diff --git a/README.md b/README.md index 55e6332e475f4e6725df6ead9f8b510211cbdea7..ed5fbba5d598c6d8c52a7026595375f07734a390 100644 --- a/README.md +++ b/README.md @@ -1,3 +1,115 @@ --- -license: cc +license: cc-by-nc-4.0 +task_categories: +- text-generation +language: +- en +tags: +- math +pretty_name: backtracing +size_categories: +- n>1k --- + +# Backtracing: Retrieving the Cause of the Query + +

+ Paper • + Code • + Video • + Citation +

+ + +**Authors:** Rose E. Wang, Pawan Wirawarn, Omar Khattab, Noah Goodman, Dorottya Demszky + +Findings of EACL, Long Paper, 2024. + +## What is Backtracing? + +![Main Figure](fig1.png) + +Many online content portals allow users to ask questions to supplement their understanding (e.g., of lectures or news articles). +While information retrieval (IR) systems may provide answers for such user queries, they do not directly assist content creators identify segments that _caused_ a user to ask those questions; this can be useful for several purposes like helping improve their content. +We introduce the task of **backtracing**, in which systems retrieve the text segment that most likely provoked a user query. + +## This Repository + +In this repository, you will find: + +1. The first **benchmark for backtracing**, composed of three heterogeneous datasets and causal retrieval tasks: understanding the cause of (a) student confusion in the _Lecture_ domain, (b) reader curiosity in the _News Article_ domain, and (c) user emotion in the _Conversation_ domain. +2. **Evaluations of a suite of retrieval systems on backtracing**, including: BM25, bi-encoder methods, cross-encoder methods, re-ranker methods, gpt-3.5-turbo-16k, and several likelihood-based methods that use pre-trained language models to estimate the probability of the query conditioned on variations of the corpus. + +Our results reveal several limitations of these methods; for example, bi-encoder methods struggle when the query and target segment share limited similarity and likelihood-based methods struggle with modeling what may be unknown information to a user. Overall, these results suggest that Backtracing is a challenging task that requires new retrieval approaches. + +We hope our benchmark serves to evaluate and improve future retrieval systems for Backtracing, and ultimately, spawns systems that empower content creators to understand user queries, refine their content and provide users with better experiences. + +## Citation + +If you find our work useful or interesting, please consider citing it! + +``` +@inproceedings{wang2024backtracing, + title = {Backtracing: Retrieving the Cause of the Query}, + booktitle = {Findings of the Association for Computational Linguistics: EACL 2024}, + publisher = {Association for Computational Linguistics}, + year = {2024}, + author = {Wang, Rose E. and Wirawarn, Pawan and Khattab, Omar and Goodman, Noah and Demszky, Dorottya}, +} +``` + +## Reproducibility + +We ran our experiments with Python 3.11 and on A6000 machines. To reproduce the results in our work, please run the following commands: + +``` +>> conda create -n backtracing python=3.11 +>> conda activate backtracing +>> pip install -r requirements.txt # install all of our requirements +>> source run_table_evaluations.sh +``` + +`run_table_evaluations.sh` outputs text files under `results//`. The text files contain the results reported in Table 2 and 3. Here is an example of what the result should look like: + +``` +>> cat results/sight/semantic_similarity.txt +Query dirs: ['data/sight/query/annotated'] +Source dirs: ['data/sight/sources/annotated'] +Output fname: results/sight/annotated/semantic_similarity.csv +Output fname: results/sight/annotated/semantic_similarity.csv +Accuracy top 1: 0.23 +Min distance top 1: 91.85 +Accuracy top 3: 0.37 +Min distance top 3: 35.22 +``` + +## Dataset Structure + + +The datasets are located under the `data` directory. +Each dataset contains the `query` directory (e.g., student question) and the `sources` directory (e.g., the lecture transcript sentences). + +``` +└── data # Backtracing Datasets + └── sight # Lecture Domain, SIGHT, derived from https://github.com/rosewang2008/sight + ├── query + └── sources + └── inquisitive # News Article Domain, Inquisitive, derived from https://github.com/wjko2/INQUISITIVE + ├── query + └── sources + └── reccon # Conversation Domain, RECCON, derived from https://github.com/declare-lab/RECCON + ├── query + └── sources +``` + + +## Retrieving from scratch + +The section above uses the cached scores. If you want to run the retrieval from scratch, then run: + + +``` +>> export OPENAI_API_KEY='yourkey' # if you want to run the gpt-3.5-turbo-16k results as well. otherwise skip. +>> source run_inference.sh +``` + diff --git a/fig1.png b/fig1.png new file mode 100644 index 0000000000000000000000000000000000000000..c1f2bb3a2a15bab519a6e9a502ca9f266cd2dffc Binary files /dev/null and b/fig1.png differ diff --git a/inquisitive/query/test/0101.json b/inquisitive/query/test/0101.json new file mode 100644 index 0000000000000000000000000000000000000000..83b1e79b133cb34e47fdc2849e8bff5745975c23 --- /dev/null +++ b/inquisitive/query/test/0101.json @@ -0,0 +1 @@ +[{"text": "What happened to the net income in the first and second quarter? ", "sentence_id": 1}, {"text": "What was done differently in the third-quarter that the net income rose 26%?", "sentence_id": 1}, {"text": "How much is 26% in dollars? ", "sentence_id": 1}, {"text": "Third-quarter net income rose because the chemical business was doing well?", "sentence_id": 1}, {"text": "What was done differently this year that was not done last year?", "sentence_id": 2}, {"text": "which year?", "sentence_id": 2}, {"text": "How did the sales shoot up 7.4% in such a short time?", "sentence_id": 3}, {"text": "When was it $540 mil?", "sentence_id": 3}, {"text": "how quickly?", "sentence_id": 3}, {"text": "Were there any losses at all?", "sentence_id": 4}, {"text": "Is there a common name for this? ", "sentence_id": 4}, {"text": "what is caustic soda?", "sentence_id": 4}, {"text": "What are gains in electrochemicals?", "sentence_id": 4}, {"text": "How did the volume increase and what was the cause of higher prices?", "sentence_id": 5}, {"text": "Who is buying the most?", "sentence_id": 5}, {"text": "what is a volume increase?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0102.json b/inquisitive/query/test/0102.json new file mode 100644 index 0000000000000000000000000000000000000000..c797bb8220238077a4fa00bf9050476f0e7c62f6 --- /dev/null +++ b/inquisitive/query/test/0102.json @@ -0,0 +1 @@ +[{"text": "Which operations will it sell?", "sentence_id": 1}, {"text": "Which year?", "sentence_id": 2}, {"text": "Why did profit drop?", "sentence_id": 2}, {"text": "Are they going to get unemployment?", "sentence_id": 4}, {"text": "Which services?", "sentence_id": 5}, {"text": "What is the number after taxes?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0103.json b/inquisitive/query/test/0103.json new file mode 100644 index 0000000000000000000000000000000000000000..ad54b2c9ed1658d0345f170b82b0a1fbac44cb95 --- /dev/null +++ b/inquisitive/query/test/0103.json @@ -0,0 +1 @@ +[{"text": "Why is Canada narrowing the trade surplus with U.S.?", "sentence_id": 1}, {"text": "Does this mean reducing the tariffs and thus reducing lost money when trading?", "sentence_id": 1}, {"text": "did it have a bad effect?", "sentence_id": 2}, {"text": "Why did imports barely rise when exports rose so much? ", "sentence_id": 2}, {"text": "How has this decrease in surplus affect trading?", "sentence_id": 3}, {"text": "Why did the trade surplus reduce so much if tariffs were cut?", "sentence_id": 3}, {"text": "which person said it?", "sentence_id": 4}, {"text": "What kind of new plant equipment?", "sentence_id": 4}, {"text": "who is the second biggest pair?", "sentence_id": 5}, {"text": "Why are they in such a hurry to come to agreements for the tariff cuts?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0104.json b/inquisitive/query/test/0104.json new file mode 100644 index 0000000000000000000000000000000000000000..0c623ed2a567e9ff2342e823dfab2421375d5e51 --- /dev/null +++ b/inquisitive/query/test/0104.json @@ -0,0 +1 @@ +[{"text": "Who is he and where did he come from?", "sentence_id": 1}, {"text": "What is this company?", "sentence_id": 2}, {"text": "Did this mean he dealt with the money required for the campaign?", "sentence_id": 3}, {"text": "What does strategy refer too in this context?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0106.json b/inquisitive/query/test/0106.json new file mode 100644 index 0000000000000000000000000000000000000000..022eca2cf9be25a4a848c7b4ee1de34d6d6dba93 --- /dev/null +++ b/inquisitive/query/test/0106.json @@ -0,0 +1 @@ +[{"text": "What are they?", "sentence_id": 1}, {"text": "What is a defunct Arkansas thrift?", "sentence_id": 1}, {"text": "How did worthless loan guarantees inflate the earnings?", "sentence_id": 1}, {"text": "why are they worthless loan guarantees?", "sentence_id": 1}, {"text": "What is a thrift in this context?", "sentence_id": 1}, {"text": "How did someone so crooked get two positions of power at this company?", "sentence_id": 2}, {"text": "is he likely to get it?", "sentence_id": 2}, {"text": "Does he have a chance of parole?", "sentence_id": 2}, {"text": "why hasnt it been set?", "sentence_id": 3}, {"text": "Why and what is the delay?", "sentence_id": 3}, {"text": "How did he think he'd get away with that?", "sentence_id": 4}, {"text": "What methods did he take to commit to this conspiracy?", "sentence_id": 4}, {"text": "Again, it doesn't let me highlight everything - just a single word. What wrongdoing were the initially accused of?", "sentence_id": 5}, {"text": "Why would these two individuals not be charged as well?", "sentence_id": 5}, {"text": "why werent they charged?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0107.json b/inquisitive/query/test/0107.json new file mode 100644 index 0000000000000000000000000000000000000000..3bcbf8c819e702d2a91999d42e299f33dc503d84 --- /dev/null +++ b/inquisitive/query/test/0107.json @@ -0,0 +1 @@ +[{"text": "How did Prospect Group Inc. gain any control, over Recognition Equipment Inc?", "sentence_id": 1}, {"text": "How was the offer hostile?", "sentence_id": 1}, {"text": "How did it gain control despite failing?", "sentence_id": 1}, {"text": "What is the name of this spokeswoman?", "sentence_id": 2}, {"text": "Who replaced those guys?", "sentence_id": 3}, {"text": "what was his reasoning for resignation?", "sentence_id": 3}, {"text": "Why did Mr, Sheinberg get promoted?", "sentence_id": 4}, {"text": "Why will he retain this role if not the other?", "sentence_id": 4}, {"text": "does he want to keep the position?", "sentence_id": 4}, {"text": "How many top spots did Recognition have?", "sentence_id": 5}, {"text": "WHAT IS A TENDER OFFER?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0108.json b/inquisitive/query/test/0108.json new file mode 100644 index 0000000000000000000000000000000000000000..8d5a600e67a4bdffc4006245b8c3d68094439846 --- /dev/null +++ b/inquisitive/query/test/0108.json @@ -0,0 +1 @@ +[{"text": "How did they help?", "sentence_id": 1}, {"text": "What does that equate to?", "sentence_id": 1}, {"text": "why is it a concern?", "sentence_id": 2}, {"text": "How does this play into things?", "sentence_id": 3}, {"text": "was this a long time ago?", "sentence_id": 3}, {"text": "How much would they dividend be?", "sentence_id": 4}, {"text": "Why did it climb?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0109.json b/inquisitive/query/test/0109.json new file mode 100644 index 0000000000000000000000000000000000000000..e90fc7545ef2ade8eb05cfcdf6e456b5be89667d --- /dev/null +++ b/inquisitive/query/test/0109.json @@ -0,0 +1 @@ +[{"text": "What happened on this date?", "sentence_id": 1}, {"text": "What is significant about Tuesday, October 17,1989?", "sentence_id": 1}, {"text": "What is this date?", "sentence_id": 1}, {"text": "Why don't interest rates always represent transactions? ", "sentence_id": 2}, {"text": "What is a good representation of actual transactions?", "sentence_id": 2}, {"text": "what do they represent?", "sentence_id": 2}, {"text": "Where is the rest of the list?", "sentence_id": 3}, {"text": "what is a prime rate?", "sentence_id": 3}, {"text": "What is this for?", "sentence_id": 3}, {"text": "What is the base rate on corporate loans at large US banks?", "sentence_id": 4}, {"text": "which banks?", "sentence_id": 4}, {"text": "How much in USD is that number?", "sentence_id": 5}, {"text": "What are federal funds?", "sentence_id": 5}, {"text": "What do Federal Funds represent?", "sentence_id": 5}, {"text": "What are these for?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0110.json b/inquisitive/query/test/0110.json new file mode 100644 index 0000000000000000000000000000000000000000..0a3b7b6026d2c0a91412e13d5226aabbaf033e47 --- /dev/null +++ b/inquisitive/query/test/0110.json @@ -0,0 +1 @@ +[{"text": "Why was there such a big debt in severance?", "sentence_id": 1}, {"text": "How big was it's database software inventories before?", "sentence_id": 1}, {"text": "Are these severance costs going to laid off employees?", "sentence_id": 1}, {"text": "What was the reason for the slide?", "sentence_id": 2}, {"text": "What was the revenue prior to this?", "sentence_id": 2}, {"text": "What happened compared to a year-ago?", "sentence_id": 3}, {"text": "What was the reason behind the decline in revenue?", "sentence_id": 3}, {"text": "Is this the exact same quarter just one year prior?", "sentence_id": 3}, {"text": "What is Ashton Tate?", "sentence_id": 4}, {"text": "What is the company's profit during this period? ", "sentence_id": 5}, {"text": "Is this time measured in quarters or months?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0112.json b/inquisitive/query/test/0112.json new file mode 100644 index 0000000000000000000000000000000000000000..24a15ce1791af53e6d013a3825271ff909962ab7 --- /dev/null +++ b/inquisitive/query/test/0112.json @@ -0,0 +1 @@ +[{"text": "who is hoping?", "sentence_id": 1}, {"text": "What does \\\"deficit-reduction legislation\\\" mean?", "sentence_id": 1}, {"text": "What does the \\\"House version\\\" consist of?", "sentence_id": 1}, {"text": "Why did the conference break down?", "sentence_id": 1}, {"text": "Which house leaders?", "sentence_id": 2}, {"text": "is this a well known budget?", "sentence_id": 2}, {"text": "What was the \\\"House-passed bill?\\\"", "sentence_id": 2}, {"text": "why do they desire it?", "sentence_id": 3}, {"text": "Why would they want to reduce the bill?", "sentence_id": 3}, {"text": "Why would it be placed into another legislation?", "sentence_id": 4}, {"text": "what are his credentials?", "sentence_id": 5}, {"text": "What is the capital-gains provision?", "sentence_id": 5}, {"text": "What is the capital-gains provision?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0113.json b/inquisitive/query/test/0113.json new file mode 100644 index 0000000000000000000000000000000000000000..74ffb65d9bde13516b98f3b5a67a9d30a2454774 --- /dev/null +++ b/inquisitive/query/test/0113.json @@ -0,0 +1 @@ +[{"text": "What is John M. Templeton's net worth?", "sentence_id": 1}, {"text": "Why is Templeton putting so much of his own money into the fund? ", "sentence_id": 1}, {"text": "What does this fund do for the public?", "sentence_id": 1}, {"text": "Who are the other funds available to?", "sentence_id": 2}, {"text": "What are some of the 33 funds?", "sentence_id": 2}, {"text": "Which countries does the Templeton Emerging Markets fund invest in?", "sentence_id": 3}, {"text": "What do these funds do?", "sentence_id": 3}, {"text": "What's the Value Fund's ROI?", "sentence_id": 4}, {"text": "Why did he add the Value Fund to the list?", "sentence_id": 4}, {"text": "Why is Mr. Templeton bullish on emerging growth stocks?", "sentence_id": 5}, {"text": "Why is Templeton so bullish on the stocks? ", "sentence_id": 5}, {"text": "Bullish in what sense?", "sentence_id": 5}, {"text": "What does this mean in terms of business?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0114.json b/inquisitive/query/test/0114.json new file mode 100644 index 0000000000000000000000000000000000000000..544ca2b24be407679b273b8a2fc07097c531c973 --- /dev/null +++ b/inquisitive/query/test/0114.json @@ -0,0 +1 @@ +[{"text": "Who are the researchers?", "sentence_id": 1}, {"text": "How does it completely prevent rejection?", "sentence_id": 1}, {"text": "What length of time indicates a success for this test?", "sentence_id": 1}, {"text": "What is the chemical makeup of the new drug?", "sentence_id": 1}, {"text": "Why are transplanted organ rejected?", "sentence_id": 1}, {"text": "What kind of long-term effects are possible?", "sentence_id": 2}, {"text": "How long has the drug been being experimented with?", "sentence_id": 2}, {"text": "What is the name of the new drug?", "sentence_id": 2}, {"text": "How long does it take to get approved?", "sentence_id": 2}, {"text": "What harmful side effects does it help prevent?", "sentence_id": 3}, {"text": "What side effects are being reduced?", "sentence_id": 3}, {"text": "How much are the rejection rates being lowered?", "sentence_id": 3}, {"text": "What is the reaction that causes the reduction in harmful side effects and the lowering of rejection rates?", "sentence_id": 3}, {"text": "How do they know it reduces side effects if it hasn't been tested long enough yet?", "sentence_id": 3}, {"text": "What is the limiting factor in terms of the number of transplants that occur?", "sentence_id": 4}, {"text": "What organ is the most commonly rejected?", "sentence_id": 4}, {"text": "How does the drug perform when other organs are being transplanted?", "sentence_id": 5}, {"text": "How many patient trials have there been?", "sentence_id": 5}, {"text": "How can they use the drug if it has not been approved yet?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0115.json b/inquisitive/query/test/0115.json new file mode 100644 index 0000000000000000000000000000000000000000..aa8a8ab43c464cab0d282dfad21b6b3eb2c80c85 --- /dev/null +++ b/inquisitive/query/test/0115.json @@ -0,0 +1 @@ +[{"text": "What is concerning about the stock market?", "sentence_id": 1}, {"text": "Why is there concern about the stock market?", "sentence_id": 1}, {"text": "does softer mean lower?", "sentence_id": 1}, {"text": "Why is there concern about the stock market?", "sentence_id": 1}, {"text": "What tumultuous ride has the stock market been on?", "sentence_id": 2}, {"text": "Why is the stock market taking a tumultuous ride?", "sentence_id": 2}, {"text": "why would it?", "sentence_id": 2}, {"text": "Why would the stock market take another tumultuous ride?", "sentence_id": 2}, {"text": "Where is California was there an earthquake?", "sentence_id": 3}, {"text": "Why would the financial impact be short lived?", "sentence_id": 3}, {"text": "Why did the earthquake create sales in Asian trade?", "sentence_id": 3}, {"text": "Why would the impact of the earthquake on financial markets be short-lived?", "sentence_id": 3}, {"text": "Why does a major earthquake in California effect Asian trade?", "sentence_id": 3}, {"text": "What makes the traders' opinion different than the performance of the dollar? ", "sentence_id": 4}, {"text": "How has it shown resilience?", "sentence_id": 5}, {"text": "is this just bad news?", "sentence_id": 5}, {"text": "How is the dollar showing resilience?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0116.json b/inquisitive/query/test/0116.json new file mode 100644 index 0000000000000000000000000000000000000000..f28482a33369739b1009b53314d0b9ea266d8202 --- /dev/null +++ b/inquisitive/query/test/0116.json @@ -0,0 +1 @@ +[{"text": "Why is it typed all in capitals?", "sentence_id": 1}, {"text": "How many billions of dollars?", "sentence_id": 1}, {"text": "Which Earthquake are we speaking of?", "sentence_id": 1}, {"text": "Where and when did the earthquake happen?", "sentence_id": 1}, {"text": "which insurers?", "sentence_id": 1}, {"text": "Which quake and where in California?", "sentence_id": 1}, {"text": "Why weren't they greatly affected and how?", "sentence_id": 2}, {"text": "What does it matter if silicon wasn't affected; where's the concern for the whole state?", "sentence_id": 2}, {"text": "why not affected?", "sentence_id": 2}, {"text": "Why do these companies not expect no long-term disruption in shipments compare to the other companies in the region?", "sentence_id": 3}, {"text": "Why are we concerned with shipments when damages need to be accounted for state wide?What kind of damage would be deemed a disruption?", "sentence_id": 3}, {"text": "but not literally?", "sentence_id": 3}, {"text": "What are the stocks that they expect to profit or suffer?", "sentence_id": 4}, {"text": "Who are these investors?", "sentence_id": 4}, {"text": "how did they single out?", "sentence_id": 4}, {"text": "Which companies?", "sentence_id": 4}, {"text": "What are the two rules the writer is referring to?", "sentence_id": 5}, {"text": "What is a leveraged buy-out?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0117.json b/inquisitive/query/test/0117.json new file mode 100644 index 0000000000000000000000000000000000000000..ca1e908cd657ddf6bf8a2b6f00e090860dce039c --- /dev/null +++ b/inquisitive/query/test/0117.json @@ -0,0 +1 @@ +[{"text": "how big was the quake?", "sentence_id": 1}, {"text": "How much damage did the earthquake do?", "sentence_id": 1}, {"text": "How strong was the earthquake?", "sentence_id": 1}, {"text": "what is a temblor?", "sentence_id": 2}, {"text": "How long did the aftershocks last?", "sentence_id": 2}, {"text": "How many people were rescued?", "sentence_id": 2}, {"text": "How many were thought to be left?", "sentence_id": 3}, {"text": "Were many cars involved?", "sentence_id": 3}, {"text": "where is that?", "sentence_id": 4}, {"text": "How strong was the tremor?", "sentence_id": 4}, {"text": "What time was it?", "sentence_id": 4}, {"text": "How long is the fault?", "sentence_id": 4}, {"text": "how many troops?", "sentence_id": 5}, {"text": "What branch of the military is responsible for this?", "sentence_id": 5}, {"text": "Was there a lot of looting?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0118.json b/inquisitive/query/test/0118.json new file mode 100644 index 0000000000000000000000000000000000000000..e7025f399578ccdfdca6d82db2ec86088008b634 --- /dev/null +++ b/inquisitive/query/test/0118.json @@ -0,0 +1 @@ +[{"text": "What does this mean?", "sentence_id": 1}, {"text": "What was the legal brawl about?", "sentence_id": 1}, {"text": "when was the last?", "sentence_id": 1}, {"text": "Which oil-producing company in Texas?", "sentence_id": 1}, {"text": "What was this legal brawl about?", "sentence_id": 1}, {"text": "What sort of legal brawl were they engaged in? ", "sentence_id": 1}, {"text": "what is a non voting issue?", "sentence_id": 2}, {"text": "What else will they provide Texaco?", "sentence_id": 3}, {"text": "what is a recoverable reserve?", "sentence_id": 4}, {"text": "when was the last indication?", "sentence_id": 5}, {"text": "Elaborate on what a reserve base is.", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0119.json b/inquisitive/query/test/0119.json new file mode 100644 index 0000000000000000000000000000000000000000..c06cc01da7e975970d9e61eb5b4ef45f6abc3a92 --- /dev/null +++ b/inquisitive/query/test/0119.json @@ -0,0 +1 @@ +[{"text": "what about a flick?", "sentence_id": 1}, {"text": "What was with a twist of the wrist?", "sentence_id": 1}, {"text": "Why would they twist their wrist?", "sentence_id": 1}, {"text": "why are they tossed?", "sentence_id": 2}, {"text": "What about boys with tops?", "sentence_id": 2}, {"text": "What is a frisbee tosser?", "sentence_id": 2}, {"text": "What are PR types?", "sentence_id": 3}, {"text": "What are P.R. types?", "sentence_id": 3}, {"text": "what is the goal?", "sentence_id": 4}, {"text": "What is their common goal?", "sentence_id": 4}, {"text": "Whats the goal that's in common?", "sentence_id": 4}, {"text": "What are they all trying?", "sentence_id": 4}, {"text": "Put the spin on what?", "sentence_id": 5}, {"text": "What is it that they are putting a spin on?", "sentence_id": 5}, {"text": "What is the spin?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0120.json b/inquisitive/query/test/0120.json new file mode 100644 index 0000000000000000000000000000000000000000..80ecad54fab435bef88e5609a03b31535cc402d5 --- /dev/null +++ b/inquisitive/query/test/0120.json @@ -0,0 +1 @@ +[{"text": "Why is he being impeached?", "sentence_id": 1}, {"text": "What were the impeachment articles?", "sentence_id": 1}, {"text": "What were the charges he was acquitted of?", "sentence_id": 2}, {"text": "Why was he removed from office if he had been acquitted?", "sentence_id": 2}, {"text": "what is this word?", "sentence_id": 2}, {"text": "Why did the jury acquit him?", "sentence_id": 2}, {"text": "How can he be convicted if he was found not guilty?", "sentence_id": 3}, {"text": "how long was the case?", "sentence_id": 3}, {"text": "What was the case?", "sentence_id": 3}, {"text": "Who was the bribe from?", "sentence_id": 3}, {"text": "who were the first five?", "sentence_id": 4}, {"text": "Who were the other five?", "sentence_id": 4}, {"text": "Why did they need 64 votes?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0121.json b/inquisitive/query/test/0121.json new file mode 100644 index 0000000000000000000000000000000000000000..ba16ef7b6cf1d409f0acf3ac800928ffc5454532 --- /dev/null +++ b/inquisitive/query/test/0121.json @@ -0,0 +1 @@ +[{"text": "How much foreign-exchange reserves does China have?", "sentence_id": 1}, {"text": "How did China manage to get into this situation?", "sentence_id": 1}, {"text": "which goverment report", "sentence_id": 1}, {"text": "Who are the authors of the report?", "sentence_id": 1}, {"text": "Why is the trade gap for China widening?", "sentence_id": 2}, {"text": "Looking back from 2020, what were the causes of this?", "sentence_id": 2}, {"text": "which one?", "sentence_id": 2}, {"text": "How and who came to this conclusion?", "sentence_id": 3}, {"text": "how many countries are healthy?", "sentence_id": 3}, {"text": "Why does the western government decline to be identified?", "sentence_id": 5}, {"text": "How can we trust the source if we cannot know the source?", "sentence_id": 5}, {"text": "which government?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0122.json b/inquisitive/query/test/0122.json new file mode 100644 index 0000000000000000000000000000000000000000..ce6aa44e2c2d51e7e5b27c05875d304e70c6963a --- /dev/null +++ b/inquisitive/query/test/0122.json @@ -0,0 +1 @@ +[{"text": "What does this word refer to and in what context?", "sentence_id": 1}, {"text": "What consumers are too deep in hock?", "sentence_id": 1}, {"text": "What would constitute being too deep?", "sentence_id": 1}, {"text": "Why would the whole economy be hurting?", "sentence_id": 2}, {"text": "Why would the observers be hurt?", "sentence_id": 2}, {"text": "Which observers?", "sentence_id": 2}, {"text": "Why are consumers being forced to cut back?", "sentence_id": 3}, {"text": "Why would a sudden cutback by consumers happen? ", "sentence_id": 3}, {"text": "Is this a global issue or specific to a region?", "sentence_id": 4}, {"text": "Why are some of these lending institutions already shaky?", "sentence_id": 4}, {"text": "Which lending institutions?", "sentence_id": 4}, {"text": "Who are the worriers and what are their facts?", "sentence_id": 5}, {"text": "How worrisome are the trends?", "sentence_id": 5}, {"text": "What were the worrisome trends ", "sentence_id": 5}, {"text": "What worrisome trends exist? ", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0123.json b/inquisitive/query/test/0123.json new file mode 100644 index 0000000000000000000000000000000000000000..1328825398cd621119e9936efa718dee4070fb75 --- /dev/null +++ b/inquisitive/query/test/0123.json @@ -0,0 +1 @@ +[{"text": "Why are they seeking to position themselves?", "sentence_id": 1}, {"text": "How would Eastman Kodak's film business be made obsolete by HDTV?", "sentence_id": 2}, {"text": "What is a virtual monopoly?", "sentence_id": 2}, {"text": "How costly is the converter?", "sentence_id": 3}, {"text": "How much does it cost?", "sentence_id": 3}] \ No newline at end of file diff --git a/inquisitive/query/test/0131.json b/inquisitive/query/test/0131.json new file mode 100644 index 0000000000000000000000000000000000000000..c8518973a5fc4f87ef64c14cda20bd589649c79c --- /dev/null +++ b/inquisitive/query/test/0131.json @@ -0,0 +1 @@ +[{"text": "Who does Secretary of State Baker work for?", "sentence_id": 5}, {"text": "what are first strike nuclear arms?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0132.json b/inquisitive/query/test/0132.json new file mode 100644 index 0000000000000000000000000000000000000000..0ed755476d32c6a413a6498d06e55222e66aab2e --- /dev/null +++ b/inquisitive/query/test/0132.json @@ -0,0 +1 @@ +[{"text": "Who estimated this amount?", "sentence_id": 1}, {"text": "Why would aid to Hurricane Hugo victims need extended further?", "sentence_id": 1}, {"text": "What were the current restrictions?", "sentence_id": 2}, {"text": "Which influential California lawmakers?", "sentence_id": 2}, {"text": "Why are they called \\\"influential\\\"?", "sentence_id": 2}, {"text": "Why would the Bush administration feel the package was excessive?", "sentence_id": 2}, {"text": "Why would lawmakers want restrictions waived?", "sentence_id": 2}, {"text": "why is it excessive?", "sentence_id": 2}, {"text": "Why was the confrontation strained?", "sentence_id": 3}, {"text": "Why was there a confrontation between Jamie Whitten and the House delegation?", "sentence_id": 3}, {"text": "why wasnt it unanimous?", "sentence_id": 3}, {"text": "Who is supposed to be jealous here?", "sentence_id": 4}, {"text": "How would there be jealousy of the Golden State?", "sentence_id": 4}, {"text": "is there no disaster fund?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0133.json b/inquisitive/query/test/0133.json new file mode 100644 index 0000000000000000000000000000000000000000..4f806f95bae506c2395b889bafdc58e05fbf6c34 --- /dev/null +++ b/inquisitive/query/test/0133.json @@ -0,0 +1 @@ +[{"text": "Where was the spill?", "sentence_id": 1}, {"text": "What were Exxon's initial efforts to treat the giant oil spill last spring?", "sentence_id": 1}, {"text": "What year was this?", "sentence_id": 1}, {"text": "What did state officials do to interfere?", "sentence_id": 1}, {"text": "Which other companies?", "sentence_id": 2}, {"text": "What year?", "sentence_id": 2}, {"text": "Which other oil companies?", "sentence_id": 2}, {"text": "What was Exxon's response?", "sentence_id": 3}, {"text": "What exactly was the response?", "sentence_id": 3}, {"text": "How many hundreds?", "sentence_id": 3}, {"text": "is that the highest court in alaska?", "sentence_id": 4}, {"text": "Which suit?", "sentence_id": 4}, {"text": "When will it be complete?", "sentence_id": 5}, {"text": "why dont they?", "sentence_id": 5}, {"text": "How was Exxon hurt, financially, by the state's suit?", "sentence_id": 5}, {"text": "When will the specific dollar claims be filed?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0134.json b/inquisitive/query/test/0134.json new file mode 100644 index 0000000000000000000000000000000000000000..34a15d36760b36d176ef1995f9821aa93d48199c --- /dev/null +++ b/inquisitive/query/test/0134.json @@ -0,0 +1 @@ +[{"text": "What is a reserve?", "sentence_id": 1}, {"text": "How did such a loss occur if there was a boost in reserves?", "sentence_id": 1}, {"text": "WHAT COUTRIES RECIEVED LOANS?", "sentence_id": 1}, {"text": "Why was this expected?", "sentence_id": 1}, {"text": "Why did they take losses on these loans?", "sentence_id": 1}, {"text": "Why was this expected?", "sentence_id": 1}, {"text": "Whose net income is this?", "sentence_id": 2}, {"text": "How is the company's situation so drastically different year-to-year?", "sentence_id": 2}, {"text": "WHAT YEAR?", "sentence_id": 2}, {"text": "What percentage loss is this?", "sentence_id": 2}, {"text": "WHY DID INTEREST INCOME RISE?", "sentence_id": 3}, {"text": "Why did interest rise that much?", "sentence_id": 3}, {"text": "What is interest income?", "sentence_id": 3}, {"text": "What does bank holding mean in this context?", "sentence_id": 4}, {"text": "How did their assets climb if they experienced a loss for the quarter?", "sentence_id": 4}, {"text": "WHY DID IT CLIMB?", "sentence_id": 4}, {"text": "Why did their assets climb so much?", "sentence_id": 4}, {"text": "How did they make more money when they lost money due to bad loans?", "sentence_id": 4}, {"text": "Why \\\"would have\\\" income increased?", "sentence_id": 5}, {"text": "WHY WOULD IT HAVE INCREASED?", "sentence_id": 5}, {"text": "Why would have it increased this much? ", "sentence_id": 5}, {"text": "What are loan-loss reserves?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0135.json b/inquisitive/query/test/0135.json new file mode 100644 index 0000000000000000000000000000000000000000..56b68ae01897bac051766b156bf7d20548053053 --- /dev/null +++ b/inquisitive/query/test/0135.json @@ -0,0 +1 @@ +[{"text": "What happened on this date?", "sentence_id": 1}, {"text": "What occurred on this day?", "sentence_id": 1}, {"text": "What happened on this day?", "sentence_id": 1}, {"text": "Which ones are key?", "sentence_id": 2}, {"text": "What are the general levels?", "sentence_id": 2}, {"text": "Why are the rates only a guide and not a set rate?", "sentence_id": 2}, {"text": "Is this the US prime rate?", "sentence_id": 3}, {"text": "What does \\\"Prime Rate\\\" mean?", "sentence_id": 3}, {"text": "How is the base rate determined?", "sentence_id": 4}, {"text": "What is a near closing bid?", "sentence_id": 5}, {"text": "What do all of the percentages mean for federal funds?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0136.json b/inquisitive/query/test/0136.json new file mode 100644 index 0000000000000000000000000000000000000000..5f347b94c1b7072028f04dabf1f863a80861b603 --- /dev/null +++ b/inquisitive/query/test/0136.json @@ -0,0 +1 @@ +[{"text": "Why is Enviropact Inc. selling its pump and tank division?", "sentence_id": 1}, {"text": "is that a lot of money?", "sentence_id": 1}, {"text": "What do these divisions contribute to Enviropact Inc as a company?", "sentence_id": 1}, {"text": "Why would GSX Chemical assume $1.6 million in debt?", "sentence_id": 2}, {"text": "where in miami?", "sentence_id": 2}, {"text": "What is included in this debt acqusition?", "sentence_id": 2}, {"text": "What divisions are they talking about?", "sentence_id": 2}, {"text": "What is common stock?", "sentence_id": 3}, {"text": "Why would Enviropact's shares go up?", "sentence_id": 4}, {"text": "What is composite trading?", "sentence_id": 4}, {"text": "Why would Enviropact sell two divisions that make up $8 million of their revenue?", "sentence_id": 5}, {"text": "which divisions?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0137.json b/inquisitive/query/test/0137.json new file mode 100644 index 0000000000000000000000000000000000000000..4e6bbf3b8eb4bce117ad897cd432ebeaed2e5d50 --- /dev/null +++ b/inquisitive/query/test/0137.json @@ -0,0 +1 @@ +[{"text": "what is a narrow range?", "sentence_id": 1}, {"text": "why did it climb?", "sentence_id": 2}, {"text": "what kind of economic data?", "sentence_id": 3}, {"text": "why were they nervous?", "sentence_id": 3}, {"text": "which day?", "sentence_id": 4}, {"text": "what do they mean by marks?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0138.json b/inquisitive/query/test/0138.json new file mode 100644 index 0000000000000000000000000000000000000000..9c33a6190683314474a2cb68955672d637a68640 --- /dev/null +++ b/inquisitive/query/test/0138.json @@ -0,0 +1 @@ +[{"text": "Why did they agree to transfer ownership to the top executives?", "sentence_id": 1}, {"text": "Who are the two top executives?", "sentence_id": 1}, {"text": "Why is this a last-ditch effort?", "sentence_id": 1}, {"text": "What is the Broker-Dealer subsidiary consist of?", "sentence_id": 1}, {"text": "Why is this a last ditch effort to keep the sales force? ", "sentence_id": 1}, {"text": "How could the financial services firm miss payments on a 1 billion dollar debt?", "sentence_id": 2}, {"text": "Why did the company miss interest payments?", "sentence_id": 2}, {"text": "Why will it exercise that right only in that particular situation?", "sentence_id": 3}, {"text": "What are the other businesses?", "sentence_id": 3}, {"text": "What are their other core businesses?", "sentence_id": 3}, {"text": "How would this right be exercised? ", "sentence_id": 3}, {"text": "Why would it want to sell the right to regain the subsidaiary?", "sentence_id": 4}, {"text": "Why are they asking permission to sell rights when theyre trying to keep its sales force and customer base?", "sentence_id": 4}, {"text": "Why was the company renamed?", "sentence_id": 5}, {"text": "Was it necessary to rename the subsidiary?", "sentence_id": 5}, {"text": "Why did the company change its name? ", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0139.json b/inquisitive/query/test/0139.json new file mode 100644 index 0000000000000000000000000000000000000000..4c3cf8b92f4a7b7afb41cf69b9db63d8d245a59b --- /dev/null +++ b/inquisitive/query/test/0139.json @@ -0,0 +1 @@ +[{"text": "How did the fiscal fourth-quarter profit plunge that much?", "sentence_id": 1}, {"text": "Why did their fourth quarter plunge so hard?", "sentence_id": 1}, {"text": "Why did the quarter profit plunge so drastically? ", "sentence_id": 1}, {"text": "What were the previously reported operating problems?", "sentence_id": 2}, {"text": "What problems were previously reported?", "sentence_id": 2}, {"text": "What did Varian do different this year than last that made their profit go up 13%?", "sentence_id": 3}, {"text": "Why was there so much growth this full fiscal year?", "sentence_id": 3}, {"text": "How did they rise the profit by that much so quickly?", "sentence_id": 3}, {"text": "How did the sales of the year rise to almost a 15% increase?", "sentence_id": 4}, {"text": "Why did sales rise almost 15%?", "sentence_id": 4}, {"text": "Why did sales rise so much?", "sentence_id": 4}, {"text": "Which division was sold?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0140.json b/inquisitive/query/test/0140.json new file mode 100644 index 0000000000000000000000000000000000000000..5ba674d6bc8aedea084c6066c3f1d6073f5090fa --- /dev/null +++ b/inquisitive/query/test/0140.json @@ -0,0 +1 @@ +[{"text": "Why did he have differences with the board?", "sentence_id": 1}, {"text": "What kind of differences did Richard W. Decker have with the board?", "sentence_id": 1}, {"text": "what were their differences?", "sentence_id": 1}, {"text": "What did the written announcement say?", "sentence_id": 2}, {"text": "How did he become such a young chief executive?", "sentence_id": 4}, {"text": "How was David Payne chosen to be the chairman?", "sentence_id": 4}, {"text": "why does this matter?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0142.json b/inquisitive/query/test/0142.json new file mode 100644 index 0000000000000000000000000000000000000000..abd9de0ec8cf5bd82ca035c5e54c06c548abbfa1 --- /dev/null +++ b/inquisitive/query/test/0142.json @@ -0,0 +1 @@ +[{"text": "What do these companies do?", "sentence_id": 1}, {"text": "What is G.M.B?", "sentence_id": 1}, {"text": "what is gmb?", "sentence_id": 1}, {"text": "Why do they want to acquire Vermont American corp?", "sentence_id": 2}, {"text": "Why has additional information been requested?", "sentence_id": 2}, {"text": "what do they do?", "sentence_id": 2}, {"text": "What additional information did the FTC request?", "sentence_id": 2}, {"text": "Why do the two companies want to acquire Vermont American Corp?", "sentence_id": 2}, {"text": "What is composite trading?", "sentence_id": 3}, {"text": "How was Vermont American able to common close at $39.75, off 25 cents?", "sentence_id": 3}, {"text": "is that a lot?", "sentence_id": 3}, {"text": "What is composite trading?", "sentence_id": 3}, {"text": "What does a full and prompt response consist of?", "sentence_id": 4}, {"text": "Why was the request not seen as unusual?", "sentence_id": 4}, {"text": "Why don't they anticipate any problems?", "sentence_id": 5}, {"text": "Why don't they anticipate any problems?", "sentence_id": 5}, {"text": "why dont they see any problems?", "sentence_id": 5}, {"text": "Who are the spokesmen?", "sentence_id": 5}, {"text": "Why has Vermont American agreed to be acquired?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0143.json b/inquisitive/query/test/0143.json new file mode 100644 index 0000000000000000000000000000000000000000..23c02479b6a0ae54040937eb0f64892e93e52f71 --- /dev/null +++ b/inquisitive/query/test/0143.json @@ -0,0 +1 @@ +[{"text": "Why is he being mock furious? ", "sentence_id": 1}, {"text": "What is a croaker?", "sentence_id": 1}, {"text": "What does \\\"pot down\\\" mean?", "sentence_id": 1}, {"text": "What kind of guide?", "sentence_id": 1}, {"text": "What is his major?", "sentence_id": 2}, {"text": "Doing what?", "sentence_id": 2}, {"text": "Why does the man take people out to fish? ", "sentence_id": 3}, {"text": "What is he fishing for?", "sentence_id": 3}, {"text": "Where exactly does he take people to fish?", "sentence_id": 3}, {"text": "Does this mean seasonally? Or as a side-gig while going to school?", "sentence_id": 3}, {"text": "What constitutes the rest?", "sentence_id": 4}, {"text": "Does he know what fish are out there based on the weather?", "sentence_id": 4}, {"text": "Is this a competition or for leisure?", "sentence_id": 5}, {"text": "How many boats are out at the same time?", "sentence_id": 5}, {"text": "is it normal to share crucial information like that?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0145.json b/inquisitive/query/test/0145.json new file mode 100644 index 0000000000000000000000000000000000000000..8469930d8471d670c2b82115ae2b7a4a4265874f --- /dev/null +++ b/inquisitive/query/test/0145.json @@ -0,0 +1 @@ +[{"text": "Is this a unit of people?", "sentence_id": 1}, {"text": "What year did this happen?", "sentence_id": 1}, {"text": "Why is Turner Broadcasting distributing movies overseas before U.S. theaters?", "sentence_id": 1}, {"text": "in which countries?", "sentence_id": 2}, {"text": "Why are Turner pictures being shown on television before theaters?", "sentence_id": 2}, {"text": "was it a popular movie?", "sentence_id": 3}, {"text": "Was there any reason these men were selected?", "sentence_id": 4}, {"text": "what are their other missions?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0146.json b/inquisitive/query/test/0146.json new file mode 100644 index 0000000000000000000000000000000000000000..97596ee3ac03e316767942a00601fc51e8e4e569 --- /dev/null +++ b/inquisitive/query/test/0146.json @@ -0,0 +1 @@ +[{"text": "is that a company?", "sentence_id": 1}, {"text": "What is the New Haven Register?", "sentence_id": 1}, {"text": "What will happen to them now?", "sentence_id": 2}, {"text": "what happened recently?", "sentence_id": 2}, {"text": "What made the association turn bitter?", "sentence_id": 2}, {"text": "Why has the relationship turned bitter?", "sentence_id": 2}, {"text": "What has Goodson been lacking according to them?", "sentence_id": 3}, {"text": "how much has inflation?", "sentence_id": 4}, {"text": "What is part of the management contract?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0147.json b/inquisitive/query/test/0147.json new file mode 100644 index 0000000000000000000000000000000000000000..3262823693cb7638ae77268d9fd4a806950ba96e --- /dev/null +++ b/inquisitive/query/test/0147.json @@ -0,0 +1 @@ +[{"text": "Who determined this was normal?", "sentence_id": 1}, {"text": "who is it associated with now?", "sentence_id": 1}, {"text": "Why do school superintendents have these reputations? ", "sentence_id": 2}, {"text": "How is Kimbrough hard-nosed?", "sentence_id": 3}, {"text": "WHAT ARE HIS CREDENTIALS?", "sentence_id": 3}, {"text": "Why did Kimbrough nearly come to blows? ", "sentence_id": 4}, {"text": "What is meant by \\\"took\\\"?", "sentence_id": 4}, {"text": "Why did Kimbrough berate reporters? ", "sentence_id": 5}, {"text": "What did he do to berate reporters?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0149.json b/inquisitive/query/test/0149.json new file mode 100644 index 0000000000000000000000000000000000000000..83686a9285a5f652741b7ba695975a4abad6e103 --- /dev/null +++ b/inquisitive/query/test/0149.json @@ -0,0 +1 @@ +[{"text": "How were the hundred injured?", "sentence_id": 1}, {"text": "Where is here?", "sentence_id": 1}, {"text": "Why were the workers unaccounted for?", "sentence_id": 2}, {"text": "How many workers were unaccounted for?", "sentence_id": 2}, {"text": "where is that in oklahoma?", "sentence_id": 3}, {"text": "How did the seal blow?", "sentence_id": 4}, {"text": "Who is the manager?", "sentence_id": 4}, {"text": "Why did a seal blow?", "sentence_id": 4}, {"text": "how did it blow?", "sentence_id": 4}, {"text": "How was the damage and cause assessed/determined?", "sentence_id": 5}, {"text": "Who are the other Phillips officials?", "sentence_id": 5}, {"text": "how long will it take to figure out?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0150.json b/inquisitive/query/test/0150.json new file mode 100644 index 0000000000000000000000000000000000000000..08f360a241fd6011c3ec371e8215dea8e1ab751f --- /dev/null +++ b/inquisitive/query/test/0150.json @@ -0,0 +1 @@ +[{"text": "Who were these analysts, and were they from inside the company?", "sentence_id": 1}, {"text": "Which analysts?", "sentence_id": 1}, {"text": "Why did analysts expect this decline?", "sentence_id": 1}, {"text": "what were the projections?", "sentence_id": 1}, {"text": "What does this common outstanding mean?", "sentence_id": 2}, {"text": "What is the meaning of common outstanding?", "sentence_id": 2}, {"text": "What evidence besides an announcement would cause shares to fall?", "sentence_id": 3}, {"text": "how far did they fall?", "sentence_id": 3}, {"text": "Does this dividend only apply to certain investors?", "sentence_id": 4}, {"text": "Which investors were disappointed?", "sentence_id": 4}, {"text": "Why would a company give special divends?", "sentence_id": 4}, {"text": "What % drop was this for the share?", "sentence_id": 5}, {"text": "How is composite trading different than other types of trading?", "sentence_id": 5}, {"text": "what is composite trading?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0501.json b/inquisitive/query/test/0501.json new file mode 100644 index 0000000000000000000000000000000000000000..1d2eddb3f805f0188feefde1be9d6424337cc6a0 --- /dev/null +++ b/inquisitive/query/test/0501.json @@ -0,0 +1 @@ +[{"text": "why cant they?", "sentence_id": 1}, {"text": "Why can't kids keep up with their parents?", "sentence_id": 1}, {"text": "Why can't kids keep up with their parents?", "sentence_id": 1}, {"text": "Why don't kids today run as fast as their parents when they were kids?", "sentence_id": 2}, {"text": "Why don't children run as fast or as far as their parents?", "sentence_id": 2}, {"text": "is that cardio?", "sentence_id": 4}, {"text": "Why has heart-related fitness declined?", "sentence_id": 4}, {"text": "is it the aha?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0502.json b/inquisitive/query/test/0502.json new file mode 100644 index 0000000000000000000000000000000000000000..7b12b2432afec383470b274278ca2f35989bd618 --- /dev/null +++ b/inquisitive/query/test/0502.json @@ -0,0 +1 @@ +[{"text": "how are they tested?", "sentence_id": 1}, {"text": "Who is Jeff Bezos?", "sentence_id": 1}, {"text": "which states?", "sentence_id": 2}, {"text": "Which states are competing to host the sites?", "sentence_id": 2}, {"text": "how will delivery drones bring more jobs than delivery drivers? ", "sentence_id": 2}, {"text": "how will they do this?", "sentence_id": 3}, {"text": "How does the FAA determine how safe this practice is?", "sentence_id": 3}, {"text": "Which types cases have been given pemission to fly unmanned?", "sentence_id": 4}, {"text": "did this happen?", "sentence_id": 5}, {"text": "How close is the company to realistically achieving this goal?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0503.json b/inquisitive/query/test/0503.json new file mode 100644 index 0000000000000000000000000000000000000000..f13354d600060c9c348cf203c82fb3623024b7bd --- /dev/null +++ b/inquisitive/query/test/0503.json @@ -0,0 +1 @@ +[{"text": "when was he born?", "sentence_id": 1}, {"text": "Which archaeologists?", "sentence_id": 1}, {"text": "nativity happens for buddha?", "sentence_id": 2}, {"text": "How do they know the evidence is connected to Buddha?", "sentence_id": 2}, {"text": "will we ever learn?", "sentence_id": 3}, {"text": "Date of birth for who?", "sentence_id": 3}, {"text": "which seems more plausible?", "sentence_id": 4}, {"text": "Why are historians wavering over dates?", "sentence_id": 4}, {"text": "Which historians?", "sentence_id": 4}, {"text": "did they have writing back then?", "sentence_id": 5}, {"text": "Why didn't they have any records written in that time?", "sentence_id": 5}, {"text": "Why wasnt there more recoreds?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0505.json b/inquisitive/query/test/0505.json new file mode 100644 index 0000000000000000000000000000000000000000..359ff0b5b1b56ef7c6a3931553f76c8a1be2c80a --- /dev/null +++ b/inquisitive/query/test/0505.json @@ -0,0 +1 @@ +[{"text": "Which islands in the East China Sea are disputed?", "sentence_id": 1}, {"text": "How did the US take Japan's side in China's opinion?", "sentence_id": 1}, {"text": "Which islands are being disputed by China and Japan?", "sentence_id": 1}, {"text": "Why did Biden appear this way?", "sentence_id": 2}, {"text": "why was he somber?", "sentence_id": 2}, {"text": "Why was Vice President Biden somber and subdued?", "sentence_id": 2}, {"text": "why is there a retricted flying zone", "sentence_id": 3}, {"text": "Why did China institute a no fly zone?", "sentence_id": 3}, {"text": "how brief was it?", "sentence_id": 3}, {"text": "Why did China newly declare a restricted flying zone?", "sentence_id": 3}, {"text": "Does the US have a positive notion about any of the countries they associate with?", "sentence_id": 4}, {"text": "What is orthodoxy?", "sentence_id": 5}, {"text": "will they get in trouble for it?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0506.json b/inquisitive/query/test/0506.json new file mode 100644 index 0000000000000000000000000000000000000000..e3bfea50d7195ff929d8a7369a66e205e078c8ea --- /dev/null +++ b/inquisitive/query/test/0506.json @@ -0,0 +1 @@ +[{"text": "why should it offend us?", "sentence_id": 2}, {"text": "What is offending?", "sentence_id": 2}, {"text": "why does he think so?", "sentence_id": 3}, {"text": "How is the income gap growing?", "sentence_id": 4}, {"text": "Which nonprofit community center?", "sentence_id": 5}, {"text": "which neighborhood?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0508.json b/inquisitive/query/test/0508.json new file mode 100644 index 0000000000000000000000000000000000000000..cb5d3efcc2287817670d1525e4fc1d0f5746a756 --- /dev/null +++ b/inquisitive/query/test/0508.json @@ -0,0 +1 @@ +[{"text": "How will the chemical weapons be destroyed? ", "sentence_id": 1}, {"text": "Why would a cargo ship help destroy?", "sentence_id": 1}, {"text": "What are their stockpiles? How much do they have?", "sentence_id": 3}, {"text": "How will the naval ship attempt to move the material? ", "sentence_id": 5}, {"text": "Why is this difficult and how does it connect to war?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0509.json b/inquisitive/query/test/0509.json new file mode 100644 index 0000000000000000000000000000000000000000..f5d0da5b745ba3ff4481d6af498c155c51947492 --- /dev/null +++ b/inquisitive/query/test/0509.json @@ -0,0 +1 @@ +[{"text": "Which media outlets?", "sentence_id": 1}, {"text": "Why have they been spying?", "sentence_id": 1}, {"text": "45", "sentence_id": 1}, {"text": "What information are they trying to gain by spying on these gamers?", "sentence_id": 1}, {"text": "Are there areas of the world that are not being spied on by these agents?", "sentence_id": 1}, {"text": "What are these agencies?", "sentence_id": 1}, {"text": "Why are terrorists using video games?", "sentence_id": 2}, {"text": "How many years?", "sentence_id": 2}, {"text": "What are some of the games?", "sentence_id": 2}, {"text": "Why do agents believe their are terrorists playing in these games?", "sentence_id": 2}, {"text": "Who is Edward Snowden?", "sentence_id": 3}, {"text": "where did he leak this information?", "sentence_id": 3}, {"text": "Who started this campaign?", "sentence_id": 3}, {"text": "What brought these two particular agencies together on this project?", "sentence_id": 3}, {"text": "What would be considered a virtual universe?", "sentence_id": 4}, {"text": "How many players, worldwide, are there at any given time?", "sentence_id": 4}, {"text": "Can real prizes be had in these fantasy games?", "sentence_id": 4}, {"text": "How much do they pay?", "sentence_id": 5}, {"text": "How much money does the average player invest in these games?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0511.json b/inquisitive/query/test/0511.json new file mode 100644 index 0000000000000000000000000000000000000000..eff84989500345bf7ac14766986da6577a48d2e9 --- /dev/null +++ b/inquisitive/query/test/0511.json @@ -0,0 +1 @@ +[{"text": "How can a magnet be flexible enough to sculp into something?", "sentence_id": 1}, {"text": "Which kind of magic tricks can Christin perform?", "sentence_id": 1}, {"text": "what does it do?", "sentence_id": 2}, {"text": "Are rare earth magnets toxic?", "sentence_id": 3}, {"text": "What classifies a magnet as rare-earth, and how many other classifications are there?", "sentence_id": 3}, {"text": "Who made her laugh?", "sentence_id": 4}, {"text": "what happened?", "sentence_id": 4}, {"text": "Why did she swallow them?", "sentence_id": 5}, {"text": "could she have died?", "sentence_id": 5}, {"text": "Why did they have to remove her intestines, colon, and appendix?", "sentence_id": 5}, {"text": "Why did this surgery happen such a long time after the incident?", "sentence_id": 5}, {"text": "How were the magnets able to travel through her digestive system to the point they reached her intestines?", "sentence_id": 5}, {"text": "How did the magnets reach her appendix?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0513.json b/inquisitive/query/test/0513.json new file mode 100644 index 0000000000000000000000000000000000000000..f4d5cfaac2a250a23021549d7d304dd187c12bf4 --- /dev/null +++ b/inquisitive/query/test/0513.json @@ -0,0 +1 @@ +[{"text": "who is rating?", "sentence_id": 1}, {"text": "What specifically are the unhappy about with the direction?", "sentence_id": 1}, {"text": "what are his credentials?", "sentence_id": 3}, {"text": "How is confidence supposed to right the ship?", "sentence_id": 3}, {"text": "what made it sharp?", "sentence_id": 5}, {"text": "What caused the sharp increase in the rating?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0514.json b/inquisitive/query/test/0514.json new file mode 100644 index 0000000000000000000000000000000000000000..3b2ffc38038d018ec109a727d7022ea18b47f227 --- /dev/null +++ b/inquisitive/query/test/0514.json @@ -0,0 +1 @@ +[{"text": "is he the new pope?", "sentence_id": 1}, {"text": "How has the Pope changed the perception of the Catholic Church?", "sentence_id": 1}, {"text": "What was the perception that changed?", "sentence_id": 1}, {"text": "What has he done to change perceptions?", "sentence_id": 1}, {"text": "How did Pope Francis change the perception of the Catholic Church?", "sentence_id": 1}, {"text": "what is a jesuit?", "sentence_id": 3}, {"text": "how did they respond?", "sentence_id": 4}] \ No newline at end of file diff --git a/inquisitive/query/test/0515.json b/inquisitive/query/test/0515.json new file mode 100644 index 0000000000000000000000000000000000000000..d6ff2b472236297ec01fcb1ef467f6f77f7adb4b --- /dev/null +++ b/inquisitive/query/test/0515.json @@ -0,0 +1 @@ +[{"text": "Who was this person?", "sentence_id": 1}, {"text": "What makes it a murky genetic past?", "sentence_id": 1}, {"text": "How ancient is this relative?", "sentence_id": 1}, {"text": "What is puzzling about the connection?", "sentence_id": 1}, {"text": "What was the puzzling connection to the Far East?", "sentence_id": 1}, {"text": "Was the remainder of the body recovered as well?", "sentence_id": 2}, {"text": "How do scientists determine this age?", "sentence_id": 2}, {"text": "What region is this cave in?", "sentence_id": 2}, {"text": "Why has the cave been termed Pit of Bones?", "sentence_id": 2}, {"text": "What time period did the Neanderthals live in?", "sentence_id": 3}, {"text": "Which other sites in Europe?", "sentence_id": 3}, {"text": "how did they surmise that?", "sentence_id": 3}, {"text": "What did they base their info on?", "sentence_id": 3}, {"text": "What other sites in Europe?", "sentence_id": 3}, {"text": "What other questions did the scientists have?", "sentence_id": 4}, {"text": "what are his credentials?", "sentence_id": 4}, {"text": "What questions does this raise?", "sentence_id": 4}, {"text": "How long has he been doing this?", "sentence_id": 4}, {"text": "What questions did the DNA raise?", "sentence_id": 4}, {"text": "What is the surprise?", "sentence_id": 5}, {"text": "should they be surprised?", "sentence_id": 5}, {"text": "Why is this a surprise, what was the original expectation?", "sentence_id": 5}, {"text": "Is this a popular publication?", "sentence_id": 5}, {"text": "What was a big surprise?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0517.json b/inquisitive/query/test/0517.json new file mode 100644 index 0000000000000000000000000000000000000000..d7815e8c52a11256e2ff6d22ac7c4256d9bfca92 --- /dev/null +++ b/inquisitive/query/test/0517.json @@ -0,0 +1 @@ +[{"text": "What are the free online courses?", "sentence_id": 1}, {"text": "why are they mixed?", "sentence_id": 1}, {"text": "What are free open online courses?", "sentence_id": 1}, {"text": "What sort of results?", "sentence_id": 1}, {"text": "are those common?", "sentence_id": 2}, {"text": "Why is the percentage for completion so low for MOOCs?", "sentence_id": 2}, {"text": "Why do they drop off?", "sentence_id": 3}, {"text": "what did the other half do?", "sentence_id": 4}, {"text": "What percentage?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0518.json b/inquisitive/query/test/0518.json new file mode 100644 index 0000000000000000000000000000000000000000..fc3b649b2831950e2b581ca22211a7dbde3ab66f --- /dev/null +++ b/inquisitive/query/test/0518.json @@ -0,0 +1 @@ +[{"text": "What sport do the college athletes play?", "sentence_id": 1}, {"text": "Why would it be too early to be relieved?", "sentence_id": 1}, {"text": "why do they say that?", "sentence_id": 1}, {"text": "Why is it too early to breathe a sigh of relief?", "sentence_id": 1}, {"text": "Who is the author of the report?", "sentence_id": 2}, {"text": "What were the worrisome changes in brain structure shown in the athletes?", "sentence_id": 2}, {"text": "What are the outward sign's of head trauma?", "sentence_id": 2}, {"text": "What were the changes in cognitive performance?", "sentence_id": 2}, {"text": "Where can I find this evidence?", "sentence_id": 3}, {"text": "like test taking?", "sentence_id": 3}, {"text": "What are some of the evidence found already that supports this?", "sentence_id": 3}, {"text": "What exactly happens when a player is hit that causes these problems?", "sentence_id": 3}, {"text": "What is the percentage that heal during the off-season?", "sentence_id": 4}, {"text": "when will we know?", "sentence_id": 4}, {"text": "How does someone heal with injuries like this?", "sentence_id": 4}, {"text": "Which scientists?", "sentence_id": 5}, {"text": "How are scientists trying to figure out how readily the brain recovers from injury?", "sentence_id": 5}, {"text": "What does cumulative mean?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0522.json b/inquisitive/query/test/0522.json new file mode 100644 index 0000000000000000000000000000000000000000..66aa73806c31ae4069427d613b676420faa2ddee --- /dev/null +++ b/inquisitive/query/test/0522.json @@ -0,0 +1 @@ +[{"text": "What does the Arctic have to do with hurricanes?", "sentence_id": 1}, {"text": "How do ice formations affect tropical storms?", "sentence_id": 1}, {"text": "Which scientists?", "sentence_id": 2}, {"text": "How does ice building up release heat?", "sentence_id": 2}, {"text": "Heat release from what?", "sentence_id": 3}, {"text": "How does heat release move the jet stream?", "sentence_id": 3}, {"text": "What shift?", "sentence_id": 4}, {"text": "How does the stream moving further south slow the storms?", "sentence_id": 4}, {"text": "How does this affect the impact of the storms?", "sentence_id": 4}, {"text": "How does the Arctic heat trigger other weather events?", "sentence_id": 5}, {"text": "How would it cause these things to happen, and where would they occur?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0524.json b/inquisitive/query/test/0524.json new file mode 100644 index 0000000000000000000000000000000000000000..575ffa5e4260531c15ed21a74f9c597f6d4fd0b8 --- /dev/null +++ b/inquisitive/query/test/0524.json @@ -0,0 +1 @@ +[{"text": "Which lawmakers are arguing that the $1 coin would save the government money?", "sentence_id": 1}, {"text": "How is paper money more durable than people realize?", "sentence_id": 2}, {"text": "why would it cost more?", "sentence_id": 2}, {"text": "What exactly helped them come to their conclusion?", "sentence_id": 3}, {"text": "what was their name?", "sentence_id": 3}, {"text": "Even though the coin may be longer- lasting, if it costs more to make, why are some congress people pushing the government to replace the $1 bill?", "sentence_id": 4}, {"text": "Who in Congress?", "sentence_id": 4}, {"text": "Which countries are included in the eurozone?", "sentence_id": 5}, {"text": "has it worked?", "sentence_id": 5}, {"text": "Why have they replaced small denomination paper?", "sentence_id": 5}, {"text": "Which other countries?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0528.json b/inquisitive/query/test/0528.json new file mode 100644 index 0000000000000000000000000000000000000000..b6a25a670d27b2ec073c5ff0a0940f3501c08b1c --- /dev/null +++ b/inquisitive/query/test/0528.json @@ -0,0 +1 @@ +[{"text": "Who are the authors of the report?", "sentence_id": 1}, {"text": "How much have the wages increased?", "sentence_id": 1}, {"text": "What are the differences in wages?", "sentence_id": 1}, {"text": "How about the husbands?", "sentence_id": 2}, {"text": "why would it slow them?", "sentence_id": 2}, {"text": "Why would motherhood slow their strides?", "sentence_id": 2}, {"text": "What was the percentage before?", "sentence_id": 3}, {"text": "why not 100 percent?", "sentence_id": 3}, {"text": "How much have wages dropped for young men?", "sentence_id": 4}, {"text": "How were they discriminated at work?", "sentence_id": 5}, {"text": "what did the 15 percent experience?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0530.json b/inquisitive/query/test/0530.json new file mode 100644 index 0000000000000000000000000000000000000000..03473831e162244b823587da5cfc9ebcfd70e068 --- /dev/null +++ b/inquisitive/query/test/0530.json @@ -0,0 +1 @@ +[{"text": "what is their body plan?", "sentence_id": 1}, {"text": "What sort of advantages?", "sentence_id": 1}, {"text": "What are the advantages of the jellyfish body plan?", "sentence_id": 1}, {"text": "What is a body plan of a jellyfish?", "sentence_id": 1}, {"text": "why did they do this?", "sentence_id": 2}, {"text": "What are the wings made from?\\nWhy do they need four wings instead of two?", "sentence_id": 2}, {"text": "What is an environmental sensor?", "sentence_id": 3}, {"text": "What things in the environment would the sensor be for?", "sentence_id": 3}, {"text": "Which engineers?", "sentence_id": 4}, {"text": "What different purposes are they envisioning for the robots?", "sentence_id": 4}, {"text": "How is a jellyfish included in things with wings?", "sentence_id": 4}, {"text": "are they successful?", "sentence_id": 5}, {"text": "What flight mechanisms did they learn from the jellyfish?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0532.json b/inquisitive/query/test/0532.json new file mode 100644 index 0000000000000000000000000000000000000000..408591371fbe433d3bbf69dbaec717464b9f9598 --- /dev/null +++ b/inquisitive/query/test/0532.json @@ -0,0 +1 @@ +[{"text": "which animal is better?", "sentence_id": 1}, {"text": "Why are humans just OK when it comes to extracting oxygen?", "sentence_id": 1}, {"text": "What is better?", "sentence_id": 1}, {"text": "how do they breath?", "sentence_id": 2}, {"text": "How are birds more efficient breathers?", "sentence_id": 2}, {"text": "What makes them more efficient?", "sentence_id": 2}, {"text": "how do we know this?", "sentence_id": 3}, {"text": "Which study?", "sentence_id": 3}, {"text": "what does that mean?", "sentence_id": 4}, {"text": "What's a tidal breather?", "sentence_id": 4}, {"text": "What is a tidal breather?", "sentence_id": 4}, {"text": "What is a tidal breather?", "sentence_id": 4}] \ No newline at end of file diff --git a/inquisitive/query/test/0536.json b/inquisitive/query/test/0536.json new file mode 100644 index 0000000000000000000000000000000000000000..0391c92373bea06c86bda28e91d895dfcf96ef17 --- /dev/null +++ b/inquisitive/query/test/0536.json @@ -0,0 +1 @@ +[{"text": "how old is he?", "sentence_id": 1}, {"text": "Which players are on the team?", "sentence_id": 2}, {"text": "does north korea have a team?", "sentence_id": 2}, {"text": "why is he named that?", "sentence_id": 3}, {"text": "Who are the streetballers?", "sentence_id": 4}, {"text": "what is a streetballer?", "sentence_id": 4}, {"text": "What are streetballers?", "sentence_id": 4}, {"text": "What is a streetballer?", "sentence_id": 4}] \ No newline at end of file diff --git a/inquisitive/query/test/0537.json b/inquisitive/query/test/0537.json new file mode 100644 index 0000000000000000000000000000000000000000..b3976a6b0a088b4f30ef3e10000490380a83a9f9 --- /dev/null +++ b/inquisitive/query/test/0537.json @@ -0,0 +1 @@ +[{"text": "Where in Chicago is this canal located?", "sentence_id": 1}, {"text": "Did the Asian carp originate in Asia?", "sentence_id": 1}, {"text": "who reported it?", "sentence_id": 2}, {"text": "How do these fish get trapped in the wake of a barge?", "sentence_id": 3}, {"text": "How does this electrified swath operate?", "sentence_id": 3}, {"text": "What is an electrified swath?", "sentence_id": 3}, {"text": "how do they electrify it?", "sentence_id": 3}, {"text": "Is it possible to stop the motors on the barges and let tug boats guide them through?", "sentence_id": 4}, {"text": "Who was the research conducted by?", "sentence_id": 4}, {"text": "How detrimental to the environment are these fish that are getting through the barriers?", "sentence_id": 5}, {"text": "Why aren't small fish sometimes incapacitated by the electrical current?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0539.json b/inquisitive/query/test/0539.json new file mode 100644 index 0000000000000000000000000000000000000000..0814374a9990752c4faa2e30657249be7df27149 --- /dev/null +++ b/inquisitive/query/test/0539.json @@ -0,0 +1 @@ +[{"text": "Why do they have headaches?", "sentence_id": 1}, {"text": "Am I getting sick?", "sentence_id": 1}, {"text": "Is the congestion from a cold?", "sentence_id": 1}, {"text": "What is making getting out of bed a chore?", "sentence_id": 1}, {"text": "How does the tiny box detect anything?", "sentence_id": 2}, {"text": "Is this test really available?", "sentence_id": 2}, {"text": "Why is this in a tiny box?", "sentence_id": 2}, {"text": "Was the virus or bacteria determined?", "sentence_id": 2}, {"text": "How long have they've been working on this test?", "sentence_id": 3}, {"text": "How would this become a staple in the real world?", "sentence_id": 3}, {"text": "How is the method being developed?", "sentence_id": 4}, {"text": "What kind of method are they developing?", "sentence_id": 4}, {"text": "How are they developing a method?", "sentence_id": 4}, {"text": "What is the current rate of recognition?", "sentence_id": 4}, {"text": "Why does rapidly copying it detect illness?", "sentence_id": 5}, {"text": "How long does it usually take now to identify the bacteria or virus DNA?", "sentence_id": 5}, {"text": "How is this obtained?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0541.json b/inquisitive/query/test/0541.json new file mode 100644 index 0000000000000000000000000000000000000000..df130e23c17d9207e8c0910479d89dd2dde98f66 --- /dev/null +++ b/inquisitive/query/test/0541.json @@ -0,0 +1 @@ +[{"text": "Who are the researchers?", "sentence_id": 1}, {"text": "What did the researchers see that shown them the Neanderthals organized their living spaces by task?", "sentence_id": 1}, {"text": "What are the artifacts?", "sentence_id": 2}, {"text": "what is that?", "sentence_id": 2}, {"text": "how did they organize?", "sentence_id": 4}, {"text": "If the site was destroyed, how do they know it hosted both Neanderthals and humans?", "sentence_id": 5}, {"text": "why did they destroy it?", "sentence_id": 5}, {"text": "What showed the researchers that this site hosted Neanderthals and humans?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0544.json b/inquisitive/query/test/0544.json new file mode 100644 index 0000000000000000000000000000000000000000..ae360d83faca5aa9c2b4bc21a10f36cdc5e2e21e --- /dev/null +++ b/inquisitive/query/test/0544.json @@ -0,0 +1 @@ +[{"text": "What states does the population growth surpass in the Northeast and Midwest?", "sentence_id": 1}, {"text": "Why does Texas, California and Florida have so many new residents?", "sentence_id": 1}, {"text": "Why does this determine political clout?", "sentence_id": 1}, {"text": "can they be limited?", "sentence_id": 2}, {"text": "How many seats does Texas have currently?", "sentence_id": 2}, {"text": "is it unfair?", "sentence_id": 3}, {"text": "How many seats do these states have currently?", "sentence_id": 3}, {"text": "have states lost or gained many seats?", "sentence_id": 5}, {"text": "How are numbers readjusted each decade?", "sentence_id": 5}, {"text": "Why does it only change every decade?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0547.json b/inquisitive/query/test/0547.json new file mode 100644 index 0000000000000000000000000000000000000000..b5dbd7c46aacd317245adbb543100ede6b240f99 --- /dev/null +++ b/inquisitive/query/test/0547.json @@ -0,0 +1 @@ +[{"text": "after what?", "sentence_id": 1}, {"text": "Fifty years of what?", "sentence_id": 1}, {"text": "After the U.S. what?", "sentence_id": 1}, {"text": "is that right?", "sentence_id": 2}, {"text": "What did the Surgeon General state as the health effects of smoking?", "sentence_id": 2}, {"text": "Why is this?", "sentence_id": 2}, {"text": "How many smokers are there worldwide?", "sentence_id": 2}, {"text": "What is the cause of this increase?", "sentence_id": 3}, {"text": "why did it jump?", "sentence_id": 4}, {"text": "Is this because of marketing?", "sentence_id": 4}, {"text": "What makes this the most comprehensive ever?", "sentence_id": 5}, {"text": "What are the examining methods used here?", "sentence_id": 5}, {"text": "What makes this a growing epidemic?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/0550.json b/inquisitive/query/test/0550.json new file mode 100644 index 0000000000000000000000000000000000000000..8c77f87458826e3f043a153865d133af06e76424 --- /dev/null +++ b/inquisitive/query/test/0550.json @@ -0,0 +1 @@ +[{"text": "how did they figure that?", "sentence_id": 1}, {"text": "Why does traffic make people unhappy?", "sentence_id": 1}, {"text": "what does this mean?", "sentence_id": 2}, {"text": "What traffic jam?", "sentence_id": 2}, {"text": "How is a traffic jam keeping penguins alive?", "sentence_id": 2}, {"text": "Which scientists are studying emperor penguins?", "sentence_id": 3}, {"text": "its like a traffic jam?", "sentence_id": 3}, {"text": "Where are they traveling to? What is the purpose of the movement and travel?", "sentence_id": 3}, {"text": "Why is the winter their breeding season?", "sentence_id": 4}] \ No newline at end of file diff --git a/inquisitive/query/test/1101.json b/inquisitive/query/test/1101.json new file mode 100644 index 0000000000000000000000000000000000000000..9881c2129465de87ebf12ccc0fb9ca9dae189143 --- /dev/null +++ b/inquisitive/query/test/1101.json @@ -0,0 +1 @@ +[{"text": "How The United Nations' new commander and supply convoys headed today for?", "sentence_id": 1}, {"text": "Who's the new commander?", "sentence_id": 1}, {"text": "Why has the fighting continued?", "sentence_id": 1}, {"text": "Why did they head for Bosnia?", "sentence_id": 1}, {"text": "How reported Sporadic fighting?", "sentence_id": 2}, {"text": "What said by Bosnian Serbs?", "sentence_id": 2}, {"text": "Why are their government soldiers attacking the Serbs? ", "sentence_id": 2}, {"text": "How peacekeeping troops in Bosnia last month?", "sentence_id": 3}, {"text": "How are there so many peacekeeping troops in Bosnia, and yet so many people within the country fighting among themselves?", "sentence_id": 3}, {"text": "What exactly is the 5th Corps Gen. Atif Dudakovic doing to bring about peace in his own country?", "sentence_id": 3}, {"text": "What has persisted in northwest Bosnia?", "sentence_id": 4}, {"text": "Why has fighting broken out even during the truce?", "sentence_id": 4}, {"text": "Why does the fighting continue when there was supposed to be a truce? What is each side fighting for?", "sentence_id": 4}, {"text": "How accord the Bosnian government and Bosnian Serbs signed the truce?", "sentence_id": 5}, {"text": "Why are renegade sects opposed to the current government?", "sentence_id": 5}, {"text": "So if they signed, why are they still fighting?", "sentence_id": 5}, {"text": "Why wouldn't the Bosnian Muslims oppose the Muslim led Bosnian government? And why wouldn't they sign for peace in their country?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1102.json b/inquisitive/query/test/1102.json new file mode 100644 index 0000000000000000000000000000000000000000..34a7e483d0c9f78b18f0b0bf25bcbd950661e051 --- /dev/null +++ b/inquisitive/query/test/1102.json @@ -0,0 +1 @@ +[{"text": "How many bombers were there?", "sentence_id": 1}, {"text": "How did this allow the bombers to avoid being detected?", "sentence_id": 1}, {"text": "where did they get uniforms?", "sentence_id": 1}, {"text": "Why did these people participate in a suicide bombing?", "sentence_id": 1}, {"text": "is that a group?", "sentence_id": 2}, {"text": "Were the people who helped the bombers believed to be aligned with Israel?", "sentence_id": 2}, {"text": "Where did the bombers reach without being caught?", "sentence_id": 3}, {"text": "of which year?", "sentence_id": 3}, {"text": "Why did the collaborators help the bombers?", "sentence_id": 3}, {"text": "Where there non-lethal injuries too?", "sentence_id": 4}, {"text": "Where did the explosion take place?", "sentence_id": 4}, {"text": "What did the uniforms look like?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1103.json b/inquisitive/query/test/1103.json new file mode 100644 index 0000000000000000000000000000000000000000..dfa2bbedff6a5c940dd56a8ed8eb0a038525c70e --- /dev/null +++ b/inquisitive/query/test/1103.json @@ -0,0 +1 @@ +[{"text": "What are the names of these teams?", "sentence_id": 1}, {"text": "Why was the young man killed?", "sentence_id": 1}, {"text": "Was this killing explicitly soccer related?", "sentence_id": 1}, {"text": "Just for going to the game?", "sentence_id": 2}, {"text": "How impactful is this?", "sentence_id": 3}, {"text": "Is he the Cardinal of Genoa?", "sentence_id": 3}, {"text": "Was support of his team the only reason the man was stabbed?", "sentence_id": 4}, {"text": "What time frame is this?", "sentence_id": 5}, {"text": "What happened during the fan riot?", "sentence_id": 5}, {"text": "Is there a history of sports related violence?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1104.json b/inquisitive/query/test/1104.json new file mode 100644 index 0000000000000000000000000000000000000000..0add9057d063d6775c9c930c42a49f0b837db81d --- /dev/null +++ b/inquisitive/query/test/1104.json @@ -0,0 +1 @@ +[{"text": "where is Grozny?", "sentence_id": 1}, {"text": "why are they seizing the districts?", "sentence_id": 1}, {"text": "Why is there still much to do?", "sentence_id": 1}, {"text": "what is the main objective of the army?", "sentence_id": 2}, {"text": "is chechnya in russia?", "sentence_id": 3}, {"text": "How has the change in control impacted the residents?", "sentence_id": 3}, {"text": "What is the importance of this town?", "sentence_id": 4}, {"text": "when is the fighting expected to end?", "sentence_id": 5}, {"text": "How do the troops shell their position?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1105.json b/inquisitive/query/test/1105.json new file mode 100644 index 0000000000000000000000000000000000000000..baf8c9f799a14ae00dbe265c77d41b45a856e502 --- /dev/null +++ b/inquisitive/query/test/1105.json @@ -0,0 +1 @@ +[{"text": "Who was hosting in the neutral territory?", "sentence_id": 1}, {"text": "Was there a mediator?", "sentence_id": 1}, {"text": "What are the accusations of mutual cease-fire violations?", "sentence_id": 1}, {"text": "Why was it a tense meeting?", "sentence_id": 1}, {"text": "What sort of accusations were being leveled?", "sentence_id": 1}, {"text": "Why are they raiding convoys?", "sentence_id": 2}, {"text": "Why would he accused the UNITA rebels?", "sentence_id": 2}, {"text": "What were the goals of the rebels?", "sentence_id": 3}, {"text": "How do they retaliate \\\"devastatingly\\\"?", "sentence_id": 3}, {"text": "What was in the peace treaty?", "sentence_id": 4}, {"text": "How is the government advancing in violation of a peace treaty?", "sentence_id": 4}, {"text": "What were the terms of the treaty?", "sentence_id": 4}, {"text": "How has leadership and communication broken down?", "sentence_id": 5}, {"text": "Why were there renegade units still operating outside of the chain of command?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1106.json b/inquisitive/query/test/1106.json new file mode 100644 index 0000000000000000000000000000000000000000..56061544e0d2b35e3a0d8c578b5c076473a9e5c1 --- /dev/null +++ b/inquisitive/query/test/1106.json @@ -0,0 +1 @@ +[{"text": "What caused the advance in jobless claims?", "sentence_id": 1}, {"text": "what is the figure which deems that level is a healthy job market?", "sentence_id": 1}, {"text": "Why were these Americans laid off?", "sentence_id": 1}, {"text": "What is considered to be a healthy job market range?", "sentence_id": 1}, {"text": "What impact does seasonality have on jobs?", "sentence_id": 2}, {"text": "what does this mean?", "sentence_id": 2}, {"text": "What was the cause of the influx?", "sentence_id": 2}, {"text": "Why was the number up from last week?", "sentence_id": 2}, {"text": "How does this first increase differ from the first advance mentioned earlier?", "sentence_id": 3}, {"text": "How does this early jump reflect difficulty when the previous sentence said it marks a healthy job market?", "sentence_id": 3}, {"text": "What sort of seasonal variations were unaccounted for?", "sentence_id": 3}, {"text": "Why did the claims shoot up?", "sentence_id": 3}, {"text": "Why were these adjustments difficult?", "sentence_id": 3}, {"text": "How does a drop back to the normal level signify a positive when the increase mentioned before is a positive as well?", "sentence_id": 4}, {"text": "What information did they have to support that?", "sentence_id": 4}, {"text": "How does it reflect that?", "sentence_id": 4}, {"text": "Where and with what company were these jobs created?", "sentence_id": 5}, {"text": "How does the creation of jobs increase the number of jobless?", "sentence_id": 5}, {"text": "Which industries had the strongest job markets?", "sentence_id": 5}, {"text": "Who created these jobs?", "sentence_id": 5}, {"text": "What industry were these jobs in?", "sentence_id": 5}, {"text": "Was the previous percentage?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1107.json b/inquisitive/query/test/1107.json new file mode 100644 index 0000000000000000000000000000000000000000..9ccfeb4a46046b7255313bf01c1b0c082858c5c5 --- /dev/null +++ b/inquisitive/query/test/1107.json @@ -0,0 +1 @@ +[{"text": "Why do they have so many non native speakers?", "sentence_id": 1}, {"text": "How many pupils are there?", "sentence_id": 1}, {"text": "Where is this school located?", "sentence_id": 1}, {"text": "What is the native language there?", "sentence_id": 1}, {"text": "How many students are enrolled?", "sentence_id": 1}, {"text": "What grade levels are taught at this school?", "sentence_id": 1}, {"text": "Why is the school so full?", "sentence_id": 2}, {"text": "How over crowded is it?", "sentence_id": 2}, {"text": "Where does the money come from for these programs?", "sentence_id": 2}, {"text": "Is this a native food for the region?", "sentence_id": 2}, {"text": "Does 'bursting at the seams' mean the school have too many students or too many student activities and events?", "sentence_id": 2}, {"text": "Why is this relevant?", "sentence_id": 3}, {"text": "Where are they coming from?", "sentence_id": 3}, {"text": "Where is this located?", "sentence_id": 3}, {"text": "Is Marvin Heights or the Peel board of education in the suburbs near Toronto?", "sentence_id": 3}, {"text": "Why are they becoming more suburban?", "sentence_id": 4}, {"text": "Why the switch?", "sentence_id": 4}, {"text": "What are these patterns?", "sentence_id": 4}, {"text": "Why is this happening?", "sentence_id": 4}, {"text": "What are the factors of this change?", "sentence_id": 4}, {"text": "Why so many people year-over-year?", "sentence_id": 5}, {"text": "Are these all immigrants?", "sentence_id": 5}, {"text": "What is the top fastest growing municipality?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1108.json b/inquisitive/query/test/1108.json new file mode 100644 index 0000000000000000000000000000000000000000..f6f1f77e508724da76762737519bdf63769b5b4c --- /dev/null +++ b/inquisitive/query/test/1108.json @@ -0,0 +1 @@ +[{"text": "Who or what is Blackburn?", "sentence_id": 1}, {"text": "Why is Blackburn responsible for the fan's actions?", "sentence_id": 1}, {"text": "Why did the fan try to commit the attack?", "sentence_id": 1}, {"text": "What do they mean by official reports? How valid are they to the situation?", "sentence_id": 2}, {"text": "What type of calls did he make that were considered controversial?", "sentence_id": 3}, {"text": "At what point does taunting become too much?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1109.json b/inquisitive/query/test/1109.json new file mode 100644 index 0000000000000000000000000000000000000000..994adcec7697e217f53e0e5048eafa00e731d74e --- /dev/null +++ b/inquisitive/query/test/1109.json @@ -0,0 +1 @@ +[{"text": "How was this WWII bomb uncovered?", "sentence_id": 1}, {"text": "When did this occur and why was there an old bomb?", "sentence_id": 1}, {"text": "Why was a 500 pound bomb there?", "sentence_id": 1}, {"text": "Why were they evacuated?", "sentence_id": 1}, {"text": "How was it uncovered?", "sentence_id": 1}, {"text": "What was under construction?", "sentence_id": 1}, {"text": "When was Oranienburg Castle built?", "sentence_id": 2}, {"text": "found by who?", "sentence_id": 2}, {"text": "Who found the bomb and how?", "sentence_id": 2}, {"text": "Why was excavation being done there?", "sentence_id": 2}, {"text": "How far from the castle?", "sentence_id": 2}, {"text": "How many others?", "sentence_id": 2}, {"text": "What took so long for this for this old bomb that didn't detonate to get rediscovered?", "sentence_id": 3}, {"text": "Is there a possibility that there are more bombs in the area?", "sentence_id": 3}, {"text": "How did they disarm it?", "sentence_id": 3}, {"text": "What caused the delay?", "sentence_id": 3}, {"text": "What is that process?", "sentence_id": 3}, {"text": "How did they disarm it?", "sentence_id": 3}, {"text": "How does a delayed-action chemical fuse work?", "sentence_id": 4}, {"text": "How was it more difficult?", "sentence_id": 4}, {"text": "How many hours?", "sentence_id": 4}, {"text": "What will happen to this antique bomb?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1110.json b/inquisitive/query/test/1110.json new file mode 100644 index 0000000000000000000000000000000000000000..92e7aed9ae11b6270ac87cbf7519ed230827c86b --- /dev/null +++ b/inquisitive/query/test/1110.json @@ -0,0 +1 @@ +[{"text": "in which ways will US help", "sentence_id": 1}, {"text": "United States is supposed to do what for their confederation?", "sentence_id": 1}, {"text": "How was the US going to assist?", "sentence_id": 1}, {"text": "Why does he want their involvement?", "sentence_id": 2}, {"text": "what will the talks be about", "sentence_id": 3}, {"text": "what is this plan? how does it apply to the US?", "sentence_id": 3}, {"text": "What is part of the plan for the confederation?", "sentence_id": 3}, {"text": "Are these talks over territory disputes?", "sentence_id": 3}, {"text": "Why is this valuable?", "sentence_id": 4}, {"text": "Are both of the groups at odds also willing to make progress to move the federation forward?", "sentence_id": 4}, {"text": "who will control the remaining percent", "sentence_id": 5}, {"text": "Who control the other 49 percent of Bosnia?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1111.json b/inquisitive/query/test/1111.json new file mode 100644 index 0000000000000000000000000000000000000000..386867dd43ee9c565425986aa5556a8014374a4b --- /dev/null +++ b/inquisitive/query/test/1111.json @@ -0,0 +1 @@ +[{"text": "Who is at war against the Kurds?", "sentence_id": 1}, {"text": "Why did they order the book seized?", "sentence_id": 1}, {"text": "What book?", "sentence_id": 1}, {"text": "Why is there a separatist rebellion amoung Turkish Kurds?", "sentence_id": 2}, {"text": "What other charges have Western governments and rights groups made?", "sentence_id": 3}, {"text": "How does Kemal's book provoke \\\"hatred and enmity\\\"?", "sentence_id": 4}, {"text": "Why is the Kemal publication considered illegal?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1112.json b/inquisitive/query/test/1112.json new file mode 100644 index 0000000000000000000000000000000000000000..cd770abba75a47d4372117f4cfa4c35c66ad5fc5 --- /dev/null +++ b/inquisitive/query/test/1112.json @@ -0,0 +1 @@ +[{"text": "Why were these regions being closed during the holidays?", "sentence_id": 1}, {"text": "Why would this cause an uprising?", "sentence_id": 1}, {"text": "Which month is the holy fasting month?", "sentence_id": 1}, {"text": "Who decides which bit is Jewish and which bit is Palestinian?", "sentence_id": 2}, {"text": "What does PLO stand for?", "sentence_id": 2}, {"text": "Who is Arafat ?", "sentence_id": 3}, {"text": "Has there been similar construction scenarios in the past, and how did the opposing groups react?", "sentence_id": 3}, {"text": "What was the evidence that this was certain to take place?", "sentence_id": 4}, {"text": "Who are the fundamentalists ?", "sentence_id": 4}, {"text": "What are the different political groups in this area?", "sentence_id": 4}, {"text": "What was the result of the 1993 negotiation attempt?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1113.json b/inquisitive/query/test/1113.json new file mode 100644 index 0000000000000000000000000000000000000000..fc977ca56df9d375d3d1add738609530cdcefd96 --- /dev/null +++ b/inquisitive/query/test/1113.json @@ -0,0 +1 @@ +[{"text": "What was the highest prior donation received by the Red Cross Society for the victims of the Kobe earthquake?", "sentence_id": 1}, {"text": "What platform did they collect donations?", "sentence_id": 1}, {"text": "When was this earthquake?", "sentence_id": 1}, {"text": "What type of damage was done by the earthquake?", "sentence_id": 1}, {"text": "What is the possible range of cost resultinf from the damage from the quake?", "sentence_id": 2}, {"text": "What was the death count of this earthquake?", "sentence_id": 2}, {"text": "What is the name of the worst hit prefecture?", "sentence_id": 2}, {"text": "What are the casualty numbers that make it so deadly?", "sentence_id": 2}, {"text": "Which prefecture is the worst hit?", "sentence_id": 2}, {"text": "Why did the calculated damage increase?", "sentence_id": 3}, {"text": "How has this number been measured?", "sentence_id": 4}, {"text": "What is the Japanese government doing to serve the newly homeless?", "sentence_id": 4}, {"text": "How long will it take to build 30,000 temporary housing units?", "sentence_id": 5}, {"text": "Where are the housing units being built?", "sentence_id": 5}, {"text": "What is the timeline for more houses being constructed?", "sentence_id": 5}, {"text": "Where will they be housed permanently?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1114.json b/inquisitive/query/test/1114.json new file mode 100644 index 0000000000000000000000000000000000000000..efa347d4964c0e844367b83e04a8cf814c04b0f1 --- /dev/null +++ b/inquisitive/query/test/1114.json @@ -0,0 +1 @@ +[{"text": "How does Silajdzic plan on settling the conflict?", "sentence_id": 1}, {"text": "Why was this decided in Washington?", "sentence_id": 1}, {"text": "What are the other efforts?", "sentence_id": 2}, {"text": "What is the war about?", "sentence_id": 2}, {"text": "Why was there war in Yugoslavia?", "sentence_id": 2}, {"text": "Why was there a war taking place in Yugoslavia?", "sentence_id": 2}, {"text": "Which countries?", "sentence_id": 3}, {"text": "What was part of this peace plan?", "sentence_id": 3}, {"text": "What did the talks cover?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1115.json b/inquisitive/query/test/1115.json new file mode 100644 index 0000000000000000000000000000000000000000..a8b4f24eaa03c4b505a72f874b09f734aef50e48 --- /dev/null +++ b/inquisitive/query/test/1115.json @@ -0,0 +1 @@ +[{"text": "Why was Art Shell fired?", "sentence_id": 1}, {"text": "why was he fired", "sentence_id": 1}, {"text": "Why was he fired?", "sentence_id": 1}, {"text": "What are the changes that need to be discussed?", "sentence_id": 3}, {"text": "What, exactly, were his accomplishments during his tenure?", "sentence_id": 4}, {"text": "what were previous super bowl scores", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1116.json b/inquisitive/query/test/1116.json new file mode 100644 index 0000000000000000000000000000000000000000..1779045c494cae8b85225c5a0acadccd6467fb74 --- /dev/null +++ b/inquisitive/query/test/1116.json @@ -0,0 +1 @@ +[{"text": "Why were the peace talks having such trouble?", "sentence_id": 1}, {"text": "Why is the process faltering?", "sentence_id": 1}, {"text": "How did they seek to revive the peace process?", "sentence_id": 1}, {"text": "Why did these leaders meet?", "sentence_id": 1}, {"text": "What makes it unprecedented?", "sentence_id": 1}, {"text": "How do they plan to revive the process?", "sentence_id": 1}, {"text": "Why are the countries unable to stop the attacks?", "sentence_id": 2}, {"text": "Why does disillusionment with the agreement run deep?", "sentence_id": 2}, {"text": "Why is their ability to stem attacks uncertain at best?", "sentence_id": 2}, {"text": "Who is disillusioned by the agreement?", "sentence_id": 2}, {"text": "What made it so dramatic?", "sentence_id": 2}, {"text": "Who is disillusioned?", "sentence_id": 2}, {"text": "Why is there ability uncertain?", "sentence_id": 2}, {"text": "What types of concessions need to be made?", "sentence_id": 3}, {"text": "Why are their positions already weak?", "sentence_id": 3}, {"text": "How are both of their positions weak", "sentence_id": 3}, {"text": "What will they find difficult?", "sentence_id": 3}, {"text": "What are the concessions?", "sentence_id": 3}, {"text": "Why are their positions weak?", "sentence_id": 3}, {"text": "Why did the PM sound a positive note?", "sentence_id": 4}, {"text": "How did he do so?", "sentence_id": 4}, {"text": "Why was the meeting held at such a late time of day?", "sentence_id": 4}, {"text": "What kind of food was served?", "sentence_id": 4}, {"text": "Why do the Muslims fast?", "sentence_id": 4}, {"text": "What makes him optimistic?", "sentence_id": 5}, {"text": "What result would be optimal?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1117.json b/inquisitive/query/test/1117.json new file mode 100644 index 0000000000000000000000000000000000000000..b08291c43eb2e54c1bcc49d418937e6937ee1cb5 --- /dev/null +++ b/inquisitive/query/test/1117.json @@ -0,0 +1 @@ +[{"text": "What does the term under par mean? ", "sentence_id": 1}, {"text": "Is this USDollars?", "sentence_id": 1}, {"text": "What does shot par mean in this context? ", "sentence_id": 2}, {"text": "What is the weather usually like then?", "sentence_id": 2}, {"text": "Is this a good score and if so why? ", "sentence_id": 3}, {"text": "What is the significance of eight at 69?", "sentence_id": 4}, {"text": "What game is this person a defending champion of? ", "sentence_id": 5}, {"text": "Why was Lanner unable to take advantage? ", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1118.json b/inquisitive/query/test/1118.json new file mode 100644 index 0000000000000000000000000000000000000000..aebc99651a33df3f87055d1ef192d47423b3f803 --- /dev/null +++ b/inquisitive/query/test/1118.json @@ -0,0 +1 @@ +[{"text": "Why Mideast leaders Thursday planned to tackle Israel's?", "sentence_id": 1}, {"text": "What does it mean to \\\"tackle\\\" the negotiations? ", "sentence_id": 1}, {"text": "Why don't even optimists expect progress?", "sentence_id": 1}, {"text": "What factors have affected negotiations between Isreal and Syria?", "sentence_id": 1}, {"text": "Why were the talks stalled out?", "sentence_id": 1}, {"text": "How President Hafez Assad, Israel's most adamant foe invited?", "sentence_id": 2}, {"text": "Why wasn't the President invited? ", "sentence_id": 2}, {"text": "Why is President Hafez Assad Isreal's most adamant foe?", "sentence_id": 2}, {"text": "Why was Assad not invited to the summit?", "sentence_id": 2}, {"text": "How Assad process of war?", "sentence_id": 3}, {"text": "What does political bachelorhood mean? ", "sentence_id": 3}, {"text": "Why is Assad hesitating entering the peace process?", "sentence_id": 3}, {"text": "When he decide?", "sentence_id": 4}, {"text": "What is the next step? ", "sentence_id": 4}] \ No newline at end of file diff --git a/inquisitive/query/test/1119.json b/inquisitive/query/test/1119.json new file mode 100644 index 0000000000000000000000000000000000000000..84165a25d0ac507e90e741c0578d15388a0f8c35 --- /dev/null +++ b/inquisitive/query/test/1119.json @@ -0,0 +1 @@ +[{"text": "What are the similarities?", "sentence_id": 5}, {"text": "Who are these other carriers?", "sentence_id": 5}, {"text": "Which other carriers does Delta have these agreements with?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1120.json b/inquisitive/query/test/1120.json new file mode 100644 index 0000000000000000000000000000000000000000..3900730ee6765f03942730360e50aabc2ac11eb4 --- /dev/null +++ b/inquisitive/query/test/1120.json @@ -0,0 +1 @@ +[{"text": "Why is the federation in such trouble?", "sentence_id": 1}, {"text": "Why is there a prospect of wider war? ", "sentence_id": 1}, {"text": "Why is the section of Croatian Serbs breaking away?", "sentence_id": 2}, {"text": "Why would Serbs aid the fight? ", "sentence_id": 2}, {"text": "Was does the UN believe this will not occur? ", "sentence_id": 3}, {"text": "What is the end result of salvaging the federation?", "sentence_id": 5}, {"text": "What is Holbrooke doing to salvage the federation? ", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1121.json b/inquisitive/query/test/1121.json new file mode 100644 index 0000000000000000000000000000000000000000..a622c23986826c9bf6635a93e44d03f3a6d7f4e6 --- /dev/null +++ b/inquisitive/query/test/1121.json @@ -0,0 +1 @@ +[{"text": "What is in the water that the locals are looking at?", "sentence_id": 1}, {"text": "What is so important that would cause them to be fixated on what they are looking at?", "sentence_id": 1}, {"text": "Why are the authorities the ones preventing the locals from dealing with what they are looking at?", "sentence_id": 1}, {"text": "Why were they in such a position?", "sentence_id": 1}, {"text": "Why are so many of them living below sea level and why is it such a big deal?", "sentence_id": 2}, {"text": "Why were the authorities telling people to leave?", "sentence_id": 3}, {"text": "Why would everyone have stayed?", "sentence_id": 3}, {"text": "Who is anticipating the flood?", "sentence_id": 4}, {"text": "What city in what country are we in?", "sentence_id": 4}] \ No newline at end of file diff --git a/inquisitive/query/test/1122.json b/inquisitive/query/test/1122.json new file mode 100644 index 0000000000000000000000000000000000000000..966074e2a05089c2e3405e2a4f68321dc7d5b81a --- /dev/null +++ b/inquisitive/query/test/1122.json @@ -0,0 +1 @@ +[{"text": "Why did the spreading of AIDS level off?", "sentence_id": 1}, {"text": "What level did it stop at?", "sentence_id": 1}, {"text": "What was behind the number of cases starting to fall at this time?", "sentence_id": 1}, {"text": "How was the report delivered?", "sentence_id": 2}, {"text": "What is different between the old and new definitions?", "sentence_id": 3}, {"text": "Why an old definition?", "sentence_id": 3}, {"text": "What was the old definition of HIV-AIDS?", "sentence_id": 3}, {"text": "How high was the rate?", "sentence_id": 4}, {"text": "What will that be caused by?", "sentence_id": 4}, {"text": "How many people had tuberculosis?", "sentence_id": 5}, {"text": "Why was it only defined by one population segment?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1123.json b/inquisitive/query/test/1123.json new file mode 100644 index 0000000000000000000000000000000000000000..5275a5cf900d5e6ae3a6322c9eadbf4ecf177e4d --- /dev/null +++ b/inquisitive/query/test/1123.json @@ -0,0 +1 @@ +[{"text": "What do the letters IRA stand for? ", "sentence_id": 1}, {"text": "How is it under threat?", "sentence_id": 1}, {"text": "Who are these convicts and what did they do?", "sentence_id": 1}, {"text": "Why are these particular convicts being freed?", "sentence_id": 1}, {"text": "Why is the government freeing them?", "sentence_id": 1}, {"text": "Why is the process under threat?", "sentence_id": 1}, {"text": "What is the prisoner issue?", "sentence_id": 1}, {"text": "Why was the Irish peace discussion having trouble?", "sentence_id": 1}, {"text": "Who arranged for the cease fire? ", "sentence_id": 2}, {"text": "Why did the IRA cease their fire?", "sentence_id": 2}, {"text": "What was the rationale for their release?", "sentence_id": 2}, {"text": "What do the words Sinn Fein mean? ", "sentence_id": 3}, {"text": "Why does he think the British government would or could follow suit?", "sentence_id": 3}, {"text": "What does unionist mean in this context? ", "sentence_id": 4}, {"text": "Who was behind the document and proposals?", "sentence_id": 4}, {"text": "Why is this alarming to the Protestant majority?", "sentence_id": 4}, {"text": "What are the settlements the proposal is detailing?", "sentence_id": 4}, {"text": "Which party does John Major represent? ", "sentence_id": 5}, {"text": "Why did the Ulster Unionist Party find this outrageous?", "sentence_id": 5}, {"text": "How would they participate?", "sentence_id": 5}, {"text": "What were the votes crucial for?", "sentence_id": 5}, {"text": "Why would the Unionists be compelled to serve both governments?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1124.json b/inquisitive/query/test/1124.json new file mode 100644 index 0000000000000000000000000000000000000000..1471434cada212e6ddc55039ce9472f9b0f175eb --- /dev/null +++ b/inquisitive/query/test/1124.json @@ -0,0 +1 @@ +[{"text": "how many member nations?", "sentence_id": 1}, {"text": "How much are the dues?", "sentence_id": 1}, {"text": "Why were so many nations delinquent?", "sentence_id": 1}, {"text": "How many assessments?", "sentence_id": 2}, {"text": "What are the payment terms, and why is it not being paid?", "sentence_id": 2}, {"text": "How much does each nation pay towards the budget?", "sentence_id": 3}, {"text": "What is the normal payment deadline?", "sentence_id": 4}, {"text": "What will happen if no one pays?", "sentence_id": 5}, {"text": "What determines how much each nation need to pay towards the overall budget?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1125.json b/inquisitive/query/test/1125.json new file mode 100644 index 0000000000000000000000000000000000000000..70fb3683e3bc9d5b000eac433781437b622cae6e --- /dev/null +++ b/inquisitive/query/test/1125.json @@ -0,0 +1 @@ +[{"text": "What exactly will the meetings entail?", "sentence_id": 1}, {"text": "Was this to be the first summit between Israel and PLO?", "sentence_id": 1}, {"text": "Why are they struggling to find ways to stop extremism?", "sentence_id": 2}, {"text": "How long have the attacks been going on?", "sentence_id": 2}, {"text": "Are there mediators to help with the negotiation progress?", "sentence_id": 3}] \ No newline at end of file diff --git a/inquisitive/query/test/1126.json b/inquisitive/query/test/1126.json new file mode 100644 index 0000000000000000000000000000000000000000..1e41e648a6a94c6a26cb14829cdf598826742aec --- /dev/null +++ b/inquisitive/query/test/1126.json @@ -0,0 +1 @@ +[{"text": "what kind of relationship did the foreign ministers reaffirmed", "sentence_id": 1}, {"text": "Which four other nations?", "sentence_id": 1}, {"text": "With which four Western European nations does Turkey reaffirm a commitment to a strong relationship?", "sentence_id": 1}, {"text": "What commitments have the foreign ministers of Turkey and four Western European nations made to each other that would support strong relationships betwee them?", "sentence_id": 1}, {"text": "Which Western European nations were involved?", "sentence_id": 1}, {"text": "How long has this relationship existed?", "sentence_id": 1}, {"text": "what are the interests of western european countries", "sentence_id": 2}, {"text": "Why was it an \\\"informal\\\" discussion.", "sentence_id": 2}, {"text": "What is the collective interest in that region?", "sentence_id": 2}, {"text": "Why do these states have a special interest in the region?", "sentence_id": 2}, {"text": "What is the civil rights situation in Turkey?", "sentence_id": 3}, {"text": "What have been the ramifications of the civil rights situation in Turkey?", "sentence_id": 3}, {"text": "What is the civil rights situation in Turkey?", "sentence_id": 3}, {"text": "what regions to kurdish people ask to have as autonomous homeland", "sentence_id": 4}, {"text": "What are the Kurdish rebels rebelling against?", "sentence_id": 4}, {"text": "What abuses have Turkish police engaged in?", "sentence_id": 4}, {"text": "Is the Turkish government killing civilians in this campaign?", "sentence_id": 4}, {"text": "Was their land taken over by Turkey?", "sentence_id": 4}, {"text": "what are the tactics", "sentence_id": 5}, {"text": "What do Turkish officials consider \\\"uncompromising\\\" tactics?", "sentence_id": 5}, {"text": "Is this referring to the campaign of violence?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1127.json b/inquisitive/query/test/1127.json new file mode 100644 index 0000000000000000000000000000000000000000..7d3a91a2cfed264f306cafa50cc7b529f2fdd611 --- /dev/null +++ b/inquisitive/query/test/1127.json @@ -0,0 +1 @@ +[{"text": "In what way did Sugihara save Jews?", "sentence_id": 1}, {"text": "How was he able to save so many people?", "sentence_id": 1}, {"text": "how did he save them?", "sentence_id": 1}, {"text": "What did he do to save all the Jews?", "sentence_id": 1}, {"text": "How much danger was Chinue Sugihara in at the time for signing the transit visas?", "sentence_id": 2}, {"text": "Where did the Jews with the transit visas signed by Sugihara escape to?", "sentence_id": 3}, {"text": "When did Sugihara pass away?", "sentence_id": 3}, {"text": "Did Japan partake in the holocaust?", "sentence_id": 4}, {"text": "Where, generally were these Jewish people sent to after landing in Japan?", "sentence_id": 4}, {"text": "How did the rescued Jews end up in Kobe from Lithuania?", "sentence_id": 4}, {"text": " hidden\tWhat is a \\hidden child\\\"?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1128.json b/inquisitive/query/test/1128.json new file mode 100644 index 0000000000000000000000000000000000000000..d688698a20e0feb52ac501687c2a9e013a905c66 --- /dev/null +++ b/inquisitive/query/test/1128.json @@ -0,0 +1 @@ +[{"text": "What are some accomplishments of Christian Fittipaldi?", "sentence_id": 1}, {"text": "is he a good prospect?", "sentence_id": 1}, {"text": "What is Formula One?", "sentence_id": 2}, {"text": "What is their relationship?", "sentence_id": 2}, {"text": "is that young for a racer?", "sentence_id": 2}, {"text": "what's a holdover?", "sentence_id": 3}, {"text": "who's quote is this?", "sentence_id": 3}, {"text": "What about them is complimentary as teammates?", "sentence_id": 4}, {"text": "Were they former teammates or competitors?", "sentence_id": 4}, {"text": "What is an oval track?", "sentence_id": 5}, {"text": "are these uncommon?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1129.json b/inquisitive/query/test/1129.json new file mode 100644 index 0000000000000000000000000000000000000000..e4a508224d153dd7d14746a0a718c6afc666e517 --- /dev/null +++ b/inquisitive/query/test/1129.json @@ -0,0 +1 @@ +[{"text": "Why was princess Diana widely tipped to visit Kobe?", "sentence_id": 1}, {"text": "Why didn't she go to Kobe after the quake?", "sentence_id": 1}, {"text": "What source tipped the news about Princess Diana's itinerary?", "sentence_id": 1}, {"text": "What changed her mind about going to the city??", "sentence_id": 1}, {"text": "What is Princess Diana planning on doing instead?", "sentence_id": 2}, {"text": "How might this happen?", "sentence_id": 3}, {"text": "How would she upstage the Imperial Family?", "sentence_id": 3}, {"text": "What caused the Japanese authorities to be concerned over this?", "sentence_id": 3}, {"text": "Why is the family showing support for the victims of the quake?", "sentence_id": 4}, {"text": "Why were they showing such little support?", "sentence_id": 4}, {"text": "What are some examples of the lackluster show of support?", "sentence_id": 4}, {"text": "Why is this official remaining anonymous?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1130.json b/inquisitive/query/test/1130.json new file mode 100644 index 0000000000000000000000000000000000000000..d2791a0e8cf1e431ba80544ac8fd9820771f2f04 --- /dev/null +++ b/inquisitive/query/test/1130.json @@ -0,0 +1 @@ +[{"text": "Which country received them?", "sentence_id": 1}, {"text": "What fungicide was used?", "sentence_id": 1}, {"text": "Where are these officials located? To what country were the American apples exported?", "sentence_id": 1}, {"text": "What type of fungicide was found on these fruits?", "sentence_id": 1}, {"text": "Which health officials specifically?", "sentence_id": 1}, {"text": "Why is it important to investigate a fungicide?", "sentence_id": 1}, {"text": "What are the name of these shops?", "sentence_id": 2}, {"text": "How many apples were included in the sample from which two were found to have fungicide?", "sentence_id": 2}, {"text": "How many pounds of the imported apples had this compound still on them?", "sentence_id": 2}, {"text": "What could be the reason of the traced amounts of fungicide?", "sentence_id": 2}, {"text": "Why would Bill Morgan say this so confidently? ", "sentence_id": 3}, {"text": "How does he know this information?", "sentence_id": 3}, {"text": "22", "sentence_id": 3}, {"text": "How can a technical issue be described?", "sentence_id": 3}, {"text": "What were the name of these shops?", "sentence_id": 4}, {"text": "Why were they 'Voluntarily' recalling them if it is a health issue?", "sentence_id": 4}, {"text": "Which stores specifically stocked and then recalled the apples so customers who purchased apples at those locations could know of a potential hazard?", "sentence_id": 4}, {"text": "What health hazards could be experienced from these fungicides?", "sentence_id": 4}, {"text": "What are the possible health hazards?", "sentence_id": 4}, {"text": "Who was this spokesman?", "sentence_id": 5}, {"text": "Why does he have no plans if this is a health issue?", "sentence_id": 5}, {"text": "Why will Daiei continue to sell apples that may have fungicide on them?", "sentence_id": 5}, {"text": "Who is the spokesman for Japan's largest supermarket chain?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1131.json b/inquisitive/query/test/1131.json new file mode 100644 index 0000000000000000000000000000000000000000..8803e43566a1707252e5641f9243daca6a53b426 --- /dev/null +++ b/inquisitive/query/test/1131.json @@ -0,0 +1 @@ +[{"text": "Why has this lasted so long?", "sentence_id": 1}, {"text": "What amount are they considering?", "sentence_id": 1}, {"text": "Why are they fighting?", "sentence_id": 1}, {"text": "What are the Tamil separatists claiming?", "sentence_id": 1}, {"text": "the government of which country?", "sentence_id": 1}, {"text": "How much is the budget?", "sentence_id": 2}, {"text": "When next week?", "sentence_id": 2}, {"text": "What is the cause of this hike?", "sentence_id": 2}, {"text": "defense spending of which nation?", "sentence_id": 2}, {"text": "who started the talks?", "sentence_id": 3}, {"text": "Why have they not made more progress?", "sentence_id": 3}, {"text": "What are their demands?", "sentence_id": 3}, {"text": "Why have the rebels increased their lists of demands?", "sentence_id": 3}, {"text": "peace talks between whom?", "sentence_id": 3}, {"text": "What are the rebels' demands?", "sentence_id": 3}, {"text": "Who started this war?", "sentence_id": 4}, {"text": "Why do the Tamils not have a homeland, in their mind?", "sentence_id": 4}, {"text": "How will it be utilized?", "sentence_id": 5}, {"text": "What is the strategy?", "sentence_id": 5}, {"text": "what strategy?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1132.json b/inquisitive/query/test/1132.json new file mode 100644 index 0000000000000000000000000000000000000000..ef076d7c91efef76fa095fce4f7a9a7f35781411 --- /dev/null +++ b/inquisitive/query/test/1132.json @@ -0,0 +1 @@ +[{"text": "how did they block the convoy of aid?", "sentence_id": 1}, {"text": "who are these renegade forces, and how are they designated renegade?", "sentence_id": 1}, {"text": "How did they block the aid?", "sentence_id": 1}, {"text": "Why did the Muslim forces ally themselves with the rebel Serbs?", "sentence_id": 1}, {"text": "Why were the civilians beleaguered?", "sentence_id": 1}, {"text": "how is it threatening the truce?", "sentence_id": 2}, {"text": "What are the details of the country-wide truce?", "sentence_id": 2}, {"text": "Truce between whom?", "sentence_id": 2}, {"text": "Why is there fighting in this area?\\n", "sentence_id": 2}, {"text": "who are they rebelling against?", "sentence_id": 3}, {"text": "Why are the Serbs and Muslims not party to the cease-fire?", "sentence_id": 3}, {"text": "Why did the peace negotiations cease?", "sentence_id": 3}, {"text": "what form did this intransigence take?", "sentence_id": 4}, {"text": "How long has the U.N. been trying to halt fighting?", "sentence_id": 4}, {"text": "How long has this been going on?", "sentence_id": 4}, {"text": "Why are the UN not capable according to Bosnia?", "sentence_id": 4}, {"text": "Why does the blame lie with them?", "sentence_id": 5}, {"text": "Why is the Bihac region to blame?", "sentence_id": 5}, {"text": "Who else is to blame?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1133.json b/inquisitive/query/test/1133.json new file mode 100644 index 0000000000000000000000000000000000000000..23873e2094dcf9fbe2932a3994ed37d6fa0b10c3 --- /dev/null +++ b/inquisitive/query/test/1133.json @@ -0,0 +1 @@ +[{"text": "Why was his quitting the post so controversial?", "sentence_id": 1}, {"text": "What human rights violations?", "sentence_id": 1}, {"text": "Which violations?", "sentence_id": 1}, {"text": "Why were his reports being ignored?", "sentence_id": 2}, {"text": "How many reports weren't acted on?", "sentence_id": 2}, {"text": "What other types of pressure are thought to be more effective?", "sentence_id": 3}, {"text": "What would be another, possibly better way?", "sentence_id": 3}, {"text": "What might other people be merely thinking other than what was already stated?", "sentence_id": 4}, {"text": "What is a denunciation?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1134.json b/inquisitive/query/test/1134.json new file mode 100644 index 0000000000000000000000000000000000000000..579886eea6860aeaa6de5cf820e2431d2ad63cf3 --- /dev/null +++ b/inquisitive/query/test/1134.json @@ -0,0 +1 @@ +[{"text": "Why are they attacking Chechnya?", "sentence_id": 1}, {"text": "What would membership in the Council of Europe entail for Russia?", "sentence_id": 1}, {"text": "Who are these 33 nations?", "sentence_id": 1}, {"text": "Why were these talks suspended?", "sentence_id": 1}, {"text": "What attacks have happened?", "sentence_id": 1}, {"text": "Who was voting?", "sentence_id": 2}, {"text": "What did they condemn?", "sentence_id": 2}, {"text": "What has specifically happened?", "sentence_id": 2}, {"text": "What are it's greatest accomplishments thus far?", "sentence_id": 3}, {"text": "Founded by whom?", "sentence_id": 3}, {"text": "How many ways do they promote unity?", "sentence_id": 3}, {"text": "Why is the council best known for the convention?", "sentence_id": 3}, {"text": "What are the criteria to enter?", "sentence_id": 4}, {"text": "Who are their members?", "sentence_id": 4}, {"text": "Why was it expanded to include more?", "sentence_id": 4}, {"text": "How could the Council demand a ceasefire if they cannot make binding law?", "sentence_id": 5}, {"text": "With what power will they demand this?", "sentence_id": 5}, {"text": "How exactly do they want altered?", "sentence_id": 5}, {"text": "Is more control necessary?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1135.json b/inquisitive/query/test/1135.json new file mode 100644 index 0000000000000000000000000000000000000000..b71a87db7b95d783d8a3cc0be31d8303764507dd --- /dev/null +++ b/inquisitive/query/test/1135.json @@ -0,0 +1 @@ +[{"text": "Why will they have a hard time/struggle?", "sentence_id": 1}, {"text": "Who is Michael Stich?", "sentence_id": 1}, {"text": "What sport is Croatia debuting in?", "sentence_id": 1}, {"text": "How did he struggle/to what extent?", "sentence_id": 2}, {"text": "What makes Michael Stich's ground strokes superior?", "sentence_id": 2}, {"text": "Why is this person unknown?", "sentence_id": 3}, {"text": "What is the Davis Cup?", "sentence_id": 3}, {"text": "Why did he take a 2.5 year absence?", "sentence_id": 3}, {"text": "What is Sasa Hirszon's background?", "sentence_id": 3}, {"text": "How did Ivanisevic become ranked no. 5 in the world?", "sentence_id": 4}, {"text": "How fast is the first serve of Ivanisevic?", "sentence_id": 5}, {"text": "Why did he lose his ability to a certain extent?", "sentence_id": 5}, {"text": "Why wasn't he able to use his first serve effectively?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1136.json b/inquisitive/query/test/1136.json new file mode 100644 index 0000000000000000000000000000000000000000..b153987aa68e7c9a42aacd4a36581bde4729b831 --- /dev/null +++ b/inquisitive/query/test/1136.json @@ -0,0 +1 @@ +[{"text": "Disarmament of who?", "sentence_id": 1}, {"text": "Which group is making these demands?", "sentence_id": 1}, {"text": "What does this have to do with the previous sentence?", "sentence_id": 2}, {"text": "Why was this practice more common in the past?", "sentence_id": 2}, {"text": "What are linking debates, and how are they commonly used during the Cold War?", "sentence_id": 2}, {"text": "How are they getting rid of the nuclear weapons?", "sentence_id": 3}, {"text": "Who are the participating countries?", "sentence_id": 3}, {"text": "Which Swiss city?", "sentence_id": 4}, {"text": "Which Swiss city is this article referring to?", "sentence_id": 4}, {"text": "What is considered a strategic weapon?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1137.json b/inquisitive/query/test/1137.json new file mode 100644 index 0000000000000000000000000000000000000000..1db3b00b8eaabd06f531cff0efc2dd7673b9e5fc --- /dev/null +++ b/inquisitive/query/test/1137.json @@ -0,0 +1 @@ +[{"text": "what is the Davis Cup?", "sentence_id": 1}, {"text": "What was the reason behind the injury?", "sentence_id": 1}, {"text": "What sport is the Davis Cup?", "sentence_id": 1}, {"text": "How was his foot injured?", "sentence_id": 1}, {"text": "what sport is this? Volleyball?", "sentence_id": 2}, {"text": "What is a forehand volley?", "sentence_id": 2}, {"text": "will Rosset be okay? how hard is the recovery process?", "sentence_id": 3}, {"text": "Did he suffer any broken bones?", "sentence_id": 3}, {"text": "what is his home town?", "sentence_id": 4}, {"text": "What team does Eltingh play for?", "sentence_id": 4}, {"text": "what kind of matches ? what sport is being talked about?", "sentence_id": 5}, {"text": "Are all matches in this tournament singles?", "sentence_id": 5}, {"text": "What is the structure of this tournament?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1138.json b/inquisitive/query/test/1138.json new file mode 100644 index 0000000000000000000000000000000000000000..3fa8f808008cf99cc8007a035c25a7c0ff7fa781 --- /dev/null +++ b/inquisitive/query/test/1138.json @@ -0,0 +1 @@ +[{"text": "Why has it taken seven years?", "sentence_id": 1}, {"text": "Why hasn't it been congenial?", "sentence_id": 2}, {"text": "In what way has the buildup not been congenial?", "sentence_id": 2}, {"text": "Why has there been such acrimony?", "sentence_id": 2}, {"text": "Why did they attack a spectator?", "sentence_id": 3}, {"text": "What sort of provocations was Moore accused of being behind?", "sentence_id": 4}] \ No newline at end of file diff --git a/inquisitive/query/test/1139.json b/inquisitive/query/test/1139.json new file mode 100644 index 0000000000000000000000000000000000000000..0eb99d9d1ba1fd0c8fca6792e2245677c989b5d1 --- /dev/null +++ b/inquisitive/query/test/1139.json @@ -0,0 +1 @@ +[{"text": "What are the seven largest economies?", "sentence_id": 1}, {"text": "what sort of economic woes / what is going on there?", "sentence_id": 1}, {"text": "What type of issues was Mexico experiencing at this time?", "sentence_id": 1}, {"text": "What caused the nosedive?", "sentence_id": 2}, {"text": "Why did the Mexican peso nosedive?", "sentence_id": 2}, {"text": "Why had the peso been struggling to keep up with other currencies?", "sentence_id": 2}, {"text": "which officials? name some from each country or the most important ones?", "sentence_id": 3}, {"text": "what date?", "sentence_id": 4}, {"text": "Which ones?", "sentence_id": 5}, {"text": "Why are the Europeans unhappy?", "sentence_id": 5}, {"text": "Why is it only a north American problem?", "sentence_id": 5}, {"text": "Why was this seen as a problem that was only North American when many economies are typically seen as linked?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1140.json b/inquisitive/query/test/1140.json new file mode 100644 index 0000000000000000000000000000000000000000..0e33737c8c75917bdcbe5b085ced27ecad07dd80 --- /dev/null +++ b/inquisitive/query/test/1140.json @@ -0,0 +1 @@ +[{"text": "How would security be increased?", "sentence_id": 1}, {"text": "How would expanding NATO into eastern Europe give Russia more security?", "sentence_id": 1}, {"text": "Why does Moscow fears that Russia will get more security?", "sentence_id": 1}, {"text": "What are some reasons why NATO expansion would give Russia more security?", "sentence_id": 1}, {"text": "Why is Willy Claes willing to cooperate with Russia?", "sentence_id": 2}, {"text": "How does he plan to cooperate with Russia?", "sentence_id": 2}, {"text": "What are the requirements to become a member of NATO? What are the benefits?", "sentence_id": 2}, {"text": "Why was Claes meeting Munich of Western defense leaders and military chiefs?", "sentence_id": 3}, {"text": "What is the objective of the meeting in Munich?", "sentence_id": 3}, {"text": "which saturday was it?", "sentence_id": 3}, {"text": "Why is Russia upset about this alliance?", "sentence_id": 4}, {"text": "Why does NATO wants former Soviet allies to join the alliance?", "sentence_id": 4}, {"text": "Why is Russia upset about this?", "sentence_id": 4}, {"text": "How many candidates are under consideration for membership?", "sentence_id": 4}, {"text": "what are they finding?", "sentence_id": 4}, {"text": "How does NATO plan on taking in Poland, Hungary and others as members?", "sentence_id": 5}, {"text": "Why did Moscow interfere in Chechnya?", "sentence_id": 5}, {"text": "is that in russia?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1141.json b/inquisitive/query/test/1141.json new file mode 100644 index 0000000000000000000000000000000000000000..22ec64c6541f81b414ffd792ef18c7397987930c --- /dev/null +++ b/inquisitive/query/test/1141.json @@ -0,0 +1 @@ +[{"text": "How bad was the anti-semitism in Yugoslavia at that time?", "sentence_id": 1}, {"text": "How did the Yugoslavs save the Jews from the Holocaust?", "sentence_id": 1}, {"text": "Which three Yugoslavs were honored?", "sentence_id": 1}, {"text": "What was their role in saving the Jews?", "sentence_id": 1}, {"text": "Who are considered Gentiles?", "sentence_id": 2}, {"text": "How big is the Jewish community in Belgrade?", "sentence_id": 3}, {"text": "Who were the one savior and two others?", "sentence_id": 3}, {"text": "How severe have these anti-Muslim sentiments been?", "sentence_id": 4}, {"text": "How did he save them? Where did he hide them?", "sentence_id": 4}, {"text": "How were the families saved during the raids?", "sentence_id": 4}, {"text": "How was Ristic tipped about the Croat raid?", "sentence_id": 5}, {"text": "How did Ristic receive his information?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1142.json b/inquisitive/query/test/1142.json new file mode 100644 index 0000000000000000000000000000000000000000..d0fc8c83cebf306a16126f6c5cccad2aa45c7621 --- /dev/null +++ b/inquisitive/query/test/1142.json @@ -0,0 +1 @@ +[{"text": "Why has there been so much violence here?", "sentence_id": 1}, {"text": "Why has there been an outbreak in violence?", "sentence_id": 1}, {"text": "What is the name?", "sentence_id": 1}, {"text": "Why has violence wracked the country?", "sentence_id": 1}, {"text": "How could the conference help end the violence?", "sentence_id": 1}, {"text": "What were the differing ideas at play?", "sentence_id": 2}, {"text": "Why is an opposition conference occurring?", "sentence_id": 2}, {"text": "Why are parties opposing each other?", "sentence_id": 2}, {"text": "How could the EU's ideas bring peace to the country?", "sentence_id": 3}, {"text": "Who posed the question?", "sentence_id": 3}, {"text": "Why was there such economic struggle in Algeria?", "sentence_id": 4}, {"text": "What are the extremist views at play?", "sentence_id": 4}, {"text": "Why is there an economic crisis in Algeria?", "sentence_id": 4}] \ No newline at end of file diff --git a/inquisitive/query/test/1143.json b/inquisitive/query/test/1143.json new file mode 100644 index 0000000000000000000000000000000000000000..16fbba42372b27d60f48554e8c24f172860adb27 --- /dev/null +++ b/inquisitive/query/test/1143.json @@ -0,0 +1 @@ +[{"text": "Why were some critical decisions delayed?", "sentence_id": 1}, {"text": "How long has it been so far?", "sentence_id": 1}, {"text": "What were each side asking for originally?", "sentence_id": 2}, {"text": "How far into their future?", "sentence_id": 2}, {"text": "Why were these issues not even touched?", "sentence_id": 3}, {"text": "Why did Amr feel this way?", "sentence_id": 4}, {"text": "Why could the meeting not discuss more specific measures?", "sentence_id": 4}, {"text": "Why can they not discuss specific ways or means?", "sentence_id": 4}] \ No newline at end of file diff --git a/inquisitive/query/test/1144.json b/inquisitive/query/test/1144.json new file mode 100644 index 0000000000000000000000000000000000000000..c87ead9dd36917a4bef606c93e7c4909c2f0f017 --- /dev/null +++ b/inquisitive/query/test/1144.json @@ -0,0 +1 @@ +[{"text": "Why is a premature return not wanted?", "sentence_id": 1}, {"text": "Where were the evacuees coming from?", "sentence_id": 1}, {"text": "Why is the return of the flooding evacuees premature?", "sentence_id": 1}, {"text": "Was the area still dangerous?", "sentence_id": 2}, {"text": "What are the risks to the people returning to Gelderland Province?", "sentence_id": 2}, {"text": "How is the exodus going to be reversed?", "sentence_id": 3}, {"text": "Was the area flooded for that long?", "sentence_id": 3}, {"text": "What negative consequences could occur upon reversal of the exodus?", "sentence_id": 3}, {"text": "Why are they concerned about looting and how will they prevent it?", "sentence_id": 4}, {"text": "How bad was the area?", "sentence_id": 4}, {"text": "Why had so many not been updated?", "sentence_id": 5}, {"text": "How can they do this relatively fast?", "sentence_id": 5}, {"text": "How many dikes were there?", "sentence_id": 5}, {"text": "How long will it tajke for emergency workers to finish shoring up weak and soggy dikes?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1145.json b/inquisitive/query/test/1145.json new file mode 100644 index 0000000000000000000000000000000000000000..0e14b8f18aee6cbab969c82d4997d60aaaad1925 --- /dev/null +++ b/inquisitive/query/test/1145.json @@ -0,0 +1 @@ +[{"text": "What does softening mean?", "sentence_id": 1}, {"text": "What does a softening economy mean?", "sentence_id": 1}, {"text": "What does that mean for a normal person?", "sentence_id": 2}, {"text": "How are stocks following higher?", "sentence_id": 3}, {"text": "What is a bond market and why is it higher?", "sentence_id": 3}, {"text": "What does dlrs stand for?", "sentence_id": 3}, {"text": "What issues are being advanced?", "sentence_id": 4}, {"text": "What is an advancing issue?", "sentence_id": 4}, {"text": "I don't understand what this means.", "sentence_id": 4}, {"text": "What is a nasdaq composite? I have no knowledge of stock lingo. ", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1147.json b/inquisitive/query/test/1147.json new file mode 100644 index 0000000000000000000000000000000000000000..6df4a924f082c0755b733659dc0c8cb5e4ce182e --- /dev/null +++ b/inquisitive/query/test/1147.json @@ -0,0 +1 @@ +[{"text": "Why do post-communist Russians like his art?", "sentence_id": 1}, {"text": "Who was the artist?", "sentence_id": 1}, {"text": "What were the specific type of monumental sculptures?", "sentence_id": 1}, {"text": "Who is this Canadian artist?", "sentence_id": 1}, {"text": "Why was this exhibition chosen to be the first?", "sentence_id": 2}, {"text": "What made it a 'major' exhibition compared to previous non-major ones?", "sentence_id": 2}, {"text": "How many pieces are in this art exhibition?", "sentence_id": 2}, {"text": "How massive are these art installations?", "sentence_id": 4}, {"text": "What does the subject 'fragile life forces' mean?", "sentence_id": 4}, {"text": "How are they trying to break free?", "sentence_id": 4}, {"text": "What is the name of this exhibition hall?", "sentence_id": 4}, {"text": "Why is the flame symbolic?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1148.json b/inquisitive/query/test/1148.json new file mode 100644 index 0000000000000000000000000000000000000000..905755f7719d238d2b08663bf169f2c6b2f9dd6a --- /dev/null +++ b/inquisitive/query/test/1148.json @@ -0,0 +1 @@ +[{"text": "Why is there a renewal of war?", "sentence_id": 1}, {"text": "Why are there tension between the nations?", "sentence_id": 1}, {"text": "What would cause a renewal of this war?", "sentence_id": 1}, {"text": "Why would Bosnian Serbs warned of turning up Balkan tension to another notch?", "sentence_id": 1}, {"text": "How is Croatia likely to attack Serbs?", "sentence_id": 2}, {"text": "How have the peacekeepers been able to do what they need to?", "sentence_id": 3}, {"text": "How did the thousands of peacekeepers enforced a brittle truce in Croatia?", "sentence_id": 3}, {"text": "Why is there an upsurge of violence in Croatia and Bosnia?", "sentence_id": 3}, {"text": "Why does their mandate expire on this date?", "sentence_id": 5}, {"text": "Why is Croatian President separating his forces from rebel Serb units?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1149.json b/inquisitive/query/test/1149.json new file mode 100644 index 0000000000000000000000000000000000000000..de35f0aea6face05dccc7acb833d398ee72e248a --- /dev/null +++ b/inquisitive/query/test/1149.json @@ -0,0 +1 @@ +[{"text": "Why had they lost enthusiasm for these efforts?", "sentence_id": 1}, {"text": "Why did they lose enthusiasm to stop expanding their auto sales?", "sentence_id": 1}, {"text": "Which newspaper is this?", "sentence_id": 1}, {"text": "Who was the newspaper's source of information?", "sentence_id": 1}, {"text": "What 'auto sales'?", "sentence_id": 1}, {"text": "Why need full access and not just some?", "sentence_id": 2}, {"text": "What are the details behind these limitations?", "sentence_id": 3}, {"text": "Why was it so difficult for Chrysler to gain access to the Japan market?", "sentence_id": 4}, {"text": "Why are they always told no when it comes to expanding to the Japanese market?", "sentence_id": 4}, {"text": "What issues are holding up these negotiations?", "sentence_id": 4}, {"text": "Why not stop the sale of Japanese-built cars and exclude them since they exclude us.", "sentence_id": 5}, {"text": "Which Japanese companies are making it more difficult for negotiators?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/query/test/1150.json b/inquisitive/query/test/1150.json new file mode 100644 index 0000000000000000000000000000000000000000..8cc14b9167962004798efd299f7173ee7a38ff2e --- /dev/null +++ b/inquisitive/query/test/1150.json @@ -0,0 +1 @@ +[{"text": "What proof do Dominican authorities have that these individuals were involved in the scandal?", "sentence_id": 1}, {"text": "Why is there a customs scandal?", "sentence_id": 1}, {"text": "Why are Dominican authorities asking for the arrest?", "sentence_id": 1}, {"text": "What is involved in a customs scandal?", "sentence_id": 1}, {"text": "How was the money stolen?", "sentence_id": 1}, {"text": "Where is Jorge Castro being extradited to?", "sentence_id": 2}, {"text": "Why was the extradition requested?", "sentence_id": 2}, {"text": "What problems prompted huge withdrawals by depositors?", "sentence_id": 3}, {"text": "Why were there huge withdrawals?", "sentence_id": 3}, {"text": "What sort of issues was the bank having?", "sentence_id": 3}, {"text": "What is a \\\"pleasure boat\\\"?", "sentence_id": 4}, {"text": "How many officials were arrested before Castro fled?", "sentence_id": 4}, {"text": "How does what Castro paid compare to the rates everyone else has had to pay?\\n", "sentence_id": 5}, {"text": "How do they know they are in Miami?", "sentence_id": 5}, {"text": "Had the banker exported legally, how much profit would he have made?", "sentence_id": 5}] \ No newline at end of file diff --git a/inquisitive/sources/test/0101.json b/inquisitive/sources/test/0101.json new file mode 100644 index 0000000000000000000000000000000000000000..ecd4bddfbd93d12ed8db5fb8639cc7e95cff804a --- /dev/null +++ b/inquisitive/sources/test/0101.json @@ -0,0 +1 @@ +[{"text": "Olin Corp. said third-quarter net income rose 26% on the strength of its chemical business."}, {"text": "Net was $24 million, or $1.15 a share, up from $19 million, or 90 cents a share, a year earlier."}, {"text": "Sales rose 7.4% to $580 million from $540 million."}, {"text": "Olin said its chemical segment had profit of $22 million, up from $15 million a year ago, largely because of gains in electrochemicals such as caustic soda."}, {"text": "The company said the gains were tied to volume increases and higher prices."}, {"text": "The market for electrochemicals include the paper, water-purification and textile industries."}, {"text": "The chemical segment had a $6 million gain on the sale of ammonia and urea businesses, which was offset by a $6 million charge for future environmental expenditures."}, {"text": "Profit in Olin's defense and ammunition segment rose to $8 million from $7 million."}, {"text": "The metals segment, hurt by a strike, had break-even results, against $3 million a year ago."}, {"text": "In the first nine months, net rose 21% to $93 million, or $4.52 a share, from $77 million, or $3.62 a share a year ago."}, {"text": "Sales rose 13% to $1.91 billion from $1.69 billion."}, {"text": "In New York Stock Exchange composite trading, Olin closed at $58.50 a share, down 25 cents."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0102.json b/inquisitive/sources/test/0102.json new file mode 100644 index 0000000000000000000000000000000000000000..1083e628750299f0eb234f161c3a7cf8b8cd081c --- /dev/null +++ b/inquisitive/sources/test/0102.json @@ -0,0 +1 @@ +[{"text": "Bank of New England Corp., seeking to streamline its business after a year of weak earnings and mounting loan problems, said it will sell some operations and lay off 4% of its work force."}, {"text": "The bank holding company also reported that third-quarter profit dropped 41%, to $42.7 million, or 61 cents a share, from the year-earlier $72.3 million, or $1.04 a share."}, {"text": "Among its restructuring measures, the company said it plans to sell 53 of its 453 branch offices and to lay off 800 employees."}, {"text": "Altogether, employment is expected to decline to less than 16,000 from the current level of about 18,000."}, {"text": "Walter Connolly, chairman, said in an interview that the company expects to record pretax gains of $100 million to $125 million from the sale of its leasing operations and of certain financial processing services."}, {"text": "In a prepared statement, the company said it expects to realize those gains before year end."}, {"text": "Nonperforming assets continued to pile up in the latest quarter, rising to $900 million, or 3.52% of loans and leases, from $667 million, or 2.68%, at the end of the second quarter."}, {"text": "Some $170 million of the $233 million increase in nonperforming loans was related to real estate, and roughly three-quarters of that was in the troubled New England market, according to Richard Driscoll, vice chairman."}, {"text": "Mr. Driscoll said that, despite continued weakness in the region's real estate market, Bank of New England expects the rate of increase in nonperforming assets to slow in coming quarters."}, {"text": "Mr. Connolly noted that net third-quarter charge-offs, at $63 million, improved slightly from the $67 million in the second quarter."}, {"text": "And he indicated that more substantial improvement is expected in the next couple of quarters."}, {"text": "The company increased its loan loss reserve to $354 million from $342 million at the end of the second quarter."}, {"text": "Total assets slipped to $31.4 billion, from $32 billion as of June 30."}, {"text": "Among other restructuring measures, the bank said it will close its loan production offices in Chicago, New York and Philadelphia."}, {"text": "The Chicago office figured prominently in the bank's problems earlier this year, when $65 million in loans to Chicago businessman William Stoecker went sour."}, {"text": "In an internal memorandum to employees, Messrs."}, {"text": "Connolly and Driscoll described the restructuring as an effort to continue rationalizing operations assembled during a series of mergers over the past five years."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0103.json b/inquisitive/sources/test/0103.json new file mode 100644 index 0000000000000000000000000000000000000000..5da41e0a0cbb746765a07d44e3ed9ad485387d0a --- /dev/null +++ b/inquisitive/sources/test/0103.json @@ -0,0 +1 @@ +[{"text": "Canada, which is preparing to speed up tariff cuts with the U.S., recorded a 47% narrowing in its trade surplus with the U.S. in August, Statistics Canada, a federal agency, reported."}, {"text": "U.S. exports to Canada jumped 11.2% in August from July while U.S. imports from Canada rose only 2.7%."}, {"text": "As a result, Canada's trade surplus with the U.S. narrowed to C$656.5 million (US$558 million) in August from C$1.23 billion (US$1.04 billion) in July."}, {"text": "U.S. exports benefited in August from heavy Canadian spending on new plant and equipment and a pickup in Canadian auto demand, Canadian officials said."}, {"text": "The U.S. and Canada, which do more trade than any other pair of nations, are to meet next month to arrange an acceleration of planned tariff cuts under the U.S.-Canada free trade agreement."}, {"text": "Industries in both countries have requested a speedup of tariff cuts on hundreds of products."}, {"text": "Some tariffs were eliminated when the trade pact took effect Jan. 1."}, {"text": "The remainder were to be phased out in five or 10 annual installments, with all tariffs eliminated by January 1998."}, {"text": "The two countries aim to reach an agreement by early December on a package of accelerated tariff cuts that would take effect early next year."}, {"text": "Canadian officials said the trade pact has kindled an export interest among many small Canadian companies that previously had little or no foreign sales."}, {"text": "For such businessmen, the Canadian government is organizing 55 missions this year to U.S. states bordering on Canada."}, {"text": "The businessmen are introduced to potential agents and distributors and instructed in trade procedures."}, {"text": "The U.S. Commerce Department is planning to try out similar trips on U.S. businessmen in coming months under its Canada First! Outreach Program."}, {"text": "Participants in the U.S. missions to Canada are to be assisted by members of the Service Corps of Retired Executives, a volunteer group, in dealing with their export challenges."}, {"text": "The Canadian government also has recently opened new trade offices in San Diego; San Juan, Puerto Rico; Miami; Princeton, N.J., and Denver, bringing the total number of such Canadian offices in the U.S. to 27."}, {"text": "The U.S. has six trade promotion offices in Canada."}, {"text": "Canada's export effort has been blunted by robust home market demand and by an 18% appreciation of the Canadian dollar against its U.S. counterpart in the past three years that has made Canadian goods more costly in the U.S."}, {"text": "Canada's trade surplus with all countries narrowed to C$203.5 million in August from C$528.3 million in July, Statistics Canada said."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0104.json b/inquisitive/sources/test/0104.json new file mode 100644 index 0000000000000000000000000000000000000000..0171631346e6d2c2a2fdcae3cc8c348b164456b8 --- /dev/null +++ b/inquisitive/sources/test/0104.json @@ -0,0 +1 @@ +[{"text": "The Federal National Mortgage Association set up a three-member office of the chairman and elected James A. Johnson as vice chairman, effective Jan. 1."}, {"text": "Mr. Johnson has been a managing director at Shearson Lehman Hutton since 1985, and before that was president of Public Strategies, a Washington consulting firm."}, {"text": "He is well-known in Democratic circles, having been executive assistant to Vice President Walter Mondale and chairman of Mr. Mondale's 1984 presidential campaign."}, {"text": "At Fannie Mae, he will take responsibility for the corporation's financial and legal areas and will work with David Maxwell, chairman and chief executive officer, and Roger Birk, president and chief operating officer, on strategic planning."}, {"text": "Mr. Johnson, 45 years old, has been a consultant on strategy to Fannie Mae for the past 3 1/2 years."}, {"text": "In an interview, he said Fannie Mae faces a number of challenges with the restructuring of the thrift industry and the push to broaden its activities overseas. 'There's no shortage of major things to do,' he said."}, {"text": "Fannie Mae also said James A. Aliber, chairman of First Federal of Michigan and a director since 1985, moved up the date of his retirement from the board to accommodate Mr. Johnson's election as a director."}, {"text": "The board has 13 members elected by holders and five presidential appointees."}, {"text": "Fannie Mae, a federally chartered, shareholder-owned corporation, operates a secondary market for mortgage loans, buying loans from lenders, packaging some into securities for sale to investors and keeping the rest in its portfolio."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0106.json b/inquisitive/sources/test/0106.json new file mode 100644 index 0000000000000000000000000000000000000000..d41e279d3cebb147ce5795050c222ee9009f46f1 --- /dev/null +++ b/inquisitive/sources/test/0106.json @@ -0,0 +1 @@ +[{"text": "The former president of FirstSouth F.A., a defunct Arkansas thrift, pleaded guilty to conspiring to inflate the institution's earnings by concealing worthless loan guarantees."}, {"text": "Roderick D. Reed III, who was also chief operating officer of FirstSouth, could receive a maximum sentence of five years in federal prison and a $250,000 fine."}, {"text": "A sentencing date hasn't been set."}, {"text": "Mr. Reed admitted he conspired to conceal an agreement not to enforce loan guarantees executed by Dallas real-estate developers A. Starke Taylor III and George S. Watson, both of whom were FirstSouth stockholders."}, {"text": "Neither Mr. Taylor nor Mr. Watson have been charged with criminal wrongdoing."}, {"text": "By concealing the non-enforcement agreement, certain transactions with Messrs."}, {"text": "Taylor and Watson were entered on FirstSouth's books as loans, allowing the thrift to report fees and interest as current income, according to the U.S. attorney's office in Little Rock, Ark."}, {"text": "The conspiracy was part of an effort by Mr. Reed to hide FirstSouth's shaky financial condition from federal regulators, according to federal prosecutors and regulators."}, {"text": "The $1.68 billion thrift was declared insolvent and closed in December 1986."}, {"text": "FirstSouth's former chairman and chief executive officer, Howard Weichern, is also charged with conspiring to conceal the agreements with Messrs."}, {"text": "Watson and Taylor."}, {"text": "Mr. Weichern is scheduled for trial Jan. 3 before federal Judge Stephen Reasoner of Little Rock."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0107.json b/inquisitive/sources/test/0107.json new file mode 100644 index 0000000000000000000000000000000000000000..6d0c932a04a9a5aecd7dfd88c868f211cb5b551f --- /dev/null +++ b/inquisitive/sources/test/0107.json @@ -0,0 +1 @@ +[{"text": "Prospect Group Inc., whose recent hostile tender offer for Recognition Equipment Inc. failed for lack of financing, apparently has gained a measure of control over the troubled company anyway."}, {"text": "As part of what a Recognition spokeswoman termed an 'amiable agreement,' Prospect Group will wind up with control of top management posts and an increased stake in the maker of data management equipment."}, {"text": "In a management restructuring, Thomas L. Ringer resigned as chairman, chief executive and a director, while Israel Sheinberg resigned as a director."}, {"text": "Mr. Sheinberg remains as executive vice president."}, {"text": "Thomas M. Hurley and Robert A. Vanourek, who had been designated to take over Recognition's top spots had Prospect's tender offer succeeded, were named co-chief executives and directors."}, {"text": "Mr. Hurley was formerly a vice president and general manager of an Avery International division; Mr. Vanourek was a former group vice president of Pitney Bowes Inc."}, {"text": "In addition, the agreement calls for Gilbert H. Lamphere, chairman of Prospect Group's executive committee, to be named chairman of a restructured board that will include four new independent directors."}, {"text": "Also named to the revised board was Thomas A. Loose, Recognition's senior vice president and general counsel."}, {"text": "Prospect, a New York-based leveraged buy-out firm, also agreed to invest $15 million in Recognition, which in turn agreed to repurchase as much as $20 million of its stock."}, {"text": "That would increase Prospect's ownership of the company's fully-diluted shares outstanding to 20% from 14.1%."}, {"text": "Under the agreement, Prospect is permitted to increase its stake in Recognition to 30%."}, {"text": "Beyond that, Prospect said it wouldn't offer to acquire additional shares for less than $11.25 a share during the next year or less than $14.06 a share during the subsequent two years."}, {"text": "Recognition also said it obtained a commitment from Chemical Bank and Bank of Boston to convert an estimated $18 million in bank debt to a new, 24-month secured term loan to be repaid through the sale of certain assets."}, {"text": "In August, Recognition said it was in violation of certain terms of its debt agreements with bank lenders because of a $3.9 million loss for the third quarter ended July 31."}, {"text": "The company attributed the loss to declining revenue and litigation costs relating to criminal charges against the company and two former executives, William G. Moore Jr. and Robert W. Reedy."}, {"text": "The former executives were indicted last October on charges of fraud, theft and conspiracy related to efforts by the company to win $400 million in Postal Service contracts."}, {"text": "Recognition Equipment said it expected to put the agreement with Prospect to a vote of its stockholders at a special meeting in January."}, {"text": "In New York Stock Exchange composite trading, Recognition rose 87.5 cents to $6.625."}, {"text": "Prospect slipped 25 cents to $10.50 in national over-the-counter trading."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0108.json b/inquisitive/sources/test/0108.json new file mode 100644 index 0000000000000000000000000000000000000000..47bd5ef3da801b9d98306dde22444c41bac489aa --- /dev/null +++ b/inquisitive/sources/test/0108.json @@ -0,0 +1 @@ +[{"text": "Tribune Co., helped by a hefty boost in performance at its broadcasting and entertainment operations, said net income jumped 21% in its third quarter ended Sept. 24 on a 3% increase in revenue."}, {"text": "The broadcasting and newspaper concern, based in Chicago, said net was $62.7 million, or 77 cents a primary share, up from $51.6 million, or 69 cents a share."}, {"text": "Per-share figures this year reflect $6.8 million in preferred-share dividends; the 1988 quarter didn't have such a payout."}, {"text": "Revenue rose to $590.7 million from $575.1 million."}, {"text": "Nine-month net climbed 19% to $174.8 million, or $2.21 a primary share, from $147.5 million, or $1.94 a share."}, {"text": "Nine-month per-share figures for 1989 reflect $12.9 million in preferred dividends that had no counterpart in the year-earlier quarter."}, {"text": "Revenue rose 4% to $1.79 billion."}, {"text": "In New York Stock Exchange composite trading Friday, Tribune closed at $49.375, down $4.75."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0109.json b/inquisitive/sources/test/0109.json new file mode 100644 index 0000000000000000000000000000000000000000..73893cdfe3e15ec771fd674b9d87c2dfb10243ca --- /dev/null +++ b/inquisitive/sources/test/0109.json @@ -0,0 +1 @@ +[{"text": "Tuesday, October 17, 1989"}, {"text": "The key U.S. and foreign annual interest rates below are a guide to general levels but don't always represent actual transactions."}, {"text": "PRIME RATE: 10 1/2%."}, {"text": "The base rate on corporate loans at large U.S. money center commercial banks."}, {"text": "FEDERAL FUNDS: 8 11/16% high, 8 5/8% low, 8 5/8% near closing bid, 8 11/16% offered."}, {"text": "Reserves traded among commercial banks for overnight use in amounts of $1 million or more."}, {"text": "Source: Fulton Prebon (U.S.A.) Inc."}, {"text": "DISCOUNT RATE: 7%."}, {"text": "The charge on loans to depository institutions by the New York Federal Reserve Bank."}, {"text": "CALL MONEY: 9 3/4% to 10%."}, {"text": "The charge on loans to brokers on stock exchange collateral."}, {"text": "COMMERCIAL PAPER placed directly by General Motors Acceptance Corp.: 8.40% 30 to 44 days; 8.325% 45 to 59 days; 8.10% 60 to 89 days; 8% 90 to 119 days; 7.85% 120 to 149 days; 7.70% 150 to 179 days; 7.375% 180 to 270 days."}, {"text": "COMMERCIAL PAPER: High-grade unsecured notes sold through dealers by major corporations in multiples of $1,000: 8.50% 30 days; 8.40% 60 days; 8.375% 90 days."}, {"text": "CERTIFICATES OF DEPOSIT: 8.05% one month; 8.02% two months; 8% three months; 7.98% six months; 7.95% one year."}, {"text": "Average of top rates paid by major New York banks on primary new issues of negotiable C.D.s, usually on amounts of $1 million and more."}, {"text": "The minimum unit is $100,000."}, {"text": "Typical rates in the secondary market: 8.50% one month; 8.50% three months; 8.45% six months."}, {"text": "BANKERS ACCEPTANCES: 8.38% 30 days; 8.28% 60 days; 8.23% 90 days; 8.13% 120 days; 8.03% 150 days; 7.93% 180 days."}, {"text": "Negotiable, bank-backed business credit instruments typically financing an import order."}, {"text": "LONDON LATE EURODOLLARS: 8 5/8% to 8 1/2% one month; 8 9/16% to 8 7/16% two months; 8 9/16% to 8 7/16% three months; 8 1/2% to 8 3/8% four months; 8 7/16% to 8 5/ 16% five months; 8 7/16% to 8 5/16% six months."}, {"text": "LONDON INTERBANK OFFERED RATES (LIBOR): 8 5/8% one month; 8 9/16% three months; 8 7/16% six months; 8 7/16% one year."}, {"text": "The average of interbank offered rates for dollar deposits in the London market based on quotations at five major banks."}, {"text": "FOREIGN PRIME RATES: Canada 13.50%; Germany 8.50%; Japan 4.875%; Switzerland 8.50%; Britain 15%."}, {"text": "These rate indications aren't directly comparable; lending practices vary widely by location."}, {"text": "TREASURY BILLS: Results of the Monday, October 16, 1989, auction of short-term U.S. government bills, sold at a discount from face value in units of $10,000 to $1 million: 7.37% 13 weeks; 7.42% 26 weeks."}, {"text": "FEDERAL HOME LOAN MORTGAGE CORP. (Freddie Mac): Posted yields on 30-year mortgage commitments for delivery within 30 days. 9.88%, standard conventional fixed-rate mortgages; 7.875%, 2% rate capped one-year adjustable rate mortgages."}, {"text": "Source: Telerate Systems Inc."}, {"text": "FEDERAL NATIONAL MORTGAGE ASSOCIATION (Fannie Mae): Posted yields on 30 year mortgage commitments for delivery within 30 days (priced at par) 9.80%, standard conventional fixed-rate mortgages; 8.70%, 6/2 rate capped one-year adjustable rate mortgages."}, {"text": "Source: Telerate Systems Inc."}, {"text": "MERRILL LYNCH READY ASSETS TRUST: 8.50%."}, {"text": "Annualized average rate of return after expenses for the past 30 days; not a forecast of future returns."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0110.json b/inquisitive/sources/test/0110.json new file mode 100644 index 0000000000000000000000000000000000000000..f16a0f615d3a14d0853effb87cda9079857f3e3e --- /dev/null +++ b/inquisitive/sources/test/0110.json @@ -0,0 +1 @@ +[{"text": "Ashton-Tate Corp. reported a net loss of $19.4 million, or 74 cents a share, for the third quarter, which was burdened by severance costs and the expense of upgrading its database software inventories."}, {"text": "The software company said revenue slid 28% to $53.9 million."}, {"text": "This contrasts with the year-ago quarter, when the company had net income of $11.7 million, or 45 cents a share, on revenue of $75.7 million."}, {"text": "For the nine months, Ashton-Tate had a loss of $27.6 million, or $1.05 a share."}, {"text": "In the year-ago period, the company had profit of $34.3 million, or $1.32 a share."}, {"text": "Revenue in the period slid almost 8% to $203.2 million from about $220 million last year."}, {"text": "Edward M. Esber, chairman, president and chief executive officer, attributed the decline to reduced domestic revenue because of $4.9 million spent to upgrade existing software inventories to the new database IV Version 1.1, and $1.8 million spent on the recent reduction in work force."}, {"text": "He said the company was 'encouraged by feedback' it received from selected customers now testing Version 1.1."}, {"text": "The red ink came as no surprise to Wall Street, but analysts said they saw ominous hints of a further delay in volume shipments of Version 1.1, a harbinger of continued losses in the fourth quarter."}, {"text": "'The loss is in line with our expectations,' said John C. Maxwell III, an analyst with Dillon, Read & Co. in New York."}, {"text": "He added gross margins and operating profit 'eroded quite dramatically' from the prior quarter, along with sales of existing software product lines like Multimate and Framework."}, {"text": "'The success of a new product in the database line is needed."}, {"text": "And while the company hasn't made a definite statement, it now looks like that's not going to be anytime soon,' Mr. Maxwell said."}, {"text": "The company said in a statement that it expects to ship new products 'during the next two quarters.'"}, {"text": "'It now looks like database IV Version 1.1 isn't going to be {widely} available until the first quarter of 1990,' said David Bayer, an analyst with Montgomery Securities in San Francisco. 'This is the second delay now in getting the product out the door."}, {"text": "It does prolong the pain somewhat.'"}, {"text": "Mr. Maxwell said unless the company can start shipments of the new product sometime this quarter, the fourth-quarter loss is likely to be 'comparable to the third quarter's.' If the company can start to ship during this quarter, it could stem some, if not all of the red ink, he said."}, {"text": "In national over-the-counter trading, Ashton-Tate closed yesterday at $10 a share, up 62.5 cents."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0112.json b/inquisitive/sources/test/0112.json new file mode 100644 index 0000000000000000000000000000000000000000..4dc4b2670215e994bbd17e3d38feed717a1a27a0 --- /dev/null +++ b/inquisitive/sources/test/0112.json @@ -0,0 +1 @@ +[{"text": "Hopes for quick enactment of pending deficit-reduction legislation faded as efforts to streamline the House version in advance of a House-Senate conference broke down."}, {"text": "House leaders had hoped to follow the Senate's lead by getting an agreement from House committee chairmen under which they would drop items that wouldn't reduce the fiscal 1990 budget deficit from the House-passed bill before the negotiations with the Senate began."}, {"text": "But the effort became snagged on the question of what would become of other issues, ranging from cutting the capital-gains tax to child care to repeal of catastrophic-illness insurance. 'Many members feel there are important features of the House bill that should be enacted,' Speaker Thomas Foley (D., Wash.) said. 'If there is any support for reducing the bill, it is conditioned on their desire to see them passed in another form.'"}, {"text": "Now those items will be discussed in a House-Senate conference, which could begin as soon as today, with the expectation that they could either be resolved there or placed into other legislation. 'You've got to give these chairmen the opportunity to see if they can work things out,' said House Budget Committee Chairman Leon Panetta (D., Calif.). 'This is a democratic process -- you can't slam-dunk anything around here.'"}, {"text": "White House Budget Director Richard Darman has said he would continue to press to keep the capital-gains provision in the final version of the bill unless the House drops many of its costly provisions."}, {"text": "Senate leaders had hoped to be able to send a compromise version of the measure to President Bush by the end of the week, but Speaker Foley said that wasn't likely."}, {"text": "Failure to pass the bill meant that $16.1 billion in across-the-board spending cuts took effect Monday under the Gramm-Rudman budget law."}, {"text": "The bill must be enacted before the cuts can be restored."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0113.json b/inquisitive/sources/test/0113.json new file mode 100644 index 0000000000000000000000000000000000000000..f94a02a96dcd4a03ff8669ffd286710baad92e81 --- /dev/null +++ b/inquisitive/sources/test/0113.json @@ -0,0 +1 @@ +[{"text": "Mutual-fund czar John M. Templeton has put his money where his moniker is, pouring $1.4 million into one of his own funds, the Templeton Value Fund."}, {"text": "Mr. Templeton owns shares in several of the 33 funds that his firm manages, but only in three of the 10 available to U.S. investors, according to filings with the Securities and Exchange Commission."}, {"text": "Those are Templeton Global Income, Templeton Emerging Markets and now the Value Fund."}, {"text": "Why did he add the Value Fund to the list?"}, {"text": "Because he's very bullish on the emerging growth stocks that make up the fund's portfolio, Mr. Templeton said from his Bahamas hideaway."}, {"text": "'Emerging growth stocks haven't been popular in America for years, they've been neglected,' he said, and their prices often trail the market as a whole."}, {"text": "Mr. Templeton's 147,300-share purchase in the closed-end fund came before the U.S. stock market's plunge last Friday, but still proved slightly profitable."}, {"text": "Mr. Templeton bought his shares in several separate purchases between Aug. 30 and Sept. 28, according to reports with the SEC."}, {"text": "He bought at share prices ranging from $9.375 to $9.625."}, {"text": "The fund closed yesterday in New York Stock Exchange composite trading at $9.625, up 12.5 cents."}, {"text": "In addition, Mr. Templeton received a dividend of 22 cents a share Oct. 5."}, {"text": "RIVER RUN: A senior vice president and a vice president at James River Corp. sold the majority of their shares in the Richmond, Va., paper-products concern in late August and early September, reports filed with the SEC show."}, {"text": "The executives, who got $30.88 a share for the stock, showed good timing."}, {"text": "In Big Board trading yesterday, James River shares closed at $28.375, down 12.5 cents."}, {"text": "On Sept. 6, Robert Joseph Sherry, the firm's senior vice president of employee and public relations, sold 4,000 shares, leaving himself with 1,062 shares of James River."}, {"text": "Including a sale of stock last February, Mr. Sherry has sold 88% of his stake in the company this year, according to SEC filings."}, {"text": "Mr. Sherry declined to comment when asked about the sales."}, {"text": "James A. Toney, a vice president, sold 1,500 shares Aug. 28."}, {"text": "He still has 1,143 shares, according to SEC files."}, {"text": "Mr. Toney also declined to comment."}, {"text": "INTEREST-RATE PLAYER: Cincinnati Gas & Electric Co. tops the companies portion of the accompanying Insider Trading table this week."}, {"text": "Three of the utility's directors have at least doubled their holdings in the company since July."}, {"text": "The largest purchase was by Dudley Taft, who bought 4,400 shares for $125,075."}, {"text": "Mr. Taft, who is also president of Taft Broadcasting Co., said he bought the shares because he keeps a utility account at the brokerage firm of Salomon Brothers Inc., which had recommended the stock as a good buy."}, {"text": "Salomon Brothers confirmed that it has had a buy recommendation on the stock for about two years."}, {"text": "'Cincinnati Gas & Electric is in good shape,' Mr. Taft said, and utilities are 'a good investment because interest rates are going down.'"}, {"text": "Mr. Taft paid an average of $28.43 for each share."}, {"text": "The stock closed yesterday on the Big Board at $28.75, down 12.5 cents."}, {"text": "The two other directors bought 1,000 and 1,900 shares, respectively, at prices between $28.15 a share and $28.75 a share, filings with the SEC show."}, {"text": "The two couldn't be reached for comment."}, {"text": "A company spokesman said he couldn't explain their sudden bullishness. 'I don't know of any news or anything unusual happening here,' said Bruce Stoecklin, director of media services."}, {"text": "Peter Pae in Pittsburgh contributed to this article."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0114.json b/inquisitive/sources/test/0114.json new file mode 100644 index 0000000000000000000000000000000000000000..e3185fff9898ba79aab0d0ddf705e4f6b2188316 --- /dev/null +++ b/inquisitive/sources/test/0114.json @@ -0,0 +1 @@ +[{"text": "A new drug to prevent the rejection of transplanted organs has been successfully used on more than 100 patients at the University of Pittsburgh, according to researchers."}, {"text": "The drug, which is still in the experimental phase, hasn't been approved yet by the Food and Drug Admistration, and its long-term effects are unknown."}, {"text": "But researchers say the drug, called FK-506, could revolutionize the transplantation field by reducing harmful side effects and by lowering rejection rates."}, {"text": "Rejection has been the major obstacle in the approximately 30,000 organ transplants performed world-wide each year."}, {"text": "Researchers began using the drug in February on patients who had received kidney, liver, heart and pancreas transplants."}, {"text": "Only two of 111 transplants have been rejected."}, {"text": "The drug, discovered in 1984, is metabolized from soil fungus found in Japan."}, {"text": "The Pittsburgh patients are the first humans to be given the drug, which is made by Fujisawa Pharmaceutical Co."}, {"text": "'We're shocked by it, because it's worked so fast,' said Dr. Thomas E. Starzl, director of the University of Pittsburgh Transplantation Program, at a news conference here yesterday. 'We consider it a life-saving drug, like one for AIDS,' said Dr. John Fung, an immunologist at the University of Pittsburgh."}, {"text": "Researchers say they believe FK-506 is 100 times more effective than the traditional anti-rejection drug, cyclosporine, made by Swiss pharmaceutical giant Sandoz Ltd."}, {"text": "They are also encouraged by the relatively mild side effects of FK-506, compared with cyclosporine, which can cause renal failure, morbidity, nausea and other problems. 'The side effects {of cyclosporine} have made the penalty for its success rather high,' Dr. Starzl said."}, {"text": "Dr. Fung said that FK-506 would not be available in the market for at least a year, and that the FDA approval process usually takes three years to five years."}, {"text": "There are no firm plans to expand the experimental program beyond the University of Pittsburgh, whose hospital performs the most transplants in the world."}, {"text": "Researchers couldn't estimate the cost of the drug when it reaches the market, but they said FK-506 will enable patients to cut hospital stays by 50% and reduce the number of blood tests used to monitor the dosage of cyclosporine and other drugs among transplant recipients."}, {"text": "Dr. Starzl said the research has been largely financed by the National Institute of Health and by university funds, and that Fujisawa didn't give the hospital any grants."}, {"text": "He said that the research team had no financial stake in the drug."}, {"text": "'We've known for six months the effect of this drug, and our advice to our people has been not to buy the company's stock,' Dr. Starzl said, adding that profiting from FK-506 wouldn't be ethical."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0115.json b/inquisitive/sources/test/0115.json new file mode 100644 index 0000000000000000000000000000000000000000..5dc3cabae88bd7d5d3229727ab40321fb91d2b5d --- /dev/null +++ b/inquisitive/sources/test/0115.json @@ -0,0 +1 @@ +[{"text": "The dollar finished softer yesterday, tilted lower by continued concern about the stock market."}, {"text": "'We're trading with a very wary eye on Wall Street,' said Trevor Woodland, chief corporate trader at Harris Trust & Savings Bank in New York. 'No one is willing to place a firm bet that the stock market won't take another tumultuous ride.'"}, {"text": "News of the major earthquake in California Tuesday triggered a round of dollar sales in early Asian trade, but most foreign-exchange dealers said they expect the impact of the quake on financial markets to be short-lived."}, {"text": "Despite the dollar's lackluster performance, some foreign-exchange traders maintain that the U.S. unit remains relatively well bid."}, {"text": "Harris Trust's Mr. Woodland noted that the unit continues to show resilience in the face of a barrage of 'headline negatives' in recent weeks, including rate increases in Europe and Japan, aggressive central bank intervention, a 190-point plunge in New York stock prices, an unexpectedly poor U.S. trade report and action by the Federal Reserve to nudge U.S. rates lower."}, {"text": "While Mr. Woodland doesn't predict a significant climb for the U.S. unit in light of recent moves in interest rates around the world, he noted that 'its downside potential is surprisingly and -- for dollar bulls -- 'impressively' limited."}, {"text": "In late New York trading yesterday, the dollar was quoted at 1.8485 marks, down from 1.8667 marks late Tuesday, and at 141.45 yen, down from 142.75 yen late Tuesday."}, {"text": "Sterling was quoted at $1.5920, up from $1.5753 late Tuesday."}, {"text": "In Tokyo Thursday, the U.S. currency opened for trading at 140.97 yen, down from Wednesday's Tokyo close of 142.10 yen."}, {"text": "Since Friday's dive in stock market prices, the Fed has injected reserves into the banking system in an effort to calm the markets and avert a repeat of 1987's stock market debacle."}, {"text": "Some analysts note that after last week's stock market tailspin and Tuesday's California earthquake, it's hard to gauge where the central bank wants the key federal funds rate."}, {"text": "They say that the earthquake, by preventing many banks from operating at full capacity, has given the Fed an additional reason to keep liquidity at a high level."}, {"text": "The Fed did, in fact, execute $1.5 billion of liquidity-enhancing customer repurchase agreements, the third set of repurchase orders in three days."}, {"text": "Analysts said the additional liquidity should tend to reduce the federal funds rate."}, {"text": "For now, traders say the foreign exchange market is scrutinizing both federal funds and events on Wall Street."}, {"text": "They note that the dollar remains extremely vulnerable to the slightest bad news from the stock exchange."}, {"text": "Indeed, the U.S. unit edged lower as the Dow Jones Industrial Average dropped about 13 points in early trading."}, {"text": "A slight recovery in the stock market gave currency traders confidence to push the dollar higher before the unit dropped back by day's end."}, {"text": "Some dealers noted that nervousness over the recent sharp dive in stock prices could intensify following suggestions by Bank of Japan Governor Satoshi Sumita that appeared to advise Japanese investors to be very careful in investing in U.S. leveraged buy-outs."}, {"text": "Dealers suggest that the only positive news on the horizon that could detract attention from equities transactions is September's U.S. consumer price data."}, {"text": "The figures, due for release Friday, are expected to show an uptick in inflation to 4.8% from 4.7% in August."}, {"text": "If the figures show a hefty rise in inflation, they could militate against easing by the Fed."}, {"text": "On the Commodity Exchange in New York, gold for current delivery rose $1.30 to $368.70 an ounce in moderate trading."}, {"text": "Estimated volume was three million ounces."}, {"text": "In early trading in Hong Kong Thursday, gold was at $368.15 an ounce."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0116.json b/inquisitive/sources/test/0116.json new file mode 100644 index 0000000000000000000000000000000000000000..2c86dff0ccbd79e293069926c696cc2ce03647f4 --- /dev/null +++ b/inquisitive/sources/test/0116.json @@ -0,0 +1 @@ +[{"text": "INSURERS ARE FACING billions of dollars in damage claims from the California quake."}, {"text": "But most businesses in the Bay area, including Silicon Valley, weren't greatly affected."}, {"text": "Computer and software companies in the region are expecting virtually no long-term disruption in shipments."}, {"text": "Also, investors quickly singled out stocks of companies expected to profit or suffer from the disaster."}, {"text": "Leveraged buy-outs may be curbed by two rules in pending congressional legislation."}, {"text": "The provisions, in deficit-reduction bills recently passed by the House and Senate, could raise the price tags of such deals by up to 10% and cool the takeover boom."}, {"text": "A bill giving the Transportation Department the power to block airline leveraged buy-outs cleared a House panel."}, {"text": "But Secretary Skinner said he would urge Bush to veto the bill."}, {"text": "Housing starts sank 5.2% in September to a seven-year low."}, {"text": "The drop, following a 6.2% decline in August, indicates the industry is still being hurt by the Fed's anti-inflation battle."}, {"text": "IBM plans to buy back $1 billion of its common shares, a move likely to help the computer giant's battered stock."}, {"text": "The buy-back, which wasn't a complete surprise, was announced after the stock market had closed."}, {"text": "A capital-gains tax cut plan has been worked out by Senate Republicans."}, {"text": "A similar proposal may be introduced soon by Senate Democrats."}, {"text": "British Airways said it is seeking improved terms and a sharply lower price in any revised bid for United Air's parent."}, {"text": "The British carrier also confirmed it isn't committed to going forward with any new bid."}, {"text": "UAL's stock fell $6.25, to $191.75."}, {"text": "Stock prices rose slightly as trading slowed, while bonds ended little changed despite a slumping dollar."}, {"text": "The Dow Jones industrials gained 4.92, to 2643.65."}, {"text": "But investors remain wary about stocks, partly because of turmoil in the junk-bond market."}, {"text": "B.A.T Industries may delay part of its defensive restructuring plan, including the sale of its Saks Fifth Avenue and Marshall Field units."}, {"text": "The British conglomerate cited the recent turmoil in financial markets."}, {"text": "WCRS Group announced a major restructuring that largely removes it from the advertising business."}, {"text": "The London-based concern will sell most of its ad unit to France's Eurocom."}, {"text": "Commodore International expects to post its second consecutive quarterly loss because of weak personal computer sales in some markets."}, {"text": "Jaguar hopes to reach a friendly accord with General Motors within a month that may involve producing a cheaper executive model."}, {"text": "Sears is negotiating to refinance its Sears Tower for close to $850 million, sources said."}, {"text": "The retailer was unable to find a buyer for the building."}, {"text": "Whitbread of Britain put its spirits division up for sale, setting off a scramble among distillers."}, {"text": "The business includes Beefeater gin."}, {"text": "Markets --"}, {"text": "Stocks: Volume 166,900,000 shares."}, {"text": "Dow Jones industrials 2643.65, up 4.92; transportation 1247.87, off 6.40; utilities 213.97, off 0.57."}, {"text": "Bonds: Shearson Lehman Hutton Treasury index 3371.36, off"}, {"text": "Commodities: Dow Jones futures index 129.90, up 0.18; spot index 130.36, up 0.39."}, {"text": "Dollar: 141.45 yen, off 1.30; 1.8485 marks, off 0.0182."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0117.json b/inquisitive/sources/test/0117.json new file mode 100644 index 0000000000000000000000000000000000000000..f0f757dd216f6b3275e2a9a46b5b2657b3a555f5 --- /dev/null +++ b/inquisitive/sources/test/0117.json @@ -0,0 +1 @@ +[{"text": "CALIFORNIA STRUGGLED with the aftermath of a Bay area earthquake."}, {"text": "As aftershocks shook the San Francisco Bay area, rescuers searched through rubble for survivors of Tuesday's temblor, and residents picked their way through glass-strewn streets."}, {"text": "In Oakland, hopes faded for finding any more survivors within the concrete and steel from the collapse of an interstate highway."}, {"text": "At least 270 people were reported killed and 1,400 injured in the rush-hour tremor that caused billions of dollars of damage along 100 miles of the San Andreas fault."}, {"text": "Bush declared the region a major disaster area and the military was mobilized to prevent looting."}, {"text": "The baseball commissioner said the third game of the World Series between the Giants and the Athletics would be played Tuesday in Candlestick Park."}, {"text": "HONECKER WAS OUSTED as leader of East Germany amid growing unrest."}, {"text": "The 77-year-old official, who oversaw the building of the Berlin Wall, was removed during a meeting of the 163-member Communist Party Central Committee in East Berlin."}, {"text": "Honecker, who was reported ill following gall-bladder surgery in August, said he was resigning for health reasons."}, {"text": "He was succeeded by internal-security chief Egon Krenz, 52, a hard-liner who quickly ruled out any sharing of power with pro-democracy groups."}, {"text": "Honecker's departure came after weeks of street protests and an exodus to the West of East Germans who had become disenchanted with his rule."}, {"text": "HUNGARY ADOPTED constitutional changes to form a democratic system."}, {"text": "At a nationally televised legislative session in Budapest, the Parliament overwhelmingly approved changes formally ending one-party domination in the country, regulating free elections by next summer and establishing the office of state president to replace a 21-member council."}, {"text": "The country was renamed the Republic of Hungary."}, {"text": "Like other Soviet bloc nations, it had been known as a 'people's republic' since"}, {"text": "The voting for new laws followed dissolution of Hungary's Communist Party this month and its replacement by a Western-style Socialist Party."}, {"text": "The space shuttle Atlantis blasted into orbit from Cape Canaveral, Fla., and its crew of five astronauts launched the nuclear-powered Galileo space probe on a flight to the planet Jupiter."}, {"text": "The $1.4 billion robot spacecraft's exploratory mission is to take six years."}, {"text": "The shuttle is slated to return Monday to California."}, {"text": "South Korea's President Roh addressed a joint House-Senate meeting and urged patience over U.S. demands for the opening of Seoul's markets to more American goods, saying trade issues would be 'resolved to mutual satisfaction.' He also said tragic results could follow any 'hint of weakening' of the U.S. defense commitment to Seoul."}, {"text": "The Census Bureau reported that 13.1% of the U.S. population, or 31.9 million people, were living in poverty in 1988."}, {"text": "Last year's figure was down from 13.4% in 1987 and marked the fifth consecutive annual decline in the poverty rate."}, {"text": "Per capita income rose 1.7% to $13,120, but median family income fell 0.2%."}, {"text": "The Bush administration accused Israeli Prime Minister Shamir of hindering peace efforts in the Mideast with 'unhelpful' and disappointing statements."}, {"text": "Shamir said Tuesday that he was prepared to risk a policy conflict with the U.S. over an Egyptian plan to hold direct Israeli-Palestinian talks, which the premier's Likud bloc opposes."}, {"text": "Cuba was elected to the U.N. Security Council for the first time since its Castro-led revolution 30 years ago."}, {"text": "The election was by secret ballot in the General Assembly."}, {"text": "The U.S. didn't openly oppose Cuba's seating as the Latin American council delegate."}, {"text": "Britain's Prime Minister Thatcher told a Commonwealth summit in Kuala Lumpur, Malaysia, that sanctions against South Africa were 'utterly irresponsible,' officials said."}, {"text": "But other nations at the opening of the 49-nation meeting of Britain and its former colonies pressed for continued or stronger embargoes in an effort to end apartheid."}, {"text": "Arab officials in Saudi Arabia said three-week-old talks by Lebanese lawmakers aimed at ending Lebanon's civil war appeared about to collapse."}, {"text": "Christian legislators are insisting on a Syrian troop pullout from Lebanon before agreeing to political changes giving the nation's Moslems a greater role in Beirut's government."}, {"text": "Colombia's judges launched a 72-hour strike to press security demands following Tuesday's murder of a High Court justice in Medellin."}, {"text": "The country's narcotics traffickers claimed responsibility for the slaying."}, {"text": "Most of the country's 20,000 judges and judicial employees joined the work stoppage."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0118.json b/inquisitive/sources/test/0118.json new file mode 100644 index 0000000000000000000000000000000000000000..d571098346f8df301200e9c6da29a48b087abe12 --- /dev/null +++ b/inquisitive/sources/test/0118.json @@ -0,0 +1 @@ +[{"text": "Texaco Inc. has purchased an oil-producing company in Texas for $476.5 million, its first major acquisition since its legal brawl with Pennzoil Co. began more than four years ago."}, {"text": "The White Plains, N.Y., oil company said Friday that it had acquired Tana Production Corp., a subsidiary of TRT Energy Holdings Inc., for $95.1 million in cash, with the rest to be paid in shares of a new, non-voting issue of preferred stock."}, {"text": "Tana, which holds properties in 17 oil and gas fields in south Texas, will provide Texaco with mostly gas reserves."}, {"text": "The fields contain recoverable reserves of 435 billion cubic feet of natural gas and four million barrels of oil."}, {"text": "'This acquisition is another indication of Texaco's commitment to increase the company's reserve base,' said Chief Executive Officer James W. Kinnear."}, {"text": "Texaco has also been attempting to sell oil properties."}, {"text": "At least two years ago, the company put 60 million barrels of oil reserves on the block."}, {"text": "They were either too small or uneconomic to maintain, the company said."}, {"text": "Not all of those parcels have yet been sold."}, {"text": "Texaco acquired Tana before it completed those sales because Tana's properties are high quality and near other fields Texaco already owns, a company spokeswoman said."}, {"text": "Texaco, like many other oil companies, has been struggling to replace its falling oil and gas reserves."}, {"text": "Texaco's situation had become particularly complex because much of its effort had for years been focused on its brawl with Pennzoil and then on New York investor Carl C. Icahn's attempt to take over the company."}, {"text": "Pennzoil had sued Texaco for improperly interfering with its acquisition of a portion of Getty Oil Co. Eventually, Texaco, which was forced into bankruptcy proceedings by that litigation, settled its fight with Pennzoil for $3 billion in 1986."}, {"text": "Mr. Icahn, who played a key role in the settlement and attempted subsequently to take control of the company, sold his stake in Texaco just last summer."}, {"text": "Completion of Texaco's acquisition of Tana is subject to government approval under the Hart-Scott-Rodino Antitrust Improvements Act."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0119.json b/inquisitive/sources/test/0119.json new file mode 100644 index 0000000000000000000000000000000000000000..d2961fff9de9fda93b8e05272f65137829f95a24 --- /dev/null +++ b/inquisitive/sources/test/0119.json @@ -0,0 +1 @@ +[{"text": "With a Twist of the Wrist"}, {"text": "Boys with tops, and Frisbee tossers,"}, {"text": "And P.R. types with bees in their bonnet,"}, {"text": "Have a goal in common, all of them try"}, {"text": "To put the right spin on it."}, {"text": "-- George O. Ludcke."}, {"text": "Net Gain"}, {"text": "Investment letters now abound,"}, {"text": "I really like to read them;"}, {"text": "If I peruse enough, I've found"}, {"text": "I've no time left to heed them!"}, {"text": "-- Bern Sharfman."}, {"text": "Daffynition"}, {"text": "TV evangelist: salesparson."}, {"text": "-- Marguerite Whitley May."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0120.json b/inquisitive/sources/test/0120.json new file mode 100644 index 0000000000000000000000000000000000000000..c8138124aca04870070c6193e2d848f85ee73937 --- /dev/null +++ b/inquisitive/sources/test/0120.json @@ -0,0 +1 @@ +[{"text": "The Senate convicted U.S. District Judge Alcee Hastings of Florida of eight impeachment articles, removing the 53-year-old judge from his $89,500-a-year, lifetime job."}, {"text": "Mr. Hastings's case was particularly nettlesome because it marked the first time a federal official was impeached and removed from office on charges of which a jury had acquitted him."}, {"text": "In 1983, Mr. Hastings was found not guilty of accepting a $150,000 bribe in a case before him, the central charge on which the Senate convicted him."}, {"text": "He was only the sixth federal judge ever ousted from office after an impeachment trial."}, {"text": "With no floor debate, the Senate on Friday voted 69-26 to convict Mr. Hastings of perjury and conspiring to accept a bribe, five votes more than needed."}, {"text": "Conviction on any single impeachment article was enough to remove Judge Hastings from office."}, {"text": "He was found not guilty of three charges, involving accusations that he had improperly disclosed information about a sensitive, government investigation."}, {"text": "The Senate didn't vote on six lesser charges."}, {"text": "Although Mr. Hastings had been acquitted by a jury, lawmakers handling the prosecution in Congress had argued that the purpose of impeachment isn't to punish an individual."}, {"text": "Instead, they argued that impeachment aims to protect public institutions from people who have abused their positions of trust, irrespective of the outcome of prior criminal or civil cases."}, {"text": "Mr. Hastings faced the senators and sat impassively during the first two roll-call votes, then quickly left the chamber."}, {"text": "In an impromptu news conference on the Capitol steps, he denounced the senators' action."}, {"text": "'Their opinion is devoid of the wisdom of the forefathers' teaching regarding impeachment,' Mr. Hastings said."}, {"text": "For the future, he said he would run for governor of Florida."}, {"text": "Mr. Hastings was appointed to the federal bench by President Carter in 1979 and was one of the few black federal judges in the country."}, {"text": "While he packed the Senate gallery with his supporters during some of the impeachment trial, most civil rights groups kept their distance from his case."}, {"text": "Following the impeachment conviction, Dr. Benjamin Hooks, executive director of the National Association for the Advancement of Colored People, issued a restrained statement, warning that the Hastings case could set a 'dangerous precedent,' but adding, 'We must respect the considered judgment of the Senate.'"}] \ No newline at end of file diff --git a/inquisitive/sources/test/0121.json b/inquisitive/sources/test/0121.json new file mode 100644 index 0000000000000000000000000000000000000000..e62877706cb564127faf8343504295eecab3bd67 --- /dev/null +++ b/inquisitive/sources/test/0121.json @@ -0,0 +1 @@ +[{"text": "China could exhaust its foreign-exchange reserves as early as next year, a Western government report says, unless imports are cut drastically to help narrow the balance-of-payments deficit."}, {"text": "According to the report, completed last month, if China's trade gap continues to widen at the pace seen in the first seven months of this year, the reserves would be wiped out either in 1990 or 1991."}, {"text": "A country is considered financially healthy if its reserves cover three months of its imports."}, {"text": "The $14 billion of reserves China had in June would cover just that much."}, {"text": "The report by the Western government, which declines to be identified, concludes that 'a near-term foreign-exchange payment problem can be avoided only if import growth drops to below 5% per annum.'"}, {"text": "According to Chinese customs figures, import growth has slowed in recent months, dropping to 16% in July and 7.1% in August from the year-earlier periods, compared with an average growth rate of 26% in the first half."}, {"text": "But before import growth slowed, China's buying spree in the first half already had taken its toll on foreign-exchange reserves."}, {"text": "The $14 billion level in June marked a drop from $19 billion at the end of April."}, {"text": "China's last big import binge sent reserves tumbling to $10.6 billion in June 1985 from $16.6 billion the previous September."}, {"text": "China might stave off a crisis if it acts as forcefully as it did to arrest the 1985 decline, when Beijing slammed the brakes on foreign-exchange spending and devalued the currency."}, {"text": "But this time, China faces a more difficult battle because of economic forces that have come into play since the Tiananmen Square killings June 4."}, {"text": "For example, China's hard-currency income is expected to suffer from the big drop in tourist arrivals since June 4."}, {"text": "Revenue from tourism this year is projected to total $1.3 billion, down from $2.2 billion last year."}, {"text": "Because of this and the huge trade gap, the deficit in China's current account, which measures trade in goods and services plus certain unilateral transfers of funds, is expected to widen sharply from the $3.8 billion deficit last year."}, {"text": "The Western government report suggests a number of scenarios for China's current-account balance, two of which are considered most likely."}, {"text": "In one, imports and exports continue to grow at the respective average rates of 25% and 5% recorded during the first seven months, and the current-account deficit widens to $13.1 billion."}, {"text": "In 1985, China had a record deficit of $11.4 billion."}, {"text": "The other scenario assumes that Beijing takes effective actions to curb imports in the coming months."}, {"text": "In this case, China would still finish the year with a current-account deficit of $8.7 billion, based on projections that imports for all of this year grow 20% and exports 10%."}, {"text": "If China were still on good terms with foreign lenders, it might be able to stem the drain on its foreign-exchange reserves by using some loan funds to offset the current-account deficit."}, {"text": "But since June, foreign bankers led by international financial institutions have virtually suspended their new loans to China."}, {"text": "Even if borrowing resumes, commercial bankers aren't expected to lend as much as before."}, {"text": "In addition, economists are forecasting a slowdown in foreign direct investments as businessmen become increasingly wary of China's deteriorating political and economic environment."}, {"text": "On top of all this, foreign-debt repayments are expected to peak in 1991 to 1992."}, {"text": "With less capital coming in, China's balance of payments would suffer."}, {"text": "The Western government report's first scenario assumes a 30% reduction in foreign borrowing and a 5% contraction in foreign direct investment."}, {"text": "In the second, foreign borrowing is projected to grow 10% and investment to drop 10%."}, {"text": "But in either case, the report says, China's balance of payments would rapidly dry up foreign reserves, which are used to finance the imbalance."}, {"text": "In the first scenario, the reserves would be exhausted next year, and in the second they would be wiped out in 1991."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0122.json b/inquisitive/sources/test/0122.json new file mode 100644 index 0000000000000000000000000000000000000000..d720469d2e7751abbc9f84430bdf2a61b50cd656 --- /dev/null +++ b/inquisitive/sources/test/0122.json @@ -0,0 +1 @@ +[{"text": "Are consumers too deep in hock?"}, {"text": "A lot of observers think so, and, if they're right, the whole economy as well as the spendthrifts among us could be hurt."}, {"text": "A sudden, forced cutback by consumers, who normally account for about two-thirds of economic activity, would damp the economy at a time when plant-and-equipment spending is slowing and deficit-racked governments can't readily take up the slack."}, {"text": "And another wave of bad loans would further batter many already-shaky lending institutions."}, {"text": "The worriers cite some worrisome trends."}, {"text": "During the almost seven-year-old economic expansion, inflation-adjusted gross national product, disposable personal income and personal consumption expenditures have risen 30%, but inflation-adjusted consumer installment credit has surged 66%."}, {"text": "And the ratio of installment debt to disposable personal income -- personal income after taxes -- has hit a high of about 18 1/2%."}, {"text": "However, these figures don't seem to worry Thomas A. Durkin, an economist at the Federal Reserve Board."}, {"text": "In a paper presented at the recent annual meeting of the National Association of Business Economists in San Francisco, Mr. Durkin comments that 'installment credit always grows rapidly in cyclical advances, and growth in this cycle is very typical of earlier experiences.' He adds: 'We are now witnessing a slowdown which, if history is a guide, could persist for a while.'"}, {"text": "But what about the debt burden?"}, {"text": "Mr. Durkin doubts that 'there is some magic level' at which the ratio of installment debt to disposable income 'indicates economic problems.' And, 'more importantly,' he says, 'the debt burden measured other ways is not really in uncharted waters.'"}, {"text": "The chart below shows why (see accompanying illustration -- WSJ Oct. 23, 1989)."}, {"text": "The ratio of consumer installment credit to disposable income, though up a bit, hasn't climbed steeply, and such debt as a percent of household assets is little changed."}, {"text": "Moreover, the burden of consumer credit payments relative to disposable income may be 'lower in this cycle than earlier,' Mr. Durkin says."}, {"text": "He notes that some 'revolving credit-card credit is actually convenience credit' being used simply as a handy way of paying bills rather than a handy way of borrowing."}, {"text": "In addition, he says, 'longer maturities on automobile and other forms of installment credit boost the stock of debt faster than the flow of repayments and the accompanying payment burden.'"}, {"text": "And if you 'consider the changing distribution of credit,' Mr. Durkin says, 'much of the increase in debt in recent years is due to increasing credit use by higher-income families,' that is, 'those probably best able to handle it.'"}, {"text": "Citing figures on home-equity loans, he notes that '11% of homeowners had home-equity credit accounts, but the proportion rises to 16% of homeowners in the $45,000-$60,000 income range and 23% of homeowners with income above $60,000.' And much home-equity credit is used conservatively. 'The most frequent use is home improvement, which presumably improves the value of the property,' Mr. Durkin says."}, {"text": "So, it isn't surprising that consumer-credit delinquencies at banks remain, as the chart shows, reassuringly below some earlier highs (see accompanying illustration -- WSJ Oct. 23, 1989)."}, {"text": "A severe recession could, of course, raise delinquency rates, but so far the current levels of consumer debt don't seem to loom as a major threat."}, {"text": "In fact, the current weakness in auto buying and department-store sales and the gradual upturn in the household saving rate suggest that consumers, conservative as ever, are already clutching their purses a bit more tightly."}, {"text": "In July, consumer installment credit outstanding fell for the first time since January 1987."}, {"text": "'Consumers appear unwilling to add to their leverage to support their spending,' Bruce Steinberg, a Merrill Lynch economist, says. 'As a result, household debt appears to be stabilizing at around 63% of GNP.'"}, {"text": "Consumers, credit cards in hand, aren't running amok through the shopping malls -- or putting the economy at any great risk."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0123.json b/inquisitive/sources/test/0123.json new file mode 100644 index 0000000000000000000000000000000000000000..52f1647c2acd210ed3c7a1656673782444ee9938 --- /dev/null +++ b/inquisitive/sources/test/0123.json @@ -0,0 +1 @@ +[{"text": "Eastman Kodak Co., seeking to position itself in the potentially huge high-definition television market, unveiled a converter that can transform conventional motion-picture film into high-definition video."}, {"text": "The move also helps the Rochester, N.Y., photographic giant ensure that its motion-picture film business -- for which it holds a virtual monopoly, supplying every Hollywood movie company -- isn't made obsolete by the upstart HDTV business."}, {"text": "While the prototype converter is costly, it's being lauded by the infant HDTV industry as a way of increasing the number of high-quality shows that can be seen on the new medium."}, {"text": "'The industry has been waiting with bated breath for the machines to come along,' says David Niles, president of Eleven Twenty Five Productions Inc., a New York pioneer in high-definition programming."}, {"text": "He notes that industry executives have until now worried that they would face a severe shortage of programs once consumers begin replacing their TV sets with HDTVs."}, {"text": "Japanese electronic giants, such as Sony Corp. and Hitachi Ltd., have focused almost entirely on HDTV hardware, and virtually ignored software or programs shot in high-definition."}, {"text": "And only a handful of small U.S. companies are engaged in high-definition software development."}, {"text": "It's estimated that just about 250 hours of HD programming is currently available for airing."}, {"text": "Kodak says its new CCD HDTV converter will help alleviate the problem by allowing programmers and broadcasters to convert movies and television programs shot in 35mm motion-picture film into high-definition video."}, {"text": "Consumers will be able to switch on their HDTV sets and get all the viewing benefits the high-tech medium offers."}, {"text": "Otherwise, they'd be watching programs that are no different in quality from what they currently view on color TVs."}, {"text": "It would be like 'watching a black and white movie on a color TV set,' says Malcolm G. Saull, chairman of the film and video department at the Rochester Institute of Technology."}, {"text": "The new converters are 'a critical link between film and the television domain,' says Joerg D. Agin, vice president and general manager of Kodak's Motion Picture and Audiovisual Products division."}, {"text": "Kodak won't disclose the cost or when its converter will be on the market, but it's estimated the machine may be available within two years."}, {"text": "A similar machine already on the market, made by Rank Sintel Ltd., a unit of Rank Organisation, costs about $500,000."}, {"text": "And the potential market is tremendous, industry experts say."}, {"text": "If HDTV takes off in the U.S., there will be demand for some 4,000 to 5,000 HDTV converters, known in the industry as telecines."}, {"text": "Demand will come first from programming production companies and then from television stations."}, {"text": "'The converter is head and shoulders above anything else I've seen,' says Richard J. Stumpf, vice president-engineering and development at MCA Inc. 's Universal City Studios."}, {"text": "And Mr. Niles, the program producer, contends that Kodak's move is 'a sound marketing decision."}, {"text": "They can't afford to stay out of HDTV.'"}, {"text": "Indeed, the stakes are high."}, {"text": "The U.S. electronics industry estimates that the HDTV market will total about $150 billion over the next two decades, with an additional $400 billion expected to go for related products."}, {"text": "HDTVs break down images into more than 1,100 lines, compared with 525 for today's televisions, providing considerably sharper detail."}, {"text": "And the sets are wider, resembling the dimensions of a movie screen."}, {"text": "But the financial rewards aren't expected soon, nor are they guaranteed."}, {"text": "Experts estimate the first sets of HDTVs won't be available for another five to 10 years, and will probably retail for more than $3,000 each in today's dollars."}, {"text": "Some critics say they won't be quickly embraced by consumers because of the high price."}, {"text": "Nevertheless, Kodak couldn't risk letting HDTV turn its motion-picture film business into a dinosaur. 'Kodak understands HDTV is where everybody is going,' says RIT's Mr. Spaull."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0131.json b/inquisitive/sources/test/0131.json new file mode 100644 index 0000000000000000000000000000000000000000..ab183ef181473d1cd02267e8cf08feb20a863edf --- /dev/null +++ b/inquisitive/sources/test/0131.json @@ -0,0 +1 @@ +[{"text": "SHEVARDNADZE ADMITTED that Moscow violated the 1972 ABM treaty."}, {"text": "In a foreign-policy address before the Soviet legislature, the foreign minister conceded that the radar station in Krasnoyarsk breached the superpower Anti-Ballistic Missile treaty and said it would be dismantled."}, {"text": "Shevardnadze said it took Gorbachev's government four years to determine that the station's location in Siberia violated the accord, as Western arms-control officials have long contended."}, {"text": "He also denounced Moscow's nine-year involvement in the war in Afghanistan, saying it involved 'gross violations of . . . civil norms and ethics.'"}, {"text": "Secretary of State Baker, in his first major arms-control speech, called for a new military relationship with Moscow to reduce 'first strike' nuclear arms."}, {"text": "BAY AREA COMMUTERS BATTLED earthquake-related transportation snarls."}, {"text": "Travelers crowded into subways, sat in traffic jams on major freeways or waited for buses in the rain, but the massive gridlock anticipated by officials in the San Francisco Bay area never materialized."}, {"text": "As the death toll from last week's temblor climbed to 61, the condition of freeway survivor Buck Helm, who spent four days trapped under rubble, improved, hospital officials said."}, {"text": "Rescue crews, however, gave up hope that others would be found alive under the collapsed roadway."}, {"text": "The House Appropriations Committee approved a $2.85 billion aid package for the quake region, less than the $3.8 billion sought by California officials."}, {"text": "Hungary declared itself a democracy and for the first time openly commemorated the anniversary of the 1956 anti-Stalinist uprising that was crushed by the Soviet Union."}, {"text": "A crowd estimated at 100,000 held a torch-lit march through Budapest as Acting President Szuros delivered a nationally televised address rejecting communist dominance."}, {"text": "About 200,000 East Germans marched in Leipzig and thousands more staged protests in three other cities in a fresh challenge to the Communist leadership to introduce democratic freedoms."}, {"text": "In an East Berlin suburb, meanwhile, employees at an electronics plant formed an independent trade union called Reform, a worker spokesman said."}, {"text": "The space shuttle Atlantis landed at a desert air strip at Edwards Air Force Base, Calif., ending a five-day mission that dispatched the Jupiter-bound Galileo space probe."}, {"text": "The five astronauts returned to Earth about three hours early because high winds had been predicted at the landing site."}, {"text": "Fog shrouded the base before touchdown."}, {"text": "Explosions shook a Phillips Petroleum Co. plastics plant near Pasadena, Texas, hurling debris and causing a fire visible from 10 miles away."}, {"text": "More than 100 people were injured, and a number of workers were missing."}, {"text": "Parts of the Houston Ship Channel were closed."}, {"text": "The White House said Bush is conferring with leaders of the Senate Intelligence Committee to ease differences over guidelines for CIA agents."}, {"text": "The statement came after officials said Bush complained at a private meeting last week that a strict interpretation of a policy requires the U.S. to notify foreign dictators of certain coup plots."}, {"text": "Lebanon's Gen. Aoun placed Christian military forces on alert in case of renewed fighting with Syrian-backed Moslems after Lebanon's two main Shiite militias rejected an Arab-sponsored peace accord."}, {"text": "The plan, approved by lawmakers and rejected Sunday by Aoun, includes political changes aimed at ending the 14-year-old civil war."}, {"text": "NATO defense ministers are expected to call for a reduction in nuclear forces in Europe when the alliance's nuclear planning group convenes a two-day session today in Portugal."}, {"text": "The ministers are to reshape NATO's defenses in Western Europe amid fast-paced changes in the Soviet bloc."}, {"text": "Iran's President Rafsanjani offered to help gain freedom for Western hostages in Lebanon, but said the assistance was contingent on U.S. aid in resolving the cases of three Iranians kidnapped in Lebanon in 1982 or the release of frozen Iranian assets."}, {"text": "Washington rejected the bid, saying the hostages weren't linked to other issues."}, {"text": "PLO leader Arafat asked Egypt to seek clarifications from the U.S. on Secretary of State Baker's plan for Mideast peace talks, an aide to Egyptian President Mubarak said."}, {"text": "The official stressed that the PLO hasn't rejected the five-point formula."}, {"text": "Commonwealth leaders turned to issues ranging from drugs to the world economy after Zimbabwe's President Mugabe called Thatcher's views on South Africa 'despicable.' At a meeting in Malaysia, Australia and Canada also assailed the British prime minister for criticizing the 49-nation group's call for Pretoria to ease apartheid."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0132.json b/inquisitive/sources/test/0132.json new file mode 100644 index 0000000000000000000000000000000000000000..6058b43e9e6cf899b2d6a870203f6e1e99323bf4 --- /dev/null +++ b/inquisitive/sources/test/0132.json @@ -0,0 +1 @@ +[{"text": "The House Appropriations Committee approved an estimated $2.85 billion in emergency funding to assist California's recovery from last week's earthquake and to extend further aid to East Coast victims of Hurricane Hugo."}, {"text": "The package was termed excessive by the Bush administration, but it also provoked a struggle with influential California lawmakers who sought unsuccessfully to add nearly $1 billion more and waive current restrictions to expedite the distribution of funds."}, {"text": "By a 26-7 margin, the committee scuttled the more expensive alternative, and the debate forced a strained confrontation between Appropriations Committee Chairman Jamie Whitten (D., Miss.) and his party's largest state delegation in the House."}, {"text": "'I have no regrets about going forward,' said Rep. Vic Fazio (D.,Calif.), who sought later to play down the sometimes hostile tone of the long evening meeting. 'We are the Golden State,' Mr. Fazio said, 'and there is a certain amount of jealousy.'"}, {"text": "The $2.85 billion package incorporates $500 million for small-business loans, $1 billion in highway construction funds, and $1.35 billion divided between general emergency assistance and a reserve to be available to President Bush to meet unanticipated costs from the two disasters."}, {"text": "The funding is attached to a stopgap bill to keep most of the government operating through Nov. 15."}, {"text": "The measure is expected to come before the House today, and Congress is under pressure to complete action before midnight EDT tomorrow, when the current continuing resolution expires."}, {"text": "Given California's size and political importance, the White House is eager to appear generous."}, {"text": "But in private meetings yesterday, Budget Director Richard Darman argued that only $1.5 billion in new federal appropriations are needed to supplement existing resources."}, {"text": "A White House budget office analysis estimates that $500 million -- or half the level in the committee bill -- is needed for highway assistance to meet California's needs, and the administration rejects the notion that new appropriations are needed to finance disaster loans by the Small Business Administration."}, {"text": "'Everybody appreciates that it is a national disaster and that we've got to address it,' said Mr. Darman, who came to the Capitol to meet with Mr. Whitten and California lawmakers before the committee session. 'I would hope very much that we wouldn't end up in a kind of situation where you have a bidding war and then a veto threat.'"}, {"text": "Although this White House pressure was clearly a factor among committee Republicans, no single influence was greater than Mr. Whitten."}, {"text": "A master of pork-barrel politics, he had crafted the $2.85 billion package in vintage style and used the full force of his chairmanship to keep the proposal intact and dismiss any alternative."}, {"text": "When Mr. Fazio offered the California-backed $3.84 billion plan, Mr. Whitten insisted that the full 14 pages be read aloud by the panel's clerk to underscore the range of legislative changes also sought by the delegation."}, {"text": "On the chairman's motion, the California package was subsequently reduced to less-binding report language, and even when this was accepted as such on a voice vote, Mr. Whitten pointedly opposed it."}, {"text": "More important than money in many cases are waivers California is seeking on current restrictions covering federal highway funds, such as a $100 million cap on how much any single state can receive in emergency funds in a year."}, {"text": "Mr. Whitten's package appears to accomplish this purpose, but the state faces more resistance in its bid for an extended waiver on having to put up any matching funds on repairs completed in the next six months."}, {"text": "A member in the House leadership and skilled legislator, Mr. Fazio nonetheless found himself burdened not only by California's needs but by Hurricane Hugo amendments he accepted in a vain effort to build support in the panel."}, {"text": "The California Democrat appeared embarrassed by provisions inserted on behalf of owners of private beaches in the Virgin Islands, and lumber interests sought to add another $100 million in federal aid to plant timber on private land in North and South Carolina."}, {"text": "California's high-priced real estate puts it in an awkward position, too."}, {"text": "One provision last night would have raised the cap on disaster loans to $500,000 from $100,000 per household to accommodate San Francisco losses."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0133.json b/inquisitive/sources/test/0133.json new file mode 100644 index 0000000000000000000000000000000000000000..4c7dd8e471467f8927331e5e7c7debc080dce401 --- /dev/null +++ b/inquisitive/sources/test/0133.json @@ -0,0 +1 @@ +[{"text": "Exxon Corp. filed suit against the state of Alaska, charging state officials interfered with the oil company's initial efforts to treat last spring's giant oil spill."}, {"text": "The action is a counterclaim to a suit filed by Alaska in August against Exxon and six other oil companies."}, {"text": "The state's suit alleges that Exxon's response to the spill failed to prevent contamination of hundreds of miles of shoreline along Prince William Sound."}, {"text": "That suit and Exxon's countersuit were filed in a state court in Anchorage."}, {"text": "Neither suit lists specific dollar claims, largely because damage assessment hasn't yet been completed."}, {"text": "Legal strategists say that damage claims against the oil giant and others could well exceed $1 billion."}, {"text": "Litigation, if not settled out of court, could drag on for years."}, {"text": "Exxon said in its suit that it will seek reimbursement from the state for that part of the cleanup costs and damage claims it says resulted from the state's conduct."}, {"text": "The oil company claims that Alaskan officials prevented Exxon from spraying dispersant onto the almost 11 million gallons of oil dumped when one of its tankers ran into an underwater reef."}, {"text": "Craig Tillery, an Alaska assistant attorney general, said in an interview last night that Exxon's accusations 'are not new."}, {"text": "Exxon has made them before, at which point the state demonstrated they were untrue."}, {"text": "The state will vigorously defend against any counterclaim.'"}, {"text": "Since the spill last March, Exxon and the state have been wrangling over whether spraying dispersant on the oil in the first hours after the spill, when the weather was clear and calm, would have helped limit the environmental damage."}, {"text": "Exxon claims that use of dispersants, which break an oil slick into microscopic droplets, was a crucial part of its immediate-response plan and that state officials banned their use during the two days of fair weather following the spill."}, {"text": "The oil company claims that it had permission from the U.S. Environmental Protection Agency prior to the spill to use dispersant during such an incident at the discretion of the U.S. Coast Guard."}, {"text": "The state's opposition to the use of dispersants, Exxon says, caused the Coast Guard 'to delay granting permission.'"}, {"text": "Alaskan and Coast Guard officials say Exxon's charges aren't relevant because tests conducted during the first two days following the spill showed that the dispersant wasn't working anyway."}, {"text": "Use of dispersants was approved when a test on the third day showed some positive results, officials said."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0134.json b/inquisitive/sources/test/0134.json new file mode 100644 index 0000000000000000000000000000000000000000..5895ebaab6553222de05980bc8590188a3172b14 --- /dev/null +++ b/inquisitive/sources/test/0134.json @@ -0,0 +1 @@ +[{"text": "Bankers Trust New York Corp., as expected, reported a third-quarter loss of $1.42 billion, or $17.39 a share, following its $1.6 billion boost in reserves for losses on loans to less-developed countries."}, {"text": "The loss compares with net income of $162.1 million, or $2.01 a share, in the year-earlier period."}, {"text": "Interest income rose 29% to about $1.35 billion from $1.05 billion."}, {"text": "The New York bank holding company's assets at Sept. 30 climbed to $59.4 billion from $57.9 billion."}, {"text": "Excluding the increase in loan-loss reserves, Bankers Trust said third-quarter net income would have increased 11% to $180 million."}, {"text": "A number of major banks have posted big losses after sharply increasing loan-loss reserves."}, {"text": "Most of the loans in question are to Third World countries in South America."}, {"text": "In New York Stock Exchange composite trading yesterday, Bankers Trust fell 12.5 cents to $50.50."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0135.json b/inquisitive/sources/test/0135.json new file mode 100644 index 0000000000000000000000000000000000000000..a8a2827c9273fa24ca55153221dd70f95e5009b9 --- /dev/null +++ b/inquisitive/sources/test/0135.json @@ -0,0 +1 @@ +[{"text": "Monday, October 23, 1989"}, {"text": "The key U.S. and foreign annual interest rates below are a guide to general levels but don't always represent actual transactions."}, {"text": "PRIME RATE: 10 1/2%."}, {"text": "The base rate on corporate loans at large U.S. money center commercial banks."}, {"text": "FEDERAL FUNDS: 8 3/4% high, 8 11/16% low, 8 11/16% near closing bid, 8 3/4% offered."}, {"text": "Reserves traded among commercial banks for overnight use in amounts of $1 million or more."}, {"text": "Source: Fulton Prebon (U.S.A.) Inc."}, {"text": "DISCOUNT RATE: 7%."}, {"text": "The charge on loans to depository institutions by the New York Federal Reserve Bank."}, {"text": "CALL MONEY: 9 3/4% to 10%."}, {"text": "The charge on loans to brokers on stock exchange collateral."}, {"text": "COMMERCIAL PAPER placed directly by General Motors Acceptance Corp.: 8.50% 2 to 44 days; 8.25% 45 to 69 days; 8.40% 70 to 89 days; 8.20% 90 to 119 days; 8.05% 120 to 149 days; 7.90% 150 to 179 days; 7.50% 180 to 270 days."}, {"text": "COMMERCIAL PAPER: High-grade unsecured notes sold through dealers by major corporations in multiples of $1,000: 8.575% 30 days; 8.50% 60 days; 8.45% 90 days."}, {"text": "CERTIFICATES OF DEPOSIT: 8.09% one month; 8.09% two months; 8.06% three months; 8% six months; 7.94% one year."}, {"text": "Average of top rates paid by major New York banks on primary new issues of negotiable C.D.s, usually on amounts of $1 million and more."}, {"text": "The minimum unit is $100,000."}, {"text": "Typical rates in the secondary market:8.60% one month; 8.60% three months; 8.40% six months."}, {"text": "BANKERS ACCEPTANCES: 8.50% 30 days; 8.32% 60 days; 8.32% 90 days; 8.16% 120 days; 8.05% 150 days; 7.96% 180 days."}, {"text": "Negotiable, bank-backed business credit instruments typically financing an import order."}, {"text": "LONDON LATE EURODOLLARS: 8 3/4% to 8 5/8% one month; 8 11/16% to 8 9/16% two months; 8 3/4% to 8 5/8% three months; 8 5/8% to 8 1/2% four months; 8 9/16% to 8 7/16% five months; 8 9/16% to 8 7/16% six months."}, {"text": "LONDON INTERBANK OFFERED RATES (LIBOR): 8 3/4% one month; 8 3/4% three months; 8 9/16% six months; 8 1/2% one year."}, {"text": "The average of interbank offered rates for dollar deposits in the London market based on quotations at five major banks."}, {"text": "FOREIGN PRIME RATES: Canada 13.50%; Germany 9%; Japan 4.875%; Switzerland 8.50%; Britain 15%."}, {"text": "These rate indications aren't directly comparable; lending practices vary widely by location."}, {"text": "Results of the Monday, October 23, 1989, auction of short-term U.S. government bills, sold at a discount from face value in units of $10,000 to $1 million: 7.52%, 13 weeks; 7.50%, 26 weeks."}, {"text": "FEDERAL HOME LOAN MORTGAGE CORP. (Freddie Mac): Posted yields on 30-year mortgage commitments for delivery within 30 days. 9.86%, standard conventional fixed-rate mortgages; 7.875%, 2% rate capped one-year adjustable rate mortgages."}, {"text": "Source: Telerate Systems Inc."}, {"text": "FEDERAL NATIONAL MORTGAGE ASSOCIATION (Fannie Mae): Posted yields on 30 year mortgage commitments for delivery within 30 days (priced at par). 9.80%, standard conventional fixed-rate mortgages; 8.75%, 6/2 rate capped one-year adjustable rate mortgages."}, {"text": "Source: Telerate Systems Inc."}, {"text": "MERRILL LYNCH READY ASSETS TRUST: 8.56%."}, {"text": "Annualized average rate of return after expenses for the past 30 days; not a forecast of future returns."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0136.json b/inquisitive/sources/test/0136.json new file mode 100644 index 0000000000000000000000000000000000000000..abdcddfd94daee03712c85ef5a7d068b07781c6c --- /dev/null +++ b/inquisitive/sources/test/0136.json @@ -0,0 +1 @@ +[{"text": "Enviropact Inc. said it entered into an agreement in principle to sell its pump and tank division and drilling division to GSX Chemical Services for $4 million."}, {"text": "The Miami-based environmental engineering concern said GSX Chemical also will assume about $1.6 million in debt related to those divisions."}, {"text": "Further, GSX will buy $1 million of Enviropact common stock, at $2.625 a share, plus an option to acquire an additional $1.5 million of common at the same price, the company said."}, {"text": "In American Stock Exchange composite trading yesterday, Enviropact closed at $3 a share, up 25 cents."}, {"text": "Enviropact said the two divisions account for about $8 million of the company's $20 million in annual revenue."}, {"text": "The transaction is expected to close within about 20 days, the company added."}, {"text": "Enviropact said the proceeds will be used as working capital for expansion and to pay its existing tax liability of about $1.5 million that was due Sept. 15."}, {"text": "GSX is a unit of Laidlaw Transportation Ltd. of Burlington, Canada."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0137.json b/inquisitive/sources/test/0137.json new file mode 100644 index 0000000000000000000000000000000000000000..1a50533bfa8faa6ed799a5b4e6e23fb445c58108 --- /dev/null +++ b/inquisitive/sources/test/0137.json @@ -0,0 +1 @@ +[{"text": "The dollar weakened in indecisive trading as foreign-exchange dealers awaited fresh economic news that they hope will jolt the U.S. unit out of its narrow ranges."}, {"text": "The Canadian dollar climbed to its highest level against the U.S. dollar since late August, prompting the Bank of Canada to sell the Canadian currency on the market."}, {"text": "Traders say that after a week of nervously tracking every development on Wall Street, the foreign-exchange market has settled back to catch its breath ahead of new U.S. economic data."}, {"text": "They noted, however, that a 26-point drop in the Dow Jones Industrial Average gave the dollar a sharp nudge downward late in the day."}, {"text": "In late New York trading yesterday, the dollar was quoted at 1.8470 marks, down from 1.8578 marks late Friday, and at 141.90 yen, down from 142.43 yen late Friday."}, {"text": "Sterling was quoted at $1.6030, up from $1.5885 late Friday."}, {"text": "In Tokyo Tuesday, the U.S. currency opened for trading at 141.80 yen, down from Monday's Tokyo close of 142.40 yen."}, {"text": "The market's attention is especially focused on a preliminary report on the U.S. third-quarter gross national product, due out Thursday, which could show the economy is continuing to expand at a relatively brisk pace."}, {"text": "The consensus view on real GNP, the total value of the U.S. output of goods and services adjusted for inflation, calls for a 2.3% gain on an annual basis, slowing somewhat from the second quarter's 2.5%, but still fairly strong."}, {"text": "Few market participants expect the U.S. unit to rally sharply on the news, if it turns out as expected."}, {"text": "Many contend that the report may overstate the economy's health and predict the third-quarter figures may be the last vigorous statistics for some time to come."}, {"text": "'Everyone is waiting for GNP,' says Walter Simon, an assistant treasurer with Bank Julius Baer & Co. 'Yet even a relatively strong number -- 2.8% to 2.9% -- won't alter the market's view that the economy is softening.'"}, {"text": "Hubert Pedroli, managing director of foreign exchange at Credit Suisse in New York, adds, 'The market sees this as the last piece of good news.'"}, {"text": "Mr. Pedroli notes that the GNP deflator, a measure of inflation, is expected to slow, which would give the Federal Reserve more room to ease key U.S. rates."}, {"text": "Analysts predict a 3.5% rise in the deflator, after climbing 4.6% in the second quarter."}, {"text": "They note that when an unexpectedly sharp widening in the U.S. trade gap in August was reported earlier this month, hopes for a sustained narrowing of the trade deficit were dashed and sentiment gripped the market that the U.S. economy was losing its momentum."}, {"text": "A 190-point plunge in U.S. stock shares compounded the view, they say."}, {"text": "'Everyone is extremely convinced the economy is slowing,' says one senior New York dealer. 'If we're not headed for a recession, we're certainly headed for a major slowdown.'"}, {"text": "While the market expects little reaction from news of U.S. durable goods orders, scheduled for release today, participants note that the figures will probably serve to reinforce this bearish sentiment."}, {"text": "U.S. durable goods orders are expected to show a decline of 1.2% in September, according to economists."}, {"text": "The anticipated drop follows a 3.9% rise in August."}, {"text": "Traders, however, are quick to point out that while there is little enthusiasm for buying dollars, the U.S. unit has found a 'natural bottom' at about 1.85 marks and 140 yen."}, {"text": "Its resilience around these levels is pegged to persistent investor demand for the greenback, especially in Japan."}, {"text": "On the Commodity Exchange in New York, gold for current delivery settled at $367 an ounce, down 30 cents."}, {"text": "Estimated volume was a very light one million ounces."}, {"text": "In early trading in Hong Kong Tuesday, gold was quoted at $366.79 an ounce."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0138.json b/inquisitive/sources/test/0138.json new file mode 100644 index 0000000000000000000000000000000000000000..03401abe40cd18bfa5d064ca18439721f4f8d280 --- /dev/null +++ b/inquisitive/sources/test/0138.json @@ -0,0 +1 @@ +[{"text": "In a last-ditch effort to keep its sales force and customer base, Integrated Resources Inc. said it agreed in principle to transfer ownership of its broker-dealer subsidiary to two of its top executives."}, {"text": "The financial-services firm, struggling since summer to avoid a bankruptcy-law filing after missing interest payments on about $1 billion of debt, will retain the right to regain the subsidiary."}, {"text": "It said it will exercise that right only if it sells substantially all of its other core businesses."}, {"text": "It also can sell the right to regain the subsidiary to another party."}, {"text": "Also, the broker-dealer subsidiary, Integrated Resources Equity Corp., was renamed Royal Alliance Associates Inc."}, {"text": "Because of Integrated's widely reported troubles, the unit's representatives had been requesting a name change."}, {"text": "Royal Alliance, to which the 3,900 representatives' licenses will be transferred, is a shell company Integrated owns."}, {"text": "In the transaction, Integrated will transfer 100% ownership of the subsidiary to Gerard M. Lavin, executive vice president of Integrated and head of back-office operations at the subsidiary, and Gary W. Krat, executive vice president of the parent and president of the subsidiary."}, {"text": "Integrated will pump $3.5 million to $4 million into Royal Alliance as initial funding."}, {"text": "In an interview, Mr. Krat said that based on criteria yet to be determined, he expects to distribute 49% of Royal Alliance to the representatives, who sell Integrated's insurance and mutual-fund products."}, {"text": "If Integrated regains Royal Alliance, the representatives will retain their 49% ownership."}, {"text": "Mr. Krat indicated that completion of the transaction could take several weeks, and it wasn't immediately clear what would happen to the broker-dealer subsidiary if Integrated files for bankruptcy-law protection in the meantime."}, {"text": "The subsidiary isn't expected to be profitable for at least one year."}, {"text": "If Integrated regains the unit, it would receive any profit the unit reports, even while the unit is independent."}, {"text": "If the deal closes, the two officers will draw salaries from the independent operation, not from Integrated."}, {"text": "Many aspects of the agreement were worked out Wednesday in Chicago, when Integrated senior managers met with about 150 representatives. 'I think it was something that we and they thought was constructive,' said Stephen D. Weinroth, chairman and co-chief executive officer of Integrated."}, {"text": "Integrated made its announcement after the market closed."}, {"text": "In New York Stock Exchange Composite trading, Integrated shares closed at $1.125, up 12.5 cents."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0139.json b/inquisitive/sources/test/0139.json new file mode 100644 index 0000000000000000000000000000000000000000..f72b41800cb0ca1d8602111f321baabd17bc3d3e --- /dev/null +++ b/inquisitive/sources/test/0139.json @@ -0,0 +1 @@ +[{"text": "Varian Associates Inc., Palo Alto, Calif., reported fiscal fourth-quarter profit plunged more than 95% to $1 million, or five cents a share, from $24.2 million, or $1.10 a share, in the year-earlier quarter."}, {"text": "The diversified electronics company blamed the decline in the quarter ended Sept. 29, on previously reported operating problems in its Electron Devices & Systems Group."}, {"text": "For the full fiscal year, Varian posted a 13% profit rise to $31.5 million, or $1.53 a share, up from $27.8 million, or $1.27 a share, last year."}, {"text": "Sales for the year rose almost 15% to $1.34 billion from $1.17 billion last year."}, {"text": "A profit last year in both the quarter and year included a net gain of $9.6 million, or 44 cents a share, from the sale of a division."}, {"text": "Additionally, the full-year profit last year reflected an after-tax restructuring charge of $22.8 million, or $1.04 a share."}, {"text": "Shares of Varian, which last month warned there would be a fourth-quarter plunge, closed at $22.75, down 62.5 cents in composite trading on the New York Stock Exchange."}, {"text": "Sales rose 18% in the fiscal fourth quarter to $364.1 million from $307.9 million on the strength in semiconductors and other products."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0140.json b/inquisitive/sources/test/0140.json new file mode 100644 index 0000000000000000000000000000000000000000..3e33cf7a568d0f80eb4275d115a907ea1db763fa --- /dev/null +++ b/inquisitive/sources/test/0140.json @@ -0,0 +1 @@ +[{"text": "Westamerica Bancorp. said Richard W. Decker resigned as president and chief executive officer after only a year on the job because of 'differences' with the board."}, {"text": "The banking company couldn't be reached to comment beyond a written announcement."}, {"text": "It didn't specify the nature of the differences, saying only that they related to 'management style' and 'strategic objectives.'"}, {"text": "Westamerica said Mr. Decker's posts were assumed by David Payne, Westamerica's chairman, who at 34 years of age becomes one of the youngest chief executives of a sizable bank in the country."}, {"text": "Mr. Decker is about 45 years old."}, {"text": "Neither Mr. Payne nor Mr. Decker could be reached to comment."}, {"text": "Westamerica has about $1.3 billion of assets and is the largest independent bank in northern California."}, {"text": "It controls about 35% of the affluent Marin County market across the Golden Gate bridge from San Francisco."}, {"text": "Mr. Decker's resignation surprised many industry officials."}, {"text": "He was brought to the company in September 1988 after 15 years at Los Angeles-based First Interstate Bancorp."}, {"text": "The bank had been suffering in late 1987 from a slew of bad real estate loans made in Arizona."}, {"text": "When he was hired, Mr. Payne lauded Mr. Decker's 'extraordinary . . . skills' and his 'outstanding reputation as one of the West's brightest bankers.'"}, {"text": "Though the bank isn't performing as well as some of its competitors in the lucrative California market, its condition has improved since Mr. Decker took over."}, {"text": "For the six months ended June 30, it earned $3.1 million, or 61 cents a share, compared with net income of $2.4 million, or 41 cents a share, a year earlier."}, {"text": "Its stock also has risen lately, at least partly because it is considered a possible takeover candidate."}, {"text": "Interstate banking is scheduled to begin in California in 1991, and larger California banks, such as Wells Fargo & Co., have been paying fat premiums to buy smaller banks to control markets before any out-of-state banks enter the fray."}, {"text": "In American Stock Exchange composite trading yesterday, Westamerica closed at $22.25 a share, down 75 cents."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0142.json b/inquisitive/sources/test/0142.json new file mode 100644 index 0000000000000000000000000000000000000000..7fd98f157d799fc90cb63fc72b899b80070e0929 --- /dev/null +++ b/inquisitive/sources/test/0142.json @@ -0,0 +1 @@ +[{"text": "Emerson Electric Co. and Robert Bosch G.m.b."}, {"text": "H. said the Federal Trade Commission has requested additional information from the two companies about their announced intention to acquire Vermont American Corp. for $40 a share, or about $440 million."}, {"text": "Yesterday, in composite trading on the American Stock Exchange, Vermont American common closed at $39.75, off 25 cents."}, {"text": "The FTC's request was 'not unusual' and Emerson will make a 'full and prompt' response, according to a spokesman."}, {"text": "Spokesmen for Emerson and Vermont American, which has agreed to be acquired, said they don't anticipate 'any problems' with the completion of the transaction."}, {"text": "An FTC spokesman said the matter is 'in a non-public posture at this time' and declined to comment further."}, {"text": "Emerson and Bosch, through their joint acquisition arm, Maple Acquisition, have begun a cash tender offer for all of Vermont's common shares outstanding."}, {"text": "The offer, set to expire Nov. 1, may be extended pending the timing and resolution of the FTC request, the companies said."}, {"text": "St. Louis-based Emerson and Stuttgart-based Bosch make electrical and electronic products, including power tools."}, {"text": "The Vermont American acquisition is designed to enhance their position in the accessories portion of the power-tool industry."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0143.json b/inquisitive/sources/test/0143.json new file mode 100644 index 0000000000000000000000000000000000000000..bf275474d44e3d99b1c8a506597c6482cae8d81f --- /dev/null +++ b/inquisitive/sources/test/0143.json @@ -0,0 +1 @@ +[{"text": "'The croaker's done gone from the hook -- damn! My language sure goes to pot down here on the coast.' The husky blond guide with the Aggie cap twists his face in mock fury. 'I got to get back to school and straighten out my English.'"}, {"text": "He has two more years at Texas A&M."}, {"text": "Right now he takes people out to fish in the bays behind the barrier islands that curve for hundreds of miles along the eastern coast of Texas, enclosing milky green lagoons behind ridges of sand and grassy scrub that rim the deep blue of the Gulf beyond."}, {"text": "There have been three days of hot, wind-swept rain, and now with the first sun we are after speckled seatrout, which with redfish provides most of the game fishing hereabouts."}, {"text": "The little radio fizzes as other boats want to see if we have found any fish -- spotting location is everything in this sport."}, {"text": "Negative answers crackle back."}, {"text": "The fish often are plentiful around the pilings of the old gas wells that dot the flat surface like the remains of sunken ships."}, {"text": "We go from one to the other."}, {"text": "The sun is hot now though it's only 8 in the morning."}, {"text": "The great silver clouds on the horizon build themselves on the pale water."}, {"text": "We cruise toward another set of pilings."}, {"text": "The guide scoops into a pail and puts a frantically wiggling croaker on the hook."}, {"text": "Then he casts out. 'Just wait for that tap-tap, that thump-thump."}, {"text": "It comes real gentle before it pulls."}, {"text": "Don't forget, trout have very soft mouths.'"}, {"text": "The radio queries again. 'Pickin' one or two,' says the guide, chuckling. 'You can tell they've got nothin'.' A pair of black skimmers zig-zag past close to the surface."}, {"text": "Soon we have our limit of the shimmering fish stippled in rose-gold and black."}, {"text": "And we are the first back at the dock, where the great blue herons stand waiting by the cleaning benches."}, {"text": "The guide is young and he knows this business but he wants a different life after college, such as working for IBM and wearing a necktie."}, {"text": "This must be the last big stretch of the American seacoast that is 'undeveloped.' There are a few ramshackle fishing towns with quiet atolls of resort houses nearby."}, {"text": "People are not apt to be self-conscious about the place or themselves."}, {"text": "Texas is big and beautiful and they live here, that's all."}, {"text": "Jutting out just to the north of us is the Blackjack Peninsula (after the oak, not the game) which forms the core of the Aransas Wildlife Refuge."}, {"text": "It is famous as the winter home of the whooping crane, that symbol of the destruction of wild America."}, {"text": "Last year a gunner shot a whooper by mistake thinking that it was a snow goose."}, {"text": "He paid an immense fine and was lucky, according to a local wag, to escape the gas chamber."}, {"text": "The peninsula comes off the vast southeastern alluvial plain with fields of rice and cotton and sorghum as far as the eye can see."}, {"text": "Near the coast there are dense coverts of live oak interspersed with marshes and prairies."}, {"text": "Deer, wild hog, armadillos and alligators are the glamour quadrupeds and the birds are innumerable, especially the herons and the spoonbills."}, {"text": "Above the blossoms of lantana and scarlet pea the inky-brown and golden palamedes butterfly floats on its lazy wingbeat."}, {"text": "Inland a few miles from the refuge there is a place called Tivoli, with a white church, a gas station and a grocery, the houses relatively close together for such a settlement in these parts. 'Tivoli Motel,' I read a sign in the usual pronunciation of the name as we whoosh through. 'Here in south Texas we say Tie-vole-ee,' my host gently corrects."}, {"text": "Mr. King is the director of the Foreign Press Center in New York."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0145.json b/inquisitive/sources/test/0145.json new file mode 100644 index 0000000000000000000000000000000000000000..b9ec36dbeba28435db14f792a707efa0796c0a8e --- /dev/null +++ b/inquisitive/sources/test/0145.json @@ -0,0 +1 @@ +[{"text": "Turner Broadcasting System Inc. said it formed a unit to make and distribute movies to theaters overseas and, eventually, to U.S. theaters, too."}, {"text": "The operator of cable-television networks said the new Turner Pictures unit will produce movies that will premiere on Turner Broadcasting's Turner Network Television channel, or TNT, and then will be released internationally in movie theaters."}, {"text": "The unit's first two offerings are slated to be 'The Secret Life of Ian Fleming,' a dramatization about the former British spy who wrote the James Bond novels, and 'Treasure Island,' produced by Charlton Heston, who also stars in the movie."}, {"text": "Ted Turner, Turner Broadcasting's chairman, was named chairman of Turner Pictures, and Gerry Hogan, president of Turner Entertainment Networks, was named president of the unit."}, {"text": "In an interview, Mr. Hogan said the subsidiary's primary mission will be to make movies for TNT and to distribute them internationally."}, {"text": "But he said Turner Broadcasting already has found some ideas that might work well as films for theatrical release in the U.S."}, {"text": "'When that occurs, and when the time is right, we'll release the films in the U.S.,' he said, adding that Turner Pictures may develop such movies next year for domestic release in 1991."}, {"text": "Turner has made several movies, docudramas and documentaries for its networks in recent years, but the company has never acted as a full-fledged movie studio and released its own pictures to theaters."}, {"text": "Mr. Hogan said 'The Secret Life of Ian Fleming' and 'Treasure Island' cost more than $6 million each to make, which is only about one-third the cost of most movies made for theatrical release."}, {"text": "The Turner move is in line with a cable-TV trend toward more original programming -- and toward finding more ways to amortize the high cost of producing films."}, {"text": "In July, Viacom Inc. formed Viacom Pictures to produce 12 low-budget movies a year that will premiere on Showtime network and be distributed later in various markets, including foreign theaters."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0146.json b/inquisitive/sources/test/0146.json new file mode 100644 index 0000000000000000000000000000000000000000..a712fdb85fe2b478c87117540d0b050284317d77 --- /dev/null +++ b/inquisitive/sources/test/0146.json @@ -0,0 +1 @@ +[{"text": "Ingersoll Publications Co. agreed to buy the New Haven Register in a transaction valued at $275 million from Goodson Newspaper Group Inc."}, {"text": "As part of the agreement, Goodson also terminated the contract under which Ingersoll manages Goodson's 66 newspapers, ending a long association between the two companies that has turned increasingly bitter recently."}, {"text": "Goodson has accused Ingersoll of paying less attention to its properties and more to such ventures as the recent launch of the St. Louis Sun."}, {"text": "Under the terms of the accord, Ingersoll will pay about $255 million for the Register, a daily that Goodson bought for about $170 million in 1986."}, {"text": "Goodson will pay the additional $20 million in settlement of the management contract."}, {"text": "Goodson also announced that it hired the former president and senior vice president of Ingersoll to run the Goodson papers."}, {"text": "Both executives left the company after clashes with Chairman Ralph Ingersoll Jr."}, {"text": "Goodson, which is based here, will use part of the proceeds to pay down debt associated with its purchase of the Morristown Daily Record for $155 million in 1987."}, {"text": "The New Jersey paper, like the New Haven, Conn., paper, was purchased by Ingersoll on Goodson's behalf as part of the management contract."}, {"text": "Industry analysts have said that the purchase price for the paper was too high, causing a strain on Goodson's finances."}, {"text": "Investment bankers familiar with the company said Goodson is seeking a new bank credit line of $190 million and may have to sell additional newspapers."}, {"text": "David N. Hurwitz, president and chief operating officer of Goodson, said in a telephone interview that the company doesn't currently have any plans to sell additional newspapers."}, {"text": "Goodson said David Carr, former president of Ingersoll Publications, and Ray Cockburn, former senior vice president, would head the new in-house management team at Goodson, which had revenue of $225 million in 1988."}, {"text": "The association between the two companies stretches back thirty years to a friendship between television producer Mark Goodson and Ingersoll founder Ralph Ingersoll."}, {"text": "The latter's son, Ralph Ingersoll Jr., took over the company and has been managing the Goodson properties and acting as an agent in the purchase of newspapers for Goodson."}, {"text": "But in recent years, Mr. Ingersoll began focusing more on expanding his own newspaper empire in partnership with investment banking firm Warburg, Pincus & Co. Ingersoll has 28 dailies and 200 other non-daily papers in the U.S. and Europe."}, {"text": "The company said its revenue will exceed $750 million this year."}, {"text": "Ingersoll President Robert M. Jelenic said in a statement that the company is 'delighted by the conclusion of the Goodson relationship' and will be able to 'concentrate all our energies' on Ingersoll's own papers."}, {"text": "Mr. Goodson, in his own statement, was less upbeat, saying 'unfortunately over the past few years, it has become increasingly clear that Ralph and I have different agendas,' and that he feels 'more comfortable with a management team whose sole interest and responsibility is in the Goodson papers.'"}] \ No newline at end of file diff --git a/inquisitive/sources/test/0147.json b/inquisitive/sources/test/0147.json new file mode 100644 index 0000000000000000000000000000000000000000..91f0c07fb08b9392745fc5a8d2a4e7bd0c4d09d0 --- /dev/null +++ b/inquisitive/sources/test/0147.json @@ -0,0 +1 @@ +[{"text": "'Hacksaw' and 'Bonecrusher' are the sort of nicknames normally associated with linebackers and heavyweight contenders."}, {"text": "Who'd have thought that the next group of tough guys carrying around reputations like that would be school superintendents?"}, {"text": "Chicago's new school chief is the hard-nosed Ted Kimbrough."}, {"text": "At his old job in Compton, Calif., he took a bitter teachers' strike and nearly came to blows with a school-board member."}, {"text": "At his first Chicago press conference, he berated the reporters."}, {"text": "In New York City, the new Chancellor, Joseph Fernandez, has landed like a 16-inch shell in the middle of a system that has been impervious to serious reform."}, {"text": "Both men fit the mood of the times -- the mood being one of a public fed up with officials' rationalizations for why their schools don't work."}, {"text": "Former Patterson, N.J., principal Joe Clark was no doubt the general public's first experience with this new breed of no-nonsense administrator."}, {"text": "The subject of the movie 'Lean on Me,' Mr. Clark controlled his school with a bullhorn and a baseball bat."}, {"text": "He may have gone overboard in his pursuit of good discipline, but isn't it interesting that some of the country's biggest, most troubled school districts are choosing new chiefs from the same gravel-chewing mold?"}, {"text": "Elena Scambio, the woman assigned to run the Jersey City school system that was taken over by the state, says her top priority will be to 'cut through the dead hand of bureaucracy.'"}, {"text": "Mr. Fernandez doesn't take control in New York until January, but already he's roiling the waters."}, {"text": "He's attacked the concept of 'building tenure,' one of the most disgraceful institutions in American public schools."}, {"text": "It means it is virtually impossible to fire or even transfer incompetent principals."}, {"text": "Once they are in the building, they stay."}, {"text": "One South Bronx principal kept his job for 16 years, despite a serious drinking problem and rarely showing up for work."}, {"text": "He was finally given leave when he was arrested for allegedly buying crack."}, {"text": "Naturally, the principals' union loves building tenure, and tenure has withstood previous challenge."}, {"text": "We suggest that Mr. Fernandez find an incompetent principal, toss him out of the building and let the forces of the status quo explain to the parents whatever it is they're defending."}, {"text": "In his old job, as Dade County chief, Mr. Fernandez forced out 92 teachers and reshuffled 48 principals."}, {"text": "He cut the dropout rate by 5.5%."}, {"text": "But the no-more-nonsense superintendents are going to have to be judicious as well; incompetent principals and administrators should go, but the good ones ought to be left alone."}, {"text": "The situation will be especially delicate for Mr. Kimbrough."}, {"text": "He takes over a school system in the midst of radical reform."}, {"text": "Chicagoans have just elected 540 neophyte school boards, one for each school."}, {"text": "This of course led to disaster in New York City."}, {"text": "Getting a community of parents to care again about its schools is essential, but in Chicago the new boards will make mistakes and Mr. Kimbrough will have to identify them."}, {"text": "The rise of superintendents such as Joseph Fernandez and Ted Kimbrough suggests plainly the process of disintegration in many school systems."}, {"text": "The schools' central mission, educating children, became subsumed by the competing interests of bureaucrats, politicians and unions."}, {"text": "The classroom itself operated on the periphery of this awful system, discipline collapsed, and kids stopped learning."}, {"text": "Mr. Chips was a nice fellow, and maybe some day he'll return."}, {"text": "Until then, it's clear that some of the people who've been keeping big-city schools down are going to be dealing with the Terminator."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0149.json b/inquisitive/sources/test/0149.json new file mode 100644 index 0000000000000000000000000000000000000000..42e8b31932c3561bb527c7dd9051f92d7649b078 --- /dev/null +++ b/inquisitive/sources/test/0149.json @@ -0,0 +1 @@ +[{"text": "A series of explosions tore through the huge Phillips Petroleum Co. plastics plant near here, injuring more than a hundred and closing parts of the Houston Ship Channel."}, {"text": "There were no immediate reports of deaths, but officials said a number of workers were still unaccounted for last night."}, {"text": "The Bartlesville, Okla., oil company late yesterday still hadn't said officially what caused the explosions and fires, which sent columns of heavy black smoke billowing high into the air."}, {"text": "One local Phillips manager said a seal blew in one of the plant's reactors."}, {"text": "Glenn Cox, Phillips' president and chief operating officer, and other Phillips officials flew from Bartlesville to assess the damage and determine the cause of the afternoon explosions."}, {"text": "In composite trading on the New York Stock Exchange, Phillips Petroleum shares fell $1.125 to $23.125."}, {"text": "The plastics plant is located on an 800-acre tract in the heart of the petrochemical corridor that reaches along the U.S. Gulf Coast."}, {"text": "The U.S. Coast Guard closed six miles of the Houston Ship Channel, where about 150 companies have operations, because the thick, black smoke obscured the area."}, {"text": "The Port of Houston closed its terminal for handling bulk cargo."}, {"text": "Broken water lines and gas leaks hindered firefighters' efforts, but by late yesterday authorities said they had the fire under control."}, {"text": "The blasts blew out windows, spewed debris for miles and crumpled the ceiling in an area elementary school."}, {"text": "The initial fireball was caught by cameras in downtown Houston, about 10 miles away."}, {"text": "Nearby Pasadena, Texas, police reported that 104 people had been taken to area hospitals, but a spokeswoman said that toll could rise."}, {"text": "The injured, including three in critical condition, were treated for burns, breathing problems and cuts from flying glass, hospital officials said."}, {"text": "The plant employs between 800 and 900 on three shifts."}, {"text": "The number working at the time of the blast wasn't known."}, {"text": "Yesterday's explosions were the second round in two months at the plastics plant."}, {"text": "In late August, four contract workers were injured and one Phillips employee died after an explosion at a fuel supply line near the facility's boiler house."}, {"text": "The Phillips facility manufactures polyethylene, polypropylene and K-resin, plastics used in a wide array of applications, including milk jugs and toys."}, {"text": "Plastics are the cornerstone of Phillips' chemicals operations, which is the biggest single contributor to the company's profits."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0150.json b/inquisitive/sources/test/0150.json new file mode 100644 index 0000000000000000000000000000000000000000..c129c3df7894d5ab2dddac1eb93f8b5488b353a9 --- /dev/null +++ b/inquisitive/sources/test/0150.json @@ -0,0 +1 @@ +[{"text": "Inco Ltd. posted a 35% decline in third-quarter net income, a performance that was in line with analysts' expectations."}, {"text": "The nickel producer also raised its quarterly dividend to 25 cents a share from 20 cents and said it may buy back as much as 4.8% of its common outstanding."}, {"text": "Inco shares fell after the announcements."}, {"text": "Analysts said some investors were disappointed that the cash-rich company had failed to announce a special dividend."}, {"text": "Inco closed at $31.125 a share, down 62.5 cents, in New York Stock Exchange composite trading."}, {"text": "Some analysts said Inco, which had cash reserves of $272 million as of Sept. 30, could still announce a special dividend in the next few months, though it would be smaller than the $10-a-share special dividend it paid last year."}, {"text": "The quarterly dividend is payable Dec. 1 to shares of record Nov. 3."}, {"text": "Inco's net fell to $129.3 million, or $1.23 a share, in the third quarter from $200.3 million, or $1.88 a share, a year earlier."}, {"text": "Sales rose 8.2% to $848.7 million from $784.5 million."}, {"text": "Excluding special gains from tax-loss carry-forwards, earnings in the latest quarter were $117.7 million, or $1.12 a share, compared with $187.4 million, or $1.76 a share."}, {"text": "Inco said the drop in earnings resulted mainly from lower nickel prices for the period and a temporary cut in nickel output at the company's Manitoba operations due to high levels of arsenic in the ore."}, {"text": "Inco said it plans to buy back as many as five million common shares over the next 12 months if nickel market conditions are favorable."}, {"text": "Under a previous buyback program, Inco has purchased 1.7 million of its shares since April."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0501.json b/inquisitive/sources/test/0501.json new file mode 100644 index 0000000000000000000000000000000000000000..5427d287f017e6a2fed22dabfce260a81caa23bf --- /dev/null +++ b/inquisitive/sources/test/0501.json @@ -0,0 +1 @@ +[{"text": "DALLAS - Today's kids can't keep up with their parents."}, {"text": "An analysis of studies on millions of children around the world finds they don't run as fast or as far as their parents did when they were young."}, {"text": "On average, it takes children 90 seconds longer to run a mile than their counterparts did 30 years ago."}, {"text": "Heart-related fitness has declined 5 percent per decade since 1975 for children ages 9 to 17."}, {"text": "The American Heart Association, whose conference featured the research on Tuesday, says it's the first to show that children's fitness has declined worldwide over the last three decades."}, {"text": "'It makes sense. We have kids that are less active than before,' said Dr. Stephen Daniels, a University of Colorado pediatrician and spokesman for the heart association."}, {"text": "Health experts recommend that children 6 and older get 60 minutes of moderately vigorous activity accumulated over a day."}, {"text": "Only one-third of American kids do now."}, {"text": "'Kids aren't getting enough opportunities to build up that activity over the course of the day,' Daniels said."}, {"text": "'Many schools, for economic reasons, don't have any physical education at all."}, {"text": "Some rely on recess' to provide exercise."}, {"text": "Sam Kass, a White House chef and head of first lady Michelle Obama's Let's Move program, stressed the role of schools in a speech to the conference on Monday."}, {"text": "'We are currently facing the most sedentary generation of children in our history,' Kass said."}, {"text": "The new study was led by Grant Tomkinson, an exercise physiologist at the University of South Australia."}, {"text": "Researchers analyzed 50 studies on running fitness - a key measure of cardiovascular health and endurance - involving 25 million children ages 9 to 17 in 28 countries from 1964 to 2010."}, {"text": "The studies measured how far children could run in 5 to 15 minutes and how quickly they ran a certain distance, ranging from half a mile to two miles."}, {"text": "Today's kids are about 15 percent less fit than their parents were, researchers concluded."}, {"text": "'The changes are very similar for boys and girls and also for various ages,' but differed by geographic region, Tomkinson said."}, {"text": "The decline in fitness seems to be leveling off in Europe, Australia and New Zealand, and perhaps in the last few years in North America."}, {"text": "However, it continues to fall in China, and Japan never had much falloff - fitness has remained fairly consistent there."}, {"text": "About 20 million of the 25 million children in the studies were from Asia."}, {"text": "In China, annual fitness test data show the country's students have become slower and fatter over the past several decades."}, {"text": "Experts and educators blame an obsession with academic testing scores for China's competitive college admissions as well as a proliferation of indoor entertainment options such gaming and web surfing for the decline."}, {"text": "China's Education Ministry data show that in 2010 male college students ran 1,000 meters (yards) 14 to 15 seconds slower on average than male students who ran a decade earlier."}, {"text": "Female students slowed by about 12 seconds in running 800 meters."}, {"text": "Motoaki Nito of the Sports and Youth Bureau at Japan's Ministry of Education, Culture, Sports, Science and Technology said there had been a decline in physical fitness among youth since the 1980s."}, {"text": "To turn that around, the government has urged municipalities and schools to promote youth fitness."}, {"text": "Nito said that this had resulted in a gradual increase of physical strength, which while not equal to levels seen in the 1980s, had reversed the trend."}, {"text": "Tomkinson and Daniels said obesity likely plays a role, since it makes it harder to run or do any aerobic exercise."}, {"text": "Too much time watching television and playing video games and unsafe neighborhoods with not enough options for outdoor play also may play a role, they said."}, {"text": "Other research discussed global declines in activity."}, {"text": "Fitness is 'pretty poor in adults and even worse in young people,' especially in the United States and eastern Europe, said Dr. Ulf Ekelund of the Norwegian School of Sport Sciences in Oslo, Norway."}, {"text": "World Health Organization numbers suggest that 80 percent of young people globally may not be getting enough exercise."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0502.json b/inquisitive/sources/test/0502.json new file mode 100644 index 0000000000000000000000000000000000000000..8db8a6c932ab8d522ca2085a456aba10b1d506d6 --- /dev/null +++ b/inquisitive/sources/test/0502.json @@ -0,0 +1 @@ +[{"text": "Not so fast, Jeff Bezos. Before Amazon.com Inc. can deploy its fleet of delivery drones, the company will have to wait for the results of drone tests at six state-run sites, which the Federal Aviation Administration will select later this month."}, {"text": "At least 24 states are competing to host these sites, which are expected to bring jobs and investment from a rapidly growing industry."}, {"text": "Congress has directed the FAA to safely integrate unmanned aerial vehicles, or unarmed drones, into the national airspace by 2015."}, {"text": "Until then, the FAA has said it will grant flight privileges to operators of unmanned aerial vehicles, or UAVs, on a case-by-case basis."}, {"text": "Bezos, the CEO of the Seattle-based e-commerce giant, said in an interview broadcast Sunday on CBS's '60 Minutes' news program that Amazon hopes to use drones to make same-day deliveries within five years of FAA approval."}, {"text": "'It will work, and it will happen, and it's gonna be a lot of fun,' Bezos said."}, {"text": "Amazon's plan is yet another example of how drones could transform everyday life."}, {"text": "Manufacturers tout the machines' ability to carry water to a wildfire, monitor storm systems, locate missing persons or even deliver pizza."}, {"text": "Governors are well aware of the technology's job potential for engineers, programmers and pilots."}, {"text": "Already, Oklahoma's Republican Gov."}, {"text": "Mary Fallin has a cabinet-level secretary dedicated to attracting drone companies to the state."}, {"text": "New Mexico, which has a long history of testing military aircraft, has already secured a site."}, {"text": "In promotional materials, Utah boasts that it is 'one of the few states with unified executive and legislative support for UAV testing'."}, {"text": "The Association of Unmanned Vehicle Systems International, the trade association for drone manufacturers, estimates that integrating drones into the national airspace will generate at least 70,000 engineering, manufacturing and piloting jobs within the first three years of FAA approval."}, {"text": "The states that win the test sites also will be charged with developing privacy policies for drones, to protect the public from surveillance by drones performing all sorts of tasks, including delivering packages."}, {"text": "During this past legislative session, eight states put limits on how law enforcement officers can use drones, and set guidelines for how long data collected from a drone can be stored in a database."}, {"text": "Still, those concerns haven't stopped the majority of states from moving ahead to attract drone businesses."}, {"text": "Even in Virginia, where tea partyers and civil libertarians worked together to pass a two-year moratorium on drone use by anyone other than the military, the economic temptation of aerospace jobs and an FAA test site persuaded the legislature and the governor to all but gut the moratorium in a special session."}, {"text": "'Not only would future job prospects dim, but current businesses and those they employ would be at risk,' warned Peter Bale, chairman of the AUVSI, in a letter to Virginia Gov."}, {"text": "Bob McDonnell, a Republican. 'More than 50 companies that manufacture UAVs have a footprint in Virginia."}, {"text": "A moratorium would create an unfriendly environment for these companies, which as a result might look to take their business, as well as jobs, elsewhere'."}, {"text": "In response, McDonnell added exemptions to the moratorium for researchers and companies to test drones, so long as they are not armed or used for surveillance."}, {"text": "Virginia and New Jersey are teaming up to apply for a joint drone test site, competing against 22 other states vying for one of the spots."}, {"text": "Republican Gov. Paul LePage of Maine also refused to sign a bill limiting drone use."}, {"text": "'This bill will harm any opportunity Maine has to create new jobs in the aerospace industry,' LePage wrote after vetoing a bill limiting law enforcement use of drones."}, {"text": "'It is the wrong message to send if we want these jobs'."}, {"text": "Instead, LePage directed the state Department of Public Safety to create guidelines for law enforcement use of drones."}, {"text": "A model drone policy from the Aerospace States Association, the Council of State Governments and the National Conference of State Legislatures urges states to require a warrant for drone surveillance of an individual; prohibit the re-use of video or photos collected by a drone for other investigations; and ban weapons from domestic drones."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0503.json b/inquisitive/sources/test/0503.json new file mode 100644 index 0000000000000000000000000000000000000000..634eff28b5bf0d59487a0cb33e26c72ebac7503b --- /dev/null +++ b/inquisitive/sources/test/0503.json @@ -0,0 +1 @@ +[{"text": "Ancient bricks, tile roofing and wood charcoal discovered beneath a Nepalese pilgrimage site are providing new evidence for the time of Buddha's birth, according to archaeologists."}, {"text": "In research published this week in the journal Antiquity, scholars wrote that the evidence supports a 6th century BC nativity for the Buddha."}, {"text": "A precise date of birth remains unknown."}, {"text": "Historians have wavered over dates ranging between 623 BC and 340 BC."}, {"text": "Much of the confusion has to do with the lack of a written record."}, {"text": "While inscriptions on monuments that were paid for and erected by the Indian emperor Asoka, or Ashoka, in the 3rd century BC provide some clues, earlier evidence is harder to come by, researchers say."}, {"text": "The Antiquity paper focused on recent archaeological work at the Maya Devi Temple at Lumbini, said to be the site of Buddha's birth."}, {"text": "The dig, which was financed by the Japanese and Nepalese governments and the National Geographic Society, was done within the shrine."}, {"text": "Robin Coningham, the paper's lead author and professor of archeology at Durham University in Britain, said the dig revealed a previously undiscovered temple built of wood beneath a succession of later brick temples."}, {"text": "The original timber structure appears to have been built around an open space that likely held a tree, the authors wrote."}, {"text": "'This central portion of the temple had always been open to the elements."}, {"text": "It had never been covered by a roof,' Coningham said."}, {"text": "'Also, the team found fragments of mineralized tree roots'."}, {"text": "According to Buddhist tradition, Siddhartha Gautama, as he was known before enlightenment, was born in a garden, beneath a tree."}, {"text": "Immediately after his delivery, Buddha is said to have stood and walked as his mother, Queen Maya Devi, held a tree branch for support."}, {"text": "Coningham said that because of this tradition, it was not surprising that a tree would feature prominently in the shrine."}, {"text": "'This is one of those rare occasions when belief, tradition, archeology and science actually come together, because here we have a very early shrine built around a tree,' Coningham said."}, {"text": "The Lumbini temple is one of four key temples associated with the life of Buddha, or 'enlightened one'."}, {"text": "The others are Bodh Gaya, where he attained enlightenment; Sarnath, where he first preached; and Kusingara, where he died at age 80."}, {"text": "The first Lumbini shrine was likely built by wealthy adherents of Buddhism at a time when the religion was considered a cult."}, {"text": "Subsequent shrines were constructed with large open areas as well, researchers said."}, {"text": "At some point the temple was forgotten and overgrown by jungle."}, {"text": "It was rediscovered in 1869 and found to have a large sandstone column with an inscription that called the site Lumbini and said that Ashoka had visited there."}, {"text": "Researchers said most of those earlier shrines at the site were covered by more recent construction, and an examination of the buried materials was not possible until now."}, {"text": "Hundreds of thousands of pilgrims visit Lumbini each year, and the temple remained open to archaeologists as they conducted their work."}, {"text": "'All of this work occurred within a living temple,' Coningham said."}, {"text": "Researchers used fragments of charcoal from the early wooden temple and grains of sand to date the structure."}, {"text": "The tests involved 'a combination of radiocarbon and optically stimulated luminescence techniques,' the authors of Monday's study said."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0505.json b/inquisitive/sources/test/0505.json new file mode 100644 index 0000000000000000000000000000000000000000..a240dc8ca488f821408afcf781254346ee6101b9 --- /dev/null +++ b/inquisitive/sources/test/0505.json @@ -0,0 +1 @@ +[{"text": "BEIJING - In a sharp rebuff, China accused Washington on Wednesday of taking Japan's side in a tense clash over disputed islands in the East China Sea, underscoring rising regional friction as visiting Vice President Joe Biden met with Beijing's leaders."}, {"text": "Emerging from a private meeting with President Xi Jinping that went considerably longer than scheduled, Biden appeared somber and subdued."}, {"text": "In a brief appearance before reporters in which he took no questions, Biden did not go into details on differences over China's newly declared restricted flying zone."}, {"text": "Instead, he spoke of a 'new model of major country cooperation,' saying U.S.-China relations must hinge on trust and a positive notion of each other's motives."}, {"text": "The awkward kickoff for a series of official meetings in Beijing followed Biden's speech earlier Wednesday urging young Chinese citizens to challenge orthodoxy and the status quo."}, {"text": "The vice president drew an implicit contrast between the authoritarian rule of China's government and the liberal, permissive intellectual culture he described in the United States."}, {"text": "Neither Biden nor Xi made public mention of the clash over disputed territory that has pitted China against the United States and its Asian allies."}, {"text": "An editorial in the state media China Daily charged, however, that Washington 'is turning a blind eye to Tokyo's provocations,' calling that the 'root cause of the tensions'."}, {"text": "It said that 'the United States is wrongly pointing an accusing finger at China for 'unilaterally' changing the 'status quo' in the East China Sea'."}, {"text": "Biden told reporters after his initial talks with Xi that the relationship between the two major powers will significantly affect the course of the 21st century."}, {"text": "If the U.S. and China can get that relationship right, the possibilities are limitless, he said to reporters who were allowed in briefly after the vice president met with Xi."}, {"text": "Biden said he came to Beijing because complex relationships require sustained engagement at high levels."}, {"text": "He said Xi's candor and constructive approach had left an impression on him."}, {"text": "'Candor generates trust,' Biden said."}, {"text": "'Trust is the basis on which real change - constructive change - is made'."}, {"text": "The two leaders had a second meeting involving larger delegations and a working dinner planned for later Wednesday."}, {"text": "Absent from Biden's public comments was any discussion of U.S. concerns over China's new air defense zone."}, {"text": "Only a day earlier, Biden pledged to raise those concerns 'with great specificity' with Xi and other Chinese leaders, adding that China's move was deeply concerning."}, {"text": "'This action has raised regional tensions and increased the risk of accidents and miscalculation,' Biden said in Tokyo Tuesday after meeting with Japanese President Shinzo Abe."}, {"text": "Japan has been on edge for the past two weeks since China unilaterally declared any planes flying through the zone must file flight plans with Beijing."}, {"text": "The airspace sits above tiny islands that are at the center of a long-running territorial dispute between China and Japan."}, {"text": "The U.S. refuses to recognize the zone, but Biden has avoided calling publicly for Beijing to retract it, wary of making demands that China is likely to snub."}, {"text": "Rather, the vice president hoped to persuade China not to enforce the zone or establish similar zones over other disputed territories."}, {"text": "After meeting with Biden, Xi said the U.S.-China relationship had gotten off to a good start this year 'and has generally maintained a momentum of positive development'."}, {"text": "But he said the global situation is changing, with more pronounced challenges and regional hotspots that keep cropping up."}, {"text": "'The world as a whole is not tranquil,' Xi said through a translator, adding that the U.S. and China shoulder important responsibilities for upholding peace."}, {"text": "'To strengthen dialogue and cooperation is the only right choice facing both of our countries'."}, {"text": "Added Biden, 'The way I was raised was to believe that change presents opportunity'."}, {"text": "In his speech earlier to young Chinese citizens waiting at the U.S. embassy to get visitor visas processed, the vice president said: 'I hope you learn that innovation can only occur where you can breathe free, challenge the government, challenge religious leaders'."}, {"text": "Biden told young Chinese citizens waiting at the U.S. embassy to get visitor visas processed."}, {"text": "'Children in America are rewarded - not punished - for challenging the status quo,' he said."}, {"text": "Biden's comments were not immediately reported by Chinese state media and were not likely to be widely known in China."}, {"text": "A one-minute excerpt of his speech posted by the Sina news website included Biden's comment about challenging the 'status quo,' but left out the one about challenging the government."}, {"text": "When Biden arrived later at the Great Hall of the People, a ceremonial edifice steps away from Tiananmen Square, any tensions between the U.S. and China were papered over as Chinese Vice President Li Yuanchao welcomed him with an elaborate honor guard."}, {"text": "A military band played the two countries' national anthems as Biden and Xi stood amid the massive hall's marble floors and crisscrossing red carpets."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0506.json b/inquisitive/sources/test/0506.json new file mode 100644 index 0000000000000000000000000000000000000000..4214059734bddf096281d77149a5ffb2e643a457 --- /dev/null +++ b/inquisitive/sources/test/0506.json @@ -0,0 +1 @@ +[{"text": "WASHINGTON - President Barack Obama prodded Congress to raise wages and secure the social safety net as he issued an overarching appeal Wednesday to correct economic inequalities that he said make it harder for a child to escape poverty."}, {"text": "'That should offend all of us,' he declared."}, {"text": "'We are a better country than this'."}, {"text": "Focusing on the pocketbook issues that Americans consistently rank as a top concern, Obama argued that the dream of upward economic mobility is breaking down and that the growing income gap is a 'defining challenge of our time'."}, {"text": "'The basic bargain at the heart of our economy has frayed,' the president said in remarks at a nonprofit community center a short drive from the White House in one of Washington's most impoverished neighborhoods."}, {"text": "Though he offered no new initiatives, Obama blended a call for Congress to act on pending short-term economic measures with an ambitious vision aimed at rectifying a growing level of income inequality in the United States."}, {"text": "Amid public doubts over Obama's stewardship of the economy, the speech served as a guide for the remaining three years of his term."}, {"text": "Still, by drawing attention to past policy proposals that have dead-ended in a divided government, Obama also laid bare the political failures and economic difficulties he has faced trying to halt widening inequality trends."}, {"text": "He acknowledged his administration's 'poor execution' in rolling out the flawed health care website that was supposed to be an easy portal for purchasing insurance, while blaming Republicans for a 'reckless' shutdown of the government."}, {"text": "'Nobody has acquitted themselves very well these past few months,' Obama said."}, {"text": "'So it's not surprising that the American people's frustrations with Washington are at an all-time high'."}, {"text": "Worse for Americans, he added, are their growing difficulties in trying to make ends meet no matter how hard they work."}, {"text": "The speech coincided with growing national and international attention to economic disparities - from the writings of Pope Francis to the protests of fast-food workers in the U.S. Obama recalled the pope's words, the deeds of past presidents as well as his own personal story as a young boy with a financially struggling mother."}, {"text": "And he noted that in the United States, a child born into the bottom 20 percent of income levels has less than a 5 percent chance of making it to the top income levels and is 10 times likelier to stay where he is - worse than other industrial countries such as Canada, Germany and France."}, {"text": "House Speaker John Boehner blamed Senate Democrats and Obama for the lack of action on jobs-related legislation."}, {"text": "He said bills passed by the Republican-controlled House that would help the economy and create jobs have been blocked in the Democratic-controlled Senate."}, {"text": "'The Senate and the president continue to stand in the way of the people's priorities,' he said on the House floor."}, {"text": "Obama conceded that 'the elephant in the room' is the politicalgridlock that has prevented congressional action."}, {"text": "But he pointed to the health care law, despite its troubled enrollment launch, as one example that he said is already helping families by providing insurance coverage to more Americans and by pushing down the costs of health care."}, {"text": "Obama specifically called on Congress to increase the federal minimum wage from the current $7.25 an hour."}, {"text": "A Democratic bill by Sen. Tom Harkin of Iowa would raise the threshold to $10.10 an hour in three steps and tie automatic annual increases to changes in the cost of living."}, {"text": "A vote in the Senate is not expected in December, when the chamber will mostly focus on stalemates over the budget and other issues."}, {"text": "Whenever it is debated, the measure seems unlikely to win the 60 votes it would need to clear the Senate due to GOP opposition."}, {"text": "Obama also pressed Congress to extend jobless benefits to 1.3 million long-term unemployed people."}, {"text": "The benefits are set to expire just three days after Christmas."}, {"text": "The additional weeks of benefits have been extended each year since 2009, but a senior Republican lawmaker, Rep. Tom Cole of Oklahoma, said Tuesday that lawmakers in his party oppose yet another extension."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0508.json b/inquisitive/sources/test/0508.json new file mode 100644 index 0000000000000000000000000000000000000000..982206e6c3f99c121a65af7a797e4d93fe8bae3e --- /dev/null +++ b/inquisitive/sources/test/0508.json @@ -0,0 +1 @@ +[{"text": "WASHINGTON - The Pentagon is outfitting a 647-foot cargo ship with high-tech equipment in an effort to safely destroy hundreds of tons of lethal chemical weapons agents that were collected in Syria after a deadly gas attack this summer sparked an international outcry."}, {"text": "Two specially developed hydrolysis machines, which use water or bleach to neutralize the chemicals that produce nerve gases, have been installed aboard the Cape Ray at the U.S. naval base in Norfolk, Va., officials said Thursday."}, {"text": "The system should be able to eliminate Syria's VX and sarin stockpiles and chemical components in 45 to 90 days, the officials said."}, {"text": "No chemicals will be dumped at sea."}, {"text": "With Syria engulfed in civil war, moving the deadly material to the U.S. naval ship over the next month may be the biggest challenge."}, {"text": "Plans call for trucking the arsenal from a series of collection sites to the Syrian port of Latakia, where it will be loaded into 150 Teflon-lined shipping containers."}, {"text": "Pentagon planners fear that even a heavily guarded convoy could be attacked en route to Latakia."}, {"text": "'Obviously, it's a challenging environment,' said a U.S. official, who briefed reporters on condition of anonymity to discuss military operations."}, {"text": "After poison gas rockets hit rebel-held suburbs of east Damascus on Aug. 21, killing more than 1,000 people, according to U.S. officials, President Bashar Assad agreed to surrender his stockpiles to international chemical weapons inspectors and thus avoid a threatened retaliatory attack led by the U.S. military."}, {"text": "Over the last few months, the teams have dismantled or destroyed Syria's chemical weapons production facilities and warheads, but they now must get rid of bulk liquid chemicals that are mixed to form the nerve gases."}, {"text": "Destroying the material at sea was chosen as a last resort when no country agreed to do it on land."}, {"text": "Norway has offered to ferry the sealed containers from Latakia to an as-yet-unnamed port outside Syria, where they will be transferred to the Cape Ray, the officials said."}, {"text": "The U.S. officials refused to say if the Cape Ray would stay in the Mediterranean Sea while the destruction process was underway or would sail elsewhere."}, {"text": "They also refused to discuss what security would be provided."}, {"text": "No U.S. government personnel will be in Syria to assist with the operation and no U.S. military forces will be involved in protecting the Syrian trucks as they transport the chemical agents to Latakia."}, {"text": "Under a timetable established by the Organization for the Prohibition of Chemical Weapons, which is working with the United Nations to carry out the disarmament, the most dangerous material must be removed from Syria by the end of this year."}, {"text": "Under a U.N. Security Council resolution, the entire stockpile must be destroyed by mid-2014."}, {"text": "The Pentagon has offered use of the ship to the Hague-based organization, which has not formally accepted the offer but is expected to shortly."}, {"text": "The modified ship is expected to undergo a sea trial this month and be ready to sail early next year."}, {"text": "It also is being outfitted with an analysis lab and a protective system that includes a large tent to prevent hazardous material from escaping the hold if an accident occurs."}, {"text": "Workers now being trained will wear protective suits."}, {"text": "The Pentagon has used hydrolysis machines to help destroy parts of its own once-vast chemical weapons stockpile, although never before on a ship."}, {"text": "The machines eliminate 99.9 percent of the chemical agents, creating a liquid byproduct that is considered hazardous waste but has a low level of toxicity, according to one of the U.S. officials."}, {"text": "The liquid will be stored aboard the Cape Ray, which will be manned by about 60 Defense Department civilians and contractors, until arrangements can be made to destroy it at a commercial waste treatment facility."}, {"text": "Most of Syria's agents are in liquid bulk form that need to be mixed to produce a usable weapon, officials said, making it easier to neutralize them instead of destroying them through incineration, a process that would have to occur on land."}, {"text": "The Cape Ray is owned by the U.S. Maritime Administration, a federal agency that maintains a reserve fleet of ships that can be leased to help the Pentagon transport vehicles and other equipment during hostilities or in other emergencies."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0509.json b/inquisitive/sources/test/0509.json new file mode 100644 index 0000000000000000000000000000000000000000..3b653a6179d34aee6420b0a8d3859d1d7bb78c45 --- /dev/null +++ b/inquisitive/sources/test/0509.json @@ -0,0 +1 @@ +[{"text": "LONDON - American and British intelligence operations have been spying on gamers across the world, media outlets reported, saying that the world's most powerful espionage agencies sent undercover agents into virtual universes to monitor activity in online fantasy games such as 'World of Warcraft'."}, {"text": "Stories carried Monday by The New York Times, the Guardian, and ProPublica said U.S. and U.K. spies have spent years trawling online games for terrorists or informants."}, {"text": "The stories, based on documents leaked by former National Security Agency (NSA) contractor Edward Snowden, offer an unusual take on America's world-spanning surveillance campaign, suggesting that even the fantasy worlds popular with children, teens, and escapists of all ages aren't beyond the attention of the NSA and its British counterpart, GCHQ."}, {"text": "Virtual universes like 'World of Warcraft' can be massively popular, drawing in millions of players who log months' worth of real-world time competing with other players for online glory, virtual treasure, and magical loot."}, {"text": "At its height, 'World of Warcraft' boasted some 12 million paying subscribers, more than the population of Greece."}, {"text": "Other virtual worlds, like Linden Labs' 'Second Life' or the various games hosted by Microsoft's Xbox - home to the popular science fiction-themed shoot-em-up 'Halo' - host millions more."}, {"text": "Spy agencies have long worried that such games serve as a good cover for terrorists or other evildoers who could use in-game messaging systems to swap information."}, {"text": "In one of the documents cited Monday by media outlets, the NSA warned that the games could give intelligence targets a place to 'hide in plain sight'."}, {"text": "Linden Labs and Microsoft Inc. did not immediately return messages seeking comment."}, {"text": "In a statement, Blizzard Entertainment said that it is 'unaware of any surveillance taking place."}, {"text": "If it was, it would have been done without our knowledge or permission'."}, {"text": "Microsoft issued a similar statement, saying it is 'not aware of any surveillance activity."}, {"text": "If it has occurred as reported, it certainly wasn't done with our consent'."}, {"text": "The 82-page-document, published on The New York Times' website, also noted that opponents could use video games to recruit other users or carry out virtual weapons training - pointing to the Sept. 11, 2001, hijackers as examples of terrorists who had used flight simulation software to hone their skills."}, {"text": "Important details - such as how the agencies secured access to gamers' data, how many players' information was compromised, or whether Americans were swept up in the spying - were not clear, the Times and ProPublica said, but the reports point to a determined effort to infiltrate a world many people associate with adolescents and shut-ins."}, {"text": "At the request of GCHQ, the NSA began extracting 'World of Warcraft' data from its global intelligence haul, trying to tie specific accounts and characters to Islamic extremism and arms dealing efforts, the Guardian reported."}, {"text": "Intelligence on the fantasy world could eventually translate to real-world espionage success, one of the documents suggested, noting that 'World of Warcraft' subscribers included 'telecom engineers, embassy drivers, scientists, the military and other intelligence agencies'."}, {"text": "'World of Warcraft' wasn't the only target."}, {"text": "Another memo noted that GCHQ had 'successfully been able to get the discussions between different game players on Xbox Live'."}, {"text": "Meanwhile, so many U.S. spies were roaming around 'Second Life' that a special 'deconfliction' unit was set up to prevent them from stepping on each other's toes."}, {"text": "Blizzard Entertainment is part of Santa Monica, Calif.-based Activision Blizzard Inc."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0511.json b/inquisitive/sources/test/0511.json new file mode 100644 index 0000000000000000000000000000000000000000..71ce649c1df930e18829c041f793c1b24f41149b --- /dev/null +++ b/inquisitive/sources/test/0511.json @@ -0,0 +1 @@ +[{"text": "ORLANDO, Fla. - Christin Rivas, 14, was fascinated by the small, round toy magnets that you can sculpt into shapes and use to perform magic tricks."}, {"text": "Put a pen on a desk, hold a magnet underneath and watch the pen move across the desktop."}, {"text": "While playing with a couple of these rare-earth magnets at her Satellite Beach, Fla., middle school last week, Christin needed both hands to grab something, so she decided to hold the mini-magnets in her mouth."}, {"text": "Someone made her laugh, and \u2026 gulp."}, {"text": "She swallowed the magnets. Five days later, Christin was at Arnold Palmer Hospital for Children in Orlando, Fla., having the magnets surgically removed from her intestines, along with a small section of her colon and her appendix."}, {"text": "Labels warning that magnets are harmful if swallowed have not stopped an increasing number of kids from putting them in their mouths or noses and then getting them stuck in their bodies, where they can cause serious harm."}, {"text": "The groups that get into the most trouble are children age 5 and younger, and tweens and teens, who use the magnets to mimic tongue, lip, cheek or nose piercings."}, {"text": "'Kids swallow a lot of objects,' said Dr. Tejas Mehta, a pediatric gastroenterologist at Arnold Palmer who treated Rivas, 'but from a GI perspective, magnets cause more damage than anything else'."}, {"text": "That risks soars when more than one magnet goes down."}, {"text": "Magnets will work so hard to find each other that their force can cause intestines to twist and become blocked."}, {"text": "The pull can also cause erosion, then ulceration, and eventually the intestine can perforate, causing infection, Mehta said."}, {"text": "Four out of five kids who swallow multiple magnets will need an invasive procedure, such as an endoscopy or surgery, said Mehta, who has heard of kids swallowing magnets and needing massive bowel resections."}, {"text": "From 2002 to 2011 magnet-related emergency-room visits among Americans younger than 21 increased fivefold, according to a recent study published in the Annals of Emergency Medicine."}, {"text": "During that 10-year period, 22,500 magnet injuries were reported."}, {"text": "Usually the kids swallowed the magnets, but about one-fourth put the magnets up their nose, said Julie Brown, an emergency-room doctor at the University of Washington, in Seattle, and lead author of the study."}, {"text": "The magnets break loose and go in, not out."}, {"text": "Based on data Brown has seen since then, the problem shows no sign of slowing."}, {"text": "'There is something very tempting about them,' Brown said."}, {"text": "'When playing with this fidgety toy, you want to put it in your mouth."}, {"text": "You want to try to separate the magnets with your teeth'."}, {"text": "To toddlers, they look just like the silver-ball candies you put on cupcakes, she said."}, {"text": "Buckyballs, a set of 216 magnets that consumers can manipulate into sculptures and chain jewelry, is one culprit."}, {"text": "Last year, the Consumer Product Safety Commission asked retailers and makers of Buckyballs and Zen Magnets, a similar toy, to stop selling them."}, {"text": "But you can still find them online, said Brown, who has researched the issue and claims more than 3 million sets of the magnet sets have been sold."}, {"text": "At 216 magnets per set, that's 600 million in circulation."}, {"text": "Other magnet-containing products are equally worrisome, she said, citing metallic bulletin boards that have little magnet pins, refrigerator magnets that look like candies or coffee beans (begging to be tasted) and fishing games that involve a magnet on a rod."}, {"text": "Many emergency-room physicians don't know how serious the problem can be."}, {"text": "When Barbara Rivas took her daughter to the emergency room at Wuesthoff Medical Center, the doctor ordered an X-ray, then sent Christin and her mother home and said the magnets would pass."}, {"text": "That advice didn't set well with Rivas, who did some online research."}, {"text": "'That's when I hit the panic button,' she said."}, {"text": "After going to another ER, she was referred to Arnold Palmer, where doctors admitted Christin and tracked her magnets' path by X-ray."}, {"text": "Normally, food or foreign objects take six to eight hours to go from entry to exit, Mehta said."}, {"text": "When the magnets Christin swallowed stalled at the neck of the large colon for 24 hours, doctors decided to operate."}, {"text": "Anyone who has surgery on the small bowel runs a 10 percent chance of developing a bowel obstruction later in life, Brown said."}, {"text": "'Don't even think about touching them or buying them,' Christin said."}, {"text": "'I messed up my intestines. I worry about that down the road'."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0513.json b/inquisitive/sources/test/0513.json new file mode 100644 index 0000000000000000000000000000000000000000..202d6c88195edc4fe0cfeedb615bb834216ac4ff --- /dev/null +++ b/inquisitive/sources/test/0513.json @@ -0,0 +1 @@ +[{"text": "WASHINGTON - The American public is unusually pessimistic about the direction of the country and increasingly fed up with Washington gridlock, a sour mood reflected in the worst disapproval ratings for President Barack Obama since he took office nearly five years ago."}, {"text": "People give elected officials unusually low grades - 31 percent rated them 'D' and 38 percent gave them an 'F,' according to a new McClatchy-Marist poll."}, {"text": "'The lack of confidence in Washington to right itself is showing up,' said Lee Miringoff, director of the Marist Institute for Public Opinion in New York."}, {"text": "Obama's disapproval rating climbed to 53 percent \u2013 the worst in 29 polls since he took office in January 2009 - while 43 percent approved of his job performance."}, {"text": "The disapproval number was up sharply from the 47 percent reading in September and tops the previous high of 52 percent in September 2011."}, {"text": "Obama retained strong support among Democrats - 77-18 percent approval - and disdain from Republicans \u2013 90-8 percent disapproval."}, {"text": "Independents disapproved 56 percent to 41 percent."}, {"text": "Obama's personal ratings were also down."}, {"text": "By 52 percent to 46 percent, people had an unfavorable impression of him, the first time since November 2011 the negative number was higher."}, {"text": "The unfavorable number was also the worst he has endured."}, {"text": "Obama in recent weeks has been battered by turmoil over his health care program."}, {"text": "The highly touted website where people could sign up for coverage proved to be a dysfunctional embarrassment, and Obama had to backtrack from his assertion that people could keep their plans if they wanted."}, {"text": "Congress fared even worse. By 74 percent to 22 percent, voters disapprove of the Republicans' performance, the highest since the question was first asked in April 2011."}, {"text": "Republicans control the House of Representatives and 45 of the Senate's 100 seats."}, {"text": "People soured on Democrats, too. Sixty-four percent disapproved of congressional Democrats, who control the Senate."}, {"text": "Both Republican and Democratic disapproval numbers were up sharply from the last poll in July."}, {"text": "The numbers show that 'the unsures have cast their vote with the negatives,' Miringoff said."}, {"text": "The key reason for the glum ratings is the economy."}, {"text": "Though indicators suggest a healthy rebound, people aren't feeling it."}, {"text": "Instead, said Miringoff, the two Washington stories that have dominated headlines in recent months were the 16-day October government shutdown and the health care chaos."}, {"text": "That helped create pessimism that found two-thirds seeing things going in the wrong direction, while 30 percent felt matters were heading in the right direction."}, {"text": "Democrats were more optimistic, with the right-wrong direction split 57 percent to 40 percent."}, {"text": "Republicans overwhelmingly saw the country moving the wrong way - 95 percent to 4 percent - and independents saw matters heading in the wrong direction, 69 percent to 26 percent."}, {"text": "The federal budget drama is the most obvious symbol of Washington inertia."}, {"text": "Lawmakers have wrangled all year, passing stopgaps after extended, often bitter debate."}, {"text": "Negotiators this week are said to be close on a deal that will avoid another shutdown when money again runs out Jan. 15."}, {"text": "Obama gets low marks for his handling of the economy."}, {"text": "Fifty-eight percent disapproved of how he's dealing with it, while 40 percent approved."}, {"text": "More people blame Republicans for the budget mess - 48 percent said it's their fault while 38 percent named Obama."}, {"text": "Obama suffered in two other areas where he had shown some strength, foreign policy and personal appeal."}, {"text": "The latest poll was conducted after the administration announced a pact with Iran that eases some sanctions on that country, in exchange for some limits on Iran's nuclear program."}, {"text": "That plan has won little congressional support, as lawmakers from both parties have expressed doubts."}, {"text": "Forty-six percent approved of Obama's handling of foreign policy, while 51 percent did not."}, {"text": "Voters have mixed views about how all this will translate in next year's elections."}, {"text": "Equal numbers - 43 percent - said they would vote for a Republican or a Democratic candidate."}, {"text": "Independents preferred Republicans, 41 percent to 34 percent, while moderates favored Democrats, 49 percent to 35 percent."}, {"text": "METHODOLOGY This survey of 1,173 adults was conducted Dec. 3-5."}, {"text": "Adults 18 years of age and older residing in the continental United States were interviewed by telephone using live interviewers."}, {"text": "Landline telephone numbers were randomly selected based upon a list of telephone exchanges from throughout the nation from ASDE Survey Sampler Inc."}, {"text": "The exchanges were selected to ensure that each region was represented in proportion to its population."}, {"text": "To increase coverage, this landline sample was supplemented by respondents reached through random dialing of cellphone numbers from Survey Sampling International."}, {"text": "The two samples were then combined and balanced to reflect the 2010 census results for age, gender, income, race and region."}, {"text": "Results are statistically significant within plus or minus 2.9 percentage points."}, {"text": "There are 988 registered voters. The results for this subset are statistically significant within plus or minus 3.1 percentage points."}, {"text": "The error margin increases for cross-tabulations."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0514.json b/inquisitive/sources/test/0514.json new file mode 100644 index 0000000000000000000000000000000000000000..ce2894ff52b5c6797d601f497a1075b4f9a79de6 --- /dev/null +++ b/inquisitive/sources/test/0514.json @@ -0,0 +1 @@ +[{"text": "NEW YORK - Time magazine selected Pope Francis as its Person of the Year on Wednesday, saying the Catholic Church's new leader has changed the perception of the 2,000-year-old institution in an extraordinary way in a short time."}, {"text": "The pope beat out NSA leaker Edward Snowden for the distinction, which the newsmagazine has been giving each year since 1927."}, {"text": "The former Argentine Cardinal Jorge Mario Bergoglio was elected in March as the first pope from Latin America and the first Jesuit."}, {"text": "Since taking over at the Vatican, he has urged the Catholic Church not to be obsessed with 'small-minded rules' and to emphasize compassion over condemnation in dealing with touchy topics like abortion, gays and contraception."}, {"text": "He has denounced the world's 'idolatry of money' and the 'global scandal' that nearly 1 billion people today go hungry, and has charmed the masses with his simple style and wry sense of humor."}, {"text": "His appearances draw tens of thousands of people and his @Pontifex Twitter account recently topped 10 million followers."}, {"text": "'He really stood out to us as someone who has changed the tone and the perception and the focus of one of the world's largest institutions in an extraordinary way,' said Nancy Gibbs, the magazine's managing editor."}, {"text": "The Vatican said the honor wasn't surprising given the resonance in the general public that Francis has had, but it nevertheless said the choice was a 'positive' recognition of spiritual values in the international media."}, {"text": "'The Holy Father is not looking to become famous or to receive honors,' said the Vatican spokesman, the Rev."}, {"text": "Federico Lombardi. 'But if the choice of Person of Year helps spread the message of the Gospel - a message of God's love for everyone - he will certainly be happy about that'."}, {"text": "It was the third time a Catholic pope had been Time's selection."}, {"text": "John Paul II was selected in 1994 and John XXIII was chosen in 1962."}, {"text": "In Argentina on Wednesday, Padre Toto, one of the many 'slum priests' the pope supported for years as archbishop of Buenos Aires, praised Time magazine's selection."}, {"text": "'I think the recognition of Time magazine is good news, because Pope Francis embodies one of the values of a church that's more missionary, closer to the people, more austere, more in keeping with the gospel,' Toto said."}, {"text": "'He had the genius of knowing how to express this sense of the church and hopefully his way of being will catch on with other political leaders, business executives, sports figures."}, {"text": "His leadership is inspiring'. Besides Snowden, Time had narrowed its finalists down to gay rights activist Edith Windsor, U.S. Sen. Ted Cruz of Texas and Syrian President Bashar Assad."}, {"text": "President Barack Obama was Time's selection for 2012."}, {"text": "Time editors make the selection. The magazine polled readers for their choice, and the winner was Egyptian General Abdel-Fattah el-Sissi, who didn't even make the top 10 of Time's final list."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0515.json b/inquisitive/sources/test/0515.json new file mode 100644 index 0000000000000000000000000000000000000000..a3bee7af221b80600275f9a08a395f89c96c24cc --- /dev/null +++ b/inquisitive/sources/test/0515.json @@ -0,0 +1 @@ +[{"text": "Peering far deeper than ever before into humanity's murky genetic past, scientists sequenced the DNA of an ancient European relative and found a puzzling connection to the Far East."}, {"text": "The genetic sample came from a 400,000-year-old thigh bone pulled from the cold, damp depths of a Spanish cave called Sima de los Huesos, or 'Pit of Bones'."}, {"text": "Researchers surmised that it belonged to an extinct species of hominin known as Homo heidelbergensis, a direct ancestor of Neanderthals, and they expected it to resemble DNA extracted from of a handful of Neanderthal bones found in Spain, Croatia and other sites in Europe."}, {"text": "They were wrong. 'This really raises more questions than it answers really,' said biologist Svante Paabo of the Max Planck Institute for Evolutionary Anthropology in Germany, a pioneer in the quest to decode ancient DNA."}, {"text": "'It's a big surprise'. Paabo and his colleagues published a report on their findings this past week in the journal Nature."}, {"text": "The DNA is the oldest known genetic material ever recovered from an early human, beating the previous record by roughly 300,000 years."}, {"text": "It was taken from cell mitochondria, tiny structures that produce energy for the cell."}, {"text": "It contains far less information than DNA from a cell nucleus, but it decays more slowly and is easier to study in ancient specimens."}, {"text": "Mitochondrial DNA is passed down virtually unchanged from mothers to children."}, {"text": "Therefore, if the mystery leg bone belonged to an ancestor of Neanderthals, it should have been quite similar."}, {"text": "Instead, the gene sleuths discovered a much closer match with the Denisovans, a little-known group of Neanderthal relatives that lived thousands of miles away in Siberia."}, {"text": "The study's authors, however, remain at a loss to explain the link between an early European hominin and another population in Asia."}, {"text": "One possibility is that the bone belonged to a member of a group that was ancestral to both Neanderthals and Denisovans and that Neanderthals acquired different mitochondrial DNA after the two groups diverged."}, {"text": "'Another alternative is that this ancestral group actually interbred with something much older, something like Homo erectus, and obtained its mitochondrial DNA from them,' Paabo said."}, {"text": "Modern humans, or Homo sapiens, are not the descendants of Neanderthals or Denisovans, although they did live as contemporaries at one time and interbred, according to scientists."}, {"text": "At some point about 30,000 years ago, all other species of the Homo genus became extinct, leaving only us."}, {"text": "Answers to this evolutionary mystery may emerge if the team is able to recover nuclear DNA from cells in the femur."}, {"text": "Paabo said scientists are already working on it, and they hope to have some results in roughly a year."}, {"text": "But success isn't something that scientists can take for granted."}, {"text": "Ancient genetic information has been extremely difficult to sequence, for at least two reasons."}, {"text": "First, DNA strands disintegrate into smaller and smaller pieces over time, making it tricky to determine their original order."}, {"text": "The second issue is one of contamination."}, {"text": "DNA from archaeologists and lab workers can get mixed up with the sample, confusing analysis."}, {"text": "Older DNA samples have been obtained for other animals - scientists recently sequenced the genome of a 700,000-year-old horse - but those specimens are usually found in permafrost conditions, far from early human remains."}, {"text": "In the case of the Spanish femur, cool, moist conditions within the cave, as well as rapid advancements in genetic sequencing techniques, allowed Paabo's team to decode much of the mitochondrial genome."}, {"text": "Alongside the femur were the remains of 28 other individuals, according to the report in Nature."}, {"text": "Fossil remains of European Neanderthals have allowed scientists to describe their appearance in detail."}, {"text": "This is not the case with Denisovans, however - evidence of their existence is based only on a fragment of bone from a child's finger and two teeth that were discovered in 2010 in the Altai Mountains of Siberia."}, {"text": "'We know quite well what Neanderthals look like."}, {"text": "They were quite more robust than modern humans ."}, {"text": "more muscular and probably more adapted to living in a harsh northerly climate,' Paabo said."}, {"text": "'What's fascinating about the Denisovans is we know next to nothing about how they looked."}, {"text": "We have their genome and we have two teeth, and those teeth are huge."}, {"text": "The only thing we can say is they must have been very big, or at least have big mouths'."}, {"text": "Confusion aside, the sequencing feat has been hailed by scientists as an incredible leap forward - albeit into the past."}, {"text": "'This is positively exciting,' said Andrea Manica, an evolutionary biologist at the University of Cambridge in England."}, {"text": "'This really pushes back the time horizon of human evolution that we can explore with genetics'."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0517.json b/inquisitive/sources/test/0517.json new file mode 100644 index 0000000000000000000000000000000000000000..b610665c87366815af7d3a3ee569472169aea106 --- /dev/null +++ b/inquisitive/sources/test/0517.json @@ -0,0 +1 @@ +[{"text": "PHILADELPHIA - The University of Pennsylvania is at the forefront of a movement to experiment with free open online courses, but the undertaking, as its own researchers are finding out, has yielded mixed results."}, {"text": "While Massive Open Online Courses (MOOCs) have attracted millions of viewers and been heralded as a potential way to address skyrocketing tuition, very few of their viewers - 4 percent on average - actually complete the courses, according to the latest study by researchers in Penn's Graduate School of Education."}, {"text": "Many who register drop off after the first week or two, the researchers found in a study they will present Thursday at a MOOC conference at the University of Texas, Arlington."}, {"text": "About half who registered viewed at least one lecture."}, {"text": "The results come on the heels of another Penn study, released last month, that showed a vast majority of students enrolled in MOOCs already hold college degrees and are taking the courses primarily to advance in their jobs, which called into question the notion that the courses were providing greater access to the world's underprivileged."}, {"text": "'The technology offers some promise of a new approach to addressing both' costs and access, said Laura Perna, a lead researcher on the new study."}, {"text": "'We just don't know to what extent this is going to be more than a promise'."}, {"text": "The researchers looked at 1 million users who registered for the 16 free courses offered from June 2012 to June 2013, among them 'Calculus: Single Variable,' 'Greek and Roman Mythology,' and 'Fundamentals of Pharmacology'."}, {"text": "The classes were taught by Penn professors and offered in partnership with Coursera, a California-based online education company and a pioneer in MOOCs."}, {"text": "The study, conducted by the newly created Alliance for Higher Education and Democracy at Penn, delved into when users enter and leave courses and when and how they participate."}, {"text": "The courses varied in use of quizzes and homework and instruction time."}, {"text": "Completion rates were slightly higher in courses with smaller workloads."}, {"text": "Most courses focused on personal enrichment or occupational skills, such as 'Cardiac Arrest, Resuscitation Science, and Hypothermia'."}, {"text": "Perna said she was a bit surprised by the results."}, {"text": "'Four percent is low. I didn't expect it to be quite this low,' she said."}, {"text": "But Ed Rock, who heads Penn's MOOC initiative, called the findings 'entirely unsurprising and not at all troubling."}, {"text": "Four or five percent of 1.6 million (current users) is still 80,000 people, and 80,000 people is a huge number to educate'."}, {"text": "Rock, senior adviser to the president and provost and director of open course initiatives, also said those who do not complete have gotten something from the experience."}, {"text": "The majority of MOOC users are doing it for leisure learning or job development, so it's not surprising that few finish, said Cathy Sandeen, vice president for education attainment and innovation at the American Council on Education."}, {"text": "'There is a place for MOOCs in terms of degree attainment, but it's probably a smaller component overall than we might have originally thought,' she said."}, {"text": "Rock acknowledged that educators have a way to go in learning how best to fit MOOCs into the educational mission."}, {"text": "Penn has partnered with 10 high schools locally and nationally whose teachers are using Penn's calculus course to supplement classroom learning."}, {"text": "'Our hope is our material will be of value."}, {"text": "We won't know that unless (high school teachers) try it out and tell us,' he said."}, {"text": "'We believe these materials have the potential to revolutionize education, but they're only going to work in a partnership'."}, {"text": "Perna, whose team includes researchers Alan Ruby, Robert Boruch, Nicole Wang, Janie Scull, Chad Evans and Seher Ahmad, agreed that MOOCs could benefit society."}, {"text": "She cited the case of a neighbor who is taking a management MOOC with co-workers, who meet each week to discuss what they've learned."}, {"text": "'I think there is something there,' she said, 'but we need to understand better what that contribution is."}, {"text": "Penn is clearly committed to exploring these issues'."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0518.json b/inquisitive/sources/test/0518.json new file mode 100644 index 0000000000000000000000000000000000000000..e1dfd2a48658f0363c1e181e1260147df4d307c0 --- /dev/null +++ b/inquisitive/sources/test/0518.json @@ -0,0 +1 @@ +[{"text": "For college athletes who get through their sport's season concussion-free, new research suggests it may be too early to breathe a sigh of relief."}, {"text": "Following a season of grueling practices and hard-fought games, football and ice hockey players who had no outward sign of head trauma showed worrisome changes in brain structure and cognitive performance that weren't shared by athletes who competed in varsity sports such as track, crew and cross-country skiing, according to a report published Wednesday in the journal Neurology."}, {"text": "The findings add to a growing body of evidence suggesting that a season-long succession of small hits - none hard enough to cause evident disorientation or draw medical attention - may prompt changes in the brain that cause problems with memory, mood or mental performance years down the road."}, {"text": "Or, they may heal during the off-season."}, {"text": "Scientists are still trying to figure out how readily the brain recovers from injury, or whether there are thresholds beyond which damage can be cumulative or irreversible."}, {"text": "The new results don't resolve the matter, but they do suggest that repetitive blows to the head are not without consequence, even when an athlete is able to get up and keep playing, said study leader Thomas McAllister, a psychiatrist at Indiana University."}, {"text": "'The management and detection of concussion is obviously important,' McAllister said."}, {"text": "'But may not be sufficient'. The study centered on 159 students at Dartmouth College in Hanover, N.H. - where McAllister worked until last year - who played on varsity teams between 2007 and 2011."}, {"text": "Except for football, all of the sports were played by both men and women."}, {"text": "The 80 athletes who played contact sports wore accelerometers in their helmets that measured the number and force of blows to the head during all practices and games."}, {"text": "In addition, all of the study participants got MRI brain scans and took wide-ranging mental performance tests before and after their seasons."}, {"text": "Looking only at athletes who were not diagnosed with a concussion during the season they were tracked, the researchers drew important connections between blows to the head and changes in brain structure as well as the students' cognitive performance weeks after their sport ended."}, {"text": "MRI scans that measured the density and integrity of the brain's white matter - the bundles of fatty tissue that speed electrical signals among neurons - showed that after a single season, football and hockey players experienced changes that were greater than anything seen in the brains of the athletes who played noncontact sports."}, {"text": "In addition, players who had the biggest changes in white matter had the worst performance on postseason tests of verbal learning and memory."}, {"text": "McAllister said the good news was that despite years of playing their sports - and presumably suffering repeated blows to the head - the white matter of contact-sport athletes at the start of their seasons was largely indistinguishable from that of athletes in noncontact sports."}, {"text": "That suggests the brains of college athletes may largely bounce back from a season's wear and tear."}, {"text": "But it will take far more research to discern whether there are certain athletes who don't heal as well, or for whom small changes in the brain structure can have outsized, and possibly delayed, effects."}, {"text": "'We know some of them heal. But some of them don't,' said Eric Nauman, a Purdue University biomechanical engineer who has spent five years tracking the effects of small and large hits meted out on high school gridirons."}, {"text": "The resolution with which MRIs can detect white matter changes is limited, so the fact that differences were seen in the Dartmouth athletes is remarkable, Nauman said."}, {"text": "'If you're seeing structural changes at the level the MRI can pick up, that is very worrisome,' said Nauman, who was not involved in the study."}, {"text": "'We're desperately trying to figure out what the long-term implications are'."}, {"text": "McAllister said his initial goal was to find a threshold for hits that were safe and hits that caused concussions."}, {"text": "But years of study have made him suspect that if such a threshold exists, it may tell only part of the story."}, {"text": "Well before they result in concussion, blows to the head change the brain's structure and the way it works, at least temporarily, he said."}, {"text": "And there's growing evidence that a succession of those smaller hits puts players at higher risk for the one that finally trips a concussion diagnosis, McAllister said."}, {"text": "'You quickly see that the emphasis on \u2018the' hit is misplaced,' he said."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0522.json b/inquisitive/sources/test/0522.json new file mode 100644 index 0000000000000000000000000000000000000000..20cd1a68d88d07b74561857eb232fe5e62d9eaca --- /dev/null +++ b/inquisitive/sources/test/0522.json @@ -0,0 +1 @@ +[{"text": "FORT LAUDERDALE, Fla. - A hurricane hunter aircraft sent to the Arctic to study ice formations returned this month with critical data that might explain why an increasing number of tropical storms seem to be taking irregular paths."}, {"text": "Scientists are trying to determine how much heat is released into the atmosphere when Arctic ice builds up in autumn."}, {"text": "That heat release is believed to shift the jet stream \u2013 a fast-moving, high altitude river of air \u2013 farther to the south."}, {"text": "That shift, in turn, might be slowing down or even stalling tropical systems, before they can re-curve east and out to sea, scientists say."}, {"text": "Kevin Wood, a University of Washington research scientist aboard the plane, said the Arctic heat release also might trigger other extreme weather events, such as flooding or severe snowstorms."}, {"text": "'That's far from proven,' he said. 'But it's one of things we're interested in understanding better'."}, {"text": "Primarily, however, scientists hope the battery of sensors onboard the National Oceanic and Atmospheric Administration WP-3 Orion might help them understand why Superstorm Sandy plowed into the East Coast last year and why eight systems aimed at Canada or the Northeast in the past three years."}, {"text": "'The very unusual path that Sandy took last year was definitely due to disruptions in the global circulation, and maybe that was related to changes in the Arctic,' said Nick Bond, a University of Washington scientist who rode on the plane during its inaugural Arctic mission."}, {"text": "In October 2012, Sandy emerged in the Caribbean as a tropical storm, grew into a hurricane and initially began to curve northeast on a path that would have taken it toward the North Atlantic."}, {"text": "Instead, Sandy curved northwest toward the New Jersey coastline, collided with a winter system and swamped much of the Mid-Atlantic and Northeast with a powerful storm surge, even though it had been downgraded to a post-tropical system just before landfall."}, {"text": "Some other hurricanes that have aimed north instead of heading east in recent years: Earl hit Nova Scotia and Igor brushed Newfoundland, both in September 2010; Irene hit the Northeast as a tropical storm in August 2011; and Ophelia hit Newfoundland as a tropical storm in October 2011."}, {"text": "The hurricane hunter, normally based at MacDill Air Force Base in Tampa, Fla., conducted eight research flights over Arctic regions between Oct. 21 and Nov. 6."}, {"text": "Flying out of Fairbanks, Alaska, it studied ice formations in the Chukchi and Beaufort seas, at times flying well north of the Arctic Circle."}, {"text": "'While we couldn't have spit on the North Pole, it wasn't that far away,' Bond said."}, {"text": "In addition to bolstering understanding of hurricane paths, the heat release study provided insight into how fast the volume of polar ice is diminishing, a primary reason for sea level rise, a critical issue in low-lying Florida."}, {"text": "Bond said the faster the ice builds up, the more heat is released into the atmosphere."}, {"text": "'We could see and feel the tremendous amount of heat coming out of the ocean,' he said."}, {"text": "'That's what it takes to make ice, to lose heat like crazy'."}, {"text": "Equipped with more sensors than a fleet of satellites, the NOAA aircraft collected a wide range of data from sea ice thickness to solar heating."}, {"text": "Much as they do when investigating tropical storms, scientists dropped probes out of the plane to better understand the atmosphere."}, {"text": "The devices measure temperature, wind direction and barometric pressure."}, {"text": "Scientists praised the WP-3 Orion's versatility."}, {"text": "'You can liken it to a weather station on steroids; you can take it anywhere,' Bond said."}, {"text": "'It allows unique measurements that you can't get any other way'."}, {"text": "One reason the plane made the Arctic trip was because the hurricane season in the Atlantic has been remarkably slow."}, {"text": "The scientists hope next year's season will be as calm so they can hop another flight over the Arctic."}, {"text": "'We know we obtained data that was unique and important,' Bond said."}, {"text": "'We're greedy, and we want more'."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0524.json b/inquisitive/sources/test/0524.json new file mode 100644 index 0000000000000000000000000000000000000000..b58035ac92b7c993278f4c14211828ed4dcc8e6f --- /dev/null +++ b/inquisitive/sources/test/0524.json @@ -0,0 +1 @@ +[{"text": "WASHINGTON - To lawmakers and others arguing that replacing the $1 bill with a $1 coin would save the government money, the Federal Reserve says, 'Don't bet on it'."}, {"text": "A new analysis by Fed staffers said the old-fashioned greenback is more durable than people realize and replacing it with a $1 coin, which is more expensive to produce, would cost the government $1.2 billion over 30 years."}, {"text": "'Based on our analysis of the benefits and costs of a currency-to-coin transition, we believe that the $1 Federal Reserve note should remain in circulation and not be replaced with a $1 coin,' concluded the authors of a Fed staff working paper released this week."}, {"text": "Some in Congress are pushing the government to replace the $1 dollar bill with the longer-lasting $1 coin."}, {"text": "Several countries, including Canada and Britain, and the eurozone have replaced small-denomination paper currency with coins."}, {"text": "Last year, the Government Accountability Office estimated a switch could save the federal government $4.4 billion over 30 years."}, {"text": "The Dollar Coin Alliance, a lobbying organization that includes government watchdogs, transit agencies, and mining and vending industry groups, touts an economic report that estimated a switch would save $13.8 billion over 30 years."}, {"text": "The organization criticized the Fed analysis, saying the central bank has a vested interest in keeping the $1 bill because it profits from the sale of paper currency."}, {"text": "'It's no surprise the Fed is fighting currency modernization, when you understand their motives behind this report,' said Shawn Smeallie, executive director of the Dollar Coin Alliance."}, {"text": "'The best interests of taxpayers, not the Fed, must come first'."}, {"text": "The Fed issues currency through its reserve banks and orders it from the Treasury's Bureau of Engraving and Printing."}, {"text": "The Fed said it is not a profit-making institution and annually turns over any profits to the Treasury Department."}, {"text": "The Fed study said estimates of costs savings for a $1 coin are way off the mark."}, {"text": "The $1 bill, made with paper that blends cotton and linen, now is more durable and lasts about 70 months compared with 18 months in 1990, the report said."}, {"text": "Small-denomination bills eliminated in other countries lasted less than 20 months."}, {"text": "Although a $1 coin has a useful life of 30 years, it also costs much more to produce."}, {"text": "A $1 bill costs about 5 cents to make while a $1 coin costs about 33 cents, the Fed said."}, {"text": "Over 30 years, the government would spend an additional $6.9 billion if it replaced $1 bills with coins."}, {"text": "At that cost, the government would make money on the switch only if $1 bills lasted less than 4.75 years."}, {"text": "With a current shelf life of 70 months, or about 5.8 years, the $1 bill is more efficient, the Fed said."}, {"text": "In addition, the shift to a $1 coin would result in additional costs to banks for extra vault storage space and equipment that would be 'perhaps in the hundreds of millions of dollars per year,' the Fed said."}, {"text": "Finally, the Fed said the public has shown no great love for $1 coins so far."}, {"text": "The latest incarnation - coins with images of American presidents - was promoted by the Fed and the U.S. Mint, but the effort 'failed to stimulate demand,' the report said."}, {"text": "As of June 30, there were 1.4 billion $1 coins sitting in Fed vaults, approximately a 40-year supply."}, {"text": "The report said polls have shown that a majority of Americans prefer the $1 bill to the $1 coin and making the switch could lead more people to shun cash for credit cards and other alternative payment methods."}, {"text": "But the Dollar Coin Alliance said polls have shown about two-thirds of Americans support a switch to a $1 coin when told of potential budget savings."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0528.json b/inquisitive/sources/test/0528.json new file mode 100644 index 0000000000000000000000000000000000000000..800ddef4bf337838d6f70ccba221a3898a35e9d0 --- /dev/null +++ b/inquisitive/sources/test/0528.json @@ -0,0 +1 @@ +[{"text": "Young women seem tantalizingly close to achieving gender equality in the workplace, at least when it comes to wages, a new report from the Pew Research Center suggests."}, {"text": "But it remains to be seen whether motherhood will slow their strides, as it did for women before them."}, {"text": "As of last year, women workers ages 25 to 34 were making 93 percent of what men of the same ages earned - much closer to wage equality than earlier generations, Pew found."}, {"text": "Between 1980 and 2012, the gap has gradually narrowed for American workers, as wages rose for women and dropped for young men."}, {"text": "Only 15 percent of young women said they had suffered discrimination because of their gender at work."}, {"text": "And unlike generations of women before them, female millennials - young women ages 18 to 32 - are statistically as likely as men to have asked their bosses for a promotion or a raise, Pew found."}, {"text": "Yet most young women - 75 percent - believe that more change is needed before men and women are equal at work, the Pew survey showed."}, {"text": "Almost 3 out of 5 say that it is easier for men to get top jobs in business and government."}, {"text": "Nearly two-thirds fear that having children will hold them back in the workplace."}, {"text": "As a graphic designer, 'I don't think I've been held back because of my gender,' said Alexandria Manson, 25, of Monrovia, Calif."}, {"text": "But in all kinds of fields, 'I can definitely see there are way more executive men than there are women - and not because of their ability'."}, {"text": "Millennials have reason to worry: Earlier generations of young women seemed to be narrowing the gender gap in wages, only to slip as they aged and many started juggling motherhood with jobs."}, {"text": "In 1995, for instance, women hitting their late 20s and early 30s earned 85 percent as much as their male counterparts, a Pew analysis of U.S. Census Bureau data shows."}, {"text": "By 2012, those same women, now in their 40s and 50s, were only making 76 percent as much as men of their same age."}, {"text": "'The question mark is, what will happen to millennials 10 or 15 years into their career?' said Kim Parker, Pew's director of social trends research."}, {"text": "'Will they slide behind?' Among Americans of all ages, mothers were almost three times as likely as fathers to have quit their jobs at some point to care for a child or other family member, the Pew survey of more than 2,000 people found."}, {"text": "Mothers were also more likely to reduce their hours or take time off for family."}, {"text": "'Nowadays, a childless woman may be able to work every bit as much as her male counterpart,' University of Illinois at Chicago sociology professor Barbara Risman said."}, {"text": "'What's holding people back is when they become parents - either mothers or egalitarian fathers, who take equal or primary responsibility for raising children'."}, {"text": "Among working parents with children younger than 18, mothers were roughly three times as likely as fathers - 51 percent vs. 16 percent - to say parenthood had hampered their careers."}, {"text": "Even among millennial parents, mothers were much more likely than fathers to say that working parents have trouble advancing."}, {"text": "When Kylie Anderson worked a string of internships and jobs in the entertainment business, dreaming of being a screenwriter, she noticed other women struggling to balance work and children."}, {"text": "None seemed to breeze through it, said Anderson, a UCLA graduate now working at a nonprofit."}, {"text": "When it comes to her own career, the 22-year-old concluded, 'having a child would be game over, at least for a while'."}, {"text": "Even among millennials, women are still less likely than men to aspire to becoming the boss."}, {"text": "Pew found that gap persists despite the fact that most millennials believe women of their age are as focused on their careers - or more so - as men."}, {"text": "'I get frustrated with my friends because they don't aspire,' said Jordan Boldt, a 30-year-old mother who decided to stay home with her daughters."}, {"text": "'It's like we grow up thinking that we can't go far'."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0530.json b/inquisitive/sources/test/0530.json new file mode 100644 index 0000000000000000000000000000000000000000..978f8b939ffa1b459904e143357fc903646a0a19 --- /dev/null +++ b/inquisitive/sources/test/0530.json @@ -0,0 +1 @@ +[{"text": "Jellyfish may not look like the most athletic of swimmers, but they're remarkably efficient and their body plan could have advantages that translate to the air."}, {"text": "A team from New York University has designed a flying jellyfish-like robot that uses four flapping wings to stay aloft."}, {"text": "The unconventional robot, described at the American Physical Society's Division of Fluid Dynamics meeting in Pittsburgh, could lead the way for flying mini-robots to be used in search-and-rescue and military operations and even as environmental sensors."}, {"text": "Engineers are trying to build all sorts of robots based on the wing motions of such animals as birds, bats, hummingbirds and butterflies."}, {"text": "Those working on the smallest robots tend to use more insect-like designs, given that the bugs have already mastered flight mechanisms on a tiny scale."}, {"text": "But the vast majority of flying insects rely on the same mechanism, with the same weaknesses: wings that sweep back and forth in a sort of S-shape."}, {"text": "(Only a few creatures, including dragonflies, move their wings in the relatively simple up-down motion that many people expect.)"}, {"text": "Such designs are 'a great place to start in terms of building a flying machine,' said lead author Leif Ristroph, an applied mathematician at New York University."}, {"text": "'But there are some technical problems with it'."}, {"text": "Bugs with flapping wings have to spend a lot of time dealing with a violent environment, sensing every gust of wind and then adjusting accordingly."}, {"text": "It takes a lot of work, and it's inherently unstable."}, {"text": "The researchers wanted to build something that can be built small, but simply, and still remain stable in the air without too much thinking."}, {"text": "'I wanted to think of something very different,' Ristroph said."}, {"text": "'So I actually tried about five or 10 different schemes, all of which failed except this one'."}, {"text": "The jellyfish, in some ways, appears ideal for this task: It's a very simple creature, lacking a brain or bones (and the complex joints that come with them)."}, {"text": "And the design works on large and small scales: The Lion's Mane jellyfish can exceed 7 feet in diameter and the Irukandji jellyfish can be just a few millimeters wide."}, {"text": "The scientists' flapping-wing robot spans 8 centimeters and weighs just 2 grams."}, {"text": "With four petal-like wings that flap up and down, it may move more like a moth than a jellyfish, given that jellies squeeze water out of smooth, unbroken bells."}, {"text": "And while this robotic flying jelly still has to be attached to a power source and can't yet be steered, this prototype shows that such a design can indeed work, perhaps for more sophisticated flying machines and on much smaller scales."}, {"text": "The design could be useful for the military, Ristroph said, though he was more excited about civilian applications."}, {"text": "Theoretically, he said, mini flying jellies could be tossed into the air from a building and float around as environmental sensors, taking data and adjusting their position when necessary."}, {"text": "'It's an excellent example of bio-inspired engineering,' said Caltech professor John Dabiri, who studies the jellyfish's swimming secrets and attended the talk at the Pittsburgh meeting."}, {"text": "'The final product doesn't copy the jellyfish body design, but it does achieve a similarly stable motion,' Dabiri said."}, {"text": "'Although it doesn't look like the jellyfish that inspired it, I'm sure they would be proud'."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0532.json b/inquisitive/sources/test/0532.json new file mode 100644 index 0000000000000000000000000000000000000000..1d2093cff7cd58fcd137c33600721995b371f075 --- /dev/null +++ b/inquisitive/sources/test/0532.json @@ -0,0 +1 @@ +[{"text": "LOS ANGELES - Little-known fact: When it comes to extracting oxygen from the air we breathe, we humans are just OK."}, {"text": "Birds are more efficient breathers than we are."}, {"text": "So are alligators and, according to a new study, monitor lizards, and probably most dinosaurs were as well."}, {"text": "Humans are what are called tidal breathers."}, {"text": "When we breathe in, fresh air moves into our lungs along progressively smaller airways, eventually ending in little sacs called alveoli, where our bloodstream picks up oxygen and deposits carbon dioxide."}, {"text": "Then the 'old' air moves out of our lungs along the same path it came in."}, {"text": "But birds, alligators and monitor lizards are 'unidirectional' breathers."}, {"text": "After the air moves into their lungs, it begins to follow a system of tubes similar to arteries, capillaries and veins."}, {"text": "In this system, the air moves through the air tubes in only one direction."}, {"text": "And, it turns out, their system is more efficient at extracting oxygen from the air than ours is."}, {"text": "Scientists discovered that birds are unidirectional breathers in the first half of the 20th century, after researchers noticed that pigeons breathing the sooty air of train stations showed just one black area on the lung."}, {"text": "If the pigeons breathed like we do, scientists would have expected the entire lung to be black."}, {"text": "'The fact that only one part of the bird lung was dark suggested the air was flowing in one direction and that the first part of the lung to receive the contaminated air was filtering the particles,' said Colleen Farmer, an associate professor of biology at the University of Utah."}, {"text": "It isn't that surprising that birds have developed a more efficient breathing system."}, {"text": "Scientists hypothesize it may have evolved to help them support their high metabolic rates, or to help them survive when they fly at high altitudes, where oxygen is scarce."}, {"text": "But in 2010, Farmer published a study showing that alligators are unidirectional breathers as well."}, {"text": "'That's when I realized it had to have a function other than supporting the high metabolic rates associated with birds,' she said."}, {"text": "'I knew cold-blooded animals spend about 80 percent of their lives holding their breaths - and so I formulated the hypothesis that this breathing would be important for mixing gases in the lungs during a breath-hold'."}, {"text": "On Wednesday, Farmer published a study in the journal Nature that shows monitor lizards are unidirectional breathers as well."}, {"text": "She believes that further studies will show that all lizards and snakes are also unidirectional breathers."}, {"text": "'(Unidirectional breathing) appears to be much more common and ancient than anyone thought,' she said in a statement."}, {"text": "The scientists are still not sure exactly when unidirectional breathing first developed, but if it all evolved from one ancestor rather than concurrently, it is possible there have been unidirectional breathers walking the planet for 270 million years - 100 million years before the first birds and 20 million years earlier than anyone thought."}, {"text": "And although it is impossible to directly study whether extinct animals like dinosaurs were unidirectional breathers, Farmer said that since alligators, birds and probably most lizards breathe this way, it's likely the system was inherited from an ancestor the dinosaurs shared as well."}, {"text": "Farmer said the next step in her research is to determine just how common unidirectional breathing is or was."}, {"text": "'We want to look at a bunch of lizards and snakes and turtles and amphibians,' she said."}, {"text": "'We have a lot of work ahead of us'."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0536.json b/inquisitive/sources/test/0536.json new file mode 100644 index 0000000000000000000000000000000000000000..d7aed7743cd8295179d64d8843b92d03b703050e --- /dev/null +++ b/inquisitive/sources/test/0536.json @@ -0,0 +1 @@ +[{"text": "PYONGYANG, North Korea - Dennis Rodman said Monday that a game he and other former National Basketball Association players are planning in North Korea will be a 'birthday present' for one of their most unlikely fans: leader Kim Jong Un."}, {"text": "Rodman's squad - featuring ex-All Stars Kenny Anderson, Cliff Robinson and Vin Baker - will play against a team of North Koreans on Wednesday, which is believed to be Kim's birthday."}, {"text": "The former NBA players, who arrived in Pyongyang on Monday, also include Eric 'Sleepy' Floyd, guard Doug Christie and Charles D. Smith, who played for the New York Knicks."}, {"text": "Four streetballers are also on the squad."}, {"text": "Rodman told The Associated Press he was glad to be in North Korea for the game, though he said he has gotten death threats for his repeated visits."}, {"text": "He said proceeds from the game would go to a charity for the deaf in North Korea."}, {"text": "'The marshal is actually trying to change this country in a great way,' Rodman said of Kim, using the leader's official title."}, {"text": "'I think that people thought that this was a joke, and Dennis Rodman is just doing this because fame and fortune'."}, {"text": "Instead, he said, he sees the game as a 'birthday present' for Kim and his country."}, {"text": "'Just to even have us here, it's an awesome feeling."}, {"text": "I want these guys here to show the world, and speak about North Korea in a great light,' he said."}, {"text": "'I hope people will have a different view about North Korea'."}, {"text": "The game will be another milestone in Rodman's surprising relationship with Kim, who rarely meets with foreigners and about whom very little is known outside of North Korea."}, {"text": "Rodman is the highest-profile American to meet Kim since the leader inherited power after his father, Kim Jong Il, died in late 2011."}, {"text": "Rodman traveled to North Korea for the first time last February with the Harlem Globetrotters for an HBO series."}, {"text": "After spending time together, Rodman called Kim a 'friend for life' and came back just before Christmas to hold tryouts for the North Korean basketball team, though he did not meet with Kim then."}, {"text": "Rodman has been given the red-carpet treatment on each of his trips, but visiting North Korea for any high-profile American is a political minefield."}, {"text": "To keep the game itself friendly, the two sides will only play against each other in the first half, and then mix together in the second."}, {"text": "Americans are regarded as enemies in North Korea since the two countries never signed a peace treaty to formally end the 1950-53 Korean War."}, {"text": "Thousands of U.S. troops are still based in South Korea, and the Demilitarized Zone between the North and South is one of the most heavily fortified borders in the world."}, {"text": "Relations are also tense because of the North's development of nuclear weapons and its threats to use them if a conflict breaks out with Washington or Seoul."}, {"text": "Rodman has also been slammed for not trying to use his influence with Kim to secure the release of Kenneth Bae, an American missionary with health problems who is being held in North Korea on charges of committing 'anti-state' crimes."}, {"text": "To make the trip more complicated, Kim's once-powerful uncle was recently executed for a long litany of alleged crimes, including trying to divide the regime and usurp power from Kim."}, {"text": "Although that has generated speculation abroad about the regime's unity, North Korean officials say the execution settled the issue and there is no instability."}, {"text": "Rodman, however, says none of that is his concern."}, {"text": "'I'm not a president, I'm not a politician, I'm not an ambassador,' he said before arriving."}, {"text": "'I'm just an athlete and the reason for me to go is to bring peace to the world, that's it."}, {"text": "That's all I want, no money. I want no money, no money'."}, {"text": "Former Knicks player Smith said he hopes the game will lead to better relations between the two countries."}, {"text": "'It's new being here, but overall the concept is not new,' he said."}, {"text": "'The team is made up of a lot of guys who really care, that's the most important, it's not about bringing dream-teamers."}, {"text": "It's about guys who are coming that want to be a part of this, that care, and really that care about humanity'."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0537.json b/inquisitive/sources/test/0537.json new file mode 100644 index 0000000000000000000000000000000000000000..354b73caa42885d17ee68b1076a2b4654a1fddbb --- /dev/null +++ b/inquisitive/sources/test/0537.json @@ -0,0 +1 @@ +[{"text": "MILWAUKEE - The electric barrier on the Chicago Sanitary and Ship Canal that is considered the last line of defense to stop an Asian carp invasion of Lake Michigan has a problem: Fish can swim through it."}, {"text": "A report by the U.S. Army Corps of Engineers and U.S."}, {"text": "Fish and Wildlife Service revealed that fish can be transported across the electrified swath of canal when they get trapped in the wake of a barge."}, {"text": "Research also shows that the metal barges can essentially suck electricity out of the water as they motor through the barrier zone, creating a moving 'bubble' of water that isn't pulsing with the intended electrical current."}, {"text": "The study also revealed that small fish are not always incapacitated by the electrical current in the water."}, {"text": "In fact, a sonar camera lowered into the canal at the barrier site regularly captured schools of fish swimming freely through the barrier."}, {"text": "States the report: 'Initial findings indicate that vessel-induced residual flows can trap fish and transport them beyond the electrical barriers, and that certain barge configurations may impact barrier electric field strength."}, {"text": "Additionally, the preliminary (sonar camera) findings identified the potential for small fish (between 2-4 inches in length) to pass the barrier array in large groups, or schools'."}, {"text": "Concerned that the barrier was too weak to repel juvenile fish, in 2011 the Army Corps increased its voltage."}, {"text": "The agency has since been operating under the assumption that the higher voltage is strong enough to repel all sizes of fish."}, {"text": "The camera told a different story. Crews dropped it in the water on 72 different occasions to capture 10 minutes of video each time."}, {"text": "Of those 72 samples, entire schools of fish, not believed to be Asian carp, were recorded swimming through the barrier 61 percent of the time."}, {"text": "Federal officials stress they do not believe Asian carp are yet probing the barrier."}, {"text": "'There is no evidence that Asian carp are bypassing the barriers."}, {"text": "Nor is there any indication that Asian carp are in the vicinity of the barriers,' states the report."}, {"text": "'The closest adult Asian carp found in the Illinois River are about 55 miles from Lake Michigan, and no small Asian carp have been observed closer than 131 miles from Lake Michigan'."}, {"text": "Yet water samples taken at the barrier site and in stretches of canal on the Lake Michigan side of the barrier have regularly tested positive for Asian carp DNA during the past four years, and a poisoning of the canal in the area around the barrier in late 2009 yielded the carcass of a single Asian carp."}, {"text": "The new study may prompt changes in the way barges are configured and how the barrier operates."}, {"text": "Safety is a big concern; some barges traveling through the electrified section of canal, about 30 miles downstream from Lake Michigan in suburban Chicago, carry flammable materials, and the threat of sparks flying between barges is real."}, {"text": "'The news is still fairly preliminary,' Felicia Y. Kirkseyv, aquatic invasive species program manager for the Army Corps in Chicago, said of the study."}, {"text": "'We're going to do more analysis and work with the barge community and the Coast Guard to see how we can move forward'."}, {"text": "The news comes just before the Jan. 6 release of the Army Corps' $25 million study examining how to re-establish the natural divide between the Great Lakes and Mississippi River basin that the Chicago canal destroyed when it opened over 100 years ago."}, {"text": "The study is expected to have a range of options, but Great Lakes advocates want the canal physically plugged to stop Asian carp and other unwanted species from swimming freely between the Great Lakes and Mississippi basin."}, {"text": "Such a project would require significant upgrades in Chicago's sewage treatment and storm-water management."}, {"text": "Josh Mogerman, a spokesman for the Natural Resources Defense Council, said news of the electrical barrier problems is further evidence that the federal government has to find a more permanent solution to the Asian carp problem."}, {"text": "'The electric barrier already had a spotty track record, but this report seems to burst any remaining implication it can be considered a solution to the carp invasion,' he said."}, {"text": "'It reinforces the broadly held belief that a permanent, physical barrier separating the watersheds is the only way to stop the dozens of dangerous critters queued up on both sides'."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0539.json b/inquisitive/sources/test/0539.json new file mode 100644 index 0000000000000000000000000000000000000000..8c5ff2b37a415578a82268c154f4a3a077a95b4b --- /dev/null +++ b/inquisitive/sources/test/0539.json @@ -0,0 +1 @@ +[{"text": "LIVERMORE, Calif. - Your head aches, you're congested and simply getting out of bed is a chore."}, {"text": "You pay a visit to your doctor, and within minutes - using a simple cheek swab placed in a tiny box - he knows precisely which virus or bacteria is causing the symptoms and prescribes the right treatment."}, {"text": "While this scene would be right at home in the 'Star Trek' sick bay, it may become a staple in real-world clinics within the decade, according to Lawrence Livermore Laboratory chemical engineer Elizabeth Wheeler."}, {"text": "Wheeler's team of engineers, biologists and chemists, headed by principal investigator Reginald Beer, is developing a method to recognize disease-causing pathogens quicker than ever before."}, {"text": "The key: obtaining the bacteria or virus DNA and rapidly copying it so there's enough to identify what's causing your illness."}, {"text": "'It's basically like you're Xeroxing it,' Wheeler said."}, {"text": "'Once you've got enough of it, you can detect it'."}, {"text": "The technique - polymerase chain reaction (PCR) - isn't a recent phenomenon."}, {"text": "Discovered in 1983 by Nobel Prize winner and University of California, Berkeley, alum Kary Mullis, it's been used for identifying human remains, food safety, and bacterial detection."}, {"text": "Just as you learned in science class, DNA has two strands."}, {"text": "Using PCR, a special enzyme is added and the DNA is heated up to 94 degrees Celsius (202 degrees Fahrenheit)."}, {"text": "The strands break apart and the enzyme 'fills in' the opposite strand."}, {"text": "By alternately heating and cooling the sample in a device the size of two toasters stacked on top of each other, the technique doubles the amount of genetic material with each cycle."}, {"text": "It takes about three minutes to run the 30 cycles needed to amplify the DNA to a size where it can be identified."}, {"text": "Wheeler, whose husband is a San Ramon physician, said the project's goal is to have Fast PCR devices in every clinician's office, allowing patients to submit a sample and have it processed while the doctor goes through his checkup routine."}, {"text": "Before the exam is over - in about the time it takes to cook a bag of microwave popcorn - the physician could make a decision on appropriate treatment."}, {"text": "'Everyone's been frustrated when you go in and it's like, \u2018is it a virus or a bacteria?' ' Wheeler said."}, {"text": "'You could run this and they can say, \u2018Yep, you have a bacterial infection, here's the antibiotic,' or \u2018it's a virus, go home and rest.' ' Dr. Stephen Bustin, a British scientist and former professor of molecular sciences, literally wrote the book on the PCR technique."}, {"text": "While reactions once took hours, Bustin said via email, they're now routinely done in tens of minutes."}, {"text": "The amplification now takes only three minutes but other preparations make the whole process longer."}, {"text": "Within a year or two, he adds, getting results in less than 10 minutes will become commonplace."}, {"text": "'This opens up all kinds of diagnostic possibilities,' Bustin wrote, including 'carrying out PCR evaluations of a patient's sample whilst talking to the doctor'."}, {"text": "Working on Fast PCR since 2010, Beer's team was responsible for speeding up the amplification part to less than three minutes."}, {"text": "In that technique, cold water is passed over a porous copper platform holding the microscopic samples, rapidly dropping the temperature to 55 degrees Celsius (131 degrees Fahrenheit)."}, {"text": "The platform is heated back up, the cycle repeats 30 times, and the results are matched to a known genetic signature."}, {"text": "As speedy as the procedure is now, Wheeler thinks the team can go even faster."}, {"text": "The Livermore researchers' next step is integrating optics into the device to detect the DNA even earlier, and finding more practical options to time-consuming sample preparation."}, {"text": "Wheeler said the pieces are already in place to allow the entire process to be done in less than 10 minutes."}, {"text": "Dr. John Leamon, head of biological research and development at CyVek, an American biotech company focused on health care, said rapid PCR could be a valuable tool in other areas where time plays a key factor."}, {"text": "It could be used to detect pathogenic agents during military conflicts, he said, or to monitor food supplies and crops."}, {"text": "Scientists could take a food sample, test it for harmful bacteria within minutes, and remove the tainted supply before it even ships."}, {"text": "Lab officials believe it could be useful during outbreaks of diseases like SARS."}, {"text": "Scientists would be able to test passengers entering the country within minutes, rather than quarantining them for days."}, {"text": "Lab spokesman Steve Wampler said two unnamed companies have already expressed interest in licensing the technology, adding that a consumer version of the device would take at least five to seven years to bring to market."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0541.json b/inquisitive/sources/test/0541.json new file mode 100644 index 0000000000000000000000000000000000000000..31a8798a4cf24eb055dc844f02514f0cb42e6f5c --- /dev/null +++ b/inquisitive/sources/test/0541.json @@ -0,0 +1 @@ +[{"text": "Ongoing excavation of a collapsed rock shelter that was used by Neanderthals suggests that our extinct human relatives organized their living spaces according to tasks, researchers say."}, {"text": "In a paper published recently in the Canadian Journal of Archaeology, researchers examined artifacts recovered at Riparo Bombrini, in northwest Italy, and concluded that their dwelling was organized around such activities as butchering animals, shaping tools and building fires."}, {"text": "'There has been this idea that Neanderthals did not have an organized use of space, something that has always been attributed to humans,' said lead study author Julien Riel-Salvatore, an assistant professor of anthropology at the University of Colorado-Denver."}, {"text": "'We found that Neanderthals did not just throw their stuff everywhere but in fact were organized and purposeful when it came to domestic space,' Riel-Salvatore said in a prepared statement."}, {"text": "The archaeological site, which was severely destroyed during railroad construction, hosted both Neanderthals and humans."}, {"text": "Researchers focused on three levels of the cave that Neanderthals used roughly 45,000 years ago."}, {"text": "Riel-Salvatore and his colleagues wrote that the cave was probably used at times as a permanent residence, and as a logistical base at other times."}, {"text": "It's for this latter use that researchers noticed the greatest organization."}, {"text": "Specifically, researchers found evidence of fire building, or 'hearths' toward the rear wall of the cave, while stone tools and chips, as well as animal materials, were found outside the cave."}, {"text": "'This may suggest an effort to keep activities associated with the production of noxious debris segregated from those parts of the shelter that were more enclosed and that, possibly, were associated with activities such as sleeping and socializing next to hearths,' authors wrote."}, {"text": "Researchers cautioned that their conclusions were made on a roughly 15-square-foot preliminary excavation, and that further work was necessary to confirm their observations."}, {"text": "Among other findings, the researchers noted the presence of edible shellfish remains throughout the cave dwelling, as well as large amounts of ochre."}, {"text": "Study authors said they were unclear as to what the ochre was used for, but speculated that it may have been used during animal butchering or in processing animal hides."}, {"text": "'Neanderthals could have used it for tanning hides, for gluing, as an antiseptic or even for symbolic purposes,' Riel Salvatore said of the ochre."}, {"text": "'We really can't tell at this point'."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0544.json b/inquisitive/sources/test/0544.json new file mode 100644 index 0000000000000000000000000000000000000000..668c146e0cb9437f3f834c4db82c330ddb090b85 --- /dev/null +++ b/inquisitive/sources/test/0544.json @@ -0,0 +1 @@ +[{"text": "WASHINGTON - Population growth in Southern and Western states, led by Texas, California and Florida, accounted for more than 80 percent of new residents nationwide over the last three years, surpassing the Northeast and Midwest in the demographic contest that plays a key role in determining states' political clout, census data released Monday show."}, {"text": "If states continue to grow at the same pace for the rest of the decade, Texas could gain three more congressional seats in 2020, according to a Los Angeles Times analysis of the Census Bureau figures."}, {"text": "Florida, North Carolina, Virginia and Colorado would stand to gain one seat each, while Illinois, Pennsylvania, Ohio, Michigan and Minnesota, West Virginia and Rhode Island would lose a seat each."}, {"text": "Population estimates are eagerly watched by state officials because the figures determine the flow of money into many federal programs and the number of seats each state receives in the House of Representatives."}, {"text": "That number gets readjusted each decade."}, {"text": "The new data reinforce a trend that has seen Southern states' growth outpace that of the Northeast and Midwest."}, {"text": "Texas, which gained four seats in the last round of congressional reapportionment, lagged behind only North Dakota and the District of Columbia in the rate of population growth since the 2010 census."}, {"text": "California, with 38,332,521 residents, and Texas, with 26,448,193, remain the nation's most populous states."}, {"text": "New York narrowly maintained its third-place spot with 19,651,127 residents, compared with Florida's 19,552,860 as of July 1."}, {"text": "But the Sunshine State will soon surpass New York because its population is growing about three times faster, according to the census estimates, which are based on data measuring births, deaths and migration."}, {"text": "As a percent of population, California's growth again outpaced the national average over the last year, rising 0.9 percent, or 332,643 new residents, compared with 0.7 percent nationwide."}, {"text": "But in raw numbers, Texas added the most residents, 387,397."}, {"text": "An improving state economy in the second half of 2013 may augur faster growth in California, but Texas still has an advantage because of its energy-based economy and a population that is trending younger."}, {"text": "Texas is 'going to keep growing a cumulative advantage in redistricting, until the oil economy turns (down) again,' said Dowell Myers, a demography expert and professor at the University of Southern California's Price School of Public Policy."}, {"text": "'But California's adding jobs more rapidly now than Texas."}, {"text": "So probably next year I would bet that California's share of the growth is up a little bit more'."}, {"text": "North Dakota is the nation's fastest-growing state, driven by a thriving oil and gas industry."}, {"text": "North Dakota's population stood at 723,393 on July 1, according to the census data, a 3.1 percent increase from 2012."}, {"text": "Since the 2010 census, North Dakota's population has grown 7.6 percent, far outpacing the national rate of 2.4 percent."}, {"text": "Kevin Iverson, manager of the North Dakota Census Office, says the biggest population growth has been among 19- to 34-year-olds, primarily through migration."}, {"text": "'The economic winds have clearly favored North Dakota,' Iverson said, attributing it mainly to the energy boom but also growth in the manufacturing and agriculture sectors."}, {"text": "'The real question begins to become, to what extent can you continue to grow?' Population in the District of Columbia also grew at a sustained clip, rising 2.1 percent from 2012 to 2013 to 646,449."}, {"text": "Utah grew the next fastest, at a rate of 1.6 percent, followed by Colorado and Texas at 1.5 percent and Nevada at 1.3 percent."}, {"text": "West Virginia and Maine saw slight population declines in the last year."}, {"text": "Pennsylvania, New Mexico, Vermont and Illinois posted the slowest population growth, all at or near a tenth of 1 percentage point."}, {"text": "The national population stood at 316,128,839 on July 1, an increase of 2.3 million."}, {"text": "But the annual growth rate nationally continues to lag behind where it was in the mid-2000s before the economic downturn."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0547.json b/inquisitive/sources/test/0547.json new file mode 100644 index 0000000000000000000000000000000000000000..053d9a39069a5904f94bf5347e0e7410ca4565be --- /dev/null +++ b/inquisitive/sources/test/0547.json @@ -0,0 +1 @@ +[{"text": "SEATTLE - Fifty years after the U.S."}, {"text": "Surgeon General first warned of the health effects of smoking, a new analysis from the University of Washington shows that the number of smokers worldwide - and the number of cigarettes consumed - has never been higher."}, {"text": "Between 1980 and 2012, the number of adults who smoke increased from 721 million to nearly 1 billion, reports the study published Tuesday in the Journal of the American Medical Association."}, {"text": "The number of cigarettes smoked globally jumped from about 5 trillion to 6.25 trillion."}, {"text": "The study, which is one of the most comprehensive ever to examine global tobacco use, shows that the remarkable reductions in smoking rates in the United States and other wealthy countries have been offset by a growing epidemic in the developing world."}, {"text": "'The University of Washington study demonstrated clearly how much further the world, particularly low- and middle-income countries, still has to go,' said Matthew Myers, president of the Washington, D.C.-based Campaign for Tobacco-Free Kids."}, {"text": "The rise in the number of smokers reflects both population growth - particularly in nations such as China and Indonesia - and the tobacco industry's heavy marketing in poorer nations, experts say."}, {"text": "Smoking statistics are usually reported in terms of rates - or the percentage of people who smoke."}, {"text": "The UW analysis confirmed that the global smoking rate dropped from 26 percent to 18.7 percent during the study period."}, {"text": "But the sheer number of smokers is most relevant when it comes to the public- health impact, said Ruth Malone, who studies global tobacco issuesat the University of California, San Francisco."}, {"text": "'It's premature deaths . and the total global burden of suffering - of preventable suffering - that we're talking about here,' said Malone, who was not involved in the UW analysis."}, {"text": "After dropping rapidly for a decade, global smoking rates have declined more slowly since the mid-2000s, said Marie Ng, lead author of the analysis from the UW's Institute for Health Metrics and Evaluation (IHME)."}, {"text": "And though the data are still uncertain, the analysis hints that the worldwide smoking rate for men may have started to climb in the past three years."}, {"text": "Since the surgeon general's 1964 report drew a clear link between smoking and lung cancer and other diseases, tobacco-control efforts in the U.S. have saved 8 million lives, according to another JAMA study."}, {"text": "The fraction of Americans who smoke has fallen by more than half, from 42 percent in 1964 to 18 percent in 2012."}, {"text": "And despite population growth, the number of smokers in the U.S. has also dropped, from 52 million in 1980 to 38 million in 2012."}, {"text": "'Tobacco control has been described, accurately, as one of the great public-health successes of the 20th century,' U.S. Centers for Disease Control and Prevention Director Thomas Frieden wrote in an editorial accompanying the studies."}, {"text": "But lung cancer remains the leading cause of cancer deaths among both men and women."}, {"text": "The World Health Organization estimates tobacco-related illness kills 5\u00e2\u20ac\u2030million people a year worldwide - more than AIDS, malaria and tuberculosis combined."}, {"text": "Ng and her colleagues spent three years compiling and analyzing more than 1,000 data sets from 182 countries."}, {"text": "An online visualization tool prepared by IHME allows anyone to parse the results by country, sex, age and other variables."}, {"text": "Those details reveal that countries with effective tobacco-control programs have all seen dramatic declines in tobacco use, Myers said."}, {"text": "Uruguay, which was the first nation to adopt a set of WHO-recommended policies, such as higher cigarette taxes and restrictions on advertising, saw smoking rates plummet 25 percent in just three years."}, {"text": "Since 1980, the smoking rate in Mexico, which requires graphic warning labels on cigarette packages, has fallen faster than in the U.S."}, {"text": "But countries such as Russia, Indonesia and China, where up to 54 percent of men still smoke, have slowed global progress, Myers said."}, {"text": "Russia, however, recently adopted some of the world's toughest anti-smoking measures, which will kick in soon."}, {"text": "'This study is not a reason for a sense of hopelessness,' Myers said."}, {"text": "'It is, however, a clarion call that in those countries that have not yet implemented tobacco-control policies, the death toll from tobacco is going to be devastating'."}] \ No newline at end of file diff --git a/inquisitive/sources/test/0550.json b/inquisitive/sources/test/0550.json new file mode 100644 index 0000000000000000000000000000000000000000..1c6c6a9d01416a3aa46120e757f01f38d8680695 --- /dev/null +++ b/inquisitive/sources/test/0550.json @@ -0,0 +1 @@ +[{"text": "LOS ANGELES - If you're in stop-and-go traffic, you're probably pretty unhappy about it."}, {"text": "If you're a male penguin balancing an egg on your feet in the freezing Antarctic, that traffic jam is probably keeping you alive."}, {"text": "Scientists studying huddles of emperor penguins in Antarctica have discovered that waves of movement travel though huddled masses of flightless birds rather as they do through cars stuck on the freeway during rush hour - but in ways that maximize the huddle's density and keep the birds warm as they incubate their eggs."}, {"text": "Emperor penguins are the only vertebrate species that breeds during the Antarctic winter, and they face freezing winds that blow as fast as 124 mph in an icy landscape that can be as cold as 58 degrees below zero."}, {"text": "So they huddle together against the harsh elements - and together, their bodies can raise the temperature within two hours to as high as 98.6 degrees."}, {"text": "At first glance, the penguins may not appear to move much."}, {"text": "The males probably can't run anywhere in a rush, in any case: The fathers-to-be cover their eggs with feathered skin known as a brood pouch, with the eggs resting on top of their feet."}, {"text": "'If you look at a penguin huddle in real time, you hardly see any movement at all - they are all standing very still,' said Richard Gerum, a physicist at University of Erlangen-Nuremberg in Germany and first author of the study published in the New Journal of Physics."}, {"text": "But watch this huddle of shuffling penguins long enough, and there emerge distinct waves of motion through the feathered masses as one penguin takes a step and the rest follow."}, {"text": "It's a way of maintaining order - something humans have trouble doing, Gerum pointed out."}, {"text": "'When a big human crowd is together, there can be accidents,' Gerum said."}, {"text": "'And this is something that never happens in a penguin huddle'."}, {"text": "To understand how these waves begin and behave, the scientists analyzed video footage gathered on penguin colonies near the French and German research bases on Antarctica."}, {"text": "Just like cars do in a traffic jam, the penguins would move to fill in an empty space."}, {"text": "But unlike cars a traffic jam, any penguin can initiate movement, whether they're in the front, to the back or to the side."}, {"text": "(A car trying to 'initiate movement' from the back would end up rear-ending the car in front of it.)"}, {"text": "The waves, said a previous study, travel through the huddle at regular intervals of 35 to 55 seconds."}, {"text": "The new study found that whenever a penguin moved a threshold distance of about 2 centimeters (less than an inch), it triggered one of these traveling waves."}, {"text": "The 2-centimeter threshold is no accident: That's roughly twice the thickness of a penguin's properly fluffed layer of insulating feathers."}, {"text": "'This suggests that the penguins touch each other only slightly when standing in a huddle, without compressing the feather layer so as to maximize the huddle density without compromising their own insulation,' the study authors wrote."}, {"text": "So if a penguin moves too far away - allowing heat to escape - the penguin next to it moves closer."}, {"text": "But if a penguin moves too close to another - crushing its neighbor's insulating layer of feathers - this will also cause the neighbor to move."}, {"text": "Such waves aren't hierarchical. Any penguin can start them, and they're a product of a simple set of rules governing the space between each penguin and its immediate neighbors."}, {"text": "And yet, these tiny movements can add up to a large-scale, complex order - akin to the impressive patterns seen in schooling fish, flocks of birds or swarms of ants."}, {"text": "These rules allow the penguins to stay organized, to maximize heat conservation and even merge two smaller penguin huddles together."}, {"text": "So although these emperor penguins don't dance like the fleet-footed characters in the 2006 animated film 'Happy Feet,' they still perform some pretty fancy footwork."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1101.json b/inquisitive/sources/test/1101.json new file mode 100644 index 0000000000000000000000000000000000000000..5c921f12422cf292ef0533c080f9c6bf8d3c4532 --- /dev/null +++ b/inquisitive/sources/test/1101.json @@ -0,0 +1 @@ +[{"text": "The United Nations' new commander and supply convoys headed today for northwest Bosnia, where persistent fighting has hindered efforts to restart peace talks."}, {"text": "Sporadic fighting was reported late Wednesday and early today in two areas of the Bihac region, around the towns of Velika Kladusa and Bihac. Bosnian Serbs said Muslim-led government soldiers attacked them farther east around Bosanska Krupa."}, {"text": "U.N. officials said Lt. Gen. Rupert Smith, who took over command of 24,000 peacekeeping troops in Bosnia last month, set off today for the Bihac area to visit Bangladeshi peacekeepers and the commander of the government's beleaguered 5th Corps, Gen. Atif Dudakovic."}, {"text": "One month into what is supposed to be a four-month truce, fighting has persisted in northwest Bosnia, impeding efforts to restart peace talks."}, {"text": "The Bosnian government and Bosnian Serbs signed the truce accord, but the Serbs' allies -- Serbs from Croatia and renegade Bosnian Muslims opposed to the Muslim-led Bosnian government -- did not."}, {"text": "Months of intense fighting in the northwest has left both peacekeepers and civilians short of food."}, {"text": "A resupply convoy for the Bangladeshis arrived in the area on Wednesday. Today, an aid convoy was on its way to civilians, said Kris Janowski, a spokesman for the U.N. High Commissioner for Refugees."}, {"text": "Janowski said the eight trucks carried 97 tons of baby food, detergents, salt and medical supplies. The convoy was expected to reach its destination on Friday."}, {"text": "U.N. officials and diplomats elsewhere were trying to shore up the cease-fire and make progress on a plan to end 34 months of war."}, {"text": "American officials said Assistant Secretary of State Richard Holbrooke would travel to Germany over the weekend for talks on bolstering a Croat-Muslim federation."}, {"text": "The federation, backed by the United States, is 10 months old and ended bitter fighting between the two sides, who started the Bosnian war as allies against the Serbs."}, {"text": "But the alliance is precarious. The two sides have done little more than institutionalize a cease-fire."}, {"text": "Some analysts suspect that President Franjo Tudjman of Croatia ordered 12,000 U.N. peacekeepers to leave his country because he and President Slobodan Milosevic of Serbia have reached an understanding about carving up the former Yugoslavia. That would mean an end to the Croat-Muslim federation."}, {"text": "Meanwhile, U.N. officials in Sarajevo said they would try to send a few more trucks with firewood along a key road into Sarajevo today."}, {"text": "The route reopened Wednesday under an agreement between Bosnian Serbs and the government, but is of limited use because the Serbs have restricted it to charities operating under the umbrella of the U.N. relief agency."}, {"text": "Those organizations already have alternate routes, but Bosnian charities that have no other options are banned from it."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1102.json b/inquisitive/sources/test/1102.json new file mode 100644 index 0000000000000000000000000000000000000000..64b1c5e5e62b5d0252650c8728d89bb3f22d3fb7 --- /dev/null +++ b/inquisitive/sources/test/1102.json @@ -0,0 +1 @@ +[{"text": "The Islamic suicide bombers who killed 21 Israelis last week dressed like soldiers to avoid detection, police said Thursday."}, {"text": "The daily Yedioth Ahronoth said the men, identified as Salah Shakr and Anwar Sukar from PLO-ruled Gaza, were aided by former Palestinian collaborators with Israel living in an Israeli-guarded enclave in the strip."}, {"text": "Yedioth said the collaborators gave the militants army uniforms that helped them leave Gaza and reach a junction in central Israel on Jan. 22 without detection."}, {"text": "Both Palestinians, 20 soldiers and a civilian died in the two blasts they detonated there."}, {"text": "Police spokesman Eric Bar-Chen confirmed the attackers were wearing either uniforms or similar clothing."}, {"text": "Israeli police, fearing an escalation of attacks to mark the holy Muslim month of Ramadan, have reinforced troops in Jerusalem."}, {"text": "There is also concern that female Palestinian Hamas activists will join the suicide attack squads, Yedioth reported. A number of Islamic women met with Hamas leaders recently asking to be allowed to participate in attacks, it said."}, {"text": "The bombing on Jan. 22 dealt a blow to Israel-PLO peace talks and sparked an intensified crackdown on Islamic militants."}, {"text": "Israeli security forces detained seven members of the Islamic Jihad and Hamas groups in the West Bank Thursday and jailed ten other Islamic militants without trial, Israel radio reported. A Hamas activist in Gaza, Ibrahim Yazouri, said Palestinian police there rounded up three Hamas activists in the past four days."}, {"text": "An Israeli official, speaking on condition of anonymity, said that in a raid last week on an east Jerusalem college, troops uncovered a Hamas ring planning to kidnap an Israeli soldier."}, {"text": "Israeli troops arrested 30 Palestinians in the raid. Four of the students in the ring were from Gaza, the official said."}, {"text": "He added that troops confiscated skullcaps of religious Jews and knives from the Palestinians' rooms."}, {"text": "A photograph published in Yedioth showed a Palestinian wearing a skullcap and the clothing of religious Jews and practicing Hebrew prayer in front of a wall painted with an Arabic inscription."}, {"text": "Islamic militant violence against Israelis has stymied talks aimed at extending the PLO-ruled Gaza-Jericho autonomy throughout the West Bank."}, {"text": "Israel demands that Yasser Arafat's Palestinian Authority take stronger measures against the Muslim extremists."}, {"text": "Prime Minister Yitzhak Rabin was to meet with Arafat and other Arab leaders in Cairo Thursday in an attempt to breathe life into the peace process."}, {"text": "The leaders were expected to make a joint statement denouncing terrorism, Israeli newspapers said."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1103.json b/inquisitive/sources/test/1103.json new file mode 100644 index 0000000000000000000000000000000000000000..6405a627ae683a4179a963b87e58442beb47fb67 --- /dev/null +++ b/inquisitive/sources/test/1103.json @@ -0,0 +1 @@ +[{"text": "Players and trainers from Genoa's two major league soccer teams joined hundreds of fans, friends and relatives Thursday for the funeral of a young man knifed to death by a rival team's supporter."}, {"text": "Vincenzo Spagnolo, 25, was stabbed near the heart as he came to Genoa's stadium for the Genoa-AC Milan game on Sunday. Police on Monday arrested Simone Barbaglia, a 19-year-old Milan fan."}, {"text": "Cardinal Giovanni Canestri led the funeral in St. Theodore's church near the port. Outside hundreds of Genoa team supporters applauded and waved the red-and-blue team flag in a show of support for the victim's family and the soccer team."}, {"text": "'One can't die for a soccer game,' the cardinal said in his homily, urging reflection."}, {"text": "Spagnolo's death touched off a fan riot and prompted Italian sports authorities to cancel all soccer games this Sunday as well as other sports events."}, {"text": "'It seems sometimes that deviant idealogies and the primitive impulses enjoy precedence' the cardinal said, 'while the values of justice, generosity and solidarity get supplanted by the culture of egoism . hedonism, of bullying, of violence.'"}, {"text": "Barbaglia claimed he was acting in self-defense when he pulled out a 10-centimeter (4 inch) knife that he said was only meant to intimidate members of a rowdy Genoa gang."}, {"text": "After his arrest Barbaglia wrote a letter, published in Italian newspapers Thursday, asking his victim to understand and forgive him."}, {"text": "'Together, maybe we shared a misunderstood passion for soccer. I didn't mean it. Forgive me,' he wrote."}, {"text": "A 17-year-old friend of Barbaglia lent Barbaglia the knife from a collection of knives he kept at home before Barbaglia set out by train to Genoa."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1104.json b/inquisitive/sources/test/1104.json new file mode 100644 index 0000000000000000000000000000000000000000..bfe4efa8f05495a80eb3da038a8216dd521d7feb --- /dev/null +++ b/inquisitive/sources/test/1104.json @@ -0,0 +1 @@ +[{"text": "Russian forces in Chechnya have seized control of three of Grozny's four districts but still have a long way to go, the commander of Interior Ministry troops said Thursday."}, {"text": "'The turning point has not been reached, but there are signs of it,' Interior Ministry Gen. Anatoly Kulikov said. 'This means the army has fulfilled its main objective. It has routed the main (rebel) armed forces.'"}, {"text": "Kulikov also claimed Russian forces now control most of northern Chechnya."}, {"text": "'Not being controlled yet is the south of the republic and (the town of) Gudermes,' he said at a news conference."}, {"text": "The fighting continued Thursday, with Russian troops continuing to shell Chechen positions in Grozny, the Chechen capital."}, {"text": "Russian Defense Minister Pavel Grachev, who recently handed over control of the operation to Kulikov, was hospitalized for a routine army physical, officials said Thursday. He is the second major official in charge of the Chechnya war to go to the hospital in the past week."}, {"text": "Grachev, 48, has been bitterly ridiculed for saying he could take Grozny in two hours with a single paratrooper regiment. Instead, tens of thousands of Russian troops have been locked in a near static struggle with a few thousand lightly armed Chechens for almost two months."}, {"text": "Russian Nationalities Minister Nikolai Yegorov was hospitalized earlier with pneumonia, and the prominent daily Izvestia printed a front-page story Thursday speculating that both men would soon be ousted."}, {"text": "Many observers expect a protracted guerrilla war once Russia imposes at least nominal control over most of Chechnya. But Kulikov rejected that notion."}, {"text": "'There will be no drawn-out guerrilla war,' he said. 'There will be acts of terrorism. '"}, {"text": "He claimed most Chechens are anxious for a Russian victory and would not back a guerrilla war. 'People with tears in their eyes are waiting for the moment when all this will stop,' he said."}, {"text": "Kulikov also acknowledged that three Russian soldiers have been charged with looting. There have several reports of Russian looting in Grozny."}, {"text": "'I regret to say that this is an inseparable, dirty part of any war,' he said."}, {"text": "Meanwhile, a new poll said the overwhelming majority of Russians oppose courts-martial for soldiers who refuse to fight in Chechnya."}, {"text": "Only 11 percent of the respondents in the poll of 1,353 people nationwide said they favored prosecuting soldiers who refuse to fight in Chechnya, the Obshchaya Gazeta newspaper said."}, {"text": "Seventy-four percent said they thought it would be wrong to bring charges and 15 percent had no opinion. The margin of error was 2.5 percent."}, {"text": "A number of Russian soldiers have surrendered rather than fight and, in a few instances, commanders refused to advance or fire on unarmed civilians."}, {"text": "The crushing morale problem is seen as one of the reasons Russian forces are bogged down in Chechnya."}, {"text": "The poll is just the latest sampling of public opinion, which has been opposed to the war in Chechnya from the outset."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1105.json b/inquisitive/sources/test/1105.json new file mode 100644 index 0000000000000000000000000000000000000000..d351d0625edef53396f3a098d57384803d08703f --- /dev/null +++ b/inquisitive/sources/test/1105.json @@ -0,0 +1 @@ +[{"text": "Angola's top government and rebel soldiers traded accusations of mutual cease-fire violations in a tense meeting on neutral territory in the southern African nation Thursday instead of sticking to a discussion of troop withdrawal."}, {"text": "Chief of Staff Joao de Matos accused UNITA rebels of ignoring the cease-fire and 'raiding at will', including an ambush on a food convoy which killed 29 civilians near the coastal city of Benguela, Portuguese TSF radio reported."}, {"text": "De Matos said government troops would retaliate 'devastatingly' against any further incursions by the rebels."}, {"text": "UNITA Gen. Arlindo Chenda Ben-Ben Pena responded angrily that government troops were provoking a battle by advancing in violation of a peace treaty signed last November."}, {"text": "Pena has attributed the attacks to small, isolated units often completely out of touch with the UNITA command."}, {"text": "After 19 years of civil war, Pena said, 'UNITA will not be pushed out of its own country now that peace is supposed to have come.'"}, {"text": "The bitter exchange came a week before the U.N. Security Council was scheduled for a critical vote on a major peacekeeping operation to the southern African nation."}, {"text": "Although U.N. Secretary-General Boutros Boutros-Ghali drafted a plan calling for a 7,000-soldier peacekeeping force, he has warned that deployment depends on a 'true commitment to peace' by the warring sides."}, {"text": "De Matos and Pena were supposed to plot safe withdrawal of their troops from the tensest parts of the war-torn nation, including Huambo, the country's second city that was held by the rebels for nearly a year."}, {"text": "More than 200,000 government and rebel troops still divide the country in a tense standoff. Severe food shortages and military tension have triggered continuous skirmishes."}, {"text": "The National Union for the Total Independence of Angola -- UNITA -- has been fighting government forces for control of the country since Portugal granted it independence in 1975."}, {"text": "More than 500,000 Angolans have died, victims of fighting and war-related famine and disease."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1106.json b/inquisitive/sources/test/1106.json new file mode 100644 index 0000000000000000000000000000000000000000..5d68e7269a6366af0b847b151996a6af91ce05f3 --- /dev/null +++ b/inquisitive/sources/test/1106.json @@ -0,0 +1 @@ +[{"text": "The number of newly laid-off Americans filing claims for jobless benefits edged up by 1,000 last week, the first advance in three weeks, but remained at a level that analysts say marks a healthy job market."}, {"text": "The Labor Department reported Thursday that new applications for unemployment insurance totaled a seasonally adjusted 326,000, up from 325,000 a week earlier."}, {"text": "It was the first increase since claims shot up by 16,000 during the week ended Jan. 7. Analysts had said the earlier jump reflected difficulties in adjustments for seasonal variations."}, {"text": "These analysts had predicted claims would drop back to about 325,000, where they have ranged since last summer. This level, they contend, reflects a strong job market."}, {"text": "Many analysts predict that 225,000 jobs were created in January following the addition of 256,000 new jobs in December. The December growth helped push the jobless rate to 5.4 percent, lowest since July 1990. The department releases the January employment report on Friday."}, {"text": "The closely-watched four-week moving average of weekly jobless claims totaled 336,000, down from 339,000 during the period ended Jan. 21 and the lowest since 334,500 during the period ended Jan. 7."}, {"text": "Analysts prefer to track the four-week average because it smooths out the spikes in the more volatile weekly reports."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1107.json b/inquisitive/sources/test/1107.json new file mode 100644 index 0000000000000000000000000000000000000000..2ce1cebf615c3f8817ae5aa2ae9c6a397f6905ee --- /dev/null +++ b/inquisitive/sources/test/1107.json @@ -0,0 +1 @@ +[{"text": "For nearly every pupil at Marvin Heights public school, English is a second or third language."}, {"text": "The school, which is bursting at the seams, offers Punjabi dance classes as well as a breakfast program. At the annual barbecue, the principal dishes up samosas and hot dogs."}, {"text": "Marvin Heights sounds like a typical downtown school with a high proportion of new immigrants. But it is part of the Peel board of education, the largest public school board in Canada, in the suburbs just west of Toronto."}, {"text": "In a switch from traditional settlement patterns, many new immigrants to Canada are not moving to the downtown city cores but are flocking to the suburbs."}, {"text": "Every year about 20,000 people arrive in Peel Region, making it the second fastest growing regional municipality in Canada between 1986 and 1991 (behind York Region, just north of Toronto)."}, {"text": "Many of those newcomers are new to Canada, says Statistics Canada. In 1992, about 10 per cent of the new immigrants in Ontario, 14,000 people, settled in Peel, often just a few kilometres from where they got off the plane at Pearson International Airport."}, {"text": "In nearby Malton, immigrants find shops, social service agencies and temples where their language is spoken. Even the local member of Parliament, Gurbax Malhi, is an immigrant from India."}, {"text": "Just a few kilometres north, in Brampton, the ubiquitous plazas have sari shops, Caribbean grocery stores and video outlets offering the latest movies from India."}, {"text": "'People still have the illusion that Brampton or Mississauga is still a traditional suburban community. It isn't,' says Harold Brathwaite, director of the Peel board of education."}, {"text": "Of all the suburban regions ringing Metropolitan Toronto, Peel has the highest proportion of visible minorities."}, {"text": "About one-quarter of the region's 700,000 residents are members of a visible minority, the same proportion as in Vancouver and second only to that of Metro Toronto. About 36 per cent of Peel's population was not born in Canada, according to the 1991 census."}, {"text": "Peel -- an amalgamation of Mississauga, Canada's ninth-largest city, Brampton and Caledon -- was created 20 years ago. Since then, it has undergone several major transitions, says Paula DeCoito, director of the region's social planning council."}, {"text": "Apple orchards and dairy farms have been paved over and most of the region has become an urban, multicultural and multiracial society."}, {"text": "Ethnic diversity has taken Peel by surprise. Suddenly, school boards, the police and social service agencies are scrambling as they realize they cannot even communicate with large segments of the community."}, {"text": "'There is a lag between the ideology of the leadership and the social reality. They're good people, but their ideas have got to go through that transition,' DeCoito said."}, {"text": "Pearson Airport and the industries that have grown up around it are a magnet for new immigrants. The region's stock of new, single-family housing is also more attractive than Toronto's older houses and highrises."}, {"text": "In the city of Mississauga (which includes Malton), 27 per cent of the population are members of visible-minority groups, while in Brampton 23 per cent are classified as such. In Caledon, the most affluent and rural of the three communities, just three per cent are visible minorities."}, {"text": "Every shift in Canadian immigration policy has changed the mix of who ends up living in Mississauga's suburban cul-de-sacs."}, {"text": "In the early 1970s, when Canada instituted a neutral point system to evaluate potential newcomers, Asian, African and Caribbean immigrants were accepted in larger numbers. At the same time, as Europe became more prosperous, the number of white European immigrants began to decline."}, {"text": "In 1981, Britain was still ranked first as the country of last permanent residence for newcomers to Peel. By 1993, the primary source countries were India, the Philippines, Poland, Hong Kong and Jamaica. Britain wasn't even in the top 10."}, {"text": "Because Canada's immigration policy has put a high priority on family reunification, once one member of a family legally enters Canada, relatives can soon follow."}, {"text": "Much of the growth of the Sikh population has come from families joining relatives in the region, said Manohar Singh Bal, secretary of the Ontario Council of Sikhs."}, {"text": "South Asians have become the biggest visible minority group in Peel, slightly more than one-third of the total visible minority population. Blacks, many of whom are first-generation immigrants from the Caribbean, make up about one-quarter."}, {"text": "Filipinos and Chinese each constitute about 10 per cent."}, {"text": "Statistics Canada says 11 per cent of the region's population are neither Catholic nor Protestant, with the largest groups being 21,300 Sikhs, 18,665 Hindus and 17,000 Muslims."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1108.json b/inquisitive/sources/test/1108.json new file mode 100644 index 0000000000000000000000000000000000000000..8e48524778e1d95bb6031bd46d3e471accd35d3b --- /dev/null +++ b/inquisitive/sources/test/1108.json @@ -0,0 +1 @@ +[{"text": "The Football Association was considering possible sanctions against Blackburn on Thursday after a fan ran onto the field and tried to attack the referee at Ewood Park."}, {"text": "The FA said it was studying official reports from Wednesday night's Premier League match against Leeds, which ended in a 1-1 draw."}, {"text": "As the players were leaving the field, a 40-year-old man jumped from the stands and grabbed referee Rodger Gifford, who had made several controversial calls during the game. Players pulled the fan away and Gifford escaped injury."}, {"text": "The fan, a season-ticket holder at Ewood Park, was arrested and faces arraignment on March 3. His name was not released."}, {"text": "It was the second incident in a week involving a spectator at a Premier League match. Last week, Manchester United star Eric Cantona attacked a Crystal Palace fan who had been taunting him at Selhurst Park."}, {"text": "The FA said it was waiting for more information before taking any action in the Blackburn incident."}, {"text": "'It is all speculation at this stage,' said spokeswoman Clare Tomlinson. 'Until we see the reports we won't know. Of course, we are the regulating body in the game and when things go wrong we can punish the club, although we do not want to prejudge the issue at this stage.'"}, {"text": "Blackburn chairman Robert Coar said the club would punish the offender itself."}, {"text": "'He will be dealt with by the club in addition to whatever penalty he may receive under the law of the land,' Coar said. 'The man is a season ticket holder and he would have had his ticket taken off him as a matter of course after the incident.'"}] \ No newline at end of file diff --git a/inquisitive/sources/test/1109.json b/inquisitive/sources/test/1109.json new file mode 100644 index 0000000000000000000000000000000000000000..9c056f8d05f3cfe77a89e0a0e1b1418b3efd262b --- /dev/null +++ b/inquisitive/sources/test/1109.json @@ -0,0 +1 @@ +[{"text": "Police on Thursday evacuated nearly 11,000 residents of Oranienburg, north of Berlin, after a 500-pound (220-kilogram) World War II bomb was uncovered at a construction site."}, {"text": "A police statement said the bomb was found late Wednesday during excavation not far from the Oranienburg Castle. Some 300 people in the immediate area were evacuated Wednesday evening, with the others told to leave Thursday."}, {"text": "After a delay of more than six hours to pump out ground water that covered the fuse section of the bomb, explosives experts disarmed it in a half-hour and residents were given the all clear to return home, police said."}, {"text": "Earlier, police had said the delayed-action chemical fuse made disarming more difficult and could take up to several hours."}, {"text": "Occupants of buildings up to a kilometer (half a mile) from the bomb were excavated to schools, sports halls and other public facilities. Main streets were closed to prevent people who had gone to work before the bomb was found from returning to their neighborhoods."}, {"text": "Some 17,000 people reside in the area, which was the site of Nazi munitions factories during the war and the target of about 6,000 bombs dropped by the Allies. Officials believe 15 to 20 percent of the bombs remained unexploded underground, and 20 old bombs have been found and disarmed in the area since 1991."}, {"text": "Discovery of old bombs is commonplace throughout Germany and other parts of Europe invaded by the Nazis during the war."}, {"text": "Last Sept. 15, three construction workers were killed when an old bomb exploded at a building project in Berlin."}, {"text": "Last October, 10,000 residents of the Rhine river town of Ludwigshafen, Chancellor Helmut Kohl's hometown, were evacuated while experts defused a nearly two ton bomb."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1110.json b/inquisitive/sources/test/1110.json new file mode 100644 index 0000000000000000000000000000000000000000..77e454687dd2ed645716c5a2d557a9032ff07b0d --- /dev/null +++ b/inquisitive/sources/test/1110.json @@ -0,0 +1 @@ +[{"text": "Secretary of State Warren Christopher today called on Bosnia's Muslims and Croats to give 'substantive content' to their planned confederation and said the United States intended to help make it work."}, {"text": "'We should work on that together,' Christopher said in asking Britain, France, Germany and Russia to join in the effort."}, {"text": "Christopher is sending Assistant Secretary of State Richard Holbrooke to Germany to try to bolster the confederation plan. Diplomats from the four other countries are expected to join the talks with Muslim and Croat leaders in Munich this weekend."}, {"text": "'We're very anxious that that process move forward,' Christopher said at a news conference. 'It is significant, it can be very valuable. . We want to make sure the federation moves beyond a concept to having the largest amount of substantive content.'"}, {"text": "Together, the Muslims and Croats would control 51 percent of Bosnia under a peace proposal by the five Western countries to end the 34-month war in the former Yugoslav republic."}, {"text": "Bosnia Serbs have rejected the plan, which would allot them control of the remaining 49 percent, about one-third less than they have captured. They say that would leave them with economically and politically ineffective fragments of Bosnia-Herzegovina."}, {"text": "The Serbs' repeated refusal to negotiate, despite assurances they could seek a better deal at the table, has stalled U.S. peace efforts while sporadic fighting threatens a shaky cease-fire."}, {"text": "An effect of Holbrooke's talks with Muslim and Croat leaders could be to isolate the Serbs diplomatically. 'We're trying to send them a political signal,' said a senior U.S. official, speaking on condition of anonymity,"}, {"text": "The Muslim-led government and Bosnian Croats agreed last March to confederate, but they have not followed up to form a joint army or to make other joint arrangements."}, {"text": "French Foreign Minister Alain Juppe has proposed, meanwhile, an international conference to deal with the impasse, but Clinton administration officials said they were cool to the idea."}, {"text": "A confederation of Muslims and Croats in Bosnia could reach across the border and establish ties with Croatia. Serbs have an opposite goal -- creation of a Greater Serbia in one form or another."}, {"text": "Bosnian Prime Minister Haris Silajdzic, in Washington for talks with Vice President Al Gore, Secretary of State Warren Christopher and congressional leaders, dismissed the French proposal."}, {"text": "'This only buys time for our enemies,' he said at a news conference. 'We don't need any more public relations conferences.'"}, {"text": "State Department spokeswoman Christine Shelly said the administration 'would want to know' how the proposed summit would relate to the peace plan devised by the United States and its partners in the so-called Contact Group."}, {"text": "Silajdzic, concluding his three-day visit, appeared exasperated that the administration declines to lift the U.N. Security Council arms embargo in Bosnia. He said a majority in Congress supported providing arms to government forces."}, {"text": "The administration's position is that the embargo should be lifted only by agreement with other members of the Security Council but that Britain and France would not go along."}, {"text": "'The international community owes us because they let other people kill us and tied our hands,' Silajdzic said. 'The arms embargo has been there long enough to prove that it only helps kill innocent people.'"}, {"text": "He goes next to Moscow where he will press for imposition of a May 1 deadline for the Serbs to accept the proposed peace plan. After that, he said, the embargo should be lifted so the Bosnians can arm themselves."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1111.json b/inquisitive/sources/test/1111.json new file mode 100644 index 0000000000000000000000000000000000000000..c8f96839d55da676c15d5c256877945e828050e9 --- /dev/null +++ b/inquisitive/sources/test/1111.json @@ -0,0 +1 @@ +[{"text": "A Turkish court on Thursday ordered Thursday the seizure of a book by a Turk who has written on the war against the Kurds, and another court ordered the confiscation of copies of a pro-Kurdish daily."}, {"text": "The author, Yasar Kemal, recently wrote in the German newsmagazine Der Spiegel that Kurdish villages were burned in an attempt to battle the 11-year separatist rebellion in southeast Turkey."}, {"text": "Western governments and rights groups have made similar charges. The government denies any military action to destroy Kurdish villages."}, {"text": "The State Security Court said it was ordering the seizure of Kemal's book, 'The Freedom of Thought and Turkey,' because it provokes 'hatred and enmity on the basis of differences in people's races and locations where they live.'"}, {"text": "Kemal and his publisher, Erdal Oz, were ordered to appear in court next week for questioning."}, {"text": "The author is awaiting arraignment on charges of making separatist Kurdish propaganda in his Der Spiegel article."}, {"text": "A prosecutor said he would face trial under an anti-terrorism law. Conviction could bring a prison sentence of two to five years."}, {"text": "In separate court developments in Istanbul, seizure was ordered for Ozgur Ulke (Free Country) daily. The court contended the paper was virtually the same publication as one banned last year on charges of making separatist propaganda. That paper was called Ozgur Gundem."}, {"text": "Baki Karadeniz, the Ozgur Ulke editor, said the paper would continue to publish even though the copies would be seized before reaching newsstands. The paper is appealing the ruling."}, {"text": "Nineteen employees of Ozgur Gundem have been killed in unsolved murders in the last three years. Thirty-five employees from the two papers are currently in jail on charges of making separatist Kurdish propaganda."}, {"text": "Kurdish guerrillas of the outlawed Kurdistan Workers' Party (PKK) have been waging war against the state since 1984 and more than 14,000 people have been killed in 11 years of bloody separatist fighting."}, {"text": "(AB-KO-KL)"}] \ No newline at end of file diff --git a/inquisitive/sources/test/1112.json b/inquisitive/sources/test/1112.json new file mode 100644 index 0000000000000000000000000000000000000000..431951ad131864839e1b5c49d1d6b1b34e8234a4 --- /dev/null +++ b/inquisitive/sources/test/1112.json @@ -0,0 +1 @@ +[{"text": "Palestinian leaders warned Thursday that the closure of West Bank and Gaza during the holy fasting month of Ramadan and stepped-up Jewish settlement construction could lead to a new uprising against Israel."}, {"text": "Faisal Husseini, a minister in the PLO's self-rule government, issued the warning a day after Jerusalem's planning council approved construction of 6,500 Jewish homes in the city's eastern sector, which is claimed by the Palestinians as a future capital."}, {"text": "Husseini said the construction would undermine support for Arafat and boost Islamic militants who oppose reconciliation with Israel."}, {"text": "'If the PLO loses the leadership, then the only ones who can assume this role are the fundamentalists. And if this happens.we will witness a new uprising and no one will be able to stop it,' Husseini said on Israel's army Radio."}, {"text": "Palestinians waged a six-year uprising against Israeli occupation that was instrumental in bringing Israel and the PLO to the negotiating table in 1993."}, {"text": "Husseini's remarks came just hours before Prime Minister Yitzhak Rabin met with Arafat and other Arab leaders in Cairo to try to rescue the failing Israel-PLO peace talks."}, {"text": "The construction dispute coincides with mounting anger among Palestinians who may be denied access to Muslim holy sites in Jerusalem during Ramadan, which began Tuesday, because of the closure imposed by Israel after a suicide bombing last week."}, {"text": "The top Muslim cleric in Jerusalem called on Palestinians to challenge the closure by trying to reach Jerusalem's Al-Aqsa mosque, the third holiest site in Islam, for the first Friday prayers of Ramadan this week."}, {"text": "'I call on Palestinians to attend the prayers at the mosque. If not (allowed), they can pray at the military roadblock,' said Ikrema Sabri, the mufti of Jerusalem."}, {"text": "He told The Associated Press that hundreds of thousands would have their observance of Ramadan impeded by the closure."}, {"text": "Israel sealed off the territories after a Jan. 22 suicide bombing by Islamic extremists in central Israel that killed 20 soldiers and a civilian."}, {"text": "Since the September 1993 Israel-PLO accord, 116 Israelis have been killed in Palestinian attacks."}, {"text": "Israeli officials, meanwhile, said they would consider easing the closure to enable Ramadan observance."}, {"text": "'If there is a sense that security arrangements are acceptable, we will allow (Palestinians) to come here for prayer,' said Police Minister Moshe Shahal, touring the area known to Jews as the Temple Mount, where the Al-Aqsa mosque is located."}, {"text": "'It can be assumed that starting next week the closure will be eased because of Ramadan. We are not interested in punishing the Palestinian population,' Shahal said later on Israel television."}, {"text": "Police commissioner Assaf Hefetz said Israeli forces were on alert in any case. Hundreds of reinforcements were deployed in Jerusalem in preparation for Friday's Ramadan prayers."}, {"text": "'We take this month very seriously,' Hefetz said, noting it was the first Ramadan since Palestinian autonomy was established in Gaza and Jericho. 'Jerusalem will be getting reinforcements (and) during Friday prayers we will deploy much larger forces.'"}, {"text": "Officials also fear militants could try to time an attack for the anniversary of the massacre of 29 Palestinian worshippers by Jewish settler Baruch Goldstein in a Hebron mosque last Feb. 25."}, {"text": "A leaflet distributed by Arafat's mainstream Fatah group warned 'the closure and settlements will lead to more escalation that would put the entire peace process in serious jeopardy.'"}] \ No newline at end of file diff --git a/inquisitive/sources/test/1113.json b/inquisitive/sources/test/1113.json new file mode 100644 index 0000000000000000000000000000000000000000..12ffa69e5621f65cbd4c65607949edf96dca24c0 --- /dev/null +++ b/inquisitive/sources/test/1113.json @@ -0,0 +1 @@ +[{"text": "Japan's Red Cross Society said Thursday it has received 30 billion yen (dlrs 300 million) in donations, mostly from other Japanese, for victims of the devastating Kobe earthquake. The total exceeded any of its previous relief campaigns."}, {"text": "Meanwhile, local officials announced that damage from the 7.2 magnitude quake, Japan's deadliest in more than 70 years, is likely to exceed dlrs 100 billion in the worst-hit prefecture."}, {"text": "The government of Hyogo prefecture, which includes Kobe, estimated damage worth 9.5 trillion yen (dlrs 95 billion), 1 trillion yen (10 billion) more than its previous calculation. It said the total would probably exceed 10 trillion yen (dlrs 100 billion)."}, {"text": "Authorities Thursday confirmed 5,104 dead, six missing and classified nearly 250,000 people as homeless from the quake."}, {"text": "The national government Thursday said it would spend almost 15 billion yen (dlrs 150 million) to build 30,000 temporary housing units. Quake victims Thursday moved into four prefab houses, the first completed since the temblor."}, {"text": "'It was wonderful. It was too good for me,' said Kimiko Ishibitsu, 70, of her new 29.1-square meter (105-square foot) space with two rooms, a bathroom, a kitchen and a toilet. The four homes are all on hard-hit Awaji Island."}, {"text": "Many people will have to spend two to three more months in shelters such as tents and converted school gymnasiums before housing is available, Rumiko Kadonaga of the Hyogo government said Thursday."}, {"text": "'We are very concerned whether volunteers can continue their activities for that long,' she said. 'We can't estimate how many volunteers are working in the quake-stricken areas. It might be 50,000 or 100,000.'"}, {"text": "In normal times, Japanese are reluctant to help people who aren't family, friends or close neighbors, and people here are also sometimes reluctant to accept gifts for fear of becoming obligated to the giver."}, {"text": "But the Kobe quake has brought out charitable impulses throughout the nation."}, {"text": "All over Japan -- at temples, convenience stores, outside train stations and even in health clubs -- collection boxes ask passersby for contributions for victims of the Jan. 17 quake."}, {"text": "Private citizens have moved to compensate for what many have criticized as insufficient government efforts."}, {"text": "In Kobe, a city of 1.4 million people 435 kilometers (270 miles) west of Tokyo, examples of good will abound. Cooked sweet potato vendors have passed out what for many was the only hot food. Some students' hands were swollen from making hundreds of rice balls a day."}, {"text": "Religious groups, companies, even organized crime syndicates have been providing baths, handing out hot meals and blankets, and giving other comfort to victims."}, {"text": "The government was giving out three meals a day, but some people who had originally been satisfied with rice balls now wanted better quality and hot food, Hyogo official Tsuyoshi Nishioka said Thursday."}, {"text": "'People keep wanting more and better,' he said. 'There's no limit. Some people even asked for a washing machine.'"}, {"text": "An aftershock Thursday registered 4.1 magnitude, but there were no reports of damage or injury. There have been more than 1,350 aftershocks in the two and a half weeks since the quake."}, {"text": "A U.S. Federal Emergency Management Agency team was touring Kobe on Thursday to assess damage and share expertise."}, {"text": "The Japan Red Cross Society, which estimated more than 90 percent of the giving came from Japanese, said its previous highest donation total was 18.5 billion yen (dlrs 185 million) after the 1993 Okushiri quake in northern Japan. That quake killed more than 200 people."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1114.json b/inquisitive/sources/test/1114.json new file mode 100644 index 0000000000000000000000000000000000000000..1b010bd2241453126a6f075f01ac68b177538bde --- /dev/null +++ b/inquisitive/sources/test/1114.json @@ -0,0 +1 @@ +[{"text": "After three days of talks in Washington, Bosnian Prime Minister Haris Silajdzic arrived in Moscow on Thursday to confer with Russian officials on settling the Bosnia conflict."}, {"text": "Foreign Ministry spokesman Grigory Karasin said Silajdzic's two-day working visit was part of Russia's efforts to bring an end to the 34-month war in the former Yugoslavia."}, {"text": "Karasin told the ITAR-Tass news agency that Silajdzic will meet with Prime Minister Viktor Chernomyrdin and Foreign Minister Andrei Kozyrev to discuss the Bosnian peace plan put together by five Western countries."}, {"text": "Russia's historical ally in the Balkans is the Serbs, fellow Orthodox Slavs."}, {"text": "In Washington, Silajdzic had held talks with Vice President Al Gore, Secretary of State Warren Christopher and congressional leaders."}, {"text": "The Bosnian prime minister appeared exasperated that the Clinton administration declined to lift the U.N. Security Council arms embargo in Bosnia. He said a majority in Congress supported providing arms to Bosnian government forces."}, {"text": "In Moscow, Silajdzic was expected to press for a May 1 deadline for the Serbs to accept the peace plan worked out by the so-called Contact Group: the United States, Russia, France, England and Germany."}, {"text": "Under the peace plan, Muslims and Croats would control 51 percent of Bosnia. Bosnian Serbs have rejected the plan, which would give them the remaining 49 percent, about one-third less than they have captured in the war."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1115.json b/inquisitive/sources/test/1115.json new file mode 100644 index 0000000000000000000000000000000000000000..73d1aeab11ea86bb7978f408ca11bb6fe85e8bc4 --- /dev/null +++ b/inquisitive/sources/test/1115.json @@ -0,0 +1 @@ +[{"text": "Art Shell was fired as coach of the Los Angeles Raiders Thursday and will be replaced by assistant Mike White."}, {"text": "Shell, an American Pro Football Hall of Famer player with the Raiders who coached the team for six years, was the first black coach in modern National Football League history. He had been with the Raiders for 27 seasons as a player, assistant and coach."}, {"text": "The team called a 1 p.m. (2100 GMT) news conference to discuss the changes."}, {"text": "'The Raiders expressed gratitude and sincere thanks to Art Shell for his tremendous contribution to the excellence of the organization throughout his 27 years as a Hall of Fame offensive tackle, as an assistant coach and as the head coach,' a team news release said."}, {"text": "The firing had been expected since the Raiders missed the playoffs with a 9-7 record after being picked as a preseason favorite to reach the Super Bowl."}, {"text": "Shell, who along with Minnesota's Dennis Green, were the only two black NFL head coaches last season. Shell became the seventh NFL coach to leave since the 1994 season began."}, {"text": "Shell succeeded Mike Shanahan as the Raiders' coach following the fourth game of the 1989 season. Shell's record with the Raiders was 56-41 and the team made the playoffs in three of his five full seasons."}, {"text": "White, a former coach at the University of California and Illinois University, was Shell's offensive line coach the past two years and has been with the team since 1990. He was to be at the news conference Thursday."}, {"text": "The Raiders were knocked out of the playoffs on the last day of the regular season after a 19-9 loss to Kansas City at the Coliseum."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1116.json b/inquisitive/sources/test/1116.json new file mode 100644 index 0000000000000000000000000000000000000000..538fd491516f1bca8c56323f2bd3cb0560fa8136 --- /dev/null +++ b/inquisitive/sources/test/1116.json @@ -0,0 +1 @@ +[{"text": "The leaders of Egypt, Israel, Jordan and the Palestinians met in Cairo on Thursday for an unprecedented summit to revive the faltering peace process or face a further descent into bloodshed."}, {"text": "The summit was a dramatic show of unity between Israel and its three Arab peace partners. But disillusionment with the Israel-PLO agreement runs deep, and their ability to stem murderous attacks by Islamic militants is uncertain at best."}, {"text": "Israeli Prime Minister Yitzhak Rabin and PLO chairman Yasser Arafat, the key players, will find it difficult to make the necessary concessions since their positions are already precariously weak."}, {"text": "The meeting got under way after sundown at the Ittahadiya presidential palace with a meal to break the daylong fast Muslims observe during the holy month of Ramadan. Prime Minister Atef Sedki of Egypt sounded a positive note as he entered the palace."}, {"text": "'I am optimistic,' he said. 'I think there will be a good result from this meeting.'"}, {"text": "Israeli officials said they hoped the meeting would produce a strong condemnation of terrorism, and Foreign Minister Shimon Peres said he expected the other foreign ministers and PLO leaders to meet next week in Washington to push forward the peace talks."}, {"text": "The group also was expected to agree on a statement pledging them to greater economic cooperation, sources close to the talks said on condition of anonymity."}, {"text": "The three visiting leaders met with President Hosni Mubarak separately before the summit, but no one commented on the meetings."}, {"text": "Earlier Thursday in Jerusalem, Rabin made it clear that an end to attacks on Israelis was the key to expanding autonomy in the West Bank and holding Palestinian elections, both elements of the Israeli-PLO accord signed in September 1993."}, {"text": "Arafat's government must 'make sure that the territory they rule -- Gaza and Jericho -- is not used as shelter, or a place to prepare, incite and execute attacks,' Rabin told members of his Labor Party before he left for Cairo."}, {"text": "'Their ability to meet it will decide more than anything both the speed and possibility of progress in implementing the solution of the Palestinian-Israeli conflict,' he said."}, {"text": "The Palestinians will push Israel to end the closure of Palestinian territories that it imposed after a Jan. 22 suicide bombing killed 21 Israelis, said Arafat adviser Nabil Abu Irdeineh. He also added a long list of demands left unresolved since the agreement was signed."}, {"text": "'The success of the summit depends on the lifting of closure, redeployment of the Israeli army from populated areas, the release of prisoners, and halting of the expansion of settlements,' he said."}, {"text": "The 1993 pact requires the Israeli army to pull back from Palestinian towns in the West Bank to make way for elections, and for the release of Palestinian prisoners. None of this has happened amid the persistent violence."}, {"text": "The Palestinians also thought the pact would freeze the expansion of Jewish settlements on occupied land. But Israel is adding thousands of homes to the Jewish enclaves."}, {"text": "Israeli officials, meanwhile, said they would consider easing the closure to enable Ramadan observance."}, {"text": "'It can be assumed that starting next week the closure will be eased because of Ramadan. We are not interested in punishing the Palestinian population,' Police Minister Moshe Shahal said on Israel television Thursday."}, {"text": "All four leaders stand to gain from the summit."}, {"text": "Jordan's King Hussein has been criticized at home for rushing into a treaty with Israel before Syria settled its quarrel. The summit could reflect Hussein's growing role as a regional broker."}, {"text": "Mubarak, meanwhile, bolsters his image as a peacemaker, currying favor with his American patrons. He's also confronted by an Islamic insurgency and has much to lose by a surge of Muslim extremism in Gaza, which lies on Egypt's Sinai border."}, {"text": "For Arafat and Rabin, their political lives depend on the agreement's success. Both have seen their popularity plummet as the expected fruits of the pact failed to materialize: jobs and independence for the Palestinians, security for the Israelis."}, {"text": "At another level, the summit marks an acceptance of Israel by Arab countries unimaginable just a few years ago. Israel has typically shied away from multilateral meetings, preferring to negotiate with Arab countries one at a time."}, {"text": "Missing at the summit was Syrian President Hafez Assad, who refuses to meet with Israeli leaders before he has a commitment for the return of land captured by Israel in 1967."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1117.json b/inquisitive/sources/test/1117.json new file mode 100644 index 0000000000000000000000000000000000000000..e1cced81a77ed41cc2b8175747480c213bc65b5e --- /dev/null +++ b/inquisitive/sources/test/1117.json @@ -0,0 +1 @@ +[{"text": "Spain's Santiago Luna shot a 5-under-par 67 Thursday to take a one-stroke lead after the first round of the dlrs 395,000 Madeira Island Open."}, {"text": "Six players were one stroke back and 68 and eight others were two strokes off the lead at 69. Fifty-two players shot par or better on a spring-like day with little or no wind."}, {"text": "Tied at 68 were Lee Westwood and Andrew Sherborne of England, Bill Malley of the United States, Jesus Maria Arruti of Spain, Alberto Binaghi of Italy and Paul Lawrie of Scotland."}, {"text": "Scotland's Andrew Coltart headed a group of eight at 69."}, {"text": "Defending champion Mats Lanner of Sweden couldn't take advantage of the low-scoring conditions and posted a 10-over 82."}, {"text": "Luna had seven birdies and with two bogeys and was satisfied with his play."}, {"text": "'The golf course is in good condition, but the greens are very fast, a bit dangerous,' he said."}, {"text": "The tournament -- the third this season on the PGA European tour but the first in Europe -- is being played on the hilly par-72, 6,606-yard (6,039 meter) Madeira Golf Club, located on a volcanic Portuguese island group situated 600 miles (1,000 kilometers) southwest of Lisbon."}, {"text": "The course is perched on a grouping of hills at around 2,300 feet (700 meters) above sea level."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1118.json b/inquisitive/sources/test/1118.json new file mode 100644 index 0000000000000000000000000000000000000000..e5b0f96cccecad6381e669233af34f0e2dd46fe0 --- /dev/null +++ b/inquisitive/sources/test/1118.json @@ -0,0 +1 @@ +[{"text": "Along with the stalled Israel-PLO talks, Mideast leaders Thursday planned to tackle Israel's even slower-paced negotiations with Syria. But not even optimists expected progress."}, {"text": "President Hafez Assad, Israel's most adamant foe, wasn't even invited to the summit of Israel, Jordan, Egypt and the Palestine Liberation Organization."}, {"text": "'It seems to me that although Assad has left behind the process of war, he has yet to enter the peace process and is in a stage of political bachelorhood,' Foreign Minister Shimon Peres told Israeli army radio."}, {"text": "'He must decide when he wants to enter the next step,' he added."}, {"text": "Syrian reaction to the meeting was muted. There was no official reaction, and Syrian newspapers kept up their standard criticism of Israel, blaming it for the deadlock in the negotiations."}, {"text": "'Israel plays the role of the triumphant in the peace process and deals with Arabs as the vanquished,' the government-owned newspaper Al-Thawra said Thursday."}, {"text": "Assad has repeatedly turned down Israeli Prime Minister Yitzhak Rabin's requests for a meeting to try to strike a deal similar to those reached with the Palestinians and Jordan."}, {"text": "Assad has said no such meetings will be possible before he has a commitment from Rabin for the return of the Golan Heights, a strategic plateau which Israel captured in the 1967 war."}, {"text": "Syria's participation, however, is crucial for a comprehensive peace. Lebanon, under the thumb of Damascus, will follow Syria's lead. Syria also has influence over opponents to the peace process."}, {"text": "Islamic Jihad, which claimed responsibility for a Jan. 22 suicide bombing that killed 21 Israelis, is based in Damascus. So are several anti-Arafat PLO groups that consider the peace accord as a sellout."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1119.json b/inquisitive/sources/test/1119.json new file mode 100644 index 0000000000000000000000000000000000000000..9b4421ce8e9516ef3739c6a5c65430d51c7d0eff --- /dev/null +++ b/inquisitive/sources/test/1119.json @@ -0,0 +1 @@ +[{"text": "Delta Air Lines Inc. and British-based Virgin Atlantic Airways won final federal approval Thursday for a joint ticketing deal that gives Delta its long-sought access to London's Heathrow Airport."}, {"text": "The Department of Transportation had been expected to approve the agreement five months ago, but took no action. Delta, which expressed anger at the time, said Thursday the DOT gave no indication why it was giving permission now."}, {"text": "Richard Mintz, a DOT spokesman in Washington, said the government decided the agreement would benefit passengers on both sides of the Atlantic."}, {"text": "Mintz declined to comment specifically on the delay. Many industry analysts have suggested that the government hoped to pressure Great Britain to give U.S. carriers more access to the British market."}, {"text": "The deal with Virgin is a 'code sharing' agreement similar to arrangements Delta has with other overseas carriers. In such deals, an airline buys a block of seats on the other carrier's flights, then sells them to travelers through its own marketing system."}, {"text": "The agreement calls for Delta to buy about dlrs 150 million worth of seats a year, according to Virgin. Delta spokesman Todd Clay said that figure was consistent with the amount of business it expects on the U.S.-London flights."}, {"text": "London-bound Delta passengers from seven U.S. cities -- Los Angeles, Newark, New York, Orlando, Miami, San Francisco and Boston -- will fly on Virgin jets. Delta will continue to use its own planes to fly to London's Gatwick Airport from Atlanta and Cincinnati."}, {"text": "Delta has struggled financially in the trans-Atlantic market since it became a major player with the 1991 acquisition of Pan American World Airways' European business. The Pan Am routes did not include any to Heathrow, a major gateway to Europe."}, {"text": "'We were at a competitive disadvantage,' Clay said, noting that rivals United Airlines and American Airlines fly in and out of Heathrow."}, {"text": "The airlines said they would put the joint deal in effect as soon as possible."}, {"text": "'This agreement will strengthen competition among all carriers serving the U.S. and U.K.,' Delta Chairman Ronald W. Allen said. 'We see it making Delta stronger in the trans-Atlantic marketplace, while enhancing our efforts to make these assets consistently profitable.'"}, {"text": "Virgin Chairman Richard Branson said the agreement allows his company to 'remain independent and competitive in the face of global alliances, while giving our customers all the benefits of flying with a major carrier.'"}, {"text": "The Delta-Virgin agreement previously was approved by the British government and the U.S. Justice Department."}, {"text": "Also Thursday, the DOT gave authorization for American Airlines to fly between Chicago and Birmingham, England, and for Tower Air to fly between New York and London's Stansted Airport."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1120.json b/inquisitive/sources/test/1120.json new file mode 100644 index 0000000000000000000000000000000000000000..2ce060f98fc2b306e7047984b2afb0aa2d332eea --- /dev/null +++ b/inquisitive/sources/test/1120.json @@ -0,0 +1 @@ +[{"text": "A projected federation of Muslims and Croats in Bosnia is in danger of falling apart as the prospect of a wider war haunts the already bloodied Balkans, a top State Department official said Thursday."}, {"text": "Due to meet this weekend with Muslim and Croat leaders in Munich, Germany, the official, Assistant Secretary of State Richard Holbrooke, said Bosnian Serbs likely would cross into Croatia and fight alongside Serbs there in the event of a conflict over a breakaway Croatian Serb enclave."}, {"text": "Croatia has threatened to expel U.N. peacekeepers, but a former U.N. commander in Bosnia predicted the threat would not materialize."}, {"text": "'The general opinion is that the Croats don't have the military ability to achieve anything significant against the Krajina Serbs,' Lt. Gen. Michael Rose said. Krajina is the state proclaimed by Croatia's rebellious Serb minority."}, {"text": "Holbrooke appeared apprehensive as he spoke with reporters at the State Department about the Balkans and his coming diplomatic effort. Holbrooke is trying to salvage the federation formed last March by Bosnian Muslims and Croats."}, {"text": "'Negative events on the federation would have a deleterious effect on an already dangerous situation,' he said. 'We're at a pretty critical time in the situation in the Balkans.'"}, {"text": "Meantime, Bosnian Serbs are refusing to negotiate with the Muslim-led government on the basis of a map dividing the country into two ethnic zones, paralyzing a peace plan proposed by the United States, Britain, France, Germany and Russia."}, {"text": "Using the map, a zone held jointly by Muslims and Croats, would control 51 percent of Bosnia. Serbs would control the country's remaining 49 percent."}, {"text": "After nearly three years of war, forces of Bosnia's Serb minority hold 70 percent of the former Yugoslav republic. They rejected the dual-zone map on the ground it would leave them with economically and politically weak fragments of the country."}, {"text": "With the peace plan stalled, the United States is focusing on the projected Muslim-Croat federation. But Holbrooke said it is in jeopardy 10 months after its creation."}, {"text": "'They're under extreme strain, and the strain is pulling them apart,' he said."}, {"text": "The two sides have failed to merge their armies or to implement other joint arrangements. Holbrooke said he would take an 'action plan' with him to Munich and will be joined by British, French, German and Russian diplomats."}, {"text": "William Perry, the U.S. defense secretary, will attend the meetings as well."}, {"text": "'The job is to assist and advise the federation in creating a unified military command out of two armies that recently fought each other but must cooperate on the ground,' Holbrooke said."}, {"text": "The United States will contribute an unspecified amount of money, Holbrooke said. 'We also are going out around the world leading an effort to get more funds for the federation from other countries. We were going to go to Japan, but the earthquake made us delay the trip for obvious reasons. And we're working with the Germans, the Austrians and others to try to form more support.'"}, {"text": "Secretary of State Warren Christopher urged Bosnia's Muslims and Croats to give 'substantive content' to the federation and said the United States intends to help make it work."}, {"text": "'We're very anxious that that process move forward,' Christopher told reporters during a joint news conference with Prime Minister Waldemar Pawlak of Poland. 'It is significant, it can be very valuable. . We want to make sure the federation moves beyond a concept to having the largest amount of substantive content.'"}] \ No newline at end of file diff --git a/inquisitive/sources/test/1121.json b/inquisitive/sources/test/1121.json new file mode 100644 index 0000000000000000000000000000000000000000..96420e6d8565a0af97cda5e5d20dd60345d92d49 --- /dev/null +++ b/inquisitive/sources/test/1121.json @@ -0,0 +1 @@ +[{"text": "If it hadn't been for the authorities, lots of the ruddy-faced locals would still be standing on the dikes, braving the stiff wind and trying to just stare the waters down."}, {"text": "With most of them living below sea level, the Dutch have been battling the principle that water runs downhill for centuries."}, {"text": "'If the authorities hadn't told people to leave, nobody would have left,' Dirk Roodbeen, who grew up among the dikes in nearby Casteren, said Thursday."}, {"text": "Anticipating the worst flood disaster since the 1953 North Sea flood that killed 1,800 people, officials here have ordered everyone in this city of 33,000 out as the swollen Maas and Waal rivers threatening to burst their dikes in this below-sea level polder region."}, {"text": "Tiel Mayor Ed van Tellingen said the financial losses in the evacuated area may run up to 700 million guilders (dlrs 409 million) a week, but that isn't likely to uproot this community among the fruit orchards and cattle pastures in the Gelderland province."}, {"text": "'People are very levelheaded. There is an attitude that `it's going to be all right in the end,' ' Roodbeen, an ambulance driver, said."}, {"text": "'You have to have faith in the water,' said Jack Benschop before leaving his home here."}, {"text": "'Fear of the water just doesn't help around here,' added retiree Johannes Serbee, survivor of the 1926 and 1953 floods. He too left, but reluctantly."}, {"text": "'I've heard no one say they will not come back immediately,' said Mayor Van Tellingen."}, {"text": "'You cannot fathom what it mean to be away from home and hearth.'"}, {"text": "Some of the dikes here in Gelderland province date from the 13th century."}, {"text": "Villages built their churches on high points. And when rivers periodically overflowed the dikes and flooded the land, everyone took refuge in the church, man and beast."}, {"text": "So when the dikes were threatened and the people fled this week, naturally the cattle went along. Tens of thousands of them were evacuated by truck and train."}, {"text": "Flooding has always been a part of life in this lowland region, about 100 kilometers (62 miles) from Amsterdam."}, {"text": "As a kid Roodbeen longed for the summers after floods when the new shallow ponds made ideal wading pools."}, {"text": "Even pensioner Ab Bouman, standing outside a Tiel wine shop before the evacuation deadline, was considering the advantages of a flood."}, {"text": "'All the wine labels will be unglued and I will be buying the best wine for the cheapest price,' he said."}, {"text": "'No,' retorted the wine shop owner. 'The worst wine for the top prices.'"}] \ No newline at end of file diff --git a/inquisitive/sources/test/1122.json b/inquisitive/sources/test/1122.json new file mode 100644 index 0000000000000000000000000000000000000000..ffef09a82121a64723d5ece5637d3ada252ac9ed --- /dev/null +++ b/inquisitive/sources/test/1122.json @@ -0,0 +1 @@ +[{"text": "The rate at which AIDS is spreading in the United States has leveled off and the number of new cases reported every year is falling, health officials said Thursday."}, {"text": "The report from the Centers for Disease Control and Prevention came just three days after the CDC announced that AIDS is now the leading killer of Americans ages 25 to 44."}, {"text": "Since the early 1980s, when AIDS cases snowballed by 200 percent a year as it spread through the white homosexual population, the disease is stabilizing at a 3 percent annual increase under an old definition of the disease, according to Dr. John Ward, the CDC's chief of HIV-AIDS surveillance."}, {"text": "'It's not growing as rapidly as in earlier years, but the rate is still unacceptably high,' he said. He predicted a similar increase in 1995."}, {"text": "The AIDS definition was expanded in 1993 to reflect the toll on women, and people with tuberculosis or depressed immune systems."}, {"text": "Last year, 80,691 new AIDS cases were reported, down from 106,618 the previous year, the CDC said."}, {"text": "'The epidemic is slowing, and we can take comfort in that -- but small comfort,' Ward said."}, {"text": "Together, the 1994 and 1993 figures represent more than 40 percent of all 441,528 AIDS cases reported since 1981, he pointed out."}, {"text": "More than half of the 1994 cases resulted from the 1993 redefinition of AIDS."}, {"text": "That demonstrates the disease's shift from the once-traditional gay male population to heterosexuals, women, blacks and Hispanics, and those living in the South and Northeast, according to Ward."}, {"text": "'This isn't a disease that's staying in one population,' said Troy Petenbrink of the National Association of People with AIDS."}, {"text": "Children with AIDS were one aspect of the report that surprised the CDC, Ward said. Their numbers jumped 8 percent, from 942 in 1993 to 1,017 last year. But the rate should soon start to slow as more pregnant women use the anti-AIDS drug AZT to protect their babies from infection, he said."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1123.json b/inquisitive/sources/test/1123.json new file mode 100644 index 0000000000000000000000000000000000000000..437ea2e6d67f30a3731963fdc5b8fffeec2d6d96 --- /dev/null +++ b/inquisitive/sources/test/1123.json @@ -0,0 +1 @@ +[{"text": "The government will free five IRA convicts from Irish jails on Friday, raising the prisoner issue again as the Northern Ireland peace process comes under threat."}, {"text": "The early releases, confirmed Thursday night, will be the second in response to the Irish Republican Army cease-fire five months ago. Nine IRA prisoners were given early release last month."}, {"text": "Pat Doherty, vice president of the IRA's Sinn Fein political allies, welcomed the announcement and said, 'I hope the British government will follow suit and free all the political prisoners.'"}, {"text": "On Wednesday, the Anglo-Irish peace effort came under threat when a leaked document dealing with proposals for a Northern Ireland settlement alarmed unionist politicians who represent the pro-British Protestant majority in Northern Ireland."}, {"text": "Members of the Ulster Unionist Party, whose nine votes are crucial to British Prime Minister John Major in the House of Commons, were outraged by a report in The Times of London that the two governments envisioned cross-border agencies in which unionists would be compelled to participate."}, {"text": "Major took to the airwaves that night to appeal for time and trust, saying nothing would be imposed on Northern Ireland."}, {"text": "Earlier in the week, the Irish government considered more early releases, but ministers said that 'minor matters of clarification' needed to be settled."}, {"text": "Pamela Kane, the only woman IRA prisoner in the republic, is among those to be freed Friday. She was jailed in 1990 for 10 years for armed robbery and had not been due for release until 1997."}, {"text": "The others to be freed are Pat Flanagan, serving a 10-year sentence for arms possession; John McBride, serving an 18-month sentence for arms possession, and Ken Gaffney and Stephen Sheedy, serving three years for arms possession. All had been due for release no later than May 1996."}, {"text": "Ulster Unionist legislator John Taylor said that Dublin had gone 'much too far' with its decision to go ahead with the releases."}, {"text": "Joe Hendron, of Northern Ireland's mainstream Catholic Social Democratic and Labor Party, welcomed the releases and said it was time Britain's Northern Ireland Office adopted a similar policy."}, {"text": "'I would like to see the same generosity and at the same time keeping in mind the sensitivities of families of people who have been murdered,' he said."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1124.json b/inquisitive/sources/test/1124.json new file mode 100644 index 0000000000000000000000000000000000000000..d521e1456f66b21a2239002ee27b5cb5ce69b60c --- /dev/null +++ b/inquisitive/sources/test/1124.json @@ -0,0 +1 @@ +[{"text": "Thirty-nine countries paid nothing toward their regular U.N. dues in 1994 and only 29 have made payments this year, the United Nations said Thursday."}, {"text": "As of the end of January, member states owed the United Nations dlrs 1.4 billion toward the regular budget and dlrs 2.2 billion for peacekeeping, which is part of a separate assessment."}, {"text": "The top debtors as of Jan. 15 were the United States, which owed dlrs 550 million toward the regular budget and dlrs 220 million toward peacekeeping, and Russia, which owed 62 million toward the regular budget and 507 million for peacekeeping."}, {"text": "Secretary-General Boutros Boutros-Ghali sent out letters on Jan. 1 asking for dues toward the dlrs 1.1 billion 1995 budget, which does not include peacekeeping charges."}, {"text": "The money was due Jan. 31, but only 19 countries paid in full while 10 countries contributed part of their dues. The list of countries paying did not include the United States or Japan, which together provide about a third of the U.N. budget."}, {"text": "Payments for the 1994 budget also fell short."}, {"text": "As of Dec. 31, only 75 of the 185 member states had paid their dues in full, leaving dlrs 480 million owed toward the regular budget. Some dlrs 1.3 billion was also owed for peacekeeping."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1125.json b/inquisitive/sources/test/1125.json new file mode 100644 index 0000000000000000000000000000000000000000..4278407f0534f4218399dc1156b22acc72f887d3 --- /dev/null +++ b/inquisitive/sources/test/1125.json @@ -0,0 +1 @@ +[{"text": "After an unprecedented summit, Israel and three Arab peace partners agreed to resume Israeli-PLO talks next week and set up a series of meetings to further the peace process."}, {"text": "Still, they came up with no new ways Thursday to stop attacks on Israelis by Muslim extremists."}, {"text": "Israel and PLO negotiators will meet again Monday in Cairo, while PLO chief Yasser Arafat and Israeli Prime Minister Yitzhak Rabin will meet Thursday at a border crossing in the Gaza Strip, said Egyptian Foreign Minister Amr Moussa."}, {"text": "Jordan's King Hussein and Egyptian President Hosni Mubarak, along with Arafat and Rabin, also condemned terrorism and agreed to work toward a nuclear-free Middle East."}, {"text": "'The four parties condemned all the outbreaks of bloodshed, terror and violence in the region and reaffirmed their intention to stand staunchly against, and put an end to, all such acts,' the leaders said in a statement read by Moussa."}, {"text": "The meeting represented a dramatic show of unity among Israel and its three Arab peace partners. But despite the declaration, disillusionment with the Israel-PLO agreement runs deep, and the leaders' ability to stem murderous attacks by Islamic militants was uncertain at best."}, {"text": "Rabin and Arafat, the key players, are facing dwindling popularity, and success of the agreement is crucial to their political careers. The Israeli-PLO talks were halted after a Jan. 22 suicide bombing that killed 21 Israelis."}, {"text": "The four also agreed to convene a meeting of the foreign ministers of Israel, Jordan and Egypt and a Palestinian representative in Washington with U.S. Secretary of State Warren Christopher on Feb. 12."}, {"text": "In Washington, Christopher said the summit showed that the four 'are standing together in the pursuit of peace and they are also standing firmly together against those who would try to stop the march towards peace.'"}, {"text": "Thursday's meeting got under way after sundown at the Ittahadiya presidential palace with a meal to break the daylong fast Muslims observe during the holy month of Ramadan."}, {"text": "The three visiting leaders met with Mubarak separately before the summit, but no one commented on the meetings."}, {"text": "Before leaving Jerusalem, Rabin made it clear that an end to attacks on Israelis was the key to expanding autonomy in the West Bank and holding Palestinian elections, both elements of the Israeli-PLO accord signed in September 1993."}, {"text": "Arafat's government must 'make sure the territory they rule -- Gaza and Jericho -- is not used as shelter, or a place to prepare, incite and execute attacks,' Rabin told members of his Labor Party."}, {"text": "For their part, the Palestinians hoped Israel would reopen the Palestinian territories closed since a Jan. 22 boming, said Arafat adviser Nabil Abu Irdeineh."}, {"text": "The Palestinians want Israel to begin withdrawing Israeli troops from Palestinian towns in the West Bank to make way for elections and the release of Palestinian prisoners. They also demand a halt to the expansion of Jewish settlements on occupied land -- even as Israel is adding thousands of homes to the Jewish enclaves."}, {"text": "The summit marked an acceptance of Israel by Arab countries unimaginable just a few years ago. Israel has typically shied away from multilateral meetings, preferring to negotiate with Arab countries one-on-one."}, {"text": "Missing at the summit was Syrian President Hafez Assad, who refuses to meet with Israeli leaders before he has a commitment for the return of land captured by Israel in 1967."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1126.json b/inquisitive/sources/test/1126.json new file mode 100644 index 0000000000000000000000000000000000000000..d40b07eaa1d4d58f4ff9239eac96af6d596a8174 --- /dev/null +++ b/inquisitive/sources/test/1126.json @@ -0,0 +1 @@ +[{"text": "The foreign ministers of Turkey and four Western European nations on Thursday reaffirmed their commitment to a strong relationship."}, {"text": "The British Foreign Office said Foreign Secretary Douglas Hurd met with the foreign ministers of Turkey, France, Germany and Italy to continue an 'intensive but informal dialogue between Turkey and Western European states with a special interest in the region.'"}, {"text": "They also discussed the civil rights situation in Turkey, as well as the need for a negotiated settlement in Cyprus, which has been divided since Turkey invaded in 1974 and occupied the northern sector."}, {"text": "Allegations of abuses by Turkish police are longstanding. Human rights groups claim the Turkish military is escalating a brutal campaign to wipe out villages considered havens for Kurdish rebels who seek an autonomous homeland."}, {"text": "Turkish officials contend uncompromising tactics are necessary to keep the nation of 60 million people together."}, {"text": "A member of the North Atlantic Treaty Organization, Turkey is seeking greater foreign assistance to stabilize its shaky economy and wants membership in the European Union."}, {"text": "The Financial Times quoted French Foreign Minister Alain Juppe as saying after the talks that agreement on a customs union between Turkey and the European Union would be reached next month."}, {"text": "Turkey's parliament is moving slowly on possible changes to the wide powers given to security forces under the law-and-order constitution written after a 1980 military coup."}, {"text": "Turkish Foreign Minister Murat Karayalcin 'emphasized the Turkish commitment to democratic values and outlined the measures the Turkish government is undertaking to reform the constitution and associated legal instruments, and to enforce the civil rights which they provide,' a Foreign Office spokesman said anonymously, in keeping with British practice."}, {"text": "The Financial Times quoted Hurd as saying the discussion on human rights was 'the most substantial' he had ever had with Turkey on the issue."}, {"text": "German Foreign Minister Klaus Kinkel and Italy's Susanna Agnelli attended the talks."}, {"text": "'Ministers reaffirmed their commitment to a strong and developing relationship between Europe and Turkey,' the Foreign Office spokesman said."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1127.json b/inquisitive/sources/test/1127.json new file mode 100644 index 0000000000000000000000000000000000000000..16a8e6f25ccd3b3fdf953e7273177ca419898e5e --- /dev/null +++ b/inquisitive/sources/test/1127.json @@ -0,0 +1 @@ +[{"text": "Fifty-four years after his act of courage, an obscure Japanese diplomat named Chinue Sugihara is finally being acknowledged as one of World War II's great heroes for having saved some 6,000 Jews from Nazi death camps."}, {"text": "Sugihara has been honored in Israel, and there is a memorial plaque and a street named after him in Lithuania, where in August of 1940 he feverishly signed thousands of transit visas that kept Jews from falling into German hands."}, {"text": "In the latest gesture, announced on Thursday at a reception for Sugihara's 81-year-old widow, Yukiko, the American Jewish World Service said it has raised dlrs 50,000 for a Kobe earthquake relief fund that has been named in Sugihara's honor."}, {"text": "Kobe, by coincidence, is where many of the Jews rescued by Sugihara in Lithuania wound up, before they were sent on to other countries as Japan itself went to war in late 1941."}, {"text": "The money will go mainly for medical supplies in the quake-ravaged port city, said Andrew Griffel, executive director of the AJWS, who himself survived the Holocaust as a 'hidden child' in Poland."}, {"text": "Yukiko Sugihara, who is visiting the United States with her son, Hiroki, recalled how her husband, as Japan's consul general in Lithuania, was ordered by Tokyo to ignore the plight of the Jews, but decided after a unanimous vote of his family to issue visas guaranteeing them safe passage across the Soviet Union to Japan and beyond."}, {"text": "Mrs. Sugihara said he signed papers 12 to 16 hours a day for a month, causing painful hand cramps. After all foreign diplomats were expelled by the Soviets, 'he was still signing and handing out visas through the window of the train' as it left the station on Sept. 1, 1940, she said."}, {"text": "Sugihara's defiance of orders from Tokyo eventually would cost him his diplomatic career, and he died in relative obscurity in 1986. Only in recent years have his deeds been honored by the Japanese government."}, {"text": "While he is sometimes called the 'Japanese Schindler,' Holocaust survivors and others at the reception rejected any glib comparison with the German industrialist whose rescue of more than 1,000 Jews in Czechoslovakia was depicted in the 1993 film, 'Schindler's List.'"}, {"text": "The 6,000 people Sugihara saved were second in number only to the tens of thousands of Jews rescued in similar manner by Swedish businessman Raoul Wallenberg. But as some speakers noted, Wallenberg had the backing of his government, which Sugihara did not."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1128.json b/inquisitive/sources/test/1128.json new file mode 100644 index 0000000000000000000000000000000000000000..5c11c7443fcd5d8b62713f06130696f4fcdce8c5 --- /dev/null +++ b/inquisitive/sources/test/1128.json @@ -0,0 +1 @@ +[{"text": "Christian Fittipaldi of Brazil, the nephew of two-time Indianapolis 500 winner Emerson Fittipaldi, has signed a contract to drive an Indy-car for Walker Racing this year."}, {"text": "The younger Fittipaldi, 24, a Formula One regular the past three years, has never driven an Indy-car. But the son of one-time Formula One driver Wilson Fittipaldi has known Walker for many years."}, {"text": "'When I was Wilson's chief mechanic in Formula One and Christian was a little boy, I told him that I would someday own a race team and that he would drive for me,' Walker said Thursday after making the announcement that Fittipaldi would team with holdover Robby Gordon."}, {"text": "'It's great to have Christian drive in this series,' Walker said. 'He and Robby will make great teammates.'"}, {"text": "Fittipaldi, considered one of the bright young stars of European racing, will be introduced to oval tracks, including the Indianapolis Motor Speedway, this year."}, {"text": "'The 1995 season is going to be really fun,' he said. 'I'm sure Uncle Emerson can help me a lot, especially on the ovals. I think Walker Racing will be very competitive. The team is in a strong position this year. . Knowing all of Robby Gordon's achievements, he's one of the quickest guys out there. He will be a nice gauge for me.'"}, {"text": "The 16-race Indy-car season opens March 5 with the Miami Grand Prix, a new event in the streets of downtown Miami."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1129.json b/inquisitive/sources/test/1129.json new file mode 100644 index 0000000000000000000000000000000000000000..0c575fb53a290cec441d8aa61ed7b6c610270ade --- /dev/null +++ b/inquisitive/sources/test/1129.json @@ -0,0 +1 @@ +[{"text": "Princess Diana, who was widely tipped to visit Kobe during her trip to Japan next week, will not after all go to the earthquake shattered city, aides said Thursday night."}, {"text": "'We have been advised by the British Embassy in Tokyo that it would be more appropriate for her to express her obvious concern for the victims by doing something in Tokyo,' said a statement by her office at St. James's Palace in London."}, {"text": "But The Times of London said Friday that observers have suggested the real reason is concern by Japanese authorities that she might upstage Japan's imperial family."}, {"text": "The paper noted the family has been widely criticized for its lackluster show of support for the victims of the quake, which struck Jan. 17, killing 5,104 people. Six more are listed missing."}, {"text": "The Times added that Japanese and British diplomats had denied the suggestion. It quoted an unnamed official at the British Embassy in Tokyo as saying Thursday: 'The princess simply decided she did not wish to overburden the local authorities in Kobe.'"}, {"text": "Diana, 33, who is separated from her husband Prince Charles, the heir to the British throne, is scheduled to fly to Japan on Sunday. She will be briefed on the quake by officials of the Japan Red Cross Society and will meet with Emperor Akihito and his wife."}, {"text": "It was never officially confirmed that Diana would visit Kobe."}, {"text": "But The times said that up until Tuesday night a visit to Kobe by her was still being negotiated by British royal aides and Japanese officials. It said members of the British media preparing to accompany her to Japan had been told unofficially that the Kobe visit would take place."}, {"text": "The Times said Diana was originally intended to pay a working visit to Tokyo as a charity ambassador from Feb. 6-9 but expressed interest in seeing relief efforts in Kobe and meeting survivors."}, {"text": "The princess is patron of the British Red Cross, which has launched a relief fund to help quake survivors."}, {"text": "A visit to Kobe by Diana would have been at her initiative and expense but depended on official Japanese approval, the paper said. But it said that from the time British royal aides first aired the suggestion, Japanese authorities discreetly signaled that the idea was not entirely welcome."}, {"text": "It said some spoke of danger from potential after-shocks and an influenza epidemic while others pointed to logistical difficulties in shepherding such a high profile VIP around the ruined city."}, {"text": "But it added: 'The real reason, commentators say, may be a combination of factors, in particular the unusually harsh criticism by popular Japanese magazines of the Japanese imperial family's response to the quake."}, {"text": "'The Emperor and Empress visited Kobe on Tuesday for the first time since the quake. The hastily arranged trip was announced two days after the Princess of Wales let her own interest be known.'"}] \ No newline at end of file diff --git a/inquisitive/sources/test/1130.json b/inquisitive/sources/test/1130.json new file mode 100644 index 0000000000000000000000000000000000000000..3dcc2faf770b93710af85dec32a78397b0af6c6f --- /dev/null +++ b/inquisitive/sources/test/1130.json @@ -0,0 +1 @@ +[{"text": "Health officials said Friday they are investigating why a fungicide that should have been cleaned off was found on apples imported from the United States."}, {"text": "In a random sampling of apples purchased at shops in the Tokyo area, two apples imported from Washington State were found to have trace amounts of the fungicide, health officials said."}, {"text": "'This is not a safety issue by any means,' said U.S. embassy spokesman Bill Morgan. 'It's a technical one. This fungicide is also commonly used by farmers in Japan.'"}, {"text": "Several stores in Tokyo that stocked apples packed by Apple King, a packer in Yakimo, Washington state, were voluntarily recalling the apples Friday because of possible health hazards, a city official said."}, {"text": "But a spokesman for Japan's largest supermarket chain, Daiei Inc., said the company has no plans to remove U.S. apples from its shelves."}, {"text": "'We buy directly from reliable packers, and do our own product quality control,' said Haruko Toyama of Daiei."}, {"text": "She added that last month the chain has sold 45,000 cases, each one 19 kilograms (42 pounds), of U.S.-grown apples."}, {"text": "The chemical is used by both Japanese and American farmers while growing the apples, but is supposed to be removed after the apples are harvested."}, {"text": "The amounts found on the apples, both Golden Delicious from Washington State, would not have a harmful effect on humans, said Satoshi Takaya of the Food and Health division at the Health Ministry."}, {"text": "The ministry has asked the U.S. exporter, through the U.S. embassy in Tokyo, to explain why the chemical was not washed from the apples."}, {"text": "After years of U.S. efforts, American apples went on sale Japan on Jan. 10. The U.S. imports were allowed on the condition that American growers follow Japan's rigorous safety procedures."}, {"text": "Of the two apples with the fungicide, one had 0.12 parts per million of the chemical, and the other had 0.1 ppm."}, {"text": "In Japan, farmers are allowed to use up to 3.0 ppm of the chemical in cultivation, but it must be removed after harvest."}, {"text": "A total of 6,116 tons of U.S.-grown apples were imported to Japan last month and sold across Japan, according to the Japanese agriculture ministry figures. U.S. growers said they hope to ship an additional 9,000 tons of apples in the next two months."}, {"text": "Japan ostensibly opened its apple market to foreign imports in 1971, but in practice banned most imports with a tangle of red tape."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1131.json b/inquisitive/sources/test/1131.json new file mode 100644 index 0000000000000000000000000000000000000000..28ba7750583e31ea31c62c0ee2da8f35fd8fd86d --- /dev/null +++ b/inquisitive/sources/test/1131.json @@ -0,0 +1 @@ +[{"text": "Despite talks to end the 11-year-old ethnic war, the government plans to spend more money on fighting the Tamil separatists this year."}, {"text": "The budget that will be presented next week is likely to hike defense spending from rupees 29 billion (dlrs 591 million) to rupees 33 billion (dlrs 673 million), according to Deputy Defense Minister Anuruddha Ratwatte."}, {"text": "Peace talks that began last October have made little progress as the rebels have been adding to their demands, President Chandrika Kumaratunga has said."}, {"text": "The war for a homeland for the nation's 3 million minority Tamils has claimed more than 34,000 lives."}, {"text": "'If this war ends forthwith, this colossal sum could be utilized toward the country's development strategy,' Ratwatte said at a ceremony during a bank opening, the state-owned Daily News reported Friday."}, {"text": "In her inauguration speech in parliament last month, President Kumaratunga said ending the conflict would save two percent of the gross domestic product."}, {"text": "The socialist People's Alliance was elected to office last August on a pledge of ending the war. The Tamils say they are subjected to discrimination by the majority Sinhalese."}, {"text": "The alliance also promised to introduce welfare for the poor and agricultural subsidies, privatize state ventures and continue a free market approach while safeguarding local industry."}, {"text": "When the budget is presented in parliament Feb. 8, economists want to see how Ms. Kumaratunga expects to reduce a soaring deficit and without reneging on her election promises."}, {"text": "The 1994 deficit is estimated at 10 percent of the gross domestic product, or 76 billion rupees (dlrs 1.55 billion)."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1132.json b/inquisitive/sources/test/1132.json new file mode 100644 index 0000000000000000000000000000000000000000..8a2465a5115f3bc71cb0de392e79eb93b799a5f0 --- /dev/null +++ b/inquisitive/sources/test/1132.json @@ -0,0 +1 @@ +[{"text": "Renegade Muslim forces allied with rebel Serbs blocked a convoy of aid for 120,000 beleaguered civilians in northwestern Bosnia, the U.N. aid agency reported Friday."}, {"text": "Fighting in that area, particularly around Velika Kladusa, headquarters of the rebel Muslim's fight against Bosnia's Muslim-led government, is threatening a country-wide truce."}, {"text": "Serb fighters from neighboring Croatia and the rebelious Muslims are not party to the cease-fire, designed as a prelude to resuming peace negotiations."}, {"text": "But international efforts to get negotiations started collapsed last week due to Bosnian Serb intransigence. Bosnia's Muslim government, impatient with U.N. inability to halt fighting, has warned the truce could collapse entirely."}, {"text": "U.N. officials expressed concern Thursday about an apparent increase of Croatian Serb tanks, artillery and troops in the contested northwest Bihac region. Most blame for the fighting lies with them, U.N. spokesman Michael Williams said."}, {"text": "Overnight, the area was reported relatively quiet. But two people were killed and six wounded Thursday in the government-controlled town of Buzim, 30 kilometers (20 miles) northwest of Bihac. There was no word on who fired."}, {"text": "The new commander of U.N. forces in Bosnia, Lt. Gen. Rupert Smith, visited the Bihac area Thursday, meeting with Bangladeshi peacekeepers. On Friday, he was in Gornji Vakuf, U.N. peacekeepers' headquarters in central Bosnia."}, {"text": "Smith took over the post from fellow Briton Sir Michael Rose last week."}, {"text": "The blocking of the convoy carrying 97 tons of medical supplies and other aid was a fresh example of the frustrations the United Nations faces in its primary mission of getting aid to besieged civilians."}, {"text": "Rebel Muslim forces demanded half the supplies, arguing that 80,000 of the 120,000 people in the Bihac region support them, said Kris Janowski, spokesman for the U.N. High Commissioner for Refugees. They usually get 20 percent of such convoy supplies."}, {"text": "U.N. aid officials refused, and the convoy returned to Zagreb, Croatia."}, {"text": "Despite the gloomy prospects for lasting peace, diplomatic efforts continued."}, {"text": "The leader of Bosnian Serbs loyal to the Muslim-led government met with senior U.S. diplomat John Menzies in Sarajevo on Thursday to discuss possible participation in the peace process."}, {"text": "Mirko Pejanovic said on Bosnian radio that such participation would rob Bosnian Serb leaders of their claim to represent all Serbs."}, {"text": "U.S. Assistant Secretary of State Richard Holbrooke was to hold weekend talks in Germany on bolstering a Croat-Muslim federation in Bosnia."}, {"text": "The federation, backed by the United States, is 10 months old and managed to end bitter fighting between Bosnian Croats and Muslims, who were allied against the Serbs at the outset of war 34 months ago."}, {"text": "But the two sides have done little more than institutionalize a cease-fire."}, {"text": "'Negative events on the federation would have a deleterious effect on an already dangerous situation,' Holbrooke told reporters at the State Department in Washington. 'We're at a pretty critical time in the situation in the Balkans.'"}] \ No newline at end of file diff --git a/inquisitive/sources/test/1133.json b/inquisitive/sources/test/1133.json new file mode 100644 index 0000000000000000000000000000000000000000..ab91826c7aefa63a9b938597707f8089b95e5e87 --- /dev/null +++ b/inquisitive/sources/test/1133.json @@ -0,0 +1 @@ +[{"text": "The U.N. expert investigating Israeli human rights violations Friday defended his controversial decision to quit, saying progress in the peace process rather condemnation of Israel was the best way to promote Palestinian rights."}, {"text": "Rene Felber, a former Swiss foreign minister, caused an outcry at the U.N. Human Rights Commission earlier this week by recommending and end to his two-year mission because it was useless to issue reports that weren't acted on."}, {"text": "In addition to focussing attention on the effectiveness of the commission -- which issues dozens of such reports each year -- Felber's action also raised wider questions about whether publicizing abuses is the best way to pressure governments into mending their ways."}, {"text": "'Maybe I said out loud what other people merely think,' Felber told a news conference. 'I don't regret it.'"}, {"text": "'You have to give priority to a political solution. There's no point issuing denunciations if there are no results from these denunciations.'"}, {"text": "'Is it better to condemn or is it better to support a peace process which leads to a concrete solution?' he said. 'For me, I support the concrete solution.'"}, {"text": "Felber said implementation of the 1993 accords, which call for Israel to withdraw its troops from the West Bank to make way for Palestinian elections, must be speeded up. Foreign governments must fulfill their promises of aid to the Gaza Strip, he said."}, {"text": "He warned otherwise there would be an 'explosion' in frustration and hatred, fomented by both Muslim and Jewish extremists who are opposed to compromise."}, {"text": "'I would like to underline that I was profoundly shocked by the oppressive atmosphere that reigned in most of the occupied territories we visited,' he said."}, {"text": "He said in general terms that it was best to criticize human rights violations, but that the Mideast peace process offered an alternative way of promoting respect for basic freedoms."}, {"text": "'I am disappointed that there doesn't seem to be any effort to understand that the political route is possible,' he said of the U.N. commission."}, {"text": "Felber said the commission would have to decide if it wanted to appoint another special investigator to succeed him. He added a separate General Assembly committee which scrutinizes Israeli abuses should continue its work."}, {"text": "Israel traditionally comes under strong fire from the U.N.'s human rights watchdog because of the Arab and Third World majority on the 53-nation body. Felber's investigation was under a procedure reserved for the worst violators, including Iraq, Iran, Burma and Sudan."}, {"text": "The commission's outgoing chairman, Peter Van Wulfften Palthe, said in a newspaper interview that Felber was irresponsible. Arab nations were outraged, leaving only Israel and its ally the United States, supporting him."}, {"text": "Private human rights groups, which devote their resources to publicizing and denouncing violations, were left in shock."}, {"text": "The International Commission of Jurists, a respected body of legal experts, accused Felber of betraying victims of human rights abuse. Amnesty International said scrutiny of Israel must continue to combat widespread torture and abuse."}, {"text": "'My aim was not to drop the victims but to find a solution which improves the situation and improves their rights,' Felber said."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1134.json b/inquisitive/sources/test/1134.json new file mode 100644 index 0000000000000000000000000000000000000000..230693960eb40b0cd1c9a38dbc3ac7e5fee82576 --- /dev/null +++ b/inquisitive/sources/test/1134.json @@ -0,0 +1 @@ +[{"text": "The 33-nation Council of Europe has suspended membership talks with Russia until Moscow stops attacking its breakaway republic of Chechnya."}, {"text": "Voting late Thursday to suspend talks, the Council's parliamentary assembly also condemned 'the indiscriminate and disproportionate use of force by the Russian military.'"}, {"text": "The council was founded in 1949 to defend human rights and parliamentary democracy. It is the oldest of the postwar organizations promoting European unity, and best known for its 1950 human rights convention."}, {"text": "Its core membership of Western European democracies has expanded to include new eastern European democracies -- Bulgaria, the Czech Republic, Estonia, Hungary, Poland, Lithuania, Romania, Slovakia and Slovenia."}, {"text": "Council spokeswoman Henriette Girard said assembly members would demand a ceasefire with Chechnya. She said they would also insist Russia alter its constitution to give its parliament more control over the executive branch."}, {"text": "Since Dec. 11, Russian troops have killed thousands of Chechens, despite obvious internal conflict over the matter in Moscow."}, {"text": "Russia has sought Council membership since May, 1992, but has been repeatedly denied acceptance because of complaints of human rights violations in Russia and its republics."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1135.json b/inquisitive/sources/test/1135.json new file mode 100644 index 0000000000000000000000000000000000000000..24ac762bb5e10cd0554dd3e12348e8a2cf9d03b5 --- /dev/null +++ b/inquisitive/sources/test/1135.json @@ -0,0 +1 @@ +[{"text": "Michael Stich made it clear on Friday that Croatia will have a hard time posting an upset over Germany in its World Group debut when he beat Goran Ivanisevic in four sets in the opening singles."}, {"text": "Ivanisevic struggled with his best weapon, his first serve, allowing the German to win 7-6 (7-3), 4-6, 6-1, 6-4 behind superior ground strokes."}, {"text": "Boris Becker, returning to Davis Cup play after a 2 1/2 year absence, is expected to give Germany a 2-0 lead Friday when he faces unknown Sasa Hirszon in the second singles later Friday."}, {"text": "The slim hopes of Croatia against Germany, a three-time Davis Cup titlist, rested on the shoulders of the hard-serving Ivanisevic. Croatia had hoped the world No. 5 could sweep both his singles against the two German aces."}, {"text": "But Ivanisevic's first serve, one of the most powerful in tennis, deserted him during the last two sets. Stich gained a decisive break in the fourth set at 3-2 after the Croatian fought off five other chances by the German."}, {"text": "'He didn't play badly, but when he has to fight on his serve, then some of his concentration gets lost,' said Stich."}, {"text": "Ivanisevic described the opening-round match against Germany as one of the biggest sporting events in the young country's history. After his loss against Stich, the 23-year-old sounded pessimistic."}, {"text": "'Our opponents are unbelievably good,' he said. 'Even when we lose 5-0, we have nothing to be ashamed about.'"}, {"text": "Becker, who has posted a 33-2 mark in Davis Cup singles, will be facing a German club player ranked 329th in the world in Hirszon."}, {"text": "Croatia will also have a hard time Saturday when Ivanisevic and Hirszon face Becker and Stich in doubles. The two Germans last teamed up to win the gold medal in doubles at the 1992 Olympics."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1136.json b/inquisitive/sources/test/1136.json new file mode 100644 index 0000000000000000000000000000000000000000..45bb423e79409269bbba984c3dfae76b46003a5e --- /dev/null +++ b/inquisitive/sources/test/1136.json @@ -0,0 +1 @@ +[{"text": "Demands that a ban on nuclear tests be completed before an agreement preventing the spread of nuclear weapons is extended are holding up the disarmament process, the Secretary-General for the world's main disarmament forum said Friday."}, {"text": "Linking debates was common during Cold War confrontational days, Vladimir Petrovsky told the Conference on Disarament but was now counter-productive."}, {"text": "Countries should concentrate instead on the progress of each individual step in the nuclear arms elimination process, he said."}, {"text": "The 38-nation conference is currently holding its spring session in this Swiss city with the successful completion of a comprehensive ban on nuclear testing its top priority."}, {"text": "The process has taken on a particular urgency in the run-up to crucial negotiations in New York in April on renewing the Nuclear Non-Proliferation Treaty which prevents the spread of strategic weapons."}, {"text": "The United States wants an indefinite extension of the 25-year-old NPT to avoid the need for further renewals in the future."}, {"text": "But many Third World countries have other ideas. They are dissatisfied nwith the way the treaty has worked and would prefer to see only a short extension."}, {"text": "They want the five declared nuclear powers -- America, Russia, Britain, France and China -- to do more to ban nuclear tests, dismantle their arsenals and provide non-nuclear weapons better security against attacks."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1137.json b/inquisitive/sources/test/1137.json new file mode 100644 index 0000000000000000000000000000000000000000..73ba94d3c4e9a41cc42f5a8b6ea10808105f24e5 --- /dev/null +++ b/inquisitive/sources/test/1137.json @@ -0,0 +1 @@ +[{"text": "Swiss hopes of defeating the Netherlands in the Davis Cup were severely hurt Friday when 15th-ranked Marc Rosset was rushed to hospital with an injured foot."}, {"text": "Rosset abandoned his match against Jacco Eltingh in the second set, while leading 6-4, 2-3. He twisted his foot while running for a forehand volley on his own service game."}, {"text": "Sobbing with pain and disappointment before the home crowd, Rosset limped off the court. He was taken to hospital for X-rays. It was not immediately clear if he would be able to play in the weekend matches."}, {"text": "'I'm not happy about winning in this manner,' Eltingh said. 'It's horrible for Rosset, especially as it happened in his home town.'"}, {"text": "Switzerland's Jakob Hlasek was due to meet the Netherlands' Richard Krajicek later. The matches are the opening singles in the first-round world group tie."}, {"text": "Rosset and Hlasek, ranked 71st, normally team up for the doubles. The reserve members of the squad are Lorenzo Manta and Patrick Mohr, ranked only 238th and 302nd respectively."}, {"text": "'It hurts Switzerland because they have only two good players,' said Stanley Franker, the Dutch coach."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1138.json b/inquisitive/sources/test/1138.json new file mode 100644 index 0000000000000000000000000000000000000000..44ca647b8a8a99ad7b14b3bb7862259362dcf3d2 --- /dev/null +++ b/inquisitive/sources/test/1138.json @@ -0,0 +1 @@ +[{"text": "It's been seven years since France beat England in rugby union, but that hasn't lessened the intensity of the cross-Channel rivalry."}, {"text": "On Saturday, the two teams meet at Twickenham in the game that is expected to decide this year's Five Nations Championship. The buildup has been anything but congenial."}, {"text": "'Playing against France in the Five Nations is like facing 15 Eric Cantonas,' said England front row forward Brian Moore, referring to the French and Manchester United soccer player who attacked a spectator during a game last week. 'They are brilliant, but brutal.'"}, {"text": "Players like Moore, nicknamed 'Pit Bull' by his England teammates, revel in the atmosphere of the France-England games. Last year, he was accused by French coach Pierre Berbizier of orchestrating on-field provocations of the French players, whose succession of penalties resulted in an 18-14 defeat."}, {"text": "Memories of that loss are just some of the many frustrations that have motivated French captain Philippe Saint-Andre for this year's game."}, {"text": "'We've not won for six years,' Saint-Andre said. 'I don't say we've got an inferiority complex, but we do tend to let them dictate the way the game is played. We have got to stamp our authority on the match for a change.'"}, {"text": "Saint-Andre and his teammates are particularly bothered that the French were pressured into dropping Olivier Merle for the game for his head-butt of Ricky Evans in the opener against Wales, while Ben Clarke has been retained by England despite receiving a yellow card for stamping on Simon Geoghegan in its game at Ireland."}, {"text": "'Let's just say we sometimes feel there are double standards involved in eliminating foul play,' Saint-Andre said. 'It certainly gives us an added incentive for winning at Twickenham.'"}, {"text": "England can attribute its winning streak over France to a brutal, forward-led attack that has capitalized on the opponent's lack of discipline. In last year's victory at Parc des Princes, for example, England won without scoring a try and 15 of the 18 points came off penalties."}, {"text": "This year, however, England has changed its tactics, emphasizing a flowing attack led by the backs. England's three tries against Ireland were more than it scored in the entire competition last year."}, {"text": "England manager Jack Rowell said he offered England's players the chance to go back to the kick-and-maul style against France, but they declined."}, {"text": "'The squad wants to stick to what we are trying to play -- more dynamic, handling rugby,' Rowell said."}, {"text": "France has always preferred the wide-open style, so Saturday's game could produce plenty of tries. But Berbizier still isn't convinced."}, {"text": "'In the past . we grew impatient and forgot the basics,' he said. 'We have to remember we cannot rely on French flair to pull us through.'"}, {"text": "With the exception of Olivier Brouzet replacing Merle in the French pack, both lineups are basically unchanged from the teams that won handily two weeks ago, England 20-8 over Ireland and France 21-9 over Wales."}, {"text": "Saturday's other game pits Scotland and Ireland at Murrayfield. Scottish captain Gavin Hastings rebuffed suggestions that the two clubs, plus Wales, had sunk to the level where they could be referred to as the 'second division' of the Five Nations."}, {"text": "'I do not support the idea there are two divisions in the Five Nations,' said Hastings, who will break the Scottish record for international appearances as he takes the field for the 53rd time."}, {"text": "Scotland broke a 10-match winless streak when it beat Canada 22-6 in a Test match two weeks ago, while Ireland's loss to England would have been a rout if the English hadn't squandered three sure tries."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1139.json b/inquisitive/sources/test/1139.json new file mode 100644 index 0000000000000000000000000000000000000000..8b1ee3b6007e70dd2fbd8302db8667ea706a311f --- /dev/null +++ b/inquisitive/sources/test/1139.json @@ -0,0 +1 @@ +[{"text": "Finance ministers and central bank officials of the world's seven largest economies gathered Friday in Toronto for talks expected to focus on the economic woes of Mexico."}, {"text": "The nosedive of the Mexican peso in recent weeks sent a shock wave through the ministries and markets of the world's rich nations, a reminder of just how closely linked the economies of the planet are today and how an economic dwarf can quickly become a giant."}, {"text": "Meeting over dinner Friday night were officials from the Group of Seven, which includes the United States, Canada, Germany, France, Britain, Italy and Japan, along with their central bankers and the chief of the International Monetary Fund."}, {"text": "The officials were scheduled to meet again Saturday morning, part of a regular series of consultations and preparatory to the G-7 summit June 15-17 in Halifax, Nova Scotia."}, {"text": "Some of the Europeans are unhappy at being dragged into what many of them see as a North American problem."}, {"text": "Several European countries abstained from voting for a Mexican rescue package Wednesday at an executive board meeting of the IMF. They complained they had not been adequately consulted before U.S. officials and the IMF worked out the agreement."}, {"text": "That agreement includes dlrs 17.8 billion U.S. in IMF assistance."}, {"text": "President Bill Clinton's plan to provide Mexico with dlrs 40 billion in loan guarantees fell apart after strong resistance from Congress. He subsequently scaled the American participation to dlrs 20 billion from a Treasury fund that he put at the disposal of Mexico through an executive order."}, {"text": "Washington's new treasury secretary, Robert Rubin, will face tough questioning from his G-7 counterparts here, concerned that huge committments of IMF funds to Mexico could drain funds for Eastern Europe."}, {"text": "'There must be a broad understanding that we really and truly are in a new world where we are dependent on other nations in ways that we never were before,' Rubin told reporters in Washington."}, {"text": "A Canadian official, who spoke on condition she not be named, said she expected the meeting to focus on the international institutions and how adequatly they to respond to crisis."}, {"text": "'Are we sure we have the right institutions in place?,' she said. 'Are we sure they are capable of responding to the dynamics of the new economy? I think Mexico has just given us an example of the deficiencies of the system.'"}, {"text": "Rubin said he hoped the G-7 finance ministers would use the crisis in Mexico as a case study that will guide them in deliberations on ways to improve the function of the IMF and other international lending organizations."}, {"text": "IMF chief Michel Camdessus no doubt will be pressed to keep a closer eye on such potential problems as Mexico."}, {"text": "The ministers also are expected to conduct their usual review of the world economic situation and spend a few minutes looking at the situation in Russia and the Ukraine, Canadian officials said."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1140.json b/inquisitive/sources/test/1140.json new file mode 100644 index 0000000000000000000000000000000000000000..4200dec1e9f317552aa9a83098557dccc4b75431 --- /dev/null +++ b/inquisitive/sources/test/1140.json @@ -0,0 +1 @@ +[{"text": "Expanding NATO into eastern Europe would give Russia more security, not less as Moscow fears, the alliance's secretary-general said Friday."}, {"text": "'We are willing to cooperate with Russia,' Willy Claes said. 'We are not trying to isolate Russia. I will sing this every day, if necessary, in order to convince Moscow that we have good intentions.'"}, {"text": "Claes was in Bonn before a Saturday meeting in Munich of Western defense leaders and military chiefs."}, {"text": "NATO is studying how former Soviet allies might join the alliance. It has named no candidates, set no entry dates. But Russia is upset and has put off a broad program of military and political cooperation with NATO."}, {"text": "Moscow is worried of being isolated if NATO takes in Poland, Hungary and others as members. Its bloody intervention in Chechnya has made east European countries especially eager to join because they could then gain the alliance's protection from Russia."}, {"text": "Claes found conciliatory words for Russia even though Western nations have voiced concern about its use of force in Chechnya."}, {"text": "NATO's enlargement would not mean isolation but 'bringing more security to Russia,' he said, because NATO is ready for broad military cooperation and an 'enhanced dialogue' on nuclear arms and security issues."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1141.json b/inquisitive/sources/test/1141.json new file mode 100644 index 0000000000000000000000000000000000000000..68a0f8d44133e12583bb58d4c384fafe79440f4b --- /dev/null +++ b/inquisitive/sources/test/1141.json @@ -0,0 +1 @@ +[{"text": "Three Yugoslavs were honored Friday for their role in saving Jews from the Holocuast."}, {"text": "Since 1953, Gentiles who saved Jews during the Nazi terror have been honored with the title of the Righteous by the Yad Vashem Holocaust museum in Israel."}, {"text": "One savior and the widows of two others received Righteous medals Friday at Belgrade's Jewish Community."}, {"text": "Risto Ristic saved 10 Jewish families -- 36 children and adults -- from a raid by Croat collaborators of the Nazis in 1941 in the town of Bijeljina, now one of the Bosnian towns from which Serbs have brutally expelled many Muslims."}, {"text": "Ristic was tipped about the Croat raid, and urged the families to flee."}, {"text": "'I will never forget what you did for us,' said Rahela Vahal, 61, one of the survivors. 'I did what I felt was my duty,' replied Ristic, a 76-year-old pensioner living in Belgrade."}, {"text": "Only 17,000 of Yugoslavia's 82,000 Jews survived World War II. Most were killed in Ukrainian, Croat or German death camps, but many were simply shot in fields outside towns where they lived."}, {"text": "A second man honored Friday, Lazar Ljubicic, saved three members of a Jewish family in his native village of Zasavica, Serbia. He saved them from having yellow ribbons attached to their clothing and then got them out a day before 1,000 Jews and 200 Gypsies were executed nearby."}, {"text": "Ljubicic's widow accepted the award for her deceased husband."}, {"text": "In Sarajevo in 1941, Olga Kukovic, now 85, dyed her Jewish friend's red hair black, put a Muslim fez on his head and found his sister a veil to cover her face. With this new identity, and false papers, the two Jews fled to the Italian-occupied part of Bosnia, where there was less persecution."}, {"text": "After the war, Vukovic visited her friends in Israel. She accepted the award on behalf of herself and her deceased husband, Janko, also a savior of Jews from the Holocaust."}, {"text": "The honor of Righteous Gentle has been awarded to 109 people in the former and the new, rump Yugoslavia, said Aca Singer, 80, head of Belgrade's dwindling Jewish Community. About half of them were from Serbia."}, {"text": "Four Croats are due to receive the title in ceremonies in now-independent Croatia in February."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1142.json b/inquisitive/sources/test/1142.json new file mode 100644 index 0000000000000000000000000000000000000000..460a03e2533d9e804a79b7686d3f981b846a6f3f --- /dev/null +++ b/inquisitive/sources/test/1142.json @@ -0,0 +1 @@ +[{"text": "A conference on Algeria organized by Europe could help end the violence that has wracked the country for three years, President Francois Mitterrand said Friday."}, {"text": "'If the European Union could, in Europe, organize a conference that draws from different ideas put forth recently, notably the opposition conference in Rome . there would perhaps be more chance to see these projects accepted by the parties opposing each other,' Mitterrand told reporters."}, {"text": "Responding to a question whether Europe could play a role in bringing peace to Algeria, Mitterrand said his comments were a 'hope' and not a 'political decision.'"}, {"text": "He said he broached the topic during informal talks with German Chancellor Helmut Kohl in Paris Thursday and the two agreed that 'terrorism and extremism strongly feed the misery and economic crisis' of Algeria."}, {"text": "Mitterrand spoke at a news conference after meeting with visiting European Union chief Jacques Santer."}, {"text": "Algeria has been engulfed in violence the government cancelled legislative elections being won by Muslim fundamentalists three years ago."}, {"text": "Opposition Algerian groups meeting in Rome last month drew up a plan to bring peace by reducing tensions in a series of steps, but the plan was rejected by the Algerian government and the more radical of armed Muslim groups waging the insurgency."}, {"text": "An estimated 30,000 people have been killed in the violence, and most foreigners have fled the country."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1143.json b/inquisitive/sources/test/1143.json new file mode 100644 index 0000000000000000000000000000000000000000..d778ca62a1f217354e35a671aa3414e748ef17be --- /dev/null +++ b/inquisitive/sources/test/1143.json @@ -0,0 +1 @@ +[{"text": "The first summit to bring together Israel and its Arab peace partners offered something for everyone. But critical decisions for a lasting peace were put off for another day."}, {"text": "Israel got a declaration on terrorism for Israel, Egypt a nod toward its goal of a nuclear-free Middle East, and the Palestinians a pledge to speed up negotiations on their future."}, {"text": "But ways to curb attacks on Israelis by Islamic militants, the most serious threat to peace, weren't even discussed at Thursday's summit."}, {"text": "'Such meetings cannot discuss specific ways and means, but to reaffirm our stand against all kinds of violence that would undermine the peace process,' Egypt's foreign minister, Amr Moussa, said after the five-hour session."}, {"text": "It was a polite way of saying nothing concrete was done."}, {"text": "In the end, the summit may well have been more symbolic than practical, marking Israel's ascent as a partner in regional politics."}, {"text": "Israel has long resisted multilateral meetings with its Arab neighbors. But televised images of the summit -- of Prime Minister Yitzhak Rabin casually sitting next to Jordan's King Hussein, PLO leader Yasser Arafat and Egyptian President Hosni Mubarak -- provided dramatic proof of the region's fast-changing landscape."}, {"text": "The images were even broadcast on Syrian television, and Al-Hayat, the London-based Arabic daily distributed throughout the Middle East, displayed a photograph of the four leaders on its front page."}, {"text": "Rabin himself was aware of the symbolism. While praising a summit statement condemning terrorism, he said the meeting as a 'peace bloc' was more important than the formal declarations."}, {"text": "Arafat secured a pledge to speed up the negotiations on Palestinian autonomy, considered crucial if he is to salvage his authority in the Gaza Strip and West Bank city of Jericho."}, {"text": "The expected fruits of the 1993 Israel-PLO peace accord -- jobs and independence -- have not come about, and Arafat has been unable or unwilling to crack down on Islamic extremists who use terrorism to undermine the accord even more. Their latest blow was a Jan. 22 suicide bombing that killed 21 Israelis."}, {"text": "Israel and the PLO will resume talks next week in Cairo, and diplomats from Egypt, Israel, Jordan and the PLO will gather in Washington on Feb. 12 to discuss everything from education to a regional nuclear-free zone."}, {"text": "But Arafat's key demands at the summit -- an end to the closure clamped on the West Bank and Gaza last week and a halt to expanding Jewish settlements -- were hardly addressed, and only then peripherally."}, {"text": "However, the Israeli Cabinet will consider this weekend a recommendation by its security forces to ease the closure, which cuts off thousands of Palestinians from their jobs in Israel."}, {"text": "As expected, Arafat's opponents were quick to condemn the summit."}, {"text": "Islamic Jihad, which claimed responsibility for the Jan. 22 bombing, said in Al-Hayat that the meeting was meant to shore up Rabin's sagging popularity, 'which is stumbling under the strikes of the crusaders.'"}, {"text": "The four summit leaders agreed to back Egypt's proposal for a 'mutually verifiable Middle East zone free of weapons of mass destruction -- nuclear, chemical and biological.'"}, {"text": "Egyptian officials have been adamant that if Israel refuses to sign the Nuclear Non-Proliferation Treaty, Egypt will not renew its commitment when the treaty is renegotiated in April. Israel has stayed mum about its nuclear capability, but is believed to possess about 200 warheads."}, {"text": "Egypt's call has drawn support from Libya, Syria and Kuwait. But it has put Egypt at a crossroads with its American patrons, who have lobbied hard to line up support for the treaty's renewal."}, {"text": "The statement and the promise of future talks may offer Egypt a way to sign the Non-Proliferation Treaty while pointing to Israel's commitment to work for a nuclear-free region."}, {"text": "Of the four leaders, Hussein had the least to gain and the least to lose."}, {"text": "Proceeding smoothly with its peace with Israel and facing a relatively tame opposition, Jordan gains credibility as a regional broker. It needs little more."}, {"text": "EDITOR'S NOTE: Anthony Shadid is an Associated Press newsman based in Cairo."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1144.json b/inquisitive/sources/test/1144.json new file mode 100644 index 0000000000000000000000000000000000000000..949abeac2a63f702e2b1597e7514d6d3fb39c4d7 --- /dev/null +++ b/inquisitive/sources/test/1144.json @@ -0,0 +1 @@ +[{"text": "More than a thousand police and soldiers were being deployed Friday in the country's southeastern region to prevent the premature return of 250,000 flooding evacuees."}, {"text": "The provincial governments were deciding Saturday whether to allow the evacuees back into the flood-threatened polder areas of Gelderland Province."}, {"text": "Reversing the largest exodus in Dutch history is likely to cause at least as much trouble as getting it started in the first place last Monday."}, {"text": "The 1,400-strong force of police and soldiers would also be there to prevent any looting, said provincial spokesman Hans Kelderman Friday night."}, {"text": "But before anyone can return, emergency workers have to finish shoring up weak and soggy dikes, many of them dating from the Middle Ages."}, {"text": "Friday the Interior Ministry confirmed that the major cost of this week's river flooding would be the strengthening of this region's 530 kilometer (328 mile) dike system."}, {"text": "No figure was issued, but it's expected to mount into the hundreds of millions of guilders (dollars)."}, {"text": "The crisis was triggered when a combination of heavy Alpine snowfall, early melting and heavy rains flooded Germany, France and Belgium. The Maas and Waal rivers drained the flood waters into the Netherlands this week."}, {"text": "This Waal River town of 33,000 in the shadow of a mammoth but weakened dike called in 200 policemen Friday to fend off any townsfolk trying to get home before the blockade of the low-lying polder areas is lifted."}, {"text": "'The danger of a broken dike is still present. Then water would stream in very quickly,' said Tiel's Mayor Ed van Tellingen."}, {"text": "Mayor Ed d'Hondt of Nijmegen, Gelderland's provincial capital, did not rule out that the first of some 250,000 evacuees could begin returning home over the weekend."}, {"text": "Some of the locals weren't so sure they even wanted to go back."}, {"text": "'The dikes might be drying but there's the danger that the bottom may be washed away,' said one old woman, who gave her name only as Mrs. Reijers from the town of Druten, where the dikes were among the weakest."}, {"text": "'I was born near the dikes . I understand what water can do,' she said at an old people's home where she took refuge."}, {"text": "'Everyone wants to go home. But if that's not possible then we can't. We just have to wait.'"}, {"text": "The evacuees have been housed in emergency shelters, as well as private homes."}, {"text": "The Maas and Waal were subsiding at up to about 50 centimeters (1.5 feet) per day."}, {"text": "But water flowing through the weakened dikes still spouted up in village streets, while emergency workers ran around trying to plug the holes with sandbags."}, {"text": "'The dikes are very wet but stable,' said Elli Willink, a spokeswoman for Gelderland Province."}, {"text": "'But we don't know yet when people can go home.'"}, {"text": "Before the evacuees can return here, workers have to ensure that the rapid fall of water and the release of outward pressure on the dikes don't cause them to crumble."}, {"text": "But all 13,000 people evacuated from Limburg Province to the south were expected to return Saturday."}, {"text": "The evacuated polder areas were filled with virtual ghost towns, except for police patrolling silently on bicycles to surprise looters in the act."}, {"text": "The evacuated area encompasses an area of about 1,000 square kilometers (400 square miles)."}, {"text": "At least 30 people were killed by the storms and high waters that began to hit areas of Germany, France, Belgium and Luxembourg last week."}, {"text": "Three of those deaths were in the Netherlands."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1145.json b/inquisitive/sources/test/1145.json new file mode 100644 index 0000000000000000000000000000000000000000..1acf3e082a6a47eee3775f3db31407c55f62932b --- /dev/null +++ b/inquisitive/sources/test/1145.json @@ -0,0 +1 @@ +[{"text": "Stocks were barrelling higher in early afternoon Friday as consensus mounted that a softening American economy should prevent further interest rate increases by the Federal Reserve."}, {"text": "At 2.30 p.m. EST (1930 GMT) the Dow Jones average of 30 industrial stocks was up 64.93 points to 3,935.71."}, {"text": "Stocks were following the bond market higher, where the 30-year U.S. Treasury bond was up more than dlrs 17 per dlrs 1,000 face value. Its yield, which falls when prices rise, slid to 7.58 percent from 7.73 percent Thursday."}, {"text": "Advancing issues led decliners by about nearly 7 to 2 on the New York Stock Exchange. Big Board volume was brisk at 301.14 million shares, up from 218.79 million on Thursday."}, {"text": "Broad market indexes were higher. The NYSE composite index was up 3.15 260.33. Standard and Poor's 500 index was up 5.83 at 478.62. The American Stock Exchange's market value index was up 3.66 at 442.11. The Nasdaq composite was up 9.70 at 773.34."}, {"text": "Stocks shot up at the opening bell, after the Labor Department said unemployment rose to 5.7 percent last month from 5.4 percent. Only 134,000 jobs were added to nonfarm payrolls."}, {"text": "The rise in unemployment surprised economists, who had expected the unemployment rate to drop by 0.1 percent, and about 300,000 jobs to be added to payrolls."}, {"text": "The numbers showed that the 'economy may be slowing down enough that the Federal Reserve won't have to raise rates again,' said Hildegard Zagorski, a stock analyst at Prudential Securities, 'but you have to be cautious, because this is only one month's numbers.'"}, {"text": "Other analysts said they believed the market was overreacting on the positive side. 'The surge in average hourly earnings and the workweek seem to suggest that the inflation seeds have taken root,' said Bob Walberg, market analyst at MMS International. 'The Fed is not going to take a look at these numbers and assume that inflation has gone away.'"}, {"text": "Wage rates rose in January by an average 7 cents an hour. The average work week was unchanged at 42.2 hours."}, {"text": "Another report released at 10 a.m. indicated robust economic growth. New factory orders rose 1.7 percent in December, led by a runup in defense orders."}, {"text": "But the University of Michigan said its consumer sentiment index fell to 97.6 from 99.1 in January. And a monthly inflation index put out by Columbia University fell in January, another indication that inflation is receding."}, {"text": "Financial stocks were soaring, as investors concluded from the economic reports that interest rates would remain stable for the time being."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1147.json b/inquisitive/sources/test/1147.json new file mode 100644 index 0000000000000000000000000000000000000000..a9213ffbfc71a9be53654a7f02fb81c2944a7dc0 --- /dev/null +++ b/inquisitive/sources/test/1147.json @@ -0,0 +1 @@ +[{"text": "A Canadian artist whose exhibition of monumental sculptures opened in Moscow on Friday says he has found post-communist Russians alive to his message of individual triumph over oppression."}, {"text": "'The Cold War is over. Welcome to the Warm War,' sculptor Noel Harding told a Russian audience at Friday's opening of Anti-Heroes, the first major Canadian art exhibition to visit post-Soviet Russia."}, {"text": "'This is a war of expressing and defining the relationship between us.'"}, {"text": "The six massive constructions on display until Feb. 27 in Moscow's main exhibition hall depict fragile life forces striving to break free from confining shells of hard, impersonal material."}, {"text": "In one, a flower thrusts defiantly through a straitjacket of ventilation pipes. In another, a symbolic flame flickers against an enormous, sterile background of white plastic sheeting."}, {"text": "'I am addressing the attempt to be an individual within the oppression of systems, no matter whether they're subtle or overt,' says Harding."}, {"text": "'This has special meaning for people in Russia, in this historical context.'"}, {"text": "The collapse of communism in 1989 inspired him to reach out to eastern Europeans, not to lecture to them, but to discover common meanings beneath apparently different experiences, Harding says."}, {"text": "Canada's ambassador to Russia, Jeremy Kinsman, called Harding's work 'politically insightful, profound and sometimes sad.'"}, {"text": "'He has something to say to all of us.'"}, {"text": "Russian viewers seemed divided."}, {"text": "'This is surprising, I couldn't imagine making art works with so many different materials,' said Natalia Belova, a 55-year-old schoolteacher."}, {"text": "'The theme of escape from control is one that has always interested we Russians.'"}, {"text": "But Irina Kachalova, a 21-year-old art student, said she found nothing new."}, {"text": "'Westerners come over here and think we've never seen any art that isn't socialist realism,' she said."}, {"text": "'But we've seen everything.'"}, {"text": "The exhibition's sponsors include the Canadian Ministry of Foreign Affairs, The Canada Council, The Province of Ontario and the Toronto Arts Council. It has already visited the ex-communist states of Hungary, Poland and Slovakia."}, {"text": "Harding, a 47-year-old artist from Toronto, has previously exhibited his work at the Art Gallery of Ontario, New York's Museum of Modern Art, Ottawa's National Art Gallery and the Palais des Beaux Arts in Brussels."}, {"text": "His three-part sculpture featuring apparently live trees recently won the international competition to represent Canada at the 1996 Cultural Olympiad as part of the 1996 Atlanta Olympic Games."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1148.json b/inquisitive/sources/test/1148.json new file mode 100644 index 0000000000000000000000000000000000000000..03c2fc0285b4a174b128dbe443258ece68d07977 --- /dev/null +++ b/inquisitive/sources/test/1148.json @@ -0,0 +1 @@ +[{"text": "A warning by Bosnian Serbs on Friday that any renewal of the war in Croatia would draw them into the fray turned up Balkan tensions another notch."}, {"text": "If Croatia attacks Serb-held parts of the republic, 'we will defend it,' Bosnian Serb leader Radovan Karadzic told Associated Press Television. 'If they squeeze . (the Serbs) in Croatia, we may unite and defend ourselves as a united country.'"}, {"text": "The warning, uttered just months before the planned departure of the thousands of peacekeepers who have enforced a brittle truce in Croatia for three years, came on the heels of United Nations cautioning of an upsurge of violence in both Croatia and Bosnia barring new peace talks."}, {"text": "The warning on Bosnia was uttered by Yasushi Akashi, the top U.N. official in former Yugoslavia; the fears about Croatia by an aide, Michael Williams."}, {"text": "Croatian President Franjo Tudjman has served notice to 12,000 peacekeepers separating his forces from rebel Serb units that they must go after their mandate expires March 31."}, {"text": "The international community is attempting to get Croat and rebel Serb agreement on a plan that would reintegrate Serb-held lands captured in 1991 back into Croatia in exchange for rights guarantees -- and in some cases substantive autonomy -- for the Serbs."}, {"text": "But the Serbs are refusing even to discuss the plan unless the peacekeepers stay. Their leader, Milan Martic, said Friday such talks were 'senseless' and warned that Bosnian Serbs and the Yugoslav army would back his side in any fight with Croatian troops."}, {"text": "Croatia, initially supportive of the plan, also said it was unacceptable Friday. Smiljko Sokol, a Tudjman advisor, told reporters it went too far in granting Serbs near autonomy in some regions."}, {"text": "Williams, asked about the situation in Croatia, said it was 'very serious and was reaching a dead-end.'"}, {"text": "Some analysts express concern that Tudjman's decision to expell the peacekeepers could mean he has reached an understanding with Serbia's president, Slobodan Milosevic. Under such a deal, Croatia would stop supporting Bosnian troops against the Serbs in Bosnia in exchange for a Serbian guarantee of non-interference in Croatia."}, {"text": "That would mean an end to Bosnia's troubled Croat-Muslim federation and almost certain defeat of Muslim-led government troops. Bosnia is sandwiched between Serbia and Croatia."}, {"text": "U.S. Assistant Secretary of State Richard Holbrooke was to hold weekend talks in Germany on bolstering the Croat-Muslim federation."}, {"text": "The federation, backed by the United States, is 10 months old and managed to end bitter fighting between Bosnian Croats and Muslims, who were allied against the Serbs at the outset of war 34 months ago."}, {"text": "But the two sides have done little more than institutionalize a cease-fire."}, {"text": "'Negative events on the federation would have a deleterious effect on an already dangerous situation,' Holbrooke told reporters Thursday at the State Department in Washington. 'We're at a pretty critical time in the situation in the Balkans.'"}, {"text": "Akashi voiced similar pessimism on Bosnia."}, {"text": "'Throughout Bosnia-Herzegovina, confrontation lines remain dangerously close, and armed forces continue their preparations for wider conflict,' Akashi warned. Without 'immediate steps to strengthen the cease-fire, the threat of renewed conflict is real,' he said."}, {"text": "'All involved must now make . a concerted effort to solve the conflict in Bihac,' Akashi said in a written statement. Fighting in that northwestern region, particularly around Velika Kladusa, headquarters of rebel Muslim leader Fikret Abdic, has vexed international efforts to anchor a month-old, Bosnia-wide truce."}, {"text": "Abdic's forces and rebel Serbs from neighboring Croatia are not party to the agreement, which was designed to halt fighting and separate forces as a prelude to resuming peace negotiations."}, {"text": "But international efforts to get negotiations started collapsed last week due to Serb intransigence. The Bosnian government, impatient with U.N. inability to halt fighting, has warned the truce could collapse entirely."}, {"text": "U.N. officials expressed concern Thursday about an apparent increase of Croatian Serb tanks, artillery and troops in the Bihac region. Most blame for the fighting lies with them, Williams said."}, {"text": "Overnight, the Bihac area was reported relatively quiet. But two people were killed and six wounded Thursday in the government-controlled town of Buzim, 30 kilometers (20 miles) northwest of Bihac. There was no word on who fired."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1149.json b/inquisitive/sources/test/1149.json new file mode 100644 index 0000000000000000000000000000000000000000..1a8d2694b8db53ce390348545d9757218aab127b --- /dev/null +++ b/inquisitive/sources/test/1149.json @@ -0,0 +1 @@ +[{"text": "Chrysler Corp. and General Motors Corp. took issue Friday with a newspaper report that suggested they had lost enthusiasm for government efforts to open Japan to U.S. auto sales."}, {"text": "'American automakers must have full access to the Japanese market if there is to be any hope of reaching our full potential in Japan,' Chrysler Chairman Robert J. Eaton said in a news release."}, {"text": "He was reacting to a report from Tokyo in Thursday's Wall Street Journal quoting him as saying Chrysler was too busy elsewhere to give high priority to expanding its sales in Japan. 'We have capacity limitations, so why bother,' Eaton said in the report."}, {"text": "The Journal story 'did not fully reflect either Chrysler's or my position concerning this issue,' Eaton said. 'It did, however, show the level of frustration I have in dealing with our constant exclusion from the Japanese market and the ongoing, laborious negotiations to gain access.'"}, {"text": "U.S. trade negotiators are pushing Japan to put pressure on its automakers to give GM, Chrysler and Ford Motor Co. access to dealer networks controlled by the Japanese companies. Japanese-built cars and trucks account for the major share of the U.S. trade deficit with Japan."}, {"text": "The Journal report quoted unidentified GM executives in Tokyo as saying high real estate prices in Japan, not access to dealer networks, were the major barrier to selling GM cars there."}, {"text": "GM President Jack Smith, in a letter Friday to the Commerce Department's international trade chief, said he was surprised by the report."}, {"text": "'Let me assure you that General Motors supports fully the administration's efforts to open the Japanese market,' Smith wrote to Jeffrey E. Garten, undersecretary of commerce for international trade."}, {"text": "'The main obstacle for us is still dealer access,' GM spokesman Michael Meyerand said Friday."}, {"text": "GM sold about 39,500 cars and trucks in Japan last year, while Chrysler sales totaled about 13,000. Foreign car sales comprised about 8 percent of the Japanese market in 1994. Sales of cars built by Japanese manufacturers account for about a quarter of the U.S. market."}] \ No newline at end of file diff --git a/inquisitive/sources/test/1150.json b/inquisitive/sources/test/1150.json new file mode 100644 index 0000000000000000000000000000000000000000..e0708f0a631e9f91b7431a9a49b48d56308e683b --- /dev/null +++ b/inquisitive/sources/test/1150.json @@ -0,0 +1 @@ +[{"text": "Dominican authorities are asking Interpol to arrest a Venezuelan banker and two Dominicans implicated in a $78 million customs scandal here."}, {"text": "Santo Domingo Judge Juan Francisco Perez y Perez, who is hearing the case, said Thursday evening he had requested the extradition of Venezuelan Jorge Castro, president of the Dominican bank Banco Latinoamericano, a subsidiary of the Venezuelan financial consortium Latinoamericano-Progreso."}, {"text": "The Dominican government closed the local bank on Dec. 22 after problems with the Venezuelan parent prompted huge withdrawals by depositors."}, {"text": "Castro left the Dominican Republic in a pleasure boat headed for Puerto Rico before his bank was closed but after authorities began arresting customs officials."}, {"text": "The banker, believed to be in Miami, is charged with exporting large amounts of merchandise and vehicles and paying only piddling amounts of taxes and tariffs."}, {"text": "Perez y Perez asked for the extradition of two other suspects in the scandal: Dominican businessman Franklin Baez Marte, who reportedly is in Miami, and former customs collector Teresa Jimenez, reportedly in Puerto Rico."}, {"text": "Thirteen customs officials, including former customs director Anisia Risi de Mercedes, are awaiting trial on charges of accepting bribes in exchange for allowing imports to enter the country without paying full customs fees."}, {"text": "Authorities say the customs scam cost the government $78 million in customs fees between April and November of last year, under the administration of Risi de Mercedes."}, {"text": "President Joaquin Balaguer has said he will reveal the names of others involved in the scam in a presentation to the parliament on Feb. 27."}, {"text": "The Venezuelan government closed Latinoamericano-Progreso in December and says it will sell it off. The banking and insurance consortium's president, Orlando Castro, is Jorge Castro's grandfather. Orlando Castro fled his country shortly after his consortium's takeover and is believed to be in Miami as well."}] \ No newline at end of file diff --git a/reccon/query/te_182.json b/reccon/query/te_182.json new file mode 100644 index 0000000000000000000000000000000000000000..9d87488556119848c89d0cbacaa9227b36645782 --- /dev/null +++ b/reccon/query/te_182.json @@ -0,0 +1,27 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Oh , I'm sorry I bothered you . I'm really sorry .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "you have misdialed .", + "I bothered you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , I'm sorry I bothered you . I'm really sorry .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_189.json b/reccon/query/te_189.json new file mode 100644 index 0000000000000000000000000000000000000000..531ff7a3a2d4b035915443bdc8193329aaf96d29 --- /dev/null +++ b/reccon/query/te_189.json @@ -0,0 +1,27 @@ +[ + { + "turn": 17, + "speaker": "A", + "utterance": "Oh , well , would you look at that ! Polarizing filters .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 16, + 17 + ], + "expanded emotion cause span": [ + "There are some right here !", + "would you look at that !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , well , would you look at that ! Polarizing filters .", + "id": 17, + "source_sentences": [ + 15 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_198.json b/reccon/query/te_198.json new file mode 100644 index 0000000000000000000000000000000000000000..572f9c6df292057573dc24682f1546ab196891a8 --- /dev/null +++ b/reccon/query/te_198.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Am I in the Twilight Zone ? You're charging me for a movie I never saw ?", + "emotion": "anger", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I had to add a $ 2 service charge to your bill .", + "You're charging me for a movie I never saw ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Am I in the Twilight Zone ? You're charging me for a movie I never saw ?", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_248.json b/reccon/query/te_248.json new file mode 100644 index 0000000000000000000000000000000000000000..915456fb8dd91d9474ee6d83965b923cc06b8a1f --- /dev/null +++ b/reccon/query/te_248.json @@ -0,0 +1,27 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "I'm really looking forward to reading your column .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13, + 14 + ], + "expanded emotion cause span": [ + "I think I could manage to bring a free copy home for you .", + "I'm really looking forward to reading your column ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm really looking forward to reading your column .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_261.json b/reccon/query/te_261.json new file mode 100644 index 0000000000000000000000000000000000000000..282a8a6a340691cdfcd1ba1be18572d18a1d62ff --- /dev/null +++ b/reccon/query/te_261.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "What ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I'm afraid all the toilets are fully occupied at the moment ." + ], + "type": [ + "inter-personal" + ], + "text": "What ?", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_266.json b/reccon/query/te_266.json new file mode 100644 index 0000000000000000000000000000000000000000..d3fe7198b4b390b3e7e819b37976625a053b901b --- /dev/null +++ b/reccon/query/te_266.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "Thank you . Please come again .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Here is four hundred yuan ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . Please come again .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_267.json b/reccon/query/te_267.json new file mode 100644 index 0000000000000000000000000000000000000000..2202d2170db153436879e81ec513dbd40697e415 --- /dev/null +++ b/reccon/query/te_267.json @@ -0,0 +1,24 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "That ' s very nice of you to offer . Here ' s your tea . Be careful , it ' s still quite hot .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "I can help with the chores while I ' m here ." + ], + "type": [ + "inter-personal" + ], + "text": "That ' s very nice of you to offer . Here ' s your tea . Be careful , it ' s still quite hot .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_277.json b/reccon/query/te_277.json new file mode 100644 index 0000000000000000000000000000000000000000..0c62b4b0ca418ab045dcdf396657ffe5e9ac7987 --- /dev/null +++ b/reccon/query/te_277.json @@ -0,0 +1,27 @@ +[ + { + "turn": 13, + "speaker": "A", + "utterance": "Are you on the level ? You're the one who called me , remember ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 12, + 13 + ], + "expanded emotion cause span": [ + "Why did you drag me into this ?", + "You're the one who called me" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Are you on the level ? You're the one who called me , remember ?", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_28.json b/reccon/query/te_28.json new file mode 100644 index 0000000000000000000000000000000000000000..6574e53e465ee94ac8c09b3a2203f1f4202ecef3 --- /dev/null +++ b/reccon/query/te_28.json @@ -0,0 +1,27 @@ +[ + { + "turn": 17, + "speaker": "A", + "utterance": "you're right . That might seem a bit rude . It's a good thing I've got you with me !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 16, + 17 + ], + "expanded emotion cause span": [ + "I think we should wait until she comes round .", + "It's a good thing I've got you with me !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "you're right . That might seem a bit rude . It's a good thing I've got you with me !", + "id": 17, + "source_sentences": [ + 15 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_282.json b/reccon/query/te_282.json new file mode 100644 index 0000000000000000000000000000000000000000..3ff49874eb137ec7c63eab6e06ee435890f0eae5 --- /dev/null +++ b/reccon/query/te_282.json @@ -0,0 +1,25 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "No problem .", + "emotion": "happiness", + "explanation": "completion of order taking", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "That'll be in a ten minutes . Please sit over there , and I'll call you over as sooner as it's ready ." + ], + "type": [ + "inter-personal" + ], + "text": "No problem .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_315.json b/reccon/query/te_315.json new file mode 100644 index 0000000000000000000000000000000000000000..d1530a75d49d1865998d64db3db097b574a5265f --- /dev/null +++ b/reccon/query/te_315.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "You know , now that I think about it , I really don't have much more to say to you at all !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 2, + 6 + ], + "expanded emotion cause span": [ + "I've already told my buddy , Mark , that I am going hunting with him in Alaska .", + "Says who ? I don't think that is necessarily the case ." + ], + "type": [ + "inter-personal" + ], + "text": "You know , now that I think about it , I really don't have much more to say to you at all !", + "id": 7, + "source_sentences": [ + 1, + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_335.json b/reccon/query/te_335.json new file mode 100644 index 0000000000000000000000000000000000000000..4374d2a53ad1870926114cbedc36a10e2fd9042f --- /dev/null +++ b/reccon/query/te_335.json @@ -0,0 +1,27 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "I ' m so lucky . You only get a chance like this once in a blue moon ! Thanks honey !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13, + 14 + ], + "expanded emotion cause span": [ + "I think you look fantastic . Happy Birthday !", + "I ' m so lucky . You only get a chance like this once in a blue moon ! Thanks honey !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I ' m so lucky . You only get a chance like this once in a blue moon ! Thanks honey !", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_352.json b/reccon/query/te_352.json new file mode 100644 index 0000000000000000000000000000000000000000..1ee563adee96b9424b4802d1643f522414896e47 --- /dev/null +++ b/reccon/query/te_352.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "That's weird !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "I've said that I've got a problem with the circus . I'm not kidding ." + ], + "type": [ + "inter-personal" + ], + "text": "That's weird !", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_361.json b/reccon/query/te_361.json new file mode 100644 index 0000000000000000000000000000000000000000..f50857a8758016e946479f89001399d9d367431c --- /dev/null +++ b/reccon/query/te_361.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Wow , it's surprising . So what do I get ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Congratulations ! You are the lucky customer of our anniversary celebration ." + ], + "type": [ + "inter-personal" + ], + "text": "Wow , it's surprising . So what do I get ?", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_41.json b/reccon/query/te_41.json new file mode 100644 index 0000000000000000000000000000000000000000..66da2c2bdc0518ac895693ac0b4ad146478a6894 --- /dev/null +++ b/reccon/query/te_41.json @@ -0,0 +1,30 @@ +[ + { + "turn": 17, + "speaker": "A", + "utterance": "Great . Then call me and let me know if she's free .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12, + 14, + 16 + ], + "expanded emotion cause span": [ + "There is a girl I know , Sara Ralston . She is 17 , and she will usually take this kind of job . I know her from my church , and I trust her completely .", + "I hope she can do it . She is very responsible .", + "I'll go home and get Sara's number . I'll call her first myself ." + ], + "type": [ + "inter-personal" + ], + "text": "Great . Then call me and let me know if she's free .", + "id": 17, + "source_sentences": [ + 11, + 13, + 15 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_435.json b/reccon/query/te_435.json new file mode 100644 index 0000000000000000000000000000000000000000..33bc41a4e74d207fbc212792dcc227735fbf540d --- /dev/null +++ b/reccon/query/te_435.json @@ -0,0 +1,24 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "Wow ! That's interesting ! It must be tough !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I don't eat or use any animal based products . I don't wear leather , eat eggs , drink milk or anything that comes from an animal ." + ], + "type": [ + "inter-personal" + ], + "text": "Wow ! That's interesting ! It must be tough !", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_469.json b/reccon/query/te_469.json new file mode 100644 index 0000000000000000000000000000000000000000..7c99a9580c419fd11297eebebdb5b16378d1cdd5 --- /dev/null +++ b/reccon/query/te_469.json @@ -0,0 +1,27 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Thank you . I'm sure I will have a wonderful time here .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "It's our pleasure to have you here . I hope you will have a pleasant stay here .", + "I'm sure I will have a wonderful time here ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you . I'm sure I will have a wonderful time here .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_478.json b/reccon/query/te_478.json new file mode 100644 index 0000000000000000000000000000000000000000..1957703ac9d577acd8772ea875b2ad2edb3e3066 --- /dev/null +++ b/reccon/query/te_478.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Very good . Now , if you will accompany me , we can take your measurements and choose the patterns for your suit and shirts .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 6 + ], + "expanded emotion cause span": [ + "I need a new suit", + "Sure . I ' ll also take some silver cuff link and a pair of silk ties ." + ], + "type": [ + "inter-personal" + ], + "text": "Very good . Now , if you will accompany me , we can take your measurements and choose the patterns for your suit and shirts .", + "id": 7, + "source_sentences": [ + 1, + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_501.json b/reccon/query/te_501.json new file mode 100644 index 0000000000000000000000000000000000000000..e69f1a8c281595ad851d7cbc55d43aa19927372c --- /dev/null +++ b/reccon/query/te_501.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "I didn ' t know it would be so big !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "there are 5000 seats", + "I didn ' t know it would be so big !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I didn ' t know it would be so big !", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_52.json b/reccon/query/te_52.json new file mode 100644 index 0000000000000000000000000000000000000000..356b08c2bbf274dc771c7a2fbe1ed55638eb3161 --- /dev/null +++ b/reccon/query/te_52.json @@ -0,0 +1,27 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Really ? I heard in America you can return rental cars in different cities .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "No , sir . We only have this office here . You will have to return it here .", + "I heard in America you can return rental cars in different cities ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Really ? I heard in America you can return rental cars in different cities .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_532.json b/reccon/query/te_532.json new file mode 100644 index 0000000000000000000000000000000000000000..c89997102d6ccaef08945e79417ecfe7b6646fb6 --- /dev/null +++ b/reccon/query/te_532.json @@ -0,0 +1,24 @@ +[ + { + "turn": 15, + "speaker": "A", + "utterance": "bye .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "promise you will let me treat you to dinner next week" + ], + "type": [ + "inter-personal" + ], + "text": "bye .", + "id": 15, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_534.json b/reccon/query/te_534.json new file mode 100644 index 0000000000000000000000000000000000000000..2a1969707d7372afb2f7674a5fd9d833e998190f --- /dev/null +++ b/reccon/query/te_534.json @@ -0,0 +1,27 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "The master suite is the best . Let ' s go look at that next .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "I love the bamboo flooring and granite countertops .", + "The master suite is the best ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "The master suite is the best . Let ' s go look at that next .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_58.json b/reccon/query/te_58.json new file mode 100644 index 0000000000000000000000000000000000000000..83b9b2cfa21d0d0337a17c65e53bc983825e014a --- /dev/null +++ b/reccon/query/te_58.json @@ -0,0 +1,27 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "To hell with you . The accident was your fault .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "if you're going to drive like you did just now , you will have to get used to a little physical pain .", + "The accident was your fault ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "To hell with you . The accident was your fault .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_598.json b/reccon/query/te_598.json new file mode 100644 index 0000000000000000000000000000000000000000..3ae99d63b6f66c1b06420c0d4a647854782fb694 --- /dev/null +++ b/reccon/query/te_598.json @@ -0,0 +1,27 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "You are welcome .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 7 + ], + "expanded emotion cause span": [ + "I am a new comer in our office .", + "It's very kind of you ." + ], + "type": [ + "inter-personal" + ], + "text": "You are welcome .", + "id": 8, + "source_sentences": [ + 0, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_601.json b/reccon/query/te_601.json new file mode 100644 index 0000000000000000000000000000000000000000..9ed4d451bccdc3c98a927e51d4dd1220e64eb443 --- /dev/null +++ b/reccon/query/te_601.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Oh , do you ? Good .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I know a very interesting place ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , do you ? Good .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_604.json b/reccon/query/te_604.json new file mode 100644 index 0000000000000000000000000000000000000000..623c5d5292e5d71673c66c5d28fcf9ced5d7b073 --- /dev/null +++ b/reccon/query/te_604.json @@ -0,0 +1,30 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Bottom's up , and you're right . This meal is incredible . I wish I had known this restaurant before . Thanks for bringing me here . I know I'll be back agile soon .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8, + 8 + ], + "expanded emotion cause span": [ + "it's the weekend . Let's taste and enjoy this meal .", + "This meal is incredible .", + "Thanks for bringing me here ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Bottom's up , and you're right . This meal is incredible . I wish I had known this restaurant before . Thanks for bringing me here . I know I'll be back agile soon .", + "id": 8, + "source_sentences": [ + 6, + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_612.json b/reccon/query/te_612.json new file mode 100644 index 0000000000000000000000000000000000000000..6f9fb494b8e9362fcbdc0b1fac7dec0cbf388156 --- /dev/null +++ b/reccon/query/te_612.json @@ -0,0 +1,27 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "Remember , real luck must be created ( by ) yourself , and then it cannot be given or taken away ...", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "Now I'll have a lucky year !", + "real luck must be created ( by ) yourself , and then it cannot be given or taken away ..." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Remember , real luck must be created ( by ) yourself , and then it cannot be given or taken away ...", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_62.json b/reccon/query/te_62.json new file mode 100644 index 0000000000000000000000000000000000000000..96196ed0f9a811619b991fdcb3711a5c8ec27cad --- /dev/null +++ b/reccon/query/te_62.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Good . Thank you . sir .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Could I have some fish ?" + ], + "type": [ + "inter-personal" + ], + "text": "Good . Thank you . sir .", + "id": 6, + "source_sentences": [ + 0 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_624.json b/reccon/query/te_624.json new file mode 100644 index 0000000000000000000000000000000000000000..575aa20d4a597123538e1ac59dbd347605fa8816 --- /dev/null +++ b/reccon/query/te_624.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Oh , I see . You're going to wear one and pretend you're married to try to attract guys .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I don't need a guy to buy a wedding ring !", + "You're going to wear one and pretend you're married to try to attract guys" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , I see . You're going to wear one and pretend you're married to try to attract guys .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_627.json b/reccon/query/te_627.json new file mode 100644 index 0000000000000000000000000000000000000000..cc6b7bba0fb1210cdd93bfc9dfe196e6fcc7a21d --- /dev/null +++ b/reccon/query/te_627.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "I didn't know you liked bird-watching .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 6 + ], + "expanded emotion cause span": [ + "that bird ... I've never seen one of those before . It's indigenous to Guiling , and an endangered species too .", + "that bird ... I've never seen one of those before . It's indigenous to Guiling , and an endangered species too ." + ], + "type": [ + "inter-personal" + ], + "text": "I didn't know you liked bird-watching .", + "id": 7, + "source_sentences": [ + 5, + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_659.json b/reccon/query/te_659.json new file mode 100644 index 0000000000000000000000000000000000000000..092d16f64da73a3606837891689cf7b705e27db7 --- /dev/null +++ b/reccon/query/te_659.json @@ -0,0 +1,25 @@ +[ + { + "turn": 19, + "speaker": "A", + "utterance": "we'll pick you up at your place at noon . Be there or be square !", + "emotion": "happiness", + "explanation": "Assuming A is happy because B agreed to go out with them.", + "expanded emotion cause evidence": [ + 18 + ], + "expanded emotion cause span": [ + "ok , where and when should I meet you ?" + ], + "type": [ + "inter-personal" + ], + "text": "we'll pick you up at your place at noon . Be there or be square !", + "id": 19, + "source_sentences": [ + 17 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_672.json b/reccon/query/te_672.json new file mode 100644 index 0000000000000000000000000000000000000000..45938eec1039bb10888be290e945b98d983e0633 --- /dev/null +++ b/reccon/query/te_672.json @@ -0,0 +1,24 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "You said it . Ok , let's go in , Sandy .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "you should start seeing someone else ." + ], + "type": [ + "inter-personal" + ], + "text": "You said it . Ok , let's go in , Sandy .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_678.json b/reccon/query/te_678.json new file mode 100644 index 0000000000000000000000000000000000000000..895903625104615b0336a9ad8ab496cd68d829e8 --- /dev/null +++ b/reccon/query/te_678.json @@ -0,0 +1,27 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "Well I have to decide which gifts to keep and which to exchange for better ones when I go to the Boxing Day sales this afternoon !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "you ' re yapping on about your new clothes !", + "I have to decide" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Well I have to decide which gifts to keep and which to exchange for better ones when I go to the Boxing Day sales this afternoon !", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_681.json b/reccon/query/te_681.json new file mode 100644 index 0000000000000000000000000000000000000000..9d08bc4c18d5ecd77a709179ba260d90b4e13b29 --- /dev/null +++ b/reccon/query/te_681.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Ok , good luck to you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "it is very nice talking with you ." + ], + "type": [ + "inter-personal" + ], + "text": "Ok , good luck to you .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_683.json b/reccon/query/te_683.json new file mode 100644 index 0000000000000000000000000000000000000000..70df8b29c5a8118bd5dde71fdee5bd82da7046f0 --- /dev/null +++ b/reccon/query/te_683.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Sure . Thank you very much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Say I've got two tickets for the concert this evening . Would you like to come with me ?" + ], + "type": [ + "inter-personal" + ], + "text": "Sure . Thank you very much .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_695.json b/reccon/query/te_695.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3d9c4e9a23a1ad47ad7498265b078b8dcd3911 --- /dev/null +++ b/reccon/query/te_695.json @@ -0,0 +1,30 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "OK . I'll be happy to join you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 5, + 6 + ], + "expanded emotion cause span": [ + "Shall we have dinner together ?", + "I know a place that has excellent food .", + "I'll be happy to join you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "OK . I'll be happy to join you .", + "id": 6, + "source_sentences": [ + 2, + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_700.json b/reccon/query/te_700.json new file mode 100644 index 0000000000000000000000000000000000000000..cd2774ba3a0892887b743fc707e000ead567a82e --- /dev/null +++ b/reccon/query/te_700.json @@ -0,0 +1,27 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "You can't be serious . How dare you not tell me you were going to marry her ?", + "emotion": "anger", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "I didn't think you'd be interested .", + "How dare you not tell me you were going to marry her ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You can't be serious . How dare you not tell me you were going to marry her ?", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_713.json b/reccon/query/te_713.json new file mode 100644 index 0000000000000000000000000000000000000000..06490d97e4b5024b1fcc5c8d571c3627b586e111 --- /dev/null +++ b/reccon/query/te_713.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Well , compared with my wife , I'm just a beginner .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "It sounds like you're a clothing expert ." + ], + "type": [ + "inter-personal" + ], + "text": "Well , compared with my wife , I'm just a beginner .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_732.json b/reccon/query/te_732.json new file mode 100644 index 0000000000000000000000000000000000000000..f537b32508b1ee7f7ce5a3237f304527868d4559 --- /dev/null +++ b/reccon/query/te_732.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Rude people are everywhere .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "This city is full of jerks .", + "Rude people are everywhere ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Rude people are everywhere .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_745.json b/reccon/query/te_745.json new file mode 100644 index 0000000000000000000000000000000000000000..f10c78e6fc30f1f145d7fbdd2fd62e2551c51445 --- /dev/null +++ b/reccon/query/te_745.json @@ -0,0 +1,27 @@ +[ + { + "turn": 17, + "speaker": "A", + "utterance": "To hell with you . The accident was your fault .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 16, + 17 + ], + "expanded emotion cause span": [ + "if you're going to drive like you did just now , you will have to get used to a little physical pain .", + "The accident was your fault ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "To hell with you . The accident was your fault .", + "id": 17, + "source_sentences": [ + 15 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_754.json b/reccon/query/te_754.json new file mode 100644 index 0000000000000000000000000000000000000000..3ad7fc9fe5ab7e75eb37b23522bdeffb0a7d5e60 --- /dev/null +++ b/reccon/query/te_754.json @@ -0,0 +1,27 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Have a nice journey , Lily .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "I ' m going to China .", + "I don ' t have to pay for my trip ." + ], + "type": [ + "inter-personal" + ], + "text": "Have a nice journey , Lily .", + "id": 8, + "source_sentences": [ + 0, + 2 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_755.json b/reccon/query/te_755.json new file mode 100644 index 0000000000000000000000000000000000000000..d216a0067b00d70c75805f00401af7c7925f5d33 --- /dev/null +++ b/reccon/query/te_755.json @@ -0,0 +1,28 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "And the host announced that he won it all !", + "emotion": "happiness", + "explanation": "10 with 9 makes the evidence stronger.", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "He really did a great job in the finale , especially in the PK round . He performed so well that the majority of the audience cast their votes for him .", + "And the host announced that he won it all !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "And the host announced that he won it all !", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_757.json b/reccon/query/te_757.json new file mode 100644 index 0000000000000000000000000000000000000000..22a6a0bc963699a27f35acd41b20ca4b5dc4cc91 --- /dev/null +++ b/reccon/query/te_757.json @@ -0,0 +1,25 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "Have a good day . Bye-Bye !", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "With your friendly smile and helpful attitude . I am sure you will win ." + ], + "type": [ + "inter-personal" + ], + "text": "Have a good day . Bye-Bye !", + "id": 14, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_786.json b/reccon/query/te_786.json new file mode 100644 index 0000000000000000000000000000000000000000..1e0e7657271df3b84bd6a4cdbe6b06a8b4ef2c49 --- /dev/null +++ b/reccon/query/te_786.json @@ -0,0 +1,30 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "So you must have had a busy and enjoyable day yesterday .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 8, + 9 + ], + "expanded emotion cause span": [ + "We went for a swim in the sea .", + "my nice tan .", + "So you must have had a busy and enjoyable day yesterday ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "So you must have had a busy and enjoyable day yesterday .", + "id": 9, + "source_sentences": [ + 7, + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_793.json b/reccon/query/te_793.json new file mode 100644 index 0000000000000000000000000000000000000000..d23d643a02ec0274fe964dc5d7f62460cb7124aa --- /dev/null +++ b/reccon/query/te_793.json @@ -0,0 +1,28 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Yes , that's a good place to spend a holiday . Last year I went there . It's really .", + "emotion": "happiness", + "explanation": "Assuming A is happy for B", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I've heard that the environment there is very good .", + "Yes , that's a good place to spend a holiday . Last year I went there . It's really ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , that's a good place to spend a holiday . Last year I went there . It's really .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_796.json b/reccon/query/te_796.json new file mode 100644 index 0000000000000000000000000000000000000000..2b0ebaca9a23033a08bee1cac5232d1a88fe49a6 --- /dev/null +++ b/reccon/query/te_796.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "That ' s my wish .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "You will be a very promising one ." + ], + "type": [ + "inter-personal" + ], + "text": "That ' s my wish .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_804.json b/reccon/query/te_804.json new file mode 100644 index 0000000000000000000000000000000000000000..e96d85bc4c7dc32630ce161ad556f5f17210123b --- /dev/null +++ b/reccon/query/te_804.json @@ -0,0 +1,24 @@ +[ + { + "turn": 16, + "speaker": "B", + "utterance": "Wow , that would be something to look forward to .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "You should get your invitation today or tomorrow ." + ], + "type": [ + "inter-personal" + ], + "text": "Wow , that would be something to look forward to .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_810.json b/reccon/query/te_810.json new file mode 100644 index 0000000000000000000000000000000000000000..36394b2d57a13fa7e8cdf7d7e6e1f87cf0c7e480 --- /dev/null +++ b/reccon/query/te_810.json @@ -0,0 +1,24 @@ +[ + { + "turn": 13, + "speaker": "A", + "utterance": "oh , I didn't know you can play the violin . Do you still play .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "I started to learn violin when I was eight ." + ], + "type": [ + "inter-personal" + ], + "text": "oh , I didn't know you can play the violin . Do you still play .", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_834.json b/reccon/query/te_834.json new file mode 100644 index 0000000000000000000000000000000000000000..b70dc4470bc0522ca005bf90df80fc77d9aa7267 --- /dev/null +++ b/reccon/query/te_834.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Thanks . That ' s terrific !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "All you have to do is ask for help ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks . That ' s terrific !", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_844.json b/reccon/query/te_844.json new file mode 100644 index 0000000000000000000000000000000000000000..48f2b236da325601ccb4bfc3ab0d1d2942377dbf --- /dev/null +++ b/reccon/query/te_844.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "I don ' t think you do . If you did , I ' d have a car . See , you know how to take the reservation , you just don ' t know how to hold the reservation and that ' s really the most important part of the reservation , the holding . Anybody can just take them .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 4, + 7 + ], + "expanded emotion cause span": [ + "unfortunately we ran out of cars .", + "you just don ' t know how to hold the reservation" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I don ' t think you do . If you did , I ' d have a car . See , you know how to take the reservation , you just don ' t know how to hold the reservation and that ' s really the most important part of the reservation , the holding . Anybody can just take them .", + "id": 7, + "source_sentences": [ + 3 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_847.json b/reccon/query/te_847.json new file mode 100644 index 0000000000000000000000000000000000000000..c111fa1601abb9a6e6d7a711d5e82f3643e50a7f --- /dev/null +++ b/reccon/query/te_847.json @@ -0,0 +1,27 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "That's so disappointing . I don't know why top athletes would feel the need to take drugs .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 6, + 9 + ], + "expanded emotion cause span": [ + "He was taking steroids to make him stronger and faster .", + "I don't know why top athletes would feel the need to take drugs ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's so disappointing . I don't know why top athletes would feel the need to take drugs .", + "id": 9, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_864.json b/reccon/query/te_864.json new file mode 100644 index 0000000000000000000000000000000000000000..fee6a2a1e6aa3e8eb77ddf6402664ee492741f00 --- /dev/null +++ b/reccon/query/te_864.json @@ -0,0 +1,27 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "Great . It's a lovely neighborhood . And it would be nice to be neighbors again . It would be just like the old days !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "you can come over and have a look .", + "It's a lovely neighborhood . And it would be nice to be neighbors again . It would be just like the old days !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Great . It's a lovely neighborhood . And it would be nice to be neighbors again . It would be just like the old days !", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_891.json b/reccon/query/te_891.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3123fb3a2ef3b5755cbc1364752327cb131112 --- /dev/null +++ b/reccon/query/te_891.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "Oh , you men ! You are all the same .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Sorry , I didn't think it mattered ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , you men ! You are all the same .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_901.json b/reccon/query/te_901.json new file mode 100644 index 0000000000000000000000000000000000000000..8581d8130a4208572e65535c6df33f4ad1519dda --- /dev/null +++ b/reccon/query/te_901.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Now that's a good idea . Thanks a lot , Brian . I'm feeling better already .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Come with me to class , and after class we can go out for dinner ." + ], + "type": [ + "inter-personal" + ], + "text": "Now that's a good idea . Thanks a lot , Brian . I'm feeling better already .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_910.json b/reccon/query/te_910.json new file mode 100644 index 0000000000000000000000000000000000000000..68c1257d9df99737f0cb2f375ee1643e8341e14a --- /dev/null +++ b/reccon/query/te_910.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Thank you very much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 6 + ], + "expanded emotion cause span": [ + "I'd like to offer you my congratulations on your birthday and best wishes for your future happiness , good health and continued success . I've asked the Fairy Flowers to send you a bunch of flowers . I hope you'll like them .", + "Now let me sing \" Happy birthday \" for you ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you very much .", + "id": 7, + "source_sentences": [ + 3, + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_913.json b/reccon/query/te_913.json new file mode 100644 index 0000000000000000000000000000000000000000..cd0109504ae4c2edc63f5fb280fa6c615f7fc8d8 --- /dev/null +++ b/reccon/query/te_913.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "That's terrific !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I'm doing really well . I got married about three years ago . I have two kids now ." + ], + "type": [ + "inter-personal" + ], + "text": "That's terrific !", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_916.json b/reccon/query/te_916.json new file mode 100644 index 0000000000000000000000000000000000000000..574419a9fae4cecd0fd80517bec72544e67a54d3 --- /dev/null +++ b/reccon/query/te_916.json @@ -0,0 +1,24 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "O . K . See you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Yeah , I will . See you then !" + ], + "type": [ + "inter-personal" + ], + "text": "O . K . See you .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_924.json b/reccon/query/te_924.json new file mode 100644 index 0000000000000000000000000000000000000000..81187cf9b26de355b7c0ac59c1cc9316f9520ab2 --- /dev/null +++ b/reccon/query/te_924.json @@ -0,0 +1,31 @@ +[ + { + "turn": 16, + "speaker": "B", + "utterance": "Yeah . I would rather get one nice watch instead of 20 mediocre ones .", + "emotion": "happiness", + "explanation": "the speaker is happy that A has approved her decision to pay more for a nice watch", + "expanded emotion cause evidence": [ + 15, + 15, + 16 + ], + "expanded emotion cause span": [ + "it looks so nice .", + "You always get what you pay for .", + "rather get one nice watch instead of 20 mediocre ones ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yeah . I would rather get one nice watch instead of 20 mediocre ones .", + "id": 16, + "source_sentences": [ + 14, + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_932.json b/reccon/query/te_932.json new file mode 100644 index 0000000000000000000000000000000000000000..68c90a51d17c761786fcc65b78ff52d53b55114b --- /dev/null +++ b/reccon/query/te_932.json @@ -0,0 +1,30 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "Thanks very much . I ' m sure it will sell well . I can ' t wait to read it . Here ' s my card . Thank you for you time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11, + 11 + ], + "expanded emotion cause span": [ + "I ' ll make sure you get an advance copy", + "I can ' t wait to read it .", + "Thank you for you time ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thanks very much . I ' m sure it will sell well . I can ' t wait to read it . Here ' s my card . Thank you for you time .", + "id": 11, + "source_sentences": [ + 9, + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_942.json b/reccon/query/te_942.json new file mode 100644 index 0000000000000000000000000000000000000000..9fdd8af6744dbb834c0ca61f037c7133d98adfe4 --- /dev/null +++ b/reccon/query/te_942.json @@ -0,0 +1,24 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "My pleasure .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Sure , I will . Thank you for inviting me ." + ], + "type": [ + "inter-personal" + ], + "text": "My pleasure .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_958.json b/reccon/query/te_958.json new file mode 100644 index 0000000000000000000000000000000000000000..0493dad40cf09b3d5567d1da3071b27252c147bb --- /dev/null +++ b/reccon/query/te_958.json @@ -0,0 +1,24 @@ +[ + { + "turn": 16, + "speaker": "B", + "utterance": "Ok . I'll talk to you later .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "I'll give you a call later . We should hang out . It's good to be around people ." + ], + "type": [ + "inter-personal" + ], + "text": "Ok . I'll talk to you later .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_968.json b/reccon/query/te_968.json new file mode 100644 index 0000000000000000000000000000000000000000..19f9a5a2b087138f84d86083e0a076ad528f99cb --- /dev/null +++ b/reccon/query/te_968.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "really ? Is he married ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I've fallen in love with my boss ." + ], + "type": [ + "inter-personal" + ], + "text": "really ? Is he married ?", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_980.json b/reccon/query/te_980.json new file mode 100644 index 0000000000000000000000000000000000000000..0b7f024fe8aba5a671adcba8ac75ad3900347017 --- /dev/null +++ b/reccon/query/te_980.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "How lovely it is !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "There is a snowman over there ." + ], + "type": [ + "inter-personal" + ], + "text": "How lovely it is !", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_982.json b/reccon/query/te_982.json new file mode 100644 index 0000000000000000000000000000000000000000..fb133ee0257d282b30e7fd5c151c32dd1d93f0e4 --- /dev/null +++ b/reccon/query/te_982.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Wow , Michael Jordan ' s slam-dunks are beautiful things to watch .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "Here comes Jordan , though .", + "Wow , Michael Jordan ' s slam-dunks are beautiful things to watch ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Wow , Michael Jordan ' s slam-dunks are beautiful things to watch .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/te_999.json b/reccon/query/te_999.json new file mode 100644 index 0000000000000000000000000000000000000000..d94b96b598433dfb83219cc8a0c33c144e521f37 --- /dev/null +++ b/reccon/query/te_999.json @@ -0,0 +1,24 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "wonderful ! I'll start packing our suitcases .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I'll make the arrangements . It will be great ." + ], + "type": [ + "inter-personal" + ], + "text": "wonderful ! I'll start packing our suitcases .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/test.test.Ses05F_script01_1.json b/reccon/query/test.test.Ses05F_script01_1.json new file mode 100644 index 0000000000000000000000000000000000000000..b0e2759696b47e8ba90d14bd069ef18e9b6d8e26 --- /dev/null +++ b/reccon/query/test.test.Ses05F_script01_1.json @@ -0,0 +1,27 @@ +[ + { + "turn": 51, + "speaker": "A", + "utterance": "Don't- you, you can't think like that! Don't think like that!", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 50, + 51 + ], + "expanded emotion cause span": [ + "It doesn't inspire me?", + "you can't think like that! Don't think like that!" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Don't- you, you can't think like that! Don't think like that!", + "id": 51, + "source_sentences": [ + 49 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/test.test.Ses05M_script03_1.json b/reccon/query/test.test.Ses05M_script03_1.json new file mode 100644 index 0000000000000000000000000000000000000000..f7b2e05fc5ea913c45e4f628683cfa1568af06cd --- /dev/null +++ b/reccon/query/test.test.Ses05M_script03_1.json @@ -0,0 +1,27 @@ +[ + { + "turn": 38, + "speaker": "A", + "utterance": "Oh, It burnt my comb and all the towels in the bathroom.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 37, + 38 + ], + "expanded emotion cause span": [ + "worst one was in Cannes when your curling iron burnt a hole in my new dressing gown?", + "It burnt my comb and all the towels in the bathroom." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh, It burnt my comb and all the towels in the bathroom.", + "id": 38, + "source_sentences": [ + 36 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_0.json b/reccon/query/tr_0.json new file mode 100644 index 0000000000000000000000000000000000000000..6c4b4d780da1981f04c2e3276cf617067d7a66a4 --- /dev/null +++ b/reccon/query/tr_0.json @@ -0,0 +1,27 @@ +[ + { + "turn": 8, + "speaker": "A", + "utterance": "Sounds great to me ! If they are willing , we could ask them to go dancing with us . That is excellent exercise and fun , too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "I hear Mary and Sally often go there to play pingpong . Perhaps we can make a foursome with them .", + "That is excellent exercise and fun , too ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Sounds great to me ! If they are willing , we could ask them to go dancing with us . That is excellent exercise and fun , too .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_10030.json b/reccon/query/tr_10030.json new file mode 100644 index 0000000000000000000000000000000000000000..869ff006c6b8ec668ba043e85608ff0a2503188b --- /dev/null +++ b/reccon/query/tr_10030.json @@ -0,0 +1,25 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "You mean I have the job ?", + "emotion": "surprise", + "flag": "F", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Can you start next week ?" + ], + "type": [ + "inter-personal" + ], + "text": "You mean I have the job ?", + "id": 12, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_10047.json b/reccon/query/tr_10047.json new file mode 100644 index 0000000000000000000000000000000000000000..e1a98fe032145ac1d189545c58841134758f675d --- /dev/null +++ b/reccon/query/tr_10047.json @@ -0,0 +1,30 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Phew ! . . . Wait a minute , CRASH ? ? ! ! Spyware ? Trojans ! What ? where ? when ? !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7, + 7, + 7 + ], + "expanded emotion cause span": [ + "your computer might have a virus", + "it crashed", + "unwanted spyware or Trojans ." + ], + "type": [ + "inter-personal" + ], + "text": "Phew ! . . . Wait a minute , CRASH ? ? ! ! Spyware ? Trojans ! What ? where ? when ? !", + "id": 8, + "source_sentences": [ + 6, + 6, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1006.json b/reccon/query/tr_1006.json new file mode 100644 index 0000000000000000000000000000000000000000..cc081e67d069f8a7454d37ed649fe7874437902a --- /dev/null +++ b/reccon/query/tr_1006.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "You think he might stay even longer ? !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "You better do something quick or he ' ll never hit the road ." + ], + "type": [ + "inter-personal" + ], + "text": "You think he might stay even longer ? !", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_10060.json b/reccon/query/tr_10060.json new file mode 100644 index 0000000000000000000000000000000000000000..052b3f6f55c7d5bf1f421c4fb885efa5a0e46379 --- /dev/null +++ b/reccon/query/tr_10060.json @@ -0,0 +1,24 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "It's my pleasure .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Thank you for your help ." + ], + "type": [ + "inter-personal" + ], + "text": "It's my pleasure .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_10095.json b/reccon/query/tr_10095.json new file mode 100644 index 0000000000000000000000000000000000000000..291aa9cf4c122149a21db0d1b7037c2cf97114e6 --- /dev/null +++ b/reccon/query/tr_10095.json @@ -0,0 +1,27 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "It's just you !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "Bingo !", + "It's just you !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It's just you !", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_10099.json b/reccon/query/tr_10099.json new file mode 100644 index 0000000000000000000000000000000000000000..bae33d29991f9a9f6e7b5b7d5e87924c3efbed79 --- /dev/null +++ b/reccon/query/tr_10099.json @@ -0,0 +1,33 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "I apologize for that . But the space is too small .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3, + 3, + 7, + 10 + ], + "expanded emotion cause span": [ + "You've just scratched my car .", + "a paint was scratched off .", + "I've just had it repainted .", + "I apologize for that ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I apologize for that . But the space is too small .", + "id": 10, + "source_sentences": [ + 2, + 2, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_10226.json b/reccon/query/tr_10226.json new file mode 100644 index 0000000000000000000000000000000000000000..fc31319b76013e36262b17b13a1d3f8bb4ca15eb --- /dev/null +++ b/reccon/query/tr_10226.json @@ -0,0 +1,28 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "She'll be very happy with this . And how do you plan to pay for it ?", + "emotion": "happiness", + "explanation": "the speaker is happy that A will be buying a product", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "A Mac it is . I'll take one home with me .", + "She'll be very happy with this ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "She'll be very happy with this . And how do you plan to pay for it ?", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1026.json b/reccon/query/tr_1026.json new file mode 100644 index 0000000000000000000000000000000000000000..4bdb2fc1ece7cd50380e52fca62eabe8f050d473 --- /dev/null +++ b/reccon/query/tr_1026.json @@ -0,0 +1,27 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "That's good for me , but do you think you'll be back by then ? I'd really like to see you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "I should have some free time next week . Say , next Wednesday evening ?", + "I'd really like to see you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's good for me , but do you think you'll be back by then ? I'd really like to see you .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_10265.json b/reccon/query/tr_10265.json new file mode 100644 index 0000000000000000000000000000000000000000..d7705e18433402b0f9a55692a49748d9c6fc9818 --- /dev/null +++ b/reccon/query/tr_10265.json @@ -0,0 +1,24 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Thanks . You ' d be ok on your own . There are loads of fashion victims out there , and you are not one of them . Have you tried it on yet ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "You have a lot of good fashion sense ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks . You ' d be ok on your own . There are loads of fashion victims out there , and you are not one of them . Have you tried it on yet ?", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_10301.json b/reccon/query/tr_10301.json new file mode 100644 index 0000000000000000000000000000000000000000..6dc3440e48d6016eabe461377fbcb5789be597db --- /dev/null +++ b/reccon/query/tr_10301.json @@ -0,0 +1,24 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Thank you , sir . I'll try my best to assist Richard in his work .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Mary is a very helpful and experienced secretary indeed , and I'm sure you will find out ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you , sir . I'll try my best to assist Richard in his work .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_10329.json b/reccon/query/tr_10329.json new file mode 100644 index 0000000000000000000000000000000000000000..2dd1bbdb99fd5f94ec4fc1dec8aeeb06717a265b --- /dev/null +++ b/reccon/query/tr_10329.json @@ -0,0 +1,24 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "Don ' t mention it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "Thank you very much ." + ], + "type": [ + "inter-personal" + ], + "text": "Don ' t mention it .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_10362.json b/reccon/query/tr_10362.json new file mode 100644 index 0000000000000000000000000000000000000000..17de2c81912b07953a901b9ed83b47915edcb5e9 --- /dev/null +++ b/reccon/query/tr_10362.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Gee . I must have left it in my hotel room .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "you can't board the plane" + ], + "type": [ + "inter-personal" + ], + "text": "Gee . I must have left it in my hotel room .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_10408.json b/reccon/query/tr_10408.json new file mode 100644 index 0000000000000000000000000000000000000000..5f972af2051d9c493668f3ddf16bd4a85e6d3f46 --- /dev/null +++ b/reccon/query/tr_10408.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Sure . What time would you like to come ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Sounds good ." + ], + "type": [ + "inter-personal" + ], + "text": "Sure . What time would you like to come ?", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_10410.json b/reccon/query/tr_10410.json new file mode 100644 index 0000000000000000000000000000000000000000..06a70a660ab24688b5bef6b8d43daa91d06337a4 --- /dev/null +++ b/reccon/query/tr_10410.json @@ -0,0 +1,27 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "I can ' t believe it ! I have all my important personal documents stored in that computer . It ' s no laughing matter .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 3, + 6 + ], + "expanded emotion cause span": [ + "I ' Ve erased your personal files accidentally .", + "I have all my important personal documents stored in that computer ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I can ' t believe it ! I have all my important personal documents stored in that computer . It ' s no laughing matter .", + "id": 6, + "source_sentences": [ + 2 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_10419.json b/reccon/query/tr_10419.json new file mode 100644 index 0000000000000000000000000000000000000000..5100090774a28f352c64ef68e99e0b942077f91c --- /dev/null +++ b/reccon/query/tr_10419.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "Bottoms up !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Here's to our friendship and health !" + ], + "type": [ + "inter-personal" + ], + "text": "Bottoms up !", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_10488.json b/reccon/query/tr_10488.json new file mode 100644 index 0000000000000000000000000000000000000000..786273903482234f18617573254725b062140881 --- /dev/null +++ b/reccon/query/tr_10488.json @@ -0,0 +1,30 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Mine are the same way . It seems like they've been overcooked .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 7, + 8, + 8 + ], + "expanded emotion cause span": [ + "vegetables are very soggy .", + "Mine are the same way .", + "they've been overcooked ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Mine are the same way . It seems like they've been overcooked .", + "id": 8, + "source_sentences": [ + 6, + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_10549.json b/reccon/query/tr_10549.json new file mode 100644 index 0000000000000000000000000000000000000000..cdf5f1dbbec4464ac2760e1998c9606bb75b151f --- /dev/null +++ b/reccon/query/tr_10549.json @@ -0,0 +1,24 @@ +[ + { + "turn": 13, + "speaker": "A", + "utterance": "It's a deal .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "275 dollars is the lowest price I can offer ." + ], + "type": [ + "inter-personal" + ], + "text": "It's a deal .", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1060.json b/reccon/query/tr_1060.json new file mode 100644 index 0000000000000000000000000000000000000000..a6db20b2c482afdd943e9a6a09563a694f1003f3 --- /dev/null +++ b/reccon/query/tr_1060.json @@ -0,0 +1,27 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Thank you . This place is nice .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "It's on me .", + "Thank you . This place is nice ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you . This place is nice .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_10620.json b/reccon/query/tr_10620.json new file mode 100644 index 0000000000000000000000000000000000000000..d449074ed9fb2d300d579355c2a7c3add2b4693c --- /dev/null +++ b/reccon/query/tr_10620.json @@ -0,0 +1,24 @@ +[ + { + "turn": 15, + "speaker": "A", + "utterance": "Enjoy yourself .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "It tastes great ." + ], + "type": [ + "inter-personal" + ], + "text": "Enjoy yourself .", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1064.json b/reccon/query/tr_1064.json new file mode 100644 index 0000000000000000000000000000000000000000..d8af9f4103a77033e306b5adb63cfe147fa75cfd --- /dev/null +++ b/reccon/query/tr_1064.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Help yourself .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Can I have a bite ?" + ], + "type": [ + "inter-personal" + ], + "text": "Help yourself .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_10644.json b/reccon/query/tr_10644.json new file mode 100644 index 0000000000000000000000000000000000000000..dc39f04e6cd63f798dc3c21b338f9be3d8bd2c1b --- /dev/null +++ b/reccon/query/tr_10644.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "I understand , and I am very sorry .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "write you a ticket ." + ], + "type": [ + "inter-personal" + ], + "text": "I understand , and I am very sorry .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_10645.json b/reccon/query/tr_10645.json new file mode 100644 index 0000000000000000000000000000000000000000..d16686a29d867c91b3fa6e8bedd8ad4a2ec5000e --- /dev/null +++ b/reccon/query/tr_10645.json @@ -0,0 +1,27 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "Yes , everything has been well designed .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "The building is quite new and well constructed . I ' m happy with the fittings too .", + "Yes , everything has been well designed ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , everything has been well designed .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_10709.json b/reccon/query/tr_10709.json new file mode 100644 index 0000000000000000000000000000000000000000..b2acf2aed74b1ca6060cb01f7f25e6f999c31406 --- /dev/null +++ b/reccon/query/tr_10709.json @@ -0,0 +1,24 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Oh , that's the worst .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "I also hate having to stand at a bus stop" + ], + "type": [ + "inter-personal" + ], + "text": "Oh , that's the worst .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1072.json b/reccon/query/tr_1072.json new file mode 100644 index 0000000000000000000000000000000000000000..4a14064e126d4c0e624fa03b508a5099261b6873 --- /dev/null +++ b/reccon/query/tr_1072.json @@ -0,0 +1,27 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Good , because my friend Wendy is getting married and I ' m organizing her party !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "If one of your friends was getting married I wouldn ' t mind you going to her bachelorette party !", + "my friend Wendy is getting married and I ' m organizing her party !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Good , because my friend Wendy is getting married and I ' m organizing her party !", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_10727.json b/reccon/query/tr_10727.json new file mode 100644 index 0000000000000000000000000000000000000000..349951a35621883caad611499ad9f9aabc36f9e9 --- /dev/null +++ b/reccon/query/tr_10727.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Ok , thank you . Goodbye .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "That's fine . please call again later ." + ], + "type": [ + "inter-personal" + ], + "text": "Ok , thank you . Goodbye .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1073.json b/reccon/query/tr_1073.json new file mode 100644 index 0000000000000000000000000000000000000000..b8676c47d22dba7cc94e7f2c64675b10b144ef98 --- /dev/null +++ b/reccon/query/tr_1073.json @@ -0,0 +1,27 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "Now there we are in agreement !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "I think that the most amazing performances are by athletes who participate in the Paralympics .", + "Now there we are in agreement !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Now there we are in agreement !", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_108.json b/reccon/query/tr_108.json new file mode 100644 index 0000000000000000000000000000000000000000..e8fc790d57140279f32d87e73d6d7e1b32c6b547 --- /dev/null +++ b/reccon/query/tr_108.json @@ -0,0 +1,27 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "You're lucky !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "I don't need a car . I walk to work .", + "You're lucky !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You're lucky !", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1084.json b/reccon/query/tr_1084.json new file mode 100644 index 0000000000000000000000000000000000000000..6823bc687b6b9eee9bd4de88fde9656bf8e4aa1d --- /dev/null +++ b/reccon/query/tr_1084.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Yes , please . Thank you for everything .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "It ' s my pleasure . Would you like another glass of champagne ?" + ], + "type": [ + "inter-personal" + ], + "text": "Yes , please . Thank you for everything .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_10853.json b/reccon/query/tr_10853.json new file mode 100644 index 0000000000000000000000000000000000000000..35f23a2867844c525bf635fc3d2e281b2eac484b --- /dev/null +++ b/reccon/query/tr_10853.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "No problem , that'll be $ 5 . 48 .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "thank you ." + ], + "type": [ + "inter-personal" + ], + "text": "No problem , that'll be $ 5 . 48 .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1090.json b/reccon/query/tr_1090.json new file mode 100644 index 0000000000000000000000000000000000000000..cf41c3acbc0f8d14469e1fc8d6a3f56c0c0fd0c1 --- /dev/null +++ b/reccon/query/tr_1090.json @@ -0,0 +1,24 @@ +[ + { + "turn": 16, + "speaker": "B", + "utterance": "ok .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "Let's go and have a drink ." + ], + "type": [ + "inter-personal" + ], + "text": "ok .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_10906.json b/reccon/query/tr_10906.json new file mode 100644 index 0000000000000000000000000000000000000000..4f8b56434716629e203e27fc65c8124689bb25e5 --- /dev/null +++ b/reccon/query/tr_10906.json @@ -0,0 +1,30 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "Merry Christmas , Mom . I love you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 11, + 12 + ], + "expanded emotion cause span": [ + "Don't worry ,", + "Merry Christmas .", + "Merry Christmas , Mom . I love you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Merry Christmas , Mom . I love you .", + "id": 12, + "source_sentences": [ + 10, + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_10916.json b/reccon/query/tr_10916.json new file mode 100644 index 0000000000000000000000000000000000000000..852e318b9f344e4f17b264e2f85163c3c907d21b --- /dev/null +++ b/reccon/query/tr_10916.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "Gross !", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Look at my smile" + ], + "type": [ + "inter-personal" + ], + "text": "Gross !", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_10955.json b/reccon/query/tr_10955.json new file mode 100644 index 0000000000000000000000000000000000000000..555d1cee53b2085a4dc6d6cb3a501551579a4f5a --- /dev/null +++ b/reccon/query/tr_10955.json @@ -0,0 +1,27 @@ +[ + { + "turn": 13, + "speaker": "A", + "utterance": "Bottom is up .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 12 + ], + "expanded emotion cause span": [ + "Would you like some more ?", + "our friendship and health !" + ], + "type": [ + "inter-personal" + ], + "text": "Bottom is up .", + "id": 13, + "source_sentences": [ + 9, + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1097.json b/reccon/query/tr_1097.json new file mode 100644 index 0000000000000000000000000000000000000000..9d7eaaec9882118d13143d4044e71fda04a2f14e --- /dev/null +++ b/reccon/query/tr_1097.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Wear red underwear ? ! Does that really work ? Are you going to try it ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "And she told me the secret to winning , wear red underwear !" + ], + "type": [ + "inter-personal" + ], + "text": "Wear red underwear ? ! Does that really work ? Are you going to try it ?", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_11018.json b/reccon/query/tr_11018.json new file mode 100644 index 0000000000000000000000000000000000000000..bd202f7ca9fa654db44e8ad2c2b2755fb48c3abd --- /dev/null +++ b/reccon/query/tr_11018.json @@ -0,0 +1,24 @@ +[ + { + "turn": 23, + "speaker": "A", + "utterance": "Damn !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 22 + ], + "expanded emotion cause span": [ + "it won't work , old buddy . They'll see that I'm not you ." + ], + "type": [ + "inter-personal" + ], + "text": "Damn !", + "id": 23, + "source_sentences": [ + 21 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_11047.json b/reccon/query/tr_11047.json new file mode 100644 index 0000000000000000000000000000000000000000..9685299616031fee352506d4db4fc96dbc3d2325 --- /dev/null +++ b/reccon/query/tr_11047.json @@ -0,0 +1,30 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "That's an attractive plan . I'll think about it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 9, + 9 + ], + "expanded emotion cause span": [ + "we can give you a 10 % discount", + "We also offer a very good financing plan .", + "no payment no interest until next June ." + ], + "type": [ + "inter-personal" + ], + "text": "That's an attractive plan . I'll think about it .", + "id": 10, + "source_sentences": [ + 8, + 8, + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_11053.json b/reccon/query/tr_11053.json new file mode 100644 index 0000000000000000000000000000000000000000..4bd462de02d37c090a655b7bb40700950ff050f0 --- /dev/null +++ b/reccon/query/tr_11053.json @@ -0,0 +1,24 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "Poor me !", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "all the medicine here is past expiration ." + ], + "type": [ + "inter-personal" + ], + "text": "Poor me !", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1106.json b/reccon/query/tr_1106.json new file mode 100644 index 0000000000000000000000000000000000000000..ca067a6d8b20f3327f91ffaa7a2e6a74adec47f3 --- /dev/null +++ b/reccon/query/tr_1106.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Wow , that's unbelievable ! You play so well , but you've never been to a real teacher . You will definitely be famous in the near future .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I taught myself by listening to some records of top players .", + "You play so well , but you've never been to a real teacher ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Wow , that's unbelievable ! You play so well , but you've never been to a real teacher . You will definitely be famous in the near future .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_11079.json b/reccon/query/tr_11079.json new file mode 100644 index 0000000000000000000000000000000000000000..a61912484ffa0309ad0221d30b5b603f33a20ac4 --- /dev/null +++ b/reccon/query/tr_11079.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "OK , bye for now !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 6 + ], + "expanded emotion cause span": [ + "I hope you have a good trip . Thanks ever so much for your cooperation , Mr . Simpson . Give my best wishes to Mr . Green .", + "all the best ." + ], + "type": [ + "inter-personal" + ], + "text": "OK , bye for now !", + "id": 7, + "source_sentences": [ + 3, + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1109.json b/reccon/query/tr_1109.json new file mode 100644 index 0000000000000000000000000000000000000000..575c7803402d8b478719ebf578622063631e4488 --- /dev/null +++ b/reccon/query/tr_1109.json @@ -0,0 +1,24 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "My pleasure .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Thank you very much . It ' s very kind of you ." + ], + "type": [ + "inter-personal" + ], + "text": "My pleasure .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1130.json b/reccon/query/tr_1130.json new file mode 100644 index 0000000000000000000000000000000000000000..2444ba30e76aaff1d436b95d1194c37f7c1e9054 --- /dev/null +++ b/reccon/query/tr_1130.json @@ -0,0 +1,24 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "That sounds really convenient . Do you pay extra money to enjoy this service ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "You can use the credit card to withdraw the money in foreign countries ." + ], + "type": [ + "inter-personal" + ], + "text": "That sounds really convenient . Do you pay extra money to enjoy this service ?", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1150.json b/reccon/query/tr_1150.json new file mode 100644 index 0000000000000000000000000000000000000000..0fc3e72aaed0bef07a80322084a9eefe8d179826 --- /dev/null +++ b/reccon/query/tr_1150.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "I ' m sure I will .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "you ' ll enjoy the trip", + "I ' m sure I will ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I ' m sure I will .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1166.json b/reccon/query/tr_1166.json new file mode 100644 index 0000000000000000000000000000000000000000..da0c7b71db3b54ee72173c97c1322dc425fbd72d --- /dev/null +++ b/reccon/query/tr_1166.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Quite well , thank you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "and you ?", + "Quite well" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Quite well , thank you .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1200.json b/reccon/query/tr_1200.json new file mode 100644 index 0000000000000000000000000000000000000000..b1f08c1fbb5fba94b7ad342d976b05eee7493f2d --- /dev/null +++ b/reccon/query/tr_1200.json @@ -0,0 +1,27 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "That would be great . I would love some .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "Can I get you some punch ?", + "That would be great . I would love some ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That would be great . I would love some .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1209.json b/reccon/query/tr_1209.json new file mode 100644 index 0000000000000000000000000000000000000000..c780fa532c3ef953863b88982f8b0d81dfd57e72 --- /dev/null +++ b/reccon/query/tr_1209.json @@ -0,0 +1,25 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "Yes , but I still don't have many friends here yet .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "your English is so good ." + ], + "type": [ + "inter-personal" + ], + "text": "Yes , but I still don't have many friends here yet .", + "id": 14, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1210.json b/reccon/query/tr_1210.json new file mode 100644 index 0000000000000000000000000000000000000000..615428698af32fea9015f35cd9b6aacc18a741a4 --- /dev/null +++ b/reccon/query/tr_1210.json @@ -0,0 +1,27 @@ +[ + { + "turn": 15, + "speaker": "A", + "utterance": "Ok . I can't wait to see it . Let's go !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14, + 15 + ], + "expanded emotion cause span": [ + "this could be a nice opportunity to enjoy it together . I bet you'd love it .", + "I can't wait to see it ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Ok . I can't wait to see it . Let's go !", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1211.json b/reccon/query/tr_1211.json new file mode 100644 index 0000000000000000000000000000000000000000..2e33b2d50a52db44bfd4f174f097cd2759f7a49e --- /dev/null +++ b/reccon/query/tr_1211.json @@ -0,0 +1,27 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "Let me have a look . Oh , no . They are Chinese poems which describe this happy scene .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "There are many Chinese characters on its body , too .", + "Oh , no . They are Chinese poems which describe this happy scene ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Let me have a look . Oh , no . They are Chinese poems which describe this happy scene .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1234.json b/reccon/query/tr_1234.json new file mode 100644 index 0000000000000000000000000000000000000000..4173e7c8bd70512ea2aec8aaad353914359ec4b3 --- /dev/null +++ b/reccon/query/tr_1234.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "You're welcome .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Thanks ." + ], + "type": [ + "inter-personal" + ], + "text": "You're welcome .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1262.json b/reccon/query/tr_1262.json new file mode 100644 index 0000000000000000000000000000000000000000..39fe4b6cc72e922f329ff083d66eaff37cc4e671 --- /dev/null +++ b/reccon/query/tr_1262.json @@ -0,0 +1,27 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Really ? That's fantastic ! Will you get a chance to do any writing ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "asked me if I was interested in becoming an assistant editor for him .", + "That's fantastic !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Really ? That's fantastic ! Will you get a chance to do any writing ?", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1266.json b/reccon/query/tr_1266.json new file mode 100644 index 0000000000000000000000000000000000000000..76843e5dd59494511f77deec8a1531b42a2fcb79 --- /dev/null +++ b/reccon/query/tr_1266.json @@ -0,0 +1,30 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "OK . See you then .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 13, + 14 + ], + "expanded emotion cause span": [ + "dancing party", + "Is that all right ?", + "See you then ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "OK . See you then .", + "id": 14, + "source_sentences": [ + 2, + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1267.json b/reccon/query/tr_1267.json new file mode 100644 index 0000000000000000000000000000000000000000..f260a62e4da4ecae57123a4580d8ea94f9ae0bad --- /dev/null +++ b/reccon/query/tr_1267.json @@ -0,0 +1,27 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "You ' re right . This year should be much more exciting than usual . What ' s you favourite award category ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "this year there are several contenders .", + "This year should be much more exciting" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You ' re right . This year should be much more exciting than usual . What ' s you favourite award category ?", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1285.json b/reccon/query/tr_1285.json new file mode 100644 index 0000000000000000000000000000000000000000..c29a3b293f4d3e276c41b9a54b384295cf4db740 --- /dev/null +++ b/reccon/query/tr_1285.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "I am glad to hear that . I'm really pleased with it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "The car has very sleek lines . I love it ." + ], + "type": [ + "inter-personal" + ], + "text": "I am glad to hear that . I'm really pleased with it .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1287.json b/reccon/query/tr_1287.json new file mode 100644 index 0000000000000000000000000000000000000000..87d5b3ad9465e0621e29e71fc8dba20934eb8226 --- /dev/null +++ b/reccon/query/tr_1287.json @@ -0,0 +1,27 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "I know life is not all roses , and I believe I will pull this through .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "I always consider you are such a guy who never gives up .", + "I believe I will pull this through ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I know life is not all roses , and I believe I will pull this through .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1288.json b/reccon/query/tr_1288.json new file mode 100644 index 0000000000000000000000000000000000000000..67b5e3004bc657fd5405ac413937bf38ff8eb6b9 --- /dev/null +++ b/reccon/query/tr_1288.json @@ -0,0 +1,24 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Thank you . He ' s very lucky indeed .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "He ' s going to be sent to Britain to study" + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . He ' s very lucky indeed .", + "id": 10, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1305.json b/reccon/query/tr_1305.json new file mode 100644 index 0000000000000000000000000000000000000000..e36d9646f8cf02572b137bfc44d32b966bbf5550 --- /dev/null +++ b/reccon/query/tr_1305.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "You bet .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 6 + ], + "expanded emotion cause span": [ + "Your house was decorated so beautiful .", + "She must have done a lot of work" + ], + "type": [ + "inter-personal" + ], + "text": "You bet .", + "id": 7, + "source_sentences": [ + 3, + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1315.json b/reccon/query/tr_1315.json new file mode 100644 index 0000000000000000000000000000000000000000..31310ddbb9484c5e5522c76d838e0939081a9dc6 --- /dev/null +++ b/reccon/query/tr_1315.json @@ -0,0 +1,33 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "Umm . I think I ' ll just stick to my old job and save myself all the hassle of trying to start up a business !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 8, + 10, + 11 + ], + "expanded emotion cause span": [ + "You couldn ' t be more wrong ! A well written business plan will include an executive summary which highlights the idea of the business in two pages or less . Then you need to describe your company with information such as what type of legal structure it has , history , etc .", + "Wait , there ' s more ! Then you need to introduce and describe your goods or services . What they are and how they are different from competitors ' ? Then comes the hard part , a market analysis . You need to investigate and analyze hundreds of variables ! You need to take into consideration socioeconomic factors from GDP per capita to how many children on average the population has ! All this information is useful so that you can move on to your strategy and implementation stage , where you will describe in detail how you will actually execute your idea .", + "Almost , the most important piece of information for your investors will be the financial analysis . Here you will calculate and estimate sales , cash flow and profits . After all , people will want to know when they will begin to see a return on their investment !", + "I think I ' ll just stick to my old job and save myself all the hassle of trying to start up a business !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Umm . I think I ' ll just stick to my old job and save myself all the hassle of trying to start up a business !", + "id": 11, + "source_sentences": [ + 5, + 7, + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1317.json b/reccon/query/tr_1317.json new file mode 100644 index 0000000000000000000000000000000000000000..3914f0a0b62f812cabcfd64288b3e9461ee82226 --- /dev/null +++ b/reccon/query/tr_1317.json @@ -0,0 +1,27 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "Great idea !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "go to a concert", + "Great idea !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Great idea !", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1353.json b/reccon/query/tr_1353.json new file mode 100644 index 0000000000000000000000000000000000000000..47dd22dd981ba7c07c0787603c2be34d60d116dc --- /dev/null +++ b/reccon/query/tr_1353.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "Talking about a barbecue , didn't you say you are organizing one next week ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "This is perfect for having a barbecue in summer ." + ], + "type": [ + "inter-personal" + ], + "text": "Talking about a barbecue , didn't you say you are organizing one next week ?", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1360.json b/reccon/query/tr_1360.json new file mode 100644 index 0000000000000000000000000000000000000000..89c6bc887ef8cd209401c41c42b015fdb1f7330d --- /dev/null +++ b/reccon/query/tr_1360.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "You ? Wow . And why don't you ever dress like that at work ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I was part of a band in school ." + ], + "type": [ + "inter-personal" + ], + "text": "You ? Wow . And why don't you ever dress like that at work ?", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1378.json b/reccon/query/tr_1378.json new file mode 100644 index 0000000000000000000000000000000000000000..1355982c460c85907586519d7d5cd9d71e7e4ad9 --- /dev/null +++ b/reccon/query/tr_1378.json @@ -0,0 +1,24 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "Thanks .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "If you want , I can give you some information I have about the city ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1392.json b/reccon/query/tr_1392.json new file mode 100644 index 0000000000000000000000000000000000000000..507001d7a919968f981dcdaf1881ad5558ba4782 --- /dev/null +++ b/reccon/query/tr_1392.json @@ -0,0 +1,27 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "What a good idea . I'm quite hungry .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "go to a restaurant to celebrate ?", + "I'm quite hungry ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "What a good idea . I'm quite hungry .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1408.json b/reccon/query/tr_1408.json new file mode 100644 index 0000000000000000000000000000000000000000..e5f76fc1c3cbf01596026784ed2112f3ec2a3ca7 --- /dev/null +++ b/reccon/query/tr_1408.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Obviously you did enjoy the concert .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "That caused a sensation . The audience were stunned by his pure tone ." + ], + "type": [ + "inter-personal" + ], + "text": "Obviously you did enjoy the concert .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1422.json b/reccon/query/tr_1422.json new file mode 100644 index 0000000000000000000000000000000000000000..67bc0961e513c837b657aab7ab226bbc0bac21b3 --- /dev/null +++ b/reccon/query/tr_1422.json @@ -0,0 +1,27 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "Good idea . Oh , by the way , would you please pick me up after the party , honey ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "leather shoes go well with your trousers .", + "Good idea ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Good idea . Oh , by the way , would you please pick me up after the party , honey ?", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_143.json b/reccon/query/tr_143.json new file mode 100644 index 0000000000000000000000000000000000000000..f7825bfdcb8e6d93615d1f5ad80db1904d7535a9 --- /dev/null +++ b/reccon/query/tr_143.json @@ -0,0 +1,24 @@ +[ + { + "turn": 15, + "speaker": "A", + "utterance": "great . I ' m looking forward to it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "maybe you can come to the bar one day and I ' ll show you around ." + ], + "type": [ + "inter-personal" + ], + "text": "great . I ' m looking forward to it .", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1432.json b/reccon/query/tr_1432.json new file mode 100644 index 0000000000000000000000000000000000000000..0824958d35bbb94024e9b0980cf3b257a430e310 --- /dev/null +++ b/reccon/query/tr_1432.json @@ -0,0 +1,27 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Yes , but not always . However , I won't let it go if I have a chance .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "swum in a river or a lake ?", + "Yes , but not always . However , I won't let it go if I have a chance ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , but not always . However , I won't let it go if I have a chance .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1443.json b/reccon/query/tr_1443.json new file mode 100644 index 0000000000000000000000000000000000000000..42d2b7f3bde0d62b394f46d5db31e41ecdcf12bb --- /dev/null +++ b/reccon/query/tr_1443.json @@ -0,0 +1,27 @@ +[ + { + "turn": 13, + "speaker": "A", + "utterance": "... and you looked so adorable with your hair all wet . I had to take a picture of you standing there in that little alley , smiling and laughing in the rain ...", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12, + 13 + ], + "expanded emotion cause span": [ + "Our trip to Italy ! I remember that day . We were going to visit the Trev fountain , and we got caught in the rain ...", + "... and you looked so adorable with your hair all wet . I had to take a picture of you standing there in that little alley , smiling and laughing in the rain ..." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "... and you looked so adorable with your hair all wet . I had to take a picture of you standing there in that little alley , smiling and laughing in the rain ...", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1453.json b/reccon/query/tr_1453.json new file mode 100644 index 0000000000000000000000000000000000000000..ded456aeabf9f98ef91483f4fe051a1ac52ebb01 --- /dev/null +++ b/reccon/query/tr_1453.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Thanks , goodbye .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "It suits us fine . We ' ll see you then ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks , goodbye .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1477.json b/reccon/query/tr_1477.json new file mode 100644 index 0000000000000000000000000000000000000000..92fb5557c6e6840d90e8c12d01ff3a93e3fab1bf --- /dev/null +++ b/reccon/query/tr_1477.json @@ -0,0 +1,24 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "Thank you very much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "Good luck with school ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you very much .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_15.json b/reccon/query/tr_15.json new file mode 100644 index 0000000000000000000000000000000000000000..315e0faf05ea5a490352d02a63ba204ca0012e40 --- /dev/null +++ b/reccon/query/tr_15.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "B", + "utterance": "That is truly amazing !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "She will be 86 next month ." + ], + "type": [ + "inter-personal" + ], + "text": "That is truly amazing !", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1515.json b/reccon/query/tr_1515.json new file mode 100644 index 0000000000000000000000000000000000000000..e0f304600d4641493c3766fe11950a8b474a12d4 --- /dev/null +++ b/reccon/query/tr_1515.json @@ -0,0 +1,27 @@ +[ + { + "turn": 18, + "speaker": "B", + "utterance": "Thanks . I plan on it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13, + 17 + ], + "expanded emotion cause span": [ + "She wants to know if you want to go to the office party with her tomorrow night .", + "Have a great time tomorrow night ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks . I plan on it .", + "id": 18, + "source_sentences": [ + 12, + 16 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1531.json b/reccon/query/tr_1531.json new file mode 100644 index 0000000000000000000000000000000000000000..c42a7093e46ab1a2dd91a812fa2b0c03611844ce --- /dev/null +++ b/reccon/query/tr_1531.json @@ -0,0 +1,27 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "It ' s very nice of you to say so . I should say you are glamorous yourself , as a matter of fact .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 5 + ], + "expanded emotion cause span": [ + "Yes , it suits you very well . It certainly is unique . I don ' t think I ' Ve seen anything like it before .", + "it matches your dress marvelously ." + ], + "type": [ + "inter-personal" + ], + "text": "It ' s very nice of you to say so . I should say you are glamorous yourself , as a matter of fact .", + "id": 6, + "source_sentences": [ + 2, + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1532.json b/reccon/query/tr_1532.json new file mode 100644 index 0000000000000000000000000000000000000000..330aaae1d1083fe633fde38a2d2648b9b5f1212b --- /dev/null +++ b/reccon/query/tr_1532.json @@ -0,0 +1,33 @@ +[ + { + "turn": 15, + "speaker": "A", + "utterance": "That's what everyone says ! I can't wait to see it for myself some day .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 4, + 14, + 15 + ], + "expanded emotion cause span": [ + "It was fantastic ,", + "Because it's off-season , we got a really good package deal to Paris , so we went there .", + "Of course ! You can't go to Paris without going to their famous art gallery ! I was surprised by how small the Mona Lisa was though .", + "I can't wait to see it for myself some day ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's what everyone says ! I can't wait to see it for myself some day .", + "id": 15, + "source_sentences": [ + 1, + 3, + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_155.json b/reccon/query/tr_155.json new file mode 100644 index 0000000000000000000000000000000000000000..e145d60cd13a9d3c3449d4e10084adb789de35ea --- /dev/null +++ b/reccon/query/tr_155.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Thanks . I'm glad you say so . Oh , the music has stopped .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "You are doing the waltz wonderfully well .", + "I'm glad you say so ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thanks . I'm glad you say so . Oh , the music has stopped .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1569.json b/reccon/query/tr_1569.json new file mode 100644 index 0000000000000000000000000000000000000000..b7576ff8f9ecc5c52ac3a55c02d5f9a9e237a195 --- /dev/null +++ b/reccon/query/tr_1569.json @@ -0,0 +1,27 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "That's a great idea . I'm going to do the same .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "Hobbies are great . I'm going to make a list of all the things I like to do .", + "I'm going to do the same ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's a great idea . I'm going to do the same .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_158.json b/reccon/query/tr_158.json new file mode 100644 index 0000000000000000000000000000000000000000..784f13d9c0ef04615003e29ee6c48b768a756f57 --- /dev/null +++ b/reccon/query/tr_158.json @@ -0,0 +1,24 @@ +[ + { + "turn": 31, + "speaker": "A", + "utterance": "You can ask me any question at any time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 30 + ], + "expanded emotion cause span": [ + "I have a lot to learn from you ." + ], + "type": [ + "inter-personal" + ], + "text": "You can ask me any question at any time .", + "id": 31, + "source_sentences": [ + 29 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1604.json b/reccon/query/tr_1604.json new file mode 100644 index 0000000000000000000000000000000000000000..c51900eb0d40f52487ddc512978edcfffab86638 --- /dev/null +++ b/reccon/query/tr_1604.json @@ -0,0 +1,24 @@ +[ + { + "turn": 18, + "speaker": "B", + "utterance": "Of course I am . Well , pleasant dreams !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 17 + ], + "expanded emotion cause span": [ + "You're being a really good friend ." + ], + "type": [ + "inter-personal" + ], + "text": "Of course I am . Well , pleasant dreams !", + "id": 18, + "source_sentences": [ + 16 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1607.json b/reccon/query/tr_1607.json new file mode 100644 index 0000000000000000000000000000000000000000..3c11f839bd8050d4a980a78db414278cfcdd8a5a --- /dev/null +++ b/reccon/query/tr_1607.json @@ -0,0 +1,27 @@ +[ + { + "turn": 19, + "speaker": "A", + "utterance": "I am very happy to hear that , Karen . It ' s good to know I'm working in such a company .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 18, + 19 + ], + "expanded emotion cause span": [ + "You shouldn't worry about Mr . Drummond . He is a very good man to work for . He is not sexist at all . He appreciates people for their ideas . And he is willing to take suggestions from men or women .", + "I am very happy to hear that , Karen . It ' s good to know I'm working in such a company ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I am very happy to hear that , Karen . It ' s good to know I'm working in such a company .", + "id": 19, + "source_sentences": [ + 17 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1614.json b/reccon/query/tr_1614.json new file mode 100644 index 0000000000000000000000000000000000000000..59e80b7b29c561106599b4838ca27e135d1b37cc --- /dev/null +++ b/reccon/query/tr_1614.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "You can't do that , Jenny !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "I'm thinking of dropping out ." + ], + "type": [ + "inter-personal" + ], + "text": "You can't do that , Jenny !", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1617.json b/reccon/query/tr_1617.json new file mode 100644 index 0000000000000000000000000000000000000000..3a5e3887607f9a8498849076175f336e377ab688 --- /dev/null +++ b/reccon/query/tr_1617.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "You're most welcome .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Thank you for your hospitality . I hope I didn't cause you too much trouble during my stay ." + ], + "type": [ + "inter-personal" + ], + "text": "You're most welcome .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1627.json b/reccon/query/tr_1627.json new file mode 100644 index 0000000000000000000000000000000000000000..eead2f9b805f8b0b7c3f620b22a9b0fd93b62157 --- /dev/null +++ b/reccon/query/tr_1627.json @@ -0,0 +1,24 @@ +[ + { + "turn": 13, + "speaker": "A", + "utterance": "I don't know about that , but my door is always open . Stop by anytime .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "Thanks . It helps to get it off my chest . You're always so easy to talk to ." + ], + "type": [ + "inter-personal" + ], + "text": "I don't know about that , but my door is always open . Stop by anytime .", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1630.json b/reccon/query/tr_1630.json new file mode 100644 index 0000000000000000000000000000000000000000..e1d755957dde3fc332f4bdbb2e4ce203767f3757 --- /dev/null +++ b/reccon/query/tr_1630.json @@ -0,0 +1,28 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "It's time to go . Bye , Ella . Hope to see you soon", + "emotion": "happiness", + "explanation": "speaker is happy to see the listener in the future", + "expanded emotion cause evidence": [ + 1, + 6 + ], + "expanded emotion cause span": [ + "I'd like to meet you again sometime .", + "Hope to see you soon" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It's time to go . Bye , Ella . Hope to see you soon", + "id": 6, + "source_sentences": [ + 0 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1634.json b/reccon/query/tr_1634.json new file mode 100644 index 0000000000000000000000000000000000000000..8d867261b81b02c594159bb74469024a5dd0e4ab --- /dev/null +++ b/reccon/query/tr_1634.json @@ -0,0 +1,29 @@ +[ + { + "turn": 20, + "speaker": "B", + "utterance": "Good point . I suppose that we all have our own individual styles .", + "emotion": "happiness", + "explanation": "the speaker is happy to hear about that A has her own personal style", + "flag": "F", + "expanded emotion cause evidence": [ + 19, + 20 + ], + "expanded emotion cause span": [ + "That's my style when I'm not in the office .", + "Good point . I suppose that we all have our own individual styles ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Good point . I suppose that we all have our own individual styles .", + "id": 20, + "source_sentences": [ + 18 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1655.json b/reccon/query/tr_1655.json new file mode 100644 index 0000000000000000000000000000000000000000..33caabbca60247349577da92a641f66c7e9d3b0e --- /dev/null +++ b/reccon/query/tr_1655.json @@ -0,0 +1,24 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Okay .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "But you have to teach me ." + ], + "type": [ + "inter-personal" + ], + "text": "Okay .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1656.json b/reccon/query/tr_1656.json new file mode 100644 index 0000000000000000000000000000000000000000..87ff8cdd331e8a40142e760f863a4d1c3348eb72 --- /dev/null +++ b/reccon/query/tr_1656.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "What does he look like ? Can people tell ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "We're very happy that he's healthy and smart ." + ], + "type": [ + "inter-personal" + ], + "text": "What does he look like ? Can people tell ?", + "id": 7, + "source_sentences": [ + 3 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1661.json b/reccon/query/tr_1661.json new file mode 100644 index 0000000000000000000000000000000000000000..44189b25c08e1723ee124d8b2258c7dcfd5a5d3b --- /dev/null +++ b/reccon/query/tr_1661.json @@ -0,0 +1,24 @@ +[ + { + "turn": 16, + "speaker": "B", + "utterance": "You are welcome ! We are neighbors !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "OK , got it ! Thank you so much . You have helped me a lot !" + ], + "type": [ + "inter-personal" + ], + "text": "You are welcome ! We are neighbors !", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1664.json b/reccon/query/tr_1664.json new file mode 100644 index 0000000000000000000000000000000000000000..7331bf4c879a590a45a15532872888c94d87f5b5 --- /dev/null +++ b/reccon/query/tr_1664.json @@ -0,0 +1,27 @@ +[ + { + "turn": 16, + "speaker": "B", + "utterance": "I believe in that . Well , the performance is about to begin . Let's be quiet .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15, + 16 + ], + "expanded emotion cause span": [ + "The right opportunity for you would come along soon .", + "the performance is about to begin" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I believe in that . Well , the performance is about to begin . Let's be quiet .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1675.json b/reccon/query/tr_1675.json new file mode 100644 index 0000000000000000000000000000000000000000..a73cb19bc3ef01e0fca2b496338dc1e737695575 --- /dev/null +++ b/reccon/query/tr_1675.json @@ -0,0 +1,25 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "Yes .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "This is what you were meant for . Say you love me , say yes , say yes ." + ], + "type": [ + "inter-personal" + ], + "text": "Yes .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1677.json b/reccon/query/tr_1677.json new file mode 100644 index 0000000000000000000000000000000000000000..862eb2c8558c9abb74e8ecdd957ac446084576d6 --- /dev/null +++ b/reccon/query/tr_1677.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Thank you . I appreciate the compliment .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I am impressed ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . I appreciate the compliment .", + "id": 8, + "source_sentences": [ + 2 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1686.json b/reccon/query/tr_1686.json new file mode 100644 index 0000000000000000000000000000000000000000..a8d55b95e86c52481ffa4968ef5f8af30ff7db23 --- /dev/null +++ b/reccon/query/tr_1686.json @@ -0,0 +1,27 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "Tragic movie ? I think it's a love story .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "I get a lump in my throat whenever I see a tragic movie .", + "I think it's a love story ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Tragic movie ? I think it's a love story .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1688.json b/reccon/query/tr_1688.json new file mode 100644 index 0000000000000000000000000000000000000000..66859e04304faafff39f5619a950c49f7c9ded1b --- /dev/null +++ b/reccon/query/tr_1688.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Oh , Miss Anna ! That's too hard ! I won't be here long .", + "emotion": "sad", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "But please don't speak to me again ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , Miss Anna ! That's too hard ! I won't be here long .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1693.json b/reccon/query/tr_1693.json new file mode 100644 index 0000000000000000000000000000000000000000..116601474a93325e0b143ddd4e69eca15cea1ff7 --- /dev/null +++ b/reccon/query/tr_1693.json @@ -0,0 +1,30 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "No problem , girl friend . I'll see you next time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 7, + 11 + ], + "expanded emotion cause span": [ + "I think it looks gorgeous .", + "I honestly think it looks great .", + "Thanks for doing such a good job ." + ], + "type": [ + "inter-personal" + ], + "text": "No problem , girl friend . I'll see you next time .", + "id": 12, + "source_sentences": [ + 4, + 6, + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1703.json b/reccon/query/tr_1703.json new file mode 100644 index 0000000000000000000000000000000000000000..e9b52a9cbade50081f722186799d5d554e216a94 --- /dev/null +++ b/reccon/query/tr_1703.json @@ -0,0 +1,27 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "That ' s great . I'd love to .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "I want to invite you to enjoy the food I cook .", + "I'd love to ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That ' s great . I'd love to .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1711.json b/reccon/query/tr_1711.json new file mode 100644 index 0000000000000000000000000000000000000000..d66ed9e126c1608f2e923dc02675deebdd494678 --- /dev/null +++ b/reccon/query/tr_1711.json @@ -0,0 +1,27 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Yes , my father gave it to me for my birthday . Do you like it ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "Is that your new bicycle ?", + "my father gave it to me for my birthday ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , my father gave it to me for my birthday . Do you like it ?", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1712.json b/reccon/query/tr_1712.json new file mode 100644 index 0000000000000000000000000000000000000000..ba35f4072233e39a94766e8990553ce2e21f28d2 --- /dev/null +++ b/reccon/query/tr_1712.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Great idea . I ' m looking forward to it . See you then .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "How about next time we meet at my place ? And I ' ll treat you to Chinese food . I know how much you like it . We can order in and watch video too . Anything you like , I promise ." + ], + "type": [ + "inter-personal" + ], + "text": "Great idea . I ' m looking forward to it . See you then .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1716.json b/reccon/query/tr_1716.json new file mode 100644 index 0000000000000000000000000000000000000000..8f3ff0db43185928f7370a35449f01fcb4bf2743 --- /dev/null +++ b/reccon/query/tr_1716.json @@ -0,0 +1,31 @@ +[ + { + "turn": 15, + "speaker": "A", + "utterance": "good luck !", + "emotion": "happiness", + "explanation": "speaker is happy to see B getting the courage to make a move", + "expanded emotion cause evidence": [ + 4, + 6, + 14 + ], + "expanded emotion cause span": [ + "the blond with the red dress ?", + "She could do anything she wants to me !", + "here I go !" + ], + "type": [ + "inter-personal" + ], + "text": "good luck !", + "id": 15, + "source_sentences": [ + 3, + 5, + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1719.json b/reccon/query/tr_1719.json new file mode 100644 index 0000000000000000000000000000000000000000..65980d5626d37d3621a5b2bbd64c1956b51fe0f0 --- /dev/null +++ b/reccon/query/tr_1719.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "You're welcome . Have a nice trip !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Thanks again for everything you have done for me ." + ], + "type": [ + "inter-personal" + ], + "text": "You're welcome . Have a nice trip !", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1725.json b/reccon/query/tr_1725.json new file mode 100644 index 0000000000000000000000000000000000000000..5cc62f266f46b0eab4ecfc4d8b78b392d3404a90 --- /dev/null +++ b/reccon/query/tr_1725.json @@ -0,0 +1,27 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "He asked me out to a dinner tonight . How about joining us ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 12 + ], + "expanded emotion cause span": [ + "Valentine's Day ?", + "He asked me out to a dinner tonight ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "He asked me out to a dinner tonight . How about joining us ?", + "id": 12, + "source_sentences": [ + 2 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1730.json b/reccon/query/tr_1730.json new file mode 100644 index 0000000000000000000000000000000000000000..daba076cd2b88ff2d3d01105e1353e9c215092da --- /dev/null +++ b/reccon/query/tr_1730.json @@ -0,0 +1,27 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "That's a good idea . Let ' s go !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "Would you like to go to the bookshop with me ?", + "That's a good idea ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's a good idea . Let ' s go !", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1734.json b/reccon/query/tr_1734.json new file mode 100644 index 0000000000000000000000000000000000000000..39b56567a3a14c3e30d8f8255fcac072baaf3123 --- /dev/null +++ b/reccon/query/tr_1734.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "Sometimes , it ' s hard to know who belongs in each section of the museum !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "There you can see british leaders , entertainers , criminals , and royalty ." + ], + "type": [ + "inter-personal" + ], + "text": "Sometimes , it ' s hard to know who belongs in each section of the museum !", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1735.json b/reccon/query/tr_1735.json new file mode 100644 index 0000000000000000000000000000000000000000..4f1bdf786f36e577577116694ae0f63892aaaa54 --- /dev/null +++ b/reccon/query/tr_1735.json @@ -0,0 +1,24 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "thanks , that was nice of you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "don't worry . Nothing bad will happen . I'll even buy your ticket for you ." + ], + "type": [ + "inter-personal" + ], + "text": "thanks , that was nice of you .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1738.json b/reccon/query/tr_1738.json new file mode 100644 index 0000000000000000000000000000000000000000..6e1d696aa8ae7907cf87b349d1a21d93ab9687c7 --- /dev/null +++ b/reccon/query/tr_1738.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "Well , it is a birch tree . It is not as old as you think .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "You are kind ." + ], + "type": [ + "inter-personal" + ], + "text": "Well , it is a birch tree . It is not as old as you think .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1739.json b/reccon/query/tr_1739.json new file mode 100644 index 0000000000000000000000000000000000000000..9e45eb4ec16d90ac69302826decc780e4d8a0419 --- /dev/null +++ b/reccon/query/tr_1739.json @@ -0,0 +1,24 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "Come on . Put the gun down .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "Oh , I love you too !" + ], + "type": [ + "inter-personal" + ], + "text": "Come on . Put the gun down .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1754.json b/reccon/query/tr_1754.json new file mode 100644 index 0000000000000000000000000000000000000000..8e108caa683d3c578ab651cb7a21a18934514a15 --- /dev/null +++ b/reccon/query/tr_1754.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "It sure is .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "This city is really comfortable to live in ." + ], + "type": [ + "inter-personal" + ], + "text": "It sure is .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_176.json b/reccon/query/tr_176.json new file mode 100644 index 0000000000000000000000000000000000000000..ff4d4ecdf15f7466351f4bff5a8bfbab06682ec3 --- /dev/null +++ b/reccon/query/tr_176.json @@ -0,0 +1,27 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "It is the symbol of laughing at hoar frost and fighting with snow . I admire the bravery of plum blossoms .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "You have a perfect taste !", + "symbol of laughing at hoar frost and fighting with snow . I admire the bravery of plum blossoms ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It is the symbol of laughing at hoar frost and fighting with snow . I admire the bravery of plum blossoms .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1775.json b/reccon/query/tr_1775.json new file mode 100644 index 0000000000000000000000000000000000000000..7561e5f6c17f3927c08289720ef4bf5cf825204d --- /dev/null +++ b/reccon/query/tr_1775.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "It's a new concert hall and the acoustics are great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "The performance is excellent .", + "It's a new concert hall and the acoustics are great ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It's a new concert hall and the acoustics are great .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1784.json b/reccon/query/tr_1784.json new file mode 100644 index 0000000000000000000000000000000000000000..e967395fd57782a6dd7be1b895cee0cf60d6a8db --- /dev/null +++ b/reccon/query/tr_1784.json @@ -0,0 +1,24 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "Goodbye .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "You too . I hope to see you soon ." + ], + "type": [ + "inter-personal" + ], + "text": "Goodbye .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_18.json b/reccon/query/tr_18.json new file mode 100644 index 0000000000000000000000000000000000000000..b44284e634e235c9f893797bb5a95261f58125e0 --- /dev/null +++ b/reccon/query/tr_18.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "A", + "utterance": "A crazy language ? Why do you say that ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "It's a crazy language ." + ], + "type": [ + "inter-personal" + ], + "text": "A crazy language ? Why do you say that ?", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_181.json b/reccon/query/tr_181.json new file mode 100644 index 0000000000000000000000000000000000000000..2593bccb695c152ef0eb36dfe262cd02211079a2 --- /dev/null +++ b/reccon/query/tr_181.json @@ -0,0 +1,27 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Congratulations ! What's your normal handicap ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 7 + ], + "expanded emotion cause span": [ + "Extremely good . I shot a 78 , including 5 birdies !", + "Extremely good . I shot a 78 , including 5 birdies !" + ], + "type": [ + "inter-personal" + ], + "text": "Congratulations ! What's your normal handicap ?", + "id": 8, + "source_sentences": [ + 6, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_183.json b/reccon/query/tr_183.json new file mode 100644 index 0000000000000000000000000000000000000000..b74224e2a021e660ac5e33641d59d128a993ca1e --- /dev/null +++ b/reccon/query/tr_183.json @@ -0,0 +1,28 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Oh , that's OK . Let's just meet at the theater before the show , around 7:30 .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1, + 1 + ], + "expanded emotion cause span": [ + "I have tickets", + "Would you like to go ?" + ], + "type": [ + "inter-personal" + ], + "text": "Oh , that's OK . Let's just meet at the theater before the show , around 7:30 .", + "id": 6, + "source_sentences": [ + 0, + 0 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1848.json b/reccon/query/tr_1848.json new file mode 100644 index 0000000000000000000000000000000000000000..bce85df848a5bdea16c81c53aa72d087b6b82275 --- /dev/null +++ b/reccon/query/tr_1848.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "All right ! Thanks !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Sure , I'd love to !" + ], + "type": [ + "inter-personal" + ], + "text": "All right ! Thanks !", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1892.json b/reccon/query/tr_1892.json new file mode 100644 index 0000000000000000000000000000000000000000..2bc2f2ebe8748bcbfa0c6fb2f05b065b3f101e44 --- /dev/null +++ b/reccon/query/tr_1892.json @@ -0,0 +1,27 @@ +[ + { + "turn": 19, + "speaker": "A", + "utterance": "Me , too ! Do you want to come over and watch the next game at my place ? I'm planning on having a few people over to watch it together .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 18, + 19 + ], + "expanded emotion cause span": [ + "I really love watching football games", + "Me , too !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Me , too ! Do you want to come over and watch the next game at my place ? I'm planning on having a few people over to watch it together .", + "id": 19, + "source_sentences": [ + 17 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_19.json b/reccon/query/tr_19.json new file mode 100644 index 0000000000000000000000000000000000000000..6f1c28f025128c55ed28f17d3061b9ae2caf2aea --- /dev/null +++ b/reccon/query/tr_19.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "A", + "utterance": "Thank you for you help .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "There are several possible sources you might use for that topic . I suggest you use the computer and the computer will give you a list of every scientific journal that talks about children and television ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you for you help .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1921.json b/reccon/query/tr_1921.json new file mode 100644 index 0000000000000000000000000000000000000000..62e5ee3f754a84eb5736c73b5e72b3eacbdf9efd --- /dev/null +++ b/reccon/query/tr_1921.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Thanks . I could eat a cow .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "It ' s my treat this time .", + "I could eat a cow ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thanks . I could eat a cow .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1928.json b/reccon/query/tr_1928.json new file mode 100644 index 0000000000000000000000000000000000000000..71a2e66bd64fb404aea80bbf263cab21fb4fe5fd --- /dev/null +++ b/reccon/query/tr_1928.json @@ -0,0 +1,27 @@ +[ + { + "turn": 25, + "speaker": "A", + "utterance": "C U here , honey .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 20, + 24 + ], + "expanded emotion cause span": [ + "Oh , I will have a sweet dream .", + "Kisssssssssss ." + ], + "type": [ + "inter-personal" + ], + "text": "C U here , honey .", + "id": 25, + "source_sentences": [ + 19, + 23 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1936.json b/reccon/query/tr_1936.json new file mode 100644 index 0000000000000000000000000000000000000000..bd82350d987412391d22a19c0248e55afa9625e5 --- /dev/null +++ b/reccon/query/tr_1936.json @@ -0,0 +1,24 @@ +[ + { + "turn": 21, + "speaker": "A", + "utterance": "I will . Thanks a lot .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 20 + ], + "expanded emotion cause span": [ + "call me if you need anything" + ], + "type": [ + "inter-personal" + ], + "text": "I will . Thanks a lot .", + "id": 21, + "source_sentences": [ + 19 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1950.json b/reccon/query/tr_1950.json new file mode 100644 index 0000000000000000000000000000000000000000..22af2ecff1e748fa9c03bce8aca2d9010917f77e --- /dev/null +++ b/reccon/query/tr_1950.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Miss , I'm very sorry for the delay , please enjoy this . Free a glass of wine for inconvenience . Again I'm terribly sorry to make you wait so long .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I ordered my dish about a half an hour ago , but it hasn't arrived yet ." + ], + "type": [ + "inter-personal" + ], + "text": "Miss , I'm very sorry for the delay , please enjoy this . Free a glass of wine for inconvenience . Again I'm terribly sorry to make you wait so long .", + "id": 6, + "source_sentences": [ + 2 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1951.json b/reccon/query/tr_1951.json new file mode 100644 index 0000000000000000000000000000000000000000..23f52695f69f4a8b960b89af997cd309a79d5351 --- /dev/null +++ b/reccon/query/tr_1951.json @@ -0,0 +1,24 @@ +[ + { + "turn": 13, + "speaker": "A", + "utterance": "Fine .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "My pleasure . Let's go and have a drink ." + ], + "type": [ + "inter-personal" + ], + "text": "Fine .", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1954.json b/reccon/query/tr_1954.json new file mode 100644 index 0000000000000000000000000000000000000000..2d42b60c98372eb1ed8ad0a2d15da9888893df0a --- /dev/null +++ b/reccon/query/tr_1954.json @@ -0,0 +1,24 @@ +[ + { + "turn": 13, + "speaker": "A", + "utterance": "Really ? What !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "There is some really good news though !" + ], + "type": [ + "inter-personal" + ], + "text": "Really ? What !", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1962.json b/reccon/query/tr_1962.json new file mode 100644 index 0000000000000000000000000000000000000000..576549d7e69ecd9b7c0a3cf3c78cd645353edbde --- /dev/null +++ b/reccon/query/tr_1962.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Yes , could you please go over this for me ? And see if there is any mistake in it ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "Do you need my help ?", + "Yes , could you please go over this for me ? And see if there is any mistake in it ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , could you please go over this for me ? And see if there is any mistake in it ?", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1963.json b/reccon/query/tr_1963.json new file mode 100644 index 0000000000000000000000000000000000000000..992dabd454566a936273a16afbfb66b29d41a583 --- /dev/null +++ b/reccon/query/tr_1963.json @@ -0,0 +1,27 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "Let me see . Yes , that's it . Where did you find it ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "Oh , what's this ? Is this your dissertation ?", + "Yes , that's it ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Let me see . Yes , that's it . Where did you find it ?", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1975.json b/reccon/query/tr_1975.json new file mode 100644 index 0000000000000000000000000000000000000000..403a1d27329fe07348cf5b7250d55f810670b601 --- /dev/null +++ b/reccon/query/tr_1975.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Really ? It's a deal . Have you ever been there ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I promise you , this summer vacation , I will take you to Huang-Shan Mountains . It is more beautiful and magnificent ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? It's a deal . Have you ever been there ?", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1980.json b/reccon/query/tr_1980.json new file mode 100644 index 0000000000000000000000000000000000000000..171da9ef8d0a3cbfc4443bff35949839d2787e18 --- /dev/null +++ b/reccon/query/tr_1980.json @@ -0,0 +1,24 @@ +[ + { + "turn": 18, + "speaker": "B", + "utterance": "Really ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 17 + ], + "expanded emotion cause span": [ + "It ' s also very different from the British education system ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ?", + "id": 18, + "source_sentences": [ + 16 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_1984.json b/reccon/query/tr_1984.json new file mode 100644 index 0000000000000000000000000000000000000000..ab3c2910b04a5169e63cd164c1e69c07efcae648 --- /dev/null +++ b/reccon/query/tr_1984.json @@ -0,0 +1,24 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "So cool . I want to be a back-packer when I grow up .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "actually almost half of all the countries over the world ." + ], + "type": [ + "inter-personal" + ], + "text": "So cool . I want to be a back-packer when I grow up .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_20.json b/reccon/query/tr_20.json new file mode 100644 index 0000000000000000000000000000000000000000..1fee603ee00af3022766978d908892a0d711791b --- /dev/null +++ b/reccon/query/tr_20.json @@ -0,0 +1,27 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Yeah , there isn ' t a bad seat in the place .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "really great place to watch a baseball game .", + "Yeah , there isn ' t a bad seat in the place ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yeah , there isn ' t a bad seat in the place .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2002.json b/reccon/query/tr_2002.json new file mode 100644 index 0000000000000000000000000000000000000000..3e2e3dedfae52a661e400d8b5846433db4ededee --- /dev/null +++ b/reccon/query/tr_2002.json @@ -0,0 +1,27 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "You are so interesting .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "But I like cold more than hot .", + "You are so interesting ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You are so interesting .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2042.json b/reccon/query/tr_2042.json new file mode 100644 index 0000000000000000000000000000000000000000..c35e2f00c5a6334e074e0979973f4e948289e177 --- /dev/null +++ b/reccon/query/tr_2042.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Oh , it ' s love at first sight .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "He is a nice guy and very considerate . I am impressed with how smart and humorous ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , it ' s love at first sight .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2061.json b/reccon/query/tr_2061.json new file mode 100644 index 0000000000000000000000000000000000000000..afbc13845055cd31b4f96541f0ba8e835d39d978 --- /dev/null +++ b/reccon/query/tr_2061.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Good idea . I'll go shopping in one of the department stores nearby . We'll go to the zoo and the park another time . After all , we can put that off .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "We can visit the country" + ], + "type": [ + "inter-personal" + ], + "text": "Good idea . I'll go shopping in one of the department stores nearby . We'll go to the zoo and the park another time . After all , we can put that off .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2066.json b/reccon/query/tr_2066.json new file mode 100644 index 0000000000000000000000000000000000000000..5d9731632901add88e6d45920cc832fe11105cac --- /dev/null +++ b/reccon/query/tr_2066.json @@ -0,0 +1,24 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "You bet it !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "Moblogging must have done a great favor for habitual bloggers" + ], + "type": [ + "inter-personal" + ], + "text": "You bet it !", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2072.json b/reccon/query/tr_2072.json new file mode 100644 index 0000000000000000000000000000000000000000..0814f6f842a3088555790f02eab1bc121623c802 --- /dev/null +++ b/reccon/query/tr_2072.json @@ -0,0 +1,27 @@ +[ + { + "turn": 16, + "speaker": "B", + "utterance": "I'll talk to my husband about it ; I'm sure he'll say yes ! He loves Switzerland !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15, + 16 + ], + "expanded emotion cause span": [ + "Would you like to go skiing with us for christmas ?", + "I'm sure he'll say yes ! He loves Switzerland !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'll talk to my husband about it ; I'm sure he'll say yes ! He loves Switzerland !", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2080.json b/reccon/query/tr_2080.json new file mode 100644 index 0000000000000000000000000000000000000000..a86a29d92c85a0a48520270ccbe7caf2113eb3d4 --- /dev/null +++ b/reccon/query/tr_2080.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Thank you for saying so .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "They are beautiful . You did a good job ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you for saying so .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_209.json b/reccon/query/tr_209.json new file mode 100644 index 0000000000000000000000000000000000000000..4cc29851a8e55fdbdea4abece9c4a357fc0f8d47 --- /dev/null +++ b/reccon/query/tr_209.json @@ -0,0 +1,25 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Let's hope it is !", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I hope we are over our financial difficulties for good ." + ], + "type": [ + "inter-personal" + ], + "text": "Let's hope it is !", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2101.json b/reccon/query/tr_2101.json new file mode 100644 index 0000000000000000000000000000000000000000..72b13b3e7704eae666cd07032d65f9fe8cc2564b --- /dev/null +++ b/reccon/query/tr_2101.json @@ -0,0 +1,33 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "They soud like the neighbours from hell !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 3, + 5, + 7, + 7 + ], + "expanded emotion cause span": [ + "They're incredibly selfish . They ' re always up until the wee hours of the night playing their music so loudly that I have to wear earplugs in order to fall asleep !", + "they were so arrogant that I didin't want to ever talk to them again !", + "They both just talk about how great they are all the time .", + "They both just talk about how great they are all the time ." + ], + "type": [ + "inter-personal" + ], + "text": "They soud like the neighbours from hell !", + "id": 8, + "source_sentences": [ + 2, + 4, + 6, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2105.json b/reccon/query/tr_2105.json new file mode 100644 index 0000000000000000000000000000000000000000..ca461fc843b8ccb173db0527e818725abdaacbcc --- /dev/null +++ b/reccon/query/tr_2105.json @@ -0,0 +1,24 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "That ' s a possibility . Thanks !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "People who play ultimate Frisbee have a positive attitude ; maybe you should join the ultimate Frisbee club ." + ], + "type": [ + "inter-personal" + ], + "text": "That ' s a possibility . Thanks !", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2122.json b/reccon/query/tr_2122.json new file mode 100644 index 0000000000000000000000000000000000000000..d36d3b896f5d39b4b2bf9489d879475fc2c120d5 --- /dev/null +++ b/reccon/query/tr_2122.json @@ -0,0 +1,30 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "Why not ? It sounds great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 11, + 12 + ], + "expanded emotion cause span": [ + "Canadian ice wine .", + "It's made from naturally frozen grapes .", + "It sounds great ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Why not ? It sounds great .", + "id": 12, + "source_sentences": [ + 8, + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2124.json b/reccon/query/tr_2124.json new file mode 100644 index 0000000000000000000000000000000000000000..bce87f4ff0658fdaf892f430afb3af327427dccd --- /dev/null +++ b/reccon/query/tr_2124.json @@ -0,0 +1,24 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "Thanks a lot .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "That is OK . Here is 20 dollars and you can keep the change ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks a lot .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2170.json b/reccon/query/tr_2170.json new file mode 100644 index 0000000000000000000000000000000000000000..9f5c1851b4ffae9cce262c34edff445ea3cb29a6 --- /dev/null +++ b/reccon/query/tr_2170.json @@ -0,0 +1,25 @@ +[ + { + "turn": 13, + "speaker": "A", + "utterance": "Not at all .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "Thank you . Thank you for the trouble you've taken ." + ], + "type": [ + "inter-personal" + ], + "text": "Not at all .", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2179.json b/reccon/query/tr_2179.json new file mode 100644 index 0000000000000000000000000000000000000000..b817bf2c403d5b79d6d475df0f81331d568bb111 --- /dev/null +++ b/reccon/query/tr_2179.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Really ? I ' m surprised .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "She ' s going to live in Paris ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? I ' m surprised .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2184.json b/reccon/query/tr_2184.json new file mode 100644 index 0000000000000000000000000000000000000000..bcdab399f12bf27618703a1b2de763180ed7eeb2 --- /dev/null +++ b/reccon/query/tr_2184.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "B", + "utterance": "Really , Mary , you ' re horrible .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "Your Rose is a fool .", + "Really , Mary , you ' re horrible ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Really , Mary , you ' re horrible .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2198.json b/reccon/query/tr_2198.json new file mode 100644 index 0000000000000000000000000000000000000000..09b5f3ee33f7c786dab4359c574007c60147510c --- /dev/null +++ b/reccon/query/tr_2198.json @@ -0,0 +1,27 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "That's not bad . Let's go .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 10 + ], + "expanded emotion cause span": [ + "I like flowers .", + "Let's enjoy the plum blossoms ." + ], + "type": [ + "inter-personal" + ], + "text": "That's not bad . Let's go .", + "id": 11, + "source_sentences": [ + 1, + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2200.json b/reccon/query/tr_2200.json new file mode 100644 index 0000000000000000000000000000000000000000..32c9df6eb2c9463b4956c76af4c041ba61a6ed05 --- /dev/null +++ b/reccon/query/tr_2200.json @@ -0,0 +1,27 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Great ! I have a coupon for free popcorn at that theater !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 8 + ], + "expanded emotion cause span": [ + "There's an action movie with Harrison Ford", + "I have a coupon for free popcorn" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Great ! I have a coupon for free popcorn at that theater !", + "id": 8, + "source_sentences": [ + 2 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_221.json b/reccon/query/tr_221.json new file mode 100644 index 0000000000000000000000000000000000000000..80cab0eb394dccde47120f21ea495c19ce01ca8d --- /dev/null +++ b/reccon/query/tr_221.json @@ -0,0 +1,27 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "Well , I don ' t mean to boast but all the designs are done by myself and some colleagues are already trying to copy some of them for their new apartments . Look , they are making photos now of my designed kitchen .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "such a nice place .", + "all the designs are done by myself and some colleagues are already trying to copy some of them for their new apartments . Look , they are making photos now of my designed kitchen ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Well , I don ' t mean to boast but all the designs are done by myself and some colleagues are already trying to copy some of them for their new apartments . Look , they are making photos now of my designed kitchen .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2210.json b/reccon/query/tr_2210.json new file mode 100644 index 0000000000000000000000000000000000000000..5b9d0f9889ba2f36067a554deb538ad333047f7d --- /dev/null +++ b/reccon/query/tr_2210.json @@ -0,0 +1,24 @@ +[ + { + "turn": 17, + "speaker": "A", + "utterance": "Days ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 16 + ], + "expanded emotion cause span": [ + "we'll probably be here for days ." + ], + "type": [ + "inter-personal" + ], + "text": "Days ?", + "id": 17, + "source_sentences": [ + 15 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2212.json b/reccon/query/tr_2212.json new file mode 100644 index 0000000000000000000000000000000000000000..64f541feb35f04bc10d7599dfb3a10d3b750ea5a --- /dev/null +++ b/reccon/query/tr_2212.json @@ -0,0 +1,27 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Thank you . Oh , it tastes excellent .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "( The waiter makes the cocktail for Mr . Bellow and hands into him . ) Here is your Shanghai cocktail , Mr . Bellow .", + "Oh , it tastes excellent ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you . Oh , it tastes excellent .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2217.json b/reccon/query/tr_2217.json new file mode 100644 index 0000000000000000000000000000000000000000..b3b2222735543c8bc35af57e8c459de6932aaffd --- /dev/null +++ b/reccon/query/tr_2217.json @@ -0,0 +1,24 @@ +[ + { + "turn": 18, + "speaker": "B", + "utterance": "Okay . See you then .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 17 + ], + "expanded emotion cause span": [ + "I'll see you there at 9pm ." + ], + "type": [ + "inter-personal" + ], + "text": "Okay . See you then .", + "id": 18, + "source_sentences": [ + 16 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_222.json b/reccon/query/tr_222.json new file mode 100644 index 0000000000000000000000000000000000000000..7e822d9db3cd03dcafb52045124bdc6294078710 --- /dev/null +++ b/reccon/query/tr_222.json @@ -0,0 +1,27 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Perhaps you are right . But I still need some time to recover from the failure .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "I'm sure you'll succeed .", + "Perhaps you are right ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Perhaps you are right . But I still need some time to recover from the failure .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2223.json b/reccon/query/tr_2223.json new file mode 100644 index 0000000000000000000000000000000000000000..ccb38c15c4bd85e6b4db717ea44476e4b29da62f --- /dev/null +++ b/reccon/query/tr_2223.json @@ -0,0 +1,27 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Amazing ! I can imagine the feeling when I hear the smooth tune around my ears .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "I got two . We can go there together .", + "I can imagine the feeling when I hear the smooth tune around my ears ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Amazing ! I can imagine the feeling when I hear the smooth tune around my ears .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_223.json b/reccon/query/tr_223.json new file mode 100644 index 0000000000000000000000000000000000000000..7bef631b58281326d11eacff33d4fb0ba72db2c7 --- /dev/null +++ b/reccon/query/tr_223.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "You dance beautifully too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "You're dancing so well .", + "You dance beautifully too ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You dance beautifully too .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2232.json b/reccon/query/tr_2232.json new file mode 100644 index 0000000000000000000000000000000000000000..10a01cacfdc75c2211b248093d1fa6f633ab82c5 --- /dev/null +++ b/reccon/query/tr_2232.json @@ -0,0 +1,27 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "I am really sorry too , maybe I can give you a call sometime .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "Sorry to hear that , I was really looking forward to spending some more time with you , I really enjoyed our last chat .", + "I am really sorry too" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I am really sorry too , maybe I can give you a call sometime .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2240.json b/reccon/query/tr_2240.json new file mode 100644 index 0000000000000000000000000000000000000000..7bd5003666a784607a11318d72c6f7113b3404e9 --- /dev/null +++ b/reccon/query/tr_2240.json @@ -0,0 +1,27 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "That ' s very generous of you . I guess that would work .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "If you lose your job , you can just move in with me until you find another job . That will save you plenty of money .", + "That ' s very generous of you . I guess that would work ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That ' s very generous of you . I guess that would work .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2250.json b/reccon/query/tr_2250.json new file mode 100644 index 0000000000000000000000000000000000000000..8b283a41b1d2328b1ad8c25aa9c4363d3cf545cb --- /dev/null +++ b/reccon/query/tr_2250.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "Really ! How fascinating .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "he's been having an affair with his secretary ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ! How fascinating .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2271.json b/reccon/query/tr_2271.json new file mode 100644 index 0000000000000000000000000000000000000000..9beccae0bfa4fe70e84a909f5379192999871745 --- /dev/null +++ b/reccon/query/tr_2271.json @@ -0,0 +1,27 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "They're neat . Now Let's take that path into the woods and see what we can see ...", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 9 + ], + "expanded emotion cause span": [ + "look ! There are some wild ducks over there in the reeds .", + "They're neat ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "They're neat . Now Let's take that path into the woods and see what we can see ...", + "id": 9, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2274.json b/reccon/query/tr_2274.json new file mode 100644 index 0000000000000000000000000000000000000000..59937389257b5b0a39cf0f6b81114d872202e6c9 --- /dev/null +++ b/reccon/query/tr_2274.json @@ -0,0 +1,24 @@ +[ + { + "turn": 15, + "speaker": "A", + "utterance": "Don't mention it . Good luck . You're going to need it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "I think that's the idea I was looking for . Thanks , man ." + ], + "type": [ + "inter-personal" + ], + "text": "Don't mention it . Good luck . You're going to need it .", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2275.json b/reccon/query/tr_2275.json new file mode 100644 index 0000000000000000000000000000000000000000..bb68a351f066db29e74ec8178dca78016627e364 --- /dev/null +++ b/reccon/query/tr_2275.json @@ -0,0 +1,24 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "Try to catch this bouquet then .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "we are beginning to make preparations ." + ], + "type": [ + "inter-personal" + ], + "text": "Try to catch this bouquet then .", + "id": 14, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_228.json b/reccon/query/tr_228.json new file mode 100644 index 0000000000000000000000000000000000000000..13ca70473a4c4ff493f8d14ff3682ffb7e07463a --- /dev/null +++ b/reccon/query/tr_228.json @@ -0,0 +1,24 @@ +[ + { + "turn": 15, + "speaker": "A", + "utterance": "Thanks for the advice . I'll talk to my fiance about it tonight .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "It'll be very romantic , I think . You'll have loads of fun ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks for the advice . I'll talk to my fiance about it tonight .", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2301.json b/reccon/query/tr_2301.json new file mode 100644 index 0000000000000000000000000000000000000000..696f29c0ddcbc5e685aa59ff47cb0553287fc841 --- /dev/null +++ b/reccon/query/tr_2301.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "OK , will do !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Would you like to play tennis with me ?" + ], + "type": [ + "inter-personal" + ], + "text": "OK , will do !", + "id": 6, + "source_sentences": [ + 2 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2306.json b/reccon/query/tr_2306.json new file mode 100644 index 0000000000000000000000000000000000000000..ceb1253c12eca40c8aa0ce109da10c2beca53241 --- /dev/null +++ b/reccon/query/tr_2306.json @@ -0,0 +1,24 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "Great . I will prepare some clothes and food for the climbing .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "You can take a bird-eye view at the glorious picture when you arrive at the top of the mountain ." + ], + "type": [ + "inter-personal" + ], + "text": "Great . I will prepare some clothes and food for the climbing .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2310.json b/reccon/query/tr_2310.json new file mode 100644 index 0000000000000000000000000000000000000000..a1b27c2c5e0683c2a5b698f4047db93ef1f76fc8 --- /dev/null +++ b/reccon/query/tr_2310.json @@ -0,0 +1,30 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Wow , you ' Ve inspired me to do something !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3, + 5 + ], + "expanded emotion cause span": [ + "you are really fantastic", + "That ' s not a big problem . There are many small schools for adults like you who can study to be certified .", + "you can easily get a student loan" + ], + "type": [ + "inter-personal" + ], + "text": "Wow , you ' Ve inspired me to do something !", + "id": 6, + "source_sentences": [ + 0, + 2, + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2311.json b/reccon/query/tr_2311.json new file mode 100644 index 0000000000000000000000000000000000000000..502ccb1231d8eef5b91c8589abfe7ca2c76d24b7 --- /dev/null +++ b/reccon/query/tr_2311.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Can I stop by ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Maybe watch a few movies ." + ], + "type": [ + "inter-personal" + ], + "text": "Can I stop by ?", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2313.json b/reccon/query/tr_2313.json new file mode 100644 index 0000000000000000000000000000000000000000..c3d38a46d9fc73f9a7baa992eb2937bbe8c315ff --- /dev/null +++ b/reccon/query/tr_2313.json @@ -0,0 +1,24 @@ +[ + { + "turn": 13, + "speaker": "A", + "utterance": "Fine .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "Let's go and have a drink ." + ], + "type": [ + "inter-personal" + ], + "text": "Fine .", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_232.json b/reccon/query/tr_232.json new file mode 100644 index 0000000000000000000000000000000000000000..37bcbe25598d588e607a1031f2c50789024ebd79 --- /dev/null +++ b/reccon/query/tr_232.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "I like the pier too , because it's beautiful at night .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I just like the pier they have at Santa Monica .", + "I like the pier too , because it's beautiful at night ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I like the pier too , because it's beautiful at night .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2330.json b/reccon/query/tr_2330.json new file mode 100644 index 0000000000000000000000000000000000000000..9a7a68720ff0d7d6d5c6e3b54b2cd43eecef7dec --- /dev/null +++ b/reccon/query/tr_2330.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "Really ? What happened ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "A colleague of mine was kidnapped once" + ], + "type": [ + "inter-personal" + ], + "text": "Really ? What happened ?", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2332.json b/reccon/query/tr_2332.json new file mode 100644 index 0000000000000000000000000000000000000000..b19d465e38f73d98d2d31a14ab8485e85ea9befd --- /dev/null +++ b/reccon/query/tr_2332.json @@ -0,0 +1,27 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "Three . Two boys and a girl .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13, + 14 + ], + "expanded emotion cause span": [ + "how many kids do you have ?", + "Three . Two boys and a girl ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Three . Two boys and a girl .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_234.json b/reccon/query/tr_234.json new file mode 100644 index 0000000000000000000000000000000000000000..b0251c0b9712728045d6a9448709b945a3c510fc --- /dev/null +++ b/reccon/query/tr_234.json @@ -0,0 +1,24 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "Really ? How long did you stay there ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I went to California to study ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? How long did you stay there ?", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2356.json b/reccon/query/tr_2356.json new file mode 100644 index 0000000000000000000000000000000000000000..f07ee9f69e6018b01cee2f24c44e3fb87c1c4e6b --- /dev/null +++ b/reccon/query/tr_2356.json @@ -0,0 +1,24 @@ +[ + { + "turn": 15, + "speaker": "A", + "utterance": "Vodka martini ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "Yes , I'll have another cocktail ." + ], + "type": [ + "inter-personal" + ], + "text": "Vodka martini ?", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2371.json b/reccon/query/tr_2371.json new file mode 100644 index 0000000000000000000000000000000000000000..a8641b2cf74846f11acc2d55025304755a3618b9 --- /dev/null +++ b/reccon/query/tr_2371.json @@ -0,0 +1,27 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "OK .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 9 + ], + "expanded emotion cause span": [ + "How do you feel about playing bridge ?", + "shall I call Janet and ask her and Tom to come over , and I'll go to the store and buy some stuff ." + ], + "type": [ + "inter-personal" + ], + "text": "OK .", + "id": 10, + "source_sentences": [ + 6, + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2372.json b/reccon/query/tr_2372.json new file mode 100644 index 0000000000000000000000000000000000000000..8c55807a3cbe7a77cb05395c74c73a560c846bac --- /dev/null +++ b/reccon/query/tr_2372.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Thank you , Steven . I accept your advice .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I hope you will have an amicable split ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you , Steven . I accept your advice .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2376.json b/reccon/query/tr_2376.json new file mode 100644 index 0000000000000000000000000000000000000000..6b9559945d1f982c9a983aef720dc3601bdefb03 --- /dev/null +++ b/reccon/query/tr_2376.json @@ -0,0 +1,24 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "OK . Then I'll be expecting you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "Sure , that would be great . I'll bring the wine ." + ], + "type": [ + "inter-personal" + ], + "text": "OK . Then I'll be expecting you .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2377.json b/reccon/query/tr_2377.json new file mode 100644 index 0000000000000000000000000000000000000000..f22dbabb051723172933df10019addcb5782c24d --- /dev/null +++ b/reccon/query/tr_2377.json @@ -0,0 +1,27 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "really ? I didn't know that it was against company policy .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "that's not just your boss . No one is allowed to send personal emails from the office .", + "I didn't know that it was against company policy ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "really ? I didn't know that it was against company policy .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2378.json b/reccon/query/tr_2378.json new file mode 100644 index 0000000000000000000000000000000000000000..aab702c3a9b53a87593a6c5b8d4f5e4e7d6bbcbb --- /dev/null +++ b/reccon/query/tr_2378.json @@ -0,0 +1,27 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "You can take me to the bank if you want to .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Can I help in anyway ?", + "take me to the bank if you want to ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You can take me to the bank if you want to .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2389.json b/reccon/query/tr_2389.json new file mode 100644 index 0000000000000000000000000000000000000000..a6ddd833e83d93eeaeab8adbccf197feeb504ad5 --- /dev/null +++ b/reccon/query/tr_2389.json @@ -0,0 +1,24 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "Thanks anyway , but I'll do it , Rebecca . Let's get to class .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "If you want I'll let him know if I run into him ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks anyway , but I'll do it , Rebecca . Let's get to class .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2400.json b/reccon/query/tr_2400.json new file mode 100644 index 0000000000000000000000000000000000000000..bd1519207a3f5304e0be5ec24caf6dd798b723f1 --- /dev/null +++ b/reccon/query/tr_2400.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "It ' s my pleasure having you here .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Yes , I ' d love another glass . You ' re a wonderful host . Thank you for everything ." + ], + "type": [ + "inter-personal" + ], + "text": "It ' s my pleasure having you here .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2421.json b/reccon/query/tr_2421.json new file mode 100644 index 0000000000000000000000000000000000000000..eccb1518a42523a37450a5583fd081e237b3b4c3 --- /dev/null +++ b/reccon/query/tr_2421.json @@ -0,0 +1,24 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Why not ? I'd love to !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "I've got some photos of our holiday in Ireland . Would you like to see them ?" + ], + "type": [ + "inter-personal" + ], + "text": "Why not ? I'd love to !", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2438.json b/reccon/query/tr_2438.json new file mode 100644 index 0000000000000000000000000000000000000000..2e8d13b00f170d261a0f4e8b81b9d3247e34a3e2 --- /dev/null +++ b/reccon/query/tr_2438.json @@ -0,0 +1,27 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "OK .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 5 + ], + "expanded emotion cause span": [ + "You had some really great ideas in there !", + "we'll go to the diner around the corner ." + ], + "type": [ + "inter-personal" + ], + "text": "OK .", + "id": 6, + "source_sentences": [ + 0, + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_246.json b/reccon/query/tr_246.json new file mode 100644 index 0000000000000000000000000000000000000000..ca7fd495c9053da26701b94b457981a4bc673ffe --- /dev/null +++ b/reccon/query/tr_246.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Oh , don't mention it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "thanks for the suggestions" + ], + "type": [ + "inter-personal" + ], + "text": "Oh , don't mention it .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2467.json b/reccon/query/tr_2467.json new file mode 100644 index 0000000000000000000000000000000000000000..e6e4f3444175f5991ff8d6a2a31e3d7f6049bba2 --- /dev/null +++ b/reccon/query/tr_2467.json @@ -0,0 +1,33 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "I can ' t believe she would do that to you . It ' s so dishonest---and rude !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 4, + 6, + 8, + 9 + ], + "expanded emotion cause span": [ + "supposed to go out for a romantic dinner for our one year anniversary , but she stood me up !", + "later that night when I saw her with another man at a club near my home !", + "I called her later that night , but she didn't answer the phone .", + "It ' s so dishonest---and rude !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I can ' t believe she would do that to you . It ' s so dishonest---and rude !", + "id": 9, + "source_sentences": [ + 3, + 5, + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2471.json b/reccon/query/tr_2471.json new file mode 100644 index 0000000000000000000000000000000000000000..29e4085ab09374aab11c7bf2afb988e4ccc0ad01 --- /dev/null +++ b/reccon/query/tr_2471.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "B", + "utterance": "Yes . Look ! Mary is going to throw the bride bouquet .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 7 + ], + "expanded emotion cause span": [ + "wonderful wedding", + "Mary is going to throw the bride bouquet ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes . Look ! Mary is going to throw the bride bouquet .", + "id": 7, + "source_sentences": [ + 1 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2484.json b/reccon/query/tr_2484.json new file mode 100644 index 0000000000000000000000000000000000000000..d5102ca1fd3f8c04b705d5ff8cf65206ca8f4eb2 --- /dev/null +++ b/reccon/query/tr_2484.json @@ -0,0 +1,24 @@ +[ + { + "turn": 15, + "speaker": "A", + "utterance": "I think so too . Let ' s go !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "This is going to be a great night !" + ], + "type": [ + "inter-personal" + ], + "text": "I think so too . Let ' s go !", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2509.json b/reccon/query/tr_2509.json new file mode 100644 index 0000000000000000000000000000000000000000..736593351827147f8a1e1d4afbf24b3cba4cb597 --- /dev/null +++ b/reccon/query/tr_2509.json @@ -0,0 +1,27 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Wow ! I am really honored you went through all this trouble just for my sake . I really appreciate that . So , what time are we going ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "I knew you were really looking forward to watching Star Wars on the opening day .", + "I am really honored you went through all this trouble just for my sake ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Wow ! I am really honored you went through all this trouble just for my sake . I really appreciate that . So , what time are we going ?", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2511.json b/reccon/query/tr_2511.json new file mode 100644 index 0000000000000000000000000000000000000000..a5ede5c27cbdf728b4a9b8c3318ff2fa37e8be81 --- /dev/null +++ b/reccon/query/tr_2511.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "You've got be joking .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "I blew the finally exam ." + ], + "type": [ + "inter-personal" + ], + "text": "You've got be joking .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2520.json b/reccon/query/tr_2520.json new file mode 100644 index 0000000000000000000000000000000000000000..b7e2f971f9f9a3458be2d16579a88f6f131497e6 --- /dev/null +++ b/reccon/query/tr_2520.json @@ -0,0 +1,24 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "That sounds like a good idea .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "I can refer him to my company . It might help ." + ], + "type": [ + "inter-personal" + ], + "text": "That sounds like a good idea .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2535.json b/reccon/query/tr_2535.json new file mode 100644 index 0000000000000000000000000000000000000000..ba064934b0f2c38498d906af4fe1b4bef76f4eb3 --- /dev/null +++ b/reccon/query/tr_2535.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "All right . Next time you will treat .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Next time lunch is on me ." + ], + "type": [ + "inter-personal" + ], + "text": "All right . Next time you will treat .", + "id": 6, + "source_sentences": [ + 2 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2552.json b/reccon/query/tr_2552.json new file mode 100644 index 0000000000000000000000000000000000000000..414faecd505d871f65d5a45c80171e2116377352 --- /dev/null +++ b/reccon/query/tr_2552.json @@ -0,0 +1,27 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "You're lucky . It's hard to find a place to stay at the beach in August", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "Oh , I don't need to do that . I'll be staying with friends", + "You're lucky" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You're lucky . It's hard to find a place to stay at the beach in August", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2553.json b/reccon/query/tr_2553.json new file mode 100644 index 0000000000000000000000000000000000000000..a97af9c7298bdd366d665684e463ebe5e07bcf81 --- /dev/null +++ b/reccon/query/tr_2553.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "That's great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "The same to you ." + ], + "type": [ + "inter-personal" + ], + "text": "That's great .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2575.json b/reccon/query/tr_2575.json new file mode 100644 index 0000000000000000000000000000000000000000..33d540bf9ea320fbd83ad755592a87ddec3aecc3 --- /dev/null +++ b/reccon/query/tr_2575.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Good .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I may take you there some day ." + ], + "type": [ + "inter-personal" + ], + "text": "Good .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2581.json b/reccon/query/tr_2581.json new file mode 100644 index 0000000000000000000000000000000000000000..e898a7a392fb464203edee90945d48a2254593bc --- /dev/null +++ b/reccon/query/tr_2581.json @@ -0,0 +1,24 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Just bring along whatever it is that you and Jake would like to drink .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Would you like some help with the food ?" + ], + "type": [ + "inter-personal" + ], + "text": "Just bring along whatever it is that you and Jake would like to drink .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2593.json b/reccon/query/tr_2593.json new file mode 100644 index 0000000000000000000000000000000000000000..03c13dbd80fda7fdd69f8ba5de4d44a94d028210 --- /dev/null +++ b/reccon/query/tr_2593.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "You know , I could really go for that . You don ' t mind being my wingman for tonight ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "let ' s get you suited up and hit the dance club tonight . I hear that an awesome DJ is playing and there will be a lot of pretty single girls there !" + ], + "type": [ + "inter-personal" + ], + "text": "You know , I could really go for that . You don ' t mind being my wingman for tonight ?", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_260.json b/reccon/query/tr_260.json new file mode 100644 index 0000000000000000000000000000000000000000..f99acc5c3bca69f638d4190d55e15756ca99d48a --- /dev/null +++ b/reccon/query/tr_260.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Yeah , I was really struggling whether I should give you this nice little car . It was the last one they had and I really like it so much myself .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "That is so nice of you ." + ], + "type": [ + "inter-personal" + ], + "text": "Yeah , I was really struggling whether I should give you this nice little car . It was the last one they had and I really like it so much myself .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2606.json b/reccon/query/tr_2606.json new file mode 100644 index 0000000000000000000000000000000000000000..7b59bd179e38ab9c42a087b53afa3364eda11e1e --- /dev/null +++ b/reccon/query/tr_2606.json @@ -0,0 +1,24 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "Really ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "His paintings sell well ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ?", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2653.json b/reccon/query/tr_2653.json new file mode 100644 index 0000000000000000000000000000000000000000..51c553c606d93e142bd4750b7644bd3d9b2c1d4e --- /dev/null +++ b/reccon/query/tr_2653.json @@ -0,0 +1,24 @@ +[ + { + "turn": 15, + "speaker": "A", + "utterance": "Good-bye . See you again sometime .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "It's been nice talking to you ." + ], + "type": [ + "inter-personal" + ], + "text": "Good-bye . See you again sometime .", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_266.json b/reccon/query/tr_266.json new file mode 100644 index 0000000000000000000000000000000000000000..0c3efac0cf0acc34db0b580753dbf44da25ff337 --- /dev/null +++ b/reccon/query/tr_266.json @@ -0,0 +1,27 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "So do I . Let ' s go to other areas to see what they have got , shall we ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "I love this art exhibition !", + "So do I ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "So do I . Let ' s go to other areas to see what they have got , shall we ?", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2678.json b/reccon/query/tr_2678.json new file mode 100644 index 0000000000000000000000000000000000000000..5bbbfbcad8496d719e7ff9a18be3364799041b02 --- /dev/null +++ b/reccon/query/tr_2678.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Don ' t mention it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "It was so kind of you ." + ], + "type": [ + "inter-personal" + ], + "text": "Don ' t mention it .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2679.json b/reccon/query/tr_2679.json new file mode 100644 index 0000000000000000000000000000000000000000..9b23b70548228998b22ad101c36bb1ef5695b338 --- /dev/null +++ b/reccon/query/tr_2679.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Hah ! OK . Let ' s go together !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "It ' s a piano solo . I'm fond of piano", + "Let ' s go together !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Hah ! OK . Let ' s go together !", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2683.json b/reccon/query/tr_2683.json new file mode 100644 index 0000000000000000000000000000000000000000..2f7292b0d73b34ee888cce4ddaa63a56d0ebebcd --- /dev/null +++ b/reccon/query/tr_2683.json @@ -0,0 +1,24 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "500 feet ! I would never be able to do that .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "We jumped off a bridge and fell 500 feet" + ], + "type": [ + "inter-personal" + ], + "text": "500 feet ! I would never be able to do that .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2684.json b/reccon/query/tr_2684.json new file mode 100644 index 0000000000000000000000000000000000000000..132845000659d943f0920e300f240c15ffe67f12 --- /dev/null +++ b/reccon/query/tr_2684.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Okay . Hey , is that a dark cloud over there ? Do you think it will rain after all ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 4, + 7 + ], + "expanded emotion cause span": [ + "The sky is clear , the sun is shining", + "is that a dark cloud over there ? Do you think it will rain after all ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Okay . Hey , is that a dark cloud over there ? Do you think it will rain after all ?", + "id": 7, + "source_sentences": [ + 3 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2695.json b/reccon/query/tr_2695.json new file mode 100644 index 0000000000000000000000000000000000000000..c49ceb78984c937da448fd5e4320a94367841b59 --- /dev/null +++ b/reccon/query/tr_2695.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Oh , yeah , that's embarrassing when that happens .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "suddenly I heard someone call my name . I turned around and there was this man looking at me . I didn't recognize him at all , but he obviously knew who I was ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , yeah , that's embarrassing when that happens .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2710.json b/reccon/query/tr_2710.json new file mode 100644 index 0000000000000000000000000000000000000000..da2ea51afb0d6abebaedf52042d61455e55b0dc1 --- /dev/null +++ b/reccon/query/tr_2710.json @@ -0,0 +1,27 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Very good . But you should talk about your family , too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "How about the last part ?", + "Very good ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Very good . But you should talk about your family , too .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2714.json b/reccon/query/tr_2714.json new file mode 100644 index 0000000000000000000000000000000000000000..230acff6843e8669904edc2882a8ebc07e7d2efb --- /dev/null +++ b/reccon/query/tr_2714.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "Now the band is playing a slow dance .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Let's disco ." + ], + "type": [ + "inter-personal" + ], + "text": "Now the band is playing a slow dance .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2717.json b/reccon/query/tr_2717.json new file mode 100644 index 0000000000000000000000000000000000000000..54aeedfac1ce74434fb82f902ab5c6338a201719 --- /dev/null +++ b/reccon/query/tr_2717.json @@ -0,0 +1,24 @@ +[ + { + "turn": 19, + "speaker": "A", + "utterance": "Ok . That sounds like a deal .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 18 + ], + "expanded emotion cause span": [ + "When you finish the book . I ' ll get the movie and watch it with you ." + ], + "type": [ + "inter-personal" + ], + "text": "Ok . That sounds like a deal .", + "id": 19, + "source_sentences": [ + 17 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2743.json b/reccon/query/tr_2743.json new file mode 100644 index 0000000000000000000000000000000000000000..4420866bd86119ba091fc206d650a05763748523 --- /dev/null +++ b/reccon/query/tr_2743.json @@ -0,0 +1,27 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "I wasn't happy with it .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "the acting", + "I wasn't happy with it ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I wasn't happy with it .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2762.json b/reccon/query/tr_2762.json new file mode 100644 index 0000000000000000000000000000000000000000..6568f5809c54a4d8244d3a35c278cb3cd9f9f7bf --- /dev/null +++ b/reccon/query/tr_2762.json @@ -0,0 +1,30 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "I always make time for family .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 7, + 8 + ], + "expanded emotion cause span": [ + "You're my cousin ! Hi cousin !", + "eat dinner and catch up ?", + "family" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I always make time for family .", + "id": 8, + "source_sentences": [ + 4, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2781.json b/reccon/query/tr_2781.json new file mode 100644 index 0000000000000000000000000000000000000000..3e2041608de1ceeb8dbfbe722a2ae9c2c321999b --- /dev/null +++ b/reccon/query/tr_2781.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "How amazing !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "A chinese girl have broken the world record in the Olympic Games" + ], + "type": [ + "inter-personal" + ], + "text": "How amazing !", + "id": 6, + "source_sentences": [ + 2 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2797.json b/reccon/query/tr_2797.json new file mode 100644 index 0000000000000000000000000000000000000000..0a2c642a11d0c9d1449e68280ddac6b512981c37 --- /dev/null +++ b/reccon/query/tr_2797.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "No hurry ! I'II tell you now , The collections include ancient cases and caskets , tea sets , abacuses , precious sea shells and conches , drama costumes , agates , ancient coins , fans , mini-musical instruments , root-carving , rare stones and rocks , model ships , model cars ...", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 6 + ], + "expanded emotion cause span": [ + "They must have excellent collections . I'II go and see each of them .", + "don't keep me in suspense !" + ], + "type": [ + "inter-personal" + ], + "text": "No hurry ! I'II tell you now , The collections include ancient cases and caskets , tea sets , abacuses , precious sea shells and conches , drama costumes , agates , ancient coins , fans , mini-musical instruments , root-carving , rare stones and rocks , model ships , model cars ...", + "id": 7, + "source_sentences": [ + 5, + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2799.json b/reccon/query/tr_2799.json new file mode 100644 index 0000000000000000000000000000000000000000..4008f7d12c27f79dbd98647ae6c864bf50b36d62 --- /dev/null +++ b/reccon/query/tr_2799.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Goodbye !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Thank you . I will if I have chance . Goodbye and happy landing !" + ], + "type": [ + "inter-personal" + ], + "text": "Goodbye !", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2803.json b/reccon/query/tr_2803.json new file mode 100644 index 0000000000000000000000000000000000000000..8f29339021fa97287ac3487561ec674dad823319 --- /dev/null +++ b/reccon/query/tr_2803.json @@ -0,0 +1,24 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "That's a good idea .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I was hoping to get a few new ties for my collection ." + ], + "type": [ + "inter-personal" + ], + "text": "That's a good idea .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2810.json b/reccon/query/tr_2810.json new file mode 100644 index 0000000000000000000000000000000000000000..980baf10dfb95ff74748cdeb5adc13049197735b --- /dev/null +++ b/reccon/query/tr_2810.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "I couldn ' t agree more .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Why don ' t we go together ? I can show you around . I think you ' ll have a better time ." + ], + "type": [ + "inter-personal" + ], + "text": "I couldn ' t agree more .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2815.json b/reccon/query/tr_2815.json new file mode 100644 index 0000000000000000000000000000000000000000..a53e32a344eca52dd688f8b7929e8ce7e8fdad02 --- /dev/null +++ b/reccon/query/tr_2815.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Ha-ha ! You got me there !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I'm not a great dancer , and you said you failed calculus ." + ], + "type": [ + "inter-personal" + ], + "text": "Ha-ha ! You got me there !", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2817.json b/reccon/query/tr_2817.json new file mode 100644 index 0000000000000000000000000000000000000000..2b41219c413ababe2d9cd443ad6af1ce792af4fd --- /dev/null +++ b/reccon/query/tr_2817.json @@ -0,0 +1,24 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "You're kidding !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "They ' re overpriced" + ], + "type": [ + "inter-personal" + ], + "text": "You're kidding !", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2820.json b/reccon/query/tr_2820.json new file mode 100644 index 0000000000000000000000000000000000000000..e2e719eb8fb8ed0882c85b5f416fa69346959f62 --- /dev/null +++ b/reccon/query/tr_2820.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "I really appreciate your kind words .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "My warmest congratulations on your entering the Oxford University .", + "I really appreciate your kind words ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I really appreciate your kind words .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2822.json b/reccon/query/tr_2822.json new file mode 100644 index 0000000000000000000000000000000000000000..d15c66752ef05c9ec8ba31bab780df6fbf824a33 --- /dev/null +++ b/reccon/query/tr_2822.json @@ -0,0 +1,24 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "Crazy !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "her fans were all screaming , trying to give her flowers and to get her autographs ." + ], + "type": [ + "inter-personal" + ], + "text": "Crazy !", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2825.json b/reccon/query/tr_2825.json new file mode 100644 index 0000000000000000000000000000000000000000..b454d7270441d98d14db4bd75f96621540e03f86 --- /dev/null +++ b/reccon/query/tr_2825.json @@ -0,0 +1,24 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "Excellent . You can borrow my Janet Jackson's CD . It's her new one .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Yes , l have two of her Cds , l'II lend them to you if you like ." + ], + "type": [ + "inter-personal" + ], + "text": "Excellent . You can borrow my Janet Jackson's CD . It's her new one .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2826.json b/reccon/query/tr_2826.json new file mode 100644 index 0000000000000000000000000000000000000000..a223194abcb19f413b3c53b23574e7c289823946 --- /dev/null +++ b/reccon/query/tr_2826.json @@ -0,0 +1,27 @@ +[ + { + "turn": 16, + "speaker": "B", + "utterance": "You're right ... I should eat something . Let's go .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13, + 15 + ], + "expanded emotion cause span": [ + "When my grandmother passed away , I frequently visited her in the cemetery . I always talked to her . Even though she wasn't there , I somehow knew she heard what I said .", + "We should get you something to eat ." + ], + "type": [ + "inter-personal" + ], + "text": "You're right ... I should eat something . Let's go .", + "id": 16, + "source_sentences": [ + 12, + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2833.json b/reccon/query/tr_2833.json new file mode 100644 index 0000000000000000000000000000000000000000..5164736dfa9c92f01b405f7b7b215c7e56bbc44a --- /dev/null +++ b/reccon/query/tr_2833.json @@ -0,0 +1,25 @@ +[ + { + "turn": 17, + "speaker": "A", + "utterance": "All right .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 16 + ], + "expanded emotion cause span": [ + "That's Okay ," + ], + "type": [ + "inter-personal" + ], + "text": "All right .", + "id": 17, + "source_sentences": [ + 15 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2880.json b/reccon/query/tr_2880.json new file mode 100644 index 0000000000000000000000000000000000000000..7d12b74212b5c42d60b6ed6344fd90b5e6624e4a --- /dev/null +++ b/reccon/query/tr_2880.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "I'm glad you're so happy .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I'm really pleased with it ." + ], + "type": [ + "inter-personal" + ], + "text": "I'm glad you're so happy .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2893.json b/reccon/query/tr_2893.json new file mode 100644 index 0000000000000000000000000000000000000000..2246c014e83dd92a2455540934db552ce978c207 --- /dev/null +++ b/reccon/query/tr_2893.json @@ -0,0 +1,24 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "I agree . I appreciate your helping me .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Very good . But you should talk about your family , too ." + ], + "type": [ + "inter-personal" + ], + "text": "I agree . I appreciate your helping me .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2911.json b/reccon/query/tr_2911.json new file mode 100644 index 0000000000000000000000000000000000000000..54f97dde448ec4db6287184218f58ad827b39715 --- /dev/null +++ b/reccon/query/tr_2911.json @@ -0,0 +1,24 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "me too . But I think I am going to bed now . my head is getting heavy . Have a nice day there !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "just give me the dates and I'll make sure I'm free . You know after all these chatting online , it will be great to meet you in real life . I look forward to seeing you soon !" + ], + "type": [ + "inter-personal" + ], + "text": "me too . But I think I am going to bed now . my head is getting heavy . Have a nice day there !", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2940.json b/reccon/query/tr_2940.json new file mode 100644 index 0000000000000000000000000000000000000000..52cf13ad4d4b2cdb29f55ec80343d3818fa5fc92 --- /dev/null +++ b/reccon/query/tr_2940.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Thank you , Steven . You are really a good friend .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Come on , buddy , cheer up . Why not do some sports with me ? Violent exercise might help to shake you out of your disappointment in love ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you , Steven . You are really a good friend .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2944.json b/reccon/query/tr_2944.json new file mode 100644 index 0000000000000000000000000000000000000000..257e4059088ec647f7057114211414c7f993f72f --- /dev/null +++ b/reccon/query/tr_2944.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "What ' s wrong with you ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Maybe you can do something useful for me ." + ], + "type": [ + "inter-personal" + ], + "text": "What ' s wrong with you ?", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2957.json b/reccon/query/tr_2957.json new file mode 100644 index 0000000000000000000000000000000000000000..728e0a466609aa7ae1caae61b10019bf3bf1e82a --- /dev/null +++ b/reccon/query/tr_2957.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Thanks . That would be really helpful .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I know a good place to hire bikes if you want ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks . That would be really helpful .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2969.json b/reccon/query/tr_2969.json new file mode 100644 index 0000000000000000000000000000000000000000..370ea4ed8dd786299e13cb4f53883ac117d0fc39 --- /dev/null +++ b/reccon/query/tr_2969.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "That ' s too bad . I ' m sorry to hear that .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 4, + 7 + ], + "expanded emotion cause span": [ + "I went to the library and lost my bag .", + "That ' s too bad . I ' m sorry to hear that ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That ' s too bad . I ' m sorry to hear that .", + "id": 7, + "source_sentences": [ + 3 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2980.json b/reccon/query/tr_2980.json new file mode 100644 index 0000000000000000000000000000000000000000..1005c2c678898dcaa3af585a522a18fa4045a2da --- /dev/null +++ b/reccon/query/tr_2980.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Fine . See you then .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "invite you over for dinner" + ], + "type": [ + "inter-personal" + ], + "text": "Fine . See you then .", + "id": 8, + "source_sentences": [ + 0 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2986.json b/reccon/query/tr_2986.json new file mode 100644 index 0000000000000000000000000000000000000000..806a289b984a95afc960477d221278cd02351b56 --- /dev/null +++ b/reccon/query/tr_2986.json @@ -0,0 +1,27 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "Wow .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6, + 8 + ], + "expanded emotion cause span": [ + "she sued her former boss for sexual harassment .", + "he was her lover and he wanted to leave her , so she got revenge . I heard him say she was a dangerous woman ." + ], + "type": [ + "inter-personal" + ], + "text": "Wow .", + "id": 9, + "source_sentences": [ + 5, + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2991.json b/reccon/query/tr_2991.json new file mode 100644 index 0000000000000000000000000000000000000000..9da1ec139f7f44ffb3f1bac20ab1d4baa23a6af5 --- /dev/null +++ b/reccon/query/tr_2991.json @@ -0,0 +1,27 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Full of energy and hope .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "I also like the rhythms .", + "Full of energy and hope ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Full of energy and hope .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_2998.json b/reccon/query/tr_2998.json new file mode 100644 index 0000000000000000000000000000000000000000..d47a741f7a2558ea7f49fb65b6c5dfb54c0c443c --- /dev/null +++ b/reccon/query/tr_2998.json @@ -0,0 +1,24 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "Yeah , I ' ll try to do the same . So , I was wondering you wanna go out to dinner Friday night ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I'll try to more considerate and to keep the noise down ." + ], + "type": [ + "inter-personal" + ], + "text": "Yeah , I ' ll try to do the same . So , I was wondering you wanna go out to dinner Friday night ?", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3002.json b/reccon/query/tr_3002.json new file mode 100644 index 0000000000000000000000000000000000000000..bf9cf17e0f396817de1f32ab89e83589a83cfd21 --- /dev/null +++ b/reccon/query/tr_3002.json @@ -0,0 +1,27 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "I'm really sick of you .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "I've never experienced such a kind of feeling .", + "I'm really sick of you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm really sick of you .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3011.json b/reccon/query/tr_3011.json new file mode 100644 index 0000000000000000000000000000000000000000..f431122c9ceb751742d1f586d5e9ddd449acf07f --- /dev/null +++ b/reccon/query/tr_3011.json @@ -0,0 +1,27 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "I think that would be horrible !", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "garlic ice cream on the menu", + "I think that would be horrible !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I think that would be horrible !", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_302.json b/reccon/query/tr_302.json new file mode 100644 index 0000000000000000000000000000000000000000..bc24cc8e44cf136c7b983ef235b1e1396f0b2eef --- /dev/null +++ b/reccon/query/tr_302.json @@ -0,0 +1,25 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "Bye .", + "emotion": "happiness", + "explanation": "Speaker is invited by the listener for coffee", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "see you later ." + ], + "type": [ + "inter-personal" + ], + "text": "Bye .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3023.json b/reccon/query/tr_3023.json new file mode 100644 index 0000000000000000000000000000000000000000..23da70936cb7adbba8f0a94129038892e1132e69 --- /dev/null +++ b/reccon/query/tr_3023.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "thank you . I can't imagine getting much done today . I'm just too exhausted !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "I can ask the boss about giving you the day off today ." + ], + "type": [ + "inter-personal" + ], + "text": "thank you . I can't imagine getting much done today . I'm just too exhausted !", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3024.json b/reccon/query/tr_3024.json new file mode 100644 index 0000000000000000000000000000000000000000..738ca1ed5b79f83a90188e91a60f83f797d961fb --- /dev/null +++ b/reccon/query/tr_3024.json @@ -0,0 +1,24 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "Thank you very much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "Yes , of course ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you very much .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3036.json b/reccon/query/tr_3036.json new file mode 100644 index 0000000000000000000000000000000000000000..d66053658e674ff962c2ea14ba253651441e77ca --- /dev/null +++ b/reccon/query/tr_3036.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "I'm so jealous of you . I've never been anywhere in Europe . I've always dreamed of traveling around and seeing the sights .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "My first time . I've traveled around Europe a lot , but this was my first time to Spain . It was amazing , and the weather was just beautiful ! No rain , and just sun , sun , sun ..." + ], + "type": [ + "inter-personal" + ], + "text": "I'm so jealous of you . I've never been anywhere in Europe . I've always dreamed of traveling around and seeing the sights .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3042.json b/reccon/query/tr_3042.json new file mode 100644 index 0000000000000000000000000000000000000000..30119c31d706113fbca0e919704ede77d66f3fae --- /dev/null +++ b/reccon/query/tr_3042.json @@ -0,0 +1,27 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Thank you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 5 + ], + "expanded emotion cause span": [ + "Do you have a garden ?", + "Your garden is really lovely ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you .", + "id": 6, + "source_sentences": [ + 2, + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3046.json b/reccon/query/tr_3046.json new file mode 100644 index 0000000000000000000000000000000000000000..6335e74628c4960773cc0831e2d8d972026b11bb --- /dev/null +++ b/reccon/query/tr_3046.json @@ -0,0 +1,24 @@ +[ + { + "turn": 15, + "speaker": "A", + "utterance": "Exactly , now , tell me the time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "OK , great Daddy , after supper , I'll embark on it ." + ], + "type": [ + "inter-personal" + ], + "text": "Exactly , now , tell me the time .", + "id": 15, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3054.json b/reccon/query/tr_3054.json new file mode 100644 index 0000000000000000000000000000000000000000..a3855ff625b857834fea339fcc02189d07610a7d --- /dev/null +++ b/reccon/query/tr_3054.json @@ -0,0 +1,27 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Yes , I usually develop and print all my own photos .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Oh , photography , It ' s really a good hobby .", + "I usually develop and print all my own photos ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , I usually develop and print all my own photos .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3060.json b/reccon/query/tr_3060.json new file mode 100644 index 0000000000000000000000000000000000000000..99a0db1e0382fd84ae398dadc34c087caa03f891 --- /dev/null +++ b/reccon/query/tr_3060.json @@ -0,0 +1,24 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "Me too . Have a great day .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "You ' re welcome . It was good seeing you again ." + ], + "type": [ + "inter-personal" + ], + "text": "Me too . Have a great day .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3071.json b/reccon/query/tr_3071.json new file mode 100644 index 0000000000000000000000000000000000000000..54aeedfac1ce74434fb82f902ab5c6338a201719 --- /dev/null +++ b/reccon/query/tr_3071.json @@ -0,0 +1,24 @@ +[ + { + "turn": 19, + "speaker": "A", + "utterance": "Ok . That sounds like a deal .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 18 + ], + "expanded emotion cause span": [ + "When you finish the book . I ' ll get the movie and watch it with you ." + ], + "type": [ + "inter-personal" + ], + "text": "Ok . That sounds like a deal .", + "id": 19, + "source_sentences": [ + 17 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3073.json b/reccon/query/tr_3073.json new file mode 100644 index 0000000000000000000000000000000000000000..5502ba9a1c40f8626bfeecdb2ed94f357fb81244 --- /dev/null +++ b/reccon/query/tr_3073.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Do you feel like a king in your castle ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I'm so excited . Finally , a yard of my own ." + ], + "type": [ + "inter-personal" + ], + "text": "Do you feel like a king in your castle ?", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3114.json b/reccon/query/tr_3114.json new file mode 100644 index 0000000000000000000000000000000000000000..21603f0c030c53653ebf2a98701f5828aaa39b94 --- /dev/null +++ b/reccon/query/tr_3114.json @@ -0,0 +1,28 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "It would be a really good choice . The movie is very suitable for lovers to see together . I'm sure you won't regret it .", + "emotion": "happiness", + "explanation": "the speaker is happy that A will have a good experience watching the movie", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "I should invite my girlfriend to go next weekend .", + "It would be a really good choice . The movie is very suitable for lovers to see together . I'm sure you won't regret it ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It would be a really good choice . The movie is very suitable for lovers to see together . I'm sure you won't regret it .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3128.json b/reccon/query/tr_3128.json new file mode 100644 index 0000000000000000000000000000000000000000..0b7526a7ed9687f3638e2a1dddf4d960d922fdb2 --- /dev/null +++ b/reccon/query/tr_3128.json @@ -0,0 +1,27 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "OK . Let's go .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 11 + ], + "expanded emotion cause span": [ + "their great love .", + "Good idea ." + ], + "type": [ + "inter-personal" + ], + "text": "OK . Let's go .", + "id": 12, + "source_sentences": [ + 4, + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3138.json b/reccon/query/tr_3138.json new file mode 100644 index 0000000000000000000000000000000000000000..e4a28f7f84bf96107e0d43b4f16966dbd0a4b238 --- /dev/null +++ b/reccon/query/tr_3138.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "Naughty ? I'm naughty ? I'm just clever . So I only do the things I am interested in .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "you are always a naughty boy ." + ], + "type": [ + "inter-personal" + ], + "text": "Naughty ? I'm naughty ? I'm just clever . So I only do the things I am interested in .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3139.json b/reccon/query/tr_3139.json new file mode 100644 index 0000000000000000000000000000000000000000..053ed7672a9ea90fd102fa17a5c08835956f7dce --- /dev/null +++ b/reccon/query/tr_3139.json @@ -0,0 +1,24 @@ +[ + { + "turn": 16, + "speaker": "B", + "utterance": "I hope not .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "Don ' t worry . You ' ll have no problem ." + ], + "type": [ + "inter-personal" + ], + "text": "I hope not .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_316.json b/reccon/query/tr_316.json new file mode 100644 index 0000000000000000000000000000000000000000..780c1f2fb1d3d814dca5504c7d838274d7586c8e --- /dev/null +++ b/reccon/query/tr_316.json @@ -0,0 +1,27 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "You ' re right . I would have to travel to the city at least once a week to go shopping and see friends . I would hate living in the country !", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "in that village there ' s nothing to do . There ' s not even a pub or restaurant . There ' s just one small shop with a poor selection of goods .", + "I would have to travel to the city at least once a week to go shopping and see friends . I would hate living in the country !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You ' re right . I would have to travel to the city at least once a week to go shopping and see friends . I would hate living in the country !", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3166.json b/reccon/query/tr_3166.json new file mode 100644 index 0000000000000000000000000000000000000000..c815fdbe1ccca665c38ebb9f3aceccf6b07e000f --- /dev/null +++ b/reccon/query/tr_3166.json @@ -0,0 +1,30 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Looks like anything fun makes you excited .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 9, + 10 + ], + "expanded emotion cause span": [ + "I always get excited the day before .", + "that makes me excited too !", + "Looks like anything fun makes you excited ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Looks like anything fun makes you excited .", + "id": 10, + "source_sentences": [ + 2, + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3169.json b/reccon/query/tr_3169.json new file mode 100644 index 0000000000000000000000000000000000000000..1e62b9e796f956676dcaa3258160f764b656c7dc --- /dev/null +++ b/reccon/query/tr_3169.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Thanks , goodbye .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "It suits us fine ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks , goodbye .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3177.json b/reccon/query/tr_3177.json new file mode 100644 index 0000000000000000000000000000000000000000..4173e7c8bd70512ea2aec8aaad353914359ec4b3 --- /dev/null +++ b/reccon/query/tr_3177.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "You're welcome .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Thanks ." + ], + "type": [ + "inter-personal" + ], + "text": "You're welcome .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3184.json b/reccon/query/tr_3184.json new file mode 100644 index 0000000000000000000000000000000000000000..a136567830b589a8604ffd8d26ee76fb14563d50 --- /dev/null +++ b/reccon/query/tr_3184.json @@ -0,0 +1,24 @@ +[ + { + "turn": 16, + "speaker": "B", + "utterance": "Perfect . See you later .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "Thanks . I ' ll stop by when I get off work ." + ], + "type": [ + "inter-personal" + ], + "text": "Perfect . See you later .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3185.json b/reccon/query/tr_3185.json new file mode 100644 index 0000000000000000000000000000000000000000..e6756694b973f35b6bf59eaae8a502e04742870b --- /dev/null +++ b/reccon/query/tr_3185.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "You must have enjoyed yourself .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Yes , a lot of friends ." + ], + "type": [ + "inter-personal" + ], + "text": "You must have enjoyed yourself .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3192.json b/reccon/query/tr_3192.json new file mode 100644 index 0000000000000000000000000000000000000000..954f9e8aa85f1f88bd6659dd05c15623c9697792 --- /dev/null +++ b/reccon/query/tr_3192.json @@ -0,0 +1,24 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Really ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "to frighten away evil spirits ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ?", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_321.json b/reccon/query/tr_321.json new file mode 100644 index 0000000000000000000000000000000000000000..8e8d81e70a37a652e6909e7686d71b4c1b2bd257 --- /dev/null +++ b/reccon/query/tr_321.json @@ -0,0 +1,24 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "it sounds like any job will be better than the one you have now !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "but frankly , it's not much of an incentive . They give us a bonus of ten dollars ." + ], + "type": [ + "inter-personal" + ], + "text": "it sounds like any job will be better than the one you have now !", + "id": 9, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3216.json b/reccon/query/tr_3216.json new file mode 100644 index 0000000000000000000000000000000000000000..cdee9785ec372b31001a4df413626bdd0b374f1f --- /dev/null +++ b/reccon/query/tr_3216.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "Yeah , I already knew that . That could be a good thing .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "he came here last year after 10 years in the military" + ], + "type": [ + "inter-personal" + ], + "text": "Yeah , I already knew that . That could be a good thing .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3233.json b/reccon/query/tr_3233.json new file mode 100644 index 0000000000000000000000000000000000000000..0d71ee95f8d27bf23a3052ed42cad35e6772b819 --- /dev/null +++ b/reccon/query/tr_3233.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Here ! Open mine first .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "( At the Party ) It's Christmas Eve ! Time to open presents !" + ], + "type": [ + "inter-personal" + ], + "text": "Here ! Open mine first .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3234.json b/reccon/query/tr_3234.json new file mode 100644 index 0000000000000000000000000000000000000000..95593f1df1b5734dc0f0065f19b960ca750c522f --- /dev/null +++ b/reccon/query/tr_3234.json @@ -0,0 +1,27 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "I'd love to .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "let's go for a spin . You can try it out .", + "I'd love to" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'd love to .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3256.json b/reccon/query/tr_3256.json new file mode 100644 index 0000000000000000000000000000000000000000..8ee647e22c83dfadaa5ca610387b648b1fc2048e --- /dev/null +++ b/reccon/query/tr_3256.json @@ -0,0 +1,27 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Good idea .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 9 + ], + "expanded emotion cause span": [ + "Let's get something to drink .", + "Let's get something to drink ." + ], + "type": [ + "inter-personal" + ], + "text": "Good idea .", + "id": 10, + "source_sentences": [ + 8, + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3261.json b/reccon/query/tr_3261.json new file mode 100644 index 0000000000000000000000000000000000000000..bd1bbf7c0ab2eda452f88758805d347bd57ceb31 --- /dev/null +++ b/reccon/query/tr_3261.json @@ -0,0 +1,25 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "That sounds good . I ' ll call you once I arrive .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "there ' s a very romantic new film starring Hugh Grant . Let ' s go and see that ." + ], + "type": [ + "inter-personal" + ], + "text": "That sounds good . I ' ll call you once I arrive .", + "id": 6, + "source_sentences": [ + 2 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3279.json b/reccon/query/tr_3279.json new file mode 100644 index 0000000000000000000000000000000000000000..44e0586a50e42096ab808490f83c64b6e55faf83 --- /dev/null +++ b/reccon/query/tr_3279.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "When the lower branches are removed , you ' ll be able to sit under the tree .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Thank you ! That would be very kind of you ." + ], + "type": [ + "inter-personal" + ], + "text": "When the lower branches are removed , you ' ll be able to sit under the tree .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3280.json b/reccon/query/tr_3280.json new file mode 100644 index 0000000000000000000000000000000000000000..c6a4d595acceb60bff38d8d4e759a42cb8525be0 --- /dev/null +++ b/reccon/query/tr_3280.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "A", + "utterance": "Really ? I ' m surprised .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "She ' s going to live in Paris ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? I ' m surprised .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3320.json b/reccon/query/tr_3320.json new file mode 100644 index 0000000000000000000000000000000000000000..2c5dcd179436d7a200131aef712d16fe51fbda71 --- /dev/null +++ b/reccon/query/tr_3320.json @@ -0,0 +1,24 @@ +[ + { + "turn": 18, + "speaker": "B", + "utterance": "No problem . Bob .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 17 + ], + "expanded emotion cause span": [ + "Thanks . Charlie !" + ], + "type": [ + "inter-personal" + ], + "text": "No problem . Bob .", + "id": 18, + "source_sentences": [ + 16 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3336.json b/reccon/query/tr_3336.json new file mode 100644 index 0000000000000000000000000000000000000000..b3390cc52e41b52968f408b564526af079954a5e --- /dev/null +++ b/reccon/query/tr_3336.json @@ -0,0 +1,27 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Sounds like you're happy with your decision .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "I was offered a good job doing marketing", + "you're happy with your decision ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Sounds like you're happy with your decision .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3342.json b/reccon/query/tr_3342.json new file mode 100644 index 0000000000000000000000000000000000000000..6a78ace467f9bb090c09ad3df492da38bee76ae9 --- /dev/null +++ b/reccon/query/tr_3342.json @@ -0,0 +1,27 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "Come on ! They only do that to get even more publicity for their films and themselves .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "I think you should give them some credit .", + "They only do that to get even more publicity for their films and themselves ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Come on ! They only do that to get even more publicity for their films and themselves .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3350.json b/reccon/query/tr_3350.json new file mode 100644 index 0000000000000000000000000000000000000000..0505869a71dca010a3499db39804ec67aa385f90 --- /dev/null +++ b/reccon/query/tr_3350.json @@ -0,0 +1,30 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "But I still love you .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 5, + 7, + 8 + ], + "expanded emotion cause span": [ + "This isn ' t working .", + "it ' s time to move on for both of us .", + "But I still love you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "But I still love you .", + "id": 8, + "source_sentences": [ + 4, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3354.json b/reccon/query/tr_3354.json new file mode 100644 index 0000000000000000000000000000000000000000..c75125c3f3cb83411e53e9200b58c540e6976cd2 --- /dev/null +++ b/reccon/query/tr_3354.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "I really appreciate your help .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I have some friends who might be able to help you find a job . I'll see what they can do ." + ], + "type": [ + "inter-personal" + ], + "text": "I really appreciate your help .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3357.json b/reccon/query/tr_3357.json new file mode 100644 index 0000000000000000000000000000000000000000..8278f602f4cc930cafaacc9ec77619e6b1b3e672 --- /dev/null +++ b/reccon/query/tr_3357.json @@ -0,0 +1,30 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "That ' s a great idea . We can really enjoy ourselves without worrying about the kids .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 5, + 6 + ], + "expanded emotion cause span": [ + "Relaxing on the beach with a nice cool drink .", + "we could try that restaurant that was recommended in the guidebook . Then we could go to a club . We haven ' t been to one for ages .", + "We can really enjoy ourselves without worrying about the kids ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That ' s a great idea . We can really enjoy ourselves without worrying about the kids .", + "id": 6, + "source_sentences": [ + 0, + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3365.json b/reccon/query/tr_3365.json new file mode 100644 index 0000000000000000000000000000000000000000..c7d74dd2ea8a43ebc91c078807997a532542df6f --- /dev/null +++ b/reccon/query/tr_3365.json @@ -0,0 +1,24 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "Oh , really ? What do you do there exactly ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "I work for American Airlines ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , really ? What do you do there exactly ?", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3376.json b/reccon/query/tr_3376.json new file mode 100644 index 0000000000000000000000000000000000000000..5cbb787b2cc60c890d95ac15fd3b6938a04ece72 --- /dev/null +++ b/reccon/query/tr_3376.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Good . Where shall we meet ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Can we have dinner together sometime this weekend ?" + ], + "type": [ + "inter-personal" + ], + "text": "Good . Where shall we meet ?", + "id": 6, + "source_sentences": [ + 0 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3386.json b/reccon/query/tr_3386.json new file mode 100644 index 0000000000000000000000000000000000000000..3c239e7008aa9350825e50d8f45cca86656d366d --- /dev/null +++ b/reccon/query/tr_3386.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "That would be wonderful . Thanks !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Well , if you want we can go together sometime . Actually I was thinking of going this afternoon , if you like , you can join me and I can show you the neighborhood along the way ." + ], + "type": [ + "inter-personal" + ], + "text": "That would be wonderful . Thanks !", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3400.json b/reccon/query/tr_3400.json new file mode 100644 index 0000000000000000000000000000000000000000..3ff31207717f16c21be382654488ae1dd7dd29ad --- /dev/null +++ b/reccon/query/tr_3400.json @@ -0,0 +1,27 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Wonderful . Just e-mail me the time and date and I'll be there .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 9 + ], + "expanded emotion cause span": [ + "We thought it would be fun to have a pool party at Jay's house .", + "Dress casually and bring your bathing suit !" + ], + "type": [ + "inter-personal" + ], + "text": "Wonderful . Just e-mail me the time and date and I'll be there .", + "id": 10, + "source_sentences": [ + 4, + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3404.json b/reccon/query/tr_3404.json new file mode 100644 index 0000000000000000000000000000000000000000..f731a648b779e4dc6e5a99b2deae1aff81821bf3 --- /dev/null +++ b/reccon/query/tr_3404.json @@ -0,0 +1,30 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "You're welcome . Good luck , bye !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 9, + 9 + ], + "expanded emotion cause span": [ + "I am having an exam at nine ,", + "It's only eight forty .", + "Thanks so much !" + ], + "type": [ + "inter-personal" + ], + "text": "You're welcome . Good luck , bye !", + "id": 10, + "source_sentences": [ + 2, + 8, + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3405.json b/reccon/query/tr_3405.json new file mode 100644 index 0000000000000000000000000000000000000000..69b545c87dc9adf649ae29b74e918a61f22ed20d --- /dev/null +++ b/reccon/query/tr_3405.json @@ -0,0 +1,25 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Let's go .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "They're all waiting for you . Let's join them . I'm going to cut the cake soon ." + ], + "type": [ + "inter-personal" + ], + "text": "Let's go .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3410.json b/reccon/query/tr_3410.json new file mode 100644 index 0000000000000000000000000000000000000000..d14663d8c8eabe1a88612ed78f25792489b189fd --- /dev/null +++ b/reccon/query/tr_3410.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "You're welcome , honey . I hope we will celebrate our golden wedding anniversary in future .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "It's so beautiful . You're so kind to me , A . Thank you !" + ], + "type": [ + "inter-personal" + ], + "text": "You're welcome , honey . I hope we will celebrate our golden wedding anniversary in future .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3421.json b/reccon/query/tr_3421.json new file mode 100644 index 0000000000000000000000000000000000000000..963044323fe7d0724f1f795955f18a696938862d --- /dev/null +++ b/reccon/query/tr_3421.json @@ -0,0 +1,27 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "That is great . Everyone says French food is wonderful .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "we went to taste the French cuisine . That was really fantastic . And no stomach problems .", + "Everyone says French food is wonderful ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That is great . Everyone says French food is wonderful .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_343.json b/reccon/query/tr_343.json new file mode 100644 index 0000000000000000000000000000000000000000..d15ad60ec518bcc3085f66da0612708788a22989 --- /dev/null +++ b/reccon/query/tr_343.json @@ -0,0 +1,25 @@ +[ + { + "turn": 16, + "speaker": "B", + "utterance": "OK , I'll meet you there .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Would you like to have lunch with me ?" + ], + "type": [ + "inter-personal" + ], + "text": "OK , I'll meet you there .", + "id": 16, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3441.json b/reccon/query/tr_3441.json new file mode 100644 index 0000000000000000000000000000000000000000..30741785eea82c632e8c6d97d94c935d5c8ae8a2 --- /dev/null +++ b/reccon/query/tr_3441.json @@ -0,0 +1,30 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Thank you for inviting me . See you then . Bye , Tom .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 9, + 10 + ], + "expanded emotion cause span": [ + "dine out together and go to the movies ?", + "I'll pick you up at 6:00 .", + "Thank you for inviting me . See you then ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you for inviting me . See you then . Bye , Tom .", + "id": 10, + "source_sentences": [ + 6, + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_345.json b/reccon/query/tr_345.json new file mode 100644 index 0000000000000000000000000000000000000000..c8de9f2dc42c33f5fda338871a9a0b1b48e4492f --- /dev/null +++ b/reccon/query/tr_345.json @@ -0,0 +1,27 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Come on , don ' t flatter me anymore . I took the job because I love being challenged . But I can ' t get this turned around without the support from you people .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "the effort pays off . You have accomplished something .", + "I took the job because I love being challenged . But I can ' t get this turned around without the support from you people ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Come on , don ' t flatter me anymore . I took the job because I love being challenged . But I can ' t get this turned around without the support from you people .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3457.json b/reccon/query/tr_3457.json new file mode 100644 index 0000000000000000000000000000000000000000..d9bea5fbd0b1eaf2e58d95f25fa939cc8a5d3632 --- /dev/null +++ b/reccon/query/tr_3457.json @@ -0,0 +1,27 @@ +[ + { + "turn": 15, + "speaker": "A", + "utterance": "You know , Tom is my best friend and he asked me to be his best man .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14, + 15 + ], + "expanded emotion cause span": [ + "Nobody is OK , but you !", + "Tom is my best friend and he asked me to be his best man ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You know , Tom is my best friend and he asked me to be his best man .", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3474.json b/reccon/query/tr_3474.json new file mode 100644 index 0000000000000000000000000000000000000000..e0d275069b93f0a4d8c1178014628d46ff2e49f4 --- /dev/null +++ b/reccon/query/tr_3474.json @@ -0,0 +1,24 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "It's very kind of you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "I can teach you ." + ], + "type": [ + "inter-personal" + ], + "text": "It's very kind of you .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3477.json b/reccon/query/tr_3477.json new file mode 100644 index 0000000000000000000000000000000000000000..4f88182e57e4f967c53a6354d5e607aa3dd8b67a --- /dev/null +++ b/reccon/query/tr_3477.json @@ -0,0 +1,30 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Yes , there is beautiful view . You can go fishing , camping and also enjoy this beautiful clean air .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 6, + 7 + ], + "expanded emotion cause span": [ + "There is a beautiful state park here .", + "so many people come out here to camp .", + "Yes , there is beautiful view . You can go fishing , camping and also enjoy this beautiful clean air ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , there is beautiful view . You can go fishing , camping and also enjoy this beautiful clean air .", + "id": 7, + "source_sentences": [ + 5, + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3481.json b/reccon/query/tr_3481.json new file mode 100644 index 0000000000000000000000000000000000000000..25b5f6601346e54d9eb163c2952f58c2519bb83b --- /dev/null +++ b/reccon/query/tr_3481.json @@ -0,0 +1,24 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "I'll be expecting you then .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I should be there some time next spring ." + ], + "type": [ + "inter-personal" + ], + "text": "I'll be expecting you then .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3504.json b/reccon/query/tr_3504.json new file mode 100644 index 0000000000000000000000000000000000000000..0e148c9eec8cedfe568ecb7b9b2dfc12cfa07de3 --- /dev/null +++ b/reccon/query/tr_3504.json @@ -0,0 +1,24 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "No , I'll go by myself , thanks .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I'll pick you up by nine o'clock and take you straight to the airport ." + ], + "type": [ + "inter-personal" + ], + "text": "No , I'll go by myself , thanks .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3548.json b/reccon/query/tr_3548.json new file mode 100644 index 0000000000000000000000000000000000000000..998efac64c5582e09a0969d2cc85042378241a03 --- /dev/null +++ b/reccon/query/tr_3548.json @@ -0,0 +1,27 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "I ask you to pass through life at my side-to be my second self and best earthly companion .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1, + 5 + ], + "expanded emotion cause span": [ + "Then I must go", + "can go anywhere now ." + ], + "type": [ + "inter-personal" + ], + "text": "I ask you to pass through life at my side-to be my second self and best earthly companion .", + "id": 6, + "source_sentences": [ + 0, + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3558.json b/reccon/query/tr_3558.json new file mode 100644 index 0000000000000000000000000000000000000000..b93c4e6fe0fc50960679dd49ac82f1d7094f76f7 --- /dev/null +++ b/reccon/query/tr_3558.json @@ -0,0 +1,30 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Yup , that ' s him . He made millions of dollars selling bonds to people and ended up with a pile of cash when they became useless .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 4, + 6, + 7 + ], + "expanded emotion cause span": [ + "he sell worthless stocks to people", + "If I remember , he got off with a light sentence .", + "He made millions of dollars selling bonds to people and ended up with a pile of cash when they became useless ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yup , that ' s him . He made millions of dollars selling bonds to people and ended up with a pile of cash when they became useless .", + "id": 7, + "source_sentences": [ + 3, + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3588.json b/reccon/query/tr_3588.json new file mode 100644 index 0000000000000000000000000000000000000000..969c15dc2179fa6758bec59825fd77101075bb82 --- /dev/null +++ b/reccon/query/tr_3588.json @@ -0,0 +1,24 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Impossible !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "It's typical Net Love , and a typical lesbians ' homosex !" + ], + "type": [ + "inter-personal" + ], + "text": "Impossible !", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3596.json b/reccon/query/tr_3596.json new file mode 100644 index 0000000000000000000000000000000000000000..0767e063b2e93363f5df81def07f7ee35d1a3141 --- /dev/null +++ b/reccon/query/tr_3596.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Good luck to you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Thank you ." + ], + "type": [ + "inter-personal" + ], + "text": "Good luck to you .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3624.json b/reccon/query/tr_3624.json new file mode 100644 index 0000000000000000000000000000000000000000..87a3865f26cccda63efb8daee9edcf5fc586b5f4 --- /dev/null +++ b/reccon/query/tr_3624.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Thank you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "if you need me , I'll always be there ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3636.json b/reccon/query/tr_3636.json new file mode 100644 index 0000000000000000000000000000000000000000..0135ad20af000e191325765cc728aa31a5c05753 --- /dev/null +++ b/reccon/query/tr_3636.json @@ -0,0 +1,27 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "Yes . I haven't been in his house for several weeks . When shall we start ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "Shall we visit our math teacher tomorrow ?", + "Yes . I haven't been in his house for several weeks ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes . I haven't been in his house for several weeks . When shall we start ?", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3647.json b/reccon/query/tr_3647.json new file mode 100644 index 0000000000000000000000000000000000000000..760430c65dc7a6c62a6edcc32357bdfdf1af11ce --- /dev/null +++ b/reccon/query/tr_3647.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "I'll surely make introductions for them .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Oh , how wonderful ! Every girl on the campus has a crush on those handsome guys ." + ], + "type": [ + "inter-personal" + ], + "text": "I'll surely make introductions for them .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3651.json b/reccon/query/tr_3651.json new file mode 100644 index 0000000000000000000000000000000000000000..5ebc65932211481ee881430840dbe6ea925de6bc --- /dev/null +++ b/reccon/query/tr_3651.json @@ -0,0 +1,24 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "Sure . Thanks .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "I'm an engineer , I work for Boeing . Say , would you like a drink ?" + ], + "type": [ + "inter-personal" + ], + "text": "Sure . Thanks .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3672.json b/reccon/query/tr_3672.json new file mode 100644 index 0000000000000000000000000000000000000000..665022a700a1504bd5bf5a6bd8fa1277b0807298 --- /dev/null +++ b/reccon/query/tr_3672.json @@ -0,0 +1,25 @@ +[ + { + "turn": 16, + "speaker": "B", + "utterance": "Will do .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "Have fun on Saturday ." + ], + "type": [ + "inter-personal" + ], + "text": "Will do .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3676.json b/reccon/query/tr_3676.json new file mode 100644 index 0000000000000000000000000000000000000000..190ca925fa00e60034b6a38cba2d4a846145645d --- /dev/null +++ b/reccon/query/tr_3676.json @@ -0,0 +1,24 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "Well . I really do have to go .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I ' m looking forward to it" + ], + "type": [ + "inter-personal" + ], + "text": "Well . I really do have to go .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3678.json b/reccon/query/tr_3678.json new file mode 100644 index 0000000000000000000000000000000000000000..8d19b3dbcb4f49d6e979698fad82c5b23244700e --- /dev/null +++ b/reccon/query/tr_3678.json @@ -0,0 +1,24 @@ +[ + { + "turn": 15, + "speaker": "A", + "utterance": "Sure , welcome anytime", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "Great ! So I'll know who to call if I ever need a lawyer ." + ], + "type": [ + "inter-personal" + ], + "text": "Sure , welcome anytime", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3685.json b/reccon/query/tr_3685.json new file mode 100644 index 0000000000000000000000000000000000000000..b9e9a0b11d5ecb9c650112f7e3238b0fa903c6c4 --- /dev/null +++ b/reccon/query/tr_3685.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Yes , please . Thank you for everything .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Would you like another glass of champagne ?" + ], + "type": [ + "inter-personal" + ], + "text": "Yes , please . Thank you for everything .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3694.json b/reccon/query/tr_3694.json new file mode 100644 index 0000000000000000000000000000000000000000..c02e02ef4ee3308d98fc7151b935828451c19521 --- /dev/null +++ b/reccon/query/tr_3694.json @@ -0,0 +1,24 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "Oh , really ? Do you know why ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "she left him last year ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , really ? Do you know why ?", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3702.json b/reccon/query/tr_3702.json new file mode 100644 index 0000000000000000000000000000000000000000..a7683d52f76a17f87093e546a332647e8ce34f63 --- /dev/null +++ b/reccon/query/tr_3702.json @@ -0,0 +1,27 @@ +[ + { + "turn": 13, + "speaker": "A", + "utterance": "I think you look fantastic . Happy Birthday !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12, + 13 + ], + "expanded emotion cause span": [ + "this is perfect !", + "you look fantastic" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I think you look fantastic . Happy Birthday !", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_371.json b/reccon/query/tr_371.json new file mode 100644 index 0000000000000000000000000000000000000000..57eac81c529ceb9dd3f801d7e174021048e3dd4f --- /dev/null +++ b/reccon/query/tr_371.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "It's a new concert hall and the acoustics are great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "The seats are excellent . We're right in the center .", + "It's a new concert hall and the acoustics are great ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It's a new concert hall and the acoustics are great .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3720.json b/reccon/query/tr_3720.json new file mode 100644 index 0000000000000000000000000000000000000000..18541c1c151db739cc6b6123b949d1a480136879 --- /dev/null +++ b/reccon/query/tr_3720.json @@ -0,0 +1,27 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Well then , I'll see you on Saturday . Thanks for asking me to go with you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "That was part of my plan .", + "I'll see you on Saturday . Thanks for asking me to go with you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Well then , I'll see you on Saturday . Thanks for asking me to go with you .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3729.json b/reccon/query/tr_3729.json new file mode 100644 index 0000000000000000000000000000000000000000..522abced2d17c9ed57b843547e16a488322d2e0a --- /dev/null +++ b/reccon/query/tr_3729.json @@ -0,0 +1,25 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "You're kidding . The story and acting were outstanding .", + "emotion": "surprise", + "explanation": "disagreement", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I can't say I agree ." + ], + "type": [ + "inter-personal" + ], + "text": "You're kidding . The story and acting were outstanding .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3734.json b/reccon/query/tr_3734.json new file mode 100644 index 0000000000000000000000000000000000000000..d68f9b4c916a932d279a1475b9513d9396695021 --- /dev/null +++ b/reccon/query/tr_3734.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "I like that joke , but I hope it's true .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "The only thing I've ever done behind your back is zipping you up ." + ], + "type": [ + "inter-personal" + ], + "text": "I like that joke , but I hope it's true .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3753.json b/reccon/query/tr_3753.json new file mode 100644 index 0000000000000000000000000000000000000000..16defce05f2e7b2729fe617c7e7538fce2adecee --- /dev/null +++ b/reccon/query/tr_3753.json @@ -0,0 +1,24 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "Thanks , Daisy .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "You made a perfect choice , Jack ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks , Daisy .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3755.json b/reccon/query/tr_3755.json new file mode 100644 index 0000000000000000000000000000000000000000..66769bfbf60f18d3e2e56c52db734e77d1b360e2 --- /dev/null +++ b/reccon/query/tr_3755.json @@ -0,0 +1,24 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "How horrible !", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "His car was hit by an express train ." + ], + "type": [ + "inter-personal" + ], + "text": "How horrible !", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_377.json b/reccon/query/tr_377.json new file mode 100644 index 0000000000000000000000000000000000000000..194d09714926c4013375173263078ab688fbd4f7 --- /dev/null +++ b/reccon/query/tr_377.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "That's exactly the way I feel .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I'd like to come back next weekend ." + ], + "type": [ + "inter-personal" + ], + "text": "That's exactly the way I feel .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3770.json b/reccon/query/tr_3770.json new file mode 100644 index 0000000000000000000000000000000000000000..575c7803402d8b478719ebf578622063631e4488 --- /dev/null +++ b/reccon/query/tr_3770.json @@ -0,0 +1,24 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "My pleasure .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Thank you very much . It ' s very kind of you ." + ], + "type": [ + "inter-personal" + ], + "text": "My pleasure .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3772.json b/reccon/query/tr_3772.json new file mode 100644 index 0000000000000000000000000000000000000000..df5b7e05a02734a2704b62b86c629b10efffeadb --- /dev/null +++ b/reccon/query/tr_3772.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "This could become a very expensive trip to be beauty parlour !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Good idea . We should also pedicures and manicures ." + ], + "type": [ + "inter-personal" + ], + "text": "This could become a very expensive trip to be beauty parlour !", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3773.json b/reccon/query/tr_3773.json new file mode 100644 index 0000000000000000000000000000000000000000..cb9fe9f33379430ad40f054ab4c3f787b058225c --- /dev/null +++ b/reccon/query/tr_3773.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Thanks .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "it looks very nice ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3777.json b/reccon/query/tr_3777.json new file mode 100644 index 0000000000000000000000000000000000000000..f7da5267a1bf3b98cfa1f3b0a67f5b3897f99fb6 --- /dev/null +++ b/reccon/query/tr_3777.json @@ -0,0 +1,24 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "Yes , that's right . You have a good memory .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I think I know the place you mean . We ate there last month , right ?" + ], + "type": [ + "inter-personal" + ], + "text": "Yes , that's right . You have a good memory .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3786.json b/reccon/query/tr_3786.json new file mode 100644 index 0000000000000000000000000000000000000000..a83881bd8daaa2a1eb8b391ea304dca70b651e5d --- /dev/null +++ b/reccon/query/tr_3786.json @@ -0,0 +1,24 @@ +[ + { + "turn": 23, + "speaker": "A", + "utterance": "See you then .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 22 + ], + "expanded emotion cause span": [ + "My pleasure , see you tomorrow evening ." + ], + "type": [ + "inter-personal" + ], + "text": "See you then .", + "id": 23, + "source_sentences": [ + 21 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3805.json b/reccon/query/tr_3805.json new file mode 100644 index 0000000000000000000000000000000000000000..6bf0af755d02b091b32beed703731c7c606fff4f --- /dev/null +++ b/reccon/query/tr_3805.json @@ -0,0 +1,33 @@ +[ + { + "turn": 16, + "speaker": "B", + "utterance": "I can't wait ! It sounds like we're going to have a great time . How much money should I bring ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15, + 15, + 16, + 16 + ], + "expanded emotion cause span": [ + "I can teach you", + "It'll be fun !", + "I can't wait !", + "we're going to have a great time ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I can't wait ! It sounds like we're going to have a great time . How much money should I bring ?", + "id": 16, + "source_sentences": [ + 14, + 14, + 15 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3807.json b/reccon/query/tr_3807.json new file mode 100644 index 0000000000000000000000000000000000000000..e2c09b8ec3ea27c1ef9ced5e50d89e6de2946b15 --- /dev/null +++ b/reccon/query/tr_3807.json @@ -0,0 +1,31 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "I'll come prepared .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 2, + 6, + 8 + ], + "expanded emotion cause span": [ + "I would love to help you prepare for your presentation .", + "easily give you some time tomorrow night .", + "write down anything you might be having trouble with ?" + ], + "type": [ + "inter-personal" + ], + "text": "I'll come prepared .", + "id": 9, + "source_sentences": [ + 1, + 5, + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3810.json b/reccon/query/tr_3810.json new file mode 100644 index 0000000000000000000000000000000000000000..6f33f47b6451ba156bdbf306dbab46ec0e5c7a12 --- /dev/null +++ b/reccon/query/tr_3810.json @@ -0,0 +1,24 @@ +[ + { + "turn": 15, + "speaker": "A", + "utterance": "cheers .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "thanks . Cheers ." + ], + "type": [ + "inter-personal" + ], + "text": "cheers .", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3813.json b/reccon/query/tr_3813.json new file mode 100644 index 0000000000000000000000000000000000000000..f79e62774709ca8b327280a7a81d5c4a27cbc014 --- /dev/null +++ b/reccon/query/tr_3813.json @@ -0,0 +1,24 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "Yes , let's do it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "Wanna have a look ?" + ], + "type": [ + "inter-personal" + ], + "text": "Yes , let's do it .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3823.json b/reccon/query/tr_3823.json new file mode 100644 index 0000000000000000000000000000000000000000..c1d2053944d45d65d298242b4e1b4ab0d7913bad --- /dev/null +++ b/reccon/query/tr_3823.json @@ -0,0 +1,24 @@ +[ + { + "turn": 15, + "speaker": "A", + "utterance": "Don't mention it . That's what friends are for !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "That's very generous of you . Thanks for the offer ." + ], + "type": [ + "inter-personal" + ], + "text": "Don't mention it . That's what friends are for !", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3842.json b/reccon/query/tr_3842.json new file mode 100644 index 0000000000000000000000000000000000000000..00058b61bb87f53d99d6b66c05b2b1ae23b79155 --- /dev/null +++ b/reccon/query/tr_3842.json @@ -0,0 +1,30 @@ +[ + { + "turn": 13, + "speaker": "A", + "utterance": "Goodbye , then . Thanks again for everything .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 6, + 13 + ], + "expanded emotion cause span": [ + "how about I come and see you off ?", + "I ' ll miss you . I hope we can see each other again soon .", + "Thanks again for everything ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Goodbye , then . Thanks again for everything .", + "id": 13, + "source_sentences": [ + 3, + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3864.json b/reccon/query/tr_3864.json new file mode 100644 index 0000000000000000000000000000000000000000..f84d4878dcc481e4e3e35e5a34d31f7e7b616b04 --- /dev/null +++ b/reccon/query/tr_3864.json @@ -0,0 +1,30 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "I am glad you are happy .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 4, + 6 + ], + "expanded emotion cause span": [ + "Perfect ! Couldn't be better .", + "It's just what I want .", + "I am really pleased with it ." + ], + "type": [ + "inter-personal" + ], + "text": "I am glad you are happy .", + "id": 7, + "source_sentences": [ + 1, + 3, + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3888.json b/reccon/query/tr_3888.json new file mode 100644 index 0000000000000000000000000000000000000000..95fb4e87f2e1ad8f0c936b323f46db48bab11fba --- /dev/null +++ b/reccon/query/tr_3888.json @@ -0,0 +1,24 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "I hope so , too . Bye ! Ben .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I hope we can get together again soon ." + ], + "type": [ + "inter-personal" + ], + "text": "I hope so , too . Bye ! Ben .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3896.json b/reccon/query/tr_3896.json new file mode 100644 index 0000000000000000000000000000000000000000..515ff9869ae4339249246c670955698346600c50 --- /dev/null +++ b/reccon/query/tr_3896.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "What ? Why didn ' t you tell me before ? What are you doing here ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I ' m a spy for the Indian government ." + ], + "type": [ + "inter-personal" + ], + "text": "What ? Why didn ' t you tell me before ? What are you doing here ?", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3897.json b/reccon/query/tr_3897.json new file mode 100644 index 0000000000000000000000000000000000000000..4aeb03c0f51f2bdd015791e7c424e967098adef7 --- /dev/null +++ b/reccon/query/tr_3897.json @@ -0,0 +1,27 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Yes , a legend , also . I still remember , his movies , Jurassic Park and Schindler's List got him nine Oscar awards in 1994 .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "Another superstar .", + "a legend" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , a legend , also . I still remember , his movies , Jurassic Park and Schindler's List got him nine Oscar awards in 1994 .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3905.json b/reccon/query/tr_3905.json new file mode 100644 index 0000000000000000000000000000000000000000..08974842281e45e4e5fecca3b4e1e633a5a2dde5 --- /dev/null +++ b/reccon/query/tr_3905.json @@ -0,0 +1,24 @@ +[ + { + "turn": 15, + "speaker": "A", + "utterance": "Great . I ' m looking forward to it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "Maybe you can come to the bar one day and I ' ll show you around ." + ], + "type": [ + "inter-personal" + ], + "text": "Great . I ' m looking forward to it .", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3906.json b/reccon/query/tr_3906.json new file mode 100644 index 0000000000000000000000000000000000000000..72d1dbdb708407d445f6ffc2b4bd219eaaa89079 --- /dev/null +++ b/reccon/query/tr_3906.json @@ -0,0 +1,27 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "That ' s why it was so weird traveling from Beijing to LA ! Because of the huge time difference , even though we left Beijing at noon and flew for more than eight hours , we still arrived in LA the same day at noon ! It ' s like we went back in time !", + "emotion": "surprised", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Remember when we were in Beijing ? Well , then we were in China Standard Time , and that ' s eight time zones east of Greenwich !", + "That ' s why it was so weird traveling from Beijing to LA ! Because of the huge time difference , even though we left Beijing at noon and flew for more than eight hours , we still arrived in LA the same day at noon ! It ' s like we went back in time !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That ' s why it was so weird traveling from Beijing to LA ! Because of the huge time difference , even though we left Beijing at noon and flew for more than eight hours , we still arrived in LA the same day at noon ! It ' s like we went back in time !", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3912.json b/reccon/query/tr_3912.json new file mode 100644 index 0000000000000000000000000000000000000000..f6538d3070320c4ea1cd12d07e45eb74ff2d16a6 --- /dev/null +++ b/reccon/query/tr_3912.json @@ -0,0 +1,24 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Great ! I can't wait .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "How about Joining our summer camp next week ?" + ], + "type": [ + "inter-personal" + ], + "text": "Great ! I can't wait .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3930.json b/reccon/query/tr_3930.json new file mode 100644 index 0000000000000000000000000000000000000000..9e7d102bae7b049561e916e9b3d7b6f9450b2c44 --- /dev/null +++ b/reccon/query/tr_3930.json @@ -0,0 +1,28 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "All right .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 4, + 8 + ], + "expanded emotion cause span": [ + "a date ?", + "Let's go to the coffee shop then ." + ], + "type": [ + "inter-personal" + ], + "text": "All right .", + "id": 11, + "source_sentences": [ + 3, + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3948.json b/reccon/query/tr_3948.json new file mode 100644 index 0000000000000000000000000000000000000000..32e75d44ae2ae1f4835b3b37415507498a27dfa6 --- /dev/null +++ b/reccon/query/tr_3948.json @@ -0,0 +1,27 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "I am really proud of you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "UCLA was my second choice , but I ' m happy knowing I ' Ve been accepted .", + "I am really proud of you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I am really proud of you .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3954.json b/reccon/query/tr_3954.json new file mode 100644 index 0000000000000000000000000000000000000000..adba5d6666f4daeb245962f86de4ea51b714dcf7 --- /dev/null +++ b/reccon/query/tr_3954.json @@ -0,0 +1,27 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "Right . The city life has made us tired and out of energy , while the natural world can bring us quite new feelings .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "We should walk into the nature and enjoy its beauty whenever we have time .", + "the natural world can bring us quite new feelings ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Right . The city life has made us tired and out of energy , while the natural world can bring us quite new feelings .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3957.json b/reccon/query/tr_3957.json new file mode 100644 index 0000000000000000000000000000000000000000..ffc1f72d21f7e989b0965ce70fae1702508bd236 --- /dev/null +++ b/reccon/query/tr_3957.json @@ -0,0 +1,24 @@ +[ + { + "turn": 19, + "speaker": "A", + "utterance": "that's a good idea . Let's discuss after work .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 18 + ], + "expanded emotion cause span": [ + "maybe we should all go out for dinner sometime ." + ], + "type": [ + "inter-personal" + ], + "text": "that's a good idea . Let's discuss after work .", + "id": 19, + "source_sentences": [ + 17 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_396.json b/reccon/query/tr_396.json new file mode 100644 index 0000000000000000000000000000000000000000..871190c48be58af45c7b3de8590baef35c7dcb8a --- /dev/null +++ b/reccon/query/tr_396.json @@ -0,0 +1,24 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "That's perfect . I will definitely do well .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "you have many opportunities to grow in this company as long as you do well ." + ], + "type": [ + "inter-personal" + ], + "text": "That's perfect . I will definitely do well .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3971.json b/reccon/query/tr_3971.json new file mode 100644 index 0000000000000000000000000000000000000000..6240eca9798061fb83120638a2c69ff6b86205dd --- /dev/null +++ b/reccon/query/tr_3971.json @@ -0,0 +1,27 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "My love will grow , like a river to flow .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "I'll never hurt you ; I'll never lie .", + "My love will grow , like a river to flow ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "My love will grow , like a river to flow .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3972.json b/reccon/query/tr_3972.json new file mode 100644 index 0000000000000000000000000000000000000000..0998c998fc2cb77b185374c75769e9be701eb364 --- /dev/null +++ b/reccon/query/tr_3972.json @@ -0,0 +1,24 @@ +[ + { + "turn": 20, + "speaker": "B", + "utterance": "Well , let's take the measurements right now .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 19 + ], + "expanded emotion cause span": [ + "Cedar is a good choice ." + ], + "type": [ + "inter-personal" + ], + "text": "Well , let's take the measurements right now .", + "id": 20, + "source_sentences": [ + 18 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3980.json b/reccon/query/tr_3980.json new file mode 100644 index 0000000000000000000000000000000000000000..5609816431e3cecb8c6b052c3236bf8721613596 --- /dev/null +++ b/reccon/query/tr_3980.json @@ -0,0 +1,27 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "Thanks very much . I ' m sure it will sell well . I can ' t wait to read it . Here ' s my card . Thank you for you time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "If you give me your", + "I can ' t wait to read it ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thanks very much . I ' m sure it will sell well . I can ' t wait to read it . Here ' s my card . Thank you for you time .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_3991.json b/reccon/query/tr_3991.json new file mode 100644 index 0000000000000000000000000000000000000000..682dd20335d441f4d60e8d9221dccfcee663d831 --- /dev/null +++ b/reccon/query/tr_3991.json @@ -0,0 +1,27 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "Here it is , and here we are .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "help me find the remote control for my garage door ?", + "Here it is , and here we are ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Here it is , and here we are .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4.json b/reccon/query/tr_4.json new file mode 100644 index 0000000000000000000000000000000000000000..5012ca98817b8844fbf51194c5af581a05bb4f75 --- /dev/null +++ b/reccon/query/tr_4.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "A", + "utterance": "Really ? I think we play you guys next week . Well , I have to go to practice . See you later .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "The Rockets ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? I think we play you guys next week . Well , I have to go to practice . See you later .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4002.json b/reccon/query/tr_4002.json new file mode 100644 index 0000000000000000000000000000000000000000..968bf3b0042bf33ff37c32245ec3545157d1d38c --- /dev/null +++ b/reccon/query/tr_4002.json @@ -0,0 +1,27 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "What ! I resent that !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6, + 8 + ], + "expanded emotion cause span": [ + "We are going to have to let you go .", + "you are a terrible employee !" + ], + "type": [ + "inter-personal" + ], + "text": "What ! I resent that !", + "id": 9, + "source_sentences": [ + 5, + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4023.json b/reccon/query/tr_4023.json new file mode 100644 index 0000000000000000000000000000000000000000..a4c9272eda0feacacb7cd60939c409ed819ad8ab --- /dev/null +++ b/reccon/query/tr_4023.json @@ -0,0 +1,24 @@ +[ + { + "turn": 19, + "speaker": "A", + "utterance": "Aright . I'll talk to you later .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 16 + ], + "expanded emotion cause span": [ + "I have a couple of guest passes . You want to check out my health club ?" + ], + "type": [ + "inter-personal" + ], + "text": "Aright . I'll talk to you later .", + "id": 19, + "source_sentences": [ + 15 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_403.json b/reccon/query/tr_403.json new file mode 100644 index 0000000000000000000000000000000000000000..ce652bae70d8b63f95c88024c2850a3f1ce99715 --- /dev/null +++ b/reccon/query/tr_403.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "I think that might work for me as well .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "Something that could calm your mind .", + "I think that might work for me as well ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I think that might work for me as well .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4049.json b/reccon/query/tr_4049.json new file mode 100644 index 0000000000000000000000000000000000000000..e09ecb6c70ef1c7e3d6f0e6328b099c8b7d2c193 --- /dev/null +++ b/reccon/query/tr_4049.json @@ -0,0 +1,30 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "That sounds good . It will give my wife a chance to dress up .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 5, + 6 + ], + "expanded emotion cause span": [ + "inviting you to a dinner party", + "it would be fun", + "It will give my wife a chance to dress up ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That sounds good . It will give my wife a chance to dress up .", + "id": 6, + "source_sentences": [ + 2, + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4066.json b/reccon/query/tr_4066.json new file mode 100644 index 0000000000000000000000000000000000000000..b0437e3d716491681e653d66664c065f769cd29b --- /dev/null +++ b/reccon/query/tr_4066.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "No kidding ! I can't believe this . You devil !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I'm already working for WebTracker ." + ], + "type": [ + "inter-personal" + ], + "text": "No kidding ! I can't believe this . You devil !", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4080.json b/reccon/query/tr_4080.json new file mode 100644 index 0000000000000000000000000000000000000000..ad03cfa47a243a37b227b1c54e433e586e646c5d --- /dev/null +++ b/reccon/query/tr_4080.json @@ -0,0 +1,24 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "I'll put the survey online this afternoon .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Yeah , that would let us know what would work best ." + ], + "type": [ + "inter-personal" + ], + "text": "I'll put the survey online this afternoon .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4087.json b/reccon/query/tr_4087.json new file mode 100644 index 0000000000000000000000000000000000000000..625262bd5b6870756ff4021402a26b36f2e0b837 --- /dev/null +++ b/reccon/query/tr_4087.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "Exactly .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "So factory tours are good for companies as well as visitors ." + ], + "type": [ + "inter-personal" + ], + "text": "Exactly .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4091.json b/reccon/query/tr_4091.json new file mode 100644 index 0000000000000000000000000000000000000000..86866a46ecfbe23648e0823b1b82308232022243 --- /dev/null +++ b/reccon/query/tr_4091.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "How do you do ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "How do you do , Mr . Wu ? Welcome .", + "How do you do ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "How do you do ?", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4092.json b/reccon/query/tr_4092.json new file mode 100644 index 0000000000000000000000000000000000000000..37f9e24f293cf37b315bb531d3d77c8dfc1c53b8 --- /dev/null +++ b/reccon/query/tr_4092.json @@ -0,0 +1,27 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "It's fantastic !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "Here is the swimming pool and we can swim later .", + "It's fantastic !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It's fantastic !", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4097.json b/reccon/query/tr_4097.json new file mode 100644 index 0000000000000000000000000000000000000000..a263e6ee2bf29c39956b2804d4afdc0fa0af95f9 --- /dev/null +++ b/reccon/query/tr_4097.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "Really ? Have you won a fortune in the lottery ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "I had some good financial news yesterday too ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? Have you won a fortune in the lottery ?", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4099.json b/reccon/query/tr_4099.json new file mode 100644 index 0000000000000000000000000000000000000000..10c742c91802c9861a5193853dd6672dc5ccabd5 --- /dev/null +++ b/reccon/query/tr_4099.json @@ -0,0 +1,24 @@ +[ + { + "turn": 17, + "speaker": "A", + "utterance": "Really ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 16 + ], + "expanded emotion cause span": [ + "the laws aren't as strict as in Taiwan . If people are arrested , and they have a little pot in their possession , they don't go to jail . They just have to pay a fine ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ?", + "id": 17, + "source_sentences": [ + 15 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4104.json b/reccon/query/tr_4104.json new file mode 100644 index 0000000000000000000000000000000000000000..ee783be1acfbfbf222f806e59577b0936b1d45c7 --- /dev/null +++ b/reccon/query/tr_4104.json @@ -0,0 +1,27 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Yeah , I like her way of teaching . She told us not to cram for exams , and to pay more attention to communicating than memorizing .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "She is a pretty good teacher ! With her help I think I can make great progress in English .", + "Yeah , I like her way of teaching . She told us not to cram for exams , and to pay more attention to communicating than memorizing ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yeah , I like her way of teaching . She told us not to cram for exams , and to pay more attention to communicating than memorizing .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4106.json b/reccon/query/tr_4106.json new file mode 100644 index 0000000000000000000000000000000000000000..054ba638d9a84b6a8360e71de4fc7ff168144877 --- /dev/null +++ b/reccon/query/tr_4106.json @@ -0,0 +1,33 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "What an attractive place ! How can I get there ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 6, + 8, + 9 + ], + "expanded emotion cause span": [ + "The scenery is so breathtaking .", + "There are thousands of hot springs and fountains .", + "Yes . The well-known Yellowstone Waterfall is formed when the Yellowstone Lake falls down into the Yellowstone Canyon .", + "an attractive place" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "What an attractive place ! How can I get there ?", + "id": 9, + "source_sentences": [ + 3, + 5, + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4132.json b/reccon/query/tr_4132.json new file mode 100644 index 0000000000000000000000000000000000000000..b64f70d3eca4e229c7ec9b21ca32d19a12575d5b --- /dev/null +++ b/reccon/query/tr_4132.json @@ -0,0 +1,27 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Thank you . He ' s very lucky indeed .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "Fantastic ! Please send him my congratulations .", + "He ' s very lucky indeed ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you . He ' s very lucky indeed .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4155.json b/reccon/query/tr_4155.json new file mode 100644 index 0000000000000000000000000000000000000000..0fc3e72aaed0bef07a80322084a9eefe8d179826 --- /dev/null +++ b/reccon/query/tr_4155.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "I ' m sure I will .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "you ' ll enjoy the trip", + "I ' m sure I will ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I ' m sure I will .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4158.json b/reccon/query/tr_4158.json new file mode 100644 index 0000000000000000000000000000000000000000..af216df83796c5c3d55243910da255585c90c886 --- /dev/null +++ b/reccon/query/tr_4158.json @@ -0,0 +1,27 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "It is so very kind of you . I'm so moved by you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13, + 14 + ], + "expanded emotion cause span": [ + "Let's sing \" Happy Birthday \" to Mary .", + "It is so very kind of you . I'm so moved by you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It is so very kind of you . I'm so moved by you .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4163.json b/reccon/query/tr_4163.json new file mode 100644 index 0000000000000000000000000000000000000000..025298227299e3039c60571f9f06fcfe766d74ab --- /dev/null +++ b/reccon/query/tr_4163.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Oh , that would be lovely . Shall we say seven o ' clock ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Would you like to have dinner with me ?" + ], + "type": [ + "inter-personal" + ], + "text": "Oh , that would be lovely . Shall we say seven o ' clock ?", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4164.json b/reccon/query/tr_4164.json new file mode 100644 index 0000000000000000000000000000000000000000..9693f025855b121e2f95ce38a665274b2dc69858 --- /dev/null +++ b/reccon/query/tr_4164.json @@ -0,0 +1,27 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Well , I just wanted to say well done . Really you did a great job .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "that was some good advice . You made some really good points .", + "Really you did a great job ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Well , I just wanted to say well done . Really you did a great job .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4165.json b/reccon/query/tr_4165.json new file mode 100644 index 0000000000000000000000000000000000000000..fe448d3532943bd62b802fdc40bf799e0e50a9e6 --- /dev/null +++ b/reccon/query/tr_4165.json @@ -0,0 +1,27 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Gorgeous ! There is another song combining Chinese and western music styles . I am crazy for it , so I hear it over and again . And I plan to make it as the ringbone of my mobile .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "What's your comment on his new album ?", + "Gorgeous ! There is another song combining Chinese and western music styles . I am crazy for it , so I hear it over and again . And I plan to make it as the ringbone of my mobile ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Gorgeous ! There is another song combining Chinese and western music styles . I am crazy for it , so I hear it over and again . And I plan to make it as the ringbone of my mobile .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4182.json b/reccon/query/tr_4182.json new file mode 100644 index 0000000000000000000000000000000000000000..0a1797bf4bb9b89b60b2fd83df6d48b4a5207b8b --- /dev/null +++ b/reccon/query/tr_4182.json @@ -0,0 +1,27 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "He will enjoy himself this weekend .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "Daniel loves the beach very much !", + "He will enjoy himself this weekend ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "He will enjoy himself this weekend .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4188.json b/reccon/query/tr_4188.json new file mode 100644 index 0000000000000000000000000000000000000000..4a4ca3efc4a2e6197ca2601da92ab45350340836 --- /dev/null +++ b/reccon/query/tr_4188.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "It's called love is blind , I think .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "So do I . You are a beautiful flower in my mind ." + ], + "type": [ + "inter-personal" + ], + "text": "It's called love is blind , I think .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4194.json b/reccon/query/tr_4194.json new file mode 100644 index 0000000000000000000000000000000000000000..48a84c0205cf8605f45ddacff559f2f716d7356d --- /dev/null +++ b/reccon/query/tr_4194.json @@ -0,0 +1,26 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "OK , I'll talk to you soon .", + "emotion": "happiness", + "explanation": "speaker and listener are happy about christmas shopping", + "flag": "F", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "go shopping with me this weekend" + ], + "type": [ + "inter-personal" + ], + "text": "OK , I'll talk to you soon .", + "id": 10, + "source_sentences": [ + 2 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4204.json b/reccon/query/tr_4204.json new file mode 100644 index 0000000000000000000000000000000000000000..720b1983ecf64d7e165c52dd3f422f8791b61d39 --- /dev/null +++ b/reccon/query/tr_4204.json @@ -0,0 +1,24 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "Bye bye ! Have a pleasant journey !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Thank you very much ." + ], + "type": [ + "inter-personal" + ], + "text": "Bye bye ! Have a pleasant journey !", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4220.json b/reccon/query/tr_4220.json new file mode 100644 index 0000000000000000000000000000000000000000..f04b1c0ce4f9e3c048127c4fbe66b13027f23372 --- /dev/null +++ b/reccon/query/tr_4220.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "No , there ' s no need . Thank you all the same .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Are you hungry ? Do you want me to buy something for you to eat ?" + ], + "type": [ + "inter-personal" + ], + "text": "No , there ' s no need . Thank you all the same .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4248.json b/reccon/query/tr_4248.json new file mode 100644 index 0000000000000000000000000000000000000000..b28a62712024884e7490fcd772eb3aa752f5537b --- /dev/null +++ b/reccon/query/tr_4248.json @@ -0,0 +1,24 @@ +[ + { + "turn": 13, + "speaker": "A", + "utterance": "Frightened ? You must be joking .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "Are you frightened ?" + ], + "type": [ + "inter-personal" + ], + "text": "Frightened ? You must be joking .", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4262.json b/reccon/query/tr_4262.json new file mode 100644 index 0000000000000000000000000000000000000000..feb69fb59349a4fd284627017a0cdbc08ab40f04 --- /dev/null +++ b/reccon/query/tr_4262.json @@ -0,0 +1,27 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "Yes , it's a good habit to have a life-long hobby . Those who practise calligraphy and Qigong always live longer .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "And I can concentrate on my study after the relaxation over the weekend .", + "Yes , it's a good habit to have a life-long hobby . Those who practise calligraphy and Qigong always live longer ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , it's a good habit to have a life-long hobby . Those who practise calligraphy and Qigong always live longer .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4266.json b/reccon/query/tr_4266.json new file mode 100644 index 0000000000000000000000000000000000000000..e014946b5d72b2716447e4b7d150e6742e2bc2d1 --- /dev/null +++ b/reccon/query/tr_4266.json @@ -0,0 +1,27 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Yeah , he tackled him so hard his helmet came off .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "What a hit !", + "he tackled him so hard" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yeah , he tackled him so hard his helmet came off .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_427.json b/reccon/query/tr_427.json new file mode 100644 index 0000000000000000000000000000000000000000..f0e0088c5ee1a0fe9e2ef1ba333e0838a5176d3e --- /dev/null +++ b/reccon/query/tr_427.json @@ -0,0 +1,27 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "I ' m sorry that you didn ' t get in .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 6, + 11 + ], + "expanded emotion cause span": [ + "I didn ' t get accepted .", + "I ' m sorry that you didn ' t get in ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I ' m sorry that you didn ' t get in .", + "id": 11, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4280.json b/reccon/query/tr_4280.json new file mode 100644 index 0000000000000000000000000000000000000000..61a54cd4626244f8684f8216e5112543da14e399 --- /dev/null +++ b/reccon/query/tr_4280.json @@ -0,0 +1,27 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Do you mean it ? I'd love to !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 5 + ], + "expanded emotion cause span": [ + "We have two weeks off !", + "why don't you come with us ? We have plenty of room ." + ], + "type": [ + "inter-personal" + ], + "text": "Do you mean it ? I'd love to !", + "id": 6, + "source_sentences": [ + 0, + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4288.json b/reccon/query/tr_4288.json new file mode 100644 index 0000000000000000000000000000000000000000..b209558c011a4019732aaa9e9f5c9f363b53e756 --- /dev/null +++ b/reccon/query/tr_4288.json @@ -0,0 +1,30 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Don ' t be silly , John . I ' m going with you . It ' s necessary for me to have a holiday too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 7, + 8 + ], + "expanded emotion cause span": [ + "That ' s very good of you , Helen", + "That ' s very kind of you , Helen .", + "I ' m going with you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Don ' t be silly , John . I ' m going with you . It ' s necessary for me to have a holiday too .", + "id": 8, + "source_sentences": [ + 4, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4291.json b/reccon/query/tr_4291.json new file mode 100644 index 0000000000000000000000000000000000000000..13dffc262ebb7760419153d0709de4ffd137883c --- /dev/null +++ b/reccon/query/tr_4291.json @@ -0,0 +1,24 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "Good . You really know how to enjoy yourself .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I'm fond of dancing ." + ], + "type": [ + "inter-personal" + ], + "text": "Good . You really know how to enjoy yourself .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4295.json b/reccon/query/tr_4295.json new file mode 100644 index 0000000000000000000000000000000000000000..6e4ec64fe885229b873651f57e89f1ae492a8087 --- /dev/null +++ b/reccon/query/tr_4295.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "OK . Here are your robes . You can go shower first .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "We'll do the seaweed wrap , the jet bath , and the foot massage ." + ], + "type": [ + "inter-personal" + ], + "text": "OK . Here are your robes . You can go shower first .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4307.json b/reccon/query/tr_4307.json new file mode 100644 index 0000000000000000000000000000000000000000..c1099224da12e2929c15c0f250e4b8f0510c549e --- /dev/null +++ b/reccon/query/tr_4307.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "I heard them warming up earlier . You're right .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 6 + ], + "expanded emotion cause span": [ + "Our bass section is really good . You're going to love singing with them .", + "Our bass section is really good . You're going to love singing with them ." + ], + "type": [ + "inter-personal" + ], + "text": "I heard them warming up earlier . You're right .", + "id": 7, + "source_sentences": [ + 5, + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4318.json b/reccon/query/tr_4318.json new file mode 100644 index 0000000000000000000000000000000000000000..ae5bbb8cfe1c55a6be6b09da8857a32e16cc7d2c --- /dev/null +++ b/reccon/query/tr_4318.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "Bye .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "All right . Can we make it another time ?" + ], + "type": [ + "inter-personal" + ], + "text": "Bye .", + "id": 11, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4332.json b/reccon/query/tr_4332.json new file mode 100644 index 0000000000000000000000000000000000000000..e73377fd1dc37846a41ca09dabb56ae3bcd040d9 --- /dev/null +++ b/reccon/query/tr_4332.json @@ -0,0 +1,24 @@ +[ + { + "turn": 16, + "speaker": "B", + "utterance": "That's too bad . They ' re such good company .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "Marcia and Paul called to cancel at the last moment ." + ], + "type": [ + "inter-personal" + ], + "text": "That's too bad . They ' re such good company .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4336.json b/reccon/query/tr_4336.json new file mode 100644 index 0000000000000000000000000000000000000000..65e68f7db4e0c7b34ef134148153bac302ebd280 --- /dev/null +++ b/reccon/query/tr_4336.json @@ -0,0 +1,27 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Are you kidding ? When I get on stage , my palms start to sweat , I get really nervous and I can hardly speak .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "public speaking is not that bad .", + "When I get on stage , my palms start to sweat , I get really nervous and I can hardly speak ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Are you kidding ? When I get on stage , my palms start to sweat , I get really nervous and I can hardly speak .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4378.json b/reccon/query/tr_4378.json new file mode 100644 index 0000000000000000000000000000000000000000..dd4f7180cad66c68ac9bcca70a159cebffd32cc2 --- /dev/null +++ b/reccon/query/tr_4378.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Really ? I'll have a try . Maybe I will get high marks next time .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I suggest you read English texts aloud every day , and try to speak more . That will be beneficial to cultivate your sense of the language ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? I'll have a try . Maybe I will get high marks next time .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4434.json b/reccon/query/tr_4434.json new file mode 100644 index 0000000000000000000000000000000000000000..34e65f32767a77917331ed7ac8978f6a27ab04e1 --- /dev/null +++ b/reccon/query/tr_4434.json @@ -0,0 +1,30 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "It deserves it . The film gave us a lot of inspiration .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 7, + 8 + ], + "expanded emotion cause span": [ + "I really enjoyed that film !", + "It has got this year's Oscar Award .", + "The film gave us a lot of inspiration ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It deserves it . The film gave us a lot of inspiration .", + "id": 8, + "source_sentences": [ + 0, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4464.json b/reccon/query/tr_4464.json new file mode 100644 index 0000000000000000000000000000000000000000..900c3dbe4ba000dae793a9a350ae73cb98ca8aa6 --- /dev/null +++ b/reccon/query/tr_4464.json @@ -0,0 +1,24 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "Thanks a lot .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "We all want you to come too ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks a lot .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4466.json b/reccon/query/tr_4466.json new file mode 100644 index 0000000000000000000000000000000000000000..af3980674e4f9ccc4093e9043d8be1b6f5cb6205 --- /dev/null +++ b/reccon/query/tr_4466.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Ok . I'll give it a try .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "it'll be fun ." + ], + "type": [ + "inter-personal" + ], + "text": "Ok . I'll give it a try .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4470.json b/reccon/query/tr_4470.json new file mode 100644 index 0000000000000000000000000000000000000000..967ea0971f3732d4ab8f049aea68a49e8cc63bf2 --- /dev/null +++ b/reccon/query/tr_4470.json @@ -0,0 +1,24 @@ +[ + { + "turn": 21, + "speaker": "A", + "utterance": "no wonder you like the class so much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 20 + ], + "expanded emotion cause span": [ + "she wanted us to relax tonight instead of doing homework ," + ], + "type": [ + "inter-personal" + ], + "text": "no wonder you like the class so much .", + "id": 21, + "source_sentences": [ + 19 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4502.json b/reccon/query/tr_4502.json new file mode 100644 index 0000000000000000000000000000000000000000..19d29a5c240f9dfdbf4b4318816a5e242cf10e03 --- /dev/null +++ b/reccon/query/tr_4502.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Sure , we call it doubt .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "You ' re great ." + ], + "type": [ + "inter-personal" + ], + "text": "Sure , we call it doubt .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4516.json b/reccon/query/tr_4516.json new file mode 100644 index 0000000000000000000000000000000000000000..5b1b3e754dfe6c7a51f8726f193dac9a7e8ce66e --- /dev/null +++ b/reccon/query/tr_4516.json @@ -0,0 +1,24 @@ +[ + { + "turn": 19, + "speaker": "A", + "utterance": "Oh , my God , you're kidding me ! He carried him back ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 18 + ], + "expanded emotion cause span": [ + "he didn't have far to carry him ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , my God , you're kidding me ! He carried him back ?", + "id": 19, + "source_sentences": [ + 17 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4525.json b/reccon/query/tr_4525.json new file mode 100644 index 0000000000000000000000000000000000000000..e56c351669eff93bd99a9c58a3cd8faa8f12c744 --- /dev/null +++ b/reccon/query/tr_4525.json @@ -0,0 +1,24 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Good ! Julie , if you could pass this plate down to Joe , I think we are all set .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "what a great dinner party !" + ], + "type": [ + "inter-personal" + ], + "text": "Good ! Julie , if you could pass this plate down to Joe , I think we are all set .", + "id": 10, + "source_sentences": [ + 0 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4533.json b/reccon/query/tr_4533.json new file mode 100644 index 0000000000000000000000000000000000000000..20afd93344b8f71ec520f9a89dfa737a73d9aeba --- /dev/null +++ b/reccon/query/tr_4533.json @@ -0,0 +1,27 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "All I know about soccer is that you can ' t use your hands and that players are always falling down , trying to get a free kick or penalty kick . It seems like a sissy sport to me !", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "It ' s a very exciting and nerve wracking sport !", + "It seems like a sissy sport to me !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "All I know about soccer is that you can ' t use your hands and that players are always falling down , trying to get a free kick or penalty kick . It seems like a sissy sport to me !", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4544.json b/reccon/query/tr_4544.json new file mode 100644 index 0000000000000000000000000000000000000000..7b1273445f1b132583ef903aa1074bf11bce9b99 --- /dev/null +++ b/reccon/query/tr_4544.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Oh , that's great . You're serious this time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I hope one day I can marry her ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , that's great . You're serious this time .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4558.json b/reccon/query/tr_4558.json new file mode 100644 index 0000000000000000000000000000000000000000..5831cd7772215c0974b79750d0a17f368234ba6d --- /dev/null +++ b/reccon/query/tr_4558.json @@ -0,0 +1,24 @@ +[ + { + "turn": 13, + "speaker": "A", + "utterance": "Thanks , Jeanine , you are a real pal . Let's go in .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "I've got you covered ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks , Jeanine , you are a real pal . Let's go in .", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4576.json b/reccon/query/tr_4576.json new file mode 100644 index 0000000000000000000000000000000000000000..02ca69640990ceba476812c0f13709351d7c5163 --- /dev/null +++ b/reccon/query/tr_4576.json @@ -0,0 +1,24 @@ +[ + { + "turn": 22, + "speaker": "B", + "utterance": "Ok . See you later .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 21 + ], + "expanded emotion cause span": [ + "I'll see you on Saturday ." + ], + "type": [ + "inter-personal" + ], + "text": "Ok . See you later .", + "id": 22, + "source_sentences": [ + 20 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4589.json b/reccon/query/tr_4589.json new file mode 100644 index 0000000000000000000000000000000000000000..58950c7a90f684969c678e0b3d2d2d7e1a61b420 --- /dev/null +++ b/reccon/query/tr_4589.json @@ -0,0 +1,24 @@ +[ + { + "turn": 15, + "speaker": "A", + "utterance": "Are you sure ? We could go Dutch .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "I'll treat you tonight ." + ], + "type": [ + "inter-personal" + ], + "text": "Are you sure ? We could go Dutch .", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4614.json b/reccon/query/tr_4614.json new file mode 100644 index 0000000000000000000000000000000000000000..49732e9f611e92c7ba146b361c4654791fa04963 --- /dev/null +++ b/reccon/query/tr_4614.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Well , thank you for coming .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I really had a good time ." + ], + "type": [ + "inter-personal" + ], + "text": "Well , thank you for coming .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4624.json b/reccon/query/tr_4624.json new file mode 100644 index 0000000000000000000000000000000000000000..1a52619b4de7a5fdb4a17a4aa48365846aea7e6c --- /dev/null +++ b/reccon/query/tr_4624.json @@ -0,0 +1,27 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "I am awfully sorry . I didn't think you would mind so much .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3, + 6 + ], + "expanded emotion cause span": [ + "What did you think you were doing ?", + "I am awfully sorry . I didn't think you would mind so much ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I am awfully sorry . I didn't think you would mind so much .", + "id": 6, + "source_sentences": [ + 2 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4627.json b/reccon/query/tr_4627.json new file mode 100644 index 0000000000000000000000000000000000000000..0793de6c4e8a70527cd885cd43c6a99fbf01acdb --- /dev/null +++ b/reccon/query/tr_4627.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "You've got to be joking .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "I blew the finally exam ." + ], + "type": [ + "inter-personal" + ], + "text": "You've got to be joking .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4633.json b/reccon/query/tr_4633.json new file mode 100644 index 0000000000000000000000000000000000000000..27ea90149a9fa07864056ef24e40d7e427b1d460 --- /dev/null +++ b/reccon/query/tr_4633.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Thank you . I wish I would .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I ' d like to wish you every success in your new venture ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . I wish I would .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4647.json b/reccon/query/tr_4647.json new file mode 100644 index 0000000000000000000000000000000000000000..1cd39f50110c0c5a567c3da9d64dd02fb3e8b38a --- /dev/null +++ b/reccon/query/tr_4647.json @@ -0,0 +1,30 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Tomorrow , I ' ll cut the grass . Then the garden will lock perfect .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 7, + 8 + ], + "expanded emotion cause span": [ + "Your garden is looking beautiful this summer . The flowers are really colorful .", + "When the lower branches are removed , you ' ll be able to sit under the tree .", + "Then the garden will lock perfect ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Tomorrow , I ' ll cut the grass . Then the garden will lock perfect .", + "id": 8, + "source_sentences": [ + 0, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4659.json b/reccon/query/tr_4659.json new file mode 100644 index 0000000000000000000000000000000000000000..e754e5ab7114d578b248e1f5a1969a47ee9353a0 --- /dev/null +++ b/reccon/query/tr_4659.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Glad to meet you , too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Glad to meet you , Ms . Baker ." + ], + "type": [ + "inter-personal" + ], + "text": "Glad to meet you , too .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4689.json b/reccon/query/tr_4689.json new file mode 100644 index 0000000000000000000000000000000000000000..fa4cb80cd51d741326253e8361cdedd367c179df --- /dev/null +++ b/reccon/query/tr_4689.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Oh , good . If you could come around six thirty or seven o'clock , that would give us some time to chat a whit over a glass of wine before dinner .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I'd be delighted to come over and celebrate your birthday with you .", + "some time to chat a whit over a glass of wine" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , good . If you could come around six thirty or seven o'clock , that would give us some time to chat a whit over a glass of wine before dinner .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4693.json b/reccon/query/tr_4693.json new file mode 100644 index 0000000000000000000000000000000000000000..59fe7dd21dc5d19d59baa594c1884a5758fb096c --- /dev/null +++ b/reccon/query/tr_4693.json @@ -0,0 +1,27 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "Good luck !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 10 + ], + "expanded emotion cause span": [ + "she's single ! Man , I could tell from the moment I saw her , she's the girl of my dreams !", + "I'll call her now and see if she is available tonight ." + ], + "type": [ + "inter-personal" + ], + "text": "Good luck !", + "id": 11, + "source_sentences": [ + 3, + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4696.json b/reccon/query/tr_4696.json new file mode 100644 index 0000000000000000000000000000000000000000..8890a0b53d06889f59760bfe4b87cfdecbd695d2 --- /dev/null +++ b/reccon/query/tr_4696.json @@ -0,0 +1,30 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "I'll never get over it . Oh , Harry , it was all so unnecessary . That man ! ! How could he do this to us after we'd put him up ?", + "emotion": "anger", + "expanded emotion cause evidence": [ + 4, + 7, + 7 + ], + "expanded emotion cause span": [ + "he simply drove off with everything in my car . That's what hurts me most .", + "it was all so unnecessary .", + "How could he do this to us" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'll never get over it . Oh , Harry , it was all so unnecessary . That man ! ! How could he do this to us after we'd put him up ?", + "id": 7, + "source_sentences": [ + 3, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4698.json b/reccon/query/tr_4698.json new file mode 100644 index 0000000000000000000000000000000000000000..c15c84c3d5ce883b36e84260be42bf320cb58de2 --- /dev/null +++ b/reccon/query/tr_4698.json @@ -0,0 +1,27 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Sure . I'd be very glad to be your tour guide .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "Can you go there with me ? I'd like someone who is familiar with that area to go with me .", + "I'd be very glad to be your tour guide ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Sure . I'd be very glad to be your tour guide .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4722.json b/reccon/query/tr_4722.json new file mode 100644 index 0000000000000000000000000000000000000000..6ec38985ce062eabf8787b483c91957e9ede5d8f --- /dev/null +++ b/reccon/query/tr_4722.json @@ -0,0 +1,24 @@ +[ + { + "turn": 17, + "speaker": "A", + "utterance": "Thanks . I'm flattered .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 16 + ], + "expanded emotion cause span": [ + "You're quite slim . In fact , if you were one of those starlets , the movie company would say you have a fabulous figure ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks . I'm flattered .", + "id": 17, + "source_sentences": [ + 15 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_475.json b/reccon/query/tr_475.json new file mode 100644 index 0000000000000000000000000000000000000000..09d200cc97f03cb023eaf201664e10b2d536f618 --- /dev/null +++ b/reccon/query/tr_475.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "See you then .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Never mind . I'll be waiting for you ." + ], + "type": [ + "inter-personal" + ], + "text": "See you then .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4750.json b/reccon/query/tr_4750.json new file mode 100644 index 0000000000000000000000000000000000000000..3283da30bfba68fe85f99c9f16e5c88cfe26083b --- /dev/null +++ b/reccon/query/tr_4750.json @@ -0,0 +1,27 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Thank you for your compliments . It's just you are a good leader . Do you like the foxtrot and tango ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "You dance beautifully too . It's lucky that I got you as a partner .", + "It's just you are a good leader ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you for your compliments . It's just you are a good leader . Do you like the foxtrot and tango ?", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4771.json b/reccon/query/tr_4771.json new file mode 100644 index 0000000000000000000000000000000000000000..fd816ee472c61eeb12bf00c4b1a4d1f9cb626951 --- /dev/null +++ b/reccon/query/tr_4771.json @@ -0,0 +1,24 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "You are so kind . Thanks .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I can help you with it" + ], + "type": [ + "inter-personal" + ], + "text": "You are so kind . Thanks .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4792.json b/reccon/query/tr_4792.json new file mode 100644 index 0000000000000000000000000000000000000000..fa98ef1285243f595a3e4e718c793087d0d558a9 --- /dev/null +++ b/reccon/query/tr_4792.json @@ -0,0 +1,24 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "sounds great . Do they serve noodles ? I am in the mood for some tasty noodles as well .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "we can try Yuanyang pot this time . You can choose the non-spicy soup base ." + ], + "type": [ + "inter-personal" + ], + "text": "sounds great . Do they serve noodles ? I am in the mood for some tasty noodles as well .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4804.json b/reccon/query/tr_4804.json new file mode 100644 index 0000000000000000000000000000000000000000..4b3cc132a2ccf4a4506af86fa88d0c9c42251f95 --- /dev/null +++ b/reccon/query/tr_4804.json @@ -0,0 +1,24 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "Well , if I'm not living here anymore , then I won't have to listen to your rules .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "maybe that'll teach you to respect my rules ." + ], + "type": [ + "inter-personal" + ], + "text": "Well , if I'm not living here anymore , then I won't have to listen to your rules .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_483.json b/reccon/query/tr_483.json new file mode 100644 index 0000000000000000000000000000000000000000..dac175a61605405ff546e0a2efec6e320d48b2cf --- /dev/null +++ b/reccon/query/tr_483.json @@ -0,0 +1,24 @@ +[ + { + "turn": 13, + "speaker": "A", + "utterance": "Oh , it's no problem . It ' s OK . You know , it only happened once .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "I promise I'll keep it down in the future ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , it's no problem . It ' s OK . You know , it only happened once .", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_487.json b/reccon/query/tr_487.json new file mode 100644 index 0000000000000000000000000000000000000000..93e5a037f99c78e4306f39dee9f920aea3ea69e3 --- /dev/null +++ b/reccon/query/tr_487.json @@ -0,0 +1,27 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "Sound like everything is great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 8 + ], + "expanded emotion cause span": [ + "Even though we are both working , we get to spend a lot of time with each other in the evening and on the weekends .", + "In the evening , we just sit and talk over dinner . But on the weekend , we try to go out to the beach or hit a nice restaurant , or go to a nice cafe ." + ], + "type": [ + "inter-personal" + ], + "text": "Sound like everything is great .", + "id": 9, + "source_sentences": [ + 5, + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4878.json b/reccon/query/tr_4878.json new file mode 100644 index 0000000000000000000000000000000000000000..e4c5355bb0e44140b2194777c79294ce86d1b1f4 --- /dev/null +++ b/reccon/query/tr_4878.json @@ -0,0 +1,24 @@ +[ + { + "turn": 15, + "speaker": "A", + "utterance": "Thank you . Do you need something else ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "I will take two bottles ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . Do you need something else ?", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4895.json b/reccon/query/tr_4895.json new file mode 100644 index 0000000000000000000000000000000000000000..c0e84cabf7bac45a36556411d9340729a29982c8 --- /dev/null +++ b/reccon/query/tr_4895.json @@ -0,0 +1,27 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Thank you . Nice to meet you , too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "Nice to meet you !", + "Nice to meet you , too ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you . Nice to meet you , too .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4911.json b/reccon/query/tr_4911.json new file mode 100644 index 0000000000000000000000000000000000000000..d065a25f25d439067d857ed47b555a162a5d4c53 --- /dev/null +++ b/reccon/query/tr_4911.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Thanks for saying so .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I ' m very pleased with your work . Your promotion will contribute to the development of the company ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks for saying so .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4915.json b/reccon/query/tr_4915.json new file mode 100644 index 0000000000000000000000000000000000000000..3b7935f206e5294789e5de82cc03939f90d7dc3e --- /dev/null +++ b/reccon/query/tr_4915.json @@ -0,0 +1,27 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Nice to see you , too , Steven . Goodbye .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "Nice to see you .", + "Nice to see you , too ," + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Nice to see you , too , Steven . Goodbye .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4936.json b/reccon/query/tr_4936.json new file mode 100644 index 0000000000000000000000000000000000000000..4ee4484581edaa739a1e474c6f0749d81938ff2e --- /dev/null +++ b/reccon/query/tr_4936.json @@ -0,0 +1,27 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "So long . Thank you for shopping here .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13, + 14 + ], + "expanded emotion cause span": [ + "Thank you for your help .", + "So long . Thank you for shopping here ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "So long . Thank you for shopping here .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4974.json b/reccon/query/tr_4974.json new file mode 100644 index 0000000000000000000000000000000000000000..77ff0e8694d3262b84660a6033421c475b7193c3 --- /dev/null +++ b/reccon/query/tr_4974.json @@ -0,0 +1,24 @@ +[ + { + "turn": 27, + "speaker": "A", + "utterance": "Oh , shut up about ties ! Forget about ties , why not ?", + "emotion": "anger", + "expanded emotion cause evidence": [ + 26 + ], + "expanded emotion cause span": [ + "A tie ?" + ], + "type": [ + "inter-personal" + ], + "text": "Oh , shut up about ties ! Forget about ties , why not ?", + "id": 27, + "source_sentences": [ + 25 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_4994.json b/reccon/query/tr_4994.json new file mode 100644 index 0000000000000000000000000000000000000000..e56466e8b1ccf52bbeda2b47633a8a96c56cacfa --- /dev/null +++ b/reccon/query/tr_4994.json @@ -0,0 +1,24 @@ +[ + { + "turn": 13, + "speaker": "A", + "utterance": "you ' re kidding ! How did that happen ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "I got sacked today ." + ], + "type": [ + "inter-personal" + ], + "text": "you ' re kidding ! How did that happen ?", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_502.json b/reccon/query/tr_502.json new file mode 100644 index 0000000000000000000000000000000000000000..04cb10ce182da0e6c07e1afa4ff3015ca2a956e0 --- /dev/null +++ b/reccon/query/tr_502.json @@ -0,0 +1,33 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "It was really an exciting moment .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 1, + 5, + 6 + ], + "expanded emotion cause span": [ + "Congratulations !", + "You won the city marathon .", + "run to the finish line .", + "It was really an exciting moment ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It was really an exciting moment .", + "id": 6, + "source_sentences": [ + 0, + 0, + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_505.json b/reccon/query/tr_505.json new file mode 100644 index 0000000000000000000000000000000000000000..154e62becf36ac6413f3d9e97482bfe2a9fca5db --- /dev/null +++ b/reccon/query/tr_505.json @@ -0,0 +1,24 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "Really ? That ' s great ! Do you speak some Spanish ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I am 40 years old and was born and raised here in the good old U . S of A , although I have some Colombian heritage ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? That ' s great ! Do you speak some Spanish ?", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_510.json b/reccon/query/tr_510.json new file mode 100644 index 0000000000000000000000000000000000000000..30a6581613f015a02bfc86888f8c3e4fa8586244 --- /dev/null +++ b/reccon/query/tr_510.json @@ -0,0 +1,24 @@ +[ + { + "turn": 20, + "speaker": "B", + "utterance": "ok ! I ' ll bring one to you next time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 19 + ], + "expanded emotion cause span": [ + "recommend one to me ?" + ], + "type": [ + "inter-personal" + ], + "text": "ok ! I ' ll bring one to you next time .", + "id": 20, + "source_sentences": [ + 18 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_5133.json b/reccon/query/tr_5133.json new file mode 100644 index 0000000000000000000000000000000000000000..c122be0c82c657812edfb6e25767dcdabb2494dc --- /dev/null +++ b/reccon/query/tr_5133.json @@ -0,0 +1,27 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "I'm glad to hear that . I think it's the nicest city in the United States .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "I really like your city .", + "I'm glad to hear that . I think it's the nicest city in the United States ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm glad to hear that . I think it's the nicest city in the United States .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_5156.json b/reccon/query/tr_5156.json new file mode 100644 index 0000000000000000000000000000000000000000..44da2b17996422a012e3c328a3b20458cb202f32 --- /dev/null +++ b/reccon/query/tr_5156.json @@ -0,0 +1,24 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "Don't worry about it , but thank you very much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I'll make sure he doesn't do that again ." + ], + "type": [ + "inter-personal" + ], + "text": "Don't worry about it , but thank you very much .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_5180.json b/reccon/query/tr_5180.json new file mode 100644 index 0000000000000000000000000000000000000000..27e40d910b54ce74b1c6290b197600fa1b7f6e79 --- /dev/null +++ b/reccon/query/tr_5180.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "No , it ' s pretty good . Why not give the landlord a call ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "It ' s looks like its in this neighborhood , $ 600 a month" + ], + "type": [ + "inter-personal" + ], + "text": "No , it ' s pretty good . Why not give the landlord a call ?", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_5190.json b/reccon/query/tr_5190.json new file mode 100644 index 0000000000000000000000000000000000000000..5b3178d3c97491f1a8e6fe90bb6fbaa098ce9a20 --- /dev/null +++ b/reccon/query/tr_5190.json @@ -0,0 +1,27 @@ +[ + { + "turn": 18, + "speaker": "B", + "utterance": "That's very unbelievable . Is it fake ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 17, + 18 + ], + "expanded emotion cause span": [ + "It's $ 60 here .", + "That's very unbelievable . Is it fake ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's very unbelievable . Is it fake ?", + "id": 18, + "source_sentences": [ + 16 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_5231.json b/reccon/query/tr_5231.json new file mode 100644 index 0000000000000000000000000000000000000000..834f6e9189f0ebd996fe9f3f94087a551b9156a0 --- /dev/null +++ b/reccon/query/tr_5231.json @@ -0,0 +1,25 @@ +[ + { + "turn": 16, + "speaker": "B", + "utterance": "Of course . I will try to buy some things at the Asian grocery down the block too . Then I can do a little cooking in my apartment .", + "emotion": "happiness", + "explanation": "The speaker is passionate about Chinese food.", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "So when you Chinese think of Chinatown , you mostly think of food ." + ], + "type": [ + "inter-personal" + ], + "text": "Of course . I will try to buy some things at the Asian grocery down the block too . Then I can do a little cooking in my apartment .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_5251.json b/reccon/query/tr_5251.json new file mode 100644 index 0000000000000000000000000000000000000000..f1999f82d76d0969ec7fd8ca0d73e790b0fe8bad --- /dev/null +++ b/reccon/query/tr_5251.json @@ -0,0 +1,25 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Me ! Me !", + "emotion": "excited", + "explanation": "The person is excited to become a volunteer", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I need a volunteer ." + ], + "type": [ + "inter-personal" + ], + "text": "Me ! Me !", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_5276.json b/reccon/query/tr_5276.json new file mode 100644 index 0000000000000000000000000000000000000000..d1990ad1e6794a36e68f16e454ee14606a83934b --- /dev/null +++ b/reccon/query/tr_5276.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "That's great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Just call me if you need anything ." + ], + "type": [ + "inter-personal" + ], + "text": "That's great .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_5278.json b/reccon/query/tr_5278.json new file mode 100644 index 0000000000000000000000000000000000000000..d6db986a553c8953794b56c8fd4144e46c3e2fe0 --- /dev/null +++ b/reccon/query/tr_5278.json @@ -0,0 +1,30 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "Wow , this is great ! I never knew Thai food was so creative and delicious !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9, + 9 + ], + "expanded emotion cause span": [ + "Ok , now for the last and best dish in my opinion . This is called Pad Thai . It's stir-fried noodles with eggs , fish sauce , tamarind juice , red chili pepper plus bean sprouts , shrimp and tofu and garnished with crushed peanuts and coriander . It's practically Thailand's national dish !", + "this is great !", + "Thai food was so creative and delicious !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Wow , this is great ! I never knew Thai food was so creative and delicious !", + "id": 9, + "source_sentences": [ + 7, + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_5293.json b/reccon/query/tr_5293.json new file mode 100644 index 0000000000000000000000000000000000000000..c2aae1fde783de0ff2775ba424022a9a52dc7f27 --- /dev/null +++ b/reccon/query/tr_5293.json @@ -0,0 +1,24 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "Not at all . Bang the door , please .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "Thanks" + ], + "type": [ + "inter-personal" + ], + "text": "Not at all . Bang the door , please .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_5297.json b/reccon/query/tr_5297.json new file mode 100644 index 0000000000000000000000000000000000000000..ece800d983c9bf923e090d68be8d6ff5acd5d49d --- /dev/null +++ b/reccon/query/tr_5297.json @@ -0,0 +1,27 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "I'm sorry . That must have really been a nightmarish day for you and your family .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "He ended up dying in the tower .", + "a nightmarish day for you and your family ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm sorry . That must have really been a nightmarish day for you and your family .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_534.json b/reccon/query/tr_534.json new file mode 100644 index 0000000000000000000000000000000000000000..c2215af505267bb16d05d54911ddbdc8cc14bea0 --- /dev/null +++ b/reccon/query/tr_534.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Really ? Is he married ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I've fallen in love with my boss ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? Is he married ?", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_5376.json b/reccon/query/tr_5376.json new file mode 100644 index 0000000000000000000000000000000000000000..3b43f7985a40298dcebae9a52f588824f2b7fb34 --- /dev/null +++ b/reccon/query/tr_5376.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Get ready for the best meal of your life !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "That sounds great ." + ], + "type": [ + "inter-personal" + ], + "text": "Get ready for the best meal of your life !", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_5414.json b/reccon/query/tr_5414.json new file mode 100644 index 0000000000000000000000000000000000000000..e7fa4dc4c590cf6aeff727a67226379ac4eb4e6d --- /dev/null +++ b/reccon/query/tr_5414.json @@ -0,0 +1,24 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "I don't need your help , jerk .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "That may be , but you're still under arrest . And you'd better stop talking ." + ], + "type": [ + "inter-personal" + ], + "text": "I don't need your help , jerk .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_5431.json b/reccon/query/tr_5431.json new file mode 100644 index 0000000000000000000000000000000000000000..0e1f75fd05e48a06920558fffc23cd3f2b38ba42 --- /dev/null +++ b/reccon/query/tr_5431.json @@ -0,0 +1,27 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "Okay . I'm in . Let's do it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 11 + ], + "expanded emotion cause span": [ + "great idea .", + "Going on a diet with a friend to back you up is a great way to succeed ." + ], + "type": [ + "inter-personal" + ], + "text": "Okay . I'm in . Let's do it .", + "id": 12, + "source_sentences": [ + 10, + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_5481.json b/reccon/query/tr_5481.json new file mode 100644 index 0000000000000000000000000000000000000000..9970b4beec3de326b7357cca6ec4994538fd1475 --- /dev/null +++ b/reccon/query/tr_5481.json @@ -0,0 +1,25 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "I will .", + "emotion": "happiness", + "explanation": "B is happy that A is asking for help", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "keep an eye for me !" + ], + "type": [ + "inter-personal" + ], + "text": "I will .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_554.json b/reccon/query/tr_554.json new file mode 100644 index 0000000000000000000000000000000000000000..a2893ab8f964625719ad99db6af311e2c18d0a11 --- /dev/null +++ b/reccon/query/tr_554.json @@ -0,0 +1,24 @@ +[ + { + "turn": 13, + "speaker": "A", + "utterance": "thanks . We should be ourselves . There are so many fashion victims out there .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "you have good fashion sense" + ], + "type": [ + "inter-personal" + ], + "text": "thanks . We should be ourselves . There are so many fashion victims out there .", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_5629.json b/reccon/query/tr_5629.json new file mode 100644 index 0000000000000000000000000000000000000000..7badcd2a61237404f16e9b28bf9a0d7c95e42fe8 --- /dev/null +++ b/reccon/query/tr_5629.json @@ -0,0 +1,27 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "He certainly looks interested , doesn ' t he ? Shall we invite him over to our table ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "I think he fancies you .", + "He certainly looks interested ," + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "He certainly looks interested , doesn ' t he ? Shall we invite him over to our table ?", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_5685.json b/reccon/query/tr_5685.json new file mode 100644 index 0000000000000000000000000000000000000000..012cff7cc8ba51a65048c8a3ff2f210903174561 --- /dev/null +++ b/reccon/query/tr_5685.json @@ -0,0 +1,27 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "Here's your change . Thank you for shopping with us .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 12 + ], + "expanded emotion cause span": [ + "I'll take it .", + "Thank you for shopping with us ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Here's your change . Thank you for shopping with us .", + "id": 12, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_5723.json b/reccon/query/tr_5723.json new file mode 100644 index 0000000000000000000000000000000000000000..b334bbef67d6d1ec2db9c4fb8fa1e91856073504 --- /dev/null +++ b/reccon/query/tr_5723.json @@ -0,0 +1,27 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "And I've never heard such good sound in a game .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "I've never seen such good graphics .", + "And I've never heard such good sound in a game ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "And I've never heard such good sound in a game .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_5729.json b/reccon/query/tr_5729.json new file mode 100644 index 0000000000000000000000000000000000000000..3c604eec23790feb33cdaa49da6d483edfe39660 --- /dev/null +++ b/reccon/query/tr_5729.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Hey ! The movie hasn't even started and they're almost gone !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Give me another pack ." + ], + "type": [ + "inter-personal" + ], + "text": "Hey ! The movie hasn't even started and they're almost gone !", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_5737.json b/reccon/query/tr_5737.json new file mode 100644 index 0000000000000000000000000000000000000000..02ae2fc8fc21b2ead333491930ccdd1789a3ed99 --- /dev/null +++ b/reccon/query/tr_5737.json @@ -0,0 +1,30 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "I know , I am sorry I ever bought it .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3, + 5, + 6 + ], + "expanded emotion cause span": [ + "I am afraid your diamond bracelet has gone ,", + "they've taken your fur coat too .", + "I am sorry I ever bought it ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I know , I am sorry I ever bought it .", + "id": 6, + "source_sentences": [ + 2, + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_5748.json b/reccon/query/tr_5748.json new file mode 100644 index 0000000000000000000000000000000000000000..c6c3d9df428e8987279a3c8f8c06ebee26bd3905 --- /dev/null +++ b/reccon/query/tr_5748.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Thanks , Mary . You ' re a real pal . I'll call now to set up an interview .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I'll help you type one up ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks , Mary . You ' re a real pal . I'll call now to set up an interview .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_58.json b/reccon/query/tr_58.json new file mode 100644 index 0000000000000000000000000000000000000000..222cc796f97f7edc4b9e2dce0b1949e0b7455d54 --- /dev/null +++ b/reccon/query/tr_58.json @@ -0,0 +1,27 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Of course it does . Everybody has his own hobby .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 7 + ], + "expanded emotion cause span": [ + "That's really interesting .", + "I like collecting matchbox" + ], + "type": [ + "inter-personal" + ], + "text": "Of course it does . Everybody has his own hobby .", + "id": 8, + "source_sentences": [ + 4, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_5802.json b/reccon/query/tr_5802.json new file mode 100644 index 0000000000000000000000000000000000000000..e89b86eaea9be56dd6c4ee60ceeb0cb5e9c92116 --- /dev/null +++ b/reccon/query/tr_5802.json @@ -0,0 +1,27 @@ +[ + { + "turn": 16, + "speaker": "B", + "utterance": "Yes . This has been fun .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15, + 16 + ], + "expanded emotion cause span": [ + "would you like to play again Wednesday ?", + "This has been fun ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes . This has been fun .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_5857.json b/reccon/query/tr_5857.json new file mode 100644 index 0000000000000000000000000000000000000000..f0e6ace6482584582c01ac952305ba2baa33ba5b --- /dev/null +++ b/reccon/query/tr_5857.json @@ -0,0 +1,27 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Here's your receipt . Have a nice day .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "Sure . Here you go .", + "Have a nice day ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Here's your receipt . Have a nice day .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_5869.json b/reccon/query/tr_5869.json new file mode 100644 index 0000000000000000000000000000000000000000..541ca5fe875b6862741486b9579a02b4a9d9d2e7 --- /dev/null +++ b/reccon/query/tr_5869.json @@ -0,0 +1,27 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "yes , I do . Let ' s go . We should be able to find something suitable . We should get him something old ... something historic .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "You know which team he supports", + "yes , I do ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "yes , I do . Let ' s go . We should be able to find something suitable . We should get him something old ... something historic .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_587.json b/reccon/query/tr_587.json new file mode 100644 index 0000000000000000000000000000000000000000..5c9f717942b5ec89a680984f2de3bb05feb26d32 --- /dev/null +++ b/reccon/query/tr_587.json @@ -0,0 +1,25 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "Just find the answer through Internet .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "we have to do something to help the people in the stricken area ." + ], + "type": [ + "inter-personal" + ], + "text": "Just find the answer through Internet .", + "id": 9, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_5961.json b/reccon/query/tr_5961.json new file mode 100644 index 0000000000000000000000000000000000000000..be5f708f21fc88199c2dc90f3b218b52ea7d1a8a --- /dev/null +++ b/reccon/query/tr_5961.json @@ -0,0 +1,24 @@ +[ + { + "turn": 19, + "speaker": "A", + "utterance": "We appreciate your business , Madam .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 18 + ], + "expanded emotion cause span": [ + "Store credit is okay with me . I'm sure I will find something I like . I shop here a lot ." + ], + "type": [ + "inter-personal" + ], + "text": "We appreciate your business , Madam .", + "id": 19, + "source_sentences": [ + 17 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_5981.json b/reccon/query/tr_5981.json new file mode 100644 index 0000000000000000000000000000000000000000..989b86d543b5da65c20e36edb1c55f5f0f54f96b --- /dev/null +++ b/reccon/query/tr_5981.json @@ -0,0 +1,24 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "Thank you !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "That's 20 dollars . Keep the change !" + ], + "type": [ + "inter-personal" + ], + "text": "Thank you !", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_5984.json b/reccon/query/tr_5984.json new file mode 100644 index 0000000000000000000000000000000000000000..ae09c2ee52006f07d8fde9e696a2e06924859684 --- /dev/null +++ b/reccon/query/tr_5984.json @@ -0,0 +1,27 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Let me see . Yes , they are perfectly matched !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 8 + ], + "expanded emotion cause span": [ + "We also have it in grey .", + "they are perfectly matched !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Let me see . Yes , they are perfectly matched !", + "id": 8, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_60.json b/reccon/query/tr_60.json new file mode 100644 index 0000000000000000000000000000000000000000..0be0eba0162024cedfebd264c2e802171c2996b3 --- /dev/null +++ b/reccon/query/tr_60.json @@ -0,0 +1,24 @@ +[ + { + "turn": 15, + "speaker": "A", + "utterance": "Ok . I'll call you Saturday morning .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "I'll give it a try . Give me a call and let's go down together ." + ], + "type": [ + "inter-personal" + ], + "text": "Ok . I'll call you Saturday morning .", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_6005.json b/reccon/query/tr_6005.json new file mode 100644 index 0000000000000000000000000000000000000000..d2286f06c2af21caac4cf9c61732bbb50d95b6e4 --- /dev/null +++ b/reccon/query/tr_6005.json @@ -0,0 +1,24 @@ +[ + { + "turn": 16, + "speaker": "B", + "utterance": "Goodbye . Thanks again .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "Hope to see you again soon . Keep in touch then" + ], + "type": [ + "inter-personal" + ], + "text": "Goodbye . Thanks again .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_6038.json b/reccon/query/tr_6038.json new file mode 100644 index 0000000000000000000000000000000000000000..213a98e5133e7f1c9cbe03d378917fba7222f338 --- /dev/null +++ b/reccon/query/tr_6038.json @@ -0,0 +1,27 @@ +[ + { + "turn": 13, + "speaker": "A", + "utterance": "Science ? What are you talking about ? Forget about your science , OK ? It's a picnic !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 12, + 13 + ], + "expanded emotion cause span": [ + "we can also teach him something about science .", + "What are you talking about ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Science ? What are you talking about ? Forget about your science , OK ? It's a picnic !", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_607.json b/reccon/query/tr_607.json new file mode 100644 index 0000000000000000000000000000000000000000..a6089dfacd5a87f59de0ce61ed06f581af263a49 --- /dev/null +++ b/reccon/query/tr_607.json @@ -0,0 +1,27 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Wow , you are going to be busy this semester ! Okay , here you go . You are registered now . you ' ll have to make your first tuition payment before classes start .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "I need to take fundamental linguistics , consumer psychology and neuroanatomy .", + "you are going to be busy this semester !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Wow , you are going to be busy this semester ! Okay , here you go . You are registered now . you ' ll have to make your first tuition payment before classes start .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_6152.json b/reccon/query/tr_6152.json new file mode 100644 index 0000000000000000000000000000000000000000..0d5df2cb2420258964f156fbed6865542872f15d --- /dev/null +++ b/reccon/query/tr_6152.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Phew ! . . . Wait a minute , CRASH ? ? ! ! Spyware ? Trojans ! What ? where ? when ? !", + "emotion": "fear", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "it has a bad program on it . Maybe that ' s why it crashed . I recommend that you run an antivirus program in order to safely remove any unwanted spyware or Trojans ." + ], + "type": [ + "inter-personal" + ], + "text": "Phew ! . . . Wait a minute , CRASH ? ? ! ! Spyware ? Trojans ! What ? where ? when ? !", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_6198.json b/reccon/query/tr_6198.json new file mode 100644 index 0000000000000000000000000000000000000000..08473576b74483a7379d6712921b0c6e6f36966f --- /dev/null +++ b/reccon/query/tr_6198.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Recliner ? In my beautifully decorated living room ? I don ' t think so !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "can you pick out a nice recliner ?", + "In my beautifully decorated living room ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Recliner ? In my beautifully decorated living room ? I don ' t think so !", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_62.json b/reccon/query/tr_62.json new file mode 100644 index 0000000000000000000000000000000000000000..377bf7f4877df92385c56534969ffa0a58c016f0 --- /dev/null +++ b/reccon/query/tr_62.json @@ -0,0 +1,27 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Wow , that does sound like it's going to be fun .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "This party is going to have a DJ , food , and drinks .", + "that does sound like it's going to be fun ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Wow , that does sound like it's going to be fun .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_6232.json b/reccon/query/tr_6232.json new file mode 100644 index 0000000000000000000000000000000000000000..72699b9d2bcca8b2575fd57ba7e5210e662ffefd --- /dev/null +++ b/reccon/query/tr_6232.json @@ -0,0 +1,24 @@ +[ + { + "turn": 29, + "speaker": "A", + "utterance": "You're very welcome . Here is my card , if you need any help .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 28 + ], + "expanded emotion cause span": [ + "thanks for your advice . I will probably come back later ." + ], + "type": [ + "inter-personal" + ], + "text": "You're very welcome . Here is my card , if you need any help .", + "id": 29, + "source_sentences": [ + 27 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_627.json b/reccon/query/tr_627.json new file mode 100644 index 0000000000000000000000000000000000000000..cd980104be278b890194b32b40dc6a6e7de33d35 --- /dev/null +++ b/reccon/query/tr_627.json @@ -0,0 +1,24 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "You can say that again .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "you're going to have a really nice vacation ." + ], + "type": [ + "inter-personal" + ], + "text": "You can say that again .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_6281.json b/reccon/query/tr_6281.json new file mode 100644 index 0000000000000000000000000000000000000000..5bd517e743264d80b9dac45a63deaf2783cef30f --- /dev/null +++ b/reccon/query/tr_6281.json @@ -0,0 +1,27 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "This isn't like you ... Well , I hope you will have a nice flight and a successful start in business", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13, + 14 + ], + "expanded emotion cause span": [ + "Thank you for being a friend of mine .", + "I hope you will have a nice flight and a successful start in business" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "This isn't like you ... Well , I hope you will have a nice flight and a successful start in business", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_6282.json b/reccon/query/tr_6282.json new file mode 100644 index 0000000000000000000000000000000000000000..2148d3a02def4cc6186eba02bf4c2a488b5ee5c5 --- /dev/null +++ b/reccon/query/tr_6282.json @@ -0,0 +1,24 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "My pleasure .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "Thank you ." + ], + "type": [ + "inter-personal" + ], + "text": "My pleasure .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_6322.json b/reccon/query/tr_6322.json new file mode 100644 index 0000000000000000000000000000000000000000..14234014421e85381db4d8b8ae51f489b9288702 --- /dev/null +++ b/reccon/query/tr_6322.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Did I ? Well , anyway , you will get your raise when the economy starts picking up .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "You said the same thing three months ago ." + ], + "type": [ + "inter-personal" + ], + "text": "Did I ? Well , anyway , you will get your raise when the economy starts picking up .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_6324.json b/reccon/query/tr_6324.json new file mode 100644 index 0000000000000000000000000000000000000000..943fca98fa229a8e73e94c893c3ad4c81c7642eb --- /dev/null +++ b/reccon/query/tr_6324.json @@ -0,0 +1,24 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "Thanks for your help .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "That will be fine ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks for your help .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_6401.json b/reccon/query/tr_6401.json new file mode 100644 index 0000000000000000000000000000000000000000..01a6eedd818d72f7a9b7deb680af8622abe5ece8 --- /dev/null +++ b/reccon/query/tr_6401.json @@ -0,0 +1,24 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "Are you really ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I am really excited for you ." + ], + "type": [ + "inter-personal" + ], + "text": "Are you really ?", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_6465.json b/reccon/query/tr_6465.json new file mode 100644 index 0000000000000000000000000000000000000000..40bf41df58f76fcf545d04fe124563964798a146 --- /dev/null +++ b/reccon/query/tr_6465.json @@ -0,0 +1,27 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Thank you . That's enough .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "Could I serve you anything else ?", + "That's enough ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you . That's enough .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_6491.json b/reccon/query/tr_6491.json new file mode 100644 index 0000000000000000000000000000000000000000..9a36057cf2b33856d0334a5f61ace2eab155b2d9 --- /dev/null +++ b/reccon/query/tr_6491.json @@ -0,0 +1,27 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "Thank you , mom . I love you so much !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "I'm proud of you !", + "I love you" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you , mom . I love you so much !", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_654.json b/reccon/query/tr_654.json new file mode 100644 index 0000000000000000000000000000000000000000..8c98a535d2c551e43ce70fd9c5d8d1e7d2491062 --- /dev/null +++ b/reccon/query/tr_654.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Now we know that they realize the real meaning of Christmas .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "We can pool the money and give it to a family who could really use it !" + ], + "type": [ + "inter-personal" + ], + "text": "Now we know that they realize the real meaning of Christmas .", + "id": 8, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_6556.json b/reccon/query/tr_6556.json new file mode 100644 index 0000000000000000000000000000000000000000..eebb42aac78c21d455772f1ea03d55b89bc51c4f --- /dev/null +++ b/reccon/query/tr_6556.json @@ -0,0 +1,25 @@ +[ + { + "turn": 20, + "speaker": "B", + "utterance": "Bye .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 17 + ], + "expanded emotion cause span": [ + "Come over to my house tonight . Let's get drunk ." + ], + "type": [ + "inter-personal" + ], + "text": "Bye .", + "id": 20, + "source_sentences": [ + 16 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_6618.json b/reccon/query/tr_6618.json new file mode 100644 index 0000000000000000000000000000000000000000..0748dfd172989c1971b5adb4dd4ba9d265929888 --- /dev/null +++ b/reccon/query/tr_6618.json @@ -0,0 +1,27 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "And look what we did to him ! Hey ... he left me his business card .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "he was just a shy guy who had a crush on you !", + "what we did to him !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "And look what we did to him ! Hey ... he left me his business card .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_6664.json b/reccon/query/tr_6664.json new file mode 100644 index 0000000000000000000000000000000000000000..321410f2c76f7a1a65823b09f0adf9c161d1f0a7 --- /dev/null +++ b/reccon/query/tr_6664.json @@ -0,0 +1,27 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "That's a lucky fruit called hong zat ! People say that if you eat them , you will have your first son very soon !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "This little red fruit looks good .", + "That's a lucky fruit" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's a lucky fruit called hong zat ! People say that if you eat them , you will have your first son very soon !", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_6700.json b/reccon/query/tr_6700.json new file mode 100644 index 0000000000000000000000000000000000000000..acba1f4aa53c882be589dfb8bed56863dfe9393f --- /dev/null +++ b/reccon/query/tr_6700.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "That does sound a lot of fun .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Usually it's the older kids going around playing Halloween , like punching the pumpkins left outside people's doors or - - someone's tree ." + ], + "type": [ + "inter-personal" + ], + "text": "That does sound a lot of fun .", + "id": 8, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_6739.json b/reccon/query/tr_6739.json new file mode 100644 index 0000000000000000000000000000000000000000..21414eef4092ec6d87a5a59fc0bb27b9c2dc1ec1 --- /dev/null +++ b/reccon/query/tr_6739.json @@ -0,0 +1,25 @@ +[ + { + "turn": 15, + "speaker": "A", + "utterance": "Goodbye .", + "emotion": "happiness", + "explanation": "F", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "Thanks" + ], + "type": [ + "inter-personal" + ], + "text": "Goodbye .", + "id": 15, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_6757.json b/reccon/query/tr_6757.json new file mode 100644 index 0000000000000000000000000000000000000000..445c467ee1fcd8920566a217994027d32bdacf13 --- /dev/null +++ b/reccon/query/tr_6757.json @@ -0,0 +1,27 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "Wonderful ! I'll start packing our suitcases .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 11 + ], + "expanded emotion cause span": [ + "It will be great .", + "I'll make the arrangements . It will be great ." + ], + "type": [ + "inter-personal" + ], + "text": "Wonderful ! I'll start packing our suitcases .", + "id": 12, + "source_sentences": [ + 10, + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_677.json b/reccon/query/tr_677.json new file mode 100644 index 0000000000000000000000000000000000000000..6310a13196968fba01649523c29ca4bea0ea9392 --- /dev/null +++ b/reccon/query/tr_677.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "Terrific ! B . A . , again and again-B . A .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "B . A . in economics" + ], + "type": [ + "inter-personal" + ], + "text": "Terrific ! B . A . , again and again-B . A .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_6796.json b/reccon/query/tr_6796.json new file mode 100644 index 0000000000000000000000000000000000000000..d1f3e392140ce06d3ae2197dd289af491c7d2f40 --- /dev/null +++ b/reccon/query/tr_6796.json @@ -0,0 +1,24 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "That's a good idea !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Let's kick off our shoes to walk on the green flag stoned roads ." + ], + "type": [ + "inter-personal" + ], + "text": "That's a good idea !", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_6828.json b/reccon/query/tr_6828.json new file mode 100644 index 0000000000000000000000000000000000000000..2dded7860810661e9d530bf2f2e3caa23b63e236 --- /dev/null +++ b/reccon/query/tr_6828.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "I don't care about that , Allen ! What did he steal ? That's the question !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "the robber broke in . Then , when he left , he left through the door . So it wasn't locked ." + ], + "type": [ + "inter-personal" + ], + "text": "I don't care about that , Allen ! What did he steal ? That's the question !", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_6847.json b/reccon/query/tr_6847.json new file mode 100644 index 0000000000000000000000000000000000000000..544947b1f6a98bd64e8e048150426fe0a0f4f99e --- /dev/null +++ b/reccon/query/tr_6847.json @@ -0,0 +1,36 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "I appreciate it very much . You've been doing great . I expect to see you be promoted pretty soon .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 6, + 8, + 8, + 9 + ], + "expanded emotion cause span": [ + "you really did great and outperformed", + "You deserved it !", + "you always have unique ideas", + "you're such a team leader .", + "You've been doing great . I expect to see you be promoted" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I appreciate it very much . You've been doing great . I expect to see you be promoted pretty soon .", + "id": 9, + "source_sentences": [ + 5, + 5, + 7, + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_6867.json b/reccon/query/tr_6867.json new file mode 100644 index 0000000000000000000000000000000000000000..5fb536572fcf46f59132878dbf96d90d78d2b01b --- /dev/null +++ b/reccon/query/tr_6867.json @@ -0,0 +1,24 @@ +[ + { + "turn": 15, + "speaker": "A", + "utterance": "Fabulous ! We should look at engagement rings then ! Now that ' s a whole other section .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "I ' m going to pop the question !" + ], + "type": [ + "inter-personal" + ], + "text": "Fabulous ! We should look at engagement rings then ! Now that ' s a whole other section .", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_6903.json b/reccon/query/tr_6903.json new file mode 100644 index 0000000000000000000000000000000000000000..cdd7fdf8b8d30a0fa627e53b4447ff76361cd43c --- /dev/null +++ b/reccon/query/tr_6903.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "Great ! Let ' s do it !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Very affordable sir . You can take it out of this lot today with 0 % down payment and no interest for the first year ! You can test drive it now and we can sign the papers when we get back ." + ], + "type": [ + "inter-personal" + ], + "text": "Great ! Let ' s do it !", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_692.json b/reccon/query/tr_692.json new file mode 100644 index 0000000000000000000000000000000000000000..c58cb73374032cfb1c640954f0b06875cf2c1bd3 --- /dev/null +++ b/reccon/query/tr_692.json @@ -0,0 +1,28 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Yes . It ' s easy and convenient to use a computer . But it takes a long time to really master it .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1, + 6 + ], + "expanded emotion cause span": [ + "bought a new computer .", + "It ' s easy and convenient to use a computer ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes . It ' s easy and convenient to use a computer . But it takes a long time to really master it .", + "id": 6, + "source_sentences": [ + 0 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_6931.json b/reccon/query/tr_6931.json new file mode 100644 index 0000000000000000000000000000000000000000..2294b42b0a099ec54660939e102a3028b5c813be --- /dev/null +++ b/reccon/query/tr_6931.json @@ -0,0 +1,27 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "I will do my best .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "good for you . I hope you can get what you want from the training .", + "I will do my best ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I will do my best .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_6984.json b/reccon/query/tr_6984.json new file mode 100644 index 0000000000000000000000000000000000000000..2fff05033862f2137e7ca3651bf6d123f69cd41c --- /dev/null +++ b/reccon/query/tr_6984.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Well , they should have called you !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I didn't reconfirm in time and they gave away half of the seats ." + ], + "type": [ + "inter-personal" + ], + "text": "Well , they should have called you !", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_7.json b/reccon/query/tr_7.json new file mode 100644 index 0000000000000000000000000000000000000000..dd0207b642117d53503bcbb687efe56ed2d14acc --- /dev/null +++ b/reccon/query/tr_7.json @@ -0,0 +1,24 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "Right , congratulations .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "my wedding" + ], + "type": [ + "inter-personal" + ], + "text": "Right , congratulations .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_7044.json b/reccon/query/tr_7044.json new file mode 100644 index 0000000000000000000000000000000000000000..a47a5f5011ee3ff62e6a2ee2863bd6794d2b508f --- /dev/null +++ b/reccon/query/tr_7044.json @@ -0,0 +1,30 @@ +[ + { + "turn": 17, + "speaker": "A", + "utterance": "Great . Then call me and let me know if she's free .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 12, + 14 + ], + "expanded emotion cause span": [ + "need a babysitter", + "I know who we can ask . There is a girl I know , Sara Ralston . She is 17 , and she will usually take this kind of job . I know her from my church , and I trust her completely .", + "She is very responsible ." + ], + "type": [ + "inter-personal" + ], + "text": "Great . Then call me and let me know if she's free .", + "id": 17, + "source_sentences": [ + 5, + 11, + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_7050.json b/reccon/query/tr_7050.json new file mode 100644 index 0000000000000000000000000000000000000000..5732f69e1f9452cbf7caaedb2bae2580ff192349 --- /dev/null +++ b/reccon/query/tr_7050.json @@ -0,0 +1,24 @@ +[ + { + "turn": 26, + "speaker": "B", + "utterance": "Don't mention it , Larry . What are friends for anyway ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 25 + ], + "expanded emotion cause span": [ + "I really appreciate your help on this ." + ], + "type": [ + "inter-personal" + ], + "text": "Don't mention it , Larry . What are friends for anyway ?", + "id": 26, + "source_sentences": [ + 24 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_710.json b/reccon/query/tr_710.json new file mode 100644 index 0000000000000000000000000000000000000000..42843b20674271dcff733d21093b3bda342653f8 --- /dev/null +++ b/reccon/query/tr_710.json @@ -0,0 +1,24 @@ +[ + { + "turn": 15, + "speaker": "A", + "utterance": "Ok . See you there in about 30 minutes .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "Let's go to Starbucks" + ], + "type": [ + "inter-personal" + ], + "text": "Ok . See you there in about 30 minutes .", + "id": 15, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_7105.json b/reccon/query/tr_7105.json new file mode 100644 index 0000000000000000000000000000000000000000..646197fbae4c8e43c5b70a1929f0c792e6cdce7f --- /dev/null +++ b/reccon/query/tr_7105.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Wow . You look great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I chose this swimming suit . Do you like it ?", + "You look great ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Wow . You look great .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_7161.json b/reccon/query/tr_7161.json new file mode 100644 index 0000000000000000000000000000000000000000..b550cd6bdb6fd1335827684244d8ed56d5a883f1 --- /dev/null +++ b/reccon/query/tr_7161.json @@ -0,0 +1,27 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "Thank you . Hopefully I won't have to call about him again .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 11 + ], + "expanded emotion cause span": [ + "That won't happen again ,", + "sorry ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . Hopefully I won't have to call about him again .", + "id": 12, + "source_sentences": [ + 10, + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_7171.json b/reccon/query/tr_7171.json new file mode 100644 index 0000000000000000000000000000000000000000..09a01455be9ad9479e3b5b6f3b6679e3a02f8a7d --- /dev/null +++ b/reccon/query/tr_7171.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Whatever . Just turn right here . . . The freeway will be packed at this hour . . . let ' s take a side street . Go on ! Get out of our way ! Move , move !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "Are you nuts ! I ' m not going to run a red light !", + "Get out of our way !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Whatever . Just turn right here . . . The freeway will be packed at this hour . . . let ' s take a side street . Go on ! Get out of our way ! Move , move !", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_7189.json b/reccon/query/tr_7189.json new file mode 100644 index 0000000000000000000000000000000000000000..e4856743a2e052271f776ba96d82fedeaad3161d --- /dev/null +++ b/reccon/query/tr_7189.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Thank you . I just got these shoes today .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "You look nice today , too .", + "I just got these shoes today ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you . I just got these shoes today .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_7197.json b/reccon/query/tr_7197.json new file mode 100644 index 0000000000000000000000000000000000000000..f57e032924252556016815914cb4f3a689cb4e1f --- /dev/null +++ b/reccon/query/tr_7197.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "I really don't think it's any of your business .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "you're trying to get off the phone so fast" + ], + "type": [ + "inter-personal" + ], + "text": "I really don't think it's any of your business .", + "id": 7, + "source_sentences": [ + 1 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_72.json b/reccon/query/tr_72.json new file mode 100644 index 0000000000000000000000000000000000000000..3e91aa0126680eee100007f1753813cbb017e572 --- /dev/null +++ b/reccon/query/tr_72.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Fine ! I want a divorce !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I am trying but , I don ' t have the willpower to just quit ." + ], + "type": [ + "inter-personal" + ], + "text": "Fine ! I want a divorce !", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_7248.json b/reccon/query/tr_7248.json new file mode 100644 index 0000000000000000000000000000000000000000..da411db30f846f25da99f6ffeb86d14b6b2dc134 --- /dev/null +++ b/reccon/query/tr_7248.json @@ -0,0 +1,27 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "But I think Eddy is going too far !", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 6, + 9 + ], + "expanded emotion cause span": [ + "He's dancing with Jack !", + "Eddy is going too far !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "But I think Eddy is going too far !", + "id": 9, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_7257.json b/reccon/query/tr_7257.json new file mode 100644 index 0000000000000000000000000000000000000000..fa67e8db444b3ba98d43491b8846229faf28d003 --- /dev/null +++ b/reccon/query/tr_7257.json @@ -0,0 +1,24 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "OK . I'll take it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "You look really beautiful in it ." + ], + "type": [ + "inter-personal" + ], + "text": "OK . I'll take it .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_7269.json b/reccon/query/tr_7269.json new file mode 100644 index 0000000000000000000000000000000000000000..65268ee22a09c5d1b24ba2e6871f489b8d9c4563 --- /dev/null +++ b/reccon/query/tr_7269.json @@ -0,0 +1,24 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "Good for you . No problem , I'll listen to the car radio", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "I finally have an inspiration ." + ], + "type": [ + "inter-personal" + ], + "text": "Good for you . No problem , I'll listen to the car radio", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_7274.json b/reccon/query/tr_7274.json new file mode 100644 index 0000000000000000000000000000000000000000..04a4ad4456e30ef07e7ecfe2da4beab1c1945956 --- /dev/null +++ b/reccon/query/tr_7274.json @@ -0,0 +1,27 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "I thought you had an unlimited SMS plan ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "I didn't have any credit on my phone .", + "I thought you had an unlimited SMS plan ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I thought you had an unlimited SMS plan ?", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_738.json b/reccon/query/tr_738.json new file mode 100644 index 0000000000000000000000000000000000000000..566cf4e8a26a78d0c52c0f1a359873a05ca48a03 --- /dev/null +++ b/reccon/query/tr_738.json @@ -0,0 +1,27 @@ +[ + { + "turn": 18, + "speaker": "B", + "utterance": "Perfect . I'll see you in front of the apartment at eleven thirty .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13, + 17 + ], + "expanded emotion cause span": [ + "there's a live outdoor concert", + "Let's meet for lunch" + ], + "type": [ + "inter-personal" + ], + "text": "Perfect . I'll see you in front of the apartment at eleven thirty .", + "id": 18, + "source_sentences": [ + 12, + 16 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_7397.json b/reccon/query/tr_7397.json new file mode 100644 index 0000000000000000000000000000000000000000..d3fe7f244ba03db7efcb561a92465dbfc5a30eec --- /dev/null +++ b/reccon/query/tr_7397.json @@ -0,0 +1,27 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "That ' s amazing . The rent is very cheap .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "It ' s only $ 725 a month .", + "The rent is very cheap ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That ' s amazing . The rent is very cheap .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_74.json b/reccon/query/tr_74.json new file mode 100644 index 0000000000000000000000000000000000000000..170c8d6f4fa383342cf02ce2e7e143295a156e1c --- /dev/null +++ b/reccon/query/tr_74.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "All-right guy ? All right . Let's talk about something else instead .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I told you that he's an all-right guy ." + ], + "type": [ + "inter-personal" + ], + "text": "All-right guy ? All right . Let's talk about something else instead .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_740.json b/reccon/query/tr_740.json new file mode 100644 index 0000000000000000000000000000000000000000..5d8fdaf91e704715ba52d2c45fe338c668ba73ad --- /dev/null +++ b/reccon/query/tr_740.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "That'll be for you to decide . I've got a new dish that I want to try out on you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I'll be there . You're still a fabulous cook", + "I've got a new dish that I want to try out on you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That'll be for you to decide . I've got a new dish that I want to try out on you .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_7481.json b/reccon/query/tr_7481.json new file mode 100644 index 0000000000000000000000000000000000000000..34abf83ed4b82f90e4af19d0f9cdd6e00d977809 --- /dev/null +++ b/reccon/query/tr_7481.json @@ -0,0 +1,27 @@ +[ + { + "turn": 22, + "speaker": "B", + "utterance": "You have made a good choice , sir . I drive an Accord myself . They are very solidly built machines , very reliable .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 21, + 22 + ], + "expanded emotion cause span": [ + "I think I want to order the new Accord then . It looks like an excellent car .", + "You have made a good choice , sir . I drive an Accord myself . They are very solidly built machines , very reliable ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You have made a good choice , sir . I drive an Accord myself . They are very solidly built machines , very reliable .", + "id": 22, + "source_sentences": [ + 20 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_7536.json b/reccon/query/tr_7536.json new file mode 100644 index 0000000000000000000000000000000000000000..446384bc70d6185e1c0f7e5a88404100a028bf39 --- /dev/null +++ b/reccon/query/tr_7536.json @@ -0,0 +1,24 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "I wasn't aware of that !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Sleeping after 12 is hurtful to our body , and I think this is your problem ." + ], + "type": [ + "inter-personal" + ], + "text": "I wasn't aware of that !", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_754.json b/reccon/query/tr_754.json new file mode 100644 index 0000000000000000000000000000000000000000..aed3bf8ceab885c20b24e0ae2cf18acfb048a5e4 --- /dev/null +++ b/reccon/query/tr_754.json @@ -0,0 +1,27 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "That's exactly the way I feel .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "What a great weekend that was !", + "I really enjoy the beach in the summer ." + ], + "type": [ + "inter-personal" + ], + "text": "That's exactly the way I feel .", + "id": 8, + "source_sentences": [ + 0, + 2 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_7551.json b/reccon/query/tr_7551.json new file mode 100644 index 0000000000000000000000000000000000000000..6f6d0a9b5e023128593c1d5088319febe1ef25da --- /dev/null +++ b/reccon/query/tr_7551.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Congratulations ! You do have the right attitude .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "my application was accepted ." + ], + "type": [ + "inter-personal" + ], + "text": "Congratulations ! You do have the right attitude .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_771.json b/reccon/query/tr_771.json new file mode 100644 index 0000000000000000000000000000000000000000..6ba42e65c5455882e4fa8e32be7189e9cc160681 --- /dev/null +++ b/reccon/query/tr_771.json @@ -0,0 +1,27 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "500 feet ! I would never be able to do that .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "We jumped off a bridge and fell 500 feet before the bungee cord caught us .", + "500 feet !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "500 feet ! I would never be able to do that .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_7727.json b/reccon/query/tr_7727.json new file mode 100644 index 0000000000000000000000000000000000000000..96565a36fbc57d3489d94efda834e6703ab8a328 --- /dev/null +++ b/reccon/query/tr_7727.json @@ -0,0 +1,24 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "My pleasure , and have a good time !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "Thank you !" + ], + "type": [ + "inter-personal" + ], + "text": "My pleasure , and have a good time !", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_7729.json b/reccon/query/tr_7729.json new file mode 100644 index 0000000000000000000000000000000000000000..870b29d04a8bbe9f7974384e6c8a9298aab47402 --- /dev/null +++ b/reccon/query/tr_7729.json @@ -0,0 +1,24 @@ +[ + { + "turn": 13, + "speaker": "A", + "utterance": "Thank you . I'm through with one steamed bread and I'd like a second helping .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "Try some beef , please ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . I'm through with one steamed bread and I'd like a second helping .", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_774.json b/reccon/query/tr_774.json new file mode 100644 index 0000000000000000000000000000000000000000..d337f9e2ea94506ba60cf3cc2d5b34e65522bd00 --- /dev/null +++ b/reccon/query/tr_774.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Let ' s just hope my teacher agrees .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "it was definitely worth all the time ." + ], + "type": [ + "inter-personal" + ], + "text": "Let ' s just hope my teacher agrees .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_778.json b/reccon/query/tr_778.json new file mode 100644 index 0000000000000000000000000000000000000000..55a43ce5e0056cf545aa423949e4de5032d62a19 --- /dev/null +++ b/reccon/query/tr_778.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Haha . Wish you good luck .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I will bite many beautiful girls on the neck tonight . Maybe I will suck their blood ." + ], + "type": [ + "inter-personal" + ], + "text": "Haha . Wish you good luck .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_784.json b/reccon/query/tr_784.json new file mode 100644 index 0000000000000000000000000000000000000000..d9a7d8419a86c6913189d0bbe1d9d5abf016f5c9 --- /dev/null +++ b/reccon/query/tr_784.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "I knew some day I would be able to profit from your love of fun !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I'm a professional party planner here in the city . I do catering and all that .", + "I would be able to profit from your love of fun !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I knew some day I would be able to profit from your love of fun !", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_7847.json b/reccon/query/tr_7847.json new file mode 100644 index 0000000000000000000000000000000000000000..3d382ea868a3dca5540344d110eb0b63a4e3bdd1 --- /dev/null +++ b/reccon/query/tr_7847.json @@ -0,0 +1,27 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Mmmm , sounds like risky business . Good luck .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 7 + ], + "expanded emotion cause span": [ + "I'm bidding on a digital video camera .", + "Thirty U . S . dollars ... and it's only been used for six months ." + ], + "type": [ + "inter-personal" + ], + "text": "Mmmm , sounds like risky business . Good luck .", + "id": 8, + "source_sentences": [ + 4, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_786.json b/reccon/query/tr_786.json new file mode 100644 index 0000000000000000000000000000000000000000..5dc19dd8c877a286ddec5038cbabdcf49814ab27 --- /dev/null +++ b/reccon/query/tr_786.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "That sounds great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Sometimes I even ski at night ." + ], + "type": [ + "inter-personal" + ], + "text": "That sounds great .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_7889.json b/reccon/query/tr_7889.json new file mode 100644 index 0000000000000000000000000000000000000000..0727cf46bc3fbde39fdbdd9da20b175aefc3e481 --- /dev/null +++ b/reccon/query/tr_7889.json @@ -0,0 +1,27 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "I think that's what I want . How much is it ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "a heavy wool scarves .", + "that's what I want ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I think that's what I want . How much is it ?", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_793.json b/reccon/query/tr_793.json new file mode 100644 index 0000000000000000000000000000000000000000..523e72dda893dafb5cf90d416f2346b3a7a01ad4 --- /dev/null +++ b/reccon/query/tr_793.json @@ -0,0 +1,24 @@ +[ + { + "turn": 15, + "speaker": "A", + "utterance": "Sounds perfect . I can't wait !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "It was hot and sunny , but there was no humidity ." + ], + "type": [ + "inter-personal" + ], + "text": "Sounds perfect . I can't wait !", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_7961.json b/reccon/query/tr_7961.json new file mode 100644 index 0000000000000000000000000000000000000000..c17d5082804598bc2d8bd938f4e4a9c7eefe7daf --- /dev/null +++ b/reccon/query/tr_7961.json @@ -0,0 +1,24 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "Great ! Can you set the table ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "the house looks really good !" + ], + "type": [ + "inter-personal" + ], + "text": "Great ! Can you set the table ?", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_797.json b/reccon/query/tr_797.json new file mode 100644 index 0000000000000000000000000000000000000000..6779f99e06f4b80ab8e0c10d2b298124fefea691 --- /dev/null +++ b/reccon/query/tr_797.json @@ -0,0 +1,27 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Oh yes , I know which one you mean . I have never been there , but I looked at their menu once and it did look good .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 8 + ], + "expanded emotion cause span": [ + "She says it is very good .", + "I looked at their menu once and it did look good ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh yes , I know which one you mean . I have never been there , but I looked at their menu once and it did look good .", + "id": 8, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_7991.json b/reccon/query/tr_7991.json new file mode 100644 index 0000000000000000000000000000000000000000..4b1e4cb4de6accfecdc8862bbf9d0ad8f366334b --- /dev/null +++ b/reccon/query/tr_7991.json @@ -0,0 +1,24 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "Absolutely unbelievable ! You people should be ashamed of yourselves .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I need to charge you $ 2 to remove this error from your file ." + ], + "type": [ + "inter-personal" + ], + "text": "Absolutely unbelievable ! You people should be ashamed of yourselves .", + "id": 9, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_7995.json b/reccon/query/tr_7995.json new file mode 100644 index 0000000000000000000000000000000000000000..73ec3904192aa09e1bc225a9bc16378b9b6e0243 --- /dev/null +++ b/reccon/query/tr_7995.json @@ -0,0 +1,27 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "Good idea . I will think it over .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13, + 14 + ], + "expanded emotion cause span": [ + "You can also seek job information on the Internet .", + "Good idea ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Good idea . I will think it over .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_7996.json b/reccon/query/tr_7996.json new file mode 100644 index 0000000000000000000000000000000000000000..32103748bfd8b2a7fd452e97f9acf6c136902d43 --- /dev/null +++ b/reccon/query/tr_7996.json @@ -0,0 +1,24 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "That's fine , because if I leave , then your rules won't matter .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "That's right , maybe then you'll respect my rules ." + ], + "type": [ + "inter-personal" + ], + "text": "That's fine , because if I leave , then your rules won't matter .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8.json b/reccon/query/tr_8.json new file mode 100644 index 0000000000000000000000000000000000000000..3f7028b2cc69ce314bf80d25c955d510d029d12b --- /dev/null +++ b/reccon/query/tr_8.json @@ -0,0 +1,24 @@ +[ + { + "turn": 12, + "speaker": "A", + "utterance": "That sounds like a good idea . I'll have to try that .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "We basically sat her down and told her how we felt about her constant criticizing , and how we welcomed her advice but hoped she'd let us do our things . She understood , and now everything is a lot more peaceful ." + ], + "type": [ + "inter-personal" + ], + "text": "That sounds like a good idea . I'll have to try that .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8014.json b/reccon/query/tr_8014.json new file mode 100644 index 0000000000000000000000000000000000000000..bd202f7ca9fa654db44e8ad2c2b2755fb48c3abd --- /dev/null +++ b/reccon/query/tr_8014.json @@ -0,0 +1,24 @@ +[ + { + "turn": 23, + "speaker": "A", + "utterance": "Damn !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 22 + ], + "expanded emotion cause span": [ + "it won't work , old buddy . They'll see that I'm not you ." + ], + "type": [ + "inter-personal" + ], + "text": "Damn !", + "id": 23, + "source_sentences": [ + 21 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_802.json b/reccon/query/tr_802.json new file mode 100644 index 0000000000000000000000000000000000000000..1518649bd8436a4ad24366193276d1fa828ece41 --- /dev/null +++ b/reccon/query/tr_802.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "Now you're talking .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "cold bottle of beer ." + ], + "type": [ + "inter-personal" + ], + "text": "Now you're talking .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8028.json b/reccon/query/tr_8028.json new file mode 100644 index 0000000000000000000000000000000000000000..04d2562a8a8b44e056941e25a61f4e9338a8a8e3 --- /dev/null +++ b/reccon/query/tr_8028.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "This PC is top of the line and I guarantee it will never freeze ! If it does , we ' ll give you your money back !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I just want to know if it ' s good and if I will be able to play solitaire without the computer crashing or freezing all the time !" + ], + "type": [ + "inter-personal" + ], + "text": "This PC is top of the line and I guarantee it will never freeze ! If it does , we ' ll give you your money back !", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8068.json b/reccon/query/tr_8068.json new file mode 100644 index 0000000000000000000000000000000000000000..6010f5ac08d8f3df5384b25b5afdce7378325b27 --- /dev/null +++ b/reccon/query/tr_8068.json @@ -0,0 +1,24 @@ +[ + { + "turn": 13, + "speaker": "A", + "utterance": "Sorry I couldn't help you .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "I am afraid I am not interested" + ], + "type": [ + "inter-personal" + ], + "text": "Sorry I couldn't help you .", + "id": 13, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8162.json b/reccon/query/tr_8162.json new file mode 100644 index 0000000000000000000000000000000000000000..b9b91319e2d5b223806a776e591a81764ab05dde --- /dev/null +++ b/reccon/query/tr_8162.json @@ -0,0 +1,27 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Dammit ! I asked for sunny side up ! How many times do I have to tell you .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "Here you go , honey , fried eggs .", + "I asked for sunny side up ! How many times do I have to tell you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Dammit ! I asked for sunny side up ! How many times do I have to tell you .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8182.json b/reccon/query/tr_8182.json new file mode 100644 index 0000000000000000000000000000000000000000..0640b4683bd53365097ea2e5de38e5ffe0f033b4 --- /dev/null +++ b/reccon/query/tr_8182.json @@ -0,0 +1,27 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Thank you . He ' s very lucky indeed .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "send him my congratulations .", + "He ' s very lucky" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you . He ' s very lucky indeed .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8184.json b/reccon/query/tr_8184.json new file mode 100644 index 0000000000000000000000000000000000000000..f9db35fbe9b7febb10a4bbec9dcb89abfb684afd --- /dev/null +++ b/reccon/query/tr_8184.json @@ -0,0 +1,24 @@ +[ + { + "turn": 20, + "speaker": "B", + "utterance": "I'm sorry , sir .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 19 + ], + "expanded emotion cause span": [ + "So we can't even assess the damages . How can we do business in this country ? Either we're buried under mud , or we're in danger of getting kidnapped ." + ], + "type": [ + "inter-personal" + ], + "text": "I'm sorry , sir .", + "id": 20, + "source_sentences": [ + 18 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8243.json b/reccon/query/tr_8243.json new file mode 100644 index 0000000000000000000000000000000000000000..3a2dc98a9205074eb2c884c0ba7bc3efaa1fefc4 --- /dev/null +++ b/reccon/query/tr_8243.json @@ -0,0 +1,30 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "I'm glad you enjoyed it . It's had long run , but the house has always been full .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6, + 6 + ], + "expanded emotion cause span": [ + "It's an excellent musical . The acting was very expressive and the songs and dancing were superb .", + "you enjoyed it", + "house has always been full ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm glad you enjoyed it . It's had long run , but the house has always been full .", + "id": 6, + "source_sentences": [ + 4, + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8244.json b/reccon/query/tr_8244.json new file mode 100644 index 0000000000000000000000000000000000000000..817fbde67768df033b69eee950e25677d6c332ca --- /dev/null +++ b/reccon/query/tr_8244.json @@ -0,0 +1,27 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "Me , too . There was always a good round of applause every time she sings .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "the leading actress who has an amazing voice .", + "There was always a good round of applause every time she sings ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Me , too . There was always a good round of applause every time she sings .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8265.json b/reccon/query/tr_8265.json new file mode 100644 index 0000000000000000000000000000000000000000..184283a712a371629fe275a86ac122511579239c --- /dev/null +++ b/reccon/query/tr_8265.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "You are welcome .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "It seems that is a better way . Thank you ." + ], + "type": [ + "inter-personal" + ], + "text": "You are welcome .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8270.json b/reccon/query/tr_8270.json new file mode 100644 index 0000000000000000000000000000000000000000..9cc2b50c2128c87b6ac901b5cd28e3e13f23df9f --- /dev/null +++ b/reccon/query/tr_8270.json @@ -0,0 +1,27 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "You certainly made a good impression on me , as well .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "I really enjoyed meeting with you .", + "You certainly made a good impression on me , as well ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You certainly made a good impression on me , as well .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8322.json b/reccon/query/tr_8322.json new file mode 100644 index 0000000000000000000000000000000000000000..0f1ef31b76989d311d46a8397daa6b05db181458 --- /dev/null +++ b/reccon/query/tr_8322.json @@ -0,0 +1,24 @@ +[ + { + "turn": 16, + "speaker": "B", + "utterance": "Thanks for saying that .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "you're very eloquent ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks for saying that .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8342.json b/reccon/query/tr_8342.json new file mode 100644 index 0000000000000000000000000000000000000000..e3896bd5389f7d6dd6816d12832ee91b026b2cb6 --- /dev/null +++ b/reccon/query/tr_8342.json @@ -0,0 +1,27 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "Well , I'm so glad to hear that she's doing well .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "Your daughter is smart and very well behaved .", + "she's doing well ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Well , I'm so glad to hear that she's doing well .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_839.json b/reccon/query/tr_839.json new file mode 100644 index 0000000000000000000000000000000000000000..393d6fa58c399a196510a1b143929b9cd8798ab3 --- /dev/null +++ b/reccon/query/tr_839.json @@ -0,0 +1,27 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Why not ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 7 + ], + "expanded emotion cause span": [ + "The lyrics of the new song are beautiful ,", + "Let's go buy their new album ." + ], + "type": [ + "inter-personal" + ], + "text": "Why not ?", + "id": 8, + "source_sentences": [ + 4, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8392.json b/reccon/query/tr_8392.json new file mode 100644 index 0000000000000000000000000000000000000000..a19813c2d10969077516be4b740d976cdf8964ce --- /dev/null +++ b/reccon/query/tr_8392.json @@ -0,0 +1,24 @@ +[ + { + "turn": 13, + "speaker": "A", + "utterance": "That ' s so unfair !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "No way !" + ], + "type": [ + "inter-personal" + ], + "text": "That ' s so unfair !", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8398.json b/reccon/query/tr_8398.json new file mode 100644 index 0000000000000000000000000000000000000000..6a3a576080d07c7025903bf5ff352da5a7c48239 --- /dev/null +++ b/reccon/query/tr_8398.json @@ -0,0 +1,27 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "Thank you ! We have really enjoyed our meal here .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "I will be right back with your desserts and drinks .", + "We have really enjoyed our meal here ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you ! We have really enjoyed our meal here .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8414.json b/reccon/query/tr_8414.json new file mode 100644 index 0000000000000000000000000000000000000000..2396122e402504da17f4c0c984d4fb87c877d0aa --- /dev/null +++ b/reccon/query/tr_8414.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Don't mention it . Just a little thing I did .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "It's very kind of you . I really don't know how I can thank you enough ." + ], + "type": [ + "inter-personal" + ], + "text": "Don't mention it . Just a little thing I did .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8433.json b/reccon/query/tr_8433.json new file mode 100644 index 0000000000000000000000000000000000000000..21b57ecdd16f7df5ae71f12b76fec1f2a0f81432 --- /dev/null +++ b/reccon/query/tr_8433.json @@ -0,0 +1,29 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "I'll take care of the lunch then , and you can take care of the other plans . What time would you like to pick me up ?", + "emotion": "happiness", + "explanation": "speaker is happy about the trip", + "flag": "F", + "expanded emotion cause evidence": [ + 5, + 7 + ], + "expanded emotion cause span": [ + "a hike to the waterfalls on Saturday .", + "that would be a perfect addition ." + ], + "type": [ + "inter-personal" + ], + "text": "I'll take care of the lunch then , and you can take care of the other plans . What time would you like to pick me up ?", + "id": 8, + "source_sentences": [ + 4, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_847.json b/reccon/query/tr_847.json new file mode 100644 index 0000000000000000000000000000000000000000..8aac4d55fa4b1468d096dc1606675ba6498946d8 --- /dev/null +++ b/reccon/query/tr_847.json @@ -0,0 +1,27 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Ok . I like fishing very much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 6 + ], + "expanded emotion cause span": [ + "We plan to go to a forest in the suburb . There is a beautiful river there . We can do some fishing .", + "I like fishing very much ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Ok . I like fishing very much .", + "id": 6, + "source_sentences": [ + 2 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8470.json b/reccon/query/tr_8470.json new file mode 100644 index 0000000000000000000000000000000000000000..182590c66f2f3b907c71511289b8d221bc218b30 --- /dev/null +++ b/reccon/query/tr_8470.json @@ -0,0 +1,27 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "That ' s great !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 8 + ], + "expanded emotion cause span": [ + "My candidate is probably the most intelligent .", + "I also agree with all his policies ." + ], + "type": [ + "inter-personal" + ], + "text": "That ' s great !", + "id": 9, + "source_sentences": [ + 5, + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8499.json b/reccon/query/tr_8499.json new file mode 100644 index 0000000000000000000000000000000000000000..b930c6efc42939fcf1fbc495935e86bdb7680e11 --- /dev/null +++ b/reccon/query/tr_8499.json @@ -0,0 +1,24 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "No problem .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "Thanks" + ], + "type": [ + "inter-personal" + ], + "text": "No problem .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_85.json b/reccon/query/tr_85.json new file mode 100644 index 0000000000000000000000000000000000000000..b219e21cb175d6335894d0dd72f6b870af422777 --- /dev/null +++ b/reccon/query/tr_85.json @@ -0,0 +1,24 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "Yeah , it sure would .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "wouldn't it be great if we could go to Thailand together sometime" + ], + "type": [ + "inter-personal" + ], + "text": "Yeah , it sure would .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8520.json b/reccon/query/tr_8520.json new file mode 100644 index 0000000000000000000000000000000000000000..63825c9c600c40ada8c2f63832f5355461a79431 --- /dev/null +++ b/reccon/query/tr_8520.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "But my sister bought this pair last month .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "We don't haven any .", + "But my sister bought this pair last month ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "But my sister bought this pair last month .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8560.json b/reccon/query/tr_8560.json new file mode 100644 index 0000000000000000000000000000000000000000..a16c8497d62750ebcf27570586226f1b9fe4babe --- /dev/null +++ b/reccon/query/tr_8560.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Good !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "let's see some pictures and know more about kung fu ." + ], + "type": [ + "inter-personal" + ], + "text": "Good !", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8576.json b/reccon/query/tr_8576.json new file mode 100644 index 0000000000000000000000000000000000000000..121dae192441cb6a2095390e2da71ba45967d0b3 --- /dev/null +++ b/reccon/query/tr_8576.json @@ -0,0 +1,24 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "The hot drinks first would be great . Thanks !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I will prepare your desserts and have someone bring you your drinks right away ." + ], + "type": [ + "inter-personal" + ], + "text": "The hot drinks first would be great . Thanks !", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8608.json b/reccon/query/tr_8608.json new file mode 100644 index 0000000000000000000000000000000000000000..291aa9cf4c122149a21db0d1b7037c2cf97114e6 --- /dev/null +++ b/reccon/query/tr_8608.json @@ -0,0 +1,27 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "It's just you !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "Bingo !", + "It's just you !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It's just you !", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8613.json b/reccon/query/tr_8613.json new file mode 100644 index 0000000000000000000000000000000000000000..5fb536572fcf46f59132878dbf96d90d78d2b01b --- /dev/null +++ b/reccon/query/tr_8613.json @@ -0,0 +1,24 @@ +[ + { + "turn": 15, + "speaker": "A", + "utterance": "Fabulous ! We should look at engagement rings then ! Now that ' s a whole other section .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "I ' m going to pop the question !" + ], + "type": [ + "inter-personal" + ], + "text": "Fabulous ! We should look at engagement rings then ! Now that ' s a whole other section .", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_864.json b/reccon/query/tr_864.json new file mode 100644 index 0000000000000000000000000000000000000000..e96d85bc4c7dc32630ce161ad556f5f17210123b --- /dev/null +++ b/reccon/query/tr_864.json @@ -0,0 +1,24 @@ +[ + { + "turn": 16, + "speaker": "B", + "utterance": "Wow , that would be something to look forward to .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "You should get your invitation today or tomorrow ." + ], + "type": [ + "inter-personal" + ], + "text": "Wow , that would be something to look forward to .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8640.json b/reccon/query/tr_8640.json new file mode 100644 index 0000000000000000000000000000000000000000..0ecee0df5a4213b4a66d98f8203cda0e77419f24 --- /dev/null +++ b/reccon/query/tr_8640.json @@ -0,0 +1,24 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "Oh , really , that's really something new . I'm afraid not everyone can accept it .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "It's the new fashion for men to wear perfumes , which is called cologne ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , really , that's really something new . I'm afraid not everyone can accept it .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8728.json b/reccon/query/tr_8728.json new file mode 100644 index 0000000000000000000000000000000000000000..c3539b0e62ea7af5c06652175ae2b2f7adfab9cc --- /dev/null +++ b/reccon/query/tr_8728.json @@ -0,0 +1,24 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "that ' s very nice of you to offer . Here ' s your tea . Be careful , it ' s still quite hot .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "I can help with the chores while I ' m here ." + ], + "type": [ + "inter-personal" + ], + "text": "that ' s very nice of you to offer . Here ' s your tea . Be careful , it ' s still quite hot .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8747.json b/reccon/query/tr_8747.json new file mode 100644 index 0000000000000000000000000000000000000000..f2e3c64f6800516527c09b5fe83af2045b59f0f2 --- /dev/null +++ b/reccon/query/tr_8747.json @@ -0,0 +1,33 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "That's not fair . We had fun . Give me a second chance . Can we meet tomorrow night for drinks at the pub ?", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3, + 3, + 5, + 6 + ], + "expanded emotion cause span": [ + "I didn't have good time ,", + "I don't really want to see you again .", + "it was you doing all the laughing at your own jokes .", + "That's not fair ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's not fair . We had fun . Give me a second chance . Can we meet tomorrow night for drinks at the pub ?", + "id": 6, + "source_sentences": [ + 2, + 2, + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8768.json b/reccon/query/tr_8768.json new file mode 100644 index 0000000000000000000000000000000000000000..5a921acd83aa9b5cee6937aad923b6b9be30a812 --- /dev/null +++ b/reccon/query/tr_8768.json @@ -0,0 +1,24 @@ +[ + { + "turn": 16, + "speaker": "B", + "utterance": "No problem .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "Thanks" + ], + "type": [ + "inter-personal" + ], + "text": "No problem .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8790.json b/reccon/query/tr_8790.json new file mode 100644 index 0000000000000000000000000000000000000000..f01b79869ca83c7bfa6c886b28617f835a55b638 --- /dev/null +++ b/reccon/query/tr_8790.json @@ -0,0 +1,27 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "No kidding ! We have only 5 bottles of beer .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "500 US dollars .", + "We have only 5 bottles of beer ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "No kidding ! We have only 5 bottles of beer .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8798.json b/reccon/query/tr_8798.json new file mode 100644 index 0000000000000000000000000000000000000000..d0c548aec0db58a1445e7ebf16d5c7f7b6430d2a --- /dev/null +++ b/reccon/query/tr_8798.json @@ -0,0 +1,24 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "Me , either ! Who decides how much money we get ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "we get our year-end bonus !" + ], + "type": [ + "inter-personal" + ], + "text": "Me , either ! Who decides how much money we get ?", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8803.json b/reccon/query/tr_8803.json new file mode 100644 index 0000000000000000000000000000000000000000..f815799d53ae269aa2515ecfbd1d3b140c44c90d --- /dev/null +++ b/reccon/query/tr_8803.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "I was never told to go to court .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "You apparently missed a court appearance .", + "I was never told to go to court ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I was never told to go to court .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8804.json b/reccon/query/tr_8804.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f696d3d900539e8db07a0894577dc5c126de7e --- /dev/null +++ b/reccon/query/tr_8804.json @@ -0,0 +1,27 @@ +[ + { + "turn": 12, + "speaker": "B", + "utterance": "That looks great . Just one more thing-you need some high heels with those jeans . Do you want a pair with a plain pattern or ones with a leopard print on them ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 12 + ], + "expanded emotion cause span": [ + "good idea . You have a lot of good fashion sense .", + "looks great ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That looks great . Just one more thing-you need some high heels with those jeans . Do you want a pair with a plain pattern or ones with a leopard print on them ?", + "id": 12, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8864.json b/reccon/query/tr_8864.json new file mode 100644 index 0000000000000000000000000000000000000000..5e95901203bce70be201e20ad7079f5f17f0ced1 --- /dev/null +++ b/reccon/query/tr_8864.json @@ -0,0 +1,33 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "I am so happy that she's doing okay .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 8, + 10, + 11 + ], + "expanded emotion cause span": [ + "enjoy having your daughter in my class .", + "She is a great addition to my class .", + "She is always behaving herself , and she's so smart .", + "she's doing okay ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I am so happy that she's doing okay .", + "id": 11, + "source_sentences": [ + 5, + 7, + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8904.json b/reccon/query/tr_8904.json new file mode 100644 index 0000000000000000000000000000000000000000..5a9fa57100a268b8fa064a643429cbd637251855 --- /dev/null +++ b/reccon/query/tr_8904.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "What ? Then what did you do ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I pay no attention to the etiquette you ' Ve told me ." + ], + "type": [ + "inter-personal" + ], + "text": "What ? Then what did you do ?", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8921.json b/reccon/query/tr_8921.json new file mode 100644 index 0000000000000000000000000000000000000000..a68e57f8fa33267427fb30f38b30e15495487b87 --- /dev/null +++ b/reccon/query/tr_8921.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "So you don't think you are fat and need to lose weight ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "it's good for her but not for me ." + ], + "type": [ + "inter-personal" + ], + "text": "So you don't think you are fat and need to lose weight ?", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8930.json b/reccon/query/tr_8930.json new file mode 100644 index 0000000000000000000000000000000000000000..d3212f33993b8189e46762dda674c2192494a4c8 --- /dev/null +++ b/reccon/query/tr_8930.json @@ -0,0 +1,27 @@ +[ + { + "turn": 16, + "speaker": "B", + "utterance": "Hope to see you again . We will provide the best service .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15, + 16 + ], + "expanded emotion cause span": [ + "Thanks a lot .", + "Hope to see you again . We will provide the best service ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Hope to see you again . We will provide the best service .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_8938.json b/reccon/query/tr_8938.json new file mode 100644 index 0000000000000000000000000000000000000000..8bbf59959de6d3d1a05f90d9d9c785b009575e47 --- /dev/null +++ b/reccon/query/tr_8938.json @@ -0,0 +1,27 @@ +[ + { + "turn": 16, + "speaker": "B", + "utterance": "That's amazing ! Really ? How could it change so much in two days ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 15, + 16 + ], + "expanded emotion cause span": [ + "They really gave me sixty pesos for the dollar .", + "How could it change so much in two days ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's amazing ! Really ? How could it change so much in two days ?", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_9046.json b/reccon/query/tr_9046.json new file mode 100644 index 0000000000000000000000000000000000000000..26726d08903cf5d45532ab959072104c22581d09 --- /dev/null +++ b/reccon/query/tr_9046.json @@ -0,0 +1,27 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "exactly ! Oh , my god ! I love Britney ! I'm going to get it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "Hey , look , that's the same shirt Britney wore in her concert .", + "Oh , my god ! I love Britney ! I'm going to get it ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "exactly ! Oh , my god ! I love Britney ! I'm going to get it .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_9076.json b/reccon/query/tr_9076.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba4f76e01d3d16dbf937219e6fd34e3e4a130ec --- /dev/null +++ b/reccon/query/tr_9076.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Don't mention it . Oh , This is a small gift for you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "You've done a lot for us . Thank you" + ], + "type": [ + "inter-personal" + ], + "text": "Don't mention it . Oh , This is a small gift for you .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_920.json b/reccon/query/tr_920.json new file mode 100644 index 0000000000000000000000000000000000000000..c9e912e07f083492c63f708f6ab62ea2bf9ffcbd --- /dev/null +++ b/reccon/query/tr_920.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "I'm glad .", + "emotion": "happy", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I'm most grateful . Everyone in our class enjoyed it ." + ], + "type": [ + "inter-personal" + ], + "text": "I'm glad .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_921.json b/reccon/query/tr_921.json new file mode 100644 index 0000000000000000000000000000000000000000..f44fd339f756ce16b0f6b5666dd8c71f1a9e4cec --- /dev/null +++ b/reccon/query/tr_921.json @@ -0,0 +1,27 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "Very good idea . Sometimes such pictures can show the house's richness .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "They don't have enough time to peel it after they harvested them , so they hung them in the tree . Then in winter , they can peel corn ears in their leisure time .", + "Very good idea ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Very good idea . Sometimes such pictures can show the house's richness .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_9249.json b/reccon/query/tr_9249.json new file mode 100644 index 0000000000000000000000000000000000000000..78ad55aa8067a4adc77aecee262d6848f0f202d4 --- /dev/null +++ b/reccon/query/tr_9249.json @@ -0,0 +1,27 @@ +[ + { + "turn": 17, + "speaker": "A", + "utterance": "it ' s too bad I did all that shopping yesterday !", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 16, + 17 + ], + "expanded emotion cause span": [ + "it ' s on sale . If you spend more than $ 100 , you get a $ 50 voucher for more clothes .", + "I did all that shopping yesterday !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "it ' s too bad I did all that shopping yesterday !", + "id": 17, + "source_sentences": [ + 15 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_9280.json b/reccon/query/tr_9280.json new file mode 100644 index 0000000000000000000000000000000000000000..b84ce55952f79a415782aff01c74d7c4dcae3d91 --- /dev/null +++ b/reccon/query/tr_9280.json @@ -0,0 +1,25 @@ +[ + { + "turn": 13, + "speaker": "A", + "utterance": "Here you go , and here ' s your receipt . Have a nice day .", + "emotion": "happiness", + "explanation": "speaker is happy for the sale", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "buy this dress ," + ], + "type": [ + "inter-personal" + ], + "text": "Here you go , and here ' s your receipt . Have a nice day .", + "id": 13, + "source_sentences": [ + 1 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_9306.json b/reccon/query/tr_9306.json new file mode 100644 index 0000000000000000000000000000000000000000..a0c380218097b992f6aeedc2d735fdbfaaf69e1c --- /dev/null +++ b/reccon/query/tr_9306.json @@ -0,0 +1,27 @@ +[ + { + "turn": 15, + "speaker": "A", + "utterance": "I'm glad you like it . I don't care for it . Why don't you finish my tiramisu so that I can try one of those fried bananas ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14, + 15 + ], + "expanded emotion cause span": [ + "it's absolutely delicious ! That is the best tiramisu I've ever had !", + "I'm glad you like it . I don't care for it . Why don't you finish my tiramisu so that I can try one of those fried bananas ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm glad you like it . I don't care for it . Why don't you finish my tiramisu so that I can try one of those fried bananas ?", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_9310.json b/reccon/query/tr_9310.json new file mode 100644 index 0000000000000000000000000000000000000000..f58bfe9779dfa5db5f96f88ec2cbed120fc48a92 --- /dev/null +++ b/reccon/query/tr_9310.json @@ -0,0 +1,24 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Thanks a lot ! I will definitely do that . Is there anything else ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "it's important that you sit with him and review his homework assignments and help him with math . I would also recommend he stay after school twice a week for tutoring sessions . It will really help a lot ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks a lot ! I will definitely do that . Is there anything else ?", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_9389.json b/reccon/query/tr_9389.json new file mode 100644 index 0000000000000000000000000000000000000000..602e3e092fda8553c1faabb4e0f1cfa772e3f29a --- /dev/null +++ b/reccon/query/tr_9389.json @@ -0,0 +1,27 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "You mean I'm among the people who have to go ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "we have to reduce some staff .", + "You mean I'm among the people who have to go ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You mean I'm among the people who have to go ?", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_945.json b/reccon/query/tr_945.json new file mode 100644 index 0000000000000000000000000000000000000000..59091c2c638981ea16796220636e22cbc588e451 --- /dev/null +++ b/reccon/query/tr_945.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "No kidding ! Jack is such a log ! He's never dated a girl .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "it's your brother , Jack ." + ], + "type": [ + "inter-personal" + ], + "text": "No kidding ! Jack is such a log ! He's never dated a girl .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_9516.json b/reccon/query/tr_9516.json new file mode 100644 index 0000000000000000000000000000000000000000..10812391d77079d6cb5e0806e17cfb7e3cc3041c --- /dev/null +++ b/reccon/query/tr_9516.json @@ -0,0 +1,27 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "Recliner ? In my beautifully decorated living room ? I don ' t think so !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 13, + 14 + ], + "expanded emotion cause span": [ + "can you pick out a nice recliner ?", + "In my beautifully decorated living room ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Recliner ? In my beautifully decorated living room ? I don ' t think so !", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_9573.json b/reccon/query/tr_9573.json new file mode 100644 index 0000000000000000000000000000000000000000..bc7102086ef981697154f9a5d3039080ff309fb4 --- /dev/null +++ b/reccon/query/tr_9573.json @@ -0,0 +1,25 @@ +[ + { + "turn": 13, + "speaker": "A", + "utterance": "Sure . As many as you want .", + "emotion": "happiness", + "explanation": "A is happy as B wants to get a service from them", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "May I have two" + ], + "type": [ + "inter-personal" + ], + "text": "Sure . As many as you want .", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_959.json b/reccon/query/tr_959.json new file mode 100644 index 0000000000000000000000000000000000000000..94698e29e0d6e9c9249df01f88a4f2061d135932 --- /dev/null +++ b/reccon/query/tr_959.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Really ? Quite a woman , isn ' t she ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "he is her sixth husband ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? Quite a woman , isn ' t she ?", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_9626.json b/reccon/query/tr_9626.json new file mode 100644 index 0000000000000000000000000000000000000000..685ee813650da9f4df6529b8a3e411aaa8cf5b61 --- /dev/null +++ b/reccon/query/tr_9626.json @@ -0,0 +1,25 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "No problem !", + "emotion": "happiness", + "explanation": "A is happy as B asks for help", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Can you use the thinning shears" + ], + "type": [ + "inter-personal" + ], + "text": "No problem !", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_9643.json b/reccon/query/tr_9643.json new file mode 100644 index 0000000000000000000000000000000000000000..298ca48bb6ee4c48c8fe0ed8005a45512ba02b4d --- /dev/null +++ b/reccon/query/tr_9643.json @@ -0,0 +1,27 @@ +[ + { + "turn": 16, + "speaker": "B", + "utterance": "Absolutely . That's why I can always get a good price .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15, + 16 + ], + "expanded emotion cause span": [ + "But I can tell that you come here often .", + "I can always get a good price ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Absolutely . That's why I can always get a good price .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_9666.json b/reccon/query/tr_9666.json new file mode 100644 index 0000000000000000000000000000000000000000..48e8469cbe42ddae7043f40308572f82f789c65d --- /dev/null +++ b/reccon/query/tr_9666.json @@ -0,0 +1,27 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "Wow . That sounds really good .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "keep doing that until most of the egg is cooked so you should have a nice thick omelet and then flip it over , you'll only have to cook that side lightly . Put your fillings on the top and fold it over and let it sit just long enough to melt the cheese .", + "sounds really good ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Wow . That sounds really good .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_9686.json b/reccon/query/tr_9686.json new file mode 100644 index 0000000000000000000000000000000000000000..d625fb26578b94c2bd801f260968c87317f2174c --- /dev/null +++ b/reccon/query/tr_9686.json @@ -0,0 +1,27 @@ +[ + { + "turn": 17, + "speaker": "A", + "utterance": "To hell with you . The accident was your fault .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 16, + 17 + ], + "expanded emotion cause span": [ + "But if you're going to drive like you did just now , you will have to get used to a little physical pain .", + "The accident was your fault ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "To hell with you . The accident was your fault .", + "id": 17, + "source_sentences": [ + 15 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_9734.json b/reccon/query/tr_9734.json new file mode 100644 index 0000000000000000000000000000000000000000..d8f2224ba972a0dccf4e63f0123715269fd38b3a --- /dev/null +++ b/reccon/query/tr_9734.json @@ -0,0 +1,24 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "Thank you , but no . This will do it for now .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Our regular price for Digital Barbie is $ 29 . 95 plus tax ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you , but no . This will do it for now .", + "id": 9, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_9779.json b/reccon/query/tr_9779.json new file mode 100644 index 0000000000000000000000000000000000000000..f5690ce6dbf967441ec3ce80cad6bc662a29acd8 --- /dev/null +++ b/reccon/query/tr_9779.json @@ -0,0 +1,24 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "So am I .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "he is our new President !" + ], + "type": [ + "inter-personal" + ], + "text": "So am I .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_9841.json b/reccon/query/tr_9841.json new file mode 100644 index 0000000000000000000000000000000000000000..133e2dccd0aaaf7d7c68b3466f4ba398ef4926f5 --- /dev/null +++ b/reccon/query/tr_9841.json @@ -0,0 +1,24 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "God ! Even talking about it makes me feel like l'm gaining weight !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "l like the traditional flavors like rum raisin , butter pecan . maple walnut , strawberry , chocolate and vanilla . But now there are some new flavors from Asia like green tea and durian ." + ], + "type": [ + "inter-personal" + ], + "text": "God ! Even talking about it makes me feel like l'm gaining weight !", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_990.json b/reccon/query/tr_990.json new file mode 100644 index 0000000000000000000000000000000000000000..7101e4e8217fa9a3fdc3df95805677107620c7bf --- /dev/null +++ b/reccon/query/tr_990.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Are you kidding ? Don't you see many people over there ? Just on your right .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "Great , it's so quiet here .", + "Don't you see many people over there ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Are you kidding ? Don't you see many people over there ? Just on your right .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/tr_9974.json b/reccon/query/tr_9974.json new file mode 100644 index 0000000000000000000000000000000000000000..2277112490e2120f90f801fe43c8c42460bd5930 --- /dev/null +++ b/reccon/query/tr_9974.json @@ -0,0 +1,27 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "In the dustbin ! Why didn't you tell me before ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "They are in the dustbin .", + "Why didn't you tell me before ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "In the dustbin ! Why didn't you tell me before ?", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/train.Ses01F_impro01.json b/reccon/query/train.Ses01F_impro01.json new file mode 100644 index 0000000000000000000000000000000000000000..a55bd7fa22c92ca31d6c15d918cf22987303f0a9 --- /dev/null +++ b/reccon/query/train.Ses01F_impro01.json @@ -0,0 +1,24 @@ +[ + { + "turn": 26, + "speaker": "A", + "utterance": "That would - I would appreciate that. Yeah.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 25 + ], + "expanded emotion cause span": [ + "Yeah. Do you want to see my supervisor? Huh? Yeah. Do you want to see my supervisor? Fine. I'll be right back." + ], + "type": [ + "inter-personal" + ], + "text": "That would - I would appreciate that. Yeah.", + "id": 26, + "source_sentences": [ + 24 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/train.Ses01F_impro07.json b/reccon/query/train.Ses01F_impro07.json new file mode 100644 index 0000000000000000000000000000000000000000..3de62559575e088b1e4029341d9adffa2e3a5fb8 --- /dev/null +++ b/reccon/query/train.Ses01F_impro07.json @@ -0,0 +1,27 @@ +[ + { + "turn": 25, + "speaker": "B", + "utterance": "Yay...School's fun.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2, + 25 + ], + "expanded emotion cause span": [ + "There's a big envelope it says, you're in", + "Yay...School's fun." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yay...School's fun.", + "id": 25, + "source_sentences": [ + 1 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/train.Ses01M_script03_2.json b/reccon/query/train.Ses01M_script03_2.json new file mode 100644 index 0000000000000000000000000000000000000000..1648ad363d969aa0d9643e92b814917e6108fa60 --- /dev/null +++ b/reccon/query/train.Ses01M_script03_2.json @@ -0,0 +1,24 @@ +[ + { + "turn": 21, + "speaker": "A", + "utterance": "You're quite insufferable, I expect it's because you're drunk.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 20 + ], + "expanded emotion cause span": [ + "I suppose you two had a riotous time, huh? No restrain at all, very enjoyable, he never had much any how." + ], + "type": [ + "inter-personal" + ], + "text": "You're quite insufferable, I expect it's because you're drunk.", + "id": 21, + "source_sentences": [ + 19 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/train.Ses02M_impro02.json b/reccon/query/train.Ses02M_impro02.json new file mode 100644 index 0000000000000000000000000000000000000000..b3d78e5c2838c38d48d85ac63a75209443dd3db9 --- /dev/null +++ b/reccon/query/train.Ses02M_impro02.json @@ -0,0 +1,27 @@ +[ + { + "turn": 9, + "speaker": "B", + "utterance": "It's- It's dangerous anywhere, honey. I mean this is -this- I'm just going to go and we'll get it over with,", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "It's dangerous; I mean how can you make sure that you'll", + "It's- It's dangerous anywhere, honey. I mean this is -this" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It's- It's dangerous anywhere, honey. I mean this is -this- I'm just going to go and we'll get it over with,", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/train.Ses03F_impro03.json b/reccon/query/train.Ses03F_impro03.json new file mode 100644 index 0000000000000000000000000000000000000000..1142f26b9c610c60f9fac5ae7cd7e398a5b491eb --- /dev/null +++ b/reccon/query/train.Ses03F_impro03.json @@ -0,0 +1,33 @@ +[ + { + "turn": 34, + "speaker": "B", + "utterance": "That's awesome. [LAUGHTER] Marriage.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 24, + 25, + 24, + 32 + ], + "expanded emotion cause span": [ + "Oh, yeah. Everyone--yeah. And people--friends of ours were in the audience, I didn't know about, like family members.", + "Yeah. It was great.", + "Everyone--yeah. And people--friends of ours were in the audience, I didn't know about, like family members.", + "like I think I want to get married--I want to have two weddings. One here, then one in Europe." + ], + "type": [ + "inter-personal" + ], + "text": "That's awesome. [LAUGHTER] Marriage.", + "id": 34, + "source_sentences": [ + 23, + 24, + 23, + 31 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/train.Ses03F_script02_1.json b/reccon/query/train.Ses03F_script02_1.json new file mode 100644 index 0000000000000000000000000000000000000000..af7ff257ca6685b675a0ef23363ae6ba9c02ece7 --- /dev/null +++ b/reccon/query/train.Ses03F_script02_1.json @@ -0,0 +1,27 @@ +[ + { + "turn": 30, + "speaker": "B", + "utterance": "We just weren't in a good spot, all right? This is a much better spot. I have a good instinct for these things. Look, is that-", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 28, + 29 + ], + "expanded emotion cause span": [ + "I got sand in my panties. We got into an argument about nothing. You got a sore throat and we never saw the grunions.", + "we've never seen the grunions. We're not going to see them." + ], + "type": [ + "inter-personal" + ], + "text": "We just weren't in a good spot, all right? This is a much better spot. I have a good instinct for these things. Look, is that-", + "id": 30, + "source_sentences": [ + 27, + 28 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/train.Ses03M_impro08b.json b/reccon/query/train.Ses03M_impro08b.json new file mode 100644 index 0000000000000000000000000000000000000000..913dac1d7cfc13b099b486ee706247dc7521e2bf --- /dev/null +++ b/reccon/query/train.Ses03M_impro08b.json @@ -0,0 +1,27 @@ +[ + { + "turn": 30, + "speaker": "A", + "utterance": "I, I, I don't want a contract. Okay. I don't want any contracts.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 29, + 30 + ], + "expanded emotion cause span": [ + "they'll hook you up with service even give you a free three months", + "Okay. I don't want any contracts." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I, I, I don't want a contract. Okay. I don't want any contracts.", + "id": 30, + "source_sentences": [ + 28 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/train.Ses03M_script01_2.json b/reccon/query/train.Ses03M_script01_2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d29d7edc3603360a5f1a015fed18178a724b047 --- /dev/null +++ b/reccon/query/train.Ses03M_script01_2.json @@ -0,0 +1,27 @@ +[ + { + "turn": 26, + "speaker": "B", + "utterance": "What do I got to hide? Huh? What the hell's the matter with you Kate?", + "emotion": "angry", + "expanded emotion cause evidence": [ + 21, + 26 + ], + "expanded emotion cause span": [ + "You above all people have got to believe.", + "What the hell's the matter with you Kate?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "What do I got to hide? Huh? What the hell's the matter with you Kate?", + "id": 26, + "source_sentences": [ + 20 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/train.Ses04F_script03_1.json b/reccon/query/train.Ses04F_script03_1.json new file mode 100644 index 0000000000000000000000000000000000000000..bf0c4280da8e53e316638d8fc328eb0c458a192b --- /dev/null +++ b/reccon/query/train.Ses04F_script03_1.json @@ -0,0 +1,30 @@ +[ + { + "turn": 18, + "speaker": "A", + "utterance": "Oh, Charles. That was his name. Charles he did wriggle so beautifully.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 15, + 17, + 18 + ], + "expanded emotion cause span": [ + "Do you remember that awful scene in Venice?", + "The one where you bought that little painted wooden snake and put it on my bed.", + "Charles he did wriggle so beautifully." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh, Charles. That was his name. Charles he did wriggle so beautifully.", + "id": 18, + "source_sentences": [ + 14, + 16 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/train.Ses04M_script02_2.json b/reccon/query/train.Ses04M_script02_2.json new file mode 100644 index 0000000000000000000000000000000000000000..e359b7d1fb2b8d58647c1792df44243601457f82 --- /dev/null +++ b/reccon/query/train.Ses04M_script02_2.json @@ -0,0 +1,27 @@ +[ + { + "turn": 51, + "speaker": "A", + "utterance": "Okay, fine. So we're in the wrong spot, but we're with the right person.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 50, + 51 + ], + "expanded emotion cause span": [ + "Actually, now that you mention it, no. I don't.", + "we're with the right person." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Okay, fine. So we're in the wrong spot, but we're with the right person.", + "id": 51, + "source_sentences": [ + 49 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/train.train.Ses01F_script01_3.json b/reccon/query/train.train.Ses01F_script01_3.json new file mode 100644 index 0000000000000000000000000000000000000000..75cff6e5007e6a287ee29bedbe5044c805a633bb --- /dev/null +++ b/reccon/query/train.train.Ses01F_script01_3.json @@ -0,0 +1,27 @@ +[ + { + "turn": 54, + "speaker": "A", + "utterance": "What would I do with a fortune?", + "emotion": "happy", + "expanded emotion cause evidence": [ + 53, + 54 + ], + "expanded emotion cause span": [ + "I just want you to know Annie.", + "What would I do with a fortune?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "What would I do with a fortune?", + "id": 54, + "source_sentences": [ + 52 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/train.train.Ses01F_script03_1.json b/reccon/query/train.train.Ses01F_script03_1.json new file mode 100644 index 0000000000000000000000000000000000000000..50f30d37846aa2d00523f02a0a70b16cc1758b0f --- /dev/null +++ b/reccon/query/train.train.Ses01F_script03_1.json @@ -0,0 +1,24 @@ +[ + { + "turn": 25, + "speaker": "B", + "utterance": "[LAUGHTER] We were very much younger then.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 23 + ], + "expanded emotion cause span": [ + "The manager came in, he found us rolling about the floor, biting and scratching like panthers. [LAUGHTER] How utterly, utterly ridiculous." + ], + "type": [ + "inter-personal" + ], + "text": "[LAUGHTER] We were very much younger then.", + "id": 25, + "source_sentences": [ + 22 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/va_101.json b/reccon/query/va_101.json new file mode 100644 index 0000000000000000000000000000000000000000..697529e91a10a57109273bf0eeb1ad89cf95a92d --- /dev/null +++ b/reccon/query/va_101.json @@ -0,0 +1,27 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "If you like to help me do the dishes , I'll be more dreadful .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 7 + ], + "expanded emotion cause span": [ + "it's delicious !", + "It's a wonderful meal . Thank you ," + ], + "type": [ + "inter-personal" + ], + "text": "If you like to help me do the dishes , I'll be more dreadful .", + "id": 8, + "source_sentences": [ + 4, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/va_184.json b/reccon/query/va_184.json new file mode 100644 index 0000000000000000000000000000000000000000..d630a68d1375adc2c88252aebb437c5b8178e806 --- /dev/null +++ b/reccon/query/va_184.json @@ -0,0 +1,24 @@ +[ + { + "turn": 13, + "speaker": "A", + "utterance": "You ' re welcome .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "I ' ll take it . Thank you" + ], + "type": [ + "inter-personal" + ], + "text": "You ' re welcome .", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/va_201.json b/reccon/query/va_201.json new file mode 100644 index 0000000000000000000000000000000000000000..c07dcd1d7a695625ed76f29139b9bbab2aaec68b --- /dev/null +++ b/reccon/query/va_201.json @@ -0,0 +1,25 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Goodbye .", + "emotion": "happiness", + "explanation": "Sharing pleasantries.", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Goodbye ." + ], + "type": [ + "inter-personal" + ], + "text": "Goodbye .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/va_227.json b/reccon/query/va_227.json new file mode 100644 index 0000000000000000000000000000000000000000..49ebdf22ced1e1b1b339ac9f4d4cb556127d5ead --- /dev/null +++ b/reccon/query/va_227.json @@ -0,0 +1,24 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Perfect ! Please add on an order of onion rings .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "another appetizer for half price" + ], + "type": [ + "inter-personal" + ], + "text": "Perfect ! Please add on an order of onion rings .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/va_330.json b/reccon/query/va_330.json new file mode 100644 index 0000000000000000000000000000000000000000..3f2796ab2801c909e3ae787eed10fa6444a11b44 --- /dev/null +++ b/reccon/query/va_330.json @@ -0,0 +1,30 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Wow !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 5, + 7 + ], + "expanded emotion cause span": [ + "It's got a built-in video camera so you can see the person you're talking to . It also takes stills and I can use the E-mail mode to send digital pictures straight to my friend's phone !", + "I can plug it into a folding keyboard to type in message mode . l can even surf the net .", + "Yes . With the 600 - second digital memory , l can record my voice and send it using voice message mode ." + ], + "type": [ + "inter-personal" + ], + "text": "Wow !", + "id": 8, + "source_sentences": [ + 2, + 4, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/va_345.json b/reccon/query/va_345.json new file mode 100644 index 0000000000000000000000000000000000000000..bc0c7fac378c34c5fbc3ebac8dc1fd76b6fba190 --- /dev/null +++ b/reccon/query/va_345.json @@ -0,0 +1,27 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "I think that's a bad idea . I'd hate anyone here to think of me as a friend . How would they ever respect me as they can do whatever they want ?", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "Just take them for your good friends", + "I'd hate anyone here to think of me as a friend . How would they ever respect me as they can do whatever they want ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I think that's a bad idea . I'd hate anyone here to think of me as a friend . How would they ever respect me as they can do whatever they want ?", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/va_371.json b/reccon/query/va_371.json new file mode 100644 index 0000000000000000000000000000000000000000..014902773721b4f9fd8d01410663b7a5b7450f67 --- /dev/null +++ b/reccon/query/va_371.json @@ -0,0 +1,27 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "Lady ! This is unfair ! I've been cheated ! I was in line before you . That should have been my ticket ! Come on , hand it over , lady !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 13, + 14 + ], + "expanded emotion cause span": [ + "I bought the last ticket ,", + "Lady ! This is unfair ! I've been cheated ! I was in line before you . That should have been my ticket !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Lady ! This is unfair ! I've been cheated ! I was in line before you . That should have been my ticket ! Come on , hand it over , lady !", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/va_410.json b/reccon/query/va_410.json new file mode 100644 index 0000000000000000000000000000000000000000..7577feb53cdac5d4fb55103eb85ab493545dbf35 --- /dev/null +++ b/reccon/query/va_410.json @@ -0,0 +1,24 @@ +[ + { + "turn": 14, + "speaker": "B", + "utterance": "Thank you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "I'll spent more time with you in the future ," + ], + "type": [ + "inter-personal" + ], + "text": "Thank you .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/va_428.json b/reccon/query/va_428.json new file mode 100644 index 0000000000000000000000000000000000000000..b54bd7213a7d1b8be7486ff5d2b80ad7cc97e6d7 --- /dev/null +++ b/reccon/query/va_428.json @@ -0,0 +1,24 @@ +[ + { + "turn": 16, + "speaker": "B", + "utterance": "OK .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "Anytime you like ." + ], + "type": [ + "inter-personal" + ], + "text": "OK .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/va_491.json b/reccon/query/va_491.json new file mode 100644 index 0000000000000000000000000000000000000000..5ef02b6b56e29353a4b8d6d413d5edad0b419a1a --- /dev/null +++ b/reccon/query/va_491.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Thanks . I found these new shoes earlier at the store .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "you look nice today too ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks . I found these new shoes earlier at the store .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/va_504.json b/reccon/query/va_504.json new file mode 100644 index 0000000000000000000000000000000000000000..520a844f55de9168d79f6256d6f4aeef7dcdc990 --- /dev/null +++ b/reccon/query/va_504.json @@ -0,0 +1,25 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Thanks again .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I will try to get a taxi for you ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks again .", + "id": 6, + "source_sentences": [ + 2 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/va_64.json b/reccon/query/va_64.json new file mode 100644 index 0000000000000000000000000000000000000000..c62ac7d710cea7907edd69b49280daf0e571b3bf --- /dev/null +++ b/reccon/query/va_64.json @@ -0,0 +1,27 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Oh , my god ! No air-conditioner !", + "emotion": "fear", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "there will be no electricity on such a hot day ?", + "No air-conditioner !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , my god ! No air-conditioner !", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/va_663.json b/reccon/query/va_663.json new file mode 100644 index 0000000000000000000000000000000000000000..051ff897a04e7fb090116703527b49f34e47f841 --- /dev/null +++ b/reccon/query/va_663.json @@ -0,0 +1,27 @@ +[ + { + "turn": 13, + "speaker": "A", + "utterance": "Grangerfield ! You were in Grangerfield ? That's a completely different town ! How could you drive to a completely different town ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 12, + 13 + ], + "expanded emotion cause span": [ + "they told us we were in Grangerfield .", + "How could you drive to a completely different town ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Grangerfield ! You were in Grangerfield ? That's a completely different town ! How could you drive to a completely different town ?", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/va_664.json b/reccon/query/va_664.json new file mode 100644 index 0000000000000000000000000000000000000000..a25364b11442362c9cbeca720846bfa0b91cb61f --- /dev/null +++ b/reccon/query/va_664.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "I'm glad you like it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "This salad looks so nice-just right for a hot day .", + "I'm glad you like it ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm glad you like it .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/va_710.json b/reccon/query/va_710.json new file mode 100644 index 0000000000000000000000000000000000000000..c076576eeebec960fa9efba316e85e33fa0aa467 --- /dev/null +++ b/reccon/query/va_710.json @@ -0,0 +1,27 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "Great ! This is our secret ! If you see my wife , say nothing to her about this !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 8 + ], + "expanded emotion cause span": [ + "I can have it ready tomorrow afternoon ,", + "Certainly ." + ], + "type": [ + "inter-personal" + ], + "text": "Great ! This is our secret ! If you see my wife , say nothing to her about this !", + "id": 9, + "source_sentences": [ + 5, + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/va_727.json b/reccon/query/va_727.json new file mode 100644 index 0000000000000000000000000000000000000000..4b424202d387b77c5f4a7c8e92ad95a0375cda50 --- /dev/null +++ b/reccon/query/va_727.json @@ -0,0 +1,27 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Don't you know that ? Are you kidding me ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "where did they get so much snow in here ?", + "Don't you know that ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Don't you know that ? Are you kidding me ?", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/va_76.json b/reccon/query/va_76.json new file mode 100644 index 0000000000000000000000000000000000000000..c36569888abc53e5e22b59979c68940885b1dec9 --- /dev/null +++ b/reccon/query/va_76.json @@ -0,0 +1,24 @@ +[ + { + "turn": 19, + "speaker": "A", + "utterance": "Oh , my God ! It's good we have food .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 18 + ], + "expanded emotion cause span": [ + "People get stranded for days ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , my God ! It's good we have food .", + "id": 19, + "source_sentences": [ + 17 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/va_835.json b/reccon/query/va_835.json new file mode 100644 index 0000000000000000000000000000000000000000..7aaa8c8862d309f2943eb96b671a6490efc61947 --- /dev/null +++ b/reccon/query/va_835.json @@ -0,0 +1,27 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "I'm always at your service .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 7 + ], + "expanded emotion cause span": [ + "Give me one ,", + "I'm always at your service ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm always at your service .", + "id": 7, + "source_sentences": [ + 3 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/va_838.json b/reccon/query/va_838.json new file mode 100644 index 0000000000000000000000000000000000000000..a8c71ad5610356be50179c8628646dfa11821dcd --- /dev/null +++ b/reccon/query/va_838.json @@ -0,0 +1,27 @@ +[ + { + "turn": 11, + "speaker": "A", + "utterance": "I'm sorry for the misunderstanding .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "I'm giving you a ticket for this .", + "I'm sorry for the misunderstanding ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm sorry for the misunderstanding .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/va_86.json b/reccon/query/va_86.json new file mode 100644 index 0000000000000000000000000000000000000000..363a34a17b4362cd074e69bcdecdad98c31b5850 --- /dev/null +++ b/reccon/query/va_86.json @@ -0,0 +1,24 @@ +[ + { + "turn": 10, + "speaker": "B", + "utterance": "Yay !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "I can get you some hamsters and we ' ll take it from there ." + ], + "type": [ + "inter-personal" + ], + "text": "Yay !", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/va_882.json b/reccon/query/va_882.json new file mode 100644 index 0000000000000000000000000000000000000000..5fa5abaf5d6d3aa1ecf0f23e3ccd16f6ecb8204d --- /dev/null +++ b/reccon/query/va_882.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Very good . Is there anything else you would like ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Let me have her ." + ], + "type": [ + "inter-personal" + ], + "text": "Very good . Is there anything else you would like ?", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/va_922.json b/reccon/query/va_922.json new file mode 100644 index 0000000000000000000000000000000000000000..c3b665b5a7215814f8049e31e1f4114ccf995770 --- /dev/null +++ b/reccon/query/va_922.json @@ -0,0 +1,27 @@ +[ + { + "turn": 9, + "speaker": "A", + "utterance": "Fine ! Get the stupid thirty dollar crayon !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "You spend as much or more money on your razors , after shave , cologne and gel ! Not to mention how much you spend on clothes and ...", + "Get the stupid thirty dollar crayon !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Fine ! Get the stupid thirty dollar crayon !", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/va_926.json b/reccon/query/va_926.json new file mode 100644 index 0000000000000000000000000000000000000000..cfc5abed4dc482b33b125f8f59ca02bb7ae7b89a --- /dev/null +++ b/reccon/query/va_926.json @@ -0,0 +1,27 @@ +[ + { + "turn": 6, + "speaker": "B", + "utterance": "Sorry . You'd better get off for taking another taxi .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Can it keep going ?", + "You'd better get off for taking another taxi ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Sorry . You'd better get off for taking another taxi .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/va_977.json b/reccon/query/va_977.json new file mode 100644 index 0000000000000000000000000000000000000000..1d2bf9e95abb7e9c2a74baebad668f5bef89a833 --- /dev/null +++ b/reccon/query/va_977.json @@ -0,0 +1,24 @@ +[ + { + "turn": 7, + "speaker": "A", + "utterance": "Really ? A foreign parrot !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "It's interesting that there is also a parrot in my English book . His mane is Polly ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? A foreign parrot !", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/va_980.json b/reccon/query/va_980.json new file mode 100644 index 0000000000000000000000000000000000000000..eadd076c6fa0a8d3b654599e33035b68578d1a38 --- /dev/null +++ b/reccon/query/va_980.json @@ -0,0 +1,24 @@ +[ + { + "turn": 8, + "speaker": "B", + "utterance": "Sounds great . Thank you for your hospitality .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I've already made a hotel reservation for you , let's go to the hotel first and drop off your things . Then , I'd like to have a drink so that we can get better acquainted . I've booked a table at an exclusive restaurant downtown . Afterwards , I've made arrangements to take you to see the city lights . Seattle ' s nightlife can be really quite exciting . How does that schedule sound to you ?" + ], + "type": [ + "inter-personal" + ], + "text": "Sounds great . Thank you for your hospitality .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/query/valid.valid.Ses04F_impro07.json b/reccon/query/valid.valid.Ses04F_impro07.json new file mode 100644 index 0000000000000000000000000000000000000000..7e6e1bab72f6dc01782e48c0243f72e40adc0ea7 --- /dev/null +++ b/reccon/query/valid.valid.Ses04F_impro07.json @@ -0,0 +1,24 @@ +[ + { + "turn": 110, + "speaker": "A", + "utterance": "me.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 107 + ], + "expanded emotion cause span": [ + "You're right though." + ], + "type": [ + "inter-personal" + ], + "text": "me.", + "id": 110, + "source_sentences": [ + 106 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_182.json b/reccon/sources/te_182.json new file mode 100644 index 0000000000000000000000000000000000000000..7034e0c771e2df53f7aa51a54bf1278bb8645878 --- /dev/null +++ b/reccon/sources/te_182.json @@ -0,0 +1,139 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello !", + "emotion": "neutral", + "text": "Hello !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hello , Is that Stefan ?", + "emotion": "neutral", + "text": "Hello , Is that Stefan ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I'm sorry , but I'm afraid you've dialed the wrong number . There is no Stefan here .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "you've dialed the wrong number ." + ], + "type": [ + "no-context" + ], + "text": "I'm sorry , but I'm afraid you've dialed the wrong number . There is no Stefan here .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Really ? Are you sure ? I called before and he was there .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "he was there ." + ], + "type": [ + "no-context" + ], + "text": "Really ? Are you sure ? I called before and he was there .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Yes . I'm sure . You have the wrong number . I have used this number for more than 20 years .", + "emotion": "neutral", + "text": "Yes . I'm sure . You have the wrong number . I have used this number for more than 20 years .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "That can't be true . I remember the number clearly . Is your number 1199886 ?", + "emotion": "neutral", + "text": "That can't be true . I remember the number clearly . Is your number 1199886 ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "No , it isn't . It's 1199866 . It seems that you have misdialed .", + "emotion": "neutral", + "text": "No , it isn't . It's 1199866 . It seems that you have misdialed .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Oh , I'm sorry I bothered you . I'm really sorry .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "you have misdialed .", + "I bothered you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , I'm sorry I bothered you . I'm really sorry .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "It doesn't matter . It happens to everyone .", + "emotion": "neutral", + "text": "It doesn't matter . It happens to everyone .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Sorry again for bothering you .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 7, + 8, + 10 + ], + "expanded emotion cause span": [ + "you have misdialed .", + "I bothered you .", + "Sorry again for bothering you ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Sorry again for bothering you .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "That's all right .", + "emotion": "neutral", + "text": "That's all right .", + "id": 11 + } +] \ No newline at end of file diff --git a/reccon/sources/te_189.json b/reccon/sources/te_189.json new file mode 100644 index 0000000000000000000000000000000000000000..ebc95e536d60338de793d2a63a3aec22d377cd13 --- /dev/null +++ b/reccon/sources/te_189.json @@ -0,0 +1,220 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello , ma ' am , can I help you find something ?", + "emotion": "neutral", + "text": "Hello , ma ' am , can I help you find something ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , actually I ' m looking to buy a camera .", + "emotion": "neutral", + "text": "Yes , actually I ' m looking to buy a camera .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "We ' Ve got a wide selection do you know if you ' d like a point-and-shoot , or something a little fancier ? Are you shopping for yourself or for someone else ?", + "emotion": "neutral", + "text": "We ' Ve got a wide selection do you know if you ' d like a point-and-shoot , or something a little fancier ? Are you shopping for yourself or for someone else ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Actually I ' m buying a camera for my husband .", + "emotion": "neutral", + "text": "Actually I ' m buying a camera for my husband .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Ah , well then I ' d recommend a nice entry-level digital SLR .", + "emotion": "neutral", + "text": "Ah , well then I ' d recommend a nice entry-level digital SLR .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yeah ? Can I take a look at the Sirs you carry ?", + "emotion": "neutral", + "text": "Yeah ? Can I take a look at the Sirs you carry ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Sure thing , follow me . This here is the .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Can I take a look at the Sirs you carry ?" + ], + "type": [ + "inter-personal" + ], + "text": "Sure thing , follow me . This here is the .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "The Canon Eos . Yeah it ' s ok , but I ' m looking for something that performs better in low light , has a better display panel , and longer battery life .", + "emotion": "neutral", + "text": "The Canon Eos . Yeah it ' s ok , but I ' m looking for something that performs better in low light , has a better display panel , and longer battery life .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Oh , ah , um the Nikon D60 is a nice option .", + "emotion": "neutral", + "text": "Oh , ah , um the Nikon D60 is a nice option .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Yeah , but what kit lens does this camera come with ? I don ' t want some bulky telephoto lens .", + "emotion": "neutral", + "text": "Yeah , but what kit lens does this camera come with ? I don ' t want some bulky telephoto lens .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Oh , well this one has the , uh .", + "emotion": "neutral", + "text": "Oh , well this one has the , uh .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Looks to me like an 18-55 mm lens . pretty standard , that will do . Not like my husband will be stalking celebrities or anything !", + "emotion": "neutral", + "text": "Looks to me like an 18-55 mm lens . pretty standard , that will do . Not like my husband will be stalking celebrities or anything !", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "So , ahem , can I interest you in any acc ...", + "emotion": "neutral", + "text": "So , ahem , can I interest you in any acc ...", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Accessories ? Do you carry polarizing filters ?", + "emotion": "neutral", + "text": "Accessories ? Do you carry polarizing filters ?", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Polarizing filter um we should ! I ' m sorry , ma ' am . It looks like we ' re sold out .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "we ' re sold out ." + ], + "type": [ + "no-context" + ], + "text": "Polarizing filter um we should ! I ' m sorry , ma ' am . It looks like we ' re sold out .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "No you ' re not ! There are some right here !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 16 + ], + "expanded emotion cause span": [ + "There are some right here !" + ], + "type": [ + "no-context" + ], + "text": "No you ' re not ! There are some right here !", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "Oh , well , would you look at that ! Polarizing filters .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 16, + 17 + ], + "expanded emotion cause span": [ + "There are some right here !", + "would you look at that !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , well , would you look at that ! Polarizing filters .", + "id": 17, + "source_sentences": [ + 15 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 18, + "speaker": "B", + "utterance": "Thanks for your help , Ralph !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 16 + ], + "expanded emotion cause span": [ + "There are some right here !" + ], + "type": [ + "self-contagion" + ], + "text": "Thanks for your help , Ralph !", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "No problem , ma ' am .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 16, + 17, + 18 + ], + "expanded emotion cause span": [ + "There are some right here !", + "would you look at that !", + "Thanks for your help" + ], + "type": [ + "hybrid" + ], + "text": "No problem , ma ' am .", + "id": 19 + } +] \ No newline at end of file diff --git a/reccon/sources/te_198.json b/reccon/sources/te_198.json new file mode 100644 index 0000000000000000000000000000000000000000..9d8daa3c0c9dd834c7e6c9ebc3f3ffae27f6c4ef --- /dev/null +++ b/reccon/sources/te_198.json @@ -0,0 +1,131 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "You guys are charging me $ 10 for a movie that I never ordered or saw .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "You guys are charging me $ 10 for a movie that I never ordered or saw ." + ], + "type": [ + "no-context" + ], + "text": "You guys are charging me $ 10 for a movie that I never ordered or saw .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Let's see , sir . According to your file , you watched ' Titanic ' Monday evening .", + "emotion": "neutral", + "text": "Let's see , sir . According to your file , you watched ' Titanic ' Monday evening .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Well , the wrong information is in my file . I was at a concert Monday night .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "You guys are charging me $ 10 for a movie that I never ordered or saw .", + "wrong information is in my file ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Well , the wrong information is in my file . I was at a concert Monday night .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Well , your word overrules the file , sir . One moment , please .", + "emotion": "neutral", + "text": "Well , your word overrules the file , sir . One moment , please .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I knew you'd see it my way .", + "emotion": "neutral", + "text": "I knew you'd see it my way .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Sir , I deleted the $ 10 , but I had to add a $ 2 service charge to your bill .", + "emotion": "neutral", + "text": "Sir , I deleted the $ 10 , but I had to add a $ 2 service charge to your bill .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Am I in the Twilight Zone ? You're charging me for a movie I never saw ?", + "emotion": "anger", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I had to add a $ 2 service charge to your bill .", + "You're charging me for a movie I never saw ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Am I in the Twilight Zone ? You're charging me for a movie I never saw ?", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Please don't blame me , sir . Blame the computer programmer .", + "emotion": "neutral", + "text": "Please don't blame me , sir . Blame the computer programmer .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "This is highway robbery . I've got a good mind to call the police !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I had to add a $ 2 service charge to your bill .", + "You're charging me for a movie I never saw ?" + ], + "type": [ + "hybrid" + ], + "text": "This is highway robbery . I've got a good mind to call the police !", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "If it makes you feel any better , other guests feel the same way .", + "emotion": "neutral", + "text": "If it makes you feel any better , other guests feel the same way .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/te_248.json b/reccon/sources/te_248.json new file mode 100644 index 0000000000000000000000000000000000000000..e068e4b4947cb86a63161c89746d507f633a813a --- /dev/null +++ b/reccon/sources/te_248.json @@ -0,0 +1,205 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "guess what ? I've got great news !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I've got great news !" + ], + "type": [ + "no-context" + ], + "text": "guess what ? I've got great news !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "what is it ?", + "emotion": "neutral", + "text": "what is it ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "well , you know how I've been working at the Economist as a proof-reader , right ?", + "emotion": "neutral", + "text": "well , you know how I've been working at the Economist as a proof-reader , right ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "yes .", + "emotion": "neutral", + "text": "yes .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "well , the editor-in-chief heard that I had experience as an editor at another magadize and asked me if I was interested in becoming an assistant editor for him .", + "emotion": "neutral", + "text": "well , the editor-in-chief heard that I had experience as an editor at another magadize and asked me if I was interested in becoming an assistant editor for him .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "really ? That's fantastic ! Will you get a chance to do any writing ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "the editor-in-chief heard that I had experience as an editor at another magadize and asked me if I was interested in becoming an assistant editor for him ." + ], + "type": [ + "inter-personal" + ], + "text": "really ? That's fantastic ! Will you get a chance to do any writing ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "she said that the columnist for the literary criticism column would be going on pregnancy leave soon and that I could be in charge of the column until she came back .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 7 + ], + "expanded emotion cause span": [ + "the editor-in-chief heard that I had experience as an editor at another magadize and asked me if I was interested in becoming an assistant editor for him .", + "I could be in charge of the column until she came back" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "she said that the columnist for the literary criticism column would be going on pregnancy leave soon and that I could be in charge of the column until she came back .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "wow ! That's really great news . How often does the magazine come out ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 7 + ], + "expanded emotion cause span": [ + "the editor-in-chief heard that I had experience as an editor at another magadize and asked me if I was interested in becoming an assistant editor for him .", + "I could be in charge of the column until she came back" + ], + "type": [ + "inter-personal" + ], + "text": "wow ! That's really great news . How often does the magazine come out ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "it's a monthly magazine , but my column will be shared with another columnist so my articles will be due fortnightly .", + "emotion": "neutral", + "text": "it's a monthly magazine , but my column will be shared with another columnist so my articles will be due fortnightly .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "are you looking forward to doing more editing work ?", + "emotion": "neutral", + "text": "are you looking forward to doing more editing work ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "yes , but I'm even more excited about getting my thoughts published again !", + "emotion": "neutral", + "text": "yes , but I'm even more excited about getting my thoughts published again !", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "do you have any order forms here so that I can get a subscription to the magazine ?", + "emotion": "neutral", + "text": "do you have any order forms here so that I can get a subscription to the magazine ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I don't have any with me , but I think I could manage to bring a free copy home for you .", + "emotion": "neutral", + "text": "I don't have any with me , but I think I could manage to bring a free copy home for you .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "I'm really looking forward to reading your column .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13, + 14 + ], + "expanded emotion cause span": [ + "I think I could manage to bring a free copy home for you .", + "I'm really looking forward to reading your column ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm really looking forward to reading your column .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 15, + "speaker": "A", + "utterance": "me , too . Do you want to go out to celebrate my good news ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I'm even more excited about getting my thoughts published again !" + ], + "type": [ + "self-contagion" + ], + "text": "me , too . Do you want to go out to celebrate my good news ?", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "sure , where would you like to go ?", + "emotion": "neutral", + "text": "sure , where would you like to go ?", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "perhaps we could go to the library festival that's going on at the local bookshop .", + "emotion": "neutral", + "text": "perhaps we could go to the library festival that's going on at the local bookshop .", + "id": 17 + } +] \ No newline at end of file diff --git a/reccon/sources/te_261.json b/reccon/sources/te_261.json new file mode 100644 index 0000000000000000000000000000000000000000..191cd92a3fa9f1491c9d14764a34b485c26e41a4 --- /dev/null +++ b/reccon/sources/te_261.json @@ -0,0 +1,117 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Are you finished ?", + "emotion": "neutral", + "text": "Are you finished ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes . May I have some more beer ?", + "emotion": "neutral", + "text": "Yes . May I have some more beer ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Oh , sure . I'll be back in a minute . Thank you for waiting . Here it is . Did you enjoy your meal ?", + "emotion": "happiness", + "explanation": "Assuming A is serving food or beverage to B. A feels happy because B is giving positive feedback to the service.", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Oh , sure . I'll be back in a minute . Thank you for waiting . Here it is . Did you enjoy your meal ?" + ], + "type": [ + "no-context" + ], + "text": "Oh , sure . I'll be back in a minute . Thank you for waiting . Here it is . Did you enjoy your meal ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes , the meal was very delicious and I enjoyed very much . I'm full .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Yes , the meal was very delicious and I enjoyed very much . I'm full ." + ], + "type": [ + "no-context" + ], + "text": "Yes , the meal was very delicious and I enjoyed very much . I'm full .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Is that so ? I'm glad you enjoyed it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Yes , the meal was very delicious and I enjoyed very much . I'm full ." + ], + "type": [ + "inter-personal" + ], + "text": "Is that so ? I'm glad you enjoyed it .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "By the way , Miss . Where is the toilet ?", + "emotion": "neutral", + "text": "By the way , Miss . Where is the toilet ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Toilets are in the rear . I'm afraid all the toilets are fully occupied at the moment .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I'm afraid all the toilets are fully occupied at the moment ." + ], + "type": [ + "no-context" + ], + "text": "Toilets are in the rear . I'm afraid all the toilets are fully occupied at the moment .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "What ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I'm afraid all the toilets are fully occupied at the moment ." + ], + "type": [ + "inter-personal" + ], + "text": "What ?", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_266.json b/reccon/sources/te_266.json new file mode 100644 index 0000000000000000000000000000000000000000..e7e907bafe3d3cc7bf26e73c4f5f9bea9bbdb224 --- /dev/null +++ b/reccon/sources/te_266.json @@ -0,0 +1,140 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Is there anything I can do for you ?", + "emotion": "neutral", + "text": "Is there anything I can do for you ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Would you please show me that mural ?", + "emotion": "neutral", + "text": "Would you please show me that mural ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Certainly . Here you are .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "please show me that mural ?" + ], + "type": [ + "inter-personal" + ], + "text": "Certainly . Here you are .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It looks so beautiful . How much is it ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "It looks so beautiful ." + ], + "type": [ + "no-context" + ], + "text": "It looks so beautiful . How much is it ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Four hundred yuan .", + "emotion": "neutral", + "text": "Four hundred yuan .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "That's a bit more than I wanted to pay . Can you cut the price down a bit ?", + "emotion": "neutral", + "text": "That's a bit more than I wanted to pay . Can you cut the price down a bit ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I'm sorry . Ours is a fixed price shop and I can assure you this is the best price you can get for a mural like this .", + "emotion": "neutral", + "text": "I'm sorry . Ours is a fixed price shop and I can assure you this is the best price you can get for a mural like this .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Maybe you are right . OK , I'll take it .", + "emotion": "neutral", + "text": "Maybe you are right . OK , I'll take it .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Well , I'll have it wrapped for you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I'll take it ." + ], + "type": [ + "inter-personal" + ], + "text": "Well , I'll have it wrapped for you .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Thank you . Here is four hundred yuan .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "I'll have it wrapped for you ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . Here is four hundred yuan .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Thank you . Please come again .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Here is four hundred yuan ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . Please come again .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_267.json b/reccon/sources/te_267.json new file mode 100644 index 0000000000000000000000000000000000000000..315c751bcf049cfbdc0e5346968a8266f44f5b90 --- /dev/null +++ b/reccon/sources/te_267.json @@ -0,0 +1,176 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "It ' s so great to be here ! I ' m so excited to help you and my daughter with your new home !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "It ' s so great to be here ! I ' m so excited to help you and my daughter with your new home !" + ], + "type": [ + "no-context" + ], + "text": "It ' s so great to be here ! I ' m so excited to help you and my daughter with your new home !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "We ' re glad that you ' re here . Would you like a tour of the house ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "It ' s so great to be here ! I ' m so excited to help you and my daughter with your new home !", + "you ' re here ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "We ' re glad that you ' re here . Would you like a tour of the house ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "That ' d be great , but could I have a cup of tea first ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "We ' re glad that you ' re here . Would you like a tour of the house ?" + ], + "type": [ + "inter-personal" + ], + "text": "That ' d be great , but could I have a cup of tea first ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Sure , I ' ll just go put the kettle on . Why don ' t you have a seat on the sofa and I ' ll go take care of things in the kitchen .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "That ' d be great" + ], + "type": [ + "inter-personal" + ], + "text": "Sure , I ' ll just go put the kettle on . Why don ' t you have a seat on the sofa and I ' ll go take care of things in the kitchen .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "That would be lovely , thanks .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Sure , I ' ll just go put the kettle on . Why don ' t you have a seat on the sofa" + ], + "type": [ + "inter-personal" + ], + "text": "That would be lovely , thanks .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Do you take milk or sugar with your tea ?", + "emotion": "neutral", + "text": "Do you take milk or sugar with your tea ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I ' ll take a little milk , but no sugar , please . Make sure you let the tea steep a few minutes before you take the tea bag out of the cup .", + "emotion": "neutral", + "text": "I ' ll take a little milk , but no sugar , please . Make sure you let the tea steep a few minutes before you take the tea bag out of the cup .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Ok . What do you think about our living room ?", + "emotion": "neutral", + "text": "Ok . What do you think about our living room ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Well , I do like the mantelpiece and the coffee table , but I don ' t really care for curtains . Did you get them at a yard sale ? They look ancient .", + "emotion": "neutral", + "text": "Well , I do like the mantelpiece and the coffee table , but I don ' t really care for curtains . Did you get them at a yard sale ? They look ancient .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "My parents gave them to us as a house warming gift .", + "emotion": "neutral", + "text": "My parents gave them to us as a house warming gift .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Oh dear . Well , I suppose they will do for now . do you ever dust in here ? It seems a bit dusty in here .", + "emotion": "neutral", + "text": "Oh dear . Well , I suppose they will do for now . do you ever dust in here ? It seems a bit dusty in here .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Your daughter usually does the dusting , and I do the vacuuming .", + "emotion": "neutral", + "text": "Your daughter usually does the dusting , and I do the vacuuming .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I see . Well , I can help with the chores while I ' m here . You two could probably use my help .", + "emotion": "neutral", + "text": "I see . Well , I can help with the chores while I ' m here . You two could probably use my help .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "That ' s very nice of you to offer . Here ' s your tea . Be careful , it ' s still quite hot .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "I can help with the chores while I ' m here ." + ], + "type": [ + "inter-personal" + ], + "text": "That ' s very nice of you to offer . Here ' s your tea . Be careful , it ' s still quite hot .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_277.json b/reccon/sources/te_277.json new file mode 100644 index 0000000000000000000000000000000000000000..c056846396fea6417162d6a36358073e5d9a1291 --- /dev/null +++ b/reccon/sources/te_277.json @@ -0,0 +1,161 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Wow , Amy , look at that number .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "that number ." + ], + "type": [ + "no-context" + ], + "text": "Wow , Amy , look at that number .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What's so great about it ?", + "emotion": "neutral", + "text": "What's so great about it ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What do you mean ? It's a scrim .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "What's so great about it ?", + "It's a scrim ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "What do you mean ? It's a scrim .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Not to me , I wouldn't be caught dead in that .", + "emotion": "neutral", + "text": "Not to me , I wouldn't be caught dead in that .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I love that kind of stuff .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I love that kind of stuff ." + ], + "type": [ + "no-context" + ], + "text": "I love that kind of stuff .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yeah , you seem to like those styles .", + "emotion": "neutral", + "text": "Yeah , you seem to like those styles .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Sure do . I get a kick out of looking punk .", + "emotion": "neutral", + "text": "Sure do . I get a kick out of looking punk .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "This one looks really expensive though .", + "emotion": "neutral", + "text": "This one looks really expensive though .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I don't care how much it costs . I'm rolling in it .", + "emotion": "neutral", + "text": "I don't care how much it costs . I'm rolling in it .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Lucky you ! I can't buy anything else . I'm flat broke .", + "emotion": "neutral", + "text": "Lucky you ! I can't buy anything else . I'm flat broke .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I got a replace my party outfit , I trashed it last week .", + "emotion": "neutral", + "text": "I got a replace my party outfit , I trashed it last week .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Why did you drag me into this ? I've spent a week salary .", + "emotion": "neutral", + "text": "Why did you drag me into this ? I've spent a week salary .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Are you on the level ? You're the one who called me , remember ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 12, + 13 + ], + "expanded emotion cause span": [ + "Why did you drag me into this ?", + "You're the one who called me" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Are you on the level ? You're the one who called me , remember ?", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Just joking , Tonia . I've got some wonderful clothes . Let's go and have a close look at your outfit .", + "emotion": "neutral", + "text": "Just joking , Tonia . I've got some wonderful clothes . Let's go and have a close look at your outfit .", + "id": 14 + } +] \ No newline at end of file diff --git a/reccon/sources/te_28.json b/reccon/sources/te_28.json new file mode 100644 index 0000000000000000000000000000000000000000..c0ab947da30cdf6abd3b49323c11d19610777182 --- /dev/null +++ b/reccon/sources/te_28.json @@ -0,0 +1,202 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "we really were lucky . We got the last available table for two---and we didn't even have a reservation ! Did you see the long lines behind us ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "we really were lucky . We got the last available table for two---and we didn't even have a reservation !" + ], + "type": [ + "no-context" + ], + "text": "we really were lucky . We got the last available table for two---and we didn't even have a reservation ! Did you see the long lines behind us ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "yeah , I'm glad that we didn't have to wait long . I'm starving !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "we really were lucky . We got the last available table for two---and we didn't even have a reservation !", + "I'm glad that we didn't have to wait long . I'm starving !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "yeah , I'm glad that we didn't have to wait long . I'm starving !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "let's take a look at the menu so we can order . Do you want to choose an appetizer for us to share ?", + "emotion": "neutral", + "text": "let's take a look at the menu so we can order . Do you want to choose an appetizer for us to share ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "what would you rather have , samosas or poppadoms ?", + "emotion": "neutral", + "text": "what would you rather have , samosas or poppadoms ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I heard that one of their specialities is the samosa .", + "emotion": "neutral", + "text": "I heard that one of their specialities is the samosa .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "well , let's get a plate of those then .", + "emotion": "neutral", + "text": "well , let's get a plate of those then .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "sounds good . What are you going to have for your main course ?", + "emotion": "neutral", + "text": "sounds good . What are you going to have for your main course ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I think I might have a dahl .", + "emotion": "neutral", + "text": "I think I might have a dahl .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "what's in a dahl ?", + "emotion": "neutral", + "text": "what's in a dahl ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "it's got chickpeas and vegetables in a spicy curry sauce with rice .", + "emotion": "neutral", + "text": "it's got chickpeas and vegetables in a spicy curry sauce with rice .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "that sounds nice . Do you want to share some kebabs as well ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "Do you want to share some kebabs as well ?" + ], + "type": [ + "no-context" + ], + "text": "that sounds nice . Do you want to share some kebabs as well ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "ok . How about some lamb kebabs ?", + "emotion": "neutral", + "text": "ok . How about some lamb kebabs ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "that's my favourite . Do you want to have some wine or beer ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "ok . How about some lamb kebabs ?" + ], + "type": [ + "inter-personal" + ], + "text": "that's my favourite . Do you want to have some wine or beer ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "I think I'll have a beer .", + "emotion": "neutral", + "text": "I think I'll have a beer .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "ok , shall I flag down the waitress ?", + "emotion": "neutral", + "text": "ok , shall I flag down the waitress ?", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "I wouldn't recommend it . I think we should wait until she comes round .", + "emotion": "neutral", + "text": "I wouldn't recommend it . I think we should wait until she comes round .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "you're right . That might seem a bit rude . It's a good thing I've got you with me !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 16, + 17 + ], + "expanded emotion cause span": [ + "I think we should wait until she comes round .", + "It's a good thing I've got you with me !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "you're right . That might seem a bit rude . It's a good thing I've got you with me !", + "id": 17, + "source_sentences": [ + 15 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 18, + "speaker": "B", + "utterance": "what would you do without me ?", + "emotion": "neutral", + "text": "what would you do without me ?", + "id": 18 + } +] \ No newline at end of file diff --git a/reccon/sources/te_282.json b/reccon/sources/te_282.json new file mode 100644 index 0000000000000000000000000000000000000000..83b9f71d81d0019d8907175b1f2e613ad22b3d65 --- /dev/null +++ b/reccon/sources/te_282.json @@ -0,0 +1,168 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Welcome , how may I help you today ?", + "emotion": "neutral", + "text": "Welcome , how may I help you today ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'm ask for a pizza , please .", + "emotion": "neutral", + "text": "I'm ask for a pizza , please .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Then you will be happy to hear that today all our pizzas are on sale . Two for one .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "you will be happy to hear that today all our pizzas are on sale . Two for one ." + ], + "type": [ + "no-context" + ], + "text": "Then you will be happy to hear that today all our pizzas are on sale . Two for one .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "You're right , that is great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "you will be happy to hear that today all our pizzas are on sale . Two for one ." + ], + "type": [ + "inter-personal" + ], + "text": "You're right , that is great .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "What size would you like ?", + "emotion": "neutral", + "text": "What size would you like ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Medium one will be perfect , thank you", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "you will be happy to hear that today all our pizzas are on sale . Two for one ." + ], + "type": [ + "inter-personal" + ], + "text": "Medium one will be perfect , thank you", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Which kind do you want ?", + "emotion": "neutral", + "text": "Which kind do you want ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I like seafood on my pizza .", + "emotion": "neutral", + "text": "I like seafood on my pizza .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "We have two seafood pizzas . Tuna and crab .", + "emotion": "neutral", + "text": "We have two seafood pizzas . Tuna and crab .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Tuna sounds good today .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "We have two seafood pizzas . Tuna and crab .", + "Tuna sounds good today ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Tuna sounds good today .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Would that be for here or take away ?", + "emotion": "neutral", + "text": "Would that be for here or take away ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "That would be to go .", + "emotion": "neutral", + "text": "That would be to go .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "That'll be in a ten minutes . Please sit over there , and I'll call you over as sooner as it's ready .", + "emotion": "neutral", + "text": "That'll be in a ten minutes . Please sit over there , and I'll call you over as sooner as it's ready .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "No problem .", + "emotion": "happiness", + "explanation": "completion of order taking", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "That'll be in a ten minutes . Please sit over there , and I'll call you over as sooner as it's ready ." + ], + "type": [ + "inter-personal" + ], + "text": "No problem .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_315.json b/reccon/sources/te_315.json new file mode 100644 index 0000000000000000000000000000000000000000..aa59d8ebc12a60f1db7116951ce816e37dcbb655 --- /dev/null +++ b/reccon/sources/te_315.json @@ -0,0 +1,137 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "John , I was looking through some magazines for ideas about where we might go on vacation this year .", + "emotion": "neutral", + "text": "John , I was looking through some magazines for ideas about where we might go on vacation this year .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I've already told my buddy , Mark , that I am going hunting with him in Alaska .", + "emotion": "neutral", + "text": "I've already told my buddy , Mark , that I am going hunting with him in Alaska .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "You can't be serious !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I've already told my buddy , Mark , that I am going hunting with him in Alaska ." + ], + "type": [ + "inter-personal" + ], + "text": "You can't be serious !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Hey , I've always gone hunting or fishing on vacation . I am sorry that bothers you .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "You can't be serious !" + ], + "type": [ + "inter-personal" + ], + "text": "Hey , I've always gone hunting or fishing on vacation . I am sorry that bothers you .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "After a year together , I thought it pretty safe to assume that we would automatically spend our vacation together .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I've already told my buddy , Mark , that I am going hunting with him in Alaska ." + ], + "type": [ + "inter-personal" + ], + "text": "After a year together , I thought it pretty safe to assume that we would automatically spend our vacation together .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Says who ? I don't think that is necessarily the case .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 3, + 5, + 6 + ], + "expanded emotion cause span": [ + "You can't be serious !", + "After a year together , I thought it pretty safe to assume that we would automatically spend our vacation together .", + "I don't think that is necessarily the case" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Says who ? I don't think that is necessarily the case .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You know , now that I think about it , I really don't have much more to say to you at all !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 2, + 6 + ], + "expanded emotion cause span": [ + "I've already told my buddy , Mark , that I am going hunting with him in Alaska .", + "Says who ? I don't think that is necessarily the case ." + ], + "type": [ + "inter-personal" + ], + "text": "You know , now that I think about it , I really don't have much more to say to you at all !", + "id": 7, + "source_sentences": [ + 1, + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Whatever you say !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 3, + 5, + 6 + ], + "expanded emotion cause span": [ + "You can't be serious !", + "After a year together , I thought it pretty safe to assume that we would automatically spend our vacation together .", + "I don't think that is necessarily the case" + ], + "type": [ + "hybrid" + ], + "text": "Whatever you say !", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/te_335.json b/reccon/sources/te_335.json new file mode 100644 index 0000000000000000000000000000000000000000..6e908b175618302523d07509099538febfc6977b --- /dev/null +++ b/reccon/sources/te_335.json @@ -0,0 +1,170 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What do you think about this store ? I heard it ' s a posh store that ' s only got branches in big cities .", + "emotion": "neutral", + "text": "What do you think about this store ? I heard it ' s a posh store that ' s only got branches in big cities .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I love this store . The only problem is that it ' s extremely expensive .", + "emotion": "neutral", + "text": "I love this store . The only problem is that it ' s extremely expensive .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Don ' t worry . I ' Ve decided that for your birthday I ' m going to take you shopping for a new dress .", + "emotion": "neutral", + "text": "Don ' t worry . I ' Ve decided that for your birthday I ' m going to take you shopping for a new dress .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Really ? I thought you hated shopping ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "for your birthday I ' m going to take you shopping for a new dress .", + "you hated shopping ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Really ? I thought you hated shopping ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I do , that ' s why you should appreciate this gift !", + "emotion": "neutral", + "text": "I do , that ' s why you should appreciate this gift !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Sure . That ' s really nice of you . Let ' s go in and try some things on .", + "emotion": "neutral", + "text": "Sure . That ' s really nice of you . Let ' s go in and try some things on .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "How about this red dress ? I think it would really suit you .", + "emotion": "neutral", + "text": "How about this red dress ? I think it would really suit you .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That ' s gorgeous ! Do they have it in a size 8 ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "That ' s gorgeous !" + ], + "type": [ + "no-context" + ], + "text": "That ' s gorgeous ! Do they have it in a size 8 ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Here you go . On any other day , it would cost me a fortune , but it ' s on special offer today .", + "emotion": "neutral", + "text": "Here you go . On any other day , it would cost me a fortune , but it ' s on special offer today .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I think this color isn ' t quite right for me . Do they have the same dress in white ?", + "emotion": "neutral", + "text": "I think this color isn ' t quite right for me . Do they have the same dress in white ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Let me look . Let ' s see ... they ' Ve got one in blue , green , pink , black ... and white . Here you are .", + "emotion": "neutral", + "text": "Let me look . Let ' s see ... they ' Ve got one in blue , green , pink , black ... and white . Here you are .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "This is perfect ! What do you think ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "This is perfect" + ], + "type": [ + "no-context" + ], + "text": "This is perfect ! What do you think ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I think you look fantastic . Happy Birthday !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "I think you look fantastic . Happy Birthday !" + ], + "type": [ + "no-context" + ], + "text": "I think you look fantastic . Happy Birthday !", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "I ' m so lucky . You only get a chance like this once in a blue moon ! Thanks honey !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13, + 14 + ], + "expanded emotion cause span": [ + "I think you look fantastic . Happy Birthday !", + "I ' m so lucky . You only get a chance like this once in a blue moon ! Thanks honey !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I ' m so lucky . You only get a chance like this once in a blue moon ! Thanks honey !", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_352.json b/reccon/sources/te_352.json new file mode 100644 index 0000000000000000000000000000000000000000..4befd46dc6a5bff38c5e265baf88c3d09f835ef7 --- /dev/null +++ b/reccon/sources/te_352.json @@ -0,0 +1,143 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey , look , there is a circus show over there .", + "emotion": "neutral", + "text": "Hey , look , there is a circus show over there .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'm not in the mood .", + "emotion": "neutral", + "text": "I'm not in the mood .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "It's the circus .", + "emotion": "neutral", + "text": "It's the circus .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I don't want to sit there and watch them torturing the animals .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "circus .", + "I don't want to sit there and watch them torturing the animals ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I don't want to sit there and watch them torturing the animals .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Oh , come on , they give them treat too . Oh , look , that little monkey is so cute .", + "emotion": "neutral", + "text": "Oh , come on , they give them treat too . Oh , look , that little monkey is so cute .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Cute ? Hope so .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "that little monkey is so cute ." + ], + "type": [ + "inter-personal" + ], + "text": "Cute ? Hope so .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Oh , it is coming to us , come on , Ben , get a banana to it .", + "emotion": "neutral", + "text": "Oh , it is coming to us , come on , Ben , get a banana to it .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Me ? No way , keep him away from me , please .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Oh , it is coming to us , come on , Ben , get a banana to it ." + ], + "type": [ + "inter-personal" + ], + "text": "Me ? No way , keep him away from me , please .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Why are you acting so strange today ?", + "emotion": "neutral", + "text": "Why are you acting so strange today ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I've said that I've got a problem with the circus . I'm not kidding .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "I've got a problem with the circus ." + ], + "type": [ + "no-context" + ], + "text": "I've said that I've got a problem with the circus . I'm not kidding .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "That's weird !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "I've said that I've got a problem with the circus . I'm not kidding ." + ], + "type": [ + "inter-personal" + ], + "text": "That's weird !", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_361.json b/reccon/sources/te_361.json new file mode 100644 index 0000000000000000000000000000000000000000..1e0e6948be9cdf71f934bf20ffcd4d44939f0eec --- /dev/null +++ b/reccon/sources/te_361.json @@ -0,0 +1,168 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Can I have my check , please .", + "emotion": "neutral", + "text": "Can I have my check , please .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Here it is . 350 Yuan all together .", + "emotion": "neutral", + "text": "Here it is . 350 Yuan all together .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "May son adores my new hairstyle so I suppose it is worth it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "May son adores my new hairstyle" + ], + "type": [ + "no-context" + ], + "text": "May son adores my new hairstyle so I suppose it is worth it .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Hearing you say that is a big reward for us . And here is the receipt .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "May son adores my new hairstyle so I suppose it is worth it .", + "Hearing you say that is a big reward for us ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Hearing you say that is a big reward for us . And here is the receipt .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Thank you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Hearing you say that is a big reward for us . And here is the receipt ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Wait ! Congratulations ! You are the lucky customer of our anniversary celebration .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "You are the lucky customer of our anniversary celebration ." + ], + "type": [ + "no-context" + ], + "text": "Wait ! Congratulations ! You are the lucky customer of our anniversary celebration .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Wow , it's surprising . So what do I get ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Congratulations ! You are the lucky customer of our anniversary celebration ." + ], + "type": [ + "inter-personal" + ], + "text": "Wow , it's surprising . So what do I get ?", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "You can have a free facial and then make up free for you . Do you want it now ?", + "emotion": "neutral", + "text": "You can have a free facial and then make up free for you . Do you want it now ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Probably not . Doing that will probably take another three hours which I can't afford now .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Probably not . Doing that will probably take another three hours which I can't afford now ." + ], + "type": [ + "no-context" + ], + "text": "Probably not . Doing that will probably take another three hours which I can't afford now .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Here is our number . Call us when you are ready to come .", + "emotion": "neutral", + "text": "Here is our number . Call us when you are ready to come .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "You mean I should make an appointment ahead of time ?", + "emotion": "neutral", + "text": "You mean I should make an appointment ahead of time ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Yes .", + "emotion": "neutral", + "text": "Yes .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Got it . Bye for now .", + "emotion": "neutral", + "text": "Got it . Bye for now .", + "id": 13 + } +] \ No newline at end of file diff --git a/reccon/sources/te_41.json b/reccon/sources/te_41.json new file mode 100644 index 0000000000000000000000000000000000000000..74a197d3393fd5d4079d5d4510076394d3007483 --- /dev/null +++ b/reccon/sources/te_41.json @@ -0,0 +1,187 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Listen , Karen , I need your help . I don't know anyone here yet .", + "emotion": "neutral", + "text": "Listen , Karen , I need your help . I don't know anyone here yet .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'm glad to help you . What's wrong ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I'm glad to help you" + ], + "type": [ + "no-context" + ], + "text": "I'm glad to help you . What's wrong ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "My mother-in-law just went into the hospital in L . A . Hank and I will be flying there tonight .", + "emotion": "neutral", + "text": "My mother-in-law just went into the hospital in L . A . Hank and I will be flying there tonight .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I'm sorry to hear it . What's wrong with her ?", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "My mother-in-law just went into the hospital in L . A ." + ], + "type": [ + "inter-personal" + ], + "text": "I'm sorry to hear it . What's wrong with her ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Doctors aren't sure yet . But the real problem is Suzy . She has a bad cold , and we don't want to take her with us . But we don't know who can stay with her .", + "emotion": "neutral", + "text": "Doctors aren't sure yet . But the real problem is Suzy . She has a bad cold , and we don't want to take her with us . But we don't know who can stay with her .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "You need a babysitter .", + "emotion": "neutral", + "text": "You need a babysitter .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yes , I'd ask Jill , the girl I've had before , but I need someone overnight . Maybe even for two nights .", + "emotion": "neutral", + "text": "Yes , I'd ask Jill , the girl I've had before , but I need someone overnight . Maybe even for two nights .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I could have Suzy stay at my place .", + "emotion": "neutral", + "text": "I could have Suzy stay at my place .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I don't want to do that to you , Karen .", + "emotion": "neutral", + "text": "I don't want to do that to you , Karen .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Why not ?", + "emotion": "neutral", + "text": "Why not ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Your own kids would get Suzy's cold . I think it would be better to have a good babysitter here . But I don't know who to ask . I need someone more mature than Jill . It might even be for two or three days .", + "emotion": "neutral", + "text": "Your own kids would get Suzy's cold . I think it would be better to have a good babysitter here . But I don't know who to ask . I need someone more mature than Jill . It might even be for two or three days .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I know who we can ask . There is a girl I know , Sara Ralston . She is 17 , and she will usually take this kind of job . I know her from my church , and I trust her completely .", + "emotion": "neutral", + "text": "I know who we can ask . There is a girl I know , Sara Ralston . She is 17 , and she will usually take this kind of job . I know her from my church , and I trust her completely .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I'd like to talk with her . This is short notice , I know . But Hank and I are leaving tonight .", + "emotion": "neutral", + "text": "I'd like to talk with her . This is short notice , I know . But Hank and I are leaving tonight .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "I'll get you her number . I hope she can do it . She is very responsible .", + "emotion": "neutral", + "text": "I'll get you her number . I hope she can do it . She is very responsible .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "I'm glad you know someone . I knew you would be the best person to ask about this . I don't want to insult Jill or her mother . I think Jill maybe could do it . But I'd rather have someone a little older .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12, + 14 + ], + "expanded emotion cause span": [ + "There is a girl I know , Sara Ralston . She is 17 , and she will usually take this kind of job . I know her from my church , and I trust her completely .", + "I hope she can do it . She is very responsible ." + ], + "type": [ + "inter-personal" + ], + "text": "I'm glad you know someone . I knew you would be the best person to ask about this . I don't want to insult Jill or her mother . I think Jill maybe could do it . But I'd rather have someone a little older .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "I'll go home and get Sara's number . I'll call her first myself .", + "emotion": "neutral", + "text": "I'll go home and get Sara's number . I'll call her first myself .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "Great . Then call me and let me know if she's free .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12, + 14, + 16 + ], + "expanded emotion cause span": [ + "There is a girl I know , Sara Ralston . She is 17 , and she will usually take this kind of job . I know her from my church , and I trust her completely .", + "I hope she can do it . She is very responsible .", + "I'll go home and get Sara's number . I'll call her first myself ." + ], + "type": [ + "inter-personal" + ], + "text": "Great . Then call me and let me know if she's free .", + "id": 17, + "source_sentences": [ + 11, + 13, + 15 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_435.json b/reccon/sources/te_435.json new file mode 100644 index 0000000000000000000000000000000000000000..5b7c4f6bd9ef40bafaae16e1283812ed383a8259 --- /dev/null +++ b/reccon/sources/te_435.json @@ -0,0 +1,142 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey Julie , you want to go grab something to eat ?", + "emotion": "neutral", + "text": "Hey Julie , you want to go grab something to eat ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Sure ! What do you feel like having ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "you want to go grab something to eat ?" + ], + "type": [ + "inter-personal" + ], + "text": "Sure ! What do you feel like having ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I really feel like having a big juicy steak !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "Sure !", + "feel like having a big juicy steak !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I really feel like having a big juicy steak !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Oh . OK . I don't eat meat , but that's fine , I am sure wherever we are going they will have other options right ?", + "emotion": "neutral", + "text": "Oh . OK . I don't eat meat , but that's fine , I am sure wherever we are going they will have other options right ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I didn't know you were a vegetarian !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "I don't eat meat ,", + "I didn't know you were a vegetarian !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I didn't know you were a vegetarian !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I'm not , I am a vegan .", + "emotion": "neutral", + "text": "I'm not , I am a vegan .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "A what ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 4, + 5, + 6 + ], + "expanded emotion cause span": [ + "I don't eat meat ,", + "I didn't know you were a vegetarian !", + "I am a vegan ." + ], + "type": [ + "hybrid" + ], + "text": "A what ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "A vegan . I don't eat or use any animal based products . I don't wear leather , eat eggs , drink milk or anything that comes from an animal . I used to be a pescatarian before , which basically means you don't eat meat , but still have fish and seafood .", + "emotion": "neutral", + "text": "A vegan . I don't eat or use any animal based products . I don't wear leather , eat eggs , drink milk or anything that comes from an animal . I used to be a pescatarian before , which basically means you don't eat meat , but still have fish and seafood .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Wow ! That's interesting ! It must be tough !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I don't eat or use any animal based products . I don't wear leather , eat eggs , drink milk or anything that comes from an animal ." + ], + "type": [ + "inter-personal" + ], + "text": "Wow ! That's interesting ! It must be tough !", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "It's a bit difficult to find vegetarian friendly restaurants sometimes , but since more and more people are vegetarians or vegans nowadays , it's getting a bit less difficult .", + "emotion": "neutral", + "text": "It's a bit difficult to find vegetarian friendly restaurants sometimes , but since more and more people are vegetarians or vegans nowadays , it's getting a bit less difficult .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/te_469.json b/reccon/sources/te_469.json new file mode 100644 index 0000000000000000000000000000000000000000..8893c2b6d42d637df4b14c11ea6f456b520c4952 --- /dev/null +++ b/reccon/sources/te_469.json @@ -0,0 +1,129 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Excuse me , are you Mrs . Green from England ?", + "emotion": "neutral", + "text": "Excuse me , are you Mrs . Green from England ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , I am .", + "emotion": "neutral", + "text": "Yes , I am .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I'm pleased to meet you , Mrs . Green . My name is Myra . I work in Beijing Institute of Technology . I came here to meet you .", + "emotion": "neutral", + "text": "I'm pleased to meet you , Mrs . Green . My name is Myra . I work in Beijing Institute of Technology . I came here to meet you .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "How do you do ?", + "emotion": "neutral", + "text": "How do you do ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "How do you do ?", + "emotion": "neutral", + "text": "How do you do ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "It's kind of you to meet me at the airport .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "meet me at the airport ." + ], + "type": [ + "no-context" + ], + "text": "It's kind of you to meet me at the airport .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Welcome to Beijing . Is this your first time in China ?", + "emotion": "neutral", + "text": "Welcome to Beijing . Is this your first time in China ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "No , I have visited China several times , but it's my first visit to Beijing and I think it's a great honor to be invited to your beautiful city .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "a great honor to be invited to your beautiful city ." + ], + "type": [ + "no-context" + ], + "text": "No , I have visited China several times , but it's my first visit to Beijing and I think it's a great honor to be invited to your beautiful city .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "It's our pleasure to have you here . I hope you will have a pleasant stay here .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "a great honor to be invited to your beautiful city .", + "It's our pleasure to have you here ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It's our pleasure to have you here . I hope you will have a pleasant stay here .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Thank you . I'm sure I will have a wonderful time here .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "It's our pleasure to have you here . I hope you will have a pleasant stay here .", + "I'm sure I will have a wonderful time here ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you . I'm sure I will have a wonderful time here .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_478.json b/reccon/sources/te_478.json new file mode 100644 index 0000000000000000000000000000000000000000..bf0b2a70f1fac4ae6bda6b95b1d5c86a438b1d93 --- /dev/null +++ b/reccon/sources/te_478.json @@ -0,0 +1,112 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello , sir , what can I do for you today ?", + "emotion": "neutral", + "text": "Hello , sir , what can I do for you today ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hello , I need a new suit . I have an important interview next week , so I really need to look sharp .", + "emotion": "neutral", + "text": "Hello , I need a new suit . I have an important interview next week , so I really need to look sharp .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "No problem ! We have a broad selection of suits , all tailored made so that it will fit perfectly .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I need a new suit" + ], + "type": [ + "inter-personal" + ], + "text": "No problem ! We have a broad selection of suits , all tailored made so that it will fit perfectly .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Great ! I want a three piece suit , preferably made from Italian cashmere or wool .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "a broad selection of suits , all tailored made so that it will fit perfectly ." + ], + "type": [ + "inter-personal" + ], + "text": "Great ! I want a three piece suit , preferably made from Italian cashmere or wool .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Very well sir . Would you like to have some shirts made also ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I need a new suit" + ], + "type": [ + "inter-personal" + ], + "text": "Very well sir . Would you like to have some shirts made also ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Sure . I ' ll also take some silver cuff link and a pair of silk ties .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Would you like to have some shirts made also ?" + ], + "type": [ + "inter-personal" + ], + "text": "Sure . I ' ll also take some silver cuff link and a pair of silk ties .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Very good . Now , if you will accompany me , we can take your measurements and choose the patterns for your suit and shirts .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 6 + ], + "expanded emotion cause span": [ + "I need a new suit", + "Sure . I ' ll also take some silver cuff link and a pair of silk ties ." + ], + "type": [ + "inter-personal" + ], + "text": "Very good . Now , if you will accompany me , we can take your measurements and choose the patterns for your suit and shirts .", + "id": 7, + "source_sentences": [ + 1, + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_501.json b/reccon/sources/te_501.json new file mode 100644 index 0000000000000000000000000000000000000000..a54d8659beb94d9409440500445a91d924f4bcd7 --- /dev/null +++ b/reccon/sources/te_501.json @@ -0,0 +1,119 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "This Olympic park is so big !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "This Olympic park is so big !" + ], + "type": [ + "no-context" + ], + "text": "This Olympic park is so big !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes . Now we are in the Olympic stadium , the center of this park .", + "emotion": "neutral", + "text": "Yes . Now we are in the Olympic stadium , the center of this park .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Splendid ! When is it gonna be finished ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "This Olympic park is so big !", + "we are in the Olympic stadium , the center of this park ." + ], + "type": [ + "hybrid" + ], + "text": "Splendid ! When is it gonna be finished ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "The whole stadium is to be finished this June .", + "emotion": "neutral", + "text": "The whole stadium is to be finished this June .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "How many seats are there in the stand ?", + "emotion": "neutral", + "text": "How many seats are there in the stand ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Oh , there are 5000 seats in total .", + "emotion": "neutral", + "text": "Oh , there are 5000 seats in total .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I didn ' t know it would be so big !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "there are 5000 seats", + "I didn ' t know it would be so big !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I didn ' t know it would be so big !", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "It is ! Look there , those are the tracks . And the jumping pit is over there .", + "emotion": "neutral", + "text": "It is ! Look there , those are the tracks . And the jumping pit is over there .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Ah ... I see . Hey , look the sign here , No climbing .", + "emotion": "neutral", + "text": "Ah ... I see . Hey , look the sign here , No climbing .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "We put many signs with English translations for foreign visitors .", + "emotion": "neutral", + "text": "We put many signs with English translations for foreign visitors .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/te_52.json b/reccon/sources/te_52.json new file mode 100644 index 0000000000000000000000000000000000000000..0f98b6993752a60cdeaf449e1c4eb3ac66fd9534 --- /dev/null +++ b/reccon/sources/te_52.json @@ -0,0 +1,160 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Take a seat inside and see what you think . So you will take the Porsche then , sir ?", + "emotion": "neutral", + "text": "Take a seat inside and see what you think . So you will take the Porsche then , sir ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , and I want to buy the insurance too . I think it's necessary .", + "emotion": "neutral", + "text": "Yes , and I want to buy the insurance too . I think it's necessary .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "You're smart to buy it . At 45 dollars for three days , it is a good deal .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 3 + ], + "expanded emotion cause span": [ + "will take the Porsche", + "and I want to buy the insurance too . I think it's necessary", + "You're smart to buy it . At 45 dollars for three days , it is a good deal ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "You're smart to buy it . At 45 dollars for three days , it is a good deal .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Can I return the car in San Francisco ?", + "emotion": "neutral", + "text": "Can I return the car in San Francisco ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "San Francisco ? No , sir . We only have this office here . You will have to return it here .", + "emotion": "neutral", + "text": "San Francisco ? No , sir . We only have this office here . You will have to return it here .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Really ? I heard in America you can return rental cars in different cities .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "No , sir . We only have this office here . You will have to return it here .", + "I heard in America you can return rental cars in different cities ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Really ? I heard in America you can return rental cars in different cities .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "No , sir . That's only with the very big companies . I'm sorry , but this car must be returned to this lot .", + "emotion": "neutral", + "text": "No , sir . That's only with the very big companies . I'm sorry , but this car must be returned to this lot .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Well , I guess I will have to drive back down then . Hmm . I didn't think of that .", + "emotion": "neutral", + "text": "Well , I guess I will have to drive back down then . Hmm . I didn't think of that .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Do you still want the car , sir ?", + "emotion": "neutral", + "text": "Do you still want the car , sir ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Yes . It will be fun . Driving back down the coast . My girlfriend will like it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "It will be fun . Driving back down the coast . My girlfriend will like it ." + ], + "type": [ + "no-context" + ], + "text": "Yes . It will be fun . Driving back down the coast . My girlfriend will like it .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "It's a beautiful drive .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10, + 11 + ], + "expanded emotion cause span": [ + "Do you still want the car ,", + "Yes . It will be fun . Driving back down the coast . My girlfriend will like it .", + "It's a beautiful drive ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "It's a beautiful drive .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Where are the keys ?", + "emotion": "neutral", + "text": "Where are the keys ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Just a moment , sir . We have to finish filling out the forms .", + "emotion": "neutral", + "text": "Just a moment , sir . We have to finish filling out the forms .", + "id": 13 + } +] \ No newline at end of file diff --git a/reccon/sources/te_532.json b/reccon/sources/te_532.json new file mode 100644 index 0000000000000000000000000000000000000000..6357c8d6f73195aa7538d8eb09038178578a0460 --- /dev/null +++ b/reccon/sources/te_532.json @@ -0,0 +1,174 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "that was a really good meal , Gordon .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "really good meal" + ], + "type": [ + "no-context" + ], + "text": "that was a really good meal , Gordon .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It sure was . I couldn't eat another bite .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "It sure was . I couldn't eat another bite ." + ], + "type": [ + "no-context" + ], + "text": "It sure was . I couldn't eat another bite .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "well , it is getting pretty late . I think we should go home .", + "emotion": "neutral", + "text": "well , it is getting pretty late . I think we should go home .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "you're right . I have to get up early to go to work tomorrow .", + "emotion": "neutral", + "text": "you're right . I have to get up early to go to work tomorrow .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "let's see how much the bill is .", + "emotion": "neutral", + "text": "let's see how much the bill is .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "don't worry about it . Tonight is my treat .", + "emotion": "neutral", + "text": "don't worry about it . Tonight is my treat .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "what are you talking about ? We'll split the bill .", + "emotion": "neutral", + "text": "what are you talking about ? We'll split the bill .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "no , I insist . I kept telling you that I would treat you to dinner but I still haven't .", + "emotion": "neutral", + "text": "no , I insist . I kept telling you that I would treat you to dinner but I still haven't .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "no way , Gordon . I know that you are a little short on cash at the moment . There's no need for you to pay for the whole bill .", + "emotion": "neutral", + "text": "no way , Gordon . I know that you are a little short on cash at the moment . There's no need for you to pay for the whole bill .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "alright , if that's the way you are going to be , we'll split the bill .", + "emotion": "neutral", + "text": "alright , if that's the way you are going to be , we'll split the bill .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "that's better . This way we will both have money to take a cab home , otherwise , you would probably have to walk .", + "emotion": "neutral", + "text": "that's better . This way we will both have money to take a cab home , otherwise , you would probably have to walk .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "just promise you will let me treat you to dinner next week , ok ?", + "emotion": "neutral", + "text": "just promise you will let me treat you to dinner next week , ok ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "you've got a deal .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "promise you will let me treat you to dinner next week" + ], + "type": [ + "inter-personal" + ], + "text": "you've got a deal .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "great . Bye .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 13 + ], + "expanded emotion cause span": [ + "I kept telling you that I would treat you to dinner but I still haven't .", + "you've got a deal ." + ], + "type": [ + "hybrid" + ], + "text": "great . Bye .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "bye .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "promise you will let me treat you to dinner next week" + ], + "type": [ + "inter-personal" + ], + "text": "bye .", + "id": 15, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_534.json b/reccon/sources/te_534.json new file mode 100644 index 0000000000000000000000000000000000000000..b86de83f1f3be2e28343e1ff030dc531788c3ff6 --- /dev/null +++ b/reccon/sources/te_534.json @@ -0,0 +1,195 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "This looks like a very nice house .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "This looks like a very nice house ." + ], + "type": [ + "no-context" + ], + "text": "This looks like a very nice house .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "You know , I fell in love with this house the first moment I laid eyes on it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I fell in love with this house the first moment I laid eyes on it ." + ], + "type": [ + "no-context" + ], + "text": "You know , I fell in love with this house the first moment I laid eyes on it .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "The style of the exterior is just what I ' Ve been looking for !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "The style of the exterior is just what I ' Ve been looking for !" + ], + "type": [ + "no-context" + ], + "text": "The style of the exterior is just what I ' Ve been looking for !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "The exterior is only half of the story . The interior is incredible .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 4 + ], + "expanded emotion cause span": [ + "I fell in love with this house the first moment I laid eyes on it .", + "The exterior is only half of the story . The interior is incredible ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "The exterior is only half of the story . The interior is incredible .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "This home is gorgeous on the inside !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "This home is gorgeous on the inside !" + ], + "type": [ + "no-context" + ], + "text": "This home is gorgeous on the inside !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Everything that you see on the walls , floors , and windows is brand new .", + "emotion": "neutral", + "text": "Everything that you see on the walls , floors , and windows is brand new .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "The wall colors totally suit the style of this house .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6, + 7 + ], + "expanded emotion cause span": [ + "This home is gorgeous on the inside !", + "Everything that you see on the walls , floors , and windows is brand new .", + "The wall colors totally suit the style of this house ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "The wall colors totally suit the style of this house .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Straight ahead is the gourmet kitchen .", + "emotion": "neutral", + "text": "Straight ahead is the gourmet kitchen .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I love the bamboo flooring and granite countertops .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "I love the bamboo flooring and granite countertops ." + ], + "type": [ + "no-context" + ], + "text": "I love the bamboo flooring and granite countertops .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "The master suite is the best . Let ' s go look at that next .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "I love the bamboo flooring and granite countertops .", + "The master suite is the best ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "The master suite is the best . Let ' s go look at that next .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 11, + "speaker": "A", + "utterance": "There is plenty of room for our king-sized bed , and I love the light in this room .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "There is plenty of room for our king-sized bed , and I love the light in this room ." + ], + "type": [ + "no-context" + ], + "text": "There is plenty of room for our king-sized bed , and I love the light in this room .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I know that you like this house , but let ' s take a look at the others before you make up your mind .", + "emotion": "neutral", + "text": "I know that you like this house , but let ' s take a look at the others before you make up your mind .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/te_58.json b/reccon/sources/te_58.json new file mode 100644 index 0000000000000000000000000000000000000000..b798c83cd57632a7ce24ace5f32c4d32f3252116 --- /dev/null +++ b/reccon/sources/te_58.json @@ -0,0 +1,138 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I have a cell phone in my car . Now it's probably on the floor on the passenger side . Why don't you get it for me , and then I can call the police ?", + "emotion": "neutral", + "text": "I have a cell phone in my car . Now it's probably on the floor on the passenger side . Why don't you get it for me , and then I can call the police ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Alright .", + "emotion": "neutral", + "text": "Alright .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "It doesn't work . It looks like it's broken . I need to get to a hospital . You should drive me there .", + "emotion": "fear", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "It doesn't work . It looks like it's broken ." + ], + "type": [ + "no-context" + ], + "text": "It doesn't work . It looks like it's broken . I need to get to a hospital . You should drive me there .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Oh , yeah ? It's better if we make a police report first . Then you can go to the hospital .", + "emotion": "neutral", + "text": "Oh , yeah ? It's better if we make a police report first . Then you can go to the hospital .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Damn it ! I'm injured here . We could wait all day for the police .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "It's better if we make a police report first ." + ], + "type": [ + "inter-personal" + ], + "text": "Damn it ! I'm injured here . We could wait all day for the police .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Well , you'll just have to wait . I'm not going to move my car until the police arrive . I'll go into one of those houses over there and use their phone . Don't worry . You'll get to the hospital in time .", + "emotion": "neutral", + "text": "Well , you'll just have to wait . I'm not going to move my car until the police arrive . I'll go into one of those houses over there and use their phone . Don't worry . You'll get to the hospital in time .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "It really hurts .", + "emotion": "neutral", + "text": "It really hurts .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yes , maybe it does . But if you're going to drive like you did just now , you will have to get used to a little physical pain . You know what I mean ?", + "emotion": "neutral", + "text": "Yes , maybe it does . But if you're going to drive like you did just now , you will have to get used to a little physical pain . You know what I mean ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "To hell with you . The accident was your fault .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "if you're going to drive like you did just now , you will have to get used to a little physical pain .", + "The accident was your fault ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "To hell with you . The accident was your fault .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I'm afraid it wasn't . And when the police get here , you will also see that it wasn't . But enough of this bickering . I'm going to go find a phone . Don ' t move that arm while I'm gone . Alright ?", + "emotion": "neutral", + "text": "I'm afraid it wasn't . And when the police get here , you will also see that it wasn't . But enough of this bickering . I'm going to go find a phone . Don ' t move that arm while I'm gone . Alright ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "To hell with you .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 8, + 9, + 10 + ], + "expanded emotion cause span": [ + "if you're going to drive like you did just now , you will have to get used to a little physical pain .", + "The accident was your fault .", + "I'm afraid it wasn't . And when the police get here , you will also see that it wasn't . But enough of this bickering . I'm going to go find a phone . Don ' t move that arm while I'm gone . Alright ?" + ], + "type": [ + "hybrid" + ], + "text": "To hell with you .", + "id": 11 + } +] \ No newline at end of file diff --git a/reccon/sources/te_598.json b/reccon/sources/te_598.json new file mode 100644 index 0000000000000000000000000000000000000000..0c54b177ba1375b44acd4728f13d660548351e35 --- /dev/null +++ b/reccon/sources/te_598.json @@ -0,0 +1,173 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Good morning ! I am a new comer in our office .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Good morning ! I am a new comer in our office ." + ], + "type": [ + "no-context" + ], + "text": "Good morning ! I am a new comer in our office .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Good morning ! Welcome to our office !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 2 + ], + "expanded emotion cause span": [ + "I am a new comer in our office .", + "Good morning !", + "Welcome" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Good morning ! Welcome to our office !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Nice to meet you ! My name is Grace Williams .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "Welcome", + "Nice to meet you !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Nice to meet you ! My name is Grace Williams .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Nice to meet you too ! I am Peter Smith .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3, + 4 + ], + "expanded emotion cause span": [ + "I am a new comer in our office .", + "Nice to meet you !", + "Nice to meet you" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Nice to meet you too ! I am Peter Smith .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Today is my first day at work !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 4, + 5 + ], + "expanded emotion cause span": [ + "Good morning ! I am a new comer in our office .", + "Nice to meet you", + "Today is my first day at work !" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Today is my first day at work !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Well , hope you will enjoy your first day ! Just ask me if you need any help .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 5, + 6 + ], + "expanded emotion cause span": [ + "I am a new comer in our office .", + "Today is my first day at work !", + "hope you will enjoy your first day !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Well , hope you will enjoy your first day ! Just ask me if you need any help .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Thank you . It's very kind of you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 6, + 6 + ], + "expanded emotion cause span": [ + "Good morning ! I am a new comer in our office .", + "hope you will enjoy your first day !", + "ask me if you need any help ." + ], + "type": [ + "hybrid" + ], + "text": "Thank you . It's very kind of you .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "You are welcome .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 7 + ], + "expanded emotion cause span": [ + "I am a new comer in our office .", + "It's very kind of you ." + ], + "type": [ + "inter-personal" + ], + "text": "You are welcome .", + "id": 8, + "source_sentences": [ + 0, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_601.json b/reccon/sources/te_601.json new file mode 100644 index 0000000000000000000000000000000000000000..93aba593b6cdb1583d8e7978984e54ae51c27e16 --- /dev/null +++ b/reccon/sources/te_601.json @@ -0,0 +1,93 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Do you have anything to do after this ?", + "emotion": "neutral", + "text": "Do you have anything to do after this ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "No , I don't .", + "emotion": "neutral", + "text": "No , I don't .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Shall we drop in somewhere for a couple of drinks ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "Do you have anything to do after this ?", + "No , I don't ." + ], + "type": [ + "hybrid" + ], + "text": "Shall we drop in somewhere for a couple of drinks ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "That sounds like a good idea .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "drop in somewhere for a couple of drinks ?" + ], + "type": [ + "inter-personal" + ], + "text": "That sounds like a good idea .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I know a very interesting place .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "good idea ." + ], + "type": [ + "inter-personal" + ], + "text": "I know a very interesting place .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Oh , do you ? Good .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I know a very interesting place ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , do you ? Good .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_604.json b/reccon/sources/te_604.json new file mode 100644 index 0000000000000000000000000000000000000000..058d2d7253be6c208590048368596da693b1748f --- /dev/null +++ b/reccon/sources/te_604.json @@ -0,0 +1,157 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Please help yourself to whatever you like , don't be shy .", + "emotion": "happiness", + "explanation": "From the context, assuming A is treating B in a restaurant.", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Please help yourself to whatever you like , don't be shy .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , thank you . I've already been helping myself .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "Please help yourself to whatever you like", + "I've already been helping myself ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , thank you . I've already been helping myself .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "This dish taste terrific . Would you like to try a little ? It is a little hot , but very good .", + "emotion": "happiness", + "explanation": "Did not include \"It is a little hot\" here", + "expanded emotion cause evidence": [ + 3, + 3 + ], + "expanded emotion cause span": [ + "This dish taste terrific .", + "very good ." + ], + "type": [ + "no-context" + ], + "text": "This dish taste terrific . Would you like to try a little ? It is a little hot , but very good .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I like hot food , especially Sichuan cuisine .", + "emotion": "happiness", + "explanation": "Including \"It is a little hot\" as I find evidence of B liking hot food.", + "expanded emotion cause evidence": [ + 3, + 3, + 4 + ], + "expanded emotion cause span": [ + "This dish taste terrific .", + "It is a little hot , but very good .", + "I like hot food" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I like hot food , especially Sichuan cuisine .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Would you like another beer ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 3, + 4 + ], + "expanded emotion cause span": [ + "This dish taste terrific .", + "very good .", + "I like hot food" + ], + "type": [ + "hybrid" + ], + "text": "Would you like another beer ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I'll have another cup of beer insist . I know I don't like to drink alone , especially there are someone sitting there next to me .", + "emotion": "neutral", + "text": "I'll have another cup of beer insist . I know I don't like to drink alone , especially there are someone sitting there next to me .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Come on , it's the weekend . Let's taste and enjoy this meal . Cheers !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "it's the weekend . Let's taste and enjoy this meal ." + ], + "type": [ + "no-context" + ], + "text": "Come on , it's the weekend . Let's taste and enjoy this meal . Cheers !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Bottom's up , and you're right . This meal is incredible . I wish I had known this restaurant before . Thanks for bringing me here . I know I'll be back agile soon .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8, + 8 + ], + "expanded emotion cause span": [ + "it's the weekend . Let's taste and enjoy this meal .", + "This meal is incredible .", + "Thanks for bringing me here ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Bottom's up , and you're right . This meal is incredible . I wish I had known this restaurant before . Thanks for bringing me here . I know I'll be back agile soon .", + "id": 8, + "source_sentences": [ + 6, + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_612.json b/reccon/sources/te_612.json new file mode 100644 index 0000000000000000000000000000000000000000..ee3b0a87adf6b916ab48e0ee6f9ea6453382072c --- /dev/null +++ b/reccon/sources/te_612.json @@ -0,0 +1,151 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Whew ! I had to wait for almost an hour to get to the front of the line .", + "emotion": "neutral", + "text": "Whew ! I had to wait for almost an hour to get to the front of the line .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "You have much patience .", + "emotion": "neutral", + "text": "You have much patience .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Wow ! Your calligraphy is very beautiful . It was worth the wait !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Your calligraphy is very beautiful ." + ], + "type": [ + "no-context" + ], + "text": "Wow ! Your calligraphy is very beautiful . It was worth the wait !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Thank you . Today I'm writing a kind of poem called a Chinese couplet .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Your calligraphy is very beautiful ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . Today I'm writing a kind of poem called a Chinese couplet .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "What does it say ?", + "emotion": "neutral", + "text": "What does it say ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "This is an especially famous one . It says \" May the passing days bring you health and longevity . May this season of renewal find you basked in riches . \"", + "emotion": "neutral", + "text": "This is an especially famous one . It says \" May the passing days bring you health and longevity . May this season of renewal find you basked in riches . \"", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "That's very nice . Is it for sale ?", + "emotion": "neutral", + "text": "That's very nice . Is it for sale ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "No . I never sell my artwork .", + "emotion": "neutral", + "text": "No . I never sell my artwork .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Really ? Then what do you do with it ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I never sell my artwork ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? Then what do you do with it ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I give it away . Here , this one is for you .", + "emotion": "neutral", + "text": "I give it away . Here , this one is for you .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Wow ! Really ? Are you sure ? Now I'll have a lucky year !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "I give it away . Here , this one is for you ." + ], + "type": [ + "inter-personal" + ], + "text": "Wow ! Really ? Are you sure ? Now I'll have a lucky year !", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Remember , real luck must be created ( by ) yourself , and then it cannot be given or taken away ...", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "Now I'll have a lucky year !", + "real luck must be created ( by ) yourself , and then it cannot be given or taken away ..." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Remember , real luck must be created ( by ) yourself , and then it cannot be given or taken away ...", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_62.json b/reccon/sources/te_62.json new file mode 100644 index 0000000000000000000000000000000000000000..a3172119ffd66c9c685b41225e6c4991a9971506 --- /dev/null +++ b/reccon/sources/te_62.json @@ -0,0 +1,126 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Could I have some fish ?", + "emotion": "neutral", + "text": "Could I have some fish ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Certainly . And what vegetables would you like ?", + "emotion": "happiness", + "explanation": "Person B is happy to fulfil the need of Person A.", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Could I have some fish ?" + ], + "type": [ + "inter-personal" + ], + "text": "Certainly . And what vegetables would you like ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Oh , spinach , I think .", + "emotion": "neutral", + "text": "Oh , spinach , I think .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Fine , And what about something to drink ?", + "emotion": "neutral", + "text": "Fine , And what about something to drink ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Just a beer , please .", + "emotion": "neutral", + "text": "Just a beer , please .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Good . Thank you . sir .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Could I have some fish ?" + ], + "type": [ + "inter-personal" + ], + "text": "Good . Thank you . sir .", + "id": 6, + "source_sentences": [ + 0 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "B", + "utterance": "Would you like to have some more beer ?", + "emotion": "neutral", + "text": "Would you like to have some more beer ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "A", + "utterance": "No , thanks . I ' Ve had enough . I'll have my bill , please .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I ' Ve had enough" + ], + "type": [ + "no-context" + ], + "text": "No , thanks . I ' Ve had enough . I'll have my bill , please .", + "id": 8 + }, + { + "turn": 9, + "speaker": "B", + "utterance": "Of course . Please wait a moment . I'll go and get it .", + "emotion": "neutral", + "text": "Of course . Please wait a moment . I'll go and get it .", + "id": 9 + }, + { + "turn": 10, + "speaker": "A", + "utterance": "Thank you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "I ' Ve had enough", + "I'll go and get it" + ], + "type": [ + "hybrid" + ], + "text": "Thank you .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/te_624.json b/reccon/sources/te_624.json new file mode 100644 index 0000000000000000000000000000000000000000..ad15009e315cfaef100dccf1dfa07ef1314c47aa --- /dev/null +++ b/reccon/sources/te_624.json @@ -0,0 +1,105 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Everything is now . I'm kind of sick of it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Everything is now . I'm kind of sick of it ." + ], + "type": [ + "no-context" + ], + "text": "Everything is now . I'm kind of sick of it .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Each ring has 3 small diamonds inside the band .", + "emotion": "neutral", + "text": "Each ring has 3 small diamonds inside the band .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Oooh ! One for each of the zeros in 2000 ! Wow !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Each ring has 3 small diamonds inside the band ." + ], + "type": [ + "inter-personal" + ], + "text": "Oooh ! One for each of the zeros in 2000 ! Wow !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Stop making fun of me .", + "emotion": "neutral", + "text": "Stop making fun of me .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "So find a guy to marry and you can get one !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "Stop making fun of me .", + "So find a guy to marry and you can get one !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "So find a guy to marry and you can get one !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I don't need a guy to buy a wedding ring !", + "emotion": "neutral", + "text": "I don't need a guy to buy a wedding ring !", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Oh , I see . You're going to wear one and pretend you're married to try to attract guys .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I don't need a guy to buy a wedding ring !", + "You're going to wear one and pretend you're married to try to attract guys" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , I see . You're going to wear one and pretend you're married to try to attract guys .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_627.json b/reccon/sources/te_627.json new file mode 100644 index 0000000000000000000000000000000000000000..c3a5e19a533e389f9454515816eb307354cb54e5 --- /dev/null +++ b/reccon/sources/te_627.json @@ -0,0 +1,153 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Wow ! What a beautiful scenic spot ! It's so open . And just breathe that fresh air , you can almost taste its freshness .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 1 + ], + "expanded emotion cause span": [ + "beautiful scenic spot ! It's so open .", + "that fresh air , you can almost taste its freshness ." + ], + "type": [ + "no-context" + ], + "text": "Wow ! What a beautiful scenic spot ! It's so open . And just breathe that fresh air , you can almost taste its freshness .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "You can have a bird view of Guiling City from the top of the mountain .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 1, + 2 + ], + "expanded emotion cause span": [ + "beautiful scenic spot ! It's so open .", + "that fresh air , you can almost taste its freshness .", + "bird view of Guiling City from the top of the mountain ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You can have a bird view of Guiling City from the top of the mountain .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Wonderful ! I'll often come here for mountain climbing .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "bird view of Guiling City from the top of the mountain ." + ], + "type": [ + "inter-personal" + ], + "text": "Wonderful ! I'll often come here for mountain climbing .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "You should . Many Guiliners , especially the old and the young , will climb mountains here in the morning .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Wonderful ! I'll often come here for mountain climbing ." + ], + "type": [ + "inter-personal" + ], + "text": "You should . Many Guiliners , especially the old and the young , will climb mountains here in the morning .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "No wonder people say", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Many Guiliners , especially the old and the young , will climb mountains here in the morning ." + ], + "type": [ + "inter-personal" + ], + "text": "No wonder people say", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Quick ! Pass me your binoculars . Look at that bird ... I've never seen one of those before . It's indigenous to Guiling , and an endangered species too . This is lucky !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "that bird ... I've never seen one of those before . It's indigenous to Guiling , and an endangered species too ." + ], + "type": [ + "no-context" + ], + "text": "Quick ! Pass me your binoculars . Look at that bird ... I've never seen one of those before . It's indigenous to Guiling , and an endangered species too . This is lucky !", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I didn't know you liked bird-watching .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 6 + ], + "expanded emotion cause span": [ + "that bird ... I've never seen one of those before . It's indigenous to Guiling , and an endangered species too .", + "that bird ... I've never seen one of those before . It's indigenous to Guiling , and an endangered species too ." + ], + "type": [ + "inter-personal" + ], + "text": "I didn't know you liked bird-watching .", + "id": 7, + "source_sentences": [ + 5, + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I don't really . I just like wildlife , and you don't get to see too much of it in the city . This place is full of it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I just like wildlife , and you don't get to see too much of it in the city . This place is full of it ." + ], + "type": [ + "no-context" + ], + "text": "I don't really . I just like wildlife , and you don't get to see too much of it in the city . This place is full of it .", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/te_659.json b/reccon/sources/te_659.json new file mode 100644 index 0000000000000000000000000000000000000000..4ff6180fbc5a554c2ab8d2061f13f5e52c151e96 --- /dev/null +++ b/reccon/sources/te_659.json @@ -0,0 +1,207 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "how are you doing , Christopher ?", + "emotion": "neutral", + "text": "how are you doing , Christopher ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "to be honest , I'm really fed up with work at the moment . I need a break !", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I'm really fed up with work at the moment ." + ], + "type": [ + "no-context" + ], + "text": "to be honest , I'm really fed up with work at the moment . I need a break !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "are you doing anything this weekend ?", + "emotion": "neutral", + "text": "are you doing anything this weekend ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I have to work on Saturday all day ! I really hate my job !", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I have to work on Saturday all day !" + ], + "type": [ + "no-context" + ], + "text": "I have to work on Saturday all day ! I really hate my job !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "are you available on Sunday ?", + "emotion": "neutral", + "text": "are you available on Sunday ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "yes , that's my only day off until Thursday .", + "emotion": "neutral", + "text": "yes , that's my only day off until Thursday .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "ok , well , my friends and I are planning on going to the beach on Sunday . We tend to leave around noon whenever we go anywhere , so you could still sleep in . Do you want to come with us ?", + "emotion": "neutral", + "text": "ok , well , my friends and I are planning on going to the beach on Sunday . We tend to leave around noon whenever we go anywhere , so you could still sleep in . Do you want to come with us ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "that'd be fantastic ! Which beach are you going to ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 7 + ], + "expanded emotion cause span": [ + "my friends and I are planning on going to the beach on Sunday .", + "Do you want to come with us ?" + ], + "type": [ + "inter-personal" + ], + "text": "that'd be fantastic ! Which beach are you going to ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "it's a quiet beach just about an hour outside of the city .", + "emotion": "neutral", + "text": "it's a quiet beach just about an hour outside of the city .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "what should I bring with me ?", + "emotion": "neutral", + "text": "what should I bring with me ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "we've got plenty of inflatables , but if you want to sit on a chair , you'll have to bring your own sunlounger .", + "emotion": "neutral", + "text": "we've got plenty of inflatables , but if you want to sit on a chair , you'll have to bring your own sunlounger .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I can just use my beach towel . I love lazing around in the sun .", + "emotion": "neutral", + "text": "I can just use my beach towel . I love lazing around in the sun .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "do you like surfing ?", + "emotion": "neutral", + "text": "do you like surfing ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "I've actually never tired . Do you have a surfboard ?", + "emotion": "neutral", + "text": "I've actually never tired . Do you have a surfboard ?", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "we've got a few . I can teach you how to surf on Sunday . It'll be fun !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "I can teach you how to surf on Sunday . It'll be fun !" + ], + "type": [ + "no-context" + ], + "text": "we've got a few . I can teach you how to surf on Sunday . It'll be fun !", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "I can't wait ! It sounds like we're going to have a great time . How much money should I bring ?", + "emotion": "neutral", + "text": "I can't wait ! It sounds like we're going to have a great time . How much money should I bring ?", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "you'll just need roughly $ 10 for food and gas money . My friend is driving , so we usually all chip in a few dollars for gas money .", + "emotion": "neutral", + "text": "you'll just need roughly $ 10 for food and gas money . My friend is driving , so we usually all chip in a few dollars for gas money .", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "ok , where and when should I meet you ?", + "emotion": "neutral", + "text": "ok , where and when should I meet you ?", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "we'll pick you up at your place at noon . Be there or be square !", + "emotion": "happiness", + "explanation": "Assuming A is happy because B agreed to go out with them.", + "expanded emotion cause evidence": [ + 18 + ], + "expanded emotion cause span": [ + "ok , where and when should I meet you ?" + ], + "type": [ + "inter-personal" + ], + "text": "we'll pick you up at your place at noon . Be there or be square !", + "id": 19, + "source_sentences": [ + 17 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_672.json b/reccon/sources/te_672.json new file mode 100644 index 0000000000000000000000000000000000000000..a9fc63d37eff2443bfbb0f5f33e857951c199593 --- /dev/null +++ b/reccon/sources/te_672.json @@ -0,0 +1,143 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Oh , hi , Jessica , are you going to see this movie too ?", + "emotion": "neutral", + "text": "Oh , hi , Jessica , are you going to see this movie too ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'd love to , the movies are smash hit .", + "emotion": "neutral", + "text": "I'd love to , the movies are smash hit .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Then let's go in .", + "emotion": "neutral", + "text": "Then let's go in .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I can't . I'm waiting for Paul , but he's late .", + "emotion": "neutral", + "text": "I can't . I'm waiting for Paul , but he's late .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I'll say the movie's starting in the minute .", + "emotion": "neutral", + "text": "I'll say the movie's starting in the minute .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I know . I wonder what's keeping him .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I'm waiting for Paul , but he's late" + ], + "type": [ + "self-contagion" + ], + "text": "I know . I wonder what's keeping him .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Looks like he won't show up . He's done this before , hasn't he ?", + "emotion": "neutral", + "text": "Looks like he won't show up . He's done this before , hasn't he ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yeah , a number of times .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 4, + 7 + ], + "expanded emotion cause span": [ + "I'm waiting for Paul , but he's late", + "Looks like he won't show up . He's done this before , hasn't he ?" + ], + "type": [ + "hybrid" + ], + "text": "Yeah , a number of times .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "What's he trying to pull anyway .", + "emotion": "neutral", + "text": "What's he trying to pull anyway .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I don't know . But this is definitely the last straw .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 4, + 7 + ], + "expanded emotion cause span": [ + "I'm waiting for Paul , but he's late", + "Looks like he won't show up . He's done this before , hasn't he ?" + ], + "type": [ + "hybrid" + ], + "text": "I don't know . But this is definitely the last straw .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Maybe you should start seeing someone else .", + "emotion": "neutral", + "text": "Maybe you should start seeing someone else .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "You said it . Ok , let's go in , Sandy .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "you should start seeing someone else ." + ], + "type": [ + "inter-personal" + ], + "text": "You said it . Ok , let's go in , Sandy .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_678.json b/reccon/sources/te_678.json new file mode 100644 index 0000000000000000000000000000000000000000..cb4d1a123bbdbaa2e5e226dbc8117549148905b3 --- /dev/null +++ b/reccon/sources/te_678.json @@ -0,0 +1,203 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What do you think of this one ?", + "emotion": "neutral", + "text": "What do you think of this one ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Eh , so so .", + "emotion": "neutral", + "text": "Eh , so so .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "And this one ? Too flashy ?", + "emotion": "neutral", + "text": "And this one ? Too flashy ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Nah , not too flashy .", + "emotion": "neutral", + "text": "Nah , not too flashy .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Hug ! And this sweater from my aunt ? Isn ' t it hideous ?", + "emotion": "neutral", + "text": "Hug ! And this sweater from my aunt ? Isn ' t it hideous ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I guess .", + "emotion": "neutral", + "text": "I guess .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Are you even listening ? I ' m trying to have a conversation with you .", + "emotion": "neutral", + "text": "Are you even listening ? I ' m trying to have a conversation with you .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "And I ' m trying to watch the game , but you ' re yapping on about your new clothes !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 7, + 8, + 8 + ], + "expanded emotion cause span": [ + "Are you even listening ?", + "I ' m trying to watch the game ,", + "you ' re yapping on about your new clothes !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "And I ' m trying to watch the game , but you ' re yapping on about your new clothes !", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Well I have to decide which gifts to keep and which to exchange for better ones when I go to the Boxing Day sales this afternoon !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "you ' re yapping on about your new clothes !", + "I have to decide" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Well I have to decide which gifts to keep and which to exchange for better ones when I go to the Boxing Day sales this afternoon !", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Well could you do me the favor of making this quick ? It ' s the third quarter and you ' Ve been blabbering on since the first !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 7, + 8, + 8, + 10 + ], + "expanded emotion cause span": [ + "Are you even listening ?", + "I ' m trying to watch the game ,", + "you ' re yapping on about your new clothes !", + "It ' s the third quarter and you ' Ve been blabbering on since the first !" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Well could you do me the favor of making this quick ? It ' s the third quarter and you ' Ve been blabbering on since the first !", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Oh , your precious game . You watch the same game every year , and each year your beloved hometown team loses by at least three goals !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 8, + 9, + 11 + ], + "expanded emotion cause span": [ + "you ' re yapping on about your new clothes !", + "I have to decide", + "You watch the same game every year , and each year your beloved hometown team loses" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Oh , your precious game . You watch the same game every year , and each year your beloved hometown team loses by at least three goals !", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Oh no you didn ' t . You didn ' t just insult the Sals-bury Seals , did you ? Why don ' t you just . just go and return all of those stupid clothes and not come back until the sales are over ?", + "emotion": "anger", + "expanded emotion cause evidence": [ + 7, + 8, + 8, + 10, + 12 + ], + "expanded emotion cause span": [ + "Are you even listening ?", + "I ' m trying to watch the game ,", + "you ' re yapping on about your new clothes !", + "It ' s the third quarter and you ' Ve been blabbering on since the first !", + "You didn ' t just insult the Sals-bury Seals , did you ?" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Oh no you didn ' t . You didn ' t just insult the Sals-bury Seals , did you ? Why don ' t you just . just go and return all of those stupid clothes and not come back until the sales are over ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I might just ! Enjoy your stupid game !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 8, + 9, + 11, + 12, + 13 + ], + "expanded emotion cause span": [ + "you ' re yapping on about your new clothes !", + "I have to decide", + "You watch the same game every year , and each year your beloved hometown team loses", + "go and return all of those stupid clothes and not come back until the sales are over ?", + "your stupid game !" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I might just ! Enjoy your stupid game !", + "id": 13 + } +] \ No newline at end of file diff --git a/reccon/sources/te_681.json b/reccon/sources/te_681.json new file mode 100644 index 0000000000000000000000000000000000000000..2f02e53c4707930a45e7c5ac3708e866baf7d6e5 --- /dev/null +++ b/reccon/sources/te_681.json @@ -0,0 +1,102 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , Monica , how is everything going ?", + "emotion": "neutral", + "text": "Hi , Monica , how is everything going ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Everything goes well , but I am thinking about quitting my current job .", + "emotion": "neutral", + "text": "Everything goes well , but I am thinking about quitting my current job .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Why ? You ' re not satisfied anymore ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I am thinking about quitting my current job ." + ], + "type": [ + "inter-personal" + ], + "text": "Why ? You ' re not satisfied anymore ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I just sense . But I cannot grow anymore . My boss is not really supporting me . I am interested in some positions in other JV companies , but I need to do some more in-depth research before I send my application letters out .", + "emotion": "neutral", + "text": "I just sense . But I cannot grow anymore . My boss is not really supporting me . I am interested in some positions in other JV companies , but I need to do some more in-depth research before I send my application letters out .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "That is important . Doing research on a company you are interested in will definitely help your application .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "That is important . Doing research on a company you are interested in will definitely help your application ." + ], + "type": [ + "no-context" + ], + "text": "That is important . Doing research on a company you are interested in will definitely help your application .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Certainly , it is very nice talking with you . But I really have to go now . Catch you later .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "That is important . Doing research on a company you are interested in will definitely help your application .", + "it is very nice talking with you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Certainly , it is very nice talking with you . But I really have to go now . Catch you later .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Ok , good luck to you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "it is very nice talking with you ." + ], + "type": [ + "inter-personal" + ], + "text": "Ok , good luck to you .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_683.json b/reccon/sources/te_683.json new file mode 100644 index 0000000000000000000000000000000000000000..e9a9428356fadf0821460b04a395fbbe23af9e00 --- /dev/null +++ b/reccon/sources/te_683.json @@ -0,0 +1,141 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello , is that Cathy speaking ?", + "emotion": "neutral", + "text": "Hello , is that Cathy speaking ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , is that you , Allen ?", + "emotion": "neutral", + "text": "Yes , is that you , Allen ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yes , how are you doing ?", + "emotion": "neutral", + "text": "Yes , how are you doing ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Not bad .", + "emotion": "happiness", + "explanation": "Assuming B is happy to talk to A", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "is that you , Allen ?" + ], + "type": [ + "self-contagion" + ], + "text": "Not bad .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Say I've got two tickets for the concert this evening . Would you like to come with me ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Say I've got two tickets for the concert this evening ." + ], + "type": [ + "no-context" + ], + "text": "Say I've got two tickets for the concert this evening . Would you like to come with me ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Sure . Thank you very much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Say I've got two tickets for the concert this evening . Would you like to come with me ?" + ], + "type": [ + "inter-personal" + ], + "text": "Sure . Thank you very much .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Then I ' ll pick you up at six thirty . OK ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Say I've got two tickets for the concert this evening . Would you like to come with me ?", + "Sure ." + ], + "type": [ + "hybrid" + ], + "text": "Then I ' ll pick you up at six thirty . OK ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Ok , see you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Say I've got two tickets for the concert this evening . Would you like to come with me ?", + "Sure ." + ], + "type": [ + "hybrid" + ], + "text": "Ok , see you .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "See you .", + "emotion": "happiness", + "explanation": "Assuming they are happy because: 1) They got two concert tickets; and 2) going to attend it together.", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Say I've got two tickets for the concert this evening . Would you like to come with me ?", + "Sure ." + ], + "type": [ + "hybrid" + ], + "text": "See you .", + "id": 9 + } +] \ No newline at end of file diff --git a/reccon/sources/te_695.json b/reccon/sources/te_695.json new file mode 100644 index 0000000000000000000000000000000000000000..1fd360cc8686a44da86e696515408826b0588eda --- /dev/null +++ b/reccon/sources/te_695.json @@ -0,0 +1,97 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Are you free tomorrow night ?", + "emotion": "neutral", + "text": "Are you free tomorrow night ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , I am .", + "emotion": "neutral", + "text": "Yes , I am .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Shall we have dinner together ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Yes , I am ." + ], + "type": [ + "inter-personal" + ], + "text": "Shall we have dinner together ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Do you have a special restaurant in mind ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Shall we have dinner together ?" + ], + "type": [ + "inter-personal" + ], + "text": "Do you have a special restaurant in mind ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Yes , I do . I know a place that has excellent food .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Yes , I am ." + ], + "type": [ + "inter-personal" + ], + "text": "Yes , I do . I know a place that has excellent food .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "OK . I'll be happy to join you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 5, + 6 + ], + "expanded emotion cause span": [ + "Shall we have dinner together ?", + "I know a place that has excellent food .", + "I'll be happy to join you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "OK . I'll be happy to join you .", + "id": 6, + "source_sentences": [ + 2, + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_700.json b/reccon/sources/te_700.json new file mode 100644 index 0000000000000000000000000000000000000000..b40187b9159120796a3346b171ca1ccf4e9e7703 --- /dev/null +++ b/reccon/sources/te_700.json @@ -0,0 +1,163 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Why didn't you tell me you had a girlfriend ?", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Why didn't you tell me you had a girlfriend ?" + ], + "type": [ + "no-context" + ], + "text": "Why didn't you tell me you had a girlfriend ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Sorry , I thought you knew .", + "emotion": "neutral", + "text": "Sorry , I thought you knew .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "But you should have told me you were in love with her .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "But you should have told me you were in love with her ." + ], + "type": [ + "no-context" + ], + "text": "But you should have told me you were in love with her .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Didn't I ?", + "emotion": "neutral", + "text": "Didn't I ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "You know you didn't .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "Didn't I ?", + "You know you didn't ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You know you didn't .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Well , I'm telling you now .", + "emotion": "neutral", + "text": "Well , I'm telling you now .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yes , but you might have told me before .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I'm telling you now .", + "you might have told me before ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , but you might have told me before .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I didn't think you'd be interested .", + "emotion": "neutral", + "text": "I didn't think you'd be interested .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "You can't be serious . How dare you not tell me you were going to marry her ?", + "emotion": "anger", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "I didn't think you'd be interested .", + "How dare you not tell me you were going to marry her ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You can't be serious . How dare you not tell me you were going to marry her ?", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Sorry , I didn't think it mattered .", + "emotion": "neutral", + "text": "Sorry , I didn't think it mattered .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Oh , you men ! You're all the same .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 9, + 10, + 11 + ], + "expanded emotion cause span": [ + "How dare you not tell me you were going to marry her ?", + "I didn't think it mattered .", + "Oh , you men ! You're all the same ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Oh , you men ! You're all the same .", + "id": 11 + } +] \ No newline at end of file diff --git a/reccon/sources/te_713.json b/reccon/sources/te_713.json new file mode 100644 index 0000000000000000000000000000000000000000..e51ead9a4fd03a82fc78f88d861d4dde47a88f81 --- /dev/null +++ b/reccon/sources/te_713.json @@ -0,0 +1,117 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Morning , Peter . Nice suit ! A new one ?", + "emotion": "happiness", + "explanation": "Appreciation", + "expanded emotion cause evidence": [ + "b", + 1 + ], + "expanded emotion cause span": [ + "b", + "Nice suit" + ], + "type": [ + "latent", + "no-context" + ], + "text": "Morning , Peter . Nice suit ! A new one ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh , yes . My wife bought it for me yesterday . Hmm , you look nice in that yellow dress . Yellow suits you really well .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 2 + ], + "expanded emotion cause span": [ + "Nice suit", + "My wife bought it for me yesterday .", + "Oh , yes . My wife bought it for me yesterday . Hmm , you look nice in that yellow dress . Yellow suits you really well ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , yes . My wife bought it for me yesterday . Hmm , you look nice in that yellow dress . Yellow suits you really well .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Maybe . Several people have suggested that I get more yellow clothes . They say the color suits me because I have a fair complexion .", + "emotion": "neutral", + "text": "Maybe . Several people have suggested that I get more yellow clothes . They say the color suits me because I have a fair complexion .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "That's right . You know , pink , green and black could also be good for you . Actually , I think that all colors are okay for a person with your complexion . It's just that different colors can give people different impressions . For example , black could make you look mature , while pink could make you look young and energetic .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3, + 4 + ], + "expanded emotion cause span": [ + "Oh , yes . My wife bought it for me yesterday . Hmm , you look nice in that yellow dress . Yellow suits you really well .", + "Several people have suggested that I get more yellow clothes . They say the color suits me because I have a fair complexion .", + "You know , pink , green and black could also be good for you . Actually , I think that all colors are okay for a person with your complexion ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "That's right . You know , pink , green and black could also be good for you . Actually , I think that all colors are okay for a person with your complexion . It's just that different colors can give people different impressions . For example , black could make you look mature , while pink could make you look young and energetic .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Thank you for your compliments . It sounds like you're a clothing expert .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "You know , pink , green and black could also be good for you . Actually , I think that all colors are okay for a person with your complexion .", + "Thank you for your compliments . It sounds like you're a clothing expert ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you for your compliments . It sounds like you're a clothing expert .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Well , compared with my wife , I'm just a beginner .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "It sounds like you're a clothing expert ." + ], + "type": [ + "inter-personal" + ], + "text": "Well , compared with my wife , I'm just a beginner .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_732.json b/reccon/sources/te_732.json new file mode 100644 index 0000000000000000000000000000000000000000..521aefe9043e3feafb1472a768973cc47b8140fe --- /dev/null +++ b/reccon/sources/te_732.json @@ -0,0 +1,185 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I hate to go outside .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I hate to go outside ." + ], + "type": [ + "no-context" + ], + "text": "I hate to go outside .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Me too .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I hate to go outside ." + ], + "type": [ + "inter-personal" + ], + "text": "Me too .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Why do you hate to go outside ?", + "emotion": "neutral", + "text": "Why do you hate to go outside ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I meet too many jerks .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I meet too many jerks ." + ], + "type": [ + "no-context" + ], + "text": "I meet too many jerks .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I agree .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I meet too many jerks ." + ], + "type": [ + "inter-personal" + ], + "text": "I agree .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "This city is full of jerks .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "This city is full of jerks ." + ], + "type": [ + "no-context" + ], + "text": "This city is full of jerks .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Rude people are everywhere .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "This city is full of jerks .", + "Rude people are everywhere ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Rude people are everywhere .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "But what can you do ?", + "emotion": "neutral", + "text": "But what can you do ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "You can yell at them .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "This city is full of jerks .", + "Rude people are everywhere ." + ], + "type": [ + "hybrid" + ], + "text": "You can yell at them .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "And they will yell back at you .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 10, + 6, + 7 + ], + "expanded emotion cause span": [ + "And they will yell back at you .", + "This city is full of jerks .", + "Rude people are everywhere ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "And they will yell back at you .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Yelling doesn't do any good .", + "emotion": "neutral", + "text": "Yelling doesn't do any good .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "No . The best thing to do is just stay home .", + "emotion": "neutral", + "text": "No . The best thing to do is just stay home .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/te_745.json b/reccon/sources/te_745.json new file mode 100644 index 0000000000000000000000000000000000000000..a012f546c189102501cac38d4b7c1e4935d49072 --- /dev/null +++ b/reccon/sources/te_745.json @@ -0,0 +1,238 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Why don't you watch where you're going ?", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Why don't you watch where you're going ?" + ], + "type": [ + "no-context" + ], + "text": "Why don't you watch where you're going ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Me ? You're the one who pulled out in front of me !", + "emotion": "neutral", + "text": "Me ? You're the one who pulled out in front of me !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "There was plenty of room for me to pull out . You didn't have to stay in the lane you were in .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "Why don't you watch where you're going ?", + "Me ? You're the one who pulled out in front of me !" + ], + "type": [ + "hybrid" + ], + "text": "There was plenty of room for me to pull out . You didn't have to stay in the lane you were in .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Hey , listen . I had every right to stay in the lane I was in . You were supposed to wait until I passed to pull out . And anyhow , you didn't give me any time to change lanes . All of a sudden--BANG--there you are right in front of me .", + "emotion": "neutral", + "text": "Hey , listen . I had every right to stay in the lane I was in . You were supposed to wait until I passed to pull out . And anyhow , you didn't give me any time to change lanes . All of a sudden--BANG--there you are right in front of me .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I think my arm is broken .", + "emotion": "neutral", + "text": "I think my arm is broken .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Sorry about your arm , but it serves you right . You need to learn how to drive . You're lucky you didn't get killed . And I'm lucky to be alive too .", + "emotion": "neutral", + "text": "Sorry about your arm , but it serves you right . You need to learn how to drive . You're lucky you didn't get killed . And I'm lucky to be alive too .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Listen , let's just wait until the police get here . Then we can decide whose fault this accident was .", + "emotion": "neutral", + "text": "Listen , let's just wait until the police get here . Then we can decide whose fault this accident was .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Fine with me . I know the laws of the road . I'm not worried .", + "emotion": "neutral", + "text": "Fine with me . I know the laws of the road . I'm not worried .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I have a cell phone in my car . Now it's probably on the floor on the passenger side . Why don't you get it for me , and then I can call the police ?", + "emotion": "neutral", + "text": "I have a cell phone in my car . Now it's probably on the floor on the passenger side . Why don't you get it for me , and then I can call the police ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Alright .", + "emotion": "neutral", + "text": "Alright .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "It doesn't work . It looks like it's broken . I need to get to a hospital . You should drive me there .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "It doesn't work . It looks like it's broken" + ], + "type": [ + "no-context" + ], + "text": "It doesn't work . It looks like it's broken . I need to get to a hospital . You should drive me there .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Oh , yeah ? It's better if we make a police report first . Then you can go to the hospital .", + "emotion": "neutral", + "text": "Oh , yeah ? It's better if we make a police report first . Then you can go to the hospital .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Damn it ! I'm injured here . We could wait all day for the police .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 11, + 12, + 13 + ], + "expanded emotion cause span": [ + "It doesn't work . It looks like it's broken", + "It's better if we make a police report first .", + "I'm injured here ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Damn it ! I'm injured here . We could wait all day for the police .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Well , you'll just have to wait . I'm not going to move my car until the police arrive . I'll go into one of those houses over there and use their phone . Don't worry . You'll get to the hospital in time .", + "emotion": "neutral", + "text": "Well , you'll just have to wait . I'm not going to move my car until the police arrive . I'll go into one of those houses over there and use their phone . Don't worry . You'll get to the hospital in time .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "It really hurts .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 11, + 12, + 13 + ], + "expanded emotion cause span": [ + "It doesn't work . It looks like it's broken", + "It's better if we make a police report first .", + "I'm injured here ." + ], + "type": [ + "hybrid" + ], + "text": "It really hurts .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Yes , maybe it does . But if you're going to drive like you did just now , you will have to get used to a little physical pain . You know what I mean ?", + "emotion": "neutral", + "text": "Yes , maybe it does . But if you're going to drive like you did just now , you will have to get used to a little physical pain . You know what I mean ?", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "To hell with you . The accident was your fault .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 16, + 17 + ], + "expanded emotion cause span": [ + "if you're going to drive like you did just now , you will have to get used to a little physical pain .", + "The accident was your fault ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "To hell with you . The accident was your fault .", + "id": 17, + "source_sentences": [ + 15 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 18, + "speaker": "B", + "utterance": "I'm afraid it wasn't . And when the police get here , you will also see that it wasn't . But enough of this bickering . I'm going to go find a phone . Don ' t move that arm while I'm gone . Alright ?", + "emotion": "neutral", + "text": "I'm afraid it wasn't . And when the police get here , you will also see that it wasn't . But enough of this bickering . I'm going to go find a phone . Don ' t move that arm while I'm gone . Alright ?", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "To hell with you .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 16, + 17 + ], + "expanded emotion cause span": [ + "if you're going to drive like you did just now , you will have to get used to a little physical pain .", + "The accident was your fault ." + ], + "type": [ + "hybrid" + ], + "text": "To hell with you .", + "id": 19 + } +] \ No newline at end of file diff --git a/reccon/sources/te_754.json b/reccon/sources/te_754.json new file mode 100644 index 0000000000000000000000000000000000000000..5ba02a5beda4ad7d8b8e93c7630c4e82a8643dc1 --- /dev/null +++ b/reccon/sources/te_754.json @@ -0,0 +1,162 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "David , I ' m going to China .", + "emotion": "neutral", + "text": "David , I ' m going to China .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Really ? How did you get the chance ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I ' m going to China ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? How did you get the chance ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "You know . I took part in the Chinese contest . I was the best and they gave me this reward . I don ' t have to pay for my trip .", + "emotion": "neutral", + "text": "You know . I took part in the Chinese contest . I was the best and they gave me this reward . I don ' t have to pay for my trip .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Congratulations . How lucky you are !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "I ' m going to China .", + "I don ' t have to pay for my trip ." + ], + "type": [ + "inter-personal" + ], + "text": "Congratulations . How lucky you are !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Thank you . I ' m leaving tomorrow morning .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 4, + 5 + ], + "expanded emotion cause span": [ + "I ' m going to China .", + "Congratulations . How lucky you are !", + "I ' m leaving tomorrow morning ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Thank you . I ' m leaving tomorrow morning .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I ' m sure you ' ll enjoy the trip . China is such a beautiful country .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "I ' m going to China .", + "I don ' t have to pay for my trip ." + ], + "type": [ + "inter-personal" + ], + "text": "I ' m sure you ' ll enjoy the trip . China is such a beautiful country .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I ' m sure I will .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I ' m sure you ' ll enjoy the trip . China is such a beautiful country .", + "I ' m sure I will ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I ' m sure I will .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Have a nice journey , Lily .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "I ' m going to China .", + "I don ' t have to pay for my trip ." + ], + "type": [ + "inter-personal" + ], + "text": "Have a nice journey , Lily .", + "id": 8, + "source_sentences": [ + 0, + 2 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Thank you , David .", + "emotion": "happiness", + "explanation": "Assuming A is happy because he will enjoy the trip to china and B is happy for A.", + "expanded emotion cause evidence": [ + 1, + 3, + 8 + ], + "expanded emotion cause span": [ + "I ' m going to China .", + "I don ' t have to pay for my trip .", + "Have a nice journey" + ], + "type": [ + "hybrid" + ], + "text": "Thank you , David .", + "id": 9 + } +] \ No newline at end of file diff --git a/reccon/sources/te_755.json b/reccon/sources/te_755.json new file mode 100644 index 0000000000000000000000000000000000000000..f22719208ec60cfbd7db1cdcb460fa56717b8920 --- /dev/null +++ b/reccon/sources/te_755.json @@ -0,0 +1,197 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Did you watch the final last night ? My favorite singer won !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "My favorite singer won !" + ], + "type": [ + "no-context" + ], + "text": "Did you watch the final last night ? My favorite singer won !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh , I love him too . He not only sings well but also shows perseverance when he encounters difficulties in the contest .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "My favorite singer won !", + "Oh , I love him too . He not only sings well but also shows perseverance when he encounters difficulties in the contest ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , I love him too . He not only sings well but also shows perseverance when he encounters difficulties in the contest .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yeah , he got booted after his initial performance in the audition , but he did not give up . He then tried at another two auditions .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "My favorite singer won !", + "Yeah , he got booted after his initial performance in the audition , but he did not give up . He then tried at another two auditions ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Yeah , he got booted after his initial performance in the audition , but he did not give up . He then tried at another two auditions .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "He had barely survived the third audition and finally got a chance to advance in the contest . Fortunately , in the third audition , he has won popularity among the audience . And that's when I started to notice him .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 4 + ], + "expanded emotion cause span": [ + "My favorite singer won !", + "Oh , I love him too . He not only sings well but also shows perseverance when he encounters difficulties in the contest .", + "He had barely survived the third audition and finally got a chance to advance in the contest . Fortunately , in the third audition , he has won popularity among the audience . And that's when I started to notice him ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "He had barely survived the third audition and finally got a chance to advance in the contest . Fortunately , in the third audition , he has won popularity among the audience . And that's when I started to notice him .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Me too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "He had barely survived the third audition and finally got a chance to advance in the contest . Fortunately , in the third audition , he has won popularity among the audience . And that's when I started to notice him ." + ], + "type": [ + "inter-personal" + ], + "text": "Me too .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Before he made the top three , I was so nervous . I just fear that he might be knocked out .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "My favorite singer won !" + ], + "type": [ + "inter-personal" + ], + "text": "Before he made the top three , I was so nervous . I just fear that he might be knocked out .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yeah , there're so many excellent candidates out there . Who knows which one will make it to the final ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "My favorite singer won !", + "Oh , I love him too . He not only sings well but also shows perseverance when he encounters difficulties in the contest ." + ], + "type": [ + "hybrid" + ], + "text": "Yeah , there're so many excellent candidates out there . Who knows which one will make it to the final ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Absolutely . That's why when he entered the final , I was so excited .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 8 + ], + "expanded emotion cause span": [ + "My favorite singer won !", + "when he entered the final" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Absolutely . That's why when he entered the final , I was so excited .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "He really did a great job in the finale , especially in the PK round . He performed so well that the majority of the audience cast their votes for him .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "He really did a great job in the finale , especially in the PK round . He performed so well that the majority of the audience cast their votes for him ." + ], + "type": [ + "no-context" + ], + "text": "He really did a great job in the finale , especially in the PK round . He performed so well that the majority of the audience cast their votes for him .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "And the host announced that he won it all !", + "emotion": "happiness", + "explanation": "10 with 9 makes the evidence stronger.", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "He really did a great job in the finale , especially in the PK round . He performed so well that the majority of the audience cast their votes for him .", + "And the host announced that he won it all !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "And the host announced that he won it all !", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_757.json b/reccon/sources/te_757.json new file mode 100644 index 0000000000000000000000000000000000000000..a74faad6f1b9b293492ced7e4a2bd7a85dd7e752 --- /dev/null +++ b/reccon/sources/te_757.json @@ -0,0 +1,177 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Excuse me , i am a new student here . Could you tell me where the English Department is ?", + "emotion": "neutral", + "text": "Excuse me , i am a new student here . Could you tell me where the English Department is ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It is in that brand new , tall building over there . On the 9th floor .", + "emotion": "neutral", + "text": "It is in that brand new , tall building over there . On the 9th floor .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Where is the school cafeteria ?", + "emotion": "neutral", + "text": "Where is the school cafeteria ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It is the basement of that red building in front of the tower with big bells .", + "emotion": "neutral", + "text": "It is the basement of that red building in front of the tower with big bells .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Where is the Computer Center ?", + "emotion": "neutral", + "text": "Where is the Computer Center ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "The Computer Center is on the first floor of the library .", + "emotion": "neutral", + "text": "The Computer Center is on the first floor of the library .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Where is the library ?", + "emotion": "neutral", + "text": "Where is the library ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "The library is next to the Adminstration Building . The Adminstration Building is over there near the school ' s main entrance . There are school maps for free in the lobby of the Admin .", + "emotion": "neutral", + "text": "The library is next to the Adminstration Building . The Adminstration Building is over there near the school ' s main entrance . There are school maps for free in the lobby of the Admin .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Thank you . I will go get one .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "There are school maps for free in the lobby of the Admin .", + "I will go get one ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you . I will go get one .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Sure . Glad to be of service . By the way , my name is Mike Sullivan . You will see me around a lot . I am running for President of the Student Government .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Glad to be of service ." + ], + "type": [ + "no-context" + ], + "text": "Sure . Glad to be of service . By the way , my name is Mike Sullivan . You will see me around a lot . I am running for President of the Student Government .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Well , hi ! My name is Eve Markowski . I am glad to meet you . With your friendly smile and helpful attitude . I am sure you will win .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I am glad to meet you . With your friendly smile and helpful attitude ." + ], + "type": [ + "no-context" + ], + "text": "Well , hi ! My name is Eve Markowski . I am glad to meet you . With your friendly smile and helpful attitude . I am sure you will win .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Thanks you for the encouragement .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "With your friendly smile and helpful attitude . I am sure you will win ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks you for the encouragement .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "You are welcome . I ' d better go . Goodbye .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "Thanks you for the encouragement ." + ], + "type": [ + "inter-personal" + ], + "text": "You are welcome . I ' d better go . Goodbye .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Have a good day . Bye-Bye !", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "With your friendly smile and helpful attitude . I am sure you will win ." + ], + "type": [ + "inter-personal" + ], + "text": "Have a good day . Bye-Bye !", + "id": 14, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_786.json b/reccon/sources/te_786.json new file mode 100644 index 0000000000000000000000000000000000000000..18d6b1b5346ef83c94daf683df28397927b61c47 --- /dev/null +++ b/reccon/sources/te_786.json @@ -0,0 +1,175 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Well , how did you enjoy your seaside trip ?", + "emotion": "neutral", + "text": "Well , how did you enjoy your seaside trip ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It was funny .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "your seaside trip", + "funny ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It was funny .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Tell me about it , will you ?", + "emotion": "neutral", + "text": "Tell me about it , will you ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Well , we drove through the valley on our way there in the morning . It was a magnificent sight .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "drove through the valley on our way there in the morning . It was a magnificent sight ." + ], + "type": [ + "no-context" + ], + "text": "Well , we drove through the valley on our way there in the morning . It was a magnificent sight .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Did you stop at the big waterfall for pictures ?", + "emotion": "neutral", + "text": "Did you stop at the big waterfall for pictures ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Sure , we wouldn't miss it for anything . After that , we took a short cut to the park . There was very little traffic , so we got there in less than an hour .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "stop at the big waterfall for pictures ?", + "Sure , we wouldn't miss it for anything . After that , we took a short cut to the park . There was very little traffic , so we got there in less than an hour ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Sure , we wouldn't miss it for anything . After that , we took a short cut to the park . There was very little traffic , so we got there in less than an hour .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You were lucky then . What did you do after that ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "There was very little traffic , so we got there in less than an hour .", + "You were lucky" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You were lucky then . What did you do after that ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "We went for a swim in the sea . That was the best part of the day . Just look at my nice tan .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 8 + ], + "expanded emotion cause span": [ + "We went for a swim in the sea .", + "my nice tan ." + ], + "type": [ + "no-context" + ], + "text": "We went for a swim in the sea . That was the best part of the day . Just look at my nice tan .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "So you must have had a busy and enjoyable day yesterday .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 8, + 9 + ], + "expanded emotion cause span": [ + "We went for a swim in the sea .", + "my nice tan .", + "So you must have had a busy and enjoyable day yesterday ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "So you must have had a busy and enjoyable day yesterday .", + "id": 9, + "source_sentences": [ + 7, + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Yes , you're right . And I was so tired that I fell asleep on the way back . My arms are still stiff from the swim yesterday .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5, + 6, + 8, + 8 + ], + "expanded emotion cause span": [ + "drove through the valley on our way there in the morning . It was a magnificent sight .", + "stop at the big waterfall for pictures ?", + "Sure , we wouldn't miss it for anything . After that , we took a short cut to the park . There was very little traffic , so we got there in less than an hour .", + "We went for a swim in the sea .", + "my nice tan ." + ], + "type": [ + "hybrid" + ], + "text": "Yes , you're right . And I was so tired that I fell asleep on the way back . My arms are still stiff from the swim yesterday .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/te_793.json b/reccon/sources/te_793.json new file mode 100644 index 0000000000000000000000000000000000000000..508b4496be400e731a59f6ea3406d250bad2575c --- /dev/null +++ b/reccon/sources/te_793.json @@ -0,0 +1,128 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "How do you arrange this summer vacation ?", + "emotion": "neutral", + "text": "How do you arrange this summer vacation ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I want to travel .", + "emotion": "neutral", + "text": "I want to travel .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Where would you like to go ?", + "emotion": "neutral", + "text": "Where would you like to go ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "The seaside .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "Where would you like to go ?", + "The seaside ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "The seaside .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "That's really a good idea . Taking a walk on the beach and lying in the sun are pretty good . I recommend you Qingdao or Dalian .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "The seaside .", + "Taking a walk on the beach and lying in the sun are pretty good ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's really a good idea . Taking a walk on the beach and lying in the sun are pretty good . I recommend you Qingdao or Dalian .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I ' Ve been to Qingdao before , so I ' ll choose Dalian . I've heard that the environment there is very good .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I've heard that the environment there is very good ." + ], + "type": [ + "no-context" + ], + "text": "I ' Ve been to Qingdao before , so I ' ll choose Dalian . I've heard that the environment there is very good .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yes , that's a good place to spend a holiday . Last year I went there . It's really .", + "emotion": "happiness", + "explanation": "Assuming A is happy for B", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I've heard that the environment there is very good .", + "Yes , that's a good place to spend a holiday . Last year I went there . It's really ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , that's a good place to spend a holiday . Last year I went there . It's really .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Thank you !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I've heard that the environment there is very good .", + "Yes , that's a good place to spend a holiday . Last year I went there . It's really ." + ], + "type": [ + "hybrid" + ], + "text": "Thank you !", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/te_796.json b/reccon/sources/te_796.json new file mode 100644 index 0000000000000000000000000000000000000000..6c583f336222aa9e49606c2e926d223d070f8423 --- /dev/null +++ b/reccon/sources/te_796.json @@ -0,0 +1,140 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Very glad to know something about you , then what are you going to do when you finish .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Very glad to know something about you" + ], + "type": [ + "no-context" + ], + "text": "Very glad to know something about you , then what are you going to do when you finish .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh , I ' ll go to shanghai to practice there .", + "emotion": "neutral", + "text": "Oh , I ' ll go to shanghai to practice there .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "That ' s a good idea . It must be easy to find a job in shanghai .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "Oh , I ' ll go to shanghai to practice there .", + "That ' s a good idea ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That ' s a good idea . It must be easy to find a job in shanghai .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I think so , you know there is a great deal of opportunity for business there .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3, + 4 + ], + "expanded emotion cause span": [ + "Oh , I ' ll go to shanghai to practice there .", + "That ' s a good idea .", + "there is a great deal of opportunity for business there ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I think so , you know there is a great deal of opportunity for business there .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "And English is very useful in your job .", + "emotion": "neutral", + "text": "And English is very useful in your job .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I think it will be very useful in many ways . Beside , shanghai is an important trade center , not only in China , but also in the world , English is useful in almost all walks of life .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3, + 4, + 6 + ], + "expanded emotion cause span": [ + "Oh , I ' ll go to shanghai to practice there .", + "That ' s a good idea .", + "there is a great deal of opportunity for business there .", + "Beside , shanghai is an important trade center , not only in China , but also in the world ," + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I think it will be very useful in many ways . Beside , shanghai is an important trade center , not only in China , but also in the world , English is useful in almost all walks of life .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You will be a very promising one .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "You will be a very promising one ." + ], + "type": [ + "no-context" + ], + "text": "You will be a very promising one .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That ' s my wish .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "You will be a very promising one ." + ], + "type": [ + "inter-personal" + ], + "text": "That ' s my wish .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_804.json b/reccon/sources/te_804.json new file mode 100644 index 0000000000000000000000000000000000000000..3f6737cd8d92389dcb659f56405d992476f28b40 --- /dev/null +++ b/reccon/sources/te_804.json @@ -0,0 +1,174 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Have you got your invitation yet ?", + "emotion": "neutral", + "text": "Have you got your invitation yet ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "My invitation ? No , I haven't . My invitation to what ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "Have you got your invitation yet ?", + "My invitation ? No , I haven't . My invitation to what ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "My invitation ? No , I haven't . My invitation to what ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "The house warming party .", + "emotion": "neutral", + "text": "The house warming party .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Whose house warming party is it ?", + "emotion": "neutral", + "text": "Whose house warming party is it ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Tom and Bill Smith . They are both working now you know ? And they've bought a new house .", + "emotion": "neutral", + "text": "Tom and Bill Smith . They are both working now you know ? And they've bought a new house .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Oh , they have ? I didn't know . I haven't seen Tom lately .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "they've bought a new house ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , they have ? I didn't know . I haven't seen Tom lately .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "It's out in the suburbs .", + "emotion": "neutral", + "text": "It's out in the suburbs .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Have you seen the house ?", + "emotion": "neutral", + "text": "Have you seen the house ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yes , I have . I went out with them last weekend .", + "emotion": "neutral", + "text": "Yes , I have . I went out with them last weekend .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Is it nice ?", + "emotion": "neutral", + "text": "Is it nice ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Yes , it is . There are three bedrooms , a living room , a dining room , and a big kitchen . There's also a garden .", + "emotion": "neutral", + "text": "Yes , it is . There are three bedrooms , a living room , a dining room , and a big kitchen . There's also a garden .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Well , that does sound nice . Have they moved in yet ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "There are three bedrooms , a living room , a dining room , and a big kitchen . There's also a garden ." + ], + "type": [ + "inter-personal" + ], + "text": "Well , that does sound nice . Have they moved in yet ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "They are moving today . Tom's taken the day off . He's rented a truck , and they should have all their furniture in the house tonight .", + "emotion": "neutral", + "text": "They are moving today . Tom's taken the day off . He's rented a truck , and they should have all their furniture in the house tonight .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "When are they going to have the party ?", + "emotion": "neutral", + "text": "When are they going to have the party ?", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Next Saturday night . You should get your invitation today or tomorrow .", + "emotion": "neutral", + "text": "Next Saturday night . You should get your invitation today or tomorrow .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Wow , that would be something to look forward to .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "You should get your invitation today or tomorrow ." + ], + "type": [ + "inter-personal" + ], + "text": "Wow , that would be something to look forward to .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_810.json b/reccon/sources/te_810.json new file mode 100644 index 0000000000000000000000000000000000000000..b032c6f8bb2bf8918573dd6fcf5c72307feecc57 --- /dev/null +++ b/reccon/sources/te_810.json @@ -0,0 +1,186 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey , Blake ! Are you still listening to Mozart ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Are you still listening to Mozart ?" + ], + "type": [ + "no-context" + ], + "text": "Hey , Blake ! Are you still listening to Mozart ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes . Do you like it ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "listening to Mozart" + ], + "type": [ + "inter-personal" + ], + "text": "Yes . Do you like it ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "It's great . and I ' Ve heard that listening to Mozart can make you more intelligent .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "It's great . and I ' Ve heard that listening to Mozart can make you more intelligent ." + ], + "type": [ + "no-context" + ], + "text": "It's great . and I ' Ve heard that listening to Mozart can make you more intelligent .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Really ? I've never heard that before . I just like it .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "I ' Ve heard that listening to Mozart can make you more intelligent .", + "I've never heard that before ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Really ? I've never heard that before . I just like it .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Is classical music your favorite ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I've never heard that before . I just like it ." + ], + "type": [ + "inter-personal" + ], + "text": "Is classical music your favorite ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yes . What about you ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Is classical music your favorite ?" + ], + "type": [ + "inter-personal" + ], + "text": "Yes . What about you ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I Like pop music best . Classical music is a bit too heavy for me . I can't get fully relaxed in it .", + "emotion": "neutral", + "text": "I Like pop music best . Classical music is a bit too heavy for me . I can't get fully relaxed in it .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Pop music doesn't have any depth for me .", + "emotion": "neutral", + "text": "Pop music doesn't have any depth for me .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yeah , that's why I can enjoy myself in it .", + "emotion": "neutral", + "text": "Yeah , that's why I can enjoy myself in it .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Did you always like pop music .", + "emotion": "neutral", + "text": "Did you always like pop music .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I think so , since I was in primary school . How long have you been interested in classical music .", + "emotion": "neutral", + "text": "I think so , since I was in primary school . How long have you been interested in classical music .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I didn't like it at all until I started to learn violin when I was eight . From then on . classical music has been an important part of my life .", + "emotion": "neutral", + "text": "I didn't like it at all until I started to learn violin when I was eight . From then on . classical music has been an important part of my life .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "oh , I didn't know you can play the violin . Do you still play .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "I started to learn violin when I was eight ." + ], + "type": [ + "inter-personal" + ], + "text": "oh , I didn't know you can play the violin . Do you still play .", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Sometimes , but these days I'm often too busy .", + "emotion": "neutral", + "text": "Sometimes , but these days I'm often too busy .", + "id": 14 + } +] \ No newline at end of file diff --git a/reccon/sources/te_834.json b/reccon/sources/te_834.json new file mode 100644 index 0000000000000000000000000000000000000000..dc99626448430cf3ec530a5445f6870ed975345c --- /dev/null +++ b/reccon/sources/te_834.json @@ -0,0 +1,129 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I am so busy today .", + "emotion": "neutral", + "text": "I am so busy today .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Can I help you ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "I am so busy today .", + "Can I help you ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Can I help you ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I ' m not sure . Perhaps you could do the shopping .", + "emotion": "neutral", + "text": "I ' m not sure . Perhaps you could do the shopping .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I ' ll be glad to help .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "you could do the shopping .", + "I ' ll be glad to help ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I ' ll be glad to help .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Or maybe make the beds .", + "emotion": "neutral", + "text": "Or maybe make the beds .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "All you have to do is ask for help .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "I ' ll be glad to help .", + "make the beds ." + ], + "type": [ + "hybrid" + ], + "text": "All you have to do is ask for help .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Thanks . That ' s terrific !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "All you have to do is ask for help ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks . That ' s terrific !", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I ' m ready and willing to help .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 7, + 8 + ], + "expanded emotion cause span": [ + "I ' ll be glad to help .", + "Thanks . That ' s terrific !", + "I ' m ready and willing to help ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I ' m ready and willing to help .", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/te_844.json b/reccon/sources/te_844.json new file mode 100644 index 0000000000000000000000000000000000000000..744de711dba368c8ceaa483f41874047570d7df6 --- /dev/null +++ b/reccon/sources/te_844.json @@ -0,0 +1,144 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , I made a reservation for a mid-size vehicle . The name is Jimmy Fox .", + "emotion": "neutral", + "text": "Hi , I made a reservation for a mid-size vehicle . The name is Jimmy Fox .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I ' m sorry , we have no mid-size available at the moment .", + "emotion": "neutral", + "text": "I ' m sorry , we have no mid-size available at the moment .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I don ' t understand , I made a reservation , do you have my reservation ?", + "emotion": "neutral", + "text": "I don ' t understand , I made a reservation , do you have my reservation ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes , we do , unfortunately we ran out of cars .", + "emotion": "neutral", + "text": "Yes , we do , unfortunately we ran out of cars .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "But the reservation keeps the car here . That ' s why you have the reservation .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "unfortunately we ran out of cars ." + ], + "type": [ + "inter-personal" + ], + "text": "But the reservation keeps the car here . That ' s why you have the reservation .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I know why we have reservations .", + "emotion": "neutral", + "text": "I know why we have reservations .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I don ' t think you do . If you did , I ' d have a car . See , you know how to take the reservation , you just don ' t know how to hold the reservation and that ' s really the most important part of the reservation , the holding . Anybody can just take them .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 4, + 7 + ], + "expanded emotion cause span": [ + "unfortunately we ran out of cars .", + "you just don ' t know how to hold the reservation" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I don ' t think you do . If you did , I ' d have a car . See , you know how to take the reservation , you just don ' t know how to hold the reservation and that ' s really the most important part of the reservation , the holding . Anybody can just take them .", + "id": 7, + "source_sentences": [ + 3 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "But we do have a compact or an SUV if you ' d like .", + "emotion": "neutral", + "text": "But we do have a compact or an SUV if you ' d like .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Fine . I ' ll take the compact .", + "emotion": "anger", + "flag": "F", + "expanded emotion cause evidence": [ + 4, + 7 + ], + "expanded emotion cause span": [ + "unfortunately we ran out of cars .", + "you just don ' t know how to hold the reservation" + ], + "type": [ + "hybrid" + ], + "text": "Fine . I ' ll take the compact .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Alright . We have a blue Ford Focus for you , Mr . Fox . Would you like insurance ?", + "emotion": "neutral", + "text": "Alright . We have a blue Ford Focus for you , Mr . Fox . Would you like insurance ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Yeah , you better give me the insurance , because I am gonna beat the hell out of this car .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 4, + 7, + 10, + 11 + ], + "expanded emotion cause span": [ + "unfortunately we ran out of cars .", + "you just don ' t know how to hold the reservation", + "Would you like insurance ?", + "I am gonna beat the hell out of this car ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Yeah , you better give me the insurance , because I am gonna beat the hell out of this car .", + "id": 11 + } +] \ No newline at end of file diff --git a/reccon/sources/te_847.json b/reccon/sources/te_847.json new file mode 100644 index 0000000000000000000000000000000000000000..ba86e117273cc361fe3f3c3e78d1c8c66c9f9eba --- /dev/null +++ b/reccon/sources/te_847.json @@ -0,0 +1,170 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What happened ? Why didn't he win ?", + "emotion": "neutral", + "text": "What happened ? Why didn't he win ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Didn't you hear ? He was disqualified .", + "emotion": "neutral", + "text": "Didn't you hear ? He was disqualified .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "How did that happen ? He's so talented ! I thought he had a great chance of winning a gold medal !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "He was disqualified ." + ], + "type": [ + "inter-personal" + ], + "text": "How did that happen ? He's so talented ! I thought he had a great chance of winning a gold medal !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "If he didn't have any drug problems , he would have won .", + "emotion": "neutral", + "text": "If he didn't have any drug problems , he would have won .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "What ? What kind of drugs was he using ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "If he didn't have any drug problems ," + ], + "type": [ + "inter-personal" + ], + "text": "What ? What kind of drugs was he using ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "He was taking steroids to make him stronger and faster .", + "emotion": "neutral", + "text": "He was taking steroids to make him stronger and faster .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I thought that all athletes were supposed to be regularly tested for drugs .", + "emotion": "disgust", + "flag": "F", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "He was taking steroids to make him stronger and faster ." + ], + "type": [ + "inter-personal" + ], + "text": "I thought that all athletes were supposed to be regularly tested for drugs .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "They are . The only reason they didn't disqualify him until after the race is because the results from the text only came back afterwards .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "He was taking steroids to make him stronger and faster ." + ], + "type": [ + "self-contagion" + ], + "text": "They are . The only reason they didn't disqualify him until after the race is because the results from the text only came back afterwards .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "That's so disappointing . I don't know why top athletes would feel the need to take drugs .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 6, + 9 + ], + "expanded emotion cause span": [ + "He was taking steroids to make him stronger and faster .", + "I don't know why top athletes would feel the need to take drugs ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's so disappointing . I don't know why top athletes would feel the need to take drugs .", + "id": 9, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I don't think it's right , but I can understand why they might . Imagine how much pressure there would be to win for your country !", + "emotion": "disgust", + "flag": "F", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "He was taking steroids to make him stronger and faster ." + ], + "type": [ + "self-contagion" + ], + "text": "I don't think it's right , but I can understand why they might . Imagine how much pressure there would be to win for your country !", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Regardless of how much pressure you're under , there's never a good reason to take drugs .", + "emotion": "neutral", + "text": "Regardless of how much pressure you're under , there's never a good reason to take drugs .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I agree . Hopefully with the new regulations , fewer athletes will try to cheat with drugs .", + "emotion": "neutral", + "text": "I agree . Hopefully with the new regulations , fewer athletes will try to cheat with drugs .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Let's hope so .", + "emotion": "neutral", + "text": "Let's hope so .", + "id": 13 + } +] \ No newline at end of file diff --git a/reccon/sources/te_864.json b/reccon/sources/te_864.json new file mode 100644 index 0000000000000000000000000000000000000000..cd9b885c1db3b29dcc64214d5fe7dde74b3b5e5e --- /dev/null +++ b/reccon/sources/te_864.json @@ -0,0 +1,198 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Matthew ? Hi !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Matthew ? Hi !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Steve ! Haven't seen you in ages ! How long's it been ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Haven't seen you in ages !" + ], + "type": [ + "no-context" + ], + "text": "Steve ! Haven't seen you in ages ! How long's it been ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "It's got to be almost a year now .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Haven't seen you in ages !" + ], + "type": [ + "inter-personal" + ], + "text": "It's got to be almost a year now .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "How have you been ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Haven't seen you in ages !" + ], + "type": [ + "self-contagion" + ], + "text": "How have you been ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I'm pretty good . I've been looking for a place to live recently . My lease runs out next month and I don't want to renew it .", + "emotion": "happiness", + "explanation": "Considering he is happy because he is seeing his friend after a long time and not because he is pretty good.", + "expanded emotion cause evidence": [ + 2, + 5 + ], + "expanded emotion cause span": [ + "Haven't seen you in ages !", + "I'm pretty good ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm pretty good . I've been looking for a place to live recently . My lease runs out next month and I don't want to renew it .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yeah , I remember the neighborhood . Have you found a place yet ?", + "emotion": "neutral", + "text": "Yeah , I remember the neighborhood . Have you found a place yet ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Not yet . But I am still looking through the classifieds . Wish me luck .", + "emotion": "neutral", + "text": "Not yet . But I am still looking through the classifieds . Wish me luck .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Well , maybe I can help . Remember my neighbor ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "maybe I can help ." + ], + "type": [ + "no-context" + ], + "text": "Well , maybe I can help . Remember my neighbor ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Mrs . Thou ?", + "emotion": "neutral", + "text": "Mrs . Thou ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Yes , her daughter's having a baby , so she's moving in with her to help out . I think if you are interested , you can come over and have a look .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 10 + ], + "expanded emotion cause span": [ + "maybe I can help .", + "she's moving in with her to help out . I think if you are interested , you can come over and have a look ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Yes , her daughter's having a baby , so she's moving in with her to help out . I think if you are interested , you can come over and have a look .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Great . It's a lovely neighborhood . And it would be nice to be neighbors again . It would be just like the old days !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "you can come over and have a look .", + "It's a lovely neighborhood . And it would be nice to be neighbors again . It would be just like the old days !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Great . It's a lovely neighborhood . And it would be nice to be neighbors again . It would be just like the old days !", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I'll ask Mrs . Thou when she's available to show the apartment and let you know . Has your number changed ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 10, + 11 + ], + "expanded emotion cause span": [ + "maybe I can help .", + "she's moving in with her to help out . I think if you are interested , you can come over and have a look .", + "It's a lovely neighborhood . And it would be nice to be neighbors again . It would be just like the old days !" + ], + "type": [ + "hybrid" + ], + "text": "I'll ask Mrs . Thou when she's available to show the apartment and let you know . Has your number changed ?", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/te_891.json b/reccon/sources/te_891.json new file mode 100644 index 0000000000000000000000000000000000000000..60a4f8f0651f2d77dc91d6c753d84bd868acefed --- /dev/null +++ b/reccon/sources/te_891.json @@ -0,0 +1,125 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Why didn't you tell me you had a girlfriend ?", + "emotion": "neutral", + "text": "Why didn't you tell me you had a girlfriend ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Sorry , I thought you knew .", + "emotion": "neutral", + "text": "Sorry , I thought you knew .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "But you should tell me you were in love with her .", + "emotion": "neutral", + "text": "But you should tell me you were in love with her .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Didn't I ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + "b", + 3 + ], + "expanded emotion cause span": [ + "b", + "But you should tell me you were in love with her ." + ], + "type": [ + "latent", + "inter-personal" + ], + "text": "Didn't I ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "You know you didn't .", + "emotion": "neutral", + "text": "You know you didn't .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Well , I am telling you now .", + "emotion": "neutral", + "text": "Well , I am telling you now .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yes , but you might have told me before .", + "emotion": "neutral", + "text": "Yes , but you might have told me before .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I didn't think you would be interested .", + "emotion": "neutral", + "text": "I didn't think you would be interested .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "You can't be serious . How dare you not tell me you are going to marry her ?", + "emotion": "anger", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "How dare you not tell me you are going to marry her ?" + ], + "type": [ + "no-context" + ], + "text": "You can't be serious . How dare you not tell me you are going to marry her ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Sorry , I didn't think it mattered .", + "emotion": "neutral", + "text": "Sorry , I didn't think it mattered .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Oh , you men ! You are all the same .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Sorry , I didn't think it mattered ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , you men ! You are all the same .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_901.json b/reccon/sources/te_901.json new file mode 100644 index 0000000000000000000000000000000000000000..663f6947340168fc3f923d4c295b6743b18b00ea --- /dev/null +++ b/reccon/sources/te_901.json @@ -0,0 +1,117 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , Victor . How are you ?", + "emotion": "neutral", + "text": "Hi , Victor . How are you ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh , I'm fine .", + "emotion": "neutral", + "text": "Oh , I'm fine .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "So , are you going to go to class tonight ?", + "emotion": "neutral", + "text": "So , are you going to go to class tonight ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Maybe ... but I don't think so .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Maybe ... but I don't think so .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Really ? What's the matter ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Maybe ... but I don't think so ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? What's the matter ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I don't know . I'm just feeling a little sad .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I don't know . I'm just feeling a little sad ." + ], + "type": [ + "no-context" + ], + "text": "I don't know . I'm just feeling a little sad .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Listen . Come with me to class , and after class we can go out for dinner .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Come with me to class , and after class we can go out for dinner ." + ], + "type": [ + "no-context" + ], + "text": "Listen . Come with me to class , and after class we can go out for dinner .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Now that's a good idea . Thanks a lot , Brian . I'm feeling better already .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Come with me to class , and after class we can go out for dinner ." + ], + "type": [ + "inter-personal" + ], + "text": "Now that's a good idea . Thanks a lot , Brian . I'm feeling better already .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_910.json b/reccon/sources/te_910.json new file mode 100644 index 0000000000000000000000000000000000000000..48f103cd9a129f24d24598a5d25962d3544751f7 --- /dev/null +++ b/reccon/sources/te_910.json @@ -0,0 +1,135 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello , Bessie .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 1 + ], + "expanded emotion cause span": [ + "b", + "Bessie" + ], + "type": [ + "latent", + "no-context" + ], + "text": "Hello , Bessie .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hello , Jack . Happy birthday !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Happy birthday !" + ], + "type": [ + "no-context" + ], + "text": "Hello , Jack . Happy birthday !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "My birthday ? I forgot it , Thank you for remembering my birthday .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Happy birthday !" + ], + "type": [ + "inter-personal" + ], + "text": "My birthday ? I forgot it , Thank you for remembering my birthday .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I'd like to offer you my congratulations on your birthday and best wishes for your future happiness , good health and continued success . I've asked the Fairy Flowers to send you a bunch of flowers . I hope you'll like them .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "Thank you for remembering my birthday", + "offer you my congratulations on your birthday and best wishes for your future happiness , good health and continued success ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'd like to offer you my congratulations on your birthday and best wishes for your future happiness , good health and continued success . I've asked the Fairy Flowers to send you a bunch of flowers . I hope you'll like them .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Thanks a lot . I'm so touched .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I'd like to offer you my congratulations on your birthday and best wishes for your future happiness , good health and continued success . I've asked the Fairy Flowers to send you a bunch of flowers . I hope you'll like them ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks a lot . I'm so touched .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Now let me sing \" Happy birthday \" for you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Happy birthday !" + ], + "type": [ + "self-contagion" + ], + "text": "Now let me sing \" Happy birthday \" for you .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Thank you very much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 6 + ], + "expanded emotion cause span": [ + "I'd like to offer you my congratulations on your birthday and best wishes for your future happiness , good health and continued success . I've asked the Fairy Flowers to send you a bunch of flowers . I hope you'll like them .", + "Now let me sing \" Happy birthday \" for you ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you very much .", + "id": 7, + "source_sentences": [ + 3, + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_913.json b/reccon/sources/te_913.json new file mode 100644 index 0000000000000000000000000000000000000000..4c51ee24bb00ffc80c24fc15f358448d63eac61b --- /dev/null +++ b/reccon/sources/te_913.json @@ -0,0 +1,142 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Diane Grant ? I haven't seen you for ages !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I haven't seen you for ages !" + ], + "type": [ + "no-context" + ], + "text": "Diane Grant ? I haven't seen you for ages !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Brian ! How have you been ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I haven't seen you for ages !" + ], + "type": [ + "inter-personal" + ], + "text": "Brian ! How have you been ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Pretty good . Say , you've really changed !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 3 + ], + "expanded emotion cause span": [ + "I haven't seen you for ages !", + "How have you been ?", + "Pretty good ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Pretty good . Say , you've really changed !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Oh , well , I've lost some weight . And my hair is longer than before .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 4, + 4 + ], + "expanded emotion cause span": [ + "I haven't seen you for ages !", + "I've lost some weight .", + "my hair is longer than before ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , well , I've lost some weight . And my hair is longer than before .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Well , you look great ! How are you ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 5 + ], + "expanded emotion cause span": [ + "I haven't seen you for ages !", + "you look great !" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Well , you look great ! How are you ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I'm doing really well . I got married about three years ago . I have two kids now .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "you look great !", + "I'm doing really well ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm doing really well . I got married about three years ago . I have two kids now .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "That's terrific !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I'm doing really well . I got married about three years ago . I have two kids now ." + ], + "type": [ + "inter-personal" + ], + "text": "That's terrific !", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_916.json b/reccon/sources/te_916.json new file mode 100644 index 0000000000000000000000000000000000000000..235dfd69d016ba6aa529afb7223e76cafebf3696 --- /dev/null +++ b/reccon/sources/te_916.json @@ -0,0 +1,123 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What ' s the Mountaineering Club doing this weekend ?", + "emotion": "neutral", + "text": "What ' s the Mountaineering Club doing this weekend ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "We are going to climb a cliff on the Colorado River .", + "emotion": "neutral", + "text": "We are going to climb a cliff on the Colorado River .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "How hard is the climb ?", + "emotion": "neutral", + "text": "How hard is the climb ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It is a very difficult climb because there are not many places to put your hands and feet .", + "emotion": "neutral", + "text": "It is a very difficult climb because there are not many places to put your hands and feet .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "What did you do last week ?", + "emotion": "neutral", + "text": "What did you do last week ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "We rappelled down the side of 300 - foot cliff . It was very exciting .", + "emotion": "neutral", + "text": "We rappelled down the side of 300 - foot cliff . It was very exciting .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Wow ! That sounds like a lot of fun . I ' m sorry I missed it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "We rappelled down the side of 300 - foot cliff . It was very exciting ." + ], + "type": [ + "inter-personal" + ], + "text": "Wow ! That sounds like a lot of fun . I ' m sorry I missed it .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Well , you should come this weekend . I think you could do the climb .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Well , you should come this weekend . I think you could do the climb ." + ], + "type": [ + "no-context" + ], + "text": "Well , you should come this weekend . I think you could do the climb .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yeah , I will . See you then !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "you should come this weekend" + ], + "type": [ + "inter-personal" + ], + "text": "Yeah , I will . See you then !", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "O . K . See you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Yeah , I will . See you then !" + ], + "type": [ + "inter-personal" + ], + "text": "O . K . See you .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_924.json b/reccon/sources/te_924.json new file mode 100644 index 0000000000000000000000000000000000000000..e9a6ddc410c84eeb58e77559374ec679e038f84b --- /dev/null +++ b/reccon/sources/te_924.json @@ -0,0 +1,260 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What a beautiful watch . It goes very well with your ring .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "beautiful watch . It goes very well with your ring ." + ], + "type": [ + "no-context" + ], + "text": "What a beautiful watch . It goes very well with your ring .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Thank you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "beautiful watch . It goes very well with your ring ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Is that your wedding ring ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "wedding ring ?" + ], + "type": [ + "no-context" + ], + "text": "Is that your wedding ring ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I'm not married yet . It's my engagement ring .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "engagement ring" + ], + "type": [ + "no-context" + ], + "text": "I'm not married yet . It's my engagement ring .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Well , congratulations . When is the big date ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "engagement", + "big date" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Well , congratulations . When is the big date ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "In June .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 5 + ], + "expanded emotion cause span": [ + "congratulations", + "big date" + ], + "type": [ + "inter-personal" + ], + "text": "In June .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Did you have the watch before getting the ring ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 1 + ], + "expanded emotion cause span": [ + "big date", + "beautiful watch . It goes very well with your ring ." + ], + "type": [ + "self-contagion" + ], + "text": "Did you have the watch before getting the ring ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Actually , we bought the ring together after I got the watch .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 8 + ], + "expanded emotion cause span": [ + "big date", + "we bought the ring together after I got the watch ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Actually , we bought the ring together after I got the watch .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "You did a fabulous job with the selection . It's gorgeous .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "It's gorgeous ." + ], + "type": [ + "no-context" + ], + "text": "You did a fabulous job with the selection . It's gorgeous .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Thank you so much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "You did a fabulous job with the selection . It's gorgeous ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you so much .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "What kind of watch is it ?", + "emotion": "neutral", + "text": "What kind of watch is it ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "It's a Tag Heer .", + "emotion": "neutral", + "text": "It's a Tag Heer .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "If you don't mind me asking , how much do they cost ?", + "emotion": "neutral", + "text": "If you don't mind me asking , how much do they cost ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "This one is $ 1500 . But they range from $ 600 to $ 3000 .", + "emotion": "neutral", + "text": "This one is $ 1500 . But they range from $ 600 to $ 3000 .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "That's why it looks so nice . I should have figured . You always get what you pay for .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "it looks so nice ." + ], + "type": [ + "no-context" + ], + "text": "That's why it looks so nice . I should have figured . You always get what you pay for .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Yeah . I would rather get one nice watch instead of 20 mediocre ones .", + "emotion": "happiness", + "explanation": "the speaker is happy that A has approved her decision to pay more for a nice watch", + "expanded emotion cause evidence": [ + 15, + 15, + 16 + ], + "expanded emotion cause span": [ + "it looks so nice .", + "You always get what you pay for .", + "rather get one nice watch instead of 20 mediocre ones ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yeah . I would rather get one nice watch instead of 20 mediocre ones .", + "id": 16, + "source_sentences": [ + 14, + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_932.json b/reccon/sources/te_932.json new file mode 100644 index 0000000000000000000000000000000000000000..8f1ca03db513467f4d2ccf65e0eee3ed29dd50d1 --- /dev/null +++ b/reccon/sources/te_932.json @@ -0,0 +1,192 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Good morning . I ' m from the New York book review . Could I ask you some questions about your latest book ?", + "emotion": "neutral", + "text": "Good morning . I ' m from the New York book review . Could I ask you some questions about your latest book ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Sure . Take a seat ... what would you like to know ?", + "emotion": "neutral", + "text": "Sure . Take a seat ... what would you like to know ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "First , I ' Ve heard that your latest book is based on a true story .", + "emotion": "neutral", + "text": "First , I ' Ve heard that your latest book is based on a true story .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "That ' s correct . It ' s a murder mystery based on actual murders that book place in Florida several years ago . The main character-the police invesigator-is based on the man who investigated the case .", + "emotion": "happiness", + "explanation": "A shows interest in B's book", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I ' Ve heard that your latest book is based on a true story ." + ], + "type": [ + "inter-personal" + ], + "text": "That ' s correct . It ' s a murder mystery based on actual murders that book place in Florida several years ago . The main character-the police invesigator-is based on the man who investigated the case .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "How do you research your books ?", + "emotion": "happiness", + "explanation": "The speaker is happy due to harmony with the fellow speaker.", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "How do you research your books ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I always visit the places that I use as setting for stories . Readers like things to be as factually correct as possible-even in fiction ! I usually base my characters on people I have met . Most character are a mixture of the characters of two or more people .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I ' Ve heard that your latest book is based on a true story ." + ], + "type": [ + "inter-personal" + ], + "text": "I always visit the places that I use as setting for stories . Readers like things to be as factually correct as possible-even in fiction ! I usually base my characters on people I have met . Most character are a mixture of the characters of two or more people .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I really like your books . I ' Ve just finished this one . I read it from cover to cover in a single day . Congratulation on making the bestseller list yet again !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 7 + ], + "expanded emotion cause span": [ + "I really like your books .", + "Congratulation" + ], + "type": [ + "no-context" + ], + "text": "I really like your books . I ' Ve just finished this one . I read it from cover to cover in a single day . Congratulation on making the bestseller list yet again !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Thank you . Let met sign it for you ... there you go .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 7 + ], + "expanded emotion cause span": [ + "I really like your books .", + "Congratulation" + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . Let met sign it for you ... there you go .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Oh ! Thank you very much . I heard that you are currently writing a collection of short stories . What are the stories about ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 7, + 8, + 9 + ], + "expanded emotion cause span": [ + "I really like your books .", + "Congratulation", + "Let met sign it for you", + "I heard that you are currently writing a collection of short stories" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Oh ! Thank you very much . I heard that you are currently writing a collection of short stories . What are the stories about ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "There ' s a real mix of stories in the book . I haven ' t finished all of them yet , though . Many of them are short detective stories , but there are also horror stories and sci-fi ones . If you give me your business card , I ' ll make sure you get an advance copy to review .", + "emotion": "happiness", + "explanation": "The speaker is happy due to the demonstrated interest on his/her work", + "expanded emotion cause evidence": [ + 7, + 7, + 9 + ], + "expanded emotion cause span": [ + "I really like your books .", + "Congratulation", + "What are the stories about ?" + ], + "type": [ + "inter-personal" + ], + "text": "There ' s a real mix of stories in the book . I haven ' t finished all of them yet , though . Many of them are short detective stories , but there are also horror stories and sci-fi ones . If you give me your business card , I ' ll make sure you get an advance copy to review .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Thanks very much . I ' m sure it will sell well . I can ' t wait to read it . Here ' s my card . Thank you for you time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11, + 11 + ], + "expanded emotion cause span": [ + "I ' ll make sure you get an advance copy", + "I can ' t wait to read it .", + "Thank you for you time ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thanks very much . I ' m sure it will sell well . I can ' t wait to read it . Here ' s my card . Thank you for you time .", + "id": 11, + "source_sentences": [ + 9, + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_942.json b/reccon/sources/te_942.json new file mode 100644 index 0000000000000000000000000000000000000000..5dd985a0017c11deecfcc5f70e1142f6388df9b3 --- /dev/null +++ b/reccon/sources/te_942.json @@ -0,0 +1,147 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "You look so happy , Anna . Any good news ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "You look so happy" + ], + "type": [ + "no-context" + ], + "text": "You look so happy , Anna . Any good news ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes . I ' Ve won the first prize in the math contest .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I ' Ve won the first prize in the math contest ." + ], + "type": [ + "no-context" + ], + "text": "Yes . I ' Ve won the first prize in the math contest .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Really ? Congratulations !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I ' Ve won the first prize in the math contest ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? Congratulations !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Thank you , Paul .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "I ' Ve won the first prize in the math contest .", + "Congratulations !" + ], + "type": [ + "hybrid" + ], + "text": "Thank you , Paul .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "By the way , would you like to have dinner with me tomorrow evening ? Tomorrow is my birthday .", + "emotion": "neutral", + "text": "By the way , would you like to have dinner with me tomorrow evening ? Tomorrow is my birthday .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Good , happy birthday to you !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Tomorrow is my birthday ." + ], + "type": [ + "inter-personal" + ], + "text": "Good , happy birthday to you !", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Not so soon . It ' s not my birthday today . Well , you ' ll come , won ' t you ?", + "emotion": "neutral", + "text": "Not so soon . It ' s not my birthday today . Well , you ' ll come , won ' t you ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Sure , I will . Thank you for inviting me .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "you ' ll come ,", + "Thank you for inviting me ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Sure , I will . Thank you for inviting me .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "My pleasure .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Sure , I will . Thank you for inviting me ." + ], + "type": [ + "inter-personal" + ], + "text": "My pleasure .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_958.json b/reccon/sources/te_958.json new file mode 100644 index 0000000000000000000000000000000000000000..e3c27a6266faf3b38e0a8a7bbff1f3325935f7b8 --- /dev/null +++ b/reccon/sources/te_958.json @@ -0,0 +1,227 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Why are you so quiet ?", + "emotion": "neutral", + "text": "Why are you so quiet ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "My girlfriend just broke up with me .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "My girlfriend just broke up with me ." + ], + "type": [ + "no-context" + ], + "text": "My girlfriend just broke up with me .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "You must feel terrible now .", + "emotion": "neutral", + "text": "You must feel terrible now .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yeah .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "My girlfriend just broke up with me ." + ], + "type": [ + "self-contagion" + ], + "text": "Yeah .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I remember my first break up . It was the worst feeling in the world . I was crying everyday for three months . And slowly , it got better . I know you'll feel better too .", + "emotion": "neutral", + "text": "I remember my first break up . It was the worst feeling in the world . I was crying everyday for three months . And slowly , it got better . I know you'll feel better too .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "You've been through this too ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I remember my first break up . It was the worst feeling in the world . I was crying everyday for three months ." + ], + "type": [ + "inter-personal" + ], + "text": "You've been through this too ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yeah . I remember it very clearly . The pain makes it easy to remember . I know you're really hurting right now , but you know many people experience break ups .", + "emotion": "neutral", + "text": "Yeah . I remember it very clearly . The pain makes it easy to remember . I know you're really hurting right now , but you know many people experience break ups .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "But it hurts too much .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2, + 8 + ], + "expanded emotion cause span": [ + "My girlfriend just broke up with me .", + "hurts too much ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "But it hurts too much .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I know it's painful , but it's only temporary . After the pain goes away , you'll find other girls .", + "emotion": "neutral", + "text": "I know it's painful , but it's only temporary . After the pain goes away , you'll find other girls .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "What if I don't want to find another girl ?", + "emotion": "neutral", + "text": "What if I don't want to find another girl ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "You'll change your mind . Look at everyone in the world . They all break up and move on . The faster you understand this , the quicker you will recover .", + "emotion": "neutral", + "text": "You'll change your mind . Look at everyone in the world . They all break up and move on . The faster you understand this , the quicker you will recover .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "You're right .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 11 + ], + "expanded emotion cause span": [ + "it's only temporary . After the pain goes away , you'll find other girls .", + "You'll change your mind . Look at everyone in the world . They all break up and move on ." + ], + "type": [ + "inter-personal" + ], + "text": "You're right .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I also know you must still have strong feelings for her , but try to think of all the bad things . You know she didn't treat you that well . Is that the person you want to spend the rest of your life with ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "You're right ." + ], + "type": [ + "inter-personal" + ], + "text": "I also know you must still have strong feelings for her , but try to think of all the bad things . You know she didn't treat you that well . Is that the person you want to spend the rest of your life with ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Yeah . Thanks for the talk .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 11, + 13 + ], + "expanded emotion cause span": [ + "it's only temporary . After the pain goes away , you'll find other girls .", + "You'll change your mind . Look at everyone in the world . They all break up and move on .", + "but try to think of all the bad things . You know she didn't treat you that well . Is that the person you want to spend the rest of your life with ?" + ], + "type": [ + "inter-personal" + ], + "text": "Yeah . Thanks for the talk .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "I'll give you a call later . We should hang out . It's good to be around people .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12, + 14 + ], + "expanded emotion cause span": [ + "You're right .", + "Yeah . Thanks for the talk ." + ], + "type": [ + "inter-personal" + ], + "text": "I'll give you a call later . We should hang out . It's good to be around people .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Ok . I'll talk to you later .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "I'll give you a call later . We should hang out . It's good to be around people ." + ], + "type": [ + "inter-personal" + ], + "text": "Ok . I'll talk to you later .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_968.json b/reccon/sources/te_968.json new file mode 100644 index 0000000000000000000000000000000000000000..59bf96537799c498e645380d3224a616a96b6164 --- /dev/null +++ b/reccon/sources/te_968.json @@ -0,0 +1,177 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What's the problem , Nada ? You look down in the dumps .", + "emotion": "neutral", + "text": "What's the problem , Nada ? You look down in the dumps .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I don't know . My life is a big mess . Everything is so complicated .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "My life is a big mess . Everything is so complicated ." + ], + "type": [ + "no-context" + ], + "text": "I don't know . My life is a big mess . Everything is so complicated .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "come on , nothing can be that bad .", + "emotion": "neutral", + "text": "come on , nothing can be that bad .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "but promise me , you'll keep it a secret .", + "emotion": "neutral", + "text": "but promise me , you'll keep it a secret .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "ok , I promise . So what's troubling you so much ?", + "emotion": "neutral", + "text": "ok , I promise . So what's troubling you so much ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I've fallen in love with my boss .", + "emotion": "neutral", + "text": "I've fallen in love with my boss .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "really ? Is he married ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I've fallen in love with my boss ." + ], + "type": [ + "inter-personal" + ], + "text": "really ? Is he married ?", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "no , of course not . He is still single .", + "emotion": "neutral", + "text": "no , of course not . He is still single .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "then what's your problem ?", + "emotion": "neutral", + "text": "then what's your problem ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I try to keep it to myself . But there is a lot of gossip about us .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "there is a lot of gossip about us ." + ], + "type": [ + "no-context" + ], + "text": "I try to keep it to myself . But there is a lot of gossip about us .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "oh , I see . Office romance tends to be the subject of gossip .", + "emotion": "neutral", + "text": "oh , I see . Office romance tends to be the subject of gossip .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "worse still , he is trying to avoid me these days .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 10, + 12 + ], + "expanded emotion cause span": [ + "there is a lot of gossip about us .", + "he is trying to avoid me these days ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "worse still , he is trying to avoid me these days .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "office romance is very tricky .", + "emotion": "neutral", + "text": "office romance is very tricky .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "it gives me a lot of pressure and I feel depressed .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 14, + 14 + ], + "expanded emotion cause span": [ + "it gives me a lot of pressure", + "I feel depressed ." + ], + "type": [ + "no-context" + ], + "text": "it gives me a lot of pressure and I feel depressed .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "cheer up , Nada . You'll be fine .", + "emotion": "neutral", + "text": "cheer up , Nada . You'll be fine .", + "id": 15 + } +] \ No newline at end of file diff --git a/reccon/sources/te_980.json b/reccon/sources/te_980.json new file mode 100644 index 0000000000000000000000000000000000000000..5356f1f409813d6f376f71b580f881b0c131a8f0 --- /dev/null +++ b/reccon/sources/te_980.json @@ -0,0 +1,174 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "It's quiet everywhere in winter .", + "emotion": "neutral", + "text": "It's quiet everywhere in winter .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes . I like winter .", + "emotion": "neutral", + "text": "Yes . I like winter .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Me too .", + "emotion": "neutral", + "text": "Me too .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It's snowing heavily . What about taking a walk ?", + "emotion": "happiness", + "explanation": "2 adds supporting evidence and close to the target utterance.", + "expanded emotion cause evidence": [ + 2, + 4 + ], + "expanded emotion cause span": [ + "Yes . I like winter .", + "It's snowing heavily ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "It's snowing heavily . What about taking a walk ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "That's a good idea . Let's go !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "What about taking a walk ?" + ], + "type": [ + "inter-personal" + ], + "text": "That's a good idea . Let's go !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "What a heavy snow ! Look ! The water is frozen .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 6 + ], + "expanded emotion cause span": [ + "I like winter .", + "What a heavy snow ! Look ! The water is frozen ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "What a heavy snow ! Look ! The water is frozen .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Take care ! Don't slip on the ground .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "What a heavy snow ! Look ! The water is frozen ." + ], + "type": [ + "inter-personal" + ], + "text": "Take care ! Don't slip on the ground .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I've got it . I like the feeling of stepping on the ice .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I like the feeling of stepping on the ice ." + ], + "type": [ + "no-context" + ], + "text": "I've got it . I like the feeling of stepping on the ice .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yes . Very wonderful .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I like the feeling of stepping on the ice ." + ], + "type": [ + "inter-personal" + ], + "text": "Yes . Very wonderful .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "There is a snowman over there .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "There is a snowman over there ." + ], + "type": [ + "no-context" + ], + "text": "There is a snowman over there .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "How lovely it is !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "There is a snowman over there ." + ], + "type": [ + "inter-personal" + ], + "text": "How lovely it is !", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/te_982.json b/reccon/sources/te_982.json new file mode 100644 index 0000000000000000000000000000000000000000..51bb838b1b274da28cb48633e9530d57aa5c496d --- /dev/null +++ b/reccon/sources/te_982.json @@ -0,0 +1,162 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Who are those guys ?", + "emotion": "neutral", + "text": "Who are those guys ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Kobe Bryant and Shaquille O ' Neal , they are the Los Angeles Lakers ' star players .", + "emotion": "neutral", + "text": "Kobe Bryant and Shaquille O ' Neal , they are the Los Angeles Lakers ' star players .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Oh .", + "emotion": "neutral", + "text": "Oh .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Wait a second . He shoots , he scores !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "He shoots , he scores !" + ], + "type": [ + "no-context" + ], + "text": "Wait a second . He shoots , he scores !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "All right !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "He shoots , he scores !" + ], + "type": [ + "inter-personal" + ], + "text": "All right !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Here comes Jordan , though .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Here comes Jordan , though ." + ], + "type": [ + "no-context" + ], + "text": "Here comes Jordan , though .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Wow , Michael Jordan ' s slam-dunks are beautiful things to watch .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "Here comes Jordan , though .", + "Wow , Michael Jordan ' s slam-dunks are beautiful things to watch ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Wow , Michael Jordan ' s slam-dunks are beautiful things to watch .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yeah . He ' s older , so he doesn ' t slam as much as he did when he was younger , but when he does , it ' s still amazing .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7, + 8 + ], + "expanded emotion cause span": [ + "Here comes Jordan , though .", + "Wow , Michael Jordan ' s slam-dunks are beautiful things to watch .", + "but when he does , it ' s still amazing ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Yeah . He ' s older , so he doesn ' t slam as much as he did when he was younger , but when he does , it ' s still amazing .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Which team do you think will win ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "Here comes Jordan , though .", + "Wow , Michael Jordan ' s slam-dunks are beautiful things to watch ." + ], + "type": [ + "hybrid" + ], + "text": "Which team do you think will win ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "The Lakers . Jordan is the only good player Washington has .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Here comes Jordan , though ." + ], + "type": [ + "self-contagion" + ], + "text": "The Lakers . Jordan is the only good player Washington has .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/te_999.json b/reccon/sources/te_999.json new file mode 100644 index 0000000000000000000000000000000000000000..d007bde32951c81061a75afc579279aec168aa4a --- /dev/null +++ b/reccon/sources/te_999.json @@ -0,0 +1,179 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What a nice day !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "What a nice day !" + ], + "type": [ + "no-context" + ], + "text": "What a nice day !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "yes . How about going out and enjoying the sunshine on the grass ?", + "emotion": "neutral", + "text": "yes . How about going out and enjoying the sunshine on the grass ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "great , let's go !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "yes . How about going out and enjoying the sunshine on the grass ?" + ], + "type": [ + "inter-personal" + ], + "text": "great , let's go !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "hey , darling , I think I might have a little heatstroke from being in the sun all day . I was so relaxed . It felt as if I were in another world .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I was so relaxed . It felt as if I were in another world ." + ], + "type": [ + "no-context" + ], + "text": "hey , darling , I think I might have a little heatstroke from being in the sun all day . I was so relaxed . It felt as if I were in another world .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "exactly . You know , the sunshine and wind remind me of our honeymoon . You remember ? The island , the sound of the waves , the salty sea air and the sunshine ...", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "I was so relaxed . It felt as if I were in another world .", + "You know , the sunshine and wind remind me of our honeymoon . You remember ? The island , the sound of the waves , the salty sea air and the sunshine ..." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "exactly . You know , the sunshine and wind remind me of our honeymoon . You remember ? The island , the sound of the waves , the salty sea air and the sunshine ...", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "yes , it was wonderful but it's already been a year . How time flies !", + "emotion": "neutral", + "text": "yes , it was wonderful but it's already been a year . How time flies !", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "why not go again to celebrate out one-year anniversary ? We can go to the same beach , stay in the same hotel and enjoy a dinner in the same restaurant .", + "emotion": "neutral", + "text": "why not go again to celebrate out one-year anniversary ? We can go to the same beach , stay in the same hotel and enjoy a dinner in the same restaurant .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "are you kidding ? Can you afford it ? Do you think we can get a room on such short notice ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "why not go again to celebrate out one-year anniversary ? We can go to the same beach , stay in the same hotel and enjoy a dinner in the same restaurant .", + "Can you afford it ? Do you think we can get a room on such short notice ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "are you kidding ? Can you afford it ? Do you think we can get a room on such short notice ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "never mind that , I'll take care of it . Are you available next week ?", + "emotion": "neutral", + "text": "never mind that , I'll take care of it . Are you available next week ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "yeah , I think so .", + "emotion": "neutral", + "text": "yeah , I think so .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "ok . I'll make the arrangements . It will be great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 9, + 10, + 11 + ], + "expanded emotion cause span": [ + "celebrate out one-year anniversary ?", + "Are you available next week ?", + "yeah , I think so .", + "It will be great ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "ok . I'll make the arrangements . It will be great .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "wonderful ! I'll start packing our suitcases .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I'll make the arrangements . It will be great ." + ], + "type": [ + "inter-personal" + ], + "text": "wonderful ! I'll start packing our suitcases .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/test.test.Ses05F_script01_1.json b/reccon/sources/test.test.Ses05F_script01_1.json new file mode 100644 index 0000000000000000000000000000000000000000..96fa51f50679d2878de99f4d606f1a1157ecc8b9 --- /dev/null +++ b/reccon/sources/test.test.Ses05F_script01_1.json @@ -0,0 +1,1133 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What's he going to say? Maybe we should tell him before he sees it.", + "emotion": "sad", + "explanation": "the speaker is sad that dad would see the crack", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "What's he going to say? Maybe we should tell him before he sees it.", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "He saw it.", + "emotion": "sad", + "flag": "F", + "expanded emotion cause evidence": [ + "b", + 2 + ], + "expanded emotion cause span": [ + "b", + "He saw it." + ], + "type": [ + "latent", + "no-context" + ], + "text": "He saw it.", + "id": 2 + }, + { + "turn": 3, + "speaker": "B", + "utterance": "He was out here when it broke.", + "emotion": "sad", + "flag": "F", + "expanded emotion cause evidence": [ + "b", + 2, + 3 + ], + "expanded emotion cause span": [ + "b", + "He saw it.", + "He was out here when it broke." + ], + "type": [ + "latent", + "no-context", + "self-contagion" + ], + "text": "He was out here when it broke.", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Around Four this morning, and there was a crack and I looked out. We're standing right there when I cracked.", + "emotion": "sad", + "flag": "F", + "expanded emotion cause evidence": [ + "b", + 2, + 3, + 4 + ], + "expanded emotion cause span": [ + "b", + "He saw it.", + "He was out here when it broke.", + "We're standing right there when I cracked." + ], + "type": [ + "latent", + "no-context", + "self-contagion" + ], + "text": "Around Four this morning, and there was a crack and I looked out. We're standing right there when I cracked.", + "id": 4 + }, + { + "turn": 5, + "speaker": "B", + "utterance": "I don't know. but When it cracked he ran back into the house and start to cry in the kitchen.", + "emotion": "sad", + "expanded emotion cause evidence": [ + "b", + 2, + 3, + 4, + 5 + ], + "expanded emotion cause span": [ + "b", + "He saw it.", + "He was out here when it broke.", + "We're standing right there when I cracked.", + "When it cracked he ran back into the house and start to cry in the kitchen." + ], + "type": [ + "latent", + "no-context", + "self-contagion" + ], + "text": "I don't know. but When it cracked he ran back into the house and start to cry in the kitchen.", + "id": 5 + }, + { + "turn": 6, + "speaker": "A", + "utterance": "Did you talk to him?", + "emotion": "sad", + "flag": "F", + "expanded emotion cause evidence": [ + "b", + 2, + 3, + 4, + 5 + ], + "expanded emotion cause span": [ + "b", + "He saw it.", + "He was out here when it broke.", + "We're standing right there when I cracked.", + "When it cracked he ran back into the house and start to cry in the kitchen." + ], + "type": [ + "latent", + "inter-personal" + ], + "text": "Did you talk to him?", + "id": 6 + }, + { + "turn": 7, + "speaker": "B", + "utterance": "No. I figured it was best to leave him alone.", + "emotion": "sad", + "expanded emotion cause evidence": [ + "b", + 2, + 3, + 4, + 5 + ], + "expanded emotion cause span": [ + "b", + "He saw it.", + "He was out here when it broke.", + "We're standing right there when I cracked.", + "When it cracked he ran back into the house and start to cry in the kitchen." + ], + "type": [ + "latent", + "self-contagion" + ], + "text": "No. I figured it was best to leave him alone.", + "id": 7 + }, + { + "turn": 8, + "speaker": "A", + "utterance": "He cried hard.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "He cried hard." + ], + "type": [ + "no-context" + ], + "text": "He cried hard.", + "id": 8 + }, + { + "turn": 9, + "speaker": "B", + "utterance": "I could hear him right through the floor of my room.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "He cried hard.", + "I could hear him right through the floor of my room." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I could hear him right through the floor of my room.", + "id": 9 + }, + { + "turn": 10, + "speaker": "A", + "utterance": "He is thinking about him again.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 8, + 9, + 10 + ], + "expanded emotion cause span": [ + "He cried hard.", + "I could hear him right through the floor of my room.", + "He is thinking about him again." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "He is thinking about him again.", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "It's getting just like after Larry died, he's having dreams, he's walking around at night.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 8, + 9, + 10, + 11 + ], + "expanded emotion cause span": [ + "He cried hard.", + "I could hear him right through the floor of my room.", + "He is thinking about him again.", + "after Larry died, he's having dreams, he's walking around at night" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "It's getting just like after Larry died, he's having dreams, he's walking around at night.", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I guess, he is.", + "emotion": "sad", + "flag": "F", + "expanded emotion cause evidence": [ + 8, + 9, + 10, + 11 + ], + "expanded emotion cause span": [ + "He cried hard.", + "I could hear him right through the floor of my room.", + "He is thinking about him again.", + "after Larry died, he's having dreams, he's walking around at night" + ], + "type": [ + "hybrid" + ], + "text": "I guess, he is.", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "What's the meaning of that?", + "emotion": "sad", + "flag": "F", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "I guess, he is." + ], + "type": [ + "inter-personal" + ], + "text": "What's the meaning of that?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "I don't know the meaning of it. But I know one thing mom did. We made a terrible mistake with dad.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "We made a terrible mistake with dad." + ], + "type": [ + "no-context" + ], + "text": "I don't know the meaning of it. But I know one thing mom did. We made a terrible mistake with dad.", + "id": 14 + }, + { + "turn": 15, + "speaker": "B", + "utterance": "Being dishonest with him. It's the kind of thing that pays off and now it's paying off.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 14, + 15 + ], + "expanded emotion cause span": [ + "We made a terrible mistake with dad.", + "Being dishonest with him. It's the kind of thing that pays off and now it's paying off." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Being dishonest with him. It's the kind of thing that pays off and now it's paying off.", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "You know that Larry's not coming back, and I know it. So why do we go on letting him think that we believe with him?", + "emotion": "sad", + "expanded emotion cause evidence": [ + 14, + 15, + 16 + ], + "expanded emotion cause span": [ + "We made a terrible mistake with dad.", + "Being dishonest with him. It's the kind of thing that pays off and now it's paying off.", + "You know that Larry's not coming back, and I know it. So why do we go on letting him think that we believe with him?" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "You know that Larry's not coming back, and I know it. So why do we go on letting him think that we believe with him?", + "id": 16 + }, + { + "turn": 17, + "speaker": "B", + "utterance": "No um, I don't want to argue with him, but it's time we realized that nobody else believes that Larry is alive.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 14, + 15, + 16, + 17 + ], + "expanded emotion cause span": [ + "We made a terrible mistake with dad.", + "Being dishonest with him. It's the kind of thing that pays off and now it's paying off.", + "You know that Larry's not coming back, and I know it. So why do we go on letting him think that we believe with him?", + "argue with him, but it's time we realized that nobody else believes that Larry is alive" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "No um, I don't want to argue with him, but it's time we realized that nobody else believes that Larry is alive.", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "Why shouldn't he dream about him, walk around during the night, looking for him um. Do we contradict him? Do we say outright that we don't have any hope anymore, that we haven't had any for years now?", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 14, + 15, + 16, + 17, + 18 + ], + "expanded emotion cause span": [ + "We made a terrible mistake with dad.", + "Being dishonest with him. It's the kind of thing that pays off and now it's paying off.", + "You know that Larry's not coming back, and I know it. So why do we go on letting him think that we believe with him?", + "argue with him, but it's time we realized that nobody else believes that Larry is alive", + "Why shouldn't he dream about him, walk around during the night, looking for him um. Do we contradict him? Do we say outright that we don't have any hope anymore, that we haven't had any for years now?" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Why shouldn't he dream about him, walk around during the night, looking for him um. Do we contradict him? Do we say outright that we don't have any hope anymore, that we haven't had any for years now?", + "id": 18 + }, + { + "turn": 19, + "speaker": "B", + "utterance": "We have to say it to him!", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 14, + 15, + 16, + 17, + 18, + 19 + ], + "expanded emotion cause span": [ + "We made a terrible mistake with dad.", + "Being dishonest with him. It's the kind of thing that pays off and now it's paying off.", + "You know that Larry's not coming back, and I know it. So why do we go on letting him think that we believe with him?", + "argue with him, but it's time we realized that nobody else believes that Larry is alive", + "Why shouldn't he dream about him, walk around during the night, looking for him um. Do we contradict him? Do we say outright that we don't have any hope anymore, that we haven't had any for years now?", + "We have to say it to him!" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "We have to say it to him!", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "For God's sake, mom, three years. Nobody comes back after three years! It's insane!", + "emotion": "angry", + "expanded emotion cause evidence": [ + 14, + 15, + 16, + 17, + 18, + 19, + 20 + ], + "expanded emotion cause span": [ + "We made a terrible mistake with dad.", + "Being dishonest with him. It's the kind of thing that pays off and now it's paying off.", + "You know that Larry's not coming back, and I know it. So why do we go on letting him think that we believe with him?", + "argue with him, but it's time we realized that nobody else believes that Larry is alive", + "Why shouldn't he dream about him, walk around during the night, looking for him um. Do we contradict him? Do we say outright that we don't have any hope anymore, that we haven't had any for years now?", + "We have to say it to him!", + "Nobody comes back after three years! It's insane!" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "For God's sake, mom, three years. Nobody comes back after three years! It's insane!", + "id": 20 + }, + { + "turn": 21, + "speaker": "A", + "utterance": "To you it is, and to me, but not to your father. Now look, you can talk yourself blue in the face, but there's no body, and there's no grave, so where are you?", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 20 + ], + "expanded emotion cause span": [ + "Nobody comes back after three years! It's insane!" + ], + "type": [ + "inter-personal" + ], + "text": "To you it is, and to me, but not to your father. Now look, you can talk yourself blue in the face, but there's no body, and there's no grave, so where are you?", + "id": 21 + }, + { + "turn": 22, + "speaker": "B", + "utterance": "Sit down, mom. I want to talk to you.", + "emotion": "frustrated", + "explanation": "the speaker wants to tell mom that he intends to marry Larry's girlfriend, but is frustrated by mom's unwillingness to make dad accept that Larry is dead", + "expanded emotion cause evidence": [ + "b", + 20 + ], + "expanded emotion cause span": [ + "b", + "Nobody comes back after three years! It's insane!" + ], + "type": [ + "latent", + "self-contagion" + ], + "text": "Sit down, mom. I want to talk to you.", + "id": 22 + }, + { + "turn": 23, + "speaker": "B", + "utterance": "All right, All right mom. Listen!", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 20 + ], + "expanded emotion cause span": [ + "Nobody comes back after three years! It's insane!" + ], + "type": [ + "self-contagion" + ], + "text": "All right, All right mom. Listen!", + "id": 23 + }, + { + "turn": 24, + "speaker": "B", + "utterance": "You know why I asked Annie here, don't you?", + "emotion": "sad", + "explanation": "the speaker wants to tell mom that he intends to marry Larry's girlfriend, but is sad because he is anticipating that mom will not accept it", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "You know why I asked Annie here, don't you?", + "id": 24 + }, + { + "turn": 25, + "speaker": "B", + "utterance": "You know.", + "emotion": "frustrated", + "flag": "F", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "You know.", + "id": 25 + }, + { + "turn": 26, + "speaker": "A", + "utterance": "Well I got an idea. But what's the story?", + "emotion": "neutral", + "text": "Well I got an idea. But what's the story?", + "id": 26 + }, + { + "turn": 27, + "speaker": "B", + "utterance": "I'm going to ask her to marry me.", + "emotion": "neutral", + "text": "I'm going to ask her to marry me.", + "id": 27 + }, + { + "turn": 28, + "speaker": "A", + "utterance": "You know that's not just my business.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 20, + 27 + ], + "expanded emotion cause span": [ + "Nobody comes back after three years! It's insane!", + "I'm going to ask her to marry me." + ], + "type": [ + "inter-personal" + ], + "text": "You know that's not just my business.", + "id": 28 + }, + { + "turn": 29, + "speaker": "B", + "utterance": "So it's all right. I can go ahead with it then?", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 20, + 27, + 28 + ], + "expanded emotion cause span": [ + "Nobody comes back after three years! It's insane!", + "I'm going to ask her to marry me.", + "You know that's not just my business." + ], + "type": [ + "hybrid" + ], + "text": "So it's all right. I can go ahead with it then?", + "id": 29 + }, + { + "turn": 30, + "speaker": "A", + "utterance": "I ignore what I got to ignore. The girl is Larry's girl.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 20, + 27, + 29 + ], + "expanded emotion cause span": [ + "Nobody comes back after three years! It's insane!", + "I'm going to ask her to marry me.", + "I can go ahead with it then?" + ], + "type": [ + "inter-personal" + ], + "text": "I ignore what I got to ignore. The girl is Larry's girl.", + "id": 30 + }, + { + "turn": 31, + "speaker": "A", + "utterance": "Now Chris you can go on from there, but I don't know what to do. I mean do you know what to do, because I don't.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 20, + 27, + 29, + 31 + ], + "expanded emotion cause span": [ + "Nobody comes back after three years! It's insane!", + "I'm going to ask her to marry me.", + "I can go ahead with it then?", + "I don't know what to do. I mean do you know what to do, because I don't." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Now Chris you can go on from there, but I don't know what to do. I mean do you know what to do, because I don't.", + "id": 31 + }, + { + "turn": 32, + "speaker": "B", + "utterance": "I don't know why it is. But every time I reach out for something I want, I have to pull back because other people will suffer. My whole bloody life, time after time, after time.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 14, + 15, + 16, + 17, + 31, + 32 + ], + "expanded emotion cause span": [ + "We made a terrible mistake with dad.", + "Being dishonest with him. It's the kind of thing that pays off and now it's paying off.", + "You know that Larry's not coming back, and I know it. So why do we go on letting him think that we believe with him?", + "argue with him, but it's time we realized that nobody else believes that Larry is alive", + "I don't know what to do. I mean do you know what to do, because I don't.", + "But every time I reach out for something I want, I have to pull back because other people will suffer. My whole bloody life, time after time, after time." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I don't know why it is. But every time I reach out for something I want, I have to pull back because other people will suffer. My whole bloody life, time after time, after time.", + "id": 32 + }, + { + "turn": 33, + "speaker": "A", + "utterance": "Well you're a considerate fellow, there's nothing wrong with that.", + "emotion": "neutral", + "text": "Well you're a considerate fellow, there's nothing wrong with that.", + "id": 33 + }, + { + "turn": 34, + "speaker": "B", + "utterance": "To hell with that!", + "emotion": "angry", + "explanation": "the speaker is angry that A is trying to convince him to pull back because of dad's issues", + "expanded emotion cause evidence": [ + 14, + 15, + 16, + 17, + 31, + 32, + 33 + ], + "expanded emotion cause span": [ + "We made a terrible mistake with dad.", + "Being dishonest with him. It's the kind of thing that pays off and now it's paying off.", + "You know that Larry's not coming back, and I know it. So why do we go on letting him think that we believe with him?", + "argue with him, but it's time we realized that nobody else believes that Larry is alive", + "I don't know what to do. I mean do you know what to do, because I don't.", + "But every time I reach out for something I want, I have to pull back because other people will suffer. My whole bloody life, time after time, after time.", + "Well you're a considerate fellow" + ], + "type": [ + "hybrid" + ], + "text": "To hell with that!", + "id": 34 + }, + { + "turn": 35, + "speaker": "A", + "utterance": "Have you asked Annie yet to marry you?", + "emotion": "neutral", + "text": "Have you asked Annie yet to marry you?", + "id": 35 + }, + { + "turn": 36, + "speaker": "A", + "utterance": "Well how did you know that she will go along with it, I mean maybe she feels the same way as your father?", + "emotion": "neutral", + "text": "Well how did you know that she will go along with it, I mean maybe she feels the same way as your father?", + "id": 36 + }, + { + "turn": 37, + "speaker": "A", + "utterance": "The trouble is you don't see enough women, you never have", + "emotion": "neutral", + "text": "The trouble is you don't see enough women, you never have", + "id": 37 + }, + { + "turn": 38, + "speaker": "B", + "utterance": "So what, I'm not fast with women.", + "emotion": "frustrated", + "explanation": "the speaker is frustrated that A is trying to convince him to pull back because of dad's issues", + "expanded emotion cause evidence": [ + 14, + 15, + 16, + 17, + 31, + 32, + 37, + 38 + ], + "expanded emotion cause span": [ + "We made a terrible mistake with dad.", + "Being dishonest with him. It's the kind of thing that pays off and now it's paying off.", + "You know that Larry's not coming back, and I know it. So why do we go on letting him think that we believe with him?", + "argue with him, but it's time we realized that nobody else believes that Larry is alive", + "I don't know what to do. I mean do you know what to do, because I don't.", + "But every time I reach out for something I want, I have to pull back because other people will suffer. My whole bloody life, time after time, after time.", + "The trouble is you don't see enough women, you never have", + "I'm not fast with women." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "So what, I'm not fast with women.", + "id": 38 + }, + { + "turn": 39, + "speaker": "A", + "utterance": "Well I just don't see why it has to be Annie.", + "emotion": "neutral", + "text": "Well I just don't see why it has to be Annie.", + "id": 39 + }, + { + "turn": 40, + "speaker": "B", + "utterance": "Because it is.", + "emotion": "frustrated", + "explanation": "the speaker is frustrated that A is trying to convince him to pull back because of dad's issues", + "expanded emotion cause evidence": [ + 14, + 15, + 16, + 17, + 31, + 32, + 39 + ], + "expanded emotion cause span": [ + "We made a terrible mistake with dad.", + "Being dishonest with him. It's the kind of thing that pays off and now it's paying off.", + "You know that Larry's not coming back, and I know it. So why do we go on letting him think that we believe with him?", + "argue with him, but it's time we realized that nobody else believes that Larry is alive", + "I don't know what to do. I mean do you know what to do, because I don't.", + "But every time I reach out for something I want, I have to pull back because other people will suffer. My whole bloody life, time after time, after time.", + "I just don't see why it has to be Annie." + ], + "type": [ + "hybrid" + ], + "text": "Because it is.", + "id": 40 + }, + { + "turn": 41, + "speaker": "B", + "utterance": "I can't help it. I know her best. I was brought up next door to here, the easiest, when I think of somebody for my wife, I think of Annie. Do you want a diagram?", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 14, + 15, + 16, + 17, + 31, + 32, + 39 + ], + "expanded emotion cause span": [ + "We made a terrible mistake with dad.", + "Being dishonest with him. It's the kind of thing that pays off and now it's paying off.", + "You know that Larry's not coming back, and I know it. So why do we go on letting him think that we believe with him?", + "argue with him, but it's time we realized that nobody else believes that Larry is alive", + "I don't know what to do. I mean do you know what to do, because I don't.", + "But every time I reach out for something I want, I have to pull back because other people will suffer. My whole bloody life, time after time, after time.", + "I just don't see why it has to be Annie." + ], + "type": [ + "hybrid" + ], + "text": "I can't help it. I know her best. I was brought up next door to here, the easiest, when I think of somebody for my wife, I think of Annie. Do you want a diagram?", + "id": 41 + }, + { + "turn": 42, + "speaker": "A", + "utterance": "No, I don't want a diagram, but, Chris, your father thinks Larry's coming back.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 20, + 27, + 30, + 31, + 42 + ], + "expanded emotion cause span": [ + "Nobody comes back after three years! It's insane!", + "I'm going to ask her to marry me.", + "The girl is Larry's girl.", + "I don't know what to do. I mean do you know what to do, because I don't.", + "your father thinks Larry's coming back." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "No, I don't want a diagram, but, Chris, your father thinks Larry's coming back.", + "id": 42 + }, + { + "turn": 43, + "speaker": "A", + "utterance": "You marry his girl, and you're pronouncing him dead. Now what's going to happen to your father, do you know? I don't.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 20, + 27, + 30, + 31, + 42, + 43 + ], + "expanded emotion cause span": [ + "Nobody comes back after three years! It's insane!", + "I'm going to ask her to marry me.", + "The girl is Larry's girl.", + "I don't know what to do. I mean do you know what to do, because I don't.", + "your father thinks Larry's coming back.", + "you're pronouncing him dead. Now what's going to happen to your father" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "You marry his girl, and you're pronouncing him dead. Now what's going to happen to your father, do you know? I don't.", + "id": 43 + }, + { + "turn": 44, + "speaker": "B", + "utterance": "All right, then, Mom.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 20, + 27, + 30, + 31, + 42, + 43 + ], + "expanded emotion cause span": [ + "Nobody comes back after three years! It's insane!", + "I'm going to ask her to marry me.", + "The girl is Larry's girl.", + "I don't know what to do. I mean do you know what to do, because I don't.", + "your father thinks Larry's coming back.", + "you're pronouncing him dead. Now what's going to happen to your father" + ], + "type": [ + "hybrid" + ], + "text": "All right, then, Mom.", + "id": 44 + }, + { + "turn": 45, + "speaker": "B", + "utterance": "I've given it three years of thought. And hope by now that he wouldn't. Can you forget about Larry an-- and we can have a regular wedding and have everybody be happy. But that can't happen here, I'm set to get out.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 20, + 27, + 30, + 31, + 42, + 43, + 45 + ], + "expanded emotion cause span": [ + "Nobody comes back after three years! It's insane!", + "I'm going to ask her to marry me.", + "The girl is Larry's girl.", + "I don't know what to do. I mean do you know what to do, because I don't.", + "your father thinks Larry's coming back.", + "you're pronouncing him dead. Now what's going to happen to your father", + "I've given it three years of thought. And hope by now that he wouldn't. Can you forget about Larry an-- and we can have a regular wedding and have everybody be happy. But that can't happen here," + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I've given it three years of thought. And hope by now that he wouldn't. Can you forget about Larry an-- and we can have a regular wedding and have everybody be happy. But that can't happen here, I'm set to get out.", + "id": 45 + }, + { + "turn": 46, + "speaker": "A", + "utterance": "What the hell is this?", + "emotion": "angry", + "expanded emotion cause evidence": [ + 45 + ], + "expanded emotion cause span": [ + "I'm set to get out." + ], + "type": [ + "inter-personal" + ], + "text": "What the hell is this?", + "id": 46 + }, + { + "turn": 47, + "speaker": "B", + "utterance": "I'll get out. I'll get married and live some place else. Maybe, maybe New York?", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 20, + 27, + 30, + 31, + 42, + 43, + 45 + ], + "expanded emotion cause span": [ + "Nobody comes back after three years! It's insane!", + "I'm going to ask her to marry me.", + "The girl is Larry's girl.", + "I don't know what to do. I mean do you know what to do, because I don't.", + "your father thinks Larry's coming back.", + "you're pronouncing him dead. Now what's going to happen to your father", + "I've given it three years of thought. And hope by now that he wouldn't. Can you forget about Larry an-- and we can have a regular wedding and have everybody be happy. But that can't happen here," + ], + "type": [ + "hybrid" + ], + "text": "I'll get out. I'll get married and live some place else. Maybe, maybe New York?", + "id": 47 + }, + { + "turn": 48, + "speaker": "A", + "utterance": "Are you crazy?", + "emotion": "angry", + "expanded emotion cause evidence": [ + 45, + 47 + ], + "expanded emotion cause span": [ + "I'm set to get out.", + "I'll get out. I'll get married and live some place else." + ], + "type": [ + "inter-personal" + ], + "text": "Are you crazy?", + "id": 48 + }, + { + "turn": 49, + "speaker": "A", + "utterance": "Wait a minute. Tell me this. Do you mean to say that you would leave the business?", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 45, + 47, + 49 + ], + "expanded emotion cause span": [ + "I'm set to get out.", + "I'll get out. I'll get married and live some place else.", + "you would leave the business?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Wait a minute. Tell me this. Do you mean to say that you would leave the business?", + "id": 49 + }, + { + "turn": 50, + "speaker": "B", + "utterance": "The business? The business? It doesn't inspire me?", + "emotion": "angry", + "expanded emotion cause evidence": [ + 49, + 50 + ], + "expanded emotion cause span": [ + "Do you mean to say that you would leave the business?", + "It doesn't inspire me?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "The business? The business? It doesn't inspire me?", + "id": 50 + }, + { + "turn": 51, + "speaker": "A", + "utterance": "Don't- you, you can't think like that! Don't think like that!", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 50, + 51 + ], + "expanded emotion cause span": [ + "It doesn't inspire me?", + "you can't think like that! Don't think like that!" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Don't- you, you can't think like that! Don't think like that!", + "id": 51, + "source_sentences": [ + 49 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 52, + "speaker": "A", + "utterance": "All right! But don't think like that, because I mean, what the hell did we do all this for, Chris? The whole business it's all for you! The whole shooting match is for you!", + "emotion": "angry", + "expanded emotion cause evidence": [ + 50, + 51, + 52 + ], + "expanded emotion cause span": [ + "It doesn't inspire me?", + "you can't think like that! Don't think like that!", + "what the hell did we do all this for, Chris? The whole business it's all for you! The whole shooting match is for you!" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "All right! But don't think like that, because I mean, what the hell did we do all this for, Chris? The whole business it's all for you! The whole shooting match is for you!", + "id": 52 + }, + { + "turn": 53, + "speaker": "A", + "utterance": "I don't understand you, do I?", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 50, + 51, + 52, + 32 + ], + "expanded emotion cause span": [ + "It doesn't inspire me?", + "you can't think like that! Don't think like that!", + "what the hell did we do all this for, Chris? The whole business it's all for you! The whole shooting match is for you!", + "I don't know why it is. But every time I reach out for something I want, I have to pull back because other people will suffer. My whole bloody life, time after time, after time." + ], + "type": [ + "hybrid" + ], + "text": "I don't understand you, do I?", + "id": 53 + } +] \ No newline at end of file diff --git a/reccon/sources/test.test.Ses05M_script03_1.json b/reccon/sources/test.test.Ses05M_script03_1.json new file mode 100644 index 0000000000000000000000000000000000000000..3f4a4ac295ddcff97ce23adf0884127b30544dde --- /dev/null +++ b/reccon/sources/test.test.Ses05M_script03_1.json @@ -0,0 +1,903 @@ +[ + { + "turn": 1, + "speaker": "B", + "utterance": "I wonder.", + "emotion": "excited", + "explanation": "the speaker is excited to be alone in a space with A without anyone else knowing", + "flag": "F", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "I wonder.", + "id": 1 + }, + { + "turn": 2, + "speaker": "A", + "utterance": "what, Nobody knows we are here except Freda and she wouldn't ring up.", + "emotion": "excited", + "explanation": "the speaker is excited to be alone in a space with B without anyone else knowing", + "expanded emotion cause evidence": [ + "b", + 2 + ], + "expanded emotion cause span": [ + "b", + "Nobody knows we are here except Freda and she wouldn't ring up." + ], + "type": [ + "latent", + "no-context" + ], + "text": "what, Nobody knows we are here except Freda and she wouldn't ring up.", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What do we do?", + "emotion": "excited", + "flag": "F", + "expanded emotion cause evidence": [ + "b", + 2 + ], + "expanded emotion cause span": [ + "b", + "Nobody knows we are here except Freda and she wouldn't ring up." + ], + "type": [ + "latent", + "self-contagion" + ], + "text": "What do we do?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "We're all right, aren't we, darling, whatever happens?", + "emotion": "neutral", + "text": "We're all right, aren't we, darling, whatever happens?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Now and always, my sweet.", + "emotion": "excited", + "expanded emotion cause evidence": [ + "b", + 2, + 4, + 5 + ], + "expanded emotion cause span": [ + "b", + "Nobody knows we are here except Freda and she wouldn't ring up.", + "We're all right, aren't we, darling, whatever happens?", + "Now and always, my sweet." + ], + "type": [ + "latent", + "no-context", + "hybrid" + ], + "text": "Now and always, my sweet.", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I don't care then.", + "emotion": "excited", + "flag": "F", + "expanded emotion cause evidence": [ + "b", + 2, + 4, + 5 + ], + "expanded emotion cause span": [ + "b", + "Nobody knows we are here except Freda and she wouldn't ring up.", + "We're all right, aren't we, darling, whatever happens?", + "Now and always, my sweet." + ], + "type": [ + "latent", + "hybrid" + ], + "text": "I don't care then.", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "It was bound to happen sooner or later.", + "emotion": "excited", + "flag": "F", + "expanded emotion cause evidence": [ + "b", + 2, + 7 + ], + "expanded emotion cause span": [ + "b", + "Nobody knows we are here except Freda and she wouldn't ring up.", + "It was bound to happen sooner or later." + ], + "type": [ + "latent", + "no-context", + "self-contagion" + ], + "text": "It was bound to happen sooner or later.", + "id": 7 + }, + { + "turn": 8, + "speaker": "A", + "utterance": "Oh, it sent shivers up my spine.", + "emotion": "excited", + "expanded emotion cause evidence": [ + "b", + 2, + 7, + 8 + ], + "expanded emotion cause span": [ + "b", + "Nobody knows we are here except Freda and she wouldn't ring up.", + "It was bound to happen sooner or later.", + "it sent shivers up my spine." + ], + "type": [ + "latent", + "no-context", + "self-contagion" + ], + "text": "Oh, it sent shivers up my spine.", + "id": 8 + }, + { + "turn": 9, + "speaker": "B", + "utterance": "Oh, what shall we do if they suddenly walk in on us.", + "emotion": "excited", + "expanded emotion cause evidence": [ + "b", + 2, + 9 + ], + "expanded emotion cause span": [ + "b", + "Nobody knows we are here except Freda and she wouldn't ring up.", + "they suddenly walk in on us." + ], + "type": [ + "latent", + "no-context", + "inter-personal" + ], + "text": "Oh, what shall we do if they suddenly walk in on us.", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "With the worst- with the most perfect poise?", + "emotion": "excited", + "expanded emotion cause evidence": [ + "b", + 2, + 9, + 10 + ], + "expanded emotion cause span": [ + "b", + "Nobody knows we are here except Freda and she wouldn't ring up.", + "they suddenly walk in on us.", + "with the most perfect poise?" + ], + "type": [ + "latent", + "no-context", + "hybrid" + ], + "text": "With the worst- with the most perfect poise?", + "id": 10 + }, + { + "turn": 11, + "speaker": "B", + "utterance": "Uhh, It's amazing how once you feel--", + "emotion": "excited", + "expanded emotion cause evidence": [ + "b", + 2, + 9, + 10, + 11 + ], + "expanded emotion cause span": [ + "b", + "Nobody knows we are here except Freda and she wouldn't ring up.", + "they suddenly walk in on us.", + "with the most perfect poise?", + "It's amazing how once you feel--" + ], + "type": [ + "latent", + "no-context", + "hybrid" + ], + "text": "Uhh, It's amazing how once you feel--", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "things that ought to matter most dreadfully don't matter at all when one's happy, do they?", + "emotion": "excited", + "expanded emotion cause evidence": [ + "b", + 2, + 9, + 10, + 11, + 12 + ], + "expanded emotion cause span": [ + "b", + "Nobody knows we are here except Freda and she wouldn't ring up.", + "they suddenly walk in on us.", + "with the most perfect poise?", + "It's amazing how once you feel--", + "things that ought to matter most dreadfully don't matter at all when one's happy," + ], + "type": [ + "latent", + "no-context", + "hybrid" + ], + "text": "things that ought to matter most dreadfully don't matter at all when one's happy, do they?", + "id": 12 + }, + { + "turn": 13, + "speaker": "B", + "utterance": "Uhh, You mustn't say that, my darling.", + "emotion": "excited", + "expanded emotion cause evidence": [ + "b", + 2, + 9, + 10, + 11, + 12 + ], + "expanded emotion cause span": [ + "b", + "Nobody knows we are here except Freda and she wouldn't ring up.", + "they suddenly walk in on us.", + "with the most perfect poise?", + "It's amazing how once you feel--", + "things that ought to matter most dreadfully don't matter at all when one's happy," + ], + "type": [ + "latent", + "hybrid" + ], + "text": "Uhh, You mustn't say that, my darling.", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Being that sacred and wonderful thing, love.", + "emotion": "excited", + "expanded emotion cause evidence": [ + "b", + 2, + 9, + 10, + 11, + 12, + 14 + ], + "expanded emotion cause span": [ + "b", + "Nobody knows we are here except Freda and she wouldn't ring up.", + "they suddenly walk in on us.", + "with the most perfect poise?", + "It's amazing how once you feel--", + "things that ought to matter most dreadfully don't matter at all when one's happy,", + "Being that sacred and wonderful thing, love." + ], + "type": [ + "latent", + "no-context", + "hybrid" + ], + "text": "Being that sacred and wonderful thing, love.", + "id": 14 + }, + { + "turn": 15, + "speaker": "B", + "utterance": "Um What does it all mean? That's what I ask myself in my endless quest for ultimate truth. Dear God, what does it all mean?", + "emotion": "excited", + "expanded emotion cause evidence": [ + "b", + 2, + 9, + 10, + 11, + 12, + 14, + 15 + ], + "expanded emotion cause span": [ + "b", + "Nobody knows we are here except Freda and she wouldn't ring up.", + "they suddenly walk in on us.", + "with the most perfect poise?", + "It's amazing how once you feel--", + "things that ought to matter most dreadfully don't matter at all when one's happy,", + "Being that sacred and wonderful thing, love.", + "What does it all mean? That's what I ask myself in my endless quest for ultimate truth. Dear God, what does it all mean?" + ], + "type": [ + "latent", + "no-context", + "hybrid" + ], + "text": "Um What does it all mean? That's what I ask myself in my endless quest for ultimate truth. Dear God, what does it all mean?", + "id": 15 + }, + { + "turn": 16, + "speaker": "A", + "utterance": "Don't laugh at me. I'm serious.", + "emotion": "neutral", + "text": "Don't laugh at me. I'm serious.", + "id": 16 + }, + { + "turn": 17, + "speaker": "B", + "utterance": "You mustn't be serious, darling. That's just what they want.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 17 + ], + "expanded emotion cause span": [ + "You mustn't be serious, darling. That's just what they want." + ], + "type": [ + "no-context" + ], + "text": "You mustn't be serious, darling. That's just what they want.", + "id": 17 + }, + { + "turn": 18, + "speaker": "A", + "utterance": "Who's they?", + "emotion": "neutral", + "text": "Who's they?", + "id": 18 + }, + { + "turn": 19, + "speaker": "B", + "utterance": "All the futile mortals who try to make life unbearable. Laugh at them, Be flippant. Laugh at everything, all their sacred shibboleths.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 17, + 19 + ], + "expanded emotion cause span": [ + "You mustn't be serious, darling. That's just what they want.", + "All the futile mortals who try to make life unbearable. Laugh at them, Be flippant. Laugh at everything, all their sacred shibboleths." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "All the futile mortals who try to make life unbearable. Laugh at them, Be flippant. Laugh at everything, all their sacred shibboleths.", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "uh- the- Being flippant brings out the acid in their damned beauty and light.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 17, + 19, + 20 + ], + "expanded emotion cause span": [ + "You mustn't be serious, darling. That's just what they want.", + "All the futile mortals who try to make life unbearable. Laugh at them, Be flippant. Laugh at everything, all their sacred shibboleths.", + "Being flippant brings out the acid in their damned beauty and light." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "uh- the- Being flippant brings out the acid in their damned beauty and light.", + "id": 20 + }, + { + "turn": 21, + "speaker": "A", + "utterance": "If I laugh at everything, then I must laugh at us too.", + "emotion": "neutral", + "text": "If I laugh at everything, then I must laugh at us too.", + "id": 21 + }, + { + "turn": 22, + "speaker": "B", + "utterance": "Certainly you must. We are figures of fun all right.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 21, + 22 + ], + "expanded emotion cause span": [ + "If I laugh at everything, then I must laugh at us too.", + "Certainly you must. We are figures of fun all right." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Certainly you must. We are figures of fun all right.", + "id": 22 + }, + { + "turn": 23, + "speaker": "A", + "utterance": "Well, will we always bicker and fight?", + "emotion": "neutral", + "text": "Well, will we always bicker and fight?", + "id": 23 + }, + { + "turn": 24, + "speaker": "B", + "utterance": "No. That fire will fade along with our passion.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 21, + 22 + ], + "expanded emotion cause span": [ + "If I laugh at everything, then I must laugh at us too.", + "Certainly you must. We are figures of fun all right." + ], + "type": [ + "hybrid" + ], + "text": "No. That fire will fade along with our passion.", + "id": 24 + }, + { + "turn": 25, + "speaker": "A", + "utterance": "What if one of us dies, does the other one laugh then?", + "emotion": "neutral", + "text": "What if one of us dies, does the other one laugh then?", + "id": 25 + }, + { + "turn": 26, + "speaker": "B", + "utterance": "Yes, yes, with all his might.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 21, + 22, + 25, + 26 + ], + "expanded emotion cause span": [ + "If I laugh at everything, then I must laugh at us too.", + "Certainly you must. We are figures of fun all right.", + "What if one of us dies, does the other one laugh then?", + "Yes, yes, with all his might." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Yes, yes, with all his might.", + "id": 26 + }, + { + "turn": 27, + "speaker": "B", + "utterance": "No, no that is quit laughable. The cutting little mystery all done with mirrors.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 21, + 22, + 25, + 26, + 27 + ], + "expanded emotion cause span": [ + "If I laugh at everything, then I must laugh at us too.", + "Certainly you must. We are figures of fun all right.", + "What if one of us dies, does the other one laugh then?", + "Yes, yes, with all his might.", + "The cutting little mystery all done with mirrors." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "No, no that is quit laughable. The cutting little mystery all done with mirrors.", + "id": 27 + }, + { + "turn": 28, + "speaker": "B", + "utterance": "So is everyone else in the long run. Let's be superficial and pity the poor philosophers. Let's blow trumpets and squeakers and enjoy the party as long as we can, like little quiet idiotic school children.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 21, + 22, + 25, + 26, + 27, + 28 + ], + "expanded emotion cause span": [ + "If I laugh at everything, then I must laugh at us too.", + "Certainly you must. We are figures of fun all right.", + "What if one of us dies, does the other one laugh then?", + "Yes, yes, with all his might.", + "The cutting little mystery all done with mirrors.", + "So is everyone else in the long run. Let's be superficial and pity the poor philosophers. Let's blow trumpets and squeakers and enjoy the party as long as we can, like little quiet idiotic school children." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "So is everyone else in the long run. Let's be superficial and pity the poor philosophers. Let's blow trumpets and squeakers and enjoy the party as long as we can, like little quiet idiotic school children.", + "id": 28 + }, + { + "turn": 29, + "speaker": "B", + "utterance": "[garbage] Darling, kiss me before your body rots and worms start popping in and out of your eye sockets.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 21, + 22, + 25, + 26, + 27, + 28, + 29 + ], + "expanded emotion cause span": [ + "If I laugh at everything, then I must laugh at us too.", + "Certainly you must. We are figures of fun all right.", + "What if one of us dies, does the other one laugh then?", + "Yes, yes, with all his might.", + "The cutting little mystery all done with mirrors.", + "So is everyone else in the long run. Let's be superficial and pity the poor philosophers. Let's blow trumpets and squeakers and enjoy the party as long as we can, like little quiet idiotic school children.", + "Darling, kiss me before your body rots and worms start popping in and out of your eye sockets." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "[garbage] Darling, kiss me before your body rots and worms start popping in and out of your eye sockets.", + "id": 29 + }, + { + "turn": 30, + "speaker": "A", + "utterance": "Elliott, worms don't pop.", + "emotion": "neutral", + "text": "Elliott, worms don't pop.", + "id": 30 + }, + { + "turn": 31, + "speaker": "B", + "utterance": "I don't care what you do. See, you could paint your body bright green and and run naked through the Place Vendome and run with every man in the world and I shan't say a word. As long as I know that you love me best.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 31 + ], + "expanded emotion cause span": [ + "you love me best." + ], + "type": [ + "no-context" + ], + "text": "I don't care what you do. See, you could paint your body bright green and and run naked through the Place Vendome and run with every man in the world and I shan't say a word. As long as I know that you love me best.", + "id": 31 + }, + { + "turn": 32, + "speaker": "B", + "utterance": "Do you remember that awful scene we had in Venice?", + "emotion": "excited", + "expanded emotion cause evidence": [ + 32 + ], + "expanded emotion cause span": [ + "that awful scene we had in Venice?" + ], + "type": [ + "no-context" + ], + "text": "Do you remember that awful scene we had in Venice?", + "id": 32 + }, + { + "turn": 33, + "speaker": "B", + "utterance": "The one where you bought that little painted wooden stake and you put it on my bed.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 32, + 33 + ], + "expanded emotion cause span": [ + "that awful scene we had in Venice?", + "you bought that little painted wooden stake and you put it on my bed." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "The one where you bought that little painted wooden stake and you put it on my bed.", + "id": 33 + }, + { + "turn": 34, + "speaker": "B", + "utterance": "Horrible thing. I hated it.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 32, + 33, + 34 + ], + "expanded emotion cause span": [ + "that awful scene we had in Venice?", + "you bought that little painted wooden stake and you put it on my bed.", + "Horrible thing. I hated it." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Horrible thing. I hated it.", + "id": 34 + }, + { + "turn": 35, + "speaker": "A", + "utterance": "I know you did. You threw it out the window into the Canal below. I don't think I'll ever forgive you for that.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 32, + 33, + 34, + 35 + ], + "expanded emotion cause span": [ + "that awful scene we had in Venice?", + "you bought that little painted wooden stake and you put it on my bed.", + "Horrible thing. I hated it.", + "You threw it out the window into the Canal below." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I know you did. You threw it out the window into the Canal below. I don't think I'll ever forgive you for that.", + "id": 35 + }, + { + "turn": 36, + "speaker": "B", + "utterance": "How long did that roue last?", + "emotion": "excited", + "expanded emotion cause evidence": [ + 32, + 33, + 34, + 35 + ], + "expanded emotion cause span": [ + "that awful scene we had in Venice?", + "you bought that little painted wooden stake and you put it on my bed.", + "Horrible thing. I hated it.", + "You threw it out the window into the Canal below." + ], + "type": [ + "hybrid" + ], + "text": "How long did that roue last?", + "id": 36 + }, + { + "turn": 37, + "speaker": "B", + "utterance": "Oh, The worst one was in Cannes when your curling iron burnt a hole in my new dressing gown?", + "emotion": "excited", + "expanded emotion cause evidence": [ + 32, + 33, + 34, + 35, + 37 + ], + "expanded emotion cause span": [ + "that awful scene we had in Venice?", + "you bought that little painted wooden stake and you put it on my bed.", + "Horrible thing. I hated it.", + "You threw it out the window into the Canal below.", + "worst one was in Cannes when your curling iron burnt a hole in my new dressing gown?" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Oh, The worst one was in Cannes when your curling iron burnt a hole in my new dressing gown?", + "id": 37 + }, + { + "turn": 38, + "speaker": "A", + "utterance": "Oh, It burnt my comb and all the towels in the bathroom.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 37, + 38 + ], + "expanded emotion cause span": [ + "worst one was in Cannes when your curling iron burnt a hole in my new dressing gown?", + "It burnt my comb and all the towels in the bathroom." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh, It burnt my comb and all the towels in the bathroom.", + "id": 38, + "source_sentences": [ + 36 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 39, + "speaker": "B", + "utterance": "[LAUGHTER] That was quit a rouser, wasn't it?", + "emotion": "excited", + "expanded emotion cause evidence": [ + 37, + 38, + 39 + ], + "expanded emotion cause span": [ + "worst one was in Cannes when your curling iron burnt a hole in my new dressing gown?", + "It burnt my comb and all the towels in the bathroom.", + "That was quit a rouser" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "[LAUGHTER] That was quit a rouser, wasn't it?", + "id": 39 + }, + { + "turn": 40, + "speaker": "B", + "utterance": "Oh, I didn't hit you very hard.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 37, + 38, + 39, + 40 + ], + "expanded emotion cause span": [ + "worst one was in Cannes when your curling iron burnt a hole in my new dressing gown?", + "It burnt my comb and all the towels in the bathroom.", + "That was quit a rouser", + "I didn't hit you very hard." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Oh, I didn't hit you very hard.", + "id": 40 + }, + { + "turn": 41, + "speaker": "B", + "utterance": "I should never forget his face. [LAUGHTER]", + "emotion": "excited", + "expanded emotion cause evidence": [ + 37, + 38, + 39, + 40, + 41 + ], + "expanded emotion cause span": [ + "worst one was in Cannes when your curling iron burnt a hole in my new dressing gown?", + "It burnt my comb and all the towels in the bathroom.", + "That was quit a rouser", + "I didn't hit you very hard.", + "I should never forget his face." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I should never forget his face. [LAUGHTER]", + "id": 41 + }, + { + "turn": 42, + "speaker": "B", + "utterance": "We were very much younger then.", + "emotion": "excited", + "flag": "F", + "expanded emotion cause evidence": [ + 37, + 38, + 39, + 40, + 41, + 42 + ], + "expanded emotion cause span": [ + "worst one was in Cannes when your curling iron burnt a hole in my new dressing gown?", + "It burnt my comb and all the towels in the bathroom.", + "That was quit a rouser", + "I didn't hit you very hard.", + "I should never forget his face.", + "We were very much younger then." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "We were very much younger then.", + "id": 42 + }, + { + "turn": 43, + "speaker": "A", + "utterance": "You knew there was nothing in that.", + "emotion": "neutral", + "text": "You knew there was nothing in that.", + "id": 43 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_0.json b/reccon/sources/tr_0.json new file mode 100644 index 0000000000000000000000000000000000000000..3534843dafb8b55cd08bd5d3d53b5affeba629f0 --- /dev/null +++ b/reccon/sources/tr_0.json @@ -0,0 +1,135 @@ +[ + { + "turn": 1, + "speaker": "B", + "utterance": "Say , Jim , how about going for a few beers after dinner ?", + "emotion": "neutral", + "text": "Say , Jim , how about going for a few beers after dinner ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "A", + "utterance": "You know that is tempting but is really not good for our fitness .", + "emotion": "neutral", + "text": "You know that is tempting but is really not good for our fitness .", + "id": 2 + }, + { + "turn": 3, + "speaker": "B", + "utterance": "What do you mean ? It will help us to relax .", + "emotion": "neutral", + "text": "What do you mean ? It will help us to relax .", + "id": 3 + }, + { + "turn": 4, + "speaker": "A", + "utterance": "Do you really think so ? I don't . It will just make us fat and act silly . Remember last time ?", + "emotion": "neutral", + "text": "Do you really think so ? I don't . It will just make us fat and act silly . Remember last time ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "B", + "utterance": "I guess you are right . But what shall we do ? I don't feel like sitting at home .", + "emotion": "neutral", + "text": "I guess you are right . But what shall we do ? I don't feel like sitting at home .", + "id": 5 + }, + { + "turn": 6, + "speaker": "A", + "utterance": "I suggest a walk over to the gym where we can play singsong and meet some of our friends .", + "emotion": "neutral", + "text": "I suggest a walk over to the gym where we can play singsong and meet some of our friends .", + "id": 6 + }, + { + "turn": 7, + "speaker": "B", + "utterance": "That's a good idea . I hear Mary and Sally often go there to play pingpong . Perhaps we can make a foursome with them .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I suggest a walk over to the gym where we can play singsong and meet some of our friends .", + "I hear Mary and Sally often go there to play pingpong . Perhaps we can make a foursome with them ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's a good idea . I hear Mary and Sally often go there to play pingpong . Perhaps we can make a foursome with them .", + "id": 7 + }, + { + "turn": 8, + "speaker": "A", + "utterance": "Sounds great to me ! If they are willing , we could ask them to go dancing with us . That is excellent exercise and fun , too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "I hear Mary and Sally often go there to play pingpong . Perhaps we can make a foursome with them .", + "That is excellent exercise and fun , too ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Sounds great to me ! If they are willing , we could ask them to go dancing with us . That is excellent exercise and fun , too .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "B", + "utterance": "Good . Let ' s go now .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7, + 8 + ], + "expanded emotion cause span": [ + "I suggest a walk over to the gym where we can play singsong and meet some of our friends .", + "I hear Mary and Sally often go there to play pingpong . Perhaps we can make a foursome with them .", + "That is excellent exercise and fun , too ." + ], + "type": [ + "hybrid" + ], + "text": "Good . Let ' s go now .", + "id": 9 + }, + { + "turn": 10, + "speaker": "A", + "utterance": "All right .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "I hear Mary and Sally often go there to play pingpong . Perhaps we can make a foursome with them .", + "That is excellent exercise and fun , too ." + ], + "type": [ + "hybrid" + ], + "text": "All right .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_10030.json b/reccon/sources/tr_10030.json new file mode 100644 index 0000000000000000000000000000000000000000..1f0c7d02a2f6d94459378335a7fc0a4087dd62a0 --- /dev/null +++ b/reccon/sources/tr_10030.json @@ -0,0 +1,139 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Can you type , Jane ?", + "emotion": "neutral", + "text": "Can you type , Jane ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , I can .", + "emotion": "neutral", + "text": "Yes , I can .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "How many words a minute ?", + "emotion": "neutral", + "text": "How many words a minute ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "About 100 words a minute .", + "emotion": "neutral", + "text": "About 100 words a minute .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "En ... and can you speak any foreign languages ?", + "emotion": "neutral", + "text": "En ... and can you speak any foreign languages ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yes , I can speak Spanish , and I can also speak Chinese .", + "emotion": "neutral", + "text": "Yes , I can speak Spanish , and I can also speak Chinese .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Really ? that ' s very good . What about French ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I can speak Spanish , and I can also speak Chinese ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? that ' s very good . What about French ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "No , I can ' t speak French . But I can speak Italian , not very well though .", + "emotion": "neutral", + "text": "No , I can ' t speak French . But I can speak Italian , not very well though .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "... Can you start next week ?", + "emotion": "neutral", + "text": "... Can you start next week ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Next week ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Can you start next week ?" + ], + "type": [ + "inter-personal" + ], + "text": "Next week ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Yes , on Monday .", + "emotion": "neutral", + "text": "Yes , on Monday .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "You mean I have the job ?", + "emotion": "surprise", + "flag": "F", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Can you start next week ?" + ], + "type": [ + "inter-personal" + ], + "text": "You mean I have the job ?", + "id": 12, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Yes , that ' s right , you have the job now .", + "emotion": "neutral", + "text": "Yes , that ' s right , you have the job now .", + "id": 13 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_10047.json b/reccon/sources/tr_10047.json new file mode 100644 index 0000000000000000000000000000000000000000..490377da62891481ecb3ec6c126893de88df220e --- /dev/null +++ b/reccon/sources/tr_10047.json @@ -0,0 +1,118 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello , thanks for calling 123 Tech Help , I ' m Todd . How can I help you ?", + "emotion": "neutral", + "text": "Hello , thanks for calling 123 Tech Help , I ' m Todd . How can I help you ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hello ? Can you help me ? My computer ! Oh man ...", + "emotion": "fear", + "explanation": "broken computer; utterance 4", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Hello ? Can you help me ? My computer ! Oh man ...", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "It ' s okay sir , calm down . What happened ?", + "emotion": "neutral", + "text": "It ' s okay sir , calm down . What happened ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I turned on my laptop and it broke ! I mean , the monitor went black !", + "emotion": "fear", + "expanded emotion cause evidence": [ + 4, + 4 + ], + "expanded emotion cause span": [ + "it broke !", + "the monitor went black !" + ], + "type": [ + "no-context" + ], + "text": "I turned on my laptop and it broke ! I mean , the monitor went black !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Ok , sir , it sounds like you might have a virus .", + "emotion": "neutral", + "text": "Ok , sir , it sounds like you might have a virus .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I don ' t feel sick , ... let me check ... Nope ! No fever , I ' m fine .", + "emotion": "fear", + "expanded emotion cause evidence": [ + 4, + 4 + ], + "expanded emotion cause span": [ + "it broke !", + "the monitor went black !" + ], + "type": [ + "self-contagion" + ], + "text": "I don ' t feel sick , ... let me check ... Nope ! No fever , I ' m fine .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "No , your computer might have a virus , I mean , it has a bad program on it . Maybe that ' s why it crashed . I recommend that you run an antivirus program in order to safely remove any unwanted spyware or Trojans .", + "emotion": "neutral", + "text": "No , your computer might have a virus , I mean , it has a bad program on it . Maybe that ' s why it crashed . I recommend that you run an antivirus program in order to safely remove any unwanted spyware or Trojans .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Phew ! . . . Wait a minute , CRASH ? ? ! ! Spyware ? Trojans ! What ? where ? when ? !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7, + 7, + 7 + ], + "expanded emotion cause span": [ + "your computer might have a virus", + "it crashed", + "unwanted spyware or Trojans ." + ], + "type": [ + "inter-personal" + ], + "text": "Phew ! . . . Wait a minute , CRASH ? ? ! ! Spyware ? Trojans ! What ? where ? when ? !", + "id": 8, + "source_sentences": [ + 6, + 6, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1006.json b/reccon/sources/tr_1006.json new file mode 100644 index 0000000000000000000000000000000000000000..03e533f4c6aaa072a9d07efd18342dee2456e7a6 --- /dev/null +++ b/reccon/sources/tr_1006.json @@ -0,0 +1,121 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey , Leo . How come you look so terrible ? What ' s going ' on ?", + "emotion": "neutral", + "text": "Hey , Leo . How come you look so terrible ? What ' s going ' on ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "You can say that again . Susan ' brother dropped in from out of town , so I offered to put him up for a few days . But he ' s driving me up a wall . This guy is bottomless pit .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "But he ' s driving me up a wall . This guy is bottomless pit ." + ], + "type": [ + "no-context" + ], + "text": "You can say that again . Susan ' brother dropped in from out of town , so I offered to put him up for a few days . But he ' s driving me up a wall . This guy is bottomless pit .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "How gross ! I can ' t handle people like that . Does he at least give you a hand around the house ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "But he ' s driving me up a wall . This guy is bottomless pit ." + ], + "type": [ + "inter-personal" + ], + "text": "How gross ! I can ' t handle people like that . Does he at least give you a hand around the house ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "He doesn ' t lift a finger ! I bend over backwards cleaning up all day and he sleeps in until noon .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 2, + 4 + ], + "expanded emotion cause span": [ + "But he ' s driving me up a wall . This guy is bottomless pit .", + "He doesn ' t lift a finger ! I bend over backwards cleaning up all day and he sleeps in until noon ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "He doesn ' t lift a finger ! I bend over backwards cleaning up all day and he sleeps in until noon .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Man , what a freeloader . You better do something quick or he ' ll never hit the road . After all , he ' s got it made in the shade here .", + "emotion": "neutral", + "text": "Man , what a freeloader . You better do something quick or he ' ll never hit the road . After all , he ' s got it made in the shade here .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "You think he might stay even longer ? !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "You better do something quick or he ' ll never hit the road ." + ], + "type": [ + "inter-personal" + ], + "text": "You think he might stay even longer ? !", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Now , don ' t go losing your temper . If you tolerated all you can , just kick him out ... but do it with gloves . I know ! Tell him a white lie like you ' re getting the house fumigated !", + "emotion": "neutral", + "text": "Now , don ' t go losing your temper . If you tolerated all you can , just kick him out ... but do it with gloves . I know ! Tell him a white lie like you ' re getting the house fumigated !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That wouldn ' t be a lie !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 2, + 4 + ], + "expanded emotion cause span": [ + "But he ' s driving me up a wall . This guy is bottomless pit .", + "He doesn ' t lift a finger ! I bend over backwards cleaning up all day and he sleeps in until noon ." + ], + "type": [ + "self-contagion" + ], + "text": "That wouldn ' t be a lie !", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_10060.json b/reccon/sources/tr_10060.json new file mode 100644 index 0000000000000000000000000000000000000000..21c447a815c4102043019d943f339cb43698d7b5 --- /dev/null +++ b/reccon/sources/tr_10060.json @@ -0,0 +1,141 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello , is Marie Ward there , please ?", + "emotion": "neutral", + "text": "Hello , is Marie Ward there , please ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'll see if she is in .", + "emotion": "neutral", + "text": "I'll see if she is in .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Ok .", + "emotion": "neutral", + "text": "Ok .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I'm afraid she's out .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 1, + 4 + ], + "expanded emotion cause span": [ + "is Marie Ward there", + "she's out ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm afraid she's out .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Can you give her a message , please ?", + "emotion": "neutral", + "text": "Can you give her a message , please ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yes , of course .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Can you give her a message" + ], + "type": [ + "inter-personal" + ], + "text": "Yes , of course .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Please tell her to give Colin a call when she gets back . She has my number .", + "emotion": "neutral", + "text": "Please tell her to give Colin a call when she gets back . She has my number .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Sure .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 7 + ], + "expanded emotion cause span": [ + "Can you give her a message", + "Please tell her to give Colin a call when she gets back ." + ], + "type": [ + "inter-personal" + ], + "text": "Sure .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Thank you for your help .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 7, + 8 + ], + "expanded emotion cause span": [ + "Can you give her a message", + "Please tell her to give Colin a call when she gets back .", + "Sure ." + ], + "type": [ + "hybrid" + ], + "text": "Thank you for your help .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "It's my pleasure .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Thank you for your help ." + ], + "type": [ + "inter-personal" + ], + "text": "It's my pleasure .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_10095.json b/reccon/sources/tr_10095.json new file mode 100644 index 0000000000000000000000000000000000000000..87691e2737ed0272be9f6ccc8e163571ff1aa00f --- /dev/null +++ b/reccon/sources/tr_10095.json @@ -0,0 +1,145 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Wow , the ferris wheel over there is so big . I'd like to take a ride on it .", + "emotion": "neutral", + "text": "Wow , the ferris wheel over there is so big . I'd like to take a ride on it .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It is called Energy Collector .", + "emotion": "neutral", + "text": "It is called Energy Collector .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Look at your right-hand . Is it the zone of the Lost Maya Kingdom ?", + "emotion": "neutral", + "text": "Look at your right-hand . Is it the zone of the Lost Maya Kingdom ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Maybe . Oh . I see the Jungle Flying Train . I once rode it . It was very exciting .", + "emotion": "neutral", + "text": "Maybe . Oh . I see the Jungle Flying Train . I once rode it . It was very exciting .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I want to have a try later .", + "emotion": "neutral", + "text": "I want to have a try later .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Me , too . Daniel , look at your left side . Can you see the Air Force Ants ?", + "emotion": "neutral", + "text": "Me , too . Daniel , look at your left side . Can you see the Air Force Ants ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Wow , that's my favorite . It's like a superman shooting right up into the sky .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "that's my favorite ." + ], + "type": [ + "no-context" + ], + "text": "Wow , that's my favorite . It's like a superman shooting right up into the sky .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Good , you can make your dream come true here .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "that's my favorite .", + "you can make your dream come true" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Good , you can make your dream come true here .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Of course . After this , I want to show you to the Haunted House .", + "emotion": "neutral", + "text": "Of course . After this , I want to show you to the Haunted House .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "So you can prove you are a man .", + "emotion": "neutral", + "text": "So you can prove you are a man .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Bingo !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "So you can prove you are a man ." + ], + "type": [ + "inter-personal" + ], + "text": "Bingo !", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "It's just you !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "Bingo !", + "It's just you !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It's just you !", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_10099.json b/reccon/sources/tr_10099.json new file mode 100644 index 0000000000000000000000000000000000000000..7b51c882b93cc15bdf1871a1f44982e56509a1b8 --- /dev/null +++ b/reccon/sources/tr_10099.json @@ -0,0 +1,176 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey , look out !", + "emotion": "neutral", + "text": "Hey , look out !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What happened ?", + "emotion": "neutral", + "text": "What happened ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "You've just scratched my car . Oh , God , a paint was scratched off .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 3, + 3 + ], + "expanded emotion cause span": [ + "You've just scratched my car .", + "a paint was scratched off ." + ], + "type": [ + "no-context" + ], + "text": "You've just scratched my car . Oh , God , a paint was scratched off .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Where ? my car ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "a paint was scratched off ." + ], + "type": [ + "inter-personal" + ], + "text": "Where ? my car ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "No , mine !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 3, + 3, + 5 + ], + "expanded emotion cause span": [ + "You've just scratched my car .", + "a paint was scratched off .", + "No , mine !" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "No , mine !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Thank goodness !", + "emotion": "neutral", + "text": "Thank goodness !", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I've just had it repainted .", + "emotion": "neutral", + "text": "I've just had it repainted .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That's terrible .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3, + 3, + 7 + ], + "expanded emotion cause span": [ + "You've just scratched my car .", + "a paint was scratched off .", + "I've just had it repainted ." + ], + "type": [ + "inter-personal" + ], + "text": "That's terrible .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I am sorry to say this , sir , but you should've been more careful .", + "emotion": "neutral", + "text": "I am sorry to say this , sir , but you should've been more careful .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I apologize for that . But the space is too small .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3, + 3, + 7, + 10 + ], + "expanded emotion cause span": [ + "You've just scratched my car .", + "a paint was scratched off .", + "I've just had it repainted .", + "I apologize for that ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I apologize for that . But the space is too small .", + "id": 10, + "source_sentences": [ + 2, + 2, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 11, + "speaker": "A", + "utterance": "What about the damage to my car ? What are you gonna do about that ?", + "emotion": "neutral", + "text": "What about the damage to my car ? What are you gonna do about that ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Can we solve this later ? I am calling the insurance company .", + "emotion": "neutral", + "text": "Can we solve this later ? I am calling the insurance company .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "OK . I gotta call mine too .", + "emotion": "neutral", + "text": "OK . I gotta call mine too .", + "id": 13 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_10226.json b/reccon/sources/tr_10226.json new file mode 100644 index 0000000000000000000000000000000000000000..413fe60fdce0f3cb4ea726b05d170261a3711040 --- /dev/null +++ b/reccon/sources/tr_10226.json @@ -0,0 +1,161 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I'd appreciate it if you could help me pick out a gift for my daughter .", + "emotion": "neutral", + "text": "I'd appreciate it if you could help me pick out a gift for my daughter .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Would she be interested in a laptop ?", + "emotion": "neutral", + "text": "Would she be interested in a laptop ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "That's exactly what I was thinking of .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "pick out a gift for my daughter .", + "Would she be interested in a laptop ?" + ], + "type": [ + "hybrid" + ], + "text": "That's exactly what I was thinking of .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "A Mac would be an excellent gift .", + "emotion": "neutral", + "text": "A Mac would be an excellent gift .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I like Macs . How much for a Mac ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I like Macs ." + ], + "type": [ + "no-context" + ], + "text": "I like Macs . How much for a Mac ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "You can take a 15 - inch Pro home right now for only $ 2,100 .", + "emotion": "neutral", + "text": "You can take a 15 - inch Pro home right now for only $ 2,100 .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "A Mac it is . I'll take one home with me .", + "emotion": "neutral", + "text": "A Mac it is . I'll take one home with me .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "She'll be very happy with this . And how do you plan to pay for it ?", + "emotion": "happiness", + "explanation": "the speaker is happy that A will be buying a product", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "A Mac it is . I'll take one home with me .", + "She'll be very happy with this ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "She'll be very happy with this . And how do you plan to pay for it ?", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I'll use my VISA , if that's okay .", + "emotion": "neutral", + "text": "I'll use my VISA , if that's okay .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Now , if you'll just sign here , the Mac is all yours .", + "emotion": "neutral", + "text": "Now , if you'll just sign here , the Mac is all yours .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Will she need anything besides what's in this box ?", + "emotion": "neutral", + "text": "Will she need anything besides what's in this box ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Everything she needs is right here in the box .", + "emotion": "neutral", + "text": "Everything she needs is right here in the box .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I appreciate your help . Maybe I'll be back for more computer stuff .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "I appreciate your help ." + ], + "type": [ + "no-context" + ], + "text": "I appreciate your help . Maybe I'll be back for more computer stuff .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Your daughter should get straight A's from now on . Good-bye .", + "emotion": "neutral", + "text": "Your daughter should get straight A's from now on . Good-bye .", + "id": 14 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1026.json b/reccon/sources/tr_1026.json new file mode 100644 index 0000000000000000000000000000000000000000..08e41bae5f42c5eb7b9b82ee742131deee997e9d --- /dev/null +++ b/reccon/sources/tr_1026.json @@ -0,0 +1,123 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello , Kevin . I hate to do this , but I have to cancel our appointment .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I hate to do this , but I have to cancel our appointment ." + ], + "type": [ + "no-context" + ], + "text": "Hello , Kevin . I hate to do this , but I have to cancel our appointment .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh , no ! Why ? I was looking forward to seeing you at my new place .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I have to cancel our appointment ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , no ! Why ? I was looking forward to seeing you at my new place .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yeah , I really wanted to come , too . But something unexpected in Shanghai have come up . I have to fly out for a few days , but I'll be back soon .", + "emotion": "neutral", + "text": "Yeah , I really wanted to come , too . But something unexpected in Shanghai have come up . I have to fly out for a few days , but I'll be back soon .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "No problem . Call me when you get back .", + "emotion": "neutral", + "text": "No problem . Call me when you get back .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I should have some free time next week . Say , next Wednesday evening ?", + "emotion": "neutral", + "text": "I should have some free time next week . Say , next Wednesday evening ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "That's good for me , but do you think you'll be back by then ? I'd really like to see you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "I should have some free time next week . Say , next Wednesday evening ?", + "I'd really like to see you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's good for me , but do you think you'll be back by then ? I'd really like to see you .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yeah , I'm expecting to come back on Tuesday .", + "emotion": "neutral", + "text": "Yeah , I'm expecting to come back on Tuesday .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Great ! That's settled then .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6, + 8 + ], + "expanded emotion cause span": [ + "I should have some free time next week . Say , next Wednesday evening ?", + "I'd really like to see you .", + "Great ! That's settled then ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Great ! That's settled then .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "OK .", + "emotion": "neutral", + "text": "OK .", + "id": 9 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_10265.json b/reccon/sources/tr_10265.json new file mode 100644 index 0000000000000000000000000000000000000000..3df01726108e9fdc7150c67f577b444e634bc007 --- /dev/null +++ b/reccon/sources/tr_10265.json @@ -0,0 +1,182 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Alright , tell me what you think .", + "emotion": "neutral", + "text": "Alright , tell me what you think .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Don't you think it ' s a bit bright ?", + "emotion": "neutral", + "text": "Don't you think it ' s a bit bright ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yeah , maybe you ' re right . How about this outfit ?", + "emotion": "neutral", + "text": "Yeah , maybe you ' re right . How about this outfit ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "This dress looks lovely on you , but it ' s not very practical , is it ?", + "emotion": "neutral", + "text": "This dress looks lovely on you , but it ' s not very practical , is it ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "No , I don't have any plans to go to a formal dance any time soon , but I love the way it looks . I just had to try it on ! What do you think about this ? It ' s casual , yet sophisticated .", + "emotion": "neutral", + "text": "No , I don't have any plans to go to a formal dance any time soon , but I love the way it looks . I just had to try it on ! What do you think about this ? It ' s casual , yet sophisticated .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I like the jeans , but you need something to go with the top . It ' s too plain on its own .", + "emotion": "neutral", + "text": "I like the jeans , but you need something to go with the top . It ' s too plain on its own .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "How about this scarf , these earrings , AMD an anklet ?", + "emotion": "neutral", + "text": "How about this scarf , these earrings , AMD an anklet ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That might be going overboard a bit . How about just that scarf with a bracelet ?", + "emotion": "neutral", + "text": "That might be going overboard a bit . How about just that scarf with a bracelet ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "That ' s a good idea . You have a lot of good fashion sense .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "How about just that scarf with a bracelet ?", + "You have a lot of good fashion sense ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That ' s a good idea . You have a lot of good fashion sense .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Thanks . You ' d be ok on your own . There are loads of fashion victims out there , and you are not one of them . Have you tried it on yet ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "You have a lot of good fashion sense ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks . You ' d be ok on your own . There are loads of fashion victims out there , and you are not one of them . Have you tried it on yet ?", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Yep . Here it is . What do you think ?", + "emotion": "neutral", + "text": "Yep . Here it is . What do you think ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "That looks great . Just one more thing---you need some high heels with those jeans . Do you want a pair with a plain pattern or ones with a leopard print on them ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "That looks great ." + ], + "type": [ + "no-context" + ], + "text": "That looks great . Just one more thing---you need some high heels with those jeans . Do you want a pair with a plain pattern or ones with a leopard print on them ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "The leopard print sounds fabulous . Are they a name brand ?", + "emotion": "neutral", + "text": "The leopard print sounds fabulous . Are they a name brand ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "No , they ' re a Prada knock-off for 1/10 of the price of the real thing .", + "emotion": "neutral", + "text": "No , they ' re a Prada knock-off for 1/10 of the price of the real thing .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "That ' s even better than the real thing .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "That ' s even better than the real thing ." + ], + "type": [ + "no-context" + ], + "text": "That ' s even better than the real thing .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "If I were you , I ' d buy that now while it ' s on sale . If you spend $ 100 , you get a $ 50 voucher for more clothes .", + "emotion": "neutral", + "text": "If I were you , I ' d buy that now while it ' s on sale . If you spend $ 100 , you get a $ 50 voucher for more clothes .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "It ' s too bad I did all that shopping yesterday !", + "emotion": "neutral", + "text": "It ' s too bad I did all that shopping yesterday !", + "id": 17 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_10301.json b/reccon/sources/tr_10301.json new file mode 100644 index 0000000000000000000000000000000000000000..79069d339459cee8318f537f3e975b7ecc53c4f6 --- /dev/null +++ b/reccon/sources/tr_10301.json @@ -0,0 +1,128 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Mary , could you please come in for a short while ?", + "emotion": "neutral", + "text": "Mary , could you please come in for a short while ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "No problem .", + "emotion": "neutral", + "text": "No problem .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Mary , I'd like you to meet Richard , Our new executive in the marketing .", + "emotion": "neutral", + "text": "Mary , I'd like you to meet Richard , Our new executive in the marketing .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Nice to meet you , Austin .", + "emotion": "neutral", + "text": "Nice to meet you , Austin .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Welcome to our department . I hope you'll like it here .", + "emotion": "neutral", + "text": "Welcome to our department . I hope you'll like it here .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "By the way , Richard will assist me in the planning work . I hope you can work well together .", + "emotion": "neutral", + "text": "By the way , Richard will assist me in the planning work . I hope you can work well together .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Sure , if you've got any problem you can ask me .", + "emotion": "happiness", + "explanation": "the speaker is happy to help Richard", + "flag": "F", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "if you've got any problem you can ask me ." + ], + "type": [ + "no-context" + ], + "text": "Sure , if you've got any problem you can ask me .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Thank you . It ' s very kind of you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "if you've got any problem you can ask me .", + "It ' s very kind of you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you . It ' s very kind of you .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Richard , Mary is a very helpful and experienced secretary indeed , and I'm sure you will find out .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Mary is a very helpful and experienced secretary indeed , and I'm sure you will find out ." + ], + "type": [ + "no-context" + ], + "text": "Richard , Mary is a very helpful and experienced secretary indeed , and I'm sure you will find out .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Thank you , sir . I'll try my best to assist Richard in his work .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Mary is a very helpful and experienced secretary indeed , and I'm sure you will find out ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you , sir . I'll try my best to assist Richard in his work .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_10329.json b/reccon/sources/tr_10329.json new file mode 100644 index 0000000000000000000000000000000000000000..9ccbdf84c249a227810e81c764f49b44c1db5537 --- /dev/null +++ b/reccon/sources/tr_10329.json @@ -0,0 +1,156 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Excuse me , What time does the next bus for Boston leave ?", + "emotion": "neutral", + "text": "Excuse me , What time does the next bus for Boston leave ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It leaves at 8", + "emotion": "neutral", + "text": "It leaves at 8", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I see . Are there any seat available ?", + "emotion": "neutral", + "text": "I see . Are there any seat available ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Just a moment please . Yes . You can have a seat .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "any seat available ?", + "Yes . You can have a seat ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Just a moment please . Yes . You can have a seat .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Good . How much is it when we take it ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "any seat available ?", + "Yes . You can have a seat ." + ], + "type": [ + "hybrid" + ], + "text": "Good . How much is it when we take it ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "It thirty-eight dollars .", + "emotion": "neutral", + "text": "It thirty-eight dollars .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "All right . Here ' s forty dollars .", + "emotion": "neutral", + "text": "All right . Here ' s forty dollars .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Here ' s your ticket and change .", + "emotion": "neutral", + "text": "Here ' s your ticket and change .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Thank you . Which gate should I go to for the bus ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Here ' s your ticket" + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . Which gate should I go to for the bus ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Go to gate No . 2 please .", + "emotion": "neutral", + "text": "Go to gate No . 2 please .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Thank you very much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "Which gate should I go to for the bus ?", + "Go to gate No . 2 please ." + ], + "type": [ + "hybrid" + ], + "text": "Thank you very much .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Don ' t mention it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "Thank you very much ." + ], + "type": [ + "inter-personal" + ], + "text": "Don ' t mention it .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_10362.json b/reccon/sources/tr_10362.json new file mode 100644 index 0000000000000000000000000000000000000000..5cb80ae8ac33511d59c04607c8b7e8bd67c70e2d --- /dev/null +++ b/reccon/sources/tr_10362.json @@ -0,0 +1,202 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Good morning , sir . Can I see your boarding pass , please ?", + "emotion": "neutral", + "text": "Good morning , sir . Can I see your boarding pass , please ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Here you are .", + "emotion": "neutral", + "text": "Here you are .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Excuse me , sir . This is your passport .", + "emotion": "neutral", + "text": "Excuse me , sir . This is your passport .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Really ? Ugh ... Is there any difference ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "This is your passport .", + "Is there any difference ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Really ? Ugh ... Is there any difference ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Yes . As a matter of fact , you can't board the plane without boarding pass .", + "emotion": "neutral", + "text": "Yes . As a matter of fact , you can't board the plane without boarding pass .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Gee . I must have left it in my hotel room .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "you can't board the plane" + ], + "type": [ + "inter-personal" + ], + "text": "Gee . I must have left it in my hotel room .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I'm sorry sir . I can't let you pass .", + "emotion": "neutral", + "text": "I'm sorry sir . I can't let you pass .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "But when does the plane take off ?", + "emotion": "neutral", + "text": "But when does the plane take off ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Ugh , in about thirty minutes , sir .", + "emotion": "neutral", + "text": "Ugh , in about thirty minutes , sir .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Oh , my God ! What do I do now ? Bone head , bone head , bone head ( He smashes his head with his hand . ) .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 6, + 7, + 8, + 9 + ], + "expanded emotion cause span": [ + "I must have left it in my hotel room .", + "I can't let you pass .", + "when does the plane take off ?", + "in about thirty minutes ," + ], + "type": [ + "hybrid" + ], + "text": "Oh , my God ! What do I do now ? Bone head , bone head , bone head ( He smashes his head with his hand . ) .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Calm down , sir . You are creating a commotion .", + "emotion": "neutral", + "text": "Calm down , sir . You are creating a commotion .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "( The speaker in the airport says , ' Mr . Benjamin , we now have a boarding pass by the name of Benjamin at Lost and Found . ' ) Is that me ?", + "emotion": "neutral", + "text": "( The speaker in the airport says , ' Mr . Benjamin , we now have a boarding pass by the name of Benjamin at Lost and Found . ' ) Is that me ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Could be .", + "emotion": "neutral", + "text": "Could be .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Oh , thank God . Thank you , I'll be right back .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "we now have a boarding pass by the name of Benjamin" + ], + "type": [ + "self-contagion" + ], + "text": "Oh , thank God . Thank you , I'll be right back .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "( Benjamin starts to run and then he seems to remember something and returns . ) Ugh , excuse me , where is the Lost and Found ?", + "emotion": "neutral", + "text": "( Benjamin starts to run and then he seems to remember something and returns . ) Ugh , excuse me , where is the Lost and Found ?", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "It's down in the lobby . Turn left at exit B .", + "emotion": "neutral", + "text": "It's down in the lobby . Turn left at exit B .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "Thank you , thank you , thanks again .", + "emotion": "happiness", + "explanation": "Speaker gets answer to his query", + "expanded emotion cause evidence": [ + 12, + 15, + 16 + ], + "expanded emotion cause span": [ + "we now have a boarding pass by the name of Benjamin", + "where is the Lost and Found ?", + "It's down in the lobby ." + ], + "type": [ + "hybrid" + ], + "text": "Thank you , thank you , thanks again .", + "id": 17 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_10408.json b/reccon/sources/tr_10408.json new file mode 100644 index 0000000000000000000000000000000000000000..1725ad24900c3a94f8c13576113810a86cceb716 --- /dev/null +++ b/reccon/sources/tr_10408.json @@ -0,0 +1,141 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello . I am calling about the apartment you advertised .", + "emotion": "neutral", + "text": "Hello . I am calling about the apartment you advertised .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , what kind of apartment are you interested in ?", + "emotion": "neutral", + "text": "Yes , what kind of apartment are you interested in ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I am interested in one-bedroom . Do you have any available ?", + "emotion": "neutral", + "text": "I am interested in one-bedroom . Do you have any available ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes , I have one . When you need it ?", + "emotion": "neutral", + "text": "Yes , I have one . When you need it ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Sometime around next week . What can you tell me about this apartment ?", + "emotion": "neutral", + "text": "Sometime around next week . What can you tell me about this apartment ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Well , It's a one-bedroom apartment . The monthly rent at 650 dollars and a 300 dollars security deposit . You pay electricity only . Gas and water is included . Both the heat and stove are gas . Let me see , what else ... Oh , you'll be assigned a sheltered parking space at no extra charge . And that's probably it .", + "emotion": "neutral", + "text": "Well , It's a one-bedroom apartment . The monthly rent at 650 dollars and a 300 dollars security deposit . You pay electricity only . Gas and water is included . Both the heat and stove are gas . Let me see , what else ... Oh , you'll be assigned a sheltered parking space at no extra charge . And that's probably it .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Sounds good . May I come over tomorrow to take a look ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "a sheltered parking space at no extra charge ." + ], + "type": [ + "inter-personal" + ], + "text": "Sounds good . May I come over tomorrow to take a look ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Sure . What time would you like to come ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Sounds good ." + ], + "type": [ + "inter-personal" + ], + "text": "Sure . What time would you like to come ?", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "How about 10 am ?", + "emotion": "neutral", + "text": "How about 10 am ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Good , May I have your name , please ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "a sheltered parking space at no extra charge ." + ], + "type": [ + "self-contagion" + ], + "text": "Good , May I have your name , please ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "My name is Blanca .", + "emotion": "neutral", + "text": "My name is Blanca .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Thanks for calling , Blanca . I'll see you tomorrow .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "a sheltered parking space at no extra charge ." + ], + "type": [ + "self-contagion" + ], + "text": "Thanks for calling , Blanca . I'll see you tomorrow .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_10410.json b/reccon/sources/tr_10410.json new file mode 100644 index 0000000000000000000000000000000000000000..6596ed0f8c47f5d428f62c15a514d200932e8bba --- /dev/null +++ b/reccon/sources/tr_10410.json @@ -0,0 +1,123 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Sam , you ' Ve got to forgive me .", + "emotion": "neutral", + "text": "Sam , you ' Ve got to forgive me .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Forgive you for what ?", + "emotion": "neutral", + "text": "Forgive you for what ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I used your computer . And I ' m afraid I ' Ve erased your personal files accidentally .", + "emotion": "neutral", + "text": "I used your computer . And I ' m afraid I ' Ve erased your personal files accidentally .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "No ! Are you kidding me ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I ' Ve erased your personal files accidentally ." + ], + "type": [ + "inter-personal" + ], + "text": "No ! Are you kidding me ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I ' m afraid not . I apologize .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I ' Ve erased your personal files accidentally ." + ], + "type": [ + "self-contagion" + ], + "text": "I ' m afraid not . I apologize .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I can ' t believe it ! I have all my important personal documents stored in that computer . It ' s no laughing matter .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 3, + 6 + ], + "expanded emotion cause span": [ + "I ' Ve erased your personal files accidentally .", + "I have all my important personal documents stored in that computer ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I can ' t believe it ! I have all my important personal documents stored in that computer . It ' s no laughing matter .", + "id": 6, + "source_sentences": [ + 2 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I told you I ' m sorry . What can I do to make it up to you ?", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3, + 6 + ], + "expanded emotion cause span": [ + "I ' Ve erased your personal files accidentally .", + "I have all my important personal documents stored in that computer ." + ], + "type": [ + "hybrid" + ], + "text": "I told you I ' m sorry . What can I do to make it up to you ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Well , you should be sorry ! Don ' t ever use my computer again ! You can ' t do anything now , it ' s too late !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 3, + 6 + ], + "expanded emotion cause span": [ + "I ' Ve erased your personal files accidentally .", + "I have all my important personal documents stored in that computer ." + ], + "type": [ + "hybrid" + ], + "text": "Well , you should be sorry ! Don ' t ever use my computer again ! You can ' t do anything now , it ' s too late !", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_10419.json b/reccon/sources/tr_10419.json new file mode 100644 index 0000000000000000000000000000000000000000..f7b161aadc6f7ede5a4d4ce691162c65db3a094c --- /dev/null +++ b/reccon/sources/tr_10419.json @@ -0,0 +1,136 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Oh . Henry . I haven't seen you in ages . Come in . Let me take your coat . How are you getting along ?", + "emotion": "neutral", + "text": "Oh . Henry . I haven't seen you in ages . Come in . Let me take your coat . How are you getting along ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Very well , thank you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 1 + ], + "expanded emotion cause span": [ + "I haven't seen you in ages .", + "How are you getting along ?" + ], + "type": [ + "inter-personal" + ], + "text": "Very well , thank you .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Please take a seat . Everything will be ready in a minute .", + "emotion": "neutral", + "text": "Please take a seat . Everything will be ready in a minute .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Here you go . We have your cocktail and there're salad . fried chicken , French fries and vanilla ice cream for dessert . Eat the chicken while it's hot . It tastes better .", + "emotion": "neutral", + "text": "Here you go . We have your cocktail and there're salad . fried chicken , French fries and vanilla ice cream for dessert . Eat the chicken while it's hot . It tastes better .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Wow ! You're right . Everything is absolutely delicious . Please pass the pepper .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "We have your cocktail and there're salad . fried chicken , French fries and vanilla ice cream for dessert . Eat the chicken while it's hot . It tastes better .", + "Everything is absolutely delicious ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Wow ! You're right . Everything is absolutely delicious . Please pass the pepper .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Here you are . Taste the French fries .", + "emotion": "neutral", + "text": "Here you are . Taste the French fries .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "They're soft .", + "emotion": "neutral", + "text": "They're soft .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Would you like some more ?", + "emotion": "neutral", + "text": "Would you like some more ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "No more . Thank you .", + "emotion": "neutral", + "text": "No more . Thank you .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Here's to our friendship and health !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Here's to our friendship and health !" + ], + "type": [ + "no-context" + ], + "text": "Here's to our friendship and health !", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Bottoms up !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Here's to our friendship and health !" + ], + "type": [ + "inter-personal" + ], + "text": "Bottoms up !", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_10488.json b/reccon/sources/tr_10488.json new file mode 100644 index 0000000000000000000000000000000000000000..6c41b429a2f30311826a8ec34a211a9e5fd92157 --- /dev/null +++ b/reccon/sources/tr_10488.json @@ -0,0 +1,123 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey George , how is your chicken ?", + "emotion": "neutral", + "text": "Hey George , how is your chicken ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "My chicken tastes all right , but it is pretty dry . How is your fish ?", + "emotion": "neutral", + "text": "My chicken tastes all right , but it is pretty dry . How is your fish ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "My fish is pretty dry too .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "fish is pretty dry" + ], + "type": [ + "no-context" + ], + "text": "My fish is pretty dry too .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It's almost as if this food has been sitting a little too long . It doesn't seem fresh .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "fish is pretty dry", + "It doesn't seem fresh ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It's almost as if this food has been sitting a little too long . It doesn't seem fresh .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Yes , it seems that way to me also .", + "emotion": "neutral", + "text": "Yes , it seems that way to me also .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "How are your vegetables ?", + "emotion": "neutral", + "text": "How are your vegetables ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "My vegetables are very soggy .", + "emotion": "neutral", + "text": "My vegetables are very soggy .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Mine are the same way . It seems like they've been overcooked .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 7, + 8, + 8 + ], + "expanded emotion cause span": [ + "vegetables are very soggy .", + "Mine are the same way .", + "they've been overcooked ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Mine are the same way . It seems like they've been overcooked .", + "id": 8, + "source_sentences": [ + 6, + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I don't usually complain , but I think that we should mention this to the waiter .", + "emotion": "neutral", + "text": "I don't usually complain , but I think that we should mention this to the waiter .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I agree . Maybe they can bring us some better food .", + "emotion": "neutral", + "text": "I agree . Maybe they can bring us some better food .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_10549.json b/reccon/sources/tr_10549.json new file mode 100644 index 0000000000000000000000000000000000000000..334ad1c7d77c5c9a88043e4fb9a63138e9848b9b --- /dev/null +++ b/reccon/sources/tr_10549.json @@ -0,0 +1,155 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Great . The bed is exactly what I have been looking for !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "The bed is exactly what I have been looking for !" + ], + "type": [ + "no-context" + ], + "text": "Great . The bed is exactly what I have been looking for !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "You have good taste . It's made of red wood .", + "emotion": "neutral", + "text": "You have good taste . It's made of red wood .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Oh , I like red wood . How much do you charge for it ?", + "emotion": "neutral", + "text": "Oh , I like red wood . How much do you charge for it ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "300 dollars .", + "emotion": "neutral", + "text": "300 dollars .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "That's sheer robbery !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 3, + 4, + 5 + ], + "expanded emotion cause span": [ + "How much do you charge for it ?", + "300 dollars .", + "That's sheer robbery !" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "That's sheer robbery !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Believe me , it's worth the price .", + "emotion": "neutral", + "text": "Believe me , it's worth the price .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "It's more than I can afford . Can I make an offer ?", + "emotion": "neutral", + "text": "It's more than I can afford . Can I make an offer ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "How much are you willing to pay ?", + "emotion": "neutral", + "text": "How much are you willing to pay ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Shall we make it 250 dollars ?", + "emotion": "neutral", + "text": "Shall we make it 250 dollars ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "No . That price would hardly cover the cost .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "Shall we make it 250 dollars ?", + "That price would hardly cover the cost ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "No . That price would hardly cover the cost .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "What about 260 dollars ?", + "emotion": "neutral", + "text": "What about 260 dollars ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "275 dollars is the lowest price I can offer .", + "emotion": "neutral", + "text": "275 dollars is the lowest price I can offer .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "It's a deal .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "275 dollars is the lowest price I can offer ." + ], + "type": [ + "inter-personal" + ], + "text": "It's a deal .", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1060.json b/reccon/sources/tr_1060.json new file mode 100644 index 0000000000000000000000000000000000000000..00993e5713ee821bb71d94d3d5e22754750a9f7a --- /dev/null +++ b/reccon/sources/tr_1060.json @@ -0,0 +1,146 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Cheer !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Cheer !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Cheer !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Cheer !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "So what time tomorrow ?", + "emotion": "neutral", + "text": "So what time tomorrow ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Half past seven in the morning .", + "emotion": "neutral", + "text": "Half past seven in the morning .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Where to meet ?", + "emotion": "neutral", + "text": "Where to meet ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "In the market .", + "emotion": "neutral", + "text": "In the market .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "OK . Bottoms up .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Where to meet ?", + "In the market ." + ], + "type": [ + "hybrid" + ], + "text": "OK . Bottoms up .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Bottoms up .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "OK . Bottoms up ." + ], + "type": [ + "inter-personal" + ], + "text": "Bottoms up .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "It's on me .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Bottoms up ." + ], + "type": [ + "inter-personal" + ], + "text": "It's on me .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Thank you . This place is nice .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "It's on me .", + "Thank you . This place is nice ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you . This place is nice .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_10620.json b/reccon/sources/tr_10620.json new file mode 100644 index 0000000000000000000000000000000000000000..1bd1866373ef2ded61b03f5ea3b44eca1a23cdda --- /dev/null +++ b/reccon/sources/tr_10620.json @@ -0,0 +1,186 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Can I get you something to drink ?", + "emotion": "neutral", + "text": "Can I get you something to drink ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Sure , but I don't drink much . So I don't know what to order .", + "emotion": "neutral", + "text": "Sure , but I don't drink much . So I don't know what to order .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "So how about an aperitif ?", + "emotion": "neutral", + "text": "So how about an aperitif ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It sounds good . I'd like to start with a Compare .", + "emotion": "neutral", + "text": "It sounds good . I'd like to start with a Compare .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Stirred or shaken ?", + "emotion": "neutral", + "text": "Stirred or shaken ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Stirred will be fine .", + "emotion": "neutral", + "text": "Stirred will be fine .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Here you are .", + "emotion": "neutral", + "text": "Here you are .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Thanks . Does the bar have a signature drink ?", + "emotion": "happiness", + "explanation": "Speaker is happy with the drinks order", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Here you are ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks . Does the bar have a signature drink ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Sure . All of our mixed drinks are excellent . You can also try a delicious non-alcoholic cocktail .", + "emotion": "neutral", + "text": "Sure . All of our mixed drinks are excellent . You can also try a delicious non-alcoholic cocktail .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Can you recommend one ?", + "emotion": "neutral", + "text": "Can you recommend one ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Try a Stinger . It has lime juice and grenadine over ice .", + "emotion": "neutral", + "text": "Try a Stinger . It has lime juice and grenadine over ice .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "It sounds interesting . I'll take one .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "Try a Stinger . It has lime juice and grenadine over ice .", + "It sounds interesting ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It sounds interesting . I'll take one .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Here we go .", + "emotion": "neutral", + "text": "Here we go .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "It tastes great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "It tastes great ." + ], + "type": [ + "no-context" + ], + "text": "It tastes great .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Enjoy yourself .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "It tastes great ." + ], + "type": [ + "inter-personal" + ], + "text": "Enjoy yourself .", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Yeah .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14, + 15 + ], + "expanded emotion cause span": [ + "It tastes great .", + "Enjoy yourself ." + ], + "type": [ + "hybrid" + ], + "text": "Yeah .", + "id": 16 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1064.json b/reccon/sources/tr_1064.json new file mode 100644 index 0000000000000000000000000000000000000000..dc75cb262bc8c61da37644ed162ea40f7dea85b7 --- /dev/null +++ b/reccon/sources/tr_1064.json @@ -0,0 +1,131 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Want to join me for a midnight snack ? I need to grab something to eat .", + "emotion": "neutral", + "text": "Want to join me for a midnight snack ? I need to grab something to eat .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Fine with me , but no more chafing dish .", + "emotion": "neutral", + "text": "Fine with me , but no more chafing dish .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Let's go to the food stall . There's a good one just around the corner .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Let's go to the food stall . There's a good one just around the corner ." + ], + "type": [ + "no-context" + ], + "text": "Let's go to the food stall . There's a good one just around the corner .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I'd love to try some snacks .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "Let's go to the food stall", + "I'd love to try some snacks ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'd love to try some snacks .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "( Later .. ) Everything looks tempting . What do you want to have ?", + "emotion": "neutral", + "text": "( Later .. ) Everything looks tempting . What do you want to have ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Kebabs and roast squid .", + "emotion": "neutral", + "text": "Kebabs and roast squid .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Can I have a bite ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Kebabs and roast squid ." + ], + "type": [ + "inter-personal" + ], + "text": "Can I have a bite ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Help yourself .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Can I have a bite ?" + ], + "type": [ + "inter-personal" + ], + "text": "Help yourself .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Super !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7, + 8 + ], + "expanded emotion cause span": [ + "Kebabs and roast squid .", + "Can I have a bite ?", + "Help yourself ." + ], + "type": [ + "hybrid" + ], + "text": "Super !", + "id": 9 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_10644.json b/reccon/sources/tr_10644.json new file mode 100644 index 0000000000000000000000000000000000000000..c1ee5f324140ea528818e5bc650367032cd1839f --- /dev/null +++ b/reccon/sources/tr_10644.json @@ -0,0 +1,130 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Is there a problem , officer ?", + "emotion": "neutral", + "text": "Is there a problem , officer ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I stopped you for driving through a red light .", + "emotion": "neutral", + "text": "I stopped you for driving through a red light .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Did I really ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "stopped you for driving through a red light ." + ], + "type": [ + "inter-personal" + ], + "text": "Did I really ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "You didn't know ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Did I really ?" + ], + "type": [ + "inter-personal" + ], + "text": "You didn't know ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I had no idea that I ran it .", + "emotion": "neutral", + "text": "I had no idea that I ran it .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Don't you know that yellow means slow down ?", + "emotion": "neutral", + "text": "Don't you know that yellow means slow down ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yes , madam .", + "emotion": "neutral", + "text": "Yes , madam .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Why'd you speed up instead ?", + "emotion": "neutral", + "text": "Why'd you speed up instead ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I really have no excuse , madam .", + "emotion": "neutral", + "text": "I really have no excuse , madam .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I'll have to write you a ticket .", + "emotion": "neutral", + "text": "I'll have to write you a ticket .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I understand , and I am very sorry .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "write you a ticket ." + ], + "type": [ + "inter-personal" + ], + "text": "I understand , and I am very sorry .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Here's your ticket .", + "emotion": "neutral", + "text": "Here's your ticket .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_10645.json b/reccon/sources/tr_10645.json new file mode 100644 index 0000000000000000000000000000000000000000..6fe57dcbc1f2a60d43638ec06ac9516636986ede --- /dev/null +++ b/reccon/sources/tr_10645.json @@ -0,0 +1,148 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I like this apartment . Do you think we can afford the mortgage ?", + "emotion": "neutral", + "text": "I like this apartment . Do you think we can afford the mortgage ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes . I think so . It ' s not a very expensive apartment . It ' s in the right area and it has everything that we are looking for . The rooms are quite large too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "It ' s not a very expensive apartment . It ' s in the right area and it has everything that we are looking for . The rooms are quite large too ." + ], + "type": [ + "no-context" + ], + "text": "Yes . I think so . It ' s not a very expensive apartment . It ' s in the right area and it has everything that we are looking for . The rooms are quite large too .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I love the balcony . We can sit outside and enjoy the sun in summer . We are on the 12th floor , so there ' s very nice view from the balcony .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I love the balcony . We can sit outside and enjoy the sun in summer . We are on the 12th floor , so there ' s very nice view from the balcony ." + ], + "type": [ + "no-context" + ], + "text": "I love the balcony . We can sit outside and enjoy the sun in summer . We are on the 12th floor , so there ' s very nice view from the balcony .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "The neighbourhood is nice too . There is a park nearby .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 4 + ], + "expanded emotion cause span": [ + "It ' s not a very expensive apartment . It ' s in the right area and it has everything that we are looking for . The rooms are quite large too .", + "The neighbourhood is nice too . There is a park nearby ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "The neighbourhood is nice too . There is a park nearby .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Yes , and there are many houses nearby . I like it that the neighbourhood isn ' t full of apartment blocks .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "the neighbourhood isn ' t full of apartment blocks ." + ], + "type": [ + "no-context" + ], + "text": "Yes , and there are many houses nearby . I like it that the neighbourhood isn ' t full of apartment blocks .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "It ' s a pity we can ' t afford a house . A garden would be so nice .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "It ' s a pity we can ' t afford a house ." + ], + "type": [ + "no-context" + ], + "text": "It ' s a pity we can ' t afford a house . A garden would be so nice .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yes , it would . Don ' t worry . There ' s a lawn outside the building and there ' s the park nearby . This place will be fine .", + "emotion": "neutral", + "text": "Yes , it would . Don ' t worry . There ' s a lawn outside the building and there ' s the park nearby . This place will be fine .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "The building is quite new and well constructed . I ' m happy with the fittings too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "The building is quite new and well constructed . I ' m happy with the fittings too ." + ], + "type": [ + "no-context" + ], + "text": "The building is quite new and well constructed . I ' m happy with the fittings too .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yes , everything has been well designed .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "The building is quite new and well constructed . I ' m happy with the fittings too .", + "Yes , everything has been well designed ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , everything has been well designed .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_10709.json b/reccon/sources/tr_10709.json new file mode 100644 index 0000000000000000000000000000000000000000..73ce5cf5faa98a03bea2db6e44b360735fce42e6 --- /dev/null +++ b/reccon/sources/tr_10709.json @@ -0,0 +1,150 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I want to get on the bus already .", + "emotion": "neutral", + "text": "I want to get on the bus already .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It just isn't on time today .", + "emotion": "neutral", + "text": "It just isn't on time today .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "It was supposed to be here thirty minutes ago .", + "emotion": "neutral", + "text": "It was supposed to be here thirty minutes ago .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I think it'll be here pretty soon .", + "emotion": "neutral", + "text": "I think it'll be here pretty soon .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I need to get to work , so it better .", + "emotion": "neutral", + "text": "I need to get to work , so it better .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I really do hate public transportation .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 2, + 6 + ], + "expanded emotion cause span": [ + "It just isn't on time today .", + "I really do hate public transportation ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I really do hate public transportation .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I agree , it's just never on time .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I really do hate public transportation .", + "I agree , it's just never on time ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I agree , it's just never on time .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That's right .", + "emotion": "neutral", + "text": "That's right .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I also hate having to stand at a bus stop in all kinds of weather .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 6, + 7, + 9 + ], + "expanded emotion cause span": [ + "I really do hate public transportation .", + "I agree , it's just never on time .", + "I also hate having to stand at a bus stop" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I also hate having to stand at a bus stop in all kinds of weather .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Oh , that's the worst .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "I also hate having to stand at a bus stop" + ], + "type": [ + "inter-personal" + ], + "text": "Oh , that's the worst .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 11, + "speaker": "A", + "utterance": "We need to get a car .", + "emotion": "neutral", + "text": "We need to get a car .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I completely agree with that .", + "emotion": "neutral", + "text": "I completely agree with that .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1072.json b/reccon/sources/tr_1072.json new file mode 100644 index 0000000000000000000000000000000000000000..3db7a35c1ec03e264f82c95f667f6311632a55ac --- /dev/null +++ b/reccon/sources/tr_1072.json @@ -0,0 +1,118 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi honey ! You ' ll never guess what ! My friends Julie and Alex are getting married !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "My friends Julie and Alex are getting married !" + ], + "type": [ + "no-context" + ], + "text": "Hi honey ! You ' ll never guess what ! My friends Julie and Alex are getting married !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Wow that ' s great news ! They ' re a great couple !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "My friends Julie and Alex are getting married !", + "They ' re a great couple !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Wow that ' s great news ! They ' re a great couple !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I know ! Anyways I just talked to Alex ' s best man and he is organizing the bachelor party It ' s gonna be so much fun ! All the groomsmen are thinking up all the wacky and crazy things we are going to do that night .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 3 + ], + "expanded emotion cause span": [ + "My friends Julie and Alex are getting married !", + "They ' re a great couple !", + "I just talked to Alex ' s best man and he is organizing the bachelor party It ' s gonna be so much fun ! All the groomsmen are thinking up all the wacky and crazy things we are going to do that night ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I know ! Anyways I just talked to Alex ' s best man and he is organizing the bachelor party It ' s gonna be so much fun ! All the groomsmen are thinking up all the wacky and crazy things we are going to do that night .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "You aren ' t going to a strip club , are you ? I don ' t want you getting a lap dance from some stripper with the excuse that it ' s your friends party .", + "emotion": "neutral", + "text": "You aren ' t going to a strip club , are you ? I don ' t want you getting a lap dance from some stripper with the excuse that it ' s your friends party .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Aw come on ! It ' s just some innocent fun ! You know how these things are ! We are gonna play drinking games , get him some gag gifts and just have a good time . Nothing too over the top .", + "emotion": "neutral", + "text": "Aw come on ! It ' s just some innocent fun ! You know how these things are ! We are gonna play drinking games , get him some gag gifts and just have a good time . Nothing too over the top .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Well , I don ' t know .", + "emotion": "neutral", + "text": "Well , I don ' t know .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Come on ! If one of your friends was getting married I wouldn ' t mind you going to her bachelorette party !", + "emotion": "neutral", + "text": "Come on ! If one of your friends was getting married I wouldn ' t mind you going to her bachelorette party !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Good , because my friend Wendy is getting married and I ' m organizing her party !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "If one of your friends was getting married I wouldn ' t mind you going to her bachelorette party !", + "my friend Wendy is getting married and I ' m organizing her party !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Good , because my friend Wendy is getting married and I ' m organizing her party !", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_10727.json b/reccon/sources/tr_10727.json new file mode 100644 index 0000000000000000000000000000000000000000..1da56c3581fac1432c15312dac8b6b74a2d4465b --- /dev/null +++ b/reccon/sources/tr_10727.json @@ -0,0 +1,102 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Marketing manage office , can I help you ?", + "emotion": "neutral", + "text": "Marketing manage office , can I help you ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Mr Green , please .", + "emotion": "neutral", + "text": "Mr Green , please .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Sorry , he's out .", + "emotion": "sadness", + "explanation": "Cant help the customer", + "expanded emotion cause evidence": [ + "b", + 3 + ], + "expanded emotion cause span": [ + "b", + "he's out ." + ], + "type": [ + "latent", + "no-context" + ], + "text": "Sorry , he's out .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "What time you suspect back them ?", + "emotion": "neutral", + "text": "What time you suspect back them ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Sorry , I am not sure , can I take a message ?", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I am not sure" + ], + "type": [ + "no-context" + ], + "text": "Sorry , I am not sure , can I take a message ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "No , thanks . I'll call back later .", + "emotion": "neutral", + "text": "No , thanks . I'll call back later .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "That's fine . please call again later .", + "emotion": "neutral", + "text": "That's fine . please call again later .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Ok , thank you . Goodbye .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "That's fine . please call again later ." + ], + "type": [ + "inter-personal" + ], + "text": "Ok , thank you . Goodbye .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1073.json b/reccon/sources/tr_1073.json new file mode 100644 index 0000000000000000000000000000000000000000..3255602937370bf28e4046758ccb9907bf7a1a1b --- /dev/null +++ b/reccon/sources/tr_1073.json @@ -0,0 +1,127 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Aren ' t you interested in watching the Olympics ? There have been some excellent performances by athletes from all over the world .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "There have been some excellent performances by athletes from all over the world ." + ], + "type": [ + "no-context" + ], + "text": "Aren ' t you interested in watching the Olympics ? There have been some excellent performances by athletes from all over the world .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I just don ' t find it very interesting .", + "emotion": "neutral", + "text": "I just don ' t find it very interesting .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I think it ' s wonderful to see people from all over the world taking part in such a great event .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I think it ' s wonderful to see people from all over the world taking part in such a great event ." + ], + "type": [ + "no-context" + ], + "text": "I think it ' s wonderful to see people from all over the world taking part in such a great event .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I think that for a lot of people , it ' s just a way to try and show their country is better than other countries .", + "emotion": "neutral", + "text": "I think that for a lot of people , it ' s just a way to try and show their country is better than other countries .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I think the Olympics help to promote world peace .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I think the Olympics help to promote world peace ." + ], + "type": [ + "no-context" + ], + "text": "I think the Olympics help to promote world peace .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I ' m not sure about that . We still have many wars in the world . I think that the idea behind the Olympics is a good one , but the reality is that during the Olympics countries compete . There ' s no real spirit of cooperation and people are usually not very friendly to each other .", + "emotion": "neutral", + "text": "I ' m not sure about that . We still have many wars in the world . I think that the idea behind the Olympics is a good one , but the reality is that during the Olympics countries compete . There ' s no real spirit of cooperation and people are usually not very friendly to each other .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You are so pessimistic ! The Olympics is a great opportunity for athletes to demonstrate their speed , skill , agility and strength . Most people hope to see someone from their country win , but I think that they are just happy to see good performances by any athlete .", + "emotion": "neutral", + "text": "You are so pessimistic ! The Olympics is a great opportunity for athletes to demonstrate their speed , skill , agility and strength . Most people hope to see someone from their country win , but I think that they are just happy to see good performances by any athlete .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Well . I think that the most amazing performances are by athletes who participate in the Paralympics .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I think that the most amazing performances are by athletes who participate in the Paralympics ." + ], + "type": [ + "no-context" + ], + "text": "Well . I think that the most amazing performances are by athletes who participate in the Paralympics .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Now there we are in agreement !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "I think that the most amazing performances are by athletes who participate in the Paralympics .", + "Now there we are in agreement !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Now there we are in agreement !", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_108.json b/reccon/sources/tr_108.json new file mode 100644 index 0000000000000000000000000000000000000000..f2b339a5c8046e8be5e65fcc2f924b1f7de695e5 --- /dev/null +++ b/reccon/sources/tr_108.json @@ -0,0 +1,126 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , Charles . What's the matter ?", + "emotion": "neutral", + "text": "Hi , Charles . What's the matter ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh ! ! My car isn't working . I'm waiting for a tow-truck .", + "emotion": "neutral", + "text": "Oh ! ! My car isn't working . I'm waiting for a tow-truck .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Do you have a ride home ?", + "emotion": "neutral", + "text": "Do you have a ride home ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes , my wife is coming to get me .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "my wife is coming to get me ." + ], + "type": [ + "no-context" + ], + "text": "Yes , my wife is coming to get me .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "That's good . Do you live near here ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "my wife is coming to get me ." + ], + "type": [ + "inter-personal" + ], + "text": "That's good . Do you live near here ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "No , we live in the suburbs . What about you ?", + "emotion": "neutral", + "text": "No , we live in the suburbs . What about you ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I live downtown , with my parents .", + "emotion": "neutral", + "text": "I live downtown , with my parents .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Do you have a car ?", + "emotion": "neutral", + "text": "Do you have a car ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I don't need a car . I walk to work .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "I don't need a car . I walk to work ." + ], + "type": [ + "no-context" + ], + "text": "I don't need a car . I walk to work .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "You're lucky !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "I don't need a car . I walk to work .", + "You're lucky !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You're lucky !", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1084.json b/reccon/sources/tr_1084.json new file mode 100644 index 0000000000000000000000000000000000000000..db963d5a8ebbea2926f907685d9beac635000559 --- /dev/null +++ b/reccon/sources/tr_1084.json @@ -0,0 +1,131 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Jenny , are you having fun here ?", + "emotion": "happiness", + "explanation": "the speaker is happy to meet B", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Jenny , are you having fun here ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , of course . This is really a nice party with wonderful people and lovely wines .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "having fun", + "This is really a nice party with wonderful people and lovely wines ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , of course . This is really a nice party with wonderful people and lovely wines .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I ' m glad you ' re enjoying it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 3 + ], + "expanded emotion cause span": [ + "having fun", + "This is really a nice party with wonderful people and lovely wines .", + "I ' m glad you ' re enjoying it ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I ' m glad you ' re enjoying it .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Thank you for the invitation .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 3, + 4 + ], + "expanded emotion cause span": [ + "having fun", + "This is really a nice party with wonderful people and lovely wines .", + "I ' m glad you ' re enjoying it .", + "invitation ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Thank you for the invitation .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "It ' s my pleasure . Would you like another glass of champagne ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 3, + 4 + ], + "expanded emotion cause span": [ + "having fun", + "This is really a nice party with wonderful people and lovely wines .", + "I ' m glad you ' re enjoying it .", + "Thank you for the invitation ." + ], + "type": [ + "hybrid" + ], + "text": "It ' s my pleasure . Would you like another glass of champagne ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yes , please . Thank you for everything .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "It ' s my pleasure . Would you like another glass of champagne ?" + ], + "type": [ + "inter-personal" + ], + "text": "Yes , please . Thank you for everything .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_10853.json b/reccon/sources/tr_10853.json new file mode 100644 index 0000000000000000000000000000000000000000..062939a83c7e1db60dba0d475cb8418bf5ec571d --- /dev/null +++ b/reccon/sources/tr_10853.json @@ -0,0 +1,170 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , what can I get for you ?", + "emotion": "neutral", + "text": "Hi , what can I get for you ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hello , may I have a double cheeseburger ?", + "emotion": "neutral", + "text": "Hello , may I have a double cheeseburger ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "With everything on it ?", + "emotion": "neutral", + "text": "With everything on it ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "That sounds great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3, + 4 + ], + "expanded emotion cause span": [ + "may I have a double cheeseburger ?", + "With everything on it ?", + "That sounds great ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "That sounds great .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Did you want fries with your order ?", + "emotion": "neutral", + "text": "Did you want fries with your order ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "May I get a large order of curly fries ?", + "emotion": "neutral", + "text": "May I get a large order of curly fries ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Did you want something to drink ?", + "emotion": "neutral", + "text": "Did you want something to drink ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Get me a medium Pepsi .", + "emotion": "neutral", + "text": "Get me a medium Pepsi .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Would you like anything else ?", + "emotion": "neutral", + "text": "Would you like anything else ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "No , thank you . That's it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3, + 4, + 6, + 8, + 10 + ], + "expanded emotion cause span": [ + "may I have a double cheeseburger ?", + "With everything on it ?", + "That sounds great .", + "large order of curly fries ?", + "medium Pepsi .", + "thank you ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "No , thank you . That's it .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "No problem , that'll be $ 5 . 48 .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "thank you ." + ], + "type": [ + "inter-personal" + ], + "text": "No problem , that'll be $ 5 . 48 .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Thanks a lot . Keep the change .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3, + 4, + 6, + 8, + 10, + 11, + 12 + ], + "expanded emotion cause span": [ + "may I have a double cheeseburger ?", + "With everything on it ?", + "That sounds great .", + "large order of curly fries ?", + "medium Pepsi .", + "thank you .", + "No problem ,", + "Thanks a lot ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Thanks a lot . Keep the change .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1090.json b/reccon/sources/tr_1090.json new file mode 100644 index 0000000000000000000000000000000000000000..002987984f84c5d001f223129b06652dad7bc865 --- /dev/null +++ b/reccon/sources/tr_1090.json @@ -0,0 +1,177 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "The band is pretty good . How do you like the music ?", + "emotion": "neutral", + "text": "The band is pretty good . How do you like the music ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "it's very nice . I haven't heard live music in a while . This is fun .", + "emotion": "neutral", + "text": "it's very nice . I haven't heard live music in a while . This is fun .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "well , then , may I invite you for the next dance ?", + "emotion": "neutral", + "text": "well , then , may I invite you for the next dance ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "of course . But I'm afraid I'm not much of a dancer ...", + "emotion": "neutral", + "text": "of course . But I'm afraid I'm not much of a dancer ...", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "don't worry . I'm not much of a dancer myself .", + "emotion": "neutral", + "text": "don't worry . I'm not much of a dancer myself .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "you're dancing so well .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "you're dancing so well ." + ], + "type": [ + "no-context" + ], + "text": "you're dancing so well .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "you dance beautifully too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "you're dancing so well .", + "you dance beautifully too ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "you dance beautifully too .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "when did you learn to dance ?", + "emotion": "neutral", + "text": "when did you learn to dance ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "in college . But I don't dance very often . What's your favourite dance ?", + "emotion": "neutral", + "text": "in college . But I don't dance very often . What's your favourite dance ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "it's hard to say . It depends . But I love the waltz .", + "emotion": "neutral", + "text": "it's hard to say . It depends . But I love the waltz .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "how about tango ?", + "emotion": "neutral", + "text": "how about tango ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "oh , I like it . It's such a beautiful dance , but I can't do it well . What about you ?", + "emotion": "neutral", + "text": "oh , I like it . It's such a beautiful dance , but I can't do it well . What about you ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Tango is my favorite . Anything but hip-hop or the foxtrot .", + "emotion": "neutral", + "text": "Tango is my favorite . Anything but hip-hop or the foxtrot .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "thank you for the dance .", + "emotion": "neutral", + "text": "thank you for the dance .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "my pleasure . Let's go and have a drink .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14, + 15 + ], + "expanded emotion cause span": [ + "thank you for the dance .", + "my pleasure ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "my pleasure . Let's go and have a drink .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "ok .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "Let's go and have a drink ." + ], + "type": [ + "inter-personal" + ], + "text": "ok .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_10906.json b/reccon/sources/tr_10906.json new file mode 100644 index 0000000000000000000000000000000000000000..1a0be713cd82706839c3cac9b31fff4f40467ac6 --- /dev/null +++ b/reccon/sources/tr_10906.json @@ -0,0 +1,207 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Merry Christmas , sweetie . How's your brother enjoying Taiwan ?", + "emotion": "neutral", + "text": "Merry Christmas , sweetie . How's your brother enjoying Taiwan ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Ryan says he wants to stay . I think he's in love with some girl who designs fruit platters ...", + "emotion": "neutral", + "text": "Ryan says he wants to stay . I think he's in love with some girl who designs fruit platters ...", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "No ! Christmas without him is bad enough . So , honey , do you have cold feet yet ?", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Christmas without him is bad enough" + ], + "type": [ + "no-context" + ], + "text": "No ! Christmas without him is bad enough . So , honey , do you have cold feet yet ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yeah , especially since Jack didn't take care of the plane reservations .", + "emotion": "neutral", + "text": "Yeah , especially since Jack didn't take care of the plane reservations .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "You're not coming ?", + "emotion": "neutral", + "text": "You're not coming ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Not until the 31st . So can you change the church reservations ?", + "emotion": "neutral", + "text": "Not until the 31st . So can you change the church reservations ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I'm afraid not . The church is booked until the year 2001 .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I'm afraid not . The church is booked" + ], + "type": [ + "no-context" + ], + "text": "I'm afraid not . The church is booked until the year 2001 .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Then where will we have the ceremony ? At home ?", + "emotion": "neutral", + "text": "Then where will we have the ceremony ? At home ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "We'll have to . We'll rehearse on the 1st and have the wedding on the 2nd .", + "emotion": "neutral", + "text": "We'll have to . We'll rehearse on the 1st and have the wedding on the 2nd .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I'm sorry , Mom .", + "emotion": "sadness", + "flag": "F", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I'm afraid not . The church is booked" + ], + "type": [ + "inter-personal" + ], + "text": "I'm sorry , Mom .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Don't worry , dear . I'm a great host . Now get some rest . Merry Christmas .", + "emotion": "happiness", + "explanation": "Sharing pleasantries", + "expanded emotion cause evidence": [ + 11, + 11 + ], + "expanded emotion cause span": [ + "Don't worry , dear . I'm a great host .", + "Merry Christmas ." + ], + "type": [ + "no-context" + ], + "text": "Don't worry , dear . I'm a great host . Now get some rest . Merry Christmas .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Merry Christmas , Mom . I love you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 11, + 12 + ], + "expanded emotion cause span": [ + "Don't worry ,", + "Merry Christmas .", + "Merry Christmas , Mom . I love you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Merry Christmas , Mom . I love you .", + "id": 12, + "source_sentences": [ + 10, + 10 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I love you , too . And forgive Jack . He's doing his best .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 11, + 12, + 13, + 13 + ], + "expanded emotion cause span": [ + "Don't worry , dear . I'm a great host .", + "Merry Christmas .", + "I love you .", + "I love you , too .", + "He's doing his best ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I love you , too . And forgive Jack . He's doing his best .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "I know . Goodnight .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 11, + 12, + 13 + ], + "expanded emotion cause span": [ + "Don't worry ,", + "Merry Christmas .", + "Merry Christmas , Mom . I love you .", + "I love you , too ." + ], + "type": [ + "hybrid" + ], + "text": "I know . Goodnight .", + "id": 14 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_10916.json b/reccon/sources/tr_10916.json new file mode 100644 index 0000000000000000000000000000000000000000..961e4ec4d0038b0181af0204d50b245548651e24 --- /dev/null +++ b/reccon/sources/tr_10916.json @@ -0,0 +1,144 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Do you know how happy I am ? The Ant Kingdom is a perfect world with colorful fairy tales . It seems like the air is fresh here .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 1 + ], + "expanded emotion cause span": [ + "a perfect world", + "the air is fresh here ." + ], + "type": [ + "no-context" + ], + "text": "Do you know how happy I am ? The Ant Kingdom is a perfect world with colorful fairy tales . It seems like the air is fresh here .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Just kids like that .", + "emotion": "neutral", + "text": "Just kids like that .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Come on baby , stop trying to pretend like a man . If you go there , you are sure to like them .", + "emotion": "neutral", + "text": "Come on baby , stop trying to pretend like a man . If you go there , you are sure to like them .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Hurry up ! Hurry up ! What lovely caterpillars are over there !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "lovely caterpillars are over there !" + ], + "type": [ + "no-context" + ], + "text": "Hurry up ! Hurry up ! What lovely caterpillars are over there !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I said you are sure to like them . There is the Grand Parade Of Ants Carnival in a few minutes in the square . You will experience a dream of fantasy .", + "emotion": "neutral", + "text": "I said you are sure to like them . There is the Grand Parade Of Ants Carnival in a few minutes in the square . You will experience a dream of fantasy .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "What's that ?", + "emotion": "neutral", + "text": "What's that ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "All kinds of insects dress themselves up . They drive straight their own Flower Cars along the Parade Avenue of Ants Kingdom .", + "emotion": "neutral", + "text": "All kinds of insects dress themselves up . They drive straight their own Flower Cars along the Parade Avenue of Ants Kingdom .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That's splendid . Can you take three pictures of me with them ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "All kinds of insects dress themselves up . They drive straight their own Flower Cars along the Parade Avenue of Ants Kingdom .", + "Can you take three pictures of me with them ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's splendid . Can you take three pictures of me with them ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I thought you had grown out of such child practices .", + "emotion": "neutral", + "text": "I thought you had grown out of such child practices .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Cut it out . Look at my smile , and it seems like the flowers in the spring . Right ?", + "emotion": "neutral", + "text": "Cut it out . Look at my smile , and it seems like the flowers in the spring . Right ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Gross !", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Look at my smile" + ], + "type": [ + "inter-personal" + ], + "text": "Gross !", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Hurry up ! The smile is frozen on my face .", + "emotion": "neutral", + "text": "Hurry up ! The smile is frozen on my face .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_10955.json b/reccon/sources/tr_10955.json new file mode 100644 index 0000000000000000000000000000000000000000..1f0411ecf8709b12b6c15abb6491062ce128fccd --- /dev/null +++ b/reccon/sources/tr_10955.json @@ -0,0 +1,169 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Dai Ling .", + "emotion": "neutral", + "text": "Dai Ling .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh , Henry , I haven't seen you for ages . Come in . Let me take your coat . How are you getting along ?", + "emotion": "neutral", + "text": "Oh , Henry , I haven't seen you for ages . Come in . Let me take your coat . How are you getting along ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Very well , thank you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 2, + 3 + ], + "expanded emotion cause span": [ + "I haven't seen you for ages .", + "Let me take your coat .", + "Very well ," + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Very well , thank you .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Please take a seat . Everything would be ready in a minute .", + "emotion": "neutral", + "text": "Please take a seat . Everything would be ready in a minute .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Can you bring me a glass of orange juice , please ? I am quite thirsty .", + "emotion": "neutral", + "text": "Can you bring me a glass of orange juice , please ? I am quite thirsty .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Here you are . Here you go . We have cocktail and salad , fried chicken , French fries and icecream for dessert . Eating chicken while it's hot . it tastes better .", + "emotion": "neutral", + "text": "Here you are . Here you go . We have cocktail and salad , fried chicken , French fries and icecream for dessert . Eating chicken while it's hot . it tastes better .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Wow , you're right . Everything is absolutely delicious . Please pass the pepper .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 6, + 7 + ], + "expanded emotion cause span": [ + "Here you are .", + "it tastes better .", + "absolutely delicious ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Wow , you're right . Everything is absolutely delicious . Please pass the pepper .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Here you are . Taste the French fries .", + "emotion": "neutral", + "text": "Here you are . Taste the French fries .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "They're soft .", + "emotion": "neutral", + "text": "They're soft .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Would you like some more ?", + "emotion": "neutral", + "text": "Would you like some more ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "No more , thank you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Would you like some more ?" + ], + "type": [ + "inter-personal" + ], + "text": "No more , thank you .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Here is to our friendship and health !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "our friendship and health !" + ], + "type": [ + "no-context" + ], + "text": "Here is to our friendship and health !", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Bottom is up .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 12 + ], + "expanded emotion cause span": [ + "Would you like some more ?", + "our friendship and health !" + ], + "type": [ + "inter-personal" + ], + "text": "Bottom is up .", + "id": 13, + "source_sentences": [ + 9, + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1097.json b/reccon/sources/tr_1097.json new file mode 100644 index 0000000000000000000000000000000000000000..f48a79549cc9a9a83f412967612bf516a78194fc --- /dev/null +++ b/reccon/sources/tr_1097.json @@ -0,0 +1,166 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Our company's wei-ya is tomorrow night ! It's your first Chinese New Year in Taiwan--you must be excited !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Our company's wei-ya is tomorrow night ! It's your first Chinese New Year in Taiwan" + ], + "type": [ + "no-context" + ], + "text": "Our company's wei-ya is tomorrow night ! It's your first Chinese New Year in Taiwan--you must be excited !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Excited ? What's there to be excited about ? It's just another company dinner , right ?", + "emotion": "neutral", + "text": "Excited ? What's there to be excited about ? It's just another company dinner , right ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "You have no idea ! There's a banquet with prizes , performances ... you name it !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "There's a banquet with prizes , performances" + ], + "type": [ + "no-context" + ], + "text": "You have no idea ! There's a banquet with prizes , performances ... you name it !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Really ? What kind of prizes ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "There's a banquet with prizes , performances" + ], + "type": [ + "inter-personal" + ], + "text": "Really ? What kind of prizes ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Well , I heard that last year Vivian from accounting won a new car !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "last year Vivian from accounting won a new car !" + ], + "type": [ + "no-context" + ], + "text": "Well , I heard that last year Vivian from accounting won a new car !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "A new car ! You're kidding !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "last year Vivian from accounting won a new car !" + ], + "type": [ + "inter-personal" + ], + "text": "A new car ! You're kidding !", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "No , really ! And she told me the secret to winning , wear red underwear !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 7 + ], + "expanded emotion cause span": [ + "last year Vivian from accounting won a new car !", + "And she told me the secret to winning , wear red underwear !" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "No , really ! And she told me the secret to winning , wear red underwear !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Wear red underwear ? ! Does that really work ? Are you going to try it ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "And she told me the secret to winning , wear red underwear !" + ], + "type": [ + "inter-personal" + ], + "text": "Wear red underwear ? ! Does that really work ? Are you going to try it ?", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Of course ! I'm not only going to wear red underwear , but I'm going to wear red socks and a red shirt , too !", + "emotion": "happiness", + "explanation": "listener is happy to try the secret to winning", + "expanded emotion cause evidence": [ + 7, + 9 + ], + "expanded emotion cause span": [ + "And she told me the secret to winning , wear red underwear !", + "Of course ! I'm not only going to wear red underwear , but I'm going to wear red socks and a red shirt , too !" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Of course ! I'm not only going to wear red underwear , but I'm going to wear red socks and a red shirt , too !", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Gee , I don't think I own any red underwear , but I can buy some !", + "emotion": "neutral", + "text": "Gee , I don't think I own any red underwear , but I can buy some !", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_11018.json b/reccon/sources/tr_11018.json new file mode 100644 index 0000000000000000000000000000000000000000..a75453e60d344f4b5e84c3be5386ef5811132179 --- /dev/null +++ b/reccon/sources/tr_11018.json @@ -0,0 +1,240 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Ah ! No ! Damn it !", + "emotion": "anger", + "explanation": "the speaker is annoyed after losing her work in a blackout", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Ah ! No ! Damn it !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It's a blackout . Now I can't see Seinfeld .", + "emotion": "neutral", + "text": "It's a blackout . Now I can't see Seinfeld .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "So what ? I just lost one hour's worth of work .", + "emotion": "neutral", + "text": "So what ? I just lost one hour's worth of work .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Really ? How could you do that ? Don't you save every couple minutes ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "I just lost one hour's worth of work .", + "Don't you save every couple minutes ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Really ? How could you do that ? Don't you save every couple minutes ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "No , I didn't save this time . Damn it ! And I'm sick of writing this paper . Now I have to write it all over again too .", + "emotion": "neutral", + "text": "No , I didn't save this time . Damn it ! And I'm sick of writing this paper . Now I have to write it all over again too .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I've had that problem too many times . So I learned to save . When I'm writing something , I save every three sentences or so . I don't want to lose anything .", + "emotion": "neutral", + "text": "I've had that problem too many times . So I learned to save . When I'm writing something , I save every three sentences or so . I don't want to lose anything .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I hate computers . Sometimes I think they cause more trouble than they're worth .", + "emotion": "neutral", + "text": "I hate computers . Sometimes I think they cause more trouble than they're worth .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "What are we going to do now ?", + "emotion": "neutral", + "text": "What are we going to do now ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I don't know . I feel like going out .", + "emotion": "neutral", + "text": "I don't know . I feel like going out .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I wonder how much of the city is down .", + "emotion": "neutral", + "text": "I wonder how much of the city is down .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "It doesn't matter . I still can go out and buy a beer .", + "emotion": "neutral", + "text": "It doesn't matter . I still can go out and buy a beer .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Maybe . But if there's a blackout , probably the pubs are closed . And besides , I know you have a political science exam tomorrow . I thought you had a lot of reading to do .", + "emotion": "neutral", + "text": "Maybe . But if there's a blackout , probably the pubs are closed . And besides , I know you have a political science exam tomorrow . I thought you had a lot of reading to do .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Yes , that's true . Damn ! I just lost half my paper , and now I can't even do my homework . This is a bad time for this to happen .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "Damn ! I just lost half my paper , and now I can't even do my homework ." + ], + "type": [ + "no-context" + ], + "text": "Yes , that's true . Damn ! I just lost half my paper , and now I can't even do my homework . This is a bad time for this to happen .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "I have a flashlight in my closet . If you want to use that to read , you can .", + "emotion": "neutral", + "text": "I have a flashlight in my closet . If you want to use that to read , you can .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Thanks . I think I will try . Where are you going ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "I have a flashlight in my closet . If you want to use that to read , you can ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks . I think I will try . Where are you going ?", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "I like your idea of getting a beer . I think I'll go out myself .", + "emotion": "neutral", + "text": "I like your idea of getting a beer . I think I'll go out myself .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "Maybe we can trade . Why don't you stay here and read for my exam , and I'll go drink beer ?", + "emotion": "neutral", + "text": "Maybe we can trade . Why don't you stay here and read for my exam , and I'll go drink beer ?", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "No , it just won't work . If I read for your exam , you won't know the answers tomorrow . I will .", + "emotion": "neutral", + "text": "No , it just won't work . If I read for your exam , you won't know the answers tomorrow . I will .", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "So ? You can go to the class for me . Just write my name on the exam book and take the exam . Why not ?", + "emotion": "neutral", + "text": "So ? You can go to the class for me . Just write my name on the exam book and take the exam . Why not ?", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "How many students are in the class ?", + "emotion": "neutral", + "text": "How many students are in the class ?", + "id": 20 + }, + { + "turn": 21, + "speaker": "A", + "utterance": "About fourteen .", + "emotion": "neutral", + "text": "About fourteen .", + "id": 21 + }, + { + "turn": 22, + "speaker": "B", + "utterance": "So it won't work , old buddy . They'll see that I'm not you . Sorry .", + "emotion": "neutral", + "text": "So it won't work , old buddy . They'll see that I'm not you . Sorry .", + "id": 22 + }, + { + "turn": 23, + "speaker": "A", + "utterance": "Damn !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 22 + ], + "expanded emotion cause span": [ + "it won't work , old buddy . They'll see that I'm not you ." + ], + "type": [ + "inter-personal" + ], + "text": "Damn !", + "id": 23, + "source_sentences": [ + 21 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_11047.json b/reccon/sources/tr_11047.json new file mode 100644 index 0000000000000000000000000000000000000000..102ad3dbf3781ac22983adbfce50738415cb66b3 --- /dev/null +++ b/reccon/sources/tr_11047.json @@ -0,0 +1,137 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , can I help you ?", + "emotion": "neutral", + "text": "Hi , can I help you ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "No , thanks . I'm just looking .", + "emotion": "happiness", + "explanation": "Sharing pleasantries", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "No , thanks . I'm just looking .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "All right . If you need any help , just let me know . My name is Greg .", + "emotion": "neutral", + "text": "All right . If you need any help , just let me know . My name is Greg .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Sure , I'll let you know if I need anything . Hm , this mattress is very firm . Jack will probably like it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "this mattress is very firm . Jack will probably like it ." + ], + "type": [ + "no-context" + ], + "text": "Sure , I'll let you know if I need anything . Hm , this mattress is very firm . Jack will probably like it .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Did you find something you like ?", + "emotion": "neutral", + "text": "Did you find something you like ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yes , this mattress is very good . It's pretty firm . The mattress I ' m now sleeping on is saggy .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5, + 6, + 6 + ], + "expanded emotion cause span": [ + "this mattress is very firm . Jack will probably like it .", + "Did you find something you like ?", + "Yes ,", + "mattress is very good . It's pretty firm ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Yes , this mattress is very good . It's pretty firm . The mattress I ' m now sleeping on is saggy .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You are right . This is very good brand . It doesn't sag easily and we offer a lifetime warranty , so you don't have to worry about its quality .", + "emotion": "neutral", + "text": "You are right . This is very good brand . It doesn't sag easily and we offer a lifetime warranty , so you don't have to worry about its quality .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Does it come with a frame ?", + "emotion": "neutral", + "text": "Does it come with a frame ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Unfortunately , it doesn't . However we can give you a 10 % discount on the frame . We also offer a very good financing plan . There is no payment no interest until next June .", + "emotion": "neutral", + "text": "Unfortunately , it doesn't . However we can give you a 10 % discount on the frame . We also offer a very good financing plan . There is no payment no interest until next June .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "That's an attractive plan . I'll think about it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 9, + 9 + ], + "expanded emotion cause span": [ + "we can give you a 10 % discount", + "We also offer a very good financing plan .", + "no payment no interest until next June ." + ], + "type": [ + "inter-personal" + ], + "text": "That's an attractive plan . I'll think about it .", + "id": 10, + "source_sentences": [ + 8, + 8, + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_11053.json b/reccon/sources/tr_11053.json new file mode 100644 index 0000000000000000000000000000000000000000..2371fe2797c6f54ae547a47cb5e126ae94b2ddb2 --- /dev/null +++ b/reccon/sources/tr_11053.json @@ -0,0 +1,147 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Poor Danny . You are so enfeebled !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "You are so enfeebled !" + ], + "type": [ + "no-context" + ], + "text": "Poor Danny . You are so enfeebled !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Don't worry . No big deal . Just a common cold .", + "emotion": "neutral", + "text": "Don't worry . No big deal . Just a common cold .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Mom called just now saying that she and Dad will be back later . Do you want to speak to them on phone ?", + "emotion": "neutral", + "text": "Mom called just now saying that she and Dad will be back later . Do you want to speak to them on phone ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "No . You can never count on the grown-ups when there is something .", + "emotion": "neutral", + "text": "No . You can never count on the grown-ups when there is something .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Whatever . Have a drink of water .", + "emotion": "neutral", + "text": "Whatever . Have a drink of water .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Come on , sister . This is the seventh glass already .", + "emotion": "neutral", + "text": "Come on , sister . This is the seventh glass already .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Maybe later . I think we have a medicine-kit .", + "emotion": "neutral", + "text": "Maybe later . I think we have a medicine-kit .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Do we ? Where is it ?", + "emotion": "neutral", + "text": "Do we ? Where is it ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Probably on the of the cabinet . I'll go and get it .", + "emotion": "neutral", + "text": "Probably on the of the cabinet . I'll go and get it .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Be careful . Now I have no one but you to depend on .", + "emotion": "neutral", + "text": "Be careful . Now I have no one but you to depend on .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Oh , here it is . Patulin . Oh , no !", + "emotion": "surprise", + "explanation": "the speaker is surprised that the medicine is expired", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Oh , here it is . Patulin . Oh , no !", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "What's the new strike ?", + "emotion": "neutral", + "text": "What's the new strike ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Keep lying down . The matter is that all the medicine here is past expiration .", + "emotion": "neutral", + "text": "Keep lying down . The matter is that all the medicine here is past expiration .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Poor me !", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "all the medicine here is past expiration ." + ], + "type": [ + "inter-personal" + ], + "text": "Poor me !", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1106.json b/reccon/sources/tr_1106.json new file mode 100644 index 0000000000000000000000000000000000000000..54e8b5795ecc4531fa33b74ebaed22e20a1dac81 --- /dev/null +++ b/reccon/sources/tr_1106.json @@ -0,0 +1,110 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey . I'm a visitor from China . I love your music . It's the best I've ever heard . Will you please spare a little bit of time for me ?", + "emotion": "neutral", + "text": "Hey . I'm a visitor from China . I love your music . It's the best I've ever heard . Will you please spare a little bit of time for me ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Sure . Thank you for saying that . Actually , those songs were sung for the first time today . I wrote them in the past two months .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I love your music . It's the best I've ever heard ." + ], + "type": [ + "inter-personal" + ], + "text": "Sure . Thank you for saying that . Actually , those songs were sung for the first time today . I wrote them in the past two months .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Oh , you wrote them all by yourself . That's amazing ! Are you a regular singer here ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "I wrote them in the past two months .", + "you wrote them all by yourself ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , you wrote them all by yourself . That's amazing ! Are you a regular singer here ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "You can say that . But my band and I also sing regularly in several other places , too .", + "emotion": "neutral", + "text": "You can say that . But my band and I also sing regularly in several other places , too .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Cool . Your guitar skills are very impressive . How did you learn to play like that ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3, + 5 + ], + "expanded emotion cause span": [ + "I wrote them in the past two months .", + "you wrote them all by yourself .", + "Your guitar skills are very impressive ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Cool . Your guitar skills are very impressive . How did you learn to play like that ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I picked up guitar at an early age , maybe around 8 years old . Afterward , I taught myself by listening to some records of top players .", + "emotion": "neutral", + "text": "I picked up guitar at an early age , maybe around 8 years old . Afterward , I taught myself by listening to some records of top players .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Wow , that's unbelievable ! You play so well , but you've never been to a real teacher . You will definitely be famous in the near future .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I taught myself by listening to some records of top players .", + "You play so well , but you've never been to a real teacher ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Wow , that's unbelievable ! You play so well , but you've never been to a real teacher . You will definitely be famous in the near future .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_11079.json b/reccon/sources/tr_11079.json new file mode 100644 index 0000000000000000000000000000000000000000..a456b289453dc9c9de579e5ddd8845f05074ad52 --- /dev/null +++ b/reccon/sources/tr_11079.json @@ -0,0 +1,145 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "It's nice of you to see me off .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "see me off ." + ], + "type": [ + "no-context" + ], + "text": "It's nice of you to see me off .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It's my pleasure . Hope you ' ll visit Beijing more often .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "It's nice of you to see me off ." + ], + "type": [ + "inter-personal" + ], + "text": "It's my pleasure . Hope you ' ll visit Beijing more often .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Thanks . Stop here now .", + "emotion": "neutral", + "text": "Thanks . Stop here now .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "OK . I hope you have a good trip . Thanks ever so much for your cooperation , Mr . Simpson . Give my best wishes to Mr . Green .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "your cooperation" + ], + "type": [ + "no-context" + ], + "text": "OK . I hope you have a good trip . Thanks ever so much for your cooperation , Mr . Simpson . Give my best wishes to Mr . Green .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "OK , I will . Goodbye and remember to look me up if ever you're in Paris .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I hope you have a good trip . Thanks ever so much for your cooperation , Mr . Simpson . Give my best wishes to Mr . Green ." + ], + "type": [ + "inter-personal" + ], + "text": "OK , I will . Goodbye and remember to look me up if ever you're in Paris .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Goodbye and all the best .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5, + 5 + ], + "expanded emotion cause span": [ + "Give my best wishes to Mr . Green .", + "OK , I will .", + "remember to look me up if ever you're in Paris ." + ], + "type": [ + "hybrid" + ], + "text": "Goodbye and all the best .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "OK , bye for now !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 6 + ], + "expanded emotion cause span": [ + "I hope you have a good trip . Thanks ever so much for your cooperation , Mr . Simpson . Give my best wishes to Mr . Green .", + "all the best ." + ], + "type": [ + "inter-personal" + ], + "text": "OK , bye for now !", + "id": 7, + "source_sentences": [ + 3, + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Bye .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5, + 5 + ], + "expanded emotion cause span": [ + "Give my best wishes to Mr . Green .", + "OK , I will .", + "remember to look me up if ever you're in Paris ." + ], + "type": [ + "hybrid" + ], + "text": "Bye .", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1109.json b/reccon/sources/tr_1109.json new file mode 100644 index 0000000000000000000000000000000000000000..72816f1822d2b4392ff5d09c2b217d05660ff49a --- /dev/null +++ b/reccon/sources/tr_1109.json @@ -0,0 +1,159 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Welcome to our university ' s fifties anniversary , Sir . Please have a seat .", + "emotion": "happiness", + "explanation": "Greeting", + "expanded emotion cause evidence": [ + 1, + 1 + ], + "expanded emotion cause span": [ + "university ' s fifties anniversary", + "Welcome" + ], + "type": [ + "no-context" + ], + "text": "Welcome to our university ' s fifties anniversary , Sir . Please have a seat .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Thank you . Wow , your school has so many honors . Congratulations !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "Welcome to our university ' s fifties anniversary", + "your school has so many honors" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you . Wow , your school has so many honors . Congratulations !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Thank you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Congratulations !" + ], + "type": [ + "inter-personal" + ], + "text": "Thank you .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Excuse me . I wonder see Dean Mr . Lee first . I was wondering if could you tell me where his office is ?", + "emotion": "neutral", + "text": "Excuse me . I wonder see Dean Mr . Lee first . I was wondering if could you tell me where his office is ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Certainly . Mr . Lee ' s office building at the south end of the campus , just beside the library .", + "emotion": "neutral", + "text": "Certainly . Mr . Lee ' s office building at the south end of the campus , just beside the library .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Excuse me ?", + "emotion": "neutral", + "text": "Excuse me ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Let me show you the way . Please follow me .", + "emotion": "happiness", + "explanation": "speaker is happy to see listener", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Let me show you the way ." + ], + "type": [ + "no-context" + ], + "text": "Let me show you the way . Please follow me .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Thank you very much . It ' s very kind of you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "Let me show you the way . Please follow me .", + "It ' s very kind of you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you very much . It ' s very kind of you .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "My pleasure .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Thank you very much . It ' s very kind of you ." + ], + "type": [ + "inter-personal" + ], + "text": "My pleasure .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "This is it ?", + "emotion": "neutral", + "text": "This is it ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "It ' s up on the second floor . You have to use the stairs . The elevator isn ' t working .", + "emotion": "neutral", + "text": "It ' s up on the second floor . You have to use the stairs . The elevator isn ' t working .", + "id": 11 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1130.json b/reccon/sources/tr_1130.json new file mode 100644 index 0000000000000000000000000000000000000000..080a6ce8c7d092b88351b779307e70f1540d204a --- /dev/null +++ b/reccon/sources/tr_1130.json @@ -0,0 +1,140 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , Jenny . You look like you are in a hurry to somewhere . Where are you going ?", + "emotion": "neutral", + "text": "Hi , Jenny . You look like you are in a hurry to somewhere . Where are you going ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I am going to the bank . I need to cash some checks .", + "emotion": "neutral", + "text": "I am going to the bank . I need to cash some checks .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "That's great . We can go to the bank together .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "We can go to the bank together ." + ], + "type": [ + "no-context" + ], + "text": "That's great . We can go to the bank together .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Why are you going there ?", + "emotion": "neutral", + "text": "Why are you going there ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I will go to Japan on business for 5 days next Tuesday . I want to exchange some Japanese yen .", + "emotion": "neutral", + "text": "I will go to Japan on business for 5 days next Tuesday . I want to exchange some Japanese yen .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I see . Will you bring a lot of money with you ?", + "emotion": "neutral", + "text": "I see . Will you bring a lot of money with you ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Not really . I plan to bring some cash and withdraw money at the ATM in Japan .", + "emotion": "neutral", + "text": "Not really . I plan to bring some cash and withdraw money at the ATM in Japan .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Do you have the bank card in Japan ?", + "emotion": "neutral", + "text": "Do you have the bank card in Japan ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Nope . You can use the credit card to withdraw the money in foreign countries .", + "emotion": "neutral", + "text": "Nope . You can use the credit card to withdraw the money in foreign countries .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "That sounds really convenient . Do you pay extra money to enjoy this service ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "You can use the credit card to withdraw the money in foreign countries ." + ], + "type": [ + "inter-personal" + ], + "text": "That sounds really convenient . Do you pay extra money to enjoy this service ?", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 11, + "speaker": "A", + "utterance": "No . It is free of charge .", + "emotion": "neutral", + "text": "No . It is free of charge .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Great ! I will apply for a credit card when I go to the bank later .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "Do you pay extra money to enjoy this service ?", + "It is free of charge ." + ], + "type": [ + "hybrid" + ], + "text": "Great ! I will apply for a credit card when I go to the bank later .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I think we are running out of time . The bank is going to close soon .", + "emotion": "neutral", + "text": "I think we are running out of time . The bank is going to close soon .", + "id": 13 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1150.json b/reccon/sources/tr_1150.json new file mode 100644 index 0000000000000000000000000000000000000000..d8f133c25e8aed22307a0056e12bb224a5640e53 --- /dev/null +++ b/reccon/sources/tr_1150.json @@ -0,0 +1,193 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "David , I ' m going to China .", + "emotion": "happiness", + "explanation": "Happy due to excitement of travelling to a place.", + "expanded emotion cause evidence": [ + 1, + "b" + ], + "expanded emotion cause span": [ + "I ' m going to China .", + "b" + ], + "type": [ + "latent", + "no-context" + ], + "text": "David , I ' m going to China .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Really ? How do you get the chance ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "I ' m going to China .", + "How do you get the chance ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Really ? How do you get the chance ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "You know . I took part in the Chinese contest . I was the best and they gave me this reward . I don ' t have to pay for my trip .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I was the best and they gave me this reward . I don ' t have to pay for my trip ." + ], + "type": [ + "no-context" + ], + "text": "You know . I took part in the Chinese contest . I was the best and they gave me this reward . I don ' t have to pay for my trip .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Congratulations . How lucky you are !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3, + 4 + ], + "expanded emotion cause span": [ + "I ' m going to China .", + "I was the best and they gave me this reward . I don ' t have to pay for my trip .", + "How lucky you are !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Congratulations . How lucky you are !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Thank you . I ' m leaving tomorrow morning .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Congratulations . How lucky you are !" + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . I ' m leaving tomorrow morning .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I ' m sure you ' ll enjoy the trip . China is such a beautiful country .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3, + 4, + 6 + ], + "expanded emotion cause span": [ + "I ' m going to China .", + "I was the best and they gave me this reward . I don ' t have to pay for my trip .", + "How lucky you are !", + "you ' ll enjoy the trip . China is such a beautiful country ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I ' m sure you ' ll enjoy the trip . China is such a beautiful country .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I ' m sure I will .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "you ' ll enjoy the trip", + "I ' m sure I will ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I ' m sure I will .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Have a nice journey , Lily .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1, + 3, + 4, + 6 + ], + "expanded emotion cause span": [ + "I ' m going to China .", + "I was the best and they gave me this reward . I don ' t have to pay for my trip .", + "How lucky you are !", + "you ' ll enjoy the trip . China is such a beautiful country ." + ], + "type": [ + "hybrid" + ], + "text": "Have a nice journey , Lily .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Thank you , David .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7, + 8 + ], + "expanded emotion cause span": [ + "you ' ll enjoy the trip", + "I ' m sure I will .", + "Have a nice journey" + ], + "type": [ + "hybrid" + ], + "text": "Thank you , David .", + "id": 9 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1166.json b/reccon/sources/tr_1166.json new file mode 100644 index 0000000000000000000000000000000000000000..707f5c5cb685e9d96247ff533f8fd2a9f0f3370c --- /dev/null +++ b/reccon/sources/tr_1166.json @@ -0,0 +1,173 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Good morning , Mr . Jones !", + "emotion": "happiness", + "explanation": "Speaker is providing cordial greetings.", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Good morning , Mr . Jones !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Good morning , Miss Bell !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Good morning" + ], + "type": [ + "inter-personal" + ], + "text": "Good morning , Miss Bell !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Nice to see you again .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Nice to see you again ." + ], + "type": [ + "no-context" + ], + "text": "Nice to see you again .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Nice to see you too . It's been a long time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Nice to see you again ." + ], + "type": [ + "inter-personal" + ], + "text": "Nice to see you too . It's been a long time .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "How is everything ?", + "emotion": "neutral", + "text": "How is everything ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Just fine , and you ?", + "emotion": "neutral", + "text": "Just fine , and you ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Quite well , thank you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "and you ?", + "Quite well" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Quite well , thank you .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Did you drive yourself to the airport ?", + "emotion": "neutral", + "text": "Did you drive yourself to the airport ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "No , I was driven by my husband .", + "emotion": "neutral", + "text": "No , I was driven by my husband .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Did someone meet you at the airport here ?", + "emotion": "neutral", + "text": "Did someone meet you at the airport here ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Yes , thanks .", + "emotion": "happiness", + "explanation": "Speaker is thankful.", + "expanded emotion cause evidence": [ + 11, + "b" + ], + "expanded emotion cause span": [ + "thanks .", + "b" + ], + "type": [ + "latent", + "no-context" + ], + "text": "Yes , thanks .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Is this where we'll be holding the meeting ?", + "emotion": "neutral", + "text": "Is this where we'll be holding the meeting ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "No , the meeting will be held on the fourth floor .", + "emotion": "neutral", + "text": "No , the meeting will be held on the fourth floor .", + "id": 13 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1200.json b/reccon/sources/tr_1200.json new file mode 100644 index 0000000000000000000000000000000000000000..de41ad604fbb0ef4d57d514ce00787d0dfd987a2 --- /dev/null +++ b/reccon/sources/tr_1200.json @@ -0,0 +1,116 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello . Are you a friend of Helen's ?", + "emotion": "neutral", + "text": "Hello . Are you a friend of Helen's ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Actually , a friend of a friend .", + "emotion": "neutral", + "text": "Actually , a friend of a friend .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "My name is Phil . What's yours ?", + "emotion": "neutral", + "text": "My name is Phil . What's yours ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Alecia .", + "emotion": "neutral", + "text": "Alecia .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Have you tried these little ditties ? They are really good .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "They are really good ." + ], + "type": [ + "no-context" + ], + "text": "Have you tried these little ditties ? They are really good .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Thanks . They look delicious .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "They are really good .", + "They look delicious ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thanks . They look delicious .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Can I get you some punch ? I was just going to go get myself some .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 7 + ], + "expanded emotion cause span": [ + "They are really good .", + "I was just going to go get myself some ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Can I get you some punch ? I was just going to go get myself some .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That would be great . I would love some .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "Can I get you some punch ?", + "That would be great . I would love some ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That would be great . I would love some .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1209.json b/reccon/sources/tr_1209.json new file mode 100644 index 0000000000000000000000000000000000000000..b65636c94858614ea9323611e11bbe947bb445ae --- /dev/null +++ b/reccon/sources/tr_1209.json @@ -0,0 +1,196 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Craig , what do you do for work ?", + "emotion": "neutral", + "text": "Craig , what do you do for work ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'm still a student .", + "emotion": "neutral", + "text": "I'm still a student .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What school do you go to ?", + "emotion": "neutral", + "text": "What school do you go to ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Boston University .", + "emotion": "neutral", + "text": "Boston University .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "That's a good school . What do you study ?", + "emotion": "neutral", + "text": "That's a good school . What do you study ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I'm studying English , math , and history . My major is English .", + "emotion": "neutral", + "text": "I'm studying English , math , and history . My major is English .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "How long have you been studying English ?", + "emotion": "neutral", + "text": "How long have you been studying English ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "More than six years .", + "emotion": "neutral", + "text": "More than six years .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "That's a long time .", + "emotion": "neutral", + "text": "That's a long time .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Yeah , I started to learn English when I was in high school .", + "emotion": "neutral", + "text": "Yeah , I started to learn English when I was in high school .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "No wonder your English is so good .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "I started to learn English when I was in high school .", + "your English is so good ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "No wonder your English is so good .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Actually , it's not that good . I can read but I can't speak very well . I haven't had a lot of chance to practice .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "your English is so good ." + ], + "type": [ + "inter-personal" + ], + "text": "Actually , it's not that good . I can read but I can't speak very well . I haven't had a lot of chance to practice .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I see . Talking with other people is very important .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "I started to learn English when I was in high school .", + "your English is so good ." + ], + "type": [ + "hybrid" + ], + "text": "I see . Talking with other people is very important .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Yes , but I still don't have many friends here yet .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "your English is so good ." + ], + "type": [ + "inter-personal" + ], + "text": "Yes , but I still don't have many friends here yet .", + "id": 14, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 15, + "speaker": "A", + "utterance": "I'm having a party tonight at my apartment . You should come .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "I'm having a party tonight at my apartment ." + ], + "type": [ + "no-context" + ], + "text": "I'm having a party tonight at my apartment . You should come .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Oh thanks for inviting me . I'd love to come .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 16 + ], + "expanded emotion cause span": [ + "thanks for inviting me . I'd love to come ." + ], + "type": [ + "no-context" + ], + "text": "Oh thanks for inviting me . I'd love to come .", + "id": 16 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1210.json b/reccon/sources/tr_1210.json new file mode 100644 index 0000000000000000000000000000000000000000..9c266c52ca846c0614dcbcfb8476f4f8d65c9d4b --- /dev/null +++ b/reccon/sources/tr_1210.json @@ -0,0 +1,217 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello , Jason , there is going to be a screening of Final Destination 3 at our campus cinema tomorrow . I plan to go to see it .", + "emotion": "neutral", + "text": "Hello , Jason , there is going to be a screening of Final Destination 3 at our campus cinema tomorrow . I plan to go to see it .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Is it a horror movie ?", + "emotion": "fear", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "screening of Final Destination 3", + "Is it a horror movie ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Is it a horror movie ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yeah , I love horror movies . Would you like to go with me tomorrow ?", + "emotion": "neutral", + "text": "Yeah , I love horror movies . Would you like to go with me tomorrow ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "No way . I will be scared out of my wits .", + "emotion": "fear", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I will be scared out of my wits ." + ], + "type": [ + "no-context" + ], + "text": "No way . I will be scared out of my wits .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "That's funny , I didn't know a big fellow like you could be so soft and timid on the inside .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I didn't know a big fellow like you could be so soft and timid on the inside ." + ], + "type": [ + "no-context" + ], + "text": "That's funny , I didn't know a big fellow like you could be so soft and timid on the inside .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Hey , how would you like to taste my fist ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "how would you like to taste my fist ?" + ], + "type": [ + "no-context" + ], + "text": "Hey , how would you like to taste my fist ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Alright , all joking aside , what kinds of moves do you like ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "all joking aside" + ], + "type": [ + "no-context" + ], + "text": "Alright , all joking aside , what kinds of moves do you like ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Um , let me see , romance , comedy . documentary , action , science fiction , animated and so on .", + "emotion": "neutral", + "text": "Um , let me see , romance , comedy . documentary , action , science fiction , animated and so on .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "That is to say , you like all genres except for horror movies .", + "emotion": "neutral", + "text": "That is to say , you like all genres except for horror movies .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Yeah . It seems like we don't speak the same language as far as movies are concerned .", + "emotion": "neutral", + "text": "Yeah . It seems like we don't speak the same language as far as movies are concerned .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Not quite . I also greatly enjoy romance and comedy .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I also greatly enjoy romance and comedy ." + ], + "type": [ + "no-context" + ], + "text": "Not quite . I also greatly enjoy romance and comedy .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "The Notebook is this type of movie .", + "emotion": "neutral", + "text": "The Notebook is this type of movie .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Really ? I haven't heard of it .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 12, + 13 + ], + "expanded emotion cause span": [ + "The Notebook is this type of movie .", + "I haven't heard of it ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Really ? I haven't heard of it .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Well then , this could be a nice opportunity to enjoy it together . I bet you'd love it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "this could be a nice opportunity to enjoy it together . I bet you'd love it ." + ], + "type": [ + "no-context" + ], + "text": "Well then , this could be a nice opportunity to enjoy it together . I bet you'd love it .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Ok . I can't wait to see it . Let's go !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14, + 15 + ], + "expanded emotion cause span": [ + "this could be a nice opportunity to enjoy it together . I bet you'd love it .", + "I can't wait to see it ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Ok . I can't wait to see it . Let's go !", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1211.json b/reccon/sources/tr_1211.json new file mode 100644 index 0000000000000000000000000000000000000000..1f24109170a658847e76a627eb7dfb259d0bdc8e --- /dev/null +++ b/reccon/sources/tr_1211.json @@ -0,0 +1,172 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Wow , there are so many lanterns to appreciate . Now , I can see why it's called the Lantern Festival . It deserves its name .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "there are so many lanterns to appreciate . Now , I can see why it's called the Lantern Festival ." + ], + "type": [ + "no-context" + ], + "text": "Wow , there are so many lanterns to appreciate . Now , I can see why it's called the Lantern Festival . It deserves its name .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yeah . People always enjoy the lighted lanterns and the gala performances .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "there are so many lanterns to appreciate . Now , I can see why it's called the Lantern Festival .", + "People always enjoy the lighted lanterns and the gala performances ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yeah . People always enjoy the lighted lanterns and the gala performances .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What are they doing over there ? People keep on gathering there .", + "emotion": "neutral", + "text": "What are they doing over there ? People keep on gathering there .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Did you notice the characters on the lanterns ?", + "emotion": "neutral", + "text": "Did you notice the characters on the lanterns ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Sure . But you know that I can't read any Chinese characters . What do they say ?", + "emotion": "neutral", + "text": "Sure . But you know that I can't read any Chinese characters . What do they say ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "They are puzzles . It's a tradition to solve the puzzles on the lanterns during the Lantern Festival .", + "emotion": "neutral", + "text": "They are puzzles . It's a tradition to solve the puzzles on the lanterns during the Lantern Festival .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Very interesting . But I'm afraid we'd better do something else . Hey , look ! There is a huge lantern there . Let's get close to it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 7 + ], + "expanded emotion cause span": [ + "People always enjoy the lighted lanterns and the gala performances .", + "Hey , look ! There is a huge lantern there . Let's get close to it ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Very interesting . But I'm afraid we'd better do something else . Hey , look ! There is a huge lantern there . Let's get close to it .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "It's really eye-catching . It's the biggest dragon lantern I've ever seen in all my life .", + "emotion": "neutral", + "text": "It's really eye-catching . It's the biggest dragon lantern I've ever seen in all my life .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Really ? Then I'm really lucky . Oh , it's spewing fireworks from its huge mouth .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "It's really eye-catching . It's the biggest dragon lantern I've ever seen in all my life .", + "Oh , it's spewing fireworks from its huge mouth ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Really ? Then I'm really lucky . Oh , it's spewing fireworks from its huge mouth .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Very impressive . It's made of glass which makes it even brighter .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "Oh , it's spewing fireworks from its huge mouth .", + "It's made of glass which makes it even brighter ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Very impressive . It's made of glass which makes it even brighter .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "There are many Chinese characters on its body , too . What are they about ? Puzzles ?", + "emotion": "neutral", + "text": "There are many Chinese characters on its body , too . What are they about ? Puzzles ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Let me have a look . Oh , no . They are Chinese poems which describe this happy scene .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "There are many Chinese characters on its body , too .", + "Oh , no . They are Chinese poems which describe this happy scene ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Let me have a look . Oh , no . They are Chinese poems which describe this happy scene .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1234.json b/reccon/sources/tr_1234.json new file mode 100644 index 0000000000000000000000000000000000000000..948b39b11add07b47aa956688b00bfb9affa5c81 --- /dev/null +++ b/reccon/sources/tr_1234.json @@ -0,0 +1,186 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "David , would you like something to eat ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "David , would you like something to eat ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "No , I'm full .", + "emotion": "neutral", + "text": "No , I'm full .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Do you want something to drink ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Do you want something to drink ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes , I'd like some coffee .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I'd like some coffee ." + ], + "type": [ + "no-context" + ], + "text": "Yes , I'd like some coffee .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Sorry , I don't have any coffee .", + "emotion": "neutral", + "text": "Sorry , I don't have any coffee .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "That's OK . I'll have a glass of water .", + "emotion": "happiness", + "explanation": "speaker is happy to see the listener", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I'd like some coffee ." + ], + "type": [ + "self-contagion" + ], + "text": "That's OK . I'll have a glass of water .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "A small glass , or a big one ?", + "emotion": "happiness", + "explanation": "speaker is happy to help the listener", + "expanded emotion cause evidence": [ + "b", + 6 + ], + "expanded emotion cause span": [ + "b", + "I'll have a glass of water ." + ], + "type": [ + "latent", + "inter-personal" + ], + "text": "A small glass , or a big one ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Small please .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I'd like some coffee ." + ], + "type": [ + "self-contagion" + ], + "text": "Small please .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Here you are .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 6 + ], + "expanded emotion cause span": [ + "b", + "I'll have a glass of water ." + ], + "type": [ + "latent", + "inter-personal" + ], + "text": "Here you are .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Thanks .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 9 + ], + "expanded emotion cause span": [ + "I'd like some coffee .", + "Here you are ." + ], + "type": [ + "hybrid" + ], + "text": "Thanks .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "You're welcome .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Thanks ." + ], + "type": [ + "inter-personal" + ], + "text": "You're welcome .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1262.json b/reccon/sources/tr_1262.json new file mode 100644 index 0000000000000000000000000000000000000000..d1dba178d97584d63c4d0941256309932fc95377 --- /dev/null +++ b/reccon/sources/tr_1262.json @@ -0,0 +1,201 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Guess what ? I've got great news !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 1 + ], + "expanded emotion cause span": [ + "b", + "I've got great news !" + ], + "type": [ + "latent", + "no-context" + ], + "text": "Guess what ? I've got great news !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What is it ?", + "emotion": "neutral", + "text": "What is it ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Well , you know how I've been working at the Economist as a proof-reader , right ?", + "emotion": "neutral", + "text": "Well , you know how I've been working at the Economist as a proof-reader , right ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes .", + "emotion": "neutral", + "text": "Yes .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Well , the editor-in-chief heard that I had experience as an editor at another magadize and asked me if I was interested in becoming an assistant editor for him .", + "emotion": "neutral", + "text": "Well , the editor-in-chief heard that I had experience as an editor at another magadize and asked me if I was interested in becoming an assistant editor for him .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Really ? That's fantastic ! Will you get a chance to do any writing ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "asked me if I was interested in becoming an assistant editor for him .", + "That's fantastic !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Really ? That's fantastic ! Will you get a chance to do any writing ?", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "She said that the columnist for the literary criticism column would be going on pregnancy leave soon and that I could be in charge of the column until she came back .", + "emotion": "neutral", + "text": "She said that the columnist for the literary criticism column would be going on pregnancy leave soon and that I could be in charge of the column until she came back .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Wow ! That's really great news . How often does the magazine come out ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6, + 7, + 8 + ], + "expanded emotion cause span": [ + "asked me if I was interested in becoming an assistant editor for him .", + "That's fantastic !", + "I could be in charge of the column until she came back .", + "Wow ! That's really great news" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Wow ! That's really great news . How often does the magazine come out ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "It's a monthly magazine , but my column will be shared with another columnist so my articles will be due fortnightly .", + "emotion": "neutral", + "text": "It's a monthly magazine , but my column will be shared with another columnist so my articles will be due fortnightly .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Are you looking forward to doing more editing work ?", + "emotion": "neutral", + "text": "Are you looking forward to doing more editing work ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Yes , but I'm even more excited about getting my thoughts published again !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I'm even more excited about getting my thoughts published again !" + ], + "type": [ + "no-context" + ], + "text": "Yes , but I'm even more excited about getting my thoughts published again !", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Do you have any order forms here so that I can get a subscription to the magazine ?", + "emotion": "neutral", + "text": "Do you have any order forms here so that I can get a subscription to the magazine ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I don't have any with me , but I think I could manage to bring a free copy home for you .", + "emotion": "neutral", + "text": "I don't have any with me , but I think I could manage to bring a free copy home for you .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "I'm really looking forward to reading your column .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "I'm really looking forward to reading your column ." + ], + "type": [ + "no-context" + ], + "text": "I'm really looking forward to reading your column .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Me , too . Do you want to go out to celebrate my good news ?", + "emotion": "neutral", + "text": "Me , too . Do you want to go out to celebrate my good news ?", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Sure , where would you like to go ?", + "emotion": "neutral", + "text": "Sure , where would you like to go ?", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "Perhaps we could go to the library festival that's going on at the local bookshop .", + "emotion": "neutral", + "text": "Perhaps we could go to the library festival that's going on at the local bookshop .", + "id": 17 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1266.json b/reccon/sources/tr_1266.json new file mode 100644 index 0000000000000000000000000000000000000000..b89e41aafd445343de75784d632905f0185441ca --- /dev/null +++ b/reccon/sources/tr_1266.json @@ -0,0 +1,258 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Are you free tonight ?", + "emotion": "neutral", + "text": "Are you free tonight ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , I am . What's wrong ?", + "emotion": "neutral", + "text": "Yes , I am . What's wrong ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Would you please go to a dancing party with me ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 3 + ], + "expanded emotion cause span": [ + "Are you free tonight ?", + "Yes , I am .", + "dancing party" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Would you please go to a dancing party with me ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "OK . No problem .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Would you please go to a dancing party with me ?" + ], + "type": [ + "inter-personal" + ], + "text": "OK . No problem .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "As a matter of fact , I haven't danced for a long time .", + "emotion": "neutral", + "text": "As a matter of fact , I haven't danced for a long time .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "But it's said that you dance wonderfully well .", + "emotion": "neutral", + "text": "But it's said that you dance wonderfully well .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Thanks for flattering me . I think you dance a lot , right ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 6, + 7 + ], + "expanded emotion cause span": [ + "dancing party", + "But it's said that you dance wonderfully well .", + "Thanks for flattering me ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Thanks for flattering me . I think you dance a lot , right ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "No . Just occasionally .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 7 + ], + "expanded emotion cause span": [ + "dancing party", + "Thanks for flattering me . I think you dance a lot" + ], + "type": [ + "inter-personal" + ], + "text": "No . Just occasionally .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "What are your favourite dances ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 9 + ], + "expanded emotion cause span": [ + "dancing party", + "favourite dances" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "What are your favourite dances ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I love rumba and waltz .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 10 + ], + "expanded emotion cause span": [ + "dancing party", + "I love rumba and waltz ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I love rumba and waltz .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "How about samba ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 10 + ], + "expanded emotion cause span": [ + "dancing party", + "I love rumba and waltz ." + ], + "type": [ + "hybrid" + ], + "text": "How about samba ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "To tell the truth , I don't like it . It's too fast .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "dancing party" + ], + "type": [ + "inter-personal" + ], + "text": "To tell the truth , I don't like it . It's too fast .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Then I'll see you at six . Is that all right ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 13 + ], + "expanded emotion cause span": [ + "dancing party", + "I'll see you at six" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Then I'll see you at six . Is that all right ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "OK . See you then .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 13, + 14 + ], + "expanded emotion cause span": [ + "dancing party", + "Is that all right ?", + "See you then ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "OK . See you then .", + "id": 14, + "source_sentences": [ + 2, + 12 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 15, + "speaker": "A", + "utterance": "See you then .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 15 + ], + "expanded emotion cause span": [ + "dancing party", + "See you then ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "See you then .", + "id": 15 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1267.json b/reccon/sources/tr_1267.json new file mode 100644 index 0000000000000000000000000000000000000000..664b6d371bc2bd95c859b01492e72eac1fe57a7c --- /dev/null +++ b/reccon/sources/tr_1267.json @@ -0,0 +1,166 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I would like to watch the Oscars on Tv tonight . How about you ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "watch the Oscars on Tv tonight ." + ], + "type": [ + "no-context" + ], + "text": "I would like to watch the Oscars on Tv tonight . How about you ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , I'd love to . It ' s interesting to see who is considered the best in their field and which film are thought to be particularly good .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "watch the Oscars on Tv tonight . How about you ?", + "I'd love to . It ' s interesting to see" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , I'd love to . It ' s interesting to see who is considered the best in their field and which film are thought to be particularly good .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I like watching it for the fashion . I like to see what the ladies are wearing . Of course , the men nearly always just wear the traditional tuxedo .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "watch the Oscars on Tv tonight .", + "I like watching it for the fashion ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I like watching it for the fashion . I like to see what the ladies are wearing . Of course , the men nearly always just wear the traditional tuxedo .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Sometimes the men wear flamboyant colours . Which films do you think will win awards this year ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 1, + 3, + 4 + ], + "expanded emotion cause span": [ + "watch the Oscars on Tv tonight . How about you ?", + "I'd love to . It ' s interesting to see", + "watch the Oscars on Tv tonight .", + "I like watching it for the fashion .", + "Sometimes the men wear flamboyant colours ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Sometimes the men wear flamboyant colours . Which films do you think will win awards this year ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I'm really not sure . Usually just one or two films look set to sweep the awards ceremony , but this year there are several contenders .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3, + 5 + ], + "expanded emotion cause span": [ + "watch the Oscars on Tv tonight .", + "I like watching it for the fashion .", + "this year there are several contenders ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I'm really not sure . Usually just one or two films look set to sweep the awards ceremony , but this year there are several contenders .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "You ' re right . This year should be much more exciting than usual . What ' s you favourite award category ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "this year there are several contenders .", + "This year should be much more exciting" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You ' re right . This year should be much more exciting than usual . What ' s you favourite award category ?", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You might think this strange , but I like the category for \" best foreign language film \" .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I like the category for \" best foreign language film \" ." + ], + "type": [ + "no-context" + ], + "text": "You might think this strange , but I like the category for \" best foreign language film \" .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "It ' s nice to see foreign language films making a little impact on Hollywood . I like the \" best actor and actress \" .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "It ' s nice to see foreign language films making a little impact on Hollywood . I like the \" best actor and actress \" ." + ], + "type": [ + "no-context" + ], + "text": "It ' s nice to see foreign language films making a little impact on Hollywood . I like the \" best actor and actress \" .", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1285.json b/reccon/sources/tr_1285.json new file mode 100644 index 0000000000000000000000000000000000000000..3a5062c4c4684d7c4d1d0aa045b79b3a20636ece --- /dev/null +++ b/reccon/sources/tr_1285.json @@ -0,0 +1,150 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "How is your new car ?", + "emotion": "neutral", + "text": "How is your new car ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Perfect . Couldn't be better .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Perfect . Couldn't be better ." + ], + "type": [ + "no-context" + ], + "text": "Perfect . Couldn't be better .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Why do you say so ? Can I see your new car ?", + "emotion": "neutral", + "text": "Why do you say so ? Can I see your new car ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Of course you can . ( Lead Carl to his garage . )", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "Perfect . Couldn't be better .", + "Can I see your new car ?" + ], + "type": [ + "hybrid" + ], + "text": "Of course you can . ( Lead Carl to his garage . )", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Wow , this new car is dynamite ! It is a shiny , beautiful car .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Wow , this new car is dynamite ! It is a shiny , beautiful car ." + ], + "type": [ + "no-context" + ], + "text": "Wow , this new car is dynamite ! It is a shiny , beautiful car .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "My car is simply a daisy . It drives smoothly .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Wow , this new car is dynamite ! It is a shiny , beautiful car .", + "My car is simply a daisy . It drives smoothly ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "My car is simply a daisy . It drives smoothly .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "The car has very sleek lines . I love it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 7 + ], + "expanded emotion cause span": [ + "Wow , this new car is dynamite ! It is a shiny , beautiful car .", + "The car has very sleek lines . I love it ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "The car has very sleek lines . I love it .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I am glad to hear that . I'm really pleased with it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "The car has very sleek lines . I love it ." + ], + "type": [ + "inter-personal" + ], + "text": "I am glad to hear that . I'm really pleased with it .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "You made a good choice .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "You made a good choice ." + ], + "type": [ + "no-context" + ], + "text": "You made a good choice .", + "id": 9 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1287.json b/reccon/sources/tr_1287.json new file mode 100644 index 0000000000000000000000000000000000000000..e10d5d3e40c8b23d829f812382469d300d1709db --- /dev/null +++ b/reccon/sources/tr_1287.json @@ -0,0 +1,145 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "How's your business ?", + "emotion": "neutral", + "text": "How's your business ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Everything seems to be getting worse . I don't know what to do with it .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Everything seems to be getting worse ." + ], + "type": [ + "no-context" + ], + "text": "Everything seems to be getting worse . I don't know what to do with it .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Things are tough all over . You should never give up !", + "emotion": "neutral", + "text": "Things are tough all over . You should never give up !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "But how can I prevent a deficit ?", + "emotion": "neutral", + "text": "But how can I prevent a deficit ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I think you should make a thorough market investigation now .", + "emotion": "happiness", + "explanation": "The market investigation would help in preventing the deficit.", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "you should make a thorough market investigation now ." + ], + "type": [ + "no-context" + ], + "text": "I think you should make a thorough market investigation now .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "OK , OK . I ' ll do my best .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "you should make a thorough market investigation now ." + ], + "type": [ + "inter-personal" + ], + "text": "OK , OK . I ' ll do my best .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I always consider you are such a guy who never gives up .", + "emotion": "happiness", + "explanation": "The speaker is providing encouragement to the other participant.", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "OK , OK . I ' ll do my best .", + "I always consider you are such a guy who never gives up ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I always consider you are such a guy who never gives up .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I know life is not all roses , and I believe I will pull this through .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "I always consider you are such a guy who never gives up .", + "I believe I will pull this through ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I know life is not all roses , and I believe I will pull this through .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yeah , you can make it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7, + 8 + ], + "expanded emotion cause span": [ + "OK , OK . I ' ll do my best .", + "I always consider you are such a guy who never gives up .", + "I believe I will pull this through ." + ], + "type": [ + "hybrid" + ], + "text": "Yeah , you can make it .", + "id": 9 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1288.json b/reccon/sources/tr_1288.json new file mode 100644 index 0000000000000000000000000000000000000000..d5012f32c9f84bded6e3c1012d3d264bc8ec203e --- /dev/null +++ b/reccon/sources/tr_1288.json @@ -0,0 +1,186 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "How are you , Sue ?", + "emotion": "happiness", + "explanation": "Greeting", + "flag": "F", + "expanded emotion cause evidence": [ + "b", + 1 + ], + "expanded emotion cause span": [ + "b", + "How are you , Sue ?" + ], + "type": [ + "latent", + "no-context" + ], + "text": "How are you , Sue ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Pretty good . I ' Ve just had my new poems published .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I ' Ve just had my new poems published ." + ], + "type": [ + "no-context" + ], + "text": "Pretty good . I ' Ve just had my new poems published .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Congratulations on your success .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 2 + ], + "expanded emotion cause span": [ + "I ' Ve just had my new poems published .", + "I ' Ve just had my new poems published ." + ], + "type": [ + "inter-personal" + ], + "text": "Congratulations on your success .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Thank you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "I ' Ve just had my new poems published .", + "Congratulations on your success ." + ], + "type": [ + "hybrid" + ], + "text": "Thank you .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "And how ' s your brother ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "And how ' s your brother ?" + ], + "type": [ + "no-context" + ], + "text": "And how ' s your brother ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "He is fine .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "He is fine ." + ], + "type": [ + "no-context" + ], + "text": "He is fine .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "He ' s going to be sent to Britain to study , really ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "He ' s going to be sent to Britain to study" + ], + "type": [ + "no-context" + ], + "text": "He ' s going to be sent to Britain to study , really ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yes . He ' s already got the passport and visa .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "He ' s going to be sent to Britain to study" + ], + "type": [ + "inter-personal" + ], + "text": "Yes . He ' s already got the passport and visa .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Fantastic ! Please send him my congratulations .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "He ' s going to be sent to Britain to study" + ], + "type": [ + "self-contagion" + ], + "text": "Fantastic ! Please send him my congratulations .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Thank you . He ' s very lucky indeed .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "He ' s going to be sent to Britain to study" + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . He ' s very lucky indeed .", + "id": 10, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1305.json b/reccon/sources/tr_1305.json new file mode 100644 index 0000000000000000000000000000000000000000..81617105cb3aa8ec4120c75f6de4c4808f3b13de --- /dev/null +++ b/reccon/sources/tr_1305.json @@ -0,0 +1,115 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Please come in !", + "emotion": "neutral", + "text": "Please come in !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hi . Steven . I just drop in and want to have a chat with you .", + "emotion": "neutral", + "text": "Hi . Steven . I just drop in and want to have a chat with you .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Oh , so nice of you to come here . Have a seat . Please make yourself at home .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "want to have a chat with you .", + "so nice of you to come here ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , so nice of you to come here . Have a seat . Please make yourself at home .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "OK . ( Sit on the sofa ) Wow ! Your house was decorated so beautiful .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Your house was decorated so beautiful ." + ], + "type": [ + "no-context" + ], + "text": "OK . ( Sit on the sofa ) Wow ! Your house was decorated so beautiful .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Thank you . My wife would be very happy to hear this .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Your house was decorated so beautiful ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . My wife would be very happy to hear this .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "She must have done a lot of work on it .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Your house was decorated so beautiful ." + ], + "type": [ + "self-contagion" + ], + "text": "She must have done a lot of work on it .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You bet .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 6 + ], + "expanded emotion cause span": [ + "Your house was decorated so beautiful .", + "She must have done a lot of work" + ], + "type": [ + "inter-personal" + ], + "text": "You bet .", + "id": 7, + "source_sentences": [ + 3, + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1315.json b/reccon/sources/tr_1315.json new file mode 100644 index 0000000000000000000000000000000000000000..b1d8f7f9442f2675bc2838222ea07c4b737b837b --- /dev/null +++ b/reccon/sources/tr_1315.json @@ -0,0 +1,145 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I ' Ve had it ! I ' m done working for a company that is taking me nowhere !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I ' m done working for a company that is taking me nowhere !" + ], + "type": [ + "no-context" + ], + "text": "I ' Ve had it ! I ' m done working for a company that is taking me nowhere !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "So what are you gonna do ? Just quit ?", + "emotion": "neutral", + "text": "So what are you gonna do ? Just quit ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "That ' s exactly what I am going to do ! I ' Ve decided to create my own company ! I ' m going to write up a business plan , get some investors and start working for myself !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I ' m done working for a company that is taking me nowhere !" + ], + "type": [ + "self-contagion" + ], + "text": "That ' s exactly what I am going to do ! I ' Ve decided to create my own company ! I ' m going to write up a business plan , get some investors and start working for myself !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Have you ever written up a business plan before ?", + "emotion": "neutral", + "text": "Have you ever written up a business plan before ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Well , no . it can ' t be that hard ! I mean , all you have to do is explain your business , how you are going to do things and that ' s it , right ?", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1, + 4, + 5 + ], + "expanded emotion cause span": [ + "I ' m done working for a company that is taking me nowhere !", + "Have you ever written up a business plan before ?", + "it can ' t be that hard !" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Well , no . it can ' t be that hard ! I mean , all you have to do is explain your business , how you are going to do things and that ' s it , right ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "You couldn ' t be more wrong ! A well written business plan will include an executive summary which highlights the idea of the business in two pages or less . Then you need to describe your company with information such as what type of legal structure it has , history , etc .", + "emotion": "neutral", + "text": "You couldn ' t be more wrong ! A well written business plan will include an executive summary which highlights the idea of the business in two pages or less . Then you need to describe your company with information such as what type of legal structure it has , history , etc .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Well , that seems easy enough .", + "emotion": "neutral", + "text": "Well , that seems easy enough .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Wait , there ' s more ! Then you need to introduce and describe your goods or services . What they are and how they are different from competitors ' ? Then comes the hard part , a market analysis . You need to investigate and analyze hundreds of variables ! You need to take into consideration socioeconomic factors from GDP per capita to how many children on average the population has ! All this information is useful so that you can move on to your strategy and implementation stage , where you will describe in detail how you will actually execute your idea .", + "emotion": "neutral", + "text": "Wait , there ' s more ! Then you need to introduce and describe your goods or services . What they are and how they are different from competitors ' ? Then comes the hard part , a market analysis . You need to investigate and analyze hundreds of variables ! You need to take into consideration socioeconomic factors from GDP per capita to how many children on average the population has ! All this information is useful so that you can move on to your strategy and implementation stage , where you will describe in detail how you will actually execute your idea .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Geez . Is that all ?", + "emotion": "neutral", + "text": "Geez . Is that all ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Almost , the most important piece of information for your investors will be the financial analysis . Here you will calculate and estimate sales , cash flow and profits . After all , people will want to know when they will begin to see a return on their investment !", + "emotion": "neutral", + "text": "Almost , the most important piece of information for your investors will be the financial analysis . Here you will calculate and estimate sales , cash flow and profits . After all , people will want to know when they will begin to see a return on their investment !", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Umm . I think I ' ll just stick to my old job and save myself all the hassle of trying to start up a business !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 8, + 10, + 11 + ], + "expanded emotion cause span": [ + "You couldn ' t be more wrong ! A well written business plan will include an executive summary which highlights the idea of the business in two pages or less . Then you need to describe your company with information such as what type of legal structure it has , history , etc .", + "Wait , there ' s more ! Then you need to introduce and describe your goods or services . What they are and how they are different from competitors ' ? Then comes the hard part , a market analysis . You need to investigate and analyze hundreds of variables ! You need to take into consideration socioeconomic factors from GDP per capita to how many children on average the population has ! All this information is useful so that you can move on to your strategy and implementation stage , where you will describe in detail how you will actually execute your idea .", + "Almost , the most important piece of information for your investors will be the financial analysis . Here you will calculate and estimate sales , cash flow and profits . After all , people will want to know when they will begin to see a return on their investment !", + "I think I ' ll just stick to my old job and save myself all the hassle of trying to start up a business !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Umm . I think I ' ll just stick to my old job and save myself all the hassle of trying to start up a business !", + "id": 11, + "source_sentences": [ + 5, + 7, + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1317.json b/reccon/sources/tr_1317.json new file mode 100644 index 0000000000000000000000000000000000000000..6c32373c0df8b6ccc667759bc4dad473fd7fb246 --- /dev/null +++ b/reccon/sources/tr_1317.json @@ -0,0 +1,164 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What are you doing this Saturday ?", + "emotion": "neutral", + "text": "What are you doing this Saturday ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Not much .", + "emotion": "neutral", + "text": "Not much .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Do you want to go see a movie ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Do you want to go see a movie ?" + ], + "type": [ + "no-context" + ], + "text": "Do you want to go see a movie ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "That sounds good .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Do you want to go see a movie ?" + ], + "type": [ + "inter-personal" + ], + "text": "That sounds good .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "What's playing at the Century Fox ?", + "emotion": "neutral", + "text": "What's playing at the Century Fox ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Candlelight in the Window", + "emotion": "neutral", + "text": "Candlelight in the Window", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Should we go see it ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Do you want to go see a movie ?" + ], + "type": [ + "self-contagion" + ], + "text": "Should we go see it ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I'd rather not . I don't like horror movies .", + "emotion": "neutral", + "text": "I'd rather not . I don't like horror movies .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "How about ' Run of the Mill ? '", + "emotion": "happiness", + "explanation": "speaker is happy on going for a movie", + "flag": "F", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Do you want to go see a movie ?" + ], + "type": [ + "self-contagion" + ], + "text": "How about ' Run of the Mill ? '", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "No . I heard that's really boring .", + "emotion": "neutral", + "text": "No . I heard that's really boring .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Why don't we go to a concert instead ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "go to a concert" + ], + "type": [ + "no-context" + ], + "text": "Why don't we go to a concert instead ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Great idea !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "go to a concert", + "Great idea !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Great idea !", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1353.json b/reccon/sources/tr_1353.json new file mode 100644 index 0000000000000000000000000000000000000000..7ae8806998edb986d2323c03cdc44a6ee8f945db --- /dev/null +++ b/reccon/sources/tr_1353.json @@ -0,0 +1,183 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Jack , what are you doing ?", + "emotion": "neutral", + "text": "Jack , what are you doing ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I am reading .", + "emotion": "neutral", + "text": "I am reading .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I can see that . But why are you reading advertisements for houses for sale ? Are you buying a house ?", + "emotion": "neutral", + "text": "I can see that . But why are you reading advertisements for houses for sale ? Are you buying a house ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "No , not yet . But I like to see what is available .", + "emotion": "neutral", + "text": "No , not yet . But I like to see what is available .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Can I have a look as well ?", + "emotion": "happiness", + "explanation": "A is probably excited to take a look or is just courteous.", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Can I have a look as well ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Of course , have a seat .", + "emotion": "happiness", + "explanation": "B is simply mirroring A's emotion.", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Of course , have a seat .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Oh , this one looks really good . And look at the garden . So beautiful .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Oh , this one looks really good . And look at the garden . So beautiful ." + ], + "type": [ + "no-context" + ], + "text": "Oh , this one looks really good . And look at the garden . So beautiful .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yes , nice . But I prefer this wooden house with a garden fence and a sloping roof .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "So beautiful .", + "I prefer this wooden house with a garden fence and a sloping roof ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , nice . But I prefer this wooden house with a garden fence and a sloping roof .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yes , but my house has large windows and so gets lots of sun . And it has a small balcony at the top .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 9 + ], + "expanded emotion cause span": [ + "Oh , this one looks really good . And look at the garden . So beautiful .", + "my house has large windows and so gets lots of sun . And it has a small balcony at the top ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Yes , but my house has large windows and so gets lots of sun . And it has a small balcony at the top .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Well , you can't compare a small balcony to this large veranda . This is perfect for having a barbecue in summer .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "This is perfect for having a barbecue in summer ." + ], + "type": [ + "no-context" + ], + "text": "Well , you can't compare a small balcony to this large veranda . This is perfect for having a barbecue in summer .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Talking about a barbecue , didn't you say you are organizing one next week ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "This is perfect for having a barbecue in summer ." + ], + "type": [ + "inter-personal" + ], + "text": "Talking about a barbecue , didn't you say you are organizing one next week ?", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Yes , next Saturday . I hope you can make it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "This is perfect for having a barbecue in summer ." + ], + "type": [ + "self-contagion" + ], + "text": "Yes , next Saturday . I hope you can make it .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1360.json b/reccon/sources/tr_1360.json new file mode 100644 index 0000000000000000000000000000000000000000..74ce2a9be02a06432937b024d48686f7f742b154 --- /dev/null +++ b/reccon/sources/tr_1360.json @@ -0,0 +1,116 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Donna , you really shocked everyone at the party last night !", + "emotion": "happiness", + "explanation": "Donna performed amazing last night that made person A happy", + "expanded emotion cause evidence": [ + "b", + 1 + ], + "expanded emotion cause span": [ + "b", + "you really shocked everyone at the party last night !" + ], + "type": [ + "latent", + "no-context" + ], + "text": "Donna , you really shocked everyone at the party last night !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "You mean with my performance ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Donna , you really shocked everyone at the party last night !" + ], + "type": [ + "inter-personal" + ], + "text": "You mean with my performance ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yes ! We have all assumed that you were the quiet , shy type .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 1, + 2 + ], + "expanded emotion cause span": [ + "b", + "you really shocked everyone at the party last night !", + "performance" + ], + "type": [ + "latent", + "hybrid" + ], + "text": "Yes ! We have all assumed that you were the quiet , shy type .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I guess everyone has a few secrets up their sleeve .", + "emotion": "neutral", + "text": "I guess everyone has a few secrets up their sleeve .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Where did you learn to sing like that ?", + "emotion": "neutral", + "text": "Where did you learn to sing like that ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I was part of a band in school .", + "emotion": "neutral", + "text": "I was part of a band in school .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You ? Wow . And why don't you ever dress like that at work ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I was part of a band in school ." + ], + "type": [ + "inter-personal" + ], + "text": "You ? Wow . And why don't you ever dress like that at work ?", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Come on ! This is work . Don't you think that would be a little weird ?", + "emotion": "neutral", + "text": "Come on ! This is work . Don't you think that would be a little weird ?", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1378.json b/reccon/sources/tr_1378.json new file mode 100644 index 0000000000000000000000000000000000000000..637910a370dbcf175628308870efe87e4d254c9e --- /dev/null +++ b/reccon/sources/tr_1378.json @@ -0,0 +1,151 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "David , what have you been up to lately ?", + "emotion": "neutral", + "text": "David , what have you been up to lately ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I went on a trip with my family last week .", + "emotion": "neutral", + "text": "I went on a trip with my family last week .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Really ? Where did you go ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Really ? Where did you go ?" + ], + "type": [ + "no-context" + ], + "text": "Really ? Where did you go ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "We went to Europe .", + "emotion": "neutral", + "text": "We went to Europe .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "What cities did you go to ?", + "emotion": "neutral", + "text": "What cities did you go to ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "London , Paris and a few other cities .", + "emotion": "neutral", + "text": "London , Paris and a few other cities .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Did you go to Berlin ?", + "emotion": "neutral", + "text": "Did you go to Berlin ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "No , We didn't go there . I'd like to go there next time .", + "emotion": "neutral", + "text": "No , We didn't go there . I'd like to go there next time .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I think this summer is a good time to visit Berlin . It's a beautiful place and the people there are very nice .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "this summer is a good time to visit Berlin . It's a beautiful place and the people there are very nice ." + ], + "type": [ + "no-context" + ], + "text": "I think this summer is a good time to visit Berlin . It's a beautiful place and the people there are very nice .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "That's what I've heard .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "this summer is a good time to visit Berlin . It's a beautiful place and the people there are very nice ." + ], + "type": [ + "inter-personal" + ], + "text": "That's what I've heard .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I went there last year . If you want , I can give you some information I have about the city .", + "emotion": "happiness", + "explanation": "the speaker is happy that B has affirmed his/her opinion", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "this summer is a good time to visit Berlin . It's a beautiful place and the people there are very nice .", + "That's what I've heard ." + ], + "type": [ + "hybrid" + ], + "text": "I went there last year . If you want , I can give you some information I have about the city .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Thanks .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "If you want , I can give you some information I have about the city ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1392.json b/reccon/sources/tr_1392.json new file mode 100644 index 0000000000000000000000000000000000000000..c875f2770f26f06b04284f3e63df7a39cb8255bd --- /dev/null +++ b/reccon/sources/tr_1392.json @@ -0,0 +1,160 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi Amy , you look very happy .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "you look very happy ." + ], + "type": [ + "no-context" + ], + "text": "Hi Amy , you look very happy .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , I'm very pleased . I've just got two tickets to see the Olympic opening ceremony .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I've just got two tickets to see the Olympic opening ceremony ." + ], + "type": [ + "no-context" + ], + "text": "Yes , I'm very pleased . I've just got two tickets to see the Olympic opening ceremony .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Wow . You must be very excited .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "I've just got two tickets to see the Olympic opening ceremony .", + "You must be very excited ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Wow . You must be very excited .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I certainly am . I would have been very disappointed if I hadn ' t got them .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I've just got two tickets to see the Olympic opening ceremony ." + ], + "type": [ + "self-contagion" + ], + "text": "I certainly am . I would have been very disappointed if I hadn ' t got them .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Shall we go to a restaurant to celebrate ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "You must be very excited .", + "I certainly am ." + ], + "type": [ + "hybrid" + ], + "text": "Shall we go to a restaurant to celebrate ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "What a good idea . I'm quite hungry .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "go to a restaurant to celebrate ?", + "I'm quite hungry ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "What a good idea . I'm quite hungry .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Me too . I feel very thirsty as well .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6, + 7 + ], + "expanded emotion cause span": [ + "go to a restaurant to celebrate ?", + "What a good idea . I'm quite hungry .", + "Me too . I feel very thirsty as well ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Me too . I feel very thirsty as well .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Let ' s go then .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6, + 7 + ], + "expanded emotion cause span": [ + "go to a restaurant to celebrate ?", + "I'm quite hungry .", + "Me too . I feel very thirsty as well ." + ], + "type": [ + "hybrid" + ], + "text": "Let ' s go then .", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1408.json b/reccon/sources/tr_1408.json new file mode 100644 index 0000000000000000000000000000000000000000..2d35bb7de4dc41cf9d32bb3e4d99fd105607287c --- /dev/null +++ b/reccon/sources/tr_1408.json @@ -0,0 +1,133 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I heard that you went to the concert the day before ? How did you like it ?", + "emotion": "neutral", + "text": "I heard that you went to the concert the day before ? How did you like it ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It was terrific . The concert was really a hit . The symphony orchestra was so good that I was completely absorbed in their performance .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "The symphony orchestra was so good that I was completely absorbed in their performance ." + ], + "type": [ + "no-context" + ], + "text": "It was terrific . The concert was really a hit . The symphony orchestra was so good that I was completely absorbed in their performance .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Who was the conductor ?", + "emotion": "neutral", + "text": "Who was the conductor ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Oh , speaking of the conductor , he is indeed a genius . He did a perfect job . His name is Menuhin , a descendent of Russian American immigrants .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "he is indeed a genius . He did a perfect job ." + ], + "type": [ + "no-context" + ], + "text": "Oh , speaking of the conductor , he is indeed a genius . He did a perfect job . His name is Menuhin , a descendent of Russian American immigrants .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Oh , I learned that he is also a legendary violinist .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "he is indeed a genius . He did a perfect job .", + "I learned that he is also a legendary violinist ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , I learned that he is also a legendary violinist .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Absolutely right . He gave a performance of Felix Mendelssohn's violin concerto . That caused a sensation . The audience were stunned by his pure tone .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "I learned that he is also a legendary violinist .", + "That caused a sensation . The audience were stunned by his pure tone ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Absolutely right . He gave a performance of Felix Mendelssohn's violin concerto . That caused a sensation . The audience were stunned by his pure tone .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Obviously you did enjoy the concert .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "That caused a sensation . The audience were stunned by his pure tone ." + ], + "type": [ + "inter-personal" + ], + "text": "Obviously you did enjoy the concert .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yes , I did .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "I learned that he is also a legendary violinist .", + "That caused a sensation . The audience were stunned by his pure tone ." + ], + "type": [ + "hybrid" + ], + "text": "Yes , I did .", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1422.json b/reccon/sources/tr_1422.json new file mode 100644 index 0000000000000000000000000000000000000000..e5cbacc0c6cd6a2fb862e0dd72a5a6aba31d1c3f --- /dev/null +++ b/reccon/sources/tr_1422.json @@ -0,0 +1,150 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Belinda , I ' m going to a party tonight . What shall I wear ?", + "emotion": "neutral", + "text": "Belinda , I ' m going to a party tonight . What shall I wear ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Is it formal or informal ?", + "emotion": "neutral", + "text": "Is it formal or informal ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I guess it ' s formal .", + "emotion": "neutral", + "text": "I guess it ' s formal .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Then , you should dress well .", + "emotion": "neutral", + "text": "Then , you should dress well .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "That ' s right .", + "emotion": "neutral", + "text": "That ' s right .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I think a white shirt with a blue tie looks nice on you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "looks nice on you ." + ], + "type": [ + "no-context" + ], + "text": "I think a white shirt with a blue tie looks nice on you .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You are smart .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "looks nice on you ." + ], + "type": [ + "inter-personal" + ], + "text": "You are smart .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Of course , the sports shoes don ' t go with the formal occasions .", + "emotion": "neutral", + "text": "Of course , the sports shoes don ' t go with the formal occasions .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "You are right . What kind of shoes should I wear ?", + "emotion": "neutral", + "text": "You are right . What kind of shoes should I wear ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "The brown leather shoes go well with your trousers .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "leather shoes go well with your trousers ." + ], + "type": [ + "no-context" + ], + "text": "The brown leather shoes go well with your trousers .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Good idea . Oh , by the way , would you please pick me up after the party , honey ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "leather shoes go well with your trousers .", + "Good idea ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Good idea . Oh , by the way , would you please pick me up after the party , honey ?", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "It ' ll be too late ; you ' d better take a taxi .", + "emotion": "neutral", + "text": "It ' ll be too late ; you ' d better take a taxi .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "OK .", + "emotion": "neutral", + "text": "OK .", + "id": 13 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_143.json b/reccon/sources/tr_143.json new file mode 100644 index 0000000000000000000000000000000000000000..cb3caa09eb86325afae7e3d2946ec913625227d6 --- /dev/null +++ b/reccon/sources/tr_143.json @@ -0,0 +1,173 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "hey , Maris , are you a part-timer ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "are you a part-timer" + ], + "type": [ + "no-context" + ], + "text": "hey , Maris , are you a part-timer ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "part-timer ? Is that a new buzzword ?", + "emotion": "neutral", + "text": "part-timer ? Is that a new buzzword ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "oh , it ' s pretty popular among my classmates these days . So are you ?", + "emotion": "neutral", + "text": "oh , it ' s pretty popular among my classmates these days . So are you ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "sure , I have a part-time job as a bartender .", + "emotion": "neutral", + "text": "sure , I have a part-time job as a bartender .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "cool ! It must be amazing to work at a bar !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "I have a part-time job as a bartender .", + "cool ! It must be amazing to work at a bar !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "cool ! It must be amazing to work at a bar !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "yeah , but I ' m not there for fun . I have to remain professional and if I get distracted , the manager would be pretty upset .", + "emotion": "neutral", + "text": "yeah , but I ' m not there for fun . I have to remain professional and if I get distracted , the manager would be pretty upset .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "that ' s true . I ' m wondering did you learn anything from the job ?", + "emotion": "neutral", + "text": "that ' s true . I ' m wondering did you learn anything from the job ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "of course . There ' s always much to learn . I got to know more about the real world .", + "emotion": "neutral", + "text": "of course . There ' s always much to learn . I got to know more about the real world .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "you mean you got working experience , right ?", + "emotion": "neutral", + "text": "you mean you got working experience , right ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "not just working experience . I would say the biggest lesson I learned is how to deal with people from all walks of life .", + "emotion": "neutral", + "text": "not just working experience . I would say the biggest lesson I learned is how to deal with people from all walks of life .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "it must be very demanding .", + "emotion": "neutral", + "text": "it must be very demanding .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "sometimes it is . But after working for a few weeks , it ' s easy to figure out .", + "emotion": "neutral", + "text": "sometimes it is . But after working for a few weeks , it ' s easy to figure out .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "really ? It sounds interesting .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 10, + 12, + 13 + ], + "expanded emotion cause span": [ + "There ' s always much to learn . I got to know more about the real world .", + "not just working experience . I would say the biggest lesson I learned is how to deal with people from all walks of life .", + "after working for a few weeks , it ' s easy to figure out .", + "It sounds interesting ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "really ? It sounds interesting .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "maybe you can come to the bar one day and I ' ll show you around .", + "emotion": "neutral", + "text": "maybe you can come to the bar one day and I ' ll show you around .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "great . I ' m looking forward to it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "maybe you can come to the bar one day and I ' ll show you around ." + ], + "type": [ + "inter-personal" + ], + "text": "great . I ' m looking forward to it .", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1432.json b/reccon/sources/tr_1432.json new file mode 100644 index 0000000000000000000000000000000000000000..332d2e91031282e1edf84d18a5c391e7a578e554 --- /dev/null +++ b/reccon/sources/tr_1432.json @@ -0,0 +1,123 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Do you like swimming ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "swimming" + ], + "type": [ + "no-context" + ], + "text": "Do you like swimming ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes . Swimming is one of my most favorite sports , indoors or out-doors .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Swimming is one of my most favorite sports , indoors or out-doors ." + ], + "type": [ + "no-context" + ], + "text": "Yes . Swimming is one of my most favorite sports , indoors or out-doors .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Me too . Swimming is a very good exercise for health . It combines water , bath , sunbath , and air bath together . It promotes the growth and haleness of muscles , bone , viscera and nerve systems .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "Swimming is one of my most favorite sports , indoors or out-doors .", + "Me too . Swimming is a very good exercise for health . It combines water , bath , sunbath , and air bath together . It promotes the growth and haleness of muscles , bone , viscera and nerve systems ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Me too . Swimming is a very good exercise for health . It combines water , bath , sunbath , and air bath together . It promotes the growth and haleness of muscles , bone , viscera and nerve systems .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I have never thought that swimming can bring us so many benefits . I only know that swimming in great waves and deep running water can train people's spirits , and enable people to be fearless of the hardships , dangers and difficulties and become brave and staunch .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3, + 4 + ], + "expanded emotion cause span": [ + "Swimming is one of my most favorite sports , indoors or out-doors .", + "Me too . Swimming is a very good exercise for health . It combines water , bath , sunbath , and air bath together . It promotes the growth and haleness of muscles , bone , viscera and nerve systems .", + "I have never thought that swimming can bring us so many benefits . I only know that swimming in great waves and deep running water can train people's spirits , and enable people to be fearless of the hardships , dangers and difficulties and become brave and staunch ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I have never thought that swimming can bring us so many benefits . I only know that swimming in great waves and deep running water can train people's spirits , and enable people to be fearless of the hardships , dangers and difficulties and become brave and staunch .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Have you ever swum in a river or a lake ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "I have never thought that swimming can bring us so many benefits .", + "swum in a river or a lake ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Have you ever swum in a river or a lake ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yes , but not always . However , I won't let it go if I have a chance .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "swum in a river or a lake ?", + "Yes , but not always . However , I won't let it go if I have a chance ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , but not always . However , I won't let it go if I have a chance .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1443.json b/reccon/sources/tr_1443.json new file mode 100644 index 0000000000000000000000000000000000000000..c6d2f581b8285ebbf8c5990cfd5de6e718c9ab6b --- /dev/null +++ b/reccon/sources/tr_1443.json @@ -0,0 +1,228 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Joanne , let ' s not make this divorce any more acrimonious than it already is , okay ? Let ' s just get down to business and start dividing this stuff up fairly , so we can go our separate ways , alright ?", + "emotion": "neutral", + "text": "Joanne , let ' s not make this divorce any more acrimonious than it already is , okay ? Let ' s just get down to business and start dividing this stuff up fairly , so we can go our separate ways , alright ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Fine with me . I just want to get this over with . It ' s important we make a clean break . I should have signed a pre-nup .", + "emotion": "neutral", + "text": "Fine with me . I just want to get this over with . It ' s important we make a clean break . I should have signed a pre-nup .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What was that ?", + "emotion": "neutral", + "text": "What was that ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Nothing ! Anyway , you ' re right , there ' s no reason this has to be nasty . My lawyer tells me you ' Ve accepted our alimony proposal and the division of property , as well as the custody agreement-I keep the cat and you get the dog . So that ' s done ... finally .", + "emotion": "neutral", + "text": "Nothing ! Anyway , you ' re right , there ' s no reason this has to be nasty . My lawyer tells me you ' Ve accepted our alimony proposal and the division of property , as well as the custody agreement-I keep the cat and you get the dog . So that ' s done ... finally .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Let ' s not go there , Joanne ! Ok , so let ' s start with the record collection , I ' ll take the albums I contributed and you can have your cheesy disco albums back .", + "emotion": "neutral", + "text": "Let ' s not go there , Joanne ! Ok , so let ' s start with the record collection , I ' ll take the albums I contributed and you can have your cheesy disco albums back .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Fine , but I ' m keeping the antique gramophone as my grandfather gave it to me .", + "emotion": "neutral", + "text": "Fine , but I ' m keeping the antique gramophone as my grandfather gave it to me .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I believe that was a wedding present to both of us , Joanne . And you hardly ever use it !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I ' m keeping the antique gramophone as my grandfather gave it to me .", + "you hardly ever use it !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I believe that was a wedding present to both of us , Joanne . And you hardly ever use it !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "He ' s my grandfather , and he never really liked you anyway !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I believe that was a wedding present to both of us , Joanne . And you hardly ever use it !" + ], + "type": [ + "inter-personal" + ], + "text": "He ' s my grandfather , and he never really liked you anyway !", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Whatever ! Alright , I ' ll concede the silly gramophone , if you ' ll agree that I get the silver tea set .", + "emotion": "neutral", + "text": "Whatever ! Alright , I ' ll concede the silly gramophone , if you ' ll agree that I get the silver tea set .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "How typical , when are you ever going to use a silver tea set ? Fine ! I don ' t want to drag this out any longer than necessary . What ' s next ? What about these old photographs ?", + "emotion": "neutral", + "text": "How typical , when are you ever going to use a silver tea set ? Fine ! I don ' t want to drag this out any longer than necessary . What ' s next ? What about these old photographs ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Which ones ? Let me have a look . Wow , look at that ! That brings back memories ... That ?", + "emotion": "neutral", + "text": "Which ones ? Let me have a look . Wow , look at that ! That brings back memories ... That ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Our trip to Italy ! I remember that day . We were going to visit the Trev fountain , and we got caught in the rain ...", + "emotion": "neutral", + "text": "Our trip to Italy ! I remember that day . We were going to visit the Trev fountain , and we got caught in the rain ...", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "... and you looked so adorable with your hair all wet . I had to take a picture of you standing there in that little alley , smiling and laughing in the rain ...", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12, + 13 + ], + "expanded emotion cause span": [ + "Our trip to Italy ! I remember that day . We were going to visit the Trev fountain , and we got caught in the rain ...", + "... and you looked so adorable with your hair all wet . I had to take a picture of you standing there in that little alley , smiling and laughing in the rain ..." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "... and you looked so adorable with your hair all wet . I had to take a picture of you standing there in that little alley , smiling and laughing in the rain ...", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Oh , we really did have fun back then , didn ' t we ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12, + 13, + 14 + ], + "expanded emotion cause span": [ + "Our trip to Italy ! I remember that day . We were going to visit the Trev fountain , and we got caught in the rain ...", + "... and you looked so adorable with your hair all wet . I had to take a picture of you standing there in that little alley , smiling and laughing in the rain ...", + "Oh , we really did have fun back then , didn ' t we ?" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Oh , we really did have fun back then , didn ' t we ?", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Oh , Joanne , are we making a big mistake ? I know our relationship has been on the rocks for sometime but are you sure we can ' t reconcile and try again ? I still love you .", + "emotion": "happiness", + "explanation": "The speaker is remembering the past memories and is questioning himself if their decision to divorce is the right one. He wants to give a try to their marraige again.", + "expanded emotion cause evidence": [ + "b", + 12, + 13, + 14, + 15 + ], + "expanded emotion cause span": [ + "b", + "Our trip to Italy ! I remember that day . We were going to visit the Trev fountain , and we got caught in the rain ...", + "... and you looked so adorable with your hair all wet . I had to take a picture of you standing there in that little alley , smiling and laughing in the rain ...", + "Oh , we really did have fun back then , didn ' t we ?", + "I still love you ." + ], + "type": [ + "latent", + "no-context", + "hybrid" + ], + "text": "Oh , Joanne , are we making a big mistake ? I know our relationship has been on the rocks for sometime but are you sure we can ' t reconcile and try again ? I still love you .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Oh Jeff ! I love you too ! I ' m so glad we didn ' t have to decide who keeps the motorcycle .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 12, + 13, + 14, + 15 + ], + "expanded emotion cause span": [ + "b", + "Our trip to Italy ! I remember that day . We were going to visit the Trev fountain , and we got caught in the rain ...", + "... and you looked so adorable with your hair all wet . I had to take a picture of you standing there in that little alley , smiling and laughing in the rain ...", + "Oh , we really did have fun back then , didn ' t we ?", + "I still love you ." + ], + "type": [ + "latent", + "hybrid" + ], + "text": "Oh Jeff ! I love you too ! I ' m so glad we didn ' t have to decide who keeps the motorcycle .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "The motorcycle ? But that ' s mine !", + "emotion": "neutral", + "text": "The motorcycle ? But that ' s mine !", + "id": 17 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1453.json b/reccon/sources/tr_1453.json new file mode 100644 index 0000000000000000000000000000000000000000..058bf5d2ed266a0b7539a8e83eec6d794bf7159b --- /dev/null +++ b/reccon/sources/tr_1453.json @@ -0,0 +1,104 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "When can we expect you and your daughter for dinner ? Next Saturday ?", + "emotion": "neutral", + "text": "When can we expect you and your daughter for dinner ? Next Saturday ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Next Saturday ? I ' m sorry . I ' Ve promised to go to a Chinese Opera with my daughter .", + "emotion": "neutral", + "text": "Next Saturday ? I ' m sorry . I ' Ve promised to go to a Chinese Opera with my daughter .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "How about Sunday then ?", + "emotion": "neutral", + "text": "How about Sunday then ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes , Sunday sounds fine . What time ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "When can we expect you and your daughter for dinner ?", + "How about Sunday then ?" + ], + "type": [ + "inter-personal" + ], + "text": "Yes , Sunday sounds fine . What time ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Does 6 thirty suit you ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Yes , Sunday sounds fine ." + ], + "type": [ + "inter-personal" + ], + "text": "Does 6 thirty suit you ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "It suits us fine . We ' ll see you then .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Does 6 thirty suit you ?", + "It suits us fine ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It suits us fine . We ' ll see you then .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Thanks , goodbye .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "It suits us fine . We ' ll see you then ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks , goodbye .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1477.json b/reccon/sources/tr_1477.json new file mode 100644 index 0000000000000000000000000000000000000000..def2143b4f927973e4366e850f2862ee74255029 --- /dev/null +++ b/reccon/sources/tr_1477.json @@ -0,0 +1,171 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , how are you doing ?", + "emotion": "neutral", + "text": "Hi , how are you doing ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'm fine . How about yourself ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "how are you doing ?", + "I'm fine ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm fine . How about yourself ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I'm pretty good . Thanks for asking .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "How about yourself ?", + "I'm pretty good ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm pretty good . Thanks for asking .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "No problem . So how have you been ?", + "emotion": "neutral", + "text": "No problem . So how have you been ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I've been great . What about you ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "how have you been ?", + "I've been great ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I've been great . What about you ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I've been good . I'm in school right now .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "What about you ?", + "I've been good ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I've been good . I'm in school right now .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "What school do you go to ?", + "emotion": "neutral", + "text": "What school do you go to ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I go to PCC .", + "emotion": "neutral", + "text": "I go to PCC .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Do you like it there ?", + "emotion": "neutral", + "text": "Do you like it there ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "It's okay . It's a really big campus .", + "emotion": "neutral", + "text": "It's okay . It's a really big campus .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Good luck with school .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "Good luck with school ." + ], + "type": [ + "no-context" + ], + "text": "Good luck with school .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Thank you very much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "Good luck with school ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you very much .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_15.json b/reccon/sources/tr_15.json new file mode 100644 index 0000000000000000000000000000000000000000..ce2ed2eaf9a6c7332bfdbac195d71d99e304bce9 --- /dev/null +++ b/reccon/sources/tr_15.json @@ -0,0 +1,72 @@ +[ + { + "turn": 1, + "speaker": "B", + "utterance": "Hi Bill , I saw your grandma yesterday .", + "emotion": "neutral", + "text": "Hi Bill , I saw your grandma yesterday .", + "id": 1 + }, + { + "turn": 2, + "speaker": "A", + "utterance": "Oh where was that ?", + "emotion": "neutral", + "text": "Oh where was that ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "B", + "utterance": "I was running around the track at my college and there she was walking around the same track .", + "emotion": "neutral", + "text": "I was running around the track at my college and there she was walking around the same track .", + "id": 3 + }, + { + "turn": 4, + "speaker": "A", + "utterance": "Grannie always tries to stay fit and healthy . She is always making us kids eat the proper foods .", + "emotion": "neutral", + "text": "Grannie always tries to stay fit and healthy . She is always making us kids eat the proper foods .", + "id": 4 + }, + { + "turn": 5, + "speaker": "B", + "utterance": "Well , it pays off for her . How old is she anyway ?", + "emotion": "neutral", + "text": "Well , it pays off for her . How old is she anyway ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "A", + "utterance": "She will be 86 next month .", + "emotion": "neutral", + "text": "She will be 86 next month .", + "id": 6 + }, + { + "turn": 7, + "speaker": "B", + "utterance": "That is truly amazing !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "She will be 86 next month ." + ], + "type": [ + "inter-personal" + ], + "text": "That is truly amazing !", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1515.json b/reccon/sources/tr_1515.json new file mode 100644 index 0000000000000000000000000000000000000000..2cd80d5c6da25f696ee24f2fa0ce127a17c86fce --- /dev/null +++ b/reccon/sources/tr_1515.json @@ -0,0 +1,245 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey , what's up ?", + "emotion": "neutral", + "text": "Hey , what's up ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh , nothing .", + "emotion": "neutral", + "text": "Oh , nothing .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What were you writing ?", + "emotion": "neutral", + "text": "What were you writing ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "( Laugh ) All right . You caught me in the act . I finally worked up the nerve to ask Diana out . I was just writing a note to put on her desk .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I finally worked up the nerve to ask Diana out ." + ], + "type": [ + "no-context" + ], + "text": "( Laugh ) All right . You caught me in the act . I finally worked up the nerve to ask Diana out . I was just writing a note to put on her desk .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "You mean you're going to ask her out in a note ? You big chicken !", + "emotion": "neutral", + "text": "You mean you're going to ask her out in a note ? You big chicken !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I admit it . I'm a wuss . I just can't do it in person .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I finally worked up the nerve to ask Diana out ." + ], + "type": [ + "self-contagion" + ], + "text": "I admit it . I'm a wuss . I just can't do it in person .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "But , you work with her everyday .", + "emotion": "neutral", + "text": "But , you work with her everyday .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That's different . When I'm working , I'm in a different frame of mind . But , when I even think about asking her out , I get tongue-tied . At least in a note , I can get the words out without turning beet red .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "At least in a note , I can get the words out without turning beet red ." + ], + "type": [ + "no-context" + ], + "text": "That's different . When I'm working , I'm in a different frame of mind . But , when I even think about asking her out , I get tongue-tied . At least in a note , I can get the words out without turning beet red .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "You've dated a lot . What's so different about Diana ?", + "emotion": "neutral", + "text": "You've dated a lot . What's so different about Diana ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Well , for one thing , she's gorgeous . She's so upbeat and sweet . Who doesn't like her ? Oh , I don't know . All I do know is that I think we have great chemistry together . But , what if I'm wrong . Maybe she's just been nice to me out of courtesy and doesn't think of me that way . Oh ... forget it . This was a bad idea .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 10 + ], + "expanded emotion cause span": [ + "she's gorgeous . She's so upbeat and sweet . Who doesn't like her ?", + "All I do know is that I think we have great chemistry together ." + ], + "type": [ + "no-context" + ], + "text": "Well , for one thing , she's gorgeous . She's so upbeat and sweet . Who doesn't like her ? Oh , I don't know . All I do know is that I think we have great chemistry together . But , what if I'm wrong . Maybe she's just been nice to me out of courtesy and doesn't think of me that way . Oh ... forget it . This was a bad idea .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Well , I guess you don't want this note , then .", + "emotion": "neutral", + "text": "Well , I guess you don't want this note , then .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "What note ?", + "emotion": "neutral", + "text": "What note ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I was looking for you to deliver this note from Diana . She wants to know if you want to go to the office party with her tomorrow night .", + "emotion": "neutral", + "text": "I was looking for you to deliver this note from Diana . She wants to know if you want to go to the office party with her tomorrow night .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "You're kidding ! I can't believe you've been standing this entire time and didn't say anything .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 13, + 14 + ], + "expanded emotion cause span": [ + "She wants to know if you want to go to the office party with her tomorrow night .", + "I can't believe you've been standing this entire time and didn't say anything ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You're kidding ! I can't believe you've been standing this entire time and didn't say anything .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Sorry . What can I say ? Now , do you want the note or what ?", + "emotion": "happiness", + "explanation": "Assuming A is happy for B and making B happy.", + "expanded emotion cause evidence": [ + 13, + 14 + ], + "expanded emotion cause span": [ + "She wants to know if you want to go to the office party with her tomorrow night .", + "You're kidding !" + ], + "type": [ + "hybrid" + ], + "text": "Sorry . What can I say ? Now , do you want the note or what ?", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Yeah , I want the note .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "She wants to know if you want to go to the office party with her tomorrow night ." + ], + "type": [ + "inter-personal" + ], + "text": "Yeah , I want the note .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "Have a great time tomorrow night .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13, + 16 + ], + "expanded emotion cause span": [ + "She wants to know if you want to go to the office party with her tomorrow night .", + "Yeah , I want the note ." + ], + "type": [ + "hybrid" + ], + "text": "Have a great time tomorrow night .", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "Thanks . I plan on it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13, + 17 + ], + "expanded emotion cause span": [ + "She wants to know if you want to go to the office party with her tomorrow night .", + "Have a great time tomorrow night ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks . I plan on it .", + "id": 18, + "source_sentences": [ + 12, + 16 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1531.json b/reccon/sources/tr_1531.json new file mode 100644 index 0000000000000000000000000000000000000000..2c05f1d288adfc6ea8b0263a3b5aa8b735908b4d --- /dev/null +++ b/reccon/sources/tr_1531.json @@ -0,0 +1,134 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello , Joanna . You are looking very charming in the new dress .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "looking very charming" + ], + "type": [ + "no-context" + ], + "text": "Hello , Joanna . You are looking very charming in the new dress .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Thanks . Does it suit me ?", + "emotion": "neutral", + "text": "Thanks . Does it suit me ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yes , it suits you very well . It certainly is unique . I don ' t think I ' Ve seen anything like it before .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "looking very charming", + "I don ' t think I ' Ve seen anything like it before ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Yes , it suits you very well . It certainly is unique . I don ' t think I ' Ve seen anything like it before .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I know . That ' s why I bought it . I hate wearing the same styles like everybody else is wearing .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Yes , it suits you very well . It certainly is unique . I don ' t think I ' Ve seen anything like it before ." + ], + "type": [ + "inter-personal" + ], + "text": "I know . That ' s why I bought it . I hate wearing the same styles like everybody else is wearing .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "And the necklace , it matches your dress marvelously .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3, + 5 + ], + "expanded emotion cause span": [ + "looking very charming", + "I don ' t think I ' Ve seen anything like it before .", + "it matches your dress marvelously ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "And the necklace , it matches your dress marvelously .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "It ' s very nice of you to say so . I should say you are glamorous yourself , as a matter of fact .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 5 + ], + "expanded emotion cause span": [ + "Yes , it suits you very well . It certainly is unique . I don ' t think I ' Ve seen anything like it before .", + "it matches your dress marvelously ." + ], + "type": [ + "inter-personal" + ], + "text": "It ' s very nice of you to say so . I should say you are glamorous yourself , as a matter of fact .", + "id": 6, + "source_sentences": [ + 2, + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Thank you for saying so .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3, + 5, + 6 + ], + "expanded emotion cause span": [ + "looking very charming", + "I don ' t think I ' Ve seen anything like it before .", + "it matches your dress marvelously .", + "you are glamorous" + ], + "type": [ + "hybrid" + ], + "text": "Thank you for saying so .", + "id": 7 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1532.json b/reccon/sources/tr_1532.json new file mode 100644 index 0000000000000000000000000000000000000000..c0163e5c5e311b8de2fd43f43e2c2e5e710d9718 --- /dev/null +++ b/reccon/sources/tr_1532.json @@ -0,0 +1,256 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Welcome back ! How was your vacation ?", + "emotion": "happiness", + "explanation": "Happy to see friend after the vacation", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Welcome back ! How was your vacation ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It was fantastic , but I'm glad to be back ! Being a tourist is really tiring !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 2 + ], + "expanded emotion cause span": [ + "b", + "It was fantastic ," + ], + "type": [ + "latent", + "no-context" + ], + "text": "It was fantastic , but I'm glad to be back ! Being a tourist is really tiring !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Where did you end up going ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "It was fantastic ," + ], + "type": [ + "inter-personal" + ], + "text": "Where did you end up going ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Because it's off-season , we got a really good package deal to Paris , so we went there .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "we got a really good package deal to Paris" + ], + "type": [ + "no-context" + ], + "text": "Because it's off-season , we got a really good package deal to Paris , so we went there .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I've always wanted to go to Paris . The Eiffel Tower is one of the most famous tourist attractions in the world ! Did you go to the top ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 4 + ], + "expanded emotion cause span": [ + "It was fantastic ,", + "Because it's off-season , we got a really good package deal to Paris , so we went there ." + ], + "type": [ + "inter-personal" + ], + "text": "I've always wanted to go to Paris . The Eiffel Tower is one of the most famous tourist attractions in the world ! Did you go to the top ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "That was the first thing we did . I have a few pictures . Do you want to see them ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 2, + 5, + 6 + ], + "expanded emotion cause span": [ + "b", + "It was fantastic ,", + "go to the top", + "That was the first thing we did . I have a few pictures ." + ], + "type": [ + "latent", + "no-context", + "hybrid" + ], + "text": "That was the first thing we did . I have a few pictures . Do you want to see them ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Sure . What's this one a picture of ?", + "emotion": "neutral", + "text": "Sure . What's this one a picture of ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Oh , that's a picture of me on our fourth day of travelling . I'm standing next to a famous foundation in the centre of the city .", + "emotion": "neutral", + "text": "Oh , that's a picture of me on our fourth day of travelling . I'm standing next to a famous foundation in the centre of the city .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "You don't look very happy in that picture .", + "emotion": "neutral", + "text": "You don't look very happy in that picture .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "No , by that time , I was sick of sightseeing . I had had enough of art galleries , cathedrals , fountains , statues , and palaces !", + "emotion": "neutral", + "text": "No , by that time , I was sick of sightseeing . I had had enough of art galleries , cathedrals , fountains , statues , and palaces !", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "So what did you do ?", + "emotion": "neutral", + "text": "So what did you do ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "We spent that afternoon walking around a flea market . We had a few coffees , watched a movie , and went for a swim in the pool at the hotel .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 2, + 12 + ], + "expanded emotion cause span": [ + "b", + "It was fantastic ,", + "We spent that afternoon walking around a flea market . We had a few coffees , watched a movie , and went for a swim in the pool at the hotel ." + ], + "type": [ + "latent", + "no-context", + "self-contagion" + ], + "text": "We spent that afternoon walking around a flea market . We had a few coffees , watched a movie , and went for a swim in the pool at the hotel .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "My travel agent always reminds me to plan a day of relaxing for every 3 days of sightseeing . Did you go to the Louvre ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 4 + ], + "expanded emotion cause span": [ + "It was fantastic ,", + "Because it's off-season , we got a really good package deal to Paris , so we went there ." + ], + "type": [ + "inter-personal" + ], + "text": "My travel agent always reminds me to plan a day of relaxing for every 3 days of sightseeing . Did you go to the Louvre ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Of course ! You can't go to Paris without going to their famous art gallery ! I was surprised by how small the Mona Lisa was though .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 2, + 14, + 14 + ], + "expanded emotion cause span": [ + "b", + "It was fantastic ,", + "I was surprised by how small the Mona Lisa was though .", + "Of course ! You can't go to Paris without going to their famous art gallery ! I was surprised by how small the Mona Lisa was though ." + ], + "type": [ + "latent", + "no-context", + "self-contagion" + ], + "text": "Of course ! You can't go to Paris without going to their famous art gallery ! I was surprised by how small the Mona Lisa was though .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "That's what everyone says ! I can't wait to see it for myself some day .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 4, + 14, + 15 + ], + "expanded emotion cause span": [ + "It was fantastic ,", + "Because it's off-season , we got a really good package deal to Paris , so we went there .", + "Of course ! You can't go to Paris without going to their famous art gallery ! I was surprised by how small the Mona Lisa was though .", + "I can't wait to see it for myself some day ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's what everyone says ! I can't wait to see it for myself some day .", + "id": 15, + "source_sentences": [ + 1, + 3, + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_155.json b/reccon/sources/tr_155.json new file mode 100644 index 0000000000000000000000000000000000000000..9a99d8689a85c3084078c5d8662f01ebf08e85c4 --- /dev/null +++ b/reccon/sources/tr_155.json @@ -0,0 +1,129 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "The music has started .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "The music has started ." + ], + "type": [ + "no-context" + ], + "text": "The music has started .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "How do you like this waltz ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "The music has started ." + ], + "type": [ + "inter-personal" + ], + "text": "How do you like this waltz ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "It's very nice .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "It's very nice ." + ], + "type": [ + "no-context" + ], + "text": "It's very nice .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "May I ask you for a dance ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "May I ask you for a dance ?" + ], + "type": [ + "no-context" + ], + "text": "May I ask you for a dance ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Certainly .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "May I ask you for a dance ?" + ], + "type": [ + "inter-personal" + ], + "text": "Certainly .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "You are doing the waltz wonderfully well .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "You are doing the waltz wonderfully well ." + ], + "type": [ + "no-context" + ], + "text": "You are doing the waltz wonderfully well .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Thanks . I'm glad you say so . Oh , the music has stopped .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "You are doing the waltz wonderfully well .", + "I'm glad you say so ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thanks . I'm glad you say so . Oh , the music has stopped .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1569.json b/reccon/sources/tr_1569.json new file mode 100644 index 0000000000000000000000000000000000000000..7b1dc2c50fd40e1284fe495cea135d35d04e8001 --- /dev/null +++ b/reccon/sources/tr_1569.json @@ -0,0 +1,137 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey Joanne . What are you up to ?", + "emotion": "neutral", + "text": "Hey Joanne . What are you up to ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'm just watching some television .", + "emotion": "neutral", + "text": "I'm just watching some television .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I'm so bored . I don't know what I'm going to do today and it is only ten in the morning .", + "emotion": "neutral", + "text": "I'm so bored . I don't know what I'm going to do today and it is only ten in the morning .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Me too . Do you think we are boring people ?", + "emotion": "neutral", + "text": "Me too . Do you think we are boring people ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I don't think we are boring . It's just that we don't have any hobbies .", + "emotion": "neutral", + "text": "I don't think we are boring . It's just that we don't have any hobbies .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "That's right . What do you think we should do as a hobby ?", + "emotion": "neutral", + "text": "That's right . What do you think we should do as a hobby ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "That all depends on what you like to do . For example , I like to doodle on the notepad , so I'm thinking about doing some real drawings .", + "emotion": "neutral", + "text": "That all depends on what you like to do . For example , I like to doodle on the notepad , so I'm thinking about doing some real drawings .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I like to play the piano for fun .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I like to play the piano for fun ." + ], + "type": [ + "no-context" + ], + "text": "I like to play the piano for fun .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yeah . That can be a good hobby .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "play the piano for fun .", + "That can be a good hobby ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yeah . That can be a good hobby .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Hobbies are great . I'm going to make a list of all the things I like to do .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Hobbies are great . I'm going to make a list of all the things I like to do ." + ], + "type": [ + "no-context" + ], + "text": "Hobbies are great . I'm going to make a list of all the things I like to do .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "That's a great idea . I'm going to do the same .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "Hobbies are great . I'm going to make a list of all the things I like to do .", + "I'm going to do the same ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's a great idea . I'm going to do the same .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_158.json b/reccon/sources/tr_158.json new file mode 100644 index 0000000000000000000000000000000000000000..d5afae1250b788e6d950999627c7546dc2058f9c --- /dev/null +++ b/reccon/sources/tr_158.json @@ -0,0 +1,308 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Han Maimed , What's your plan for the weekend ?", + "emotion": "neutral", + "text": "Han Maimed , What's your plan for the weekend ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I plan to travel around Harvard University and know more about it . To tell you the truth , I plan to apply for Harvard after graduation from high school . It ' s better to get to know it . What about you ?", + "emotion": "neutral", + "text": "I plan to travel around Harvard University and know more about it . To tell you the truth , I plan to apply for Harvard after graduation from high school . It ' s better to get to know it . What about you ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I get together with my Christian brothers on Saturdays .", + "emotion": "neutral", + "text": "I get together with my Christian brothers on Saturdays .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Oh , my God ! John , I didn ' t know you are religious . You just look like a scientific kook , like Leonard in the Big Bang Theory .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "I get together with my Christian brothers on Saturdays .", + "I didn ' t know you are religious . You just look like a scientific kook ," + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , my God ! John , I didn ' t know you are religious . You just look like a scientific kook , like Leonard in the Big Bang Theory .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Come on , Han Maimed , don ' t make a fuss . A lot of Americans , including many scientists , believe in religion .", + "emotion": "neutral", + "text": "Come on , Han Maimed , don ' t make a fuss . A lot of Americans , including many scientists , believe in religion .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "But I ' m really surprised . I thought science and religion are not compatible , are they ?", + "emotion": "neutral", + "text": "But I ' m really surprised . I thought science and religion are not compatible , are they ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yes , they are compatible . Actually , the U . S . is both the most developed and the most religious country in the world .", + "emotion": "neutral", + "text": "Yes , they are compatible . Actually , the U . S . is both the most developed and the most religious country in the world .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I've heard about it a little bit before , but I don ' t understand . How can people believe in God since they know God doesn't exist ?", + "emotion": "neutral", + "text": "I've heard about it a little bit before , but I don ' t understand . How can people believe in God since they know God doesn't exist ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "That ' s a little complicated . You ' ll get to know it when you are acquainted with the U . S . history later on . Religion was and is a part of American people ' s life . Guess what ? Even Harvard University , which is a highly academic institution , is in a sense the product of religion .", + "emotion": "neutral", + "text": "That ' s a little complicated . You ' ll get to know it when you are acquainted with the U . S . history later on . Religion was and is a part of American people ' s life . Guess what ? Even Harvard University , which is a highly academic institution , is in a sense the product of religion .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Really ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Even Harvard University , which is a highly academic institution , is in a sense the product of religion ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Absolutely ! It was founded by a group of Puritan immigrants from England .", + "emotion": "neutral", + "text": "Absolutely ! It was founded by a group of Puritan immigrants from England .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Why was it founded by the Puritans ? Where were the atheistic educators ?", + "emotion": "neutral", + "text": "Why was it founded by the Puritans ? Where were the atheistic educators ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Because most of the first English immigrants who came to the United States were Puritans .", + "emotion": "neutral", + "text": "Because most of the first English immigrants who came to the United States were Puritans .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "How come ? I mean why most of them were religious people ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "Because most of the first English immigrants who came to the United States were Puritans ." + ], + "type": [ + "inter-personal" + ], + "text": "How come ? I mean why most of them were religious people ?", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "That ' s because in the 16th and 17th century , there was a series of religious reforms in England . Many religious separatists were persecuted and fled to other countries .", + "emotion": "neutral", + "text": "That ' s because in the 16th and 17th century , there was a series of religious reforms in England . Many religious separatists were persecuted and fled to other countries .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "So , you mean people didn't enjoy religious freedom in England ?", + "emotion": "neutral", + "text": "So , you mean people didn't enjoy religious freedom in England ?", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "Yes , that's why Puritans moved to the New World , where they believed they could establish a heaven for Puritans . Later on , it was these Puritans who founded Harvard College .", + "emotion": "neutral", + "text": "Yes , that's why Puritans moved to the New World , where they believed they could establish a heaven for Puritans . Later on , it was these Puritans who founded Harvard College .", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "Why did they want to found a college ?", + "emotion": "neutral", + "text": "Why did they want to found a college ?", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "Many Puritans had received classic style of higher education in Oxford University and Cambridge University back in England . They hoped that their descendants could receive this kind of education as well .", + "emotion": "neutral", + "text": "Many Puritans had received classic style of higher education in Oxford University and Cambridge University back in England . They hoped that their descendants could receive this kind of education as well .", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "Oh , I see .", + "emotion": "neutral", + "text": "Oh , I see .", + "id": 20 + }, + { + "turn": 21, + "speaker": "A", + "utterance": "Actually Harvard was first named ' New College ' , without a formal name .", + "emotion": "neutral", + "text": "Actually Harvard was first named ' New College ' , without a formal name .", + "id": 21 + }, + { + "turn": 22, + "speaker": "B", + "utterance": "When did it begin to be called Harvard University ?", + "emotion": "neutral", + "text": "When did it begin to be called Harvard University ?", + "id": 22 + }, + { + "turn": 23, + "speaker": "A", + "utterance": "In 1639 , it was renamed after its major benefactor John Harvard . Interestingly , JohnHarvard himself was a clergyman .", + "emotion": "neutral", + "text": "In 1639 , it was renamed after its major benefactor John Harvard . Interestingly , JohnHarvard himself was a clergyman .", + "id": 23 + }, + { + "turn": 24, + "speaker": "B", + "utterance": "It seems that Harvard was predestined to be influenced by religion .", + "emotion": "neutral", + "text": "It seems that Harvard was predestined to be influenced by religion .", + "id": 24 + }, + { + "turn": 25, + "speaker": "A", + "utterance": "Therefore , it ' s not exaggerate to claim that had there not been religion , there would note Harvard .", + "emotion": "neutral", + "text": "Therefore , it ' s not exaggerate to claim that had there not been religion , there would note Harvard .", + "id": 25 + }, + { + "turn": 26, + "speaker": "B", + "utterance": "Wow , I didn ' t know that religion had played such an important role in Harvard history .", + "emotion": "neutral", + "text": "Wow , I didn ' t know that religion had played such an important role in Harvard history .", + "id": 26 + }, + { + "turn": 27, + "speaker": "A", + "utterance": "Religion has been playing an indispensible part in Harvard history as well as the U . S .", + "emotion": "neutral", + "text": "Religion has been playing an indispensible part in Harvard history as well as the U . S .", + "id": 27 + }, + { + "turn": 28, + "speaker": "B", + "utterance": "I finally begin to get to know Harvard . It seems that my knowledge of Harvard is rather poor . I have a lot work to do before applying for Harvard .", + "emotion": "neutral", + "text": "I finally begin to get to know Harvard . It seems that my knowledge of Harvard is rather poor . I have a lot work to do before applying for Harvard .", + "id": 28 + }, + { + "turn": 29, + "speaker": "A", + "utterance": "Remember that Harvard is a part of the United States . So you have to know the U . S . history and culture if you want to have in-depth knowledge of Harvard . The two are closely related .", + "emotion": "neutral", + "text": "Remember that Harvard is a part of the United States . So you have to know the U . S . history and culture if you want to have in-depth knowledge of Harvard . The two are closely related .", + "id": 29 + }, + { + "turn": 30, + "speaker": "B", + "utterance": "That ' s right . I have a lot to learn from you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 29, + 30 + ], + "expanded emotion cause span": [ + "I plan to travel around Harvard University and know more about it . To tell you the truth , I plan to apply for Harvard after graduation from high school .", + "you have to know the U . S . history and culture if you want to have in-depth knowledge of Harvard .", + "I have a lot to learn from you ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "That ' s right . I have a lot to learn from you .", + "id": 30 + }, + { + "turn": 31, + "speaker": "A", + "utterance": "You can ask me any question at any time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 30 + ], + "expanded emotion cause span": [ + "I have a lot to learn from you ." + ], + "type": [ + "inter-personal" + ], + "text": "You can ask me any question at any time .", + "id": 31, + "source_sentences": [ + 29 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1604.json b/reccon/sources/tr_1604.json new file mode 100644 index 0000000000000000000000000000000000000000..3cc7d86dc05d02261248c741650d5d7931928665 --- /dev/null +++ b/reccon/sources/tr_1604.json @@ -0,0 +1,228 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What would you say if I told you I was going to quit school ?", + "emotion": "neutral", + "text": "What would you say if I told you I was going to quit school ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I ' d say , think twice about it . Well , you are not going to quit school , are you ?", + "emotion": "neutral", + "text": "I ' d say , think twice about it . Well , you are not going to quit school , are you ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I don't know . I failed my exam .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "you are not going to quit school , are you ?", + "I failed my exam ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I don't know . I failed my exam .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "What did you get ?", + "emotion": "neutral", + "text": "What did you get ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "A B plus .", + "emotion": "neutral", + "text": "A B plus .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "That's not bad .", + "emotion": "neutral", + "text": "That's not bad .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "But I should have aced it . I mean I finished the paper so quickly , thinking it's a piece of cake . But when I knew my result , I was like what ? That can't be true !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "But I should have aced it . I mean I finished the paper so quickly , thinking it's a piece of cake . But when I knew my result , I was like what ? That can't be true !" + ], + "type": [ + "no-context" + ], + "text": "But I should have aced it . I mean I finished the paper so quickly , thinking it's a piece of cake . But when I knew my result , I was like what ? That can't be true !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Listen , John . I understand that you are such an excellent student and I know you must have lots of stress , but you really want to give up ?", + "emotion": "neutral", + "text": "Listen , John . I understand that you are such an excellent student and I know you must have lots of stress , but you really want to give up ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "No , I don't . I just don't know how to handle this . This is my first time , you know .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2, + 3, + 9 + ], + "expanded emotion cause span": [ + "you are not going to quit school , are you ?", + "I failed my exam .", + "I just don't know how to handle this . This is my first time , you know ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "No , I don't . I just don't know how to handle this . This is my first time , you know .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I know . Don't worry . Do you know what you should do ?", + "emotion": "neutral", + "text": "I know . Don't worry . Do you know what you should do ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "What ?", + "emotion": "neutral", + "text": "What ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "You need to blow off some steam . The world is not on your shoulder .", + "emotion": "neutral", + "text": "You need to blow off some steam . The world is not on your shoulder .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "How ?", + "emotion": "neutral", + "text": "How ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Forget about school and exams . Come over to my house and have fun . I have some really good DVDs .", + "emotion": "neutral", + "text": "Forget about school and exams . Come over to my house and have fun . I have some really good DVDs .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Thanks . But I really don't feel like watching movies tonight . I have to get an early start in the morning .", + "emotion": "neutral", + "text": "Thanks . But I really don't feel like watching movies tonight . I have to get an early start in the morning .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Then go to bed and have a good sleep .", + "emotion": "neutral", + "text": "Then go to bed and have a good sleep .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "I guess that's what I need . Thanks . You're being a really good friend .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 16, + 17 + ], + "expanded emotion cause span": [ + "Then go to bed and have a good sleep .", + "I guess that's what I need . Thanks . You're being a really good friend ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I guess that's what I need . Thanks . You're being a really good friend .", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "Of course I am . Well , pleasant dreams !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 17 + ], + "expanded emotion cause span": [ + "You're being a really good friend ." + ], + "type": [ + "inter-personal" + ], + "text": "Of course I am . Well , pleasant dreams !", + "id": 18, + "source_sentences": [ + 16 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 19, + "speaker": "A", + "utterance": "Thanks , bye .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 16, + 17, + 18 + ], + "expanded emotion cause span": [ + "Then go to bed and have a good sleep .", + "I guess that's what I need . Thanks . You're being a really good friend .", + "pleasant dreams !" + ], + "type": [ + "hybrid" + ], + "text": "Thanks , bye .", + "id": 19 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1607.json b/reccon/sources/tr_1607.json new file mode 100644 index 0000000000000000000000000000000000000000..f19694baa0b3e9ce356c6b86eaf3f56cae8d97b5 --- /dev/null +++ b/reccon/sources/tr_1607.json @@ -0,0 +1,241 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Karen , do you have a minute ? I'd like to ask you about something .", + "emotion": "neutral", + "text": "Karen , do you have a minute ? I'd like to ask you about something .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Sure . What is it ?", + "emotion": "neutral", + "text": "Sure . What is it ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I think you can give me some advice . You have worked here longer , and I just want to know what you think .", + "emotion": "neutral", + "text": "I think you can give me some advice . You have worked here longer , and I just want to know what you think .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I'm glad to help you . But what is it you want to ask about ?", + "emotion": "neutral", + "text": "I'm glad to help you . But what is it you want to ask about ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I am worried about the meeting this morning .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "worried about the meeting this morning ." + ], + "type": [ + "no-context" + ], + "text": "I am worried about the meeting this morning .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Why ? I think the meeting went well .", + "emotion": "neutral", + "text": "Why ? I think the meeting went well .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Really ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "worried about the meeting this morning .", + "I think the meeting went well ." + ], + "type": [ + "hybrid" + ], + "text": "Really ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yes . But what are you worried about ?", + "emotion": "neutral", + "text": "Yes . But what are you worried about ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I'm afraid I was too rude .", + "emotion": "neutral", + "text": "I'm afraid I was too rude .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Rude ? You weren't rude at all , Annie . Why do you think you were rude ?", + "emotion": "neutral", + "text": "Rude ? You weren't rude at all , Annie . Why do you think you were rude ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Well , I maybe talked to Mr . Drummond too directly . I thought I maybe said too much . I don't want him to be angry .", + "emotion": "neutral", + "text": "Well , I maybe talked to Mr . Drummond too directly . I thought I maybe said too much . I don't want him to be angry .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I understand . But really you weren't rude at all . You said what you thought . I think he appreciates that .", + "emotion": "neutral", + "text": "I understand . But really you weren't rude at all . You said what you thought . I think he appreciates that .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Really ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 9, + 11, + 12 + ], + "expanded emotion cause span": [ + "I'm afraid I was too rude .", + "I maybe talked to Mr . Drummond too directly . I thought I maybe said too much .", + "But really you weren't rude at all . You said what you thought . I think he appreciates that ." + ], + "type": [ + "hybrid" + ], + "text": "Really ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Yes .", + "emotion": "neutral", + "text": "Yes .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "But I am new here , and I'm not sure he is used to that .", + "emotion": "neutral", + "text": "But I am new here , and I'm not sure he is used to that .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "You mean because you are a woman ?", + "emotion": "neutral", + "text": "You mean because you are a woman ?", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "Yes . And he is the president of the company .", + "emotion": "neutral", + "text": "Yes . And he is the president of the company .", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "Listen , Annie . You shouldn't worry about Mr . Drummond . He is a very good man to work for . He is not sexist at all . He appreciates people for their ideas . And he is willing to take suggestions from men or women .", + "emotion": "neutral", + "text": "Listen , Annie . You shouldn't worry about Mr . Drummond . He is a very good man to work for . He is not sexist at all . He appreciates people for their ideas . And he is willing to take suggestions from men or women .", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "I am very happy to hear that , Karen . It ' s good to know I'm working in such a company .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 18, + 19 + ], + "expanded emotion cause span": [ + "You shouldn't worry about Mr . Drummond . He is a very good man to work for . He is not sexist at all . He appreciates people for their ideas . And he is willing to take suggestions from men or women .", + "I am very happy to hear that , Karen . It ' s good to know I'm working in such a company ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I am very happy to hear that , Karen . It ' s good to know I'm working in such a company .", + "id": 19, + "source_sentences": [ + 17 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 20, + "speaker": "B", + "utterance": "I agree with you on that , Annie . I've worked for Derek Drummond for nine years now . I feel he appreciates his employees for their work , not their gender . I would never change jobs .", + "emotion": "neutral", + "text": "I agree with you on that , Annie . I've worked for Derek Drummond for nine years now . I feel he appreciates his employees for their work , not their gender . I would never change jobs .", + "id": 20 + }, + { + "turn": 21, + "speaker": "A", + "utterance": "Good . Thank you for telling me this .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 18, + 19, + 20 + ], + "expanded emotion cause span": [ + "You shouldn't worry about Mr . Drummond . He is a very good man to work for . He is not sexist at all . He appreciates people for their ideas . And he is willing to take suggestions from men or women .", + "I am very happy to hear that , Karen . It ' s good to know I'm working in such a company .", + "I agree with you on that , Annie . I've worked for Derek Drummond for nine years now . I feel he appreciates his employees for their work , not their gender . I would never change jobs ." + ], + "type": [ + "hybrid" + ], + "text": "Good . Thank you for telling me this .", + "id": 21 + }, + { + "turn": 22, + "speaker": "B", + "utterance": "Any time . If you have a good idea , don't be afraid to speak up . This is a company that appreciates initiative .", + "emotion": "neutral", + "text": "Any time . If you have a good idea , don't be afraid to speak up . This is a company that appreciates initiative .", + "id": 22 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1614.json b/reccon/sources/tr_1614.json new file mode 100644 index 0000000000000000000000000000000000000000..8056917df2f9534b11ac0f4e96049653eb298d5c --- /dev/null +++ b/reccon/sources/tr_1614.json @@ -0,0 +1,195 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Jenny , you look terrible . What's eating you ?", + "emotion": "neutral", + "text": "Jenny , you look terrible . What's eating you ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Don't brother me !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "you look terrible . What's eating you ?" + ], + "type": [ + "inter-personal" + ], + "text": "Don't brother me !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Hey , chill out , I'm just trying to help .", + "emotion": "neutral", + "text": "Hey , chill out , I'm just trying to help .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Sorry , Sally , it's not your fault .", + "emotion": "sadness", + "explanation": "Self realization of agrressive behavior", + "expanded emotion cause evidence": [ + 3, + 4, + "b" + ], + "expanded emotion cause span": [ + "I'm just trying to help .", + "Sorry , Sally", + "b" + ], + "type": [ + "latent", + "no-context", + "inter-personal" + ], + "text": "Sorry , Sally , it's not your fault .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "So , what's the problem ?", + "emotion": "neutral", + "text": "So , what's the problem ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I drew a blank on the algebra test .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I drew a blank on the algebra test ." + ], + "type": [ + "no-context" + ], + "text": "I drew a blank on the algebra test .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "No kidding ! Didn't you study for it ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I drew a blank on the algebra test ." + ], + "type": [ + "inter-personal" + ], + "text": "No kidding ! Didn't you study for it ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yeah , but nothing was clear during the test .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I drew a blank on the algebra test ." + ], + "type": [ + "self-contagion" + ], + "text": "Yeah , but nothing was clear during the test .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "That's too bad , anyway , I'm sure things will turn around next semester .", + "emotion": "neutral", + "text": "That's too bad , anyway , I'm sure things will turn around next semester .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I'm thinking of dropping out .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 6, + 10 + ], + "expanded emotion cause span": [ + "I drew a blank on the algebra test .", + "I'm thinking of dropping out ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I'm thinking of dropping out .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "You can't do that , Jenny !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "I'm thinking of dropping out ." + ], + "type": [ + "inter-personal" + ], + "text": "You can't do that , Jenny !", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I'm dead serious about this , Sally .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 6, + 10 + ], + "expanded emotion cause span": [ + "I drew a blank on the algebra test .", + "I'm thinking of dropping out ." + ], + "type": [ + "self-contagion" + ], + "text": "I'm dead serious about this , Sally .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Come on , let's talk about it .", + "emotion": "neutral", + "text": "Come on , let's talk about it .", + "id": 13 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1617.json b/reccon/sources/tr_1617.json new file mode 100644 index 0000000000000000000000000000000000000000..ea1bf473e5435019c0749dff8f4973b2a86a5fb5 --- /dev/null +++ b/reccon/sources/tr_1617.json @@ -0,0 +1,129 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Thank you for coming to see me off .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "coming to see me off ." + ], + "type": [ + "no-context" + ], + "text": "Thank you for coming to see me off .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Not at all .", + "emotion": "happiness", + "explanation": "seeing off friend", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Not at all .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "If have time , I'll come again .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "coming to see me off .", + "I'll come again ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "If have time , I'll come again .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "You're welcome at any time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "If have time , I'll come again ." + ], + "type": [ + "inter-personal" + ], + "text": "You're welcome at any time .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Thank you for your hospitality . I hope I didn't cause you too much trouble during my stay .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "your hospitality ." + ], + "type": [ + "no-context" + ], + "text": "Thank you for your hospitality . I hope I didn't cause you too much trouble during my stay .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "You're most welcome .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Thank you for your hospitality . I hope I didn't cause you too much trouble during my stay ." + ], + "type": [ + "inter-personal" + ], + "text": "You're most welcome .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I'm afraid I have to go now . The plane will take off soon .", + "emotion": "neutral", + "text": "I'm afraid I have to go now . The plane will take off soon .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Call us as soon as you get home .", + "emotion": "neutral", + "text": "Call us as soon as you get home .", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1627.json b/reccon/sources/tr_1627.json new file mode 100644 index 0000000000000000000000000000000000000000..268e88ac022dfae4dffa726a40586192f07578eb --- /dev/null +++ b/reccon/sources/tr_1627.json @@ -0,0 +1,186 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , long time no see . How have you been ?", + "emotion": "neutral", + "text": "Hi , long time no see . How have you been ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh , I've been fine , but I'm having some trouble with my son .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I'm having some trouble with my son ." + ], + "type": [ + "no-context" + ], + "text": "Oh , I've been fine , but I'm having some trouble with my son .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Tell me all about it .", + "emotion": "neutral", + "text": "Tell me all about it .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Oh , he's 14 and in the past few months , he's become quieter and a bit secretive . He locks himself in his room and I think he's running around with the wrong crowd .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2, + 4 + ], + "expanded emotion cause span": [ + "I'm having some trouble with my son .", + "he's become quieter and a bit secretive . He locks himself in his room and I think he's running around with the wrong crowd ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Oh , he's 14 and in the past few months , he's become quieter and a bit secretive . He locks himself in his room and I think he's running around with the wrong crowd .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Oh , I see . What makes you think that ?", + "emotion": "neutral", + "text": "Oh , I see . What makes you think that ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Well , he's become friends with a couple of older boys who are in a band . And one night last weekend , he came home really late , way past his curfew .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2, + 4, + 6 + ], + "expanded emotion cause span": [ + "I'm having some trouble with my son .", + "he's become quieter and a bit secretive . He locks himself in his room and I think he's running around with the wrong crowd .", + "one night last weekend , he came home really late , way past his curfew ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Well , he's become friends with a couple of older boys who are in a band . And one night last weekend , he came home really late , way past his curfew .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Really ? What happened ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "one night last weekend , he came home really late , way past his curfew ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? What happened ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "He told me that his friend's car broke down and they had to walk home .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2, + 4, + 6 + ], + "expanded emotion cause span": [ + "I'm having some trouble with my son .", + "he's become quieter and a bit secretive . He locks himself in his room and I think he's running around with the wrong crowd .", + "one night last weekend , he came home really late , way past his curfew ." + ], + "type": [ + "self-contagion" + ], + "text": "He told me that his friend's car broke down and they had to walk home .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I see what you mean . I understand why you're concerned . Have you tried talking to your son about it ?", + "emotion": "neutral", + "text": "I see what you mean . I understand why you're concerned . Have you tried talking to your son about it ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I haven't yet . I just keep hoping it's just a phase he's going through .", + "emotion": "neutral", + "text": "I haven't yet . I just keep hoping it's just a phase he's going through .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "You may be right , but it doesn't hurt to find out more about what's going on in his life .", + "emotion": "neutral", + "text": "You may be right , but it doesn't hurt to find out more about what's going on in his life .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "You're right . I should talk to him . Sometimes , it's not easy being a parent . Thanks . It helps to get it off my chest . You're always so easy to talk to .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "Thanks . It helps to get it off my chest . You're always so easy to talk to ." + ], + "type": [ + "no-context" + ], + "text": "You're right . I should talk to him . Sometimes , it's not easy being a parent . Thanks . It helps to get it off my chest . You're always so easy to talk to .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I don't know about that , but my door is always open . Stop by anytime .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "Thanks . It helps to get it off my chest . You're always so easy to talk to ." + ], + "type": [ + "inter-personal" + ], + "text": "I don't know about that , but my door is always open . Stop by anytime .", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1630.json b/reccon/sources/tr_1630.json new file mode 100644 index 0000000000000000000000000000000000000000..06c0c79d16012bebbf74a79a7075bdb1489998b2 --- /dev/null +++ b/reccon/sources/tr_1630.json @@ -0,0 +1,142 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I'd like to meet you again sometime .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 1 + ], + "expanded emotion cause span": [ + "b", + "I'd like to meet you again sometime ." + ], + "type": [ + "latent", + "no-context" + ], + "text": "I'd like to meet you again sometime .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "That would be great . Actually , can I get your phone number , Ella ? That's assuming you don't mind if I call you sometime .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I'd like to meet you again sometime ." + ], + "type": [ + "inter-personal" + ], + "text": "That would be great . Actually , can I get your phone number , Ella ? That's assuming you don't mind if I call you sometime .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Anytime . You can reach me at 5558929 .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 1 + ], + "expanded emotion cause span": [ + "b", + "I'd like to meet you again sometime ." + ], + "type": [ + "latent", + "self-contagion" + ], + "text": "Anytime . You can reach me at 5558929 .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Ok , got it . I will call you sometime next week .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I'd like to meet you again sometime ." + ], + "type": [ + "inter-personal" + ], + "text": "Ok , got it . I will call you sometime next week .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Fine .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 1 + ], + "expanded emotion cause span": [ + "b", + "I'd like to meet you again sometime ." + ], + "type": [ + "latent", + "self-contagion" + ], + "text": "Fine .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "It's time to go . Bye , Ella . Hope to see you soon", + "emotion": "happiness", + "explanation": "speaker is happy to see the listener in the future", + "expanded emotion cause evidence": [ + 1, + 6 + ], + "expanded emotion cause span": [ + "I'd like to meet you again sometime .", + "Hope to see you soon" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It's time to go . Bye , Ella . Hope to see you soon", + "id": 6, + "source_sentences": [ + 0 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Bye , Jason .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 1 + ], + "expanded emotion cause span": [ + "b", + "I'd like to meet you again sometime ." + ], + "type": [ + "latent", + "self-contagion" + ], + "text": "Bye , Jason .", + "id": 7 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1634.json b/reccon/sources/tr_1634.json new file mode 100644 index 0000000000000000000000000000000000000000..fb044c78d8cf05b8262496ed1d7ffe1612710ba9 --- /dev/null +++ b/reccon/sources/tr_1634.json @@ -0,0 +1,229 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey , That's a really nice outfit you have on .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "That's a really nice outfit you have on ." + ], + "type": [ + "no-context" + ], + "text": "Hey , That's a really nice outfit you have on .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Why , thank you . I wasn't sure if it looked okay or not . I can't believe all the words the salesgirl said .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "That's a really nice outfit you have on ." + ], + "type": [ + "inter-personal" + ], + "text": "Why , thank you . I wasn't sure if it looked okay or not . I can't believe all the words the salesgirl said .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Oh , you look stunning . Your dress really goes well with your shoes .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "you look stunning . Your dress really goes well with your shoes ." + ], + "type": [ + "no-context" + ], + "text": "Oh , you look stunning . Your dress really goes well with your shoes .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I'm glad that you think so . I thought it might be a bit too revealing .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "you look stunning . Your dress really goes well with your shoes ." + ], + "type": [ + "inter-personal" + ], + "text": "I'm glad that you think so . I thought it might be a bit too revealing .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "No , not at all . It looks really classy on you . Where did you pick that up ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "I thought it might be a bit too revealing .", + "No , not at all . It looks really classy on you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "No , not at all . It looks really classy on you . Where did you pick that up ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I got it on sale down at the department store .", + "emotion": "neutral", + "text": "I got it on sale down at the department store .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "When did you go there ?", + "emotion": "neutral", + "text": "When did you go there ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I was just there a couple of days ago . You know , you should go down there too . They have a lot of stylish clothes on sale .", + "emotion": "neutral", + "text": "I was just there a couple of days ago . You know , you should go down there too . They have a lot of stylish clothes on sale .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I might just do that . What style of clothes do they have ?", + "emotion": "neutral", + "text": "I might just do that . What style of clothes do they have ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Anything you want . They have both casual and formal styles .", + "emotion": "neutral", + "text": "Anything you want . They have both casual and formal styles .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I was hoping to get a few new ties for my collection .", + "emotion": "neutral", + "text": "I was hoping to get a few new ties for my collection .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "That's a good idea . Some of your ties are pretty outdated .", + "emotion": "neutral", + "text": "That's a good idea . Some of your ties are pretty outdated .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Well , I spent a lot of money on getting my shirts tailor-made , so I couldn't afford to buy any new ties .", + "emotion": "neutral", + "text": "Well , I spent a lot of money on getting my shirts tailor-made , so I couldn't afford to buy any new ties .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Anyways , are you going to the party tonight ?", + "emotion": "neutral", + "text": "Anyways , are you going to the party tonight ?", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Yes , I am . Say , are you going to wear that outfit to the party ?", + "emotion": "neutral", + "text": "Yes , I am . Say , are you going to wear that outfit to the party ?", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "I don't think so . It is a little too formal . I'm probably going to wear something more laid back .", + "emotion": "neutral", + "text": "I don't think so . It is a little too formal . I'm probably going to wear something more laid back .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "Me too . I will probably go dressed in a T-shirt and jeans .", + "emotion": "neutral", + "text": "Me too . I will probably go dressed in a T-shirt and jeans .", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "I guess that you will really be dressing down .", + "emotion": "neutral", + "text": "I guess that you will really be dressing down .", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "That's my style when I'm not in the office .", + "emotion": "neutral", + "text": "That's my style when I'm not in the office .", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "Good point . I suppose that we all have our own individual styles .", + "emotion": "happiness", + "explanation": "the speaker is happy to hear about that A has her own personal style", + "flag": "F", + "expanded emotion cause evidence": [ + 19, + 20 + ], + "expanded emotion cause span": [ + "That's my style when I'm not in the office .", + "Good point . I suppose that we all have our own individual styles ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Good point . I suppose that we all have our own individual styles .", + "id": 20, + "source_sentences": [ + 18 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1655.json b/reccon/sources/tr_1655.json new file mode 100644 index 0000000000000000000000000000000000000000..cc3c2c97991807cc7d1be80e72b9b27b14573247 --- /dev/null +++ b/reccon/sources/tr_1655.json @@ -0,0 +1,124 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey , Tom , I want to learn how to play golf .", + "emotion": "happiness", + "explanation": "Excited about playing golf", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Hey , Tom , I want to learn how to play golf .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "You're really sporty !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I want to learn how to play golf ." + ], + "type": [ + "inter-personal" + ], + "text": "You're really sporty !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I want to do everything I can .", + "emotion": "neutral", + "text": "I want to do everything I can .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Do you have clubs ?", + "emotion": "neutral", + "text": "Do you have clubs ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "No . Can I rent clubs ?", + "emotion": "neutral", + "text": "No . Can I rent clubs ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "There are clubs for beginners . It's cheaper to buy those rather than rent them a few times .", + "emotion": "neutral", + "text": "There are clubs for beginners . It's cheaper to buy those rather than rent them a few times .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "What kinds of clubs ?", + "emotion": "neutral", + "text": "What kinds of clubs ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Like the seven-piece set . It's only $ 120 .", + "emotion": "neutral", + "text": "Like the seven-piece set . It's only $ 120 .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I'll buy a set . But you have to teach me .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "It's only $ 120 ." + ], + "type": [ + "inter-personal" + ], + "text": "I'll buy a set . But you have to teach me .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Okay .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "But you have to teach me ." + ], + "type": [ + "inter-personal" + ], + "text": "Okay .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1656.json b/reccon/sources/tr_1656.json new file mode 100644 index 0000000000000000000000000000000000000000..36b1e17feabd63244e9ce9b960b1159f453a04d2 --- /dev/null +++ b/reccon/sources/tr_1656.json @@ -0,0 +1,144 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "You are married to a foreigner , aren't you ? So what's it like ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "You are married to a foreigner , aren't you ? So what's it like ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Well , in the first year of our marriage , we had great difficulties in getting along . The things that are important to me are not important to him . We had a lot of conflicts .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Well , in the first year of our marriage , we had great difficulties in getting along . The things that are important to me are not important to him . We had a lot of conflicts .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yeah , I know what you mean . The first year of any marriage is difficult for all couples , not to mention two people from different cultures .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Yeah , I know what you mean . The first year of any marriage is difficult for all couples , not to mention two people from different cultures .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Now we have a two-year-old boy . We're very happy that he's healthy and smart .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "We're very happy that he's healthy and smart ." + ], + "type": [ + "no-context" + ], + "text": "Now we have a two-year-old boy . We're very happy that he's healthy and smart .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Oh , so he's half Chinese and half American . That's unusual . What languages does he speak , then ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "We're very happy that he's healthy and smart ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , so he's half Chinese and half American . That's unusual . What languages does he speak , then ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Right now he speaks mostly English , and he can say a few Chinese words . But he will learn in the future .", + "emotion": "happiness", + "explanation": "speaker and listener are happy to discuss attributes of the speaker's son", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "We're very happy that he's healthy and smart ." + ], + "type": [ + "self-contagion" + ], + "text": "Right now he speaks mostly English , and he can say a few Chinese words . But he will learn in the future .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "What does he look like ? Can people tell ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "We're very happy that he's healthy and smart ." + ], + "type": [ + "inter-personal" + ], + "text": "What does he look like ? Can people tell ?", + "id": 7, + "source_sentences": [ + 3 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yes , people surely can . He's whiter than the Chinese kids , and his hair is a little blonde . My husband says his eyes are very Chinese though .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "We're very happy that he's healthy and smart ." + ], + "type": [ + "self-contagion" + ], + "text": "Yes , people surely can . He's whiter than the Chinese kids , and his hair is a little blonde . My husband says his eyes are very Chinese though .", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1661.json b/reccon/sources/tr_1661.json new file mode 100644 index 0000000000000000000000000000000000000000..efdfb2ce279f325f8f693844fd0ac4c33f744924 --- /dev/null +++ b/reccon/sources/tr_1661.json @@ -0,0 +1,295 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey , Shirley . The party has been wonderful . My husband and my children have enjoyed it very much , and me too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "The party has been wonderful . My husband and my children have enjoyed it very much" + ], + "type": [ + "no-context" + ], + "text": "Hey , Shirley . The party has been wonderful . My husband and my children have enjoyed it very much , and me too .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I've said you will enjoy your life here !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "The party has been wonderful . My husband and my children have enjoyed it very much" + ], + "type": [ + "inter-personal" + ], + "text": "I've said you will enjoy your life here !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I surely will . By the way , is the party like this held every weekend in our neighborhood ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "The party has been wonderful . My husband and my children have enjoyed it very much" + ], + "type": [ + "self-contagion" + ], + "text": "I surely will . By the way , is the party like this held every weekend in our neighborhood ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Oh , I've forgotten to tell you . The party is held every other week . And every family gives their own performance each time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 4 + ], + "expanded emotion cause span": [ + "The party has been wonderful . My husband and my children have enjoyed it very much", + "The party is held every other week . And every family gives their own performance each time ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , I've forgotten to tell you . The party is held every other week . And every family gives their own performance each time .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "My children would like that ; they like dancing very much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "Oh , I've forgotten to tell you . The party is held every other week . And every family gives their own performance each time .", + "My children would like that" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "My children would like that ; they like dancing very much .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "That's good !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "My children would like that ; they like dancing very much ." + ], + "type": [ + "inter-personal" + ], + "text": "That's good !", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Look ! Who is that guy on the stage ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Who is that guy on the stage ?" + ], + "type": [ + "no-context" + ], + "text": "Look ! Who is that guy on the stage ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Oh , my God ! That's my husband , Benjamin .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Who is that guy on the stage ?" + ], + "type": [ + "inter-personal" + ], + "text": "Oh , my God ! That's my husband , Benjamin .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Really ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "Who is that guy on the stage ?", + "That's my husband" + ], + "type": [ + "hybrid" + ], + "text": "Really ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "He likes American Idol very much , and he always imitates the contestant at home . I can't believe he got on the stage himself .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7, + 10 + ], + "expanded emotion cause span": [ + "Who is that guy on the stage ?", + "I can't believe he got on the stage himself ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "He likes American Idol very much , and he always imitates the contestant at home . I can't believe he got on the stage himself .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "He performs very well . He is so funny !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "He performs very well . He is so funny !" + ], + "type": [ + "no-context" + ], + "text": "He performs very well . He is so funny !", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "OK , just ignore him . I've noticed there are lots of exercise facilities in our community . After dinner you can go there for a walk with your family !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 10 + ], + "expanded emotion cause span": [ + "Who is that guy on the stage ?", + "I can't believe he got on the stage himself ." + ], + "type": [ + "hybrid" + ], + "text": "OK , just ignore him . I've noticed there are lots of exercise facilities in our community . After dinner you can go there for a walk with your family !", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "OK , that's perfect ! By the way , is there any playground in our neighborhood ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "I've noticed there are lots of exercise facilities in our community . After dinner you can go there for a walk with your family !" + ], + "type": [ + "inter-personal" + ], + "text": "OK , that's perfect ! By the way , is there any playground in our neighborhood ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Yes , there is one behind our building . And you can play tennis there . But if you want to play tennis there , they will change you 30 Yuan per hour .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "there is one behind our building" + ], + "type": [ + "no-context" + ], + "text": "Yes , there is one behind our building . And you can play tennis there . But if you want to play tennis there , they will change you 30 Yuan per hour .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "OK , got it ! Thank you so much . You have helped me a lot !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14, + 15 + ], + "expanded emotion cause span": [ + "there is one behind our building", + "You have helped me a lot !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "OK , got it ! Thank you so much . You have helped me a lot !", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "You are welcome ! We are neighbors !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "OK , got it ! Thank you so much . You have helped me a lot !" + ], + "type": [ + "inter-personal" + ], + "text": "You are welcome ! We are neighbors !", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1664.json b/reccon/sources/tr_1664.json new file mode 100644 index 0000000000000000000000000000000000000000..d794d6d4e9d219f768b88e19b28ad50cc5c8a80b --- /dev/null +++ b/reccon/sources/tr_1664.json @@ -0,0 +1,337 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "You said you like classical music very much . Then who is your favorite opera star ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "You said you like classical music very much . Then who is your favorite opera star ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "There are three of them , the Three Tenors .", + "emotion": "happiness", + "explanation": "Sharing experience", + "expanded emotion cause evidence": [ + "b", + 1, + 2 + ], + "expanded emotion cause span": [ + "b", + "You said you like classical music very much . Then who is your favorite opera star ?", + "There are three of them , the Three Tenors ." + ], + "type": [ + "latent", + "no-context", + "inter-personal" + ], + "text": "There are three of them , the Three Tenors .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Oh , you mean Pavarotti , Domingo and Carreras . Have you been to their live shows ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 2 + ], + "expanded emotion cause span": [ + "b", + "There are three of them , the Three Tenors ." + ], + "type": [ + "latent", + "inter-personal" + ], + "text": "Oh , you mean Pavarotti , Domingo and Carreras . Have you been to their live shows ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yeah , it's really a unique experience . It's a solo concert by Pavarotti . He put on the performance in the Forbidden City in Beijing .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 1, + 2, + 4 + ], + "expanded emotion cause span": [ + "b", + "You said you like classical music very much . Then who is your favorite opera star ?", + "There are three of them , the Three Tenors .", + "it's really a unique experience ." + ], + "type": [ + "latent", + "no-context", + "hybrid" + ], + "text": "Yeah , it's really a unique experience . It's a solo concert by Pavarotti . He put on the performance in the Forbidden City in Beijing .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I've heard of that one . It was also his swan song .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "it's really a unique experience ." + ], + "type": [ + "inter-personal" + ], + "text": "I've heard of that one . It was also his swan song .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Besides , speaking of classical music , we should never forget about the New Year's Concert .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 1, + 2, + 4, + 6 + ], + "expanded emotion cause span": [ + "b", + "You said you like classical music very much . Then who is your favorite opera star ?", + "There are three of them , the Three Tenors .", + "it's really a unique experience .", + "New Year's Concert" + ], + "type": [ + "latent", + "no-context", + "hybrid" + ], + "text": "Besides , speaking of classical music , we should never forget about the New Year's Concert .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Of course not . People all over the world watch it on TV , or listen to it on the radio .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "New Year's Concert" + ], + "type": [ + "inter-personal" + ], + "text": "Of course not . People all over the world watch it on TV , or listen to it on the radio .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Sure . It's undoubtedly one of the biggest classical music events . Have you ever been to the live show ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "New Year's Concert" + ], + "type": [ + "self-contagion" + ], + "text": "Sure . It's undoubtedly one of the biggest classical music events . Have you ever been to the live show ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yes , I went to the New Year's Concert in 2005 .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 9 + ], + "expanded emotion cause span": [ + "New Year's Concert", + "I went to the New Year's Concert in 2005 ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , I went to the New Year's Concert in 2005 .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Wow , you are so lucky . I saw that one on TV . But it must be so different to be there in the concert hall .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Yes , I went to the New Year's Concert in 2005 ." + ], + "type": [ + "inter-personal" + ], + "text": "Wow , you are so lucky . I saw that one on TV . But it must be so different to be there in the concert hall .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "That's for sure . You know , it's really amazing to be in the best concert hall , listening to the performance by the best orchestra . I had the greatest time ever .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 9, + 11 + ], + "expanded emotion cause span": [ + "New Year's Concert", + "I went to the New Year's Concert in 2005 .", + "it's really amazing to be in the best concert hall , listening to the performance by the best orchestra . I had the greatest time ever ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "That's for sure . You know , it's really amazing to be in the best concert hall , listening to the performance by the best orchestra . I had the greatest time ever .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Who was the conductor at that event ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 11 + ], + "expanded emotion cause span": [ + "Yes , I went to the New Year's Concert in 2005 .", + "it's really amazing to be in the best concert hall , listening to the performance by the best orchestra . I had the greatest time ever ." + ], + "type": [ + "inter-personal" + ], + "text": "Who was the conductor at that event ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Lorin Maazel . He did an amazing job . Moreover , he just celebrated his 75th birthday .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 9, + 11, + 13 + ], + "expanded emotion cause span": [ + "New Year's Concert", + "I went to the New Year's Concert in 2005 .", + "it's really amazing to be in the best concert hall , listening to the performance by the best orchestra . I had the greatest time ever .", + "He did an amazing job ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Lorin Maazel . He did an amazing job . Moreover , he just celebrated his 75th birthday .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "So cool . I wish I can go to the live New Year's Concert someday in the future .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 11, + 13 + ], + "expanded emotion cause span": [ + "Yes , I went to the New Year's Concert in 2005 .", + "it's really amazing to be in the best concert hall , listening to the performance by the best orchestra . I had the greatest time ever .", + "Lorin Maazel . He did an amazing job ." + ], + "type": [ + "inter-personal" + ], + "text": "So cool . I wish I can go to the live New Year's Concert someday in the future .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "The right opportunity for you would come along soon . You know , music is transnational .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 9, + 11, + 13 + ], + "expanded emotion cause span": [ + "New Year's Concert", + "I went to the New Year's Concert in 2005 .", + "it's really amazing to be in the best concert hall , listening to the performance by the best orchestra . I had the greatest time ever .", + "He did an amazing job ." + ], + "type": [ + "hybrid" + ], + "text": "The right opportunity for you would come along soon . You know , music is transnational .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "I believe in that . Well , the performance is about to begin . Let's be quiet .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15, + 16 + ], + "expanded emotion cause span": [ + "The right opportunity for you would come along soon .", + "the performance is about to begin" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I believe in that . Well , the performance is about to begin . Let's be quiet .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1675.json b/reccon/sources/tr_1675.json new file mode 100644 index 0000000000000000000000000000000000000000..ed67c8c26cd3c716de3079817aee43e0e9cb889d --- /dev/null +++ b/reccon/sources/tr_1675.json @@ -0,0 +1,200 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I want to say ...", + "emotion": "neutral", + "text": "I want to say ...", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Say it ! What is it ?", + "emotion": "neutral", + "text": "Say it ! What is it ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "That I can't go on any longer without you .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I can't go on any longer without you ." + ], + "type": [ + "no-context" + ], + "text": "That I can't go on any longer without you .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "You know you shouldn't say that at a time like this .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "I can't go on any longer without you .", + "you shouldn't say that at a time like this ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You know you shouldn't say that at a time like this .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Nancy , I made up my mind you were the only woman for me at the first sight .", + "emotion": "neutral", + "text": "Nancy , I made up my mind you were the only woman for me at the first sight .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Too sudden ! I'm not ready for it .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3, + 4, + 5, + 6 + ], + "expanded emotion cause span": [ + "I can't go on any longer without you .", + "you shouldn't say that at a time like this .", + "you were the only woman for me at the first sight .", + "Too sudden !" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Too sudden ! I'm not ready for it .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Forgive me for startling you with the impetuosity of my sentiments .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I'm not ready for it .", + "Forgive me for startling you" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Forgive me for startling you with the impetuosity of my sentiments .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Stop it . No more of that talk .", + "emotion": "neutral", + "text": "Stop it . No more of that talk .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I really love you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "I really love you ." + ], + "type": [ + "no-context" + ], + "text": "I really love you .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "No , I shall faint .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3, + 4, + 5, + 6, + 9 + ], + "expanded emotion cause span": [ + "I can't go on any longer without you .", + "you shouldn't say that at a time like this .", + "you were the only woman for me at the first sight .", + "Too sudden !", + "I really love you ." + ], + "type": [ + "hybrid" + ], + "text": "No , I shall faint .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "And I hope so . This is what you were meant for . Say you love me , say yes , say yes .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "I shall faint .", + "This is what you were meant for ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "And I hope so . This is what you were meant for . Say you love me , say yes , say yes .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Yes .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "This is what you were meant for . Say you love me , say yes , say yes ." + ], + "type": [ + "inter-personal" + ], + "text": "Yes .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1677.json b/reccon/sources/tr_1677.json new file mode 100644 index 0000000000000000000000000000000000000000..f99889ece60ca2add18161be7330c4496177c8ad --- /dev/null +++ b/reccon/sources/tr_1677.json @@ -0,0 +1,143 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Your knowledge of English is really surprising .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Your knowledge of English is really surprising ." + ], + "type": [ + "no-context" + ], + "text": "Your knowledge of English is really surprising .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh , it's nothing to speak of .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Your knowledge of English is really surprising ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , it's nothing to speak of .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "No , seriously . I am impressed .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I am impressed ." + ], + "type": [ + "no-context" + ], + "text": "No , seriously . I am impressed .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Thank you . I appreciate the compliment .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I am impressed ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . I appreciate the compliment .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Your knowledge of English is really surprising .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Your knowledge of English is really surprising ." + ], + "type": [ + "self-contagion" + ], + "text": "Your knowledge of English is really surprising .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Oh , it's nothing to speak of .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Your knowledge of English is really surprising ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , it's nothing to speak of .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "No , seriously . I am impressed .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I am impressed ." + ], + "type": [ + "self-contagion" + ], + "text": "No , seriously . I am impressed .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Thank you . I appreciate the compliment .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I am impressed ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . I appreciate the compliment .", + "id": 8, + "source_sentences": [ + 2 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1686.json b/reccon/sources/tr_1686.json new file mode 100644 index 0000000000000000000000000000000000000000..da3b377f5f41457a954c91112c85a4248304d515 --- /dev/null +++ b/reccon/sources/tr_1686.json @@ -0,0 +1,162 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Are you going to the movie theater with me tonight ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "movie theater with me tonight ?" + ], + "type": [ + "no-context" + ], + "text": "Are you going to the movie theater with me tonight ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Is there anything good playing ?", + "emotion": "neutral", + "text": "Is there anything good playing ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Titanic is playing tonight . It's a blockbuster .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Titanic is playing tonight . It's a blockbuster ." + ], + "type": [ + "no-context" + ], + "text": "Titanic is playing tonight . It's a blockbuster .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Really ? I want to go , too .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Titanic is playing tonight . It's a blockbuster ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? I want to go , too .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "OK , let's meet at the movie theater entrance tonight . Don ' t be late .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I want to go , too ." + ], + "type": [ + "inter-personal" + ], + "text": "OK , let's meet at the movie theater entrance tonight . Don ' t be late .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "No problem .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 5 + ], + "expanded emotion cause span": [ + "Titanic is playing tonight . It's a blockbuster .", + "let's meet at the movie theater entrance tonight ." + ], + "type": [ + "inter-personal" + ], + "text": "No problem .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "( After watching the movie . ) Are you crying ?", + "emotion": "neutral", + "text": "( After watching the movie . ) Are you crying ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I get a lump in my throat whenever I see a tragic movie .", + "emotion": "neutral", + "text": "I get a lump in my throat whenever I see a tragic movie .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Tragic movie ? I think it's a love story .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "I get a lump in my throat whenever I see a tragic movie .", + "I think it's a love story ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Tragic movie ? I think it's a love story .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "But their love is touching !", + "emotion": "neutral", + "text": "But their love is touching !", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Ah , you're just too emotional .", + "emotion": "neutral", + "text": "Ah , you're just too emotional .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I am not !", + "emotion": "neutral", + "text": "I am not !", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1688.json b/reccon/sources/tr_1688.json new file mode 100644 index 0000000000000000000000000000000000000000..cecee410f7f16c6ef0b858d677f1b0fd029b2e9f --- /dev/null +++ b/reccon/sources/tr_1688.json @@ -0,0 +1,131 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I couldn't look at you , and say you aren't beautiful !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I couldn't look at you , and say you aren't beautiful !" + ], + "type": [ + "no-context" + ], + "text": "I couldn't look at you , and say you aren't beautiful !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "You are pretending !", + "emotion": "happiness", + "explanation": "Flirtery", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I couldn't look at you , and say you aren't beautiful !" + ], + "type": [ + "inter-personal" + ], + "text": "You are pretending !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "No , Miss Anna , you must let me say how lovely you are ! What's wrong with that ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I couldn't look at you , and say you aren't beautiful !" + ], + "type": [ + "self-contagion" + ], + "text": "No , Miss Anna , you must let me say how lovely you are ! What's wrong with that ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It's wrong because---it isn't true .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I couldn't look at you , and say you aren't beautiful !" + ], + "type": [ + "inter-personal" + ], + "text": "It's wrong because---it isn't true .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "You know that everybody notices how beautiful you are , don't you ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 5 + ], + "expanded emotion cause span": [ + "I couldn't look at you , and say you aren't beautiful !", + "how beautiful you are" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "You know that everybody notices how beautiful you are , don't you ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Well , no-that is , I've heard Linda say they do , but ... Thank you . But please don't speak to me again .", + "emotion": "disgust", + "explanation": "Tired of constant flirting by the other speaker.", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "please don't speak to me again ." + ], + "type": [ + "no-context" + ], + "text": "Well , no-that is , I've heard Linda say they do , but ... Thank you . But please don't speak to me again .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Oh , Miss Anna ! That's too hard ! I won't be here long .", + "emotion": "sad", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "But please don't speak to me again ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , Miss Anna ! That's too hard ! I won't be here long .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1693.json b/reccon/sources/tr_1693.json new file mode 100644 index 0000000000000000000000000000000000000000..86d4955d1077668413538e3728d340596cfa6193 --- /dev/null +++ b/reccon/sources/tr_1693.json @@ -0,0 +1,210 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Will you be done doing my hair soon ?", + "emotion": "neutral", + "text": "Will you be done doing my hair soon ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Give me a little while longer .", + "emotion": "neutral", + "text": "Give me a little while longer .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "How much time do you need ?", + "emotion": "neutral", + "text": "How much time do you need ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "There you go . How do you like it ?", + "emotion": "happiness", + "explanation": "the speaker is happy to have finished his/her job", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "There you go ." + ], + "type": [ + "no-context" + ], + "text": "There you go . How do you like it ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I think it looks gorgeous .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I think it looks gorgeous ." + ], + "type": [ + "no-context" + ], + "text": "I think it looks gorgeous .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "You think it looks nice ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I think it looks gorgeous ." + ], + "type": [ + "inter-personal" + ], + "text": "You think it looks nice ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I honestly think it looks great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 7 + ], + "expanded emotion cause span": [ + "I think it looks gorgeous .", + "I honestly think it looks great ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I honestly think it looks great .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Thanks . I'm glad that I did a good job .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 7, + 8 + ], + "expanded emotion cause span": [ + "I think it looks gorgeous .", + "I honestly think it looks great .", + "I did a good job ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thanks . I'm glad that I did a good job .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "How much is it for my hair ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 7 + ], + "expanded emotion cause span": [ + "I think it looks gorgeous .", + "I honestly think it looks great ." + ], + "type": [ + "self-contagion" + ], + "text": "How much is it for my hair ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Just give me $ 55 .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 7, + 8 + ], + "expanded emotion cause span": [ + "I think it looks gorgeous .", + "I honestly think it looks great .", + "I did a good job ." + ], + "type": [ + "hybrid" + ], + "text": "Just give me $ 55 .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Thanks for doing such a good job .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 7, + 11 + ], + "expanded emotion cause span": [ + "I think it looks gorgeous .", + "I honestly think it looks great .", + "Thanks for doing such a good job ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Thanks for doing such a good job .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "No problem , girl friend . I'll see you next time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 7, + 11 + ], + "expanded emotion cause span": [ + "I think it looks gorgeous .", + "I honestly think it looks great .", + "Thanks for doing such a good job ." + ], + "type": [ + "inter-personal" + ], + "text": "No problem , girl friend . I'll see you next time .", + "id": 12, + "source_sentences": [ + 4, + 6, + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1703.json b/reccon/sources/tr_1703.json new file mode 100644 index 0000000000000000000000000000000000000000..984dc07a5e4b14d20d092b3d46603c2a2a00ca30 --- /dev/null +++ b/reccon/sources/tr_1703.json @@ -0,0 +1,166 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello , Tom . How do you find the dinner of yesterday ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "How do you find the dinner of yesterday ?" + ], + "type": [ + "no-context" + ], + "text": "Hello , Tom . How do you find the dinner of yesterday ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Very good . That may be the most delicious food I have ever eaten .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "That may be the most delicious food I have ever eaten ." + ], + "type": [ + "no-context" + ], + "text": "Very good . That may be the most delicious food I have ever eaten .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "It's nice of you to say so .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Very good . That may be the most delicious food I have ever eaten ." + ], + "type": [ + "inter-personal" + ], + "text": "It's nice of you to say so .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I really appreciate you for having invited me .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I really appreciate you for having invited me ." + ], + "type": [ + "no-context" + ], + "text": "I really appreciate you for having invited me .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Don't mention it . You know , we ' re old friends .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I really appreciate you for having invited me ." + ], + "type": [ + "inter-personal" + ], + "text": "Don't mention it . You know , we ' re old friends .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Anyway , I owe you one . Are you free tonight ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I really appreciate you for having invited me ." + ], + "type": [ + "self-contagion" + ], + "text": "Anyway , I owe you one . Are you free tonight ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yes . Why ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Anyway , I owe you one . Are you free tonight ?" + ], + "type": [ + "inter-personal" + ], + "text": "Yes . Why ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I want to invite you to enjoy the food I cook .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 8 + ], + "expanded emotion cause span": [ + "I really appreciate you for having invited me .", + "I want to invite you to enjoy the food I cook ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I want to invite you to enjoy the food I cook .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "That ' s great . I'd love to .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "I want to invite you to enjoy the food I cook .", + "I'd love to ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That ' s great . I'd love to .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1711.json b/reccon/sources/tr_1711.json new file mode 100644 index 0000000000000000000000000000000000000000..ce85ef654797b2072351747f80caac02478fc89a --- /dev/null +++ b/reccon/sources/tr_1711.json @@ -0,0 +1,236 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Are you ready to go the concert ?", + "emotion": "neutral", + "text": "Are you ready to go the concert ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes . Should we go there by bus so we aren't late ?", + "emotion": "neutral", + "text": "Yes . Should we go there by bus so we aren't late ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Actually , why don't we go there by bike ? We could get stuck in traffic if we travel by bus in rush hour .", + "emotion": "happiness", + "explanation": "Speaker is happy to travel by bike", + "flag": "F", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Actually , why don't we go there by bike ?" + ], + "type": [ + "no-context" + ], + "text": "Actually , why don't we go there by bike ? We could get stuck in traffic if we travel by bus in rush hour .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "That's true . Cycling is good for our environment , too . Let me just get my helmet then .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "Actually , why don't we go there by bike ?", + "Cycling is good for our environment , too ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's true . Cycling is good for our environment , too . Let me just get my helmet then .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Is your helmet comfortable ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Actually , why don't we go there by bike ?" + ], + "type": [ + "self-contagion" + ], + "text": "Is your helmet comfortable ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Not really , but I liked the design , so I got it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I liked the design ," + ], + "type": [ + "no-context" + ], + "text": "Not really , but I liked the design , so I got it .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Maybe you should think about getting a round helmet ; they're better .", + "emotion": "happiness", + "explanation": "speaker feels comfortable in round helmet", + "flag": "F", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "you should think about getting a round helmet ; they're better ." + ], + "type": [ + "no-context" + ], + "text": "Maybe you should think about getting a round helmet ; they're better .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I'll think about it .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "you should think about getting a round helmet ; they're better ." + ], + "type": [ + "inter-personal" + ], + "text": "I'll think about it .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Is that your new bicycle ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Is that your new bicycle ?" + ], + "type": [ + "no-context" + ], + "text": "Is that your new bicycle ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Yes , my father gave it to me for my birthday . Do you like it ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "Is that your new bicycle ?", + "my father gave it to me for my birthday ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , my father gave it to me for my birthday . Do you like it ?", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 11, + "speaker": "A", + "utterance": "It's the newest 10 speed cycling mountain bike . These are really expensive !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "It's the newest 10 speed cycling mountain bike ." + ], + "type": [ + "no-context" + ], + "text": "It's the newest 10 speed cycling mountain bike . These are really expensive !", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Nothing but the best from my dad . I like everything about it except for the brakes . They are a bit sticky .", + "emotion": "neutral", + "text": "Nothing but the best from my dad . I like everything about it except for the brakes . They are a bit sticky .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I can fix those for you . Is there anything else wrong with it ?", + "emotion": "neutral", + "text": "I can fix those for you . Is there anything else wrong with it ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Well , my saddle is too low for me . Do you know how to change the height ?", + "emotion": "neutral", + "text": "Well , my saddle is too low for me . Do you know how to change the height ?", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "That's easy . It's important to have the saddle high enough so that your legs can extend fully when you are on your bicycle .", + "emotion": "neutral", + "text": "That's easy . It's important to have the saddle high enough so that your legs can extend fully when you are on your bicycle .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Is that why my knees have felt sore after every time I've ridden my bike ?", + "emotion": "neutral", + "text": "Is that why my knees have felt sore after every time I've ridden my bike ?", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "It's possible . Give me a minute and I can fix these for you and then we can go .", + "emotion": "neutral", + "text": "It's possible . Give me a minute and I can fix these for you and then we can go .", + "id": 17 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1712.json b/reccon/sources/tr_1712.json new file mode 100644 index 0000000000000000000000000000000000000000..8a1bd57e8e4bdb4597c88a80094783f58458fa23 --- /dev/null +++ b/reccon/sources/tr_1712.json @@ -0,0 +1,134 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Oh , God . It ' s late . I ' m afraid I have to leave .", + "emotion": "fear", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Oh , God . It ' s late ." + ], + "type": [ + "no-context" + ], + "text": "Oh , God . It ' s late . I ' m afraid I have to leave .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "But you just got here . Can ' t you stay a little longer and have some tea ?", + "emotion": "neutral", + "text": "But you just got here . Can ' t you stay a little longer and have some tea ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "That ' s very kind of you . But if I don ' t go now I ' ll miss the last bus .", + "emotion": "neutral", + "text": "That ' s very kind of you . But if I don ' t go now I ' ll miss the last bus .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "That ' s too bad .", + "emotion": "neutral", + "text": "That ' s too bad .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Thank you for your hospitality .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Thank you for your hospitality ." + ], + "type": [ + "no-context" + ], + "text": "Thank you for your hospitality .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Thanks for coming .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Thank you for your hospitality .", + "Thanks for coming ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thanks for coming .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "How about next time we meet at my place ? And I ' ll treat you to Chinese food . I know how much you like it . We can order in and watch video too . Anything you like , I promise .", + "emotion": "neutral", + "text": "How about next time we meet at my place ? And I ' ll treat you to Chinese food . I know how much you like it . We can order in and watch video too . Anything you like , I promise .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Great idea . I ' m looking forward to it . See you then .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "How about next time we meet at my place ? And I ' ll treat you to Chinese food . I know how much you like it . We can order in and watch video too . Anything you like , I promise ." + ], + "type": [ + "inter-personal" + ], + "text": "Great idea . I ' m looking forward to it . See you then .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Well . I really do have to go .", + "emotion": "neutral", + "text": "Well . I really do have to go .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Good night then .", + "emotion": "neutral", + "text": "Good night then .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "See you tomorrow .", + "emotion": "neutral", + "text": "See you tomorrow .", + "id": 11 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1716.json b/reccon/sources/tr_1716.json new file mode 100644 index 0000000000000000000000000000000000000000..99b9face67964ecbc192663d77dfb536349fdf81 --- /dev/null +++ b/reccon/sources/tr_1716.json @@ -0,0 +1,179 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "this party rocks !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "this party rocks !" + ], + "type": [ + "no-context" + ], + "text": "this party rocks !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "you said it . Good beer , good music , and on top of that , there are so many hot girls here !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "this party rocks !", + "Good beer , good music , and on top of that , there are so many hot girls here !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "you said it . Good beer , good music , and on top of that , there are so many hot girls here !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I'm with you on that . Check out that one over there . I think I'm in love !", + "emotion": "neutral", + "text": "I'm with you on that . Check out that one over there . I think I'm in love !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "well , she's alright , but not really my cup of tea . What about the blond with the red dress ?", + "emotion": "neutral", + "text": "well , she's alright , but not really my cup of tea . What about the blond with the red dress ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "oh , that's Janice . She's just new in town . You have a thing for blonds , eh ?", + "emotion": "neutral", + "text": "oh , that's Janice . She's just new in town . You have a thing for blonds , eh ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "yeah ! She could do anything she wants to me !", + "emotion": "neutral", + "text": "yeah ! She could do anything she wants to me !", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I bet . Why not go over and talk to her ? She's really nice .", + "emotion": "neutral", + "text": "I bet . Why not go over and talk to her ? She's really nice .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I don't think so . I get so nervous talking to girls . I always put my foot in my mouth , scare her off , and end up looking like a real fool . Besides , she is way out of my league .", + "emotion": "neutral", + "text": "I don't think so . I get so nervous talking to girls . I always put my foot in my mouth , scare her off , and end up looking like a real fool . Besides , she is way out of my league .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "come on ! Man up ! You'll never know until you try .", + "emotion": "neutral", + "text": "come on ! Man up ! You'll never know until you try .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "okay okay , just let me have another cup of beers to get my head in the game .", + "emotion": "neutral", + "text": "okay okay , just let me have another cup of beers to get my head in the game .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "all right . But I think you ought to move soon .", + "emotion": "neutral", + "text": "all right . But I think you ought to move soon .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "why ?", + "emotion": "neutral", + "text": "why ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I can see five other guys eying her up .", + "emotion": "neutral", + "text": "I can see five other guys eying her up .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "okay , here I go !", + "emotion": "happiness", + "explanation": "speaker is happy to talk to the girl", + "expanded emotion cause evidence": [ + 4, + 6, + 14 + ], + "expanded emotion cause span": [ + "the blond with the red dress ?", + "She could do anything she wants to me !", + "here I go !" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "okay , here I go !", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "good luck !", + "emotion": "happiness", + "explanation": "speaker is happy to see B getting the courage to make a move", + "expanded emotion cause evidence": [ + 4, + 6, + 14 + ], + "expanded emotion cause span": [ + "the blond with the red dress ?", + "She could do anything she wants to me !", + "here I go !" + ], + "type": [ + "inter-personal" + ], + "text": "good luck !", + "id": 15, + "source_sentences": [ + 3, + 5, + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1719.json b/reccon/sources/tr_1719.json new file mode 100644 index 0000000000000000000000000000000000000000..9f556342977d8069262fe94b9cdce38249a1cdc1 --- /dev/null +++ b/reccon/sources/tr_1719.json @@ -0,0 +1,135 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello ! So you are leaving today .", + "emotion": "neutral", + "text": "Hello ! So you are leaving today .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hello . Thank you for seeing me off . You actually don't need to bother .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Thank you for seeing me off ." + ], + "type": [ + "no-context" + ], + "text": "Hello . Thank you for seeing me off . You actually don't need to bother .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "It is my pleasure to see you off .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "Thank you for seeing me off .", + "my pleasure" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It is my pleasure to see you off .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Thanks a lot . I hope to see you again .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 4 + ], + "expanded emotion cause span": [ + "Thank you for seeing me off .", + "I hope to see you again ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Thanks a lot . I hope to see you again .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I hope so , too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 4, + 4, + 5 + ], + "expanded emotion cause span": [ + "Thank you for seeing me off .", + "I hope to see you again .", + "I hope to see you again .", + "I hope so , too ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I hope so , too .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Thanks again for everything you have done for me .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 4, + 6 + ], + "expanded emotion cause span": [ + "Thank you for seeing me off .", + "I hope to see you again .", + "Thanks again for everything you have done for me ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Thanks again for everything you have done for me .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You're welcome . Have a nice trip !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Thanks again for everything you have done for me ." + ], + "type": [ + "inter-personal" + ], + "text": "You're welcome . Have a nice trip !", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1725.json b/reccon/sources/tr_1725.json new file mode 100644 index 0000000000000000000000000000000000000000..52f0d75170ff1c048a8fc88933b1cbb0d7cb9f5f --- /dev/null +++ b/reccon/sources/tr_1725.json @@ -0,0 +1,199 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What date is it today ?", + "emotion": "neutral", + "text": "What date is it today ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Why ?", + "emotion": "neutral", + "text": "Why ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Look at the girls in the street . They all have a bunch of flowers . Is it Valentine's Day ?", + "emotion": "neutral", + "text": "Look at the girls in the street . They all have a bunch of flowers . Is it Valentine's Day ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Oh , yes ! I completely forgot about it .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "Valentine's Day ?", + "I completely forgot about it ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , yes ! I completely forgot about it .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Did you have a fight with Jack ?", + "emotion": "neutral", + "text": "Did you have a fight with Jack ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "No , but now he'll be in trouble . What's a boyfriend for ? To forget about Valentine's Day ?", + "emotion": "anger", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "What's a boyfriend for ? To forget about Valentine's Day ?" + ], + "type": [ + "no-context" + ], + "text": "No , but now he'll be in trouble . What's a boyfriend for ? To forget about Valentine's Day ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Come on , dear ! You forgot it , too .", + "emotion": "neutral", + "text": "Come on , dear ! You forgot it , too .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "You know , it's OK for a girl to forget these \" big days \" , but for a guy , to do that is unforgivable .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 6, + 8 + ], + "expanded emotion cause span": [ + "What's a boyfriend for ? To forget about Valentine's Day ?", + "but for a guy , to do that is unforgivable ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "You know , it's OK for a girl to forget these \" big days \" , but for a guy , to do that is unforgivable .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Is that your phone ?", + "emotion": "neutral", + "text": "Is that your phone ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Oh , it's Jack . Excuse me .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 6, + 8, + 10 + ], + "expanded emotion cause span": [ + "Valentine's Day ?", + "What's a boyfriend for ? To forget about Valentine's Day ?", + "but for a guy , to do that is unforgivable .", + "it's Jack ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Oh , it's Jack . Excuse me .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Wow ! Good timing .", + "emotion": "neutral", + "text": "Wow ! Good timing .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "He asked me out to a dinner tonight . How about joining us ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 12 + ], + "expanded emotion cause span": [ + "Valentine's Day ?", + "He asked me out to a dinner tonight ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "He asked me out to a dinner tonight . How about joining us ?", + "id": 12, + "source_sentences": [ + 2 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Come on ! Three's a crowd !", + "emotion": "neutral", + "text": "Come on ! Three's a crowd !", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "So what ?", + "emotion": "neutral", + "text": "So what ?", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Just go ! It's Valentine's Day !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 12 + ], + "expanded emotion cause span": [ + "Valentine's Day ?", + "He asked me out to a dinner tonight . How about joining us ?" + ], + "type": [ + "hybrid" + ], + "text": "Just go ! It's Valentine's Day !", + "id": 15 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1730.json b/reccon/sources/tr_1730.json new file mode 100644 index 0000000000000000000000000000000000000000..244816ed6428d528e5203005d9d13e72e4dc25a3 --- /dev/null +++ b/reccon/sources/tr_1730.json @@ -0,0 +1,150 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What's your favorite book ?", + "emotion": "neutral", + "text": "What's your favorite book ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It's Gone With the Wind .", + "emotion": "neutral", + "text": "It's Gone With the Wind .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Why do you like it best ?", + "emotion": "neutral", + "text": "Why do you like it best ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I enjoy the various characters and the plot .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I enjoy the various characters and the plot ." + ], + "type": [ + "no-context" + ], + "text": "I enjoy the various characters and the plot .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Well . I like the Thom Birds best .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I like the Thom Birds best ." + ], + "type": [ + "no-context" + ], + "text": "Well . I like the Thom Birds best .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Is it very interesting ?", + "emotion": "neutral", + "text": "Is it very interesting ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Sure . I like the writer's language , too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 7 + ], + "expanded emotion cause span": [ + "I like the Thom Birds best .", + "like the writer's language , too ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Sure . I like the writer's language , too .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "If I have a chance , I'll enjoy the book .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "I like the writer's language", + "I'll enjoy the book ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "If I have a chance , I'll enjoy the book .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Would you like to go to the bookshop with me ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Would you like to go to the bookshop with me ?" + ], + "type": [ + "no-context" + ], + "text": "Would you like to go to the bookshop with me ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "That's a good idea . Let ' s go !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "Would you like to go to the bookshop with me ?", + "That's a good idea ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's a good idea . Let ' s go !", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1734.json b/reccon/sources/tr_1734.json new file mode 100644 index 0000000000000000000000000000000000000000..8dd0da0ddf294d1f2d95f696142d33fdfe793e92 --- /dev/null +++ b/reccon/sources/tr_1734.json @@ -0,0 +1,200 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "London is such a historical city ! There ' s history everywhere you look . There ' s nelson ' s column , built as a monument to one of the Britain ' s great admirals and his important victory . He won the battle of Trafalgar in 1805 .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "London is such a historical city ! There ' s history everywhere you look ." + ], + "type": [ + "no-context" + ], + "text": "London is such a historical city ! There ' s history everywhere you look . There ' s nelson ' s column , built as a monument to one of the Britain ' s great admirals and his important victory . He won the battle of Trafalgar in 1805 .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I ' m looking forward to seeing Westminster abbey , where many historical figures are buried , like Isaac Newton , the great mathematician and Winston Churchill , the great wartime leader .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I ' m looking forward to seeing Westminster abbey , where many historical figures are buried , like Isaac Newton , the great mathematician and Winston Churchill , the great wartime leader ." + ], + "type": [ + "no-context" + ], + "text": "I ' m looking forward to seeing Westminster abbey , where many historical figures are buried , like Isaac Newton , the great mathematician and Winston Churchill , the great wartime leader .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Nearby , on the banks of the thames , there ' s the statue of Boadicea . She fought the Romans when they invaded Britain .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Nearby , on the banks of the thames , there ' s the statue of Boadicea" + ], + "type": [ + "no-context" + ], + "text": "Nearby , on the banks of the thames , there ' s the statue of Boadicea . She fought the Romans when they invaded Britain .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Women have often played an important role in British history . Queen Elizabeth I built a navy strong enough to fight off the Spanish armada in 1588 . more recently , Margaret thatcher transformed british society in the 1980 ' s .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "She fought the Romans when they invaded Britain .", + "Women have often played an important role in British history . Queen Elizabeth I built a navy strong enough to fight off the Spanish armada in 1588 . more recently , Margaret thatcher transformed british society in the 1980 ' s ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Women have often played an important role in British history . Queen Elizabeth I built a navy strong enough to fight off the Spanish armada in 1588 . more recently , Margaret thatcher transformed british society in the 1980 ' s .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "She was a very controversial leader . Are we going to visit the famous tower of London later ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Are we going to visit the famous tower of London later ?" + ], + "type": [ + "no-context" + ], + "text": "She was a very controversial leader . Are we going to visit the famous tower of London later ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "There ' s a lot to see there . Perhaps we should go tomorrow .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "There ' s a lot to see there . Perhaps we should go tomorrow ." + ], + "type": [ + "no-context" + ], + "text": "There ' s a lot to see there . Perhaps we should go tomorrow .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I ' m looking forward to seeing the famous castle and prison . Many historic figures were imprisoned there in the past . I really want to see the crown jewels too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I ' m looking forward to seeing the famous castle and prison . Many historic figures were imprisoned there in the past . I really want to see the crown jewels too ." + ], + "type": [ + "no-context" + ], + "text": "I ' m looking forward to seeing the famous castle and prison . Many historic figures were imprisoned there in the past . I really want to see the crown jewels too .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I ' Ve seen them before . They ' re quite incredible . If you want to see historical figures in London , there ' s one place you have to go .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I ' Ve seen them before . They ' re quite incredible ." + ], + "type": [ + "no-context" + ], + "text": "I ' Ve seen them before . They ' re quite incredible . If you want to see historical figures in London , there ' s one place you have to go .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Where ' s that ? Oh , I know ! Madame Tussaud ' s the waxworks museum .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "If you want to see historical figures in London , there ' s one place you have to go ." + ], + "type": [ + "inter-personal" + ], + "text": "Where ' s that ? Oh , I know ! Madame Tussaud ' s the waxworks museum .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "There you can see british leaders , entertainers , criminals , and royalty .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 10 + ], + "expanded emotion cause span": [ + "If you want to see historical figures in London , there ' s one place you have to go .", + "There you can see british leaders , entertainers , criminals , and royalty ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "There you can see british leaders , entertainers , criminals , and royalty .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Sometimes , it ' s hard to know who belongs in each section of the museum !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "There you can see british leaders , entertainers , criminals , and royalty ." + ], + "type": [ + "inter-personal" + ], + "text": "Sometimes , it ' s hard to know who belongs in each section of the museum !", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1735.json b/reccon/sources/tr_1735.json new file mode 100644 index 0000000000000000000000000000000000000000..772f4f7baf1ab06d0eb67cd5961ce35cd8606a60 --- /dev/null +++ b/reccon/sources/tr_1735.json @@ -0,0 +1,172 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "so , how should we go to the theatre ?", + "emotion": "neutral", + "text": "so , how should we go to the theatre ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "let's take the bus .", + "emotion": "neutral", + "text": "let's take the bus .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I hate the bus system in London ! The bus drivers are rude , the buses are never on time , and there are few people around who can help you .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "The bus drivers are rude , the buses are never on time , and there are few people around who can help you ." + ], + "type": [ + "no-context" + ], + "text": "I hate the bus system in London ! The bus drivers are rude , the buses are never on time , and there are few people around who can help you .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "it's not that bad . You probably just had a bad experience once .", + "emotion": "neutral", + "text": "it's not that bad . You probably just had a bad experience once .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "it wasn't just once . Every single time I take the bus , something bad happens to me or to someone else on the bus .", + "emotion": "neutral", + "text": "it wasn't just once . Every single time I take the bus , something bad happens to me or to someone else on the bus .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "we could take the subway , but we'd have to go three stops along one line and then change trains twice .", + "emotion": "neutral", + "text": "we could take the subway , but we'd have to go three stops along one line and then change trains twice .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "train fares are twice as expensive as the bus fare , too .", + "emotion": "neutral", + "text": "train fares are twice as expensive as the bus fare , too .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "if we don't hurry up , we'll miss the show . Should we take the bus ?", + "emotion": "neutral", + "text": "if we don't hurry up , we'll miss the show . Should we take the bus ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "we're already late , so I think we had better take a taxi .", + "emotion": "neutral", + "text": "we're already late , so I think we had better take a taxi .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I don't think we'll be able to find a taxi very easily during hush hours . Let's just take the bus .", + "emotion": "neutral", + "text": "I don't think we'll be able to find a taxi very easily during hush hours . Let's just take the bus .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "fine . Have a look at the timetable to find out when the next one arrives .", + "emotion": "neutral", + "text": "fine . Have a look at the timetable to find out when the next one arrives .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "it looks like it should be here in just a few minutes .", + "emotion": "neutral", + "text": "it looks like it should be here in just a few minutes .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "don't worry . Nothing bad will happen . I'll even buy your ticket for you .", + "emotion": "happiness", + "explanation": "Assuring, Eager to help", + "expanded emotion cause evidence": [ + "b", + 13 + ], + "expanded emotion cause span": [ + "b", + "Nothing bad will happen . I'll even buy your ticket for you ." + ], + "type": [ + "latent", + "no-context" + ], + "text": "don't worry . Nothing bad will happen . I'll even buy your ticket for you .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "thanks , that was nice of you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "don't worry . Nothing bad will happen . I'll even buy your ticket for you ." + ], + "type": [ + "inter-personal" + ], + "text": "thanks , that was nice of you .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 15, + "speaker": "A", + "utterance": "see , now something good has happened to you on a bus trip !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 13, + 14 + ], + "expanded emotion cause span": [ + "b", + "Nothing bad will happen . I'll even buy your ticket for you .", + "thanks , that was nice of you ." + ], + "type": [ + "latent", + "hybrid" + ], + "text": "see , now something good has happened to you on a bus trip !", + "id": 15 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1738.json b/reccon/sources/tr_1738.json new file mode 100644 index 0000000000000000000000000000000000000000..296e499e17f14ea7f42307ca196f3674c9ef65ff --- /dev/null +++ b/reccon/sources/tr_1738.json @@ -0,0 +1,240 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "It's wonderful to be in the mountains after a hustle bustle week .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "It's wonderful to be in the mountains after a hustle bustle week ." + ], + "type": [ + "no-context" + ], + "text": "It's wonderful to be in the mountains after a hustle bustle week .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Indeed . I love the smell of the grass and trees . They certainly refresh my mind .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "It's wonderful to be in the mountains after a hustle bustle week .", + "I love the smell of the grass and trees . They certainly refresh my mind ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Indeed . I love the smell of the grass and trees . They certainly refresh my mind .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Can we stop here for a while ? My backpack is very heavy .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "It's wonderful to be in the mountains after a hustle bustle week ." + ], + "type": [ + "self-contagion" + ], + "text": "Can we stop here for a while ? My backpack is very heavy .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Sure . Did you hear anything ? Look ! An eagle is hovering in the sky .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "It's wonderful to be in the mountains after a hustle bustle week .", + "I love the smell of the grass and trees . They certainly refresh my mind ." + ], + "type": [ + "hybrid" + ], + "text": "Sure . Did you hear anything ? Look ! An eagle is hovering in the sky .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Let me see . It's not an eagle . I think it's a vulture .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "It's wonderful to be in the mountains after a hustle bustle week ." + ], + "type": [ + "self-contagion" + ], + "text": "Let me see . It's not an eagle . I think it's a vulture .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yes . Will it hurt us ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "It's wonderful to be in the mountains after a hustle bustle week .", + "I love the smell of the grass and trees . They certainly refresh my mind ." + ], + "type": [ + "hybrid" + ], + "text": "Yes . Will it hurt us ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I don't think so . Let's walk by the stream . I am sure we can find the waterfall on the map .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 7 + ], + "expanded emotion cause span": [ + "It's wonderful to be in the mountains after a hustle bustle week .", + "I am sure we can find the waterfall on the map ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I don't think so . Let's walk by the stream . I am sure we can find the waterfall on the map .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "OK . I have a good pair of hiking boots . It should not be a big problem .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "I am sure we can find the waterfall on the map .", + "OK . I have a good pair of hiking boots . It should not be a big problem ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "OK . I have a good pair of hiking boots . It should not be a big problem .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I also brought a bottle of water and some provisions . If you are hungry , you can let me know .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 1, + 7 + ], + "expanded emotion cause span": [ + "It's wonderful to be in the mountains after a hustle bustle week .", + "It's wonderful to be in the mountains after a hustle bustle week .", + "I am sure we can find the waterfall on the map ." + ], + "type": [ + "self-contagion" + ], + "text": "I also brought a bottle of water and some provisions . If you are hungry , you can let me know .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "You are kind . Look there is a big tree over there , it looks like a thousand-year-old tree .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "If you are hungry , you can let me know .", + "it looks like a thousand-year-old tree ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You are kind . Look there is a big tree over there , it looks like a thousand-year-old tree .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Well , it is a birch tree . It is not as old as you think .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "You are kind ." + ], + "type": [ + "inter-personal" + ], + "text": "Well , it is a birch tree . It is not as old as you think .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "How do you know ?", + "emotion": "neutral", + "text": "How do you know ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Because its trunk is not thick enough to be like a thousand-year-old tree .", + "emotion": "happiness", + "explanation": "The cause is latent", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Because its trunk is not thick enough to be like a thousand-year-old tree .", + "id": 13 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1739.json b/reccon/sources/tr_1739.json new file mode 100644 index 0000000000000000000000000000000000000000..f5c488a4f4a5f900038eb0eebe76994caab49cb0 --- /dev/null +++ b/reccon/sources/tr_1739.json @@ -0,0 +1,190 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Can we talk ?", + "emotion": "neutral", + "text": "Can we talk ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Sure , honey , we ' re talking now , aren ' t we ?", + "emotion": "neutral", + "text": "Sure , honey , we ' re talking now , aren ' t we ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "You know what I mean .", + "emotion": "neutral", + "text": "You know what I mean .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yeah . I know .", + "emotion": "neutral", + "text": "Yeah . I know .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I want to know where this relationship is going . I ' m in love with you and I need to know ...", + "emotion": "neutral", + "text": "I want to know where this relationship is going . I ' m in love with you and I need to know ...", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "You know , I think you ' re awesome .", + "emotion": "neutral", + "text": "You know , I think you ' re awesome .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I ' m awesome . Well , I guess that ' s my answer , isn ' t it .", + "emotion": "neutral", + "text": "I ' m awesome . Well , I guess that ' s my answer , isn ' t it .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Honey ...", + "emotion": "neutral", + "text": "Honey ...", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Look , if you don ' t love me , it ' s not a thing , alright , we ' Ve had our laughs , but I don ' t appreciate ... maybe it ' s just time we ...", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "if you don ' t love me , it ' s not a thing , alright , we ' Ve had our laughs , but I don ' t appreciate ... maybe it ' s just time we ..." + ], + "type": [ + "no-context" + ], + "text": "Look , if you don ' t love me , it ' s not a thing , alright , we ' Ve had our laughs , but I don ' t appreciate ... maybe it ' s just time we ...", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Baby , I love you so much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Baby , I love you so much ." + ], + "type": [ + "no-context" + ], + "text": "Baby , I love you so much .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "You do ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Baby , I love you so much ." + ], + "type": [ + "inter-personal" + ], + "text": "You do ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I love you . And I think you ' re awesome .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "I love you . And I think you ' re awesome ." + ], + "type": [ + "no-context" + ], + "text": "I love you . And I think you ' re awesome .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Oh , I love you too !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "I love you . And I think you ' re awesome ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , I love you too !", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Come on . Put the gun down .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "Oh , I love you too !" + ], + "type": [ + "inter-personal" + ], + "text": "Come on . Put the gun down .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Oh baby , I ' m so sorry .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "Oh , I love you too !" + ], + "type": [ + "self-contagion" + ], + "text": "Oh baby , I ' m so sorry .", + "id": 15 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1754.json b/reccon/sources/tr_1754.json new file mode 100644 index 0000000000000000000000000000000000000000..f65dbace514475f38a507201b003b3421a9b76fc --- /dev/null +++ b/reccon/sources/tr_1754.json @@ -0,0 +1,150 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Dalian is a beautiful city . Do you agree ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Dalian is a beautiful city ." + ], + "type": [ + "no-context" + ], + "text": "Dalian is a beautiful city . Do you agree ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I suppose I do .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Dalian is a beautiful city ." + ], + "type": [ + "inter-personal" + ], + "text": "I suppose I do .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "The climate here is pleasant .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "The climate here is pleasant ." + ], + "type": [ + "no-context" + ], + "text": "The climate here is pleasant .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "You said it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "The climate here is pleasant ." + ], + "type": [ + "inter-personal" + ], + "text": "You said it .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "This city is really comfortable to live in .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "This city is really comfortable to live in ." + ], + "type": [ + "no-context" + ], + "text": "This city is really comfortable to live in .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "It sure is .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "This city is really comfortable to live in ." + ], + "type": [ + "inter-personal" + ], + "text": "It sure is .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "No other city can match it . It's heaven .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "No other city can match it . It's heaven ." + ], + "type": [ + "no-context" + ], + "text": "No other city can match it . It's heaven .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Well , if you live in other cities as long as enough , you will love them just as much .", + "emotion": "neutral", + "text": "Well , if you live in other cities as long as enough , you will love them just as much .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Maybe .", + "emotion": "neutral", + "text": "Maybe .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "That's for sure .", + "emotion": "neutral", + "text": "That's for sure .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_176.json b/reccon/sources/tr_176.json new file mode 100644 index 0000000000000000000000000000000000000000..28a33154ab41c7df50837c5b049d1f3c8fe6d83b --- /dev/null +++ b/reccon/sources/tr_176.json @@ -0,0 +1,212 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Do you like flowers ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "flowers" + ], + "type": [ + "no-context" + ], + "text": "Do you like flowers ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Of course , I like .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "flowers", + "Of course , I like ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Of course , I like .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What's your favorite flower ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "flowers", + "Of course , I like ." + ], + "type": [ + "hybrid" + ], + "text": "What's your favorite flower ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Forsythia . It's also called winter jasmine which is the symbol of the spring's arrival .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4, + 4 + ], + "expanded emotion cause span": [ + "favorite flower ?", + "Forsythia .", + "symbol of the spring's arrival ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Forsythia . It's also called winter jasmine which is the symbol of the spring's arrival .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Spring is a lively season .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "symbol of the spring's arrival .", + "Spring is a lively season ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Spring is a lively season .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yes . How about you ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "symbol of the spring's arrival .", + "Spring is a lively season ." + ], + "type": [ + "hybrid" + ], + "text": "Yes . How about you ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I admire plum blossoms very much . It seems that only it can blossom in the cold winter .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7, + 7 + ], + "expanded emotion cause span": [ + "How about you ?", + "I admire plum blossoms very much .", + "only it can blossom in the cold winter ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I admire plum blossoms very much . It seems that only it can blossom in the cold winter .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "You have a perfect taste !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 7, + 8 + ], + "expanded emotion cause span": [ + "I admire plum blossoms very much .", + "only it can blossom in the cold winter .", + "perfect taste !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You have a perfect taste !", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "It is the symbol of laughing at hoar frost and fighting with snow . I admire the bravery of plum blossoms .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "You have a perfect taste !", + "symbol of laughing at hoar frost and fighting with snow . I admire the bravery of plum blossoms ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It is the symbol of laughing at hoar frost and fighting with snow . I admire the bravery of plum blossoms .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "But it used to be ignored by many people .", + "emotion": "neutral", + "text": "But it used to be ignored by many people .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "The bright people will remember it forever .", + "emotion": "neutral", + "text": "The bright people will remember it forever .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Well , it's snowing . Let's enjoy the plum blossoms when snowing .", + "emotion": "neutral", + "text": "Well , it's snowing . Let's enjoy the plum blossoms when snowing .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1775.json b/reccon/sources/tr_1775.json new file mode 100644 index 0000000000000000000000000000000000000000..b2acca2d9f499b34a1c8e0053bb87bb5f1a6d77d --- /dev/null +++ b/reccon/sources/tr_1775.json @@ -0,0 +1,196 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Would you like to stretch your legs ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Would you like to stretch your legs ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Why not ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Why not ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Let's get a soft drink .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Let's get a soft drink .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Do we have enough time ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Do we have enough time ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Yes , we do .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Yes , we do .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "The performance is excellent .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "The performance is excellent ." + ], + "type": [ + "no-context" + ], + "text": "The performance is excellent .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "It's a new concert hall and the acoustics are great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "The performance is excellent .", + "It's a new concert hall and the acoustics are great ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It's a new concert hall and the acoustics are great .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I couldn't agree more .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "The performance is excellent .", + "It's a new concert hall and the acoustics are great ." + ], + "type": [ + "hybrid" + ], + "text": "I couldn't agree more .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Is this your first time to come to a symphony concert ?", + "emotion": "neutral", + "text": "Is this your first time to come to a symphony concert ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Yes , it is .", + "emotion": "neutral", + "text": "Yes , it is .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Do you have concert halls in your city ?", + "emotion": "neutral", + "text": "Do you have concert halls in your city ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Yes , but it's much smaller .", + "emotion": "neutral", + "text": "Yes , but it's much smaller .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Well , we'd better get back to our seats . It's about to start .", + "emotion": "neutral", + "text": "Well , we'd better get back to our seats . It's about to start .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "OK .", + "emotion": "neutral", + "text": "OK .", + "id": 14 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1784.json b/reccon/sources/tr_1784.json new file mode 100644 index 0000000000000000000000000000000000000000..11b7a2cb5c8098a753a92fd1f86a897e67fafeb5 --- /dev/null +++ b/reccon/sources/tr_1784.json @@ -0,0 +1,139 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi ! How are you going ?", + "emotion": "neutral", + "text": "Hi ! How are you going ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Fine , thank you . How are you doing this morning ?", + "emotion": "neutral", + "text": "Fine , thank you . How are you doing this morning ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Not bad . How about you ? Haven't seen you for a long time .", + "emotion": "neutral", + "text": "Not bad . How about you ? Haven't seen you for a long time .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes . I've been to New York . I got back only yesterday .", + "emotion": "neutral", + "text": "Yes . I've been to New York . I got back only yesterday .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Did you enjoy yourself ?", + "emotion": "neutral", + "text": "Did you enjoy yourself ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Very much . New York is such a nice place . Shall I show you some photographs ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5, + 6 + ], + "expanded emotion cause span": [ + "I've been to New York .", + "Did you enjoy yourself ?", + "Very much . New York is such a nice place ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Very much . New York is such a nice place . Shall I show you some photographs ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Thanks , I like looking at photographs . How nice ! Oh , I'm afraid I must be going now . I've got an appointment . Have a good day .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5, + 6, + 6, + 7 + ], + "expanded emotion cause span": [ + "I've been to New York .", + "Did you enjoy yourself ?", + "Very much . New York is such a nice place .", + "Shall I show you some photographs ?", + "Thanks , I like looking at photographs . How nice !" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Thanks , I like looking at photographs . How nice ! Oh , I'm afraid I must be going now . I've got an appointment . Have a good day .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "You too . I hope to see you soon . Goodbye .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5, + 6, + 6, + 7, + 7 + ], + "expanded emotion cause span": [ + "I've been to New York .", + "Did you enjoy yourself ?", + "Very much . New York is such a nice place .", + "Shall I show you some photographs ?", + "Thanks , I like looking at photographs . How nice !", + "Have a good day ." + ], + "type": [ + "hybrid" + ], + "text": "You too . I hope to see you soon . Goodbye .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Goodbye .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "You too . I hope to see you soon ." + ], + "type": [ + "inter-personal" + ], + "text": "Goodbye .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_18.json b/reccon/sources/tr_18.json new file mode 100644 index 0000000000000000000000000000000000000000..d866fbc2c960cee401c9a63723c7d0edd1619a26 --- /dev/null +++ b/reccon/sources/tr_18.json @@ -0,0 +1,80 @@ +[ + { + "turn": 1, + "speaker": "B", + "utterance": "Hi , my name is Lean , and I'm from Russia .", + "emotion": "neutral", + "text": "Hi , my name is Lean , and I'm from Russia .", + "id": 1 + }, + { + "turn": 2, + "speaker": "A", + "utterance": "Nice to meet you , Lean . My name is Alike . I'm from Japan .", + "emotion": "neutral", + "text": "Nice to meet you , Lean . My name is Alike . I'm from Japan .", + "id": 2 + }, + { + "turn": 3, + "speaker": "B", + "utterance": "To me English is a difficult language .", + "emotion": "neutral", + "text": "To me English is a difficult language .", + "id": 3 + }, + { + "turn": 4, + "speaker": "A", + "utterance": "A second language is always difficult .", + "emotion": "neutral", + "text": "A second language is always difficult .", + "id": 4 + }, + { + "turn": 5, + "speaker": "B", + "utterance": "True , but English is harder than most . It's a crazy language .", + "emotion": "neutral", + "text": "True , but English is harder than most . It's a crazy language .", + "id": 5 + }, + { + "turn": 6, + "speaker": "A", + "utterance": "A crazy language ? Why do you say that ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "It's a crazy language ." + ], + "type": [ + "inter-personal" + ], + "text": "A crazy language ? Why do you say that ?", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "B", + "utterance": "One letter can have several pronunciations and one word can have several meanings .", + "emotion": "neutral", + "text": "One letter can have several pronunciations and one word can have several meanings .", + "id": 7 + }, + { + "turn": 8, + "speaker": "A", + "utterance": "No wonder you say English is a crazy language .", + "emotion": "neutral", + "text": "No wonder you say English is a crazy language .", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_181.json b/reccon/sources/tr_181.json new file mode 100644 index 0000000000000000000000000000000000000000..e607473346c99c679d7b0f6b0902e52dd7a39762 --- /dev/null +++ b/reccon/sources/tr_181.json @@ -0,0 +1,134 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Well , I am a regular member of this club .", + "emotion": "neutral", + "text": "Well , I am a regular member of this club .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Do you have to pay to join ?", + "emotion": "neutral", + "text": "Do you have to pay to join ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yes , membership fees vary depending on the club but usually they run into tens of thousands of dollars .", + "emotion": "neutral", + "text": "Yes , membership fees vary depending on the club but usually they run into tens of thousands of dollars .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Wow , that much ? Don't they have any public courses ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "usually they run into tens of thousands of dollars ." + ], + "type": [ + "inter-personal" + ], + "text": "Wow , that much ? Don't they have any public courses ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Very few , unfortunately .", + "emotion": "neutral", + "text": "Very few , unfortunately .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "How was your game today ?", + "emotion": "neutral", + "text": "How was your game today ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Extremely good . I shot a 78 , including 5 birdies !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Extremely good . I shot a 78 , including 5 birdies !" + ], + "type": [ + "no-context" + ], + "text": "Extremely good . I shot a 78 , including 5 birdies !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Congratulations ! What's your normal handicap ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 7 + ], + "expanded emotion cause span": [ + "Extremely good . I shot a 78 , including 5 birdies !", + "Extremely good . I shot a 78 , including 5 birdies !" + ], + "type": [ + "inter-personal" + ], + "text": "Congratulations ! What's your normal handicap ?", + "id": 8, + "source_sentences": [ + 6, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Ten . How did your game go ?", + "emotion": "neutral", + "text": "Ten . How did your game go ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "My drives were terrible today . I kept slicing the ball into the roughs and sand traps .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "My drives were terrible today . I kept slicing the ball into the roughs and sand traps ." + ], + "type": [ + "no-context" + ], + "text": "My drives were terrible today . I kept slicing the ball into the roughs and sand traps .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Maybe you can correct it by going to a driving range before you play again .", + "emotion": "neutral", + "text": "Maybe you can correct it by going to a driving range before you play again .", + "id": 11 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_183.json b/reccon/sources/tr_183.json new file mode 100644 index 0000000000000000000000000000000000000000..5fabbc78914d03caa102af4f9d46677ff12e3977 --- /dev/null +++ b/reccon/sources/tr_183.json @@ -0,0 +1,124 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I have tickets to The Phantom of the Opera on Friday night . Would you like to go ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I have tickets" + ], + "type": [ + "no-context" + ], + "text": "I have tickets to The Phantom of the Opera on Friday night . Would you like to go ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Thanks . I'd love to . What time is the show ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 1 + ], + "expanded emotion cause span": [ + "I have tickets", + "Would you like to go ?" + ], + "type": [ + "inter-personal" + ], + "text": "Thanks . I'd love to . What time is the show ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "It's at 8: 00 .", + "emotion": "neutral", + "text": "It's at 8: 00 .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "That sounds great . So , do you want to have dinner at 6:00 ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1, + 1 + ], + "expanded emotion cause span": [ + "I have tickets", + "Would you like to go ?" + ], + "type": [ + "inter-personal" + ], + "text": "That sounds great . So , do you want to have dinner at 6:00 ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Uh , I'd like to , but I have to work late .", + "emotion": "neutral", + "text": "Uh , I'd like to , but I have to work late .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Oh , that's OK . Let's just meet at the theater before the show , around 7:30 .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1, + 1 + ], + "expanded emotion cause span": [ + "I have tickets", + "Would you like to go ?" + ], + "type": [ + "inter-personal" + ], + "text": "Oh , that's OK . Let's just meet at the theater before the show , around 7:30 .", + "id": 6, + "source_sentences": [ + 0, + 0 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "That sounds fine .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 6, + 7 + ], + "expanded emotion cause span": [ + "I have tickets", + "I'd love to .", + "meet at the theater", + "sounds fine ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "That sounds fine .", + "id": 7 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1848.json b/reccon/sources/tr_1848.json new file mode 100644 index 0000000000000000000000000000000000000000..35cd67d83f49a6020f0e31ad2eafa939c4a1b094 --- /dev/null +++ b/reccon/sources/tr_1848.json @@ -0,0 +1,112 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Say , Anna , what are you doing tonight ? Would you like to go out ?", + "emotion": "happiness", + "explanation": "Asking friend to go out tonight.", + "expanded emotion cause evidence": [ + "b", + 1 + ], + "expanded emotion cause span": [ + "b", + "go out" + ], + "type": [ + "latent", + "no-context" + ], + "text": "Say , Anna , what are you doing tonight ? Would you like to go out ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh , sorry , I can't . I'm going to work late tonight . I have to finish this report .", + "emotion": "neutral", + "text": "Oh , sorry , I can't . I'm going to work late tonight . I have to finish this report .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Well , how about tomorrow night ? Are you doing anything then ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 1 + ], + "expanded emotion cause span": [ + "b", + "go out" + ], + "type": [ + "latent", + "self-contagion" + ], + "text": "Well , how about tomorrow night ? Are you doing anything then ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "No , I'm not . What are you planning to do ?", + "emotion": "neutral", + "text": "No , I'm not . What are you planning to do ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I'm going to see a musical . Would you like to come ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 1, + 5 + ], + "expanded emotion cause span": [ + "b", + "go out", + "I'm going to see a musical ." + ], + "type": [ + "latent", + "no-context", + "self-contagion" + ], + "text": "I'm going to see a musical . Would you like to come ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Sure , I'd love to ! But let me pay for the tickets this time . It's my turn .", + "emotion": "neutral", + "text": "Sure , I'd love to ! But let me pay for the tickets this time . It's my turn .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "All right ! Thanks !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Sure , I'd love to !" + ], + "type": [ + "inter-personal" + ], + "text": "All right ! Thanks !", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1892.json b/reccon/sources/tr_1892.json new file mode 100644 index 0000000000000000000000000000000000000000..4154d50c3026acbfb28992907ddd9d75e70e9871 --- /dev/null +++ b/reccon/sources/tr_1892.json @@ -0,0 +1,236 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What did you do last night ?", + "emotion": "neutral", + "text": "What did you do last night ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I just stayed at home and watched TV .", + "emotion": "neutral", + "text": "I just stayed at home and watched TV .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Did you watch the Barcelona versus Madrid game ?", + "emotion": "neutral", + "text": "Did you watch the Barcelona versus Madrid game ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes , it was a very evenly matched game .", + "emotion": "neutral", + "text": "Yes , it was a very evenly matched game .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "What were the results of the game ?", + "emotion": "neutral", + "text": "What were the results of the game ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "It ended in a tie .", + "emotion": "neutral", + "text": "It ended in a tie .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "What was the actual score ?", + "emotion": "neutral", + "text": "What was the actual score ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "It was three all .", + "emotion": "neutral", + "text": "It was three all .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Really ? I thought Barcelona was going to win . They are a much better team than Madrid .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "It was three all .", + "I thought Barcelona was going to win ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Really ? I thought Barcelona was going to win . They are a much better team than Madrid .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "If Barcelona had played as they normally do , they should have won .", + "emotion": "neutral", + "text": "If Barcelona had played as they normally do , they should have won .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "What happened ?", + "emotion": "neutral", + "text": "What happened ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Their goalkeepers got injured after the first goal , but he kept on playing anyway .", + "emotion": "neutral", + "text": "Their goalkeepers got injured after the first goal , but he kept on playing anyway .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "That explains it .", + "emotion": "neutral", + "text": "That explains it .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "How many more games are left this season ?", + "emotion": "neutral", + "text": "How many more games are left this season ?", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "That was the last game before the playoffs .", + "emotion": "neutral", + "text": "That was the last game before the playoffs .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "When do the playoffs start ?", + "emotion": "neutral", + "text": "When do the playoffs start ?", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "In a few weeks . Are you planning on watching them ?", + "emotion": "neutral", + "text": "In a few weeks . Are you planning on watching them ?", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "Of course ! I really love watching football games on TV .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 18 + ], + "expanded emotion cause span": [ + "I really love watching football games" + ], + "type": [ + "no-context" + ], + "text": "Of course ! I really love watching football games on TV .", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "Me , too ! Do you want to come over and watch the next game at my place ? I'm planning on having a few people over to watch it together .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 18, + 19 + ], + "expanded emotion cause span": [ + "I really love watching football games", + "Me , too !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Me , too ! Do you want to come over and watch the next game at my place ? I'm planning on having a few people over to watch it together .", + "id": 19, + "source_sentences": [ + 17 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 20, + "speaker": "B", + "utterance": "Sure , that would be great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 18, + 19, + 19 + ], + "expanded emotion cause span": [ + "I really love watching football games", + "Me , too !", + "Do you want to come over and watch the next game" + ], + "type": [ + "hybrid" + ], + "text": "Sure , that would be great .", + "id": 20 + }, + { + "turn": 21, + "speaker": "A", + "utterance": "Ok , it's a date then !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 18, + 19, + 19, + 20 + ], + "expanded emotion cause span": [ + "I really love watching football games", + "Me , too !", + "Do you want to come over and watch the next game", + "Sure" + ], + "type": [ + "hybrid" + ], + "text": "Ok , it's a date then !", + "id": 21 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_19.json b/reccon/sources/tr_19.json new file mode 100644 index 0000000000000000000000000000000000000000..df9dd6c2f79c21ca43db626e40fccd80fa429658 --- /dev/null +++ b/reccon/sources/tr_19.json @@ -0,0 +1,64 @@ +[ + { + "turn": 1, + "speaker": "B", + "utterance": "Can I help you ?", + "emotion": "neutral", + "text": "Can I help you ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "A", + "utterance": "I hope so . I'm looking for some material for a paper I'm writing , and I'm not quite sure where to look .", + "emotion": "neutral", + "text": "I hope so . I'm looking for some material for a paper I'm writing , and I'm not quite sure where to look .", + "id": 2 + }, + { + "turn": 3, + "speaker": "B", + "utterance": "I'll certainly try to help you . What topic is your paper on ?", + "emotion": "neutral", + "text": "I'll certainly try to help you . What topic is your paper on ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "A", + "utterance": "My paper is on the influence of television on children .", + "emotion": "neutral", + "text": "My paper is on the influence of television on children .", + "id": 4 + }, + { + "turn": 5, + "speaker": "B", + "utterance": "There are several possible sources you might use for that topic . I suggest you use the computer and the computer will give you a list of every scientific journal that talks about children and television .", + "emotion": "neutral", + "text": "There are several possible sources you might use for that topic . I suggest you use the computer and the computer will give you a list of every scientific journal that talks about children and television .", + "id": 5 + }, + { + "turn": 6, + "speaker": "A", + "utterance": "Thank you for you help .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "There are several possible sources you might use for that topic . I suggest you use the computer and the computer will give you a list of every scientific journal that talks about children and television ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you for you help .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1921.json b/reccon/sources/tr_1921.json new file mode 100644 index 0000000000000000000000000000000000000000..cdb4fe94e82bca7e05a38877d2409d6abd16f027 --- /dev/null +++ b/reccon/sources/tr_1921.json @@ -0,0 +1,107 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello ?", + "emotion": "neutral", + "text": "Hello ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hi , Kathy . Have you had lunch ?", + "emotion": "neutral", + "text": "Hi , Kathy . Have you had lunch ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Not yet . And I ' m really hungry now .", + "emotion": "neutral", + "text": "Not yet . And I ' m really hungry now .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I ' m starving , too . There is a new Chinese restaurant close by . Do you want to go there for lunch ?", + "emotion": "happiness", + "explanation": "The speaker is happy to realize that they share the same feeling of hunger as the counterpart.", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "I ' m really hungry now .", + "I ' m starving , too . There is a new Chinese restaurant close by ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I ' m starving , too . There is a new Chinese restaurant close by . Do you want to go there for lunch ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Why not ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I ' m starving , too . There is a new Chinese restaurant close by ." + ], + "type": [ + "inter-personal" + ], + "text": "Why not ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "It ' s my treat this time .", + "emotion": "happiness", + "explanation": "The cause for happiness is latent.", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "It ' s my treat this time .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Thanks . I could eat a cow .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "It ' s my treat this time .", + "I could eat a cow ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thanks . I could eat a cow .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1928.json b/reccon/sources/tr_1928.json new file mode 100644 index 0000000000000000000000000000000000000000..ada592613e7019e80d59b8d34df4d4ee7d2491dd --- /dev/null +++ b/reccon/sources/tr_1928.json @@ -0,0 +1,386 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Do you have a bf ?", + "emotion": "neutral", + "text": "Do you have a bf ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , I had a bf before .", + "emotion": "neutral", + "text": "Yes , I had a bf before .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Why you say bf before ?", + "emotion": "neutral", + "text": "Why you say bf before ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "We parted from each other last month .", + "emotion": "neutral", + "text": "We parted from each other last month .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Have you got a new one ?", + "emotion": "neutral", + "text": "Have you got a new one ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Mmmm , no . How about you ?", + "emotion": "neutral", + "text": "Mmmm , no . How about you ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I am single , I have no real of , only an E-gf , that is you .", + "emotion": "neutral", + "text": "I am single , I have no real of , only an E-gf , that is you .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Haha , so you are my E-bf .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "only an E-gf , that is you ." + ], + "type": [ + "inter-personal" + ], + "text": "Haha , so you are my E-bf .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I like you . Do you agree to be my of ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "I like you ." + ], + "type": [ + "no-context" + ], + "text": "I like you . Do you agree to be my of ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Mmmm . .. OK , let's try to be .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "I like you . Do you agree to be my of ?", + "let's try to be ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Mmmm . .. OK , let's try to be .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Wow ! Blablablabla . . .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Mmmm . .. OK , let's try to be ." + ], + "type": [ + "inter-personal" + ], + "text": "Wow ! Blablablabla . . .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Hey ! What is it ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "I like you . Do you agree to be my of ?", + "let's try to be ." + ], + "type": [ + "hybrid" + ], + "text": "Hey ! What is it ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I am flying like a bird .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Mmmm . .. OK , let's try to be ." + ], + "type": [ + "inter-personal" + ], + "text": "I am flying like a bird .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "LL", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "I like you . Do you agree to be my of ?", + "let's try to be ." + ], + "type": [ + "hybrid" + ], + "text": "LL", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "I am so happy . I want to drink a cup of champagne .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Mmmm . .. OK , let's try to be ." + ], + "type": [ + "inter-personal" + ], + "text": "I am so happy . I want to drink a cup of champagne .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "I have no champagne right now . How about this ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "I like you . Do you agree to be my of ?", + "let's try to be ." + ], + "type": [ + "hybrid" + ], + "text": "I have no champagne right now . How about this ?", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "It's OK , so I send you this .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Mmmm . .. OK , let's try to be ." + ], + "type": [ + "inter-personal" + ], + "text": "It's OK , so I send you this .", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "Is it made of chocolate ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 17 + ], + "expanded emotion cause span": [ + "so I send you this ." + ], + "type": [ + "inter-personal" + ], + "text": "Is it made of chocolate ?", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "It's my heart ; it's made of what you like .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 19 + ], + "expanded emotion cause span": [ + "It's my heart ; it's made of what you like ." + ], + "type": [ + "no-context" + ], + "text": "It's my heart ; it's made of what you like .", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "Oh , I will have a sweet dream .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 19 + ], + "expanded emotion cause span": [ + "It's my heart ; it's made of what you like ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , I will have a sweet dream .", + "id": 20 + }, + { + "turn": 21, + "speaker": "A", + "utterance": "Are you sleepy ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 20 + ], + "expanded emotion cause span": [ + "Oh , I will have a sweet dream ." + ], + "type": [ + "inter-personal" + ], + "text": "Are you sleepy ?", + "id": 21 + }, + { + "turn": 22, + "speaker": "B", + "utterance": "A little bit . I have to go to sleep though I don't want to .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 20, + 22 + ], + "expanded emotion cause span": [ + "Oh , I will have a sweet dream .", + "I have to go to sleep though I don't want to ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "A little bit . I have to go to sleep though I don't want to .", + "id": 22 + }, + { + "turn": 23, + "speaker": "A", + "utterance": "Yes , I do not want to see ur sleeping in the office .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 20 + ], + "expanded emotion cause span": [ + "Oh , I will have a sweet dream ." + ], + "type": [ + "inter-personal" + ], + "text": "Yes , I do not want to see ur sleeping in the office .", + "id": 23 + }, + { + "turn": 24, + "speaker": "B", + "utterance": "Thx . Bye for now . Kisssssssssss .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 20, + 23 + ], + "expanded emotion cause span": [ + "Oh , I will have a sweet dream .", + "I do not want to see ur sleeping in the office ." + ], + "type": [ + "hybrid" + ], + "text": "Thx . Bye for now . Kisssssssssss .", + "id": 24 + }, + { + "turn": 25, + "speaker": "A", + "utterance": "C U here , honey .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 20, + 24 + ], + "expanded emotion cause span": [ + "Oh , I will have a sweet dream .", + "Kisssssssssss ." + ], + "type": [ + "inter-personal" + ], + "text": "C U here , honey .", + "id": 25, + "source_sentences": [ + 19, + 23 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1936.json b/reccon/sources/tr_1936.json new file mode 100644 index 0000000000000000000000000000000000000000..448a8110f411f695760aabaf77ed0a4ffd843bc8 --- /dev/null +++ b/reccon/sources/tr_1936.json @@ -0,0 +1,246 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "That was a great dinner . I didn't know that you knew how yo cook .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "That was a great dinner ." + ], + "type": [ + "no-context" + ], + "text": "That was a great dinner . I didn't know that you knew how yo cook .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'm glad you liked it . Are you ready for dessert ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "That was a great dinner ." + ], + "type": [ + "inter-personal" + ], + "text": "I'm glad you liked it . Are you ready for dessert ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I don't know . I'm pretty full . What are we having ?", + "emotion": "neutral", + "text": "I don't know . I'm pretty full . What are we having ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I made strawberry shortcake .", + "emotion": "neutral", + "text": "I made strawberry shortcake .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Ooh , that's my favorite . Maybe I'll have a small slice .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "I made strawberry shortcake .", + "that's my favorite ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Ooh , that's my favorite . Maybe I'll have a small slice .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Great . Would you like coffee or tea with that ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 5 + ], + "expanded emotion cause span": [ + "that's my favorite .", + "I'll have a small slice ." + ], + "type": [ + "inter-personal" + ], + "text": "Great . Would you like coffee or tea with that ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I'll have a cup of tea .", + "emotion": "neutral", + "text": "I'll have a cup of tea .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Do you take cream or sugar with your tea ?", + "emotion": "neutral", + "text": "Do you take cream or sugar with your tea ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Actually , could I have some milk with that ?", + "emotion": "neutral", + "text": "Actually , could I have some milk with that ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Definitely . Would you like skim or whole milk ?", + "emotion": "neutral", + "text": "Definitely . Would you like skim or whole milk ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Skim , please . That'd be very nice . Thanks ... oh no . Janna , I'm so sorry , but I've got to go .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I've got to go ." + ], + "type": [ + "no-context" + ], + "text": "Skim , please . That'd be very nice . Thanks ... oh no . Janna , I'm so sorry , but I've got to go .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "What happened ?", + "emotion": "neutral", + "text": "What happened ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I just got a message from my sister saying that she's been in a car accident . I need to go pick her up .", + "emotion": "neutral", + "text": "I just got a message from my sister saying that she's been in a car accident . I need to go pick her up .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "I'll go with you . Where is she ?", + "emotion": "neutral", + "text": "I'll go with you . Where is she ?", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "She's on the M40 , near Reading .", + "emotion": "neutral", + "text": "She's on the M40 , near Reading .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Is she alright ?", + "emotion": "neutral", + "text": "Is she alright ?", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "I don't know , she didn't say . I'm so sorry about this .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 11, + 17 + ], + "expanded emotion cause span": [ + "I've got to go .", + "I don't know , she didn't say ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I don't know , she didn't say . I'm so sorry about this .", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "Don't worry . Family comes first . Come on , let's go .", + "emotion": "neutral", + "text": "Don't worry . Family comes first . Come on , let's go .", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "Actually , I've only got a two-seater . I'll have to go on my own .", + "emotion": "neutral", + "text": "Actually , I've only got a two-seater . I'll have to go on my own .", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "Ok . Just call me if you need anything then .", + "emotion": "neutral", + "text": "Ok . Just call me if you need anything then .", + "id": 20 + }, + { + "turn": 21, + "speaker": "A", + "utterance": "I will . Thanks a lot .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 20 + ], + "expanded emotion cause span": [ + "call me if you need anything" + ], + "type": [ + "inter-personal" + ], + "text": "I will . Thanks a lot .", + "id": 21, + "source_sentences": [ + 19 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1950.json b/reccon/sources/tr_1950.json new file mode 100644 index 0000000000000000000000000000000000000000..8e9431187d6cffcb44444e0697f22e8b07c59b8e --- /dev/null +++ b/reccon/sources/tr_1950.json @@ -0,0 +1,101 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Excuse me .", + "emotion": "neutral", + "text": "Excuse me .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , Miss , what can I do for you ?", + "emotion": "neutral", + "text": "Yes , Miss , what can I do for you ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I ordered my dish about a half an hour ago , but it hasn't arrived yet .", + "emotion": "neutral", + "text": "I ordered my dish about a half an hour ago , but it hasn't arrived yet .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I'm sorry for that , I'm going to check with the chef right now . Miss , I just checked with the kitchen , and they said your order will be coming right up next . Oh , here comes .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I ordered my dish about a half an hour ago , but it hasn't arrived yet ." + ], + "type": [ + "inter-personal" + ], + "text": "I'm sorry for that , I'm going to check with the chef right now . Miss , I just checked with the kitchen , and they said your order will be coming right up next . Oh , here comes .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Thank you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "your order will be coming right up next . Oh , here comes ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Miss , I'm very sorry for the delay , please enjoy this . Free a glass of wine for inconvenience . Again I'm terribly sorry to make you wait so long .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I ordered my dish about a half an hour ago , but it hasn't arrived yet ." + ], + "type": [ + "inter-personal" + ], + "text": "Miss , I'm very sorry for the delay , please enjoy this . Free a glass of wine for inconvenience . Again I'm terribly sorry to make you wait so long .", + "id": 6, + "source_sentences": [ + 2 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "It doesn't matter .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 6 + ], + "expanded emotion cause span": [ + "I ordered my dish about a half an hour ago , but it hasn't arrived yet .", + "Free a glass of wine for inconvenience ." + ], + "type": [ + "hybrid" + ], + "text": "It doesn't matter .", + "id": 7 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1951.json b/reccon/sources/tr_1951.json new file mode 100644 index 0000000000000000000000000000000000000000..9d77b384680f5faaf92bdbf15a904fa87fc80b25 --- /dev/null +++ b/reccon/sources/tr_1951.json @@ -0,0 +1,287 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "How do you like this waltz ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "this waltz" + ], + "type": [ + "no-context" + ], + "text": "How do you like this waltz ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It's very nice , I like it very much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "this waltz", + "It's very nice , I like it very much ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It's very nice , I like it very much .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Well , then , may I invite you for the first dance ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 3 + ], + "expanded emotion cause span": [ + "this waltz", + "It's very nice , I like it very much .", + "first dance ?" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Well , then , may I invite you for the first dance ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "My pleasure . But I'm afraid I'm not much of a dancer , and I suppose you dance often .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 3 + ], + "expanded emotion cause span": [ + "this waltz", + "It's very nice , I like it very much .", + "may I invite you for the first dance ?" + ], + "type": [ + "hybrid" + ], + "text": "My pleasure . But I'm afraid I'm not much of a dancer , and I suppose you dance often .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Me ? Oh , no . In fact , I took up dancing quite recently .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "I suppose you dance often .", + "I took up dancing quite recently ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Me ? Oh , no . In fact , I took up dancing quite recently .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Oh , really ? But you're doing the waltz wonderfully well .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "I took up dancing quite recently .", + "But you're doing the waltz wonderfully well ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , really ? But you're doing the waltz wonderfully well .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I'm glad you say so , you dance beautifully too . It's lucky that I got a partner .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 3, + 6, + 7 + ], + "expanded emotion cause span": [ + "this waltz", + "It's very nice , I like it very much .", + "first dance ?", + "But you're doing the waltz wonderfully well .", + "you dance beautifully too . It's lucky that I got a partner ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I'm glad you say so , you dance beautifully too . It's lucky that I got a partner .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Thank you for your compliments . It ' s just that you are a good leader . Do you like the fox-trot and tango ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 3, + 7 + ], + "expanded emotion cause span": [ + "this waltz", + "It's very nice , I like it very much .", + "first dance ?", + "you dance beautifully too" + ], + "type": [ + "hybrid" + ], + "text": "Thank you for your compliments . It ' s just that you are a good leader . Do you like the fox-trot and tango ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yes . And what dances do you do best ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 3, + 8 + ], + "expanded emotion cause span": [ + "this waltz", + "It's very nice , I like it very much .", + "first dance ?", + "It ' s just that you are a good leader . Do you like the fox-trot and tango ?" + ], + "type": [ + "hybrid" + ], + "text": "Yes . And what dances do you do best ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Disco is my favorite . I like it better than any other dances because it can release one's pent-up feelings , and is a healthy exercise . But I don't do the rock and roll and the break dance .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 3, + 10 + ], + "expanded emotion cause span": [ + "this waltz", + "It's very nice , I like it very much .", + "first dance ?", + "Disco is my favorite . I like it better than any other dances because it can release one's pent-up feelings , and is a healthy exercise ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Disco is my favorite . I like it better than any other dances because it can release one's pent-up feelings , and is a healthy exercise . But I don't do the rock and roll and the break dance .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Oh , well , the music has stopped . Thank you for the dance .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 3, + 11 + ], + "expanded emotion cause span": [ + "this waltz", + "It's very nice , I like it very much .", + "first dance ?", + "Thank you for the dance ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Oh , well , the music has stopped . Thank you for the dance .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "My pleasure . Let's go and have a drink .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 3, + 11 + ], + "expanded emotion cause span": [ + "this waltz", + "It's very nice , I like it very much .", + "first dance ?", + "Thank you for the dance ." + ], + "type": [ + "hybrid" + ], + "text": "My pleasure . Let's go and have a drink .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Fine .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "My pleasure . Let's go and have a drink ." + ], + "type": [ + "inter-personal" + ], + "text": "Fine .", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1954.json b/reccon/sources/tr_1954.json new file mode 100644 index 0000000000000000000000000000000000000000..c49610531973c1f0bba0cb7df94a046b89f3b107 --- /dev/null +++ b/reccon/sources/tr_1954.json @@ -0,0 +1,173 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "... Now that we have been over the gory details of our disastrous first quarter , Ed ! Give us some good news . How are things looking for us in terms sales this month ?", + "emotion": "neutral", + "text": "... Now that we have been over the gory details of our disastrous first quarter , Ed ! Give us some good news . How are things looking for us in terms sales this month ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Uh well ... would you like the bad news first or the really bad news ?", + "emotion": "neutral", + "text": "Uh well ... would you like the bad news first or the really bad news ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What ? Ed , don ' t tell me you only have bad news !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "would you like the bad news first or the really bad news ?" + ], + "type": [ + "inter-personal" + ], + "text": "What ? Ed , don ' t tell me you only have bad news !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Well sir , our sales have dropped , no plunged , fifty percent in the past month alone . We are currently overstocked and overstaffed and our profits refalling fast . The market is in recession and we have no way of moving our inventory , or getting rid of our staff . If we consider redundancies , it would cost us a fortune because of the new regulations governing compensation packages . It ' s a real mess .", + "emotion": "neutral", + "text": "Well sir , our sales have dropped , no plunged , fifty percent in the past month alone . We are currently overstocked and overstaffed and our profits refalling fast . The market is in recession and we have no way of moving our inventory , or getting rid of our staff . If we consider redundancies , it would cost us a fortune because of the new regulations governing compensation packages . It ' s a real mess .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "For crying out loud ... How fast are we losing money ?", + "emotion": "anger", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "How fast are we losing money ?" + ], + "type": [ + "no-context" + ], + "text": "For crying out loud ... How fast are we losing money ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Um ... how can I put this ? Let ' s just say that at this pace , we will be filing for Chapter eleven in less than three months .", + "emotion": "neutral", + "text": "Um ... how can I put this ? Let ' s just say that at this pace , we will be filing for Chapter eleven in less than three months .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "What ! Geez ! How could this have happened ? So what ' s the bad news ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "at this pace , we will be filing for Chapter eleven in less than three months ." + ], + "type": [ + "inter-personal" + ], + "text": "What ! Geez ! How could this have happened ? So what ' s the bad news ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Oh , that ' s the really bad news . Our supplier suffered QC problems and , well , half of our production is faulty . We ' re going to have to recall all itemssold in the last quarter . And the worst part ? We ' re going to have to shoulder this cost .", + "emotion": "neutral", + "text": "Oh , that ' s the really bad news . Our supplier suffered QC problems and , well , half of our production is faulty . We ' re going to have to recall all itemssold in the last quarter . And the worst part ? We ' re going to have to shoulder this cost .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Are you joking ? Get the supplier on the line now ! They have to assume the costs of this mess !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Oh , that ' s the really bad news . Our supplier suffered QC problems and , well , half of our production is faulty . We ' re going to have to recall all itemssold in the last quarter . And the worst part ? We ' re going to have to shoulder this cost ." + ], + "type": [ + "inter-personal" + ], + "text": "Are you joking ? Get the supplier on the line now ! They have to assume the costs of this mess !", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "We tried that , sir . The factory has gone under and the owner apparently has fled the country .", + "emotion": "neutral", + "text": "We tried that , sir . The factory has gone under and the owner apparently has fled the country .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "We ' re doomed !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "The factory has gone under and the owner apparently has fled the country ." + ], + "type": [ + "inter-personal" + ], + "text": "We ' re doomed !", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "There is some really good news though !", + "emotion": "neutral", + "text": "There is some really good news though !", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Really ? What !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "There is some really good news though !" + ], + "type": [ + "inter-personal" + ], + "text": "Really ? What !", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 14, + "speaker": "B", + "utterance": "I got offered a new job !", + "emotion": "neutral", + "text": "I got offered a new job !", + "id": 14 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1962.json b/reccon/sources/tr_1962.json new file mode 100644 index 0000000000000000000000000000000000000000..bbacdba2045d0f54ed1126955e3cb1ec5fd38051 --- /dev/null +++ b/reccon/sources/tr_1962.json @@ -0,0 +1,132 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , Jenny . Are still working ?", + "emotion": "neutral", + "text": "Hi , Jenny . Are still working ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hi , Nancy . Come in please . I'm just putting away on my books .", + "emotion": "neutral", + "text": "Hi , Nancy . Come in please . I'm just putting away on my books .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "So , you are leaving , aren't you ?", + "emotion": "neutral", + "text": "So , you are leaving , aren't you ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes , I ' m going to take a holiday tomorrow .", + "emotion": "neutral", + "text": "Yes , I ' m going to take a holiday tomorrow .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "How nice ! I can see you are busying packing . I'm sorry to interrupt you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I ' m going to take a holiday tomorrow ." + ], + "type": [ + "inter-personal" + ], + "text": "How nice ! I can see you are busying packing . I'm sorry to interrupt you .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "That's all right . I'm almost finished . Do you need my help ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "I ' m going to take a holiday tomorrow .", + "How nice !" + ], + "type": [ + "hybrid" + ], + "text": "That's all right . I'm almost finished . Do you need my help ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yes , could you please go over this for me ? And see if there is any mistake in it ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "Do you need my help ?", + "Yes , could you please go over this for me ? And see if there is any mistake in it ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , could you please go over this for me ? And see if there is any mistake in it ?", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Oh . All right I'll read it soon .", + "emotion": "neutral", + "text": "Oh . All right I'll read it soon .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Excuse me for taking your time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7, + 8 + ], + "expanded emotion cause span": [ + "Do you need my help ?", + "Yes , could you please go over this for me ? And see if there is any mistake in it ?", + "I'll read it soon ." + ], + "type": [ + "hybrid" + ], + "text": "Excuse me for taking your time .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "It's nothing Nancy .", + "emotion": "neutral", + "text": "It's nothing Nancy .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1963.json b/reccon/sources/tr_1963.json new file mode 100644 index 0000000000000000000000000000000000000000..89bb38daa3d772079cac34e99c1aa185e1150393 --- /dev/null +++ b/reccon/sources/tr_1963.json @@ -0,0 +1,190 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Why do you look so gloomy ? What are you looking for ?", + "emotion": "neutral", + "text": "Why do you look so gloomy ? What are you looking for ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "My dissertation . I put it somewhere last night and I can't find it now .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "My dissertation . I put it somewhere last night and I can't find it now ." + ], + "type": [ + "no-context" + ], + "text": "My dissertation . I put it somewhere last night and I can't find it now .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Did you finish typing it yesterday ?", + "emotion": "neutral", + "text": "Did you finish typing it yesterday ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes , I kept on typing it until midnight , but it is lost .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "My dissertation . I put it somewhere last night and I can't find it now ." + ], + "type": [ + "self-contagion" + ], + "text": "Yes , I kept on typing it until midnight , but it is lost .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Don't worry about it . It must be somewhere in your room . Let's see where you put it . Have you searched your drawers and the desk ?", + "emotion": "neutral", + "text": "Don't worry about it . It must be somewhere in your room . Let's see where you put it . Have you searched your drawers and the desk ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yes , but there is nothing inside the drawers or on the desk .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "My dissertation . I put it somewhere last night and I can't find it now ." + ], + "type": [ + "self-contagion" + ], + "text": "Yes , but there is nothing inside the drawers or on the desk .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "How about the shelf ?", + "emotion": "neutral", + "text": "How about the shelf ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I've searched everywhere . Where on earth did I put it ?", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "My dissertation . I put it somewhere last night and I can't find it now ." + ], + "type": [ + "self-contagion" + ], + "text": "I've searched everywhere . Where on earth did I put it ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Don't get upset over it . At least you have another week to go .", + "emotion": "neutral", + "text": "Don't get upset over it . At least you have another week to go .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I have been working on it for a whole month and it's too late to write another . Just think of all my hard work that goes for nothing . How could I do such a thing ?", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2, + 10 + ], + "expanded emotion cause span": [ + "My dissertation . I put it somewhere last night and I can't find it now .", + "Just think of all my hard work that goes for nothing ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I have been working on it for a whole month and it's too late to write another . Just think of all my hard work that goes for nothing . How could I do such a thing ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Cheer up ! What I meant was that you can find it sometime during a week . There is no need to write a new one . Oh , what's this ? Is this your dissertation ?", + "emotion": "neutral", + "text": "Cheer up ! What I meant was that you can find it sometime during a week . There is no need to write a new one . Oh , what's this ? Is this your dissertation ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Let me see . Yes , that's it . Where did you find it ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "Oh , what's this ? Is this your dissertation ?", + "Yes , that's it ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Let me see . Yes , that's it . Where did you find it ?", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 13, + "speaker": "A", + "utterance": "You ' Ve put it among these journals .", + "emotion": "neutral", + "text": "You ' Ve put it among these journals .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "My poor memory . Thank you very much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "Oh , what's this ? Is this your dissertation ?", + "Yes , that's it ." + ], + "type": [ + "hybrid" + ], + "text": "My poor memory . Thank you very much .", + "id": 14 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1975.json b/reccon/sources/tr_1975.json new file mode 100644 index 0000000000000000000000000000000000000000..bb44f0aeb3676df7537e15cd9a78bc6e6f50867d --- /dev/null +++ b/reccon/sources/tr_1975.json @@ -0,0 +1,142 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Wow , the view from the peak is so grand !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Wow , the view from the peak is so grand !" + ], + "type": [ + "no-context" + ], + "text": "Wow , the view from the peak is so grand !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Look , most of the maple leaves have turned red .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "Wow , the view from the peak is so grand !", + "most of the maple leaves have turned red ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Look , most of the maple leaves have turned red .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Did you ever see this kind of beautiful scene ?", + "emotion": "neutral", + "text": "Did you ever see this kind of beautiful scene ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Of course , my father used to take me to Kiang Shan or somewhere like that as a child .", + "emotion": "neutral", + "text": "Of course , my father used to take me to Kiang Shan or somewhere like that as a child .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "But my father did not . He didn't have much time .", + "emotion": "neutral", + "text": "But my father did not . He didn't have much time .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Honey , I'm sorry . I promise you , this summer vacation , I will take you to Huang-Shan Mountains . It is more beautiful and magnificent .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I promise you , this summer vacation , I will take you to Huang-Shan Mountains . It is more beautiful and magnificent ." + ], + "type": [ + "no-context" + ], + "text": "Honey , I'm sorry . I promise you , this summer vacation , I will take you to Huang-Shan Mountains . It is more beautiful and magnificent .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Really ? It's a deal . Have you ever been there ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I promise you , this summer vacation , I will take you to Huang-Shan Mountains . It is more beautiful and magnificent ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? It's a deal . Have you ever been there ?", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yes , I went there five years ago . You were still a baby at that time .", + "emotion": "neutral", + "text": "Yes , I went there five years ago . You were still a baby at that time .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "It really gets me interested . Is it higher than Kiang Shan ?", + "emotion": "neutral", + "text": "It really gets me interested . Is it higher than Kiang Shan ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Surely . You can enjoy the beauty of numerous streams and waterfalls . The sea of clouds has a fairy tale beauty .", + "emotion": "neutral", + "text": "Surely . You can enjoy the beauty of numerous streams and waterfalls . The sea of clouds has a fairy tale beauty .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Can I see the rainbow ?", + "emotion": "neutral", + "text": "Can I see the rainbow ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "That depends . If you are lucky , you can see a vivid rainbow across over two peaks .", + "emotion": "neutral", + "text": "That depends . If you are lucky , you can see a vivid rainbow across over two peaks .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1980.json b/reccon/sources/tr_1980.json new file mode 100644 index 0000000000000000000000000000000000000000..ab337c9cd4b8fc13b40c0c53b679d4d6b3496048 --- /dev/null +++ b/reccon/sources/tr_1980.json @@ -0,0 +1,253 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Guess what came in the mail today ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "came in the mail today" + ], + "type": [ + "no-context" + ], + "text": "Guess what came in the mail today ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What ?", + "emotion": "neutral", + "text": "What ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "My acceptance letter to Yale !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "came in the mail today", + "My acceptance letter to Yale !" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "My acceptance letter to Yale !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Wow ! Congratulation ! When do classes start ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "My acceptance letter to Yale !" + ], + "type": [ + "inter-personal" + ], + "text": "Wow ! Congratulation ! When do classes start ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Freshman orientation is the last week of august , but I want to go two weeks before that to get settled in .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "came in the mail today", + "My acceptance letter to Yale !" + ], + "type": [ + "self-contagion" + ], + "text": "Freshman orientation is the last week of august , but I want to go two weeks before that to get settled in .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "You ' re so lucky ! Do you have to do many things before you leave ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 6 + ], + "expanded emotion cause span": [ + "My acceptance letter to Yale !", + "You ' re so lucky !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You ' re so lucky ! Do you have to do many things before you leave ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yes . I ' ll be very busy ! I have to get a visa , buy a plane ticket , and pack my things . But first , I want to register for classes .", + "emotion": "neutral", + "text": "Yes . I ' ll be very busy ! I have to get a visa , buy a plane ticket , and pack my things . But first , I want to register for classes .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "When can you do that ?", + "emotion": "neutral", + "text": "When can you do that ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Well , they sent me their prospectus , so I can start looking now . do you want to help me decide which classed to take ?", + "emotion": "neutral", + "text": "Well , they sent me their prospectus , so I can start looking now . do you want to help me decide which classed to take ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Sure . What can you choose from ?", + "emotion": "neutral", + "text": "Sure . What can you choose from ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Well , I have to take all the fundamental course , plus a few from my major .", + "emotion": "neutral", + "text": "Well , I have to take all the fundamental course , plus a few from my major .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "What is your major ?", + "emotion": "neutral", + "text": "What is your major ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I hope to major in English literature , but the admissions counselor told me that many people change their major many times in their first year , so we ' ll see .", + "emotion": "neutral", + "text": "I hope to major in English literature , but the admissions counselor told me that many people change their major many times in their first year , so we ' ll see .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "What are the fundamental course ?", + "emotion": "neutral", + "text": "What are the fundamental course ?", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "In order to graduate , every student must take a certain amount of classes in history , math , English , philosophy , science and art .", + "emotion": "neutral", + "text": "In order to graduate , every student must take a certain amount of classes in history , math , English , philosophy , science and art .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Interesting . That ' s very different from the Chinese education system .", + "emotion": "neutral", + "text": "Interesting . That ' s very different from the Chinese education system .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "Yes , it is . It ' s also very different from the British education system .", + "emotion": "neutral", + "text": "Yes , it is . It ' s also very different from the British education system .", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "Really ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 17 + ], + "expanded emotion cause span": [ + "It ' s also very different from the British education system ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ?", + "id": 18, + "source_sentences": [ + 16 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 19, + "speaker": "A", + "utterance": "oh , sure . In British , students don ' t have to take the foundation course .", + "emotion": "neutral", + "text": "oh , sure . In British , students don ' t have to take the foundation course .", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "why not ?", + "emotion": "neutral", + "text": "why not ?", + "id": 20 + }, + { + "turn": 21, + "speaker": "A", + "utterance": "maybe because they think they know everything already ! ha ha .", + "emotion": "happiness", + "explanation": "Cracking a joke", + "expanded emotion cause evidence": [ + "b", + 21, + 19 + ], + "expanded emotion cause span": [ + "b", + "because they think they know everything already", + "In British , students don ' t have to take the foundation course ." + ], + "type": [ + "latent", + "no-context", + "self-contagion" + ], + "text": "maybe because they think they know everything already ! ha ha .", + "id": 21 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_1984.json b/reccon/sources/tr_1984.json new file mode 100644 index 0000000000000000000000000000000000000000..51623aa569fa9f5255abee230f368757c0269bba --- /dev/null +++ b/reccon/sources/tr_1984.json @@ -0,0 +1,163 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Excuse me . Is there any body here ?", + "emotion": "neutral", + "text": "Excuse me . Is there any body here ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes .", + "emotion": "neutral", + "text": "Yes .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I've finished up all my water . I would kill for a sip of water .", + "emotion": "neutral", + "text": "I've finished up all my water . I would kill for a sip of water .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Sure , come on in .", + "emotion": "neutral", + "text": "Sure , come on in .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Thank you very much . Are you here alone ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "I've finished up all my water . I would kill for a sip of water .", + "Sure , come on in ." + ], + "type": [ + "hybrid" + ], + "text": "Thank you very much . Are you here alone ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "My father and sister are out to photographing . What about you ?", + "emotion": "neutral", + "text": "My father and sister are out to photographing . What about you ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I'm a back-packer from America .", + "emotion": "neutral", + "text": "I'm a back-packer from America .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "What is a back-packer ?", + "emotion": "neutral", + "text": "What is a back-packer ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "It means a hiker who loves traveling around the world .", + "emotion": "neutral", + "text": "It means a hiker who loves traveling around the world .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Cool . You must have been to a lot of places .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "a hiker who loves traveling around the world .", + "Cool . You must have been to a lot of places ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Cool . You must have been to a lot of places .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Yes , actually almost half of all the countries over the world . I love traveling places .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "Cool . You must have been to a lot of places .", + "Yes , actually almost half of all the countries over the world . I love traveling places ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , actually almost half of all the countries over the world . I love traveling places .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "So cool . I want to be a back-packer when I grow up .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "actually almost half of all the countries over the world ." + ], + "type": [ + "inter-personal" + ], + "text": "So cool . I want to be a back-packer when I grow up .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 13, + "speaker": "A", + "utterance": "You can do it . But do work hard on your English to make it easier .", + "emotion": "neutral", + "text": "You can do it . But do work hard on your English to make it easier .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "I'll try my best .", + "emotion": "neutral", + "text": "I'll try my best .", + "id": 14 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_20.json b/reccon/sources/tr_20.json new file mode 100644 index 0000000000000000000000000000000000000000..65e0803f3b7d34cbc3124687f50b16163c02b63a --- /dev/null +++ b/reccon/sources/tr_20.json @@ -0,0 +1,165 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Here ' s your hot dog and beer . What happened ? Did I miss anything ?", + "emotion": "neutral", + "text": "Here ' s your hot dog and beer . What happened ? Did I miss anything ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yeah , Cal Ripen just hit a home run .", + "emotion": "neutral", + "text": "Yeah , Cal Ripen just hit a home run .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What ' s the score ?", + "emotion": "neutral", + "text": "What ' s the score ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Well it was 3 to 4 , but Ripen ' s home run made it 5 to 4 since another player was on first base .", + "emotion": "neutral", + "text": "Well it was 3 to 4 , but Ripen ' s home run made it 5 to 4 since another player was on first base .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "So Baltimore is winning ?", + "emotion": "neutral", + "text": "So Baltimore is winning ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Right .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Baltimore is winning ?" + ], + "type": [ + "inter-personal" + ], + "text": "Right .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "This is a really great place to watch a baseball game .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "really great place to watch a baseball game ." + ], + "type": [ + "no-context" + ], + "text": "This is a really great place to watch a baseball game .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yeah , there isn ' t a bad seat in the place .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "really great place to watch a baseball game .", + "Yeah , there isn ' t a bad seat in the place ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yeah , there isn ' t a bad seat in the place .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "The fans are great here , too . Not like in Philadelphia .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "The fans are great here" + ], + "type": [ + "no-context" + ], + "text": "The fans are great here , too . Not like in Philadelphia .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "It was a great idea to spend a day watching a game .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8, + 9, + 10 + ], + "expanded emotion cause span": [ + "really great place to watch a baseball game .", + "Yeah , there isn ' t a bad seat in the place .", + "The fans are great here", + "great idea to spend a day watching a game ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "It was a great idea to spend a day watching a game .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Yeah , it reminds you why they say baseball is America ' s favorite pastime .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8, + 9, + 10 + ], + "expanded emotion cause span": [ + "really great place to watch a baseball game .", + "Yeah , there isn ' t a bad seat in the place .", + "The fans are great here", + "great idea to spend a day watching a game ." + ], + "type": [ + "hybrid" + ], + "text": "Yeah , it reminds you why they say baseball is America ' s favorite pastime .", + "id": 11 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2002.json b/reccon/sources/tr_2002.json new file mode 100644 index 0000000000000000000000000000000000000000..2a21d544c84379f3df5e6d8f6e2eddd5a045bc41 --- /dev/null +++ b/reccon/sources/tr_2002.json @@ -0,0 +1,174 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "It's snowing outside .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "snowing outside" + ], + "type": [ + "no-context" + ], + "text": "It's snowing outside .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh , how could it be ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "snowing outside" + ], + "type": [ + "inter-personal" + ], + "text": "Oh , how could it be ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Let's go out and have a look .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "snowing outside" + ], + "type": [ + "self-contagion" + ], + "text": "Let's go out and have a look .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "OK . Wait a minute .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "snowing outside" + ], + "type": [ + "inter-personal" + ], + "text": "OK . Wait a minute .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Look at the snow , it's so beautiful .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 5 + ], + "expanded emotion cause span": [ + "snowing outside", + "it's so beautiful" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Look at the snow , it's so beautiful .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yes . It's really snowing .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "snowing outside" + ], + "type": [ + "inter-personal" + ], + "text": "Yes . It's really snowing .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I love winter , I love snow .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 5, + 7 + ], + "expanded emotion cause span": [ + "snowing outside", + "it's so beautiful", + "I love winter , I love snow ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I love winter , I love snow .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "But don't you think it's a little too cold ?", + "emotion": "neutral", + "text": "But don't you think it's a little too cold ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "But I like cold more than hot .", + "emotion": "neutral", + "text": "But I like cold more than hot .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "You are so interesting .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "But I like cold more than hot .", + "You are so interesting ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You are so interesting .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2042.json b/reccon/sources/tr_2042.json new file mode 100644 index 0000000000000000000000000000000000000000..45c51aa2dc2cefdbe63a4bc685fef9e9e8156db8 --- /dev/null +++ b/reccon/sources/tr_2042.json @@ -0,0 +1,123 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Mary , how was your date with John ?", + "emotion": "neutral", + "text": "Mary , how was your date with John ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It ' s OK . It seems we have a lot in common .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "It seems we have a lot in common ." + ], + "type": [ + "no-context" + ], + "text": "It ' s OK . It seems we have a lot in common .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Oh , really ? That is great news . What does he look like ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "It seems we have a lot in common ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , really ? That is great news . What does he look like ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "He is tall and slim , fair-haired .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 4 + ], + "expanded emotion cause span": [ + "It seems we have a lot in common .", + "He is tall and slim , fair-haired ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "He is tall and slim , fair-haired .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Sounds like he is pretty cute . What do you think of him ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "He is tall and slim , fair-haired .", + "Sounds like he is pretty cute ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Sounds like he is pretty cute . What do you think of him ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "He is a nice guy and very considerate . I am impressed with how smart and humorous .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "He is a nice guy and very considerate . I am impressed with how smart and humorous ." + ], + "type": [ + "no-context" + ], + "text": "He is a nice guy and very considerate . I am impressed with how smart and humorous .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Oh , it ' s love at first sight .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "He is a nice guy and very considerate . I am impressed with how smart and humorous ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , it ' s love at first sight .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2061.json b/reccon/sources/tr_2061.json new file mode 100644 index 0000000000000000000000000000000000000000..068778ea0256225ccfcfbb4a2232755699094751 --- /dev/null +++ b/reccon/sources/tr_2061.json @@ -0,0 +1,123 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Rose , the weekend is coming . Let's discuss what we will do .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "the weekend is coming" + ], + "type": [ + "no-context" + ], + "text": "Rose , the weekend is coming . Let's discuss what we will do .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What about going to the zoo on Saturday and to the park on Sunday ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "the weekend is coming", + "going to the zoo on Saturday and to the park on Sunday" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "What about going to the zoo on Saturday and to the park on Sunday ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Sounds good . But on Saturday there's a football final .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "What about going to the zoo on Saturday and to the park on Sunday ?" + ], + "type": [ + "inter-personal" + ], + "text": "Sounds good . But on Saturday there's a football final .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Then , what shall we do on Sunday .", + "emotion": "neutral", + "text": "Then , what shall we do on Sunday .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Let me see . We can visit the country . We haven't done that for such a long time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 5 + ], + "expanded emotion cause span": [ + "What about going to the zoo on Saturday and to the park on Sunday ?", + "We can visit the country" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Let me see . We can visit the country . We haven't done that for such a long time .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Good idea . I'll go shopping in one of the department stores nearby . We'll go to the zoo and the park another time . After all , we can put that off .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "We can visit the country" + ], + "type": [ + "inter-personal" + ], + "text": "Good idea . I'll go shopping in one of the department stores nearby . We'll go to the zoo and the park another time . After all , we can put that off .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "OK .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "We can visit the country" + ], + "type": [ + "self-contagion" + ], + "text": "OK .", + "id": 7 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2066.json b/reccon/sources/tr_2066.json new file mode 100644 index 0000000000000000000000000000000000000000..b290488bc5951f6b7ea29b5ca5386ec344ea03e5 --- /dev/null +++ b/reccon/sources/tr_2066.json @@ -0,0 +1,179 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What are you doing there with your mobile phone ?", + "emotion": "happiness", + "explanation": "A is happy for some unkown reason", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "What are you doing there with your mobile phone ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'm moblogging !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I'm moblogging !" + ], + "type": [ + "no-context" + ], + "text": "I'm moblogging !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Moblogging ? what does that mean ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Moblogging ? what does that mean ?" + ], + "type": [ + "no-context" + ], + "text": "Moblogging ? what does that mean ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Oh , moblogging is a combination of the word ' mobile ' and ' blogging ' . It's another form of blogging . Users can publish blog entries to the web from a mobile phone or other mobile devices .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I'm moblogging !" + ], + "type": [ + "self-contagion" + ], + "text": "Oh , moblogging is a combination of the word ' mobile ' and ' blogging ' . It's another form of blogging . Users can publish blog entries to the web from a mobile phone or other mobile devices .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Sounds interesting ! That must be very convenient .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Sounds interesting ! That must be very convenient ." + ], + "type": [ + "no-context" + ], + "text": "Sounds interesting ! That must be very convenient .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yes , you're right . I can blog wherever and whenever I'm on the move . It's especially good when I'm on a business trip and my laptop happens to be away from me .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 6 + ], + "expanded emotion cause span": [ + "I'm moblogging !", + "I can blog wherever and whenever I'm on the move . It's especially good when I'm on a business trip and my laptop happens to be away from me ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Yes , you're right . I can blog wherever and whenever I'm on the move . It's especially good when I'm on a business trip and my laptop happens to be away from me .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "How can you do that ?", + "emotion": "neutral", + "text": "How can you do that ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Well , if I simply want to write a few words , I'll send it by email or edit it all from the cell phone browser .", + "emotion": "neutral", + "text": "Well , if I simply want to write a few words , I'll send it by email or edit it all from the cell phone browser .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "What if you want to publish some photos ?", + "emotion": "neutral", + "text": "What if you want to publish some photos ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Then I'll shoot some pictures , re-size the images and upload them with text descriptions to my blog .", + "emotion": "neutral", + "text": "Then I'll shoot some pictures , re-size the images and upload them with text descriptions to my blog .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I see . Moblogging must have done a great favor for habitual bloggers like you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "Moblogging must have done a great favor for habitual bloggers" + ], + "type": [ + "no-context" + ], + "text": "I see . Moblogging must have done a great favor for habitual bloggers like you .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "You bet it !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "Moblogging must have done a great favor for habitual bloggers" + ], + "type": [ + "inter-personal" + ], + "text": "You bet it !", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2072.json b/reccon/sources/tr_2072.json new file mode 100644 index 0000000000000000000000000000000000000000..c429c1eba8e6145056e9ec192bc8b52bb5d314f5 --- /dev/null +++ b/reccon/sources/tr_2072.json @@ -0,0 +1,278 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Well , how was your honeymoon ?", + "emotion": "neutral", + "text": "Well , how was your honeymoon ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It was fantastic ! We had such a good time . The only problem was that because it was their high season , we spent hours queuing .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "It was fantastic ! We had such a good time ." + ], + "type": [ + "no-context" + ], + "text": "It was fantastic ! We had such a good time . The only problem was that because it was their high season , we spent hours queuing .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Peak periods always entail hours of queuing . At least you got a nice tan though !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "It was fantastic ! We had such a good time . The only problem was that because it was their high season , we spent hours queuing .", + "At least you got a nice tan though !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Peak periods always entail hours of queuing . At least you got a nice tan though !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes , Florida had great weather while we were there . You look tan , too . Did you go somewhere ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 4 + ], + "expanded emotion cause span": [ + "It was fantastic ! We had such a good time .", + "Florida had great weather while we were there" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Yes , Florida had great weather while we were there . You look tan , too . Did you go somewhere ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "My friends and I just got back from Bali .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "My friends and I just got back from Bali ." + ], + "type": [ + "no-context" + ], + "text": "My friends and I just got back from Bali .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Wow ! Bali Islands have some of the best beaches in the world , don't they ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "My friends and I just got back from Bali .", + "Bali Islands have some of the best beaches in the world" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Wow ! Bali Islands have some of the best beaches in the world , don't they ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yes , we were lucky . My friend's father owns a resort on one of the islands , so we were able to stay for free .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 7 + ], + "expanded emotion cause span": [ + "My friends and I just got back from Bali .", + "My friend's father owns a resort on one of the islands , so we were able to stay for free ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Yes , we were lucky . My friend's father owns a resort on one of the islands , so we were able to stay for free .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Did you go diving while you were there ?", + "emotion": "neutral", + "text": "Did you go diving while you were there ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I took a few diving classes , but I didn't really like it , so I did snorkeling instead !", + "emotion": "neutral", + "text": "I took a few diving classes , but I didn't really like it , so I did snorkeling instead !", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Did you take any pictures in the ocean ?", + "emotion": "neutral", + "text": "Did you take any pictures in the ocean ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I've got quite a few pictures of all different kinds of fish . I'll show them to you next time I see you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "ve got quite a few pictures of all different kinds of fish ." + ], + "type": [ + "no-context" + ], + "text": "I've got quite a few pictures of all different kinds of fish . I'll show them to you next time I see you .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Have you started planning your christmas vacation yet ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "Have you started planning your christmas vacation yet ?" + ], + "type": [ + "no-context" + ], + "text": "Have you started planning your christmas vacation yet ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "We're planning on going skiing in Switzerland . Do you ski ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "We're planning on going skiing in Switzerland" + ], + "type": [ + "no-context" + ], + "text": "We're planning on going skiing in Switzerland . Do you ski ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "No , but I do like snowboarding .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "I do like snowboarding ." + ], + "type": [ + "no-context" + ], + "text": "No , but I do like snowboarding .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Would you like to go skiing with us for christmas ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "Would you like to go skiing with us for christmas ?" + ], + "type": [ + "no-context" + ], + "text": "Would you like to go skiing with us for christmas ?", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "I'll talk to my husband about it ; I'm sure he'll say yes ! He loves Switzerland !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15, + 16 + ], + "expanded emotion cause span": [ + "Would you like to go skiing with us for christmas ?", + "I'm sure he'll say yes ! He loves Switzerland !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'll talk to my husband about it ; I'm sure he'll say yes ! He loves Switzerland !", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 17, + "speaker": "A", + "utterance": "It is Europe's spotless land of lakes and mountains ! Let me know as soon as you can so we can get a discount .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15, + 17 + ], + "expanded emotion cause span": [ + "Would you like to go skiing with us for christmas ?", + "It is Europe's spotless land of lakes and mountains !" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "It is Europe's spotless land of lakes and mountains ! Let me know as soon as you can so we can get a discount .", + "id": 17 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2080.json b/reccon/sources/tr_2080.json new file mode 100644 index 0000000000000000000000000000000000000000..9099c409ae0646271c09e9407a6f1cc2a1c84479 --- /dev/null +++ b/reccon/sources/tr_2080.json @@ -0,0 +1,112 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What do you like to do in your spare time ?", + "emotion": "neutral", + "text": "What do you like to do in your spare time ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I like taking photos .", + "emotion": "neutral", + "text": "I like taking photos .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Really ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I like taking photos ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes , look at the photos I took .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Yes , look at the photos I took ." + ], + "type": [ + "no-context" + ], + "text": "Yes , look at the photos I took .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "They are beautiful . You did a good job .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "They are beautiful . You did a good job ." + ], + "type": [ + "no-context" + ], + "text": "They are beautiful . You did a good job .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Thank you for saying so .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "They are beautiful . You did a good job ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you for saying so .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "As a matter of fact , you are really a terrific photographer .", + "emotion": "happiness", + "explanation": "Appreciation", + "expanded emotion cause evidence": [ + 5, + 7 + ], + "expanded emotion cause span": [ + "They are beautiful . You did a good job .", + "you are really a terrific photographer ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "As a matter of fact , you are really a terrific photographer .", + "id": 7 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_209.json b/reccon/sources/tr_209.json new file mode 100644 index 0000000000000000000000000000000000000000..f0afbbb8d93f41eaf5a4d4a41ba30c6d079cf03a --- /dev/null +++ b/reccon/sources/tr_209.json @@ -0,0 +1,127 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Did you see the information on sales for last year ? The sales review was made at our last board meeting . There's a great news for our shareholders .", + "emotion": "neutral", + "text": "Did you see the information on sales for last year ? The sales review was made at our last board meeting . There's a great news for our shareholders .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yeah , I went over the figures this morning . We're finally started making money again !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "We're finally started making money again !" + ], + "type": [ + "no-context" + ], + "text": "Yeah , I went over the figures this morning . We're finally started making money again !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "We've never sold this much before , our growth this year has been phenomenal . We have captured 8 % of the market , up from last year by 120 % . Our strategy is working !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "We're finally started making money again !", + "We've never sold this much before , our growth this year has been phenomenal . We have captured 8 % of the market , up from last year by 120 % . Our strategy is working !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "We've never sold this much before , our growth this year has been phenomenal . We have captured 8 % of the market , up from last year by 120 % . Our strategy is working !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "not only our annual sales brake a record , but our month by month earnings exceeded our forecast as well . After a two-year slump , we finally back in the black .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3, + 4, + 4 + ], + "expanded emotion cause span": [ + "We're finally started making money again !", + "We've never sold this much before , our growth this year has been phenomenal . We have captured 8 % of the market , up from last year by 120 % . Our strategy is working !", + "our month by month earnings exceeded our forecast", + "we finally back in the black ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "not only our annual sales brake a record , but our month by month earnings exceeded our forecast as well . After a two-year slump , we finally back in the black .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "The company's performance has improved since Wallace became president . He's made our little business into a real lucrative operation . Products are selling like hotcakes .", + "emotion": "neutral", + "text": "The company's performance has improved since Wallace became president . He's made our little business into a real lucrative operation . Products are selling like hotcakes .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I think our success is partly because of Wallace's contribution , and partly because of our new marketing strategy . Because of the new advertising campaign , we have become the top sellers in the field .", + "emotion": "neutral", + "text": "I think our success is partly because of Wallace's contribution , and partly because of our new marketing strategy . Because of the new advertising campaign , we have become the top sellers in the field .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Let's hope this stroke of good luck lasts . I hope we are over our financial difficulties for good .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I hope we are over our financial difficulties for good ." + ], + "type": [ + "no-context" + ], + "text": "Let's hope this stroke of good luck lasts . I hope we are over our financial difficulties for good .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Let's hope it is !", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I hope we are over our financial difficulties for good ." + ], + "type": [ + "inter-personal" + ], + "text": "Let's hope it is !", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2101.json b/reccon/sources/tr_2101.json new file mode 100644 index 0000000000000000000000000000000000000000..94fdf70f9b2c9e1160ca1a8b481b4ee14c284422 --- /dev/null +++ b/reccon/sources/tr_2101.json @@ -0,0 +1,266 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I don't know what to do about the people who live in the flat above me !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "the people who live in the flat above me" + ], + "type": [ + "no-context" + ], + "text": "I don't know what to do about the people who live in the flat above me !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Why ? What are they like ?", + "emotion": "neutral", + "text": "Why ? What are they like ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "They're incredibly selfish . They ' re always up until the wee hours of the night playing their music so loudly that I have to wear earplugs in order to fall asleep !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "They're incredibly selfish . They ' re always up until the wee hours of the night playing their music so loudly that I have to wear earplugs in order to fall asleep !" + ], + "type": [ + "no-context" + ], + "text": "They're incredibly selfish . They ' re always up until the wee hours of the night playing their music so loudly that I have to wear earplugs in order to fall asleep !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Have you ever talked to them about it ?", + "emotion": "neutral", + "text": "Have you ever talked to them about it ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I tried to introduce myself to them when they moved in , but they were so arrogant that I didin't want to ever talk to them again !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 3, + 5 + ], + "expanded emotion cause span": [ + "They're incredibly selfish . They ' re always up until the wee hours of the night playing their music so loudly that I have to wear earplugs in order to fall asleep !", + "they were so arrogant that I didin't want to ever talk to them again !" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I tried to introduce myself to them when they moved in , but they were so arrogant that I didin't want to ever talk to them again !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "What did they say ?", + "emotion": "neutral", + "text": "What did they say ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "They both just talk about how great they are all the time .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 3, + 5, + 7 + ], + "expanded emotion cause span": [ + "They're incredibly selfish . They ' re always up until the wee hours of the night playing their music so loudly that I have to wear earplugs in order to fall asleep !", + "they were so arrogant that I didin't want to ever talk to them again !", + "They both just talk about how great they are all the time ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "They both just talk about how great they are all the time .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "They soud like the neighbours from hell !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 3, + 5, + 7, + 7 + ], + "expanded emotion cause span": [ + "They're incredibly selfish . They ' re always up until the wee hours of the night playing their music so loudly that I have to wear earplugs in order to fall asleep !", + "they were so arrogant that I didin't want to ever talk to them again !", + "They both just talk about how great they are all the time .", + "They both just talk about how great they are all the time ." + ], + "type": [ + "inter-personal" + ], + "text": "They soud like the neighbours from hell !", + "id": 8, + "source_sentences": [ + 2, + 4, + 6, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "They are ! Besides being loud and arrogant , they're also terrible gossips . They're always talking about everybody else in the apartment .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 3, + 5, + 7, + 9 + ], + "expanded emotion cause span": [ + "They're incredibly selfish . They ' re always up until the wee hours of the night playing their music so loudly that I have to wear earplugs in order to fall asleep !", + "they were so arrogant that I didin't want to ever talk to them again !", + "They both just talk about how great they are all the time .", + "Besides being loud and arrogant , they're also terrible gossips . They're always talking about everybody else in the apartment ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "They are ! Besides being loud and arrogant , they're also terrible gossips . They're always talking about everybody else in the apartment .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I thought you didn't talk to them much .", + "emotion": "neutral", + "text": "I thought you didn't talk to them much .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I don't , but they talk so loudly that I can hear what they're talking about from my bedroom - and it's not very nice .", + "emotion": "neutral", + "text": "I don't , but they talk so loudly that I can hear what they're talking about from my bedroom - and it's not very nice .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "What do the other people in your apartment think about them ?", + "emotion": "neutral", + "text": "What do the other people in your apartment think about them ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Most of my other neighbours are scared of them .", + "emotion": "neutral", + "text": "Most of my other neighbours are scared of them .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Maybe you should think about moving .", + "emotion": "neutral", + "text": "Maybe you should think about moving .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "I can't afford to move right now .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 3, + 5, + 7, + 9, + 15 + ], + "expanded emotion cause span": [ + "They're incredibly selfish . They ' re always up until the wee hours of the night playing their music so loudly that I have to wear earplugs in order to fall asleep !", + "they were so arrogant that I didin't want to ever talk to them again !", + "They both just talk about how great they are all the time .", + "Besides being loud and arrogant , they're also terrible gossips . They're always talking about everybody else in the apartment .", + "I can't afford to move right now ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I can't afford to move right now .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Well , perhaps you should have a party and try to get to know them better . Maybe once you get to know them , they'll turn out to be more sensitive .", + "emotion": "neutral", + "text": "Well , perhaps you should have a party and try to get to know them better . Maybe once you get to know them , they'll turn out to be more sensitive .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "I think you're being a bit optimistic . If you met them , you'd understand .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 3, + 5, + 7, + 9, + 15, + 16 + ], + "expanded emotion cause span": [ + "They're incredibly selfish . They ' re always up until the wee hours of the night playing their music so loudly that I have to wear earplugs in order to fall asleep !", + "they were so arrogant that I didin't want to ever talk to them again !", + "They both just talk about how great they are all the time .", + "Besides being loud and arrogant , they're also terrible gossips . They're always talking about everybody else in the apartment .", + "I can't afford to move right now .", + "perhaps you should have a party and try to get to know them better ." + ], + "type": [ + "hybrid" + ], + "text": "I think you're being a bit optimistic . If you met them , you'd understand .", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "Well , I don't know what else you could do then . Do you think bribing them with chocolate would work ?", + "emotion": "neutral", + "text": "Well , I don't know what else you could do then . Do you think bribing them with chocolate would work ?", + "id": 18 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2105.json b/reccon/sources/tr_2105.json new file mode 100644 index 0000000000000000000000000000000000000000..3485c0b3f044b4128927e18917520a1cc9958fef --- /dev/null +++ b/reccon/sources/tr_2105.json @@ -0,0 +1,155 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "How are you doing , Andrew ?", + "emotion": "neutral", + "text": "How are you doing , Andrew ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Not well . I ' Ve been feeling pretty lonely lately .", + "emotion": "neutral", + "text": "Not well . I ' Ve been feeling pretty lonely lately .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "But you have so many friends ! How could you be lonely ?", + "emotion": "neutral", + "text": "But you have so many friends ! How could you be lonely ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "You know what they say'a friend to all is a friend to none ' . I don ' t feel like I really know any of my friends . In fact , I should probably call them acquaintances , not friends .", + "emotion": "neutral", + "text": "You know what they say'a friend to all is a friend to none ' . I don ' t feel like I really know any of my friends . In fact , I should probably call them acquaintances , not friends .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "What about me ? I ' m your friend .", + "emotion": "neutral", + "text": "What about me ? I ' m your friend .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I know you are , you are my girlfriend . I wish I had a guy friend to hang out with sometimes .", + "emotion": "neutral", + "text": "I know you are , you are my girlfriend . I wish I had a guy friend to hang out with sometimes .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I know what you mean . I find it difficult to make new friends , too . It ' s not as easy as it was when we were young , is it ?", + "emotion": "neutral", + "text": "I know what you mean . I find it difficult to make new friends , too . It ' s not as easy as it was when we were young , is it ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Not at all .", + "emotion": "neutral", + "text": "Not at all .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I ' Ve made a lot of new friends since I started learning English . Maybe you could join a club or take a class to make some new friends .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "I ' Ve made a lot of new friends since I started learning English ." + ], + "type": [ + "no-context" + ], + "text": "I ' Ve made a lot of new friends since I started learning English . Maybe you could join a club or take a class to make some new friends .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "That ' s a good idea .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Maybe you could join a club or take a class to make some new friends ." + ], + "type": [ + "inter-personal" + ], + "text": "That ' s a good idea .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "What kind of qualities do you look for in a friend ?", + "emotion": "neutral", + "text": "What kind of qualities do you look for in a friend ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I ' m not sure . I guess I ' d like to meet some people who have a positive attitude and want to have a good time .", + "emotion": "neutral", + "text": "I ' m not sure . I guess I ' d like to meet some people who have a positive attitude and want to have a good time .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "People who play ultimate Frisbee have a positive attitude ; maybe you should join the ultimate Frisbee club .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "People who play ultimate Frisbee have a positive attitude ; maybe you should join the ultimate Frisbee club ." + ], + "type": [ + "no-context" + ], + "text": "People who play ultimate Frisbee have a positive attitude ; maybe you should join the ultimate Frisbee club .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "That ' s a possibility . Thanks !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "People who play ultimate Frisbee have a positive attitude ; maybe you should join the ultimate Frisbee club ." + ], + "type": [ + "inter-personal" + ], + "text": "That ' s a possibility . Thanks !", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2122.json b/reccon/sources/tr_2122.json new file mode 100644 index 0000000000000000000000000000000000000000..0734c1d6a8a6d30502e2c3314543fd06ece8a4bc --- /dev/null +++ b/reccon/sources/tr_2122.json @@ -0,0 +1,309 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "The dinner was really good . It knocked my socks off .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "The dinner was really good . It knocked my socks off ." + ], + "type": [ + "no-context" + ], + "text": "The dinner was really good . It knocked my socks off .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "That's very kind of you to say so . Let's try some after-dinner wines .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "The dinner was really good . It knocked my socks off .", + "That's very kind of you to say so . Let's try some after-dinner wines ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's very kind of you to say so . Let's try some after-dinner wines .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Great . Sweet wines are my favorite . They always make a great finish to a decisions meal .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "Let's try some after-dinner wines .", + "Sweet wines are my favorite . They always make a great finish to a decisions meal ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Great . Sweet wines are my favorite . They always make a great finish to a decisions meal .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Do you prefer brandy or ports .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Sweet wines are my favorite . They always make a great finish to a decisions meal ." + ], + "type": [ + "inter-personal" + ], + "text": "Do you prefer brandy or ports .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Port , please .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3, + 4 + ], + "expanded emotion cause span": [ + "Let's try some after-dinner wines .", + "Sweet wines are my favorite . They always make a great finish to a decisions meal .", + "Do you prefer brandy or ports ." + ], + "type": [ + "hybrid" + ], + "text": "Port , please .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Excellent choice . I love its smooth flavor .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Port", + "Excellent choice . I love its smooth flavor ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Excellent choice . I love its smooth flavor .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "The port is quite exquisite . It must have spent years aging in barrels . Am I right ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6, + 7 + ], + "expanded emotion cause span": [ + "Port", + "Excellent choice . I love its smooth flavor .", + "The port is quite exquisite . It must have spent years aging in barrels ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "The port is quite exquisite . It must have spent years aging in barrels . Am I right ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yes . You always have a good nose for wines .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "The port is quite exquisite . It must have spent years aging in barrels ." + ], + "type": [ + "inter-personal" + ], + "text": "Yes . You always have a good nose for wines .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Next time we are about to dinner we should try some Canadian ice wine .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8, + 9 + ], + "expanded emotion cause span": [ + "The port is quite exquisite . It must have spent years aging in barrels .", + "You always have a good nose for wines .", + "Next time we are about to dinner we should try some Canadian ice wine ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Next time we are about to dinner we should try some Canadian ice wine .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Oh , what's that ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Canadian ice wine ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , what's that ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "It's made from naturally frozen grapes .", + "emotion": "happiness", + "explanation": "the speaker is glad that B is asking more about the wine he/she brought up", + "expanded emotion cause evidence": [ + 9, + 10, + 11 + ], + "expanded emotion cause span": [ + "Canadian ice wine .", + "Oh , what's that ?", + "It's made from naturally frozen grapes ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "It's made from naturally frozen grapes .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Why not ? It sounds great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 11, + 12 + ], + "expanded emotion cause span": [ + "Canadian ice wine .", + "It's made from naturally frozen grapes .", + "It sounds great ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Why not ? It sounds great .", + "id": 12, + "source_sentences": [ + 8, + 10 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 13, + "speaker": "A", + "utterance": "OK , here's to your health .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 11, + 12 + ], + "expanded emotion cause span": [ + "Canadian ice wine .", + "It's made from naturally frozen grapes .", + "It sounds great ." + ], + "type": [ + "hybrid" + ], + "text": "OK , here's to your health .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Thanks . Cheers .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6, + 13 + ], + "expanded emotion cause span": [ + "Port", + "Excellent choice . I love its smooth flavor .", + "OK , here's to your health ." + ], + "type": [ + "hybrid" + ], + "text": "Thanks . Cheers .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Cheers .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6, + 14 + ], + "expanded emotion cause span": [ + "Port", + "Excellent choice . I love its smooth flavor .", + "Thanks . Cheers ." + ], + "type": [ + "hybrid" + ], + "text": "Cheers .", + "id": 15 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2124.json b/reccon/sources/tr_2124.json new file mode 100644 index 0000000000000000000000000000000000000000..8b0a937288fec4baad70ac17f06774209e41b358 --- /dev/null +++ b/reccon/sources/tr_2124.json @@ -0,0 +1,118 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Good evening , sir . What can I do for you ?", + "emotion": "neutral", + "text": "Good evening , sir . What can I do for you ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Bourbon , please .", + "emotion": "neutral", + "text": "Bourbon , please .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "How would you like your Bourbon , straight or on the rock ?", + "emotion": "neutral", + "text": "How would you like your Bourbon , straight or on the rock ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "With iced water , please .", + "emotion": "neutral", + "text": "With iced water , please .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Here you are , sir . Bourbon with iced water .", + "emotion": "neutral", + "text": "Here you are , sir . Bourbon with iced water .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Thank you . Now how much do I owe you ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Here you are , sir . Bourbon with iced water ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . Now how much do I owe you ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "The bourbon is 15 dollars plus 10 % service charge . So the total is 16 . 5 dollars .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "how much do I owe you ?" + ], + "type": [ + "inter-personal" + ], + "text": "The bourbon is 15 dollars plus 10 % service charge . So the total is 16 . 5 dollars .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That is OK . Here is 20 dollars and you can keep the change .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "The bourbon is 15 dollars plus 10 % service charge . So the total is 16 . 5 dollars .", + "That is OK ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That is OK . Here is 20 dollars and you can keep the change .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Thanks a lot .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "That is OK . Here is 20 dollars and you can keep the change ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks a lot .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2170.json b/reccon/sources/tr_2170.json new file mode 100644 index 0000000000000000000000000000000000000000..03d48965f5569ff32ffb6f8b00a34b008d2597b5 --- /dev/null +++ b/reccon/sources/tr_2170.json @@ -0,0 +1,196 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello , Jill .", + "emotion": "neutral", + "text": "Hello , Jill .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Tom , You're back , come in please . How are you ?", + "emotion": "neutral", + "text": "Tom , You're back , come in please . How are you ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Fine , only a little tired .", + "emotion": "neutral", + "text": "Fine , only a little tired .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "You'll recover after a good night's sleep .", + "emotion": "neutral", + "text": "You'll recover after a good night's sleep .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Thank you very much for looking after my house in my absence .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Thank you very much for looking after my house in my absence ." + ], + "type": [ + "no-context" + ], + "text": "Thank you very much for looking after my house in my absence .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "That's all right . Would you have a cup of coffee ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Thank you very much for looking after my house in my absence ." + ], + "type": [ + "inter-personal" + ], + "text": "That's all right . Would you have a cup of coffee ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yes , Please . It ' s very kind of you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Would you have a cup of coffee ?" + ], + "type": [ + "inter-personal" + ], + "text": "Yes , Please . It ' s very kind of you .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Don't mention it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Yes , Please . It ' s very kind of you ." + ], + "type": [ + "inter-personal" + ], + "text": "Don't mention it .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "The rooms are very tidy and the flowers grew very well . You are very helpful . I want to thank you for everything you've done for me .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "The rooms are very tidy and the flowers grew very well . You are very helpful . I want to thank you for everything you've done for me ." + ], + "type": [ + "no-context" + ], + "text": "The rooms are very tidy and the flowers grew very well . You are very helpful . I want to thank you for everything you've done for me .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "It's my pleasure .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "The rooms are very tidy and the flowers grew very well . You are very helpful . I want to thank you for everything you've done for me ." + ], + "type": [ + "inter-personal" + ], + "text": "It's my pleasure .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I bought you some books on literature , I don't know if you would like them .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "The rooms are very tidy and the flowers grew very well . You are very helpful . I want to thank you for everything you've done for me .", + "It's my pleasure ." + ], + "type": [ + "hybrid" + ], + "text": "I bought you some books on literature , I don't know if you would like them .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Thank you . Thank you for the trouble you've taken .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I bought you some books on literature ," + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . Thank you for the trouble you've taken .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Not at all .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "Thank you . Thank you for the trouble you've taken ." + ], + "type": [ + "inter-personal" + ], + "text": "Not at all .", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2179.json b/reccon/sources/tr_2179.json new file mode 100644 index 0000000000000000000000000000000000000000..06c2916f05dfed45fb8e921c33fbd49ed8ccb901 --- /dev/null +++ b/reccon/sources/tr_2179.json @@ -0,0 +1,107 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Listen to this . Mary got married .", + "emotion": "neutral", + "text": "Listen to this . Mary got married .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Is she really ? I can ' t believe it !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Mary got married ." + ], + "type": [ + "inter-personal" + ], + "text": "Is she really ? I can ' t believe it !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yes . Yesterday .", + "emotion": "neutral", + "text": "Yes . Yesterday .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Good gracious . That ' s incredible !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Mary got married ." + ], + "type": [ + "inter-personal" + ], + "text": "Good gracious . That ' s incredible !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "She married Jerrod .", + "emotion": "neutral", + "text": "She married Jerrod .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "You ' re kidding .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "She married Jerrod ." + ], + "type": [ + "inter-personal" + ], + "text": "You ' re kidding .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "She ' s going to live in Paris .", + "emotion": "neutral", + "text": "She ' s going to live in Paris .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Really ? I ' m surprised .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "She ' s going to live in Paris ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? I ' m surprised .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2184.json b/reccon/sources/tr_2184.json new file mode 100644 index 0000000000000000000000000000000000000000..4532bd0c1987ef40a77a1cd89443045785053e77 --- /dev/null +++ b/reccon/sources/tr_2184.json @@ -0,0 +1,126 @@ +[ + { + "turn": 1, + "speaker": "B", + "utterance": "Mary , it was wrong of you to be so late . Mother ' s very worried .", + "emotion": "neutral", + "text": "Mary , it was wrong of you to be so late . Mother ' s very worried .", + "id": 1 + }, + { + "turn": 2, + "speaker": "A", + "utterance": "I ' m so sorry I ' m late . But Henry ' s car broke down .", + "emotion": "neutral", + "text": "I ' m so sorry I ' m late . But Henry ' s car broke down .", + "id": 2 + }, + { + "turn": 3, + "speaker": "B", + "utterance": "I don ' t really like Henry . I like my Rose .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I don ' t really like Henry ." + ], + "type": [ + "no-context" + ], + "text": "I don ' t really like Henry . I like my Rose .", + "id": 3 + }, + { + "turn": 4, + "speaker": "A", + "utterance": "I don ' t like your Rose . And I do love Henry . And I ' m going to marry him .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "I don ' t really like Henry .", + "I don ' t like your Rose ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I don ' t like your Rose . And I do love Henry . And I ' m going to marry him .", + "id": 4 + }, + { + "turn": 5, + "speaker": "B", + "utterance": "But my Rose is great .", + "emotion": "neutral", + "text": "But my Rose is great .", + "id": 5 + }, + { + "turn": 6, + "speaker": "A", + "utterance": "Your Rose is a fool .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Your Rose is a fool ." + ], + "type": [ + "no-context" + ], + "text": "Your Rose is a fool .", + "id": 6 + }, + { + "turn": 7, + "speaker": "B", + "utterance": "Really , Mary , you ' re horrible .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "Your Rose is a fool .", + "Really , Mary , you ' re horrible ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Really , Mary , you ' re horrible .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "A", + "utterance": "Why don ' t you marry Rose , then ?", + "emotion": "anger", + "expanded emotion cause evidence": [ + 3, + 4, + 7 + ], + "expanded emotion cause span": [ + "I don ' t really like Henry . I like my Rose .", + "I don ' t like your Rose . And I do love Henry . And I ' m going to marry him .", + "Really , Mary , you ' re horrible ." + ], + "type": [ + "hybrid" + ], + "text": "Why don ' t you marry Rose , then ?", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2198.json b/reccon/sources/tr_2198.json new file mode 100644 index 0000000000000000000000000000000000000000..0981d15ae50952b1b37822009b120ed97cd7687e --- /dev/null +++ b/reccon/sources/tr_2198.json @@ -0,0 +1,238 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Do you like flowers ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Do you like flowers ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Of course , I like flowers .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I like flowers ." + ], + "type": [ + "no-context" + ], + "text": "Of course , I like flowers .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What's your favorite flower ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 2 + ], + "expanded emotion cause span": [ + "I like flowers .", + "I like flowers ." + ], + "type": [ + "inter-personal" + ], + "text": "What's your favorite flower ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I like peach blossom , because I like spring .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 2, + 4 + ], + "expanded emotion cause span": [ + "I like flowers .", + "I like flowers .", + "I like peach blossom , because I like spring ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I like peach blossom , because I like spring .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Peach blossom is really beautiful .", + "emotion": "happiness", + "explanation": "speaker and listener are happy to discuss on thier mutual love for flowers", + "expanded emotion cause evidence": [ + 2, + 2, + 4, + 5 + ], + "expanded emotion cause span": [ + "I like flowers .", + "I like flowers .", + "I like peach blossom , because I like spring .", + "Peach blossom is really beautiful ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Peach blossom is really beautiful .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yes . How about you ?", + "emotion": "happiness", + "explanation": "speaker and listener are happy to discuss on thier mutual love for flowers", + "expanded emotion cause evidence": [ + 2, + 2, + 4 + ], + "expanded emotion cause span": [ + "I like flowers .", + "I like flowers .", + "I like peach blossom , because I like spring ." + ], + "type": [ + "self-contagion" + ], + "text": "Yes . How about you ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I like lotus .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 2, + 7 + ], + "expanded emotion cause span": [ + "I like flowers .", + "I like flowers .", + "I like lotus ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I like lotus .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "You have a perfect taste !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 2, + 7, + 8 + ], + "expanded emotion cause span": [ + "I like flowers .", + "I like flowers .", + "I like lotus .", + "You have a perfect taste !" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "You have a perfect taste !", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "But there aren't any lotus now .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 2, + 7, + 8 + ], + "expanded emotion cause span": [ + "I like flowers .", + "I like flowers .", + "I like lotus .", + "You have a perfect taste !" + ], + "type": [ + "hybrid" + ], + "text": "But there aren't any lotus now .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Yes . It's snowing outside . Let's enjoy the plum blossoms .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 10 + ], + "expanded emotion cause span": [ + "I like flowers .", + "Let's enjoy the plum blossoms ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Yes . It's snowing outside . Let's enjoy the plum blossoms .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "That's not bad . Let's go .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 10 + ], + "expanded emotion cause span": [ + "I like flowers .", + "Let's enjoy the plum blossoms ." + ], + "type": [ + "inter-personal" + ], + "text": "That's not bad . Let's go .", + "id": 11, + "source_sentences": [ + 1, + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2200.json b/reccon/sources/tr_2200.json new file mode 100644 index 0000000000000000000000000000000000000000..43794642b130f76f0a5443184ffda979c323c206 --- /dev/null +++ b/reccon/sources/tr_2200.json @@ -0,0 +1,111 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "There's a double feature at the cinema this Saturday . Do you want to go with me ?", + "emotion": "neutral", + "text": "There's a double feature at the cinema this Saturday . Do you want to go with me ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What are the movies that are playing ?", + "emotion": "neutral", + "text": "What are the movies that are playing ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "There's an action movie with Harrison Ford and a chick flick with Susan Abandon .", + "emotion": "neutral", + "text": "There's an action movie with Harrison Ford and a chick flick with Susan Abandon .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I've never seen a movie I don't like that had Harrison Ford in it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "There's an action movie with Harrison Ford" + ], + "type": [ + "inter-personal" + ], + "text": "I've never seen a movie I don't like that had Harrison Ford in it .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "So , is that a yes ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I've never seen a movie I don't like that had Harrison Ford in it ." + ], + "type": [ + "inter-personal" + ], + "text": "So , is that a yes ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yes . What time does it start and do you want to meet me there ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "There's an action movie with Harrison Ford" + ], + "type": [ + "inter-personal" + ], + "text": "Yes . What time does it start and do you want to meet me there ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "It starts at one and yea , let's meet there . It's the cinema on the corner of Lincoln and Main .", + "emotion": "neutral", + "text": "It starts at one and yea , let's meet there . It's the cinema on the corner of Lincoln and Main .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Great ! I have a coupon for free popcorn at that theater !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 8 + ], + "expanded emotion cause span": [ + "There's an action movie with Harrison Ford", + "I have a coupon for free popcorn" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Great ! I have a coupon for free popcorn at that theater !", + "id": 8, + "source_sentences": [ + 2 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_221.json b/reccon/sources/tr_221.json new file mode 100644 index 0000000000000000000000000000000000000000..8b93d891177efc743691d5124a254802fdaf1441 --- /dev/null +++ b/reccon/sources/tr_221.json @@ -0,0 +1,132 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Come on in . I am so glad you are here . We have been expecting you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "you are here . We have been expecting you ." + ], + "type": [ + "no-context" + ], + "text": "Come on in . I am so glad you are here . We have been expecting you .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Am I late for the party ? Looks everyone is already here . Hope I didn ' t miss something interesting .", + "emotion": "neutral", + "text": "Am I late for the party ? Looks everyone is already here . Hope I didn ' t miss something interesting .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "No , you are just on time . We haven ' t really started yet .", + "emotion": "neutral", + "text": "No , you are just on time . We haven ' t really started yet .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Great , here are some flowers for you . I hope you like them . I was not sure if the color will suit your new apartment .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "Hope I didn ' t miss something interesting .", + "No , you are just on time . We haven ' t really started yet ." + ], + "type": [ + "hybrid" + ], + "text": "Great , here are some flowers for you . I hope you like them . I was not sure if the color will suit your new apartment .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Thank you , they ' re beautiful . You can hang your coat over there . Try this new couch , it is so comfortable . You will love it . Want something to drink , tea , coffee , juice or Cola ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "here are some flowers for you .", + "they ' re beautiful" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you , they ' re beautiful . You can hang your coat over there . Try this new couch , it is so comfortable . You will love it . Want something to drink , tea , coffee , juice or Cola ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Don ' t bother . I will help myself .", + "emotion": "neutral", + "text": "Don ' t bother . I will help myself .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Make yourself at home .", + "emotion": "neutral", + "text": "Make yourself at home .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "It is such a nice place .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "such a nice place ." + ], + "type": [ + "no-context" + ], + "text": "It is such a nice place .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Well , I don ' t mean to boast but all the designs are done by myself and some colleagues are already trying to copy some of them for their new apartments . Look , they are making photos now of my designed kitchen .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "such a nice place .", + "all the designs are done by myself and some colleagues are already trying to copy some of them for their new apartments . Look , they are making photos now of my designed kitchen ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Well , I don ' t mean to boast but all the designs are done by myself and some colleagues are already trying to copy some of them for their new apartments . Look , they are making photos now of my designed kitchen .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2210.json b/reccon/sources/tr_2210.json new file mode 100644 index 0000000000000000000000000000000000000000..94d40a1ef347c9ebec35c0b9334f1d5dc710ee92 --- /dev/null +++ b/reccon/sources/tr_2210.json @@ -0,0 +1,223 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What are we going to do ? I can't get the car out of this ditch . I'm stuck !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I can't get the car out of this ditch . I'm stuck !" + ], + "type": [ + "no-context" + ], + "text": "What are we going to do ? I can't get the car out of this ditch . I'm stuck !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'm worried , Tom . I haven't seen any other cars for almost an hour .", + "emotion": "neutral", + "text": "I'm worried , Tom . I haven't seen any other cars for almost an hour .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I know . This is terrible . What can we do ? This snow doesn't stop falling !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "I can't get the car out of this ditch . I'm stuck !", + "This snow doesn't stop falling !" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I know . This is terrible . What can we do ? This snow doesn't stop falling !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I told you we should have stayed in town today . The weather report said 100 percent chance of snow . Why did you want to come up here ?", + "emotion": "neutral", + "text": "I told you we should have stayed in town today . The weather report said 100 percent chance of snow . Why did you want to come up here ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I wanted to show you the cabin . We only had another half-hour to go .", + "emotion": "neutral", + "text": "I wanted to show you the cabin . We only had another half-hour to go .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Well , now we're stuck . What can we do ?", + "emotion": "neutral", + "text": "Well , now we're stuck . What can we do ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I don't know .", + "emotion": "neutral", + "text": "I don't know .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I've heard that when this happens , it's important to save energy .", + "emotion": "neutral", + "text": "I've heard that when this happens , it's important to save energy .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "What do you mean ?", + "emotion": "neutral", + "text": "What do you mean ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "We're stranded here , Tom . We may be here a long time . We need to conserve the gas in the car . The car's energy is what will keep us warm .", + "emotion": "neutral", + "text": "We're stranded here , Tom . We may be here a long time . We need to conserve the gas in the car . The car's energy is what will keep us warm .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I have plenty of gas .", + "emotion": "neutral", + "text": "I have plenty of gas .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Yes , but the gas and the battery both have to stay working . We can't just let the car run and run . If we do , it will die soon . Then we'll freeze .", + "emotion": "neutral", + "text": "Yes , but the gas and the battery both have to stay working . We can't just let the car run and run . If we do , it will die soon . Then we'll freeze .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "So what can we do ?", + "emotion": "neutral", + "text": "So what can we do ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Turn the lights off . Then , run the car and the heater only about fifteen minutes every hour . That will conserve the heat as long as possible .", + "emotion": "neutral", + "text": "Turn the lights off . Then , run the car and the heater only about fifteen minutes every hour . That will conserve the heat as long as possible .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Alright . That's a good idea .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "That will conserve the heat as long as possible ." + ], + "type": [ + "inter-personal" + ], + "text": "Alright . That's a good idea .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "I wish we hadn't come up here . Now we'll probably be here for days .", + "emotion": "neutral", + "text": "I wish we hadn't come up here . Now we'll probably be here for days .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "Days ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 16 + ], + "expanded emotion cause span": [ + "we'll probably be here for days ." + ], + "type": [ + "inter-personal" + ], + "text": "Days ?", + "id": 17, + "source_sentences": [ + 15 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 18, + "speaker": "B", + "utterance": "Yes , it happens . That is what happens in big snowstorms . People get stranded for days .", + "emotion": "neutral", + "text": "Yes , it happens . That is what happens in big snowstorms . People get stranded for days .", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "Oh , my God ! It's good we have food .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 19 + ], + "expanded emotion cause span": [ + "It's good we have food ." + ], + "type": [ + "no-context" + ], + "text": "Oh , my God ! It's good we have food .", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "Probably we'll survive . But turn the car off for about forty-five minutes . Then we'll turn it on again .", + "emotion": "neutral", + "text": "Probably we'll survive . But turn the car off for about forty-five minutes . Then we'll turn it on again .", + "id": 20 + }, + { + "turn": 21, + "speaker": "A", + "utterance": "Okay , I'll follow your advice .", + "emotion": "neutral", + "text": "Okay , I'll follow your advice .", + "id": 21 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2212.json b/reccon/sources/tr_2212.json new file mode 100644 index 0000000000000000000000000000000000000000..7595911141035f771cd6e3aab1c4521740147d80 --- /dev/null +++ b/reccon/sources/tr_2212.json @@ -0,0 +1,99 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Mr . Bellow , have you anything in mind as to what to drink or may I make a few suggestions ?", + "emotion": "neutral", + "text": "Mr . Bellow , have you anything in mind as to what to drink or may I make a few suggestions ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I have had enough gin fizz and bloody mary . But I have no idea about Chinese cocktails .", + "emotion": "neutral", + "text": "I have had enough gin fizz and bloody mary . But I have no idea about Chinese cocktails .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Would you prefer our cocktail -- Shanghai cocktail ? It's a mixture of real Chinese ingredients .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "But I have no idea about Chinese cocktails .", + "our cocktail -- Shanghai cocktail ? It's a mixture of real Chinese ingredients ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Would you prefer our cocktail -- Shanghai cocktail ? It's a mixture of real Chinese ingredients .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "That ' s good .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "But I have no idea about Chinese cocktails .", + "our cocktail -- Shanghai cocktail ? It's a mixture of real Chinese ingredients ." + ], + "type": [ + "hybrid" + ], + "text": "That ' s good .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "( The waiter makes the cocktail for Mr . Bellow and hands into him . ) Here is your Shanghai cocktail , Mr . Bellow .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "That ' s good ." + ], + "type": [ + "inter-personal" + ], + "text": "( The waiter makes the cocktail for Mr . Bellow and hands into him . ) Here is your Shanghai cocktail , Mr . Bellow .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Thank you . Oh , it tastes excellent .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "( The waiter makes the cocktail for Mr . Bellow and hands into him . ) Here is your Shanghai cocktail , Mr . Bellow .", + "Oh , it tastes excellent ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you . Oh , it tastes excellent .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2217.json b/reccon/sources/tr_2217.json new file mode 100644 index 0000000000000000000000000000000000000000..1386a294d0c8fcfd59b1db438028161db709b44a --- /dev/null +++ b/reccon/sources/tr_2217.json @@ -0,0 +1,240 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Will you be joining Billy and I at the Bar ?", + "emotion": "neutral", + "text": "Will you be joining Billy and I at the Bar ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Which one will you be going to ?", + "emotion": "neutral", + "text": "Which one will you be going to ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "We are going to try the new one that opened up on 17th Street .", + "emotion": "neutral", + "text": "We are going to try the new one that opened up on 17th Street .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Sure , I've been meaning to visit that place myself .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "We are going to try the new one that opened up on 17th Street .", + "I've been meaning to visit that place myself ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Sure , I've been meaning to visit that place myself .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I want to stop off at my apartment to get changed so I should be there by 9 pm .", + "emotion": "neutral", + "text": "I want to stop off at my apartment to get changed so I should be there by 9 pm .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "OK , can I bring a date with me ?", + "emotion": "neutral", + "text": "OK , can I bring a date with me ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Certainly . But if there are going to be four of us , I had better make reservations .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "can I bring a date with me ?", + "if there are going to be four of us , I had better make reservations ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Certainly . But if there are going to be four of us , I had better make reservations .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yes . that is a very good idea . It would be a shame if we could not find a place to sit .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "But if there are going to be four of us , I had better make reservations .", + "that is a very good idea" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes . that is a very good idea . It would be a shame if we could not find a place to sit .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Then I'II make reservations for 9 pm for a party of four .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "can I bring a date with me ?", + "if there are going to be four of us , I had better make reservations ." + ], + "type": [ + "hybrid" + ], + "text": "Then I'II make reservations for 9 pm for a party of four .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I'll be there . Oh , is there a cover charge at the bar ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "Then I'II make reservations for 9 pm for a party of four .", + "I'll be there ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'll be there . Oh , is there a cover charge at the bar ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Not that I know of . Why do you ask ?", + "emotion": "neutral", + "text": "Not that I know of . Why do you ask ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I want to make sure I bring enough money for my date and I .", + "emotion": "neutral", + "text": "I want to make sure I bring enough money for my date and I .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I hear the drinks and food there are moderately priced . You should be fine .", + "emotion": "neutral", + "text": "I hear the drinks and food there are moderately priced . You should be fine .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "One last question . Is there a dress code there ?", + "emotion": "neutral", + "text": "One last question . Is there a dress code there ?", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "No , its very casual there . Leave your jacket and tie at home .", + "emotion": "neutral", + "text": "No , its very casual there . Leave your jacket and tie at home .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Perfect . I wanted to have a casual evening tonight .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15, + 16 + ], + "expanded emotion cause span": [ + "No , its very casual there . Leave your jacket and tie at home .", + "Perfect . I wanted to have a casual evening tonight ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Perfect . I wanted to have a casual evening tonight .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "I'll see you there at 9pm .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 17 + ], + "expanded emotion cause span": [ + "I'll see you there at 9pm ." + ], + "type": [ + "no-context" + ], + "text": "I'll see you there at 9pm .", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "Okay . See you then .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 17 + ], + "expanded emotion cause span": [ + "I'll see you there at 9pm ." + ], + "type": [ + "inter-personal" + ], + "text": "Okay . See you then .", + "id": 18, + "source_sentences": [ + 16 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_222.json b/reccon/sources/tr_222.json new file mode 100644 index 0000000000000000000000000000000000000000..31745397d50fde04b03120a17c5b1dff66f6b9f1 --- /dev/null +++ b/reccon/sources/tr_222.json @@ -0,0 +1,166 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Steven , would you like to go dance with us tonight ?", + "emotion": "neutral", + "text": "Steven , would you like to go dance with us tonight ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "John , I am just not in the mood for this .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "not in the mood for this ." + ], + "type": [ + "no-context" + ], + "text": "John , I am just not in the mood for this .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "You look so upset . What's going on ?", + "emotion": "neutral", + "text": "You look so upset . What's going on ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I lost the table tennis game yesterday .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I lost the table tennis game yesterday ." + ], + "type": [ + "no-context" + ], + "text": "I lost the table tennis game yesterday .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Oh , what a pity !", + "emotion": "neutral", + "text": "Oh , what a pity !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I just don ' t want to play table tennis any more .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 4, + 6 + ], + "expanded emotion cause span": [ + "I lost the table tennis game yesterday .", + "I just don ' t want to play table tennis any more ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I just don ' t want to play table tennis any more .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Is it that bad ? It ' s nothing more than a game .", + "emotion": "neutral", + "text": "Is it that bad ? It ' s nothing more than a game .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "My opponent bowled me with the very first ball . I was wondering if it's appropriate for me to play table tennis .", + "emotion": "sadness", + "flag": "F", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I lost the table tennis game yesterday ." + ], + "type": [ + "self-contagion" + ], + "text": "My opponent bowled me with the very first ball . I was wondering if it's appropriate for me to play table tennis .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Oh , come on ! Failure is the mother of success . Don ' t lose heart . I'm sure you'll succeed .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "I'm sure you'll succeed ." + ], + "type": [ + "no-context" + ], + "text": "Oh , come on ! Failure is the mother of success . Don ' t lose heart . I'm sure you'll succeed .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Perhaps you are right . But I still need some time to recover from the failure .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "I'm sure you'll succeed .", + "Perhaps you are right ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Perhaps you are right . But I still need some time to recover from the failure .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I understand .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "I'm sure you'll succeed ." + ], + "type": [ + "self-contagion" + ], + "text": "I understand .", + "id": 11 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2223.json b/reccon/sources/tr_2223.json new file mode 100644 index 0000000000000000000000000000000000000000..e6ff94f72bb56d606e96f09a2b6b32f711975655 --- /dev/null +++ b/reccon/sources/tr_2223.json @@ -0,0 +1,139 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Rachel , do you like music ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Rachel , do you like music ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Of course . I can't live without it , so I always bring my CD with me no matter where I go .", + "emotion": "happiness", + "explanation": "Person B sharing her personal belief and choice with happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I can't live without it , so I always bring my CD with me no matter where I go ." + ], + "type": [ + "no-context" + ], + "text": "Of course . I can't live without it , so I always bring my CD with me no matter where I go .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What kind of music do you like best ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "What kind of music do you like best ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Light music and classic music .", + "emotion": "happiness", + "explanation": "Person B sharing her personal belief and choice with happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I can't live without it , so I always bring my CD with me no matter where I go ." + ], + "type": [ + "self-contagion" + ], + "text": "Light music and classic music .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Really ? I can't believe this . I am also keen on classic music . And do you know there is a concert of classic music tomorrow evening ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Light music and classic music ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? I can't believe this . I am also keen on classic music . And do you know there is a concert of classic music tomorrow evening ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "But I didn't get the ticket . And it is said that they were sold out yesterday .", + "emotion": "neutral", + "text": "But I didn't get the ticket . And it is said that they were sold out yesterday .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I got two . We can go there together .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I got two . We can go there together ." + ], + "type": [ + "no-context" + ], + "text": "I got two . We can go there together .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Amazing ! I can imagine the feeling when I hear the smooth tune around my ears .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "I got two . We can go there together .", + "I can imagine the feeling when I hear the smooth tune around my ears ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Amazing ! I can imagine the feeling when I hear the smooth tune around my ears .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_223.json b/reccon/sources/tr_223.json new file mode 100644 index 0000000000000000000000000000000000000000..a1886bcd410c4bdbfdafc67679b8b92584d5b7d5 --- /dev/null +++ b/reccon/sources/tr_223.json @@ -0,0 +1,339 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "The band is pretty good . How do you like the music ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "The band is pretty good ." + ], + "type": [ + "no-context" + ], + "text": "The band is pretty good . How do you like the music ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It's very nice . I haven't heard live music in a while . This is fun .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "The band is pretty good .", + "It's very nice . I haven't heard live music in a while . This is fun ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It's very nice . I haven't heard live music in a while . This is fun .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Well , then , may I invite you for the next dance ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 3 + ], + "expanded emotion cause span": [ + "The band is pretty good .", + "It's very nice . I haven't heard live music in a while . This is fun .", + "next dance" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Well , then , may I invite you for the next dance ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Of course . But I'm afraid I'm not much of a dancer ...", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 3 + ], + "expanded emotion cause span": [ + "The band is pretty good .", + "It's very nice . I haven't heard live music in a while . This is fun .", + "may I invite you for the next dance ?" + ], + "type": [ + "hybrid" + ], + "text": "Of course . But I'm afraid I'm not much of a dancer ...", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Don't worry . I'm not much of a dancer myself .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Of course ." + ], + "type": [ + "inter-personal" + ], + "text": "Don't worry . I'm not much of a dancer myself .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "You're dancing so well .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "You're dancing so well ." + ], + "type": [ + "no-context" + ], + "text": "You're dancing so well .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You dance beautifully too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "You're dancing so well .", + "You dance beautifully too ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You dance beautifully too .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "When did you learn to dance ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "You're dancing so well .", + "You dance beautifully too ." + ], + "type": [ + "hybrid" + ], + "text": "When did you learn to dance ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "In college . But I don't dance very often . What's your favourite dance ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7, + 8 + ], + "expanded emotion cause span": [ + "You're dancing so well .", + "You dance beautifully too .", + "When did you learn to dance ?" + ], + "type": [ + "hybrid" + ], + "text": "In college . But I don't dance very often . What's your favourite dance ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "It's hard to say . It depends . But I love the waltz .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7, + 9, + 10 + ], + "expanded emotion cause span": [ + "You're dancing so well .", + "You dance beautifully too .", + "What's your favourite dance ?", + "I love the waltz ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "It's hard to say . It depends . But I love the waltz .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "How about tango ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7, + 11 + ], + "expanded emotion cause span": [ + "You're dancing so well .", + "You dance beautifully too .", + "tango" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "How about tango ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Oh , I like it . It's such a beautiful dance , but I can't do it well . What about you ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7, + 11, + 12 + ], + "expanded emotion cause span": [ + "You're dancing so well .", + "You dance beautifully too .", + "tango", + "Oh , I like it . It's such a beautiful dance" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Oh , I like it . It's such a beautiful dance , but I can't do it well . What about you ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Tango is my favorite . Anything but hip-hop or the foxtrot . ( the music has stopped )", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7, + 13 + ], + "expanded emotion cause span": [ + "You're dancing so well .", + "You dance beautifully too .", + "Tango is my favorite ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Tango is my favorite . Anything but hip-hop or the foxtrot . ( the music has stopped )", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Thank you for the dance .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7, + 14 + ], + "expanded emotion cause span": [ + "You're dancing so well .", + "You dance beautifully too .", + "Thank you for the dance ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Thank you for the dance .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "My pleasure . Let's go and have a drink .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7, + 14 + ], + "expanded emotion cause span": [ + "You're dancing so well .", + "You dance beautifully too .", + "Thank you for the dance ." + ], + "type": [ + "hybrid" + ], + "text": "My pleasure . Let's go and have a drink .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "OK .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7, + 14, + 15 + ], + "expanded emotion cause span": [ + "You're dancing so well .", + "You dance beautifully too .", + "Thank you for the dance .", + "My pleasure . Let's go and have a drink ." + ], + "type": [ + "hybrid" + ], + "text": "OK .", + "id": 16 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2232.json b/reccon/sources/tr_2232.json new file mode 100644 index 0000000000000000000000000000000000000000..ac6001ac08452ab26430631c9c7b7736da92686b --- /dev/null +++ b/reccon/sources/tr_2232.json @@ -0,0 +1,129 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Jane , I was wondering if you you had any plans for saturday afternoon .", + "emotion": "neutral", + "text": "Jane , I was wondering if you you had any plans for saturday afternoon .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "A friend and I are planing to go out , why ? what's up ?", + "emotion": "neutral", + "text": "A friend and I are planing to go out , why ? what's up ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "There is a special exhibition of french sculptures at the museum , I was hoping you ' d like to come with me .", + "emotion": "neutral", + "text": "There is a special exhibition of french sculptures at the museum , I was hoping you ' d like to come with me .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I am afraid I can't I am going to be out all day .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "There is a special exhibition of french sculptures at the museum , I was hoping you ' d like to come with me .", + "I can't I am going to be out all day ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I am afraid I can't I am going to be out all day .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "What about sunday ?", + "emotion": "neutral", + "text": "What about sunday ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I wish I could , but it's my mums birthday .", + "emotion": "neutral", + "text": "I wish I could , but it's my mums birthday .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Maybe next week .", + "emotion": "neutral", + "text": "Maybe next week .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Much as I ' d like to , I am afraid i wont be free next week , I have a lot of work .", + "emotion": "neutral", + "text": "Much as I ' d like to , I am afraid i wont be free next week , I have a lot of work .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Sorry to hear that , I was really looking forward to spending some more time with you , I really enjoyed our last chat .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3, + 4, + 6, + 8, + 9 + ], + "expanded emotion cause span": [ + "There is a special exhibition of french sculptures at the museum , I was hoping you ' d like to come with me .", + "I can't I am going to be out all day .", + "I wish I could , but it's my mums birthday .", + "Much as I ' d like to , I am afraid i wont be free next week , I have a lot of work .", + "Sorry to hear that , I was really looking forward to spending some more time with you , I really enjoyed our last chat ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Sorry to hear that , I was really looking forward to spending some more time with you , I really enjoyed our last chat .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I am really sorry too , maybe I can give you a call sometime .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "Sorry to hear that , I was really looking forward to spending some more time with you , I really enjoyed our last chat .", + "I am really sorry too" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I am really sorry too , maybe I can give you a call sometime .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2240.json b/reccon/sources/tr_2240.json new file mode 100644 index 0000000000000000000000000000000000000000..1e4f332d23211dfe9ed1d098f474c7d21fe12048 --- /dev/null +++ b/reccon/sources/tr_2240.json @@ -0,0 +1,157 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I don ' t know what I ' m going to do ! It ' s going to be impossible to make ends meet if I lose my job !", + "emotion": "neutral", + "text": "I don ' t know what I ' m going to do ! It ' s going to be impossible to make ends meet if I lose my job !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Don ' t worry . I don't think you ' re going to lose your job over one mistake .", + "emotion": "neutral", + "text": "Don ' t worry . I don't think you ' re going to lose your job over one mistake .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "It was a rather big mistake . When you work as an investment adviser , one small mistake can cost the company millions .", + "emotion": "neutral", + "text": "It was a rather big mistake . When you work as an investment adviser , one small mistake can cost the company millions .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "But it wasn ' t just you who was involved , right ? You were only doing what your supervisor told you to do .", + "emotion": "neutral", + "text": "But it wasn ' t just you who was involved , right ? You were only doing what your supervisor told you to do .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "That ' s true , but my supervisor is very dishonest . There ' s no reason he needs to tell our boss the truth . I ' m sure he will tell our boss that it was all my fault , and there ' s nothing I can do about that . My boss won ' t believe me if I tell him the truth .", + "emotion": "neutral", + "text": "That ' s true , but my supervisor is very dishonest . There ' s no reason he needs to tell our boss the truth . I ' m sure he will tell our boss that it was all my fault , and there ' s nothing I can do about that . My boss won ' t believe me if I tell him the truth .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Let ' s think realistically about what might happen . How much money do you have in your savings ?", + "emotion": "neutral", + "text": "Let ' s think realistically about what might happen . How much money do you have in your savings ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I have enough to live off of for about 3 months . But I really don't want to spend my life savings on just living ! I ' d rather invest my money somehow .", + "emotion": "neutral", + "text": "I have enough to live off of for about 3 months . But I really don't want to spend my life savings on just living ! I ' d rather invest my money somehow .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Well , you can't have everything . Let's just figure out what you will do if you lose your job . When is your contract up on your apartment ?", + "emotion": "neutral", + "text": "Well , you can't have everything . Let's just figure out what you will do if you lose your job . When is your contract up on your apartment ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Next month . So I can either move out then or renew my contract for another year .", + "emotion": "neutral", + "text": "Next month . So I can either move out then or renew my contract for another year .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Well , that ' s good . If you lose your job , you can just move in with me until you find another job . That will save you plenty of money .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "Next month . So I can either move out then or renew my contract for another year .", + "If you lose your job , you can just move in with me until you find another job . That will save you plenty of money ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Well , that ' s good . If you lose your job , you can just move in with me until you find another job . That will save you plenty of money .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "That ' s very generous of you . I guess that would work .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "If you lose your job , you can just move in with me until you find another job . That will save you plenty of money .", + "That ' s very generous of you . I guess that would work ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That ' s very generous of you . I guess that would work .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "If you lose your job , you just have to go for a few months without buying all the junk you usually buy . If you live frugally , you ' ll save plenty of money .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "If you lose your job , you just have to go for a few months without buying all the junk you usually buy . If you live frugally , you ' ll save plenty of money ." + ], + "type": [ + "no-context" + ], + "text": "If you lose your job , you just have to go for a few months without buying all the junk you usually buy . If you live frugally , you ' ll save plenty of money .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I guess working with so much money has made me rather greedy . Maybe losing my job would be a good thing !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11, + 12 + ], + "expanded emotion cause span": [ + "If you lose your job , you can just move in with me until you find another job . That will save you plenty of money .", + "That ' s very generous of you . I guess that would work .", + "If you lose your job , you just have to go for a few months without buying all the junk you usually buy . If you live frugally , you ' ll save plenty of money ." + ], + "type": [ + "hybrid" + ], + "text": "I guess working with so much money has made me rather greedy . Maybe losing my job would be a good thing !", + "id": 13 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2250.json b/reccon/sources/tr_2250.json new file mode 100644 index 0000000000000000000000000000000000000000..383e34b416540e492d20f8d184d85104e00f815b --- /dev/null +++ b/reccon/sources/tr_2250.json @@ -0,0 +1,155 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Who's that man over there talking to James ?", + "emotion": "neutral", + "text": "Who's that man over there talking to James ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Where ? Oh , that's Henry .", + "emotion": "neutral", + "text": "Where ? Oh , that's Henry .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "He's very handsome , isn't he ? What's he like ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "He's very handsome ," + ], + "type": [ + "no-context" + ], + "text": "He's very handsome , isn't he ? What's he like ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "He's very nice , actually , but rather eccentric .", + "emotion": "neutral", + "text": "He's very nice , actually , but rather eccentric .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Really ? I love eccentric people .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "but rather eccentric ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? I love eccentric people .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yes , but he may be too eccentric even for you .", + "emotion": "neutral", + "text": "Yes , but he may be too eccentric even for you .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Why ? What do you mean by that ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "he may be too eccentric even for you ." + ], + "type": [ + "inter-personal" + ], + "text": "Why ? What do you mean by that ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Well , haven't you heard ?", + "emotion": "neutral", + "text": "Well , haven't you heard ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Heard what ? No one ever tells me anything .", + "emotion": "neutral", + "text": "Heard what ? No one ever tells me anything .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Well , apparently , he's been having an affair with his secretary .", + "emotion": "neutral", + "text": "Well , apparently , he's been having an affair with his secretary .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Really ! How fascinating .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "he's been having an affair with his secretary ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ! How fascinating .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "According to Mary , he's divorcing his wife and there's a big fight going on about the children . I thought everyone knew .", + "emotion": "neutral", + "text": "According to Mary , he's divorcing his wife and there's a big fight going on about the children . I thought everyone knew .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Well , what can I say ? I didn't know . Oh , I meant to tell you earlier , your blouse doesn't really match your skirt . Those colors don't really suit you either .", + "emotion": "neutral", + "text": "Well , what can I say ? I didn't know . Oh , I meant to tell you earlier , your blouse doesn't really match your skirt . Those colors don't really suit you either .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Oh . Thanks . Look , I must just go and say hello to someone . I'll be right back .", + "emotion": "neutral", + "text": "Oh . Thanks . Look , I must just go and say hello to someone . I'll be right back .", + "id": 14 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2271.json b/reccon/sources/tr_2271.json new file mode 100644 index 0000000000000000000000000000000000000000..ea05b475eeb953b0aa3eaa1bb8b3a7d1f9fe1460 --- /dev/null +++ b/reccon/sources/tr_2271.json @@ -0,0 +1,160 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "The summers are so great here ! Not hot at all . I love the cooling breezes , the clear air , all the greenery .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "The summers are so great here ! Not hot at all . I love the cooling breezes , the clear air , all the greenery ." + ], + "type": [ + "no-context" + ], + "text": "The summers are so great here ! Not hot at all . I love the cooling breezes , the clear air , all the greenery .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "This really has been a wonderful holiday for us . Shall we take a walk around the pond or into those woods for a while ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "This really has been a wonderful holiday for us ." + ], + "type": [ + "no-context" + ], + "text": "This really has been a wonderful holiday for us . Shall we take a walk around the pond or into those woods for a while ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Let's do both ! Are we in a rush or anything", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 3 + ], + "expanded emotion cause span": [ + "The summers are so great here ! Not hot at all . I love the cooling breezes , the clear air , all the greenery .", + "we take a walk around the pond or into those woods", + "Let's do both !" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Let's do both ! Are we in a rush or anything", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "No , not really . I had thought we'd stay in Hamburg tonight , but we can't unless we rush it . Let's stay in Bremen instead . Tomorrow we can have lunch in Hamburg , then check into a hostel in Copenhagen and have dinner there .", + "emotion": "neutral", + "text": "No , not really . I had thought we'd stay in Hamburg tonight , but we can't unless we rush it . Let's stay in Bremen instead . Tomorrow we can have lunch in Hamburg , then check into a hostel in Copenhagen and have dinner there .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Sounds fine to me . Whatever , let's enjoy this pond first .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "let's enjoy this pond first ." + ], + "type": [ + "no-context" + ], + "text": "Sounds fine to me . Whatever , let's enjoy this pond first .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Sure . We can walk around to that path that leads into the woods there . Hey , look ! There are some wild ducks over there in the reeds .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "look ! There are some wild ducks over there in the reeds ." + ], + "type": [ + "no-context" + ], + "text": "Sure . We can walk around to that path that leads into the woods there . Hey , look ! There are some wild ducks over there in the reeds .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I see them ! Wow ! How do you know they're wild ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "look ! There are some wild ducks over there in the reeds ." + ], + "type": [ + "inter-personal" + ], + "text": "I see them ! Wow ! How do you know they're wild ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I used to go hunting with my uncle , that's how .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "look ! There are some wild ducks over there in the reeds ." + ], + "type": [ + "self-contagion" + ], + "text": "I used to go hunting with my uncle , that's how .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "They're neat . Now Let's take that path into the woods and see what we can see ...", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 9 + ], + "expanded emotion cause span": [ + "look ! There are some wild ducks over there in the reeds .", + "They're neat ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "They're neat . Now Let's take that path into the woods and see what we can see ...", + "id": 9, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2274.json b/reccon/sources/tr_2274.json new file mode 100644 index 0000000000000000000000000000000000000000..66ba9a4b30304666d41fdb742d2445a25ba7a4f0 --- /dev/null +++ b/reccon/sources/tr_2274.json @@ -0,0 +1,169 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey Jack . What's going on ?", + "emotion": "neutral", + "text": "Hey Jack . What's going on ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hey Matt . I'm going to ask Martha to marry me ?", + "emotion": "neutral", + "text": "Hey Matt . I'm going to ask Martha to marry me ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Really ? When did you decide this ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I'm going to ask Martha to marry me ?" + ], + "type": [ + "inter-personal" + ], + "text": "Really ? When did you decide this ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I always knew she was the one , but I decided to pop the big question about 2 weeks ago . I'm just debating on how to do it .", + "emotion": "neutral", + "text": "I always knew she was the one , but I decided to pop the big question about 2 weeks ago . I'm just debating on how to do it .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "That's exciting , man .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "I decided to pop the big question about 2 weeks ago .", + "That's exciting" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's exciting , man .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "So how did you propose ?", + "emotion": "neutral", + "text": "So how did you propose ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You shouldn't use my example . It wasn't special . I kind of wish I made it more special but it's too late now .", + "emotion": "neutral", + "text": "You shouldn't use my example . It wasn't special . I kind of wish I made it more special but it's too late now .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "What do you think I should do ?", + "emotion": "neutral", + "text": "What do you think I should do ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "There are a lot of options . You can surprise her over dinner , or ask her in a public area , or if you have the balls , ask her father in front of her .", + "emotion": "neutral", + "text": "There are a lot of options . You can surprise her over dinner , or ask her in a public area , or if you have the balls , ask her father in front of her .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I never thought about that .", + "emotion": "neutral", + "text": "I never thought about that .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Thought about what ?", + "emotion": "neutral", + "text": "Thought about what ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Asking her father in front of her . How do you think she will react ?", + "emotion": "neutral", + "text": "Asking her father in front of her . How do you think she will react ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I don't know . You should know how she's going to react . She is your girlfriend .", + "emotion": "neutral", + "text": "I don't know . You should know how she's going to react . She is your girlfriend .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "I think that's the idea I was looking for . Thanks , man .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 14 + ], + "expanded emotion cause span": [ + "ask her father in front of her .", + "that's the idea I was looking for ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I think that's the idea I was looking for . Thanks , man .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Don't mention it . Good luck . You're going to need it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "I think that's the idea I was looking for . Thanks , man ." + ], + "type": [ + "inter-personal" + ], + "text": "Don't mention it . Good luck . You're going to need it .", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2275.json b/reccon/sources/tr_2275.json new file mode 100644 index 0000000000000000000000000000000000000000..95c5d5fbe81d9e7218f6724e312031631e37fcd8 --- /dev/null +++ b/reccon/sources/tr_2275.json @@ -0,0 +1,202 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "The bridegroom looks a bit nervous .", + "emotion": "neutral", + "text": "The bridegroom looks a bit nervous .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "On this occasion , most people do .", + "emotion": "neutral", + "text": "On this occasion , most people do .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Oh , they are playing the wedding March . Here they come .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "they are playing the wedding March ." + ], + "type": [ + "no-context" + ], + "text": "Oh , they are playing the wedding March . Here they come .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "She is a beautiful bride .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "She is a beautiful bride ." + ], + "type": [ + "no-context" + ], + "text": "She is a beautiful bride .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I am so happy for them .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I am so happy for them ." + ], + "type": [ + "no-context" + ], + "text": "I am so happy for them .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Are you crying ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "She is a beautiful bride .", + "I am so happy for them ." + ], + "type": [ + "hybrid" + ], + "text": "Are you crying ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yes , I always cry at weddings .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I am so happy for them ." + ], + "type": [ + "self-contagion" + ], + "text": "Yes , I always cry at weddings .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Harris and Anne are perfect for each other .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Harris and Anne are perfect for each other ." + ], + "type": [ + "no-context" + ], + "text": "Harris and Anne are perfect for each other .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yes , they are .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Harris and Anne are perfect for each other ." + ], + "type": [ + "inter-personal" + ], + "text": "Yes , they are .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "You and Tom also make a great couple .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "You and Tom also make a great couple ." + ], + "type": [ + "no-context" + ], + "text": "You and Tom also make a great couple .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "In fact , we are beginning to make preparations .", + "emotion": "neutral", + "text": "In fact , we are beginning to make preparations .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "For the wedding ?", + "emotion": "neutral", + "text": "For the wedding ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "No , no , for the engagement .", + "emotion": "neutral", + "text": "No , no , for the engagement .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Try to catch this bouquet then .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "we are beginning to make preparations ." + ], + "type": [ + "inter-personal" + ], + "text": "Try to catch this bouquet then .", + "id": 14, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_228.json b/reccon/sources/tr_228.json new file mode 100644 index 0000000000000000000000000000000000000000..aebece83d15e94f185de15290e0cf66ee9129ab2 --- /dev/null +++ b/reccon/sources/tr_228.json @@ -0,0 +1,236 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Have you been ever been to Disneyworld ?", + "emotion": "neutral", + "text": "Have you been ever been to Disneyworld ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "When I was young , my parents took me to the one in California . I always forget which -- is that one Disneyland or Disneyworld ?", + "emotion": "neutral", + "text": "When I was young , my parents took me to the one in California . I always forget which -- is that one Disneyland or Disneyworld ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "The one in Florida is Disneyworld and the one in California is Disneyland , so you must have been to Disneyland .", + "emotion": "neutral", + "text": "The one in Florida is Disneyworld and the one in California is Disneyland , so you must have been to Disneyland .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "That's right . Why do you ask ?", + "emotion": "neutral", + "text": "That's right . Why do you ask ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Well , I've never been to either so I was thinking of going to Disneyworld for my honeymoon .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I was thinking of going to Disneyworld for my honeymoon ." + ], + "type": [ + "no-context" + ], + "text": "Well , I've never been to either so I was thinking of going to Disneyworld for my honeymoon .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "When are getting married ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "my honeymoon .", + "getting married" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "When are getting married ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Some time next year . We haven't set the date yet .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "getting married", + "Some time next year ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Some time next year . We haven't set the date yet .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Congratulations ! I had no idea .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "getting married", + "Some time next year ." + ], + "type": [ + "hybrid" + ], + "text": "Congratulations ! I had no idea .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Thank you . So what do you think ? Would we have a good time ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 8 + ], + "expanded emotion cause span": [ + "I was thinking of going to Disneyworld for my honeymoon .", + "Congratulations !" + ], + "type": [ + "hybrid" + ], + "text": "Thank you . So what do you think ? Would we have a good time ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Do you like amusement parks ?", + "emotion": "neutral", + "text": "Do you like amusement parks ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "For the most part , yes . Some of the rides are bit too scary for me , though .", + "emotion": "neutral", + "text": "For the most part , yes . Some of the rides are bit too scary for me , though .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "If you don't think twice about the rides and go on every ride that you can , you'll have a good time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "If you don't think twice about the rides and go on every ride that you can , you'll have a good time ." + ], + "type": [ + "no-context" + ], + "text": "If you don't think twice about the rides and go on every ride that you can , you'll have a good time .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Even the roller coasters that go through tunnels in the dark ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "If you don't think twice about the rides and go on every ride that you can , you'll have a good time ." + ], + "type": [ + "inter-personal" + ], + "text": "Even the roller coasters that go through tunnels in the dark ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Even those . It'll be very romantic , I think . You'll have loads of fun .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "It'll be very romantic , I think . You'll have loads of fun ." + ], + "type": [ + "no-context" + ], + "text": "Even those . It'll be very romantic , I think . You'll have loads of fun .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Thanks for the advice . I'll talk to my fiance about it tonight .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "It'll be very romantic , I think . You'll have loads of fun ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks for the advice . I'll talk to my fiance about it tonight .", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 16, + "speaker": "B", + "utterance": "I'm sure he'll love the idea . Just throw yourself into it and you'll enjoy it !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 16 + ], + "expanded emotion cause span": [ + "I'm sure he'll love the idea . Just throw yourself into it and you'll enjoy it !" + ], + "type": [ + "no-context" + ], + "text": "I'm sure he'll love the idea . Just throw yourself into it and you'll enjoy it !", + "id": 16 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2301.json b/reccon/sources/tr_2301.json new file mode 100644 index 0000000000000000000000000000000000000000..b58de1f63f4264c1ac024efdcb1bf28e134448f3 --- /dev/null +++ b/reccon/sources/tr_2301.json @@ -0,0 +1,91 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , Lucy . What are you going to do this weekend ?", + "emotion": "neutral", + "text": "Hi , Lucy . What are you going to do this weekend ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I have no idea yet . Do you have any suggestions ?", + "emotion": "neutral", + "text": "I have no idea yet . Do you have any suggestions ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Would you like to play tennis with me ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Would you like to play tennis with me ?" + ], + "type": [ + "no-context" + ], + "text": "Would you like to play tennis with me ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I'd like to .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Would you like to play tennis with me ?" + ], + "type": [ + "inter-personal" + ], + "text": "I'd like to .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Be sure to get to the sports hall at nine o'clock on Sunday morning .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Would you like to play tennis with me ?" + ], + "type": [ + "self-contagion" + ], + "text": "Be sure to get to the sports hall at nine o'clock on Sunday morning .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "OK , will do !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Would you like to play tennis with me ?" + ], + "type": [ + "inter-personal" + ], + "text": "OK , will do !", + "id": 6, + "source_sentences": [ + 2 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2306.json b/reccon/sources/tr_2306.json new file mode 100644 index 0000000000000000000000000000000000000000..68ff1dd07a567e2c4353bd37358d9ec6cf649f09 --- /dev/null +++ b/reccon/sources/tr_2306.json @@ -0,0 +1,227 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Do you like climbing ?", + "emotion": "happiness", + "explanation": "It is not clear if A is happy about climbing sport.", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Do you like climbing ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , I like it very much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "Do you like climbing ?", + "Yes , I like it very much ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , I like it very much .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "How about climbing up the Fragrant Mountain tomorrow ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 3 + ], + "expanded emotion cause span": [ + "b", + "How about climbing up the Fragrant Mountain tomorrow ?" + ], + "type": [ + "latent", + "no-context" + ], + "text": "How about climbing up the Fragrant Mountain tomorrow ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Where is it ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "climbing up the Fragrant Mountain tomorrow ?" + ], + "type": [ + "inter-personal" + ], + "text": "Where is it ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "It is located at the east foot of Western Mountain of Beijing , in a park with the same name . There are some huge stones within the mountain which look like the censer , so it is called ' Fragrant Mountain ' .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 3 + ], + "expanded emotion cause span": [ + "b", + "How about climbing up the Fragrant Mountain tomorrow ?" + ], + "type": [ + "latent", + "self-contagion" + ], + "text": "It is located at the east foot of Western Mountain of Beijing , in a park with the same name . There are some huge stones within the mountain which look like the censer , so it is called ' Fragrant Mountain ' .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Have you visited it before ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "climbing up the Fragrant Mountain tomorrow ?" + ], + "type": [ + "inter-personal" + ], + "text": "Have you visited it before ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Many times . Except climbing , there are many attractions worth visiting .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 3, + 7 + ], + "expanded emotion cause span": [ + "b", + "How about climbing up the Fragrant Mountain tomorrow ?", + "there are many attractions worth visiting ." + ], + "type": [ + "latent", + "no-context", + "self-contagion" + ], + "text": "Many times . Except climbing , there are many attractions worth visiting .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Like what ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "there are many attractions worth visiting ." + ], + "type": [ + "inter-personal" + ], + "text": "Like what ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "It is the best season to view red leaves from the Mid-October to the first ten days of November . During the period , thousands of hectares of maples on the sloping field are so red that you would recognize them as fallen petals by mistake if looking from a further area . The bright red , pink , scarlet , and peach-puff leaves are distributed in different layout , with some green pines and cypresses dotted in between .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "It is the best season to view red leaves from the Mid-October to the first ten days of November . During the period , thousands of hectares of maples on the sloping field are so red that you would recognize them as fallen petals by mistake if looking from a further area . The bright red , pink , scarlet , and peach-puff leaves are distributed in different layout , with some green pines and cypresses dotted in between ." + ], + "type": [ + "no-context" + ], + "text": "It is the best season to view red leaves from the Mid-October to the first ten days of November . During the period , thousands of hectares of maples on the sloping field are so red that you would recognize them as fallen petals by mistake if looking from a further area . The bright red , pink , scarlet , and peach-puff leaves are distributed in different layout , with some green pines and cypresses dotted in between .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Sounds marvelous .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "It is the best season to view red leaves from the Mid-October to the first ten days of November . During the period , thousands of hectares of maples on the sloping field are so red that you would recognize them as fallen petals by mistake if looking from a further area . The bright red , pink , scarlet , and peach-puff leaves are distributed in different layout , with some green pines and cypresses dotted in between ." + ], + "type": [ + "inter-personal" + ], + "text": "Sounds marvelous .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "You can take a bird-eye view at the glorious picture when you arrive at the top of the mountain .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "You can take a bird-eye view at the glorious picture when you arrive at the top of the mountain ." + ], + "type": [ + "no-context" + ], + "text": "You can take a bird-eye view at the glorious picture when you arrive at the top of the mountain .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Great . I will prepare some clothes and food for the climbing .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "You can take a bird-eye view at the glorious picture when you arrive at the top of the mountain ." + ], + "type": [ + "inter-personal" + ], + "text": "Great . I will prepare some clothes and food for the climbing .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2310.json b/reccon/sources/tr_2310.json new file mode 100644 index 0000000000000000000000000000000000000000..df31dc1530f40083bc691d0c4ef17aab071674c5 --- /dev/null +++ b/reccon/sources/tr_2310.json @@ -0,0 +1,119 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Lester , you are really fantastic at automobile repair .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "you are really fantastic" + ], + "type": [ + "no-context" + ], + "text": "Lester , you are really fantastic at automobile repair .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Thanks , June . But I think I need to be certified as a mechanic before I ' m allowed to repair cars for a living .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "you are really fantastic" + ], + "type": [ + "inter-personal" + ], + "text": "Thanks , June . But I think I need to be certified as a mechanic before I ' m allowed to repair cars for a living .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "That ' s not a big problem . There are many small schools for adults like you who can study to be certified .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "you are really fantastic" + ], + "type": [ + "self-contagion" + ], + "text": "That ' s not a big problem . There are many small schools for adults like you who can study to be certified .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I guess I never thought of that before .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "you are really fantastic", + "That ' s not a big problem . There are many small schools for adults like you who can study to be certified ." + ], + "type": [ + "inter-personal" + ], + "text": "I guess I never thought of that before .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "And you can easily get a student loan from a vocational school , or from the government .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "you are really fantastic" + ], + "type": [ + "self-contagion" + ], + "text": "And you can easily get a student loan from a vocational school , or from the government .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Wow , you ' Ve inspired me to do something !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3, + 5 + ], + "expanded emotion cause span": [ + "you are really fantastic", + "That ' s not a big problem . There are many small schools for adults like you who can study to be certified .", + "you can easily get a student loan" + ], + "type": [ + "inter-personal" + ], + "text": "Wow , you ' Ve inspired me to do something !", + "id": 6, + "source_sentences": [ + 0, + 2, + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2311.json b/reccon/sources/tr_2311.json new file mode 100644 index 0000000000000000000000000000000000000000..12cbd6e0d63bec9ad1542f9e5c6c6a1ec944f487 --- /dev/null +++ b/reccon/sources/tr_2311.json @@ -0,0 +1,139 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey , Ted . What are you up to this Friday ?", + "emotion": "neutral", + "text": "Hey , Ted . What are you up to this Friday ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Well , I have the day off from work .", + "emotion": "neutral", + "text": "Well , I have the day off from work .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "That ' s great ! Do you have any plans ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I have the day off from work ." + ], + "type": [ + "inter-personal" + ], + "text": "That ' s great ! Do you have any plans ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Well , I ' Ve been working so hard lately , so I ' ll probably just take it easy .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "That ' s great !", + "I ' Ve been working so hard lately , so I ' ll probably just take it easy ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Well , I ' Ve been working so hard lately , so I ' ll probably just take it easy .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Sounds nice .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I ' ll probably just take it easy ." + ], + "type": [ + "inter-personal" + ], + "text": "Sounds nice .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yeah , I ' ll probably just stay in and relax . Maybe watch a few movies .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4, + 6 + ], + "expanded emotion cause span": [ + "That ' s great !", + "I ' Ve been working so hard lately , so I ' ll probably just take it easy .", + "I ' ll probably just stay in and relax . Maybe watch a few movies ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Yeah , I ' ll probably just stay in and relax . Maybe watch a few movies .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Can I stop by ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Maybe watch a few movies ." + ], + "type": [ + "inter-personal" + ], + "text": "Can I stop by ?", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Sure . Any time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4, + 6, + 7 + ], + "expanded emotion cause span": [ + "That ' s great !", + "I ' Ve been working so hard lately , so I ' ll probably just take it easy .", + "I ' ll probably just stay in and relax . Maybe watch a few movies .", + "Can I stop by ?" + ], + "type": [ + "hybrid" + ], + "text": "Sure . Any time .", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2313.json b/reccon/sources/tr_2313.json new file mode 100644 index 0000000000000000000000000000000000000000..a078ff530becf55b5451351425742308cf3c16ae --- /dev/null +++ b/reccon/sources/tr_2313.json @@ -0,0 +1,248 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "How do you like waltz ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "How do you like waltz ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It's very nice , I like it very much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 3 + ], + "expanded emotion cause span": [ + "b", + "May I invite you for the first dance ?" + ], + "type": [ + "latent", + "inter-personal" + ], + "text": "It's very nice , I like it very much .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "May I invite you for the first dance ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "It's very nice , I like it very much .", + "I invite you for the first dance" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "May I invite you for the first dance ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "My pleasure . But I'm afraid I'm not much of a dancer .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "May I invite you for the first dance ?" + ], + "type": [ + "inter-personal" + ], + "text": "My pleasure . But I'm afraid I'm not much of a dancer .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "In fact , I took up dancing quite recently , too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "It's very nice , I like it very much .", + "I invite you for the first dance" + ], + "type": [ + "hybrid" + ], + "text": "In fact , I took up dancing quite recently , too .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Oh , really ? But you're doing the tango wonderfully well .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "you're doing the tango wonderfully well ." + ], + "type": [ + "no-context" + ], + "text": "Oh , really ? But you're doing the tango wonderfully well .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I'm glad you say so , you dance beautifully too . It's lucky that I got a partner .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "you're doing the tango wonderfully well .", + "It's lucky that I got a partner ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm glad you say so , you dance beautifully too . It's lucky that I got a partner .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Thank you for your compliments . It's just that you are a good leader . Do you like the samba and waltz ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "you're doing the tango wonderfully well ." + ], + "type": [ + "self-contagion" + ], + "text": "Thank you for your compliments . It's just that you are a good leader . Do you like the samba and waltz ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yes . And what dances do you like best ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "you're doing the tango wonderfully well .", + "It's lucky that I got a partner ." + ], + "type": [ + "hybrid" + ], + "text": "Yes . And what dances do you like best ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Waltz is my favorite . I like it better than any other dances .", + "emotion": "happiness", + "explanation": "explaining personal preference", + "expanded emotion cause evidence": [ + "b", + 10 + ], + "expanded emotion cause span": [ + "b", + "Waltz is my favorite ." + ], + "type": [ + "latent", + "no-context" + ], + "text": "Waltz is my favorite . I like it better than any other dances .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Oh , the music has stopped . Thank you for the dance .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 11 + ], + "expanded emotion cause span": [ + "b", + "Thank you for the dance ." + ], + "type": [ + "latent", + "no-context" + ], + "text": "Oh , the music has stopped . Thank you for the dance .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "My pleasure . Let's go and have a drink .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "Thank you for the dance ." + ], + "type": [ + "inter-personal" + ], + "text": "My pleasure . Let's go and have a drink .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Fine .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "Let's go and have a drink ." + ], + "type": [ + "inter-personal" + ], + "text": "Fine .", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_232.json b/reccon/sources/tr_232.json new file mode 100644 index 0000000000000000000000000000000000000000..1e7f1acd644593d0fd70b57ddd8ee9000cf9a15a --- /dev/null +++ b/reccon/sources/tr_232.json @@ -0,0 +1,173 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Do you want to go to the beach tonight ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Do you want to go to the beach tonight ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Sure , which beach are we going to ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Do you want to go to the beach tonight ?" + ], + "type": [ + "inter-personal" + ], + "text": "Sure , which beach are we going to ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I wanted to go to Malibu beach .", + "emotion": "neutral", + "text": "I wanted to go to Malibu beach .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I like Santa Monica .", + "emotion": "neutral", + "text": "I like Santa Monica .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "The water there looks so dirty .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "The water there looks so dirty ." + ], + "type": [ + "no-context" + ], + "text": "The water there looks so dirty .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I just like the pier they have at Santa Monica .", + "emotion": "neutral", + "text": "I just like the pier they have at Santa Monica .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I like the pier too , because it's beautiful at night .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I just like the pier they have at Santa Monica .", + "I like the pier too , because it's beautiful at night ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I like the pier too , because it's beautiful at night .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Is Malibu beach nice ?", + "emotion": "neutral", + "text": "Is Malibu beach nice ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "It's a lot nicer , and I really like it better .", + "emotion": "neutral", + "text": "It's a lot nicer , and I really like it better .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "So you want to go to Malibu ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "Is Malibu beach nice ?", + "It's a lot nicer , and I really like it better ." + ], + "type": [ + "hybrid" + ], + "text": "So you want to go to Malibu ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "If that's okay with you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "It's a lot nicer , and I really like it better ." + ], + "type": [ + "self-contagion" + ], + "text": "If that's okay with you .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Sure , let's go to Malibu .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "Is Malibu beach nice ?", + "It's a lot nicer , and I really like it better ." + ], + "type": [ + "hybrid" + ], + "text": "Sure , let's go to Malibu .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2330.json b/reccon/sources/tr_2330.json new file mode 100644 index 0000000000000000000000000000000000000000..ac9b7255617894cecf140c59e1b653ddc7974276 --- /dev/null +++ b/reccon/sources/tr_2330.json @@ -0,0 +1,155 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Have you seen this ?", + "emotion": "neutral", + "text": "Have you seen this ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What ?", + "emotion": "neutral", + "text": "What ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "They killed another hostage .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "They killed another hostage ." + ], + "type": [ + "no-context" + ], + "text": "They killed another hostage .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Oh , how awful . What a terrible thing to do .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "They killed another hostage .", + "how awful ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , how awful . What a terrible thing to do .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I agree completely . I just don't understand what's wrong with them . Don't they have any humanity ?", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 3, + 4, + 5 + ], + "expanded emotion cause span": [ + "They killed another hostage .", + "how awful .", + "Don't they have any humanity ?" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I agree completely . I just don't understand what's wrong with them . Don't they have any humanity ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Well , maybe they've got a point . I mean , I suspect that they think the same about us .", + "emotion": "neutral", + "text": "Well , maybe they've got a point . I mean , I suspect that they think the same about us .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yes , but that doesn't make them right , does it ? Just because they think so ?", + "emotion": "neutral", + "text": "Yes , but that doesn't make them right , does it ? Just because they think so ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I guess not . My view is that we should give in to their demands , so that innocent people can stop getting killed .", + "emotion": "neutral", + "text": "I guess not . My view is that we should give in to their demands , so that innocent people can stop getting killed .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Come on , you can't be serious ! We should never give in to terrorist's demands , otherwise where would we be ?", + "emotion": "neutral", + "text": "Come on , you can't be serious ! We should never give in to terrorist's demands , otherwise where would we be ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Well , that's probably true , but I don't think we should be dogmatic about it . A colleague of mine was kidnapped once , so perhaps I have a different view of things .", + "emotion": "neutral", + "text": "Well , that's probably true , but I don't think we should be dogmatic about it . A colleague of mine was kidnapped once , so perhaps I have a different view of things .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Really ? What happened ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "A colleague of mine was kidnapped once" + ], + "type": [ + "inter-personal" + ], + "text": "Really ? What happened ?", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Well , it was in the Balkans during the war . He was only held for three days , and then they simply released him . It was a case of mistaken identity , and they just let him go when they found out he was no use to them . It was lucky they didn't kill him .", + "emotion": "neutral", + "text": "Well , it was in the Balkans during the war . He was only held for three days , and then they simply released him . It was a case of mistaken identity , and they just let him go when they found out he was no use to them . It was lucky they didn't kill him .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Oh , sure .", + "emotion": "neutral", + "text": "Oh , sure .", + "id": 13 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2332.json b/reccon/sources/tr_2332.json new file mode 100644 index 0000000000000000000000000000000000000000..76e53592b5b16f773638937c9ee6998b7fe163c8 --- /dev/null +++ b/reccon/sources/tr_2332.json @@ -0,0 +1,188 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Where did you get your mobile ? It's really cute .", + "emotion": "neutral", + "text": "Where did you get your mobile ? It's really cute .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh , this ? I got it in Singapore . Here , do you want to take a look ?", + "emotion": "neutral", + "text": "Oh , this ? I got it in Singapore . Here , do you want to take a look ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Thanks . Gee , it's really light !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "it's really light !" + ], + "type": [ + "no-context" + ], + "text": "Thanks . Gee , it's really light !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes , it is , isn't it ? A bit too light , really . What make have you got ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "it's really light !" + ], + "type": [ + "inter-personal" + ], + "text": "Yes , it is , isn't it ? A bit too light , really . What make have you got ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I've got an old Ericsson . Here . Take a look .", + "emotion": "neutral", + "text": "I've got an old Ericsson . Here . Take a look .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Wow , that's really old .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "that's really old ." + ], + "type": [ + "no-context" + ], + "text": "Wow , that's really old .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yes , I like collecting antiques .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "that's really old .", + "I like collecting antiques ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , I like collecting antiques .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Why don't you get a new one ?", + "emotion": "neutral", + "text": "Why don't you get a new one ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I don't know . I like this one , and I don't have any need for all the bells and whistles you get on the new ones .", + "emotion": "neutral", + "text": "I don't know . I like this one , and I don't have any need for all the bells and whistles you get on the new ones .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Really , what makes you say that ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "I don't have any need for all the bells and whistles you get on the new ones ." + ], + "type": [ + "inter-personal" + ], + "text": "Really , what makes you say that ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Well , I just need to make and receive calls , and it's quite reliable . I find that the more fancy stuff they put into these things , the more likely they are to break bown or go wrong , you know ? I mean , this camera function , for instance-how often do you use it ?", + "emotion": "neutral", + "text": "Well , I just need to make and receive calls , and it's quite reliable . I find that the more fancy stuff they put into these things , the more likely they are to break bown or go wrong , you know ? I mean , this camera function , for instance-how often do you use it ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Sometimes , but I guess not very often . It's more for fun . Sometimes when I'm on a trip , for example , I can take a picture and send it to my kids . Or I can send a picture of a sample back to my office and get it costed up immediately .", + "emotion": "neutral", + "text": "Sometimes , but I guess not very often . It's more for fun . Sometimes when I'm on a trip , for example , I can take a picture and send it to my kids . Or I can send a picture of a sample back to my office and get it costed up immediately .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Well , that's nice I guess . So how many kids do you have ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "It's more for fun . Sometimes when I'm on a trip , for example , I can take a picture and send it to my kids . Or I can send a picture of a sample back to my office and get it costed up immediately ." + ], + "type": [ + "inter-personal" + ], + "text": "Well , that's nice I guess . So how many kids do you have ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Three . Two boys and a girl .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13, + 14 + ], + "expanded emotion cause span": [ + "how many kids do you have ?", + "Three . Two boys and a girl ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Three . Two boys and a girl .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_234.json b/reccon/sources/tr_234.json new file mode 100644 index 0000000000000000000000000000000000000000..54cb79665a2961c353b86619e6cf4e6e35002332 --- /dev/null +++ b/reccon/sources/tr_234.json @@ -0,0 +1,139 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Kathy ! How are you ? It's been ages ! What are you doing these days ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Kathy ! How are you ? It's been ages !" + ], + "type": [ + "no-context" + ], + "text": "Kathy ! How are you ? It's been ages ! What are you doing these days ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I just opened my own restaurant . I'm also head chef .", + "emotion": "neutral", + "text": "I just opened my own restaurant . I'm also head chef .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "You're kidding ! You've always hated cooking !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I just opened my own restaurant . I'm also head chef ." + ], + "type": [ + "inter-personal" + ], + "text": "You're kidding ! You've always hated cooking !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Well , I used to hate cooking , but now I love it .", + "emotion": "neutral", + "text": "Well , I used to hate cooking , but now I love it .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "When did you change your mind ?", + "emotion": "neutral", + "text": "When did you change your mind ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "After I tried French food . Before that , I used to cook really boring things for my family .", + "emotion": "neutral", + "text": "After I tried French food . Before that , I used to cook really boring things for my family .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I still can't believe it ! So , did you go to cooking school or something ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I just opened my own restaurant . I'm also head chef ." + ], + "type": [ + "inter-personal" + ], + "text": "I still can't believe it ! So , did you go to cooking school or something ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yeah . I went to California to study .", + "emotion": "neutral", + "text": "Yeah . I went to California to study .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Really ? How long did you stay there ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I went to California to study ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? How long did you stay there ?", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I was there between 88 and 90 .", + "emotion": "neutral", + "text": "I was there between 88 and 90 .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "And what did you do after that ?", + "emotion": "neutral", + "text": "And what did you do after that ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Then I came back here . I worked for about three years to get some experience .", + "emotion": "neutral", + "text": "Then I came back here . I worked for about three years to get some experience .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2356.json b/reccon/sources/tr_2356.json new file mode 100644 index 0000000000000000000000000000000000000000..039b2b3dbd1cd142f57b9e31eb1d35890017e76f --- /dev/null +++ b/reccon/sources/tr_2356.json @@ -0,0 +1,229 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Who's that tall guy over there ?", + "emotion": "neutral", + "text": "Who's that tall guy over there ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh , that's George . He looks very drunk .", + "emotion": "neutral", + "text": "Oh , that's George . He looks very drunk .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What's he like normally ?", + "emotion": "neutral", + "text": "What's he like normally ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Oh , he's really reserved , normally . But , from what I hear , he's got lots of problems .", + "emotion": "neutral", + "text": "Oh , he's really reserved , normally . But , from what I hear , he's got lots of problems .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Really ? What kind of problems ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "he's got lots of problems ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? What kind of problems ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Well , off the record , of course , but I hear that he's got terrible debts . He has his own company , and it's not going very well .", + "emotion": "neutral", + "text": "Well , off the record , of course , but I hear that he's got terrible debts . He has his own company , and it's not going very well .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Really ? Well , I hate to say this , but I'm not surprised .", + "emotion": "neutral", + "text": "Really ? Well , I hate to say this , but I'm not surprised .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Really ? What makes you say that ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I'm not surprised ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? What makes you say that ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Well , he doesn't look very honest .", + "emotion": "neutral", + "text": "Well , he doesn't look very honest .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I know , that's the problem . He can't find any customers . It's a pity , really , because his products are very good . Oh , that reminds me . Did I tell you about my new laptop ?", + "emotion": "neutral", + "text": "I know , that's the problem . He can't find any customers . It's a pity , really , because his products are very good . Oh , that reminds me . Did I tell you about my new laptop ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Oh , don't talk to me about laptops . Mine crashed on Friday and I lost everything . I hate them .", + "emotion": "neutral", + "text": "Oh , don't talk to me about laptops . Mine crashed on Friday and I lost everything . I hate them .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Oh , really ?", + "emotion": "neutral", + "text": "Oh , really ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Look , I need another drink . Do you want one ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "I need another drink . Do you want one ?" + ], + "type": [ + "no-context" + ], + "text": "Look , I need another drink . Do you want one ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Yes , I'll have another cocktail .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "I need another drink . Do you want one ?" + ], + "type": [ + "inter-personal" + ], + "text": "Yes , I'll have another cocktail .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Vodka martini ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "Yes , I'll have another cocktail ." + ], + "type": [ + "inter-personal" + ], + "text": "Vodka martini ?", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Absolutely .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14, + 15 + ], + "expanded emotion cause span": [ + "Yes , I'll have another cocktail .", + "Vodka martini ?" + ], + "type": [ + "hybrid" + ], + "text": "Absolutely .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "I'll be back in a sec .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15, + 16 + ], + "expanded emotion cause span": [ + "Vodka martini ?", + "Absolutely ." + ], + "type": [ + "hybrid" + ], + "text": "I'll be back in a sec .", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "OK . I'll wait here for you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15, + 16 + ], + "expanded emotion cause span": [ + "Vodka martini ?", + "Absolutely ." + ], + "type": [ + "hybrid" + ], + "text": "OK . I'll wait here for you .", + "id": 18 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2371.json b/reccon/sources/tr_2371.json new file mode 100644 index 0000000000000000000000000000000000000000..571672d6fdcace7290f7a3bcd79c776eaabc3160 --- /dev/null +++ b/reccon/sources/tr_2371.json @@ -0,0 +1,148 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Would you like to come by and play bridge ?", + "emotion": "neutral", + "text": "Would you like to come by and play bridge ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Well , let's see . Why don't we go dancing for a change ? We haven't done that for a long time .", + "emotion": "neutral", + "text": "Well , let's see . Why don't we go dancing for a change ? We haven't done that for a long time .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Well , to tell the truth , I don't really feel like it tonight . I had a pretty hard day and I'm sort of tired .", + "emotion": "neutral", + "text": "Well , to tell the truth , I don't really feel like it tonight . I had a pretty hard day and I'm sort of tired .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Hmm . Well , in that case , we could go to the movies .", + "emotion": "neutral", + "text": "Hmm . Well , in that case , we could go to the movies .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Oh , we always go to the movies . Can ' t we do something different ?", + "emotion": "neutral", + "text": "Oh , we always go to the movies . Can ' t we do something different ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Well , do you have any suggestions ?", + "emotion": "neutral", + "text": "Well , do you have any suggestions ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Let's see . How do you feel about playing bridge ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "How do you feel about playing bridge ?" + ], + "type": [ + "no-context" + ], + "text": "Let's see . How do you feel about playing bridge ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "It's OK with me , but we don't have any beer and things .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "How do you feel about playing bridge ?" + ], + "type": [ + "inter-personal" + ], + "text": "It's OK with me , but we don't have any beer and things .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Well , shall I call Janet and ask her and Tom to come over , and I'll go to the store and buy some stuff .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8, + 9 + ], + "expanded emotion cause span": [ + "How do you feel about playing bridge ?", + "It's OK with me ,", + "shall I call Janet and ask her and Tom to come over , and I'll go to the store and buy some stuff ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Well , shall I call Janet and ask her and Tom to come over , and I'll go to the store and buy some stuff .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "OK .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 9 + ], + "expanded emotion cause span": [ + "How do you feel about playing bridge ?", + "shall I call Janet and ask her and Tom to come over , and I'll go to the store and buy some stuff ." + ], + "type": [ + "inter-personal" + ], + "text": "OK .", + "id": 10, + "source_sentences": [ + 6, + 8 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Hello , Janet . It ' s me ... Oh , fine . Just fine . Say , Janet , I was wondering if you and Tom were doing anything tonight ... No ? Well . would you like to come by our place and play a few hands of bridge ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "would you like to come by our place and play a few hands of bridge ?" + ], + "type": [ + "no-context" + ], + "text": "Hello , Janet . It ' s me ... Oh , fine . Just fine . Say , Janet , I was wondering if you and Tom were doing anything tonight ... No ? Well . would you like to come by our place and play a few hands of bridge ?", + "id": 11 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2372.json b/reccon/sources/tr_2372.json new file mode 100644 index 0000000000000000000000000000000000000000..6ae676f9599dbe3f6e58407b3ff1b8ac1bbfdc30 --- /dev/null +++ b/reccon/sources/tr_2372.json @@ -0,0 +1,113 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello , Tom . I'm really glad to meet you here .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "meet you here ." + ], + "type": [ + "no-context" + ], + "text": "Hello , Tom . I'm really glad to meet you here .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'm glad too . Steven , I want to tell you that I'm going to divorce my wife .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "I'm really glad to meet you here .", + "I'm glad too ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm glad too . Steven , I want to tell you that I'm going to divorce my wife .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I'm so surprised , B . Why did you decide to end your marriage suddenly ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "I want to tell you that I'm going to divorce my wife .", + "end your marriage suddenly ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm so surprised , B . Why did you decide to end your marriage suddenly ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "We don't get along well with each other and fight a lot .", + "emotion": "neutral", + "text": "We don't get along well with each other and fight a lot .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I didn't know that . I thought that you were happy together .", + "emotion": "neutral", + "text": "I didn't know that . I thought that you were happy together .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "That isn't true . Actually , we have been separated for six months .", + "emotion": "neutral", + "text": "That isn't true . Actually , we have been separated for six months .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I can't believe it . But if you both determine to divorce , I hope you will have an amicable split .", + "emotion": "neutral", + "text": "I can't believe it . But if you both determine to divorce , I hope you will have an amicable split .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Thank you , Steven . I accept your advice .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I hope you will have an amicable split ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you , Steven . I accept your advice .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2376.json b/reccon/sources/tr_2376.json new file mode 100644 index 0000000000000000000000000000000000000000..74f80eee10277ba5c278e4dc01d8125a50aa25f7 --- /dev/null +++ b/reccon/sources/tr_2376.json @@ -0,0 +1,192 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi Rose , what are you busy with right now ?", + "emotion": "neutral", + "text": "Hi Rose , what are you busy with right now ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hi Jack , I'm working on these documents . The manager wants them for half an hour .", + "emotion": "neutral", + "text": "Hi Jack , I'm working on these documents . The manager wants them for half an hour .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Well , Rose ,", + "emotion": "neutral", + "text": "Well , Rose ,", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Is there something you need ?", + "emotion": "neutral", + "text": "Is there something you need ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Are your free this weekend ?", + "emotion": "neutral", + "text": "Are your free this weekend ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yes , I have nothing to do .", + "emotion": "neutral", + "text": "Yes , I have nothing to do .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Great , Is it convenient if i visit you this weekend ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Are your free this weekend ?", + "Yes , I have nothing to do ." + ], + "type": [ + "hybrid" + ], + "text": "Great , Is it convenient if i visit you this weekend ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I beg your pardon ?", + "emotion": "neutral", + "text": "I beg your pardon ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I'd like to call on you this weekend . I just want to a drop in for a chat .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "I'd like to call on you this weekend . I just want to a drop in for a chat ." + ], + "type": [ + "no-context" + ], + "text": "I'd like to call on you this weekend . I just want to a drop in for a chat .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Really ? well , ok , you're welcome .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "I'd like to call on you this weekend . I just want to a drop in for a chat ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? well , ok , you're welcome .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Is 5 PM . a good time for you ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "you're welcome ." + ], + "type": [ + "inter-personal" + ], + "text": "Is 5 PM . a good time for you ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Hmm , how about seven ? I can treat you to dinner .", + "emotion": "neutral", + "text": "Hmm , how about seven ? I can treat you to dinner .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Sure , that would be great . I'll bring the wine .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "I can treat you to dinner ." + ], + "type": [ + "inter-personal" + ], + "text": "Sure , that would be great . I'll bring the wine .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "OK . Then I'll be expecting you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "Sure , that would be great . I'll bring the wine ." + ], + "type": [ + "inter-personal" + ], + "text": "OK . Then I'll be expecting you .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 15, + "speaker": "A", + "utterance": "I'll be there on time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "Sure , that would be great . I'll bring the wine ." + ], + "type": [ + "self-contagion" + ], + "text": "I'll be there on time .", + "id": 15 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2377.json b/reccon/sources/tr_2377.json new file mode 100644 index 0000000000000000000000000000000000000000..c1a7a9d0d339d80a97bbbf52983c9bb69912e3f1 --- /dev/null +++ b/reccon/sources/tr_2377.json @@ -0,0 +1,178 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "you're rather energetic today . What's going on ?", + "emotion": "neutral", + "text": "you're rather energetic today . What's going on ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "nothing really . I think I've had a few too many coffees .", + "emotion": "neutral", + "text": "nothing really . I think I've had a few too many coffees .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "free coffee is one of the perks at this place , isn't it ?", + "emotion": "neutral", + "text": "free coffee is one of the perks at this place , isn't it ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "it's the only perk of this job ! How's your day going ?", + "emotion": "neutral", + "text": "it's the only perk of this job ! How's your day going ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "not that well . I've got that Monday morning feeling today .", + "emotion": "neutral", + "text": "not that well . I've got that Monday morning feeling today .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "why is that ?", + "emotion": "neutral", + "text": "why is that ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "my boss has been breathing down my neck all day . I can't wait for the weekend !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "my boss has been breathing down my neck all day ." + ], + "type": [ + "no-context" + ], + "text": "my boss has been breathing down my neck all day . I can't wait for the weekend !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "your boss is a real salve-driver , isn't he ?", + "emotion": "neutral", + "text": "your boss is a real salve-driver , isn't he ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "you can say that again ! He won't even let us check our personal email at work !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 7, + 8, + 9 + ], + "expanded emotion cause span": [ + "my boss has been breathing down my neck all day .", + "your boss is a real salve-driver ,", + "He won't even let us check our personal email at work !" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "you can say that again ! He won't even let us check our personal email at work !", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "that's not just your boss . No one is allowed to send personal emails from the office .", + "emotion": "neutral", + "text": "that's not just your boss . No one is allowed to send personal emails from the office .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "really ? I didn't know that it was against company policy .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "that's not just your boss . No one is allowed to send personal emails from the office .", + "I didn't know that it was against company policy ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "really ? I didn't know that it was against company policy .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "maybe your boss isn't so horrible after all !", + "emotion": "neutral", + "text": "maybe your boss isn't so horrible after all !", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "no , he is . Some bosses will bend the rules a bit sometimes , but not my boss . He always follows the rules to a T .", + "emotion": "neutral", + "text": "no , he is . Some bosses will bend the rules a bit sometimes , but not my boss . He always follows the rules to a T .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "try not to let it bother you too much .", + "emotion": "neutral", + "text": "try not to let it bother you too much .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "thanks . I better get back to my work before my boss yells at me again !", + "emotion": "neutral", + "text": "thanks . I better get back to my work before my boss yells at me again !", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "ok , I'll see you in a bit .", + "emotion": "neutral", + "text": "ok , I'll see you in a bit .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "alright . See you later !", + "emotion": "neutral", + "text": "alright . See you later !", + "id": 17 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2378.json b/reccon/sources/tr_2378.json new file mode 100644 index 0000000000000000000000000000000000000000..339d74ede64fa70a2a419de299cd5d664e3603ae --- /dev/null +++ b/reccon/sources/tr_2378.json @@ -0,0 +1,95 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , Mr . James , what's the rush ?", + "emotion": "neutral", + "text": "Hi , Mr . James , what's the rush ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "The bank closes in 30 minutes and I need to cash a check .", + "emotion": "neutral", + "text": "The bank closes in 30 minutes and I need to cash a check .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I can lend you some money .", + "emotion": "neutral", + "text": "I can lend you some money .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Thanks . But it's necessary for me to buy a TV set .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I can lend you some money ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks . But it's necessary for me to buy a TV set .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Can I help in anyway ?", + "emotion": "neutral", + "text": "Can I help in anyway ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "You can take me to the bank if you want to .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Can I help in anyway ?", + "take me to the bank if you want to ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You can take me to the bank if you want to .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Sure . Let ' s go .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Can I help in anyway ?", + "take me to the bank if you want to ." + ], + "type": [ + "hybrid" + ], + "text": "Sure . Let ' s go .", + "id": 7 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2389.json b/reccon/sources/tr_2389.json new file mode 100644 index 0000000000000000000000000000000000000000..5bdf5fc5f61fbf8ca1f57cf8d60134cfeb1196bc --- /dev/null +++ b/reccon/sources/tr_2389.json @@ -0,0 +1,176 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Did you enjoy that new movie ?", + "emotion": "neutral", + "text": "Did you enjoy that new movie ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "That movie's just a lot of noise , same as Simon .", + "emotion": "neutral", + "text": "That movie's just a lot of noise , same as Simon .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Oh , what happened , Carole ?", + "emotion": "neutral", + "text": "Oh , what happened , Carole ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I had to go by myself , he couldn't make it .", + "emotion": "neutral", + "text": "I had to go by myself , he couldn't make it .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "What ? I met him just before I took off from Kitty's , he said he was coming .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I had to go by myself , he couldn't make it ." + ], + "type": [ + "inter-personal" + ], + "text": "What ? I met him just before I took off from Kitty's , he said he was coming .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Kitty's ? He sure gets around , doesn't he ?", + "emotion": "neutral", + "text": "Kitty's ? He sure gets around , doesn't he ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Looks like it . So how did he handle it to ?", + "emotion": "neutral", + "text": "Looks like it . So how did he handle it to ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "His excuse was familiar . He said his car died again .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "He said his car died again ." + ], + "type": [ + "no-context" + ], + "text": "His excuse was familiar . He said his car died again .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I think that's a bunch of nonsense . It seemed ok to me .", + "emotion": "neutral", + "text": "I think that's a bunch of nonsense . It seemed ok to me .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I know . Last week he gave me a lie about being too busy .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 8, + 9, + 10 + ], + "expanded emotion cause span": [ + "He said his car died again .", + "I think that's a bunch of nonsense .", + "Last week he gave me a lie about being too busy ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I know . Last week he gave me a lie about being too busy .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Doesn't sound promising .", + "emotion": "neutral", + "text": "Doesn't sound promising .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Well , I think it's the time to pull the plug .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 8, + 9, + 10, + 12 + ], + "expanded emotion cause span": [ + "He said his car died again .", + "I think that's a bunch of nonsense .", + "Last week he gave me a lie about being too busy .", + "Well , I think it's the time to pull the plug ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Well , I think it's the time to pull the plug .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "If you want I'll let him know if I run into him .", + "emotion": "neutral", + "text": "If you want I'll let him know if I run into him .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Thanks anyway , but I'll do it , Rebecca . Let's get to class .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "If you want I'll let him know if I run into him ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks anyway , but I'll do it , Rebecca . Let's get to class .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2400.json b/reccon/sources/tr_2400.json new file mode 100644 index 0000000000000000000000000000000000000000..f566fd49b3b4f060456c4195cb9bd2c8e1b3018c --- /dev/null +++ b/reccon/sources/tr_2400.json @@ -0,0 +1,128 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Jenny , are you having a good time ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Jenny , are you having a good time ?" + ], + "type": [ + "no-context" + ], + "text": "Jenny , are you having a good time ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , of course . This is a really wonderful party with interesting people and great food .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "This is a really wonderful party with interesting people and great food ." + ], + "type": [ + "no-context" + ], + "text": "Yes , of course . This is a really wonderful party with interesting people and great food .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I ' m glad you are enjoying yourself .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Yes , of course . This is a really wonderful party with interesting people and great food ." + ], + "type": [ + "inter-personal" + ], + "text": "I ' m glad you are enjoying yourself .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Thank you for the invitation .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Thank you for the invitation ." + ], + "type": [ + "no-context" + ], + "text": "Thank you for the invitation .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "It ' s my pleasure . Can I get you another glass of champagne ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Thank you for the invitation ." + ], + "type": [ + "inter-personal" + ], + "text": "It ' s my pleasure . Can I get you another glass of champagne ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yes , I ' d love another glass . You ' re a wonderful host . Thank you for everything .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 5 + ], + "expanded emotion cause span": [ + "This is a really wonderful party with interesting people and great food .", + "Can I get you another glass of champagne ?" + ], + "type": [ + "hybrid" + ], + "text": "Yes , I ' d love another glass . You ' re a wonderful host . Thank you for everything .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "It ' s my pleasure having you here .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Yes , I ' d love another glass . You ' re a wonderful host . Thank you for everything ." + ], + "type": [ + "inter-personal" + ], + "text": "It ' s my pleasure having you here .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2421.json b/reccon/sources/tr_2421.json new file mode 100644 index 0000000000000000000000000000000000000000..0f5266cfc6e7c294750b9e7a4b3fc51392ed52a7 --- /dev/null +++ b/reccon/sources/tr_2421.json @@ -0,0 +1,183 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Come and sit down . Would you like a drink ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Would you like a drink ?" + ], + "type": [ + "no-context" + ], + "text": "Come and sit down . Would you like a drink ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh , yes please ! I'd love a gin and tonic .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "Would you like a drink ?", + "I'd love a gin and tonic ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , yes please ! I'd love a gin and tonic .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Do you like olives ? Or would you prefer crisps ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Would you like a drink ?" + ], + "type": [ + "self-contagion" + ], + "text": "Do you like olives ? Or would you prefer crisps ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Oh , just olives please . What music is this ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Do you like olives ? Or would you prefer crisps ?" + ], + "type": [ + "inter-personal" + ], + "text": "Oh , just olives please . What music is this ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Do you like it ? It's Irish music .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "It's Irish music ." + ], + "type": [ + "no-context" + ], + "text": "Do you like it ? It's Irish music .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "It's great ! Where did you get the CD ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "It's Irish music ." + ], + "type": [ + "inter-personal" + ], + "text": "It's great ! Where did you get the CD ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Arm - I think it was in the CD shop in the Mall . Have you been there ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "It's Irish music ." + ], + "type": [ + "self-contagion" + ], + "text": "Arm - I think it was in the CD shop in the Mall . Have you been there ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yes . I buy a lot of stuff from there . It's a good shop , isn't it ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 8 + ], + "expanded emotion cause span": [ + "It's Irish music .", + "It's a good shop ," + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes . I buy a lot of stuff from there . It's a good shop , isn't it ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yes . Hey , I've got some photos of our holiday in Ireland . Would you like to see them ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "I've got some photos of our holiday in Ireland ." + ], + "type": [ + "no-context" + ], + "text": "Yes . Hey , I've got some photos of our holiday in Ireland . Would you like to see them ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Why not ? I'd love to !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "I've got some photos of our holiday in Ireland . Would you like to see them ?" + ], + "type": [ + "inter-personal" + ], + "text": "Why not ? I'd love to !", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2438.json b/reccon/sources/tr_2438.json new file mode 100644 index 0000000000000000000000000000000000000000..af135e091cf39301c86828bdffcda8ca1402acdd --- /dev/null +++ b/reccon/sources/tr_2438.json @@ -0,0 +1,118 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Well , Jeff , that was a very productive meeting , I thought . You had some really great ideas in there !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 1 + ], + "expanded emotion cause span": [ + "that was a very productive meeting ,", + "You had some really great ideas in there !" + ], + "type": [ + "no-context" + ], + "text": "Well , Jeff , that was a very productive meeting , I thought . You had some really great ideas in there !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Really ? Well , thanks for saying so .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "You had some really great ideas in there !" + ], + "type": [ + "inter-personal" + ], + "text": "Really ? Well , thanks for saying so .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "No , I mean it . Look , are you hungry ? Shall we go get something to eat ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "that was a very productive meeting ,", + "thanks for saying so ." + ], + "type": [ + "hybrid" + ], + "text": "No , I mean it . Look , are you hungry ? Shall we go get something to eat ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Sure . Why not ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "You had some really great ideas in there !", + "No , I mean it . Look , are you hungry ? Shall we go get something to eat ?" + ], + "type": [ + "inter-personal" + ], + "text": "Sure . Why not ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "OK , well , let me just get my coat and we'll go to the diner around the corner .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Sure . Why not ?" + ], + "type": [ + "inter-personal" + ], + "text": "OK , well , let me just get my coat and we'll go to the diner around the corner .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "OK .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 5 + ], + "expanded emotion cause span": [ + "You had some really great ideas in there !", + "we'll go to the diner around the corner ." + ], + "type": [ + "inter-personal" + ], + "text": "OK .", + "id": 6, + "source_sentences": [ + 0, + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_246.json b/reccon/sources/tr_246.json new file mode 100644 index 0000000000000000000000000000000000000000..22a5d6c013d21aa0cf00627b85a2d1778ad88e22 --- /dev/null +++ b/reccon/sources/tr_246.json @@ -0,0 +1,107 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Oh dear , Miss , you are soaked ! Wow , it's really raining heavily outside .", + "emotion": "neutral", + "text": "Oh dear , Miss , you are soaked ! Wow , it's really raining heavily outside .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , it sure is . I had to run here from work ! I need to rush as I'm on my lunch break .", + "emotion": "neutral", + "text": "Yes , it sure is . I had to run here from work ! I need to rush as I'm on my lunch break .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Well please , why don't you go ahead of me in line ? I'm in no hurry .", + "emotion": "neutral", + "text": "Well please , why don't you go ahead of me in line ? I'm in no hurry .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Oh , that's so nice of you ! Thank you very much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "why don't you go ahead of me in line" + ], + "type": [ + "inter-personal" + ], + "text": "Oh , that's so nice of you ! Thank you very much .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "My pleasure Miss . Actually , could you recommend what to eat here ? I've never been here before .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Oh , that's so nice of you ! Thank you very much ." + ], + "type": [ + "inter-personal" + ], + "text": "My pleasure Miss . Actually , could you recommend what to eat here ? I've never been here before .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Sure . Well , the avocado sandwich is delicious , and it's the healthiest thing on the menu . Personally , I think the beef salad is the tastiest choice . I usually get that . Also , the milkshakes are the best milkshakes in town !", + "emotion": "neutral", + "text": "Sure . Well , the avocado sandwich is delicious , and it's the healthiest thing on the menu . Personally , I think the beef salad is the tastiest choice . I usually get that . Also , the milkshakes are the best milkshakes in town !", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Well , thanks for the suggestions .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "the avocado sandwich is delicious , and it's the healthiest thing on the menu . Personally , I think the beef salad is the tastiest choice . I usually get that . Also , the milkshakes are the best milkshakes in town !" + ], + "type": [ + "inter-personal" + ], + "text": "Well , thanks for the suggestions .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Oh , don't mention it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "thanks for the suggestions" + ], + "type": [ + "inter-personal" + ], + "text": "Oh , don't mention it .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2467.json b/reccon/sources/tr_2467.json new file mode 100644 index 0000000000000000000000000000000000000000..628555d9d040aafd862c5c03a510aa2a4cb0e699 --- /dev/null +++ b/reccon/sources/tr_2467.json @@ -0,0 +1,217 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "How is everything going with your girlfriend ?", + "emotion": "neutral", + "text": "How is everything going with your girlfriend ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Didn ' t I tell you ? It ' s over !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "everything going with your girlfriend ?", + "Didn ' t I tell you ? It ' s over !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Didn ' t I tell you ? It ' s over !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Oh , I am sorry to hear that . I did ' t know that you had split up . What happened ?", + "emotion": "neutral", + "text": "Oh , I am sorry to hear that . I did ' t know that you had split up . What happened ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It was a few things . The first thing that happened was that we were supposed to go out for a romantic dinner for our one year anniversary , but she stood me up !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1, + 2, + 4 + ], + "expanded emotion cause span": [ + "everything going with your girlfriend ?", + "Didn ' t I tell you ? It ' s over !", + "It was a few things . The first thing that happened was that we were supposed to go out for a romantic dinner for our one year anniversary , but she stood me up !" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "It was a few things . The first thing that happened was that we were supposed to go out for a romantic dinner for our one year anniversary , but she stood me up !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Really ! Did she tell you why she didn ' t show up ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "supposed to go out for a romantic dinner for our one year anniversary , but she stood me up !" + ], + "type": [ + "inter-personal" + ], + "text": "Really ! Did she tell you why she didn ' t show up ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "No , but I ended up finding out later that night when I saw her with another man at a club near my home !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1, + 2, + 4, + 6 + ], + "expanded emotion cause span": [ + "everything going with your girlfriend ?", + "Didn ' t I tell you ? It ' s over !", + "It was a few things . The first thing that happened was that we were supposed to go out for a romantic dinner for our one year anniversary , but she stood me up !", + "later that night when I saw her with another man at a club near my home !" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "No , but I ended up finding out later that night when I saw her with another man at a club near my home !", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "What was she thinking ? Did you confront her about it when you saw her ?", + "emotion": "neutral", + "text": "What was she thinking ? Did you confront her about it when you saw her ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I wanted to , but I knew that if I spoke to her , I'd just blow up at her , so I decided to just go home . I called her later that night , but she didn't answer the phone .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1, + 2, + 4, + 6, + 8 + ], + "expanded emotion cause span": [ + "everything going with your girlfriend ?", + "Didn ' t I tell you ? It ' s over !", + "It was a few things . The first thing that happened was that we were supposed to go out for a romantic dinner for our one year anniversary , but she stood me up !", + "later that night when I saw her with another man at a club near my home !", + "I called her later that night , but she didn't answer the phone ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I wanted to , but I knew that if I spoke to her , I'd just blow up at her , so I decided to just go home . I called her later that night , but she didn't answer the phone .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I can ' t believe she would do that to you . It ' s so dishonest---and rude !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 4, + 6, + 8, + 9 + ], + "expanded emotion cause span": [ + "supposed to go out for a romantic dinner for our one year anniversary , but she stood me up !", + "later that night when I saw her with another man at a club near my home !", + "I called her later that night , but she didn't answer the phone .", + "It ' s so dishonest---and rude !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I can ' t believe she would do that to you . It ' s so dishonest---and rude !", + "id": 9, + "source_sentences": [ + 3, + 5, + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I know . I still haven ' t heard from her . The good thing is that I ' m so angry with her that I don ' t feel sad about not having her around .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1, + 2, + 4, + 6, + 8, + 9 + ], + "expanded emotion cause span": [ + "everything going with your girlfriend ?", + "Didn ' t I tell you ? It ' s over !", + "It was a few things . The first thing that happened was that we were supposed to go out for a romantic dinner for our one year anniversary , but she stood me up !", + "later that night when I saw her with another man at a club near my home !", + "I called her later that night , but she didn't answer the phone .", + "It ' s so dishonest---and rude !" + ], + "type": [ + "hybrid" + ], + "text": "I know . I still haven ' t heard from her . The good thing is that I ' m so angry with her that I don ' t feel sad about not having her around .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I bet you she regrets what she ' s done . You were such a good catch ! She really lost out , didn ' t she ?", + "emotion": "neutral", + "text": "I bet you she regrets what she ' s done . You were such a good catch ! She really lost out , didn ' t she ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I guess so . It would be nice to know why she did this though .", + "emotion": "neutral", + "text": "I guess so . It would be nice to know why she did this though .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I know . It ' s always nice to have some closure , but I don ' t think you ' ll have a problem finding another girlfriend .", + "emotion": "neutral", + "text": "I know . It ' s always nice to have some closure , but I don ' t think you ' ll have a problem finding another girlfriend .", + "id": 13 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2471.json b/reccon/sources/tr_2471.json new file mode 100644 index 0000000000000000000000000000000000000000..3dd692e6c62ccc851154865511048447a60c8be6 --- /dev/null +++ b/reccon/sources/tr_2471.json @@ -0,0 +1,148 @@ +[ + { + "turn": 1, + "speaker": "B", + "utterance": "Hi , Lucy !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Lucy !" + ], + "type": [ + "no-context" + ], + "text": "Hi , Lucy !", + "id": 1 + }, + { + "turn": 2, + "speaker": "A", + "utterance": "Hi . It ' s a wonderful wedding , isn't it ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "It ' s a wonderful wedding" + ], + "type": [ + "no-context" + ], + "text": "Hi . It ' s a wonderful wedding , isn't it ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "B", + "utterance": "Yes , It's very great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "wonderful wedding" + ], + "type": [ + "inter-personal" + ], + "text": "Yes , It's very great .", + "id": 3 + }, + { + "turn": 4, + "speaker": "A", + "utterance": "Mary's father is a rich man , isn't he ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "It ' s a wonderful wedding" + ], + "type": [ + "self-contagion" + ], + "text": "Mary's father is a rich man , isn't he ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "B", + "utterance": "You are right , Mary's father is responsible for the entire wedding-arrangement , costs , etc . I think he must spend much money .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "wonderful wedding" + ], + "type": [ + "inter-personal" + ], + "text": "You are right , Mary's father is responsible for the entire wedding-arrangement , costs , etc . I think he must spend much money .", + "id": 5 + }, + { + "turn": 6, + "speaker": "A", + "utterance": "Will Mary and her husband be ready to leave for their honeymoon ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "It ' s a wonderful wedding" + ], + "type": [ + "self-contagion" + ], + "text": "Will Mary and her husband be ready to leave for their honeymoon ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "B", + "utterance": "Yes . Look ! Mary is going to throw the bride bouquet .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 7 + ], + "expanded emotion cause span": [ + "wonderful wedding", + "Mary is going to throw the bride bouquet ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes . Look ! Mary is going to throw the bride bouquet .", + "id": 7, + "source_sentences": [ + 1 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "A", + "utterance": "Oh , I'll try to catch it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 7 + ], + "expanded emotion cause span": [ + "It ' s a wonderful wedding", + "Mary is going to throw the bride bouquet ." + ], + "type": [ + "hybrid" + ], + "text": "Oh , I'll try to catch it .", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2484.json b/reccon/sources/tr_2484.json new file mode 100644 index 0000000000000000000000000000000000000000..2d6407f5bc61c70b1d0b6a55048397206e656cea --- /dev/null +++ b/reccon/sources/tr_2484.json @@ -0,0 +1,183 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I've been thinking of taking I've been thinking of taking a Crazy English course . Do you think it's a good idea", + "emotion": "neutral", + "text": "I've been thinking of taking I've been thinking of taking a Crazy English course . Do you think it's a good idea", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Sure ! You should do anything you can to improve your English .", + "emotion": "neutral", + "text": "Sure ! You should do anything you can to improve your English .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Really ? Do you think English is that important ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "You should do anything you can to improve your English .", + "Do you think English is that important ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Really ? Do you think English is that important ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Of course it is . In fact , I'll even take the course with you if you want .", + "emotion": "neutral", + "text": "Of course it is . In fact , I'll even take the course with you if you want .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Great ! It's always better to do things with a friend .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I'll even take the course with you" + ], + "type": [ + "inter-personal" + ], + "text": "Great ! It's always better to do things with a friend .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Do you have the phone number ? I need to call for registration .", + "emotion": "neutral", + "text": "Do you have the phone number ? I need to call for registration .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "No , I left it at home . Sorry !", + "emotion": "neutral", + "text": "No , I left it at home . Sorry !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That's OK . I can get it from you later .", + "emotion": "neutral", + "text": "That's OK . I can get it from you later .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "So , do you want to go somewhere for dinner and practice our English together tonight ?", + "emotion": "neutral", + "text": "So , do you want to go somewhere for dinner and practice our English together tonight ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "All right . I know a great restaurant near here . But , it's a little expensive and I don't have much money with me .", + "emotion": "neutral", + "text": "All right . I know a great restaurant near here . But , it's a little expensive and I don't have much money with me .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "No problem . I just got paid . It ' s my treat .", + "emotion": "neutral", + "text": "No problem . I just got paid . It ' s my treat .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Thank you ! I'll be sure to return the favor after our first class , OK ?", + "emotion": "neutral", + "text": "Thank you ! I'll be sure to return the favor after our first class , OK ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Forget it ! That's what friends are for ! Besides , I have a VIP card for a discount .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12, + 13 + ], + "expanded emotion cause span": [ + "I'll be sure to return the favor", + "I have a VIP card for a discount ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Forget it ! That's what friends are for ! Besides , I have a VIP card for a discount .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Good job ! This is going to be a great night !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13, + 13, + 14 + ], + "expanded emotion cause span": [ + "Forget it ! That's what friends are for !", + "I have a VIP card for a discount .", + "This is going to be a great night !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Good job ! This is going to be a great night !", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "I think so too . Let ' s go !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "This is going to be a great night !" + ], + "type": [ + "inter-personal" + ], + "text": "I think so too . Let ' s go !", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2509.json b/reccon/sources/tr_2509.json new file mode 100644 index 0000000000000000000000000000000000000000..ccd50743b72d77743eb416351306b82c6231c143 --- /dev/null +++ b/reccon/sources/tr_2509.json @@ -0,0 +1,188 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , Ann . I was wondering if you are free tomorrow night ?", + "emotion": "neutral", + "text": "Hi , Ann . I was wondering if you are free tomorrow night ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Well , George . I guess I am . Why do you ask ?", + "emotion": "neutral", + "text": "Well , George . I guess I am . Why do you ask ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I've just gotten a pair of pre-sale Star Wars movie tickets from a friend and was thinking of inviting you along for the opening premiere . Are you interested ?", + "emotion": "neutral", + "text": "I've just gotten a pair of pre-sale Star Wars movie tickets from a friend and was thinking of inviting you along for the opening premiere . Are you interested ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yeah , definitely ! Thanks for inviting me .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "I've just gotten a pair of pre-sale Star Wars movie tickets from a friend and was thinking of inviting you along for the opening premiere . Are you interested ?", + "for inviting me ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yeah , definitely ! Thanks for inviting me .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "My pleasure .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Thanks for inviting me ." + ], + "type": [ + "inter-personal" + ], + "text": "My pleasure .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I really wanted to watch the Star Wars on the opening day , but the pre-sale tickets were sold out . How did you manage to get hold of them ?", + "emotion": "neutral", + "text": "I really wanted to watch the Star Wars on the opening day , but the pre-sale tickets were sold out . How did you manage to get hold of them ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "A friend of mine works at the corporate headquarters of Pepsi , which is a major sponsor of the movie . He was able to get the tickets for free , and then he sold two more for me for 50 dollars a piece .", + "emotion": "neutral", + "text": "A friend of mine works at the corporate headquarters of Pepsi , which is a major sponsor of the movie . He was able to get the tickets for free , and then he sold two more for me for 50 dollars a piece .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "You paid 50 dollars for each ticket ? That's a huge premium over the regular price .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "he sold two more for me for 50 dollars a piece .", + "That's a huge premium over the regular price ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You paid 50 dollars for each ticket ? That's a huge premium over the regular price .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Not really . Considering the fact that other people were willing to pay as much as 200 dollars each on the black market . Besides , I knew you were really looking forward to watching Star Wars on the opening day .", + "emotion": "neutral", + "text": "Not really . Considering the fact that other people were willing to pay as much as 200 dollars each on the black market . Besides , I knew you were really looking forward to watching Star Wars on the opening day .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Wow ! I am really honored you went through all this trouble just for my sake . I really appreciate that . So , what time are we going ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "I knew you were really looking forward to watching Star Wars on the opening day .", + "I am really honored you went through all this trouble just for my sake ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Wow ! I am really honored you went through all this trouble just for my sake . I really appreciate that . So , what time are we going ?", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Well , let's see . The movie stars at 10 . We should be there at least 1 hour earlier , because there is a big line . I could pick you up at your house at 8 , if that's ok with you .", + "emotion": "neutral", + "text": "Well , let's see . The movie stars at 10 . We should be there at least 1 hour earlier , because there is a big line . I could pick you up at your house at 8 , if that's ok with you .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "8 pm , that's fine with me .", + "emotion": "neutral", + "text": "8 pm , that's fine with me .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Okay .", + "emotion": "neutral", + "text": "Okay .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "So I'll see you tomorrow then at 8 .", + "emotion": "neutral", + "text": "So I'll see you tomorrow then at 8 .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Yeah , that's great . I'll see you tomorrow night .", + "emotion": "neutral", + "text": "Yeah , that's great . I'll see you tomorrow night .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Ok , George . Bye !", + "emotion": "neutral", + "text": "Ok , George . Bye !", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "Bye , Ann !", + "emotion": "neutral", + "text": "Bye , Ann !", + "id": 17 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2511.json b/reccon/sources/tr_2511.json new file mode 100644 index 0000000000000000000000000000000000000000..8e1e35f5e763a6c4601def663a9efe7b85f21fe0 --- /dev/null +++ b/reccon/sources/tr_2511.json @@ -0,0 +1,149 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi . Ed , what's up ?", + "emotion": "neutral", + "text": "Hi . Ed , what's up ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Nothing .", + "emotion": "neutral", + "text": "Nothing .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Doesn't look like it to me .", + "emotion": "neutral", + "text": "Doesn't look like it to me .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Just get out of my face !", + "emotion": "anger", + "explanation": "The cause for anger is latent.", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Just get out of my face !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Woo , easy .", + "emotion": "neutral", + "text": "Woo , easy .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Leave me alone !", + "emotion": "anger", + "explanation": "The cause for anger is latent.", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Leave me alone !", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "What are you so ticked off about ?", + "emotion": "neutral", + "text": "What are you so ticked off about ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I don't want to talk about it .", + "emotion": "neutral", + "text": "I don't want to talk about it .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Maybe I could help .", + "emotion": "neutral", + "text": "Maybe I could help .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I blew the finally exam .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "I blew the finally exam ." + ], + "type": [ + "no-context" + ], + "text": "I blew the finally exam .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "You've got be joking .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "I blew the finally exam ." + ], + "type": [ + "inter-personal" + ], + "text": "You've got be joking .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "No , I'm not .", + "emotion": "neutral", + "text": "No , I'm not .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Well , don't get bend on a ship about it .", + "emotion": "neutral", + "text": "Well , don't get bend on a ship about it .", + "id": 13 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2520.json b/reccon/sources/tr_2520.json new file mode 100644 index 0000000000000000000000000000000000000000..f28527b859b9b655bc2b00c9a13241d33177ea3a --- /dev/null +++ b/reccon/sources/tr_2520.json @@ -0,0 +1,207 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey Matt . I just got a job at a consulting firm .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I just got a job at a consulting firm ." + ], + "type": [ + "no-context" + ], + "text": "Hey Matt . I just got a job at a consulting firm .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Congratulations . That's great !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 1 + ], + "expanded emotion cause span": [ + "I just got a job at a consulting firm .", + "I just got a job at a consulting firm ." + ], + "type": [ + "inter-personal" + ], + "text": "Congratulations . That's great !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I'm so happy . I don't have to worry about finding a job and interviewing anymore .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "I just got a job at a consulting firm .", + "I don't have to worry about finding a job and interviewing anymore ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I'm so happy . I don't have to worry about finding a job and interviewing anymore .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "When do you start ?", + "emotion": "neutral", + "text": "When do you start ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I start next Monday .", + "emotion": "neutral", + "text": "I start next Monday .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "You're going to have to put in a lot of hours you know .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I'm so happy . I don't have to worry about finding a job and interviewing anymore ." + ], + "type": [ + "inter-personal" + ], + "text": "You're going to have to put in a lot of hours you know .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I know . I'm a little nervous , but it's pretty exciting .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "it's pretty exciting ." + ], + "type": [ + "no-context" + ], + "text": "I know . I'm a little nervous , but it's pretty exciting .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I bet . You must be stoked .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 7 + ], + "expanded emotion cause span": [ + "I'm so happy . I don't have to worry about finding a job and interviewing anymore .", + "I know . I'm a little nervous , but it's pretty exciting ." + ], + "type": [ + "inter-personal" + ], + "text": "I bet . You must be stoked .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yeah . I'm going to celebrate tonight . Wanna hang out ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "I'm going to celebrate tonight . Wanna hang out ?" + ], + "type": [ + "no-context" + ], + "text": "Yeah . I'm going to celebrate tonight . Wanna hang out ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Sure . It's on you right ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Yeah . I'm going to celebrate tonight . Wanna hang out ?" + ], + "type": [ + "inter-personal" + ], + "text": "Sure . It's on you right ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Of course . How about Toby ? Should we call him ?", + "emotion": "neutral", + "text": "Of course . How about Toby ? Should we call him ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I don't know . He's a little depressed . He's having a hard time finding a job right now .", + "emotion": "neutral", + "text": "I don't know . He's a little depressed . He's having a hard time finding a job right now .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I should still tell him . In the least , I can refer him to my company . It might help .", + "emotion": "neutral", + "text": "I should still tell him . In the least , I can refer him to my company . It might help .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "That sounds like a good idea .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "I can refer him to my company . It might help ." + ], + "type": [ + "inter-personal" + ], + "text": "That sounds like a good idea .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2535.json b/reccon/sources/tr_2535.json new file mode 100644 index 0000000000000000000000000000000000000000..fefc5f09577f59928848c2503cfc4e47f4db2e61 --- /dev/null +++ b/reccon/sources/tr_2535.json @@ -0,0 +1,130 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Thanks for lunch . It was delicious .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "lunch . It was delicious ." + ], + "type": [ + "no-context" + ], + "text": "Thanks for lunch . It was delicious .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It's OK .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Thanks for lunch . It was delicious ." + ], + "type": [ + "inter-personal" + ], + "text": "It's OK .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Next time lunch is on me .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "lunch . It was delicious ." + ], + "type": [ + "self-contagion" + ], + "text": "Next time lunch is on me .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Don't be silly .", + "emotion": "surprise", + "explanation": "The speaker appreciates person A's gesture but happily replies that speaker A is not required organize a payback lunch.", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Next time lunch is on me ." + ], + "type": [ + "inter-personal" + ], + "text": "Don't be silly .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I'm serious .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "lunch . It was delicious ." + ], + "type": [ + "self-contagion" + ], + "text": "I'm serious .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "All right . Next time you will treat .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Next time lunch is on me ." + ], + "type": [ + "inter-personal" + ], + "text": "All right . Next time you will treat .", + "id": 6, + "source_sentences": [ + 2 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "It's a deal .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 6 + ], + "expanded emotion cause span": [ + "lunch . It was delicious .", + "Next time you will treat ." + ], + "type": [ + "hybrid" + ], + "text": "It's a deal .", + "id": 7 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2552.json b/reccon/sources/tr_2552.json new file mode 100644 index 0000000000000000000000000000000000000000..4c0d7cc0b189cf634d9a6f5f70e983e690467258 --- /dev/null +++ b/reccon/sources/tr_2552.json @@ -0,0 +1,135 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "When is your vacation going to start ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "When is your vacation going to start ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'll be leaving on the fifth of August for the vacation", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I'll be leaving on the fifth of August for the vacation" + ], + "type": [ + "no-context" + ], + "text": "I'll be leaving on the fifth of August for the vacation", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Oh , that's only a few days from now ! How many weeks are you going to be taking ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I'll be leaving on the fifth of August for the vacation" + ], + "type": [ + "inter-personal" + ], + "text": "Oh , that's only a few days from now ! How many weeks are you going to be taking ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I'm taking two weeks now . but I want to save the other week and take it sometime during the winter .", + "emotion": "neutral", + "text": "I'm taking two weeks now . but I want to save the other week and take it sometime during the winter .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Where are you going now .", + "emotion": "neutral", + "text": "Where are you going now .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "To the beach", + "emotion": "neutral", + "text": "To the beach", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Have you made your hotel reservation yet ?", + "emotion": "neutral", + "text": "Have you made your hotel reservation yet ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Oh , I don't need to do that . I'll be staying with friends", + "emotion": "neutral", + "text": "Oh , I don't need to do that . I'll be staying with friends", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "You're lucky . It's hard to find a place to stay at the beach in August", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "Oh , I don't need to do that . I'll be staying with friends", + "You're lucky" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You're lucky . It's hard to find a place to stay at the beach in August", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Just think , in a few days , I'll be swimming and lying in the sun and just taking it easy .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "in a few days , I'll be swimming and lying in the sun and just taking it easy ." + ], + "type": [ + "no-context" + ], + "text": "Just think , in a few days , I'll be swimming and lying in the sun and just taking it easy .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2553.json b/reccon/sources/tr_2553.json new file mode 100644 index 0000000000000000000000000000000000000000..7e374334f5c5730862613e0668e1407c3ab858b6 --- /dev/null +++ b/reccon/sources/tr_2553.json @@ -0,0 +1,113 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What a hot day !", + "emotion": "neutral", + "text": "What a hot day !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , summer is coming .", + "emotion": "neutral", + "text": "Yes , summer is coming .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Where are you going this summer vacation ?", + "emotion": "neutral", + "text": "Where are you going this summer vacation ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I'd like to go to Tianjin .", + "emotion": "neutral", + "text": "I'd like to go to Tianjin .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Do you want to go to the beach there ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I'd like to go to Tianjin ." + ], + "type": [ + "inter-personal" + ], + "text": "Do you want to go to the beach there ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yes , of course . And what's your plan ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Do you want to go to the beach there ?", + "Yes , of course ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , of course . And what's your plan ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "The same to you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "Yes , of course . And what's your plan ?", + "The same to you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "The same to you .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That's great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "The same to you ." + ], + "type": [ + "inter-personal" + ], + "text": "That's great .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2575.json b/reccon/sources/tr_2575.json new file mode 100644 index 0000000000000000000000000000000000000000..37c1f840d404d7e53de170e0e77c5cba9644a0e3 --- /dev/null +++ b/reccon/sources/tr_2575.json @@ -0,0 +1,155 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I often go to a place of leisure .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I often go to a place of leisure ." + ], + "type": [ + "no-context" + ], + "text": "I often go to a place of leisure .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Really ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I often go to a place of leisure ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I very much like to go to a cafe and doze in the afternoon sunshine .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "I often go to a place of leisure .", + "go to a cafe and doze in the afternoon sunshine ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I very much like to go to a cafe and doze in the afternoon sunshine .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Sounds great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I very much like to go to a cafe and doze in the afternoon sunshine ." + ], + "type": [ + "inter-personal" + ], + "text": "Sounds great .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "The coffee , books , music and sunshine are just beautiful there .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3, + 5 + ], + "expanded emotion cause span": [ + "I often go to a place of leisure .", + "go to a cafe and doze in the afternoon sunshine .", + "The coffee , books , music and sunshine are just beautiful there ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "The coffee , books , music and sunshine are just beautiful there .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "How nice .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "The coffee , books , music and sunshine are just beautiful there ." + ], + "type": [ + "inter-personal" + ], + "text": "How nice .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I may take you there some day .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3, + 5 + ], + "expanded emotion cause span": [ + "I often go to a place of leisure .", + "go to a cafe and doze in the afternoon sunshine .", + "The coffee , books , music and sunshine are just beautiful there ." + ], + "type": [ + "self-contagion" + ], + "text": "I may take you there some day .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Good .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I may take you there some day ." + ], + "type": [ + "inter-personal" + ], + "text": "Good .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2581.json b/reccon/sources/tr_2581.json new file mode 100644 index 0000000000000000000000000000000000000000..1adbfd34edb25327c4e12e67408ecc27f4e9c2f5 --- /dev/null +++ b/reccon/sources/tr_2581.json @@ -0,0 +1,197 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Joe , how are you doing ?", + "emotion": "happiness", + "explanation": "the speaker is happy to meet B", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "how are you doing ?" + ], + "type": [ + "no-context" + ], + "text": "Joe , how are you doing ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Pretty good . Mary , I was wondering if you would like to come to a party on Friday night ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "how are you doing ?", + "party on Friday night ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Pretty good . Mary , I was wondering if you would like to come to a party on Friday night ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I am free that night , and a party sounds good .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "I was wondering if you would like to come to a party on Friday night ?", + "I am free that night , and a party sounds good ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I am free that night , and a party sounds good .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Fine . It will be at my house . Do you know how to get there ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "party on Friday night ?", + "I am free that night , and a party sounds good ." + ], + "type": [ + "hybrid" + ], + "text": "Fine . It will be at my house . Do you know how to get there ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I kind of know where you live , but could you e-mail me your address ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "I was wondering if you would like to come to a party on Friday night ?", + "I am free that night , and a party sounds good ." + ], + "type": [ + "hybrid" + ], + "text": "I kind of know where you live , but could you e-mail me your address ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I can do that . Do you have anyone that you would like to bring with you to the party ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "party on Friday night ?", + "I am free that night , and a party sounds good ." + ], + "type": [ + "hybrid" + ], + "text": "I can do that . Do you have anyone that you would like to bring with you to the party ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I would really like to bring my friend Jake , if that would be OK .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "Do you have anyone that you would like to bring with you to the party ?", + "I would really like to bring my friend Jake ," + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I would really like to bring my friend Jake , if that would be OK .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Oh yeah , I remember Jake . That would be fine .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I would really like to bring my friend Jake ," + ], + "type": [ + "inter-personal" + ], + "text": "Oh yeah , I remember Jake . That would be fine .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Would you like some help with the food ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7, + 8 + ], + "expanded emotion cause span": [ + "Do you have anyone that you would like to bring with you to the party ?", + "I would really like to bring my friend Jake ,", + "I remember Jake . That would be fine ." + ], + "type": [ + "hybrid" + ], + "text": "Would you like some help with the food ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Just bring along whatever it is that you and Jake would like to drink .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Would you like some help with the food ?" + ], + "type": [ + "inter-personal" + ], + "text": "Just bring along whatever it is that you and Jake would like to drink .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2593.json b/reccon/sources/tr_2593.json new file mode 100644 index 0000000000000000000000000000000000000000..d4bda37380d8c48926e31ef3a78a4c200ff24360 --- /dev/null +++ b/reccon/sources/tr_2593.json @@ -0,0 +1,123 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Tom ! How are you ? We missed you at the party last night . Are you OK ?", + "emotion": "neutral", + "text": "Tom ! How are you ? We missed you at the party last night . Are you OK ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I don ' t know . I didn ' t really feel like going out . I guess I ' m feeling a little homesick .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I ' m feeling a little homesick ." + ], + "type": [ + "no-context" + ], + "text": "I don ' t know . I didn ' t really feel like going out . I guess I ' m feeling a little homesick .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Come on . We ' Ve been through this already ! Look , I know the adjustment was hard when you first got here , but we agreed that you were gonna try and deal with it .", + "emotion": "neutral", + "text": "Come on . We ' Ve been through this already ! Look , I know the adjustment was hard when you first got here , but we agreed that you were gonna try and deal with it .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I was . It ' s just that the holidays are coming up and I won ' t be able to home because I can ' t afford the airfare . I ' m just longing for some of the comforts of home , like my mom ' s cooking and being around my family .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "It ' s just that the holidays are coming up and I won ' t be able to home because I can ' t afford the airfare . I ' m just longing for some of the comforts of home , like my mom ' s cooking and being around my family ." + ], + "type": [ + "no-context" + ], + "text": "I was . It ' s just that the holidays are coming up and I won ' t be able to home because I can ' t afford the airfare . I ' m just longing for some of the comforts of home , like my mom ' s cooking and being around my family .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Yeah , it can get pretty lonely over the holidays . When I first got here , I ' d get depressed and nostalgic for anything that reminded me of home . I almost let it get to me , but then I started going out , keeping myself busy and before I knew it , I was used to to it .", + "emotion": "neutral", + "text": "Yeah , it can get pretty lonely over the holidays . When I first got here , I ' d get depressed and nostalgic for anything that reminded me of home . I almost let it get to me , but then I started going out , keeping myself busy and before I knew it , I was used to to it .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I see what you mean , but I ' m still bummed out .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "It ' s just that the holidays are coming up and I won ' t be able to home because I can ' t afford the airfare . I ' m just longing for some of the comforts of home , like my mom ' s cooking and being around my family ." + ], + "type": [ + "self-contagion" + ], + "text": "I see what you mean , but I ' m still bummed out .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "OK . how does this sound . let ' s get you suited up and hit the dance club tonight . I hear that an awesome DJ is playing and there will be a lot of pretty single girls there !", + "emotion": "neutral", + "text": "OK . how does this sound . let ' s get you suited up and hit the dance club tonight . I hear that an awesome DJ is playing and there will be a lot of pretty single girls there !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "You know , I could really go for that . You don ' t mind being my wingman for tonight ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "let ' s get you suited up and hit the dance club tonight . I hear that an awesome DJ is playing and there will be a lot of pretty single girls there !" + ], + "type": [ + "inter-personal" + ], + "text": "You know , I could really go for that . You don ' t mind being my wingman for tonight ?", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Not at all ! It be fun ! It will be like a boys ' night out ... well kinda ...", + "emotion": "neutral", + "text": "Not at all ! It be fun ! It will be like a boys ' night out ... well kinda ...", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Great ! I must warn you though , whatever happens , don ' t let me go on a drinking binge . Trust me , it ' s not a pretty picture !", + "emotion": "neutral", + "text": "Great ! I must warn you though , whatever happens , don ' t let me go on a drinking binge . Trust me , it ' s not a pretty picture !", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_260.json b/reccon/sources/tr_260.json new file mode 100644 index 0000000000000000000000000000000000000000..ce9a71f9186fb27ba26f2bb26fb1c32f7d0df95c --- /dev/null +++ b/reccon/sources/tr_260.json @@ -0,0 +1,114 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Welcome to my birthday party , I am so happy you can come .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "you can come ." + ], + "type": [ + "no-context" + ], + "text": "Welcome to my birthday party , I am so happy you can come .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Thanks for inviting me . Here is the gift for you . Happy birthday , Francis ! Many more happy and healthy years for you !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "Welcome to my birthday party , I am so happy you can come .", + "Thanks for inviting me . Here is the gift for you . Happy birthday , Francis ! Many more happy and healthy years for you !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thanks for inviting me . Here is the gift for you . Happy birthday , Francis ! Many more happy and healthy years for you !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Thank you , shall I open it now ?", + "emotion": "neutral", + "text": "Thank you , shall I open it now ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes , please do .", + "emotion": "neutral", + "text": "Yes , please do .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Wow , a remote car model and my favorite brand . I really like it . That is so nice of you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "a remote car model and my favorite brand . I really like it ." + ], + "type": [ + "no-context" + ], + "text": "Wow , a remote car model and my favorite brand . I really like it . That is so nice of you .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yeah , I was really struggling whether I should give you this nice little car . It was the last one they had and I really like it so much myself .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "That is so nice of you ." + ], + "type": [ + "inter-personal" + ], + "text": "Yeah , I was really struggling whether I should give you this nice little car . It was the last one they had and I really like it so much myself .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Typical you , always wanting to keep the best things for yourself . The more I appreciate the gift now .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 7 + ], + "expanded emotion cause span": [ + "a remote car model and my favorite brand . I really like it .", + "The more I appreciate the gift now ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Typical you , always wanting to keep the best things for yourself . The more I appreciate the gift now .", + "id": 7 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2606.json b/reccon/sources/tr_2606.json new file mode 100644 index 0000000000000000000000000000000000000000..f0b316fc9d36532af132ea523d6aa36b330da4ed --- /dev/null +++ b/reccon/sources/tr_2606.json @@ -0,0 +1,214 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Come on , you must tell me everything about him .", + "emotion": "neutral", + "text": "Come on , you must tell me everything about him .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Well , he's very tall and handsome .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "tell me everything about him .", + "he's very tall and handsome ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Well , he's very tall and handsome .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Hmm ...", + "emotion": "neutral", + "text": "Hmm ...", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "He has big blue eyes and long blonde hair .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 4 + ], + "expanded emotion cause span": [ + "tell me everything about him .", + "he's very tall and handsome .", + "big blue eyes and long blonde hair ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "He has big blue eyes and long blonde hair .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Oh , how long ?", + "emotion": "neutral", + "text": "Oh , how long ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Down to his shoulders . It's beautiful , like gold .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 4, + 6 + ], + "expanded emotion cause span": [ + "tell me everything about him .", + "he's very tall and handsome .", + "big blue eyes and long blonde hair .", + "It's beautiful , like gold ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Down to his shoulders . It's beautiful , like gold .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "OK . OK . You'd better tell me what he does .", + "emotion": "neutral", + "text": "OK . OK . You'd better tell me what he does .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "He's a very creative painter . His paintings sell well .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 4, + 6, + 8 + ], + "expanded emotion cause span": [ + "tell me everything about him .", + "he's very tall and handsome .", + "big blue eyes and long blonde hair .", + "It's beautiful , like gold .", + "He's a very creative painter . His paintings sell well ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "He's a very creative painter . His paintings sell well .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Really ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "His paintings sell well ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ?", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "He's quite a patient teacher , too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 4, + 6, + 8, + 10 + ], + "expanded emotion cause span": [ + "tell me everything about him .", + "he's very tall and handsome .", + "big blue eyes and long blonde hair .", + "It's beautiful , like gold .", + "He's a very creative painter . His paintings sell well .", + "He's quite a patient teacher" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "He's quite a patient teacher , too .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Fine .", + "emotion": "neutral", + "text": "Fine .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "You're going to like him . Everybody says he's a nice guy .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 4, + 6, + 8, + 10, + 12 + ], + "expanded emotion cause span": [ + "tell me everything about him .", + "he's very tall and handsome .", + "big blue eyes and long blonde hair .", + "It's beautiful , like gold .", + "He's a very creative painter . His paintings sell well .", + "He's quite a patient teacher", + "Everybody says he's a nice guy ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "You're going to like him . Everybody says he's a nice guy .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2653.json b/reccon/sources/tr_2653.json new file mode 100644 index 0000000000000000000000000000000000000000..00c039ace7c90533847ae43b06fd59eef924695b --- /dev/null +++ b/reccon/sources/tr_2653.json @@ -0,0 +1,194 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello , John . How are you ?", + "emotion": "neutral", + "text": "Hello , John . How are you ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'm fine , thanks . And you ?", + "emotion": "neutral", + "text": "I'm fine , thanks . And you ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Very well , thanks . Nice to see you again . I haven't seen you for a long time . What have you been doing lately ?", + "emotion": "neutral", + "text": "Very well , thanks . Nice to see you again . I haven't seen you for a long time . What have you been doing lately ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Oh , nothing much really . And how is everything with you ?", + "emotion": "neutral", + "text": "Oh , nothing much really . And how is everything with you ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Fine , thanks . I've been busy lately .", + "emotion": "neutral", + "text": "Fine , thanks . I've been busy lately .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "What have you been doing ?", + "emotion": "neutral", + "text": "What have you been doing ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I've been studying for my exams . My school exams will begin next month .", + "emotion": "neutral", + "text": "I've been studying for my exams . My school exams will begin next month .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Really ? Good luck for them .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "My school exams will begin next month ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? Good luck for them .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Thanks . And how are your parents ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Good luck for them ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks . And how are your parents ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "They're both very well , thanks .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "And how are your parents ?", + "They're both very well , thanks ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "They're both very well , thanks .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Where are you going now ?", + "emotion": "neutral", + "text": "Where are you going now ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I'm going to do some shopping . Why don't you come with me ?", + "emotion": "happiness", + "explanation": "Assuming asking somone to come along is a cause of happiness from socialization.", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "I'm going to do some shopping . Why don't you come with me ?" + ], + "type": [ + "no-context" + ], + "text": "I'm going to do some shopping . Why don't you come with me ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I can't . I have to meet someone .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "I'm going to do some shopping . Why don't you come with me ?" + ], + "type": [ + "inter-personal" + ], + "text": "I can't . I have to meet someone .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "It's been nice talking to you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "It's been nice talking to you ." + ], + "type": [ + "no-context" + ], + "text": "It's been nice talking to you .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Good-bye . See you again sometime .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "It's been nice talking to you ." + ], + "type": [ + "inter-personal" + ], + "text": "Good-bye . See you again sometime .", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_266.json b/reccon/sources/tr_266.json new file mode 100644 index 0000000000000000000000000000000000000000..ec629e5ac913fea2a8eb912e19e191d8154b21ca --- /dev/null +++ b/reccon/sources/tr_266.json @@ -0,0 +1,172 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Mike , come and look at this painting of shrimp ! It is so simple yet so vivid !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "this painting of shrimp ! It is so simple yet so vivid !" + ], + "type": [ + "no-context" + ], + "text": "Mike , come and look at this painting of shrimp ! It is so simple yet so vivid !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yeah . It is incredible ! Is it the work of Qi Bakshi ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "this painting of shrimp ! It is so simple yet so vivid !", + "It is incredible ! Is it the work of Qi Bakshi ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yeah . It is incredible ! Is it the work of Qi Bakshi ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yes , it is . How do you know that ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "Is it the work of Qi Bakshi ?", + "Yes , it is . How do you know that ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , it is . How do you know that ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Well , Qi is famous all over the world , isn ' t he ? Besides I am quite interested in Chinese painting .", + "emotion": "neutral", + "text": "Well , Qi is famous all over the world , isn ' t he ? Besides I am quite interested in Chinese painting .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Cool ! What kind of Chinese painting do you prefer , free sketch or claborate-style painting ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I am quite interested in Chinese painting ." + ], + "type": [ + "inter-personal" + ], + "text": "Cool ! What kind of Chinese painting do you prefer , free sketch or claborate-style painting ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I prefer free sketch , especially the landscape paintings . I can always feel peace and harmony from those landscape paintings .", + "emotion": "neutral", + "text": "I prefer free sketch , especially the landscape paintings . I can always feel peace and harmony from those landscape paintings .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "That's true . Chinese art stresses the harmony between man and nature , which is an important part of China's traditional culture .", + "emotion": "neutral", + "text": "That's true . Chinese art stresses the harmony between man and nature , which is an important part of China's traditional culture .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I love this art exhibition !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 8 + ], + "expanded emotion cause span": [ + "this painting of shrimp ! It is so simple yet so vivid !", + "It is incredible ! Is it the work of Qi Bakshi ?", + "I love this art exhibition !" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I love this art exhibition !", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "So do I . Let ' s go to other areas to see what they have got , shall we ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "I love this art exhibition !", + "So do I ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "So do I . Let ' s go to other areas to see what they have got , shall we ?", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "OK .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 8, + 9, + 9 + ], + "expanded emotion cause span": [ + "this painting of shrimp ! It is so simple yet so vivid !", + "It is incredible ! Is it the work of Qi Bakshi ?", + "I love this art exhibition !", + "So do I .", + "Let ' s go to other areas to see what they have got" + ], + "type": [ + "hybrid" + ], + "text": "OK .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2678.json b/reccon/sources/tr_2678.json new file mode 100644 index 0000000000000000000000000000000000000000..9d130cd8a0bd89c4be504ff95ae08eeda9bb086b --- /dev/null +++ b/reccon/sources/tr_2678.json @@ -0,0 +1,147 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "You ' re all set now ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "You ' re all set now ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh , thank you so much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "You ' re all set now ?" + ], + "type": [ + "inter-personal" + ], + "text": "Oh , thank you so much .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Really , it was nothing .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "You ' re all set now ?", + "Oh , thank you so much ." + ], + "type": [ + "hybrid" + ], + "text": "Really , it was nothing .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I really appreciated it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "You ' re all set now ?" + ], + "type": [ + "inter-personal" + ], + "text": "I really appreciated it .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I was happy to help .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I really appreciated it ." + ], + "type": [ + "inter-personal" + ], + "text": "I was happy to help .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "It was so kind of you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 5 + ], + "expanded emotion cause span": [ + "You ' re all set now ?", + "I was happy to help ." + ], + "type": [ + "inter-personal" + ], + "text": "It was so kind of you .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Don ' t mention it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "It was so kind of you ." + ], + "type": [ + "inter-personal" + ], + "text": "Don ' t mention it .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "You ' re a real friend in need .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "You ' re a real friend in need ." + ], + "type": [ + "no-context" + ], + "text": "You ' re a real friend in need .", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2679.json b/reccon/sources/tr_2679.json new file mode 100644 index 0000000000000000000000000000000000000000..851603541110f5f04e77d2de152ee7e25455f92f --- /dev/null +++ b/reccon/sources/tr_2679.json @@ -0,0 +1,124 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , Jason !", + "emotion": "neutral", + "text": "Hi , Jason !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hi , Linda . I have two concert complimentary tickets . Will you go with me tonight ?", + "emotion": "neutral", + "text": "Hi , Linda . I have two concert complimentary tickets . Will you go with me tonight ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "With the greatest pleasure ! Where is the concert held this evening ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I have two concert complimentary tickets . Will you go with me tonight ?" + ], + "type": [ + "inter-personal" + ], + "text": "With the greatest pleasure ! Where is the concert held this evening ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It will be held at the Central Music Hall .", + "emotion": "neutral", + "text": "It will be held at the Central Music Hall .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "What is on the program ?", + "emotion": "neutral", + "text": "What is on the program ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "It ' s a piano solo . I'm fond of piano , you know .", + "emotion": "neutral", + "text": "It ' s a piano solo . I'm fond of piano , you know .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Hah ! OK . Let ' s go together !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "It ' s a piano solo . I'm fond of piano", + "Let ' s go together !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Hah ! OK . Let ' s go together !", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Let ' s meet at the park at 6:00 .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "It ' s a piano solo . I'm fond of piano", + "Let ' s go together !" + ], + "type": [ + "hybrid" + ], + "text": "Let ' s meet at the park at 6:00 .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "See you then .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "It ' s a piano solo . I'm fond of piano", + "Let ' s go together !" + ], + "type": [ + "hybrid" + ], + "text": "See you then .", + "id": 9 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2683.json b/reccon/sources/tr_2683.json new file mode 100644 index 0000000000000000000000000000000000000000..ee2659211e61da91c0287c9df85d40f2d4fb214e --- /dev/null +++ b/reccon/sources/tr_2683.json @@ -0,0 +1,131 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , John ! How was your vacation ?", + "emotion": "neutral", + "text": "Hi , John ! How was your vacation ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "We went to Malaysia and Thailand .", + "emotion": "neutral", + "text": "We went to Malaysia and Thailand .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "That must have been wonderful . Do anything interesting ?", + "emotion": "neutral", + "text": "That must have been wonderful . Do anything interesting ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Well . We went bungee jumping when we were in Malaysia .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "We went bungee jumping when we were in Malaysia ." + ], + "type": [ + "no-context" + ], + "text": "Well . We went bungee jumping when we were in Malaysia .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Wow , isn't that dangerous ?", + "emotion": "neutral", + "text": "Wow , isn't that dangerous ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "A little , but the rush was worth it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 6 + ], + "expanded emotion cause span": [ + "We went bungee jumping when we were in Malaysia .", + "the rush was worth it ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "A little , but the rush was worth it .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Tell me about it .", + "emotion": "neutral", + "text": "Tell me about it .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "We jumped off a bridge and fell 500 feet before the bungee cord caught us .", + "emotion": "neutral", + "text": "We jumped off a bridge and fell 500 feet before the bungee cord caught us .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "500 feet ! I would never be able to do that .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "We jumped off a bridge and fell 500 feet" + ], + "type": [ + "inter-personal" + ], + "text": "500 feet ! I would never be able to do that .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Yeah , It was scary but exhilarating .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 6, + 10 + ], + "expanded emotion cause span": [ + "We went bungee jumping when we were in Malaysia .", + "the rush was worth it .", + "exhilarating" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Yeah , It was scary but exhilarating .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2684.json b/reccon/sources/tr_2684.json new file mode 100644 index 0000000000000000000000000000000000000000..408192cb327322dba83a73f63a0ba2de3d0e6ae2 --- /dev/null +++ b/reccon/sources/tr_2684.json @@ -0,0 +1,186 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "It's a lovely day , isn't it ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "It's a lovely day" + ], + "type": [ + "no-context" + ], + "text": "It's a lovely day , isn't it ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , the weather sure is nice today .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "It's a lovely day", + "Yes , the weather sure is nice today ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , the weather sure is nice today .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I love it when the weather is like this . Why don't we sit down outside and have our lunch ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 3 + ], + "expanded emotion cause span": [ + "It's a lovely day", + "Yes , the weather sure is nice today .", + "I love it when the weather is like this ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I love it when the weather is like this . Why don't we sit down outside and have our lunch ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "That sounds like a good idea . The sky is clear , the sun is shining and there's a nice cool breeze , so it is not too hot .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 3, + 3, + 4 + ], + "expanded emotion cause span": [ + "It's a lovely day", + "Yes , the weather sure is nice today .", + "I love it when the weather is like this .", + "Why don't we sit down outside and have our lunch ?", + "That sounds like a good idea . The sky is clear , the sun is shining and there's a nice cool breeze , so it is not too hot ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "That sounds like a good idea . The sky is clear , the sun is shining and there's a nice cool breeze , so it is not too hot .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I really miss the change of seasons like we have in Colorado ; but I must admit , this sure is a nice spring day .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 3, + 3, + 4, + 5 + ], + "expanded emotion cause span": [ + "It's a lovely day", + "Yes , the weather sure is nice today .", + "I love it when the weather is like this .", + "Why don't we sit down outside and have our lunch ?", + "That sounds like a good idea . The sky is clear , the sun is shining and there's a nice cool breeze , so it is not too hot .", + "this sure is a nice spring day ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I really miss the change of seasons like we have in Colorado ; but I must admit , this sure is a nice spring day .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Hey , this spot in the shade looks really comfortable .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 3, + 3, + 4, + 5, + 6 + ], + "expanded emotion cause span": [ + "It's a lovely day", + "Yes , the weather sure is nice today .", + "I love it when the weather is like this .", + "Why don't we sit down outside and have our lunch ?", + "That sounds like a good idea . The sky is clear , the sun is shining and there's a nice cool breeze , so it is not too hot .", + "this sure is a nice spring day .", + "this spot in the shade looks really comfortable ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Hey , this spot in the shade looks really comfortable .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Okay . Hey , is that a dark cloud over there ? Do you think it will rain after all ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 4, + 7 + ], + "expanded emotion cause span": [ + "The sky is clear , the sun is shining", + "is that a dark cloud over there ? Do you think it will rain after all ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Okay . Hey , is that a dark cloud over there ? Do you think it will rain after all ?", + "id": 7, + "source_sentences": [ + 3 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I don't think so . I say the weather report last night , and it said the weather should be fine all day .", + "emotion": "neutral", + "text": "I don't think so . I say the weather report last night , and it said the weather should be fine all day .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "If the weather stays nice perhaps we can go to the beach this weekend . It ' s been a while since I've not really gotten some sun .", + "emotion": "neutral", + "text": "If the weather stays nice perhaps we can go to the beach this weekend . It ' s been a while since I've not really gotten some sun .", + "id": 9 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2695.json b/reccon/sources/tr_2695.json new file mode 100644 index 0000000000000000000000000000000000000000..bbc848149492d27d89c8beb22ba289bdbc82871b --- /dev/null +++ b/reccon/sources/tr_2695.json @@ -0,0 +1,150 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "A funny thing happened to me the other day .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "A funny thing happened to me the other day ." + ], + "type": [ + "no-context" + ], + "text": "A funny thing happened to me the other day .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh , yes ?", + "emotion": "neutral", + "text": "Oh , yes ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I was just thinking about someone I went to school with , this boy I was quite friendly with in third grade . We used to hang out together - he lived next door - but then my parents moved and I changed schools and never saw him again .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "A funny thing happened to me the other day ." + ], + "type": [ + "self-contagion" + ], + "text": "I was just thinking about someone I went to school with , this boy I was quite friendly with in third grade . We used to hang out together - he lived next door - but then my parents moved and I changed schools and never saw him again .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Mmm .", + "emotion": "neutral", + "text": "Mmm .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Well , I was walking down Nan Jing Dong Lu ( Nan-Jing E . Rd . ) during my lunch break thinking about this boy-I have no idea why I was thinking about him .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "A funny thing happened to me the other day ." + ], + "type": [ + "self-contagion" + ], + "text": "Well , I was walking down Nan Jing Dong Lu ( Nan-Jing E . Rd . ) during my lunch break thinking about this boy-I have no idea why I was thinking about him .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Really ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I have no idea why I was thinking about him ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yes . And suddenly I heard someone call my name . I turned around and there was this man looking at me . I didn't recognize him at all , but he obviously knew who I was .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 7 + ], + "expanded emotion cause span": [ + "A funny thing happened to me the other day .", + "And suddenly I heard someone call my name . I turned around and there was this man looking at me . I didn't recognize him at all , but he obviously knew who I was ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Yes . And suddenly I heard someone call my name . I turned around and there was this man looking at me . I didn't recognize him at all , but he obviously knew who I was .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Oh , yeah , that's embarrassing when that happens .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "suddenly I heard someone call my name . I turned around and there was this man looking at me . I didn't recognize him at all , but he obviously knew who I was ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , yeah , that's embarrassing when that happens .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "You got it . Well , he walked up to me and said my name again and then I realized it was the boy I had been thinking about , the one from third grade !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 7, + 9 + ], + "expanded emotion cause span": [ + "A funny thing happened to me the other day .", + "And suddenly I heard someone call my name . I turned around and there was this man looking at me . I didn't recognize him at all , but he obviously knew who I was .", + "he walked up to me and said my name again and then I realized it was the boy I had been thinking about , the one from third grade !" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "You got it . Well , he walked up to me and said my name again and then I realized it was the boy I had been thinking about , the one from third grade !", + "id": 9 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2710.json b/reccon/sources/tr_2710.json new file mode 100644 index 0000000000000000000000000000000000000000..9f35f84ab28a681c508af9d51bafcba4a9b6e51d --- /dev/null +++ b/reccon/sources/tr_2710.json @@ -0,0 +1,140 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Betty , would you please read this letter of application I've just written ? I'd like to have your opinion .", + "emotion": "neutral", + "text": "Betty , would you please read this letter of application I've just written ? I'd like to have your opinion .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'd be glad to tell you what I think .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "I'd like to have your opinion .", + "I'd be glad to tell you" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'd be glad to tell you what I think .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Good ! I'm interested in your advice .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "I'd be glad to tell you", + "I'm interested in your advice ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Good ! I'm interested in your advice .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "If I were you , I would change the beginning . You should write about your education first because we like to judge a man by his abilities .", + "emotion": "neutral", + "text": "If I were you , I would change the beginning . You should write about your education first because we like to judge a man by his abilities .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Good idea , Betty . What would you think about the second part ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3, + 4, + 5 + ], + "expanded emotion cause span": [ + "I'd be glad to tell you", + "I'm interested in your advice .", + "I would change the beginning .", + "Good idea" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Good idea , Betty . What would you think about the second part ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I think it's too short . You'd better say something about your work experience .", + "emotion": "neutral", + "text": "I think it's too short . You'd better say something about your work experience .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You're right , I'll change it . How about the last part ?", + "emotion": "neutral", + "text": "You're right , I'll change it . How about the last part ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Very good . But you should talk about your family , too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "How about the last part ?", + "Very good ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Very good . But you should talk about your family , too .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I agree . I appreciate your helping me .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "I appreciate your helping me ." + ], + "type": [ + "no-context" + ], + "text": "I agree . I appreciate your helping me .", + "id": 9 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2714.json b/reccon/sources/tr_2714.json new file mode 100644 index 0000000000000000000000000000000000000000..a37cff3082d345528fd74b7de9d6dfcf51cc6644 --- /dev/null +++ b/reccon/sources/tr_2714.json @@ -0,0 +1,250 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "How is night life in Beijing ?", + "emotion": "happiness", + "explanation": "the speaker is excited to try night life in Beijing", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "night life in Beijing" + ], + "type": [ + "no-context" + ], + "text": "How is night life in Beijing ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Very interesting !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "night life in Beijing", + "Very interesting !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Very interesting !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What do you suggest then ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "night life in Beijing", + "Very interesting !" + ], + "type": [ + "hybrid" + ], + "text": "What do you suggest then ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "How about going to dance ? There is a very good nightclub nearby .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "How about going to dance ? There is a very good nightclub nearby ." + ], + "type": [ + "no-context" + ], + "text": "How about going to dance ? There is a very good nightclub nearby .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "That's a great idea . Let's go ... Oh , the dance hall looks very nice and the music is wonderful .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "How about going to dance ? There is a very good nightclub nearby .", + "the dance hall looks very nice and the music is wonderful ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's a great idea . Let's go ... Oh , the dance hall looks very nice and the music is wonderful .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I'm glad you like it . The band is called \" Four and One \" . They are especially good at playing rock and roll .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5, + 6 + ], + "expanded emotion cause span": [ + "How about going to dance ? There is a very good nightclub nearby .", + "the dance hall looks very nice and the music is wonderful .", + "I'm glad you like it . The band is called \" Four and One \" . They are especially good at playing rock and roll ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I'm glad you like it . The band is called \" Four and One \" . They are especially good at playing rock and roll .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "That's great ! I love to dance to fast music .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I'm glad you like it . The band is called \" Four and One \" . They are especially good at playing rock and roll .", + "I love to dance to fast music ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's great ! I love to dance to fast music .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Then you must be interested in disco dancing , aren't you ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "I love to dance to fast music .", + "you must be interested in disco dancing" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Then you must be interested in disco dancing , aren't you ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yes , disco dancing is my favorite . It ' s great fun and good exercise as well .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "you must be interested in disco dancing", + "disco dancing is my favorite . It ' s great fun and good exercise as well ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , disco dancing is my favorite . It ' s great fun and good exercise as well .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "OK . Let's disco .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "disco dancing is my favorite . It ' s great fun and good exercise as well ." + ], + "type": [ + "inter-personal" + ], + "text": "OK . Let's disco .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Now the band is playing a slow dance .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Let's disco ." + ], + "type": [ + "inter-personal" + ], + "text": "Now the band is playing a slow dance .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "That's a waltz . Would you like to try it ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "That's a waltz ." + ], + "type": [ + "no-context" + ], + "text": "That's a waltz . Would you like to try it ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Sorry , I think I'Il sit out the next dance .", + "emotion": "neutral", + "text": "Sorry , I think I'Il sit out the next dance .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "All right . Let me get you something to drink .", + "emotion": "neutral", + "text": "All right . Let me get you something to drink .", + "id": 14 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2717.json b/reccon/sources/tr_2717.json new file mode 100644 index 0000000000000000000000000000000000000000..01ae00ef730b7d3824517ca7b58b6cf3a44d6876 --- /dev/null +++ b/reccon/sources/tr_2717.json @@ -0,0 +1,207 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I can ' t believe my English teacher is making me read pride and prejudice !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I can ' t believe my English teacher is making me read pride and prejudice !" + ], + "type": [ + "no-context" + ], + "text": "I can ' t believe my English teacher is making me read pride and prejudice !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Why not ! It ' s a classic ; in fact , it ' s one of my favorite novels .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I can ' t believe" + ], + "type": [ + "inter-personal" + ], + "text": "Why not ! It ' s a classic ; in fact , it ' s one of my favorite novels .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "But it ' s so old .", + "emotion": "neutral", + "text": "But it ' s so old .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Don ' t judge a book by its cover . Do you Kwon what it ' s about ?", + "emotion": "neutral", + "text": "Don ' t judge a book by its cover . Do you Kwon what it ' s about ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "No , not at all .", + "emotion": "neutral", + "text": "No , not at all .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "First of all , it ' s a romance novel , set in the early 19th century .", + "emotion": "neutral", + "text": "First of all , it ' s a romance novel , set in the early 19th century .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I didn ' t realize it was a romance novel . What ' s the main storyline ?", + "emotion": "neutral", + "text": "I didn ' t realize it was a romance novel . What ' s the main storyline ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "It ' s basically about a father who tried to marry off one of his five girls .", + "emotion": "neutral", + "text": "It ' s basically about a father who tried to marry off one of his five girls .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Why does he want to do that ?", + "emotion": "neutral", + "text": "Why does he want to do that ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Since he doesn ' t have a son , he hopes that one of the girls will marry a wealthy man . That way , all of his daughters will be cared for .", + "emotion": "neutral", + "text": "Since he doesn ' t have a son , he hopes that one of the girls will marry a wealthy man . That way , all of his daughters will be cared for .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Won ' t they get his inheritance ?", + "emotion": "neutral", + "text": "Won ' t they get his inheritance ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "No , that ' s the problem . Though they are well-off , once he dies , his house will go to his cousin . So , when he dies , the girls will have nothing .", + "emotion": "neutral", + "text": "No , that ' s the problem . Though they are well-off , once he dies , his house will go to his cousin . So , when he dies , the girls will have nothing .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I see . This sounds interesting ! Maybe my teacher isn ' t so horrible after all .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "This sounds interesting ! Maybe my teacher isn ' t so horrible after all ." + ], + "type": [ + "no-context" + ], + "text": "I see . This sounds interesting ! Maybe my teacher isn ' t so horrible after all .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "So , are you going to read the novel or watch the movie ?", + "emotion": "neutral", + "text": "So , are you going to read the novel or watch the movie ?", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "There ' s movie ? My teacher didn ' t tell me that !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 14, + 15 + ], + "expanded emotion cause span": [ + "are you going to read the novel or watch the movie ?", + "There ' s movie ? My teacher didn ' t tell me that !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "There ' s movie ? My teacher didn ' t tell me that !", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "That ' s probably because she wants you to read the book first .", + "emotion": "neutral", + "text": "That ' s probably because she wants you to read the book first .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "It would take a lot less time ..", + "emotion": "neutral", + "text": "It would take a lot less time ..", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "How about this . When you finish the book . I ' ll get the movie and watch it with you .", + "emotion": "neutral", + "text": "How about this . When you finish the book . I ' ll get the movie and watch it with you .", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "Ok . That sounds like a deal .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 18 + ], + "expanded emotion cause span": [ + "When you finish the book . I ' ll get the movie and watch it with you ." + ], + "type": [ + "inter-personal" + ], + "text": "Ok . That sounds like a deal .", + "id": 19, + "source_sentences": [ + 17 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2743.json b/reccon/sources/tr_2743.json new file mode 100644 index 0000000000000000000000000000000000000000..0c862c35e45d792d7677d869a0da84717d96c850 --- /dev/null +++ b/reccon/sources/tr_2743.json @@ -0,0 +1,99 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "How was the movie last night ?", + "emotion": "neutral", + "text": "How was the movie last night ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I didn't really like it .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "movie last night ?", + "I didn't really like it ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I didn't really like it .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Mary said that she was really pleased with the photography .", + "emotion": "neutral", + "text": "Mary said that she was really pleased with the photography .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I found it very disappointing .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "photography .", + "I found it very disappointing ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I found it very disappointing .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "She liked the acting , too , because that's what she wanted to see .", + "emotion": "neutral", + "text": "She liked the acting , too , because that's what she wanted to see .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I wasn't happy with it .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "the acting", + "I wasn't happy with it ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I wasn't happy with it .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Nothing is to your satisfaction .", + "emotion": "neutral", + "text": "Nothing is to your satisfaction .", + "id": 7 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2762.json b/reccon/sources/tr_2762.json new file mode 100644 index 0000000000000000000000000000000000000000..936af0a2237ebfe1302576c9c80b062e0e91774b --- /dev/null +++ b/reccon/sources/tr_2762.json @@ -0,0 +1,130 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "You really look familiar .", + "emotion": "neutral", + "text": "You really look familiar .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Really ? My name is Gretchen Hammer . What is your name ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "You really look familiar ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? My name is Gretchen Hammer . What is your name ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "My name is Phillip Hammer . I think we are related . Who is your dad ?", + "emotion": "neutral", + "text": "My name is Phillip Hammer . I think we are related . Who is your dad ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Jacob Hammer . He is originally from Holland .", + "emotion": "neutral", + "text": "Jacob Hammer . He is originally from Holland .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "That's my uncle . You're my cousin ! Hi cousin !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3, + 4, + 5 + ], + "expanded emotion cause span": [ + "I think we are related . Who is your dad ?", + "Jacob Hammer . He is originally from Holland .", + "That's my uncle . You're my cousin !" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "That's my uncle . You're my cousin ! Hi cousin !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "It's really a small world , isn't it ! The Hammer family isn't very big .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "That's my uncle . You're my cousin !", + "The Hammer family isn't very big ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It's really a small world , isn't it ! The Hammer family isn't very big .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "It really is . Do you have time to eat dinner and catch up ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "You're my cousin ! Hi cousin !" + ], + "type": [ + "self-contagion" + ], + "text": "It really is . Do you have time to eat dinner and catch up ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I always make time for family .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 7, + 8 + ], + "expanded emotion cause span": [ + "You're my cousin ! Hi cousin !", + "eat dinner and catch up ?", + "family" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I always make time for family .", + "id": 8, + "source_sentences": [ + 4, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2781.json b/reccon/sources/tr_2781.json new file mode 100644 index 0000000000000000000000000000000000000000..da1dc4e06796088318dc3664c742700fb99f1151 --- /dev/null +++ b/reccon/sources/tr_2781.json @@ -0,0 +1,82 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "My goodness . She is thirty seconds faster than the world records in five thousand meters race .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "She is thirty seconds faster than the world records in five thousand meters race ." + ], + "type": [ + "no-context" + ], + "text": "My goodness . She is thirty seconds faster than the world records in five thousand meters race .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Excuse me . What did you say ?", + "emotion": "neutral", + "text": "Excuse me . What did you say ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "A chinese girl have broken the world record in the Olympic Games", + "emotion": "neutral", + "text": "A chinese girl have broken the world record in the Olympic Games", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "That's incredible . I cann't believe it .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "A chinese girl have broken the world record in the Olympic Games" + ], + "type": [ + "inter-personal" + ], + "text": "That's incredible . I cann't believe it .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "You have to . It's sure .", + "emotion": "neutral", + "text": "You have to . It's sure .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "How amazing !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "A chinese girl have broken the world record in the Olympic Games" + ], + "type": [ + "inter-personal" + ], + "text": "How amazing !", + "id": 6, + "source_sentences": [ + 2 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2797.json b/reccon/sources/tr_2797.json new file mode 100644 index 0000000000000000000000000000000000000000..c060491946fcebb45639d93d7b8e66aec2650ccc --- /dev/null +++ b/reccon/sources/tr_2797.json @@ -0,0 +1,125 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Tomorrow I'll take you to some places that I'm sure you will have interest in .", + "emotion": "neutral", + "text": "Tomorrow I'll take you to some places that I'm sure you will have interest in .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Where else haven't we been to yet ?", + "emotion": "neutral", + "text": "Where else haven't we been to yet ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "They are the Folk Antique Handicrafts and Collectibles Exhibition Halls .", + "emotion": "neutral", + "text": "They are the Folk Antique Handicrafts and Collectibles Exhibition Halls .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Sounds great ! How many kinds of folk collections do they have ?", + "emotion": "happiness", + "explanation": "Speaker is excited hearing this.", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "Tomorrow I'll take you to some places that I'm sure you will have interest in .", + "the Folk Antique Handicrafts and Collectibles Exhibition Halls ." + ], + "type": [ + "inter-personal" + ], + "text": "Sounds great ! How many kinds of folk collections do they have ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Well . there're actually over 200 kinds of folk collections in this city . That's half the collections of antique objects in China . There's one exhibition half for multiple collection , and several individual display rooms for private collectors .", + "emotion": "neutral", + "text": "Well . there're actually over 200 kinds of folk collections in this city . That's half the collections of antique objects in China . There's one exhibition half for multiple collection , and several individual display rooms for private collectors .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Private collectors ! They must have excellent collections . I'II go and see each of them . What kinds of collections can I see ? Come on , don't keep me in suspense !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3, + 6 + ], + "expanded emotion cause span": [ + "Tomorrow I'll take you to some places that I'm sure you will have interest in .", + "the Folk Antique Handicrafts and Collectibles Exhibition Halls .", + "They must have excellent collections . I'II go and see each of them ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Private collectors ! They must have excellent collections . I'II go and see each of them . What kinds of collections can I see ? Come on , don't keep me in suspense !", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "No hurry ! I'II tell you now , The collections include ancient cases and caskets , tea sets , abacuses , precious sea shells and conches , drama costumes , agates , ancient coins , fans , mini-musical instruments , root-carving , rare stones and rocks , model ships , model cars ...", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 6 + ], + "expanded emotion cause span": [ + "They must have excellent collections . I'II go and see each of them .", + "don't keep me in suspense !" + ], + "type": [ + "inter-personal" + ], + "text": "No hurry ! I'II tell you now , The collections include ancient cases and caskets , tea sets , abacuses , precious sea shells and conches , drama costumes , agates , ancient coins , fans , mini-musical instruments , root-carving , rare stones and rocks , model ships , model cars ...", + "id": 7, + "source_sentences": [ + 5, + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Enough ! I can't wait anymore .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3, + 6, + 8 + ], + "expanded emotion cause span": [ + "Tomorrow I'll take you to some places that I'm sure you will have interest in .", + "the Folk Antique Handicrafts and Collectibles Exhibition Halls .", + "They must have excellent collections . I'II go and see each of them .", + "I can't wait anymore ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Enough ! I can't wait anymore .", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2799.json b/reccon/sources/tr_2799.json new file mode 100644 index 0000000000000000000000000000000000000000..55abf9f7f1815212d2a914416bd76fae227ec979 --- /dev/null +++ b/reccon/sources/tr_2799.json @@ -0,0 +1,146 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Now , you are to board the plane . We ' re sorry that we haven't done much to help you when you stayed in China .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "we haven't done much to help you when you stayed in China ." + ], + "type": [ + "no-context" + ], + "text": "Now , you are to board the plane . We ' re sorry that we haven't done much to help you when you stayed in China .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I appreciate what you have done for me . Everything I have seen here has left a deep impression on me . I really don't know how to express my thanks to you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I appreciate what you have done for me . Everything I have seen here has left a deep impression on me ." + ], + "type": [ + "no-context" + ], + "text": "I appreciate what you have done for me . Everything I have seen here has left a deep impression on me . I really don't know how to express my thanks to you .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "We are ready to help you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I appreciate what you have done for me . Everything I have seen here has left a deep impression on me . I really don't know how to express my thanks to you ." + ], + "type": [ + "inter-personal" + ], + "text": "We are ready to help you .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Will you be kind to say \" Thank you \" to Mr . Zhang and other friends for me ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "We are ready to help you ." + ], + "type": [ + "inter-personal" + ], + "text": "Will you be kind to say \" Thank you \" to Mr . Zhang and other friends for me ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I'd like to . I'm sure your visit will help to promote the friendship and understanding between both of us . Welcome to China again .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "Will you be kind to say \" Thank you \" to Mr . Zhang and other friends for me ?", + "I'm sure your visit will help to promote the friendship and understanding between both of us ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'd like to . I'm sure your visit will help to promote the friendship and understanding between both of us . Welcome to China again .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Of course , I will . Well , it's time for me to say goodbye . The plane will take off soon . Hope some day you will come to America for a visit .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I'd like to . I'm sure your visit will help to promote the friendship and understanding between both of us . Welcome to China again ." + ], + "type": [ + "inter-personal" + ], + "text": "Of course , I will . Well , it's time for me to say goodbye . The plane will take off soon . Hope some day you will come to America for a visit .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Thank you . I will if I have chance . Goodbye and happy landing !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Hope some day you will come to America for a visit ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . I will if I have chance . Goodbye and happy landing !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Goodbye !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Thank you . I will if I have chance . Goodbye and happy landing !" + ], + "type": [ + "inter-personal" + ], + "text": "Goodbye !", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2803.json b/reccon/sources/tr_2803.json new file mode 100644 index 0000000000000000000000000000000000000000..a3cd0c64fb88f00dad1f8e66e10a214b4938c8f9 --- /dev/null +++ b/reccon/sources/tr_2803.json @@ -0,0 +1,160 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey , that's a really nice outfit you have on .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "that's a really nice outfit you have on ." + ], + "type": [ + "no-context" + ], + "text": "Hey , that's a really nice outfit you have on .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Thank you . I wasn't sure if it looked okay or not .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "that's a really nice outfit you have on ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . I wasn't sure if it looked okay or not .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Oh , you look stunning . Your dress really goes well with your shoes .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Oh , you look stunning . Your dress really goes well with your shoes ." + ], + "type": [ + "no-context" + ], + "text": "Oh , you look stunning . Your dress really goes well with your shoes .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I'm glad that you think so . I thought it might be a bit too revealing .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Oh , you look stunning . Your dress really goes well with your shoes ." + ], + "type": [ + "inter-personal" + ], + "text": "I'm glad that you think so . I thought it might be a bit too revealing .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "No , not at all . It looks really classy on you . Where did you pick that up ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "I'm glad that you think so .", + "It looks really classy on you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "No , not at all . It looks really classy on you . Where did you pick that up ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I got it on sale down at the department store .", + "emotion": "neutral", + "text": "I got it on sale down at the department store .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "When did you go there ?", + "emotion": "neutral", + "text": "When did you go there ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I was just there a couple of days ago . You know , you should go down there too . They have a lot of stylish clothes on sale .", + "emotion": "neutral", + "text": "I was just there a couple of days ago . You know , you should go down there too . They have a lot of stylish clothes on sale .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I might just do that . What style of clothes do they have ?", + "emotion": "neutral", + "text": "I might just do that . What style of clothes do they have ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Anything you want . They have both casual and formal styles .", + "emotion": "neutral", + "text": "Anything you want . They have both casual and formal styles .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I was hoping to get a few new ties for my collection .", + "emotion": "neutral", + "text": "I was hoping to get a few new ties for my collection .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "That's a good idea .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I was hoping to get a few new ties for my collection ." + ], + "type": [ + "inter-personal" + ], + "text": "That's a good idea .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2810.json b/reccon/sources/tr_2810.json new file mode 100644 index 0000000000000000000000000000000000000000..76842ca34ed785155606a221c93fbd9e2eaa4d5a --- /dev/null +++ b/reccon/sources/tr_2810.json @@ -0,0 +1,147 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Beautiful weather , isn ' t it ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Beautiful weather" + ], + "type": [ + "no-context" + ], + "text": "Beautiful weather , isn ' t it ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , it is . Are you here on business ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Beautiful weather" + ], + "type": [ + "inter-personal" + ], + "text": "Yes , it is . Are you here on business ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "No , I ' m on a vacation to see the famous Three Gorges .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I ' m on a vacation to see the famous Three Gorges ." + ], + "type": [ + "no-context" + ], + "text": "No , I ' m on a vacation to see the famous Three Gorges .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I ' m going there for a tour , too . Is this your first trip to China ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I ' m going there for a tour" + ], + "type": [ + "no-context" + ], + "text": "I ' m going there for a tour , too . Is this your first trip to China ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Yes , it is .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "I ' m on a vacation to see the famous Three Gorges .", + "first trip to China" + ], + "type": [ + "hybrid" + ], + "text": "Yes , it is .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Why don ' t we go together ? I can show you around . I think you ' ll have a better time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Why don ' t we go together ? I can show you around . I think you ' ll have a better time ." + ], + "type": [ + "no-context" + ], + "text": "Why don ' t we go together ? I can show you around . I think you ' ll have a better time .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I couldn ' t agree more .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Why don ' t we go together ? I can show you around . I think you ' ll have a better time ." + ], + "type": [ + "inter-personal" + ], + "text": "I couldn ' t agree more .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Great , let ' s go !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "Why don ' t we go together ? I can show you around . I think you ' ll have a better time .", + "I couldn ' t agree more ." + ], + "type": [ + "hybrid" + ], + "text": "Great , let ' s go !", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2815.json b/reccon/sources/tr_2815.json new file mode 100644 index 0000000000000000000000000000000000000000..461b10f0cf6910b499c7ef414fc0486b8f7e73b9 --- /dev/null +++ b/reccon/sources/tr_2815.json @@ -0,0 +1,126 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Here's some dancing . See those guys stomping , clapping and shouting ? They're practicing step-dancing .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Here's some dancing . See those guys stomping , clapping and shouting ? They're practicing step-dancing ." + ], + "type": [ + "no-context" + ], + "text": "Here's some dancing . See those guys stomping , clapping and shouting ? They're practicing step-dancing .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It sounds cool . The rhythms look really difficult .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "Here's some dancing . See those guys stomping , clapping and shouting ? They're practicing step-dancing .", + "It sounds cool ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It sounds cool . The rhythms look really difficult .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "They basically turn their bodies into drums . There's a national step competition every year .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 3 + ], + "expanded emotion cause span": [ + "Here's some dancing . See those guys stomping , clapping and shouting ? They're practicing step-dancing .", + "It sounds cool .", + "national step competition every year ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "They basically turn their bodies into drums . There's a national step competition every year .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Well , black people are supposed to be great dancers .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 3, + 3 + ], + "expanded emotion cause span": [ + "Here's some dancing . See those guys stomping , clapping and shouting ? They're practicing step-dancing .", + "It sounds cool .", + "national step competition every year .", + "turn their bodies into drums ." + ], + "type": [ + "hybrid" + ], + "text": "Well , black people are supposed to be great dancers .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Wen ! That's only a stereotype . Like all Asians are supposed to be math geniuses . I'm not a great dancer , and you said you failed calculus .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "black people are supposed to be great dancers .", + "That's only a stereotype . Like all Asians are supposed to be math geniuses . I'm not a great dancer , and you said you failed calculus ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Wen ! That's only a stereotype . Like all Asians are supposed to be math geniuses . I'm not a great dancer , and you said you failed calculus .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Ha-ha ! You got me there !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I'm not a great dancer , and you said you failed calculus ." + ], + "type": [ + "inter-personal" + ], + "text": "Ha-ha ! You got me there !", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2817.json b/reccon/sources/tr_2817.json new file mode 100644 index 0000000000000000000000000000000000000000..8b4b5ec753450650b932cafc54330056de7279a3 --- /dev/null +++ b/reccon/sources/tr_2817.json @@ -0,0 +1,130 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What's the bonus like at your company ?", + "emotion": "neutral", + "text": "What's the bonus like at your company ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Well , it's OK , I suppose . We get about the equivalent of six months ' salary .", + "emotion": "neutral", + "text": "Well , it's OK , I suppose . We get about the equivalent of six months ' salary .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Six months ' salary ? Are you serious ? That's incredible !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "We get about the equivalent of six months ' salary ." + ], + "type": [ + "inter-personal" + ], + "text": "Six months ' salary ? Are you serious ? That's incredible !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Maybe . But you'd be amazed at how little's left after the credit companies have deducted their share from my account .", + "emotion": "neutral", + "text": "Maybe . But you'd be amazed at how little's left after the credit companies have deducted their share from my account .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Hey , I know what that's like . I bought a BMW on my Visa card . Now the payments really hurt .", + "emotion": "neutral", + "text": "Hey , I know what that's like . I bought a BMW on my Visa card . Now the payments really hurt .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Well , you're lucky that you're still able to make your payments . I missed a credit payment last month . Now my bank account's overdrawn , and the company is threatening to take back my purchases .", + "emotion": "neutral", + "text": "Well , you're lucky that you're still able to make your payments . I missed a credit payment last month . Now my bank account's overdrawn , and the company is threatening to take back my purchases .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "What did you buy ?", + "emotion": "neutral", + "text": "What did you buy ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "A new home health monitor .", + "emotion": "neutral", + "text": "A new home health monitor .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Health Monitor ? I read an article about that racket . They ' re overpriced to begin with ! Listen , if I were you , I'd let them take back their monitor and spend my money on something more practical .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "home health monitor ." + ], + "type": [ + "inter-personal" + ], + "text": "Health Monitor ? I read an article about that racket . They ' re overpriced to begin with ! Listen , if I were you , I'd let them take back their monitor and spend my money on something more practical .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "You're kidding !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "They ' re overpriced" + ], + "type": [ + "inter-personal" + ], + "text": "You're kidding !", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 11, + "speaker": "A", + "utterance": "No joke !", + "emotion": "neutral", + "text": "No joke !", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "That's something else ! Maybe I'll return it to them .", + "emotion": "neutral", + "text": "That's something else ! Maybe I'll return it to them .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2820.json b/reccon/sources/tr_2820.json new file mode 100644 index 0000000000000000000000000000000000000000..8e772b7df9b1756d1746b4e22669a4ea7151659b --- /dev/null +++ b/reccon/sources/tr_2820.json @@ -0,0 +1,124 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I have just had my new paper published .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I have just had my new paper published ." + ], + "type": [ + "no-context" + ], + "text": "I have just had my new paper published .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "You have done excellent work .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 1 + ], + "expanded emotion cause span": [ + "I have just had my new paper published .", + "I have just had my new paper published ." + ], + "type": [ + "inter-personal" + ], + "text": "You have done excellent work .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I'm going to Britain .", + "emotion": "neutral", + "text": "I'm going to Britain .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Really ? How did you get the chance ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I'm going to Britain ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? How did you get the chance ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I have been accepted by Oxford University on PhD .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I have been accepted by Oxford University on PhD ." + ], + "type": [ + "no-context" + ], + "text": "I have been accepted by Oxford University on PhD .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "My warmest congratulations on your entering the Oxford University .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 5 + ], + "expanded emotion cause span": [ + "I have been accepted by Oxford University on PhD .", + "I have been accepted by Oxford University on PhD ." + ], + "type": [ + "inter-personal" + ], + "text": "My warmest congratulations on your entering the Oxford University .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I really appreciate your kind words .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "My warmest congratulations on your entering the Oxford University .", + "I really appreciate your kind words ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I really appreciate your kind words .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2822.json b/reccon/sources/tr_2822.json new file mode 100644 index 0000000000000000000000000000000000000000..d8428f5eda75ecceb45fd2fd292cbc33408ded3b --- /dev/null +++ b/reccon/sources/tr_2822.json @@ -0,0 +1,149 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Guess who I saw yesterday ?", + "emotion": "neutral", + "text": "Guess who I saw yesterday ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I don't know . Who ?", + "emotion": "neutral", + "text": "I don't know . Who ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Avril Lavigen !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "Guess who I saw yesterday ?", + "Avril Lavigen !" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Avril Lavigen !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "The Canadian rock singer ? But I heard you had a part-time job yesterday . How did you see her ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Avril Lavigen !" + ], + "type": [ + "inter-personal" + ], + "text": "The Canadian rock singer ? But I heard you had a part-time job yesterday . How did you see her ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Yeah , I worked as temporary staff in her concert . Look , her poster , a CD ...", + "emotion": "neutral", + "text": "Yeah , I worked as temporary staff in her concert . Look , her poster , a CD ...", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "So you're a big fan , eh ?", + "emotion": "neutral", + "text": "So you're a big fan , eh ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Not really . But I like some of her songs . She's actually very talented . She's a song writer and fashion designer , too .", + "emotion": "neutral", + "text": "Not really . But I like some of her songs . She's actually very talented . She's a song writer and fashion designer , too .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "And she was in a movie once again , right ?", + "emotion": "neutral", + "text": "And she was in a movie once again , right ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yeah , though I don't think her acting skills are that great .", + "emotion": "neutral", + "text": "Yeah , though I don't think her acting skills are that great .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "What was your impression of her when you saw her in person ?", + "emotion": "neutral", + "text": "What was your impression of her when you saw her in person ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "She looked sweeter than her pictures .", + "emotion": "neutral", + "text": "She looked sweeter than her pictures .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Did you take a photo with her ?", + "emotion": "neutral", + "text": "Did you take a photo with her ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "No , there were too many people . When she got out of the car , her fans were all screaming , trying to give her flowers and to get her autographs .", + "emotion": "neutral", + "text": "No , there were too many people . When she got out of the car , her fans were all screaming , trying to give her flowers and to get her autographs .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Crazy !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "her fans were all screaming , trying to give her flowers and to get her autographs ." + ], + "type": [ + "inter-personal" + ], + "text": "Crazy !", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2825.json b/reccon/sources/tr_2825.json new file mode 100644 index 0000000000000000000000000000000000000000..3f3550d27adcbc45ac4d2f526c510d6836918ed4 --- /dev/null +++ b/reccon/sources/tr_2825.json @@ -0,0 +1,142 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Okay , show me your card hand . Here's mine . I have three Kings and a pair of Aces .", + "emotion": "neutral", + "text": "Okay , show me your card hand . Here's mine . I have three Kings and a pair of Aces .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "How did you get that ? No need to show you my hand , I lose . This is not as much fun as the music concert we just saw .", + "emotion": "neutral", + "text": "How did you get that ? No need to show you my hand , I lose . This is not as much fun as the music concert we just saw .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Thanks again for buying the tickets . That was the most exciting live concert I've ever seen . That silver electric guitar was really cool .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "That was the most exciting live concert I've ever seen . That silver electric guitar was really cool ." + ], + "type": [ + "no-context" + ], + "text": "Thanks again for buying the tickets . That was the most exciting live concert I've ever seen . That silver electric guitar was really cool .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "They're quite popular now . Wasn't her voice good ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "That was the most exciting live concert I've ever seen . That silver electric guitar was really cool .", + "They're quite popular now . Wasn't her voice good ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "They're quite popular now . Wasn't her voice good ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "That , My Heart Will Go On . It warms my heart . you know , JanetJackson , Shanna Twain and Celine Dion are so very different .", + "emotion": "neutral", + "text": "That , My Heart Will Go On . It warms my heart . you know , JanetJackson , Shanna Twain and Celine Dion are so very different .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Janet Jackson is more pop music . Shania sings country music . Celine just seems to hit all the right notes .", + "emotion": "neutral", + "text": "Janet Jackson is more pop music . Shania sings country music . Celine just seems to hit all the right notes .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Have you heard Maria Carey ?", + "emotion": "neutral", + "text": "Have you heard Maria Carey ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yes , l have two of her Cds , l'II lend them to you if you like .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Maria Carey" + ], + "type": [ + "inter-personal" + ], + "text": "Yes , l have two of her Cds , l'II lend them to you if you like .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Excellent . You can borrow my Janet Jackson's CD . It's her new one .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Yes , l have two of her Cds , l'II lend them to you if you like ." + ], + "type": [ + "inter-personal" + ], + "text": "Excellent . You can borrow my Janet Jackson's CD . It's her new one .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I hope you have a good stereo .", + "emotion": "neutral", + "text": "I hope you have a good stereo .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Why ?", + "emotion": "neutral", + "text": "Why ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Because you have to hear it really loud to get the full concert effect .", + "emotion": "neutral", + "text": "Because you have to hear it really loud to get the full concert effect .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2826.json b/reccon/sources/tr_2826.json new file mode 100644 index 0000000000000000000000000000000000000000..6d87ad5f7d7d645726f610c5a9752f74c75f347f --- /dev/null +++ b/reccon/sources/tr_2826.json @@ -0,0 +1,186 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Sarah . You look terrible . What's wrong ?", + "emotion": "neutral", + "text": "Sarah . You look terrible . What's wrong ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "My grandmother just passed away .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "My grandmother just passed away ." + ], + "type": [ + "no-context" + ], + "text": "My grandmother just passed away .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I'm so sorry to hear that . When did this happen ?", + "emotion": "neutral", + "text": "I'm so sorry to hear that . When did this happen ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "A couple of days ago . I just go back from the funeral .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "My grandmother just passed away ." + ], + "type": [ + "self-contagion" + ], + "text": "A couple of days ago . I just go back from the funeral .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Is there anything I can do ?", + "emotion": "neutral", + "text": "Is there anything I can do ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "No ... not really . The sad thing is that I wasn't there when she died . I really wanted to be there one last time .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2, + 6 + ], + "expanded emotion cause span": [ + "My grandmother just passed away .", + "The sad thing is that I wasn't there when she died . I really wanted to be there one last time ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "No ... not really . The sad thing is that I wasn't there when she died . I really wanted to be there one last time .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I'm sure she knew you loved her . Did she pass away in the hospital ?", + "emotion": "neutral", + "text": "I'm sure she knew you loved her . Did she pass away in the hospital ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yeah . She died in her sleep .", + "emotion": "neutral", + "text": "Yeah . She died in her sleep .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I'm sorry she's gone .", + "emotion": "neutral", + "text": "I'm sorry she's gone .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "At least she didn't suffer .", + "emotion": "neutral", + "text": "At least she didn't suffer .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I think your grandmother would want you to think of all the good times you spent together .", + "emotion": "neutral", + "text": "I think your grandmother would want you to think of all the good times you spent together .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I know . But I miss her .", + "emotion": "neutral", + "text": "I know . But I miss her .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "When my grandmother passed away , I frequently visited her in the cemetery . I always talked to her . Even though she wasn't there , I somehow knew she heard what I said .", + "emotion": "neutral", + "text": "When my grandmother passed away , I frequently visited her in the cemetery . I always talked to her . Even though she wasn't there , I somehow knew she heard what I said .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Yeah ? That's what I was thinking too . Thanks .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "When my grandmother passed away , I frequently visited her in the cemetery . I always talked to her . Even though she wasn't there , I somehow knew she heard what I said ." + ], + "type": [ + "inter-personal" + ], + "text": "Yeah ? That's what I was thinking too . Thanks .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "It looks like you haven't eaten anything all day . We should get you something to eat .", + "emotion": "neutral", + "text": "It looks like you haven't eaten anything all day . We should get you something to eat .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "You're right ... I should eat something . Let's go .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13, + 15 + ], + "expanded emotion cause span": [ + "When my grandmother passed away , I frequently visited her in the cemetery . I always talked to her . Even though she wasn't there , I somehow knew she heard what I said .", + "We should get you something to eat ." + ], + "type": [ + "inter-personal" + ], + "text": "You're right ... I should eat something . Let's go .", + "id": 16, + "source_sentences": [ + 12, + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2833.json b/reccon/sources/tr_2833.json new file mode 100644 index 0000000000000000000000000000000000000000..9f43470e7832f36ccb0052959b6ce1b3397e9139 --- /dev/null +++ b/reccon/sources/tr_2833.json @@ -0,0 +1,193 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi . Bob ! We've been working hard at our lessons for a fortnight . So why don't we take it easy this weekend ?", + "emotion": "neutral", + "text": "Hi . Bob ! We've been working hard at our lessons for a fortnight . So why don't we take it easy this weekend ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Okay ! What do you suggest ?", + "emotion": "neutral", + "text": "Okay ! What do you suggest ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "How about seeing a play ? I hear Hamlet is on at the National Theater .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "seeing a play ? I hear Hamlet is on at the National Theater ." + ], + "type": [ + "no-context" + ], + "text": "How about seeing a play ? I hear Hamlet is on at the National Theater .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Is that so ? Why not ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "seeing a play ? I hear Hamlet is on at the National Theater ." + ], + "type": [ + "inter-personal" + ], + "text": "Is that so ? Why not ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "( looking at a newspaper ) Oh , dear me ! There's no performance at the National theater this weekend . So we have to go to cinema instead .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "There's no performance at the National theater this weekend ." + ], + "type": [ + "no-context" + ], + "text": "( looking at a newspaper ) Oh , dear me ! There's no performance at the National theater this weekend . So we have to go to cinema instead .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "What's on ?", + "emotion": "neutral", + "text": "What's on ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Let me see .. um . Gone With the Wind . It is on at six cinemas on Saturday night .", + "emotion": "neutral", + "text": "Let me see .. um . Gone With the Wind . It is on at six cinemas on Saturday night .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That sounds interesting . Which is the nearest ?", + "emotion": "neutral", + "text": "That sounds interesting . Which is the nearest ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Ah . The Royal , I think .", + "emotion": "neutral", + "text": "Ah . The Royal , I think .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "What time does it start ?", + "emotion": "neutral", + "text": "What time does it start ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Why don't we go to the 7:30 show ? It is convenient to us , I think .", + "emotion": "neutral", + "text": "Why don't we go to the 7:30 show ? It is convenient to us , I think .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "But we won't have enough time for dinner .", + "emotion": "neutral", + "text": "But we won't have enough time for dinner .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Do you want to go to the earlier or the later show ?", + "emotion": "neutral", + "text": "Do you want to go to the earlier or the later show ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Ah ... I fancy going to the later show .", + "emotion": "neutral", + "text": "Ah ... I fancy going to the later show .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Then , there's a 9:30 show .", + "emotion": "neutral", + "text": "Then , there's a 9:30 show .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "That's Okay , I think .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 14, + 15 + ], + "expanded emotion cause span": [ + "I fancy going to the later show .", + "there's a 9:30 show ." + ], + "type": [ + "hybrid" + ], + "text": "That's Okay , I think .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "All right .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 16 + ], + "expanded emotion cause span": [ + "That's Okay ," + ], + "type": [ + "inter-personal" + ], + "text": "All right .", + "id": 17, + "source_sentences": [ + 15 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2880.json b/reccon/sources/tr_2880.json new file mode 100644 index 0000000000000000000000000000000000000000..4e7c5d89c796219145e2642ccf145c5fbe90120f --- /dev/null +++ b/reccon/sources/tr_2880.json @@ -0,0 +1,149 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "How's your new car ?", + "emotion": "neutral", + "text": "How's your new car ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Perfect . Couldn't be better !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 2 + ], + "expanded emotion cause span": [ + "b", + "Perfect . Couldn't be better !" + ], + "type": [ + "latent", + "no-context" + ], + "text": "Perfect . Couldn't be better !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "You made a good choice , then ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Perfect . Couldn't be better !" + ], + "type": [ + "inter-personal" + ], + "text": "You made a good choice , then ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It's just what I wanted .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 2, + 4 + ], + "expanded emotion cause span": [ + "b", + "Perfect . Couldn't be better !", + "It's just what I wanted ." + ], + "type": [ + "latent", + "no-context", + "self-contagion" + ], + "text": "It's just what I wanted .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "No regrets ?", + "emotion": "neutral", + "text": "No regrets ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I'm really pleased with it . Thanks .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 2, + 4, + 6 + ], + "expanded emotion cause span": [ + "b", + "Perfect . Couldn't be better !", + "It's just what I wanted .", + "I'm really pleased with it" + ], + "type": [ + "latent", + "no-context", + "self-contagion" + ], + "text": "I'm really pleased with it . Thanks .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I'm glad you're so happy .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I'm really pleased with it ." + ], + "type": [ + "inter-personal" + ], + "text": "I'm glad you're so happy .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "It's super .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 2, + 4, + 6 + ], + "expanded emotion cause span": [ + "b", + "Perfect . Couldn't be better !", + "It's just what I wanted .", + "I'm really pleased with it" + ], + "type": [ + "latent", + "self-contagion" + ], + "text": "It's super .", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2893.json b/reccon/sources/tr_2893.json new file mode 100644 index 0000000000000000000000000000000000000000..2f4e289b980c4de451be0f51a17ef9039c9f4baf --- /dev/null +++ b/reccon/sources/tr_2893.json @@ -0,0 +1,130 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Betty , would you please read this letter of application I've just written ? I'd like to have your opinion .", + "emotion": "neutral", + "text": "Betty , would you please read this letter of application I've just written ? I'd like to have your opinion .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'd be glad to tell you what I think .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I'd like to have your opinion ." + ], + "type": [ + "inter-personal" + ], + "text": "I'd be glad to tell you what I think .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Good ! I'm interested in your advice .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I'd be glad to tell you what I think ." + ], + "type": [ + "inter-personal" + ], + "text": "Good ! I'm interested in your advice .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "If I were you , I would change the beginning . You should write about your education first because we like to judge a man by his abilities .", + "emotion": "neutral", + "text": "If I were you , I would change the beginning . You should write about your education first because we like to judge a man by his abilities .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Good idea , Betty . What would you think about the second part ?", + "emotion": "happiness", + "explanation": "Assuming getting constructive feedback as a cause of happiness as long as the feedback is asked for.", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "I'm interested in your advice .", + "If I were you , I would change the beginning . You should write about your education first because we like to judge a man by his abilities ." + ], + "type": [ + "hybrid" + ], + "text": "Good idea , Betty . What would you think about the second part ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I think it's too short . You'd better say something about your work experience .", + "emotion": "neutral", + "text": "I think it's too short . You'd better say something about your work experience .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You're right , I'll change it . How about the last part ?", + "emotion": "neutral", + "text": "You're right , I'll change it . How about the last part ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Very good . But you should talk about your family , too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "You're right , I'll change it . How about the last part ?", + "Very good ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Very good . But you should talk about your family , too .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I agree . I appreciate your helping me .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Very good . But you should talk about your family , too ." + ], + "type": [ + "inter-personal" + ], + "text": "I agree . I appreciate your helping me .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2911.json b/reccon/sources/tr_2911.json new file mode 100644 index 0000000000000000000000000000000000000000..79171dfa979600e876bb21ffaacceea1a83483dc --- /dev/null +++ b/reccon/sources/tr_2911.json @@ -0,0 +1,142 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "ORG ! It must be so late where you are . What time is it ?", + "emotion": "neutral", + "text": "ORG ! It must be so late where you are . What time is it ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "just after 2 am .", + "emotion": "neutral", + "text": "just after 2 am .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "what's wrong ? Can't sleep ?", + "emotion": "neutral", + "text": "what's wrong ? Can't sleep ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "nope , actually I was waiting for you . I have something big to tell you .", + "emotion": "neutral", + "text": "nope , actually I was waiting for you . I have something big to tell you .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "really ? What is it ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I was waiting for you . I have something big to tell you ." + ], + "type": [ + "inter-personal" + ], + "text": "really ? What is it ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I have an offer to work for a company in your city today ?", + "emotion": "neutral", + "text": "I have an offer to work for a company in your city today ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I can't believe it ! Is it real ? You're moving here ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I have an offer to work for a company in your city today ?" + ], + "type": [ + "inter-personal" + ], + "text": "I can't believe it ! Is it real ? You're moving here ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I haven't accepted the position yet and with the upcoming holiday I think it's the perfect chance to visit the city and take a good look at the company before deciding . If you have time I think we c", + "emotion": "neutral", + "text": "I haven't accepted the position yet and with the upcoming holiday I think it's the perfect chance to visit the city and take a good look at the company before deciding . If you have time I think we c", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "just give me the dates and I'll make sure I'm free . You know after all these chatting online , it will be great to meet you in real life . I look forward to seeing you soon !", + "emotion": "neutral", + "text": "just give me the dates and I'll make sure I'm free . You know after all these chatting online , it will be great to meet you in real life . I look forward to seeing you soon !", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "me too . But I think I am going to bed now . my head is getting heavy . Have a nice day there !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "just give me the dates and I'll make sure I'm free . You know after all these chatting online , it will be great to meet you in real life . I look forward to seeing you soon !" + ], + "type": [ + "inter-personal" + ], + "text": "me too . But I think I am going to bed now . my head is getting heavy . Have a nice day there !", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 11, + "speaker": "A", + "utterance": "thanks . This is so exciting . Sleep tight and sweet dreams !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 11 + ], + "expanded emotion cause span": [ + "just give me the dates and I'll make sure I'm free . You know after all these chatting online , it will be great to meet you in real life . I look forward to seeing you soon !", + "This is so exciting ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "thanks . This is so exciting . Sleep tight and sweet dreams !", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "talk to you later .", + "emotion": "neutral", + "text": "talk to you later .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2940.json b/reccon/sources/tr_2940.json new file mode 100644 index 0000000000000000000000000000000000000000..676b787fd0f9b56d51d4dc3e8f0da007f148ad50 --- /dev/null +++ b/reccon/sources/tr_2940.json @@ -0,0 +1,119 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Tom , you look thoughtful and unhappy recently . What's wrong with you ?", + "emotion": "neutral", + "text": "Tom , you look thoughtful and unhappy recently . What's wrong with you ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Lily broke up with me last week . In fact , she dumped me .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Lily broke up with me last week . In fact , she dumped me ." + ], + "type": [ + "no-context" + ], + "text": "Lily broke up with me last week . In fact , she dumped me .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Why ? I mean , why did she part company with you after seven years together ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "Lily broke up with me last week . In fact , she dumped me .", + "after seven years together ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Why ? I mean , why did she part company with you after seven years together ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "She said it was because we had very different ideas about life .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Lily broke up with me last week . In fact , she dumped me ." + ], + "type": [ + "self-contagion" + ], + "text": "She said it was because we had very different ideas about life .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Do you believe her excuse ?", + "emotion": "neutral", + "text": "Do you believe her excuse ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Of course not . I knew she had fallen in love with another guy . It is difficult to see her move on so quickly .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I knew she had fallen in love with another guy . It is difficult to see her move on so quickly ." + ], + "type": [ + "no-context" + ], + "text": "Of course not . I knew she had fallen in love with another guy . It is difficult to see her move on so quickly .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Come on , buddy , cheer up . Why not do some sports with me ? Violent exercise might help to shake you out of your disappointment in love .", + "emotion": "neutral", + "text": "Come on , buddy , cheer up . Why not do some sports with me ? Violent exercise might help to shake you out of your disappointment in love .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Thank you , Steven . You are really a good friend .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Come on , buddy , cheer up . Why not do some sports with me ? Violent exercise might help to shake you out of your disappointment in love ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you , Steven . You are really a good friend .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2944.json b/reccon/sources/tr_2944.json new file mode 100644 index 0000000000000000000000000000000000000000..5abe19019f25dc66b8a7775d0ff1e1e852db0bbb --- /dev/null +++ b/reccon/sources/tr_2944.json @@ -0,0 +1,138 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello , this is Helen speaking .", + "emotion": "neutral", + "text": "Hello , this is Helen speaking .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hello , Helen . This is John . How are you ?", + "emotion": "neutral", + "text": "Hello , Helen . This is John . How are you ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Fine , thank you . And you ?", + "emotion": "happiness", + "explanation": "Helen is happy to meet John", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "This is John . How are you ?" + ], + "type": [ + "inter-personal" + ], + "text": "Fine , thank you . And you ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Fine , thanks . I ' ll have a party next Sunday at home . I ' m calling to ask whether you can come or not .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "Fine , thank you . And you ?", + "I ' ll have a party next Sunday at home ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Fine , thanks . I ' ll have a party next Sunday at home . I ' m calling to ask whether you can come or not .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Oh , how wonderful . I ' ll be glad to .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I ' ll have a party next Sunday at home ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , how wonderful . I ' ll be glad to .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Okay , now you are a famous star .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "I ' ll have a party next Sunday at home .", + "how wonderful . I ' ll be glad to ." + ], + "type": [ + "hybrid" + ], + "text": "Okay , now you are a famous star .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Hum , don ' t say that . Maybe you can do something useful for me .", + "emotion": "neutral", + "text": "Hum , don ' t say that . Maybe you can do something useful for me .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "What ' s wrong with you ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Maybe you can do something useful for me ." + ], + "type": [ + "inter-personal" + ], + "text": "What ' s wrong with you ?", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I ' ll tell you at the party .", + "emotion": "neutral", + "text": "I ' ll tell you at the party .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Okay .", + "emotion": "neutral", + "text": "Okay .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2957.json b/reccon/sources/tr_2957.json new file mode 100644 index 0000000000000000000000000000000000000000..23cd87ee814fed538e5bcc6aaf596955af57ae90 --- /dev/null +++ b/reccon/sources/tr_2957.json @@ -0,0 +1,102 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What are your plans for this weekend ?", + "emotion": "neutral", + "text": "What are your plans for this weekend ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'd like to hire a bike . I think it would be a good idea to do some cycling on Sunday .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I'd like to hire a bike . I think it would be a good idea to do some cycling on Sunday ." + ], + "type": [ + "no-context" + ], + "text": "I'd like to hire a bike . I think it would be a good idea to do some cycling on Sunday .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "If the weather's fine .", + "emotion": "neutral", + "text": "If the weather's fine .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I am sure it will be . It's been good so far this weekend .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 4 + ], + "expanded emotion cause span": [ + "I'd like to hire a bike . I think it would be a good idea to do some cycling on Sunday .", + "It's been good so far this weekend ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I am sure it will be . It's been good so far this weekend .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I know a good place to hire bikes if you want .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I know a good place to hire bikes if you want ." + ], + "type": [ + "no-context" + ], + "text": "I know a good place to hire bikes if you want .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Thanks . That would be really helpful .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I know a good place to hire bikes if you want ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks . That would be really helpful .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "But remember , be careful when you ride a bike . The traffic in Beijing can be dangerous .", + "emotion": "neutral", + "text": "But remember , be careful when you ride a bike . The traffic in Beijing can be dangerous .", + "id": 7 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2969.json b/reccon/sources/tr_2969.json new file mode 100644 index 0000000000000000000000000000000000000000..f750ef119765015ce5650d4a767ba7e6428b8b8a --- /dev/null +++ b/reccon/sources/tr_2969.json @@ -0,0 +1,96 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What ' s the matter , Sally ? You look so unhappy .", + "emotion": "neutral", + "text": "What ' s the matter , Sally ? You look so unhappy .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I had a bad day yesterday .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I had a bad day yesterday ." + ], + "type": [ + "no-context" + ], + "text": "I had a bad day yesterday .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What happened ?", + "emotion": "neutral", + "text": "What happened ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I went to the library and lost my bag .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2, + 4 + ], + "expanded emotion cause span": [ + "I had a bad day yesterday .", + "I went to the library and lost my bag ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I went to the library and lost my bag .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Your bag ? Did you get it back ?", + "emotion": "neutral", + "text": "Your bag ? Did you get it back ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I went back for it . But it was already gone .", + "emotion": "neutral", + "text": "I went back for it . But it was already gone .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "That ' s too bad . I ' m sorry to hear that .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 4, + 7 + ], + "expanded emotion cause span": [ + "I went to the library and lost my bag .", + "That ' s too bad . I ' m sorry to hear that ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That ' s too bad . I ' m sorry to hear that .", + "id": 7, + "source_sentences": [ + 3 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2980.json b/reccon/sources/tr_2980.json new file mode 100644 index 0000000000000000000000000000000000000000..366b0df82a9a13d4486c460ea56cd576db9177f8 --- /dev/null +++ b/reccon/sources/tr_2980.json @@ -0,0 +1,143 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "We'd like to invite you over for dinner this Friday evening . Can you come ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "invite you over for dinner" + ], + "type": [ + "no-context" + ], + "text": "We'd like to invite you over for dinner this Friday evening . Can you come ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "This Friday evening ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "invite you over for dinner" + ], + "type": [ + "inter-personal" + ], + "text": "This Friday evening ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yes . We hope you'll be able to join us .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "invite you over for dinner" + ], + "type": [ + "self-contagion" + ], + "text": "Yes . We hope you'll be able to join us .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Thank you for the invitation . I'll be very happy to go .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "invite you over for dinner" + ], + "type": [ + "inter-personal" + ], + "text": "Thank you for the invitation . I'll be very happy to go .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Good !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I'll be very happy to go ." + ], + "type": [ + "inter-personal" + ], + "text": "Good !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "What time should I arrive ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "invite you over for dinner" + ], + "type": [ + "inter-personal" + ], + "text": "What time should I arrive ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "How about 6:00 ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I'll be very happy to go ." + ], + "type": [ + "inter-personal" + ], + "text": "How about 6:00 ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Fine . See you then .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "invite you over for dinner" + ], + "type": [ + "inter-personal" + ], + "text": "Fine . See you then .", + "id": 8, + "source_sentences": [ + 0 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2986.json b/reccon/sources/tr_2986.json new file mode 100644 index 0000000000000000000000000000000000000000..7998b37dde7e342e7335ad3c0e4e2687d7d98b59 --- /dev/null +++ b/reccon/sources/tr_2986.json @@ -0,0 +1,152 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Who's that striking woman over there ?", + "emotion": "neutral", + "text": "Who's that striking woman over there ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hm ? Oh , that's Alice . She's totally mad . Don't get yourself in a room alone with her .", + "emotion": "neutral", + "text": "Hm ? Oh , that's Alice . She's totally mad . Don't get yourself in a room alone with her .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Really ? Why not ? She looks great .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "She's totally mad . Don't get yourself in a room alone with her .", + "She looks great ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Really ? Why not ? She looks great .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes , I know , but she's dangerous .", + "emotion": "neutral", + "text": "Yes , I know , but she's dangerous .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Really ? Tell me more .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "she's dangerous ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? Tell me more .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Well , I'm not one to gossip , as you know , but rumor has it that she sued her former boss for sexual harassment .", + "emotion": "neutral", + "text": "Well , I'm not one to gossip , as you know , but rumor has it that she sued her former boss for sexual harassment .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Wow , crikey . So what happened ?", + "emotion": "neutral", + "text": "Wow , crikey . So what happened ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Well , this is just between ourselves , of course , but he was her lover and he wanted to leave her , so she got revenge . I heard him say she was a dangerous woman .", + "emotion": "neutral", + "text": "Well , this is just between ourselves , of course , but he was her lover and he wanted to leave her , so she got revenge . I heard him say she was a dangerous woman .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Wow .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6, + 8 + ], + "expanded emotion cause span": [ + "she sued her former boss for sexual harassment .", + "he was her lover and he wanted to leave her , so she got revenge . I heard him say she was a dangerous woman ." + ], + "type": [ + "inter-personal" + ], + "text": "Wow .", + "id": 9, + "source_sentences": [ + 5, + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Oh , while we're on the subject , what happened to you and your secretary ?", + "emotion": "neutral", + "text": "Oh , while we're on the subject , what happened to you and your secretary ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I have no idea what you're talking about .", + "emotion": "neutral", + "text": "I have no idea what you're talking about .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Oh , come on . Everybody knows .", + "emotion": "neutral", + "text": "Oh , come on . Everybody knows .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Could you excuse me a moment ? I have to make a phone call", + "emotion": "neutral", + "text": "Could you excuse me a moment ? I have to make a phone call", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Oh , sure .", + "emotion": "neutral", + "text": "Oh , sure .", + "id": 14 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2991.json b/reccon/sources/tr_2991.json new file mode 100644 index 0000000000000000000000000000000000000000..3c0ba5db327167335cf5b880bfb973d1b38e97ce --- /dev/null +++ b/reccon/sources/tr_2991.json @@ -0,0 +1,192 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Do you like music ?", + "emotion": "neutral", + "text": "Do you like music ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Well , it depends .", + "emotion": "neutral", + "text": "Well , it depends .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Do you think the music is well-matched ?", + "emotion": "neutral", + "text": "Do you think the music is well-matched ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "No , I think the music is too fast .", + "emotion": "neutral", + "text": "No , I think the music is too fast .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "How about the words of the song ?", + "emotion": "neutral", + "text": "How about the words of the song ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "It sounds nice .", + "emotion": "neutral", + "text": "It sounds nice .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I like it . Naturally it can arouse your feelings .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "It sounds nice .", + "I like it . Naturally it can arouse your feelings ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I like it . Naturally it can arouse your feelings .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yes , I think so . It's very emotional .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "Naturally it can arouse your feelings .", + "It's very emotional ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , I think so . It's very emotional .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Of course , and I also like the rhythms .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8, + 9 + ], + "expanded emotion cause span": [ + "Naturally it can arouse your feelings .", + "It's very emotional .", + "I also like the rhythms ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Of course , and I also like the rhythms .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Full of energy and hope .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "I also like the rhythms .", + "Full of energy and hope ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Full of energy and hope .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Really . It's worth listening to and enjoying .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8, + 9, + 10, + 11 + ], + "expanded emotion cause span": [ + "Naturally it can arouse your feelings .", + "It's very emotional .", + "I also like the rhythms .", + "Full of energy and hope .", + "Really . It's worth listening to and enjoying ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Really . It's worth listening to and enjoying .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Certainly it is . It's worth an Academy Award .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8, + 7, + 8, + 9, + 10, + 11 + ], + "expanded emotion cause span": [ + "Naturally it can arouse your feelings .", + "It's very emotional .", + "Naturally it can arouse your feelings .", + "It's very emotional .", + "I also like the rhythms .", + "Full of energy and hope .", + "Really . It's worth listening to and enjoying ." + ], + "type": [ + "hybrid" + ], + "text": "Certainly it is . It's worth an Academy Award .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_2998.json b/reccon/sources/tr_2998.json new file mode 100644 index 0000000000000000000000000000000000000000..665659cf4984bcf154d94dec7690f2ec63d8becc --- /dev/null +++ b/reccon/sources/tr_2998.json @@ -0,0 +1,137 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey , Mary , can you cut that out ?", + "emotion": "neutral", + "text": "Hey , Mary , can you cut that out ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Cut what out I ' m not doing anything .", + "emotion": "neutral", + "text": "Cut what out I ' m not doing anything .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "The tapping of your pen on your desk . It ' s driving me crazy .", + "emotion": "neutral", + "text": "The tapping of your pen on your desk . It ' s driving me crazy .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Fine ! By the way would you mind not slurping your coffee every time you have a cup !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "The tapping of your pen on your desk . It ' s driving me crazy .", + "slurping your coffee every time you have a cup !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Fine ! By the way would you mind not slurping your coffee every time you have a cup !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I don ' t slurp my coffee . And plus , how can you hear it when you ' re shouting into your phone all the time ?", + "emotion": "anger", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "would you mind not slurping your coffee every time you have a cup !", + "you ' re shouting into your phone all the time" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I don ' t slurp my coffee . And plus , how can you hear it when you ' re shouting into your phone all the time ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "You ' Ve got to be kidding me ! You ' re complaining about me talking on the phone when you go out for a cigarette break ten times a day to shoot the breeze ?", + "emotion": "anger", + "expanded emotion cause evidence": [ + 3, + 4, + 5, + 6 + ], + "expanded emotion cause span": [ + "The tapping of your pen on your desk . It ' s driving me crazy .", + "slurping your coffee every time you have a cup !", + "how can you hear it when you ' re shouting into your phone all the time ?", + "You ' re complaining about me talking on the phone" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "You ' Ve got to be kidding me ! You ' re complaining about me talking on the phone when you go out for a cigarette break ten times a day to shoot the breeze ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Look , we have a lot of accumulated anger from working in these conditions , and it ' s probably okay to let off steam once in a while . But , it ' s probably not a good idea to keep it up I ' m willing to forgive and forget and if you are .", + "emotion": "neutral", + "text": "Look , we have a lot of accumulated anger from working in these conditions , and it ' s probably okay to let off steam once in a while . But , it ' s probably not a good idea to keep it up I ' m willing to forgive and forget and if you are .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Fine . Let's call a truce . I'll try to more considerate and to keep the noise down .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "it ' s probably not a good idea to keep it up I ' m willing to forgive and forget and if you are ." + ], + "type": [ + "inter-personal" + ], + "text": "Fine . Let's call a truce . I'll try to more considerate and to keep the noise down .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yeah , I ' ll try to do the same . So , I was wondering you wanna go out to dinner Friday night ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I'll try to more considerate and to keep the noise down ." + ], + "type": [ + "inter-personal" + ], + "text": "Yeah , I ' ll try to do the same . So , I was wondering you wanna go out to dinner Friday night ?", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3002.json b/reccon/sources/tr_3002.json new file mode 100644 index 0000000000000000000000000000000000000000..3a55fc9569c0f0d73861cea0a0366552b65850e2 --- /dev/null +++ b/reccon/sources/tr_3002.json @@ -0,0 +1,115 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Bob , put on your shoes , your feet are really smelly .", + "emotion": "neutral", + "text": "Bob , put on your shoes , your feet are really smelly .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "No foot gives out scent .", + "emotion": "neutral", + "text": "No foot gives out scent .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "But don't forget you are in a cafe .", + "emotion": "neutral", + "text": "But don't forget you are in a cafe .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Never mind , the odour of my feet will quicken their eating speed .", + "emotion": "neutral", + "text": "Never mind , the odour of my feet will quicken their eating speed .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I simply can't bear your barbaric behavior .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "the odour of my feet will quicken their eating speed .", + "can't bear your barbaric behavior ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I simply can't bear your barbaric behavior .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Don ' t pretend you are a good God .", + "emotion": "neutral", + "text": "Don ' t pretend you are a good God .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You should feel shameful for your behavior .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "Don ' t pretend you are a good God .", + "You should feel shameful for your behavior ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You should feel shameful for your behavior .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I've never experienced such a kind of feeling .", + "emotion": "neutral", + "text": "I've never experienced such a kind of feeling .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I'm really sick of you .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "I've never experienced such a kind of feeling .", + "I'm really sick of you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm really sick of you .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3011.json b/reccon/sources/tr_3011.json new file mode 100644 index 0000000000000000000000000000000000000000..2d0a52518a67ff20debccfe47c1a1b1c0e441d0c --- /dev/null +++ b/reccon/sources/tr_3011.json @@ -0,0 +1,137 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I have never seen so many flavors of ice cream in one place !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I have never seen so many flavors of ice cream in one place !" + ], + "type": [ + "no-context" + ], + "text": "I have never seen so many flavors of ice cream in one place !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "There certainly are a lot . Can you choose a favorite ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I have never seen so many flavors of ice cream in one place !" + ], + "type": [ + "inter-personal" + ], + "text": "There certainly are a lot . Can you choose a favorite ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Vanilla with toppings is my favorite .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "I have never seen so many flavors of ice cream in one place !", + "Can you choose a favorite ?" + ], + "type": [ + "hybrid" + ], + "text": "Vanilla with toppings is my favorite .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Is there anything as good as a hot fudge sundae ?", + "emotion": "neutral", + "text": "Is there anything as good as a hot fudge sundae ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "No way ! Do you have a flavors you don't like ?", + "emotion": "neutral", + "text": "No way ! Do you have a flavors you don't like ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I don't like ice cream with too many different flavors in it .", + "emotion": "neutral", + "text": "I don't like ice cream with too many different flavors in it .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I agree with that , it just doesn't work for me .", + "emotion": "neutral", + "text": "I agree with that , it just doesn't work for me .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I saw garlic ice cream on the menu once .", + "emotion": "neutral", + "text": "I saw garlic ice cream on the menu once .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I think that would be horrible !", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "garlic ice cream on the menu", + "I think that would be horrible !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I think that would be horrible !", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I think I'll stick with a more traditional choice today !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "I think I'll stick with a more traditional choice today !" + ], + "type": [ + "no-context" + ], + "text": "I think I'll stick with a more traditional choice today !", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_302.json b/reccon/sources/tr_302.json new file mode 100644 index 0000000000000000000000000000000000000000..2e5aec0c060e81816f0dbf74a0319b4b8ceecad2 --- /dev/null +++ b/reccon/sources/tr_302.json @@ -0,0 +1,187 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello ! I'm Penny , I moved here just now .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I moved here just now ." + ], + "type": [ + "no-context" + ], + "text": "Hello ! I'm Penny , I moved here just now .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh , Penny , I'm Leonard , glad to meet you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "glad to meet you ." + ], + "type": [ + "no-context" + ], + "text": "Oh , Penny , I'm Leonard , glad to meet you .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Nice to meet you , too . I thought I should come and say hello to you . I haven't known anybody .", + "emotion": "neutral", + "text": "Nice to meet you , too . I thought I should come and say hello to you . I haven't known anybody .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It is hard to get used to a new place , isn't it ?", + "emotion": "neutral", + "text": "It is hard to get used to a new place , isn't it ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Yes . Would you like to come here later to have a coffee ? Bring all your family .", + "emotion": "happiness", + "explanation": "Eagerness to meet", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "come here later to have a coffee" + ], + "type": [ + "no-context" + ], + "text": "Yes . Would you like to come here later to have a coffee ? Bring all your family .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "We'd like to . Can you tell me when we go ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Would you like to come here later to have a coffee ?", + "We'd like to ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "We'd like to . Can you tell me when we go ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "About 4 .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "come here later to have a coffee" + ], + "type": [ + "self-contagion" + ], + "text": "About 4 .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "OK . Do you want us to bring something ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Would you like to come here later to have a coffee ?", + "We'd like to ." + ], + "type": [ + "hybrid" + ], + "text": "OK . Do you want us to bring something ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "No , just come here .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "come here later to have a coffee" + ], + "type": [ + "self-contagion" + ], + "text": "No , just come here .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "OK , see you later .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6, + 9 + ], + "expanded emotion cause span": [ + "Would you like to come here later to have a coffee ?", + "We'd like to .", + "just come here" + ], + "type": [ + "hybrid" + ], + "text": "OK , see you later .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Bye .", + "emotion": "happiness", + "explanation": "Speaker is invited by the listener for coffee", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "see you later ." + ], + "type": [ + "inter-personal" + ], + "text": "Bye .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3023.json b/reccon/sources/tr_3023.json new file mode 100644 index 0000000000000000000000000000000000000000..b37421bfa3df2ed91fff4692d1bb371482270b82 --- /dev/null +++ b/reccon/sources/tr_3023.json @@ -0,0 +1,168 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "did you get my email ?", + "emotion": "neutral", + "text": "did you get my email ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I certainly did . Do you want to come in and give me some feedback about your weekend ?", + "emotion": "neutral", + "text": "I certainly did . Do you want to come in and give me some feedback about your weekend ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "sure .", + "emotion": "neutral", + "text": "sure .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "how did the business trip go ?", + "emotion": "neutral", + "text": "how did the business trip go ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "well , to be honest , nothing is more stressful than going on a business trip with our boss .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "nothing is more stressful than going on a business trip with our boss ." + ], + "type": [ + "no-context" + ], + "text": "well , to be honest , nothing is more stressful than going on a business trip with our boss .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I understand . The last time I went on a business trip with the boss , I didn't even have enough to eat !", + "emotion": "neutral", + "text": "I understand . The last time I went on a business trip with the boss , I didn't even have enough to eat !", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I also think the company is pretty cheap with travel expenses . I spent half of the weekend on a train ! Surely they could have afforded to buy a few plane tickets !", + "emotion": "neutral", + "text": "I also think the company is pretty cheap with travel expenses . I spent half of the weekend on a train ! Surely they could have afforded to buy a few plane tickets !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "our company is quite conscious of the environmental problems that frequent flying causes .", + "emotion": "neutral", + "text": "our company is quite conscious of the environmental problems that frequent flying causes .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I see . Well , then perhaps they could give me a few days off after a business trip . It was really tiring for me .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "It was really tiring for me ." + ], + "type": [ + "no-context" + ], + "text": "I see . Well , then perhaps they could give me a few days off after a business trip . It was really tiring for me .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I can ask the boss about giving you the day off today .", + "emotion": "happiness", + "explanation": "willingness to help", + "expanded emotion cause evidence": [ + "b", + 9, + 10 + ], + "expanded emotion cause span": [ + "b", + "then perhaps they could give me a few days off after a business trip . It was really tiring for me .", + "I can ask the boss about giving you the day off today ." + ], + "type": [ + "latent", + "no-context", + "inter-personal" + ], + "text": "I can ask the boss about giving you the day off today .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "thank you . I can't imagine getting much done today . I'm just too exhausted !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "I can ask the boss about giving you the day off today ." + ], + "type": [ + "inter-personal" + ], + "text": "thank you . I can't imagine getting much done today . I'm just too exhausted !", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "no problem . Did you bring any gifts back for your department ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 9, + 10 + ], + "expanded emotion cause span": [ + "b", + "then perhaps they could give me a few days off after a business trip . It was really tiring for me .", + "I can ask the boss about giving you the day off today ." + ], + "type": [ + "latent", + "hybrid" + ], + "text": "no problem . Did you bring any gifts back for your department ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "no , should I have ?", + "emotion": "neutral", + "text": "no , should I have ?", + "id": 13 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3024.json b/reccon/sources/tr_3024.json new file mode 100644 index 0000000000000000000000000000000000000000..2bc348dae84b0f0a573456a92ee3229b4a6f6450 --- /dev/null +++ b/reccon/sources/tr_3024.json @@ -0,0 +1,142 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello !", + "emotion": "neutral", + "text": "Hello !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Is that the box-office ?", + "emotion": "neutral", + "text": "Is that the box-office ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yes .", + "emotion": "neutral", + "text": "Yes .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I'd like to book two tickets for the film ' Jane Eyre ' for this evening , please .", + "emotion": "neutral", + "text": "I'd like to book two tickets for the film ' Jane Eyre ' for this evening , please .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Just a minute please . Oh , I'm sorry , all the tickets for tonight have been sold out .", + "emotion": "neutral", + "text": "Just a minute please . Oh , I'm sorry , all the tickets for tonight have been sold out .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "What a pity ! How about tomorrow evening ?", + "emotion": "neutral", + "text": "What a pity ! How about tomorrow evening ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Oh , you're lucky , there are just two tickets left . Do you want to take them ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "you're lucky" + ], + "type": [ + "no-context" + ], + "text": "Oh , you're lucky , there are just two tickets left . Do you want to take them ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Wonderful , I'll take them .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 7 + ], + "expanded emotion cause span": [ + "you're lucky", + "you're lucky" + ], + "type": [ + "inter-personal" + ], + "text": "Wonderful , I'll take them .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "OK , your name and telephone number please .", + "emotion": "neutral", + "text": "OK , your name and telephone number please .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Wang Min . Telephone number is 13811658 . Can I pick the tickets this afternoon ?", + "emotion": "neutral", + "text": "Wang Min . Telephone number is 13811658 . Can I pick the tickets this afternoon ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Yes , of course .", + "emotion": "happiness", + "explanation": "The speaker is able to accept counterpart's request", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Yes , of course .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Thank you very much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "Yes , of course ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you very much .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3036.json b/reccon/sources/tr_3036.json new file mode 100644 index 0000000000000000000000000000000000000000..17e6d7f278e6c94daa73455e0480ebcdadb4ff17 --- /dev/null +++ b/reccon/sources/tr_3036.json @@ -0,0 +1,99 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey Michelle . Good to see you . Are you at lunch ?", + "emotion": "neutral", + "text": "Hey Michelle . Good to see you . Are you at lunch ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh hi Jim . No I just got back . I thought you were on vacation now .", + "emotion": "neutral", + "text": "Oh hi Jim . No I just got back . I thought you were on vacation now .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "No , I wish I was ! I just got back from Spain actually .", + "emotion": "neutral", + "text": "No , I wish I was ! I just got back from Spain actually .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Oh wonderful ! Have you been there before or was it your first time ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I just got back from Spain actually ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh wonderful ! Have you been there before or was it your first time ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "My first time . I've traveled around Europe a lot , but this was my first time to Spain . It was amazing , and the weather was just beautiful ! No rain , and just sun , sun , sun ...", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "this was my first time to Spain . It was amazing , and the weather was just beautiful ! No rain , and just sun , sun , sun ..." + ], + "type": [ + "no-context" + ], + "text": "My first time . I've traveled around Europe a lot , but this was my first time to Spain . It was amazing , and the weather was just beautiful ! No rain , and just sun , sun , sun ...", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I'm so jealous of you . I've never been anywhere in Europe . I've always dreamed of traveling around and seeing the sights .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "My first time . I've traveled around Europe a lot , but this was my first time to Spain . It was amazing , and the weather was just beautiful ! No rain , and just sun , sun , sun ..." + ], + "type": [ + "inter-personal" + ], + "text": "I'm so jealous of you . I've never been anywhere in Europe . I've always dreamed of traveling around and seeing the sights .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Well , I really recommend Spain . You really should go . Anyway , it's been great to catch up , but I must be going , this is my floor . Speak again soon I hope .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "this was my first time to Spain . It was amazing , and the weather was just beautiful ! No rain , and just sun , sun , sun ..." + ], + "type": [ + "self-contagion" + ], + "text": "Well , I really recommend Spain . You really should go . Anyway , it's been great to catch up , but I must be going , this is my floor . Speak again soon I hope .", + "id": 7 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3042.json b/reccon/sources/tr_3042.json new file mode 100644 index 0000000000000000000000000000000000000000..7f6c75580b39634782b32eee61e2c3ee70f14fa8 --- /dev/null +++ b/reccon/sources/tr_3042.json @@ -0,0 +1,129 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Do you have any hobbies ?", + "emotion": "neutral", + "text": "Do you have any hobbies ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes . I like gardening .", + "emotion": "neutral", + "text": "Yes . I like gardening .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Oh , that's interesting . Do you have a garden ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I like gardening ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , that's interesting . Do you have a garden ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes , follow me . Here it is .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Do you have a garden ?" + ], + "type": [ + "inter-personal" + ], + "text": "Yes , follow me . Here it is .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Your garden is really lovely .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 5 + ], + "expanded emotion cause span": [ + "I like gardening .", + "Your garden is really lovely ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Your garden is really lovely .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Thank you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 5 + ], + "expanded emotion cause span": [ + "Do you have a garden ?", + "Your garden is really lovely ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you .", + "id": 6, + "source_sentences": [ + 2, + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Do you take care of them everyday ?", + "emotion": "neutral", + "text": "Do you take care of them everyday ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yes , I do .", + "emotion": "neutral", + "text": "Yes , I do .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Don't you feel dull ?", + "emotion": "neutral", + "text": "Don't you feel dull ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I don't . I like the work .", + "emotion": "neutral", + "text": "I don't . I like the work .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3046.json b/reccon/sources/tr_3046.json new file mode 100644 index 0000000000000000000000000000000000000000..4013bc8134805091fc88a2e72df8630a66c74f30 --- /dev/null +++ b/reccon/sources/tr_3046.json @@ -0,0 +1,192 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey , Daniel , how's it going ?", + "emotion": "neutral", + "text": "Hey , Daniel , how's it going ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hey , Daddy , today I had really a fantastic history class .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "today I had really a fantastic history class ." + ], + "type": [ + "no-context" + ], + "text": "Hey , Daddy , today I had really a fantastic history class .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Wow , it's so strange for you to say things like that . What had happened ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "today I had really a fantastic history class .", + "it's so strange for you to say things like that ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Wow , it's so strange for you to say things like that . What had happened ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "We've learnt the story of Zheg He Sailing to West Ocean . He is a real great navigator .", + "emotion": "neutral", + "text": "We've learnt the story of Zheg He Sailing to West Ocean . He is a real great navigator .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Did your teacher tell you the route he took ?", + "emotion": "neutral", + "text": "Did your teacher tell you the route he took ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yeah , he , with his fleet , came across the Indian Ocean , and arrived at the east coast of Africa .", + "emotion": "neutral", + "text": "Yeah , he , with his fleet , came across the Indian Ocean , and arrived at the east coast of Africa .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Great , do you still remember when he started his voyage ?", + "emotion": "neutral", + "text": "Great , do you still remember when he started his voyage ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Of course , that is from 1405 to 1433 , which is in Ming dynasty .", + "emotion": "neutral", + "text": "Of course , that is from 1405 to 1433 , which is in Ming dynasty .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Good , by the way , do you finish reading the book Robinson Crusoe I've bought for you ?", + "emotion": "neutral", + "text": "Good , by the way , do you finish reading the book Robinson Crusoe I've bought for you ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Not yet , you know I have a lot of homework to do .", + "emotion": "neutral", + "text": "Not yet , you know I have a lot of homework to do .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "You should speed up , because the story of Robinson can give you a better understanding about what you learned today .", + "emotion": "neutral", + "text": "You should speed up , because the story of Robinson can give you a better understanding about what you learned today .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "OK , great Daddy , after supper , I'll embark on it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "the story of Robinson can give you a better understanding about what you learned today ." + ], + "type": [ + "inter-personal" + ], + "text": "OK , great Daddy , after supper , I'll embark on it .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "That's my boy ! Wait , Daniel , when is Pirates of the Caribbean on ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "OK , great Daddy , after supper , I'll embark on it ." + ], + "type": [ + "inter-personal" + ], + "text": "That's my boy ! Wait , Daniel , when is Pirates of the Caribbean on ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Is it about Captain Jack Sparrow , who wants to find the treasure on the sea ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "the story of Robinson can give you a better understanding about what you learned today ." + ], + "type": [ + "inter-personal" + ], + "text": "Is it about Captain Jack Sparrow , who wants to find the treasure on the sea ?", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Exactly , now , tell me the time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "OK , great Daddy , after supper , I'll embark on it ." + ], + "type": [ + "inter-personal" + ], + "text": "Exactly , now , tell me the time .", + "id": 15, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 16, + "speaker": "B", + "utterance": "I won't tell you , unless you promise to let me watch it with you .", + "emotion": "neutral", + "text": "I won't tell you , unless you promise to let me watch it with you .", + "id": 16 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3054.json b/reccon/sources/tr_3054.json new file mode 100644 index 0000000000000000000000000000000000000000..66ab7986d17347dafa939eed28be968ea2c6cd14 --- /dev/null +++ b/reccon/sources/tr_3054.json @@ -0,0 +1,121 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "How do you usually spend your leisure time ? I mean , do you have any special interests out of your job ?", + "emotion": "neutral", + "text": "How do you usually spend your leisure time ? I mean , do you have any special interests out of your job ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Of course . You see , almost everyone has some kind of hobby .", + "emotion": "neutral", + "text": "Of course . You see , almost everyone has some kind of hobby .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yeah , you ' re quite right and what ' s your hobby ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Yeah , you ' re quite right and what ' s your hobby ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I like taking photos out of doors .", + "emotion": "neutral", + "text": "I like taking photos out of doors .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Oh , photography , It ' s really a good hobby .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "I like taking photos out of doors .", + "photography , It ' s really a good hobby ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , photography , It ' s really a good hobby .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yes , I usually develop and print all my own photos .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Oh , photography , It ' s really a good hobby .", + "I usually develop and print all my own photos ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , I usually develop and print all my own photos .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You yourself have a photo studio ?", + "emotion": "neutral", + "text": "You yourself have a photo studio ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yes , simple as it is . It does work .", + "emotion": "happiness", + "explanation": "Assuming B is happy because A is interested in his hobby.", + "expanded emotion cause evidence": [ + 5, + 6, + 7, + 8 + ], + "expanded emotion cause span": [ + "Oh , photography , It ' s really a good hobby .", + "I usually develop and print all my own photos .", + "You yourself have a photo studio ?", + "It does work ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Yes , simple as it is . It does work .", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3060.json b/reccon/sources/tr_3060.json new file mode 100644 index 0000000000000000000000000000000000000000..7abcd4fe805c68201bf8b1307b75cd71a59a6aab --- /dev/null +++ b/reccon/sources/tr_3060.json @@ -0,0 +1,121 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , Francis .", + "emotion": "neutral", + "text": "Hi , Francis .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh , Mike . How are you doing ?", + "emotion": "neutral", + "text": "Oh , Mike . How are you doing ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Not bad . It seems you are super yogurt lover . You have so many in your cart .", + "emotion": "neutral", + "text": "Not bad . It seems you are super yogurt lover . You have so many in your cart .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Well , I prefer yogurt to all the other drinks . Have you ever tried a kind of yogurt with old milk in it ? It tastes great and very healthy too .", + "emotion": "neutral", + "text": "Well , I prefer yogurt to all the other drinks . Have you ever tried a kind of yogurt with old milk in it ? It tastes great and very healthy too .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Oh , I haven ' t noticed that before . Maybe I will try next time .", + "emotion": "neutral", + "text": "Oh , I haven ' t noticed that before . Maybe I will try next time .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Why don ' t you go ahead of me ? I have more items than you .", + "emotion": "happiness", + "explanation": "the speaker is happy that A is willing to try his yogurt suggestion", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "Have you ever tried a kind of yogurt with old milk in it ? It tastes great and very healthy too .", + "Maybe I will try next time ." + ], + "type": [ + "hybrid" + ], + "text": "Why don ' t you go ahead of me ? I have more items than you .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Thank you . In fact , I am in a hurry . My wife is waiting for me at the parking lot .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "Why don ' t you go ahead of me ?", + "I am in a hurry . My wife is waiting for me at the parking lot ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you . In fact , I am in a hurry . My wife is waiting for me at the parking lot .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "You ' re welcome . It was good seeing you again .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Thank you . In fact , I am in a hurry . My wife is waiting for me at the parking lot ." + ], + "type": [ + "inter-personal" + ], + "text": "You ' re welcome . It was good seeing you again .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Me too . Have a great day .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "You ' re welcome . It was good seeing you again ." + ], + "type": [ + "inter-personal" + ], + "text": "Me too . Have a great day .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3071.json b/reccon/sources/tr_3071.json new file mode 100644 index 0000000000000000000000000000000000000000..2bd8da6091940bed7a887b7bc6f4380c037a0b6f --- /dev/null +++ b/reccon/sources/tr_3071.json @@ -0,0 +1,195 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I can ' t believe my English teacher is making me read pride and prejudice !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "my English teacher is making me read pride and prejudice !" + ], + "type": [ + "no-context" + ], + "text": "I can ' t believe my English teacher is making me read pride and prejudice !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Why not ! It ' s a classic . In fact , it ' s one of my favorite novels .", + "emotion": "neutral", + "text": "Why not ! It ' s a classic . In fact , it ' s one of my favorite novels .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "But it ' s so old .", + "emotion": "neutral", + "text": "But it ' s so old .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Don ' t judge a book by its cover . Do you know what it ' s about ?", + "emotion": "neutral", + "text": "Don ' t judge a book by its cover . Do you know what it ' s about ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "No , not at all .", + "emotion": "neutral", + "text": "No , not at all .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "First of all , it ' s a romance novel , set in the early 19th century .", + "emotion": "neutral", + "text": "First of all , it ' s a romance novel , set in the early 19th century .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I didn ' t realize it was a romance novel . What ' s the main storyline ?", + "emotion": "neutral", + "text": "I didn ' t realize it was a romance novel . What ' s the main storyline ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "It ' s basically about a father who tried to marry off one of his five girls .", + "emotion": "neutral", + "text": "It ' s basically about a father who tried to marry off one of his five girls .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Why does he want to do that ?", + "emotion": "neutral", + "text": "Why does he want to do that ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Since he doesn ' t have a son , he hopes that one of the girls will marry a wealthy man . That way , all of his daughters will be cared for .", + "emotion": "neutral", + "text": "Since he doesn ' t have a son , he hopes that one of the girls will marry a wealthy man . That way , all of his daughters will be cared for .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Won ' t they get his inheritance ?", + "emotion": "neutral", + "text": "Won ' t they get his inheritance ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "No , that ' s the problem . Though they are well-off , once he dies , his house will go to his cousin . So , when he dies , the girls will have nothing .", + "emotion": "neutral", + "text": "No , that ' s the problem . Though they are well-off , once he dies , his house will go to his cousin . So , when he dies , the girls will have nothing .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I see . This sounds interesting ! Maybe my teacher isn ' t so horrible after all .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "This sounds interesting !" + ], + "type": [ + "no-context" + ], + "text": "I see . This sounds interesting ! Maybe my teacher isn ' t so horrible after all .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "So , are you going to read the novel or watch the movie ?", + "emotion": "neutral", + "text": "So , are you going to read the novel or watch the movie ?", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "There ' s movie ? My teacher didn ' t tell me that !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "watch the movie ?" + ], + "type": [ + "inter-personal" + ], + "text": "There ' s movie ? My teacher didn ' t tell me that !", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "That ' s probably because she wants you to read the book first .", + "emotion": "neutral", + "text": "That ' s probably because she wants you to read the book first .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "It would take a lot less time ...", + "emotion": "neutral", + "text": "It would take a lot less time ...", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "How about this . When you finish the book . I ' ll get the movie and watch it with you .", + "emotion": "neutral", + "text": "How about this . When you finish the book . I ' ll get the movie and watch it with you .", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "Ok . That sounds like a deal .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 18 + ], + "expanded emotion cause span": [ + "When you finish the book . I ' ll get the movie and watch it with you ." + ], + "type": [ + "inter-personal" + ], + "text": "Ok . That sounds like a deal .", + "id": 19, + "source_sentences": [ + 17 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3073.json b/reccon/sources/tr_3073.json new file mode 100644 index 0000000000000000000000000000000000000000..7307988f016964e5953f89d92e3ac2e35082f654 --- /dev/null +++ b/reccon/sources/tr_3073.json @@ -0,0 +1,127 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "When do you want to have the open house party ?", + "emotion": "neutral", + "text": "When do you want to have the open house party ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "How about next Friday ?", + "emotion": "neutral", + "text": "How about next Friday ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Friday sounds good .", + "emotion": "happiness", + "explanation": "speaker is happy about the house party and that B has confirmed attendance", + "expanded emotion cause evidence": [ + 1, + 2, + 3 + ], + "expanded emotion cause span": [ + "have the open house party ?", + "How about next Friday ?", + "Friday sounds good ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Friday sounds good .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "How do you feel about hiring that clown to come and entertain the kids ?", + "emotion": "neutral", + "text": "How do you feel about hiring that clown to come and entertain the kids ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I like that . Then the adults will be more free to mingle and relax .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "hiring that clown to come and entertain the kids", + "the adults will be more free to mingle and relax ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I like that . Then the adults will be more free to mingle and relax .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "That's what I was thinking .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "hiring that clown to come and entertain the kids", + "the adults will be more free to mingle and relax ." + ], + "type": [ + "hybrid" + ], + "text": "That's what I was thinking .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I'm so excited . Finally , a yard of my own .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I'm so excited . Finally , a yard of my own ." + ], + "type": [ + "no-context" + ], + "text": "I'm so excited . Finally , a yard of my own .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Do you feel like a king in your castle ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I'm so excited . Finally , a yard of my own ." + ], + "type": [ + "inter-personal" + ], + "text": "Do you feel like a king in your castle ?", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3114.json b/reccon/sources/tr_3114.json new file mode 100644 index 0000000000000000000000000000000000000000..eee830b6e01fdf01bb42157c07bd16dde0c6eca5 --- /dev/null +++ b/reccon/sources/tr_3114.json @@ -0,0 +1,139 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "How did you spend the weekend ?", + "emotion": "neutral", + "text": "How did you spend the weekend ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I went to a movie with my boyfriend .", + "emotion": "neutral", + "text": "I went to a movie with my boyfriend .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Really ? How was it ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I went to a movie with my boyfriend ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? How was it ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It was great . The director took a lot of care while framing . They say be has good chance at winning the Oscar for best director . Also I like the actors , some really great new young actors .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "It was great . The director took a lot of care while framing . They say be has good chance at winning the Oscar for best director . Also I like the actors , some really great new young actors ." + ], + "type": [ + "no-context" + ], + "text": "It was great . The director took a lot of care while framing . They say be has good chance at winning the Oscar for best director . Also I like the actors , some really great new young actors .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Oh , yeah ? What's it about ?", + "emotion": "neutral", + "text": "Oh , yeah ? What's it about ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Well , it's the classic love story between two people from conflicting backgrounds . But besides a beautiful story , the cinematography is great . There is some really dramatic footage . It's really quite a visual feast . And the soundtrack is moving .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Well , it's the classic love story between two people from conflicting backgrounds . But besides a beautiful story , the cinematography is great . There is some really dramatic footage . It's really quite a visual feast . And the soundtrack is moving ." + ], + "type": [ + "no-context" + ], + "text": "Well , it's the classic love story between two people from conflicting backgrounds . But besides a beautiful story , the cinematography is great . There is some really dramatic footage . It's really quite a visual feast . And the soundtrack is moving .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Sounds pretty good . Is it a tragedy ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "Well , it's the classic love story between two people from conflicting backgrounds . But besides a beautiful story , the cinematography is great . There is some really dramatic footage . It's really quite a visual feast . And the soundtrack is moving .", + "Sounds pretty good ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Sounds pretty good . Is it a tragedy ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "The ending is a bit of a surprise . I don't want to ruin it for you .", + "emotion": "neutral", + "text": "The ending is a bit of a surprise . I don't want to ruin it for you .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Oh , I like movies with surprise endings , although , sometimes they can be frustrating . Maybe I should invite my girlfriend to go next weekend .", + "emotion": "neutral", + "text": "Oh , I like movies with surprise endings , although , sometimes they can be frustrating . Maybe I should invite my girlfriend to go next weekend .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "It would be a really good choice . The movie is very suitable for lovers to see together . I'm sure you won't regret it .", + "emotion": "happiness", + "explanation": "the speaker is happy that A will have a good experience watching the movie", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "I should invite my girlfriend to go next weekend .", + "It would be a really good choice . The movie is very suitable for lovers to see together . I'm sure you won't regret it ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It would be a really good choice . The movie is very suitable for lovers to see together . I'm sure you won't regret it .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3128.json b/reccon/sources/tr_3128.json new file mode 100644 index 0000000000000000000000000000000000000000..fb81fe9b19f8d338a438aa321209d22708d904ea --- /dev/null +++ b/reccon/sources/tr_3128.json @@ -0,0 +1,152 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "There's a new play tonight .", + "emotion": "neutral", + "text": "There's a new play tonight .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What's its name ?", + "emotion": "neutral", + "text": "What's its name ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "' Romeo and Juliet ' .", + "emotion": "neutral", + "text": "' Romeo and Juliet ' .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "What is it about ?", + "emotion": "neutral", + "text": "What is it about ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "It's about their great love .", + "emotion": "neutral", + "text": "It's about their great love .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Sounds interesting .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "their great love ." + ], + "type": [ + "inter-personal" + ], + "text": "Sounds interesting .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Of course . Do you want to see it ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Sounds interesting ." + ], + "type": [ + "inter-personal" + ], + "text": "Of course . Do you want to see it ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yes , do you have tickets ?", + "emotion": "neutral", + "text": "Yes , do you have tickets ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "No , I don't .", + "emotion": "neutral", + "text": "No , I don't .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Let's go to the theater and buy two tickets now , shall we ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "their great love ." + ], + "type": [ + "inter-personal" + ], + "text": "Let's go to the theater and buy two tickets now , shall we ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Good idea . Let's goa", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Let's go to the theater and buy two tickets now" + ], + "type": [ + "inter-personal" + ], + "text": "Good idea . Let's goa", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "OK . Let's go .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 11 + ], + "expanded emotion cause span": [ + "their great love .", + "Good idea ." + ], + "type": [ + "inter-personal" + ], + "text": "OK . Let's go .", + "id": 12, + "source_sentences": [ + 4, + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3138.json b/reccon/sources/tr_3138.json new file mode 100644 index 0000000000000000000000000000000000000000..ab831f4c7cc367cbcc4e1793fee1d21ee44dc541 --- /dev/null +++ b/reccon/sources/tr_3138.json @@ -0,0 +1,139 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "School has added several new courses to our grade this semester . I have more homework to do now .", + "emotion": "neutral", + "text": "School has added several new courses to our grade this semester . I have more homework to do now .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What's your favorite course , Daniel ?", + "emotion": "neutral", + "text": "What's your favorite course , Daniel ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I like science most .", + "emotion": "neutral", + "text": "I like science most .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Science ? That's a surprise .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I like science most ." + ], + "type": [ + "inter-personal" + ], + "text": "Science ? That's a surprise .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Surprise ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "That's a surprise ." + ], + "type": [ + "inter-personal" + ], + "text": "Surprise ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I thought you would like PE .", + "emotion": "neutral", + "text": "I thought you would like PE .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I do like PE , but I am interested in science .", + "emotion": "neutral", + "text": "I do like PE , but I am interested in science .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Are you interested in science ? I can't believe it .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I am interested in science ." + ], + "type": [ + "inter-personal" + ], + "text": "Are you interested in science ? I can't believe it .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Through this course , I can learn more about the world around us clearly .", + "emotion": "neutral", + "text": "Through this course , I can learn more about the world around us clearly .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Your parents would be happy if they knew that . Because you are always a naughty boy .", + "emotion": "neutral", + "text": "Your parents would be happy if they knew that . Because you are always a naughty boy .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Naughty ? I'm naughty ? I'm just clever . So I only do the things I am interested in .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "you are always a naughty boy ." + ], + "type": [ + "inter-personal" + ], + "text": "Naughty ? I'm naughty ? I'm just clever . So I only do the things I am interested in .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Hope so .", + "emotion": "neutral", + "text": "Hope so .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3139.json b/reccon/sources/tr_3139.json new file mode 100644 index 0000000000000000000000000000000000000000..0ccfb194ccdb9bde152c82d9517061829f133d41 --- /dev/null +++ b/reccon/sources/tr_3139.json @@ -0,0 +1,206 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , Tony . Haven ' t seen you for a long time . How have you been ?", + "emotion": "neutral", + "text": "Hi , Tony . Haven ' t seen you for a long time . How have you been ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "OK , I ' Ve been looking for a job for days , and I haven ' t found one yet . It's so hard finding work these days . Have you had any luck ?", + "emotion": "neutral", + "text": "OK , I ' Ve been looking for a job for days , and I haven ' t found one yet . It's so hard finding work these days . Have you had any luck ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yes , I've got a job , a waiter's job in a restaurant .", + "emotion": "neutral", + "text": "Yes , I've got a job , a waiter's job in a restaurant .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Are you well paid ?", + "emotion": "neutral", + "text": "Are you well paid ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Well , $ 10 per hour , but I can keep the tips . That comes to roughly $ 80 every evening", + "emotion": "neutral", + "text": "Well , $ 10 per hour , but I can keep the tips . That comes to roughly $ 80 every evening", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Not bad .", + "emotion": "neutral", + "text": "Not bad .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Actually , there's still another opening . If you are interested , you ' ll surely get it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "there's still another opening ." + ], + "type": [ + "no-context" + ], + "text": "Actually , there's still another opening . If you are interested , you ' ll surely get it .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That ' s great ! I ' ll go there right now and speak with the boss .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 7, + 8 + ], + "expanded emotion cause span": [ + "there's still another opening .", + "there's still another opening . If you are interested , you ' ll surely get it .", + "That ' s great !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That ' s great ! I ' ll go there right now and speak with the boss .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "There ' s no rush . You can see him tomorrow . I ' Ve told him about you . He promised to give you the job .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 9 + ], + "expanded emotion cause span": [ + "there's still another opening .", + "He promised to give you the job ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "There ' s no rush . You can see him tomorrow . I ' Ve told him about you . He promised to give you the job .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "That was nice of you , Susan . Thanks a lot .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 7, + 8, + 9 + ], + "expanded emotion cause span": [ + "there's still another opening .", + "there's still another opening . If you are interested , you ' ll surely get it .", + "That ' s great !", + "I ' Ve told him about you . He promised to give you the job ." + ], + "type": [ + "hybrid" + ], + "text": "That was nice of you , Susan . Thanks a lot .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Think nothing of it , Tony . I ' m sure you ' d do the same for me .", + "emotion": "neutral", + "text": "Think nothing of it , Tony . I ' m sure you ' d do the same for me .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Could you tell me a bit more about the work there ? I mean , those dos and don'ts . I am a green hand , you know .", + "emotion": "neutral", + "text": "Could you tell me a bit more about the work there ? I mean , those dos and don'ts . I am a green hand , you know .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "First of all , you must be punctual . You should be there before 6 p . m . so that you will have half an hour for preparation changing clothes and things like that . Then , remember you should smile . Smile to your customers all the time . Never pull a long face even If you feel awful that day . Anything else ? Oh , yes . Never argue with your boss . Learn to say ' Yes , sir . '", + "emotion": "neutral", + "text": "First of all , you must be punctual . You should be there before 6 p . m . so that you will have half an hour for preparation changing clothes and things like that . Then , remember you should smile . Smile to your customers all the time . Never pull a long face even If you feel awful that day . Anything else ? Oh , yes . Never argue with your boss . Learn to say ' Yes , sir . '", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Be a yes-man , you mean ?", + "emotion": "neutral", + "text": "Be a yes-man , you mean ?", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "You may put it that way if you like . Don ' t worry . You ' ll have no problem .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14, + 15 + ], + "expanded emotion cause span": [ + "Be a yes-man", + "Don ' t worry . You ' ll have no problem ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You may put it that way if you like . Don ' t worry . You ' ll have no problem .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "I hope not .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "Don ' t worry . You ' ll have no problem ." + ], + "type": [ + "inter-personal" + ], + "text": "I hope not .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_316.json b/reccon/sources/tr_316.json new file mode 100644 index 0000000000000000000000000000000000000000..c49757f75e454d81af0bcef173c149e75bfa3789 --- /dev/null +++ b/reccon/sources/tr_316.json @@ -0,0 +1,171 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "It ' s so relaxing , taking a walk in the country . The air is so fresh and clean .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "It ' s so relaxing , taking a walk in the country . The air is so fresh and clean ." + ], + "type": [ + "no-context" + ], + "text": "It ' s so relaxing , taking a walk in the country . The air is so fresh and clean .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "would you like to live in the country ? I ' m not sure I ' d like it .", + "emotion": "neutral", + "text": "would you like to live in the country ? I ' m not sure I ' d like it .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I can see a lot of advantage and disadvantage . The problem is that , for me , each advantage has its own disadvantage .", + "emotion": "neutral", + "text": "I can see a lot of advantage and disadvantage . The problem is that , for me , each advantage has its own disadvantage .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "What do you mean ?", + "emotion": "neutral", + "text": "What do you mean ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Well , I hate the noise in the city , but I love being around lost of people . The problem is that you can ' t have lots of people and have peace and quiet . The two just don ' t go together .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I hate the noise in the city" + ], + "type": [ + "no-context" + ], + "text": "Well , I hate the noise in the city , but I love being around lost of people . The problem is that you can ' t have lots of people and have peace and quiet . The two just don ' t go together .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I see what you mean . I love being far away from a city , but I hate being so far away department stores and sports facilities .", + "emotion": "neutral", + "text": "I see what you mean . I love being far away from a city , but I hate being so far away department stores and sports facilities .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "People can ' t have it both ways . If you live in the country , it is often less convenient . If you live in a city , it is noisy , but there ' s more to do .", + "emotion": "neutral", + "text": "People can ' t have it both ways . If you live in the country , it is often less convenient . If you live in a city , it is noisy , but there ' s more to do .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I would love to be surrounded by hills and streams . They ' re so much better to look at than concrete , rows of parked cars and tall buildings .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 8 + ], + "expanded emotion cause span": [ + "It ' s so relaxing , taking a walk in the country . The air is so fresh and clean .", + "I would love to be surrounded by hills and streams . They ' re so much better to look at than concrete , rows of parked cars and tall buildings ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I would love to be surrounded by hills and streams . They ' re so much better to look at than concrete , rows of parked cars and tall buildings .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I would love to hear the birds singing and feel the fresh breeze on my face . When the wind blows in the city , you get dust in your mouth and in your eyes .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 9 + ], + "expanded emotion cause span": [ + "It ' s so relaxing , taking a walk in the country . The air is so fresh and clean .", + "I would love to hear the birds singing and feel the fresh breeze on my face ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I would love to hear the birds singing and feel the fresh breeze on my face . When the wind blows in the city , you get dust in your mouth and in your eyes .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "The view from the hill is so beautiful and relaxing . There ' s so sign of pollution . The village looks so peaceful .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 8, + 10 + ], + "expanded emotion cause span": [ + "It ' s so relaxing , taking a walk in the country . The air is so fresh and clean .", + "I would love to be surrounded by hills and streams . They ' re so much better to look at than concrete , rows of parked cars and tall buildings .", + "The view from the hill is so beautiful and relaxing . There ' s so sign of pollution . The village looks so peaceful ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "The view from the hill is so beautiful and relaxing . There ' s so sign of pollution . The village looks so peaceful .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Just remember that in that village there ' s nothing to do . There ' s not even a pub or restaurant . There ' s just one small shop with a poor selection of goods .", + "emotion": "neutral", + "text": "Just remember that in that village there ' s nothing to do . There ' s not even a pub or restaurant . There ' s just one small shop with a poor selection of goods .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "You ' re right . I would have to travel to the city at least once a week to go shopping and see friends . I would hate living in the country !", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "in that village there ' s nothing to do . There ' s not even a pub or restaurant . There ' s just one small shop with a poor selection of goods .", + "I would have to travel to the city at least once a week to go shopping and see friends . I would hate living in the country !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You ' re right . I would have to travel to the city at least once a week to go shopping and see friends . I would hate living in the country !", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3166.json b/reccon/sources/tr_3166.json new file mode 100644 index 0000000000000000000000000000000000000000..70aba4ebd5b8e4848b8b36ceb42dd20fc96fc326 --- /dev/null +++ b/reccon/sources/tr_3166.json @@ -0,0 +1,197 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I can't wait to go skiing tomorrow .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I can't wait to go skiing tomorrow ." + ], + "type": [ + "no-context" + ], + "text": "I can't wait to go skiing tomorrow .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I know . It's going to be so much fun .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 2 + ], + "expanded emotion cause span": [ + "It's going to be so much fun .", + "I know . It's going to be so much fun ." + ], + "type": [ + "no-context" + ], + "text": "I know . It's going to be so much fun .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I always get excited the day before .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I can't wait to go skiing tomorrow ." + ], + "type": [ + "self-contagion" + ], + "text": "I always get excited the day before .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I used to be like that . But I go skiing so often that I don't get excited anymore .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 2 + ], + "expanded emotion cause span": [ + "It's going to be so much fun .", + "I know . It's going to be so much fun ." + ], + "type": [ + "self-contagion" + ], + "text": "I used to be like that . But I go skiing so often that I don't get excited anymore .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I only go skiing twice a year , so it's a real treat for me .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 5 + ], + "expanded emotion cause span": [ + "I can't wait to go skiing tomorrow .", + "it's a real treat for me ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I only go skiing twice a year , so it's a real treat for me .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "That makes sense .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 2, + 2 + ], + "expanded emotion cause span": [ + "It's going to be so much fun .", + "I know . It's going to be so much fun ." + ], + "type": [ + "self-contagion" + ], + "text": "That makes sense .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "What things make you excited ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I can't wait to go skiing tomorrow ." + ], + "type": [ + "self-contagion" + ], + "text": "What things make you excited ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Whenever I go to Vegas , I get really excited .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Whenever I go to Vegas , I get really excited ." + ], + "type": [ + "no-context" + ], + "text": "Whenever I go to Vegas , I get really excited .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Oh ... that makes me excited too !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 8 + ], + "expanded emotion cause span": [ + "Whenever I go to Vegas , I get really excited .", + "Whenever I go to Vegas , I get really excited ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh ... that makes me excited too !", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Looks like anything fun makes you excited .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 9, + 10 + ], + "expanded emotion cause span": [ + "I always get excited the day before .", + "that makes me excited too !", + "Looks like anything fun makes you excited ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Looks like anything fun makes you excited .", + "id": 10, + "source_sentences": [ + 2, + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3169.json b/reccon/sources/tr_3169.json new file mode 100644 index 0000000000000000000000000000000000000000..b338f4b9aebee18cd1aca368a5c5051321a722d6 --- /dev/null +++ b/reccon/sources/tr_3169.json @@ -0,0 +1,100 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "When can we expect you and your daughter for dinner ? Next Saturday ?", + "emotion": "neutral", + "text": "When can we expect you and your daughter for dinner ? Next Saturday ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Next Saturday ? I ' m sorry . I ' Ve promised to go to a Chinese Opera with my daughter .", + "emotion": "neutral", + "text": "Next Saturday ? I ' m sorry . I ' Ve promised to go to a Chinese Opera with my daughter .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "How about Sunday then ?", + "emotion": "neutral", + "text": "How about Sunday then ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes , Sunday sounds fine . What time ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Sunday sounds fine ." + ], + "type": [ + "no-context" + ], + "text": "Yes , Sunday sounds fine . What time ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Does six thirty suit you ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Sunday sounds fine ." + ], + "type": [ + "inter-personal" + ], + "text": "Does six thirty suit you ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "It suits us fine . We ' ll see you then .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Sunday sounds fine ." + ], + "type": [ + "self-contagion" + ], + "text": "It suits us fine . We ' ll see you then .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Thanks , goodbye .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "It suits us fine ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks , goodbye .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3177.json b/reccon/sources/tr_3177.json new file mode 100644 index 0000000000000000000000000000000000000000..d82bd192f3a411178b42a4794211f8c34f06daaf --- /dev/null +++ b/reccon/sources/tr_3177.json @@ -0,0 +1,131 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Excuse me , what's your name ?", + "emotion": "neutral", + "text": "Excuse me , what's your name ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "My name is Jessica . What's yours ?", + "emotion": "neutral", + "text": "My name is Jessica . What's yours ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "John .", + "emotion": "neutral", + "text": "John .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "You speak English very well .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "You speak English very well ." + ], + "type": [ + "no-context" + ], + "text": "You speak English very well .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Thank you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "You speak English very well ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Do you know what time it is ?", + "emotion": "neutral", + "text": "Do you know what time it is ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Sure . It's 5:10 PM .", + "emotion": "neutral", + "text": "Sure . It's 5:10 PM .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "What did you say ?", + "emotion": "neutral", + "text": "What did you say ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I said it's 5:10 PM .", + "emotion": "neutral", + "text": "I said it's 5:10 PM .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Thanks .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "it's 5:10 PM ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "You're welcome .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Thanks ." + ], + "type": [ + "inter-personal" + ], + "text": "You're welcome .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3184.json b/reccon/sources/tr_3184.json new file mode 100644 index 0000000000000000000000000000000000000000..416ff7a224cba7d19f0322cf994cf6f98ac6ccb0 --- /dev/null +++ b/reccon/sources/tr_3184.json @@ -0,0 +1,184 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey , Susie , what health club do you belong to ?", + "emotion": "neutral", + "text": "Hey , Susie , what health club do you belong to ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Total Fitness , why ?", + "emotion": "neutral", + "text": "Total Fitness , why ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Well , I ' Ve been going to Athletic Express , but I don ' t like it there .", + "emotion": "neutral", + "text": "Well , I ' Ve been going to Athletic Express , but I don ' t like it there .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Really ? Why not ? I hear it ' s pretty good .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "I ' Ve been going to Athletic Express , but I don ' t like it there .", + "I hear it ' s pretty good ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Really ? Why not ? I hear it ' s pretty good .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "The people don ' t really work out there . They just stand around and talk all the time .", + "emotion": "neutral", + "text": "The people don ' t really work out there . They just stand around and talk all the time .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Oh , it ' s one of those places .", + "emotion": "neutral", + "text": "Oh , it ' s one of those places .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yeah , is your club different ?", + "emotion": "neutral", + "text": "Yeah , is your club different ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Well , they have different rooms . I lift weights by the pool where there aren ' t so many people .", + "emotion": "neutral", + "text": "Well , they have different rooms . I lift weights by the pool where there aren ' t so many people .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Do they have a lot of equipment ?", + "emotion": "neutral", + "text": "Do they have a lot of equipment ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Yeah , they have all the machines , a pool , and a steam room and sauna .", + "emotion": "neutral", + "text": "Yeah , they have all the machines , a pool , and a steam room and sauna .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Sounds nice . What about classes ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "they have all the machines , a pool , and a steam room and sauna ." + ], + "type": [ + "inter-personal" + ], + "text": "Sounds nice . What about classes ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "The usual . Aerobics , kickboxing , yoga . They just started a Tai Chi class too .", + "emotion": "neutral", + "text": "The usual . Aerobics , kickboxing , yoga . They just started a Tai Chi class too .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Wow , that sounds great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 12 + ], + "expanded emotion cause span": [ + "they have all the machines , a pool , and a steam room and sauna .", + "Aerobics , kickboxing , yoga . They just started a Tai Chi class too ." + ], + "type": [ + "inter-personal" + ], + "text": "Wow , that sounds great .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Well , I have a guest pass . Why don ' t you come with me tonight ?", + "emotion": "neutral", + "text": "Well , I have a guest pass . Why don ' t you come with me tonight ?", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Really ? Thanks . I ' ll stop by when I get off work .", + "emotion": "neutral", + "text": "Really ? Thanks . I ' ll stop by when I get off work .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Perfect . See you later .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "Thanks . I ' ll stop by when I get off work ." + ], + "type": [ + "inter-personal" + ], + "text": "Perfect . See you later .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 17, + "speaker": "A", + "utterance": "O . K . , see you .", + "emotion": "neutral", + "text": "O . K . , see you .", + "id": 17 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3185.json b/reccon/sources/tr_3185.json new file mode 100644 index 0000000000000000000000000000000000000000..cdac6e0b97983e5733b15be06a013c1b86ef3ec0 --- /dev/null +++ b/reccon/sources/tr_3185.json @@ -0,0 +1,140 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Do you like traveling ?", + "emotion": "neutral", + "text": "Do you like traveling ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , I've just come back from Scotland .", + "emotion": "neutral", + "text": "Yes , I've just come back from Scotland .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Where did you visit ?", + "emotion": "neutral", + "text": "Where did you visit ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I only had time to visit Edinburgh .", + "emotion": "neutral", + "text": "I only had time to visit Edinburgh .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "How did you like it ?", + "emotion": "neutral", + "text": "How did you like it ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "It's fantastic .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "It's fantastic ." + ], + "type": [ + "no-context" + ], + "text": "It's fantastic .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Why did you go there ?", + "emotion": "neutral", + "text": "Why did you go there ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I went there on business .", + "emotion": "neutral", + "text": "I went there on business .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "And do you have friends there ?", + "emotion": "neutral", + "text": "And do you have friends there ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Yes , a lot of friends .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Yes , a lot of friends ." + ], + "type": [ + "no-context" + ], + "text": "Yes , a lot of friends .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "You must have enjoyed yourself .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Yes , a lot of friends ." + ], + "type": [ + "inter-personal" + ], + "text": "You must have enjoyed yourself .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Yes , and I took many pictures .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Yes , a lot of friends ." + ], + "type": [ + "self-contagion" + ], + "text": "Yes , and I took many pictures .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3192.json b/reccon/sources/tr_3192.json new file mode 100644 index 0000000000000000000000000000000000000000..60754868a1fb3afe4e5254d108d0ede32d9b6277 --- /dev/null +++ b/reccon/sources/tr_3192.json @@ -0,0 +1,154 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I'm so glad that the Spring Festival is near at hand .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I'm so glad that the Spring Festival is near at hand ." + ], + "type": [ + "no-context" + ], + "text": "I'm so glad that the Spring Festival is near at hand .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Me too . I like the festival best of all .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "I'm so glad that the Spring Festival is near at hand .", + "I like the festival best of all ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Me too . I like the festival best of all .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Think of the big face down the eve , hmm .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Think of the big face down the eve ," + ], + "type": [ + "no-context" + ], + "text": "Think of the big face down the eve , hmm .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "And special TV programs , fire crackers and the games to play .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "Think of the big face down the eve ,", + "And special TV programs , fire crackers and the games to play ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "And special TV programs , fire crackers and the games to play .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Hey , do you know any mystery belief serve the festival ?", + "emotion": "neutral", + "text": "Hey , do you know any mystery belief serve the festival ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Such as ?", + "emotion": "neutral", + "text": "Such as ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You know why fire crackers are set off in festival .", + "emotion": "neutral", + "text": "You know why fire crackers are set off in festival .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Why ? To welcome the new year of course ?", + "emotion": "neutral", + "text": "Why ? To welcome the new year of course ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "And also to frighten away evil spirits .", + "emotion": "neutral", + "text": "And also to frighten away evil spirits .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Really ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "to frighten away evil spirits ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ?", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 11, + "speaker": "A", + "utterance": "And my parents say the whole year will be as good or as bad as new year day itself and bad or rude words on the day will bring a bad year .", + "emotion": "neutral", + "text": "And my parents say the whole year will be as good or as bad as new year day itself and bad or rude words on the day will bring a bad year .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Oh , that's why my parents never scold me that day . They always try to avoid tears and quarrels .", + "emotion": "neutral", + "text": "Oh , that's why my parents never scold me that day . They always try to avoid tears and quarrels .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_321.json b/reccon/sources/tr_321.json new file mode 100644 index 0000000000000000000000000000000000000000..d4e769ab12e544a1f63196a7fe1a495f58006e34 --- /dev/null +++ b/reccon/sources/tr_321.json @@ -0,0 +1,106 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "are you working overtime again ? Over the last two weeks , you have worked overtime every day without a break ! Your company is draining the life out of you !", + "emotion": "neutral", + "text": "are you working overtime again ? Over the last two weeks , you have worked overtime every day without a break ! Your company is draining the life out of you !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I know , but I don't have a choice , my boss has complete control over our work schedules . I haven't made it out of the office before 9 PM a single day this week .", + "emotion": "neutral", + "text": "I know , but I don't have a choice , my boss has complete control over our work schedules . I haven't made it out of the office before 9 PM a single day this week .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Well , I hope they're paying you the big bucks for all this work ...", + "emotion": "neutral", + "text": "Well , I hope they're paying you the big bucks for all this work ...", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "No , not exactly , I'm working for minimum wage . And they don't give extra pay for overtime . Overtime is our own time .", + "emotion": "neutral", + "text": "No , not exactly , I'm working for minimum wage . And they don't give extra pay for overtime . Overtime is our own time .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "What ? ! Isn't there a law against that , I think there is some legislation that requires employers to give their employees a fair rate of wages . You should know your rights ! If you are putting in so many hours , they should give you some kind of compensation .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "they don't give extra pay for overtime . Overtime is our own time ." + ], + "type": [ + "inter-personal" + ], + "text": "What ? ! Isn't there a law against that , I think there is some legislation that requires employers to give their employees a fair rate of wages . You should know your rights ! If you are putting in so many hours , they should give you some kind of compensation .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "They do give bonuses at the end of the year for the employees with highest productivity numbers , but frankly , it's not much of an incentive . They give us a bonus of ten dollars .", + "emotion": "neutral", + "text": "They do give bonuses at the end of the year for the employees with highest productivity numbers , but frankly , it's not much of an incentive . They give us a bonus of ten dollars .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "That's just wrong ! why don't you just quit ?", + "emotion": "anger", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "but frankly , it's not much of an incentive . They give us a bonus of ten dollars ." + ], + "type": [ + "inter-personal" + ], + "text": "That's just wrong ! why don't you just quit ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I would , but I'm afraid I would't be able to find another job . I don't have very many job marketable skills , there aren't so many jobs that I'm qualified for .", + "emotion": "neutral", + "text": "I would , but I'm afraid I would't be able to find another job . I don't have very many job marketable skills , there aren't so many jobs that I'm qualified for .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "it sounds like any job will be better than the one you have now !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "but frankly , it's not much of an incentive . They give us a bonus of ten dollars ." + ], + "type": [ + "inter-personal" + ], + "text": "it sounds like any job will be better than the one you have now !", + "id": 9, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3216.json b/reccon/sources/tr_3216.json new file mode 100644 index 0000000000000000000000000000000000000000..5163e4d6704ea3aa36a3828f1e287df7fe031cdb --- /dev/null +++ b/reccon/sources/tr_3216.json @@ -0,0 +1,143 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Would you talk to me about taking one of Dr . Miller's classes ?", + "emotion": "neutral", + "text": "Would you talk to me about taking one of Dr . Miller's classes ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes . Have you ever been in one of his classes ?", + "emotion": "neutral", + "text": "Yes . Have you ever been in one of his classes ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I'm thinking about taking his class next semester .", + "emotion": "neutral", + "text": "I'm thinking about taking his class next semester .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "He was a very easy teacher . Are you thinking of taking a class with him ?", + "emotion": "neutral", + "text": "He was a very easy teacher . Are you thinking of taking a class with him ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I'm not sure because I really need to learn something , but I also worry about grades .", + "emotion": "neutral", + "text": "I'm not sure because I really need to learn something , but I also worry about grades .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Grades are important , but don't you think that gaining the knowledge is important , too ?", + "emotion": "neutral", + "text": "Grades are important , but don't you think that gaining the knowledge is important , too ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I really need to learn this stuff .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I really need to learn this stuff ." + ], + "type": [ + "no-context" + ], + "text": "I really need to learn this stuff .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "He made everything so interesting that the time just flew by . Do you know what I mean ?", + "emotion": "neutral", + "text": "He made everything so interesting that the time just flew by . Do you know what I mean ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yes , that sounds right for me .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "He made everything so interesting that the time just flew by .", + "that sounds right for me ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , that sounds right for me .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Did you know that he came here last year after 10 years in the military ?", + "emotion": "neutral", + "text": "Did you know that he came here last year after 10 years in the military ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Yeah , I already knew that . That could be a good thing .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "he came here last year after 10 years in the military" + ], + "type": [ + "inter-personal" + ], + "text": "Yeah , I already knew that . That could be a good thing .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I think you know that you have to make the best decision for you . Enjoy your year !", + "emotion": "happiness", + "explanation": "Wishing/appreciation", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "I think you know that you have to make the best decision for you . Enjoy your year !", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3233.json b/reccon/sources/tr_3233.json new file mode 100644 index 0000000000000000000000000000000000000000..6c93738ec27942214f05a5e23113d2c8a5770f3e --- /dev/null +++ b/reccon/sources/tr_3233.json @@ -0,0 +1,173 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "( Before Christmas Party ) Are you ready for the Christmas party tonight", + "emotion": "happiness", + "explanation": "There might be some additional underlying cause for happiness.", + "expanded emotion cause evidence": [ + 1, + "b" + ], + "expanded emotion cause span": [ + "Christmas party tonight", + "b" + ], + "type": [ + "latent", + "no-context" + ], + "text": "( Before Christmas Party ) Are you ready for the Christmas party tonight", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Almost . I have to get dressed . It's a formal party and I have special party make up !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I have special party make up !" + ], + "type": [ + "no-context" + ], + "text": "Almost . I have to get dressed . It's a formal party and I have special party make up !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Use this lipstick and it will make your lips shine !", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1, + "b" + ], + "expanded emotion cause span": [ + "Christmas party tonight", + "b" + ], + "type": [ + "latent", + "self-contagion" + ], + "text": "Use this lipstick and it will make your lips shine !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Great ! Uh , remember that there's a gift exchange , too . We all have to bring a gift .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "I have special party make up !", + "it will make your lips shine" + ], + "type": [ + "hybrid" + ], + "text": "Great ! Uh , remember that there's a gift exchange , too . We all have to bring a gift .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I've already got mine .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I've already got mine ." + ], + "type": [ + "no-context" + ], + "text": "I've already got mine .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "( At the Party ) It's Christmas Eve ! Time to open presents !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "( At the Party ) It's Christmas Eve ! Time to open presents !" + ], + "type": [ + "no-context" + ], + "text": "( At the Party ) It's Christmas Eve ! Time to open presents !", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Here ! Open mine first .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "( At the Party ) It's Christmas Eve ! Time to open presents !" + ], + "type": [ + "inter-personal" + ], + "text": "Here ! Open mine first .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Wow ! It's just what I wanted !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 8 + ], + "expanded emotion cause span": [ + "( At the Party ) It's Christmas Eve ! Time to open presents !", + "It's just what I wanted !" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Wow ! It's just what I wanted !", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Hey ! Why don't I have any presents !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Why don't I have any presents !" + ], + "type": [ + "no-context" + ], + "text": "Hey ! Why don't I have any presents !", + "id": 9 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3234.json b/reccon/sources/tr_3234.json new file mode 100644 index 0000000000000000000000000000000000000000..40b21d5cd9673784f2afd80b1e2fe107d0e9db63 --- /dev/null +++ b/reccon/sources/tr_3234.json @@ -0,0 +1,224 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , Mike , what gives ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Hi , Mike , what gives ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hi , Bill , this is my new car .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "this is my new car ." + ], + "type": [ + "no-context" + ], + "text": "Hi , Bill , this is my new car .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Hey , great set of wheels .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "great set of wheels ." + ], + "type": [ + "no-context" + ], + "text": "Hey , great set of wheels .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "You like it , huh ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "this is my new car .", + "great set of wheels ." + ], + "type": [ + "hybrid" + ], + "text": "You like it , huh ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Who wouldn't ? Wow , that's out of this world .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 5 + ], + "expanded emotion cause span": [ + "great set of wheels .", + "that's out of this world ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Who wouldn't ? Wow , that's out of this world .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "It is special , isn't it ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "that's out of this world ." + ], + "type": [ + "inter-personal" + ], + "text": "It is special , isn't it ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yeah , too cool . How much did they sold you for ?", + "emotion": "happiness", + "explanation": "the speaker and listener are happy due to the background context and the car", + "expanded emotion cause evidence": [ + 3, + 5 + ], + "expanded emotion cause span": [ + "great set of wheels .", + "that's out of this world ." + ], + "type": [ + "self-contagion" + ], + "text": "Yeah , too cool . How much did they sold you for ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Lots . Looks like I'll have to moonlight for the next two years .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "this is my new car ." + ], + "type": [ + "self-contagion" + ], + "text": "Lots . Looks like I'll have to moonlight for the next two years .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I can imagine .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 5 + ], + "expanded emotion cause span": [ + "great set of wheels .", + "that's out of this world ." + ], + "type": [ + "self-contagion" + ], + "text": "I can imagine .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Hey , let's go for a spin . You can try it out .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "let's go for a spin . You can try it out ." + ], + "type": [ + "no-context" + ], + "text": "Hey , let's go for a spin . You can try it out .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I'd love to .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "let's go for a spin . You can try it out .", + "I'd love to" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'd love to .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Ok , let's go .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "let's go for a spin . You can try it out ." + ], + "type": [ + "self-contagion" + ], + "text": "Ok , let's go .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3256.json b/reccon/sources/tr_3256.json new file mode 100644 index 0000000000000000000000000000000000000000..d0126a8ea457a5c67475aea3cc8be8cd1e09901c --- /dev/null +++ b/reccon/sources/tr_3256.json @@ -0,0 +1,139 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What dances do you like ?", + "emotion": "neutral", + "text": "What dances do you like ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I love to dance the fast music .", + "emotion": "happiness", + "explanation": "sharing personal preferences", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I love to dance the fast music ." + ], + "type": [ + "no-context" + ], + "text": "I love to dance the fast music .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Then you must be interested in disco .", + "emotion": "neutral", + "text": "Then you must be interested in disco .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes , it's my favorite .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "I love to dance the fast music .", + "Then you must be interested in disco ." + ], + "type": [ + "hybrid" + ], + "text": "Yes , it's my favorite .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Oh , it's a disco . Let's dance .", + "emotion": "neutral", + "text": "Oh , it's a disco . Let's dance .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "You're a good dancer .", + "emotion": "happiness", + "explanation": "complimenting the other person", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "You're a good dancer ." + ], + "type": [ + "no-context" + ], + "text": "You're a good dancer .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Thank you . Now they are playing a rumba . Would you have a try ?", + "emotion": "neutral", + "text": "Thank you . Now they are playing a rumba . Would you have a try ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Sorry . I feel like sitting out the next dance .", + "emotion": "neutral", + "text": "Sorry . I feel like sitting out the next dance .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "OK . Let's get something to drink .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Let's get something to drink ." + ], + "type": [ + "no-context" + ], + "text": "OK . Let's get something to drink .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Good idea .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 9 + ], + "expanded emotion cause span": [ + "Let's get something to drink .", + "Let's get something to drink ." + ], + "type": [ + "inter-personal" + ], + "text": "Good idea .", + "id": 10, + "source_sentences": [ + 8, + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3261.json b/reccon/sources/tr_3261.json new file mode 100644 index 0000000000000000000000000000000000000000..e3f5d4de14ae7db9a078af540cfffc90f24fb058 --- /dev/null +++ b/reccon/sources/tr_3261.json @@ -0,0 +1,131 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Why don ' t we go the cinema tonight ?", + "emotion": "happiness", + "explanation": "There might be some underlying cause for the happiness too.", + "expanded emotion cause evidence": [ + 1, + "b" + ], + "expanded emotion cause span": [ + "we go the cinema tonight", + "b" + ], + "type": [ + "latent", + "no-context" + ], + "text": "Why don ' t we go the cinema tonight ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "That sounds good but I don ' t know what ' s on .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Why don ' t we go the cinema tonight ?" + ], + "type": [ + "inter-personal" + ], + "text": "That sounds good but I don ' t know what ' s on .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I think there ' s a very romantic new film starring Hugh Grant . Let ' s go and see that .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + "b", + 2, + 3 + ], + "expanded emotion cause span": [ + "we go the cinema tonight", + "b", + "That sounds good", + "there ' s a very romantic new film" + ], + "type": [ + "latent", + "no-context", + "hybrid" + ], + "text": "I think there ' s a very romantic new film starring Hugh Grant . Let ' s go and see that .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Ok , that ' s a good idea . Where shall we meet ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "there ' s a very romantic new film starring Hugh Grant . Let ' s go and see that ." + ], + "type": [ + "inter-personal" + ], + "text": "Ok , that ' s a good idea . Where shall we meet ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Well how about meeting at my place ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + "b", + 2, + 3, + 4 + ], + "expanded emotion cause span": [ + "we go the cinema tonight", + "b", + "That sounds good", + "there ' s a very romantic new film", + "that ' s a good idea" + ], + "type": [ + "latent", + "hybrid" + ], + "text": "Well how about meeting at my place ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "That sounds good . I ' ll call you once I arrive .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "there ' s a very romantic new film starring Hugh Grant . Let ' s go and see that ." + ], + "type": [ + "inter-personal" + ], + "text": "That sounds good . I ' ll call you once I arrive .", + "id": 6, + "source_sentences": [ + 2 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3279.json b/reccon/sources/tr_3279.json new file mode 100644 index 0000000000000000000000000000000000000000..1b5a8292ffbdf67a8f4f8a2a870ccc200fea1210 --- /dev/null +++ b/reccon/sources/tr_3279.json @@ -0,0 +1,172 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Your garden is looking very beautiful this summer . The flowers are really colorful .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 1 + ], + "expanded emotion cause span": [ + "garden is looking very beautiful", + "flowers are really colorful ." + ], + "type": [ + "no-context" + ], + "text": "Your garden is looking very beautiful this summer . The flowers are really colorful .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Thank you . I have roses , tulips , and daffodils . Do you like the rockery with the smaller flowers ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 1 + ], + "expanded emotion cause span": [ + "Your garden is looking very beautiful", + "flowers are really colorful ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . I have roses , tulips , and daffodils . Do you like the rockery with the smaller flowers ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yes , I do . Those are violets , aren ' t they ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1, + 1 + ], + "expanded emotion cause span": [ + "garden is looking very beautiful", + "flowers are really colorful ." + ], + "type": [ + "self-contagion" + ], + "text": "Yes , I do . Those are violets , aren ' t they ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes , they are . This afternoon , I ' m going to prune the hedge .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1, + 1 + ], + "expanded emotion cause span": [ + "Your garden is looking very beautiful", + "flowers are really colorful ." + ], + "type": [ + "inter-personal" + ], + "text": "Yes , they are . This afternoon , I ' m going to prune the hedge .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "The lower branches on that tree are hanging very low . Would you like me to cut them off for you ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1, + 1 + ], + "expanded emotion cause span": [ + "garden is looking very beautiful", + "flowers are really colorful ." + ], + "type": [ + "self-contagion" + ], + "text": "The lower branches on that tree are hanging very low . Would you like me to cut them off for you ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Thank you ! That would be very kind of you . I have a saw in the garden shed .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Would you like me to cut them off for you ?", + "That would be very kind of you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you ! That would be very kind of you . I have a saw in the garden shed .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "When the lower branches are removed , you ' ll be able to sit under the tree .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Thank you ! That would be very kind of you ." + ], + "type": [ + "inter-personal" + ], + "text": "When the lower branches are removed , you ' ll be able to sit under the tree .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Tomorrow , I ' ll cut the grass . Then the garden will look perfect .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6, + 8 + ], + "expanded emotion cause span": [ + "Would you like me to cut them off for you ?", + "That would be very kind of you .", + "the garden will look perfect ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Tomorrow , I ' ll cut the grass . Then the garden will look perfect .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Just make sure children don ' t play in the flower beds and destroy the flowers .", + "emotion": "neutral", + "text": "Just make sure children don ' t play in the flower beds and destroy the flowers .", + "id": 9 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3280.json b/reccon/sources/tr_3280.json new file mode 100644 index 0000000000000000000000000000000000000000..329fc023626bae8b00e8e5869acda390cd374775 --- /dev/null +++ b/reccon/sources/tr_3280.json @@ -0,0 +1,116 @@ +[ + { + "turn": 1, + "speaker": "B", + "utterance": "Listen to this . Mary got married .", + "emotion": "neutral", + "text": "Listen to this . Mary got married .", + "id": 1 + }, + { + "turn": 2, + "speaker": "A", + "utterance": "Is she really ? I can ' t believe it !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Mary got married ." + ], + "type": [ + "inter-personal" + ], + "text": "Is she really ? I can ' t believe it !", + "id": 2 + }, + { + "turn": 3, + "speaker": "B", + "utterance": "Yes . Yesterday .", + "emotion": "neutral", + "text": "Yes . Yesterday .", + "id": 3 + }, + { + "turn": 4, + "speaker": "A", + "utterance": "Good gracious . That ' s incredible !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Mary got married ." + ], + "type": [ + "inter-personal" + ], + "text": "Good gracious . That ' s incredible !", + "id": 4 + }, + { + "turn": 5, + "speaker": "B", + "utterance": "She married Jerrod .", + "emotion": "neutral", + "text": "She married Jerrod .", + "id": 5 + }, + { + "turn": 6, + "speaker": "A", + "utterance": "You ' re kidding .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "She married Jerrod ." + ], + "type": [ + "inter-personal" + ], + "text": "You ' re kidding .", + "id": 6 + }, + { + "turn": 7, + "speaker": "B", + "utterance": "She ' s going to live in Paris .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "She ' s going to live in Paris ." + ], + "type": [ + "no-context" + ], + "text": "She ' s going to live in Paris .", + "id": 7 + }, + { + "turn": 8, + "speaker": "A", + "utterance": "Really ? I ' m surprised .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "She ' s going to live in Paris ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? I ' m surprised .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3320.json b/reccon/sources/tr_3320.json new file mode 100644 index 0000000000000000000000000000000000000000..a4d618a8a44f7a821a0181854820abe1f463451a --- /dev/null +++ b/reccon/sources/tr_3320.json @@ -0,0 +1,210 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , Charlie ! What are you reading ?", + "emotion": "neutral", + "text": "Hi , Charlie ! What are you reading ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hi , bob . I ' m reading a biography ?", + "emotion": "neutral", + "text": "Hi , bob . I ' m reading a biography ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Who ' s it about ?", + "emotion": "neutral", + "text": "Who ' s it about ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It ' s about Bob Dylan .", + "emotion": "neutral", + "text": "It ' s about Bob Dylan .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Who is he ?", + "emotion": "neutral", + "text": "Who is he ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "He ' s a famous American musician .", + "emotion": "neutral", + "text": "He ' s a famous American musician .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Who ' s the author ?", + "emotion": "neutral", + "text": "Who ' s the author ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "It was written by Howard Sounds .", + "emotion": "neutral", + "text": "It was written by Howard Sounds .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "What do you think about it ?", + "emotion": "neutral", + "text": "What do you think about it ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "It ' s great ! I ' Ve learned a lot from reading it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "It ' s great ! I ' Ve learned a lot from reading it ." + ], + "type": [ + "no-context" + ], + "text": "It ' s great ! I ' Ve learned a lot from reading it .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Can I read it when you ' re done ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "It ' s great ! I ' Ve learned a lot from reading it ." + ], + "type": [ + "inter-personal" + ], + "text": "Can I read it when you ' re done ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Sure , bob ! I ' m on chapter 12 now , so I ' m almost finished .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "It ' s great ! I ' Ve learned a lot from reading it .", + "Can I read it when you ' re done ?" + ], + "type": [ + "hybrid" + ], + "text": "Sure , bob ! I ' m on chapter 12 now , so I ' m almost finished .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "How many chapters does the book have ?", + "emotion": "neutral", + "text": "How many chapters does the book have ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "There are 15 chapters in total .", + "emotion": "neutral", + "text": "There are 15 chapters in total .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "When do you think you ' ll have finished reading it ?", + "emotion": "neutral", + "text": "When do you think you ' ll have finished reading it ?", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "I should be done by Friday . I ' ll give it to you in class then .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 16 + ], + "expanded emotion cause span": [ + "It ' s great ! I ' Ve learned a lot from reading it .", + "I should be done by Friday ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I should be done by Friday . I ' ll give it to you in class then .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "Thanks . Charlie !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 16 + ], + "expanded emotion cause span": [ + "I should be done by Friday . I ' ll give it to you in class then ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks . Charlie !", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "No problem . Bob .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 17 + ], + "expanded emotion cause span": [ + "Thanks . Charlie !" + ], + "type": [ + "inter-personal" + ], + "text": "No problem . Bob .", + "id": 18, + "source_sentences": [ + 16 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3336.json b/reccon/sources/tr_3336.json new file mode 100644 index 0000000000000000000000000000000000000000..aefcfa610a9c6846abf5dd0e28ef90ec22a86c1c --- /dev/null +++ b/reccon/sources/tr_3336.json @@ -0,0 +1,197 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I'll always remember my college days .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "my college days" + ], + "type": [ + "no-context" + ], + "text": "I'll always remember my college days .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh yeah ?", + "emotion": "neutral", + "text": "Oh yeah ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "It was one of the best times in my life . It was tough , but I made it . I became a college graduate .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "my college days", + "It was one of the best times in my life . It was tough , but I made it . I became a college graduate ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "It was one of the best times in my life . It was tough , but I made it . I became a college graduate .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "How did you feel when you graduated ?", + "emotion": "neutral", + "text": "How did you feel when you graduated ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "It was a round day for me . My family attend the graduation ceremony . I was so nervous . I couldn't find my cap and gown , but all worked out in the end .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 5, + 5 + ], + "expanded emotion cause span": [ + "It was tough , but I made it . I became a college graduate .", + "My family attend the graduation ceremony .", + "all worked out in the end ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "It was a round day for me . My family attend the graduation ceremony . I was so nervous . I couldn't find my cap and gown , but all worked out in the end .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "What did you do after graduation ?", + "emotion": "neutral", + "text": "What did you do after graduation ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I was planning to attend gradate school , but then I was offered a good job doing marketing , so I changed my mind .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I was offered a good job doing marketing" + ], + "type": [ + "no-context" + ], + "text": "I was planning to attend gradate school , but then I was offered a good job doing marketing , so I changed my mind .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Sounds like you're happy with your decision .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "I was offered a good job doing marketing", + "you're happy with your decision ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Sounds like you're happy with your decision .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I sure am . So what about you ? How did you feel when you graduated ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8, + 9 + ], + "expanded emotion cause span": [ + "I was offered a good job doing marketing", + "you're happy with your decision .", + "I sure am ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I sure am . So what about you ? How did you feel when you graduated ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "It was also a proud day for me , but I also felt like a kind of loss that day .", + "emotion": "neutral", + "text": "It was also a proud day for me , but I also felt like a kind of loss that day .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "How could it be ?", + "emotion": "neutral", + "text": "How could it be ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "While seeing others going to work or continue their study , I didn't know what I would do .", + "emotion": "neutral", + "text": "While seeing others going to work or continue their study , I didn't know what I would do .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "You didn't have an offer ?", + "emotion": "neutral", + "text": "You didn't have an offer ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "I had one , but I didn't like the job very much . I wanted to attend graduate school , but I was afraid it would be too tough .", + "emotion": "neutral", + "text": "I had one , but I didn't like the job very much . I wanted to attend graduate school , but I was afraid it would be too tough .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "I think you lack in the power of decision . Once you make your decision , don't be overtaken by misgivings and fear . Just go full steam ahead !", + "emotion": "neutral", + "text": "I think you lack in the power of decision . Once you make your decision , don't be overtaken by misgivings and fear . Just go full steam ahead !", + "id": 15 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3342.json b/reccon/sources/tr_3342.json new file mode 100644 index 0000000000000000000000000000000000000000..5f982c077a37cfc9b754ec74c8672190d7b1ce77 --- /dev/null +++ b/reccon/sources/tr_3342.json @@ -0,0 +1,112 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I think that show biz stars have a really easy life . They have lots of money , so they can buy almost anything they want . They ' re famous , so everyone loves them .", + "emotion": "neutral", + "text": "I think that show biz stars have a really easy life . They have lots of money , so they can buy almost anything they want . They ' re famous , so everyone loves them .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I think they must have horrible lives . All the paparazzi take photos of them wherever they go and whatever they do . They must get sick of it .", + "emotion": "neutral", + "text": "I think they must have horrible lives . All the paparazzi take photos of them wherever they go and whatever they do . They must get sick of it .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I bet they love it really . Sure , they complain about it , but that just gets them more publicity , doesn ' t it ?", + "emotion": "neutral", + "text": "I bet they love it really . Sure , they complain about it , but that just gets them more publicity , doesn ' t it ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I think that few of the show biz stars want any publicity for themselves . They only want it for their films .", + "emotion": "neutral", + "text": "I think that few of the show biz stars want any publicity for themselves . They only want it for their films .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "No way ! They want publicity for themselves , so that they get invited to make more films , go to lots of cocktail parties , and even make albums ! They have such an easy life . They don ' t even pay for Drin", + "emotion": "anger", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "I think that few of the show biz stars want any publicity for themselves . They only want it for their films .", + "No way ! They want publicity for themselves , so that they get invited to make more films , go to lots of cocktail parties , and even make albums ! They have such an easy life . They don ' t even pay for Drin" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "No way ! They want publicity for themselves , so that they get invited to make more films , go to lots of cocktail parties , and even make albums ! They have such an easy life . They don ' t even pay for Drin", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Show biz stars have plenty of expenses . That ' s why they need so much money . They need million of dollars to buy big , seclude houses and wonderful dresses . I bet most show biz stars would prefer to Wea", + "emotion": "neutral", + "text": "Show biz stars have plenty of expenses . That ' s why they need so much money . They need million of dollars to buy big , seclude houses and wonderful dresses . I bet most show biz stars would prefer to Wea", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I don ' t understand how you can have any sympathy for show biz stars . They ' re overpaid , over-ambitious , and over-adored .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "you can have any sympathy for show biz stars . They ' re overpaid , over-ambitious , and over-adored ." + ], + "type": [ + "no-context" + ], + "text": "I don ' t understand how you can have any sympathy for show biz stars . They ' re overpaid , over-ambitious , and over-adored .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I think you should give them some credit . They ' re very talented people and they deserve all the money they earn . They even donate money to charity to help people who are less fortunate than themselves", + "emotion": "neutral", + "text": "I think you should give them some credit . They ' re very talented people and they deserve all the money they earn . They even donate money to charity to help people who are less fortunate than themselves", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Come on ! They only do that to get even more publicity for their films and themselves .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "I think you should give them some credit .", + "They only do that to get even more publicity for their films and themselves ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Come on ! They only do that to get even more publicity for their films and themselves .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3350.json b/reccon/sources/tr_3350.json new file mode 100644 index 0000000000000000000000000000000000000000..96d019099ca36c3f9e6f1203adb39353aab75694 --- /dev/null +++ b/reccon/sources/tr_3350.json @@ -0,0 +1,239 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "This is tough to say , Jordan , but I think we should break up .", + "emotion": "neutral", + "text": "This is tough to say , Jordan , but I think we should break up .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Are you serious ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I think we should break up ." + ], + "type": [ + "inter-personal" + ], + "text": "Are you serious ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yes , I mean it .", + "emotion": "neutral", + "text": "Yes , I mean it .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "But why ? Did I do anything wrong ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "I think we should break up .", + "Yes , I mean it ." + ], + "type": [ + "inter-personal" + ], + "text": "But why ? Did I do anything wrong ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "No , we are just too different . This isn ' t working .", + "emotion": "neutral", + "text": "No , we are just too different . This isn ' t working .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Hey , come on . It ' s too early to say that . We can fix things .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "This isn ' t working ." + ], + "type": [ + "inter-personal" + ], + "text": "Hey , come on . It ' s too early to say that . We can fix things .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I have thought about it for a while . I think it ' s time to move on for both of us .", + "emotion": "neutral", + "text": "I have thought about it for a while . I think it ' s time to move on for both of us .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "But I still love you .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 5, + 7, + 8 + ], + "expanded emotion cause span": [ + "This isn ' t working .", + "it ' s time to move on for both of us .", + "But I still love you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "But I still love you .", + "id": 8, + "source_sentences": [ + 4, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I ' m sorry .", + "emotion": "neutral", + "text": "I ' m sorry .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I knew this would happen some day ...", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 5, + 7, + 8 + ], + "expanded emotion cause span": [ + "This isn ' t working .", + "it ' s time to move on for both of us .", + "But I still love you ." + ], + "type": [ + "hybrid" + ], + "text": "I knew this would happen some day ...", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Then why didn ' t you talk to me ?", + "emotion": "neutral", + "text": "Then why didn ' t you talk to me ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Well . It ' s not all my fault , Anna ...", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 5, + 7, + 8 + ], + "expanded emotion cause span": [ + "This isn ' t working .", + "it ' s time to move on for both of us .", + "But I still love you ." + ], + "type": [ + "hybrid" + ], + "text": "Well . It ' s not all my fault , Anna ...", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I don't want to argue with you anymore . This is going to be tough , but Let ' s try and be friends .", + "emotion": "neutral", + "text": "I don't want to argue with you anymore . This is going to be tough , but Let ' s try and be friends .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "I would like that Anna , but I think I ' ll need a little space for a bit .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 5, + 7, + 8 + ], + "expanded emotion cause span": [ + "This isn ' t working .", + "it ' s time to move on for both of us .", + "But I still love you ." + ], + "type": [ + "hybrid" + ], + "text": "I would like that Anna , but I think I ' ll need a little space for a bit .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "I think we ' ll be better off if we are apart .", + "emotion": "neutral", + "text": "I think we ' ll be better off if we are apart .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Shall we keep pur friendship ?", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 5, + 7, + 8 + ], + "expanded emotion cause span": [ + "This isn ' t working .", + "it ' s time to move on for both of us .", + "But I still love you ." + ], + "type": [ + "hybrid" + ], + "text": "Shall we keep pur friendship ?", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "Sure , let ' s just be friends .", + "emotion": "neutral", + "text": "Sure , let ' s just be friends .", + "id": 17 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3354.json b/reccon/sources/tr_3354.json new file mode 100644 index 0000000000000000000000000000000000000000..bd7bcf36f671e72732530092cd0d28ada053e335 --- /dev/null +++ b/reccon/sources/tr_3354.json @@ -0,0 +1,131 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "You don't look too well . What's going on ?", + "emotion": "neutral", + "text": "You don't look too well . What's going on ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I just lost my job . I'm just worried about how I'm going to pay the bills .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I just lost my job . I'm just worried about how I'm going to pay the bills ." + ], + "type": [ + "no-context" + ], + "text": "I just lost my job . I'm just worried about how I'm going to pay the bills .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I'm sorry to hear that . Have you been looking for another job ?", + "emotion": "neutral", + "text": "I'm sorry to hear that . Have you been looking for another job ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I just started , but the job market is very bad right now . I'm not optimistic about it .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2, + 4, + 4 + ], + "expanded emotion cause span": [ + "I just lost my job . I'm just worried about how I'm going to pay the bills .", + "the job market is very bad", + "I'm not optimistic about it ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I just started , but the job market is very bad right now . I'm not optimistic about it .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "That's tough . What does your wife think about this ?", + "emotion": "neutral", + "text": "That's tough . What does your wife think about this ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "She's trying to be supportive , but I can tell she is very worried about our financial situation as well .", + "emotion": "neutral", + "text": "She's trying to be supportive , but I can tell she is very worried about our financial situation as well .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I have some friends who might be able to help you find a job . I'll see what they can do .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I have some friends who might be able to help you find a job ." + ], + "type": [ + "no-context" + ], + "text": "I have some friends who might be able to help you find a job . I'll see what they can do .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I really appreciate your help .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I have some friends who might be able to help you find a job . I'll see what they can do ." + ], + "type": [ + "inter-personal" + ], + "text": "I really appreciate your help .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "No problem . In the meantime , don't try to worry so much . You'll get through this .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "I have some friends who might be able to help you find a job .", + "I really appreciate your help ." + ], + "type": [ + "hybrid" + ], + "text": "No problem . In the meantime , don't try to worry so much . You'll get through this .", + "id": 9 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3357.json b/reccon/sources/tr_3357.json new file mode 100644 index 0000000000000000000000000000000000000000..3c27ddf1e0fcd92fbec14beb45799f413d86859a --- /dev/null +++ b/reccon/sources/tr_3357.json @@ -0,0 +1,149 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "This is how a holiday should be . Relaxing on the beach with a nice cool drink .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Relaxing on the beach with a nice cool drink ." + ], + "type": [ + "no-context" + ], + "text": "This is how a holiday should be . Relaxing on the beach with a nice cool drink .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Isn ' t it wonderful here ? The kids are enjoying themselves in the swimming pool . I hope it ' s safe .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "Relaxing on the beach with a nice cool drink .", + "The kids are enjoying themselves in the swimming pool ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Isn ' t it wonderful here ? The kids are enjoying themselves in the swimming pool . I hope it ' s safe .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Don ' t worry about them . They ' re very responsible . Besides , there are many people there and there ' s lifeguard employed by the hotel . Waiter ! Could I have another drink pleas ? Thank you . So , what shall we do this evening ?", + "emotion": "happiness", + "explanation": "Speaker and listener are happy about relaxing in the beach", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "Relaxing on the beach with a nice cool drink .", + "what shall we do this evening ?" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Don ' t worry about them . They ' re very responsible . Besides , there are many people there and there ' s lifeguard employed by the hotel . Waiter ! Could I have another drink pleas ? Thank you . So , what shall we do this evening ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "The kids said that they wanted to go to a party at the hotel . There ' s a special one just for kids .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Relaxing on the beach with a nice cool drink ." + ], + "type": [ + "inter-personal" + ], + "text": "The kids said that they wanted to go to a party at the hotel . There ' s a special one just for kids .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "So , we could try that restaurant that was recommended in the guidebook . Then we could go to a club . We haven ' t been to one for ages .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 5 + ], + "expanded emotion cause span": [ + "Relaxing on the beach with a nice cool drink .", + "we could try that restaurant that was recommended in the guidebook . Then we could go to a club . We haven ' t been to one for ages ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "So , we could try that restaurant that was recommended in the guidebook . Then we could go to a club . We haven ' t been to one for ages .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "That ' s a great idea . We can really enjoy ourselves without worrying about the kids .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 5, + 6 + ], + "expanded emotion cause span": [ + "Relaxing on the beach with a nice cool drink .", + "we could try that restaurant that was recommended in the guidebook . Then we could go to a club . We haven ' t been to one for ages .", + "We can really enjoy ourselves without worrying about the kids ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That ' s a great idea . We can really enjoy ourselves without worrying about the kids .", + "id": 6, + "source_sentences": [ + 0, + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Now , how about going for a swim in the sea ? We shouldn ' t sunbathe all day .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 5, + 6, + 7 + ], + "expanded emotion cause span": [ + "Relaxing on the beach with a nice cool drink .", + "we could try that restaurant that was recommended in the guidebook . Then we could go to a club . We haven ' t been to one for ages .", + "We can really enjoy ourselves without worrying about the kids .", + "how about going for a swim in the sea ?" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Now , how about going for a swim in the sea ? We shouldn ' t sunbathe all day .", + "id": 7 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3365.json b/reccon/sources/tr_3365.json new file mode 100644 index 0000000000000000000000000000000000000000..d9a3dc9c3b0255d23720dd7d556c4ca5a3254cbe --- /dev/null +++ b/reccon/sources/tr_3365.json @@ -0,0 +1,166 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "An interesting meeting , isn't it ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "interesting meeting" + ], + "type": [ + "no-context" + ], + "text": "An interesting meeting , isn't it ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , very . I thought the last speaker was especially good .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "interesting meeting", + "Yes , very . I thought the last speaker was especially good ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , very . I thought the last speaker was especially good .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Let me introduce myself , by the way . My name's Thomas Bradley .", + "emotion": "neutral", + "text": "Let me introduce myself , by the way . My name's Thomas Bradley .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "How do you do ? I'm Ted Nugent .", + "emotion": "neutral", + "text": "How do you do ? I'm Ted Nugent .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Sorry , what was your last name again ?", + "emotion": "neutral", + "text": "Sorry , what was your last name again ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "It's Nugent , N-U-G-E-N-T , but just call me Ted .", + "emotion": "neutral", + "text": "It's Nugent , N-U-G-E-N-T , but just call me Ted .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Ok , I'm Tom .", + "emotion": "neutral", + "text": "Ok , I'm Tom .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Glad to meet you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "meet you ." + ], + "type": [ + "no-context" + ], + "text": "Glad to meet you .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "And what do you do , Ted ?", + "emotion": "neutral", + "text": "And what do you do , Ted ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Me ? I'm in the car business .", + "emotion": "neutral", + "text": "Me ? I'm in the car business .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Salesman ?", + "emotion": "neutral", + "text": "Salesman ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Yes , that's right . And how about you ?", + "emotion": "neutral", + "text": "Yes , that's right . And how about you ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I work for American Airlines .", + "emotion": "neutral", + "text": "I work for American Airlines .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Oh , really ? What do you do there exactly ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "I work for American Airlines ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , really ? What do you do there exactly ?", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 15, + "speaker": "A", + "utterance": "I'm in the Personnel Department .", + "emotion": "neutral", + "text": "I'm in the Personnel Department .", + "id": 15 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3376.json b/reccon/sources/tr_3376.json new file mode 100644 index 0000000000000000000000000000000000000000..9a03efae2470dcf637bb4adb573aa70b13d71384 --- /dev/null +++ b/reccon/sources/tr_3376.json @@ -0,0 +1,110 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Can we have dinner together sometime this weekend ?", + "emotion": "happiness", + "explanation": "they want to have dinner together", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Can we have dinner together sometime this weekend ?" + ], + "type": [ + "no-context" + ], + "text": "Can we have dinner together sometime this weekend ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Ok , you name the day .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Can we have dinner together sometime this weekend ?" + ], + "type": [ + "inter-personal" + ], + "text": "Ok , you name the day .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "How about the second of March ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Can we have dinner together sometime this weekend ?" + ], + "type": [ + "self-contagion" + ], + "text": "How about the second of March ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "What day is that ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Can we have dinner together sometime this weekend ?" + ], + "type": [ + "inter-personal" + ], + "text": "What day is that ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "It's Friday .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Can we have dinner together sometime this weekend ?" + ], + "type": [ + "self-contagion" + ], + "text": "It's Friday .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Good . Where shall we meet ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Can we have dinner together sometime this weekend ?" + ], + "type": [ + "inter-personal" + ], + "text": "Good . Where shall we meet ?", + "id": 6, + "source_sentences": [ + 0 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3386.json b/reccon/sources/tr_3386.json new file mode 100644 index 0000000000000000000000000000000000000000..05c8b82bc6b6b55d90979fca3b1c377d8c217302 --- /dev/null +++ b/reccon/sources/tr_3386.json @@ -0,0 +1,208 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , I'm Lucas , I just moved in next door .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Hi , I'm Lucas , I just moved in next door .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh , hi Lucas , come on in . I'm Barbara . Nice to meet you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Nice to meet you ." + ], + "type": [ + "no-context" + ], + "text": "Oh , hi Lucas , come on in . I'm Barbara . Nice to meet you .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Nice to meet you too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Nice to meet you ." + ], + "type": [ + "inter-personal" + ], + "text": "Nice to meet you too .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Would you like something to drink ? I've got tea and some grape juice .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Nice to meet you ." + ], + "type": [ + "self-contagion" + ], + "text": "Would you like something to drink ? I've got tea and some grape juice .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Thanks . Some tea would be nice . Chinese tea is great . I really like your tea set . Where did you get it ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "Would you like something to drink ? I've got tea", + "I really like your tea set" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thanks . Some tea would be nice . Chinese tea is great . I really like your tea set . Where did you get it ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Oh , there is a supermarket not far from here . But there is also a tea house around the corner , where you can get tea , taste tea and get a tea set as well .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I really like your tea set" + ], + "type": [ + "inter-personal" + ], + "text": "Oh , there is a supermarket not far from here . But there is also a tea house around the corner , where you can get tea , taste tea and get a tea set as well .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Oh yeah , I saw the tea house the other day . I think I might go and have a look sometime . It's a nice neighborhood here .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5, + 7 + ], + "expanded emotion cause span": [ + "Would you like something to drink ? I've got tea", + "I really like your tea set", + "It's a nice neighborhood here ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Oh yeah , I saw the tea house the other day . I think I might go and have a look sometime . It's a nice neighborhood here .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "You are right about that . It's quiet and very convenient . You can get to the bus and the subway stations within ten minutes ' walk . There's a grocery store , a book store , a gym , and many restaurants along the street .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "It's a nice neighborhood here .", + "It's quiet and very convenient ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You are right about that . It's quiet and very convenient . You can get to the bus and the subway stations within ten minutes ' walk . There's a grocery store , a book store , a gym , and many restaurants along the street .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "There's a gym nearby ? That's exciting ! I really want to start to go to gym as soon as possible . I've been lazy this summer holiday and have put on some weight .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "a gym", + "I really want to start to go to gym as soon as possible ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "There's a gym nearby ? That's exciting ! I really want to start to go to gym as soon as possible . I've been lazy this summer holiday and have put on some weight .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Well , if you want we can go together sometime . Actually I was thinking of going this afternoon , if you like , you can join me and I can show you the neighborhood along the way .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "That's exciting ! I really want to start to go to gym as soon as possible ." + ], + "type": [ + "inter-personal" + ], + "text": "Well , if you want we can go together sometime . Actually I was thinking of going this afternoon , if you like , you can join me and I can show you the neighborhood along the way .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "That would be wonderful . Thanks !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Well , if you want we can go together sometime . Actually I was thinking of going this afternoon , if you like , you can join me and I can show you the neighborhood along the way ." + ], + "type": [ + "inter-personal" + ], + "text": "That would be wonderful . Thanks !", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3400.json b/reccon/sources/tr_3400.json new file mode 100644 index 0000000000000000000000000000000000000000..f0905711f7299701cdac1c6a55eca899f535dd49 --- /dev/null +++ b/reccon/sources/tr_3400.json @@ -0,0 +1,162 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey , Robert , what are you doing this weekend ?", + "emotion": "neutral", + "text": "Hey , Robert , what are you doing this weekend ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I didn't have any big plans .", + "emotion": "neutral", + "text": "I didn't have any big plans .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "We are putting together a birthday party for Mary .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "We are putting together a birthday party for Mary ." + ], + "type": [ + "no-context" + ], + "text": "We are putting together a birthday party for Mary .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "That sounds like fun . Where will it be ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "We are putting together a birthday party for Mary ." + ], + "type": [ + "inter-personal" + ], + "text": "That sounds like fun . Where will it be ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "We thought it would be fun to have a pool party at Jay's house .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "We are putting together a birthday party for Mary ." + ], + "type": [ + "self-contagion" + ], + "text": "We thought it would be fun to have a pool party at Jay's house .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Oh good ! Can I bring anything ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "We thought it would be fun to have a pool party at Jay's house ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh good ! Can I bring anything ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "We will be providing hot dogs , hamburgers , and cake , but people can bring side dishes .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "We are putting together a birthday party for Mary ." + ], + "type": [ + "self-contagion" + ], + "text": "We will be providing hot dogs , hamburgers , and cake , but people can bring side dishes .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I am assuming that the dress is casual .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "We thought it would be fun to have a pool party at Jay's house ." + ], + "type": [ + "inter-personal" + ], + "text": "I am assuming that the dress is casual .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Dress casually and bring your bathing suit !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "We are putting together a birthday party for Mary ." + ], + "type": [ + "self-contagion" + ], + "text": "Dress casually and bring your bathing suit !", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Wonderful . Just e-mail me the time and date and I'll be there .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 9 + ], + "expanded emotion cause span": [ + "We thought it would be fun to have a pool party at Jay's house .", + "Dress casually and bring your bathing suit !" + ], + "type": [ + "inter-personal" + ], + "text": "Wonderful . Just e-mail me the time and date and I'll be there .", + "id": 10, + "source_sentences": [ + 4, + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3404.json b/reccon/sources/tr_3404.json new file mode 100644 index 0000000000000000000000000000000000000000..b826e486c5decb68a880a7eb732a2c4591107af4 --- /dev/null +++ b/reccon/sources/tr_3404.json @@ -0,0 +1,186 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Good morning Mike !", + "emotion": "neutral", + "text": "Good morning Mike !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Morning Sally ! What's up ? you seem in a hurry !", + "emotion": "neutral", + "text": "Morning Sally ! What's up ? you seem in a hurry !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I am having an exam at nine , It's already eight thirty .", + "emotion": "neutral", + "text": "I am having an exam at nine , It's already eight thirty .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Don't worry , I'll drive you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Don't worry , I'll drive you ." + ], + "type": [ + "no-context" + ], + "text": "Don't worry , I'll drive you .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Thank you very much !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Don't worry , I'll drive you ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you very much !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "How are your cases coming along ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Don't worry , I'll drive you ." + ], + "type": [ + "self-contagion" + ], + "text": "How are your cases coming along ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Very well , thanks , I will probably finish next week , but this is still a lot of work , I have been worked on in for six months , and i ' m so closed to end . I can feel it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Very well , thanks , I will probably finish next week" + ], + "type": [ + "no-context" + ], + "text": "Very well , thanks , I will probably finish next week , but this is still a lot of work , I have been worked on in for six months , and i ' m so closed to end . I can feel it .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Wow , Good for you . It sounds like a lot of work . I'm proud of you ! Is this the right building ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8, + 8 + ], + "expanded emotion cause span": [ + "Very well , thanks , I will probably finish next week", + "Wow , Good for you .", + "I'm proud of you !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Wow , Good for you . It sounds like a lot of work . I'm proud of you ! Is this the right building ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yes , It's only eight forty . Thanks so much !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 9 + ], + "expanded emotion cause span": [ + "I am having an exam at nine ,", + "It's only eight forty ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Yes , It's only eight forty . Thanks so much !", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "You're welcome . Good luck , bye !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 9, + 9 + ], + "expanded emotion cause span": [ + "I am having an exam at nine ,", + "It's only eight forty .", + "Thanks so much !" + ], + "type": [ + "inter-personal" + ], + "text": "You're welcome . Good luck , bye !", + "id": 10, + "source_sentences": [ + 2, + 8, + 8 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Have a nice day , bye !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 9, + 10 + ], + "expanded emotion cause span": [ + "I am having an exam at nine ,", + "It's only eight forty .", + "Good luck ," + ], + "type": [ + "hybrid" + ], + "text": "Have a nice day , bye !", + "id": 11 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3405.json b/reccon/sources/tr_3405.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c414571b9703608839ed75a2876ab4a381714 --- /dev/null +++ b/reccon/sources/tr_3405.json @@ -0,0 +1,118 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Oh , Mary , come in , please . I'm so happy to see you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I'm so happy to see you ." + ], + "type": [ + "no-context" + ], + "text": "Oh , Mary , come in , please . I'm so happy to see you .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Happy birthday , George . Many happy returns of the day . Here's a present for you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "I'm so happy to see you .", + "Happy birthday , George . Many happy returns of the day . Here's a present for you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Happy birthday , George . Many happy returns of the day . Here's a present for you .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Oh , thank you , Mary . You're so nice .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "I'm so happy to see you .", + "Happy birthday , George . Many happy returns of the day . Here's a present for you ." + ], + "type": [ + "hybrid" + ], + "text": "Oh , thank you , Mary . You're so nice .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I hope you like it . Oh , have the other guys arrived ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "thank you , Mary . You're so nice ." + ], + "type": [ + "inter-personal" + ], + "text": "I hope you like it . Oh , have the other guys arrived ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "They're all waiting for you . Let's join them . I'm going to cut the cake soon .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "I hope you like it .", + "I'm going to cut the cake soon ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "They're all waiting for you . Let's join them . I'm going to cut the cake soon .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Let's go .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "They're all waiting for you . Let's join them . I'm going to cut the cake soon ." + ], + "type": [ + "inter-personal" + ], + "text": "Let's go .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3410.json b/reccon/sources/tr_3410.json new file mode 100644 index 0000000000000000000000000000000000000000..fe050f7e3b5175e857dbdc24727f051b7edea9f1 --- /dev/null +++ b/reccon/sources/tr_3410.json @@ -0,0 +1,139 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Julia , why have you prepared a candlelight dinner ? Anything special to celebrate ? Did you get a promotion ?", + "emotion": "neutral", + "text": "Julia , why have you prepared a candlelight dinner ? Anything special to celebrate ? Did you get a promotion ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Honey , don't tell me that you forgot our anniversary , did you ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "Julia , why have you prepared a candlelight dinner ? Anything special to celebrate ? Did you get a promotion ?", + "you forgot our anniversary" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Honey , don't tell me that you forgot our anniversary , did you ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Oh , my dear , how can I forget such an important day ? I was just kidding . Look at this box .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3, + 3 + ], + "expanded emotion cause span": [ + "anniversary", + "such an important day", + "I was just kidding ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , my dear , how can I forget such an important day ? I was just kidding . Look at this box .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "What's in it ?", + "emotion": "neutral", + "text": "What's in it ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Have a guess .", + "emotion": "neutral", + "text": "Have a guess .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "A necklace ?", + "emotion": "neutral", + "text": "A necklace ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "No .", + "emotion": "neutral", + "text": "No .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I have no idea .", + "emotion": "neutral", + "text": "I have no idea .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Open it now .", + "emotion": "neutral", + "text": "Open it now .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Oh , my god . A diamond brooch . It's so beautiful . You're so kind to me , A . Thank you !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "A diamond brooch . It's so beautiful ." + ], + "type": [ + "no-context" + ], + "text": "Oh , my god . A diamond brooch . It's so beautiful . You're so kind to me , A . Thank you !", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "You're welcome , honey . I hope we will celebrate our golden wedding anniversary in future .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "It's so beautiful . You're so kind to me , A . Thank you !" + ], + "type": [ + "inter-personal" + ], + "text": "You're welcome , honey . I hope we will celebrate our golden wedding anniversary in future .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3421.json b/reccon/sources/tr_3421.json new file mode 100644 index 0000000000000000000000000000000000000000..468a64408bafae71314713e1f56163a03c6024d8 --- /dev/null +++ b/reccon/sources/tr_3421.json @@ -0,0 +1,236 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey Lucas , how was your trip to Paris ?", + "emotion": "happiness", + "explanation": "the speaker is excited to hear about B's trip to Paris", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "your trip to Paris" + ], + "type": [ + "no-context" + ], + "text": "Hey Lucas , how was your trip to Paris ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It was wonderful , but I was so tired .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "your trip to Paris", + "It was wonderful" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It was wonderful , but I was so tired .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Did you go to the top of the Eiffel Tower .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 3 + ], + "expanded emotion cause span": [ + "your trip to Paris", + "It was wonderful", + "top of the Eiffel Tower" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Did you go to the top of the Eiffel Tower .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes , that was the first thing we did . We went all the way to the top . There were visitorsfrom all over the world taking photos there .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "top of the Eiffel Tower", + "Yes , that was the first thing we did . We went all the way to the top ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , that was the first thing we did . We went all the way to the top . There were visitorsfrom all over the world taking photos there .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "What else did you see ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "What else did you see ?" + ], + "type": [ + "no-context" + ], + "text": "What else did you see ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Art galleries , cathedrals , statues , fountains , palaces , bistros , there's really too much to say .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Art galleries , cathedrals , statues , fountains , palaces , bistros , there's really too much to say ." + ], + "type": [ + "no-context" + ], + "text": "Art galleries , cathedrals , statues , fountains , palaces , bistros , there's really too much to say .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You must have had a great time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "Art galleries , cathedrals , statues , fountains , palaces , bistros , there's really too much to say .", + "You must have had a great time ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You must have had a great time .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yes , at the beginning we were all excited and had lots of fun . However , on the third day of travelling in the city , I felt sick I think I had something bad to eat but it passed by the evening .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 8 + ], + "expanded emotion cause span": [ + "Art galleries , cathedrals , statues , fountains , palaces , bistros , there's really too much to say .", + "Yes , at the beginning we were all excited and had lots of fun ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Yes , at the beginning we were all excited and had lots of fun . However , on the third day of travelling in the city , I felt sick I think I had something bad to eat but it passed by the evening .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yes . you need to be careful with what you eat when you're abroad . sometimes new food might disagree with you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 8 + ], + "expanded emotion cause span": [ + "Art galleries , cathedrals , statues , fountains , palaces , bistros , there's really too much to say .", + "Yes , at the beginning we were all excited and had lots of fun ." + ], + "type": [ + "inter-personal" + ], + "text": "Yes . you need to be careful with what you eat when you're abroad . sometimes new food might disagree with you .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "On the fourth day , we went to taste the French cuisine . That was really fantastic . And no stomach problems .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "we went to taste the French cuisine . That was really fantastic . And no stomach problems ." + ], + "type": [ + "no-context" + ], + "text": "On the fourth day , we went to taste the French cuisine . That was really fantastic . And no stomach problems .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "That is great . Everyone says French food is wonderful .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "we went to taste the French cuisine . That was really fantastic . And no stomach problems .", + "Everyone says French food is wonderful ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That is great . Everyone says French food is wonderful .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "You'll have to try for yourself some day .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "we went to taste the French cuisine . That was really fantastic . And no stomach problems .", + "Everyone says French food is wonderful ." + ], + "type": [ + "hybrid" + ], + "text": "You'll have to try for yourself some day .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_343.json b/reccon/sources/tr_343.json new file mode 100644 index 0000000000000000000000000000000000000000..6bf893b6c48a9ccd04d0f6bd295f193ba0511e20 --- /dev/null +++ b/reccon/sources/tr_343.json @@ -0,0 +1,215 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi Mark .", + "emotion": "neutral", + "text": "Hi Mark .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hi .", + "emotion": "neutral", + "text": "Hi .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What are you planning to do today ?", + "emotion": "neutral", + "text": "What are you planning to do today ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I'm not sure yet .", + "emotion": "neutral", + "text": "I'm not sure yet .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Would you like to have lunch with me ?", + "emotion": "happiness", + "explanation": "Speaker is excited to have lunch with a friend", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Would you like to have lunch with me ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yes . When ?", + "emotion": "happiness", + "explanation": "Speaker is getting invited", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Would you like to have lunch with me ?" + ], + "type": [ + "inter-personal" + ], + "text": "Yes . When ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Is 11:30 AM OK ?", + "emotion": "neutral", + "text": "Is 11:30 AM OK ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Sorry , I didn't hear you . Can you say that again please ?", + "emotion": "neutral", + "text": "Sorry , I didn't hear you . Can you say that again please ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I said , 11:30 AM .", + "emotion": "neutral", + "text": "I said , 11:30 AM .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Oh , I'm busy then . Can we meet a little later ?", + "emotion": "neutral", + "text": "Oh , I'm busy then . Can we meet a little later ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "OK , how about 12:30 PM ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "OK , how about 12:30 PM ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "OK . Where ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Would you like to have lunch with me ?" + ], + "type": [ + "inter-personal" + ], + "text": "OK . Where ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "How about Bill's Seafood Restaurant ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "How about Bill's Seafood Restaurant ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Oh , Where is that ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Would you like to have lunch with me ?" + ], + "type": [ + "inter-personal" + ], + "text": "Oh , Where is that ?", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "It's on 7th Street .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "It's on 7th Street .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "OK , I'll meet you there .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Would you like to have lunch with me ?" + ], + "type": [ + "inter-personal" + ], + "text": "OK , I'll meet you there .", + "id": 16, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3441.json b/reccon/sources/tr_3441.json new file mode 100644 index 0000000000000000000000000000000000000000..1cd0baf3e23c37ab91b9e9fd2b9df5fc5ff8c7fa --- /dev/null +++ b/reccon/sources/tr_3441.json @@ -0,0 +1,143 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello . May I speak to Mary , please ?", + "emotion": "neutral", + "text": "Hello . May I speak to Mary , please ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Speaking . Who's calling , please ?", + "emotion": "neutral", + "text": "Speaking . Who's calling , please ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Hi , Mary . This is Tom .", + "emotion": "neutral", + "text": "Hi , Mary . This is Tom .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Oh , hi , Tom . How've you been ?", + "emotion": "neutral", + "text": "Oh , hi , Tom . How've you been ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Just fine . I say . Aren't you busy tomorrow evening ?", + "emotion": "neutral", + "text": "Just fine . I say . Aren't you busy tomorrow evening ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Let me see . Uh-huh ... no , I guess I'll be free .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I guess I'll be free ." + ], + "type": [ + "no-context" + ], + "text": "Let me see . Uh-huh ... no , I guess I'll be free .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Well , uh ... why not dine out together and go to the movies ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I guess I'll be free .", + "dine out together and go to the movies ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Well , uh ... why not dine out together and go to the movies ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Sounds like a good idea .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "dine out together and go to the movies ?" + ], + "type": [ + "inter-personal" + ], + "text": "Sounds like a good idea .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Okay . I'll pick you up at 6:00 .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "dine out together and go to the movies ?", + "Sounds like a good idea ." + ], + "type": [ + "hybrid" + ], + "text": "Okay . I'll pick you up at 6:00 .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Thank you for inviting me . See you then . Bye , Tom .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 9, + 10 + ], + "expanded emotion cause span": [ + "dine out together and go to the movies ?", + "I'll pick you up at 6:00 .", + "Thank you for inviting me . See you then ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you for inviting me . See you then . Bye , Tom .", + "id": 10, + "source_sentences": [ + 6, + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_345.json b/reccon/sources/tr_345.json new file mode 100644 index 0000000000000000000000000000000000000000..12f7b0851cc4f86f8c8d3a65858c396571276587 --- /dev/null +++ b/reccon/sources/tr_345.json @@ -0,0 +1,125 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , Monica , congratulations ! Your presentation at the meeting was very successful and everyone was impressed by your speech . And it was so persuasive and I bet our clients will be convinced to invest their money in this project . You really made a big contribution to our company .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "congratulations ! Your presentation at the meeting was very successful and everyone was impressed by your speech . And it was so persuasive and I bet our clients will be convinced to invest their money in this project . You really made a big contribution to our company ." + ], + "type": [ + "no-context" + ], + "text": "Hi , Monica , congratulations ! Your presentation at the meeting was very successful and everyone was impressed by your speech . And it was so persuasive and I bet our clients will be convinced to invest their money in this project . You really made a big contribution to our company .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Thank you , I just tried my best . I am very happy to know you like it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "congratulations ! Your presentation at the meeting was very successful and everyone was impressed by your speech . And it was so persuasive and I bet our clients will be convinced to invest their money in this project . You really made a big contribution to our company .", + "I just tried my best . I am very happy to know you like it ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you , I just tried my best . I am very happy to know you like it .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "You must have been prepared for a long time . Some statistics in this presentation are not easy to find , right ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "congratulations ! Your presentation at the meeting was very successful and everyone was impressed by your speech . And it was so persuasive and I bet our clients will be convinced to invest their money in this project . You really made a big contribution to our company .", + "I just tried my best . I am very happy to know you like it ." + ], + "type": [ + "hybrid" + ], + "text": "You must have been prepared for a long time . Some statistics in this presentation are not easy to find , right ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Well , yes . Several colleagues from different departments helped me with that . They are very supportive . I consulted an economic expert last week . He was very kind to give valuable suggestions .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 3, + 4 + ], + "expanded emotion cause span": [ + "congratulations ! Your presentation at the meeting was very successful and everyone was impressed by your speech . And it was so persuasive and I bet our clients will be convinced to invest their money in this project . You really made a big contribution to our company .", + "I just tried my best . I am very happy to know you like it .", + "You must have been prepared for a long time . Some statistics in this presentation are not easy to find", + "Several colleagues from different departments helped me with that . They are very supportive . I consulted an economic expert last week . He was very kind to give valuable suggestions ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Well , yes . Several colleagues from different departments helped me with that . They are very supportive . I consulted an economic expert last week . He was very kind to give valuable suggestions .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Now , the effort pays off . You have accomplished something .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "the effort pays off . You have accomplished something ." + ], + "type": [ + "no-context" + ], + "text": "Now , the effort pays off . You have accomplished something .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Come on , don ' t flatter me anymore . I took the job because I love being challenged . But I can ' t get this turned around without the support from you people .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "the effort pays off . You have accomplished something .", + "I took the job because I love being challenged . But I can ' t get this turned around without the support from you people ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Come on , don ' t flatter me anymore . I took the job because I love being challenged . But I can ' t get this turned around without the support from you people .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3457.json b/reccon/sources/tr_3457.json new file mode 100644 index 0000000000000000000000000000000000000000..f307441249672c4579e9838515a32cfbbde4dc39 --- /dev/null +++ b/reccon/sources/tr_3457.json @@ -0,0 +1,317 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I have some good news for you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I have some good news" + ], + "type": [ + "no-context" + ], + "text": "I have some good news for you .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What's that ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I have some good news" + ], + "type": [ + "inter-personal" + ], + "text": "What's that ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Jenny is getting married .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Jenny is getting married ." + ], + "type": [ + "no-context" + ], + "text": "Jenny is getting married .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Great ! Who's the bridegroom ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Jenny is getting married ." + ], + "type": [ + "inter-personal" + ], + "text": "Great ! Who's the bridegroom ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Tom , that lucky guy .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Tom , that lucky guy ." + ], + "type": [ + "no-context" + ], + "text": "Tom , that lucky guy .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "The guy always hands the girls in a line . When did he propose ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Tom , that lucky guy ." + ], + "type": [ + "inter-personal" + ], + "text": "The guy always hands the girls in a line . When did he propose ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Last week , It said that he fell in love with Jenny at Mrs . Whit ' s party last Monday as soon as he saw her .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Last week , It said that he fell in love with Jenny at Mrs . Whit ' s party last Monday as soon as he saw her ." + ], + "type": [ + "no-context" + ], + "text": "Last week , It said that he fell in love with Jenny at Mrs . Whit ' s party last Monday as soon as he saw her .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "My gosh ! How romantic ! When's the big day ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "My gosh ! How romantic ! When's the big day ?" + ], + "type": [ + "no-context" + ], + "text": "My gosh ! How romantic ! When's the big day ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "July 4 , the National Holiday .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Jenny is getting married ." + ], + "type": [ + "self-contagion" + ], + "text": "July 4 , the National Holiday .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Will it be a church wedding or a civil ceremony ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Jenny is getting married ." + ], + "type": [ + "inter-personal" + ], + "text": "Will it be a church wedding or a civil ceremony ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Jenny plans to hold it in church .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Jenny is getting married ." + ], + "type": [ + "self-contagion" + ], + "text": "Jenny plans to hold it in church .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Who is the best man ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Jenny is getting married ." + ], + "type": [ + "inter-personal" + ], + "text": "Who is the best man ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Guess !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 12 + ], + "expanded emotion cause span": [ + "Jenny is getting married .", + "Who is the best man ?" + ], + "type": [ + "hybrid" + ], + "text": "Guess !", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Nobody is OK , but you !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 14 + ], + "expanded emotion cause span": [ + "Jenny is getting married .", + "Nobody is OK , but you !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Nobody is OK , but you !", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "You know , Tom is my best friend and he asked me to be his best man .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14, + 15 + ], + "expanded emotion cause span": [ + "Nobody is OK , but you !", + "Tom is my best friend and he asked me to be his best man ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You know , Tom is my best friend and he asked me to be his best man .", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Did you promise him ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14, + 15, + 16 + ], + "expanded emotion cause span": [ + "Nobody is OK , but you !", + "Tom is my best friend and he asked me to be his best man .", + "promise him" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Did you promise him ?", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "Yes , I did .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14, + 15, + 16 + ], + "expanded emotion cause span": [ + "Nobody is OK , but you !", + "Tom is my best friend and he asked me to be his best man .", + "promise him" + ], + "type": [ + "hybrid" + ], + "text": "Yes , I did .", + "id": 17 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3474.json b/reccon/sources/tr_3474.json new file mode 100644 index 0000000000000000000000000000000000000000..01cac2268401c3b30cc2526117a3ac8a25e91fc4 --- /dev/null +++ b/reccon/sources/tr_3474.json @@ -0,0 +1,123 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Good afternoon , Sam .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Good afternoon , Sam ." + ], + "type": [ + "no-context" + ], + "text": "Good afternoon , Sam .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Good afternoon , Tina .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Good afternoon , Tina ." + ], + "type": [ + "no-context" + ], + "text": "Good afternoon , Tina .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What are you going to do tomorrow ?", + "emotion": "neutral", + "text": "What are you going to do tomorrow ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I'm not sure yet . And you ?", + "emotion": "neutral", + "text": "I'm not sure yet . And you ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I would like to go skating . Feel like going with me ?", + "emotion": "neutral", + "text": "I would like to go skating . Feel like going with me ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Is skating interesting ?", + "emotion": "neutral", + "text": "Is skating interesting ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I think so . Fresh air , white snow . It's so comfortable .", + "emotion": "neutral", + "text": "I think so . Fresh air , white snow . It's so comfortable .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "But I can't skate well .", + "emotion": "neutral", + "text": "But I can't skate well .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "It doesn't matter , I can teach you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "I can teach you ." + ], + "type": [ + "no-context" + ], + "text": "It doesn't matter , I can teach you .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "It's very kind of you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "I can teach you ." + ], + "type": [ + "inter-personal" + ], + "text": "It's very kind of you .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3477.json b/reccon/sources/tr_3477.json new file mode 100644 index 0000000000000000000000000000000000000000..9d5442370d8e5045e4ccf8ec934135bf8709a04a --- /dev/null +++ b/reccon/sources/tr_3477.json @@ -0,0 +1,177 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What a beautiful view .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "What a beautiful view ." + ], + "type": [ + "no-context" + ], + "text": "What a beautiful view .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It sure is . The Grand Canyon is truly a masterpiece . No man could ever make anything like this .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "What a beautiful view .", + "The Grand Canyon is truly a masterpiece . No man could ever make anything like this ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It sure is . The Grand Canyon is truly a masterpiece . No man could ever make anything like this .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What is that below ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "What a beautiful view .", + "The Grand Canyon is truly a masterpiece . No man could ever make anything like this ." + ], + "type": [ + "hybrid" + ], + "text": "What is that below ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It is the Colorado River . You can go down the river in a boat if you wish .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "What a beautiful view .", + "The Grand Canyon is truly a masterpiece . No man could ever make anything like this ." + ], + "type": [ + "hybrid" + ], + "text": "It is the Colorado River . You can go down the river in a boat if you wish .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "No . Thank you . It looks a bit too dangerous for me .", + "emotion": "neutral", + "text": "No . Thank you . It looks a bit too dangerous for me .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "There is a beautiful state park here . I can see why so many people come out here to camp .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 6 + ], + "expanded emotion cause span": [ + "There is a beautiful state park here .", + "so many people come out here to camp ." + ], + "type": [ + "no-context" + ], + "text": "There is a beautiful state park here . I can see why so many people come out here to camp .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yes , there is beautiful view . You can go fishing , camping and also enjoy this beautiful clean air .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 6, + 7 + ], + "expanded emotion cause span": [ + "There is a beautiful state park here .", + "so many people come out here to camp .", + "Yes , there is beautiful view . You can go fishing , camping and also enjoy this beautiful clean air ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , there is beautiful view . You can go fishing , camping and also enjoy this beautiful clean air .", + "id": 7, + "source_sentences": [ + 5, + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "It definitely is a nice change from the polluted and crowded city .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 6, + 8 + ], + "expanded emotion cause span": [ + "There is a beautiful state park here .", + "so many people come out here to camp .", + "It definitely is a nice change from the polluted and crowded city ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "It definitely is a nice change from the polluted and crowded city .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "That's true .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 6, + 7, + 8 + ], + "expanded emotion cause span": [ + "There is a beautiful state park here .", + "so many people come out here to camp .", + "Yes , there is beautiful view . You can go fishing , camping and also enjoy this beautiful clean air .", + "It definitely is a nice change from the polluted and crowded city ." + ], + "type": [ + "hybrid" + ], + "text": "That's true .", + "id": 9 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3481.json b/reccon/sources/tr_3481.json new file mode 100644 index 0000000000000000000000000000000000000000..77a817cd1efb20e8ad3b2763ed72c0d4ce341175 --- /dev/null +++ b/reccon/sources/tr_3481.json @@ -0,0 +1,175 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "The time has come to say goodbye .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "The time has come to say goodbye ." + ], + "type": [ + "no-context" + ], + "text": "The time has come to say goodbye .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "So soon . It seems as if you just got here .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "The time has come to say goodbye ." + ], + "type": [ + "inter-personal" + ], + "text": "So soon . It seems as if you just got here .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I feel that way , too . But all good things must come to an end , as they say .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "The time has come to say goodbye .", + "But all good things must come to an end , as they say ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I feel that way , too . But all good things must come to an end , as they say .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It certainly has been a pleasure seeing you again and renewing old memories .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "seeing you again and renewing old memories ." + ], + "type": [ + "no-context" + ], + "text": "It certainly has been a pleasure seeing you again and renewing old memories .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I've had a great time and thank you for your spending so much time showing me around .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "seeing you again and renewing old memories .", + "I've had a great time and thank you for your spending so much time showing me around ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I've had a great time and thank you for your spending so much time showing me around .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "It was fun for me , too . It gave me a chance to get away from my routine .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "I've had a great time and thank you for your spending so much time showing me around .", + "It was fun for me , too . It gave me a chance to get away from my routine ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It was fun for me , too . It gave me a chance to get away from my routine .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You'll be out to see me next year , as you promised ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "It was fun for me , too . It gave me a chance to get away from my routine .", + "You'll be out to see me next year , as you promised ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You'll be out to see me next year , as you promised ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Oh , yes . I should be there some time next spring .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "You'll be out to see me next year , as you promised ?", + "I should be there some time next spring ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , yes . I should be there some time next spring .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I'll be expecting you then .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I should be there some time next spring ." + ], + "type": [ + "inter-personal" + ], + "text": "I'll be expecting you then .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3504.json b/reccon/sources/tr_3504.json new file mode 100644 index 0000000000000000000000000000000000000000..e6e3c2f5c15b76551a4a4497608ed7889576d4bb --- /dev/null +++ b/reccon/sources/tr_3504.json @@ -0,0 +1,130 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello , Mr . Black , I'm calling to say goodbye .", + "emotion": "neutral", + "text": "Hello , Mr . Black , I'm calling to say goodbye .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "You're leaving so soon ? I wish you stayed a little longer .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "I'm calling to say goodbye .", + "You're leaving so soon" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You're leaving so soon ? I wish you stayed a little longer .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I wish I could stay a little longer , but a lot of things to do back home .", + "emotion": "neutral", + "text": "I wish I could stay a little longer , but a lot of things to do back home .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Have you got the ticket ?", + "emotion": "neutral", + "text": "Have you got the ticket ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Yes , I did .", + "emotion": "neutral", + "text": "Yes , I did .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "What time are you going ?", + "emotion": "neutral", + "text": "What time are you going ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "At 11:00 o'clock .", + "emotion": "neutral", + "text": "At 11:00 o'clock .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I'll pick you up by nine o'clock and take you straight to the airport .", + "emotion": "happiness", + "explanation": "happy because offering to see off a freind at the airport", + "expanded emotion cause evidence": [ + "b", + 8 + ], + "expanded emotion cause span": [ + "b", + "I'll pick you up by nine o'clock and take you straight to the airport ." + ], + "type": [ + "latent", + "no-context" + ], + "text": "I'll pick you up by nine o'clock and take you straight to the airport .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "No , I'll go by myself , thanks .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I'll pick you up by nine o'clock and take you straight to the airport ." + ], + "type": [ + "inter-personal" + ], + "text": "No , I'll go by myself , thanks .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "OK , goodbye .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "OK , goodbye .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3548.json b/reccon/sources/tr_3548.json new file mode 100644 index 0000000000000000000000000000000000000000..749aca049e16db2e5d047ced09148d70371e0b25 --- /dev/null +++ b/reccon/sources/tr_3548.json @@ -0,0 +1,103 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Then I must go-you have said it yourself .", + "emotion": "neutral", + "text": "Then I must go-you have said it yourself .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "No , you must stay ! I swear it , and the oath shall be kept .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Then I must go" + ], + "type": [ + "inter-personal" + ], + "text": "No , you must stay ! I swear it , and the oath shall be kept .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I tell you I must go !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "No , you must stay ! I swear it , and the oath shall be kept ." + ], + "type": [ + "inter-personal" + ], + "text": "I tell you I must go !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Where ?", + "emotion": "neutral", + "text": "Where ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I have spoken my mind , and can go anywhere now .", + "emotion": "neutral", + "text": "I have spoken my mind , and can go anywhere now .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I ask you to pass through life at my side-to be my second self and best earthly companion .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1, + 5 + ], + "expanded emotion cause span": [ + "Then I must go", + "can go anywhere now ." + ], + "type": [ + "inter-personal" + ], + "text": "I ask you to pass through life at my side-to be my second self and best earthly companion .", + "id": 6, + "source_sentences": [ + 0, + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I'll never again come to your side ; I am turn away now and can't return .", + "emotion": "anger", + "explanation": "The person wants to break up", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "I'll never again come to your side ; I am turn away now and can't return .", + "id": 7 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3558.json b/reccon/sources/tr_3558.json new file mode 100644 index 0000000000000000000000000000000000000000..a2bbb4007a08c831a2fbfbcd1608367f587529d0 --- /dev/null +++ b/reccon/sources/tr_3558.json @@ -0,0 +1,139 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Can you believe the headlines ?", + "emotion": "neutral", + "text": "Can you believe the headlines ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What are you reading ?", + "emotion": "neutral", + "text": "What are you reading ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I ' m reading about Michael Milliken , the Bond King .", + "emotion": "neutral", + "text": "I ' m reading about Michael Milliken , the Bond King .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Didn ' t he sell worthless stocks to people or something ? He got arrested for that , didn ' t he ?", + "emotion": "neutral", + "text": "Didn ' t he sell worthless stocks to people or something ? He got arrested for that , didn ' t he ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "He got arrested all right .", + "emotion": "neutral", + "text": "He got arrested all right .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "If I remember , he got off with a light sentence . Something like three years in a minimum-security prison .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 4, + 6 + ], + "expanded emotion cause span": [ + "he sell worthless stocks to people", + "If I remember , he got off with a light sentence ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "If I remember , he got off with a light sentence . Something like three years in a minimum-security prison .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yup , that ' s him . He made millions of dollars selling bonds to people and ended up with a pile of cash when they became useless .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 4, + 6, + 7 + ], + "expanded emotion cause span": [ + "he sell worthless stocks to people", + "If I remember , he got off with a light sentence .", + "He made millions of dollars selling bonds to people and ended up with a pile of cash when they became useless ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yup , that ' s him . He made millions of dollars selling bonds to people and ended up with a pile of cash when they became useless .", + "id": 7, + "source_sentences": [ + 3, + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I think the government fined him a small amount , and he kept the rest in his foreign bank accounts . He ' s still a millionaire .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 4, + 6, + 7, + 8 + ], + "expanded emotion cause span": [ + "he sell worthless stocks to people", + "If I remember , he got off with a light sentence .", + "He made millions of dollars selling bonds to people and ended up with a pile of cash when they became useless .", + "I think the government fined him a small amount , and he kept the rest in his foreign bank accounts . He ' s still a millionaire ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I think the government fined him a small amount , and he kept the rest in his foreign bank accounts . He ' s still a millionaire .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "That ' s the kind of thing in America that gets me mad . Some guy pulls off a stock scheme and makes millions while spending the bare minimum sentence in jail .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Some guy pulls off a stock scheme and makes millions while spending the bare minimum sentence in jail ." + ], + "type": [ + "no-context" + ], + "text": "That ' s the kind of thing in America that gets me mad . Some guy pulls off a stock scheme and makes millions while spending the bare minimum sentence in jail .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I know . And some poor guy that robs a liquor store makes $ 500 at most and ends up in jail for five to ten years .", + "emotion": "neutral", + "text": "I know . And some poor guy that robs a liquor store makes $ 500 at most and ends up in jail for five to ten years .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3588.json b/reccon/sources/tr_3588.json new file mode 100644 index 0000000000000000000000000000000000000000..ca79345c7e24d0146ee926e92034e1e4d16a4b65 --- /dev/null +++ b/reccon/sources/tr_3588.json @@ -0,0 +1,120 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Recently , there prevails ' Net Love ' !", + "emotion": "neutral", + "text": "Recently , there prevails ' Net Love ' !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What's Net Love ?", + "emotion": "neutral", + "text": "What's Net Love ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Two people chat on the Net and step by step fall into love ! It's Net Love .", + "emotion": "neutral", + "text": "Two people chat on the Net and step by step fall into love ! It's Net Love .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Ridiculous ! They haven't met ! Maybe they're the same sex !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "Two people chat on the Net and step by step fall into love !", + "They haven't met ! Maybe they're the same sex !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Ridiculous ! They haven't met ! Maybe they're the same sex !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Maybe yesterday you've received a man's woos . He's called ' Beast ' ?", + "emotion": "neutral", + "text": "Maybe yesterday you've received a man's woos . He's called ' Beast ' ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "How could you know ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Maybe yesterday you've received a man's woos . He's called ' Beast ' ?", + "How could you know ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "How could you know ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I watched the screen display !", + "emotion": "neutral", + "text": "I watched the screen display !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Do you know ' He ' is Ms . Rebecca !", + "emotion": "neutral", + "text": "Do you know ' He ' is Ms . Rebecca !", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "It's typical Net Love , and a typical lesbians ' homosex ! HA !", + "emotion": "neutral", + "text": "It's typical Net Love , and a typical lesbians ' homosex ! HA !", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Impossible !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "It's typical Net Love , and a typical lesbians ' homosex !" + ], + "type": [ + "inter-personal" + ], + "text": "Impossible !", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3596.json b/reccon/sources/tr_3596.json new file mode 100644 index 0000000000000000000000000000000000000000..8e19ba353df421cf3a5a004d74ed9dffefcbd92f --- /dev/null +++ b/reccon/sources/tr_3596.json @@ -0,0 +1,108 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "You ' re going to set up your own law office , aren ' t you ?", + "emotion": "neutral", + "text": "You ' re going to set up your own law office , aren ' t you ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes . After so many years of hard work , I ' d rather I had an office of my own .", + "emotion": "neutral", + "text": "Yes . After so many years of hard work , I ' d rather I had an office of my own .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "If you need help , don ' t hesitate to ask me .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "After so many years of hard work , I ' d rather I had an office of my own ." + ], + "type": [ + "inter-personal" + ], + "text": "If you need help , don ' t hesitate to ask me .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I ' ll be very glad if you would help .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "If you need help , don ' t hesitate to ask me ." + ], + "type": [ + "inter-personal" + ], + "text": "I ' ll be very glad if you would help .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I ' d like to wish you every success in your new venture .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I ' ll be very glad if you would help ." + ], + "type": [ + "inter-personal" + ], + "text": "I ' d like to wish you every success in your new venture .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Thank you . I wish I would .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I ' d like to wish you every success in your new venture ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . I wish I would .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Good luck to you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Thank you ." + ], + "type": [ + "inter-personal" + ], + "text": "Good luck to you .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3624.json b/reccon/sources/tr_3624.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff6b3645959e23702f4e770358ce3c9ffea50d8 --- /dev/null +++ b/reccon/sources/tr_3624.json @@ -0,0 +1,107 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What's the matter with you ? You look so upset and tired .", + "emotion": "neutral", + "text": "What's the matter with you ? You look so upset and tired .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "My father failed in business .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "My father failed in business ." + ], + "type": [ + "no-context" + ], + "text": "My father failed in business .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Oh , that's really tough .", + "emotion": "neutral", + "text": "Oh , that's really tough .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Maybe it is the most difficult period of my family have experienced .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "it is the most difficult period of my family have experienced ." + ], + "type": [ + "no-context" + ], + "text": "Maybe it is the most difficult period of my family have experienced .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I can understand . By the way , is there anyway I can help ?", + "emotion": "neutral", + "text": "I can understand . By the way , is there anyway I can help ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "No , not now . I have found a part-time job . So perhaps I can help my family to come over the difficulties .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "it is the most difficult period of my family have experienced ." + ], + "type": [ + "self-contagion" + ], + "text": "No , not now . I have found a part-time job . So perhaps I can help my family to come over the difficulties .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Oh , that's so great , bless you ! if you need me , I'll always be there .", + "emotion": "neutral", + "text": "Oh , that's so great , bless you ! if you need me , I'll always be there .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Thank you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "if you need me , I'll always be there ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3636.json b/reccon/sources/tr_3636.json new file mode 100644 index 0000000000000000000000000000000000000000..dfbcabab3d5282db0e0a4e681a3775c9f652a2b8 --- /dev/null +++ b/reccon/sources/tr_3636.json @@ -0,0 +1,262 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Is this Zhang Lin's home ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Is this Zhang Lin's home ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes . Oh , it's you , Linda . I haven't seen you for a long time . Well , come in and sit down . How about something to drink ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I haven't seen you for a long time ." + ], + "type": [ + "no-context" + ], + "text": "Yes . Oh , it's you , Linda . I haven't seen you for a long time . Well , come in and sit down . How about something to drink ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yes , please . I'm a little thirsty , actually .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I haven't seen you for a long time . Well , come in and sit down . How about something to drink ?" + ], + "type": [ + "inter-personal" + ], + "text": "Yes , please . I'm a little thirsty , actually .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Would you like tea or coffee ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I haven't seen you for a long time ." + ], + "type": [ + "self-contagion" + ], + "text": "Would you like tea or coffee ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Coffee , please .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "I'm a little thirsty", + "Would you like tea or coffee ?" + ], + "type": [ + "hybrid" + ], + "text": "Coffee , please .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Here you are .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I haven't seen you for a long time ." + ], + "type": [ + "self-contagion" + ], + "text": "Here you are .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Would you like to talk over a drink ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "Here you are .", + "Would you like to talk over a drink ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Would you like to talk over a drink ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That sounds good . How are you doing , Linda ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Would you like to talk over a drink ?" + ], + "type": [ + "inter-personal" + ], + "text": "That sounds good . How are you doing , Linda ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Just fine . Are you busy now ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "That sounds good . How are you doing , Linda ?", + "Just fine ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Just fine . Are you busy now ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "No . I'm just killing time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 9 + ], + "expanded emotion cause span": [ + "I haven't seen you for a long time .", + "Just fine ." + ], + "type": [ + "hybrid" + ], + "text": "No . I'm just killing time .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Shall we visit our math teacher tomorrow ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "Shall we visit our math teacher tomorrow ?" + ], + "type": [ + "no-context" + ], + "text": "Shall we visit our math teacher tomorrow ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Yes . I haven't been in his house for several weeks . When shall we start ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "Shall we visit our math teacher tomorrow ?", + "Yes . I haven't been in his house for several weeks ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes . I haven't been in his house for several weeks . When shall we start ?", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 13, + "speaker": "A", + "utterance": "How about eight o'clock tomorrow morning ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "Shall we visit our math teacher tomorrow ?", + "Yes . I haven't been in his house for several weeks ." + ], + "type": [ + "hybrid" + ], + "text": "How about eight o'clock tomorrow morning ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "All right . See you tomorrow .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "Shall we visit our math teacher tomorrow ?", + "Yes . I haven't been in his house for several weeks ." + ], + "type": [ + "hybrid" + ], + "text": "All right . See you tomorrow .", + "id": 14 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3647.json b/reccon/sources/tr_3647.json new file mode 100644 index 0000000000000000000000000000000000000000..fab4859a278779102dce899eda4beec348a05aea --- /dev/null +++ b/reccon/sources/tr_3647.json @@ -0,0 +1,114 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "It ' s a wonderful party , Joan , The food , the drink , the atmosphere ... Everyone is enjoying himself .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "It ' s a wonderful party , Joan , The food , the drink , the atmosphere ... Everyone is enjoying himself ." + ], + "type": [ + "no-context" + ], + "text": "It ' s a wonderful party , Joan , The food , the drink , the atmosphere ... Everyone is enjoying himself .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Thanks to your help . To our friendship .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "It ' s a wonderful party , Joan , The food , the drink , the atmosphere ... Everyone is enjoying himself ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks to your help . To our friendship .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Bottoms up ! By the way what kind of entertainment are we gonna have ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "It ' s a wonderful party , Joan , The food , the drink , the atmosphere ... Everyone is enjoying himself .", + "Thanks to your help . To our friendship ." + ], + "type": [ + "hybrid" + ], + "text": "Bottoms up ! By the way what kind of entertainment are we gonna have ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Dancing . The boys from the Campus Band have promised to play music for us .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Dancing . The boys from the Campus Band have promised to play music for us ." + ], + "type": [ + "no-context" + ], + "text": "Dancing . The boys from the Campus Band have promised to play music for us .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Oh , how wonderful ! Every girl on the campus has a crush on those handsome guys .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "Dancing . The boys from the Campus Band have promised to play music for us .", + "Every girl on the campus has a crush on those handsome guys ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , how wonderful ! Every girl on the campus has a crush on those handsome guys .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I'll surely make introductions for them .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Oh , how wonderful ! Every girl on the campus has a crush on those handsome guys ." + ], + "type": [ + "inter-personal" + ], + "text": "I'll surely make introductions for them .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3651.json b/reccon/sources/tr_3651.json new file mode 100644 index 0000000000000000000000000000000000000000..beecae566b0da08ce9a076c74c94237016fabd11 --- /dev/null +++ b/reccon/sources/tr_3651.json @@ -0,0 +1,155 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hot in here , isn't it ?", + "emotion": "neutral", + "text": "Hot in here , isn't it ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yeah , really .", + "emotion": "neutral", + "text": "Yeah , really .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Is it Ok if I sit here ?", + "emotion": "neutral", + "text": "Is it Ok if I sit here ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Of course . Suit yourself .", + "emotion": "neutral", + "text": "Of course . Suit yourself .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Thanks . My name's Bill Peters , by the way .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Of course . Suit yourself ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks . My name's Bill Peters , by the way .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Hi , I'm Susan Jackson .", + "emotion": "neutral", + "text": "Hi , I'm Susan Jackson .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Nice to meet you . And what do you do , Susan ?", + "emotion": "neutral", + "text": "Nice to meet you . And what do you do , Susan ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I'm a student at UCLA .", + "emotion": "neutral", + "text": "I'm a student at UCLA .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Oh , are you ? And what are you studying ?", + "emotion": "neutral", + "text": "Oh , are you ? And what are you studying ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Medicine .", + "emotion": "neutral", + "text": "Medicine .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Really ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Medicine ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Yes , I want to be a doctor one of these days . What about you ?", + "emotion": "neutral", + "text": "Yes , I want to be a doctor one of these days . What about you ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I'm an engineer , I work for Boeing . Say , would you like a drink ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "Yes , I want to be a doctor one of these days . What about you ?" + ], + "type": [ + "inter-personal" + ], + "text": "I'm an engineer , I work for Boeing . Say , would you like a drink ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Sure . Thanks .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "I'm an engineer , I work for Boeing . Say , would you like a drink ?" + ], + "type": [ + "inter-personal" + ], + "text": "Sure . Thanks .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3672.json b/reccon/sources/tr_3672.json new file mode 100644 index 0000000000000000000000000000000000000000..eab11ebb2bcba00d9cfb73cc423371dc9118abd3 --- /dev/null +++ b/reccon/sources/tr_3672.json @@ -0,0 +1,182 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey Steve . When's the next time you're going to play golf ?", + "emotion": "neutral", + "text": "Hey Steve . When's the next time you're going to play golf ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'm going out this Saturday .", + "emotion": "neutral", + "text": "I'm going out this Saturday .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Do you already have a foursome ?", + "emotion": "neutral", + "text": "Do you already have a foursome ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Unfortunately , we do . Let's plan for something together for Wednesday . We can go right after work .", + "emotion": "neutral", + "text": "Unfortunately , we do . Let's plan for something together for Wednesday . We can go right after work .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "That sounds good . Where do you want to play ?", + "emotion": "neutral", + "text": "That sounds good . Where do you want to play ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "We won't have much time , so let's play somewhere close to work .", + "emotion": "neutral", + "text": "We won't have much time , so let's play somewhere close to work .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "How about Bellevue ? It's pretty close .", + "emotion": "neutral", + "text": "How about Bellevue ? It's pretty close .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "How much does it cost over there ?", + "emotion": "neutral", + "text": "How much does it cost over there ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Twilight rates are 21 dollars .", + "emotion": "neutral", + "text": "Twilight rates are 21 dollars .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "That's pretty good . Let's do it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Twilight rates are 21 dollars ." + ], + "type": [ + "inter-personal" + ], + "text": "That's pretty good . Let's do it .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Aright . I'll get a tee time for Wednesday at about 4", + "emotion": "neutral", + "text": "Aright . I'll get a tee time for Wednesday at about 4", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Make it 4", + "emotion": "neutral", + "text": "Make it 4", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Ok . I'll call you later when I get a tee time .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "I'll call you later when I get a tee time ." + ], + "type": [ + "no-context" + ], + "text": "Ok . I'll call you later when I get a tee time .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Sounds good . I'll see you on Wednesday then .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "I'll see you on Wednesday then ." + ], + "type": [ + "no-context" + ], + "text": "Sounds good . I'll see you on Wednesday then .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Aright . Have fun on Saturday .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "I'll see you on Wednesday then ." + ], + "type": [ + "inter-personal" + ], + "text": "Aright . Have fun on Saturday .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Will do .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "Have fun on Saturday ." + ], + "type": [ + "inter-personal" + ], + "text": "Will do .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3676.json b/reccon/sources/tr_3676.json new file mode 100644 index 0000000000000000000000000000000000000000..f6283a072b55dbe2704950284f1e181599d87aa6 --- /dev/null +++ b/reccon/sources/tr_3676.json @@ -0,0 +1,188 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Oh , God . It ' s late . I ' m afraid I have to leave .", + "emotion": "neutral", + "text": "Oh , God . It ' s late . I ' m afraid I have to leave .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "But you just got here . Can ' t you stay a little longer and have some tea ?", + "emotion": "neutral", + "text": "But you just got here . Can ' t you stay a little longer and have some tea ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "That ' s very kind of you . But if I don ' t go now I ' ll miss the last bus .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "have some tea ?", + "That ' s very kind of you" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That ' s very kind of you . But if I don ' t go now I ' ll miss the last bus .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "That ' s too bad .", + "emotion": "neutral", + "text": "That ' s too bad .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Thank you for your hospitality .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3, + 5 + ], + "expanded emotion cause span": [ + "have some tea ?", + "That ' s very kind of you", + "Thank you for your hospitality ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Thank you for your hospitality .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Thanks for coming .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Thanks for coming ." + ], + "type": [ + "no-context" + ], + "text": "Thanks for coming .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "How about next time we meet at my place ? And I ' ll treat you to Chinese food . I know how much you like it . We can order in and watch video too . Anything you like , I promise .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3, + 5, + 7 + ], + "expanded emotion cause span": [ + "have some tea ?", + "That ' s very kind of you", + "Thank you for your hospitality .", + "How about next time we meet at my place ?" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "How about next time we meet at my place ? And I ' ll treat you to Chinese food . I know how much you like it . We can order in and watch video too . Anything you like , I promise .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Great idea . I ' m looking forward to it . See you then .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7, + 7 + ], + "expanded emotion cause span": [ + "Thanks for coming .", + "How about next time we meet at my place ?", + "Anything you like , I promise ." + ], + "type": [ + "hybrid" + ], + "text": "Great idea . I ' m looking forward to it . See you then .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Well . I really do have to go .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I ' m looking forward to it" + ], + "type": [ + "inter-personal" + ], + "text": "Well . I really do have to go .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Good night then .", + "emotion": "happiness", + "explanation": "Sharing pleasantries", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Good night then .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "See you tomorrow .", + "emotion": "happiness", + "explanation": "Sharing pleasantries", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "See you tomorrow .", + "id": 11 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3678.json b/reccon/sources/tr_3678.json new file mode 100644 index 0000000000000000000000000000000000000000..516a0eb182f616201dd667cac9517e7a759964a6 --- /dev/null +++ b/reccon/sources/tr_3678.json @@ -0,0 +1,187 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , Daisy !", + "emotion": "neutral", + "text": "Hi , Daisy !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hi Simon . Nice to meet you again", + "emotion": "neutral", + "text": "Hi Simon . Nice to meet you again", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I hope you are Settling in at school !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Hi Simon . Nice to meet you again" + ], + "type": [ + "inter-personal" + ], + "text": "I hope you are Settling in at school !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I am ! I've made lots of friends and I really enjoy my courses .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "I hope you are Settling in at school !", + "I am ! I've made lots of friends and I really enjoy my courses ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I am ! I've made lots of friends and I really enjoy my courses .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Good ! Me too ! By the way . you didn't tell me what you are studying here .", + "emotion": "neutral", + "text": "Good ! Me too ! By the way . you didn't tell me what you are studying here .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Didn't I ? I'm doing business studies .", + "emotion": "neutral", + "text": "Didn't I ? I'm doing business studies .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Really ? That's great . You hope to join a company after graduating ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I'm doing business studies ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? That's great . You hope to join a company after graduating ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Maybe . My parents moved to Canada the year when I was born . We are living in Toronto . Suppose I might get a job in Toronto when I graduate . It's too soon to say really .", + "emotion": "neutral", + "text": "Maybe . My parents moved to Canada the year when I was born . We are living in Toronto . Suppose I might get a job in Toronto when I graduate . It's too soon to say really .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "What about your friend Zoe", + "emotion": "neutral", + "text": "What about your friend Zoe", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "She's from Australia . She lives in Sydney . Her father runs a hotel business there and she is doing a degree in accountancy .", + "emotion": "neutral", + "text": "She's from Australia . She lives in Sydney . Her father runs a hotel business there and she is doing a degree in accountancy .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Accountancy ? Really ? She must be very good at figures .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "she is doing a degree in accountancy ." + ], + "type": [ + "inter-personal" + ], + "text": "Accountancy ? Really ? She must be very good at figures .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I guess so . What about you , Simon ?", + "emotion": "neutral", + "text": "I guess so . What about you , Simon ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I'm studying law .", + "emotion": "neutral", + "text": "I'm studying law .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Great ! So I'll know who to call if I ever need a lawyer .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13, + 14 + ], + "expanded emotion cause span": [ + "I'm studying law .", + "I'll know who to call if I ever need a lawyer ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Great ! So I'll know who to call if I ever need a lawyer .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Sure , welcome anytime", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "Great ! So I'll know who to call if I ever need a lawyer ." + ], + "type": [ + "inter-personal" + ], + "text": "Sure , welcome anytime", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3685.json b/reccon/sources/tr_3685.json new file mode 100644 index 0000000000000000000000000000000000000000..6bd6a6777981815f4987b2c34760e6b112c2ab36 --- /dev/null +++ b/reccon/sources/tr_3685.json @@ -0,0 +1,114 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Jenny , are you having fun here ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Jenny , are you having fun here ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , of course . This is really a nice party with wonderful people and lovely wines .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "This is really a nice party with wonderful people and lovely wines ." + ], + "type": [ + "no-context" + ], + "text": "Yes , of course . This is really a nice party with wonderful people and lovely wines .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I ' m glad you ' re enjoying it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "This is really a nice party with wonderful people and lovely wines .", + "you ' re enjoying it ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I ' m glad you ' re enjoying it .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Thank you for the invitation .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Thank you for the invitation ." + ], + "type": [ + "no-context" + ], + "text": "Thank you for the invitation .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "It ' s my pleasure . Would you like another glass of champagne ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 4 + ], + "expanded emotion cause span": [ + "Yes , of course . This is really a nice party with wonderful people and lovely wines .", + "Thank you for the invitation ." + ], + "type": [ + "inter-personal" + ], + "text": "It ' s my pleasure . Would you like another glass of champagne ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yes , please . Thank you for everything .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Would you like another glass of champagne ?" + ], + "type": [ + "inter-personal" + ], + "text": "Yes , please . Thank you for everything .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3694.json b/reccon/sources/tr_3694.json new file mode 100644 index 0000000000000000000000000000000000000000..085e2987ef63cf637994be7adcef0b7767c8a9dc --- /dev/null +++ b/reccon/sources/tr_3694.json @@ -0,0 +1,202 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Did you hear what happened to Mike in Accounts ?", + "emotion": "neutral", + "text": "Did you hear what happened to Mike in Accounts ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "No . What ?", + "emotion": "neutral", + "text": "No . What ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "He got arrested on Friday night and spent the night in jail .", + "emotion": "neutral", + "text": "He got arrested on Friday night and spent the night in jail .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "No . Really , what happened ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "He got arrested on Friday night and spent the night in jail ." + ], + "type": [ + "inter-personal" + ], + "text": "No . Really , what happened ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Well , it was all a big mistake , actually . He got home on Friday night really late , and apparently he'd been out drinking with some clients , so he was really drunk .", + "emotion": "neutral", + "text": "Well , it was all a big mistake , actually . He got home on Friday night really late , and apparently he'd been out drinking with some clients , so he was really drunk .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Was he out with the guys from the bank ?", + "emotion": "neutral", + "text": "Was he out with the guys from the bank ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yes , I think so .", + "emotion": "neutral", + "text": "Yes , I think so .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Oh , yeah , they always get really drunk .", + "emotion": "neutral", + "text": "Oh , yeah , they always get really drunk .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Well , anyway , he'd somehow lost his wallet and his house keys , so he couldn't get in . He lives alone , you know .", + "emotion": "neutral", + "text": "Well , anyway , he'd somehow lost his wallet and his house keys , so he couldn't get in . He lives alone , you know .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Oh , really . I thought he lived with his wife .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "He lives alone , you know ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , really . I thought he lived with his wife .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "No , she left him last year .", + "emotion": "neutral", + "text": "No , she left him last year .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Oh , really ? Do you know why ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "she left him last year ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , really ? Do you know why ?", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Hang on , let me finish telling you what happened . Where was I ?", + "emotion": "neutral", + "text": "Hang on , let me finish telling you what happened . Where was I ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "He lost his wallet and keys .", + "emotion": "neutral", + "text": "He lost his wallet and keys .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Oh yes , well , he tried to climb in through the bathroom window , but apparently he slipped and broke the glass with his foot . The neighbors heard him and thought a robbery was in progress , so they called the police .", + "emotion": "neutral", + "text": "Oh yes , well , he tried to climb in through the bathroom window , but apparently he slipped and broke the glass with his foot . The neighbors heard him and thought a robbery was in progress , so they called the police .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Oh , no .", + "emotion": "neutral", + "text": "Oh , no .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "Yes . So when the cops arrived , they didn't believe his story", + "emotion": "neutral", + "text": "Yes . So when the cops arrived , they didn't believe his story", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "So then what happened ?", + "emotion": "neutral", + "text": "So then what happened ?", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "Well , when he sobered up , he called someone from work to come and bail him out .", + "emotion": "neutral", + "text": "Well , when he sobered up , he called someone from work to come and bail him out .", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "Well , that's a bit of a tricky situation .", + "emotion": "neutral", + "text": "Well , that's a bit of a tricky situation .", + "id": 20 + }, + { + "turn": 21, + "speaker": "A", + "utterance": "Yes , I know .", + "emotion": "neutral", + "text": "Yes , I know .", + "id": 21 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3702.json b/reccon/sources/tr_3702.json new file mode 100644 index 0000000000000000000000000000000000000000..93baee2a32ffc6b1390dd85d985b29d5d9c01204 --- /dev/null +++ b/reccon/sources/tr_3702.json @@ -0,0 +1,258 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "what do you think about this store ? I heard it ' s a posh store that ' s only got branches in big cities .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "it ' s a posh store that ' s only got branches in big cities ." + ], + "type": [ + "no-context" + ], + "text": "what do you think about this store ? I heard it ' s a posh store that ' s only got branches in big cities .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I love this store . The only problem is that it ' s extremely expensive .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I love this store ." + ], + "type": [ + "no-context" + ], + "text": "I love this store . The only problem is that it ' s extremely expensive .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "don ' t worry . I ' Ve decided that for your birthday I ' m going to take you shopping for a new dress .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "I love this store . The only problem is that it ' s extremely expensive .", + "don ' t worry . I ' Ve decided that for your birthday I ' m going to take you shopping for a new dress ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "don ' t worry . I ' Ve decided that for your birthday I ' m going to take you shopping for a new dress .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "really ? I thought you hated shopping ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I ' Ve decided that for your birthday I ' m going to take you shopping for a new dress ." + ], + "type": [ + "inter-personal" + ], + "text": "really ? I thought you hated shopping ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I do , that ' s why you should appreciate this gift !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I thought you hated shopping ?" + ], + "type": [ + "inter-personal" + ], + "text": "I do , that ' s why you should appreciate this gift !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "sure . That ' s really nice of you . Let ' s go in and try some things on .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "I thought you hated shopping ?", + "you should appreciate this gift !" + ], + "type": [ + "hybrid" + ], + "text": "sure . That ' s really nice of you . Let ' s go in and try some things on .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "how about this red dress ? I think it would really suit you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "it would really suit you ." + ], + "type": [ + "no-context" + ], + "text": "how about this red dress ? I think it would really suit you .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "that ' s gorgeous ! Do they have it in a size 8 ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "it would really suit you ." + ], + "type": [ + "inter-personal" + ], + "text": "that ' s gorgeous ! Do they have it in a size 8 ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "here you go . On any other day , it would cost me a fortune , but it ' s on special offer today .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "it ' s on special offer today ." + ], + "type": [ + "no-context" + ], + "text": "here you go . On any other day , it would cost me a fortune , but it ' s on special offer today .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I think this color isn ' t quite right for me . Do they have the same dress in white ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "it would really suit you ." + ], + "type": [ + "inter-personal" + ], + "text": "I think this color isn ' t quite right for me . Do they have the same dress in white ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "let me look . Let ' s see ... they ' Ve got one in blue , green , pink , black ... and white . Here you are .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "they ' Ve got one in blue , green , pink , black ... and white ." + ], + "type": [ + "no-context" + ], + "text": "let me look . Let ' s see ... they ' Ve got one in blue , green , pink , black ... and white . Here you are .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "this is perfect ! What do you think ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "this is perfect !" + ], + "type": [ + "no-context" + ], + "text": "this is perfect ! What do you think ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I think you look fantastic . Happy Birthday !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12, + 13 + ], + "expanded emotion cause span": [ + "this is perfect !", + "you look fantastic" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I think you look fantastic . Happy Birthday !", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 14, + "speaker": "B", + "utterance": "I ' m so lucky . You only get a chance like this once in a blue moon ! Thanks honey !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12, + 13, + 14 + ], + "expanded emotion cause span": [ + "this is perfect !", + "you look fantastic", + "I ' m so lucky . You only get a chance like this once in a blue moon ! Thanks honey !" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I ' m so lucky . You only get a chance like this once in a blue moon ! Thanks honey !", + "id": 14 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_371.json b/reccon/sources/tr_371.json new file mode 100644 index 0000000000000000000000000000000000000000..249c386827c4e47dcbdb5a924ad609c19201030b --- /dev/null +++ b/reccon/sources/tr_371.json @@ -0,0 +1,192 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Would you like to stretch your legs ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + "b", + 1 + ], + "expanded emotion cause span": [ + "b", + "Would you like to stretch your legs ?" + ], + "type": [ + "latent", + "no-context" + ], + "text": "Would you like to stretch your legs ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Sure .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + "b", + 1 + ], + "expanded emotion cause span": [ + "b", + "Would you like to stretch your legs ?" + ], + "type": [ + "latent", + "inter-personal" + ], + "text": "Sure .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Let's get a soft drink .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 3 + ], + "expanded emotion cause span": [ + "b", + "Let's get a soft drink ." + ], + "type": [ + "latent", + "no-context" + ], + "text": "Let's get a soft drink .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Do we have enough time ?", + "emotion": "neutral", + "text": "Do we have enough time ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "It's a fifteen-minute intermission .", + "emotion": "neutral", + "text": "It's a fifteen-minute intermission .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "The seats are excellent . We're right in the center .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "The seats are excellent . We're right in the center ." + ], + "type": [ + "no-context" + ], + "text": "The seats are excellent . We're right in the center .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "It's a new concert hall and the acoustics are great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "The seats are excellent . We're right in the center .", + "It's a new concert hall and the acoustics are great ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It's a new concert hall and the acoustics are great .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I can't agree more .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "The seats are excellent . We're right in the center .", + "It's a new concert hall and the acoustics are great ." + ], + "type": [ + "hybrid" + ], + "text": "I can't agree more .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Is this your first time to come to a symphony concert ?", + "emotion": "neutral", + "text": "Is this your first time to come to a symphony concert ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "In the United States , yes . But back in China , I went to concerts a couple of times with my parents .", + "emotion": "neutral", + "text": "In the United States , yes . But back in China , I went to concerts a couple of times with my parents .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Do you have large concert halls in your city ?", + "emotion": "neutral", + "text": "Do you have large concert halls in your city ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "We have two . One is like this one . The other is a little smaller .", + "emotion": "neutral", + "text": "We have two . One is like this one . The other is a little smaller .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "That's great . Well , we'd better get back to our seats . It's about to start .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13, + 13 + ], + "expanded emotion cause span": [ + "That's great . Well , we'd better get back to our seats . It's about to start .", + "It's about to start ." + ], + "type": [ + "no-context" + ], + "text": "That's great . Well , we'd better get back to our seats . It's about to start .", + "id": 13 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3720.json b/reccon/sources/tr_3720.json new file mode 100644 index 0000000000000000000000000000000000000000..61978d641ab0384d2fe6cb83524088b8db068c5d --- /dev/null +++ b/reccon/sources/tr_3720.json @@ -0,0 +1,165 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What are you doing this weekend ?", + "emotion": "neutral", + "text": "What are you doing this weekend ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I am not sure . What are you doing ?", + "emotion": "neutral", + "text": "I am not sure . What are you doing ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I was thinking of maybe taking a drive to the beach .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "taking a drive to the beach ." + ], + "type": [ + "no-context" + ], + "text": "I was thinking of maybe taking a drive to the beach .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "That sounds like a great idea !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "taking a drive to the beach ." + ], + "type": [ + "inter-personal" + ], + "text": "That sounds like a great idea !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Would you be interested in joining me ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "That sounds like a great idea !" + ], + "type": [ + "inter-personal" + ], + "text": "Would you be interested in joining me ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Sure , I would love to go with you . When would you be leaving ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Would you be interested in joining me ?", + "Sure , I would love to go with you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Sure , I would love to go with you . When would you be leaving ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I thought that we could leave around 8", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Sure , I would love to go with you ." + ], + "type": [ + "inter-personal" + ], + "text": "I thought that we could leave around 8", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That would give us plenty of time to explore . Did you know that there is a music festival on the beach in Santa Barbara ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "That would give us plenty of time to explore . Did you know that there is a music festival on the beach in Santa Barbara ?" + ], + "type": [ + "no-context" + ], + "text": "That would give us plenty of time to explore . Did you know that there is a music festival on the beach in Santa Barbara ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "That was part of my plan .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "music festival on the beach in Santa Barbara ?" + ], + "type": [ + "inter-personal" + ], + "text": "That was part of my plan .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Well then , I'll see you on Saturday . Thanks for asking me to go with you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "That was part of my plan .", + "I'll see you on Saturday . Thanks for asking me to go with you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Well then , I'll see you on Saturday . Thanks for asking me to go with you .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3729.json b/reccon/sources/tr_3729.json new file mode 100644 index 0000000000000000000000000000000000000000..e51052d07fa27d858254e76c39a2158eb4aae4e8 --- /dev/null +++ b/reccon/sources/tr_3729.json @@ -0,0 +1,117 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What was the last movie you saw ?", + "emotion": "neutral", + "text": "What was the last movie you saw ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "A Korean film called Friends , starring Sang Dong-gun .", + "emotion": "neutral", + "text": "A Korean film called Friends , starring Sang Dong-gun .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Really ? I've seen that movie , too .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "A Korean film called Friends , starring Sang Dong-gun ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? I've seen that movie , too .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "How did you like the movie ?", + "emotion": "neutral", + "text": "How did you like the movie ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I thought it was pretty good .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "it was pretty good ." + ], + "type": [ + "no-context" + ], + "text": "I thought it was pretty good .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Really ? I can't say I agree .", + "emotion": "surprise", + "explanation": "disagreement", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I thought it was pretty good ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? I can't say I agree .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You're kidding . The story and acting were outstanding .", + "emotion": "surprise", + "explanation": "disagreement", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I can't say I agree ." + ], + "type": [ + "inter-personal" + ], + "text": "You're kidding . The story and acting were outstanding .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I guess I expected too much from the movie , so I was a bit disappointed .", + "emotion": "neutral", + "text": "I guess I expected too much from the movie , so I was a bit disappointed .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I guess it could happen .", + "emotion": "neutral", + "text": "I guess it could happen .", + "id": 9 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3734.json b/reccon/sources/tr_3734.json new file mode 100644 index 0000000000000000000000000000000000000000..e08f5dd475a8122a2d1cf32bc9e854d03a26bb51 --- /dev/null +++ b/reccon/sources/tr_3734.json @@ -0,0 +1,110 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "The Blacks got divorced .", + "emotion": "neutral", + "text": "The Blacks got divorced .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Really ? Why ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "The Blacks got divorced ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? Why ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Mr . Black has been getting a little on the side .", + "emotion": "neutral", + "text": "Mr . Black has been getting a little on the side .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Really ? I am surprised . He doesn't look like a guy who'd ever cheat on his wife , does he ?", + "emotion": "neutral", + "text": "Really ? I am surprised . He doesn't look like a guy who'd ever cheat on his wife , does he ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "No , he doesn't . Anyway , his wife found out that he has been two-timing for a long time .", + "emotion": "neutral", + "text": "No , he doesn't . Anyway , his wife found out that he has been two-timing for a long time .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Well , I am really surprised . By the way , have you done anything behind my back ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "He doesn't look like a guy who'd ever cheat on his wife", + "his wife found out that he has been two-timing for a long time ." + ], + "type": [ + "hybrid" + ], + "text": "Well , I am really surprised . By the way , have you done anything behind my back ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "No . The only thing I've ever done behind your back is zipping you up .", + "emotion": "happiness", + "explanation": "the speaker is making a joke", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "The only thing I've ever done behind your back is zipping you up ." + ], + "type": [ + "no-context" + ], + "text": "No . The only thing I've ever done behind your back is zipping you up .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I like that joke , but I hope it's true .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "The only thing I've ever done behind your back is zipping you up ." + ], + "type": [ + "inter-personal" + ], + "text": "I like that joke , but I hope it's true .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3753.json b/reccon/sources/tr_3753.json new file mode 100644 index 0000000000000000000000000000000000000000..5c8feb5f7260d426408ed3ecfbcfa5c58e739001 --- /dev/null +++ b/reccon/sources/tr_3753.json @@ -0,0 +1,238 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey , Jack , where's your car ?", + "emotion": "neutral", + "text": "Hey , Jack , where's your car ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I got rid of that clunker . This is my new one .", + "emotion": "neutral", + "text": "I got rid of that clunker . This is my new one .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Is that right ? This sure beats the old one ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I got rid of that clunker . This is my new one ." + ], + "type": [ + "inter-personal" + ], + "text": "Is that right ? This sure beats the old one ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Hop in , I'll give you a ride .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 4 + ], + "expanded emotion cause span": [ + "I got rid of that clunker . This is my new one .", + "I'll give you a ride ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Hop in , I'll give you a ride .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Ok . Boy , this looks expensive .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "I'll give you a ride .", + "this looks expensive ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Ok . Boy , this looks expensive .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yeah , it costed a bundle , alright ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "this looks expensive ." + ], + "type": [ + "inter-personal" + ], + "text": "Yeah , it costed a bundle , alright ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Wow , this thing can haul .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "this thing can haul ." + ], + "type": [ + "no-context" + ], + "text": "Wow , this thing can haul .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yeah , this sucker is the fastest thing I've ever owned .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "this sucker is the fastest thing I've ever owned ." + ], + "type": [ + "no-context" + ], + "text": "Yeah , this sucker is the fastest thing I've ever owned .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I believe it . Hoo , this car corners like it's on rails .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "this sucker is the fastest thing I've ever owned .", + "this car corners like it's on rails ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I believe it . Hoo , this car corners like it's on rails .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "We are on the high way . Find the pound shade ..", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "this sucker is the fastest thing I've ever owned .", + "this car corners like it's on rails ." + ], + "type": [ + "hybrid" + ], + "text": "We are on the high way . Find the pound shade ..", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Wow , this car can really burn rubber .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "this car can really burn rubber ." + ], + "type": [ + "no-context" + ], + "text": "Wow , this car can really burn rubber .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "It's a great feeling .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "this car can really burn rubber ." + ], + "type": [ + "inter-personal" + ], + "text": "It's a great feeling .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "You made a perfect choice , Jack .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "You made a perfect choice ," + ], + "type": [ + "no-context" + ], + "text": "You made a perfect choice , Jack .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Thanks , Daisy .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "You made a perfect choice , Jack ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks , Daisy .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3755.json b/reccon/sources/tr_3755.json new file mode 100644 index 0000000000000000000000000000000000000000..f86c98a8af4120e1a8c24317a1bede138c5ce3d4 --- /dev/null +++ b/reccon/sources/tr_3755.json @@ -0,0 +1,130 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello , Ellen .", + "emotion": "neutral", + "text": "Hello , Ellen .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hello , Helen , have you heard the news ? There ' s been a horrible accident .", + "emotion": "neutral", + "text": "Hello , Helen , have you heard the news ? There ' s been a horrible accident .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Oh , no ! What happened ?", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "There ' s been a horrible accident ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , no ! What happened ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Hilda Harris husband , Henry had an accident on his way home from work .", + "emotion": "neutral", + "text": "Hilda Harris husband , Henry had an accident on his way home from work .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "How awful ! Was he hurt ?", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Henry had an accident on his way home from work ." + ], + "type": [ + "inter-personal" + ], + "text": "How awful ! Was he hurt ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yes . He was taken to the hospital in an ambulance .", + "emotion": "neutral", + "text": "Yes . He was taken to the hospital in an ambulance .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "How did it happen ?", + "emotion": "neutral", + "text": "How did it happen ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "His car was hit by an express train . It happened at the crossing just behind his house .", + "emotion": "neutral", + "text": "His car was hit by an express train . It happened at the crossing just behind his house .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "How horrible !", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "His car was hit by an express train ." + ], + "type": [ + "inter-personal" + ], + "text": "How horrible !", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "He ' s having an operation in the hospital now . Poor Hilda ! You can imagine how unhappy she is .", + "emotion": "neutral", + "text": "He ' s having an operation in the hospital now . Poor Hilda ! You can imagine how unhappy she is .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I hope he ' ll be all right .", + "emotion": "neutral", + "text": "I hope he ' ll be all right .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I hope so , too .", + "emotion": "neutral", + "text": "I hope so , too .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_377.json b/reccon/sources/tr_377.json new file mode 100644 index 0000000000000000000000000000000000000000..95edd564a899b5ba93490259ca542bdec4d5c6c2 --- /dev/null +++ b/reccon/sources/tr_377.json @@ -0,0 +1,146 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What a great weekend that was !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "What a great weekend that was !" + ], + "type": [ + "no-context" + ], + "text": "What a great weekend that was !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "My feelings exactly .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "What a great weekend that was !" + ], + "type": [ + "inter-personal" + ], + "text": "My feelings exactly .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I really enjoy the beach in the summer .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I really enjoy the beach in the summer ." + ], + "type": [ + "no-context" + ], + "text": "I really enjoy the beach in the summer .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I couldn't agree with you more .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I really enjoy the beach in the summer ." + ], + "type": [ + "inter-personal" + ], + "text": "I couldn't agree with you more .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "We should come here more often .", + "emotion": "happiness", + "explanation": "Assuming the phrase of suggestion is not the actual cause of happiness emotion.", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I really enjoy the beach in the summer ." + ], + "type": [ + "self-contagion" + ], + "text": "We should come here more often .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "You are absolutely right .", + "emotion": "happiness", + "explanation": "Assuming B is happy because A wants to come with them again.", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "We should come here more often ." + ], + "type": [ + "inter-personal" + ], + "text": "You are absolutely right .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I'd like to come back next weekend .", + "emotion": "happiness", + "explanation": "Assuming A is happy because they can come back on next weekend.", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I'd like to come back next weekend ." + ], + "type": [ + "no-context" + ], + "text": "I'd like to come back next weekend .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That's exactly the way I feel .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I'd like to come back next weekend ." + ], + "type": [ + "inter-personal" + ], + "text": "That's exactly the way I feel .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3770.json b/reccon/sources/tr_3770.json new file mode 100644 index 0000000000000000000000000000000000000000..1398efc78457f425897693e04cddd435c29a9e81 --- /dev/null +++ b/reccon/sources/tr_3770.json @@ -0,0 +1,154 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Welcome to our university ' s fifties anniversary , Sir . Please have a seat .", + "emotion": "happiness", + "explanation": "Greetings", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "university ' s fifties anniversary" + ], + "type": [ + "no-context" + ], + "text": "Welcome to our university ' s fifties anniversary , Sir . Please have a seat .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Thank you . Wow , your school has so many honors . Congratulations !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "Welcome to our university ' s fifties anniversary , Sir . Please have a seat .", + "Wow , your school has so many honors . Congratulations !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you . Wow , your school has so many honors . Congratulations !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Thank you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Wow , your school has so many honors . Congratulations !" + ], + "type": [ + "inter-personal" + ], + "text": "Thank you .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Excuse me . I wonder see Dean Mr . Lee first . I was wondering if could you tell me where his office is ?", + "emotion": "neutral", + "text": "Excuse me . I wonder see Dean Mr . Lee first . I was wondering if could you tell me where his office is ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Certainly . Mr . Lee ' s office building at the south end of the campus , just beside the library .", + "emotion": "neutral", + "text": "Certainly . Mr . Lee ' s office building at the south end of the campus , just beside the library .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Excuse me ?", + "emotion": "neutral", + "text": "Excuse me ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Let me show you the way . Please follow me .", + "emotion": "happiness", + "explanation": "speaker is happy to help", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Let me show you the way ." + ], + "type": [ + "no-context" + ], + "text": "Let me show you the way . Please follow me .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Thank you very much . It ' s very kind of you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Let me show you the way ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you very much . It ' s very kind of you .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "My pleasure .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Thank you very much . It ' s very kind of you ." + ], + "type": [ + "inter-personal" + ], + "text": "My pleasure .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "This is it ?", + "emotion": "neutral", + "text": "This is it ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "It ' s up on the second floor . You have to use the stairs . The elevator isn ' t working .", + "emotion": "neutral", + "text": "It ' s up on the second floor . You have to use the stairs . The elevator isn ' t working .", + "id": 11 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3772.json b/reccon/sources/tr_3772.json new file mode 100644 index 0000000000000000000000000000000000000000..45b79d9fe66a7fb00f31d221372e23687053c79f --- /dev/null +++ b/reccon/sources/tr_3772.json @@ -0,0 +1,172 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I ' m going to the beauty parlor . Do you want to come too ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I ' m going to the beauty parlor ." + ], + "type": [ + "no-context" + ], + "text": "I ' m going to the beauty parlor . Do you want to come too ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Sure . Let ' s go . What are you going to have done ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I ' m going to the beauty parlor . Do you want to come too ?" + ], + "type": [ + "inter-personal" + ], + "text": "Sure . Let ' s go . What are you going to have done ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I want to have a foot massage and haircut .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "Sure . Let ' s go .", + "I want to have a foot massage and haircut ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I want to have a foot massage and haircut .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "A foot massage sounds like a great idea . They are very relaxing . I ' d also like to have a mudpack on my face . It ' s supposed to help with your complexion .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "A foot massage sounds like a great idea . They are very relaxing . I ' d also like to have a mudpack on my face . It ' s supposed to help with your complexion ." + ], + "type": [ + "no-context" + ], + "text": "A foot massage sounds like a great idea . They are very relaxing . I ' d also like to have a mudpack on my face . It ' s supposed to help with your complexion .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Good idea . We should also pedicures and manicures .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "A foot massage sounds like a great idea . They are very relaxing . I ' d also like to have a mudpack on my face . It ' s supposed to help with your complexion .", + "We should also pedicures and manicures ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Good idea . We should also pedicures and manicures .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "This could become a very expensive trip to be beauty parlour !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Good idea . We should also pedicures and manicures ." + ], + "type": [ + "inter-personal" + ], + "text": "This could become a very expensive trip to be beauty parlour !", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I think it ' s a good idea to pamper yourself occasionally . Don ' t you agree ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "it ' s a good idea to pamper yourself occasionally" + ], + "type": [ + "no-context" + ], + "text": "I think it ' s a good idea to pamper yourself occasionally . Don ' t you agree ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Oh , I agree . We both work hard and a little beauty treatment can relieve stress .", + "emotion": "neutral", + "text": "Oh , I agree . We both work hard and a little beauty treatment can relieve stress .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Maybe we should try a thai massage too .", + "emotion": "neutral", + "text": "Maybe we should try a thai massage too .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "What ' s special about a thai massage ?", + "emotion": "neutral", + "text": "What ' s special about a thai massage ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "That ' s when the masseuse walk on your back and massage you with her feet .", + "emotion": "neutral", + "text": "That ' s when the masseuse walk on your back and massage you with her feet .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Sounds painful !", + "emotion": "neutral", + "text": "Sounds painful !", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3773.json b/reccon/sources/tr_3773.json new file mode 100644 index 0000000000000000000000000000000000000000..579899411cc48547676f33afdb33e0a48dfbb7a8 --- /dev/null +++ b/reccon/sources/tr_3773.json @@ -0,0 +1,99 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I just love your hair that way .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I just love your hair that way ." + ], + "type": [ + "no-context" + ], + "text": "I just love your hair that way .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Thanks .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I just love your hair that way ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Where did you have it done ?", + "emotion": "neutral", + "text": "Where did you have it done ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "My sister did it . When did you get yours cut ?", + "emotion": "neutral", + "text": "My sister did it . When did you get yours cut ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Just yesterday . I'm still getting used to it .", + "emotion": "neutral", + "text": "Just yesterday . I'm still getting used to it .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Well , it looks very nice .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "it looks very nice ." + ], + "type": [ + "no-context" + ], + "text": "Well , it looks very nice .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Thanks .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "it looks very nice ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3777.json b/reccon/sources/tr_3777.json new file mode 100644 index 0000000000000000000000000000000000000000..bc5f64516dbfde994efea7386b1ad9fb9072a226 --- /dev/null +++ b/reccon/sources/tr_3777.json @@ -0,0 +1,214 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Paul , what kind of music do you like to listen to ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Paul , what kind of music do you like to listen to ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "All kinds , but mostly Pop , rock and classical . Why ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Paul , what kind of music do you like to listen to ?" + ], + "type": [ + "inter-personal" + ], + "text": "All kinds , but mostly Pop , rock and classical . Why ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I have tickets to a show . Do you want to go with me ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "All kinds , but mostly Pop , rock and classical ." + ], + "type": [ + "inter-personal" + ], + "text": "I have tickets to a show . Do you want to go with me ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "What kind of music is it ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I have tickets to a show . Do you want to go with me ?" + ], + "type": [ + "inter-personal" + ], + "text": "What kind of music is it ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Pop . It's Maria Carey .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Pop . It's Maria Carey ." + ], + "type": [ + "no-context" + ], + "text": "Pop . It's Maria Carey .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "When is it ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Pop . It's Maria Carey ." + ], + "type": [ + "inter-personal" + ], + "text": "When is it ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "At 8P M tomorrow night .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "When is it ?" + ], + "type": [ + "inter-personal" + ], + "text": "At 8P M tomorrow night .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yeah , I'd like to go . Do you think we should have dinner first ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "At 8P M tomorrow night ." + ], + "type": [ + "inter-personal" + ], + "text": "Yeah , I'd like to go . Do you think we should have dinner first ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yes , that's a good idea .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Yeah , I'd like to go . Do you think we should have dinner first ?" + ], + "type": [ + "inter-personal" + ], + "text": "Yes , that's a good idea .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Let's eat at the restaurant across the street from my apartment .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Yes , that's a good idea ." + ], + "type": [ + "inter-personal" + ], + "text": "Let's eat at the restaurant across the street from my apartment .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Oh , I think I know the place you mean . We ate there last month , right ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "Let's eat at the restaurant across the street from my apartment .", + "Oh , I think I know the place you mean . We ate there last month , right ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , I think I know the place you mean . We ate there last month , right ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Yes , that's right . You have a good memory .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I think I know the place you mean . We ate there last month , right ?" + ], + "type": [ + "inter-personal" + ], + "text": "Yes , that's right . You have a good memory .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3786.json b/reccon/sources/tr_3786.json new file mode 100644 index 0000000000000000000000000000000000000000..4d9e0a3d7c1540873199f5f225639c6d8b53190d --- /dev/null +++ b/reccon/sources/tr_3786.json @@ -0,0 +1,227 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello , could you arrange a dinner for us ?", + "emotion": "neutral", + "text": "Hello , could you arrange a dinner for us ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Sure , what time ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "could you arrange a dinner for us ?" + ], + "type": [ + "inter-personal" + ], + "text": "Sure , what time ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Eight o'clock tomorrow evening .", + "emotion": "neutral", + "text": "Eight o'clock tomorrow evening .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "For how many people ?", + "emotion": "neutral", + "text": "For how many people ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Ten .", + "emotion": "neutral", + "text": "Ten .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Western food or Chinese food ?", + "emotion": "neutral", + "text": "Western food or Chinese food ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Chinese food .", + "emotion": "neutral", + "text": "Chinese food .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Do you want an expensive meal ?", + "emotion": "neutral", + "text": "Do you want an expensive meal ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "No , not too lavish .", + "emotion": "neutral", + "text": "No , not too lavish .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "How much would you like to spend for each person ?", + "emotion": "neutral", + "text": "How much would you like to spend for each person ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "What is the usual thing here ?", + "emotion": "neutral", + "text": "What is the usual thing here ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Forty to eighty RIB Yuan a plate .", + "emotion": "neutral", + "text": "Forty to eighty RIB Yuan a plate .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Let's say sixty Yuan then .", + "emotion": "neutral", + "text": "Let's say sixty Yuan then .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "OK . Is there anything special you'd like to have on the menu ?", + "emotion": "neutral", + "text": "OK . Is there anything special you'd like to have on the menu ?", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "We'd like to have typical Chinese food .", + "emotion": "neutral", + "text": "We'd like to have typical Chinese food .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Anything you'd rather not have ?", + "emotion": "neutral", + "text": "Anything you'd rather not have ?", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "No snakes , please .", + "emotion": "neutral", + "text": "No snakes , please .", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "How about drinks ?", + "emotion": "neutral", + "text": "How about drinks ?", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "Mao Tai and Qingdao Beer .", + "emotion": "neutral", + "text": "Mao Tai and Qingdao Beer .", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "Well . Dinner for ten at sixty Yuan a plate , drink's extra , at 8 o'clock tomorrow evening . Is that all right ?", + "emotion": "neutral", + "text": "Well . Dinner for ten at sixty Yuan a plate , drink's extra , at 8 o'clock tomorrow evening . Is that all right ?", + "id": 20 + }, + { + "turn": 21, + "speaker": "A", + "utterance": "Right , thanks .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 20 + ], + "expanded emotion cause span": [ + "Dinner for ten at sixty Yuan a plate , drink's extra , at 8 o'clock tomorrow evening . Is that all right ?" + ], + "type": [ + "inter-personal" + ], + "text": "Right , thanks .", + "id": 21 + }, + { + "turn": 22, + "speaker": "B", + "utterance": "My pleasure , see you tomorrow evening .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 21 + ], + "expanded emotion cause span": [ + "Right , thanks ." + ], + "type": [ + "inter-personal" + ], + "text": "My pleasure , see you tomorrow evening .", + "id": 22 + }, + { + "turn": 23, + "speaker": "A", + "utterance": "See you then .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 22 + ], + "expanded emotion cause span": [ + "My pleasure , see you tomorrow evening ." + ], + "type": [ + "inter-personal" + ], + "text": "See you then .", + "id": 23, + "source_sentences": [ + 21 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3805.json b/reccon/sources/tr_3805.json new file mode 100644 index 0000000000000000000000000000000000000000..237293ba74bf5f995bf2bb107faef5b0afe14c2f --- /dev/null +++ b/reccon/sources/tr_3805.json @@ -0,0 +1,345 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "How are you doing , Christopher ?", + "emotion": "neutral", + "text": "How are you doing , Christopher ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "To be honest , I'm really fed up with work at the moment . I need a break !", + "emotion": "neutral", + "text": "To be honest , I'm really fed up with work at the moment . I need a break !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Are you doing anything this weekend ?", + "emotion": "neutral", + "text": "Are you doing anything this weekend ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I have to work on Saturday all day ! I really hate my job !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I have to work on Saturday all day !" + ], + "type": [ + "no-context" + ], + "text": "I have to work on Saturday all day ! I really hate my job !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Are you available on Sunday ?", + "emotion": "neutral", + "text": "Are you available on Sunday ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yes , that's my only day off until Thursday .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Are you available on Sunday ?", + "Yes , that's my only day off until Thursday ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , that's my only day off until Thursday .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Ok , well , my friends and I are planning on going to the beach on Sunday . We tend to leave around noon whenever we go anywhere , so you could still sleep in . Do you want to come with us ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "my friends and I are planning on going to the beach" + ], + "type": [ + "no-context" + ], + "text": "Ok , well , my friends and I are planning on going to the beach on Sunday . We tend to leave around noon whenever we go anywhere , so you could still sleep in . Do you want to come with us ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That'd be fantastic ! Which beach are you going to ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 7 + ], + "expanded emotion cause span": [ + "my friends and I are planning on going to the beach", + "Do you want to come with us ?" + ], + "type": [ + "inter-personal" + ], + "text": "That'd be fantastic ! Which beach are you going to ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "It's a quiet beach just about an hour outside of the city .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 9 + ], + "expanded emotion cause span": [ + "my friends and I are planning on going to the beach", + "It's a quiet beach just about an hour outside of the city ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "It's a quiet beach just about an hour outside of the city .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "What should I bring with me ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 7, + 7 + ], + "expanded emotion cause span": [ + "my friends and I are planning on going to the beach", + "Do you want to come with us ?" + ], + "type": [ + "inter-personal" + ], + "text": "What should I bring with me ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "We've got plenty of inflatables , but if you want to sit on a chair , you'll have to bring your own sunlounger .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 9, + 11 + ], + "expanded emotion cause span": [ + "my friends and I are planning on going to the beach", + "It's a quiet beach just about an hour outside of the city .", + "We've got plenty of inflatables ," + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "We've got plenty of inflatables , but if you want to sit on a chair , you'll have to bring your own sunlounger .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I can just use my beach towel . I love lazing around in the sun .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "I love lazing around in the sun ." + ], + "type": [ + "no-context" + ], + "text": "I can just use my beach towel . I love lazing around in the sun .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Do you like surfing ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 13 + ], + "expanded emotion cause span": [ + "my friends and I are planning on going to the beach", + "like surfing ?" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Do you like surfing ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "I've actually never tried . Do you have a surfboard ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "Do you like surfing ?" + ], + "type": [ + "inter-personal" + ], + "text": "I've actually never tried . Do you have a surfboard ?", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "We've got a few . I can teach you how to surf on Sunday . It'll be fun !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 15, + 15 + ], + "expanded emotion cause span": [ + "my friends and I are planning on going to the beach", + "I can teach", + "It'll be fun !" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "We've got a few . I can teach you how to surf on Sunday . It'll be fun !", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "I can't wait ! It sounds like we're going to have a great time . How much money should I bring ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15, + 15, + 16, + 16 + ], + "expanded emotion cause span": [ + "I can teach you", + "It'll be fun !", + "I can't wait !", + "we're going to have a great time ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I can't wait ! It sounds like we're going to have a great time . How much money should I bring ?", + "id": 16, + "source_sentences": [ + 14, + 14, + 15 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 17, + "speaker": "A", + "utterance": "You'll just need roughly $ 10 for food and gas money . My friend is driving , so we usually all chip in a few dollars for gas money .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 7, + 15, + 15 + ], + "expanded emotion cause span": [ + "my friends and I are planning on going to the beach", + "I can teach", + "It'll be fun !" + ], + "type": [ + "self-contagion" + ], + "text": "You'll just need roughly $ 10 for food and gas money . My friend is driving , so we usually all chip in a few dollars for gas money .", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "Ok , where and when should I meet you ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 15, + 15, + 16, + 16 + ], + "expanded emotion cause span": [ + "I can teach you", + "It'll be fun !", + "I can't wait !", + "we're going to have a great time ." + ], + "type": [ + "hybrid" + ], + "text": "Ok , where and when should I meet you ?", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "We'll pick you up at your place at noon . Be there or be square !", + "emotion": "happiness", + "explanation": "The speaker is in general excited to go to the beach.", + "flag": "F", + "expanded emotion cause evidence": [ + 7, + 15, + 15 + ], + "expanded emotion cause span": [ + "my friends and I are planning on going to the beach", + "I can teach", + "It'll be fun !" + ], + "type": [ + "self-contagion" + ], + "text": "We'll pick you up at your place at noon . Be there or be square !", + "id": 19 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3807.json b/reccon/sources/tr_3807.json new file mode 100644 index 0000000000000000000000000000000000000000..512f11b478841de39d13675f4bd42433a674815e --- /dev/null +++ b/reccon/sources/tr_3807.json @@ -0,0 +1,155 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Could you help me prepare for my presentation on Friday ?", + "emotion": "neutral", + "text": "Could you help me prepare for my presentation on Friday ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I would love to help you prepare for your presentation .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I would love to help you prepare for your presentation ." + ], + "type": [ + "no-context" + ], + "text": "I would love to help you prepare for your presentation .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I hate to ask you to do something like that .", + "emotion": "neutral", + "text": "I hate to ask you to do something like that .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "This will not interfere with my work . I promise you that .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I would love to help you prepare for your presentation ." + ], + "type": [ + "self-contagion" + ], + "text": "This will not interfere with my work . I promise you that .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "When could we get together ?", + "emotion": "neutral", + "text": "When could we get together ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I could easily give you some time tomorrow night .", + "emotion": "neutral", + "text": "I could easily give you some time tomorrow night .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Would you like to meet me at the coffee house next door ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 2, + 6 + ], + "expanded emotion cause span": [ + "I would love to help you prepare for your presentation .", + "easily give you some time tomorrow night ." + ], + "type": [ + "inter-personal" + ], + "text": "Would you like to meet me at the coffee house next door ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yes , and could you write down anything you might be having trouble with ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 2, + 6 + ], + "expanded emotion cause span": [ + "I would love to help you prepare for your presentation .", + "easily give you some time tomorrow night ." + ], + "type": [ + "self-contagion" + ], + "text": "Yes , and could you write down anything you might be having trouble with ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I'll come prepared .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 2, + 6, + 8 + ], + "expanded emotion cause span": [ + "I would love to help you prepare for your presentation .", + "easily give you some time tomorrow night .", + "write down anything you might be having trouble with ?" + ], + "type": [ + "inter-personal" + ], + "text": "I'll come prepared .", + "id": 9, + "source_sentences": [ + 1, + 5, + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Goodbye until then . I promise you that you'll do well after we meet .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "I promise you that you'll do well after we meet ." + ], + "type": [ + "no-context" + ], + "text": "Goodbye until then . I promise you that you'll do well after we meet .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3810.json b/reccon/sources/tr_3810.json new file mode 100644 index 0000000000000000000000000000000000000000..adda429b6c0311d6dfec1880d3e8dab56a4730f9 --- /dev/null +++ b/reccon/sources/tr_3810.json @@ -0,0 +1,277 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "the dinner was really good . It knocked my socks off .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "the dinner was really good ." + ], + "type": [ + "no-context" + ], + "text": "the dinner was really good . It knocked my socks off .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "that's very kind of you to say so . Let's try some after-dinner wines .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "the dinner was really good ." + ], + "type": [ + "inter-personal" + ], + "text": "that's very kind of you to say so . Let's try some after-dinner wines .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "great . Sweet wines are my favorite . They always make a great finish to a decisions meal .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "Let's try some after-dinner wines .", + "Sweet wines are my favorite . They always make a great finish to a decisions meal ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "great . Sweet wines are my favorite . They always make a great finish to a decisions meal .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "do you prefer brandy or ports .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "great . Sweet wines are my favorite . They always make a great finish to a decisions meal ." + ], + "type": [ + "inter-personal" + ], + "text": "do you prefer brandy or ports .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "port , please .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "Let's try some after-dinner wines .", + "Sweet wines are my favorite . They always make a great finish to a decisions meal ." + ], + "type": [ + "hybrid" + ], + "text": "port , please .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "excellent choice . I love its smooth flavor .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "port", + "I love its smooth flavor ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "excellent choice . I love its smooth flavor .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "the port is exquisite . It must have spent years aging in barrels . Am I right ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "excellent choice . I love its smooth flavor .", + "the port is exquisite . It must have spent years aging in barrels ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "the port is exquisite . It must have spent years aging in barrels . Am I right ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "yes . You always have a good nose for wines .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "the port is exquisite . It must have spent years aging in barrels ." + ], + "type": [ + "inter-personal" + ], + "text": "yes . You always have a good nose for wines .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "next time we are about to dinner we should try some Canadian ice wine .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "we should try some Canadian ice wine ." + ], + "type": [ + "no-context" + ], + "text": "next time we are about to dinner we should try some Canadian ice wine .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "oh , what's that ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "we should try some Canadian ice wine ." + ], + "type": [ + "inter-personal" + ], + "text": "oh , what's that ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "it's made from naturally frozen grapes .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "we should try some Canadian ice wine ." + ], + "type": [ + "self-contagion" + ], + "text": "it's made from naturally frozen grapes .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "why not ? It sounds great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 11 + ], + "expanded emotion cause span": [ + "we should try some Canadian ice wine .", + "naturally frozen grapes ." + ], + "type": [ + "inter-personal" + ], + "text": "why not ? It sounds great .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "oh , here's to your health .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "It sounds great ." + ], + "type": [ + "inter-personal" + ], + "text": "oh , here's to your health .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "thanks . Cheers .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12, + 13 + ], + "expanded emotion cause span": [ + "It sounds great .", + "here's to your health ." + ], + "type": [ + "hybrid" + ], + "text": "thanks . Cheers .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "cheers .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "thanks . Cheers ." + ], + "type": [ + "inter-personal" + ], + "text": "cheers .", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3813.json b/reccon/sources/tr_3813.json new file mode 100644 index 0000000000000000000000000000000000000000..9c090dd6c002b3bf776ae4b9e1cb1f660019de3e --- /dev/null +++ b/reccon/sources/tr_3813.json @@ -0,0 +1,201 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "We came too early . There're still three hours before the performance starts .", + "emotion": "neutral", + "text": "We came too early . There're still three hours before the performance starts .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I know . Sorry , I shouldn't have rushed you , but I just couldn't stay at home and wait .", + "emotion": "neutral", + "text": "I know . Sorry , I shouldn't have rushed you , but I just couldn't stay at home and wait .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Never mind . What about taking a look around the theater ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "What about taking a look around the theater ?" + ], + "type": [ + "no-context" + ], + "text": "Never mind . What about taking a look around the theater ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Why not ? I'd love to do that .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "What about taking a look around the theater ?", + "I'd love to do that ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Why not ? I'd love to do that .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Here we go . There is a museum of the Beijing Opera art .", + "emotion": "neutral", + "text": "Here we go . There is a museum of the Beijing Opera art .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Wow . Look at this . So delicate and beautiful . Did ancient Chinese people really wear them ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Wow . Look at this . So delicate and beautiful ." + ], + "type": [ + "no-context" + ], + "text": "Wow . Look at this . So delicate and beautiful . Did ancient Chinese people really wear them ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Not really . They are just opera costumes . Do you like the embroidery ?", + "emotion": "neutral", + "text": "Not really . They are just opera costumes . Do you like the embroidery ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I surely do . They must have had advanced machines in ancient China to do that .", + "emotion": "neutral", + "text": "I surely do . They must have had advanced machines in ancient China to do that .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "No , no , no . They are all handmade , girl . You know , the ancient Chinese women were supposed to be good at needlework .", + "emotion": "neutral", + "text": "No , no , no . They are all handmade , girl . You know , the ancient Chinese women were supposed to be good at needlework .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Unbelievable ! I could never do that .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "They are all handmade , girl ." + ], + "type": [ + "inter-personal" + ], + "text": "Unbelievable ! I could never do that .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Very few can . That's why these clothes only appear in the museum .", + "emotion": "neutral", + "text": "Very few can . That's why these clothes only appear in the museum .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Listen ! Some people are singing outside . Is it the opera ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "Listen ! Some people are singing outside ." + ], + "type": [ + "no-context" + ], + "text": "Listen ! Some people are singing outside . Is it the opera ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Oh , yes . I heard there was an opera fans club . They are probably practicing now . Wanna have a look ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "Listen ! Some people are singing outside ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , yes . I heard there was an opera fans club . They are probably practicing now . Wanna have a look ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Yes , let's do it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "Wanna have a look ?" + ], + "type": [ + "inter-personal" + ], + "text": "Yes , let's do it .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Follow me . Make sure not to interrupt them .", + "emotion": "neutral", + "text": "Follow me . Make sure not to interrupt them .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Of course not . We don't do that .", + "emotion": "neutral", + "text": "Of course not . We don't do that .", + "id": 16 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3823.json b/reccon/sources/tr_3823.json new file mode 100644 index 0000000000000000000000000000000000000000..4350f70327d48f205828fe29830cdf8fa5e4c379 --- /dev/null +++ b/reccon/sources/tr_3823.json @@ -0,0 +1,166 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Are you alright , Ethan ? You don't seem to be as cheerful as you normally are .", + "emotion": "neutral", + "text": "Are you alright , Ethan ? You don't seem to be as cheerful as you normally are .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "To be honest , Ava , I've just had a really bad day .", + "emotion": "neutral", + "text": "To be honest , Ava , I've just had a really bad day .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What happened ?", + "emotion": "neutral", + "text": "What happened ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "First , I slept through my alarm and ended up two hours late to work .", + "emotion": "neutral", + "text": "First , I slept through my alarm and ended up two hours late to work .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "What did your boss say ?", + "emotion": "neutral", + "text": "What did your boss say ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "He told me that if I showed up late one more time , he'd fire me . He's so mean !", + "emotion": "neutral", + "text": "He told me that if I showed up late one more time , he'd fire me . He's so mean !", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "That's horrible . Was that the first time you'd shown up late to work ?", + "emotion": "anger", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "He told me that if I showed up late one more time , he'd fire me . He's so mean !" + ], + "type": [ + "inter-personal" + ], + "text": "That's horrible . Was that the first time you'd shown up late to work ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That was my second time . The first time , I was in a car accident .", + "emotion": "neutral", + "text": "That was my second time . The first time , I was in a car accident .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Is your boss Chinese ?", + "emotion": "neutral", + "text": "Is your boss Chinese ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "No , he's from Australia . Before I met him , I thought Australians were supposed to be relaxed and easy-going . I had no idea he'd be so fussy about things .", + "emotion": "neutral", + "text": "No , he's from Australia . Before I met him , I thought Australians were supposed to be relaxed and easy-going . I had no idea he'd be so fussy about things .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "What are you going to do ?", + "emotion": "neutral", + "text": "What are you going to do ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I think I'm going to look for another job . I need to find a boss that is a bit more sensitive and optimistic than my current boss .", + "emotion": "neutral", + "text": "I think I'm going to look for another job . I need to find a boss that is a bit more sensitive and optimistic than my current boss .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "That sounds like a sensible plan . Do you want me to help you with your job search ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "I think I'm going to look for another job ." + ], + "type": [ + "inter-personal" + ], + "text": "That sounds like a sensible plan . Do you want me to help you with your job search ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "That's very generous of you . Thanks for the offer .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13, + 14 + ], + "expanded emotion cause span": [ + "Do you want me to help you with your job search ?", + "That's very generous of you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's very generous of you . Thanks for the offer .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Don't mention it . That's what friends are for !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "That's very generous of you . Thanks for the offer ." + ], + "type": [ + "inter-personal" + ], + "text": "Don't mention it . That's what friends are for !", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3842.json b/reccon/sources/tr_3842.json new file mode 100644 index 0000000000000000000000000000000000000000..4008b2d0c5e9a2339409ad666610d3378c8b41f0 --- /dev/null +++ b/reccon/sources/tr_3842.json @@ -0,0 +1,246 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I want to say goodbye to everyone .", + "emotion": "neutral", + "text": "I want to say goodbye to everyone .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "You ' re leaving so soon . When are you off ?", + "emotion": "neutral", + "text": "You ' re leaving so soon . When are you off ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I ' m catching the nine fifteen train tomorrow morning .", + "emotion": "neutral", + "text": "I ' m catching the nine fifteen train tomorrow morning .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "how about I come and see you off ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "how about I come and see you off ?" + ], + "type": [ + "no-context" + ], + "text": "how about I come and see you off ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "You really don ' t need to .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "how about I come and see you off ?" + ], + "type": [ + "inter-personal" + ], + "text": "You really don ' t need to .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Ok . I ' ll miss you . I hope we can see each other again soon .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5, + 6 + ], + "expanded emotion cause span": [ + "how about I come and see you off ?", + "You really don ' t need to .", + "I hope we can see each other again soon ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Ok . I ' ll miss you . I hope we can see each other again soon .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I hope so , too . Thank you , Lily . Thank you for everything .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 6 + ], + "expanded emotion cause span": [ + "how about I come and see you off ?", + "I ' ll miss you . I hope we can see each other again soon ." + ], + "type": [ + "inter-personal" + ], + "text": "I hope so , too . Thank you , Lily . Thank you for everything .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "You ' re welcome .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5, + 6, + 7 + ], + "expanded emotion cause span": [ + "how about I come and see you off ?", + "You really don ' t need to .", + "I hope we can see each other again soon .", + "Thank you for everything ." + ], + "type": [ + "hybrid" + ], + "text": "You ' re welcome .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Please say goodbye to the rest of the family for me .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 4, + 6 + ], + "expanded emotion cause span": [ + "how about I come and see you off ?", + "I ' ll miss you . I hope we can see each other again soon ." + ], + "type": [ + "inter-personal" + ], + "text": "Please say goodbye to the rest of the family for me .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Ok . Take care . I hope you have a good journey .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5, + 6, + 9, + 10 + ], + "expanded emotion cause span": [ + "how about I come and see you off ?", + "You really don ' t need to .", + "I hope we can see each other again soon .", + "say goodbye to the rest of the family", + "have a good journey ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Ok . Take care . I hope you have a good journey .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Thank you . Remember to look me up if you ' re ever in Washington .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 6, + 10 + ], + "expanded emotion cause span": [ + "how about I come and see you off ?", + "I ' ll miss you . I hope we can see each other again soon .", + "have a good journey ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . Remember to look me up if you ' re ever in Washington .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Of course . I will .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5, + 6, + 9, + 10, + 11 + ], + "expanded emotion cause span": [ + "how about I come and see you off ?", + "You really don ' t need to .", + "I hope we can see each other again soon .", + "say goodbye to the rest of the family", + "have a good journey .", + "look me up if you ' re ever in Washington ." + ], + "type": [ + "hybrid" + ], + "text": "Of course . I will .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Goodbye , then . Thanks again for everything .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 6, + 13 + ], + "expanded emotion cause span": [ + "how about I come and see you off ?", + "I ' ll miss you . I hope we can see each other again soon .", + "Thanks again for everything ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Goodbye , then . Thanks again for everything .", + "id": 13, + "source_sentences": [ + 3, + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3864.json b/reccon/sources/tr_3864.json new file mode 100644 index 0000000000000000000000000000000000000000..35362a71184c19be4dd682e1123741039e8ed89a --- /dev/null +++ b/reccon/sources/tr_3864.json @@ -0,0 +1,158 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "How's your new car ?", + "emotion": "happiness", + "explanation": "happy becuase asking someone about his/her new car", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "How's your new car ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Perfect ! Couldn't be better .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Perfect ! Couldn't be better ." + ], + "type": [ + "no-context" + ], + "text": "Perfect ! Couldn't be better .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "You made a good choice , then ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Perfect ! Couldn't be better ." + ], + "type": [ + "inter-personal" + ], + "text": "You made a good choice , then ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It's just what I want .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 4 + ], + "expanded emotion cause span": [ + "Perfect ! Couldn't be better .", + "It's just what I want ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "It's just what I want .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "No regrets .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "It's just what I want ." + ], + "type": [ + "inter-personal" + ], + "text": "No regrets .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I am really pleased with it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 4, + 6 + ], + "expanded emotion cause span": [ + "Perfect ! Couldn't be better .", + "It's just what I want .", + "I am really pleased with it ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I am really pleased with it .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I am glad you are happy .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 4, + 6 + ], + "expanded emotion cause span": [ + "Perfect ! Couldn't be better .", + "It's just what I want .", + "I am really pleased with it ." + ], + "type": [ + "inter-personal" + ], + "text": "I am glad you are happy .", + "id": 7, + "source_sentences": [ + 1, + 3, + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "It's super .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Perfect ! Couldn't be better ." + ], + "type": [ + "self-contagion" + ], + "text": "It's super .", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3888.json b/reccon/sources/tr_3888.json new file mode 100644 index 0000000000000000000000000000000000000000..f6faa54fc717c7d10cf6ed4e5409147e2b654a94 --- /dev/null +++ b/reccon/sources/tr_3888.json @@ -0,0 +1,184 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I really should be on my way .", + "emotion": "neutral", + "text": "I really should be on my way .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh , don ' t go yet . Let ' s at least have one more .", + "emotion": "neutral", + "text": "Oh , don ' t go yet . Let ' s at least have one more .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "No , thank you . I can ' t .", + "emotion": "neutral", + "text": "No , thank you . I can ' t .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It ' s too bad that you have to leave so early .", + "emotion": "neutral", + "text": "It ' s too bad that you have to leave so early .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Thank you very much . I had a really good time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "too bad that you have to leave so early .", + "I had a really good time ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you very much . I had a really good time .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Thanks for coming ! We should meet again sometime soon .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "I had a really good time .", + "Thanks for coming !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thanks for coming ! We should meet again sometime soon .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "That would be great ! Actually , can I get your phone number , Ella ? That ' s assuming you don ' t mind if I call you sometime .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "We should meet again sometime soon ." + ], + "type": [ + "inter-personal" + ], + "text": "That would be great ! Actually , can I get your phone number , Ella ? That ' s assuming you don ' t mind if I call you sometime .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Anytime . You can reach me 5558929 .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "We should meet again sometime soon ." + ], + "type": [ + "self-contagion" + ], + "text": "Anytime . You can reach me 5558929 .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "ok , got it . I ' ll call you sometime next week .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "I ' ll call you sometime next week ." + ], + "type": [ + "no-context" + ], + "text": "ok , got it . I ' ll call you sometime next week .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Fine .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "I ' ll call you sometime next week ." + ], + "type": [ + "inter-personal" + ], + "text": "Fine .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "It ' s time to go and I hope we can get together again soon .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I hope we can get together again soon ." + ], + "type": [ + "no-context" + ], + "text": "It ' s time to go and I hope we can get together again soon .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I hope so , too . Bye ! Ben .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I hope we can get together again soon ." + ], + "type": [ + "inter-personal" + ], + "text": "I hope so , too . Bye ! Ben .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3896.json b/reccon/sources/tr_3896.json new file mode 100644 index 0000000000000000000000000000000000000000..38a7a5ed56e34139e09e0e687e7807b05bb899f6 --- /dev/null +++ b/reccon/sources/tr_3896.json @@ -0,0 +1,140 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Veronica ! Veronica ! Veronica ! Are you OK ?", + "emotion": "neutral", + "text": "Veronica ! Veronica ! Veronica ! Are you OK ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Steven ! What ' s going on ! Who were those guys ? I didn ' t know you have a gun ! What ' s going on !", + "emotion": "fear", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "What ' s going on ! Who were those guys ? I didn ' t know you have a gun ! What ' s going on !" + ], + "type": [ + "no-context" + ], + "text": "Steven ! What ' s going on ! Who were those guys ? I didn ' t know you have a gun ! What ' s going on !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I will come clean as soon as we get to safety , OK ? For now , you have to trust me , please ! I would never do anything to hurt you .", + "emotion": "neutral", + "text": "I will come clean as soon as we get to safety , OK ? For now , you have to trust me , please ! I would never do anything to hurt you .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Steven , I ...", + "emotion": "fear", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "What ' s going on ! Who were those guys ? I didn ' t know you have a gun ! What ' s going on !" + ], + "type": [ + "self-contagion" + ], + "text": "Steven , I ...", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I haven ' t been completely honest with you Veronica , I ' m sorry . I ' m not a fireman . I ' m not even from the United States . I ' m a spy for the Indian government .", + "emotion": "neutral", + "text": "I haven ' t been completely honest with you Veronica , I ' m sorry . I ' m not a fireman . I ' m not even from the United States . I ' m a spy for the Indian government .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "What ? Why didn ' t you tell me before ? What are you doing here ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I ' m a spy for the Indian government ." + ], + "type": [ + "inter-personal" + ], + "text": "What ? Why didn ' t you tell me before ? What are you doing here ?", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "When I was a young boy , I used to play cricket my father back in my hometown of Hyderabad . It was a peaceful town , and my father was a renowned chemist . One day , he was approached by members of the CIA , claiming that my father had made the discovery of the millennium in his small lab back at the university where he taught bio-chemistry . I never saw him again . I vowed to discover the whereabouts of my father and consequently joined the Indian Intelligence Bureau .", + "emotion": "neutral", + "text": "When I was a young boy , I used to play cricket my father back in my hometown of Hyderabad . It was a peaceful town , and my father was a renowned chemist . One day , he was approached by members of the CIA , claiming that my father had made the discovery of the millennium in his small lab back at the university where he taught bio-chemistry . I never saw him again . I vowed to discover the whereabouts of my father and consequently joined the Indian Intelligence Bureau .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "What does that have to do with those men shooting at us ? Most importantly , why did you lie to me !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "why did you lie to me !" + ], + "type": [ + "no-context" + ], + "text": "What does that have to do with those men shooting at us ? Most importantly , why did you lie to me !", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I ' m sorry , I wasn ' t supposed to meet you . I wasn ' t supposed to fall in love with you , but you have to believe me when I tell you that what I feel for you is real .", + "emotion": "neutral", + "text": "I ' m sorry , I wasn ' t supposed to meet you . I wasn ' t supposed to fall in love with you , but you have to believe me when I tell you that what I feel for you is real .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I can ' t believe this ! Why are all these things happening to me ! I can ' t take it anymore ! Let me out of the car !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "why did you lie to me !" + ], + "type": [ + "self-contagion" + ], + "text": "I can ' t believe this ! Why are all these things happening to me ! I can ' t take it anymore ! Let me out of the car !", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Veronica , wait !", + "emotion": "neutral", + "text": "Veronica , wait !", + "id": 11 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3897.json b/reccon/sources/tr_3897.json new file mode 100644 index 0000000000000000000000000000000000000000..4b27e2483b8fba469f469a9bb3612b4370504e8a --- /dev/null +++ b/reccon/sources/tr_3897.json @@ -0,0 +1,213 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey , May . How about getting together for a movie tonight ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "getting together for a movie" + ], + "type": [ + "no-context" + ], + "text": "Hey , May . How about getting together for a movie tonight ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Sure . What's playing ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "getting together for a movie" + ], + "type": [ + "inter-personal" + ], + "text": "Sure . What's playing ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Well , Let me check the newspaper . What about The Terminal ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 1, + 2 + ], + "expanded emotion cause span": [ + "getting together for a movie", + "How about getting together for a movie", + "Sure . What's playing ?" + ], + "type": [ + "hybrid" + ], + "text": "Well , Let me check the newspaper . What about The Terminal ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Wow , it stars Catherine Zeta-Jones , my favorite actress .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 4 + ], + "expanded emotion cause span": [ + "getting together for a movie", + "my favorite actress ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Wow , it stars Catherine Zeta-Jones , my favorite actress .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Well , birds of a feather flock together . I like her too . She was in a lot of dramas .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I like her too . She was in a lot of dramas ." + ], + "type": [ + "no-context" + ], + "text": "Well , birds of a feather flock together . I like her too . She was in a lot of dramas .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "She is so beautiful and elegant . And she is famous for her fine acting .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "She is so beautiful and elegant ." + ], + "type": [ + "no-context" + ], + "text": "She is so beautiful and elegant . And she is famous for her fine acting .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "What's more , she doesn't have scandals . And she likes to take part in the charitable activities .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 7 + ], + "expanded emotion cause span": [ + "she doesn't have scandals .", + "she likes to take part in the charitable activities ." + ], + "type": [ + "no-context" + ], + "text": "What's more , she doesn't have scandals . And she likes to take part in the charitable activities .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Who is the director ?", + "emotion": "neutral", + "text": "Who is the director ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Steven Spielberg . Another superstar .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Another superstar ." + ], + "type": [ + "no-context" + ], + "text": "Steven Spielberg . Another superstar .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Yes , a legend , also . I still remember , his movies , Jurassic Park and Schindler's List got him nine Oscar awards in 1994 .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "Another superstar .", + "a legend" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , a legend , also . I still remember , his movies , Jurassic Park and Schindler's List got him nine Oscar awards in 1994 .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Can you introduce the story of The Terminal briefly ?", + "emotion": "neutral", + "text": "Can you introduce the story of The Terminal briefly ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "It tells a romantic and humorous love story .", + "emotion": "neutral", + "text": "It tells a romantic and humorous love story .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "This is really exciting movie . Lets go to this one .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "This is really exciting movie ." + ], + "type": [ + "no-context" + ], + "text": "This is really exciting movie . Lets go to this one .", + "id": 13 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3905.json b/reccon/sources/tr_3905.json new file mode 100644 index 0000000000000000000000000000000000000000..be4ed6aa3f5b1df76ceeae343c6ea26ac2de1926 --- /dev/null +++ b/reccon/sources/tr_3905.json @@ -0,0 +1,165 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey , Maris , are you a part-timer ?", + "emotion": "neutral", + "text": "Hey , Maris , are you a part-timer ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Part-timer ? Is that a new buzzword ?", + "emotion": "neutral", + "text": "Part-timer ? Is that a new buzzword ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Oh , it ' s pretty popular among my classmates these days . So are you ?", + "emotion": "neutral", + "text": "Oh , it ' s pretty popular among my classmates these days . So are you ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Sure , I have a part-time job as a bartender .", + "emotion": "neutral", + "text": "Sure , I have a part-time job as a bartender .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Cool ! It must be amazing to work at a bar !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I have a part-time job as a bartender ." + ], + "type": [ + "inter-personal" + ], + "text": "Cool ! It must be amazing to work at a bar !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yeah , but I ' m not there for fun . I have to remain professional and if I get distracted , the manager would be pretty upset .", + "emotion": "neutral", + "text": "Yeah , but I ' m not there for fun . I have to remain professional and if I get distracted , the manager would be pretty upset .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "That ' s true . I ' m wondering did you learn anything from the job ?", + "emotion": "neutral", + "text": "That ' s true . I ' m wondering did you learn anything from the job ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Of course . There ' s always much to learn . I got to know more about the real world .", + "emotion": "neutral", + "text": "Of course . There ' s always much to learn . I got to know more about the real world .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "You mean you got working experience , right ?", + "emotion": "neutral", + "text": "You mean you got working experience , right ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Not just working experience . I would say the biggest lesson I learned is how to deal with people from all walks of life .", + "emotion": "neutral", + "text": "Not just working experience . I would say the biggest lesson I learned is how to deal with people from all walks of life .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "It must be very demanding .", + "emotion": "neutral", + "text": "It must be very demanding .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Sometimes it is . But after working for a few weeks , it ' s easy to figure out .", + "emotion": "neutral", + "text": "Sometimes it is . But after working for a few weeks , it ' s easy to figure out .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Really ? It sounds interesting .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "It must be very demanding .", + "Sometimes it is . But after working for a few weeks , it ' s easy to figure out ." + ], + "type": [ + "hybrid" + ], + "text": "Really ? It sounds interesting .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Maybe you can come to the bar one day and I ' ll show you around .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "It sounds interesting ." + ], + "type": [ + "inter-personal" + ], + "text": "Maybe you can come to the bar one day and I ' ll show you around .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Great . I ' m looking forward to it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "Maybe you can come to the bar one day and I ' ll show you around ." + ], + "type": [ + "inter-personal" + ], + "text": "Great . I ' m looking forward to it .", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3906.json b/reccon/sources/tr_3906.json new file mode 100644 index 0000000000000000000000000000000000000000..0deb4e8be5689038d124e5c20a70edce25429c8d --- /dev/null +++ b/reccon/sources/tr_3906.json @@ -0,0 +1,85 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Did you set your clock forward for daylight savings time ?", + "emotion": "neutral", + "text": "Did you set your clock forward for daylight savings time ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What ? Why do we have to do that ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Did you set your clock forward for daylight savings time ?" + ], + "type": [ + "inter-personal" + ], + "text": "What ? Why do we have to do that ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Well , at the start of the spring we usually have more daylight in the mornings and less in the afternoon . This is basically due to our position on the planet and the rotation of the earth . In any case , to take better advantage of the daylight available , we compensate by moving our clocks forward one hour .", + "emotion": "neutral", + "text": "Well , at the start of the spring we usually have more daylight in the mornings and less in the afternoon . This is basically due to our position on the planet and the rotation of the earth . In any case , to take better advantage of the daylight available , we compensate by moving our clocks forward one hour .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I see . That ' s convenient ! I never understood things like this , such as GMT . I never know what time zone we are in or when to change my clock !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I never understood things like this , such as GMT . I never know what time zone we are in or when to change my clock !" + ], + "type": [ + "no-context" + ], + "text": "I see . That ' s convenient ! I never understood things like this , such as GMT . I never know what time zone we are in or when to change my clock !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "That just stands for Greenwich Mean Time . Here in California , we are in Pacific Standard Time , that is eight time zones west of Greenwich . Remember when we were in Beijing ? Well , then we were in China Standard Time , and that ' s eight time zones east of Greenwich !", + "emotion": "neutral", + "text": "That just stands for Greenwich Mean Time . Here in California , we are in Pacific Standard Time , that is eight time zones west of Greenwich . Remember when we were in Beijing ? Well , then we were in China Standard Time , and that ' s eight time zones east of Greenwich !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "That ' s why it was so weird traveling from Beijing to LA ! Because of the huge time difference , even though we left Beijing at noon and flew for more than eight hours , we still arrived in LA the same day at noon ! It ' s like we went back in time !", + "emotion": "surprised", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Remember when we were in Beijing ? Well , then we were in China Standard Time , and that ' s eight time zones east of Greenwich !", + "That ' s why it was so weird traveling from Beijing to LA ! Because of the huge time difference , even though we left Beijing at noon and flew for more than eight hours , we still arrived in LA the same day at noon ! It ' s like we went back in time !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That ' s why it was so weird traveling from Beijing to LA ! Because of the huge time difference , even though we left Beijing at noon and flew for more than eight hours , we still arrived in LA the same day at noon ! It ' s like we went back in time !", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3912.json b/reccon/sources/tr_3912.json new file mode 100644 index 0000000000000000000000000000000000000000..64c54e95d4b91ede99a03cf7ae67578612003328 --- /dev/null +++ b/reccon/sources/tr_3912.json @@ -0,0 +1,144 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Mr . Lin , what are you interested in ?", + "emotion": "neutral", + "text": "Mr . Lin , what are you interested in ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I enjoy camping .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I enjoy camping ." + ], + "type": [ + "no-context" + ], + "text": "I enjoy camping .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Really ? I'm not much of an outdoor person . What do you like about it ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I enjoy camping ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? I'm not much of an outdoor person . What do you like about it ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I love the fresh air , the scenery the exercise , and the time to think .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I love the fresh air , the scenery the exercise , and the time to think ." + ], + "type": [ + "no-context" + ], + "text": "I love the fresh air , the scenery the exercise , and the time to think .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Do you hike or fish on your trips ?", + "emotion": "neutral", + "text": "Do you hike or fish on your trips ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yes , both . Last trip I fished a little and hiked five miles .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Do you hike or fish on your trips ?", + "Yes , both . Last trip I fished a little and hiked five miles ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , both . Last trip I fished a little and hiked five miles .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Did you catch anything ?", + "emotion": "neutral", + "text": "Did you catch anything ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yes , but I threw them back .", + "emotion": "neutral", + "text": "Yes , but I threw them back .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "How about Joining our summer camp next week ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "How about Joining our summer camp next week ?" + ], + "type": [ + "no-context" + ], + "text": "How about Joining our summer camp next week ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Great ! I can't wait .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "How about Joining our summer camp next week ?" + ], + "type": [ + "inter-personal" + ], + "text": "Great ! I can't wait .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3930.json b/reccon/sources/tr_3930.json new file mode 100644 index 0000000000000000000000000000000000000000..47433969e4ae175103653cc04489f273c39416f1 --- /dev/null +++ b/reccon/sources/tr_3930.json @@ -0,0 +1,156 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Julia , are you free tonight ?", + "emotion": "neutral", + "text": "Julia , are you free tonight ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What's up ?", + "emotion": "neutral", + "text": "What's up ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I want to invite you to go to the movies .", + "emotion": "neutral", + "text": "I want to invite you to go to the movies .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Are you asking me for a date ?", + "emotion": "neutral", + "text": "Are you asking me for a date ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Yes .", + "emotion": "neutral", + "text": "Yes .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I don ' t like to go to the movies on a date . It's noisy there .", + "emotion": "neutral", + "text": "I don ' t like to go to the movies on a date . It's noisy there .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Where do you want to meet ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Where do you want to meet ?" + ], + "type": [ + "no-context" + ], + "text": "Where do you want to meet ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Let's go to the coffee shop then . It's quiet there .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 4, + 8 + ], + "expanded emotion cause span": [ + "a date ?", + "Let's go to the coffee shop then ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Let's go to the coffee shop then . It's quiet there .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "What time should we meet ?", + "emotion": "happiness", + "explanation": "speaker is happy because listener agrred on the date", + "flag": "F", + "expanded emotion cause evidence": [ + 4, + 8 + ], + "expanded emotion cause span": [ + "a date ?", + "Let's go to the coffee shop then ." + ], + "type": [ + "inter-personal" + ], + "text": "What time should we meet ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "How about seven ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 4, + 8 + ], + "expanded emotion cause span": [ + "a date ?", + "Let's go to the coffee shop then ." + ], + "type": [ + "self-contagion" + ], + "text": "How about seven ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "All right .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 4, + 8 + ], + "expanded emotion cause span": [ + "a date ?", + "Let's go to the coffee shop then ." + ], + "type": [ + "inter-personal" + ], + "text": "All right .", + "id": 11, + "source_sentences": [ + 3, + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3948.json b/reccon/sources/tr_3948.json new file mode 100644 index 0000000000000000000000000000000000000000..457cfddaae364f00f671478887bc72b738a34ffe --- /dev/null +++ b/reccon/sources/tr_3948.json @@ -0,0 +1,174 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Here ' s a letter for you .", + "emotion": "neutral", + "text": "Here ' s a letter for you .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Let me see it .", + "emotion": "neutral", + "text": "Let me see it .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Who ' s the letter from ?", + "emotion": "neutral", + "text": "Who ' s the letter from ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It ' s a letter from UCLA about my acceptance .", + "emotion": "neutral", + "text": "It ' s a letter from UCLA about my acceptance .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Read it !", + "emotion": "neutral", + "text": "Read it !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "UCLA accepted me !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "UCLA accepted me !" + ], + "type": [ + "no-context" + ], + "text": "UCLA accepted me !", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Really ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "UCLA accepted me !" + ], + "type": [ + "inter-personal" + ], + "text": "Really ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I ' m not joking . I got accepted !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 8 + ], + "expanded emotion cause span": [ + "UCLA accepted me !", + "I got accepted !" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I ' m not joking . I got accepted !", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I ' m so happy for you !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 8 + ], + "expanded emotion cause span": [ + "UCLA accepted me !", + "I got accepted !" + ], + "type": [ + "inter-personal" + ], + "text": "I ' m so happy for you !", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "UCLA was my second choice , but I ' m happy knowing I ' Ve been accepted .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "UCLA was my second choice , but I ' m happy knowing I ' Ve been accepted ." + ], + "type": [ + "no-context" + ], + "text": "UCLA was my second choice , but I ' m happy knowing I ' Ve been accepted .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I am really proud of you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "UCLA was my second choice , but I ' m happy knowing I ' Ve been accepted .", + "I am really proud of you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I am really proud of you .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "You have no idea how proud I am of myself .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "UCLA accepted me !" + ], + "type": [ + "self-contagion" + ], + "text": "You have no idea how proud I am of myself .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3954.json b/reccon/sources/tr_3954.json new file mode 100644 index 0000000000000000000000000000000000000000..e751d1c580c02635a8016b82480b5e7be4832e42 --- /dev/null +++ b/reccon/sources/tr_3954.json @@ -0,0 +1,203 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What a good day !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "What a good day !" + ], + "type": [ + "no-context" + ], + "text": "What a good day !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes . It's really wonderful here The grass is greener and the air is fresher than those in the city .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "What a good day !", + "Yes . It's really wonderful here The grass is greener and the air is fresher than those in the city ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes . It's really wonderful here The grass is greener and the air is fresher than those in the city .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Right . Let's go out and enjoy the beautiful natural scenery .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "Yes . It's really wonderful here The grass is greener and the air is fresher than those in the city .", + "Right . Let's go out and enjoy the beautiful natural scenery ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Right . Let's go out and enjoy the beautiful natural scenery .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Great , let's go .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Right . Let's go out and enjoy the beautiful natural scenery ." + ], + "type": [ + "inter-personal" + ], + "text": "Great , let's go .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Wow , what a beautiful lake ! The green hills and clear water really provide magnificent scenery .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "what a beautiful lake ! The green hills and clear water really provide magnificent scenery ." + ], + "type": [ + "no-context" + ], + "text": "Wow , what a beautiful lake ! The green hills and clear water really provide magnificent scenery .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "En , it's so beautiful that I don't want to move my eyes from it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "it's so beautiful that I don't want to move my eyes from it ." + ], + "type": [ + "no-context" + ], + "text": "En , it's so beautiful that I don't want to move my eyes from it .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I feel as if I'm living in a different world , honey .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I feel as if I'm living in a different world , honey ." + ], + "type": [ + "no-context" + ], + "text": "I feel as if I'm living in a different world , honey .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "The same to me . All the things here make me happy , the mountain , the water , the grass , the birds , the sunshine ...", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "All the things here make me happy , the mountain , the water , the grass , the birds , the sunshine ..." + ], + "type": [ + "no-context" + ], + "text": "The same to me . All the things here make me happy , the mountain , the water , the grass , the birds , the sunshine ...", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I think we should go out more frequently . The natural scenery can do us good .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "I think we should go out more frequently . The natural scenery can do us good ." + ], + "type": [ + "no-context" + ], + "text": "I think we should go out more frequently . The natural scenery can do us good .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "That's the point . We should walk into the nature and enjoy its beauty whenever we have time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "We should walk into the nature and enjoy its beauty whenever we have time ." + ], + "type": [ + "no-context" + ], + "text": "That's the point . We should walk into the nature and enjoy its beauty whenever we have time .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Right . The city life has made us tired and out of energy , while the natural world can bring us quite new feelings .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "We should walk into the nature and enjoy its beauty whenever we have time .", + "the natural world can bring us quite new feelings ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Right . The city life has made us tired and out of energy , while the natural world can bring us quite new feelings .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3957.json b/reccon/sources/tr_3957.json new file mode 100644 index 0000000000000000000000000000000000000000..4bd3b9d6d8ef0e3269f280b266924d7f493d8839 --- /dev/null +++ b/reccon/sources/tr_3957.json @@ -0,0 +1,282 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "what a nice uniform !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "what a nice uniform !" + ], + "type": [ + "no-context" + ], + "text": "what a nice uniform !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "thanks ; do you like it ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "what a nice uniform !" + ], + "type": [ + "inter-personal" + ], + "text": "thanks ; do you like it ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "not really . I was being sarcastic . Does it come with the job ?", + "emotion": "neutral", + "text": "not really . I was being sarcastic . Does it come with the job ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "yes , everyone on the sales floor has to wear one . They're supposed to make us look more professional .", + "emotion": "neutral", + "text": "yes , everyone on the sales floor has to wear one . They're supposed to make us look more professional .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "they're not actually that bad . They could be worse . What do you think about it ?", + "emotion": "neutral", + "text": "they're not actually that bad . They could be worse . What do you think about it ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I don't mind it , actually . I don't have to worry about what I'm going to wear every day .", + "emotion": "neutral", + "text": "I don't mind it , actually . I don't have to worry about what I'm going to wear every day .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "so are you enjoying your new job ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I don't have to worry about what I'm going to wear every day ." + ], + "type": [ + "inter-personal" + ], + "text": "so are you enjoying your new job ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "it's much better than my old one . My new boss is great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "it's much better than my old one . My new boss is great ." + ], + "type": [ + "no-context" + ], + "text": "it's much better than my old one . My new boss is great .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "how do you like working in sales ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "it's much better than my old one . My new boss is great ." + ], + "type": [ + "inter-personal" + ], + "text": "how do you like working in sales ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I like the fact that I get to work with people . It makes the day go by much faster .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "I like the fact that I get to work with people ." + ], + "type": [ + "no-context" + ], + "text": "I like the fact that I get to work with people . It makes the day go by much faster .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "that's good . Have you met Jane yet ? She's the intern in the international travel department .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "I like the fact that I get to work with people ." + ], + "type": [ + "inter-personal" + ], + "text": "that's good . Have you met Jane yet ? She's the intern in the international travel department .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "yeah , I've met her . She's a genius saleswoman !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "I've met her . She's a genius saleswoman !" + ], + "type": [ + "no-context" + ], + "text": "yeah , I've met her . She's a genius saleswoman !", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I know ! She could sell fridges to Eskimos !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "I've met her . She's a genius saleswoman !" + ], + "type": [ + "inter-personal" + ], + "text": "I know ! She could sell fridges to Eskimos !", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "how do you know her ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 13, + 14 + ], + "expanded emotion cause span": [ + "She could sell fridges to Eskimos !", + "how do you know her ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "how do you know her ?", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "she's my cousin .", + "emotion": "neutral", + "text": "she's my cousin .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "why didn't you tell me about that before ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "she's my cousin ." + ], + "type": [ + "inter-personal" + ], + "text": "why didn't you tell me about that before ?", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "I don't know . I didn't think it was that interesting .", + "emotion": "neutral", + "text": "I don't know . I didn't think it was that interesting .", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "well , now that I know that , maybe we should all go out for dinner sometime .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 18 + ], + "expanded emotion cause span": [ + "maybe we should all go out for dinner sometime ." + ], + "type": [ + "no-context" + ], + "text": "well , now that I know that , maybe we should all go out for dinner sometime .", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "that's a good idea . Let's discuss after work .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 18 + ], + "expanded emotion cause span": [ + "maybe we should all go out for dinner sometime ." + ], + "type": [ + "inter-personal" + ], + "text": "that's a good idea . Let's discuss after work .", + "id": 19, + "source_sentences": [ + 17 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_396.json b/reccon/sources/tr_396.json new file mode 100644 index 0000000000000000000000000000000000000000..c1acd9ab2af5e9dad0644e35695ee4f6e2b10360 --- /dev/null +++ b/reccon/sources/tr_396.json @@ -0,0 +1,149 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "How do you like your job here , Linda ?", + "emotion": "neutral", + "text": "How do you like your job here , Linda ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It's interesting , I like being an editor .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "It's interesting , I like being an editor ." + ], + "type": [ + "no-context" + ], + "text": "It's interesting , I like being an editor .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Why ?", + "emotion": "neutral", + "text": "Why ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I like talking to writers , I get to meet a lot of interesting people .", + "emotion": "happiness", + "explanation": "happily sharing his experience", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I like talking to writers , I get to meet a lot of interesting people ." + ], + "type": [ + "no-context" + ], + "text": "I like talking to writers , I get to meet a lot of interesting people .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I'm happy to hear that , but publishing is more than just talking to writers . it involves a lot of work , patience and responsibility . Most of the work is boring .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 4 + ], + "expanded emotion cause span": [ + "It's interesting , I like being an editor .", + "I like talking to writers , I get to meet a lot of interesting people ." + ], + "type": [ + "inter-personal" + ], + "text": "I'm happy to hear that , but publishing is more than just talking to writers . it involves a lot of work , patience and responsibility . Most of the work is boring .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I don't feel bored at all . I'm getting along with my colleagues . I will enjoy working with them . People are great in this industry .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 4, + 6 + ], + "expanded emotion cause span": [ + "It's interesting , I like being an editor .", + "I like talking to writers , I get to meet a lot of interesting people .", + "I don't feel bored at all . I'm getting along with my colleagues . I will enjoy working with them . People are great in this industry ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I don't feel bored at all . I'm getting along with my colleagues . I will enjoy working with them . People are great in this industry .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Do you have any complaints ?", + "emotion": "neutral", + "text": "Do you have any complaints ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "No , I have no complaints . I hear there are many opportunities to move up in this company . is that true ?", + "emotion": "neutral", + "text": "No , I have no complaints . I hear there are many opportunities to move up in this company . is that true ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yes , you have many opportunities to grow in this company as long as you do well .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "you have many opportunities to grow in this company as long as you do well ." + ], + "type": [ + "no-context" + ], + "text": "Yes , you have many opportunities to grow in this company as long as you do well .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "That's perfect . I will definitely do well .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "you have many opportunities to grow in this company as long as you do well ." + ], + "type": [ + "inter-personal" + ], + "text": "That's perfect . I will definitely do well .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3971.json b/reccon/sources/tr_3971.json new file mode 100644 index 0000000000000000000000000000000000000000..5bf1e40aa33c579bbf51afc6cee5c50f35240a58 --- /dev/null +++ b/reccon/sources/tr_3971.json @@ -0,0 +1,272 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Can you believe me ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Can you believe me ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Sure .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Sure .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Please count on my love .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 3 + ], + "expanded emotion cause span": [ + "b", + "Please count on my love ." + ], + "type": [ + "latent", + "no-context" + ], + "text": "Please count on my love .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I will .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + "b", + 3 + ], + "expanded emotion cause span": [ + "b", + "Please count on my love ." + ], + "type": [ + "latent", + "inter-personal" + ], + "text": "I will .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I'll be yours through endless time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 3, + 5 + ], + "expanded emotion cause span": [ + "b", + "Please count on my love .", + "I'll be yours through endless time ." + ], + "type": [ + "latent", + "no-context", + "self-contagion" + ], + "text": "I'll be yours through endless time .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I see . And I'll always be devoted to you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "I'll be yours through endless time .", + "I'll always be devoted to you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I see . And I'll always be devoted to you .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Thank you . I know I've nothing to offer you , but I'll never give you reason to cry .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 3, + 6, + 7 + ], + "expanded emotion cause span": [ + "b", + "Please count on my love .", + "I'll always be devoted to you .", + "I'll never give you reason to cry ." + ], + "type": [ + "latent", + "no-context", + "hybrid" + ], + "text": "Thank you . I know I've nothing to offer you , but I'll never give you reason to cry .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I'll never hurt you ; I'll never lie .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7, + 8 + ], + "expanded emotion cause span": [ + "I'll always be devoted to you .", + "I'll never give you reason to cry .", + "I'll never hurt you ; I'll never lie ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I'll never hurt you ; I'll never lie .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "My love will grow , like a river to flow .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "I'll never hurt you ; I'll never lie .", + "My love will grow , like a river to flow ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "My love will grow , like a river to flow .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "It can't be dry , and can't die .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 9 + ], + "expanded emotion cause span": [ + "I'll always be devoted to you .", + "My love will grow , like a river to flow ." + ], + "type": [ + "hybrid" + ], + "text": "It can't be dry , and can't die .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I don't know whether we are in a dream .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 8, + 9, + 11 + ], + "expanded emotion cause span": [ + "I'll always be devoted to you .", + "I'll never hurt you ; I'll never lie .", + "My love will grow , like a river to flow .", + "I don't know whether we are in a dream ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I don't know whether we are in a dream .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Aha , Aha ...", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 3, + 5, + 6, + 7, + 9, + 6, + 8, + 9, + 11 + ], + "expanded emotion cause span": [ + "b", + "Please count on my love .", + "I'll be yours through endless time .", + "I'll always be devoted to you .", + "I'll never give you reason to cry .", + "My love will grow , like a river to flow .", + "I'll always be devoted to you .", + "I'll never hurt you ; I'll never lie .", + "My love will grow , like a river to flow .", + "I don't know whether we are in a dream ." + ], + "type": [ + "latent", + "hybrid" + ], + "text": "Aha , Aha ...", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3972.json b/reccon/sources/tr_3972.json new file mode 100644 index 0000000000000000000000000000000000000000..71509d4518067fa6edec8574f9ad094ed7861a6a --- /dev/null +++ b/reccon/sources/tr_3972.json @@ -0,0 +1,256 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , Sara , what are you reading ?", + "emotion": "neutral", + "text": "Hi , Sara , what are you reading ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hi , John , I am trying to find a carpenter .", + "emotion": "neutral", + "text": "Hi , John , I am trying to find a carpenter .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Why ?", + "emotion": "neutral", + "text": "Why ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Well , I want to build a deck in my back yard .", + "emotion": "neutral", + "text": "Well , I want to build a deck in my back yard .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "What for ?", + "emotion": "neutral", + "text": "What for ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "So I can have a special place to hang out with friends , and also do some barbecuing on weekends .", + "emotion": "neutral", + "text": "So I can have a special place to hang out with friends , and also do some barbecuing on weekends .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "That sounds cool . Do you mind if I recommend myself for the job ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I can have a special place to hang out with friends , and also do some barbecuing on weekends ." + ], + "type": [ + "inter-personal" + ], + "text": "That sounds cool . Do you mind if I recommend myself for the job ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "You ? Do you have a carpenter's license ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Do you mind if I recommend myself for the job ?" + ], + "type": [ + "inter-personal" + ], + "text": "You ? Do you have a carpenter's license ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yes , of course . But I only freelance on weekends with my uncle .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "Do you have a carpenter's license ?", + "Yes , of course ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , of course . But I only freelance on weekends with my uncle .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Wow ! That's cool . So , let me give you some details about the deck I want .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "Do you have a carpenter's license ?", + "Yes , of course ." + ], + "type": [ + "hybrid" + ], + "text": "Wow ! That's cool . So , let me give you some details about the deck I want .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Please go ahead , I am listening .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Wow ! That's cool . So , let me give you some details about the deck I want ." + ], + "type": [ + "inter-personal" + ], + "text": "Please go ahead , I am listening .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I'd like my deck to be at the same level as the back door .", + "emotion": "neutral", + "text": "I'd like my deck to be at the same level as the back door .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Is your back door higher than the ground level ?", + "emotion": "neutral", + "text": "Is your back door higher than the ground level ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Yes , the back door is about four or five steps higher than the ground .", + "emotion": "neutral", + "text": "Yes , the back door is about four or five steps higher than the ground .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Okay , then you need a deck with a guardrail .", + "emotion": "neutral", + "text": "Okay , then you need a deck with a guardrail .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "I don't like things to be fancy .", + "emotion": "neutral", + "text": "I don't like things to be fancy .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "Don't worry . I will build your deck with a simple but classic look .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 17 + ], + "expanded emotion cause span": [ + "I will build your deck with a simple but classic look ." + ], + "type": [ + "no-context" + ], + "text": "Don't worry . I will build your deck with a simple but classic look .", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "Hmm , that's good . Can you use cedar or redwood to build it ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 17 + ], + "expanded emotion cause span": [ + "I will build your deck with a simple but classic look ." + ], + "type": [ + "inter-personal" + ], + "text": "Hmm , that's good . Can you use cedar or redwood to build it ?", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "Cedar is a good choice .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 18, + 19 + ], + "expanded emotion cause span": [ + "Hmm , that's good . Can you use cedar or redwood to build it ?", + "Cedar is a good choice ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Cedar is a good choice .", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "Well , let's take the measurements right now .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 19 + ], + "expanded emotion cause span": [ + "Cedar is a good choice ." + ], + "type": [ + "inter-personal" + ], + "text": "Well , let's take the measurements right now .", + "id": 20, + "source_sentences": [ + 18 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3980.json b/reccon/sources/tr_3980.json new file mode 100644 index 0000000000000000000000000000000000000000..c074149e12adfd7d7cab363f4e5ea77caa8d504b --- /dev/null +++ b/reccon/sources/tr_3980.json @@ -0,0 +1,143 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Good morning . I ' m from the new york book review . Could I ask you some question about your latest book ?", + "emotion": "neutral", + "text": "Good morning . I ' m from the new york book review . Could I ask you some question about your latest book ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Sure . Take a seat ... what would you like to know ?", + "emotion": "neutral", + "text": "Sure . Take a seat ... what would you like to know ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "First , I ' Ve heard that your latest book is based on a true story .", + "emotion": "neutral", + "text": "First , I ' Ve heard that your latest book is based on a true story .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "That ' s correct . It ' s a murder mystery based on actual murders that book place in florida several years ago . The main character-the police invesigator-is based on the man who investigated the case .", + "emotion": "neutral", + "text": "That ' s correct . It ' s a murder mystery based on actual murders that book place in florida several years ago . The main character-the police invesigator-is based on the man who investigated the case .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "How do you research your books ?", + "emotion": "neutral", + "text": "How do you research your books ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I always visit the places that I use as setting for stories . Readers like things to be as factually correct as possible-even in fiction ! I usually base my characters on people I have met . Most charact", + "emotion": "neutral", + "text": "I always visit the places that I use as setting for stories . Readers like things to be as factually correct as possible-even in fiction ! I usually base my characters on people I have met . Most charact", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I really like your books . I ' Ve just finished this one . I read it from cover to cover in a single day . Congratulation on making the bestseller list yet again !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I really like your books ." + ], + "type": [ + "no-context" + ], + "text": "I really like your books . I ' Ve just finished this one . I read it from cover to cover in a single day . Congratulation on making the bestseller list yet again !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Thank you . Let met sign it for you ... there you go .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I really like your books ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . Let met sign it for you ... there you go .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Oh ! Thank you very much . I heard that you are currently writing a collection of short stories . What are the stories about ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Let met sign it for you ... there you go ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh ! Thank you very much . I heard that you are currently writing a collection of short stories . What are the stories about ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "There ' s a real mix of stories in the book . I haven ' t finished all of them yet , though . Many of them are short detective stories , but there are also horror stories and sci-fi ones . If you give me your", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I really like your books ." + ], + "type": [ + "inter-personal" + ], + "text": "There ' s a real mix of stories in the book . I haven ' t finished all of them yet , though . Many of them are short detective stories , but there are also horror stories and sci-fi ones . If you give me your", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Thanks very much . I ' m sure it will sell well . I can ' t wait to read it . Here ' s my card . Thank you for you time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "If you give me your", + "I can ' t wait to read it ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thanks very much . I ' m sure it will sell well . I can ' t wait to read it . Here ' s my card . Thank you for you time .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_3991.json b/reccon/sources/tr_3991.json new file mode 100644 index 0000000000000000000000000000000000000000..c54432fb543ed270b352875ce22648183d8ef460 --- /dev/null +++ b/reccon/sources/tr_3991.json @@ -0,0 +1,182 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "It's time to leave the office for the night . Firstly I log off my computer , then I set the electronic security system .", + "emotion": "neutral", + "text": "It's time to leave the office for the night . Firstly I log off my computer , then I set the electronic security system .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "That's pretty advanced .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "Firstly I log off my computer , then I set the electronic security system .", + "That's pretty advanced ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's pretty advanced .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Now I'll quickly send a short message to my wife and take the elevator down to the basement .", + "emotion": "neutral", + "text": "Now I'll quickly send a short message to my wife and take the elevator down to the basement .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Is that where you park ?", + "emotion": "neutral", + "text": "Is that where you park ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Yes , the car park is under constant video surveillance , so my car is quite safe . Please get in .", + "emotion": "neutral", + "text": "Yes , the car park is under constant video surveillance , so my car is quite safe . Please get in .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Thank you . Where is your key ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "my car is quite safe . Please get in ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . Where is your key ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "There's no need , I have keyless entry , and the steering wheel recognizes my finger prints before starting the car . Now , we can look at the navigation system to find the best route home .", + "emotion": "neutral", + "text": "There's no need , I have keyless entry , and the steering wheel recognizes my finger prints before starting the car . Now , we can look at the navigation system to find the best route home .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That's amazing , it even shows all the roads that are congested at the moment .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "we can look at the navigation system to find the best route home .", + "it even shows all the roads that are congested at the moment ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's amazing , it even shows all the roads that are congested at the moment .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Using GPS I can rely on this to direct me home . Now I just need to find my E-Card to automatically open the gate and we can drive out .", + "emotion": "neutral", + "text": "Using GPS I can rely on this to direct me home . Now I just need to find my E-Card to automatically open the gate and we can drive out .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Pretty soon cars will be driving themselves .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Pretty soon cars will be driving themselves ." + ], + "type": [ + "no-context" + ], + "text": "Pretty soon cars will be driving themselves .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Maybe , but in the meantime why not help me find the remote control for my garage door ?", + "emotion": "neutral", + "text": "Maybe , but in the meantime why not help me find the remote control for my garage door ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Here it is , and here we are .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "help me find the remote control for my garage door ?", + "Here it is , and here we are ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Here it is , and here we are .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 13, + "speaker": "A", + "utterance": "When I turn off my home alarm , the house will automatically tum on the lights and set the climate to a comfortable level .", + "emotion": "neutral", + "text": "When I turn off my home alarm , the house will automatically tum on the lights and set the climate to a comfortable level .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "I have to get home , but I don't need all of this fancy technology , I think I'll just walk .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "I don't need all of this fancy technology , I think I'll just walk ." + ], + "type": [ + "no-context" + ], + "text": "I have to get home , but I don't need all of this fancy technology , I think I'll just walk .", + "id": 14 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4.json b/reccon/sources/tr_4.json new file mode 100644 index 0000000000000000000000000000000000000000..ca8fce964d27c889f680bb37aaeadda7e8794f7f --- /dev/null +++ b/reccon/sources/tr_4.json @@ -0,0 +1,97 @@ +[ + { + "turn": 1, + "speaker": "B", + "utterance": "Hey John , nice skates . Are they new ?", + "emotion": "neutral", + "text": "Hey John , nice skates . Are they new ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "A", + "utterance": "Yeah , I just got them . I started playing ice hockey in a community league . So , I finally got myself new skates .", + "emotion": "neutral", + "text": "Yeah , I just got them . I started playing ice hockey in a community league . So , I finally got myself new skates .", + "id": 2 + }, + { + "turn": 3, + "speaker": "B", + "utterance": "What position do you play ?", + "emotion": "neutral", + "text": "What position do you play ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "A", + "utterance": "I ' m a defender . It ' s a lot of fun . You don ' t have to be able to skate as fast on defense .", + "emotion": "neutral", + "text": "I ' m a defender . It ' s a lot of fun . You don ' t have to be able to skate as fast on defense .", + "id": 4 + }, + { + "turn": 5, + "speaker": "B", + "utterance": "Yeah , you ' re a pretty big guy . I play goalie , myself .", + "emotion": "neutral", + "text": "Yeah , you ' re a pretty big guy . I play goalie , myself .", + "id": 5 + }, + { + "turn": 6, + "speaker": "A", + "utterance": "Oh , yeah ? Which team ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I play goalie , myself ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , yeah ? Which team ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "B", + "utterance": "The Rockets .", + "emotion": "neutral", + "text": "The Rockets .", + "id": 7 + }, + { + "turn": 8, + "speaker": "A", + "utterance": "Really ? I think we play you guys next week . Well , I have to go to practice . See you later .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "The Rockets ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? I think we play you guys next week . Well , I have to go to practice . See you later .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "B", + "utterance": "All right , see you later .", + "emotion": "neutral", + "text": "All right , see you later .", + "id": 9 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4002.json b/reccon/sources/tr_4002.json new file mode 100644 index 0000000000000000000000000000000000000000..b1768dfbb18c16e68f4df6a8b522d74f60f27f0e --- /dev/null +++ b/reccon/sources/tr_4002.json @@ -0,0 +1,117 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi Isabel ! You wanted to see me ?", + "emotion": "neutral", + "text": "Hi Isabel ! You wanted to see me ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes Anthony , come on in . Have a seat .", + "emotion": "neutral", + "text": "Yes Anthony , come on in . Have a seat .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Is everything okay ? You seem a bit preoccupied .", + "emotion": "neutral", + "text": "Is everything okay ? You seem a bit preoccupied .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Well , Anthony , this is not going to be an easy conversation . The company has made some decisions which will have a direct impact on your employment .", + "emotion": "neutral", + "text": "Well , Anthony , this is not going to be an easy conversation . The company has made some decisions which will have a direct impact on your employment .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Okay ...", + "emotion": "neutral", + "text": "Okay ...", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I don ' t want to beat around the bush so I ' m just gonna come out with it . We are going to have to let you go .", + "emotion": "neutral", + "text": "I don ' t want to beat around the bush so I ' m just gonna come out with it . We are going to have to let you go .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "What ? Why ? I mean ... just like that ? I ' m fired ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "We are going to have to let you go ." + ], + "type": [ + "inter-personal" + ], + "text": "What ? Why ? I mean ... just like that ? I ' m fired ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I ' m sorry but , to be honest , you are a terrible employee !", + "emotion": "neutral", + "text": "I ' m sorry but , to be honest , you are a terrible employee !", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "What ! I resent that !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6, + 8 + ], + "expanded emotion cause span": [ + "We are going to have to let you go .", + "you are a terrible employee !" + ], + "type": [ + "inter-personal" + ], + "text": "What ! I resent that !", + "id": 9, + "source_sentences": [ + 5, + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Anthony , you were caught making international calls from the office phone , you called in sick in eight times this month and you smell like alcohol !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "you were caught making international calls from the office phone , you called in sick in eight times this month and you smell like alcohol !" + ], + "type": [ + "no-context" + ], + "text": "Anthony , you were caught making international calls from the office phone , you called in sick in eight times this month and you smell like alcohol !", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4023.json b/reccon/sources/tr_4023.json new file mode 100644 index 0000000000000000000000000000000000000000..b22b15ab76d6706eb8b2c272b013df8d9c30e949 --- /dev/null +++ b/reccon/sources/tr_4023.json @@ -0,0 +1,244 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Steve . Is that you ?", + "emotion": "surprise", + "explanation": "Person A is surprised to see Person B suddenly.", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Is that you ?" + ], + "type": [ + "no-context" + ], + "text": "Steve . Is that you ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yeah . What's going on ?", + "emotion": "neutral", + "text": "Yeah . What's going on ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Not much . What a surprise to see you here .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "What a surprise to see you here ." + ], + "type": [ + "no-context" + ], + "text": "Not much . What a surprise to see you here .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yeah . It's been a couple of months since I saw you .", + "emotion": "neutral", + "text": "Yeah . It's been a couple of months since I saw you .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "What have you been up to ?", + "emotion": "neutral", + "text": "What have you been up to ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I just started working out .", + "emotion": "neutral", + "text": "I just started working out .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Really ? Where do you work out at ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I just started working out ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? Where do you work out at ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I joined the Samsung Health Club last month .", + "emotion": "neutral", + "text": "I joined the Samsung Health Club last month .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "What do you mostly do during your workout ?", + "emotion": "neutral", + "text": "What do you mostly do during your workout ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I concentrate mostly on my legs , chest , arms and stomach .", + "emotion": "neutral", + "text": "I concentrate mostly on my legs , chest , arms and stomach .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I should start exercising more .", + "emotion": "neutral", + "text": "I should start exercising more .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "It's hard work while exercising , but it is a great feeling when I get done .", + "emotion": "neutral", + "text": "It's hard work while exercising , but it is a great feeling when I get done .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I have a running machine at home . I used to use it , but I already got sick of it .", + "emotion": "neutral", + "text": "I have a running machine at home . I used to use it , but I already got sick of it .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Exercising at home is hard . The environment is not suited for exercising .", + "emotion": "neutral", + "text": "Exercising at home is hard . The environment is not suited for exercising .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "If I want to exercise , I will need to join a gym .", + "emotion": "neutral", + "text": "If I want to exercise , I will need to join a gym .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "I have a couple of guest passes . You want to check out my health club ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 16 + ], + "expanded emotion cause span": [ + "I have a couple of guest passes ." + ], + "type": [ + "no-context" + ], + "text": "I have a couple of guest passes . You want to check out my health club ?", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "That's a good idea . Let's go over the weekend .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 16 + ], + "expanded emotion cause span": [ + "I have a couple of guest passes . You want to check out my health club ?" + ], + "type": [ + "inter-personal" + ], + "text": "That's a good idea . Let's go over the weekend .", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "Great . I'll call you Saturday morning .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 16, + 17 + ], + "expanded emotion cause span": [ + "I have a couple of guest passes . You want to check out my health club ?", + "That's a good idea . Let's go over the weekend ." + ], + "type": [ + "hybrid" + ], + "text": "Great . I'll call you Saturday morning .", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "Aright . I'll talk to you later .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 16 + ], + "expanded emotion cause span": [ + "I have a couple of guest passes . You want to check out my health club ?" + ], + "type": [ + "inter-personal" + ], + "text": "Aright . I'll talk to you later .", + "id": 19, + "source_sentences": [ + 15 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 20, + "speaker": "B", + "utterance": "Ok . Bye .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 16, + 17 + ], + "expanded emotion cause span": [ + "I have a couple of guest passes . You want to check out my health club ?", + "That's a good idea . Let's go over the weekend ." + ], + "type": [ + "hybrid" + ], + "text": "Ok . Bye .", + "id": 20 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_403.json b/reccon/sources/tr_403.json new file mode 100644 index 0000000000000000000000000000000000000000..455d688ce08c380bbca1ac02847dfd9e2929deb0 --- /dev/null +++ b/reccon/sources/tr_403.json @@ -0,0 +1,129 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What do you do when you are angry ?", + "emotion": "neutral", + "text": "What do you do when you are angry ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I usually calm down first and think about the reason that caused my anger .", + "emotion": "neutral", + "text": "I usually calm down first and think about the reason that caused my anger .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "That ' s smart . What do you usually do to relieve your anger ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "I usually calm down first and think about the reason that caused my anger .", + "That ' s smart ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That ' s smart . What do you usually do to relieve your anger ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Something like listening to music is a good idea .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Something like listening to music is a good idea ." + ], + "type": [ + "no-context" + ], + "text": "Something like listening to music is a good idea .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Oh , what kind of music do you listen to ?", + "emotion": "neutral", + "text": "Oh , what kind of music do you listen to ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Classic . Something that could calm your mind .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Classic . Something that could calm your mind ." + ], + "type": [ + "no-context" + ], + "text": "Classic . Something that could calm your mind .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I think that might work for me as well .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "Something that could calm your mind .", + "I think that might work for me as well ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I think that might work for me as well .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Working out is another good way to relieve anger .", + "emotion": "neutral", + "text": "Working out is another good way to relieve anger .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Like what ?", + "emotion": "neutral", + "text": "Like what ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Jogging , yoga , or even just taking a walk .", + "emotion": "neutral", + "text": "Jogging , yoga , or even just taking a walk .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4049.json b/reccon/sources/tr_4049.json new file mode 100644 index 0000000000000000000000000000000000000000..b5b077ebff66bc3ad633830b7a9fb463e2588db6 --- /dev/null +++ b/reccon/sources/tr_4049.json @@ -0,0 +1,193 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Mr . Lee , I was wondering if you and your wife had plans for next Friday night ?", + "emotion": "neutral", + "text": "Mr . Lee , I was wondering if you and your wife had plans for next Friday night ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , I think we might be free . What did you have in mind ?", + "emotion": "neutral", + "text": "Yes , I think we might be free . What did you have in mind ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I've mailed a formal written invitation to your home inviting you to a dinner party at my home .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 2, + 3 + ], + "expanded emotion cause span": [ + "Yes ,", + "I think we might be free .", + "inviting you to a dinner party" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I've mailed a formal written invitation to your home inviting you to a dinner party at my home .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "That sounds great . Is it casual ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "inviting you to a dinner party" + ], + "type": [ + "inter-personal" + ], + "text": "That sounds great . Is it casual ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Actually , we thought it would be fun to have a formal sit-down dinner for the holidays .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 2, + 3, + 5 + ], + "expanded emotion cause span": [ + "Yes ,", + "I think we might be free .", + "inviting you to a dinner party", + "it would be fun" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Actually , we thought it would be fun to have a formal sit-down dinner for the holidays .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "That sounds good . It will give my wife a chance to dress up .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 5, + 6 + ], + "expanded emotion cause span": [ + "inviting you to a dinner party", + "it would be fun", + "It will give my wife a chance to dress up ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That sounds good . It will give my wife a chance to dress up .", + "id": 6, + "source_sentences": [ + 2, + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yes , we've invited four other couples , so it should be a good mix of people .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 2, + 3, + 5, + 7 + ], + "expanded emotion cause span": [ + "Yes ,", + "I think we might be free .", + "inviting you to a dinner party", + "it would be fun", + "a good mix of people ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Yes , we've invited four other couples , so it should be a good mix of people .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That sounds wonderful . Will there be anyone there that I know ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 5, + 6, + 7 + ], + "expanded emotion cause span": [ + "inviting you to a dinner party", + "it would be fun", + "It will give my wife a chance to dress up .", + "a good mix of people ." + ], + "type": [ + "hybrid" + ], + "text": "That sounds wonderful . Will there be anyone there that I know ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Oh yes , everyone we are inviting is from our company .", + "emotion": "neutral", + "text": "Oh yes , everyone we are inviting is from our company .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Great ! I'll look forward to it . We'll make sure and check the mail for our invitation .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 5, + 6, + 7, + 8, + 9 + ], + "expanded emotion cause span": [ + "inviting you to a dinner party", + "it would be fun", + "It will give my wife a chance to dress up .", + "a good mix of people .", + "Will there be anyone there that I know ?", + "everyone we are inviting is from our company ." + ], + "type": [ + "hybrid" + ], + "text": "Great ! I'll look forward to it . We'll make sure and check the mail for our invitation .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4066.json b/reccon/sources/tr_4066.json new file mode 100644 index 0000000000000000000000000000000000000000..f57fa13f30a26837286320967a51dee445bc066d --- /dev/null +++ b/reccon/sources/tr_4066.json @@ -0,0 +1,122 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "This is going to surprise you , but I'm happy . I think you're making the right move .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I think you're making the right move ." + ], + "type": [ + "no-context" + ], + "text": "This is going to surprise you , but I'm happy . I think you're making the right move .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "You do ?", + "emotion": "neutral", + "text": "You do ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Look , maybe I shouldn't tell you this , but I'v going over to WebTracker , too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "but I'v going over to WebTracker , too ." + ], + "type": [ + "no-context" + ], + "text": "Look , maybe I shouldn't tell you this , but I'v going over to WebTracker , too .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "No way ! That's great ! Then we'll still be together !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "but I'v going over to WebTracker , too ." + ], + "type": [ + "inter-personal" + ], + "text": "No way ! That's great ! Then we'll still be together !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Actually , I'm already working for WebTracker . Vince never wanted to give me what I was worth , so I figured , what the heck .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 5 + ], + "expanded emotion cause span": [ + "but I'v going over to WebTracker , too .", + "I'm already working for WebTracker ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Actually , I'm already working for WebTracker . Vince never wanted to give me what I was worth , so I figured , what the heck .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "No kidding ! I can't believe this . You devil !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I'm already working for WebTracker ." + ], + "type": [ + "inter-personal" + ], + "text": "No kidding ! I can't believe this . You devil !", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "It's kind of cool , isn't it ? I'm sort of like a secret agent .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 5 + ], + "expanded emotion cause span": [ + "but I'v going over to WebTracker , too .", + "I'm already working for WebTracker ." + ], + "type": [ + "self-contagion" + ], + "text": "It's kind of cool , isn't it ? I'm sort of like a secret agent .", + "id": 7 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4080.json b/reccon/sources/tr_4080.json new file mode 100644 index 0000000000000000000000000000000000000000..b3d021a063924211edda4bbb239b692f9855c162 --- /dev/null +++ b/reccon/sources/tr_4080.json @@ -0,0 +1,183 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I think that the company retreat should be in the mountains this year .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "the company retreat should be in the mountains this year ." + ], + "type": [ + "no-context" + ], + "text": "I think that the company retreat should be in the mountains this year .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What a great idea !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "the company retreat should be in the mountains this year ." + ], + "type": [ + "inter-personal" + ], + "text": "What a great idea !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "January would be a good month for a mountain retreat .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "What a great idea !" + ], + "type": [ + "inter-personal" + ], + "text": "January would be a good month for a mountain retreat .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I like the mountain idea , but I am not so sure about the month of January .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I like the mountain idea" + ], + "type": [ + "no-context" + ], + "text": "I like the mountain idea , but I am not so sure about the month of January .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "You know , now that I think about it , you might be right .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I like the mountain idea , but I am not so sure about the month of January ." + ], + "type": [ + "inter-personal" + ], + "text": "You know , now that I think about it , you might be right .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "April might be nice . It is far enough away to make the necessary arrangements .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "you might be right .", + "April might be nice ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "April might be nice . It is far enough away to make the necessary arrangements .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "That is a good suggestion .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "April might be nice . It is far enough away to make the necessary arrangements ." + ], + "type": [ + "inter-personal" + ], + "text": "That is a good suggestion .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "We could ask everyone what would be the best time for them .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "That is a good suggestion ." + ], + "type": [ + "inter-personal" + ], + "text": "We could ask everyone what would be the best time for them .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yeah , that would let us know what would work best .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "We could ask everyone what would be the best time for them .", + "Yeah , that would let us know what would work best ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yeah , that would let us know what would work best .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I'll put the survey online this afternoon .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Yeah , that would let us know what would work best ." + ], + "type": [ + "inter-personal" + ], + "text": "I'll put the survey online this afternoon .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4087.json b/reccon/sources/tr_4087.json new file mode 100644 index 0000000000000000000000000000000000000000..07e315976cbf3920512d2916aedc6a8148f820c5 --- /dev/null +++ b/reccon/sources/tr_4087.json @@ -0,0 +1,202 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "We still have one more day to go before we return home . What will we see tomorrow ?", + "emotion": "neutral", + "text": "We still have one more day to go before we return home . What will we see tomorrow ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "No idea . We've enjoyed both the natural scenery and the city sights . What else is there to see ?", + "emotion": "neutral", + "text": "No idea . We've enjoyed both the natural scenery and the city sights . What else is there to see ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What about a factory tour ?", + "emotion": "neutral", + "text": "What about a factory tour ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "You mean visit a factory ?", + "emotion": "neutral", + "text": "You mean visit a factory ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Yes . I heard there's a lager motor company nearby which is open to the public every weekend . We can go to see how a car is manufactured and learn more about the automobile industry .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I heard there's a lager motor company nearby which is open to the public every weekend . We can go to see how a car is manufactured and learn more about the automobile industry ." + ], + "type": [ + "no-context" + ], + "text": "Yes . I heard there's a lager motor company nearby which is open to the public every weekend . We can go to see how a car is manufactured and learn more about the automobile industry .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Good idea ! I've always been interested in that . How much is the entrance fee ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "I heard there's a lager motor company nearby which is open to the public every weekend . We can go to see how a car is manufactured and learn more about the automobile industry .", + "I've always been interested in that ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Good idea ! I've always been interested in that . How much is the entrance fee ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I'm not sure , but as far as I know , most factory tours are free . They are sponsored by the company providing the tour .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I've always been interested in that .", + "most factory tours are free . They are sponsored by the company providing the tour ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm not sure , but as far as I know , most factory tours are free . They are sponsored by the company providing the tour .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Really ? What do the companies do that for ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "most factory tours are free . They are sponsored by the company providing the tour ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? What do the companies do that for ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I believe most of them think it as good public relations . They can promote their product and make their company better-known .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "most factory tours are free . They are sponsored by the company providing the tour ." + ], + "type": [ + "self-contagion" + ], + "text": "I believe most of them think it as good public relations . They can promote their product and make their company better-known .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Oh , ISEE . So factory tours are good for companies as well as visitors .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "So factory tours are good for companies as well as visitors ." + ], + "type": [ + "no-context" + ], + "text": "Oh , ISEE . So factory tours are good for companies as well as visitors .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Exactly .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "So factory tours are good for companies as well as visitors ." + ], + "type": [ + "inter-personal" + ], + "text": "Exactly .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Do we need an appointment beforehand ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I've always been interested in that .", + "most factory tours are free . They are sponsored by the company providing the tour ." + ], + "type": [ + "hybrid" + ], + "text": "Do we need an appointment beforehand ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I'll call the tourist information centre to check .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I've always been interested in that .", + "most factory tours are free . They are sponsored by the company providing the tour ." + ], + "type": [ + "hybrid" + ], + "text": "I'll call the tourist information centre to check .", + "id": 13 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4091.json b/reccon/sources/tr_4091.json new file mode 100644 index 0000000000000000000000000000000000000000..4971512918323bb6a71d4a1b7308ea080571ac88 --- /dev/null +++ b/reccon/sources/tr_4091.json @@ -0,0 +1,163 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Good evening , Mr . Wu .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Good evening ," + ], + "type": [ + "no-context" + ], + "text": "Good evening , Mr . Wu .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Good evening , Mr . Smith .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "Good evening ,", + "Good evening ," + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Good evening , Mr . Smith .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Have you met my wife , Mary ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "Good evening ,", + "Good evening ," + ], + "type": [ + "hybrid" + ], + "text": "Have you met my wife , Mary ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "No . I haven ' t had the pleasure .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "Have you met my wife , Mary ?", + "No . I haven ' t had the pleasure ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "No . I haven ' t had the pleasure .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Mary , this is Mr . Wu , my new Chinese friend .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4, + 5 + ], + "expanded emotion cause span": [ + "Have you met my wife , Mary ?", + "No . I haven ' t had the pleasure .", + "my new Chinese friend ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Mary , this is Mr . Wu , my new Chinese friend .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "How do you do , Mr . Wu ? Welcome .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "my new Chinese friend .", + "How do you do , Mr . Wu ? Welcome ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "How do you do , Mr . Wu ? Welcome .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "How do you do ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "How do you do , Mr . Wu ? Welcome .", + "How do you do ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "How do you do ?", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Have a glass of wine , Mr . Wu ? And let me introduce you to some of my guests .", + "emotion": "happiness", + "explanation": "Assuming offering someone help/food/drinks, and introducing someone as happiness inducing behavior", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Have a glass of wine , Mr . Wu ? And let me introduce you to some of my guests ." + ], + "type": [ + "no-context" + ], + "text": "Have a glass of wine , Mr . Wu ? And let me introduce you to some of my guests .", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4092.json b/reccon/sources/tr_4092.json new file mode 100644 index 0000000000000000000000000000000000000000..301614de29ea40afc444420f115f2280633fd1de --- /dev/null +++ b/reccon/sources/tr_4092.json @@ -0,0 +1,155 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "This is my house . Let me show you around it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "This is my house . Let me show you around it ." + ], + "type": [ + "no-context" + ], + "text": "This is my house . Let me show you around it .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "How beautiful the detached house is !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "How beautiful the detached house is !" + ], + "type": [ + "no-context" + ], + "text": "How beautiful the detached house is !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Follow me to the back-yard .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "How beautiful the detached house is !", + "the back-yard" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Follow me to the back-yard .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It's marvelous ! The lawn looks like a green carpet , and the garden with so many lovely flowers .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "It's marvelous ! The lawn looks like a green carpet , and the garden with so many lovely flowers ." + ], + "type": [ + "no-context" + ], + "text": "It's marvelous ! The lawn looks like a green carpet , and the garden with so many lovely flowers .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "We had the grass cut and the flowers trimmed this morning .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "It's marvelous ! The lawn looks like a green carpet , and the garden with so many lovely flowers .", + "We had the grass cut and the flowers trimmed this morning ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "We had the grass cut and the flowers trimmed this morning .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "No wonder it smells fragrant .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "No wonder it smells fragrant ." + ], + "type": [ + "no-context" + ], + "text": "No wonder it smells fragrant .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Here is the swimming pool and we can swim later .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "No wonder it smells fragrant .", + "Here is the swimming pool and we can swim later ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Here is the swimming pool and we can swim later .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "It's fantastic !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "Here is the swimming pool and we can swim later .", + "It's fantastic !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It's fantastic !", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4097.json b/reccon/sources/tr_4097.json new file mode 100644 index 0000000000000000000000000000000000000000..80bb26d36200c5b5f42da3c2cb843433a2912d24 --- /dev/null +++ b/reccon/sources/tr_4097.json @@ -0,0 +1,141 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I heard that Janet has got a new job . She ' s working for the united investment group . I heard that they pay very well .", + "emotion": "neutral", + "text": "I heard that Janet has got a new job . She ' s working for the united investment group . I heard that they pay very well .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I heard that too . She must be making a pocket . Well , good for her .", + "emotion": "neutral", + "text": "I heard that too . She must be making a pocket . Well , good for her .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Now , she ' ll be able to save up for that holiday in the united states .", + "emotion": "neutral", + "text": "Now , she ' ll be able to save up for that holiday in the united states .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes , she will . At the moment , the exchange rate is very favorable , so she should try to go as soon as possible , while it ' s cheaper .", + "emotion": "neutral", + "text": "Yes , she will . At the moment , the exchange rate is very favorable , so she should try to go as soon as possible , while it ' s cheaper .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "You ' re right . By the way , did you hear that Tom inherited some money recently ?", + "emotion": "neutral", + "text": "You ' re right . By the way , did you hear that Tom inherited some money recently ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Really ? I thought his parents had died several years ago .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Tom inherited some money recently ?", + "I thought his parents had died several years ago ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Really ? I thought his parents had died several years ago .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "They did . He inherited the money from an uncle . I hope he doesn ' t lose a lot of it in taxed to the government .", + "emotion": "neutral", + "text": "They did . He inherited the money from an uncle . I hope he doesn ' t lose a lot of it in taxed to the government .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Dying can be very expensive nowadays ! What ' s he going to do with it ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I hope he doesn ' t lose a lot of it in taxed to the government ." + ], + "type": [ + "inter-personal" + ], + "text": "Dying can be very expensive nowadays ! What ' s he going to do with it ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "He said that he would probably invest most of it . He ' s got a well-paid job , so he doesn ' t need the money to cover day-to day expenses . He just wants some extra money available for when he retires .", + "emotion": "neutral", + "text": "He said that he would probably invest most of it . He ' s got a well-paid job , so he doesn ' t need the money to cover day-to day expenses . He just wants some extra money available for when he retires .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I had some good financial news yesterday too .", + "emotion": "neutral", + "text": "I had some good financial news yesterday too .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Really ? Have you won a fortune in the lottery ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "I had some good financial news yesterday too ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? Have you won a fortune in the lottery ?", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "No , but I got a pay rise of 5 % and a bonus for all the hard work I ' Ve put in recently . I think it was very nice for my boss to show his appreciation in that way .", + "emotion": "neutral", + "text": "No , but I got a pay rise of 5 % and a bonus for all the hard work I ' Ve put in recently . I think it was very nice for my boss to show his appreciation in that way .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "It certainly was ! So , what are you going to do with your windfall ?", + "emotion": "neutral", + "text": "It certainly was ! So , what are you going to do with your windfall ?", + "id": 13 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4099.json b/reccon/sources/tr_4099.json new file mode 100644 index 0000000000000000000000000000000000000000..25147015953f7cd93bb3aea057c7f40fd61a35e2 --- /dev/null +++ b/reccon/sources/tr_4099.json @@ -0,0 +1,253 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I think I'm going to go home .", + "emotion": "neutral", + "text": "I think I'm going to go home .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Why ? We just got here .", + "emotion": "neutral", + "text": "Why ? We just got here .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I know , but it's 12", + "emotion": "neutral", + "text": "I know , but it's 12", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "12", + "emotion": "neutral", + "text": "12", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Three or four o'clock ?", + "emotion": "neutral", + "text": "Three or four o'clock ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yes .", + "emotion": "neutral", + "text": "Yes .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I never stay out that late . That's too late .", + "emotion": "neutral", + "text": "I never stay out that late . That's too late .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "But why is it too late ? It's Saturday night . You have nothing to do tomorrow . Why not stay out and drink with us ?", + "emotion": "neutral", + "text": "But why is it too late ? It's Saturday night . You have nothing to do tomorrow . Why not stay out and drink with us ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Were you so wild when you were still in Taipei , Sharon ?", + "emotion": "neutral", + "text": "Were you so wild when you were still in Taipei , Sharon ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Yes , I was . And I like living here . People know how to party here . In Taipei , some people know how to party . But here , everyone does .", + "emotion": "neutral", + "text": "Yes , I was . And I like living here . People know how to party here . In Taipei , some people know how to party . But here , everyone does .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "What is that they're doing on the couch ?", + "emotion": "neutral", + "text": "What is that they're doing on the couch ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "They're smoking pot . Don't worry about it .", + "emotion": "neutral", + "text": "They're smoking pot . Don't worry about it .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Pot ? Isn't that marijuana ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "They're smoking pot ." + ], + "type": [ + "inter-personal" + ], + "text": "Pot ? Isn't that marijuana ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Yes , it is .", + "emotion": "neutral", + "text": "Yes , it is .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "But , Sharon , that's illegal ! The police could come , and we could go to jail .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 12, + 15 + ], + "expanded emotion cause span": [ + "They're smoking pot .", + "that's illegal !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "But , Sharon , that's illegal ! The police could come , and we could go to jail .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Don't worry about it . It is true that pot is illegal in America . But the laws aren't as strict as in Taiwan . If people are arrested , and they have a little pot in their possession , they don't go to jail . They just have to pay a fine .", + "emotion": "neutral", + "text": "Don't worry about it . It is true that pot is illegal in America . But the laws aren't as strict as in Taiwan . If people are arrested , and they have a little pot in their possession , they don't go to jail . They just have to pay a fine .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "Really ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 16 + ], + "expanded emotion cause span": [ + "the laws aren't as strict as in Taiwan . If people are arrested , and they have a little pot in their possession , they don't go to jail . They just have to pay a fine ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ?", + "id": 17, + "source_sentences": [ + 15 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 18, + "speaker": "B", + "utterance": "Yes .", + "emotion": "neutral", + "text": "Yes .", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "I didn't know you had such wild friends . Do you smoke marijuana too ?", + "emotion": "neutral", + "text": "I didn't know you had such wild friends . Do you smoke marijuana too ?", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "I tried it a couple times . But I don't like it . I like alcohol better . Don ' t worry about them , though . If you don't want to smoke pot , you don't have to .", + "emotion": "neutral", + "text": "I tried it a couple times . But I don't like it . I like alcohol better . Don ' t worry about them , though . If you don't want to smoke pot , you don't have to .", + "id": 20 + }, + { + "turn": 21, + "speaker": "A", + "utterance": "I don't want to .", + "emotion": "neutral", + "text": "I don't want to .", + "id": 21 + }, + { + "turn": 22, + "speaker": "B", + "utterance": "That's alright . But you really should have another drink . People will probably start dancing soon .", + "emotion": "neutral", + "text": "That's alright . But you really should have another drink . People will probably start dancing soon .", + "id": 22 + }, + { + "turn": 23, + "speaker": "A", + "utterance": "I don't know if I can drink more . I already had two drinks .", + "emotion": "neutral", + "text": "I don't know if I can drink more . I already had two drinks .", + "id": 23 + }, + { + "turn": 24, + "speaker": "B", + "utterance": "You had two drinks at nine o'clock . C'mon , Ann , you are in an American university now ! You have to learn how to drink .", + "emotion": "neutral", + "text": "You had two drinks at nine o'clock . C'mon , Ann , you are in an American university now ! You have to learn how to drink .", + "id": 24 + }, + { + "turn": 25, + "speaker": "A", + "utterance": "I thought a university was for studying .", + "emotion": "neutral", + "text": "I thought a university was for studying .", + "id": 25 + }, + { + "turn": 26, + "speaker": "B", + "utterance": "It is . We study hard all week . And then , on the weekend , we party hard . That's the best way to live .", + "emotion": "neutral", + "text": "It is . We study hard all week . And then , on the weekend , we party hard . That's the best way to live .", + "id": 26 + }, + { + "turn": 27, + "speaker": "A", + "utterance": "Alright . I'll have another drink .", + "emotion": "neutral", + "text": "Alright . I'll have another drink .", + "id": 27 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4104.json b/reccon/sources/tr_4104.json new file mode 100644 index 0000000000000000000000000000000000000000..7f349904e37474b2df05f6d4e842d62951d79624 --- /dev/null +++ b/reccon/sources/tr_4104.json @@ -0,0 +1,126 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "There are lots of new teachers in our class this semester .", + "emotion": "neutral", + "text": "There are lots of new teachers in our class this semester .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yeah , so what do you think about the teachers ?", + "emotion": "neutral", + "text": "Yeah , so what do you think about the teachers ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "To be honest , I like all of them , except for the math teacher . Though he must be quite young , he seems like an old person . He's so boring .", + "emotion": "neutral", + "text": "To be honest , I like all of them , except for the math teacher . Though he must be quite young , he seems like an old person . He's so boring .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I think so too . I don't like him either . Well , who do you like best ?", + "emotion": "neutral", + "text": "I think so too . I don't like him either . Well , who do you like best ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "It might be the English teacher . What about you ?", + "emotion": "neutral", + "text": "It might be the English teacher . What about you ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Me , too . She speaks very clearly and doesn't use very complicated words so that it is easy for us to understand her .", + "emotion": "neutral", + "text": "Me , too . She speaks very clearly and doesn't use very complicated words so that it is easy for us to understand her .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "She is a pretty good teacher ! With her help I think I can make great progress in English .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "She is a pretty good teacher ! With her help I think I can make great progress in English ." + ], + "type": [ + "no-context" + ], + "text": "She is a pretty good teacher ! With her help I think I can make great progress in English .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yeah , I like her way of teaching . She told us not to cram for exams , and to pay more attention to communicating than memorizing .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "She is a pretty good teacher ! With her help I think I can make great progress in English .", + "Yeah , I like her way of teaching . She told us not to cram for exams , and to pay more attention to communicating than memorizing ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yeah , I like her way of teaching . She told us not to cram for exams , and to pay more attention to communicating than memorizing .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I think it's a good way to develop our language ability .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "it's a good way to develop our language ability ." + ], + "type": [ + "no-context" + ], + "text": "I think it's a good way to develop our language ability .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Actually , our new math teacher is a good person . He just can't find an appropriate way to teach us .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "our new math teacher is a good person ." + ], + "type": [ + "no-context" + ], + "text": "Actually , our new math teacher is a good person . He just can't find an appropriate way to teach us .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4106.json b/reccon/sources/tr_4106.json new file mode 100644 index 0000000000000000000000000000000000000000..a8d9e4ef34d43a8bad2a7480facd008762784ff3 --- /dev/null +++ b/reccon/sources/tr_4106.json @@ -0,0 +1,138 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Can you recommend a resort to me ?", + "emotion": "neutral", + "text": "Can you recommend a resort to me ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What about the Yellowstone National Park ?", + "emotion": "neutral", + "text": "What about the Yellowstone National Park ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Have you ever been there ?", + "emotion": "neutral", + "text": "Have you ever been there ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes . The scenery is so breathtaking .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "The scenery is so breathtaking ." + ], + "type": [ + "no-context" + ], + "text": "Yes . The scenery is so breathtaking .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "What is especially impressive ?", + "emotion": "neutral", + "text": "What is especially impressive ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "There are thousands of hot springs and fountains . The park is known for them .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 6 + ], + "expanded emotion cause span": [ + "The scenery is so breathtaking .", + "There are thousands of hot springs and fountains ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "There are thousands of hot springs and fountains . The park is known for them .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Is there a waterfall ?", + "emotion": "neutral", + "text": "Is there a waterfall ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yes . The well-known Yellowstone Waterfall is formed when the Yellowstone Lake falls down into the Yellowstone Canyon .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 4, + 6 + ], + "expanded emotion cause span": [ + "The scenery is so breathtaking .", + "There are thousands of hot springs and fountains ." + ], + "type": [ + "self-contagion" + ], + "text": "Yes . The well-known Yellowstone Waterfall is formed when the Yellowstone Lake falls down into the Yellowstone Canyon .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "What an attractive place ! How can I get there ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 6, + 8, + 9 + ], + "expanded emotion cause span": [ + "The scenery is so breathtaking .", + "There are thousands of hot springs and fountains .", + "Yes . The well-known Yellowstone Waterfall is formed when the Yellowstone Lake falls down into the Yellowstone Canyon .", + "an attractive place" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "What an attractive place ! How can I get there ?", + "id": 9, + "source_sentences": [ + 3, + 5, + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "You can take No . 2 bus .", + "emotion": "neutral", + "text": "You can take No . 2 bus .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4132.json b/reccon/sources/tr_4132.json new file mode 100644 index 0000000000000000000000000000000000000000..0e4b1366ac3967174f46904942b1dbd66ee98655 --- /dev/null +++ b/reccon/sources/tr_4132.json @@ -0,0 +1,135 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "How are you , Sue ?", + "emotion": "neutral", + "text": "How are you , Sue ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Pretty good . I ' Ve just had my new poems published .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I ' Ve just had my new poems published ." + ], + "type": [ + "no-context" + ], + "text": "Pretty good . I ' Ve just had my new poems published .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Congratulations on your success .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I ' Ve just had my new poems published ." + ], + "type": [ + "inter-personal" + ], + "text": "Congratulations on your success .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Thank you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Congratulations on your success ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "And how ' s your brother ?", + "emotion": "neutral", + "text": "And how ' s your brother ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "He is fine .", + "emotion": "neutral", + "text": "He is fine .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "He ' s going to be sent to Britain to study , really ?", + "emotion": "neutral", + "text": "He ' s going to be sent to Britain to study , really ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yes . He ' s already got the passport and visa .", + "emotion": "neutral", + "text": "Yes . He ' s already got the passport and visa .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Fantastic ! Please send him my congratulations .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "He ' s already got the passport and visa ." + ], + "type": [ + "inter-personal" + ], + "text": "Fantastic ! Please send him my congratulations .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Thank you . He ' s very lucky indeed .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "Fantastic ! Please send him my congratulations .", + "He ' s very lucky indeed ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you . He ' s very lucky indeed .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4155.json b/reccon/sources/tr_4155.json new file mode 100644 index 0000000000000000000000000000000000000000..b35ea82b166420177ebd12e1747096ddec36216a --- /dev/null +++ b/reccon/sources/tr_4155.json @@ -0,0 +1,171 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "David , I ' m going to China .", + "emotion": "neutral", + "text": "David , I ' m going to China .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Really ? How do you get the chance ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "I ' m going to China .", + "How do you get the chance ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Really ? How do you get the chance ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "You know . I took part in the Chinese contest . I was the best and they gave me this reward . I don ' t have to pay for my trip .", + "emotion": "neutral", + "text": "You know . I took part in the Chinese contest . I was the best and they gave me this reward . I don ' t have to pay for my trip .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Congratulations . How lucky you are !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3, + 4 + ], + "expanded emotion cause span": [ + "I ' m going to China .", + "I was the best and they gave me this reward . I don ' t have to pay for my trip .", + "How lucky you are !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Congratulations . How lucky you are !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Thank you . I ' m leaving tomorrow morning .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Congratulations . How lucky you are !" + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . I ' m leaving tomorrow morning .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I ' m sure you ' ll enjoy the trip . China is such a beautiful country .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3, + 4, + 6 + ], + "expanded emotion cause span": [ + "I ' m going to China .", + "I was the best and they gave me this reward . I don ' t have to pay for my trip .", + "How lucky you are !", + "you ' ll enjoy the trip . China is such a beautiful country ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I ' m sure you ' ll enjoy the trip . China is such a beautiful country .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I ' m sure I will .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "you ' ll enjoy the trip", + "I ' m sure I will ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I ' m sure I will .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Have a nice journey , Lily .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1, + 3, + 4, + 6 + ], + "expanded emotion cause span": [ + "I ' m going to China .", + "I was the best and they gave me this reward . I don ' t have to pay for my trip .", + "How lucky you are !", + "you ' ll enjoy the trip . China is such a beautiful country ." + ], + "type": [ + "hybrid" + ], + "text": "Have a nice journey , Lily .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Thank you , David .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7, + 8 + ], + "expanded emotion cause span": [ + "you ' ll enjoy the trip", + "I ' m sure I will .", + "Have a nice journey" + ], + "type": [ + "hybrid" + ], + "text": "Thank you , David .", + "id": 9 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4158.json b/reccon/sources/tr_4158.json new file mode 100644 index 0000000000000000000000000000000000000000..a15e71b640b68a66d046c20ed142047b6f22e814 --- /dev/null +++ b/reccon/sources/tr_4158.json @@ -0,0 +1,259 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Happy Birthday , Mary !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Happy Birthday , Mary !" + ], + "type": [ + "no-context" + ], + "text": "Happy Birthday , Mary !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Thank you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Happy Birthday , Mary !" + ], + "type": [ + "inter-personal" + ], + "text": "Thank you .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Here is a gift for you . I hope you like it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "Happy Birthday , Mary !", + "Here is a gift for you ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Here is a gift for you . I hope you like it .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "What a lovely dog ! How did you know I love things like this ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "What a lovely dog ! How did you know I love things like this ?" + ], + "type": [ + "no-context" + ], + "text": "What a lovely dog ! How did you know I love things like this ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I had my own ways of finding out . It ' s a secret . You look so beautiful today . Your new shirt goes well with your skirt .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "What a lovely dog ! How did you know I love things like this ?", + "I had my own ways of finding out . It ' s a secret . You look so beautiful today . Your new shirt goes well with your skirt ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I had my own ways of finding out . It ' s a secret . You look so beautiful today . Your new shirt goes well with your skirt .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Maybe you won't believe this , but it was made by my grandmother .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Your new shirt goes well with your skirt .", + "it was made by my grandmother ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Maybe you won't believe this , but it was made by my grandmother .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Really ? It looks so nice .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "it was made by my grandmother ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? It looks so nice .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Thank you , Please have a cup of tea .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "It looks so nice ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you , Please have a cup of tea .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "All right .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Please have a cup of tea ." + ], + "type": [ + "inter-personal" + ], + "text": "All right .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "How about some fish ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Happy Birthday , Mary !" + ], + "type": [ + "inter-personal" + ], + "text": "How about some fish ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "No , thanks . I've had enough . Now , Mary , before you blow out the birthday candles , you have to make a wish . After that , you may cut the cake .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Happy Birthday , Mary !" + ], + "type": [ + "self-contagion" + ], + "text": "No , thanks . I've had enough . Now , Mary , before you blow out the birthday candles , you have to make a wish . After that , you may cut the cake .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "OK . Let me make a wish ... Do you want a big piece of cake ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "you have to make a wish ." + ], + "type": [ + "inter-personal" + ], + "text": "OK . Let me make a wish ... Do you want a big piece of cake ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "No , just a small one . Next Let's sing \" Happy Birthday \" to Mary .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "Let's sing \" Happy Birthday \" to Mary ." + ], + "type": [ + "no-context" + ], + "text": "No , just a small one . Next Let's sing \" Happy Birthday \" to Mary .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "It is so very kind of you . I'm so moved by you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13, + 14 + ], + "expanded emotion cause span": [ + "Let's sing \" Happy Birthday \" to Mary .", + "It is so very kind of you . I'm so moved by you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It is so very kind of you . I'm so moved by you .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4163.json b/reccon/sources/tr_4163.json new file mode 100644 index 0000000000000000000000000000000000000000..b3aa3abc5b275d2b23fc169a1408b53663d954af --- /dev/null +++ b/reccon/sources/tr_4163.json @@ -0,0 +1,105 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What are you doing this weekend ?", + "emotion": "neutral", + "text": "What are you doing this weekend ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Nothing much . I ' m going to the cinema on Friday night but that ' s all I have planned .", + "emotion": "neutral", + "text": "Nothing much . I ' m going to the cinema on Friday night but that ' s all I have planned .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "So you ' re free on Saturday night ?", + "emotion": "neutral", + "text": "So you ' re free on Saturday night ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "That ' s right .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "you ' re free on Saturday night ?" + ], + "type": [ + "inter-personal" + ], + "text": "That ' s right .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Would you like to have dinner with me ?", + "emotion": "happiness", + "explanation": "The person inviting person B in dinner and thus happy", + "flag": "F", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Would you like to have dinner with me ?" + ], + "type": [ + "no-context" + ], + "text": "Would you like to have dinner with me ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Oh , that would be lovely . Shall we say seven o ' clock ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Would you like to have dinner with me ?" + ], + "type": [ + "inter-personal" + ], + "text": "Oh , that would be lovely . Shall we say seven o ' clock ?", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Perfect . I ' ll pick you up then .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Would you like to have dinner with me ?", + "that would be lovely ." + ], + "type": [ + "hybrid" + ], + "text": "Perfect . I ' ll pick you up then .", + "id": 7 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4164.json b/reccon/sources/tr_4164.json new file mode 100644 index 0000000000000000000000000000000000000000..ae9aeb6857fa515b18c09c5eef3b77f505321dd4 --- /dev/null +++ b/reccon/sources/tr_4164.json @@ -0,0 +1,123 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "And so , that concludes my outline for our marketing strategy next year . Thank you very much for your time .", + "emotion": "neutral", + "text": "And so , that concludes my outline for our marketing strategy next year . Thank you very much for your time .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hey , that was quite the presentation ! Honestly , I was completely blown away by your strategy outline . I've gotta say , Alex , you really wowed me today .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2, + 2 + ], + "expanded emotion cause span": [ + "that was quite the presentation ! Honestly , I was completely blown away by your strategy outline .", + "you really wowed me today ." + ], + "type": [ + "no-context" + ], + "text": "Hey , that was quite the presentation ! Honestly , I was completely blown away by your strategy outline . I've gotta say , Alex , you really wowed me today .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Aw , come on , it was nothing . I'm just doing my job .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 2 + ], + "expanded emotion cause span": [ + "that was quite the presentation ! Honestly , I was completely blown away by your strategy outline .", + "you really wowed me today ." + ], + "type": [ + "inter-personal" + ], + "text": "Aw , come on , it was nothing . I'm just doing my job .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "No , I think you deserve some recognition here ; I mean , if I look back on your previous presentations , this is a huge improvement .", + "emotion": "neutral", + "text": "No , I think you deserve some recognition here ; I mean , if I look back on your previous presentations , this is a huge improvement .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Well , Kristin did give me a hand with the slides . She ' s a real wiz on PowerPoint .", + "emotion": "neutral", + "text": "Well , Kristin did give me a hand with the slides . She ' s a real wiz on PowerPoint .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "And I saw that you took on board my feedback about pricing strategies . I really appreciate you taking the time to think though my suggestions .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "you took on board my feedback about pricing strategies . I really appreciate you taking the time to think though my suggestions ." + ], + "type": [ + "no-context" + ], + "text": "And I saw that you took on board my feedback about pricing strategies . I really appreciate you taking the time to think though my suggestions .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yeah , well , that was some good advice . You made some really good points .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "you took on board my feedback about pricing strategies . I really appreciate you taking the time to think though my suggestions ." + ], + "type": [ + "inter-personal" + ], + "text": "Yeah , well , that was some good advice . You made some really good points .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Well , I just wanted to say well done . Really you did a great job .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "that was some good advice . You made some really good points .", + "Really you did a great job ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Well , I just wanted to say well done . Really you did a great job .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4165.json b/reccon/sources/tr_4165.json new file mode 100644 index 0000000000000000000000000000000000000000..67d858ace3d6405019846ca7bd1da2ed6a24fae7 --- /dev/null +++ b/reccon/sources/tr_4165.json @@ -0,0 +1,145 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What are you listening now , Fred ?", + "emotion": "neutral", + "text": "What are you listening now , Fred ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What ?", + "emotion": "neutral", + "text": "What ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Hey ! Man , put your earphone out . I said which song you are listening to .", + "emotion": "neutral", + "text": "Hey ! Man , put your earphone out . I said which song you are listening to .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Jay Chou's title song in his new album .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Jay Chou's title song in his new album ." + ], + "type": [ + "no-context" + ], + "text": "Jay Chou's title song in his new album .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "What's your comment on his new album ?", + "emotion": "happiness", + "explanation": "Latent reason behind happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "What's your comment on his new album ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Gorgeous ! There is another song combining Chinese and western music styles . I am crazy for it , so I hear it over and again . And I plan to make it as the ringbone of my mobile .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "What's your comment on his new album ?", + "Gorgeous ! There is another song combining Chinese and western music styles . I am crazy for it , so I hear it over and again . And I plan to make it as the ringbone of my mobile ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Gorgeous ! There is another song combining Chinese and western music styles . I am crazy for it , so I hear it over and again . And I plan to make it as the ringbone of my mobile .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Let me enjoy it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Let me enjoy it ." + ], + "type": [ + "no-context" + ], + "text": "Let me enjoy it .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I suppose this song can be the No . 1 on the top chart .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6, + 8 + ], + "expanded emotion cause span": [ + "What's your comment on his new album ?", + "Gorgeous ! There is another song combining Chinese and western music styles . I am crazy for it , so I hear it over and again . And I plan to make it as the ringbone of my mobile .", + "I suppose this song can be the No . 1 on the top chart ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I suppose this song can be the No . 1 on the top chart .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I cann't wait for buying his CD now .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 9 + ], + "expanded emotion cause span": [ + "Let me enjoy it .", + "I cann't wait for buying his CD now ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I cann't wait for buying his CD now .", + "id": 9 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4182.json b/reccon/sources/tr_4182.json new file mode 100644 index 0000000000000000000000000000000000000000..c90a5a5ae8306823db124800231043b72a4e0d1f --- /dev/null +++ b/reccon/sources/tr_4182.json @@ -0,0 +1,231 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Nice weather , honey !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Nice weather" + ], + "type": [ + "no-context" + ], + "text": "Nice weather , honey !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "The days are getting longer !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "Nice weather", + "The days are getting longer !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "The days are getting longer !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "May and Daniel often like this kind of weather .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "Nice weather", + "often like this kind of weather ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "May and Daniel often like this kind of weather .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yeah , they can enjoy themselves in the day time and it is not so hot .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 4 + ], + "expanded emotion cause span": [ + "Nice weather", + "The days are getting longer !", + "they can enjoy themselves in the day time and it is not so hot ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Yeah , they can enjoy themselves in the day time and it is not so hot .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Honey , how about taking them to the beach this weekend ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "taking them to the beach this weekend ?" + ], + "type": [ + "no-context" + ], + "text": "Honey , how about taking them to the beach this weekend ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "That's great !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "taking them to the beach this weekend ?" + ], + "type": [ + "inter-personal" + ], + "text": "That's great !", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Since last time we've climbed the mountain , we haven't gone out for a long time .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "taking them to the beach this weekend ?" + ], + "type": [ + "self-contagion" + ], + "text": "Since last time we've climbed the mountain , we haven't gone out for a long time .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "And this kind of weather is rare for the season either .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 8 + ], + "expanded emotion cause span": [ + "Nice weather", + "The days are getting longer !", + "And this kind of weather is rare for the season either ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "And this kind of weather is rare for the season either .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yes , I remember last year this time , the weather is so hot .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "this kind of weather is rare for the season either ." + ], + "type": [ + "inter-personal" + ], + "text": "Yes , I remember last year this time , the weather is so hot .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "So we must seize this chance to go the beach .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "So we must seize this chance to go the beach ." + ], + "type": [ + "no-context" + ], + "text": "So we must seize this chance to go the beach .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Daniel loves the beach very much !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "Daniel loves the beach very much !" + ], + "type": [ + "no-context" + ], + "text": "Daniel loves the beach very much !", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "He will enjoy himself this weekend .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "Daniel loves the beach very much !", + "He will enjoy himself this weekend ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "He will enjoy himself this weekend .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4188.json b/reccon/sources/tr_4188.json new file mode 100644 index 0000000000000000000000000000000000000000..4f83cc6414999de00b1350adf107ceff887732c2 --- /dev/null +++ b/reccon/sources/tr_4188.json @@ -0,0 +1,118 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , dear , I've got your voice at last .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "dear , I've got your voice at last ." + ], + "type": [ + "no-context" + ], + "text": "Hi , dear , I've got your voice at last .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hi , darling , I am thinking it is the time of your calling .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "dear , I've got your voice at last .", + "darling , I am thinking it is the time of your calling ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Hi , darling , I am thinking it is the time of your calling .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Are you OK today ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "darling , I am thinking it is the time of your calling ." + ], + "type": [ + "inter-personal" + ], + "text": "Are you OK today ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Quite good except thinking of you so much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "Are you OK today ?", + "thinking of you so much ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Quite good except thinking of you so much .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "So do I . You are a beautiful flower in my mind .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "Quite good except thinking of you so much .", + "You are a beautiful flower in my mind ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "So do I . You are a beautiful flower in my mind .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "It's called love is blind , I think .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "So do I . You are a beautiful flower in my mind ." + ], + "type": [ + "inter-personal" + ], + "text": "It's called love is blind , I think .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4194.json b/reccon/sources/tr_4194.json new file mode 100644 index 0000000000000000000000000000000000000000..cd8df9efab4315aaec1fb8d3811d3db69b674ed4 --- /dev/null +++ b/reccon/sources/tr_4194.json @@ -0,0 +1,157 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "It's almost Christmas . What are you doing this weekend ?", + "emotion": "neutral", + "text": "It's almost Christmas . What are you doing this weekend ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Nothing special , just working . Why do you ask ?", + "emotion": "neutral", + "text": "Nothing special , just working . Why do you ask ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Well , I still haven't finished my Christmas shopping . Do you want to go shopping with me this weekend ?", + "emotion": "neutral", + "text": "Well , I still haven't finished my Christmas shopping . Do you want to go shopping with me this weekend ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I'd like to , but I'm not sure if I can . Work has been really busy lately . Why don't we go on Friday instead ?", + "emotion": "neutral", + "text": "I'd like to , but I'm not sure if I can . Work has been really busy lately . Why don't we go on Friday instead ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Friday's not good . I think the stores will be very crowded and I have to work .", + "emotion": "neutral", + "text": "Friday's not good . I think the stores will be very crowded and I have to work .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "OK , then let's try to go this weekend . I should know if I can go by Friday . Is it OK if I call you then ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "go shopping with me this weekend" + ], + "type": [ + "inter-personal" + ], + "text": "OK , then let's try to go this weekend . I should know if I can go by Friday . Is it OK if I call you then ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yeah , that's fine .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 3, + 6 + ], + "expanded emotion cause span": [ + "go shopping with me this weekend", + "I should know if I can go by Friday ." + ], + "type": [ + "hybrid" + ], + "text": "Yeah , that's fine .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "What's your number ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "go shopping with me this weekend" + ], + "type": [ + "inter-personal" + ], + "text": "What's your number ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "233-331-8828 . Let me give you my email address too . It's Tom861@gmail . com", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "go shopping with me this weekend" + ], + "type": [ + "self-contagion" + ], + "text": "233-331-8828 . Let me give you my email address too . It's Tom861@gmail . com", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "OK , I'll talk to you soon .", + "emotion": "happiness", + "explanation": "speaker and listener are happy about christmas shopping", + "flag": "F", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "go shopping with me this weekend" + ], + "type": [ + "inter-personal" + ], + "text": "OK , I'll talk to you soon .", + "id": 10, + "source_sentences": [ + 2 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 11, + "speaker": "A", + "utterance": "OK .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "go shopping with me this weekend" + ], + "type": [ + "self-contagion" + ], + "text": "OK .", + "id": 11 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4204.json b/reccon/sources/tr_4204.json new file mode 100644 index 0000000000000000000000000000000000000000..b869dc3e68cae3d4ccb80bb5ce123dad652cada1 --- /dev/null +++ b/reccon/sources/tr_4204.json @@ -0,0 +1,166 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Mr . Martin , we're on arrival .", + "emotion": "happiness", + "explanation": "A is happy to see B off at the airport", + "expanded emotion cause evidence": [ + "b", + 1 + ], + "expanded emotion cause span": [ + "b", + "we're on arrival ." + ], + "type": [ + "latent", + "no-context" + ], + "text": "Mr . Martin , we're on arrival .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It's nice of you to see my off at the airport . Thank you very much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "It's nice of you to see my off at the airport ." + ], + "type": [ + "no-context" + ], + "text": "It's nice of you to see my off at the airport . Thank you very much .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "We'll miss you . I hope we'll keep in touch .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "It's nice of you to see my off at the airport . Thank you very much ." + ], + "type": [ + "inter-personal" + ], + "text": "We'll miss you . I hope we'll keep in touch .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Sure . You've given a great help to me in the past days .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "We'll miss you . I hope we'll keep in touch ." + ], + "type": [ + "inter-personal" + ], + "text": "Sure . You've given a great help to me in the past days .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "It's my pleasure . We hope you'll visit Beijing again .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Sure . You've given a great help to me in the past days ." + ], + "type": [ + "inter-personal" + ], + "text": "It's my pleasure . We hope you'll visit Beijing again .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Certainly . I'll be glad to .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "It's my pleasure . We hope you'll visit Beijing again ." + ], + "type": [ + "inter-personal" + ], + "text": "Certainly . I'll be glad to .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "It's almost time to get aboard .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Certainly . I'll be glad to ." + ], + "type": [ + "inter-personal" + ], + "text": "It's almost time to get aboard .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yes , we should go . Thank you very much . Goodbye !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "Certainly . I'll be glad to .", + "It's almost time to get aboard ." + ], + "type": [ + "hybrid" + ], + "text": "Yes , we should go . Thank you very much . Goodbye !", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Bye bye ! Have a pleasant journey !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Thank you very much ." + ], + "type": [ + "inter-personal" + ], + "text": "Bye bye ! Have a pleasant journey !", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4220.json b/reccon/sources/tr_4220.json new file mode 100644 index 0000000000000000000000000000000000000000..5bb1cf6b2f586ba7be89a1bb94d322c1e850515d --- /dev/null +++ b/reccon/sources/tr_4220.json @@ -0,0 +1,94 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "How are you feeling , John ?", + "emotion": "neutral", + "text": "How are you feeling , John ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh , not too bad , but I've got to stay in bed .", + "emotion": "neutral", + "text": "Oh , not too bad , but I've got to stay in bed .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Do more exercises after you are healthy .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "not too bad" + ], + "type": [ + "inter-personal" + ], + "text": "Do more exercises after you are healthy .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Ok , I will . You have said that many times .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "Do more exercises after you are healthy .", + "You have said that many times ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Ok , I will . You have said that many times .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Are you hungry ? Do you want me to buy something for you to eat ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Ok , I will . You have said that many times ." + ], + "type": [ + "inter-personal" + ], + "text": "Are you hungry ? Do you want me to buy something for you to eat ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "No , there ' s no need . Thank you all the same .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Are you hungry ? Do you want me to buy something for you to eat ?" + ], + "type": [ + "inter-personal" + ], + "text": "No , there ' s no need . Thank you all the same .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4248.json b/reccon/sources/tr_4248.json new file mode 100644 index 0000000000000000000000000000000000000000..7426a0c817e6f0f25f49997ac6c3865eba925b1f --- /dev/null +++ b/reccon/sources/tr_4248.json @@ -0,0 +1,151 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Have you seen that house ?", + "emotion": "happiness", + "explanation": "Loves the house as mentioned in utterance 3", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Have you seen that house ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , it looks interesting .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "it looks interesting ." + ], + "type": [ + "no-context" + ], + "text": "Yes , it looks interesting .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "You're right . I love it very much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "it looks interesting .", + "I love it very much ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You're right . I love it very much .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It must be old .", + "emotion": "neutral", + "text": "It must be old .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "At least more than 100 years old .", + "emotion": "neutral", + "text": "At least more than 100 years old .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Let's enter it !", + "emotion": "neutral", + "text": "Let's enter it !", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I can't open the door .", + "emotion": "neutral", + "text": "I can't open the door .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "It must be locked .", + "emotion": "neutral", + "text": "It must be locked .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Let me ask the old woman in that reception office .", + "emotion": "neutral", + "text": "Let me ask the old woman in that reception office .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "She can't answer you .", + "emotion": "neutral", + "text": "She can't answer you .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "She must be deaf .", + "emotion": "neutral", + "text": "She must be deaf .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "It must be a haunted house . Are you frightened ?", + "emotion": "neutral", + "text": "It must be a haunted house . Are you frightened ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Frightened ? You must be joking .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "Are you frightened ?" + ], + "type": [ + "inter-personal" + ], + "text": "Frightened ? You must be joking .", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4262.json b/reccon/sources/tr_4262.json new file mode 100644 index 0000000000000000000000000000000000000000..b989366b621c3a076935d353f3ffc661109c8c97 --- /dev/null +++ b/reccon/sources/tr_4262.json @@ -0,0 +1,170 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "It's weekend again , I'm glad I can arrange for my personal matters .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "It's weekend again , I'm glad I can arrange for my personal matters ." + ], + "type": [ + "no-context" + ], + "text": "It's weekend again , I'm glad I can arrange for my personal matters .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What do you mean by that ?", + "emotion": "neutral", + "text": "What do you mean by that ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Oh , that means I can do whatever I like without few interruptions .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I can do whatever I like without few interruptions ." + ], + "type": [ + "no-context" + ], + "text": "Oh , that means I can do whatever I like without few interruptions .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "You've been always active and versatile . It seems that you are interested in everything .", + "emotion": "neutral", + "text": "You've been always active and versatile . It seems that you are interested in everything .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Oh , really ? I just have lots of hobbies in my spare time ; such as going to the concert , painting , handwriting , reading novels and reading fashion magazines . What about yours ?", + "emotion": "neutral", + "text": "Oh , really ? I just have lots of hobbies in my spare time ; such as going to the concert , painting , handwriting , reading novels and reading fashion magazines . What about yours ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I have fewer hobbies than yours . That's why I find campus life a bit dull and uninteresting .", + "emotion": "neutral", + "text": "I have fewer hobbies than yours . That's why I find campus life a bit dull and uninteresting .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Oh , you can't think like that . We young people should try our best to learn new things and accept new ideas . You like taking photos and going to photography shows , why not practise the technique and catch something unforgeable ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "You like taking photos and going to photography shows , why not practise the technique and catch something unforgeable ?" + ], + "type": [ + "no-context" + ], + "text": "Oh , you can't think like that . We young people should try our best to learn new things and accept new ideas . You like taking photos and going to photography shows , why not practise the technique and catch something unforgeable ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That's a good suggestion . It's fine today . Maybe I can take photos on the scenery of the lake at sunset . It must be fantastic .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "You like taking photos and going to photography shows , why not practise the technique and catch something unforgeable ?", + "That's a good suggestion . It's fine today . Maybe I can take photos on the scenery of the lake at sunset . It must be fantastic ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's a good suggestion . It's fine today . Maybe I can take photos on the scenery of the lake at sunset . It must be fantastic .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I quite agree with you . With our hobbies , our life can be more colorful and exciting .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "That's a good suggestion . It's fine today . Maybe I can take photos on the scenery of the lake at sunset . It must be fantastic .", + "I quite agree with you . With our hobbies , our life can be more colorful and exciting ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I quite agree with you . With our hobbies , our life can be more colorful and exciting .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "And I can concentrate on my study after the relaxation over the weekend .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "I quite agree with you . With our hobbies , our life can be more colorful and exciting .", + "And I can concentrate on my study after the relaxation over the weekend ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "And I can concentrate on my study after the relaxation over the weekend .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Yes , it's a good habit to have a life-long hobby . Those who practise calligraphy and Qigong always live longer .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "And I can concentrate on my study after the relaxation over the weekend .", + "Yes , it's a good habit to have a life-long hobby . Those who practise calligraphy and Qigong always live longer ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , it's a good habit to have a life-long hobby . Those who practise calligraphy and Qigong always live longer .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4266.json b/reccon/sources/tr_4266.json new file mode 100644 index 0000000000000000000000000000000000000000..5600f4ba5f9ce7d15b15cfd6f09f8f01dc2de33d --- /dev/null +++ b/reccon/sources/tr_4266.json @@ -0,0 +1,171 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Wow , American football is more exciting than I thought .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "American football is more exciting than I thought ." + ], + "type": [ + "no-context" + ], + "text": "Wow , American football is more exciting than I thought .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "You ' re in America now , my British friend . We just call it football .", + "emotion": "neutral", + "text": "You ' re in America now , my British friend . We just call it football .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Oh , right . So , I can ' t quite follow what ' s going on ... who ' s winning ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "American football is more exciting than I thought ." + ], + "type": [ + "self-contagion" + ], + "text": "Oh , right . So , I can ' t quite follow what ' s going on ... who ' s winning ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "The Giants are up by three points because of the field goal they kicked , but the Redskins have the ball and there pretty close to the end zone .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "The Giants are up by three points because of the field goal they kicked , but the Redskins have the ball and there pretty close to the end zone ." + ], + "type": [ + "no-context" + ], + "text": "The Giants are up by three points because of the field goal they kicked , but the Redskins have the ball and there pretty close to the end zone .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Wow ! What a hit !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1, + 5 + ], + "expanded emotion cause span": [ + "American football is more exciting than I thought .", + "What a hit !" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Wow ! What a hit !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yeah , he tackled him so hard his helmet came off .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "What a hit !", + "he tackled him so hard" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yeah , he tackled him so hard his helmet came off .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Is he ok ?", + "emotion": "neutral", + "text": "Is he ok ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "It looks like it , he ' s getting up .", + "emotion": "neutral", + "text": "It looks like it , he ' s getting up .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I guess he hit him too hard ; the referee just called a penalty on the home team .", + "emotion": "neutral", + "text": "I guess he hit him too hard ; the referee just called a penalty on the home team .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "The Giants ?", + "emotion": "neutral", + "text": "The Giants ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Yeah .", + "emotion": "neutral", + "text": "Yeah .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Well , here we go again .", + "emotion": "neutral", + "text": "Well , here we go again .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "What happened ? Why did everyone get so quiet ?", + "emotion": "neutral", + "text": "What happened ? Why did everyone get so quiet ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "The Redskin ' s quarterback just threw a touchdown pass for seven points . We ' re losing again .", + "emotion": "neutral", + "text": "The Redskin ' s quarterback just threw a touchdown pass for seven points . We ' re losing again .", + "id": 14 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_427.json b/reccon/sources/tr_427.json new file mode 100644 index 0000000000000000000000000000000000000000..7bc99d1fed8f0a5c75882b44427486b6be67f7ce --- /dev/null +++ b/reccon/sources/tr_427.json @@ -0,0 +1,133 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "You got a letter in the mail .", + "emotion": "neutral", + "text": "You got a letter in the mail .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Give it to me .", + "emotion": "neutral", + "text": "Give it to me .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What is it ?", + "emotion": "neutral", + "text": "What is it ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It ' s from NYU .", + "emotion": "neutral", + "text": "It ' s from NYU .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "What does it say ?", + "emotion": "neutral", + "text": "What does it say ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I didn ' t get accepted .", + "emotion": "neutral", + "text": "I didn ' t get accepted .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You can ' t be serious !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I didn ' t get accepted ." + ], + "type": [ + "inter-personal" + ], + "text": "You can ' t be serious !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I ' m serious .", + "emotion": "neutral", + "text": "I ' m serious .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Are you all right ?", + "emotion": "neutral", + "text": "Are you all right ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "NYU was my first choice .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I didn ' t get accepted ." + ], + "type": [ + "self-contagion" + ], + "text": "NYU was my first choice .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I ' m sorry that you didn ' t get in .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 6, + 11 + ], + "expanded emotion cause span": [ + "I didn ' t get accepted .", + "I ' m sorry that you didn ' t get in ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I ' m sorry that you didn ' t get in .", + "id": 11, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I ' ll just have to wait for UCLA .", + "emotion": "neutral", + "text": "I ' ll just have to wait for UCLA .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4280.json b/reccon/sources/tr_4280.json new file mode 100644 index 0000000000000000000000000000000000000000..340d1475ae6f182b38b6cc697f22fddd229b4b73 --- /dev/null +++ b/reccon/sources/tr_4280.json @@ -0,0 +1,123 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I'm so excited ! We have two weeks off ! What are you going to do ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "We have two weeks off !" + ], + "type": [ + "no-context" + ], + "text": "I'm so excited ! We have two weeks off ! What are you going to do ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'm not sure . I guess I'll just stay at home . Maybe I'll catch up on my reading . What about you ? Any plans ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "We have two weeks off !", + "I'll catch up on my reading ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm not sure . I guess I'll just stay at home . Maybe I'll catch up on my reading . What about you ? Any plans ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Well , my parents have rented a condominium in Florida . I'm going to take long walks along the beach every day and do lots of swimming .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "We have two weeks off !", + "I'm going to take long walks along the beach every day and do lots of swimming ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Well , my parents have rented a condominium in Florida . I'm going to take long walks along the beach every day and do lots of swimming .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Sounds great !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "We have two weeks off !", + "I'm going to take long walks along the beach every day and do lots of swimming ." + ], + "type": [ + "inter-personal" + ], + "text": "Sounds great !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Say , why don't you come with us ? We have plenty of room .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 5 + ], + "expanded emotion cause span": [ + "We have two weeks off !", + "why don't you come with us ? We have plenty of room ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Say , why don't you come with us ? We have plenty of room .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Do you mean it ? I'd love to !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 5 + ], + "expanded emotion cause span": [ + "We have two weeks off !", + "why don't you come with us ? We have plenty of room ." + ], + "type": [ + "inter-personal" + ], + "text": "Do you mean it ? I'd love to !", + "id": 6, + "source_sentences": [ + 0, + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4288.json b/reccon/sources/tr_4288.json new file mode 100644 index 0000000000000000000000000000000000000000..9b3be9fa4e6169091fba73b0e19157c39fc94b36 --- /dev/null +++ b/reccon/sources/tr_4288.json @@ -0,0 +1,115 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Do I need a visa ?", + "emotion": "neutral", + "text": "Do I need a visa ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "No , I shouldn ' t think so . But you must take your passport of course .", + "emotion": "neutral", + "text": "No , I shouldn ' t think so . But you must take your passport of course .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yes , I know . I must get my traveler ' s check and some foreign currency .", + "emotion": "neutral", + "text": "Yes , I know . I must get my traveler ' s check and some foreign currency .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes , you need the traveler ' s check but you needn ' t get any foreign currency . You can have my US Dollars , I don ' t need them .", + "emotion": "neutral", + "text": "Yes , you need the traveler ' s check but you needn ' t get any foreign currency . You can have my US Dollars , I don ' t need them .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Really ? That ' s very good of you , Helen . But I must get a new suitcase , my old one needs repairing .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "You can have my US Dollars" + ], + "type": [ + "inter-personal" + ], + "text": "Really ? That ' s very good of you , Helen . But I must get a new suitcase , my old one needs repairing .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "You needn ' t buy one . You can have mine .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "That ' s very good of you , Helen" + ], + "type": [ + "inter-personal" + ], + "text": "You needn ' t buy one . You can have mine .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "That ' s very kind of you , Helen . I hope you don ' t mind my leaving you like this . I need a holiday . It won ' t be long .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 6 + ], + "expanded emotion cause span": [ + "You can have my US Dollars", + "You needn ' t buy one . You can have mine ." + ], + "type": [ + "inter-personal" + ], + "text": "That ' s very kind of you , Helen . I hope you don ' t mind my leaving you like this . I need a holiday . It won ' t be long .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Don ' t be silly , John . I ' m going with you . It ' s necessary for me to have a holiday too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 7, + 8 + ], + "expanded emotion cause span": [ + "That ' s very good of you , Helen", + "That ' s very kind of you , Helen .", + "I ' m going with you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Don ' t be silly , John . I ' m going with you . It ' s necessary for me to have a holiday too .", + "id": 8, + "source_sentences": [ + 4, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4291.json b/reccon/sources/tr_4291.json new file mode 100644 index 0000000000000000000000000000000000000000..1e9b71a5d95ae76b463ca94f3c4e10af48a348f8 --- /dev/null +++ b/reccon/sources/tr_4291.json @@ -0,0 +1,130 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What are your weekend arrangements ?", + "emotion": "neutral", + "text": "What are your weekend arrangements ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "There're many things I can do on weekends .", + "emotion": "neutral", + "text": "There're many things I can do on weekends .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What sort of things are you interested in ?", + "emotion": "neutral", + "text": "What sort of things are you interested in ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I'm keen on talking short trips to nearby scenic spots . More often than not , I go with some of my friends . By the way , what are your favorites ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 4 + ], + "expanded emotion cause span": [ + "I'm keen on talking short trips to nearby scenic spots .", + "I go with some of my friends ." + ], + "type": [ + "no-context" + ], + "text": "I'm keen on talking short trips to nearby scenic spots . More often than not , I go with some of my friends . By the way , what are your favorites ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I love swimming and cycling . On Sunday morning I have swimming practice for an hour . In the afternoon , I just ride my bike around the city or along the country roads for almost two hours .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I love swimming and cycling . On Sunday morning I have swimming practice for an hour . In the afternoon , I just ride my bike around the city or along the country roads for almost two hours ." + ], + "type": [ + "no-context" + ], + "text": "I love swimming and cycling . On Sunday morning I have swimming practice for an hour . In the afternoon , I just ride my bike around the city or along the country roads for almost two hours .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "That's great ! I think they do you a lot of good . Where do you swim ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 4, + 5 + ], + "expanded emotion cause span": [ + "I'm keen on talking short trips to nearby scenic spots .", + "I go with some of my friends .", + "I love swimming and cycling . On Sunday morning I have swimming practice for an hour . In the afternoon , I just ride my bike around the city or along the country roads for almost two hours ." + ], + "type": [ + "hybrid" + ], + "text": "That's great ! I think they do you a lot of good . Where do you swim ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Mostly in the city's swimming pool . But on occasion , I go to the beach with friends . Well , what do you do at leisure ?", + "emotion": "neutral", + "text": "Mostly in the city's swimming pool . But on occasion , I go to the beach with friends . Well , what do you do at leisure ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I'm fond of dancing .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I'm fond of dancing ." + ], + "type": [ + "no-context" + ], + "text": "I'm fond of dancing .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Good . You really know how to enjoy yourself .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I'm fond of dancing ." + ], + "type": [ + "inter-personal" + ], + "text": "Good . You really know how to enjoy yourself .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4295.json b/reccon/sources/tr_4295.json new file mode 100644 index 0000000000000000000000000000000000000000..7fcded6d143e9f5c6820299ca7b2fef23401cd81 --- /dev/null +++ b/reccon/sources/tr_4295.json @@ -0,0 +1,112 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "We'd like a half-day package .", + "emotion": "happiness", + "explanation": "A is excited about ordering something that is desired.", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "We'd like a half-day package .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "We offer many different sea water treatments .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "We'd like a half-day package ." + ], + "type": [ + "inter-personal" + ], + "text": "We offer many different sea water treatments .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "How many can we choose ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "We offer many different sea water treatments ." + ], + "type": [ + "inter-personal" + ], + "text": "How many can we choose ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "The aquamedic pool is included . You can choose three .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 1 + ], + "expanded emotion cause span": [ + "We'd like a half-day package .", + "We'd like a half-day package ." + ], + "type": [ + "inter-personal" + ], + "text": "The aquamedic pool is included . You can choose three .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "We'll do the seaweed wrap , the jet bath , and the foot massage .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "The aquamedic pool is included . You can choose three ." + ], + "type": [ + "inter-personal" + ], + "text": "We'll do the seaweed wrap , the jet bath , and the foot massage .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "OK . Here are your robes . You can go shower first .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "We'll do the seaweed wrap , the jet bath , and the foot massage ." + ], + "type": [ + "inter-personal" + ], + "text": "OK . Here are your robes . You can go shower first .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4307.json b/reccon/sources/tr_4307.json new file mode 100644 index 0000000000000000000000000000000000000000..a49c91d0e6542e7b46515ca73005b8f41ab47ed5 --- /dev/null +++ b/reccon/sources/tr_4307.json @@ -0,0 +1,114 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , I'm Jake . I'm new to the choir . What's your name ?", + "emotion": "neutral", + "text": "Hi , I'm Jake . I'm new to the choir . What's your name ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hello , there , my name is Tonia .", + "emotion": "neutral", + "text": "Hello , there , my name is Tonia .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Do you sing alto ?", + "emotion": "neutral", + "text": "Do you sing alto ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Actually , I can do both soprano and alto but the director asked me to sing alto for the next perforate . What about you .", + "emotion": "neutral", + "text": "Actually , I can do both soprano and alto but the director asked me to sing alto for the next perforate . What about you .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Looks like we both float back and forth . I'm baritone .", + "emotion": "happiness", + "explanation": "The cause for A is latent.", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Looks like we both float back and forth . I'm baritone .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Our bass section is really good . You're going to love singing with them .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Our bass section is really good . You're going to love singing with them ." + ], + "type": [ + "no-context" + ], + "text": "Our bass section is really good . You're going to love singing with them .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I heard them warming up earlier . You're right .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 6 + ], + "expanded emotion cause span": [ + "Our bass section is really good . You're going to love singing with them .", + "Our bass section is really good . You're going to love singing with them ." + ], + "type": [ + "inter-personal" + ], + "text": "I heard them warming up earlier . You're right .", + "id": 7, + "source_sentences": [ + 5, + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "It's good to have you in the group . We can always use a good baritone !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 8 + ], + "expanded emotion cause span": [ + "Our bass section is really good . You're going to love singing with them .", + "It's good to have you in the group . We can always use a good baritone !" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "It's good to have you in the group . We can always use a good baritone !", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4318.json b/reccon/sources/tr_4318.json new file mode 100644 index 0000000000000000000000000000000000000000..7306a4aa38552099e8c9dc975fe553d0d643901c --- /dev/null +++ b/reccon/sources/tr_4318.json @@ -0,0 +1,135 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello ?", + "emotion": "neutral", + "text": "Hello ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hi , Shelley . Have you had lunch ?", + "emotion": "neutral", + "text": "Hi , Shelley . Have you had lunch ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Not yet .", + "emotion": "neutral", + "text": "Not yet .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "So shall we have lunch together ? I ' d like to take you this time .", + "emotion": "neutral", + "text": "So shall we have lunch together ? I ' d like to take you this time .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I ' d like to , but I can ' t .", + "emotion": "neutral", + "text": "I ' d like to , but I can ' t .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "How come ?", + "emotion": "neutral", + "text": "How come ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I ' Ve a lot of paper work to do right now . I ' m behind schedule .", + "emotion": "neutral", + "text": "I ' Ve a lot of paper work to do right now . I ' m behind schedule .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "All right . Can we make it another time ?", + "emotion": "happiness", + "explanation": "B might be happy only for courtesy. Actual cause is latent.", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "All right . Can we make it another time ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Sure , thanks .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "All right . Can we make it another time ?" + ], + "type": [ + "inter-personal" + ], + "text": "Sure , thanks .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I ' ll call you later . Bye .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 9 + ], + "expanded emotion cause span": [ + "b", + "Sure , thanks ." + ], + "type": [ + "latent", + "inter-personal" + ], + "text": "I ' ll call you later . Bye .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Bye .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "All right . Can we make it another time ?" + ], + "type": [ + "inter-personal" + ], + "text": "Bye .", + "id": 11, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4332.json b/reccon/sources/tr_4332.json new file mode 100644 index 0000000000000000000000000000000000000000..f504d9d498380fafd97e6e77cb68af2665f2645e --- /dev/null +++ b/reccon/sources/tr_4332.json @@ -0,0 +1,195 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , come on in . Can I take your coat ?", + "emotion": "neutral", + "text": "Hi , come on in . Can I take your coat ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Sure , thanks . I brought you a bottle of wine as well .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Sure , thanks . I brought you a bottle of wine as well .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "You're the first guest to arrive . I'll just put your coat away and then I'll get you something to drink .", + "emotion": "neutral", + "text": "You're the first guest to arrive . I'll just put your coat away and then I'll get you something to drink .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Should I take my shoes off ?", + "emotion": "neutral", + "text": "Should I take my shoes off ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Whatever you prefer .", + "emotion": "neutral", + "text": "Whatever you prefer .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "This is a very nice place . How long have you been living here now ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "This is a very nice place ." + ], + "type": [ + "no-context" + ], + "text": "This is a very nice place . How long have you been living here now ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Just over three weeks . Would you like a drink ?", + "emotion": "neutral", + "text": "Just over three weeks . Would you like a drink ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Sure , what do you have ?", + "emotion": "neutral", + "text": "Sure , what do you have ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I've got white wine , red wine , gin and tonics , ginger ale , lemonade , orange juice , and sprite .", + "emotion": "neutral", + "text": "I've got white wine , red wine , gin and tonics , ginger ale , lemonade , orange juice , and sprite .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I'll have a glass of red wine please .", + "emotion": "neutral", + "text": "I'll have a glass of red wine please .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "One glass of red wine coming up !", + "emotion": "happiness", + "explanation": "Hapy because of the aura", + "expanded emotion cause evidence": [ + "b", + 11 + ], + "expanded emotion cause span": [ + "b", + "One glass of red wine coming up !" + ], + "type": [ + "latent", + "no-context" + ], + "text": "One glass of red wine coming up !", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "So how many people are coming for the dinner tonight ?", + "emotion": "neutral", + "text": "So how many people are coming for the dinner tonight ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "There's just going to be 6 of us tonight .", + "emotion": "neutral", + "text": "There's just going to be 6 of us tonight .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Oh , I thought there were going to be eight . who isn't coming ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 13, + 14 + ], + "expanded emotion cause span": [ + "There's just going to be 6 of us tonight .", + "I thought there were going to be eight ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , I thought there were going to be eight . who isn't coming ?", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Marcia and Paul called to cancel at the last moment . Paul was running late and Marcia wasn't feeling well .", + "emotion": "neutral", + "text": "Marcia and Paul called to cancel at the last moment . Paul was running late and Marcia wasn't feeling well .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "That's too bad . They ' re such good company .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "Marcia and Paul called to cancel at the last moment ." + ], + "type": [ + "inter-personal" + ], + "text": "That's too bad . They ' re such good company .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 17, + "speaker": "A", + "utterance": "I think there's someone at the door . Excuse me while I go and get that .", + "emotion": "neutral", + "text": "I think there's someone at the door . Excuse me while I go and get that .", + "id": 17 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4336.json b/reccon/sources/tr_4336.json new file mode 100644 index 0000000000000000000000000000000000000000..4690f957e5cd8bc4be0fd56416173d763ab0c15b --- /dev/null +++ b/reccon/sources/tr_4336.json @@ -0,0 +1,126 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Are you excited about your trip next month ?", + "emotion": "neutral", + "text": "Are you excited about your trip next month ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes and no . I can ' t wait to go to Europe , but at the same time I am terrified .", + "emotion": "neutral", + "text": "Yes and no . I can ' t wait to go to Europe , but at the same time I am terrified .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Why ?", + "emotion": "neutral", + "text": "Why ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Well , I have acrophobia . I have a chronic fear of flying .", + "emotion": "fear", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I have acrophobia . I have a chronic fear of flying ." + ], + "type": [ + "no-context" + ], + "text": "Well , I have acrophobia . I have a chronic fear of flying .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Oh really ? I have an uncle who is also terrified of flying . It ' s not that bad though , I mean , it is pretty scary to be in this big machine flying through the air at seven hundred miles per hour . I actually have arachnophobia .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I have acrophobia . I have a chronic fear of flying ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh really ? I have an uncle who is also terrified of flying . It ' s not that bad though , I mean , it is pretty scary to be in this big machine flying through the air at seven hundred miles per hour . I actually have arachnophobia .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "You ' re scared of spiders ? I actually have two more phobias . Acrophobia and glossophobia .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I actually have arachnophobia ." + ], + "type": [ + "inter-personal" + ], + "text": "You ' re scared of spiders ? I actually have two more phobias . Acrophobia and glossophobia .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I guess that explains why you are afraid of flying , but public speaking is not that bad .", + "emotion": "neutral", + "text": "I guess that explains why you are afraid of flying , but public speaking is not that bad .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Are you kidding ? When I get on stage , my palms start to sweat , I get really nervous and I can hardly speak .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "public speaking is not that bad .", + "When I get on stage , my palms start to sweat , I get really nervous and I can hardly speak ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Are you kidding ? When I get on stage , my palms start to sweat , I get really nervous and I can hardly speak .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Well , I must confess I am a bit claustrophobic . I hate being in an elevator for more than 5 seconds .", + "emotion": "neutral", + "text": "Well , I must confess I am a bit claustrophobic . I hate being in an elevator for more than 5 seconds .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "We are such weirdos right ?", + "emotion": "neutral", + "text": "We are such weirdos right ?", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4378.json b/reccon/sources/tr_4378.json new file mode 100644 index 0000000000000000000000000000000000000000..a2cc30e5276ad466edb7397a5eadaa50854db913 --- /dev/null +++ b/reccon/sources/tr_4378.json @@ -0,0 +1,85 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What's wrong , Dave ? You look down today .", + "emotion": "neutral", + "text": "What's wrong , Dave ? You look down today .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I didn't pass the English exam . How to learn English well ? Can you give me some suggestions ?", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I didn't pass the English exam ." + ], + "type": [ + "no-context" + ], + "text": "I didn't pass the English exam . How to learn English well ? Can you give me some suggestions ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Well , English is a \" paper tiger \" . Its natural enemy is adequate practice .", + "emotion": "neutral", + "text": "Well , English is a \" paper tiger \" . Its natural enemy is adequate practice .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I have done a lot of reading comprehension exercises , and I also spend much time in memorizing English words .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "English is a \" paper tiger \" . Its natural enemy is adequate practice .", + "I have done a lot of reading comprehension exercises , and I also spend much time in memorizing English words ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I have done a lot of reading comprehension exercises , and I also spend much time in memorizing English words .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I suggest you read English texts aloud every day , and try to speak more . That will be beneficial to cultivate your sense of the language .", + "emotion": "neutral", + "text": "I suggest you read English texts aloud every day , and try to speak more . That will be beneficial to cultivate your sense of the language .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Really ? I'll have a try . Maybe I will get high marks next time .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I suggest you read English texts aloud every day , and try to speak more . That will be beneficial to cultivate your sense of the language ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? I'll have a try . Maybe I will get high marks next time .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4434.json b/reccon/sources/tr_4434.json new file mode 100644 index 0000000000000000000000000000000000000000..9809fc82d872cf4b656e705a26ac7068786383cd --- /dev/null +++ b/reccon/sources/tr_4434.json @@ -0,0 +1,167 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I really enjoyed that film ! What about you ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I really enjoyed that film !" + ], + "type": [ + "no-context" + ], + "text": "I really enjoyed that film ! What about you ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "So did I . At first , I thought it was going to be boring , but then it turned to be good .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I thought it was going to be boring , but then it turned to be good ." + ], + "type": [ + "no-context" + ], + "text": "So did I . At first , I thought it was going to be boring , but then it turned to be good .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What part of the film do you like best ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "I really enjoyed that film !", + "I thought it was going to be boring , but then it turned to be good ." + ], + "type": [ + "hybrid" + ], + "text": "What part of the film do you like best ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Well , the scene of the hero's struggle with enemies impressed me the most .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "the scene of the hero's struggle with enemies impressed me the most ." + ], + "type": [ + "no-context" + ], + "text": "Well , the scene of the hero's struggle with enemies impressed me the most .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I loved it , too . To tell you the truth , I even dropped tears .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5, + 5 + ], + "expanded emotion cause span": [ + "the scene of the hero's struggle with enemies impressed me the most .", + "I loved it , too .", + "I even dropped tears ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I loved it , too . To tell you the truth , I even dropped tears .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Actually , tears also came to my eyes .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5, + 5, + 6 + ], + "expanded emotion cause span": [ + "the scene of the hero's struggle with enemies impressed me the most .", + "I loved it , too .", + "I even dropped tears .", + "tears also came to my eyes ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Actually , tears also came to my eyes .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "It has got this year's Oscar Award .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 7 + ], + "expanded emotion cause span": [ + "I really enjoyed that film !", + "It has got this year's Oscar Award ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "It has got this year's Oscar Award .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "It deserves it . The film gave us a lot of inspiration .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 7, + 8 + ], + "expanded emotion cause span": [ + "I really enjoyed that film !", + "It has got this year's Oscar Award .", + "The film gave us a lot of inspiration ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It deserves it . The film gave us a lot of inspiration .", + "id": 8, + "source_sentences": [ + 0, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4464.json b/reccon/sources/tr_4464.json new file mode 100644 index 0000000000000000000000000000000000000000..336789b0a482089feafa45115226b2e3fb1f99c4 --- /dev/null +++ b/reccon/sources/tr_4464.json @@ -0,0 +1,142 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "How do you like this dress ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "do you like this dress ?" + ], + "type": [ + "no-context" + ], + "text": "How do you like this dress ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It's nice . But what kind of dress are you looking for ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "do you like this dress ?", + "It's nice ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It's nice . But what kind of dress are you looking for ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Something attractive and dressy . Maybe a little sexy too . New Year's Eve is a special occasion and it only happens once a year , right ?", + "emotion": "neutral", + "text": "Something attractive and dressy . Maybe a little sexy too . New Year's Eve is a special occasion and it only happens once a year , right ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Of course . It's common too that we wear something special for our Chinese New Year .", + "emotion": "neutral", + "text": "Of course . It's common too that we wear something special for our Chinese New Year .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "People here always wear the best clothes they have . Many people go out and buy clothes especially for New Year's Eve .", + "emotion": "neutral", + "text": "People here always wear the best clothes they have . Many people go out and buy clothes especially for New Year's Eve .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Any other common customs of your New Year ?", + "emotion": "neutral", + "text": "Any other common customs of your New Year ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Before the New Year , we always send greeting cards to our relatives and friends to wish them a happy year . On the street and in stores people usually greet others with a ' Happy New Year ' . It's also common for people to make a New Year's resolution .", + "emotion": "neutral", + "text": "Before the New Year , we always send greeting cards to our relatives and friends to wish them a happy year . On the street and in stores people usually greet others with a ' Happy New Year ' . It's also common for people to make a New Year's resolution .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "What's that ?", + "emotion": "neutral", + "text": "What's that ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "It's when people quit a bad habit or do something they find hard to do . Many people resolve to quit smoking , lose weight , or stop nagging their wife , etc . However , it usually lasts only for a few days !", + "emotion": "neutral", + "text": "It's when people quit a bad habit or do something they find hard to do . Many people resolve to quit smoking , lose weight , or stop nagging their wife , etc . However , it usually lasts only for a few days !", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "By the way , where are you going on New Year's Eve ?", + "emotion": "neutral", + "text": "By the way , where are you going on New Year's Eve ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "We're going to a night club for dinner and dancing , then we'll go down to the city square for the big celebration . There's always a fireworks display put on by the local government . We all want you to come too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "We're going to a night club for dinner and dancing , then we'll go down to the city square for the big celebration . There's always a fireworks display put on by the local government . We all want you to come too ." + ], + "type": [ + "no-context" + ], + "text": "We're going to a night club for dinner and dancing , then we'll go down to the city square for the big celebration . There's always a fireworks display put on by the local government . We all want you to come too .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Thanks a lot .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "We all want you to come too ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks a lot .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4466.json b/reccon/sources/tr_4466.json new file mode 100644 index 0000000000000000000000000000000000000000..d1cc6944bd2faa7336c32e677acab416fb68f74e --- /dev/null +++ b/reccon/sources/tr_4466.json @@ -0,0 +1,128 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey , you wanna see a movie tomorrow ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "see a movie tomorrow ?" + ], + "type": [ + "no-context" + ], + "text": "Hey , you wanna see a movie tomorrow ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Sounds like a good plan . What do you want to see ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "see a movie tomorrow ?" + ], + "type": [ + "inter-personal" + ], + "text": "Sounds like a good plan . What do you want to see ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "How about Legally Blonde .", + "emotion": "neutral", + "text": "How about Legally Blonde .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Ah , my girlfriend wanted to see that movie . I have to take her later so I don't want to watch it ahead of time . How about The Cube ?", + "emotion": "neutral", + "text": "Ah , my girlfriend wanted to see that movie . I have to take her later so I don't want to watch it ahead of time . How about The Cube ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Isn't that a scary movie ?", + "emotion": "neutral", + "text": "Isn't that a scary movie ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "How scary can it be ? Come on , it'll be fun .", + "emotion": "neutral", + "text": "How scary can it be ? Come on , it'll be fun .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Ok . I'll give it a try .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "it'll be fun ." + ], + "type": [ + "inter-personal" + ], + "text": "Ok . I'll give it a try .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That's the spirit . I'll see you tomorrow after class .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "it'll be fun .", + "Ok . I'll give it a try ." + ], + "type": [ + "hybrid" + ], + "text": "That's the spirit . I'll see you tomorrow after class .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Ok . See you tomorrow .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 6 + ], + "expanded emotion cause span": [ + "see a movie tomorrow ?", + "it'll be fun ." + ], + "type": [ + "hybrid" + ], + "text": "Ok . See you tomorrow .", + "id": 9 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4470.json b/reccon/sources/tr_4470.json new file mode 100644 index 0000000000000000000000000000000000000000..b20cd660db50dfdf4a6e05fa60ba2e16abdc0a7d --- /dev/null +++ b/reccon/sources/tr_4470.json @@ -0,0 +1,231 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Lucy , you ' re back . How was your first day of school ?", + "emotion": "neutral", + "text": "Lucy , you ' re back . How was your first day of school ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It was great . I had a really good time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "your first day of school ?", + "I had a really good time ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It was great . I had a really good time .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What classes did you have ?", + "emotion": "neutral", + "text": "What classes did you have ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Well , I had English from 9 o'clock to 11 o'clock , art from 12 o'clock to 2 o'clock , and math from 2 o'clock to 4 o'clock .", + "emotion": "neutral", + "text": "Well , I had English from 9 o'clock to 11 o'clock , art from 12 o'clock to 2 o'clock , and math from 2 o'clock to 4 o'clock .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "What do you think about the teachers ?", + "emotion": "neutral", + "text": "What do you think about the teachers ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "To be honest , I liked all of them , except for the math teacher . Though he must be quite young , he seem like an old person . He ' s so boring !", + "emotion": "neutral", + "text": "To be honest , I liked all of them , except for the math teacher . Though he must be quite young , he seem like an old person . He ' s so boring !", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "That ' s too bad . How was your English teacher ?", + "emotion": "neutral", + "text": "That ' s too bad . How was your English teacher ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "She was great . In today ' s class , she gave us a lecture on how to be a good student . She told us not to arm for exams , and to pay more attention on communicating than memorizing .", + "emotion": "neutral", + "text": "She was great . In today ' s class , she gave us a lecture on how to be a good student . She told us not to arm for exams , and to pay more attention on communicating than memorizing .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Where is she from ?", + "emotion": "neutral", + "text": "Where is she from ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "She said that she ' s from a small town in the middle of America .", + "emotion": "neutral", + "text": "She said that she ' s from a small town in the middle of America .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Were you able to understand everything that she said ?", + "emotion": "neutral", + "text": "Were you able to understand everything that she said ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Not everything , but nearly . She speaks very clearly and doesn ' t use very complex words so that it is easy for us to understand her .", + "emotion": "neutral", + "text": "Not everything , but nearly . She speaks very clearly and doesn ' t use very complex words so that it is easy for us to understand her .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "She sounds like a good teacher . Do you think you ' ll pass her class ?", + "emotion": "neutral", + "text": "She sounds like a good teacher . Do you think you ' ll pass her class ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Yes ... with flying colors !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13, + 14 + ], + "expanded emotion cause span": [ + "Do you think you ' ll pass her class ?", + "Yes ... with flying colors !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes ... with flying colors !", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "What does that mean ?", + "emotion": "neutral", + "text": "What does that mean ?", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "It ' s a new phrase that she taught us today . It means that I will not only pass the class , but I will do extremely well !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13, + 14, + 16 + ], + "expanded emotion cause span": [ + "Do you think you ' ll pass her class ?", + "Yes ... with flying colors !", + "but I will do extremely well !" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "It ' s a new phrase that she taught us today . It means that I will not only pass the class , but I will do extremely well !", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "If you like the class this much already , I ' m sure you will .", + "emotion": "neutral", + "text": "If you like the class this much already , I ' m sure you will .", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "I hope so .", + "emotion": "neutral", + "text": "I hope so .", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "did she give you any homework ?", + "emotion": "neutral", + "text": "did she give you any homework ?", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "not today . She said she wanted us to relax tonight instead of doing homework ,", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 20 + ], + "expanded emotion cause span": [ + "she wanted us to relax tonight instead of doing homework ," + ], + "type": [ + "no-context" + ], + "text": "not today . She said she wanted us to relax tonight instead of doing homework ,", + "id": 20 + }, + { + "turn": 21, + "speaker": "A", + "utterance": "no wonder you like the class so much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 20 + ], + "expanded emotion cause span": [ + "she wanted us to relax tonight instead of doing homework ," + ], + "type": [ + "inter-personal" + ], + "text": "no wonder you like the class so much .", + "id": 21, + "source_sentences": [ + 19 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4502.json b/reccon/sources/tr_4502.json new file mode 100644 index 0000000000000000000000000000000000000000..68f830e8572d1566798b2b35a72afb930abaf8ca --- /dev/null +++ b/reccon/sources/tr_4502.json @@ -0,0 +1,109 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "It ' s very kind of you to invite me to dinner .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "It ' s very kind of you" + ], + "type": [ + "no-context" + ], + "text": "It ' s very kind of you to invite me to dinner .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Please sit down and make yourself at home . Please don ' t stand on ceremony .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "It ' s very kind of you" + ], + "type": [ + "inter-personal" + ], + "text": "Please sit down and make yourself at home . Please don ' t stand on ceremony .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "This dish is really delicious .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "This dish is really delicious ." + ], + "type": [ + "no-context" + ], + "text": "This dish is really delicious .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I ' m glad that you like it . This is only the first time that I made it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "This dish is really delicious ." + ], + "type": [ + "inter-personal" + ], + "text": "I ' m glad that you like it . This is only the first time that I made it .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "You ' re great . Could you say it in Chinese ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "This is only the first time that I made it ." + ], + "type": [ + "inter-personal" + ], + "text": "You ' re great . Could you say it in Chinese ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Sure , we call it doubt .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "You ' re great ." + ], + "type": [ + "inter-personal" + ], + "text": "Sure , we call it doubt .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4516.json b/reccon/sources/tr_4516.json new file mode 100644 index 0000000000000000000000000000000000000000..88ff94e4dcea8c2b30a30db93ff019622aa39191 --- /dev/null +++ b/reccon/sources/tr_4516.json @@ -0,0 +1,221 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Good game ?", + "emotion": "neutral", + "text": "Good game ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Not bad . But too hot for me today .", + "emotion": "neutral", + "text": "Not bad . But too hot for me today .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yes , I know . Kind of hard to concentrate , isn't it ?", + "emotion": "neutral", + "text": "Yes , I know . Kind of hard to concentrate , isn't it ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Absolutely . Who were you playing with ?", + "emotion": "neutral", + "text": "Absolutely . Who were you playing with ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Oh , just on my own . I just joined , so I don't really have any partners .", + "emotion": "neutral", + "text": "Oh , just on my own . I just joined , so I don't really have any partners .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Really ? Oh , well , in that case we should play together some time . What's your handicap ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I don't really have any partners ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? Oh , well , in that case we should play together some time . What's your handicap ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "16 . Yours ?", + "emotion": "neutral", + "text": "16 . Yours ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "No kidding ! I'm 16 , too . We should definitely play together some time . My name's Bob .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "We should definitely play together some time ." + ], + "type": [ + "no-context" + ], + "text": "No kidding ! I'm 16 , too . We should definitely play together some time . My name's Bob .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Jane . Nice to meet you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "We should definitely play together some time ." + ], + "type": [ + "inter-personal" + ], + "text": "Jane . Nice to meet you .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Me too . So , do you like the course ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Nice to meet you ." + ], + "type": [ + "inter-personal" + ], + "text": "Me too . So , do you like the course ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Yes , it's fine . However , I personally think the fairways between the greens are a bit too long , especially for such a hot climate . Don't they have carts ?", + "emotion": "neutral", + "text": "Yes , it's fine . However , I personally think the fairways between the greens are a bit too long , especially for such a hot climate . Don't they have carts ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Well , they used to , but they got rid of them because of environmental concerns .", + "emotion": "neutral", + "text": "Well , they used to , but they got rid of them because of environmental concerns .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Oh , that's good . I guess the caddies were pleased .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "they got rid of them because of environmental concerns ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , that's good . I guess the caddies were pleased .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Actually , in my opinion , the carts were better because you don't have to tip them .", + "emotion": "neutral", + "text": "Actually , in my opinion , the carts were better because you don't have to tip them .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Yes , but look at it this way , getting rid of the carts probably gives more work to local people , which is a good thing , right ?", + "emotion": "neutral", + "text": "Yes , but look at it this way , getting rid of the carts probably gives more work to local people , which is a good thing , right ?", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Possibly , but I still miss them ! What bothers me is that the heat makes the caddies ' life quite hard . One member's caddy fainted last week !", + "emotion": "neutral", + "text": "Possibly , but I still miss them ! What bothers me is that the heat makes the caddies ' life quite hard . One member's caddy fainted last week !", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "How awful , poor guy .", + "emotion": "neutral", + "text": "How awful , poor guy .", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "Right . Luckily it was on the eighteen hole , quite near the clubhouse , so he didn't have far to carry him .", + "emotion": "neutral", + "text": "Right . Luckily it was on the eighteen hole , quite near the clubhouse , so he didn't have far to carry him .", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "Oh , my God , you're kidding me ! He carried him back ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 18 + ], + "expanded emotion cause span": [ + "he didn't have far to carry him ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , my God , you're kidding me ! He carried him back ?", + "id": 19, + "source_sentences": [ + 17 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 20, + "speaker": "B", + "utterance": "Yup .", + "emotion": "neutral", + "text": "Yup .", + "id": 20 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4525.json b/reccon/sources/tr_4525.json new file mode 100644 index 0000000000000000000000000000000000000000..5ccc05510d8c0950abaa09974ec377ba972aaf94 --- /dev/null +++ b/reccon/sources/tr_4525.json @@ -0,0 +1,200 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Ashley , what a great dinner party !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "what a great dinner party !" + ], + "type": [ + "no-context" + ], + "text": "Ashley , what a great dinner party !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Thank you , Joe . What would you like to drink with your meal ? I can offer you wine , mango juice , or water .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "what a great dinner party !" + ], + "type": [ + "inter-personal" + ], + "text": "Thank you , Joe . What would you like to drink with your meal ? I can offer you wine , mango juice , or water .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Just water would be fine .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "what a great dinner party !", + "What would you like to drink with your meal ? I can offer you wine , mango juice , or water ." + ], + "type": [ + "hybrid" + ], + "text": "Just water would be fine .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Excellent choice . Can I dish you up some chicken ?", + "emotion": "happiness", + "explanation": "speaker and listener are happy about the great party", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "what a great dinner party !" + ], + "type": [ + "inter-personal" + ], + "text": "Excellent choice . Can I dish you up some chicken ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Yes , the chicken looks wonderful !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 4, + 5 + ], + "expanded emotion cause span": [ + "what a great dinner party !", + "Can I dish you up some chicken ?", + "the chicken looks wonderful !" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Yes , the chicken looks wonderful !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "How about some salad to go with your chicken ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1, + 4, + 5 + ], + "expanded emotion cause span": [ + "what a great dinner party !", + "Can I dish you up some chicken ?", + "the chicken looks wonderful !" + ], + "type": [ + "hybrid" + ], + "text": "How about some salad to go with your chicken ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Sure , I love salad !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 6, + 7 + ], + "expanded emotion cause span": [ + "what a great dinner party !", + "some salad to go with your chicken ?", + "I love salad !" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Sure , I love salad !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Would you like to have rice with your chicken ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "what a great dinner party !" + ], + "type": [ + "inter-personal" + ], + "text": "Would you like to have rice with your chicken ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yes , I think that rice will go perfectly with my chicken !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 9 + ], + "expanded emotion cause span": [ + "what a great dinner party !", + "rice will go perfectly with my chicken !" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Yes , I think that rice will go perfectly with my chicken !", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Good ! Julie , if you could pass this plate down to Joe , I think we are all set .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "what a great dinner party !" + ], + "type": [ + "inter-personal" + ], + "text": "Good ! Julie , if you could pass this plate down to Joe , I think we are all set .", + "id": 10, + "source_sentences": [ + 0 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4533.json b/reccon/sources/tr_4533.json new file mode 100644 index 0000000000000000000000000000000000000000..66d4c967b17a7e5e0e18ec273a349a105da04f5c --- /dev/null +++ b/reccon/sources/tr_4533.json @@ -0,0 +1,145 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What are you doing ?", + "emotion": "neutral", + "text": "What are you doing ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What am I doing ? What am I doing ? Don ' t you know what day it is ?", + "emotion": "neutral", + "text": "What am I doing ? What am I doing ? Don ' t you know what day it is ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Mumm . no .", + "emotion": "neutral", + "text": "Mumm . no .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It ' s only the day when the world ' s biggest sporting event is kicking off .", + "emotion": "neutral", + "text": "It ' s only the day when the world ' s biggest sporting event is kicking off .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "What ?", + "emotion": "neutral", + "text": "What ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "The World Cup ! The first match is today ! It ' s Mexico vs . South Africa ! It ' s going to be a really good match ! Both teams have a very strong offense and have skilled players . I think that South Africa", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "It ' s going to be a really good match !" + ], + "type": [ + "no-context" + ], + "text": "The World Cup ! The first match is today ! It ' s Mexico vs . South Africa ! It ' s going to be a really good match ! Both teams have a very strong offense and have skilled players . I think that South Africa", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I have no idea what you ' re talking about . The only sporting event we watch at home is the Super Bowl .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "It ' s going to be a really good match !", + "The only sporting event we watch at home is the Super Bowl ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I have no idea what you ' re talking about . The only sporting event we watch at home is the Super Bowl .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "This is bigger than the Super Bowl , man ! Teams from 32 countries compete against each other every four years and fight to win that trophy . They first start in a group stage with bigger groups , each g", + "emotion": "neutral", + "text": "This is bigger than the Super Bowl , man ! Teams from 32 countries compete against each other every four years and fight to win that trophy . They first start in a group stage with bigger groups , each g", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Sounds interesting , but soccer doesn ' t really appeal to me .", + "emotion": "neutral", + "text": "Sounds interesting , but soccer doesn ' t really appeal to me .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Are you kidding ? Over seven hundred million people watched the final match of the World Cup ! It ' s a very exciting and nerve wracking sport ! Each nation is cheering on their team , hoping they will bec", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "soccer doesn ' t really appeal to me ." + ], + "type": [ + "inter-personal" + ], + "text": "Are you kidding ? Over seven hundred million people watched the final match of the World Cup ! It ' s a very exciting and nerve wracking sport ! Each nation is cheering on their team , hoping they will bec", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "All I know about soccer is that you can ' t use your hands and that players are always falling down , trying to get a free kick or penalty kick . It seems like a sissy sport to me !", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "It ' s a very exciting and nerve wracking sport !", + "It seems like a sissy sport to me !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "All I know about soccer is that you can ' t use your hands and that players are always falling down , trying to get a free kick or penalty kick . It seems like a sissy sport to me !", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Whatever , I ' m going to go watch the opening match .", + "emotion": "neutral", + "text": "Whatever , I ' m going to go watch the opening match .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4544.json b/reccon/sources/tr_4544.json new file mode 100644 index 0000000000000000000000000000000000000000..ab8d299650ae0e0170ab128e3c557338e9d9b889 --- /dev/null +++ b/reccon/sources/tr_4544.json @@ -0,0 +1,111 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , Bill . I saw you yesterday with a pretty girl .", + "emotion": "neutral", + "text": "Hi , Bill . I saw you yesterday with a pretty girl .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , she is my favorite girl . I've decided to go steady with her .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "she is my favorite girl . I've decided to go steady with her ." + ], + "type": [ + "no-context" + ], + "text": "Yes , she is my favorite girl . I've decided to go steady with her .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Are you sure she is the right girl ?", + "emotion": "neutral", + "text": "Are you sure she is the right girl ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Sure . She is the ideal girl , the one I had dreamed of .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 4, + 4 + ], + "expanded emotion cause span": [ + "she is my favorite girl . I've decided to go steady with her .", + "She is the ideal girl ,", + "I had dreamed of ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Sure . She is the ideal girl , the one I had dreamed of .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "What type of girl is she ?", + "emotion": "neutral", + "text": "What type of girl is she ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "She is the mature , stable , feminine type . I hope one day I can marry her .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 4, + 4, + 6 + ], + "expanded emotion cause span": [ + "she is my favorite girl . I've decided to go steady with her .", + "She is the ideal girl ,", + "I had dreamed of .", + "She is the mature , stable , feminine type . I hope one day I can marry her ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "She is the mature , stable , feminine type . I hope one day I can marry her .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Oh , that's great . You're serious this time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I hope one day I can marry her ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , that's great . You're serious this time .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4558.json b/reccon/sources/tr_4558.json new file mode 100644 index 0000000000000000000000000000000000000000..c64573b33d7e51b77826a886a25c58df8e594bbc --- /dev/null +++ b/reccon/sources/tr_4558.json @@ -0,0 +1,211 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hoo , I'm getting tired , Jeanine , been a long day .", + "emotion": "neutral", + "text": "Hoo , I'm getting tired , Jeanine , been a long day .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'm not quitting yet . You know my favourite slogan , don't you ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "I'm not quitting yet . You know my favourite slogan , don't you ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yeah , I know . Shop till you drop .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I'm not quitting yet ." + ], + "type": [ + "inter-personal" + ], + "text": "Yeah , I know . Shop till you drop .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Right !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I'm not quitting yet ." + ], + "type": [ + "self-contagion" + ], + "text": "Right !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I'm getting a little short on cash . Let's just window shop a little .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Shop till you drop ." + ], + "type": [ + "self-contagion" + ], + "text": "I'm getting a little short on cash . Let's just window shop a little .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Ok .", + "emotion": "neutral", + "text": "Ok .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Hey , Jeanine , get a load of that . It's beautiful .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "get a load of that . It's beautiful ." + ], + "type": [ + "no-context" + ], + "text": "Hey , Jeanine , get a load of that . It's beautiful .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Ahahah , and I thought you were tired .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "get a load of that . It's beautiful ." + ], + "type": [ + "inter-personal" + ], + "text": "Ahahah , and I thought you were tired .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "You know .. I have a weakness for long dresses .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "get a load of that . It's beautiful ." + ], + "type": [ + "self-contagion" + ], + "text": "You know .. I have a weakness for long dresses .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "It sure looks special , looks expensive too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "It sure looks special , looks expensive too ." + ], + "type": [ + "no-context" + ], + "text": "It sure looks special , looks expensive too .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Sure does . Hey , can I sponge a little cash of you ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "It sure looks special , looks expensive too ." + ], + "type": [ + "inter-personal" + ], + "text": "Sure does . Hey , can I sponge a little cash of you ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Don't worry , Mary , I've got you covered .", + "emotion": "happiness", + "explanation": "Helping happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "I've got you covered ." + ], + "type": [ + "no-context" + ], + "text": "Don't worry , Mary , I've got you covered .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Thanks , Jeanine , you are a real pal . Let's go in .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "I've got you covered ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks , Jeanine , you are a real pal . Let's go in .", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4576.json b/reccon/sources/tr_4576.json new file mode 100644 index 0000000000000000000000000000000000000000..1c79d817ab4ba5e242a67619aa2d9640b6f460e2 --- /dev/null +++ b/reccon/sources/tr_4576.json @@ -0,0 +1,231 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "How are you doing ?", + "emotion": "neutral", + "text": "How are you doing ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'm doing great .", + "emotion": "neutral", + "text": "I'm doing great .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What movies have you seen lately ?", + "emotion": "neutral", + "text": "What movies have you seen lately ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I saw Forrest Gump the other day .", + "emotion": "neutral", + "text": "I saw Forrest Gump the other day .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "What type of movie is that ?", + "emotion": "neutral", + "text": "What type of movie is that ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "The movie type is drama .", + "emotion": "neutral", + "text": "The movie type is drama .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I can't believe you are watching movies . The weather is great . You should be outside .", + "emotion": "neutral", + "text": "I can't believe you are watching movies . The weather is great . You should be outside .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I hate the hot weather . I'd rather stay indoors with the air conditioner .", + "emotion": "neutral", + "text": "I hate the hot weather . I'd rather stay indoors with the air conditioner .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "What else do you like to do besides watching movies ?", + "emotion": "neutral", + "text": "What else do you like to do besides watching movies ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I like to play computer games , read books , go shopping , and play pool .", + "emotion": "neutral", + "text": "I like to play computer games , read books , go shopping , and play pool .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Out of those what is your favorite ?", + "emotion": "neutral", + "text": "Out of those what is your favorite ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "My favorite is to play computer games .", + "emotion": "neutral", + "text": "My favorite is to play computer games .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "What is your favorite computer game ?", + "emotion": "neutral", + "text": "What is your favorite computer game ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "My favorite is Diablo . It used to be Star Craft , but it is getting a little old .", + "emotion": "neutral", + "text": "My favorite is Diablo . It used to be Star Craft , but it is getting a little old .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "If you like to play so much , when do you ever exercise ?", + "emotion": "neutral", + "text": "If you like to play so much , when do you ever exercise ?", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Although I hate to exercise , I go jogging at least twice a week .", + "emotion": "neutral", + "text": "Although I hate to exercise , I go jogging at least twice a week .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "That's pretty good . By the way , what are you doing next Saturday ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 16, + 17 + ], + "expanded emotion cause span": [ + "I go jogging at least twice a week .", + "That's pretty good ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's pretty good . By the way , what are you doing next Saturday ?", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "I am going to go to the bookstore .", + "emotion": "neutral", + "text": "I am going to go to the bookstore .", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "I am having a party Saturday night at my house . If you have time , you should come .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 19 + ], + "expanded emotion cause span": [ + "I am having a party Saturday night at my house ." + ], + "type": [ + "no-context" + ], + "text": "I am having a party Saturday night at my house . If you have time , you should come .", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "That sounds like fun .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 19 + ], + "expanded emotion cause span": [ + "I am having a party Saturday night at my house . If you have time , you should come ." + ], + "type": [ + "inter-personal" + ], + "text": "That sounds like fun .", + "id": 20 + }, + { + "turn": 21, + "speaker": "A", + "utterance": "Great . I'll see you on Saturday .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 20 + ], + "expanded emotion cause span": [ + "That sounds like fun ." + ], + "type": [ + "inter-personal" + ], + "text": "Great . I'll see you on Saturday .", + "id": 21 + }, + { + "turn": 22, + "speaker": "B", + "utterance": "Ok . See you later .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 21 + ], + "expanded emotion cause span": [ + "I'll see you on Saturday ." + ], + "type": [ + "inter-personal" + ], + "text": "Ok . See you later .", + "id": 22, + "source_sentences": [ + 20 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4589.json b/reccon/sources/tr_4589.json new file mode 100644 index 0000000000000000000000000000000000000000..070b11b33611e16e00369b6f2ce66551b88db65e --- /dev/null +++ b/reccon/sources/tr_4589.json @@ -0,0 +1,353 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Do you want to go out for dinner tonight ?", + "emotion": "happiness", + "explanation": "A might be generally happy out of courtesy or genuinely happy about dinner. The actual cause is latent.", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Do you want to go out for dinner tonight ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Sure . Have you got anywhere in mind ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Do you want to go out for dinner tonight ?" + ], + "type": [ + "inter-personal" + ], + "text": "Sure . Have you got anywhere in mind ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I'm starving , so maybe we could go somewhere with large portions .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 3 + ], + "expanded emotion cause span": [ + "b", + "go somewhere with large portions ." + ], + "type": [ + "latent", + "no-context" + ], + "text": "I'm starving , so maybe we could go somewhere with large portions .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "That Italian restaurant in the city centre always has large portions . Do you want to go there ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Do you want to go out for dinner tonight ?" + ], + "type": [ + "inter-personal" + ], + "text": "That Italian restaurant in the city centre always has large portions . Do you want to go there ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I'm not really in the mood for Italian , actually . I was thinking of something a bit spicy .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + "b", + 3 + ], + "expanded emotion cause span": [ + "b", + "go somewhere with large portions ." + ], + "type": [ + "latent", + "self-contagion" + ], + "text": "I'm not really in the mood for Italian , actually . I was thinking of something a bit spicy .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "If you want spicy food , then I'd recommend going to a Thai , Indian or Chinese restaurant . How about that Chinese buffet on Cowley Road ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Do you want to go out for dinner tonight ?" + ], + "type": [ + "inter-personal" + ], + "text": "If you want spicy food , then I'd recommend going to a Thai , Indian or Chinese restaurant . How about that Chinese buffet on Cowley Road ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I really like that restaurant ; you get a lot for your money there . But , they've westernized their food , so it's not actually that spicy .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 3, + 7 + ], + "expanded emotion cause span": [ + "b", + "go somewhere with large portions .", + "I really like that restaurant ; you get a lot for your money there ." + ], + "type": [ + "latent", + "no-context", + "self-contagion" + ], + "text": "I really like that restaurant ; you get a lot for your money there . But , they've westernized their food , so it's not actually that spicy .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "You're right . Most of their dishes have sweet sauces . We could try that Indian restaurant just down the road from us .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Do you want to go out for dinner tonight ?" + ], + "type": [ + "inter-personal" + ], + "text": "You're right . Most of their dishes have sweet sauces . We could try that Indian restaurant just down the road from us .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "The Taj ? They're a bit expensive , but they do serve large portions of very hot food .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 3, + 9 + ], + "expanded emotion cause span": [ + "b", + "go somewhere with large portions .", + "they do serve large portions of very hot food ." + ], + "type": [ + "latent", + "no-context", + "self-contagion" + ], + "text": "The Taj ? They're a bit expensive , but they do serve large portions of very hot food .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "The Taj it is then .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 9 + ], + "expanded emotion cause span": [ + "Do you want to go out for dinner tonight ?", + "they do serve large portions of very hot food ." + ], + "type": [ + "inter-personal" + ], + "text": "The Taj it is then .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Shall we bring our own bottle of wine to save some money ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + "b", + 3, + 9 + ], + "expanded emotion cause span": [ + "b", + "go somewhere with large portions .", + "they do serve large portions of very hot food ." + ], + "type": [ + "latent", + "self-contagion" + ], + "text": "Shall we bring our own bottle of wine to save some money ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "They'll still charge us a corkage fee .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1, + 9 + ], + "expanded emotion cause span": [ + "Do you want to go out for dinner tonight ?", + "they do serve large portions of very hot food ." + ], + "type": [ + "inter-personal" + ], + "text": "They'll still charge us a corkage fee .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "That's right . It'll probably work out to be about the same then anyway .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + "b", + 3, + 9 + ], + "expanded emotion cause span": [ + "b", + "go somewhere with large portions .", + "they do serve large portions of very hot food ." + ], + "type": [ + "latent", + "self-contagion" + ], + "text": "That's right . It'll probably work out to be about the same then anyway .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Don't worry about money . I'll treat you tonight .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 9, + 14 + ], + "expanded emotion cause span": [ + "Do you want to go out for dinner tonight ?", + "they do serve large portions of very hot food .", + "I'll treat you" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Don't worry about money . I'll treat you tonight .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Are you sure ? We could go Dutch .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "I'll treat you tonight ." + ], + "type": [ + "inter-personal" + ], + "text": "Are you sure ? We could go Dutch .", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 16, + "speaker": "B", + "utterance": "No , I'll pay . It's my turn anyway . You paid last time .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1, + 9, + 14 + ], + "expanded emotion cause span": [ + "Do you want to go out for dinner tonight ?", + "they do serve large portions of very hot food .", + "I'll treat you" + ], + "type": [ + "hybrid" + ], + "text": "No , I'll pay . It's my turn anyway . You paid last time .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "I won't argue with that ! Let's go !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 3, + 9, + 14 + ], + "expanded emotion cause span": [ + "b", + "go somewhere with large portions .", + "they do serve large portions of very hot food .", + "Don't worry about money . I'll treat you tonight ." + ], + "type": [ + "latent", + "hybrid" + ], + "text": "I won't argue with that ! Let's go !", + "id": 17 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4614.json b/reccon/sources/tr_4614.json new file mode 100644 index 0000000000000000000000000000000000000000..ad1ca2a1edd0bd2a6de15e05a32d8a2890e43d79 --- /dev/null +++ b/reccon/sources/tr_4614.json @@ -0,0 +1,111 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I really should be on my way .", + "emotion": "neutral", + "text": "I really should be on my way .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh , not yet . At least have one for the road .", + "emotion": "neutral", + "text": "Oh , not yet . At least have one for the road .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "No , thanks all the same .", + "emotion": "neutral", + "text": "No , thanks all the same .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Well , I am sorry you have to leave so early .", + "emotion": "neutral", + "text": "Well , I am sorry you have to leave so early .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Thank you very much . I really had a good time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I really had a good time ." + ], + "type": [ + "no-context" + ], + "text": "Thank you very much . I really had a good time .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Well , thank you for coming .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I really had a good time ." + ], + "type": [ + "inter-personal" + ], + "text": "Well , thank you for coming .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "So see you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "I really had a good time .", + "thank you for coming ." + ], + "type": [ + "hybrid" + ], + "text": "So see you .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Bye .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "I really had a good time .", + "thank you for coming ." + ], + "type": [ + "hybrid" + ], + "text": "Bye .", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4624.json b/reccon/sources/tr_4624.json new file mode 100644 index 0000000000000000000000000000000000000000..fe8e52d4130614d870f239c4528aa8bf2c7c84a5 --- /dev/null +++ b/reccon/sources/tr_4624.json @@ -0,0 +1,130 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I wish I knew who had moved our flower pots .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "who had moved our flower pots ." + ], + "type": [ + "no-context" + ], + "text": "I wish I knew who had moved our flower pots .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It was me . I am so sorry .", + "emotion": "neutral", + "text": "It was me . I am so sorry .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What did you think you were doing ?", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1, + 1, + 2 + ], + "expanded emotion cause span": [ + "who had moved our flower pots .", + "who had moved our flower pots .", + "It was me ." + ], + "type": [ + "hybrid" + ], + "text": "What did you think you were doing ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I had to move it , so that I can get my bike through .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "What did you think you were doing ?" + ], + "type": [ + "inter-personal" + ], + "text": "I had to move it , so that I can get my bike through .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "How dare you be so inconsiderate ? That's wrong .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1, + 1, + 2, + 5 + ], + "expanded emotion cause span": [ + "who had moved our flower pots .", + "who had moved our flower pots .", + "It was me .", + "How dare you be so inconsiderate ?" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "How dare you be so inconsiderate ? That's wrong .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I am awfully sorry . I didn't think you would mind so much .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3, + 6 + ], + "expanded emotion cause span": [ + "What did you think you were doing ?", + "I am awfully sorry . I didn't think you would mind so much ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I am awfully sorry . I didn't think you would mind so much .", + "id": 6, + "source_sentences": [ + 2 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Never do that again .", + "emotion": "neutral", + "text": "Never do that again .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I promise .", + "emotion": "neutral", + "text": "I promise .", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4627.json b/reccon/sources/tr_4627.json new file mode 100644 index 0000000000000000000000000000000000000000..e0d5051e008278009a522ecd030e71b1e4b8a513 --- /dev/null +++ b/reccon/sources/tr_4627.json @@ -0,0 +1,143 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi ! Ed , what's up ?", + "emotion": "neutral", + "text": "Hi ! Ed , what's up ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Nothing .", + "emotion": "neutral", + "text": "Nothing .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Doesn't look like it to me .", + "emotion": "neutral", + "text": "Doesn't look like it to me .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Just get out of my face !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "Nothing .", + "Doesn't look like it to me ." + ], + "type": [ + "hybrid" + ], + "text": "Just get out of my face !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Woo , easy .", + "emotion": "neutral", + "text": "Woo , easy .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Leave me alone !", + "emotion": "anger", + "flag": "F", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "Nothing .", + "Doesn't look like it to me ." + ], + "type": [ + "hybrid" + ], + "text": "Leave me alone !", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "What are you so ticked off about ?", + "emotion": "neutral", + "text": "What are you so ticked off about ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I don't want to talk about it .", + "emotion": "neutral", + "text": "I don't want to talk about it .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Maybe I can help .", + "emotion": "neutral", + "text": "Maybe I can help .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I blew the finally exam .", + "emotion": "neutral", + "text": "I blew the finally exam .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "You've got to be joking .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "I blew the finally exam ." + ], + "type": [ + "inter-personal" + ], + "text": "You've got to be joking .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "No , I'm not .", + "emotion": "neutral", + "text": "No , I'm not .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Well , don't get bend on a ship about it .", + "emotion": "neutral", + "text": "Well , don't get bend on a ship about it .", + "id": 13 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4633.json b/reccon/sources/tr_4633.json new file mode 100644 index 0000000000000000000000000000000000000000..050a45e28ce2e70e25d5c3e60df30a5b07b4a0bd --- /dev/null +++ b/reccon/sources/tr_4633.json @@ -0,0 +1,120 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "You ' re going to set up your own law office , aren ' t you ?", + "emotion": "neutral", + "text": "You ' re going to set up your own law office , aren ' t you ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes . After so many years of hard work , I ' d rather I had an office of my own .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I ' d rather I had an office of my own ." + ], + "type": [ + "no-context" + ], + "text": "Yes . After so many years of hard work , I ' d rather I had an office of my own .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "If you need help , don ' t hesitate to ask me .", + "emotion": "happiness", + "explanation": "A is happy to offer help", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "If you need help , don ' t hesitate to ask me ." + ], + "type": [ + "no-context" + ], + "text": "If you need help , don ' t hesitate to ask me .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I ' ll be very glad if you would help .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "If you need help , don ' t hesitate to ask me ." + ], + "type": [ + "inter-personal" + ], + "text": "I ' ll be very glad if you would help .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I ' d like to wish you every success in your new venture .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I ' ll be very glad if you would help ." + ], + "type": [ + "inter-personal" + ], + "text": "I ' d like to wish you every success in your new venture .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Thank you . I wish I would .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I ' d like to wish you every success in your new venture ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . I wish I would .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Good luck to you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "I ' ll be very glad if you would help .", + "I ' d like to wish you every success in your new venture ." + ], + "type": [ + "hybrid" + ], + "text": "Good luck to you .", + "id": 7 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4647.json b/reccon/sources/tr_4647.json new file mode 100644 index 0000000000000000000000000000000000000000..f49838700e31a7b3f6878655ffe1c5b013ffaea0 --- /dev/null +++ b/reccon/sources/tr_4647.json @@ -0,0 +1,181 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Your garden is looking beautiful this summer . The flowers are really colorful .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Your garden is looking beautiful this summer . The flowers are really colorful ." + ], + "type": [ + "no-context" + ], + "text": "Your garden is looking beautiful this summer . The flowers are really colorful .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Thank you . I have roses , tulips , and daffodils . Do you like the rockery with the smaller flowers ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Your garden is looking beautiful this summer . The flowers are really colorful ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . I have roses , tulips , and daffodils . Do you like the rockery with the smaller flowers ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yes , I do . Those are violets , aren ' t they ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "Your garden is looking beautiful this summer . The flowers are really colorful .", + "the rockery with the smaller flowers ?" + ], + "type": [ + "hybrid" + ], + "text": "Yes , I do . Those are violets , aren ' t they ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes , they are . This afternoon , I ' m going to prune the hedge .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Your garden is looking beautiful this summer . The flowers are really colorful ." + ], + "type": [ + "inter-personal" + ], + "text": "Yes , they are . This afternoon , I ' m going to prune the hedge .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "The lower branches on that tree are hanging very low . Would you like me to cut them off for you ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Your garden is looking beautiful this summer . The flowers are really colorful ." + ], + "type": [ + "self-contagion" + ], + "text": "The lower branches on that tree are hanging very low . Would you like me to cut them off for you ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Thank you ! That would be very kind of you . I have a saw in the garden shed .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 5 + ], + "expanded emotion cause span": [ + "Your garden is looking beautiful this summer . The flowers are really colorful .", + "Would you like me to cut them off for you ?" + ], + "type": [ + "inter-personal" + ], + "text": "Thank you ! That would be very kind of you . I have a saw in the garden shed .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "When the lower branches are removed , you ' ll be able to sit under the tree .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 7 + ], + "expanded emotion cause span": [ + "Your garden is looking beautiful this summer . The flowers are really colorful .", + "When the lower branches are removed , you ' ll be able to sit under the tree ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "When the lower branches are removed , you ' ll be able to sit under the tree .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Tomorrow , I ' ll cut the grass . Then the garden will lock perfect .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 7, + 8 + ], + "expanded emotion cause span": [ + "Your garden is looking beautiful this summer . The flowers are really colorful .", + "When the lower branches are removed , you ' ll be able to sit under the tree .", + "Then the garden will lock perfect ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Tomorrow , I ' ll cut the grass . Then the garden will lock perfect .", + "id": 8, + "source_sentences": [ + 0, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Just make sure children don ' t play in the flower beds and destroy the flowers .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1, + 7, + 8 + ], + "expanded emotion cause span": [ + "Your garden is looking beautiful this summer . The flowers are really colorful .", + "When the lower branches are removed , you ' ll be able to sit under the tree .", + "Then the garden will lock perfect ." + ], + "type": [ + "hybrid" + ], + "text": "Just make sure children don ' t play in the flower beds and destroy the flowers .", + "id": 9 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4659.json b/reccon/sources/tr_4659.json new file mode 100644 index 0000000000000000000000000000000000000000..92e02b129afaa0f360dfbd13f8fdfb157f520c36 --- /dev/null +++ b/reccon/sources/tr_4659.json @@ -0,0 +1,152 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Good evening . Welcome to our program .", + "emotion": "happiness", + "explanation": "Person A is happy because he got a new participant in their program", + "expanded emotion cause evidence": [ + "b", + 1 + ], + "expanded emotion cause span": [ + "b", + "Welcome to our program ." + ], + "type": [ + "latent", + "no-context" + ], + "text": "Good evening . Welcome to our program .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Thank you . Good evening , Mr . Dean .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Welcome to our program ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . Good evening , Mr . Dean .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Would you tell us your name , please ?", + "emotion": "neutral", + "text": "Would you tell us your name , please ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I'm Helen Baker .", + "emotion": "neutral", + "text": "I'm Helen Baker .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Glad to meet you , Ms . Baker .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 1, + 4 + ], + "expanded emotion cause span": [ + "b", + "Welcome to our program .", + "I'm Helen Baker ." + ], + "type": [ + "latent", + "hybrid" + ], + "text": "Glad to meet you , Ms . Baker .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Glad to meet you , too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Glad to meet you , Ms . Baker ." + ], + "type": [ + "inter-personal" + ], + "text": "Glad to meet you , too .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Where are you from , Ms . Baker ?", + "emotion": "neutral", + "text": "Where are you from , Ms . Baker ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I'm from New Zealand .", + "emotion": "neutral", + "text": "I'm from New Zealand .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "What do you do for a living ?", + "emotion": "neutral", + "text": "What do you do for a living ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I'm a teacher .", + "emotion": "neutral", + "text": "I'm a teacher .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Thank you for coming , Ms . baker .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 1 + ], + "expanded emotion cause span": [ + "b", + "Welcome to our program ." + ], + "type": [ + "latent", + "self-contagion" + ], + "text": "Thank you for coming , Ms . baker .", + "id": 11 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4689.json b/reccon/sources/tr_4689.json new file mode 100644 index 0000000000000000000000000000000000000000..ef87462cffc0b9dcf21dc9709529ae071d1d7c1a --- /dev/null +++ b/reccon/sources/tr_4689.json @@ -0,0 +1,151 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Good morning , Mary !", + "emotion": "happiness", + "explanation": "A is happy to greet", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Good morning ," + ], + "type": [ + "no-context" + ], + "text": "Good morning , Mary !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Good morning , John !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Good morning , Mary !" + ], + "type": [ + "inter-personal" + ], + "text": "Good morning , John !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I want to have a few friends over for a dinner party to celebrate my birthday . Would you be able to come the next weekend on Saturday ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I want to have a few friends over for a dinner party to celebrate my birthday ." + ], + "type": [ + "no-context" + ], + "text": "I want to have a few friends over for a dinner party to celebrate my birthday . Would you be able to come the next weekend on Saturday ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I'd be delighted to , John . Saturday did you say ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Would you be able to come the next weekend on Saturday ?" + ], + "type": [ + "inter-personal" + ], + "text": "I'd be delighted to , John . Saturday did you say ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Yes , if that's all right for you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "I want to have a few friends over for a dinner party to celebrate my birthday .", + "I'd be delighted to ," + ], + "type": [ + "hybrid" + ], + "text": "Yes , if that's all right for you .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I'm pretty sure I'll be all right . In fact , I'd be delighted to come over and celebrate your birthday with you . What time are you planning to start ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I'd be delighted to come over and celebrate your birthday with you ." + ], + "type": [ + "no-context" + ], + "text": "I'm pretty sure I'll be all right . In fact , I'd be delighted to come over and celebrate your birthday with you . What time are you planning to start ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Oh , good . If you could come around six thirty or seven o'clock , that would give us some time to chat a whit over a glass of wine before dinner .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I'd be delighted to come over and celebrate your birthday with you .", + "some time to chat a whit over a glass of wine" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , good . If you could come around six thirty or seven o'clock , that would give us some time to chat a whit over a glass of wine before dinner .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That sounds fine . I'll be there around seven .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I'd be delighted to come over and celebrate your birthday with you .", + "some time to chat a whit over a glass of wine" + ], + "type": [ + "hybrid" + ], + "text": "That sounds fine . I'll be there around seven .", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4693.json b/reccon/sources/tr_4693.json new file mode 100644 index 0000000000000000000000000000000000000000..558240b3d062589594191b61c3e3cf9b790622db --- /dev/null +++ b/reccon/sources/tr_4693.json @@ -0,0 +1,158 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "It's a lovely day , isn't it ?", + "emotion": "neutral", + "text": "It's a lovely day , isn't it ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yeah , and most excitingly , I met the girl living under me today . She's really nice .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "most excitingly , I met the girl living under me today . She's really nice ." + ], + "type": [ + "no-context" + ], + "text": "Yeah , and most excitingly , I met the girl living under me today . She's really nice .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Is she American ?", + "emotion": "neutral", + "text": "Is she American ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yeah , and most importantly , she's single ! Man , I could tell from the moment I saw her , she's the girl of my dreams !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "she's single ! Man , I could tell from the moment I saw her , she's the girl of my dreams !" + ], + "type": [ + "no-context" + ], + "text": "Yeah , and most importantly , she's single ! Man , I could tell from the moment I saw her , she's the girl of my dreams !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "So I take it you two are hitting it off ? I know it's very convenient to be in a relationship with your neighbor , but what if you break up ?", + "emotion": "neutral", + "text": "So I take it you two are hitting it off ? I know it's very convenient to be in a relationship with your neighbor , but what if you break up ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I don't know . I am not really worried about that . I don't wanna lose before even starting . Besides I think the other two American guys have also fallen for her .", + "emotion": "neutral", + "text": "I don't know . I am not really worried about that . I don't wanna lose before even starting . Besides I think the other two American guys have also fallen for her .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Sounds like you've got some competition . You made a move already ?", + "emotion": "neutral", + "text": "Sounds like you've got some competition . You made a move already ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Not yet . But I am thinking of inviting her to dinner sometime . I know some good restaurants nearby .", + "emotion": "neutral", + "text": "Not yet . But I am thinking of inviting her to dinner sometime . I know some good restaurants nearby .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "That's nice . Having been here a little while surely gives you the advantage , eh ?", + "emotion": "neutral", + "text": "That's nice . Having been here a little while surely gives you the advantage , eh ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "You bet . Now that you mentioned it , I think I'll call her now and see if she is available tonight .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 10 + ], + "expanded emotion cause span": [ + "she's single ! Man , I could tell from the moment I saw her , she's the girl of my dreams !", + "I'll call her now and see if she is available tonight ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "You bet . Now that you mentioned it , I think I'll call her now and see if she is available tonight .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Good luck !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 10 + ], + "expanded emotion cause span": [ + "she's single ! Man , I could tell from the moment I saw her , she's the girl of my dreams !", + "I'll call her now and see if she is available tonight ." + ], + "type": [ + "inter-personal" + ], + "text": "Good luck !", + "id": 11, + "source_sentences": [ + 3, + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Thanks !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 10, + 11 + ], + "expanded emotion cause span": [ + "she's single ! Man , I could tell from the moment I saw her , she's the girl of my dreams !", + "I'll call her now and see if she is available tonight .", + "Good luck !" + ], + "type": [ + "hybrid" + ], + "text": "Thanks !", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4696.json b/reccon/sources/tr_4696.json new file mode 100644 index 0000000000000000000000000000000000000000..ced915f66f387793a2f72ae5003496fdc3647e0b --- /dev/null +++ b/reccon/sources/tr_4696.json @@ -0,0 +1,122 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Oh !", + "emotion": "neutral", + "text": "Oh !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What fools we were !", + "emotion": "sadness", + "explanation": "B is sad over some incident that is not mentioned.", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "What fools we were !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "To think of it ! All my old silver ! It meant so much to me .", + "emotion": "neutral", + "text": "To think of it ! All my old silver ! It meant so much to me .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "And my new car . To think that he simply drove off with everything in my car . That's what hurts me most .", + "emotion": "neutral", + "text": "And my new car . To think that he simply drove off with everything in my car . That's what hurts me most .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "What's so terrible too , is the fools we've made of ourselves .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + "b", + 5 + ], + "expanded emotion cause span": [ + "b", + "What's so terrible too , is the fools we've made of ourselves ." + ], + "type": [ + "latent", + "no-context" + ], + "text": "What's so terrible too , is the fools we've made of ourselves .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I hardly dare call the police . They'll just laugh at us .", + "emotion": "neutral", + "text": "I hardly dare call the police . They'll just laugh at us .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I'll never get over it . Oh , Harry , it was all so unnecessary . That man ! ! How could he do this to us after we'd put him up ?", + "emotion": "anger", + "expanded emotion cause evidence": [ + 4, + 7, + 7 + ], + "expanded emotion cause span": [ + "he simply drove off with everything in my car . That's what hurts me most .", + "it was all so unnecessary .", + "How could he do this to us" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'll never get over it . Oh , Harry , it was all so unnecessary . That man ! ! How could he do this to us after we'd put him up ?", + "id": 7, + "source_sentences": [ + 3, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "And his story didn't even hold together . I feel such an idiot .", + "emotion": "anger", + "flag": "F", + "expanded emotion cause evidence": [ + 4, + 7, + 7 + ], + "expanded emotion cause span": [ + "he simply drove off with everything in my car . That's what hurts me most .", + "it was all so unnecessary .", + "How could he do this to us" + ], + "type": [ + "hybrid" + ], + "text": "And his story didn't even hold together . I feel such an idiot .", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4698.json b/reccon/sources/tr_4698.json new file mode 100644 index 0000000000000000000000000000000000000000..b026e22602be883bbb56ba52ecaf78cc0ffb3f01 --- /dev/null +++ b/reccon/sources/tr_4698.json @@ -0,0 +1,152 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Do you know how to go to the Fragrant Hills in Beijing ? I heard that they are very famous in China .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Fragrant Hills in Beijing ? I heard that they are very famous in China ." + ], + "type": [ + "no-context" + ], + "text": "Do you know how to go to the Fragrant Hills in Beijing ? I heard that they are very famous in China .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes . Especially in autumn , the red leaves of the maple trees make the whole mountain red .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Yes . Especially in autumn , the red leaves of the maple trees make the whole mountain red ." + ], + "type": [ + "no-context" + ], + "text": "Yes . Especially in autumn , the red leaves of the maple trees make the whole mountain red .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "That must be very beautiful .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "Yes . Especially in autumn , the red leaves of the maple trees make the whole mountain red .", + "That must be very beautiful ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That must be very beautiful .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes , it can make people feel as if they were in the land of fairies .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Yes , it can make people feel as if they were in the land of fairies ." + ], + "type": [ + "no-context" + ], + "text": "Yes , it can make people feel as if they were in the land of fairies .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Really ? Have you ever been there ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Yes , it can make people feel as if they were in the land of fairies ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? Have you ever been there ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "A couple of times .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "A couple of times ." + ], + "type": [ + "no-context" + ], + "text": "A couple of times .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Can you go there with me ? I'd like someone who is familiar with that area to go with me .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "A couple of times .", + "Can you go there with me ? I'd like someone who is familiar with that area to go with me ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Can you go there with me ? I'd like someone who is familiar with that area to go with me .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Sure . I'd be very glad to be your tour guide .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "Can you go there with me ? I'd like someone who is familiar with that area to go with me .", + "I'd be very glad to be your tour guide ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Sure . I'd be very glad to be your tour guide .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4722.json b/reccon/sources/tr_4722.json new file mode 100644 index 0000000000000000000000000000000000000000..6d8f7efb04a80af305fd1591fdbc385342959ebd --- /dev/null +++ b/reccon/sources/tr_4722.json @@ -0,0 +1,330 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What a nice dress , Jean . You look marvelous !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "What a nice dress , Jean . You look marvelous !" + ], + "type": [ + "no-context" + ], + "text": "What a nice dress , Jean . You look marvelous !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "You , too . Where did you get your new hat ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "What a nice dress , Jean . You look marvelous !", + "You , too . Where did you get your new hat ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You , too . Where did you get your new hat ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "From the Crown's . Oh , what lovely earrings you have ! Are they diamond ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "You , too . Where did you get your new hat ?", + "Oh , what lovely earrings you have ! Are they diamond ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "From the Crown's . Oh , what lovely earrings you have ! Are they diamond ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes . It's a birthday present from my husband !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "Oh , what lovely earrings you have ! Are they diamond ?", + "Yes . It's a birthday present from my husband !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes . It's a birthday present from my husband !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Well , you are lucky to have such a considerate husband . Mine hasn't brought me a single rose since we married .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "you are lucky to have such a considerate husband ." + ], + "type": [ + "no-context" + ], + "text": "Well , you are lucky to have such a considerate husband . Mine hasn't brought me a single rose since we married .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "He'll come out with surprises . Just wait and see . Look at that woman , with the white chiffon !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "you are lucky to have such a considerate husband .", + "Look at that woman , with the white chiffon !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "He'll come out with surprises . Just wait and see . Look at that woman , with the white chiffon !", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "She's chic , isn't she ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "She's chic" + ], + "type": [ + "no-context" + ], + "text": "She's chic , isn't she ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yes . I like the dress . It must be the latest fashion . Look , the hem has lowered , and the waist narrowed .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Yes . I like the dress . It must be the latest fashion . Look , the hem has lowered , and the waist narrowed ." + ], + "type": [ + "no-context" + ], + "text": "Yes . I like the dress . It must be the latest fashion . Look , the hem has lowered , and the waist narrowed .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "It makes me feel rather shabby . That woman has a good taste in dressing , I would say .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "That woman has a good taste in dressing" + ], + "type": [ + "no-context" + ], + "text": "It makes me feel rather shabby . That woman has a good taste in dressing , I would say .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Yes . She dressed with an individual flair . I rather envy her .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Yes . She dressed with an individual flair ." + ], + "type": [ + "no-context" + ], + "text": "Yes . She dressed with an individual flair . I rather envy her .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Most women follow fashion like sheep . They don't know any better than imitate .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "Most women follow fashion like sheep . They don't know any better than imitate ." + ], + "type": [ + "no-context" + ], + "text": "Most women follow fashion like sheep . They don't know any better than imitate .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I quite agree with you . See the woman there ? I dare say she hasn't got any eyes . How could she match the mauve gown with the green handbag ? And all that jewelry !", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "I dare say she hasn't got any eyes . How could she match the mauve gown with the green handbag ? And all that jewelry !" + ], + "type": [ + "no-context" + ], + "text": "I quite agree with you . See the woman there ? I dare say she hasn't got any eyes . How could she match the mauve gown with the green handbag ? And all that jewelry !", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "The gown is quite expensive , believe me .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "How could she match the mauve gown with the green handbag" + ], + "type": [ + "inter-personal" + ], + "text": "The gown is quite expensive , believe me .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "So what ? It only makes her look cheap and vulgar .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 12, + 13, + 14 + ], + "expanded emotion cause span": [ + "I dare say she hasn't got any eyes . How could she match the mauve gown with the green handbag ? And all that jewelry !", + "The gown is quite expensive", + "It only makes her look cheap and vulgar ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "So what ? It only makes her look cheap and vulgar .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "You know those upstarts . They're all show-offs ! I think I'd better have a diet ; otherwise I'd look like a ballon soon .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "They're all show-offs ! I think I'd better have a diet ; otherwise I'd look like a ballon soon ." + ], + "type": [ + "no-context" + ], + "text": "You know those upstarts . They're all show-offs ! I think I'd better have a diet ; otherwise I'd look like a ballon soon .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "You're quite slim . In fact , if you were one of those starlets , the movie company would say you have a fabulous figure .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 16 + ], + "expanded emotion cause span": [ + "You're quite slim . In fact , if you were one of those starlets , the movie company would say you have a fabulous figure ." + ], + "type": [ + "no-context" + ], + "text": "You're quite slim . In fact , if you were one of those starlets , the movie company would say you have a fabulous figure .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "Thanks . I'm flattered .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 16 + ], + "expanded emotion cause span": [ + "You're quite slim . In fact , if you were one of those starlets , the movie company would say you have a fabulous figure ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks . I'm flattered .", + "id": 17, + "source_sentences": [ + 15 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 18, + "speaker": "B", + "utterance": "Oh , my shoes pinch me . Let's find a seat and sit a while .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 18 + ], + "expanded emotion cause span": [ + "my shoes pinch me ." + ], + "type": [ + "no-context" + ], + "text": "Oh , my shoes pinch me . Let's find a seat and sit a while .", + "id": 18 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_475.json b/reccon/sources/tr_475.json new file mode 100644 index 0000000000000000000000000000000000000000..1a3419d6fd1a309c24c638bdb93290eedff25665 --- /dev/null +++ b/reccon/sources/tr_475.json @@ -0,0 +1,116 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Let's get together this weekend , is that all right ?", + "emotion": "neutral", + "text": "Let's get together this weekend , is that all right ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Sounds good , when ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Let's get together this weekend" + ], + "type": [ + "inter-personal" + ], + "text": "Sounds good , when ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "When is it convenient for you ?", + "emotion": "neutral", + "text": "When is it convenient for you ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Any time is fine .", + "emotion": "neutral", + "text": "Any time is fine .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Could you and your wife be ready at nine o'clock ?", + "emotion": "neutral", + "text": "Could you and your wife be ready at nine o'clock ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Please wait for us even if we're a little late .", + "emotion": "neutral", + "text": "Please wait for us even if we're a little late .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Never mind . I'll be waiting for you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Never mind . I'll be waiting for you .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "See you then .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Never mind . I'll be waiting for you ." + ], + "type": [ + "inter-personal" + ], + "text": "See you then .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "OK . Bye !", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "OK . Bye !", + "id": 9 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4750.json b/reccon/sources/tr_4750.json new file mode 100644 index 0000000000000000000000000000000000000000..099bcd99cac9ae628bb441eda0c52367529a8af0 --- /dev/null +++ b/reccon/sources/tr_4750.json @@ -0,0 +1,245 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "How do you like this waltz ?", + "emotion": "happiness", + "explanation": "A is happy for a latent reason", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "How do you like this waltz ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It's very nice . I like it very much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "It's very nice . I like it very much ." + ], + "type": [ + "no-context" + ], + "text": "It's very nice . I like it very much .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Well , then , may I invite you for the first dance ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "It's very nice . I like it very much ." + ], + "type": [ + "inter-personal" + ], + "text": "Well , then , may I invite you for the first dance ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "My pleasure . But I'm afraid I'm not much of a dancer , and I suppose you dance often .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "It's very nice . I like it very much .", + "I invite you for the first dance ?" + ], + "type": [ + "hybrid" + ], + "text": "My pleasure . But I'm afraid I'm not much of a dancer , and I suppose you dance often .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Me ? Oh , no . In fact , I only took up dancing quite recently .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I suppose you dance often ." + ], + "type": [ + "inter-personal" + ], + "text": "Me ? Oh , no . In fact , I only took up dancing quite recently .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Oh , really ? But you're doing the waltz wonderfully well .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "I only took up dancing quite recently .", + "you're doing the waltz wonderfully well ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , really ? But you're doing the waltz wonderfully well .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I'm glad you say so . You dance beautifully too . It's lucky that I got you as a partner .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "you're doing the waltz wonderfully well .", + "You dance beautifully too . It's lucky that I got you as a partner ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm glad you say so . You dance beautifully too . It's lucky that I got you as a partner .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Thank you for your compliments . It's just you are a good leader . Do you like the foxtrot and tango ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "You dance beautifully too . It's lucky that I got you as a partner .", + "It's just you are a good leader ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you for your compliments . It's just you are a good leader . Do you like the foxtrot and tango ?", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yes . And what dances do you like best ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7, + 8 + ], + "expanded emotion cause span": [ + "you're doing the waltz wonderfully well .", + "You dance beautifully too . It's lucky that I got you as a partner .", + "It's just you are a good leader ." + ], + "type": [ + "hybrid" + ], + "text": "Yes . And what dances do you like best ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Disco is my favorite . I like it better than any other dances because it can release one's hidden feelings , and is a healthy exercise . But I don't do the rock and roll nor break-dancing .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8, + 10, + 10 + ], + "expanded emotion cause span": [ + "You dance beautifully too . It's lucky that I got you as a partner .", + "It's just you are a good leader .", + "I like it better than any other dances", + "it can release one's hidden feelings , and is a healthy exercise ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Disco is my favorite . I like it better than any other dances because it can release one's hidden feelings , and is a healthy exercise . But I don't do the rock and roll nor break-dancing .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Oh , well , the music has stopped . Thank you for the dance .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7, + 8, + 11 + ], + "expanded emotion cause span": [ + "you're doing the waltz wonderfully well .", + "You dance beautifully too . It's lucky that I got you as a partner .", + "It's just you are a good leader .", + "Thank you for the dance ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Oh , well , the music has stopped . Thank you for the dance .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "My pleasure .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8, + 11 + ], + "expanded emotion cause span": [ + "You dance beautifully too . It's lucky that I got you as a partner .", + "It's just you are a good leader .", + "Thank you for the dance ." + ], + "type": [ + "hybrid" + ], + "text": "My pleasure .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4771.json b/reccon/sources/tr_4771.json new file mode 100644 index 0000000000000000000000000000000000000000..46bf860570ce5984cb177992465f65b4aa0d018b --- /dev/null +++ b/reccon/sources/tr_4771.json @@ -0,0 +1,160 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Come here ! I can see the tall camphor trees from here .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Come here ! I can see the tall camphor trees from here .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , we can also see some yew trees .", + "emotion": "neutral", + "text": "Yes , we can also see some yew trees .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "This is a great botanical garden in the city .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "This is a great botanical garden in the city ." + ], + "type": [ + "no-context" + ], + "text": "This is a great botanical garden in the city .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Listen to the sound of nature ! It's like music .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Listen to the sound of nature ! It's like music ." + ], + "type": [ + "no-context" + ], + "text": "Listen to the sound of nature ! It's like music .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Yeah , I agree . It makes you feel really good .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "Listen to the sound of nature ! It's like music .", + "Yeah , I agree . It makes you feel really good ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yeah , I agree . It makes you feel really good .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "What are those . Miss Liu ?", + "emotion": "neutral", + "text": "What are those . Miss Liu ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Do you mean the red flowers ? They are peony flowers ?", + "emotion": "neutral", + "text": "Do you mean the red flowers ? They are peony flowers ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "The red and yellow peony flowers are so beautiful .", + "emotion": "neutral", + "text": "The red and yellow peony flowers are so beautiful .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yes , you like them very much . right ?", + "emotion": "neutral", + "text": "Yes , you like them very much . right ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Sure . I'm going to take more pictures today .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "The red and yellow peony flowers are so beautiful ." + ], + "type": [ + "self-contagion" + ], + "text": "Sure . I'm going to take more pictures today .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I can help you with it", + "emotion": "neutral", + "text": "I can help you with it", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "You are so kind . Thanks .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I can help you with it" + ], + "type": [ + "inter-personal" + ], + "text": "You are so kind . Thanks .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4792.json b/reccon/sources/tr_4792.json new file mode 100644 index 0000000000000000000000000000000000000000..2fe900a73a242003f306e4d60f74f4bf130d0a68 --- /dev/null +++ b/reccon/sources/tr_4792.json @@ -0,0 +1,144 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I'm so hungry . Shall we go eat now , Rick ?", + "emotion": "neutral", + "text": "I'm so hungry . Shall we go eat now , Rick ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "sure . Where do you want to go ? Are you in the mood for anything in particular ?", + "emotion": "neutral", + "text": "sure . Where do you want to go ? Are you in the mood for anything in particular ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "how about some dumplings ? I just can't get enough of them .", + "emotion": "neutral", + "text": "how about some dumplings ? I just can't get enough of them .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "dumplings again ? ! Oh , Amy , let's try something new !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "how about some dumplings ? I just can't get enough of them ." + ], + "type": [ + "inter-personal" + ], + "text": "dumplings again ? ! Oh , Amy , let's try something new !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "well , what do you have in mind ?", + "emotion": "neutral", + "text": "well , what do you have in mind ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "how about the Mongolian hot pot ?", + "emotion": "neutral", + "text": "how about the Mongolian hot pot ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "oh , it's too spicy for me . Don't you remember last time when I tasted the lamb ? It was so spicy my eyes teared up !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "how about the Mongolian hot pot ?", + "it's too spicy for me . Don't you remember last time when I tasted the lamb ? It was so spicy my eyes teared up !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "oh , it's too spicy for me . Don't you remember last time when I tasted the lamb ? It was so spicy my eyes teared up !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "maybe we can try Yuanyang pot this time . You can choose the non-spicy soup base .", + "emotion": "neutral", + "text": "maybe we can try Yuanyang pot this time . You can choose the non-spicy soup base .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "sounds great . Do they serve noodles ? I am in the mood for some tasty noodles as well .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "we can try Yuanyang pot this time . You can choose the non-spicy soup base ." + ], + "type": [ + "inter-personal" + ], + "text": "sounds great . Do they serve noodles ? I am in the mood for some tasty noodles as well .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "yes . The sliced noodles they offer are among the most authentic Shanti cuisines .", + "emotion": "neutral", + "text": "yes . The sliced noodles they offer are among the most authentic Shanti cuisines .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "great . Let's go !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "I am in the mood for some tasty noodles as well .", + "The sliced noodles they offer are among the most authentic Shanti cuisines ." + ], + "type": [ + "hybrid" + ], + "text": "great . Let's go !", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "wait a minute . Let me throw on a sweater .", + "emotion": "neutral", + "text": "wait a minute . Let me throw on a sweater .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4804.json b/reccon/sources/tr_4804.json new file mode 100644 index 0000000000000000000000000000000000000000..4cf871114b9b2bf10103d1aabba74a7491ab63e6 --- /dev/null +++ b/reccon/sources/tr_4804.json @@ -0,0 +1,165 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Do you have any idea what time it is ?", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "any idea what time it is ?" + ], + "type": [ + "no-context" + ], + "text": "Do you have any idea what time it is ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "My bad . I didn't realize that it was so late .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I didn't realize that it was so late ." + ], + "type": [ + "no-context" + ], + "text": "My bad . I didn't realize that it was so late .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Do you really think that that excuses your tardiness ?", + "emotion": "neutral", + "text": "Do you really think that that excuses your tardiness ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Of course not . I really did lose track of time .", + "emotion": "neutral", + "text": "Of course not . I really did lose track of time .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Didn't I tell you to call when you're running late ?", + "emotion": "neutral", + "text": "Didn't I tell you to call when you're running late ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yeah , you did . I just forgot to call .", + "emotion": "neutral", + "text": "Yeah , you did . I just forgot to call .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "It doesn't matter , you should have called and let me know .", + "emotion": "neutral", + "text": "It doesn't matter , you should have called and let me know .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That's true . My bad for not calling .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2, + 8 + ], + "expanded emotion cause span": [ + "I didn't realize that it was so late .", + "My bad for not calling ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "That's true . My bad for not calling .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "If you do this again , don't even bother coming home .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "you should have called and let me know .", + "My bad for not calling ." + ], + "type": [ + "hybrid" + ], + "text": "If you do this again , don't even bother coming home .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "You're going to kick me out over this ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "don't even bother coming home .", + "You're going to kick me out over this ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You're going to kick me out over this ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Exactly , maybe that'll teach you to respect my rules .", + "emotion": "neutral", + "text": "Exactly , maybe that'll teach you to respect my rules .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Well , if I'm not living here anymore , then I won't have to listen to your rules .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "maybe that'll teach you to respect my rules ." + ], + "type": [ + "inter-personal" + ], + "text": "Well , if I'm not living here anymore , then I won't have to listen to your rules .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_483.json b/reccon/sources/tr_483.json new file mode 100644 index 0000000000000000000000000000000000000000..5ad9d45fb989e6b8a19ad7e9787003e591e48d5f --- /dev/null +++ b/reccon/sources/tr_483.json @@ -0,0 +1,158 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi .", + "emotion": "neutral", + "text": "Hi .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hi , Mary , Hi , Ken I hate to bring this up , but that new stereo , system you got ...", + "emotion": "neutral", + "text": "Hi , Mary , Hi , Ken I hate to bring this up , but that new stereo , system you got ...", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yeah ?", + "emotion": "neutral", + "text": "Yeah ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "You were playing it very late last night .", + "emotion": "neutral", + "text": "You were playing it very late last night .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Yeah ?", + "emotion": "neutral", + "text": "Yeah ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "It kept me awake .", + "emotion": "neutral", + "text": "It kept me awake .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Oh , I'm sorry .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "It kept me awake ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , I'm sorry .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "It kept me awake a couple of hours .", + "emotion": "neutral", + "text": "It kept me awake a couple of hours .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I'm so sorry , I .. I didn't realize it was that loud .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "It kept me awake a couple of hours .", + "I didn't realize it was that loud ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm so sorry , I .. I didn't realize it was that loud .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "It was that loud , and it was pretty late , and check with Mary if you don't believe me .", + "emotion": "neutral", + "text": "It was that loud , and it was pretty late , and check with Mary if you don't believe me .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "It's true . It was a bit loud .", + "emotion": "neutral", + "text": "It's true . It was a bit loud .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I'm very sorry . I didn't realize it . I promise I'll keep it down in the future .", + "emotion": "neutral", + "text": "I'm very sorry . I didn't realize it . I promise I'll keep it down in the future .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Oh , it's no problem . It ' s OK . You know , it only happened once .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "I promise I'll keep it down in the future ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , it's no problem . It ' s OK . You know , it only happened once .", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 14, + "speaker": "B", + "utterance": "I am glad we've straightened everything out .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "I am glad we've straightened everything out ." + ], + "type": [ + "no-context" + ], + "text": "I am glad we've straightened everything out .", + "id": 14 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_487.json b/reccon/sources/tr_487.json new file mode 100644 index 0000000000000000000000000000000000000000..17bfa61510189ad3b9b7d08af8c0dbbf5d7dfcae --- /dev/null +++ b/reccon/sources/tr_487.json @@ -0,0 +1,153 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey Jane . How are you doing these days ?", + "emotion": "neutral", + "text": "Hey Jane . How are you doing these days ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hi Martha . Everything is perfect .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Everything is perfect ." + ], + "type": [ + "no-context" + ], + "text": "Hi Martha . Everything is perfect .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Are you enjoying married life ?", + "emotion": "neutral", + "text": "Are you enjoying married life ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It couldn't be better . My husband is so supportive with my work and he helps around the house so much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "It couldn't be better . My husband is so supportive with my work and he helps around the house so much ." + ], + "type": [ + "no-context" + ], + "text": "It couldn't be better . My husband is so supportive with my work and he helps around the house so much .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "You're so lucky . I hope to get married to a guy like that .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "It couldn't be better . My husband is so supportive with my work and he helps around the house so much ." + ], + "type": [ + "inter-personal" + ], + "text": "You're so lucky . I hope to get married to a guy like that .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I'm so happy . Even though we are both working , we get to spend a lot of time with each other in the evening and on the weekends .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 6 + ], + "expanded emotion cause span": [ + "It couldn't be better . My husband is so supportive with my work and he helps around the house so much .", + "Even though we are both working , we get to spend a lot of time with each other in the evening and on the weekends ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I'm so happy . Even though we are both working , we get to spend a lot of time with each other in the evening and on the weekends .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Do you guys do anything special ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I'm so happy . Even though we are both working , we get to spend a lot of time with each other in the evening and on the weekends ." + ], + "type": [ + "inter-personal" + ], + "text": "Do you guys do anything special ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "In the evening , we just sit and talk over dinner . But on the weekend , we try to go out to the beach or hit a nice restaurant , or go to a nice cafe .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 6, + 8 + ], + "expanded emotion cause span": [ + "It couldn't be better . My husband is so supportive with my work and he helps around the house so much .", + "Even though we are both working , we get to spend a lot of time with each other in the evening and on the weekends .", + "In the evening , we just sit and talk over dinner . But on the weekend , we try to go out to the beach or hit a nice restaurant , or go to a nice cafe ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "In the evening , we just sit and talk over dinner . But on the weekend , we try to go out to the beach or hit a nice restaurant , or go to a nice cafe .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Sound like everything is great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 8 + ], + "expanded emotion cause span": [ + "Even though we are both working , we get to spend a lot of time with each other in the evening and on the weekends .", + "In the evening , we just sit and talk over dinner . But on the weekend , we try to go out to the beach or hit a nice restaurant , or go to a nice cafe ." + ], + "type": [ + "inter-personal" + ], + "text": "Sound like everything is great .", + "id": 9, + "source_sentences": [ + 5, + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4878.json b/reccon/sources/tr_4878.json new file mode 100644 index 0000000000000000000000000000000000000000..5e99939b88ae3631f79f12af21c5004ca05c609c --- /dev/null +++ b/reccon/sources/tr_4878.json @@ -0,0 +1,187 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Good afternoon , madam . May I help you ?", + "emotion": "neutral", + "text": "Good afternoon , madam . May I help you ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Do you have some new perfume ?", + "emotion": "neutral", + "text": "Do you have some new perfume ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I am sorry , madam . I didn't hear you . It's too noisy here . Could you please say it again ?", + "emotion": "neutral", + "text": "I am sorry , madam . I didn't hear you . It's too noisy here . Could you please say it again ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Well , I wanna buy some new perfume .", + "emotion": "neutral", + "text": "Well , I wanna buy some new perfume .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Would you please wait a minute ? I will get one for you at once .", + "emotion": "neutral", + "text": "Would you please wait a minute ? I will get one for you at once .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "That's all right .", + "emotion": "neutral", + "text": "That's all right .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Here you are .", + "emotion": "neutral", + "text": "Here you are .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Can I open it ?", + "emotion": "neutral", + "text": "Can I open it ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yes , certainly , madam .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Can I open it ?" + ], + "type": [ + "inter-personal" + ], + "text": "Yes , certainly , madam .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "It smells sweet .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9, + 10 + ], + "expanded emotion cause span": [ + "Can I open it ?", + "Yes , certainly ,", + "It smells sweet ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "It smells sweet .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Yes , it is . This perfume just arrived yesterday , and it's the latest products of Chanel .", + "emotion": "neutral", + "text": "Yes , it is . This perfume just arrived yesterday , and it's the latest products of Chanel .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Really ? How much is it ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "This perfume just arrived yesterday , and it's the latest products of Chanel ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? How much is it ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "55 dollars , madam .", + "emotion": "neutral", + "text": "55 dollars , madam .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Ok , I will take two bottles .", + "emotion": "neutral", + "text": "Ok , I will take two bottles .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Thank you . Do you need something else ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "I will take two bottles ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . Do you need something else ?", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 16, + "speaker": "B", + "utterance": "No , thanks .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14, + 15 + ], + "expanded emotion cause span": [ + "I will take two bottles .", + "Thank you ." + ], + "type": [ + "hybrid" + ], + "text": "No , thanks .", + "id": 16 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4895.json b/reccon/sources/tr_4895.json new file mode 100644 index 0000000000000000000000000000000000000000..cae3eb78239a2b68a9ae414543da9348ea072bbe --- /dev/null +++ b/reccon/sources/tr_4895.json @@ -0,0 +1,124 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Ten sheets of rice paper , 25 brushes , two boxes of oil color and two boxes of water color . All these come up to $ 35 . 50 , sir .", + "emotion": "neutral", + "text": "Ten sheets of rice paper , 25 brushes , two boxes of oil color and two boxes of water color . All these come up to $ 35 . 50 , sir .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Ok , here is $ 50 . Oh , can you make out an invoice for me ?", + "emotion": "neutral", + "text": "Ok , here is $ 50 . Oh , can you make out an invoice for me ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Sure , just a minute . Are you an artist , sir ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Are you an artist" + ], + "type": [ + "no-context" + ], + "text": "Sure , just a minute . Are you an artist , sir ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "No , I am a teacher . I teach art .", + "emotion": "neutral", + "text": "No , I am a teacher . I teach art .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "That must be a very interesting job .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4, + 5 + ], + "expanded emotion cause span": [ + "Are you an artist", + "I teach art .", + "very interesting job ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "That must be a very interesting job .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "It is . You must be new here . I do my shopping here regularly , once a week .", + "emotion": "neutral", + "text": "It is . You must be new here . I do my shopping here regularly , once a week .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Do you ? Nice to meet you ! And here is the invoice and your change .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4, + 5, + 6, + 7 + ], + "expanded emotion cause span": [ + "Are you an artist", + "I teach art .", + "very interesting job .", + "I do my shopping here regularly ,", + "Nice to meet you !" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Do you ? Nice to meet you ! And here is the invoice and your change .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Thank you . Nice to meet you , too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "Nice to meet you !", + "Nice to meet you , too ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you . Nice to meet you , too .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4911.json b/reccon/sources/tr_4911.json new file mode 100644 index 0000000000000000000000000000000000000000..0c8dacdf79a34efd576474effa5d39a426702a04 --- /dev/null +++ b/reccon/sources/tr_4911.json @@ -0,0 +1,149 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey , you have been promoted to president of the department .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "you have been promoted to president of the department ." + ], + "type": [ + "no-context" + ], + "text": "Hey , you have been promoted to president of the department .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "All this is thanks to the efforts of my superiors and colleagues .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "you have been promoted to president of the department ." + ], + "type": [ + "inter-personal" + ], + "text": "All this is thanks to the efforts of my superiors and colleagues .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "You are so smart . Your efforts in the success of the plan were outstanding .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "You are so smart . Your efforts in the success of the plan were outstanding ." + ], + "type": [ + "no-context" + ], + "text": "You are so smart . Your efforts in the success of the plan were outstanding .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I just did what I should have done .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "You are so smart . Your efforts in the success of the plan were outstanding ." + ], + "type": [ + "inter-personal" + ], + "text": "I just did what I should have done .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "You ' Ve got a great personality .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I just did what I should have done ." + ], + "type": [ + "inter-personal" + ], + "text": "You ' Ve got a great personality .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Thank you for your compliments . I will try even harder to repay the company and your support .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "You are so smart . Your efforts in the success of the plan were outstanding .", + "I just did what I should have done ." + ], + "type": [ + "hybrid" + ], + "text": "Thank you for your compliments . I will try even harder to repay the company and your support .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I believe you will . I ' m very pleased with your work . Your promotion will contribute to the development of the company .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I will try even harder to repay the company and your support .", + "I ' m very pleased with your work . Your promotion will contribute to the development of the company ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I believe you will . I ' m very pleased with your work . Your promotion will contribute to the development of the company .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Thanks for saying so .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I ' m very pleased with your work . Your promotion will contribute to the development of the company ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks for saying so .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4915.json b/reccon/sources/tr_4915.json new file mode 100644 index 0000000000000000000000000000000000000000..7a0e79c972b2fa0a2df10076f0749cb3517df7f3 --- /dev/null +++ b/reccon/sources/tr_4915.json @@ -0,0 +1,137 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello , Helen .", + "emotion": "neutral", + "text": "Hello , Helen .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hi , Steven .", + "emotion": "neutral", + "text": "Hi , Steven .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "How are you today ?", + "emotion": "neutral", + "text": "How are you today ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I ' m very well , Thank you . And you ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "How are you today ?", + "I ' m very well ," + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I ' m very well , Thank you . And you ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I ' m fine , thanks . How is Tony ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "And you ?", + "I ' m fine ," + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I ' m fine , thanks . How is Tony ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "He ' s fine , Thanks . How ' s Emma ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4, + 6 + ], + "expanded emotion cause span": [ + "How are you today ?", + "I ' m very well ,", + "He ' s fine ," + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "He ' s fine , Thanks . How ' s Emma ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "She ' s very well , too , Helen . Goodbye , Helen . Nice to see you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5, + 7, + 7 + ], + "expanded emotion cause span": [ + "And you ?", + "I ' m fine ,", + "She ' s very well ,", + "Nice to see you ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "She ' s very well , too , Helen . Goodbye , Helen . Nice to see you .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Nice to see you , too , Steven . Goodbye .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "Nice to see you .", + "Nice to see you , too ," + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Nice to see you , too , Steven . Goodbye .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4936.json b/reccon/sources/tr_4936.json new file mode 100644 index 0000000000000000000000000000000000000000..37eb81c86a132e1e21eb52f83e897d92fa43168d --- /dev/null +++ b/reccon/sources/tr_4936.json @@ -0,0 +1,167 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Can you help me pick out a gift for my daughter ?", + "emotion": "neutral", + "text": "Can you help me pick out a gift for my daughter ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "She might like a laptop computer .", + "emotion": "neutral", + "text": "She might like a laptop computer .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yes , that sounds like a good idea .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "laptop computer ." + ], + "type": [ + "inter-personal" + ], + "text": "Yes , that sounds like a good idea .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Might I suggest a Mac ?", + "emotion": "neutral", + "text": "Might I suggest a Mac ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Okay . How much ?", + "emotion": "neutral", + "text": "Okay . How much ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Well , a 15 - inch Pro is $ 2,100 .", + "emotion": "neutral", + "text": "Well , a 15 - inch Pro is $ 2,100 .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Oh , that sounds great . I'll take it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "a 15 - inch Pro is $ 2,100 ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , that sounds great . I'll take it .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Great . How would you like to pay for it ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I'll take it ." + ], + "type": [ + "inter-personal" + ], + "text": "Great . How would you like to pay for it ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Here's my VISA .", + "emotion": "neutral", + "text": "Here's my VISA .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Let me ring you up . Okay , sign here , please .", + "emotion": "neutral", + "text": "Let me ring you up . Okay , sign here , please .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Everything I need is in this box ?", + "emotion": "neutral", + "text": "Everything I need is in this box ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "It'll take her only a few minutes to get online .", + "emotion": "neutral", + "text": "It'll take her only a few minutes to get online .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Thank you for your help .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "It'll take her only a few minutes to get online ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you for your help .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "So long . Thank you for shopping here .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13, + 14 + ], + "expanded emotion cause span": [ + "Thank you for your help .", + "So long . Thank you for shopping here ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "So long . Thank you for shopping here .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4974.json b/reccon/sources/tr_4974.json new file mode 100644 index 0000000000000000000000000000000000000000..da0283a3b17d3a5935f16b3c887930b8b08c954b --- /dev/null +++ b/reccon/sources/tr_4974.json @@ -0,0 +1,279 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What should I get Uncle Teddy ?", + "emotion": "neutral", + "text": "What should I get Uncle Teddy ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "You could get him a tie .", + "emotion": "neutral", + "text": "You could get him a tie .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Are you kidding ? That's the stupidest gift one can buy . I don't want to get a tie .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "You could get him a tie .", + "That's the stupidest gift one can buy ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Are you kidding ? That's the stupidest gift one can buy . I don't want to get a tie .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Why not ?", + "emotion": "neutral", + "text": "Why not ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Everybody gets men ties for Christmas . It's too boring . Everybody buys either ties or sweaters . I want a more unique gift .", + "emotion": "neutral", + "text": "Everybody gets men ties for Christmas . It's too boring . Everybody buys either ties or sweaters . I want a more unique gift .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Well , you can buy him a pet iguana then .", + "emotion": "neutral", + "text": "Well , you can buy him a pet iguana then .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "That's a cool idea . At least it would be a surprise . But I'm afraid he wouldn't take care of it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "you can buy him a pet iguana" + ], + "type": [ + "inter-personal" + ], + "text": "That's a cool idea . At least it would be a surprise . But I'm afraid he wouldn't take care of it .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "He would think you were crazy , Caroline .", + "emotion": "neutral", + "text": "He would think you were crazy , Caroline .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yes . An iguana is too strange for a gift , and a tie is too normal . So I have to find something halfway between .", + "emotion": "neutral", + "text": "Yes . An iguana is too strange for a gift , and a tie is too normal . So I have to find something halfway between .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "How much do you want to spend ?", + "emotion": "neutral", + "text": "How much do you want to spend ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Well , he was very good to me . He helped me edit my essay for the scholarship contest . So I want to spend at least 75 dollars .", + "emotion": "neutral", + "text": "Well , he was very good to me . He helped me edit my essay for the scholarship contest . So I want to spend at least 75 dollars .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Alright , I have an idea . You know he carries that conservative-looking briefcase every day .", + "emotion": "neutral", + "text": "Alright , I have an idea . You know he carries that conservative-looking briefcase every day .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Yes .", + "emotion": "neutral", + "text": "Yes .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Well , he isn't a lawyer , so I don't think he needs to have a briefcase like that .", + "emotion": "neutral", + "text": "Well , he isn't a lawyer , so I don't think he needs to have a briefcase like that .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "What should he have then ?", + "emotion": "neutral", + "text": "What should he have then ?", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "I think he would appreciate having a very fine leather bag . But more like a workbag or shoulder bag . You know , not so hard and square like a briefcase .", + "emotion": "neutral", + "text": "I think he would appreciate having a very fine leather bag . But more like a workbag or shoulder bag . You know , not so hard and square like a briefcase .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "I think that's a great idea . Men look great with that kind of bag . Where can we buy one ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 16 + ], + "expanded emotion cause span": [ + "I think he would appreciate having a very fine leather bag . But more like a workbag or shoulder bag . You know , not so hard and square like a briefcase ." + ], + "type": [ + "inter-personal" + ], + "text": "I think that's a great idea . Men look great with that kind of bag . Where can we buy one ?", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "I don't think this mall has a leather goods store . So we have to go to State Street .", + "emotion": "neutral", + "text": "I don't think this mall has a leather goods store . So we have to go to State Street .", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "Alright . We can go later then .", + "emotion": "neutral", + "text": "Alright . We can go later then .", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "We can buy something for Mom and Dad here , and then go buy Uncle Teddy's gift on State Street .", + "emotion": "neutral", + "text": "We can buy something for Mom and Dad here , and then go buy Uncle Teddy's gift on State Street .", + "id": 20 + }, + { + "turn": 21, + "speaker": "A", + "utterance": "Good plan . What should we get for Mom though ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 20 + ], + "expanded emotion cause span": [ + "We can buy something for Mom and Dad here , and then go buy Uncle Teddy's gift on State Street ." + ], + "type": [ + "inter-personal" + ], + "text": "Good plan . What should we get for Mom though ?", + "id": 21 + }, + { + "turn": 22, + "speaker": "B", + "utterance": "She said she wants one of those automatic foot massagers . I think they sell them at Sears .", + "emotion": "neutral", + "text": "She said she wants one of those automatic foot massagers . I think they sell them at Sears .", + "id": 22 + }, + { + "turn": 23, + "speaker": "A", + "utterance": "Alright . We can go check at Sears and see if they have them . And what about Dad ?", + "emotion": "neutral", + "text": "Alright . We can go check at Sears and see if they have them . And what about Dad ?", + "id": 23 + }, + { + "turn": 24, + "speaker": "B", + "utterance": "How about the iguana ?", + "emotion": "neutral", + "text": "How about the iguana ?", + "id": 24 + }, + { + "turn": 25, + "speaker": "A", + "utterance": "I think it would be a great joke . But I know we'd have to take the iguana back . And the pet store might not let us . So why don't we get him something else ? Some clothes maybe .", + "emotion": "neutral", + "text": "I think it would be a great joke . But I know we'd have to take the iguana back . And the pet store might not let us . So why don't we get him something else ? Some clothes maybe .", + "id": 25 + }, + { + "turn": 26, + "speaker": "B", + "utterance": "A tie ?", + "emotion": "neutral", + "text": "A tie ?", + "id": 26 + }, + { + "turn": 27, + "speaker": "A", + "utterance": "Oh , shut up about ties ! Forget about ties , why not ?", + "emotion": "anger", + "expanded emotion cause evidence": [ + 26 + ], + "expanded emotion cause span": [ + "A tie ?" + ], + "type": [ + "inter-personal" + ], + "text": "Oh , shut up about ties ! Forget about ties , why not ?", + "id": 27, + "source_sentences": [ + 25 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 28, + "speaker": "B", + "utterance": "I was just kidding .", + "emotion": "neutral", + "text": "I was just kidding .", + "id": 28 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_4994.json b/reccon/sources/tr_4994.json new file mode 100644 index 0000000000000000000000000000000000000000..dea0bc8e63176b3db0f90e9e591c2bcb1d9d02f9 --- /dev/null +++ b/reccon/sources/tr_4994.json @@ -0,0 +1,195 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "how was your day ?", + "emotion": "neutral", + "text": "how was your day ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "let ' s start with you . How was yours ?", + "emotion": "neutral", + "text": "let ' s start with you . How was yours ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "it was really busy . I had to work straight through my lunch break .", + "emotion": "neutral", + "text": "it was really busy . I had to work straight through my lunch break .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "did you get to leave early then ?", + "emotion": "neutral", + "text": "did you get to leave early then ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "my boss told me that I could either go home early or take a long lunch break another day , so I decided to wait and take a long lunch break another time .", + "emotion": "neutral", + "text": "my boss told me that I could either go home early or take a long lunch break another day , so I decided to wait and take a long lunch break another time .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "it was nice of your boss to give you an option . My boss would never do that .", + "emotion": "neutral", + "text": "it was nice of your boss to give you an option . My boss would never do that .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "let ' s get back to you . How was your day ?", + "emotion": "neutral", + "text": "let ' s get back to you . How was your day ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "it was horrible ! It was just one thing after another .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "it was horrible ! It was just one thing after another ." + ], + "type": [ + "no-context" + ], + "text": "it was horrible ! It was just one thing after another .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "you look pretty upset . Are you ok ?", + "emotion": "neutral", + "text": "you look pretty upset . Are you ok ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I ' m fine . But I have bad news .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "I have bad news ." + ], + "type": [ + "no-context" + ], + "text": "I ' m fine . But I have bad news .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "what ' s that ?", + "emotion": "neutral", + "text": "what ' s that ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I got sacked today .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "I got sacked today ." + ], + "type": [ + "no-context" + ], + "text": "I got sacked today .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "you ' re kidding ! How did that happen ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "I got sacked today ." + ], + "type": [ + "inter-personal" + ], + "text": "you ' re kidding ! How did that happen ?", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 14, + "speaker": "B", + "utterance": "well , I was late to work today . It was the third time I was late this week .", + "emotion": "neutral", + "text": "well , I was late to work today . It was the third time I was late this week .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "how late were you ?", + "emotion": "neutral", + "text": "how late were you ?", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "only about 5 minutes .", + "emotion": "neutral", + "text": "only about 5 minutes .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "you got fired for being a few minutes late ?", + "emotion": "neutral", + "text": "you got fired for being a few minutes late ?", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "my boss is really picky about that . He never arrives late , usually works over-time , and always gets his work done on time .", + "emotion": "neutral", + "text": "my boss is really picky about that . He never arrives late , usually works over-time , and always gets his work done on time .", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "oh well . You never really liked your boss anyway , did you ?", + "emotion": "neutral", + "text": "oh well . You never really liked your boss anyway , did you ?", + "id": 19 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_502.json b/reccon/sources/tr_502.json new file mode 100644 index 0000000000000000000000000000000000000000..f6b4b0c2022c1afb36a16764e3c7ca9d91de518c --- /dev/null +++ b/reccon/sources/tr_502.json @@ -0,0 +1,137 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Congratulations ! Mr . Stuart ! You won the city marathon .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 1 + ], + "expanded emotion cause span": [ + "Congratulations !", + "You won the city marathon ." + ], + "type": [ + "no-context" + ], + "text": "Congratulations ! Mr . Stuart ! You won the city marathon .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Thank you . I am very excited .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 1 + ], + "expanded emotion cause span": [ + "Congratulations !", + "You won the city marathon ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . I am very excited .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "We are all very proud of you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 1, + 3 + ], + "expanded emotion cause span": [ + "Congratulations !", + "You won the city marathon .", + "We are all very proud of you ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "We are all very proud of you .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I am very happy , too . It was a big game and I won .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 1, + 4 + ], + "expanded emotion cause span": [ + "Congratulations !", + "You won the city marathon .", + "It was a big game and I won ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I am very happy , too . It was a big game and I won .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I watched the race with my children . We saw you run to the finish line . We all screamed with excitement .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 1, + 5 + ], + "expanded emotion cause span": [ + "Congratulations !", + "You won the city marathon .", + "We saw you run to the finish line ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I watched the race with my children . We saw you run to the finish line . We all screamed with excitement .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "It was really an exciting moment .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 1, + 5, + 6 + ], + "expanded emotion cause span": [ + "Congratulations !", + "You won the city marathon .", + "run to the finish line .", + "It was really an exciting moment ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It was really an exciting moment .", + "id": 6, + "source_sentences": [ + 0, + 0, + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_505.json b/reccon/sources/tr_505.json new file mode 100644 index 0000000000000000000000000000000000000000..4b65f13d2aedf31e05d5171925307cdc326a1868 --- /dev/null +++ b/reccon/sources/tr_505.json @@ -0,0 +1,180 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Where to , miss ?", + "emotion": "neutral", + "text": "Where to , miss ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hi ! Crenshaw and Hawthorne , at the Holiday Inn that is on that corner .", + "emotion": "neutral", + "text": "Hi ! Crenshaw and Hawthorne , at the Holiday Inn that is on that corner .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Sure thing . So , where are you flying in from ?", + "emotion": "neutral", + "text": "Sure thing . So , where are you flying in from ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "From China .", + "emotion": "neutral", + "text": "From China .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Really ? You don ' t look very Chinese to me , if you don ' t mind me saying so .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "From China .", + "You don ' t look very Chinese to me ," + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Really ? You don ' t look very Chinese to me , if you don ' t mind me saying so .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "It ' s fine . I am actually from Mexico . I was in China on a business trip , visiting some local companies that manufacture bathroom products .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "You don ' t look very Chinese to me ," + ], + "type": [ + "inter-personal" + ], + "text": "It ' s fine . I am actually from Mexico . I was in China on a business trip , visiting some local companies that manufacture bathroom products .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Wow sounds interesting ! Excuse me if I am being a bit nosy but , how old are you ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "You don ' t look very Chinese to me ,", + "I am actually from Mexico . I was in China on a business trip , visiting some local companies that manufacture bathroom products ." + ], + "type": [ + "hybrid" + ], + "text": "Wow sounds interesting ! Excuse me if I am being a bit nosy but , how old are you ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Don ' t you know it ' s rude to ask a lady her age ?", + "emotion": "neutral", + "text": "Don ' t you know it ' s rude to ask a lady her age ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Don ' t get me wrong ! It ' s just that you seem so young and already doing business overseas !", + "emotion": "neutral", + "text": "Don ' t get me wrong ! It ' s just that you seem so young and already doing business overseas !", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Well thank you ! In that case , I am 26 years old , and what about yourself ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "It ' s just that you seem so young and already doing business overseas !" + ], + "type": [ + "inter-personal" + ], + "text": "Well thank you ! In that case , I am 26 years old , and what about yourself ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I am 40 years old and was born and raised here in the good old U . S of A , although I have some Colombian heritage .", + "emotion": "neutral", + "text": "I am 40 years old and was born and raised here in the good old U . S of A , although I have some Colombian heritage .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Really ? That ' s great ! Do you speak some Spanish ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I am 40 years old and was born and raised here in the good old U . S of A , although I have some Colombian heritage ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? That ' s great ! Do you speak some Spanish ?", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Uh ... yeah .. of course !", + "emotion": "neutral", + "text": "Uh ... yeah .. of course !", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Que bien ! Sentences poems habeas en espanol !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12, + 13 + ], + "expanded emotion cause span": [ + "Do you speak some Spanish ?", + "Uh ... yeah .. of course !" + ], + "type": [ + "hybrid" + ], + "text": "Que bien ! Sentences poems habeas en espanol !", + "id": 14 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_510.json b/reccon/sources/tr_510.json new file mode 100644 index 0000000000000000000000000000000000000000..3c8b783229b31412f8f0ada8543d47c13346bc1b --- /dev/null +++ b/reccon/sources/tr_510.json @@ -0,0 +1,232 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Who was the best teacher that you ever had ?", + "emotion": "neutral", + "text": "Who was the best teacher that you ever had ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "That would have to be Miss Baymler , my fourth grade teacher .", + "emotion": "neutral", + "text": "That would have to be Miss Baymler , my fourth grade teacher .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What was she like ?", + "emotion": "neutral", + "text": "What was she like ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "She was patient , kind , fun , smart , caring , and yet strict , too . I really learned a lot from her .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 4 + ], + "expanded emotion cause span": [ + "best teacher that you ever had ?", + "She was patient , kind , fun , smart , caring , and yet strict , too . I really learned a lot from her ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "She was patient , kind , fun , smart , caring , and yet strict , too . I really learned a lot from her .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "What kind of things did you learn ?", + "emotion": "neutral", + "text": "What kind of things did you learn ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "She taught us that you can do anything that you want to do .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "She taught us that you can do anything that you want to do ." + ], + "type": [ + "no-context" + ], + "text": "She taught us that you can do anything that you want to do .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Anything ? Do you really believe that we can do anything ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "She taught us that you can do anything that you want to do ." + ], + "type": [ + "inter-personal" + ], + "text": "Anything ? Do you really believe that we can do anything ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "If you really want to do something and you work hard at it , I believe you can do it .", + "emotion": "neutral", + "text": "If you really want to do something and you work hard at it , I believe you can do it .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "You said she was strict . Did she have a lot of rules ?", + "emotion": "neutral", + "text": "You said she was strict . Did she have a lot of rules ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "She had some rules that helped us to feel comfortable . For example , the students had to treat each other with respect , or they would be disciplined .", + "emotion": "neutral", + "text": "She had some rules that helped us to feel comfortable . For example , the students had to treat each other with respect , or they would be disciplined .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I see . She sounds like she really cared about her students .", + "emotion": "neutral", + "text": "I see . She sounds like she really cared about her students .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Yes . She treated us all fairly . She don ' t have any teacher ' s pets .", + "emotion": "neutral", + "text": "Yes . She treated us all fairly . She don ' t have any teacher ' s pets .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Really ? Doesn ' t every teacher have a teacher ' s pet ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 12, + 13 + ], + "expanded emotion cause span": [ + "She treated us all fairly . She don ' t have any teacher ' s pets .", + "Doesn ' t every teacher have a teacher ' s pet ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Really ? Doesn ' t every teacher have a teacher ' s pet ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Well . To be honest , I usually sucked up to teachers because I wanted them to give me good grades . However , Miss Baymler didn ' t treat me any differently . She really didn ' t have any teacher ' s pets .", + "emotion": "neutral", + "text": "Well . To be honest , I usually sucked up to teachers because I wanted them to give me good grades . However , Miss Baymler didn ' t treat me any differently . She really didn ' t have any teacher ' s pets .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Do you know what she is doing now ?", + "emotion": "neutral", + "text": "Do you know what she is doing now ?", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "As a matter of fact , I do . After she taught our class , she got married and moved to another city . Then , she started writing children ' s book .", + "emotion": "neutral", + "text": "As a matter of fact , I do . After she taught our class , she got married and moved to another city . Then , she started writing children ' s book .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "Have you ever read one of the books ?", + "emotion": "neutral", + "text": "Have you ever read one of the books ?", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "Of course ! Both children and adults enjoy her books .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 4, + 18 + ], + "expanded emotion cause span": [ + "best teacher that you ever had ?", + "She was patient , kind , fun , smart , caring , and yet strict , too . I really learned a lot from her .", + "Both children and adults enjoy her books ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Of course ! Both children and adults enjoy her books .", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "Why don ' t you recommend one to me ?", + "emotion": "neutral", + "text": "Why don ' t you recommend one to me ?", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "ok ! I ' ll bring one to you next time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 19 + ], + "expanded emotion cause span": [ + "recommend one to me ?" + ], + "type": [ + "inter-personal" + ], + "text": "ok ! I ' ll bring one to you next time .", + "id": 20, + "source_sentences": [ + 18 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_5133.json b/reccon/sources/tr_5133.json new file mode 100644 index 0000000000000000000000000000000000000000..b0380ad70ebeeb39817d05034c207865a6ac16f5 --- /dev/null +++ b/reccon/sources/tr_5133.json @@ -0,0 +1,97 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Good evening ! I don't believe we've met before . May I introduce myself ? My name is Jack .", + "emotion": "neutral", + "text": "Good evening ! I don't believe we've met before . May I introduce myself ? My name is Jack .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It's a pleasure to meet you . My name is Lucy .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "Good evening !", + "It's a pleasure to meet you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It's a pleasure to meet you . My name is Lucy .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I'm very happy to meet you . You're from the United States , aren't you ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "It's a pleasure to meet you ." + ], + "type": [ + "inter-personal" + ], + "text": "I'm very happy to meet you . You're from the United States , aren't you ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes , I'm from Salt Lake City .", + "emotion": "neutral", + "text": "Yes , I'm from Salt Lake City .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I've been to Salt Lake City a few times . I really like your city .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I really like your city ." + ], + "type": [ + "no-context" + ], + "text": "I've been to Salt Lake City a few times . I really like your city .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I'm glad to hear that . I think it's the nicest city in the United States .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "I really like your city .", + "I'm glad to hear that . I think it's the nicest city in the United States ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm glad to hear that . I think it's the nicest city in the United States .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_5156.json b/reccon/sources/tr_5156.json new file mode 100644 index 0000000000000000000000000000000000000000..38d7bf58ebb583d15363b323afbc5fe3cc35f3f0 --- /dev/null +++ b/reccon/sources/tr_5156.json @@ -0,0 +1,139 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I believe that you called me ?", + "emotion": "neutral", + "text": "I believe that you called me ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh , hi . Thanks for getting back to me quickly .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Thanks for getting back to me quickly ." + ], + "type": [ + "no-context" + ], + "text": "Oh , hi . Thanks for getting back to me quickly .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Why did you call me ?", + "emotion": "neutral", + "text": "Why did you call me ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I was calling about your son .", + "emotion": "neutral", + "text": "I was calling about your son .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Did he do something wrong ?", + "emotion": "neutral", + "text": "Did he do something wrong ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Your son was acting up in class .", + "emotion": "neutral", + "text": "Your son was acting up in class .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "What do you mean ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Your son was acting up in class ." + ], + "type": [ + "inter-personal" + ], + "text": "What do you mean ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "He was talking and causing a disturbance during class .", + "emotion": "neutral", + "text": "He was talking and causing a disturbance during class .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "That's really not like him .", + "emotion": "neutral", + "text": "That's really not like him .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "If you could just talk to him , I would greatly appreciate it .", + "emotion": "neutral", + "text": "If you could just talk to him , I would greatly appreciate it .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I apologize , and I'll make sure he doesn't do that again .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "He was talking and causing a disturbance during class ." + ], + "type": [ + "inter-personal" + ], + "text": "I apologize , and I'll make sure he doesn't do that again .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Don't worry about it , but thank you very much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I'll make sure he doesn't do that again ." + ], + "type": [ + "inter-personal" + ], + "text": "Don't worry about it , but thank you very much .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_5180.json b/reccon/sources/tr_5180.json new file mode 100644 index 0000000000000000000000000000000000000000..5083cbf2ec49f37ca4d7084071698d4a51b98a9f --- /dev/null +++ b/reccon/sources/tr_5180.json @@ -0,0 +1,124 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I need to find a new place to live .", + "emotion": "neutral", + "text": "I need to find a new place to live .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yeah ? Why ? Don ' t you like living with me ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I need to find a new place to live ." + ], + "type": [ + "inter-personal" + ], + "text": "Yeah ? Why ? Don ' t you like living with me ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Oh , it ' s not you . I just want my own place .", + "emotion": "neutral", + "text": "Oh , it ' s not you . I just want my own place .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Well , check the newspaper .", + "emotion": "neutral", + "text": "Well , check the newspaper .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Jeez ... I didn ' t realize a single bedroom apartment went for so much these days .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "a single bedroom apartment went for so much these days ." + ], + "type": [ + "no-context" + ], + "text": "Jeez ... I didn ' t realize a single bedroom apartment went for so much these days .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yeah , prices have really gone up the past couple of years .", + "emotion": "neutral", + "text": "Yeah , prices have really gone up the past couple of years .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Oh , here ' s one . It ' s looks like its in this neighborhood , $ 600 a month . That ' s not to bad .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "It ' s looks like its in this neighborhood , $ 600 a month" + ], + "type": [ + "no-context" + ], + "text": "Oh , here ' s one . It ' s looks like its in this neighborhood , $ 600 a month . That ' s not to bad .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "No , it ' s pretty good . Why not give the landlord a call ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "It ' s looks like its in this neighborhood , $ 600 a month" + ], + "type": [ + "inter-personal" + ], + "text": "No , it ' s pretty good . Why not give the landlord a call ?", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Hello . I ' m calling about the one bedroom in Lincoln Park . Could I take a look at it ? Yes . Tonight at six is fine . Thanks .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "It ' s looks like its in this neighborhood , $ 600 a month" + ], + "type": [ + "self-contagion" + ], + "text": "Hello . I ' m calling about the one bedroom in Lincoln Park . Could I take a look at it ? Yes . Tonight at six is fine . Thanks .", + "id": 9 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_5190.json b/reccon/sources/tr_5190.json new file mode 100644 index 0000000000000000000000000000000000000000..edb1bd8c61d70c170affec3da2a0ee26553bf5d4 --- /dev/null +++ b/reccon/sources/tr_5190.json @@ -0,0 +1,212 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Can I help you , sir ?", + "emotion": "neutral", + "text": "Can I help you , sir ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , please . I'm picking out some presents for my children and wife .", + "emotion": "neutral", + "text": "Yes , please . I'm picking out some presents for my children and wife .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What kind of presents do you want ?", + "emotion": "neutral", + "text": "What kind of presents do you want ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Actually , I don't know exactly . Do you have anything recommended ?", + "emotion": "neutral", + "text": "Actually , I don't know exactly . Do you have anything recommended ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "OK . How about some very cool sneakers for your children ? Anyway , it won't cost you much . It's only around $ 59 . 95 for each pair . It might be cheaper than that in America .", + "emotion": "neutral", + "text": "OK . How about some very cool sneakers for your children ? Anyway , it won't cost you much . It's only around $ 59 . 95 for each pair . It might be cheaper than that in America .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Hey , How did you know I came from America ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "It might be cheaper than that in America .", + "How did you know I came from America ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Hey , How did you know I came from America ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Just a hunch , sir .", + "emotion": "neutral", + "text": "Just a hunch , sir .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "How much again ?", + "emotion": "neutral", + "text": "How much again ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "$ 59 . 95 .", + "emotion": "neutral", + "text": "$ 59 . 95 .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "That's really cheap for shoes like those . OK , I'll take 5 pairs .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "That's really cheap for shoes like those ." + ], + "type": [ + "no-context" + ], + "text": "That's really cheap for shoes like those . OK , I'll take 5 pairs .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Sorry , sir .", + "emotion": "neutral", + "text": "Sorry , sir .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Why not ?", + "emotion": "neutral", + "text": "Why not ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Because in this duty-free shop , your total expenditure cannot be over $ 300 and you also have one more present to buy for your wife .", + "emotion": "neutral", + "text": "Because in this duty-free shop , your total expenditure cannot be over $ 300 and you also have one more present to buy for your wife .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Oh , my God . I've totally forgotten about that . Anyway , I think she would like a bottle of perfume .", + "emotion": "neutral", + "text": "Oh , my God . I've totally forgotten about that . Anyway , I think she would like a bottle of perfume .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "That's good . And I can also recommend you a good one . It's the brand of DENY .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14, + 15 + ], + "expanded emotion cause span": [ + "I think she would like a bottle of perfume .", + "I can also recommend you a good one ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's good . And I can also recommend you a good one . It's the brand of DENY .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "DENY ? That's very expensive in America . It costs nearly $ 70 for only 50ml . DKNY ?", + "emotion": "neutral", + "text": "DENY ? That's very expensive in America . It costs nearly $ 70 for only 50ml . DKNY ?", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "It's $ 60 here .", + "emotion": "neutral", + "text": "It's $ 60 here .", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "That's very unbelievable . Is it fake ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 17, + 18 + ], + "expanded emotion cause span": [ + "It's $ 60 here .", + "That's very unbelievable . Is it fake ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's very unbelievable . Is it fake ?", + "id": 18, + "source_sentences": [ + 16 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 19, + "speaker": "A", + "utterance": "Of course not , sir .", + "emotion": "neutral", + "text": "Of course not , sir .", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "OK , I'll take one .", + "emotion": "neutral", + "text": "OK , I'll take one .", + "id": 20 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_5231.json b/reccon/sources/tr_5231.json new file mode 100644 index 0000000000000000000000000000000000000000..f5944b2b8f158d384fe7201fd122f0c7a8cee44d --- /dev/null +++ b/reccon/sources/tr_5231.json @@ -0,0 +1,270 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I'm glad we came here . This is really delicious !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I'm glad we came here . This is really delicious !" + ], + "type": [ + "no-context" + ], + "text": "I'm glad we came here . This is really delicious !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I was worried you would think it was too far to drive .", + "emotion": "neutral", + "text": "I was worried you would think it was too far to drive .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Well , it's true I've never driven two hours just to get lunch . But really , I think it's worth it .", + "emotion": "neutral", + "text": "Well , it's true I've never driven two hours just to get lunch . But really , I think it's worth it .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I think if you try some more authentic Chinese food , you might understand how we students from Taiwan suffer .", + "emotion": "neutral", + "text": "I think if you try some more authentic Chinese food , you might understand how we students from Taiwan suffer .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "How do you mean \" suffer \" ?", + "emotion": "neutral", + "text": "How do you mean \" suffer \" ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I mean , in Milwaukee there is no good Chinese food . So we miss the food in Taiwan too much . Sometimes we just have to drive down here to Chicago to find something better .", + "emotion": "neutral", + "text": "I mean , in Milwaukee there is no good Chinese food . So we miss the food in Taiwan too much . Sometimes we just have to drive down here to Chicago to find something better .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Even in the winter ?", + "emotion": "neutral", + "text": "Even in the winter ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yes , even in the winter .", + "emotion": "neutral", + "text": "Yes , even in the winter .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "And even if it takes two hours , huh ?", + "emotion": "neutral", + "text": "And even if it takes two hours , huh ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Why not ? I've been craving good food for three weeks now . I'm too sick of hamburgers and pizza !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "I've been craving good food for three weeks now ." + ], + "type": [ + "no-context" + ], + "text": "Why not ? I've been craving good food for three weeks now . I'm too sick of hamburgers and pizza !", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Well , this really is delicious , I have to admit . I can understand better now why you and your friends are always whining .", + "emotion": "neutral", + "text": "Well , this really is delicious , I have to admit . I can understand better now why you and your friends are always whining .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Don't tease me ! Good food is really important to Chinese !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "this really is delicious , I have to admit ." + ], + "type": [ + "inter-personal" + ], + "text": "Don't tease me ! Good food is really important to Chinese !", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I know . I can see that . This is what is called \" dim sum , \" right ?", + "emotion": "neutral", + "text": "I know . I can see that . This is what is called \" dim sum , \" right ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Yes , all these dishes are different \" dim sum \" dishes . You can't find this kind of thing except for in a few cities in America .", + "emotion": "neutral", + "text": "Yes , all these dishes are different \" dim sum \" dishes . You can't find this kind of thing except for in a few cities in America .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "So when you Chinese think of Chinatown , you mostly think of food . Is that right ?", + "emotion": "neutral", + "text": "So when you Chinese think of Chinatown , you mostly think of food . Is that right ?", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Of course . I will try to buy some things at the Asian grocery down the block too . Then I can do a little cooking in my apartment .", + "emotion": "happiness", + "explanation": "The speaker is passionate about Chinese food.", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "So when you Chinese think of Chinatown , you mostly think of food ." + ], + "type": [ + "inter-personal" + ], + "text": "Of course . I will try to buy some things at the Asian grocery down the block too . Then I can do a little cooking in my apartment .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 17, + "speaker": "A", + "utterance": "And maybe we can go to a good Italian restaurant for dinner , after the museum . Chicago has some great Italian restaurants .", + "emotion": "neutral", + "text": "And maybe we can go to a good Italian restaurant for dinner , after the museum . Chicago has some great Italian restaurants .", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "No way !", + "emotion": "neutral", + "text": "No way !", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "What do you mean ?", + "emotion": "neutral", + "text": "What do you mean ?", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "We're going up to the \" new \" Chinatown for dinner . I already know where we're going to go .", + "emotion": "neutral", + "text": "We're going up to the \" new \" Chinatown for dinner . I already know where we're going to go .", + "id": 20 + }, + { + "turn": 21, + "speaker": "A", + "utterance": "Alright , alright . I am happy to try more Chinese food . Will it be dim sum again ?", + "emotion": "neutral", + "text": "Alright , alright . I am happy to try more Chinese food . Will it be dim sum again ?", + "id": 21 + }, + { + "turn": 22, + "speaker": "B", + "utterance": "No , dim sum is usually eaten around lunch time , or sometimes closer to breakfast . We ' ll try more Taiwanese style up at the \" new \" Chinatown .", + "emotion": "neutral", + "text": "No , dim sum is usually eaten around lunch time , or sometimes closer to breakfast . We ' ll try more Taiwanese style up at the \" new \" Chinatown .", + "id": 22 + }, + { + "turn": 23, + "speaker": "A", + "utterance": "Taiwanese style ? Isn't dim sum Taiwanese style ?", + "emotion": "neutral", + "text": "Taiwanese style ? Isn't dim sum Taiwanese style ?", + "id": 23 + }, + { + "turn": 24, + "speaker": "B", + "utterance": "No , dim sum is more Cantonese style . But of course you can buy it in Taiwan .", + "emotion": "neutral", + "text": "No , dim sum is more Cantonese style . But of course you can buy it in Taiwan .", + "id": 24 + }, + { + "turn": 25, + "speaker": "A", + "utterance": "I wonder if you can cook things this good .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 25 + ], + "expanded emotion cause span": [ + "if you can cook things this good ." + ], + "type": [ + "no-context" + ], + "text": "I wonder if you can cook things this good .", + "id": 25 + }, + { + "turn": 26, + "speaker": "B", + "utterance": "I'm a great cook actually . You will see .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 26 + ], + "expanded emotion cause span": [ + "I'm a great cook" + ], + "type": [ + "no-context" + ], + "text": "I'm a great cook actually . You will see .", + "id": 26 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_5251.json b/reccon/sources/tr_5251.json new file mode 100644 index 0000000000000000000000000000000000000000..2a2537c27671ad592ab7575903eb1cabd5c1468b --- /dev/null +++ b/reccon/sources/tr_5251.json @@ -0,0 +1,141 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello everyone , and welcome to our CPR for beginners course . First of all , does anyone know what CPR stands for ?", + "emotion": "neutral", + "text": "Hello everyone , and welcome to our CPR for beginners course . First of all , does anyone know what CPR stands for ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Cardiopulmonary resuscitation !", + "emotion": "happiness", + "explanation": "knowing the answer to the question", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Cardiopulmonary resuscitation !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "That ' s right ! We apply CPR in the case of cardiac arrest or pulmonary arrest .", + "emotion": "neutral", + "text": "That ' s right ! We apply CPR in the case of cardiac arrest or pulmonary arrest .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "What does that mean ?", + "emotion": "neutral", + "text": "What does that mean ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Well , basically if your heart stops pumping blood , or your lungs stop pumping air , then we need to get them going again ! That ' s when we have to apply this procedure . Let ' s begin ! I need a volunteer .", + "emotion": "neutral", + "text": "Well , basically if your heart stops pumping blood , or your lungs stop pumping air , then we need to get them going again ! That ' s when we have to apply this procedure . Let ' s begin ! I need a volunteer .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Me ! Me !", + "emotion": "excited", + "explanation": "The person is excited to become a volunteer", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I need a volunteer ." + ], + "type": [ + "inter-personal" + ], + "text": "Me ! Me !", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Alright , come here and lay flat on your back . Let ' s suppose this young woman has stopped breathing . We must lift the person ' s chin so that we clear a pathway for air to get into the lungs . Then we place our mouth over the other person ' s mouth and blow air two or three times , like this .", + "emotion": "neutral", + "text": "Alright , come here and lay flat on your back . Let ' s suppose this young woman has stopped breathing . We must lift the person ' s chin so that we clear a pathway for air to get into the lungs . Then we place our mouth over the other person ' s mouth and blow air two or three times , like this .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Wait , what are you doing ? I ' m a married woman ! You can ' t just try to kiss me like this !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "You can ' t just try to kiss me like this !" + ], + "type": [ + "no-context" + ], + "text": "Wait , what are you doing ? I ' m a married woman ! You can ' t just try to kiss me like this !", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Madam I ' m not trying to kiss you ! I am trying to demonstrate how to apply CPR in the case of an emergency .", + "emotion": "neutral", + "text": "Madam I ' m not trying to kiss you ! I am trying to demonstrate how to apply CPR in the case of an emergency .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Well , OK . But no French kissing !", + "emotion": "neutral", + "text": "Well , OK . But no French kissing !", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "As I was saying , we blow air through the mouth in this manner . Once this is done , we must try to get the heart going again . To do this , we place our hands over the person ' s chest , and press down firmly two or three times .", + "emotion": "neutral", + "text": "As I was saying , we blow air through the mouth in this manner . Once this is done , we must try to get the heart going again . To do this , we place our hands over the person ' s chest , and press down firmly two or three times .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Wait , what are you doing ! You can ' t just kiss me then go for second base !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "You can ' t just kiss me then go for second base !" + ], + "type": [ + "no-context" + ], + "text": "Wait , what are you doing ! You can ' t just kiss me then go for second base !", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_5276.json b/reccon/sources/tr_5276.json new file mode 100644 index 0000000000000000000000000000000000000000..8f1272814ad7004e7fa225b5fc115bca6b478cdb --- /dev/null +++ b/reccon/sources/tr_5276.json @@ -0,0 +1,169 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Good morning , Mr . Huang . It's a pleasure to meet you again .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 1 + ], + "expanded emotion cause span": [ + "b", + "It's a pleasure to meet you again ." + ], + "type": [ + "latent", + "no-context" + ], + "text": "Good morning , Mr . Huang . It's a pleasure to meet you again .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Pleased to see you . Welcome to our company . I hope you have a good day .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 1, + 2 + ], + "expanded emotion cause span": [ + "b", + "It's a pleasure to meet you again .", + "Pleased to see you ." + ], + "type": [ + "latent", + "no-context", + "inter-personal" + ], + "text": "Pleased to see you . Welcome to our company . I hope you have a good day .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Thank you . Can I meet my colleagues ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 1, + 2 + ], + "expanded emotion cause span": [ + "b", + "It's a pleasure to meet you again .", + "Pleased to see you . Welcome to our company ." + ], + "type": [ + "latent", + "hybrid" + ], + "text": "Thank you . Can I meet my colleagues ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Sure , come with me . Hello , Michael , this is Steven . He will be part of your team .", + "emotion": "neutral", + "text": "Sure , come with me . Hello , Michael , this is Steven . He will be part of your team .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Hi , Steven , welcome to join us !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "welcome to join us !" + ], + "type": [ + "no-context" + ], + "text": "Hi , Steven , welcome to join us !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I ' Ve been looking forward to meeting you . I am new to the working world and would appreciate your guidance .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "welcome", + "I ' Ve been looking forward to meeting you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I ' Ve been looking forward to meeting you . I am new to the working world and would appreciate your guidance .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "That ' s right . Just call me if you need anything .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "welcome", + "I ' Ve been looking forward to meeting you ." + ], + "type": [ + "hybrid" + ], + "text": "That ' s right . Just call me if you need anything .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That's great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Just call me if you need anything ." + ], + "type": [ + "inter-personal" + ], + "text": "That's great .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Well , as the other guys are still not in , I ' ll introduce you to them later .", + "emotion": "neutral", + "text": "Well , as the other guys are still not in , I ' ll introduce you to them later .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "All right .", + "emotion": "neutral", + "text": "All right .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_5278.json b/reccon/sources/tr_5278.json new file mode 100644 index 0000000000000000000000000000000000000000..28d55a755cb08d1ec9723ccb4a5716c169036825 --- /dev/null +++ b/reccon/sources/tr_5278.json @@ -0,0 +1,179 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What did you cook ?", + "emotion": "neutral", + "text": "What did you cook ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Well , as you know I was in Thailand last month , and I took a cooking class ! So I prepared some of my favorite dishes .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I prepared some of my favorite dishes ." + ], + "type": [ + "no-context" + ], + "text": "Well , as you know I was in Thailand last month , and I took a cooking class ! So I prepared some of my favorite dishes .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Great idea ! As long as I don't get food poisoning ! So what is on the menu tonight ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "So I prepared some of my favorite dishes ." + ], + "type": [ + "inter-personal" + ], + "text": "Great idea ! As long as I don't get food poisoning ! So what is on the menu tonight ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Ok , for starters we have Tom Yam soup . It's a bit spicy , but really good !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 4 + ], + "expanded emotion cause span": [ + "I prepared some of my favorite dishes .", + "It's a bit spicy , but really good !" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Ok , for starters we have Tom Yam soup . It's a bit spicy , but really good !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "This is delicious ! The ginger and lemongrass really gives it a nice taste !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "This is delicious ! The ginger and lemongrass really gives it a nice taste !" + ], + "type": [ + "no-context" + ], + "text": "This is delicious ! The ginger and lemongrass really gives it a nice taste !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Now this next dish is one of the most famous . Foreigners call it papaya salad but the proper name is Tom Sam . It is a spicy salad made from a mix of fresh vegetables including shredded unripened papaya and tomato .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 6 + ], + "expanded emotion cause span": [ + "I prepared some of my favorite dishes .", + "Now this next dish is one of the most famous ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Now this next dish is one of the most famous . Foreigners call it papaya salad but the proper name is Tom Sam . It is a spicy salad made from a mix of fresh vegetables including shredded unripened papaya and tomato .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "This is delicious ! The combination of sour and spicy is really interesting ! I could have this everyday !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "This is delicious ! The combination of sour and spicy is really interesting !" + ], + "type": [ + "no-context" + ], + "text": "This is delicious ! The combination of sour and spicy is really interesting ! I could have this everyday !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Ok , now for the last and best dish in my opinion . This is called Pad Thai . It's stir-fried noodles with eggs , fish sauce , tamarind juice , red chili pepper plus bean sprouts , shrimp and tofu and garnished with crushed peanuts and coriander . It's practically Thailand's national dish !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I prepared some of my favorite dishes ." + ], + "type": [ + "self-contagion" + ], + "text": "Ok , now for the last and best dish in my opinion . This is called Pad Thai . It's stir-fried noodles with eggs , fish sauce , tamarind juice , red chili pepper plus bean sprouts , shrimp and tofu and garnished with crushed peanuts and coriander . It's practically Thailand's national dish !", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Wow , this is great ! I never knew Thai food was so creative and delicious !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9, + 9 + ], + "expanded emotion cause span": [ + "Ok , now for the last and best dish in my opinion . This is called Pad Thai . It's stir-fried noodles with eggs , fish sauce , tamarind juice , red chili pepper plus bean sprouts , shrimp and tofu and garnished with crushed peanuts and coriander . It's practically Thailand's national dish !", + "this is great !", + "Thai food was so creative and delicious !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Wow , this is great ! I never knew Thai food was so creative and delicious !", + "id": 9, + "source_sentences": [ + 7, + 8 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Want some more ?", + "emotion": "neutral", + "text": "Want some more ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I'm stuffed !", + "emotion": "neutral", + "text": "I'm stuffed !", + "id": 11 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_5293.json b/reccon/sources/tr_5293.json new file mode 100644 index 0000000000000000000000000000000000000000..5ffb7dfd20d04407a4a8cc07859cb087ad3af51e --- /dev/null +++ b/reccon/sources/tr_5293.json @@ -0,0 +1,175 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey , Taxi . Over here !", + "emotion": "neutral", + "text": "Hey , Taxi . Over here !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Did you call for a car service", + "emotion": "neutral", + "text": "Did you call for a car service", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yes , are you engaged", + "emotion": "neutral", + "text": "Yes , are you engaged", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Not at the moment . Where would you like me to take you", + "emotion": "neutral", + "text": "Not at the moment . Where would you like me to take you", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I am going to the airport , and I have to catch the 930 flight to New York .", + "emotion": "neutral", + "text": "I am going to the airport , and I have to catch the 930 flight to New York .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Well , it's a long way and there is roadwork near Broadway . I am not sure I can snake it in half an hour .", + "emotion": "neutral", + "text": "Well , it's a long way and there is roadwork near Broadway . I am not sure I can snake it in half an hour .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "But I can't miss the flight . It's an important meeting and it ' s waiting for me .", + "emotion": "neutral", + "text": "But I can't miss the flight . It's an important meeting and it ' s waiting for me .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "All right , I will try my best . If there aren ' t any holdups , I think we can get there in time .", + "emotion": "neutral", + "text": "All right , I will try my best . If there aren ' t any holdups , I think we can get there in time .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "That's great . How much is it to the airport", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 8 + ], + "expanded emotion cause span": [ + "I will try my best .", + "I think we can get there in time ." + ], + "type": [ + "inter-personal" + ], + "text": "That's great . How much is it to the airport", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "About $ 25 , tips not included .", + "emotion": "neutral", + "text": "About $ 25 , tips not included .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Fine . Will you please help me with the luggage", + "emotion": "neutral", + "text": "Fine . Will you please help me with the luggage", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Oh , yes , sure . Let me put it in the boot .", + "emotion": "neutral", + "text": "Oh , yes , sure . Let me put it in the boot .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Thanks very much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "Will you please help me with the luggage", + "yes , sure ." + ], + "type": [ + "hybrid" + ], + "text": "Thanks very much .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Not at all . Bang the door , please .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "Thanks" + ], + "type": [ + "inter-personal" + ], + "text": "Not at all . Bang the door , please .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Ok , let's hurry .", + "emotion": "neutral", + "text": "Ok , let's hurry .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "You are in luck . The traffic is not heavy today .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 16 + ], + "expanded emotion cause span": [ + "You are in luck . The traffic is not heavy today ." + ], + "type": [ + "no-context" + ], + "text": "You are in luck . The traffic is not heavy today .", + "id": 16 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_5297.json b/reccon/sources/tr_5297.json new file mode 100644 index 0000000000000000000000000000000000000000..88b05f3fb8e64850b0f3667176eb172dafdff5eb --- /dev/null +++ b/reccon/sources/tr_5297.json @@ -0,0 +1,149 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "do you remember where you were for the terrorist attacks on 9-11 ?", + "emotion": "neutral", + "text": "do you remember where you were for the terrorist attacks on 9-11 ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "yes , I was in my apartment in Beijing . Where were you ?", + "emotion": "neutral", + "text": "yes , I was in my apartment in Beijing . Where were you ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I was at home with my parents in New York City .", + "emotion": "neutral", + "text": "I was at home with my parents in New York City .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "really ? Did you see the hijacked planes crash into and destroy the twin towers ?", + "emotion": "neutral", + "text": "really ? Did you see the hijacked planes crash into and destroy the twin towers ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I didn't see the crash itself , but I did see the smoke and everything afterwards from my parents ' apartment building .", + "emotion": "neutral", + "text": "I didn't see the crash itself , but I did see the smoke and everything afterwards from my parents ' apartment building .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "that must have been horrible . Did you go out at all that day to see what was going on ?", + "emotion": "neutral", + "text": "that must have been horrible . Did you go out at all that day to see what was going on ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "no , we decided to stay in our apartment . With all the buses out of service and the underground trains at a halt , many people had no choice but to walk home . It was utter chaos .", + "emotion": "neutral", + "text": "no , we decided to stay in our apartment . With all the buses out of service and the underground trains at a halt , many people had no choice but to walk home . It was utter chaos .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "did you know anyone who worked in the World Trade Center ?", + "emotion": "neutral", + "text": "did you know anyone who worked in the World Trade Center ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "yes , my uncle's firm had an office in one of the towers .", + "emotion": "neutral", + "text": "yes , my uncle's firm had an office in one of the towers .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "did he survive ?", + "emotion": "neutral", + "text": "did he survive ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "unfortunately , he wasn't able to evacuate in time . He ended up dying in the tower .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "unfortunately , he wasn't able to evacuate in time . He ended up dying in the tower ." + ], + "type": [ + "no-context" + ], + "text": "unfortunately , he wasn't able to evacuate in time . He ended up dying in the tower .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I'm sorry . That must have really been a nightmarish day for you and your family .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "He ended up dying in the tower .", + "a nightmarish day for you and your family ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm sorry . That must have really been a nightmarish day for you and your family .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 13, + "speaker": "A", + "utterance": "it was . The hijackers didn't have any respect for human life not even their own .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "hijackers didn't have any respect for human life not even their own ." + ], + "type": [ + "no-context" + ], + "text": "it was . The hijackers didn't have any respect for human life not even their own .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "terrorist acts are deliberate and deadly and can affect every walk of life .", + "emotion": "neutral", + "text": "terrorist acts are deliberate and deadly and can affect every walk of life .", + "id": 14 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_534.json b/reccon/sources/tr_534.json new file mode 100644 index 0000000000000000000000000000000000000000..17f1e7758c232f1b3415e497b420ec19ef64e3b6 --- /dev/null +++ b/reccon/sources/tr_534.json @@ -0,0 +1,171 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What's the problem , Nada ? You look down in the dumps .", + "emotion": "neutral", + "text": "What's the problem , Nada ? You look down in the dumps .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I don't know . My life is a big mess . Everything is so complicated .", + "emotion": "neutral", + "text": "I don't know . My life is a big mess . Everything is so complicated .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Come on , nothing can be that bad .", + "emotion": "neutral", + "text": "Come on , nothing can be that bad .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "But promise me , you'll keep it a secret .", + "emotion": "neutral", + "text": "But promise me , you'll keep it a secret .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Ok , I promise . So what's troubling you so much ?", + "emotion": "neutral", + "text": "Ok , I promise . So what's troubling you so much ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I've fallen in love with my boss .", + "emotion": "neutral", + "text": "I've fallen in love with my boss .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Really ? Is he married ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I've fallen in love with my boss ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? Is he married ?", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Bo , of course not . He is still single .", + "emotion": "neutral", + "text": "Bo , of course not . He is still single .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Then what's your problem ?", + "emotion": "neutral", + "text": "Then what's your problem ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I try to keep it to myself . But there is a lot of gossip about us .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "I try to keep it to myself . But there is a lot of gossip about us ." + ], + "type": [ + "no-context" + ], + "text": "I try to keep it to myself . But there is a lot of gossip about us .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Oh , I see . Office romance tends to be the subject of gossip .", + "emotion": "neutral", + "text": "Oh , I see . Office romance tends to be the subject of gossip .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Worse still , he is trying to avoid me these days .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 10, + 12 + ], + "expanded emotion cause span": [ + "I try to keep it to myself . But there is a lot of gossip about us .", + "he is trying to avoid me these days ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Worse still , he is trying to avoid me these days .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Office romance is very tricky .", + "emotion": "neutral", + "text": "Office romance is very tricky .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "It gives me a lot of pressure and I feel depressed .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 10, + 12, + 14 + ], + "expanded emotion cause span": [ + "I try to keep it to myself . But there is a lot of gossip about us .", + "he is trying to avoid me these days .", + "It gives me a lot of pressure" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "It gives me a lot of pressure and I feel depressed .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Cheer up , Nada . You'll be fine .", + "emotion": "neutral", + "text": "Cheer up , Nada . You'll be fine .", + "id": 15 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_5376.json b/reccon/sources/tr_5376.json new file mode 100644 index 0000000000000000000000000000000000000000..df87b54fdbee95fd89a417a785ffed24b5dcfdcd --- /dev/null +++ b/reccon/sources/tr_5376.json @@ -0,0 +1,107 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I love Chinese food .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I love Chinese food ." + ], + "type": [ + "no-context" + ], + "text": "I love Chinese food .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What's your favorite dish or dishes ?", + "emotion": "neutral", + "text": "What's your favorite dish or dishes ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Well , I always order fried spring rolls when I go to Chinatown .", + "emotion": "neutral", + "text": "Well , I always order fried spring rolls when I go to Chinatown .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "But a Chinese person would never order that .", + "emotion": "neutral", + "text": "But a Chinese person would never order that .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Really ? But they're delicious !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "a Chinese person would never order that ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? But they're delicious !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Alex , you don't know what to order . Let's go to a Chinese restaurant together next time .", + "emotion": "neutral", + "text": "Alex , you don't know what to order . Let's go to a Chinese restaurant together next time .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "That sounds great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Let's go to a Chinese restaurant together next time ." + ], + "type": [ + "inter-personal" + ], + "text": "That sounds great .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Get ready for the best meal of your life !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "That sounds great ." + ], + "type": [ + "inter-personal" + ], + "text": "Get ready for the best meal of your life !", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_5414.json b/reccon/sources/tr_5414.json new file mode 100644 index 0000000000000000000000000000000000000000..f183f5b5ae74589b519b130636c4696524fb03dc --- /dev/null +++ b/reccon/sources/tr_5414.json @@ -0,0 +1,149 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Freeze ! Police ! Put your hands over your head !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Freeze ! Police ! Put your hands over your head !" + ], + "type": [ + "no-context" + ], + "text": "Freeze ! Police ! Put your hands over your head !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What did I do ? I haven't done anything .", + "emotion": "neutral", + "text": "What did I do ? I haven't done anything .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "You're under arrest for concealing illegal drugs .", + "emotion": "neutral", + "text": "You're under arrest for concealing illegal drugs .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "What do you mean ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "You're under arrest for concealing illegal drugs ." + ], + "type": [ + "inter-personal" + ], + "text": "What do you mean ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "You are suspected of hiding illegal drugs . So we are taking you into custody .", + "emotion": "neutral", + "text": "You are suspected of hiding illegal drugs . So we are taking you into custody .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I didn't do anything .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "You are suspected of hiding illegal drugs ." + ], + "type": [ + "inter-personal" + ], + "text": "I didn't do anything .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "We've found some heroin at your house .", + "emotion": "neutral", + "text": "We've found some heroin at your house .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "No , I didn't . I'm innocent . Those aren't mine . Whatever you found is someone else's stuff . You can't prove anything . I wasn't there when you went in , and you can't prove it's my stuff .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "We've found some heroin at your house ." + ], + "type": [ + "inter-personal" + ], + "text": "No , I didn't . I'm innocent . Those aren't mine . Whatever you found is someone else's stuff . You can't prove anything . I wasn't there when you went in , and you can't prove it's my stuff .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "That may be , but you're still under arrest . And you'd better stop talking .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "No , I didn't . I'm innocent . Those aren't mine . Whatever you found is someone else's stuff . You can't prove anything . I wasn't there when you went in , and you can't prove it's my stuff ." + ], + "type": [ + "inter-personal" + ], + "text": "That may be , but you're still under arrest . And you'd better stop talking .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I don't need your help , jerk .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "That may be , but you're still under arrest . And you'd better stop talking ." + ], + "type": [ + "inter-personal" + ], + "text": "I don't need your help , jerk .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Whatever you say .", + "emotion": "neutral", + "text": "Whatever you say .", + "id": 11 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_5431.json b/reccon/sources/tr_5431.json new file mode 100644 index 0000000000000000000000000000000000000000..c4ac6e57270f96847cba6c83e875157a0e0ee27a --- /dev/null +++ b/reccon/sources/tr_5431.json @@ -0,0 +1,164 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Can you believe her ? She is not even a hundred pounds and she is going off on how she wants to go on a diet .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "She is not even a hundred pounds and she is going off on how she wants to go on a diet ." + ], + "type": [ + "no-context" + ], + "text": "Can you believe her ? She is not even a hundred pounds and she is going off on how she wants to go on a diet .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Tell me about it . If I was as small as her , I wouldn't think about going on a diet .", + "emotion": "neutral", + "text": "Tell me about it . If I was as small as her , I wouldn't think about going on a diet .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Me too . But what are we going to do ? I have been on 4 different diets and I can't seem to lose weight .", + "emotion": "neutral", + "text": "Me too . But what are we going to do ? I have been on 4 different diets and I can't seem to lose weight .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "That's because you don't exercise . If you were more active , you wouldn't have a dieting problem .", + "emotion": "neutral", + "text": "That's because you don't exercise . If you were more active , you wouldn't have a dieting problem .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "What do you know ? You are over weight too .", + "emotion": "neutral", + "text": "What do you know ? You are over weight too .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I'm not on a diet though .", + "emotion": "neutral", + "text": "I'm not on a diet though .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I know . But I don't have someone to diet with . If we help each other and motivate each other , then I think we can lose some weight .", + "emotion": "neutral", + "text": "I know . But I don't have someone to diet with . If we help each other and motivate each other , then I think we can lose some weight .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I like ice cream too much though .", + "emotion": "neutral", + "text": "I like ice cream too much though .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "C'mon . You'll feel better and look better and as a reward you can eat a little bit of ice cream here and there .", + "emotion": "neutral", + "text": "C'mon . You'll feel better and look better and as a reward you can eat a little bit of ice cream here and there .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "It does sound appealing .", + "emotion": "neutral", + "text": "It does sound appealing .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "It's a great idea . I can't believe I didn't think of this earlier . Going on a diet with a friend to back you up is a great way to succeed .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 11 + ], + "expanded emotion cause span": [ + "great idea .", + "Going on a diet with a friend to back you up is a great way to succeed ." + ], + "type": [ + "no-context" + ], + "text": "It's a great idea . I can't believe I didn't think of this earlier . Going on a diet with a friend to back you up is a great way to succeed .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Okay . I'm in . Let's do it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 11 + ], + "expanded emotion cause span": [ + "great idea .", + "Going on a diet with a friend to back you up is a great way to succeed ." + ], + "type": [ + "inter-personal" + ], + "text": "Okay . I'm in . Let's do it .", + "id": 12, + "source_sentences": [ + 10, + 10 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Great . I'll get our plan started right away .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 11, + 12 + ], + "expanded emotion cause span": [ + "great idea .", + "Going on a diet with a friend to back you up is a great way to succeed .", + "I'm in . Let's do it ." + ], + "type": [ + "hybrid" + ], + "text": "Great . I'll get our plan started right away .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Can we start tomorrow though ?", + "emotion": "neutral", + "text": "Can we start tomorrow though ?", + "id": 14 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_5481.json b/reccon/sources/tr_5481.json new file mode 100644 index 0000000000000000000000000000000000000000..a8f9a6f7af2e3759994ea37553ac312ca9c70284 --- /dev/null +++ b/reccon/sources/tr_5481.json @@ -0,0 +1,164 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Mary , it seems that your family and friends have been calling you recently , am I right ?", + "emotion": "neutral", + "text": "Mary , it seems that your family and friends have been calling you recently , am I right ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , they have been concerned about me finding a job .", + "emotion": "neutral", + "text": "Yes , they have been concerned about me finding a job .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What do they say ?", + "emotion": "neutral", + "text": "What do they say ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "They want to recommend some jobs to me .", + "emotion": "neutral", + "text": "They want to recommend some jobs to me .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Really ? What jobs are they ?", + "emotion": "neutral", + "text": "Really ? What jobs are they ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "My father wants me to work as a trainee in his company .", + "emotion": "neutral", + "text": "My father wants me to work as a trainee in his company .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "It's great !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 6 + ], + "expanded emotion cause span": [ + "They want to recommend", + "My father wants me to work as a trainee in his company ." + ], + "type": [ + "inter-personal" + ], + "text": "It's great !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "My aunt says her company is in need of an assistant now , and she wants me to give it a try .", + "emotion": "neutral", + "text": "My aunt says her company is in need of an assistant now , and she wants me to give it a try .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "This is a good opportunity .", + "emotion": "neutral", + "text": "This is a good opportunity .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "One of my friends tells me that his company is hiring in a large scale and he wants me to go for an interview .", + "emotion": "neutral", + "text": "One of my friends tells me that his company is hiring in a large scale and he wants me to go for an interview .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "You can give it a try ! May be you will succeed .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "One of my friends tells me that his company is hiring in a large scale and he wants me to go for an interview .", + "ou will succeed ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You can give it a try ! May be you will succeed .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I know . Let me think it over .", + "emotion": "neutral", + "text": "I know . Let me think it over .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "If you have any good jobs , keep an eye for me !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 13 + ], + "expanded emotion cause span": [ + "May be you will succeed .", + "If you have any good jobs , keep an eye for me !" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "If you have any good jobs , keep an eye for me !", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "I will .", + "emotion": "happiness", + "explanation": "B is happy that A is asking for help", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "keep an eye for me !" + ], + "type": [ + "inter-personal" + ], + "text": "I will .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_554.json b/reccon/sources/tr_554.json new file mode 100644 index 0000000000000000000000000000000000000000..e7108b978f1886d915bb148ce03e4630c266fdc8 --- /dev/null +++ b/reccon/sources/tr_554.json @@ -0,0 +1,266 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "it's getting cold .", + "emotion": "neutral", + "text": "it's getting cold .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "yes . I bought a scarf yesterday . It's really nice and warm . Have a look .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I bought a scarf yesterday . It's really nice and warm ." + ], + "type": [ + "no-context" + ], + "text": "yes . I bought a scarf yesterday . It's really nice and warm . Have a look .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Oh , it's made of wool . I like the striped pattern .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I like the striped pattern ." + ], + "type": [ + "no-context" + ], + "text": "Oh , it's made of wool . I like the striped pattern .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "yes , I adore simple fashions . How does it look on me ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "I like the striped pattern .", + "I adore simple fashions" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "yes , I adore simple fashions . How does it look on me ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "it looks great , but you need something to go with it . It's too plain on its own .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "it looks great" + ], + "type": [ + "no-context" + ], + "text": "it looks great , but you need something to go with it . It's too plain on its own .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "how about this blue sweater ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 5, + 5, + 6 + ], + "expanded emotion cause span": [ + "it looks great", + "you need something to go with it . It's too plain on its own .", + "blue sweater ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "how about this blue sweater ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "that's a good idea . When did you buy it ? Is it a name brand ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "that's a good idea" + ], + "type": [ + "no-context" + ], + "text": "that's a good idea . When did you buy it ? Is it a name brand ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "yes , but I bought it when it was on sale , 50 % off the original price . OK , what do you think ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 7, + 8 + ], + "expanded emotion cause span": [ + "that's a good idea", + "name brand ?", + "yes , but I bought it when it was on sale , 50 % off the original price ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "yes , but I bought it when it was on sale , 50 % off the original price . OK , what do you think ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "that looks lovely . Just one more thing---you need a pair of earrings .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "that looks lovely" + ], + "type": [ + "no-context" + ], + "text": "that looks lovely . Just one more thing---you need a pair of earrings .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I've got a pair of pearl earrings . Here it is .", + "emotion": "happiness", + "explanation": "the speaker is getting help and appreciation from the listener on getting dressed", + "expanded emotion cause evidence": [ + 9, + 9, + 10 + ], + "expanded emotion cause span": [ + "that looks lovely", + "you need a pair of earrings .", + "I've got a pair of pearl earrings ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I've got a pair of pearl earrings . Here it is .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "perfect !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 9, + 10, + 11 + ], + "expanded emotion cause span": [ + "that looks lovely", + "you need a pair of earrings .", + "I've got a pair of pearl earrings .", + "perfect !" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "perfect !", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "you have good fashion sense , Karen .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "perfect !", + "you have good fashion sense" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "you have good fashion sense , Karen .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "thanks . We should be ourselves . There are so many fashion victims out there .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "you have good fashion sense" + ], + "type": [ + "inter-personal" + ], + "text": "thanks . We should be ourselves . There are so many fashion victims out there .", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 14, + "speaker": "B", + "utterance": "yes , but with our sense we'll always look good .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "with our sense we'll always look good ." + ], + "type": [ + "no-context" + ], + "text": "yes , but with our sense we'll always look good .", + "id": 14 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_5629.json b/reccon/sources/tr_5629.json new file mode 100644 index 0000000000000000000000000000000000000000..c9a2f421712bb614058660436c13f2944f970701 --- /dev/null +++ b/reccon/sources/tr_5629.json @@ -0,0 +1,151 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello Mary . I haven ' t seen you for ages . Are you still seeing Paul ?", + "emotion": "neutral", + "text": "Hello Mary . I haven ' t seen you for ages . Are you still seeing Paul ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "No . We broke up last month . I ' m taking a break from dating for a while .", + "emotion": "neutral", + "text": "No . We broke up last month . I ' m taking a break from dating for a while .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Did you break up amicably ? Sometimes couples row a lot before splitting up .", + "emotion": "neutral", + "text": "Did you break up amicably ? Sometimes couples row a lot before splitting up .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "We just decided to stop seeing each other . It was all very amicable . Are you still going out with mike ?", + "emotion": "neutral", + "text": "We just decided to stop seeing each other . It was all very amicable . Are you still going out with mike ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Yes , I am . We ' re thinking about getting engaged . We ' Ve been dating for over a year now .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "We ' re thinking about getting engaged . We ' Ve been dating for over a year now ." + ], + "type": [ + "no-context" + ], + "text": "Yes , I am . We ' re thinking about getting engaged . We ' Ve been dating for over a year now .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Good for you ! Have you seen Kelly recently ? Is she still dating nick ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "We ' re thinking about getting engaged . We ' Ve been dating for over a year now ." + ], + "type": [ + "inter-personal" + ], + "text": "Good for you ! Have you seen Kelly recently ? Is she still dating nick ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I havn't seen her for a while . She stopped seeing nick because he was cheating on her . He was seeing a girl form his office . One day , she saw them holding hands and ended the relationship immediately .", + "emotion": "neutral", + "text": "I havn't seen her for a while . She stopped seeing nick because he was cheating on her . He was seeing a girl form his office . One day , she saw them holding hands and ended the relationship immediately .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "She was right to do that . I heard the Neil and Tina getting married soon .", + "emotion": "neutral", + "text": "She was right to do that . I heard the Neil and Tina getting married soon .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Really ? They ' Ve been together for a long time . When are they getting married ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "the Neil and Tina getting married" + ], + "type": [ + "inter-personal" + ], + "text": "Really ? They ' Ve been together for a long time . When are they getting married ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I think it ' s 26th September . I ' ll check and make sure that Tina remembers to invite you to the hen night .", + "emotion": "neutral", + "text": "I think it ' s 26th September . I ' ll check and make sure that Tina remembers to invite you to the hen night .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Thanks . Hey , look at that guy over there . I think he fancies you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "I ' ll check and make sure that Tina remembers to invite you" + ], + "type": [ + "inter-personal" + ], + "text": "Thanks . Hey , look at that guy over there . I think he fancies you .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "He certainly looks interested , doesn ' t he ? Shall we invite him over to our table ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "I think he fancies you .", + "He certainly looks interested ," + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "He certainly looks interested , doesn ' t he ? Shall we invite him over to our table ?", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_5685.json b/reccon/sources/tr_5685.json new file mode 100644 index 0000000000000000000000000000000000000000..bde200c511d06da27d0fd43549c709b41708cf99 --- /dev/null +++ b/reccon/sources/tr_5685.json @@ -0,0 +1,144 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Can you help me pick out a gift for my niece ?", + "emotion": "neutral", + "text": "Can you help me pick out a gift for my niece ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Most normal little girls go wild over Barbie dolls .", + "emotion": "neutral", + "text": "Most normal little girls go wild over Barbie dolls .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "That sounds good . Let me see one .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "little girls go wild over Barbie dolls ." + ], + "type": [ + "inter-personal" + ], + "text": "That sounds good . Let me see one .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Here's the latest model -- Digital Barbie .", + "emotion": "neutral", + "text": "Here's the latest model -- Digital Barbie .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Oh , she's nice . How much is she ?", + "emotion": "neutral", + "text": "Oh , she's nice . How much is she ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Why , she's only $ 29 . 95 .", + "emotion": "neutral", + "text": "Why , she's only $ 29 . 95 .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Well , that's reasonable . I'll take it .", + "emotion": "neutral", + "text": "Well , that's reasonable . I'll take it .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Excellent . Would you like anything else ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I'll take it ." + ], + "type": [ + "inter-personal" + ], + "text": "Excellent . Would you like anything else ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "No , thank you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "Well , that's reasonable . I'll take it .", + "Would you like anything else ?" + ], + "type": [ + "hybrid" + ], + "text": "No , thank you .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "The total will be $ 32 . 42 . Will that be cash ?", + "emotion": "neutral", + "text": "The total will be $ 32 . 42 . Will that be cash ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Oh , cash will be fine .", + "emotion": "neutral", + "text": "Oh , cash will be fine .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Here's your change . Thank you for shopping with us .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 12 + ], + "expanded emotion cause span": [ + "I'll take it .", + "Thank you for shopping with us ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Here's your change . Thank you for shopping with us .", + "id": 12, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_5723.json b/reccon/sources/tr_5723.json new file mode 100644 index 0000000000000000000000000000000000000000..f30791a2cff490efb5f35a7ae8eda2565467fcf8 --- /dev/null +++ b/reccon/sources/tr_5723.json @@ -0,0 +1,151 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Have you bought War Craft 2 yet ?", + "emotion": "neutral", + "text": "Have you bought War Craft 2 yet ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yeah ! I bought it the day it was released .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Yeah ! I bought it the day it was released ." + ], + "type": [ + "no-context" + ], + "text": "Yeah ! I bought it the day it was released .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "How do you like it ?", + "emotion": "neutral", + "text": "How do you like it ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It's a great game . There are a lot of new characters .", + "emotion": "neutral", + "text": "It's a great game . There are a lot of new characters .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Did it cost very much", + "emotion": "neutral", + "text": "Did it cost very much", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "It cost about thirty . Most games cost about that much .", + "emotion": "neutral", + "text": "It cost about thirty . Most games cost about that much .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Mechwarrior is such a good game . The graphics are awesome !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Mechwarrior is such a good game . The graphics are awesome !" + ], + "type": [ + "no-context" + ], + "text": "Mechwarrior is such a good game . The graphics are awesome !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Oh , I know what you mean . I'm addicted to that game .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Mechwarrior is such a good game . The graphics are awesome !" + ], + "type": [ + "inter-personal" + ], + "text": "Oh , I know what you mean . I'm addicted to that game .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "My roommate always wants to play it . But I told her to buy her own game .", + "emotion": "neutral", + "text": "My roommate always wants to play it . But I told her to buy her own game .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Yeah , my roommate likes to watch me play . He says it's like watching a movie .", + "emotion": "neutral", + "text": "Yeah , my roommate likes to watch me play . He says it's like watching a movie .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I've never seen such good graphics .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I've never seen such good graphics ." + ], + "type": [ + "no-context" + ], + "text": "I've never seen such good graphics .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "And I've never heard such good sound in a game .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "I've never seen such good graphics .", + "And I've never heard such good sound in a game ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "And I've never heard such good sound in a game .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_5729.json b/reccon/sources/tr_5729.json new file mode 100644 index 0000000000000000000000000000000000000000..df005a28b63154cf24cf9fff48e0a49e4bfcdba6 --- /dev/null +++ b/reccon/sources/tr_5729.json @@ -0,0 +1,91 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Mmm . Nice and crunchy . And they leave a space uncovered for you to hold ...", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Mmm . Nice and crunchy . And they leave a space uncovered for you to hold ..." + ], + "type": [ + "no-context" + ], + "text": "Mmm . Nice and crunchy . And they leave a space uncovered for you to hold ...", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "They're so much fun to eat . You can suck all the coating off first ...", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "They're so much fun to eat . You can suck all the coating off first ..." + ], + "type": [ + "no-context" + ], + "text": "They're so much fun to eat . You can suck all the coating off first ...", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Or just stuff the whole thing in your mouth at once !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Or just stuff the whole thing in your mouth at once !" + ], + "type": [ + "no-context" + ], + "text": "Or just stuff the whole thing in your mouth at once !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "But that way you're not savoring it .", + "emotion": "neutral", + "text": "But that way you're not savoring it .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Whatever . Give me another pack .", + "emotion": "neutral", + "text": "Whatever . Give me another pack .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Hey ! The movie hasn't even started and they're almost gone !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Give me another pack ." + ], + "type": [ + "inter-personal" + ], + "text": "Hey ! The movie hasn't even started and they're almost gone !", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_5737.json b/reccon/sources/tr_5737.json new file mode 100644 index 0000000000000000000000000000000000000000..3c907dc3f2f7d0697aead212aa9ef47d6ebe296a --- /dev/null +++ b/reccon/sources/tr_5737.json @@ -0,0 +1,112 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "They must have got in through the kitchen window .", + "emotion": "neutral", + "text": "They must have got in through the kitchen window .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "If only we'd remember to close it .", + "emotion": "neutral", + "text": "If only we'd remember to close it .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I am afraid your diamond bracelet has gone , darling !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I am afraid your diamond bracelet has gone ," + ], + "type": [ + "no-context" + ], + "text": "I am afraid your diamond bracelet has gone , darling !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I wish I'd put it in the bank .", + "emotion": "neutral", + "text": "I wish I'd put it in the bank .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Look ! they've taken your fur coat too .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "they've taken your fur coat too ." + ], + "type": [ + "no-context" + ], + "text": "Look ! they've taken your fur coat too .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I know , I am sorry I ever bought it .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3, + 5, + 6 + ], + "expanded emotion cause span": [ + "I am afraid your diamond bracelet has gone ,", + "they've taken your fur coat too .", + "I am sorry I ever bought it ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I know , I am sorry I ever bought it .", + "id": 6, + "source_sentences": [ + 2, + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I noticed they've taken our radio and left the television .", + "emotion": "neutral", + "text": "I noticed they've taken our radio and left the television .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "It's a pity they didn't take the tele . We need a new one . Anyway we can claim for all this from the insurance company .", + "emotion": "neutral", + "text": "It's a pity they didn't take the tele . We need a new one . Anyway we can claim for all this from the insurance company .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I wish we could , but we can't , you see , we are not insured .", + "emotion": "neutral", + "text": "I wish we could , but we can't , you see , we are not insured .", + "id": 9 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_5748.json b/reccon/sources/tr_5748.json new file mode 100644 index 0000000000000000000000000000000000000000..f9ab28987e9641de2c34a7f839c226fd0905f979 --- /dev/null +++ b/reccon/sources/tr_5748.json @@ -0,0 +1,107 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey Ted , I saw this ad in the paper . You should take a look .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "saw this ad in the paper" + ], + "type": [ + "no-context" + ], + "text": "Hey Ted , I saw this ad in the paper . You should take a look .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What is it ?", + "emotion": "neutral", + "text": "What is it ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "It ' s for a job . It looks perfect for you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "It looks perfect for you ." + ], + "type": [ + "no-context" + ], + "text": "It ' s for a job . It looks perfect for you .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Let ' s see ... ' Wanted , manager for up-and-coming firm . Must have good organizational skills . Experience a plus . Please contact Betty Sue . ' Oh , I don ' t know ...", + "emotion": "neutral", + "text": "Let ' s see ... ' Wanted , manager for up-and-coming firm . Must have good organizational skills . Experience a plus . Please contact Betty Sue . ' Oh , I don ' t know ...", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Come on , what have you got to lose ?", + "emotion": "neutral", + "text": "Come on , what have you got to lose ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "What about my resume ?", + "emotion": "neutral", + "text": "What about my resume ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Here , I'll help you type one up .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "It looks perfect for you ." + ], + "type": [ + "self-contagion" + ], + "text": "Here , I'll help you type one up .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Thanks , Mary . You ' re a real pal . I'll call now to set up an interview .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I'll help you type one up ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks , Mary . You ' re a real pal . I'll call now to set up an interview .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_58.json b/reccon/sources/tr_58.json new file mode 100644 index 0000000000000000000000000000000000000000..52242bf655a53e6fdd0f3d2d4211b90e84f55b85 --- /dev/null +++ b/reccon/sources/tr_58.json @@ -0,0 +1,110 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What do you do in your free time , Nancy ?", + "emotion": "neutral", + "text": "What do you do in your free time , Nancy ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Well , I like playing the violin .", + "emotion": "neutral", + "text": "Well , I like playing the violin .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Really ? How long have you been playing the violin ?", + "emotion": "neutral", + "text": "Really ? How long have you been playing the violin ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "About ten years so far . I started learning when I was in middle school .", + "emotion": "neutral", + "text": "About ten years so far . I started learning when I was in middle school .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "That's really interesting .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "About ten years so far . I started learning when I was in middle school ." + ], + "type": [ + "inter-personal" + ], + "text": "That's really interesting .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Sure . So what about you ? Do you have any hobbies ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "That's really interesting ." + ], + "type": [ + "inter-personal" + ], + "text": "Sure . So what about you ? Do you have any hobbies ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Well , I like collecting matchbox ! I'm not sure if that counts , though .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I like collecting matchbox !" + ], + "type": [ + "no-context" + ], + "text": "Well , I like collecting matchbox ! I'm not sure if that counts , though .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Of course it does . Everybody has his own hobby .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 7 + ], + "expanded emotion cause span": [ + "That's really interesting .", + "I like collecting matchbox" + ], + "type": [ + "inter-personal" + ], + "text": "Of course it does . Everybody has his own hobby .", + "id": 8, + "source_sentences": [ + 4, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_5802.json b/reccon/sources/tr_5802.json new file mode 100644 index 0000000000000000000000000000000000000000..e18beb38ee7810cb34085936f2b70b8442cdeb02 --- /dev/null +++ b/reccon/sources/tr_5802.json @@ -0,0 +1,177 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What a busy week !", + "emotion": "neutral", + "text": "What a busy week !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Really ! I've never seen so much work .", + "emotion": "neutral", + "text": "Really ! I've never seen so much work .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Right . How are you going to spend your weekend ?", + "emotion": "neutral", + "text": "Right . How are you going to spend your weekend ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I don't know . I have no idea .", + "emotion": "neutral", + "text": "I don't know . I have no idea .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Would you like to play some tennis with me before going home ?", + "emotion": "neutral", + "text": "Would you like to play some tennis with me before going home ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I'm not good at sports , I have never played tennis , and I know I would be terrible .", + "emotion": "neutral", + "text": "I'm not good at sports , I have never played tennis , and I know I would be terrible .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You should try it . It ' s a great game . Come on , let me help you . I'm a good player , and a good teacher , too . What do you say ?", + "emotion": "neutral", + "text": "You should try it . It ' s a great game . Come on , let me help you . I'm a good player , and a good teacher , too . What do you say ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "OK , but don't say I didn't warn you .", + "emotion": "neutral", + "text": "OK , but don't say I didn't warn you .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "That was a pretty good shot , Mary .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "That was a pretty good shot" + ], + "type": [ + "no-context" + ], + "text": "That was a pretty good shot , Mary .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Thanks . This is fun !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "That was a pretty good shot", + "This is fun !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thanks . This is fun !", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Let me help you with your serve .", + "emotion": "neutral", + "text": "Let me help you with your serve .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "No one has ever tried to show me how to play a sport before . Maybe I should learn to do something .", + "emotion": "neutral", + "text": "No one has ever tried to show me how to play a sport before . Maybe I should learn to do something .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Of course , you can . All you need is a little help and a lot of practice .", + "emotion": "neutral", + "text": "Of course , you can . All you need is a little help and a lot of practice .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Do you really think I can be a good player ?", + "emotion": "neutral", + "text": "Do you really think I can be a good player ?", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Well , maybe not a Michael Zhang , but better than the average . Person would you like to play again Wednesday ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "better than the average ." + ], + "type": [ + "no-context" + ], + "text": "Well , maybe not a Michael Zhang , but better than the average . Person would you like to play again Wednesday ?", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Yes . This has been fun .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15, + 16 + ], + "expanded emotion cause span": [ + "would you like to play again Wednesday ?", + "This has been fun ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes . This has been fun .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_5857.json b/reccon/sources/tr_5857.json new file mode 100644 index 0000000000000000000000000000000000000000..e6f47ec7bdeed5383029c7a728a0c6001f8bdb0b --- /dev/null +++ b/reccon/sources/tr_5857.json @@ -0,0 +1,114 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What do you think ?", + "emotion": "neutral", + "text": "What do you think ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It looks great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "looks great ." + ], + "type": [ + "no-context" + ], + "text": "It looks great .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I would like to purchase it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "looks great .", + "I would like to purchase it ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I would like to purchase it .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Will this be cash or charge ?", + "emotion": "neutral", + "text": "Will this be cash or charge ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Here , take my credit card .", + "emotion": "neutral", + "text": "Here , take my credit card .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Just sign here , please .", + "emotion": "neutral", + "text": "Just sign here , please .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Sure . Here you go .", + "emotion": "happiness", + "explanation": "A is happy for a latent reason", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Sure . Here you go .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Here's your receipt . Have a nice day .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "Sure . Here you go .", + "Have a nice day ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Here's your receipt . Have a nice day .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_5869.json b/reccon/sources/tr_5869.json new file mode 100644 index 0000000000000000000000000000000000000000..ecfb69cdd9441bb23cf86b125e16ba79fa71c4d0 --- /dev/null +++ b/reccon/sources/tr_5869.json @@ -0,0 +1,145 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "have you bought a present for jim ' s birthday yet ?", + "emotion": "neutral", + "text": "have you bought a present for jim ' s birthday yet ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "no , I haven ' t . I can ' t think of anything to get him .", + "emotion": "neutral", + "text": "no , I haven ' t . I can ' t think of anything to get him .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I ' m having the same problem . I want to get something really special . Jim always seem to know exactly what to get people as gifts .", + "emotion": "neutral", + "text": "I ' m having the same problem . I want to get something really special . Jim always seem to know exactly what to get people as gifts .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I know . He bought me that beautiful sweater for my birthday . It was exactly what I wanted . And it fit me perfectly !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "Jim always seem to know exactly what to get people as gifts .", + "He bought me that beautiful sweater for my birthday . It was exactly what I wanted . And it fit me perfectly !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I know . He bought me that beautiful sweater for my birthday . It was exactly what I wanted . And it fit me perfectly !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "he bought me an iron .", + "emotion": "neutral", + "text": "he bought me an iron .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "that doesn ' t sound like a great present .", + "emotion": "neutral", + "text": "that doesn ' t sound like a great present .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "maybe not , but my iron was getting old . In fact , it stopped working the week after jim bought me the new one . It ' s as if he knew that my old iron would soon stop working !", + "emotion": "neutral", + "text": "maybe not , but my iron was getting old . In fact , it stopped working the week after jim bought me the new one . It ' s as if he knew that my old iron would soon stop working !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "let ' s think . He loves football , doesn ' t he ? I saw signed photographs of famous footballers in a shop near hear . Let ' s go and have a look . You know which team he supports , don ' t you ?", + "emotion": "neutral", + "text": "let ' s think . He loves football , doesn ' t he ? I saw signed photographs of famous footballers in a shop near hear . Let ' s go and have a look . You know which team he supports , don ' t you ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "yes , I do . Let ' s go . We should be able to find something suitable . We should get him something old ... something historic .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "You know which team he supports", + "yes , I do ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "yes , I do . Let ' s go . We should be able to find something suitable . We should get him something old ... something historic .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "it ' ll be an expensive present , but we can share the cost .", + "emotion": "neutral", + "text": "it ' ll be an expensive present , but we can share the cost .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I ' ll be happy to get him something special , even if it coasts a little extra .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I ' ll be happy to get him something special" + ], + "type": [ + "no-context" + ], + "text": "I ' ll be happy to get him something special , even if it coasts a little extra .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "yes . He always get us special gift . We should repay his kindness .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "yes . He always get us special gift . We should repay his kindness ." + ], + "type": [ + "no-context" + ], + "text": "yes . He always get us special gift . We should repay his kindness .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_587.json b/reccon/sources/tr_587.json new file mode 100644 index 0000000000000000000000000000000000000000..dd7fba35d6a33c60acbca2959ee045a7378e343a --- /dev/null +++ b/reccon/sources/tr_587.json @@ -0,0 +1,125 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Steven , why are you so depressed ?", + "emotion": "neutral", + "text": "Steven , why are you so depressed ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'm feeling very sad . I just read the newspaper .", + "emotion": "neutral", + "text": "I'm feeling very sad . I just read the newspaper .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What's the news ?", + "emotion": "neutral", + "text": "What's the news ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "According to the newspaper , the town was razed by an earthquake and more than 10 thousand people died in the earthquake .", + "emotion": "neutral", + "text": "According to the newspaper , the town was razed by an earthquake and more than 10 thousand people died in the earthquake .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "It's horrible .", + "emotion": "neutral", + "text": "It's horrible .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yeah , we have to do something to help the people in the stricken area .", + "emotion": "neutral", + "text": "Yeah , we have to do something to help the people in the stricken area .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yes . How about donating some money ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "we have to do something to help the people in the stricken area ." + ], + "type": [ + "inter-personal" + ], + "text": "Yes . How about donating some money ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "It's a good idea . But where can we donate money ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "How about donating some money ?" + ], + "type": [ + "inter-personal" + ], + "text": "It's a good idea . But where can we donate money ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Just find the answer through Internet .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "we have to do something to help the people in the stricken area ." + ], + "type": [ + "inter-personal" + ], + "text": "Just find the answer through Internet .", + "id": 9, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Yes , let's do it now .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "let's do it now ." + ], + "type": [ + "no-context" + ], + "text": "Yes , let's do it now .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_5961.json b/reccon/sources/tr_5961.json new file mode 100644 index 0000000000000000000000000000000000000000..8041d1f7eeb49856d9530c9bfb41507b4fb4a71f --- /dev/null +++ b/reccon/sources/tr_5961.json @@ -0,0 +1,213 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "May I help you ?", + "emotion": "neutral", + "text": "May I help you ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , I would like to return these slacks .", + "emotion": "neutral", + "text": "Yes , I would like to return these slacks .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Alright . Do you have your receipt ?", + "emotion": "neutral", + "text": "Alright . Do you have your receipt ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes . Here it is . I bought them last week .", + "emotion": "neutral", + "text": "Yes . Here it is . I bought them last week .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "And why are you returning them ?", + "emotion": "neutral", + "text": "And why are you returning them ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I bought them to go with a blouse of mine . But they don't really match .", + "emotion": "neutral", + "text": "I bought them to go with a blouse of mine . But they don't really match .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I see . Oh , wait . Ma'am , I'm sorry . These slacks were on sale .", + "emotion": "sadness", + "explanation": "Cant process the return request as the items are not on sale anymore", + "expanded emotion cause evidence": [ + 7, + 9 + ], + "expanded emotion cause span": [ + "These slacks were on sale .", + "we don't allow returns on sale items ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I see . Oh , wait . Ma'am , I'm sorry . These slacks were on sale .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yes , they were thirty percent off .", + "emotion": "neutral", + "text": "Yes , they were thirty percent off .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I'm sorry , but we don't allow returns on sale items .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 7, + 9 + ], + "expanded emotion cause span": [ + "These slacks were on sale .", + "we don't allow returns on sale items ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I'm sorry , but we don't allow returns on sale items .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I know many stores have that policy . But I have returned sale items here before .", + "emotion": "neutral", + "text": "I know many stores have that policy . But I have returned sale items here before .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I'm sorry , but we usually don't do it . It is our policy .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 7, + 9 + ], + "expanded emotion cause span": [ + "These slacks were on sale .", + "we don't allow returns on sale items ." + ], + "type": [ + "self-contagion" + ], + "text": "I'm sorry , but we usually don't do it . It is our policy .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I just bought these slacks a week ago . And I am a regular customer here . Can you make an exception this time ?", + "emotion": "neutral", + "text": "I just bought these slacks a week ago . And I am a regular customer here . Can you make an exception this time ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Well . Let me talk to the manager for a moment . Madam , the manager says can do it this time .", + "emotion": "neutral", + "text": "Well . Let me talk to the manager for a moment . Madam , the manager says can do it this time .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Good . I'm a regular customer here . I am glad you can make an exception for me .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "the manager says can do it this time ." + ], + "type": [ + "inter-personal" + ], + "text": "Good . I'm a regular customer here . I am glad you can make an exception for me .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Please show me your receipt again .", + "emotion": "neutral", + "text": "Please show me your receipt again .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Here it is .", + "emotion": "neutral", + "text": "Here it is .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "I will have to give you store credit , Madam . If you can find something else you like in the store , you can use the credit .", + "emotion": "neutral", + "text": "I will have to give you store credit , Madam . If you can find something else you like in the store , you can use the credit .", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "Store credit is okay with me . I'm sure I will find something I like . I shop here a lot .", + "emotion": "neutral", + "text": "Store credit is okay with me . I'm sure I will find something I like . I shop here a lot .", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "We appreciate your business , Madam .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 18 + ], + "expanded emotion cause span": [ + "Store credit is okay with me . I'm sure I will find something I like . I shop here a lot ." + ], + "type": [ + "inter-personal" + ], + "text": "We appreciate your business , Madam .", + "id": 19, + "source_sentences": [ + 17 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_5981.json b/reccon/sources/tr_5981.json new file mode 100644 index 0000000000000000000000000000000000000000..85dcac4f87a9f480780b865ff44286834757702f --- /dev/null +++ b/reccon/sources/tr_5981.json @@ -0,0 +1,140 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Taxi .", + "emotion": "neutral", + "text": "Taxi .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Get on , PLS . Where do you wanna go ?", + "emotion": "neutral", + "text": "Get on , PLS . Where do you wanna go ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Thank you . Pls hurry , I am late . Can I get to the Battery Park before 4 ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Get on , PLS ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . Pls hurry , I am late . Can I get to the Battery Park before 4 ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "All right , Miss . I think we will get there if there are no delays on the way .", + "emotion": "neutral", + "text": "All right , Miss . I think we will get there if there are no delays on the way .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "How exactly do you figure out the car fare ?", + "emotion": "neutral", + "text": "How exactly do you figure out the car fare ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "According to the kilometer rate , the first five kilometers are 4 dollars and every kilometer extra costs 50 cents .", + "emotion": "neutral", + "text": "According to the kilometer rate , the first five kilometers are 4 dollars and every kilometer extra costs 50 cents .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Oh , I see .", + "emotion": "neutral", + "text": "Oh , I see .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Here we are , Miss .", + "emotion": "neutral", + "text": "Here we are , Miss .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Thank you . How much do I owe you ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Here we are" + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . How much do I owe you ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "You owe me 19 dollars .", + "emotion": "neutral", + "text": "You owe me 19 dollars .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "That's 20 dollars . Keep the change !", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Here we are" + ], + "type": [ + "inter-personal" + ], + "text": "That's 20 dollars . Keep the change !", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Thank you !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "That's 20 dollars . Keep the change !" + ], + "type": [ + "inter-personal" + ], + "text": "Thank you !", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_5984.json b/reccon/sources/tr_5984.json new file mode 100644 index 0000000000000000000000000000000000000000..05cef13e049caa747cb38108b5f33ce28cac1540 --- /dev/null +++ b/reccon/sources/tr_5984.json @@ -0,0 +1,113 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Can I help you , Madam ?", + "emotion": "neutral", + "text": "Can I help you , Madam ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes . I'd like to buy a sweater for my husband . Which style is the latest ?", + "emotion": "neutral", + "text": "Yes . I'd like to buy a sweater for my husband . Which style is the latest ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "These are all the latest fashion . How do you like this white turtleneck one ?", + "emotion": "neutral", + "text": "These are all the latest fashion . How do you like this white turtleneck one ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I like this style . But do you have any other colors ? I feel that this color doesn't suit his complexion .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I like this style ." + ], + "type": [ + "no-context" + ], + "text": "I like this style . But do you have any other colors ? I feel that this color doesn't suit his complexion .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "We also have it in grey .", + "emotion": "neutral", + "text": "We also have it in grey .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Great ! I will take it . And could you suggest a pair of trousers to match this sweater ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "We also have it in grey ." + ], + "type": [ + "inter-personal" + ], + "text": "Great ! I will take it . And could you suggest a pair of trousers to match this sweater ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "It's my pleasure . I think this pair of jeans will suit the sweater well .", + "emotion": "happiness", + "explanation": "A is happy about B asking suggestion", + "expanded emotion cause evidence": [ + 6, + 6 + ], + "expanded emotion cause span": [ + "I will take it .", + "could you suggest" + ], + "type": [ + "inter-personal" + ], + "text": "It's my pleasure . I think this pair of jeans will suit the sweater well .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Let me see . Yes , they are perfectly matched !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 8 + ], + "expanded emotion cause span": [ + "We also have it in grey .", + "they are perfectly matched !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Let me see . Yes , they are perfectly matched !", + "id": 8, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_60.json b/reccon/sources/tr_60.json new file mode 100644 index 0000000000000000000000000000000000000000..8427d42b81f409396cf33ff09162e5662b8c6145 --- /dev/null +++ b/reccon/sources/tr_60.json @@ -0,0 +1,186 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What sports do you like to play ?", + "emotion": "neutral", + "text": "What sports do you like to play ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I like baseball and basketball .", + "emotion": "neutral", + "text": "I like baseball and basketball .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "How about football ?", + "emotion": "neutral", + "text": "How about football ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "In my country football is brand new , so I never learned the game when I was younger .", + "emotion": "neutral", + "text": "In my country football is brand new , so I never learned the game when I was younger .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "It's a very popular game in America .", + "emotion": "neutral", + "text": "It's a very popular game in America .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yeah . I heard a lot about it . Is it really that fun ?", + "emotion": "neutral", + "text": "Yeah . I heard a lot about it . Is it really that fun ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "For me , it's one of those games that are fun to both watch and play .", + "emotion": "neutral", + "text": "For me , it's one of those games that are fun to both watch and play .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Are you a football player ?", + "emotion": "neutral", + "text": "Are you a football player ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "No , I just for fun with my friends . We play two hand touch or flag football . We're too old to play tackle football .", + "emotion": "neutral", + "text": "No , I just for fun with my friends . We play two hand touch or flag football . We're too old to play tackle football .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "What is two hand touch and flag football ?", + "emotion": "neutral", + "text": "What is two hand touch and flag football ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Instead of tackling somebody , you just have to touch them with two hands , or if it is flag football , grab the flag that the ball carrier is wearing .", + "emotion": "neutral", + "text": "Instead of tackling somebody , you just have to touch them with two hands , or if it is flag football , grab the flag that the ball carrier is wearing .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I see . It's safer then right ?", + "emotion": "neutral", + "text": "I see . It's safer then right ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Exactly . We play every Saturdays on the field by the tennis courts . If you want to learn and play a little , you're welcome to join us .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 9, + 12, + 13 + ], + "expanded emotion cause span": [ + "fun to both watch and play .", + "I just for fun with my friends .", + "It's safer then right ?", + "We play every Saturdays on the field by the tennis courts ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Exactly . We play every Saturdays on the field by the tennis courts . If you want to learn and play a little , you're welcome to join us .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "I'll give it a try . Give me a call and let's go down together .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 12, + 13 + ], + "expanded emotion cause span": [ + "fun to both watch and play .", + "It's safer then right ?", + "If you want to learn and play a little , you're welcome to join us ." + ], + "type": [ + "hybrid" + ], + "text": "I'll give it a try . Give me a call and let's go down together .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Ok . I'll call you Saturday morning .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "I'll give it a try . Give me a call and let's go down together ." + ], + "type": [ + "inter-personal" + ], + "text": "Ok . I'll call you Saturday morning .", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 12, + 13 + ], + "expanded emotion cause span": [ + "fun to both watch and play .", + "It's safer then right ?", + "If you want to learn and play a little , you're welcome to join us ." + ], + "type": [ + "hybrid" + ], + "text": "Great .", + "id": 16 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_6005.json b/reccon/sources/tr_6005.json new file mode 100644 index 0000000000000000000000000000000000000000..68f3e8dfbf5ce8f37a7a5d850d3b008486d43a26 --- /dev/null +++ b/reccon/sources/tr_6005.json @@ -0,0 +1,212 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello , Mr . Green . This is Lin Tong . How are you ?", + "emotion": "neutral", + "text": "Hello , Mr . Green . This is Lin Tong . How are you ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hi , Mr . Lin . I am leaving tomorrow and I am just packing .", + "emotion": "neutral", + "text": "Hi , Mr . Lin . I am leaving tomorrow and I am just packing .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Oh , sorry to interrupt you . But I am calling to say goodbye to you . I am awfully sorry to tell you that I am afraid I could not see you off at the airport tomorrow , because I will have to attend a very important meeting .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I am afraid I could not see you off" + ], + "type": [ + "no-context" + ], + "text": "Oh , sorry to interrupt you . But I am calling to say goodbye to you . I am awfully sorry to tell you that I am afraid I could not see you off at the airport tomorrow , because I will have to attend a very important meeting .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It doesn't matter , Mr . Lin . I can understand . I know you are always very busy . Work must come first .", + "emotion": "neutral", + "text": "It doesn't matter , Mr . Lin . I can understand . I know you are always very busy . Work must come first .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Thanks a lot . You have been here for almost three weeks . How time flies !", + "emotion": "neutral", + "text": "Thanks a lot . You have been here for almost three weeks . How time flies !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yes . And I would like to convey my thanks to you for your help during my stay here in Nanjing .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "thanks to you for your help" + ], + "type": [ + "no-context" + ], + "text": "Yes . And I would like to convey my thanks to you for your help during my stay here in Nanjing .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "It is our pleasure . It has been a great pleasure to work with you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "thanks to you for your help", + "a great pleasure to work with you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It is our pleasure . It has been a great pleasure to work with you .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Me too . I am looking forward to cooperating with you again .", + "emotion": "neutral", + "text": "Me too . I am looking forward to cooperating with you again .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Really ? Great ! We will . Well , what's your flight number ? When are you leaving tomorrow ?", + "emotion": "neutral", + "text": "Really ? Great ! We will . Well , what's your flight number ? When are you leaving tomorrow ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "It's Flight No . 104 , Northey Airlines , which leaves at ten O'dock tomorrow evening .", + "emotion": "neutral", + "text": "It's Flight No . 104 , Northey Airlines , which leaves at ten O'dock tomorrow evening .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "OK , I will send someone to see you off .", + "emotion": "neutral", + "text": "OK , I will send someone to see you off .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "That is so thoughtful of you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I will send someone to see you off ." + ], + "type": [ + "inter-personal" + ], + "text": "That is so thoughtful of you .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "My pleasure . Take care and have a nice trip .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "That is so thoughtful of you ." + ], + "type": [ + "inter-personal" + ], + "text": "My pleasure . Take care and have a nice trip .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Thanks a lot . My wife and I will be welcoming and looking forward to your visit .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 13 + ], + "expanded emotion cause span": [ + "I will send someone to see you off .", + "Take care and have a nice trip ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks a lot . My wife and I will be welcoming and looking forward to your visit .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Let's call it a deal . Hope to see you again soon . Keep in touch then . Byebye .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "My wife and I will be welcoming and looking forward to your visit ." + ], + "type": [ + "inter-personal" + ], + "text": "Let's call it a deal . Hope to see you again soon . Keep in touch then . Byebye .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Goodbye . Thanks again .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "Hope to see you again soon . Keep in touch then" + ], + "type": [ + "inter-personal" + ], + "text": "Goodbye . Thanks again .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_6038.json b/reccon/sources/tr_6038.json new file mode 100644 index 0000000000000000000000000000000000000000..fc93a43be717b8da4a9722e72604a6fa4ee267c7 --- /dev/null +++ b/reccon/sources/tr_6038.json @@ -0,0 +1,234 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I love breathing fresh air in the suburb places , while sitting in the morning sunshine .", + "emotion": "happiness", + "explanation": "A is happy to share what they like", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I love breathing fresh air in the suburb places , while sitting in the morning sunshine ." + ], + "type": [ + "no-context" + ], + "text": "I love breathing fresh air in the suburb places , while sitting in the morning sunshine .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I can't agree more , honey . We need to get away from work from time to time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "I love breathing fresh air in the suburb places , while sitting in the morning sunshine .", + "I can't agree more ," + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I can't agree more , honey . We need to get away from work from time to time .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yeah , just return to nature and feel the thrills of its beauty .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "I love breathing fresh air in the suburb places , while sitting in the morning sunshine .", + "I can't agree more ," + ], + "type": [ + "hybrid" + ], + "text": "Yeah , just return to nature and feel the thrills of its beauty .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "We are nor alone here . So many other families !", + "emotion": "happiness", + "explanation": "B is happy to see other people also enjoy the same ambience", + "expanded emotion cause evidence": [ + 1, + 2, + 4, + 4 + ], + "expanded emotion cause span": [ + "I love breathing fresh air in the suburb places , while sitting in the morning sunshine .", + "I can't agree more ,", + "We are nor alone here .", + "many other families !" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "We are nor alone here . So many other families !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Sure . The sunny days of spring are ideal for outdoor gatherings .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 4, + 4, + 5 + ], + "expanded emotion cause span": [ + "I love breathing fresh air in the suburb places , while sitting in the morning sunshine .", + "We are nor alone here .", + "many other families !", + "The sunny days of spring are ideal for outdoor gatherings ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Sure . The sunny days of spring are ideal for outdoor gatherings .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Well , let's go over there and put a blanket on the lawn .", + "emotion": "neutral", + "text": "Well , let's go over there and put a blanket on the lawn .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "OK , you go back to our car and fetch the picnic stuff .", + "emotion": "neutral", + "text": "OK , you go back to our car and fetch the picnic stuff .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Oh , so heavy ! What have you put in here ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "so heavy !" + ], + "type": [ + "no-context" + ], + "text": "Oh , so heavy ! What have you put in here ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Nothing special . Food , drinks , and Daniel's kangaroo toys .", + "emotion": "neutral", + "text": "Nothing special . Food , drinks , and Daniel's kangaroo toys .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Toys ? Why do we need toys for a picnic ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "toys .", + "Why do we need toys" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Toys ? Why do we need toys for a picnic ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "He said he would like to be our tour director and he lined up many things to do .", + "emotion": "neutral", + "text": "He said he would like to be our tour director and he lined up many things to do .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Sure , then . May it really be a day of enjoyment . Other than that , we can also teach him something about science .", + "emotion": "neutral", + "text": "Sure , then . May it really be a day of enjoyment . Other than that , we can also teach him something about science .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Science ? What are you talking about ? Forget about your science , OK ? It's a picnic !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 12, + 13 + ], + "expanded emotion cause span": [ + "we can also teach him something about science .", + "What are you talking about ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Science ? What are you talking about ? Forget about your science , OK ? It's a picnic !", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 14, + "speaker": "B", + "utterance": "I mean we can inspire him for a deeper understanding of the natural world .", + "emotion": "neutral", + "text": "I mean we can inspire him for a deeper understanding of the natural world .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "I can't agree on that . Just cut it out . Give him a break and don't spoil the day .", + "emotion": "neutral", + "text": "I can't agree on that . Just cut it out . Give him a break and don't spoil the day .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Well , OK . you are always right .", + "emotion": "neutral", + "text": "Well , OK . you are always right .", + "id": 16 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_607.json b/reccon/sources/tr_607.json new file mode 100644 index 0000000000000000000000000000000000000000..02bbe4e0788eee5a713fce16a1cbd81996572650 --- /dev/null +++ b/reccon/sources/tr_607.json @@ -0,0 +1,99 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Excuse me ? Is this where I register ? I ' d like to sign up for my courses for next semester .", + "emotion": "neutral", + "text": "Excuse me ? Is this where I register ? I ' d like to sign up for my courses for next semester .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , of course . I need your student ID please .", + "emotion": "neutral", + "text": "Yes , of course . I need your student ID please .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Here you are .", + "emotion": "neutral", + "text": "Here you are .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Okay , Susan . It says here that you are a business major and you are in your second year . Is this information correct ?", + "emotion": "neutral", + "text": "Okay , Susan . It says here that you are a business major and you are in your second year . Is this information correct ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Yes . I do want to take some additional credits this year to get a minor in psychology .", + "emotion": "neutral", + "text": "Yes . I do want to take some additional credits this year to get a minor in psychology .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Sure . That ' s not a problem . Do you have the list of courses you want to taketh semester ?", + "emotion": "neutral", + "text": "Sure . That ' s not a problem . Do you have the list of courses you want to taketh semester ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yeah . Here ' s my list . I ' m not sure if the class schedule will allow me to take all of them though .", + "emotion": "neutral", + "text": "Yeah . Here ' s my list . I ' m not sure if the class schedule will allow me to take all of them though .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yeah , that ' s perfect . What about the subjects for your minor ?", + "emotion": "neutral", + "text": "Yeah , that ' s perfect . What about the subjects for your minor ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Oh yeah ! Almost forgot ! I need to take fundamental linguistics , consumer psychology and neuroanatomy .", + "emotion": "neutral", + "text": "Oh yeah ! Almost forgot ! I need to take fundamental linguistics , consumer psychology and neuroanatomy .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Wow , you are going to be busy this semester ! Okay , here you go . You are registered now . you ' ll have to make your first tuition payment before classes start .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "I need to take fundamental linguistics , consumer psychology and neuroanatomy .", + "you are going to be busy this semester !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Wow , you are going to be busy this semester ! Okay , here you go . You are registered now . you ' ll have to make your first tuition payment before classes start .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_6152.json b/reccon/sources/tr_6152.json new file mode 100644 index 0000000000000000000000000000000000000000..cf3c94610e9ab7bfe342bf8310b21a0f303657db --- /dev/null +++ b/reccon/sources/tr_6152.json @@ -0,0 +1,107 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello , thanks for calling 123 Tech Help , I ' m Todd . How can I help you ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "thanks for calling 123 Tech Help" + ], + "type": [ + "no-context" + ], + "text": "Hello , thanks for calling 123 Tech Help , I ' m Todd . How can I help you ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hello ? Can you help me ? My computer ! Oh man ...", + "emotion": "neutral", + "text": "Hello ? Can you help me ? My computer ! Oh man ...", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "It ' s okay sir , calm down . What happened ?", + "emotion": "neutral", + "text": "It ' s okay sir , calm down . What happened ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I turned on my laptop and it broke ! I mean , the monitor went black !", + "emotion": "fear", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I turned on my laptop and it broke ! I mean , the monitor went black !" + ], + "type": [ + "no-context" + ], + "text": "I turned on my laptop and it broke ! I mean , the monitor went black !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Ok , sir , it sounds like you might have a virus .", + "emotion": "neutral", + "text": "Ok , sir , it sounds like you might have a virus .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I don ' t feel sick , ... let me check ... Nope ! No fever , I ' m fine .", + "emotion": "fear", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "it sounds like you might have a virus ." + ], + "type": [ + "inter-personal" + ], + "text": "I don ' t feel sick , ... let me check ... Nope ! No fever , I ' m fine .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "No , your computer might have a virus , I mean , it has a bad program on it . Maybe that ' s why it crashed . I recommend that you run an antivirus program in order to safely remove any unwanted spyware or Trojans .", + "emotion": "neutral", + "text": "No , your computer might have a virus , I mean , it has a bad program on it . Maybe that ' s why it crashed . I recommend that you run an antivirus program in order to safely remove any unwanted spyware or Trojans .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Phew ! . . . Wait a minute , CRASH ? ? ! ! Spyware ? Trojans ! What ? where ? when ? !", + "emotion": "fear", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "it has a bad program on it . Maybe that ' s why it crashed . I recommend that you run an antivirus program in order to safely remove any unwanted spyware or Trojans ." + ], + "type": [ + "inter-personal" + ], + "text": "Phew ! . . . Wait a minute , CRASH ? ? ! ! Spyware ? Trojans ! What ? where ? when ? !", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_6198.json b/reccon/sources/tr_6198.json new file mode 100644 index 0000000000000000000000000000000000000000..c24d70c18f1dca2cf614dfedb34711178007a811 --- /dev/null +++ b/reccon/sources/tr_6198.json @@ -0,0 +1,102 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "How about this floor lamp ?", + "emotion": "neutral", + "text": "How about this floor lamp ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Fine , just get it ! We have been shopping for furniture for five hours ! I ' m so tired !", + "emotion": "angry", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "We have been shopping for furniture for five hours ! I ' m so tired !" + ], + "type": [ + "no-context" + ], + "text": "Fine , just get it ! We have been shopping for furniture for five hours ! I ' m so tired !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "We still need to find an armoire and a dresser .", + "emotion": "neutral", + "text": "We still need to find an armoire and a dresser .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Fine ! I am going to go home and drop off this nightstand , coffee table and love seat while you look for the rest of the things .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I am going to go home" + ], + "type": [ + "no-context" + ], + "text": "Fine ! I am going to go home and drop off this nightstand , coffee table and love seat while you look for the rest of the things .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Great ! Pick me up in about an hour because I think I ' ll also get a bean bag and a dining set .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Fine ! I am going to go home and drop off this nightstand , coffee table and love seat while you look for the rest of the things ." + ], + "type": [ + "inter-personal" + ], + "text": "Great ! Pick me up in about an hour because I think I ' ll also get a bean bag and a dining set .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "While you are at it can you pick out a nice recliner ? I really want one so I can watch TV .", + "emotion": "neutral", + "text": "While you are at it can you pick out a nice recliner ? I really want one so I can watch TV .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Recliner ? In my beautifully decorated living room ? I don ' t think so !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "can you pick out a nice recliner ?", + "In my beautifully decorated living room ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Recliner ? In my beautifully decorated living room ? I don ' t think so !", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_62.json b/reccon/sources/tr_62.json new file mode 100644 index 0000000000000000000000000000000000000000..280e00ce12d4299a82e8e42c0f95ce976f45a159 --- /dev/null +++ b/reccon/sources/tr_62.json @@ -0,0 +1,173 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Are you going to the party on Saturday ?", + "emotion": "neutral", + "text": "Are you going to the party on Saturday ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I was thinking about it . Are you ?", + "emotion": "neutral", + "text": "I was thinking about it . Are you ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yeah , I heard it's going to be a lot of fun .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "party on Saturday ?", + "I heard it's going to be a lot of fun ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Yeah , I heard it's going to be a lot of fun .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Really ? Well , what time does it start ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "party on Saturday ?", + "I heard it's going to be a lot of fun ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? Well , what time does it start ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "It starts at 8", + "emotion": "neutral", + "text": "It starts at 8", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Well , who all is going to be there ?", + "emotion": "neutral", + "text": "Well , who all is going to be there ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Everyone from school .", + "emotion": "neutral", + "text": "Everyone from school .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "How do you know it's going to be so fun ?", + "emotion": "neutral", + "text": "How do you know it's going to be so fun ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "This party is going to have a DJ , food , and drinks .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "This party is going to have a DJ , food , and drinks ." + ], + "type": [ + "no-context" + ], + "text": "This party is going to have a DJ , food , and drinks .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Wow , that does sound like it's going to be fun .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "This party is going to have a DJ , food , and drinks .", + "that does sound like it's going to be fun ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Wow , that does sound like it's going to be fun .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 11, + "speaker": "A", + "utterance": "So am I going to see you at the party ?", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "This party is going to have a DJ , food , and drinks .", + "that does sound like it's going to be fun ." + ], + "type": [ + "hybrid" + ], + "text": "So am I going to see you at the party ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Yeah , I will be there .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 9, + 10, + 11 + ], + "expanded emotion cause span": [ + "This party is going to have a DJ , food , and drinks .", + "that does sound like it's going to be fun .", + "am I going to see you at the party ?" + ], + "type": [ + "hybrid" + ], + "text": "Yeah , I will be there .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_6232.json b/reccon/sources/tr_6232.json new file mode 100644 index 0000000000000000000000000000000000000000..0c043aa2d51234d12a7345aedf4ae16df680f47e --- /dev/null +++ b/reccon/sources/tr_6232.json @@ -0,0 +1,329 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Can I help you ?", + "emotion": "neutral", + "text": "Can I help you ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , I need to buy a computer for this semester . I was told it is cheaper to buy computers here .", + "emotion": "neutral", + "text": "Yes , I need to buy a computer for this semester . I was told it is cheaper to buy computers here .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Well , you heard right . You can get an excellent deal on a new computer here . We have great discounts for students .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 2 + ], + "expanded emotion cause span": [ + "I need to buy a computer", + "I was told it is cheaper to buy computers here ." + ], + "type": [ + "inter-personal" + ], + "text": "Well , you heard right . You can get an excellent deal on a new computer here . We have great discounts for students .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I don't know much about computers . But I know I want a desktop computer with a lot of memory . And I need a printer .", + "emotion": "neutral", + "text": "I don't know much about computers . But I know I want a desktop computer with a lot of memory . And I need a printer .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Well , first let's consider your computer . Here , for example , is a system I highly recommend--the Power Macintosh G3 . It comes with 64 megabytes of total memory .", + "emotion": "neutral", + "text": "Well , first let's consider your computer . Here , for example , is a system I highly recommend--the Power Macintosh G3 . It comes with 64 megabytes of total memory .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Is that a lot ? Sixty-four ?", + "emotion": "neutral", + "text": "Is that a lot ? Sixty-four ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yes , it is . It should be enough for any student needs you might have . What department are you in ?", + "emotion": "neutral", + "text": "Yes , it is . It should be enough for any student needs you might have . What department are you in ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "History .", + "emotion": "neutral", + "text": "History .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Well , so you will mostly be using word processing , for writing papers . I recommend the Corel Word Perfect program for word processing . We can talk about software later . Let's talk about your", + "emotion": "neutral", + "text": "Well , so you will mostly be using word processing , for writing papers . I recommend the Corel Word Perfect program for word processing . We can talk about software later . Let's talk about your", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Thirty percent ?", + "emotion": "neutral", + "text": "Thirty percent ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Yes .", + "emotion": "neutral", + "text": "Yes .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Wow . That's really good . And you think this is really a good system for a graduate student ?", + "emotion": "happiness", + "explanation": "Latent cause of happiness", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Wow . That's really good . And you think this is really a good system for a graduate student ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Yes . It's an excellent system .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12, + 13 + ], + "expanded emotion cause span": [ + "That's really good .", + "It's an excellent system ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes . It's an excellent system .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Hmm . Hey , wait . This has an Apple on it . Is this an Apple computer ?", + "emotion": "neutral", + "text": "Hmm . Hey , wait . This has an Apple on it . Is this an Apple computer ?", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Yes , it's a Macintosh . It's Apple . Macintosh and Apple are the same thing .", + "emotion": "neutral", + "text": "Yes , it's a Macintosh . It's Apple . Macintosh and Apple are the same thing .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "I don't want Macintosh . I want PC .", + "emotion": "neutral", + "text": "I don't want Macintosh . I want PC .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "I'm sorry , but our university computer center only sells Macintosh equipment .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 17 + ], + "expanded emotion cause span": [ + "our university computer center only sells Macintosh equipment ." + ], + "type": [ + "no-context" + ], + "text": "I'm sorry , but our university computer center only sells Macintosh equipment .", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "What ? Are you serious ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 17 + ], + "expanded emotion cause span": [ + "our university computer center only sells Macintosh equipment ." + ], + "type": [ + "inter-personal" + ], + "text": "What ? Are you serious ?", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "Yes .", + "emotion": "neutral", + "text": "Yes .", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "But nobody uses Macintosh !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 17, + 20 + ], + "expanded emotion cause span": [ + "our university computer center only sells Macintosh equipment .", + "nobody uses Macintosh !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "But nobody uses Macintosh !", + "id": 20 + }, + { + "turn": 21, + "speaker": "A", + "utterance": "That's not true . Most of the students and professors in the university here use Macintosh . They find it is better for writing and word-processing , and that is what students mostly do . Ma", + "emotion": "neutral", + "text": "That's not true . Most of the students and professors in the university here use Macintosh . They find it is better for writing and word-processing , and that is what students mostly do . Ma", + "id": 21 + }, + { + "turn": 22, + "speaker": "B", + "utterance": "Yes , I'm from Taiwan .", + "emotion": "neutral", + "text": "Yes , I'm from Taiwan .", + "id": 22 + }, + { + "turn": 23, + "speaker": "A", + "utterance": "Well , I know that in most Asian countries Apple is not very popular . But here in America , especially in universities and publishing companies , Apple is very commonly used .", + "emotion": "neutral", + "text": "Well , I know that in most Asian countries Apple is not very popular . But here in America , especially in universities and publishing companies , Apple is very commonly used .", + "id": 23 + }, + { + "turn": 24, + "speaker": "B", + "utterance": "But I need a computer that can handle writing in Chinese .", + "emotion": "neutral", + "text": "But I need a computer that can handle writing in Chinese .", + "id": 24 + }, + { + "turn": 25, + "speaker": "A", + "utterance": "There are several Chinese writing programs you can use with Macintosh . Chinese is no problem for Apple .", + "emotion": "neutral", + "text": "There are several Chinese writing programs you can use with Macintosh . Chinese is no problem for Apple .", + "id": 25 + }, + { + "turn": 26, + "speaker": "B", + "utterance": "Hmm . I think I should ask some of my friends for advice before I make a decision . I'm sorry .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 26 + ], + "expanded emotion cause span": [ + "I should ask some of my friends for advice before I make a decision . I'm sorry ." + ], + "type": [ + "no-context" + ], + "text": "Hmm . I think I should ask some of my friends for advice before I make a decision . I'm sorry .", + "id": 26 + }, + { + "turn": 27, + "speaker": "A", + "utterance": "No , don't be sorry . It's reasonable to ask your friends . But believe me , most of the students here in the university--Asian students included--most of them use Apple .", + "emotion": "neutral", + "text": "No , don't be sorry . It's reasonable to ask your friends . But believe me , most of the students here in the university--Asian students included--most of them use Apple .", + "id": 27 + }, + { + "turn": 28, + "speaker": "B", + "utterance": "Well , thanks for your advice . I will probably come back later .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 28 + ], + "expanded emotion cause span": [ + "thanks for your advice ." + ], + "type": [ + "no-context" + ], + "text": "Well , thanks for your advice . I will probably come back later .", + "id": 28 + }, + { + "turn": 29, + "speaker": "A", + "utterance": "You're very welcome . Here is my card , if you need any help .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 28 + ], + "expanded emotion cause span": [ + "thanks for your advice . I will probably come back later ." + ], + "type": [ + "inter-personal" + ], + "text": "You're very welcome . Here is my card , if you need any help .", + "id": 29, + "source_sentences": [ + 27 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_627.json b/reccon/sources/tr_627.json new file mode 100644 index 0000000000000000000000000000000000000000..833027f202dbdd2ab18826f2955e19892056df93 --- /dev/null +++ b/reccon/sources/tr_627.json @@ -0,0 +1,140 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Are you going anywhere for your vacation ?", + "emotion": "neutral", + "text": "Are you going anywhere for your vacation ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , we're making plans for a tour .", + "emotion": "neutral", + "text": "Yes , we're making plans for a tour .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "That'll be lovely . Where are you going ?", + "emotion": "neutral", + "text": "That'll be lovely . Where are you going ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Well start out from Long Island this Friday . We've planned a four day drive to Salt Lake City , where we'll join my brother and his family on his fortieth birthday .", + "emotion": "neutral", + "text": "Well start out from Long Island this Friday . We've planned a four day drive to Salt Lake City , where we'll join my brother and his family on his fortieth birthday .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Well , you've got to prepare a lot of food and enough sleeping bags then .", + "emotion": "neutral", + "text": "Well , you've got to prepare a lot of food and enough sleeping bags then .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Oh , we'll spend the nights in hotels and enjoy local food as we pass by . How does it sound , David ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "we'll spend the nights in hotels and enjoy local food as we pass by ." + ], + "type": [ + "no-context" + ], + "text": "Oh , we'll spend the nights in hotels and enjoy local food as we pass by . How does it sound , David ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "It sounds good . You can do a lot of sightseeing , too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "we'll spend the nights in hotels and enjoy local food as we pass by .", + "You can do a lot of sightseeing , too ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It sounds good . You can do a lot of sightseeing , too .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yes , we'll take our time . And we'll go to Five-lake Strict and the Wall Street .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7, + 8 + ], + "expanded emotion cause span": [ + "we'll spend the nights in hotels and enjoy local food as we pass by .", + "You can do a lot of sightseeing , too .", + "And we'll go to Five-lake Strict and the Wall Street ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Yes , we'll take our time . And we'll go to Five-lake Strict and the Wall Street .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "So , you're going to have a really nice vacation .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "you're going to have a really nice vacation ." + ], + "type": [ + "no-context" + ], + "text": "So , you're going to have a really nice vacation .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "You can say that again .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "you're going to have a really nice vacation ." + ], + "type": [ + "inter-personal" + ], + "text": "You can say that again .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_6281.json b/reccon/sources/tr_6281.json new file mode 100644 index 0000000000000000000000000000000000000000..b760e32ba7332c733cab9f87706a327fde347ef7 --- /dev/null +++ b/reccon/sources/tr_6281.json @@ -0,0 +1,180 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Where is Pamela ?", + "emotion": "neutral", + "text": "Where is Pamela ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Is she coming ?", + "emotion": "neutral", + "text": "Is she coming ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "She told me she'd be here .", + "emotion": "neutral", + "text": "She told me she'd be here .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "They are announcing your flight . You'd better board the plane .", + "emotion": "neutral", + "text": "They are announcing your flight . You'd better board the plane .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Are you rushing me ?", + "emotion": "neutral", + "text": "Are you rushing me ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I am just reminding you about the time . You don't want to miss the plane , do you ?", + "emotion": "neutral", + "text": "I am just reminding you about the time . You don't want to miss the plane , do you ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I know what I am doing . Don't worry . Can you do me a favor ?", + "emotion": "neutral", + "text": "I know what I am doing . Don't worry . Can you do me a favor ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Name it and I'll do it for you .", + "emotion": "neutral", + "text": "Name it and I'll do it for you .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Take care of Pamela when I am away . She is a nice girl . I don't want her to get hurt or anything .", + "emotion": "neutral", + "text": "Take care of Pamela when I am away . She is a nice girl . I don't want her to get hurt or anything .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I've got it .", + "emotion": "neutral", + "text": "I've got it .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Thank you . Now I see that you are my true friend . Most of my so-called friends left me at the moment my company went bankrupt . You are the only one who has stood by me the whole time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11, + 11 + ], + "expanded emotion cause span": [ + "I've got it .", + "you are my true friend .", + "You are the only one who has stood by me the whole time ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you . Now I see that you are my true friend . Most of my so-called friends left me at the moment my company went bankrupt . You are the only one who has stood by me the whole time .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I am just doing what I think I should do .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 11 + ], + "expanded emotion cause span": [ + "you are my true friend .", + "You are the only one who has stood by me the whole time ." + ], + "type": [ + "inter-personal" + ], + "text": "I am just doing what I think I should do .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Thank you for being a friend of mine .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11, + 11, + 13 + ], + "expanded emotion cause span": [ + "I've got it .", + "you are my true friend .", + "You are the only one who has stood by me the whole time .", + "Thank you for being a friend" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Thank you for being a friend of mine .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "This isn't like you ... Well , I hope you will have a nice flight and a successful start in business", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13, + 14 + ], + "expanded emotion cause span": [ + "Thank you for being a friend of mine .", + "I hope you will have a nice flight and a successful start in business" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "This isn't like you ... Well , I hope you will have a nice flight and a successful start in business", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Thank you . I have to leave now . If you see Pamela , tell her I'll write to her .", + "emotion": "neutral", + "text": "Thank you . I have to leave now . If you see Pamela , tell her I'll write to her .", + "id": 15 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_6282.json b/reccon/sources/tr_6282.json new file mode 100644 index 0000000000000000000000000000000000000000..395119bcff59333ae53f45971c1e07cdcf5eca91 --- /dev/null +++ b/reccon/sources/tr_6282.json @@ -0,0 +1,155 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Excuse me , is this the Guyon Travel Agency ?", + "emotion": "neutral", + "text": "Excuse me , is this the Guyon Travel Agency ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , sir . What can I do for you ?", + "emotion": "neutral", + "text": "Yes , sir . What can I do for you ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I want to travel to the ancient town in the south of China . Would you please tell me something about it ?", + "emotion": "neutral", + "text": "I want to travel to the ancient town in the south of China . Would you please tell me something about it ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Sure . There's network of canals . And there are white walls , black tiles , small bridges , flowing rivers , flagstones roads , blue sky and white clouds . Few places have preserved the past like this place . Walking on the ancient road makes us back to our sense .", + "emotion": "neutral", + "text": "Sure . There's network of canals . And there are white walls , black tiles , small bridges , flowing rivers , flagstones roads , blue sky and white clouds . Few places have preserved the past like this place . Walking on the ancient road makes us back to our sense .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Wonderful . That's just what I expect , where is my first place if I go there ?", + "emotion": "neutral", + "text": "Wonderful . That's just what I expect , where is my first place if I go there ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Zhouzhuang .", + "emotion": "neutral", + "text": "Zhouzhuang .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "How long does the tour take ?", + "emotion": "neutral", + "text": "How long does the tour take ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "It's about two days .", + "emotion": "neutral", + "text": "It's about two days .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "what's the cost ?", + "emotion": "neutral", + "text": "what's the cost ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "It's about 300 yuan .", + "emotion": "neutral", + "text": "It's about 300 yuan .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I know . Thank you very much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I know ." + ], + "type": [ + "no-context" + ], + "text": "I know . Thank you very much .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "That's all right . May you have a good trip !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "Thank you very much ." + ], + "type": [ + "inter-personal" + ], + "text": "That's all right . May you have a good trip !", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Thank you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "May you have a good trip !" + ], + "type": [ + "inter-personal" + ], + "text": "Thank you .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "My pleasure .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "Thank you ." + ], + "type": [ + "inter-personal" + ], + "text": "My pleasure .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_6322.json b/reccon/sources/tr_6322.json new file mode 100644 index 0000000000000000000000000000000000000000..4d2a56100722a147e6fe1e35008bd9a647def097 --- /dev/null +++ b/reccon/sources/tr_6322.json @@ -0,0 +1,149 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "May I come in ?", + "emotion": "neutral", + "text": "May I come in ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Come in , please .", + "emotion": "neutral", + "text": "Come in , please .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I'm sorry to trouble you , but I'd like to ask when I will get a raise .", + "emotion": "neutral", + "text": "I'm sorry to trouble you , but I'd like to ask when I will get a raise .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "In 3 months or so .", + "emotion": "neutral", + "text": "In 3 months or so .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "You said the same thing three months ago .", + "emotion": "neutral", + "text": "You said the same thing three months ago .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Did I ? Well , anyway , you will get your raise when the economy starts picking up .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "You said the same thing three months ago ." + ], + "type": [ + "inter-personal" + ], + "text": "Did I ? Well , anyway , you will get your raise when the economy starts picking up .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You mean that I won't get a raise until the recession ends ?", + "emotion": "neutral", + "text": "You mean that I won't get a raise until the recession ends ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yes .", + "emotion": "neutral", + "text": "Yes .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I got the message . I'm quiting .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "You mean that I won't get a raise until the recession ends ?" + ], + "type": [ + "self-contagion" + ], + "text": "I got the message . I'm quiting .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Nah , don't be so fast . We like your work here , but this company is on hard times . and I can't be handing out raises for anyone .", + "emotion": "neutral", + "text": "Nah , don't be so fast . We like your work here , but this company is on hard times . and I can't be handing out raises for anyone .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I've been here for 3 years , and I haven't had a raise in all that time . If you like my work , it should be reflected in my pay , and I feel it isn't .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I've been here for 3 years , and I haven't had a raise in all that time ." + ], + "type": [ + "no-context" + ], + "text": "I've been here for 3 years , and I haven't had a raise in all that time . If you like my work , it should be reflected in my pay , and I feel it isn't .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I hear what you're saying , and I wish there were something I could do .", + "emotion": "neutral", + "text": "I hear what you're saying , and I wish there were something I could do .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Very well , consider me gone .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "I've been here for 3 years , and I haven't had a raise in all that time .", + "I wish there were something I could do ." + ], + "type": [ + "hybrid" + ], + "text": "Very well , consider me gone .", + "id": 13 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_6324.json b/reccon/sources/tr_6324.json new file mode 100644 index 0000000000000000000000000000000000000000..6b78a663c3eae8af082ba2d097df9985bb749fa2 --- /dev/null +++ b/reccon/sources/tr_6324.json @@ -0,0 +1,142 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "How are you doing ?", + "emotion": "neutral", + "text": "How are you doing ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Everything ' s fine with me .", + "emotion": "neutral", + "text": "Everything ' s fine with me .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What can I do for you today ?", + "emotion": "neutral", + "text": "What can I do for you today ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Is it possible for me to view the apartment today ?", + "emotion": "neutral", + "text": "Is it possible for me to view the apartment today ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Unfortunately , you will not be able to view it today .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "you will not be able to view it today" + ], + "type": [ + "no-context" + ], + "text": "Unfortunately , you will not be able to view it today .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Why can ' t I view it today ?", + "emotion": "neutral", + "text": "Why can ' t I view it today ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You ' ll need to make an appointment to view the apartment .", + "emotion": "neutral", + "text": "You ' ll need to make an appointment to view the apartment .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I understand . May I make an appointment then ?", + "emotion": "neutral", + "text": "I understand . May I make an appointment then ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "How does this Friday sound ?", + "emotion": "neutral", + "text": "How does this Friday sound ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Friday at 6 pm . would be perfect .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "How does this Friday sound ?" + ], + "type": [ + "inter-personal" + ], + "text": "Friday at 6 pm . would be perfect .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "That will be fine .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "Friday at 6 pm . would be perfect .", + "That will be fine ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That will be fine .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Thanks for your help .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "That will be fine ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks for your help .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_6401.json b/reccon/sources/tr_6401.json new file mode 100644 index 0000000000000000000000000000000000000000..27c2ded6f5a5b810a0a1100cdc203a8b151b7ad1 --- /dev/null +++ b/reccon/sources/tr_6401.json @@ -0,0 +1,175 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Have you heard my good news ?", + "emotion": "neutral", + "text": "Have you heard my good news ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "You haven't told me anything yet .", + "emotion": "neutral", + "text": "You haven't told me anything yet .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I got a promotion at work earlier this week .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I got a promotion at work earlier this week ." + ], + "type": [ + "no-context" + ], + "text": "I got a promotion at work earlier this week .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Is that right ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I got a promotion at work earlier this week ." + ], + "type": [ + "inter-personal" + ], + "text": "Is that right ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "It's the truth . I am really happy .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I got a promotion at work earlier this week ." + ], + "type": [ + "self-contagion" + ], + "text": "It's the truth . I am really happy .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Congratulations on your promotion .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Congratulations on your promotion ." + ], + "type": [ + "no-context" + ], + "text": "Congratulations on your promotion .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Thank you very much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Congratulations on your promotion ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you very much .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I am really excited for you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I am really excited for you ." + ], + "type": [ + "no-context" + ], + "text": "I am really excited for you .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Are you really ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I am really excited for you ." + ], + "type": [ + "inter-personal" + ], + "text": "Are you really ?", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I'm serious . You deserved this promotion .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "You deserved this promotion ." + ], + "type": [ + "no-context" + ], + "text": "I'm serious . You deserved this promotion .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Is that what you really think ?", + "emotion": "neutral", + "text": "Is that what you really think ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Yes , I do .", + "emotion": "neutral", + "text": "Yes , I do .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_6465.json b/reccon/sources/tr_6465.json new file mode 100644 index 0000000000000000000000000000000000000000..c53225844d1e6763bffebf982385d1448987d350 --- /dev/null +++ b/reccon/sources/tr_6465.json @@ -0,0 +1,152 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "May I take your order now ?", + "emotion": "neutral", + "text": "May I take your order now ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , please . What's special today ? Any special recommendations ?", + "emotion": "neutral", + "text": "Yes , please . What's special today ? Any special recommendations ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Certainly . I would recommend ' Songshuguiyu ' .", + "emotion": "neutral", + "text": "Certainly . I would recommend ' Songshuguiyu ' .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "The name sounds fascinating . What is it exactly ?", + "emotion": "neutral", + "text": "The name sounds fascinating . What is it exactly ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Well , it is sweet and sour fried Mandarin fish .", + "emotion": "neutral", + "text": "Well , it is sweet and sour fried Mandarin fish .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Sorry , I'm not interested in vinegar .", + "emotion": "neutral", + "text": "Sorry , I'm not interested in vinegar .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Then , how about this one ?", + "emotion": "neutral", + "text": "Then , how about this one ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "OK . I'll have that .", + "emotion": "neutral", + "text": "OK . I'll have that .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Very good . Could I serve you anything else ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "how about this one ?", + "I'll have that ." + ], + "type": [ + "hybrid" + ], + "text": "Very good . Could I serve you anything else ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Thank you . That's enough .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "Could I serve you anything else ?", + "That's enough ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you . That's enough .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 11, + "speaker": "A", + "utterance": "My pleasure . Just a little while , your order will be ready very soon . Please enjoy your lunch .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8, + 10 + ], + "expanded emotion cause span": [ + "how about this one ?", + "I'll have that .", + "Thank you ." + ], + "type": [ + "hybrid" + ], + "text": "My pleasure . Just a little while , your order will be ready very soon . Please enjoy your lunch .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Thanks .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10, + 11 + ], + "expanded emotion cause span": [ + "Could I serve you anything else ?", + "That's enough .", + "your order will be ready very soon . Please enjoy your lunch ." + ], + "type": [ + "hybrid" + ], + "text": "Thanks .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_6491.json b/reccon/sources/tr_6491.json new file mode 100644 index 0000000000000000000000000000000000000000..40dca2e20c1c963c528c7bcc433189125b97b889 --- /dev/null +++ b/reccon/sources/tr_6491.json @@ -0,0 +1,227 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Mom , Happy mother's Day ! Here's my card .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Happy mother's Day !" + ], + "type": [ + "no-context" + ], + "text": "Mom , Happy mother's Day ! Here's my card .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What a surprise ! Thanks . It ' s beautiful .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 2 + ], + "expanded emotion cause span": [ + "Happy mother's Day !", + "What a surprise !", + "It ' s beautiful ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "What a surprise ! Thanks . It ' s beautiful .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Thank you for your love and care over the years , I appreciate it , mom .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 3, + 3 + ], + "expanded emotion cause span": [ + "Happy mother's Day !", + "It ' s beautiful .", + "Thank you for your love and care", + "I appreciate it ," + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Thank you for your love and care over the years , I appreciate it , mom .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "This is the best card I ever received .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 2, + 4 + ], + "expanded emotion cause span": [ + "Happy mother's Day !", + "What a surprise !", + "It ' s beautiful .", + "the best card I ever received ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "This is the best card I ever received .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Mom , what can I do for you today ?", + "emotion": "neutral", + "text": "Mom , what can I do for you today ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Nothing , son . I'm already very happy .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 2, + 4, + 5 + ], + "expanded emotion cause span": [ + "Happy mother's Day !", + "What a surprise !", + "It ' s beautiful .", + "the best card I ever received .", + "what can I do for you today ?" + ], + "type": [ + "hybrid" + ], + "text": "Nothing , son . I'm already very happy .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "How about dinner tonight ? My treat .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I'm already very happy ." + ], + "type": [ + "inter-personal" + ], + "text": "How about dinner tonight ? My treat .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Actually . I prefer we eat at home . We ' ll have more time to catch up that way .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 2, + 4, + 5, + 7 + ], + "expanded emotion cause span": [ + "Happy mother's Day !", + "What a surprise !", + "It ' s beautiful .", + "the best card I ever received .", + "what can I do for you today ?", + "My treat ." + ], + "type": [ + "hybrid" + ], + "text": "Actually . I prefer we eat at home . We ' ll have more time to catch up that way .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I'm sorry I haven't dropped in that much these past few years . Business kept me too busy , I apologize .", + "emotion": "neutral", + "text": "I'm sorry I haven't dropped in that much these past few years . Business kept me too busy , I apologize .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Oh , don't mention it . I'm proud of you !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 2, + 4, + 5, + 10 + ], + "expanded emotion cause span": [ + "Happy mother's Day !", + "What a surprise !", + "It ' s beautiful .", + "the best card I ever received .", + "what can I do for you today ?", + "I'm proud of you !" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Oh , don't mention it . I'm proud of you !", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Thank you , mom . I love you so much !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "I'm proud of you !", + "I love you" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you , mom . I love you so much !", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_654.json b/reccon/sources/tr_654.json new file mode 100644 index 0000000000000000000000000000000000000000..d3b1dbd219e49fc92a7aa3446d615af89996fb4d --- /dev/null +++ b/reccon/sources/tr_654.json @@ -0,0 +1,107 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I have an idea for Christmas this year .", + "emotion": "neutral", + "text": "I have an idea for Christmas this year .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What is it ?", + "emotion": "neutral", + "text": "What is it ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Let's not exchange any gifts at all .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Let's not exchange any gifts at all ." + ], + "type": [ + "no-context" + ], + "text": "Let's not exchange any gifts at all .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "You big scrooge !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Let's not exchange any gifts at all ." + ], + "type": [ + "inter-personal" + ], + "text": "You big scrooge !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Hear me out . We can pool the money and give it to a family who could really use it !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "We can pool the money and give it to a family who could really use it !" + ], + "type": [ + "no-context" + ], + "text": "Hear me out . We can pool the money and give it to a family who could really use it !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "But you may have some trouble convincing the kids .", + "emotion": "neutral", + "text": "But you may have some trouble convincing the kids .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Actual 1y , it was their idea first .", + "emotion": "neutral", + "text": "Actual 1y , it was their idea first .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Now we know that they realize the real meaning of Christmas .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "We can pool the money and give it to a family who could really use it !" + ], + "type": [ + "inter-personal" + ], + "text": "Now we know that they realize the real meaning of Christmas .", + "id": 8, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_6556.json b/reccon/sources/tr_6556.json new file mode 100644 index 0000000000000000000000000000000000000000..aa827bef6fcbef4b9b961b91fe8ad8072ae9d281 --- /dev/null +++ b/reccon/sources/tr_6556.json @@ -0,0 +1,246 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello , Anna speaking !", + "emotion": "neutral", + "text": "Hello , Anna speaking !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hey , Anna , this is Jason .", + "emotion": "neutral", + "text": "Hey , Anna , this is Jason .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Jason , where have you been hiding lately ? You know it's been a long time since your last call . Have you been good ?", + "emotion": "neutral", + "text": "Jason , where have you been hiding lately ? You know it's been a long time since your last call . Have you been good ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes . How are you , Anna ?", + "emotion": "neutral", + "text": "Yes . How are you , Anna ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I am fine . What have you been doing ?", + "emotion": "neutral", + "text": "I am fine . What have you been doing ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Working . I've been really busy these days . I got a promotion .", + "emotion": "neutral", + "text": "Working . I've been really busy these days . I got a promotion .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "That's great , congratulations !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I got a promotion ." + ], + "type": [ + "inter-personal" + ], + "text": "That's great , congratulations !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Thanks . I am feeling pretty good about myself too . You know , bigger office , a raise and even an assistant .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "That's great , congratulations !", + "I am feeling pretty good about myself too . You know , bigger office , a raise and even an assistant ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thanks . I am feeling pretty good about myself too . You know , bigger office , a raise and even an assistant .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "That's good . So I guess I'll have to make an appointment to see you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I am feeling pretty good about myself too . You know , bigger office , a raise and even an assistant ." + ], + "type": [ + "inter-personal" + ], + "text": "That's good . So I guess I'll have to make an appointment to see you .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "You are kidding .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "I guess I'll have to make an appointment to see you ." + ], + "type": [ + "inter-personal" + ], + "text": "You are kidding .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "How long have you been working there ?", + "emotion": "neutral", + "text": "How long have you been working there ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "A bit over two years . This is a fast-moving company , and seniority isn ' t the only factor in deciding promotions .", + "emotion": "neutral", + "text": "A bit over two years . This is a fast-moving company , and seniority isn ' t the only factor in deciding promotions .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "How do you like your new boss ?", + "emotion": "neutral", + "text": "How do you like your new boss ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "She is very nice and open-minded .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 14 + ], + "expanded emotion cause span": [ + "I got a promotion .", + "She is very nice and open-minded ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "She is very nice and open-minded .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Much better than the last one , huh ?", + "emotion": "neutral", + "text": "Much better than the last one , huh ?", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Yeah . He was a real slave driver . He probably would have loved it if we were robots .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "Much better than the last one" + ], + "type": [ + "inter-personal" + ], + "text": "Yeah . He was a real slave driver . He probably would have loved it if we were robots .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "Forget about him . Come over to my house tonight . Let's get drunk .", + "emotion": "neutral", + "text": "Forget about him . Come over to my house tonight . Let's get drunk .", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "Good . Tonight 8 o'clock .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 17 + ], + "expanded emotion cause span": [ + "Come over to my house tonight . Let's get drunk ." + ], + "type": [ + "inter-personal" + ], + "text": "Good . Tonight 8 o'clock .", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "8 it is . See you then .", + "emotion": "neutral", + "text": "8 it is . See you then .", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "Bye .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 17 + ], + "expanded emotion cause span": [ + "Come over to my house tonight . Let's get drunk ." + ], + "type": [ + "inter-personal" + ], + "text": "Bye .", + "id": 20, + "source_sentences": [ + 16 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_6618.json b/reccon/sources/tr_6618.json new file mode 100644 index 0000000000000000000000000000000000000000..0f45e4c94be86c6fdf5ba81436fe3459a2ac8625 --- /dev/null +++ b/reccon/sources/tr_6618.json @@ -0,0 +1,120 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What's in the box ?", + "emotion": "neutral", + "text": "What's in the box ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Sandy , I think we made a mistake ...", + "emotion": "neutral", + "text": "Sandy , I think we made a mistake ...", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What do you mean ?", + "emotion": "neutral", + "text": "What do you mean ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It's a cute little teddy bear !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "a cute little teddy bear !" + ], + "type": [ + "no-context" + ], + "text": "It's a cute little teddy bear !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "How sweet ! Maybe he was just a shy guy who had a crush on you !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 4, + 5, + 5 + ], + "expanded emotion cause span": [ + "How sweet !", + "a cute little teddy bear !", + "a shy guy", + "a crush on you !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "How sweet ! Maybe he was just a shy guy who had a crush on you !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "And look what we did to him ! Hey ... he left me his business card .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "he was just a shy guy who had a crush on you !", + "what we did to him !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "And look what we did to him ! Hey ... he left me his business card .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Wow ! Call him tonight ! You guys will really have an interesting love story to tell everyone !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 4, + 5, + 5, + 6, + 7 + ], + "expanded emotion cause span": [ + "How sweet !", + "a cute little teddy bear !", + "a shy guy", + "a crush on you !", + "he left me his business card .", + "interesting love story" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Wow ! Call him tonight ! You guys will really have an interesting love story to tell everyone !", + "id": 7 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_6664.json b/reccon/sources/tr_6664.json new file mode 100644 index 0000000000000000000000000000000000000000..42054282c0826e029d089738c348cd8472701019 --- /dev/null +++ b/reccon/sources/tr_6664.json @@ -0,0 +1,150 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "OK ... well , then how much is one jin ?", + "emotion": "neutral", + "text": "OK ... well , then how much is one jin ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Ginseng comes in 6 different grades . It runs from 5,000 to 30,000 NT a jin .", + "emotion": "neutral", + "text": "Ginseng comes in 6 different grades . It runs from 5,000 to 30,000 NT a jin .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "30,000 NT for ginseng ? ! Do I have to buy a whole jin ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "5,000 to 30,000 NT a jin .", + "Do I have to buy a whole jin ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "30,000 NT for ginseng ? ! Do I have to buy a whole jin ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "You can get a liang if you want . A liang is one-sixteenth of a jin . That would be 330NT .", + "emotion": "neutral", + "text": "You can get a liang if you want . A liang is one-sixteenth of a jin . That would be 330NT .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Whew ! That sounds more like my price range . I'll take two liangs .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "A liang is one-sixteenth of a jin .", + "That sounds more like my price range ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Whew ! That sounds more like my price range . I'll take two liangs .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I'll have my brother cut some for you .", + "emotion": "neutral", + "text": "I'll have my brother cut some for you .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "This little red fruit looks good . What's it good for ?", + "emotion": "neutral", + "text": "This little red fruit looks good . What's it good for ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That's a lucky fruit called hong zat ! People say that if you eat them , you will have your first son very soon !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "This little red fruit looks good .", + "That's a lucky fruit" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's a lucky fruit called hong zat ! People say that if you eat them , you will have your first son very soon !", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Uh ... , I'm not even married yet . How about this brown dried fruit ?", + "emotion": "neutral", + "text": "Uh ... , I'm not even married yet . How about this brown dried fruit ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Gui yuan are lucky , too ! If you eat them , you'll have a very sweet life !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 10 + ], + "expanded emotion cause span": [ + "Gui yuan are lucky ,", + "you'll have a very sweet life !" + ], + "type": [ + "no-context" + ], + "text": "Gui yuan are lucky , too ! If you eat them , you'll have a very sweet life !", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "And how about these little brown chips ?", + "emotion": "neutral", + "text": "And how about these little brown chips ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Oh , that's deer horn . That helps you ... umm , how should I put it ?", + "emotion": "neutral", + "text": "Oh , that's deer horn . That helps you ... umm , how should I put it ?", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_6700.json b/reccon/sources/tr_6700.json new file mode 100644 index 0000000000000000000000000000000000000000..563a84827d1c9850ffcb79d31ac4bfe22de8d7b7 --- /dev/null +++ b/reccon/sources/tr_6700.json @@ -0,0 +1,109 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Tomorrow is Halloween , I know I'm ready . I bought two pumpkins and a big bags of candy . Do you want to help me a jack-o-lantern ?", + "emotion": "neutral", + "text": "Tomorrow is Halloween , I know I'm ready . I bought two pumpkins and a big bags of candy . Do you want to help me a jack-o-lantern ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'd love to . I heard about Halloween when I was in Beijing . It's kind of a children's day . Small kids get dressed up , then walk around with paper bags or baskets , knocking on the neighbor's", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 1 + ], + "expanded emotion cause span": [ + "Tomorrow is Halloween ,", + "Do you want to help me a jack-o-lantern ?" + ], + "type": [ + "inter-personal" + ], + "text": "I'd love to . I heard about Halloween when I was in Beijing . It's kind of a children's day . Small kids get dressed up , then walk around with paper bags or baskets , knocking on the neighbor's", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "They are supposed to say trick or treat ? Then the neighbors are supposed to hand up the candy .", + "emotion": "neutral", + "text": "They are supposed to say trick or treat ? Then the neighbors are supposed to hand up the candy .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "That's kind of cool . But what's the trick mean ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "They are supposed to say trick or treat ? Then the neighbors are supposed to hand up the candy ." + ], + "type": [ + "inter-personal" + ], + "text": "That's kind of cool . But what's the trick mean ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Usually it's the older kids going around playing Halloween , like punching the pumpkins left outside people's doors or - - someone's tree . They usually do it late at night after little kids go", + "emotion": "neutral", + "text": "Usually it's the older kids going around playing Halloween , like punching the pumpkins left outside people's doors or - - someone's tree . They usually do it late at night after little kids go", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "That sounds kind of fun , maybe I can get tighter with my friends that night .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Usually it's the older kids going around playing Halloween , like punching the pumpkins left outside people's doors or - - someone's tree ." + ], + "type": [ + "inter-personal" + ], + "text": "That sounds kind of fun , maybe I can get tighter with my friends that night .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Usually be adults , you don't have kids have a big party in get dressed up too .", + "emotion": "neutral", + "text": "Usually be adults , you don't have kids have a big party in get dressed up too .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That does sound a lot of fun .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Usually it's the older kids going around playing Halloween , like punching the pumpkins left outside people's doors or - - someone's tree ." + ], + "type": [ + "inter-personal" + ], + "text": "That does sound a lot of fun .", + "id": 8, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_6739.json b/reccon/sources/tr_6739.json new file mode 100644 index 0000000000000000000000000000000000000000..0979af0f5e90206f2fd48d6248b8be64f02d3704 --- /dev/null +++ b/reccon/sources/tr_6739.json @@ -0,0 +1,174 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello , this is Rich .", + "emotion": "neutral", + "text": "Hello , this is Rich .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hi , Rich . Is Jim here ?", + "emotion": "neutral", + "text": "Hi , Rich . Is Jim here ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "He ' s not in at the moment . Can I take a message ?", + "emotion": "neutral", + "text": "He ' s not in at the moment . Can I take a message ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Sure . This is Claire .", + "emotion": "neutral", + "text": "Sure . This is Claire .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Does have your telephone number ?", + "emotion": "neutral", + "text": "Does have your telephone number ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "No , it ' s 3725019281 .", + "emotion": "neutral", + "text": "No , it ' s 3725019281 .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "3725015281 ?", + "emotion": "neutral", + "text": "3725015281 ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "No , it ' s 3725019281 , it ' s a 9 , not a 5 .", + "emotion": "neutral", + "text": "No , it ' s 3725019281 , it ' s a 9 , not a 5 .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Right . I ' ll have him call you back .", + "emotion": "neutral", + "text": "Right . I ' ll have him call you back .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Can you tell him that it ' s urgent ?", + "emotion": "neutral", + "text": "Can you tell him that it ' s urgent ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Sure can .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Can you tell him" + ], + "type": [ + "inter-personal" + ], + "text": "Sure can .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Thanks a lot .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "Sure can ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks a lot .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "No problem .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "Thanks" + ], + "type": [ + "inter-personal" + ], + "text": "No problem .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Bye .", + "emotion": "happiness", + "explanation": "F", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "Sure can ." + ], + "type": [ + "inter-personal" + ], + "text": "Bye .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Goodbye .", + "emotion": "happiness", + "explanation": "F", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "Thanks" + ], + "type": [ + "inter-personal" + ], + "text": "Goodbye .", + "id": 15, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_6757.json b/reccon/sources/tr_6757.json new file mode 100644 index 0000000000000000000000000000000000000000..5a64268f460eafe62e86e86d99cab6956ccdc23f --- /dev/null +++ b/reccon/sources/tr_6757.json @@ -0,0 +1,200 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What a nice day !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "What a nice day !" + ], + "type": [ + "no-context" + ], + "text": "What a nice day !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes . How about going out and enjoying the sunshine on the grass ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "What a nice day !", + "going out and enjoying" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes . How about going out and enjoying the sunshine on the grass ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Great , let's go !", + "emotion": "neutral", + "text": "Great , let's go !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Hey , darling , I think I might have a little heatstroke from being in the sun all day . I was so relaxed . It felt as if I were in another world .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 4 + ], + "expanded emotion cause span": [ + "What a nice day !", + "going out and enjoying", + "I was so relaxed . It felt as if I were in another world ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Hey , darling , I think I might have a little heatstroke from being in the sun all day . I was so relaxed . It felt as if I were in another world .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Exactly . You know , the sunshine and wind remind me of our honeymoon . You remember ? The island , the sound of the waves , the salty sea air and the sunshine ...", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 4, + 5 + ], + "expanded emotion cause span": [ + "What a nice day !", + "going out and enjoying", + "I was so relaxed . It felt as if I were in another world .", + "the sunshine and wind remind me of our honeymoon ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Exactly . You know , the sunshine and wind remind me of our honeymoon . You remember ? The island , the sound of the waves , the salty sea air and the sunshine ...", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yes , it was wonderful but it's already been a year . How time flies !", + "emotion": "neutral", + "text": "Yes , it was wonderful but it's already been a year . How time flies !", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Why not go again to celebrate our one-year anniversary ? We can go to the same beach , stay in the same hotel and enjoy a dinner in the same restaurant .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 4, + 5, + 7, + 7 + ], + "expanded emotion cause span": [ + "What a nice day !", + "going out and enjoying", + "I was so relaxed . It felt as if I were in another world .", + "the sunshine and wind remind me of our honeymoon .", + "go again to celebrate", + "enjoy a dinner" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Why not go again to celebrate our one-year anniversary ? We can go to the same beach , stay in the same hotel and enjoy a dinner in the same restaurant .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Are you kidding ? Can you afford it ? Do you think we can get a room on such short voice ?", + "emotion": "neutral", + "text": "Are you kidding ? Can you afford it ? Do you think we can get a room on such short voice ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Never mind that , I'll take care of it . Are you available next week ?", + "emotion": "neutral", + "text": "Never mind that , I'll take care of it . Are you available next week ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Yeah , I think so .", + "emotion": "neutral", + "text": "Yeah , I think so .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Ok . I'll make the arrangements . It will be great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 7, + 11 + ], + "expanded emotion cause span": [ + "go again to celebrate", + "enjoy a dinner", + "It will be great ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Ok . I'll make the arrangements . It will be great .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Wonderful ! I'll start packing our suitcases .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 11 + ], + "expanded emotion cause span": [ + "It will be great .", + "I'll make the arrangements . It will be great ." + ], + "type": [ + "inter-personal" + ], + "text": "Wonderful ! I'll start packing our suitcases .", + "id": 12, + "source_sentences": [ + 10, + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_677.json b/reccon/sources/tr_677.json new file mode 100644 index 0000000000000000000000000000000000000000..668b03c035a605a5db4de3eb5d805fab20e59684 --- /dev/null +++ b/reccon/sources/tr_677.json @@ -0,0 +1,138 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Could you tell me what university you want to go to , John ?", + "emotion": "neutral", + "text": "Could you tell me what university you want to go to , John ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Pardon ?", + "emotion": "surprise", + "explanation": "The speaker is confused by the question", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Pardon ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What university would you enter ?", + "emotion": "neutral", + "text": "What university would you enter ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "University ? Why ? You asked me last year .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "What university would you enter ?", + "You asked me last year ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "University ? Why ? You asked me last year .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Oh , I forget . Sorry .", + "emotion": "neutral", + "text": "Oh , I forget . Sorry .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I went to Harvard University .", + "emotion": "neutral", + "text": "I went to Harvard University .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Did you ? And what course did you take there ?", + "emotion": "neutral", + "text": "Did you ? And what course did you take there ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "God save me ! Is there anything wrong with you ? Didn't I tell you ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "what course did you take there ?", + "Didn't I tell you ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "God save me ! Is there anything wrong with you ? Didn't I tell you ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I've not known . Perhaps , I've got a bad memory .", + "emotion": "neutral", + "text": "I've not known . Perhaps , I've got a bad memory .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I did a B . A . in economics . Remember ?", + "emotion": "neutral", + "text": "I did a B . A . in economics . Remember ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Terrific ! B . A . , again and again-B . A .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "B . A . in economics" + ], + "type": [ + "inter-personal" + ], + "text": "Terrific ! B . A . , again and again-B . A .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_6796.json b/reccon/sources/tr_6796.json new file mode 100644 index 0000000000000000000000000000000000000000..31ae9ab70591eea6f2a2b5053c5ef69fbae1d249 --- /dev/null +++ b/reccon/sources/tr_6796.json @@ -0,0 +1,124 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What a wonderful sight !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "a wonderful sight" + ], + "type": [ + "no-context" + ], + "text": "What a wonderful sight !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes . I've dreamed a thousand times that I could lie down here to relax .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Yes . I've dreamed a thousand times that I could lie down here to relax ." + ], + "type": [ + "no-context" + ], + "text": "Yes . I've dreamed a thousand times that I could lie down here to relax .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "We are tired of jobs and competition . We need a quiet place .", + "emotion": "neutral", + "text": "We are tired of jobs and competition . We need a quiet place .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I'd like to stay here for all my life if possible .", + "emotion": "neutral", + "text": "I'd like to stay here for all my life if possible .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "So would I . Look , it might be going to rain .", + "emotion": "neutral", + "text": "So would I . Look , it might be going to rain .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I don't think it will spoil our trip .", + "emotion": "neutral", + "text": "I don't think it will spoil our trip .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "It will give us better feeling and atmosphere if it rains .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "It will give us better feeling and atmosphere if it rains ." + ], + "type": [ + "no-context" + ], + "text": "It will give us better feeling and atmosphere if it rains .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Let's kick off our shoes to walk on the green flag stoned roads .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Let's kick off our shoes to walk on the green flag stoned roads ." + ], + "type": [ + "no-context" + ], + "text": "Let's kick off our shoes to walk on the green flag stoned roads .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "That's a good idea !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Let's kick off our shoes to walk on the green flag stoned roads ." + ], + "type": [ + "inter-personal" + ], + "text": "That's a good idea !", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_6828.json b/reccon/sources/tr_6828.json new file mode 100644 index 0000000000000000000000000000000000000000..cb80b6a91f3f9d16671348cf236ca0daf15331ce --- /dev/null +++ b/reccon/sources/tr_6828.json @@ -0,0 +1,165 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Oh , my God ! What's this ?", + "emotion": "neutral", + "text": "Oh , my God ! What's this ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What ?", + "emotion": "neutral", + "text": "What ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Look ! This window is open .", + "emotion": "neutral", + "text": "Look ! This window is open .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Did you open it before we left ?", + "emotion": "neutral", + "text": "Did you open it before we left ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Are you kidding ? It's winter . Why would I open it ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "Did you open it before we left ?", + "It's winter ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Are you kidding ? It's winter . Why would I open it ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I don't know . Wait . Is this yours ?", + "emotion": "neutral", + "text": "I don't know . Wait . Is this yours ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "No ! Oh , my God ! Someone has broken into the house .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Someone has broken into the house ." + ], + "type": [ + "no-context" + ], + "text": "No ! Oh , my God ! Someone has broken into the house .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "It looks that way . That's probably why the door wasn't locked when we came in .", + "emotion": "neutral", + "text": "It looks that way . That's probably why the door wasn't locked when we came in .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I locked it when I left though .", + "emotion": "neutral", + "text": "I locked it when I left though .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Yes , but the robber broke in . Then , when he left , he left through the door . So it wasn't locked .", + "emotion": "neutral", + "text": "Yes , but the robber broke in . Then , when he left , he left through the door . So it wasn't locked .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I don't care about that , Allen ! What did he steal ? That's the question !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "the robber broke in . Then , when he left , he left through the door . So it wasn't locked ." + ], + "type": [ + "inter-personal" + ], + "text": "I don't care about that , Allen ! What did he steal ? That's the question !", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Look around .", + "emotion": "neutral", + "text": "Look around .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "The TV's still here .", + "emotion": "neutral", + "text": "The TV's still here .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "And your stereo too . So what did he steal ? We have to go look upstairs .", + "emotion": "neutral", + "text": "And your stereo too . So what did he steal ? We have to go look upstairs .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "But what if someone's still up there ?", + "emotion": "neutral", + "text": "But what if someone's still up there ?", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "I don't think there will be . He left through the door , remember ?", + "emotion": "neutral", + "text": "I don't think there will be . He left through the door , remember ?", + "id": 16 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_6847.json b/reccon/sources/tr_6847.json new file mode 100644 index 0000000000000000000000000000000000000000..e6b00d9ea12173edd5219ed0d4433c044536667c --- /dev/null +++ b/reccon/sources/tr_6847.json @@ -0,0 +1,211 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I've got some great news for you !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "great news" + ], + "type": [ + "no-context" + ], + "text": "I've got some great news for you !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "did you get the position you wanted ?", + "emotion": "neutral", + "text": "did you get the position you wanted ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "yes , I'll be promoted to department manager .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "great news", + "I'll be promoted" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "yes , I'll be promoted to department manager .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I'm glad to hear that . Congratulations !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "great news", + "I'll be promoted" + ], + "type": [ + "inter-personal" + ], + "text": "I'm glad to hear that . Congratulations !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "thank you . Actually , I could not believe it at first . You know , there're so many outstanding people in our company . Many of them are qualified to fill that position .", + "emotion": "neutral", + "text": "thank you . Actually , I could not believe it at first . You know , there're so many outstanding people in our company . Many of them are qualified to fill that position .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "sure , but you really did great and outperformed the others . You deserved it !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3, + 6, + 6 + ], + "expanded emotion cause span": [ + "great news", + "I'll be promoted", + "you really did great and outperformed", + "You deserved it !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "sure , but you really did great and outperformed the others . You deserved it !", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "thank you very much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 6 + ], + "expanded emotion cause span": [ + "you really did great and outperformed", + "You deserved it !" + ], + "type": [ + "inter-personal" + ], + "text": "thank you very much .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "you always have unique ideas and you're such a team leader .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3, + 6, + 6, + 8, + 8 + ], + "expanded emotion cause span": [ + "great news", + "I'll be promoted", + "you really did great and outperformed", + "You deserved it !", + "you always have unique ideas", + "you're such a team leader ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "you always have unique ideas and you're such a team leader .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I appreciate it very much . You've been doing great . I expect to see you be promoted pretty soon .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 6, + 8, + 8, + 9 + ], + "expanded emotion cause span": [ + "you really did great and outperformed", + "You deserved it !", + "you always have unique ideas", + "you're such a team leader .", + "You've been doing great . I expect to see you be promoted" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I appreciate it very much . You've been doing great . I expect to see you be promoted pretty soon .", + "id": 9, + "source_sentences": [ + 5, + 5, + 7, + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "that's very nice of you to say so . I'll try my best . When will you start at the new position ?", + "emotion": "neutral", + "text": "that's very nice of you to say so . I'll try my best . When will you start at the new position ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "next week .", + "emotion": "neutral", + "text": "next week .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "so by then , you'll be in charge of the whole department .", + "emotion": "neutral", + "text": "so by then , you'll be in charge of the whole department .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "absolutely .", + "emotion": "neutral", + "text": "absolutely .", + "id": 13 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_6867.json b/reccon/sources/tr_6867.json new file mode 100644 index 0000000000000000000000000000000000000000..971eadda45821dde2213ab42813a3d7f7ca543aa --- /dev/null +++ b/reccon/sources/tr_6867.json @@ -0,0 +1,166 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Good afternoon , sir , is there anything I can help you with today ?", + "emotion": "neutral", + "text": "Good afternoon , sir , is there anything I can help you with today ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "umm ... yeah ! I ' m looking for a nice gift to give my girlfriend . Our fifth anniversary ' s next Friday .", + "emotion": "neutral", + "text": "umm ... yeah ! I ' m looking for a nice gift to give my girlfriend . Our fifth anniversary ' s next Friday .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Well , I would be happy to assist you in choosing the perfect gift for her . Is there anything particular that you have in mind ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I would be happy to assist you in choosing the perfect gift" + ], + "type": [ + "no-context" + ], + "text": "Well , I would be happy to assist you in choosing the perfect gift for her . Is there anything particular that you have in mind ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "No , not really ... I ' m completely at a loss .", + "emotion": "neutral", + "text": "No , not really ... I ' m completely at a loss .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Well , you can give her a set of pearl earrings , or this beautiful heart-shaped pendant . What is her favorite gemstone ?", + "emotion": "neutral", + "text": "Well , you can give her a set of pearl earrings , or this beautiful heart-shaped pendant . What is her favorite gemstone ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "That purple one . I ' m sorry ... I ' Ve never bought jewellery for anyone and I ' m kind of nervous .", + "emotion": "neutral", + "text": "That purple one . I ' m sorry ... I ' Ve never bought jewellery for anyone and I ' m kind of nervous .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Don ' t worry , we specialize in providing our customers a relaxed , pressure-free shopping environment . That stone is an amethyst . We have a range of beautiful amethyst pieces . Take a look at this bracelet . It ' s 18K rose-gold , studded with amethyst and blue topaz . It ' s a great statement piece .", + "emotion": "neutral", + "text": "Don ' t worry , we specialize in providing our customers a relaxed , pressure-free shopping environment . That stone is an amethyst . We have a range of beautiful amethyst pieces . Take a look at this bracelet . It ' s 18K rose-gold , studded with amethyst and blue topaz . It ' s a great statement piece .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Oh ... wow . That ' s really pretty . Jess would love that . But ... I was thinking of something a little more delicate , perhaps a necklace ?", + "emotion": "neutral", + "text": "Oh ... wow . That ' s really pretty . Jess would love that . But ... I was thinking of something a little more delicate , perhaps a necklace ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "We have this beautiful platinum pendant , or you could also get her a locket . You could also get her a timepiece -- it ' s both glamorous yet functional . If you tell me a little more about your girlfriend , maybe I can help you find something for her .", + "emotion": "neutral", + "text": "We have this beautiful platinum pendant , or you could also get her a locket . You could also get her a timepiece -- it ' s both glamorous yet functional . If you tell me a little more about your girlfriend , maybe I can help you find something for her .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Jess ? Well , she ' s very smart , and has a great sense of humor . She ' s very feminine ...", + "emotion": "neutral", + "text": "Jess ? Well , she ' s very smart , and has a great sense of humor . She ' s very feminine ...", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Perhaps you could give her a ring ?", + "emotion": "neutral", + "text": "Perhaps you could give her a ring ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Well ... actually ... I was thinking about asking Jess to marry me ... I ' Ve just been so nervous .", + "emotion": "neutral", + "text": "Well ... actually ... I was thinking about asking Jess to marry me ... I ' Ve just been so nervous .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Well sir , I believe your fifth anniversary is a great time to propose !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "I believe your fifth anniversary is a great time" + ], + "type": [ + "no-context" + ], + "text": "Well sir , I believe your fifth anniversary is a great time to propose !", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Okay , I ' Ve decided . I ' m going to pop the question !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13, + 14 + ], + "expanded emotion cause span": [ + "your fifth anniversary is a great time", + "I ' m going to pop the question !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Okay , I ' Ve decided . I ' m going to pop the question !", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Fabulous ! We should look at engagement rings then ! Now that ' s a whole other section .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "I ' m going to pop the question !" + ], + "type": [ + "inter-personal" + ], + "text": "Fabulous ! We should look at engagement rings then ! Now that ' s a whole other section .", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_6903.json b/reccon/sources/tr_6903.json new file mode 100644 index 0000000000000000000000000000000000000000..e2f6a9af32d5db8cee32f29eeabd2b5144195efd --- /dev/null +++ b/reccon/sources/tr_6903.json @@ -0,0 +1,152 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi there ! I am looking for a new car . I have this old Ford Pinto that I would like to trade in .", + "emotion": "neutral", + "text": "Hi there ! I am looking for a new car . I have this old Ford Pinto that I would like to trade in .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I see . You are in luck this month because all of our models are on sale ! it is a perfect time to buy a new car since it ' s the end of the year .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I am looking for a new car ." + ], + "type": [ + "inter-personal" + ], + "text": "I see . You are in luck this month because all of our models are on sale ! it is a perfect time to buy a new car since it ' s the end of the year .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Perfect ! I like this one .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "You are in luck this month because all of our models are on sale ! it is a perfect time to buy a new car since it ' s the end of the year ." + ], + "type": [ + "inter-personal" + ], + "text": "Perfect ! I like this one .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "That is the Ford Focus . A very light but powerful vehicle . It comes with dual side airbags , power steering and power windows , tinted windows and your choice of either automatic or manual transmission .", + "emotion": "neutral", + "text": "That is the Ford Focus . A very light but powerful vehicle . It comes with dual side airbags , power steering and power windows , tinted windows and your choice of either automatic or manual transmission .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Sounds like a good car ! How many miles to the gallon ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "A very light but powerful vehicle . It comes with dual side airbags , power steering and power windows , tinted windows and your choice of either automatic or manual transmission ." + ], + "type": [ + "inter-personal" + ], + "text": "Sounds like a good car ! How many miles to the gallon ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "It is a very fuel efficient vehicle giving you about 34 miles in the city and 40 on the highway .", + "emotion": "neutral", + "text": "It is a very fuel efficient vehicle giving you about 34 miles in the city and 40 on the highway .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "That is really convenient . Especially now that fuel prices are so high ! What ' s under the hood ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "very fuel efficient vehicle giving you about 34 miles in the city and 40 on the highway ." + ], + "type": [ + "inter-personal" + ], + "text": "That is really convenient . Especially now that fuel prices are so high ! What ' s under the hood ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "A very powerful 2 . 5- liter turbocharged engine , Trust me , this car is fast !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "What ' s under the hood ?", + "A very powerful 2 . 5- liter turbocharged engine , Trust me , this car is fast !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "A very powerful 2 . 5- liter turbocharged engine , Trust me , this car is fast !", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Now for the most difficult question . What is the price tag for this lovely vehicle ?", + "emotion": "neutral", + "text": "Now for the most difficult question . What is the price tag for this lovely vehicle ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Very affordable sir . You can take it out of this lot today with 0 % down payment and no interest for the first year ! You can test drive it now and we can sign the papers when we get back .", + "emotion": "neutral", + "text": "Very affordable sir . You can take it out of this lot today with 0 % down payment and no interest for the first year ! You can test drive it now and we can sign the papers when we get back .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Great ! Let ' s do it !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Very affordable sir . You can take it out of this lot today with 0 % down payment and no interest for the first year ! You can test drive it now and we can sign the papers when we get back ." + ], + "type": [ + "inter-personal" + ], + "text": "Great ! Let ' s do it !", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_692.json b/reccon/sources/tr_692.json new file mode 100644 index 0000000000000000000000000000000000000000..8d43084352856c7ecb5111ab8f7bc7d65bf7e0e6 --- /dev/null +++ b/reccon/sources/tr_692.json @@ -0,0 +1,104 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Jim , I heard you ' Ve bought a new computer .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I heard you ' Ve bought a new computer ." + ], + "type": [ + "no-context" + ], + "text": "Jim , I heard you ' Ve bought a new computer .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes . Look , it is on my desk .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "bought a new computer ." + ], + "type": [ + "inter-personal" + ], + "text": "Yes . Look , it is on my desk .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Your office looks different with a computer . By the way , is it difficult to use a computer ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Your office looks different with a computer ." + ], + "type": [ + "no-context" + ], + "text": "Your office looks different with a computer . By the way , is it difficult to use a computer ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Not at all . It ' s a piece of cake .", + "emotion": "neutral", + "text": "Not at all . It ' s a piece of cake .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "A piece of cake ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "A piece of cake ?" + ], + "type": [ + "no-context" + ], + "text": "A piece of cake ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yes . It ' s easy and convenient to use a computer . But it takes a long time to really master it .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 1, + 6 + ], + "expanded emotion cause span": [ + "bought a new computer .", + "It ' s easy and convenient to use a computer ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes . It ' s easy and convenient to use a computer . But it takes a long time to really master it .", + "id": 6, + "source_sentences": [ + 0 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_6931.json b/reccon/sources/tr_6931.json new file mode 100644 index 0000000000000000000000000000000000000000..367d8fba0f03b948f9aa8596e9436fae1353297e --- /dev/null +++ b/reccon/sources/tr_6931.json @@ -0,0 +1,104 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Congratulations ! I heard that you are going to take a two-week training course in the headquarter .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Congratulations !" + ], + "type": [ + "no-context" + ], + "text": "Congratulations ! I heard that you are going to take a two-week training course in the headquarter .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Thank you . I am very happy to have this opportunity to learn something new . You know information and knowledge in this field update very fast .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "Congratulations !", + "happy to have this opportunity" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you . I am very happy to have this opportunity to learn something new . You know information and knowledge in this field update very fast .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Sure it is . This is a changing world . Does the training course cover the new law and regulation issued last month ? They are very useful for us .", + "emotion": "neutral", + "text": "Sure it is . This is a changing world . Does the training course cover the new law and regulation issued last month ? They are very useful for us .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes , according to the agenda , there will be a seminar on these issues at the very beginning of the training course .", + "emotion": "neutral", + "text": "Yes , according to the agenda , there will be a seminar on these issues at the very beginning of the training course .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Well , good for you . I hope you can get what you want from the training .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4, + 4, + 5 + ], + "expanded emotion cause span": [ + "Does the training course cover the new law and regulation", + "Yes ,", + "there will be a seminar on these issues", + "I hope you can get what you want from the training ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Well , good for you . I hope you can get what you want from the training .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I will do my best .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "good for you . I hope you can get what you want from the training .", + "I will do my best ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I will do my best .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_6984.json b/reccon/sources/tr_6984.json new file mode 100644 index 0000000000000000000000000000000000000000..ad33326e5e201e026581a2362accbdf49e5b206b --- /dev/null +++ b/reccon/sources/tr_6984.json @@ -0,0 +1,194 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Brooke , I have bad news .", + "emotion": "neutral", + "text": "Brooke , I have bad news .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I have bad news ." + ], + "type": [ + "inter-personal" + ], + "text": "What !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I called the airlines to reconfirm the reservations today .", + "emotion": "neutral", + "text": "I called the airlines to reconfirm the reservations today .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Don't you dare tell me that ...", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "I have bad news .", + "I called the airlines to reconfirm the reservations today ." + ], + "type": [ + "inter-personal" + ], + "text": "Don't you dare tell me that ...", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I'm sorry . I didn't reconfirm in time and they gave away half of the seats .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I'm sorry . I didn't reconfirm in time and they gave away half of the seats ." + ], + "type": [ + "no-context" + ], + "text": "I'm sorry . I didn't reconfirm in time and they gave away half of the seats .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Well , they should have called you !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I didn't reconfirm in time and they gave away half of the seats ." + ], + "type": [ + "inter-personal" + ], + "text": "Well , they should have called you !", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "They said that they did . I've been so busy ...", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "They said that they did ." + ], + "type": [ + "no-context" + ], + "text": "They said that they did . I've been so busy ...", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "And you didn't think to leave them my cell phone ?", + "emotion": "anger", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "you didn't think to leave them my cell phone ?" + ], + "type": [ + "no-context" + ], + "text": "And you didn't think to leave them my cell phone ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I didn't think there would be a problem .", + "emotion": "neutral", + "text": "I didn't think there would be a problem .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "It's the holidays ! Everybody knows how hard it is to get tickets !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "It's the holidays ! Everybody knows how hard it is to get tickets !" + ], + "type": [ + "no-context" + ], + "text": "It's the holidays ! Everybody knows how hard it is to get tickets !", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I'm sorry . We're still going . I got reservations for all of us on the 31st . It will be OK . Trust me .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I'm sorry ." + ], + "type": [ + "no-context" + ], + "text": "I'm sorry . We're still going . I got reservations for all of us on the 31st . It will be OK . Trust me .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Trust you ! You can't even handle simple plane reservations !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "You can't even handle simple plane reservations !" + ], + "type": [ + "no-context" + ], + "text": "Trust you ! You can't even handle simple plane reservations !", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Brooke !", + "emotion": "neutral", + "text": "Brooke !", + "id": 13 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_7.json b/reccon/sources/tr_7.json new file mode 100644 index 0000000000000000000000000000000000000000..e97e272b4154e8a0e5feed56f2bb5b85ec9aa407 --- /dev/null +++ b/reccon/sources/tr_7.json @@ -0,0 +1,187 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I hear you bought a new house in the northern suburbs .", + "emotion": "neutral", + "text": "I hear you bought a new house in the northern suburbs .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "That ' s right , we bought it the same day we came on the market .", + "emotion": "neutral", + "text": "That ' s right , we bought it the same day we came on the market .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What kind of house is it ?", + "emotion": "neutral", + "text": "What kind of house is it ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It ' s a wonderful Spanish style .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "wonderful Spanish style ." + ], + "type": [ + "no-context" + ], + "text": "It ' s a wonderful Spanish style .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Oh , I love the roof tiles on Spanish style houses .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "wonderful Spanish style .", + "I love the roof tiles on Spanish style houses ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , I love the roof tiles on Spanish style houses .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "And it ' s a bargaining . A house like this in river side costs double the price .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5, + 6 + ], + "expanded emotion cause span": [ + "wonderful Spanish style .", + "I love the roof tiles on Spanish style houses .", + "And it ' s a bargaining . A house like this in river side costs double the price ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "And it ' s a bargaining . A house like this in river side costs double the price .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Great , is it a two bedroom house ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "And it ' s a bargaining . A house like this in river side costs double the price ." + ], + "type": [ + "inter-personal" + ], + "text": "Great , is it a two bedroom house ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "No , it has three bedrooms and three beds , and has a living room with a twelve-foot ceiling . There ' s a two-car garage .", + "emotion": "neutral", + "text": "No , it has three bedrooms and three beds , and has a living room with a twelve-foot ceiling . There ' s a two-car garage .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "That ' s a nice area too . It ' ll be a good investment for you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "three bedrooms and three beds , and has a living room with a twelve-foot ceiling . There ' s a two-car garage .", + "nice area too . It ' ll be a good investment for you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That ' s a nice area too . It ' ll be a good investment for you .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Yeas , when will you buy a house ?", + "emotion": "neutral", + "text": "Yeas , when will you buy a house ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Not untill the end of this year , you know , just before my wedding .", + "emotion": "neutral", + "text": "Not untill the end of this year , you know , just before my wedding .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Right , congratulations .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "my wedding" + ], + "type": [ + "inter-personal" + ], + "text": "Right , congratulations .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Thank you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "my wedding", + "congratulations" + ], + "type": [ + "hybrid" + ], + "text": "Thank you .", + "id": 13 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_7044.json b/reccon/sources/tr_7044.json new file mode 100644 index 0000000000000000000000000000000000000000..244671058afe83ae685d6355a86d459489311a18 --- /dev/null +++ b/reccon/sources/tr_7044.json @@ -0,0 +1,198 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Listen , Karen , I need your help . I don't know anyone here yet .", + "emotion": "neutral", + "text": "Listen , Karen , I need your help . I don't know anyone here yet .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'm glad to help you . What's wrong ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I'm glad to help you ." + ], + "type": [ + "no-context" + ], + "text": "I'm glad to help you . What's wrong ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "My mother-in-law just went into the hospital in L . A . Hank and I will be flying there tonight .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "My mother-in-law just went into the hospital in L . A" + ], + "type": [ + "no-context" + ], + "text": "My mother-in-law just went into the hospital in L . A . Hank and I will be flying there tonight .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I'm sorry to hear it . What's wrong with her ?", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "My mother-in-law just went into the hospital in L . A" + ], + "type": [ + "inter-personal" + ], + "text": "I'm sorry to hear it . What's wrong with her ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Doctors aren't sure yet . But the real problem is Suzy . She has a bad cold , and we don't want to take her with us . But we don't know who can stay with her .", + "emotion": "neutral", + "text": "Doctors aren't sure yet . But the real problem is Suzy . She has a bad cold , and we don't want to take her with us . But we don't know who can stay with her .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "You need a babysitter .", + "emotion": "neutral", + "text": "You need a babysitter .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yes , I'd ask Jill , the girl I've had before , but I need someone overnight . Maybe even for two nights .", + "emotion": "neutral", + "text": "Yes , I'd ask Jill , the girl I've had before , but I need someone overnight . Maybe even for two nights .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I could have Suzy stay at my place .", + "emotion": "neutral", + "text": "I could have Suzy stay at my place .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I don't want to do that to you , Karen .", + "emotion": "neutral", + "text": "I don't want to do that to you , Karen .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Why not ?", + "emotion": "neutral", + "text": "Why not ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Your own kids would get Suzy's cold . I think it would be better to have a good babysitter here . But I don't know who to ask . I need someone more mature than Jill . It might even be for two or three days .", + "emotion": "neutral", + "text": "Your own kids would get Suzy's cold . I think it would be better to have a good babysitter here . But I don't know who to ask . I need someone more mature than Jill . It might even be for two or three days .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I know who we can ask . There is a girl I know , Sara Ralston . She is 17 , and she will usually take this kind of job . I know her from my church , and I trust her completely .", + "emotion": "neutral", + "text": "I know who we can ask . There is a girl I know , Sara Ralston . She is 17 , and she will usually take this kind of job . I know her from my church , and I trust her completely .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I'd like to talk with her . This is short notice , I know . But Hank and I are leaving tonight .", + "emotion": "neutral", + "text": "I'd like to talk with her . This is short notice , I know . But Hank and I are leaving tonight .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "I'll get you her number . I hope she can do it . She is very responsible .", + "emotion": "neutral", + "text": "I'll get you her number . I hope she can do it . She is very responsible .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "I'm glad you know someone . I knew you would be the best person to ask about this . I don't want to insult Jill or her mother . I think Jill maybe could do it . But I'd rather have someone a little older .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 12, + 14 + ], + "expanded emotion cause span": [ + "need a babysitter", + "I know who we can ask . There is a girl I know , Sara Ralston . She is 17 , and she will usually take this kind of job . I know her from my church , and I trust her completely .", + "She is very responsible ." + ], + "type": [ + "inter-personal" + ], + "text": "I'm glad you know someone . I knew you would be the best person to ask about this . I don't want to insult Jill or her mother . I think Jill maybe could do it . But I'd rather have someone a little older .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "I'll go home and get Sara's number . I'll call her first myself .", + "emotion": "neutral", + "text": "I'll go home and get Sara's number . I'll call her first myself .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "Great . Then call me and let me know if she's free .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 12, + 14 + ], + "expanded emotion cause span": [ + "need a babysitter", + "I know who we can ask . There is a girl I know , Sara Ralston . She is 17 , and she will usually take this kind of job . I know her from my church , and I trust her completely .", + "She is very responsible ." + ], + "type": [ + "inter-personal" + ], + "text": "Great . Then call me and let me know if she's free .", + "id": 17, + "source_sentences": [ + 5, + 11, + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_7050.json b/reccon/sources/tr_7050.json new file mode 100644 index 0000000000000000000000000000000000000000..4020a9d76efaac06525c1db3ad14577d46512a0a --- /dev/null +++ b/reccon/sources/tr_7050.json @@ -0,0 +1,272 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I really appreciate your driving me around .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I really appreciate your driving me around ." + ], + "type": [ + "no-context" + ], + "text": "I really appreciate your driving me around .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It's no problem . I have time today , and I think it's important that you find a good place .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I really appreciate your driving me around ." + ], + "type": [ + "inter-personal" + ], + "text": "It's no problem . I have time today , and I think it's important that you find a good place .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "It would be hard for just me to do it . I don't know the city at all .", + "emotion": "neutral", + "text": "It would be hard for just me to do it . I don't know the city at all .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "So what do you see in there ?", + "emotion": "neutral", + "text": "So what do you see in there ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "This one sounds good . Efficiency with view of the lake . Utilities and parking included . Newly remodeled kitchen . $ 470 .", + "emotion": "neutral", + "text": "This one sounds good . Efficiency with view of the lake . Utilities and parking included . Newly remodeled kitchen . $ 470 .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Can you afford that much ?", + "emotion": "neutral", + "text": "Can you afford that much ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "No , I guess not . But that's what I want , isn't it ? An efficiency .", + "emotion": "neutral", + "text": "No , I guess not . But that's what I want , isn't it ? An efficiency .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yes , an efficiency is a small apartment . Usually one large room and a small bathroom . There is often a small kitchen too . So it's good for one person .", + "emotion": "neutral", + "text": "Yes , an efficiency is a small apartment . Usually one large room and a small bathroom . There is often a small kitchen too . So it's good for one person .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "How about this one ? Downtown efficiency . Furnished ... What does furnished mean ?", + "emotion": "neutral", + "text": "How about this one ? Downtown efficiency . Furnished ... What does furnished mean ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "That means the apartment has furniture in it .", + "emotion": "neutral", + "text": "That means the apartment has furniture in it .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "That's good .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "That means the apartment has furniture in it ." + ], + "type": [ + "inter-personal" + ], + "text": "That's good .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Sometimes it's good , sometimes it's bad . You have to like the furniture .", + "emotion": "neutral", + "text": "Sometimes it's good , sometimes it's bad . You have to like the furniture .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Furnished . Parking included . $ 400 .", + "emotion": "neutral", + "text": "Furnished . Parking included . $ 400 .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "It's still pretty expensive .", + "emotion": "neutral", + "text": "It's still pretty expensive .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Yes , but it's downtown . I would like to take look at this one .", + "emotion": "neutral", + "text": "Yes , but it's downtown . I would like to take look at this one .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Alright . What's the phone number ?", + "emotion": "neutral", + "text": "Alright . What's the phone number ?", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "256-7797 .", + "emotion": "neutral", + "text": "256-7797 .", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "Got it . What else do you see ?", + "emotion": "neutral", + "text": "Got it . What else do you see ?", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "This one . Two male grad students seeking roommate . Must be quiet . Comfortable downtown apartment . Does this mean I have to share a room with them ?", + "emotion": "neutral", + "text": "This one . Two male grad students seeking roommate . Must be quiet . Comfortable downtown apartment . Does this mean I have to share a room with them ?", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "No . It probably means they have a large apartment . Probably a living room , kitchen and three bedrooms . They need someone for the empty bedroom .", + "emotion": "neutral", + "text": "No . It probably means they have a large apartment . Probably a living room , kitchen and three bedrooms . They need someone for the empty bedroom .", + "id": 20 + }, + { + "turn": 21, + "speaker": "A", + "utterance": "That sounds alright .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 20 + ], + "expanded emotion cause span": [ + "They need someone for the empty bedroom ." + ], + "type": [ + "inter-personal" + ], + "text": "That sounds alright .", + "id": 21 + }, + { + "turn": 22, + "speaker": "B", + "utterance": "Yes , it might be an advantage for you . You are a foreigner , after all . If they're alright roommates , you could learn a lot from them .", + "emotion": "neutral", + "text": "Yes , it might be an advantage for you . You are a foreigner , after all . If they're alright roommates , you could learn a lot from them .", + "id": 22 + }, + { + "turn": 23, + "speaker": "A", + "utterance": "Here's the number , 256-4367 .", + "emotion": "neutral", + "text": "Here's the number , 256-4367 .", + "id": 23 + }, + { + "turn": 24, + "speaker": "B", + "utterance": "Got it . Let ' s call these two and see if we can make appointments to see the apartments .", + "emotion": "neutral", + "text": "Got it . Let ' s call these two and see if we can make appointments to see the apartments .", + "id": 24 + }, + { + "turn": 25, + "speaker": "A", + "utterance": "Sounds good to me . I really appreciate your help on this .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 24, + 25 + ], + "expanded emotion cause span": [ + "Let ' s call these two and see if we can make appointments to see the apartments .", + "Sounds good to me . I really appreciate your help on this ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Sounds good to me . I really appreciate your help on this .", + "id": 25 + }, + { + "turn": 26, + "speaker": "B", + "utterance": "Don't mention it , Larry . What are friends for anyway ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 25 + ], + "expanded emotion cause span": [ + "I really appreciate your help on this ." + ], + "type": [ + "inter-personal" + ], + "text": "Don't mention it , Larry . What are friends for anyway ?", + "id": 26, + "source_sentences": [ + 24 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_710.json b/reccon/sources/tr_710.json new file mode 100644 index 0000000000000000000000000000000000000000..9a35283e173d3d61ddf02deef34ec2adb0668658 --- /dev/null +++ b/reccon/sources/tr_710.json @@ -0,0 +1,171 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey Mark . What are you doing ?", + "emotion": "neutral", + "text": "Hey Mark . What are you doing ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Just watching some TV .", + "emotion": "neutral", + "text": "Just watching some TV .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Anything interesting on ?", + "emotion": "neutral", + "text": "Anything interesting on ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Not really . Just watching the sports highlight on ESPN .", + "emotion": "neutral", + "text": "Not really . Just watching the sports highlight on ESPN .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "So I take it you're pretty bored too .", + "emotion": "neutral", + "text": "So I take it you're pretty bored too .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Just killing time until I find something to do . What are you going to do ?", + "emotion": "neutral", + "text": "Just killing time until I find something to do . What are you going to do ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "It's Saturday and we are sitting at home doing nothing . What's wrong with us ?", + "emotion": "neutral", + "text": "It's Saturday and we are sitting at home doing nothing . What's wrong with us ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "You wanna shoot some hoops ?", + "emotion": "neutral", + "text": "You wanna shoot some hoops ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I already tried to call up some of the guys , but they are all busy .", + "emotion": "neutral", + "text": "I already tried to call up some of the guys , but they are all busy .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Where's your girlfriend ? I thought you were going out with her today .", + "emotion": "neutral", + "text": "Where's your girlfriend ? I thought you were going out with her today .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "She's out shopping with her friends .", + "emotion": "neutral", + "text": "She's out shopping with her friends .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Let's go to Starbucks and think of something to do then .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "Let's go to Starbucks" + ], + "type": [ + "no-context" + ], + "text": "Let's go to Starbucks and think of something to do then .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Aright . Do you have any cigarettes ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "Let's go to Starbucks" + ], + "type": [ + "inter-personal" + ], + "text": "Aright . Do you have any cigarettes ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "I only have a couple left . Why don't you pick some up on the way .", + "emotion": "neutral", + "text": "I only have a couple left . Why don't you pick some up on the way .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Ok . See you there in about 30 minutes .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "Let's go to Starbucks" + ], + "type": [ + "inter-personal" + ], + "text": "Ok . See you there in about 30 minutes .", + "id": 15, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Aright . See you there .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "Let's go to Starbucks" + ], + "type": [ + "self-contagion" + ], + "text": "Aright . See you there .", + "id": 16 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_7105.json b/reccon/sources/tr_7105.json new file mode 100644 index 0000000000000000000000000000000000000000..11f16dde88a851aec6c6d654f50c73939b64a74e --- /dev/null +++ b/reccon/sources/tr_7105.json @@ -0,0 +1,125 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I'm so glad we decided to go on a cruise for our vacation .", + "emotion": "neutral", + "text": "I'm so glad we decided to go on a cruise for our vacation .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Are you even glad that we get to buy new clothes too ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "cruise for our vacation .", + "we get to buy new clothes too ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Are you even glad that we get to buy new clothes too ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Ah , that's all part of the fun . What do you think of these shorts ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 3 + ], + "expanded emotion cause span": [ + "cruise for our vacation .", + "we get to buy new clothes too ?", + "these shorts ?" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Ah , that's all part of the fun . What do you think of these shorts ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "They look really good on you . They look comfortable too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 3, + 4 + ], + "expanded emotion cause span": [ + "cruise for our vacation .", + "we get to buy new clothes too ?", + "these shorts ?", + "They look really good on you . They look comfortable too ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "They look really good on you . They look comfortable too .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "They are . I think I'm going to get a hat too .", + "emotion": "neutral", + "text": "They are . I think I'm going to get a hat too .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Okay . I chose this swimming suit . Do you like it ?", + "emotion": "neutral", + "text": "Okay . I chose this swimming suit . Do you like it ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Wow . You look great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I chose this swimming suit . Do you like it ?", + "You look great ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Wow . You look great .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Great and white ! Which reminds me , let's pick up some heavy duty sunscreen !", + "emotion": "neutral", + "text": "Great and white ! Which reminds me , let's pick up some heavy duty sunscreen !", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_7161.json b/reccon/sources/tr_7161.json new file mode 100644 index 0000000000000000000000000000000000000000..fdebd80ae9e8a7f61f41c49014ca1b88568148b3 --- /dev/null +++ b/reccon/sources/tr_7161.json @@ -0,0 +1,144 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Did you call me ?", + "emotion": "neutral", + "text": "Did you call me ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Thank you for returning my call .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "returning my call ." + ], + "type": [ + "no-context" + ], + "text": "Thank you for returning my call .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What was your call about ?", + "emotion": "neutral", + "text": "What was your call about ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I wanted to have a talk with you about your son .", + "emotion": "neutral", + "text": "I wanted to have a talk with you about your son .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "What did he do ?", + "emotion": "neutral", + "text": "What did he do ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "He was messing around last week in class .", + "emotion": "neutral", + "text": "He was messing around last week in class .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Exactly what did he do ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "He was messing around" + ], + "type": [ + "inter-personal" + ], + "text": "Exactly what did he do ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Even though I asked him not to , he kept speaking out in class .", + "emotion": "neutral", + "text": "Even though I asked him not to , he kept speaking out in class .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I don't know what his problem is .", + "emotion": "neutral", + "text": "I don't know what his problem is .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I need you to talk to him , if you don't mind .", + "emotion": "neutral", + "text": "I need you to talk to him , if you don't mind .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "That won't happen again , I'm sorry .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "he kept speaking out in class .", + "I don't know what his problem is ." + ], + "type": [ + "hybrid" + ], + "text": "That won't happen again , I'm sorry .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Thank you . Hopefully I won't have to call about him again .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 11 + ], + "expanded emotion cause span": [ + "That won't happen again ,", + "sorry ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . Hopefully I won't have to call about him again .", + "id": 12, + "source_sentences": [ + 10, + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_7171.json b/reccon/sources/tr_7171.json new file mode 100644 index 0000000000000000000000000000000000000000..f91741aa2aca0b5cde3473b4a7ddff9a520e849d --- /dev/null +++ b/reccon/sources/tr_7171.json @@ -0,0 +1,146 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hurry up , get in .", + "emotion": "neutral", + "text": "Hurry up , get in .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I ' m in , let ' s go !", + "emotion": "neutral", + "text": "I ' m in , let ' s go !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "OK , make a left here . . . no wait , I meant make a right . Come on , speed up !", + "emotion": "neutral", + "text": "OK , make a left here . . . no wait , I meant make a right . Come on , speed up !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Geez ! What ' s the rush ?", + "emotion": "neutral", + "text": "Geez ! What ' s the rush ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Don ' t worry about it , just drive . Oh , no , the light is about to change . . . step on it !", + "emotion": "neutral", + "text": "Don ' t worry about it , just drive . Oh , no , the light is about to change . . . step on it !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Are you nuts ! I ' m not going to run a red light !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "step on it !" + ], + "type": [ + "inter-personal" + ], + "text": "Are you nuts ! I ' m not going to run a red light !", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Whatever . Just turn right here . . . The freeway will be packed at this hour . . . let ' s take a side street . Go on ! Get out of our way ! Move , move !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "Are you nuts ! I ' m not going to run a red light !", + "Get out of our way !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Whatever . Just turn right here . . . The freeway will be packed at this hour . . . let ' s take a side street . Go on ! Get out of our way ! Move , move !", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "What ' s your problem ! Geez . Having a fit is not going to help !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 8, + 8 + ], + "expanded emotion cause span": [ + "What ' s your problem !", + "Having a fit is not going to help !" + ], + "type": [ + "no-context" + ], + "text": "What ' s your problem ! Geez . Having a fit is not going to help !", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Here , I know a short cut ... just go down here , and we ' ll cut though Ashburn Heights . Let ' s go , let ' s go ! Watch out for that lady !", + "emotion": "neutral", + "text": "Here , I know a short cut ... just go down here , and we ' ll cut though Ashburn Heights . Let ' s go , let ' s go ! Watch out for that lady !", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I ' m going as fast as I can !", + "emotion": "neutral", + "text": "I ' m going as fast as I can !", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Yes ! We made it . 5 fifty-eight , just before the library closes .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 11 + ], + "expanded emotion cause span": [ + "We made it .", + "before the library closes ." + ], + "type": [ + "no-context" + ], + "text": "Yes ! We made it . 5 fifty-eight , just before the library closes .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "You ' re such a geek !", + "emotion": "neutral", + "text": "You ' re such a geek !", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_7189.json b/reccon/sources/tr_7189.json new file mode 100644 index 0000000000000000000000000000000000000000..1fc1bf4c7c5e4a17abb1874d666da9abddce5d93 --- /dev/null +++ b/reccon/sources/tr_7189.json @@ -0,0 +1,142 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "You look really nice today .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "You look really nice today ." + ], + "type": [ + "no-context" + ], + "text": "You look really nice today .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Thank you . I just got this outfit the other day .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "You look really nice today ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . I just got this outfit the other day .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Really , where did you get it ?", + "emotion": "neutral", + "text": "Really , where did you get it ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I got it from Macy's .", + "emotion": "neutral", + "text": "I got it from Macy's .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "It's really nice .", + "emotion": "neutral", + "text": "It's really nice .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Thanks again . You look nice today , too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "It's really nice ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks again . You look nice today , too .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Thank you . I just got these shoes today .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "You look nice today , too .", + "I just got these shoes today ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you . I just got these shoes today .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Really ? What kind of shoes are they ?", + "emotion": "neutral", + "text": "Really ? What kind of shoes are they ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "These are called All Star Chuck Taylors .", + "emotion": "neutral", + "text": "These are called All Star Chuck Taylors .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I really like those . How much did they cost ?", + "emotion": "neutral", + "text": "I really like those . How much did they cost ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "They were about forty dollars .", + "emotion": "neutral", + "text": "They were about forty dollars .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I think I'm going to go buy myself a pair .", + "emotion": "neutral", + "text": "I think I'm going to go buy myself a pair .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_7197.json b/reccon/sources/tr_7197.json new file mode 100644 index 0000000000000000000000000000000000000000..8de89298c15e1a25f97a90dff28f2969e6ec5255 --- /dev/null +++ b/reccon/sources/tr_7197.json @@ -0,0 +1,143 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I've enjoyed conversing with you .", + "emotion": "neutral", + "text": "I've enjoyed conversing with you .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Is there a reason why you're trying to get off the phone so fast ?", + "emotion": "anger", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "you're trying to get off the phone so fast" + ], + "type": [ + "no-context" + ], + "text": "Is there a reason why you're trying to get off the phone so fast ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I've got to go .", + "emotion": "neutral", + "text": "I've got to go .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I wasn't done talking to you .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 2, + 4 + ], + "expanded emotion cause span": [ + "you're trying to get off the phone so fast", + "I wasn't done talking to you ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I wasn't done talking to you .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I have to do some things , and besides , it's not polite to be nosey .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "I wasn't done talking to you .", + "it's not polite to be nosey ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I have to do some things , and besides , it's not polite to be nosey .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I'm not being nosey . I'm just asking .", + "emotion": "neutral", + "text": "I'm not being nosey . I'm just asking .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I really don't think it's any of your business .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "you're trying to get off the phone so fast" + ], + "type": [ + "inter-personal" + ], + "text": "I really don't think it's any of your business .", + "id": 7, + "source_sentences": [ + 1 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That's not nice .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 2, + 7, + 8 + ], + "expanded emotion cause span": [ + "you're trying to get off the phone so fast", + "I really don't think it's any of your business .", + "That's not nice ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "That's not nice .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I apologize , but I'm getting off the phone now .", + "emotion": "neutral", + "text": "I apologize , but I'm getting off the phone now .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Okay .", + "emotion": "neutral", + "text": "Okay .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_72.json b/reccon/sources/tr_72.json new file mode 100644 index 0000000000000000000000000000000000000000..0d98eb76788547f6546f3268bbcb1b9c23b2a202 --- /dev/null +++ b/reccon/sources/tr_72.json @@ -0,0 +1,109 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "It smells like an ashtray in here !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "It smells like an ashtray in here !" + ], + "type": [ + "no-context" + ], + "text": "It smells like an ashtray in here !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hi honey ! What ' s wrong ? Why do you have that look on your face ?", + "emotion": "neutral", + "text": "Hi honey ! What ' s wrong ? Why do you have that look on your face ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What ' s wrong ? I thought we agreed that you were gonna quit smoking .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "It smells like an ashtray in here !", + "I thought we agreed that you were gonna quit smoking ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "What ' s wrong ? I thought we agreed that you were gonna quit smoking .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "No ! I said I was going to cut down which is very different . You can ' t just expect me to go cold turkey overnight !", + "emotion": "neutral", + "text": "No ! I said I was going to cut down which is very different . You can ' t just expect me to go cold turkey overnight !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Look , there are other ways to quit . You can try the nicotine patch , or nicotine chewing gum . We spend a fortune on cigarettes every month and now laws are cracking down and not allowing smoking in any public place . It ' s not like you can just light up like before .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1, + 3, + 4, + 5 + ], + "expanded emotion cause span": [ + "It smells like an ashtray in here !", + "I thought we agreed that you were gonna quit smoking .", + "I said I was going to cut down which is very different . You can ' t just expect me to go cold turkey overnight !", + "there are other ways to quit . You can try the nicotine patch , or nicotine chewing gum . We spend a fortune on cigarettes every month" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Look , there are other ways to quit . You can try the nicotine patch , or nicotine chewing gum . We spend a fortune on cigarettes every month and now laws are cracking down and not allowing smoking in any public place . It ' s not like you can just light up like before .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I know , I know . I am trying but , I don ' t have the willpower to just quit . I can ' t fight with the urge to reach for my pack of smokes in the morning with coffee or after lunch ! Please understand ?", + "emotion": "neutral", + "text": "I know , I know . I am trying but , I don ' t have the willpower to just quit . I can ' t fight with the urge to reach for my pack of smokes in the morning with coffee or after lunch ! Please understand ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Fine ! I want a divorce !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I am trying but , I don ' t have the willpower to just quit ." + ], + "type": [ + "inter-personal" + ], + "text": "Fine ! I want a divorce !", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_7248.json b/reccon/sources/tr_7248.json new file mode 100644 index 0000000000000000000000000000000000000000..cdb17d1d30d6a707cf3f58838ee5489997dd9a3d --- /dev/null +++ b/reccon/sources/tr_7248.json @@ -0,0 +1,154 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Next is a ballet performance , but who is the dancer ?", + "emotion": "neutral", + "text": "Next is a ballet performance , but who is the dancer ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'd swear that's Eddy from circulation .", + "emotion": "neutral", + "text": "I'd swear that's Eddy from circulation .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Since when did Eddy start doing ballet ? !", + "emotion": "neutral", + "text": "Since when did Eddy start doing ballet ? !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Not very long from the looks of it !", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Not very long from the looks of it !" + ], + "type": [ + "no-context" + ], + "text": "Not very long from the looks of it !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Look ! He has a partner !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "He has a partner !" + ], + "type": [ + "no-context" + ], + "text": "Look ! He has a partner !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "He's dancing with Jack !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "He has a partner !", + "He's dancing with Jack !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "He's dancing with Jack !", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Gross !", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "He's dancing with Jack !" + ], + "type": [ + "inter-personal" + ], + "text": "Gross !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "The wei-ya is the one time a year you can make fun of the boss .", + "emotion": "neutral", + "text": "The wei-ya is the one time a year you can make fun of the boss .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "But I think Eddy is going too far !", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 6, + 9 + ], + "expanded emotion cause span": [ + "He's dancing with Jack !", + "Eddy is going too far !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "But I think Eddy is going too far !", + "id": 9, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "You're right . They are spinning pretty fast . Aren't they getting dizzy ? What if they fall ...", + "emotion": "neutral", + "text": "You're right . They are spinning pretty fast . Aren't they getting dizzy ? What if they fall ...", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Oh ! Ouch ! That must've hurt !", + "emotion": "neutral", + "text": "Oh ! Ouch ! That must've hurt !", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "How embarrassing !", + "emotion": "neutral", + "text": "How embarrassing !", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_7257.json b/reccon/sources/tr_7257.json new file mode 100644 index 0000000000000000000000000000000000000000..6dc34bfaa361945bf963cabe6e4c8aedf2cee2ce --- /dev/null +++ b/reccon/sources/tr_7257.json @@ -0,0 +1,133 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Can I help you ?", + "emotion": "neutral", + "text": "Can I help you ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Could you show me the coat on the shelf ?", + "emotion": "neutral", + "text": "Could you show me the coat on the shelf ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Sure . Please come this way .", + "emotion": "happiness", + "explanation": "speaker is happy to help", + "flag": "F", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "Could you show me the coat on the shelf ?", + "Sure . Please come this way ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Sure . Please come this way .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "May I try it on ?", + "emotion": "neutral", + "text": "May I try it on ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Of course . Here is the fitting room .", + "emotion": "happiness", + "explanation": "speaker is happy to help", + "flag": "F", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "May I try it on ?", + "Of course . Here is the fitting room ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Of course . Here is the fitting room .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "It doesn't fit quite right . It feels a little tight in the waist . Do you have this in a larger size ?", + "emotion": "neutral", + "text": "It doesn't fit quite right . It feels a little tight in the waist . Do you have this in a larger size ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yes , here it is .", + "emotion": "neutral", + "text": "Yes , here it is .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Well , how do I look in this one ?", + "emotion": "neutral", + "text": "Well , how do I look in this one ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "You look really beautiful in it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "You look really beautiful in it ." + ], + "type": [ + "no-context" + ], + "text": "You look really beautiful in it .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "OK . I'll take it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "You look really beautiful in it ." + ], + "type": [ + "inter-personal" + ], + "text": "OK . I'll take it .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_7269.json b/reccon/sources/tr_7269.json new file mode 100644 index 0000000000000000000000000000000000000000..5b65a0f5a72d88a712ea93a5eb41dbddb7c9bb77 --- /dev/null +++ b/reccon/sources/tr_7269.json @@ -0,0 +1,170 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "My Goodness ! What a busy line so early in the morning ! Hello .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "What a busy line so early in the morning !" + ], + "type": [ + "no-context" + ], + "text": "My Goodness ! What a busy line so early in the morning ! Hello .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Ruth ? Basil .", + "emotion": "neutral", + "text": "Ruth ? Basil .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Hi , Basil .", + "emotion": "neutral", + "text": "Hi , Basil .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Want a ride to the office ?", + "emotion": "neutral", + "text": "Want a ride to the office ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Yes , by all means . I was just about to leave .", + "emotion": "neutral", + "text": "Yes , by all means . I was just about to leave .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Hold on . Just 5 minutes .", + "emotion": "neutral", + "text": "Hold on . Just 5 minutes .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I'll wait on the sidewalk . It's very kind of you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "Hold on . Just 5 minutes .", + "It's very kind of you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'll wait on the sidewalk . It's very kind of you .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "It's my pleasure . See you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "It's very kind of you .", + "It's my pleasure ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It's my pleasure . See you .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Hi , Basil .", + "emotion": "neutral", + "text": "Hi , Basil .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Hi , Ruth . Hop in .", + "emotion": "neutral", + "text": "Hi , Ruth . Hop in .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Do you mind if I take some notes while we drive ?", + "emotion": "neutral", + "text": "Do you mind if I take some notes while we drive ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Of course I don't mind . For your report ?", + "emotion": "neutral", + "text": "Of course I don't mind . For your report ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Yes , I finally have an inspiration .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "I finally have an inspiration ." + ], + "type": [ + "no-context" + ], + "text": "Yes , I finally have an inspiration .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Good for you . No problem , I'll listen to the car radio", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "I finally have an inspiration ." + ], + "type": [ + "inter-personal" + ], + "text": "Good for you . No problem , I'll listen to the car radio", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_7274.json b/reccon/sources/tr_7274.json new file mode 100644 index 0000000000000000000000000000000000000000..42dd72b2fc9558195ddf7644dd5fd44c31b7716b --- /dev/null +++ b/reccon/sources/tr_7274.json @@ -0,0 +1,104 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Why didn't you text me last night ?", + "emotion": "neutral", + "text": "Why didn't you text me last night ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What ? I sent you three or four messages !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "Why didn't you text me last night ?", + "I sent you three or four messages !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "What ? I sent you three or four messages !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I didn't get any of them . I was waiting for you to text me the address of where the party was and I never got your message .", + "emotion": "neutral", + "text": "I didn't get any of them . I was waiting for you to text me the address of where the party was and I never got your message .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Why didn't you just call ? I hate sending SMS messages .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Why didn't you just call ?" + ], + "type": [ + "no-context" + ], + "text": "Why didn't you just call ? I hate sending SMS messages .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Well , because I didn't have any credit on my phone . I used it all up this month .", + "emotion": "neutral", + "text": "Well , because I didn't have any credit on my phone . I used it all up this month .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I thought you had an unlimited SMS plan ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "I didn't have any credit on my phone .", + "I thought you had an unlimited SMS plan ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I thought you had an unlimited SMS plan ?", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I do , but if I don't have any credit in my phone , it won't let me call or send messages .", + "emotion": "neutral", + "text": "I do , but if I don't have any credit in my phone , it won't let me call or send messages .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "No wonder you didn't get my texts !", + "emotion": "neutral", + "text": "No wonder you didn't get my texts !", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_738.json b/reccon/sources/tr_738.json new file mode 100644 index 0000000000000000000000000000000000000000..c5e63059207edabf3dc78bfd5057974c4289dd07 --- /dev/null +++ b/reccon/sources/tr_738.json @@ -0,0 +1,220 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello ?", + "emotion": "neutral", + "text": "Hello ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hi Steve . This is Mike . What are you doing ?", + "emotion": "neutral", + "text": "Hi Steve . This is Mike . What are you doing ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Oh , hi . I was just watching TV .", + "emotion": "neutral", + "text": "Oh , hi . I was just watching TV .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "There's nothing to watch right now .", + "emotion": "neutral", + "text": "There's nothing to watch right now .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I know . I was watching a re-run . I have nothing to do and I was bored .", + "emotion": "neutral", + "text": "I know . I was watching a re-run . I have nothing to do and I was bored .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Me too . Let's get together and do something .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Let's get together and do something ." + ], + "type": [ + "no-context" + ], + "text": "Me too . Let's get together and do something .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I'd like to , but I have to meet my parents in an hour for dinner . How about tomorrow ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Let's get together and do something ." + ], + "type": [ + "inter-personal" + ], + "text": "I'd like to , but I have to meet my parents in an hour for dinner . How about tomorrow ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yeah . Let's plan something tomorrow .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I'd like to ," + ], + "type": [ + "inter-personal" + ], + "text": "Yeah . Let's plan something tomorrow .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Did you hear the weather forecast for tomorrow ?", + "emotion": "neutral", + "text": "Did you hear the weather forecast for tomorrow ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I think it is going to be the same as today . Clear and sunny .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Clear and sunny ." + ], + "type": [ + "no-context" + ], + "text": "I think it is going to be the same as today . Clear and sunny .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "That's great . We can do something outdoors then .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "Clear and sunny .", + "We can do something outdoors" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's great . We can do something outdoors then .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Are there any special events going on tomorrow ?", + "emotion": "neutral", + "text": "Are there any special events going on tomorrow ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Yeah . I think there's a live outdoor concert by the river tomorrow .", + "emotion": "neutral", + "text": "Yeah . I think there's a live outdoor concert by the river tomorrow .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Oh yeah . I heard about that too . Let's go check it out .", + "emotion": "neutral", + "text": "Oh yeah . I heard about that too . Let's go check it out .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Do you know what time it starts ?", + "emotion": "neutral", + "text": "Do you know what time it starts ?", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "It starts at one PM .", + "emotion": "neutral", + "text": "It starts at one PM .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "Let's meet for lunch at eleven thirty and afterwards , we can head over there .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "there's a live outdoor concert" + ], + "type": [ + "self-contagion" + ], + "text": "Let's meet for lunch at eleven thirty and afterwards , we can head over there .", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "Perfect . I'll see you in front of the apartment at eleven thirty .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13, + 17 + ], + "expanded emotion cause span": [ + "there's a live outdoor concert", + "Let's meet for lunch" + ], + "type": [ + "inter-personal" + ], + "text": "Perfect . I'll see you in front of the apartment at eleven thirty .", + "id": 18, + "source_sentences": [ + 12, + 16 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_7397.json b/reccon/sources/tr_7397.json new file mode 100644 index 0000000000000000000000000000000000000000..7a307c4f80980db8975744a2c67a0129faa7ec0a --- /dev/null +++ b/reccon/sources/tr_7397.json @@ -0,0 +1,151 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I think I may rent out this apartment that I found .", + "emotion": "neutral", + "text": "I think I may rent out this apartment that I found .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh , really ? Where ' d you find it ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I may rent out this apartment that I found ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , really ? Where ' d you find it ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I was looking through the ads today , and I found it in there .", + "emotion": "neutral", + "text": "I was looking through the ads today , and I found it in there .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "In the ads ? Are you serious ?", + "emotion": "neutral", + "text": "In the ads ? Are you serious ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Yeah , and it ' s affordable too .", + "emotion": "neutral", + "text": "Yeah , and it ' s affordable too .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I ' d like to hear about this apartment .", + "emotion": "neutral", + "text": "I ' d like to hear about this apartment .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "First of all , it ' s absolutely gorgeous .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "it ' s absolutely gorgeous ." + ], + "type": [ + "no-context" + ], + "text": "First of all , it ' s absolutely gorgeous .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "What is the rent each month ?", + "emotion": "neutral", + "text": "What is the rent each month ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "It ' s only $ 725 a month .", + "emotion": "neutral", + "text": "It ' s only $ 725 a month .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "That ' s amazing . The rent is very cheap .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "It ' s only $ 725 a month .", + "The rent is very cheap ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That ' s amazing . The rent is very cheap .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I know it is .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I know it is ." + ], + "type": [ + "no-context" + ], + "text": "I know it is .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "It ' s a good thing that you read that ad today .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "It ' s a good thing that you read that ad today ." + ], + "type": [ + "no-context" + ], + "text": "It ' s a good thing that you read that ad today .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_74.json b/reccon/sources/tr_74.json new file mode 100644 index 0000000000000000000000000000000000000000..2a1a01a145a6d60788724747e7d45df859aacef2 --- /dev/null +++ b/reccon/sources/tr_74.json @@ -0,0 +1,110 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "It seems that you get antsy when you hear I praise another guy .", + "emotion": "neutral", + "text": "It seems that you get antsy when you hear I praise another guy .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I get antsy not because you praise a guy , but because you may be taken for a ride by a guy like him .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "you may be taken for a ride by a guy like him ." + ], + "type": [ + "no-context" + ], + "text": "I get antsy not because you praise a guy , but because you may be taken for a ride by a guy like him .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "How come you think of him that way ?", + "emotion": "neutral", + "text": "How come you think of him that way ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Because you seem to have lost your vigilance . You should be on the watch out .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "you seem to have lost your vigilance ." + ], + "type": [ + "no-context" + ], + "text": "Because you seem to have lost your vigilance . You should be on the watch out .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I have no reason to distrust him . He's never caused any harm .", + "emotion": "neutral", + "text": "I have no reason to distrust him . He's never caused any harm .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Isn't there anything that sounds fishy ?", + "emotion": "anger", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "I have no reason to distrust him . He's never caused any harm .", + "sounds fishy ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Isn't there anything that sounds fishy ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Nothing smells a rat . I told you that he's an all-right guy .", + "emotion": "neutral", + "text": "Nothing smells a rat . I told you that he's an all-right guy .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "All-right guy ? All right . Let's talk about something else instead .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I told you that he's an all-right guy ." + ], + "type": [ + "inter-personal" + ], + "text": "All-right guy ? All right . Let's talk about something else instead .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_740.json b/reccon/sources/tr_740.json new file mode 100644 index 0000000000000000000000000000000000000000..b9da1ca08bcbd2a9bbdc0dabe61b1d68e9f88ce5 --- /dev/null +++ b/reccon/sources/tr_740.json @@ -0,0 +1,138 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "When can we expect you for dinner ? Can you come tonight ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "When can we expect you for dinner ?" + ], + "type": [ + "no-context" + ], + "text": "When can we expect you for dinner ? Can you come tonight ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Not tonight . I promised to go to a concert with my sister .", + "emotion": "neutral", + "text": "Not tonight . I promised to go to a concert with my sister .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Well ... How about Friday then ?", + "emotion": "neutral", + "text": "Well ... How about Friday then ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "That sounds fine .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3, + 4 + ], + "expanded emotion cause span": [ + "When can we expect you for dinner ?", + "How about Friday", + "sounds fine ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That sounds fine .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Good . Shall we say seven o'clock ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "sounds fine ." + ], + "type": [ + "inter-personal" + ], + "text": "Good . Shall we say seven o'clock ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I'll be there . You're still a fabulous cook , aren't you ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 6 + ], + "expanded emotion cause span": [ + "When can we expect you for dinner ?", + "fabulous cook" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'll be there . You're still a fabulous cook , aren't you ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "That'll be for you to decide . I've got a new dish that I want to try out on you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I'll be there . You're still a fabulous cook", + "I've got a new dish that I want to try out on you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That'll be for you to decide . I've got a new dish that I want to try out on you .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I'm ready . I'll look forward to it all Friday !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "fabulous cook", + "I've got a new dish that I want to try out on you ." + ], + "type": [ + "hybrid" + ], + "text": "I'm ready . I'll look forward to it all Friday !", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_7481.json b/reccon/sources/tr_7481.json new file mode 100644 index 0000000000000000000000000000000000000000..adaff8104551551913829be64596320d2e23aadc --- /dev/null +++ b/reccon/sources/tr_7481.json @@ -0,0 +1,257 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I like the Honda Accord you showed me before . I think it's more practical for my needs .", + "emotion": "neutral", + "text": "I like the Honda Accord you showed me before . I think it's more practical for my needs .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Alright , sir . You are making a good choice . Honda has made a lot of design improvements in the new Accord .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "I like the Honda Accord you showed me before .", + "You are making a good choice . Honda has made a lot of design improvements in the new Accord ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Alright , sir . You are making a good choice . Honda has made a lot of design improvements in the new Accord .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What does it come with standard ?", + "emotion": "neutral", + "text": "What does it come with standard ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "On all our new cars , the standards includeair conditioning , anti-lock brakes , air bags , and an AM / FM stereo with a CD player . But on the Accord , there is another standard item as well . The Accord com", + "emotion": "neutral", + "text": "On all our new cars , the standards includeair conditioning , anti-lock brakes , air bags , and an AM / FM stereo with a CD player . But on the Accord , there is another standard item as well . The Accord com", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Cruise control ? I don't like that .", + "emotion": "neutral", + "text": "Cruise control ? I don't like that .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Why not , sir ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Cruise control ? I don't like that ." + ], + "type": [ + "inter-personal" + ], + "text": "Why not , sir ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I think it's dangerous . What if I can't turn it off ?", + "emotion": "neutral", + "text": "I think it's dangerous . What if I can't turn it off ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Well , sir , I know some of our customers are concerned about cruise control . But Honda has never had a single cruise control malfunction that led to an accident .", + "emotion": "neutral", + "text": "Well , sir , I know some of our customers are concerned about cruise control . But Honda has never had a single cruise control malfunction that led to an accident .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I wish it didn't have cruise control . My wife doesn't like it either .", + "emotion": "neutral", + "text": "I wish it didn't have cruise control . My wife doesn't like it either .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "You know , sir , you don't have to use it . You can turn it on or off . If you don't want to use it , you just never turn it on .", + "emotion": "neutral", + "text": "You know , sir , you don't have to use it . You can turn it on or off . If you don't want to use it , you just never turn it on .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I suppose . And what about the sunroof ? Is that standard ?", + "emotion": "neutral", + "text": "I suppose . And what about the sunroof ? Is that standard ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "No , the sunroof is optional , sir .", + "emotion": "neutral", + "text": "No , the sunroof is optional , sir .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I see . Another important question is the time I can get this car . I need a new car rather soon .", + "emotion": "neutral", + "text": "I see . Another important question is the time I can get this car . I need a new car rather soon .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Well , I can say that the new models will be here in August . If you order one now , we will have it for you in August .", + "emotion": "neutral", + "text": "Well , I can say that the new models will be here in August . If you order one now , we will have it for you in August .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "That's good enough , I think . What colors does the new Accord come in ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13, + 14 + ], + "expanded emotion cause span": [ + "I need a new car rather soon .", + "If you order one now , we will have it for you in August ." + ], + "type": [ + "hybrid" + ], + "text": "That's good enough , I think . What colors does the new Accord come in ?", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "We have this new model in red , white , black , or silver . These are the standard colors . Of course you could specially order from various other colors too .", + "emotion": "neutral", + "text": "We have this new model in red , white , black , or silver . These are the standard colors . Of course you could specially order from various other colors too .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "My brother has last year's Accord . And his car is a kind of soft purple color mixed with silver . I really like that color . I wonder if I can get that color on my Accord .", + "emotion": "neutral", + "text": "My brother has last year's Accord . And his car is a kind of soft purple color mixed with silver . I really like that color . I wonder if I can get that color on my Accord .", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "I know the color you mean . Is this it , sir ?", + "emotion": "neutral", + "text": "I know the color you mean . Is this it , sir ?", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "Yes , I think that's it . Can I get that on the Accord ?", + "emotion": "neutral", + "text": "Yes , I think that's it . Can I get that on the Accord ?", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "Yes , you can . That color is very popular with Honda buyers . So we've kept it available .", + "emotion": "neutral", + "text": "Yes , you can . That color is very popular with Honda buyers . So we've kept it available .", + "id": 20 + }, + { + "turn": 21, + "speaker": "A", + "utterance": "Well , I think I want to order the new Accord then . It looks like an excellent car .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 17, + 20, + 21 + ], + "expanded emotion cause span": [ + "soft purple color mixed with silver . I really like that color . I wonder if I can get that color on my Accord .", + "we've kept it available .", + "It looks like an excellent car ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Well , I think I want to order the new Accord then . It looks like an excellent car .", + "id": 21 + }, + { + "turn": 22, + "speaker": "B", + "utterance": "You have made a good choice , sir . I drive an Accord myself . They are very solidly built machines , very reliable .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 21, + 22 + ], + "expanded emotion cause span": [ + "I think I want to order the new Accord then . It looks like an excellent car .", + "You have made a good choice , sir . I drive an Accord myself . They are very solidly built machines , very reliable ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You have made a good choice , sir . I drive an Accord myself . They are very solidly built machines , very reliable .", + "id": 22, + "source_sentences": [ + 20 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 23, + "speaker": "A", + "utterance": "Yes , I know . I think Honda is the most reliable car on the road . I would never change to anything else . The Honda I have now almost never has service problems . It runs smooth as silk .", + "emotion": "neutral", + "text": "Yes , I know . I think Honda is the most reliable car on the road . I would never change to anything else . The Honda I have now almost never has service problems . It runs smooth as silk .", + "id": 23 + }, + { + "turn": 24, + "speaker": "B", + "utterance": "Alright , sir . I will get the paperwork ready for you . Just a moment .", + "emotion": "neutral", + "text": "Alright , sir . I will get the paperwork ready for you . Just a moment .", + "id": 24 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_7536.json b/reccon/sources/tr_7536.json new file mode 100644 index 0000000000000000000000000000000000000000..6e1e8172c402f68b7f9f8a1696d9e95fbadf97ca --- /dev/null +++ b/reccon/sources/tr_7536.json @@ -0,0 +1,115 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Ann , it's terrible !", + "emotion": "anger", + "explanation": "What is terrible is not mentioned.", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Ann , it's terrible !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What's up ?", + "emotion": "neutral", + "text": "What's up ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Look , this is a pimple !", + "emotion": "neutral", + "text": "Look , this is a pimple !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Oh , I think it is .", + "emotion": "neutral", + "text": "Oh , I think it is .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "How come ?", + "emotion": "neutral", + "text": "How come ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I think it's because of your bad habits !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "it's because of your bad habits !" + ], + "type": [ + "no-context" + ], + "text": "I think it's because of your bad habits !", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I have no bad habit . I sleep eight hours a day , never eat spicy food , clean the face twice a day and so on . I have done a lot .", + "emotion": "neutral", + "text": "I have no bad habit . I sleep eight hours a day , never eat spicy food , clean the face twice a day and so on . I have done a lot .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I know you have done a lot , but you always sleep very late . Sleeping eight hours a day doesn't mean it is healthy . Sleeping after 12 is hurtful to our body , and I think this is your problem .", + "emotion": "neutral", + "text": "I know you have done a lot , but you always sleep very late . Sleeping eight hours a day doesn't mean it is healthy . Sleeping after 12 is hurtful to our body , and I think this is your problem .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I wasn't aware of that !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Sleeping after 12 is hurtful to our body , and I think this is your problem ." + ], + "type": [ + "inter-personal" + ], + "text": "I wasn't aware of that !", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "You should do better later .", + "emotion": "neutral", + "text": "You should do better later .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_754.json b/reccon/sources/tr_754.json new file mode 100644 index 0000000000000000000000000000000000000000..b4a9857617f21a574d151cd084d4da0d0bd42f94 --- /dev/null +++ b/reccon/sources/tr_754.json @@ -0,0 +1,161 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What a great weekend that was !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "What a great weekend that was !" + ], + "type": [ + "no-context" + ], + "text": "What a great weekend that was !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "My feelings exactly .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "What a great weekend that was !" + ], + "type": [ + "inter-personal" + ], + "text": "My feelings exactly .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I really enjoy the beach in the summer .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "What a great weekend that was !", + "I really enjoy the beach in the summer ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I really enjoy the beach in the summer .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I couldn't agree with you more .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 1, + 3 + ], + "expanded emotion cause span": [ + "What a great weekend that was !", + "What a great weekend that was !", + "I really enjoy the beach in the summer ." + ], + "type": [ + "inter-personal" + ], + "text": "I couldn't agree with you more .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "We should come here more often .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "What a great weekend that was !", + "I really enjoy the beach in the summer ." + ], + "type": [ + "self-contagion" + ], + "text": "We should come here more often .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "You are absolutely right .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 1, + 3 + ], + "expanded emotion cause span": [ + "What a great weekend that was !", + "What a great weekend that was !", + "I really enjoy the beach in the summer ." + ], + "type": [ + "inter-personal" + ], + "text": "You are absolutely right .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I'd like to come back next weekend .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "What a great weekend that was !", + "I really enjoy the beach in the summer ." + ], + "type": [ + "self-contagion" + ], + "text": "I'd like to come back next weekend .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That's exactly the way I feel .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "What a great weekend that was !", + "I really enjoy the beach in the summer ." + ], + "type": [ + "inter-personal" + ], + "text": "That's exactly the way I feel .", + "id": 8, + "source_sentences": [ + 0, + 2 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_7551.json b/reccon/sources/tr_7551.json new file mode 100644 index 0000000000000000000000000000000000000000..101a49c2ebd8ff5e4dab0bff7cdc8eead0c36e58 --- /dev/null +++ b/reccon/sources/tr_7551.json @@ -0,0 +1,102 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "How is your job search 1 going , Janet ?", + "emotion": "neutral", + "text": "How is your job search 1 going , Janet ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I found the ideal position . I ' m working for a plumbing company .", + "emotion": "neutral", + "text": "I found the ideal position . I ' m working for a plumbing company .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Are you serious ? You studied mathematics at college for four years , and now you have a job working with your hands !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "I ' m working for a plumbing company .", + "You studied mathematics at college for four years , and now you have a job working with your hands !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Are you serious ? You studied mathematics at college for four years , and now you have a job working with your hands !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Plumbing work requires mathematics knowledge , and creativity . I love this job .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Plumbing work requires mathematics knowledge , and creativity . I love this job ." + ], + "type": [ + "no-context" + ], + "text": "Plumbing work requires mathematics knowledge , and creativity . I love this job .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I can see that . But I didn ' t know you had experience in that line of work .", + "emotion": "neutral", + "text": "I can see that . But I didn ' t know you had experience in that line of work .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I didn ' t , but I applied for an apprenticeship , and since I studied math , AND I have a good attitude 4 , my application was accepted .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I didn ' t , but I applied for an apprenticeship , and since I studied math , AND I have a good attitude 4 , my application was accepted ." + ], + "type": [ + "no-context" + ], + "text": "I didn ' t , but I applied for an apprenticeship , and since I studied math , AND I have a good attitude 4 , my application was accepted .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Congratulations ! You do have the right attitude .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "my application was accepted ." + ], + "type": [ + "inter-personal" + ], + "text": "Congratulations ! You do have the right attitude .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_771.json b/reccon/sources/tr_771.json new file mode 100644 index 0000000000000000000000000000000000000000..0af0b062eae08be1c41a42be0f423315d8cbbbab --- /dev/null +++ b/reccon/sources/tr_771.json @@ -0,0 +1,126 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , John , how was your vacation ?", + "emotion": "neutral", + "text": "Hi , John , how was your vacation ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Awesome , we went to Australia and New Zealand .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "we went to Australia and New Zealand" + ], + "type": [ + "no-context" + ], + "text": "Awesome , we went to Australia and New Zealand .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "That must have been wonderful . Do anything interesting ?", + "emotion": "neutral", + "text": "That must have been wonderful . Do anything interesting ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Well , we went bungee jumping when we were in Australia .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Well , we went bungee jumping when we were in Australia ." + ], + "type": [ + "no-context" + ], + "text": "Well , we went bungee jumping when we were in Australia .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Wow ! Isn ' t that dangerous ?", + "emotion": "neutral", + "text": "Wow ! Isn ' t that dangerous ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "A little , but the rush was worth it .", + "emotion": "neutral", + "text": "A little , but the rush was worth it .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Tell me about it .", + "emotion": "neutral", + "text": "Tell me about it .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "We jumped off a bridge and fell 500 feet before the bungee cord caught us .", + "emotion": "neutral", + "text": "We jumped off a bridge and fell 500 feet before the bungee cord caught us .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "500 feet ! I would never be able to do that .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "We jumped off a bridge and fell 500 feet before the bungee cord caught us .", + "500 feet !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "500 feet ! I would never be able to do that .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Yeah , It was scary , but exhilarating .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "It was scary , but exhilarating ." + ], + "type": [ + "no-context" + ], + "text": "Yeah , It was scary , but exhilarating .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_7727.json b/reccon/sources/tr_7727.json new file mode 100644 index 0000000000000000000000000000000000000000..50d6f5495e32b641df13b2a562de4ec81c964d98 --- /dev/null +++ b/reccon/sources/tr_7727.json @@ -0,0 +1,158 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Excuse me , is this the way to the Great Wall ?", + "emotion": "neutral", + "text": "Excuse me , is this the way to the Great Wall ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh , it is really far from here . You ' re going in the wrong direction actually .", + "emotion": "neutral", + "text": "Oh , it is really far from here . You ' re going in the wrong direction actually .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I must have taken a wrong turn .", + "emotion": "neutral", + "text": "I must have taken a wrong turn .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It doesn ' t matter . Go back the way you came . After about five kilometers , you ' ll see a hotel on the side of the road . It ' s a big one . You can ' t miss it .", + "emotion": "neutral", + "text": "It doesn ' t matter . Go back the way you came . After about five kilometers , you ' ll see a hotel on the side of the road . It ' s a big one . You can ' t miss it .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "And then ?", + "emotion": "neutral", + "text": "And then ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Take the next right . Drive about one click further , and you ' ll see the entrance of the highway to the Great Wall .", + "emotion": "neutral", + "text": "Take the next right . Drive about one click further , and you ' ll see the entrance of the highway to the Great Wall .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Thanks a lot .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 6 + ], + "expanded emotion cause span": [ + "I must have taken a wrong turn .", + "Take the next right ." + ], + "type": [ + "hybrid" + ], + "text": "Thanks a lot .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "You ' re welcome .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Thanks" + ], + "type": [ + "inter-personal" + ], + "text": "You ' re welcome .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "By the way , how long does it take ?", + "emotion": "neutral", + "text": "By the way , how long does it take ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Without traffic , it takes about an hour .", + "emotion": "neutral", + "text": "Without traffic , it takes about an hour .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I heard the Great Wall closes early in the afternoon . Do you think I can make it before closing ?", + "emotion": "neutral", + "text": "I heard the Great Wall closes early in the afternoon . Do you think I can make it before closing ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Yes , I think so . It doesn ' t close until 5 o ' clock . You still have plenty of time .", + "emotion": "neutral", + "text": "Yes , I think so . It doesn ' t close until 5 o ' clock . You still have plenty of time .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Great ! Thank you !", + "emotion": "happiness", + "explanation": "The speaker is grateful for the provided help.", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "You still have plenty of time ." + ], + "type": [ + "inter-personal" + ], + "text": "Great ! Thank you !", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "My pleasure , and have a good time !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "Thank you !" + ], + "type": [ + "inter-personal" + ], + "text": "My pleasure , and have a good time !", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_7729.json b/reccon/sources/tr_7729.json new file mode 100644 index 0000000000000000000000000000000000000000..ebca08f8fb9a854c575c6cd39e43549ed608e958 --- /dev/null +++ b/reccon/sources/tr_7729.json @@ -0,0 +1,166 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "All the food smells tasty today and makes my mouth water .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "food smells tasty" + ], + "type": [ + "no-context" + ], + "text": "All the food smells tasty today and makes my mouth water .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Let's line up here . This line seems a little shorter .", + "emotion": "neutral", + "text": "Let's line up here . This line seems a little shorter .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What's on the menu today ?", + "emotion": "neutral", + "text": "What's on the menu today ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Fish , beef , pork , chicken , vegetables and beancurd . For staple food we have rice , steamed bread , stuffed buns and noodles .", + "emotion": "neutral", + "text": "Fish , beef , pork , chicken , vegetables and beancurd . For staple food we have rice , steamed bread , stuffed buns and noodles .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Oh , we're lucky today , aren't we ?", + "emotion": "neutral", + "text": "Oh , we're lucky today , aren't we ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I'd rather take stewed cabbage with beef .", + "emotion": "neutral", + "text": "I'd rather take stewed cabbage with beef .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I think I'll take fried fish , because fish is one of my favorites .", + "emotion": "neutral", + "text": "I think I'll take fried fish , because fish is one of my favorites .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That's good , we can share what we have . Here we are . You go ahead .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "fish is one of my favorites .", + "we can share" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's good , we can share what we have . Here we are . You go ahead .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "( They get everything ready ) Here is a free table . Let's sit down . Help yourself to some fish please . Isn't it delicious and appetizing ?", + "emotion": "neutral", + "text": "( They get everything ready ) Here is a free table . Let's sit down . Help yourself to some fish please . Isn't it delicious and appetizing ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I'm sorry I don't like it's a little too salty .", + "emotion": "neutral", + "text": "I'm sorry I don't like it's a little too salty .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I see . You people from south prefer sweet , don't you ?", + "emotion": "neutral", + "text": "I see . You people from south prefer sweet , don't you ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Yes , I like the fish cooked in sweet and sour sauce best . Try some beef , please .", + "emotion": "neutral", + "text": "Yes , I like the fish cooked in sweet and sour sauce best . Try some beef , please .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Thank you . I'm through with one steamed bread and I'd like a second helping .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "Try some beef , please ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . I'm through with one steamed bread and I'd like a second helping .", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Your appetite is good .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "Your appetite is good ." + ], + "type": [ + "no-context" + ], + "text": "Your appetite is good .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "I'm always feeling hungry .", + "emotion": "neutral", + "text": "I'm always feeling hungry .", + "id": 15 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_774.json b/reccon/sources/tr_774.json new file mode 100644 index 0000000000000000000000000000000000000000..ec60081f01083deda11a4120b29d8e798d230b35 --- /dev/null +++ b/reccon/sources/tr_774.json @@ -0,0 +1,129 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Mom , I just finished my paper . Can you proofread it before I hand it in ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I just finished my paper ." + ], + "type": [ + "no-context" + ], + "text": "Mom , I just finished my paper . Can you proofread it before I hand it in ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Sure , let ' s take a look . Sweetie , this is terrific . Your ideas are so original .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "this is terrific . Your ideas are so original ." + ], + "type": [ + "no-context" + ], + "text": "Sure , let ' s take a look . Sweetie , this is terrific . Your ideas are so original .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Thanks .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "this is terrific . Your ideas are so original ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I can tell you worked hard on it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "this is terrific . Your ideas are so original ." + ], + "type": [ + "self-contagion" + ], + "text": "I can tell you worked hard on it .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I really did ! I started thinking about what I wanted to say three weeks ago .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I can tell you worked hard on it ." + ], + "type": [ + "inter-personal" + ], + "text": "I really did ! I started thinking about what I wanted to say three weeks ago .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Well , it was definitely worth all the time .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "I started thinking about what I wanted to say three weeks ago .", + "it was definitely worth all the time ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Well , it was definitely worth all the time .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Let ' s just hope my teacher agrees .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "it was definitely worth all the time ." + ], + "type": [ + "inter-personal" + ], + "text": "Let ' s just hope my teacher agrees .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_778.json b/reccon/sources/tr_778.json new file mode 100644 index 0000000000000000000000000000000000000000..6db22cf214b15410cecb044250d0bc70752e4087 --- /dev/null +++ b/reccon/sources/tr_778.json @@ -0,0 +1,122 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Bill , Happy Halloween !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Happy Halloween !" + ], + "type": [ + "no-context" + ], + "text": "Bill , Happy Halloween !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Happy Halloween ! What creature are you going to dress up as ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "Happy Halloween !", + "What creature are you going to dress up as ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Happy Halloween ! What creature are you going to dress up as ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I will dress up as a vampire with big fangs .", + "emotion": "neutral", + "text": "I will dress up as a vampire with big fangs .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "May I have a look at your costume ?", + "emotion": "neutral", + "text": "May I have a look at your costume ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Sure . Wait a moment . ( Several minutes later ) Here you are .", + "emotion": "neutral", + "text": "Sure . Wait a moment . ( Several minutes later ) Here you are .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I like your black clothes and your fangs are cool .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I like your black clothes and your fangs are cool ." + ], + "type": [ + "no-context" + ], + "text": "I like your black clothes and your fangs are cool .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I will bite many beautiful girls on the neck tonight . Maybe I will suck their blood .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I like your black clothes and your fangs are cool .", + "I will bite many beautiful girls on the neck tonight . Maybe I will suck their blood ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I will bite many beautiful girls on the neck tonight . Maybe I will suck their blood .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Haha . Wish you good luck .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I will bite many beautiful girls on the neck tonight . Maybe I will suck their blood ." + ], + "type": [ + "inter-personal" + ], + "text": "Haha . Wish you good luck .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_784.json b/reccon/sources/tr_784.json new file mode 100644 index 0000000000000000000000000000000000000000..972e3bad6fb5d327ca6d4373b84ed260b2d2ba1b --- /dev/null +++ b/reccon/sources/tr_784.json @@ -0,0 +1,123 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Linda ? Is that you ? I haven't seen you in ages !", + "emotion": "surprise", + "explanation": "Person A is surprised to suddenly see person B after a long time", + "expanded emotion cause evidence": [ + "b", + 1 + ], + "expanded emotion cause span": [ + "b", + "haven't seen you in age" + ], + "type": [ + "latent", + "no-context" + ], + "text": "Linda ? Is that you ? I haven't seen you in ages !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hi George ! It's good to see you !", + "emotion": "surprise", + "explanation": "Person B is surprised to suddenly see person A after a long time", + "expanded emotion cause evidence": [ + "b", + 1, + 2 + ], + "expanded emotion cause span": [ + "b", + "haven't seen you in age", + "It's good to see you !" + ], + "type": [ + "latent", + "no-context", + "inter-personal" + ], + "text": "Hi George ! It's good to see you !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What have you been up to ?", + "emotion": "neutral", + "text": "What have you been up to ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I just opened up my own business not long ago .", + "emotion": "neutral", + "text": "I just opened up my own business not long ago .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Good for you ! What are you doing ?", + "emotion": "neutral", + "text": "Good for you ! What are you doing ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I'm a professional party planner here in the city . I do catering and all that .", + "emotion": "neutral", + "text": "I'm a professional party planner here in the city . I do catering and all that .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I knew some day I would be able to profit from your love of fun !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I'm a professional party planner here in the city . I do catering and all that .", + "I would be able to profit from your love of fun !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I knew some day I would be able to profit from your love of fun !", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Well , I don't know about the profit part yet . But I am really having fun !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 8 + ], + "expanded emotion cause span": [ + "I am really having fun !", + "Well , I don't know about the profit part yet . But I am really having fun !" + ], + "type": [ + "no-context" + ], + "text": "Well , I don't know about the profit part yet . But I am really having fun !", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_7847.json b/reccon/sources/tr_7847.json new file mode 100644 index 0000000000000000000000000000000000000000..0f5b8f088d49cf9faa3239056405d313e99ff4ca --- /dev/null +++ b/reccon/sources/tr_7847.json @@ -0,0 +1,110 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Guess what , Gilly ? I won both bids .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I won both bids ." + ], + "type": [ + "no-context" + ], + "text": "Guess what , Gilly ? I won both bids .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Good for you . Did you use Paypal ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I won both bids ." + ], + "type": [ + "inter-personal" + ], + "text": "Good for you . Did you use Paypal ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yeah . It was so easy and super-fast , once I figured it out .", + "emotion": "neutral", + "text": "Yeah . It was so easy and super-fast , once I figured it out .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "That's the beauty of it , and the danger .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "It was so easy and super-fast , once I figured it out ." + ], + "type": [ + "inter-personal" + ], + "text": "That's the beauty of it , and the danger .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I should get the items within a week . But in the meantime I'm bidding on a digital video camera .", + "emotion": "neutral", + "text": "I should get the items within a week . But in the meantime I'm bidding on a digital video camera .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "How much ?", + "emotion": "neutral", + "text": "How much ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Thirty U . S . dollars ... and it's only been used for six months .", + "emotion": "neutral", + "text": "Thirty U . S . dollars ... and it's only been used for six months .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Mmmm , sounds like risky business . Good luck .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 7 + ], + "expanded emotion cause span": [ + "I'm bidding on a digital video camera .", + "Thirty U . S . dollars ... and it's only been used for six months ." + ], + "type": [ + "inter-personal" + ], + "text": "Mmmm , sounds like risky business . Good luck .", + "id": 8, + "source_sentences": [ + 4, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_786.json b/reccon/sources/tr_786.json new file mode 100644 index 0000000000000000000000000000000000000000..84e92b7505d6cfedba8f2b0026044c50dda391f9 --- /dev/null +++ b/reccon/sources/tr_786.json @@ -0,0 +1,142 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "How do you like skiing , Pat ?", + "emotion": "neutral", + "text": "How do you like skiing , Pat ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I love it . All my life I wanted to learn to ski . Finally I took lessons last year .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "All my life I wanted to learn to ski . Finally I took lessons last year ." + ], + "type": [ + "no-context" + ], + "text": "I love it . All my life I wanted to learn to ski . Finally I took lessons last year .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I suppose skiing is easy for you .", + "emotion": "neutral", + "text": "I suppose skiing is easy for you .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "No , quite the opposite . I thought I'd never stop falling down . Then all of a sudden I started skiing much better .", + "emotion": "neutral", + "text": "No , quite the opposite . I thought I'd never stop falling down . Then all of a sudden I started skiing much better .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I see . Do you ski often ?", + "emotion": "neutral", + "text": "I see . Do you ski often ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Every chance I get . On weekends I ski all day long . Sometimes I even ski at night .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Every chance I get . On weekends I ski all day long . Sometimes I even ski at night ." + ], + "type": [ + "no-context" + ], + "text": "Every chance I get . On weekends I ski all day long . Sometimes I even ski at night .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "That sounds great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Sometimes I even ski at night ." + ], + "type": [ + "inter-personal" + ], + "text": "That sounds great .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Oh , yes . The ski slopes are well lit . It's really nice to ski at night . Why don't you learn to ski ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "The ski slopes are well lit . It's really nice to ski at night ." + ], + "type": [ + "no-context" + ], + "text": "Oh , yes . The ski slopes are well lit . It's really nice to ski at night . Why don't you learn to ski ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Not on your life ! I know I'd break my leg", + "emotion": "fear", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "I know I'd break my leg" + ], + "type": [ + "no-context" + ], + "text": "Not on your life ! I know I'd break my leg", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Don't be so frightened . It's just a skill .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "The ski slopes are well lit . It's really nice to ski at night ." + ], + "type": [ + "self-contagion" + ], + "text": "Don't be so frightened . It's just a skill .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_7889.json b/reccon/sources/tr_7889.json new file mode 100644 index 0000000000000000000000000000000000000000..12202ccd563ce5171b70ed9bf36d21557e90c5af --- /dev/null +++ b/reccon/sources/tr_7889.json @@ -0,0 +1,154 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , are you being helped ?", + "emotion": "neutral", + "text": "Hi , are you being helped ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "No , I'm not . I am interested in some scarves .", + "emotion": "neutral", + "text": "No , I'm not . I am interested in some scarves .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "All our scarves are in this section . What do you think of this one here ? It's made of silk .", + "emotion": "neutral", + "text": "All our scarves are in this section . What do you think of this one here ? It's made of silk .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Hm , It looks nice , but I ' d like to have something warm for the winter .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "It's made of silk .", + "looks nice ," + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Hm , It looks nice , but I ' d like to have something warm for the winter .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Maybe you would like a heavy wool scarves . How about this one ?", + "emotion": "neutral", + "text": "Maybe you would like a heavy wool scarves . How about this one ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I think that's what I want . How much is it ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "a heavy wool scarves .", + "that's what I want ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I think that's what I want . How much is it ?", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "It's 75 dollars plus tax .", + "emotion": "neutral", + "text": "It's 75 dollars plus tax .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "It's a little expensive . Do you think it's possible to get a discount ?", + "emotion": "neutral", + "text": "It's a little expensive . Do you think it's possible to get a discount ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Since you like it so much , how about a 10 % discount ? That's the best I can offer .", + "emotion": "neutral", + "text": "Since you like it so much , how about a 10 % discount ? That's the best I can offer .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "That's good . Could you wrap it for me ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6, + 9 + ], + "expanded emotion cause span": [ + "a heavy wool scarves .", + "that's what I want .", + "a 10 % discount ?" + ], + "type": [ + "hybrid" + ], + "text": "That's good . Could you wrap it for me ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Sure . Is there anything else I can get for you ?", + "emotion": "neutral", + "text": "Sure . Is there anything else I can get for you ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "No , that should be it . Thank you !", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 5, + 6, + 9 + ], + "expanded emotion cause span": [ + "a heavy wool scarves .", + "that's what I want .", + "a 10 % discount ?" + ], + "type": [ + "hybrid" + ], + "text": "No , that should be it . Thank you !", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_793.json b/reccon/sources/tr_793.json new file mode 100644 index 0000000000000000000000000000000000000000..18759ab7343f01aca3b8a2b385896c98c58432ae --- /dev/null +++ b/reccon/sources/tr_793.json @@ -0,0 +1,181 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Have you ever been to Japan ? I'm going in the fall .", + "emotion": "neutral", + "text": "Have you ever been to Japan ? I'm going in the fall .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yeah , I've been there twice .", + "emotion": "neutral", + "text": "Yeah , I've been there twice .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Really ? Tell me about it . What's it like ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I've been there twice ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? Tell me about it . What's it like ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Oh , it's fantastic .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Oh , it's fantastic ." + ], + "type": [ + "no-context" + ], + "text": "Oh , it's fantastic .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Where did you go ?", + "emotion": "neutral", + "text": "Where did you go ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "On my first trip I went to Tokyo , and on my second trip I visited Kyoto .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Oh , it's fantastic ." + ], + "type": [ + "self-contagion" + ], + "text": "On my first trip I went to Tokyo , and on my second trip I visited Kyoto .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "What did you think of Tokyo ?", + "emotion": "neutral", + "text": "What did you think of Tokyo ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Very big and exciting , but very crowded , too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Very big and exciting ," + ], + "type": [ + "no-context" + ], + "text": "Very big and exciting , but very crowded , too .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yeah . I've seen pictures of the crowds !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Very big and exciting ," + ], + "type": [ + "inter-personal" + ], + "text": "Yeah . I've seen pictures of the crowds !", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "And the restaurant are excellent ... but they're kind of expensive .", + "emotion": "neutral", + "text": "And the restaurant are excellent ... but they're kind of expensive .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "And how about Kyoto ?", + "emotion": "neutral", + "text": "And how about Kyoto ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Kyoto is lovely . It's full of beautiful old temples and gardens . It ' s a very historic city .", + "emotion": "neutral", + "text": "Kyoto is lovely . It's full of beautiful old temples and gardens . It ' s a very historic city .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "How was the weather ?", + "emotion": "neutral", + "text": "How was the weather ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "I was in Tokyo in August , and it was really hot and humid . I went to Kyoto in October . It was hot and sunny , but there was no humidity .", + "emotion": "neutral", + "text": "I was in Tokyo in August , and it was really hot and humid . I went to Kyoto in October . It was hot and sunny , but there was no humidity .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Sounds perfect . I can't wait !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "It was hot and sunny , but there was no humidity ." + ], + "type": [ + "inter-personal" + ], + "text": "Sounds perfect . I can't wait !", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_7961.json b/reccon/sources/tr_7961.json new file mode 100644 index 0000000000000000000000000000000000000000..9cbbd7147b67d02b98c81534667486ef1f515301 --- /dev/null +++ b/reccon/sources/tr_7961.json @@ -0,0 +1,131 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Honey , the house is such a mess ! I need you to help me tidy up a bit . My boss and her husband are coming over for dinner and the house needs to be spotless !", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "the house is such a mess !" + ], + "type": [ + "no-context" + ], + "text": "Honey , the house is such a mess ! I need you to help me tidy up a bit . My boss and her husband are coming over for dinner and the house needs to be spotless !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I ' m in the middle of something right now . I ' ll be there in a second .", + "emotion": "neutral", + "text": "I ' m in the middle of something right now . I ' ll be there in a second .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "This can ' t wait ! I need your help now !", + "emotion": "fear", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "This can ' t wait ! I need your help now !" + ], + "type": [ + "no-context" + ], + "text": "This can ' t wait ! I need your help now !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Alright , alright . I ' m coming .", + "emotion": "neutral", + "text": "Alright , alright . I ' m coming .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Ok , here ' s a list of chores we need to get done . I'll do the dishes and get all the groceries for tonight . You can sweep and mop the floors . Oh , and the furniture needs to be dusted .", + "emotion": "neutral", + "text": "Ok , here ' s a list of chores we need to get done . I'll do the dishes and get all the groceries for tonight . You can sweep and mop the floors . Oh , and the furniture needs to be dusted .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "You know what , I have to pick something up at the mall , so why don ' t you clean the floors and I'll go to the supermarket and get all the groceries .", + "emotion": "neutral", + "text": "You know what , I have to pick something up at the mall , so why don ' t you clean the floors and I'll go to the supermarket and get all the groceries .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Sure that ' s fine . Here is the list of all the things you need to get . Don't forget anything ! And can you pick up a bottle of wine on your way home ?", + "emotion": "neutral", + "text": "Sure that ' s fine . Here is the list of all the things you need to get . Don't forget anything ! And can you pick up a bottle of wine on your way home ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Hey , honey I ' m back . Wow , the house looks really good !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "the house looks really good !" + ], + "type": [ + "no-context" + ], + "text": "Hey , honey I ' m back . Wow , the house looks really good !", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Great ! Can you set the table ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "the house looks really good !" + ], + "type": [ + "inter-personal" + ], + "text": "Great ! Can you set the table ?", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Just a sec I ' m just gonna vacuum this rug real fast .", + "emotion": "neutral", + "text": "Just a sec I ' m just gonna vacuum this rug real fast .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Wait ! Don ' t turn it on ...", + "emotion": "neutral", + "text": "Wait ! Don ' t turn it on ...", + "id": 11 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_797.json b/reccon/sources/tr_797.json new file mode 100644 index 0000000000000000000000000000000000000000..67bbe09dcaa7baadee1de278d8a57db7b6278bfa --- /dev/null +++ b/reccon/sources/tr_797.json @@ -0,0 +1,171 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi Sam , would you like to come for a curry with us next Friday ?", + "emotion": "neutral", + "text": "Hi Sam , would you like to come for a curry with us next Friday ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Sure , I love curry . Who else is coming ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "come for a curry with us next Friday ?", + "I love curry ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Sure , I love curry . Who else is coming ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Jane , Susan , Pete and two colleagues of mine from work .", + "emotion": "neutral", + "text": "Jane , Susan , Pete and two colleagues of mine from work .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I have no plans for Friday , so curry would be great . Which restaurant do you have in mind ?", + "emotion": "neutral", + "text": "I have no plans for Friday , so curry would be great . Which restaurant do you have in mind ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Susan suggested the one on Main Street . She says it is very good .", + "emotion": "neutral", + "text": "Susan suggested the one on Main Street . She says it is very good .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Which one is that ?", + "emotion": "neutral", + "text": "Which one is that ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You know , the one just on the corner with Oxford Street . There is a large pharmacy next door .", + "emotion": "neutral", + "text": "You know , the one just on the corner with Oxford Street . There is a large pharmacy next door .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Oh yes , I know which one you mean . I have never been there , but I looked at their menu once and it did look good .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 8 + ], + "expanded emotion cause span": [ + "She says it is very good .", + "I looked at their menu once and it did look good ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh yes , I know which one you mean . I have never been there , but I looked at their menu once and it did look good .", + "id": 8, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Okay then . I think we will all meet outside ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 8 + ], + "expanded emotion cause span": [ + "She says it is very good .", + "I looked at their menu once and it did look good ." + ], + "type": [ + "hybrid" + ], + "text": "Okay then . I think we will all meet outside ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "What time ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 8 + ], + "expanded emotion cause span": [ + "She says it is very good .", + "I looked at their menu once and it did look good ." + ], + "type": [ + "hybrid" + ], + "text": "What time ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "At 8 o'clock . I will make the reservation .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 8 + ], + "expanded emotion cause span": [ + "She says it is very good .", + "I looked at their menu once and it did look good ." + ], + "type": [ + "hybrid" + ], + "text": "At 8 o'clock . I will make the reservation .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "That's good . See you on Friday .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 8 + ], + "expanded emotion cause span": [ + "She says it is very good .", + "I looked at their menu once and it did look good ." + ], + "type": [ + "hybrid" + ], + "text": "That's good . See you on Friday .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_7991.json b/reccon/sources/tr_7991.json new file mode 100644 index 0000000000000000000000000000000000000000..b1e34d7607a671a2c2a387ad33a86ed6b59dde2c --- /dev/null +++ b/reccon/sources/tr_7991.json @@ -0,0 +1,117 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I just discovered that I owe $ 10 for a movie that I never ordered .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I owe $ 10 for a movie that I never ordered ." + ], + "type": [ + "no-context" + ], + "text": "I just discovered that I owe $ 10 for a movie that I never ordered .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Let me check , sir . You were charged for watching ' Titanic ' Monday night .", + "emotion": "neutral", + "text": "Let me check , sir . You were charged for watching ' Titanic ' Monday night .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "That is absolutely incorrect ! I was out on the town Monday night .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "You were charged for watching ' Titanic ' Monday night .", + "I was out on the town Monday night ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That is absolutely incorrect ! I was out on the town Monday night .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Okay , sir , bear with me a moment .", + "emotion": "neutral", + "text": "Okay , sir , bear with me a moment .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Thank you for taking my word over the computer's word .", + "emotion": "neutral", + "text": "Thank you for taking my word over the computer's word .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "One slight problem , sir . I need to charge you $ 2 to remove this error from your file .", + "emotion": "neutral", + "text": "One slight problem , sir . I need to charge you $ 2 to remove this error from your file .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You can", + "emotion": "neutral", + "text": "You can", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I feel your pain , sir .", + "emotion": "neutral", + "text": "I feel your pain , sir .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Absolutely unbelievable ! You people should be ashamed of yourselves .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I need to charge you $ 2 to remove this error from your file ." + ], + "type": [ + "inter-personal" + ], + "text": "Absolutely unbelievable ! You people should be ashamed of yourselves .", + "id": 9, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I agree with you , sir , but all I do is work here .", + "emotion": "neutral", + "text": "I agree with you , sir , but all I do is work here .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_7995.json b/reccon/sources/tr_7995.json new file mode 100644 index 0000000000000000000000000000000000000000..ecf252f638c1588deb3f5cf307a649e0a9e9a393 --- /dev/null +++ b/reccon/sources/tr_7995.json @@ -0,0 +1,160 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , Mary , I have decided to look for a job as a salesman .", + "emotion": "neutral", + "text": "Hi , Mary , I have decided to look for a job as a salesman .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Good ! Have you got the recruitment information on marketing ?", + "emotion": "neutral", + "text": "Good ! Have you got the recruitment information on marketing ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yes . I have found some through different channels .", + "emotion": "neutral", + "text": "Yes . I have found some through different channels .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Really ? That's great ! Tell me .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "Have you got the recruitment information on marketing ?", + "Yes ." + ], + "type": [ + "hybrid" + ], + "text": "Really ? That's great ! Tell me .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "OK . The first piece of job information I got was from the Internet , and it is about selling medicines .", + "emotion": "neutral", + "text": "OK . The first piece of job information I got was from the Internet , and it is about selling medicines .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "What do you think of this job ?", + "emotion": "neutral", + "text": "What do you think of this job ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I am not familiar with the medicine industry , and I don't think it fits me well .", + "emotion": "neutral", + "text": "I am not familiar with the medicine industry , and I don't think it fits me well .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Then how about the others ?", + "emotion": "neutral", + "text": "Then how about the others ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Another is about electronic commerce , and its products are mainly large machinery equipments .", + "emotion": "neutral", + "text": "Another is about electronic commerce , and its products are mainly large machinery equipments .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I have heard about electronic commerce , and many people say it has good prospects for development .", + "emotion": "neutral", + "text": "I have heard about electronic commerce , and many people say it has good prospects for development .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I also feel it's nice . I want to give it a try .", + "emotion": "neutral", + "text": "I also feel it's nice . I want to give it a try .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Come on ! I believe you will succeed .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "I believe you will succeed ." + ], + "type": [ + "no-context" + ], + "text": "Come on ! I believe you will succeed .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Thanks . You can also seek job information on the Internet .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "I believe you will succeed ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks . You can also seek job information on the Internet .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Good idea . I will think it over .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13, + 14 + ], + "expanded emotion cause span": [ + "You can also seek job information on the Internet .", + "Good idea ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Good idea . I will think it over .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_7996.json b/reccon/sources/tr_7996.json new file mode 100644 index 0000000000000000000000000000000000000000..93135a26c29f413f15c260a68e715aa13926d3ff --- /dev/null +++ b/reccon/sources/tr_7996.json @@ -0,0 +1,177 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Do you know how late it is ?", + "emotion": "anger", + "explanation": "Person B is late which made Person 1 angry.", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Do you know how late it is ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "My fault . I didn't realize what time it was .", + "emotion": "sad", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "Do you know how late it is ?", + "I didn't realize what time it was ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "My fault . I didn't realize what time it was .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I hope you don't think that excuse lets you off the hook .", + "emotion": "anger", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "I hope you don't think that excuse lets you off the hook .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Not really . I'm telling the truth .", + "emotion": "neutral", + "text": "Not really . I'm telling the truth .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Haven't I asked you to call if you're going to be home late ?", + "emotion": "anger", + "explanation": "Person A is angry because person B is late and have not give a prior call to person A as agreed upon.", + "expanded emotion cause evidence": [ + "b", + 5 + ], + "expanded emotion cause span": [ + "b", + "I asked you to call if you're going to be home late" + ], + "type": [ + "latent", + "no-context" + ], + "text": "Haven't I asked you to call if you're going to be home late ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "This is true , but it must've slipped my mind .", + "emotion": "neutral", + "text": "This is true , but it must've slipped my mind .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Regardless , all you had to do was give a call .", + "emotion": "neutral", + "text": "Regardless , all you had to do was give a call .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I know . I should've called .", + "emotion": "neutral", + "text": "I know . I should've called .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Come home late one more time , and you'll find your stuff outside .", + "emotion": "anger", + "expanded emotion cause evidence": [ + "b", + 5 + ], + "expanded emotion cause span": [ + "b", + "I asked you to call if you're going to be home late" + ], + "type": [ + "latent", + "self-contagion" + ], + "text": "Come home late one more time , and you'll find your stuff outside .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "You want to throw me out over this ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Come home late one more time , and you'll find your stuff outside ." + ], + "type": [ + "inter-personal" + ], + "text": "You want to throw me out over this ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "That's right , maybe then you'll respect my rules .", + "emotion": "neutral", + "text": "That's right , maybe then you'll respect my rules .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "That's fine , because if I leave , then your rules won't matter .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "That's right , maybe then you'll respect my rules ." + ], + "type": [ + "inter-personal" + ], + "text": "That's fine , because if I leave , then your rules won't matter .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8.json b/reccon/sources/tr_8.json new file mode 100644 index 0000000000000000000000000000000000000000..a5bb0d3e1b9125b6c966aaaf62bf4b131bb588ef --- /dev/null +++ b/reccon/sources/tr_8.json @@ -0,0 +1,112 @@ +[ + { + "turn": 1, + "speaker": "B", + "utterance": "Hi , Becky , what's up ?", + "emotion": "neutral", + "text": "Hi , Becky , what's up ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "A", + "utterance": "Not much , except that my mother-in-law is driving me up the wall .", + "emotion": "neutral", + "text": "Not much , except that my mother-in-law is driving me up the wall .", + "id": 2 + }, + { + "turn": 3, + "speaker": "B", + "utterance": "What's the problem ?", + "emotion": "neutral", + "text": "What's the problem ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "A", + "utterance": "She loves to nit-pick and criticizes everything that I do . I can never do anything right when she's around .", + "emotion": "neutral", + "text": "She loves to nit-pick and criticizes everything that I do . I can never do anything right when she's around .", + "id": 4 + }, + { + "turn": 5, + "speaker": "B", + "utterance": "For example ?", + "emotion": "neutral", + "text": "For example ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "A", + "utterance": "Well , last week I invited her over to dinner . My husband and I had no problem with the food , but if you listened to her , then it would seem like I fed her old meat and rotten vegetables . There's just nothing can please her .", + "emotion": "neutral", + "text": "Well , last week I invited her over to dinner . My husband and I had no problem with the food , but if you listened to her , then it would seem like I fed her old meat and rotten vegetables . There's just nothing can please her .", + "id": 6 + }, + { + "turn": 7, + "speaker": "B", + "utterance": "No , I can't see that happening . I know you're a good cook and nothing like that would ever happen .", + "emotion": "neutral", + "text": "No , I can't see that happening . I know you're a good cook and nothing like that would ever happen .", + "id": 7 + }, + { + "turn": 8, + "speaker": "A", + "utterance": "It's not just that . She also criticizes how we raise the kids .", + "emotion": "neutral", + "text": "It's not just that . She also criticizes how we raise the kids .", + "id": 8 + }, + { + "turn": 9, + "speaker": "B", + "utterance": "My mother-in-law used to do the same thing to us . If it wasn't disciplining them enough , then we were disciplining them too much . She also complained about the food we fed them , the schools we sent them too , and everything else under the sun .", + "emotion": "neutral", + "text": "My mother-in-law used to do the same thing to us . If it wasn't disciplining them enough , then we were disciplining them too much . She also complained about the food we fed them , the schools we sent them too , and everything else under the sun .", + "id": 9 + }, + { + "turn": 10, + "speaker": "A", + "utterance": "You said she used to ? How did you stop her ?", + "emotion": "neutral", + "text": "You said she used to ? How did you stop her ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "B", + "utterance": "We basically sat her down and told her how we felt about her constant criticizing , and how we welcomed her advice but hoped she'd let us do our things . She understood , and now everything is a lot more peaceful .", + "emotion": "neutral", + "text": "We basically sat her down and told her how we felt about her constant criticizing , and how we welcomed her advice but hoped she'd let us do our things . She understood , and now everything is a lot more peaceful .", + "id": 11 + }, + { + "turn": 12, + "speaker": "A", + "utterance": "That sounds like a good idea . I'll have to try that .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "We basically sat her down and told her how we felt about her constant criticizing , and how we welcomed her advice but hoped she'd let us do our things . She understood , and now everything is a lot more peaceful ." + ], + "type": [ + "inter-personal" + ], + "text": "That sounds like a good idea . I'll have to try that .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8014.json b/reccon/sources/tr_8014.json new file mode 100644 index 0000000000000000000000000000000000000000..7287081df42993750b8272c536722f7749439bd1 --- /dev/null +++ b/reccon/sources/tr_8014.json @@ -0,0 +1,251 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Ah ! No ! Damn it !", + "emotion": "anger", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Ah ! No ! Damn it !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It's a blackout . Now I can't see Seinfeld .", + "emotion": "neutral", + "text": "It's a blackout . Now I can't see Seinfeld .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "So what ? I just lost one hour's worth of work .", + "emotion": "neutral", + "text": "So what ? I just lost one hour's worth of work .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Really ? How could you do that ? Don't you save every couple minutes ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "I just lost one hour's worth of work .", + "Don't you save every couple minutes ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Really ? How could you do that ? Don't you save every couple minutes ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "No , I didn't save this time . Damn it ! And I'm sick of writing this paper . Now I have to write it all over again too .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I didn't save this time . Damn it ! And I'm sick of writing this paper . Now I have to write it all over again too ." + ], + "type": [ + "no-context" + ], + "text": "No , I didn't save this time . Damn it ! And I'm sick of writing this paper . Now I have to write it all over again too .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I've had that problem too many times . So I learned to save . When I'm writing something , I save every three sentences or so . I don't want to lose anything .", + "emotion": "neutral", + "text": "I've had that problem too many times . So I learned to save . When I'm writing something , I save every three sentences or so . I don't want to lose anything .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I hate computers . Sometimes I think they cause more trouble than they're worth .", + "emotion": "neutral", + "text": "I hate computers . Sometimes I think they cause more trouble than they're worth .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "What are we going to do now ?", + "emotion": "neutral", + "text": "What are we going to do now ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I don't know . I feel like going out .", + "emotion": "neutral", + "text": "I don't know . I feel like going out .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I wonder how much of the city is down .", + "emotion": "neutral", + "text": "I wonder how much of the city is down .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "It doesn't matter . I still can go out and buy a beer .", + "emotion": "neutral", + "text": "It doesn't matter . I still can go out and buy a beer .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Maybe . But if there's a blackout , probably the pubs are closed . And besides , I know you have a political science exam tomorrow . I thought you had a lot of reading to do .", + "emotion": "neutral", + "text": "Maybe . But if there's a blackout , probably the pubs are closed . And besides , I know you have a political science exam tomorrow . I thought you had a lot of reading to do .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Yes , that's true . Damn ! I just lost half my paper , and now I can't even do my homework . This is a bad time for this to happen .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 12, + 13 + ], + "expanded emotion cause span": [ + "you have a political science exam tomorrow . I thought you had a lot of reading to do .", + "I just lost half my paper , and now I can't even do my homework ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , that's true . Damn ! I just lost half my paper , and now I can't even do my homework . This is a bad time for this to happen .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "I have a flashlight in my closet . If you want to use that to read , you can .", + "emotion": "neutral", + "text": "I have a flashlight in my closet . If you want to use that to read , you can .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Thanks . I think I will try . Where are you going ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "I have a flashlight in my closet . If you want to use that to read , you can ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks . I think I will try . Where are you going ?", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "I like your idea of getting a beer . I think I'll go out myself .", + "emotion": "neutral", + "text": "I like your idea of getting a beer . I think I'll go out myself .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "Maybe we can trade . Why don't you stay here and read for my exam , and I'll go drink beer ?", + "emotion": "neutral", + "text": "Maybe we can trade . Why don't you stay here and read for my exam , and I'll go drink beer ?", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "No , it just won't work . If I read for your exam , you won't know the answers tomorrow . I will .", + "emotion": "neutral", + "text": "No , it just won't work . If I read for your exam , you won't know the answers tomorrow . I will .", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "So ? You can go to the class for me . Just write my name on the exam book and take the exam . Why not ?", + "emotion": "neutral", + "text": "So ? You can go to the class for me . Just write my name on the exam book and take the exam . Why not ?", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "How many students are in the class ?", + "emotion": "neutral", + "text": "How many students are in the class ?", + "id": 20 + }, + { + "turn": 21, + "speaker": "A", + "utterance": "About fourteen .", + "emotion": "neutral", + "text": "About fourteen .", + "id": 21 + }, + { + "turn": 22, + "speaker": "B", + "utterance": "So it won't work , old buddy . They'll see that I'm not you . Sorry .", + "emotion": "neutral", + "text": "So it won't work , old buddy . They'll see that I'm not you . Sorry .", + "id": 22 + }, + { + "turn": 23, + "speaker": "A", + "utterance": "Damn !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 22 + ], + "expanded emotion cause span": [ + "it won't work , old buddy . They'll see that I'm not you ." + ], + "type": [ + "inter-personal" + ], + "text": "Damn !", + "id": 23, + "source_sentences": [ + 21 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_802.json b/reccon/sources/tr_802.json new file mode 100644 index 0000000000000000000000000000000000000000..1796d704a35050f4e0bcc8ee85c60eb105fccebe --- /dev/null +++ b/reccon/sources/tr_802.json @@ -0,0 +1,166 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Why is the long face ?", + "emotion": "neutral", + "text": "Why is the long face ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'm getting sick of work man . I can't take the political bull in the company any more .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I'm getting sick of work man . I can't take the political bull in the company any more ." + ], + "type": [ + "no-context" + ], + "text": "I'm getting sick of work man . I can't take the political bull in the company any more .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Did you just get your review or something ?", + "emotion": "neutral", + "text": "Did you just get your review or something ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yeah , but that's not why I am upset . I just found out another guy got a promotion . He doesn't know how to do anything . He sits there and kisses the managers butt all day long .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I just found out another guy got a promotion . He doesn't know how to do anything . He sits there and kisses the managers butt all day long ." + ], + "type": [ + "no-context" + ], + "text": "Yeah , but that's not why I am upset . I just found out another guy got a promotion . He doesn't know how to do anything . He sits there and kisses the managers butt all day long .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "That sucks .", + "emotion": "neutral", + "text": "That sucks .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I'm just pissed that management can't see behind his smooth talking lies .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 2, + 4, + 6 + ], + "expanded emotion cause span": [ + "I'm getting sick of work man . I can't take the political bull in the company any more .", + "I just found out another guy got a promotion . He doesn't know how to do anything . He sits there and kisses the managers butt all day long .", + "management can't see behind his smooth talking lies ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I'm just pissed that management can't see behind his smooth talking lies .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Look on the bright side . At least you have a job .", + "emotion": "neutral", + "text": "Look on the bright side . At least you have a job .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yeah . I shouldn't stress about this anymore . It's not like I can do anything about it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "At least you have a job ." + ], + "type": [ + "inter-personal" + ], + "text": "Yeah . I shouldn't stress about this anymore . It's not like I can do anything about it .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Exactly . Instead , we should have some drinks tonight .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I shouldn't stress about this anymore ." + ], + "type": [ + "inter-personal" + ], + "text": "Exactly . Instead , we should have some drinks tonight .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "How about a cold bottle of beer .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "we should have some drinks tonight .", + "cold bottle of beer ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "How about a cold bottle of beer .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Now you're talking .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "cold bottle of beer ." + ], + "type": [ + "inter-personal" + ], + "text": "Now you're talking .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8028.json b/reccon/sources/tr_8028.json new file mode 100644 index 0000000000000000000000000000000000000000..bf44ee9ff17692f9ee4662732a47286b6a86ec72 --- /dev/null +++ b/reccon/sources/tr_8028.json @@ -0,0 +1,101 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "So can you fix it ?", + "emotion": "neutral", + "text": "So can you fix it ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I ' m sorry sir . This computer is not broken or damaged . It ' s simply just too old ! That ' s why your programs and applications are running slow . There really isn ' t much I can do .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "There really isn ' t much I can do ." + ], + "type": [ + "no-context" + ], + "text": "I ' m sorry sir . This computer is not broken or damaged . It ' s simply just too old ! That ' s why your programs and applications are running slow . There really isn ' t much I can do .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What do you mean ? I bought this computer just three years ago !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "It ' s simply just too old ! That ' s why your programs and applications are running slow .", + "I bought this computer just three years ago !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "What do you mean ? I bought this computer just three years ago !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes , but technology is ever changing and technology is becoming obsolete faster and faster !", + "emotion": "neutral", + "text": "Yes , but technology is ever changing and technology is becoming obsolete faster and faster !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "OK , I know where this is going . How much will it cost me to get a new computer ?", + "emotion": "neutral", + "text": "OK , I know where this is going . How much will it cost me to get a new computer ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Well , this desktop over here is our latest model . It has a four gigahertz processor with sixteen gigabytes in RAM and a hard disk with one terabyte . Of course , it includes a mouse , keyboard and desk speakers .", + "emotion": "neutral", + "text": "Well , this desktop over here is our latest model . It has a four gigahertz processor with sixteen gigabytes in RAM and a hard disk with one terabyte . Of course , it includes a mouse , keyboard and desk speakers .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I have no idea what you are talking about . I just want to know if it ' s good and if I will be able to play solitaire without the computer crashing or freezing all the time !", + "emotion": "neutral", + "text": "I have no idea what you are talking about . I just want to know if it ' s good and if I will be able to play solitaire without the computer crashing or freezing all the time !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "This PC is top of the line and I guarantee it will never freeze ! If it does , we ' ll give you your money back !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I just want to know if it ' s good and if I will be able to play solitaire without the computer crashing or freezing all the time !" + ], + "type": [ + "inter-personal" + ], + "text": "This PC is top of the line and I guarantee it will never freeze ! If it does , we ' ll give you your money back !", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8068.json b/reccon/sources/tr_8068.json new file mode 100644 index 0000000000000000000000000000000000000000..dd2a540cf5e6f574d25d7e91b84ee5fd2efae574 --- /dev/null +++ b/reccon/sources/tr_8068.json @@ -0,0 +1,138 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Would you like to see our new shirts ?", + "emotion": "neutral", + "text": "Would you like to see our new shirts ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Sorry , but I'm not really that interested in those things .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "not really that interested" + ], + "type": [ + "no-context" + ], + "text": "Sorry , but I'm not really that interested in those things .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Well , they are very nice you know .", + "emotion": "neutral", + "text": "Well , they are very nice you know .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Really ?", + "emotion": "neutral", + "text": "Really ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "And not expensive either .", + "emotion": "neutral", + "text": "And not expensive either .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Oh , I don't care about that .", + "emotion": "neutral", + "text": "Oh , I don't care about that .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Everybody is buying them .", + "emotion": "neutral", + "text": "Everybody is buying them .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Are they ?", + "emotion": "neutral", + "text": "Are they ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yes , they are very fashionable , you see .", + "emotion": "neutral", + "text": "Yes , they are very fashionable , you see .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I am afraid I am not interested in fashion .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "I am afraid I am not interested" + ], + "type": [ + "no-context" + ], + "text": "I am afraid I am not interested in fashion .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I see .", + "emotion": "neutral", + "text": "I see .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "But thank you very much all the same .", + "emotion": "neutral", + "text": "But thank you very much all the same .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Sorry I couldn't help you .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "I am afraid I am not interested" + ], + "type": [ + "inter-personal" + ], + "text": "Sorry I couldn't help you .", + "id": 13, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8162.json b/reccon/sources/tr_8162.json new file mode 100644 index 0000000000000000000000000000000000000000..6931de2d83089da886824cfe19910e032e29c6c9 --- /dev/null +++ b/reccon/sources/tr_8162.json @@ -0,0 +1,131 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Wow , you ' re up early today ! What ' s for breakfast ?", + "emotion": "excited", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "you ' re up early today" + ], + "type": [ + "no-context" + ], + "text": "Wow , you ' re up early today ! What ' s for breakfast ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Well , I felt like baking , so I made some muffins .", + "emotion": "neutral", + "text": "Well , I felt like baking , so I made some muffins .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Smells good ! I ' ll make some coffee . Do you want me to make you some eggs ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "I made some muffins .", + "Smells good !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Smells good ! I ' ll make some coffee . Do you want me to make you some eggs ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Sure , I'll take mine , sunny side up .", + "emotion": "neutral", + "text": "Sure , I'll take mine , sunny side up .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Www , I don ' t know how you can eat your eggs like that ! Ever since I was small , I ' Ve had eggs and soldiers .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "I made some muffins .", + "Smells good !" + ], + "type": [ + "hybrid" + ], + "text": "Www , I don ' t know how you can eat your eggs like that ! Ever since I was small , I ' Ve had eggs and soldiers .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "You know , my dad had scrambled eggs every morning for twenty years . It drove my mom crazy !", + "emotion": "neutral", + "text": "You know , my dad had scrambled eggs every morning for twenty years . It drove my mom crazy !", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You know what really drives me crazy ? When I ask for soft boiled eggs , and they overcook them , so they come out hard boiled ! How can you dipyour toast into a hard boiled egg ?", + "emotion": "neutral", + "text": "You know what really drives me crazy ? When I ask for soft boiled eggs , and they overcook them , so they come out hard boiled ! How can you dipyour toast into a hard boiled egg ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "You ' re so picky sometimes .", + "emotion": "neutral", + "text": "You ' re so picky sometimes .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Here you go , honey , fried eggs .", + "emotion": "neutral", + "text": "Here you go , honey , fried eggs .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Dammit ! I asked for sunny side up ! How many times do I have to tell you .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "Here you go , honey , fried eggs .", + "I asked for sunny side up ! How many times do I have to tell you ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Dammit ! I asked for sunny side up ! How many times do I have to tell you .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8182.json b/reccon/sources/tr_8182.json new file mode 100644 index 0000000000000000000000000000000000000000..68c099a4c8202aaf6f6b04b76f106abc6cfe2764 --- /dev/null +++ b/reccon/sources/tr_8182.json @@ -0,0 +1,139 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "How are you , Sue ?", + "emotion": "neutral", + "text": "How are you , Sue ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Pretty good . I ' Ve just had my new poems published .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I ' Ve just had my new poems published ." + ], + "type": [ + "no-context" + ], + "text": "Pretty good . I ' Ve just had my new poems published .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Congratulations on your success .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I ' Ve just had my new poems published ." + ], + "type": [ + "inter-personal" + ], + "text": "Congratulations on your success .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Thank you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "I ' Ve just had my new poems published .", + "Congratulations" + ], + "type": [ + "hybrid" + ], + "text": "Thank you .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "And how ' s your brother ?", + "emotion": "neutral", + "text": "And how ' s your brother ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "He is fine .", + "emotion": "neutral", + "text": "He is fine .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "He ' s going to be sent to Britain to study , really ?", + "emotion": "neutral", + "text": "He ' s going to be sent to Britain to study , really ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yes . He ' s already got the passport and visa .", + "emotion": "neutral", + "text": "Yes . He ' s already got the passport and visa .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Fantastic ! Please send him my congratulations .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "He ' s going to be sent to Britain to study , really ?", + "Yes . He ' s already got the passport and visa ." + ], + "type": [ + "hybrid" + ], + "text": "Fantastic ! Please send him my congratulations .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Thank you . He ' s very lucky indeed .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "send him my congratulations .", + "He ' s very lucky" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you . He ' s very lucky indeed .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8184.json b/reccon/sources/tr_8184.json new file mode 100644 index 0000000000000000000000000000000000000000..c249fbe23a1d627479ec4f6a736aded8a09d6e33 --- /dev/null +++ b/reccon/sources/tr_8184.json @@ -0,0 +1,238 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Well , Yuri , tell me about it .", + "emotion": "neutral", + "text": "Well , Yuri , tell me about it .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'm sorry I can't bring better news , sir . The site is a disaster .", + "emotion": "neutral", + "text": "I'm sorry I can't bring better news , sir . The site is a disaster .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "That's what I was afraid of .", + "emotion": "neutral", + "text": "That's what I was afraid of .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It is not only the earthquake , sir . But the mudslides . Much of the north half of the site has been covered over by mud .", + "emotion": "neutral", + "text": "It is not only the earthquake , sir . But the mudslides . Much of the north half of the site has been covered over by mud .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Mud ? But Ivan told me there were no mudslides in that district . I thought all the mudslides were down in Chichitango .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "the mudslides . Much of the north half of the site has been covered over by mud .", + "Ivan told me there were no mudslides in that district . I thought all the mudslides were down in Chichitango ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Mud ? But Ivan told me there were no mudslides in that district . I thought all the mudslides were down in Chichitango .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "That's what we thought , sir . That's what the news reported . But there was one little mudslide in our district too . Right above our site .", + "emotion": "neutral", + "text": "That's what we thought , sir . That's what the news reported . But there was one little mudslide in our district too . Right above our site .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Oh , that's terrible ! What bad luck ! I wish we had never come to this country . But , if it isn't the strikes and the revolutionaries , it's the earthquakes . Our operations here are finished !", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "there was one little mudslide in our district too . Right above our site .", + "I wish we had never come to this country . But , if it isn't the strikes and the revolutionaries , it's the earthquakes . Our operations here are finished !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , that's terrible ! What bad luck ! I wish we had never come to this country . But , if it isn't the strikes and the revolutionaries , it's the earthquakes . Our operations here are finished !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I'm sorry , sir .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I wish we had never come to this country . But , if it isn't the strikes and the revolutionaries , it's the earthquakes . Our operations here are finished !" + ], + "type": [ + "inter-personal" + ], + "text": "I'm sorry , sir .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "It's not your fault , Yuri . But tell me . When will Ivan be able to get out there ?", + "emotion": "neutral", + "text": "It's not your fault , Yuri . But tell me . When will Ivan be able to get out there ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Well , it took me about nine hours to get back here by car . If Ivan leaves tonight , I think he should be there by tomorrow lunch .", + "emotion": "neutral", + "text": "Well , it took me about nine hours to get back here by car . If Ivan leaves tonight , I think he should be there by tomorrow lunch .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Good . I want an estimate of damages as soon as possible .", + "emotion": "neutral", + "text": "Good . I want an estimate of damages as soon as possible .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "But sir ...", + "emotion": "neutral", + "text": "But sir ...", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Yes , Yuri ?", + "emotion": "neutral", + "text": "Yes , Yuri ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "I wouldn't recommend sending Ivan now . Especially not at night . The roads aren't safe .", + "emotion": "neutral", + "text": "I wouldn't recommend sending Ivan now . Especially not at night . The roads aren't safe .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Has the earthquake damaged the bridges too ?", + "emotion": "neutral", + "text": "Has the earthquake damaged the bridges too ?", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "No , sir . The bridges are fine . But I've heard rumors that the revolutionaries are coming down from the mountains . There has been fighting , sir .", + "emotion": "neutral", + "text": "No , sir . The bridges are fine . But I've heard rumors that the revolutionaries are coming down from the mountains . There has been fighting , sir .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "Are you serious ? Fighting ? But I didn't hear anything on the news .", + "emotion": "neutral", + "text": "Are you serious ? Fighting ? But I didn't hear anything on the news .", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "You know the government controls the press here , sir . They don't want it reported .", + "emotion": "neutral", + "text": "You know the government controls the press here , sir . They don't want it reported .", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "Oh , this is terrible , Yuri . Terrible ! So we can't even assess the damages . How can we do business in this country ? Either we're buried under mud , or we're in danger of getting kidnapped . No , I can't believe this mess !", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 19 + ], + "expanded emotion cause span": [ + "So we can't even assess the damages . How can we do business in this country ? Either we're buried under mud , or we're in danger of getting kidnapped ." + ], + "type": [ + "no-context" + ], + "text": "Oh , this is terrible , Yuri . Terrible ! So we can't even assess the damages . How can we do business in this country ? Either we're buried under mud , or we're in danger of getting kidnapped . No , I can't believe this mess !", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "I'm sorry , sir .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 19 + ], + "expanded emotion cause span": [ + "So we can't even assess the damages . How can we do business in this country ? Either we're buried under mud , or we're in danger of getting kidnapped ." + ], + "type": [ + "inter-personal" + ], + "text": "I'm sorry , sir .", + "id": 20, + "source_sentences": [ + 18 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 21, + "speaker": "A", + "utterance": "You don't have to keep saying that , Yuri . It's not your fault . But me--I'm the one who should be sorry . It was me who suggested operations here in the first place ! Oh , what can we do ?", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 19, + 21 + ], + "expanded emotion cause span": [ + "So we can't even assess the damages . How can we do business in this country ? Either we're buried under mud , or we're in danger of getting kidnapped .", + "I'm the one who should be sorry . It was me who suggested operations here in the first place ! Oh , what can we do ?" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "You don't have to keep saying that , Yuri . It's not your fault . But me--I'm the one who should be sorry . It was me who suggested operations here in the first place ! Oh , what can we do ?", + "id": 21 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8243.json b/reccon/sources/tr_8243.json new file mode 100644 index 0000000000000000000000000000000000000000..364701ce5dc90014c5c0bf6fa1c00d6a654d9026 --- /dev/null +++ b/reccon/sources/tr_8243.json @@ -0,0 +1,131 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I enjoy the folk song and dance show very much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I enjoy the folk song and dance show very much ." + ], + "type": [ + "no-context" + ], + "text": "I enjoy the folk song and dance show very much .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'm glad you appreciate our folk music . But a live performance is much more interesting .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "I enjoy the folk song and dance show very much .", + "you appreciate our folk music ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm glad you appreciate our folk music . But a live performance is much more interesting .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I can't wait anymore . When does the performance start ?", + "emotion": "neutral", + "text": "I can't wait anymore . When does the performance start ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "The show starts at 7 and is over at around 10 o'clock p . m .", + "emotion": "neutral", + "text": "The show starts at 7 and is over at around 10 o'clock p . m .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "( After the show ) It's an excellent musical . The acting was very expressive and the songs and dancing were superb .", + "emotion": "neutral", + "text": "( After the show ) It's an excellent musical . The acting was very expressive and the songs and dancing were superb .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I'm glad you enjoyed it . It's had long run , but the house has always been full .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6, + 6 + ], + "expanded emotion cause span": [ + "It's an excellent musical . The acting was very expressive and the songs and dancing were superb .", + "you enjoyed it", + "house has always been full ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm glad you enjoyed it . It's had long run , but the house has always been full .", + "id": 6, + "source_sentences": [ + 4, + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "What do you think of the leading actors ?", + "emotion": "neutral", + "text": "What do you think of the leading actors ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Personally I liked the main character . He was true to type .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6, + 6, + 8 + ], + "expanded emotion cause span": [ + "It's an excellent musical . The acting was very expressive and the songs and dancing were superb .", + "you enjoyed it", + "house has always been full .", + "I liked the main character ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Personally I liked the main character . He was true to type .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "You are a better judge . I don't know the play well enough .", + "emotion": "neutral", + "text": "You are a better judge . I don't know the play well enough .", + "id": 9 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8244.json b/reccon/sources/tr_8244.json new file mode 100644 index 0000000000000000000000000000000000000000..855f0aa70e25b880dcf3b2744309dc2f018e1469 --- /dev/null +++ b/reccon/sources/tr_8244.json @@ -0,0 +1,222 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Are you OK ?", + "emotion": "neutral", + "text": "Are you OK ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'm fine . I'm just so touched by the sad story .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "so touched by the sad story ." + ], + "type": [ + "no-context" + ], + "text": "I'm fine . I'm just so touched by the sad story .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "So I can say now that you must have enjoyed the opera . Which scene is your favorite ?", + "emotion": "neutral", + "text": "So I can say now that you must have enjoyed the opera . Which scene is your favorite ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I love them all . But if I had to name one as the best , I would say it's the ending .", + "emotion": "neutral", + "text": "I love them all . But if I had to name one as the best , I would say it's the ending .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "What's it about ? You know , I couldn't help falling asleep .", + "emotion": "neutral", + "text": "What's it about ? You know , I couldn't help falling asleep .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Did you ? I didn't notice that . But still you should know it , for you have seen it with Laura before .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I couldn't help falling asleep ." + ], + "type": [ + "inter-personal" + ], + "text": "Did you ? I didn't notice that . But still you should know it , for you have seen it with Laura before .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I guess I've done the same thing last time I was here with her , too . I mean falling asleep . For me , this one is not that attractive .", + "emotion": "neutral", + "text": "I guess I've done the same thing last time I was here with her , too . I mean falling asleep . For me , this one is not that attractive .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Then I doubt if you like operas at all .", + "emotion": "neutral", + "text": "Then I doubt if you like operas at all .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yes . I like Carmen very much . But I don't mind if you want to tell me about this one .", + "emotion": "neutral", + "text": "Yes . I like Carmen very much . But I don't mind if you want to tell me about this one .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "OK , then . The man was old and he was visiting his wife's grave , with a rose in his hand . When he got there , he saw someone already put a rose on her grave .", + "emotion": "neutral", + "text": "OK , then . The man was old and he was visiting his wife's grave , with a rose in his hand . When he got there , he saw someone already put a rose on her grave .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Very impressive . And I do like the leading actress who has an amazing voice .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11, + 11 + ], + "expanded emotion cause span": [ + "The man was old and he was visiting his wife's grave , with a rose in his hand . When he got there , he saw someone already put a rose on her grave .", + "Very impressive .", + "the leading actress who has an amazing voice ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Very impressive . And I do like the leading actress who has an amazing voice .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Me , too . There was always a good round of applause every time she sings .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "the leading actress who has an amazing voice .", + "There was always a good round of applause every time she sings ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Me , too . There was always a good round of applause every time she sings .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Yes , the applause ! That was what kept waking me up during the show .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "the applause !" + ], + "type": [ + "no-context" + ], + "text": "Yes , the applause ! That was what kept waking me up during the show .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "And it's been such a faultless performance with the perfect lighting , and music . Just amazing !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "it's been such a faultless performance with the perfect lighting , and music . Just amazing !" + ], + "type": [ + "no-context" + ], + "text": "And it's been such a faultless performance with the perfect lighting , and music . Just amazing !", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "No doubt , it's not a simple thing to put on a ' phantom show ' .", + "emotion": "happiness", + "explanation": "the speaker is happy because he thinks the show is amazing and he enjoyed the show", + "expanded emotion cause evidence": [ + 10, + 11, + 11, + 14 + ], + "expanded emotion cause span": [ + "The man was old and he was visiting his wife's grave , with a rose in his hand . When he got there , he saw someone already put a rose on her grave .", + "Very impressive .", + "the leading actress who has an amazing voice .", + "it's been such a faultless performance with the perfect lighting , and music . Just amazing !" + ], + "type": [ + "hybrid" + ], + "text": "No doubt , it's not a simple thing to put on a ' phantom show ' .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Exactly .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "it's been such a faultless performance with the perfect lighting , and music . Just amazing !" + ], + "type": [ + "self-contagion" + ], + "text": "Exactly .", + "id": 16 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8265.json b/reccon/sources/tr_8265.json new file mode 100644 index 0000000000000000000000000000000000000000..f0382040b3952ba03862ebb94fc69fa6987e3df4 --- /dev/null +++ b/reccon/sources/tr_8265.json @@ -0,0 +1,107 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey , don ' t walk on the lawn .", + "emotion": "neutral", + "text": "Hey , don ' t walk on the lawn .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Sorry , I ' m looking for my wallet .", + "emotion": "sadness", + "explanation": "B is said as their wallet is lost", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Sorry , I ' m looking for my wallet .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "You lost your wallet ? Anything important in it ?", + "emotion": "neutral", + "text": "You lost your wallet ? Anything important in it ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes . A lot of cash . Almost forty thousand pounds .", + "emotion": "neutral", + "text": "Yes . A lot of cash . Almost forty thousand pounds .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Oh , I ' m sorry to hear that . I think you ' d better talk to the police officer walking there .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3, + 4, + 4 + ], + "expanded emotion cause span": [ + "Anything important in it ?", + "Yes . A lot of cash .", + "forty thousand pounds ." + ], + "type": [ + "hybrid" + ], + "text": "Oh , I ' m sorry to hear that . I think you ' d better talk to the police officer walking there .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "It seems that is a better way . Thank you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "talk to the police officer", + "It seems that is a better way ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It seems that is a better way . Thank you .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You are welcome .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "It seems that is a better way . Thank you ." + ], + "type": [ + "inter-personal" + ], + "text": "You are welcome .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8270.json b/reccon/sources/tr_8270.json new file mode 100644 index 0000000000000000000000000000000000000000..7708783d5a2ae9aeaafb67ad095c1a8993fc1d51 --- /dev/null +++ b/reccon/sources/tr_8270.json @@ -0,0 +1,150 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello , BCD Company , can I help you ?", + "emotion": "neutral", + "text": "Hello , BCD Company , can I help you ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hello , may I speak to Mrs Smith ?", + "emotion": "neutral", + "text": "Hello , may I speak to Mrs Smith ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "This is Mrs Smith , may I have your name ?", + "emotion": "neutral", + "text": "This is Mrs Smith , may I have your name ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "This is Sun , and I interviewed with you yesterday .", + "emotion": "neutral", + "text": "This is Sun , and I interviewed with you yesterday .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Hello , Mr . Sun .", + "emotion": "neutral", + "text": "Hello , Mr . Sun .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I am calling to thank you for giving me the interview for the Sales Manager position yesterday .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "thank you for giving me the interview for the Sales Manager position yesterday ." + ], + "type": [ + "no-context" + ], + "text": "I am calling to thank you for giving me the interview for the Sales Manager position yesterday .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You are welcome , Mr . Sun .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I am calling to thank you for giving me the interview for the Sales Manager position yesterday ." + ], + "type": [ + "inter-personal" + ], + "text": "You are welcome , Mr . Sun .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I really enjoyed meeting with you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I really enjoyed meeting with you ." + ], + "type": [ + "no-context" + ], + "text": "I really enjoyed meeting with you .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "You certainly made a good impression on me , as well .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "I really enjoyed meeting with you .", + "You certainly made a good impression on me , as well ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You certainly made a good impression on me , as well .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I am very interested in this position .", + "emotion": "neutral", + "text": "I am very interested in this position .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "We'll be making the decision by the end of this week and we'll contact you as soon as possible .", + "emotion": "neutral", + "text": "We'll be making the decision by the end of this week and we'll contact you as soon as possible .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Well , thank you for your time and consideration again .", + "emotion": "neutral", + "text": "Well , thank you for your time and consideration again .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "You are welcome .", + "emotion": "neutral", + "text": "You are welcome .", + "id": 13 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8322.json b/reccon/sources/tr_8322.json new file mode 100644 index 0000000000000000000000000000000000000000..e81a447deb6526611700b4ff7fbfca3deadfe94f --- /dev/null +++ b/reccon/sources/tr_8322.json @@ -0,0 +1,197 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I can't stand the stupid guy any longer . It's unbelievable .", + "emotion": "anger", + "explanation": "Something intolerable and unexpected happened to person A causing his anger", + "expanded emotion cause evidence": [ + "b", + 1 + ], + "expanded emotion cause span": [ + "b", + "It's unbelievable ." + ], + "type": [ + "latent", + "no-context" + ], + "text": "I can't stand the stupid guy any longer . It's unbelievable .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh , my dear lady , take it easy . You should forgive a green hand like him .", + "emotion": "neutral", + "text": "Oh , my dear lady , take it easy . You should forgive a green hand like him .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "He does everything so mindlessly that he is going to drive me crazy .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "He does everything so mindlessly that he is going to drive me crazy ." + ], + "type": [ + "no-context" + ], + "text": "He does everything so mindlessly that he is going to drive me crazy .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I suggest you talk with him and teach him how to deal with the problems .", + "emotion": "neutral", + "text": "I suggest you talk with him and teach him how to deal with the problems .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I've told him how to do that several times , but he's never listened to me .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 3, + 5 + ], + "expanded emotion cause span": [ + "He does everything so mindlessly that he is going to drive me crazy .", + "I've told him how to do that several times , but he's never listened to me ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I've told him how to do that several times , but he's never listened to me .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Maybe you should communicate with him just like a friend , not a boss .", + "emotion": "neutral", + "text": "Maybe you should communicate with him just like a friend , not a boss .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Oh , I always have difficulty in getting along with the staff .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I always have difficulty in getting along with the staff ." + ], + "type": [ + "no-context" + ], + "text": "Oh , I always have difficulty in getting along with the staff .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Just take them for your good friends and have a talk with them as we do . Make sure you won't lose your temper !", + "emotion": "neutral", + "text": "Just take them for your good friends and have a talk with them as we do . Make sure you won't lose your temper !", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Oh , so bad . I'm afraid I'll change the image of myself .", + "emotion": "neutral", + "text": "Oh , so bad . I'm afraid I'll change the image of myself .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "No , it's unnecessary . Just respect the staff and their own opinions .", + "emotion": "neutral", + "text": "No , it's unnecessary . Just respect the staff and their own opinions .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "But sometimes they offer some useless proposals , it's awfully useless .", + "emotion": "neutral", + "text": "But sometimes they offer some useless proposals , it's awfully useless .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Oh , no one is perfect .", + "emotion": "neutral", + "text": "Oh , no one is perfect .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "That's right . I should speak to them in a polite way .", + "emotion": "neutral", + "text": "That's right . I should speak to them in a polite way .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "We have the equal partnership in team .", + "emotion": "neutral", + "text": "We have the equal partnership in team .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Thanks very much and you're very eloquent .", + "emotion": "happiness", + "explanation": "Appreciation", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "We have the equal partnership in team ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks very much and you're very eloquent .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Thanks for saying that .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "you're very eloquent ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks for saying that .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8342.json b/reccon/sources/tr_8342.json new file mode 100644 index 0000000000000000000000000000000000000000..3f79a47382559a3bcd83107d9733e63848f68ee3 --- /dev/null +++ b/reccon/sources/tr_8342.json @@ -0,0 +1,200 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello , it's nice to meet you .", + "emotion": "neutral", + "text": "Hello , it's nice to meet you .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'm glad we're meeting today . Thank you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "it's nice to meet you .", + "we're meeting today ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm glad we're meeting today . Thank you .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "You're welcome .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I'm glad we're meeting today . Thank you ." + ], + "type": [ + "inter-personal" + ], + "text": "You're welcome .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I would like to talk to you about your daughter .", + "emotion": "neutral", + "text": "I would like to talk to you about your daughter .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Is there a problem ?", + "emotion": "neutral", + "text": "Is there a problem ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "No , your daughter is great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "your daughter is great ." + ], + "type": [ + "no-context" + ], + "text": "No , your daughter is great .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "That's great news .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "your daughter is great ." + ], + "type": [ + "inter-personal" + ], + "text": "That's great news .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Your daughter is a wonderful student .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 8 + ], + "expanded emotion cause span": [ + "your daughter is great .", + "Your daughter is a wonderful student ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Your daughter is a wonderful student .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "She isn't messing up in class ?", + "emotion": "neutral", + "text": "She isn't messing up in class ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Of course not . Your daughter is smart and very well behaved .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 8, + 10, + 10 + ], + "expanded emotion cause span": [ + "your daughter is great .", + "Your daughter is a wonderful student .", + "Of course not .", + "Your daughter is smart and very well behaved ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Of course not . Your daughter is smart and very well behaved .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Well , I'm so glad to hear that she's doing well .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "Your daughter is smart and very well behaved .", + "she's doing well ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Well , I'm so glad to hear that she's doing well .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "It is my pleasure to have her in my class .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 8, + 10, + 10, + 12 + ], + "expanded emotion cause span": [ + "your daughter is great .", + "Your daughter is a wonderful student .", + "Of course not .", + "Your daughter is smart and very well behaved .", + "my pleasure to have her in my class ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "It is my pleasure to have her in my class .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_839.json b/reccon/sources/tr_839.json new file mode 100644 index 0000000000000000000000000000000000000000..6168ec44cf2aa0eabf10e37bc5e5214285e45263 --- /dev/null +++ b/reccon/sources/tr_839.json @@ -0,0 +1,154 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I went to Super Junior's concert last night . It was fantastic .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 1 + ], + "expanded emotion cause span": [ + "b", + "I went to Super Junior's concert last night . It was fantastic ." + ], + "type": [ + "latent", + "no-context" + ], + "text": "I went to Super Junior's concert last night . It was fantastic .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Really ? Their songs are very popular all round Asia now . I am also a big fan of theirs .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I am also a big fan of theirs ." + ], + "type": [ + "no-context" + ], + "text": "Really ? Their songs are very popular all round Asia now . I am also a big fan of theirs .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yes , their new album just came out last week . It is number one on the billboard .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Really ? Their songs are very popular all round Asia now . I am also a big fan of theirs ." + ], + "type": [ + "inter-personal" + ], + "text": "Yes , their new album just came out last week . It is number one on the billboard .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I really love their dancing . They are all excellent dancers .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I really love their dancing ." + ], + "type": [ + "no-context" + ], + "text": "I really love their dancing . They are all excellent dancers .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "The lyrics of the new song are beautiful , too . Can you sing ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "The lyrics of the new song are beautiful ," + ], + "type": [ + "no-context" + ], + "text": "The lyrics of the new song are beautiful , too . Can you sing ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Sure . I think you can hear the song everywhere you go now .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "I really love their dancing .", + "The lyrics of the new song are beautiful ," + ], + "type": [ + "hybrid" + ], + "text": "Sure . I think you can hear the song everywhere you go now .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Let's go buy their new album . Want to come with me ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 7 + ], + "expanded emotion cause span": [ + "The lyrics of the new song are beautiful ,", + "Let's go buy their new album ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Let's go buy their new album . Want to come with me ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Why not ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 7 + ], + "expanded emotion cause span": [ + "The lyrics of the new song are beautiful ,", + "Let's go buy their new album ." + ], + "type": [ + "inter-personal" + ], + "text": "Why not ?", + "id": 8, + "source_sentences": [ + 4, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8392.json b/reccon/sources/tr_8392.json new file mode 100644 index 0000000000000000000000000000000000000000..f0beaf009c0ad57bad8b382b93b06a5a36cc38d3 --- /dev/null +++ b/reccon/sources/tr_8392.json @@ -0,0 +1,162 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey daddy ! You look great today . I like your tie ! By the way , I was wondering can I ...", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "You look great today . I like your tie !" + ], + "type": [ + "no-context" + ], + "text": "Hey daddy ! You look great today . I like your tie ! By the way , I was wondering can I ...", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "NO !", + "emotion": "neutral", + "text": "NO !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I haven't even told you what it is yet !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "NO !", + "I haven't even told you what it is yet !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I haven't even told you what it is yet !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Okay , okay , what do you want ?", + "emotion": "neutral", + "text": "Okay , okay , what do you want ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Do you think I could borrow the car ? I ' m going to a concert tonight .", + "emotion": "neutral", + "text": "Do you think I could borrow the car ? I ' m going to a concert tonight .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Um .. I don ' t think so . I need the car tonight to pick up your mother .", + "emotion": "neutral", + "text": "Um .. I don ' t think so . I need the car tonight to pick up your mother .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Egg ! I told you about it last week ! Smelly Toes is playing , and Eric asked if I would go with him !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I don ' t think so . I need the car tonight to pick up your mother .", + "I told you about it last week ! Smelly Toes is playing , and Eric asked if I would go with him !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Egg ! I told you about it last week ! Smelly Toes is playing , and Eric asked if I would go with him !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Who's this Eric guy ?", + "emotion": "neutral", + "text": "Who's this Eric guy ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Duh ! He's like the hottest and most popular guy at school ! Come on , dad ! Please !", + "emotion": "neutral", + "text": "Duh ! He's like the hottest and most popular guy at school ! Come on , dad ! Please !", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "No can do ... sorry .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "No can do ... sorry ." + ], + "type": [ + "no-context" + ], + "text": "No can do ... sorry .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Fine then ! Would you mind giving me 100 bucks ?", + "emotion": "neutral", + "text": "Fine then ! Would you mind giving me 100 bucks ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "No way !", + "emotion": "neutral", + "text": "No way !", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "That ' s so unfair !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "No way !" + ], + "type": [ + "inter-personal" + ], + "text": "That ' s so unfair !", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8398.json b/reccon/sources/tr_8398.json new file mode 100644 index 0000000000000000000000000000000000000000..31e4f3984e3104c8c55714314458ed3d64cac621 --- /dev/null +++ b/reccon/sources/tr_8398.json @@ -0,0 +1,147 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Did you enjoy your meal ?", + "emotion": "neutral", + "text": "Did you enjoy your meal ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , we really enjoyed it .", + "emotion": "neutral", + "text": "Yes , we really enjoyed it .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "May I interest you in some dessert ?", + "emotion": "neutral", + "text": "May I interest you in some dessert ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes , that sounds great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "May I interest you in some dessert ?" + ], + "type": [ + "inter-personal" + ], + "text": "Yes , that sounds great .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Well , we have chocolate mousse cake , homemade fresh strawberry shortcake , and a spicy rum apple crisp for our specials .", + "emotion": "neutral", + "text": "Well , we have chocolate mousse cake , homemade fresh strawberry shortcake , and a spicy rum apple crisp for our specials .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "The apple crisp sounds great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 5 + ], + "expanded emotion cause span": [ + "dessert", + "a spicy rum apple crisp" + ], + "type": [ + "inter-personal" + ], + "text": "The apple crisp sounds great .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Since there are four of you , would you like to split a second dessert ?", + "emotion": "neutral", + "text": "Since there are four of you , would you like to split a second dessert ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Good suggestion . Could you please bring us a chocolate mousse cake and four dessert forks , please ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "Since there are four of you , would you like to split a second dessert ?", + "bring us a chocolate mousse cake and four dessert forks" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Good suggestion . Could you please bring us a chocolate mousse cake and four dessert forks , please ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Would you like coffee or tea with your dessert ?", + "emotion": "neutral", + "text": "Would you like coffee or tea with your dessert ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Let's have four coffees , please .", + "emotion": "neutral", + "text": "Let's have four coffees , please .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "OK . I will be right back with your desserts and drinks .", + "emotion": "neutral", + "text": "OK . I will be right back with your desserts and drinks .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Thank you ! We have really enjoyed our meal here .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "I will be right back with your desserts and drinks .", + "We have really enjoyed our meal here ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you ! We have really enjoyed our meal here .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8414.json b/reccon/sources/tr_8414.json new file mode 100644 index 0000000000000000000000000000000000000000..ace5cce386b4f1220942c1b9e1f0c699f2e336b7 --- /dev/null +++ b/reccon/sources/tr_8414.json @@ -0,0 +1,116 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Mr . Mass , here is a gift for you .", + "emotion": "neutral", + "text": "Mr . Mass , here is a gift for you .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh . Thanks a million .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "here is a gift for you ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh . Thanks a million .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "It's a souvenir I bought for you from Rome .", + "emotion": "neutral", + "text": "It's a souvenir I bought for you from Rome .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "How beautiful ! I love it at all .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "souvenir I bought for you from Rome .", + "How beautiful ! I love it at all ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "How beautiful ! I love it at all .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I'm glad you like it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "How beautiful ! I love it at all .", + "I'm glad you like it ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm glad you like it .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "It's very kind of you . I really don't know how I can thank you enough .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "here is a gift for you .", + "souvenir I bought for you from Rome ." + ], + "type": [ + "inter-personal" + ], + "text": "It's very kind of you . I really don't know how I can thank you enough .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Don't mention it . Just a little thing I did .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "It's very kind of you . I really don't know how I can thank you enough ." + ], + "type": [ + "inter-personal" + ], + "text": "Don't mention it . Just a little thing I did .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8433.json b/reccon/sources/tr_8433.json new file mode 100644 index 0000000000000000000000000000000000000000..fe0b8fce27e104ec5386690584ce8b6c0a5d97ee --- /dev/null +++ b/reccon/sources/tr_8433.json @@ -0,0 +1,168 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Linda , this is Todd calling .", + "emotion": "neutral", + "text": "Linda , this is Todd calling .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Todd , I am so happy you called !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "this is Todd calling ." + ], + "type": [ + "inter-personal" + ], + "text": "Todd , I am so happy you called !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Linda , I wanted to tell you how much I enjoyed our time together last Friday night .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "I am so happy you called !", + "I wanted to tell you how much I enjoyed our time together last Friday night ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Linda , I wanted to tell you how much I enjoyed our time together last Friday night .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Boy , Todd , that was one great movie you picked out ! Thanks for asking me to go with you !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3, + 4 + ], + "expanded emotion cause span": [ + "I am so happy you called !", + "I wanted to tell you how much I enjoyed our time together last Friday night .", + "that was one great movie you picked out ! Thanks for asking me to go with you !" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Boy , Todd , that was one great movie you picked out ! Thanks for asking me to go with you !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I had a great time too and was thinking that maybe you might want to join me for a hike to the waterfalls on Saturday .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "that was one great movie you picked out ! Thanks for asking me to go with you !", + "I had a great time too and was thinking that maybe you might want to join me for a hike to the waterfalls on Saturday ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I had a great time too and was thinking that maybe you might want to join me for a hike to the waterfalls on Saturday .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "A hike would be great ! Let me pack us a nice picnic lunch , OK ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "that was one great movie you picked out ! Thanks for asking me to go with you !", + "I had a great time too and was thinking that maybe you might want to join me for a hike to the waterfalls on Saturday ." + ], + "type": [ + "hybrid" + ], + "text": "A hike would be great ! Let me pack us a nice picnic lunch , OK ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Linda , that would be a perfect addition .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "hike would be great ! Let me pack us a nice picnic lunch ," + ], + "type": [ + "inter-personal" + ], + "text": "Linda , that would be a perfect addition .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I'll take care of the lunch then , and you can take care of the other plans . What time would you like to pick me up ?", + "emotion": "happiness", + "explanation": "speaker is happy about the trip", + "flag": "F", + "expanded emotion cause evidence": [ + 5, + 7 + ], + "expanded emotion cause span": [ + "a hike to the waterfalls on Saturday .", + "that would be a perfect addition ." + ], + "type": [ + "inter-personal" + ], + "text": "I'll take care of the lunch then , and you can take care of the other plans . What time would you like to pick me up ?", + "id": 8, + "source_sentences": [ + 4, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I was hoping to leave by 9 o'clock so that it won \\ ' t be too hot for the hike .", + "emotion": "neutral", + "text": "I was hoping to leave by 9 o'clock so that it won \\ ' t be too hot for the hike .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Nine is a great time to get started . I'll see you on Saturday !", + "emotion": "neutral", + "text": "Nine is a great time to get started . I'll see you on Saturday !", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_847.json b/reccon/sources/tr_847.json new file mode 100644 index 0000000000000000000000000000000000000000..772ee085bd388f40a3a8c04ae3a225b382519cfa --- /dev/null +++ b/reccon/sources/tr_847.json @@ -0,0 +1,113 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Can you take part in our picnic this Saturday ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "take part in our picnic" + ], + "type": [ + "no-context" + ], + "text": "Can you take part in our picnic this Saturday ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "That would be fine . Where are you going ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "take part in our picnic" + ], + "type": [ + "inter-personal" + ], + "text": "That would be fine . Where are you going ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "We plan to go to a forest in the suburb . There is a beautiful river there . We can do some fishing .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "We plan to go to a forest in the suburb . There is a beautiful river there . We can do some fishing ." + ], + "type": [ + "no-context" + ], + "text": "We plan to go to a forest in the suburb . There is a beautiful river there . We can do some fishing .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "We plan to go to a forest in the suburb . There is a beautiful river there . We can do some fishing ." + ], + "type": [ + "inter-personal" + ], + "text": "Great .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "And don't forget your fishing tackle .", + "emotion": "happiness", + "explanation": "speaker is happy for the picnic", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "We plan to go to a forest in the suburb . There is a beautiful river there . We can do some fishing ." + ], + "type": [ + "self-contagion" + ], + "text": "And don't forget your fishing tackle .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Ok . I like fishing very much .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 6 + ], + "expanded emotion cause span": [ + "We plan to go to a forest in the suburb . There is a beautiful river there . We can do some fishing .", + "I like fishing very much ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Ok . I like fishing very much .", + "id": 6, + "source_sentences": [ + 2 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8470.json b/reccon/sources/tr_8470.json new file mode 100644 index 0000000000000000000000000000000000000000..6146fff10052e88be722e8c891c54f65b6e4262d --- /dev/null +++ b/reccon/sources/tr_8470.json @@ -0,0 +1,254 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Are you going to vote this Tuesday ?", + "emotion": "neutral", + "text": "Are you going to vote this Tuesday ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , I am , and I am so excited .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 2 + ], + "expanded emotion cause span": [ + "Are you going to vote", + "Yes ,", + "I am so excited ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , I am , and I am so excited .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Have you figured out who you ' re going to vote for ?", + "emotion": "neutral", + "text": "Have you figured out who you ' re going to vote for ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I love my candidate .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 2, + 4 + ], + "expanded emotion cause span": [ + "Are you going to vote", + "Yes ,", + "I am so excited .", + "I love my candidate ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I love my candidate .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Why is that ?", + "emotion": "neutral", + "text": "Why is that ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "My candidate is probably the most intelligent .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 2, + 4, + 6 + ], + "expanded emotion cause span": [ + "Are you going to vote", + "Yes ,", + "I am so excited .", + "I love my candidate .", + "My candidate is probably the most intelligent ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "My candidate is probably the most intelligent .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Is that right ?", + "emotion": "neutral", + "text": "Is that right ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I also agree with all his policies .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 2, + 4, + 6, + 8 + ], + "expanded emotion cause span": [ + "Are you going to vote", + "Yes ,", + "I am so excited .", + "I love my candidate .", + "My candidate is probably the most intelligent .", + "I also agree with all his policies ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I also agree with all his policies .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "That ' s great !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 8 + ], + "expanded emotion cause span": [ + "My candidate is probably the most intelligent .", + "I also agree with all his policies ." + ], + "type": [ + "inter-personal" + ], + "text": "That ' s great !", + "id": 9, + "source_sentences": [ + 5, + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I know he ' s going to be the next President .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 2, + 4, + 6, + 8, + 10 + ], + "expanded emotion cause span": [ + "Are you going to vote", + "Yes ,", + "I am so excited .", + "I love my candidate .", + "My candidate is probably the most intelligent .", + "I also agree with all his policies .", + "he ' s going to be the next President ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I know he ' s going to be the next President .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Hopefully , he will be .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 8, + 1, + 2, + 2, + 4, + 6, + 8, + 10 + ], + "expanded emotion cause span": [ + "My candidate is probably the most intelligent .", + "I also agree with all his policies .", + "Are you going to vote", + "Yes ,", + "I am so excited .", + "I love my candidate .", + "My candidate is probably the most intelligent .", + "I also agree with all his policies .", + "he ' s going to be the next President ." + ], + "type": [ + "hybrid" + ], + "text": "Hopefully , he will be .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I can ' t wait to vote .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 2, + 4, + 6, + 8, + 10, + 12 + ], + "expanded emotion cause span": [ + "Are you going to vote", + "Yes ,", + "I am so excited .", + "I love my candidate .", + "My candidate is probably the most intelligent .", + "I also agree with all his policies .", + "he ' s going to be the next President .", + "I can ' t wait" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I can ' t wait to vote .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8499.json b/reccon/sources/tr_8499.json new file mode 100644 index 0000000000000000000000000000000000000000..89c4f1ab66845641e0fdd32281a06afa50098cf1 --- /dev/null +++ b/reccon/sources/tr_8499.json @@ -0,0 +1,143 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , John , this is Mary , your tenant up in Lincoln Park .", + "emotion": "neutral", + "text": "Hi , John , this is Mary , your tenant up in Lincoln Park .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh , hi , Mary , what can I do for you ?", + "emotion": "neutral", + "text": "Oh , hi , Mary , what can I do for you ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I was wondering when trash collection day was .", + "emotion": "neutral", + "text": "I was wondering when trash collection day was .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It ' s on Tuesdays and Fridays .", + "emotion": "neutral", + "text": "It ' s on Tuesdays and Fridays .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "wondering when trash collection day was .", + "It ' s on Tuesdays and Fridays ." + ], + "type": [ + "hybrid" + ], + "text": "Great .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "You could save a couple of dollars by taking it to the dump yourself , though .", + "emotion": "neutral", + "text": "You could save a couple of dollars by taking it to the dump yourself , though .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Oh , o . k . Where ' s that ?", + "emotion": "neutral", + "text": "Oh , o . k . Where ' s that ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "It ' s at the corner of that street .", + "emotion": "neutral", + "text": "It ' s at the corner of that street .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Thanks . Who do I call for trash collection ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "Where ' s that ?", + "It ' s at the corner of that street ." + ], + "type": [ + "hybrid" + ], + "text": "Thanks . Who do I call for trash collection ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Just leave the stuff by the curb . The company ' ll send a guy out next month to give you the bill .", + "emotion": "neutral", + "text": "Just leave the stuff by the curb . The company ' ll send a guy out next month to give you the bill .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "All right . Thanks a lot .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Just leave the stuff by the curb . The company ' ll send a guy out next month to give you the bill ." + ], + "type": [ + "inter-personal" + ], + "text": "All right . Thanks a lot .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "No problem .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "Thanks" + ], + "type": [ + "inter-personal" + ], + "text": "No problem .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_85.json b/reccon/sources/tr_85.json new file mode 100644 index 0000000000000000000000000000000000000000..c1a2293cbaed581d47472cd1bf1f912ba01b43aa --- /dev/null +++ b/reccon/sources/tr_85.json @@ -0,0 +1,218 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey , Mark , long time no see .", + "emotion": "happiness", + "explanation": "Meeting friend after a long time", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Hey , Mark , long time no see .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Julie ! It's good to see you again . How have you been ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "It's good to see you again ." + ], + "type": [ + "no-context" + ], + "text": "Julie ! It's good to see you again . How have you been ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Great . I just got back from a week's vacation in Thailand .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I just got back from a week's vacation in Thailand ." + ], + "type": [ + "no-context" + ], + "text": "Great . I just got back from a week's vacation in Thailand .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Really ? How was it ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Great . I just got back from a week's vacation in Thailand ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? How was it ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Fantastic ! I didn't want to come back .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 5 + ], + "expanded emotion cause span": [ + "Great . I just got back from a week's vacation in Thailand .", + "Fantastic ! I didn't want to come back ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Fantastic ! I didn't want to come back .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I hear the beaches in Thailand are beautiful .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I hear the beaches in Thailand are beautiful ." + ], + "type": [ + "no-context" + ], + "text": "I hear the beaches in Thailand are beautiful .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "They are . And not only that the people are friendly , but also the food is delicious , not to mention cheap .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "I hear the beaches in Thailand are beautiful .", + "They are . And not only that the people are friendly , but also the food is delicious , not to mention cheap ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "They are . And not only that the people are friendly , but also the food is delicious , not to mention cheap .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I do like Thai food . Did you see much of Bangkok ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I do like Thai food" + ], + "type": [ + "no-context" + ], + "text": "I do like Thai food . Did you see much of Bangkok ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Not much . I've got enough city life in Beijing .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "I've got enough city life in Beijing ." + ], + "type": [ + "no-context" + ], + "text": "Not much . I've got enough city life in Beijing .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I know what you mean . I could use a vacation myself .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "I could use a vacation myself ." + ], + "type": [ + "no-context" + ], + "text": "I know what you mean . I could use a vacation myself .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Hey , wouldn't it be great if we could go to Thailand together sometime ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "wouldn't it be great if we could go to Thailand together sometime" + ], + "type": [ + "no-context" + ], + "text": "Hey , wouldn't it be great if we could go to Thailand together sometime ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Yeah , it sure would .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "wouldn't it be great if we could go to Thailand together sometime" + ], + "type": [ + "inter-personal" + ], + "text": "Yeah , it sure would .", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8520.json b/reccon/sources/tr_8520.json new file mode 100644 index 0000000000000000000000000000000000000000..26a5abb0611e60ab9d79e49d6034700d93af2c68 --- /dev/null +++ b/reccon/sources/tr_8520.json @@ -0,0 +1,154 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Do you have any shoes like these ?", + "emotion": "neutral", + "text": "Do you have any shoes like these ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What size ?", + "emotion": "neutral", + "text": "What size ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Size five .", + "emotion": "neutral", + "text": "Size five .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "What colour ?", + "emotion": "neutral", + "text": "What colour ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Black .", + "emotion": "neutral", + "text": "Black .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I ' m sorry . We don't haven any .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "We don't haven any ." + ], + "type": [ + "no-context" + ], + "text": "I ' m sorry . We don't haven any .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "But my sister bought this pair last month .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "We don't haven any .", + "But my sister bought this pair last month ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "But my sister bought this pair last month .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Did she buy them here ?", + "emotion": "neutral", + "text": "Did she buy them here ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "No , she bought them in the U . S .", + "emotion": "neutral", + "text": "No , she bought them in the U . S .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "We had some shoes like those a month ago , but we don't have any now .", + "emotion": "neutral", + "text": "We had some shoes like those a month ago , but we don't have any now .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Can you get a pair for me please ?", + "emotion": "neutral", + "text": "Can you get a pair for me please ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I ' m afraid that I can ' t . They were in fashion last year and the year before last . But they ' re not in fashion this year . These shoes are in fashion now .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 10, + 11, + 12 + ], + "expanded emotion cause span": [ + "we don't have", + "Can you get a pair for me please ?", + "I can ' t ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I ' m afraid that I can ' t . They were in fashion last year and the year before last . But they ' re not in fashion this year . These shoes are in fashion now .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "They look very uncomfortable .", + "emotion": "neutral", + "text": "They look very uncomfortable .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "They are very uncomfortable . But women always wear uncomfortable shoes !", + "emotion": "neutral", + "text": "They are very uncomfortable . But women always wear uncomfortable shoes !", + "id": 14 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8560.json b/reccon/sources/tr_8560.json new file mode 100644 index 0000000000000000000000000000000000000000..8da859282b338c4650c3adb4bd895cf0458931b6 --- /dev/null +++ b/reccon/sources/tr_8560.json @@ -0,0 +1,116 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Steven , we are preparing a martial arts show for the New Year's party . Would you like to join us ?", + "emotion": "neutral", + "text": "Steven , we are preparing a martial arts show for the New Year's party . Would you like to join us ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'd love to ! But I have never learned martial arts , and there is only a month left before the New Year .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "we are preparing a martial arts show for the New Year's party . Would you like to join us ?" + ], + "type": [ + "inter-personal" + ], + "text": "I'd love to ! But I have never learned martial arts , and there is only a month left before the New Year .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "That's OK . A month is enough for you to learn the basic movements . It would be great to have you with us on the show .", + "emotion": "neutral", + "text": "That's OK . A month is enough for you to learn the basic movements . It would be great to have you with us on the show .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Sounds great ! Shall I learn the actions that Jet Li did in the movies ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "A month is enough for you to learn the basic movements . It would be great to have you with us on the show ." + ], + "type": [ + "inter-personal" + ], + "text": "Sounds great ! Shall I learn the actions that Jet Li did in the movies ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "No . You know , there are many schools and styles of kung fu . What we will perform is a set of Chinese shadow boxing .", + "emotion": "neutral", + "text": "No . You know , there are many schools and styles of kung fu . What we will perform is a set of Chinese shadow boxing .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Whatever ! I'm glad to learn something of Chinese kung fu . Thanks for asking me .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I'm glad to learn something of Chinese kung fu ." + ], + "type": [ + "no-context" + ], + "text": "Whatever ! I'm glad to learn something of Chinese kung fu . Thanks for asking me .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Thank you for joining us ! Now let's see some pictures and know more about kung fu .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Thank you for joining us !" + ], + "type": [ + "no-context" + ], + "text": "Thank you for joining us ! Now let's see some pictures and know more about kung fu .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Good !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "let's see some pictures and know more about kung fu ." + ], + "type": [ + "inter-personal" + ], + "text": "Good !", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8576.json b/reccon/sources/tr_8576.json new file mode 100644 index 0000000000000000000000000000000000000000..1dd8f956dc433b0eb1987f85ba56e40dd6d34e1d --- /dev/null +++ b/reccon/sources/tr_8576.json @@ -0,0 +1,145 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Did your meal meet with your approval ?", + "emotion": "neutral", + "text": "Did your meal meet with your approval ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Our meal was absolutely perfect !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "meal was absolutely perfect !" + ], + "type": [ + "no-context" + ], + "text": "Our meal was absolutely perfect !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "How about a dessert to top off that wonderful meal ?", + "emotion": "neutral", + "text": "How about a dessert to top off that wonderful meal ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Dessert sounds perfect , but I would like to split something with my friends .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "meal was absolutely perfect !", + "How about a dessert" + ], + "type": [ + "hybrid" + ], + "text": "Dessert sounds perfect , but I would like to split something with my friends .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "On this evening's dessert list , we have chocolate mousse cake , homemade fresh strawberry shortcake , and a spicy rum apple crisp .", + "emotion": "neutral", + "text": "On this evening's dessert list , we have chocolate mousse cake , homemade fresh strawberry shortcake , and a spicy rum apple crisp .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I think that the apple crisp would be wonderful .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3, + 5 + ], + "expanded emotion cause span": [ + "meal was absolutely perfect !", + "How about a dessert", + "spicy rum apple crisp ." + ], + "type": [ + "hybrid" + ], + "text": "I think that the apple crisp would be wonderful .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "One dessert will serve two , so would you like to split a second one ?", + "emotion": "neutral", + "text": "One dessert will serve two , so would you like to split a second one ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "We would also like a piece of chocolate mousse cake . Could you bring us four dessert forks , please ?", + "emotion": "neutral", + "text": "We would also like a piece of chocolate mousse cake . Could you bring us four dessert forks , please ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "How about some coffee and tea as well ?", + "emotion": "neutral", + "text": "How about some coffee and tea as well ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "We are all tea drinkers . Please bring us four teas .", + "emotion": "neutral", + "text": "We are all tea drinkers . Please bring us four teas .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I will prepare your desserts and have someone bring you your drinks right away .", + "emotion": "neutral", + "text": "I will prepare your desserts and have someone bring you your drinks right away .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "The hot drinks first would be great . Thanks !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I will prepare your desserts and have someone bring you your drinks right away ." + ], + "type": [ + "inter-personal" + ], + "text": "The hot drinks first would be great . Thanks !", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8608.json b/reccon/sources/tr_8608.json new file mode 100644 index 0000000000000000000000000000000000000000..9d7e84df075bb1634375a9a7606825713780022a --- /dev/null +++ b/reccon/sources/tr_8608.json @@ -0,0 +1,163 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Wow , the ferris wheel over there is so big . I'd like to take a ride on it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "ferris wheel over there is so big . I'd like to take a ride" + ], + "type": [ + "no-context" + ], + "text": "Wow , the ferris wheel over there is so big . I'd like to take a ride on it .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It is called Energy Collector .", + "emotion": "neutral", + "text": "It is called Energy Collector .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Look at your right-hand . Is it the zone of the Lost Maya Kingdom ?", + "emotion": "neutral", + "text": "Look at your right-hand . Is it the zone of the Lost Maya Kingdom ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Maybe . Oh , I see the Jungle Flying Train . I once rode it . It was very exciting .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "I see the Jungle Flying Train . I once rode it . It was very exciting ." + ], + "type": [ + "no-context" + ], + "text": "Maybe . Oh , I see the Jungle Flying Train . I once rode it . It was very exciting .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I want to have a try later .", + "emotion": "neutral", + "text": "I want to have a try later .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Me too . Daniel , look at your left side . Can you see the Air Force Ants ?", + "emotion": "neutral", + "text": "Me too . Daniel , look at your left side . Can you see the Air Force Ants ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Wow , that's my favorite . It's like a superman shooting right up into the sky .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "that's my favorite ." + ], + "type": [ + "no-context" + ], + "text": "Wow , that's my favorite . It's like a superman shooting right up into the sky .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Good , you can make your dream come true here .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "that's my favorite .", + "you can make your dream come true" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Good , you can make your dream come true here .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Of course . After this , I want to show you to the Haunted House .", + "emotion": "neutral", + "text": "Of course . After this , I want to show you to the Haunted House .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "So you can prove you are a man .", + "emotion": "neutral", + "text": "So you can prove you are a man .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Bingo !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "So you can prove you are a man" + ], + "type": [ + "inter-personal" + ], + "text": "Bingo !", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "It's just you !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "Bingo !", + "It's just you !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It's just you !", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8613.json b/reccon/sources/tr_8613.json new file mode 100644 index 0000000000000000000000000000000000000000..31ecf43a812cb363cb3e914ae081fd7e209d9176 --- /dev/null +++ b/reccon/sources/tr_8613.json @@ -0,0 +1,166 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Good afternoon , sir , is there anything I can help you with today ?", + "emotion": "neutral", + "text": "Good afternoon , sir , is there anything I can help you with today ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "umm ... yeah ! I ' m looking for a nice gift to give my girlfriend . Our fifth anniversary ' s next Friday .", + "emotion": "neutral", + "text": "umm ... yeah ! I ' m looking for a nice gift to give my girlfriend . Our fifth anniversary ' s next Friday .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Well , I would be happy to assist you in choosing the perfect gift for her . Is there anything particular that you have in mind ?", + "emotion": "neutral", + "text": "Well , I would be happy to assist you in choosing the perfect gift for her . Is there anything particular that you have in mind ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "No , not really ... I ' m completely at a loss .", + "emotion": "neutral", + "text": "No , not really ... I ' m completely at a loss .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Well , you can give her a set of pearl earrings , or this beautiful heart-shaped pendant . What is her favorite gemstone ?", + "emotion": "neutral", + "text": "Well , you can give her a set of pearl earrings , or this beautiful heart-shaped pendant . What is her favorite gemstone ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "That purple one . I ' m sorry ... I ' Ve never bought jewellery for anyone and I ' m kind of nervous .", + "emotion": "neutral", + "text": "That purple one . I ' m sorry ... I ' Ve never bought jewellery for anyone and I ' m kind of nervous .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Don ' t worry , we specialize in providing our customers a relaxed , pressure-free shopping environment . That stone is an amethyst . We have a range of beautiful amethyst pieces . Take a look at this bracelet . It ' s 18K rose-gold , studded with amethyst and blue topaz . It ' s a great statement piece .", + "emotion": "neutral", + "text": "Don ' t worry , we specialize in providing our customers a relaxed , pressure-free shopping environment . That stone is an amethyst . We have a range of beautiful amethyst pieces . Take a look at this bracelet . It ' s 18K rose-gold , studded with amethyst and blue topaz . It ' s a great statement piece .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Oh ... wow . That ' s really pretty . Jess would love that . But ... I was thinking of something a little more delicate , perhaps a necklace ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "Take a look at this bracelet . It ' s 18K rose-gold , studded with amethyst and blue topaz . It ' s a great statement piece .", + "That ' s really pretty . Jess would love that ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh ... wow . That ' s really pretty . Jess would love that . But ... I was thinking of something a little more delicate , perhaps a necklace ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "We have this beautiful platinum pendant , or you could also get her a locket . You could also get her a timepiece -- it ' s both glamorous yet functional . If you tell me a little more about your girlfriend , maybe I can help you find something for her .", + "emotion": "neutral", + "text": "We have this beautiful platinum pendant , or you could also get her a locket . You could also get her a timepiece -- it ' s both glamorous yet functional . If you tell me a little more about your girlfriend , maybe I can help you find something for her .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Jess ? Well , she ' s very smart , and has a great sense of humor . She ' s very feminine ...", + "emotion": "neutral", + "text": "Jess ? Well , she ' s very smart , and has a great sense of humor . She ' s very feminine ...", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Perhaps you could give her a ring ?", + "emotion": "neutral", + "text": "Perhaps you could give her a ring ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Well ... actually ... I was thinking about asking Jess to marry me ... I ' Ve just been so nervous .", + "emotion": "neutral", + "text": "Well ... actually ... I was thinking about asking Jess to marry me ... I ' Ve just been so nervous .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Well sir , I believe your fifth anniversary is a great time to propose !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "I was thinking about asking Jess to marry me" + ], + "type": [ + "inter-personal" + ], + "text": "Well sir , I believe your fifth anniversary is a great time to propose !", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Okay , I ' Ve decided . I ' m going to pop the question !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "I believe your fifth anniversary is a great time to propose !" + ], + "type": [ + "inter-personal" + ], + "text": "Okay , I ' Ve decided . I ' m going to pop the question !", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Fabulous ! We should look at engagement rings then ! Now that ' s a whole other section .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "I ' m going to pop the question !" + ], + "type": [ + "inter-personal" + ], + "text": "Fabulous ! We should look at engagement rings then ! Now that ' s a whole other section .", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_864.json b/reccon/sources/tr_864.json new file mode 100644 index 0000000000000000000000000000000000000000..3f6737cd8d92389dcb659f56405d992476f28b40 --- /dev/null +++ b/reccon/sources/tr_864.json @@ -0,0 +1,174 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Have you got your invitation yet ?", + "emotion": "neutral", + "text": "Have you got your invitation yet ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "My invitation ? No , I haven't . My invitation to what ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "Have you got your invitation yet ?", + "My invitation ? No , I haven't . My invitation to what ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "My invitation ? No , I haven't . My invitation to what ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "The house warming party .", + "emotion": "neutral", + "text": "The house warming party .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Whose house warming party is it ?", + "emotion": "neutral", + "text": "Whose house warming party is it ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Tom and Bill Smith . They are both working now you know ? And they've bought a new house .", + "emotion": "neutral", + "text": "Tom and Bill Smith . They are both working now you know ? And they've bought a new house .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Oh , they have ? I didn't know . I haven't seen Tom lately .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "they've bought a new house ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , they have ? I didn't know . I haven't seen Tom lately .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "It's out in the suburbs .", + "emotion": "neutral", + "text": "It's out in the suburbs .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Have you seen the house ?", + "emotion": "neutral", + "text": "Have you seen the house ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yes , I have . I went out with them last weekend .", + "emotion": "neutral", + "text": "Yes , I have . I went out with them last weekend .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Is it nice ?", + "emotion": "neutral", + "text": "Is it nice ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Yes , it is . There are three bedrooms , a living room , a dining room , and a big kitchen . There's also a garden .", + "emotion": "neutral", + "text": "Yes , it is . There are three bedrooms , a living room , a dining room , and a big kitchen . There's also a garden .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Well , that does sound nice . Have they moved in yet ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "There are three bedrooms , a living room , a dining room , and a big kitchen . There's also a garden ." + ], + "type": [ + "inter-personal" + ], + "text": "Well , that does sound nice . Have they moved in yet ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "They are moving today . Tom's taken the day off . He's rented a truck , and they should have all their furniture in the house tonight .", + "emotion": "neutral", + "text": "They are moving today . Tom's taken the day off . He's rented a truck , and they should have all their furniture in the house tonight .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "When are they going to have the party ?", + "emotion": "neutral", + "text": "When are they going to have the party ?", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Next Saturday night . You should get your invitation today or tomorrow .", + "emotion": "neutral", + "text": "Next Saturday night . You should get your invitation today or tomorrow .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Wow , that would be something to look forward to .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "You should get your invitation today or tomorrow ." + ], + "type": [ + "inter-personal" + ], + "text": "Wow , that would be something to look forward to .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8640.json b/reccon/sources/tr_8640.json new file mode 100644 index 0000000000000000000000000000000000000000..d776f3beeb5da5a4db78c0a0a1866f238621e995 --- /dev/null +++ b/reccon/sources/tr_8640.json @@ -0,0 +1,174 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Wow ! They've got everything here . All the world's famous brands . Aunt Cindy , what is your favorite brand ?", + "emotion": "neutral", + "text": "Wow ! They've got everything here . All the world's famous brands . Aunt Cindy , what is your favorite brand ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I love all the fashionable things . But my favorite brand is Chanel .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I love all the fashionable things . But my favorite brand is Chanel ." + ], + "type": [ + "no-context" + ], + "text": "I love all the fashionable things . But my favorite brand is Chanel .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Oh , that's a very expensive brand , but with good reason .", + "emotion": "neutral", + "text": "Oh , that's a very expensive brand , but with good reason .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yeah . Each style is specially designed by world's top designers . So they can always make you look amazing .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 4 + ], + "expanded emotion cause span": [ + "I love all the fashionable things . But my favorite brand is Chanel .", + "Each style is specially designed by world's top designers . So they can always make you look amazing ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Yeah . Each style is specially designed by world's top designers . So they can always make you look amazing .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I see . Come here . The high heels here look really attractive . But I wonder whether it's comfortable to wear any of them ?", + "emotion": "neutral", + "text": "I see . Come here . The high heels here look really attractive . But I wonder whether it's comfortable to wear any of them ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Not really , especially at the beginning , if you wear high heels all day long , your feet would hurt . But , no big deal . Women can always get used to that .", + "emotion": "neutral", + "text": "Not really , especially at the beginning , if you wear high heels all day long , your feet would hurt . But , no big deal . Women can always get used to that .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "It's not a simple thing to be beautiful .", + "emotion": "neutral", + "text": "It's not a simple thing to be beautiful .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Sure . But everyone loves to be beautiful . Hey , do you think this pair of sunglasses matches the handbag well ?", + "emotion": "neutral", + "text": "Sure . But everyone loves to be beautiful . Hey , do you think this pair of sunglasses matches the handbag well ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yeah , very tasteful . And with them , you look even more fashionable . Oh , there are so many French perfumers . Oops , perfumes for guys ? So strange !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "perfumes for guys ? So strange !" + ], + "type": [ + "no-context" + ], + "text": "Yeah , very tasteful . And with them , you look even more fashionable . Oh , there are so many French perfumers . Oops , perfumes for guys ? So strange !", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Come on . Fashion is not only for women . Men also share the equal right to chase fashion . It's the new fashion for men to wear perfumes , which is called cologne .", + "emotion": "neutral", + "text": "Come on . Fashion is not only for women . Men also share the equal right to chase fashion . It's the new fashion for men to wear perfumes , which is called cologne .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Oh , really , that's really something new . I'm afraid not everyone can accept it .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "It's the new fashion for men to wear perfumes , which is called cologne ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , really , that's really something new . I'm afraid not everyone can accept it .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "It takes time for that . But people's consuming attitudes are changing quickly .", + "emotion": "neutral", + "text": "It takes time for that . But people's consuming attitudes are changing quickly .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "That's true . Well , it's obvious that fashion is not a cheap thing . So , do you spend all your money on it ?", + "emotion": "neutral", + "text": "That's true . Well , it's obvious that fashion is not a cheap thing . So , do you spend all your money on it ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "No . Fashion is just part of my life , which improves its quality . But also , I'm good at financing . I have a credit card , but I never overdraft .", + "emotion": "neutral", + "text": "No . Fashion is just part of my life , which improves its quality . But also , I'm good at financing . I have a credit card , but I never overdraft .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "How is it that you are my mom's sis ? You two are so different . She always picks up bargains and spends more than she earns . You do so much better than her .", + "emotion": "neutral", + "text": "How is it that you are my mom's sis ? You two are so different . She always picks up bargains and spends more than she earns . You do so much better than her .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "I have to say that's just the result of difference of our consumptive habits .", + "emotion": "neutral", + "text": "I have to say that's just the result of difference of our consumptive habits .", + "id": 16 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8728.json b/reccon/sources/tr_8728.json new file mode 100644 index 0000000000000000000000000000000000000000..4eed7b981786a4ceed1b2ee18dda2a3b772ad8fd --- /dev/null +++ b/reccon/sources/tr_8728.json @@ -0,0 +1,155 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "it ' s so great to be here ! I ' m so excited to help you and my daughter with your new home !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "it ' s so great to be here ! I ' m so excited to help you and my daughter with your new home !" + ], + "type": [ + "no-context" + ], + "text": "it ' s so great to be here ! I ' m so excited to help you and my daughter with your new home !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "we ' re glad that you ' re here . Would you like a tour of the house ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "we ' re glad that you ' re here ." + ], + "type": [ + "no-context" + ], + "text": "we ' re glad that you ' re here . Would you like a tour of the house ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "that ' d be great , but could I have a cup of tea first ?", + "emotion": "neutral", + "text": "that ' d be great , but could I have a cup of tea first ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "sure , I ' ll just go put the kettle on . Why don ' t you have a seat on the sofa and I ' ll go take care of things in the kitchen .", + "emotion": "neutral", + "text": "sure , I ' ll just go put the kettle on . Why don ' t you have a seat on the sofa and I ' ll go take care of things in the kitchen .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "that would be lovely , thanks .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "sure , I ' ll just go put the kettle on ." + ], + "type": [ + "inter-personal" + ], + "text": "that would be lovely , thanks .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "do you take milk or sugar with your tea ?", + "emotion": "neutral", + "text": "do you take milk or sugar with your tea ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I ' ll take a little milk , but no sugar , please . Make sure you let the tea steep a few minutes before you take the tea bag out of the cup .", + "emotion": "neutral", + "text": "I ' ll take a little milk , but no sugar , please . Make sure you let the tea steep a few minutes before you take the tea bag out of the cup .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "ok . What do you think about our living room ?", + "emotion": "neutral", + "text": "ok . What do you think about our living room ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "well , I do like the mantelpiece and the coffee table , but I don ' t really care for curtains . Did you get them at a yard sale ? They look ancient .", + "emotion": "neutral", + "text": "well , I do like the mantelpiece and the coffee table , but I don ' t really care for curtains . Did you get them at a yard sale ? They look ancient .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "my parents gave them to us as a house warming gift .", + "emotion": "neutral", + "text": "my parents gave them to us as a house warming gift .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "oh dear . Well , I suppose they will do for now . do you ever dust in here ? It seems a bit dusty in here .", + "emotion": "neutral", + "text": "oh dear . Well , I suppose they will do for now . do you ever dust in here ? It seems a bit dusty in here .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "your daughter usually does the dusting , and I do the vacuuming .", + "emotion": "neutral", + "text": "your daughter usually does the dusting , and I do the vacuuming .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I see . Well , I can help with the chores while I ' m here . You two could probably use my help .", + "emotion": "neutral", + "text": "I see . Well , I can help with the chores while I ' m here . You two could probably use my help .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "that ' s very nice of you to offer . Here ' s your tea . Be careful , it ' s still quite hot .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "I can help with the chores while I ' m here ." + ], + "type": [ + "inter-personal" + ], + "text": "that ' s very nice of you to offer . Here ' s your tea . Be careful , it ' s still quite hot .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8747.json b/reccon/sources/tr_8747.json new file mode 100644 index 0000000000000000000000000000000000000000..5f744c9399ec299dd99459b1d977762f1f1325b5 --- /dev/null +++ b/reccon/sources/tr_8747.json @@ -0,0 +1,164 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello , three-five .", + "emotion": "neutral", + "text": "Hello , three-five .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Is that Anne ?", + "emotion": "neutral", + "text": "Is that Anne ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I'm sorry , I'm very tired . I'm going to bed early . I didn't have good time , and I don't really want to see you again .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 3, + 3, + 3 + ], + "expanded emotion cause span": [ + "I'm very tired .", + "I didn't have good time ,", + "I don't really want to see you again ." + ], + "type": [ + "no-context" + ], + "text": "I'm sorry , I'm very tired . I'm going to bed early . I didn't have good time , and I don't really want to see you again .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "What are you talking about ? We had a great time . We laughed and talked all night last time .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3, + 3, + 4 + ], + "expanded emotion cause span": [ + "I didn't have good time ,", + "I don't really want to see you again .", + "What are you talking about ? We had a great time ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "What are you talking about ? We had a great time . We laughed and talked all night last time .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "It was hardly all night . And I recall it was you doing all the laughing at your own jokes .", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 3, + 3, + 3, + 5 + ], + "expanded emotion cause span": [ + "I'm very tired .", + "I didn't have good time ,", + "I don't really want to see you again .", + "it was you doing all the laughing at your own jokes ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "It was hardly all night . And I recall it was you doing all the laughing at your own jokes .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "That's not fair . We had fun . Give me a second chance . Can we meet tomorrow night for drinks at the pub ?", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3, + 3, + 5, + 6 + ], + "expanded emotion cause span": [ + "I didn't have good time ,", + "I don't really want to see you again .", + "it was you doing all the laughing at your own jokes .", + "That's not fair ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's not fair . We had fun . Give me a second chance . Can we meet tomorrow night for drinks at the pub ?", + "id": 6, + "source_sentences": [ + 2, + 2, + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "No , I ' m sorry . I'm going to meet some friends tomorrow evening . And I ' m too tired now . I have to go to sleep . Goodbye .", + "emotion": "disgust", + "flag": "F", + "expanded emotion cause evidence": [ + 3, + 3, + 3, + 5 + ], + "expanded emotion cause span": [ + "I'm very tired .", + "I didn't have good time ,", + "I don't really want to see you again .", + "it was you doing all the laughing at your own jokes ." + ], + "type": [ + "self-contagion" + ], + "text": "No , I ' m sorry . I'm going to meet some friends tomorrow evening . And I ' m too tired now . I have to go to sleep . Goodbye .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "But Anne ...", + "emotion": "sadness", + "flag": "F", + "expanded emotion cause evidence": [ + 3, + 3, + 5, + 6 + ], + "expanded emotion cause span": [ + "I didn't have good time ,", + "I don't really want to see you again .", + "it was you doing all the laughing at your own jokes .", + "That's not fair ." + ], + "type": [ + "hybrid" + ], + "text": "But Anne ...", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8768.json b/reccon/sources/tr_8768.json new file mode 100644 index 0000000000000000000000000000000000000000..64e3adbd6e6e4ea36a9b5dbc8a8de228bf761b44 --- /dev/null +++ b/reccon/sources/tr_8768.json @@ -0,0 +1,173 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi Barbara . Have you lost weight ?", + "emotion": "neutral", + "text": "Hi Barbara . Have you lost weight ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hi Julie . Yeah . I've been on a diet for a couple of months now .", + "emotion": "neutral", + "text": "Hi Julie . Yeah . I've been on a diet for a couple of months now .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Wow . You look great .", + "emotion": "neutral", + "text": "Wow . You look great .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Thanks for noticing .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "Have you lost weight ?", + "You look great ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks for noticing .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "What type of diet were you on ?", + "emotion": "neutral", + "text": "What type of diet were you on ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I joined a health club and my trainer gave me tips on eating . With a combination of eating better and exercising , I managed to lose 15 pounds in 2 months .", + "emotion": "neutral", + "text": "I joined a health club and my trainer gave me tips on eating . With a combination of eating better and exercising , I managed to lose 15 pounds in 2 months .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "That's amazing . What tips did your trainer give you ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I managed to lose 15 pounds" + ], + "type": [ + "inter-personal" + ], + "text": "That's amazing . What tips did your trainer give you ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Mostly on how to exercise , but the best advice I got was changing my eating habits . Instead of eating 3 times a day , she told me to eat 5 times a day .", + "emotion": "neutral", + "text": "Mostly on how to exercise , but the best advice I got was changing my eating habits . Instead of eating 3 times a day , she told me to eat 5 times a day .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "That doesn't make sense . If you eat more , than how do you lose weight ?", + "emotion": "neutral", + "text": "That doesn't make sense . If you eat more , than how do you lose weight ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Actually , I'm eating the same amount . I eat 5 smaller meals a day . Basically , it naturally speeds up the metabolism and helps to burn fat at a faster rate .", + "emotion": "neutral", + "text": "Actually , I'm eating the same amount . I eat 5 smaller meals a day . Basically , it naturally speeds up the metabolism and helps to burn fat at a faster rate .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "That makes sense . I'm going to try that .", + "emotion": "neutral", + "text": "That makes sense . I'm going to try that .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "You don't need to lose weight .", + "emotion": "neutral", + "text": "You don't need to lose weight .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I have a little gut I have been trying to get rid of .", + "emotion": "neutral", + "text": "I have a little gut I have been trying to get rid of .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Ah ... but remember to incorporate a little exercise into your diet .", + "emotion": "neutral", + "text": "Ah ... but remember to incorporate a little exercise into your diet .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Thanks for the advice .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "incorporate a little exercise into your diet ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks for the advice .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "No problem .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "Thanks" + ], + "type": [ + "inter-personal" + ], + "text": "No problem .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8790.json b/reccon/sources/tr_8790.json new file mode 100644 index 0000000000000000000000000000000000000000..6fa94a2e31a21c58db5c1126801635efb2115433 --- /dev/null +++ b/reccon/sources/tr_8790.json @@ -0,0 +1,145 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "You are from Japan , aren't you ?", + "emotion": "neutral", + "text": "You are from Japan , aren't you ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh , yes !", + "emotion": "neutral", + "text": "Oh , yes !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I love Japan a lot .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I love Japan" + ], + "type": [ + "no-context" + ], + "text": "I love Japan a lot .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I am glad to hear that .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I love Japan" + ], + "type": [ + "inter-personal" + ], + "text": "I am glad to hear that .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Let's go to another place where my friend is working , let me pay here .", + "emotion": "neutral", + "text": "Let's go to another place where my friend is working , let me pay here .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Thank you , I ' ll pay next then .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 5 + ], + "expanded emotion cause span": [ + "I love Japan", + "let me pay" + ], + "type": [ + "inter-personal" + ], + "text": "Thank you , I ' ll pay next then .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Oh , I must be going now ; it was nice talking with you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "nice talking" + ], + "type": [ + "no-context" + ], + "text": "Oh , I must be going now ; it was nice talking with you .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Check , please .", + "emotion": "neutral", + "text": "Check , please .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "500 US dollars .", + "emotion": "neutral", + "text": "500 US dollars .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "No kidding ! We have only 5 bottles of beer .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "500 US dollars .", + "We have only 5 bottles of beer ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "No kidding ! We have only 5 bottles of beer .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 11, + "speaker": "A", + "utterance": "You had champagne for the girl .", + "emotion": "neutral", + "text": "You had champagne for the girl .", + "id": 11 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8798.json b/reccon/sources/tr_8798.json new file mode 100644 index 0000000000000000000000000000000000000000..a5f1e7e86f4de86366da190bc48d03d08de48310 --- /dev/null +++ b/reccon/sources/tr_8798.json @@ -0,0 +1,142 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "See how many people are here !", + "emotion": "neutral", + "text": "See how many people are here !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yeah ! Do all these people work in the company ? Everyone and their dog is here !", + "emotion": "neutral", + "text": "Yeah ! Do all these people work in the company ? Everyone and their dog is here !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Other than the employees , our boss Jack invited some friends of the company .", + "emotion": "neutral", + "text": "Other than the employees , our boss Jack invited some friends of the company .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Can we just sit wherever we want ?", + "emotion": "neutral", + "text": "Can we just sit wherever we want ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Of course not ! We have to sit at our assigned seats . I think our table is over there in the back .", + "emotion": "neutral", + "text": "Of course not ! We have to sit at our assigned seats . I think our table is over there in the back .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Hmm . We don't exactly have the best seats in the house , do we ?", + "emotion": "neutral", + "text": "Hmm . We don't exactly have the best seats in the house , do we ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Look who you get to sit next to--Tim from purchasing !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Look who you get to sit next to--Tim from purchasing !" + ], + "type": [ + "no-context" + ], + "text": "Look who you get to sit next to--Tim from purchasing !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Www ! That weirdo ? ! He really gives me the creeps !", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "Look who you get to sit next to--Tim from purchasing !", + "That weirdo ? ! He really gives me the creeps !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Www ! That weirdo ? ! He really gives me the creeps !", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Don't worry . I'm also sitting next to you .", + "emotion": "neutral", + "text": "Don't worry . I'm also sitting next to you .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I just hope he doesn't start bragging again !", + "emotion": "neutral", + "text": "I just hope he doesn't start bragging again !", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I can't wait until we get our year-end bonus !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "we get our year-end bonus !" + ], + "type": [ + "no-context" + ], + "text": "I can't wait until we get our year-end bonus !", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Me , either ! Who decides how much money we get ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "we get our year-end bonus !" + ], + "type": [ + "inter-personal" + ], + "text": "Me , either ! Who decides how much money we get ?", + "id": 12, + "source_sentences": [ + 10 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8803.json b/reccon/sources/tr_8803.json new file mode 100644 index 0000000000000000000000000000000000000000..704318b2619a27db46d81045a40225aa10fe4050 --- /dev/null +++ b/reccon/sources/tr_8803.json @@ -0,0 +1,194 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Why am I being arrested ?", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "being arrested" + ], + "type": [ + "no-context" + ], + "text": "Why am I being arrested ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "You have a warrant out for your arrest .", + "emotion": "neutral", + "text": "You have a warrant out for your arrest .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I don't have a warrant .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "You have a warrant out for your arrest .", + "I don't have a warrant ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I don't have a warrant .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "My computer shows that you have a bench warrant .", + "emotion": "neutral", + "text": "My computer shows that you have a bench warrant .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I don't know what a bench warrant is .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "My computer shows that you have a bench warrant .", + "I don't know what a bench warrant is ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I don't know what a bench warrant is .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "You apparently missed a court appearance .", + "emotion": "neutral", + "text": "You apparently missed a court appearance .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I was never told to go to court .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "You apparently missed a court appearance .", + "I was never told to go to court ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I was never told to go to court .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "There's nothing I can do about that .", + "emotion": "neutral", + "text": "There's nothing I can do about that .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "This isn't fair .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 2, + 3, + 4, + 5, + 6, + 7, + 9 + ], + "expanded emotion cause span": [ + "You have a warrant out for your arrest .", + "I don't have a warrant .", + "My computer shows that you have a bench warrant .", + "I don't know what a bench warrant is .", + "You apparently missed a court appearance .", + "I was never told to go to court .", + "isn't fair ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "This isn't fair .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "That's life .", + "emotion": "neutral", + "text": "That's life .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "What about my rights ?", + "emotion": "anger", + "expanded emotion cause evidence": [ + 2, + 3, + 4, + 5, + 6, + 7, + 9, + 11 + ], + "expanded emotion cause span": [ + "You have a warrant out for your arrest .", + "I don't have a warrant .", + "My computer shows that you have a bench warrant .", + "I don't know what a bench warrant is .", + "You apparently missed a court appearance .", + "I was never told to go to court .", + "isn't fair .", + "What about my rights ?" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "What about my rights ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Anything you say can and will be used against you in a court of law .", + "emotion": "neutral", + "text": "Anything you say can and will be used against you in a court of law .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8804.json b/reccon/sources/tr_8804.json new file mode 100644 index 0000000000000000000000000000000000000000..a1f2d5e4cb5c20a7099b2f23cdfd1f63ca7defc2 --- /dev/null +++ b/reccon/sources/tr_8804.json @@ -0,0 +1,167 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Alright , tell me what you think about this one .", + "emotion": "neutral", + "text": "Alright , tell me what you think about this one .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Don't you think it's a bit bright ?", + "emotion": "neutral", + "text": "Don't you think it's a bit bright ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yeah , maybe you're right . How about this outfit ?", + "emotion": "neutral", + "text": "Yeah , maybe you're right . How about this outfit ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "That dress looks lovely on you , but it's not very practical , is it ?", + "emotion": "neutral", + "text": "That dress looks lovely on you , but it's not very practical , is it ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "No , I don't have any plans to go to a formal dance any time soon , but I love the way it looks . I just want to try it on ! What do you think about this ? It's casual , yet sophisticated .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5, + 5 + ], + "expanded emotion cause span": [ + "looks lovely on you ,", + "I love the way it looks .", + "It's casual , yet sophisticated ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "No , I don't have any plans to go to a formal dance any time soon , but I love the way it looks . I just want to try it on ! What do you think about this ? It's casual , yet sophisticated .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I like the jeans , but you need something to go with the top . It's too plain on its own .", + "emotion": "neutral", + "text": "I like the jeans , but you need something to go with the top . It's too plain on its own .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "How about this scarf , these earrings , and an anklet ?", + "emotion": "neutral", + "text": "How about this scarf , these earrings , and an anklet ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That might be going overboard a bit . How about just that scarf with a bracelet ?", + "emotion": "neutral", + "text": "That might be going overboard a bit . How about just that scarf with a bracelet ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "That's a good idea . You have a lot of good fashion sense .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "scarf with a bracelet ?", + "good idea . You have a lot of good fashion sense ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's a good idea . You have a lot of good fashion sense .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Thanks . You'd be OK on your own . There are loads of fashion victims out there , and you are not one of them . Have you tried it on yet ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "good idea . You have a lot of good fashion sense ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks . You'd be OK on your own . There are loads of fashion victims out there , and you are not one of them . Have you tried it on yet ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Yep . Here it is . What do you think ?", + "emotion": "neutral", + "text": "Yep . Here it is . What do you think ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "That looks great . Just one more thing-you need some high heels with those jeans . Do you want a pair with a plain pattern or ones with a leopard print on them ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 12 + ], + "expanded emotion cause span": [ + "good idea . You have a lot of good fashion sense .", + "looks great ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That looks great . Just one more thing-you need some high heels with those jeans . Do you want a pair with a plain pattern or ones with a leopard print on them ?", + "id": 12, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 13, + "speaker": "A", + "utterance": "The leopard print sounds fabulous . OK , I'll take it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "sounds fabulous ." + ], + "type": [ + "no-context" + ], + "text": "The leopard print sounds fabulous . OK , I'll take it .", + "id": 13 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8864.json b/reccon/sources/tr_8864.json new file mode 100644 index 0000000000000000000000000000000000000000..090d1d59b8c805291325b7f44354fba40e7134ef --- /dev/null +++ b/reccon/sources/tr_8864.json @@ -0,0 +1,190 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "We finally get a chance to meet .", + "emotion": "neutral", + "text": "We finally get a chance to meet .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Thank you for meeting me here .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "get a chance to meet .", + "Thank you for meeting me here ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you for meeting me here .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "It's no problem .", + "emotion": "neutral", + "text": "It's no problem .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I need to speak with you about your daughter .", + "emotion": "neutral", + "text": "I need to speak with you about your daughter .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Is there something wrong ?", + "emotion": "neutral", + "text": "Is there something wrong ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I enjoy having your daughter in my class .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "enjoy having your daughter in my class ." + ], + "type": [ + "no-context" + ], + "text": "I enjoy having your daughter in my class .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I'm glad to hear it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "enjoy having your daughter in my class ." + ], + "type": [ + "inter-personal" + ], + "text": "I'm glad to hear it .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "She is a great addition to my class .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 8 + ], + "expanded emotion cause span": [ + "enjoy having your daughter in my class .", + "She is a great addition to my class ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "She is a great addition to my class .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "You don't have anything bad to say about her ?", + "emotion": "neutral", + "text": "You don't have anything bad to say about her ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "She is always behaving herself , and she's so smart .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 8, + 10 + ], + "expanded emotion cause span": [ + "enjoy having your daughter in my class .", + "She is a great addition to my class .", + "She is always behaving herself , and she's so smart ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "She is always behaving herself , and she's so smart .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I am so happy that she's doing okay .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 8, + 10, + 11 + ], + "expanded emotion cause span": [ + "enjoy having your daughter in my class .", + "She is a great addition to my class .", + "She is always behaving herself , and she's so smart .", + "she's doing okay ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I am so happy that she's doing okay .", + "id": 11, + "source_sentences": [ + 5, + 7, + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I'm more than happy having her in my class .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 8, + 10 + ], + "expanded emotion cause span": [ + "enjoy having your daughter in my class .", + "She is a great addition to my class .", + "She is always behaving herself , and she's so smart ." + ], + "type": [ + "self-contagion" + ], + "text": "I'm more than happy having her in my class .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8904.json b/reccon/sources/tr_8904.json new file mode 100644 index 0000000000000000000000000000000000000000..d351c6ca1119a5647f977528491a855a67a9a04f --- /dev/null +++ b/reccon/sources/tr_8904.json @@ -0,0 +1,125 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello , Pratt . How was your interview yesterday ?", + "emotion": "neutral", + "text": "Hello , Pratt . How was your interview yesterday ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hello , Finn . I did a wonderful job and I was employed . How about you ?", + "emotion": "neutral", + "text": "Hello , Finn . I did a wonderful job and I was employed . How about you ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I am sorry to tell you that I have lost the opportunity .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I am sorry to tell you that I have lost the opportunity ." + ], + "type": [ + "no-context" + ], + "text": "I am sorry to tell you that I have lost the opportunity .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Why ? You are so excellent . I think you are the most suitable person for the job .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "I am sorry to tell you that I have lost the opportunity .", + "You are so excellent . I think you are the most suitable person for the job ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Why ? You are so excellent . I think you are the most suitable person for the job .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Yes , I know I am excellent , but I pay no attention to the etiquette you ' Ve told me .", + "emotion": "neutral", + "text": "Yes , I know I am excellent , but I pay no attention to the etiquette you ' Ve told me .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "What ? Then what did you do ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I pay no attention to the etiquette you ' Ve told me ." + ], + "type": [ + "inter-personal" + ], + "text": "What ? Then what did you do ?", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "When I entered the room , I forgot to close the door . Later , I couldn ' t help smoking , you know I am a heavy-smoker . What ' s more , I forgot to polish my shoes . There is some dirt on it .", + "emotion": "neutral", + "text": "When I entered the room , I forgot to close the door . Later , I couldn ' t help smoking , you know I am a heavy-smoker . What ' s more , I forgot to polish my shoes . There is some dirt on it .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "You are so careless . You know they are the basic rules you should follow before you attend an interview . Do remember not to smoke any more , otherwise , you can ' t find a job .", + "emotion": "neutral", + "text": "You are so careless . You know they are the basic rules you should follow before you attend an interview . Do remember not to smoke any more , otherwise , you can ' t find a job .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yes , I know . And next time I must make good preparations .", + "emotion": "neutral", + "text": "Yes , I know . And next time I must make good preparations .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Good luck next time .", + "emotion": "neutral", + "text": "Good luck next time .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Thank you .", + "emotion": "neutral", + "text": "Thank you .", + "id": 11 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8921.json b/reccon/sources/tr_8921.json new file mode 100644 index 0000000000000000000000000000000000000000..d39852b331521e6522124e680b5b5a7782f27a73 --- /dev/null +++ b/reccon/sources/tr_8921.json @@ -0,0 +1,141 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "My friend Emily recently lost 18 pounds .", + "emotion": "neutral", + "text": "My friend Emily recently lost 18 pounds .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh , really ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Emily recently lost 18 pounds ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , really ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "The point is that she has been persuading me to lose weight too .", + "emotion": "neutral", + "text": "The point is that she has been persuading me to lose weight too .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Well , it's a good thing for you .", + "emotion": "neutral", + "text": "Well , it's a good thing for you .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Good ? Yes , it's good for her but not for me . You see , she tells me that I'll feel better about myself if I slim down . She keeps giving me newspaper clippings about the latest miracle diet and insists that I join a health club , as she has .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "it's a good thing for you .", + "it's good for her but not for me ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Good ? Yes , it's good for her but not for me . You see , she tells me that I'll feel better about myself if I slim down . She keeps giving me newspaper clippings about the latest miracle diet and insists that I join a health club , as she has .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "So you don't think you are fat and need to lose weight ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "it's good for her but not for me ." + ], + "type": [ + "inter-personal" + ], + "text": "So you don't think you are fat and need to lose weight ?", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I just can't bear it that Emily made me feel like a baby who always pigs out on junk food .", + "emotion": "neutral", + "text": "I just can't bear it that Emily made me feel like a baby who always pigs out on junk food .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "junk food is not good for your health . Too much of it will make you fat .", + "emotion": "neutral", + "text": "junk food is not good for your health . Too much of it will make you fat .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "But junk food is so easy . It requires no silverware or plates , no rigid mealtimes , no pleases and thank yous .", + "emotion": "neutral", + "text": "But junk food is so easy . It requires no silverware or plates , no rigid mealtimes , no pleases and thank yous .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Ok , but junk food has many disadvantages . As junk food contains high amount of oil and fat , you'll feel sleepy , but not be able to concentrate when you have a lot of it .", + "emotion": "neutral", + "text": "Ok , but junk food has many disadvantages . As junk food contains high amount of oil and fat , you'll feel sleepy , but not be able to concentrate when you have a lot of it .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Yes , but life without chips , ice cream and coca cola is boring .", + "emotion": "neutral", + "text": "Yes , but life without chips , ice cream and coca cola is boring .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Let me see . You could exercise more to keep fit .", + "emotion": "neutral", + "text": "Let me see . You could exercise more to keep fit .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Well , that sounds better than giving it up .", + "emotion": "neutral", + "text": "Well , that sounds better than giving it up .", + "id": 13 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8930.json b/reccon/sources/tr_8930.json new file mode 100644 index 0000000000000000000000000000000000000000..2dd412496063872e1abae85788e08fac0dcefd9f --- /dev/null +++ b/reccon/sources/tr_8930.json @@ -0,0 +1,198 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , I come to pick up my laundry . This is the invoice .", + "emotion": "neutral", + "text": "Hi , I come to pick up my laundry . This is the invoice .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Here you are . We've ironed them for you already . Please check and see if there is any damage .", + "emotion": "neutral", + "text": "Here you are . We've ironed them for you already . Please check and see if there is any damage .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I'm afraid that a button is missing .", + "emotion": "neutral", + "text": "I'm afraid that a button is missing .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I'm terribly sorry . You know we are so busy today and we forget to sew the button back on . Please wait a moment . It will be ready soon .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "I'm afraid that a button is missing .", + "we forget to sew the button back on ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm terribly sorry . You know we are so busy today and we forget to sew the button back on . Please wait a moment . It will be ready soon .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "OK , please .", + "emotion": "neutral", + "text": "OK , please .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Would you like to have a look ? Is it to your satisfaction ?", + "emotion": "neutral", + "text": "Would you like to have a look ? Is it to your satisfaction ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Well , oh my God , there is another problem , I'm afraid . There is still a stain on the shirt .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "There is still a stain on the shirt ." + ], + "type": [ + "no-context" + ], + "text": "Well , oh my God , there is another problem , I'm afraid . There is still a stain on the shirt .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "It doesn't seem like that . Sorry , sir , we've tried everything , but we're not able to get it off the shirt . It was from the sugar I think .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "There is still a stain on the shirt .", + "we've tried everything , but we're not able to get it off the shirt ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It doesn't seem like that . Sorry , sir , we've tried everything , but we're not able to get it off the shirt . It was from the sugar I think .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "It's been several days now , I am not sure .", + "emotion": "neutral", + "text": "It's been several days now , I am not sure .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Yes , the sugar was burnt during the dry-cleaning process . And there you go .", + "emotion": "neutral", + "text": "Yes , the sugar was burnt during the dry-cleaning process . And there you go .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Oh , that's so bad . I know little about that . Is there a remedy for it ?", + "emotion": "neutral", + "text": "Oh , that's so bad . I know little about that . Is there a remedy for it ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I am awfully sorry . Please tell us about the stains before the dry-cleaning next time .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "the sugar was burnt during the dry-cleaning process ." + ], + "type": [ + "self-contagion" + ], + "text": "I am awfully sorry . Please tell us about the stains before the dry-cleaning next time .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "OK , I will .", + "emotion": "neutral", + "text": "OK , I will .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "This is a membership card . You can get a 20 percent discount next time .", + "emotion": "neutral", + "text": "This is a membership card . You can get a 20 percent discount next time .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Thanks a lot .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "This is a membership card . You can get a 20 percent discount next time ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks a lot .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Hope to see you again . We will provide the best service .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15, + 16 + ], + "expanded emotion cause span": [ + "Thanks a lot .", + "Hope to see you again . We will provide the best service ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Hope to see you again . We will provide the best service .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_8938.json b/reccon/sources/tr_8938.json new file mode 100644 index 0000000000000000000000000000000000000000..b36e2f720036c0d4076dd29da56a0ebc1e5e8e85 --- /dev/null +++ b/reccon/sources/tr_8938.json @@ -0,0 +1,188 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "You won't believe what just happened .", + "emotion": "neutral", + "text": "You won't believe what just happened .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What ?", + "emotion": "neutral", + "text": "What ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I went down to change some money , right ?", + "emotion": "neutral", + "text": "I went down to change some money , right ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Yes . We need some . How much did you change ?", + "emotion": "neutral", + "text": "Yes . We need some . How much did you change ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I wanted to change around 5000 dollars . And you know the exchange rate .", + "emotion": "neutral", + "text": "I wanted to change around 5000 dollars . And you know the exchange rate .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yes , it's about 35 pesos for every Taiwan dollar , right ?", + "emotion": "neutral", + "text": "Yes , it's about 35 pesos for every Taiwan dollar , right ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Not today .", + "emotion": "neutral", + "text": "Not today .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "What do you mean ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "it's about 35 pesos for every Taiwan dollar ,", + "Not today ." + ], + "type": [ + "hybrid" + ], + "text": "What do you mean ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I went into the bank with my money , and I looked at the exchange board . At first I couldn't believe it . I thought I was reading the board wrong or something .", + "emotion": "neutral", + "text": "I went into the bank with my money , and I looked at the exchange board . At first I couldn't believe it . I thought I was reading the board wrong or something .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Why ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "At first I couldn't believe it . I thought I was reading the board wrong or something ." + ], + "type": [ + "inter-personal" + ], + "text": "Why ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Because the board said 60 pesos for every Taiwan dollar .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6, + 11 + ], + "expanded emotion cause span": [ + "it's about 35 pesos for every Taiwan dollar ,", + "60 pesos for every Taiwan dollar ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Because the board said 60 pesos for every Taiwan dollar .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Sixty ? That's too much . How can that be ?", + "emotion": "neutral", + "text": "Sixty ? That's too much . How can that be ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I thought it was wrong too . It didn't make sense .", + "emotion": "neutral", + "text": "I thought it was wrong too . It didn't make sense .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Just two days ago it was 35 . How can it be 60 ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "Just two days ago it was 35 . How can it be 60 ?" + ], + "type": [ + "no-context" + ], + "text": "Just two days ago it was 35 . How can it be 60 ?", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "So , I went up to the teller and started to exchange the money . And it's true . They really gave me sixty pesos for the dollar .", + "emotion": "neutral", + "text": "So , I went up to the teller and started to exchange the money . And it's true . They really gave me sixty pesos for the dollar .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "That's amazing ! Really ? How could it change so much in two days ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 15, + 16 + ], + "expanded emotion cause span": [ + "They really gave me sixty pesos for the dollar .", + "How could it change so much in two days ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's amazing ! Really ? How could it change so much in two days ?", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_9046.json b/reccon/sources/tr_9046.json new file mode 100644 index 0000000000000000000000000000000000000000..f9318edaece5664a3460baf38e2ec5bddc9cfe9a --- /dev/null +++ b/reccon/sources/tr_9046.json @@ -0,0 +1,175 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "oh , the clothes here are so expensive ! No wonder there are few people .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "the clothes here are so expensive !" + ], + "type": [ + "no-context" + ], + "text": "oh , the clothes here are so expensive ! No wonder there are few people .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Beauty costs , dear ! What do you think of this dress ? Do you think it suits me ?", + "emotion": "neutral", + "text": "Beauty costs , dear ! What do you think of this dress ? Do you think it suits me ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "yeah , it's lovely , but to be frank , it's not the most practical . You don't have many formal events in your calendar , do you ?", + "emotion": "neutral", + "text": "yeah , it's lovely , but to be frank , it's not the most practical . You don't have many formal events in your calendar , do you ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "come on , you sound like my Mom . Look at that , it's beautiful !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Look at that , it's beautiful !" + ], + "type": [ + "no-context" + ], + "text": "come on , you sound like my Mom . Look at that , it's beautiful !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "when you buy clothes , you must think about the material , quality and price .", + "emotion": "neutral", + "text": "when you buy clothes , you must think about the material , quality and price .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "maybe you have a point .", + "emotion": "neutral", + "text": "maybe you have a point .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "make sure you buy what you need and your clothes can be worn for various occasions .", + "emotion": "neutral", + "text": "make sure you buy what you need and your clothes can be worn for various occasions .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "all right . How about this black shirt ? It can be worn for anything---a party , a job interview and even a funeral !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "this black shirt ? It can be worn for anything---a party , a job interview and even a funeral !" + ], + "type": [ + "no-context" + ], + "text": "all right . How about this black shirt ? It can be worn for anything---a party , a job interview and even a funeral !", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "that's true , but you already have two back coats and one black sweater .", + "emotion": "neutral", + "text": "that's true , but you already have two back coats and one black sweater .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "oh ! Hey , look , that's the same shirt Britney wore in her concert .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Hey , look , that's the same shirt Britney wore in her concert ." + ], + "type": [ + "no-context" + ], + "text": "oh ! Hey , look , that's the same shirt Britney wore in her concert .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "exactly ! Oh , my god ! I love Britney ! I'm going to get it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "Hey , look , that's the same shirt Britney wore in her concert .", + "Oh , my god ! I love Britney ! I'm going to get it ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "exactly ! Oh , my god ! I love Britney ! I'm going to get it .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "why not try it on ?", + "emotion": "neutral", + "text": "why not try it on ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "it's just the right size--a perfect fit ! I'll take it . Oh , no , I'm a little short . Did you bring your credit card ?", + "emotion": "neutral", + "text": "it's just the right size--a perfect fit ! I'll take it . Oh , no , I'm a little short . Did you bring your credit card ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "yes .", + "emotion": "neutral", + "text": "yes .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "I promise I'll pay you back as soon as we get home .", + "emotion": "neutral", + "text": "I promise I'll pay you back as soon as we get home .", + "id": 15 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_9076.json b/reccon/sources/tr_9076.json new file mode 100644 index 0000000000000000000000000000000000000000..6fae335aded0fe8dde4b09958dfcbd28415fd084 --- /dev/null +++ b/reccon/sources/tr_9076.json @@ -0,0 +1,143 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "We have been here for about five days and I have to leave now .", + "emotion": "neutral", + "text": "We have been here for about five days and I have to leave now .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Ok ! You know you're always welcome here . Did you enjoy your stay ?", + "emotion": "neutral", + "text": "Ok ! You know you're always welcome here . Did you enjoy your stay ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yes , we have a very pleasant time . Thank you for being so nice for us .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3, + 3 + ], + "expanded emotion cause span": [ + "you're always welcome", + "we have a very pleasant time .", + "Thank you for being so nice" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes , we have a very pleasant time . Thank you for being so nice for us .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It's our pleasure . And is there anything else we can do for you before you leave here ?", + "emotion": "neutral", + "text": "It's our pleasure . And is there anything else we can do for you before you leave here ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "No , thanks . You've done a lot for us . Thank you for everything .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3, + 3, + 5 + ], + "expanded emotion cause span": [ + "you're always welcome", + "we have a very pleasant time .", + "Thank you for being so nice", + "You've done a lot for us ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "No , thanks . You've done a lot for us . Thank you for everything .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Don't mention it . Oh , This is a small gift for you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "You've done a lot for us . Thank you" + ], + "type": [ + "inter-personal" + ], + "text": "Don't mention it . Oh , This is a small gift for you .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Oh ! Thank you ! It's very kind of you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3, + 3, + 5, + 6 + ], + "expanded emotion cause span": [ + "you're always welcome", + "we have a very pleasant time .", + "Thank you for being so nice", + "You've done a lot for us .", + "a small gift for you ." + ], + "type": [ + "hybrid" + ], + "text": "Oh ! Thank you ! It's very kind of you .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "We hope you could visit our company again .", + "emotion": "neutral", + "text": "We hope you could visit our company again .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "We're sure we will . And welcome to our corporation next year . We're expecting you .", + "emotion": "neutral", + "text": "We're sure we will . And welcome to our corporation next year . We're expecting you .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Ok ! We'll definitely go to visit your company .", + "emotion": "neutral", + "text": "Ok ! We'll definitely go to visit your company .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_920.json b/reccon/sources/tr_920.json new file mode 100644 index 0000000000000000000000000000000000000000..fa7fb2a4019996f7c1fb76e9e877a85d2c357fb0 --- /dev/null +++ b/reccon/sources/tr_920.json @@ -0,0 +1,114 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I really like the record you lent me the other day .", + "emotion": "happy", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I really like the record you lent me the other day ." + ], + "type": [ + "no-context" + ], + "text": "I really like the record you lent me the other day .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'm glad you like it .", + "emotion": "happy", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I'm glad you like it ." + ], + "type": [ + "no-context" + ], + "text": "I'm glad you like it .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "And thank you very much for letting me keep it so long .", + "emotion": "happy", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "I really like the record you lent me the other day .", + "for letting me keep it so long ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "And thank you very much for letting me keep it so long .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Not at all .", + "emotion": "neutral", + "text": "Not at all .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I'm most grateful . Everyone in our class enjoyed it .", + "emotion": "happy", + "expanded emotion cause evidence": [ + 1, + 5 + ], + "expanded emotion cause span": [ + "I really like the record you lent me the other day .", + "Everyone in our class enjoyed it ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I'm most grateful . Everyone in our class enjoyed it .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I'm glad .", + "emotion": "happy", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I'm most grateful . Everyone in our class enjoyed it ." + ], + "type": [ + "inter-personal" + ], + "text": "I'm glad .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Would you mind my keeping it for another week ?", + "emotion": "neutral", + "text": "Would you mind my keeping it for another week ?", + "id": 7 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_921.json b/reccon/sources/tr_921.json new file mode 100644 index 0000000000000000000000000000000000000000..68aa814a6f4e884cbd72ef4ee45536582f61c4a6 --- /dev/null +++ b/reccon/sources/tr_921.json @@ -0,0 +1,135 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "We'd like to have a look around your house ?", + "emotion": "neutral", + "text": "We'd like to have a look around your house ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , of course , please follow me .", + "emotion": "happiness", + "explanation": "The statement of person A comes as an appreciation of person B's house which makes person B happy.", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "We'd like to have a look around your house ?" + ], + "type": [ + "inter-personal" + ], + "text": "Yes , of course , please follow me .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Thank you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Yes , of course , please follow me ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "This is our courtyard .", + "emotion": "neutral", + "text": "This is our courtyard .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "It's so spacious , about 40 square metres , right ?", + "emotion": "neutral", + "text": "It's so spacious , about 40 square metres , right ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yes , about 46 square metres .", + "emotion": "neutral", + "text": "Yes , about 46 square metres .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Are these corn ears hanging on the tree branch ?", + "emotion": "neutral", + "text": "Are these corn ears hanging on the tree branch ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Yes .", + "emotion": "neutral", + "text": "Yes .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Very beautiful and very interesting . But why do you hang them in the tree ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Very beautiful and very interesting ." + ], + "type": [ + "no-context" + ], + "text": "Very beautiful and very interesting . But why do you hang them in the tree ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "They don't have enough time to peel it after they harvested them , so they hung them in the tree . Then in winter , they can peel corn ears in their leisure time .", + "emotion": "neutral", + "text": "They don't have enough time to peel it after they harvested them , so they hung them in the tree . Then in winter , they can peel corn ears in their leisure time .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Very good idea . Sometimes such pictures can show the house's richness .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "They don't have enough time to peel it after they harvested them , so they hung them in the tree . Then in winter , they can peel corn ears in their leisure time .", + "Very good idea ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Very good idea . Sometimes such pictures can show the house's richness .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_9249.json b/reccon/sources/tr_9249.json new file mode 100644 index 0000000000000000000000000000000000000000..909fb4947af5f42bf8372ceb5fe368d0b799511e --- /dev/null +++ b/reccon/sources/tr_9249.json @@ -0,0 +1,189 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "alright , tell me what you think .", + "emotion": "neutral", + "text": "alright , tell me what you think .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "don't you think it ' s a bit bright ?", + "emotion": "neutral", + "text": "don't you think it ' s a bit bright ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "yeah , maybe you ' re right . How about this outfit ?", + "emotion": "neutral", + "text": "yeah , maybe you ' re right . How about this outfit ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "that dress looks lovely on you , but it ' s not very practical , is it ?", + "emotion": "neutral", + "text": "that dress looks lovely on you , but it ' s not very practical , is it ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "no , I don't have an plans to go to a formal dance any time soon , but I love the way it looks . I just had to try it on ! What do you think about this ? It ' s casual , yet sophisticated .", + "emotion": "neutral", + "text": "no , I don't have an plans to go to a formal dance any time soon , but I love the way it looks . I just had to try it on ! What do you think about this ? It ' s casual , yet sophisticated .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I like the jeans , but you need something to go with the top . It ' s too plain on its own .", + "emotion": "neutral", + "text": "I like the jeans , but you need something to go with the top . It ' s too plain on its own .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "how about this scarf , these earrings , and an anklet ?", + "emotion": "neutral", + "text": "how about this scarf , these earrings , and an anklet ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "that might be going overboard a bit . How about just that scarf with a bracelet ?", + "emotion": "neutral", + "text": "that might be going overboard a bit . How about just that scarf with a bracelet ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "that ' s a good idea . You have a lot of good fashion sense .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7, + 8 + ], + "expanded emotion cause span": [ + "I like the jeans , but you need something to go with the top . It ' s too plain on its own .", + "how about this scarf , these earrings , and an anklet ?", + "that might be going overboard a bit . How about just that scarf with a bracelet ?" + ], + "type": [ + "hybrid" + ], + "text": "that ' s a good idea . You have a lot of good fashion sense .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "thanks . You ' d be ok on your own . There are loads of fashion victims out there , and you are not one of them . Have you tried it on yet ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "that ' s a good idea . You have a lot of good fashion sense ." + ], + "type": [ + "inter-personal" + ], + "text": "thanks . You ' d be ok on your own . There are loads of fashion victims out there , and you are not one of them . Have you tried it on yet ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "yep . Here it is . What do you think ?", + "emotion": "neutral", + "text": "yep . Here it is . What do you think ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "that looks great . Just one more thing---you need some high heels with those jeans . Do you want a pair with a plain pattern or ones with a leopard print on them ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "What do you think ?", + "that looks great ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "that looks great . Just one more thing---you need some high heels with those jeans . Do you want a pair with a plain pattern or ones with a leopard print on them ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "the leopard print sounds fabulous . Are they a name brand ?", + "emotion": "neutral", + "text": "the leopard print sounds fabulous . Are they a name brand ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "no , they ' re a Prada knock-off for 1/10 of the price of the real thing .", + "emotion": "neutral", + "text": "no , they ' re a Prada knock-off for 1/10 of the price of the real thing .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "that ' s even better than the real thing .", + "emotion": "neutral", + "text": "that ' s even better than the real thing .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "if I were you , I ' d buy that now while it ' s on sale . If you spend more than $ 100 , you get a $ 50 voucher for more clothes .", + "emotion": "neutral", + "text": "if I were you , I ' d buy that now while it ' s on sale . If you spend more than $ 100 , you get a $ 50 voucher for more clothes .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "it ' s too bad I did all that shopping yesterday !", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 16, + 17 + ], + "expanded emotion cause span": [ + "it ' s on sale . If you spend more than $ 100 , you get a $ 50 voucher for more clothes .", + "I did all that shopping yesterday !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "it ' s too bad I did all that shopping yesterday !", + "id": 17, + "source_sentences": [ + 15 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_9280.json b/reccon/sources/tr_9280.json new file mode 100644 index 0000000000000000000000000000000000000000..e63f8c6ecc759322444b3a8875d3f5495c6c64a9 --- /dev/null +++ b/reccon/sources/tr_9280.json @@ -0,0 +1,178 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Good afternoon , miss , can I help you ?", + "emotion": "neutral", + "text": "Good afternoon , miss , can I help you ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , I ' d like to buy this dress , please .", + "emotion": "neutral", + "text": "Yes , I ' d like to buy this dress , please .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "It ' s certainly a pretty dress . I can ring you up at the register over here .", + "emotion": "neutral", + "text": "It ' s certainly a pretty dress . I can ring you up at the register over here .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Great .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "It ' s certainly a pretty dress . I can ring you up at the register over here ." + ], + "type": [ + "inter-personal" + ], + "text": "Great .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Will you be paying by cash , check , or credit card ?", + "emotion": "neutral", + "text": "Will you be paying by cash , check , or credit card ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I want to use a credit card . Do you take Discover ?", + "emotion": "neutral", + "text": "I want to use a credit card . Do you take Discover ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Sorry , no . We only take MasterCard or Visa .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Sorry , no . We only take MasterCard or Visa ." + ], + "type": [ + "no-context" + ], + "text": "Sorry , no . We only take MasterCard or Visa .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I ' ll put it on my Visa card , then .", + "emotion": "neutral", + "text": "I ' ll put it on my Visa card , then .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Very well , ma ' am . Oh , there seems to be a problem , it says it ' s rejected .", + "emotion": "neutral", + "text": "Very well , ma ' am . Oh , there seems to be a problem , it says it ' s rejected .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "There must be something wrong with the system . Try my MasterCard .", + "emotion": "neutral", + "text": "There must be something wrong with the system . Try my MasterCard .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Alright . Thank you . Yes , it seems to be working fine . Your total is $ 199 . 00 , sign here , please .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "Yes , it seems to be working fine ." + ], + "type": [ + "no-context" + ], + "text": "Alright . Thank you . Yes , it seems to be working fine . Your total is $ 199 . 00 , sign here , please .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Sure .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "buy this dress ," + ], + "type": [ + "self-contagion" + ], + "text": "Sure .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Here you go , and here ' s your receipt . Have a nice day .", + "emotion": "happiness", + "explanation": "speaker is happy for the sale", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "buy this dress ," + ], + "type": [ + "inter-personal" + ], + "text": "Here you go , and here ' s your receipt . Have a nice day .", + "id": 13, + "source_sentences": [ + 1 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Thanks . You have a good one , too .", + "emotion": "happiness", + "explanation": "speaker is happy for buying the dress", + "expanded emotion cause evidence": [ + 2, + 13 + ], + "expanded emotion cause span": [ + "buy this dress ,", + "Have a nice day ." + ], + "type": [ + "hybrid" + ], + "text": "Thanks . You have a good one , too .", + "id": 14 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_9306.json b/reccon/sources/tr_9306.json new file mode 100644 index 0000000000000000000000000000000000000000..b3ebbbb9f766eba33f8b7fcfd8066bf0adcf8e8e --- /dev/null +++ b/reccon/sources/tr_9306.json @@ -0,0 +1,265 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "It's time for desserts ! Are you still hungry ?", + "emotion": "neutral", + "text": "It's time for desserts ! Are you still hungry ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I've always got room for something sweet !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "desserts", + "I've always got room for something sweet !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I've always got room for something sweet !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "what are you going to try first ?", + "emotion": "neutral", + "text": "what are you going to try first ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I've never tried traditional Greek yogurt , so I want to try that first .", + "emotion": "neutral", + "text": "I've never tried traditional Greek yogurt , so I want to try that first .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "do they serve the yogurt with anything ?", + "emotion": "neutral", + "text": "do they serve the yogurt with anything ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I believe they add locally produced honey to it .", + "emotion": "neutral", + "text": "I believe they add locally produced honey to it .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "that sounds good . I'm going to start with an Italian tiramisu .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6, + 7 + ], + "expanded emotion cause span": [ + "serve the yogurt with anything ?", + "add locally produced honey to it .", + "start with an Italian tiramisu ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "that sounds good . I'm going to start with an Italian tiramisu .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "do you want to try some of my yogurt . It's a favorite everyday dessert in Greece .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "that sounds good . I'm going to start with an Italian tiramisu .", + "my yogurt . It's a favorite everyday dessert in Greece ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "do you want to try some of my yogurt . It's a favorite everyday dessert in Greece .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "ok . Mmm .", + "emotion": "neutral", + "text": "ok . Mmm .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "what do you think ? How does it taste ?", + "emotion": "neutral", + "text": "what do you think ? How does it taste ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "it's nice , but it's rather plain . Do you want to try my tiramisu ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "it's nice" + ], + "type": [ + "no-context" + ], + "text": "it's nice , but it's rather plain . Do you want to try my tiramisu ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "sure . I'll just have a bite .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "Do you want to try my tiramisu ?" + ], + "type": [ + "inter-personal" + ], + "text": "sure . I'll just have a bite .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "what do you think ? Does it taste good ?", + "emotion": "neutral", + "text": "what do you think ? Does it taste good ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "it's absolutely delicious ! That is the best tiramisu I've ever had !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "it's absolutely delicious ! That is the best tiramisu I've ever had !" + ], + "type": [ + "no-context" + ], + "text": "it's absolutely delicious ! That is the best tiramisu I've ever had !", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "I'm glad you like it . I don't care for it . Why don't you finish my tiramisu so that I can try one of those fried bananas ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 14, + 15 + ], + "expanded emotion cause span": [ + "it's absolutely delicious ! That is the best tiramisu I've ever had !", + "I'm glad you like it . I don't care for it . Why don't you finish my tiramisu so that I can try one of those fried bananas ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm glad you like it . I don't care for it . Why don't you finish my tiramisu so that I can try one of those fried bananas ?", + "id": 15, + "source_sentences": [ + 13 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 16, + "speaker": "B", + "utterance": "ok . I've had one of those before . They're really sweet and crunchy .", + "emotion": "neutral", + "text": "ok . I've had one of those before . They're really sweet and crunchy .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "do you know where they are from .", + "emotion": "neutral", + "text": "do you know where they are from .", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "I believe they are a local delicacy in the South .", + "emotion": "neutral", + "text": "I believe they are a local delicacy in the South .", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "do you want me to get you one , too ?", + "emotion": "neutral", + "text": "do you want me to get you one , too ?", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "yeah , why not ? We've already pigged out as it is !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15, + 16, + 19 + ], + "expanded emotion cause span": [ + "fried bananas ?", + "really sweet and crunchy .", + "do you want me to get you one" + ], + "type": [ + "hybrid" + ], + "text": "yeah , why not ? We've already pigged out as it is !", + "id": 20 + }, + { + "turn": 21, + "speaker": "A", + "utterance": "ok , I'll be back with two fried bananas in a few minutes . Wait for me here !", + "emotion": "neutral", + "text": "ok , I'll be back with two fried bananas in a few minutes . Wait for me here !", + "id": 21 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_9310.json b/reccon/sources/tr_9310.json new file mode 100644 index 0000000000000000000000000000000000000000..c960118e68f0ad06a5af3649816b9e2272780a8c --- /dev/null +++ b/reccon/sources/tr_9310.json @@ -0,0 +1,107 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Thank you for coming tonight , Mrs . Webber . As a teacher , it's great seeing the kid's parents assist our parent-teacher conference night .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "it's great seeing the kid's parents assist our parent-teacher conference night ." + ], + "type": [ + "no-context" + ], + "text": "Thank you for coming tonight , Mrs . Webber . As a teacher , it's great seeing the kid's parents assist our parent-teacher conference night .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Of course ! I am very interested to know how my child is doing and also get some insight from you as to how he can improve .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "I am very interested to know how my child is doing and also get some insight from you as to how he can improve ." + ], + "type": [ + "no-context" + ], + "text": "Of course ! I am very interested to know how my child is doing and also get some insight from you as to how he can improve .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Well Allen is a great student . He is a hard worker and very well behaved , however he does struggle a bit with math .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Allen is a great student . He is a hard worker and very well behaved ," + ], + "type": [ + "no-context" + ], + "text": "Well Allen is a great student . He is a hard worker and very well behaved , however he does struggle a bit with math .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I guess he gets that from me , I never did well in math when I was a kid . What can I do at home to compliment what he is learning in the classroom .", + "emotion": "neutral", + "text": "I guess he gets that from me , I never did well in math when I was a kid . What can I do at home to compliment what he is learning in the classroom .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Well , it's important that you sit with him and review his homework assignments and help him with math . I would also recommend he stay after school twice a week for tutoring sessions . It will really help a lot .", + "emotion": "neutral", + "text": "Well , it's important that you sit with him and review his homework assignments and help him with math . I would also recommend he stay after school twice a week for tutoring sessions . It will really help a lot .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Thanks a lot ! I will definitely do that . Is there anything else ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "it's important that you sit with him and review his homework assignments and help him with math . I would also recommend he stay after school twice a week for tutoring sessions . It will really help a lot ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks a lot ! I will definitely do that . Is there anything else ?", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Um ... yes . Here is a notice from our financial department , seems your child's Tumion is overdue .", + "emotion": "neutral", + "text": "Um ... yes . Here is a notice from our financial department , seems your child's Tumion is overdue .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Oh yes , I ...", + "emotion": "neutral", + "text": "Oh yes , I ...", + "id": 8 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_9389.json b/reccon/sources/tr_9389.json new file mode 100644 index 0000000000000000000000000000000000000000..557168b19c7adb298507908a2b0d61ba2b5d7d25 --- /dev/null +++ b/reccon/sources/tr_9389.json @@ -0,0 +1,132 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Please come in , Steven .", + "emotion": "neutral", + "text": "Please come in , Steven .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "All right , Mr . Green .", + "emotion": "neutral", + "text": "All right , Mr . Green .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Have a seat over there . How are things going out in the office ?", + "emotion": "neutral", + "text": "Have a seat over there . How are things going out in the office ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Pretty well . Everyone is working hard .", + "emotion": "neutral", + "text": "Pretty well . Everyone is working hard .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "But , our business has been going down sharply the couple of months and we have to reduce some staff .", + "emotion": "neutral", + "text": "But , our business has been going down sharply the couple of months and we have to reduce some staff .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "You mean I'm among the people who have to go ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "we have to reduce some staff .", + "You mean I'm among the people who have to go ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "You mean I'm among the people who have to go ?", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I'm afraid so .", + "emotion": "neutral", + "text": "I'm afraid so .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Did I do something wrong ?", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "You mean I'm among the people who have to go ?", + "I'm afraid so ." + ], + "type": [ + "hybrid" + ], + "text": "Did I do something wrong ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "You're the sales manager , but our sales didn't go up .", + "emotion": "neutral", + "text": "You're the sales manager , but our sales didn't go up .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "But you know I've been working very hard . And I have a family to support .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 6, + 7, + 10 + ], + "expanded emotion cause span": [ + "You mean I'm among the people who have to go ?", + "I'm afraid so .", + "I have a family to support ." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "But you know I've been working very hard . And I have a family to support .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I feel sorry , but that's the decision of the directorate .", + "emotion": "neutral", + "text": "I feel sorry , but that's the decision of the directorate .", + "id": 11 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_945.json b/reccon/sources/tr_945.json new file mode 100644 index 0000000000000000000000000000000000000000..9884f30c69f7209e44422dddf9977f12a6cd274d --- /dev/null +++ b/reccon/sources/tr_945.json @@ -0,0 +1,125 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Did you hear about Joe ? She hasn't eaten for days .", + "emotion": "neutral", + "text": "Did you hear about Joe ? She hasn't eaten for days .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Why ? What's eating her ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "She hasn't eaten for days ." + ], + "type": [ + "inter-personal" + ], + "text": "Why ? What's eating her ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Love sick . You know who she's in love with ?", + "emotion": "neutral", + "text": "Love sick . You know who she's in love with ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I don't have the slightest idea .", + "emotion": "neutral", + "text": "I don't have the slightest idea .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Someone you're living with .", + "emotion": "neutral", + "text": "Someone you're living with .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "What ? Not my Dad , I hope ! ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Someone you're living with .", + "What ? Not my Dad , I hope ! ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "What ? Not my Dad , I hope ! ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Come on , Mary , it's your brother , Jack .", + "emotion": "neutral", + "text": "Come on , Mary , it's your brother , Jack .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "No kidding ! Jack is such a log ! He's never dated a girl .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "it's your brother , Jack ." + ], + "type": [ + "inter-personal" + ], + "text": "No kidding ! Jack is such a log ! He's never dated a girl .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "The problem with Joe is that she's too shy to tell him .", + "emotion": "neutral", + "text": "The problem with Joe is that she's too shy to tell him .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "And the problem with Jack is that he seems to have no interest in girls . He's putting his heart into his stamp collection .", + "emotion": "neutral", + "text": "And the problem with Jack is that he seems to have no interest in girls . He's putting his heart into his stamp collection .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Well , if you want to help your friend , you should do something about it .", + "emotion": "neutral", + "text": "Well , if you want to help your friend , you should do something about it .", + "id": 11 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_9516.json b/reccon/sources/tr_9516.json new file mode 100644 index 0000000000000000000000000000000000000000..39e3960bf8b56961ed597c4191033e526c30e3ea --- /dev/null +++ b/reccon/sources/tr_9516.json @@ -0,0 +1,187 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "How about this floor lamp ?", + "emotion": "neutral", + "text": "How about this floor lamp ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Fine , just get it ! We have been shopping for furniture for five hours ! I ' m so tired !", + "emotion": "neutral", + "text": "Fine , just get it ! We have been shopping for furniture for five hours ! I ' m so tired !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "We still need to find an armoire and a dresser .", + "emotion": "neutral", + "text": "We still need to find an armoire and a dresser .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Fine ! I am going to go home and drop off this nightstand , coffee table and love seat while you look for the rest of the things .", + "emotion": "neutral", + "text": "Fine ! I am going to go home and drop off this nightstand , coffee table and love seat while you look for the rest of the things .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Great ! Pick me up in about an hour because I think I ' ll also get a bean bag and a dining set .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "I am going to go home and drop off this nightstand , coffee table and love seat while you look for the rest of the things .", + "I ' ll also get a bean bag and a dining set ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Great ! Pick me up in about an hour because I think I ' ll also get a bean bag and a dining set .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "While you are at it can you pick out a nice recliner ? I really want one so I can watch TV .", + "emotion": "neutral", + "text": "While you are at it can you pick out a nice recliner ? I really want one so I can watch TV .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Recliner ? In my beautifully decorated living room ? I don ' t think so !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "can you pick out a nice recliner ?", + "In my beautifully decorated living room ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Recliner ? In my beautifully decorated living room ? I don ' t think so !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "How about this floor lamp ?", + "emotion": "neutral", + "text": "How about this floor lamp ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Fine , just get it ! We have been shopping for furniture for five hours ! I ' m so tired !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "We have been shopping for furniture for five hours ! I ' m so tired !" + ], + "type": [ + "no-context" + ], + "text": "Fine , just get it ! We have been shopping for furniture for five hours ! I ' m so tired !", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "We still need to find an armoire and a dresser .", + "emotion": "neutral", + "text": "We still need to find an armoire and a dresser .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Fine ! I am going to go home and drop off this nightstand , coffee table and love seat while you look for the rest of the things .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "We have been shopping for furniture for five hours ! I ' m so tired !", + "We still need to find an armoire and a dresser ." + ], + "type": [ + "hybrid" + ], + "text": "Fine ! I am going to go home and drop off this nightstand , coffee table and love seat while you look for the rest of the things .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Great ! Pick me up in about an hour because I think I ' ll also get a bean bag and a dining set .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11, + 12 + ], + "expanded emotion cause span": [ + "I am going to go home and drop off this nightstand , coffee table and love seat while you look for the rest of the things .", + "I ' ll also get a bean bag and a dining set ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Great ! Pick me up in about an hour because I think I ' ll also get a bean bag and a dining set .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "While you are at it can you pick out a nice recliner ? I really want one so I can watch TV .", + "emotion": "neutral", + "text": "While you are at it can you pick out a nice recliner ? I really want one so I can watch TV .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Recliner ? In my beautifully decorated living room ? I don ' t think so !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 13, + 14 + ], + "expanded emotion cause span": [ + "can you pick out a nice recliner ?", + "In my beautifully decorated living room ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Recliner ? In my beautifully decorated living room ? I don ' t think so !", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_9573.json b/reccon/sources/tr_9573.json new file mode 100644 index 0000000000000000000000000000000000000000..b39f481bde9d19d6303b3510824173046635de1f --- /dev/null +++ b/reccon/sources/tr_9573.json @@ -0,0 +1,160 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Can I help you , Ma'am ?", + "emotion": "neutral", + "text": "Can I help you , Ma'am ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I need a phone card for this new cell phone .", + "emotion": "neutral", + "text": "I need a phone card for this new cell phone .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Cool phone . What kind of phone card do you want ?", + "emotion": "happiness", + "explanation": "A is happy as B wants to get a service from them", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "I need a phone card", + "Cool phone ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Cool phone . What kind of phone card do you want ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It's for my daughter who is still a senior high school student .", + "emotion": "neutral", + "text": "It's for my daughter who is still a senior high school student .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Then the M-Zone will be suitable .", + "emotion": "neutral", + "text": "Then the M-Zone will be suitable .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "What's special with the service ?", + "emotion": "neutral", + "text": "What's special with the service ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You know students use tested message service . And they provide favorable service for that .", + "emotion": "neutral", + "text": "You know students use tested message service . And they provide favorable service for that .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That's nice . And I need a pre-paid phone card .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "they provide favorable service" + ], + "type": [ + "inter-personal" + ], + "text": "That's nice . And I need a pre-paid phone card .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Oh , there is a sales promotion for it now .", + "emotion": "neutral", + "text": "Oh , there is a sales promotion for it now .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Oh , good . Then what is it ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "there is a sales promotion" + ], + "type": [ + "inter-personal" + ], + "text": "Oh , good . Then what is it ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "If you buy a pre-paid phone card worth 100 yuan today , you will get 50 yuan for free .", + "emotion": "neutral", + "text": "If you buy a pre-paid phone card worth 100 yuan today , you will get 50 yuan for free .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "May I have two of them ?", + "emotion": "neutral", + "text": "May I have two of them ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Sure . As many as you want .", + "emotion": "happiness", + "explanation": "A is happy as B wants to get a service from them", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "May I have two" + ], + "type": [ + "inter-personal" + ], + "text": "Sure . As many as you want .", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Okay , then a third one for my husband too .", + "emotion": "neutral", + "text": "Okay , then a third one for my husband too .", + "id": 14 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_959.json b/reccon/sources/tr_959.json new file mode 100644 index 0000000000000000000000000000000000000000..42f08baf26a2d1eaa75ae2a68b0b902e1dfed1c3 --- /dev/null +++ b/reccon/sources/tr_959.json @@ -0,0 +1,110 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Do you know who ' s just got married ? Old McDonald .", + "emotion": "neutral", + "text": "Do you know who ' s just got married ? Old McDonald .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Never ! He ' s over 80 , isn ' t he ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "Do you know who ' s just got married ? Old McDonald .", + "He ' s over 80" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Never ! He ' s over 80 , isn ' t he ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "He ' s nearly 90 .", + "emotion": "neutral", + "text": "He ' s nearly 90 .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Good gracious ! Are you sure ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "He ' s nearly 90 ." + ], + "type": [ + "inter-personal" + ], + "text": "Good gracious ! Are you sure ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I am . What ' s more , his wife is 84 .", + "emotion": "neutral", + "text": "I am . What ' s more , his wife is 84 .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Is she really ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "his wife is 84 ." + ], + "type": [ + "inter-personal" + ], + "text": "Is she really ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yes , she is . And guess what , he is her sixth husband .", + "emotion": "neutral", + "text": "Yes , she is . And guess what , he is her sixth husband .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Really ? Quite a woman , isn ' t she ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "he is her sixth husband ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? Quite a woman , isn ' t she ?", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_9626.json b/reccon/sources/tr_9626.json new file mode 100644 index 0000000000000000000000000000000000000000..c910ec4f5e7d02dca1933d9f5ef0418809413dc5 --- /dev/null +++ b/reccon/sources/tr_9626.json @@ -0,0 +1,161 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi , I'm back ! Hmm ... your hair is pretty damaged , and you've got split ends .", + "emotion": "neutral", + "text": "Hi , I'm back ! Hmm ... your hair is pretty damaged , and you've got split ends .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Really ? What can I do ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1, + 1 + ], + "expanded emotion cause span": [ + "your hair is pretty damaged", + "you've got split ends ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? What can I do ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Well , the trim should fix the split ends , but you might need a deep conditioning treatment .", + "emotion": "neutral", + "text": "Well , the trim should fix the split ends , but you might need a deep conditioning treatment .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Umm , OK . Whatever you think will help .", + "emotion": "neutral", + "text": "Umm , OK . Whatever you think will help .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I'm also going to add some layers to frame your face .", + "emotion": "neutral", + "text": "I'm also going to add some layers to frame your face .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Can you use the thinning shears on top , too ? My hair is really thick .", + "emotion": "neutral", + "text": "Can you use the thinning shears on top , too ? My hair is really thick .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "No problem !", + "emotion": "happiness", + "explanation": "A is happy as B asks for help", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Can you use the thinning shears" + ], + "type": [ + "inter-personal" + ], + "text": "No problem !", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Hi , I'm back ! Hmm ... your hair is pretty damaged , and you've got split ends .", + "emotion": "neutral", + "text": "Hi , I'm back ! Hmm ... your hair is pretty damaged , and you've got split ends .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Really ? What can I do ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1, + 1 + ], + "expanded emotion cause span": [ + "your hair is pretty damaged", + "you've got split ends ." + ], + "type": [ + "self-contagion" + ], + "text": "Really ? What can I do ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Well , the trim should fix the split ends , but you might need a deep conditioning treatment .", + "emotion": "neutral", + "text": "Well , the trim should fix the split ends , but you might need a deep conditioning treatment .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Umm , OK . Whatever you think will help .", + "emotion": "neutral", + "text": "Umm , OK . Whatever you think will help .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I'm also going to add some layers to frame your face .", + "emotion": "neutral", + "text": "I'm also going to add some layers to frame your face .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Can you use the thinning shears on top , too ? My hair is really thick .", + "emotion": "neutral", + "text": "Can you use the thinning shears on top , too ? My hair is really thick .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "No problem !", + "emotion": "happiness", + "explanation": "A is happy as B asks for help", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Can you use the thinning shears" + ], + "type": [ + "self-contagion" + ], + "text": "No problem !", + "id": 14 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_9643.json b/reccon/sources/tr_9643.json new file mode 100644 index 0000000000000000000000000000000000000000..71cee2e6942774099c9f3f636354bb252d29286d --- /dev/null +++ b/reccon/sources/tr_9643.json @@ -0,0 +1,198 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Sis , why did you ask me to come to this bargain market ? It's so crowded , and you can't find anything that you really want .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "why did you ask me to come to this bargain market ? It's so crowded , and you can't find anything that you really want ." + ], + "type": [ + "no-context" + ], + "text": "Sis , why did you ask me to come to this bargain market ? It's so crowded , and you can't find anything that you really want .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "You just don't get it . Looking for bargains can be really interesting .", + "emotion": "neutral", + "text": "You just don't get it . Looking for bargains can be really interesting .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Are you serious ? How can that be ?", + "emotion": "neutral", + "text": "Are you serious ? How can that be ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Bargaining is a game , or even a battle . You feel like a winner when you get a good price .", + "emotion": "neutral", + "text": "Bargaining is a game , or even a battle . You feel like a winner when you get a good price .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Come on . You know , you can never really win . The salesperson never loses . They make their living out of it .", + "emotion": "neutral", + "text": "Come on . You know , you can never really win . The salesperson never loses . They make their living out of it .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "That's true . But I just love it . Come here !", + "emotion": "neutral", + "text": "That's true . But I just love it . Come here !", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Oh , this silk carpet is really beautiful . Look at the pattern , and how delicate it is !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "this silk carpet is really beautiful . Look at the pattern , and how delicate it is !" + ], + "type": [ + "no-context" + ], + "text": "Oh , this silk carpet is really beautiful . Look at the pattern , and how delicate it is !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "You do have great taste . That's the most expensive stuff here .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "this silk carpet is really beautiful . Look at the pattern , and how delicate it is !" + ], + "type": [ + "inter-personal" + ], + "text": "You do have great taste . That's the most expensive stuff here .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Really ? Oh , this one . I like the cloisonn vase .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "You do have great taste . That's the most expensive stuff here .", + "cloisonn vase ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Really ? Oh , this one . I like the cloisonn vase .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Are you kidding me ? I bought a same one last week . It's surprising that there is something we both like . Well , what do you think of these ceramic cups ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "cloisonn vase .", + "I bought a same one last week . It's surprising that there is something we both like ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Are you kidding me ? I bought a same one last week . It's surprising that there is something we both like . Well , what do you think of these ceramic cups ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Come on . They look so cheap . Something else , please .", + "emotion": "neutral", + "text": "Come on . They look so cheap . Something else , please .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "What about this picture ? I think Benjamin would like it .", + "emotion": "neutral", + "text": "What about this picture ? I think Benjamin would like it .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Don't underestimate his taste . I don't think he'd like it .", + "emotion": "neutral", + "text": "Don't underestimate his taste . I don't think he'd like it .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Don't be so sure . He loves the vase I bought here last week .", + "emotion": "neutral", + "text": "Don't be so sure . He loves the vase I bought here last week .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Yeah . Well , anyway , it's up to you . But I can tell that you come here often .", + "emotion": "neutral", + "text": "Yeah . Well , anyway , it's up to you . But I can tell that you come here often .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Absolutely . That's why I can always get a good price .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15, + 16 + ], + "expanded emotion cause span": [ + "But I can tell that you come here often .", + "I can always get a good price ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Absolutely . That's why I can always get a good price .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_9666.json b/reccon/sources/tr_9666.json new file mode 100644 index 0000000000000000000000000000000000000000..1617506b171c7a579bdeefc8804af538a6cb0d9c --- /dev/null +++ b/reccon/sources/tr_9666.json @@ -0,0 +1,122 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Oh , hey , Keri ! You cook , right ! You're a pretty good cook .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "You're a pretty good cook ." + ], + "type": [ + "no-context" + ], + "text": "Oh , hey , Keri ! You cook , right ! You're a pretty good cook .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'm OK .", + "emotion": "neutral", + "text": "I'm OK .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I want to make an omelet , so actually this is really silly , I've never made one before . How do you make an omelet ?", + "emotion": "neutral", + "text": "I want to make an omelet , so actually this is really silly , I've never made one before . How do you make an omelet ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Well , I can teach you how I make them , which is the same way my father and grandmother make them , which is a little special .", + "emotion": "neutral", + "text": "Well , I can teach you how I make them , which is the same way my father and grandmother make them , which is a little special .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "OK . Yeah ! Yeah !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 3, + 4 + ], + "expanded emotion cause span": [ + "I want to make an omelet", + "I've never made one before . How do you make an omelet ?", + "I can teach you how I make them , which is the same way my father and grandmother make them , which is a little special ." + ], + "type": [ + "hybrid" + ], + "text": "OK . Yeah ! Yeah !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "First you take some eggs and crack them in a bowl , and whisk them up , quite , so they're quite high and fluffy , and in a hot pan , and you need a pan that's that's kind of small , that the sides go up at an angle . You put some oil and heat it up , so it's quite hot , and then you take your whipped up eggs , or whisked up eggs , and pour them into the pan , and as it's cooking , if you take a spatula , and push the bottom layer of the egg , to the side , to the sides , and then to the middle , so the uncooked egg gets to the bottom of the pan .", + "emotion": "neutral", + "text": "First you take some eggs and crack them in a bowl , and whisk them up , quite , so they're quite high and fluffy , and in a hot pan , and you need a pan that's that's kind of small , that the sides go up at an angle . You put some oil and heat it up , so it's quite hot , and then you take your whipped up eggs , or whisked up eggs , and pour them into the pan , and as it's cooking , if you take a spatula , and push the bottom layer of the egg , to the side , to the sides , and then to the middle , so the uncooked egg gets to the bottom of the pan .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Oh , OK . Wow !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "First you take some eggs and crack them in a bowl , and whisk them up , quite , so they're quite high and fluffy , and in a hot pan , and you need a pan that's that's kind of small , that the sides go up at an angle . You put some oil and heat it up , so it's quite hot , and then you take your whipped up eggs , or whisked up eggs , and pour them into the pan , and as it's cooking , if you take a spatula , and push the bottom layer of the egg , to the side , to the sides , and then to the middle , so the uncooked egg gets to the bottom of the pan ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , OK . Wow !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "OK . And keep doing that until most of the egg is cooked so you should have a nice thick omelet and then flip it over , you'll only have to cook that side lightly . Put your fillings on the top and fold it over and let it sit just long enough to melt the cheese .", + "emotion": "neutral", + "text": "OK . And keep doing that until most of the egg is cooked so you should have a nice thick omelet and then flip it over , you'll only have to cook that side lightly . Put your fillings on the top and fold it over and let it sit just long enough to melt the cheese .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Wow . That sounds really good .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "keep doing that until most of the egg is cooked so you should have a nice thick omelet and then flip it over , you'll only have to cook that side lightly . Put your fillings on the top and fold it over and let it sit just long enough to melt the cheese .", + "sounds really good ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Wow . That sounds really good .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/tr_9686.json b/reccon/sources/tr_9686.json new file mode 100644 index 0000000000000000000000000000000000000000..ada4d0e807514caa1a0586ef3b93225f6952316e --- /dev/null +++ b/reccon/sources/tr_9686.json @@ -0,0 +1,227 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Why don't you watch where you're going ?", + "emotion": "neutral", + "text": "Why don't you watch where you're going ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Me ? You're the one who pulled out in front of me !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "Why don't you watch where you're going ?", + "You're the one who pulled out in front of me !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Me ? You're the one who pulled out in front of me !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "There was plenty of room for me to pull out . You didn't have to stay in the lane you were in .", + "emotion": "neutral", + "text": "There was plenty of room for me to pull out . You didn't have to stay in the lane you were in .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Hey , listen . I had every right to stay in the lane I was in . You were supposed to wait until I passed to pull out . And anyhow , you didn't give me any time to change lanes . All of a sudden--BANG--there you are right in front of me .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "There was plenty of room for me to pull out . You didn't have to stay in the lane you were in .", + "I had every right to stay in the lane I was in . You were supposed to wait until I passed to pull out ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Hey , listen . I had every right to stay in the lane I was in . You were supposed to wait until I passed to pull out . And anyhow , you didn't give me any time to change lanes . All of a sudden--BANG--there you are right in front of me .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I think my arm is broken .", + "emotion": "neutral", + "text": "I think my arm is broken .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Sorry about your arm , but it serves you right . You need to learn how to drive . You're lucky you didn't get killed . And I'm lucky to be alive too .", + "emotion": "neutral", + "text": "Sorry about your arm , but it serves you right . You need to learn how to drive . You're lucky you didn't get killed . And I'm lucky to be alive too .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Listen , let's just wait until the police get here . Then we can decide whose fault this accident was .", + "emotion": "neutral", + "text": "Listen , let's just wait until the police get here . Then we can decide whose fault this accident was .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Fine with me . I know the laws of the road . I'm not worried .", + "emotion": "neutral", + "text": "Fine with me . I know the laws of the road . I'm not worried .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I have a cell phone in my car . Now it's probably on the floor on the passenger side . Why don't you get it for me , and then I can call the police ?", + "emotion": "neutral", + "text": "I have a cell phone in my car . Now it's probably on the floor on the passenger side . Why don't you get it for me , and then I can call the police ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Alright .", + "emotion": "neutral", + "text": "Alright .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "It doesn't work . It looks like it's broken . I need to get to a hospital . You should drive me there .", + "emotion": "neutral", + "text": "It doesn't work . It looks like it's broken . I need to get to a hospital . You should drive me there .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Oh , yeah ? It's better if we make a police report first . Then you can go to the hospital .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "It looks like it's broken . I need to get to a hospital . You should drive me there ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , yeah ? It's better if we make a police report first . Then you can go to the hospital .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Damn it ! I'm injured here . We could wait all day for the police .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 12, + 13 + ], + "expanded emotion cause span": [ + "It's better if we make a police report first . Then you can go to the hospital .", + "I'm injured here . We could wait all day for the police ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Damn it ! I'm injured here . We could wait all day for the police .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Well , you'll just have to wait . I'm not going to move my car until the police arrive . I'll go into one of those houses over there and use their phone . Don't worry . You'll get to the hospital in time .", + "emotion": "neutral", + "text": "Well , you'll just have to wait . I'm not going to move my car until the police arrive . I'll go into one of those houses over there and use their phone . Don't worry . You'll get to the hospital in time .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "It really hurts .", + "emotion": "neutral", + "text": "It really hurts .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Yes , maybe it does . But if you're going to drive like you did just now , you will have to get used to a little physical pain . You know what I mean ?", + "emotion": "neutral", + "text": "Yes , maybe it does . But if you're going to drive like you did just now , you will have to get used to a little physical pain . You know what I mean ?", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "To hell with you . The accident was your fault .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 16, + 17 + ], + "expanded emotion cause span": [ + "But if you're going to drive like you did just now , you will have to get used to a little physical pain .", + "The accident was your fault ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "To hell with you . The accident was your fault .", + "id": 17, + "source_sentences": [ + 15 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 18, + "speaker": "B", + "utterance": "I'm afraid it wasn't . And when the police get here , you will also see that it wasn't . But enough of this bickering . I'm going to go find a phone . Don ' t move that arm while I'm gone . Alright ?", + "emotion": "neutral", + "text": "I'm afraid it wasn't . And when the police get here , you will also see that it wasn't . But enough of this bickering . I'm going to go find a phone . Don ' t move that arm while I'm gone . Alright ?", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "To hell with you .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 17, + 18 + ], + "expanded emotion cause span": [ + "The accident was your fault .", + "I'm afraid it wasn't . And when the police get here , you will also see that it wasn't ." + ], + "type": [ + "hybrid" + ], + "text": "To hell with you .", + "id": 19 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_9734.json b/reccon/sources/tr_9734.json new file mode 100644 index 0000000000000000000000000000000000000000..d1c8dcc0a202078965f54c1db0e27977f5f72788 --- /dev/null +++ b/reccon/sources/tr_9734.json @@ -0,0 +1,139 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Can you help me find a nice gift for my young niece ?", + "emotion": "neutral", + "text": "Can you help me find a nice gift for my young niece ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Barbie dolls are quite popular , you know .", + "emotion": "neutral", + "text": "Barbie dolls are quite popular , you know .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "You're right . Girls love Barbie . Show me a Barbie doll .", + "emotion": "neutral", + "text": "You're right . Girls love Barbie . Show me a Barbie doll .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Take a look at the newest Barbie -- Digital Barbie .", + "emotion": "neutral", + "text": "Take a look at the newest Barbie -- Digital Barbie .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "She's beautiful . What's the price for Digital Barbie ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "She's beautiful ." + ], + "type": [ + "no-context" + ], + "text": "She's beautiful . What's the price for Digital Barbie ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Our regular price for Digital Barbie is $ 29 . 95 plus tax .", + "emotion": "neutral", + "text": "Our regular price for Digital Barbie is $ 29 . 95 plus tax .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Only $ 29 . 95 ? I'll buy it , of course .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Our regular price for Digital Barbie is $ 29 . 95 plus tax ." + ], + "type": [ + "inter-personal" + ], + "text": "Only $ 29 . 95 ? I'll buy it , of course .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Another one sold . Do you see anything else you would like ?", + "emotion": "neutral", + "text": "Another one sold . Do you see anything else you would like ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Thank you , but no . This will do it for now .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "Our regular price for Digital Barbie is $ 29 . 95 plus tax ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you , but no . This will do it for now .", + "id": 9, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Tax brings your total to $ 32 . 42 . How would you like to pay ?", + "emotion": "neutral", + "text": "Tax brings your total to $ 32 . 42 . How would you like to pay ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Cash , please .", + "emotion": "neutral", + "text": "Cash , please .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Here's your change . Thank you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Another one sold ." + ], + "type": [ + "self-contagion" + ], + "text": "Here's your change . Thank you .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_9779.json b/reccon/sources/tr_9779.json new file mode 100644 index 0000000000000000000000000000000000000000..9c136e62fd9f080745dda5ba520a996570fb13a1 --- /dev/null +++ b/reccon/sources/tr_9779.json @@ -0,0 +1,142 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Did you hear who won the election ?", + "emotion": "neutral", + "text": "Did you hear who won the election ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I can ' t believe that Obama won .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Obama won ." + ], + "type": [ + "no-context" + ], + "text": "I can ' t believe that Obama won .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I couldn ' t be happier to know that he ' s our new President .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 3 + ], + "expanded emotion cause span": [ + "Obama won .", + "he ' s our new President ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I couldn ' t be happier to know that he ' s our new President .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I know ! He just made history !", + "emotion": "neutral", + "text": "I know ! He just made history !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "You voted for him , right ?", + "emotion": "neutral", + "text": "You voted for him , right ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I did . Did you ?", + "emotion": "neutral", + "text": "I did . Did you ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I voted for him .", + "emotion": "neutral", + "text": "I voted for him .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I am so happy that he is our new President !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "he is our new President !" + ], + "type": [ + "no-context" + ], + "text": "I am so happy that he is our new President !", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "So am I .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "he is our new President !" + ], + "type": [ + "inter-personal" + ], + "text": "So am I .", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I hope that he brings change to America .", + "emotion": "neutral", + "text": "I hope that he brings change to America .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I have faith in him .", + "emotion": "neutral", + "text": "I have faith in him .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I have faith in our new President .", + "emotion": "neutral", + "text": "I have faith in our new President .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_9841.json b/reccon/sources/tr_9841.json new file mode 100644 index 0000000000000000000000000000000000000000..fa7c70de38b4382775d7ade0f22a1a7af69f70d6 --- /dev/null +++ b/reccon/sources/tr_9841.json @@ -0,0 +1,130 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Wow ! It's hot today ! Do you want to get an ice cream cone ?", + "emotion": "neutral", + "text": "Wow ! It's hot today ! Do you want to get an ice cream cone ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "No Let's go to an ice cream parlor ! They have way more flavors to choose from there . I feel like having something special like Neapolitan ice cream .", + "emotion": "neutral", + "text": "No Let's go to an ice cream parlor ! They have way more flavors to choose from there . I feel like having something special like Neapolitan ice cream .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What's that ?", + "emotion": "neutral", + "text": "What's that ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It's three different flavors mixed together . Chocolate , strawberry and something green with candied fruit .", + "emotion": "neutral", + "text": "It's three different flavors mixed together . Chocolate , strawberry and something green with candied fruit .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Do they have ice cream bars . frozen yogurt or frozen chocolate mousse ?", + "emotion": "neutral", + "text": "Do they have ice cream bars . frozen yogurt or frozen chocolate mousse ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Absolutely ! They also have real Italian Galatian and French sorbets . They do a great baked Alaska .", + "emotion": "happiness", + "explanation": "the speaker is happy that A can have his ice cream wishes fulfilled", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Do they have ice cream bars . frozen yogurt or frozen chocolate mousse ?", + "Absolutely ! They also have real Italian Galatian and French sorbets . They do a great baked Alaska ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Absolutely ! They also have real Italian Galatian and French sorbets . They do a great baked Alaska .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Maybe a vanilla ice cream milkshake would be good . What's your favorite flavor ?", + "emotion": "neutral", + "text": "Maybe a vanilla ice cream milkshake would be good . What's your favorite flavor ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Well ... l like the traditional flavors like rum raisin , butter pecan . maple walnut , strawberry , chocolate and vanilla . But now there are some new flavors from Asia like green tea and durian .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "favorite flavor ?", + "l like the traditional flavors like rum raisin , butter pecan . maple walnut , strawberry , chocolate and vanilla . But now there are some new flavors from Asia like green tea and durian ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Well ... l like the traditional flavors like rum raisin , butter pecan . maple walnut , strawberry , chocolate and vanilla . But now there are some new flavors from Asia like green tea and durian .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "God ! Even talking about it makes me feel like l'm gaining weight !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "l like the traditional flavors like rum raisin , butter pecan . maple walnut , strawberry , chocolate and vanilla . But now there are some new flavors from Asia like green tea and durian ." + ], + "type": [ + "inter-personal" + ], + "text": "God ! Even talking about it makes me feel like l'm gaining weight !", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "That's OK . We can go jogging , after we eat !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "l like the traditional flavors like rum raisin , butter pecan . maple walnut , strawberry , chocolate and vanilla . But now there are some new flavors from Asia like green tea and durian ." + ], + "type": [ + "self-contagion" + ], + "text": "That's OK . We can go jogging , after we eat !", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_990.json b/reccon/sources/tr_990.json new file mode 100644 index 0000000000000000000000000000000000000000..cd0f2434ef8b017f919a666e4dd6ad69ad3b5e4d --- /dev/null +++ b/reccon/sources/tr_990.json @@ -0,0 +1,121 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello , Mary . Nice day , isn't it ?", + "emotion": "neutral", + "text": "Hello , Mary . Nice day , isn't it ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , what a wonderful day ! The sky has cleared up in the end .", + "emotion": "neutral", + "text": "Yes , what a wonderful day ! The sky has cleared up in the end .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I do feel like an outdoor exercise . After all , we haven't had such a beautiful day for a long time .", + "emotion": "neutral", + "text": "I do feel like an outdoor exercise . After all , we haven't had such a beautiful day for a long time .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "How about taking a walk in the park ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "what a wonderful day ! The sky has cleared up in the end ." + ], + "type": [ + "self-contagion" + ], + "text": "How about taking a walk in the park ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "OK . It's delightful to have a walk in the park with the air so fresh .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "It's delightful to have a walk in the park with the air so fresh ." + ], + "type": [ + "no-context" + ], + "text": "OK . It's delightful to have a walk in the park with the air so fresh .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "( After they entering the park ) Great , it's so quiet here . We have the park to ourselves , only you and me .", + "emotion": "neutral", + "text": "( After they entering the park ) Great , it's so quiet here . We have the park to ourselves , only you and me .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Are you kidding ? Don't you see many people over there ? Just on your right .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "Great , it's so quiet here .", + "Don't you see many people over there ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Are you kidding ? Don't you see many people over there ? Just on your right .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Oh , I see them . Beautiful weather should be shared by all the people .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 8 + ], + "expanded emotion cause span": [ + "Great , it's so quiet here .", + "Beautiful weather should be shared by all the people ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Oh , I see them . Beautiful weather should be shared by all the people .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Ah , you changed so fast .", + "emotion": "neutral", + "text": "Ah , you changed so fast .", + "id": 9 + } +] \ No newline at end of file diff --git a/reccon/sources/tr_9974.json b/reccon/sources/tr_9974.json new file mode 100644 index 0000000000000000000000000000000000000000..c69fa164e9165de1619e0b90ef883d1579e4a467 --- /dev/null +++ b/reccon/sources/tr_9974.json @@ -0,0 +1,131 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Mike ! Look at the floor !", + "emotion": "neutral", + "text": "Mike ! Look at the floor !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What's wrong with it ?", + "emotion": "neutral", + "text": "What's wrong with it ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What's wrong with it ? It's filthy !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "It's filthy !" + ], + "type": [ + "no-context" + ], + "text": "What's wrong with it ? It's filthy !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Oh ...", + "emotion": "neutral", + "text": "Oh ...", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "It's filthy because you never wipe your shoes .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 3, + 5 + ], + "expanded emotion cause span": [ + "It's filthy !", + "It's filthy because you never wipe your shoes ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "It's filthy because you never wipe your shoes .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Sorry , love .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3, + 5 + ], + "expanded emotion cause span": [ + "It's filthy !", + "It's filthy because you never wipe your shoes ." + ], + "type": [ + "inter-personal" + ], + "text": "Sorry , love .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "What are you looking for now ?", + "emotion": "neutral", + "text": "What are you looking for now ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "My cigarettes .", + "emotion": "neutral", + "text": "My cigarettes .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Well , they ' re not here . They are in the dustbin .", + "emotion": "neutral", + "text": "Well , they ' re not here . They are in the dustbin .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "In the dustbin ! Why didn't you tell me before ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "They are in the dustbin .", + "Why didn't you tell me before ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "In the dustbin ! Why didn't you tell me before ?", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/train.Ses01F_impro01.json b/reccon/sources/train.Ses01F_impro01.json new file mode 100644 index 0000000000000000000000000000000000000000..4f03fc9a6fcc8bf40d54f3ff6352f55954e0113f --- /dev/null +++ b/reccon/sources/train.Ses01F_impro01.json @@ -0,0 +1,438 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Excuse me.", + "emotion": "neutral", + "text": "Excuse me.", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Do you have your forms?", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Do you have your forms?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Yeah.", + "emotion": "neutral", + "text": "Yeah.", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Let me see them.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Let me see them.", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Is there a problem?", + "emotion": "neutral", + "text": "Is there a problem?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Who told you to get in this line?", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Who told you to get in this line?", + "id": 6 + }, + { + "turn": 7, + "speaker": "B", + "utterance": "Okay. But I didn't tell you to get in this line if you are filling out this particular form.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 7, + "b" + ], + "expanded emotion cause span": [ + "I didn't tell you to get in this line if you are filling out this particular form", + "b" + ], + "type": [ + "latent", + "no-context" + ], + "text": "Okay. But I didn't tell you to get in this line if you are filling out this particular form.", + "id": 7 + }, + { + "turn": 8, + "speaker": "A", + "utterance": "Well what's the problem? Let me change it.", + "emotion": "neutral", + "text": "Well what's the problem? Let me change it.", + "id": 8 + }, + { + "turn": 9, + "speaker": "B", + "utterance": "This form is a Z.X.four.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 9, + 7, + "b" + ], + "expanded emotion cause span": [ + "This form is a Z.X.four.", + "I didn't tell you to get in this line if you are filling out this particular form", + "b" + ], + "type": [ + "latent", + "no-context", + "self-contagion" + ], + "text": "This form is a Z.X.four.", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "You can't-- This is not the line for Z.X.four. If you're going to fill out the Z.X.four, you need to have a different form of ID.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 10, + 7, + "b" + ], + "expanded emotion cause span": [ + "You can't-- This is not the line for Z.X.four. If you're going to fill out the Z.X.four, you need to have a different form of ID.", + "I didn't tell you to get in this line if you are filling out this particular form", + "b" + ], + "type": [ + "latent", + "no-context", + "self-contagion" + ], + "text": "You can't-- This is not the line for Z.X.four. If you're going to fill out the Z.X.four, you need to have a different form of ID.", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "What? I'm getting an ID. This is why I'm here. My wallet was stolen.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 11, + 10 + ], + "expanded emotion cause span": [ + "What? I'm getting an ID. This is why I'm here. My wallet was stolen.", + "If you're going to fill out the Z.X.four, you need to have a different form of ID" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "What? I'm getting an ID. This is why I'm here. My wallet was stolen.", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "No. I need another set of ID to prove this is actually you.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "No. I need another set of ID to prove this is actually you." + ], + "type": [ + "no-context" + ], + "text": "No. I need another set of ID to prove this is actually you.", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "How am I supposed to get an ID without an ID? How does a person get an ID in the first place?", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "How am I supposed to get an ID without an ID? How does a person get an ID in the first place?" + ], + "type": [ + "no-context" + ], + "text": "How am I supposed to get an ID without an ID? How does a person get an ID in the first place?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "I don't know. But I need an ID to pass this form along. I can't just send it along without an ID.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 14, + 13 + ], + "expanded emotion cause span": [ + "I don't know. But I need an ID to pass this form along. I can't just send it along without an ID.", + "How am I supposed to get an ID without an ID? How does a person get an ID in the first place?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I don't know. But I need an ID to pass this form along. I can't just send it along without an ID.", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "I'm here to get an ID.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "But I need an ID to pass this form along. I can't just send it along without an ID." + ], + "type": [ + "inter-personal" + ], + "text": "I'm here to get an ID.", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "No. I need another ID, a separate one.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 16 + ], + "expanded emotion cause span": [ + "No. I need another ID, a separate one." + ], + "type": [ + "no-context" + ], + "text": "No. I need another ID, a separate one.", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "Like what? Like a birth certificate?", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 16 + ], + "expanded emotion cause span": [ + "No. I need another ID, a separate one." + ], + "type": [ + "inter-personal" + ], + "text": "Like what? Like a birth certificate?", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "A birth certificate, a passport...a student ID; didn't you go to school? Anything?", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 16, + 17 + ], + "expanded emotion cause span": [ + "No. I need another ID, a separate one.", + "Like what? Like a birth certificate?" + ], + "type": [ + "hybrid" + ], + "text": "A birth certificate, a passport...a student ID; didn't you go to school? Anything?", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "Yes but my wallet was stolen, I don't have anything. I don't have any credit cards, I don't have my ID. Don't you have things on file here?", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 19, + 18 + ], + "expanded emotion cause span": [ + "my wallet was stolen, I don't have anything. I don't have any credit cards, I don't have my ID.", + "didn't you go to school?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes but my wallet was stolen, I don't have anything. I don't have any credit cards, I don't have my ID. Don't you have things on file here?", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "Yeah. We keep it on file, but we need an ID to access that file.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 20 + ], + "expanded emotion cause span": [ + "We keep it on file, but we need an ID to access that file" + ], + "type": [ + "no-context" + ], + "text": "Yeah. We keep it on file, but we need an ID to access that file.", + "id": 20 + }, + { + "turn": 21, + "speaker": "A", + "utterance": "That's out of control.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 21, + 20 + ], + "expanded emotion cause span": [ + "That's out of control.", + "Yeah. We keep it on file, but we need an ID to access that file." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's out of control.", + "id": 21 + }, + { + "turn": 22, + "speaker": "B", + "utterance": "I don't understand why this is so complicated for people when they get here. It's just a simple form. I just need an ID.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 22, + 21 + ], + "expanded emotion cause span": [ + "I don't understand why this is so complicated for people when they get here", + "That's out of control." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I don't understand why this is so complicated for people when they get here. It's just a simple form. I just need an ID.", + "id": 22 + }, + { + "turn": 23, + "speaker": "A", + "utterance": "How long have you been working here?", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 21, + 22 + ], + "expanded emotion cause span": [ + "That's out of control.", + "I don't understand why this is so complicated for people when they get here." + ], + "type": [ + "hybrid" + ], + "text": "How long have you been working here?", + "id": 23 + }, + { + "turn": 24, + "speaker": "A", + "utterance": "Clearly. You know, do you have like a supervisor or something?", + "emotion": "neutral", + "text": "Clearly. You know, do you have like a supervisor or something?", + "id": 24 + }, + { + "turn": 25, + "speaker": "B", + "utterance": "Yeah. Do you want to see my supervisor? Huh? Yeah. Do you want to see my supervisor? Fine. I'll be right back.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 24 + ], + "expanded emotion cause span": [ + "do you have like a supervisor or something?" + ], + "type": [ + "inter-personal" + ], + "text": "Yeah. Do you want to see my supervisor? Huh? Yeah. Do you want to see my supervisor? Fine. I'll be right back.", + "id": 25 + }, + { + "turn": 26, + "speaker": "A", + "utterance": "That would - I would appreciate that. Yeah.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 25 + ], + "expanded emotion cause span": [ + "Yeah. Do you want to see my supervisor? Huh? Yeah. Do you want to see my supervisor? Fine. I'll be right back." + ], + "type": [ + "inter-personal" + ], + "text": "That would - I would appreciate that. Yeah.", + "id": 26, + "source_sentences": [ + 24 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/train.Ses01F_impro07.json b/reccon/sources/train.Ses01F_impro07.json new file mode 100644 index 0000000000000000000000000000000000000000..17160db52d63cdc7e909a5a820d981eb4acee37b --- /dev/null +++ b/reccon/sources/train.Ses01F_impro07.json @@ -0,0 +1,497 @@ +[ + { + "turn": 1, + "speaker": "B", + "utterance": "Did you get the letter?", + "emotion": "excited", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Did you get the letter?", + "id": 1 + }, + { + "turn": 2, + "speaker": "A", + "utterance": "Yes. There's a big envelope it says, you're in. I know.", + "emotion": "excited", + "expanded emotion cause evidence": [ + "b", + 2 + ], + "expanded emotion cause span": [ + "b", + "There's a big envelope it says, you're in" + ], + "type": [ + "latent", + "no-context" + ], + "text": "Yes. There's a big envelope it says, you're in. I know.", + "id": 2 + }, + { + "turn": 3, + "speaker": "B", + "utterance": "Yeah. That is so awesome.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "There's a big envelope it says, you're in" + ], + "type": [ + "inter-personal" + ], + "text": "Yeah. That is so awesome.", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Oh my God. What are you going to do? [LAUGHTER]", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "There's a big envelope it says, you're in" + ], + "type": [ + "inter-personal" + ], + "text": "Oh my God. What are you going to do? [LAUGHTER]", + "id": 4 + }, + { + "turn": 5, + "speaker": "B", + "utterance": "Oh-Yeah, I bet you're really excited. Oh. That's what loans are for? Right? Exactly.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 5, + 2 + ], + "expanded emotion cause span": [ + "That's what loans are for", + "There's a big envelope it says, you're in." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh-Yeah, I bet you're really excited. Oh. That's what loans are for? Right? Exactly.", + "id": 5 + }, + { + "turn": 6, + "speaker": "A", + "utterance": "I'm really excited. Yeah. I don't know how I'm going to pay for anything, but... I also- Yeah. Loans, too, yeah. I applied, though, for a bunch of grants and scholarships so I'm still waiting to hear on that.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 5, + 2 + ], + "expanded emotion cause span": [ + "That's what loans are for", + "There's a big envelope it says, you're in." + ], + "type": [ + "hybrid" + ], + "text": "I'm really excited. Yeah. I don't know how I'm going to pay for anything, but... I also- Yeah. Loans, too, yeah. I applied, though, for a bunch of grants and scholarships so I'm still waiting to hear on that.", + "id": 6 + }, + { + "turn": 7, + "speaker": "B", + "utterance": "Oh. Good, good. That's awesome. Are you going to stay around here? Or are you going to like get a different neighborhood- you going to move to a different neighborhood?", + "emotion": "excited", + "expanded emotion cause evidence": [ + 5, + 2 + ], + "expanded emotion cause span": [ + "That's what loans are for", + "There's a big envelope it says, you're in." + ], + "type": [ + "hybrid" + ], + "text": "Oh. Good, good. That's awesome. Are you going to stay around here? Or are you going to like get a different neighborhood- you going to move to a different neighborhood?", + "id": 7 + }, + { + "turn": 8, + "speaker": "A", + "utterance": "Oh- I know, I know, I know, I know.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 7, + 5, + 2 + ], + "expanded emotion cause span": [ + "move to a different neighborhood", + "That's what loans are for", + "There's a big envelope it says, you're in." + ], + "type": [ + "hybrid" + ], + "text": "Oh- I know, I know, I know, I know.", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I don't know. I spend so much time commuting as it is, I'd rather.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 7, + 5, + 2 + ], + "expanded emotion cause span": [ + "move to a different neighborhood", + "That's what loans are for", + "There's a big envelope it says, you're in." + ], + "type": [ + "hybrid" + ], + "text": "I don't know. I spend so much time commuting as it is, I'd rather.", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "This is so- I am so happy that you're going to stay. You're not going to...We should totally throw a party.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "I spend so much time commuting as it is, I'd rather.", + "you're going to stay. You're not going to...We should totally throw a party." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "This is so- I am so happy that you're going to stay. You're not going to...We should totally throw a party.", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I know. We should throw a party.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 5, + 2, + 10, + 11 + ], + "expanded emotion cause span": [ + "That's what loans are for", + "There's a big envelope it says, you're in.", + "This is so- I am so happy that you're going to stay. You're not going to...We should totally throw a party.", + "throw a party." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I know. We should throw a party.", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "A rapper party ho. Yeah. Okay.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I know. We should throw a party." + ], + "type": [ + "inter-personal" + ], + "text": "A rapper party ho. Yeah. Okay.", + "id": 12 + }, + { + "turn": 13, + "speaker": "B", + "utterance": "I am just- Yeah. I'm sticking around, I'm just doing my thing. I'm living here. I'm so glad you're going to stay, I'm so glad you're going to be here. Yeah. Woo.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "I'm so glad you're going to stay, I'm so glad you're going to be here." + ], + "type": [ + "no-context" + ], + "text": "I am just- Yeah. I'm sticking around, I'm just doing my thing. I'm living here. I'm so glad you're going to stay, I'm so glad you're going to be here. Yeah. Woo.", + "id": 13 + }, + { + "turn": 14, + "speaker": "A", + "utterance": "It's a relief too. I mean I was thinking I was going to have to pack up all of my stuff but yeah. Hooray for U.S.C.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "It's a relief too. I mean I was thinking I was going to have to pack up all of my stuff but yeah" + ], + "type": [ + "no-context" + ], + "text": "It's a relief too. I mean I was thinking I was going to have to pack up all of my stuff but yeah. Hooray for U.S.C.", + "id": 14 + }, + { + "turn": 15, + "speaker": "B", + "utterance": "Yeah. Big time.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "Hooray for U.S.C." + ], + "type": [ + "inter-personal" + ], + "text": "Yeah. Big time.", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Mmhmm. Mmhmm. Yay. So what major? What are you doing?", + "emotion": "excited", + "expanded emotion cause evidence": [ + 15, + 13 + ], + "expanded emotion cause span": [ + "Yeah. Big time.", + "I'm so glad you're going to stay, I'm so glad you're going to be here" + ], + "type": [ + "self-contagion" + ], + "text": "Mmhmm. Mmhmm. Yay. So what major? What are you doing?", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "Yeah. I'm not sure.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "There's a big envelope it says, you're in" + ], + "type": [ + "self-contagion" + ], + "text": "Yeah. I'm not sure.", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "Is this a Masters or a P.h.D.? Or can you...? Nice", + "emotion": "neutral", + "text": "Is this a Masters or a P.h.D.? Or can you...? Nice", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "Umm...P.h.D. [LAUGHTER]", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2, + 19 + ], + "expanded emotion cause span": [ + "There's a big envelope it says, you're in", + "P.h.D." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Umm...P.h.D. [LAUGHTER]", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "That's good. Don't you have to like teach a class, too, when you do that?", + "emotion": "neutral", + "text": "That's good. Don't you have to like teach a class, too, when you do that?", + "id": 20 + }, + { + "turn": 21, + "speaker": "B", + "utterance": "Teacher. Mrs. Nash, I have a question.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 20 + ], + "expanded emotion cause span": [ + "Don't you have to like teach a class, too," + ], + "type": [ + "self-contagion" + ], + "text": "Teacher. Mrs. Nash, I have a question.", + "id": 21 + }, + { + "turn": 22, + "speaker": "A", + "utterance": "So I get to mold young minds. Mrs.? That's my mother.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 22 + ], + "expanded emotion cause span": [ + "So I get to mold young minds" + ], + "type": [ + "no-context" + ], + "text": "So I get to mold young minds. Mrs.? That's my mother.", + "id": 22 + }, + { + "turn": 23, + "speaker": "B", + "utterance": "You have to get married. Well you are married to Chuck. You're Mrs. Nash. Not to be confused with Mrs. Dash which is the popular seasoning.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "There's a big envelope it says, you're in" + ], + "type": [ + "inter-personal" + ], + "text": "You have to get married. Well you are married to Chuck. You're Mrs. Nash. Not to be confused with Mrs. Dash which is the popular seasoning.", + "id": 23 + }, + { + "turn": 24, + "speaker": "A", + "utterance": "I would be like- Oh. Right, right, right.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "There's a big envelope it says, you're in" + ], + "type": [ + "self-contagion" + ], + "text": "I would be like- Oh. Right, right, right.", + "id": 24 + }, + { + "turn": 25, + "speaker": "B", + "utterance": "Yay...School's fun.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2, + 25 + ], + "expanded emotion cause span": [ + "There's a big envelope it says, you're in", + "Yay...School's fun." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yay...School's fun.", + "id": 25, + "source_sentences": [ + 1 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 26, + "speaker": "B", + "utterance": "Of course, right. That's where the real money is, being a student.", + "emotion": "neutral", + "text": "Of course, right. That's where the real money is, being a student.", + "id": 26 + }, + { + "turn": 27, + "speaker": "B", + "utterance": "That's how you get the big bucks. Are you messing with the chair? Don't ruin it.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 26, + 27, + 2 + ], + "expanded emotion cause span": [ + "That's where the real money is, being a student", + "That's how you get the big bucks", + "There's a big envelope it says, you're in" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "That's how you get the big bucks. Are you messing with the chair? Don't ruin it.", + "id": 27 + }, + { + "turn": 28, + "speaker": "A", + "utterance": "I know. I made such a mess of it, the entire time. The last three things I've done, I've ruined everything, I think. Mm-hmm. Yeah.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "There's a big envelope it says, you're in" + ], + "type": [ + "self-contagion" + ], + "text": "I know. I made such a mess of it, the entire time. The last three things I've done, I've ruined everything, I think. Mm-hmm. Yeah.", + "id": 28 + } +] \ No newline at end of file diff --git a/reccon/sources/train.Ses01M_script03_2.json b/reccon/sources/train.Ses01M_script03_2.json new file mode 100644 index 0000000000000000000000000000000000000000..768a2efadac4452fd8e1e414bf3930805965523f --- /dev/null +++ b/reccon/sources/train.Ses01M_script03_2.json @@ -0,0 +1,717 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Well, what of it?", + "emotion": "neutral", + "text": "Well, what of it?", + "id": 1 + }, + { + "turn": 2, + "speaker": "A", + "utterance": "No, thank you.", + "emotion": "neutral", + "text": "No, thank you.", + "id": 2 + }, + { + "turn": 3, + "speaker": "B", + "utterance": "I'll have a little, I think.", + "emotion": "neutral", + "text": "I'll have a little, I think.", + "id": 3 + }, + { + "turn": 4, + "speaker": "A", + "utterance": "I don't see why you want any you already had two glasses.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "I'll have a little, I think.", + "I don't see why you want any you already had two glasses." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I don't see why you want any you already had two glasses.", + "id": 4 + }, + { + "turn": 5, + "speaker": "B", + "utterance": "Oh, you know no particular reason besides they are very small glasses.", + "emotion": "neutral", + "text": "Oh, you know no particular reason besides they are very small glasses.", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Really, Amanda.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "they are very small glasses" + ], + "type": [ + "self-contagion" + ], + "text": "Really, Amanda.", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Don't be stupid, what?", + "emotion": "angry", + "expanded emotion cause evidence": [ + 5, + 3, + 4 + ], + "expanded emotion cause span": [ + "they are very small glasses", + "I'll have a little, I think.", + "I don't see why you want any you already had two glasses." + ], + "type": [ + "hybrid" + ], + "text": "Don't be stupid, what?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Nothing.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Don't be stupid, what?" + ], + "type": [ + "inter-personal" + ], + "text": "Nothing.", + "id": 8 + }, + { + "turn": 9, + "speaker": "B", + "utterance": "Are you going out somewhere dear?", + "emotion": "neutral", + "text": "Are you going out somewhere dear?", + "id": 9 + }, + { + "turn": 10, + "speaker": "A", + "utterance": "Well it's a woman's duty to allure the man. Watch me a minute will you?", + "emotion": "angry", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I'll have a little, I think." + ], + "type": [ + "inter-personal" + ], + "text": "Well it's a woman's duty to allure the man. Watch me a minute will you?", + "id": 10 + }, + { + "turn": 11, + "speaker": "B", + "utterance": "You know, it's a pity you didn't have any more brandy. It would have made you just a little less disagreeable.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Well it's a woman's duty to allure the man" + ], + "type": [ + "inter-personal" + ], + "text": "You know, it's a pity you didn't have any more brandy. It would have made you just a little less disagreeable.", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "You know what? You snap, you snap, you snap you're like a little adder.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Well it's a woman's duty to allure the man" + ], + "type": [ + "inter-personal" + ], + "text": "You know what? You snap, you snap, you snap you're like a little adder.", + "id": 12 + }, + { + "turn": 13, + "speaker": "B", + "utterance": "Nonsense. They have a bag of venom behind of fangs and they snap.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "Well it's a woman's duty to allure the man" + ], + "type": [ + "inter-personal" + ], + "text": "Nonsense. They have a bag of venom behind of fangs and they snap.", + "id": 13 + }, + { + "turn": 14, + "speaker": "A", + "utterance": "They sting.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 3, + 4, + 12 + ], + "expanded emotion cause span": [ + "I'll have a little, I think.", + "I don't see why you want any you already had two glasses.", + "You snap, you snap, you snap you're like a little adder" + ], + "type": [ + "hybrid" + ], + "text": "They sting.", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "I don't care. I don't care, do you understand? I don't mind if they bark and they roll about like hoops.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 3, + 4, + 12 + ], + "expanded emotion cause span": [ + "I'll have a little, I think.", + "I don't see why you want any you already had two glasses.", + "You snap, you snap, you snap you're like a little adder" + ], + "type": [ + "hybrid" + ], + "text": "I don't care. I don't care, do you understand? I don't mind if they bark and they roll about like hoops.", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Did you see much of Peter Burden after our divorce?", + "emotion": "angry", + "expanded emotion cause evidence": [ + 16 + ], + "expanded emotion cause span": [ + "Did you see much of Peter Burden after our divorce?" + ], + "type": [ + "no-context" + ], + "text": "Did you see much of Peter Burden after our divorce?", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "Yes, I did quite a lot.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 3, + 4, + 12 + ], + "expanded emotion cause span": [ + "I'll have a little, I think.", + "I don't see why you want any you already had two glasses.", + "You snap, you snap, you snap you're like a little adder" + ], + "type": [ + "hybrid" + ], + "text": "Yes, I did quite a lot.", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "I suppose you let him just kiss you or good deal more than too.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 17, + 18 + ], + "expanded emotion cause span": [ + "Yes, I did quite a lot.", + "I suppose you let him just kiss you or good deal more than too." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I suppose you let him just kiss you or good deal more than too.", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "Oh, mind you own business.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 18 + ], + "expanded emotion cause span": [ + "I suppose you let him just kiss you or good deal more than too." + ], + "type": [ + "inter-personal" + ], + "text": "Oh, mind you own business.", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "I suppose you two had a riotous time, huh? No restrain at all, very enjoyable, he never had much any how.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 20 + ], + "expanded emotion cause span": [ + "I suppose you two had a riotous time, huh" + ], + "type": [ + "no-context" + ], + "text": "I suppose you two had a riotous time, huh? No restrain at all, very enjoyable, he never had much any how.", + "id": 20 + }, + { + "turn": 21, + "speaker": "A", + "utterance": "You're quite insufferable, I expect it's because you're drunk.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 20 + ], + "expanded emotion cause span": [ + "I suppose you two had a riotous time, huh? No restrain at all, very enjoyable, he never had much any how." + ], + "type": [ + "inter-personal" + ], + "text": "You're quite insufferable, I expect it's because you're drunk.", + "id": 21, + "source_sentences": [ + 19 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 22, + "speaker": "B", + "utterance": "I am not in the least bit drunk.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 18, + 20, + 21 + ], + "expanded emotion cause span": [ + "I suppose you let him just kiss you or good deal more than too.", + "I suppose you two had a riotous time, huh? No restrain at all, very enjoyable, he never had much any how.", + "You're quite insufferable, I expect it's because you're drunk." + ], + "type": [ + "hybrid" + ], + "text": "I am not in the least bit drunk.", + "id": 22 + }, + { + "turn": 23, + "speaker": "A", + "utterance": "You always had a weak head.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 18, + 20, + 21 + ], + "expanded emotion cause span": [ + "I suppose you let him just kiss you or good deal more than too.", + "I suppose you two had a riotous time, huh? No restrain at all, very enjoyable, he never had much any how.", + "You're quite insufferable, I expect it's because you're drunk." + ], + "type": [ + "hybrid" + ], + "text": "You always had a weak head.", + "id": 23 + }, + { + "turn": 24, + "speaker": "B", + "utterance": "I think I told you once before that I had three minute liquor glasses the whole evening long. A Child of two cannot get drunk on that.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 18, + 20, + 21 + ], + "expanded emotion cause span": [ + "I suppose you let him just kiss you or good deal more than too.", + "I suppose you two had a riotous time, huh? No restrain at all, very enjoyable, he never had much any how.", + "You're quite insufferable, I expect it's because you're drunk." + ], + "type": [ + "hybrid" + ], + "text": "I think I told you once before that I had three minute liquor glasses the whole evening long. A Child of two cannot get drunk on that.", + "id": 24 + }, + { + "turn": 25, + "speaker": "A", + "utterance": "On the contrary, a child two could get violently drunk on only one glass of brandy.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 18, + 20, + 21 + ], + "expanded emotion cause span": [ + "I suppose you let him just kiss you or good deal more than too.", + "I suppose you two had a riotous time, huh? No restrain at all, very enjoyable, he never had much any how.", + "You're quite insufferable, I expect it's because you're drunk." + ], + "type": [ + "hybrid" + ], + "text": "On the contrary, a child two could get violently drunk on only one glass of brandy.", + "id": 25 + }, + { + "turn": 26, + "speaker": "B", + "utterance": "Oh very, very interesting Amanda. How about the child of uh... four, six or maybe nine---you know, we could work up a splendid little debate about it, you know? Intemperate tots.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 18, + 20, + 21 + ], + "expanded emotion cause span": [ + "I suppose you let him just kiss you or good deal more than too.", + "I suppose you two had a riotous time, huh? No restrain at all, very enjoyable, he never had much any how.", + "You're quite insufferable, I expect it's because you're drunk." + ], + "type": [ + "hybrid" + ], + "text": "Oh very, very interesting Amanda. How about the child of uh... four, six or maybe nine---you know, we could work up a splendid little debate about it, you know? Intemperate tots.", + "id": 26 + }, + { + "turn": 27, + "speaker": "A", + "utterance": "Shut up.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 26, + 18, + 20, + 21 + ], + "expanded emotion cause span": [ + "Oh very, very interesting Amanda. How about the child of uh... four, six or maybe nine---you know, we could work up a splendid little debate about it, you know? Intemperate tots.", + "I suppose you let him just kiss you or good deal more than too.", + "I suppose you two had a riotous time, huh? No restrain at all, very enjoyable, he never had much any how.", + "You're quite insufferable, I expect it's because you're drunk." + ], + "type": [ + "hybrid" + ], + "text": "Shut up.", + "id": 27 + }, + { + "turn": 28, + "speaker": "A", + "utterance": "Not very funny darling. Why don't you have some more brandy?", + "emotion": "angry", + "expanded emotion cause evidence": [ + 26, + 18, + 20, + 21 + ], + "expanded emotion cause span": [ + "Oh very, very interesting Amanda. How about the child of uh... four, six or maybe nine---you know, we could work up a splendid little debate about it, you know? Intemperate tots.", + "I suppose you let him just kiss you or good deal more than too.", + "I suppose you two had a riotous time, huh? No restrain at all, very enjoyable, he never had much any how.", + "You're quite insufferable, I expect it's because you're drunk." + ], + "type": [ + "hybrid" + ], + "text": "Not very funny darling. Why don't you have some more brandy?", + "id": 28 + }, + { + "turn": 29, + "speaker": "B", + "utterance": "That's a very good idea I think I will.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 18, + 20, + 21 + ], + "expanded emotion cause span": [ + "I suppose you let him just kiss you or good deal more than too.", + "I suppose you two had a riotous time, huh? No restrain at all, very enjoyable, he never had much any how.", + "You're quite insufferable, I expect it's because you're drunk." + ], + "type": [ + "hybrid" + ], + "text": "That's a very good idea I think I will.", + "id": 29 + }, + { + "turn": 30, + "speaker": "B", + "utterance": "Would you uh...turn that off please? You're going to wake the people upstairs.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 18, + 20, + 21 + ], + "expanded emotion cause span": [ + "I suppose you let him just kiss you or good deal more than too.", + "I suppose you two had a riotous time, huh? No restrain at all, very enjoyable, he never had much any how.", + "You're quite insufferable, I expect it's because you're drunk." + ], + "type": [ + "hybrid" + ], + "text": "Would you uh...turn that off please? You're going to wake the people upstairs.", + "id": 30 + }, + { + "turn": 31, + "speaker": "A", + "utterance": "Why?", + "emotion": "angry", + "expanded emotion cause evidence": [ + 30, + 18, + 20, + 21 + ], + "expanded emotion cause span": [ + "Would you uh...turn that off please? You're going to wake the people upstairs.", + "I suppose you let him just kiss you or good deal more than too.", + "I suppose you two had a riotous time, huh? No restrain at all, very enjoyable, he never had much any how.", + "You're quite insufferable, I expect it's because you're drunk." + ], + "type": [ + "hybrid" + ], + "text": "Why?", + "id": 31 + }, + { + "turn": 32, + "speaker": "B", + "utterance": "Well then you'll wake the people downstairs.", + "emotion": "angry", + "text": "Well then you'll wake the people downstairs.", + "id": 32 + }, + { + "turn": 33, + "speaker": "A", + "utterance": "They are away in Tunis.", + "emotion": "angry", + "text": "They are away in Tunis.", + "id": 33 + }, + { + "turn": 34, + "speaker": "B", + "utterance": "This is no time a year for Tunis.", + "emotion": "angry", + "text": "This is no time a year for Tunis.", + "id": 34 + }, + { + "turn": 35, + "speaker": "A", + "utterance": "Turn it on again, please.", + "emotion": "angry", + "text": "Turn it on again, please.", + "id": 35 + }, + { + "turn": 36, + "speaker": "B", + "utterance": "I will do no such thing.", + "emotion": "angry", + "text": "I will do no such thing.", + "id": 36 + }, + { + "turn": 37, + "speaker": "A", + "utterance": "Very well if you insist on being boorish and idiotic.", + "emotion": "angry", + "text": "Very well if you insist on being boorish and idiotic.", + "id": 37 + }, + { + "turn": 38, + "speaker": "B", + "utterance": "Turn it off. It's driving me mad.", + "emotion": "angry", + "text": "Turn it off. It's driving me mad.", + "id": 38 + }, + { + "turn": 39, + "speaker": "A", + "utterance": "I won't.", + "emotion": "angry", + "text": "I won't.", + "id": 39 + }, + { + "turn": 40, + "speaker": "B", + "utterance": "Turn it off.", + "emotion": "angry", + "text": "Turn it off.", + "id": 40 + }, + { + "turn": 41, + "speaker": "A", + "utterance": "Stop it. No. Go away.", + "emotion": "angry", + "text": "Stop it. No. Go away.", + "id": 41 + }, + { + "turn": 42, + "speaker": "B", + "utterance": "Amanda listen. Listen.", + "emotion": "angry", + "text": "Amanda listen. Listen.", + "id": 42 + }, + { + "turn": 43, + "speaker": "A", + "utterance": "listen Oh I'm sick and tired of listening to you, you damn sadistic bully.", + "emotion": "angry", + "text": "listen Oh I'm sick and tired of listening to you, you damn sadistic bully.", + "id": 43 + }, + { + "turn": 44, + "speaker": "B", + "utterance": "That's very amusing indeed.", + "emotion": "angry", + "text": "That's very amusing indeed.", + "id": 44 + }, + { + "turn": 45, + "speaker": "A", + "utterance": "Oh you're cruel you're...you're...I hate you, I hate you. Go away. You're conceited. You're overbearing. You're utterly impossible.", + "emotion": "angry", + "text": "Oh you're cruel you're...you're...I hate you, I hate you. Go away. You're conceited. You're overbearing. You're utterly impossible.", + "id": 45 + }, + { + "turn": 46, + "speaker": "B", + "utterance": "You...You're an evil minded, self-centered little wench and I never want to see you again.", + "emotion": "angry", + "text": "You...You're an evil minded, self-centered little wench and I never want to see you again.", + "id": 46 + }, + { + "turn": 47, + "speaker": "A", + "utterance": "This is the end do you hear me? Finally and forever.", + "emotion": "angry", + "text": "This is the end do you hear me? Finally and forever.", + "id": 47 + }, + { + "turn": 48, + "speaker": "B", + "utterance": "You're not going like this.", + "emotion": "angry", + "text": "You're not going like this.", + "id": 48 + }, + { + "turn": 49, + "speaker": "A", + "utterance": "Oh yes I am...Oh yes I am. Let go of me. You let go. You...urgh...You're a cruel friend. I loathe and I hate you. Marry you again...Ha...Never, never, never, never. I hope you die in torment. You beast.", + "emotion": "angry", + "text": "Oh yes I am...Oh yes I am. Let go of me. You let go. You...urgh...You're a cruel friend. I loathe and I hate you. Marry you again...Ha...Never, never, never, never. I hope you die in torment. You beast.", + "id": 49 + }, + { + "turn": 50, + "speaker": "B", + "utterance": "No you're not.", + "emotion": "angry", + "text": "No you're not.", + "id": 50 + }, + { + "turn": 51, + "speaker": "B", + "utterance": "Shut up. Shut up. I wouldn't marry you again if you came crawling back to me on a bended knee. You are an evil tempered little vampire and I never want to see you again as long as I live.", + "emotion": "angry", + "text": "Shut up. Shut up. I wouldn't marry you again if you came crawling back to me on a bended knee. You are an evil tempered little vampire and I never want to see you again as long as I live.", + "id": 51 + } +] \ No newline at end of file diff --git a/reccon/sources/train.Ses02M_impro02.json b/reccon/sources/train.Ses02M_impro02.json new file mode 100644 index 0000000000000000000000000000000000000000..6e021e995f5f8e66b903ac0ba9b80e53c543dece --- /dev/null +++ b/reccon/sources/train.Ses02M_impro02.json @@ -0,0 +1,543 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I don't want you to go.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I don't want you to go." + ], + "type": [ + "no-context" + ], + "text": "I don't want you to go.", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I know, I know. I don't want to go either baby. I love you know. And I'm going to miss you a lot.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 2, + 2 + ], + "expanded emotion cause span": [ + "I don't want to go either baby.", + "And I'm going to miss you a lot." + ], + "type": [ + "no-context" + ], + "text": "I know, I know. I don't want to go either baby. I love you know. And I'm going to miss you a lot.", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I'm going to miss you too; I don't know what I'm going to do here without you. It's going to be so lonely, and so hard.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I'm going to miss you too; I don't know what I'm going to do here without you. It's going to be so lonely, and so hard." + ], + "type": [ + "no-context" + ], + "text": "I'm going to miss you too; I don't know what I'm going to do here without you. It's going to be so lonely, and so hard.", + "id": 3 + }, + { + "turn": 4, + "speaker": "A", + "utterance": "I don't want to be a single mom.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "I'm going to miss you too; I don't know what I'm going to do here without you. It's going to be so lonely, and so hard.", + "I don't want to be a single mom." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I don't want to be a single mom.", + "id": 4 + }, + { + "turn": 5, + "speaker": "B", + "utterance": "You won't be. I'll be back; I'll be back before you know it. All right, and", + "emotion": "sad", + "expanded emotion cause evidence": [ + 2, + 2, + 4 + ], + "expanded emotion cause span": [ + "I don't want to go either baby.", + "And I'm going to miss you a lot.", + "I don't want to be a single mom." + ], + "type": [ + "hybrid" + ], + "text": "You won't be. I'll be back; I'll be back before you know it. All right, and", + "id": 5 + }, + { + "turn": 6, + "speaker": "A", + "utterance": "but", + "emotion": "sad", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "I'm going to miss you too; I don't know what I'm going to do here without you. It's going to be so lonely, and so hard.", + "I don't want to be a single mom." + ], + "type": [ + "self-contagion" + ], + "text": "but", + "id": 6 + }, + { + "turn": 7, + "speaker": "B", + "utterance": "and", + "emotion": "sad", + "expanded emotion cause evidence": [ + 2, + 2, + 4 + ], + "expanded emotion cause span": [ + "I don't want to go either baby.", + "And I'm going to miss you a lot.", + "I don't want to be a single mom." + ], + "type": [ + "hybrid" + ], + "text": "and", + "id": 7 + }, + { + "turn": 8, + "speaker": "A", + "utterance": "It's dangerous; I mean how can you make sure that you'll", + "emotion": "sad", + "expanded emotion cause evidence": [ + 3, + 4, + 8 + ], + "expanded emotion cause span": [ + "I'm going to miss you too; I don't know what I'm going to do here without you. It's going to be so lonely, and so hard.", + "I don't want to be a single mom.", + "It's dangerous" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "It's dangerous; I mean how can you make sure that you'll", + "id": 8 + }, + { + "turn": 9, + "speaker": "B", + "utterance": "It's- It's dangerous anywhere, honey. I mean this is -this- I'm just going to go and we'll get it over with,", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "It's dangerous; I mean how can you make sure that you'll", + "It's- It's dangerous anywhere, honey. I mean this is -this" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It's- It's dangerous anywhere, honey. I mean this is -this- I'm just going to go and we'll get it over with,", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "A", + "utterance": "I hope so.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 3, + 4, + 8 + ], + "expanded emotion cause span": [ + "I'm going to miss you too; I don't know what I'm going to do here without you. It's going to be so lonely, and so hard.", + "I don't want to be a single mom.", + "It's dangerous" + ], + "type": [ + "self-contagion" + ], + "text": "I hope so.", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I hope so.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 3, + 4, + 8 + ], + "expanded emotion cause span": [ + "I'm going to miss you too; I don't know what I'm going to do here without you. It's going to be so lonely, and so hard.", + "I don't want to be a single mom.", + "It's dangerous" + ], + "type": [ + "self-contagion" + ], + "text": "I hope so.", + "id": 11 + }, + { + "turn": 12, + "speaker": "A", + "utterance": "It's going to be really rough.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 3, + 4, + 8, + 12 + ], + "expanded emotion cause span": [ + "I'm going to miss you too; I don't know what I'm going to do here without you. It's going to be so lonely, and so hard.", + "I don't want to be a single mom.", + "It's dangerous", + "It's going to be really rough." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "It's going to be really rough.", + "id": 12 + }, + { + "turn": 13, + "speaker": "B", + "utterance": "You gotta take care of our baby for me, alright?", + "emotion": "sad", + "expanded emotion cause evidence": [ + 2, + 2 + ], + "expanded emotion cause span": [ + "I don't want to go either baby.", + "And I'm going to miss you a lot." + ], + "type": [ + "self-contagion" + ], + "text": "You gotta take care of our baby for me, alright?", + "id": 13 + }, + { + "turn": 14, + "speaker": "A", + "utterance": "I'll send you lots of pictures.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 3, + 4, + 8, + 12 + ], + "expanded emotion cause span": [ + "I'm going to miss you too; I don't know what I'm going to do here without you. It's going to be so lonely, and so hard.", + "I don't want to be a single mom.", + "It's dangerous", + "It's going to be really rough." + ], + "type": [ + "self-contagion" + ], + "text": "I'll send you lots of pictures.", + "id": 14 + }, + { + "turn": 15, + "speaker": "B", + "utterance": "I hope so, because I'm not going to be able to survive without all that. I don't know what I'm going to do.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 2, + 2, + 15 + ], + "expanded emotion cause span": [ + "I don't want to go either baby.", + "And I'm going to miss you a lot.", + "I hope so, because I'm not going to be able to survive without all that. I don't know what I'm going to do." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I hope so, because I'm not going to be able to survive without all that. I don't know what I'm going to do.", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "I've never been - I've never been away from you for two weeks let alone a year.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 2, + 2, + 15 + ], + "expanded emotion cause span": [ + "I don't want to go either baby.", + "And I'm going to miss you a lot.", + "I hope so, because I'm not going to be able to survive without all that. I don't know what I'm going to do." + ], + "type": [ + "self-contagion" + ], + "text": "I've never been - I've never been away from you for two weeks let alone a year.", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "Well, just promise me that you going to be safe.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 3, + 4, + 8, + 12 + ], + "expanded emotion cause span": [ + "I'm going to miss you too; I don't know what I'm going to do here without you. It's going to be so lonely, and so hard.", + "I don't want to be a single mom.", + "It's dangerous", + "It's going to be really rough." + ], + "type": [ + "self-contagion" + ], + "text": "Well, just promise me that you going to be safe.", + "id": 17 + }, + { + "turn": 18, + "speaker": "A", + "utterance": "I mean can't they put you in like, you know kitchen work or something where you won't get", + "emotion": "sad", + "expanded emotion cause evidence": [ + 3, + 4, + 8, + 12 + ], + "expanded emotion cause span": [ + "I'm going to miss you too; I don't know what I'm going to do here without you. It's going to be so lonely, and so hard.", + "I don't want to be a single mom.", + "It's dangerous", + "It's going to be really rough." + ], + "type": [ + "self-contagion" + ], + "text": "I mean can't they put you in like, you know kitchen work or something where you won't get", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "It doesn't make any sense; I don't know why we have to be at war in the first place.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 19 + ], + "expanded emotion cause span": [ + "It doesn't make any sense; I don't know why we have to be at war in the first place." + ], + "type": [ + "no-context" + ], + "text": "It doesn't make any sense; I don't know why we have to be at war in the first place.", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "there's people that thought it was the right thing to do so now we have to- we have to do what we have to do for our country", + "emotion": "sad", + "expanded emotion cause evidence": [ + 2, + 2, + 20 + ], + "expanded emotion cause span": [ + "I don't want to go either baby.", + "And I'm going to miss you a lot.", + "there's people that thought it was the right thing to do so now we have to- we have to do what we have to do for our country" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "there's people that thought it was the right thing to do so now we have to- we have to do what we have to do for our country", + "id": 20 + }, + { + "turn": 21, + "speaker": "B", + "utterance": "and it'll work out you know, go there and do that. Yeah, I'll be back", + "emotion": "neutral", + "text": "and it'll work out you know, go there and do that. Yeah, I'll be back", + "id": 21 + }, + { + "turn": 22, + "speaker": "A", + "utterance": "Will you write me letters, paper ones?", + "emotion": "sad", + "expanded emotion cause evidence": [ + 3, + 4, + 8, + 12 + ], + "expanded emotion cause span": [ + "I'm going to miss you too; I don't know what I'm going to do here without you. It's going to be so lonely, and so hard.", + "I don't want to be a single mom.", + "It's dangerous", + "It's going to be really rough." + ], + "type": [ + "self-contagion" + ], + "text": "Will you write me letters, paper ones?", + "id": 22 + }, + { + "turn": 23, + "speaker": "A", + "utterance": "Our baby needs a dad; you can't leave. Okay, you can't disappear.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 3, + 4, + 8, + 12, + 23 + ], + "expanded emotion cause span": [ + "I'm going to miss you too; I don't know what I'm going to do here without you. It's going to be so lonely, and so hard.", + "I don't want to be a single mom.", + "It's dangerous", + "It's going to be really rough.", + "you can't leave. Okay, you can't disappear." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Our baby needs a dad; you can't leave. Okay, you can't disappear.", + "id": 23 + }, + { + "turn": 24, + "speaker": "B", + "utterance": "Our baby has a dad, alright. Daddy is going to be back soon.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 2, + 2 + ], + "expanded emotion cause span": [ + "I don't want to go either baby.", + "And I'm going to miss you a lot." + ], + "type": [ + "self-contagion" + ], + "text": "Our baby has a dad, alright. Daddy is going to be back soon.", + "id": 24 + }, + { + "turn": 25, + "speaker": "B", + "utterance": "I want you to, you know, take lots of video; pictures and I can see you when I get back or while I'm there. I'm going to miss you.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 2, + 2, + 25 + ], + "expanded emotion cause span": [ + "I don't want to go either baby.", + "And I'm going to miss you a lot.", + "I'm going to miss you." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I want you to, you know, take lots of video; pictures and I can see you when I get back or while I'm there. I'm going to miss you.", + "id": 25 + }, + { + "turn": 26, + "speaker": "A", + "utterance": "I'll miss you too.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 3, + 4, + 8, + 12, + 26 + ], + "expanded emotion cause span": [ + "I'm going to miss you too; I don't know what I'm going to do here without you. It's going to be so lonely, and so hard.", + "I don't want to be a single mom.", + "It's dangerous", + "It's going to be really rough.", + "I'll miss you too." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I'll miss you too.", + "id": 26 + } +] \ No newline at end of file diff --git a/reccon/sources/train.Ses03F_impro03.json b/reccon/sources/train.Ses03F_impro03.json new file mode 100644 index 0000000000000000000000000000000000000000..e54398c73fc5bc543bfb1af0aba1bea813c2d0b5 --- /dev/null +++ b/reccon/sources/train.Ses03F_impro03.json @@ -0,0 +1,699 @@ +[ + { + "turn": 1, + "speaker": "B", + "utterance": "Oh, my God, look at that. Huh-oh, how many carats is that?", + "emotion": "excited", + "explanation": "Seeing a diamond ring", + "expanded emotion cause evidence": [ + "b", + 1 + ], + "expanded emotion cause span": [ + "b", + "how many carats is that?" + ], + "type": [ + "latent", + "no-context" + ], + "text": "Oh, my God, look at that. Huh-oh, how many carats is that?", + "id": 1 + }, + { + "turn": 2, + "speaker": "A", + "utterance": "I know. [LAUGHTER]. Dude, I don't know. It's- Probably. It's huge. I don't even know how to like wear it. My hand is like going down like really low. I can't believe it.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 2, + 2 + ], + "expanded emotion cause span": [ + "It's huge.", + "My hand is like going down like really low. I can't believe it." + ], + "type": [ + "no-context" + ], + "text": "I know. [LAUGHTER]. Dude, I don't know. It's- Probably. It's huge. I don't even know how to like wear it. My hand is like going down like really low. I can't believe it.", + "id": 2 + }, + { + "turn": 3, + "speaker": "B", + "utterance": "Like eighteen? [LAUGHTER]", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "My hand is like going down like really low. I can't believe it." + ], + "type": [ + "inter-personal" + ], + "text": "Like eighteen? [LAUGHTER]", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Oh, Jesus.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "My hand is like going down like really low. I can't believe it." + ], + "type": [ + "inter-personal" + ], + "text": "Oh, Jesus.", + "id": 4 + }, + { + "turn": 5, + "speaker": "B", + "utterance": "Is it-", + "emotion": "happy", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "My hand is like going down like really low. I can't believe it." + ], + "type": [ + "inter-personal" + ], + "text": "Is it-", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "yeah [LAUGHTER]", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "My hand is like going down like really low. I can't believe it." + ], + "type": [ + "inter-personal" + ], + "text": "yeah [LAUGHTER]", + "id": 6 + }, + { + "turn": 7, + "speaker": "B", + "utterance": "Yeah, The Lousy Chaperone. [LAUGHTER] Uh huh.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2, + 7 + ], + "expanded emotion cause span": [ + "My hand is like going down like really low. I can't believe it.", + "The Lousy Chaperone" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yeah, The Lousy Chaperone. [LAUGHTER] Uh huh.", + "id": 7 + }, + { + "turn": 8, + "speaker": "A", + "utterance": "Right. Right. Right. So, and there's like a whole like wedding scene in it. All right, not the--Drowsy, Drowsy [LAUGHTER] --not the Lousy. [LAUGHTER]. Um - So Drowsy. So I go to see this Drowsy Chaperone. And uh-", + "emotion": "happy", + "expanded emotion cause evidence": [ + 7, + 8, + 8 + ], + "expanded emotion cause span": [ + "Yeah, The Lousy Chaperone. [LAUGHTER] Uh huh.", + "here's like a whole like wedding scene in it", + "So Drowsy. So I go to see this Drowsy Chaperone" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Right. Right. Right. So, and there's like a whole like wedding scene in it. All right, not the--Drowsy, Drowsy [LAUGHTER] --not the Lousy. [LAUGHTER]. Um - So Drowsy. So I go to see this Drowsy Chaperone. And uh-", + "id": 8 + }, + { + "turn": 9, + "speaker": "B", + "utterance": "[LAUGHTER] Uh- Drowsy.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "So Drowsy. So I go to see this Drowsy Chaperone" + ], + "type": [ + "inter-personal" + ], + "text": "[LAUGHTER] Uh- Drowsy.", + "id": 9 + }, + { + "turn": 10, + "speaker": "A", + "utterance": "at the end of the performance, you know, like we're all clapping and stuff. And all of a sudden I look over and", + "emotion": "excited", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "at the end of the performance, you know, like we're all clapping and stuff. And all of a sudden I look over and", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Joe's gone. -where did he go, you know?", + "emotion": "excited", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "Joe's gone" + ], + "type": [ + "no-context" + ], + "text": "Joe's gone. -where did he go, you know?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Uh huh. Oh-", + "emotion": "happy", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "Joe's gone" + ], + "type": [ + "inter-personal" + ], + "text": "Uh huh. Oh-", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "And I'm like oh, he went to the- -the bathroom, but he didn't tell me, I didn't even notice him leaving. And all of a sudden, I swear to God, I'm sitting there and-", + "emotion": "excited", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "Joe's gone" + ], + "type": [ + "self-contagion" + ], + "text": "And I'm like oh, he went to the- -the bathroom, but he didn't tell me, I didn't even notice him leaving. And all of a sudden, I swear to God, I'm sitting there and-", + "id": 13 + }, + { + "turn": 14, + "speaker": "A", + "utterance": "he comes up onstage-- And the entire cast everyone just like", + "emotion": "excited", + "expanded emotion cause evidence": [ + 11, + 14 + ], + "expanded emotion cause span": [ + "Joe's gone", + "he comes up onstage" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "he comes up onstage-- And the entire cast everyone just like", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "goes up there and everyone's clapping and he's standing there and they put a spotlight on him.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 11, + 14, + 15 + ], + "expanded emotion cause span": [ + "Joe's gone", + "he comes up onstage", + "goes up there and everyone's clapping and he's standing there and they put a spotlight on him." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "goes up there and everyone's clapping and he's standing there and they put a spotlight on him.", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Oh, my God.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "goes up there and everyone's clapping and he's standing there and they put a spotlight on him." + ], + "type": [ + "inter-personal" + ], + "text": "Oh, my God.", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "And I'm like freaking out. I'm like what the hell's going on, you know. I don't know what's going on. And so he's like standing there and then all of a sudden they give him a microphone-", + "emotion": "excited", + "expanded emotion cause evidence": [ + 11, + 14, + 15, + 17 + ], + "expanded emotion cause span": [ + "Joe's gone", + "he comes up onstage", + "goes up there and everyone's clapping and he's standing there and they put a spotlight on him.", + "so he's like standing there and then all of a sudden they give him a microphone-" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "And I'm like freaking out. I'm like what the hell's going on, you know. I don't know what's going on. And so he's like standing there and then all of a sudden they give him a microphone-", + "id": 17 + }, + { + "turn": 18, + "speaker": "A", + "utterance": "and he just starts doing like this little spiel about me and like", + "emotion": "happy", + "expanded emotion cause evidence": [ + 18 + ], + "expanded emotion cause span": [ + "and he just starts doing like this little spiel about me and like" + ], + "type": [ + "no-context" + ], + "text": "and he just starts doing like this little spiel about me and like", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "he asked me to marry him, like- onstage. I was like, I couldn't believe--and I had to walk up there and I was, like I think I tripped or something.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 19 + ], + "expanded emotion cause span": [ + "he asked me to marry him, like- onstage. I was like, I couldn't believe" + ], + "type": [ + "no-context" + ], + "text": "he asked me to marry him, like- onstage. I was like, I couldn't believe--and I had to walk up there and I was, like I think I tripped or something.", + "id": 19 + }, + { + "turn": 20, + "speaker": "A", + "utterance": "Yeah, I said yes, but I, yeah, I mean,", + "emotion": "excited", + "expanded emotion cause evidence": [ + 19, + 20 + ], + "expanded emotion cause span": [ + "he asked me to marry him, like- onstage. I was like, I couldn't believe", + "I said yes" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Yeah, I said yes, but I, yeah, I mean,", + "id": 20 + }, + { + "turn": 21, + "speaker": "A", + "utterance": "I don't know- it just like took me, took me by surprise.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 19, + 21 + ], + "expanded emotion cause span": [ + "he asked me to marry him, like- onstage. I was like, I couldn't believe", + "it just like took me, took me by surprise" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I don't know- it just like took me, took me by surprise.", + "id": 21 + }, + { + "turn": 22, + "speaker": "A", + "utterance": "He scored points.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 19, + 20 + ], + "expanded emotion cause span": [ + "he asked me to marry him, like- onstage. I was like, I couldn't believe", + "I said yes" + ], + "type": [ + "self-contagion" + ], + "text": "He scored points.", + "id": 22 + }, + { + "turn": 23, + "speaker": "B", + "utterance": "Did you get a standing ovation?", + "emotion": "happy", + "expanded emotion cause evidence": [ + 19, + 20 + ], + "expanded emotion cause span": [ + "he asked me to marry him, like- onstage. I was like, I couldn't believe--and I had to walk up there and I was, like I think I tripped or something.", + "Yeah, I said yes, but I, yeah, I mean," + ], + "type": [ + "inter-personal" + ], + "text": "Did you get a standing ovation?", + "id": 23 + }, + { + "turn": 24, + "speaker": "A", + "utterance": "Oh, yeah. Everyone--yeah. And people--friends of ours were in the audience, I didn't know about, like family members.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 23, + 24 + ], + "expanded emotion cause span": [ + "standing ovation", + "Everyone--yeah. And people--friends of ours were in the audience, I didn't know about, like family members." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh, yeah. Everyone--yeah. And people--friends of ours were in the audience, I didn't know about, like family members.", + "id": 24 + }, + { + "turn": 25, + "speaker": "A", + "utterance": "Yeah. It was great.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 23, + 24, + 25 + ], + "expanded emotion cause span": [ + "standing ovation", + "Everyone--yeah. And people--friends of ours were in the audience, I didn't know about, like family members.", + "It was great." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Yeah. It was great.", + "id": 25 + }, + { + "turn": 26, + "speaker": "A", + "utterance": "It was--I cried,", + "emotion": "excited", + "expanded emotion cause evidence": [ + 23, + 24, + 25 + ], + "expanded emotion cause span": [ + "standing ovation", + "Everyone--yeah. And people--friends of ours were in the audience, I didn't know about, like family members.", + "It was great." + ], + "type": [ + "hybrid" + ], + "text": "It was--I cried,", + "id": 26 + }, + { + "turn": 27, + "speaker": "B", + "utterance": "No, you deserve to cry. I mean, tears of happiness.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 24, + 25, + 24 + ], + "expanded emotion cause span": [ + "Oh, yeah. Everyone--yeah. And people--friends of ours were in the audience, I didn't know about, like family members.", + "Yeah. It was great.", + "Everyone--yeah. And people--friends of ours were in the audience, I didn't know about, like family members." + ], + "type": [ + "inter-personal" + ], + "text": "No, you deserve to cry. I mean, tears of happiness.", + "id": 27 + }, + { + "turn": 28, + "speaker": "A", + "utterance": "like a loser, I cried.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 23, + 24, + 25 + ], + "expanded emotion cause span": [ + "standing ovation", + "Everyone--yeah. And people--friends of ours were in the audience, I didn't know about, like family members.", + "It was great." + ], + "type": [ + "hybrid" + ], + "text": "like a loser, I cried.", + "id": 28 + }, + { + "turn": 29, + "speaker": "A", + "utterance": "But, I don't know, I--it's so weird to think I'm marrying somebody 'cause I feel so young, you know?", + "emotion": "happy", + "expanded emotion cause evidence": [ + 23, + 24, + 25 + ], + "expanded emotion cause span": [ + "standing ovation", + "Everyone--yeah. And people--friends of ours were in the audience, I didn't know about, like family members.", + "It was great." + ], + "type": [ + "hybrid" + ], + "text": "But, I don't know, I--it's so weird to think I'm marrying somebody 'cause I feel so young, you know?", + "id": 29 + }, + { + "turn": 30, + "speaker": "B", + "utterance": "So where- where- where is this--have you talked about where it's going to be?", + "emotion": "happy", + "expanded emotion cause evidence": [ + 24, + 25, + 24 + ], + "expanded emotion cause span": [ + "Oh, yeah. Everyone--yeah. And people--friends of ours were in the audience, I didn't know about, like family members.", + "Yeah. It was great.", + "Everyone--yeah. And people--friends of ours were in the audience, I didn't know about, like family members." + ], + "type": [ + "inter-personal" + ], + "text": "So where- where- where is this--have you talked about where it's going to be?", + "id": 30 + }, + { + "turn": 31, + "speaker": "A", + "utterance": "No. No plans. or any- and probably", + "emotion": "happy", + "expanded emotion cause evidence": [ + 23, + 24, + 25 + ], + "expanded emotion cause span": [ + "standing ovation", + "Everyone--yeah. And people--friends of ours were in the audience, I didn't know about, like family members.", + "It was great." + ], + "type": [ + "hybrid" + ], + "text": "No. No plans. or any- and probably", + "id": 31 + }, + { + "turn": 32, + "speaker": "A", + "utterance": "like I think I want to get married--I want to have two weddings. One here, then one in Europe.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 23, + 24, + 25, + 32 + ], + "expanded emotion cause span": [ + "standing ovation", + "Everyone--yeah. And people--friends of ours were in the audience, I didn't know about, like family members.", + "It was great.", + "like I think I want to get married--I want to have two weddings. One here, then one in Europe." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "like I think I want to get married--I want to have two weddings. One here, then one in Europe.", + "id": 32 + }, + { + "turn": 33, + "speaker": "B", + "utterance": "He's rich enough. Maybe you can rent out the Eiffel Tower for your--", + "emotion": "happy", + "expanded emotion cause evidence": [ + 24, + 25, + 24, + 32 + ], + "expanded emotion cause span": [ + "Oh, yeah. Everyone--yeah. And people--friends of ours were in the audience, I didn't know about, like family members.", + "Yeah. It was great.", + "Everyone--yeah. And people--friends of ours were in the audience, I didn't know about, like family members.", + "like I think I want to get married--I want to have two weddings. One here, then one in Europe." + ], + "type": [ + "inter-personal" + ], + "text": "He's rich enough. Maybe you can rent out the Eiffel Tower for your--", + "id": 33 + }, + { + "turn": 34, + "speaker": "B", + "utterance": "That's awesome. [LAUGHTER] Marriage.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 24, + 25, + 24, + 32 + ], + "expanded emotion cause span": [ + "Oh, yeah. Everyone--yeah. And people--friends of ours were in the audience, I didn't know about, like family members.", + "Yeah. It was great.", + "Everyone--yeah. And people--friends of ours were in the audience, I didn't know about, like family members.", + "like I think I want to get married--I want to have two weddings. One here, then one in Europe." + ], + "type": [ + "inter-personal" + ], + "text": "That's awesome. [LAUGHTER] Marriage.", + "id": 34, + "source_sentences": [ + 23, + 24, + 23, + 31 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 35, + "speaker": "A", + "utterance": "Yeah. I'm so excited. [LAUGHTER].", + "emotion": "excited", + "expanded emotion cause evidence": [ + 23, + 24, + 25 + ], + "expanded emotion cause span": [ + "standing ovation", + "Everyone--yeah. And people--friends of ours were in the audience, I didn't know about, like family members.", + "It was great." + ], + "type": [ + "hybrid" + ], + "text": "Yeah. I'm so excited. [LAUGHTER].", + "id": 35 + } +] \ No newline at end of file diff --git a/reccon/sources/train.Ses03F_script02_1.json b/reccon/sources/train.Ses03F_script02_1.json new file mode 100644 index 0000000000000000000000000000000000000000..abf7c0a2ff1b56a3e495672425042138f4dda439 --- /dev/null +++ b/reccon/sources/train.Ses03F_script02_1.json @@ -0,0 +1,650 @@ +[ + { + "turn": 1, + "speaker": "B", + "utterance": "Hey, what time is it? They're supposed to run around midnight, right? God, this is great, isn't it?", + "emotion": "excited", + "expanded emotion cause evidence": [ + 1, + 1 + ], + "expanded emotion cause span": [ + "They're supposed to run around midnight", + "this is great" + ], + "type": [ + "no-context" + ], + "text": "Hey, what time is it? They're supposed to run around midnight, right? God, this is great, isn't it?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Look at the night we got; couldn't be better.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 1, + 1, + 2 + ], + "expanded emotion cause span": [ + "They're supposed to run around midnight", + "this is great", + "Look at the night we got; couldn't be better." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Look at the night we got; couldn't be better.", + "id": 2 + }, + { + "turn": 3, + "speaker": "B", + "utterance": "You know actually, I wanted to go a little further up the coast to get away from all the, the people and the lights, and uh- but I thought we'd miss it. Hey, how you doing?", + "emotion": "excited", + "expanded emotion cause evidence": [ + 1, + 1, + 2 + ], + "expanded emotion cause span": [ + "They're supposed to run around midnight", + "this is great", + "Look at the night we got; couldn't be better." + ], + "type": [ + "self-contagion" + ], + "text": "You know actually, I wanted to go a little further up the coast to get away from all the, the people and the lights, and uh- but I thought we'd miss it. Hey, how you doing?", + "id": 3 + }, + { + "turn": 4, + "speaker": "A", + "utterance": "Fine.", + "emotion": "sad", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Fine.", + "id": 4 + }, + { + "turn": 5, + "speaker": "B", + "utterance": "Oh, is that-is that-now, is that just foam, uhh, I can't even tell.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 1, + 1, + 2, + 5 + ], + "expanded emotion cause span": [ + "They're supposed to run around midnight", + "this is great", + "Look at the night we got; couldn't be better.", + "Oh, is that-is that-now, is that just foam" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Oh, is that-is that-now, is that just foam, uhh, I can't even tell.", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Oh, though if I can't tell it probably isn't them, right? It probably would be unmistakable, wouldn't you think? Hey, how you doing?", + "emotion": "excited", + "expanded emotion cause evidence": [ + 1, + 1 + ], + "expanded emotion cause span": [ + "They're supposed to run around midnight", + "this is great" + ], + "type": [ + "self-contagion" + ], + "text": "Oh, though if I can't tell it probably isn't them, right? It probably would be unmistakable, wouldn't you think? Hey, how you doing?", + "id": 6 + }, + { + "turn": 7, + "speaker": "B", + "utterance": "Oh, do you know what I forgot? I forgot my flashlight. How could I be so stupid. Oh, I-I should have brought my flashlight.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 1, + 1, + 2, + 7 + ], + "expanded emotion cause span": [ + "They're supposed to run around midnight", + "this is great", + "Look at the night we got; couldn't be better.", + "I forgot my flashlight. How could I be so stupid." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Oh, do you know what I forgot? I forgot my flashlight. How could I be so stupid. Oh, I-I should have brought my flashlight.", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Uh- you know, the flashlight. The silver one. There's only one, isn't there?", + "emotion": "excited", + "expanded emotion cause evidence": [ + 1, + 1, + 2, + 7 + ], + "expanded emotion cause span": [ + "They're supposed to run around midnight", + "this is great", + "Look at the night we got; couldn't be better.", + "I forgot my flashlight. How could I be so stupid." + ], + "type": [ + "self-contagion" + ], + "text": "Uh- you know, the flashlight. The silver one. There's only one, isn't there?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I don't understand why you're always saying oh, it's mine, it's mine. It's not like it's just your flashlight. I mean, how do you think that makes me feel?", + "emotion": "angry", + "expanded emotion cause evidence": [ + 7, + 9 + ], + "expanded emotion cause span": [ + "I forgot my flashlight", + "don't understand why you're always saying oh, it's mine, it's mine. It's not like it's just your flashlight." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I don't understand why you're always saying oh, it's mine, it's mine. It's not like it's just your flashlight. I mean, how do you think that makes me feel?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "We should have brought our flashlight. I can't believe we forgot to bring it.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "We should have brought our flashlight. I can't believe we forgot to bring it." + ], + "type": [ + "no-context" + ], + "text": "We should have brought our flashlight. I can't believe we forgot to bring it.", + "id": 10 + }, + { + "turn": 11, + "speaker": "B", + "utterance": "I hope the moon stays out.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 10 + ], + "expanded emotion cause span": [ + "We should have brought our flashlight. I can't believe we forgot to bring it." + ], + "type": [ + "self-contagion" + ], + "text": "I hope the moon stays out.", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Hey, do they always run during a full moon? I can't remember if it was full last year. Do you remember?", + "emotion": "excited", + "expanded emotion cause evidence": [ + 1, + 1, + 2, + 7 + ], + "expanded emotion cause span": [ + "They're supposed to run around midnight", + "this is great", + "Look at the night we got; couldn't be better.", + "I forgot my flashlight. How could I be so stupid." + ], + "type": [ + "self-contagion" + ], + "text": "Hey, do they always run during a full moon? I can't remember if it was full last year. Do you remember?", + "id": 12 + }, + { + "turn": 13, + "speaker": "B", + "utterance": "We should have brought the blanket. Oh, why didn't we bring the blanket? Our blanket.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "We should have brought the blanket." + ], + "type": [ + "no-context" + ], + "text": "We should have brought the blanket. Oh, why didn't we bring the blanket? Our blanket.", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "You know what would be good right now? A six-pack. Ah, I can't believe I forgot a six-pack. A six-pack would be just the ticket right about now.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "Ah, I can't believe I forgot a six-pack. A six-pack would be just the ticket right about now." + ], + "type": [ + "no-context" + ], + "text": "You know what would be good right now? A six-pack. Ah, I can't believe I forgot a six-pack. A six-pack would be just the ticket right about now.", + "id": 14 + }, + { + "turn": 15, + "speaker": "B", + "utterance": "I'm so stupid. I'm like a little kid. I-it's amazing I get out of the house with my fly zipped. Oh- [LAUGHTER].", + "emotion": "excited", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "I-it's amazing I get out of the house with my fly zipped" + ], + "type": [ + "no-context" + ], + "text": "I'm so stupid. I'm like a little kid. I-it's amazing I get out of the house with my fly zipped. Oh- [LAUGHTER].", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "I wonder if they can hear us talk. Or hear the vibrations in the sand when we move.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 16 + ], + "expanded emotion cause span": [ + "I wonder if they can hear us talk. Or hear the vibrations in the sand when we move." + ], + "type": [ + "no-context" + ], + "text": "I wonder if they can hear us talk. Or hear the vibrations in the sand when we move.", + "id": 16 + }, + { + "turn": 17, + "speaker": "B", + "utterance": "Do you want my jacket?", + "emotion": "neutral", + "text": "Do you want my jacket?", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "Right.", + "emotion": "neutral", + "text": "Right.", + "id": 18 + }, + { + "turn": 19, + "speaker": "B", + "utterance": "Yeah, that's my point too.", + "emotion": "neutral", + "text": "Yeah, that's my point too.", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "No. No, no, no, that's not my point. My point is there's no point in coming down here if we just turn around and leave.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 16 + ], + "expanded emotion cause span": [ + "I wonder if they can hear us talk. Or hear the vibrations in the sand when we move." + ], + "type": [ + "self-contagion" + ], + "text": "No. No, no, no, that's not my point. My point is there's no point in coming down here if we just turn around and leave.", + "id": 20 + }, + { + "turn": 21, + "speaker": "B", + "utterance": "I mean, don't you want to see it?", + "emotion": "neutral", + "text": "I mean, don't you want to see it?", + "id": 21 + }, + { + "turn": 22, + "speaker": "A", + "utterance": "Not particularly.", + "emotion": "sad", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Not particularly.", + "id": 22 + }, + { + "turn": 23, + "speaker": "B", + "utterance": "Why not?", + "emotion": "neutral", + "text": "Why not?", + "id": 23 + }, + { + "turn": 24, + "speaker": "A", + "utterance": "I don't know. I just don't.", + "emotion": "sad", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "I don't know. I just don't.", + "id": 24 + }, + { + "turn": 25, + "speaker": "A", + "utterance": "Pass up what? A bunch of fish. They swim up to the beach and they flop around and they swim away and then they die.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 16, + 20, + 23 + ], + "expanded emotion cause span": [ + "I wonder if they can hear us talk. Or hear the vibrations in the sand when we move.", + "No. No, no, no, that's not my point. My point is there's no point in coming down here if we just turn around and leave.", + "Why not?" + ], + "type": [ + "inter-personal" + ], + "text": "Pass up what? A bunch of fish. They swim up to the beach and they flop around and they swim away and then they die.", + "id": 25 + }, + { + "turn": 26, + "speaker": "A", + "utterance": "I don't know why you're getting so excited. I mean, it's not like the landing of the moon or something. It's just fish. Fish that nobody eats.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 16, + 20, + 26 + ], + "expanded emotion cause span": [ + "I wonder if they can hear us talk. Or hear the vibrations in the sand when we move.", + "No. No, no, no, that's not my point. My point is there's no point in coming down here if we just turn around and leave.", + "I don't know why you're getting so excited." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I don't know why you're getting so excited. I mean, it's not like the landing of the moon or something. It's just fish. Fish that nobody eats.", + "id": 26 + }, + { + "turn": 27, + "speaker": "A", + "utterance": "Oh, God, Augie.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 16, + 20, + 26 + ], + "expanded emotion cause span": [ + "I wonder if they can hear us talk. Or hear the vibrations in the sand when we move.", + "No. No, no, no, that's not my point. My point is there's no point in coming down here if we just turn around and leave.", + "I don't know why you're getting so excited." + ], + "type": [ + "hybrid" + ], + "text": "Oh, God, Augie.", + "id": 27 + }, + { + "turn": 28, + "speaker": "A", + "utterance": "Yes, and if you also remember, I got sand in my panties. We got into an argument about nothing. You got a sore throat and we never saw the grunions.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 28 + ], + "expanded emotion cause span": [ + "I got sand in my panties. We got into an argument about nothing. You got a sore throat and we never saw the grunions." + ], + "type": [ + "no-context" + ], + "text": "Yes, and if you also remember, I got sand in my panties. We got into an argument about nothing. You got a sore throat and we never saw the grunions.", + "id": 28 + }, + { + "turn": 29, + "speaker": "A", + "utterance": "No, for God's sakes, we've never seen the grunions. We're not going to see them.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 28, + 29 + ], + "expanded emotion cause span": [ + "I got sand in my panties. We got into an argument about nothing. You got a sore throat and we never saw the grunions.", + "we've never seen the grunions. We're not going to see them." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "No, for God's sakes, we've never seen the grunions. We're not going to see them.", + "id": 29 + }, + { + "turn": 30, + "speaker": "B", + "utterance": "We just weren't in a good spot, all right? This is a much better spot. I have a good instinct for these things. Look, is that-", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 28, + 29 + ], + "expanded emotion cause span": [ + "I got sand in my panties. We got into an argument about nothing. You got a sore throat and we never saw the grunions.", + "we've never seen the grunions. We're not going to see them." + ], + "type": [ + "inter-personal" + ], + "text": "We just weren't in a good spot, all right? This is a much better spot. I have a good instinct for these things. Look, is that-", + "id": 30, + "source_sentences": [ + 27, + 28 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 31, + "speaker": "B", + "utterance": "I wouldn't miss this for anything. I mean, think about this. Okay, I know you're not interested, but just think about this for a minute.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 1, + 1, + 2, + 31 + ], + "expanded emotion cause span": [ + "They're supposed to run around midnight", + "this is great", + "Look at the night we got; couldn't be better.", + "I wouldn't miss this for anything." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I wouldn't miss this for anything. I mean, think about this. Okay, I know you're not interested, but just think about this for a minute.", + "id": 31 + }, + { + "turn": 32, + "speaker": "B", + "utterance": "And they all, all as one, turned as one and formed this line as big as the California coast and started swimming this way. Swimming as if that's the only thing that matters.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 32 + ], + "expanded emotion cause span": [ + "And they all, all as one, turned as one and formed this line as big as the California coast and started swimming this way. Swimming as if that's the only thing that matters." + ], + "type": [ + "no-context" + ], + "text": "And they all, all as one, turned as one and formed this line as big as the California coast and started swimming this way. Swimming as if that's the only thing that matters.", + "id": 32 + }, + { + "turn": 33, + "speaker": "B", + "utterance": "You know, they didn't ask it a question. They didn't, they didn't take a vote. They didn't have an invitation or a map; they just started swimming as one.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 33 + ], + "expanded emotion cause span": [ + "You know, they didn't ask it a question. They didn't, they didn't take a vote. They didn't have an invitation or a map; they just started swimming as one." + ], + "type": [ + "no-context" + ], + "text": "You know, they didn't ask it a question. They didn't, they didn't take a vote. They didn't have an invitation or a map; they just started swimming as one.", + "id": 33 + }, + { + "turn": 34, + "speaker": "B", + "utterance": "its single-mindedness with one mind. Urgency that's pure urge. You know, they don't give it a name.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 34 + ], + "expanded emotion cause span": [ + "its single-mindedness with one mind. Urgency that's pure urge. You know, they don't give it a name." + ], + "type": [ + "no-context" + ], + "text": "its single-mindedness with one mind. Urgency that's pure urge. You know, they don't give it a name.", + "id": 34 + }, + { + "turn": 35, + "speaker": "B", + "utterance": "They don't ask it a question. They just, they just, they don't know what drives them. They just turn as one and start the swim that brings them to here", + "emotion": "excited", + "expanded emotion cause evidence": [ + 35 + ], + "expanded emotion cause span": [ + "They don't ask it a question. They just, they just, they don't know what drives them. They just turn as one and start the swim that brings them to here" + ], + "type": [ + "no-context" + ], + "text": "They don't ask it a question. They just, they just, they don't know what drives them. They just turn as one and start the swim that brings them to here", + "id": 35 + }, + { + "turn": 36, + "speaker": "B", + "utterance": "where we stand for a massive celebration of sex and death. Oh, God, I'm giving myself goosebumps. Look, I'm all-all my hairs on my arms is sticking up.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 36 + ], + "expanded emotion cause span": [ + "where we stand for a massive celebration of sex and death. Oh, God, I'm giving myself goosebumps." + ], + "type": [ + "no-context" + ], + "text": "where we stand for a massive celebration of sex and death. Oh, God, I'm giving myself goosebumps. Look, I'm all-all my hairs on my arms is sticking up.", + "id": 36 + }, + { + "turn": 37, + "speaker": "B", + "utterance": "About what I just said.", + "emotion": "neutral", + "text": "About what I just said.", + "id": 37 + } +] \ No newline at end of file diff --git a/reccon/sources/train.Ses03M_impro08b.json b/reccon/sources/train.Ses03M_impro08b.json new file mode 100644 index 0000000000000000000000000000000000000000..07030bc18bcca1cb21df993a824c2f92138dae51 --- /dev/null +++ b/reccon/sources/train.Ses03M_impro08b.json @@ -0,0 +1,539 @@ +[ + { + "turn": 1, + "speaker": "B", + "utterance": "Hello?", + "emotion": "neutral", + "text": "Hello?", + "id": 1 + }, + { + "turn": 2, + "speaker": "A", + "utterance": "Oh God I finally got...you know how long I've been waiting on line? You put on hold for like five hours. Geez.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "you know how long I've been waiting on line? You put on hold for like five hours." + ], + "type": [ + "no-context" + ], + "text": "Oh God I finally got...you know how long I've been waiting on line? You put on hold for like five hours. Geez.", + "id": 2 + }, + { + "turn": 3, + "speaker": "B", + "utterance": "I'm sorry ma'am. What's the nature of your problem? But first can I get you to tell me your first and last name?", + "emotion": "neutral", + "text": "I'm sorry ma'am. What's the nature of your problem? But first can I get you to tell me your first and last name?", + "id": 3 + }, + { + "turn": 4, + "speaker": "A", + "utterance": "I've already been through this five times with these people. I've been calling every single day.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 2, + 4 + ], + "expanded emotion cause span": [ + "you know how long I've been waiting on line? You put on hold for like five hours.", + "I've already been through this five times with these people. I've been calling every single day." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I've already been through this five times with these people. I've been calling every single day.", + "id": 4 + }, + { + "turn": 5, + "speaker": "B", + "utterance": "I know I just need to verify every time. I'm sorry.", + "emotion": "neutral", + "text": "I know I just need to verify every time. I'm sorry.", + "id": 5 + }, + { + "turn": 6, + "speaker": "A", + "utterance": "Olivia Brown.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 2, + 4 + ], + "expanded emotion cause span": [ + "you know how long I've been waiting on line? You put on hold for like five hours.", + "I've already been through this five times with these people. I've been calling every single day." + ], + "type": [ + "self-contagion" + ], + "text": "Olivia Brown.", + "id": 6 + }, + { + "turn": 7, + "speaker": "B", + "utterance": "Alright Ms. Brown what's the nature of your problem?", + "emotion": "neutral", + "text": "Alright Ms. Brown what's the nature of your problem?", + "id": 7 + }, + { + "turn": 8, + "speaker": "A", + "utterance": "Well my phone isn't working and it hasn't been working for the last five days.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "my phone isn't working and it hasn't been working for the last five days." + ], + "type": [ + "no-context" + ], + "text": "Well my phone isn't working and it hasn't been working for the last five days.", + "id": 8 + }, + { + "turn": 9, + "speaker": "B", + "utterance": "Oh. I'm sorry. Um- Did you drop it in water?", + "emotion": "neutral", + "text": "Oh. I'm sorry. Um- Did you drop it in water?", + "id": 9 + }, + { + "turn": 10, + "speaker": "A", + "utterance": "Yeah, yeah, yeah you better be sorry.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 2, + 4 + ], + "expanded emotion cause span": [ + "you know how long I've been waiting on line? You put on hold for like five hours.", + "I've already been through this five times with these people. I've been calling every single day." + ], + "type": [ + "self-contagion" + ], + "text": "Yeah, yeah, yeah you better be sorry.", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "No I did not drop my phone in water. I'm not five years old and just dropped my phone anywhere I see it. Okay this is my business.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 2, + 4, + 9 + ], + "expanded emotion cause span": [ + "you know how long I've been waiting on line? You put on hold for like five hours.", + "I've already been through this five times with these people. I've been calling every single day.", + "Did you drop it in water?" + ], + "type": [ + "hybrid" + ], + "text": "No I did not drop my phone in water. I'm not five years old and just dropped my phone anywhere I see it. Okay this is my business.", + "id": 11 + }, + { + "turn": 12, + "speaker": "A", + "utterance": "Okay? And it [GARBAGE]. My business is failing because my phone isn't working and I don't have a land line and I really can't handle this right now.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "My business is failing because my phone isn't working and I don't have a land line and I really can't handle this right now." + ], + "type": [ + "no-context" + ], + "text": "Okay? And it [GARBAGE]. My business is failing because my phone isn't working and I don't have a land line and I really can't handle this right now.", + "id": 12 + }, + { + "turn": 13, + "speaker": "B", + "utterance": "Um- well it's probably easy. Can you any more symptoms either you're not receiving calls----ok, you're not receiving calls, not getting calls.", + "emotion": "neutral", + "text": "Um- well it's probably easy. Can you any more symptoms either you're not receiving calls----ok, you're not receiving calls, not getting calls.", + "id": 13 + }, + { + "turn": 14, + "speaker": "A", + "utterance": "the symptoms- This [GARBAGE] a doctor's office. I'm not receiving calls...I can't receive- no, it's, it cuts me off--", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 12, + 14 + ], + "expanded emotion cause span": [ + "My business is failing because my phone isn't working and I don't have a land line and I really can't handle this right now.", + "I'm not receiving calls...I can't receive- no, it's, it cuts me off--" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "the symptoms- This [GARBAGE] a doctor's office. I'm not receiving calls...I can't receive- no, it's, it cuts me off--", + "id": 14 + }, + { + "turn": 15, + "speaker": "B", + "utterance": "Is the phone turned on?", + "emotion": "neutral", + "text": "Is the phone turned on?", + "id": 15 + }, + { + "turn": 16, + "speaker": "A", + "utterance": "Yes the phone turns on. No I mean I'm using it not turning on the phone. Of course it turns on.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 12, + 14 + ], + "expanded emotion cause span": [ + "My business is failing because my phone isn't working and I don't have a land line and I really can't handle this right now.", + "I'm not receiving calls...I can't receive- no, it's, it cuts me off--" + ], + "type": [ + "self-contagion" + ], + "text": "Yes the phone turns on. No I mean I'm using it not turning on the phone. Of course it turns on.", + "id": 16 + }, + { + "turn": 17, + "speaker": "B", + "utterance": "Well, um- okay. Your sim card is in- didn't fall out-", + "emotion": "neutral", + "text": "Well, um- okay. Your sim card is in- didn't fall out-", + "id": 17 + }, + { + "turn": 18, + "speaker": "A", + "utterance": "No- I don't have a sim card because it's Verizon and you guys don't use sim cards.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 12, + 14 + ], + "expanded emotion cause span": [ + "My business is failing because my phone isn't working and I don't have a land line and I really can't handle this right now.", + "I'm not receiving calls...I can't receive- no, it's, it cuts me off--" + ], + "type": [ + "self-contagion" + ], + "text": "No- I don't have a sim card because it's Verizon and you guys don't use sim cards.", + "id": 18 + }, + { + "turn": 19, + "speaker": "B", + "utterance": "Alright. Um- Well that could be the problem. cause--", + "emotion": "neutral", + "text": "Alright. Um- Well that could be the problem. cause--", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "you might have an older phone where we would use sim cards but probably not.", + "emotion": "neutral", + "text": "you might have an older phone where we would use sim cards but probably not.", + "id": 20 + }, + { + "turn": 21, + "speaker": "A", + "utterance": "Okay no. Sir, this is the deal. My phone isn't working and I don't care what the problem is but it needs to work. That's why I'm paying you guys to fix it.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 12, + 14, + 19, + 20, + 21 + ], + "expanded emotion cause span": [ + "My business is failing because my phone isn't working and I don't have a land line and I really can't handle this right now.", + "I'm not receiving calls...I can't receive- no, it's, it cuts me off--", + "Alright. Um- Well that could be the problem. cause--", + "you might have an older phone where we would use sim cards but probably not.", + "My phone isn't working" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Okay no. Sir, this is the deal. My phone isn't working and I don't care what the problem is but it needs to work. That's why I'm paying you guys to fix it.", + "id": 21 + }, + { + "turn": 22, + "speaker": "B", + "utterance": "Okay. How about this we'll send you a brand new camera phone with palm pilot-- and-", + "emotion": "neutral", + "text": "Okay. How about this we'll send you a brand new camera phone with palm pilot-- and-", + "id": 22 + }, + { + "turn": 23, + "speaker": "A", + "utterance": "I don't know even how to use that stuff it's too complicated. I just want my flip phone to work----that's all I need", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 12, + 14, + 21, + 23 + ], + "expanded emotion cause span": [ + "My business is failing because my phone isn't working and I don't have a land line and I really can't handle this right now.", + "I'm not receiving calls...I can't receive- no, it's, it cuts me off--", + "My phone isn't working", + "I don't know even how to use that stuff it's too complicated." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I don't know even how to use that stuff it's too complicated. I just want my flip phone to work----that's all I need", + "id": 23 + }, + { + "turn": 24, + "speaker": "B", + "utterance": "So we'll send it- And we'll give you, how about a free year's service?", + "emotion": "neutral", + "text": "So we'll send it- And we'll give you, how about a free year's service?", + "id": 24 + }, + { + "turn": 25, + "speaker": "A", + "utterance": "Look, I am on the road all the time. Do you understand how important? I'm a woman, a single mother by herself working...what?", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 12, + 14, + 21, + 23 + ], + "expanded emotion cause span": [ + "My business is failing because my phone isn't working and I don't have a land line and I really can't handle this right now.", + "I'm not receiving calls...I can't receive- no, it's, it cuts me off--", + "My phone isn't working", + "I don't know even how to use that stuff it's too complicated." + ], + "type": [ + "self-contagion" + ], + "text": "Look, I am on the road all the time. Do you understand how important? I'm a woman, a single mother by herself working...what?", + "id": 25 + }, + { + "turn": 26, + "speaker": "B", + "utterance": "Tell them my name. My name is Brent Backersen.", + "emotion": "neutral", + "text": "Tell them my name. My name is Brent Backersen.", + "id": 26 + }, + { + "turn": 27, + "speaker": "A", + "utterance": "Brent Backersen, I am writing this down, Brent Backersen. Alright.", + "emotion": "frustrated", + "flag": "F", + "expanded emotion cause evidence": [ + 12, + 14, + 21, + 23 + ], + "expanded emotion cause span": [ + "My business is failing because my phone isn't working and I don't have a land line and I really can't handle this right now.", + "I'm not receiving calls...I can't receive- no, it's, it cuts me off--", + "My phone isn't working", + "I don't know even how to use that stuff it's too complicated." + ], + "type": [ + "self-contagion" + ], + "text": "Brent Backersen, I am writing this down, Brent Backersen. Alright.", + "id": 27 + }, + { + "turn": 28, + "speaker": "B", + "utterance": "Okay. Tell them my - my ID number is two one three five.", + "emotion": "neutral", + "text": "Okay. Tell them my - my ID number is two one three five.", + "id": 28 + }, + { + "turn": 29, + "speaker": "B", + "utterance": "Tell them that. You can go in, get a brand new phone, they'll hook you up with service even give you a free three months--", + "emotion": "neutral", + "text": "Tell them that. You can go in, get a brand new phone, they'll hook you up with service even give you a free three months--", + "id": 29 + }, + { + "turn": 30, + "speaker": "A", + "utterance": "I, I, I don't want a contract. Okay. I don't want any contracts.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 29, + 30 + ], + "expanded emotion cause span": [ + "they'll hook you up with service even give you a free three months", + "Okay. I don't want any contracts." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I, I, I don't want a contract. Okay. I don't want any contracts.", + "id": 30, + "source_sentences": [ + 28 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 31, + "speaker": "B", + "utterance": "It will be free. No contract okay?", + "emotion": "neutral", + "text": "It will be free. No contract okay?", + "id": 31 + }, + { + "turn": 32, + "speaker": "A", + "utterance": "Really? No contract?", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 29, + 30 + ], + "expanded emotion cause span": [ + "they'll hook you up with service even give you a free three months", + "Okay. I don't want any contracts." + ], + "type": [ + "hybrid" + ], + "text": "Really? No contract?", + "id": 32 + }, + { + "turn": 33, + "speaker": "B", + "utterance": "Go in there, yeah, go in there. Tell them Brent Backersen sent you.", + "emotion": "neutral", + "text": "Go in there, yeah, go in there. Tell them Brent Backersen sent you.", + "id": 33 + }, + { + "turn": 34, + "speaker": "B", + "utterance": "the top of the line camera phone, game boy, anything you want. For free. And palm pilot.", + "emotion": "neutral", + "text": "the top of the line camera phone, game boy, anything you want. For free. And palm pilot.", + "id": 34 + }, + { + "turn": 35, + "speaker": "B", + "utterance": "They might only have orange.", + "emotion": "neutral", + "text": "They might only have orange.", + "id": 35 + }, + { + "turn": 36, + "speaker": "B", + "utterance": "Okay. They can figure out pink for you. So go in there and just tell them that and they'll hook you up with other goodies, stuff like that free service, no contract, no nothing. Just for being a good customer", + "emotion": "neutral", + "text": "Okay. They can figure out pink for you. So go in there and just tell them that and they'll hook you up with other goodies, stuff like that free service, no contract, no nothing. Just for being a good customer", + "id": 36 + }, + { + "turn": 37, + "speaker": "B", + "utterance": "and battling through with us.", + "emotion": "neutral", + "text": "and battling through with us.", + "id": 37 + }, + { + "turn": 38, + "speaker": "A", + "utterance": "Alright. Well- I guess - I guess that's okay but,", + "emotion": "neutral", + "text": "Alright. Well- I guess - I guess that's okay but,", + "id": 38 + }, + { + "turn": 39, + "speaker": "B", + "utterance": "Yes. You just tell them Brent Backersen sent you.", + "emotion": "neutral", + "text": "Yes. You just tell them Brent Backersen sent you.", + "id": 39 + }, + { + "turn": 40, + "speaker": "A", + "utterance": "Okay.", + "emotion": "neutral", + "text": "Okay.", + "id": 40 + }, + { + "turn": 41, + "speaker": "B", + "utterance": "Alright? Great. Have a nice evening.", + "emotion": "neutral", + "text": "Alright? Great. Have a nice evening.", + "id": 41 + }, + { + "turn": 42, + "speaker": "A", + "utterance": "Alright Thanks.", + "emotion": "neutral", + "text": "Alright Thanks.", + "id": 42 + } +] \ No newline at end of file diff --git a/reccon/sources/train.Ses03M_script01_2.json b/reccon/sources/train.Ses03M_script01_2.json new file mode 100644 index 0000000000000000000000000000000000000000..d610291fbb17419575f5a2af8698ea0af50c2470 --- /dev/null +++ b/reccon/sources/train.Ses03M_script01_2.json @@ -0,0 +1,447 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Why did he invite her here?", + "emotion": "angry", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "he invite her here" + ], + "type": [ + "no-context" + ], + "text": "Why did he invite her here?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Why does that bother you?", + "emotion": "frustrated", + "explanation": "Speaker B is frustrated to hear the question by A which seems to be unreaonable according to speaker B.", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Why did he invite her here?" + ], + "type": [ + "inter-personal" + ], + "text": "Why does that bother you?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Well she's been away for three and a half years in New York and suddenly she just shows up.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "he invite her here", + "Well she's been away for three and a half years in New York and suddenly she just shows up." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Well she's been away for three and a half years in New York and suddenly she just shows up.", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Well maybe, maybe he just wanted to see her.", + "emotion": "neutral", + "text": "Well maybe, maybe he just wanted to see her.", + "id": 4 + }, + { + "turn": 5, + "speaker": "B", + "utterance": "uh-uh What do you mean? They grew up next to each other their entire lives. Why shouldn't he want to see her?", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Well she's been away for three and a half years in New York and suddenly she just shows up." + ], + "type": [ + "inter-personal" + ], + "text": "uh-uh What do you mean? They grew up next to each other their entire lives. Why shouldn't he want to see her?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Hey don't look at me like that. I don't know anymore than you.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 3, + 6 + ], + "expanded emotion cause span": [ + "Well she's been away for three and a half years in New York and suddenly she just shows up.", + "Hey don't look at me like that." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Hey don't look at me like that. I don't know anymore than you.", + "id": 6 + }, + { + "turn": 7, + "speaker": "B", + "utterance": "Who said he even thought about that?", + "emotion": "neutral", + "text": "Who said he even thought about that?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Well, so what?", + "emotion": "neutral", + "text": "Well, so what?", + "id": 8 + }, + { + "turn": 9, + "speaker": "B", + "utterance": "Now listen kid...", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 3, + 6 + ], + "expanded emotion cause span": [ + "Well she's been away for three and a half years in New York and suddenly she just shows up.", + "Hey don't look at me like that." + ], + "type": [ + "hybrid" + ], + "text": "Now listen kid...", + "id": 9 + }, + { + "turn": 10, + "speaker": "A", + "utterance": "No. She's not his girl Joe and she knows that.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 1, + 3, + 5 + ], + "expanded emotion cause span": [ + "he invite her here", + "Well she's been away for three and a half years in New York and suddenly she just shows up.", + "uh-uh What do you mean? They grew up next to each other their entire lives. Why shouldn't he want to see her?" + ], + "type": [ + "hybrid" + ], + "text": "No. She's not his girl Joe and she knows that.", + "id": 10 + }, + { + "turn": 11, + "speaker": "B", + "utterance": "How do you know why she's waited? Hmmm?", + "emotion": "neutral", + "text": "How do you know why she's waited? Hmmm?", + "id": 11 + }, + { + "turn": 12, + "speaker": "A", + "utterance": "I mean, her faith is stronger than a rock.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "he invite her here", + "Well she's been away for three and a half years in New York and suddenly she just shows up." + ], + "type": [ + "self-contagion" + ], + "text": "I mean, her faith is stronger than a rock.", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "My worst times I think about her, you know, and I", + "emotion": "sad", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "My worst times I think about her, you know, and I" + ], + "type": [ + "no-context" + ], + "text": "My worst times I think about her, you know, and I", + "id": 13 + }, + { + "turn": 14, + "speaker": "A", + "utterance": "it's like I know as long as she's waiting I'm right again.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 13, + 14 + ], + "expanded emotion cause span": [ + "My worst times I think about her, you know, and I", + "it's like I know as long as she's waiting I'm right again." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "it's like I know as long as she's waiting I'm right again.", + "id": 14 + }, + { + "turn": 15, + "speaker": "B", + "utterance": "Look at how nice the day is. What are we arguing for?", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 3, + 6, + 15 + ], + "expanded emotion cause span": [ + "Well she's been away for three and a half years in New York and suddenly she just shows up.", + "Hey don't look at me like that.", + "What are we arguing for?" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Look at how nice the day is. What are we arguing for?", + "id": 15 + }, + { + "turn": 16, + "speaker": "A", + "utterance": "No. Nobody in my house better dare and challenge her faith. You know and maybe strangers but not his father, not his brother.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 1, + 16 + ], + "expanded emotion cause span": [ + "he invite her here", + "Nobody in my house better dare and challenge her faith." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "No. Nobody in my house better dare and challenge her faith. You know and maybe strangers but not his father, not his brother.", + "id": 16 + }, + { + "turn": 17, + "speaker": "B", + "utterance": "What do you want me to do? What do you want?", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 16 + ], + "expanded emotion cause span": [ + "No. Nobody in my house better dare and challenge her faith. You know and maybe strangers but not his father, not his brother." + ], + "type": [ + "inter-personal" + ], + "text": "What do you want me to do? What do you want?", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "But Kate...", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 16 + ], + "expanded emotion cause span": [ + "No. Nobody in my house better dare and challenge her faith. You know and maybe strangers but not his father, not his brother." + ], + "type": [ + "inter-personal" + ], + "text": "But Kate...", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "Laugh, laugh at me but I will. Because you know what happened when she came here? When she came back she slept in his room, the memorial broke into pieces. Joe, look. Look at it. You got to believe with me.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 1, + 16, + 19 + ], + "expanded emotion cause span": [ + "he invite her here", + "Nobody in my house better dare and challenge her faith.", + "When she came back she slept in his room, the memorial broke into pieces." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Laugh, laugh at me but I will. Because you know what happened when she came here? When she came back she slept in his room, the memorial broke into pieces. Joe, look. Look at it. You got to believe with me.", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "Okay. Calm yourself. Just calm yourself.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 16 + ], + "expanded emotion cause span": [ + "No. Nobody in my house better dare and challenge her faith. You know and maybe strangers but not his father, not his brother." + ], + "type": [ + "inter-personal" + ], + "text": "Okay. Calm yourself. Just calm yourself.", + "id": 20 + }, + { + "turn": 21, + "speaker": "A", + "utterance": "Look, it was just last week that Detroit, some boy came back he had been away longer than Larry, you can read it for yourself. You above all people have got to believe.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 21 + ], + "expanded emotion cause span": [ + "it was just last week that Detroit, some boy came back he had been away longer than Larry, you can read it for yourself." + ], + "type": [ + "no-context" + ], + "text": "Look, it was just last week that Detroit, some boy came back he had been away longer than Larry, you can read it for yourself. You above all people have got to believe.", + "id": 21 + }, + { + "turn": 22, + "speaker": "B", + "utterance": "Alright, alright, calm yourself okay? Calm yourself. Wait, wait. What do you mean, me above all?", + "emotion": "angry", + "expanded emotion cause evidence": [ + 21 + ], + "expanded emotion cause span": [ + "You above all people have got to believe." + ], + "type": [ + "inter-personal" + ], + "text": "Alright, alright, calm yourself okay? Calm yourself. Wait, wait. What do you mean, me above all?", + "id": 22 + }, + { + "turn": 23, + "speaker": "B", + "utterance": "Wait, what does that mean? Me above all?", + "emotion": "angry", + "expanded emotion cause evidence": [ + 21 + ], + "expanded emotion cause span": [ + "You above all people have got to believe." + ], + "type": [ + "inter-personal" + ], + "text": "Wait, what does that mean? Me above all?", + "id": 23 + }, + { + "turn": 24, + "speaker": "B", + "utterance": "Look at you, you're shaking.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 21 + ], + "expanded emotion cause span": [ + "You above all people have got to believe." + ], + "type": [ + "inter-personal" + ], + "text": "Look at you, you're shaking.", + "id": 24 + }, + { + "turn": 25, + "speaker": "A", + "utterance": "I can't help it.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 21 + ], + "expanded emotion cause span": [ + "it was just last week that Detroit, some boy came back he had been away longer than Larry, you can read it for yourself." + ], + "type": [ + "self-contagion" + ], + "text": "I can't help it.", + "id": 25 + }, + { + "turn": 26, + "speaker": "B", + "utterance": "What do I got to hide? Huh? What the hell's the matter with you Kate?", + "emotion": "angry", + "expanded emotion cause evidence": [ + 21, + 26 + ], + "expanded emotion cause span": [ + "You above all people have got to believe.", + "What the hell's the matter with you Kate?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "What do I got to hide? Huh? What the hell's the matter with you Kate?", + "id": 26, + "source_sentences": [ + 20 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/train.Ses04F_script03_1.json b/reccon/sources/train.Ses04F_script03_1.json new file mode 100644 index 0000000000000000000000000000000000000000..1f1d219128160a3148e8f30c288225ac974616cc --- /dev/null +++ b/reccon/sources/train.Ses04F_script03_1.json @@ -0,0 +1,420 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Ahh. It sent shivers up my spine.", + "emotion": "excited", + "expanded emotion cause evidence": [ + "b", + 1 + ], + "expanded emotion cause span": [ + "b", + "It sent shivers up my spine." + ], + "type": [ + "latent", + "no-context" + ], + "text": "Ahh. It sent shivers up my spine.", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What shall we do if they suddenly walk in on us?", + "emotion": "excited", + "expanded emotion cause evidence": [ + "b", + "b", + 1, + 2 + ], + "expanded emotion cause span": [ + "b", + "b", + "It sent shivers up my spine.", + "if they suddenly walk in on us?" + ], + "type": [ + "latent", + "no-context", + "inter-personal" + ], + "text": "What shall we do if they suddenly walk in on us?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Behave exquisitely.", + "emotion": "excited", + "expanded emotion cause evidence": [ + "b", + 1 + ], + "expanded emotion cause span": [ + "b", + "It sent shivers up my spine." + ], + "type": [ + "latent", + "self-contagion" + ], + "text": "Behave exquisitely.", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "With the most perfect poise.", + "emotion": "excited", + "expanded emotion cause evidence": [ + "b", + "b", + 1, + 2 + ], + "expanded emotion cause span": [ + "b", + "b", + "It sent shivers up my spine.", + "if they suddenly walk in on us?" + ], + "type": [ + "latent", + "hybrid" + ], + "text": "With the most perfect poise.", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Certainly I shall probably do a court curtsy.", + "emotion": "excited", + "expanded emotion cause evidence": [ + "b", + 1 + ], + "expanded emotion cause span": [ + "b", + "It sent shivers up my spine." + ], + "type": [ + "latent", + "self-contagion" + ], + "text": "Certainly I shall probably do a court curtsy.", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Things that ought to matter dreadfully don't matter at all when one's happy, do they?", + "emotion": "excited", + "expanded emotion cause evidence": [ + "b", + "b", + 1, + 2 + ], + "expanded emotion cause span": [ + "b", + "b", + "It sent shivers up my spine.", + "if they suddenly walk in on us?" + ], + "type": [ + "latent", + "hybrid" + ], + "text": "Things that ought to matter dreadfully don't matter at all when one's happy, do they?", + "id": 6 + }, + { + "turn": 7, + "speaker": "B", + "utterance": "Don't say that, my darling.", + "emotion": "neutral", + "text": "Don't say that, my darling.", + "id": 7 + }, + { + "turn": 8, + "speaker": "A", + "utterance": "It's true the whole business is very poor joke.", + "emotion": "excited", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "It's true the whole business is very poor joke.", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Don't laugh at me. I'm serious.", + "emotion": "excited", + "expanded emotion cause evidence": [ + "b", + 9 + ], + "expanded emotion cause span": [ + "b", + "Don't laugh at me. I'm serious." + ], + "type": [ + "latent", + "no-context" + ], + "text": "Don't laugh at me. I'm serious.", + "id": 9 + }, + { + "turn": 10, + "speaker": "A", + "utterance": "Who's they?", + "emotion": "neutral", + "text": "Who's they?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Oh, how long will it last, this ludicrous, over-bearing love of ours?", + "emotion": "excited", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "how long will it last, this ludicrous" + ], + "type": [ + "no-context" + ], + "text": "Oh, how long will it last, this ludicrous, over-bearing love of ours?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Well who knows?", + "emotion": "neutral", + "text": "Well who knows?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "What happens if one of us dies? Does the one that's left still laugh?", + "emotion": "neutral", + "text": "What happens if one of us dies? Does the one that's left still laugh?", + "id": 13 + }, + { + "turn": 14, + "speaker": "A", + "utterance": "Thank you, dear. The same applies to you except that if I catch you so much as looking at another woman, I'll kill you.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "The same applies to you except that if I catch you so much as looking at another woman" + ], + "type": [ + "no-context" + ], + "text": "Thank you, dear. The same applies to you except that if I catch you so much as looking at another woman, I'll kill you.", + "id": 14 + }, + { + "turn": 15, + "speaker": "B", + "utterance": "Do you remember that awful scene in Venice?", + "emotion": "neutral", + "text": "Do you remember that awful scene in Venice?", + "id": 15 + }, + { + "turn": 16, + "speaker": "A", + "utterance": "Which particular one?", + "emotion": "excited", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "Do you remember that awful scene in Venice?" + ], + "type": [ + "inter-personal" + ], + "text": "Which particular one?", + "id": 16 + }, + { + "turn": 17, + "speaker": "B", + "utterance": "The one where you bought that little painted wooden snake and put it on my bed.", + "emotion": "neutral", + "text": "The one where you bought that little painted wooden snake and put it on my bed.", + "id": 17 + }, + { + "turn": 18, + "speaker": "A", + "utterance": "Oh, Charles. That was his name. Charles he did wriggle so beautifully.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 15, + 17, + 18 + ], + "expanded emotion cause span": [ + "Do you remember that awful scene in Venice?", + "The one where you bought that little painted wooden snake and put it on my bed.", + "Charles he did wriggle so beautifully." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh, Charles. That was his name. Charles he did wriggle so beautifully.", + "id": 18, + "source_sentences": [ + 14, + 16 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 19, + "speaker": "B", + "utterance": "Horrible thing. I hated it.", + "emotion": "neutral", + "text": "Horrible thing. I hated it.", + "id": 19 + }, + { + "turn": 20, + "speaker": "A", + "utterance": "Yes, I know you did. You threw him out of the window into the Grand Canal. I don't think I'll ever forgive you for that.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 20 + ], + "expanded emotion cause span": [ + "You threw him out of the window into the Grand Canal." + ], + "type": [ + "no-context" + ], + "text": "Yes, I know you did. You threw him out of the window into the Grand Canal. I don't think I'll ever forgive you for that.", + "id": 20 + }, + { + "turn": 21, + "speaker": "B", + "utterance": "How long did that row last?", + "emotion": "neutral", + "text": "How long did that row last?", + "id": 21 + }, + { + "turn": 22, + "speaker": "B", + "utterance": "The worst one was in Cannes when your curling irons burnt holes in my dressing gown.", + "emotion": "neutral", + "text": "The worst one was in Cannes when your curling irons burnt holes in my dressing gown.", + "id": 22 + }, + { + "turn": 23, + "speaker": "A", + "utterance": "It burnt my comb too and all the towels in the bathroom.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 23 + ], + "expanded emotion cause span": [ + "It burnt my comb too and all the towels in the bathroom." + ], + "type": [ + "no-context" + ], + "text": "It burnt my comb too and all the towels in the bathroom.", + "id": 23 + }, + { + "turn": 24, + "speaker": "A", + "utterance": "Then the manager came in and found us rolling about on the floor biting and scratching like panthers.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 23, + 24 + ], + "expanded emotion cause span": [ + "It burnt my comb too and all the towels in the bathroom.", + "Then the manager came in and found us rolling about on the floor biting and scratching like panthers." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Then the manager came in and found us rolling about on the floor biting and scratching like panthers.", + "id": 24 + }, + { + "turn": 25, + "speaker": "A", + "utterance": "How ridiculous. How utterly, utterly ridiculous.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 23, + 24, + 25 + ], + "expanded emotion cause span": [ + "It burnt my comb too and all the towels in the bathroom.", + "Then the manager came in and found us rolling about on the floor biting and scratching like panthers.", + "How ridiculous. How utterly, utterly ridiculous." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "How ridiculous. How utterly, utterly ridiculous.", + "id": 25 + }, + { + "turn": 26, + "speaker": "A", + "utterance": "And very much sillier.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 23, + 24, + 25 + ], + "expanded emotion cause span": [ + "It burnt my comb too and all the towels in the bathroom.", + "Then the manager came in and found us rolling about on the floor biting and scratching like panthers.", + "How ridiculous. How utterly, utterly ridiculous." + ], + "type": [ + "self-contagion" + ], + "text": "And very much sillier.", + "id": 26 + } +] \ No newline at end of file diff --git a/reccon/sources/train.Ses04M_script02_2.json b/reccon/sources/train.Ses04M_script02_2.json new file mode 100644 index 0000000000000000000000000000000000000000..d46e10a5878f2bda3255e92c781f9b9e669b91b5 --- /dev/null +++ b/reccon/sources/train.Ses04M_script02_2.json @@ -0,0 +1,1009 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Look at this, goose bumps.", + "emotion": "neutral", + "text": "Look at this, goose bumps.", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Well so what'd you think?", + "emotion": "neutral", + "text": "Well so what'd you think?", + "id": 2 + }, + { + "turn": 3, + "speaker": "B", + "utterance": "What I said.", + "emotion": "neutral", + "text": "What I said.", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Certainly is not. It's slightly exaggerated scientific fact.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 1, + 4 + ], + "expanded emotion cause span": [ + "Look at this, goose bumps.", + "It's slightly exaggerated scientific fact." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Certainly is not. It's slightly exaggerated scientific fact.", + "id": 4 + }, + { + "turn": 5, + "speaker": "B", + "utterance": "Carla, can I ask you something? Don't take this the wrong way, but are you having your period?", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 1, + 4 + ], + "expanded emotion cause span": [ + "Look at this, goose bumps.", + "It's slightly exaggerated scientific fact." + ], + "type": [ + "hybrid" + ], + "text": "Carla, can I ask you something? Don't take this the wrong way, but are you having your period?", + "id": 5 + }, + { + "turn": 6, + "speaker": "A", + "utterance": "Goddamn it, Augie, don't ask me that. I hate it when you ask me that. You always ask me that. It's insulting.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "but are you having your period?", + "I hate it when you ask me that. You always ask me that. It's insulting." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Goddamn it, Augie, don't ask me that. I hate it when you ask me that. You always ask me that. It's insulting.", + "id": 6 + }, + { + "turn": 7, + "speaker": "B", + "utterance": "Well what's bugging you?", + "emotion": "angry", + "expanded emotion cause evidence": [ + 1, + 1, + 4 + ], + "expanded emotion cause span": [ + "Look at this, goose bumps.", + "Look at this, goose bumps.", + "It's slightly exaggerated scientific fact." + ], + "type": [ + "hybrid" + ], + "text": "Well what's bugging you?", + "id": 7 + }, + { + "turn": 8, + "speaker": "A", + "utterance": "We just have different ideas about what this evening is supposed to look like.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 5, + 6, + 8 + ], + "expanded emotion cause span": [ + "but are you having your period?", + "I hate it when you ask me that. You always ask me that. It's insulting.", + "We just have different ideas about what this evening is supposed to look like." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "We just have different ideas about what this evening is supposed to look like.", + "id": 8 + }, + { + "turn": 9, + "speaker": "B", + "utterance": "There's nothing to it. We come down here. The grunions arrive. They do their little fish business. We go ooh, ah, look at the fish. They go home. We go home.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 1, + 4, + 8, + 9 + ], + "expanded emotion cause span": [ + "Look at this, goose bumps.", + "It's slightly exaggerated scientific fact.", + "We just have different ideas about what this evening is supposed to look like.", + "There's nothing to it. We come down here. The grunions arrive. They do their little fish business. We go ooh, ah, look at the fish. They go home. We go home." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "There's nothing to it. We come down here. The grunions arrive. They do their little fish business. We go ooh, ah, look at the fish. They go home. We go home.", + "id": 9 + }, + { + "turn": 10, + "speaker": "A", + "utterance": "We never do, do we? Have we ever?", + "emotion": "angry", + "expanded emotion cause evidence": [ + 5, + 6, + 8 + ], + "expanded emotion cause span": [ + "but are you having your period?", + "I hate it when you ask me that. You always ask me that. It's insulting.", + "We just have different ideas about what this evening is supposed to look like." + ], + "type": [ + "hybrid" + ], + "text": "We never do, do we? Have we ever?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Twice is every time we've tried. That's ever.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "There's nothing to it. We come down here. The grunions arrive. They do their little fish business. We go ooh, ah, look at the fish. They go home. We go home.", + "We never do, do we? Have we ever?" + ], + "type": [ + "hybrid" + ], + "text": "Twice is every time we've tried. That's ever.", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "We'll see them this year.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "Twice is every time we've tried. That's ever." + ], + "type": [ + "inter-personal" + ], + "text": "We'll see them this year.", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "You don't have any idea what I'm saying.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 9, + 10, + 12 + ], + "expanded emotion cause span": [ + "There's nothing to it. We come down here. The grunions arrive. They do their little fish business. We go ooh, ah, look at the fish. They go home. We go home.", + "We never do, do we? Have we ever?", + "We'll see them this year." + ], + "type": [ + "hybrid" + ], + "text": "You don't have any idea what I'm saying.", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "No, of course, not.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 9, + 10, + 13 + ], + "expanded emotion cause span": [ + "There's nothing to it. We come down here. The grunions arrive. They do their little fish business. We go ooh, ah, look at the fish. They go home. We go home.", + "We never do, do we? Have we ever?", + "You don't have any idea what I'm saying." + ], + "type": [ + "hybrid" + ], + "text": "No, of course, not.", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "I did want to see it. I always do. I keep thinking this time will be the time, but it never is.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 5, + 6, + 8, + 14 + ], + "expanded emotion cause span": [ + "but are you having your period?", + "I hate it when you ask me that. You always ask me that. It's insulting.", + "We just have different ideas about what this evening is supposed to look like.", + "No, of course, not." + ], + "type": [ + "hybrid" + ], + "text": "I did want to see it. I always do. I keep thinking this time will be the time, but it never is.", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "It's just fish; nothing to get traumatized over.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 15, + 16 + ], + "expanded emotion cause span": [ + "I did want to see it. I always do. I keep thinking this time will be the time, but it never is.", + "It's just fish" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "It's just fish; nothing to get traumatized over.", + "id": 16 + }, + { + "turn": 17, + "speaker": "B", + "utterance": "I've been trying to work this backwards, but I can't seem to pinpoint the moment when we took a turn for the worse.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 15, + 16, + 17 + ], + "expanded emotion cause span": [ + "I did want to see it. I always do. I keep thinking this time will be the time, but it never is.", + "It's just fish", + "I can't seem to pinpoint the moment when we took a turn for the worse." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I've been trying to work this backwards, but I can't seem to pinpoint the moment when we took a turn for the worse.", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "You were fine during the phone call from Marge. Dinner was okay. Doing the dishes was no problem. Let's see, I took a shower. Uh, you watched the news. You said the grunions are running tonight. I said great, let's go. I feel lucky tonight.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 15, + 16, + 17 + ], + "expanded emotion cause span": [ + "I did want to see it. I always do. I keep thinking this time will be the time, but it never is.", + "It's just fish", + "I can't seem to pinpoint the moment when we took a turn for the worse." + ], + "type": [ + "hybrid" + ], + "text": "You were fine during the phone call from Marge. Dinner was okay. Doing the dishes was no problem. Let's see, I took a shower. Uh, you watched the news. You said the grunions are running tonight. I said great, let's go. I feel lucky tonight.", + "id": 18 + }, + { + "turn": 19, + "speaker": "B", + "utterance": "Uh,okay. So I'm putting on my jacket; putting out the animals;", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 15, + 16, + 17 + ], + "expanded emotion cause span": [ + "I did want to see it. I always do. I keep thinking this time will be the time, but it never is.", + "It's just fish", + "I can't seem to pinpoint the moment when we took a turn for the worse." + ], + "type": [ + "hybrid" + ], + "text": "Uh,okay. So I'm putting on my jacket; putting out the animals;", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "uh, taking the car out of the gara- out of the garage.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 15, + 16, + 17 + ], + "expanded emotion cause span": [ + "I did want to see it. I always do. I keep thinking this time will be the time, but it never is.", + "It's just fish", + "I can't seem to pinpoint the moment when we took a turn for the worse." + ], + "type": [ + "hybrid" + ], + "text": "uh, taking the car out of the gara- out of the garage.", + "id": 20 + }, + { + "turn": 21, + "speaker": "B", + "utterance": "Uh.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 15, + 16, + 17 + ], + "expanded emotion cause span": [ + "I did want to see it. I always do. I keep thinking this time will be the time, but it never is.", + "It's just fish", + "I can't seem to pinpoint the moment when we took a turn for the worse." + ], + "type": [ + "hybrid" + ], + "text": "Uh.", + "id": 21 + }, + { + "turn": 22, + "speaker": "A", + "utterance": "It was about four years ago, right after we got married. We thought I was pregnant and we had a bottle of champagne but no glasses. You asked me to dance. So we took off our shoes and you popped the cork.", + "emotion": "sad", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "It was about four years ago, right after we got married. We thought I was pregnant and we had a bottle of champagne but no glasses. You asked me to dance. So we took off our shoes and you popped the cork.", + "id": 22 + }, + { + "turn": 23, + "speaker": "B", + "utterance": "Wait a minute, I've got it.", + "emotion": "neutral", + "text": "Wait a minute, I've got it.", + "id": 23 + }, + { + "turn": 24, + "speaker": "A", + "utterance": "Dancing barefoot in the sand; drinking champagne from the bottle.", + "emotion": "sad", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Dancing barefoot in the sand; drinking champagne from the bottle.", + "id": 24 + }, + { + "turn": 25, + "speaker": "B", + "utterance": "It was in the car, right? Driving past the Knickerbocker Liquor Locker? You said let's get some champagne and I said times a wasting or something like that. Right? That's it, right? You want this to be like the other time. That's it. Of course.", + "emotion": "neutral", + "text": "It was in the car, right? Driving past the Knickerbocker Liquor Locker? You said let's get some champagne and I said times a wasting or something like that. Right? That's it, right? You want this to be like the other time. That's it. Of course.", + "id": 25 + }, + { + "turn": 26, + "speaker": "A", + "utterance": "I'd rather not remember some things. I'd rather not hope for some things.", + "emotion": "sad", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "I'd rather not remember some things. I'd rather not hope for some things.", + "id": 26 + }, + { + "turn": 27, + "speaker": "A", + "utterance": "No.", + "emotion": "sad", + "expanded emotion cause evidence": [ + "b", + 24 + ], + "expanded emotion cause span": [ + "b", + "Dancing barefoot in the sand; drinking champagne from the bottle." + ], + "type": [ + "latent", + "self-contagion" + ], + "text": "No.", + "id": 27 + }, + { + "turn": 28, + "speaker": "A", + "utterance": "No.", + "emotion": "sad", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "No.", + "id": 28 + }, + { + "turn": 29, + "speaker": "B", + "utterance": "What, you want me to breathe in your ear?", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 26 + ], + "expanded emotion cause span": [ + "I'd rather not remember some things. I'd rather not hope for some things." + ], + "type": [ + "inter-personal" + ], + "text": "What, you want me to breathe in your ear?", + "id": 29 + }, + { + "turn": 30, + "speaker": "A", + "utterance": "No.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 29 + ], + "expanded emotion cause span": [ + "What, you want me to breathe in your ear?" + ], + "type": [ + "inter-personal" + ], + "text": "No.", + "id": 30 + }, + { + "turn": 31, + "speaker": "B", + "utterance": "You want to get married again?", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 26 + ], + "expanded emotion cause span": [ + "I'd rather not remember some things. I'd rather not hope for some things." + ], + "type": [ + "inter-personal" + ], + "text": "You want to get married again?", + "id": 31 + }, + { + "turn": 32, + "speaker": "A", + "utterance": "No.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 31 + ], + "expanded emotion cause span": [ + "You want to get married again?" + ], + "type": [ + "inter-personal" + ], + "text": "No.", + "id": 32 + }, + { + "turn": 33, + "speaker": "B", + "utterance": "What, you want a divorce?", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 26 + ], + "expanded emotion cause span": [ + "I'd rather not remember some things. I'd rather not hope for some things." + ], + "type": [ + "inter-personal" + ], + "text": "What, you want a divorce?", + "id": 33 + }, + { + "turn": 34, + "speaker": "A", + "utterance": "No.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 33 + ], + "expanded emotion cause span": [ + "What, you want a divorce?" + ], + "type": [ + "inter-personal" + ], + "text": "No.", + "id": 34 + }, + { + "turn": 35, + "speaker": "B", + "utterance": "A vacation?", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 26 + ], + "expanded emotion cause span": [ + "I'd rather not remember some things. I'd rather not hope for some things." + ], + "type": [ + "inter-personal" + ], + "text": "A vacation?", + "id": 35 + }, + { + "turn": 36, + "speaker": "A", + "utterance": "No.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 29, + 31, + 33, + 35 + ], + "expanded emotion cause span": [ + "What, you want me to breathe in your ear?", + "You want to get married again?", + "What, you want a divorce?", + "A vacation?" + ], + "type": [ + "inter-personal" + ], + "text": "No.", + "id": 36 + }, + { + "turn": 37, + "speaker": "A", + "utterance": "I want something to turn out the way it's supposed to.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 29, + 31, + 33, + 35 + ], + "expanded emotion cause span": [ + "What, you want me to breathe in your ear?", + "You want to get married again?", + "What, you want a divorce?", + "A vacation?" + ], + "type": [ + "inter-personal" + ], + "text": "I want something to turn out the way it's supposed to.", + "id": 37 + }, + { + "turn": 38, + "speaker": "B", + "utterance": "Well welcome to the human race. You think this is what I had in mind? You think that when I proposed, I had this great fantasy going that four years down the line, we'd come to the beach and yell at each other over fish? No.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 37, + 38 + ], + "expanded emotion cause span": [ + "I want something to turn out the way it's supposed to.", + "You think that when I proposed, I had this great fantasy going that four years down the line, we'd come to the beach and yell at each other over fish?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Well welcome to the human race. You think this is what I had in mind? You think that when I proposed, I had this great fantasy going that four years down the line, we'd come to the beach and yell at each other over fish? No.", + "id": 38 + }, + { + "turn": 39, + "speaker": "B", + "utterance": "And we'll have three fat rosy kids and ha, ha, ha, baby, the joke's on us, 'cause you know what you get, Carla? You know what you get? This.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 37, + 38 + ], + "expanded emotion cause span": [ + "I want something to turn out the way it's supposed to.", + "You think that when I proposed, I had this great fantasy going that four years down the line, we'd come to the beach and yell at each other over fish?" + ], + "type": [ + "hybrid" + ], + "text": "And we'll have three fat rosy kids and ha, ha, ha, baby, the joke's on us, 'cause you know what you get, Carla? You know what you get? This.", + "id": 39 + }, + { + "turn": 40, + "speaker": "A", + "utterance": "This what? What is this? This isn't even anything.", + "emotion": "angry", + "expanded emotion cause evidence": [ + "b", + 39 + ], + "expanded emotion cause span": [ + "b", + "And we'll have three fat rosy kids and ha, ha, ha, baby, the joke's on us, 'cause you know what you get, Carla? You know what you get? This." + ], + "type": [ + "latent", + "inter-personal" + ], + "text": "This what? What is this? This isn't even anything.", + "id": 40 + }, + { + "turn": 41, + "speaker": "B", + "utterance": "Yes, it is.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 37, + 38 + ], + "expanded emotion cause span": [ + "I want something to turn out the way it's supposed to.", + "You think that when I proposed, I had this great fantasy going that four years down the line, we'd come to the beach and yell at each other over fish?" + ], + "type": [ + "hybrid" + ], + "text": "Yes, it is.", + "id": 41 + }, + { + "turn": 42, + "speaker": "A", + "utterance": "Oh, right, sure. This is standing on the beach. This is waiting. This is fighting.", + "emotion": "angry", + "expanded emotion cause evidence": [ + "b", + 41, + 42 + ], + "expanded emotion cause span": [ + "b", + "Yes, it is.", + "This is fighting" + ], + "type": [ + "latent", + "no-context", + "inter-personal" + ], + "text": "Oh, right, sure. This is standing on the beach. This is waiting. This is fighting.", + "id": 42 + }, + { + "turn": 43, + "speaker": "B", + "utterance": "Right.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 37, + 38, + 42 + ], + "expanded emotion cause span": [ + "I want something to turn out the way it's supposed to.", + "You think that when I proposed, I had this great fantasy going that four years down the line, we'd come to the beach and yell at each other over fish?", + "This is fighting" + ], + "type": [ + "hybrid" + ], + "text": "Right.", + "id": 43 + }, + { + "turn": 44, + "speaker": "A", + "utterance": "But this isn't anything like I thought anything would be like.", + "emotion": "angry", + "expanded emotion cause evidence": [ + "b", + 5, + 6, + 8, + 44 + ], + "expanded emotion cause span": [ + "b", + "but are you having your period?", + "I hate it when you ask me that. You always ask me that. It's insulting.", + "We just have different ideas about what this evening is supposed to look like.", + "But this isn't anything like I thought anything would be like." + ], + "type": [ + "latent", + "no-context", + "hybrid" + ], + "text": "But this isn't anything like I thought anything would be like.", + "id": 44 + }, + { + "turn": 45, + "speaker": "B", + "utterance": "No, I know, me neither.", + "emotion": "angry", + "expanded emotion cause evidence": [ + 5, + 6, + 8 + ], + "expanded emotion cause span": [ + "but are you having your period?", + "I hate it when you ask me that. You always ask me that. It's insulting.", + "We just have different ideas about what this evening is supposed to look like." + ], + "type": [ + "hybrid" + ], + "text": "No, I know, me neither.", + "id": 45 + }, + { + "turn": 46, + "speaker": "B", + "utterance": "I'm doing the best I can.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 5, + 6, + 8 + ], + "expanded emotion cause span": [ + "but are you having your period?", + "I hate it when you ask me that. You always ask me that. It's insulting.", + "We just have different ideas about what this evening is supposed to look like." + ], + "type": [ + "hybrid" + ], + "text": "I'm doing the best I can.", + "id": 46 + }, + { + "turn": 47, + "speaker": "A", + "utterance": "I know you are, Augie. Really, I do. I know you meant for this to be special and nice and it's the full moon and the sand and everything. But I just couldn't help thinking about being somewhere else.", + "emotion": "frustrated", + "expanded emotion cause evidence": [ + 47 + ], + "expanded emotion cause span": [ + "But I just couldn't help thinking about being somewhere else." + ], + "type": [ + "no-context" + ], + "text": "I know you are, Augie. Really, I do. I know you meant for this to be special and nice and it's the full moon and the sand and everything. But I just couldn't help thinking about being somewhere else.", + "id": 47 + }, + { + "turn": 48, + "speaker": "A", + "utterance": "I didn't say that.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 47 + ], + "expanded emotion cause span": [ + "But I just couldn't help thinking about being somewhere else." + ], + "type": [ + "self-contagion" + ], + "text": "I didn't say that.", + "id": 48 + }, + { + "turn": 49, + "speaker": "B", + "utterance": "No, I know. But still. I know I don't make you happy.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 49 + ], + "expanded emotion cause span": [ + "I know I don't make you happy." + ], + "type": [ + "no-context" + ], + "text": "No, I know. But still. I know I don't make you happy.", + "id": 49 + }, + { + "turn": 50, + "speaker": "B", + "utterance": "Actually, now that you mention it, no. I don't.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 49 + ], + "expanded emotion cause span": [ + "I know I don't make you happy." + ], + "type": [ + "self-contagion" + ], + "text": "Actually, now that you mention it, no. I don't.", + "id": 50 + }, + { + "turn": 51, + "speaker": "A", + "utterance": "Okay, fine. So we're in the wrong spot, but we're with the right person.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 50, + 51 + ], + "expanded emotion cause span": [ + "Actually, now that you mention it, no. I don't.", + "we're with the right person." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Okay, fine. So we're in the wrong spot, but we're with the right person.", + "id": 51, + "source_sentences": [ + 49 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 52, + "speaker": "B", + "utterance": "I don't know. It seemed like a good spot to me. I mean, look at the view you've got of the moon from here.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 52 + ], + "expanded emotion cause span": [ + "It seemed like a good spot to me. I mean, look at the view you've got of the moon from here." + ], + "type": [ + "no-context" + ], + "text": "I don't know. It seemed like a good spot to me. I mean, look at the view you've got of the moon from here.", + "id": 52 + }, + { + "turn": 53, + "speaker": "A", + "utterance": "Yeah, I noticed that. Looks pretty on the water, doesn't it? Big ol' white moon. I'm sorry, Augie.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 53 + ], + "expanded emotion cause span": [ + "Looks pretty on the water, doesn't it? Big ol' white moon." + ], + "type": [ + "no-context" + ], + "text": "Yeah, I noticed that. Looks pretty on the water, doesn't it? Big ol' white moon. I'm sorry, Augie.", + "id": 53 + }, + { + "turn": 54, + "speaker": "B", + "utterance": "Shh. If we're very quiet, the fish might come.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 51, + 52, + 54 + ], + "expanded emotion cause span": [ + "we're with the right person.", + "It seemed like a good spot to me. I mean, look at the view you've got of the moon from here.", + "the fish might come." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Shh. If we're very quiet, the fish might come.", + "id": 54 + } +] \ No newline at end of file diff --git a/reccon/sources/train.train.Ses01F_script01_3.json b/reccon/sources/train.train.Ses01F_script01_3.json new file mode 100644 index 0000000000000000000000000000000000000000..73a42fe01e86e406c2f225f0077874ee7f33d67b --- /dev/null +++ b/reccon/sources/train.train.Ses01F_script01_3.json @@ -0,0 +1,770 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "You're the only one who still loves his parents.", + "emotion": "neutral", + "text": "You're the only one who still loves his parents.", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I know. It kind of went out of style, didn't it?", + "emotion": "neutral", + "text": "I know. It kind of went out of style, didn't it?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "It's not so bad; it's a good thing.", + "emotion": "neutral", + "text": "It's not so bad; it's a good thing.", + "id": 3 + }, + { + "turn": 4, + "speaker": "A", + "utterance": "[BREATHING] You know, it's lovely here. The air is sweet.", + "emotion": "neutral", + "text": "[BREATHING] You know, it's lovely here. The air is sweet.", + "id": 4 + }, + { + "turn": 5, + "speaker": "B", + "utterance": "You're not sorry you came.", + "emotion": "neutral", + "text": "You're not sorry you came.", + "id": 5 + }, + { + "turn": 6, + "speaker": "A", + "utterance": "I'm not sorry, no. But I'm...I can't stay.", + "emotion": "neutral", + "text": "I'm not sorry, no. But I'm...I can't stay.", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "For one thing, your mother much as told me to go.", + "emotion": "neutral", + "text": "For one thing, your mother much as told me to go.", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Well.", + "emotion": "neutral", + "text": "Well.", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "And then, you. You've been kind of...", + "emotion": "neutral", + "text": "And then, you. You've been kind of...", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "What?", + "emotion": "neutral", + "text": "What?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Sort of embarrassed ever since I got here.", + "emotion": "neutral", + "text": "Sort of embarrassed ever since I got here.", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Well I was kind of planning of sneaking up on you over the course of a week or so. They just take it for granted that we're all set.", + "emotion": "neutral", + "text": "Well I was kind of planning of sneaking up on you over the course of a week or so. They just take it for granted that we're all set.", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I knew they would.", + "emotion": "neutral", + "text": "I knew they would.", + "id": 13 + }, + { + "turn": 14, + "speaker": "A", + "utterance": "Well sure, from your mother's point of view. Why else would I come?", + "emotion": "neutral", + "text": "Well sure, from your mother's point of view. Why else would I come?", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "I, umm. I guess, I guess that's kind of why I came.", + "emotion": "neutral", + "text": "I, umm. I guess, I guess that's kind of why I came.", + "id": 15 + }, + { + "turn": 16, + "speaker": "A", + "utterance": "[BREATHING]", + "emotion": "happy", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "I'm not sorry, no." + ], + "type": [ + "self-contagion" + ], + "text": "[BREATHING]", + "id": 16 + }, + { + "turn": 17, + "speaker": "B", + "utterance": "I love you. Annie, I love you.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 17 + ], + "expanded emotion cause span": [ + "I love you. Annie, I love you." + ], + "type": [ + "no-context" + ], + "text": "I love you. Annie, I love you.", + "id": 17 + }, + { + "turn": 18, + "speaker": "A", + "utterance": "[LAUGHTER]", + "emotion": "happy", + "expanded emotion cause evidence": [ + 17 + ], + "expanded emotion cause span": [ + "I love you. Annie, I love you." + ], + "type": [ + "inter-personal" + ], + "text": "[LAUGHTER]", + "id": 18 + }, + { + "turn": 19, + "speaker": "B", + "utterance": "I don't really have any imagination, that's all I know how to say.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 17 + ], + "expanded emotion cause span": [ + "I love you. Annie, I love you." + ], + "type": [ + "self-contagion" + ], + "text": "I don't really have any imagination, that's all I know how to say.", + "id": 19 + }, + { + "turn": 20, + "speaker": "A", + "utterance": "[LAUGHTER]", + "emotion": "happy", + "expanded emotion cause evidence": [ + 17 + ], + "expanded emotion cause span": [ + "I love you. Annie, I love you." + ], + "type": [ + "inter-personal" + ], + "text": "[LAUGHTER]", + "id": 20 + }, + { + "turn": 21, + "speaker": "B", + "utterance": "Am I embarrassing you? Are you - See, I didn't want to do it here with this yard, on this porch. I wanted it to be somewhere new, some place fresh for both of us.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 17 + ], + "expanded emotion cause span": [ + "I love you. Annie, I love you." + ], + "type": [ + "self-contagion" + ], + "text": "Am I embarrassing you? Are you - See, I didn't want to do it here with this yard, on this porch. I wanted it to be somewhere new, some place fresh for both of us.", + "id": 21 + }, + { + "turn": 22, + "speaker": "A", + "utterance": "No. No", + "emotion": "happy", + "expanded emotion cause evidence": [ + 17 + ], + "expanded emotion cause span": [ + "I love you. Annie, I love you." + ], + "type": [ + "inter-personal" + ], + "text": "No. No", + "id": 22 + }, + { + "turn": 23, + "speaker": "A", + "utterance": "Chris, I've been ready a long, long, time.", + "emotion": "neutral", + "text": "Chris, I've been ready a long, long, time.", + "id": 23 + }, + { + "turn": 24, + "speaker": "A", + "utterance": "I almost got married two years ago.", + "emotion": "neutral", + "text": "I almost got married two years ago.", + "id": 24 + }, + { + "turn": 25, + "speaker": "A", + "utterance": "You started to write me.", + "emotion": "neutral", + "text": "You started to write me.", + "id": 25 + }, + { + "turn": 26, + "speaker": "A", + "utterance": "Every day since.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 23, + 26 + ], + "expanded emotion cause span": [ + "I've been ready a long, long, time", + "Every day since." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Every day since.", + "id": 26 + }, + { + "turn": 27, + "speaker": "B", + "utterance": "Why didn't you let me know?", + "emotion": "happy", + "expanded emotion cause evidence": [ + 23, + 26 + ], + "expanded emotion cause span": [ + "I've been ready a long, long, time", + "Every day since." + ], + "type": [ + "inter-personal" + ], + "text": "Why didn't you let me know?", + "id": 27 + }, + { + "turn": 28, + "speaker": "B", + "utterance": "Give me a...", + "emotion": "happy", + "expanded emotion cause evidence": [ + 23, + 26 + ], + "expanded emotion cause span": [ + "I've been ready a long, long, time", + "Every day since." + ], + "type": [ + "inter-personal" + ], + "text": "Give me a...", + "id": 28 + }, + { + "turn": 29, + "speaker": "B", + "utterance": "Give me a kiss.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 17, + 23, + 26 + ], + "expanded emotion cause span": [ + "I love you. Annie, I love you.", + "I've been ready a long, long, time", + "Every day since." + ], + "type": [ + "hybrid" + ], + "text": "Give me a kiss.", + "id": 29 + }, + { + "turn": 30, + "speaker": "A", + "utterance": "beating around the bush.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 17, + 23, + 26 + ], + "expanded emotion cause span": [ + "I love you. Annie, I love you.", + "I've been ready a long, long, time", + "Every day since." + ], + "type": [ + "hybrid" + ], + "text": "beating around the bush.", + "id": 30 + }, + { + "turn": 31, + "speaker": "A", + "utterance": "I will never forgive you. All I'd done was sit around wondering if I was crazy waiting so long, wondering if you were thinking about me.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 17, + 23, + 26, + 31 + ], + "expanded emotion cause span": [ + "I love you. Annie, I love you.", + "I've been ready a long, long, time", + "Every day since.", + "wondering if you were thinking about me." + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I will never forgive you. All I'd done was sit around wondering if I was crazy waiting so long, wondering if you were thinking about me.", + "id": 31 + }, + { + "turn": 32, + "speaker": "B", + "utterance": "Oh Annie, we are going to live now. I am going to make you so happy.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 32 + ], + "expanded emotion cause span": [ + "I am going to make you so happy." + ], + "type": [ + "no-context" + ], + "text": "Oh Annie, we are going to live now. I am going to make you so happy.", + "id": 32 + }, + { + "turn": 33, + "speaker": "A", + "utterance": "Not like that you're not.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 32 + ], + "expanded emotion cause span": [ + "I am going to make you so happy." + ], + "type": [ + "inter-personal" + ], + "text": "Not like that you're not.", + "id": 33 + }, + { + "turn": 34, + "speaker": "B", + "utterance": "I kissed you.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 34 + ], + "expanded emotion cause span": [ + "I kissed you." + ], + "type": [ + "no-context" + ], + "text": "I kissed you.", + "id": 34 + }, + { + "turn": 35, + "speaker": "A", + "utterance": "Like Larry's brother. Do it like you, Chris.", + "emotion": "neutral", + "text": "Like Larry's brother. Do it like you, Chris.", + "id": 35 + }, + { + "turn": 36, + "speaker": "B", + "utterance": "Hey, let's drive some place. Huh? Let's get out of here.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 33, + 36 + ], + "expanded emotion cause span": [ + "Not like that you're not.", + "Let's get out of here." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Hey, let's drive some place. Huh? Let's get out of here.", + "id": 36 + }, + { + "turn": 37, + "speaker": "B", + "utterance": "No it's nothing like that. It's-", + "emotion": "sad", + "expanded emotion cause evidence": [ + 36 + ], + "expanded emotion cause span": [ + "Let's get out of here." + ], + "type": [ + "self-contagion" + ], + "text": "No it's nothing like that. It's-", + "id": 37 + }, + { + "turn": 38, + "speaker": "B", + "utterance": "Yeah. I suppose I have been. But it's going from me.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 36 + ], + "expanded emotion cause span": [ + "Let's get out of here." + ], + "type": [ + "self-contagion" + ], + "text": "Yeah. I suppose I have been. But it's going from me.", + "id": 38 + }, + { + "turn": 39, + "speaker": "B", + "utterance": "I don't even know how to start.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 36, + 39 + ], + "expanded emotion cause span": [ + "Let's get out of here.", + "I don't even know how to start." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I don't even know how to start.", + "id": 39 + }, + { + "turn": 40, + "speaker": "B", + "utterance": "It's just all mixed up with so many other things, you know? You know overseas I was in command of a company?", + "emotion": "sad", + "expanded emotion cause evidence": [ + 39, + 40, + 40 + ], + "expanded emotion cause span": [ + "I don't even know how to start.", + "all mixed up with so many other things", + "overseas I was in command of a company" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "It's just all mixed up with so many other things, you know? You know overseas I was in command of a company?", + "id": 40 + }, + { + "turn": 41, + "speaker": "A", + "utterance": "Yeah, sure.", + "emotion": "neutral", + "text": "Yeah, sure.", + "id": 41 + }, + { + "turn": 42, + "speaker": "B", + "utterance": "Well I lost them.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 40, + 42 + ], + "expanded emotion cause span": [ + "overseas I was in command of a company", + "I lost them." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Well I lost them.", + "id": 42 + }, + { + "turn": 43, + "speaker": "A", + "utterance": "How many?", + "emotion": "neutral", + "text": "How many?", + "id": 43 + }, + { + "turn": 44, + "speaker": "B", + "utterance": "Pretty much all.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 42 + ], + "expanded emotion cause span": [ + "I lost them." + ], + "type": [ + "self-contagion" + ], + "text": "Pretty much all.", + "id": 44 + }, + { + "turn": 45, + "speaker": "A", + "utterance": "Aw, geez.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 42, + 44 + ], + "expanded emotion cause span": [ + "I lost them.", + "Pretty much all." + ], + "type": [ + "inter-personal" + ], + "text": "Aw, geez.", + "id": 45 + }, + { + "turn": 46, + "speaker": "B", + "utterance": "You can't just toss off a thing like that because they weren't just men. You know?", + "emotion": "sad", + "expanded emotion cause evidence": [ + 46 + ], + "expanded emotion cause span": [ + "You can't just toss off a thing like that" + ], + "type": [ + "no-context" + ], + "text": "You can't just toss off a thing like that because they weren't just men. You know?", + "id": 46 + }, + { + "turn": 47, + "speaker": "B", + "utterance": "Like for instance, there was this one time it had been raining for several days and this kid he just came up to me and he gave me his last pair of dry socks. He just put them in my pocket. That's a little thing, you know, but that's what kind of guys I had.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 46, + 47 + ], + "expanded emotion cause span": [ + "You can't just toss off a thing like that", + "That's a little thing, you know, but that's what kind of guys I had." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Like for instance, there was this one time it had been raining for several days and this kid he just came up to me and he gave me his last pair of dry socks. He just put them in my pocket. That's a little thing, you know, but that's what kind of guys I had.", + "id": 47 + }, + { + "turn": 48, + "speaker": "B", + "utterance": "They didn't die, they killed themselves for each other. I mean that, exactly. Just a little more selfish and they would all be here today.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 48, + 48 + ], + "expanded emotion cause span": [ + "They didn't die, they killed themselves for each other", + "they would all be here today." + ], + "type": [ + "no-context" + ], + "text": "They didn't die, they killed themselves for each other. I mean that, exactly. Just a little more selfish and they would all be here today.", + "id": 48 + }, + { + "turn": 49, + "speaker": "A", + "utterance": "Mmhmm.", + "emotion": "neutral", + "text": "Mmhmm.", + "id": 49 + }, + { + "turn": 50, + "speaker": "B", + "utterance": "To bring that on to the earth again, you know, is like some kind of monument and I thought I would just make a difference to them.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 50 + ], + "expanded emotion cause span": [ + "I thought I would just make a difference to them." + ], + "type": [ + "no-context" + ], + "text": "To bring that on to the earth again, you know, is like some kind of monument and I thought I would just make a difference to them.", + "id": 50 + }, + { + "turn": 51, + "speaker": "B", + "utterance": "But then I came home and it was incredible, you know? The whole thing was just kind of this random bus accident. You know, I went back to the rat race again, I went to work.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 50, + 51 + ], + "expanded emotion cause span": [ + "I thought I would just make a difference to them.", + "I went back to the rat race again, I went to work." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "But then I came home and it was incredible, you know? The whole thing was just kind of this random bus accident. You know, I went back to the rat race again, I went to work.", + "id": 51 + }, + { + "turn": 52, + "speaker": "B", + "utterance": "And I didn't want any of it. I guess that included you.", + "emotion": "sad", + "expanded emotion cause evidence": [ + 51, + 52 + ], + "expanded emotion cause span": [ + "I went back to the rat race again, I went to work.", + "And I didn't want any of it." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "And I didn't want any of it. I guess that included you.", + "id": 52 + }, + { + "turn": 53, + "speaker": "B", + "utterance": "I just want you to know Annie.", + "emotion": "neutral", + "text": "I just want you to know Annie.", + "id": 53 + }, + { + "turn": 54, + "speaker": "A", + "utterance": "What would I do with a fortune?", + "emotion": "happy", + "expanded emotion cause evidence": [ + 53, + 54 + ], + "expanded emotion cause span": [ + "I just want you to know Annie.", + "What would I do with a fortune?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "What would I do with a fortune?", + "id": 54, + "source_sentences": [ + 52 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/train.train.Ses01F_script03_1.json b/reccon/sources/train.train.Ses01F_script03_1.json new file mode 100644 index 0000000000000000000000000000000000000000..10bbe00ac170f24ec2da6e7a514aff1957074806 --- /dev/null +++ b/reccon/sources/train.train.Ses01F_script03_1.json @@ -0,0 +1,377 @@ +[ + { + "turn": 1, + "speaker": "B", + "utterance": "I don't care then.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I don't care then." + ], + "type": [ + "no-context" + ], + "text": "I don't care then.", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "No. Wrong number. [LAUGHTER]", + "emotion": "happy", + "expanded emotion cause evidence": [ + "b", + 2 + ], + "expanded emotion cause span": [ + "b", + "No. Wrong number. [LAUGHTER]" + ], + "type": [ + "latent", + "no-context" + ], + "text": "No. Wrong number. [LAUGHTER]", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "[LAUGHTER] That sent shivers up my spine.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I don't care then." + ], + "type": [ + "inter-personal" + ], + "text": "[LAUGHTER] That sent shivers up my spine.", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "What shall we do if they suddenly walk in on us.[LAUGHTER]", + "emotion": "happy", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "What shall we do if they suddenly walk in on us.[LAUGHTER]", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "We'll behave exquisitely.", + "emotion": "excited", + "text": "We'll behave exquisitely.", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "With perfect poise.", + "emotion": "happy", + "text": "With perfect poise.", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I think I shall do a curtsy.", + "emotion": "excited", + "text": "I think I shall do a curtsy.", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "It's strange; things that ought to matter dreadfully, they just don't matter at all when one's happy. Do they?", + "emotion": "happy", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "things that ought to matter dreadfully, they just don't matter at all when one's happy." + ], + "type": [ + "no-context" + ], + "text": "It's strange; things that ought to matter dreadfully, they just don't matter at all when one's happy. Do they?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Yes. Meaning just that.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "things that ought to matter dreadfully, they just don't matter at all when one's happy.", + "Yes. Meaning just that." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Yes. Meaning just that.", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Well what does it all mean? That's what I ask myself in my quest for ultimate truth. Dear God, what does it all mean?", + "emotion": "happy", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "things that ought to matter dreadfully, they just don't matter at all when one's happy." + ], + "type": [ + "self-contagion" + ], + "text": "Well what does it all mean? That's what I ask myself in my quest for ultimate truth. Dear God, what does it all mean?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Don't laugh at me. I'm being serious.", + "emotion": "happy", + "text": "Don't laugh at me. I'm being serious.", + "id": 11 + }, + { + "turn": 12, + "speaker": "A", + "utterance": "Who's they?", + "emotion": "excited", + "text": "Who's they?", + "id": 12 + }, + { + "turn": 13, + "speaker": "B", + "utterance": "Who knows?", + "emotion": "happy", + "text": "Who knows?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Yes. Yes with all of his might.", + "emotion": "excited", + "text": "Yes. Yes with all of his might.", + "id": 14 + }, + { + "turn": 15, + "speaker": "B", + "utterance": "Let's be superficial, and just pity those poor philosophers, huh? Let's blow trumpets and squeakers and enjoy the party for as long as we can, you know, like small, idiotic school children.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "Let's blow trumpets and squeakers and enjoy the party for as long as we can" + ], + "type": [ + "no-context" + ], + "text": "Let's be superficial, and just pity those poor philosophers, huh? Let's blow trumpets and squeakers and enjoy the party for as long as we can, you know, like small, idiotic school children.", + "id": 15 + }, + { + "turn": 16, + "speaker": "A", + "utterance": "[LAUGHTER]", + "emotion": "happy", + "text": "[LAUGHTER]", + "id": 16 + }, + { + "turn": 17, + "speaker": "B", + "utterance": "Oh Come and kiss me darling before your body rots and worms pop out of your eye sockets.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 17 + ], + "expanded emotion cause span": [ + "Oh Come and kiss me darling" + ], + "type": [ + "no-context" + ], + "text": "Oh Come and kiss me darling before your body rots and worms pop out of your eye sockets.", + "id": 17 + }, + { + "turn": 18, + "speaker": "A", + "utterance": "Oh Elliott, worms don't pop.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 17 + ], + "expanded emotion cause span": [ + "kiss me darling before your body rots and worms pop out of your eye sockets" + ], + "type": [ + "inter-personal" + ], + "text": "Oh Elliott, worms don't pop.", + "id": 18 + }, + { + "turn": 19, + "speaker": "B", + "utterance": "Oh See, I don't care what you do, see. You can paint yourself green and run naked through the Place Vendome and run off with all of the men of the world. I shan't say a word, just as long as you love me best.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 19 + ], + "expanded emotion cause span": [ + "Oh See, I don't care what you do, see." + ], + "type": [ + "no-context" + ], + "text": "Oh See, I don't care what you do, see. You can paint yourself green and run naked through the Place Vendome and run off with all of the men of the world. I shan't say a word, just as long as you love me best.", + "id": 19 + }, + { + "turn": 20, + "speaker": "A", + "utterance": "Aw. Thank you, darling. The same applies to you too, except that if you so much as look at another woman I'll kill you.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 20 + ], + "expanded emotion cause span": [ + "Aw. Thank you, darling." + ], + "type": [ + "no-context" + ], + "text": "Aw. Thank you, darling. The same applies to you too, except that if you so much as look at another woman I'll kill you.", + "id": 20 + }, + { + "turn": 21, + "speaker": "A", + "utterance": "Oh Charles, that was his name. He did wiggle so beautifully.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 20, + 21 + ], + "expanded emotion cause span": [ + "if you so much as look at another woman I'll kill you.", + "Oh Charles, that was his name. He did wiggle so beautifully." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Oh Charles, that was his name. He did wiggle so beautifully.", + "id": 21 + }, + { + "turn": 22, + "speaker": "B", + "utterance": "That was a rouser, wasn't it?", + "emotion": "happy", + "text": "That was a rouser, wasn't it?", + "id": 22 + }, + { + "turn": 23, + "speaker": "A", + "utterance": "The manager came in, he found us rolling about the floor, biting and scratching like panthers. [LAUGHTER] How utterly, utterly ridiculous.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 23 + ], + "expanded emotion cause span": [ + "The manager came in, he found us rolling about the floor, biting and scratching like panthers. [LAUGHTER] How utterly, utterly ridiculous." + ], + "type": [ + "no-context" + ], + "text": "The manager came in, he found us rolling about the floor, biting and scratching like panthers. [LAUGHTER] How utterly, utterly ridiculous.", + "id": 23 + }, + { + "turn": 24, + "speaker": "B", + "utterance": "[LAUGHTER] I'll never forget his face. [LAUGHTER]", + "emotion": "happy", + "expanded emotion cause evidence": [ + 23 + ], + "expanded emotion cause span": [ + "The manager came in, he found us rolling about the floor, biting and scratching like panthers. [LAUGHTER] How utterly, utterly ridiculous." + ], + "type": [ + "inter-personal" + ], + "text": "[LAUGHTER] I'll never forget his face. [LAUGHTER]", + "id": 24 + }, + { + "turn": 25, + "speaker": "B", + "utterance": "[LAUGHTER] We were very much younger then.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 23 + ], + "expanded emotion cause span": [ + "The manager came in, he found us rolling about the floor, biting and scratching like panthers. [LAUGHTER] How utterly, utterly ridiculous." + ], + "type": [ + "inter-personal" + ], + "text": "[LAUGHTER] We were very much younger then.", + "id": 25, + "source_sentences": [ + 22 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 26, + "speaker": "A", + "utterance": "[LAUGHTER] And very much sillier.", + "emotion": "happy", + "expanded emotion cause evidence": [ + 23 + ], + "expanded emotion cause span": [ + "The manager came in, he found us rolling about the floor, biting and scratching like panthers. [LAUGHTER] How utterly, utterly ridiculous." + ], + "type": [ + "self-contagion" + ], + "text": "[LAUGHTER] And very much sillier.", + "id": 26 + } +] \ No newline at end of file diff --git a/reccon/sources/va_101.json b/reccon/sources/va_101.json new file mode 100644 index 0000000000000000000000000000000000000000..b747330d5840eb5c1b839633c00c915c4d9cf5f5 --- /dev/null +++ b/reccon/sources/va_101.json @@ -0,0 +1,121 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Am I ever hungry ? When will supper be ready ?", + "emotion": "neutral", + "text": "Am I ever hungry ? When will supper be ready ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It's almost ready . Can you set the table ?", + "emotion": "neutral", + "text": "It's almost ready . Can you set the table ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "All right .", + "emotion": "neutral", + "text": "All right .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Want to taste this dish ?", + "emotion": "neutral", + "text": "Want to taste this dish ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Yeah . Oh , it's delicious !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "it's delicious !" + ], + "type": [ + "no-context" + ], + "text": "Yeah . Oh , it's delicious !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Really ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "it's delicious !" + ], + "type": [ + "inter-personal" + ], + "text": "Really ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Definitely . It's a wonderful meal . Thank you , Honey .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 7 + ], + "expanded emotion cause span": [ + "it's delicious !", + "It's a wonderful meal ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Definitely . It's a wonderful meal . Thank you , Honey .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "If you like to help me do the dishes , I'll be more dreadful .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 7 + ], + "expanded emotion cause span": [ + "it's delicious !", + "It's a wonderful meal . Thank you ," + ], + "type": [ + "inter-personal" + ], + "text": "If you like to help me do the dishes , I'll be more dreadful .", + "id": 8, + "source_sentences": [ + 4, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I wish I could , but I won't .", + "emotion": "neutral", + "text": "I wish I could , but I won't .", + "id": 9 + } +] \ No newline at end of file diff --git a/reccon/sources/va_184.json b/reccon/sources/va_184.json new file mode 100644 index 0000000000000000000000000000000000000000..d7c295efe079d60fd53502128ebd946bdb55a0e4 --- /dev/null +++ b/reccon/sources/va_184.json @@ -0,0 +1,182 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hello , ma ' am . Can I help you ?", + "emotion": "neutral", + "text": "Hello , ma ' am . Can I help you ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I ' m looking for a sweater .", + "emotion": "neutral", + "text": "I ' m looking for a sweater .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What size are you looking for ?", + "emotion": "neutral", + "text": "What size are you looking for ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Well , I ' m looking for size 10 but you don ' t have it .", + "emotion": "neutral", + "text": "Well , I ' m looking for size 10 but you don ' t have it .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "How about this one ? I think it looks terrific on you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "it looks terrific" + ], + "type": [ + "no-context" + ], + "text": "How about this one ? I think it looks terrific on you .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Yes , I like the color . Can I try it on ?", + "emotion": "neutral", + "text": "Yes , I like the color . Can I try it on ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Sure . The fitting room is on your right .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "it looks terrific", + "I like the color ." + ], + "type": [ + "hybrid" + ], + "text": "Sure . The fitting room is on your right .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "It fits well . I like it a lot . What do you think ?", + "emotion": "neutral", + "text": "It fits well . I like it a lot . What do you think ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "You look pretty in red .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6, + 8, + 9 + ], + "expanded emotion cause span": [ + "it looks terrific", + "I like the color .", + "It fits well . I like it a lot .", + "You look pretty" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "You look pretty in red .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Oh , it ' s my favorite . How much is it ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "You look pretty in red .", + "it ' s my favorite ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , it ' s my favorite . How much is it ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "$ 29 . 99 .", + "emotion": "neutral", + "text": "$ 29 . 99 .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Okay . I ' ll take it . Thank you very much for your help .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9, + 10, + 12 + ], + "expanded emotion cause span": [ + "You look pretty in red .", + "it ' s my favorite .", + "Thank you" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "Okay . I ' ll take it . Thank you very much for your help .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "You ' re welcome .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "I ' ll take it . Thank you" + ], + "type": [ + "inter-personal" + ], + "text": "You ' re welcome .", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/va_201.json b/reccon/sources/va_201.json new file mode 100644 index 0000000000000000000000000000000000000000..41b2b7ac00f9c4ee616dd80500d1e45bca2bdb2a --- /dev/null +++ b/reccon/sources/va_201.json @@ -0,0 +1,93 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Good morning .", + "emotion": "neutral", + "text": "Good morning .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Good morning . This is Mary . Can I speak to Anne please ?", + "emotion": "neutral", + "text": "Good morning . This is Mary . Can I speak to Anne please ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I ' m sorry She isn ' t in at the momment . She will come back at half past nineCan I take a message for her ?", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "She isn ' t in at the momment ." + ], + "type": [ + "no-context" + ], + "text": "I ' m sorry She isn ' t in at the momment . She will come back at half past nineCan I take a message for her ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Thank you . But I will call her later", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Can I take a message for her ?" + ], + "type": [ + "inter-personal" + ], + "text": "Thank you . But I will call her later", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "OK . Goodbye .", + "emotion": "happiness", + "explanation": "Sharing pleasantries.", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Thank you ." + ], + "type": [ + "inter-personal" + ], + "text": "OK . Goodbye .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Goodbye .", + "emotion": "happiness", + "explanation": "Sharing pleasantries.", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "Goodbye ." + ], + "type": [ + "inter-personal" + ], + "text": "Goodbye .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/va_227.json b/reccon/sources/va_227.json new file mode 100644 index 0000000000000000000000000000000000000000..a531fe1b56f1f2288365a61b80625b8cc5f49c0a --- /dev/null +++ b/reccon/sources/va_227.json @@ -0,0 +1,130 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "My name is Mary , and I will be your waitress tonight .", + "emotion": "neutral", + "text": "My name is Mary , and I will be your waitress tonight .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Thank you , Mary . We have been looking forward to trying out this restaurant .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "I will be your waitress tonight .", + "We have been looking forward to trying out this restaurant ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Thank you , Mary . We have been looking forward to trying out this restaurant .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Before your main course , would you like to order an appetizer ?", + "emotion": "neutral", + "text": "Before your main course , would you like to order an appetizer ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Sure , that sounds great . Where are your appetizers listed ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 3 + ], + "expanded emotion cause span": [ + "I will be your waitress tonight .", + "We have been looking forward to trying out this restaurant .", + "would you like to order an appetizer ?" + ], + "type": [ + "hybrid" + ], + "text": "Sure , that sounds great . Where are your appetizers listed ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "There is a special appetizer menu right here in the center of the table .", + "emotion": "neutral", + "text": "There is a special appetizer menu right here in the center of the table .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "The chicken and cheese quesadilla looks good . Is that pretty good ?", + "emotion": "neutral", + "text": "The chicken and cheese quesadilla looks good . Is that pretty good ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You know , that is one of my favorites !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "that is one of my favorites !" + ], + "type": [ + "no-context" + ], + "text": "You know , that is one of my favorites !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "OK , I'll take one order of that .", + "emotion": "neutral", + "text": "OK , I'll take one order of that .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "You could choose another appetizer for half price to share .", + "emotion": "neutral", + "text": "You could choose another appetizer for half price to share .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Perfect ! Please add on an order of onion rings .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "another appetizer for half price" + ], + "type": [ + "inter-personal" + ], + "text": "Perfect ! Please add on an order of onion rings .", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/va_330.json b/reccon/sources/va_330.json new file mode 100644 index 0000000000000000000000000000000000000000..d17e3e3e6c4ec2ca20e925443d6236b7a6fec356 --- /dev/null +++ b/reccon/sources/va_330.json @@ -0,0 +1,144 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hey ! I just bought one of those new Japanese cell phones ! It's loaded with extras .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "It's loaded with extras ." + ], + "type": [ + "no-context" + ], + "text": "Hey ! I just bought one of those new Japanese cell phones ! It's loaded with extras .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What does it do ?", + "emotion": "neutral", + "text": "What does it do ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "It's got a built-in video camera so you can see the person you're talking to . It also takes stills and I can use the E-mail mode to send digital pictures straight to my friend's phone !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "It's loaded with extras .", + "It's got a built-in video camera so you can see the person you're talking to . It also takes stills and I can use the E-mail mode to send digital pictures straight to my friend's phone !" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "It's got a built-in video camera so you can see the person you're talking to . It also takes stills and I can use the E-mail mode to send digital pictures straight to my friend's phone !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Wow ! What else does it do ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "It's got a built-in video camera so you can see the person you're talking to . It also takes stills and I can use the E-mail mode to send digital pictures straight to my friend's phone !" + ], + "type": [ + "inter-personal" + ], + "text": "Wow ! What else does it do ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I can plug it into a folding keyboard to type in message mode . l can even surf the net .", + "emotion": "neutral", + "text": "I can plug it into a folding keyboard to type in message mode . l can even surf the net .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Cool ! Anything else ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 5 + ], + "expanded emotion cause span": [ + "It's got a built-in video camera so you can see the person you're talking to . It also takes stills and I can use the E-mail mode to send digital pictures straight to my friend's phone !", + "I can plug it into a folding keyboard to type in message mode . l can even surf the net ." + ], + "type": [ + "inter-personal" + ], + "text": "Cool ! Anything else ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Yes . With the 600 - second digital memory , l can record my voice and send it using voice message mode .", + "emotion": "neutral", + "text": "Yes . With the 600 - second digital memory , l can record my voice and send it using voice message mode .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Wow !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 5, + 7 + ], + "expanded emotion cause span": [ + "It's got a built-in video camera so you can see the person you're talking to . It also takes stills and I can use the E-mail mode to send digital pictures straight to my friend's phone !", + "I can plug it into a folding keyboard to type in message mode . l can even surf the net .", + "Yes . With the 600 - second digital memory , l can record my voice and send it using voice message mode ." + ], + "type": [ + "inter-personal" + ], + "text": "Wow !", + "id": 8, + "source_sentences": [ + 2, + 4, + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "You'll love this ! I can use a stylus to draw a map on the touch screen and then use the fax mode to send it to another phone .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "You'll love this !" + ], + "type": [ + "no-context" + ], + "text": "You'll love this ! I can use a stylus to draw a map on the touch screen and then use the fax mode to send it to another phone .", + "id": 9 + } +] \ No newline at end of file diff --git a/reccon/sources/va_345.json b/reccon/sources/va_345.json new file mode 100644 index 0000000000000000000000000000000000000000..d9f89c6d83d172b43c3beaa43d6b49090783372f --- /dev/null +++ b/reccon/sources/va_345.json @@ -0,0 +1,138 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I can't stand the stupid guy any longer . It ' s unbelievable !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I can't stand the stupid guy any longer ." + ], + "type": [ + "no-context" + ], + "text": "I can't stand the stupid guy any longer . It ' s unbelievable !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Oh , my dear lady . Take it easy . You should forgive a green hand like him .", + "emotion": "neutral", + "text": "Oh , my dear lady . Take it easy . You should forgive a green hand like him .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "He does everything so mindlessly that he is going to drive me crazy .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "I can't stand the stupid guy any longer .", + "He does everything so mindlessly" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "He does everything so mindlessly that he is going to drive me crazy .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I suggest you talk with him and teach him how to deal with the problems .", + "emotion": "neutral", + "text": "I suggest you talk with him and teach him how to deal with the problems .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I have told him how to do it several times , but he's never listened to me .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I have told him how to do it several times , but he's never listened to me ." + ], + "type": [ + "no-context" + ], + "text": "I have told him how to do it several times , but he's never listened to me .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Maybe you should communicate with him just like a friend and not a boss .", + "emotion": "neutral", + "text": "Maybe you should communicate with him just like a friend and not a boss .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Oh , I always have difficulty in getting along with the staff .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Oh , I always have difficulty in getting along with the staff ." + ], + "type": [ + "no-context" + ], + "text": "Oh , I always have difficulty in getting along with the staff .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Just take them for your good friends and have a talk with them as we do , make sure you don't lose your temper .", + "emotion": "neutral", + "text": "Just take them for your good friends and have a talk with them as we do , make sure you don't lose your temper .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I think that's a bad idea . I'd hate anyone here to think of me as a friend . How would they ever respect me as they can do whatever they want ?", + "emotion": "disgust", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "Just take them for your good friends", + "I'd hate anyone here to think of me as a friend . How would they ever respect me as they can do whatever they want ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I think that's a bad idea . I'd hate anyone here to think of me as a friend . How would they ever respect me as they can do whatever they want ?", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I disagree . All you have to do is respect the staff and their opinions .", + "emotion": "neutral", + "text": "I disagree . All you have to do is respect the staff and their opinions .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/va_371.json b/reccon/sources/va_371.json new file mode 100644 index 0000000000000000000000000000000000000000..e4529ce048128d03e20037bbc37ec6e2c3f676b5 --- /dev/null +++ b/reccon/sources/va_371.json @@ -0,0 +1,208 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Ahem ... uh , sir , I beg your pardon ... Uh , mister , are you waiting to buy a ticket for the movie ?", + "emotion": "neutral", + "text": "Ahem ... uh , sir , I beg your pardon ... Uh , mister , are you waiting to buy a ticket for the movie ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What's it look like , lady ? This is the ticket line I'm standing in , isn't it ?", + "emotion": "neutral", + "text": "What's it look like , lady ? This is the ticket line I'm standing in , isn't it ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Well , yes , it is , but ...", + "emotion": "neutral", + "text": "Well , yes , it is , but ...", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "So , what's your beef anyway , lady ?", + "emotion": "neutral", + "text": "So , what's your beef anyway , lady ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "You just cut into line , in front of me and everyone else , that's what ! Go take your place back at the end of the line , like every - one else !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "You just cut into line , in front of me and everyone else" + ], + "type": [ + "no-context" + ], + "text": "You just cut into line , in front of me and everyone else , that's what ! Go take your place back at the end of the line , like every - one else !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Oh sure , lady , and fat chance I'd get a ticket before they're sold out . I'm staying right here , understand ? So be a nice lady and butt out !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Go take your place back at the end of the line , like every - one else !", + "fat chance I'd get a ticket before they're sold out . I'm staying right here , understand ? So be a nice lady and butt out !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh sure , lady , and fat chance I'd get a ticket before they're sold out . I'm staying right here , understand ? So be a nice lady and butt out !", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Just what gives you the right ... ?", + "emotion": "anger", + "expanded emotion cause evidence": [ + 5, + 5, + 6 + ], + "expanded emotion cause span": [ + "You just cut into line , in front of me and everyone else", + "Go take your place back at the end of the line , like every - one else !", + "I'm staying right here , understand ? So be a nice lady and butt out !" + ], + "type": [ + "hybrid" + ], + "text": "Just what gives you the right ... ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Because I'm no sucker ; only suckers go to the end of the line . It's as simple as that , lady .", + "emotion": "anger", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "Because I'm no sucker ; only suckers go to the end of the line ." + ], + "type": [ + "no-context" + ], + "text": "Because I'm no sucker ; only suckers go to the end of the line . It's as simple as that , lady .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Well , you're no gentleman , either .", + "emotion": "neutral", + "text": "Well , you're no gentleman , either .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Okay , lady , just to show what a gentleman I really am , I'll let you go in front of me . Now , just buy your ticket and shut your trap , will you , lady ?", + "emotion": "neutral", + "text": "Okay , lady , just to show what a gentleman I really am , I'll let you go in front of me . Now , just buy your ticket and shut your trap , will you , lady ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Whew ! I got the last one . This must be my lucky day !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "Whew ! I got the last one ." + ], + "type": [ + "no-context" + ], + "text": "Whew ! I got the last one . This must be my lucky day !", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "What was that you just said ? Last one ... ? Hey , they've closed the ticket window !", + "emotion": "neutral", + "text": "What was that you just said ? Last one ... ? Hey , they've closed the ticket window !", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Yes , I'm afraid I bought the last ticket , and to think , if you hadn't been such a gentleman . . .", + "emotion": "neutral", + "text": "Yes , I'm afraid I bought the last ticket , and to think , if you hadn't been such a gentleman . . .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Lady ! This is unfair ! I've been cheated ! I was in line before you . That should have been my ticket ! Come on , hand it over , lady !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 13, + 14 + ], + "expanded emotion cause span": [ + "I bought the last ticket ,", + "Lady ! This is unfair ! I've been cheated ! I was in line before you . That should have been my ticket !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Lady ! This is unfair ! I've been cheated ! I was in line before you . That should have been my ticket ! Come on , hand it over , lady !", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Gentleman ! Hah ! Fat chance ! Hah ! Eat your heart out , sucker ! Hah !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 5, + 5, + 6, + 13, + 14 + ], + "expanded emotion cause span": [ + "You just cut into line , in front of me and everyone else", + "Go take your place back at the end of the line , like every - one else !", + "I'm staying right here , understand ? So be a nice lady and butt out !", + "I bought the last ticket ,", + "Lady ! This is unfair ! I've been cheated ! I was in line before you . That should have been my ticket !" + ], + "type": [ + "hybrid" + ], + "text": "Gentleman ! Hah ! Fat chance ! Hah ! Eat your heart out , sucker ! Hah !", + "id": 15 + } +] \ No newline at end of file diff --git a/reccon/sources/va_410.json b/reccon/sources/va_410.json new file mode 100644 index 0000000000000000000000000000000000000000..6fb95c2c725f65cfd7dff813df69d867b5f1cd2c --- /dev/null +++ b/reccon/sources/va_410.json @@ -0,0 +1,156 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What time is it ?", + "emotion": "neutral", + "text": "What time is it ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Ten to nine .", + "emotion": "neutral", + "text": "Ten to nine .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Your watch is ten minutes slow . So it's should be nine sharp . I'm gonna be late again . What will be my excuse this time ? It should be set the alarm for seven thirty .", + "emotion": "neutral", + "text": "Your watch is ten minutes slow . So it's should be nine sharp . I'm gonna be late again . What will be my excuse this time ? It should be set the alarm for seven thirty .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Don't cry over spilled milk , Fred ? Could you stay with me a few minutes ?", + "emotion": "neutral", + "text": "Don't cry over spilled milk , Fred ? Could you stay with me a few minutes ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "What ? Why ? What's wrong with you ?", + "emotion": "neutral", + "text": "What ? Why ? What's wrong with you ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I just hate being alone at home with nothing to do about listen to the clock ticking . It ' s so lonely and boring . My sickness makes it worse . When will I recover ?", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "being alone at home with nothing to do about listen to the clock ticking . It ' s so lonely and boring . My sickness makes it worse ." + ], + "type": [ + "no-context" + ], + "text": "I just hate being alone at home with nothing to do about listen to the clock ticking . It ' s so lonely and boring . My sickness makes it worse . When will I recover ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You will be fine in the couple of month , just be patient . I've got to woke now , I'll be late .", + "emotion": "neutral", + "text": "You will be fine in the couple of month , just be patient . I've got to woke now , I'll be late .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "You only care about your work .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "You only care about your work ." + ], + "type": [ + "no-context" + ], + "text": "You only care about your work .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Sorry , baby , you are everything to me . all I do just for our family .", + "emotion": "neutral", + "text": "Sorry , baby , you are everything to me . all I do just for our family .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Stay just a few minutes longer , OK ?", + "emotion": "neutral", + "text": "Stay just a few minutes longer , OK ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "OK , I'll leave at 9:15 , Is that all right ?", + "emotion": "neutral", + "text": "OK , I'll leave at 9:15 , Is that all right ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Yes .", + "emotion": "happiness", + "explanation": "speaker is happy that the listener will stay longer", + "expanded emotion cause evidence": [ + 11 + ], + "expanded emotion cause span": [ + "I'll leave at 9:15 ," + ], + "type": [ + "inter-personal" + ], + "text": "Yes .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "I'll spent more time with you in the future , Dina .", + "emotion": "neutral", + "text": "I'll spent more time with you in the future , Dina .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Thank you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "I'll spent more time with you in the future ," + ], + "type": [ + "inter-personal" + ], + "text": "Thank you .", + "id": 14, + "source_sentences": [ + 12 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/va_428.json b/reccon/sources/va_428.json new file mode 100644 index 0000000000000000000000000000000000000000..4650cea75c94d81d8e8f864db6a3dd383a520c67 --- /dev/null +++ b/reccon/sources/va_428.json @@ -0,0 +1,184 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I am a student in Cambridge University . I read your ad , I want to know something more about your room , please ?", + "emotion": "neutral", + "text": "I am a student in Cambridge University . I read your ad , I want to know something more about your room , please ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It's a big bedroom with a drawing room , facing a beautiful wood .", + "emotion": "neutral", + "text": "It's a big bedroom with a drawing room , facing a beautiful wood .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Is there a bathroom ?", + "emotion": "neutral", + "text": "Is there a bathroom ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "No , but there is one downstairs , which my daughter used some years ago .", + "emotion": "neutral", + "text": "No , but there is one downstairs , which my daughter used some years ago .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "It sounds good . Could I go and see it myself ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 2, + 4 + ], + "expanded emotion cause span": [ + "It's a big bedroom with a drawing room , facing a beautiful wood .", + "No , but there is one downstairs , which my daughter used some years ago ." + ], + "type": [ + "inter-personal" + ], + "text": "It sounds good . Could I go and see it myself ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Certainly , you're welcome anytime .", + "emotion": "neutral", + "text": "Certainly , you're welcome anytime .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "See you later !", + "emotion": "neutral", + "text": "See you later !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "( after a while ) Good afternoon , Mrs . Smith . I called you just now .", + "emotion": "neutral", + "text": "( after a while ) Good afternoon , Mrs . Smith . I called you just now .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Welcome ! Come in , please !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8 + ], + "expanded emotion cause span": [ + "I called you just now" + ], + "type": [ + "inter-personal" + ], + "text": "Welcome ! Come in , please !", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Yes .", + "emotion": "neutral", + "text": "Yes .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "This way please . Your room is upstairs ... Here it is .", + "emotion": "neutral", + "text": "This way please . Your room is upstairs ... Here it is .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Wonderful ! A modest , comfortable room . Ah , a beautiful window , through which I can see a beautiful scene , and hear the birds singing . How nice !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12 + ], + "expanded emotion cause span": [ + "A modest , comfortable room . Ah , a beautiful window , through which I can see a beautiful scene , and hear the birds singing ." + ], + "type": [ + "no-context" + ], + "text": "Wonderful ! A modest , comfortable room . Ah , a beautiful window , through which I can see a beautiful scene , and hear the birds singing . How nice !", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Yes , if you want to wash something , there is a separate lavatory room outside .", + "emotion": "neutral", + "text": "Yes , if you want to wash something , there is a separate lavatory room outside .", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Excellent ! I like it ! When can I move in ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 12, + 13 + ], + "expanded emotion cause span": [ + "A modest , comfortable room . Ah , a beautiful window , through which I can see a beautiful scene , and hear the birds singing .", + "Yes , if you want to wash something , there is a separate lavatory room outside ." + ], + "type": [ + "hybrid" + ], + "text": "Excellent ! I like it ! When can I move in ?", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Anytime you like .", + "emotion": "neutral", + "text": "Anytime you like .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "OK .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 15 + ], + "expanded emotion cause span": [ + "Anytime you like ." + ], + "type": [ + "inter-personal" + ], + "text": "OK .", + "id": 16, + "source_sentences": [ + 14 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/va_491.json b/reccon/sources/va_491.json new file mode 100644 index 0000000000000000000000000000000000000000..fab759420cbc5296ebed46394b203b3b86690fd8 --- /dev/null +++ b/reccon/sources/va_491.json @@ -0,0 +1,157 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I think that you look very cute today .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "you look very cute" + ], + "type": [ + "no-context" + ], + "text": "I think that you look very cute today .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Is that right ? This is a brand new outfit .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "you look very cute today .", + "This is a brand new" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Is that right ? This is a brand new outfit .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What store did you get it from ?", + "emotion": "neutral", + "text": "What store did you get it from ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I went to Macy's and picked it out .", + "emotion": "neutral", + "text": "I went to Macy's and picked it out .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I love your outfit right now .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 5 + ], + "expanded emotion cause span": [ + "you look very cute", + "I love your outfit" + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I love your outfit right now .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Well , I think you look nice today too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "I love your outfit", + "you look nice today too ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Well , I think you look nice today too .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Thanks . I found these new shoes earlier at the store .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "you look nice today too ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks . I found these new shoes earlier at the store .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I think that those are some really nice shoes . What kind are they ?", + "emotion": "neutral", + "text": "I think that those are some really nice shoes . What kind are they ?", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "These are Chucks .", + "emotion": "neutral", + "text": "These are Chucks .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Your shoes look really nice . How much did you get them for ?", + "emotion": "neutral", + "text": "Your shoes look really nice . How much did you get them for ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "They only cost me about forty dollars .", + "emotion": "neutral", + "text": "They only cost me about forty dollars .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "I'm going to go get a pair for myself .", + "emotion": "neutral", + "text": "I'm going to go get a pair for myself .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/va_504.json b/reccon/sources/va_504.json new file mode 100644 index 0000000000000000000000000000000000000000..551293bc7729859141f78d150ad011440b028f24 --- /dev/null +++ b/reccon/sources/va_504.json @@ -0,0 +1,94 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Good afternoon , madam . Is there anything I can do for you ?", + "emotion": "neutral", + "text": "Good afternoon , madam . Is there anything I can do for you ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , I spent so much time sightseeing here . It is already so late now . I am afraid I can't catch the last bus back to downtown .", + "emotion": "neutral", + "text": "Yes , I spent so much time sightseeing here . It is already so late now . I am afraid I can't catch the last bus back to downtown .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Don't worry . I will try to get a taxi for you . You can take it to the bus station .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "Don't worry . I will try to get a taxi for you ." + ], + "type": [ + "no-context" + ], + "text": "Don't worry . I will try to get a taxi for you . You can take it to the bus station .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I am very grateful to your help .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I will try to get a taxi for you ." + ], + "type": [ + "inter-personal" + ], + "text": "I am very grateful to your help .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Don't mention it . It is my duty .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 4 + ], + "expanded emotion cause span": [ + "Don't worry . I will try to get a taxi for you .", + "I am very grateful" + ], + "type": [ + "hybrid" + ], + "text": "Don't mention it . It is my duty .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Thanks again .", + "emotion": "happiness", + "flag": "F", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "I will try to get a taxi for you ." + ], + "type": [ + "inter-personal" + ], + "text": "Thanks again .", + "id": 6, + "source_sentences": [ + 2 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/va_64.json b/reccon/sources/va_64.json new file mode 100644 index 0000000000000000000000000000000000000000..11136d1aa99809de23034c7f370cfa4173747241 --- /dev/null +++ b/reccon/sources/va_64.json @@ -0,0 +1,145 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Oh , come on , Ultraman !", + "emotion": "anger", + "explanation": "A is angry on B for some latent cause.", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Oh , come on , Ultraman !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "What's up , Bro ? What's in the bulletin ?", + "emotion": "neutral", + "text": "What's up , Bro ? What's in the bulletin ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "It says that there will be a blackout from 5 p . m . to 7 p . m . in our neighborhood today .", + "emotion": "neutral", + "text": "It says that there will be a blackout from 5 p . m . to 7 p . m . in our neighborhood today .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Blackout ? Even the TV has the limit .", + "emotion": "neutral", + "text": "Blackout ? Even the TV has the limit .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Don't you know you will look like a monster in the blackout ?", + "emotion": "neutral", + "text": "Don't you know you will look like a monster in the blackout ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Oops , no , Daddy can't watch American Idol , either !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 3, + 6 + ], + "expanded emotion cause span": [ + "there will be a blackout", + "Daddy can't watch American Idol ," + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oops , no , Daddy can't watch American Idol , either !", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "That's not the point . Come on , can you imagine that there will be no electricity on such a hot day ?", + "emotion": "neutral", + "text": "That's not the point . Come on , can you imagine that there will be no electricity on such a hot day ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Oh , my god ! No air-conditioner !", + "emotion": "fear", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "there will be no electricity on such a hot day ?", + "No air-conditioner !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Oh , my god ! No air-conditioner !", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "OK , since you are the smart one , can you come up with a better plan ? So that we won't be baked like cookies here .", + "emotion": "neutral", + "text": "OK , since you are the smart one , can you come up with a better plan ? So that we won't be baked like cookies here .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "How about playing Barbie out there in the neighborhood ?", + "emotion": "neutral", + "text": "How about playing Barbie out there in the neighborhood ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Barbie ? You know , I might be seven , but I'm not a girl .", + "emotion": "neutral", + "text": "Barbie ? You know , I might be seven , but I'm not a girl .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Do you have a better plan ?", + "emotion": "neutral", + "text": "Do you have a better plan ?", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "All right , all right .", + "emotion": "neutral", + "text": "All right , all right .", + "id": 13 + } +] \ No newline at end of file diff --git a/reccon/sources/va_663.json b/reccon/sources/va_663.json new file mode 100644 index 0000000000000000000000000000000000000000..b3ae7ebddef19eeebac656f8d64cee0d9632d5a5 --- /dev/null +++ b/reccon/sources/va_663.json @@ -0,0 +1,222 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Well , I'm glad you're finally back . I was wondering what happened .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "you're finally back ." + ], + "type": [ + "no-context" + ], + "text": "Well , I'm glad you're finally back . I was wondering what happened .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I feel kind of stupid .", + "emotion": "neutral", + "text": "I feel kind of stupid .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Why ?", + "emotion": "neutral", + "text": "Why ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "We got lost coming back . I guess I don't really know this town yet .", + "emotion": "neutral", + "text": "We got lost coming back . I guess I don't really know this town yet .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "You got lost . You're kidding !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "We got lost coming back ." + ], + "type": [ + "inter-personal" + ], + "text": "You got lost . You're kidding !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "No . We took a wrong turn somewhere . And Joseph doesn't know the town at all . So I started giving him directions . But I didn't really know where we were . So we got seriously lost .", + "emotion": "neutral", + "text": "No . We took a wrong turn somewhere . And Joseph doesn't know the town at all . So I started giving him directions . But I didn't really know where we were . So we got seriously lost .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You could have called .", + "emotion": "neutral", + "text": "You could have called .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I know I could have . But finally we asked someone where we were .", + "emotion": "neutral", + "text": "I know I could have . But finally we asked someone where we were .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "You've been gone for two hours . How could you get lost for so long ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "You've been gone for two hours . How could you get lost for so long ?" + ], + "type": [ + "no-context" + ], + "text": "You've been gone for two hours . How could you get lost for so long ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Guess where we ended up .", + "emotion": "neutral", + "text": "Guess where we ended up .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I don't know . Where ?", + "emotion": "neutral", + "text": "I don't know . Where ?", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "When we finally decided to ask someone , they told us we were in Grangerfield .", + "emotion": "neutral", + "text": "When we finally decided to ask someone , they told us we were in Grangerfield .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Grangerfield ! You were in Grangerfield ? That's a completely different town ! How could you drive to a completely different town ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 12, + 13 + ], + "expanded emotion cause span": [ + "they told us we were in Grangerfield .", + "How could you drive to a completely different town ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Grangerfield ! You were in Grangerfield ? That's a completely different town ! How could you drive to a completely different town ?", + "id": 13, + "source_sentences": [ + 11 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 14, + "speaker": "B", + "utterance": "I don't know . The person we asked had to give us directions to the highway to get back here .", + "emotion": "neutral", + "text": "I don't know . The person we asked had to give us directions to the highway to get back here .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Grangerfield is like a dozen miles away from here .", + "emotion": "neutral", + "text": "Grangerfield is like a dozen miles away from here .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "I know it is . I don't know how it happened .", + "emotion": "neutral", + "text": "I know it is . I don't know how it happened .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "Hmm , maybe I do .", + "emotion": "neutral", + "text": "Hmm , maybe I do .", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "What ?", + "emotion": "neutral", + "text": "What ?", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "Maybe I have an idea how it happened .", + "emotion": "neutral", + "text": "Maybe I have an idea how it happened .", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "How ?", + "emotion": "neutral", + "text": "How ?", + "id": 20 + }, + { + "turn": 21, + "speaker": "A", + "utterance": "You were too busy looking at Joseph , and you weren't paying attention to the road .", + "emotion": "neutral", + "text": "You were too busy looking at Joseph , and you weren't paying attention to the road .", + "id": 21 + }, + { + "turn": 22, + "speaker": "B", + "utterance": "Oh , that's what you think , huh ?", + "emotion": "neutral", + "text": "Oh , that's what you think , huh ?", + "id": 22 + } +] \ No newline at end of file diff --git a/reccon/sources/va_664.json b/reccon/sources/va_664.json new file mode 100644 index 0000000000000000000000000000000000000000..25953db590d452da30e107878a2deda31de335ee --- /dev/null +++ b/reccon/sources/va_664.json @@ -0,0 +1,146 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Won't you have some of this ?", + "emotion": "neutral", + "text": "Won't you have some of this ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yes , thanks .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "Won't you have some of this ?" + ], + "type": [ + "inter-personal" + ], + "text": "Yes , thanks .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "It's my grandmother's favorite recipe for barbecue .", + "emotion": "neutral", + "text": "It's my grandmother's favorite recipe for barbecue .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It's very good . How do you make it ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "It's very good ." + ], + "type": [ + "no-context" + ], + "text": "It's very good . How do you make it ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I use a special dressing and homemade catsup .", + "emotion": "neutral", + "text": "I use a special dressing and homemade catsup .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "This salad looks so nice-just right for a hot day .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 6 + ], + "expanded emotion cause span": [ + "It's very good .", + "This salad looks so nice-just right for a hot day ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "This salad looks so nice-just right for a hot day .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I'm glad you like it .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "This salad looks so nice-just right for a hot day .", + "I'm glad you like it ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm glad you like it .", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "You Americans usually have nutritious food .", + "emotion": "neutral", + "text": "You Americans usually have nutritious food .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Oh , but Chinese food is so delicious . I wish I knew how to cook Chinese food . Do you follow recipes ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "Chinese food is so delicious . I wish I knew how to cook Chinese food ." + ], + "type": [ + "no-context" + ], + "text": "Oh , but Chinese food is so delicious . I wish I knew how to cook Chinese food . Do you follow recipes ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "We use different spices but few people use recipes . They learn to cook by experience .", + "emotion": "neutral", + "text": "We use different spices but few people use recipes . They learn to cook by experience .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I always use a recipe but my grandmother never did . She was a great cook . She would make clam chowder and cornbread every Sunday night .", + "emotion": "neutral", + "text": "I always use a recipe but my grandmother never did . She was a great cook . She would make clam chowder and cornbread every Sunday night .", + "id": 11 + } +] \ No newline at end of file diff --git a/reccon/sources/va_710.json b/reccon/sources/va_710.json new file mode 100644 index 0000000000000000000000000000000000000000..8b21ced0f447add1b935af4b303fe1833a9562a9 --- /dev/null +++ b/reccon/sources/va_710.json @@ -0,0 +1,122 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Thank god you are open ! I have an emergency !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + "b", + 1 + ], + "expanded emotion cause span": [ + "b", + "Thank god you are open !" + ], + "type": [ + "latent", + "no-context" + ], + "text": "Thank god you are open ! I have an emergency !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Hello , Mr . Henderson what can I do for you ?", + "emotion": "neutral", + "text": "Hello , Mr . Henderson what can I do for you ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I need this dress and this suit dry cleaned ASAP !", + "emotion": "neutral", + "text": "I need this dress and this suit dry cleaned ASAP !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "OK , I can have it ready by the end of the week .", + "emotion": "neutral", + "text": "OK , I can have it ready by the end of the week .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "No , you don ' t understand , I need this tomorrow morning ! I accidentally spilled beer all over my wife ' s dress and we have a wedding to attend tomorrow ! She ' s gonna kill me !", + "emotion": "fear", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "She ' s gonna kill me !" + ], + "type": [ + "no-context" + ], + "text": "No , you don ' t understand , I need this tomorrow morning ! I accidentally spilled beer all over my wife ' s dress and we have a wedding to attend tomorrow ! She ' s gonna kill me !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "OK , I can have it ready tomorrow afternoon , but this suit is also very stained . I can ' t guarantee we can remove it completely .", + "emotion": "neutral", + "text": "OK , I can have it ready tomorrow afternoon , but this suit is also very stained . I can ' t guarantee we can remove it completely .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Fine ! Can you also iron and starch this shirt ?", + "emotion": "neutral", + "text": "Fine ! Can you also iron and starch this shirt ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Certainly .", + "emotion": "happiness", + "explanation": "The speaker is happy to fulfil the need of the customer", + "expanded emotion cause evidence": [ + "b" + ], + "expanded emotion cause span": [ + "b" + ], + "type": [ + "latent" + ], + "text": "Certainly .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Great ! This is our secret ! If you see my wife , say nothing to her about this !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 8 + ], + "expanded emotion cause span": [ + "I can have it ready tomorrow afternoon ,", + "Certainly ." + ], + "type": [ + "inter-personal" + ], + "text": "Great ! This is our secret ! If you see my wife , say nothing to her about this !", + "id": 9, + "source_sentences": [ + 5, + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/va_727.json b/reccon/sources/va_727.json new file mode 100644 index 0000000000000000000000000000000000000000..e2b6deee19353c6e6bcfbad2b184047b80aed0f4 --- /dev/null +++ b/reccon/sources/va_727.json @@ -0,0 +1,193 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Wow , this is amazing . I'm glad we've come here . So cool .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "this is amazing . I'm glad we've come here . So cool ." + ], + "type": [ + "no-context" + ], + "text": "Wow , this is amazing . I'm glad we've come here . So cool .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I always love skiing . You know , it's a cool game for cool people . Stay with me and you will be cool , too .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 2 + ], + "expanded emotion cause span": [ + "this is amazing . I'm glad we've come here . So cool .", + "I always love skiing .", + "it's a cool game for cool people ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I always love skiing . You know , it's a cool game for cool people . Stay with me and you will be cool , too .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Hey , look over there . It seems that there is something interesting going on . Let's go and have a look .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 3 + ], + "expanded emotion cause span": [ + "this is amazing . I'm glad we've come here . So cool .", + "there is something interesting going on ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Hey , look over there . It seems that there is something interesting going on . Let's go and have a look .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Sure . It's probably the skiing show . Adam told me there were many skiing clubs whose members put on shows to attract more visitors .", + "emotion": "neutral", + "text": "Sure . It's probably the skiing show . Adam told me there were many skiing clubs whose members put on shows to attract more visitors .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "See that . It's so dangerous . My mom would never allow me to do that .", + "emotion": "neutral", + "text": "See that . It's so dangerous . My mom would never allow me to do that .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Hey , don't be so pathetic . It's a maximal sports show . What else can they do to attract more visitors ? Stop all this fuss and enjoy the show .", + "emotion": "neutral", + "text": "Hey , don't be so pathetic . It's a maximal sports show . What else can they do to attract more visitors ? Stop all this fuss and enjoy the show .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "You are right . But what if the avalanche happened ?", + "emotion": "neutral", + "text": "You are right . But what if the avalanche happened ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "They are all very experienced and great skiers . So I suppose the chance for them to be buried by an avalanche is slim .", + "emotion": "neutral", + "text": "They are all very experienced and great skiers . So I suppose the chance for them to be buried by an avalanche is slim .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Anyway , the show is breathtaking . By the way , where did they get so much snow in here ?", + "emotion": "neutral", + "text": "Anyway , the show is breathtaking . By the way , where did they get so much snow in here ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Don't you know that ? Are you kidding me ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 9, + 10 + ], + "expanded emotion cause span": [ + "where did they get so much snow in here ?", + "Don't you know that ?" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Don't you know that ? Are you kidding me ?", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Hey , not everyone is as lucky as you to have a father who is a scientist .", + "emotion": "neutral", + "text": "Hey , not everyone is as lucky as you to have a father who is a scientist .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Sorry . Well , they have the most advanced snowmaking machine .", + "emotion": "neutral", + "text": "Sorry . Well , they have the most advanced snowmaking machine .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "Do you think the snowmaking may cause pollution ?", + "emotion": "neutral", + "text": "Do you think the snowmaking may cause pollution ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "It's possible . But the boss here said they were doing whatever they can .", + "emotion": "neutral", + "text": "It's possible . But the boss here said they were doing whatever they can .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "It's a good thing . OK , let's go skiing .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 13, + 14 + ], + "expanded emotion cause span": [ + "snowmaking may cause pollution ?", + "the boss here said they were doing whatever they can ." + ], + "type": [ + "hybrid" + ], + "text": "It's a good thing . OK , let's go skiing .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "Here we go .", + "emotion": "neutral", + "text": "Here we go .", + "id": 16 + } +] \ No newline at end of file diff --git a/reccon/sources/va_76.json b/reccon/sources/va_76.json new file mode 100644 index 0000000000000000000000000000000000000000..169f4bf2bad886a9e397ec159a00287d52d068e4 --- /dev/null +++ b/reccon/sources/va_76.json @@ -0,0 +1,212 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What are we going to do ? I can't get the car out of this ditch . I'm stuck !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "I can't get the car out of this ditch . I'm stuck !" + ], + "type": [ + "no-context" + ], + "text": "What are we going to do ? I can't get the car out of this ditch . I'm stuck !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'm worried , Tom . I haven't seen any other cars for almost an hour .", + "emotion": "neutral", + "text": "I'm worried , Tom . I haven't seen any other cars for almost an hour .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I know . This is terrible . What can we do ? This snow doesn't stop falling !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1, + 2, + 3 + ], + "expanded emotion cause span": [ + "I can't get the car out of this ditch . I'm stuck !", + "I haven't seen any other cars for almost an hour .", + "This snow doesn't stop falling !" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "I know . This is terrible . What can we do ? This snow doesn't stop falling !", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I told you we should have stayed in town today . The weather report said 100 percent chance of snow . Why did you want to come up here ?", + "emotion": "neutral", + "text": "I told you we should have stayed in town today . The weather report said 100 percent chance of snow . Why did you want to come up here ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I wanted to show you the cabin . We only had another half-hour to go .", + "emotion": "neutral", + "text": "I wanted to show you the cabin . We only had another half-hour to go .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Well , now we're stuck . What can we do ?", + "emotion": "neutral", + "text": "Well , now we're stuck . What can we do ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I don't know .", + "emotion": "neutral", + "text": "I don't know .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "I've heard that when this happens , it's important to save energy .", + "emotion": "neutral", + "text": "I've heard that when this happens , it's important to save energy .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "What do you mean ?", + "emotion": "neutral", + "text": "What do you mean ?", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "We're stranded here , Tom . We may be here a long time . We need to conserve the gas in the car . The car's energy is what will keep us warm .", + "emotion": "neutral", + "text": "We're stranded here , Tom . We may be here a long time . We need to conserve the gas in the car . The car's energy is what will keep us warm .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I have plenty of gas .", + "emotion": "neutral", + "text": "I have plenty of gas .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Yes , but the gas and the battery both have to stay working . We can't just let the car run and run . If we do , it will die soon . Then we'll freeze .", + "emotion": "neutral", + "text": "Yes , but the gas and the battery both have to stay working . We can't just let the car run and run . If we do , it will die soon . Then we'll freeze .", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "So what can we do ?", + "emotion": "neutral", + "text": "So what can we do ?", + "id": 13 + }, + { + "turn": 14, + "speaker": "B", + "utterance": "Turn the lights off . Then , run the car and the heater only about fifteen minutes every hour . That will conserve the heat as long as possible .", + "emotion": "neutral", + "text": "Turn the lights off . Then , run the car and the heater only about fifteen minutes every hour . That will conserve the heat as long as possible .", + "id": 14 + }, + { + "turn": 15, + "speaker": "A", + "utterance": "Alright . That's a good idea .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 8, + 10, + 14 + ], + "expanded emotion cause span": [ + "I've heard that when this happens , it's important to save energy .", + "We need to conserve the gas in the car . The car's energy is what will keep us warm .", + "run the car and the heater only about fifteen minutes every hour . That will conserve the heat as long as possible ." + ], + "type": [ + "inter-personal" + ], + "text": "Alright . That's a good idea .", + "id": 15 + }, + { + "turn": 16, + "speaker": "B", + "utterance": "I wish we hadn't come up here . Now we'll probably be here for days .", + "emotion": "neutral", + "text": "I wish we hadn't come up here . Now we'll probably be here for days .", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "Days ?", + "emotion": "neutral", + "text": "Days ?", + "id": 17 + }, + { + "turn": 18, + "speaker": "B", + "utterance": "Yes , it happens . That is what happens in big snowstorms . People get stranded for days .", + "emotion": "neutral", + "text": "Yes , it happens . That is what happens in big snowstorms . People get stranded for days .", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "Oh , my God ! It's good we have food .", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 18 + ], + "expanded emotion cause span": [ + "People get stranded for days ." + ], + "type": [ + "inter-personal" + ], + "text": "Oh , my God ! It's good we have food .", + "id": 19, + "source_sentences": [ + 17 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 20, + "speaker": "B", + "utterance": "Probably we'll survive . But turn the car off for about forty-five minutes . Then we'll turn it on again .", + "emotion": "neutral", + "text": "Probably we'll survive . But turn the car off for about forty-five minutes . Then we'll turn it on again .", + "id": 20 + } +] \ No newline at end of file diff --git a/reccon/sources/va_835.json b/reccon/sources/va_835.json new file mode 100644 index 0000000000000000000000000000000000000000..6ebeecabf3f4e6d8b5cfdfd900ced020dc51ea44 --- /dev/null +++ b/reccon/sources/va_835.json @@ -0,0 +1,104 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What would you have ?", + "emotion": "neutral", + "text": "What would you have ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'll try Chinese wine .", + "emotion": "neutral", + "text": "I'll try Chinese wine .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "What about this dry red ? It's good indeed , it never goes to the head .", + "emotion": "neutral", + "text": "What about this dry red ? It's good indeed , it never goes to the head .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "OK . Give me one , please .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3 + ], + "expanded emotion cause span": [ + "It's good indeed ," + ], + "type": [ + "inter-personal" + ], + "text": "OK . Give me one , please .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Here it is .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "Give me one ," + ], + "type": [ + "inter-personal" + ], + "text": "Here it is .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Thank you .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 3, + 5 + ], + "expanded emotion cause span": [ + "It's good indeed ,", + "Here it is ." + ], + "type": [ + "inter-personal" + ], + "text": "Thank you .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I'm always at your service .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 7 + ], + "expanded emotion cause span": [ + "Give me one ,", + "I'm always at your service ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm always at your service .", + "id": 7, + "source_sentences": [ + 3 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/va_838.json b/reccon/sources/va_838.json new file mode 100644 index 0000000000000000000000000000000000000000..a6c73350a408ab0a40da919c52ecd24de8b9f15c --- /dev/null +++ b/reccon/sources/va_838.json @@ -0,0 +1,133 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "What's wrong , officer ?", + "emotion": "neutral", + "text": "What's wrong , officer ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "You do realize that you ran a red light , don't you ?", + "emotion": "neutral", + "text": "You do realize that you ran a red light , don't you ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "I did ?", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "you ran a red light" + ], + "type": [ + "inter-personal" + ], + "text": "I did ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "You didn't see the red light ?", + "emotion": "neutral", + "text": "You didn't see the red light ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "I'm sorry for running it , but I really didn't know .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I'm sorry for running it" + ], + "type": [ + "no-context" + ], + "text": "I'm sorry for running it , but I really didn't know .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Didn't you learn that red means stop ?", + "emotion": "neutral", + "text": "Didn't you learn that red means stop ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I know that .", + "emotion": "neutral", + "text": "I know that .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Then tell me why you sped up on the yellow light .", + "emotion": "neutral", + "text": "Then tell me why you sped up on the yellow light .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I'm not sure .", + "emotion": "neutral", + "text": "I'm not sure .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "I'm giving you a ticket for this .", + "emotion": "neutral", + "text": "I'm giving you a ticket for this .", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I'm sorry for the misunderstanding .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 10, + 11 + ], + "expanded emotion cause span": [ + "I'm giving you a ticket for this .", + "I'm sorry for the misunderstanding ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm sorry for the misunderstanding .", + "id": 11, + "source_sentences": [ + 9 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Maybe you'll think about this before you decide to run another light .", + "emotion": "neutral", + "text": "Maybe you'll think about this before you decide to run another light .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/va_86.json b/reccon/sources/va_86.json new file mode 100644 index 0000000000000000000000000000000000000000..40ecbfb9c8ea95839c18655ca74f38f0de2188ee --- /dev/null +++ b/reccon/sources/va_86.json @@ -0,0 +1,123 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "We have been over this a hundred times ! We are not getting a pet !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "We have been over this a hundred times !" + ], + "type": [ + "no-context" + ], + "text": "We have been over this a hundred times ! We are not getting a pet !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Why not ? Come on ! Just a cute little puppy or a kitty !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "We are not getting a pet !" + ], + "type": [ + "inter-personal" + ], + "text": "Why not ? Come on ! Just a cute little puppy or a kitty !", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Who is going to look after a dog or a cat ?", + "emotion": "neutral", + "text": "Who is going to look after a dog or a cat ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "I will ! I ' ll feed it , bathe it and walk it every day ! We can get a Labrador or a German Shepard !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "We are not getting a pet !" + ], + "type": [ + "inter-personal" + ], + "text": "I will ! I ' ll feed it , bathe it and walk it every day ! We can get a Labrador or a German Shepard !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "What if we want to take a vacation ? Who will we leave it with ? Plus , our apartment is too small for that breed of dog .", + "emotion": "neutral", + "text": "What if we want to take a vacation ? Who will we leave it with ? Plus , our apartment is too small for that breed of dog .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Ok . How about we get a cat or a ferret ?", + "emotion": "neutral", + "text": "Ok . How about we get a cat or a ferret ?", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "We ' re planning on having children soon , I don ' t think those animals are a good idea with a baby in the house .", + "emotion": "neutral", + "text": "We ' re planning on having children soon , I don ' t think those animals are a good idea with a baby in the house .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Fine ! Let ' s get a bird then ! We can keep it in its cage and teach it to talk ! A parrot would be awesome !", + "emotion": "neutral", + "text": "Fine ! Let ' s get a bird then ! We can keep it in its cage and teach it to talk ! A parrot would be awesome !", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "I ' ll tell you what , I can get you some hamsters and we ' ll take it from there .", + "emotion": "neutral", + "text": "I ' ll tell you what , I can get you some hamsters and we ' ll take it from there .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Yay !", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 9 + ], + "expanded emotion cause span": [ + "I can get you some hamsters and we ' ll take it from there ." + ], + "type": [ + "inter-personal" + ], + "text": "Yay !", + "id": 10, + "source_sentences": [ + 8 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/va_882.json b/reccon/sources/va_882.json new file mode 100644 index 0000000000000000000000000000000000000000..5053e0798b515ba44f28ec664b597c55361a2e40 --- /dev/null +++ b/reccon/sources/va_882.json @@ -0,0 +1,161 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Hi . I'm looking for a gift for my niece .", + "emotion": "neutral", + "text": "Hi . I'm looking for a gift for my niece .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Well , little girls seem to love Barbie dolls .", + "emotion": "neutral", + "text": "Well , little girls seem to love Barbie dolls .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "That's perfect . I want to see one .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 1, + 2, + 3 + ], + "expanded emotion cause span": [ + "I'm looking for a gift for my niece .", + "little girls seem to love Barbie dolls .", + "That's perfect" + ], + "type": [ + "no-context", + "hybrid" + ], + "text": "That's perfect . I want to see one .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Here you are -- she's called Digital Barbie .", + "emotion": "neutral", + "text": "Here you are -- she's called Digital Barbie .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Oh , I like Digital Barbie ! How much does she cost ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "I like Digital Barbie !" + ], + "type": [ + "no-context" + ], + "text": "Oh , I like Digital Barbie ! How much does she cost ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "This Barbie is only $ 29 . 95 .", + "emotion": "neutral", + "text": "This Barbie is only $ 29 . 95 .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "That's perfect . Let me have her .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "This Barbie is only $ 29 . 95 .", + "That's perfect ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's perfect . Let me have her .", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Very good . Is there anything else you would like ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "Let me have her ." + ], + "type": [ + "inter-personal" + ], + "text": "Very good . Is there anything else you would like ?", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 9, + "speaker": "A", + "utterance": "No , that'll do it for now .", + "emotion": "neutral", + "text": "No , that'll do it for now .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Including tax , your total will be $ 32 . 42 . Cash or charge ?", + "emotion": "neutral", + "text": "Including tax , your total will be $ 32 . 42 . Cash or charge ?", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "Let me give you cash , please .", + "emotion": "neutral", + "text": "Let me give you cash , please .", + "id": 11 + }, + { + "turn": 12, + "speaker": "B", + "utterance": "Here's your change and receipt . Thank you .", + "emotion": "happiness", + "explanation": "Speaker is happy for the sale", + "expanded emotion cause evidence": [ + 6, + 7, + 11 + ], + "expanded emotion cause span": [ + "This Barbie is only $ 29 . 95 .", + "That's perfect .", + "Let me give you cash ," + ], + "type": [ + "hybrid" + ], + "text": "Here's your change and receipt . Thank you .", + "id": 12 + } +] \ No newline at end of file diff --git a/reccon/sources/va_922.json b/reccon/sources/va_922.json new file mode 100644 index 0000000000000000000000000000000000000000..671f9ee86defe6fec37f142c7c858d11515966f1 --- /dev/null +++ b/reccon/sources/va_922.json @@ -0,0 +1,127 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "I ' m hungry , let ' s go grab a bite to eat .", + "emotion": "neutral", + "text": "I ' m hungry , let ' s go grab a bite to eat .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Yeah me too . Oh ! Can we stop at the shop really fast ? I lost my makeup bag at the airport and I want to pick up a few things .", + "emotion": "neutral", + "text": "Yeah me too . Oh ! Can we stop at the shop really fast ? I lost my makeup bag at the airport and I want to pick up a few things .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Will you take long ?", + "emotion": "neutral", + "text": "Will you take long ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "No ! Five minutes I promise !", + "emotion": "neutral", + "text": "No ! Five minutes I promise !", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Come on ! We have been here for almost an hour ! I thought you said you were only going to get a few things ! How long does it take you to pick out a lipstick and some nail polish !", + "emotion": "neutral", + "text": "Come on ! We have been here for almost an hour ! I thought you said you were only going to get a few things ! How long does it take you to pick out a lipstick and some nail polish !", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Are you crazy ? You have no idea what you are talking about ! Just for my eyes I have to get eye-liner , an eyelash curler , eye shadow , an eyebrow pencil and mascara . Then I need to get foundation , liq", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "I thought you said you were only going to get a few things ! How long does it take you to pick out a lipstick and some nail polish !", + "You have no idea what you are talking about ! Just for my eyes I have to get eye-liner , an eyelash curler , eye shadow , an eyebrow pencil and mascara . Then I need to get foundation , liq" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Are you crazy ? You have no idea what you are talking about ! Just for my eyes I have to get eye-liner , an eyelash curler , eye shadow , an eyebrow pencil and mascara . Then I need to get foundation , liq", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Whoa whoa whoa ! Are you nuts ? How much is all this going to cost ? I ' m looking at the price at each one of these little things and it ' s outrageous ! This is basically a crayon !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 6, + 7 + ], + "expanded emotion cause span": [ + "Just for my eyes I have to get eye-liner , an eyelash curler , eye shadow , an eyebrow pencil and mascara . Then I need to get foundation , liq", + "How much is all this going to cost ? I ' m looking at the price at each one of these little things and it ' s outrageous ! This is basically a crayon !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Whoa whoa whoa ! Are you nuts ? How much is all this going to cost ? I ' m looking at the price at each one of these little things and it ' s outrageous ! This is basically a crayon !", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "What about you ? You spend as much or more money on your razors , after shave , cologne and gel ! Not to mention how much you spend on clothes and ...", + "emotion": "anger", + "expanded emotion cause evidence": [ + 7, + 8 + ], + "expanded emotion cause span": [ + "Are you nuts ? How much is all this going to cost ? I ' m looking at the price at each one of these little things and it ' s outrageous !", + "You spend as much or more money on your razors , after shave , cologne and gel ! Not to mention how much you spend on clothes and ..." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "What about you ? You spend as much or more money on your razors , after shave , cologne and gel ! Not to mention how much you spend on clothes and ...", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Fine ! Get the stupid thirty dollar crayon !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 8, + 9 + ], + "expanded emotion cause span": [ + "You spend as much or more money on your razors , after shave , cologne and gel ! Not to mention how much you spend on clothes and ...", + "Get the stupid thirty dollar crayon !" + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Fine ! Get the stupid thirty dollar crayon !", + "id": 9, + "source_sentences": [ + 7 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/va_926.json b/reccon/sources/va_926.json new file mode 100644 index 0000000000000000000000000000000000000000..924039737edef6da04df4b568e5b14fe4c693900 --- /dev/null +++ b/reccon/sources/va_926.json @@ -0,0 +1,88 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "How slowly you drive !", + "emotion": "anger", + "expanded emotion cause evidence": [ + 1 + ], + "expanded emotion cause span": [ + "How slowly you drive !" + ], + "type": [ + "no-context" + ], + "text": "How slowly you drive !", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "I'm sorry . Something is wrong with my taxi .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 1, + 2 + ], + "expanded emotion cause span": [ + "How slowly you drive !", + "Something is wrong with my taxi ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "I'm sorry . Something is wrong with my taxi .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Where does it go wrong ?", + "emotion": "neutral", + "text": "Where does it go wrong ?", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Let me stop my car for check . Oh , my god . I got a flat tyre .", + "emotion": "neutral", + "text": "Let me stop my car for check . Oh , my god . I got a flat tyre .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Can it keep going ?", + "emotion": "neutral", + "text": "Can it keep going ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "Sorry . You'd better get off for taking another taxi .", + "emotion": "sadness", + "expanded emotion cause evidence": [ + 5, + 6 + ], + "expanded emotion cause span": [ + "Can it keep going ?", + "You'd better get off for taking another taxi ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Sorry . You'd better get off for taking another taxi .", + "id": 6, + "source_sentences": [ + 4 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/va_977.json b/reccon/sources/va_977.json new file mode 100644 index 0000000000000000000000000000000000000000..be57addadacff92bd123443c2519d19af2367410 --- /dev/null +++ b/reccon/sources/va_977.json @@ -0,0 +1,126 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Good morning , May . Good girl , you are reading English books again .", + "emotion": "neutral", + "text": "Good morning , May . Good girl , you are reading English books again .", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "Good morning . There is no reason to miss so beautiful a morning . Is that a new bird ?", + "emotion": "neutral", + "text": "Good morning . There is no reason to miss so beautiful a morning . Is that a new bird ?", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "Oh , yes , my daughter bought it yesterday . We call her Lulu .", + "emotion": "neutral", + "text": "Oh , yes , my daughter bought it yesterday . We call her Lulu .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "It looks so cute . Is it a parrot ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "It looks so cute ." + ], + "type": [ + "no-context" + ], + "text": "It looks so cute . Is it a parrot ?", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Yes . Just look at her colorful feathers . What else can it be ?", + "emotion": "neutral", + "text": "Yes . Just look at her colorful feathers . What else can it be ?", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "I see . It's interesting that there is also a parrot in my English book . His mane is Polly .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "It looks so cute ." + ], + "type": [ + "self-contagion" + ], + "text": "I see . It's interesting that there is also a parrot in my English book . His mane is Polly .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Really ? A foreign parrot !", + "emotion": "surprise", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "It's interesting that there is also a parrot in my English book . His mane is Polly ." + ], + "type": [ + "inter-personal" + ], + "text": "Really ? A foreign parrot !", + "id": 7, + "source_sentences": [ + 5 + ], + "has_target": true, + "annotator": "ground_truth" + }, + { + "turn": 8, + "speaker": "B", + "utterance": "He can speak English , too .", + "emotion": "neutral", + "text": "He can speak English , too .", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Maybe you can teach Lulu some English words .", + "emotion": "neutral", + "text": "Maybe you can teach Lulu some English words .", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "Lulu . Lulu . Say hello . hello . Oh , she is so smart . Good bird .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 4, + 10 + ], + "expanded emotion cause span": [ + "It looks so cute .", + "Oh , she is so smart . Good bird ." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Lulu . Lulu . Say hello . hello . Oh , she is so smart . Good bird .", + "id": 10 + } +] \ No newline at end of file diff --git a/reccon/sources/va_980.json b/reccon/sources/va_980.json new file mode 100644 index 0000000000000000000000000000000000000000..d228eb6f14d01e1fcde65ada77fdd3731fa33793 --- /dev/null +++ b/reccon/sources/va_980.json @@ -0,0 +1,111 @@ +[ + { + "turn": 1, + "speaker": "A", + "utterance": "Mr . Bryant ? Hi , I'm Mike from Florence Incorporated . I'll glad you made it okay . How was your flight ?", + "emotion": "neutral", + "text": "Mr . Bryant ? Hi , I'm Mike from Florence Incorporated . I'll glad you made it okay . How was your flight ?", + "id": 1 + }, + { + "turn": 2, + "speaker": "B", + "utterance": "It was pretty bumpy , also a bit long , all together about 5 hours .", + "emotion": "neutral", + "text": "It was pretty bumpy , also a bit long , all together about 5 hours .", + "id": 2 + }, + { + "turn": 3, + "speaker": "A", + "utterance": "That is a long flight . You had a layover too , is that right ? You must be tired .", + "emotion": "neutral", + "text": "That is a long flight . You had a layover too , is that right ? You must be tired .", + "id": 3 + }, + { + "turn": 4, + "speaker": "B", + "utterance": "Actually I feel quite rested . I was able to sleep on the plane .", + "emotion": "neutral", + "text": "Actually I feel quite rested . I was able to sleep on the plane .", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "Good ! Here , let me help you with your bag . Is it your first time to Seattle ? I'd be happy to take you around this city and show you the sights tonight if you're up to it .", + "emotion": "happiness", + "explanation": "The person shows happiness to make the customer feel good. In other words, the person is happy to server his customers.", + "expanded emotion cause evidence": [ + 4, + 5 + ], + "expanded emotion cause span": [ + "Actually I feel quite rested . I was able to sleep on the plane .", + "happy to take you around this city and show you the sights tonight if you're up to it ." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Good ! Here , let me help you with your bag . Is it your first time to Seattle ? I'd be happy to take you around this city and show you the sights tonight if you're up to it .", + "id": 5 + }, + { + "turn": 6, + "speaker": "B", + "utterance": "That will be very nice . You're too kind .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 5 + ], + "expanded emotion cause span": [ + "happy to take you around this city and show you the sights tonight if you're up to it ." + ], + "type": [ + "inter-personal" + ], + "text": "That will be very nice . You're too kind .", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "I've already made a hotel reservation for you , let's go to the hotel first and drop off your things . Then , I'd like to have a drink so that we can get better acquainted . I've booked a table at an exclusive restaurant downtown . Afterwards , I've made arrangements to take you to see the city lights . Seattle ' s nightlife can be really quite exciting . How does that schedule sound to you ?", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 6 + ], + "expanded emotion cause span": [ + "That will be very nice . You're too kind ." + ], + "type": [ + "inter-personal" + ], + "text": "I've already made a hotel reservation for you , let's go to the hotel first and drop off your things . Then , I'd like to have a drink so that we can get better acquainted . I've booked a table at an exclusive restaurant downtown . Afterwards , I've made arrangements to take you to see the city lights . Seattle ' s nightlife can be really quite exciting . How does that schedule sound to you ?", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "Sounds great . Thank you for your hospitality .", + "emotion": "happiness", + "expanded emotion cause evidence": [ + 7 + ], + "expanded emotion cause span": [ + "I've already made a hotel reservation for you , let's go to the hotel first and drop off your things . Then , I'd like to have a drink so that we can get better acquainted . I've booked a table at an exclusive restaurant downtown . Afterwards , I've made arrangements to take you to see the city lights . Seattle ' s nightlife can be really quite exciting . How does that schedule sound to you ?" + ], + "type": [ + "inter-personal" + ], + "text": "Sounds great . Thank you for your hospitality .", + "id": 8, + "source_sentences": [ + 6 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/reccon/sources/valid.valid.Ses04F_impro07.json b/reccon/sources/valid.valid.Ses04F_impro07.json new file mode 100644 index 0000000000000000000000000000000000000000..ca0e2165d26e333c13258f26c805a8d2773e8678 --- /dev/null +++ b/reccon/sources/valid.valid.Ses04F_impro07.json @@ -0,0 +1,1615 @@ +[ + { + "turn": 1, + "speaker": "B", + "utterance": "Hey, what's up?", + "emotion": "neutral", + "text": "Hey, what's up?", + "id": 1 + }, + { + "turn": 2, + "speaker": "A", + "utterance": "Guess what came today?", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Guess what came today?" + ], + "type": [ + "no-context" + ], + "text": "Guess what came today?", + "id": 2 + }, + { + "turn": 3, + "speaker": "B", + "utterance": "What?", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Guess what came today?" + ], + "type": [ + "inter-personal" + ], + "text": "What?", + "id": 3 + }, + { + "turn": 4, + "speaker": "A", + "utterance": "My acceptance letter.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "My acceptance letter." + ], + "type": [ + "no-context" + ], + "text": "My acceptance letter.", + "id": 4 + }, + { + "turn": 5, + "speaker": "A", + "utterance": "From U.S.C..", + "emotion": "excited", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "My acceptance letter." + ], + "type": [ + "self-contagion" + ], + "text": "From U.S.C..", + "id": 5 + }, + { + "turn": 6, + "speaker": "A", + "utterance": "Yes, I am.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "My acceptance letter." + ], + "type": [ + "self-contagion" + ], + "text": "Yes, I am.", + "id": 6 + }, + { + "turn": 7, + "speaker": "A", + "utterance": "Well yeah, that's the general idea. [LAUGHTER]", + "emotion": "excited", + "expanded emotion cause evidence": [ + 4 + ], + "expanded emotion cause span": [ + "My acceptance letter." + ], + "type": [ + "self-contagion" + ], + "text": "Well yeah, that's the general idea. [LAUGHTER]", + "id": 7 + }, + { + "turn": 8, + "speaker": "B", + "utterance": "That's awesome. Congratulations.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Guess what came today?" + ], + "type": [ + "inter-personal" + ], + "text": "That's awesome. Congratulations.", + "id": 8 + }, + { + "turn": 9, + "speaker": "A", + "utterance": "Big bad acceptance packet with all the information. I'm going to U.S.C..", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2, + 9 + ], + "expanded emotion cause span": [ + "Guess what came today?", + "'m going to U.S.C.." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Big bad acceptance packet with all the information. I'm going to U.S.C..", + "id": 9 + }, + { + "turn": 10, + "speaker": "B", + "utterance": "That's amazing. Wow.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2, + 9, + 10 + ], + "expanded emotion cause span": [ + "Guess what came today?", + "'m going to U.S.C..", + "That's amazing. Wow." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's amazing. Wow.", + "id": 10 + }, + { + "turn": 11, + "speaker": "A", + "utterance": "I know. [LAUGHTER]", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2, + 9 + ], + "expanded emotion cause span": [ + "Guess what came today?", + "'m going to U.S.C.." + ], + "type": [ + "self-contagion" + ], + "text": "I know. [LAUGHTER]", + "id": 11 + }, + { + "turn": 12, + "speaker": "A", + "utterance": "[LAUGHTER] Yeah, uh. No.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2, + 9 + ], + "expanded emotion cause span": [ + "Guess what came today?", + "'m going to U.S.C.." + ], + "type": [ + "self-contagion" + ], + "text": "[LAUGHTER] Yeah, uh. No.", + "id": 12 + }, + { + "turn": 13, + "speaker": "A", + "utterance": "[LAUGHTER] It's safe around there.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 13 + ], + "expanded emotion cause span": [ + "It's safe around there." + ], + "type": [ + "no-context" + ], + "text": "[LAUGHTER] It's safe around there.", + "id": 13 + }, + { + "turn": 14, + "speaker": "A", + "utterance": "The campus is beautiful. I'm so excited.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 14 + ], + "expanded emotion cause span": [ + "The campus is beautiful" + ], + "type": [ + "no-context" + ], + "text": "The campus is beautiful. I'm so excited.", + "id": 14 + }, + { + "turn": 15, + "speaker": "B", + "utterance": "I know but you should get like a taser or something. I mean walking around the campus at night-", + "emotion": "neutral", + "text": "I know but you should get like a taser or something. I mean walking around the campus at night-", + "id": 15 + }, + { + "turn": 16, + "speaker": "A", + "utterance": "Do you want to buy me some mace for my, you know, going away present?", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2, + 9, + 15 + ], + "expanded emotion cause span": [ + "Guess what came today?", + "'m going to U.S.C..", + "I know but you should get like a taser or something. I mean walking around the campus at night-" + ], + "type": [ + "hybrid" + ], + "text": "Do you want to buy me some mace for my, you know, going away present?", + "id": 16 + }, + { + "turn": 17, + "speaker": "A", + "utterance": "There we go. Perfect.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2, + 9, + 15 + ], + "expanded emotion cause span": [ + "Guess what came today?", + "'m going to U.S.C..", + "I know but you should get like a taser or something. I mean walking around the campus at night-" + ], + "type": [ + "hybrid" + ], + "text": "There we go. Perfect.", + "id": 17 + }, + { + "turn": 18, + "speaker": "A", + "utterance": "And a taser. Excellent. Just make sure it's a big knife.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 16 + ], + "expanded emotion cause span": [ + "Do you want to buy me some mace for my, you know, going away present?" + ], + "type": [ + "self-contagion" + ], + "text": "And a taser. Excellent. Just make sure it's a big knife.", + "id": 18 + }, + { + "turn": 19, + "speaker": "A", + "utterance": "I don't want any of those little puny ones.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 16 + ], + "expanded emotion cause span": [ + "Do you want to buy me some mace for my, you know, going away present?" + ], + "type": [ + "self-contagion" + ], + "text": "I don't want any of those little puny ones.", + "id": 19 + }, + { + "turn": 20, + "speaker": "B", + "utterance": "So, um- so what are you going to- what are you going to major in?", + "emotion": "neutral", + "text": "So, um- so what are you going to- what are you going to major in?", + "id": 20 + }, + { + "turn": 21, + "speaker": "A", + "utterance": "Well I was thinking maybe underwater basket weaving.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2, + 21 + ], + "expanded emotion cause span": [ + "Guess what came today?", + "I was thinking maybe underwater basket weaving." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Well I was thinking maybe underwater basket weaving.", + "id": 21 + }, + { + "turn": 22, + "speaker": "A", + "utterance": "U.S.C. has a major in that, right.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2, + 21 + ], + "expanded emotion cause span": [ + "Guess what came today?", + "I was thinking maybe underwater basket weaving." + ], + "type": [ + "self-contagion" + ], + "text": "U.S.C. has a major in that, right.", + "id": 22 + }, + { + "turn": 23, + "speaker": "A", + "utterance": "They have - U.S.C. has everything because U.S.C. is the best school ever.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2, + 21, + 23 + ], + "expanded emotion cause span": [ + "Guess what came today?", + "I was thinking maybe underwater basket weaving.", + "U.S.C. is the best school ever." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "They have - U.S.C. has everything because U.S.C. is the best school ever.", + "id": 23 + }, + { + "turn": 24, + "speaker": "B", + "utterance": "they have that as a major?", + "emotion": "neutral", + "text": "they have that as a major?", + "id": 24 + }, + { + "turn": 25, + "speaker": "B", + "utterance": "That's ridiculous. I don't believe that.", + "emotion": "neutral", + "text": "That's ridiculous. I don't believe that.", + "id": 25 + }, + { + "turn": 26, + "speaker": "A", + "utterance": "Okay. Well I'm lying but-", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2, + 21, + 23 + ], + "expanded emotion cause span": [ + "Guess what came today?", + "I was thinking maybe underwater basket weaving.", + "U.S.C. is the best school ever." + ], + "type": [ + "self-contagion" + ], + "text": "Okay. Well I'm lying but-", + "id": 26 + }, + { + "turn": 27, + "speaker": "B", + "utterance": "Seriously, what's your major?", + "emotion": "neutral", + "text": "Seriously, what's your major?", + "id": 27 + }, + { + "turn": 28, + "speaker": "A", + "utterance": "Well, I haven't decided yet. I want to try some things out.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2, + 28 + ], + "expanded emotion cause span": [ + "Guess what came today?", + "I want to try some things out." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Well, I haven't decided yet. I want to try some things out.", + "id": 28 + }, + { + "turn": 29, + "speaker": "B", + "utterance": "So you're undecided?", + "emotion": "neutral", + "text": "So you're undecided?", + "id": 29 + }, + { + "turn": 30, + "speaker": "B", + "utterance": "Hey, that's cool.", + "emotion": "neutral", + "text": "Hey, that's cool.", + "id": 30 + }, + { + "turn": 31, + "speaker": "B", + "utterance": "No, no. It's totally cool. I mean, like, this friend of mine he was- he's been undecided now for, like, the past like eleven years of his life.", + "emotion": "neutral", + "text": "No, no. It's totally cool. I mean, like, this friend of mine he was- he's been undecided now for, like, the past like eleven years of his life.", + "id": 31 + }, + { + "turn": 32, + "speaker": "A", + "utterance": "okay. Well I'm not going to be undecided forever. [LAUGHTER]", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2, + 28 + ], + "expanded emotion cause span": [ + "Guess what came today?", + "I want to try some things out." + ], + "type": [ + "self-contagion" + ], + "text": "okay. Well I'm not going to be undecided forever. [LAUGHTER]", + "id": 32 + }, + { + "turn": 33, + "speaker": "B", + "utterance": "Uh, well-", + "emotion": "neutral", + "text": "Uh, well-", + "id": 33 + }, + { + "turn": 34, + "speaker": "A", + "utterance": "And it's so close so you can come visit me all the time.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 34 + ], + "expanded emotion cause span": [ + "it's so close so you can come visit me all the time." + ], + "type": [ + "no-context" + ], + "text": "And it's so close so you can come visit me all the time.", + "id": 34 + }, + { + "turn": 35, + "speaker": "B", + "utterance": "You- you- you'll find.", + "emotion": "neutral", + "text": "You- you- you'll find.", + "id": 35 + }, + { + "turn": 36, + "speaker": "A", + "utterance": "So this works out perfectly. Because I was worried if I didn't get in to U.S.C., then I would have to go somewhere far away and then-", + "emotion": "excited", + "expanded emotion cause evidence": [ + 36 + ], + "expanded emotion cause span": [ + "So this works out perfectly." + ], + "type": [ + "no-context" + ], + "text": "So this works out perfectly. Because I was worried if I didn't get in to U.S.C., then I would have to go somewhere far away and then-", + "id": 36 + }, + { + "turn": 37, + "speaker": "B", + "utterance": "You'd have to, like go somewhere else, and, you know, we would be apart, and that would suck.", + "emotion": "neutral", + "text": "You'd have to, like go somewhere else, and, you know, we would be apart, and that would suck.", + "id": 37 + }, + { + "turn": 38, + "speaker": "A", + "utterance": "Everything worked out perfectly.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 38 + ], + "expanded emotion cause span": [ + "Everything worked out perfectly." + ], + "type": [ + "no-context" + ], + "text": "Everything worked out perfectly.", + "id": 38 + }, + { + "turn": 39, + "speaker": "B", + "utterance": "That's awesome.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 38 + ], + "expanded emotion cause span": [ + "Everything worked out perfectly." + ], + "type": [ + "inter-personal" + ], + "text": "That's awesome.", + "id": 39 + }, + { + "turn": 40, + "speaker": "A", + "utterance": "I know. We should have a party.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 38, + 40 + ], + "expanded emotion cause span": [ + "Everything worked out perfectly.", + "We should have a party." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "I know. We should have a party.", + "id": 40 + }, + { + "turn": 41, + "speaker": "A", + "utterance": "An I got accepted to U.S.C. party.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 38, + 40 + ], + "expanded emotion cause span": [ + "Everything worked out perfectly.", + "We should have a party." + ], + "type": [ + "self-contagion" + ], + "text": "An I got accepted to U.S.C. party.", + "id": 41 + }, + { + "turn": 42, + "speaker": "A", + "utterance": "No. An I got accepted to U.S.C. party. [LAUGHTER]", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2, + 40 + ], + "expanded emotion cause span": [ + "Guess what came today?", + "We should have a party." + ], + "type": [ + "self-contagion" + ], + "text": "No. An I got accepted to U.S.C. party. [LAUGHTER]", + "id": 42 + }, + { + "turn": 43, + "speaker": "B", + "utterance": "Oh, that's right. Okay, I see. Right, right, right.", + "emotion": "neutral", + "text": "Oh, that's right. Okay, I see. Right, right, right.", + "id": 43 + }, + { + "turn": 44, + "speaker": "B", + "utterance": "A party celebrating your acceptance.", + "emotion": "neutral", + "text": "A party celebrating your acceptance.", + "id": 44 + }, + { + "turn": 45, + "speaker": "A", + "utterance": "Right. Now you're with me.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 44, + 45 + ], + "expanded emotion cause span": [ + "A party celebrating your acceptance.", + "Right. Now you're with me." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Right. Now you're with me.", + "id": 45 + }, + { + "turn": 46, + "speaker": "B", + "utterance": "That's cool.", + "emotion": "neutral", + "text": "That's cool.", + "id": 46 + }, + { + "turn": 47, + "speaker": "A", + "utterance": "That is why I got accepted.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 47 + ], + "expanded emotion cause span": [ + "I got accepted." + ], + "type": [ + "no-context" + ], + "text": "That is why I got accepted.", + "id": 47 + }, + { + "turn": 48, + "speaker": "B", + "utterance": "Well, that's really cool that you're going to be staying in the same city and everything. so umm", + "emotion": "excited", + "expanded emotion cause evidence": [ + 48 + ], + "expanded emotion cause span": [ + "that's really cool that you're going to be staying in the same city" + ], + "type": [ + "no-context" + ], + "text": "Well, that's really cool that you're going to be staying in the same city and everything. so umm", + "id": 48 + }, + { + "turn": 49, + "speaker": "A", + "utterance": "I know.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 48 + ], + "expanded emotion cause span": [ + "Well, that's really cool that you're going to be staying in the same city and everything. so umm" + ], + "type": [ + "inter-personal" + ], + "text": "I know.", + "id": 49 + }, + { + "turn": 50, + "speaker": "B", + "utterance": "I don't know are you, like, I don't know. Are you, like, available or anything?", + "emotion": "neutral", + "text": "I don't know are you, like, I don't know. Are you, like, available or anything?", + "id": 50 + }, + { + "turn": 51, + "speaker": "B", + "utterance": "Well I mean I don't know. It's like you know I kind of had a crush on you throughout high school and, like", + "emotion": "excited", + "expanded emotion cause evidence": [ + 51 + ], + "expanded emotion cause span": [ + "It's like you know I kind of had a crush on you throughout high school" + ], + "type": [ + "no-context" + ], + "text": "Well I mean I don't know. It's like you know I kind of had a crush on you throughout high school and, like", + "id": 51 + }, + { + "turn": 52, + "speaker": "B", + "utterance": "I don't know I just thought that, you know, maybe we could, you know, I don't know. It's like, you know, just test the waters anyway. I don't see what the problem is.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 51 + ], + "expanded emotion cause span": [ + "It's like you know I kind of had a crush on you throughout high school" + ], + "type": [ + "self-contagion" + ], + "text": "I don't know I just thought that, you know, maybe we could, you know, I don't know. It's like, you know, just test the waters anyway. I don't see what the problem is.", + "id": 52 + }, + { + "turn": 53, + "speaker": "A", + "utterance": "What- what did you have in mind?", + "emotion": "excited", + "expanded emotion cause evidence": [ + 51 + ], + "expanded emotion cause span": [ + "It's like you know I kind of had a crush on you throughout high school" + ], + "type": [ + "inter-personal" + ], + "text": "What- what did you have in mind?", + "id": 53 + }, + { + "turn": 54, + "speaker": "B", + "utterance": "Movies- movie, we'll go to a movie and a dinner and- and", + "emotion": "excited", + "expanded emotion cause evidence": [ + 51 + ], + "expanded emotion cause span": [ + "It's like you know I kind of had a crush on you throughout high school" + ], + "type": [ + "self-contagion" + ], + "text": "Movies- movie, we'll go to a movie and a dinner and- and", + "id": 54 + }, + { + "turn": 55, + "speaker": "B", + "utterance": "actually, you know, there's this- there's this really cool restaurant, um, I don't know if you- it's Red Lobster. It's like down on", + "emotion": "excited", + "expanded emotion cause evidence": [ + 51 + ], + "expanded emotion cause span": [ + "It's like you know I kind of had a crush on you throughout high school" + ], + "type": [ + "self-contagion" + ], + "text": "actually, you know, there's this- there's this really cool restaurant, um, I don't know if you- it's Red Lobster. It's like down on", + "id": 55 + }, + { + "turn": 56, + "speaker": "A", + "utterance": "[LAUGHTER]", + "emotion": "excited", + "expanded emotion cause evidence": [ + 51 + ], + "expanded emotion cause span": [ + "It's like you know I kind of had a crush on you throughout high school" + ], + "type": [ + "inter-personal" + ], + "text": "[LAUGHTER]", + "id": 56 + }, + { + "turn": 57, + "speaker": "B", + "utterance": "Vermont.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 51 + ], + "expanded emotion cause span": [ + "It's like you know I kind of had a crush on you throughout high school" + ], + "type": [ + "self-contagion" + ], + "text": "Vermont.", + "id": 57 + }, + { + "turn": 58, + "speaker": "B", + "utterance": "Wait, you've been there before?", + "emotion": "excited", + "expanded emotion cause evidence": [ + 51 + ], + "expanded emotion cause span": [ + "It's like you know I kind of had a crush on you throughout high school" + ], + "type": [ + "self-contagion" + ], + "text": "Wait, you've been there before?", + "id": 58 + }, + { + "turn": 59, + "speaker": "A", + "utterance": "On occasion I've heard of it.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 51 + ], + "expanded emotion cause span": [ + "It's like you know I kind of had a crush on you throughout high school" + ], + "type": [ + "inter-personal" + ], + "text": "On occasion I've heard of it.", + "id": 59 + }, + { + "turn": 60, + "speaker": "B", + "utterance": "Oh, so well then you know that it's awesome.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 51, + 60 + ], + "expanded emotion cause span": [ + "It's like you know I kind of had a crush on you throughout high school", + "it's awesome." + ], + "type": [ + "no-context", + "self-contagion" + ], + "text": "Oh, so well then you know that it's awesome.", + "id": 60 + }, + { + "turn": 61, + "speaker": "A", + "utterance": "Yeah. Totally.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 51, + 60 + ], + "expanded emotion cause span": [ + "It's like you know I kind of had a crush on you throughout high school", + "it's awesome." + ], + "type": [ + "inter-personal" + ], + "text": "Yeah. Totally.", + "id": 61 + }, + { + "turn": 62, + "speaker": "B", + "utterance": "Right, so we'll go there and then- and then we'll get some ice cream and maybe we'll go putt-putt golfing.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 62 + ], + "expanded emotion cause span": [ + "Right, so we'll go there and then- and then we'll get some ice cream and maybe we'll go putt-putt golfing." + ], + "type": [ + "no-context" + ], + "text": "Right, so we'll go there and then- and then we'll get some ice cream and maybe we'll go putt-putt golfing.", + "id": 62 + }, + { + "turn": 63, + "speaker": "A", + "utterance": "I am totally down with the ice cream.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 63 + ], + "expanded emotion cause span": [ + "I am totally down with the ice cream." + ], + "type": [ + "no-context" + ], + "text": "I am totally down with the ice cream.", + "id": 63 + }, + { + "turn": 64, + "speaker": "B", + "utterance": "Okay. Putt-putt golfing?", + "emotion": "neutral", + "text": "Okay. Putt-putt golfing?", + "id": 64 + }, + { + "turn": 65, + "speaker": "A", + "utterance": "Eh, we can work that part out.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 63 + ], + "expanded emotion cause span": [ + "I am totally down with the ice cream." + ], + "type": [ + "self-contagion" + ], + "text": "Eh, we can work that part out.", + "id": 65 + }, + { + "turn": 66, + "speaker": "B", + "utterance": "Yeah, you want to go. No, you want to go. You want to go.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 62 + ], + "expanded emotion cause span": [ + "Right, so we'll go there and then- and then we'll get some ice cream and maybe we'll go putt-putt golfing." + ], + "type": [ + "self-contagion" + ], + "text": "Yeah, you want to go. No, you want to go. You want to go.", + "id": 66 + }, + { + "turn": 67, + "speaker": "A", + "utterance": "Alright.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 63 + ], + "expanded emotion cause span": [ + "I am totally down with the ice cream." + ], + "type": [ + "self-contagion" + ], + "text": "Alright.", + "id": 67 + }, + { + "turn": 68, + "speaker": "B", + "utterance": "I can see it in your eyes. You want to go.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 68 + ], + "expanded emotion cause span": [ + "I can see it in your eyes. You want to go." + ], + "type": [ + "no-context" + ], + "text": "I can see it in your eyes. You want to go.", + "id": 68 + }, + { + "turn": 69, + "speaker": "A", + "utterance": "party.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2 + ], + "expanded emotion cause span": [ + "Guess what came today?" + ], + "type": [ + "self-contagion" + ], + "text": "party.", + "id": 69 + }, + { + "turn": 70, + "speaker": "B", + "utterance": "Good. Alright we're so happy.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 63, + 70 + ], + "expanded emotion cause span": [ + "I am totally down with the ice cream.", + "we're so happy." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "Good. Alright we're so happy.", + "id": 70 + }, + { + "turn": 71, + "speaker": "B", + "utterance": "That's right. Um, so U.S.C. is a really nice school.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2, + 71 + ], + "expanded emotion cause span": [ + "Guess what came today?", + "U.S.C. is a really nice school." + ], + "type": [ + "no-context", + "inter-personal" + ], + "text": "That's right. Um, so U.S.C. is a really nice school.", + "id": 71 + }, + { + "turn": 72, + "speaker": "A", + "utterance": "I know.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 2, + 71 + ], + "expanded emotion cause span": [ + "Guess what came today?", + "U.S.C. is a really nice school." + ], + "type": [ + "hybrid" + ], + "text": "I know.", + "id": 72 + }, + { + "turn": 73, + "speaker": "B", + "utterance": "Are you going to take out loans or-", + "emotion": "neutral", + "text": "Are you going to take out loans or-", + "id": 73 + }, + { + "turn": 74, + "speaker": "A", + "utterance": "Okay well that's not a happy part. We don't want to talk about that.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 74 + ], + "expanded emotion cause span": [ + "Okay well that's not a happy part. We don't want to talk about that." + ], + "type": [ + "no-context" + ], + "text": "Okay well that's not a happy part. We don't want to talk about that.", + "id": 74 + }, + { + "turn": 75, + "speaker": "A", + "utterance": "Well no. I mean I have some scholarships and some financial aid and stuff but I'll have to, you know, I'll get a job", + "emotion": "excited", + "expanded emotion cause evidence": [ + 75 + ], + "expanded emotion cause span": [ + "I mean I have some scholarships and some financial aid and stuff but I'll have to, you know, I'll get a job" + ], + "type": [ + "no-context" + ], + "text": "Well no. I mean I have some scholarships and some financial aid and stuff but I'll have to, you know, I'll get a job", + "id": 75 + }, + { + "turn": 76, + "speaker": "A", + "utterance": "while I'm in school. It'll be good.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 76 + ], + "expanded emotion cause span": [ + "while I'm in school. It'll be good." + ], + "type": [ + "no-context" + ], + "text": "while I'm in school. It'll be good.", + "id": 76 + }, + { + "turn": 77, + "speaker": "A", + "utterance": "Yeah. It will work out. Maybe I could work at Red Lobster.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 77 + ], + "expanded emotion cause span": [ + "It will work out." + ], + "type": [ + "no-context" + ], + "text": "Yeah. It will work out. Maybe I could work at Red Lobster.", + "id": 77 + }, + { + "turn": 78, + "speaker": "A", + "utterance": "I know. Right down the street.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 77 + ], + "expanded emotion cause span": [ + "It will work out." + ], + "type": [ + "self-contagion" + ], + "text": "I know. Right down the street.", + "id": 78 + }, + { + "turn": 79, + "speaker": "B", + "utterance": "But, um-", + "emotion": "neutral", + "text": "But, um-", + "id": 79 + }, + { + "turn": 80, + "speaker": "B", + "utterance": "I mean, like, I don't know. I'm just saying if you need to make some extra cash. You can, you know", + "emotion": "neutral", + "text": "I mean, like, I don't know. I'm just saying if you need to make some extra cash. You can, you know", + "id": 80 + }, + { + "turn": 81, + "speaker": "B", + "utterance": "Or library.", + "emotion": "neutral", + "text": "Or library.", + "id": 81 + }, + { + "turn": 82, + "speaker": "B", + "utterance": "I just said the library", + "emotion": "neutral", + "text": "I just said the library", + "id": 82 + }, + { + "turn": 83, + "speaker": "B", + "utterance": "or, um, campus cruiser. You can drive people around.", + "emotion": "neutral", + "text": "or, um, campus cruiser. You can drive people around.", + "id": 83 + }, + { + "turn": 84, + "speaker": "A", + "utterance": "Excellent. Drive drunk people around because you know that's all campus cruisers for.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 84 + ], + "expanded emotion cause span": [ + "Drive drunk people around because you know that's all campus cruisers for." + ], + "type": [ + "no-context" + ], + "text": "Excellent. Drive drunk people around because you know that's all campus cruisers for.", + "id": 84 + }, + { + "turn": 85, + "speaker": "B", + "utterance": "Right or you can run for student counsel.", + "emotion": "neutral", + "text": "Right or you can run for student counsel.", + "id": 85 + }, + { + "turn": 86, + "speaker": "A", + "utterance": "Okay. No, that's dorky.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 84 + ], + "expanded emotion cause span": [ + "Drive drunk people around because you know that's all campus cruisers for." + ], + "type": [ + "self-contagion" + ], + "text": "Okay. No, that's dorky.", + "id": 86 + }, + { + "turn": 87, + "speaker": "B", + "utterance": "Dorky?", + "emotion": "neutral", + "text": "Dorky?", + "id": 87 + }, + { + "turn": 88, + "speaker": "A", + "utterance": "Yeah.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 84 + ], + "expanded emotion cause span": [ + "Drive drunk people around because you know that's all campus cruisers for." + ], + "type": [ + "self-contagion" + ], + "text": "Yeah.", + "id": 88 + }, + { + "turn": 89, + "speaker": "B", + "utterance": "It's important.", + "emotion": "neutral", + "text": "It's important.", + "id": 89 + }, + { + "turn": 90, + "speaker": "A", + "utterance": "Student counsel?", + "emotion": "excited", + "expanded emotion cause evidence": [ + 84 + ], + "expanded emotion cause span": [ + "Drive drunk people around because you know that's all campus cruisers for." + ], + "type": [ + "self-contagion" + ], + "text": "Student counsel?", + "id": 90 + }, + { + "turn": 91, + "speaker": "A", + "utterance": "No, it's dorky.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 84 + ], + "expanded emotion cause span": [ + "Drive drunk people around because you know that's all campus cruisers for." + ], + "type": [ + "self-contagion" + ], + "text": "No, it's dorky.", + "id": 91 + }, + { + "turn": 92, + "speaker": "B", + "utterance": "Fine. It's dorky.", + "emotion": "neutral", + "text": "Fine. It's dorky.", + "id": 92 + }, + { + "turn": 93, + "speaker": "A", + "utterance": "Social life. Hello.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 93 + ], + "expanded emotion cause span": [ + "Social life" + ], + "type": [ + "no-context" + ], + "text": "Social life. Hello.", + "id": 93 + }, + { + "turn": 94, + "speaker": "B", + "utterance": "But that'll fit you because you're a dork.", + "emotion": "neutral", + "text": "But that'll fit you because you're a dork.", + "id": 94 + }, + { + "turn": 95, + "speaker": "A", + "utterance": "[LAUGHTER].", + "emotion": "excited", + "expanded emotion cause evidence": [ + 93 + ], + "expanded emotion cause span": [ + "Social life" + ], + "type": [ + "self-contagion" + ], + "text": "[LAUGHTER].", + "id": 95 + }, + { + "turn": 96, + "speaker": "A", + "utterance": "[LAUGHTER].", + "emotion": "excited", + "expanded emotion cause evidence": [ + 93 + ], + "expanded emotion cause span": [ + "Social life" + ], + "type": [ + "self-contagion" + ], + "text": "[LAUGHTER].", + "id": 96 + }, + { + "turn": 97, + "speaker": "B", + "utterance": "I dork.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 93 + ], + "expanded emotion cause span": [ + "Social life" + ], + "type": [ + "inter-personal" + ], + "text": "I dork.", + "id": 97 + }, + { + "turn": 98, + "speaker": "A", + "utterance": "No. But I'm thinking I might, you know, like audition for a play or something. I don't really want to do the sorority thing. I'm not really feeling that vibe with the", + "emotion": "excited", + "expanded emotion cause evidence": [ + 98 + ], + "expanded emotion cause span": [ + "I don't really want to do the sorority thing. I'm not really feeling that vibe with the" + ], + "type": [ + "no-context" + ], + "text": "No. But I'm thinking I might, you know, like audition for a play or something. I don't really want to do the sorority thing. I'm not really feeling that vibe with the", + "id": 98 + }, + { + "turn": 99, + "speaker": "B", + "utterance": "Yeah, you don't want to do the sorority thing because you'll probably get used and abused by", + "emotion": "neutral", + "text": "Yeah, you don't want to do the sorority thing because you'll probably get used and abused by", + "id": 99 + }, + { + "turn": 100, + "speaker": "B", + "utterance": "lots of drunk frat boys", + "emotion": "neutral", + "text": "lots of drunk frat boys", + "id": 100 + }, + { + "turn": 101, + "speaker": "B", + "utterance": "Yeah.", + "emotion": "neutral", + "text": "Yeah.", + "id": 101 + }, + { + "turn": 102, + "speaker": "A", + "utterance": "What have you heard about the Greek system?", + "emotion": "excited", + "expanded emotion cause evidence": [ + 102 + ], + "expanded emotion cause span": [ + "What have you heard about the Greek system?" + ], + "type": [ + "no-context" + ], + "text": "What have you heard about the Greek system?", + "id": 102 + }, + { + "turn": 103, + "speaker": "B", + "utterance": "I mean it's not really free because you have to pay for it, but yeah.", + "emotion": "neutral", + "text": "I mean it's not really free because you have to pay for it, but yeah.", + "id": 103 + }, + { + "turn": 104, + "speaker": "B", + "utterance": "Well do you think you're going to live on campus or off campus your first year?", + "emotion": "neutral", + "text": "Well do you think you're going to live on campus or off campus your first year?", + "id": 104 + }, + { + "turn": 105, + "speaker": "B", + "utterance": "I hate to break this to you but you meet people by being cool, so-", + "emotion": "neutral", + "text": "I hate to break this to you but you meet people by being cool, so-", + "id": 105 + }, + { + "turn": 106, + "speaker": "A", + "utterance": "Oh, oh, I'm sorry, my bad. I'll have to, like, sign up for summer lessons from you before I go. You can teach me how to be cool before I go to college.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 106 + ], + "expanded emotion cause span": [ + "sign up for summer lessons from you before I go" + ], + "type": [ + "no-context" + ], + "text": "Oh, oh, I'm sorry, my bad. I'll have to, like, sign up for summer lessons from you before I go. You can teach me how to be cool before I go to college.", + "id": 106 + }, + { + "turn": 107, + "speaker": "B", + "utterance": "No, no, no. You're right though. I mean, you know, dorms are definitely the way to meet people. I know that I was in an apartment off campus", + "emotion": "neutral", + "text": "No, no, no. You're right though. I mean, you know, dorms are definitely the way to meet people. I know that I was in an apartment off campus", + "id": 107 + }, + { + "turn": 108, + "speaker": "B", + "utterance": "that happened, you know, that was going on.", + "emotion": "neutral", + "text": "that happened, you know, that was going on.", + "id": 108 + }, + { + "turn": 109, + "speaker": "A", + "utterance": "That's what you're saying. I'm right. [LAUGHTER]", + "emotion": "excited", + "expanded emotion cause evidence": [ + 107 + ], + "expanded emotion cause span": [ + "You're right though." + ], + "type": [ + "inter-personal" + ], + "text": "That's what you're saying. I'm right. [LAUGHTER]", + "id": 109 + }, + { + "turn": 110, + "speaker": "A", + "utterance": "me.", + "emotion": "excited", + "expanded emotion cause evidence": [ + 107 + ], + "expanded emotion cause span": [ + "You're right though." + ], + "type": [ + "inter-personal" + ], + "text": "me.", + "id": 110, + "source_sentences": [ + 106 + ], + "has_target": true, + "annotator": "ground_truth" + } +] \ No newline at end of file diff --git a/sight/query/annotated/0Qws8BuK3RQ.json b/sight/query/annotated/0Qws8BuK3RQ.json new file mode 100644 index 0000000000000000000000000000000000000000..31c097d2f762cb36383b9e65bfdfaaf4ced749be --- /dev/null +++ b/sight/query/annotated/0Qws8BuK3RQ.json @@ -0,0 +1,30 @@ +[ + { + "file_id": "0Qws8BuK3RQ", + "query_id": 0, + "timestamp": 1684701645936.0, + "annotatedSourceSentencesIndices": [ + 4, + 25, + 29 + ], + "names": [ + "annotator2" + ], + "text": "Is the distance matrix right?" + }, + { + "file_id": "0Qws8BuK3RQ", + "query_id": 1, + "timestamp": 1684701685821.0, + "annotatedSourceSentencesIndices": [ + 62, + 63, + 73 + ], + "names": [ + "annotator2" + ], + "text": "where can i find the proof of procrustes problem?" + } +] \ No newline at end of file diff --git a/sight/query/annotated/0h43aV4aH7I.json b/sight/query/annotated/0h43aV4aH7I.json new file mode 100644 index 0000000000000000000000000000000000000000..5e001baa7b5354a36405ad5a6c51c7c2b66d9662 --- /dev/null +++ b/sight/query/annotated/0h43aV4aH7I.json @@ -0,0 +1,105 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 0, + "timestamp": 1684520869368.0, + "annotatedSourceSentencesIndices": [ + 370 + ], + "names": [ + "annotator1" + ], + "text": "Isnt there a mistake @ 46:24 ? Shouldn\u2019t the position 8,1 of matrix A contain a8,1 and not a1,8? Same for position 8,2, shouldn\u2019t it contain a8,2 instead of a2,8? And same for position 1,2? Great lecture thanks!" + }, + { + "file_id": "0h43aV4aH7I", + "query_id": 1, + "timestamp": 1684700727042.0, + "annotatedSourceSentencesIndices": [ + 81 + ], + "names": [ + "annotator2" + ], + "text": "How the imaginary parts are taken care of in Fourier Basis for JPEG?" + }, + { + "file_id": "0h43aV4aH7I", + "query_id": 2, + "timestamp": 1684700837277.0, + "annotatedSourceSentencesIndices": [ + 27, + 28 + ], + "names": [ + "annotator2" + ], + "text": "I'm fairly certain x includes 255 in the domain. [4:15]\nCan anyone confirm or clarify? \n(should be x is less than or equal to 255, rather than strictly less than)" + }, + { + "file_id": "0h43aV4aH7I", + "query_id": 3, + "timestamp": 1684700983228.0, + "annotatedSourceSentencesIndices": [ + 365, + 366 + ], + "names": [ + "annotator2" + ], + "text": "Excuse me, does it mean that the basis of the input space and that of the output space is the same {v1, v2, ..., v8} at 45:25?\nThen, if this is true, when does change of basis happen?\nI get confused here, please help me, thanks a lot!" + }, + { + "file_id": "0h43aV4aH7I", + "query_id": 4, + "timestamp": 1684701306384.0, + "annotatedSourceSentencesIndices": [ + 345, + 357, + 358, + 365, + 366 + ], + "names": [ + "annotator2" + ], + "text": "Got extremely confused when he brought transformations in at the end. Why did the original basis vector \"x\" change to \"v\", then why does he compute a T(x) from \"knowing\" T(v1), ... T(v8) BEFORE writing what the actual values of T(v1) .. T(v8) are, and what is this T(x) even used for? and then where does the \"a\" come from?" + }, + { + "file_id": "0h43aV4aH7I", + "query_id": 5, + "timestamp": 1684701331681.0, + "annotatedSourceSentencesIndices": [ + 27, + 28 + ], + "names": [ + "annotator2" + ], + "text": "4:17, x[i] <256 , right?" + }, + { + "file_id": "0h43aV4aH7I", + "query_id": 6, + "timestamp": 1684701411849.0, + "annotatedSourceSentencesIndices": [ + 291 + ], + "names": [ + "annotator2" + ], + "text": "Is it just me? Is that a mistake? He writes x=Wc at 37:11, where x represents vector in the old basis, and c the vector in the new basis, and W the columns of new basis vectors. Should it be c=Wx instead?" + }, + { + "file_id": "0h43aV4aH7I", + "query_id": 7, + "timestamp": 1684701455485.0, + "annotatedSourceSentencesIndices": [ + 121 + ], + "names": [ + "annotator2" + ], + "text": "He never taught the compression step right? ie., c -> c(hat)" + } +] \ No newline at end of file diff --git a/sight/query/annotated/13r9QY6cmjc.json b/sight/query/annotated/13r9QY6cmjc.json new file mode 100644 index 0000000000000000000000000000000000000000..80fb77cf0c95c499c2a4c57fd3cc1d8d063a1a9a --- /dev/null +++ b/sight/query/annotated/13r9QY6cmjc.json @@ -0,0 +1,328 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 0, + "timestamp": 1684723011392.0, + "annotatedSourceSentencesIndices": [ + 246, + 276 + ], + "names": [ + "annotator2" + ], + "text": "i'm still a little confused, what is u naught supposed to represent? Are those just the linear combination of the eigenvectors?" + }, + { + "file_id": "13r9QY6cmjc", + "query_id": 1, + "timestamp": 1684723178257.0, + "annotatedSourceSentencesIndices": [ + 289, + 290 + ], + "names": [ + "annotator2" + ], + "text": "I dont undertand why the eigenvectors are [lamba_1 \u00a01] and [lamba_2 1] at 49:19...\nsince it is NOT true that ((1 - lamba) * (lamba)) + 1 is lamba^2 - lamba - 1 ... or it is? or what is happening?\u00a0" + }, + { + "file_id": "13r9QY6cmjc", + "query_id": 2, + "timestamp": 1684723273690.0, + "annotatedSourceSentencesIndices": [ + 105, + 106 + ], + "names": [ + "annotator2" + ], + "text": "I don't understand 11:25 why A square can be written in the way on the blackboard. I think A^2 should be (S Lambda S^-1)^T (S Lambda S^-1), the result differs from the one on the blackboard. Could someone explain this?" + }, + { + "file_id": "13r9QY6cmjc", + "query_id": 5, + "timestamp": 1684723528088.0, + "annotatedSourceSentencesIndices": [ + 351, + 352, + 357, + 358, + 361 + ], + "names": [ + "annotator2" + ], + "text": "So, the second component of u(k+1) is useless, right? The actual value is given by the first component." + }, + { + "file_id": "13r9QY6cmjc", + "query_id": 6, + "timestamp": 1684723821969.0, + "annotatedSourceSentencesIndices": [ + 429, + 433 + ], + "names": [ + "annotator2" + ], + "text": "Excuse me, why doesn't the calculation of F_100 at \"46:08\" time the eigenvector X_1? Am i missing something?" + }, + { + "file_id": "13r9QY6cmjc", + "query_id": 7, + "timestamp": 1684725468449.0, + "annotatedSourceSentencesIndices": [ + 213 + ], + "names": [ + "annotator2" + ], + "text": "-0.618 1\n 1 -1.618\nThe Null Space of the given matrix should be the zero vector because the RREF will become:\n1 0\n0 1\nWhich means the Null Space(and hence the Eigenvector) is the zero vector for the first Eigenvalue?\nCorrect me if I'm wrong?" + }, + { + "file_id": "13r9QY6cmjc", + "query_id": 9, + "timestamp": 1684725523482.0, + "annotatedSourceSentencesIndices": [ + 346 + ], + "names": [ + "annotator2" + ], + "text": "for anyone wondering how he turned the fibonaci sequence to a matrix @ 37:00 you are not alone , check this video out https://www.youtube.com/watch?v=iVNoIwY0UV8" + }, + { + "file_id": "13r9QY6cmjc", + "query_id": 10, + "timestamp": 1684725950887.0, + "annotatedSourceSentencesIndices": [ + 1, + 485 + ], + "names": [ + "annotator2" + ], + "text": "so it seems like the professor emphasized the importance of the eigenvalue here, that's nice. but is the eigenvector of any importance? what's a good example of eigenvectors?" + }, + { + "file_id": "13r9QY6cmjc", + "query_id": 11, + "timestamp": 1684726006688.0, + "annotatedSourceSentencesIndices": [ + 276 + ], + "names": [ + "annotator2" + ], + "text": "Why u_0 can be written as a linear combination of eigenvector of A? 29:55" + }, + { + "file_id": "13r9QY6cmjc", + "query_id": 13, + "timestamp": 1684726031554.0, + "annotatedSourceSentencesIndices": [ + 276 + ], + "names": [ + "annotator2" + ], + "text": "Did we ever prove that if the set of eigenvalues are distinct, the set of eigenvectors are linearly independent? I ask because at ~ 32:00 taking u_o = c1*x1 + c2*x2 + ... + cn*xn requires the eigenvectors to form a basis for an n-dimensional vector space (i.e. span the column space of an invertible matrix). It feels right but I have no solid background for how to think about it" + }, + { + "file_id": "13r9QY6cmjc", + "query_id": 14, + "timestamp": 1684726883847.0, + "annotatedSourceSentencesIndices": [ + 313, + 361 + ], + "names": [ + "annotator2" + ], + "text": "why are we representing mu(k) vector as the combination of eigen vectors in the problem of Fibonacci sequence?" + }, + { + "file_id": "13r9QY6cmjc", + "query_id": 15, + "timestamp": 1684726895777.0, + "annotatedSourceSentencesIndices": [ + 276 + ], + "names": [ + "annotator2" + ], + "text": "In u naught = c1x1 + c2x2 .... Cnxn what are X's the vectors of?" + }, + { + "file_id": "13r9QY6cmjc", + "query_id": 17, + "timestamp": 1684727650779.0, + "annotatedSourceSentencesIndices": [ + 485 + ], + "names": [ + "annotator2" + ], + "text": "Notes for future ref.)\n(7:16) there are _some_ matrices that do _NOT_ have n-independent eigenvectors, but _most_ of the matrices we deal with do have n-independent eigenvectors.\n(17:14) If all evalues are different, there _must_ be n-indep evectors. But if there are same evalues, it's possible _no_ n-indep evectors. (Identity matrix is an example of having the same evalues but still having n-indep evectors)\n* Also, the position of Lambda and S should be changed(32:36). You'll see why by just thinking matrix multiplication, and it can also be viewed by knowing A^100=S*Lambda^100*S^-1 and u_0=S*c.\n Thus, it should be S*Lambda^100*c, and this also can be thought of as 'transformation' between the two different bases - one of the two is the set of the egenvectors of A.\n* Also, (43:34) How prof. Strang could calculate that?? Actually that number _1.618033988749894..._ is called the 'golden ratio'.\n* (8:15) Note that A and Lambda are 'similar'. (And, S and S_-1(S inverse) transforms the coordinates.. you know what I mean.. both A and Lambda can be though of as some \"transformation\" based on different basis.. and S(or S_-1) transforms the coord between those two world.)" + }, + { + "file_id": "13r9QY6cmjc", + "query_id": 18, + "timestamp": 1684727704997.0, + "annotatedSourceSentencesIndices": [ + 358 + ], + "names": [ + "annotator2" + ], + "text": "39:03 where the A (1,1,1,0) comes from? help....." + }, + { + "file_id": "13r9QY6cmjc", + "query_id": 21, + "timestamp": 1684727831398.0, + "annotatedSourceSentencesIndices": [ + 255 + ], + "names": [ + "annotator2" + ], + "text": "Can't you also use the determinant to figure out that A\u1d4f \u2192 0 as K \u2192 \u221e ? i.e. if det A < 1 then A\u1d4f \u2192 0" + }, + { + "file_id": "13r9QY6cmjc", + "query_id": 22, + "timestamp": 1684727876048.0, + "annotatedSourceSentencesIndices": [ + 302 + ], + "names": [ + "annotator2" + ], + "text": "Is there an error at 32:30? Shouldn't S be multiplied before (lamda matrix)^100?" + }, + { + "file_id": "13r9QY6cmjc", + "query_id": 23, + "timestamp": 1684727933448.0, + "annotatedSourceSentencesIndices": [ + 276 + ], + "names": [ + "annotator2" + ], + "text": "I have a doubt in Difference equations part. He writes u_0 as a combination of eigen-vectors of A. Why should this be true?" + }, + { + "file_id": "13r9QY6cmjc", + "query_id": 25, + "timestamp": 1684727944948.0, + "annotatedSourceSentencesIndices": [ + 276 + ], + "names": [ + "annotator2" + ], + "text": "https://www.youtube.com/watch?v=13r9QY6cmjc#t=29m29s how does one know that u0 can be expressed in terms of eigenvectors, i.e. how do we know what u0 is in the span of eigenvectors?" + }, + { + "file_id": "13r9QY6cmjc", + "query_id": 26, + "timestamp": 1684728060182.0, + "annotatedSourceSentencesIndices": [ + 105, + 106 + ], + "names": [ + "annotator2" + ], + "text": "In the computation of the Eigen values for A\u00b2, he used A = S\u028cS\u02c9\u00b9 to derive that \u028c\u00b2 represents its Eigen value matrix. However this can be true only if S is invertible for A\u00b2, which need not be always true.\n\nFor example, for the matrix below (say A), the Eigen values are 1, -1(refer previous lecture). This would imply that A\u00b2 has only one Eigen value of 1. This would imply that S has 2 columns which are same (if it has only one column then it is no longer square and hence inverse doesn't apply) and hence non invertible. This implies that this proof cannot be used for all the cases of the matrix A.\n\u00a0_\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 _\u00a0\n\u2502 0\u00a0 1 \u2502\n\u2502\u00a01 \u00a00 \u2502\n \u00af\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00af\nIs there something I'm missing here?" + }, + { + "file_id": "13r9QY6cmjc", + "query_id": 27, + "timestamp": 1684728093599.0, + "annotatedSourceSentencesIndices": [ + 433 + ], + "names": [ + "annotator2" + ], + "text": "45:50\nWhy does he add the constant c1?" + }, + { + "file_id": "13r9QY6cmjc", + "query_id": 30, + "timestamp": 1684728116666.0, + "annotatedSourceSentencesIndices": [ + 485 + ], + "names": [ + "annotator2" + ], + "text": "Why the skew-symmetric matrix have zero or imaginary eigenvalue?" + }, + { + "file_id": "13r9QY6cmjc", + "query_id": 31, + "timestamp": 1684728216400.0, + "annotatedSourceSentencesIndices": [ + 458 + ], + "names": [ + "annotator2" + ], + "text": "Could someone explain why vector, lambda and 1 is a solution to the nullspace at 48:43? First component, (1-lambda)*lambda+1 is not 0 or different from lambda^2 - lambda -1." + }, + { + "file_id": "13r9QY6cmjc", + "query_id": 32, + "timestamp": 1684728378616.0, + "annotatedSourceSentencesIndices": [ + 413 + ], + "names": [ + "annotator2" + ], + "text": "@ 44:00 why summation of both eigen values are 1?? have i missed any concept behind this?? : (" + }, + { + "file_id": "13r9QY6cmjc", + "query_id": 36, + "timestamp": 1684728416886.0, + "annotatedSourceSentencesIndices": [ + 166, + 167 + ], + "names": [ + "annotator2" + ], + "text": "Can anyone direct me to a good proof for 19:36?" + }, + { + "file_id": "13r9QY6cmjc", + "query_id": 37, + "timestamp": 1684728431252.0, + "annotatedSourceSentencesIndices": [ + 433 + ], + "names": [ + "annotator2" + ], + "text": "But how do you find c1?" + }, + { + "file_id": "13r9QY6cmjc", + "query_id": 38, + "timestamp": 1684728490619.0, + "annotatedSourceSentencesIndices": [ + 10, + 12, + 16 + ], + "names": [ + "annotator2" + ], + "text": "Just wondering...what keeps us from calling the eigenvector matrix E instead of S ? Is E already used for something else ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated/1RLctDS2hUQ.json b/sight/query/annotated/1RLctDS2hUQ.json new file mode 100644 index 0000000000000000000000000000000000000000..4eb2909867be69806c71d6d606f73e5f95038719 --- /dev/null +++ b/sight/query/annotated/1RLctDS2hUQ.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "1RLctDS2hUQ", + "query_id": 0, + "timestamp": 1684511409384.0, + "annotatedSourceSentencesIndices": [ + 443 + ], + "names": [ + "annotator1" + ], + "text": "43:00 where did he get 1/18(u^6) from?" + } +] \ No newline at end of file diff --git a/sight/query/annotated/4HRhg4eUiMo.json b/sight/query/annotated/4HRhg4eUiMo.json new file mode 100644 index 0000000000000000000000000000000000000000..5e82f3d5dc1cf25d3d6c3b145b5014ce47a796de --- /dev/null +++ b/sight/query/annotated/4HRhg4eUiMo.json @@ -0,0 +1,77 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [ + 805 + ], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + }, + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [ + 444 + ], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + }, + { + "file_id": "4HRhg4eUiMo", + "query_id": 2, + "timestamp": 1684518443888.0, + "annotatedSourceSentencesIndices": [ + 614 + ], + "names": [ + "annotator1" + ], + "text": "What about non parameric testing ?" + }, + { + "file_id": "4HRhg4eUiMo", + "query_id": 3, + "timestamp": 1684518521013.0, + "annotatedSourceSentencesIndices": [ + 148, + 150 + ], + "names": [ + "annotator1" + ], + "text": "the power of the test shouldn't it be 95% ? 1-alpha ?" + }, + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [ + 399, + 400 + ], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + }, + { + "file_id": "4HRhg4eUiMo", + "query_id": 5, + "timestamp": 1684518647036.0, + "annotatedSourceSentencesIndices": [ + 810, + 835 + ], + "names": [ + "annotator1" + ], + "text": "why can we treat the mean of x equal to 0?" + } +] \ No newline at end of file diff --git a/sight/query/annotated/7K1sB05pE0A.json b/sight/query/annotated/7K1sB05pE0A.json new file mode 100644 index 0000000000000000000000000000000000000000..dcb98028333b7f5bb983a824a65e7db7556a6522 --- /dev/null +++ b/sight/query/annotated/7K1sB05pE0A.json @@ -0,0 +1,666 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 2, + "timestamp": 1684514464480.0, + "annotatedSourceSentencesIndices": [ + 414 + ], + "names": [ + "annotator1" + ], + "text": "I have just one question: How 1/2 (2Xo)(2Yo)= 2XoYo=2? If we do 1/2 *2 (XoYo) we are left with XoYo which i don't think is equal to 2 :X\u00a0" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 3, + "timestamp": 1684514482386.0, + "annotatedSourceSentencesIndices": [ + 3 + ], + "names": [ + "annotator1" + ], + "text": "Is this entire course a combination of calc 1 and 2? Or just calc 1. I see the next course is multi-variable which is often known as calc 3." + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 5, + "timestamp": 1684514746641.0, + "annotatedSourceSentencesIndices": [ + 414, + 415 + ], + "names": [ + "annotator1" + ], + "text": "Where do x(sub naught) and y(sub naught) go at 40:59? It may be a rudimentary question, but I've been out of math classes for a number of years now. I am able to follow along with all of this except that one piece, and it's bugging me. What did I forget?" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 6, + "timestamp": 1684514906495.0, + "annotatedSourceSentencesIndices": [ + 7, + 8, + 9, + 10, + 11, + 12, + 23, + 28 + ], + "names": [ + "annotator1" + ], + "text": "Why aren't they giving a meaningful description of what a derivative is in plain English? E.g. The derivative of a function is the function that evaluates to the rate of change for a given input." + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 8, + "timestamp": 1684514986976.0, + "annotatedSourceSentencesIndices": [ + 3 + ], + "names": [ + "annotator1" + ], + "text": "Today I have statrted this course. This is really awesome. I just want to know which book I should follow for this course?" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 10, + "timestamp": 1684515014648.0, + "annotatedSourceSentencesIndices": [ + 3 + ], + "names": [ + "annotator1" + ], + "text": "May I ask you guys a question, do Single Variable Calculus and Multivariable Calculus cover all the content of calculus and real analysis?" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 11, + "timestamp": 1684515253951.0, + "annotatedSourceSentencesIndices": [ + 489, + 490 + ], + "names": [ + "annotator1" + ], + "text": "I am confused with the Binomial part, especially about how to get the nX\u02c6n-1\u25b3x from formula X\u02c6n+ nX\u02c6n-1\u25b3x+ Junk?" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 14, + "timestamp": 1684515267034.0, + "annotatedSourceSentencesIndices": [ + 0, + 1, + 2, + 3 + ], + "names": [ + "annotator1" + ], + "text": "Is this intro calc? Like if you've taken advanced algebra and trig, is this the best place to start? I have a textbook and a fair bit of free time at the moment. Is this video the right way to begin? Thanks :)" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 15, + "timestamp": 1684515294082.0, + "annotatedSourceSentencesIndices": [ + 106 + ], + "names": [ + "annotator1" + ], + "text": "Lecture 1 of calculus he uses Limit, but he doesn't define it anywhere ... was that done in a previous course? otherwise I believe the course is incomplete..." + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 16, + "timestamp": 1684515383068.0, + "annotatedSourceSentencesIndices": [ + 175 + ], + "names": [ + "annotator1" + ], + "text": "how did you factored that 19:53 diference equation?" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 17, + "timestamp": 1684515562316.0, + "annotatedSourceSentencesIndices": [ + 147, + 414 + ], + "names": [ + "annotator1" + ], + "text": "why is x_0y_0 = 1 ?\nmiddle schooler here, please don't mock..." + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 20, + "timestamp": 1684516142439.0, + "annotatedSourceSentencesIndices": [ + 239 + ], + "names": [ + "annotator1" + ], + "text": "24:56 how did he figure out what the numerator had to be at 25:17? I am sure this is some simple algebra, but it's been a while :)" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 21, + "timestamp": 1684516169620.0, + "annotatedSourceSentencesIndices": [ + 3, + 524 + ], + "names": [ + "annotator1" + ], + "text": "Which math course is better to do after this?" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 22, + "timestamp": 1684516183458.0, + "annotatedSourceSentencesIndices": [ + 7 + ], + "names": [ + "annotator1" + ], + "text": "why do you start with derivatives without going through limits and continuity first ?" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 24, + "timestamp": 1684516213076.0, + "annotatedSourceSentencesIndices": [ + 464, + 465, + 466, + 467 + ], + "names": [ + "annotator1" + ], + "text": "Why use binomial theorem instead of Taylor expansion?\n\nAnd professor said it is single variable calculus, but there may have many variables like x0,y0 to confuse peoples. But I think there is only one variable x, x0 is just one value of x." + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 26, + "timestamp": 1684516220556.0, + "annotatedSourceSentencesIndices": [ + 414 + ], + "names": [ + "annotator1" + ], + "text": "why is 2xo(yo) = 2?" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 27, + "timestamp": 1684516284253.0, + "annotatedSourceSentencesIndices": [ + 415 + ], + "names": [ + "annotator1" + ], + "text": "When he solves for the area of the triangle, why does he say it doesn't matter what X0 and Y0 are? Does he just mean that all values of f(x) = 1/x will result in the area of the triangle of the tangent line to be 2?" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 28, + "timestamp": 1684516405044.0, + "annotatedSourceSentencesIndices": [ + 402, + 403 + ], + "names": [ + "annotator1" + ], + "text": "Can someone explain how to calculate the y-intercept? If you replace y0 with 1/x and plug x = 0, wouldn't you get a division by zero error?" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 29, + "timestamp": 1684516519367.0, + "annotatedSourceSentencesIndices": [ + 334 + ], + "names": [ + "annotator1" + ], + "text": "I have a question. At 33 minutes, where did the negative of the x/Xo^2 go when he added the 1/Xo to the other side?" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 30, + "timestamp": 1684516528894.0, + "annotatedSourceSentencesIndices": [ + 524 + ], + "names": [ + "annotator1" + ], + "text": "I'm looking to learn calculus and coming to the end of this video, it seems I'm missing lots of information.\nWhat previous math categories should I learn to continue on with calculus?" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 31, + "timestamp": 1684516539061.0, + "annotatedSourceSentencesIndices": [ + 3 + ], + "names": [ + "annotator1" + ], + "text": "It seems that this course is a combination of what is usually separated into two courses typically named \"Calculus 1\" and \"Calculus 2\". Is that correct?" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 32, + "timestamp": 1684516614873.0, + "annotatedSourceSentencesIndices": [ + 342, + 343 + ], + "names": [ + "annotator1" + ], + "text": "Does anyone understand the symmetry thing he was talking about? Which equation did he stare at XD" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 33, + "timestamp": 1684516837318.0, + "annotatedSourceSentencesIndices": [ + 187 + ], + "names": [ + "annotator1" + ], + "text": "wait, why did delta F when finding the derivative of \u00a0f(1/x) become the inverse of the previous delta f?\u00a0" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 36, + "timestamp": 1684516848252.0, + "annotatedSourceSentencesIndices": [ + 3 + ], + "names": [ + "annotator1" + ], + "text": "Does this class include what is generally Calc 2 as well? I see the next class up is multivariable which is often known as calc 3 at some uni's." + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 38, + "timestamp": 1684516879122.0, + "annotatedSourceSentencesIndices": [ + 336 + ], + "names": [ + "annotator1" + ], + "text": "At around 33:35 he defines the x-int as (2x0,0), following the same logic and using the original point slope form, I got y-int as (0,2/x0). I don't think I am wrong, but can any confirm?" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 42, + "timestamp": 1684516889278.0, + "annotatedSourceSentencesIndices": [ + 0 + ], + "names": [ + "annotator1" + ], + "text": "2+ 2 = 4?" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 43, + "timestamp": 1684516900629.0, + "annotatedSourceSentencesIndices": [ + 414 + ], + "names": [ + "annotator1" + ], + "text": "Why always 2?? is there a prove?" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 47, + "timestamp": 1684516942994.0, + "annotatedSourceSentencesIndices": [ + 166 + ], + "names": [ + "annotator1" + ], + "text": "How does he get 1 / \u03b4 x at 19:40?" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 48, + "timestamp": 1684517008407.0, + "annotatedSourceSentencesIndices": [ + 196, + 203 + ], + "names": [ + "annotator1" + ], + "text": "I have a question in 22:00 if x0 go to infinitive then the value would be bigger and bigger isn\u2019t it? for example -1/1 < -1/1000" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 49, + "timestamp": 1684517025478.0, + "annotatedSourceSentencesIndices": [ + 342 + ], + "names": [ + "annotator1" + ], + "text": "Can someone kindly compute y-intercept for me? Where x = 0 into the asterisk eqn. I would just like to prove that y = 2y0. Thanks!" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 52, + "timestamp": 1684517036117.0, + "annotatedSourceSentencesIndices": [ + 3, + 7 + ], + "names": [ + "annotator1" + ], + "text": "Is this equivalent to calculus 1 and 2? Derivatives, integrals, and sequences and series?" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 55, + "timestamp": 1684517099986.0, + "annotatedSourceSentencesIndices": [ + 183 + ], + "names": [ + "annotator1" + ], + "text": "At 20:29, why does x0-(x0+deltaX) simplify to -deltaX? Shouldn't x0 - x0 equal 0, and adding 0 to deltaX = deltaX?" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 58, + "timestamp": 1684517285810.0, + "annotatedSourceSentencesIndices": [ + 452, + 453, + 454, + 475 + ], + "names": [ + "annotator1" + ], + "text": "Hi friends,\n\nCan someone please clarify below 2 doubts, please \n\n1. What does those junk terms exactly look like? One example string would be good\n\n2. Why did prof didn\u2019t substitute with x0 in last calculation \n\nThank You very much in advance \ud83d\ude4f\ud83c\udffb" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 60, + "timestamp": 1684517399324.0, + "annotatedSourceSentencesIndices": [ + 122, + 127 + ], + "names": [ + "annotator1" + ], + "text": "Hey in defining slope why we should take delta x tends to zero because for the point Q to be P it is both delta x and y both should be zero right??" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 63, + "timestamp": 1684517523119.0, + "annotatedSourceSentencesIndices": [ + 124, + 309, + 310, + 311, + 312 + ], + "names": [ + "annotator1" + ], + "text": "This professor is not the best I've seen on youtube. Not that he doesnt understand what he explains but his methodology is not essentialising the obscure concepts. First, he should have discribed the slope as delta x on delta y....( why f(x))?...or the obscure equation y-yo= m (x-xo)... could have been easyer as m= delta x/delta y...." + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 64, + "timestamp": 1684517528984.0, + "annotatedSourceSentencesIndices": [ + 3 + ], + "names": [ + "annotator1" + ], + "text": "Is there any prerequisite required?" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 65, + "timestamp": 1684517557050.0, + "annotatedSourceSentencesIndices": [ + 124, + 132 + ], + "names": [ + "annotator1" + ], + "text": "Why is it Delta F instead of Delta Q?" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 66, + "timestamp": 1684517573504.0, + "annotatedSourceSentencesIndices": [ + 106 + ], + "names": [ + "annotator1" + ], + "text": "Did he ever define what a limit is ? where ?" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 67, + "timestamp": 1684517591721.0, + "annotatedSourceSentencesIndices": [ + 487 + ], + "names": [ + "annotator1" + ], + "text": "I didn't quite understand how (x+\u2206x).....(x+\u2206x) got us the term nx^n-1\u2206x. Won't \u2206x be multiplied n-1 times instead of n?" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 70, + "timestamp": 1684517599157.0, + "annotatedSourceSentencesIndices": [ + 414 + ], + "names": [ + "annotator1" + ], + "text": "How is it 2 40:50?" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 72, + "timestamp": 1684517721236.0, + "annotatedSourceSentencesIndices": [ + 139, + 140, + 141, + 142, + 143 + ], + "names": [ + "annotator1" + ], + "text": "guys i have a question \nif we have something like this one -->\nf(x)>x^2 +e and this is true for every real x\nCan i differentate this and say\nFirst derivative of f (x) >= 2*x ?\nPlease i need help on this one" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 73, + "timestamp": 1684517826734.0, + "annotatedSourceSentencesIndices": [ + 235, + 237, + 238 + ], + "names": [ + "annotator1" + ], + "text": "24:51 seriously? Basic LCM is a doubt in an MIT class?" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 74, + "timestamp": 1684517837500.0, + "annotatedSourceSentencesIndices": [ + 127 + ], + "names": [ + "annotator1" + ], + "text": "I have a question. Why does he let the limit be delta x to zero? Can it be done with the limit being delta y to zero?" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 75, + "timestamp": 1684517841432.0, + "annotatedSourceSentencesIndices": [ + 3 + ], + "names": [ + "annotator1" + ], + "text": "Are there any pre-requisites for taking this course?" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 76, + "timestamp": 1684517855869.0, + "annotatedSourceSentencesIndices": [ + 3, + 468 + ], + "names": [ + "annotator1" + ], + "text": "Can anyone tell me which book should i prefer with these lectures.??" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 77, + "timestamp": 1684518035758.0, + "annotatedSourceSentencesIndices": [ + 194 + ], + "names": [ + "annotator1" + ], + "text": "At 21:20, he says \"I set this delta x to zero.\" So just like that? You can just set it to zero randomly? I'm so confused as to why/how it is zero, then magically disappears." + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 78, + "timestamp": 1684518045810.0, + "annotatedSourceSentencesIndices": [ + 414 + ], + "names": [ + "annotator1" + ], + "text": "thank you\nwas following till 40'57\"\nhow does 2x0y0 = 2 ?\n\nrealise this lecture is 13 yo but anyone out there\nappreciate any advice\nmark" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 79, + "timestamp": 1684518138072.0, + "annotatedSourceSentencesIndices": [ + 378, + 379, + 380, + 381 + ], + "names": [ + "annotator1" + ], + "text": "I didn't really understand what he said around 37:42. Can someone please clarify a little bit? Thank you!" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 80, + "timestamp": 1684518147548.0, + "annotatedSourceSentencesIndices": [ + 7 + ], + "names": [ + "annotator1" + ], + "text": "Why do they teach derivatives before limits in MIT? Aren't limits the basis for both differential and integral calculus?" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 82, + "timestamp": 1684518162850.0, + "annotatedSourceSentencesIndices": [ + 478 + ], + "names": [ + "annotator1" + ], + "text": "48:37 A little confusion here. Don't you have to use a lower bound for that junk terms? Big O is an upper bound. And (delta x)^2 cannot be an upperbound for, say, (delta x)^3." + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 83, + "timestamp": 1684518178554.0, + "annotatedSourceSentencesIndices": [ + 106 + ], + "names": [ + "annotator1" + ], + "text": "Why don't he tell definition of limit and also refer about epsilon-delta staff?" + }, + { + "file_id": "7K1sB05pE0A", + "query_id": 84, + "timestamp": 1684518187429.0, + "annotatedSourceSentencesIndices": [ + 468 + ], + "names": [ + "annotator1" + ], + "text": "Which book does they follow?" + } +] \ No newline at end of file diff --git a/sight/query/annotated/Cx5Z-OslNWE.json b/sight/query/annotated/Cx5Z-OslNWE.json new file mode 100644 index 0000000000000000000000000000000000000000..a889f83b36d695f310b5e70cda68b65304e949b1 --- /dev/null +++ b/sight/query/annotated/Cx5Z-OslNWE.json @@ -0,0 +1,16 @@ +[ + { + "file_id": "Cx5Z-OslNWE", + "query_id": 0, + "timestamp": 1684191216689.0, + "annotatedSourceSentencesIndices": [ + 3, + 0 + ], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks to MIT and professor Strang. Is 18.06 is prerequisite to this course or it will be covered in this course?" + } +] \ No newline at end of file diff --git a/sight/query/annotated/KAySmSEGc9U.json b/sight/query/annotated/KAySmSEGc9U.json new file mode 100644 index 0000000000000000000000000000000000000000..1d5223a06b6ccef0bf81079f821593f2f5ec5544 --- /dev/null +++ b/sight/query/annotated/KAySmSEGc9U.json @@ -0,0 +1,31 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 0, + "timestamp": 1684706671595.0, + "annotatedSourceSentencesIndices": [ + 258, + 261, + 262, + 264 + ], + "names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + }, + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [ + 461, + 462, + 490 + ], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated/MsIvs_6vC38.json b/sight/query/annotated/MsIvs_6vC38.json new file mode 100644 index 0000000000000000000000000000000000000000..ec429aca066beee3a4ead6bb617e1e2b3d8162bf --- /dev/null +++ b/sight/query/annotated/MsIvs_6vC38.json @@ -0,0 +1,445 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 0, + "timestamp": 1684707989274.0, + "annotatedSourceSentencesIndices": [ + 39, + 428 + ], + "names": [ + "annotator2" + ], + "text": "How did transpose suddenly come into the picture?" + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 2, + "timestamp": 1684708398925.0, + "annotatedSourceSentencesIndices": [ + 189, + 279 + ], + "names": [ + "annotator2" + ], + "text": "Can someone explain why A=LU is better than EA=U?" + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 3, + "timestamp": 1684708441242.0, + "annotatedSourceSentencesIndices": [ + 10 + ], + "names": [ + "annotator2" + ], + "text": "In A=LU part, what do L and U stand for? (Like \"E\" for elimination )" + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 4, + "timestamp": 1684708849693.0, + "annotatedSourceSentencesIndices": [ + 341, + 342, + 343, + 344, + 353 + ], + "names": [ + "annotator2" + ], + "text": "at 32:35 => Should not the first cost be 99*2 instead of 100^2 because there are 99 rows below first one. For pivoting each row below, you need to multiply the first row by some constant then subtract from the row you are pivoting. So, essentially are we not ending up having 2 operations per row for those 99 rows, hence, 99*2 instead of 100^2 ???" + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 5, + "timestamp": 1684708888995.0, + "annotatedSourceSentencesIndices": [ + 341, + 342, + 343, + 344 + ], + "names": [ + "annotator2" + ], + "text": "sorry i'm confused at 32:22, it is 100 ^2, but i think it is 100, why it isn't 100? could anyone explain that to me? thx alot" + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 6, + "timestamp": 1684709130696.0, + "annotatedSourceSentencesIndices": [ + 515, + 516 + ], + "names": [ + "annotator2" + ], + "text": "How come 4x4 Matrix has 24 P's ?" + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 7, + "timestamp": 1684709988672.0, + "annotatedSourceSentencesIndices": [ + 48 + ], + "names": [ + "annotator2" + ], + "text": "4:57 if i transpose these guys, that product, then again, ... : why did he jump suddenly to this theorem without any definition of transpose nor the logical derivation? Did I miss something?" + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 8, + "timestamp": 1684710001490.0, + "annotatedSourceSentencesIndices": [ + 341, + 342, + 343, + 344 + ], + "names": [ + "annotator2" + ], + "text": "33\uff1a06 why it's 100^2?" + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 9, + "timestamp": 1684710020923.0, + "annotatedSourceSentencesIndices": [ + 341, + 342, + 343, + 344, + 353 + ], + "names": [ + "annotator2" + ], + "text": "Can someone explain why the computatinal expense is roughly 100^2 for the first step? I thought it would be roughly proportional to n = 100" + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 10, + "timestamp": 1684710094057.0, + "annotatedSourceSentencesIndices": [ + 185 + ], + "names": [ + "annotator2" + ], + "text": "Why is L always inverse of E? Like how can we see that geometrically?" + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 12, + "timestamp": 1684710326625.0, + "annotatedSourceSentencesIndices": [ + 281, + 282 + ], + "names": [ + "annotator2" + ], + "text": "My doubt is what were we trying to prove while calculating the cost of operation during elimination. And how EA is costlier than LU?" + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 13, + "timestamp": 1684719774461.0, + "annotatedSourceSentencesIndices": [ + 419 + ], + "names": [ + "annotator2" + ], + "text": "Can anyone explain to me why the answer for cost of B is $n^2$ around 40:00?" + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 14, + "timestamp": 1684719853045.0, + "annotatedSourceSentencesIndices": [ + 9 + ], + "names": [ + "annotator2" + ], + "text": "Hi. Is U the b in Ax = b?" + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 15, + "timestamp": 1684719893863.0, + "annotatedSourceSentencesIndices": [ + 271 + ], + "names": [ + "annotator2" + ], + "text": "At 24:20 when he says that the multiplier goes directly into L, he means the negative right? If you keep a track of the operation on the left side, it inverts while bringing it to the right side." + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 16, + "timestamp": 1684719946478.0, + "annotatedSourceSentencesIndices": [ + 162 + ], + "names": [ + "annotator2" + ], + "text": "It is the best linear algebra lecture ever!!! But I do not get where the Identity matrix E31 comes from (at 16:47) ? Could anyone pls help me with this?" + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 17, + "timestamp": 1684719965960.0, + "annotatedSourceSentencesIndices": [ + 341, + 342, + 343, + 344 + ], + "names": [ + "annotator2" + ], + "text": "Can someone please explain how did he get 100^2 and not 100 x 2 (multiply+substract) operations at 33:22?" + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 18, + "timestamp": 1684720220360.0, + "annotatedSourceSentencesIndices": [ + 341, + 353, + 355, + 356, + 360, + 419 + ], + "names": [ + "annotator2" + ], + "text": "26:10\n\nI have a question about the cost of elimination.\nAx=b\n\nFor an nxn matrix A\nFor the 1st pivot, instead of 100^2, shouldn\u2019t it cost 100*99?\n2nd pivot, instead of 99^2, shouldn\u2019t it cost 99*98?\n3rd pivot, instead of 98^2, shouldn\u2019t it cost 98*87?\n\nSo, instead of n^2+(n-1)^2+(n-2)^2+...., shouldn\u2019t it be n(n-1)+(n-1)(n-2)+(n-2)(n-3)+.... instead?\n\n\nAlso, how did he get n^2 for the matrix b?" + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 20, + "timestamp": 1684720264277.0, + "annotatedSourceSentencesIndices": [ + 91 + ], + "names": [ + "annotator2" + ], + "text": "8:55 Min why does he want to avoid A to be singular? don\u00b4t quite understand...the only reason i see (in hindsight), is that the step, he does at 12:30 Min (rewriting LU with a diagonal matrix in the middle) wouldn\u00b4t be unique. But i assume, there must be another reason." + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 21, + "timestamp": 1684720310343.0, + "annotatedSourceSentencesIndices": [ + 102 + ], + "names": [ + "annotator2" + ], + "text": "At 10:27 how are we calculating E21( elimination matrix)?" + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 22, + "timestamp": 1684720431225.0, + "annotatedSourceSentencesIndices": [ + 381, + 386 + ], + "names": [ + "annotator2" + ], + "text": "Great video! I love this series. In this lecture, Dr. Strang briefly mentions that the cost of operations for the det(A) will be (n!) He also shows us how the cost of getting A into upper triangular form U will be (1/3)n^3. But from Lecture 2 we know that one way of finding det(A) is to get A into U and then simply find the product of all n pivots. So it seems like the cost for finding det(A) would just be a bit more than (1/3)n^3, perhaps (1/3)n^3 + n. I must be missing something here; any thoughts?" + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 23, + "timestamp": 1684720563078.0, + "annotatedSourceSentencesIndices": [ + 31, + 94, + 132 + ], + "names": [ + "annotator2" + ], + "text": "hmm is there a complementary book we must follow? I'm puzzled as I don't think we've introduced the elementary matrices in previous lectures, or Upper/lower matrices. I feel this is not beginner friendly." + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 24, + "timestamp": 1684720668792.0, + "annotatedSourceSentencesIndices": [ + 220, + 221, + 222, + 223 + ], + "names": [ + "annotator2" + ], + "text": "I'm a bit unsure as to why he doesn't like the 10 in the matrix E around 19:00? Are we assuming we already have A and U defined, and just need to find a matrix that relates them? Is it because the L parts, like the E parts (E21, E31, E32) can simply be stated, but to calculate the final L and E, final L can be stated (just like it's parts), where as E has to be calculated?" + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 28, + "timestamp": 1684720790293.0, + "annotatedSourceSentencesIndices": [ + 185 + ], + "names": [ + "annotator2" + ], + "text": "Can anyone tell me why can't we obtain the Lower triangular matrix L directly from the combined E which could just be derived from using gaussian elimination? Thanksss" + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 30, + "timestamp": 1684721031176.0, + "annotatedSourceSentencesIndices": [ + 235, + 236, + 237, + 240 + ], + "names": [ + "annotator2" + ], + "text": "On 21 minute I don't understand where these matrices come from and why we need them. Anyone care to elaborate?" + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 31, + "timestamp": 1684721039024.0, + "annotatedSourceSentencesIndices": [ + 516 + ], + "names": [ + "annotator2" + ], + "text": "can someone explain how he got 24P's at the end?" + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 32, + "timestamp": 1684721377675.0, + "annotatedSourceSentencesIndices": [ + 142, + 143 + ], + "names": [ + "annotator2" + ], + "text": "How did he work out at 12:50?" + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 34, + "timestamp": 1684721404907.0, + "annotatedSourceSentencesIndices": [ + 417, + 419 + ], + "names": [ + "annotator2" + ], + "text": "Why the number of operation is equal to n^2 ? Can anyone ?" + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 36, + "timestamp": 1684722009555.0, + "annotatedSourceSentencesIndices": [ + 10, + 69, + 111, + 261, + 270 + ], + "names": [ + "annotator2" + ], + "text": "I don't get the point of A = LU. You need to know U to solve for x in Ax=b. You need E to find U, you can't get U from L. Once you have U, you're basically done. What do you need L for?\n\nI understand the point that L is less costly than E -- but what use is L if you don't know U yet? What am I missing?" + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 39, + "timestamp": 1684722160238.0, + "annotatedSourceSentencesIndices": [ + 236, + 240 + ], + "names": [ + "annotator2" + ], + "text": "At 26:00 how did he find the inverses of E21 & E32 so easily? is he using some formula? I'm watching the videos in the MITs required order, but looks like I missed somewhere something" + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 40, + "timestamp": 1684722350405.0, + "annotatedSourceSentencesIndices": [ + 491, + 516 + ], + "names": [ + "annotator2" + ], + "text": "Why does a 4x4 matrix have 24 Permutationmatrices when a 3x3 Matrix has 6? I don't get how they calculated it so quickly." + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 42, + "timestamp": 1684722535272.0, + "annotatedSourceSentencesIndices": [ + 170, + 171, + 185 + ], + "names": [ + "annotator2" + ], + "text": "how do we know that E-1 will be a lower triangular matrix?" + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 43, + "timestamp": 1684722576236.0, + "annotatedSourceSentencesIndices": [ + 318 + ], + "names": [ + "annotator2" + ], + "text": "can someone pls explain how n,n^2 , n^3....n! come ? ?? at 29:46 ." + }, + { + "file_id": "MsIvs_6vC38", + "query_id": 44, + "timestamp": 1684722640153.0, + "annotatedSourceSentencesIndices": [ + 384, + 386, + 389 + ], + "names": [ + "annotator2" + ], + "text": "The complexity of matrix multiplication is of the order O(n^3), that's fine. But in every step in the we are changing just one row...therefore, shouldn't the cost be n+ (n-1)+ (n-2) + ........+1, ie O(n^2), if we have a suitable algorithm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated/RD9AWDdj-Yk.json b/sight/query/annotated/RD9AWDdj-Yk.json new file mode 100644 index 0000000000000000000000000000000000000000..4b0eec813298cc4db824d56da13711c68c6afa50 --- /dev/null +++ b/sight/query/annotated/RD9AWDdj-Yk.json @@ -0,0 +1,16 @@ +[ + { + "file_id": "RD9AWDdj-Yk", + "query_id": 0, + "timestamp": 1684192371630.0, + "annotatedSourceSentencesIndices": [ + 255, + 243 + ], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Proof of TRL neglects edges inside clusters?" + } +] \ No newline at end of file diff --git a/sight/query/annotated/TSkDZbGS94k.json b/sight/query/annotated/TSkDZbGS94k.json new file mode 100644 index 0000000000000000000000000000000000000000..666f77568fe1a5b77fa4d2923f3ad657cb5f1012 --- /dev/null +++ b/sight/query/annotated/TSkDZbGS94k.json @@ -0,0 +1,27 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 0, + "timestamp": 1684520696821.0, + "annotatedSourceSentencesIndices": [ + 844 + ], + "names": [ + "annotator1" + ], + "text": "at time 1:12:36, the instructor stated the expectation to be P. What is P representing here? In the case of the statistical model, P represents the Family of Distributions......" + }, + { + "file_id": "TSkDZbGS94k", + "query_id": 1, + "timestamp": 1684520806354.0, + "annotatedSourceSentencesIndices": [ + 702, + 703 + ], + "names": [ + "annotator1" + ], + "text": "Why are the parameters of one of the normal distributions he describes identifiable and the others aren't?" + } +] \ No newline at end of file diff --git a/sight/query/annotated/TX_vooSnhm8.json b/sight/query/annotated/TX_vooSnhm8.json new file mode 100644 index 0000000000000000000000000000000000000000..f92db211f60b4e77f448d7aed5444d11ded1e9fc --- /dev/null +++ b/sight/query/annotated/TX_vooSnhm8.json @@ -0,0 +1,87 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 1, + "timestamp": 1684512167597.0, + "annotatedSourceSentencesIndices": [ + 261, + 262, + 263, + 264, + 265, + 266 + ], + "names": [ + "annotator1" + ], + "text": "@ 26:04 I have to admit, that took me a second to figure it out. \nProf Strang didn't actually have anything wrong, he just couldn't see while in the middle of it why that was the case. He actually had it at 26:44 but let it slip through his hands.\nFor that you have to go back to when he was computing matrix \"V\". The evec associated with eval of 18 was [1;-1] but it also can be written as [-1;1]\n\nHe chose the [1;-1] which had the effect once we made it to the final calculation of U * Diag^2 * V^t that it SWAPPED THE COLUMNS of A\nHis original A was [4,4;-3,3] and the calc'd one was [4,4;3,-3]\nHad he chosen the 'other version' of the evec associated with Lambda = 18 when figuring out \"V\", he would have gotten back the same \"A\" he started with instead of the column-swapped version.\nBut what could go wrong? :-)" + }, + { + "file_id": "TX_vooSnhm8", + "query_id": 2, + "timestamp": 1684512339083.0, + "annotatedSourceSentencesIndices": [ + 381 + ], + "names": [ + "annotator1" + ], + "text": "Professor Strang mentions that U and V form bases for the four fundamental subspaces of A, but it's not clear to me how C(A) = C(Ur) and C(A') = C (Vr'). I know that U and V were determined by the eigenvectors of AA' and A'A, respectively, but how are these related to the column and row spaces of A?" + }, + { + "file_id": "TX_vooSnhm8", + "query_id": 7, + "timestamp": 1684512390426.0, + "annotatedSourceSentencesIndices": [ + 207 + ], + "names": [ + "annotator1" + ], + "text": "at 20:35, why use the positive square roots instead of negative ones?" + }, + { + "file_id": "TX_vooSnhm8", + "query_id": 8, + "timestamp": 1684512455481.0, + "annotatedSourceSentencesIndices": [ + 87 + ], + "names": [ + "annotator1" + ], + "text": "Hi, can anyone explain why 10:20 sigma_1 and sigma_2 greater than 0? Thanks!" + }, + { + "file_id": "TX_vooSnhm8", + "query_id": 10, + "timestamp": 1684512534435.0, + "annotatedSourceSentencesIndices": [ + 265, + 266, + 267 + ], + "names": [ + "annotator1" + ], + "text": "Regarding the problem at 26:28\nIt would be solved if the matrix U was [1 0; 0 -1]. (Replace the 1 at the bottom right of the 2x2 identity with -1).\nThis can be found by following the argument that Prof Strang makes in this video: https://youtu.be/rYz83XPxiZo?t=1177 (Skip to 19:37). \nThe problem is that here the eigenvectors of U that we found are [1, 0]' and [0, 1]', but they should be [1, 0]' and [0, -1]'.\nThe negative in the 2nd eigenvector allows the scaling term (sigma) to be strictly positive. \n\nLet S = Sigma (for ease of typing).\nI think the main problem is that the general form A = U*S*V' does not mathematically enforce that S should be a strictly positive matrix.\nSo even though A'A and AA' will output the squares of the eigenvalues, simply choosing the positive roots is not enough.\nWe would need to choose the right sign for the eigenvector that corresponds to the positive root. E.g. [1,0] and [-1,0] can both have the same eigenvalue, so we have to decide which to use.\nHence, we need to check the cases and manually negate the vectors in U or V so that S can be positive.\nHowever, if we follow what Prof Strang does in the video whose URL ive included in the earlier part of this comment, then this is accounted for by the computation." + }, + { + "file_id": "TX_vooSnhm8", + "query_id": 4, + "timestamp": 1684192467807.0, + "annotatedSourceSentencesIndices": [ + 179, + 188, + 179, + 180, + 188, + 193 + ], + "names": [ + "annotator1", + "annotator2" + ], + "text": "how did we get 32 and 18 as squares of sigma1 and sigma2 ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated/UYe98CcxPbs.json b/sight/query/annotated/UYe98CcxPbs.json new file mode 100644 index 0000000000000000000000000000000000000000..35bbf1fc7811886b3eb600828afa0b07402e76e4 --- /dev/null +++ b/sight/query/annotated/UYe98CcxPbs.json @@ -0,0 +1,117 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 0, + "timestamp": 1684480825133.0, + "annotatedSourceSentencesIndices": [ + 55, + 57, + 51, + 52, + 55 + ], + "names": [ + "annotator1", + "annotator2" + ], + "text": "where can I find a complete derivation of the formula z=z0 + a(x-x0) + b(y-y0) using parametric equations as he suggested at 8:38? I tried to do what he said but no luck!" + }, + { + "file_id": "UYe98CcxPbs", + "query_id": 2, + "timestamp": 1684480921899.0, + "annotatedSourceSentencesIndices": [ + 51, + 52 + ], + "names": [ + "annotator1" + ], + "text": "08:10 how do you express the plan formed by two lines in general? " + }, + { + "file_id": "UYe98CcxPbs", + "query_id": 3, + "timestamp": 1684510062486.0, + "annotatedSourceSentencesIndices": [ + 293 + ], + "names": [ + "annotator1" + ], + "text": "why is it the the deviation formula is squared? i know it must be equal to zero." + }, + { + "file_id": "UYe98CcxPbs", + "query_id": 4, + "timestamp": 1684510080674.0, + "annotatedSourceSentencesIndices": [ + 293 + ], + "names": [ + "annotator1" + ], + "text": "Why do we do square deviation, but not ordinary one? I don`t understand the precondition for squares. If anyone can explain, do it, please." + }, + { + "file_id": "UYe98CcxPbs", + "query_id": 5, + "timestamp": 1684510172054.0, + "annotatedSourceSentencesIndices": [ + 198 + ], + "names": [ + "annotator1" + ], + "text": "25:57\nWhy he wrote f(-1,0)?" + }, + { + "file_id": "UYe98CcxPbs", + "query_id": 7, + "timestamp": 1684510713476.0, + "annotatedSourceSentencesIndices": [ + 51 + ], + "names": [ + "annotator1" + ], + "text": "For z = z0 + a(x-x0) + b(y-y0),\nwouldn't that mean:\n-1(z-z0) + a(x-x0) + b(y-y0) = 0\nso from lecture 4 the normal vector for any f(x,y) tangent plane is <-1, a, b> ?\nI'm missing something about the -1 I'm sure" + }, + { + "file_id": "UYe98CcxPbs", + "query_id": 9, + "timestamp": 1684510838484.0, + "annotatedSourceSentencesIndices": [ + 284, + 285 + ], + "names": [ + "annotator1" + ], + "text": "34:58 would using perpendicular distance (instead of vertical distance) make better sense? \n" + }, + { + "file_id": "UYe98CcxPbs", + "query_id": 12, + "timestamp": 1684510931819.0, + "annotatedSourceSentencesIndices": [ + 43 + ], + "names": [ + "annotator1" + ], + "text": "6:34, how is that z=z0 + dz/dx(x-x0) a equation of straight line. y=mx+c is a eqaution of straight line in 2D space. and x = x0 + st is vector form of equaiton in higher dimension. how is the above euqation realted to this? Thanks in advance" + }, + { + "file_id": "UYe98CcxPbs", + "query_id": 1, + "timestamp": 1684191408602.0, + "annotatedSourceSentencesIndices": [ + 0 + ], + "names": [ + "annotator1" + ], + "text": "Would any one please explain what did the professor mean between 13:13 and 13:44?" + } +] \ No newline at end of file diff --git a/sight/query/annotated/WfEQabCGAqI.json b/sight/query/annotated/WfEQabCGAqI.json new file mode 100644 index 0000000000000000000000000000000000000000..df20066303eda135765d2eedfd9f84de11e4b930 --- /dev/null +++ b/sight/query/annotated/WfEQabCGAqI.json @@ -0,0 +1,68 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 3, + "timestamp": 1684511496045.0, + "annotatedSourceSentencesIndices": [ + 196, + 197 + ], + "names": [ + "annotator1" + ], + "text": "Do maths/science/engineering students take this class or some other multivariable calculus course like 18.024?" + }, + { + "file_id": "WfEQabCGAqI", + "query_id": 5, + "timestamp": 1684511772657.0, + "annotatedSourceSentencesIndices": [ + 161 + ], + "names": [ + "annotator1" + ], + "text": "18:09 why the range of r goes from 0 to 1? I think the definition of S in this problem needs further clarification. S should be a paraboloid of z = x^2 + y^2 between z=0 and z=1. It is a little confusing by justing saying \"above the unit disk\". " + }, + { + "file_id": "WfEQabCGAqI", + "query_id": 7, + "timestamp": 1684511834173.0, + "annotatedSourceSentencesIndices": [ + 359, + 361 + ], + "names": [ + "annotator1" + ], + "text": "Isn't this theorem called after Ostrogradsky, since he is the first one to prove it?" + }, + { + "file_id": "WfEQabCGAqI", + "query_id": 8, + "timestamp": 1684512043723.0, + "annotatedSourceSentencesIndices": [ + 226, + 227, + 264 + ], + "names": [ + "annotator1" + ], + "text": "Wait, did he ever account for vector N not being a unit vector? He never required that the N vector represented the area of the delta slanted plane did he?" + }, + { + "file_id": "WfEQabCGAqI", + "query_id": 1, + "timestamp": 1684192120438.0, + "annotatedSourceSentencesIndices": [ + 331, + 331 + ], + "names": [ + "annotator1", + "annotator2" + ], + "text": "I did not understand the last step replacing dA by dxdy. The proof contained slanted plane with an angle alpha to only one axis and not a general slant in both directions. Does this proof apply when we are considering a general slant to both x and y ? Will dA=dS Cos theta still be applicable?" + } +] \ No newline at end of file diff --git a/sight/query/annotated/X-ix97pw0xY.json b/sight/query/annotated/X-ix97pw0xY.json new file mode 100644 index 0000000000000000000000000000000000000000..fec5137015bf7c667542dbffb244dd139d7b48ee --- /dev/null +++ b/sight/query/annotated/X-ix97pw0xY.json @@ -0,0 +1,43 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [ + 697, + 697 + ], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + }, + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [ + 62, + 63, + 64 + ], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + }, + { + "file_id": "X-ix97pw0xY", + "query_id": 0, + "timestamp": 1684191675943.0, + "annotatedSourceSentencesIndices": [ + 188, + 252 + ], + "names": [ + "annotator1" + ], + "text": "Sorry I'm having trouble keeping up, but for the Poisson example, where does that expression for mu(x) come from?\n\n\nThis is terrific by the way- thank you MIT for helping me stay even a little afloat in one of my classes." + } +] \ No newline at end of file diff --git a/sight/query/annotated/Xa2jPbURTjQ.json b/sight/query/annotated/Xa2jPbURTjQ.json new file mode 100644 index 0000000000000000000000000000000000000000..542ed0270a0c75a276e6b5e5d6e6c316dd93fb78 --- /dev/null +++ b/sight/query/annotated/Xa2jPbURTjQ.json @@ -0,0 +1,66 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 0, + "timestamp": 1684512668939.0, + "annotatedSourceSentencesIndices": [ + 427, + 428 + ], + "names": [ + "annotator1" + ], + "text": "can anyone explain how the 5th column of w8 came out to be?" + }, + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [ + 316, + 317, + 318, + 319, + 320, + 321, + 322, + 323, + 324 + ], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + }, + { + "file_id": "Xa2jPbURTjQ", + "query_id": 3, + "timestamp": 1684512777130.0, + "annotatedSourceSentencesIndices": [ + 221 + ], + "names": [ + "annotator1" + ], + "text": "In 17.03, Why UU transpose is symmetric?" + }, + { + "file_id": "Xa2jPbURTjQ", + "query_id": 5, + "timestamp": 1684192613269.0, + "annotatedSourceSentencesIndices": [ + 81, + 82, + 93, + 79, + 81, + 82, + 93 + ], + "names": [ + "annotator1", + "annotator2" + ], + "text": "for a square matrix with orthogonal columns will ||Qx||^2 = || x ||^2 hold or the columns have to be orthonormal for this equality to hold ??? a bit confused please help" + } +] \ No newline at end of file diff --git a/sight/query/annotated/XsYXACeIklU.json b/sight/query/annotated/XsYXACeIklU.json new file mode 100644 index 0000000000000000000000000000000000000000..fff24f84d84fc40a5c51831a61e94ff8d26c2b08 --- /dev/null +++ b/sight/query/annotated/XsYXACeIklU.json @@ -0,0 +1,112 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 0, + "timestamp": 1684520066474.0, + "annotatedSourceSentencesIndices": [ + 185, + 186, + 187 + ], + "names": [ + "annotator1" + ], + "text": "For the Expected number of fish ( ~ 19:00 ), shouldn't he include the possibility of catching N fish during the first two hours? Is the probability of 3 or more fish in 0 < t < 2 insignificant?" + }, + { + "file_id": "XsYXACeIklU", + "query_id": 2, + "timestamp": 1684520098328.0, + "annotatedSourceSentencesIndices": [ + 155 + ], + "names": [ + "annotator1" + ], + "text": "Shouldn't the answer to the fish question at 15:46 be equal to p(0,2)*p(1,3) instead of p(0,2)*(1-p(0,3))\nI say this because the fisherman should fish for no longer than 1 fish. In the case of 1-p(0,3), he's considering all the possibilities that he could fish 1,2,3,4,5,6,7..... any number of fishes during that interval? from hour 2....5" + }, + { + "file_id": "XsYXACeIklU", + "query_id": 3, + "timestamp": 1684520173396.0, + "annotatedSourceSentencesIndices": [ + 194, + 196, + 197, + 198 + ], + "names": [ + "annotator1" + ], + "text": "The first terms in part d and f of the examples should be weighted with the probability that scenario 1 occurs, right?" + }, + { + "file_id": "XsYXACeIklU", + "query_id": 5, + "timestamp": 1684520219876.0, + "annotatedSourceSentencesIndices": [ + 99 + ], + "names": [ + "annotator1" + ], + "text": "But is the life of a light bulb actually modeled by the memoryless Poisson process? I would think the past takes it's toll on the filament." + }, + { + "file_id": "XsYXACeIklU", + "query_id": 6, + "timestamp": 1684520305601.0, + "annotatedSourceSentencesIndices": [ + 193, + 194, + 196, + 197, + 198, + 199, + 200, + 201 + ], + "names": [ + "annotator1" + ], + "text": "Thank you very much \nI think that there is a missing factor (1-P(0,2)) in the response to the questions d and f. Is this true?" + }, + { + "file_id": "XsYXACeIklU", + "query_id": 7, + "timestamp": 1684520381503.0, + "annotatedSourceSentencesIndices": [ + 375, + 388 + ], + "names": [ + "annotator1" + ], + "text": "The bus inter-arrival time example is a bad/counteractive example. If buses are running at the rate of 4 per hour, You go at a random time for many days and your average waiting time should be 7.5 minutes. Why would the bus company foll people by saying we are running buses whose time is determined by poisson process and not a uniform/predetermined time?" + }, + { + "file_id": "XsYXACeIklU", + "query_id": 8, + "timestamp": 1684520433574.0, + "annotatedSourceSentencesIndices": [ + 200 + ], + "names": [ + "annotator1" + ], + "text": "what does 1 over lambda represent in the fishing example?" + }, + { + "file_id": "XsYXACeIklU", + "query_id": 9, + "timestamp": 1684520498170.0, + "annotatedSourceSentencesIndices": [ + 465, + 466 + ], + "names": [ + "annotator1" + ], + "text": "45:57 we assume equally likely, bu prof. wrote 1/3 and 2/3 ? why" + } +] \ No newline at end of file diff --git a/sight/query/annotated/cxTmmasBiC8.json b/sight/query/annotated/cxTmmasBiC8.json new file mode 100644 index 0000000000000000000000000000000000000000..5478bdfaa341a297e386a1fa1c5d66f1f40e9ae7 --- /dev/null +++ b/sight/query/annotated/cxTmmasBiC8.json @@ -0,0 +1,33 @@ +[ + { + "file_id": "cxTmmasBiC8", + "query_id": 1, + "timestamp": 1684480753122.0, + "annotatedSourceSentencesIndices": [ + 291, + 265, + 266, + 267, + 269, + 270 + ], + "names": [ + "annotator1", + "annotator2" + ], + "text": "The first two eigenvalues are 0 and 2 which correspond to the eigenvectors (1,1,1,1), (0,0,-1,1). He says some of the components in this second eigenvectors are positive and some are negative which tells you which cluster each node is in. But he never carries it out and explain the 0 components? See wolfram-alpha https://tinyurl.com/y7vdkhua for decomposition." + }, + { + "file_id": "cxTmmasBiC8", + "query_id": 0, + "timestamp": 1684191388833.0, + "annotatedSourceSentencesIndices": [ + 36, + 38 + ], + "names": [ + "annotator1" + ], + "text": "3:08 how do you take (a_i - x) if a_i and x are not adjacent nodes?" + } +] \ No newline at end of file diff --git a/sight/query/annotated/d32WV1rKoVk.json b/sight/query/annotated/d32WV1rKoVk.json new file mode 100644 index 0000000000000000000000000000000000000000..374dfa20895007fb3689c32166fb026c63bcb3cc --- /dev/null +++ b/sight/query/annotated/d32WV1rKoVk.json @@ -0,0 +1,87 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 0, + "timestamp": 1684518790918.0, + "annotatedSourceSentencesIndices": [ + 211 + ], + "names": [ + "annotator1" + ], + "text": "so...how to find the proper \"shift\"?" + }, + { + "file_id": "d32WV1rKoVk", + "query_id": 1, + "timestamp": 1684518968338.0, + "annotatedSourceSentencesIndices": [ + 35 + ], + "names": [ + "annotator1" + ], + "text": "How do we get A2 from A1 ??" + }, + { + "file_id": "d32WV1rKoVk", + "query_id": 2, + "timestamp": 1684519128837.0, + "annotatedSourceSentencesIndices": [ + 65 + ], + "names": [ + "annotator1" + ], + "text": "Should we not use A0 = QR , A1=RQ => A0 = QRQ^-1 since we know Q is orthogonal and hence invertible? Where as R is not invertible unless A is?" + }, + { + "file_id": "d32WV1rKoVk", + "query_id": 3, + "timestamp": 1684519167076.0, + "annotatedSourceSentencesIndices": [ + 337 + ], + "names": [ + "annotator1" + ], + "text": "Is he talking about Galois or Abel?" + }, + { + "file_id": "d32WV1rKoVk", + "query_id": 4, + "timestamp": 1684519760474.0, + "annotatedSourceSentencesIndices": [ + 250 + ], + "names": [ + "annotator1" + ], + "text": "why cannot simple steps to get upper triangle? still don't get it from this lecture" + }, + { + "file_id": "d32WV1rKoVk", + "query_id": 6, + "timestamp": 1684519784891.0, + "annotatedSourceSentencesIndices": [ + 250 + ], + "names": [ + "annotator1" + ], + "text": "At around the 21 minute mark, he says that it\u2019s too much to hope for to reduce the matrix A0 to an upper triangular matrix. He immediately follows up with a statement that it\u2019s impossible to solve a 5x5 system with simple steps. And this is why you instead reduce A0 to an upper Hessenberg matrix instead.\n\nI got lost trying to follow this argument, so I did a bit of research. Can someone tell me if I've got it right:\n1) The eigenvalues of a triangular matrix are just its diagonal elements.\n2) The Abel-Ruffini theorem says that's impossible, using radicals, to find the roots of a 5th order polynomial.\n3) If you were to try to solve det(A - lambda I) = 0 for a 5x5 triangular matrix, you'd be trying to find the roots of a 5th order polynomial. Though doesn't it automatically come perfectly factored for you to read off the eigenvalues?\n\nCombining all of these, does the Abel-Ruffini theorem imply that you can't transform a 5x5 matrix into triangular form via orthogonal transformations (e.g. Householder reflections) which preserve the eigenvalues? This doesn't sit right with me, so I'm thinking that can't be it." + }, + { + "file_id": "d32WV1rKoVk", + "query_id": 7, + "timestamp": 1684519933908.0, + "annotatedSourceSentencesIndices": [ + 211, + 214 + ], + "names": [ + "annotator1" + ], + "text": "What happens when the eigenvalues are complex? It doesn't seem like the QR method would converge as all the numbers resulting from this method would be real." + } +] \ No newline at end of file diff --git a/sight/query/annotated/lZrIPRnoGQQ.json b/sight/query/annotated/lZrIPRnoGQQ.json new file mode 100644 index 0000000000000000000000000000000000000000..4147178bbfd6f6ecc550de2d1aeae8d35bd0db28 --- /dev/null +++ b/sight/query/annotated/lZrIPRnoGQQ.json @@ -0,0 +1,17 @@ +[ + { + "file_id": "lZrIPRnoGQQ", + "query_id": 0, + "timestamp": 1684707834591.0, + "annotatedSourceSentencesIndices": [ + 373, + 379, + 382, + 420 + ], + "names": [ + "annotator2" + ], + "text": "but if the input nodes count in NN is lower than num. of outputs then the forward mode changes to backprop from the other side, I mean if you compute Jacobians and use them in successive computations in the right order, is that so?" + } +] \ No newline at end of file diff --git a/sight/query/annotated/nHlE7EgJFds.json b/sight/query/annotated/nHlE7EgJFds.json new file mode 100644 index 0000000000000000000000000000000000000000..1a8d62bf9fd3143ecb6ea1a9dcb62e5679e7f852 --- /dev/null +++ b/sight/query/annotated/nHlE7EgJFds.json @@ -0,0 +1,231 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 0, + "timestamp": 1684702121808.0, + "annotatedSourceSentencesIndices": [ + 206, + 207, + 208 + ], + "names": [ + "annotator2" + ], + "text": "May I say that the vectors in R span the same space as vectors in A after row operation because you can do a reverse ROW operation and construct the same vectors in A from R? It can't be true for column space because after row operations you most likely can't reverse and reconstruct the original column vectors from R through COLUMN combinations." + }, + { + "file_id": "nHlE7EgJFds", + "query_id": 2, + "timestamp": 1684702165910.0, + "annotatedSourceSentencesIndices": [ + 20 + ], + "names": [ + "annotator2" + ], + "text": "\"But, after class - TO MY SORROW - a student tells me, 'Wait a minute that [third vector] is not independent...'\"\nI love it. \u00a0What other professor brings this kind of passion to linear algebra? \u00a0This is what makes real in the flesh lectures worthwhile. \u00a0" + }, + { + "file_id": "nHlE7EgJFds", + "query_id": 3, + "timestamp": 1684702398013.0, + "annotatedSourceSentencesIndices": [ + 0 + ], + "names": [ + "annotator2" + ], + "text": "40:41 why empty again?" + }, + { + "file_id": "nHlE7EgJFds", + "query_id": 5, + "timestamp": 1684702466780.0, + "annotatedSourceSentencesIndices": [ + 300 + ], + "names": [ + "annotator2" + ], + "text": "35:55 Size of identity matrix should be be nxn so that its conformable, shouldn't it?" + }, + { + "file_id": "nHlE7EgJFds", + "query_id": 9, + "timestamp": 1684702633715.0, + "annotatedSourceSentencesIndices": [ + 2 + ], + "names": [ + "annotator2" + ], + "text": "00:00 Error from last lecture, row dependent.\n04:28 4 Fundamental subspaces.\n08:30 Where are those spaces?\n11:45 Dimension of those spaces.\n21:20 Basis for those space.\n30:00 N(A^T) \"Left nullspace\"?\n42:10 New \"matrix\" space?" + }, + { + "file_id": "nHlE7EgJFds", + "query_id": 11, + "timestamp": 1684702962651.0, + "annotatedSourceSentencesIndices": [ + 14, + 439, + 440 + ], + "names": [ + "annotator2" + ], + "text": "Can anyone explain how \"length of the linearly independent list \u2264 length of spanning list\"?\nTY in advance." + }, + { + "file_id": "nHlE7EgJFds", + "query_id": 13, + "timestamp": 1684703194452.0, + "annotatedSourceSentencesIndices": [ + 351 + ], + "names": [ + "annotator2" + ], + "text": "In the 3X4 matrix example, shouldn't the dim Null(A transpose) be 4-2= 2 instead of 3-2=1?" + }, + { + "file_id": "nHlE7EgJFds", + "query_id": 14, + "timestamp": 1684703307354.0, + "annotatedSourceSentencesIndices": [ + 15, + 79 + ], + "names": [ + "annotator2" + ], + "text": "how do we define vector?" + }, + { + "file_id": "nHlE7EgJFds", + "query_id": 16, + "timestamp": 1684703606756.0, + "annotatedSourceSentencesIndices": [ + 144 + ], + "names": [ + "annotator2" + ], + "text": "*Question:* what is the relationship between rank(A) and rank(A^T)? Does rank(A) = rank(A^T) in general?\n\nThe professor seems to be hinting at this, but rref(A) only preserves the column space, so it doesn\u2019t seem so trivial to me. Any insight is highly appreciated.\n\nEdit: I found the answer. rank(A) = rank(A^T) by virtue of the fact that linear independence of the columns implies linear independence of the rows, even for non-square matrices. I proved this for myself this evening. The main idea for the proof (at least how I did it) is that if you have two linearly dependent rows, one above the other say, row reduction kills the lower one (reduces number of possibly independent rows). Killing off the row (making the row all zeros) also makes it so that the given row can\u2019t have a pivot. Thus, we\u2019ve reduced the number of potential pivot columns by one. That\u2019s the relationship in a nutshell. The math is only slightly more involved" + }, + { + "file_id": "nHlE7EgJFds", + "query_id": 17, + "timestamp": 1684703913122.0, + "annotatedSourceSentencesIndices": [ + 84, + 86 + ], + "names": [ + "annotator2" + ], + "text": "m is a number of rows, and the column space is in R^m?" + }, + { + "file_id": "nHlE7EgJFds", + "query_id": 20, + "timestamp": 1684703963640.0, + "annotatedSourceSentencesIndices": [ + 312, + 315 + ], + "names": [ + "annotator2" + ], + "text": "What's the chapter 2 he's referring at #37:30?" + }, + { + "file_id": "nHlE7EgJFds", + "query_id": 21, + "timestamp": 1684704008241.0, + "annotatedSourceSentencesIndices": [ + 397 + ], + "names": [ + "annotator2" + ], + "text": "What are 8 rule for vector space.. which he never wrote. Any answer ???" + }, + { + "file_id": "nHlE7EgJFds", + "query_id": 22, + "timestamp": 1684704082641.0, + "annotatedSourceSentencesIndices": [ + 208 + ], + "names": [ + "annotator2" + ], + "text": "@ 24:30 why is row operation able to preserve row space and not column space? as Prof Strang mentioned that 111 can longer be found in C(R) so column space is not preserved. However, I don't see any row in A being found in R as well?. To put my question simply, how do I know if certain space is preserved after certain operation?" + }, + { + "file_id": "nHlE7EgJFds", + "query_id": 24, + "timestamp": 1684704215642.0, + "annotatedSourceSentencesIndices": [ + 208 + ], + "names": [ + "annotator2" + ], + "text": "25:06 So performing row eliminations doesn't change the row space but changes the column space?\n\nSo to get the basis for the column space, would you have to do column elimination for matrix [A]? Or could you take the transpose, do row elimination, and just use that row basis for [A] transpose as the column basis for [A]?" + }, + { + "file_id": "nHlE7EgJFds", + "query_id": 26, + "timestamp": 1684704349825.0, + "annotatedSourceSentencesIndices": [ + 81 + ], + "names": [ + "annotator2" + ], + "text": "I don't understand how vectors of N(A) can be in R^m ! If A is a m*n matrix, we need a R^n vector to have the 0 matrix, no ?" + }, + { + "file_id": "nHlE7EgJFds", + "query_id": 27, + "timestamp": 1684704442760.0, + "annotatedSourceSentencesIndices": [ + 91, + 106, + 110, + 431 + ], + "names": [ + "annotator2" + ], + "text": "What did he mean by the Dimensions?" + }, + { + "file_id": "nHlE7EgJFds", + "query_id": 28, + "timestamp": 1684705683645.0, + "annotatedSourceSentencesIndices": [ + 81, + 159 + ], + "names": [ + "annotator2" + ], + "text": "suppose I'm in 3D if nullspace is a plane can we not simply write nullspace as an equation of that plane and every x,y,z be the possible values that give b of zeroes similarly if column space is plane and vice versa for row space and null space of A^t?\np.s I do understand we can't write any of four subspace as a line in 3D because there is no equation of a line in 3D it's just the equation of the plane" + }, + { + "file_id": "nHlE7EgJFds", + "query_id": 32, + "timestamp": 1684705846181.0, + "annotatedSourceSentencesIndices": [ + 129, + 130, + 132 + ], + "names": [ + "annotator2" + ], + "text": "How to prove the dimension of A and A transpose are the same?or Why they are the same value?can any one explan to me ?thanks" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk0.json b/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..9c602df53cd5a3ad16a5b096e66ff89115d4fb60 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk0.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "0Qws8BuK3RQ", + "query_id": 0, + "timestamp": 1684701645936.0, + "annotatedSourceSentencesIndices": [ + 4 + ], + "names": [ + "annotator2" + ], + "text": "Is the distance matrix right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk1.json 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0, + "timestamp": 1684701645936.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is the distance matrix right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk9.json b/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..9872b348efccca32f665233311d7bd4530cb500d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0Qws8BuK3RQ", + "query_id": 0, + "timestamp": 1684701645936.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is the distance matrix right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk0.json b/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk0.json new file mode 100644 index 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procrustes problem?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk10.json b/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..2ad73af08339688dcd7b250cdb79cc2da68d468b --- /dev/null +++ b/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0Qws8BuK3RQ", + "query_id": 1, + "timestamp": 1684701685821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "where can i find the proof of procrustes problem?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk11.json b/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..2ad73af08339688dcd7b250cdb79cc2da68d468b --- /dev/null +++ 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"query_id": 1, + "timestamp": 1684701685821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "where can i find the proof of procrustes problem?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk3.json b/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..30a22d1290a6a3b39eb5d6a16fd2324ea96aa977 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk3.json @@ -0,0 +1,16 @@ +[ + { + "file_id": "0Qws8BuK3RQ", + "query_id": 1, + "timestamp": 1684701685821.0, + "annotatedSourceSentencesIndices": [ + 2, + 3, + 13 + ], + "names": [ + "annotator2" + ], + "text": "where can i find the proof of procrustes problem?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk4.json b/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..2ad73af08339688dcd7b250cdb79cc2da68d468b --- /dev/null +++ b/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0Qws8BuK3RQ", + "query_id": 1, + "timestamp": 1684701685821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "where can i find the proof of procrustes problem?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk5.json b/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..2ad73af08339688dcd7b250cdb79cc2da68d468b --- /dev/null +++ b/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0Qws8BuK3RQ", + "query_id": 1, + "timestamp": 1684701685821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "where can i find the proof of procrustes problem?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk6.json b/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..2ad73af08339688dcd7b250cdb79cc2da68d468b --- /dev/null +++ b/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0Qws8BuK3RQ", + "query_id": 1, + "timestamp": 1684701685821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "where can i find the proof of procrustes problem?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk7.json b/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..2ad73af08339688dcd7b250cdb79cc2da68d468b --- /dev/null +++ b/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0Qws8BuK3RQ", + "query_id": 1, + "timestamp": 1684701685821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "where can i find the proof of procrustes problem?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk8.json b/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..2ad73af08339688dcd7b250cdb79cc2da68d468b --- /dev/null +++ b/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0Qws8BuK3RQ", + "query_id": 1, + "timestamp": 1684701685821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "where can i find the proof of procrustes problem?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk9.json b/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..2ad73af08339688dcd7b250cdb79cc2da68d468b --- /dev/null +++ b/sight/query/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0Qws8BuK3RQ", + "query_id": 1, + "timestamp": 1684701685821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "where can i find the proof of procrustes problem?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk0.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..cfbb824a1e789d2cbff152f1f4da818dab620cc1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 0, + "timestamp": 1684520869368.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Isnt there a mistake @ 46:24 ? Shouldn\u2019t the position 8,1 of matrix A contain a8,1 and not a1,8? Same for position 8,2, shouldn\u2019t it contain a8,2 instead of a2,8? And same for position 1,2? Great lecture thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk1.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..cfbb824a1e789d2cbff152f1f4da818dab620cc1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 0, + "timestamp": 1684520869368.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Isnt there a mistake @ 46:24 ? Shouldn\u2019t the position 8,1 of matrix A contain a8,1 and not a1,8? Same for position 8,2, shouldn\u2019t it contain a8,2 instead of a2,8? And same for position 1,2? Great lecture thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk10.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..cfbb824a1e789d2cbff152f1f4da818dab620cc1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 0, + "timestamp": 1684520869368.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Isnt there a mistake @ 46:24 ? Shouldn\u2019t the position 8,1 of matrix A contain a8,1 and not a1,8? Same for position 8,2, shouldn\u2019t it contain a8,2 instead of a2,8? And same for position 1,2? Great lecture thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk11.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..cfbb824a1e789d2cbff152f1f4da818dab620cc1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 0, + "timestamp": 1684520869368.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Isnt there a mistake @ 46:24 ? Shouldn\u2019t the position 8,1 of matrix A contain a8,1 and not a1,8? Same for position 8,2, shouldn\u2019t it contain a8,2 instead of a2,8? And same for position 1,2? Great lecture thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk12.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..cfbb824a1e789d2cbff152f1f4da818dab620cc1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 0, + "timestamp": 1684520869368.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Isnt there a mistake @ 46:24 ? Shouldn\u2019t the position 8,1 of matrix A contain a8,1 and not a1,8? Same for position 8,2, shouldn\u2019t it contain a8,2 instead of a2,8? And same for position 1,2? Great lecture thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk13.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..cfbb824a1e789d2cbff152f1f4da818dab620cc1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 0, + "timestamp": 1684520869368.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Isnt there a mistake @ 46:24 ? Shouldn\u2019t the position 8,1 of matrix A contain a8,1 and not a1,8? Same for position 8,2, shouldn\u2019t it contain a8,2 instead of a2,8? And same for position 1,2? Great lecture thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk14.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..cfbb824a1e789d2cbff152f1f4da818dab620cc1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 0, + "timestamp": 1684520869368.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Isnt there a mistake @ 46:24 ? Shouldn\u2019t the position 8,1 of matrix A contain a8,1 and not a1,8? Same for position 8,2, shouldn\u2019t it contain a8,2 instead of a2,8? And same for position 1,2? Great lecture thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk15.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..cfbb824a1e789d2cbff152f1f4da818dab620cc1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 0, + "timestamp": 1684520869368.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Isnt there a mistake @ 46:24 ? Shouldn\u2019t the position 8,1 of matrix A contain a8,1 and not a1,8? Same for position 8,2, shouldn\u2019t it contain a8,2 instead of a2,8? And same for position 1,2? Great lecture thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk16.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..cfbb824a1e789d2cbff152f1f4da818dab620cc1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 0, + "timestamp": 1684520869368.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Isnt there a mistake @ 46:24 ? Shouldn\u2019t the position 8,1 of matrix A contain a8,1 and not a1,8? Same for position 8,2, shouldn\u2019t it contain a8,2 instead of a2,8? And same for position 1,2? Great lecture thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk17.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..cfbb824a1e789d2cbff152f1f4da818dab620cc1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 0, + "timestamp": 1684520869368.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Isnt there a mistake @ 46:24 ? Shouldn\u2019t the position 8,1 of matrix A contain a8,1 and not a1,8? Same for position 8,2, shouldn\u2019t it contain a8,2 instead of a2,8? And same for position 1,2? Great lecture thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk18.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..8f1d18ecd2b9707757b8654fdbd1a70efc68eb29 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk18.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 0, + "timestamp": 1684520869368.0, + "annotatedSourceSentencesIndices": [ + 10 + ], + "names": [ + "annotator1" + ], + "text": "Isnt there a mistake @ 46:24 ? Shouldn\u2019t the position 8,1 of matrix A contain a8,1 and not a1,8? Same for position 8,2, shouldn\u2019t it contain a8,2 instead of a2,8? And same for position 1,2? Great lecture thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk19.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..cfbb824a1e789d2cbff152f1f4da818dab620cc1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 0, + "timestamp": 1684520869368.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Isnt there a mistake @ 46:24 ? Shouldn\u2019t the position 8,1 of matrix A contain a8,1 and not a1,8? Same for position 8,2, shouldn\u2019t it contain a8,2 instead of a2,8? And same for position 1,2? Great lecture thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk2.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..cfbb824a1e789d2cbff152f1f4da818dab620cc1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 0, + "timestamp": 1684520869368.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Isnt there a mistake @ 46:24 ? Shouldn\u2019t the position 8,1 of matrix A contain a8,1 and not a1,8? Same for position 8,2, shouldn\u2019t it contain a8,2 instead of a2,8? And same for position 1,2? Great lecture thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk20.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..cfbb824a1e789d2cbff152f1f4da818dab620cc1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 0, + "timestamp": 1684520869368.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Isnt there a mistake @ 46:24 ? Shouldn\u2019t the position 8,1 of matrix A contain a8,1 and not a1,8? Same for position 8,2, shouldn\u2019t it contain a8,2 instead of a2,8? And same for position 1,2? Great lecture thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk3.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..cfbb824a1e789d2cbff152f1f4da818dab620cc1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 0, + "timestamp": 1684520869368.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Isnt there a mistake @ 46:24 ? Shouldn\u2019t the position 8,1 of matrix A contain a8,1 and not a1,8? Same for position 8,2, shouldn\u2019t it contain a8,2 instead of a2,8? And same for position 1,2? Great lecture thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk4.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..cfbb824a1e789d2cbff152f1f4da818dab620cc1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 0, + "timestamp": 1684520869368.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Isnt there a mistake @ 46:24 ? Shouldn\u2019t the position 8,1 of matrix A contain a8,1 and not a1,8? Same for position 8,2, shouldn\u2019t it contain a8,2 instead of a2,8? And same for position 1,2? Great lecture thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk5.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..cfbb824a1e789d2cbff152f1f4da818dab620cc1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 0, + "timestamp": 1684520869368.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Isnt there a mistake @ 46:24 ? Shouldn\u2019t the position 8,1 of matrix A contain a8,1 and not a1,8? Same for position 8,2, shouldn\u2019t it contain a8,2 instead of a2,8? And same for position 1,2? Great lecture thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk6.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..cfbb824a1e789d2cbff152f1f4da818dab620cc1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 0, + "timestamp": 1684520869368.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Isnt there a mistake @ 46:24 ? Shouldn\u2019t the position 8,1 of matrix A contain a8,1 and not a1,8? Same for position 8,2, shouldn\u2019t it contain a8,2 instead of a2,8? And same for position 1,2? Great lecture thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk7.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..cfbb824a1e789d2cbff152f1f4da818dab620cc1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 0, + "timestamp": 1684520869368.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Isnt there a mistake @ 46:24 ? Shouldn\u2019t the position 8,1 of matrix A contain a8,1 and not a1,8? Same for position 8,2, shouldn\u2019t it contain a8,2 instead of a2,8? And same for position 1,2? Great lecture thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk8.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..cfbb824a1e789d2cbff152f1f4da818dab620cc1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 0, + "timestamp": 1684520869368.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Isnt there a mistake @ 46:24 ? Shouldn\u2019t the position 8,1 of matrix A contain a8,1 and not a1,8? Same for position 8,2, shouldn\u2019t it contain a8,2 instead of a2,8? And same for position 1,2? Great lecture thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk9.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..cfbb824a1e789d2cbff152f1f4da818dab620cc1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_0_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 0, + "timestamp": 1684520869368.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Isnt there a mistake @ 46:24 ? Shouldn\u2019t the position 8,1 of matrix A contain a8,1 and not a1,8? Same for position 8,2, shouldn\u2019t it contain a8,2 instead of a2,8? And same for position 1,2? Great lecture thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk0.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..05b0bd65aed53cf025756cc6420650dbe1a880ae --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 1, + "timestamp": 1684700727042.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "How the imaginary parts are taken care of in Fourier Basis for JPEG?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk1.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..05b0bd65aed53cf025756cc6420650dbe1a880ae --- /dev/null +++ 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a/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk11.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..05b0bd65aed53cf025756cc6420650dbe1a880ae --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 1, + "timestamp": 1684700727042.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "How the imaginary parts are taken care of in Fourier Basis for JPEG?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk12.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..05b0bd65aed53cf025756cc6420650dbe1a880ae --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 1, + "timestamp": 1684700727042.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "How the imaginary parts are taken care of in Fourier Basis for JPEG?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk13.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..05b0bd65aed53cf025756cc6420650dbe1a880ae --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 1, + "timestamp": 1684700727042.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "How the imaginary parts are taken care of in Fourier Basis for JPEG?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk14.json 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"annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "How the imaginary parts are taken care of in Fourier Basis for JPEG?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk16.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..05b0bd65aed53cf025756cc6420650dbe1a880ae --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 1, + "timestamp": 1684700727042.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "How the imaginary parts are taken care of in Fourier Basis for JPEG?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk17.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk17.json new file mode 100644 index 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imaginary parts are taken care of in Fourier Basis for JPEG?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk19.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..05b0bd65aed53cf025756cc6420650dbe1a880ae --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 1, + "timestamp": 1684700727042.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "How the imaginary parts are taken care of in Fourier Basis for JPEG?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk2.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..05b0bd65aed53cf025756cc6420650dbe1a880ae --- /dev/null +++ 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a/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk3.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..05b0bd65aed53cf025756cc6420650dbe1a880ae --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 1, + "timestamp": 1684700727042.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "How the imaginary parts are taken care of in Fourier Basis for JPEG?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk4.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..ca3aa151a1eeb33f36b78946734cee392fec4681 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk4.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 1, + "timestamp": 1684700727042.0, + "annotatedSourceSentencesIndices": [ + 1 + ], + "names": [ + "annotator2" + ], + "text": "How the imaginary parts are taken care of in Fourier Basis for JPEG?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk5.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..05b0bd65aed53cf025756cc6420650dbe1a880ae --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 1, + "timestamp": 1684700727042.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "How the imaginary parts are taken care of in Fourier Basis for JPEG?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk6.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..05b0bd65aed53cf025756cc6420650dbe1a880ae --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 1, + "timestamp": 1684700727042.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "How the imaginary parts are taken care of in Fourier Basis for JPEG?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk7.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..05b0bd65aed53cf025756cc6420650dbe1a880ae --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 1, + "timestamp": 1684700727042.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "How the imaginary parts are taken care of in Fourier Basis for JPEG?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk8.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..05b0bd65aed53cf025756cc6420650dbe1a880ae --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 1, + "timestamp": 1684700727042.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "How the imaginary parts are taken care of in Fourier Basis for JPEG?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk9.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..05b0bd65aed53cf025756cc6420650dbe1a880ae --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_1_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 1, + "timestamp": 1684700727042.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "How the imaginary parts are taken care of in Fourier Basis for JPEG?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk0.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..16274411b020921c5c2bfb00690b28e81d258743 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 2, + "timestamp": 1684700837277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm fairly certain x includes 255 in the domain. [4:15]\nCan anyone confirm or clarify? \n(should be x is less than or equal to 255, rather than strictly less than)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk1.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..88d682f2c8f2e29a237487fb83becda067de6644 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk1.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 2, + "timestamp": 1684700837277.0, + "annotatedSourceSentencesIndices": [ + 7, + 8 + ], + "names": [ + "annotator2" + ], + "text": "I'm fairly certain x includes 255 in the domain. [4:15]\nCan anyone confirm or clarify? \n(should be x is less than or equal to 255, rather than strictly less than)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk10.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..16274411b020921c5c2bfb00690b28e81d258743 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 2, + "timestamp": 1684700837277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm fairly certain x includes 255 in the domain. [4:15]\nCan anyone confirm or clarify? \n(should be x is less than or equal to 255, rather than strictly less than)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk11.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..16274411b020921c5c2bfb00690b28e81d258743 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 2, + "timestamp": 1684700837277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm fairly certain x includes 255 in the domain. [4:15]\nCan anyone confirm or clarify? \n(should be x is less than or equal to 255, rather than strictly less than)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk12.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..16274411b020921c5c2bfb00690b28e81d258743 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 2, + "timestamp": 1684700837277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm fairly certain x includes 255 in the domain. [4:15]\nCan anyone confirm or clarify? \n(should be x is less than or equal to 255, rather than strictly less than)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk13.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..16274411b020921c5c2bfb00690b28e81d258743 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 2, + "timestamp": 1684700837277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm fairly certain x includes 255 in the domain. [4:15]\nCan anyone confirm or clarify? \n(should be x is less than or equal to 255, rather than strictly less than)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk14.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..16274411b020921c5c2bfb00690b28e81d258743 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 2, + "timestamp": 1684700837277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm fairly certain x includes 255 in the domain. [4:15]\nCan anyone confirm or clarify? \n(should be x is less than or equal to 255, rather than strictly less than)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk15.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..16274411b020921c5c2bfb00690b28e81d258743 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 2, + "timestamp": 1684700837277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm fairly certain x includes 255 in the domain. [4:15]\nCan anyone confirm or clarify? \n(should be x is less than or equal to 255, rather than strictly less than)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk16.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..16274411b020921c5c2bfb00690b28e81d258743 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 2, + "timestamp": 1684700837277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm fairly certain x includes 255 in the domain. [4:15]\nCan anyone confirm or clarify? \n(should be x is less than or equal to 255, rather than strictly less than)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk17.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..16274411b020921c5c2bfb00690b28e81d258743 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 2, + "timestamp": 1684700837277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm fairly certain x includes 255 in the domain. [4:15]\nCan anyone confirm or clarify? \n(should be x is less than or equal to 255, rather than strictly less than)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk18.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..16274411b020921c5c2bfb00690b28e81d258743 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 2, + "timestamp": 1684700837277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm fairly certain x includes 255 in the domain. [4:15]\nCan anyone confirm or clarify? \n(should be x is less than or equal to 255, rather than strictly less than)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk19.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..16274411b020921c5c2bfb00690b28e81d258743 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 2, + "timestamp": 1684700837277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm fairly certain x includes 255 in the domain. [4:15]\nCan anyone confirm or clarify? \n(should be x is less than or equal to 255, rather than strictly less than)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk2.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..16274411b020921c5c2bfb00690b28e81d258743 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 2, + "timestamp": 1684700837277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm fairly certain x includes 255 in the domain. [4:15]\nCan anyone confirm or clarify? \n(should be x is less than or equal to 255, rather than strictly less than)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk20.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..16274411b020921c5c2bfb00690b28e81d258743 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 2, + "timestamp": 1684700837277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm fairly certain x includes 255 in the domain. [4:15]\nCan anyone confirm or clarify? \n(should be x is less than or equal to 255, rather than strictly less than)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk3.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..16274411b020921c5c2bfb00690b28e81d258743 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 2, + "timestamp": 1684700837277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm fairly certain x includes 255 in the domain. [4:15]\nCan anyone confirm or clarify? \n(should be x is less than or equal to 255, rather than strictly less than)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk4.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..16274411b020921c5c2bfb00690b28e81d258743 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 2, + "timestamp": 1684700837277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm fairly certain x includes 255 in the domain. [4:15]\nCan anyone confirm or clarify? \n(should be x is less than or equal to 255, rather than strictly less than)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk5.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..16274411b020921c5c2bfb00690b28e81d258743 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 2, + "timestamp": 1684700837277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm fairly certain x includes 255 in the domain. [4:15]\nCan anyone confirm or clarify? \n(should be x is less than or equal to 255, rather than strictly less than)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk6.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..16274411b020921c5c2bfb00690b28e81d258743 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 2, + "timestamp": 1684700837277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm fairly certain x includes 255 in the domain. [4:15]\nCan anyone confirm or clarify? \n(should be x is less than or equal to 255, rather than strictly less than)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk7.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..16274411b020921c5c2bfb00690b28e81d258743 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 2, + "timestamp": 1684700837277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm fairly certain x includes 255 in the domain. [4:15]\nCan anyone confirm or clarify? \n(should be x is less than or equal to 255, rather than strictly less than)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk8.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..16274411b020921c5c2bfb00690b28e81d258743 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 2, + "timestamp": 1684700837277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm fairly certain x includes 255 in the domain. [4:15]\nCan anyone confirm or clarify? \n(should be x is less than or equal to 255, rather than strictly less than)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk9.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..16274411b020921c5c2bfb00690b28e81d258743 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_2_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 2, + "timestamp": 1684700837277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm fairly certain x includes 255 in the domain. [4:15]\nCan anyone confirm or clarify? \n(should be x is less than or equal to 255, rather than strictly less than)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk0.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..3415d45c4a8a2ba2f6d5da08def601f4403cf58d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 3, + "timestamp": 1684700983228.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, does it mean that the basis of the input space and that of the output space is the same {v1, v2, ..., v8} at 45:25?\nThen, if this is true, when does change of basis happen?\nI get confused here, please help me, thanks a lot!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk1.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3415d45c4a8a2ba2f6d5da08def601f4403cf58d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 3, + "timestamp": 1684700983228.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, does it mean that the basis of the input space and that of the output space is the same {v1, v2, ..., v8} at 45:25?\nThen, if this is true, when does change of basis happen?\nI get confused here, please help me, thanks a lot!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk10.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..3415d45c4a8a2ba2f6d5da08def601f4403cf58d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 3, + "timestamp": 1684700983228.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, does it mean that the basis of the input space and that of the output space is the same {v1, v2, ..., v8} at 45:25?\nThen, if this is true, when does change of basis happen?\nI get confused here, please help me, thanks a lot!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk11.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..3415d45c4a8a2ba2f6d5da08def601f4403cf58d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 3, + "timestamp": 1684700983228.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, does it mean that the basis of the input space and that of the output space is the same {v1, v2, ..., v8} at 45:25?\nThen, if this is true, when does change of basis happen?\nI get confused here, please help me, thanks a lot!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk12.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..3415d45c4a8a2ba2f6d5da08def601f4403cf58d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 3, + "timestamp": 1684700983228.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, does it mean that the basis of the input space and that of the output space is the same {v1, v2, ..., v8} at 45:25?\nThen, if this is true, when does change of basis happen?\nI get confused here, please help me, thanks a lot!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk13.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..3415d45c4a8a2ba2f6d5da08def601f4403cf58d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 3, + "timestamp": 1684700983228.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, does it mean that the basis of the input space and that of the output space is the same {v1, v2, ..., v8} at 45:25?\nThen, if this is true, when does change of basis happen?\nI get confused here, please help me, thanks a lot!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk14.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..3415d45c4a8a2ba2f6d5da08def601f4403cf58d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 3, + "timestamp": 1684700983228.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, does it mean that the basis of the input space and that of the output space is the same {v1, v2, ..., v8} at 45:25?\nThen, if this is true, when does change of basis happen?\nI get confused here, please help me, thanks a lot!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk15.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3415d45c4a8a2ba2f6d5da08def601f4403cf58d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 3, + "timestamp": 1684700983228.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, does it mean that the basis of the input space and that of the output space is the same {v1, v2, ..., v8} at 45:25?\nThen, if this is true, when does change of basis happen?\nI get confused here, please help me, thanks a lot!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk16.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..3415d45c4a8a2ba2f6d5da08def601f4403cf58d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 3, + "timestamp": 1684700983228.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, does it mean that the basis of the input space and that of the output space is the same {v1, v2, ..., v8} at 45:25?\nThen, if this is true, when does change of basis happen?\nI get confused here, please help me, thanks a lot!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk17.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..3415d45c4a8a2ba2f6d5da08def601f4403cf58d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 3, + "timestamp": 1684700983228.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, does it mean that the basis of the input space and that of the output space is the same {v1, v2, ..., v8} at 45:25?\nThen, if this is true, when does change of basis happen?\nI get confused here, please help me, thanks a lot!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk18.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..5dd76945e6559db9ae35bdb5435f470bb7eec250 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk18.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 3, + "timestamp": 1684700983228.0, + "annotatedSourceSentencesIndices": [ + 5, + 6 + ], + "names": [ + "annotator2" + ], + "text": "Excuse me, does it mean that the basis of the input space and that of the output space is the same {v1, v2, ..., v8} at 45:25?\nThen, if this is true, when does change of basis happen?\nI get confused here, please help me, thanks a lot!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk19.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..3415d45c4a8a2ba2f6d5da08def601f4403cf58d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 3, + "timestamp": 1684700983228.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, does it mean that the basis of the input space and that of the output space is the same {v1, v2, ..., v8} at 45:25?\nThen, if this is true, when does change of basis happen?\nI get confused here, please help me, thanks a lot!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk2.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..3415d45c4a8a2ba2f6d5da08def601f4403cf58d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 3, + "timestamp": 1684700983228.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, does it mean that the basis of the input space and that of the output space is the same {v1, v2, ..., v8} at 45:25?\nThen, if this is true, when does change of basis happen?\nI get confused here, please help me, thanks a lot!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk20.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..3415d45c4a8a2ba2f6d5da08def601f4403cf58d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 3, + "timestamp": 1684700983228.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, does it mean that the basis of the input space and that of the output space is the same {v1, v2, ..., v8} at 45:25?\nThen, if this is true, when does change of basis happen?\nI get confused here, please help me, thanks a lot!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk3.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..3415d45c4a8a2ba2f6d5da08def601f4403cf58d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 3, + "timestamp": 1684700983228.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, does it mean that the basis of the input space and that of the output space is the same {v1, v2, ..., v8} at 45:25?\nThen, if this is true, when does change of basis happen?\nI get confused here, please help me, thanks a lot!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk4.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..3415d45c4a8a2ba2f6d5da08def601f4403cf58d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 3, + "timestamp": 1684700983228.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, does it mean that the basis of the input space and that of the output space is the same {v1, v2, ..., v8} at 45:25?\nThen, if this is true, when does change of basis happen?\nI get confused here, please help me, thanks a lot!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk5.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..3415d45c4a8a2ba2f6d5da08def601f4403cf58d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 3, + "timestamp": 1684700983228.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, does it mean that the basis of the input space and that of the output space is the same {v1, v2, ..., v8} at 45:25?\nThen, if this is true, when does change of basis happen?\nI get confused here, please help me, thanks a lot!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk6.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..3415d45c4a8a2ba2f6d5da08def601f4403cf58d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 3, + "timestamp": 1684700983228.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, does it mean that the basis of the input space and that of the output space is the same {v1, v2, ..., v8} at 45:25?\nThen, if this is true, when does change of basis happen?\nI get confused here, please help me, thanks a lot!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk7.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..3415d45c4a8a2ba2f6d5da08def601f4403cf58d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 3, + "timestamp": 1684700983228.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, does it mean that the basis of the input space and that of the output space is the same {v1, v2, ..., v8} at 45:25?\nThen, if this is true, when does change of basis happen?\nI get confused here, please help me, thanks a lot!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk8.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..3415d45c4a8a2ba2f6d5da08def601f4403cf58d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 3, + "timestamp": 1684700983228.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, does it mean that the basis of the input space and that of the output space is the same {v1, v2, ..., v8} at 45:25?\nThen, if this is true, when does change of basis happen?\nI get confused here, please help me, thanks a lot!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk9.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..3415d45c4a8a2ba2f6d5da08def601f4403cf58d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_3_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 3, + "timestamp": 1684700983228.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, does it mean that the basis of the input space and that of the output space is the same {v1, v2, ..., v8} at 45:25?\nThen, if this is true, when does change of basis happen?\nI get confused here, please help me, thanks a lot!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk0.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..640e3267d382c0652757bc17a559154be83c0f1d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 4, + "timestamp": 1684701306384.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Got extremely confused when he brought transformations in at the end. Why did the original basis vector \"x\" change to \"v\", then why does he compute a T(x) from \"knowing\" T(v1), ... T(v8) BEFORE writing what the actual values of T(v1) .. T(v8) are, and what is this T(x) even used for? and then where does the \"a\" come from?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk1.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..640e3267d382c0652757bc17a559154be83c0f1d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 4, + "timestamp": 1684701306384.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Got extremely confused when he brought transformations in at the end. Why did the original basis vector \"x\" change to \"v\", then why does he compute a T(x) from \"knowing\" T(v1), ... T(v8) BEFORE writing what the actual values of T(v1) .. T(v8) are, and what is this T(x) even used for? and then where does the \"a\" come from?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk10.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..640e3267d382c0652757bc17a559154be83c0f1d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 4, + "timestamp": 1684701306384.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Got extremely confused when he brought transformations in at the end. Why did the original basis vector \"x\" change to \"v\", then why does he compute a T(x) from \"knowing\" T(v1), ... T(v8) BEFORE writing what the actual values of T(v1) .. T(v8) are, and what is this T(x) even used for? and then where does the \"a\" come from?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk11.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..640e3267d382c0652757bc17a559154be83c0f1d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 4, + "timestamp": 1684701306384.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Got extremely confused when he brought transformations in at the end. Why did the original basis vector \"x\" change to \"v\", then why does he compute a T(x) from \"knowing\" T(v1), ... T(v8) BEFORE writing what the actual values of T(v1) .. T(v8) are, and what is this T(x) even used for? and then where does the \"a\" come from?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk12.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..640e3267d382c0652757bc17a559154be83c0f1d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 4, + "timestamp": 1684701306384.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Got extremely confused when he brought transformations in at the end. Why did the original basis vector \"x\" change to \"v\", then why does he compute a T(x) from \"knowing\" T(v1), ... T(v8) BEFORE writing what the actual values of T(v1) .. T(v8) are, and what is this T(x) even used for? and then where does the \"a\" come from?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk13.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..640e3267d382c0652757bc17a559154be83c0f1d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 4, + "timestamp": 1684701306384.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Got extremely confused when he brought transformations in at the end. Why did the original basis vector \"x\" change to \"v\", then why does he compute a T(x) from \"knowing\" T(v1), ... T(v8) BEFORE writing what the actual values of T(v1) .. T(v8) are, and what is this T(x) even used for? and then where does the \"a\" come from?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk14.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..640e3267d382c0652757bc17a559154be83c0f1d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 4, + "timestamp": 1684701306384.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Got extremely confused when he brought transformations in at the end. Why did the original basis vector \"x\" change to \"v\", then why does he compute a T(x) from \"knowing\" T(v1), ... T(v8) BEFORE writing what the actual values of T(v1) .. T(v8) are, and what is this T(x) even used for? and then where does the \"a\" come from?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk15.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..640e3267d382c0652757bc17a559154be83c0f1d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 4, + "timestamp": 1684701306384.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Got extremely confused when he brought transformations in at the end. Why did the original basis vector \"x\" change to \"v\", then why does he compute a T(x) from \"knowing\" T(v1), ... T(v8) BEFORE writing what the actual values of T(v1) .. T(v8) are, and what is this T(x) even used for? and then where does the \"a\" come from?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk16.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..640e3267d382c0652757bc17a559154be83c0f1d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 4, + "timestamp": 1684701306384.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Got extremely confused when he brought transformations in at the end. Why did the original basis vector \"x\" change to \"v\", then why does he compute a T(x) from \"knowing\" T(v1), ... T(v8) BEFORE writing what the actual values of T(v1) .. T(v8) are, and what is this T(x) even used for? and then where does the \"a\" come from?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk17.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..2f85d2145697f0cd469c3ff8dbd360088f1c9867 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk17.json @@ -0,0 +1,16 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 4, + "timestamp": 1684701306384.0, + "annotatedSourceSentencesIndices": [ + 5, + 17, + 18 + ], + "names": [ + "annotator2" + ], + "text": "Got extremely confused when he brought transformations in at the end. Why did the original basis vector \"x\" change to \"v\", then why does he compute a T(x) from \"knowing\" T(v1), ... T(v8) BEFORE writing what the actual values of T(v1) .. T(v8) are, and what is this T(x) even used for? and then where does the \"a\" come from?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk18.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..c00bc69cec39379cbf87d91bb99d7d97ea1a0d40 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk18.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 4, + "timestamp": 1684701306384.0, + "annotatedSourceSentencesIndices": [ + 5, + 6 + ], + "names": [ + "annotator2" + ], + "text": "Got extremely confused when he brought transformations in at the end. Why did the original basis vector \"x\" change to \"v\", then why does he compute a T(x) from \"knowing\" T(v1), ... T(v8) BEFORE writing what the actual values of T(v1) .. T(v8) are, and what is this T(x) even used for? and then where does the \"a\" come from?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk19.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..640e3267d382c0652757bc17a559154be83c0f1d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 4, + "timestamp": 1684701306384.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Got extremely confused when he brought transformations in at the end. Why did the original basis vector \"x\" change to \"v\", then why does he compute a T(x) from \"knowing\" T(v1), ... T(v8) BEFORE writing what the actual values of T(v1) .. T(v8) are, and what is this T(x) even used for? and then where does the \"a\" come from?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk2.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..640e3267d382c0652757bc17a559154be83c0f1d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 4, + "timestamp": 1684701306384.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Got extremely confused when he brought transformations in at the end. Why did the original basis vector \"x\" change to \"v\", then why does he compute a T(x) from \"knowing\" T(v1), ... T(v8) BEFORE writing what the actual values of T(v1) .. T(v8) are, and what is this T(x) even used for? and then where does the \"a\" come from?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk20.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..640e3267d382c0652757bc17a559154be83c0f1d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 4, + "timestamp": 1684701306384.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Got extremely confused when he brought transformations in at the end. Why did the original basis vector \"x\" change to \"v\", then why does he compute a T(x) from \"knowing\" T(v1), ... T(v8) BEFORE writing what the actual values of T(v1) .. T(v8) are, and what is this T(x) even used for? and then where does the \"a\" come from?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk3.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..640e3267d382c0652757bc17a559154be83c0f1d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 4, + "timestamp": 1684701306384.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Got extremely confused when he brought transformations in at the end. Why did the original basis vector \"x\" change to \"v\", then why does he compute a T(x) from \"knowing\" T(v1), ... T(v8) BEFORE writing what the actual values of T(v1) .. T(v8) are, and what is this T(x) even used for? and then where does the \"a\" come from?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk4.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..640e3267d382c0652757bc17a559154be83c0f1d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 4, + "timestamp": 1684701306384.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Got extremely confused when he brought transformations in at the end. Why did the original basis vector \"x\" change to \"v\", then why does he compute a T(x) from \"knowing\" T(v1), ... T(v8) BEFORE writing what the actual values of T(v1) .. T(v8) are, and what is this T(x) even used for? and then where does the \"a\" come from?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk5.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..640e3267d382c0652757bc17a559154be83c0f1d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 4, + "timestamp": 1684701306384.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Got extremely confused when he brought transformations in at the end. Why did the original basis vector \"x\" change to \"v\", then why does he compute a T(x) from \"knowing\" T(v1), ... T(v8) BEFORE writing what the actual values of T(v1) .. T(v8) are, and what is this T(x) even used for? and then where does the \"a\" come from?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk6.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..640e3267d382c0652757bc17a559154be83c0f1d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 4, + "timestamp": 1684701306384.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Got extremely confused when he brought transformations in at the end. Why did the original basis vector \"x\" change to \"v\", then why does he compute a T(x) from \"knowing\" T(v1), ... T(v8) BEFORE writing what the actual values of T(v1) .. T(v8) are, and what is this T(x) even used for? and then where does the \"a\" come from?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk7.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..640e3267d382c0652757bc17a559154be83c0f1d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 4, + "timestamp": 1684701306384.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Got extremely confused when he brought transformations in at the end. Why did the original basis vector \"x\" change to \"v\", then why does he compute a T(x) from \"knowing\" T(v1), ... T(v8) BEFORE writing what the actual values of T(v1) .. T(v8) are, and what is this T(x) even used for? and then where does the \"a\" come from?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk8.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..640e3267d382c0652757bc17a559154be83c0f1d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 4, + "timestamp": 1684701306384.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Got extremely confused when he brought transformations in at the end. Why did the original basis vector \"x\" change to \"v\", then why does he compute a T(x) from \"knowing\" T(v1), ... T(v8) BEFORE writing what the actual values of T(v1) .. T(v8) are, and what is this T(x) even used for? and then where does the \"a\" come from?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk9.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..640e3267d382c0652757bc17a559154be83c0f1d --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_4_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 4, + "timestamp": 1684701306384.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Got extremely confused when he brought transformations in at the end. Why did the original basis vector \"x\" change to \"v\", then why does he compute a T(x) from \"knowing\" T(v1), ... T(v8) BEFORE writing what the actual values of T(v1) .. T(v8) are, and what is this T(x) even used for? and then where does the \"a\" come from?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk0.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a9775bd93b5f5f90d95004affb88d550a278e015 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 5, + "timestamp": 1684701331681.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:17, x[i] <256 , right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk1.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..07d89b32d758af6b4949a524b28f30b80071822e --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk1.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 5, + "timestamp": 1684701331681.0, + "annotatedSourceSentencesIndices": [ + 7, + 8 + ], + "names": [ + "annotator2" + ], + "text": "4:17, x[i] <256 , right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk10.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..a9775bd93b5f5f90d95004affb88d550a278e015 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 5, + "timestamp": 1684701331681.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:17, x[i] <256 , right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk11.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..a9775bd93b5f5f90d95004affb88d550a278e015 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 5, + "timestamp": 1684701331681.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:17, x[i] <256 , right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk12.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..a9775bd93b5f5f90d95004affb88d550a278e015 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 5, + "timestamp": 1684701331681.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:17, x[i] <256 , right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk13.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..a9775bd93b5f5f90d95004affb88d550a278e015 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 5, + "timestamp": 1684701331681.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:17, x[i] <256 , right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk14.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..a9775bd93b5f5f90d95004affb88d550a278e015 --- /dev/null +++ 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b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..a9775bd93b5f5f90d95004affb88d550a278e015 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 5, + "timestamp": 1684701331681.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:17, x[i] <256 , right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk17.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a9775bd93b5f5f90d95004affb88d550a278e015 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 5, + "timestamp": 1684701331681.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:17, x[i] <256 , right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk18.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..a9775bd93b5f5f90d95004affb88d550a278e015 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 5, + "timestamp": 1684701331681.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:17, x[i] <256 , right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk19.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..a9775bd93b5f5f90d95004affb88d550a278e015 --- /dev/null +++ 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b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..a9775bd93b5f5f90d95004affb88d550a278e015 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 5, + "timestamp": 1684701331681.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:17, x[i] <256 , right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk3.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..a9775bd93b5f5f90d95004affb88d550a278e015 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 5, + "timestamp": 1684701331681.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:17, x[i] <256 , right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk4.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..a9775bd93b5f5f90d95004affb88d550a278e015 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 5, + "timestamp": 1684701331681.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:17, x[i] <256 , right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk5.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..a9775bd93b5f5f90d95004affb88d550a278e015 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 5, + "timestamp": 1684701331681.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:17, x[i] <256 , right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk6.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..a9775bd93b5f5f90d95004affb88d550a278e015 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 5, + "timestamp": 1684701331681.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:17, x[i] <256 , right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk7.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..a9775bd93b5f5f90d95004affb88d550a278e015 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 5, + "timestamp": 1684701331681.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:17, x[i] <256 , right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk8.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..a9775bd93b5f5f90d95004affb88d550a278e015 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 5, + "timestamp": 1684701331681.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:17, x[i] <256 , right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk9.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..a9775bd93b5f5f90d95004affb88d550a278e015 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_5_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 5, + "timestamp": 1684701331681.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:17, x[i] <256 , right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk0.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..f8e8fe77e65492bf5641a84854e7ee2cbb496aa1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 6, + "timestamp": 1684701411849.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is it just me? Is that a mistake? He writes x=Wc at 37:11, where x represents vector in the old basis, and c the vector in the new basis, and W the columns of new basis vectors. Should it be c=Wx instead?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk1.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..f8e8fe77e65492bf5641a84854e7ee2cbb496aa1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 6, + "timestamp": 1684701411849.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is it just me? Is that a mistake? He writes x=Wc at 37:11, where x represents vector in the old basis, and c the vector in the new basis, and W the columns of new basis vectors. Should it be c=Wx instead?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk10.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..f8e8fe77e65492bf5641a84854e7ee2cbb496aa1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 6, + "timestamp": 1684701411849.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is it just me? Is that a mistake? He writes x=Wc at 37:11, where x represents vector in the old basis, and c the vector in the new basis, and W the columns of new basis vectors. Should it be c=Wx instead?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk11.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..f8e8fe77e65492bf5641a84854e7ee2cbb496aa1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 6, + "timestamp": 1684701411849.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is it just me? Is that a mistake? He writes x=Wc at 37:11, where x represents vector in the old basis, and c the vector in the new basis, and W the columns of new basis vectors. Should it be c=Wx instead?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk12.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..f8e8fe77e65492bf5641a84854e7ee2cbb496aa1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 6, + "timestamp": 1684701411849.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is it just me? Is that a mistake? He writes x=Wc at 37:11, where x represents vector in the old basis, and c the vector in the new basis, and W the columns of new basis vectors. Should it be c=Wx instead?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk13.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..f8e8fe77e65492bf5641a84854e7ee2cbb496aa1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 6, + "timestamp": 1684701411849.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is it just me? Is that a mistake? He writes x=Wc at 37:11, where x represents vector in the old basis, and c the vector in the new basis, and W the columns of new basis vectors. Should it be c=Wx instead?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk14.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..b563bb319fbf6e1c3be76b9b41791709b9005cad --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk14.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 6, + "timestamp": 1684701411849.0, + "annotatedSourceSentencesIndices": [ + 11 + ], + "names": [ + "annotator2" + ], + "text": "Is it just me? Is that a mistake? He writes x=Wc at 37:11, where x represents vector in the old basis, and c the vector in the new basis, and W the columns of new basis vectors. Should it be c=Wx instead?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk15.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..f8e8fe77e65492bf5641a84854e7ee2cbb496aa1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 6, + "timestamp": 1684701411849.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is it just me? Is that a mistake? He writes x=Wc at 37:11, where x represents vector in the old basis, and c the vector in the new basis, and W the columns of new basis vectors. Should it be c=Wx instead?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk16.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f8e8fe77e65492bf5641a84854e7ee2cbb496aa1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 6, + "timestamp": 1684701411849.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is it just me? Is that a mistake? He writes x=Wc at 37:11, where x represents vector in the old basis, and c the vector in the new basis, and W the columns of new basis vectors. Should it be c=Wx instead?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk17.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..f8e8fe77e65492bf5641a84854e7ee2cbb496aa1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 6, + "timestamp": 1684701411849.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is it just me? Is that a mistake? He writes x=Wc at 37:11, where x represents vector in the old basis, and c the vector in the new basis, and W the columns of new basis vectors. Should it be c=Wx instead?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk18.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..f8e8fe77e65492bf5641a84854e7ee2cbb496aa1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 6, + "timestamp": 1684701411849.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is it just me? Is that a mistake? He writes x=Wc at 37:11, where x represents vector in the old basis, and c the vector in the new basis, and W the columns of new basis vectors. Should it be c=Wx instead?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk19.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..f8e8fe77e65492bf5641a84854e7ee2cbb496aa1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 6, + "timestamp": 1684701411849.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is it just me? Is that a mistake? He writes x=Wc at 37:11, where x represents vector in the old basis, and c the vector in the new basis, and W the columns of new basis vectors. Should it be c=Wx instead?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk2.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..f8e8fe77e65492bf5641a84854e7ee2cbb496aa1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 6, + "timestamp": 1684701411849.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is it just me? Is that a mistake? He writes x=Wc at 37:11, where x represents vector in the old basis, and c the vector in the new basis, and W the columns of new basis vectors. Should it be c=Wx instead?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk20.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..f8e8fe77e65492bf5641a84854e7ee2cbb496aa1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 6, + "timestamp": 1684701411849.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is it just me? Is that a mistake? He writes x=Wc at 37:11, where x represents vector in the old basis, and c the vector in the new basis, and W the columns of new basis vectors. Should it be c=Wx instead?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk3.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..f8e8fe77e65492bf5641a84854e7ee2cbb496aa1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 6, + "timestamp": 1684701411849.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is it just me? Is that a mistake? He writes x=Wc at 37:11, where x represents vector in the old basis, and c the vector in the new basis, and W the columns of new basis vectors. Should it be c=Wx instead?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk4.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..f8e8fe77e65492bf5641a84854e7ee2cbb496aa1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 6, + "timestamp": 1684701411849.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is it just me? Is that a mistake? He writes x=Wc at 37:11, where x represents vector in the old basis, and c the vector in the new basis, and W the columns of new basis vectors. Should it be c=Wx instead?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk5.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..f8e8fe77e65492bf5641a84854e7ee2cbb496aa1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 6, + "timestamp": 1684701411849.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is it just me? Is that a mistake? He writes x=Wc at 37:11, where x represents vector in the old basis, and c the vector in the new basis, and W the columns of new basis vectors. Should it be c=Wx instead?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk6.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..f8e8fe77e65492bf5641a84854e7ee2cbb496aa1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 6, + "timestamp": 1684701411849.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is it just me? Is that a mistake? He writes x=Wc at 37:11, where x represents vector in the old basis, and c the vector in the new basis, and W the columns of new basis vectors. Should it be c=Wx instead?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk7.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..f8e8fe77e65492bf5641a84854e7ee2cbb496aa1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 6, + "timestamp": 1684701411849.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is it just me? Is that a mistake? He writes x=Wc at 37:11, where x represents vector in the old basis, and c the vector in the new basis, and W the columns of new basis vectors. Should it be c=Wx instead?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk8.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f8e8fe77e65492bf5641a84854e7ee2cbb496aa1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 6, + "timestamp": 1684701411849.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is it just me? Is that a mistake? He writes x=Wc at 37:11, where x represents vector in the old basis, and c the vector in the new basis, and W the columns of new basis vectors. Should it be c=Wx instead?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk9.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..f8e8fe77e65492bf5641a84854e7ee2cbb496aa1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_6_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 6, + "timestamp": 1684701411849.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is it just me? Is that a mistake? He writes x=Wc at 37:11, where x represents vector in the old basis, and c the vector in the new basis, and W the columns of new basis vectors. Should it be c=Wx instead?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk0.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..1c5e684f741fab2fd90131ccee7414dd29ff6496 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 7, + "timestamp": 1684701455485.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "He never taught the compression step right? ie., c -> c(hat)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk1.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..1c5e684f741fab2fd90131ccee7414dd29ff6496 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 7, + "timestamp": 1684701455485.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "He never taught the compression step right? ie., c -> c(hat)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk10.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..1c5e684f741fab2fd90131ccee7414dd29ff6496 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 7, + "timestamp": 1684701455485.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "He never taught the compression step right? ie., c -> c(hat)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk11.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..1c5e684f741fab2fd90131ccee7414dd29ff6496 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 7, + "timestamp": 1684701455485.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "He never taught the compression step right? ie., c -> c(hat)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk12.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..1c5e684f741fab2fd90131ccee7414dd29ff6496 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 7, + "timestamp": 1684701455485.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "He never taught the compression step right? ie., c -> c(hat)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk13.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1c5e684f741fab2fd90131ccee7414dd29ff6496 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 7, + "timestamp": 1684701455485.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "He never taught the compression step right? ie., c -> c(hat)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk14.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..1c5e684f741fab2fd90131ccee7414dd29ff6496 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 7, + "timestamp": 1684701455485.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "He never taught the compression step right? ie., c -> c(hat)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk15.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..1c5e684f741fab2fd90131ccee7414dd29ff6496 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 7, + "timestamp": 1684701455485.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "He never taught the compression step right? ie., c -> c(hat)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk16.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..1c5e684f741fab2fd90131ccee7414dd29ff6496 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 7, + "timestamp": 1684701455485.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "He never taught the compression step right? ie., c -> c(hat)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk17.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..1c5e684f741fab2fd90131ccee7414dd29ff6496 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 7, + "timestamp": 1684701455485.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "He never taught the compression step right? ie., c -> c(hat)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk18.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..1c5e684f741fab2fd90131ccee7414dd29ff6496 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 7, + "timestamp": 1684701455485.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "He never taught the compression step right? ie., c -> c(hat)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk19.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1c5e684f741fab2fd90131ccee7414dd29ff6496 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 7, + "timestamp": 1684701455485.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "He never taught the compression step right? ie., c -> c(hat)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk2.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1c5e684f741fab2fd90131ccee7414dd29ff6496 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 7, + "timestamp": 1684701455485.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "He never taught the compression step right? ie., c -> c(hat)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk20.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..1c5e684f741fab2fd90131ccee7414dd29ff6496 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 7, + "timestamp": 1684701455485.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "He never taught the compression step right? ie., c -> c(hat)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk3.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1c5e684f741fab2fd90131ccee7414dd29ff6496 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 7, + "timestamp": 1684701455485.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "He never taught the compression step right? ie., c -> c(hat)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk4.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..1c5e684f741fab2fd90131ccee7414dd29ff6496 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 7, + "timestamp": 1684701455485.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "He never taught the compression step right? ie., c -> c(hat)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk5.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..1c5e684f741fab2fd90131ccee7414dd29ff6496 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 7, + "timestamp": 1684701455485.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "He never taught the compression step right? ie., c -> c(hat)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk6.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..b692ae2c0736058893feb271a48247c90692d885 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk6.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 7, + "timestamp": 1684701455485.0, + "annotatedSourceSentencesIndices": [ + 1 + ], + "names": [ + "annotator2" + ], + "text": "He never taught the compression step right? ie., c -> c(hat)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk7.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..1c5e684f741fab2fd90131ccee7414dd29ff6496 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 7, + "timestamp": 1684701455485.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "He never taught the compression step right? ie., c -> c(hat)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk8.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..1c5e684f741fab2fd90131ccee7414dd29ff6496 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 7, + "timestamp": 1684701455485.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "He never taught the compression step right? ie., c -> c(hat)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk9.json b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..1c5e684f741fab2fd90131ccee7414dd29ff6496 --- /dev/null +++ b/sight/query/annotated_chunks_window20/0h43aV4aH7I_7_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "0h43aV4aH7I", + "query_id": 7, + "timestamp": 1684701455485.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "He never taught the compression step right? ie., c -> c(hat)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk0.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..f12e0f56c26a7ee7b9ea40824716bbf332fa2384 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 0, + "timestamp": 1684723011392.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "i'm still a little confused, what is u naught supposed to represent? Are those just the linear combination of the eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk1.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..f12e0f56c26a7ee7b9ea40824716bbf332fa2384 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 0, + "timestamp": 1684723011392.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "i'm still a little confused, what is u naught supposed to represent? Are those just the linear combination of the eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk10.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..f12e0f56c26a7ee7b9ea40824716bbf332fa2384 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 0, + "timestamp": 1684723011392.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "i'm still a little confused, what is u naught supposed to represent? Are those just the linear combination of the eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk11.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..f12e0f56c26a7ee7b9ea40824716bbf332fa2384 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 0, + "timestamp": 1684723011392.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "i'm still a little confused, what is u naught supposed to represent? Are those just the linear combination of the eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk12.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..12a6c3ab2e731b264ebd61eb641bcae577d85e3e --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk12.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 0, + "timestamp": 1684723011392.0, + "annotatedSourceSentencesIndices": [ + 6 + ], + "names": [ + "annotator2" + ], + "text": "i'm still a little confused, what is u naught supposed to represent? Are those just the linear combination of the eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk13.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..20635ac7a3a10dc12504d51bad400ae1f77afdfc --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk13.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 0, + "timestamp": 1684723011392.0, + "annotatedSourceSentencesIndices": [ + 16 + ], + "names": [ + "annotator2" + ], + "text": "i'm still a little confused, what is u naught supposed to represent? Are those just the linear combination of the eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk14.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..f12e0f56c26a7ee7b9ea40824716bbf332fa2384 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 0, + "timestamp": 1684723011392.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "i'm still a little confused, what is u naught supposed to represent? Are those just the linear combination of the eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk15.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..f12e0f56c26a7ee7b9ea40824716bbf332fa2384 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 0, + "timestamp": 1684723011392.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "i'm still a little confused, what is u naught supposed to represent? Are those just the linear combination of the eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk16.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f12e0f56c26a7ee7b9ea40824716bbf332fa2384 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 0, + "timestamp": 1684723011392.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "i'm still a little confused, what is u naught supposed to represent? Are those just the linear combination of the eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk17.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..f12e0f56c26a7ee7b9ea40824716bbf332fa2384 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 0, + "timestamp": 1684723011392.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "i'm still a little confused, what is u naught supposed to represent? Are those just the linear combination of the eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk18.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..f12e0f56c26a7ee7b9ea40824716bbf332fa2384 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 0, + "timestamp": 1684723011392.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "i'm still a little confused, what is u naught supposed to represent? Are those just the linear combination of the eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk19.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..f12e0f56c26a7ee7b9ea40824716bbf332fa2384 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 0, + "timestamp": 1684723011392.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "i'm still a little confused, what is u naught supposed to represent? Are those just the linear combination of the eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk2.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..f12e0f56c26a7ee7b9ea40824716bbf332fa2384 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 0, + "timestamp": 1684723011392.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "i'm still a little confused, what is u naught supposed to represent? Are those just the linear combination of the eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk20.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..f12e0f56c26a7ee7b9ea40824716bbf332fa2384 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 0, + "timestamp": 1684723011392.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "i'm still a little confused, what is u naught supposed to represent? Are those just the linear combination of the eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk21.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f12e0f56c26a7ee7b9ea40824716bbf332fa2384 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 0, + "timestamp": 1684723011392.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "i'm still a little confused, what is u naught supposed to represent? Are those just the linear combination of the eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk22.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..f12e0f56c26a7ee7b9ea40824716bbf332fa2384 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 0, + "timestamp": 1684723011392.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "i'm still a little confused, what is u naught supposed to represent? Are those just the linear combination of the eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk23.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..f12e0f56c26a7ee7b9ea40824716bbf332fa2384 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 0, + "timestamp": 1684723011392.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "i'm still a little confused, what is u naught supposed to represent? Are those just the linear combination of the eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk24.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..f12e0f56c26a7ee7b9ea40824716bbf332fa2384 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 0, + "timestamp": 1684723011392.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "i'm still a little confused, what is u naught supposed to represent? Are those just the linear combination of the eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk3.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..f12e0f56c26a7ee7b9ea40824716bbf332fa2384 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 0, + "timestamp": 1684723011392.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "i'm still a little confused, what is u naught supposed to represent? Are those just the linear combination of the eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk4.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..f12e0f56c26a7ee7b9ea40824716bbf332fa2384 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 0, + "timestamp": 1684723011392.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "i'm still a little confused, what is u naught supposed to represent? Are those just the linear combination of the eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk5.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..f12e0f56c26a7ee7b9ea40824716bbf332fa2384 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 0, + "timestamp": 1684723011392.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "i'm still a little confused, what is u naught supposed to represent? Are those just the linear combination of the eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk6.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..f12e0f56c26a7ee7b9ea40824716bbf332fa2384 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 0, + "timestamp": 1684723011392.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "i'm still a little confused, what is u naught supposed to represent? Are those just the linear combination of the eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk7.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..f12e0f56c26a7ee7b9ea40824716bbf332fa2384 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 0, + "timestamp": 1684723011392.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "i'm still a little confused, what is u naught supposed to represent? Are those just the linear combination of the eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk8.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f12e0f56c26a7ee7b9ea40824716bbf332fa2384 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 0, + "timestamp": 1684723011392.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "i'm still a little confused, what is u naught supposed to represent? Are those just the linear combination of the eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk9.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..f12e0f56c26a7ee7b9ea40824716bbf332fa2384 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_0_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 0, + "timestamp": 1684723011392.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "i'm still a little confused, what is u naught supposed to represent? Are those just the linear combination of the eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_10_chunk0.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_10_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..e169d865a3bbe932d4ab160d43102eaee27e484f --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_10_chunk0.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 10, + "timestamp": 1684725950887.0, + "annotatedSourceSentencesIndices": [ + 1 + ], + "names": [ + "annotator2" + ], + "text": "so it seems like the professor emphasized the importance of the eigenvalue here, that's nice. but is the eigenvector of any importance? what's a good example of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_10_chunk1.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_10_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..9c3da7b21d3b8accbb47788ddc1e9a41b4d1f6f7 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_10_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 10, + "timestamp": 1684725950887.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "so it seems like the professor emphasized the importance of the eigenvalue here, that's nice. but is the eigenvector of any importance? what's a good example of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_10_chunk10.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_10_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..9c3da7b21d3b8accbb47788ddc1e9a41b4d1f6f7 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_10_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 10, + "timestamp": 1684725950887.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "so it seems like the professor emphasized the importance of the eigenvalue here, that's nice. but is the eigenvector of any importance? what's a good example of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_10_chunk11.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_10_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..9c3da7b21d3b8accbb47788ddc1e9a41b4d1f6f7 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_10_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 10, + "timestamp": 1684725950887.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "so it seems like the professor emphasized the importance of the eigenvalue here, that's nice. but is the eigenvector of any importance? what's a good example of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_10_chunk12.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_10_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..9c3da7b21d3b8accbb47788ddc1e9a41b4d1f6f7 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_10_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 10, + "timestamp": 1684725950887.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "so it seems like the professor emphasized the importance of the eigenvalue here, that's nice. but is the eigenvector of any importance? what's a good example of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_10_chunk13.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_10_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..9c3da7b21d3b8accbb47788ddc1e9a41b4d1f6f7 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_10_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 10, + "timestamp": 1684725950887.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "so it seems like the professor emphasized the importance of the eigenvalue here, that's nice. but is the eigenvector of any importance? what's a good example of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_10_chunk14.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_10_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..9c3da7b21d3b8accbb47788ddc1e9a41b4d1f6f7 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_10_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 10, + "timestamp": 1684725950887.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "so it seems like the professor emphasized the importance of the eigenvalue here, that's nice. but is the eigenvector of any importance? what's a good example of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_10_chunk15.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_10_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..9c3da7b21d3b8accbb47788ddc1e9a41b4d1f6f7 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_10_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 10, + "timestamp": 1684725950887.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "so it seems like the professor emphasized the importance of the eigenvalue here, that's nice. but is the eigenvector of any importance? 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29:55" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk17.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..08ff3b35bd4a4eb946fa56141550110a18075f55 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 11, + "timestamp": 1684726006688.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why u_0 can be written as a linear combination of eigenvector of A? 29:55" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk18.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..08ff3b35bd4a4eb946fa56141550110a18075f55 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 11, + "timestamp": 1684726006688.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why u_0 can be written as a linear combination of eigenvector of A? 29:55" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk19.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..08ff3b35bd4a4eb946fa56141550110a18075f55 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 11, + "timestamp": 1684726006688.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why u_0 can be written as a linear combination of eigenvector of A? 29:55" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk2.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..08ff3b35bd4a4eb946fa56141550110a18075f55 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 11, + "timestamp": 1684726006688.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why u_0 can be written as a linear combination of eigenvector of A? 29:55" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk20.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..08ff3b35bd4a4eb946fa56141550110a18075f55 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 11, + "timestamp": 1684726006688.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why u_0 can be written as a linear combination of eigenvector of A? 29:55" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk21.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..08ff3b35bd4a4eb946fa56141550110a18075f55 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 11, + "timestamp": 1684726006688.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why u_0 can be written as a linear combination of eigenvector of A? 29:55" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk22.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..08ff3b35bd4a4eb946fa56141550110a18075f55 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 11, + "timestamp": 1684726006688.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why u_0 can be written as a linear combination of eigenvector of A? 29:55" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk23.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..08ff3b35bd4a4eb946fa56141550110a18075f55 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 11, + "timestamp": 1684726006688.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why u_0 can be written as a linear combination of eigenvector of A? 29:55" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk24.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..08ff3b35bd4a4eb946fa56141550110a18075f55 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 11, + "timestamp": 1684726006688.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why u_0 can be written as a linear combination of eigenvector of A? 29:55" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk3.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..08ff3b35bd4a4eb946fa56141550110a18075f55 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 11, + "timestamp": 1684726006688.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why u_0 can be written as a linear combination of eigenvector of A? 29:55" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk4.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..08ff3b35bd4a4eb946fa56141550110a18075f55 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 11, + "timestamp": 1684726006688.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why u_0 can be written as a linear combination of eigenvector of A? 29:55" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk5.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..08ff3b35bd4a4eb946fa56141550110a18075f55 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 11, + "timestamp": 1684726006688.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why u_0 can be written as a linear combination of eigenvector of A? 29:55" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk6.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..08ff3b35bd4a4eb946fa56141550110a18075f55 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 11, + "timestamp": 1684726006688.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why u_0 can be written as a linear combination of eigenvector of A? 29:55" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk7.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..08ff3b35bd4a4eb946fa56141550110a18075f55 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 11, + "timestamp": 1684726006688.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why u_0 can be written as a linear combination of eigenvector of A? 29:55" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk8.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..08ff3b35bd4a4eb946fa56141550110a18075f55 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 11, + "timestamp": 1684726006688.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why u_0 can be written as a linear combination of eigenvector of A? 29:55" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk9.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..08ff3b35bd4a4eb946fa56141550110a18075f55 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_11_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 11, + "timestamp": 1684726006688.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why u_0 can be written as a linear combination of eigenvector of A? 29:55" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk0.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..5a5995e812e560682079997e58eb7a39255f90ad --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 13, + "timestamp": 1684726031554.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Did we ever prove that if the set of eigenvalues are distinct, the set of eigenvectors are linearly independent? I ask because at ~ 32:00 taking u_o = c1*x1 + c2*x2 + ... + cn*xn requires the eigenvectors to form a basis for an n-dimensional vector space (i.e. span the column space of an invertible matrix). It feels right but I have no solid background for how to think about it" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk1.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..5a5995e812e560682079997e58eb7a39255f90ad --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 13, + "timestamp": 1684726031554.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Did we ever prove that if the set of eigenvalues are distinct, the set of eigenvectors are linearly independent? I ask because at ~ 32:00 taking u_o = c1*x1 + c2*x2 + ... + cn*xn requires the eigenvectors to form a basis for an n-dimensional vector space (i.e. span the column space of an invertible matrix). It feels right but I have no solid background for how to think about it" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk10.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..5a5995e812e560682079997e58eb7a39255f90ad --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 13, + "timestamp": 1684726031554.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Did we ever prove that if the set of eigenvalues are distinct, the set of eigenvectors are linearly independent? I ask because at ~ 32:00 taking u_o = c1*x1 + c2*x2 + ... + cn*xn requires the eigenvectors to form a basis for an n-dimensional vector space (i.e. span the column space of an invertible matrix). It feels right but I have no solid background for how to think about it" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk11.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..5a5995e812e560682079997e58eb7a39255f90ad --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 13, + "timestamp": 1684726031554.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Did we ever prove that if the set of eigenvalues are distinct, the set of eigenvectors are linearly independent? I ask because at ~ 32:00 taking u_o = c1*x1 + c2*x2 + ... + cn*xn requires the eigenvectors to form a basis for an n-dimensional vector space (i.e. span the column space of an invertible matrix). It feels right but I have no solid background for how to think about it" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk12.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..5a5995e812e560682079997e58eb7a39255f90ad --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 13, + "timestamp": 1684726031554.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Did we ever prove that if the set of eigenvalues are distinct, the set of eigenvectors are linearly independent? I ask because at ~ 32:00 taking u_o = c1*x1 + c2*x2 + ... + cn*xn requires the eigenvectors to form a basis for an n-dimensional vector space (i.e. span the column space of an invertible matrix). It feels right but I have no solid background for how to think about it" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk13.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..68bdc173af4be4fc1aaa6579aa10f9a5a0a67894 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk13.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 13, + "timestamp": 1684726031554.0, + "annotatedSourceSentencesIndices": [ + 16 + ], + "names": [ + "annotator2" + ], + "text": "Did we ever prove that if the set of eigenvalues are distinct, the set of eigenvectors are linearly independent? I ask because at ~ 32:00 taking u_o = c1*x1 + c2*x2 + ... + cn*xn requires the eigenvectors to form a basis for an n-dimensional vector space (i.e. span the column space of an invertible matrix). It feels right but I have no solid background for how to think about it" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk14.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..5a5995e812e560682079997e58eb7a39255f90ad --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 13, + "timestamp": 1684726031554.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Did we ever prove that if the set of eigenvalues are distinct, the set of eigenvectors are linearly independent? I ask because at ~ 32:00 taking u_o = c1*x1 + c2*x2 + ... + cn*xn requires the eigenvectors to form a basis for an n-dimensional vector space (i.e. span the column space of an invertible matrix). It feels right but I have no solid background for how to think about it" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk15.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..5a5995e812e560682079997e58eb7a39255f90ad --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 13, + "timestamp": 1684726031554.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Did we ever prove that if the set of eigenvalues are distinct, the set of eigenvectors are linearly independent? I ask because at ~ 32:00 taking u_o = c1*x1 + c2*x2 + ... + cn*xn requires the eigenvectors to form a basis for an n-dimensional vector space (i.e. span the column space of an invertible matrix). It feels right but I have no solid background for how to think about it" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk16.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..5a5995e812e560682079997e58eb7a39255f90ad --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 13, + "timestamp": 1684726031554.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Did we ever prove that if the set of eigenvalues are distinct, the set of eigenvectors are linearly independent? I ask because at ~ 32:00 taking u_o = c1*x1 + c2*x2 + ... + cn*xn requires the eigenvectors to form a basis for an n-dimensional vector space (i.e. span the column space of an invertible matrix). It feels right but I have no solid background for how to think about it" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk17.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..5a5995e812e560682079997e58eb7a39255f90ad --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 13, + "timestamp": 1684726031554.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Did we ever prove that if the set of eigenvalues are distinct, the set of eigenvectors are linearly independent? I ask because at ~ 32:00 taking u_o = c1*x1 + c2*x2 + ... + cn*xn requires the eigenvectors to form a basis for an n-dimensional vector space (i.e. span the column space of an invertible matrix). It feels right but I have no solid background for how to think about it" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk18.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..5a5995e812e560682079997e58eb7a39255f90ad --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 13, + "timestamp": 1684726031554.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Did we ever prove that if the set of eigenvalues are distinct, the set of eigenvectors are linearly independent? I ask because at ~ 32:00 taking u_o = c1*x1 + c2*x2 + ... + cn*xn requires the eigenvectors to form a basis for an n-dimensional vector space (i.e. span the column space of an invertible matrix). It feels right but I have no solid background for how to think about it" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk19.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..5a5995e812e560682079997e58eb7a39255f90ad --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 13, + "timestamp": 1684726031554.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Did we ever prove that if the set of eigenvalues are distinct, the set of eigenvectors are linearly independent? I ask because at ~ 32:00 taking u_o = c1*x1 + c2*x2 + ... + cn*xn requires the eigenvectors to form a basis for an n-dimensional vector space (i.e. span the column space of an invertible matrix). It feels right but I have no solid background for how to think about it" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk2.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..5a5995e812e560682079997e58eb7a39255f90ad --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 13, + "timestamp": 1684726031554.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Did we ever prove that if the set of eigenvalues are distinct, the set of eigenvectors are linearly independent? I ask because at ~ 32:00 taking u_o = c1*x1 + c2*x2 + ... + cn*xn requires the eigenvectors to form a basis for an n-dimensional vector space (i.e. span the column space of an invertible matrix). It feels right but I have no solid background for how to think about it" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk20.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..5a5995e812e560682079997e58eb7a39255f90ad --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 13, + "timestamp": 1684726031554.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Did we ever prove that if the set of eigenvalues are distinct, the set of eigenvectors are linearly independent? I ask because at ~ 32:00 taking u_o = c1*x1 + c2*x2 + ... + cn*xn requires the eigenvectors to form a basis for an n-dimensional vector space (i.e. span the column space of an invertible matrix). It feels right but I have no solid background for how to think about it" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk21.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..5a5995e812e560682079997e58eb7a39255f90ad --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 13, + "timestamp": 1684726031554.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Did we ever prove that if the set of eigenvalues are distinct, the set of eigenvectors are linearly independent? I ask because at ~ 32:00 taking u_o = c1*x1 + c2*x2 + ... + cn*xn requires the eigenvectors to form a basis for an n-dimensional vector space (i.e. span the column space of an invertible matrix). It feels right but I have no solid background for how to think about it" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk22.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..5a5995e812e560682079997e58eb7a39255f90ad --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 13, + "timestamp": 1684726031554.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Did we ever prove that if the set of eigenvalues are distinct, the set of eigenvectors are linearly independent? I ask because at ~ 32:00 taking u_o = c1*x1 + c2*x2 + ... + cn*xn requires the eigenvectors to form a basis for an n-dimensional vector space (i.e. span the column space of an invertible matrix). It feels right but I have no solid background for how to think about it" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk23.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..5a5995e812e560682079997e58eb7a39255f90ad --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 13, + "timestamp": 1684726031554.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Did we ever prove that if the set of eigenvalues are distinct, the set of eigenvectors are linearly independent? I ask because at ~ 32:00 taking u_o = c1*x1 + c2*x2 + ... + cn*xn requires the eigenvectors to form a basis for an n-dimensional vector space (i.e. span the column space of an invertible matrix). It feels right but I have no solid background for how to think about it" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk24.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..5a5995e812e560682079997e58eb7a39255f90ad --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 13, + "timestamp": 1684726031554.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Did we ever prove that if the set of eigenvalues are distinct, the set of eigenvectors are linearly independent? I ask because at ~ 32:00 taking u_o = c1*x1 + c2*x2 + ... + cn*xn requires the eigenvectors to form a basis for an n-dimensional vector space (i.e. span the column space of an invertible matrix). It feels right but I have no solid background for how to think about it" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk3.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..5a5995e812e560682079997e58eb7a39255f90ad --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 13, + "timestamp": 1684726031554.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Did we ever prove that if the set of eigenvalues are distinct, the set of eigenvectors are linearly independent? I ask because at ~ 32:00 taking u_o = c1*x1 + c2*x2 + ... + cn*xn requires the eigenvectors to form a basis for an n-dimensional vector space (i.e. span the column space of an invertible matrix). It feels right but I have no solid background for how to think about it" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk4.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..5a5995e812e560682079997e58eb7a39255f90ad --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 13, + "timestamp": 1684726031554.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Did we ever prove that if the set of eigenvalues are distinct, the set of eigenvectors are linearly independent? I ask because at ~ 32:00 taking u_o = c1*x1 + c2*x2 + ... + cn*xn requires the eigenvectors to form a basis for an n-dimensional vector space (i.e. span the column space of an invertible matrix). It feels right but I have no solid background for how to think about it" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk5.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5a5995e812e560682079997e58eb7a39255f90ad --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 13, + "timestamp": 1684726031554.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Did we ever prove that if the set of eigenvalues are distinct, the set of eigenvectors are linearly independent? I ask because at ~ 32:00 taking u_o = c1*x1 + c2*x2 + ... + cn*xn requires the eigenvectors to form a basis for an n-dimensional vector space (i.e. span the column space of an invertible matrix). It feels right but I have no solid background for how to think about it" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk6.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..5a5995e812e560682079997e58eb7a39255f90ad --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 13, + "timestamp": 1684726031554.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Did we ever prove that if the set of eigenvalues are distinct, the set of eigenvectors are linearly independent? I ask because at ~ 32:00 taking u_o = c1*x1 + c2*x2 + ... + cn*xn requires the eigenvectors to form a basis for an n-dimensional vector space (i.e. span the column space of an invertible matrix). It feels right but I have no solid background for how to think about it" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk7.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..5a5995e812e560682079997e58eb7a39255f90ad --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 13, + "timestamp": 1684726031554.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Did we ever prove that if the set of eigenvalues are distinct, the set of eigenvectors are linearly independent? I ask because at ~ 32:00 taking u_o = c1*x1 + c2*x2 + ... + cn*xn requires the eigenvectors to form a basis for an n-dimensional vector space (i.e. span the column space of an invertible matrix). It feels right but I have no solid background for how to think about it" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk8.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..5a5995e812e560682079997e58eb7a39255f90ad --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 13, + "timestamp": 1684726031554.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Did we ever prove that if the set of eigenvalues are distinct, the set of eigenvectors are linearly independent? I ask because at ~ 32:00 taking u_o = c1*x1 + c2*x2 + ... + cn*xn requires the eigenvectors to form a basis for an n-dimensional vector space (i.e. span the column space of an invertible matrix). It feels right but I have no solid background for how to think about it" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk9.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..5a5995e812e560682079997e58eb7a39255f90ad --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_13_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 13, + "timestamp": 1684726031554.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Did we ever prove that if the set of eigenvalues are distinct, the set of eigenvectors are linearly independent? I ask because at ~ 32:00 taking u_o = c1*x1 + c2*x2 + ... + cn*xn requires the eigenvectors to form a basis for an n-dimensional vector space (i.e. span the column space of an invertible matrix). It feels right but I have no solid background for how to think about it" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk0.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..e2acf04d4c68d73458293062dfe0e572a3bc788c --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 14, + "timestamp": 1684726883847.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "why are we representing mu(k) vector as the combination of eigen vectors in the problem of Fibonacci sequence?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk1.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..e2acf04d4c68d73458293062dfe0e572a3bc788c --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 14, + "timestamp": 1684726883847.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "why are we representing mu(k) vector as the combination of eigen vectors in the problem of Fibonacci sequence?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk10.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..e2acf04d4c68d73458293062dfe0e572a3bc788c --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 14, + "timestamp": 1684726883847.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "why are we representing mu(k) vector as the combination of eigen vectors in the problem of Fibonacci sequence?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk11.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..e2acf04d4c68d73458293062dfe0e572a3bc788c --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 14, + "timestamp": 1684726883847.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "why are we representing mu(k) vector as the combination of eigen vectors in the problem of Fibonacci sequence?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk12.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..e2acf04d4c68d73458293062dfe0e572a3bc788c --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 14, + "timestamp": 1684726883847.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "why are we representing mu(k) vector as the combination of eigen vectors in the problem of Fibonacci sequence?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk13.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..e2acf04d4c68d73458293062dfe0e572a3bc788c --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 14, + "timestamp": 1684726883847.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "why are we representing mu(k) vector as the combination of eigen vectors in the problem of Fibonacci sequence?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk14.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..e2acf04d4c68d73458293062dfe0e572a3bc788c --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 14, + "timestamp": 1684726883847.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "why are we representing mu(k) vector as the combination of eigen vectors in the problem of Fibonacci sequence?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk15.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..c50e19af26e6b1b853c649da9609d2d39d96753f --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk15.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 14, + "timestamp": 1684726883847.0, + "annotatedSourceSentencesIndices": [ + 13 + ], + "names": [ + "annotator2" + ], + "text": "why are we representing mu(k) vector as the combination of eigen vectors in the problem of Fibonacci sequence?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk16.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..e2acf04d4c68d73458293062dfe0e572a3bc788c --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 14, + "timestamp": 1684726883847.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "why are we representing mu(k) vector as the combination of eigen vectors in the problem of Fibonacci sequence?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk17.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..e2acf04d4c68d73458293062dfe0e572a3bc788c --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 14, + "timestamp": 1684726883847.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "why are we representing mu(k) vector as the combination of eigen vectors in the problem of Fibonacci sequence?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk18.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..b35e6c7e0ee3905b87f373fd039b8f1b755703c2 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk18.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 14, + "timestamp": 1684726883847.0, + "annotatedSourceSentencesIndices": [ + 1 + ], + "names": [ + "annotator2" + ], + "text": "why are we representing mu(k) vector as the combination of eigen vectors in the problem of Fibonacci sequence?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk19.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_14_chunk19.json new file mode 100644 index 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Cnxn what are X's the vectors of?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_15_chunk22.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_15_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..ffad83f2ba81c142b641110fe1c179d38981fbb3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_15_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 15, + "timestamp": 1684726895777.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In u naught = c1x1 + c2x2 .... Cnxn what are X's the vectors of?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_15_chunk23.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_15_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..ffad83f2ba81c142b641110fe1c179d38981fbb3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_15_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 15, + "timestamp": 1684726895777.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In u naught = c1x1 + c2x2 .... Cnxn what are X's the vectors of?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_15_chunk24.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_15_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ffad83f2ba81c142b641110fe1c179d38981fbb3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_15_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 15, + "timestamp": 1684726895777.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In u naught = c1x1 + c2x2 .... Cnxn what are X's the vectors of?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_15_chunk3.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_15_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..ffad83f2ba81c142b641110fe1c179d38981fbb3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_15_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 15, + "timestamp": 1684726895777.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In u naught = c1x1 + c2x2 .... Cnxn what are X's the vectors of?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_15_chunk4.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_15_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..ffad83f2ba81c142b641110fe1c179d38981fbb3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_15_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 15, + "timestamp": 1684726895777.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In u naught = c1x1 + c2x2 .... Cnxn what are X's the vectors of?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_15_chunk5.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_15_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..ffad83f2ba81c142b641110fe1c179d38981fbb3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_15_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 15, + "timestamp": 1684726895777.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In u naught = c1x1 + c2x2 .... Cnxn what are X's the vectors of?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_15_chunk6.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_15_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..ffad83f2ba81c142b641110fe1c179d38981fbb3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_15_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 15, + "timestamp": 1684726895777.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In u naught = c1x1 + c2x2 .... Cnxn what are X's the vectors of?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_15_chunk7.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_15_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..ffad83f2ba81c142b641110fe1c179d38981fbb3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_15_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 15, + "timestamp": 1684726895777.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In u naught = c1x1 + c2x2 .... Cnxn what are X's the vectors of?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_15_chunk8.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_15_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..ffad83f2ba81c142b641110fe1c179d38981fbb3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_15_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 15, + "timestamp": 1684726895777.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In u naught = c1x1 + c2x2 .... Cnxn what are X's the vectors of?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_15_chunk9.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_15_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..ffad83f2ba81c142b641110fe1c179d38981fbb3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_15_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 15, + "timestamp": 1684726895777.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In u naught = c1x1 + c2x2 .... Cnxn what are X's the vectors of?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk0.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..b8a64f1e33abb7e7901b5228ccc774fb40b6197a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 17, + "timestamp": 1684727650779.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Notes for future ref.)\n(7:16) there are _some_ matrices that do _NOT_ have n-independent eigenvectors, but _most_ of the matrices we deal with do have n-independent eigenvectors.\n(17:14) If all evalues are different, there _must_ be n-indep evectors. But if there are same evalues, it's possible _no_ n-indep evectors. (Identity matrix is an example of having the same evalues but still having n-indep evectors)\n* Also, the position of Lambda and S should be changed(32:36). You'll see why by just thinking matrix multiplication, and it can also be viewed by knowing A^100=S*Lambda^100*S^-1 and u_0=S*c.\n Thus, it should be S*Lambda^100*c, and this also can be thought of as 'transformation' between the two different bases - one of the two is the set of the egenvectors of A.\n* Also, (43:34) How prof. Strang could calculate that?? Actually that number _1.618033988749894..._ is called the 'golden ratio'.\n* (8:15) Note that A and Lambda are 'similar'. (And, S and S_-1(S inverse) transforms the coordinates.. you know what I mean.. both A and Lambda can be though of as some \"transformation\" based on different basis.. and S(or S_-1) transforms the coord between those two world.)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk1.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..b8a64f1e33abb7e7901b5228ccc774fb40b6197a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 17, + "timestamp": 1684727650779.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Notes for future ref.)\n(7:16) there are _some_ matrices that do _NOT_ have n-independent eigenvectors, but _most_ of the matrices we deal with do have n-independent eigenvectors.\n(17:14) If all evalues are different, there _must_ be n-indep evectors. But if there are same evalues, it's possible _no_ n-indep evectors. (Identity matrix is an example of having the same evalues but still having n-indep evectors)\n* Also, the position of Lambda and S should be changed(32:36). You'll see why by just thinking matrix multiplication, and it can also be viewed by knowing A^100=S*Lambda^100*S^-1 and u_0=S*c.\n Thus, it should be S*Lambda^100*c, and this also can be thought of as 'transformation' between the two different bases - one of the two is the set of the egenvectors of A.\n* Also, (43:34) How prof. Strang could calculate that?? Actually that number _1.618033988749894..._ is called the 'golden ratio'.\n* (8:15) Note that A and Lambda are 'similar'. (And, S and S_-1(S inverse) transforms the coordinates.. you know what I mean.. both A and Lambda can be though of as some \"transformation\" based on different basis.. and S(or S_-1) transforms the coord between those two world.)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk10.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..b8a64f1e33abb7e7901b5228ccc774fb40b6197a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 17, + "timestamp": 1684727650779.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Notes for future ref.)\n(7:16) there are _some_ matrices that do _NOT_ have n-independent eigenvectors, but _most_ of the matrices we deal with do have n-independent eigenvectors.\n(17:14) If all evalues are different, there _must_ be n-indep evectors. But if there are same evalues, it's possible _no_ n-indep evectors. (Identity matrix is an example of having the same evalues but still having n-indep evectors)\n* Also, the position of Lambda and S should be changed(32:36). You'll see why by just thinking matrix multiplication, and it can also be viewed by knowing A^100=S*Lambda^100*S^-1 and u_0=S*c.\n Thus, it should be S*Lambda^100*c, and this also can be thought of as 'transformation' between the two different bases - one of the two is the set of the egenvectors of A.\n* Also, (43:34) How prof. Strang could calculate that?? Actually that number _1.618033988749894..._ is called the 'golden ratio'.\n* (8:15) Note that A and Lambda are 'similar'. (And, S and S_-1(S inverse) transforms the coordinates.. you know what I mean.. both A and Lambda can be though of as some \"transformation\" based on different basis.. and S(or S_-1) transforms the coord between those two world.)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk11.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b8a64f1e33abb7e7901b5228ccc774fb40b6197a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 17, + "timestamp": 1684727650779.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Notes for future ref.)\n(7:16) there are _some_ matrices that do _NOT_ have n-independent eigenvectors, but _most_ of the matrices we deal with do have n-independent eigenvectors.\n(17:14) If all evalues are different, there _must_ be n-indep evectors. But if there are same evalues, it's possible _no_ n-indep evectors. (Identity matrix is an example of having the same evalues but still having n-indep evectors)\n* Also, the position of Lambda and S should be changed(32:36). You'll see why by just thinking matrix multiplication, and it can also be viewed by knowing A^100=S*Lambda^100*S^-1 and u_0=S*c.\n Thus, it should be S*Lambda^100*c, and this also can be thought of as 'transformation' between the two different bases - one of the two is the set of the egenvectors of A.\n* Also, (43:34) How prof. Strang could calculate that?? Actually that number _1.618033988749894..._ is called the 'golden ratio'.\n* (8:15) Note that A and Lambda are 'similar'. (And, S and S_-1(S inverse) transforms the coordinates.. you know what I mean.. both A and Lambda can be though of as some \"transformation\" based on different basis.. and S(or S_-1) transforms the coord between those two world.)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk12.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..b8a64f1e33abb7e7901b5228ccc774fb40b6197a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 17, + "timestamp": 1684727650779.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Notes for future ref.)\n(7:16) there are _some_ matrices that do _NOT_ have n-independent eigenvectors, but _most_ of the matrices we deal with do have n-independent eigenvectors.\n(17:14) If all evalues are different, there _must_ be n-indep evectors. But if there are same evalues, it's possible _no_ n-indep evectors. (Identity matrix is an example of having the same evalues but still having n-indep evectors)\n* Also, the position of Lambda and S should be changed(32:36). You'll see why by just thinking matrix multiplication, and it can also be viewed by knowing A^100=S*Lambda^100*S^-1 and u_0=S*c.\n Thus, it should be S*Lambda^100*c, and this also can be thought of as 'transformation' between the two different bases - one of the two is the set of the egenvectors of A.\n* Also, (43:34) How prof. Strang could calculate that?? Actually that number _1.618033988749894..._ is called the 'golden ratio'.\n* (8:15) Note that A and Lambda are 'similar'. (And, S and S_-1(S inverse) transforms the coordinates.. you know what I mean.. both A and Lambda can be though of as some \"transformation\" based on different basis.. and S(or S_-1) transforms the coord between those two world.)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk13.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..b8a64f1e33abb7e7901b5228ccc774fb40b6197a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 17, + "timestamp": 1684727650779.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Notes for future ref.)\n(7:16) there are _some_ matrices that do _NOT_ have n-independent eigenvectors, but _most_ of the matrices we deal with do have n-independent eigenvectors.\n(17:14) If all evalues are different, there _must_ be n-indep evectors. But if there are same evalues, it's possible _no_ n-indep evectors. (Identity matrix is an example of having the same evalues but still having n-indep evectors)\n* Also, the position of Lambda and S should be changed(32:36). You'll see why by just thinking matrix multiplication, and it can also be viewed by knowing A^100=S*Lambda^100*S^-1 and u_0=S*c.\n Thus, it should be S*Lambda^100*c, and this also can be thought of as 'transformation' between the two different bases - one of the two is the set of the egenvectors of A.\n* Also, (43:34) How prof. Strang could calculate that?? Actually that number _1.618033988749894..._ is called the 'golden ratio'.\n* (8:15) Note that A and Lambda are 'similar'. (And, S and S_-1(S inverse) transforms the coordinates.. you know what I mean.. both A and Lambda can be though of as some \"transformation\" based on different basis.. and S(or S_-1) transforms the coord between those two world.)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk14.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..b8a64f1e33abb7e7901b5228ccc774fb40b6197a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 17, + "timestamp": 1684727650779.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Notes for future ref.)\n(7:16) there are _some_ matrices that do _NOT_ have n-independent eigenvectors, but _most_ of the matrices we deal with do have n-independent eigenvectors.\n(17:14) If all evalues are different, there _must_ be n-indep evectors. But if there are same evalues, it's possible _no_ n-indep evectors. (Identity matrix is an example of having the same evalues but still having n-indep evectors)\n* Also, the position of Lambda and S should be changed(32:36). You'll see why by just thinking matrix multiplication, and it can also be viewed by knowing A^100=S*Lambda^100*S^-1 and u_0=S*c.\n Thus, it should be S*Lambda^100*c, and this also can be thought of as 'transformation' between the two different bases - one of the two is the set of the egenvectors of A.\n* Also, (43:34) How prof. Strang could calculate that?? Actually that number _1.618033988749894..._ is called the 'golden ratio'.\n* (8:15) Note that A and Lambda are 'similar'. (And, S and S_-1(S inverse) transforms the coordinates.. you know what I mean.. both A and Lambda can be though of as some \"transformation\" based on different basis.. and S(or S_-1) transforms the coord between those two world.)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk15.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..b8a64f1e33abb7e7901b5228ccc774fb40b6197a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 17, + "timestamp": 1684727650779.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Notes for future ref.)\n(7:16) there are _some_ matrices that do _NOT_ have n-independent eigenvectors, but _most_ of the matrices we deal with do have n-independent eigenvectors.\n(17:14) If all evalues are different, there _must_ be n-indep evectors. But if there are same evalues, it's possible _no_ n-indep evectors. (Identity matrix is an example of having the same evalues but still having n-indep evectors)\n* Also, the position of Lambda and S should be changed(32:36). You'll see why by just thinking matrix multiplication, and it can also be viewed by knowing A^100=S*Lambda^100*S^-1 and u_0=S*c.\n Thus, it should be S*Lambda^100*c, and this also can be thought of as 'transformation' between the two different bases - one of the two is the set of the egenvectors of A.\n* Also, (43:34) How prof. Strang could calculate that?? Actually that number _1.618033988749894..._ is called the 'golden ratio'.\n* (8:15) Note that A and Lambda are 'similar'. (And, S and S_-1(S inverse) transforms the coordinates.. you know what I mean.. both A and Lambda can be though of as some \"transformation\" based on different basis.. and S(or S_-1) transforms the coord between those two world.)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk16.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..b8a64f1e33abb7e7901b5228ccc774fb40b6197a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 17, + "timestamp": 1684727650779.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Notes for future ref.)\n(7:16) there are _some_ matrices that do _NOT_ have n-independent eigenvectors, but _most_ of the matrices we deal with do have n-independent eigenvectors.\n(17:14) If all evalues are different, there _must_ be n-indep evectors. But if there are same evalues, it's possible _no_ n-indep evectors. (Identity matrix is an example of having the same evalues but still having n-indep evectors)\n* Also, the position of Lambda and S should be changed(32:36). You'll see why by just thinking matrix multiplication, and it can also be viewed by knowing A^100=S*Lambda^100*S^-1 and u_0=S*c.\n Thus, it should be S*Lambda^100*c, and this also can be thought of as 'transformation' between the two different bases - one of the two is the set of the egenvectors of A.\n* Also, (43:34) How prof. Strang could calculate that?? Actually that number _1.618033988749894..._ is called the 'golden ratio'.\n* (8:15) Note that A and Lambda are 'similar'. (And, S and S_-1(S inverse) transforms the coordinates.. you know what I mean.. both A and Lambda can be though of as some \"transformation\" based on different basis.. and S(or S_-1) transforms the coord between those two world.)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk17.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b8a64f1e33abb7e7901b5228ccc774fb40b6197a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 17, + "timestamp": 1684727650779.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Notes for future ref.)\n(7:16) there are _some_ matrices that do _NOT_ have n-independent eigenvectors, but _most_ of the matrices we deal with do have n-independent eigenvectors.\n(17:14) If all evalues are different, there _must_ be n-indep evectors. But if there are same evalues, it's possible _no_ n-indep evectors. (Identity matrix is an example of having the same evalues but still having n-indep evectors)\n* Also, the position of Lambda and S should be changed(32:36). You'll see why by just thinking matrix multiplication, and it can also be viewed by knowing A^100=S*Lambda^100*S^-1 and u_0=S*c.\n Thus, it should be S*Lambda^100*c, and this also can be thought of as 'transformation' between the two different bases - one of the two is the set of the egenvectors of A.\n* Also, (43:34) How prof. Strang could calculate that?? Actually that number _1.618033988749894..._ is called the 'golden ratio'.\n* (8:15) Note that A and Lambda are 'similar'. (And, S and S_-1(S inverse) transforms the coordinates.. you know what I mean.. both A and Lambda can be though of as some \"transformation\" based on different basis.. and S(or S_-1) transforms the coord between those two world.)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk18.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..b8a64f1e33abb7e7901b5228ccc774fb40b6197a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 17, + "timestamp": 1684727650779.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Notes for future ref.)\n(7:16) there are _some_ matrices that do _NOT_ have n-independent eigenvectors, but _most_ of the matrices we deal with do have n-independent eigenvectors.\n(17:14) If all evalues are different, there _must_ be n-indep evectors. But if there are same evalues, it's possible _no_ n-indep evectors. (Identity matrix is an example of having the same evalues but still having n-indep evectors)\n* Also, the position of Lambda and S should be changed(32:36). You'll see why by just thinking matrix multiplication, and it can also be viewed by knowing A^100=S*Lambda^100*S^-1 and u_0=S*c.\n Thus, it should be S*Lambda^100*c, and this also can be thought of as 'transformation' between the two different bases - one of the two is the set of the egenvectors of A.\n* Also, (43:34) How prof. Strang could calculate that?? Actually that number _1.618033988749894..._ is called the 'golden ratio'.\n* (8:15) Note that A and Lambda are 'similar'. (And, S and S_-1(S inverse) transforms the coordinates.. you know what I mean.. both A and Lambda can be though of as some \"transformation\" based on different basis.. and S(or S_-1) transforms the coord between those two world.)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk19.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..b8a64f1e33abb7e7901b5228ccc774fb40b6197a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 17, + "timestamp": 1684727650779.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Notes for future ref.)\n(7:16) there are _some_ matrices that do _NOT_ have n-independent eigenvectors, but _most_ of the matrices we deal with do have n-independent eigenvectors.\n(17:14) If all evalues are different, there _must_ be n-indep evectors. But if there are same evalues, it's possible _no_ n-indep evectors. (Identity matrix is an example of having the same evalues but still having n-indep evectors)\n* Also, the position of Lambda and S should be changed(32:36). You'll see why by just thinking matrix multiplication, and it can also be viewed by knowing A^100=S*Lambda^100*S^-1 and u_0=S*c.\n Thus, it should be S*Lambda^100*c, and this also can be thought of as 'transformation' between the two different bases - one of the two is the set of the egenvectors of A.\n* Also, (43:34) How prof. Strang could calculate that?? Actually that number _1.618033988749894..._ is called the 'golden ratio'.\n* (8:15) Note that A and Lambda are 'similar'. (And, S and S_-1(S inverse) transforms the coordinates.. you know what I mean.. both A and Lambda can be though of as some \"transformation\" based on different basis.. and S(or S_-1) transforms the coord between those two world.)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk2.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..b8a64f1e33abb7e7901b5228ccc774fb40b6197a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 17, + "timestamp": 1684727650779.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Notes for future ref.)\n(7:16) there are _some_ matrices that do _NOT_ have n-independent eigenvectors, but _most_ of the matrices we deal with do have n-independent eigenvectors.\n(17:14) If all evalues are different, there _must_ be n-indep evectors. But if there are same evalues, it's possible _no_ n-indep evectors. (Identity matrix is an example of having the same evalues but still having n-indep evectors)\n* Also, the position of Lambda and S should be changed(32:36). You'll see why by just thinking matrix multiplication, and it can also be viewed by knowing A^100=S*Lambda^100*S^-1 and u_0=S*c.\n Thus, it should be S*Lambda^100*c, and this also can be thought of as 'transformation' between the two different bases - one of the two is the set of the egenvectors of A.\n* Also, (43:34) How prof. Strang could calculate that?? Actually that number _1.618033988749894..._ is called the 'golden ratio'.\n* (8:15) Note that A and Lambda are 'similar'. (And, S and S_-1(S inverse) transforms the coordinates.. you know what I mean.. both A and Lambda can be though of as some \"transformation\" based on different basis.. and S(or S_-1) transforms the coord between those two world.)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk20.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..b8a64f1e33abb7e7901b5228ccc774fb40b6197a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 17, + "timestamp": 1684727650779.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Notes for future ref.)\n(7:16) there are _some_ matrices that do _NOT_ have n-independent eigenvectors, but _most_ of the matrices we deal with do have n-independent eigenvectors.\n(17:14) If all evalues are different, there _must_ be n-indep evectors. But if there are same evalues, it's possible _no_ n-indep evectors. (Identity matrix is an example of having the same evalues but still having n-indep evectors)\n* Also, the position of Lambda and S should be changed(32:36). You'll see why by just thinking matrix multiplication, and it can also be viewed by knowing A^100=S*Lambda^100*S^-1 and u_0=S*c.\n Thus, it should be S*Lambda^100*c, and this also can be thought of as 'transformation' between the two different bases - one of the two is the set of the egenvectors of A.\n* Also, (43:34) How prof. Strang could calculate that?? Actually that number _1.618033988749894..._ is called the 'golden ratio'.\n* (8:15) Note that A and Lambda are 'similar'. (And, S and S_-1(S inverse) transforms the coordinates.. you know what I mean.. both A and Lambda can be though of as some \"transformation\" based on different basis.. and S(or S_-1) transforms the coord between those two world.)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk21.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..b8a64f1e33abb7e7901b5228ccc774fb40b6197a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 17, + "timestamp": 1684727650779.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Notes for future ref.)\n(7:16) there are _some_ matrices that do _NOT_ have n-independent eigenvectors, but _most_ of the matrices we deal with do have n-independent eigenvectors.\n(17:14) If all evalues are different, there _must_ be n-indep evectors. But if there are same evalues, it's possible _no_ n-indep evectors. (Identity matrix is an example of having the same evalues but still having n-indep evectors)\n* Also, the position of Lambda and S should be changed(32:36). You'll see why by just thinking matrix multiplication, and it can also be viewed by knowing A^100=S*Lambda^100*S^-1 and u_0=S*c.\n Thus, it should be S*Lambda^100*c, and this also can be thought of as 'transformation' between the two different bases - one of the two is the set of the egenvectors of A.\n* Also, (43:34) How prof. Strang could calculate that?? Actually that number _1.618033988749894..._ is called the 'golden ratio'.\n* (8:15) Note that A and Lambda are 'similar'. (And, S and S_-1(S inverse) transforms the coordinates.. you know what I mean.. both A and Lambda can be though of as some \"transformation\" based on different basis.. and S(or S_-1) transforms the coord between those two world.)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk22.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..b8a64f1e33abb7e7901b5228ccc774fb40b6197a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 17, + "timestamp": 1684727650779.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Notes for future ref.)\n(7:16) there are _some_ matrices that do _NOT_ have n-independent eigenvectors, but _most_ of the matrices we deal with do have n-independent eigenvectors.\n(17:14) If all evalues are different, there _must_ be n-indep evectors. But if there are same evalues, it's possible _no_ n-indep evectors. (Identity matrix is an example of having the same evalues but still having n-indep evectors)\n* Also, the position of Lambda and S should be changed(32:36). You'll see why by just thinking matrix multiplication, and it can also be viewed by knowing A^100=S*Lambda^100*S^-1 and u_0=S*c.\n Thus, it should be S*Lambda^100*c, and this also can be thought of as 'transformation' between the two different bases - one of the two is the set of the egenvectors of A.\n* Also, (43:34) How prof. Strang could calculate that?? Actually that number _1.618033988749894..._ is called the 'golden ratio'.\n* (8:15) Note that A and Lambda are 'similar'. (And, S and S_-1(S inverse) transforms the coordinates.. you know what I mean.. both A and Lambda can be though of as some \"transformation\" based on different basis.. and S(or S_-1) transforms the coord between those two world.)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk23.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..b8a64f1e33abb7e7901b5228ccc774fb40b6197a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 17, + "timestamp": 1684727650779.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Notes for future ref.)\n(7:16) there are _some_ matrices that do _NOT_ have n-independent eigenvectors, but _most_ of the matrices we deal with do have n-independent eigenvectors.\n(17:14) If all evalues are different, there _must_ be n-indep evectors. But if there are same evalues, it's possible _no_ n-indep evectors. (Identity matrix is an example of having the same evalues but still having n-indep evectors)\n* Also, the position of Lambda and S should be changed(32:36). You'll see why by just thinking matrix multiplication, and it can also be viewed by knowing A^100=S*Lambda^100*S^-1 and u_0=S*c.\n Thus, it should be S*Lambda^100*c, and this also can be thought of as 'transformation' between the two different bases - one of the two is the set of the egenvectors of A.\n* Also, (43:34) How prof. Strang could calculate that?? Actually that number _1.618033988749894..._ is called the 'golden ratio'.\n* (8:15) Note that A and Lambda are 'similar'. (And, S and S_-1(S inverse) transforms the coordinates.. you know what I mean.. both A and Lambda can be though of as some \"transformation\" based on different basis.. and S(or S_-1) transforms the coord between those two world.)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk24.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..dbe592e499656f49cfdb96b0c35bc1cce686005a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk24.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 17, + "timestamp": 1684727650779.0, + "annotatedSourceSentencesIndices": [ + 5 + ], + "names": [ + "annotator2" + ], + "text": "Notes for future ref.)\n(7:16) there are _some_ matrices that do _NOT_ have n-independent eigenvectors, but _most_ of the matrices we deal with do have n-independent eigenvectors.\n(17:14) If all evalues are different, there _must_ be n-indep evectors. But if there are same evalues, it's possible _no_ n-indep evectors. (Identity matrix is an example of having the same evalues but still having n-indep evectors)\n* Also, the position of Lambda and S should be changed(32:36). You'll see why by just thinking matrix multiplication, and it can also be viewed by knowing A^100=S*Lambda^100*S^-1 and u_0=S*c.\n Thus, it should be S*Lambda^100*c, and this also can be thought of as 'transformation' between the two different bases - one of the two is the set of the egenvectors of A.\n* Also, (43:34) How prof. Strang could calculate that?? Actually that number _1.618033988749894..._ is called the 'golden ratio'.\n* (8:15) Note that A and Lambda are 'similar'. (And, S and S_-1(S inverse) transforms the coordinates.. you know what I mean.. both A and Lambda can be though of as some \"transformation\" based on different basis.. and S(or S_-1) transforms the coord between those two world.)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk3.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..b8a64f1e33abb7e7901b5228ccc774fb40b6197a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 17, + "timestamp": 1684727650779.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Notes for future ref.)\n(7:16) there are _some_ matrices that do _NOT_ have n-independent eigenvectors, but _most_ of the matrices we deal with do have n-independent eigenvectors.\n(17:14) If all evalues are different, there _must_ be n-indep evectors. But if there are same evalues, it's possible _no_ n-indep evectors. (Identity matrix is an example of having the same evalues but still having n-indep evectors)\n* Also, the position of Lambda and S should be changed(32:36). You'll see why by just thinking matrix multiplication, and it can also be viewed by knowing A^100=S*Lambda^100*S^-1 and u_0=S*c.\n Thus, it should be S*Lambda^100*c, and this also can be thought of as 'transformation' between the two different bases - one of the two is the set of the egenvectors of A.\n* Also, (43:34) How prof. Strang could calculate that?? Actually that number _1.618033988749894..._ is called the 'golden ratio'.\n* (8:15) Note that A and Lambda are 'similar'. (And, S and S_-1(S inverse) transforms the coordinates.. you know what I mean.. both A and Lambda can be though of as some \"transformation\" based on different basis.. and S(or S_-1) transforms the coord between those two world.)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk4.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..b8a64f1e33abb7e7901b5228ccc774fb40b6197a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 17, + "timestamp": 1684727650779.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Notes for future ref.)\n(7:16) there are _some_ matrices that do _NOT_ have n-independent eigenvectors, but _most_ of the matrices we deal with do have n-independent eigenvectors.\n(17:14) If all evalues are different, there _must_ be n-indep evectors. But if there are same evalues, it's possible _no_ n-indep evectors. (Identity matrix is an example of having the same evalues but still having n-indep evectors)\n* Also, the position of Lambda and S should be changed(32:36). You'll see why by just thinking matrix multiplication, and it can also be viewed by knowing A^100=S*Lambda^100*S^-1 and u_0=S*c.\n Thus, it should be S*Lambda^100*c, and this also can be thought of as 'transformation' between the two different bases - one of the two is the set of the egenvectors of A.\n* Also, (43:34) How prof. Strang could calculate that?? Actually that number _1.618033988749894..._ is called the 'golden ratio'.\n* (8:15) Note that A and Lambda are 'similar'. (And, S and S_-1(S inverse) transforms the coordinates.. you know what I mean.. both A and Lambda can be though of as some \"transformation\" based on different basis.. and S(or S_-1) transforms the coord between those two world.)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk5.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..b8a64f1e33abb7e7901b5228ccc774fb40b6197a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 17, + "timestamp": 1684727650779.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Notes for future ref.)\n(7:16) there are _some_ matrices that do _NOT_ have n-independent eigenvectors, but _most_ of the matrices we deal with do have n-independent eigenvectors.\n(17:14) If all evalues are different, there _must_ be n-indep evectors. But if there are same evalues, it's possible _no_ n-indep evectors. (Identity matrix is an example of having the same evalues but still having n-indep evectors)\n* Also, the position of Lambda and S should be changed(32:36). You'll see why by just thinking matrix multiplication, and it can also be viewed by knowing A^100=S*Lambda^100*S^-1 and u_0=S*c.\n Thus, it should be S*Lambda^100*c, and this also can be thought of as 'transformation' between the two different bases - one of the two is the set of the egenvectors of A.\n* Also, (43:34) How prof. Strang could calculate that?? Actually that number _1.618033988749894..._ is called the 'golden ratio'.\n* (8:15) Note that A and Lambda are 'similar'. (And, S and S_-1(S inverse) transforms the coordinates.. you know what I mean.. both A and Lambda can be though of as some \"transformation\" based on different basis.. and S(or S_-1) transforms the coord between those two world.)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk6.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..b8a64f1e33abb7e7901b5228ccc774fb40b6197a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 17, + "timestamp": 1684727650779.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Notes for future ref.)\n(7:16) there are _some_ matrices that do _NOT_ have n-independent eigenvectors, but _most_ of the matrices we deal with do have n-independent eigenvectors.\n(17:14) If all evalues are different, there _must_ be n-indep evectors. But if there are same evalues, it's possible _no_ n-indep evectors. (Identity matrix is an example of having the same evalues but still having n-indep evectors)\n* Also, the position of Lambda and S should be changed(32:36). You'll see why by just thinking matrix multiplication, and it can also be viewed by knowing A^100=S*Lambda^100*S^-1 and u_0=S*c.\n Thus, it should be S*Lambda^100*c, and this also can be thought of as 'transformation' between the two different bases - one of the two is the set of the egenvectors of A.\n* Also, (43:34) How prof. Strang could calculate that?? Actually that number _1.618033988749894..._ is called the 'golden ratio'.\n* (8:15) Note that A and Lambda are 'similar'. (And, S and S_-1(S inverse) transforms the coordinates.. you know what I mean.. both A and Lambda can be though of as some \"transformation\" based on different basis.. and S(or S_-1) transforms the coord between those two world.)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk7.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b8a64f1e33abb7e7901b5228ccc774fb40b6197a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 17, + "timestamp": 1684727650779.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Notes for future ref.)\n(7:16) there are _some_ matrices that do _NOT_ have n-independent eigenvectors, but _most_ of the matrices we deal with do have n-independent eigenvectors.\n(17:14) If all evalues are different, there _must_ be n-indep evectors. But if there are same evalues, it's possible _no_ n-indep evectors. (Identity matrix is an example of having the same evalues but still having n-indep evectors)\n* Also, the position of Lambda and S should be changed(32:36). You'll see why by just thinking matrix multiplication, and it can also be viewed by knowing A^100=S*Lambda^100*S^-1 and u_0=S*c.\n Thus, it should be S*Lambda^100*c, and this also can be thought of as 'transformation' between the two different bases - one of the two is the set of the egenvectors of A.\n* Also, (43:34) How prof. Strang could calculate that?? Actually that number _1.618033988749894..._ is called the 'golden ratio'.\n* (8:15) Note that A and Lambda are 'similar'. (And, S and S_-1(S inverse) transforms the coordinates.. you know what I mean.. both A and Lambda can be though of as some \"transformation\" based on different basis.. and S(or S_-1) transforms the coord between those two world.)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk8.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..b8a64f1e33abb7e7901b5228ccc774fb40b6197a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 17, + "timestamp": 1684727650779.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Notes for future ref.)\n(7:16) there are _some_ matrices that do _NOT_ have n-independent eigenvectors, but _most_ of the matrices we deal with do have n-independent eigenvectors.\n(17:14) If all evalues are different, there _must_ be n-indep evectors. But if there are same evalues, it's possible _no_ n-indep evectors. (Identity matrix is an example of having the same evalues but still having n-indep evectors)\n* Also, the position of Lambda and S should be changed(32:36). You'll see why by just thinking matrix multiplication, and it can also be viewed by knowing A^100=S*Lambda^100*S^-1 and u_0=S*c.\n Thus, it should be S*Lambda^100*c, and this also can be thought of as 'transformation' between the two different bases - one of the two is the set of the egenvectors of A.\n* Also, (43:34) How prof. Strang could calculate that?? Actually that number _1.618033988749894..._ is called the 'golden ratio'.\n* (8:15) Note that A and Lambda are 'similar'. (And, S and S_-1(S inverse) transforms the coordinates.. you know what I mean.. both A and Lambda can be though of as some \"transformation\" based on different basis.. and S(or S_-1) transforms the coord between those two world.)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk9.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..b8a64f1e33abb7e7901b5228ccc774fb40b6197a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_17_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 17, + "timestamp": 1684727650779.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Notes for future ref.)\n(7:16) there are _some_ matrices that do _NOT_ have n-independent eigenvectors, but _most_ of the matrices we deal with do have n-independent eigenvectors.\n(17:14) If all evalues are different, there _must_ be n-indep evectors. But if there are same evalues, it's possible _no_ n-indep evectors. (Identity matrix is an example of having the same evalues but still having n-indep evectors)\n* Also, the position of Lambda and S should be changed(32:36). You'll see why by just thinking matrix multiplication, and it can also be viewed by knowing A^100=S*Lambda^100*S^-1 and u_0=S*c.\n Thus, it should be S*Lambda^100*c, and this also can be thought of as 'transformation' between the two different bases - one of the two is the set of the egenvectors of A.\n* Also, (43:34) How prof. Strang could calculate that?? Actually that number _1.618033988749894..._ is called the 'golden ratio'.\n* (8:15) Note that A and Lambda are 'similar'. (And, S and S_-1(S inverse) transforms the coordinates.. you know what I mean.. both A and Lambda can be though of as some \"transformation\" based on different basis.. and S(or S_-1) transforms the coord between those two world.)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk0.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..99cead80e6a29a3170e52c182c854235a0bb47a4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 18, + "timestamp": 1684727704997.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "39:03 where the A (1,1,1,0) comes from? help....." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk1.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..99cead80e6a29a3170e52c182c854235a0bb47a4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 18, + "timestamp": 1684727704997.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "39:03 where the A (1,1,1,0) comes from? help....." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk10.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..99cead80e6a29a3170e52c182c854235a0bb47a4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 18, + "timestamp": 1684727704997.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "39:03 where the A (1,1,1,0) comes from? help....." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk11.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..99cead80e6a29a3170e52c182c854235a0bb47a4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 18, + "timestamp": 1684727704997.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "39:03 where the A (1,1,1,0) comes from? help....." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk12.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..99cead80e6a29a3170e52c182c854235a0bb47a4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 18, + "timestamp": 1684727704997.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "39:03 where the A (1,1,1,0) comes from? help....." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk13.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..99cead80e6a29a3170e52c182c854235a0bb47a4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 18, + "timestamp": 1684727704997.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "39:03 where the A (1,1,1,0) comes from? help....." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk14.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..99cead80e6a29a3170e52c182c854235a0bb47a4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 18, + "timestamp": 1684727704997.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "39:03 where the A (1,1,1,0) comes from? help....." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk15.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..99cead80e6a29a3170e52c182c854235a0bb47a4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 18, + "timestamp": 1684727704997.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "39:03 where the A (1,1,1,0) comes from? help....." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk16.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..99cead80e6a29a3170e52c182c854235a0bb47a4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 18, + "timestamp": 1684727704997.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "39:03 where the A (1,1,1,0) comes from? help....." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk17.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..474c4823066c1499d4c97c29503f76e98729d26e --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk17.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 18, + "timestamp": 1684727704997.0, + "annotatedSourceSentencesIndices": [ + 18 + ], + "names": [ + "annotator2" + ], + "text": "39:03 where the A (1,1,1,0) comes from? help....." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk18.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..99cead80e6a29a3170e52c182c854235a0bb47a4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 18, + "timestamp": 1684727704997.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "39:03 where the A (1,1,1,0) comes from? help....." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk19.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..99cead80e6a29a3170e52c182c854235a0bb47a4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 18, + "timestamp": 1684727704997.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "39:03 where the A (1,1,1,0) comes from? help....." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk2.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..99cead80e6a29a3170e52c182c854235a0bb47a4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 18, + "timestamp": 1684727704997.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "39:03 where the A (1,1,1,0) comes from? help....." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk20.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..99cead80e6a29a3170e52c182c854235a0bb47a4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 18, + "timestamp": 1684727704997.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "39:03 where the A (1,1,1,0) comes from? help....." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk21.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..99cead80e6a29a3170e52c182c854235a0bb47a4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 18, + "timestamp": 1684727704997.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "39:03 where the A (1,1,1,0) comes from? help....." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk22.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..99cead80e6a29a3170e52c182c854235a0bb47a4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 18, + "timestamp": 1684727704997.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "39:03 where the A (1,1,1,0) comes from? help....." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk23.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..99cead80e6a29a3170e52c182c854235a0bb47a4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 18, + "timestamp": 1684727704997.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "39:03 where the A (1,1,1,0) comes from? help....." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk24.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..99cead80e6a29a3170e52c182c854235a0bb47a4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 18, + "timestamp": 1684727704997.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "39:03 where the A (1,1,1,0) comes from? help....." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk3.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..99cead80e6a29a3170e52c182c854235a0bb47a4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 18, + "timestamp": 1684727704997.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "39:03 where the A (1,1,1,0) comes from? help....." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk4.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..99cead80e6a29a3170e52c182c854235a0bb47a4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 18, + "timestamp": 1684727704997.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "39:03 where the A (1,1,1,0) comes from? help....." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk5.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..99cead80e6a29a3170e52c182c854235a0bb47a4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 18, + "timestamp": 1684727704997.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "39:03 where the A (1,1,1,0) comes from? help....." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk6.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..99cead80e6a29a3170e52c182c854235a0bb47a4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 18, + "timestamp": 1684727704997.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "39:03 where the A (1,1,1,0) comes from? help....." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk7.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..99cead80e6a29a3170e52c182c854235a0bb47a4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 18, + "timestamp": 1684727704997.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "39:03 where the A (1,1,1,0) comes from? help....." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk8.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..99cead80e6a29a3170e52c182c854235a0bb47a4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 18, + "timestamp": 1684727704997.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "39:03 where the A (1,1,1,0) comes from? help....." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk9.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..99cead80e6a29a3170e52c182c854235a0bb47a4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_18_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 18, + "timestamp": 1684727704997.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "39:03 where the A (1,1,1,0) comes from? help....." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk0.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..ced9d1e8fba81bf02ffdb1910b3ec67301b048e6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 1, + "timestamp": 1684723178257.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I dont undertand why the eigenvectors are [lamba_1 \u00a01] and [lamba_2 1] at 49:19...\nsince it is NOT true that ((1 - lamba) * (lamba)) + 1 is lamba^2 - lamba - 1 ... or it is? or what is happening?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk1.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..ced9d1e8fba81bf02ffdb1910b3ec67301b048e6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 1, + "timestamp": 1684723178257.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I dont undertand why the eigenvectors are [lamba_1 \u00a01] and [lamba_2 1] at 49:19...\nsince it is NOT true that ((1 - lamba) * (lamba)) + 1 is lamba^2 - lamba - 1 ... or it is? or what is happening?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk10.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..ced9d1e8fba81bf02ffdb1910b3ec67301b048e6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 1, + "timestamp": 1684723178257.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I dont undertand why the eigenvectors are [lamba_1 \u00a01] and [lamba_2 1] at 49:19...\nsince it is NOT true that ((1 - lamba) * (lamba)) + 1 is lamba^2 - lamba - 1 ... or it is? or what is happening?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk11.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..ced9d1e8fba81bf02ffdb1910b3ec67301b048e6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 1, + "timestamp": 1684723178257.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I dont undertand why the eigenvectors are [lamba_1 \u00a01] and [lamba_2 1] at 49:19...\nsince it is NOT true that ((1 - lamba) * (lamba)) + 1 is lamba^2 - lamba - 1 ... or it is? or what is happening?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk12.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..ced9d1e8fba81bf02ffdb1910b3ec67301b048e6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 1, + "timestamp": 1684723178257.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I dont undertand why the eigenvectors are [lamba_1 \u00a01] and [lamba_2 1] at 49:19...\nsince it is NOT true that ((1 - lamba) * (lamba)) + 1 is lamba^2 - lamba - 1 ... or it is? or what is happening?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk13.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..ced9d1e8fba81bf02ffdb1910b3ec67301b048e6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 1, + "timestamp": 1684723178257.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I dont undertand why the eigenvectors are [lamba_1 \u00a01] and [lamba_2 1] at 49:19...\nsince it is NOT true that ((1 - lamba) * (lamba)) + 1 is lamba^2 - lamba - 1 ... or it is? or what is happening?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk14.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..ba07bfb9fcd8a619612ebeec9d77fcfe20a05199 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk14.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 1, + "timestamp": 1684723178257.0, + "annotatedSourceSentencesIndices": [ + 9, + 10 + ], + "names": [ + "annotator2" + ], + "text": "I dont undertand why the eigenvectors are [lamba_1 \u00a01] and [lamba_2 1] at 49:19...\nsince it is NOT true that ((1 - lamba) * (lamba)) + 1 is lamba^2 - lamba - 1 ... or it is? or what is happening?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk15.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..ced9d1e8fba81bf02ffdb1910b3ec67301b048e6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 1, + "timestamp": 1684723178257.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I dont undertand why the eigenvectors are [lamba_1 \u00a01] and [lamba_2 1] at 49:19...\nsince it is NOT true that ((1 - lamba) * (lamba)) + 1 is lamba^2 - lamba - 1 ... or it is? or what is happening?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk16.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..ced9d1e8fba81bf02ffdb1910b3ec67301b048e6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 1, + "timestamp": 1684723178257.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I dont undertand why the eigenvectors are [lamba_1 \u00a01] and [lamba_2 1] at 49:19...\nsince it is NOT true that ((1 - lamba) * (lamba)) + 1 is lamba^2 - lamba - 1 ... or it is? or what is happening?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk17.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..ced9d1e8fba81bf02ffdb1910b3ec67301b048e6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 1, + "timestamp": 1684723178257.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I dont undertand why the eigenvectors are [lamba_1 \u00a01] and [lamba_2 1] at 49:19...\nsince it is NOT true that ((1 - lamba) * (lamba)) + 1 is lamba^2 - lamba - 1 ... or it is? or what is happening?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk18.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..ced9d1e8fba81bf02ffdb1910b3ec67301b048e6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 1, + "timestamp": 1684723178257.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I dont undertand why the eigenvectors are [lamba_1 \u00a01] and [lamba_2 1] at 49:19...\nsince it is NOT true that ((1 - lamba) * (lamba)) + 1 is lamba^2 - lamba - 1 ... or it is? or what is happening?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk19.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..ced9d1e8fba81bf02ffdb1910b3ec67301b048e6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 1, + "timestamp": 1684723178257.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I dont undertand why the eigenvectors are [lamba_1 \u00a01] and [lamba_2 1] at 49:19...\nsince it is NOT true that ((1 - lamba) * (lamba)) + 1 is lamba^2 - lamba - 1 ... or it is? or what is happening?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk2.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..ced9d1e8fba81bf02ffdb1910b3ec67301b048e6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 1, + "timestamp": 1684723178257.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I dont undertand why the eigenvectors are [lamba_1 \u00a01] and [lamba_2 1] at 49:19...\nsince it is NOT true that ((1 - lamba) * (lamba)) + 1 is lamba^2 - lamba - 1 ... or it is? or what is happening?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk20.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ced9d1e8fba81bf02ffdb1910b3ec67301b048e6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 1, + "timestamp": 1684723178257.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I dont undertand why the eigenvectors are [lamba_1 \u00a01] and [lamba_2 1] at 49:19...\nsince it is NOT true that ((1 - lamba) * (lamba)) + 1 is lamba^2 - lamba - 1 ... or it is? or what is happening?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk21.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..ced9d1e8fba81bf02ffdb1910b3ec67301b048e6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 1, + "timestamp": 1684723178257.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I dont undertand why the eigenvectors are [lamba_1 \u00a01] and [lamba_2 1] at 49:19...\nsince it is NOT true that ((1 - lamba) * (lamba)) + 1 is lamba^2 - lamba - 1 ... or it is? or what is happening?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk22.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..ced9d1e8fba81bf02ffdb1910b3ec67301b048e6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 1, + "timestamp": 1684723178257.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I dont undertand why the eigenvectors are [lamba_1 \u00a01] and [lamba_2 1] at 49:19...\nsince it is NOT true that ((1 - lamba) * (lamba)) + 1 is lamba^2 - lamba - 1 ... or it is? or what is happening?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk23.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..ced9d1e8fba81bf02ffdb1910b3ec67301b048e6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 1, + "timestamp": 1684723178257.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I dont undertand why the eigenvectors are [lamba_1 \u00a01] and [lamba_2 1] at 49:19...\nsince it is NOT true that ((1 - lamba) * (lamba)) + 1 is lamba^2 - lamba - 1 ... or it is? or what is happening?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk24.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ced9d1e8fba81bf02ffdb1910b3ec67301b048e6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 1, + "timestamp": 1684723178257.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I dont undertand why the eigenvectors are [lamba_1 \u00a01] and [lamba_2 1] at 49:19...\nsince it is NOT true that ((1 - lamba) * (lamba)) + 1 is lamba^2 - lamba - 1 ... or it is? or what is happening?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk3.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..ced9d1e8fba81bf02ffdb1910b3ec67301b048e6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 1, + "timestamp": 1684723178257.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I dont undertand why the eigenvectors are [lamba_1 \u00a01] and [lamba_2 1] at 49:19...\nsince it is NOT true that ((1 - lamba) * (lamba)) + 1 is lamba^2 - lamba - 1 ... or it is? or what is happening?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk4.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..ced9d1e8fba81bf02ffdb1910b3ec67301b048e6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 1, + "timestamp": 1684723178257.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I dont undertand why the eigenvectors are [lamba_1 \u00a01] and [lamba_2 1] at 49:19...\nsince it is NOT true that ((1 - lamba) * (lamba)) + 1 is lamba^2 - lamba - 1 ... or it is? or what is happening?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk5.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..ced9d1e8fba81bf02ffdb1910b3ec67301b048e6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 1, + "timestamp": 1684723178257.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I dont undertand why the eigenvectors are [lamba_1 \u00a01] and [lamba_2 1] at 49:19...\nsince it is NOT true that ((1 - lamba) * (lamba)) + 1 is lamba^2 - lamba - 1 ... or it is? or what is happening?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk6.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..ced9d1e8fba81bf02ffdb1910b3ec67301b048e6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 1, + "timestamp": 1684723178257.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I dont undertand why the eigenvectors are [lamba_1 \u00a01] and [lamba_2 1] at 49:19...\nsince it is NOT true that ((1 - lamba) * (lamba)) + 1 is lamba^2 - lamba - 1 ... or it is? or what is happening?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk7.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..ced9d1e8fba81bf02ffdb1910b3ec67301b048e6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 1, + "timestamp": 1684723178257.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I dont undertand why the eigenvectors are [lamba_1 \u00a01] and [lamba_2 1] at 49:19...\nsince it is NOT true that ((1 - lamba) * (lamba)) + 1 is lamba^2 - lamba - 1 ... or it is? or what is happening?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk8.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..ced9d1e8fba81bf02ffdb1910b3ec67301b048e6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 1, + "timestamp": 1684723178257.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I dont undertand why the eigenvectors are [lamba_1 \u00a01] and [lamba_2 1] at 49:19...\nsince it is NOT true that ((1 - lamba) * (lamba)) + 1 is lamba^2 - lamba - 1 ... or it is? or what is happening?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk9.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..ced9d1e8fba81bf02ffdb1910b3ec67301b048e6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_1_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 1, + "timestamp": 1684723178257.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I dont undertand why the eigenvectors are [lamba_1 \u00a01] and [lamba_2 1] at 49:19...\nsince it is NOT true that ((1 - lamba) * (lamba)) + 1 is lamba^2 - lamba - 1 ... or it is? or what is happening?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk0.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..628ae8ec3cd050bd7120d7fff57738f2c633319e --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 21, + "timestamp": 1684727831398.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can't you also use the determinant to figure out that A\u1d4f \u2192 0 as K \u2192 \u221e ? i.e. if det A < 1 then A\u1d4f \u2192 0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk1.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..628ae8ec3cd050bd7120d7fff57738f2c633319e --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 21, + "timestamp": 1684727831398.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can't you also use the determinant to figure out that A\u1d4f \u2192 0 as K \u2192 \u221e ? i.e. if det A < 1 then A\u1d4f \u2192 0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk10.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..628ae8ec3cd050bd7120d7fff57738f2c633319e --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 21, + "timestamp": 1684727831398.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can't you also use the determinant to figure out that A\u1d4f \u2192 0 as K \u2192 \u221e ? i.e. if det A < 1 then A\u1d4f \u2192 0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk11.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..628ae8ec3cd050bd7120d7fff57738f2c633319e --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 21, + "timestamp": 1684727831398.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can't you also use the determinant to figure out that A\u1d4f \u2192 0 as K \u2192 \u221e ? i.e. if det A < 1 then A\u1d4f \u2192 0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk12.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..ce307b8baed62778ae137a32914dd4eee0f2cb32 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk12.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 21, + "timestamp": 1684727831398.0, + "annotatedSourceSentencesIndices": [ + 15 + ], + "names": [ + "annotator2" + ], + "text": "Can't you also use the determinant to figure out that A\u1d4f \u2192 0 as K \u2192 \u221e ? i.e. if det A < 1 then A\u1d4f \u2192 0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk13.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..628ae8ec3cd050bd7120d7fff57738f2c633319e --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 21, + "timestamp": 1684727831398.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can't you also use the determinant to figure out that A\u1d4f \u2192 0 as K \u2192 \u221e ? i.e. if det A < 1 then A\u1d4f \u2192 0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk14.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..628ae8ec3cd050bd7120d7fff57738f2c633319e --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 21, + "timestamp": 1684727831398.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can't you also use the determinant to figure out that A\u1d4f \u2192 0 as K \u2192 \u221e ? i.e. if det A < 1 then A\u1d4f \u2192 0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk15.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..628ae8ec3cd050bd7120d7fff57738f2c633319e --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 21, + "timestamp": 1684727831398.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can't you also use the determinant to figure out that A\u1d4f \u2192 0 as K \u2192 \u221e ? i.e. if det A < 1 then A\u1d4f \u2192 0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk16.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..628ae8ec3cd050bd7120d7fff57738f2c633319e --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 21, + "timestamp": 1684727831398.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can't you also use the determinant to figure out that A\u1d4f \u2192 0 as K \u2192 \u221e ? i.e. if det A < 1 then A\u1d4f \u2192 0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk17.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..628ae8ec3cd050bd7120d7fff57738f2c633319e --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 21, + "timestamp": 1684727831398.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can't you also use the determinant to figure out that A\u1d4f \u2192 0 as K \u2192 \u221e ? i.e. if det A < 1 then A\u1d4f \u2192 0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk18.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..628ae8ec3cd050bd7120d7fff57738f2c633319e --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 21, + "timestamp": 1684727831398.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can't you also use the determinant to figure out that A\u1d4f \u2192 0 as K \u2192 \u221e ? i.e. if det A < 1 then A\u1d4f \u2192 0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk19.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..628ae8ec3cd050bd7120d7fff57738f2c633319e --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 21, + "timestamp": 1684727831398.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can't you also use the determinant to figure out that A\u1d4f \u2192 0 as K \u2192 \u221e ? i.e. if det A < 1 then A\u1d4f \u2192 0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk2.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..628ae8ec3cd050bd7120d7fff57738f2c633319e --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 21, + "timestamp": 1684727831398.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can't you also use the determinant to figure out that A\u1d4f \u2192 0 as K \u2192 \u221e ? i.e. if det A < 1 then A\u1d4f \u2192 0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk20.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..628ae8ec3cd050bd7120d7fff57738f2c633319e --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 21, + "timestamp": 1684727831398.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can't you also use the determinant to figure out that A\u1d4f \u2192 0 as K \u2192 \u221e ? i.e. if det A < 1 then A\u1d4f \u2192 0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk21.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..628ae8ec3cd050bd7120d7fff57738f2c633319e --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 21, + "timestamp": 1684727831398.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can't you also use the determinant to figure out that A\u1d4f \u2192 0 as K \u2192 \u221e ? i.e. if det A < 1 then A\u1d4f \u2192 0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk22.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..628ae8ec3cd050bd7120d7fff57738f2c633319e --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 21, + "timestamp": 1684727831398.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can't you also use the determinant to figure out that A\u1d4f \u2192 0 as K \u2192 \u221e ? i.e. if det A < 1 then A\u1d4f \u2192 0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk23.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..628ae8ec3cd050bd7120d7fff57738f2c633319e --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 21, + "timestamp": 1684727831398.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can't you also use the determinant to figure out that A\u1d4f \u2192 0 as K \u2192 \u221e ? i.e. if det A < 1 then A\u1d4f \u2192 0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk24.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..628ae8ec3cd050bd7120d7fff57738f2c633319e --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 21, + "timestamp": 1684727831398.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can't you also use the determinant to figure out that A\u1d4f \u2192 0 as K \u2192 \u221e ? i.e. if det A < 1 then A\u1d4f \u2192 0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk3.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..628ae8ec3cd050bd7120d7fff57738f2c633319e --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 21, + "timestamp": 1684727831398.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can't you also use the determinant to figure out that A\u1d4f \u2192 0 as K \u2192 \u221e ? i.e. if det A < 1 then A\u1d4f \u2192 0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk4.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..628ae8ec3cd050bd7120d7fff57738f2c633319e --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 21, + "timestamp": 1684727831398.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can't you also use the determinant to figure out that A\u1d4f \u2192 0 as K \u2192 \u221e ? i.e. if det A < 1 then A\u1d4f \u2192 0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk5.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..628ae8ec3cd050bd7120d7fff57738f2c633319e --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 21, + "timestamp": 1684727831398.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can't you also use the determinant to figure out that A\u1d4f \u2192 0 as K \u2192 \u221e ? i.e. if det A < 1 then A\u1d4f \u2192 0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk6.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..628ae8ec3cd050bd7120d7fff57738f2c633319e --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 21, + "timestamp": 1684727831398.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can't you also use the determinant to figure out that A\u1d4f \u2192 0 as K \u2192 \u221e ? i.e. if det A < 1 then A\u1d4f \u2192 0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk7.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..628ae8ec3cd050bd7120d7fff57738f2c633319e --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 21, + "timestamp": 1684727831398.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can't you also use the determinant to figure out that A\u1d4f \u2192 0 as K \u2192 \u221e ? i.e. if det A < 1 then A\u1d4f \u2192 0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk8.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..628ae8ec3cd050bd7120d7fff57738f2c633319e --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 21, + "timestamp": 1684727831398.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can't you also use the determinant to figure out that A\u1d4f \u2192 0 as K \u2192 \u221e ? i.e. if det A < 1 then A\u1d4f \u2192 0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk9.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..628ae8ec3cd050bd7120d7fff57738f2c633319e --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_21_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 21, + "timestamp": 1684727831398.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can't you also use the determinant to figure out that A\u1d4f \u2192 0 as K \u2192 \u221e ? i.e. if det A < 1 then A\u1d4f \u2192 0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk0.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..e1d2d03ebc49dbf2daf0df04bbcae2ef6b63987a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 22, + "timestamp": 1684727876048.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is there an error at 32:30? Shouldn't S be multiplied before (lamda matrix)^100?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk1.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..e1d2d03ebc49dbf2daf0df04bbcae2ef6b63987a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 22, + "timestamp": 1684727876048.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is there an error at 32:30? Shouldn't S be multiplied before (lamda matrix)^100?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk10.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..e1d2d03ebc49dbf2daf0df04bbcae2ef6b63987a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 22, + "timestamp": 1684727876048.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is there an error at 32:30? Shouldn't S be multiplied before (lamda matrix)^100?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk11.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..e1d2d03ebc49dbf2daf0df04bbcae2ef6b63987a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 22, + "timestamp": 1684727876048.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is there an error at 32:30? Shouldn't S be multiplied before (lamda matrix)^100?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk12.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..e1d2d03ebc49dbf2daf0df04bbcae2ef6b63987a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 22, + "timestamp": 1684727876048.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is there an error at 32:30? Shouldn't S be multiplied before (lamda matrix)^100?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk13.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..e1d2d03ebc49dbf2daf0df04bbcae2ef6b63987a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 22, + "timestamp": 1684727876048.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is there an error at 32:30? Shouldn't S be multiplied before (lamda matrix)^100?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk14.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..e1d2d03ebc49dbf2daf0df04bbcae2ef6b63987a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 22, + "timestamp": 1684727876048.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is there an error at 32:30? Shouldn't S be multiplied before (lamda matrix)^100?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk15.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..47ee62fde793158706034adbf7337e8f5a5266e5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk15.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 22, + "timestamp": 1684727876048.0, + "annotatedSourceSentencesIndices": [ + 2 + ], + "names": [ + "annotator2" + ], + "text": "Is there an error at 32:30? Shouldn't S be multiplied before (lamda matrix)^100?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk16.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..e1d2d03ebc49dbf2daf0df04bbcae2ef6b63987a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 22, + "timestamp": 1684727876048.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is there an error at 32:30? Shouldn't S be multiplied before (lamda matrix)^100?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk17.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..e1d2d03ebc49dbf2daf0df04bbcae2ef6b63987a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 22, + "timestamp": 1684727876048.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is there an error at 32:30? Shouldn't S be multiplied before (lamda matrix)^100?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk18.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..e1d2d03ebc49dbf2daf0df04bbcae2ef6b63987a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 22, + "timestamp": 1684727876048.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is there an error at 32:30? Shouldn't S be multiplied before (lamda matrix)^100?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk19.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..e1d2d03ebc49dbf2daf0df04bbcae2ef6b63987a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 22, + "timestamp": 1684727876048.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is there an error at 32:30? Shouldn't S be multiplied before (lamda matrix)^100?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk2.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..e1d2d03ebc49dbf2daf0df04bbcae2ef6b63987a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 22, + "timestamp": 1684727876048.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is there an error at 32:30? Shouldn't S be multiplied before (lamda matrix)^100?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk20.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..e1d2d03ebc49dbf2daf0df04bbcae2ef6b63987a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 22, + "timestamp": 1684727876048.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is there an error at 32:30? Shouldn't S be multiplied before (lamda matrix)^100?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk21.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..e1d2d03ebc49dbf2daf0df04bbcae2ef6b63987a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 22, + "timestamp": 1684727876048.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is there an error at 32:30? Shouldn't S be multiplied before (lamda matrix)^100?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk22.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1d2d03ebc49dbf2daf0df04bbcae2ef6b63987a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 22, + "timestamp": 1684727876048.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is there an error at 32:30? Shouldn't S be multiplied before (lamda matrix)^100?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk23.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e1d2d03ebc49dbf2daf0df04bbcae2ef6b63987a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 22, + "timestamp": 1684727876048.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is there an error at 32:30? Shouldn't S be multiplied before (lamda matrix)^100?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk24.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..e1d2d03ebc49dbf2daf0df04bbcae2ef6b63987a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 22, + "timestamp": 1684727876048.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is there an error at 32:30? Shouldn't S be multiplied before (lamda matrix)^100?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk3.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..e1d2d03ebc49dbf2daf0df04bbcae2ef6b63987a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 22, + "timestamp": 1684727876048.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is there an error at 32:30? Shouldn't S be multiplied before (lamda matrix)^100?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk4.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..e1d2d03ebc49dbf2daf0df04bbcae2ef6b63987a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 22, + "timestamp": 1684727876048.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is there an error at 32:30? Shouldn't S be multiplied before (lamda matrix)^100?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk5.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..e1d2d03ebc49dbf2daf0df04bbcae2ef6b63987a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 22, + "timestamp": 1684727876048.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is there an error at 32:30? Shouldn't S be multiplied before (lamda matrix)^100?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk6.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..e1d2d03ebc49dbf2daf0df04bbcae2ef6b63987a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 22, + "timestamp": 1684727876048.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is there an error at 32:30? Shouldn't S be multiplied before (lamda matrix)^100?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk7.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..e1d2d03ebc49dbf2daf0df04bbcae2ef6b63987a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 22, + "timestamp": 1684727876048.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is there an error at 32:30? Shouldn't S be multiplied before (lamda matrix)^100?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk8.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..e1d2d03ebc49dbf2daf0df04bbcae2ef6b63987a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 22, + "timestamp": 1684727876048.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is there an error at 32:30? Shouldn't S be multiplied before (lamda matrix)^100?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk9.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..e1d2d03ebc49dbf2daf0df04bbcae2ef6b63987a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_22_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 22, + "timestamp": 1684727876048.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Is there an error at 32:30? Shouldn't S be multiplied before (lamda matrix)^100?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk0.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..ab64c6792f3f15f4f170829f35dea7b7ccb670e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 23, + "timestamp": 1684727933448.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I have a doubt in Difference equations part. He writes u_0 as a combination of eigen-vectors of A. Why should this be true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk1.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..ab64c6792f3f15f4f170829f35dea7b7ccb670e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 23, + "timestamp": 1684727933448.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I have a doubt in Difference equations part. He writes u_0 as a combination of eigen-vectors of A. Why should this be true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk10.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..ab64c6792f3f15f4f170829f35dea7b7ccb670e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 23, + "timestamp": 1684727933448.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I have a doubt in Difference equations part. He writes u_0 as a combination of eigen-vectors of A. Why should this be true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk11.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..ab64c6792f3f15f4f170829f35dea7b7ccb670e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 23, + "timestamp": 1684727933448.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I have a doubt in Difference equations part. He writes u_0 as a combination of eigen-vectors of A. Why should this be true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk12.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..ab64c6792f3f15f4f170829f35dea7b7ccb670e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 23, + "timestamp": 1684727933448.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I have a doubt in Difference equations part. He writes u_0 as a combination of eigen-vectors of A. Why should this be true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk13.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..e6dd2adcfb179bd03995d167449ba03be085ffa4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk13.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 23, + "timestamp": 1684727933448.0, + "annotatedSourceSentencesIndices": [ + 16 + ], + "names": [ + "annotator2" + ], + "text": "I have a doubt in Difference equations part. He writes u_0 as a combination of eigen-vectors of A. Why should this be true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk14.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..ab64c6792f3f15f4f170829f35dea7b7ccb670e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 23, + "timestamp": 1684727933448.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I have a doubt in Difference equations part. He writes u_0 as a combination of eigen-vectors of A. Why should this be true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk15.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..ab64c6792f3f15f4f170829f35dea7b7ccb670e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 23, + "timestamp": 1684727933448.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I have a doubt in Difference equations part. He writes u_0 as a combination of eigen-vectors of A. Why should this be true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk16.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..ab64c6792f3f15f4f170829f35dea7b7ccb670e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 23, + "timestamp": 1684727933448.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I have a doubt in Difference equations part. He writes u_0 as a combination of eigen-vectors of A. Why should this be true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk17.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..ab64c6792f3f15f4f170829f35dea7b7ccb670e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 23, + "timestamp": 1684727933448.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I have a doubt in Difference equations part. He writes u_0 as a combination of eigen-vectors of A. Why should this be true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk18.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..ab64c6792f3f15f4f170829f35dea7b7ccb670e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 23, + "timestamp": 1684727933448.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I have a doubt in Difference equations part. He writes u_0 as a combination of eigen-vectors of A. Why should this be true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk19.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..ab64c6792f3f15f4f170829f35dea7b7ccb670e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 23, + "timestamp": 1684727933448.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I have a doubt in Difference equations part. He writes u_0 as a combination of eigen-vectors of A. Why should this be true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk2.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..ab64c6792f3f15f4f170829f35dea7b7ccb670e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 23, + "timestamp": 1684727933448.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I have a doubt in Difference equations part. He writes u_0 as a combination of eigen-vectors of A. Why should this be true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk20.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ab64c6792f3f15f4f170829f35dea7b7ccb670e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 23, + "timestamp": 1684727933448.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I have a doubt in Difference equations part. He writes u_0 as a combination of eigen-vectors of A. Why should this be true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk21.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..ab64c6792f3f15f4f170829f35dea7b7ccb670e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 23, + "timestamp": 1684727933448.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I have a doubt in Difference equations part. He writes u_0 as a combination of eigen-vectors of A. Why should this be true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk22.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..ab64c6792f3f15f4f170829f35dea7b7ccb670e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 23, + "timestamp": 1684727933448.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I have a doubt in Difference equations part. He writes u_0 as a combination of eigen-vectors of A. Why should this be true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk23.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..ab64c6792f3f15f4f170829f35dea7b7ccb670e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 23, + "timestamp": 1684727933448.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I have a doubt in Difference equations part. He writes u_0 as a combination of eigen-vectors of A. Why should this be true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk24.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ab64c6792f3f15f4f170829f35dea7b7ccb670e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 23, + "timestamp": 1684727933448.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I have a doubt in Difference equations part. He writes u_0 as a combination of eigen-vectors of A. Why should this be true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk3.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..ab64c6792f3f15f4f170829f35dea7b7ccb670e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 23, + "timestamp": 1684727933448.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I have a doubt in Difference equations part. He writes u_0 as a combination of eigen-vectors of A. Why should this be true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk4.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..ab64c6792f3f15f4f170829f35dea7b7ccb670e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 23, + "timestamp": 1684727933448.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I have a doubt in Difference equations part. He writes u_0 as a combination of eigen-vectors of A. Why should this be true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk5.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..ab64c6792f3f15f4f170829f35dea7b7ccb670e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 23, + "timestamp": 1684727933448.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I have a doubt in Difference equations part. He writes u_0 as a combination of eigen-vectors of A. Why should this be true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk6.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..ab64c6792f3f15f4f170829f35dea7b7ccb670e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 23, + "timestamp": 1684727933448.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I have a doubt in Difference equations part. He writes u_0 as a combination of eigen-vectors of A. Why should this be true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk7.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..ab64c6792f3f15f4f170829f35dea7b7ccb670e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 23, + "timestamp": 1684727933448.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I have a doubt in Difference equations part. He writes u_0 as a combination of eigen-vectors of A. Why should this be true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk8.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..ab64c6792f3f15f4f170829f35dea7b7ccb670e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 23, + "timestamp": 1684727933448.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I have a doubt in Difference equations part. He writes u_0 as a combination of eigen-vectors of A. Why should this be true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk9.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..ab64c6792f3f15f4f170829f35dea7b7ccb670e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_23_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 23, + "timestamp": 1684727933448.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I have a doubt in Difference equations part. He writes u_0 as a combination of eigen-vectors of A. Why should this be true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk0.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..14cbf591b1ca79fd5d894a48ae042345feb72605 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 25, + "timestamp": 1684727944948.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "https://www.youtube.com/watch?v=13r9QY6cmjc#t=29m29s how does one know that u0 can be expressed in terms of eigenvectors, i.e. how do we know what u0 is in the span of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk1.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..14cbf591b1ca79fd5d894a48ae042345feb72605 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 25, + "timestamp": 1684727944948.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "https://www.youtube.com/watch?v=13r9QY6cmjc#t=29m29s how does one know that u0 can be expressed in terms of eigenvectors, i.e. how do we know what u0 is in the span of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk10.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..14cbf591b1ca79fd5d894a48ae042345feb72605 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 25, + "timestamp": 1684727944948.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "https://www.youtube.com/watch?v=13r9QY6cmjc#t=29m29s how does one know that u0 can be expressed in terms of eigenvectors, i.e. how do we know what u0 is in the span of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk11.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..14cbf591b1ca79fd5d894a48ae042345feb72605 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 25, + "timestamp": 1684727944948.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "https://www.youtube.com/watch?v=13r9QY6cmjc#t=29m29s how does one know that u0 can be expressed in terms of eigenvectors, i.e. how do we know what u0 is in the span of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk12.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..14cbf591b1ca79fd5d894a48ae042345feb72605 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 25, + "timestamp": 1684727944948.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "https://www.youtube.com/watch?v=13r9QY6cmjc#t=29m29s how does one know that u0 can be expressed in terms of eigenvectors, i.e. how do we know what u0 is in the span of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk13.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..6cf8069c1a5a6fa51346eaba4953e9222533c384 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk13.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 25, + "timestamp": 1684727944948.0, + "annotatedSourceSentencesIndices": [ + 16 + ], + "names": [ + "annotator2" + ], + "text": "https://www.youtube.com/watch?v=13r9QY6cmjc#t=29m29s how does one know that u0 can be expressed in terms of eigenvectors, i.e. how do we know what u0 is in the span of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk14.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..14cbf591b1ca79fd5d894a48ae042345feb72605 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 25, + "timestamp": 1684727944948.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "https://www.youtube.com/watch?v=13r9QY6cmjc#t=29m29s how does one know that u0 can be expressed in terms of eigenvectors, i.e. how do we know what u0 is in the span of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk15.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..14cbf591b1ca79fd5d894a48ae042345feb72605 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 25, + "timestamp": 1684727944948.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "https://www.youtube.com/watch?v=13r9QY6cmjc#t=29m29s how does one know that u0 can be expressed in terms of eigenvectors, i.e. how do we know what u0 is in the span of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk16.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..14cbf591b1ca79fd5d894a48ae042345feb72605 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 25, + "timestamp": 1684727944948.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "https://www.youtube.com/watch?v=13r9QY6cmjc#t=29m29s how does one know that u0 can be expressed in terms of eigenvectors, i.e. how do we know what u0 is in the span of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk17.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..14cbf591b1ca79fd5d894a48ae042345feb72605 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 25, + "timestamp": 1684727944948.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "https://www.youtube.com/watch?v=13r9QY6cmjc#t=29m29s how does one know that u0 can be expressed in terms of eigenvectors, i.e. how do we know what u0 is in the span of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk18.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..14cbf591b1ca79fd5d894a48ae042345feb72605 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 25, + "timestamp": 1684727944948.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "https://www.youtube.com/watch?v=13r9QY6cmjc#t=29m29s how does one know that u0 can be expressed in terms of eigenvectors, i.e. how do we know what u0 is in the span of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk19.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..14cbf591b1ca79fd5d894a48ae042345feb72605 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 25, + "timestamp": 1684727944948.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "https://www.youtube.com/watch?v=13r9QY6cmjc#t=29m29s how does one know that u0 can be expressed in terms of eigenvectors, i.e. how do we know what u0 is in the span of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk2.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..14cbf591b1ca79fd5d894a48ae042345feb72605 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 25, + "timestamp": 1684727944948.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "https://www.youtube.com/watch?v=13r9QY6cmjc#t=29m29s how does one know that u0 can be expressed in terms of eigenvectors, i.e. how do we know what u0 is in the span of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk20.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..14cbf591b1ca79fd5d894a48ae042345feb72605 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 25, + "timestamp": 1684727944948.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "https://www.youtube.com/watch?v=13r9QY6cmjc#t=29m29s how does one know that u0 can be expressed in terms of eigenvectors, i.e. how do we know what u0 is in the span of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk21.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..14cbf591b1ca79fd5d894a48ae042345feb72605 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 25, + "timestamp": 1684727944948.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "https://www.youtube.com/watch?v=13r9QY6cmjc#t=29m29s how does one know that u0 can be expressed in terms of eigenvectors, i.e. how do we know what u0 is in the span of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk22.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..14cbf591b1ca79fd5d894a48ae042345feb72605 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 25, + "timestamp": 1684727944948.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "https://www.youtube.com/watch?v=13r9QY6cmjc#t=29m29s how does one know that u0 can be expressed in terms of eigenvectors, i.e. how do we know what u0 is in the span of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk23.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..14cbf591b1ca79fd5d894a48ae042345feb72605 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 25, + "timestamp": 1684727944948.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "https://www.youtube.com/watch?v=13r9QY6cmjc#t=29m29s how does one know that u0 can be expressed in terms of eigenvectors, i.e. how do we know what u0 is in the span of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk24.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..14cbf591b1ca79fd5d894a48ae042345feb72605 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 25, + "timestamp": 1684727944948.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "https://www.youtube.com/watch?v=13r9QY6cmjc#t=29m29s how does one know that u0 can be expressed in terms of eigenvectors, i.e. how do we know what u0 is in the span of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk3.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..14cbf591b1ca79fd5d894a48ae042345feb72605 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 25, + "timestamp": 1684727944948.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "https://www.youtube.com/watch?v=13r9QY6cmjc#t=29m29s how does one know that u0 can be expressed in terms of eigenvectors, i.e. how do we know what u0 is in the span of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk4.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..14cbf591b1ca79fd5d894a48ae042345feb72605 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 25, + "timestamp": 1684727944948.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "https://www.youtube.com/watch?v=13r9QY6cmjc#t=29m29s how does one know that u0 can be expressed in terms of eigenvectors, i.e. how do we know what u0 is in the span of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk5.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..14cbf591b1ca79fd5d894a48ae042345feb72605 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 25, + "timestamp": 1684727944948.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "https://www.youtube.com/watch?v=13r9QY6cmjc#t=29m29s how does one know that u0 can be expressed in terms of eigenvectors, i.e. how do we know what u0 is in the span of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk6.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..14cbf591b1ca79fd5d894a48ae042345feb72605 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 25, + "timestamp": 1684727944948.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "https://www.youtube.com/watch?v=13r9QY6cmjc#t=29m29s how does one know that u0 can be expressed in terms of eigenvectors, i.e. how do we know what u0 is in the span of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk7.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..14cbf591b1ca79fd5d894a48ae042345feb72605 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 25, + "timestamp": 1684727944948.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "https://www.youtube.com/watch?v=13r9QY6cmjc#t=29m29s how does one know that u0 can be expressed in terms of eigenvectors, i.e. how do we know what u0 is in the span of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk8.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..14cbf591b1ca79fd5d894a48ae042345feb72605 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 25, + "timestamp": 1684727944948.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "https://www.youtube.com/watch?v=13r9QY6cmjc#t=29m29s how does one know that u0 can be expressed in terms of eigenvectors, i.e. how do we know what u0 is in the span of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk9.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..14cbf591b1ca79fd5d894a48ae042345feb72605 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_25_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 25, + "timestamp": 1684727944948.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "https://www.youtube.com/watch?v=13r9QY6cmjc#t=29m29s how does one know that u0 can be expressed in terms of eigenvectors, i.e. how do we know what u0 is in the span of eigenvectors?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk0.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..fca1dd38b5ef4fe4b69d0e2445a5013d8a3f3107 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 26, + "timestamp": 1684728060182.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In the computation of the Eigen values for A\u00b2, he used A = S\u028cS\u02c9\u00b9 to derive that \u028c\u00b2 represents its Eigen value matrix. However this can be true only if S is invertible for A\u00b2, which need not be always true.\n\nFor example, for the matrix below (say A), the Eigen values are 1, -1(refer previous lecture). This would imply that A\u00b2 has only one Eigen value of 1. This would imply that S has 2 columns which are same (if it has only one column then it is no longer square and hence inverse doesn't apply) and hence non invertible. This implies that this proof cannot be used for all the cases of the matrix A.\n\u00a0_\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 _\u00a0\n\u2502 0\u00a0 1 \u2502\n\u2502\u00a01 \u00a00 \u2502\n \u00af\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00af\nIs there something I'm missing here?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk1.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..fca1dd38b5ef4fe4b69d0e2445a5013d8a3f3107 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 26, + "timestamp": 1684728060182.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In the computation of the Eigen values for A\u00b2, he used A = S\u028cS\u02c9\u00b9 to derive that \u028c\u00b2 represents its Eigen value matrix. However this can be true only if S is invertible for A\u00b2, which need not be always true.\n\nFor example, for the matrix below (say A), the Eigen values are 1, -1(refer previous lecture). This would imply that A\u00b2 has only one Eigen value of 1. This would imply that S has 2 columns which are same (if it has only one column then it is no longer square and hence inverse doesn't apply) and hence non invertible. This implies that this proof cannot be used for all the cases of the matrix A.\n\u00a0_\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 _\u00a0\n\u2502 0\u00a0 1 \u2502\n\u2502\u00a01 \u00a00 \u2502\n \u00af\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00af\nIs there something I'm missing here?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk10.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..fca1dd38b5ef4fe4b69d0e2445a5013d8a3f3107 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 26, + "timestamp": 1684728060182.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In the computation of the Eigen values for A\u00b2, he used A = S\u028cS\u02c9\u00b9 to derive that \u028c\u00b2 represents its Eigen value matrix. However this can be true only if S is invertible for A\u00b2, which need not be always true.\n\nFor example, for the matrix below (say A), the Eigen values are 1, -1(refer previous lecture). This would imply that A\u00b2 has only one Eigen value of 1. This would imply that S has 2 columns which are same (if it has only one column then it is no longer square and hence inverse doesn't apply) and hence non invertible. This implies that this proof cannot be used for all the cases of the matrix A.\n\u00a0_\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 _\u00a0\n\u2502 0\u00a0 1 \u2502\n\u2502\u00a01 \u00a00 \u2502\n \u00af\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00af\nIs there something I'm missing here?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk11.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..fca1dd38b5ef4fe4b69d0e2445a5013d8a3f3107 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 26, + "timestamp": 1684728060182.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In the computation of the Eigen values for A\u00b2, he used A = S\u028cS\u02c9\u00b9 to derive that \u028c\u00b2 represents its Eigen value matrix. However this can be true only if S is invertible for A\u00b2, which need not be always true.\n\nFor example, for the matrix below (say A), the Eigen values are 1, -1(refer previous lecture). This would imply that A\u00b2 has only one Eigen value of 1. This would imply that S has 2 columns which are same (if it has only one column then it is no longer square and hence inverse doesn't apply) and hence non invertible. This implies that this proof cannot be used for all the cases of the matrix A.\n\u00a0_\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 _\u00a0\n\u2502 0\u00a0 1 \u2502\n\u2502\u00a01 \u00a00 \u2502\n \u00af\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00af\nIs there something I'm missing here?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk12.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..fca1dd38b5ef4fe4b69d0e2445a5013d8a3f3107 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 26, + "timestamp": 1684728060182.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In the computation of the Eigen values for A\u00b2, he used A = S\u028cS\u02c9\u00b9 to derive that \u028c\u00b2 represents its Eigen value matrix. However this can be true only if S is invertible for A\u00b2, which need not be always true.\n\nFor example, for the matrix below (say A), the Eigen values are 1, -1(refer previous lecture). This would imply that A\u00b2 has only one Eigen value of 1. This would imply that S has 2 columns which are same (if it has only one column then it is no longer square and hence inverse doesn't apply) and hence non invertible. This implies that this proof cannot be used for all the cases of the matrix A.\n\u00a0_\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 _\u00a0\n\u2502 0\u00a0 1 \u2502\n\u2502\u00a01 \u00a00 \u2502\n \u00af\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00af\nIs there something I'm missing here?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk13.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..fca1dd38b5ef4fe4b69d0e2445a5013d8a3f3107 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 26, + "timestamp": 1684728060182.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In the computation of the Eigen values for A\u00b2, he used A = S\u028cS\u02c9\u00b9 to derive that \u028c\u00b2 represents its Eigen value matrix. However this can be true only if S is invertible for A\u00b2, which need not be always true.\n\nFor example, for the matrix below (say A), the Eigen values are 1, -1(refer previous lecture). This would imply that A\u00b2 has only one Eigen value of 1. This would imply that S has 2 columns which are same (if it has only one column then it is no longer square and hence inverse doesn't apply) and hence non invertible. This implies that this proof cannot be used for all the cases of the matrix A.\n\u00a0_\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 _\u00a0\n\u2502 0\u00a0 1 \u2502\n\u2502\u00a01 \u00a00 \u2502\n \u00af\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00af\nIs there something I'm missing here?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk14.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..fca1dd38b5ef4fe4b69d0e2445a5013d8a3f3107 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 26, + "timestamp": 1684728060182.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In the computation of the Eigen values for A\u00b2, he used A = S\u028cS\u02c9\u00b9 to derive that \u028c\u00b2 represents its Eigen value matrix. However this can be true only if S is invertible for A\u00b2, which need not be always true.\n\nFor example, for the matrix below (say A), the Eigen values are 1, -1(refer previous lecture). This would imply that A\u00b2 has only one Eigen value of 1. This would imply that S has 2 columns which are same (if it has only one column then it is no longer square and hence inverse doesn't apply) and hence non invertible. This implies that this proof cannot be used for all the cases of the matrix A.\n\u00a0_\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 _\u00a0\n\u2502 0\u00a0 1 \u2502\n\u2502\u00a01 \u00a00 \u2502\n \u00af\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00af\nIs there something I'm missing here?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk15.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..fca1dd38b5ef4fe4b69d0e2445a5013d8a3f3107 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 26, + "timestamp": 1684728060182.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In the computation of the Eigen values for A\u00b2, he used A = S\u028cS\u02c9\u00b9 to derive that \u028c\u00b2 represents its Eigen value matrix. However this can be true only if S is invertible for A\u00b2, which need not be always true.\n\nFor example, for the matrix below (say A), the Eigen values are 1, -1(refer previous lecture). This would imply that A\u00b2 has only one Eigen value of 1. This would imply that S has 2 columns which are same (if it has only one column then it is no longer square and hence inverse doesn't apply) and hence non invertible. This implies that this proof cannot be used for all the cases of the matrix A.\n\u00a0_\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 _\u00a0\n\u2502 0\u00a0 1 \u2502\n\u2502\u00a01 \u00a00 \u2502\n \u00af\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00af\nIs there something I'm missing here?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk16.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..fca1dd38b5ef4fe4b69d0e2445a5013d8a3f3107 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 26, + "timestamp": 1684728060182.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In the computation of the Eigen values for A\u00b2, he used A = S\u028cS\u02c9\u00b9 to derive that \u028c\u00b2 represents its Eigen value matrix. However this can be true only if S is invertible for A\u00b2, which need not be always true.\n\nFor example, for the matrix below (say A), the Eigen values are 1, -1(refer previous lecture). This would imply that A\u00b2 has only one Eigen value of 1. This would imply that S has 2 columns which are same (if it has only one column then it is no longer square and hence inverse doesn't apply) and hence non invertible. This implies that this proof cannot be used for all the cases of the matrix A.\n\u00a0_\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 _\u00a0\n\u2502 0\u00a0 1 \u2502\n\u2502\u00a01 \u00a00 \u2502\n \u00af\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00af\nIs there something I'm missing here?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk17.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..fca1dd38b5ef4fe4b69d0e2445a5013d8a3f3107 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 26, + "timestamp": 1684728060182.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In the computation of the Eigen values for A\u00b2, he used A = S\u028cS\u02c9\u00b9 to derive that \u028c\u00b2 represents its Eigen value matrix. However this can be true only if S is invertible for A\u00b2, which need not be always true.\n\nFor example, for the matrix below (say A), the Eigen values are 1, -1(refer previous lecture). This would imply that A\u00b2 has only one Eigen value of 1. This would imply that S has 2 columns which are same (if it has only one column then it is no longer square and hence inverse doesn't apply) and hence non invertible. This implies that this proof cannot be used for all the cases of the matrix A.\n\u00a0_\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 _\u00a0\n\u2502 0\u00a0 1 \u2502\n\u2502\u00a01 \u00a00 \u2502\n \u00af\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00af\nIs there something I'm missing here?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk18.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..fca1dd38b5ef4fe4b69d0e2445a5013d8a3f3107 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 26, + "timestamp": 1684728060182.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In the computation of the Eigen values for A\u00b2, he used A = S\u028cS\u02c9\u00b9 to derive that \u028c\u00b2 represents its Eigen value matrix. However this can be true only if S is invertible for A\u00b2, which need not be always true.\n\nFor example, for the matrix below (say A), the Eigen values are 1, -1(refer previous lecture). This would imply that A\u00b2 has only one Eigen value of 1. This would imply that S has 2 columns which are same (if it has only one column then it is no longer square and hence inverse doesn't apply) and hence non invertible. This implies that this proof cannot be used for all the cases of the matrix A.\n\u00a0_\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 _\u00a0\n\u2502 0\u00a0 1 \u2502\n\u2502\u00a01 \u00a00 \u2502\n \u00af\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00af\nIs there something I'm missing here?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk19.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..fca1dd38b5ef4fe4b69d0e2445a5013d8a3f3107 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 26, + "timestamp": 1684728060182.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In the computation of the Eigen values for A\u00b2, he used A = S\u028cS\u02c9\u00b9 to derive that \u028c\u00b2 represents its Eigen value matrix. However this can be true only if S is invertible for A\u00b2, which need not be always true.\n\nFor example, for the matrix below (say A), the Eigen values are 1, -1(refer previous lecture). This would imply that A\u00b2 has only one Eigen value of 1. This would imply that S has 2 columns which are same (if it has only one column then it is no longer square and hence inverse doesn't apply) and hence non invertible. This implies that this proof cannot be used for all the cases of the matrix A.\n\u00a0_\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 _\u00a0\n\u2502 0\u00a0 1 \u2502\n\u2502\u00a01 \u00a00 \u2502\n \u00af\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00af\nIs there something I'm missing here?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk2.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..fca1dd38b5ef4fe4b69d0e2445a5013d8a3f3107 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 26, + "timestamp": 1684728060182.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In the computation of the Eigen values for A\u00b2, he used A = S\u028cS\u02c9\u00b9 to derive that \u028c\u00b2 represents its Eigen value matrix. However this can be true only if S is invertible for A\u00b2, which need not be always true.\n\nFor example, for the matrix below (say A), the Eigen values are 1, -1(refer previous lecture). This would imply that A\u00b2 has only one Eigen value of 1. This would imply that S has 2 columns which are same (if it has only one column then it is no longer square and hence inverse doesn't apply) and hence non invertible. This implies that this proof cannot be used for all the cases of the matrix A.\n\u00a0_\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 _\u00a0\n\u2502 0\u00a0 1 \u2502\n\u2502\u00a01 \u00a00 \u2502\n \u00af\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00af\nIs there something I'm missing here?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk20.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..fca1dd38b5ef4fe4b69d0e2445a5013d8a3f3107 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 26, + "timestamp": 1684728060182.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In the computation of the Eigen values for A\u00b2, he used A = S\u028cS\u02c9\u00b9 to derive that \u028c\u00b2 represents its Eigen value matrix. However this can be true only if S is invertible for A\u00b2, which need not be always true.\n\nFor example, for the matrix below (say A), the Eigen values are 1, -1(refer previous lecture). This would imply that A\u00b2 has only one Eigen value of 1. This would imply that S has 2 columns which are same (if it has only one column then it is no longer square and hence inverse doesn't apply) and hence non invertible. This implies that this proof cannot be used for all the cases of the matrix A.\n\u00a0_\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 _\u00a0\n\u2502 0\u00a0 1 \u2502\n\u2502\u00a01 \u00a00 \u2502\n \u00af\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00af\nIs there something I'm missing here?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk21.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..fca1dd38b5ef4fe4b69d0e2445a5013d8a3f3107 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 26, + "timestamp": 1684728060182.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In the computation of the Eigen values for A\u00b2, he used A = S\u028cS\u02c9\u00b9 to derive that \u028c\u00b2 represents its Eigen value matrix. However this can be true only if S is invertible for A\u00b2, which need not be always true.\n\nFor example, for the matrix below (say A), the Eigen values are 1, -1(refer previous lecture). This would imply that A\u00b2 has only one Eigen value of 1. This would imply that S has 2 columns which are same (if it has only one column then it is no longer square and hence inverse doesn't apply) and hence non invertible. This implies that this proof cannot be used for all the cases of the matrix A.\n\u00a0_\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 _\u00a0\n\u2502 0\u00a0 1 \u2502\n\u2502\u00a01 \u00a00 \u2502\n \u00af\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00af\nIs there something I'm missing here?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk22.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..fca1dd38b5ef4fe4b69d0e2445a5013d8a3f3107 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 26, + "timestamp": 1684728060182.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In the computation of the Eigen values for A\u00b2, he used A = S\u028cS\u02c9\u00b9 to derive that \u028c\u00b2 represents its Eigen value matrix. However this can be true only if S is invertible for A\u00b2, which need not be always true.\n\nFor example, for the matrix below (say A), the Eigen values are 1, -1(refer previous lecture). This would imply that A\u00b2 has only one Eigen value of 1. This would imply that S has 2 columns which are same (if it has only one column then it is no longer square and hence inverse doesn't apply) and hence non invertible. This implies that this proof cannot be used for all the cases of the matrix A.\n\u00a0_\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 _\u00a0\n\u2502 0\u00a0 1 \u2502\n\u2502\u00a01 \u00a00 \u2502\n \u00af\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00af\nIs there something I'm missing here?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk23.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..fca1dd38b5ef4fe4b69d0e2445a5013d8a3f3107 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 26, + "timestamp": 1684728060182.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In the computation of the Eigen values for A\u00b2, he used A = S\u028cS\u02c9\u00b9 to derive that \u028c\u00b2 represents its Eigen value matrix. However this can be true only if S is invertible for A\u00b2, which need not be always true.\n\nFor example, for the matrix below (say A), the Eigen values are 1, -1(refer previous lecture). This would imply that A\u00b2 has only one Eigen value of 1. This would imply that S has 2 columns which are same (if it has only one column then it is no longer square and hence inverse doesn't apply) and hence non invertible. This implies that this proof cannot be used for all the cases of the matrix A.\n\u00a0_\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 _\u00a0\n\u2502 0\u00a0 1 \u2502\n\u2502\u00a01 \u00a00 \u2502\n \u00af\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00af\nIs there something I'm missing here?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk24.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..fca1dd38b5ef4fe4b69d0e2445a5013d8a3f3107 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 26, + "timestamp": 1684728060182.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In the computation of the Eigen values for A\u00b2, he used A = S\u028cS\u02c9\u00b9 to derive that \u028c\u00b2 represents its Eigen value matrix. However this can be true only if S is invertible for A\u00b2, which need not be always true.\n\nFor example, for the matrix below (say A), the Eigen values are 1, -1(refer previous lecture). This would imply that A\u00b2 has only one Eigen value of 1. This would imply that S has 2 columns which are same (if it has only one column then it is no longer square and hence inverse doesn't apply) and hence non invertible. This implies that this proof cannot be used for all the cases of the matrix A.\n\u00a0_\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 _\u00a0\n\u2502 0\u00a0 1 \u2502\n\u2502\u00a01 \u00a00 \u2502\n \u00af\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00af\nIs there something I'm missing here?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk3.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..fca1dd38b5ef4fe4b69d0e2445a5013d8a3f3107 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 26, + "timestamp": 1684728060182.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In the computation of the Eigen values for A\u00b2, he used A = S\u028cS\u02c9\u00b9 to derive that \u028c\u00b2 represents its Eigen value matrix. However this can be true only if S is invertible for A\u00b2, which need not be always true.\n\nFor example, for the matrix below (say A), the Eigen values are 1, -1(refer previous lecture). This would imply that A\u00b2 has only one Eigen value of 1. This would imply that S has 2 columns which are same (if it has only one column then it is no longer square and hence inverse doesn't apply) and hence non invertible. This implies that this proof cannot be used for all the cases of the matrix A.\n\u00a0_\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 _\u00a0\n\u2502 0\u00a0 1 \u2502\n\u2502\u00a01 \u00a00 \u2502\n \u00af\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00af\nIs there something I'm missing here?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk4.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..fca1dd38b5ef4fe4b69d0e2445a5013d8a3f3107 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 26, + "timestamp": 1684728060182.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In the computation of the Eigen values for A\u00b2, he used A = S\u028cS\u02c9\u00b9 to derive that \u028c\u00b2 represents its Eigen value matrix. However this can be true only if S is invertible for A\u00b2, which need not be always true.\n\nFor example, for the matrix below (say A), the Eigen values are 1, -1(refer previous lecture). This would imply that A\u00b2 has only one Eigen value of 1. This would imply that S has 2 columns which are same (if it has only one column then it is no longer square and hence inverse doesn't apply) and hence non invertible. This implies that this proof cannot be used for all the cases of the matrix A.\n\u00a0_\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 _\u00a0\n\u2502 0\u00a0 1 \u2502\n\u2502\u00a01 \u00a00 \u2502\n \u00af\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00af\nIs there something I'm missing here?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk5.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..f46561804d83edf2c8ad3c9280fc80103fe83a0e --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk5.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 26, + "timestamp": 1684728060182.0, + "annotatedSourceSentencesIndices": [ + 5, + 6 + ], + "names": [ + "annotator2" + ], + "text": "In the computation of the Eigen values for A\u00b2, he used A = S\u028cS\u02c9\u00b9 to derive that \u028c\u00b2 represents its Eigen value matrix. However this can be true only if S is invertible for A\u00b2, which need not be always true.\n\nFor example, for the matrix below (say A), the Eigen values are 1, -1(refer previous lecture). This would imply that A\u00b2 has only one Eigen value of 1. This would imply that S has 2 columns which are same (if it has only one column then it is no longer square and hence inverse doesn't apply) and hence non invertible. This implies that this proof cannot be used for all the cases of the matrix A.\n\u00a0_\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 _\u00a0\n\u2502 0\u00a0 1 \u2502\n\u2502\u00a01 \u00a00 \u2502\n \u00af\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00af\nIs there something I'm missing here?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk6.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..fca1dd38b5ef4fe4b69d0e2445a5013d8a3f3107 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 26, + "timestamp": 1684728060182.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In the computation of the Eigen values for A\u00b2, he used A = S\u028cS\u02c9\u00b9 to derive that \u028c\u00b2 represents its Eigen value matrix. However this can be true only if S is invertible for A\u00b2, which need not be always true.\n\nFor example, for the matrix below (say A), the Eigen values are 1, -1(refer previous lecture). This would imply that A\u00b2 has only one Eigen value of 1. This would imply that S has 2 columns which are same (if it has only one column then it is no longer square and hence inverse doesn't apply) and hence non invertible. This implies that this proof cannot be used for all the cases of the matrix A.\n\u00a0_\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 _\u00a0\n\u2502 0\u00a0 1 \u2502\n\u2502\u00a01 \u00a00 \u2502\n \u00af\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00af\nIs there something I'm missing here?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk7.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..fca1dd38b5ef4fe4b69d0e2445a5013d8a3f3107 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 26, + "timestamp": 1684728060182.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In the computation of the Eigen values for A\u00b2, he used A = S\u028cS\u02c9\u00b9 to derive that \u028c\u00b2 represents its Eigen value matrix. However this can be true only if S is invertible for A\u00b2, which need not be always true.\n\nFor example, for the matrix below (say A), the Eigen values are 1, -1(refer previous lecture). This would imply that A\u00b2 has only one Eigen value of 1. This would imply that S has 2 columns which are same (if it has only one column then it is no longer square and hence inverse doesn't apply) and hence non invertible. This implies that this proof cannot be used for all the cases of the matrix A.\n\u00a0_\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 _\u00a0\n\u2502 0\u00a0 1 \u2502\n\u2502\u00a01 \u00a00 \u2502\n \u00af\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00af\nIs there something I'm missing here?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk8.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..fca1dd38b5ef4fe4b69d0e2445a5013d8a3f3107 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 26, + "timestamp": 1684728060182.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In the computation of the Eigen values for A\u00b2, he used A = S\u028cS\u02c9\u00b9 to derive that \u028c\u00b2 represents its Eigen value matrix. However this can be true only if S is invertible for A\u00b2, which need not be always true.\n\nFor example, for the matrix below (say A), the Eigen values are 1, -1(refer previous lecture). This would imply that A\u00b2 has only one Eigen value of 1. This would imply that S has 2 columns which are same (if it has only one column then it is no longer square and hence inverse doesn't apply) and hence non invertible. This implies that this proof cannot be used for all the cases of the matrix A.\n\u00a0_\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 _\u00a0\n\u2502 0\u00a0 1 \u2502\n\u2502\u00a01 \u00a00 \u2502\n \u00af\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00af\nIs there something I'm missing here?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk9.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..fca1dd38b5ef4fe4b69d0e2445a5013d8a3f3107 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_26_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 26, + "timestamp": 1684728060182.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In the computation of the Eigen values for A\u00b2, he used A = S\u028cS\u02c9\u00b9 to derive that \u028c\u00b2 represents its Eigen value matrix. However this can be true only if S is invertible for A\u00b2, which need not be always true.\n\nFor example, for the matrix below (say A), the Eigen values are 1, -1(refer previous lecture). This would imply that A\u00b2 has only one Eigen value of 1. This would imply that S has 2 columns which are same (if it has only one column then it is no longer square and hence inverse doesn't apply) and hence non invertible. This implies that this proof cannot be used for all the cases of the matrix A.\n\u00a0_\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 _\u00a0\n\u2502 0\u00a0 1 \u2502\n\u2502\u00a01 \u00a00 \u2502\n \u00af\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00af\nIs there something I'm missing here?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk0.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..58f34b82138942902403955aed5f891cd9b67ca1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 27, + "timestamp": 1684728093599.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "45:50\nWhy does he add the constant c1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk1.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..58f34b82138942902403955aed5f891cd9b67ca1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 27, + "timestamp": 1684728093599.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "45:50\nWhy does he add the constant c1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk10.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..58f34b82138942902403955aed5f891cd9b67ca1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 27, + "timestamp": 1684728093599.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "45:50\nWhy does he add the constant c1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk11.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..58f34b82138942902403955aed5f891cd9b67ca1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 27, + "timestamp": 1684728093599.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "45:50\nWhy does he add the constant c1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk12.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..58f34b82138942902403955aed5f891cd9b67ca1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 27, + "timestamp": 1684728093599.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "45:50\nWhy does he add the constant c1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk13.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..58f34b82138942902403955aed5f891cd9b67ca1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 27, + "timestamp": 1684728093599.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "45:50\nWhy does he add the constant c1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk14.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..58f34b82138942902403955aed5f891cd9b67ca1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 27, + "timestamp": 1684728093599.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "45:50\nWhy does he add the constant c1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk15.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..58f34b82138942902403955aed5f891cd9b67ca1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 27, + "timestamp": 1684728093599.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "45:50\nWhy does he add the constant c1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk16.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..58f34b82138942902403955aed5f891cd9b67ca1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 27, + "timestamp": 1684728093599.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "45:50\nWhy does he add the constant c1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk17.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..58f34b82138942902403955aed5f891cd9b67ca1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 27, + "timestamp": 1684728093599.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "45:50\nWhy does he add the constant c1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk18.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..58f34b82138942902403955aed5f891cd9b67ca1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_27_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 27, + "timestamp": 1684728093599.0, + 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I think A^2 should be (S Lambda S^-1)^T (S Lambda S^-1), the result differs from the one on the blackboard. Could someone explain this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk1.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..9afce9c3da329baaaa61ef63fe905555eea93af6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 2, + "timestamp": 1684723273690.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand 11:25 why A square can be written in the way on the blackboard. I think A^2 should be (S Lambda S^-1)^T (S Lambda S^-1), the result differs from the one on the blackboard. Could someone explain this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk10.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..9afce9c3da329baaaa61ef63fe905555eea93af6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 2, + "timestamp": 1684723273690.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand 11:25 why A square can be written in the way on the blackboard. I think A^2 should be (S Lambda S^-1)^T (S Lambda S^-1), the result differs from the one on the blackboard. Could someone explain this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk11.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..9afce9c3da329baaaa61ef63fe905555eea93af6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 2, + "timestamp": 1684723273690.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand 11:25 why A square can be written in the way on the blackboard. I think A^2 should be (S Lambda S^-1)^T (S Lambda S^-1), the result differs from the one on the blackboard. Could someone explain this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk12.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..9afce9c3da329baaaa61ef63fe905555eea93af6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 2, + "timestamp": 1684723273690.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand 11:25 why A square can be written in the way on the blackboard. I think A^2 should be (S Lambda S^-1)^T (S Lambda S^-1), the result differs from the one on the blackboard. 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Could someone explain this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk14.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..9afce9c3da329baaaa61ef63fe905555eea93af6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 2, + "timestamp": 1684723273690.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand 11:25 why A square can be written in the way on the blackboard. I think A^2 should be (S Lambda S^-1)^T (S Lambda S^-1), the result differs from the one on the blackboard. Could someone explain this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk15.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..9afce9c3da329baaaa61ef63fe905555eea93af6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 2, + "timestamp": 1684723273690.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand 11:25 why A square can be written in the way on the blackboard. I think A^2 should be (S Lambda S^-1)^T (S Lambda S^-1), the result differs from the one on the blackboard. Could someone explain this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk16.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..9afce9c3da329baaaa61ef63fe905555eea93af6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 2, + "timestamp": 1684723273690.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand 11:25 why A square can be written in the way on the blackboard. I think A^2 should be (S Lambda S^-1)^T (S Lambda S^-1), the result differs from the one on the blackboard. Could someone explain this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk17.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..9afce9c3da329baaaa61ef63fe905555eea93af6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 2, + "timestamp": 1684723273690.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand 11:25 why A square can be written in the way on the blackboard. I think A^2 should be (S Lambda S^-1)^T (S Lambda S^-1), the result differs from the one on the blackboard. Could someone explain this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk18.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..9afce9c3da329baaaa61ef63fe905555eea93af6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 2, + "timestamp": 1684723273690.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand 11:25 why A square can be written in the way on the blackboard. I think A^2 should be (S Lambda S^-1)^T (S Lambda S^-1), the result differs from the one on the blackboard. Could someone explain this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk19.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..9afce9c3da329baaaa61ef63fe905555eea93af6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 2, + "timestamp": 1684723273690.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand 11:25 why A square can be written in the way on the blackboard. I think A^2 should be (S Lambda S^-1)^T (S Lambda S^-1), the result differs from the one on the blackboard. Could someone explain this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk2.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..9afce9c3da329baaaa61ef63fe905555eea93af6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 2, + "timestamp": 1684723273690.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand 11:25 why A square can be written in the way on the blackboard. I think A^2 should be (S Lambda S^-1)^T (S Lambda S^-1), the result differs from the one on the blackboard. Could someone explain this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk20.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..9afce9c3da329baaaa61ef63fe905555eea93af6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 2, + "timestamp": 1684723273690.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand 11:25 why A square can be written in the way on the blackboard. I think A^2 should be (S Lambda S^-1)^T (S Lambda S^-1), the result differs from the one on the blackboard. Could someone explain this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk21.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..9afce9c3da329baaaa61ef63fe905555eea93af6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 2, + "timestamp": 1684723273690.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand 11:25 why A square can be written in the way on the blackboard. I think A^2 should be (S Lambda S^-1)^T (S Lambda S^-1), the result differs from the one on the blackboard. Could someone explain this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk22.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..9afce9c3da329baaaa61ef63fe905555eea93af6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 2, + "timestamp": 1684723273690.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand 11:25 why A square can be written in the way on the blackboard. I think A^2 should be (S Lambda S^-1)^T (S Lambda S^-1), the result differs from the one on the blackboard. Could someone explain this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk23.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..9afce9c3da329baaaa61ef63fe905555eea93af6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 2, + "timestamp": 1684723273690.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand 11:25 why A square can be written in the way on the blackboard. I think A^2 should be (S Lambda S^-1)^T (S Lambda S^-1), the result differs from the one on the blackboard. Could someone explain this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk24.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9afce9c3da329baaaa61ef63fe905555eea93af6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 2, + "timestamp": 1684723273690.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand 11:25 why A square can be written in the way on the blackboard. I think A^2 should be (S Lambda S^-1)^T (S Lambda S^-1), the result differs from the one on the blackboard. Could someone explain this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk3.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..9afce9c3da329baaaa61ef63fe905555eea93af6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 2, + "timestamp": 1684723273690.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand 11:25 why A square can be written in the way on the blackboard. I think A^2 should be (S Lambda S^-1)^T (S Lambda S^-1), the result differs from the one on the blackboard. Could someone explain this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk4.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..9afce9c3da329baaaa61ef63fe905555eea93af6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 2, + "timestamp": 1684723273690.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand 11:25 why A square can be written in the way on the blackboard. I think A^2 should be (S Lambda S^-1)^T (S Lambda S^-1), the result differs from the one on the blackboard. Could someone explain this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk5.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5a093afd6ebe4bc08b8c50e1de847089901b08fe --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk5.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 2, + "timestamp": 1684723273690.0, + "annotatedSourceSentencesIndices": [ + 5, + 6 + ], + "names": [ + "annotator2" + ], + "text": "I don't understand 11:25 why A square can be written in the way on the blackboard. I think A^2 should be (S Lambda S^-1)^T (S Lambda S^-1), the result differs from the one on the blackboard. Could someone explain this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk6.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9afce9c3da329baaaa61ef63fe905555eea93af6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 2, + "timestamp": 1684723273690.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand 11:25 why A square can be written in the way on the blackboard. I think A^2 should be (S Lambda S^-1)^T (S Lambda S^-1), the result differs from the one on the blackboard. Could someone explain this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk7.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..9afce9c3da329baaaa61ef63fe905555eea93af6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 2, + "timestamp": 1684723273690.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand 11:25 why A square can be written in the way on the blackboard. I think A^2 should be (S Lambda S^-1)^T (S Lambda S^-1), the result differs from the one on the blackboard. Could someone explain this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk8.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..9afce9c3da329baaaa61ef63fe905555eea93af6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 2, + "timestamp": 1684723273690.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand 11:25 why A square can be written in the way on the blackboard. I think A^2 should be (S Lambda S^-1)^T (S Lambda S^-1), the result differs from the one on the blackboard. Could someone explain this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk9.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..9afce9c3da329baaaa61ef63fe905555eea93af6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_2_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 2, + "timestamp": 1684723273690.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand 11:25 why A square can be written in the way on the blackboard. I think A^2 should be (S Lambda S^-1)^T (S Lambda S^-1), the result differs from the one on the blackboard. Could someone explain this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_30_chunk0.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_30_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6fcf4c5fea1df2973846c8cd12b4c55cda894554 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_30_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 30, + "timestamp": 1684728116666.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why the skew-symmetric matrix have zero or imaginary eigenvalue?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_30_chunk1.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_30_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..6fcf4c5fea1df2973846c8cd12b4c55cda894554 --- /dev/null +++ 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"annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why the skew-symmetric matrix have zero or imaginary eigenvalue?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_30_chunk16.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_30_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..6fcf4c5fea1df2973846c8cd12b4c55cda894554 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_30_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 30, + "timestamp": 1684728116666.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why the skew-symmetric matrix have zero or imaginary eigenvalue?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_30_chunk17.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_30_chunk17.json new file mode 100644 index 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skew-symmetric matrix have zero or imaginary eigenvalue?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_30_chunk19.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_30_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..6fcf4c5fea1df2973846c8cd12b4c55cda894554 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_30_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 30, + "timestamp": 1684728116666.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why the skew-symmetric matrix have zero or imaginary eigenvalue?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_30_chunk2.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_30_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6fcf4c5fea1df2973846c8cd12b4c55cda894554 --- /dev/null +++ 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First component, (1-lambda)*lambda+1 is not 0 or different from lambda^2 - lambda -1." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_31_chunk23.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_31_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..66b37619661342236a4110bf95a9031e301e66b8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_31_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 31, + "timestamp": 1684728216400.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Could someone explain why vector, lambda and 1 is a solution to the nullspace at 48:43? First component, (1-lambda)*lambda+1 is not 0 or different from lambda^2 - lambda -1." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_31_chunk24.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_31_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..66b37619661342236a4110bf95a9031e301e66b8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_31_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 31, + "timestamp": 1684728216400.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Could someone explain why vector, lambda and 1 is a solution to the nullspace at 48:43? First component, (1-lambda)*lambda+1 is not 0 or different from lambda^2 - lambda -1." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_31_chunk3.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_31_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..66b37619661342236a4110bf95a9031e301e66b8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_31_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 31, + "timestamp": 1684728216400.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Could someone explain why vector, lambda and 1 is a solution to the nullspace at 48:43? First component, (1-lambda)*lambda+1 is not 0 or different from lambda^2 - lambda -1." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_31_chunk4.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_31_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..66b37619661342236a4110bf95a9031e301e66b8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_31_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 31, + "timestamp": 1684728216400.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Could someone explain why vector, lambda and 1 is a solution to the nullspace at 48:43? First component, (1-lambda)*lambda+1 is not 0 or different from lambda^2 - lambda -1." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_31_chunk5.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_31_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..66b37619661342236a4110bf95a9031e301e66b8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_31_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 31, + "timestamp": 1684728216400.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Could someone explain why vector, lambda and 1 is a solution to the nullspace at 48:43? First component, (1-lambda)*lambda+1 is not 0 or different from lambda^2 - lambda -1." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_31_chunk6.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_31_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..66b37619661342236a4110bf95a9031e301e66b8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_31_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 31, + "timestamp": 1684728216400.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Could someone explain why vector, lambda and 1 is a solution to the nullspace at 48:43? First component, (1-lambda)*lambda+1 is not 0 or different from lambda^2 - lambda -1." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_31_chunk7.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_31_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..66b37619661342236a4110bf95a9031e301e66b8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_31_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 31, + "timestamp": 1684728216400.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Could someone explain why vector, lambda and 1 is a solution to the nullspace at 48:43? First component, (1-lambda)*lambda+1 is not 0 or different from lambda^2 - lambda -1." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_31_chunk8.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_31_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..66b37619661342236a4110bf95a9031e301e66b8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_31_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 31, + "timestamp": 1684728216400.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Could someone explain why vector, lambda and 1 is a solution to the nullspace at 48:43? First component, (1-lambda)*lambda+1 is not 0 or different from lambda^2 - lambda -1." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_31_chunk9.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_31_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..66b37619661342236a4110bf95a9031e301e66b8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_31_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 31, + "timestamp": 1684728216400.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Could someone explain why vector, lambda and 1 is a solution to the nullspace at 48:43? First component, (1-lambda)*lambda+1 is not 0 or different from lambda^2 - lambda -1." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk0.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..f964f3d6deee2411ee70dbdf73a266014255532d --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 32, + "timestamp": 1684728378616.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 44:00 why summation of both eigen values are 1?? have i missed any concept behind this?? : (" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk1.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..f964f3d6deee2411ee70dbdf73a266014255532d --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 32, + "timestamp": 1684728378616.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 44:00 why summation of both eigen values are 1?? have i missed any concept behind this?? : (" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk10.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..f964f3d6deee2411ee70dbdf73a266014255532d --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 32, + "timestamp": 1684728378616.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 44:00 why summation of both eigen values are 1?? have i missed any concept behind this?? : (" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk11.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..f964f3d6deee2411ee70dbdf73a266014255532d --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 32, + "timestamp": 1684728378616.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 44:00 why summation of both eigen values are 1?? have i missed any concept behind this?? : (" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk12.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..f964f3d6deee2411ee70dbdf73a266014255532d --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 32, + "timestamp": 1684728378616.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 44:00 why summation of both eigen values are 1?? have i missed any concept behind this?? : (" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk13.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..f964f3d6deee2411ee70dbdf73a266014255532d --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 32, + "timestamp": 1684728378616.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 44:00 why summation of both eigen values are 1?? have i missed any concept behind this?? : (" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk14.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..f964f3d6deee2411ee70dbdf73a266014255532d --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 32, + "timestamp": 1684728378616.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 44:00 why summation of both eigen values are 1?? have i missed any concept behind this?? : (" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk15.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..f964f3d6deee2411ee70dbdf73a266014255532d --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 32, + "timestamp": 1684728378616.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 44:00 why summation of both eigen values are 1?? have i missed any concept behind this?? : (" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk16.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f964f3d6deee2411ee70dbdf73a266014255532d --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 32, + "timestamp": 1684728378616.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 44:00 why summation of both eigen values are 1?? have i missed any concept behind this?? : (" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk17.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..f964f3d6deee2411ee70dbdf73a266014255532d --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 32, + "timestamp": 1684728378616.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 44:00 why summation of both eigen values are 1?? have i missed any concept behind this?? : (" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk18.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..f964f3d6deee2411ee70dbdf73a266014255532d --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 32, + "timestamp": 1684728378616.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 44:00 why summation of both eigen values are 1?? have i missed any concept behind this?? : (" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk19.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..f964f3d6deee2411ee70dbdf73a266014255532d --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 32, + "timestamp": 1684728378616.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 44:00 why summation of both eigen values are 1?? have i missed any concept behind this?? : (" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk2.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..f964f3d6deee2411ee70dbdf73a266014255532d --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 32, + "timestamp": 1684728378616.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 44:00 why summation of both eigen values are 1?? have i missed any concept behind this?? : (" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk20.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583014ae21fb8eb7cab8fb86d7e98751d4275c6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk20.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 32, + "timestamp": 1684728378616.0, + "annotatedSourceSentencesIndices": [ + 13 + ], + "names": [ + "annotator2" + ], + "text": "@ 44:00 why summation of both eigen values are 1?? have i missed any concept behind this?? : (" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk21.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f964f3d6deee2411ee70dbdf73a266014255532d --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 32, + "timestamp": 1684728378616.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 44:00 why summation of both eigen values are 1?? have i missed any concept behind this?? : (" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk22.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..f964f3d6deee2411ee70dbdf73a266014255532d --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 32, + "timestamp": 1684728378616.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 44:00 why summation of both eigen values are 1?? have i missed any concept behind this?? : (" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk23.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..f964f3d6deee2411ee70dbdf73a266014255532d --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 32, + "timestamp": 1684728378616.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 44:00 why summation of both eigen values are 1?? have i missed any concept behind this?? : (" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk24.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..f964f3d6deee2411ee70dbdf73a266014255532d --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 32, + "timestamp": 1684728378616.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 44:00 why summation of both eigen values are 1?? have i missed any concept behind this?? : (" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk3.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..f964f3d6deee2411ee70dbdf73a266014255532d --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 32, + "timestamp": 1684728378616.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 44:00 why summation of both eigen values are 1?? have i missed any concept behind this?? : (" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk4.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..f964f3d6deee2411ee70dbdf73a266014255532d --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 32, + "timestamp": 1684728378616.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 44:00 why summation of both eigen values are 1?? have i missed any concept behind this?? : (" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk5.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..f964f3d6deee2411ee70dbdf73a266014255532d --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 32, + "timestamp": 1684728378616.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 44:00 why summation of both eigen values are 1?? have i missed any concept behind this?? : (" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk6.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..f964f3d6deee2411ee70dbdf73a266014255532d --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 32, + "timestamp": 1684728378616.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 44:00 why summation of both eigen values are 1?? have i missed any concept behind this?? : (" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk7.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..f964f3d6deee2411ee70dbdf73a266014255532d --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 32, + "timestamp": 1684728378616.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 44:00 why summation of both eigen values are 1?? have i missed any concept behind this?? : (" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk8.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f964f3d6deee2411ee70dbdf73a266014255532d --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 32, + "timestamp": 1684728378616.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 44:00 why summation of both eigen values are 1?? have i missed any concept behind this?? : (" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk9.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..f964f3d6deee2411ee70dbdf73a266014255532d --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_32_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 32, + "timestamp": 1684728378616.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 44:00 why summation of both eigen values are 1?? have i missed any concept behind this?? : (" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk0.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..27fc1423d7760a96f4373fc4649069b67ba3f89a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 36, + "timestamp": 1684728416886.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone direct me to a good proof for 19:36?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk1.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..27fc1423d7760a96f4373fc4649069b67ba3f89a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 36, + "timestamp": 1684728416886.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone direct me to a good proof for 19:36?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk10.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..27fc1423d7760a96f4373fc4649069b67ba3f89a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 36, + "timestamp": 1684728416886.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone direct me to a good proof for 19:36?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk11.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..27fc1423d7760a96f4373fc4649069b67ba3f89a --- /dev/null +++ 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a/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk13.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..27fc1423d7760a96f4373fc4649069b67ba3f89a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 36, + "timestamp": 1684728416886.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone direct me to a good proof for 19:36?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk14.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..27fc1423d7760a96f4373fc4649069b67ba3f89a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 36, + "timestamp": 1684728416886.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone direct me to a good proof for 19:36?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk15.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..27fc1423d7760a96f4373fc4649069b67ba3f89a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 36, + "timestamp": 1684728416886.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone direct me to a good proof for 19:36?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk16.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk16.json new file mode 100644 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a good proof for 19:36?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk18.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..27fc1423d7760a96f4373fc4649069b67ba3f89a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 36, + "timestamp": 1684728416886.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone direct me to a good proof for 19:36?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk19.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..27fc1423d7760a96f4373fc4649069b67ba3f89a --- /dev/null +++ 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"query_id": 36, + "timestamp": 1684728416886.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone direct me to a good proof for 19:36?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk22.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..27fc1423d7760a96f4373fc4649069b67ba3f89a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 36, + "timestamp": 1684728416886.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone direct me to a good proof for 19:36?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk23.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk23.json new file mode 100644 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a good proof for 19:36?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk3.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..27fc1423d7760a96f4373fc4649069b67ba3f89a --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 36, + "timestamp": 1684728416886.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone direct me to a good proof for 19:36?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk4.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..27fc1423d7760a96f4373fc4649069b67ba3f89a --- /dev/null +++ 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"query_id": 36, + "timestamp": 1684728416886.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone direct me to a good proof for 19:36?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk8.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..d88f620a786401308845ce03963fb2c71a4c1aa5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk8.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 36, + "timestamp": 1684728416886.0, + "annotatedSourceSentencesIndices": [ + 6, + 7 + ], + "names": [ + "annotator2" + ], + "text": "Can anyone direct me to a good proof for 19:36?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk9.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_36_chunk9.json new file mode 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c1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_37_chunk1.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_37_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..8b3fffcba99247e1e37510ce405f5d0e9e362b01 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_37_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 37, + "timestamp": 1684728431252.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "But how do you find c1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_37_chunk10.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_37_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..8b3fffcba99247e1e37510ce405f5d0e9e362b01 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_37_chunk10.json @@ -0,0 +1,12 @@ +[ + { + 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calling the eigenvector matrix E instead of S ? Is E already used for something else ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk1.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..626250e82e1dab7edb0554fa4aef932f0f427b08 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 38, + "timestamp": 1684728490619.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Just wondering...what keeps us from calling the eigenvector matrix E instead of S ? 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Is E already used for something else ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk11.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..626250e82e1dab7edb0554fa4aef932f0f427b08 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 38, + "timestamp": 1684728490619.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Just wondering...what keeps us from calling the eigenvector matrix E instead of S ? Is E already used for something else ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk12.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..626250e82e1dab7edb0554fa4aef932f0f427b08 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 38, + "timestamp": 1684728490619.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Just wondering...what keeps us from calling the eigenvector matrix E instead of S ? Is E already used for something else ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk13.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..626250e82e1dab7edb0554fa4aef932f0f427b08 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 38, + "timestamp": 1684728490619.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Just wondering...what keeps us from calling the eigenvector matrix E instead of S ? Is E already used for something else ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk14.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..626250e82e1dab7edb0554fa4aef932f0f427b08 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 38, + "timestamp": 1684728490619.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Just wondering...what keeps us from calling the eigenvector matrix E instead of S ? Is E already used for something else ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk15.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..626250e82e1dab7edb0554fa4aef932f0f427b08 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 38, + "timestamp": 1684728490619.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Just wondering...what keeps us from calling the eigenvector matrix E instead of S ? Is E already used for something else ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk16.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..626250e82e1dab7edb0554fa4aef932f0f427b08 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 38, + "timestamp": 1684728490619.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Just wondering...what keeps us from calling the eigenvector matrix E instead of S ? Is E already used for something else ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk17.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..626250e82e1dab7edb0554fa4aef932f0f427b08 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 38, + "timestamp": 1684728490619.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Just wondering...what keeps us from calling the eigenvector matrix E instead of S ? Is E already used for something else ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk18.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..626250e82e1dab7edb0554fa4aef932f0f427b08 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 38, + "timestamp": 1684728490619.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Just wondering...what keeps us from calling the eigenvector matrix E instead of S ? Is E already used for something else ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk19.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..626250e82e1dab7edb0554fa4aef932f0f427b08 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 38, + "timestamp": 1684728490619.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Just wondering...what keeps us from calling the eigenvector matrix E instead of S ? Is E already used for something else ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk2.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..626250e82e1dab7edb0554fa4aef932f0f427b08 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 38, + "timestamp": 1684728490619.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Just wondering...what keeps us from calling the eigenvector matrix E instead of S ? Is E already used for something else ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk20.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..626250e82e1dab7edb0554fa4aef932f0f427b08 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 38, + "timestamp": 1684728490619.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Just wondering...what keeps us from calling the eigenvector matrix E instead of S ? Is E already used for something else ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk21.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..626250e82e1dab7edb0554fa4aef932f0f427b08 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 38, + "timestamp": 1684728490619.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Just wondering...what keeps us from calling the eigenvector matrix E instead of S ? Is E already used for something else ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk22.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..626250e82e1dab7edb0554fa4aef932f0f427b08 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 38, + "timestamp": 1684728490619.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Just wondering...what keeps us from calling the eigenvector matrix E instead of S ? Is E already used for something else ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk23.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..626250e82e1dab7edb0554fa4aef932f0f427b08 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 38, + "timestamp": 1684728490619.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Just wondering...what keeps us from calling the eigenvector matrix E instead of S ? Is E already used for something else ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk24.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..626250e82e1dab7edb0554fa4aef932f0f427b08 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 38, + "timestamp": 1684728490619.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Just wondering...what keeps us from calling the eigenvector matrix E instead of S ? Is E already used for something else ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk3.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..626250e82e1dab7edb0554fa4aef932f0f427b08 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 38, + "timestamp": 1684728490619.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Just wondering...what keeps us from calling the eigenvector matrix E instead of S ? Is E already used for something else ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk4.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..626250e82e1dab7edb0554fa4aef932f0f427b08 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 38, + "timestamp": 1684728490619.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Just wondering...what keeps us from calling the eigenvector matrix E instead of S ? Is E already used for something else ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk5.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..626250e82e1dab7edb0554fa4aef932f0f427b08 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 38, + "timestamp": 1684728490619.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Just wondering...what keeps us from calling the eigenvector matrix E instead of S ? Is E already used for something else ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk6.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..626250e82e1dab7edb0554fa4aef932f0f427b08 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 38, + "timestamp": 1684728490619.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Just wondering...what keeps us from calling the eigenvector matrix E instead of S ? Is E already used for something else ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk7.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..626250e82e1dab7edb0554fa4aef932f0f427b08 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 38, + "timestamp": 1684728490619.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Just wondering...what keeps us from calling the eigenvector matrix E instead of S ? Is E already used for something else ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk8.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..626250e82e1dab7edb0554fa4aef932f0f427b08 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 38, + "timestamp": 1684728490619.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Just wondering...what keeps us from calling the eigenvector matrix E instead of S ? Is E already used for something else ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk9.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..626250e82e1dab7edb0554fa4aef932f0f427b08 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_38_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 38, + "timestamp": 1684728490619.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Just wondering...what keeps us from calling the eigenvector matrix E instead of S ? Is E already used for something else ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk0.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..22b026725ebf7827722c727c63218e6180a34bf2 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 5, + "timestamp": 1684723528088.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "So, the second component of u(k+1) is useless, right? The actual value is given by the first component." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk1.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..22b026725ebf7827722c727c63218e6180a34bf2 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 5, + "timestamp": 1684723528088.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "So, the second component of u(k+1) is useless, right? The actual value is given by the first component." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk10.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..22b026725ebf7827722c727c63218e6180a34bf2 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 5, + "timestamp": 1684723528088.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "So, the second component of u(k+1) is useless, right? The actual value is given by the first component." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk11.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..22b026725ebf7827722c727c63218e6180a34bf2 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 5, + "timestamp": 1684723528088.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "So, the second component of u(k+1) is useless, right? The actual value is given by the first component." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk12.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..22b026725ebf7827722c727c63218e6180a34bf2 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 5, + "timestamp": 1684723528088.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "So, the second component of u(k+1) is useless, right? The actual value is given by the first component." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk13.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..22b026725ebf7827722c727c63218e6180a34bf2 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 5, + "timestamp": 1684723528088.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "So, the second component of u(k+1) is useless, right? The actual value is given by the first component." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk14.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22b026725ebf7827722c727c63218e6180a34bf2 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 5, + "timestamp": 1684723528088.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "So, the second component of u(k+1) is useless, right? The actual value is given by the first component." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk15.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..22b026725ebf7827722c727c63218e6180a34bf2 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 5, + "timestamp": 1684723528088.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "So, the second component of u(k+1) is useless, right? The actual value is given by the first component." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk16.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..22b026725ebf7827722c727c63218e6180a34bf2 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 5, + "timestamp": 1684723528088.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "So, the second component of u(k+1) is useless, right? The actual value is given by the first component." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk17.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..90dcf576b8d0cb2922c03b4b97374a739f44ae71 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk17.json @@ -0,0 +1,17 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 5, + "timestamp": 1684723528088.0, + "annotatedSourceSentencesIndices": [ + 11, + 12, + 17, + 18 + ], + "names": [ + "annotator2" + ], + "text": "So, the second component of u(k+1) is useless, right? The actual value is given by the first component." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk18.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..3a612436931e8cdcaa7ddf11a0c4db4f76471146 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk18.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 5, + "timestamp": 1684723528088.0, + "annotatedSourceSentencesIndices": [ + 1 + ], + "names": [ + "annotator2" + ], + "text": "So, the second component of u(k+1) is useless, right? The actual value is given by the first component." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk19.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..22b026725ebf7827722c727c63218e6180a34bf2 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 5, + "timestamp": 1684723528088.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "So, the second component of u(k+1) is useless, right? The actual value is given by the first component." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk2.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..22b026725ebf7827722c727c63218e6180a34bf2 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 5, + "timestamp": 1684723528088.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "So, the second component of u(k+1) is useless, right? The actual value is given by the first component." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk20.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..22b026725ebf7827722c727c63218e6180a34bf2 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 5, + "timestamp": 1684723528088.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "So, the second component of u(k+1) is useless, right? The actual value is given by the first component." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk21.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..22b026725ebf7827722c727c63218e6180a34bf2 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 5, + "timestamp": 1684723528088.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "So, the second component of u(k+1) is useless, right? The actual value is given by the first component." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk22.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..22b026725ebf7827722c727c63218e6180a34bf2 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 5, + "timestamp": 1684723528088.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "So, the second component of u(k+1) is useless, right? The actual value is given by the first component." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk23.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..22b026725ebf7827722c727c63218e6180a34bf2 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 5, + "timestamp": 1684723528088.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "So, the second component of u(k+1) is useless, right? The actual value is given by the first component." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk24.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..22b026725ebf7827722c727c63218e6180a34bf2 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 5, + "timestamp": 1684723528088.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "So, the second component of u(k+1) is useless, right? The actual value is given by the first component." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk3.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..22b026725ebf7827722c727c63218e6180a34bf2 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 5, + "timestamp": 1684723528088.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "So, the second component of u(k+1) is useless, right? The actual value is given by the first component." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk4.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..22b026725ebf7827722c727c63218e6180a34bf2 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 5, + "timestamp": 1684723528088.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "So, the second component of u(k+1) is useless, right? The actual value is given by the first component." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk5.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..22b026725ebf7827722c727c63218e6180a34bf2 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 5, + "timestamp": 1684723528088.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "So, the second component of u(k+1) is useless, right? The actual value is given by the first component." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk6.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..22b026725ebf7827722c727c63218e6180a34bf2 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 5, + "timestamp": 1684723528088.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "So, the second component of u(k+1) is useless, right? The actual value is given by the first component." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk7.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..22b026725ebf7827722c727c63218e6180a34bf2 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 5, + "timestamp": 1684723528088.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "So, the second component of u(k+1) is useless, right? The actual value is given by the first component." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk8.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..22b026725ebf7827722c727c63218e6180a34bf2 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 5, + "timestamp": 1684723528088.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "So, the second component of u(k+1) is useless, right? The actual value is given by the first component." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk9.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..22b026725ebf7827722c727c63218e6180a34bf2 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_5_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 5, + "timestamp": 1684723528088.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "So, the second component of u(k+1) is useless, right? The actual value is given by the first component." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk0.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6ede483dc930bf844d421703f285dbbb5d3d8dde --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 6, + "timestamp": 1684723821969.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, why doesn't the calculation of F_100 at \"46:08\" time the eigenvector X_1? Am i missing something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk1.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..6ede483dc930bf844d421703f285dbbb5d3d8dde --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 6, + "timestamp": 1684723821969.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, why doesn't the calculation of F_100 at \"46:08\" time the eigenvector X_1? Am i missing something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk10.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..6ede483dc930bf844d421703f285dbbb5d3d8dde --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 6, + "timestamp": 1684723821969.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, why doesn't the calculation of F_100 at \"46:08\" time the eigenvector X_1? Am i missing something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk11.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..6ede483dc930bf844d421703f285dbbb5d3d8dde --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 6, + "timestamp": 1684723821969.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, why doesn't the calculation of F_100 at \"46:08\" time the eigenvector X_1? Am i missing something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk12.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..6ede483dc930bf844d421703f285dbbb5d3d8dde --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 6, + "timestamp": 1684723821969.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, why doesn't the calculation of F_100 at \"46:08\" time the eigenvector X_1? Am i missing something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk13.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..6ede483dc930bf844d421703f285dbbb5d3d8dde --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 6, + "timestamp": 1684723821969.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, why doesn't the calculation of F_100 at \"46:08\" time the eigenvector X_1? Am i missing something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk14.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..6ede483dc930bf844d421703f285dbbb5d3d8dde --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 6, + "timestamp": 1684723821969.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, why doesn't the calculation of F_100 at \"46:08\" time the eigenvector X_1? Am i missing something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk15.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..6ede483dc930bf844d421703f285dbbb5d3d8dde --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 6, + "timestamp": 1684723821969.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, why doesn't the calculation of F_100 at \"46:08\" time the eigenvector X_1? Am i missing something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk16.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..6ede483dc930bf844d421703f285dbbb5d3d8dde --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 6, + "timestamp": 1684723821969.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, why doesn't the calculation of F_100 at \"46:08\" time the eigenvector X_1? Am i missing something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk17.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..6ede483dc930bf844d421703f285dbbb5d3d8dde --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 6, + "timestamp": 1684723821969.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, why doesn't the calculation of F_100 at \"46:08\" time the eigenvector X_1? Am i missing something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk18.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..6ede483dc930bf844d421703f285dbbb5d3d8dde --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 6, + "timestamp": 1684723821969.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, why doesn't the calculation of F_100 at \"46:08\" time the eigenvector X_1? Am i missing something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk19.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..6ede483dc930bf844d421703f285dbbb5d3d8dde --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 6, + "timestamp": 1684723821969.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, why doesn't the calculation of F_100 at \"46:08\" time the eigenvector X_1? Am i missing something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk2.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6ede483dc930bf844d421703f285dbbb5d3d8dde --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 6, + "timestamp": 1684723821969.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, why doesn't the calculation of F_100 at \"46:08\" time the eigenvector X_1? Am i missing something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk20.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6ede483dc930bf844d421703f285dbbb5d3d8dde --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 6, + "timestamp": 1684723821969.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, why doesn't the calculation of F_100 at \"46:08\" time the eigenvector X_1? Am i missing something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk21.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..eb95778ed400a8002681f9cc8dd1bb9914964830 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk21.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 6, + "timestamp": 1684723821969.0, + "annotatedSourceSentencesIndices": [ + 9, + 13 + ], + "names": [ + "annotator2" + ], + "text": "Excuse me, why doesn't the calculation of F_100 at \"46:08\" time the eigenvector X_1? Am i missing something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk22.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..6ede483dc930bf844d421703f285dbbb5d3d8dde --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 6, + "timestamp": 1684723821969.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, why doesn't the calculation of F_100 at \"46:08\" time the eigenvector X_1? Am i missing something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk23.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..6ede483dc930bf844d421703f285dbbb5d3d8dde --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 6, + "timestamp": 1684723821969.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, why doesn't the calculation of F_100 at \"46:08\" time the eigenvector X_1? Am i missing something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk24.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..6ede483dc930bf844d421703f285dbbb5d3d8dde --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 6, + "timestamp": 1684723821969.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, why doesn't the calculation of F_100 at \"46:08\" time the eigenvector X_1? Am i missing something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk3.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..6ede483dc930bf844d421703f285dbbb5d3d8dde --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 6, + "timestamp": 1684723821969.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, why doesn't the calculation of F_100 at \"46:08\" time the eigenvector X_1? Am i missing something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk4.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..6ede483dc930bf844d421703f285dbbb5d3d8dde --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 6, + "timestamp": 1684723821969.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, why doesn't the calculation of F_100 at \"46:08\" time the eigenvector X_1? Am i missing something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk5.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..6ede483dc930bf844d421703f285dbbb5d3d8dde --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 6, + "timestamp": 1684723821969.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, why doesn't the calculation of F_100 at \"46:08\" time the eigenvector X_1? Am i missing something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk6.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..6ede483dc930bf844d421703f285dbbb5d3d8dde --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 6, + "timestamp": 1684723821969.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, why doesn't the calculation of F_100 at \"46:08\" time the eigenvector X_1? Am i missing something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk7.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..6ede483dc930bf844d421703f285dbbb5d3d8dde --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 6, + "timestamp": 1684723821969.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, why doesn't the calculation of F_100 at \"46:08\" time the eigenvector X_1? Am i missing something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk8.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..6ede483dc930bf844d421703f285dbbb5d3d8dde --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 6, + "timestamp": 1684723821969.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, why doesn't the calculation of F_100 at \"46:08\" time the eigenvector X_1? Am i missing something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk9.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..6ede483dc930bf844d421703f285dbbb5d3d8dde --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_6_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 6, + "timestamp": 1684723821969.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Excuse me, why doesn't the calculation of F_100 at \"46:08\" time the eigenvector X_1? Am i missing something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk0.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..bfd376faf05344d286e4e89674fc6ea8a56c3409 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 7, + "timestamp": 1684725468449.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "-0.618 1\n 1 -1.618\nThe Null Space of the given matrix should be the zero vector because the RREF will become:\n1 0\n0 1\nWhich means the Null Space(and hence the Eigenvector) is the zero vector for the first Eigenvalue?\nCorrect me if I'm wrong?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk1.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..bfd376faf05344d286e4e89674fc6ea8a56c3409 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 7, + "timestamp": 1684725468449.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "-0.618 1\n 1 -1.618\nThe Null Space of the given matrix should be the zero vector because the RREF will become:\n1 0\n0 1\nWhich means the Null Space(and hence the Eigenvector) is the zero vector for the first Eigenvalue?\nCorrect me if I'm wrong?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk10.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..5e31ad9face48f548b33010ab8989467ba19f490 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk10.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 7, + "timestamp": 1684725468449.0, + "annotatedSourceSentencesIndices": [ + 13 + ], + "names": [ + "annotator2" + ], + "text": "-0.618 1\n 1 -1.618\nThe Null Space of the given matrix should be the zero vector because the RREF will become:\n1 0\n0 1\nWhich means the Null Space(and hence the Eigenvector) is the zero vector for the first Eigenvalue?\nCorrect me if I'm wrong?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk11.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..bfd376faf05344d286e4e89674fc6ea8a56c3409 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 7, + "timestamp": 1684725468449.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "-0.618 1\n 1 -1.618\nThe Null Space of the given matrix should be the zero vector because the RREF will become:\n1 0\n0 1\nWhich means the Null Space(and hence the Eigenvector) is the zero vector for the first Eigenvalue?\nCorrect me if I'm wrong?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk12.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..bfd376faf05344d286e4e89674fc6ea8a56c3409 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 7, + "timestamp": 1684725468449.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "-0.618 1\n 1 -1.618\nThe Null Space of the given matrix should be the zero vector because the RREF will become:\n1 0\n0 1\nWhich means the Null Space(and hence the Eigenvector) is the zero vector for the first Eigenvalue?\nCorrect me if I'm wrong?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk13.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..bfd376faf05344d286e4e89674fc6ea8a56c3409 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 7, + "timestamp": 1684725468449.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "-0.618 1\n 1 -1.618\nThe Null Space of the given matrix should be the zero vector because the RREF will become:\n1 0\n0 1\nWhich means the Null Space(and hence the Eigenvector) is the zero vector for the first Eigenvalue?\nCorrect me if I'm wrong?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk14.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..bfd376faf05344d286e4e89674fc6ea8a56c3409 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 7, + "timestamp": 1684725468449.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "-0.618 1\n 1 -1.618\nThe Null Space of the given matrix should be the zero vector because the RREF will become:\n1 0\n0 1\nWhich means the Null Space(and hence the Eigenvector) is the zero vector for the first Eigenvalue?\nCorrect me if I'm wrong?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk15.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..bfd376faf05344d286e4e89674fc6ea8a56c3409 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 7, + "timestamp": 1684725468449.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "-0.618 1\n 1 -1.618\nThe Null Space of the given matrix should be the zero vector because the RREF will become:\n1 0\n0 1\nWhich means the Null Space(and hence the Eigenvector) is the zero vector for the first Eigenvalue?\nCorrect me if I'm wrong?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk16.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..bfd376faf05344d286e4e89674fc6ea8a56c3409 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 7, + "timestamp": 1684725468449.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "-0.618 1\n 1 -1.618\nThe Null Space of the given matrix should be the zero vector because the RREF will become:\n1 0\n0 1\nWhich means the Null Space(and hence the Eigenvector) is the zero vector for the first Eigenvalue?\nCorrect me if I'm wrong?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk17.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..bfd376faf05344d286e4e89674fc6ea8a56c3409 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 7, + "timestamp": 1684725468449.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "-0.618 1\n 1 -1.618\nThe Null Space of the given matrix should be the zero vector because the RREF will become:\n1 0\n0 1\nWhich means the Null Space(and hence the Eigenvector) is the zero vector for the first Eigenvalue?\nCorrect me if I'm wrong?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk18.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..bfd376faf05344d286e4e89674fc6ea8a56c3409 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 7, + "timestamp": 1684725468449.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "-0.618 1\n 1 -1.618\nThe Null Space of the given matrix should be the zero vector because the RREF will become:\n1 0\n0 1\nWhich means the Null Space(and hence the Eigenvector) is the zero vector for the first Eigenvalue?\nCorrect me if I'm wrong?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk19.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..bfd376faf05344d286e4e89674fc6ea8a56c3409 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 7, + "timestamp": 1684725468449.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "-0.618 1\n 1 -1.618\nThe Null Space of the given matrix should be the zero vector because the RREF will become:\n1 0\n0 1\nWhich means the Null Space(and hence the Eigenvector) is the zero vector for the first Eigenvalue?\nCorrect me if I'm wrong?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk2.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..bfd376faf05344d286e4e89674fc6ea8a56c3409 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 7, + "timestamp": 1684725468449.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "-0.618 1\n 1 -1.618\nThe Null Space of the given matrix should be the zero vector because the RREF will become:\n1 0\n0 1\nWhich means the Null Space(and hence the Eigenvector) is the zero vector for the first Eigenvalue?\nCorrect me if I'm wrong?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk20.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..bfd376faf05344d286e4e89674fc6ea8a56c3409 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 7, + "timestamp": 1684725468449.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "-0.618 1\n 1 -1.618\nThe Null Space of the given matrix should be the zero vector because the RREF will become:\n1 0\n0 1\nWhich means the Null Space(and hence the Eigenvector) is the zero vector for the first Eigenvalue?\nCorrect me if I'm wrong?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk21.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..bfd376faf05344d286e4e89674fc6ea8a56c3409 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 7, + "timestamp": 1684725468449.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "-0.618 1\n 1 -1.618\nThe Null Space of the given matrix should be the zero vector because the RREF will become:\n1 0\n0 1\nWhich means the Null Space(and hence the Eigenvector) is the zero vector for the first Eigenvalue?\nCorrect me if I'm wrong?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk22.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..bfd376faf05344d286e4e89674fc6ea8a56c3409 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 7, + "timestamp": 1684725468449.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "-0.618 1\n 1 -1.618\nThe Null Space of the given matrix should be the zero vector because the RREF will become:\n1 0\n0 1\nWhich means the Null Space(and hence the Eigenvector) is the zero vector for the first Eigenvalue?\nCorrect me if I'm wrong?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk23.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..bfd376faf05344d286e4e89674fc6ea8a56c3409 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 7, + "timestamp": 1684725468449.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "-0.618 1\n 1 -1.618\nThe Null Space of the given matrix should be the zero vector because the RREF will become:\n1 0\n0 1\nWhich means the Null Space(and hence the Eigenvector) is the zero vector for the first Eigenvalue?\nCorrect me if I'm wrong?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk24.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..bfd376faf05344d286e4e89674fc6ea8a56c3409 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 7, + "timestamp": 1684725468449.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "-0.618 1\n 1 -1.618\nThe Null Space of the given matrix should be the zero vector because the RREF will become:\n1 0\n0 1\nWhich means the Null Space(and hence the Eigenvector) is the zero vector for the first Eigenvalue?\nCorrect me if I'm wrong?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk3.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..bfd376faf05344d286e4e89674fc6ea8a56c3409 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 7, + "timestamp": 1684725468449.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "-0.618 1\n 1 -1.618\nThe Null Space of the given matrix should be the zero vector because the RREF will become:\n1 0\n0 1\nWhich means the Null Space(and hence the Eigenvector) is the zero vector for the first Eigenvalue?\nCorrect me if I'm wrong?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk4.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..bfd376faf05344d286e4e89674fc6ea8a56c3409 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 7, + "timestamp": 1684725468449.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "-0.618 1\n 1 -1.618\nThe Null Space of the given matrix should be the zero vector because the RREF will become:\n1 0\n0 1\nWhich means the Null Space(and hence the Eigenvector) is the zero vector for the first Eigenvalue?\nCorrect me if I'm wrong?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk5.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..bfd376faf05344d286e4e89674fc6ea8a56c3409 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 7, + "timestamp": 1684725468449.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "-0.618 1\n 1 -1.618\nThe Null Space of the given matrix should be the zero vector because the RREF will become:\n1 0\n0 1\nWhich means the Null Space(and hence the Eigenvector) is the zero vector for the first Eigenvalue?\nCorrect me if I'm wrong?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk6.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..bfd376faf05344d286e4e89674fc6ea8a56c3409 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 7, + "timestamp": 1684725468449.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "-0.618 1\n 1 -1.618\nThe Null Space of the given matrix should be the zero vector because the RREF will become:\n1 0\n0 1\nWhich means the Null Space(and hence the Eigenvector) is the zero vector for the first Eigenvalue?\nCorrect me if I'm wrong?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk7.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..bfd376faf05344d286e4e89674fc6ea8a56c3409 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 7, + "timestamp": 1684725468449.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "-0.618 1\n 1 -1.618\nThe Null Space of the given matrix should be the zero vector because the RREF will become:\n1 0\n0 1\nWhich means the Null Space(and hence the Eigenvector) is the zero vector for the first Eigenvalue?\nCorrect me if I'm wrong?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_7_chunk8.json 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"annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "for anyone wondering how he turned the fibonaci sequence to a matrix @ 37:00 you are not alone , check this video out https://www.youtube.com/watch?v=iVNoIwY0UV8" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_9_chunk1.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_9_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..aaa136d3bf6e32aa0baaabab5dbbdf030fb31fdc --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_9_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 9, + "timestamp": 1684725523482.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "for anyone wondering how he turned the fibonaci sequence to a matrix @ 37:00 you are not alone , check this video out https://www.youtube.com/watch?v=iVNoIwY0UV8" + } +] \ No newline at end of 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wondering how he turned the fibonaci sequence to a matrix @ 37:00 you are not alone , check this video out https://www.youtube.com/watch?v=iVNoIwY0UV8" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_9_chunk13.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_9_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..aaa136d3bf6e32aa0baaabab5dbbdf030fb31fdc --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_9_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 9, + "timestamp": 1684725523482.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "for anyone wondering how he turned the fibonaci sequence to a matrix @ 37:00 you are not alone , check this video out https://www.youtube.com/watch?v=iVNoIwY0UV8" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_9_chunk14.json 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this video out https://www.youtube.com/watch?v=iVNoIwY0UV8" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_9_chunk17.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_9_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..190b23aa7c7b92b359137c67bebe3ab3a2e3de87 --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_9_chunk17.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 9, + "timestamp": 1684725523482.0, + "annotatedSourceSentencesIndices": [ + 6 + ], + "names": [ + "annotator2" + ], + "text": "for anyone wondering how he turned the fibonaci sequence to a matrix @ 37:00 you are not alone , check this video out https://www.youtube.com/watch?v=iVNoIwY0UV8" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_9_chunk18.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_9_chunk18.json new file mode 100644 index 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wondering how he turned the fibonaci sequence to a matrix @ 37:00 you are not alone , check this video out https://www.youtube.com/watch?v=iVNoIwY0UV8" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_9_chunk23.json b/sight/query/annotated_chunks_window20/13r9QY6cmjc_9_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..aaa136d3bf6e32aa0baaabab5dbbdf030fb31fdc --- /dev/null +++ b/sight/query/annotated_chunks_window20/13r9QY6cmjc_9_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "13r9QY6cmjc", + "query_id": 9, + "timestamp": 1684725523482.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "for anyone wondering how he turned the fibonaci sequence to a matrix @ 37:00 you are not alone , check this video out https://www.youtube.com/watch?v=iVNoIwY0UV8" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/13r9QY6cmjc_9_chunk24.json 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Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk1.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk10.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk11.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk12.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk13.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk14.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk15.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk16.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk17.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk18.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk19.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk2.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk20.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk21.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk22.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk23.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk24.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk25.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk26.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk27.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk27.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk27.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk28.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk28.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk28.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk29.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk29.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk29.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk3.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk30.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk30.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk30.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk31.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk31.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk31.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk32.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk32.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk32.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk33.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk33.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk33.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk34.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk34.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk34.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk35.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk35.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk35.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk36.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk36.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk36.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk37.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk37.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk37.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk38.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk38.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk38.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk39.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk39.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk39.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk4.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk40.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk40.json new file mode 100644 index 0000000000000000000000000000000000000000..33c6b8c25911bfce143306c159310a5ab02ee2ff --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk40.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [ + 5 + ], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk41.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk41.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk41.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk42.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk42.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk42.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk43.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk43.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk43.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk5.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk6.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk7.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk8.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk9.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..25adedd3f7481a440cc8e97e9876d3b1fe97591a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_0_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 0, + "timestamp": 1684518259177.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk0.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk1.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk10.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk11.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk12.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk13.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk14.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk15.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk16.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk17.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk18.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk19.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk2.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk20.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk21.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk22.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..2c806c2f120b54d44cf94b63791dfdbbb7e08c4e --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk22.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [ + 4 + ], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk23.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk24.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk25.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk26.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk27.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk27.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk27.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk28.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk28.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk28.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk29.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk29.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk29.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk3.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk30.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk30.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk30.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk31.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk31.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk31.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk32.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk32.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk32.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk33.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk33.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk33.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk34.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk34.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk34.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk35.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk35.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk35.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk36.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk36.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk36.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk37.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk37.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk37.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk38.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk38.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk38.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk39.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk39.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk39.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk4.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk40.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk40.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk40.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk41.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk41.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk41.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk42.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk42.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk42.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk43.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk43.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk43.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk5.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk6.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk7.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk8.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk9.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..24a7581c48a397ecf2829f146e9a8464e07e3eba --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_1_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 1, + "timestamp": 1684518329514.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 43:20 isn\u2019t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk0.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..5560224f3654f4714eb4d62d0ccd154e342675d9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 2, + "timestamp": 1684518443888.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What about non parameric testing ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk1.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk1.json new file mode 100644 index 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newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk11.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..5560224f3654f4714eb4d62d0ccd154e342675d9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 2, + "timestamp": 1684518443888.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What about non parameric testing ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk12.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..5560224f3654f4714eb4d62d0ccd154e342675d9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 2, + "timestamp": 1684518443888.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What about non parameric testing ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk13.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..5560224f3654f4714eb4d62d0ccd154e342675d9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 2, + "timestamp": 1684518443888.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What about non parameric testing ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk14.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk14.json new file mode 100644 index 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newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk16.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..5560224f3654f4714eb4d62d0ccd154e342675d9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 2, + "timestamp": 1684518443888.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What about non parameric testing ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk17.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..5560224f3654f4714eb4d62d0ccd154e342675d9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 2, + "timestamp": 1684518443888.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What about non parameric testing ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk18.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..5560224f3654f4714eb4d62d0ccd154e342675d9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 2, + "timestamp": 1684518443888.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What about non parameric testing ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk19.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk19.json new file mode 100644 index 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newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk20.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..5560224f3654f4714eb4d62d0ccd154e342675d9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 2, + "timestamp": 1684518443888.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What about non parameric testing ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk21.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..5560224f3654f4714eb4d62d0ccd154e342675d9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": 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newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk25.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..5560224f3654f4714eb4d62d0ccd154e342675d9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 2, + "timestamp": 1684518443888.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What about non parameric testing ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk26.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..5560224f3654f4714eb4d62d0ccd154e342675d9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": 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newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk3.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..5560224f3654f4714eb4d62d0ccd154e342675d9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 2, + "timestamp": 1684518443888.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What about non parameric testing ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk30.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk30.json new file mode 100644 index 0000000000000000000000000000000000000000..22a7a2a443cd8cac327ac43cedaf003eceb4b93a --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_2_chunk30.json @@ -0,0 +1,14 @@ +[ + { + "file_id": 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"query_id": 3, + "timestamp": 1684518521013.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "the power of the test shouldn't it be 95% ? 1-alpha ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_3_chunk7.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_3_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..43daca000cd859db99f6a8e9325280f8ff340b82 --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_3_chunk7.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 3, + "timestamp": 1684518521013.0, + "annotatedSourceSentencesIndices": [ + 8, + 10 + ], + "names": [ + "annotator1" + ], + "text": "the power of the test shouldn't it be 95% ? 1-alpha ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_3_chunk8.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_3_chunk8.json new file 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test shouldn't it be 95% ? 1-alpha ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk0.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk1.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk10.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk11.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk12.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk13.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk14.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk15.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk16.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk17.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk18.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk19.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..5967dcc194cb66825723b878ec801c0cf8525fec --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk19.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [ + 19 + ], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk2.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk20.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..e8824b48f29b40c245969daae3cf3974f1a9250d --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk20.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [ + 0 + ], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk21.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk22.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk23.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk24.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk25.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk26.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk27.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk27.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk27.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk28.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk28.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk28.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk29.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk29.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk29.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk3.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk30.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk30.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk30.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk31.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk31.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk31.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk32.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk32.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk32.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk33.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk33.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk33.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk34.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk34.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk34.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk35.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk35.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk35.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk36.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk36.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk36.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk37.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk37.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk37.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk38.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk38.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk38.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk39.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk39.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk39.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk4.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk40.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk40.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk40.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk41.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk41.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk41.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? 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He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk43.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk43.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk43.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? 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He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk7.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? 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He said in a previous lecture it is not Gaussian." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk9.json b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f2ee40d5cdc1e7c03c622d9481944a349223b --- /dev/null +++ b/sight/query/annotated_chunks_window20/4HRhg4eUiMo_4_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "4HRhg4eUiMo", + "query_id": 4, + "timestamp": 1684518589095.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? 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"annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I am confused with the Binomial part, especially about how to get the nX\u02c6n-1\u25b3x from formula X\u02c6n+ nX\u02c6n-1\u25b3x+ Junk?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk1.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..fb67b29f2d481c26e748d7be735549c509ca20b7 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 11, + "timestamp": 1684515253951.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I am confused with the Binomial part, especially about how to get the nX\u02c6n-1\u25b3x from formula X\u02c6n+ nX\u02c6n-1\u25b3x+ Junk?" + } +] \ No newline at end of file diff --git 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especially about how to get the nX\u02c6n-1\u25b3x from formula X\u02c6n+ nX\u02c6n-1\u25b3x+ Junk?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk13.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..fb67b29f2d481c26e748d7be735549c509ca20b7 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 11, + "timestamp": 1684515253951.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I am confused with the Binomial part, especially about how to get the nX\u02c6n-1\u25b3x from formula X\u02c6n+ nX\u02c6n-1\u25b3x+ Junk?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk14.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk14.json new file mode 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"annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I am confused with the Binomial part, especially about how to get the nX\u02c6n-1\u25b3x from formula X\u02c6n+ nX\u02c6n-1\u25b3x+ Junk?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk16.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..fb67b29f2d481c26e748d7be735549c509ca20b7 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 11, + "timestamp": 1684515253951.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I am confused with the Binomial part, especially about how to get the nX\u02c6n-1\u25b3x from formula X\u02c6n+ nX\u02c6n-1\u25b3x+ Junk?" + } +] \ No newline at end of file diff --git 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especially about how to get the nX\u02c6n-1\u25b3x from formula X\u02c6n+ nX\u02c6n-1\u25b3x+ Junk?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk2.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..fb67b29f2d481c26e748d7be735549c509ca20b7 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 11, + "timestamp": 1684515253951.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I am confused with the Binomial part, especially about how to get the nX\u02c6n-1\u25b3x from formula X\u02c6n+ nX\u02c6n-1\u25b3x+ Junk?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk20.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..fb67b29f2d481c26e748d7be735549c509ca20b7 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 11, + "timestamp": 1684515253951.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I am confused with the Binomial part, especially about how to get the nX\u02c6n-1\u25b3x from formula X\u02c6n+ nX\u02c6n-1\u25b3x+ Junk?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk21.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..fb67b29f2d481c26e748d7be735549c509ca20b7 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 11, + "timestamp": 1684515253951.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I am confused with the Binomial part, especially about how to get the nX\u02c6n-1\u25b3x from formula X\u02c6n+ nX\u02c6n-1\u25b3x+ Junk?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk22.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..fb67b29f2d481c26e748d7be735549c509ca20b7 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 11, + "timestamp": 1684515253951.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I am confused with the Binomial part, especially about how to get the nX\u02c6n-1\u25b3x from formula X\u02c6n+ nX\u02c6n-1\u25b3x+ Junk?" + } +] \ No newline at end of file diff --git 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Binomial part, especially about how to get the nX\u02c6n-1\u25b3x from formula X\u02c6n+ nX\u02c6n-1\u25b3x+ Junk?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk26.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..fb67b29f2d481c26e748d7be735549c509ca20b7 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 11, + "timestamp": 1684515253951.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I am confused with the Binomial part, especially about how to get the nX\u02c6n-1\u25b3x from formula X\u02c6n+ nX\u02c6n-1\u25b3x+ Junk?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk3.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..fb67b29f2d481c26e748d7be735549c509ca20b7 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 11, + "timestamp": 1684515253951.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I am confused with the Binomial part, especially about how to get the nX\u02c6n-1\u25b3x from formula X\u02c6n+ nX\u02c6n-1\u25b3x+ Junk?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk4.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..fb67b29f2d481c26e748d7be735549c509ca20b7 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 11, + "timestamp": 1684515253951.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I am confused with the Binomial part, especially about how to get the nX\u02c6n-1\u25b3x from formula X\u02c6n+ nX\u02c6n-1\u25b3x+ Junk?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk5.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..fb67b29f2d481c26e748d7be735549c509ca20b7 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 11, + "timestamp": 1684515253951.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I am confused with the Binomial part, especially about how to get the nX\u02c6n-1\u25b3x from formula X\u02c6n+ nX\u02c6n-1\u25b3x+ Junk?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk6.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..fb67b29f2d481c26e748d7be735549c509ca20b7 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 11, + "timestamp": 1684515253951.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I am confused with the Binomial part, especially about how to get the nX\u02c6n-1\u25b3x from formula X\u02c6n+ nX\u02c6n-1\u25b3x+ Junk?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk7.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..fb67b29f2d481c26e748d7be735549c509ca20b7 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 11, + "timestamp": 1684515253951.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I am confused with the Binomial part, especially about how to get the nX\u02c6n-1\u25b3x from formula X\u02c6n+ nX\u02c6n-1\u25b3x+ Junk?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk8.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..fb67b29f2d481c26e748d7be735549c509ca20b7 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 11, + "timestamp": 1684515253951.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I am confused with the Binomial part, especially about how to get the nX\u02c6n-1\u25b3x from formula X\u02c6n+ nX\u02c6n-1\u25b3x+ Junk?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk9.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..fb67b29f2d481c26e748d7be735549c509ca20b7 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_11_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 11, + "timestamp": 1684515253951.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I am confused with the Binomial part, especially about how to get the nX\u02c6n-1\u25b3x from formula X\u02c6n+ nX\u02c6n-1\u25b3x+ Junk?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk0.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..f69d8b3daa05315791fe010b6dda8d2225d51ca6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk0.json @@ -0,0 +1,17 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 14, + "timestamp": 1684515267034.0, + "annotatedSourceSentencesIndices": [ + 0, + 1, + 2, + 3 + ], + "names": [ + "annotator1" + ], + "text": "Is this intro calc? Like if you've taken advanced algebra and trig, is this the best place to start? I have a textbook and a fair bit of free time at the moment. Is this video the right way to begin? Thanks :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk1.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..bf1e2e18ad71ffb48d29b65f325bf58499a5e965 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 14, + "timestamp": 1684515267034.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this intro calc? Like if you've taken advanced algebra and trig, is this the best place to start? I have a textbook and a fair bit of free time at the moment. Is this video the right way to begin? Thanks :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk10.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..bf1e2e18ad71ffb48d29b65f325bf58499a5e965 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 14, + "timestamp": 1684515267034.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this intro calc? Like if you've taken advanced algebra and trig, is this the best place to start? I have a textbook and a fair bit of free time at the moment. Is this video the right way to begin? Thanks :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk11.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..bf1e2e18ad71ffb48d29b65f325bf58499a5e965 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 14, + "timestamp": 1684515267034.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this intro calc? Like if you've taken advanced algebra and trig, is this the best place to start? I have a textbook and a fair bit of free time at the moment. Is this video the right way to begin? Thanks :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk12.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..bf1e2e18ad71ffb48d29b65f325bf58499a5e965 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 14, + "timestamp": 1684515267034.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this intro calc? Like if you've taken advanced algebra and trig, is this the best place to start? I have a textbook and a fair bit of free time at the moment. Is this video the right way to begin? Thanks :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk13.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..bf1e2e18ad71ffb48d29b65f325bf58499a5e965 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 14, + "timestamp": 1684515267034.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this intro calc? Like if you've taken advanced algebra and trig, is this the best place to start? I have a textbook and a fair bit of free time at the moment. Is this video the right way to begin? Thanks :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk14.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..bf1e2e18ad71ffb48d29b65f325bf58499a5e965 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 14, + "timestamp": 1684515267034.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this intro calc? Like if you've taken advanced algebra and trig, is this the best place to start? I have a textbook and a fair bit of free time at the moment. Is this video the right way to begin? Thanks :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk15.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..bf1e2e18ad71ffb48d29b65f325bf58499a5e965 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 14, + "timestamp": 1684515267034.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this intro calc? Like if you've taken advanced algebra and trig, is this the best place to start? I have a textbook and a fair bit of free time at the moment. Is this video the right way to begin? Thanks :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk16.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..bf1e2e18ad71ffb48d29b65f325bf58499a5e965 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 14, + "timestamp": 1684515267034.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this intro calc? Like if you've taken advanced algebra and trig, is this the best place to start? I have a textbook and a fair bit of free time at the moment. Is this video the right way to begin? Thanks :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk17.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..bf1e2e18ad71ffb48d29b65f325bf58499a5e965 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 14, + "timestamp": 1684515267034.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this intro calc? Like if you've taken advanced algebra and trig, is this the best place to start? I have a textbook and a fair bit of free time at the moment. Is this video the right way to begin? Thanks :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk18.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..bf1e2e18ad71ffb48d29b65f325bf58499a5e965 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 14, + "timestamp": 1684515267034.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this intro calc? Like if you've taken advanced algebra and trig, is this the best place to start? I have a textbook and a fair bit of free time at the moment. Is this video the right way to begin? Thanks :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk19.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..bf1e2e18ad71ffb48d29b65f325bf58499a5e965 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 14, + "timestamp": 1684515267034.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this intro calc? Like if you've taken advanced algebra and trig, is this the best place to start? I have a textbook and a fair bit of free time at the moment. Is this video the right way to begin? Thanks :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk2.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..bf1e2e18ad71ffb48d29b65f325bf58499a5e965 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 14, + "timestamp": 1684515267034.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this intro calc? Like if you've taken advanced algebra and trig, is this the best place to start? I have a textbook and a fair bit of free time at the moment. Is this video the right way to begin? Thanks :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk20.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..bf1e2e18ad71ffb48d29b65f325bf58499a5e965 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 14, + "timestamp": 1684515267034.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this intro calc? Like if you've taken advanced algebra and trig, is this the best place to start? I have a textbook and a fair bit of free time at the moment. Is this video the right way to begin? Thanks :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk21.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..bf1e2e18ad71ffb48d29b65f325bf58499a5e965 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 14, + "timestamp": 1684515267034.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this intro calc? Like if you've taken advanced algebra and trig, is this the best place to start? I have a textbook and a fair bit of free time at the moment. Is this video the right way to begin? Thanks :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk22.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..bf1e2e18ad71ffb48d29b65f325bf58499a5e965 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 14, + "timestamp": 1684515267034.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this intro calc? Like if you've taken advanced algebra and trig, is this the best place to start? I have a textbook and a fair bit of free time at the moment. Is this video the right way to begin? Thanks :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk23.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..bf1e2e18ad71ffb48d29b65f325bf58499a5e965 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 14, + "timestamp": 1684515267034.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this intro calc? Like if you've taken advanced algebra and trig, is this the best place to start? I have a textbook and a fair bit of free time at the moment. Is this video the right way to begin? Thanks :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk24.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..bf1e2e18ad71ffb48d29b65f325bf58499a5e965 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 14, + "timestamp": 1684515267034.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this intro calc? Like if you've taken advanced algebra and trig, is this the best place to start? I have a textbook and a fair bit of free time at the moment. Is this video the right way to begin? Thanks :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk25.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..bf1e2e18ad71ffb48d29b65f325bf58499a5e965 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 14, + "timestamp": 1684515267034.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this intro calc? Like if you've taken advanced algebra and trig, is this the best place to start? I have a textbook and a fair bit of free time at the moment. Is this video the right way to begin? Thanks :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk26.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..bf1e2e18ad71ffb48d29b65f325bf58499a5e965 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 14, + "timestamp": 1684515267034.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this intro calc? Like if you've taken advanced algebra and trig, is this the best place to start? I have a textbook and a fair bit of free time at the moment. Is this video the right way to begin? Thanks :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk3.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..bf1e2e18ad71ffb48d29b65f325bf58499a5e965 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 14, + "timestamp": 1684515267034.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this intro calc? Like if you've taken advanced algebra and trig, is this the best place to start? I have a textbook and a fair bit of free time at the moment. Is this video the right way to begin? Thanks :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk4.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..bf1e2e18ad71ffb48d29b65f325bf58499a5e965 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 14, + "timestamp": 1684515267034.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this intro calc? Like if you've taken advanced algebra and trig, is this the best place to start? I have a textbook and a fair bit of free time at the moment. Is this video the right way to begin? Thanks :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk5.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..bf1e2e18ad71ffb48d29b65f325bf58499a5e965 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 14, + "timestamp": 1684515267034.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this intro calc? Like if you've taken advanced algebra and trig, is this the best place to start? I have a textbook and a fair bit of free time at the moment. Is this video the right way to begin? Thanks :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk6.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..bf1e2e18ad71ffb48d29b65f325bf58499a5e965 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 14, + "timestamp": 1684515267034.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this intro calc? Like if you've taken advanced algebra and trig, is this the best place to start? I have a textbook and a fair bit of free time at the moment. Is this video the right way to begin? Thanks :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk7.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..bf1e2e18ad71ffb48d29b65f325bf58499a5e965 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 14, + "timestamp": 1684515267034.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this intro calc? Like if you've taken advanced algebra and trig, is this the best place to start? I have a textbook and a fair bit of free time at the moment. Is this video the right way to begin? Thanks :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk8.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..bf1e2e18ad71ffb48d29b65f325bf58499a5e965 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 14, + "timestamp": 1684515267034.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this intro calc? Like if you've taken advanced algebra and trig, is this the best place to start? I have a textbook and a fair bit of free time at the moment. Is this video the right way to begin? Thanks :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk9.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bf1e2e18ad71ffb48d29b65f325bf58499a5e965 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_14_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 14, + "timestamp": 1684515267034.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this intro calc? Like if you've taken advanced algebra and trig, is this the best place to start? I have a textbook and a fair bit of free time at the moment. Is this video the right way to begin? Thanks :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_15_chunk0.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_15_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..29d9a91b9d05b02f38e8c755f1d50c1fe8ae18d9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_15_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 15, + "timestamp": 1684515294082.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Lecture 1 of calculus he uses Limit, but he doesn't define it anywhere ... was that done in a previous course? otherwise I believe the course is incomplete..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_15_chunk1.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_15_chunk1.json new file mode 100644 index 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"why is x_0y_0 = 1 ?\nmiddle schooler here, please don't mock..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_17_chunk10.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_17_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..4b7dbff19de350936f7421f58f8d91f222961d03 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_17_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 17, + "timestamp": 1684515562316.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why is x_0y_0 = 1 ?\nmiddle schooler here, please don't mock..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_17_chunk11.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_17_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..4b7dbff19de350936f7421f58f8d91f222961d03 --- 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diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_17_chunk13.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_17_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..4b7dbff19de350936f7421f58f8d91f222961d03 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_17_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 17, + "timestamp": 1684515562316.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why is x_0y_0 = 1 ?\nmiddle schooler here, please don't mock..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_17_chunk14.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_17_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..4b7dbff19de350936f7421f58f8d91f222961d03 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_17_chunk14.json @@ -0,0 +1,12 @@ +[ + { + 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"annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why is x_0y_0 = 1 ?\nmiddle schooler here, please don't mock..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_17_chunk4.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_17_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..4b7dbff19de350936f7421f58f8d91f222961d03 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_17_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 17, + "timestamp": 1684515562316.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why is x_0y_0 = 1 ?\nmiddle schooler here, please don't mock..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_17_chunk5.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_17_chunk5.json new file mode 100644 index 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?\nmiddle schooler here, please don't mock..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_17_chunk7.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_17_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..1bf6af4210e6f3f37f46011017348745318b818a --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_17_chunk7.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 17, + "timestamp": 1684515562316.0, + "annotatedSourceSentencesIndices": [ + 7 + ], + "names": [ + "annotator1" + ], + "text": "why is x_0y_0 = 1 ?\nmiddle schooler here, please don't mock..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_17_chunk8.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_17_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..4b7dbff19de350936f7421f58f8d91f222961d03 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_17_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 17, + "timestamp": 1684515562316.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why is x_0y_0 = 1 ?\nmiddle schooler here, please don't mock..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_17_chunk9.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_17_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4b7dbff19de350936f7421f58f8d91f222961d03 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_17_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 17, + "timestamp": 1684515562316.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why is x_0y_0 = 1 ?\nmiddle schooler here, please don't mock..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk0.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..e90df68594a3bc06213df76c7e60cc00ac4067ba --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 20, + "timestamp": 1684516142439.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:56 how did he figure out what the numerator had to be at 25:17? I am sure this is some simple algebra, but it's been a while :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk1.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..e90df68594a3bc06213df76c7e60cc00ac4067ba --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 20, + "timestamp": 1684516142439.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:56 how did he figure out what the numerator had to be at 25:17? I am sure this is some simple algebra, but it's been a while :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk10.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..e90df68594a3bc06213df76c7e60cc00ac4067ba --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 20, + "timestamp": 1684516142439.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:56 how did he figure out what the numerator had to be at 25:17? I am sure this is some simple algebra, but it's been a while :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk11.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..5b7ca5c986b0a285c80736cfad04dfe5b621d19f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk11.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 20, + "timestamp": 1684516142439.0, + "annotatedSourceSentencesIndices": [ + 19 + ], + "names": [ + "annotator1" + ], + "text": "24:56 how did he figure out what the numerator had to be at 25:17? I am sure this is some simple algebra, but it's been a while :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk12.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..e90df68594a3bc06213df76c7e60cc00ac4067ba --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 20, + "timestamp": 1684516142439.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:56 how did he figure out what the numerator had to be at 25:17? I am sure this is some simple algebra, but it's been a while :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk13.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..e90df68594a3bc06213df76c7e60cc00ac4067ba --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 20, + "timestamp": 1684516142439.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:56 how did he figure out what the numerator had to be at 25:17? I am sure this is some simple algebra, but it's been a while :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk14.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..e90df68594a3bc06213df76c7e60cc00ac4067ba --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 20, + "timestamp": 1684516142439.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:56 how did he figure out what the numerator had to be at 25:17? I am sure this is some simple algebra, but it's been a while :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk15.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..e90df68594a3bc06213df76c7e60cc00ac4067ba --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 20, + "timestamp": 1684516142439.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:56 how did he figure out what the numerator had to be at 25:17? I am sure this is some simple algebra, but it's been a while :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk16.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..e90df68594a3bc06213df76c7e60cc00ac4067ba --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 20, + "timestamp": 1684516142439.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:56 how did he figure out what the numerator had to be at 25:17? I am sure this is some simple algebra, but it's been a while :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk17.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..e90df68594a3bc06213df76c7e60cc00ac4067ba --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 20, + "timestamp": 1684516142439.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:56 how did he figure out what the numerator had to be at 25:17? I am sure this is some simple algebra, but it's been a while :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk18.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..e90df68594a3bc06213df76c7e60cc00ac4067ba --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 20, + "timestamp": 1684516142439.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:56 how did he figure out what the numerator had to be at 25:17? I am sure this is some simple algebra, but it's been a while :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk19.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..e90df68594a3bc06213df76c7e60cc00ac4067ba --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 20, + "timestamp": 1684516142439.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:56 how did he figure out what the numerator had to be at 25:17? I am sure this is some simple algebra, but it's been a while :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk2.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..e90df68594a3bc06213df76c7e60cc00ac4067ba --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 20, + "timestamp": 1684516142439.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:56 how did he figure out what the numerator had to be at 25:17? I am sure this is some simple algebra, but it's been a while :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk20.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..e90df68594a3bc06213df76c7e60cc00ac4067ba --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 20, + "timestamp": 1684516142439.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:56 how did he figure out what the numerator had to be at 25:17? I am sure this is some simple algebra, but it's been a while :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk21.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..e90df68594a3bc06213df76c7e60cc00ac4067ba --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 20, + "timestamp": 1684516142439.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:56 how did he figure out what the numerator had to be at 25:17? I am sure this is some simple algebra, but it's been a while :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk22.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e90df68594a3bc06213df76c7e60cc00ac4067ba --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 20, + "timestamp": 1684516142439.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:56 how did he figure out what the numerator had to be at 25:17? I am sure this is some simple algebra, but it's been a while :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk23.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e90df68594a3bc06213df76c7e60cc00ac4067ba --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 20, + "timestamp": 1684516142439.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:56 how did he figure out what the numerator had to be at 25:17? I am sure this is some simple algebra, but it's been a while :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk24.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..e90df68594a3bc06213df76c7e60cc00ac4067ba --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 20, + "timestamp": 1684516142439.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:56 how did he figure out what the numerator had to be at 25:17? I am sure this is some simple algebra, but it's been a while :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk25.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..e90df68594a3bc06213df76c7e60cc00ac4067ba --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 20, + "timestamp": 1684516142439.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:56 how did he figure out what the numerator had to be at 25:17? I am sure this is some simple algebra, but it's been a while :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk26.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..e90df68594a3bc06213df76c7e60cc00ac4067ba --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 20, + "timestamp": 1684516142439.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:56 how did he figure out what the numerator had to be at 25:17? I am sure this is some simple algebra, but it's been a while :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk3.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..e90df68594a3bc06213df76c7e60cc00ac4067ba --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 20, + "timestamp": 1684516142439.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:56 how did he figure out what the numerator had to be at 25:17? I am sure this is some simple algebra, but it's been a while :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk4.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..e90df68594a3bc06213df76c7e60cc00ac4067ba --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 20, + "timestamp": 1684516142439.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:56 how did he figure out what the numerator had to be at 25:17? I am sure this is some simple algebra, but it's been a while :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk5.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..e90df68594a3bc06213df76c7e60cc00ac4067ba --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 20, + "timestamp": 1684516142439.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:56 how did he figure out what the numerator had to be at 25:17? I am sure this is some simple algebra, but it's been a while :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk6.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..e90df68594a3bc06213df76c7e60cc00ac4067ba --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 20, + "timestamp": 1684516142439.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:56 how did he figure out what the numerator had to be at 25:17? I am sure this is some simple algebra, but it's been a while :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk7.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..e90df68594a3bc06213df76c7e60cc00ac4067ba --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 20, + "timestamp": 1684516142439.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:56 how did he figure out what the numerator had to be at 25:17? I am sure this is some simple algebra, but it's been a while :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk8.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..e90df68594a3bc06213df76c7e60cc00ac4067ba --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 20, + "timestamp": 1684516142439.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:56 how did he figure out what the numerator had to be at 25:17? I am sure this is some simple algebra, but it's been a while :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk9.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..e90df68594a3bc06213df76c7e60cc00ac4067ba --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_20_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 20, + "timestamp": 1684516142439.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:56 how did he figure out what the numerator had to be at 25:17? I am sure this is some simple algebra, but it's been a while :)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_21_chunk0.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_21_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..77841399a1de93f2e9f4dac37787028cf7e63b06 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_21_chunk0.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 21, + "timestamp": 1684516169620.0, + "annotatedSourceSentencesIndices": [ + 3 + ], + "names": [ + "annotator1" + ], + "text": "Which math course is better to do after this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_21_chunk1.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_21_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3953171ae2b4978aee2f5dbe958257fb47e3be07 --- /dev/null +++ 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But I think there is only one variable x, x0 is just one value of x." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk18.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..5afd96a8076cddc0cf5d51a5acb58452e61baa22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 24, + "timestamp": 1684516213076.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why use binomial theorem instead of Taylor expansion?\n\nAnd professor said it is single variable calculus, but there may have many variables like x0,y0 to confuse peoples. But I think there is only one variable x, x0 is just one value of x." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk19.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..5afd96a8076cddc0cf5d51a5acb58452e61baa22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 24, + "timestamp": 1684516213076.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why use binomial theorem instead of Taylor expansion?\n\nAnd professor said it is single variable calculus, but there may have many variables like x0,y0 to confuse peoples. But I think there is only one variable x, x0 is just one value of x." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk2.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..5afd96a8076cddc0cf5d51a5acb58452e61baa22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 24, + "timestamp": 1684516213076.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why use binomial theorem instead of Taylor expansion?\n\nAnd professor said it is single variable calculus, but there may have many variables like x0,y0 to confuse peoples. But I think there is only one variable x, x0 is just one value of x." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk20.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..5afd96a8076cddc0cf5d51a5acb58452e61baa22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 24, + "timestamp": 1684516213076.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why use binomial theorem instead of Taylor expansion?\n\nAnd professor said it is single variable calculus, but there may have many variables like x0,y0 to confuse peoples. But I think there is only one variable x, x0 is just one value of x." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk21.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..5afd96a8076cddc0cf5d51a5acb58452e61baa22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 24, + "timestamp": 1684516213076.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why use binomial theorem instead of Taylor expansion?\n\nAnd professor said it is single variable calculus, but there may have many variables like x0,y0 to confuse peoples. 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But I think there is only one variable x, x0 is just one value of x." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk23.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..fc4665b9b6b0bdf6e5c5006c8d70779554a15e79 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk23.json @@ -0,0 +1,17 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 24, + "timestamp": 1684516213076.0, + "annotatedSourceSentencesIndices": [ + 4, + 5, + 6, + 7 + ], + "names": [ + "annotator1" + ], + "text": "Why use binomial theorem instead of Taylor expansion?\n\nAnd professor said it is single variable calculus, but there may have many variables like x0,y0 to confuse peoples. But I think there is only one variable x, x0 is just one value of x." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk24.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..5afd96a8076cddc0cf5d51a5acb58452e61baa22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 24, + "timestamp": 1684516213076.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why use binomial theorem instead of Taylor expansion?\n\nAnd professor said it is single variable calculus, but there may have many variables like x0,y0 to confuse peoples. But I think there is only one variable x, x0 is just one value of x." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk25.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..5afd96a8076cddc0cf5d51a5acb58452e61baa22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 24, + "timestamp": 1684516213076.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why use binomial theorem instead of Taylor expansion?\n\nAnd professor said it is single variable calculus, but there may have many variables like x0,y0 to confuse peoples. But I think there is only one variable x, x0 is just one value of x." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk26.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..5afd96a8076cddc0cf5d51a5acb58452e61baa22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 24, + "timestamp": 1684516213076.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why use binomial theorem instead of Taylor expansion?\n\nAnd professor said it is single variable calculus, but there may have many variables like x0,y0 to confuse peoples. But I think there is only one variable x, x0 is just one value of x." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk3.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..5afd96a8076cddc0cf5d51a5acb58452e61baa22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 24, + "timestamp": 1684516213076.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why use binomial theorem instead of Taylor expansion?\n\nAnd professor said it is single variable calculus, but there may have many variables like x0,y0 to confuse peoples. But I think there is only one variable x, x0 is just one value of x." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk4.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..5afd96a8076cddc0cf5d51a5acb58452e61baa22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 24, + "timestamp": 1684516213076.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why use binomial theorem instead of Taylor expansion?\n\nAnd professor said it is single variable calculus, but there may have many variables like x0,y0 to confuse peoples. But I think there is only one variable x, x0 is just one value of x." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk5.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5afd96a8076cddc0cf5d51a5acb58452e61baa22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 24, + "timestamp": 1684516213076.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why use binomial theorem instead of Taylor expansion?\n\nAnd professor said it is single variable calculus, but there may have many variables like x0,y0 to confuse peoples. But I think there is only one variable x, x0 is just one value of x." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk6.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..5afd96a8076cddc0cf5d51a5acb58452e61baa22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 24, + "timestamp": 1684516213076.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why use binomial theorem instead of Taylor expansion?\n\nAnd professor said it is single variable calculus, but there may have many variables like x0,y0 to confuse peoples. But I think there is only one variable x, x0 is just one value of x." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk7.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..5afd96a8076cddc0cf5d51a5acb58452e61baa22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 24, + "timestamp": 1684516213076.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why use binomial theorem instead of Taylor expansion?\n\nAnd professor said it is single variable calculus, but there may have many variables like x0,y0 to confuse peoples. But I think there is only one variable x, x0 is just one value of x." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk8.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..5afd96a8076cddc0cf5d51a5acb58452e61baa22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 24, + "timestamp": 1684516213076.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why use binomial theorem instead of Taylor expansion?\n\nAnd professor said it is single variable calculus, but there may have many variables like x0,y0 to confuse peoples. But I think there is only one variable x, x0 is just one value of x." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk9.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..5afd96a8076cddc0cf5d51a5acb58452e61baa22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_24_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 24, + "timestamp": 1684516213076.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why use binomial theorem instead of Taylor expansion?\n\nAnd professor said it is single variable calculus, but there may have many variables like x0,y0 to confuse peoples. But I think there is only one variable x, x0 is just one value of x." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_26_chunk0.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_26_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..97c03ecc3ce560011f69107e97a5441b97f07e6f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_26_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 26, + "timestamp": 1684516220556.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why is 2xo(yo) = 2?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_26_chunk1.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_26_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..97c03ecc3ce560011f69107e97a5441b97f07e6f --- /dev/null +++ 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Does he just mean that all values of f(x) = 1/x will result in the area of the triangle of the tangent line to be 2?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_27_chunk9.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_27_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..43c7b45f786d340c11dbd0b04f292b8d3b1cb119 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_27_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 27, + "timestamp": 1684516284253.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "When he solves for the area of the triangle, why does he say it doesn't matter what X0 and Y0 are? Does he just mean that all values of f(x) = 1/x will result in the area of the triangle of the tangent line to be 2?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk0.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..e0e5e9bc1c926891f658cb6802950e5d3f2a3b50 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 28, + "timestamp": 1684516405044.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone explain how to calculate the y-intercept? If you replace y0 with 1/x and plug x = 0, wouldn't you get a division by zero error?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk1.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..e0e5e9bc1c926891f658cb6802950e5d3f2a3b50 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 28, + "timestamp": 1684516405044.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone explain how to calculate the y-intercept? If you replace y0 with 1/x and plug x = 0, wouldn't you get a division by zero error?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk10.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..e0e5e9bc1c926891f658cb6802950e5d3f2a3b50 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 28, + "timestamp": 1684516405044.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone explain how to calculate the y-intercept? If you replace y0 with 1/x and plug x = 0, wouldn't you get a division by zero error?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk11.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..e0e5e9bc1c926891f658cb6802950e5d3f2a3b50 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 28, + "timestamp": 1684516405044.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone explain how to calculate the y-intercept? If you replace y0 with 1/x and plug x = 0, wouldn't you get a division by zero error?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk12.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..e0e5e9bc1c926891f658cb6802950e5d3f2a3b50 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 28, + "timestamp": 1684516405044.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone explain how to calculate the y-intercept? If you replace y0 with 1/x and plug x = 0, wouldn't you get a division by zero error?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk13.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..e0e5e9bc1c926891f658cb6802950e5d3f2a3b50 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 28, + "timestamp": 1684516405044.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone explain how to calculate the y-intercept? If you replace y0 with 1/x and plug x = 0, wouldn't you get a division by zero error?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk14.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..e0e5e9bc1c926891f658cb6802950e5d3f2a3b50 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 28, + "timestamp": 1684516405044.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone explain how to calculate the y-intercept? If you replace y0 with 1/x and plug x = 0, wouldn't you get a division by zero error?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk15.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..e0e5e9bc1c926891f658cb6802950e5d3f2a3b50 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 28, + "timestamp": 1684516405044.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone explain how to calculate the y-intercept? If you replace y0 with 1/x and plug x = 0, wouldn't you get a division by zero error?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk16.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..e0e5e9bc1c926891f658cb6802950e5d3f2a3b50 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 28, + "timestamp": 1684516405044.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone explain how to calculate the y-intercept? If you replace y0 with 1/x and plug x = 0, wouldn't you get a division by zero error?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk17.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..e0e5e9bc1c926891f658cb6802950e5d3f2a3b50 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 28, + "timestamp": 1684516405044.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone explain how to calculate the y-intercept? If you replace y0 with 1/x and plug x = 0, wouldn't you get a division by zero error?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk18.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..e0e5e9bc1c926891f658cb6802950e5d3f2a3b50 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 28, + "timestamp": 1684516405044.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone explain how to calculate the y-intercept? If you replace y0 with 1/x and plug x = 0, wouldn't you get a division by zero error?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk19.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..e0e5e9bc1c926891f658cb6802950e5d3f2a3b50 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 28, + "timestamp": 1684516405044.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone explain how to calculate the y-intercept? If you replace y0 with 1/x and plug x = 0, wouldn't you get a division by zero error?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk2.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..e0e5e9bc1c926891f658cb6802950e5d3f2a3b50 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 28, + "timestamp": 1684516405044.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone explain how to calculate the y-intercept? If you replace y0 with 1/x and plug x = 0, wouldn't you get a division by zero error?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk20.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6d8c18c5a24943bef9fb7024ef4cdd82c0667455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk20.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 28, + "timestamp": 1684516405044.0, + "annotatedSourceSentencesIndices": [ + 2, + 3 + ], + "names": [ + "annotator1" + ], + "text": "Can someone explain how to calculate the y-intercept? If you replace y0 with 1/x and plug x = 0, wouldn't you get a division by zero error?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk21.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..e0e5e9bc1c926891f658cb6802950e5d3f2a3b50 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 28, + "timestamp": 1684516405044.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone explain how to calculate the y-intercept? If you replace y0 with 1/x and plug x = 0, wouldn't you get a division by zero error?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk22.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e0e5e9bc1c926891f658cb6802950e5d3f2a3b50 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 28, + "timestamp": 1684516405044.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone explain how to calculate the y-intercept? If you replace y0 with 1/x and plug x = 0, wouldn't you get a division by zero error?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk23.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e0e5e9bc1c926891f658cb6802950e5d3f2a3b50 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 28, + "timestamp": 1684516405044.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone explain how to calculate the y-intercept? If you replace y0 with 1/x and plug x = 0, wouldn't you get a division by zero error?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk24.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..e0e5e9bc1c926891f658cb6802950e5d3f2a3b50 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 28, + "timestamp": 1684516405044.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone explain how to calculate the y-intercept? If you replace y0 with 1/x and plug x = 0, wouldn't you get a division by zero error?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk25.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..e0e5e9bc1c926891f658cb6802950e5d3f2a3b50 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 28, + "timestamp": 1684516405044.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone explain how to calculate the y-intercept? If you replace y0 with 1/x and plug x = 0, wouldn't you get a division by zero error?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk26.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..e0e5e9bc1c926891f658cb6802950e5d3f2a3b50 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 28, + "timestamp": 1684516405044.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone explain how to calculate the y-intercept? If you replace y0 with 1/x and plug x = 0, wouldn't you get a division by zero error?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk3.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..e0e5e9bc1c926891f658cb6802950e5d3f2a3b50 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 28, + "timestamp": 1684516405044.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone explain how to calculate the y-intercept? If you replace y0 with 1/x and plug x = 0, wouldn't you get a division by zero error?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk4.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..e0e5e9bc1c926891f658cb6802950e5d3f2a3b50 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 28, + "timestamp": 1684516405044.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone explain how to calculate the y-intercept? If you replace y0 with 1/x and plug x = 0, wouldn't you get a division by zero error?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk5.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..e0e5e9bc1c926891f658cb6802950e5d3f2a3b50 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 28, + "timestamp": 1684516405044.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone explain how to calculate the y-intercept? If you replace y0 with 1/x and plug x = 0, wouldn't you get a division by zero error?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk6.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..e0e5e9bc1c926891f658cb6802950e5d3f2a3b50 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 28, + "timestamp": 1684516405044.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone explain how to calculate the y-intercept? If you replace y0 with 1/x and plug x = 0, wouldn't you get a division by zero error?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk7.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..e0e5e9bc1c926891f658cb6802950e5d3f2a3b50 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 28, + "timestamp": 1684516405044.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone explain how to calculate the y-intercept? If you replace y0 with 1/x and plug x = 0, wouldn't you get a division by zero error?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk8.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..e0e5e9bc1c926891f658cb6802950e5d3f2a3b50 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 28, + "timestamp": 1684516405044.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone explain how to calculate the y-intercept? If you replace y0 with 1/x and plug x = 0, wouldn't you get a division by zero error?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk9.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..e0e5e9bc1c926891f658cb6802950e5d3f2a3b50 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_28_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 28, + "timestamp": 1684516405044.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone explain how to calculate the y-intercept? If you replace y0 with 1/x and plug x = 0, wouldn't you get a division by zero error?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk0.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d60625fe39fd65fa216ab70d631b3944f729ca22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 29, + "timestamp": 1684516519367.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. At 33 minutes, where did the negative of the x/Xo^2 go when he added the 1/Xo to the other side?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk1.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..d60625fe39fd65fa216ab70d631b3944f729ca22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 29, + "timestamp": 1684516519367.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. At 33 minutes, where did the negative of the x/Xo^2 go when he added the 1/Xo to the other side?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk10.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..d60625fe39fd65fa216ab70d631b3944f729ca22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 29, + "timestamp": 1684516519367.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. At 33 minutes, where did the negative of the x/Xo^2 go when he added the 1/Xo to the other side?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk11.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d60625fe39fd65fa216ab70d631b3944f729ca22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 29, + "timestamp": 1684516519367.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. At 33 minutes, where did the negative of the x/Xo^2 go when he added the 1/Xo to the other side?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk12.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..d60625fe39fd65fa216ab70d631b3944f729ca22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 29, + "timestamp": 1684516519367.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. At 33 minutes, where did the negative of the x/Xo^2 go when he added the 1/Xo to the other side?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk13.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..d60625fe39fd65fa216ab70d631b3944f729ca22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 29, + "timestamp": 1684516519367.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. At 33 minutes, where did the negative of the x/Xo^2 go when he added the 1/Xo to the other side?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk14.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d60625fe39fd65fa216ab70d631b3944f729ca22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 29, + "timestamp": 1684516519367.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. At 33 minutes, where did the negative of the x/Xo^2 go when he added the 1/Xo to the other side?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk15.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..d60625fe39fd65fa216ab70d631b3944f729ca22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 29, + "timestamp": 1684516519367.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. At 33 minutes, where did the negative of the x/Xo^2 go when he added the 1/Xo to the other side?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk16.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..0cac9b3fb603fe93702ecc9ae15d81426652a822 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk16.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 29, + "timestamp": 1684516519367.0, + "annotatedSourceSentencesIndices": [ + 14 + ], + "names": [ + "annotator1" + ], + "text": "I have a question. At 33 minutes, where did the negative of the x/Xo^2 go when he added the 1/Xo to the other side?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk17.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..d60625fe39fd65fa216ab70d631b3944f729ca22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 29, + "timestamp": 1684516519367.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. At 33 minutes, where did the negative of the x/Xo^2 go when he added the 1/Xo to the other side?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk18.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..d60625fe39fd65fa216ab70d631b3944f729ca22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 29, + "timestamp": 1684516519367.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. At 33 minutes, where did the negative of the x/Xo^2 go when he added the 1/Xo to the other side?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk19.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..d60625fe39fd65fa216ab70d631b3944f729ca22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 29, + "timestamp": 1684516519367.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. At 33 minutes, where did the negative of the x/Xo^2 go when he added the 1/Xo to the other side?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk2.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..d60625fe39fd65fa216ab70d631b3944f729ca22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 29, + "timestamp": 1684516519367.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. At 33 minutes, where did the negative of the x/Xo^2 go when he added the 1/Xo to the other side?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk20.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..d60625fe39fd65fa216ab70d631b3944f729ca22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 29, + "timestamp": 1684516519367.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. At 33 minutes, where did the negative of the x/Xo^2 go when he added the 1/Xo to the other side?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk21.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..d60625fe39fd65fa216ab70d631b3944f729ca22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 29, + "timestamp": 1684516519367.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. At 33 minutes, where did the negative of the x/Xo^2 go when he added the 1/Xo to the other side?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk22.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..d60625fe39fd65fa216ab70d631b3944f729ca22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 29, + "timestamp": 1684516519367.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. At 33 minutes, where did the negative of the x/Xo^2 go when he added the 1/Xo to the other side?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk23.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..d60625fe39fd65fa216ab70d631b3944f729ca22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 29, + "timestamp": 1684516519367.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. At 33 minutes, where did the negative of the x/Xo^2 go when he added the 1/Xo to the other side?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk24.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..d60625fe39fd65fa216ab70d631b3944f729ca22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 29, + "timestamp": 1684516519367.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. At 33 minutes, where did the negative of the x/Xo^2 go when he added the 1/Xo to the other side?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk25.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d60625fe39fd65fa216ab70d631b3944f729ca22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 29, + "timestamp": 1684516519367.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. At 33 minutes, where did the negative of the x/Xo^2 go when he added the 1/Xo to the other side?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk26.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..d60625fe39fd65fa216ab70d631b3944f729ca22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 29, + "timestamp": 1684516519367.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. At 33 minutes, where did the negative of the x/Xo^2 go when he added the 1/Xo to the other side?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk3.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..d60625fe39fd65fa216ab70d631b3944f729ca22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 29, + "timestamp": 1684516519367.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. At 33 minutes, where did the negative of the x/Xo^2 go when he added the 1/Xo to the other side?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk4.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..d60625fe39fd65fa216ab70d631b3944f729ca22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 29, + "timestamp": 1684516519367.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. At 33 minutes, where did the negative of the x/Xo^2 go when he added the 1/Xo to the other side?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk5.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..d60625fe39fd65fa216ab70d631b3944f729ca22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 29, + "timestamp": 1684516519367.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. At 33 minutes, where did the negative of the x/Xo^2 go when he added the 1/Xo to the other side?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk6.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..d60625fe39fd65fa216ab70d631b3944f729ca22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 29, + "timestamp": 1684516519367.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. At 33 minutes, where did the negative of the x/Xo^2 go when he added the 1/Xo to the other side?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk7.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..d60625fe39fd65fa216ab70d631b3944f729ca22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 29, + "timestamp": 1684516519367.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. At 33 minutes, where did the negative of the x/Xo^2 go when he added the 1/Xo to the other side?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk8.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..d60625fe39fd65fa216ab70d631b3944f729ca22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 29, + "timestamp": 1684516519367.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. At 33 minutes, where did the negative of the x/Xo^2 go when he added the 1/Xo to the other side?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk9.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..d60625fe39fd65fa216ab70d631b3944f729ca22 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_29_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 29, + "timestamp": 1684516519367.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. At 33 minutes, where did the negative of the x/Xo^2 go when he added the 1/Xo to the other side?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk0.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..9945cf3eb425f031031a987c459572ee8694bf33 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 2, + "timestamp": 1684514464480.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have just one question: How 1/2 (2Xo)(2Yo)= 2XoYo=2? If we do 1/2 *2 (XoYo) we are left with XoYo which i don't think is equal to 2 :X\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk1.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..9945cf3eb425f031031a987c459572ee8694bf33 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 2, + "timestamp": 1684514464480.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have just one question: How 1/2 (2Xo)(2Yo)= 2XoYo=2? If we do 1/2 *2 (XoYo) we are left with XoYo which i don't think is equal to 2 :X\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk10.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..9945cf3eb425f031031a987c459572ee8694bf33 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 2, + "timestamp": 1684514464480.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have just one question: How 1/2 (2Xo)(2Yo)= 2XoYo=2? If we do 1/2 *2 (XoYo) we are left with XoYo which i don't think is equal to 2 :X\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk11.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..9945cf3eb425f031031a987c459572ee8694bf33 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 2, + "timestamp": 1684514464480.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have just one question: How 1/2 (2Xo)(2Yo)= 2XoYo=2? If we do 1/2 *2 (XoYo) we are left with XoYo which i don't think is equal to 2 :X\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk12.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..9945cf3eb425f031031a987c459572ee8694bf33 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 2, + "timestamp": 1684514464480.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have just one question: How 1/2 (2Xo)(2Yo)= 2XoYo=2? If we do 1/2 *2 (XoYo) we are left with XoYo which i don't think is equal to 2 :X\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk13.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..9945cf3eb425f031031a987c459572ee8694bf33 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 2, + "timestamp": 1684514464480.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have just one question: How 1/2 (2Xo)(2Yo)= 2XoYo=2? If we do 1/2 *2 (XoYo) we are left with XoYo which i don't think is equal to 2 :X\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk14.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..9945cf3eb425f031031a987c459572ee8694bf33 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 2, + "timestamp": 1684514464480.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have just one question: How 1/2 (2Xo)(2Yo)= 2XoYo=2? If we do 1/2 *2 (XoYo) we are left with XoYo which i don't think is equal to 2 :X\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk15.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..9945cf3eb425f031031a987c459572ee8694bf33 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 2, + "timestamp": 1684514464480.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have just one question: How 1/2 (2Xo)(2Yo)= 2XoYo=2? If we do 1/2 *2 (XoYo) we are left with XoYo which i don't think is equal to 2 :X\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk16.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..9945cf3eb425f031031a987c459572ee8694bf33 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 2, + "timestamp": 1684514464480.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have just one question: How 1/2 (2Xo)(2Yo)= 2XoYo=2? If we do 1/2 *2 (XoYo) we are left with XoYo which i don't think is equal to 2 :X\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk17.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..9945cf3eb425f031031a987c459572ee8694bf33 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 2, + "timestamp": 1684514464480.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have just one question: How 1/2 (2Xo)(2Yo)= 2XoYo=2? If we do 1/2 *2 (XoYo) we are left with XoYo which i don't think is equal to 2 :X\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk18.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..9945cf3eb425f031031a987c459572ee8694bf33 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 2, + "timestamp": 1684514464480.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have just one question: How 1/2 (2Xo)(2Yo)= 2XoYo=2? If we do 1/2 *2 (XoYo) we are left with XoYo which i don't think is equal to 2 :X\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk19.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..9945cf3eb425f031031a987c459572ee8694bf33 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 2, + "timestamp": 1684514464480.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have just one question: How 1/2 (2Xo)(2Yo)= 2XoYo=2? If we do 1/2 *2 (XoYo) we are left with XoYo which i don't think is equal to 2 :X\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk2.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..9945cf3eb425f031031a987c459572ee8694bf33 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 2, + "timestamp": 1684514464480.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have just one question: How 1/2 (2Xo)(2Yo)= 2XoYo=2? If we do 1/2 *2 (XoYo) we are left with XoYo which i don't think is equal to 2 :X\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk20.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..fb336be97b0acf90bd5b0e82780aa5b63a6d4b0a --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk20.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 2, + "timestamp": 1684514464480.0, + "annotatedSourceSentencesIndices": [ + 14 + ], + "names": [ + "annotator1" + ], + "text": "I have just one question: How 1/2 (2Xo)(2Yo)= 2XoYo=2? If we do 1/2 *2 (XoYo) we are left with XoYo which i don't think is equal to 2 :X\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk21.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..9945cf3eb425f031031a987c459572ee8694bf33 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 2, + "timestamp": 1684514464480.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have just one question: How 1/2 (2Xo)(2Yo)= 2XoYo=2? If we do 1/2 *2 (XoYo) we are left with XoYo which i don't think is equal to 2 :X\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk22.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..9945cf3eb425f031031a987c459572ee8694bf33 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 2, + "timestamp": 1684514464480.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have just one question: How 1/2 (2Xo)(2Yo)= 2XoYo=2? If we do 1/2 *2 (XoYo) we are left with XoYo which i don't think is equal to 2 :X\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk23.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..9945cf3eb425f031031a987c459572ee8694bf33 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 2, + "timestamp": 1684514464480.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have just one question: How 1/2 (2Xo)(2Yo)= 2XoYo=2? If we do 1/2 *2 (XoYo) we are left with XoYo which i don't think is equal to 2 :X\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk24.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9945cf3eb425f031031a987c459572ee8694bf33 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 2, + "timestamp": 1684514464480.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have just one question: How 1/2 (2Xo)(2Yo)= 2XoYo=2? If we do 1/2 *2 (XoYo) we are left with XoYo which i don't think is equal to 2 :X\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk25.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..9945cf3eb425f031031a987c459572ee8694bf33 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 2, + "timestamp": 1684514464480.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have just one question: How 1/2 (2Xo)(2Yo)= 2XoYo=2? If we do 1/2 *2 (XoYo) we are left with XoYo which i don't think is equal to 2 :X\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk26.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..9945cf3eb425f031031a987c459572ee8694bf33 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 2, + "timestamp": 1684514464480.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have just one question: How 1/2 (2Xo)(2Yo)= 2XoYo=2? If we do 1/2 *2 (XoYo) we are left with XoYo which i don't think is equal to 2 :X\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk3.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..9945cf3eb425f031031a987c459572ee8694bf33 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 2, + "timestamp": 1684514464480.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have just one question: How 1/2 (2Xo)(2Yo)= 2XoYo=2? If we do 1/2 *2 (XoYo) we are left with XoYo which i don't think is equal to 2 :X\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk4.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..9945cf3eb425f031031a987c459572ee8694bf33 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 2, + "timestamp": 1684514464480.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have just one question: How 1/2 (2Xo)(2Yo)= 2XoYo=2? If we do 1/2 *2 (XoYo) we are left with XoYo which i don't think is equal to 2 :X\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk5.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..9945cf3eb425f031031a987c459572ee8694bf33 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 2, + "timestamp": 1684514464480.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have just one question: How 1/2 (2Xo)(2Yo)= 2XoYo=2? If we do 1/2 *2 (XoYo) we are left with XoYo which i don't think is equal to 2 :X\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk6.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9945cf3eb425f031031a987c459572ee8694bf33 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 2, + "timestamp": 1684514464480.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have just one question: How 1/2 (2Xo)(2Yo)= 2XoYo=2? If we do 1/2 *2 (XoYo) we are left with XoYo which i don't think is equal to 2 :X\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk7.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..9945cf3eb425f031031a987c459572ee8694bf33 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 2, + "timestamp": 1684514464480.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have just one question: How 1/2 (2Xo)(2Yo)= 2XoYo=2? If we do 1/2 *2 (XoYo) we are left with XoYo which i don't think is equal to 2 :X\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk8.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..9945cf3eb425f031031a987c459572ee8694bf33 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 2, + "timestamp": 1684514464480.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have just one question: How 1/2 (2Xo)(2Yo)= 2XoYo=2? If we do 1/2 *2 (XoYo) we are left with XoYo which i don't think is equal to 2 :X\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk9.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..9945cf3eb425f031031a987c459572ee8694bf33 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_2_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 2, + "timestamp": 1684514464480.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have just one question: How 1/2 (2Xo)(2Yo)= 2XoYo=2? If we do 1/2 *2 (XoYo) we are left with XoYo which i don't think is equal to 2 :X\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk0.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..e8b3078107ae6c7d195f5c59a97e94fc6c6cf1c4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 30, + "timestamp": 1684516528894.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I'm looking to learn calculus and coming to the end of this video, it seems I'm missing lots of information.\nWhat previous math categories should I learn to continue on with calculus?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk1.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..e8b3078107ae6c7d195f5c59a97e94fc6c6cf1c4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 30, + "timestamp": 1684516528894.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I'm looking to learn calculus and coming to the end of this video, it seems I'm missing lots of information.\nWhat previous math categories should I learn to continue on with calculus?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk10.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..e8b3078107ae6c7d195f5c59a97e94fc6c6cf1c4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 30, + "timestamp": 1684516528894.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I'm looking to learn calculus and coming to the end of this video, it seems I'm missing lots of information.\nWhat previous math categories should I learn to continue on with calculus?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk11.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..e8b3078107ae6c7d195f5c59a97e94fc6c6cf1c4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 30, + "timestamp": 1684516528894.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I'm looking to learn calculus and coming to the end of this video, it seems I'm missing lots of information.\nWhat previous math categories should I learn to continue on with calculus?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk12.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..e8b3078107ae6c7d195f5c59a97e94fc6c6cf1c4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 30, + "timestamp": 1684516528894.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I'm looking to learn calculus and coming to the end of this video, it seems I'm missing lots of information.\nWhat previous math categories should I learn to continue on with calculus?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk13.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..e8b3078107ae6c7d195f5c59a97e94fc6c6cf1c4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 30, + "timestamp": 1684516528894.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I'm looking to learn calculus and coming to the end of this video, it seems I'm missing lots of information.\nWhat previous math categories should I learn to continue on with calculus?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk14.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..e8b3078107ae6c7d195f5c59a97e94fc6c6cf1c4 --- 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categories should I learn to continue on with calculus?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk20.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..e8b3078107ae6c7d195f5c59a97e94fc6c6cf1c4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 30, + "timestamp": 1684516528894.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I'm looking to learn calculus and coming to the end of this video, it seems I'm missing lots of information.\nWhat previous math categories should I learn to continue on with calculus?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk21.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk21.json new file 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previous math categories should I learn to continue on with calculus?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk24.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..e8b3078107ae6c7d195f5c59a97e94fc6c6cf1c4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 30, + "timestamp": 1684516528894.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I'm looking to learn calculus and coming to the end of this video, it seems I'm missing lots of information.\nWhat previous math categories should I learn to continue on with calculus?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk25.json 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"text": "I'm looking to learn calculus and coming to the end of this video, it seems I'm missing lots of information.\nWhat previous math categories should I learn to continue on with calculus?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk4.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..e8b3078107ae6c7d195f5c59a97e94fc6c6cf1c4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 30, + "timestamp": 1684516528894.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I'm looking to learn calculus and coming to the end of this video, it seems I'm missing lots of information.\nWhat previous math categories should I learn to continue on with calculus?" + } +] \ No newline at end of file diff --git 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+ ], + "text": "I'm looking to learn calculus and coming to the end of this video, it seems I'm missing lots of information.\nWhat previous math categories should I learn to continue on with calculus?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk8.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..e8b3078107ae6c7d195f5c59a97e94fc6c6cf1c4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_30_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 30, + "timestamp": 1684516528894.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I'm looking to learn calculus and coming to the end of this video, it seems I'm missing lots of information.\nWhat previous math categories should I learn to continue on with calculus?" + } +] \ No newline at end of file diff --git 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Is that correct?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk1.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..9a3b870cedb208a508be16a30d4331b31d946f23 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 31, + "timestamp": 1684516539061.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It seems that this course is a combination of what is usually separated into two courses typically named \"Calculus 1\" and \"Calculus 2\". Is that correct?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk10.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..9a3b870cedb208a508be16a30d4331b31d946f23 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 31, + "timestamp": 1684516539061.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It seems that this course is a combination of what is usually separated into two courses typically named \"Calculus 1\" and \"Calculus 2\". Is that correct?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk11.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..9a3b870cedb208a508be16a30d4331b31d946f23 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 31, + "timestamp": 1684516539061.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It seems that this course is a combination of what is usually separated into two courses typically named \"Calculus 1\" and \"Calculus 2\". Is that correct?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk12.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..9a3b870cedb208a508be16a30d4331b31d946f23 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 31, + "timestamp": 1684516539061.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It seems that this course is a combination of what is usually separated into two courses typically named \"Calculus 1\" and \"Calculus 2\". Is that correct?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk13.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..9a3b870cedb208a508be16a30d4331b31d946f23 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 31, + "timestamp": 1684516539061.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It seems that this course is a combination of what is usually separated into two courses typically named \"Calculus 1\" and \"Calculus 2\". Is that correct?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk14.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..9a3b870cedb208a508be16a30d4331b31d946f23 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 31, + "timestamp": 1684516539061.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It seems that this course is a combination of what is usually separated into two courses typically named \"Calculus 1\" and \"Calculus 2\". Is that correct?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk15.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..9a3b870cedb208a508be16a30d4331b31d946f23 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 31, + "timestamp": 1684516539061.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It seems that this course is a combination of what is usually separated into two courses typically named \"Calculus 1\" and \"Calculus 2\". Is that correct?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk16.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..9a3b870cedb208a508be16a30d4331b31d946f23 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 31, + "timestamp": 1684516539061.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It seems that this course is a combination of what is usually separated into two courses typically named \"Calculus 1\" and \"Calculus 2\". Is that correct?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk17.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..9a3b870cedb208a508be16a30d4331b31d946f23 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 31, + "timestamp": 1684516539061.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It seems that this course is a combination of what is usually separated into two courses typically named \"Calculus 1\" and \"Calculus 2\". Is that correct?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk18.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..9a3b870cedb208a508be16a30d4331b31d946f23 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 31, + "timestamp": 1684516539061.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It seems that this course is a combination of what is usually separated into two courses typically named \"Calculus 1\" and \"Calculus 2\". Is that correct?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk19.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..9a3b870cedb208a508be16a30d4331b31d946f23 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 31, + "timestamp": 1684516539061.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It seems that this course is a combination of what is usually separated into two courses typically named \"Calculus 1\" and \"Calculus 2\". Is that correct?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk2.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..9a3b870cedb208a508be16a30d4331b31d946f23 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 31, + "timestamp": 1684516539061.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It seems that this course is a combination of what is usually separated into two courses typically named \"Calculus 1\" and \"Calculus 2\". Is that correct?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk20.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..9a3b870cedb208a508be16a30d4331b31d946f23 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 31, + "timestamp": 1684516539061.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It seems that this course is a combination of what is usually separated into two courses typically named \"Calculus 1\" and \"Calculus 2\". Is that correct?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk21.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..9a3b870cedb208a508be16a30d4331b31d946f23 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 31, + "timestamp": 1684516539061.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It seems that this course is a combination of what is usually separated into two courses typically named \"Calculus 1\" and \"Calculus 2\". Is that correct?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk22.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..9a3b870cedb208a508be16a30d4331b31d946f23 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 31, + "timestamp": 1684516539061.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It seems that this course is a combination of what is usually separated into two courses typically named \"Calculus 1\" and \"Calculus 2\". Is that correct?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk23.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..9a3b870cedb208a508be16a30d4331b31d946f23 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 31, + "timestamp": 1684516539061.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It seems that this course is a combination of what is usually separated into two courses typically named \"Calculus 1\" and \"Calculus 2\". Is that correct?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk24.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9a3b870cedb208a508be16a30d4331b31d946f23 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 31, + "timestamp": 1684516539061.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It seems that this course is a combination of what is usually separated into two courses typically named \"Calculus 1\" and \"Calculus 2\". Is that correct?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk25.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..9a3b870cedb208a508be16a30d4331b31d946f23 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 31, + "timestamp": 1684516539061.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It seems that this course is a combination of what is usually separated into two courses typically named \"Calculus 1\" and \"Calculus 2\". Is that correct?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk26.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..9a3b870cedb208a508be16a30d4331b31d946f23 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 31, + "timestamp": 1684516539061.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It seems that this course is a combination of what is usually separated into two courses typically named \"Calculus 1\" and \"Calculus 2\". Is that correct?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk3.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..9a3b870cedb208a508be16a30d4331b31d946f23 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 31, + "timestamp": 1684516539061.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It seems that this course is a combination of what is usually separated into two courses typically named \"Calculus 1\" and \"Calculus 2\". Is that correct?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk4.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..9a3b870cedb208a508be16a30d4331b31d946f23 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 31, + "timestamp": 1684516539061.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It seems that this course is a combination of what is usually separated into two courses typically named \"Calculus 1\" and \"Calculus 2\". Is that correct?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk5.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..9a3b870cedb208a508be16a30d4331b31d946f23 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 31, + "timestamp": 1684516539061.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It seems that this course is a combination of what is usually separated into two courses typically named \"Calculus 1\" and \"Calculus 2\". Is that correct?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk6.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9a3b870cedb208a508be16a30d4331b31d946f23 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 31, + "timestamp": 1684516539061.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It seems that this course is a combination of what is usually separated into two courses typically named \"Calculus 1\" and \"Calculus 2\". Is that correct?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk7.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..9a3b870cedb208a508be16a30d4331b31d946f23 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 31, + "timestamp": 1684516539061.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It seems that this course is a combination of what is usually separated into two courses typically named \"Calculus 1\" and \"Calculus 2\". Is that correct?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk8.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..9a3b870cedb208a508be16a30d4331b31d946f23 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 31, + "timestamp": 1684516539061.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It seems that this course is a combination of what is usually separated into two courses typically named \"Calculus 1\" and \"Calculus 2\". Is that correct?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk9.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..9a3b870cedb208a508be16a30d4331b31d946f23 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_31_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 31, + "timestamp": 1684516539061.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It seems that this course is a combination of what is usually separated into two courses typically named \"Calculus 1\" and \"Calculus 2\". Is that correct?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_32_chunk0.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_32_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..be0dc0460a126ca5d41f9c0965bfe84d6964163f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_32_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 32, + "timestamp": 1684516614873.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Does anyone understand the symmetry thing he was talking about? Which equation did he stare at XD" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_32_chunk1.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_32_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..be0dc0460a126ca5d41f9c0965bfe84d6964163f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_32_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 32, + "timestamp": 1684516614873.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Does anyone understand the symmetry thing he was talking about? Which equation did he stare at XD" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_32_chunk10.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_32_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..be0dc0460a126ca5d41f9c0965bfe84d6964163f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_32_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 32, + "timestamp": 1684516614873.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Does anyone understand the symmetry thing he was talking about? Which equation did he stare at XD" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_32_chunk11.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_32_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..be0dc0460a126ca5d41f9c0965bfe84d6964163f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_32_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 32, + "timestamp": 1684516614873.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Does anyone understand the symmetry thing he was talking about? Which equation did he stare at XD" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_32_chunk12.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_32_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..be0dc0460a126ca5d41f9c0965bfe84d6964163f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_32_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 32, + "timestamp": 1684516614873.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Does anyone understand the symmetry thing he was talking about? 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\u00a0f(1/x) become the inverse of the previous delta f?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_33_chunk18.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_33_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..46a33ad48c695cb5bc1e468717ea9dce5c13602c --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_33_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 33, + "timestamp": 1684516837318.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "wait, why did delta F when finding the derivative of \u00a0f(1/x) become the inverse of the previous delta f?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_33_chunk19.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_33_chunk19.json new file mode 100644 index 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\u00a0f(1/x) become the inverse of the previous delta f?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_33_chunk3.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_33_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..46a33ad48c695cb5bc1e468717ea9dce5c13602c --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_33_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 33, + "timestamp": 1684516837318.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "wait, why did delta F when finding the derivative of \u00a0f(1/x) become the inverse of the previous delta f?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_33_chunk4.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_33_chunk4.json new file mode 100644 index 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[ + "annotator1" + ], + "text": "wait, why did delta F when finding the derivative of \u00a0f(1/x) become the inverse of the previous delta f?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_33_chunk6.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_33_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..46a33ad48c695cb5bc1e468717ea9dce5c13602c --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_33_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 33, + "timestamp": 1684516837318.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "wait, why did delta F when finding the derivative of \u00a0f(1/x) become the inverse of the previous delta f?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_33_chunk7.json 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"query_id": 33, + "timestamp": 1684516837318.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "wait, why did delta F when finding the derivative of \u00a0f(1/x) become the inverse of the previous delta f?\u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_33_chunk9.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_33_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..8c1b4464a80d804e8b7608ebab5ecb15499efef3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_33_chunk9.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 33, + "timestamp": 1684516837318.0, + "annotatedSourceSentencesIndices": [ + 7 + ], + "names": [ + "annotator1" + ], + "text": "wait, why did delta F when finding the derivative of \u00a0f(1/x) become the inverse of the previous delta f?\u00a0" + } +] \ No newline at end of file diff --git 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I see the next class up is multivariable which is often known as calc 3 at some uni's." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk1.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..8b2cdfa2cea3197e562a4b13ecf656c49faf894a --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 36, + "timestamp": 1684516848252.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Does this class include what is generally Calc 2 as well? I see the next class up is multivariable which is often known as calc 3 at some uni's." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk10.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..8b2cdfa2cea3197e562a4b13ecf656c49faf894a --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 36, + "timestamp": 1684516848252.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Does this class include what is generally Calc 2 as well? I see the next class up is multivariable which is often known as calc 3 at some uni's." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk11.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..8b2cdfa2cea3197e562a4b13ecf656c49faf894a --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 36, + "timestamp": 1684516848252.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Does this class include what is generally Calc 2 as well? I see the next class up is multivariable which is often known as calc 3 at some uni's." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk12.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..8b2cdfa2cea3197e562a4b13ecf656c49faf894a --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 36, + "timestamp": 1684516848252.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Does this class include what is generally Calc 2 as well? I see the next class up is multivariable which is often known as calc 3 at some uni's." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk13.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..8b2cdfa2cea3197e562a4b13ecf656c49faf894a --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 36, + "timestamp": 1684516848252.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Does this class include what is generally Calc 2 as well? I see the next class up is multivariable which is often known as calc 3 at some uni's." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk14.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..8b2cdfa2cea3197e562a4b13ecf656c49faf894a --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 36, + "timestamp": 1684516848252.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Does this class include what is generally Calc 2 as well? I see the next class up is multivariable which is often known as calc 3 at some uni's." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk15.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..8b2cdfa2cea3197e562a4b13ecf656c49faf894a --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 36, + "timestamp": 1684516848252.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Does this class include what is generally Calc 2 as well? I see the next class up is multivariable which is often known as calc 3 at some uni's." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk16.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..8b2cdfa2cea3197e562a4b13ecf656c49faf894a --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 36, + "timestamp": 1684516848252.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Does this class include what is generally Calc 2 as well? I see the next class up is multivariable which is often known as calc 3 at some uni's." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk17.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..8b2cdfa2cea3197e562a4b13ecf656c49faf894a --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 36, + "timestamp": 1684516848252.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Does this class include what is generally Calc 2 as well? I see the next class up is multivariable which is often known as calc 3 at some uni's." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk18.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..8b2cdfa2cea3197e562a4b13ecf656c49faf894a --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 36, + "timestamp": 1684516848252.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Does this class include what is generally Calc 2 as well? I see the next class up is multivariable which is often known as calc 3 at some uni's." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk19.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..8b2cdfa2cea3197e562a4b13ecf656c49faf894a --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 36, + "timestamp": 1684516848252.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Does this class include what is generally Calc 2 as well? I see the next class up is multivariable which is often known as calc 3 at some uni's." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk2.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..8b2cdfa2cea3197e562a4b13ecf656c49faf894a --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 36, + "timestamp": 1684516848252.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Does this class include what is generally Calc 2 as well? I see the next class up is multivariable which is often known as calc 3 at some uni's." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk20.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..8b2cdfa2cea3197e562a4b13ecf656c49faf894a --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 36, + "timestamp": 1684516848252.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Does this class include what is generally Calc 2 as well? I see the next class up is multivariable which is often known as calc 3 at some uni's." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk21.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..8b2cdfa2cea3197e562a4b13ecf656c49faf894a --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 36, + "timestamp": 1684516848252.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Does this class include what is generally Calc 2 as well? I see the next class up is multivariable which is often known as calc 3 at some uni's." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk22.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..8b2cdfa2cea3197e562a4b13ecf656c49faf894a --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 36, + "timestamp": 1684516848252.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Does this class include what is generally Calc 2 as well? I see the next class up is multivariable which is often known as calc 3 at some uni's." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk23.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..8b2cdfa2cea3197e562a4b13ecf656c49faf894a --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 36, + "timestamp": 1684516848252.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Does this class include what is generally Calc 2 as well? I see the next class up is multivariable which is often known as calc 3 at some uni's." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk24.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..8b2cdfa2cea3197e562a4b13ecf656c49faf894a --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 36, + "timestamp": 1684516848252.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Does this class include what is generally Calc 2 as well? I see the next class up is multivariable which is often known as calc 3 at some uni's." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk25.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..8b2cdfa2cea3197e562a4b13ecf656c49faf894a --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 36, + "timestamp": 1684516848252.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Does this class include what is generally Calc 2 as well? I see the next class up is multivariable which is often known as calc 3 at some uni's." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk26.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..8b2cdfa2cea3197e562a4b13ecf656c49faf894a --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 36, + "timestamp": 1684516848252.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Does this class include what is generally Calc 2 as well? I see the next class up is multivariable which is often known as calc 3 at some uni's." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk3.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..8b2cdfa2cea3197e562a4b13ecf656c49faf894a --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 36, + "timestamp": 1684516848252.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Does this class include what is generally Calc 2 as well? I see the next class up is multivariable which is often known as calc 3 at some uni's." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk4.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..8b2cdfa2cea3197e562a4b13ecf656c49faf894a --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 36, + "timestamp": 1684516848252.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Does this class include what is generally Calc 2 as well? I see the next class up is multivariable which is often known as calc 3 at some uni's." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk5.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..8b2cdfa2cea3197e562a4b13ecf656c49faf894a --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 36, + "timestamp": 1684516848252.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Does this class include what is generally Calc 2 as well? I see the next class up is multivariable which is often known as calc 3 at some uni's." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk6.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..8b2cdfa2cea3197e562a4b13ecf656c49faf894a --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 36, + "timestamp": 1684516848252.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Does this class include what is generally Calc 2 as well? I see the next class up is multivariable which is often known as calc 3 at some uni's." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk7.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..8b2cdfa2cea3197e562a4b13ecf656c49faf894a --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 36, + "timestamp": 1684516848252.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Does this class include what is generally Calc 2 as well? I see the next class up is multivariable which is often known as calc 3 at some uni's." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk8.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8b2cdfa2cea3197e562a4b13ecf656c49faf894a --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 36, + "timestamp": 1684516848252.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Does this class include what is generally Calc 2 as well? I see the next class up is multivariable which is often known as calc 3 at some uni's." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk9.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..8b2cdfa2cea3197e562a4b13ecf656c49faf894a --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_36_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 36, + "timestamp": 1684516848252.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Does this class include what is generally Calc 2 as well? I see the next class up is multivariable which is often known as calc 3 at some uni's." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk0.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..b8094bb0a2338091c0dc087777705d1087751717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 38, + "timestamp": 1684516879122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around 33:35 he defines the x-int as (2x0,0), following the same logic and using the original point slope form, I got y-int as (0,2/x0). I don't think I am wrong, but can any confirm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk1.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..b8094bb0a2338091c0dc087777705d1087751717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 38, + "timestamp": 1684516879122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around 33:35 he defines the x-int as (2x0,0), following the same logic and using the original point slope form, I got y-int as (0,2/x0). I don't think I am wrong, but can any confirm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk10.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..b8094bb0a2338091c0dc087777705d1087751717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 38, + "timestamp": 1684516879122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around 33:35 he defines the x-int as (2x0,0), following the same logic and using the original point slope form, I got y-int as (0,2/x0). I don't think I am wrong, but can any confirm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk11.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b8094bb0a2338091c0dc087777705d1087751717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 38, + "timestamp": 1684516879122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around 33:35 he defines the x-int as (2x0,0), following the same logic and using the original point slope form, I got y-int as (0,2/x0). I don't think I am wrong, but can any confirm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk12.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..b8094bb0a2338091c0dc087777705d1087751717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 38, + "timestamp": 1684516879122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around 33:35 he defines the x-int as (2x0,0), following the same logic and using the original point slope form, I got y-int as (0,2/x0). I don't think I am wrong, but can any confirm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk13.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..b8094bb0a2338091c0dc087777705d1087751717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 38, + "timestamp": 1684516879122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around 33:35 he defines the x-int as (2x0,0), following the same logic and using the original point slope form, I got y-int as (0,2/x0). I don't think I am wrong, but can any confirm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk14.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..b8094bb0a2338091c0dc087777705d1087751717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 38, + "timestamp": 1684516879122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around 33:35 he defines the x-int as (2x0,0), following the same logic and using the original point slope form, I got y-int as (0,2/x0). I don't think I am wrong, but can any confirm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk15.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..b8094bb0a2338091c0dc087777705d1087751717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 38, + "timestamp": 1684516879122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around 33:35 he defines the x-int as (2x0,0), following the same logic and using the original point slope form, I got y-int as (0,2/x0). I don't think I am wrong, but can any confirm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk16.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..e89565d6271a102423449141573295e42aa35920 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk16.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 38, + "timestamp": 1684516879122.0, + "annotatedSourceSentencesIndices": [ + 16 + ], + "names": [ + "annotator1" + ], + "text": "At around 33:35 he defines the x-int as (2x0,0), following the same logic and using the original point slope form, I got y-int as (0,2/x0). I don't think I am wrong, but can any confirm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk17.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b8094bb0a2338091c0dc087777705d1087751717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 38, + "timestamp": 1684516879122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around 33:35 he defines the x-int as (2x0,0), following the same logic and using the original point slope form, I got y-int as (0,2/x0). I don't think I am wrong, but can any confirm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk18.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..b8094bb0a2338091c0dc087777705d1087751717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 38, + "timestamp": 1684516879122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around 33:35 he defines the x-int as (2x0,0), following the same logic and using the original point slope form, I got y-int as (0,2/x0). I don't think I am wrong, but can any confirm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk19.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..b8094bb0a2338091c0dc087777705d1087751717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 38, + "timestamp": 1684516879122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around 33:35 he defines the x-int as (2x0,0), following the same logic and using the original point slope form, I got y-int as (0,2/x0). I don't think I am wrong, but can any confirm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk2.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..b8094bb0a2338091c0dc087777705d1087751717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 38, + "timestamp": 1684516879122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around 33:35 he defines the x-int as (2x0,0), following the same logic and using the original point slope form, I got y-int as (0,2/x0). I don't think I am wrong, but can any confirm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk20.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..b8094bb0a2338091c0dc087777705d1087751717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 38, + "timestamp": 1684516879122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around 33:35 he defines the x-int as (2x0,0), following the same logic and using the original point slope form, I got y-int as (0,2/x0). I don't think I am wrong, but can any confirm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk21.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..b8094bb0a2338091c0dc087777705d1087751717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 38, + "timestamp": 1684516879122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around 33:35 he defines the x-int as (2x0,0), following the same logic and using the original point slope form, I got y-int as (0,2/x0). I don't think I am wrong, but can any confirm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk22.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..b8094bb0a2338091c0dc087777705d1087751717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 38, + "timestamp": 1684516879122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around 33:35 he defines the x-int as (2x0,0), following the same logic and using the original point slope form, I got y-int as (0,2/x0). I don't think I am wrong, but can any confirm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk23.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..b8094bb0a2338091c0dc087777705d1087751717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 38, + "timestamp": 1684516879122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around 33:35 he defines the x-int as (2x0,0), following the same logic and using the original point slope form, I got y-int as (0,2/x0). I don't think I am wrong, but can any confirm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk24.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..b8094bb0a2338091c0dc087777705d1087751717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 38, + "timestamp": 1684516879122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around 33:35 he defines the x-int as (2x0,0), following the same logic and using the original point slope form, I got y-int as (0,2/x0). I don't think I am wrong, but can any confirm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk25.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..b8094bb0a2338091c0dc087777705d1087751717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 38, + "timestamp": 1684516879122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around 33:35 he defines the x-int as (2x0,0), following the same logic and using the original point slope form, I got y-int as (0,2/x0). I don't think I am wrong, but can any confirm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk26.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..b8094bb0a2338091c0dc087777705d1087751717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 38, + "timestamp": 1684516879122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around 33:35 he defines the x-int as (2x0,0), following the same logic and using the original point slope form, I got y-int as (0,2/x0). I don't think I am wrong, but can any confirm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk3.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..b8094bb0a2338091c0dc087777705d1087751717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 38, + "timestamp": 1684516879122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around 33:35 he defines the x-int as (2x0,0), following the same logic and using the original point slope form, I got y-int as (0,2/x0). I don't think I am wrong, but can any confirm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk4.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..b8094bb0a2338091c0dc087777705d1087751717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 38, + "timestamp": 1684516879122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around 33:35 he defines the x-int as (2x0,0), following the same logic and using the original point slope form, I got y-int as (0,2/x0). I don't think I am wrong, but can any confirm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk5.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..b8094bb0a2338091c0dc087777705d1087751717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 38, + "timestamp": 1684516879122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around 33:35 he defines the x-int as (2x0,0), following the same logic and using the original point slope form, I got y-int as (0,2/x0). I don't think I am wrong, but can any confirm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk6.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..b8094bb0a2338091c0dc087777705d1087751717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 38, + "timestamp": 1684516879122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around 33:35 he defines the x-int as (2x0,0), following the same logic and using the original point slope form, I got y-int as (0,2/x0). I don't think I am wrong, but can any confirm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk7.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b8094bb0a2338091c0dc087777705d1087751717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 38, + "timestamp": 1684516879122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around 33:35 he defines the x-int as (2x0,0), following the same logic and using the original point slope form, I got y-int as (0,2/x0). I don't think I am wrong, but can any confirm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk8.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..b8094bb0a2338091c0dc087777705d1087751717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 38, + "timestamp": 1684516879122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around 33:35 he defines the x-int as (2x0,0), following the same logic and using the original point slope form, I got y-int as (0,2/x0). I don't think I am wrong, but can any confirm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk9.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..b8094bb0a2338091c0dc087777705d1087751717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_38_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 38, + "timestamp": 1684516879122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around 33:35 he defines the x-int as (2x0,0), following the same logic and using the original point slope form, I got y-int as (0,2/x0). I don't think I am wrong, but can any confirm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk0.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..266431867cb897c51a4e11092e668ceab6a423e3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk0.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 3, + "timestamp": 1684514482386.0, + "annotatedSourceSentencesIndices": [ + 3 + ], + "names": [ + "annotator1" + ], + "text": "Is this entire course a combination of calc 1 and 2? Or just calc 1. I see the next course is multi-variable which is often known as calc 3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk1.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..12f2aa21d0edd337d7aef4a6d485851d185d1831 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 3, + "timestamp": 1684514482386.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this entire course a combination of calc 1 and 2? Or just calc 1. I see the next course is multi-variable which is often known as calc 3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk10.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..12f2aa21d0edd337d7aef4a6d485851d185d1831 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 3, + "timestamp": 1684514482386.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this entire course a combination of calc 1 and 2? Or just calc 1. I see the next course is multi-variable which is often known as calc 3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk11.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..12f2aa21d0edd337d7aef4a6d485851d185d1831 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 3, + "timestamp": 1684514482386.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this entire course a combination of calc 1 and 2? Or just calc 1. I see the next course is multi-variable which is often known as calc 3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk12.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..12f2aa21d0edd337d7aef4a6d485851d185d1831 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 3, + "timestamp": 1684514482386.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this entire course a combination of calc 1 and 2? Or just calc 1. I see the next course is multi-variable which is often known as calc 3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk13.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..12f2aa21d0edd337d7aef4a6d485851d185d1831 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 3, + "timestamp": 1684514482386.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this entire course a combination of calc 1 and 2? Or just calc 1. I see the next course is multi-variable which is often known as calc 3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk14.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..12f2aa21d0edd337d7aef4a6d485851d185d1831 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 3, + "timestamp": 1684514482386.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this entire course a combination of calc 1 and 2? Or just calc 1. I see the next course is multi-variable which is often known as calc 3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk15.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..12f2aa21d0edd337d7aef4a6d485851d185d1831 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 3, + "timestamp": 1684514482386.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this entire course a combination of calc 1 and 2? Or just calc 1. I see the next course is multi-variable which is often known as calc 3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk16.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..12f2aa21d0edd337d7aef4a6d485851d185d1831 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 3, + "timestamp": 1684514482386.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this entire course a combination of calc 1 and 2? Or just calc 1. I see the next course is multi-variable which is often known as calc 3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk17.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..12f2aa21d0edd337d7aef4a6d485851d185d1831 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 3, + "timestamp": 1684514482386.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this entire course a combination of calc 1 and 2? Or just calc 1. I see the next course is multi-variable which is often known as calc 3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk18.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..12f2aa21d0edd337d7aef4a6d485851d185d1831 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 3, + "timestamp": 1684514482386.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this entire course a combination of calc 1 and 2? Or just calc 1. I see the next course is multi-variable which is often known as calc 3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk19.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..12f2aa21d0edd337d7aef4a6d485851d185d1831 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 3, + "timestamp": 1684514482386.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this entire course a combination of calc 1 and 2? Or just calc 1. I see the next course is multi-variable which is often known as calc 3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk2.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..12f2aa21d0edd337d7aef4a6d485851d185d1831 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 3, + "timestamp": 1684514482386.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this entire course a combination of calc 1 and 2? Or just calc 1. I see the next course is multi-variable which is often known as calc 3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk20.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..12f2aa21d0edd337d7aef4a6d485851d185d1831 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 3, + "timestamp": 1684514482386.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this entire course a combination of calc 1 and 2? Or just calc 1. I see the next course is multi-variable which is often known as calc 3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk21.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..12f2aa21d0edd337d7aef4a6d485851d185d1831 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 3, + "timestamp": 1684514482386.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this entire course a combination of calc 1 and 2? Or just calc 1. I see the next course is multi-variable which is often known as calc 3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk22.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..12f2aa21d0edd337d7aef4a6d485851d185d1831 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 3, + "timestamp": 1684514482386.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this entire course a combination of calc 1 and 2? Or just calc 1. I see the next course is multi-variable which is often known as calc 3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk23.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..12f2aa21d0edd337d7aef4a6d485851d185d1831 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 3, + "timestamp": 1684514482386.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this entire course a combination of calc 1 and 2? Or just calc 1. I see the next course is multi-variable which is often known as calc 3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk24.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..12f2aa21d0edd337d7aef4a6d485851d185d1831 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 3, + "timestamp": 1684514482386.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this entire course a combination of calc 1 and 2? Or just calc 1. I see the next course is multi-variable which is often known as calc 3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk25.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..12f2aa21d0edd337d7aef4a6d485851d185d1831 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 3, + "timestamp": 1684514482386.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this entire course a combination of calc 1 and 2? Or just calc 1. I see the next course is multi-variable which is often known as calc 3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk26.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..12f2aa21d0edd337d7aef4a6d485851d185d1831 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 3, + "timestamp": 1684514482386.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this entire course a combination of calc 1 and 2? Or just calc 1. I see the next course is multi-variable which is often known as calc 3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk3.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..12f2aa21d0edd337d7aef4a6d485851d185d1831 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 3, + "timestamp": 1684514482386.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this entire course a combination of calc 1 and 2? Or just calc 1. I see the next course is multi-variable which is often known as calc 3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk4.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..12f2aa21d0edd337d7aef4a6d485851d185d1831 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 3, + "timestamp": 1684514482386.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this entire course a combination of calc 1 and 2? Or just calc 1. I see the next course is multi-variable which is often known as calc 3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk5.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..12f2aa21d0edd337d7aef4a6d485851d185d1831 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 3, + "timestamp": 1684514482386.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this entire course a combination of calc 1 and 2? Or just calc 1. I see the next course is multi-variable which is often known as calc 3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk6.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..12f2aa21d0edd337d7aef4a6d485851d185d1831 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 3, + "timestamp": 1684514482386.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this entire course a combination of calc 1 and 2? Or just calc 1. I see the next course is multi-variable which is often known as calc 3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk7.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..12f2aa21d0edd337d7aef4a6d485851d185d1831 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 3, + "timestamp": 1684514482386.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this entire course a combination of calc 1 and 2? Or just calc 1. I see the next course is multi-variable which is often known as calc 3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk8.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..12f2aa21d0edd337d7aef4a6d485851d185d1831 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 3, + "timestamp": 1684514482386.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this entire course a combination of calc 1 and 2? Or just calc 1. I see the next course is multi-variable which is often known as calc 3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk9.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..12f2aa21d0edd337d7aef4a6d485851d185d1831 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_3_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 3, + "timestamp": 1684514482386.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is this entire course a combination of calc 1 and 2? Or just calc 1. I see the next course is multi-variable which is often known as calc 3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_42_chunk0.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_42_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..16fdfbfd30fbff8ff792d607f03d58ed99f2b1ce --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_42_chunk0.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 42, + "timestamp": 1684516889278.0, + "annotatedSourceSentencesIndices": [ + 0 + ], + "names": [ + "annotator1" + ], + "text": "2+ 2 = 4?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_42_chunk1.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_42_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..c505fc4cefaa59a276f586910808ad5b275410a0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_42_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 42, + "timestamp": 1684516889278.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "2+ 2 = 4?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_42_chunk10.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_42_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c505fc4cefaa59a276f586910808ad5b275410a0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_42_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 42, + "timestamp": 1684516889278.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "2+ 2 = 4?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_42_chunk11.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_42_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..c505fc4cefaa59a276f586910808ad5b275410a0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_42_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 42, + "timestamp": 1684516889278.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "2+ 2 = 4?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_42_chunk12.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_42_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..c505fc4cefaa59a276f586910808ad5b275410a0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_42_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 42, + "timestamp": 1684516889278.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "2+ 2 = 4?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_42_chunk13.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_42_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..c505fc4cefaa59a276f586910808ad5b275410a0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_42_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 42, + "timestamp": 1684516889278.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "2+ 2 = 4?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_42_chunk14.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_42_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..c505fc4cefaa59a276f586910808ad5b275410a0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_42_chunk14.json @@ 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"annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question in 22:00 if x0 go to infinitive then the value would be bigger and bigger isn\u2019t it? for example -1/1 < -1/1000" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_48_chunk23.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_48_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..8602085d7a1db484d858cfab054840edac7eef10 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_48_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 48, + "timestamp": 1684517008407.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question in 22:00 if x0 go to infinitive then the value would be bigger and bigger isn\u2019t it? for example -1/1 < -1/1000" + } +] \ No newline at end of file diff --git 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infinitive then the value would be bigger and bigger isn\u2019t it? for example -1/1 < -1/1000" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_48_chunk3.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_48_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..8602085d7a1db484d858cfab054840edac7eef10 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_48_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 48, + "timestamp": 1684517008407.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question in 22:00 if x0 go to infinitive then the value would be bigger and bigger isn\u2019t it? for example -1/1 < -1/1000" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_48_chunk4.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_48_chunk4.json new file mode 100644 index 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"annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question in 22:00 if x0 go to infinitive then the value would be bigger and bigger isn\u2019t it? for example -1/1 < -1/1000" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_48_chunk6.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_48_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..8602085d7a1db484d858cfab054840edac7eef10 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_48_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 48, + "timestamp": 1684517008407.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question in 22:00 if x0 go to infinitive then the value would be bigger and bigger isn\u2019t it? for example -1/1 < -1/1000" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_48_chunk7.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_48_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..8602085d7a1db484d858cfab054840edac7eef10 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_48_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 48, + "timestamp": 1684517008407.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question in 22:00 if x0 go to infinitive then the value would be bigger and bigger isn\u2019t it? for example -1/1 < -1/1000" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_48_chunk8.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_48_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8602085d7a1db484d858cfab054840edac7eef10 --- /dev/null +++ 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infinitive then the value would be bigger and bigger isn\u2019t it? for example -1/1 < -1/1000" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk0.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..8790abba422eeffc0b973e678cc54b1542c81fa6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 49, + "timestamp": 1684517025478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone kindly compute y-intercept for me? Where x = 0 into the asterisk eqn. I would just like to prove that y = 2y0. Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk1.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..8790abba422eeffc0b973e678cc54b1542c81fa6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 49, + "timestamp": 1684517025478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone kindly compute y-intercept for me? Where x = 0 into the asterisk eqn. I would just like to prove that y = 2y0. Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk10.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..8790abba422eeffc0b973e678cc54b1542c81fa6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 49, + "timestamp": 1684517025478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone kindly compute y-intercept for me? Where x = 0 into the asterisk eqn. I would just like to prove that y = 2y0. Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk11.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..8790abba422eeffc0b973e678cc54b1542c81fa6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 49, + "timestamp": 1684517025478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone kindly compute y-intercept for me? Where x = 0 into the asterisk eqn. I would just like to prove that y = 2y0. Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk12.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..8790abba422eeffc0b973e678cc54b1542c81fa6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 49, + "timestamp": 1684517025478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone kindly compute y-intercept for me? Where x = 0 into the asterisk eqn. I would just like to prove that y = 2y0. Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk13.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..8790abba422eeffc0b973e678cc54b1542c81fa6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 49, + "timestamp": 1684517025478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone kindly compute y-intercept for me? Where x = 0 into the asterisk eqn. I would just like to prove that y = 2y0. Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk14.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..8790abba422eeffc0b973e678cc54b1542c81fa6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 49, + "timestamp": 1684517025478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone kindly compute y-intercept for me? Where x = 0 into the asterisk eqn. I would just like to prove that y = 2y0. Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk15.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..8790abba422eeffc0b973e678cc54b1542c81fa6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 49, + "timestamp": 1684517025478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone kindly compute y-intercept for me? Where x = 0 into the asterisk eqn. I would just like to prove that y = 2y0. Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk16.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..8790abba422eeffc0b973e678cc54b1542c81fa6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 49, + "timestamp": 1684517025478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone kindly compute y-intercept for me? Where x = 0 into the asterisk eqn. I would just like to prove that y = 2y0. Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk17.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..7818d7acff3bb5a0f72d978f2a83391dabf3bb8f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk17.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 49, + "timestamp": 1684517025478.0, + "annotatedSourceSentencesIndices": [ + 2 + ], + "names": [ + "annotator1" + ], + "text": "Can someone kindly compute y-intercept for me? Where x = 0 into the asterisk eqn. I would just like to prove that y = 2y0. Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk18.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..8790abba422eeffc0b973e678cc54b1542c81fa6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 49, + "timestamp": 1684517025478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone kindly compute y-intercept for me? Where x = 0 into the asterisk eqn. I would just like to prove that y = 2y0. Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk19.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..8790abba422eeffc0b973e678cc54b1542c81fa6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 49, + "timestamp": 1684517025478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone kindly compute y-intercept for me? Where x = 0 into the asterisk eqn. I would just like to prove that y = 2y0. Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk2.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..8790abba422eeffc0b973e678cc54b1542c81fa6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 49, + "timestamp": 1684517025478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone kindly compute y-intercept for me? Where x = 0 into the asterisk eqn. I would just like to prove that y = 2y0. Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk20.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..8790abba422eeffc0b973e678cc54b1542c81fa6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 49, + "timestamp": 1684517025478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone kindly compute y-intercept for me? Where x = 0 into the asterisk eqn. I would just like to prove that y = 2y0. Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk21.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..8790abba422eeffc0b973e678cc54b1542c81fa6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_49_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 49, + "timestamp": 1684517025478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can someone kindly compute y-intercept for me? Where x = 0 into the asterisk eqn. I would just like to prove that y = 2y0. 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Shouldn't x0 - x0 equal 0, and adding 0 to deltaX = deltaX?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk23.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4cf1f87109c3bf923debf7241b97e499af26fa47 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 55, + "timestamp": 1684517099986.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 20:29, why does x0-(x0+deltaX) simplify to -deltaX? Shouldn't x0 - x0 equal 0, and adding 0 to deltaX = deltaX?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk24.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..4cf1f87109c3bf923debf7241b97e499af26fa47 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 55, + "timestamp": 1684517099986.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 20:29, why does x0-(x0+deltaX) simplify to -deltaX? Shouldn't x0 - x0 equal 0, and adding 0 to deltaX = deltaX?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk25.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4cf1f87109c3bf923debf7241b97e499af26fa47 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 55, + "timestamp": 1684517099986.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 20:29, why does x0-(x0+deltaX) simplify to -deltaX? Shouldn't x0 - x0 equal 0, and adding 0 to deltaX = deltaX?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk26.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..4cf1f87109c3bf923debf7241b97e499af26fa47 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 55, + "timestamp": 1684517099986.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 20:29, why does x0-(x0+deltaX) simplify to -deltaX? Shouldn't x0 - x0 equal 0, and adding 0 to deltaX = deltaX?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk3.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..4cf1f87109c3bf923debf7241b97e499af26fa47 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 55, + "timestamp": 1684517099986.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 20:29, why does x0-(x0+deltaX) simplify to -deltaX? Shouldn't x0 - x0 equal 0, and adding 0 to deltaX = deltaX?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk4.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..4cf1f87109c3bf923debf7241b97e499af26fa47 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 55, + "timestamp": 1684517099986.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 20:29, why does x0-(x0+deltaX) simplify to -deltaX? Shouldn't x0 - x0 equal 0, and adding 0 to deltaX = deltaX?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk5.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..4cf1f87109c3bf923debf7241b97e499af26fa47 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 55, + "timestamp": 1684517099986.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 20:29, why does x0-(x0+deltaX) simplify to -deltaX? Shouldn't x0 - x0 equal 0, and adding 0 to deltaX = deltaX?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk6.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..4cf1f87109c3bf923debf7241b97e499af26fa47 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 55, + "timestamp": 1684517099986.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 20:29, why does x0-(x0+deltaX) simplify to -deltaX? Shouldn't x0 - x0 equal 0, and adding 0 to deltaX = deltaX?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk7.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..4cf1f87109c3bf923debf7241b97e499af26fa47 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 55, + "timestamp": 1684517099986.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 20:29, why does x0-(x0+deltaX) simplify to -deltaX? Shouldn't x0 - x0 equal 0, and adding 0 to deltaX = deltaX?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk8.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..4cf1f87109c3bf923debf7241b97e499af26fa47 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 55, + "timestamp": 1684517099986.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 20:29, why does x0-(x0+deltaX) simplify to -deltaX? Shouldn't x0 - x0 equal 0, and adding 0 to deltaX = deltaX?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk9.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..eeb05393d4b63600abbb419a32d3760e862d9850 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_55_chunk9.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 55, + "timestamp": 1684517099986.0, + "annotatedSourceSentencesIndices": [ + 3 + ], + "names": [ + "annotator1" + ], + "text": "At 20:29, why does x0-(x0+deltaX) simplify to -deltaX? Shouldn't x0 - x0 equal 0, and adding 0 to deltaX = deltaX?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk0.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..4d1a8d3d2d04a697ac38b8305927fa2b22e7977f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 58, + "timestamp": 1684517285810.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi friends,\n\nCan someone please clarify below 2 doubts, please \n\n1. What does those junk terms exactly look like? One example string would be good\n\n2. Why did prof didn\u2019t substitute with x0 in last calculation \n\nThank You very much in advance \ud83d\ude4f\ud83c\udffb" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk1.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..4d1a8d3d2d04a697ac38b8305927fa2b22e7977f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 58, + "timestamp": 1684517285810.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi friends,\n\nCan someone please clarify below 2 doubts, please \n\n1. What does those junk terms exactly look like? One example string would be good\n\n2. Why did prof didn\u2019t substitute with x0 in last calculation \n\nThank You very much in advance \ud83d\ude4f\ud83c\udffb" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk10.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..4d1a8d3d2d04a697ac38b8305927fa2b22e7977f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 58, + "timestamp": 1684517285810.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi friends,\n\nCan someone please clarify below 2 doubts, please \n\n1. What does those junk terms exactly look like? One example string would be good\n\n2. Why did prof didn\u2019t substitute with x0 in last calculation \n\nThank You very much in advance \ud83d\ude4f\ud83c\udffb" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk11.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..4d1a8d3d2d04a697ac38b8305927fa2b22e7977f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 58, + "timestamp": 1684517285810.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi friends,\n\nCan someone please clarify below 2 doubts, please \n\n1. What does those junk terms exactly look like? One example string would be good\n\n2. Why did prof didn\u2019t substitute with x0 in last calculation \n\nThank You very much in advance \ud83d\ude4f\ud83c\udffb" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk12.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..4d1a8d3d2d04a697ac38b8305927fa2b22e7977f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 58, + "timestamp": 1684517285810.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi friends,\n\nCan someone please clarify below 2 doubts, please \n\n1. What does those junk terms exactly look like? One example string would be good\n\n2. Why did prof didn\u2019t substitute with x0 in last calculation \n\nThank You very much in advance \ud83d\ude4f\ud83c\udffb" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk13.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..4d1a8d3d2d04a697ac38b8305927fa2b22e7977f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 58, + "timestamp": 1684517285810.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi friends,\n\nCan someone please clarify below 2 doubts, please \n\n1. What does those junk terms exactly look like? One example string would be good\n\n2. Why did prof didn\u2019t substitute with x0 in last calculation \n\nThank You very much in advance \ud83d\ude4f\ud83c\udffb" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk14.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..4d1a8d3d2d04a697ac38b8305927fa2b22e7977f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 58, + "timestamp": 1684517285810.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi friends,\n\nCan someone please clarify below 2 doubts, please \n\n1. What does those junk terms exactly look like? One example string would be good\n\n2. Why did prof didn\u2019t substitute with x0 in last calculation \n\nThank You very much in advance \ud83d\ude4f\ud83c\udffb" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk15.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..4d1a8d3d2d04a697ac38b8305927fa2b22e7977f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 58, + "timestamp": 1684517285810.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi friends,\n\nCan someone please clarify below 2 doubts, please \n\n1. What does those junk terms exactly look like? One example string would be good\n\n2. Why did prof didn\u2019t substitute with x0 in last calculation \n\nThank You very much in advance \ud83d\ude4f\ud83c\udffb" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk16.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..4d1a8d3d2d04a697ac38b8305927fa2b22e7977f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 58, + "timestamp": 1684517285810.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi friends,\n\nCan someone please clarify below 2 doubts, please \n\n1. What does those junk terms exactly look like? One example string would be good\n\n2. Why did prof didn\u2019t substitute with x0 in last calculation \n\nThank You very much in advance \ud83d\ude4f\ud83c\udffb" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk17.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..4d1a8d3d2d04a697ac38b8305927fa2b22e7977f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 58, + "timestamp": 1684517285810.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi friends,\n\nCan someone please clarify below 2 doubts, please \n\n1. What does those junk terms exactly look like? One example string would be good\n\n2. Why did prof didn\u2019t substitute with x0 in last calculation \n\nThank You very much in advance \ud83d\ude4f\ud83c\udffb" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk18.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4d1a8d3d2d04a697ac38b8305927fa2b22e7977f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 58, + "timestamp": 1684517285810.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi friends,\n\nCan someone please clarify below 2 doubts, please \n\n1. What does those junk terms exactly look like? One example string would be good\n\n2. Why did prof didn\u2019t substitute with x0 in last calculation \n\nThank You very much in advance \ud83d\ude4f\ud83c\udffb" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk19.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..4d1a8d3d2d04a697ac38b8305927fa2b22e7977f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 58, + "timestamp": 1684517285810.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi friends,\n\nCan someone please clarify below 2 doubts, please \n\n1. What does those junk terms exactly look like? One example string would be good\n\n2. Why did prof didn\u2019t substitute with x0 in last calculation \n\nThank You very much in advance \ud83d\ude4f\ud83c\udffb" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk2.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..4d1a8d3d2d04a697ac38b8305927fa2b22e7977f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 58, + "timestamp": 1684517285810.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi friends,\n\nCan someone please clarify below 2 doubts, please \n\n1. What does those junk terms exactly look like? One example string would be good\n\n2. Why did prof didn\u2019t substitute with x0 in last calculation \n\nThank You very much in advance \ud83d\ude4f\ud83c\udffb" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk20.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..4d1a8d3d2d04a697ac38b8305927fa2b22e7977f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 58, + "timestamp": 1684517285810.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi friends,\n\nCan someone please clarify below 2 doubts, please \n\n1. What does those junk terms exactly look like? One example string would be good\n\n2. Why did prof didn\u2019t substitute with x0 in last calculation \n\nThank You very much in advance \ud83d\ude4f\ud83c\udffb" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk21.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..4d1a8d3d2d04a697ac38b8305927fa2b22e7977f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 58, + "timestamp": 1684517285810.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi friends,\n\nCan someone please clarify below 2 doubts, please \n\n1. What does those junk terms exactly look like? One example string would be good\n\n2. Why did prof didn\u2019t substitute with x0 in last calculation \n\nThank You very much in advance \ud83d\ude4f\ud83c\udffb" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk22.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..7e0517489cc240705d36046be3d752ee11b6e5c1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk22.json @@ -0,0 +1,16 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 58, + "timestamp": 1684517285810.0, + "annotatedSourceSentencesIndices": [ + 12, + 13, + 14 + ], + "names": [ + "annotator1" + ], + "text": "Hi friends,\n\nCan someone please clarify below 2 doubts, please \n\n1. What does those junk terms exactly look like? One example string would be good\n\n2. Why did prof didn\u2019t substitute with x0 in last calculation \n\nThank You very much in advance \ud83d\ude4f\ud83c\udffb" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk23.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..d190f4836825e7a530325de622605d30b0ae2891 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk23.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 58, + "timestamp": 1684517285810.0, + "annotatedSourceSentencesIndices": [ + 15 + ], + "names": [ + "annotator1" + ], + "text": "Hi friends,\n\nCan someone please clarify below 2 doubts, please \n\n1. What does those junk terms exactly look like? One example string would be good\n\n2. Why did prof didn\u2019t substitute with x0 in last calculation \n\nThank You very much in advance \ud83d\ude4f\ud83c\udffb" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk24.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..4d1a8d3d2d04a697ac38b8305927fa2b22e7977f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 58, + "timestamp": 1684517285810.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi friends,\n\nCan someone please clarify below 2 doubts, please \n\n1. What does those junk terms exactly look like? One example string would be good\n\n2. Why did prof didn\u2019t substitute with x0 in last calculation \n\nThank You very much in advance \ud83d\ude4f\ud83c\udffb" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk25.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4d1a8d3d2d04a697ac38b8305927fa2b22e7977f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 58, + "timestamp": 1684517285810.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi friends,\n\nCan someone please clarify below 2 doubts, please \n\n1. What does those junk terms exactly look like? One example string would be good\n\n2. Why did prof didn\u2019t substitute with x0 in last calculation \n\nThank You very much in advance \ud83d\ude4f\ud83c\udffb" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk26.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..4d1a8d3d2d04a697ac38b8305927fa2b22e7977f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 58, + "timestamp": 1684517285810.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi friends,\n\nCan someone please clarify below 2 doubts, please \n\n1. What does those junk terms exactly look like? One example string would be good\n\n2. Why did prof didn\u2019t substitute with x0 in last calculation \n\nThank You very much in advance \ud83d\ude4f\ud83c\udffb" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk3.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..4d1a8d3d2d04a697ac38b8305927fa2b22e7977f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 58, + "timestamp": 1684517285810.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi friends,\n\nCan someone please clarify below 2 doubts, please \n\n1. What does those junk terms exactly look like? One example string would be good\n\n2. Why did prof didn\u2019t substitute with x0 in last calculation \n\nThank You very much in advance \ud83d\ude4f\ud83c\udffb" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk4.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..4d1a8d3d2d04a697ac38b8305927fa2b22e7977f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 58, + "timestamp": 1684517285810.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi friends,\n\nCan someone please clarify below 2 doubts, please \n\n1. What does those junk terms exactly look like? One example string would be good\n\n2. Why did prof didn\u2019t substitute with x0 in last calculation \n\nThank You very much in advance \ud83d\ude4f\ud83c\udffb" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk5.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..4d1a8d3d2d04a697ac38b8305927fa2b22e7977f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 58, + "timestamp": 1684517285810.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi friends,\n\nCan someone please clarify below 2 doubts, please \n\n1. What does those junk terms exactly look like? One example string would be good\n\n2. Why did prof didn\u2019t substitute with x0 in last calculation \n\nThank You very much in advance \ud83d\ude4f\ud83c\udffb" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk6.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..4d1a8d3d2d04a697ac38b8305927fa2b22e7977f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 58, + "timestamp": 1684517285810.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi friends,\n\nCan someone please clarify below 2 doubts, please \n\n1. What does those junk terms exactly look like? One example string would be good\n\n2. Why did prof didn\u2019t substitute with x0 in last calculation \n\nThank You very much in advance \ud83d\ude4f\ud83c\udffb" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk7.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..4d1a8d3d2d04a697ac38b8305927fa2b22e7977f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 58, + "timestamp": 1684517285810.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi friends,\n\nCan someone please clarify below 2 doubts, please \n\n1. What does those junk terms exactly look like? One example string would be good\n\n2. Why did prof didn\u2019t substitute with x0 in last calculation \n\nThank You very much in advance \ud83d\ude4f\ud83c\udffb" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk8.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..4d1a8d3d2d04a697ac38b8305927fa2b22e7977f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 58, + "timestamp": 1684517285810.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi friends,\n\nCan someone please clarify below 2 doubts, please \n\n1. What does those junk terms exactly look like? One example string would be good\n\n2. Why did prof didn\u2019t substitute with x0 in last calculation \n\nThank You very much in advance \ud83d\ude4f\ud83c\udffb" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk9.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4d1a8d3d2d04a697ac38b8305927fa2b22e7977f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_58_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 58, + "timestamp": 1684517285810.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi friends,\n\nCan someone please clarify below 2 doubts, please \n\n1. What does those junk terms exactly look like? One example string would be good\n\n2. Why did prof didn\u2019t substitute with x0 in last calculation \n\nThank You very much in advance \ud83d\ude4f\ud83c\udffb" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk0.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..2e425e742331800a5aca45686f21d9d294157a86 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 5, + "timestamp": 1684514746641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Where do x(sub naught) and y(sub naught) go at 40:59? It may be a rudimentary question, but I've been out of math classes for a number of years now. I am able to follow along with all of this except that one piece, and it's bugging me. What did I forget?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk1.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..2e425e742331800a5aca45686f21d9d294157a86 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 5, + "timestamp": 1684514746641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Where do x(sub naught) and y(sub naught) go at 40:59? It may be a rudimentary question, but I've been out of math classes for a number of years now. I am able to follow along with all of this except that one piece, and it's bugging me. What did I forget?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk10.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..2e425e742331800a5aca45686f21d9d294157a86 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 5, + "timestamp": 1684514746641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Where do x(sub naught) and y(sub naught) go at 40:59? It may be a rudimentary question, but I've been out of math classes for a number of years now. I am able to follow along with all of this except that one piece, and it's bugging me. What did I forget?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk11.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..2e425e742331800a5aca45686f21d9d294157a86 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 5, + "timestamp": 1684514746641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Where do x(sub naught) and y(sub naught) go at 40:59? It may be a rudimentary question, but I've been out of math classes for a number of years now. I am able to follow along with all of this except that one piece, and it's bugging me. What did I forget?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk12.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..2e425e742331800a5aca45686f21d9d294157a86 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 5, + "timestamp": 1684514746641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Where do x(sub naught) and y(sub naught) go at 40:59? It may be a rudimentary question, but I've been out of math classes for a number of years now. I am able to follow along with all of this except that one piece, and it's bugging me. What did I forget?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk13.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2e425e742331800a5aca45686f21d9d294157a86 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 5, + "timestamp": 1684514746641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Where do x(sub naught) and y(sub naught) go at 40:59? It may be a rudimentary question, but I've been out of math classes for a number of years now. I am able to follow along with all of this except that one piece, and it's bugging me. What did I forget?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk14.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..2e425e742331800a5aca45686f21d9d294157a86 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 5, + "timestamp": 1684514746641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Where do x(sub naught) and y(sub naught) go at 40:59? It may be a rudimentary question, but I've been out of math classes for a number of years now. I am able to follow along with all of this except that one piece, and it's bugging me. What did I forget?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk15.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..2e425e742331800a5aca45686f21d9d294157a86 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 5, + "timestamp": 1684514746641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Where do x(sub naught) and y(sub naught) go at 40:59? It may be a rudimentary question, but I've been out of math classes for a number of years now. I am able to follow along with all of this except that one piece, and it's bugging me. What did I forget?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk16.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..2e425e742331800a5aca45686f21d9d294157a86 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 5, + "timestamp": 1684514746641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Where do x(sub naught) and y(sub naught) go at 40:59? It may be a rudimentary question, but I've been out of math classes for a number of years now. I am able to follow along with all of this except that one piece, and it's bugging me. What did I forget?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk17.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..2e425e742331800a5aca45686f21d9d294157a86 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 5, + "timestamp": 1684514746641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Where do x(sub naught) and y(sub naught) go at 40:59? It may be a rudimentary question, but I've been out of math classes for a number of years now. I am able to follow along with all of this except that one piece, and it's bugging me. What did I forget?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk18.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2e425e742331800a5aca45686f21d9d294157a86 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 5, + "timestamp": 1684514746641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Where do x(sub naught) and y(sub naught) go at 40:59? It may be a rudimentary question, but I've been out of math classes for a number of years now. I am able to follow along with all of this except that one piece, and it's bugging me. What did I forget?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk19.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..2e425e742331800a5aca45686f21d9d294157a86 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 5, + "timestamp": 1684514746641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Where do x(sub naught) and y(sub naught) go at 40:59? It may be a rudimentary question, but I've been out of math classes for a number of years now. I am able to follow along with all of this except that one piece, and it's bugging me. What did I forget?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk2.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..2e425e742331800a5aca45686f21d9d294157a86 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 5, + "timestamp": 1684514746641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Where do x(sub naught) and y(sub naught) go at 40:59? It may be a rudimentary question, but I've been out of math classes for a number of years now. I am able to follow along with all of this except that one piece, and it's bugging me. What did I forget?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk20.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ad6b2e4c50ec4d5ac8f0f9d08420f8b99c2e47ff --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk20.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 5, + "timestamp": 1684514746641.0, + "annotatedSourceSentencesIndices": [ + 14, + 15 + ], + "names": [ + "annotator1" + ], + "text": "Where do x(sub naught) and y(sub naught) go at 40:59? It may be a rudimentary question, but I've been out of math classes for a number of years now. I am able to follow along with all of this except that one piece, and it's bugging me. What did I forget?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk21.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..2e425e742331800a5aca45686f21d9d294157a86 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 5, + "timestamp": 1684514746641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Where do x(sub naught) and y(sub naught) go at 40:59? It may be a rudimentary question, but I've been out of math classes for a number of years now. I am able to follow along with all of this except that one piece, and it's bugging me. What did I forget?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk22.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..2e425e742331800a5aca45686f21d9d294157a86 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 5, + "timestamp": 1684514746641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Where do x(sub naught) and y(sub naught) go at 40:59? It may be a rudimentary question, but I've been out of math classes for a number of years now. I am able to follow along with all of this except that one piece, and it's bugging me. What did I forget?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk23.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..2e425e742331800a5aca45686f21d9d294157a86 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 5, + "timestamp": 1684514746641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Where do x(sub naught) and y(sub naught) go at 40:59? It may be a rudimentary question, but I've been out of math classes for a number of years now. I am able to follow along with all of this except that one piece, and it's bugging me. What did I forget?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk24.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..2e425e742331800a5aca45686f21d9d294157a86 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 5, + "timestamp": 1684514746641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Where do x(sub naught) and y(sub naught) go at 40:59? It may be a rudimentary question, but I've been out of math classes for a number of years now. I am able to follow along with all of this except that one piece, and it's bugging me. What did I forget?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk25.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..2e425e742331800a5aca45686f21d9d294157a86 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 5, + "timestamp": 1684514746641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Where do x(sub naught) and y(sub naught) go at 40:59? It may be a rudimentary question, but I've been out of math classes for a number of years now. I am able to follow along with all of this except that one piece, and it's bugging me. What did I forget?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk26.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..2e425e742331800a5aca45686f21d9d294157a86 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 5, + "timestamp": 1684514746641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Where do x(sub naught) and y(sub naught) go at 40:59? It may be a rudimentary question, but I've been out of math classes for a number of years now. I am able to follow along with all of this except that one piece, and it's bugging me. What did I forget?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk3.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..2e425e742331800a5aca45686f21d9d294157a86 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 5, + "timestamp": 1684514746641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Where do x(sub naught) and y(sub naught) go at 40:59? It may be a rudimentary question, but I've been out of math classes for a number of years now. I am able to follow along with all of this except that one piece, and it's bugging me. What did I forget?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk4.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..2e425e742331800a5aca45686f21d9d294157a86 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 5, + "timestamp": 1684514746641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Where do x(sub naught) and y(sub naught) go at 40:59? It may be a rudimentary question, but I've been out of math classes for a number of years now. I am able to follow along with all of this except that one piece, and it's bugging me. What did I forget?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk5.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..2e425e742331800a5aca45686f21d9d294157a86 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 5, + "timestamp": 1684514746641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Where do x(sub naught) and y(sub naught) go at 40:59? It may be a rudimentary question, but I've been out of math classes for a number of years now. I am able to follow along with all of this except that one piece, and it's bugging me. What did I forget?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk6.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..2e425e742331800a5aca45686f21d9d294157a86 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 5, + "timestamp": 1684514746641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Where do x(sub naught) and y(sub naught) go at 40:59? It may be a rudimentary question, but I've been out of math classes for a number of years now. I am able to follow along with all of this except that one piece, and it's bugging me. What did I forget?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk7.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..2e425e742331800a5aca45686f21d9d294157a86 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 5, + "timestamp": 1684514746641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Where do x(sub naught) and y(sub naught) go at 40:59? It may be a rudimentary question, but I've been out of math classes for a number of years now. I am able to follow along with all of this except that one piece, and it's bugging me. What did I forget?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk8.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..2e425e742331800a5aca45686f21d9d294157a86 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 5, + "timestamp": 1684514746641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Where do x(sub naught) and y(sub naught) go at 40:59? It may be a rudimentary question, but I've been out of math classes for a number of years now. I am able to follow along with all of this except that one piece, and it's bugging me. What did I forget?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk9.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..2e425e742331800a5aca45686f21d9d294157a86 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_5_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 5, + "timestamp": 1684514746641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Where do x(sub naught) and y(sub naught) go at 40:59? It may be a rudimentary question, but I've been out of math classes for a number of years now. I am able to follow along with all of this except that one piece, and it's bugging me. What did I forget?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_60_chunk0.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_60_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..843df8670ba2278b9ccf4cc263425f3f11f8451f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_60_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 60, + "timestamp": 1684517399324.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hey in defining slope why we should take delta x tends to zero because for the point Q to be P it is both delta x and y both should be zero right??" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_60_chunk1.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_60_chunk1.json new file mode 100644 index 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"annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hey in defining slope why we should take delta x tends to zero because for the point Q to be P it is both delta x and y both should be zero right??" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_60_chunk11.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_60_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..843df8670ba2278b9ccf4cc263425f3f11f8451f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_60_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 60, + "timestamp": 1684517399324.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hey in defining slope why we should take delta x tends to zero because for the point Q to be P it is both delta x and y both should be zero right??" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_60_chunk12.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_60_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..843df8670ba2278b9ccf4cc263425f3f11f8451f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_60_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 60, + "timestamp": 1684517399324.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hey in defining slope why we should take delta x tends to zero because for the point Q to be P it is both delta x and y both should be zero right??" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_60_chunk13.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_60_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..843df8670ba2278b9ccf4cc263425f3f11f8451f --- /dev/null +++ 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should take delta x tends to zero because for the point Q to be P it is both delta x and y both should be zero right??" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_60_chunk15.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_60_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..843df8670ba2278b9ccf4cc263425f3f11f8451f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_60_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 60, + "timestamp": 1684517399324.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hey in defining slope why we should take delta x tends to zero because for the point Q to be P it is both delta x and y both should be zero right??" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_60_chunk16.json 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both should be zero right??" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_60_chunk19.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_60_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..843df8670ba2278b9ccf4cc263425f3f11f8451f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_60_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 60, + "timestamp": 1684517399324.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hey in defining slope why we should take delta x tends to zero because for the point Q to be P it is both delta x and y both should be zero right??" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_60_chunk2.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_60_chunk2.json new file mode 100644 index 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should take delta x tends to zero because for the point Q to be P it is both delta x and y both should be zero right??" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_60_chunk25.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_60_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..843df8670ba2278b9ccf4cc263425f3f11f8451f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_60_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 60, + "timestamp": 1684517399324.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hey in defining slope why we should take delta x tends to zero because for the point Q to be P it is both delta x and y both should be zero right??" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_60_chunk26.json 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"annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hey in defining slope why we should take delta x tends to zero because for the point Q to be P it is both delta x and y both should be zero right??" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_60_chunk8.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_60_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..843df8670ba2278b9ccf4cc263425f3f11f8451f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_60_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 60, + "timestamp": 1684517399324.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hey in defining slope why we should take delta x tends to zero because for the point Q to be P it is both delta x and y both should be zero right??" + } +] \ No newline at end of file diff --git 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Not that he doesnt understand what he explains but his methodology is not essentialising the obscure concepts. First, he should have discribed the slope as delta x on delta y....( why f(x))?...or the obscure equation y-yo= m (x-xo)... could have been easyer as m= delta x/delta y...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk1.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..31da50f39e8d8fb5cb06d527b65462213aa29767 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 63, + "timestamp": 1684517523119.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "This professor is not the best I've seen on youtube. Not that he doesnt understand what he explains but his methodology is not essentialising the obscure concepts. First, he should have discribed the slope as delta x on delta y....( why f(x))?...or the obscure equation y-yo= m (x-xo)... could have been easyer as m= delta x/delta y...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk10.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..31da50f39e8d8fb5cb06d527b65462213aa29767 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 63, + "timestamp": 1684517523119.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "This professor is not the best I've seen on youtube. Not that he doesnt understand what he explains but his methodology is not essentialising the obscure concepts. First, he should have discribed the slope as delta x on delta y....( why f(x))?...or the obscure equation y-yo= m (x-xo)... could have been easyer as m= delta x/delta y...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk11.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..31da50f39e8d8fb5cb06d527b65462213aa29767 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 63, + "timestamp": 1684517523119.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "This professor is not the best I've seen on youtube. Not that he doesnt understand what he explains but his methodology is not essentialising the obscure concepts. First, he should have discribed the slope as delta x on delta y....( why f(x))?...or the obscure equation y-yo= m (x-xo)... could have been easyer as m= delta x/delta y...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk12.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..31da50f39e8d8fb5cb06d527b65462213aa29767 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 63, + "timestamp": 1684517523119.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "This professor is not the best I've seen on youtube. Not that he doesnt understand what he explains but his methodology is not essentialising the obscure concepts. First, he should have discribed the slope as delta x on delta y....( why f(x))?...or the obscure equation y-yo= m (x-xo)... could have been easyer as m= delta x/delta y...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk13.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..31da50f39e8d8fb5cb06d527b65462213aa29767 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 63, + "timestamp": 1684517523119.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "This professor is not the best I've seen on youtube. Not that he doesnt understand what he explains but his methodology is not essentialising the obscure concepts. First, he should have discribed the slope as delta x on delta y....( why f(x))?...or the obscure equation y-yo= m (x-xo)... could have been easyer as m= delta x/delta y...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk14.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..31da50f39e8d8fb5cb06d527b65462213aa29767 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 63, + "timestamp": 1684517523119.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "This professor is not the best I've seen on youtube. Not that he doesnt understand what he explains but his methodology is not essentialising the obscure concepts. First, he should have discribed the slope as delta x on delta y....( why f(x))?...or the obscure equation y-yo= m (x-xo)... could have been easyer as m= delta x/delta y...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk15.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..432bc20f00c3ce6f13b92a165c65c4d9a3daf2f6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk15.json @@ -0,0 +1,17 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 63, + "timestamp": 1684517523119.0, + "annotatedSourceSentencesIndices": [ + 9, + 10, + 11, + 12 + ], + "names": [ + "annotator1" + ], + "text": "This professor is not the best I've seen on youtube. Not that he doesnt understand what he explains but his methodology is not essentialising the obscure concepts. First, he should have discribed the slope as delta x on delta y....( why f(x))?...or the obscure equation y-yo= m (x-xo)... could have been easyer as m= delta x/delta y...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk16.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..31da50f39e8d8fb5cb06d527b65462213aa29767 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 63, + "timestamp": 1684517523119.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "This professor is not the best I've seen on youtube. Not that he doesnt understand what he explains but his methodology is not essentialising the obscure concepts. First, he should have discribed the slope as delta x on delta y....( why f(x))?...or the obscure equation y-yo= m (x-xo)... could have been easyer as m= delta x/delta y...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk17.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..31da50f39e8d8fb5cb06d527b65462213aa29767 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 63, + "timestamp": 1684517523119.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "This professor is not the best I've seen on youtube. Not that he doesnt understand what he explains but his methodology is not essentialising the obscure concepts. First, he should have discribed the slope as delta x on delta y....( why f(x))?...or the obscure equation y-yo= m (x-xo)... could have been easyer as m= delta x/delta y...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk18.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..31da50f39e8d8fb5cb06d527b65462213aa29767 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 63, + "timestamp": 1684517523119.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "This professor is not the best I've seen on youtube. Not that he doesnt understand what he explains but his methodology is not essentialising the obscure concepts. First, he should have discribed the slope as delta x on delta y....( why f(x))?...or the obscure equation y-yo= m (x-xo)... could have been easyer as m= delta x/delta y...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk19.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..31da50f39e8d8fb5cb06d527b65462213aa29767 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 63, + "timestamp": 1684517523119.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "This professor is not the best I've seen on youtube. Not that he doesnt understand what he explains but his methodology is not essentialising the obscure concepts. First, he should have discribed the slope as delta x on delta y....( why f(x))?...or the obscure equation y-yo= m (x-xo)... could have been easyer as m= delta x/delta y...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk2.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..31da50f39e8d8fb5cb06d527b65462213aa29767 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 63, + "timestamp": 1684517523119.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "This professor is not the best I've seen on youtube. Not that he doesnt understand what he explains but his methodology is not essentialising the obscure concepts. First, he should have discribed the slope as delta x on delta y....( why f(x))?...or the obscure equation y-yo= m (x-xo)... could have been easyer as m= delta x/delta y...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk20.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..31da50f39e8d8fb5cb06d527b65462213aa29767 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 63, + "timestamp": 1684517523119.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "This professor is not the best I've seen on youtube. Not that he doesnt understand what he explains but his methodology is not essentialising the obscure concepts. First, he should have discribed the slope as delta x on delta y....( why f(x))?...or the obscure equation y-yo= m (x-xo)... could have been easyer as m= delta x/delta y...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk21.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..31da50f39e8d8fb5cb06d527b65462213aa29767 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 63, + "timestamp": 1684517523119.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "This professor is not the best I've seen on youtube. Not that he doesnt understand what he explains but his methodology is not essentialising the obscure concepts. First, he should have discribed the slope as delta x on delta y....( why f(x))?...or the obscure equation y-yo= m (x-xo)... could have been easyer as m= delta x/delta y...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk22.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..31da50f39e8d8fb5cb06d527b65462213aa29767 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 63, + "timestamp": 1684517523119.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "This professor is not the best I've seen on youtube. Not that he doesnt understand what he explains but his methodology is not essentialising the obscure concepts. First, he should have discribed the slope as delta x on delta y....( why f(x))?...or the obscure equation y-yo= m (x-xo)... could have been easyer as m= delta x/delta y...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk23.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..31da50f39e8d8fb5cb06d527b65462213aa29767 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 63, + "timestamp": 1684517523119.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "This professor is not the best I've seen on youtube. Not that he doesnt understand what he explains but his methodology is not essentialising the obscure concepts. First, he should have discribed the slope as delta x on delta y....( why f(x))?...or the obscure equation y-yo= m (x-xo)... could have been easyer as m= delta x/delta y...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk24.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..31da50f39e8d8fb5cb06d527b65462213aa29767 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 63, + "timestamp": 1684517523119.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "This professor is not the best I've seen on youtube. Not that he doesnt understand what he explains but his methodology is not essentialising the obscure concepts. First, he should have discribed the slope as delta x on delta y....( why f(x))?...or the obscure equation y-yo= m (x-xo)... could have been easyer as m= delta x/delta y...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk25.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..31da50f39e8d8fb5cb06d527b65462213aa29767 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 63, + "timestamp": 1684517523119.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "This professor is not the best I've seen on youtube. Not that he doesnt understand what he explains but his methodology is not essentialising the obscure concepts. First, he should have discribed the slope as delta x on delta y....( why f(x))?...or the obscure equation y-yo= m (x-xo)... could have been easyer as m= delta x/delta y...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk26.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..31da50f39e8d8fb5cb06d527b65462213aa29767 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 63, + "timestamp": 1684517523119.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "This professor is not the best I've seen on youtube. Not that he doesnt understand what he explains but his methodology is not essentialising the obscure concepts. First, he should have discribed the slope as delta x on delta y....( why f(x))?...or the obscure equation y-yo= m (x-xo)... could have been easyer as m= delta x/delta y...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk3.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..31da50f39e8d8fb5cb06d527b65462213aa29767 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 63, + "timestamp": 1684517523119.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "This professor is not the best I've seen on youtube. Not that he doesnt understand what he explains but his methodology is not essentialising the obscure concepts. First, he should have discribed the slope as delta x on delta y....( why f(x))?...or the obscure equation y-yo= m (x-xo)... could have been easyer as m= delta x/delta y...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk4.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..31da50f39e8d8fb5cb06d527b65462213aa29767 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 63, + "timestamp": 1684517523119.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "This professor is not the best I've seen on youtube. Not that he doesnt understand what he explains but his methodology is not essentialising the obscure concepts. First, he should have discribed the slope as delta x on delta y....( why f(x))?...or the obscure equation y-yo= m (x-xo)... could have been easyer as m= delta x/delta y...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk5.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..31da50f39e8d8fb5cb06d527b65462213aa29767 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 63, + "timestamp": 1684517523119.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "This professor is not the best I've seen on youtube. Not that he doesnt understand what he explains but his methodology is not essentialising the obscure concepts. First, he should have discribed the slope as delta x on delta y....( why f(x))?...or the obscure equation y-yo= m (x-xo)... could have been easyer as m= delta x/delta y...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk6.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9b8a0ea6fde29a6ee36fcd573db17aa0e0eee9d6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk6.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 63, + "timestamp": 1684517523119.0, + "annotatedSourceSentencesIndices": [ + 4 + ], + "names": [ + "annotator1" + ], + "text": "This professor is not the best I've seen on youtube. Not that he doesnt understand what he explains but his methodology is not essentialising the obscure concepts. First, he should have discribed the slope as delta x on delta y....( why f(x))?...or the obscure equation y-yo= m (x-xo)... could have been easyer as m= delta x/delta y...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk7.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..31da50f39e8d8fb5cb06d527b65462213aa29767 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 63, + "timestamp": 1684517523119.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "This professor is not the best I've seen on youtube. Not that he doesnt understand what he explains but his methodology is not essentialising the obscure concepts. First, he should have discribed the slope as delta x on delta y....( why f(x))?...or the obscure equation y-yo= m (x-xo)... could have been easyer as m= delta x/delta y...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk8.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..31da50f39e8d8fb5cb06d527b65462213aa29767 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 63, + "timestamp": 1684517523119.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "This professor is not the best I've seen on youtube. Not that he doesnt understand what he explains but his methodology is not essentialising the obscure concepts. First, he should have discribed the slope as delta x on delta y....( why f(x))?...or the obscure equation y-yo= m (x-xo)... could have been easyer as m= delta x/delta y...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk9.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..31da50f39e8d8fb5cb06d527b65462213aa29767 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_63_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 63, + "timestamp": 1684517523119.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "This professor is not the best I've seen on youtube. Not that he doesnt understand what he explains but his methodology is not essentialising the obscure concepts. First, he should have discribed the slope as delta x on delta y....( why f(x))?...or the obscure equation y-yo= m (x-xo)... could have been easyer as m= delta x/delta y...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_64_chunk0.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_64_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..f41ca10841467059701d70cec36f51e6ce31fa8e --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_64_chunk0.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 64, + "timestamp": 1684517528984.0, + "annotatedSourceSentencesIndices": [ + 3 + ], + "names": [ + "annotator1" + ], + "text": "Is there any prerequisite required?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_64_chunk1.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_64_chunk1.json new file mode 100644 index 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\ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_64_chunk11.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_64_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..edec9402ed9c061a9d74f31569b906e1b59ae4a3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_64_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 64, + "timestamp": 1684517528984.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is there any prerequisite required?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_64_chunk12.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_64_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..edec9402ed9c061a9d74f31569b906e1b59ae4a3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_64_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 64, + "timestamp": 1684517528984.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is there any prerequisite required?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_64_chunk13.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_64_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..edec9402ed9c061a9d74f31569b906e1b59ae4a3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_64_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 64, + "timestamp": 1684517528984.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is there any prerequisite required?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_64_chunk14.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_64_chunk14.json new file mode 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Won't \u2206x be multiplied n-1 times instead of n?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk20.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..bdc548d9ee144e022bbe16996828afd659285426 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 67, + "timestamp": 1684517591721.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I didn't quite understand how (x+\u2206x).....(x+\u2206x) got us the term nx^n-1\u2206x. Won't \u2206x be multiplied n-1 times instead of n?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk21.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..bdc548d9ee144e022bbe16996828afd659285426 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 67, + "timestamp": 1684517591721.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I didn't quite understand how (x+\u2206x).....(x+\u2206x) got us the term nx^n-1\u2206x. Won't \u2206x be multiplied n-1 times instead of n?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk22.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..bdc548d9ee144e022bbe16996828afd659285426 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 67, + "timestamp": 1684517591721.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I didn't quite understand how (x+\u2206x).....(x+\u2206x) got us the term nx^n-1\u2206x. Won't \u2206x be multiplied n-1 times instead of n?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk23.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..bdc548d9ee144e022bbe16996828afd659285426 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 67, + "timestamp": 1684517591721.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I didn't quite understand how (x+\u2206x).....(x+\u2206x) got us the term nx^n-1\u2206x. Won't \u2206x be multiplied n-1 times instead of n?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk24.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..844a08f7b9460b20baf053b712d3fdcc2206c79d --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk24.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 67, + "timestamp": 1684517591721.0, + "annotatedSourceSentencesIndices": [ + 7 + ], + "names": [ + "annotator1" + ], + "text": "I didn't quite understand how (x+\u2206x).....(x+\u2206x) got us the term nx^n-1\u2206x. Won't \u2206x be multiplied n-1 times instead of n?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk25.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..bdc548d9ee144e022bbe16996828afd659285426 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 67, + "timestamp": 1684517591721.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I didn't quite understand how (x+\u2206x).....(x+\u2206x) got us the term nx^n-1\u2206x. Won't \u2206x be multiplied n-1 times instead of n?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk26.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..bdc548d9ee144e022bbe16996828afd659285426 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 67, + "timestamp": 1684517591721.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I didn't quite understand how (x+\u2206x).....(x+\u2206x) got us the term nx^n-1\u2206x. Won't \u2206x be multiplied n-1 times instead of n?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk3.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..bdc548d9ee144e022bbe16996828afd659285426 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 67, + "timestamp": 1684517591721.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I didn't quite understand how (x+\u2206x).....(x+\u2206x) got us the term nx^n-1\u2206x. Won't \u2206x be multiplied n-1 times instead of n?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk4.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..bdc548d9ee144e022bbe16996828afd659285426 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 67, + "timestamp": 1684517591721.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I didn't quite understand how (x+\u2206x).....(x+\u2206x) got us the term nx^n-1\u2206x. Won't \u2206x be multiplied n-1 times instead of n?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk5.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..bdc548d9ee144e022bbe16996828afd659285426 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 67, + "timestamp": 1684517591721.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I didn't quite understand how (x+\u2206x).....(x+\u2206x) got us the term nx^n-1\u2206x. Won't \u2206x be multiplied n-1 times instead of n?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk6.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..bdc548d9ee144e022bbe16996828afd659285426 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 67, + "timestamp": 1684517591721.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I didn't quite understand how (x+\u2206x).....(x+\u2206x) got us the term nx^n-1\u2206x. Won't \u2206x be multiplied n-1 times instead of n?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk7.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..bdc548d9ee144e022bbe16996828afd659285426 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 67, + "timestamp": 1684517591721.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I didn't quite understand how (x+\u2206x).....(x+\u2206x) got us the term nx^n-1\u2206x. Won't \u2206x be multiplied n-1 times instead of n?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk8.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..bdc548d9ee144e022bbe16996828afd659285426 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 67, + "timestamp": 1684517591721.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I didn't quite understand how (x+\u2206x).....(x+\u2206x) got us the term nx^n-1\u2206x. Won't \u2206x be multiplied n-1 times instead of n?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk9.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bdc548d9ee144e022bbe16996828afd659285426 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_67_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 67, + "timestamp": 1684517591721.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I didn't quite understand how (x+\u2206x).....(x+\u2206x) got us the term nx^n-1\u2206x. Won't \u2206x be multiplied n-1 times instead of n?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk0.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..c720f6d5df5c984bc8ac51cff07dd1704ca971db --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk0.json @@ -0,0 +1,19 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 6, + "timestamp": 1684514906495.0, + "annotatedSourceSentencesIndices": [ + 7, + 8, + 9, + 10, + 11, + 12 + ], + "names": [ + "annotator1" + ], + "text": "Why aren't they giving a meaningful description of what a derivative is in plain English? E.g. The derivative of a function is the function that evaluates to the rate of change for a given input." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk1.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..d96383475a1cbf75eca6433dadddc3f9e8b80358 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk1.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 6, + "timestamp": 1684514906495.0, + "annotatedSourceSentencesIndices": [ + 3, + 8 + ], + "names": [ + "annotator1" + ], + "text": "Why aren't they giving a meaningful description of what a derivative is in plain English? E.g. The derivative of a function is the function that evaluates to the rate of change for a given input." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk10.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..4546c2b7223cac433897a318852bd14298eaae7b --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 6, + "timestamp": 1684514906495.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why aren't they giving a meaningful description of what a derivative is in plain English? E.g. The derivative of a function is the function that evaluates to the rate of change for a given input." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk11.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..4546c2b7223cac433897a318852bd14298eaae7b --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 6, + "timestamp": 1684514906495.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why aren't they giving a meaningful description of what a derivative is in plain English? E.g. The derivative of a function is the function that evaluates to the rate of change for a given input." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk12.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..4546c2b7223cac433897a318852bd14298eaae7b --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 6, + "timestamp": 1684514906495.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why aren't they giving a meaningful description of what a derivative is in plain English? E.g. The derivative of a function is the function that evaluates to the rate of change for a given input." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk13.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..4546c2b7223cac433897a318852bd14298eaae7b --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 6, + "timestamp": 1684514906495.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why aren't they giving a meaningful description of what a derivative is in plain English? E.g. The derivative of a function is the function that evaluates to the rate of change for a given input." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk14.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..4546c2b7223cac433897a318852bd14298eaae7b --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 6, + "timestamp": 1684514906495.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why aren't they giving a meaningful description of what a derivative is in plain English? E.g. The derivative of a function is the function that evaluates to the rate of change for a given input." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk15.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..4546c2b7223cac433897a318852bd14298eaae7b --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 6, + "timestamp": 1684514906495.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why aren't they giving a meaningful description of what a derivative is in plain English? E.g. The derivative of a function is the function that evaluates to the rate of change for a given input." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk16.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..4546c2b7223cac433897a318852bd14298eaae7b --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 6, + "timestamp": 1684514906495.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why aren't they giving a meaningful description of what a derivative is in plain English? E.g. The derivative of a function is the function that evaluates to the rate of change for a given input." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk17.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..4546c2b7223cac433897a318852bd14298eaae7b --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 6, + "timestamp": 1684514906495.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why aren't they giving a meaningful description of what a derivative is in plain English? E.g. The derivative of a function is the function that evaluates to the rate of change for a given input." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk18.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4546c2b7223cac433897a318852bd14298eaae7b --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 6, + "timestamp": 1684514906495.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why aren't they giving a meaningful description of what a derivative is in plain English? E.g. The derivative of a function is the function that evaluates to the rate of change for a given input." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk19.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..4546c2b7223cac433897a318852bd14298eaae7b --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_6_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 6, + "timestamp": 1684514906495.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why aren't they giving a meaningful description of what a derivative is in plain English? E.g. 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"names": [ + "annotator1" + ], + "text": "How is it 2 40:50?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_70_chunk3.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_70_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..94783c038f73e1eb26e3c349747f2e25774c6466 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_70_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 70, + "timestamp": 1684517599157.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "How is it 2 40:50?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_70_chunk4.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_70_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..94783c038f73e1eb26e3c349747f2e25774c6466 --- /dev/null +++ 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+ "annotator1" + ], + "text": "How is it 2 40:50?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_70_chunk8.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_70_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..94783c038f73e1eb26e3c349747f2e25774c6466 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_70_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 70, + "timestamp": 1684517599157.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "How is it 2 40:50?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_70_chunk9.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_70_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..94783c038f73e1eb26e3c349747f2e25774c6466 --- /dev/null +++ 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f (x) >= 2*x ?\nPlease i need help on this one" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk1.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..1d939db8c24da4ea1194dceb703b696b2b771206 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 72, + "timestamp": 1684517721236.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "guys i have a question \nif we have something like this one -->\nf(x)>x^2 +e and this is true for every real x\nCan i differentate this and say\nFirst derivative of f (x) >= 2*x ?\nPlease i need help on this one" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk10.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..1d939db8c24da4ea1194dceb703b696b2b771206 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 72, + "timestamp": 1684517721236.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "guys i have a question \nif we have something like this one -->\nf(x)>x^2 +e and this is true for every real x\nCan i differentate this and say\nFirst derivative of f (x) >= 2*x ?\nPlease i need help on this one" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk11.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..1d939db8c24da4ea1194dceb703b696b2b771206 --- /dev/null +++ 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[ + "annotator1" + ], + "text": "guys i have a question \nif we have something like this one -->\nf(x)>x^2 +e and this is true for every real x\nCan i differentate this and say\nFirst derivative of f (x) >= 2*x ?\nPlease i need help on this one" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk13.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1d939db8c24da4ea1194dceb703b696b2b771206 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 72, + "timestamp": 1684517721236.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "guys i have a question \nif we have something like this one -->\nf(x)>x^2 +e and this is true for every real x\nCan i differentate this and say\nFirst derivative of f (x) >= 2*x ?\nPlease i need help on this one" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk14.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..1d939db8c24da4ea1194dceb703b696b2b771206 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 72, + "timestamp": 1684517721236.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "guys i have a question \nif we have something like this one -->\nf(x)>x^2 +e and this is true for every real x\nCan i differentate this and say\nFirst derivative of f (x) >= 2*x ?\nPlease i need help on this one" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk15.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..1d939db8c24da4ea1194dceb703b696b2b771206 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 72, + "timestamp": 1684517721236.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "guys i have a question \nif we have something like this one -->\nf(x)>x^2 +e and this is true for every real x\nCan i differentate this and say\nFirst derivative of f (x) >= 2*x ?\nPlease i need help on this one" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk16.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..1d939db8c24da4ea1194dceb703b696b2b771206 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 72, + "timestamp": 1684517721236.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "guys i have a question \nif we have something like this one -->\nf(x)>x^2 +e and this is true for every real x\nCan i differentate this and say\nFirst derivative of f (x) >= 2*x ?\nPlease i need help on this one" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk17.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..1d939db8c24da4ea1194dceb703b696b2b771206 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 72, + "timestamp": 1684517721236.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "guys i have a question \nif we have something like this one -->\nf(x)>x^2 +e and this is true for every real x\nCan i differentate this and say\nFirst derivative of f (x) >= 2*x ?\nPlease i need help on this one" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk18.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..1d939db8c24da4ea1194dceb703b696b2b771206 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 72, + "timestamp": 1684517721236.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "guys i have a question \nif we have something like this one -->\nf(x)>x^2 +e and this is true for every real x\nCan i differentate this and say\nFirst derivative of f (x) >= 2*x ?\nPlease i need help on this one" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk19.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1d939db8c24da4ea1194dceb703b696b2b771206 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 72, + "timestamp": 1684517721236.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "guys i have a question \nif we have something like this one -->\nf(x)>x^2 +e and this is true for every real x\nCan i differentate this and say\nFirst derivative of f (x) >= 2*x ?\nPlease i need help on this one" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk2.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d939db8c24da4ea1194dceb703b696b2b771206 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 72, + "timestamp": 1684517721236.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "guys i have a question \nif we have something like this one -->\nf(x)>x^2 +e and this is true for every real x\nCan i differentate this and say\nFirst derivative of f (x) >= 2*x ?\nPlease i need help on this one" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk20.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..1d939db8c24da4ea1194dceb703b696b2b771206 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 72, + "timestamp": 1684517721236.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "guys i have a question \nif we have something like this one -->\nf(x)>x^2 +e and this is true for every real x\nCan i differentate this and say\nFirst derivative of f (x) >= 2*x ?\nPlease i need help on this one" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk21.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..1d939db8c24da4ea1194dceb703b696b2b771206 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 72, + "timestamp": 1684517721236.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "guys i have a question \nif we have something like this one -->\nf(x)>x^2 +e and this is true for every real x\nCan i differentate this and say\nFirst derivative of f (x) >= 2*x ?\nPlease i need help on this one" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk22.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..1d939db8c24da4ea1194dceb703b696b2b771206 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 72, + "timestamp": 1684517721236.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "guys i have a question \nif we have something like this one -->\nf(x)>x^2 +e and this is true for every real x\nCan i differentate this and say\nFirst derivative of f (x) >= 2*x ?\nPlease i need help on this one" + } +] \ No newline at end of file diff --git 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"query_id": 72, + "timestamp": 1684517721236.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "guys i have a question \nif we have something like this one -->\nf(x)>x^2 +e and this is true for every real x\nCan i differentate this and say\nFirst derivative of f (x) >= 2*x ?\nPlease i need help on this one" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk26.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..1d939db8c24da4ea1194dceb703b696b2b771206 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 72, + "timestamp": 1684517721236.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "guys i have a question \nif we have something like this one -->\nf(x)>x^2 +e and this is true for every real x\nCan i differentate this and say\nFirst derivative of f (x) >= 2*x ?\nPlease i need help on this one" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk3.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1d939db8c24da4ea1194dceb703b696b2b771206 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 72, + "timestamp": 1684517721236.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "guys i have a question \nif we have something like this one -->\nf(x)>x^2 +e and this is true for every real x\nCan i differentate this and say\nFirst derivative of f (x) >= 2*x ?\nPlease i need help on this one" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk4.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..1d939db8c24da4ea1194dceb703b696b2b771206 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 72, + "timestamp": 1684517721236.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "guys i have a question \nif we have something like this one -->\nf(x)>x^2 +e and this is true for every real x\nCan i differentate this and say\nFirst derivative of f (x) >= 2*x ?\nPlease i need help on this one" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk5.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk5.json new file mode 100644 index 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"query_id": 72, + "timestamp": 1684517721236.0, + "annotatedSourceSentencesIndices": [ + 19 + ], + "names": [ + "annotator1" + ], + "text": "guys i have a question \nif we have something like this one -->\nf(x)>x^2 +e and this is true for every real x\nCan i differentate this and say\nFirst derivative of f (x) >= 2*x ?\nPlease i need help on this one" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk7.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..74b2e1aca0f3acddc469c8a0624b886c33b0b102 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk7.json @@ -0,0 +1,17 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 72, + "timestamp": 1684517721236.0, + "annotatedSourceSentencesIndices": [ + 0, + 1, + 2, + 3 + ], + "names": [ + "annotator1" + ], + "text": "guys i have a question \nif we have something like this one -->\nf(x)>x^2 +e and this is true for every real x\nCan i differentate this and say\nFirst derivative of f (x) >= 2*x ?\nPlease i need help on this one" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk8.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..1d939db8c24da4ea1194dceb703b696b2b771206 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 72, + "timestamp": 1684517721236.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "guys i have a question \nif we have something like this one -->\nf(x)>x^2 +e and this is true for every real x\nCan i differentate this and say\nFirst derivative of f (x) >= 2*x ?\nPlease i need help on this one" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk9.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..1d939db8c24da4ea1194dceb703b696b2b771206 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_72_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 72, + "timestamp": 1684517721236.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "guys i have a question \nif we have something like this one -->\nf(x)>x^2 +e and this is true for every real x\nCan i differentate this and say\nFirst derivative of f (x) >= 2*x ?\nPlease i need help on this one" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk0.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk0.json new file mode 100644 index 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Basic LCM is a doubt in an MIT class?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk1.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..015a87882df97cdc7e15057d2f0d282db5cdd484 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 73, + "timestamp": 1684517826734.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:51 seriously? Basic LCM is a doubt in an MIT class?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk10.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..015a87882df97cdc7e15057d2f0d282db5cdd484 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 73, + "timestamp": 1684517826734.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:51 seriously? Basic LCM is a doubt in an MIT class?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk11.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b7052d67c53070240b75c4acf8499854d78cf99a --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk11.json @@ -0,0 +1,16 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 73, + "timestamp": 1684517826734.0, + "annotatedSourceSentencesIndices": [ + 15, + 17, + 18 + ], + "names": [ + "annotator1" + ], + "text": "24:51 seriously? Basic LCM is a doubt in an MIT class?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk12.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..015a87882df97cdc7e15057d2f0d282db5cdd484 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 73, + "timestamp": 1684517826734.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:51 seriously? Basic LCM is a doubt in an MIT class?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk13.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..015a87882df97cdc7e15057d2f0d282db5cdd484 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 73, + "timestamp": 1684517826734.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:51 seriously? Basic LCM is a doubt in an MIT class?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk14.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..015a87882df97cdc7e15057d2f0d282db5cdd484 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 73, + "timestamp": 1684517826734.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:51 seriously? Basic LCM is a doubt in an MIT class?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk15.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..015a87882df97cdc7e15057d2f0d282db5cdd484 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 73, + "timestamp": 1684517826734.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:51 seriously? Basic LCM is a doubt in an MIT class?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk16.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..015a87882df97cdc7e15057d2f0d282db5cdd484 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 73, + "timestamp": 1684517826734.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:51 seriously? Basic LCM is a doubt in an MIT class?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk17.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..015a87882df97cdc7e15057d2f0d282db5cdd484 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 73, + "timestamp": 1684517826734.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:51 seriously? Basic LCM is a doubt in an MIT class?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk18.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..015a87882df97cdc7e15057d2f0d282db5cdd484 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 73, + "timestamp": 1684517826734.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:51 seriously? Basic LCM is a doubt in an MIT class?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk19.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..015a87882df97cdc7e15057d2f0d282db5cdd484 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 73, + "timestamp": 1684517826734.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:51 seriously? 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Basic LCM is a doubt in an MIT class?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk20.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..015a87882df97cdc7e15057d2f0d282db5cdd484 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 73, + "timestamp": 1684517826734.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:51 seriously? 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Basic LCM is a doubt in an MIT class?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk3.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..015a87882df97cdc7e15057d2f0d282db5cdd484 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 73, + "timestamp": 1684517826734.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:51 seriously? 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Basic LCM is a doubt in an MIT class?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk5.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..015a87882df97cdc7e15057d2f0d282db5cdd484 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 73, + "timestamp": 1684517826734.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:51 seriously? Basic LCM is a doubt in an MIT class?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk6.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..015a87882df97cdc7e15057d2f0d282db5cdd484 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 73, + "timestamp": 1684517826734.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:51 seriously? Basic LCM is a doubt in an MIT class?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk7.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..015a87882df97cdc7e15057d2f0d282db5cdd484 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 73, + "timestamp": 1684517826734.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:51 seriously? Basic LCM is a doubt in an MIT class?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk8.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..015a87882df97cdc7e15057d2f0d282db5cdd484 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 73, + "timestamp": 1684517826734.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:51 seriously? Basic LCM is a doubt in an MIT class?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk9.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..015a87882df97cdc7e15057d2f0d282db5cdd484 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_73_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 73, + "timestamp": 1684517826734.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "24:51 seriously? Basic LCM is a doubt in an MIT class?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk0.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..c16049135733761bf942dc024c9327d583e2dda9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 74, + "timestamp": 1684517837500.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. Why does he let the limit be delta x to zero? Can it be done with the limit being delta y to zero?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk1.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..c16049135733761bf942dc024c9327d583e2dda9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 74, + "timestamp": 1684517837500.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. Why does he let the limit be delta x to zero? Can it be done with the limit being delta y to zero?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk10.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c16049135733761bf942dc024c9327d583e2dda9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 74, + "timestamp": 1684517837500.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. Why does he let the limit be delta x to zero? Can it be done with the limit being delta y to zero?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk11.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..c16049135733761bf942dc024c9327d583e2dda9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 74, + "timestamp": 1684517837500.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. Why does he let the limit be delta x to zero? Can it be done with the limit being delta y to zero?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk12.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..c16049135733761bf942dc024c9327d583e2dda9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 74, + "timestamp": 1684517837500.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. Why does he let the limit be delta x to zero? Can it be done with the limit being delta y to zero?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk13.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..c16049135733761bf942dc024c9327d583e2dda9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 74, + "timestamp": 1684517837500.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. Why does he let the limit be delta x to zero? Can it be done with the limit being delta y to zero?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk14.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..c16049135733761bf942dc024c9327d583e2dda9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 74, + "timestamp": 1684517837500.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. Why does he let the limit be delta x to zero? Can it be done with the limit being delta y to zero?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk15.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..c16049135733761bf942dc024c9327d583e2dda9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 74, + "timestamp": 1684517837500.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. Why does he let the limit be delta x to zero? Can it be done with the limit being delta y to zero?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk16.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..c16049135733761bf942dc024c9327d583e2dda9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 74, + "timestamp": 1684517837500.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. Why does he let the limit be delta x to zero? Can it be done with the limit being delta y to zero?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk17.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..c16049135733761bf942dc024c9327d583e2dda9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 74, + "timestamp": 1684517837500.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. Why does he let the limit be delta x to zero? Can it be done with the limit being delta y to zero?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk18.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..c16049135733761bf942dc024c9327d583e2dda9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 74, + "timestamp": 1684517837500.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. Why does he let the limit be delta x to zero? Can it be done with the limit being delta y to zero?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk19.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..c16049135733761bf942dc024c9327d583e2dda9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 74, + "timestamp": 1684517837500.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. Why does he let the limit be delta x to zero? Can it be done with the limit being delta y to zero?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk2.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..c16049135733761bf942dc024c9327d583e2dda9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 74, + "timestamp": 1684517837500.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. Why does he let the limit be delta x to zero? Can it be done with the limit being delta y to zero?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk20.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c16049135733761bf942dc024c9327d583e2dda9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 74, + "timestamp": 1684517837500.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. Why does he let the limit be delta x to zero? Can it be done with the limit being delta y to zero?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk21.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..c16049135733761bf942dc024c9327d583e2dda9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 74, + "timestamp": 1684517837500.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. Why does he let the limit be delta x to zero? Can it be done with the limit being delta y to zero?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk22.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..c16049135733761bf942dc024c9327d583e2dda9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 74, + "timestamp": 1684517837500.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. Why does he let the limit be delta x to zero? Can it be done with the limit being delta y to zero?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk23.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..c16049135733761bf942dc024c9327d583e2dda9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 74, + "timestamp": 1684517837500.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. Why does he let the limit be delta x to zero? Can it be done with the limit being delta y to zero?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk24.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..c16049135733761bf942dc024c9327d583e2dda9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 74, + "timestamp": 1684517837500.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. Why does he let the limit be delta x to zero? Can it be done with the limit being delta y to zero?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk25.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..c16049135733761bf942dc024c9327d583e2dda9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 74, + "timestamp": 1684517837500.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. Why does he let the limit be delta x to zero? Can it be done with the limit being delta y to zero?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk26.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..c16049135733761bf942dc024c9327d583e2dda9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 74, + "timestamp": 1684517837500.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. Why does he let the limit be delta x to zero? Can it be done with the limit being delta y to zero?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk3.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c16049135733761bf942dc024c9327d583e2dda9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 74, + "timestamp": 1684517837500.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. Why does he let the limit be delta x to zero? Can it be done with the limit being delta y to zero?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk4.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c16049135733761bf942dc024c9327d583e2dda9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 74, + "timestamp": 1684517837500.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. Why does he let the limit be delta x to zero? Can it be done with the limit being delta y to zero?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk5.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..c16049135733761bf942dc024c9327d583e2dda9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 74, + "timestamp": 1684517837500.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. Why does he let the limit be delta x to zero? Can it be done with the limit being delta y to zero?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk6.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..f8f5ea635a787364808187cfc1e0d296a3baea52 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk6.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 74, + "timestamp": 1684517837500.0, + "annotatedSourceSentencesIndices": [ + 7 + ], + "names": [ + "annotator1" + ], + "text": "I have a question. Why does he let the limit be delta x to zero? Can it be done with the limit being delta y to zero?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk7.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..c16049135733761bf942dc024c9327d583e2dda9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 74, + "timestamp": 1684517837500.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. Why does he let the limit be delta x to zero? 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Can it be done with the limit being delta y to zero?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk9.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..c16049135733761bf942dc024c9327d583e2dda9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_74_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 74, + "timestamp": 1684517837500.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I have a question. Why does he let the limit be delta x to zero? 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end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_76_chunk3.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_76_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..cb1830a2233a8185f0aa64ff4d0653753f5a306e --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_76_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 76, + "timestamp": 1684517855869.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can anyone tell me which book should i prefer with these lectures.??" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_76_chunk4.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_76_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..cb1830a2233a8185f0aa64ff4d0653753f5a306e --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_76_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 76, + "timestamp": 1684517855869.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can anyone tell me which book should i prefer with these lectures.??" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_76_chunk5.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_76_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..cb1830a2233a8185f0aa64ff4d0653753f5a306e --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_76_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 76, + "timestamp": 1684517855869.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can anyone tell me which book should i prefer with these lectures.??" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_76_chunk6.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_76_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..cb1830a2233a8185f0aa64ff4d0653753f5a306e --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_76_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 76, + "timestamp": 1684517855869.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can anyone tell me which book should i prefer with these lectures.??" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_76_chunk7.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_76_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..cb1830a2233a8185f0aa64ff4d0653753f5a306e --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_76_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 76, + "timestamp": 1684517855869.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can anyone tell me which book should i prefer with these lectures.??" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_76_chunk8.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_76_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..cb1830a2233a8185f0aa64ff4d0653753f5a306e --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_76_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 76, + "timestamp": 1684517855869.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can anyone tell me which book should i prefer with these lectures.??" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_76_chunk9.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_76_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..cb1830a2233a8185f0aa64ff4d0653753f5a306e --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_76_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 76, + "timestamp": 1684517855869.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Can anyone tell me which book should i prefer with these lectures.??" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk0.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..4b0d70d9616671652242e233a2ecb35d16d66ec4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 77, + "timestamp": 1684518035758.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 21:20, he says \"I set this delta x to zero.\" So just like that? You can just set it to zero randomly? I'm so confused as to why/how it is zero, then magically disappears." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk1.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..4b0d70d9616671652242e233a2ecb35d16d66ec4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 77, + "timestamp": 1684518035758.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 21:20, he says \"I set this delta x to zero.\" So just like that? You can just set it to zero randomly? I'm so confused as to why/how it is zero, then magically disappears." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk10.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..4b0d70d9616671652242e233a2ecb35d16d66ec4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 77, + "timestamp": 1684518035758.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 21:20, he says \"I set this delta x to zero.\" So just like that? You can just set it to zero randomly? I'm so confused as to why/how it is zero, then magically disappears." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk11.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..4b0d70d9616671652242e233a2ecb35d16d66ec4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 77, + "timestamp": 1684518035758.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 21:20, he says \"I set this delta x to zero.\" So just like that? You can just set it to zero randomly? I'm so confused as to why/how it is zero, then magically disappears." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk12.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..4b0d70d9616671652242e233a2ecb35d16d66ec4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 77, + "timestamp": 1684518035758.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 21:20, he says \"I set this delta x to zero.\" So just like that? You can just set it to zero randomly? I'm so confused as to why/how it is zero, then magically disappears." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk13.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..4b0d70d9616671652242e233a2ecb35d16d66ec4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 77, + "timestamp": 1684518035758.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 21:20, he says \"I set this delta x to zero.\" So just like that? You can just set it to zero randomly? I'm so confused as to why/how it is zero, then magically disappears." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk14.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..4b0d70d9616671652242e233a2ecb35d16d66ec4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 77, + "timestamp": 1684518035758.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 21:20, he says \"I set this delta x to zero.\" So just like that? You can just set it to zero randomly? I'm so confused as to why/how it is zero, then magically disappears." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk15.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..4b0d70d9616671652242e233a2ecb35d16d66ec4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 77, + "timestamp": 1684518035758.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 21:20, he says \"I set this delta x to zero.\" So just like that? You can just set it to zero randomly? I'm so confused as to why/how it is zero, then magically disappears." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk16.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..4b0d70d9616671652242e233a2ecb35d16d66ec4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 77, + "timestamp": 1684518035758.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 21:20, he says \"I set this delta x to zero.\" So just like that? You can just set it to zero randomly? I'm so confused as to why/how it is zero, then magically disappears." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk17.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..4b0d70d9616671652242e233a2ecb35d16d66ec4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 77, + "timestamp": 1684518035758.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 21:20, he says \"I set this delta x to zero.\" So just like that? You can just set it to zero randomly? I'm so confused as to why/how it is zero, then magically disappears." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk18.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4b0d70d9616671652242e233a2ecb35d16d66ec4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 77, + "timestamp": 1684518035758.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 21:20, he says \"I set this delta x to zero.\" So just like that? You can just set it to zero randomly? I'm so confused as to why/how it is zero, then magically disappears." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk19.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..4b0d70d9616671652242e233a2ecb35d16d66ec4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 77, + "timestamp": 1684518035758.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 21:20, he says \"I set this delta x to zero.\" So just like that? You can just set it to zero randomly? I'm so confused as to why/how it is zero, then magically disappears." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk2.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..4b0d70d9616671652242e233a2ecb35d16d66ec4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 77, + "timestamp": 1684518035758.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 21:20, he says \"I set this delta x to zero.\" So just like that? You can just set it to zero randomly? I'm so confused as to why/how it is zero, then magically disappears." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk20.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..4b0d70d9616671652242e233a2ecb35d16d66ec4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 77, + "timestamp": 1684518035758.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 21:20, he says \"I set this delta x to zero.\" So just like that? You can just set it to zero randomly? I'm so confused as to why/how it is zero, then magically disappears." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk21.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..4b0d70d9616671652242e233a2ecb35d16d66ec4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 77, + "timestamp": 1684518035758.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 21:20, he says \"I set this delta x to zero.\" So just like that? You can just set it to zero randomly? I'm so confused as to why/how it is zero, then magically disappears." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk22.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..4b0d70d9616671652242e233a2ecb35d16d66ec4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 77, + "timestamp": 1684518035758.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 21:20, he says \"I set this delta x to zero.\" So just like that? You can just set it to zero randomly? I'm so confused as to why/how it is zero, then magically disappears." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk23.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4b0d70d9616671652242e233a2ecb35d16d66ec4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 77, + "timestamp": 1684518035758.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 21:20, he says \"I set this delta x to zero.\" So just like that? You can just set it to zero randomly? I'm so confused as to why/how it is zero, then magically disappears." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk24.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..4b0d70d9616671652242e233a2ecb35d16d66ec4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 77, + "timestamp": 1684518035758.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 21:20, he says \"I set this delta x to zero.\" So just like that? You can just set it to zero randomly? I'm so confused as to why/how it is zero, then magically disappears." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk25.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4b0d70d9616671652242e233a2ecb35d16d66ec4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 77, + "timestamp": 1684518035758.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 21:20, he says \"I set this delta x to zero.\" So just like that? You can just set it to zero randomly? I'm so confused as to why/how it is zero, then magically disappears." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk26.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..4b0d70d9616671652242e233a2ecb35d16d66ec4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 77, + "timestamp": 1684518035758.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 21:20, he says \"I set this delta x to zero.\" So just like that? You can just set it to zero randomly? I'm so confused as to why/how it is zero, then magically disappears." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk3.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..4b0d70d9616671652242e233a2ecb35d16d66ec4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 77, + "timestamp": 1684518035758.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 21:20, he says \"I set this delta x to zero.\" So just like that? You can just set it to zero randomly? I'm so confused as to why/how it is zero, then magically disappears." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk4.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..4b0d70d9616671652242e233a2ecb35d16d66ec4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 77, + "timestamp": 1684518035758.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 21:20, he says \"I set this delta x to zero.\" So just like that? You can just set it to zero randomly? I'm so confused as to why/how it is zero, then magically disappears." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk5.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..4b0d70d9616671652242e233a2ecb35d16d66ec4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 77, + "timestamp": 1684518035758.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 21:20, he says \"I set this delta x to zero.\" So just like that? You can just set it to zero randomly? I'm so confused as to why/how it is zero, then magically disappears." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk6.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..4b0d70d9616671652242e233a2ecb35d16d66ec4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 77, + "timestamp": 1684518035758.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 21:20, he says \"I set this delta x to zero.\" So just like that? You can just set it to zero randomly? I'm so confused as to why/how it is zero, then magically disappears." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk7.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..4b0d70d9616671652242e233a2ecb35d16d66ec4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 77, + "timestamp": 1684518035758.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 21:20, he says \"I set this delta x to zero.\" So just like that? You can just set it to zero randomly? I'm so confused as to why/how it is zero, then magically disappears." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk8.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..4b0d70d9616671652242e233a2ecb35d16d66ec4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 77, + "timestamp": 1684518035758.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At 21:20, he says \"I set this delta x to zero.\" So just like that? You can just set it to zero randomly? I'm so confused as to why/how it is zero, then magically disappears." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk9.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..451d135873e6a6141f436e7e8e8f0ce50622d49d --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_77_chunk9.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 77, + "timestamp": 1684518035758.0, + "annotatedSourceSentencesIndices": [ + 14 + ], + "names": [ + "annotator1" + ], + "text": "At 21:20, he says \"I set this delta x to zero.\" So just like that? You can just set it to zero randomly? I'm so confused as to why/how it is zero, then magically disappears." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_78_chunk0.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_78_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..2b685d38b3ed2d84665814a89d3d18f1939dd8a6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_78_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 78, + "timestamp": 1684518045810.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "thank you\nwas following till 40'57\"\nhow does 2x0y0 = 2 ?\n\nrealise this lecture is 13 yo but anyone out there\nappreciate any advice\nmark" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_78_chunk1.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_78_chunk1.json new file mode 100644 index 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"annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "thank you\nwas following till 40'57\"\nhow does 2x0y0 = 2 ?\n\nrealise this lecture is 13 yo but anyone out there\nappreciate any advice\nmark" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_78_chunk11.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_78_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..2b685d38b3ed2d84665814a89d3d18f1939dd8a6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_78_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 78, + "timestamp": 1684518045810.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "thank you\nwas following till 40'57\"\nhow does 2x0y0 = 2 ?\n\nrealise this lecture is 13 yo but anyone out there\nappreciate any advice\nmark" + } +] \ No newline at end of file diff --git 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40'57\"\nhow does 2x0y0 = 2 ?\n\nrealise this lecture is 13 yo but anyone out there\nappreciate any advice\nmark" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_78_chunk15.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_78_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..2b685d38b3ed2d84665814a89d3d18f1939dd8a6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_78_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 78, + "timestamp": 1684518045810.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "thank you\nwas following till 40'57\"\nhow does 2x0y0 = 2 ?\n\nrealise this lecture is 13 yo but anyone out there\nappreciate any advice\nmark" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_78_chunk16.json 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"annotatedSourceSentencesIndices": [ + 14 + ], + "names": [ + "annotator1" + ], + "text": "thank you\nwas following till 40'57\"\nhow does 2x0y0 = 2 ?\n\nrealise this lecture is 13 yo but anyone out there\nappreciate any advice\nmark" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_78_chunk21.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_78_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..2b685d38b3ed2d84665814a89d3d18f1939dd8a6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_78_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 78, + "timestamp": 1684518045810.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "thank you\nwas following till 40'57\"\nhow does 2x0y0 = 2 ?\n\nrealise this lecture is 13 yo but anyone out there\nappreciate any advice\nmark" + } +] \ No newline at end of file diff --git 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40'57\"\nhow does 2x0y0 = 2 ?\n\nrealise this lecture is 13 yo but anyone out there\nappreciate any advice\nmark" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_78_chunk25.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_78_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..2b685d38b3ed2d84665814a89d3d18f1939dd8a6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_78_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 78, + "timestamp": 1684518045810.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "thank you\nwas following till 40'57\"\nhow does 2x0y0 = 2 ?\n\nrealise this lecture is 13 yo but anyone out there\nappreciate any advice\nmark" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_78_chunk26.json 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Can someone please clarify a little bit? Thank you!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk1.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..48fb9df7fc532c6fd87e6ed7607c9d65bb0ede74 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 79, + "timestamp": 1684518138072.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I didn't really understand what he said around 37:42. Can someone please clarify a little bit? Thank you!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk10.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..48fb9df7fc532c6fd87e6ed7607c9d65bb0ede74 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 79, + "timestamp": 1684518138072.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I didn't really understand what he said around 37:42. Can someone please clarify a little bit? Thank you!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk11.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..48fb9df7fc532c6fd87e6ed7607c9d65bb0ede74 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 79, + "timestamp": 1684518138072.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I didn't really understand what he said around 37:42. Can someone please clarify a little bit? Thank you!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk12.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..48fb9df7fc532c6fd87e6ed7607c9d65bb0ede74 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 79, + "timestamp": 1684518138072.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I didn't really understand what he said around 37:42. Can someone please clarify a little bit? Thank you!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk13.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..48fb9df7fc532c6fd87e6ed7607c9d65bb0ede74 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 79, + "timestamp": 1684518138072.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I didn't really understand what he said around 37:42. Can someone please clarify a little bit? Thank you!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk14.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..48fb9df7fc532c6fd87e6ed7607c9d65bb0ede74 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 79, + "timestamp": 1684518138072.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I didn't really understand what he said around 37:42. Can someone please clarify a little bit? Thank you!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk15.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..48fb9df7fc532c6fd87e6ed7607c9d65bb0ede74 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 79, + "timestamp": 1684518138072.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I didn't really understand what he said around 37:42. Can someone please clarify a little bit? Thank you!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk16.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..48fb9df7fc532c6fd87e6ed7607c9d65bb0ede74 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 79, + "timestamp": 1684518138072.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I didn't really understand what he said around 37:42. Can someone please clarify a little bit? Thank you!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk17.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..48fb9df7fc532c6fd87e6ed7607c9d65bb0ede74 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 79, + "timestamp": 1684518138072.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I didn't really understand what he said around 37:42. Can someone please clarify a little bit? Thank you!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk18.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..bc52549e5b464cd9ebd5a58a736397767815f69d --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk18.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 79, + "timestamp": 1684518138072.0, + "annotatedSourceSentencesIndices": [ + 18, + 19 + ], + "names": [ + "annotator1" + ], + "text": "I didn't really understand what he said around 37:42. Can someone please clarify a little bit? Thank you!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk19.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..2855e59197e6c3046afcb008427b62ab44d6e0d9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk19.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 79, + "timestamp": 1684518138072.0, + "annotatedSourceSentencesIndices": [ + 0, + 1 + ], + "names": [ + "annotator1" + ], + "text": "I didn't really understand what he said around 37:42. Can someone please clarify a little bit? Thank you!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk2.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..48fb9df7fc532c6fd87e6ed7607c9d65bb0ede74 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 79, + "timestamp": 1684518138072.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I didn't really understand what he said around 37:42. Can someone please clarify a little bit? Thank you!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk20.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..48fb9df7fc532c6fd87e6ed7607c9d65bb0ede74 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 79, + "timestamp": 1684518138072.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I didn't really understand what he said around 37:42. Can someone please clarify a little bit? Thank you!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk21.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..48fb9df7fc532c6fd87e6ed7607c9d65bb0ede74 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 79, + "timestamp": 1684518138072.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I didn't really understand what he said around 37:42. Can someone please clarify a little bit? Thank you!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk22.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..48fb9df7fc532c6fd87e6ed7607c9d65bb0ede74 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 79, + "timestamp": 1684518138072.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I didn't really understand what he said around 37:42. Can someone please clarify a little bit? Thank you!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk23.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..48fb9df7fc532c6fd87e6ed7607c9d65bb0ede74 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 79, + "timestamp": 1684518138072.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I didn't really understand what he said around 37:42. Can someone please clarify a little bit? Thank you!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk24.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..48fb9df7fc532c6fd87e6ed7607c9d65bb0ede74 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 79, + "timestamp": 1684518138072.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I didn't really understand what he said around 37:42. Can someone please clarify a little bit? Thank you!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk25.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..48fb9df7fc532c6fd87e6ed7607c9d65bb0ede74 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 79, + "timestamp": 1684518138072.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I didn't really understand what he said around 37:42. Can someone please clarify a little bit? Thank you!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk26.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..48fb9df7fc532c6fd87e6ed7607c9d65bb0ede74 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 79, + "timestamp": 1684518138072.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I didn't really understand what he said around 37:42. Can someone please clarify a little bit? Thank you!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk3.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..48fb9df7fc532c6fd87e6ed7607c9d65bb0ede74 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_79_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 79, + "timestamp": 1684518138072.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "I didn't really understand what he said around 37:42. Can someone please clarify a little bit? 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Aren't limits the basis for both differential and integral calculus?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_80_chunk6.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_80_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..12a390ba7734fe72f6f2b3ad1efdbaca74a7eb09 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_80_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 80, + "timestamp": 1684518147548.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why do they teach derivatives before limits in MIT? Aren't limits the basis for both differential and integral calculus?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_80_chunk7.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_80_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..12a390ba7734fe72f6f2b3ad1efdbaca74a7eb09 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_80_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 80, + "timestamp": 1684518147548.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why do they teach derivatives before limits in MIT? Aren't limits the basis for both differential and integral calculus?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_80_chunk8.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_80_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..12a390ba7734fe72f6f2b3ad1efdbaca74a7eb09 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_80_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 80, + "timestamp": 1684518147548.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why do they teach derivatives before limits in MIT? Aren't limits the basis for both differential and integral calculus?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_80_chunk9.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_80_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..12a390ba7734fe72f6f2b3ad1efdbaca74a7eb09 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_80_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 80, + "timestamp": 1684518147548.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why do they teach derivatives before limits in MIT? Aren't limits the basis for both differential and integral calculus?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk0.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..815532d7a3278915e1cc34546500f45d2a624e77 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 82, + "timestamp": 1684518162850.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "48:37 A little confusion here. Don't you have to use a lower bound for that junk terms? Big O is an upper bound. And (delta x)^2 cannot be an upperbound for, say, (delta x)^3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk1.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..815532d7a3278915e1cc34546500f45d2a624e77 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 82, + "timestamp": 1684518162850.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "48:37 A little confusion here. Don't you have to use a lower bound for that junk terms? Big O is an upper bound. And (delta x)^2 cannot be an upperbound for, say, (delta x)^3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk10.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..815532d7a3278915e1cc34546500f45d2a624e77 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 82, + "timestamp": 1684518162850.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "48:37 A little confusion here. Don't you have to use a lower bound for that junk terms? Big O is an upper bound. And (delta x)^2 cannot be an upperbound for, say, (delta x)^3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk11.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..815532d7a3278915e1cc34546500f45d2a624e77 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 82, + "timestamp": 1684518162850.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "48:37 A little confusion here. Don't you have to use a lower bound for that junk terms? Big O is an upper bound. And (delta x)^2 cannot be an upperbound for, say, (delta x)^3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk12.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..815532d7a3278915e1cc34546500f45d2a624e77 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 82, + "timestamp": 1684518162850.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "48:37 A little confusion here. Don't you have to use a lower bound for that junk terms? Big O is an upper bound. And (delta x)^2 cannot be an upperbound for, say, (delta x)^3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk13.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..815532d7a3278915e1cc34546500f45d2a624e77 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 82, + "timestamp": 1684518162850.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "48:37 A little confusion here. Don't you have to use a lower bound for that junk terms? Big O is an upper bound. And (delta x)^2 cannot be an upperbound for, say, (delta x)^3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk14.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..815532d7a3278915e1cc34546500f45d2a624e77 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 82, + "timestamp": 1684518162850.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "48:37 A little confusion here. Don't you have to use a lower bound for that junk terms? Big O is an upper bound. And (delta x)^2 cannot be an upperbound for, say, (delta x)^3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk15.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..815532d7a3278915e1cc34546500f45d2a624e77 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 82, + "timestamp": 1684518162850.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "48:37 A little confusion here. Don't you have to use a lower bound for that junk terms? Big O is an upper bound. And (delta x)^2 cannot be an upperbound for, say, (delta x)^3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk16.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..815532d7a3278915e1cc34546500f45d2a624e77 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 82, + "timestamp": 1684518162850.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "48:37 A little confusion here. Don't you have to use a lower bound for that junk terms? Big O is an upper bound. And (delta x)^2 cannot be an upperbound for, say, (delta x)^3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk17.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..815532d7a3278915e1cc34546500f45d2a624e77 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 82, + "timestamp": 1684518162850.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "48:37 A little confusion here. Don't you have to use a lower bound for that junk terms? Big O is an upper bound. And (delta x)^2 cannot be an upperbound for, say, (delta x)^3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk18.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..815532d7a3278915e1cc34546500f45d2a624e77 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 82, + "timestamp": 1684518162850.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "48:37 A little confusion here. Don't you have to use a lower bound for that junk terms? Big O is an upper bound. And (delta x)^2 cannot be an upperbound for, say, (delta x)^3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk19.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..815532d7a3278915e1cc34546500f45d2a624e77 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 82, + "timestamp": 1684518162850.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "48:37 A little confusion here. Don't you have to use a lower bound for that junk terms? Big O is an upper bound. And (delta x)^2 cannot be an upperbound for, say, (delta x)^3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk2.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..815532d7a3278915e1cc34546500f45d2a624e77 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 82, + "timestamp": 1684518162850.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "48:37 A little confusion here. Don't you have to use a lower bound for that junk terms? Big O is an upper bound. And (delta x)^2 cannot be an upperbound for, say, (delta x)^3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk20.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..815532d7a3278915e1cc34546500f45d2a624e77 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 82, + "timestamp": 1684518162850.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "48:37 A little confusion here. Don't you have to use a lower bound for that junk terms? Big O is an upper bound. And (delta x)^2 cannot be an upperbound for, say, (delta x)^3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk21.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..815532d7a3278915e1cc34546500f45d2a624e77 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 82, + "timestamp": 1684518162850.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "48:37 A little confusion here. Don't you have to use a lower bound for that junk terms? Big O is an upper bound. And (delta x)^2 cannot be an upperbound for, say, (delta x)^3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk22.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..815532d7a3278915e1cc34546500f45d2a624e77 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 82, + "timestamp": 1684518162850.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "48:37 A little confusion here. Don't you have to use a lower bound for that junk terms? Big O is an upper bound. And (delta x)^2 cannot be an upperbound for, say, (delta x)^3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk23.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..ac3ec52bfe9115cd230a7c7f2ccf9989f0ecc00f --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk23.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 82, + "timestamp": 1684518162850.0, + "annotatedSourceSentencesIndices": [ + 18 + ], + "names": [ + "annotator1" + ], + "text": "48:37 A little confusion here. Don't you have to use a lower bound for that junk terms? Big O is an upper bound. And (delta x)^2 cannot be an upperbound for, say, (delta x)^3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk24.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..815532d7a3278915e1cc34546500f45d2a624e77 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 82, + "timestamp": 1684518162850.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "48:37 A little confusion here. Don't you have to use a lower bound for that junk terms? Big O is an upper bound. And (delta x)^2 cannot be an upperbound for, say, (delta x)^3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk25.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..815532d7a3278915e1cc34546500f45d2a624e77 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 82, + "timestamp": 1684518162850.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "48:37 A little confusion here. Don't you have to use a lower bound for that junk terms? Big O is an upper bound. And (delta x)^2 cannot be an upperbound for, say, (delta x)^3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk26.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..815532d7a3278915e1cc34546500f45d2a624e77 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 82, + "timestamp": 1684518162850.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "48:37 A little confusion here. Don't you have to use a lower bound for that junk terms? Big O is an upper bound. And (delta x)^2 cannot be an upperbound for, say, (delta x)^3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk3.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..815532d7a3278915e1cc34546500f45d2a624e77 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 82, + "timestamp": 1684518162850.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "48:37 A little confusion here. Don't you have to use a lower bound for that junk terms? Big O is an upper bound. And (delta x)^2 cannot be an upperbound for, say, (delta x)^3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk4.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..815532d7a3278915e1cc34546500f45d2a624e77 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 82, + "timestamp": 1684518162850.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "48:37 A little confusion here. Don't you have to use a lower bound for that junk terms? Big O is an upper bound. And (delta x)^2 cannot be an upperbound for, say, (delta x)^3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk5.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..815532d7a3278915e1cc34546500f45d2a624e77 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 82, + "timestamp": 1684518162850.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "48:37 A little confusion here. Don't you have to use a lower bound for that junk terms? Big O is an upper bound. And (delta x)^2 cannot be an upperbound for, say, (delta x)^3." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk6.json b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..815532d7a3278915e1cc34546500f45d2a624e77 --- /dev/null +++ b/sight/query/annotated_chunks_window20/7K1sB05pE0A_82_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "7K1sB05pE0A", + "query_id": 82, + "timestamp": 1684518162850.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "48:37 A little confusion here. Don't you have to use a lower bound for that junk terms? Big O is an upper bound. 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I just want to know which book I should follow for this course?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk0.json b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..0c861d8653dc728173b8e675cf480d41585435ec --- /dev/null +++ b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk0.json @@ -0,0 +1,16 @@ +[ + { + "file_id": "Cx5Z-OslNWE", + "query_id": 0, + "timestamp": 1684191216689.0, + "annotatedSourceSentencesIndices": [ + 0, + 3 + ], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks to MIT and professor Strang. Is 18.06 is prerequisite to this course or it will be covered in this course?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk1.json b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..f97b096d91c43795c2e4557342b85f0c3fed4ce1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk1.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Cx5Z-OslNWE", + "query_id": 0, + "timestamp": 1684191216689.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks to MIT and professor Strang. Is 18.06 is prerequisite to this course or it will be covered in this course?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk10.json b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..f97b096d91c43795c2e4557342b85f0c3fed4ce1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk10.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Cx5Z-OslNWE", + "query_id": 0, + "timestamp": 1684191216689.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks to MIT and professor Strang. Is 18.06 is prerequisite to this course or it will be covered in this course?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk11.json b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..f97b096d91c43795c2e4557342b85f0c3fed4ce1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk11.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Cx5Z-OslNWE", + "query_id": 0, + "timestamp": 1684191216689.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks to MIT and professor Strang. Is 18.06 is prerequisite to this course or it will be covered in this course?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk12.json b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..f97b096d91c43795c2e4557342b85f0c3fed4ce1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk12.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Cx5Z-OslNWE", + "query_id": 0, + "timestamp": 1684191216689.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks to MIT and professor Strang. Is 18.06 is prerequisite to this course or it will be covered in this course?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk13.json b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..f97b096d91c43795c2e4557342b85f0c3fed4ce1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk13.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Cx5Z-OslNWE", + "query_id": 0, + "timestamp": 1684191216689.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks to MIT and professor Strang. Is 18.06 is prerequisite to this course or it will be covered in this course?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk14.json b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..f97b096d91c43795c2e4557342b85f0c3fed4ce1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk14.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Cx5Z-OslNWE", + "query_id": 0, + "timestamp": 1684191216689.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks to MIT and professor Strang. Is 18.06 is prerequisite to this course or it will be covered in this course?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk15.json b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..f97b096d91c43795c2e4557342b85f0c3fed4ce1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk15.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Cx5Z-OslNWE", + "query_id": 0, + "timestamp": 1684191216689.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks to MIT and professor Strang. Is 18.06 is prerequisite to this course or it will be covered in this course?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk16.json b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f97b096d91c43795c2e4557342b85f0c3fed4ce1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk16.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Cx5Z-OslNWE", + "query_id": 0, + "timestamp": 1684191216689.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks to MIT and professor Strang. Is 18.06 is prerequisite to this course or it will be covered in this course?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk2.json b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..f97b096d91c43795c2e4557342b85f0c3fed4ce1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk2.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Cx5Z-OslNWE", + "query_id": 0, + "timestamp": 1684191216689.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks to MIT and professor Strang. Is 18.06 is prerequisite to this course or it will be covered in this course?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk3.json b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..f97b096d91c43795c2e4557342b85f0c3fed4ce1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk3.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Cx5Z-OslNWE", + "query_id": 0, + "timestamp": 1684191216689.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks to MIT and professor Strang. Is 18.06 is prerequisite to this course or it will be covered in this course?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk4.json b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..f97b096d91c43795c2e4557342b85f0c3fed4ce1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk4.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Cx5Z-OslNWE", + "query_id": 0, + "timestamp": 1684191216689.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks to MIT and professor Strang. Is 18.06 is prerequisite to this course or it will be covered in this course?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk5.json b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..f97b096d91c43795c2e4557342b85f0c3fed4ce1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk5.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Cx5Z-OslNWE", + "query_id": 0, + "timestamp": 1684191216689.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks to MIT and professor Strang. Is 18.06 is prerequisite to this course or it will be covered in this course?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk6.json b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..f97b096d91c43795c2e4557342b85f0c3fed4ce1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk6.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Cx5Z-OslNWE", + "query_id": 0, + "timestamp": 1684191216689.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks to MIT and professor Strang. Is 18.06 is prerequisite to this course or it will be covered in this course?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk7.json b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..f97b096d91c43795c2e4557342b85f0c3fed4ce1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk7.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Cx5Z-OslNWE", + "query_id": 0, + "timestamp": 1684191216689.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks to MIT and professor Strang. Is 18.06 is prerequisite to this course or it will be covered in this course?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk8.json b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f97b096d91c43795c2e4557342b85f0c3fed4ce1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk8.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Cx5Z-OslNWE", + "query_id": 0, + "timestamp": 1684191216689.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks to MIT and professor Strang. Is 18.06 is prerequisite to this course or it will be covered in this course?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk9.json b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..f97b096d91c43795c2e4557342b85f0c3fed4ce1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk9.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Cx5Z-OslNWE", + "query_id": 0, + "timestamp": 1684191216689.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks to MIT and professor Strang. Is 18.06 is prerequisite to this course or it will be covered in this course?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk0.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..5c8e8f39b93604496073ae8d34ffd13c34f1bce3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 0, + "timestamp": 1684706671595.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk1.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..5c8e8f39b93604496073ae8d34ffd13c34f1bce3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 0, + "timestamp": 1684706671595.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk10.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..5c8e8f39b93604496073ae8d34ffd13c34f1bce3 --- /dev/null +++ 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"names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk12.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..ae999057d6c9f6893aae0dd4357eaaf3d44c750b --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk12.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 0, + "timestamp": 1684706671595.0, + "annotatedSourceSentencesIndices": [ + 18 + ], + "names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk13.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..12c0b8920845840807e92f0cad17a0a269441869 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk13.json @@ -0,0 +1,16 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 0, + "timestamp": 1684706671595.0, + "annotatedSourceSentencesIndices": [ + 1, + 2, + 4 + ], + "names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk14.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..5c8e8f39b93604496073ae8d34ffd13c34f1bce3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 0, + "timestamp": 1684706671595.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk15.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..5c8e8f39b93604496073ae8d34ffd13c34f1bce3 --- /dev/null +++ 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"names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk17.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..5c8e8f39b93604496073ae8d34ffd13c34f1bce3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 0, + "timestamp": 1684706671595.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk18.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..5c8e8f39b93604496073ae8d34ffd13c34f1bce3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 0, + "timestamp": 1684706671595.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk19.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..5c8e8f39b93604496073ae8d34ffd13c34f1bce3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 0, + "timestamp": 1684706671595.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk2.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..5c8e8f39b93604496073ae8d34ffd13c34f1bce3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 0, + "timestamp": 1684706671595.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk20.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..5c8e8f39b93604496073ae8d34ffd13c34f1bce3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 0, + "timestamp": 1684706671595.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk21.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..5c8e8f39b93604496073ae8d34ffd13c34f1bce3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 0, + "timestamp": 1684706671595.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk22.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..5c8e8f39b93604496073ae8d34ffd13c34f1bce3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 0, + "timestamp": 1684706671595.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk23.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..5c8e8f39b93604496073ae8d34ffd13c34f1bce3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 0, + "timestamp": 1684706671595.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk24.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..5c8e8f39b93604496073ae8d34ffd13c34f1bce3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 0, + "timestamp": 1684706671595.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk25.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..5c8e8f39b93604496073ae8d34ffd13c34f1bce3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 0, + "timestamp": 1684706671595.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk26.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..5c8e8f39b93604496073ae8d34ffd13c34f1bce3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 0, + "timestamp": 1684706671595.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk27.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk27.json new file mode 100644 index 0000000000000000000000000000000000000000..5c8e8f39b93604496073ae8d34ffd13c34f1bce3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk27.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 0, + "timestamp": 1684706671595.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk28.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk28.json new file mode 100644 index 0000000000000000000000000000000000000000..5c8e8f39b93604496073ae8d34ffd13c34f1bce3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk28.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 0, + "timestamp": 1684706671595.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk29.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk29.json new file mode 100644 index 0000000000000000000000000000000000000000..5c8e8f39b93604496073ae8d34ffd13c34f1bce3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk29.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 0, + "timestamp": 1684706671595.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk3.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..5c8e8f39b93604496073ae8d34ffd13c34f1bce3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 0, + "timestamp": 1684706671595.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk30.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk30.json new file mode 100644 index 0000000000000000000000000000000000000000..5c8e8f39b93604496073ae8d34ffd13c34f1bce3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk30.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 0, + "timestamp": 1684706671595.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk31.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk31.json new file mode 100644 index 0000000000000000000000000000000000000000..5c8e8f39b93604496073ae8d34ffd13c34f1bce3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk31.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 0, + "timestamp": 1684706671595.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk32.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk32.json new file mode 100644 index 0000000000000000000000000000000000000000..5c8e8f39b93604496073ae8d34ffd13c34f1bce3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk32.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 0, + "timestamp": 1684706671595.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk33.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk33.json new file mode 100644 index 0000000000000000000000000000000000000000..5c8e8f39b93604496073ae8d34ffd13c34f1bce3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk33.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 0, + "timestamp": 1684706671595.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk4.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..5c8e8f39b93604496073ae8d34ffd13c34f1bce3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 0, + "timestamp": 1684706671595.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk5.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5c8e8f39b93604496073ae8d34ffd13c34f1bce3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 0, + "timestamp": 1684706671595.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk6.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..5c8e8f39b93604496073ae8d34ffd13c34f1bce3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 0, + "timestamp": 1684706671595.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk7.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..5c8e8f39b93604496073ae8d34ffd13c34f1bce3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 0, + "timestamp": 1684706671595.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk8.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..5c8e8f39b93604496073ae8d34ffd13c34f1bce3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 0, + "timestamp": 1684706671595.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk9.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..5c8e8f39b93604496073ae8d34ffd13c34f1bce3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_0_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 0, + "timestamp": 1684706671595.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk0.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..4c99bb812bf82f7246fc82a6644a0114134eeba4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk1.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..4c99bb812bf82f7246fc82a6644a0114134eeba4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk10.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..4c99bb812bf82f7246fc82a6644a0114134eeba4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk11.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..4c99bb812bf82f7246fc82a6644a0114134eeba4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk12.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..4c99bb812bf82f7246fc82a6644a0114134eeba4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk13.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..4c99bb812bf82f7246fc82a6644a0114134eeba4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk14.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..4c99bb812bf82f7246fc82a6644a0114134eeba4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk15.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..4c99bb812bf82f7246fc82a6644a0114134eeba4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk16.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..4c99bb812bf82f7246fc82a6644a0114134eeba4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk17.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..4c99bb812bf82f7246fc82a6644a0114134eeba4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk18.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4c99bb812bf82f7246fc82a6644a0114134eeba4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk19.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..4c99bb812bf82f7246fc82a6644a0114134eeba4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk2.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..4c99bb812bf82f7246fc82a6644a0114134eeba4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk20.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..4c99bb812bf82f7246fc82a6644a0114134eeba4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk21.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..4c99bb812bf82f7246fc82a6644a0114134eeba4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk22.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..4c99bb812bf82f7246fc82a6644a0114134eeba4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk23.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..06e1c7c214d24b9a0c1b2fae15dba395b6ce2c0b --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk23.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [ + 1, + 2 + ], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk24.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..1c44533467efef18c4281cec9972d62028aeccd5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk24.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [ + 10 + ], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk25.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4c99bb812bf82f7246fc82a6644a0114134eeba4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk26.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..4c99bb812bf82f7246fc82a6644a0114134eeba4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk27.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk27.json new file mode 100644 index 0000000000000000000000000000000000000000..4c99bb812bf82f7246fc82a6644a0114134eeba4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk27.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk28.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk28.json new file mode 100644 index 0000000000000000000000000000000000000000..4c99bb812bf82f7246fc82a6644a0114134eeba4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk28.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk29.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk29.json new file mode 100644 index 0000000000000000000000000000000000000000..4c99bb812bf82f7246fc82a6644a0114134eeba4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk29.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk3.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..4c99bb812bf82f7246fc82a6644a0114134eeba4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk30.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk30.json new file mode 100644 index 0000000000000000000000000000000000000000..4c99bb812bf82f7246fc82a6644a0114134eeba4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk30.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk31.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk31.json new file mode 100644 index 0000000000000000000000000000000000000000..4c99bb812bf82f7246fc82a6644a0114134eeba4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk31.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk32.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk32.json new file mode 100644 index 0000000000000000000000000000000000000000..4c99bb812bf82f7246fc82a6644a0114134eeba4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk32.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk33.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk33.json new file mode 100644 index 0000000000000000000000000000000000000000..4c99bb812bf82f7246fc82a6644a0114134eeba4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk33.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk4.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..4c99bb812bf82f7246fc82a6644a0114134eeba4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. 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We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk6.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..4c99bb812bf82f7246fc82a6644a0114134eeba4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk7.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..4c99bb812bf82f7246fc82a6644a0114134eeba4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk8.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..4c99bb812bf82f7246fc82a6644a0114134eeba4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk9.json b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4c99bb812bf82f7246fc82a6644a0114134eeba4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/KAySmSEGc9U_1_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "KAySmSEGc9U", + "query_id": 1, + "timestamp": 1684706796695.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "anyone mind explaining why, when we're trying to prove D is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.\nwhy is that not possible? is it because 01 is same as 01010101...." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_0_chunk0.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_0_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6d0cff647823d142a967f33807767b2770a48ad4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_0_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 0, + "timestamp": 1684707989274.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "How did transpose suddenly come into the picture?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_0_chunk1.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_0_chunk1.json new file mode 100644 index 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come into the picture?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_0_chunk19.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_0_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..6d0cff647823d142a967f33807767b2770a48ad4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_0_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 0, + "timestamp": 1684707989274.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "How did transpose suddenly come into the picture?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_0_chunk2.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_0_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6d0cff647823d142a967f33807767b2770a48ad4 --- /dev/null +++ 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Like how can we see that geometrically?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_10_chunk3.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_10_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..f038a90a82e1ed7ec1d97f6f374c5e7c527f6545 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_10_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 10, + "timestamp": 1684710094057.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why is L always inverse of E? Like how can we see that geometrically?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_10_chunk4.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_10_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..f038a90a82e1ed7ec1d97f6f374c5e7c527f6545 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_10_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 10, + "timestamp": 1684710094057.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why is L always inverse of E? Like how can we see that geometrically?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_10_chunk5.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_10_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..f038a90a82e1ed7ec1d97f6f374c5e7c527f6545 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_10_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 10, + "timestamp": 1684710094057.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why is L always inverse of E? Like how can we see that geometrically?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_10_chunk6.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_10_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..f038a90a82e1ed7ec1d97f6f374c5e7c527f6545 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_10_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 10, + "timestamp": 1684710094057.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why is L always inverse of E? Like how can we see that geometrically?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_10_chunk7.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_10_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..f038a90a82e1ed7ec1d97f6f374c5e7c527f6545 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_10_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 10, + "timestamp": 1684710094057.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why is L always inverse of E? Like how can we see that geometrically?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_10_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_10_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f038a90a82e1ed7ec1d97f6f374c5e7c527f6545 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_10_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 10, + "timestamp": 1684710094057.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why is L always inverse of E? Like how can we see that geometrically?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_10_chunk9.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_10_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..609afcbaedcdc9f8d7cc20ff9b3fe1b5fb093cbe --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_10_chunk9.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 10, + "timestamp": 1684710094057.0, + "annotatedSourceSentencesIndices": [ + 5 + ], + "names": [ + "annotator2" + ], + "text": "Why is L always inverse of E? Like how can we see that geometrically?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk0.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..eda7f89d61995f4439b255c66d161d47f3654262 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 12, + "timestamp": 1684710326625.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "My doubt is what were we trying to prove while calculating the cost of operation during elimination. And how EA is costlier than LU?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk1.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..eda7f89d61995f4439b255c66d161d47f3654262 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 12, + "timestamp": 1684710326625.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "My doubt is what were we trying to prove while calculating the cost of operation during elimination. And how EA is costlier than LU?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk10.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..eda7f89d61995f4439b255c66d161d47f3654262 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 12, + "timestamp": 1684710326625.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "My doubt is what were we trying to prove while calculating the cost of operation during elimination. And how EA is costlier than LU?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk11.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..eda7f89d61995f4439b255c66d161d47f3654262 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 12, + "timestamp": 1684710326625.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "My doubt is what were we trying to prove while calculating the cost of operation during elimination. And how EA is costlier than LU?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk12.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..eda7f89d61995f4439b255c66d161d47f3654262 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 12, + "timestamp": 1684710326625.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "My doubt is what were we trying to prove while calculating the cost of operation during elimination. And how EA is costlier than LU?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk13.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..eda7f89d61995f4439b255c66d161d47f3654262 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 12, + "timestamp": 1684710326625.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "My doubt is what were we trying to prove while calculating the cost of operation during elimination. And how EA is costlier than LU?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk14.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d2050d63635dc7b9c9c5aa1a3774e9d5cc38d421 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk14.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 12, + "timestamp": 1684710326625.0, + "annotatedSourceSentencesIndices": [ + 1, + 2 + ], + "names": [ + "annotator2" + ], + "text": "My doubt is what were we trying to prove while calculating the cost of operation during elimination. And how EA is costlier than LU?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk15.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eda7f89d61995f4439b255c66d161d47f3654262 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 12, + "timestamp": 1684710326625.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "My doubt is what were we trying to prove while calculating the cost of operation during elimination. And how EA is costlier than LU?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk16.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..eda7f89d61995f4439b255c66d161d47f3654262 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 12, + "timestamp": 1684710326625.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "My doubt is what were we trying to prove while calculating the cost of operation during elimination. And how EA is costlier than LU?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk17.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..eda7f89d61995f4439b255c66d161d47f3654262 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 12, + "timestamp": 1684710326625.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "My doubt is what were we trying to prove while calculating the cost of operation during elimination. And how EA is costlier than LU?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk18.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..eda7f89d61995f4439b255c66d161d47f3654262 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 12, + "timestamp": 1684710326625.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "My doubt is what were we trying to prove while calculating the cost of operation during elimination. And how EA is costlier than LU?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk19.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..eda7f89d61995f4439b255c66d161d47f3654262 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 12, + "timestamp": 1684710326625.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "My doubt is what were we trying to prove while calculating the cost of operation during elimination. And how EA is costlier than LU?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk2.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..eda7f89d61995f4439b255c66d161d47f3654262 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 12, + "timestamp": 1684710326625.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "My doubt is what were we trying to prove while calculating the cost of operation during elimination. And how EA is costlier than LU?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk20.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..eda7f89d61995f4439b255c66d161d47f3654262 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 12, + "timestamp": 1684710326625.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "My doubt is what were we trying to prove while calculating the cost of operation during elimination. And how EA is costlier than LU?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk21.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..eda7f89d61995f4439b255c66d161d47f3654262 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 12, + "timestamp": 1684710326625.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "My doubt is what were we trying to prove while calculating the cost of operation during elimination. And how EA is costlier than LU?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk22.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..eda7f89d61995f4439b255c66d161d47f3654262 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 12, + "timestamp": 1684710326625.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "My doubt is what were we trying to prove while calculating the cost of operation during elimination. And how EA is costlier than LU?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk23.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..eda7f89d61995f4439b255c66d161d47f3654262 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 12, + "timestamp": 1684710326625.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "My doubt is what were we trying to prove while calculating the cost of operation during elimination. And how EA is costlier than LU?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk24.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..eda7f89d61995f4439b255c66d161d47f3654262 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 12, + "timestamp": 1684710326625.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "My doubt is what were we trying to prove while calculating the cost of operation during elimination. And how EA is costlier than LU?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk25.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..eda7f89d61995f4439b255c66d161d47f3654262 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 12, + "timestamp": 1684710326625.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "My doubt is what were we trying to prove while calculating the cost of operation during elimination. And how EA is costlier than LU?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk26.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..eda7f89d61995f4439b255c66d161d47f3654262 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 12, + "timestamp": 1684710326625.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "My doubt is what were we trying to prove while calculating the cost of operation during elimination. And how EA is costlier than LU?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk3.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..eda7f89d61995f4439b255c66d161d47f3654262 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 12, + "timestamp": 1684710326625.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "My doubt is what were we trying to prove while calculating the cost of operation during elimination. And how EA is costlier than LU?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk4.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..eda7f89d61995f4439b255c66d161d47f3654262 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 12, + "timestamp": 1684710326625.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "My doubt is what were we trying to prove while calculating the cost of operation during elimination. And how EA is costlier than LU?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk5.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eda7f89d61995f4439b255c66d161d47f3654262 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 12, + "timestamp": 1684710326625.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "My doubt is what were we trying to prove while calculating the cost of operation during elimination. And how EA is costlier than LU?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk6.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..eda7f89d61995f4439b255c66d161d47f3654262 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 12, + "timestamp": 1684710326625.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "My doubt is what were we trying to prove while calculating the cost of operation during elimination. And how EA is costlier than LU?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk7.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..eda7f89d61995f4439b255c66d161d47f3654262 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 12, + "timestamp": 1684710326625.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "My doubt is what were we trying to prove while calculating the cost of operation during elimination. And how EA is costlier than LU?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..eda7f89d61995f4439b255c66d161d47f3654262 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 12, + "timestamp": 1684710326625.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "My doubt is what were we trying to prove while calculating the cost of operation during elimination. And how EA is costlier than LU?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk9.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..eda7f89d61995f4439b255c66d161d47f3654262 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_12_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 12, + "timestamp": 1684710326625.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "My doubt is what were we trying to prove while calculating the cost of operation during elimination. And how EA is costlier than LU?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk0.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..f77dde840b2c2a468ee2463ae67383c6b1c6f1e4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 13, + "timestamp": 1684719774461.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain to me why the answer for cost of B is $n^2$ around 40:00?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk1.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..f77dde840b2c2a468ee2463ae67383c6b1c6f1e4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 13, + "timestamp": 1684719774461.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain to me why the answer for cost of B is $n^2$ around 40:00?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk10.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..f77dde840b2c2a468ee2463ae67383c6b1c6f1e4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 13, + "timestamp": 1684719774461.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain to me why the answer for cost of B is $n^2$ around 40:00?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk11.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..f77dde840b2c2a468ee2463ae67383c6b1c6f1e4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 13, + "timestamp": 1684719774461.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain to me why the answer for cost of B is $n^2$ around 40:00?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk12.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..f77dde840b2c2a468ee2463ae67383c6b1c6f1e4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 13, + "timestamp": 1684719774461.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain to me why the answer for cost of B is $n^2$ around 40:00?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk13.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..f77dde840b2c2a468ee2463ae67383c6b1c6f1e4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 13, + "timestamp": 1684719774461.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain to me why the answer for cost of B is $n^2$ around 40:00?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk14.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..f77dde840b2c2a468ee2463ae67383c6b1c6f1e4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 13, + "timestamp": 1684719774461.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain to me why the answer for cost of B is $n^2$ around 40:00?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk15.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..f77dde840b2c2a468ee2463ae67383c6b1c6f1e4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 13, + "timestamp": 1684719774461.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain to me why the answer for cost of B is $n^2$ around 40:00?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk16.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f77dde840b2c2a468ee2463ae67383c6b1c6f1e4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 13, + "timestamp": 1684719774461.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain to me why the answer for cost of B is $n^2$ around 40:00?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk17.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..f77dde840b2c2a468ee2463ae67383c6b1c6f1e4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 13, + "timestamp": 1684719774461.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain to me why the answer for cost of B is $n^2$ around 40:00?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk18.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..f77dde840b2c2a468ee2463ae67383c6b1c6f1e4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 13, + "timestamp": 1684719774461.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain to me why the answer for cost of B is $n^2$ around 40:00?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk19.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..f77dde840b2c2a468ee2463ae67383c6b1c6f1e4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 13, + "timestamp": 1684719774461.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain to me why the answer for cost of B is $n^2$ around 40:00?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk2.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..f77dde840b2c2a468ee2463ae67383c6b1c6f1e4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 13, + "timestamp": 1684719774461.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain to me why the answer for cost of B is $n^2$ around 40:00?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk20.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6b5f1179d675b43dab47bf5c49a128a2a282165a --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk20.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 13, + "timestamp": 1684719774461.0, + "annotatedSourceSentencesIndices": [ + 19 + ], + "names": [ + "annotator2" + ], + "text": "Can anyone explain to me why the answer for cost of B is $n^2$ around 40:00?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk21.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f77dde840b2c2a468ee2463ae67383c6b1c6f1e4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 13, + "timestamp": 1684719774461.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain to me why the answer for cost of B is $n^2$ around 40:00?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk22.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..f77dde840b2c2a468ee2463ae67383c6b1c6f1e4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 13, + "timestamp": 1684719774461.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain to me why the answer for cost of B is $n^2$ around 40:00?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk23.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..f77dde840b2c2a468ee2463ae67383c6b1c6f1e4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 13, + "timestamp": 1684719774461.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain to me why the answer for cost of B is $n^2$ around 40:00?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk24.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..f77dde840b2c2a468ee2463ae67383c6b1c6f1e4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 13, + "timestamp": 1684719774461.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain to me why the answer for cost of B is $n^2$ around 40:00?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk25.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..f77dde840b2c2a468ee2463ae67383c6b1c6f1e4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 13, + "timestamp": 1684719774461.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain to me why the answer for cost of B is $n^2$ around 40:00?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk26.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f77dde840b2c2a468ee2463ae67383c6b1c6f1e4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 13, + "timestamp": 1684719774461.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain to me why the answer for cost of B is $n^2$ around 40:00?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk3.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..f77dde840b2c2a468ee2463ae67383c6b1c6f1e4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 13, + "timestamp": 1684719774461.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain to me why the answer for cost of B is $n^2$ around 40:00?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk4.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..f77dde840b2c2a468ee2463ae67383c6b1c6f1e4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 13, + "timestamp": 1684719774461.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain to me why the answer for cost of B is $n^2$ around 40:00?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk5.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..f77dde840b2c2a468ee2463ae67383c6b1c6f1e4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 13, + "timestamp": 1684719774461.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain to me why the answer for cost of B is $n^2$ around 40:00?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk6.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..f77dde840b2c2a468ee2463ae67383c6b1c6f1e4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 13, + "timestamp": 1684719774461.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain to me why the answer for cost of B is $n^2$ around 40:00?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk7.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..f77dde840b2c2a468ee2463ae67383c6b1c6f1e4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 13, + "timestamp": 1684719774461.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain to me why the answer for cost of B is $n^2$ around 40:00?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f77dde840b2c2a468ee2463ae67383c6b1c6f1e4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 13, + "timestamp": 1684719774461.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain to me why the answer for cost of B is $n^2$ around 40:00?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk9.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..f77dde840b2c2a468ee2463ae67383c6b1c6f1e4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_13_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 13, + "timestamp": 1684719774461.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain to me why the answer for cost of B is $n^2$ around 40:00?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk0.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..4522f672286f453fe486c8b4261707a5aad126a3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk0.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 14, + "timestamp": 1684719853045.0, + "annotatedSourceSentencesIndices": [ + 9 + ], + "names": [ + "annotator2" + ], + "text": "Hi. Is U the b in Ax = b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk1.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..ee21c9e4351279bbf81da2d3c89f4a04c7468862 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 14, + "timestamp": 1684719853045.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Hi. Is U the b in Ax = b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk10.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..ee21c9e4351279bbf81da2d3c89f4a04c7468862 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 14, + "timestamp": 1684719853045.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Hi. Is U the b in Ax = b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk11.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..ee21c9e4351279bbf81da2d3c89f4a04c7468862 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 14, + "timestamp": 1684719853045.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Hi. Is U the b in Ax = b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk12.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..ee21c9e4351279bbf81da2d3c89f4a04c7468862 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 14, + "timestamp": 1684719853045.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Hi. Is U the b in Ax = b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk13.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..ee21c9e4351279bbf81da2d3c89f4a04c7468862 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 14, + "timestamp": 1684719853045.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Hi. Is U the b in Ax = b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk14.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..ee21c9e4351279bbf81da2d3c89f4a04c7468862 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 14, + "timestamp": 1684719853045.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Hi. Is U the b in Ax = b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk15.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..ee21c9e4351279bbf81da2d3c89f4a04c7468862 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 14, + "timestamp": 1684719853045.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Hi. Is U the b in Ax = b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk16.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..ee21c9e4351279bbf81da2d3c89f4a04c7468862 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 14, + "timestamp": 1684719853045.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Hi. Is U the b in Ax = b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk17.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..ee21c9e4351279bbf81da2d3c89f4a04c7468862 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 14, + "timestamp": 1684719853045.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Hi. Is U the b in Ax = b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk18.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..ee21c9e4351279bbf81da2d3c89f4a04c7468862 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 14, + "timestamp": 1684719853045.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Hi. Is U the b in Ax = b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk19.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..ee21c9e4351279bbf81da2d3c89f4a04c7468862 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 14, + "timestamp": 1684719853045.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Hi. Is U the b in Ax = b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk2.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..ee21c9e4351279bbf81da2d3c89f4a04c7468862 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 14, + "timestamp": 1684719853045.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Hi. Is U the b in Ax = b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk20.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ee21c9e4351279bbf81da2d3c89f4a04c7468862 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 14, + "timestamp": 1684719853045.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Hi. Is U the b in Ax = b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk21.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..ee21c9e4351279bbf81da2d3c89f4a04c7468862 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 14, + "timestamp": 1684719853045.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Hi. Is U the b in Ax = b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk22.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..ee21c9e4351279bbf81da2d3c89f4a04c7468862 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 14, + "timestamp": 1684719853045.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Hi. Is U the b in Ax = b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk23.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..ee21c9e4351279bbf81da2d3c89f4a04c7468862 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 14, + "timestamp": 1684719853045.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Hi. Is U the b in Ax = b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk24.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ee21c9e4351279bbf81da2d3c89f4a04c7468862 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 14, + "timestamp": 1684719853045.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Hi. Is U the b in Ax = b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk25.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..ee21c9e4351279bbf81da2d3c89f4a04c7468862 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 14, + "timestamp": 1684719853045.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Hi. Is U the b in Ax = b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk26.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ee21c9e4351279bbf81da2d3c89f4a04c7468862 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 14, + "timestamp": 1684719853045.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Hi. Is U the b in Ax = b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk3.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..ee21c9e4351279bbf81da2d3c89f4a04c7468862 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 14, + "timestamp": 1684719853045.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Hi. Is U the b in Ax = b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk4.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..ee21c9e4351279bbf81da2d3c89f4a04c7468862 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 14, + "timestamp": 1684719853045.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Hi. Is U the b in Ax = b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk5.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..ee21c9e4351279bbf81da2d3c89f4a04c7468862 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 14, + "timestamp": 1684719853045.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Hi. Is U the b in Ax = b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk6.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..ee21c9e4351279bbf81da2d3c89f4a04c7468862 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 14, + "timestamp": 1684719853045.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Hi. Is U the b in Ax = b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk7.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..ee21c9e4351279bbf81da2d3c89f4a04c7468862 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 14, + "timestamp": 1684719853045.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Hi. Is U the b in Ax = b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..ee21c9e4351279bbf81da2d3c89f4a04c7468862 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 14, + "timestamp": 1684719853045.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Hi. Is U the b in Ax = b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk9.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..ee21c9e4351279bbf81da2d3c89f4a04c7468862 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_14_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 14, + "timestamp": 1684719853045.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Hi. Is U the b in Ax = b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk0.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..607b1862d0bffecb760c74995c10c1c7112fde56 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 15, + "timestamp": 1684719893863.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 24:20 when he says that the multiplier goes directly into L, he means the negative right? If you keep a track of the operation on the left side, it inverts while bringing it to the right side." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk1.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..607b1862d0bffecb760c74995c10c1c7112fde56 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 15, + "timestamp": 1684719893863.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 24:20 when he says that the multiplier goes directly into L, he means the negative right? If you keep a track of the operation on the left side, it inverts while bringing it to the right side." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk10.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..607b1862d0bffecb760c74995c10c1c7112fde56 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 15, + "timestamp": 1684719893863.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 24:20 when he says that the multiplier goes directly into L, he means the negative right? If you keep a track of the operation on the left side, it inverts while bringing it to the right side." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk11.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..607b1862d0bffecb760c74995c10c1c7112fde56 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 15, + "timestamp": 1684719893863.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 24:20 when he says that the multiplier goes directly into L, he means the negative right? If you keep a track of the operation on the left side, it inverts while bringing it to the right side." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk12.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..607b1862d0bffecb760c74995c10c1c7112fde56 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 15, + "timestamp": 1684719893863.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 24:20 when he says that the multiplier goes directly into L, he means the negative right? If you keep a track of the operation on the left side, it inverts while bringing it to the right side." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk13.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..011468b4b84908db7b185c63b91b083a10d20c57 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk13.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 15, + "timestamp": 1684719893863.0, + "annotatedSourceSentencesIndices": [ + 11 + ], + "names": [ + "annotator2" + ], + "text": "At 24:20 when he says that the multiplier goes directly into L, he means the negative right? If you keep a track of the operation on the left side, it inverts while bringing it to the right side." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk14.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..607b1862d0bffecb760c74995c10c1c7112fde56 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 15, + "timestamp": 1684719893863.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 24:20 when he says that the multiplier goes directly into L, he means the negative right? If you keep a track of the operation on the left side, it inverts while bringing it to the right side." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk15.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..607b1862d0bffecb760c74995c10c1c7112fde56 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 15, + "timestamp": 1684719893863.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 24:20 when he says that the multiplier goes directly into L, he means the negative right? If you keep a track of the operation on the left side, it inverts while bringing it to the right side." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk16.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..607b1862d0bffecb760c74995c10c1c7112fde56 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 15, + "timestamp": 1684719893863.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 24:20 when he says that the multiplier goes directly into L, he means the negative right? If you keep a track of the operation on the left side, it inverts while bringing it to the right side." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk17.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..607b1862d0bffecb760c74995c10c1c7112fde56 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 15, + "timestamp": 1684719893863.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 24:20 when he says that the multiplier goes directly into L, he means the negative right? If you keep a track of the operation on the left side, it inverts while bringing it to the right side." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk18.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..607b1862d0bffecb760c74995c10c1c7112fde56 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 15, + "timestamp": 1684719893863.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 24:20 when he says that the multiplier goes directly into L, he means the negative right? If you keep a track of the operation on the left side, it inverts while bringing it to the right side." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk19.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..607b1862d0bffecb760c74995c10c1c7112fde56 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 15, + "timestamp": 1684719893863.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 24:20 when he says that the multiplier goes directly into L, he means the negative right? If you keep a track of the operation on the left side, it inverts while bringing it to the right side." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk2.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..607b1862d0bffecb760c74995c10c1c7112fde56 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 15, + "timestamp": 1684719893863.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 24:20 when he says that the multiplier goes directly into L, he means the negative right? If you keep a track of the operation on the left side, it inverts while bringing it to the right side." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk20.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..607b1862d0bffecb760c74995c10c1c7112fde56 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 15, + "timestamp": 1684719893863.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 24:20 when he says that the multiplier goes directly into L, he means the negative right? If you keep a track of the operation on the left side, it inverts while bringing it to the right side." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk21.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..607b1862d0bffecb760c74995c10c1c7112fde56 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 15, + "timestamp": 1684719893863.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 24:20 when he says that the multiplier goes directly into L, he means the negative right? If you keep a track of the operation on the left side, it inverts while bringing it to the right side." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk22.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..607b1862d0bffecb760c74995c10c1c7112fde56 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 15, + "timestamp": 1684719893863.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 24:20 when he says that the multiplier goes directly into L, he means the negative right? If you keep a track of the operation on the left side, it inverts while bringing it to the right side." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk23.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..607b1862d0bffecb760c74995c10c1c7112fde56 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 15, + "timestamp": 1684719893863.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 24:20 when he says that the multiplier goes directly into L, he means the negative right? If you keep a track of the operation on the left side, it inverts while bringing it to the right side." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk24.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..607b1862d0bffecb760c74995c10c1c7112fde56 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 15, + "timestamp": 1684719893863.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 24:20 when he says that the multiplier goes directly into L, he means the negative right? If you keep a track of the operation on the left side, it inverts while bringing it to the right side." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk25.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..607b1862d0bffecb760c74995c10c1c7112fde56 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 15, + "timestamp": 1684719893863.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 24:20 when he says that the multiplier goes directly into L, he means the negative right? If you keep a track of the operation on the left side, it inverts while bringing it to the right side." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk26.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..607b1862d0bffecb760c74995c10c1c7112fde56 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 15, + "timestamp": 1684719893863.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 24:20 when he says that the multiplier goes directly into L, he means the negative right? If you keep a track of the operation on the left side, it inverts while bringing it to the right side." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk3.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..607b1862d0bffecb760c74995c10c1c7112fde56 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 15, + "timestamp": 1684719893863.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 24:20 when he says that the multiplier goes directly into L, he means the negative right? If you keep a track of the operation on the left side, it inverts while bringing it to the right side." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk4.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..607b1862d0bffecb760c74995c10c1c7112fde56 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 15, + "timestamp": 1684719893863.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 24:20 when he says that the multiplier goes directly into L, he means the negative right? If you keep a track of the operation on the left side, it inverts while bringing it to the right side." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk5.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..607b1862d0bffecb760c74995c10c1c7112fde56 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 15, + "timestamp": 1684719893863.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 24:20 when he says that the multiplier goes directly into L, he means the negative right? If you keep a track of the operation on the left side, it inverts while bringing it to the right side." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk6.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..607b1862d0bffecb760c74995c10c1c7112fde56 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 15, + "timestamp": 1684719893863.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 24:20 when he says that the multiplier goes directly into L, he means the negative right? If you keep a track of the operation on the left side, it inverts while bringing it to the right side." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk7.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..607b1862d0bffecb760c74995c10c1c7112fde56 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 15, + "timestamp": 1684719893863.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 24:20 when he says that the multiplier goes directly into L, he means the negative right? If you keep a track of the operation on the left side, it inverts while bringing it to the right side." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..607b1862d0bffecb760c74995c10c1c7112fde56 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 15, + "timestamp": 1684719893863.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 24:20 when he says that the multiplier goes directly into L, he means the negative right? If you keep a track of the operation on the left side, it inverts while bringing it to the right side." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk9.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..607b1862d0bffecb760c74995c10c1c7112fde56 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_15_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 15, + "timestamp": 1684719893863.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 24:20 when he says that the multiplier goes directly into L, he means the negative right? If you keep a track of the operation on the left side, it inverts while bringing it to the right side." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk0.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..3f31b0f519aec2289242e988585d97fc4584a40e --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 16, + "timestamp": 1684719946478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "It is the best linear algebra lecture ever!!! But I do not get where the Identity matrix E31 comes from (at 16:47) ? Could anyone pls help me with this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk1.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3f31b0f519aec2289242e988585d97fc4584a40e --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 16, + "timestamp": 1684719946478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "It is the best linear algebra lecture ever!!! But I do not get where the Identity matrix E31 comes from (at 16:47) ? Could anyone pls help me with this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk10.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..3f31b0f519aec2289242e988585d97fc4584a40e --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 16, + "timestamp": 1684719946478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "It is the best linear algebra lecture ever!!! But I do not get where the Identity matrix E31 comes from (at 16:47) ? Could anyone pls help me with this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk11.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..3f31b0f519aec2289242e988585d97fc4584a40e --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 16, + "timestamp": 1684719946478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "It is the best linear algebra lecture ever!!! But I do not get where the Identity matrix E31 comes from (at 16:47) ? Could anyone pls help me with this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk12.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..3f31b0f519aec2289242e988585d97fc4584a40e --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 16, + "timestamp": 1684719946478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "It is the best linear algebra lecture ever!!! But I do not get where the Identity matrix E31 comes from (at 16:47) ? Could anyone pls help me with this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk13.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..3f31b0f519aec2289242e988585d97fc4584a40e --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 16, + "timestamp": 1684719946478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "It is the best linear algebra lecture ever!!! But I do not get where the Identity matrix E31 comes from (at 16:47) ? Could anyone pls help me with this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk14.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..3f31b0f519aec2289242e988585d97fc4584a40e --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 16, + "timestamp": 1684719946478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "It is the best linear algebra lecture ever!!! But I do not get where the Identity matrix E31 comes from (at 16:47) ? Could anyone pls help me with this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk15.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3f31b0f519aec2289242e988585d97fc4584a40e --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 16, + "timestamp": 1684719946478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "It is the best linear algebra lecture ever!!! But I do not get where the Identity matrix E31 comes from (at 16:47) ? Could anyone pls help me with this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk16.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..3f31b0f519aec2289242e988585d97fc4584a40e --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 16, + "timestamp": 1684719946478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "It is the best linear algebra lecture ever!!! But I do not get where the Identity matrix E31 comes from (at 16:47) ? Could anyone pls help me with this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk17.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..3f31b0f519aec2289242e988585d97fc4584a40e --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 16, + "timestamp": 1684719946478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "It is the best linear algebra lecture ever!!! But I do not get where the Identity matrix E31 comes from (at 16:47) ? Could anyone pls help me with this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk18.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..3f31b0f519aec2289242e988585d97fc4584a40e --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 16, + "timestamp": 1684719946478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "It is the best linear algebra lecture ever!!! But I do not get where the Identity matrix E31 comes from (at 16:47) ? Could anyone pls help me with this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk19.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..3f31b0f519aec2289242e988585d97fc4584a40e --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 16, + "timestamp": 1684719946478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "It is the best linear algebra lecture ever!!! But I do not get where the Identity matrix E31 comes from (at 16:47) ? Could anyone pls help me with this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk2.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..3f31b0f519aec2289242e988585d97fc4584a40e --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 16, + "timestamp": 1684719946478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "It is the best linear algebra lecture ever!!! But I do not get where the Identity matrix E31 comes from (at 16:47) ? Could anyone pls help me with this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk20.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..3f31b0f519aec2289242e988585d97fc4584a40e --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 16, + "timestamp": 1684719946478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "It is the best linear algebra lecture ever!!! But I do not get where the Identity matrix E31 comes from (at 16:47) ? Could anyone pls help me with this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk21.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..3f31b0f519aec2289242e988585d97fc4584a40e --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 16, + "timestamp": 1684719946478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "It is the best linear algebra lecture ever!!! But I do not get where the Identity matrix E31 comes from (at 16:47) ? Could anyone pls help me with this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk22.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..3f31b0f519aec2289242e988585d97fc4584a40e --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 16, + "timestamp": 1684719946478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "It is the best linear algebra lecture ever!!! But I do not get where the Identity matrix E31 comes from (at 16:47) ? Could anyone pls help me with this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk23.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..3f31b0f519aec2289242e988585d97fc4584a40e --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 16, + "timestamp": 1684719946478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "It is the best linear algebra lecture ever!!! But I do not get where the Identity matrix E31 comes from (at 16:47) ? Could anyone pls help me with this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk24.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..3f31b0f519aec2289242e988585d97fc4584a40e --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 16, + "timestamp": 1684719946478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "It is the best linear algebra lecture ever!!! But I do not get where the Identity matrix E31 comes from (at 16:47) ? Could anyone pls help me with this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk25.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..3f31b0f519aec2289242e988585d97fc4584a40e --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 16, + "timestamp": 1684719946478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "It is the best linear algebra lecture ever!!! But I do not get where the Identity matrix E31 comes from (at 16:47) ? Could anyone pls help me with this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk26.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..3f31b0f519aec2289242e988585d97fc4584a40e --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 16, + "timestamp": 1684719946478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "It is the best linear algebra lecture ever!!! But I do not get where the Identity matrix E31 comes from (at 16:47) ? Could anyone pls help me with this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk3.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..3f31b0f519aec2289242e988585d97fc4584a40e --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 16, + "timestamp": 1684719946478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "It is the best linear algebra lecture ever!!! But I do not get where the Identity matrix E31 comes from (at 16:47) ? Could anyone pls help me with this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk4.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..3f31b0f519aec2289242e988585d97fc4584a40e --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 16, + "timestamp": 1684719946478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "It is the best linear algebra lecture ever!!! But I do not get where the Identity matrix E31 comes from (at 16:47) ? Could anyone pls help me with this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk5.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..3f31b0f519aec2289242e988585d97fc4584a40e --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 16, + "timestamp": 1684719946478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "It is the best linear algebra lecture ever!!! But I do not get where the Identity matrix E31 comes from (at 16:47) ? Could anyone pls help me with this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk6.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..3f31b0f519aec2289242e988585d97fc4584a40e --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 16, + "timestamp": 1684719946478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "It is the best linear algebra lecture ever!!! But I do not get where the Identity matrix E31 comes from (at 16:47) ? Could anyone pls help me with this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk7.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..3f31b0f519aec2289242e988585d97fc4584a40e --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 16, + "timestamp": 1684719946478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "It is the best linear algebra lecture ever!!! But I do not get where the Identity matrix E31 comes from (at 16:47) ? Could anyone pls help me with this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..d8c680311b4518495ae3a26010ca54b2d5958bd6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk8.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 16, + "timestamp": 1684719946478.0, + "annotatedSourceSentencesIndices": [ + 2 + ], + "names": [ + "annotator2" + ], + "text": "It is the best linear algebra lecture ever!!! But I do not get where the Identity matrix E31 comes from (at 16:47) ? Could anyone pls help me with this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk9.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..3f31b0f519aec2289242e988585d97fc4584a40e --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_16_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 16, + "timestamp": 1684719946478.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "It is the best linear algebra lecture ever!!! But I do not get where the Identity matrix E31 comes from (at 16:47) ? Could anyone pls help me with this?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk0.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..7d6f5eaf80275a41f8a2b93f3c1850cdd310c455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 17, + "timestamp": 1684719965960.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone please explain how did he get 100^2 and not 100 x 2 (multiply+substract) operations at 33:22?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk1.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..7d6f5eaf80275a41f8a2b93f3c1850cdd310c455 --- 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x 2 (multiply+substract) operations at 33:22?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk11.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..7d6f5eaf80275a41f8a2b93f3c1850cdd310c455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 17, + "timestamp": 1684719965960.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone please explain how did he get 100^2 and not 100 x 2 (multiply+substract) operations at 33:22?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk12.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..7d6f5eaf80275a41f8a2b93f3c1850cdd310c455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 17, + "timestamp": 1684719965960.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone please explain how did he get 100^2 and not 100 x 2 (multiply+substract) operations at 33:22?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk13.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..7d6f5eaf80275a41f8a2b93f3c1850cdd310c455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 17, + "timestamp": 1684719965960.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone please explain how did he get 100^2 and not 100 x 2 (multiply+substract) operations at 33:22?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk14.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7d6f5eaf80275a41f8a2b93f3c1850cdd310c455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 17, + "timestamp": 1684719965960.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone please explain how did he get 100^2 and not 100 x 2 (multiply+substract) operations at 33:22?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk15.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7d6f5eaf80275a41f8a2b93f3c1850cdd310c455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 17, + "timestamp": 1684719965960.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone please explain how did he get 100^2 and not 100 x 2 (multiply+substract) operations at 33:22?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk16.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..7d6f5eaf80275a41f8a2b93f3c1850cdd310c455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 17, + "timestamp": 1684719965960.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone please explain how did he get 100^2 and not 100 x 2 (multiply+substract) operations at 33:22?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk17.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b84d78790428e5c0932c2f37eccf101525db5073 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk17.json @@ -0,0 +1,17 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 17, + "timestamp": 1684719965960.0, + "annotatedSourceSentencesIndices": [ + 1, + 2, + 3, + 4 + ], + "names": [ + "annotator2" + ], + "text": "Can someone please explain how did he get 100^2 and not 100 x 2 (multiply+substract) operations at 33:22?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk18.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..7d6f5eaf80275a41f8a2b93f3c1850cdd310c455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 17, + "timestamp": 1684719965960.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone please explain how did he get 100^2 and not 100 x 2 (multiply+substract) operations at 33:22?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk19.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..7d6f5eaf80275a41f8a2b93f3c1850cdd310c455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 17, + "timestamp": 1684719965960.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone please explain how did he get 100^2 and not 100 x 2 (multiply+substract) operations at 33:22?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk2.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..7d6f5eaf80275a41f8a2b93f3c1850cdd310c455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 17, + "timestamp": 1684719965960.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone please explain how did he get 100^2 and not 100 x 2 (multiply+substract) operations at 33:22?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk20.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..7d6f5eaf80275a41f8a2b93f3c1850cdd310c455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 17, + "timestamp": 1684719965960.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone please explain how did he get 100^2 and not 100 x 2 (multiply+substract) operations at 33:22?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk21.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7d6f5eaf80275a41f8a2b93f3c1850cdd310c455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 17, + "timestamp": 1684719965960.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone please explain how did he get 100^2 and not 100 x 2 (multiply+substract) operations at 33:22?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk22.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..7d6f5eaf80275a41f8a2b93f3c1850cdd310c455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 17, + "timestamp": 1684719965960.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone please explain how did he get 100^2 and not 100 x 2 (multiply+substract) operations at 33:22?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk23.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..7d6f5eaf80275a41f8a2b93f3c1850cdd310c455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 17, + "timestamp": 1684719965960.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone please explain how did he get 100^2 and not 100 x 2 (multiply+substract) operations at 33:22?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk24.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..7d6f5eaf80275a41f8a2b93f3c1850cdd310c455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 17, + "timestamp": 1684719965960.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone please explain how did he get 100^2 and not 100 x 2 (multiply+substract) operations at 33:22?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk25.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..7d6f5eaf80275a41f8a2b93f3c1850cdd310c455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 17, + "timestamp": 1684719965960.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone please explain how did he get 100^2 and not 100 x 2 (multiply+substract) operations at 33:22?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk26.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..7d6f5eaf80275a41f8a2b93f3c1850cdd310c455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 17, + "timestamp": 1684719965960.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone please explain how did he get 100^2 and not 100 x 2 (multiply+substract) operations at 33:22?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk3.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..7d6f5eaf80275a41f8a2b93f3c1850cdd310c455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 17, + "timestamp": 1684719965960.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone please explain how did he get 100^2 and not 100 x 2 (multiply+substract) operations at 33:22?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk4.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..7d6f5eaf80275a41f8a2b93f3c1850cdd310c455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 17, + "timestamp": 1684719965960.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone please explain how did he get 100^2 and not 100 x 2 (multiply+substract) operations at 33:22?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk5.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..7d6f5eaf80275a41f8a2b93f3c1850cdd310c455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 17, + "timestamp": 1684719965960.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone please explain how did he get 100^2 and not 100 x 2 (multiply+substract) operations at 33:22?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk6.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..7d6f5eaf80275a41f8a2b93f3c1850cdd310c455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 17, + "timestamp": 1684719965960.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone please explain how did he get 100^2 and not 100 x 2 (multiply+substract) operations at 33:22?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk7.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..7d6f5eaf80275a41f8a2b93f3c1850cdd310c455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 17, + "timestamp": 1684719965960.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone please explain how did he get 100^2 and not 100 x 2 (multiply+substract) operations at 33:22?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..7d6f5eaf80275a41f8a2b93f3c1850cdd310c455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 17, + "timestamp": 1684719965960.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone please explain how did he get 100^2 and not 100 x 2 (multiply+substract) operations at 33:22?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk9.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..7d6f5eaf80275a41f8a2b93f3c1850cdd310c455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_17_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 17, + "timestamp": 1684719965960.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone please explain how did he get 100^2 and not 100 x 2 (multiply+substract) operations at 33:22?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk0.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..542a9ad88b358c78d273030de37cf51b649ee455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 18, + "timestamp": 1684720220360.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "26:10\n\nI have a question about the cost of elimination.\nAx=b\n\nFor an nxn matrix A\nFor the 1st pivot, instead of 100^2, shouldn\u2019t it cost 100*99?\n2nd pivot, instead of 99^2, shouldn\u2019t it cost 99*98?\n3rd pivot, instead of 98^2, shouldn\u2019t it cost 98*87?\n\nSo, instead of n^2+(n-1)^2+(n-2)^2+...., shouldn\u2019t it be n(n-1)+(n-1)(n-2)+(n-2)(n-3)+.... instead?\n\n\nAlso, how did he get n^2 for the matrix b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk1.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..542a9ad88b358c78d273030de37cf51b649ee455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 18, + "timestamp": 1684720220360.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "26:10\n\nI have a question about the cost of elimination.\nAx=b\n\nFor an nxn matrix A\nFor the 1st pivot, instead of 100^2, shouldn\u2019t it cost 100*99?\n2nd pivot, instead of 99^2, shouldn\u2019t it cost 99*98?\n3rd pivot, instead of 98^2, shouldn\u2019t it cost 98*87?\n\nSo, instead of n^2+(n-1)^2+(n-2)^2+...., shouldn\u2019t it be n(n-1)+(n-1)(n-2)+(n-2)(n-3)+.... instead?\n\n\nAlso, how did he get n^2 for the matrix b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk10.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..542a9ad88b358c78d273030de37cf51b649ee455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 18, + "timestamp": 1684720220360.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "26:10\n\nI have a question about the cost of elimination.\nAx=b\n\nFor an nxn matrix A\nFor the 1st pivot, instead of 100^2, shouldn\u2019t it cost 100*99?\n2nd pivot, instead of 99^2, shouldn\u2019t it cost 99*98?\n3rd pivot, instead of 98^2, shouldn\u2019t it cost 98*87?\n\nSo, instead of n^2+(n-1)^2+(n-2)^2+...., shouldn\u2019t it be n(n-1)+(n-1)(n-2)+(n-2)(n-3)+.... instead?\n\n\nAlso, how did he get n^2 for the matrix b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk11.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..542a9ad88b358c78d273030de37cf51b649ee455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 18, + "timestamp": 1684720220360.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "26:10\n\nI have a question about the cost of elimination.\nAx=b\n\nFor an nxn matrix A\nFor the 1st pivot, instead of 100^2, shouldn\u2019t it cost 100*99?\n2nd pivot, instead of 99^2, shouldn\u2019t it cost 99*98?\n3rd pivot, instead of 98^2, shouldn\u2019t it cost 98*87?\n\nSo, instead of n^2+(n-1)^2+(n-2)^2+...., shouldn\u2019t it be n(n-1)+(n-1)(n-2)+(n-2)(n-3)+.... instead?\n\n\nAlso, how did he get n^2 for the matrix b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk12.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..542a9ad88b358c78d273030de37cf51b649ee455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 18, + "timestamp": 1684720220360.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "26:10\n\nI have a question about the cost of elimination.\nAx=b\n\nFor an nxn matrix A\nFor the 1st pivot, instead of 100^2, shouldn\u2019t it cost 100*99?\n2nd pivot, instead of 99^2, shouldn\u2019t it cost 99*98?\n3rd pivot, instead of 98^2, shouldn\u2019t it cost 98*87?\n\nSo, instead of n^2+(n-1)^2+(n-2)^2+...., shouldn\u2019t it be n(n-1)+(n-1)(n-2)+(n-2)(n-3)+.... instead?\n\n\nAlso, how did he get n^2 for the matrix b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk13.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..542a9ad88b358c78d273030de37cf51b649ee455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 18, + "timestamp": 1684720220360.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "26:10\n\nI have a question about the cost of elimination.\nAx=b\n\nFor an nxn matrix A\nFor the 1st pivot, instead of 100^2, shouldn\u2019t it cost 100*99?\n2nd pivot, instead of 99^2, shouldn\u2019t it cost 99*98?\n3rd pivot, instead of 98^2, shouldn\u2019t it cost 98*87?\n\nSo, instead of n^2+(n-1)^2+(n-2)^2+...., shouldn\u2019t it be n(n-1)+(n-1)(n-2)+(n-2)(n-3)+.... instead?\n\n\nAlso, how did he get n^2 for the matrix b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk14.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..542a9ad88b358c78d273030de37cf51b649ee455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 18, + "timestamp": 1684720220360.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "26:10\n\nI have a question about the cost of elimination.\nAx=b\n\nFor an nxn matrix A\nFor the 1st pivot, instead of 100^2, shouldn\u2019t it cost 100*99?\n2nd pivot, instead of 99^2, shouldn\u2019t it cost 99*98?\n3rd pivot, instead of 98^2, shouldn\u2019t it cost 98*87?\n\nSo, instead of n^2+(n-1)^2+(n-2)^2+...., shouldn\u2019t it be n(n-1)+(n-1)(n-2)+(n-2)(n-3)+.... instead?\n\n\nAlso, how did he get n^2 for the matrix b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk15.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..542a9ad88b358c78d273030de37cf51b649ee455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 18, + "timestamp": 1684720220360.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "26:10\n\nI have a question about the cost of elimination.\nAx=b\n\nFor an nxn matrix A\nFor the 1st pivot, instead of 100^2, shouldn\u2019t it cost 100*99?\n2nd pivot, instead of 99^2, shouldn\u2019t it cost 99*98?\n3rd pivot, instead of 98^2, shouldn\u2019t it cost 98*87?\n\nSo, instead of n^2+(n-1)^2+(n-2)^2+...., shouldn\u2019t it be n(n-1)+(n-1)(n-2)+(n-2)(n-3)+.... instead?\n\n\nAlso, how did he get n^2 for the matrix b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk16.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..542a9ad88b358c78d273030de37cf51b649ee455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 18, + "timestamp": 1684720220360.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "26:10\n\nI have a question about the cost of elimination.\nAx=b\n\nFor an nxn matrix A\nFor the 1st pivot, instead of 100^2, shouldn\u2019t it cost 100*99?\n2nd pivot, instead of 99^2, shouldn\u2019t it cost 99*98?\n3rd pivot, instead of 98^2, shouldn\u2019t it cost 98*87?\n\nSo, instead of n^2+(n-1)^2+(n-2)^2+...., shouldn\u2019t it be n(n-1)+(n-1)(n-2)+(n-2)(n-3)+.... instead?\n\n\nAlso, how did he get n^2 for the matrix b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk17.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..1e874ca2abae8b55596009d4d6f4ab484f15424f --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk17.json @@ -0,0 +1,18 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 18, + "timestamp": 1684720220360.0, + "annotatedSourceSentencesIndices": [ + 1, + 13, + 15, + 16, + 19 + ], + "names": [ + "annotator2" + ], + "text": "26:10\n\nI have a question about the cost of elimination.\nAx=b\n\nFor an nxn matrix A\nFor the 1st pivot, instead of 100^2, shouldn\u2019t it cost 100*99?\n2nd pivot, instead of 99^2, shouldn\u2019t it cost 99*98?\n3rd pivot, instead of 98^2, shouldn\u2019t it cost 98*87?\n\nSo, instead of n^2+(n-1)^2+(n-2)^2+...., shouldn\u2019t it be n(n-1)+(n-1)(n-2)+(n-2)(n-3)+.... instead?\n\n\nAlso, how did he get n^2 for the matrix b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk18.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..cb4d876a7908d5dee0a360c9700e07415b65ac1e --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk18.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 18, + "timestamp": 1684720220360.0, + "annotatedSourceSentencesIndices": [ + 0 + ], + "names": [ + "annotator2" + ], + "text": "26:10\n\nI have a question about the cost of elimination.\nAx=b\n\nFor an nxn matrix A\nFor the 1st pivot, instead of 100^2, shouldn\u2019t it cost 100*99?\n2nd pivot, instead of 99^2, shouldn\u2019t it cost 99*98?\n3rd pivot, instead of 98^2, shouldn\u2019t it cost 98*87?\n\nSo, instead of n^2+(n-1)^2+(n-2)^2+...., shouldn\u2019t it be n(n-1)+(n-1)(n-2)+(n-2)(n-3)+.... instead?\n\n\nAlso, how did he get n^2 for the matrix b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk19.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..542a9ad88b358c78d273030de37cf51b649ee455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 18, + "timestamp": 1684720220360.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "26:10\n\nI have a question about the cost of elimination.\nAx=b\n\nFor an nxn matrix A\nFor the 1st pivot, instead of 100^2, shouldn\u2019t it cost 100*99?\n2nd pivot, instead of 99^2, shouldn\u2019t it cost 99*98?\n3rd pivot, instead of 98^2, shouldn\u2019t it cost 98*87?\n\nSo, instead of n^2+(n-1)^2+(n-2)^2+...., shouldn\u2019t it be n(n-1)+(n-1)(n-2)+(n-2)(n-3)+.... instead?\n\n\nAlso, how did he get n^2 for the matrix b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk2.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..542a9ad88b358c78d273030de37cf51b649ee455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 18, + "timestamp": 1684720220360.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "26:10\n\nI have a question about the cost of elimination.\nAx=b\n\nFor an nxn matrix A\nFor the 1st pivot, instead of 100^2, shouldn\u2019t it cost 100*99?\n2nd pivot, instead of 99^2, shouldn\u2019t it cost 99*98?\n3rd pivot, instead of 98^2, shouldn\u2019t it cost 98*87?\n\nSo, instead of n^2+(n-1)^2+(n-2)^2+...., shouldn\u2019t it be n(n-1)+(n-1)(n-2)+(n-2)(n-3)+.... instead?\n\n\nAlso, how did he get n^2 for the matrix b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk20.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c9b08d5c63a22d548e3b01866aed802d4db3ce29 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk20.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 18, + "timestamp": 1684720220360.0, + "annotatedSourceSentencesIndices": [ + 19 + ], + "names": [ + "annotator2" + ], + "text": "26:10\n\nI have a question about the cost of elimination.\nAx=b\n\nFor an nxn matrix A\nFor the 1st pivot, instead of 100^2, shouldn\u2019t it cost 100*99?\n2nd pivot, instead of 99^2, shouldn\u2019t it cost 99*98?\n3rd pivot, instead of 98^2, shouldn\u2019t it cost 98*87?\n\nSo, instead of n^2+(n-1)^2+(n-2)^2+...., shouldn\u2019t it be n(n-1)+(n-1)(n-2)+(n-2)(n-3)+.... instead?\n\n\nAlso, how did he get n^2 for the matrix b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk21.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..542a9ad88b358c78d273030de37cf51b649ee455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 18, + "timestamp": 1684720220360.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "26:10\n\nI have a question about the cost of elimination.\nAx=b\n\nFor an nxn matrix A\nFor the 1st pivot, instead of 100^2, shouldn\u2019t it cost 100*99?\n2nd pivot, instead of 99^2, shouldn\u2019t it cost 99*98?\n3rd pivot, instead of 98^2, shouldn\u2019t it cost 98*87?\n\nSo, instead of n^2+(n-1)^2+(n-2)^2+...., shouldn\u2019t it be n(n-1)+(n-1)(n-2)+(n-2)(n-3)+.... instead?\n\n\nAlso, how did he get n^2 for the matrix b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk22.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..542a9ad88b358c78d273030de37cf51b649ee455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 18, + "timestamp": 1684720220360.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "26:10\n\nI have a question about the cost of elimination.\nAx=b\n\nFor an nxn matrix A\nFor the 1st pivot, instead of 100^2, shouldn\u2019t it cost 100*99?\n2nd pivot, instead of 99^2, shouldn\u2019t it cost 99*98?\n3rd pivot, instead of 98^2, shouldn\u2019t it cost 98*87?\n\nSo, instead of n^2+(n-1)^2+(n-2)^2+...., shouldn\u2019t it be n(n-1)+(n-1)(n-2)+(n-2)(n-3)+.... instead?\n\n\nAlso, how did he get n^2 for the matrix b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk23.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..542a9ad88b358c78d273030de37cf51b649ee455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 18, + "timestamp": 1684720220360.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "26:10\n\nI have a question about the cost of elimination.\nAx=b\n\nFor an nxn matrix A\nFor the 1st pivot, instead of 100^2, shouldn\u2019t it cost 100*99?\n2nd pivot, instead of 99^2, shouldn\u2019t it cost 99*98?\n3rd pivot, instead of 98^2, shouldn\u2019t it cost 98*87?\n\nSo, instead of n^2+(n-1)^2+(n-2)^2+...., shouldn\u2019t it be n(n-1)+(n-1)(n-2)+(n-2)(n-3)+.... instead?\n\n\nAlso, how did he get n^2 for the matrix b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk24.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..542a9ad88b358c78d273030de37cf51b649ee455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 18, + "timestamp": 1684720220360.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "26:10\n\nI have a question about the cost of elimination.\nAx=b\n\nFor an nxn matrix A\nFor the 1st pivot, instead of 100^2, shouldn\u2019t it cost 100*99?\n2nd pivot, instead of 99^2, shouldn\u2019t it cost 99*98?\n3rd pivot, instead of 98^2, shouldn\u2019t it cost 98*87?\n\nSo, instead of n^2+(n-1)^2+(n-2)^2+...., shouldn\u2019t it be n(n-1)+(n-1)(n-2)+(n-2)(n-3)+.... instead?\n\n\nAlso, how did he get n^2 for the matrix b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk25.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..542a9ad88b358c78d273030de37cf51b649ee455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 18, + "timestamp": 1684720220360.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "26:10\n\nI have a question about the cost of elimination.\nAx=b\n\nFor an nxn matrix A\nFor the 1st pivot, instead of 100^2, shouldn\u2019t it cost 100*99?\n2nd pivot, instead of 99^2, shouldn\u2019t it cost 99*98?\n3rd pivot, instead of 98^2, shouldn\u2019t it cost 98*87?\n\nSo, instead of n^2+(n-1)^2+(n-2)^2+...., shouldn\u2019t it be n(n-1)+(n-1)(n-2)+(n-2)(n-3)+.... instead?\n\n\nAlso, how did he get n^2 for the matrix b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk26.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..542a9ad88b358c78d273030de37cf51b649ee455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 18, + "timestamp": 1684720220360.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "26:10\n\nI have a question about the cost of elimination.\nAx=b\n\nFor an nxn matrix A\nFor the 1st pivot, instead of 100^2, shouldn\u2019t it cost 100*99?\n2nd pivot, instead of 99^2, shouldn\u2019t it cost 99*98?\n3rd pivot, instead of 98^2, shouldn\u2019t it cost 98*87?\n\nSo, instead of n^2+(n-1)^2+(n-2)^2+...., shouldn\u2019t it be n(n-1)+(n-1)(n-2)+(n-2)(n-3)+.... instead?\n\n\nAlso, how did he get n^2 for the matrix b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk3.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..542a9ad88b358c78d273030de37cf51b649ee455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 18, + "timestamp": 1684720220360.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "26:10\n\nI have a question about the cost of elimination.\nAx=b\n\nFor an nxn matrix A\nFor the 1st pivot, instead of 100^2, shouldn\u2019t it cost 100*99?\n2nd pivot, instead of 99^2, shouldn\u2019t it cost 99*98?\n3rd pivot, instead of 98^2, shouldn\u2019t it cost 98*87?\n\nSo, instead of n^2+(n-1)^2+(n-2)^2+...., shouldn\u2019t it be n(n-1)+(n-1)(n-2)+(n-2)(n-3)+.... instead?\n\n\nAlso, how did he get n^2 for the matrix b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk4.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..542a9ad88b358c78d273030de37cf51b649ee455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 18, + "timestamp": 1684720220360.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "26:10\n\nI have a question about the cost of elimination.\nAx=b\n\nFor an nxn matrix A\nFor the 1st pivot, instead of 100^2, shouldn\u2019t it cost 100*99?\n2nd pivot, instead of 99^2, shouldn\u2019t it cost 99*98?\n3rd pivot, instead of 98^2, shouldn\u2019t it cost 98*87?\n\nSo, instead of n^2+(n-1)^2+(n-2)^2+...., shouldn\u2019t it be n(n-1)+(n-1)(n-2)+(n-2)(n-3)+.... instead?\n\n\nAlso, how did he get n^2 for the matrix b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk5.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..542a9ad88b358c78d273030de37cf51b649ee455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 18, + "timestamp": 1684720220360.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "26:10\n\nI have a question about the cost of elimination.\nAx=b\n\nFor an nxn matrix A\nFor the 1st pivot, instead of 100^2, shouldn\u2019t it cost 100*99?\n2nd pivot, instead of 99^2, shouldn\u2019t it cost 99*98?\n3rd pivot, instead of 98^2, shouldn\u2019t it cost 98*87?\n\nSo, instead of n^2+(n-1)^2+(n-2)^2+...., shouldn\u2019t it be n(n-1)+(n-1)(n-2)+(n-2)(n-3)+.... instead?\n\n\nAlso, how did he get n^2 for the matrix b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk6.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..542a9ad88b358c78d273030de37cf51b649ee455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 18, + "timestamp": 1684720220360.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "26:10\n\nI have a question about the cost of elimination.\nAx=b\n\nFor an nxn matrix A\nFor the 1st pivot, instead of 100^2, shouldn\u2019t it cost 100*99?\n2nd pivot, instead of 99^2, shouldn\u2019t it cost 99*98?\n3rd pivot, instead of 98^2, shouldn\u2019t it cost 98*87?\n\nSo, instead of n^2+(n-1)^2+(n-2)^2+...., shouldn\u2019t it be n(n-1)+(n-1)(n-2)+(n-2)(n-3)+.... instead?\n\n\nAlso, how did he get n^2 for the matrix b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk7.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..542a9ad88b358c78d273030de37cf51b649ee455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 18, + "timestamp": 1684720220360.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "26:10\n\nI have a question about the cost of elimination.\nAx=b\n\nFor an nxn matrix A\nFor the 1st pivot, instead of 100^2, shouldn\u2019t it cost 100*99?\n2nd pivot, instead of 99^2, shouldn\u2019t it cost 99*98?\n3rd pivot, instead of 98^2, shouldn\u2019t it cost 98*87?\n\nSo, instead of n^2+(n-1)^2+(n-2)^2+...., shouldn\u2019t it be n(n-1)+(n-1)(n-2)+(n-2)(n-3)+.... instead?\n\n\nAlso, how did he get n^2 for the matrix b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..542a9ad88b358c78d273030de37cf51b649ee455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 18, + "timestamp": 1684720220360.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "26:10\n\nI have a question about the cost of elimination.\nAx=b\n\nFor an nxn matrix A\nFor the 1st pivot, instead of 100^2, shouldn\u2019t it cost 100*99?\n2nd pivot, instead of 99^2, shouldn\u2019t it cost 99*98?\n3rd pivot, instead of 98^2, shouldn\u2019t it cost 98*87?\n\nSo, instead of n^2+(n-1)^2+(n-2)^2+...., shouldn\u2019t it be n(n-1)+(n-1)(n-2)+(n-2)(n-3)+.... instead?\n\n\nAlso, how did he get n^2 for the matrix b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk9.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..542a9ad88b358c78d273030de37cf51b649ee455 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_18_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 18, + "timestamp": 1684720220360.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "26:10\n\nI have a question about the cost of elimination.\nAx=b\n\nFor an nxn matrix A\nFor the 1st pivot, instead of 100^2, shouldn\u2019t it cost 100*99?\n2nd pivot, instead of 99^2, shouldn\u2019t it cost 99*98?\n3rd pivot, instead of 98^2, shouldn\u2019t it cost 98*87?\n\nSo, instead of n^2+(n-1)^2+(n-2)^2+...., shouldn\u2019t it be n(n-1)+(n-1)(n-2)+(n-2)(n-3)+.... instead?\n\n\nAlso, how did he get n^2 for the matrix b?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk0.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..cd902f1e20fc340383bfce26e804888d14cac9aa --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 20, + "timestamp": 1684720264277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "8:55 Min why does he want to avoid A to be singular? don\u00b4t quite understand...the only reason i see (in hindsight), is that the step, he does at 12:30 Min (rewriting LU with a diagonal matrix in the middle) wouldn\u00b4t be unique. But i assume, there must be another reason." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk1.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..cd902f1e20fc340383bfce26e804888d14cac9aa --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 20, + "timestamp": 1684720264277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "8:55 Min why does he want to avoid A to be singular? don\u00b4t quite understand...the only reason i see (in hindsight), is that the step, he does at 12:30 Min (rewriting LU with a diagonal matrix in the middle) wouldn\u00b4t be unique. But i assume, there must be another reason." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk10.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..cd902f1e20fc340383bfce26e804888d14cac9aa --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 20, + "timestamp": 1684720264277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "8:55 Min why does he want to avoid A to be singular? don\u00b4t quite understand...the only reason i see (in hindsight), is that the step, he does at 12:30 Min (rewriting LU with a diagonal matrix in the middle) wouldn\u00b4t be unique. But i assume, there must be another reason." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk11.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..cd902f1e20fc340383bfce26e804888d14cac9aa --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 20, + "timestamp": 1684720264277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "8:55 Min why does he want to avoid A to be singular? don\u00b4t quite understand...the only reason i see (in hindsight), is that the step, he does at 12:30 Min (rewriting LU with a diagonal matrix in the middle) wouldn\u00b4t be unique. But i assume, there must be another reason." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk12.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..cd902f1e20fc340383bfce26e804888d14cac9aa --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 20, + "timestamp": 1684720264277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "8:55 Min why does he want to avoid A to be singular? don\u00b4t quite understand...the only reason i see (in hindsight), is that the step, he does at 12:30 Min (rewriting LU with a diagonal matrix in the middle) wouldn\u00b4t be unique. But i assume, there must be another reason." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk13.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..cd902f1e20fc340383bfce26e804888d14cac9aa --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 20, + "timestamp": 1684720264277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "8:55 Min why does he want to avoid A to be singular? don\u00b4t quite understand...the only reason i see (in hindsight), is that the step, he does at 12:30 Min (rewriting LU with a diagonal matrix in the middle) wouldn\u00b4t be unique. But i assume, there must be another reason." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk14.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..cd902f1e20fc340383bfce26e804888d14cac9aa --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 20, + "timestamp": 1684720264277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "8:55 Min why does he want to avoid A to be singular? don\u00b4t quite understand...the only reason i see (in hindsight), is that the step, he does at 12:30 Min (rewriting LU with a diagonal matrix in the middle) wouldn\u00b4t be unique. But i assume, there must be another reason." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk15.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..cd902f1e20fc340383bfce26e804888d14cac9aa --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 20, + "timestamp": 1684720264277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "8:55 Min why does he want to avoid A to be singular? don\u00b4t quite understand...the only reason i see (in hindsight), is that the step, he does at 12:30 Min (rewriting LU with a diagonal matrix in the middle) wouldn\u00b4t be unique. But i assume, there must be another reason." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk16.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..cd902f1e20fc340383bfce26e804888d14cac9aa --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 20, + "timestamp": 1684720264277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "8:55 Min why does he want to avoid A to be singular? don\u00b4t quite understand...the only reason i see (in hindsight), is that the step, he does at 12:30 Min (rewriting LU with a diagonal matrix in the middle) wouldn\u00b4t be unique. But i assume, there must be another reason." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk17.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..cd902f1e20fc340383bfce26e804888d14cac9aa --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 20, + "timestamp": 1684720264277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "8:55 Min why does he want to avoid A to be singular? don\u00b4t quite understand...the only reason i see (in hindsight), is that the step, he does at 12:30 Min (rewriting LU with a diagonal matrix in the middle) wouldn\u00b4t be unique. But i assume, there must be another reason." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk18.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..cd902f1e20fc340383bfce26e804888d14cac9aa --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 20, + "timestamp": 1684720264277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "8:55 Min why does he want to avoid A to be singular? don\u00b4t quite understand...the only reason i see (in hindsight), is that the step, he does at 12:30 Min (rewriting LU with a diagonal matrix in the middle) wouldn\u00b4t be unique. But i assume, there must be another reason." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk19.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..cd902f1e20fc340383bfce26e804888d14cac9aa --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 20, + "timestamp": 1684720264277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "8:55 Min why does he want to avoid A to be singular? don\u00b4t quite understand...the only reason i see (in hindsight), is that the step, he does at 12:30 Min (rewriting LU with a diagonal matrix in the middle) wouldn\u00b4t be unique. But i assume, there must be another reason." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk2.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..cd902f1e20fc340383bfce26e804888d14cac9aa --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 20, + "timestamp": 1684720264277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "8:55 Min why does he want to avoid A to be singular? don\u00b4t quite understand...the only reason i see (in hindsight), is that the step, he does at 12:30 Min (rewriting LU with a diagonal matrix in the middle) wouldn\u00b4t be unique. But i assume, there must be another reason." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk20.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..cd902f1e20fc340383bfce26e804888d14cac9aa --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 20, + "timestamp": 1684720264277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "8:55 Min why does he want to avoid A to be singular? don\u00b4t quite understand...the only reason i see (in hindsight), is that the step, he does at 12:30 Min (rewriting LU with a diagonal matrix in the middle) wouldn\u00b4t be unique. But i assume, there must be another reason." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk21.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..cd902f1e20fc340383bfce26e804888d14cac9aa --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 20, + "timestamp": 1684720264277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "8:55 Min why does he want to avoid A to be singular? don\u00b4t quite understand...the only reason i see (in hindsight), is that the step, he does at 12:30 Min (rewriting LU with a diagonal matrix in the middle) wouldn\u00b4t be unique. But i assume, there must be another reason." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk22.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..cd902f1e20fc340383bfce26e804888d14cac9aa --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 20, + "timestamp": 1684720264277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "8:55 Min why does he want to avoid A to be singular? don\u00b4t quite understand...the only reason i see (in hindsight), is that the step, he does at 12:30 Min (rewriting LU with a diagonal matrix in the middle) wouldn\u00b4t be unique. But i assume, there must be another reason." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk23.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..cd902f1e20fc340383bfce26e804888d14cac9aa --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 20, + "timestamp": 1684720264277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "8:55 Min why does he want to avoid A to be singular? don\u00b4t quite understand...the only reason i see (in hindsight), is that the step, he does at 12:30 Min (rewriting LU with a diagonal matrix in the middle) wouldn\u00b4t be unique. But i assume, there must be another reason." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk24.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..cd902f1e20fc340383bfce26e804888d14cac9aa --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 20, + "timestamp": 1684720264277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "8:55 Min why does he want to avoid A to be singular? don\u00b4t quite understand...the only reason i see (in hindsight), is that the step, he does at 12:30 Min (rewriting LU with a diagonal matrix in the middle) wouldn\u00b4t be unique. But i assume, there must be another reason." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk25.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..cd902f1e20fc340383bfce26e804888d14cac9aa --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 20, + "timestamp": 1684720264277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "8:55 Min why does he want to avoid A to be singular? don\u00b4t quite understand...the only reason i see (in hindsight), is that the step, he does at 12:30 Min (rewriting LU with a diagonal matrix in the middle) wouldn\u00b4t be unique. But i assume, there must be another reason." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk26.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..cd902f1e20fc340383bfce26e804888d14cac9aa --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 20, + "timestamp": 1684720264277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "8:55 Min why does he want to avoid A to be singular? don\u00b4t quite understand...the only reason i see (in hindsight), is that the step, he does at 12:30 Min (rewriting LU with a diagonal matrix in the middle) wouldn\u00b4t be unique. But i assume, there must be another reason." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk3.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..cd902f1e20fc340383bfce26e804888d14cac9aa --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 20, + "timestamp": 1684720264277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "8:55 Min why does he want to avoid A to be singular? don\u00b4t quite understand...the only reason i see (in hindsight), is that the step, he does at 12:30 Min (rewriting LU with a diagonal matrix in the middle) wouldn\u00b4t be unique. But i assume, there must be another reason." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk4.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..57cea6f9899ef4cff2c1f696cd141bc7479fd83a --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk4.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 20, + "timestamp": 1684720264277.0, + "annotatedSourceSentencesIndices": [ + 11 + ], + "names": [ + "annotator2" + ], + "text": "8:55 Min why does he want to avoid A to be singular? don\u00b4t quite understand...the only reason i see (in hindsight), is that the step, he does at 12:30 Min (rewriting LU with a diagonal matrix in the middle) wouldn\u00b4t be unique. But i assume, there must be another reason." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk5.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..cd902f1e20fc340383bfce26e804888d14cac9aa --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 20, + "timestamp": 1684720264277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "8:55 Min why does he want to avoid A to be singular? don\u00b4t quite understand...the only reason i see (in hindsight), is that the step, he does at 12:30 Min (rewriting LU with a diagonal matrix in the middle) wouldn\u00b4t be unique. But i assume, there must be another reason." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk6.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..cd902f1e20fc340383bfce26e804888d14cac9aa --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 20, + "timestamp": 1684720264277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "8:55 Min why does he want to avoid A to be singular? don\u00b4t quite understand...the only reason i see (in hindsight), is that the step, he does at 12:30 Min (rewriting LU with a diagonal matrix in the middle) wouldn\u00b4t be unique. But i assume, there must be another reason." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk7.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..cd902f1e20fc340383bfce26e804888d14cac9aa --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 20, + "timestamp": 1684720264277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "8:55 Min why does he want to avoid A to be singular? don\u00b4t quite understand...the only reason i see (in hindsight), is that the step, he does at 12:30 Min (rewriting LU with a diagonal matrix in the middle) wouldn\u00b4t be unique. But i assume, there must be another reason." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..cd902f1e20fc340383bfce26e804888d14cac9aa --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 20, + "timestamp": 1684720264277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "8:55 Min why does he want to avoid A to be singular? don\u00b4t quite understand...the only reason i see (in hindsight), is that the step, he does at 12:30 Min (rewriting LU with a diagonal matrix in the middle) wouldn\u00b4t be unique. But i assume, there must be another reason." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk9.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..cd902f1e20fc340383bfce26e804888d14cac9aa --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_20_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 20, + "timestamp": 1684720264277.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "8:55 Min why does he want to avoid A to be singular? don\u00b4t quite understand...the only reason i see (in hindsight), is that the step, he does at 12:30 Min (rewriting LU with a diagonal matrix in the middle) wouldn\u00b4t be unique. But i assume, there must be another reason." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk0.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..3260d0b57802d675c0dbb097175a18d830c65c81 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 21, + "timestamp": 1684720310343.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 10:27 how are we calculating E21( elimination matrix)?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk1.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3260d0b57802d675c0dbb097175a18d830c65c81 --- /dev/null +++ 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"annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 10:27 how are we calculating E21( elimination matrix)?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk16.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..3260d0b57802d675c0dbb097175a18d830c65c81 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 21, + "timestamp": 1684720310343.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 10:27 how are we calculating E21( elimination matrix)?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk17.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk17.json new file mode 100644 index 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calculating E21( elimination matrix)?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk19.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..3260d0b57802d675c0dbb097175a18d830c65c81 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 21, + "timestamp": 1684720310343.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 10:27 how are we calculating E21( elimination matrix)?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk2.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..3260d0b57802d675c0dbb097175a18d830c65c81 --- /dev/null +++ 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"MsIvs_6vC38", + "query_id": 21, + "timestamp": 1684720310343.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 10:27 how are we calculating E21( elimination matrix)?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk23.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..3260d0b57802d675c0dbb097175a18d830c65c81 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 21, + "timestamp": 1684720310343.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 10:27 how are we calculating E21( elimination matrix)?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk24.json 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"annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 10:27 how are we calculating E21( elimination matrix)?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk26.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..3260d0b57802d675c0dbb097175a18d830c65c81 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 21, + "timestamp": 1684720310343.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 10:27 how are we calculating E21( elimination matrix)?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk3.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..3260d0b57802d675c0dbb097175a18d830c65c81 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 21, + "timestamp": 1684720310343.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 10:27 how are we calculating E21( elimination matrix)?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk4.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..3260d0b57802d675c0dbb097175a18d830c65c81 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 21, + "timestamp": 1684720310343.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 10:27 how are we calculating E21( elimination matrix)?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk5.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..a991a4ec3e47f69e094b4946179dc99e9bf22652 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk5.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 21, + "timestamp": 1684720310343.0, + "annotatedSourceSentencesIndices": [ + 2 + ], + "names": [ + "annotator2" + ], + "text": "At 10:27 how are we calculating E21( elimination matrix)?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk6.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..3260d0b57802d675c0dbb097175a18d830c65c81 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 21, + "timestamp": 1684720310343.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 10:27 how are we calculating E21( elimination matrix)?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk7.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..3260d0b57802d675c0dbb097175a18d830c65c81 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 21, + "timestamp": 1684720310343.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 10:27 how are we calculating E21( elimination matrix)?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..3260d0b57802d675c0dbb097175a18d830c65c81 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 21, + "timestamp": 1684720310343.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 10:27 how are we calculating E21( elimination matrix)?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk9.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..3260d0b57802d675c0dbb097175a18d830c65c81 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_21_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 21, + "timestamp": 1684720310343.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 10:27 how are we calculating E21( elimination matrix)?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk0.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..5f39499908c469014396d6eee03c8b7762fe62b9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 22, + "timestamp": 1684720431225.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Great video! I love this series. In this lecture, Dr. Strang briefly mentions that the cost of operations for the det(A) will be (n!) He also shows us how the cost of getting A into upper triangular form U will be (1/3)n^3. But from Lecture 2 we know that one way of finding det(A) is to get A into U and then simply find the product of all n pivots. So it seems like the cost for finding det(A) would just be a bit more than (1/3)n^3, perhaps (1/3)n^3 + n. I must be missing something here; any thoughts?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk1.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..5f39499908c469014396d6eee03c8b7762fe62b9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 22, + "timestamp": 1684720431225.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Great video! I love this series. In this lecture, Dr. Strang briefly mentions that the cost of operations for the det(A) will be (n!) He also shows us how the cost of getting A into upper triangular form U will be (1/3)n^3. But from Lecture 2 we know that one way of finding det(A) is to get A into U and then simply find the product of all n pivots. So it seems like the cost for finding det(A) would just be a bit more than (1/3)n^3, perhaps (1/3)n^3 + n. I must be missing something here; any thoughts?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk10.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..5f39499908c469014396d6eee03c8b7762fe62b9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 22, + "timestamp": 1684720431225.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Great video! I love this series. In this lecture, Dr. Strang briefly mentions that the cost of operations for the det(A) will be (n!) He also shows us how the cost of getting A into upper triangular form U will be (1/3)n^3. But from Lecture 2 we know that one way of finding det(A) is to get A into U and then simply find the product of all n pivots. So it seems like the cost for finding det(A) would just be a bit more than (1/3)n^3, perhaps (1/3)n^3 + n. I must be missing something here; any thoughts?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk11.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..5f39499908c469014396d6eee03c8b7762fe62b9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 22, + "timestamp": 1684720431225.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Great video! I love this series. In this lecture, Dr. Strang briefly mentions that the cost of operations for the det(A) will be (n!) He also shows us how the cost of getting A into upper triangular form U will be (1/3)n^3. But from Lecture 2 we know that one way of finding det(A) is to get A into U and then simply find the product of all n pivots. So it seems like the cost for finding det(A) would just be a bit more than (1/3)n^3, perhaps (1/3)n^3 + n. I must be missing something here; any thoughts?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk12.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..5f39499908c469014396d6eee03c8b7762fe62b9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 22, + "timestamp": 1684720431225.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Great video! I love this series. In this lecture, Dr. Strang briefly mentions that the cost of operations for the det(A) will be (n!) He also shows us how the cost of getting A into upper triangular form U will be (1/3)n^3. But from Lecture 2 we know that one way of finding det(A) is to get A into U and then simply find the product of all n pivots. So it seems like the cost for finding det(A) would just be a bit more than (1/3)n^3, perhaps (1/3)n^3 + n. I must be missing something here; any thoughts?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk13.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..5f39499908c469014396d6eee03c8b7762fe62b9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 22, + "timestamp": 1684720431225.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Great video! I love this series. In this lecture, Dr. Strang briefly mentions that the cost of operations for the det(A) will be (n!) He also shows us how the cost of getting A into upper triangular form U will be (1/3)n^3. But from Lecture 2 we know that one way of finding det(A) is to get A into U and then simply find the product of all n pivots. So it seems like the cost for finding det(A) would just be a bit more than (1/3)n^3, perhaps (1/3)n^3 + n. I must be missing something here; any thoughts?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk14.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..5f39499908c469014396d6eee03c8b7762fe62b9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 22, + "timestamp": 1684720431225.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Great video! I love this series. In this lecture, Dr. Strang briefly mentions that the cost of operations for the det(A) will be (n!) He also shows us how the cost of getting A into upper triangular form U will be (1/3)n^3. But from Lecture 2 we know that one way of finding det(A) is to get A into U and then simply find the product of all n pivots. So it seems like the cost for finding det(A) would just be a bit more than (1/3)n^3, perhaps (1/3)n^3 + n. I must be missing something here; any thoughts?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk15.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..5f39499908c469014396d6eee03c8b7762fe62b9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 22, + "timestamp": 1684720431225.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Great video! I love this series. In this lecture, Dr. Strang briefly mentions that the cost of operations for the det(A) will be (n!) He also shows us how the cost of getting A into upper triangular form U will be (1/3)n^3. But from Lecture 2 we know that one way of finding det(A) is to get A into U and then simply find the product of all n pivots. So it seems like the cost for finding det(A) would just be a bit more than (1/3)n^3, perhaps (1/3)n^3 + n. I must be missing something here; any thoughts?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk16.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..5f39499908c469014396d6eee03c8b7762fe62b9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 22, + "timestamp": 1684720431225.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Great video! I love this series. In this lecture, Dr. Strang briefly mentions that the cost of operations for the det(A) will be (n!) He also shows us how the cost of getting A into upper triangular form U will be (1/3)n^3. But from Lecture 2 we know that one way of finding det(A) is to get A into U and then simply find the product of all n pivots. So it seems like the cost for finding det(A) would just be a bit more than (1/3)n^3, perhaps (1/3)n^3 + n. I must be missing something here; any thoughts?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk17.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..5f39499908c469014396d6eee03c8b7762fe62b9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 22, + "timestamp": 1684720431225.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Great video! I love this series. In this lecture, Dr. Strang briefly mentions that the cost of operations for the det(A) will be (n!) He also shows us how the cost of getting A into upper triangular form U will be (1/3)n^3. But from Lecture 2 we know that one way of finding det(A) is to get A into U and then simply find the product of all n pivots. So it seems like the cost for finding det(A) would just be a bit more than (1/3)n^3, perhaps (1/3)n^3 + n. I must be missing something here; any thoughts?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk18.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..5f39499908c469014396d6eee03c8b7762fe62b9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 22, + "timestamp": 1684720431225.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Great video! I love this series. In this lecture, Dr. Strang briefly mentions that the cost of operations for the det(A) will be (n!) He also shows us how the cost of getting A into upper triangular form U will be (1/3)n^3. But from Lecture 2 we know that one way of finding det(A) is to get A into U and then simply find the product of all n pivots. So it seems like the cost for finding det(A) would just be a bit more than (1/3)n^3, perhaps (1/3)n^3 + n. I must be missing something here; any thoughts?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk19.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1d2d6bffd8aa80b28859b6103b6b237396e20445 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk19.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 22, + "timestamp": 1684720431225.0, + "annotatedSourceSentencesIndices": [ + 1, + 6 + ], + "names": [ + "annotator2" + ], + "text": "Great video! I love this series. In this lecture, Dr. Strang briefly mentions that the cost of operations for the det(A) will be (n!) He also shows us how the cost of getting A into upper triangular form U will be (1/3)n^3. But from Lecture 2 we know that one way of finding det(A) is to get A into U and then simply find the product of all n pivots. So it seems like the cost for finding det(A) would just be a bit more than (1/3)n^3, perhaps (1/3)n^3 + n. I must be missing something here; any thoughts?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk2.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..5f39499908c469014396d6eee03c8b7762fe62b9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 22, + "timestamp": 1684720431225.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Great video! I love this series. In this lecture, Dr. Strang briefly mentions that the cost of operations for the det(A) will be (n!) He also shows us how the cost of getting A into upper triangular form U will be (1/3)n^3. But from Lecture 2 we know that one way of finding det(A) is to get A into U and then simply find the product of all n pivots. So it seems like the cost for finding det(A) would just be a bit more than (1/3)n^3, perhaps (1/3)n^3 + n. I must be missing something here; any thoughts?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk20.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..5f39499908c469014396d6eee03c8b7762fe62b9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 22, + "timestamp": 1684720431225.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Great video! I love this series. In this lecture, Dr. Strang briefly mentions that the cost of operations for the det(A) will be (n!) He also shows us how the cost of getting A into upper triangular form U will be (1/3)n^3. But from Lecture 2 we know that one way of finding det(A) is to get A into U and then simply find the product of all n pivots. So it seems like the cost for finding det(A) would just be a bit more than (1/3)n^3, perhaps (1/3)n^3 + n. I must be missing something here; any thoughts?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk21.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..5f39499908c469014396d6eee03c8b7762fe62b9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 22, + "timestamp": 1684720431225.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Great video! I love this series. In this lecture, Dr. Strang briefly mentions that the cost of operations for the det(A) will be (n!) He also shows us how the cost of getting A into upper triangular form U will be (1/3)n^3. But from Lecture 2 we know that one way of finding det(A) is to get A into U and then simply find the product of all n pivots. So it seems like the cost for finding det(A) would just be a bit more than (1/3)n^3, perhaps (1/3)n^3 + n. I must be missing something here; any thoughts?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk22.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..5f39499908c469014396d6eee03c8b7762fe62b9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 22, + "timestamp": 1684720431225.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Great video! I love this series. In this lecture, Dr. Strang briefly mentions that the cost of operations for the det(A) will be (n!) He also shows us how the cost of getting A into upper triangular form U will be (1/3)n^3. But from Lecture 2 we know that one way of finding det(A) is to get A into U and then simply find the product of all n pivots. So it seems like the cost for finding det(A) would just be a bit more than (1/3)n^3, perhaps (1/3)n^3 + n. I must be missing something here; any thoughts?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk23.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..5f39499908c469014396d6eee03c8b7762fe62b9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 22, + "timestamp": 1684720431225.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Great video! I love this series. In this lecture, Dr. Strang briefly mentions that the cost of operations for the det(A) will be (n!) He also shows us how the cost of getting A into upper triangular form U will be (1/3)n^3. But from Lecture 2 we know that one way of finding det(A) is to get A into U and then simply find the product of all n pivots. So it seems like the cost for finding det(A) would just be a bit more than (1/3)n^3, perhaps (1/3)n^3 + n. I must be missing something here; any thoughts?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk24.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..5f39499908c469014396d6eee03c8b7762fe62b9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 22, + "timestamp": 1684720431225.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Great video! I love this series. In this lecture, Dr. Strang briefly mentions that the cost of operations for the det(A) will be (n!) He also shows us how the cost of getting A into upper triangular form U will be (1/3)n^3. But from Lecture 2 we know that one way of finding det(A) is to get A into U and then simply find the product of all n pivots. So it seems like the cost for finding det(A) would just be a bit more than (1/3)n^3, perhaps (1/3)n^3 + n. I must be missing something here; any thoughts?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk25.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..5f39499908c469014396d6eee03c8b7762fe62b9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 22, + "timestamp": 1684720431225.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Great video! I love this series. In this lecture, Dr. Strang briefly mentions that the cost of operations for the det(A) will be (n!) He also shows us how the cost of getting A into upper triangular form U will be (1/3)n^3. But from Lecture 2 we know that one way of finding det(A) is to get A into U and then simply find the product of all n pivots. So it seems like the cost for finding det(A) would just be a bit more than (1/3)n^3, perhaps (1/3)n^3 + n. I must be missing something here; any thoughts?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk26.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..5f39499908c469014396d6eee03c8b7762fe62b9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 22, + "timestamp": 1684720431225.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Great video! I love this series. In this lecture, Dr. Strang briefly mentions that the cost of operations for the det(A) will be (n!) He also shows us how the cost of getting A into upper triangular form U will be (1/3)n^3. But from Lecture 2 we know that one way of finding det(A) is to get A into U and then simply find the product of all n pivots. So it seems like the cost for finding det(A) would just be a bit more than (1/3)n^3, perhaps (1/3)n^3 + n. I must be missing something here; any thoughts?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk3.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..5f39499908c469014396d6eee03c8b7762fe62b9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 22, + "timestamp": 1684720431225.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Great video! I love this series. In this lecture, Dr. Strang briefly mentions that the cost of operations for the det(A) will be (n!) He also shows us how the cost of getting A into upper triangular form U will be (1/3)n^3. But from Lecture 2 we know that one way of finding det(A) is to get A into U and then simply find the product of all n pivots. So it seems like the cost for finding det(A) would just be a bit more than (1/3)n^3, perhaps (1/3)n^3 + n. I must be missing something here; any thoughts?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk4.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..5f39499908c469014396d6eee03c8b7762fe62b9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 22, + "timestamp": 1684720431225.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Great video! I love this series. In this lecture, Dr. Strang briefly mentions that the cost of operations for the det(A) will be (n!) He also shows us how the cost of getting A into upper triangular form U will be (1/3)n^3. But from Lecture 2 we know that one way of finding det(A) is to get A into U and then simply find the product of all n pivots. So it seems like the cost for finding det(A) would just be a bit more than (1/3)n^3, perhaps (1/3)n^3 + n. I must be missing something here; any thoughts?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk5.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5f39499908c469014396d6eee03c8b7762fe62b9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 22, + "timestamp": 1684720431225.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Great video! I love this series. In this lecture, Dr. Strang briefly mentions that the cost of operations for the det(A) will be (n!) He also shows us how the cost of getting A into upper triangular form U will be (1/3)n^3. But from Lecture 2 we know that one way of finding det(A) is to get A into U and then simply find the product of all n pivots. So it seems like the cost for finding det(A) would just be a bit more than (1/3)n^3, perhaps (1/3)n^3 + n. I must be missing something here; any thoughts?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk6.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..5f39499908c469014396d6eee03c8b7762fe62b9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 22, + "timestamp": 1684720431225.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Great video! I love this series. In this lecture, Dr. Strang briefly mentions that the cost of operations for the det(A) will be (n!) He also shows us how the cost of getting A into upper triangular form U will be (1/3)n^3. But from Lecture 2 we know that one way of finding det(A) is to get A into U and then simply find the product of all n pivots. So it seems like the cost for finding det(A) would just be a bit more than (1/3)n^3, perhaps (1/3)n^3 + n. I must be missing something here; any thoughts?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk7.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..5f39499908c469014396d6eee03c8b7762fe62b9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 22, + "timestamp": 1684720431225.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Great video! I love this series. In this lecture, Dr. Strang briefly mentions that the cost of operations for the det(A) will be (n!) He also shows us how the cost of getting A into upper triangular form U will be (1/3)n^3. But from Lecture 2 we know that one way of finding det(A) is to get A into U and then simply find the product of all n pivots. So it seems like the cost for finding det(A) would just be a bit more than (1/3)n^3, perhaps (1/3)n^3 + n. I must be missing something here; any thoughts?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..5f39499908c469014396d6eee03c8b7762fe62b9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 22, + "timestamp": 1684720431225.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Great video! I love this series. In this lecture, Dr. Strang briefly mentions that the cost of operations for the det(A) will be (n!) He also shows us how the cost of getting A into upper triangular form U will be (1/3)n^3. But from Lecture 2 we know that one way of finding det(A) is to get A into U and then simply find the product of all n pivots. So it seems like the cost for finding det(A) would just be a bit more than (1/3)n^3, perhaps (1/3)n^3 + n. I must be missing something here; any thoughts?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk9.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..5f39499908c469014396d6eee03c8b7762fe62b9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_22_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 22, + "timestamp": 1684720431225.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Great video! I love this series. In this lecture, Dr. Strang briefly mentions that the cost of operations for the det(A) will be (n!) He also shows us how the cost of getting A into upper triangular form U will be (1/3)n^3. But from Lecture 2 we know that one way of finding det(A) is to get A into U and then simply find the product of all n pivots. So it seems like the cost for finding det(A) would just be a bit more than (1/3)n^3, perhaps (1/3)n^3 + n. I must be missing something here; any thoughts?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk0.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..0e34bb755b3f8af68a1452658954efab7a3aade8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 23, + "timestamp": 1684720563078.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "hmm is there a complementary book we must follow? I'm puzzled as I don't think we've introduced the elementary matrices in previous lectures, or Upper/lower matrices. I feel this is not beginner friendly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk1.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..06bc467828b8ae0696327ba70a95698af524b2d4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk1.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 23, + "timestamp": 1684720563078.0, + "annotatedSourceSentencesIndices": [ + 11 + ], + "names": [ + "annotator2" + ], + "text": "hmm is there a complementary book we must follow? I'm puzzled as I don't think we've introduced the elementary matrices in previous lectures, or Upper/lower matrices. I feel this is not beginner friendly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk10.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..0e34bb755b3f8af68a1452658954efab7a3aade8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 23, + "timestamp": 1684720563078.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "hmm is there a complementary book we must follow? I'm puzzled as I don't think we've introduced the elementary matrices in previous lectures, or Upper/lower matrices. I feel this is not beginner friendly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk11.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..0e34bb755b3f8af68a1452658954efab7a3aade8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 23, + "timestamp": 1684720563078.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "hmm is there a complementary book we must follow? I'm puzzled as I don't think we've introduced the elementary matrices in previous lectures, or Upper/lower matrices. I feel this is not beginner friendly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk12.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0e34bb755b3f8af68a1452658954efab7a3aade8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 23, + "timestamp": 1684720563078.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "hmm is there a complementary book we must follow? I'm puzzled as I don't think we've introduced the elementary matrices in previous lectures, or Upper/lower matrices. I feel this is not beginner friendly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk13.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..0e34bb755b3f8af68a1452658954efab7a3aade8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 23, + "timestamp": 1684720563078.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "hmm is there a complementary book we must follow? I'm puzzled as I don't think we've introduced the elementary matrices in previous lectures, or Upper/lower matrices. I feel this is not beginner friendly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk14.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..0e34bb755b3f8af68a1452658954efab7a3aade8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 23, + "timestamp": 1684720563078.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "hmm is there a complementary book we must follow? I'm puzzled as I don't think we've introduced the elementary matrices in previous lectures, or Upper/lower matrices. I feel this is not beginner friendly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk15.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..0e34bb755b3f8af68a1452658954efab7a3aade8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 23, + "timestamp": 1684720563078.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "hmm is there a complementary book we must follow? I'm puzzled as I don't think we've introduced the elementary matrices in previous lectures, or Upper/lower matrices. I feel this is not beginner friendly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk16.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..0e34bb755b3f8af68a1452658954efab7a3aade8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 23, + "timestamp": 1684720563078.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "hmm is there a complementary book we must follow? I'm puzzled as I don't think we've introduced the elementary matrices in previous lectures, or Upper/lower matrices. I feel this is not beginner friendly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk17.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..0e34bb755b3f8af68a1452658954efab7a3aade8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 23, + "timestamp": 1684720563078.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "hmm is there a complementary book we must follow? I'm puzzled as I don't think we've introduced the elementary matrices in previous lectures, or Upper/lower matrices. I feel this is not beginner friendly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk18.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..0e34bb755b3f8af68a1452658954efab7a3aade8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 23, + "timestamp": 1684720563078.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "hmm is there a complementary book we must follow? I'm puzzled as I don't think we've introduced the elementary matrices in previous lectures, or Upper/lower matrices. I feel this is not beginner friendly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk19.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..0e34bb755b3f8af68a1452658954efab7a3aade8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 23, + "timestamp": 1684720563078.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "hmm is there a complementary book we must follow? I'm puzzled as I don't think we've introduced the elementary matrices in previous lectures, or Upper/lower matrices. I feel this is not beginner friendly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk2.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..0e34bb755b3f8af68a1452658954efab7a3aade8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 23, + "timestamp": 1684720563078.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "hmm is there a complementary book we must follow? I'm puzzled as I don't think we've introduced the elementary matrices in previous lectures, or Upper/lower matrices. I feel this is not beginner friendly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk20.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..0e34bb755b3f8af68a1452658954efab7a3aade8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 23, + "timestamp": 1684720563078.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "hmm is there a complementary book we must follow? I'm puzzled as I don't think we've introduced the elementary matrices in previous lectures, or Upper/lower matrices. I feel this is not beginner friendly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk21.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..0e34bb755b3f8af68a1452658954efab7a3aade8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 23, + "timestamp": 1684720563078.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "hmm is there a complementary book we must follow? I'm puzzled as I don't think we've introduced the elementary matrices in previous lectures, or Upper/lower matrices. I feel this is not beginner friendly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk22.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0e34bb755b3f8af68a1452658954efab7a3aade8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 23, + "timestamp": 1684720563078.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "hmm is there a complementary book we must follow? I'm puzzled as I don't think we've introduced the elementary matrices in previous lectures, or Upper/lower matrices. I feel this is not beginner friendly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk23.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..0e34bb755b3f8af68a1452658954efab7a3aade8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 23, + "timestamp": 1684720563078.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "hmm is there a complementary book we must follow? I'm puzzled as I don't think we've introduced the elementary matrices in previous lectures, or Upper/lower matrices. I feel this is not beginner friendly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk24.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..0e34bb755b3f8af68a1452658954efab7a3aade8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 23, + "timestamp": 1684720563078.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "hmm is there a complementary book we must follow? I'm puzzled as I don't think we've introduced the elementary matrices in previous lectures, or Upper/lower matrices. I feel this is not beginner friendly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk25.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..0e34bb755b3f8af68a1452658954efab7a3aade8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 23, + "timestamp": 1684720563078.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "hmm is there a complementary book we must follow? I'm puzzled as I don't think we've introduced the elementary matrices in previous lectures, or Upper/lower matrices. I feel this is not beginner friendly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk26.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..0e34bb755b3f8af68a1452658954efab7a3aade8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 23, + "timestamp": 1684720563078.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "hmm is there a complementary book we must follow? I'm puzzled as I don't think we've introduced the elementary matrices in previous lectures, or Upper/lower matrices. I feel this is not beginner friendly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk3.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..0e34bb755b3f8af68a1452658954efab7a3aade8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 23, + "timestamp": 1684720563078.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "hmm is there a complementary book we must follow? I'm puzzled as I don't think we've introduced the elementary matrices in previous lectures, or Upper/lower matrices. I feel this is not beginner friendly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk4.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..8f2b341c595dd7cdef503cadfa204c1ddaa29a71 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk4.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 23, + "timestamp": 1684720563078.0, + "annotatedSourceSentencesIndices": [ + 14 + ], + "names": [ + "annotator2" + ], + "text": "hmm is there a complementary book we must follow? I'm puzzled as I don't think we've introduced the elementary matrices in previous lectures, or Upper/lower matrices. I feel this is not beginner friendly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk5.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..0e34bb755b3f8af68a1452658954efab7a3aade8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 23, + "timestamp": 1684720563078.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "hmm is there a complementary book we must follow? I'm puzzled as I don't think we've introduced the elementary matrices in previous lectures, or Upper/lower matrices. I feel this is not beginner friendly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk6.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..c0cfeca7b984b2f8781fe4eb4ad3bdcb0fd8c657 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk6.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 23, + "timestamp": 1684720563078.0, + "annotatedSourceSentencesIndices": [ + 12 + ], + "names": [ + "annotator2" + ], + "text": "hmm is there a complementary book we must follow? I'm puzzled as I don't think we've introduced the elementary matrices in previous lectures, or Upper/lower matrices. I feel this is not beginner friendly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk7.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e34bb755b3f8af68a1452658954efab7a3aade8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 23, + "timestamp": 1684720563078.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "hmm is there a complementary book we must follow? I'm puzzled as I don't think we've introduced the elementary matrices in previous lectures, or Upper/lower matrices. I feel this is not beginner friendly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..0e34bb755b3f8af68a1452658954efab7a3aade8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 23, + "timestamp": 1684720563078.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "hmm is there a complementary book we must follow? I'm puzzled as I don't think we've introduced the elementary matrices in previous lectures, or Upper/lower matrices. I feel this is not beginner friendly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk9.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..0e34bb755b3f8af68a1452658954efab7a3aade8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_23_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 23, + "timestamp": 1684720563078.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "hmm is there a complementary book we must follow? I'm puzzled as I don't think we've introduced the elementary matrices in previous lectures, or Upper/lower matrices. I feel this is not beginner friendly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk0.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..f6ee1f2642f6e42c2091d5d976cd91051febc23c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 24, + "timestamp": 1684720668792.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm a bit unsure as to why he doesn't like the 10 in the matrix E around 19:00? Are we assuming we already have A and U defined, and just need to find a matrix that relates them? Is it because the L parts, like the E parts (E21, E31, E32) can simply be stated, but to calculate the final L and E, final L can be stated (just like it's parts), where as E has to be calculated?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk1.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..f6ee1f2642f6e42c2091d5d976cd91051febc23c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 24, + "timestamp": 1684720668792.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm a bit unsure as to why he doesn't like the 10 in the matrix E around 19:00? Are we assuming we already have A and U defined, and just need to find a matrix that relates them? Is it because the L parts, like the E parts (E21, E31, E32) can simply be stated, but to calculate the final L and E, final L can be stated (just like it's parts), where as E has to be calculated?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk10.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..f6ee1f2642f6e42c2091d5d976cd91051febc23c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 24, + "timestamp": 1684720668792.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm a bit unsure as to why he doesn't like the 10 in the matrix E around 19:00? Are we assuming we already have A and U defined, and just need to find a matrix that relates them? Is it because the L parts, like the E parts (E21, E31, E32) can simply be stated, but to calculate the final L and E, final L can be stated (just like it's parts), where as E has to be calculated?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk11.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..35a5ba35a6f39374537d7f11b2f4cb591e7c0b99 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk11.json @@ -0,0 +1,17 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 24, + "timestamp": 1684720668792.0, + "annotatedSourceSentencesIndices": [ + 0, + 1, + 2, + 3 + ], + "names": [ + "annotator2" + ], + "text": "I'm a bit unsure as to why he doesn't like the 10 in the matrix E around 19:00? Are we assuming we already have A and U defined, and just need to find a matrix that relates them? Is it because the L parts, like the E parts (E21, E31, E32) can simply be stated, but to calculate the final L and E, final L can be stated (just like it's parts), where as E has to be calculated?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk12.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..f6ee1f2642f6e42c2091d5d976cd91051febc23c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 24, + "timestamp": 1684720668792.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm a bit unsure as to why he doesn't like the 10 in the matrix E around 19:00? Are we assuming we already have A and U defined, and just need to find a matrix that relates them? Is it because the L parts, like the E parts (E21, E31, E32) can simply be stated, but to calculate the final L and E, final L can be stated (just like it's parts), where as E has to be calculated?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk13.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..f6ee1f2642f6e42c2091d5d976cd91051febc23c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 24, + "timestamp": 1684720668792.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm a bit unsure as to why he doesn't like the 10 in the matrix E around 19:00? Are we assuming we already have A and U defined, and just need to find a matrix that relates them? Is it because the L parts, like the E parts (E21, E31, E32) can simply be stated, but to calculate the final L and E, final L can be stated (just like it's parts), where as E has to be calculated?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk14.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..f6ee1f2642f6e42c2091d5d976cd91051febc23c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 24, + "timestamp": 1684720668792.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm a bit unsure as to why he doesn't like the 10 in the matrix E around 19:00? Are we assuming we already have A and U defined, and just need to find a matrix that relates them? Is it because the L parts, like the E parts (E21, E31, E32) can simply be stated, but to calculate the final L and E, final L can be stated (just like it's parts), where as E has to be calculated?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk15.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..f6ee1f2642f6e42c2091d5d976cd91051febc23c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 24, + "timestamp": 1684720668792.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm a bit unsure as to why he doesn't like the 10 in the matrix E around 19:00? Are we assuming we already have A and U defined, and just need to find a matrix that relates them? Is it because the L parts, like the E parts (E21, E31, E32) can simply be stated, but to calculate the final L and E, final L can be stated (just like it's parts), where as E has to be calculated?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk16.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f6ee1f2642f6e42c2091d5d976cd91051febc23c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 24, + "timestamp": 1684720668792.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm a bit unsure as to why he doesn't like the 10 in the matrix E around 19:00? Are we assuming we already have A and U defined, and just need to find a matrix that relates them? Is it because the L parts, like the E parts (E21, E31, E32) can simply be stated, but to calculate the final L and E, final L can be stated (just like it's parts), where as E has to be calculated?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk17.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..f6ee1f2642f6e42c2091d5d976cd91051febc23c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 24, + "timestamp": 1684720668792.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm a bit unsure as to why he doesn't like the 10 in the matrix E around 19:00? Are we assuming we already have A and U defined, and just need to find a matrix that relates them? Is it because the L parts, like the E parts (E21, E31, E32) can simply be stated, but to calculate the final L and E, final L can be stated (just like it's parts), where as E has to be calculated?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk18.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..f6ee1f2642f6e42c2091d5d976cd91051febc23c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 24, + "timestamp": 1684720668792.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm a bit unsure as to why he doesn't like the 10 in the matrix E around 19:00? Are we assuming we already have A and U defined, and just need to find a matrix that relates them? Is it because the L parts, like the E parts (E21, E31, E32) can simply be stated, but to calculate the final L and E, final L can be stated (just like it's parts), where as E has to be calculated?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk19.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..f6ee1f2642f6e42c2091d5d976cd91051febc23c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 24, + "timestamp": 1684720668792.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm a bit unsure as to why he doesn't like the 10 in the matrix E around 19:00? Are we assuming we already have A and U defined, and just need to find a matrix that relates them? Is it because the L parts, like the E parts (E21, E31, E32) can simply be stated, but to calculate the final L and E, final L can be stated (just like it's parts), where as E has to be calculated?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk2.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..f6ee1f2642f6e42c2091d5d976cd91051febc23c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 24, + "timestamp": 1684720668792.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm a bit unsure as to why he doesn't like the 10 in the matrix E around 19:00? Are we assuming we already have A and U defined, and just need to find a matrix that relates them? Is it because the L parts, like the E parts (E21, E31, E32) can simply be stated, but to calculate the final L and E, final L can be stated (just like it's parts), where as E has to be calculated?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk20.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..f6ee1f2642f6e42c2091d5d976cd91051febc23c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 24, + "timestamp": 1684720668792.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm a bit unsure as to why he doesn't like the 10 in the matrix E around 19:00? Are we assuming we already have A and U defined, and just need to find a matrix that relates them? Is it because the L parts, like the E parts (E21, E31, E32) can simply be stated, but to calculate the final L and E, final L can be stated (just like it's parts), where as E has to be calculated?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk21.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f6ee1f2642f6e42c2091d5d976cd91051febc23c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 24, + "timestamp": 1684720668792.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm a bit unsure as to why he doesn't like the 10 in the matrix E around 19:00? Are we assuming we already have A and U defined, and just need to find a matrix that relates them? Is it because the L parts, like the E parts (E21, E31, E32) can simply be stated, but to calculate the final L and E, final L can be stated (just like it's parts), where as E has to be calculated?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk22.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..f6ee1f2642f6e42c2091d5d976cd91051febc23c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 24, + "timestamp": 1684720668792.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm a bit unsure as to why he doesn't like the 10 in the matrix E around 19:00? Are we assuming we already have A and U defined, and just need to find a matrix that relates them? Is it because the L parts, like the E parts (E21, E31, E32) can simply be stated, but to calculate the final L and E, final L can be stated (just like it's parts), where as E has to be calculated?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk23.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..f6ee1f2642f6e42c2091d5d976cd91051febc23c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 24, + "timestamp": 1684720668792.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm a bit unsure as to why he doesn't like the 10 in the matrix E around 19:00? Are we assuming we already have A and U defined, and just need to find a matrix that relates them? Is it because the L parts, like the E parts (E21, E31, E32) can simply be stated, but to calculate the final L and E, final L can be stated (just like it's parts), where as E has to be calculated?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk24.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..f6ee1f2642f6e42c2091d5d976cd91051febc23c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 24, + "timestamp": 1684720668792.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm a bit unsure as to why he doesn't like the 10 in the matrix E around 19:00? Are we assuming we already have A and U defined, and just need to find a matrix that relates them? Is it because the L parts, like the E parts (E21, E31, E32) can simply be stated, but to calculate the final L and E, final L can be stated (just like it's parts), where as E has to be calculated?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk25.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..f6ee1f2642f6e42c2091d5d976cd91051febc23c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 24, + "timestamp": 1684720668792.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm a bit unsure as to why he doesn't like the 10 in the matrix E around 19:00? Are we assuming we already have A and U defined, and just need to find a matrix that relates them? Is it because the L parts, like the E parts (E21, E31, E32) can simply be stated, but to calculate the final L and E, final L can be stated (just like it's parts), where as E has to be calculated?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk26.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f6ee1f2642f6e42c2091d5d976cd91051febc23c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 24, + "timestamp": 1684720668792.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm a bit unsure as to why he doesn't like the 10 in the matrix E around 19:00? Are we assuming we already have A and U defined, and just need to find a matrix that relates them? Is it because the L parts, like the E parts (E21, E31, E32) can simply be stated, but to calculate the final L and E, final L can be stated (just like it's parts), where as E has to be calculated?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk3.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..f6ee1f2642f6e42c2091d5d976cd91051febc23c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 24, + "timestamp": 1684720668792.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm a bit unsure as to why he doesn't like the 10 in the matrix E around 19:00? Are we assuming we already have A and U defined, and just need to find a matrix that relates them? Is it because the L parts, like the E parts (E21, E31, E32) can simply be stated, but to calculate the final L and E, final L can be stated (just like it's parts), where as E has to be calculated?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk4.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..f6ee1f2642f6e42c2091d5d976cd91051febc23c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 24, + "timestamp": 1684720668792.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm a bit unsure as to why he doesn't like the 10 in the matrix E around 19:00? Are we assuming we already have A and U defined, and just need to find a matrix that relates them? Is it because the L parts, like the E parts (E21, E31, E32) can simply be stated, but to calculate the final L and E, final L can be stated (just like it's parts), where as E has to be calculated?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk5.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..f6ee1f2642f6e42c2091d5d976cd91051febc23c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 24, + "timestamp": 1684720668792.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm a bit unsure as to why he doesn't like the 10 in the matrix E around 19:00? Are we assuming we already have A and U defined, and just need to find a matrix that relates them? Is it because the L parts, like the E parts (E21, E31, E32) can simply be stated, but to calculate the final L and E, final L can be stated (just like it's parts), where as E has to be calculated?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk6.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..f6ee1f2642f6e42c2091d5d976cd91051febc23c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 24, + "timestamp": 1684720668792.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm a bit unsure as to why he doesn't like the 10 in the matrix E around 19:00? Are we assuming we already have A and U defined, and just need to find a matrix that relates them? Is it because the L parts, like the E parts (E21, E31, E32) can simply be stated, but to calculate the final L and E, final L can be stated (just like it's parts), where as E has to be calculated?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk7.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..f6ee1f2642f6e42c2091d5d976cd91051febc23c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 24, + "timestamp": 1684720668792.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm a bit unsure as to why he doesn't like the 10 in the matrix E around 19:00? Are we assuming we already have A and U defined, and just need to find a matrix that relates them? Is it because the L parts, like the E parts (E21, E31, E32) can simply be stated, but to calculate the final L and E, final L can be stated (just like it's parts), where as E has to be calculated?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f6ee1f2642f6e42c2091d5d976cd91051febc23c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 24, + "timestamp": 1684720668792.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm a bit unsure as to why he doesn't like the 10 in the matrix E around 19:00? Are we assuming we already have A and U defined, and just need to find a matrix that relates them? Is it because the L parts, like the E parts (E21, E31, E32) can simply be stated, but to calculate the final L and E, final L can be stated (just like it's parts), where as E has to be calculated?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk9.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..f6ee1f2642f6e42c2091d5d976cd91051febc23c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_24_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 24, + "timestamp": 1684720668792.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I'm a bit unsure as to why he doesn't like the 10 in the matrix E around 19:00? Are we assuming we already have A and U defined, and just need to find a matrix that relates them? Is it because the L parts, like the E parts (E21, E31, E32) can simply be stated, but to calculate the final L and E, final L can be stated (just like it's parts), where as E has to be calculated?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk0.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6889b98e38bdb5d237a3d8b0381f0bfb04ea7cb8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 28, + "timestamp": 1684720790293.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone tell me why can't we obtain the Lower triangular matrix L directly from the combined E which could just be derived from using gaussian elimination? Thanksss" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk1.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..6889b98e38bdb5d237a3d8b0381f0bfb04ea7cb8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 28, + "timestamp": 1684720790293.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone tell me why can't we obtain the Lower triangular matrix L directly from the combined E which could just be derived from using gaussian elimination? Thanksss" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk10.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..6889b98e38bdb5d237a3d8b0381f0bfb04ea7cb8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 28, + "timestamp": 1684720790293.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone tell me why can't we obtain the Lower triangular matrix L directly from the combined E which could just be derived from using gaussian elimination? Thanksss" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk11.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..6889b98e38bdb5d237a3d8b0381f0bfb04ea7cb8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 28, + "timestamp": 1684720790293.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone tell me why can't we obtain the Lower triangular matrix L directly from the combined E which could just be derived from using gaussian elimination? Thanksss" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk12.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..6889b98e38bdb5d237a3d8b0381f0bfb04ea7cb8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 28, + "timestamp": 1684720790293.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone tell me why can't we obtain the Lower triangular matrix L directly from the combined E which could just be derived from using gaussian elimination? Thanksss" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk13.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..6889b98e38bdb5d237a3d8b0381f0bfb04ea7cb8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 28, + "timestamp": 1684720790293.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone tell me why can't we obtain the Lower triangular matrix L directly from the combined E which could just be derived from using gaussian elimination? Thanksss" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk14.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..6889b98e38bdb5d237a3d8b0381f0bfb04ea7cb8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 28, + "timestamp": 1684720790293.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone tell me why can't we obtain the Lower triangular matrix L directly from the combined E which could just be derived from using gaussian elimination? Thanksss" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk15.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..6889b98e38bdb5d237a3d8b0381f0bfb04ea7cb8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 28, + "timestamp": 1684720790293.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone tell me why can't we obtain the Lower triangular matrix L directly from the combined E which could just be derived from using gaussian elimination? Thanksss" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk16.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..6889b98e38bdb5d237a3d8b0381f0bfb04ea7cb8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 28, + "timestamp": 1684720790293.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone tell me why can't we obtain the Lower triangular matrix L directly from the combined E which could just be derived from using gaussian elimination? Thanksss" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk17.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..6889b98e38bdb5d237a3d8b0381f0bfb04ea7cb8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 28, + "timestamp": 1684720790293.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone tell me why can't we obtain the Lower triangular matrix L directly from the combined E which could just be derived from using gaussian elimination? Thanksss" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk18.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..6889b98e38bdb5d237a3d8b0381f0bfb04ea7cb8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 28, + "timestamp": 1684720790293.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone tell me why can't we obtain the Lower triangular matrix L directly from the combined E which could just be derived from using gaussian elimination? Thanksss" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk19.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..6889b98e38bdb5d237a3d8b0381f0bfb04ea7cb8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 28, + "timestamp": 1684720790293.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone tell me why can't we obtain the Lower triangular matrix L directly from the combined E which could just be derived from using gaussian elimination? Thanksss" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk2.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6889b98e38bdb5d237a3d8b0381f0bfb04ea7cb8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 28, + "timestamp": 1684720790293.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone tell me why can't we obtain the Lower triangular matrix L directly from the combined E which could just be derived from using gaussian elimination? Thanksss" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk20.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6889b98e38bdb5d237a3d8b0381f0bfb04ea7cb8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 28, + "timestamp": 1684720790293.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone tell me why can't we obtain the Lower triangular matrix L directly from the combined E which could just be derived from using gaussian elimination? Thanksss" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk21.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..6889b98e38bdb5d237a3d8b0381f0bfb04ea7cb8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 28, + "timestamp": 1684720790293.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone tell me why can't we obtain the Lower triangular matrix L directly from the combined E which could just be derived from using gaussian elimination? Thanksss" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk22.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..6889b98e38bdb5d237a3d8b0381f0bfb04ea7cb8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 28, + "timestamp": 1684720790293.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone tell me why can't we obtain the Lower triangular matrix L directly from the combined E which could just be derived from using gaussian elimination? Thanksss" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk23.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..6889b98e38bdb5d237a3d8b0381f0bfb04ea7cb8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 28, + "timestamp": 1684720790293.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone tell me why can't we obtain the Lower triangular matrix L directly from the combined E which could just be derived from using gaussian elimination? Thanksss" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk24.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..6889b98e38bdb5d237a3d8b0381f0bfb04ea7cb8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 28, + "timestamp": 1684720790293.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone tell me why can't we obtain the Lower triangular matrix L directly from the combined E which could just be derived from using gaussian elimination? Thanksss" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk25.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..6889b98e38bdb5d237a3d8b0381f0bfb04ea7cb8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 28, + "timestamp": 1684720790293.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone tell me why can't we obtain the Lower triangular matrix L directly from the combined E which could just be derived from using gaussian elimination? Thanksss" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk26.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..6889b98e38bdb5d237a3d8b0381f0bfb04ea7cb8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 28, + "timestamp": 1684720790293.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone tell me why can't we obtain the Lower triangular matrix L directly from the combined E which could just be derived from using gaussian elimination? Thanksss" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk3.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..6889b98e38bdb5d237a3d8b0381f0bfb04ea7cb8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 28, + "timestamp": 1684720790293.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone tell me why can't we obtain the Lower triangular matrix L directly from the combined E which could just be derived from using gaussian elimination? Thanksss" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk4.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..6889b98e38bdb5d237a3d8b0381f0bfb04ea7cb8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 28, + "timestamp": 1684720790293.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone tell me why can't we obtain the Lower triangular matrix L directly from the combined E which could just be derived from using gaussian elimination? Thanksss" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk5.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..6889b98e38bdb5d237a3d8b0381f0bfb04ea7cb8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 28, + "timestamp": 1684720790293.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone tell me why can't we obtain the Lower triangular matrix L directly from the combined E which could just be derived from using gaussian elimination? Thanksss" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk6.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..6889b98e38bdb5d237a3d8b0381f0bfb04ea7cb8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 28, + "timestamp": 1684720790293.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone tell me why can't we obtain the Lower triangular matrix L directly from the combined E which could just be derived from using gaussian elimination? Thanksss" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk7.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..6889b98e38bdb5d237a3d8b0381f0bfb04ea7cb8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 28, + "timestamp": 1684720790293.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone tell me why can't we obtain the Lower triangular matrix L directly from the combined E which could just be derived from using gaussian elimination? Thanksss" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..6889b98e38bdb5d237a3d8b0381f0bfb04ea7cb8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 28, + "timestamp": 1684720790293.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone tell me why can't we obtain the Lower triangular matrix L directly from the combined E which could just be derived from using gaussian elimination? Thanksss" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk9.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..ae65ff13f6a1e4829902a9c4de4ef4fc5324a42f --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_28_chunk9.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 28, + "timestamp": 1684720790293.0, + "annotatedSourceSentencesIndices": [ + 5 + ], + "names": [ + "annotator2" + ], + "text": "Can anyone tell me why can't we obtain the Lower triangular matrix L directly from the combined E which could just be derived from using gaussian elimination? Thanksss" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk0.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..15b246f2a18ce7816c5b520a761f9be408b0b17f --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 2, + "timestamp": 1684708398925.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why A=LU is better than EA=U?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk1.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..15b246f2a18ce7816c5b520a761f9be408b0b17f --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk1.json @@ -0,0 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"annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why A=LU is better than EA=U?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk13.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..ac4926c2a3cfdd1ac4ef5f1305622b70d7605ef3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk13.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 2, + "timestamp": 1684708398925.0, + "annotatedSourceSentencesIndices": [ + 19 + ], + "names": [ + "annotator2" + ], + "text": "Can someone explain why A=LU is better than EA=U?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk14.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk14.json new file mode 100644 index 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better than EA=U?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk16.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..15b246f2a18ce7816c5b520a761f9be408b0b17f --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 2, + "timestamp": 1684708398925.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why A=LU is better than EA=U?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk17.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..15b246f2a18ce7816c5b520a761f9be408b0b17f --- /dev/null +++ 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"query_id": 2, + "timestamp": 1684708398925.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why A=LU is better than EA=U?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk20.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..15b246f2a18ce7816c5b520a761f9be408b0b17f --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 2, + "timestamp": 1684708398925.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why A=LU is better than EA=U?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk21.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk21.json new file mode 100644 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is better than EA=U?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk23.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..15b246f2a18ce7816c5b520a761f9be408b0b17f --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 2, + "timestamp": 1684708398925.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why A=LU is better than EA=U?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk24.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..15b246f2a18ce7816c5b520a761f9be408b0b17f --- /dev/null +++ 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"query_id": 2, + "timestamp": 1684708398925.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why A=LU is better than EA=U?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk4.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..15b246f2a18ce7816c5b520a761f9be408b0b17f --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 2, + "timestamp": 1684708398925.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why A=LU is better than EA=U?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk5.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk5.json new file mode 100644 index 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than EA=U?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk7.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..15b246f2a18ce7816c5b520a761f9be408b0b17f --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 2, + "timestamp": 1684708398925.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why A=LU is better than EA=U?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..15b246f2a18ce7816c5b520a761f9be408b0b17f --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_2_chunk8.json @@ -0,0 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b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..7872a0c59c4d744efa3055d4f4645cca20251b92 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 30, + "timestamp": 1684721031176.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "On 21 minute I don't understand where these matrices come from and why we need them. Anyone care to elaborate?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk1.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..7872a0c59c4d744efa3055d4f4645cca20251b92 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 30, + "timestamp": 1684721031176.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "On 21 minute I don't understand where these matrices come from and why we need them. Anyone care to elaborate?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk10.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..7872a0c59c4d744efa3055d4f4645cca20251b92 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 30, + "timestamp": 1684721031176.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "On 21 minute I don't understand where these matrices come from and why we need them. Anyone care to elaborate?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk11.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..45c73fb027982404c9b9869dfdfcf3458630cb34 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk11.json @@ -0,0 +1,16 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 30, + "timestamp": 1684721031176.0, + "annotatedSourceSentencesIndices": [ + 15, + 16, + 17 + ], + "names": [ + "annotator2" + ], + "text": "On 21 minute I don't understand where these matrices come from and why we need them. Anyone care to elaborate?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk12.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..e89f591b58016501e2b617549c3f9998f27d329d --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk12.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 30, + "timestamp": 1684721031176.0, + "annotatedSourceSentencesIndices": [ + 0 + ], + "names": [ + "annotator2" + ], + "text": "On 21 minute I don't understand where these matrices come from and why we need them. Anyone care to elaborate?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk13.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..7872a0c59c4d744efa3055d4f4645cca20251b92 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 30, + "timestamp": 1684721031176.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "On 21 minute I don't understand where these matrices come from and why we need them. Anyone care to elaborate?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk14.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7872a0c59c4d744efa3055d4f4645cca20251b92 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 30, + "timestamp": 1684721031176.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "On 21 minute I don't understand where these matrices come from and why we need them. Anyone care to elaborate?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk15.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7872a0c59c4d744efa3055d4f4645cca20251b92 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 30, + "timestamp": 1684721031176.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "On 21 minute I don't understand where these matrices come from and why we need them. Anyone care to elaborate?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk16.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..7872a0c59c4d744efa3055d4f4645cca20251b92 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 30, + "timestamp": 1684721031176.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "On 21 minute I don't understand where these matrices come from and why we need them. Anyone care to elaborate?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk17.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..7872a0c59c4d744efa3055d4f4645cca20251b92 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 30, + "timestamp": 1684721031176.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "On 21 minute I don't understand where these matrices come from and why we need them. Anyone care to elaborate?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk18.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..7872a0c59c4d744efa3055d4f4645cca20251b92 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 30, + "timestamp": 1684721031176.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "On 21 minute I don't understand where these matrices come from and why we need them. Anyone care to elaborate?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk19.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..7872a0c59c4d744efa3055d4f4645cca20251b92 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 30, + "timestamp": 1684721031176.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "On 21 minute I don't understand where these matrices come from and why we need them. Anyone care to elaborate?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk2.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..7872a0c59c4d744efa3055d4f4645cca20251b92 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 30, + "timestamp": 1684721031176.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "On 21 minute I don't understand where these matrices come from and why we need them. Anyone care to elaborate?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk20.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..7872a0c59c4d744efa3055d4f4645cca20251b92 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 30, + "timestamp": 1684721031176.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "On 21 minute I don't understand where these matrices come from and why we need them. Anyone care to elaborate?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk21.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7872a0c59c4d744efa3055d4f4645cca20251b92 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 30, + "timestamp": 1684721031176.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "On 21 minute I don't understand where these matrices come from and why we need them. Anyone care to elaborate?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk22.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..7872a0c59c4d744efa3055d4f4645cca20251b92 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 30, + "timestamp": 1684721031176.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "On 21 minute I don't understand where these matrices come from and why we need them. Anyone care to elaborate?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk23.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..7872a0c59c4d744efa3055d4f4645cca20251b92 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 30, + "timestamp": 1684721031176.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "On 21 minute I don't understand where these matrices come from and why we need them. Anyone care to elaborate?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk24.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..7872a0c59c4d744efa3055d4f4645cca20251b92 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 30, + "timestamp": 1684721031176.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "On 21 minute I don't understand where these matrices come from and why we need them. Anyone care to elaborate?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk25.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..7872a0c59c4d744efa3055d4f4645cca20251b92 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 30, + "timestamp": 1684721031176.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "On 21 minute I don't understand where these matrices come from and why we need them. Anyone care to elaborate?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk26.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..7872a0c59c4d744efa3055d4f4645cca20251b92 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 30, + "timestamp": 1684721031176.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "On 21 minute I don't understand where these matrices come from and why we need them. Anyone care to elaborate?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk3.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..7872a0c59c4d744efa3055d4f4645cca20251b92 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 30, + "timestamp": 1684721031176.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "On 21 minute I don't understand where these matrices come from and why we need them. Anyone care to elaborate?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk4.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..7872a0c59c4d744efa3055d4f4645cca20251b92 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 30, + "timestamp": 1684721031176.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "On 21 minute I don't understand where these matrices come from and why we need them. Anyone care to elaborate?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk5.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..7872a0c59c4d744efa3055d4f4645cca20251b92 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 30, + "timestamp": 1684721031176.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "On 21 minute I don't understand where these matrices come from and why we need them. Anyone care to elaborate?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk6.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..7872a0c59c4d744efa3055d4f4645cca20251b92 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 30, + "timestamp": 1684721031176.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "On 21 minute I don't understand where these matrices come from and why we need them. Anyone care to elaborate?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk7.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..7872a0c59c4d744efa3055d4f4645cca20251b92 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 30, + "timestamp": 1684721031176.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "On 21 minute I don't understand where these matrices come from and why we need them. Anyone care to elaborate?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..7872a0c59c4d744efa3055d4f4645cca20251b92 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 30, + "timestamp": 1684721031176.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "On 21 minute I don't understand where these matrices come from and why we need them. Anyone care to elaborate?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk9.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..7872a0c59c4d744efa3055d4f4645cca20251b92 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_30_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 30, + "timestamp": 1684721031176.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "On 21 minute I don't understand where these matrices come from and why we need them. Anyone care to elaborate?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk0.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..8139e73c697f828680f0067624a7caeed4f03c31 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 31, + "timestamp": 1684721039024.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "can someone explain how he got 24P's at the end?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk1.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..8139e73c697f828680f0067624a7caeed4f03c31 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 31, + "timestamp": 1684721039024.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "can someone explain how he got 24P's at the end?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk10.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..8139e73c697f828680f0067624a7caeed4f03c31 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 31, + "timestamp": 1684721039024.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "can someone explain how he got 24P's at the end?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk11.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..8139e73c697f828680f0067624a7caeed4f03c31 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 31, + "timestamp": 1684721039024.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "can someone explain how he got 24P's at the end?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk12.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..8139e73c697f828680f0067624a7caeed4f03c31 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 31, + "timestamp": 1684721039024.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "can someone explain how he got 24P's at the end?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk13.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..8139e73c697f828680f0067624a7caeed4f03c31 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 31, + "timestamp": 1684721039024.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "can someone explain how he got 24P's at the end?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk14.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..8139e73c697f828680f0067624a7caeed4f03c31 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 31, + "timestamp": 1684721039024.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "can someone explain how he got 24P's at the end?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk15.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..8139e73c697f828680f0067624a7caeed4f03c31 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 31, + "timestamp": 1684721039024.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "can someone explain how he got 24P's at the end?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk16.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..8139e73c697f828680f0067624a7caeed4f03c31 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 31, + "timestamp": 1684721039024.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "can someone explain how he got 24P's at the end?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk17.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..8139e73c697f828680f0067624a7caeed4f03c31 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 31, + "timestamp": 1684721039024.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "can someone explain how he got 24P's at the end?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk18.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..8139e73c697f828680f0067624a7caeed4f03c31 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 31, + "timestamp": 1684721039024.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "can someone explain how he got 24P's at the end?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk19.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..8139e73c697f828680f0067624a7caeed4f03c31 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 31, + "timestamp": 1684721039024.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "can someone explain how he got 24P's at the end?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk2.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..8139e73c697f828680f0067624a7caeed4f03c31 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 31, + "timestamp": 1684721039024.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "can someone explain how he got 24P's at the end?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk20.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..8139e73c697f828680f0067624a7caeed4f03c31 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 31, + "timestamp": 1684721039024.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "can someone explain how he got 24P's at the end?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk21.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk21.json new file mode 100644 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he got 24P's at the end?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk23.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..8139e73c697f828680f0067624a7caeed4f03c31 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 31, + "timestamp": 1684721039024.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "can someone explain how he got 24P's at the end?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk24.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..8139e73c697f828680f0067624a7caeed4f03c31 --- /dev/null +++ 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got 24P's at the end?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk7.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..8139e73c697f828680f0067624a7caeed4f03c31 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 31, + "timestamp": 1684721039024.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "can someone explain how he got 24P's at the end?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_31_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8139e73c697f828680f0067624a7caeed4f03c31 --- /dev/null +++ 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newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_32_chunk3.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_32_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..ee4481ccc505545071d56dc6d49a3788775edbc5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_32_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 32, + "timestamp": 1684721377675.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "How did he work out at 12:50?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_32_chunk4.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_32_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..ee4481ccc505545071d56dc6d49a3788775edbc5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_32_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": 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No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_32_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_32_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..ee4481ccc505545071d56dc6d49a3788775edbc5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_32_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 32, + "timestamp": 1684721377675.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "How did he work out at 12:50?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_32_chunk9.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_32_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..ee4481ccc505545071d56dc6d49a3788775edbc5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_32_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 32, + "timestamp": 1684721377675.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "How did he work out at 12:50?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk0.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..7db403961dafbaac264c0b3deca91ef895152faf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 34, + "timestamp": 1684721404907.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why the number of operation is equal to n^2 ? Can anyone ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk1.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..7db403961dafbaac264c0b3deca91ef895152faf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 34, + "timestamp": 1684721404907.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why the number of operation is equal to n^2 ? Can anyone ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk10.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..7db403961dafbaac264c0b3deca91ef895152faf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 34, + "timestamp": 1684721404907.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why the number of operation is equal to n^2 ? Can anyone ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk11.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..7db403961dafbaac264c0b3deca91ef895152faf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 34, + "timestamp": 1684721404907.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why the number of operation is equal to n^2 ? Can anyone ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk12.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..7db403961dafbaac264c0b3deca91ef895152faf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 34, + "timestamp": 1684721404907.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why the number of operation is equal to n^2 ? Can anyone ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk13.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..7db403961dafbaac264c0b3deca91ef895152faf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 34, + "timestamp": 1684721404907.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why the number of operation is equal to n^2 ? Can anyone ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk14.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7db403961dafbaac264c0b3deca91ef895152faf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 34, + "timestamp": 1684721404907.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why the number of operation is equal to n^2 ? Can anyone ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk15.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7db403961dafbaac264c0b3deca91ef895152faf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 34, + "timestamp": 1684721404907.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why the number of operation is equal to n^2 ? Can anyone ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk16.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..7db403961dafbaac264c0b3deca91ef895152faf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 34, + "timestamp": 1684721404907.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why the number of operation is equal to n^2 ? Can anyone ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk17.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..7db403961dafbaac264c0b3deca91ef895152faf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 34, + "timestamp": 1684721404907.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why the number of operation is equal to n^2 ? Can anyone ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk18.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..7db403961dafbaac264c0b3deca91ef895152faf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 34, + "timestamp": 1684721404907.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why the number of operation is equal to n^2 ? Can anyone ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk19.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..7db403961dafbaac264c0b3deca91ef895152faf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 34, + "timestamp": 1684721404907.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why the number of operation is equal to n^2 ? Can anyone ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk2.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..7db403961dafbaac264c0b3deca91ef895152faf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 34, + "timestamp": 1684721404907.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why the number of operation is equal to n^2 ? Can anyone ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk20.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..deb3c3eb009598f7f633526bc17af20c30f79ba3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk20.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 34, + "timestamp": 1684721404907.0, + "annotatedSourceSentencesIndices": [ + 17, + 19 + ], + "names": [ + "annotator2" + ], + "text": "Why the number of operation is equal to n^2 ? Can anyone ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk21.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7db403961dafbaac264c0b3deca91ef895152faf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 34, + "timestamp": 1684721404907.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why the number of operation is equal to n^2 ? Can anyone ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk22.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..7db403961dafbaac264c0b3deca91ef895152faf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 34, + "timestamp": 1684721404907.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why the number of operation is equal to n^2 ? Can anyone ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk23.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..7db403961dafbaac264c0b3deca91ef895152faf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 34, + "timestamp": 1684721404907.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why the number of operation is equal to n^2 ? Can anyone ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk24.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..7db403961dafbaac264c0b3deca91ef895152faf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 34, + "timestamp": 1684721404907.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why the number of operation is equal to n^2 ? Can anyone ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk25.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..7db403961dafbaac264c0b3deca91ef895152faf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 34, + "timestamp": 1684721404907.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why the number of operation is equal to n^2 ? Can anyone ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk26.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..7db403961dafbaac264c0b3deca91ef895152faf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 34, + "timestamp": 1684721404907.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why the number of operation is equal to n^2 ? Can anyone ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk3.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..7db403961dafbaac264c0b3deca91ef895152faf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 34, + "timestamp": 1684721404907.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why the number of operation is equal to n^2 ? Can anyone ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk4.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..7db403961dafbaac264c0b3deca91ef895152faf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 34, + "timestamp": 1684721404907.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why the number of operation is equal to n^2 ? Can anyone ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk5.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..7db403961dafbaac264c0b3deca91ef895152faf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 34, + "timestamp": 1684721404907.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why the number of operation is equal to n^2 ? Can anyone ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk6.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..7db403961dafbaac264c0b3deca91ef895152faf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 34, + "timestamp": 1684721404907.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why the number of operation is equal to n^2 ? Can anyone ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk7.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..7db403961dafbaac264c0b3deca91ef895152faf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 34, + "timestamp": 1684721404907.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why the number of operation is equal to n^2 ? Can anyone ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..7db403961dafbaac264c0b3deca91ef895152faf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 34, + "timestamp": 1684721404907.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why the number of operation is equal to n^2 ? Can anyone ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk9.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..7db403961dafbaac264c0b3deca91ef895152faf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_34_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 34, + "timestamp": 1684721404907.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why the number of operation is equal to n^2 ? Can anyone ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk0.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..029ed95058127ae501a03622666ed19826f3d159 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk0.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 36, + "timestamp": 1684722009555.0, + "annotatedSourceSentencesIndices": [ + 10 + ], + "names": [ + "annotator2" + ], + "text": "I don't get the point of A = LU. You need to know U to solve for x in Ax=b. You need E to find U, you can't get U from L. Once you have U, you're basically done. What do you need L for?\n\nI understand the point that L is less costly than E -- but what use is L if you don't know U yet? What am I missing?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk1.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..44d8db21d2bdad222bcb961b440dd860b1d91db0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 36, + "timestamp": 1684722009555.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't get the point of A = LU. You need to know U to solve for x in Ax=b. You need E to find U, you can't get U from L. Once you have U, you're basically done. What do you need L for?\n\nI understand the point that L is less costly than E -- but what use is L if you don't know U yet? What am I missing?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk10.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..44d8db21d2bdad222bcb961b440dd860b1d91db0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 36, + "timestamp": 1684722009555.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't get the point of A = LU. You need to know U to solve for x in Ax=b. You need E to find U, you can't get U from L. Once you have U, you're basically done. What do you need L for?\n\nI understand the point that L is less costly than E -- but what use is L if you don't know U yet? What am I missing?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk11.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..44d8db21d2bdad222bcb961b440dd860b1d91db0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 36, + "timestamp": 1684722009555.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't get the point of A = LU. You need to know U to solve for x in Ax=b. You need E to find U, you can't get U from L. Once you have U, you're basically done. What do you need L for?\n\nI understand the point that L is less costly than E -- but what use is L if you don't know U yet? What am I missing?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk12.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..44d8db21d2bdad222bcb961b440dd860b1d91db0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 36, + "timestamp": 1684722009555.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't get the point of A = LU. You need to know U to solve for x in Ax=b. You need E to find U, you can't get U from L. Once you have U, you're basically done. What do you need L for?\n\nI understand the point that L is less costly than E -- but what use is L if you don't know U yet? What am I missing?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk13.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..3f26899992eedca7d140cd4488697f8e327eef6d --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk13.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 36, + "timestamp": 1684722009555.0, + "annotatedSourceSentencesIndices": [ + 1, + 10 + ], + "names": [ + "annotator2" + ], + "text": "I don't get the point of A = LU. You need to know U to solve for x in Ax=b. You need E to find U, you can't get U from L. Once you have U, you're basically done. What do you need L for?\n\nI understand the point that L is less costly than E -- but what use is L if you don't know U yet? What am I missing?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk14.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..44d8db21d2bdad222bcb961b440dd860b1d91db0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 36, + "timestamp": 1684722009555.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't get the point of A = LU. You need to know U to solve for x in Ax=b. You need E to find U, you can't get U from L. Once you have U, you're basically done. What do you need L for?\n\nI understand the point that L is less costly than E -- but what use is L if you don't know U yet? What am I missing?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk15.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..44d8db21d2bdad222bcb961b440dd860b1d91db0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 36, + "timestamp": 1684722009555.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't get the point of A = LU. You need to know U to solve for x in Ax=b. You need E to find U, you can't get U from L. Once you have U, you're basically done. What do you need L for?\n\nI understand the point that L is less costly than E -- but what use is L if you don't know U yet? What am I missing?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk16.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..44d8db21d2bdad222bcb961b440dd860b1d91db0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 36, + "timestamp": 1684722009555.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't get the point of A = LU. You need to know U to solve for x in Ax=b. You need E to find U, you can't get U from L. Once you have U, you're basically done. What do you need L for?\n\nI understand the point that L is less costly than E -- but what use is L if you don't know U yet? What am I missing?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk17.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..44d8db21d2bdad222bcb961b440dd860b1d91db0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 36, + "timestamp": 1684722009555.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't get the point of A = LU. You need to know U to solve for x in Ax=b. You need E to find U, you can't get U from L. Once you have U, you're basically done. What do you need L for?\n\nI understand the point that L is less costly than E -- but what use is L if you don't know U yet? What am I missing?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk18.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..44d8db21d2bdad222bcb961b440dd860b1d91db0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 36, + "timestamp": 1684722009555.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't get the point of A = LU. You need to know U to solve for x in Ax=b. You need E to find U, you can't get U from L. Once you have U, you're basically done. What do you need L for?\n\nI understand the point that L is less costly than E -- but what use is L if you don't know U yet? What am I missing?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk19.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..44d8db21d2bdad222bcb961b440dd860b1d91db0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 36, + "timestamp": 1684722009555.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't get the point of A = LU. You need to know U to solve for x in Ax=b. You need E to find U, you can't get U from L. Once you have U, you're basically done. What do you need L for?\n\nI understand the point that L is less costly than E -- but what use is L if you don't know U yet? What am I missing?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk2.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..44d8db21d2bdad222bcb961b440dd860b1d91db0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 36, + "timestamp": 1684722009555.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't get the point of A = LU. You need to know U to solve for x in Ax=b. You need E to find U, you can't get U from L. Once you have U, you're basically done. What do you need L for?\n\nI understand the point that L is less costly than E -- but what use is L if you don't know U yet? What am I missing?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk20.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..44d8db21d2bdad222bcb961b440dd860b1d91db0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 36, + "timestamp": 1684722009555.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't get the point of A = LU. You need to know U to solve for x in Ax=b. You need E to find U, you can't get U from L. Once you have U, you're basically done. What do you need L for?\n\nI understand the point that L is less costly than E -- but what use is L if you don't know U yet? What am I missing?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk21.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..44d8db21d2bdad222bcb961b440dd860b1d91db0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 36, + "timestamp": 1684722009555.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't get the point of A = LU. You need to know U to solve for x in Ax=b. You need E to find U, you can't get U from L. Once you have U, you're basically done. What do you need L for?\n\nI understand the point that L is less costly than E -- but what use is L if you don't know U yet? What am I missing?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk22.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..44d8db21d2bdad222bcb961b440dd860b1d91db0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 36, + "timestamp": 1684722009555.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't get the point of A = LU. You need to know U to solve for x in Ax=b. You need E to find U, you can't get U from L. Once you have U, you're basically done. What do you need L for?\n\nI understand the point that L is less costly than E -- but what use is L if you don't know U yet? What am I missing?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk23.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..44d8db21d2bdad222bcb961b440dd860b1d91db0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 36, + "timestamp": 1684722009555.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't get the point of A = LU. You need to know U to solve for x in Ax=b. You need E to find U, you can't get U from L. Once you have U, you're basically done. What do you need L for?\n\nI understand the point that L is less costly than E -- but what use is L if you don't know U yet? What am I missing?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk24.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..44d8db21d2bdad222bcb961b440dd860b1d91db0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 36, + "timestamp": 1684722009555.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't get the point of A = LU. You need to know U to solve for x in Ax=b. You need E to find U, you can't get U from L. Once you have U, you're basically done. What do you need L for?\n\nI understand the point that L is less costly than E -- but what use is L if you don't know U yet? What am I missing?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk25.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..44d8db21d2bdad222bcb961b440dd860b1d91db0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 36, + "timestamp": 1684722009555.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't get the point of A = LU. You need to know U to solve for x in Ax=b. You need E to find U, you can't get U from L. Once you have U, you're basically done. What do you need L for?\n\nI understand the point that L is less costly than E -- but what use is L if you don't know U yet? What am I missing?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk26.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..44d8db21d2bdad222bcb961b440dd860b1d91db0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 36, + "timestamp": 1684722009555.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't get the point of A = LU. You need to know U to solve for x in Ax=b. You need E to find U, you can't get U from L. Once you have U, you're basically done. What do you need L for?\n\nI understand the point that L is less costly than E -- but what use is L if you don't know U yet? What am I missing?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk3.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..85b129d849278b39c754cef7b2965ad5b26da958 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk3.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 36, + "timestamp": 1684722009555.0, + "annotatedSourceSentencesIndices": [ + 9 + ], + "names": [ + "annotator2" + ], + "text": "I don't get the point of A = LU. You need to know U to solve for x in Ax=b. You need E to find U, you can't get U from L. Once you have U, you're basically done. What do you need L for?\n\nI understand the point that L is less costly than E -- but what use is L if you don't know U yet? What am I missing?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk4.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..44d8db21d2bdad222bcb961b440dd860b1d91db0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 36, + "timestamp": 1684722009555.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't get the point of A = LU. You need to know U to solve for x in Ax=b. You need E to find U, you can't get U from L. Once you have U, you're basically done. What do you need L for?\n\nI understand the point that L is less costly than E -- but what use is L if you don't know U yet? What am I missing?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk5.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..6400b4760c91be1ae6807cada70474c8a3abb971 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk5.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 36, + "timestamp": 1684722009555.0, + "annotatedSourceSentencesIndices": [ + 11 + ], + "names": [ + "annotator2" + ], + "text": "I don't get the point of A = LU. You need to know U to solve for x in Ax=b. You need E to find U, you can't get U from L. Once you have U, you're basically done. What do you need L for?\n\nI understand the point that L is less costly than E -- but what use is L if you don't know U yet? What am I missing?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk6.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..44d8db21d2bdad222bcb961b440dd860b1d91db0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 36, + "timestamp": 1684722009555.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't get the point of A = LU. You need to know U to solve for x in Ax=b. You need E to find U, you can't get U from L. Once you have U, you're basically done. What do you need L for?\n\nI understand the point that L is less costly than E -- but what use is L if you don't know U yet? What am I missing?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk7.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..44d8db21d2bdad222bcb961b440dd860b1d91db0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 36, + "timestamp": 1684722009555.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't get the point of A = LU. You need to know U to solve for x in Ax=b. You need E to find U, you can't get U from L. Once you have U, you're basically done. What do you need L for?\n\nI understand the point that L is less costly than E -- but what use is L if you don't know U yet? What am I missing?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..44d8db21d2bdad222bcb961b440dd860b1d91db0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 36, + "timestamp": 1684722009555.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't get the point of A = LU. You need to know U to solve for x in Ax=b. You need E to find U, you can't get U from L. Once you have U, you're basically done. What do you need L for?\n\nI understand the point that L is less costly than E -- but what use is L if you don't know U yet? What am I missing?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk9.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..44d8db21d2bdad222bcb961b440dd860b1d91db0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_36_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 36, + "timestamp": 1684722009555.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't get the point of A = LU. You need to know U to solve for x in Ax=b. You need E to find U, you can't get U from L. Once you have U, you're basically done. What do you need L for?\n\nI understand the point that L is less costly than E -- but what use is L if you don't know U yet? What am I missing?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk0.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..dddff9c53d74f0deb882afcb5c83f67c1d468516 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 39, + "timestamp": 1684722160238.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 26:00 how did he find the inverses of E21 & E32 so easily? is he using some formula? I'm watching the videos in the MITs required order, but looks like I missed somewhere something" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk1.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..dddff9c53d74f0deb882afcb5c83f67c1d468516 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 39, + "timestamp": 1684722160238.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 26:00 how did he find the inverses of E21 & E32 so easily? is he using some formula? I'm watching the videos in the MITs required order, but looks like I missed somewhere something" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk10.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..dddff9c53d74f0deb882afcb5c83f67c1d468516 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 39, + "timestamp": 1684722160238.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 26:00 how did he find the inverses of E21 & E32 so easily? is he using some formula? I'm watching the videos in the MITs required order, but looks like I missed somewhere something" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk11.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..f11351d23f9bbed08db36ec702103febb0850988 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk11.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 39, + "timestamp": 1684722160238.0, + "annotatedSourceSentencesIndices": [ + 16 + ], + "names": [ + "annotator2" + ], + "text": "At 26:00 how did he find the inverses of E21 & E32 so easily? is he using some formula? I'm watching the videos in the MITs required order, but looks like I missed somewhere something" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk12.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..7b6e3ef6f0635e7c7205683b429a510fab6e8340 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk12.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 39, + "timestamp": 1684722160238.0, + "annotatedSourceSentencesIndices": [ + 0 + ], + "names": [ + "annotator2" + ], + "text": "At 26:00 how did he find the inverses of E21 & E32 so easily? is he using some formula? I'm watching the videos in the MITs required order, but looks like I missed somewhere something" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk13.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..dddff9c53d74f0deb882afcb5c83f67c1d468516 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 39, + "timestamp": 1684722160238.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 26:00 how did he find the inverses of E21 & E32 so easily? is he using some formula? I'm watching the videos in the MITs required order, but looks like I missed somewhere something" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk14.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..dddff9c53d74f0deb882afcb5c83f67c1d468516 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 39, + "timestamp": 1684722160238.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 26:00 how did he find the inverses of E21 & E32 so easily? is he using some formula? I'm watching the videos in the MITs required order, but looks like I missed somewhere something" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk15.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..dddff9c53d74f0deb882afcb5c83f67c1d468516 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 39, + "timestamp": 1684722160238.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 26:00 how did he find the inverses of E21 & E32 so easily? is he using some formula? I'm watching the videos in the MITs required order, but looks like I missed somewhere something" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk16.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..dddff9c53d74f0deb882afcb5c83f67c1d468516 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 39, + "timestamp": 1684722160238.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 26:00 how did he find the inverses of E21 & E32 so easily? is he using some formula? I'm watching the videos in the MITs required order, but looks like I missed somewhere something" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk17.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..dddff9c53d74f0deb882afcb5c83f67c1d468516 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 39, + "timestamp": 1684722160238.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 26:00 how did he find the inverses of E21 & E32 so easily? is he using some formula? I'm watching the videos in the MITs required order, but looks like I missed somewhere something" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk18.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..dddff9c53d74f0deb882afcb5c83f67c1d468516 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 39, + "timestamp": 1684722160238.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 26:00 how did he find the inverses of E21 & E32 so easily? is he using some formula? I'm watching the videos in the MITs required order, but looks like I missed somewhere something" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk19.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..dddff9c53d74f0deb882afcb5c83f67c1d468516 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 39, + "timestamp": 1684722160238.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 26:00 how did he find the inverses of E21 & E32 so easily? is he using some formula? I'm watching the videos in the MITs required order, but looks like I missed somewhere something" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk2.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..dddff9c53d74f0deb882afcb5c83f67c1d468516 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 39, + "timestamp": 1684722160238.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 26:00 how did he find the inverses of E21 & E32 so easily? is he using some formula? I'm watching the videos in the MITs required order, but looks like I missed somewhere something" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk20.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..dddff9c53d74f0deb882afcb5c83f67c1d468516 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 39, + "timestamp": 1684722160238.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 26:00 how did he find the inverses of E21 & E32 so easily? is he using some formula? I'm watching the videos in the MITs required order, but looks like I missed somewhere something" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk21.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..dddff9c53d74f0deb882afcb5c83f67c1d468516 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 39, + "timestamp": 1684722160238.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 26:00 how did he find the inverses of E21 & E32 so easily? is he using some formula? I'm watching the videos in the MITs required order, but looks like I missed somewhere something" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk22.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..dddff9c53d74f0deb882afcb5c83f67c1d468516 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 39, + "timestamp": 1684722160238.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 26:00 how did he find the inverses of E21 & E32 so easily? is he using some formula? I'm watching the videos in the MITs required order, but looks like I missed somewhere something" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk23.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..dddff9c53d74f0deb882afcb5c83f67c1d468516 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 39, + "timestamp": 1684722160238.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 26:00 how did he find the inverses of E21 & E32 so easily? is he using some formula? I'm watching the videos in the MITs required order, but looks like I missed somewhere something" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk24.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..dddff9c53d74f0deb882afcb5c83f67c1d468516 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 39, + "timestamp": 1684722160238.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 26:00 how did he find the inverses of E21 & E32 so easily? is he using some formula? I'm watching the videos in the MITs required order, but looks like I missed somewhere something" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk25.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..dddff9c53d74f0deb882afcb5c83f67c1d468516 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 39, + "timestamp": 1684722160238.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 26:00 how did he find the inverses of E21 & E32 so easily? is he using some formula? I'm watching the videos in the MITs required order, but looks like I missed somewhere something" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk26.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..dddff9c53d74f0deb882afcb5c83f67c1d468516 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 39, + "timestamp": 1684722160238.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 26:00 how did he find the inverses of E21 & E32 so easily? is he using some formula? I'm watching the videos in the MITs required order, but looks like I missed somewhere something" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk3.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..dddff9c53d74f0deb882afcb5c83f67c1d468516 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 39, + "timestamp": 1684722160238.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 26:00 how did he find the inverses of E21 & E32 so easily? is he using some formula? I'm watching the videos in the MITs required order, but looks like I missed somewhere something" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk4.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..dddff9c53d74f0deb882afcb5c83f67c1d468516 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 39, + "timestamp": 1684722160238.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 26:00 how did he find the inverses of E21 & E32 so easily? is he using some formula? I'm watching the videos in the MITs required order, but looks like I missed somewhere something" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk5.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..dddff9c53d74f0deb882afcb5c83f67c1d468516 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 39, + "timestamp": 1684722160238.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 26:00 how did he find the inverses of E21 & E32 so easily? is he using some formula? I'm watching the videos in the MITs required order, but looks like I missed somewhere something" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk6.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..dddff9c53d74f0deb882afcb5c83f67c1d468516 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 39, + "timestamp": 1684722160238.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 26:00 how did he find the inverses of E21 & E32 so easily? is he using some formula? I'm watching the videos in the MITs required order, but looks like I missed somewhere something" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk7.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..dddff9c53d74f0deb882afcb5c83f67c1d468516 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 39, + "timestamp": 1684722160238.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 26:00 how did he find the inverses of E21 & E32 so easily? is he using some formula? I'm watching the videos in the MITs required order, but looks like I missed somewhere something" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..dddff9c53d74f0deb882afcb5c83f67c1d468516 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 39, + "timestamp": 1684722160238.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 26:00 how did he find the inverses of E21 & E32 so easily? is he using some formula? I'm watching the videos in the MITs required order, but looks like I missed somewhere something" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk9.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..dddff9c53d74f0deb882afcb5c83f67c1d468516 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_39_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 39, + "timestamp": 1684722160238.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "At 26:00 how did he find the inverses of E21 & E32 so easily? is he using some formula? I'm watching the videos in the MITs required order, but looks like I missed somewhere something" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk0.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6a1b0d4d572459b1150240c6303b3983088c2e5d --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk0.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 3, + "timestamp": 1684708441242.0, + "annotatedSourceSentencesIndices": [ + 10 + ], + "names": [ + "annotator2" + ], + "text": "In A=LU part, what do L and U stand for? (Like \"E\" for elimination )" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk1.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..98a291dccc256d8e997202017ded96160aa10ad8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 3, + "timestamp": 1684708441242.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In A=LU part, what do L and U stand for? (Like \"E\" for elimination )" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk10.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..98a291dccc256d8e997202017ded96160aa10ad8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 3, + "timestamp": 1684708441242.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In A=LU part, what do L and U stand for? (Like \"E\" for elimination )" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk11.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..98a291dccc256d8e997202017ded96160aa10ad8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 3, + "timestamp": 1684708441242.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In A=LU part, what do L and U stand for? (Like \"E\" for elimination )" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk12.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..98a291dccc256d8e997202017ded96160aa10ad8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 3, + "timestamp": 1684708441242.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In A=LU part, what do L and U stand for? (Like \"E\" for elimination )" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk13.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..98a291dccc256d8e997202017ded96160aa10ad8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 3, + "timestamp": 1684708441242.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In A=LU part, what do L and U stand for? (Like \"E\" for elimination )" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk14.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..98a291dccc256d8e997202017ded96160aa10ad8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 3, + "timestamp": 1684708441242.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In A=LU part, what do L and U stand for? (Like \"E\" for elimination )" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk15.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..98a291dccc256d8e997202017ded96160aa10ad8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 3, + "timestamp": 1684708441242.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In A=LU part, what do L and U stand for? (Like \"E\" for elimination )" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk16.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..98a291dccc256d8e997202017ded96160aa10ad8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 3, + "timestamp": 1684708441242.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In A=LU part, what do L and U stand for? (Like \"E\" for elimination )" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk17.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..98a291dccc256d8e997202017ded96160aa10ad8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 3, + "timestamp": 1684708441242.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In A=LU part, what do L and U stand for? (Like \"E\" for elimination )" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk18.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..98a291dccc256d8e997202017ded96160aa10ad8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 3, + "timestamp": 1684708441242.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In A=LU part, what do L and U stand for? (Like \"E\" for elimination )" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk19.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..98a291dccc256d8e997202017ded96160aa10ad8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 3, + "timestamp": 1684708441242.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In A=LU part, what do L and U stand for? (Like \"E\" for elimination )" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk2.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..98a291dccc256d8e997202017ded96160aa10ad8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 3, + "timestamp": 1684708441242.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In A=LU part, what do L and U stand for? (Like \"E\" for elimination )" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk20.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..98a291dccc256d8e997202017ded96160aa10ad8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 3, + "timestamp": 1684708441242.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In A=LU part, what do L and U stand for? (Like \"E\" for elimination )" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk21.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..98a291dccc256d8e997202017ded96160aa10ad8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 3, + "timestamp": 1684708441242.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In A=LU part, what do L and U stand for? (Like \"E\" for elimination )" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk22.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..98a291dccc256d8e997202017ded96160aa10ad8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 3, + "timestamp": 1684708441242.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In A=LU part, what do L and U stand for? (Like \"E\" for elimination )" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk23.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..98a291dccc256d8e997202017ded96160aa10ad8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 3, + "timestamp": 1684708441242.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In A=LU part, what do L and U stand for? (Like \"E\" for elimination )" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk24.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..98a291dccc256d8e997202017ded96160aa10ad8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 3, + "timestamp": 1684708441242.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In A=LU part, what do L and U stand for? (Like \"E\" for elimination )" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk25.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..98a291dccc256d8e997202017ded96160aa10ad8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 3, + "timestamp": 1684708441242.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In A=LU part, what do L and U stand for? (Like \"E\" for elimination )" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk26.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..98a291dccc256d8e997202017ded96160aa10ad8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 3, + "timestamp": 1684708441242.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In A=LU part, what do L and U stand for? (Like \"E\" for elimination )" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk3.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..98a291dccc256d8e997202017ded96160aa10ad8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 3, + "timestamp": 1684708441242.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In A=LU part, what do L and U stand for? (Like \"E\" for elimination )" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk4.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..98a291dccc256d8e997202017ded96160aa10ad8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 3, + "timestamp": 1684708441242.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In A=LU part, what do L and U stand for? (Like \"E\" for elimination )" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk5.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..98a291dccc256d8e997202017ded96160aa10ad8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 3, + "timestamp": 1684708441242.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In A=LU part, what do L and U stand for? (Like \"E\" for elimination )" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk6.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..98a291dccc256d8e997202017ded96160aa10ad8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 3, + "timestamp": 1684708441242.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In A=LU part, what do L and U stand for? (Like \"E\" for elimination )" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk7.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..98a291dccc256d8e997202017ded96160aa10ad8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 3, + "timestamp": 1684708441242.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In A=LU part, what do L and U stand for? (Like \"E\" for elimination )" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..98a291dccc256d8e997202017ded96160aa10ad8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 3, + "timestamp": 1684708441242.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In A=LU part, what do L and U stand for? (Like \"E\" for elimination )" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk9.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..98a291dccc256d8e997202017ded96160aa10ad8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_3_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 3, + "timestamp": 1684708441242.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "In A=LU part, what do L and U stand for? (Like \"E\" for elimination )" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk0.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..064d92c0280d610986d720f4b503ce12d56d840d --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 40, + "timestamp": 1684722350405.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why does a 4x4 matrix have 24 Permutationmatrices when a 3x3 Matrix has 6? I don't get how they calculated it so quickly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk1.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..064d92c0280d610986d720f4b503ce12d56d840d --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 40, + "timestamp": 1684722350405.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why does a 4x4 matrix have 24 Permutationmatrices when a 3x3 Matrix has 6? I don't get how they calculated it so quickly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk10.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..064d92c0280d610986d720f4b503ce12d56d840d --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 40, + "timestamp": 1684722350405.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why does a 4x4 matrix have 24 Permutationmatrices when a 3x3 Matrix has 6? I don't get how they calculated it so quickly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk11.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..064d92c0280d610986d720f4b503ce12d56d840d --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 40, + "timestamp": 1684722350405.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why does a 4x4 matrix have 24 Permutationmatrices when a 3x3 Matrix has 6? I don't get how they calculated it so quickly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk12.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..064d92c0280d610986d720f4b503ce12d56d840d --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 40, + "timestamp": 1684722350405.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why does a 4x4 matrix have 24 Permutationmatrices when a 3x3 Matrix has 6? I don't get how they calculated it so quickly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk13.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..064d92c0280d610986d720f4b503ce12d56d840d --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 40, + "timestamp": 1684722350405.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why does a 4x4 matrix have 24 Permutationmatrices when a 3x3 Matrix has 6? I don't get how they calculated it so quickly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk14.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..064d92c0280d610986d720f4b503ce12d56d840d --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 40, + "timestamp": 1684722350405.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why does a 4x4 matrix have 24 Permutationmatrices when a 3x3 Matrix has 6? I don't get how they calculated it so quickly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk15.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..064d92c0280d610986d720f4b503ce12d56d840d --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 40, + "timestamp": 1684722350405.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why does a 4x4 matrix have 24 Permutationmatrices when a 3x3 Matrix has 6? I don't get how they calculated it so quickly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk16.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..064d92c0280d610986d720f4b503ce12d56d840d --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 40, + "timestamp": 1684722350405.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why does a 4x4 matrix have 24 Permutationmatrices when a 3x3 Matrix has 6? I don't get how they calculated it so quickly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk17.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..064d92c0280d610986d720f4b503ce12d56d840d --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 40, + "timestamp": 1684722350405.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why does a 4x4 matrix have 24 Permutationmatrices when a 3x3 Matrix has 6? I don't get how they calculated it so quickly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk18.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..064d92c0280d610986d720f4b503ce12d56d840d --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 40, + "timestamp": 1684722350405.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why does a 4x4 matrix have 24 Permutationmatrices when a 3x3 Matrix has 6? I don't get how they calculated it so quickly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk19.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..064d92c0280d610986d720f4b503ce12d56d840d --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 40, + "timestamp": 1684722350405.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why does a 4x4 matrix have 24 Permutationmatrices when a 3x3 Matrix has 6? I don't get how they calculated it so quickly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk2.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..064d92c0280d610986d720f4b503ce12d56d840d --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 40, + "timestamp": 1684722350405.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why does a 4x4 matrix have 24 Permutationmatrices when a 3x3 Matrix has 6? I don't get how they calculated it so quickly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk20.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..064d92c0280d610986d720f4b503ce12d56d840d --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 40, + "timestamp": 1684722350405.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why does a 4x4 matrix have 24 Permutationmatrices when a 3x3 Matrix has 6? I don't get how they calculated it so quickly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk21.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..064d92c0280d610986d720f4b503ce12d56d840d --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 40, + "timestamp": 1684722350405.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why does a 4x4 matrix have 24 Permutationmatrices when a 3x3 Matrix has 6? I don't get how they calculated it so quickly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk22.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..064d92c0280d610986d720f4b503ce12d56d840d --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 40, + "timestamp": 1684722350405.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why does a 4x4 matrix have 24 Permutationmatrices when a 3x3 Matrix has 6? I don't get how they calculated it so quickly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk23.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..064d92c0280d610986d720f4b503ce12d56d840d --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 40, + "timestamp": 1684722350405.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why does a 4x4 matrix have 24 Permutationmatrices when a 3x3 Matrix has 6? I don't get how they calculated it so quickly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk24.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..5b077f0af1219dec2e5e8f3075b6a395722283b3 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk24.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 40, + "timestamp": 1684722350405.0, + "annotatedSourceSentencesIndices": [ + 11 + ], + "names": [ + "annotator2" + ], + "text": "Why does a 4x4 matrix have 24 Permutationmatrices when a 3x3 Matrix has 6? I don't get how they calculated it so quickly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk25.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..1b501a059cf3e2242eba13c07eb77b2935b23a9a --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk25.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 40, + "timestamp": 1684722350405.0, + "annotatedSourceSentencesIndices": [ + 16 + ], + "names": [ + "annotator2" + ], + "text": "Why does a 4x4 matrix have 24 Permutationmatrices when a 3x3 Matrix has 6? I don't get how they calculated it so quickly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk26.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..064d92c0280d610986d720f4b503ce12d56d840d --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 40, + "timestamp": 1684722350405.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why does a 4x4 matrix have 24 Permutationmatrices when a 3x3 Matrix has 6? I don't get how they calculated it so quickly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk3.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..064d92c0280d610986d720f4b503ce12d56d840d --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 40, + "timestamp": 1684722350405.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why does a 4x4 matrix have 24 Permutationmatrices when a 3x3 Matrix has 6? I don't get how they calculated it so quickly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk4.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..064d92c0280d610986d720f4b503ce12d56d840d --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 40, + "timestamp": 1684722350405.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why does a 4x4 matrix have 24 Permutationmatrices when a 3x3 Matrix has 6? I don't get how they calculated it so quickly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk5.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..064d92c0280d610986d720f4b503ce12d56d840d --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 40, + "timestamp": 1684722350405.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why does a 4x4 matrix have 24 Permutationmatrices when a 3x3 Matrix has 6? I don't get how they calculated it so quickly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk6.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..064d92c0280d610986d720f4b503ce12d56d840d --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 40, + "timestamp": 1684722350405.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why does a 4x4 matrix have 24 Permutationmatrices when a 3x3 Matrix has 6? I don't get how they calculated it so quickly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk7.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..064d92c0280d610986d720f4b503ce12d56d840d --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 40, + "timestamp": 1684722350405.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why does a 4x4 matrix have 24 Permutationmatrices when a 3x3 Matrix has 6? I don't get how they calculated it so quickly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..064d92c0280d610986d720f4b503ce12d56d840d --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 40, + "timestamp": 1684722350405.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why does a 4x4 matrix have 24 Permutationmatrices when a 3x3 Matrix has 6? I don't get how they calculated it so quickly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk9.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..064d92c0280d610986d720f4b503ce12d56d840d --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_40_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 40, + "timestamp": 1684722350405.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Why does a 4x4 matrix have 24 Permutationmatrices when a 3x3 Matrix has 6? I don't get how they calculated it so quickly." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk0.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..005da9714ea2bf0b61161595f1d3d03bd08f236c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 42, + "timestamp": 1684722535272.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "how do we know that E-1 will be a lower triangular matrix?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk1.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..005da9714ea2bf0b61161595f1d3d03bd08f236c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 42, + "timestamp": 1684722535272.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "how do we know that E-1 will be a lower triangular matrix?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk10.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..005da9714ea2bf0b61161595f1d3d03bd08f236c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 42, + "timestamp": 1684722535272.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "how do we know that E-1 will be a lower triangular matrix?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk11.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..005da9714ea2bf0b61161595f1d3d03bd08f236c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 42, + "timestamp": 1684722535272.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "how do we know that E-1 will be a lower triangular matrix?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk12.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..005da9714ea2bf0b61161595f1d3d03bd08f236c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 42, + "timestamp": 1684722535272.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "how do we know that E-1 will be a lower triangular matrix?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk13.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..005da9714ea2bf0b61161595f1d3d03bd08f236c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 42, + "timestamp": 1684722535272.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "how do we know that E-1 will be a lower triangular matrix?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk14.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..005da9714ea2bf0b61161595f1d3d03bd08f236c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 42, + "timestamp": 1684722535272.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "how do we know that E-1 will be a lower triangular matrix?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk15.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..005da9714ea2bf0b61161595f1d3d03bd08f236c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 42, + "timestamp": 1684722535272.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "how do we know that E-1 will be a lower triangular matrix?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk16.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..005da9714ea2bf0b61161595f1d3d03bd08f236c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 42, + "timestamp": 1684722535272.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "how do we know that E-1 will be a lower triangular matrix?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk17.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk17.json new file mode 100644 index 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E-1 will be a lower triangular matrix?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk19.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..005da9714ea2bf0b61161595f1d3d03bd08f236c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 42, + "timestamp": 1684722535272.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "how do we know that E-1 will be a lower triangular matrix?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk2.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..005da9714ea2bf0b61161595f1d3d03bd08f236c --- /dev/null +++ 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a/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk21.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..005da9714ea2bf0b61161595f1d3d03bd08f236c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 42, + "timestamp": 1684722535272.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "how do we know that E-1 will be a lower triangular matrix?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk22.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..005da9714ea2bf0b61161595f1d3d03bd08f236c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 42, + "timestamp": 1684722535272.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "how do we know that E-1 will be a lower triangular matrix?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk23.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..005da9714ea2bf0b61161595f1d3d03bd08f236c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 42, + "timestamp": 1684722535272.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "how do we know that E-1 will be a lower triangular matrix?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk24.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..005da9714ea2bf0b61161595f1d3d03bd08f236c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 42, + "timestamp": 1684722535272.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "how do we know that E-1 will be a lower triangular matrix?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk25.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..005da9714ea2bf0b61161595f1d3d03bd08f236c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 42, + "timestamp": 1684722535272.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "how do we know that E-1 will be a lower triangular matrix?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk26.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..005da9714ea2bf0b61161595f1d3d03bd08f236c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 42, + "timestamp": 1684722535272.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "how do we know that E-1 will be a lower triangular matrix?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk3.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk3.json new file mode 100644 index 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will be a lower triangular matrix?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk5.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..005da9714ea2bf0b61161595f1d3d03bd08f236c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 42, + "timestamp": 1684722535272.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "how do we know that E-1 will be a lower triangular matrix?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk6.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..005da9714ea2bf0b61161595f1d3d03bd08f236c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 42, + "timestamp": 1684722535272.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "how do we know that E-1 will be a lower triangular matrix?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk7.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..005da9714ea2bf0b61161595f1d3d03bd08f236c --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 42, + "timestamp": 1684722535272.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "how do we know that E-1 will be a lower triangular matrix?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..ff25fe0ad7fb2cd6eed80fc0bd6cd45bf551842d --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk8.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 42, + "timestamp": 1684722535272.0, + "annotatedSourceSentencesIndices": [ + 10, + 11 + ], + "names": [ + "annotator2" + ], + "text": "how do we know that E-1 will be a lower triangular matrix?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk9.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..d3b1224679ce0f47653b0b56d17627ef60bf59c8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_42_chunk9.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 42, + "timestamp": 1684722535272.0, + "annotatedSourceSentencesIndices": [ + 5 + ], + "names": [ + "annotator2" + ], + "text": "how do we know that E-1 will be a lower triangular matrix?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_43_chunk0.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_43_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..9fa243a167850275b20b42ea980a008933c1bea5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_43_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 43, + "timestamp": 1684722576236.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "can someone pls explain how n,n^2 , n^3....n! come ? ?? at 29:46 ." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_43_chunk1.json 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pls explain how n,n^2 , n^3....n! come ? ?? at 29:46 ." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_43_chunk14.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_43_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..9fa243a167850275b20b42ea980a008933c1bea5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_43_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 43, + "timestamp": 1684722576236.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "can someone pls explain how n,n^2 , n^3....n! come ? ?? at 29:46 ." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_43_chunk15.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_43_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..f64156007a7f404294263b647027d00b017e5cd2 --- /dev/null +++ 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pls explain how n,n^2 , n^3....n! come ? ?? at 29:46 ." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_43_chunk24.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_43_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9fa243a167850275b20b42ea980a008933c1bea5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_43_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 43, + "timestamp": 1684722576236.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "can someone pls explain how n,n^2 , n^3....n! come ? ?? at 29:46 ." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_43_chunk25.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_43_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..9fa243a167850275b20b42ea980a008933c1bea5 --- /dev/null +++ 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"annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "can someone pls explain how n,n^2 , n^3....n! come ? ?? at 29:46 ." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_43_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_43_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..9fa243a167850275b20b42ea980a008933c1bea5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_43_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 43, + "timestamp": 1684722576236.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "can someone pls explain how n,n^2 , n^3....n! come ? ?? at 29:46 ." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_43_chunk9.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_43_chunk9.json new file mode 100644 index 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of matrix multiplication is of the order O(n^3), that's fine. But in every step in the we are changing just one row...therefore, shouldn't the cost be n+ (n-1)+ (n-2) + ........+1, ie O(n^2), if we have a suitable algorithm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk1.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..1c8031f5331732c86162c0ea15252b3df1263cfc --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 44, + "timestamp": 1684722640153.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "The complexity of matrix multiplication is of the order O(n^3), that's fine. But in every step in the we are changing just one row...therefore, shouldn't the cost be n+ (n-1)+ (n-2) + ........+1, ie O(n^2), if we have a suitable algorithm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk10.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..1c8031f5331732c86162c0ea15252b3df1263cfc --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 44, + "timestamp": 1684722640153.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "The complexity of matrix multiplication is of the order O(n^3), that's fine. But in every step in the we are changing just one row...therefore, shouldn't the cost be n+ (n-1)+ (n-2) + ........+1, ie O(n^2), if we have a suitable algorithm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk11.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..1c8031f5331732c86162c0ea15252b3df1263cfc --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 44, + "timestamp": 1684722640153.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "The complexity of matrix multiplication is of the order O(n^3), that's fine. But in every step in the we are changing just one row...therefore, shouldn't the cost be n+ (n-1)+ (n-2) + ........+1, ie O(n^2), if we have a suitable algorithm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk12.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..1c8031f5331732c86162c0ea15252b3df1263cfc --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 44, + "timestamp": 1684722640153.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "The complexity of matrix multiplication is of the order O(n^3), that's fine. But in every step in the we are changing just one row...therefore, shouldn't the cost be n+ (n-1)+ (n-2) + ........+1, ie O(n^2), if we have a suitable algorithm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk13.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1c8031f5331732c86162c0ea15252b3df1263cfc --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 44, + "timestamp": 1684722640153.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "The complexity of matrix multiplication is of the order O(n^3), that's fine. But in every step in the we are changing just one row...therefore, shouldn't the cost be n+ (n-1)+ (n-2) + ........+1, ie O(n^2), if we have a suitable algorithm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk14.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..1c8031f5331732c86162c0ea15252b3df1263cfc --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 44, + "timestamp": 1684722640153.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "The complexity of matrix multiplication is of the order O(n^3), that's fine. But in every step in the we are changing just one row...therefore, shouldn't the cost be n+ (n-1)+ (n-2) + ........+1, ie O(n^2), if we have a suitable algorithm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk15.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..1c8031f5331732c86162c0ea15252b3df1263cfc --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 44, + "timestamp": 1684722640153.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "The complexity of matrix multiplication is of the order O(n^3), that's fine. But in every step in the we are changing just one row...therefore, shouldn't the cost be n+ (n-1)+ (n-2) + ........+1, ie O(n^2), if we have a suitable algorithm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk16.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..1c8031f5331732c86162c0ea15252b3df1263cfc --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 44, + "timestamp": 1684722640153.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "The complexity of matrix multiplication is of the order O(n^3), that's fine. But in every step in the we are changing just one row...therefore, shouldn't the cost be n+ (n-1)+ (n-2) + ........+1, ie O(n^2), if we have a suitable algorithm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk17.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..1c8031f5331732c86162c0ea15252b3df1263cfc --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 44, + "timestamp": 1684722640153.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "The complexity of matrix multiplication is of the order O(n^3), that's fine. But in every step in the we are changing just one row...therefore, shouldn't the cost be n+ (n-1)+ (n-2) + ........+1, ie O(n^2), if we have a suitable algorithm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk18.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..1c8031f5331732c86162c0ea15252b3df1263cfc --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 44, + "timestamp": 1684722640153.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "The complexity of matrix multiplication is of the order O(n^3), that's fine. But in every step in the we are changing just one row...therefore, shouldn't the cost be n+ (n-1)+ (n-2) + ........+1, ie O(n^2), if we have a suitable algorithm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk19.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..72baffff11ff2ae5f97c1a2a43030196552a85b6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk19.json @@ -0,0 +1,16 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 44, + "timestamp": 1684722640153.0, + "annotatedSourceSentencesIndices": [ + 4, + 6, + 9 + ], + "names": [ + "annotator2" + ], + "text": "The complexity of matrix multiplication is of the order O(n^3), that's fine. But in every step in the we are changing just one row...therefore, shouldn't the cost be n+ (n-1)+ (n-2) + ........+1, ie O(n^2), if we have a suitable algorithm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk2.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1c8031f5331732c86162c0ea15252b3df1263cfc --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 44, + "timestamp": 1684722640153.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "The complexity of matrix multiplication is of the order O(n^3), that's fine. But in every step in the we are changing just one row...therefore, shouldn't the cost be n+ (n-1)+ (n-2) + ........+1, ie O(n^2), if we have a suitable algorithm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk20.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..1c8031f5331732c86162c0ea15252b3df1263cfc --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 44, + "timestamp": 1684722640153.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "The complexity of matrix multiplication is of the order O(n^3), that's fine. But in every step in the we are changing just one row...therefore, shouldn't the cost be n+ (n-1)+ (n-2) + ........+1, ie O(n^2), if we have a suitable algorithm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk21.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..1c8031f5331732c86162c0ea15252b3df1263cfc --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 44, + "timestamp": 1684722640153.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "The complexity of matrix multiplication is of the order O(n^3), that's fine. But in every step in the we are changing just one row...therefore, shouldn't the cost be n+ (n-1)+ (n-2) + ........+1, ie O(n^2), if we have a suitable algorithm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk22.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..1c8031f5331732c86162c0ea15252b3df1263cfc --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 44, + "timestamp": 1684722640153.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "The complexity of matrix multiplication is of the order O(n^3), that's fine. But in every step in the we are changing just one row...therefore, shouldn't the cost be n+ (n-1)+ (n-2) + ........+1, ie O(n^2), if we have a suitable algorithm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk23.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..1c8031f5331732c86162c0ea15252b3df1263cfc --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 44, + "timestamp": 1684722640153.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "The complexity of matrix multiplication is of the order O(n^3), that's fine. But in every step in the we are changing just one row...therefore, shouldn't the cost be n+ (n-1)+ (n-2) + ........+1, ie O(n^2), if we have a suitable algorithm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk24.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..1c8031f5331732c86162c0ea15252b3df1263cfc --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 44, + "timestamp": 1684722640153.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "The complexity of matrix multiplication is of the order O(n^3), that's fine. But in every step in the we are changing just one row...therefore, shouldn't the cost be n+ (n-1)+ (n-2) + ........+1, ie O(n^2), if we have a suitable algorithm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk25.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..1c8031f5331732c86162c0ea15252b3df1263cfc --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 44, + "timestamp": 1684722640153.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "The complexity of matrix multiplication is of the order O(n^3), that's fine. But in every step in the we are changing just one row...therefore, shouldn't the cost be n+ (n-1)+ (n-2) + ........+1, ie O(n^2), if we have a suitable algorithm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk26.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..1c8031f5331732c86162c0ea15252b3df1263cfc --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 44, + "timestamp": 1684722640153.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "The complexity of matrix multiplication is of the order O(n^3), that's fine. But in every step in the we are changing just one row...therefore, shouldn't the cost be n+ (n-1)+ (n-2) + ........+1, ie O(n^2), if we have a suitable algorithm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk3.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1c8031f5331732c86162c0ea15252b3df1263cfc --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 44, + "timestamp": 1684722640153.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "The complexity of matrix multiplication is of the order O(n^3), that's fine. But in every step in the we are changing just one row...therefore, shouldn't the cost be n+ (n-1)+ (n-2) + ........+1, ie O(n^2), if we have a suitable algorithm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk4.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..1c8031f5331732c86162c0ea15252b3df1263cfc --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 44, + "timestamp": 1684722640153.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "The complexity of matrix multiplication is of the order O(n^3), that's fine. But in every step in the we are changing just one row...therefore, shouldn't the cost be n+ (n-1)+ (n-2) + ........+1, ie O(n^2), if we have a suitable algorithm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk5.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..1c8031f5331732c86162c0ea15252b3df1263cfc --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 44, + "timestamp": 1684722640153.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "The complexity of matrix multiplication is of the order O(n^3), that's fine. But in every step in the we are changing just one row...therefore, shouldn't the cost be n+ (n-1)+ (n-2) + ........+1, ie O(n^2), if we have a suitable algorithm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk6.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..1c8031f5331732c86162c0ea15252b3df1263cfc --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 44, + "timestamp": 1684722640153.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "The complexity of matrix multiplication is of the order O(n^3), that's fine. But in every step in the we are changing just one row...therefore, shouldn't the cost be n+ (n-1)+ (n-2) + ........+1, ie O(n^2), if we have a suitable algorithm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk7.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..1c8031f5331732c86162c0ea15252b3df1263cfc --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 44, + "timestamp": 1684722640153.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "The complexity of matrix multiplication is of the order O(n^3), that's fine. But in every step in the we are changing just one row...therefore, shouldn't the cost be n+ (n-1)+ (n-2) + ........+1, ie O(n^2), if we have a suitable algorithm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..1c8031f5331732c86162c0ea15252b3df1263cfc --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 44, + "timestamp": 1684722640153.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "The complexity of matrix multiplication is of the order O(n^3), that's fine. But in every step in the we are changing just one row...therefore, shouldn't the cost be n+ (n-1)+ (n-2) + ........+1, ie O(n^2), if we have a suitable algorithm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk9.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..1c8031f5331732c86162c0ea15252b3df1263cfc --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_44_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 44, + "timestamp": 1684722640153.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "The complexity of matrix multiplication is of the order O(n^3), that's fine. But in every step in the we are changing just one row...therefore, shouldn't the cost be n+ (n-1)+ (n-2) + ........+1, ie O(n^2), if we have a suitable algorithm?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk0.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..0c36744e58fabb6a3245dc9d958d1f27684ed520 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 4, + "timestamp": 1684708849693.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "at 32:35 => Should not the first cost be 99*2 instead of 100^2 because there are 99 rows below first one. For pivoting each row below, you need to multiply the first row by some constant then subtract from the row you are pivoting. So, essentially are we not ending up having 2 operations per row for those 99 rows, hence, 99*2 instead of 100^2 ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk1.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..0c36744e58fabb6a3245dc9d958d1f27684ed520 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 4, + "timestamp": 1684708849693.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "at 32:35 => Should not the first cost be 99*2 instead of 100^2 because there are 99 rows below first one. For pivoting each row below, you need to multiply the first row by some constant then subtract from the row you are pivoting. So, essentially are we not ending up having 2 operations per row for those 99 rows, hence, 99*2 instead of 100^2 ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk10.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..0c36744e58fabb6a3245dc9d958d1f27684ed520 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 4, + "timestamp": 1684708849693.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "at 32:35 => Should not the first cost be 99*2 instead of 100^2 because there are 99 rows below first one. For pivoting each row below, you need to multiply the first row by some constant then subtract from the row you are pivoting. So, essentially are we not ending up having 2 operations per row for those 99 rows, hence, 99*2 instead of 100^2 ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk11.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..0c36744e58fabb6a3245dc9d958d1f27684ed520 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 4, + "timestamp": 1684708849693.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "at 32:35 => Should not the first cost be 99*2 instead of 100^2 because there are 99 rows below first one. For pivoting each row below, you need to multiply the first row by some constant then subtract from the row you are pivoting. So, essentially are we not ending up having 2 operations per row for those 99 rows, hence, 99*2 instead of 100^2 ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk12.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0c36744e58fabb6a3245dc9d958d1f27684ed520 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 4, + "timestamp": 1684708849693.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "at 32:35 => Should not the first cost be 99*2 instead of 100^2 because there are 99 rows below first one. For pivoting each row below, you need to multiply the first row by some constant then subtract from the row you are pivoting. So, essentially are we not ending up having 2 operations per row for those 99 rows, hence, 99*2 instead of 100^2 ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk13.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..0c36744e58fabb6a3245dc9d958d1f27684ed520 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 4, + "timestamp": 1684708849693.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "at 32:35 => Should not the first cost be 99*2 instead of 100^2 because there are 99 rows below first one. For pivoting each row below, you need to multiply the first row by some constant then subtract from the row you are pivoting. So, essentially are we not ending up having 2 operations per row for those 99 rows, hence, 99*2 instead of 100^2 ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk14.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..0c36744e58fabb6a3245dc9d958d1f27684ed520 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 4, + "timestamp": 1684708849693.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "at 32:35 => Should not the first cost be 99*2 instead of 100^2 because there are 99 rows below first one. For pivoting each row below, you need to multiply the first row by some constant then subtract from the row you are pivoting. So, essentially are we not ending up having 2 operations per row for those 99 rows, hence, 99*2 instead of 100^2 ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk15.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..0c36744e58fabb6a3245dc9d958d1f27684ed520 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 4, + "timestamp": 1684708849693.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "at 32:35 => Should not the first cost be 99*2 instead of 100^2 because there are 99 rows below first one. For pivoting each row below, you need to multiply the first row by some constant then subtract from the row you are pivoting. So, essentially are we not ending up having 2 operations per row for those 99 rows, hence, 99*2 instead of 100^2 ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk16.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..0c36744e58fabb6a3245dc9d958d1f27684ed520 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 4, + "timestamp": 1684708849693.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "at 32:35 => Should not the first cost be 99*2 instead of 100^2 because there are 99 rows below first one. For pivoting each row below, you need to multiply the first row by some constant then subtract from the row you are pivoting. So, essentially are we not ending up having 2 operations per row for those 99 rows, hence, 99*2 instead of 100^2 ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk17.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..51ccbf7ccb1bca75159c5c8fc3f13147348cd31f --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk17.json @@ -0,0 +1,18 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 4, + "timestamp": 1684708849693.0, + "annotatedSourceSentencesIndices": [ + 1, + 2, + 3, + 4, + 13 + ], + "names": [ + "annotator2" + ], + "text": "at 32:35 => Should not the first cost be 99*2 instead of 100^2 because there are 99 rows below first one. For pivoting each row below, you need to multiply the first row by some constant then subtract from the row you are pivoting. So, essentially are we not ending up having 2 operations per row for those 99 rows, hence, 99*2 instead of 100^2 ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk18.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..0c36744e58fabb6a3245dc9d958d1f27684ed520 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 4, + "timestamp": 1684708849693.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "at 32:35 => Should not the first cost be 99*2 instead of 100^2 because there are 99 rows below first one. For pivoting each row below, you need to multiply the first row by some constant then subtract from the row you are pivoting. So, essentially are we not ending up having 2 operations per row for those 99 rows, hence, 99*2 instead of 100^2 ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk19.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..0c36744e58fabb6a3245dc9d958d1f27684ed520 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 4, + "timestamp": 1684708849693.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "at 32:35 => Should not the first cost be 99*2 instead of 100^2 because there are 99 rows below first one. For pivoting each row below, you need to multiply the first row by some constant then subtract from the row you are pivoting. So, essentially are we not ending up having 2 operations per row for those 99 rows, hence, 99*2 instead of 100^2 ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk2.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..0c36744e58fabb6a3245dc9d958d1f27684ed520 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 4, + "timestamp": 1684708849693.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "at 32:35 => Should not the first cost be 99*2 instead of 100^2 because there are 99 rows below first one. For pivoting each row below, you need to multiply the first row by some constant then subtract from the row you are pivoting. So, essentially are we not ending up having 2 operations per row for those 99 rows, hence, 99*2 instead of 100^2 ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk20.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..0c36744e58fabb6a3245dc9d958d1f27684ed520 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 4, + "timestamp": 1684708849693.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "at 32:35 => Should not the first cost be 99*2 instead of 100^2 because there are 99 rows below first one. For pivoting each row below, you need to multiply the first row by some constant then subtract from the row you are pivoting. So, essentially are we not ending up having 2 operations per row for those 99 rows, hence, 99*2 instead of 100^2 ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk21.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..0c36744e58fabb6a3245dc9d958d1f27684ed520 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 4, + "timestamp": 1684708849693.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "at 32:35 => Should not the first cost be 99*2 instead of 100^2 because there are 99 rows below first one. For pivoting each row below, you need to multiply the first row by some constant then subtract from the row you are pivoting. So, essentially are we not ending up having 2 operations per row for those 99 rows, hence, 99*2 instead of 100^2 ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk22.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0c36744e58fabb6a3245dc9d958d1f27684ed520 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 4, + "timestamp": 1684708849693.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "at 32:35 => Should not the first cost be 99*2 instead of 100^2 because there are 99 rows below first one. For pivoting each row below, you need to multiply the first row by some constant then subtract from the row you are pivoting. So, essentially are we not ending up having 2 operations per row for those 99 rows, hence, 99*2 instead of 100^2 ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk23.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..0c36744e58fabb6a3245dc9d958d1f27684ed520 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 4, + "timestamp": 1684708849693.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "at 32:35 => Should not the first cost be 99*2 instead of 100^2 because there are 99 rows below first one. For pivoting each row below, you need to multiply the first row by some constant then subtract from the row you are pivoting. So, essentially are we not ending up having 2 operations per row for those 99 rows, hence, 99*2 instead of 100^2 ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk24.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..0c36744e58fabb6a3245dc9d958d1f27684ed520 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 4, + "timestamp": 1684708849693.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "at 32:35 => Should not the first cost be 99*2 instead of 100^2 because there are 99 rows below first one. For pivoting each row below, you need to multiply the first row by some constant then subtract from the row you are pivoting. So, essentially are we not ending up having 2 operations per row for those 99 rows, hence, 99*2 instead of 100^2 ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk25.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..0c36744e58fabb6a3245dc9d958d1f27684ed520 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 4, + "timestamp": 1684708849693.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "at 32:35 => Should not the first cost be 99*2 instead of 100^2 because there are 99 rows below first one. For pivoting each row below, you need to multiply the first row by some constant then subtract from the row you are pivoting. So, essentially are we not ending up having 2 operations per row for those 99 rows, hence, 99*2 instead of 100^2 ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk26.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..0c36744e58fabb6a3245dc9d958d1f27684ed520 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 4, + "timestamp": 1684708849693.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "at 32:35 => Should not the first cost be 99*2 instead of 100^2 because there are 99 rows below first one. For pivoting each row below, you need to multiply the first row by some constant then subtract from the row you are pivoting. So, essentially are we not ending up having 2 operations per row for those 99 rows, hence, 99*2 instead of 100^2 ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk3.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..0c36744e58fabb6a3245dc9d958d1f27684ed520 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 4, + "timestamp": 1684708849693.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "at 32:35 => Should not the first cost be 99*2 instead of 100^2 because there are 99 rows below first one. For pivoting each row below, you need to multiply the first row by some constant then subtract from the row you are pivoting. So, essentially are we not ending up having 2 operations per row for those 99 rows, hence, 99*2 instead of 100^2 ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk4.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0c36744e58fabb6a3245dc9d958d1f27684ed520 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 4, + "timestamp": 1684708849693.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "at 32:35 => Should not the first cost be 99*2 instead of 100^2 because there are 99 rows below first one. For pivoting each row below, you need to multiply the first row by some constant then subtract from the row you are pivoting. So, essentially are we not ending up having 2 operations per row for those 99 rows, hence, 99*2 instead of 100^2 ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk5.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..0c36744e58fabb6a3245dc9d958d1f27684ed520 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 4, + "timestamp": 1684708849693.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "at 32:35 => Should not the first cost be 99*2 instead of 100^2 because there are 99 rows below first one. For pivoting each row below, you need to multiply the first row by some constant then subtract from the row you are pivoting. So, essentially are we not ending up having 2 operations per row for those 99 rows, hence, 99*2 instead of 100^2 ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk6.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..0c36744e58fabb6a3245dc9d958d1f27684ed520 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 4, + "timestamp": 1684708849693.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "at 32:35 => Should not the first cost be 99*2 instead of 100^2 because there are 99 rows below first one. For pivoting each row below, you need to multiply the first row by some constant then subtract from the row you are pivoting. So, essentially are we not ending up having 2 operations per row for those 99 rows, hence, 99*2 instead of 100^2 ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk7.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0c36744e58fabb6a3245dc9d958d1f27684ed520 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 4, + "timestamp": 1684708849693.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "at 32:35 => Should not the first cost be 99*2 instead of 100^2 because there are 99 rows below first one. For pivoting each row below, you need to multiply the first row by some constant then subtract from the row you are pivoting. So, essentially are we not ending up having 2 operations per row for those 99 rows, hence, 99*2 instead of 100^2 ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..0c36744e58fabb6a3245dc9d958d1f27684ed520 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 4, + "timestamp": 1684708849693.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "at 32:35 => Should not the first cost be 99*2 instead of 100^2 because there are 99 rows below first one. For pivoting each row below, you need to multiply the first row by some constant then subtract from the row you are pivoting. So, essentially are we not ending up having 2 operations per row for those 99 rows, hence, 99*2 instead of 100^2 ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk9.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..0c36744e58fabb6a3245dc9d958d1f27684ed520 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_4_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 4, + "timestamp": 1684708849693.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "at 32:35 => Should not the first cost be 99*2 instead of 100^2 because there are 99 rows below first one. For pivoting each row below, you need to multiply the first row by some constant then subtract from the row you are pivoting. So, essentially are we not ending up having 2 operations per row for those 99 rows, hence, 99*2 instead of 100^2 ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk0.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..448a83920ca0dae29373841fc845de1e0f5d0978 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 5, + "timestamp": 1684708888995.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "sorry i'm confused at 32:22, it is 100 ^2, but i think it is 100, why it isn't 100? could anyone explain that to me? thx alot" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk1.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..448a83920ca0dae29373841fc845de1e0f5d0978 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 5, + "timestamp": 1684708888995.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "sorry i'm confused at 32:22, it is 100 ^2, but i think it is 100, why it isn't 100? could anyone explain that to me? thx alot" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk10.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..448a83920ca0dae29373841fc845de1e0f5d0978 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 5, + "timestamp": 1684708888995.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "sorry i'm confused at 32:22, it is 100 ^2, but i think it is 100, why it isn't 100? could anyone explain that to me? thx alot" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk11.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..448a83920ca0dae29373841fc845de1e0f5d0978 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 5, + "timestamp": 1684708888995.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "sorry i'm confused at 32:22, it is 100 ^2, but i think it is 100, why it isn't 100? could anyone explain that to me? thx alot" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk12.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..448a83920ca0dae29373841fc845de1e0f5d0978 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 5, + "timestamp": 1684708888995.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "sorry i'm confused at 32:22, it is 100 ^2, but i think it is 100, why it isn't 100? could anyone explain that to me? thx alot" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk13.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..448a83920ca0dae29373841fc845de1e0f5d0978 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 5, + "timestamp": 1684708888995.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "sorry i'm confused at 32:22, it is 100 ^2, but i think it is 100, why it isn't 100? could anyone explain that to me? thx alot" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk14.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..448a83920ca0dae29373841fc845de1e0f5d0978 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 5, + "timestamp": 1684708888995.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "sorry i'm confused at 32:22, it is 100 ^2, but i think it is 100, why it isn't 100? could anyone explain that to me? thx alot" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk15.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..448a83920ca0dae29373841fc845de1e0f5d0978 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 5, + "timestamp": 1684708888995.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "sorry i'm confused at 32:22, it is 100 ^2, but i think it is 100, why it isn't 100? could anyone explain that to me? thx alot" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk16.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..448a83920ca0dae29373841fc845de1e0f5d0978 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 5, + "timestamp": 1684708888995.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "sorry i'm confused at 32:22, it is 100 ^2, but i think it is 100, why it isn't 100? could anyone explain that to me? thx alot" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk17.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a0c5b6604622271154df2c95ab7ca4d9d8d3925e --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk17.json @@ -0,0 +1,17 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 5, + "timestamp": 1684708888995.0, + "annotatedSourceSentencesIndices": [ + 1, + 2, + 3, + 4 + ], + "names": [ + "annotator2" + ], + "text": "sorry i'm confused at 32:22, it is 100 ^2, but i think it is 100, why it isn't 100? could anyone explain that to me? thx alot" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk18.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..448a83920ca0dae29373841fc845de1e0f5d0978 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 5, + "timestamp": 1684708888995.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "sorry i'm confused at 32:22, it is 100 ^2, but i think it is 100, why it isn't 100? could anyone explain that to me? thx alot" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk19.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..448a83920ca0dae29373841fc845de1e0f5d0978 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 5, + "timestamp": 1684708888995.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "sorry i'm confused at 32:22, it is 100 ^2, but i think it is 100, why it isn't 100? could anyone explain that to me? thx alot" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk2.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..448a83920ca0dae29373841fc845de1e0f5d0978 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 5, + "timestamp": 1684708888995.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "sorry i'm confused at 32:22, it is 100 ^2, but i think it is 100, why it isn't 100? could anyone explain that to me? thx alot" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk20.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..448a83920ca0dae29373841fc845de1e0f5d0978 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 5, + "timestamp": 1684708888995.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "sorry i'm confused at 32:22, it is 100 ^2, but i think it is 100, why it isn't 100? could anyone explain that to me? thx alot" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk21.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..448a83920ca0dae29373841fc845de1e0f5d0978 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 5, + "timestamp": 1684708888995.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "sorry i'm confused at 32:22, it is 100 ^2, but i think it is 100, why it isn't 100? could anyone explain that to me? thx alot" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk22.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..448a83920ca0dae29373841fc845de1e0f5d0978 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 5, + "timestamp": 1684708888995.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "sorry i'm confused at 32:22, it is 100 ^2, but i think it is 100, why it isn't 100? could anyone explain that to me? thx alot" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk23.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..448a83920ca0dae29373841fc845de1e0f5d0978 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 5, + "timestamp": 1684708888995.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "sorry i'm confused at 32:22, it is 100 ^2, but i think it is 100, why it isn't 100? could anyone explain that to me? thx alot" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk24.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..448a83920ca0dae29373841fc845de1e0f5d0978 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 5, + "timestamp": 1684708888995.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "sorry i'm confused at 32:22, it is 100 ^2, but i think it is 100, why it isn't 100? could anyone explain that to me? thx alot" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk25.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..448a83920ca0dae29373841fc845de1e0f5d0978 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 5, + "timestamp": 1684708888995.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "sorry i'm confused at 32:22, it is 100 ^2, but i think it is 100, why it isn't 100? could anyone explain that to me? thx alot" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk26.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..448a83920ca0dae29373841fc845de1e0f5d0978 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 5, + "timestamp": 1684708888995.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "sorry i'm confused at 32:22, it is 100 ^2, but i think it is 100, why it isn't 100? could anyone explain that to me? thx alot" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk3.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..448a83920ca0dae29373841fc845de1e0f5d0978 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 5, + "timestamp": 1684708888995.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "sorry i'm confused at 32:22, it is 100 ^2, but i think it is 100, why it isn't 100? could anyone explain that to me? thx alot" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk4.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..448a83920ca0dae29373841fc845de1e0f5d0978 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 5, + "timestamp": 1684708888995.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "sorry i'm confused at 32:22, it is 100 ^2, but i think it is 100, why it isn't 100? could anyone explain that to me? thx alot" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk5.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..448a83920ca0dae29373841fc845de1e0f5d0978 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 5, + "timestamp": 1684708888995.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "sorry i'm confused at 32:22, it is 100 ^2, but i think it is 100, why it isn't 100? could anyone explain that to me? thx alot" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk6.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..448a83920ca0dae29373841fc845de1e0f5d0978 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 5, + "timestamp": 1684708888995.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "sorry i'm confused at 32:22, it is 100 ^2, but i think it is 100, why it isn't 100? could anyone explain that to me? thx alot" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk7.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..448a83920ca0dae29373841fc845de1e0f5d0978 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 5, + "timestamp": 1684708888995.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "sorry i'm confused at 32:22, it is 100 ^2, but i think it is 100, why it isn't 100? could anyone explain that to me? thx alot" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..448a83920ca0dae29373841fc845de1e0f5d0978 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 5, + "timestamp": 1684708888995.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "sorry i'm confused at 32:22, it is 100 ^2, but i think it is 100, why it isn't 100? could anyone explain that to me? thx alot" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk9.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..448a83920ca0dae29373841fc845de1e0f5d0978 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_5_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 5, + "timestamp": 1684708888995.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "sorry i'm confused at 32:22, it is 100 ^2, but i think it is 100, why it isn't 100? could anyone explain that to me? thx alot" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_6_chunk0.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_6_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..fa6edaed9de5bc759e67afe08e180bcefe366e31 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_6_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 6, + "timestamp": 1684709130696.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "How come 4x4 Matrix has 24 P's ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_6_chunk1.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_6_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..fa6edaed9de5bc759e67afe08e180bcefe366e31 --- /dev/null +++ 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"names": [ + "annotator2" + ], + "text": "How come 4x4 Matrix has 24 P's ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_6_chunk13.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_6_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..fa6edaed9de5bc759e67afe08e180bcefe366e31 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_6_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 6, + "timestamp": 1684709130696.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "How come 4x4 Matrix has 24 P's ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_6_chunk14.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_6_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..fa6edaed9de5bc759e67afe08e180bcefe366e31 --- /dev/null +++ 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"names": [ + "annotator2" + ], + "text": "How come 4x4 Matrix has 24 P's ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_6_chunk18.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_6_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..fa6edaed9de5bc759e67afe08e180bcefe366e31 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_6_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 6, + "timestamp": 1684709130696.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "How come 4x4 Matrix has 24 P's ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_6_chunk19.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_6_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..fa6edaed9de5bc759e67afe08e180bcefe366e31 --- /dev/null +++ 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"names": [ + "annotator2" + ], + "text": "How come 4x4 Matrix has 24 P's ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_6_chunk22.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_6_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..fa6edaed9de5bc759e67afe08e180bcefe366e31 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_6_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 6, + "timestamp": 1684709130696.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "How come 4x4 Matrix has 24 P's ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_6_chunk23.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_6_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..fa6edaed9de5bc759e67afe08e180bcefe366e31 --- /dev/null +++ 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"annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "How come 4x4 Matrix has 24 P's ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_6_chunk3.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_6_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..fa6edaed9de5bc759e67afe08e180bcefe366e31 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_6_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 6, + "timestamp": 1684709130696.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "How come 4x4 Matrix has 24 P's ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_6_chunk4.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_6_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..fa6edaed9de5bc759e67afe08e180bcefe366e31 --- 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"timestamp": 1684709130696.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "How come 4x4 Matrix has 24 P's ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_6_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_6_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..fa6edaed9de5bc759e67afe08e180bcefe366e31 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_6_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 6, + "timestamp": 1684709130696.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "How come 4x4 Matrix has 24 P's ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_6_chunk9.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_6_chunk9.json new file mode 100644 index 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again, ... : why did he jump suddenly to this theorem without any definition of transpose nor the logical derivation? Did I miss something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk1.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..2aa215b68c7fa04ca91d619b29e2dc3f971cd1e9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 7, + "timestamp": 1684709988672.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:57 if i transpose these guys, that product, then again, ... : why did he jump suddenly to this theorem without any definition of transpose nor the logical derivation? Did I miss something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk10.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..2aa215b68c7fa04ca91d619b29e2dc3f971cd1e9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 7, + "timestamp": 1684709988672.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:57 if i transpose these guys, that product, then again, ... : why did he jump suddenly to this theorem without any definition of transpose nor the logical derivation? Did I miss something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk11.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..2aa215b68c7fa04ca91d619b29e2dc3f971cd1e9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 7, + "timestamp": 1684709988672.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:57 if i transpose these guys, that product, then again, ... : why did he jump suddenly to this theorem without any definition of transpose nor the logical derivation? Did I miss something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk12.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..2aa215b68c7fa04ca91d619b29e2dc3f971cd1e9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 7, + "timestamp": 1684709988672.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:57 if i transpose these guys, that product, then again, ... : why did he jump suddenly to this theorem without any definition of transpose nor the logical derivation? Did I miss something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk13.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2aa215b68c7fa04ca91d619b29e2dc3f971cd1e9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 7, + "timestamp": 1684709988672.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:57 if i transpose these guys, that product, then again, ... : why did he jump suddenly to this theorem without any definition of transpose nor the logical derivation? Did I miss something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk14.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..2aa215b68c7fa04ca91d619b29e2dc3f971cd1e9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 7, + "timestamp": 1684709988672.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:57 if i transpose these guys, that product, then again, ... : why did he jump suddenly to this theorem without any definition of transpose nor the logical derivation? Did I miss something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk15.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..2aa215b68c7fa04ca91d619b29e2dc3f971cd1e9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 7, + "timestamp": 1684709988672.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:57 if i transpose these guys, that product, then again, ... : why did he jump suddenly to this theorem without any definition of transpose nor the logical derivation? Did I miss something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk16.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..2aa215b68c7fa04ca91d619b29e2dc3f971cd1e9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 7, + "timestamp": 1684709988672.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:57 if i transpose these guys, that product, then again, ... : why did he jump suddenly to this theorem without any definition of transpose nor the logical derivation? Did I miss something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk17.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..2aa215b68c7fa04ca91d619b29e2dc3f971cd1e9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 7, + "timestamp": 1684709988672.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:57 if i transpose these guys, that product, then again, ... : why did he jump suddenly to this theorem without any definition of transpose nor the logical derivation? Did I miss something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk18.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2aa215b68c7fa04ca91d619b29e2dc3f971cd1e9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 7, + "timestamp": 1684709988672.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:57 if i transpose these guys, that product, then again, ... : why did he jump suddenly to this theorem without any definition of transpose nor the logical derivation? Did I miss something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk19.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..2aa215b68c7fa04ca91d619b29e2dc3f971cd1e9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 7, + "timestamp": 1684709988672.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:57 if i transpose these guys, that product, then again, ... : why did he jump suddenly to this theorem without any definition of transpose nor the logical derivation? Did I miss something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk2.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..981b914df3773748a51780c7c8b5227307abb643 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk2.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 7, + "timestamp": 1684709988672.0, + "annotatedSourceSentencesIndices": [ + 8 + ], + "names": [ + "annotator2" + ], + "text": "4:57 if i transpose these guys, that product, then again, ... : why did he jump suddenly to this theorem without any definition of transpose nor the logical derivation? Did I miss something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk20.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..2aa215b68c7fa04ca91d619b29e2dc3f971cd1e9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 7, + "timestamp": 1684709988672.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:57 if i transpose these guys, that product, then again, ... : why did he jump suddenly to this theorem without any definition of transpose nor the logical derivation? Did I miss something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk21.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..2aa215b68c7fa04ca91d619b29e2dc3f971cd1e9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 7, + "timestamp": 1684709988672.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:57 if i transpose these guys, that product, then again, ... : why did he jump suddenly to this theorem without any definition of transpose nor the logical derivation? Did I miss something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk22.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..2aa215b68c7fa04ca91d619b29e2dc3f971cd1e9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 7, + "timestamp": 1684709988672.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:57 if i transpose these guys, that product, then again, ... : why did he jump suddenly to this theorem without any definition of transpose nor the logical derivation? Did I miss something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk23.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..2aa215b68c7fa04ca91d619b29e2dc3f971cd1e9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 7, + "timestamp": 1684709988672.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:57 if i transpose these guys, that product, then again, ... : why did he jump suddenly to this theorem without any definition of transpose nor the logical derivation? Did I miss something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk24.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..2aa215b68c7fa04ca91d619b29e2dc3f971cd1e9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 7, + "timestamp": 1684709988672.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:57 if i transpose these guys, that product, then again, ... : why did he jump suddenly to this theorem without any definition of transpose nor the logical derivation? Did I miss something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk25.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..2aa215b68c7fa04ca91d619b29e2dc3f971cd1e9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 7, + "timestamp": 1684709988672.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:57 if i transpose these guys, that product, then again, ... : why did he jump suddenly to this theorem without any definition of transpose nor the logical derivation? Did I miss something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk26.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..2aa215b68c7fa04ca91d619b29e2dc3f971cd1e9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 7, + "timestamp": 1684709988672.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:57 if i transpose these guys, that product, then again, ... : why did he jump suddenly to this theorem without any definition of transpose nor the logical derivation? Did I miss something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk3.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..2aa215b68c7fa04ca91d619b29e2dc3f971cd1e9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 7, + "timestamp": 1684709988672.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:57 if i transpose these guys, that product, then again, ... : why did he jump suddenly to this theorem without any definition of transpose nor the logical derivation? Did I miss something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk4.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..2aa215b68c7fa04ca91d619b29e2dc3f971cd1e9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 7, + "timestamp": 1684709988672.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:57 if i transpose these guys, that product, then again, ... : why did he jump suddenly to this theorem without any definition of transpose nor the logical derivation? Did I miss something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk5.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..2aa215b68c7fa04ca91d619b29e2dc3f971cd1e9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 7, + "timestamp": 1684709988672.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:57 if i transpose these guys, that product, then again, ... : why did he jump suddenly to this theorem without any definition of transpose nor the logical derivation? Did I miss something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk6.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..2aa215b68c7fa04ca91d619b29e2dc3f971cd1e9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 7, + "timestamp": 1684709988672.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:57 if i transpose these guys, that product, then again, ... : why did he jump suddenly to this theorem without any definition of transpose nor the logical derivation? Did I miss something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk7.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..2aa215b68c7fa04ca91d619b29e2dc3f971cd1e9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 7, + "timestamp": 1684709988672.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:57 if i transpose these guys, that product, then again, ... : why did he jump suddenly to this theorem without any definition of transpose nor the logical derivation? Did I miss something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..2aa215b68c7fa04ca91d619b29e2dc3f971cd1e9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 7, + "timestamp": 1684709988672.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:57 if i transpose these guys, that product, then again, ... : why did he jump suddenly to this theorem without any definition of transpose nor the logical derivation? Did I miss something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk9.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..2aa215b68c7fa04ca91d619b29e2dc3f971cd1e9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_7_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 7, + "timestamp": 1684709988672.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "4:57 if i transpose these guys, that product, then again, ... : why did he jump suddenly to this theorem without any definition of transpose nor the logical derivation? Did I miss something?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk0.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..68baf38ebc4f13c7e00daa88511919ecd5aceedf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 8, + "timestamp": 1684710001490.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "33\uff1a06 why it's 100^2?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk1.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..68baf38ebc4f13c7e00daa88511919ecd5aceedf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk1.json @@ -0,0 +1,12 @@ +[ 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\ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk18.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..68baf38ebc4f13c7e00daa88511919ecd5aceedf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 8, + "timestamp": 1684710001490.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "33\uff1a06 why it's 100^2?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk19.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..68baf38ebc4f13c7e00daa88511919ecd5aceedf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": 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file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk22.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..68baf38ebc4f13c7e00daa88511919ecd5aceedf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 8, + "timestamp": 1684710001490.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "33\uff1a06 why it's 100^2?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk23.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..68baf38ebc4f13c7e00daa88511919ecd5aceedf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 8, + "timestamp": 1684710001490.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "33\uff1a06 why it's 100^2?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk24.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..68baf38ebc4f13c7e00daa88511919ecd5aceedf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 8, + "timestamp": 1684710001490.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "33\uff1a06 why it's 100^2?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk25.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk25.json new file mode 100644 index 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file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk3.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..68baf38ebc4f13c7e00daa88511919ecd5aceedf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 8, + "timestamp": 1684710001490.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "33\uff1a06 why it's 100^2?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk4.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..68baf38ebc4f13c7e00daa88511919ecd5aceedf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 8, + "timestamp": 1684710001490.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "33\uff1a06 why it's 100^2?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk5.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..68baf38ebc4f13c7e00daa88511919ecd5aceedf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 8, + "timestamp": 1684710001490.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "33\uff1a06 why it's 100^2?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk6.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk6.json new file mode 100644 index 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file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..68baf38ebc4f13c7e00daa88511919ecd5aceedf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 8, + "timestamp": 1684710001490.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "33\uff1a06 why it's 100^2?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk9.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..68baf38ebc4f13c7e00daa88511919ecd5aceedf --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_8_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 8, + "timestamp": 1684710001490.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "33\uff1a06 why it's 100^2?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk0.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d0684e48fac6f8d9ef0ccd3fa2719efaf6c43b24 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 9, + "timestamp": 1684710020923.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why the computatinal expense is roughly 100^2 for the first step? I thought it would be roughly proportional to n = 100" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk1.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..d0684e48fac6f8d9ef0ccd3fa2719efaf6c43b24 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 9, + "timestamp": 1684710020923.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why the computatinal expense is roughly 100^2 for the first step? I thought it would be roughly proportional to n = 100" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk10.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..d0684e48fac6f8d9ef0ccd3fa2719efaf6c43b24 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 9, + "timestamp": 1684710020923.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why the computatinal expense is roughly 100^2 for the first step? I thought it would be roughly proportional to n = 100" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk11.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d0684e48fac6f8d9ef0ccd3fa2719efaf6c43b24 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 9, + "timestamp": 1684710020923.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why the computatinal expense is roughly 100^2 for the first step? I thought it would be roughly proportional to n = 100" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk12.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..d0684e48fac6f8d9ef0ccd3fa2719efaf6c43b24 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 9, + "timestamp": 1684710020923.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why the computatinal expense is roughly 100^2 for the first step? I thought it would be roughly proportional to n = 100" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk13.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..d0684e48fac6f8d9ef0ccd3fa2719efaf6c43b24 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 9, + "timestamp": 1684710020923.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why the computatinal expense is roughly 100^2 for the first step? I thought it would be roughly proportional to n = 100" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk14.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d0684e48fac6f8d9ef0ccd3fa2719efaf6c43b24 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 9, + "timestamp": 1684710020923.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why the computatinal expense is roughly 100^2 for the first step? I thought it would be roughly proportional to n = 100" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk15.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..d0684e48fac6f8d9ef0ccd3fa2719efaf6c43b24 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 9, + "timestamp": 1684710020923.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why the computatinal expense is roughly 100^2 for the first step? I thought it would be roughly proportional to n = 100" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk16.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..d0684e48fac6f8d9ef0ccd3fa2719efaf6c43b24 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 9, + "timestamp": 1684710020923.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why the computatinal expense is roughly 100^2 for the first step? I thought it would be roughly proportional to n = 100" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk17.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..132707990773feb7ddfd2c516d08a96532c73792 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk17.json @@ -0,0 +1,18 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 9, + "timestamp": 1684710020923.0, + "annotatedSourceSentencesIndices": [ + 1, + 2, + 3, + 4, + 13 + ], + "names": [ + "annotator2" + ], + "text": "Can someone explain why the computatinal expense is roughly 100^2 for the first step? I thought it would be roughly proportional to n = 100" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk18.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..d0684e48fac6f8d9ef0ccd3fa2719efaf6c43b24 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 9, + "timestamp": 1684710020923.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why the computatinal expense is roughly 100^2 for the first step? I thought it would be roughly proportional to n = 100" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk19.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..d0684e48fac6f8d9ef0ccd3fa2719efaf6c43b24 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 9, + "timestamp": 1684710020923.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why the computatinal expense is roughly 100^2 for the first step? I thought it would be roughly proportional to n = 100" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk2.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..d0684e48fac6f8d9ef0ccd3fa2719efaf6c43b24 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 9, + "timestamp": 1684710020923.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why the computatinal expense is roughly 100^2 for the first step? I thought it would be roughly proportional to n = 100" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk20.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..d0684e48fac6f8d9ef0ccd3fa2719efaf6c43b24 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 9, + "timestamp": 1684710020923.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why the computatinal expense is roughly 100^2 for the first step? I thought it would be roughly proportional to n = 100" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk21.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..d0684e48fac6f8d9ef0ccd3fa2719efaf6c43b24 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 9, + "timestamp": 1684710020923.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why the computatinal expense is roughly 100^2 for the first step? I thought it would be roughly proportional to n = 100" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk22.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..d0684e48fac6f8d9ef0ccd3fa2719efaf6c43b24 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 9, + "timestamp": 1684710020923.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why the computatinal expense is roughly 100^2 for the first step? I thought it would be roughly proportional to n = 100" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk23.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..d0684e48fac6f8d9ef0ccd3fa2719efaf6c43b24 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 9, + "timestamp": 1684710020923.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why the computatinal expense is roughly 100^2 for the first step? I thought it would be roughly proportional to n = 100" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk24.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..d0684e48fac6f8d9ef0ccd3fa2719efaf6c43b24 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 9, + "timestamp": 1684710020923.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why the computatinal expense is roughly 100^2 for the first step? I thought it would be roughly proportional to n = 100" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk25.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0684e48fac6f8d9ef0ccd3fa2719efaf6c43b24 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 9, + "timestamp": 1684710020923.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why the computatinal expense is roughly 100^2 for the first step? I thought it would be roughly proportional to n = 100" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk26.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..d0684e48fac6f8d9ef0ccd3fa2719efaf6c43b24 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 9, + "timestamp": 1684710020923.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why the computatinal expense is roughly 100^2 for the first step? I thought it would be roughly proportional to n = 100" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk3.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..d0684e48fac6f8d9ef0ccd3fa2719efaf6c43b24 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 9, + "timestamp": 1684710020923.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why the computatinal expense is roughly 100^2 for the first step? I thought it would be roughly proportional to n = 100" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk4.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..d0684e48fac6f8d9ef0ccd3fa2719efaf6c43b24 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 9, + "timestamp": 1684710020923.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why the computatinal expense is roughly 100^2 for the first step? I thought it would be roughly proportional to n = 100" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk5.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..d0684e48fac6f8d9ef0ccd3fa2719efaf6c43b24 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 9, + "timestamp": 1684710020923.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why the computatinal expense is roughly 100^2 for the first step? I thought it would be roughly proportional to n = 100" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk6.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..d0684e48fac6f8d9ef0ccd3fa2719efaf6c43b24 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 9, + "timestamp": 1684710020923.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why the computatinal expense is roughly 100^2 for the first step? I thought it would be roughly proportional to n = 100" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk7.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..d0684e48fac6f8d9ef0ccd3fa2719efaf6c43b24 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 9, + "timestamp": 1684710020923.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why the computatinal expense is roughly 100^2 for the first step? I thought it would be roughly proportional to n = 100" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk8.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..d0684e48fac6f8d9ef0ccd3fa2719efaf6c43b24 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 9, + "timestamp": 1684710020923.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why the computatinal expense is roughly 100^2 for the first step? I thought it would be roughly proportional to n = 100" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk9.json b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..d0684e48fac6f8d9ef0ccd3fa2719efaf6c43b24 --- /dev/null +++ b/sight/query/annotated_chunks_window20/MsIvs_6vC38_9_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "MsIvs_6vC38", + "query_id": 9, + "timestamp": 1684710020923.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can someone explain why the computatinal expense is roughly 100^2 for the first step? I thought it would be roughly proportional to n = 100" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk0.json b/sight/query/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..fca7d748d405def78063d8ed74ecc020a7dc62cb --- /dev/null +++ b/sight/query/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk0.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "RD9AWDdj-Yk", + "query_id": 0, + "timestamp": 1684192371630.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Proof of TRL neglects edges inside clusters?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk1.json b/sight/query/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..fca7d748d405def78063d8ed74ecc020a7dc62cb --- /dev/null +++ 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"annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Proof of TRL neglects edges inside clusters?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk16.json b/sight/query/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..fca7d748d405def78063d8ed74ecc020a7dc62cb --- /dev/null +++ b/sight/query/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk16.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "RD9AWDdj-Yk", + "query_id": 0, + "timestamp": 1684192371630.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Proof of TRL neglects edges inside clusters?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk17.json b/sight/query/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk17.json new file mode 100644 index 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In the case of the statistical model, P represents the Family of Distributions......" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk2.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..60ca18ae111c4d39af8d7c2510fafd29a79ca6cc --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 0, + "timestamp": 1684520696821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at time 1:12:36, the instructor stated the expectation to be P. What is P representing here? In the case of the statistical model, P represents the Family of Distributions......" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk20.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..60ca18ae111c4d39af8d7c2510fafd29a79ca6cc --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 0, + "timestamp": 1684520696821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at time 1:12:36, the instructor stated the expectation to be P. What is P representing here? In the case of the statistical model, P represents the Family of Distributions......" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk21.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..60ca18ae111c4d39af8d7c2510fafd29a79ca6cc --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 0, + "timestamp": 1684520696821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at time 1:12:36, the instructor stated the expectation to be P. What is P representing here? In the case of the statistical model, P represents the Family of Distributions......" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk22.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..60ca18ae111c4d39af8d7c2510fafd29a79ca6cc --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 0, + "timestamp": 1684520696821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at time 1:12:36, the instructor stated the expectation to be P. What is P representing here? In the case of the statistical model, P represents the Family of Distributions......" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk23.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..60ca18ae111c4d39af8d7c2510fafd29a79ca6cc --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 0, + "timestamp": 1684520696821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at time 1:12:36, the instructor stated the expectation to be P. What is P representing here? In the case of the statistical model, P represents the Family of Distributions......" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk24.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..60ca18ae111c4d39af8d7c2510fafd29a79ca6cc --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 0, + "timestamp": 1684520696821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at time 1:12:36, the instructor stated the expectation to be P. What is P representing here? In the case of the statistical model, P represents the Family of Distributions......" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk25.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..60ca18ae111c4d39af8d7c2510fafd29a79ca6cc --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 0, + "timestamp": 1684520696821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at time 1:12:36, the instructor stated the expectation to be P. What is P representing here? 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In the case of the statistical model, P represents the Family of Distributions......" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk29.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk29.json new file mode 100644 index 0000000000000000000000000000000000000000..60ca18ae111c4d39af8d7c2510fafd29a79ca6cc --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk29.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 0, + "timestamp": 1684520696821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at time 1:12:36, the instructor stated the expectation to be P. What is P representing here? 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In the case of the statistical model, P represents the Family of Distributions......" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk33.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk33.json new file mode 100644 index 0000000000000000000000000000000000000000..60ca18ae111c4d39af8d7c2510fafd29a79ca6cc --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk33.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 0, + "timestamp": 1684520696821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at time 1:12:36, the instructor stated the expectation to be P. What is P representing here? In the case of the statistical model, P represents the Family of Distributions......" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk34.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk34.json new file mode 100644 index 0000000000000000000000000000000000000000..60ca18ae111c4d39af8d7c2510fafd29a79ca6cc --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk34.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 0, + "timestamp": 1684520696821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at time 1:12:36, the instructor stated the expectation to be P. What is P representing here? In the case of the statistical model, P represents the Family of Distributions......" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk35.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk35.json new file mode 100644 index 0000000000000000000000000000000000000000..60ca18ae111c4d39af8d7c2510fafd29a79ca6cc --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk35.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 0, + "timestamp": 1684520696821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at time 1:12:36, the instructor stated the expectation to be P. What is P representing here? 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In the case of the statistical model, P represents the Family of Distributions......" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk37.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk37.json new file mode 100644 index 0000000000000000000000000000000000000000..60ca18ae111c4d39af8d7c2510fafd29a79ca6cc --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk37.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 0, + "timestamp": 1684520696821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at time 1:12:36, the instructor stated the expectation to be P. What is P representing here? In the case of the statistical model, P represents the Family of Distributions......" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk38.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk38.json new file mode 100644 index 0000000000000000000000000000000000000000..60ca18ae111c4d39af8d7c2510fafd29a79ca6cc --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk38.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 0, + "timestamp": 1684520696821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at time 1:12:36, the instructor stated the expectation to be P. What is P representing here? In the case of the statistical model, P represents the Family of Distributions......" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk39.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk39.json new file mode 100644 index 0000000000000000000000000000000000000000..60ca18ae111c4d39af8d7c2510fafd29a79ca6cc --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk39.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 0, + "timestamp": 1684520696821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at time 1:12:36, the instructor stated the expectation to be P. What is P representing here? In the case of the statistical model, P represents the Family of Distributions......" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk4.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..60ca18ae111c4d39af8d7c2510fafd29a79ca6cc --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 0, + "timestamp": 1684520696821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at time 1:12:36, the instructor stated the expectation to be P. What is P representing here? In the case of the statistical model, P represents the Family of Distributions......" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk40.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk40.json new file mode 100644 index 0000000000000000000000000000000000000000..60ca18ae111c4d39af8d7c2510fafd29a79ca6cc --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk40.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 0, + "timestamp": 1684520696821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at time 1:12:36, the instructor stated the expectation to be P. What is P representing here? In the case of the statistical model, P represents the Family of Distributions......" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk41.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk41.json new file mode 100644 index 0000000000000000000000000000000000000000..60ca18ae111c4d39af8d7c2510fafd29a79ca6cc --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk41.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 0, + "timestamp": 1684520696821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at time 1:12:36, the instructor stated the expectation to be P. What is P representing here? In the case of the statistical model, P represents the Family of Distributions......" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk42.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk42.json new file mode 100644 index 0000000000000000000000000000000000000000..d888a357ebfc9ce6ea1f0316c973f63c6bc05f26 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk42.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 0, + "timestamp": 1684520696821.0, + "annotatedSourceSentencesIndices": [ + 4 + ], + "names": [ + "annotator1" + ], + "text": "at time 1:12:36, the instructor stated the expectation to be P. What is P representing here? In the case of the statistical model, P represents the Family of Distributions......" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk43.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk43.json new file mode 100644 index 0000000000000000000000000000000000000000..60ca18ae111c4d39af8d7c2510fafd29a79ca6cc --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk43.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 0, + "timestamp": 1684520696821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at time 1:12:36, the instructor stated the expectation to be P. What is P representing here? In the case of the statistical model, P represents the Family of Distributions......" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk44.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk44.json new file mode 100644 index 0000000000000000000000000000000000000000..60ca18ae111c4d39af8d7c2510fafd29a79ca6cc --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk44.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 0, + "timestamp": 1684520696821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at time 1:12:36, the instructor stated the expectation to be P. What is P representing here? In the case of the statistical model, P represents the Family of Distributions......" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk45.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk45.json new file mode 100644 index 0000000000000000000000000000000000000000..60ca18ae111c4d39af8d7c2510fafd29a79ca6cc --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk45.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 0, + "timestamp": 1684520696821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at time 1:12:36, the instructor stated the expectation to be P. What is P representing here? In the case of the statistical model, P represents the Family of Distributions......" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk46.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk46.json new file mode 100644 index 0000000000000000000000000000000000000000..60ca18ae111c4d39af8d7c2510fafd29a79ca6cc --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk46.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 0, + "timestamp": 1684520696821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at time 1:12:36, the instructor stated the expectation to be P. What is P representing here? In the case of the statistical model, P represents the Family of Distributions......" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk47.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk47.json new file mode 100644 index 0000000000000000000000000000000000000000..60ca18ae111c4d39af8d7c2510fafd29a79ca6cc --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk47.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 0, + "timestamp": 1684520696821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at time 1:12:36, the instructor stated the expectation to be P. What is P representing here? In the case of the statistical model, P represents the Family of Distributions......" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk5.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60ca18ae111c4d39af8d7c2510fafd29a79ca6cc --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 0, + "timestamp": 1684520696821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at time 1:12:36, the instructor stated the expectation to be P. What is P representing here? In the case of the statistical model, P represents the Family of Distributions......" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk6.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..60ca18ae111c4d39af8d7c2510fafd29a79ca6cc --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 0, + "timestamp": 1684520696821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at time 1:12:36, the instructor stated the expectation to be P. What is P representing here? In the case of the statistical model, P represents the Family of Distributions......" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk7.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..60ca18ae111c4d39af8d7c2510fafd29a79ca6cc --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 0, + "timestamp": 1684520696821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at time 1:12:36, the instructor stated the expectation to be P. What is P representing here? In the case of the statistical model, P represents the Family of Distributions......" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk8.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..60ca18ae111c4d39af8d7c2510fafd29a79ca6cc --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 0, + "timestamp": 1684520696821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at time 1:12:36, the instructor stated the expectation to be P. What is P representing here? In the case of the statistical model, P represents the Family of Distributions......" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk9.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..60ca18ae111c4d39af8d7c2510fafd29a79ca6cc --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_0_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 0, + "timestamp": 1684520696821.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at time 1:12:36, the instructor stated the expectation to be P. What is P representing here? In the case of the statistical model, P represents the Family of Distributions......" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk0.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6a0989ce09d801f105dacf35a8890d16d579d9ce --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 1, + "timestamp": 1684520806354.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why are the parameters of one of the normal distributions he describes identifiable and the others aren't?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk1.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk1.json new file mode 100644 index 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"names": [ + "annotator1" + ], + "text": "Why are the parameters of one of the normal distributions he describes identifiable and the others aren't?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk14.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..6a0989ce09d801f105dacf35a8890d16d579d9ce --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 1, + "timestamp": 1684520806354.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why are the parameters of one of the normal distributions he describes identifiable and the others aren't?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk15.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk15.json 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"annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why are the parameters of one of the normal distributions he describes identifiable and the others aren't?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk17.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..6a0989ce09d801f105dacf35a8890d16d579d9ce --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 1, + "timestamp": 1684520806354.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why are the parameters of one of the normal distributions he describes identifiable and the others aren't?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk18.json 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identifiable and the others aren't?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk26.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..6a0989ce09d801f105dacf35a8890d16d579d9ce --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 1, + "timestamp": 1684520806354.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why are the parameters of one of the normal distributions he describes identifiable and the others aren't?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk27.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk27.json new file mode 100644 index 0000000000000000000000000000000000000000..6a0989ce09d801f105dacf35a8890d16d579d9ce --- 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describes identifiable and the others aren't?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk29.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk29.json new file mode 100644 index 0000000000000000000000000000000000000000..6a0989ce09d801f105dacf35a8890d16d579d9ce --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk29.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 1, + "timestamp": 1684520806354.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why are the parameters of one of the normal distributions he describes identifiable and the others aren't?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk3.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk3.json new file mode 100644 index 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"annotator1" + ], + "text": "Why are the parameters of one of the normal distributions he describes identifiable and the others aren't?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk31.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk31.json new file mode 100644 index 0000000000000000000000000000000000000000..6a0989ce09d801f105dacf35a8890d16d579d9ce --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk31.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 1, + "timestamp": 1684520806354.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why are the parameters of one of the normal distributions he describes identifiable and the others aren't?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk32.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk32.json new file mode 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"names": [ + "annotator1" + ], + "text": "Why are the parameters of one of the normal distributions he describes identifiable and the others aren't?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk34.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk34.json new file mode 100644 index 0000000000000000000000000000000000000000..6a0989ce09d801f105dacf35a8890d16d579d9ce --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk34.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 1, + "timestamp": 1684520806354.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why are the parameters of one of the normal distributions he describes identifiable and the others aren't?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk35.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk35.json 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"annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why are the parameters of one of the normal distributions he describes identifiable and the others aren't?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk37.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk37.json new file mode 100644 index 0000000000000000000000000000000000000000..6a0989ce09d801f105dacf35a8890d16d579d9ce --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk37.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 1, + "timestamp": 1684520806354.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why are the parameters of one of the normal distributions he describes identifiable and the others aren't?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk38.json 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+ "timestamp": 1684520806354.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why are the parameters of one of the normal distributions he describes identifiable and the others aren't?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk4.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..6a0989ce09d801f105dacf35a8890d16d579d9ce --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 1, + "timestamp": 1684520806354.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why are the parameters of one of the normal distributions he describes identifiable and the others aren't?" + } +] \ No newline at end of file diff --git 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--git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk43.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk43.json new file mode 100644 index 0000000000000000000000000000000000000000..6a0989ce09d801f105dacf35a8890d16d579d9ce --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk43.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 1, + "timestamp": 1684520806354.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why are the parameters of one of the normal distributions he describes identifiable and the others aren't?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk44.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk44.json new file mode 100644 index 0000000000000000000000000000000000000000..6a0989ce09d801f105dacf35a8890d16d579d9ce --- /dev/null +++ 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identifiable and the others aren't?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk46.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk46.json new file mode 100644 index 0000000000000000000000000000000000000000..6a0989ce09d801f105dacf35a8890d16d579d9ce --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk46.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 1, + "timestamp": 1684520806354.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why are the parameters of one of the normal distributions he describes identifiable and the others aren't?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk47.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk47.json new file mode 100644 index 0000000000000000000000000000000000000000..6a0989ce09d801f105dacf35a8890d16d579d9ce --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk47.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 1, + "timestamp": 1684520806354.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why are the parameters of one of the normal distributions he describes identifiable and the others aren't?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk5.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..6a0989ce09d801f105dacf35a8890d16d579d9ce --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 1, + "timestamp": 1684520806354.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why are the parameters of one of the normal distributions he describes identifiable and the others aren't?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk6.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..6a0989ce09d801f105dacf35a8890d16d579d9ce --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 1, + "timestamp": 1684520806354.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why are the parameters of one of the normal distributions he describes identifiable and the others aren't?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk7.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..6a0989ce09d801f105dacf35a8890d16d579d9ce --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 1, + "timestamp": 1684520806354.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why are the parameters of one of the normal distributions he describes identifiable and the others aren't?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk8.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..6a0989ce09d801f105dacf35a8890d16d579d9ce --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 1, + "timestamp": 1684520806354.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why are the parameters of one of the normal distributions he describes identifiable and the others aren't?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk9.json b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..6a0989ce09d801f105dacf35a8890d16d579d9ce --- /dev/null +++ b/sight/query/annotated_chunks_window20/TSkDZbGS94k_1_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TSkDZbGS94k", + "query_id": 1, + "timestamp": 1684520806354.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why are the parameters of one of the normal distributions he describes identifiable and the others aren't?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk0.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..eb0e4d0cdf554a9ac84a1e3b655b16c9c12a75a5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 10, + "timestamp": 1684512534435.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Regarding the problem at 26:28\nIt would be solved if the matrix U was [1 0; 0 -1]. (Replace the 1 at the bottom right of the 2x2 identity with -1).\nThis can be found by following the argument that Prof Strang makes in this video: https://youtu.be/rYz83XPxiZo?t=1177 (Skip to 19:37). \nThe problem is that here the eigenvectors of U that we found are [1, 0]' and [0, 1]', but they should be [1, 0]' and [0, -1]'.\nThe negative in the 2nd eigenvector allows the scaling term (sigma) to be strictly positive. \n\nLet S = Sigma (for ease of typing).\nI think the main problem is that the general form A = U*S*V' does not mathematically enforce that S should be a strictly positive matrix.\nSo even though A'A and AA' will output the squares of the eigenvalues, simply choosing the positive roots is not enough.\nWe would need to choose the right sign for the eigenvector that corresponds to the positive root. E.g. [1,0] and [-1,0] can both have the same eigenvalue, so we have to decide which to use.\nHence, we need to check the cases and manually negate the vectors in U or V so that S can be positive.\nHowever, if we follow what Prof Strang does in the video whose URL ive included in the earlier part of this comment, then this is accounted for by the computation." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk1.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..eb0e4d0cdf554a9ac84a1e3b655b16c9c12a75a5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 10, + "timestamp": 1684512534435.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Regarding the problem at 26:28\nIt would be solved if the matrix U was [1 0; 0 -1]. (Replace the 1 at the bottom right of the 2x2 identity with -1).\nThis can be found by following the argument that Prof Strang makes in this video: https://youtu.be/rYz83XPxiZo?t=1177 (Skip to 19:37). \nThe problem is that here the eigenvectors of U that we found are [1, 0]' and [0, 1]', but they should be [1, 0]' and [0, -1]'.\nThe negative in the 2nd eigenvector allows the scaling term (sigma) to be strictly positive. \n\nLet S = Sigma (for ease of typing).\nI think the main problem is that the general form A = U*S*V' does not mathematically enforce that S should be a strictly positive matrix.\nSo even though A'A and AA' will output the squares of the eigenvalues, simply choosing the positive roots is not enough.\nWe would need to choose the right sign for the eigenvector that corresponds to the positive root. E.g. [1,0] and [-1,0] can both have the same eigenvalue, so we have to decide which to use.\nHence, we need to check the cases and manually negate the vectors in U or V so that S can be positive.\nHowever, if we follow what Prof Strang does in the video whose URL ive included in the earlier part of this comment, then this is accounted for by the computation." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk10.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..eb0e4d0cdf554a9ac84a1e3b655b16c9c12a75a5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 10, + "timestamp": 1684512534435.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Regarding the problem at 26:28\nIt would be solved if the matrix U was [1 0; 0 -1]. (Replace the 1 at the bottom right of the 2x2 identity with -1).\nThis can be found by following the argument that Prof Strang makes in this video: https://youtu.be/rYz83XPxiZo?t=1177 (Skip to 19:37). \nThe problem is that here the eigenvectors of U that we found are [1, 0]' and [0, 1]', but they should be [1, 0]' and [0, -1]'.\nThe negative in the 2nd eigenvector allows the scaling term (sigma) to be strictly positive. \n\nLet S = Sigma (for ease of typing).\nI think the main problem is that the general form A = U*S*V' does not mathematically enforce that S should be a strictly positive matrix.\nSo even though A'A and AA' will output the squares of the eigenvalues, simply choosing the positive roots is not enough.\nWe would need to choose the right sign for the eigenvector that corresponds to the positive root. E.g. [1,0] and [-1,0] can both have the same eigenvalue, so we have to decide which to use.\nHence, we need to check the cases and manually negate the vectors in U or V so that S can be positive.\nHowever, if we follow what Prof Strang does in the video whose URL ive included in the earlier part of this comment, then this is accounted for by the computation." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk11.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..eb0e4d0cdf554a9ac84a1e3b655b16c9c12a75a5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 10, + "timestamp": 1684512534435.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Regarding the problem at 26:28\nIt would be solved if the matrix U was [1 0; 0 -1]. (Replace the 1 at the bottom right of the 2x2 identity with -1).\nThis can be found by following the argument that Prof Strang makes in this video: https://youtu.be/rYz83XPxiZo?t=1177 (Skip to 19:37). \nThe problem is that here the eigenvectors of U that we found are [1, 0]' and [0, 1]', but they should be [1, 0]' and [0, -1]'.\nThe negative in the 2nd eigenvector allows the scaling term (sigma) to be strictly positive. \n\nLet S = Sigma (for ease of typing).\nI think the main problem is that the general form A = U*S*V' does not mathematically enforce that S should be a strictly positive matrix.\nSo even though A'A and AA' will output the squares of the eigenvalues, simply choosing the positive roots is not enough.\nWe would need to choose the right sign for the eigenvector that corresponds to the positive root. E.g. [1,0] and [-1,0] can both have the same eigenvalue, so we have to decide which to use.\nHence, we need to check the cases and manually negate the vectors in U or V so that S can be positive.\nHowever, if we follow what Prof Strang does in the video whose URL ive included in the earlier part of this comment, then this is accounted for by the computation." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk12.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..eb0e4d0cdf554a9ac84a1e3b655b16c9c12a75a5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 10, + "timestamp": 1684512534435.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Regarding the problem at 26:28\nIt would be solved if the matrix U was [1 0; 0 -1]. (Replace the 1 at the bottom right of the 2x2 identity with -1).\nThis can be found by following the argument that Prof Strang makes in this video: https://youtu.be/rYz83XPxiZo?t=1177 (Skip to 19:37). \nThe problem is that here the eigenvectors of U that we found are [1, 0]' and [0, 1]', but they should be [1, 0]' and [0, -1]'.\nThe negative in the 2nd eigenvector allows the scaling term (sigma) to be strictly positive. \n\nLet S = Sigma (for ease of typing).\nI think the main problem is that the general form A = U*S*V' does not mathematically enforce that S should be a strictly positive matrix.\nSo even though A'A and AA' will output the squares of the eigenvalues, simply choosing the positive roots is not enough.\nWe would need to choose the right sign for the eigenvector that corresponds to the positive root. E.g. [1,0] and [-1,0] can both have the same eigenvalue, so we have to decide which to use.\nHence, we need to check the cases and manually negate the vectors in U or V so that S can be positive.\nHowever, if we follow what Prof Strang does in the video whose URL ive included in the earlier part of this comment, then this is accounted for by the computation." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk13.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..948638788b6ad6412741c25a0802428f776b521e --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk13.json @@ -0,0 +1,16 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 10, + "timestamp": 1684512534435.0, + "annotatedSourceSentencesIndices": [ + 5, + 6, + 7 + ], + "names": [ + "annotator1" + ], + "text": "Regarding the problem at 26:28\nIt would be solved if the matrix U was [1 0; 0 -1]. (Replace the 1 at the bottom right of the 2x2 identity with -1).\nThis can be found by following the argument that Prof Strang makes in this video: https://youtu.be/rYz83XPxiZo?t=1177 (Skip to 19:37). \nThe problem is that here the eigenvectors of U that we found are [1, 0]' and [0, 1]', but they should be [1, 0]' and [0, -1]'.\nThe negative in the 2nd eigenvector allows the scaling term (sigma) to be strictly positive. \n\nLet S = Sigma (for ease of typing).\nI think the main problem is that the general form A = U*S*V' does not mathematically enforce that S should be a strictly positive matrix.\nSo even though A'A and AA' will output the squares of the eigenvalues, simply choosing the positive roots is not enough.\nWe would need to choose the right sign for the eigenvector that corresponds to the positive root. E.g. [1,0] and [-1,0] can both have the same eigenvalue, so we have to decide which to use.\nHence, we need to check the cases and manually negate the vectors in U or V so that S can be positive.\nHowever, if we follow what Prof Strang does in the video whose URL ive included in the earlier part of this comment, then this is accounted for by the computation." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk14.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..eb0e4d0cdf554a9ac84a1e3b655b16c9c12a75a5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 10, + "timestamp": 1684512534435.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Regarding the problem at 26:28\nIt would be solved if the matrix U was [1 0; 0 -1]. (Replace the 1 at the bottom right of the 2x2 identity with -1).\nThis can be found by following the argument that Prof Strang makes in this video: https://youtu.be/rYz83XPxiZo?t=1177 (Skip to 19:37). \nThe problem is that here the eigenvectors of U that we found are [1, 0]' and [0, 1]', but they should be [1, 0]' and [0, -1]'.\nThe negative in the 2nd eigenvector allows the scaling term (sigma) to be strictly positive. \n\nLet S = Sigma (for ease of typing).\nI think the main problem is that the general form A = U*S*V' does not mathematically enforce that S should be a strictly positive matrix.\nSo even though A'A and AA' will output the squares of the eigenvalues, simply choosing the positive roots is not enough.\nWe would need to choose the right sign for the eigenvector that corresponds to the positive root. E.g. [1,0] and [-1,0] can both have the same eigenvalue, so we have to decide which to use.\nHence, we need to check the cases and manually negate the vectors in U or V so that S can be positive.\nHowever, if we follow what Prof Strang does in the video whose URL ive included in the earlier part of this comment, then this is accounted for by the computation." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk15.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eb0e4d0cdf554a9ac84a1e3b655b16c9c12a75a5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 10, + "timestamp": 1684512534435.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Regarding the problem at 26:28\nIt would be solved if the matrix U was [1 0; 0 -1]. (Replace the 1 at the bottom right of the 2x2 identity with -1).\nThis can be found by following the argument that Prof Strang makes in this video: https://youtu.be/rYz83XPxiZo?t=1177 (Skip to 19:37). \nThe problem is that here the eigenvectors of U that we found are [1, 0]' and [0, 1]', but they should be [1, 0]' and [0, -1]'.\nThe negative in the 2nd eigenvector allows the scaling term (sigma) to be strictly positive. \n\nLet S = Sigma (for ease of typing).\nI think the main problem is that the general form A = U*S*V' does not mathematically enforce that S should be a strictly positive matrix.\nSo even though A'A and AA' will output the squares of the eigenvalues, simply choosing the positive roots is not enough.\nWe would need to choose the right sign for the eigenvector that corresponds to the positive root. E.g. [1,0] and [-1,0] can both have the same eigenvalue, so we have to decide which to use.\nHence, we need to check the cases and manually negate the vectors in U or V so that S can be positive.\nHowever, if we follow what Prof Strang does in the video whose URL ive included in the earlier part of this comment, then this is accounted for by the computation." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk16.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..eb0e4d0cdf554a9ac84a1e3b655b16c9c12a75a5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 10, + "timestamp": 1684512534435.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Regarding the problem at 26:28\nIt would be solved if the matrix U was [1 0; 0 -1]. (Replace the 1 at the bottom right of the 2x2 identity with -1).\nThis can be found by following the argument that Prof Strang makes in this video: https://youtu.be/rYz83XPxiZo?t=1177 (Skip to 19:37). \nThe problem is that here the eigenvectors of U that we found are [1, 0]' and [0, 1]', but they should be [1, 0]' and [0, -1]'.\nThe negative in the 2nd eigenvector allows the scaling term (sigma) to be strictly positive. \n\nLet S = Sigma (for ease of typing).\nI think the main problem is that the general form A = U*S*V' does not mathematically enforce that S should be a strictly positive matrix.\nSo even though A'A and AA' will output the squares of the eigenvalues, simply choosing the positive roots is not enough.\nWe would need to choose the right sign for the eigenvector that corresponds to the positive root. E.g. [1,0] and [-1,0] can both have the same eigenvalue, so we have to decide which to use.\nHence, we need to check the cases and manually negate the vectors in U or V so that S can be positive.\nHowever, if we follow what Prof Strang does in the video whose URL ive included in the earlier part of this comment, then this is accounted for by the computation." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk17.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..eb0e4d0cdf554a9ac84a1e3b655b16c9c12a75a5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 10, + "timestamp": 1684512534435.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Regarding the problem at 26:28\nIt would be solved if the matrix U was [1 0; 0 -1]. (Replace the 1 at the bottom right of the 2x2 identity with -1).\nThis can be found by following the argument that Prof Strang makes in this video: https://youtu.be/rYz83XPxiZo?t=1177 (Skip to 19:37). \nThe problem is that here the eigenvectors of U that we found are [1, 0]' and [0, 1]', but they should be [1, 0]' and [0, -1]'.\nThe negative in the 2nd eigenvector allows the scaling term (sigma) to be strictly positive. \n\nLet S = Sigma (for ease of typing).\nI think the main problem is that the general form A = U*S*V' does not mathematically enforce that S should be a strictly positive matrix.\nSo even though A'A and AA' will output the squares of the eigenvalues, simply choosing the positive roots is not enough.\nWe would need to choose the right sign for the eigenvector that corresponds to the positive root. E.g. [1,0] and [-1,0] can both have the same eigenvalue, so we have to decide which to use.\nHence, we need to check the cases and manually negate the vectors in U or V so that S can be positive.\nHowever, if we follow what Prof Strang does in the video whose URL ive included in the earlier part of this comment, then this is accounted for by the computation." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk18.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..eb0e4d0cdf554a9ac84a1e3b655b16c9c12a75a5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 10, + "timestamp": 1684512534435.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Regarding the problem at 26:28\nIt would be solved if the matrix U was [1 0; 0 -1]. (Replace the 1 at the bottom right of the 2x2 identity with -1).\nThis can be found by following the argument that Prof Strang makes in this video: https://youtu.be/rYz83XPxiZo?t=1177 (Skip to 19:37). \nThe problem is that here the eigenvectors of U that we found are [1, 0]' and [0, 1]', but they should be [1, 0]' and [0, -1]'.\nThe negative in the 2nd eigenvector allows the scaling term (sigma) to be strictly positive. \n\nLet S = Sigma (for ease of typing).\nI think the main problem is that the general form A = U*S*V' does not mathematically enforce that S should be a strictly positive matrix.\nSo even though A'A and AA' will output the squares of the eigenvalues, simply choosing the positive roots is not enough.\nWe would need to choose the right sign for the eigenvector that corresponds to the positive root. E.g. [1,0] and [-1,0] can both have the same eigenvalue, so we have to decide which to use.\nHence, we need to check the cases and manually negate the vectors in U or V so that S can be positive.\nHowever, if we follow what Prof Strang does in the video whose URL ive included in the earlier part of this comment, then this is accounted for by the computation." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk19.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..eb0e4d0cdf554a9ac84a1e3b655b16c9c12a75a5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 10, + "timestamp": 1684512534435.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Regarding the problem at 26:28\nIt would be solved if the matrix U was [1 0; 0 -1]. (Replace the 1 at the bottom right of the 2x2 identity with -1).\nThis can be found by following the argument that Prof Strang makes in this video: https://youtu.be/rYz83XPxiZo?t=1177 (Skip to 19:37). \nThe problem is that here the eigenvectors of U that we found are [1, 0]' and [0, 1]', but they should be [1, 0]' and [0, -1]'.\nThe negative in the 2nd eigenvector allows the scaling term (sigma) to be strictly positive. \n\nLet S = Sigma (for ease of typing).\nI think the main problem is that the general form A = U*S*V' does not mathematically enforce that S should be a strictly positive matrix.\nSo even though A'A and AA' will output the squares of the eigenvalues, simply choosing the positive roots is not enough.\nWe would need to choose the right sign for the eigenvector that corresponds to the positive root. E.g. [1,0] and [-1,0] can both have the same eigenvalue, so we have to decide which to use.\nHence, we need to check the cases and manually negate the vectors in U or V so that S can be positive.\nHowever, if we follow what Prof Strang does in the video whose URL ive included in the earlier part of this comment, then this is accounted for by the computation." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk2.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..eb0e4d0cdf554a9ac84a1e3b655b16c9c12a75a5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 10, + "timestamp": 1684512534435.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Regarding the problem at 26:28\nIt would be solved if the matrix U was [1 0; 0 -1]. (Replace the 1 at the bottom right of the 2x2 identity with -1).\nThis can be found by following the argument that Prof Strang makes in this video: https://youtu.be/rYz83XPxiZo?t=1177 (Skip to 19:37). \nThe problem is that here the eigenvectors of U that we found are [1, 0]' and [0, 1]', but they should be [1, 0]' and [0, -1]'.\nThe negative in the 2nd eigenvector allows the scaling term (sigma) to be strictly positive. \n\nLet S = Sigma (for ease of typing).\nI think the main problem is that the general form A = U*S*V' does not mathematically enforce that S should be a strictly positive matrix.\nSo even though A'A and AA' will output the squares of the eigenvalues, simply choosing the positive roots is not enough.\nWe would need to choose the right sign for the eigenvector that corresponds to the positive root. E.g. [1,0] and [-1,0] can both have the same eigenvalue, so we have to decide which to use.\nHence, we need to check the cases and manually negate the vectors in U or V so that S can be positive.\nHowever, if we follow what Prof Strang does in the video whose URL ive included in the earlier part of this comment, then this is accounted for by the computation." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk3.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..eb0e4d0cdf554a9ac84a1e3b655b16c9c12a75a5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 10, + "timestamp": 1684512534435.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Regarding the problem at 26:28\nIt would be solved if the matrix U was [1 0; 0 -1]. (Replace the 1 at the bottom right of the 2x2 identity with -1).\nThis can be found by following the argument that Prof Strang makes in this video: https://youtu.be/rYz83XPxiZo?t=1177 (Skip to 19:37). \nThe problem is that here the eigenvectors of U that we found are [1, 0]' and [0, 1]', but they should be [1, 0]' and [0, -1]'.\nThe negative in the 2nd eigenvector allows the scaling term (sigma) to be strictly positive. \n\nLet S = Sigma (for ease of typing).\nI think the main problem is that the general form A = U*S*V' does not mathematically enforce that S should be a strictly positive matrix.\nSo even though A'A and AA' will output the squares of the eigenvalues, simply choosing the positive roots is not enough.\nWe would need to choose the right sign for the eigenvector that corresponds to the positive root. E.g. [1,0] and [-1,0] can both have the same eigenvalue, so we have to decide which to use.\nHence, we need to check the cases and manually negate the vectors in U or V so that S can be positive.\nHowever, if we follow what Prof Strang does in the video whose URL ive included in the earlier part of this comment, then this is accounted for by the computation." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk4.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..eb0e4d0cdf554a9ac84a1e3b655b16c9c12a75a5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 10, + "timestamp": 1684512534435.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Regarding the problem at 26:28\nIt would be solved if the matrix U was [1 0; 0 -1]. (Replace the 1 at the bottom right of the 2x2 identity with -1).\nThis can be found by following the argument that Prof Strang makes in this video: https://youtu.be/rYz83XPxiZo?t=1177 (Skip to 19:37). \nThe problem is that here the eigenvectors of U that we found are [1, 0]' and [0, 1]', but they should be [1, 0]' and [0, -1]'.\nThe negative in the 2nd eigenvector allows the scaling term (sigma) to be strictly positive. \n\nLet S = Sigma (for ease of typing).\nI think the main problem is that the general form A = U*S*V' does not mathematically enforce that S should be a strictly positive matrix.\nSo even though A'A and AA' will output the squares of the eigenvalues, simply choosing the positive roots is not enough.\nWe would need to choose the right sign for the eigenvector that corresponds to the positive root. E.g. [1,0] and [-1,0] can both have the same eigenvalue, so we have to decide which to use.\nHence, we need to check the cases and manually negate the vectors in U or V so that S can be positive.\nHowever, if we follow what Prof Strang does in the video whose URL ive included in the earlier part of this comment, then this is accounted for by the computation." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk5.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb0e4d0cdf554a9ac84a1e3b655b16c9c12a75a5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 10, + "timestamp": 1684512534435.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Regarding the problem at 26:28\nIt would be solved if the matrix U was [1 0; 0 -1]. (Replace the 1 at the bottom right of the 2x2 identity with -1).\nThis can be found by following the argument that Prof Strang makes in this video: https://youtu.be/rYz83XPxiZo?t=1177 (Skip to 19:37). \nThe problem is that here the eigenvectors of U that we found are [1, 0]' and [0, 1]', but they should be [1, 0]' and [0, -1]'.\nThe negative in the 2nd eigenvector allows the scaling term (sigma) to be strictly positive. \n\nLet S = Sigma (for ease of typing).\nI think the main problem is that the general form A = U*S*V' does not mathematically enforce that S should be a strictly positive matrix.\nSo even though A'A and AA' will output the squares of the eigenvalues, simply choosing the positive roots is not enough.\nWe would need to choose the right sign for the eigenvector that corresponds to the positive root. E.g. [1,0] and [-1,0] can both have the same eigenvalue, so we have to decide which to use.\nHence, we need to check the cases and manually negate the vectors in U or V so that S can be positive.\nHowever, if we follow what Prof Strang does in the video whose URL ive included in the earlier part of this comment, then this is accounted for by the computation." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk6.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..eb0e4d0cdf554a9ac84a1e3b655b16c9c12a75a5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 10, + "timestamp": 1684512534435.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Regarding the problem at 26:28\nIt would be solved if the matrix U was [1 0; 0 -1]. (Replace the 1 at the bottom right of the 2x2 identity with -1).\nThis can be found by following the argument that Prof Strang makes in this video: https://youtu.be/rYz83XPxiZo?t=1177 (Skip to 19:37). \nThe problem is that here the eigenvectors of U that we found are [1, 0]' and [0, 1]', but they should be [1, 0]' and [0, -1]'.\nThe negative in the 2nd eigenvector allows the scaling term (sigma) to be strictly positive. \n\nLet S = Sigma (for ease of typing).\nI think the main problem is that the general form A = U*S*V' does not mathematically enforce that S should be a strictly positive matrix.\nSo even though A'A and AA' will output the squares of the eigenvalues, simply choosing the positive roots is not enough.\nWe would need to choose the right sign for the eigenvector that corresponds to the positive root. E.g. [1,0] and [-1,0] can both have the same eigenvalue, so we have to decide which to use.\nHence, we need to check the cases and manually negate the vectors in U or V so that S can be positive.\nHowever, if we follow what Prof Strang does in the video whose URL ive included in the earlier part of this comment, then this is accounted for by the computation." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk7.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..eb0e4d0cdf554a9ac84a1e3b655b16c9c12a75a5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 10, + "timestamp": 1684512534435.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Regarding the problem at 26:28\nIt would be solved if the matrix U was [1 0; 0 -1]. (Replace the 1 at the bottom right of the 2x2 identity with -1).\nThis can be found by following the argument that Prof Strang makes in this video: https://youtu.be/rYz83XPxiZo?t=1177 (Skip to 19:37). \nThe problem is that here the eigenvectors of U that we found are [1, 0]' and [0, 1]', but they should be [1, 0]' and [0, -1]'.\nThe negative in the 2nd eigenvector allows the scaling term (sigma) to be strictly positive. \n\nLet S = Sigma (for ease of typing).\nI think the main problem is that the general form A = U*S*V' does not mathematically enforce that S should be a strictly positive matrix.\nSo even though A'A and AA' will output the squares of the eigenvalues, simply choosing the positive roots is not enough.\nWe would need to choose the right sign for the eigenvector that corresponds to the positive root. E.g. [1,0] and [-1,0] can both have the same eigenvalue, so we have to decide which to use.\nHence, we need to check the cases and manually negate the vectors in U or V so that S can be positive.\nHowever, if we follow what Prof Strang does in the video whose URL ive included in the earlier part of this comment, then this is accounted for by the computation." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk8.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..eb0e4d0cdf554a9ac84a1e3b655b16c9c12a75a5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 10, + "timestamp": 1684512534435.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Regarding the problem at 26:28\nIt would be solved if the matrix U was [1 0; 0 -1]. (Replace the 1 at the bottom right of the 2x2 identity with -1).\nThis can be found by following the argument that Prof Strang makes in this video: https://youtu.be/rYz83XPxiZo?t=1177 (Skip to 19:37). \nThe problem is that here the eigenvectors of U that we found are [1, 0]' and [0, 1]', but they should be [1, 0]' and [0, -1]'.\nThe negative in the 2nd eigenvector allows the scaling term (sigma) to be strictly positive. \n\nLet S = Sigma (for ease of typing).\nI think the main problem is that the general form A = U*S*V' does not mathematically enforce that S should be a strictly positive matrix.\nSo even though A'A and AA' will output the squares of the eigenvalues, simply choosing the positive roots is not enough.\nWe would need to choose the right sign for the eigenvector that corresponds to the positive root. E.g. [1,0] and [-1,0] can both have the same eigenvalue, so we have to decide which to use.\nHence, we need to check the cases and manually negate the vectors in U or V so that S can be positive.\nHowever, if we follow what Prof Strang does in the video whose URL ive included in the earlier part of this comment, then this is accounted for by the computation." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk9.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..eb0e4d0cdf554a9ac84a1e3b655b16c9c12a75a5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_10_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 10, + "timestamp": 1684512534435.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Regarding the problem at 26:28\nIt would be solved if the matrix U was [1 0; 0 -1]. (Replace the 1 at the bottom right of the 2x2 identity with -1).\nThis can be found by following the argument that Prof Strang makes in this video: https://youtu.be/rYz83XPxiZo?t=1177 (Skip to 19:37). \nThe problem is that here the eigenvectors of U that we found are [1, 0]' and [0, 1]', but they should be [1, 0]' and [0, -1]'.\nThe negative in the 2nd eigenvector allows the scaling term (sigma) to be strictly positive. \n\nLet S = Sigma (for ease of typing).\nI think the main problem is that the general form A = U*S*V' does not mathematically enforce that S should be a strictly positive matrix.\nSo even though A'A and AA' will output the squares of the eigenvalues, simply choosing the positive roots is not enough.\nWe would need to choose the right sign for the eigenvector that corresponds to the positive root. E.g. [1,0] and [-1,0] can both have the same eigenvalue, so we have to decide which to use.\nHence, we need to check the cases and manually negate the vectors in U or V so that S can be positive.\nHowever, if we follow what Prof Strang does in the video whose URL ive included in the earlier part of this comment, then this is accounted for by the computation." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk0.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..fbabade74419d05d2ed6ee623feb6130ef0f2904 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 1, + "timestamp": 1684512167597.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "@ 26:04 I have to admit, that took me a second to figure it out. \nProf Strang didn't actually have anything wrong, he just couldn't see while in the middle of it why that was the case. He actually had it at 26:44 but let it slip through his hands.\nFor that you have to go back to when he was computing matrix \"V\". The evec associated with eval of 18 was [1;-1] but it also can be written as [-1;1]\n\nHe chose the [1;-1] which had the effect once we made it to the final calculation of U * Diag^2 * V^t that it SWAPPED THE COLUMNS of A\nHis original A was [4,4;-3,3] and the calc'd one was [4,4;3,-3]\nHad he chosen the 'other version' of the evec associated with Lambda = 18 when figuring out \"V\", he would have gotten back the same \"A\" he started with instead of the column-swapped version.\nBut what could go wrong? :-)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk1.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..fbabade74419d05d2ed6ee623feb6130ef0f2904 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 1, + "timestamp": 1684512167597.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "@ 26:04 I have to admit, that took me a second to figure it out. \nProf Strang didn't actually have anything wrong, he just couldn't see while in the middle of it why that was the case. He actually had it at 26:44 but let it slip through his hands.\nFor that you have to go back to when he was computing matrix \"V\". The evec associated with eval of 18 was [1;-1] but it also can be written as [-1;1]\n\nHe chose the [1;-1] which had the effect once we made it to the final calculation of U * Diag^2 * V^t that it SWAPPED THE COLUMNS of A\nHis original A was [4,4;-3,3] and the calc'd one was [4,4;3,-3]\nHad he chosen the 'other version' of the evec associated with Lambda = 18 when figuring out \"V\", he would have gotten back the same \"A\" he started with instead of the column-swapped version.\nBut what could go wrong? :-)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk10.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..fbabade74419d05d2ed6ee623feb6130ef0f2904 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 1, + "timestamp": 1684512167597.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "@ 26:04 I have to admit, that took me a second to figure it out. \nProf Strang didn't actually have anything wrong, he just couldn't see while in the middle of it why that was the case. He actually had it at 26:44 but let it slip through his hands.\nFor that you have to go back to when he was computing matrix \"V\". The evec associated with eval of 18 was [1;-1] but it also can be written as [-1;1]\n\nHe chose the [1;-1] which had the effect once we made it to the final calculation of U * Diag^2 * V^t that it SWAPPED THE COLUMNS of A\nHis original A was [4,4;-3,3] and the calc'd one was [4,4;3,-3]\nHad he chosen the 'other version' of the evec associated with Lambda = 18 when figuring out \"V\", he would have gotten back the same \"A\" he started with instead of the column-swapped version.\nBut what could go wrong? :-)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk11.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..fbabade74419d05d2ed6ee623feb6130ef0f2904 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 1, + "timestamp": 1684512167597.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "@ 26:04 I have to admit, that took me a second to figure it out. \nProf Strang didn't actually have anything wrong, he just couldn't see while in the middle of it why that was the case. He actually had it at 26:44 but let it slip through his hands.\nFor that you have to go back to when he was computing matrix \"V\". The evec associated with eval of 18 was [1;-1] but it also can be written as [-1;1]\n\nHe chose the [1;-1] which had the effect once we made it to the final calculation of U * Diag^2 * V^t that it SWAPPED THE COLUMNS of A\nHis original A was [4,4;-3,3] and the calc'd one was [4,4;3,-3]\nHad he chosen the 'other version' of the evec associated with Lambda = 18 when figuring out \"V\", he would have gotten back the same \"A\" he started with instead of the column-swapped version.\nBut what could go wrong? :-)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk12.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..fbabade74419d05d2ed6ee623feb6130ef0f2904 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 1, + "timestamp": 1684512167597.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "@ 26:04 I have to admit, that took me a second to figure it out. \nProf Strang didn't actually have anything wrong, he just couldn't see while in the middle of it why that was the case. He actually had it at 26:44 but let it slip through his hands.\nFor that you have to go back to when he was computing matrix \"V\". The evec associated with eval of 18 was [1;-1] but it also can be written as [-1;1]\n\nHe chose the [1;-1] which had the effect once we made it to the final calculation of U * Diag^2 * V^t that it SWAPPED THE COLUMNS of A\nHis original A was [4,4;-3,3] and the calc'd one was [4,4;3,-3]\nHad he chosen the 'other version' of the evec associated with Lambda = 18 when figuring out \"V\", he would have gotten back the same \"A\" he started with instead of the column-swapped version.\nBut what could go wrong? :-)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk13.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..b1a2b5c267f28668c4d39be952ff21117c12bc4b --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk13.json @@ -0,0 +1,22 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 1, + "timestamp": 1684512167597.0, + "annotatedSourceSentencesIndices": [ + 1, + 2, + 3, + 4, + 5, + 6, + 10, + 11, + 18 + ], + "names": [ + "annotator1" + ], + "text": "@ 26:04 I have to admit, that took me a second to figure it out. \nProf Strang didn't actually have anything wrong, he just couldn't see while in the middle of it why that was the case. He actually had it at 26:44 but let it slip through his hands.\nFor that you have to go back to when he was computing matrix \"V\". The evec associated with eval of 18 was [1;-1] but it also can be written as [-1;1]\n\nHe chose the [1;-1] which had the effect once we made it to the final calculation of U * Diag^2 * V^t that it SWAPPED THE COLUMNS of A\nHis original A was [4,4;-3,3] and the calc'd one was [4,4;3,-3]\nHad he chosen the 'other version' of the evec associated with Lambda = 18 when figuring out \"V\", he would have gotten back the same \"A\" he started with instead of the column-swapped version.\nBut what could go wrong? :-)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk14.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..fbabade74419d05d2ed6ee623feb6130ef0f2904 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 1, + "timestamp": 1684512167597.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "@ 26:04 I have to admit, that took me a second to figure it out. \nProf Strang didn't actually have anything wrong, he just couldn't see while in the middle of it why that was the case. He actually had it at 26:44 but let it slip through his hands.\nFor that you have to go back to when he was computing matrix \"V\". The evec associated with eval of 18 was [1;-1] but it also can be written as [-1;1]\n\nHe chose the [1;-1] which had the effect once we made it to the final calculation of U * Diag^2 * V^t that it SWAPPED THE COLUMNS of A\nHis original A was [4,4;-3,3] and the calc'd one was [4,4;3,-3]\nHad he chosen the 'other version' of the evec associated with Lambda = 18 when figuring out \"V\", he would have gotten back the same \"A\" he started with instead of the column-swapped version.\nBut what could go wrong? :-)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk15.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..fbabade74419d05d2ed6ee623feb6130ef0f2904 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 1, + "timestamp": 1684512167597.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "@ 26:04 I have to admit, that took me a second to figure it out. \nProf Strang didn't actually have anything wrong, he just couldn't see while in the middle of it why that was the case. He actually had it at 26:44 but let it slip through his hands.\nFor that you have to go back to when he was computing matrix \"V\". The evec associated with eval of 18 was [1;-1] but it also can be written as [-1;1]\n\nHe chose the [1;-1] which had the effect once we made it to the final calculation of U * Diag^2 * V^t that it SWAPPED THE COLUMNS of A\nHis original A was [4,4;-3,3] and the calc'd one was [4,4;3,-3]\nHad he chosen the 'other version' of the evec associated with Lambda = 18 when figuring out \"V\", he would have gotten back the same \"A\" he started with instead of the column-swapped version.\nBut what could go wrong? :-)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk16.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..fbabade74419d05d2ed6ee623feb6130ef0f2904 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 1, + "timestamp": 1684512167597.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "@ 26:04 I have to admit, that took me a second to figure it out. \nProf Strang didn't actually have anything wrong, he just couldn't see while in the middle of it why that was the case. He actually had it at 26:44 but let it slip through his hands.\nFor that you have to go back to when he was computing matrix \"V\". The evec associated with eval of 18 was [1;-1] but it also can be written as [-1;1]\n\nHe chose the [1;-1] which had the effect once we made it to the final calculation of U * Diag^2 * V^t that it SWAPPED THE COLUMNS of A\nHis original A was [4,4;-3,3] and the calc'd one was [4,4;3,-3]\nHad he chosen the 'other version' of the evec associated with Lambda = 18 when figuring out \"V\", he would have gotten back the same \"A\" he started with instead of the column-swapped version.\nBut what could go wrong? :-)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk17.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..fbabade74419d05d2ed6ee623feb6130ef0f2904 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 1, + "timestamp": 1684512167597.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "@ 26:04 I have to admit, that took me a second to figure it out. \nProf Strang didn't actually have anything wrong, he just couldn't see while in the middle of it why that was the case. He actually had it at 26:44 but let it slip through his hands.\nFor that you have to go back to when he was computing matrix \"V\". The evec associated with eval of 18 was [1;-1] but it also can be written as [-1;1]\n\nHe chose the [1;-1] which had the effect once we made it to the final calculation of U * Diag^2 * V^t that it SWAPPED THE COLUMNS of A\nHis original A was [4,4;-3,3] and the calc'd one was [4,4;3,-3]\nHad he chosen the 'other version' of the evec associated with Lambda = 18 when figuring out \"V\", he would have gotten back the same \"A\" he started with instead of the column-swapped version.\nBut what could go wrong? :-)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk18.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..fbabade74419d05d2ed6ee623feb6130ef0f2904 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 1, + "timestamp": 1684512167597.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "@ 26:04 I have to admit, that took me a second to figure it out. \nProf Strang didn't actually have anything wrong, he just couldn't see while in the middle of it why that was the case. He actually had it at 26:44 but let it slip through his hands.\nFor that you have to go back to when he was computing matrix \"V\". The evec associated with eval of 18 was [1;-1] but it also can be written as [-1;1]\n\nHe chose the [1;-1] which had the effect once we made it to the final calculation of U * Diag^2 * V^t that it SWAPPED THE COLUMNS of A\nHis original A was [4,4;-3,3] and the calc'd one was [4,4;3,-3]\nHad he chosen the 'other version' of the evec associated with Lambda = 18 when figuring out \"V\", he would have gotten back the same \"A\" he started with instead of the column-swapped version.\nBut what could go wrong? :-)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk19.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..fbabade74419d05d2ed6ee623feb6130ef0f2904 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 1, + "timestamp": 1684512167597.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "@ 26:04 I have to admit, that took me a second to figure it out. \nProf Strang didn't actually have anything wrong, he just couldn't see while in the middle of it why that was the case. He actually had it at 26:44 but let it slip through his hands.\nFor that you have to go back to when he was computing matrix \"V\". The evec associated with eval of 18 was [1;-1] but it also can be written as [-1;1]\n\nHe chose the [1;-1] which had the effect once we made it to the final calculation of U * Diag^2 * V^t that it SWAPPED THE COLUMNS of A\nHis original A was [4,4;-3,3] and the calc'd one was [4,4;3,-3]\nHad he chosen the 'other version' of the evec associated with Lambda = 18 when figuring out \"V\", he would have gotten back the same \"A\" he started with instead of the column-swapped version.\nBut what could go wrong? :-)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk2.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..fbabade74419d05d2ed6ee623feb6130ef0f2904 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 1, + "timestamp": 1684512167597.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "@ 26:04 I have to admit, that took me a second to figure it out. \nProf Strang didn't actually have anything wrong, he just couldn't see while in the middle of it why that was the case. He actually had it at 26:44 but let it slip through his hands.\nFor that you have to go back to when he was computing matrix \"V\". The evec associated with eval of 18 was [1;-1] but it also can be written as [-1;1]\n\nHe chose the [1;-1] which had the effect once we made it to the final calculation of U * Diag^2 * V^t that it SWAPPED THE COLUMNS of A\nHis original A was [4,4;-3,3] and the calc'd one was [4,4;3,-3]\nHad he chosen the 'other version' of the evec associated with Lambda = 18 when figuring out \"V\", he would have gotten back the same \"A\" he started with instead of the column-swapped version.\nBut what could go wrong? :-)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk3.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..fbabade74419d05d2ed6ee623feb6130ef0f2904 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 1, + "timestamp": 1684512167597.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "@ 26:04 I have to admit, that took me a second to figure it out. \nProf Strang didn't actually have anything wrong, he just couldn't see while in the middle of it why that was the case. He actually had it at 26:44 but let it slip through his hands.\nFor that you have to go back to when he was computing matrix \"V\". The evec associated with eval of 18 was [1;-1] but it also can be written as [-1;1]\n\nHe chose the [1;-1] which had the effect once we made it to the final calculation of U * Diag^2 * V^t that it SWAPPED THE COLUMNS of A\nHis original A was [4,4;-3,3] and the calc'd one was [4,4;3,-3]\nHad he chosen the 'other version' of the evec associated with Lambda = 18 when figuring out \"V\", he would have gotten back the same \"A\" he started with instead of the column-swapped version.\nBut what could go wrong? :-)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk4.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..fbabade74419d05d2ed6ee623feb6130ef0f2904 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 1, + "timestamp": 1684512167597.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "@ 26:04 I have to admit, that took me a second to figure it out. \nProf Strang didn't actually have anything wrong, he just couldn't see while in the middle of it why that was the case. He actually had it at 26:44 but let it slip through his hands.\nFor that you have to go back to when he was computing matrix \"V\". The evec associated with eval of 18 was [1;-1] but it also can be written as [-1;1]\n\nHe chose the [1;-1] which had the effect once we made it to the final calculation of U * Diag^2 * V^t that it SWAPPED THE COLUMNS of A\nHis original A was [4,4;-3,3] and the calc'd one was [4,4;3,-3]\nHad he chosen the 'other version' of the evec associated with Lambda = 18 when figuring out \"V\", he would have gotten back the same \"A\" he started with instead of the column-swapped version.\nBut what could go wrong? :-)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk5.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..fbabade74419d05d2ed6ee623feb6130ef0f2904 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 1, + "timestamp": 1684512167597.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "@ 26:04 I have to admit, that took me a second to figure it out. \nProf Strang didn't actually have anything wrong, he just couldn't see while in the middle of it why that was the case. He actually had it at 26:44 but let it slip through his hands.\nFor that you have to go back to when he was computing matrix \"V\". The evec associated with eval of 18 was [1;-1] but it also can be written as [-1;1]\n\nHe chose the [1;-1] which had the effect once we made it to the final calculation of U * Diag^2 * V^t that it SWAPPED THE COLUMNS of A\nHis original A was [4,4;-3,3] and the calc'd one was [4,4;3,-3]\nHad he chosen the 'other version' of the evec associated with Lambda = 18 when figuring out \"V\", he would have gotten back the same \"A\" he started with instead of the column-swapped version.\nBut what could go wrong? :-)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk6.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..fbabade74419d05d2ed6ee623feb6130ef0f2904 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 1, + "timestamp": 1684512167597.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "@ 26:04 I have to admit, that took me a second to figure it out. \nProf Strang didn't actually have anything wrong, he just couldn't see while in the middle of it why that was the case. He actually had it at 26:44 but let it slip through his hands.\nFor that you have to go back to when he was computing matrix \"V\". The evec associated with eval of 18 was [1;-1] but it also can be written as [-1;1]\n\nHe chose the [1;-1] which had the effect once we made it to the final calculation of U * Diag^2 * V^t that it SWAPPED THE COLUMNS of A\nHis original A was [4,4;-3,3] and the calc'd one was [4,4;3,-3]\nHad he chosen the 'other version' of the evec associated with Lambda = 18 when figuring out \"V\", he would have gotten back the same \"A\" he started with instead of the column-swapped version.\nBut what could go wrong? :-)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk7.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..fbabade74419d05d2ed6ee623feb6130ef0f2904 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 1, + "timestamp": 1684512167597.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "@ 26:04 I have to admit, that took me a second to figure it out. \nProf Strang didn't actually have anything wrong, he just couldn't see while in the middle of it why that was the case. He actually had it at 26:44 but let it slip through his hands.\nFor that you have to go back to when he was computing matrix \"V\". The evec associated with eval of 18 was [1;-1] but it also can be written as [-1;1]\n\nHe chose the [1;-1] which had the effect once we made it to the final calculation of U * Diag^2 * V^t that it SWAPPED THE COLUMNS of A\nHis original A was [4,4;-3,3] and the calc'd one was [4,4;3,-3]\nHad he chosen the 'other version' of the evec associated with Lambda = 18 when figuring out \"V\", he would have gotten back the same \"A\" he started with instead of the column-swapped version.\nBut what could go wrong? :-)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk8.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..fbabade74419d05d2ed6ee623feb6130ef0f2904 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 1, + "timestamp": 1684512167597.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "@ 26:04 I have to admit, that took me a second to figure it out. \nProf Strang didn't actually have anything wrong, he just couldn't see while in the middle of it why that was the case. He actually had it at 26:44 but let it slip through his hands.\nFor that you have to go back to when he was computing matrix \"V\". The evec associated with eval of 18 was [1;-1] but it also can be written as [-1;1]\n\nHe chose the [1;-1] which had the effect once we made it to the final calculation of U * Diag^2 * V^t that it SWAPPED THE COLUMNS of A\nHis original A was [4,4;-3,3] and the calc'd one was [4,4;3,-3]\nHad he chosen the 'other version' of the evec associated with Lambda = 18 when figuring out \"V\", he would have gotten back the same \"A\" he started with instead of the column-swapped version.\nBut what could go wrong? :-)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk9.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..fbabade74419d05d2ed6ee623feb6130ef0f2904 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_1_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 1, + "timestamp": 1684512167597.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "@ 26:04 I have to admit, that took me a second to figure it out. \nProf Strang didn't actually have anything wrong, he just couldn't see while in the middle of it why that was the case. He actually had it at 26:44 but let it slip through his hands.\nFor that you have to go back to when he was computing matrix \"V\". The evec associated with eval of 18 was [1;-1] but it also can be written as [-1;1]\n\nHe chose the [1;-1] which had the effect once we made it to the final calculation of U * Diag^2 * V^t that it SWAPPED THE COLUMNS of A\nHis original A was [4,4;-3,3] and the calc'd one was [4,4;3,-3]\nHad he chosen the 'other version' of the evec associated with Lambda = 18 when figuring out \"V\", he would have gotten back the same \"A\" he started with instead of the column-swapped version.\nBut what could go wrong? :-)" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk0.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..0da1e66e7e1e700efd23a7d9824f5cd31ccedbcd --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 2, + "timestamp": 1684512339083.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Professor Strang mentions that U and V form bases for the four fundamental subspaces of A, but it's not clear to me how C(A) = C(Ur) and C(A') = C (Vr'). I know that U and V were determined by the eigenvectors of AA' and A'A, respectively, but how are these related to the column and row spaces of A?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk1.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..0da1e66e7e1e700efd23a7d9824f5cd31ccedbcd --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 2, + "timestamp": 1684512339083.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Professor Strang mentions that U and V form bases for the four fundamental subspaces of A, but it's not clear to me how C(A) = C(Ur) and C(A') = C (Vr'). I know that U and V were determined by the eigenvectors of AA' and A'A, respectively, but how are these related to the column and row spaces of A?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk10.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..0da1e66e7e1e700efd23a7d9824f5cd31ccedbcd --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 2, + "timestamp": 1684512339083.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Professor Strang mentions that U and V form bases for the four fundamental subspaces of A, but it's not clear to me how C(A) = C(Ur) and C(A') = C (Vr'). I know that U and V were determined by the eigenvectors of AA' and A'A, respectively, but how are these related to the column and row spaces of A?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk11.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..0da1e66e7e1e700efd23a7d9824f5cd31ccedbcd --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 2, + "timestamp": 1684512339083.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Professor Strang mentions that U and V form bases for the four fundamental subspaces of A, but it's not clear to me how C(A) = C(Ur) and C(A') = C (Vr'). I know that U and V were determined by the eigenvectors of AA' and A'A, respectively, but how are these related to the column and row spaces of A?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk12.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0da1e66e7e1e700efd23a7d9824f5cd31ccedbcd --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 2, + "timestamp": 1684512339083.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Professor Strang mentions that U and V form bases for the four fundamental subspaces of A, but it's not clear to me how C(A) = C(Ur) and C(A') = C (Vr'). I know that U and V were determined by the eigenvectors of AA' and A'A, respectively, but how are these related to the column and row spaces of A?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk13.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..0da1e66e7e1e700efd23a7d9824f5cd31ccedbcd --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 2, + "timestamp": 1684512339083.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Professor Strang mentions that U and V form bases for the four fundamental subspaces of A, but it's not clear to me how C(A) = C(Ur) and C(A') = C (Vr'). I know that U and V were determined by the eigenvectors of AA' and A'A, respectively, but how are these related to the column and row spaces of A?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk14.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..0da1e66e7e1e700efd23a7d9824f5cd31ccedbcd --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 2, + "timestamp": 1684512339083.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Professor Strang mentions that U and V form bases for the four fundamental subspaces of A, but it's not clear to me how C(A) = C(Ur) and C(A') = C (Vr'). I know that U and V were determined by the eigenvectors of AA' and A'A, respectively, but how are these related to the column and row spaces of A?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk15.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..0da1e66e7e1e700efd23a7d9824f5cd31ccedbcd --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 2, + "timestamp": 1684512339083.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Professor Strang mentions that U and V form bases for the four fundamental subspaces of A, but it's not clear to me how C(A) = C(Ur) and C(A') = C (Vr'). I know that U and V were determined by the eigenvectors of AA' and A'A, respectively, but how are these related to the column and row spaces of A?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk16.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..0da1e66e7e1e700efd23a7d9824f5cd31ccedbcd --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 2, + "timestamp": 1684512339083.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Professor Strang mentions that U and V form bases for the four fundamental subspaces of A, but it's not clear to me how C(A) = C(Ur) and C(A') = C (Vr'). I know that U and V were determined by the eigenvectors of AA' and A'A, respectively, but how are these related to the column and row spaces of A?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk17.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..0da1e66e7e1e700efd23a7d9824f5cd31ccedbcd --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 2, + "timestamp": 1684512339083.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Professor Strang mentions that U and V form bases for the four fundamental subspaces of A, but it's not clear to me how C(A) = C(Ur) and C(A') = C (Vr'). I know that U and V were determined by the eigenvectors of AA' and A'A, respectively, but how are these related to the column and row spaces of A?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk18.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..0da1e66e7e1e700efd23a7d9824f5cd31ccedbcd --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 2, + "timestamp": 1684512339083.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Professor Strang mentions that U and V form bases for the four fundamental subspaces of A, but it's not clear to me how C(A) = C(Ur) and C(A') = C (Vr'). I know that U and V were determined by the eigenvectors of AA' and A'A, respectively, but how are these related to the column and row spaces of A?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk19.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..e2b82262f3ba0048afcde9d1ffb6fa21329d5b56 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk19.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 2, + "timestamp": 1684512339083.0, + "annotatedSourceSentencesIndices": [ + 1 + ], + "names": [ + "annotator1" + ], + "text": "Professor Strang mentions that U and V form bases for the four fundamental subspaces of A, but it's not clear to me how C(A) = C(Ur) and C(A') = C (Vr'). I know that U and V were determined by the eigenvectors of AA' and A'A, respectively, but how are these related to the column and row spaces of A?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk2.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..0da1e66e7e1e700efd23a7d9824f5cd31ccedbcd --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 2, + "timestamp": 1684512339083.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Professor Strang mentions that U and V form bases for the four fundamental subspaces of A, but it's not clear to me how C(A) = C(Ur) and C(A') = C (Vr'). I know that U and V were determined by the eigenvectors of AA' and A'A, respectively, but how are these related to the column and row spaces of A?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk3.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..0da1e66e7e1e700efd23a7d9824f5cd31ccedbcd --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 2, + "timestamp": 1684512339083.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Professor Strang mentions that U and V form bases for the four fundamental subspaces of A, but it's not clear to me how C(A) = C(Ur) and C(A') = C (Vr'). I know that U and V were determined by the eigenvectors of AA' and A'A, respectively, but how are these related to the column and row spaces of A?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk4.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0da1e66e7e1e700efd23a7d9824f5cd31ccedbcd --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 2, + "timestamp": 1684512339083.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Professor Strang mentions that U and V form bases for the four fundamental subspaces of A, but it's not clear to me how C(A) = C(Ur) and C(A') = C (Vr'). I know that U and V were determined by the eigenvectors of AA' and A'A, respectively, but how are these related to the column and row spaces of A?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk5.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..0da1e66e7e1e700efd23a7d9824f5cd31ccedbcd --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 2, + "timestamp": 1684512339083.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Professor Strang mentions that U and V form bases for the four fundamental subspaces of A, but it's not clear to me how C(A) = C(Ur) and C(A') = C (Vr'). I know that U and V were determined by the eigenvectors of AA' and A'A, respectively, but how are these related to the column and row spaces of A?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk6.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..0da1e66e7e1e700efd23a7d9824f5cd31ccedbcd --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 2, + "timestamp": 1684512339083.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Professor Strang mentions that U and V form bases for the four fundamental subspaces of A, but it's not clear to me how C(A) = C(Ur) and C(A') = C (Vr'). I know that U and V were determined by the eigenvectors of AA' and A'A, respectively, but how are these related to the column and row spaces of A?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk7.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0da1e66e7e1e700efd23a7d9824f5cd31ccedbcd --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 2, + "timestamp": 1684512339083.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Professor Strang mentions that U and V form bases for the four fundamental subspaces of A, but it's not clear to me how C(A) = C(Ur) and C(A') = C (Vr'). I know that U and V were determined by the eigenvectors of AA' and A'A, respectively, but how are these related to the column and row spaces of A?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk8.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..0da1e66e7e1e700efd23a7d9824f5cd31ccedbcd --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 2, + "timestamp": 1684512339083.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Professor Strang mentions that U and V form bases for the four fundamental subspaces of A, but it's not clear to me how C(A) = C(Ur) and C(A') = C (Vr'). I know that U and V were determined by the eigenvectors of AA' and A'A, respectively, but how are these related to the column and row spaces of A?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk9.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..0da1e66e7e1e700efd23a7d9824f5cd31ccedbcd --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_2_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 2, + "timestamp": 1684512339083.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Professor Strang mentions that U and V form bases for the four fundamental subspaces of A, but it's not clear to me how C(A) = C(Ur) and C(A') = C (Vr'). I know that U and V were determined by the eigenvectors of AA' and A'A, respectively, but how are these related to the column and row spaces of A?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_4_chunk0.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_4_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..00157422a98c9e0381189f68b8df733aa2396155 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_4_chunk0.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 4, + "timestamp": 1684192467807.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "how did we get 32 and 18 as squares of sigma1 and sigma2 ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_4_chunk1.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_4_chunk1.json new file mode 100644 index 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"text": "how did we get 32 and 18 as squares of sigma1 and sigma2 ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_4_chunk11.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_4_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..00157422a98c9e0381189f68b8df733aa2396155 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_4_chunk11.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 4, + "timestamp": 1684192467807.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "how did we get 32 and 18 as squares of sigma1 and sigma2 ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_4_chunk12.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_4_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..00157422a98c9e0381189f68b8df733aa2396155 --- 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"annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "how did we get 32 and 18 as squares of sigma1 and sigma2 ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_4_chunk4.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_4_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..00157422a98c9e0381189f68b8df733aa2396155 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_4_chunk4.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 4, + "timestamp": 1684192467807.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "how did we get 32 and 18 as squares of sigma1 and sigma2 ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_4_chunk5.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_4_chunk5.json new file mode 100644 index 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"text": "how did we get 32 and 18 as squares of sigma1 and sigma2 ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_4_chunk7.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_4_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..00157422a98c9e0381189f68b8df733aa2396155 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_4_chunk7.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 4, + "timestamp": 1684192467807.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "how did we get 32 and 18 as squares of sigma1 and sigma2 ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_4_chunk8.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_4_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..e2d274922a739fd8ec430d5ab4351b8f90c210bc --- 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?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk0.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..902d3382303c1332c4611d86ccfb6f34845f1510 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 7, + "timestamp": 1684512390426.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 20:35, why use the positive square roots instead of negative ones?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk1.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..902d3382303c1332c4611d86ccfb6f34845f1510 --- /dev/null +++ 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diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk11.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..902d3382303c1332c4611d86ccfb6f34845f1510 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 7, + "timestamp": 1684512390426.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 20:35, why use the positive square roots instead of negative ones?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk12.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..902d3382303c1332c4611d86ccfb6f34845f1510 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 7, + "timestamp": 1684512390426.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 20:35, why use the positive square roots instead of negative ones?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk13.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..902d3382303c1332c4611d86ccfb6f34845f1510 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 7, + "timestamp": 1684512390426.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 20:35, why use the positive square roots instead of negative ones?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk14.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..902d3382303c1332c4611d86ccfb6f34845f1510 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 7, + "timestamp": 1684512390426.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 20:35, why use the positive square roots instead of negative ones?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk15.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..902d3382303c1332c4611d86ccfb6f34845f1510 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 7, + "timestamp": 1684512390426.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 20:35, why use the positive square roots instead of negative ones?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk16.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..902d3382303c1332c4611d86ccfb6f34845f1510 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 7, + "timestamp": 1684512390426.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 20:35, why use the positive square roots instead of negative ones?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk17.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk17.json new file mode 100644 index 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use the positive square roots instead of negative ones?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk19.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..902d3382303c1332c4611d86ccfb6f34845f1510 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 7, + "timestamp": 1684512390426.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 20:35, why use the positive square roots instead of negative ones?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk2.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..902d3382303c1332c4611d86ccfb6f34845f1510 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 7, + "timestamp": 1684512390426.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 20:35, why use the positive square roots instead of negative ones?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk3.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..902d3382303c1332c4611d86ccfb6f34845f1510 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 7, + "timestamp": 1684512390426.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 20:35, why use the positive square roots instead of negative ones?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk4.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..902d3382303c1332c4611d86ccfb6f34845f1510 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 7, + "timestamp": 1684512390426.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 20:35, why use the positive square roots instead of negative ones?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk5.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..902d3382303c1332c4611d86ccfb6f34845f1510 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 7, + "timestamp": 1684512390426.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 20:35, why use the positive square roots instead of negative ones?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk6.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..902d3382303c1332c4611d86ccfb6f34845f1510 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 7, + "timestamp": 1684512390426.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 20:35, why use the positive square roots instead of negative ones?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk7.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..902d3382303c1332c4611d86ccfb6f34845f1510 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 7, + "timestamp": 1684512390426.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 20:35, why use the positive square roots instead of negative ones?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk8.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..902d3382303c1332c4611d86ccfb6f34845f1510 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 7, + "timestamp": 1684512390426.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 20:35, why use the positive square roots instead of negative ones?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk9.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..902d3382303c1332c4611d86ccfb6f34845f1510 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_7_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 7, + "timestamp": 1684512390426.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "at 20:35, why use the positive square roots instead of negative ones?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk0.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..f5eefbfc4541ac57b575a52709ab793a1c5a7606 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 8, + "timestamp": 1684512455481.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi, can anyone explain why 10:20 sigma_1 and sigma_2 greater than 0? Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk1.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..f5eefbfc4541ac57b575a52709ab793a1c5a7606 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 8, + "timestamp": 1684512455481.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi, can anyone explain why 10:20 sigma_1 and sigma_2 greater than 0? Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk10.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..f5eefbfc4541ac57b575a52709ab793a1c5a7606 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 8, + "timestamp": 1684512455481.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi, can anyone explain why 10:20 sigma_1 and sigma_2 greater than 0? Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk11.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..f5eefbfc4541ac57b575a52709ab793a1c5a7606 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 8, + "timestamp": 1684512455481.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi, can anyone explain why 10:20 sigma_1 and sigma_2 greater than 0? Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk12.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..f5eefbfc4541ac57b575a52709ab793a1c5a7606 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 8, + "timestamp": 1684512455481.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi, can anyone explain why 10:20 sigma_1 and sigma_2 greater than 0? Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk13.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..f5eefbfc4541ac57b575a52709ab793a1c5a7606 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 8, + "timestamp": 1684512455481.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi, can anyone explain why 10:20 sigma_1 and sigma_2 greater than 0? Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk14.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..f5eefbfc4541ac57b575a52709ab793a1c5a7606 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 8, + "timestamp": 1684512455481.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi, can anyone explain why 10:20 sigma_1 and sigma_2 greater than 0? Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk15.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..f5eefbfc4541ac57b575a52709ab793a1c5a7606 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 8, + "timestamp": 1684512455481.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi, can anyone explain why 10:20 sigma_1 and sigma_2 greater than 0? Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk16.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f5eefbfc4541ac57b575a52709ab793a1c5a7606 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 8, + "timestamp": 1684512455481.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi, can anyone explain why 10:20 sigma_1 and sigma_2 greater than 0? Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk17.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..f5eefbfc4541ac57b575a52709ab793a1c5a7606 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 8, + "timestamp": 1684512455481.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi, can anyone explain why 10:20 sigma_1 and sigma_2 greater than 0? Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk18.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..f5eefbfc4541ac57b575a52709ab793a1c5a7606 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 8, + "timestamp": 1684512455481.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi, can anyone explain why 10:20 sigma_1 and sigma_2 greater than 0? Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk19.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..f5eefbfc4541ac57b575a52709ab793a1c5a7606 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 8, + "timestamp": 1684512455481.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi, can anyone explain why 10:20 sigma_1 and sigma_2 greater than 0? Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk2.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..f5eefbfc4541ac57b575a52709ab793a1c5a7606 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 8, + "timestamp": 1684512455481.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi, can anyone explain why 10:20 sigma_1 and sigma_2 greater than 0? Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk3.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..f5eefbfc4541ac57b575a52709ab793a1c5a7606 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 8, + "timestamp": 1684512455481.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi, can anyone explain why 10:20 sigma_1 and sigma_2 greater than 0? Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk4.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..cbe80d5b7aa4ed7710a4d2b72205ab7c69ff54bd --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk4.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 8, + "timestamp": 1684512455481.0, + "annotatedSourceSentencesIndices": [ + 7 + ], + "names": [ + "annotator1" + ], + "text": "Hi, can anyone explain why 10:20 sigma_1 and sigma_2 greater than 0? Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk5.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..f5eefbfc4541ac57b575a52709ab793a1c5a7606 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 8, + "timestamp": 1684512455481.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi, can anyone explain why 10:20 sigma_1 and sigma_2 greater than 0? Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk6.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..f5eefbfc4541ac57b575a52709ab793a1c5a7606 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 8, + "timestamp": 1684512455481.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi, can anyone explain why 10:20 sigma_1 and sigma_2 greater than 0? Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk7.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..f5eefbfc4541ac57b575a52709ab793a1c5a7606 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 8, + "timestamp": 1684512455481.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi, can anyone explain why 10:20 sigma_1 and sigma_2 greater than 0? Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk8.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f5eefbfc4541ac57b575a52709ab793a1c5a7606 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 8, + "timestamp": 1684512455481.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi, can anyone explain why 10:20 sigma_1 and sigma_2 greater than 0? Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk9.json b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..f5eefbfc4541ac57b575a52709ab793a1c5a7606 --- /dev/null +++ b/sight/query/annotated_chunks_window20/TX_vooSnhm8_8_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "TX_vooSnhm8", + "query_id": 8, + "timestamp": 1684512455481.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Hi, can anyone explain why 10:20 sigma_1 and sigma_2 greater than 0? Thanks!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk0.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..60e8db448c856f17755fa06ebfc5799a985a7735 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk0.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 0, + "timestamp": 1684480825133.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "where can I find a complete derivation of the formula z=z0 + a(x-x0) + b(y-y0) using parametric equations as he suggested at 8:38? I tried to do what he said but no luck!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk1.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..60e8db448c856f17755fa06ebfc5799a985a7735 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk1.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 0, + "timestamp": 1684480825133.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "where can I find a complete derivation of the formula z=z0 + a(x-x0) + b(y-y0) using parametric equations as he suggested at 8:38? I tried to do what he said but no luck!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk10.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..60e8db448c856f17755fa06ebfc5799a985a7735 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk10.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 0, + "timestamp": 1684480825133.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "where can I find a complete derivation of the formula z=z0 + a(x-x0) + b(y-y0) using parametric equations as he suggested at 8:38? I tried to do what he said but no luck!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk11.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..60e8db448c856f17755fa06ebfc5799a985a7735 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk11.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 0, + "timestamp": 1684480825133.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "where can I find a complete derivation of the formula z=z0 + a(x-x0) + b(y-y0) using parametric equations as he suggested at 8:38? I tried to do what he said but no luck!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk12.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..60e8db448c856f17755fa06ebfc5799a985a7735 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk12.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 0, + "timestamp": 1684480825133.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "where can I find a complete derivation of the formula z=z0 + a(x-x0) + b(y-y0) using parametric equations as he suggested at 8:38? I tried to do what he said but no luck!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk13.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..60e8db448c856f17755fa06ebfc5799a985a7735 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk13.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 0, + "timestamp": 1684480825133.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "where can I find a complete derivation of the formula z=z0 + a(x-x0) + b(y-y0) using parametric equations as he suggested at 8:38? I tried to do what he said but no luck!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk14.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..60e8db448c856f17755fa06ebfc5799a985a7735 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk14.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 0, + "timestamp": 1684480825133.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "where can I find a complete derivation of the formula z=z0 + a(x-x0) + b(y-y0) using parametric equations as he suggested at 8:38? I tried to do what he said but no luck!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk15.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..60e8db448c856f17755fa06ebfc5799a985a7735 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk15.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 0, + "timestamp": 1684480825133.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "where can I find a complete derivation of the formula z=z0 + a(x-x0) + b(y-y0) using parametric equations as he suggested at 8:38? I tried to do what he said but no luck!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk16.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..60e8db448c856f17755fa06ebfc5799a985a7735 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk16.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 0, + "timestamp": 1684480825133.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "where can I find a complete derivation of the formula z=z0 + a(x-x0) + b(y-y0) using parametric equations as he suggested at 8:38? I tried to do what he said but no luck!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk17.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..60e8db448c856f17755fa06ebfc5799a985a7735 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk17.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 0, + "timestamp": 1684480825133.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "where can I find a complete derivation of the formula z=z0 + a(x-x0) + b(y-y0) using parametric equations as he suggested at 8:38? I tried to do what he said but no luck!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk18.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..60e8db448c856f17755fa06ebfc5799a985a7735 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk18.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 0, + "timestamp": 1684480825133.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "where can I find a complete derivation of the formula z=z0 + a(x-x0) + b(y-y0) using parametric equations as he suggested at 8:38? I tried to do what he said but no luck!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk19.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..60e8db448c856f17755fa06ebfc5799a985a7735 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk19.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 0, + "timestamp": 1684480825133.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "where can I find a complete derivation of the formula z=z0 + a(x-x0) + b(y-y0) using parametric equations as he suggested at 8:38? I tried to do what he said but no luck!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk2.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..8fcca2c735527e15515c5c89afe3c6ce5dace5d0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk2.json @@ -0,0 +1,18 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 0, + "timestamp": 1684480825133.0, + "annotatedSourceSentencesIndices": [ + 11, + 12, + 15, + 17 + ], + "names": [ + "annotator1", + "annotator2" + ], + "text": "where can I find a complete derivation of the formula z=z0 + a(x-x0) + b(y-y0) using parametric equations as he suggested at 8:38? I tried to do what he said but no luck!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk3.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..60e8db448c856f17755fa06ebfc5799a985a7735 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk3.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 0, + "timestamp": 1684480825133.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "where can I find a complete derivation of the formula z=z0 + a(x-x0) + b(y-y0) using parametric equations as he suggested at 8:38? I tried to do what he said but no luck!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk4.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..60e8db448c856f17755fa06ebfc5799a985a7735 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk4.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 0, + "timestamp": 1684480825133.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "where can I find a complete derivation of the formula z=z0 + a(x-x0) + b(y-y0) using parametric equations as he suggested at 8:38? I tried to do what he said but no luck!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk5.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e8db448c856f17755fa06ebfc5799a985a7735 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk5.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 0, + "timestamp": 1684480825133.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "where can I find a complete derivation of the formula z=z0 + a(x-x0) + b(y-y0) using parametric equations as he suggested at 8:38? I tried to do what he said but no luck!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk6.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..60e8db448c856f17755fa06ebfc5799a985a7735 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk6.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 0, + "timestamp": 1684480825133.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "where can I find a complete derivation of the formula z=z0 + a(x-x0) + b(y-y0) using parametric equations as he suggested at 8:38? I tried to do what he said but no luck!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk7.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..60e8db448c856f17755fa06ebfc5799a985a7735 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk7.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 0, + "timestamp": 1684480825133.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "where can I find a complete derivation of the formula z=z0 + a(x-x0) + b(y-y0) using parametric equations as he suggested at 8:38? I tried to do what he said but no luck!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk8.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..60e8db448c856f17755fa06ebfc5799a985a7735 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk8.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 0, + "timestamp": 1684480825133.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "where can I find a complete derivation of the formula z=z0 + a(x-x0) + b(y-y0) using parametric equations as he suggested at 8:38? I tried to do what he said but no luck!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk9.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..60e8db448c856f17755fa06ebfc5799a985a7735 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_0_chunk9.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 0, + "timestamp": 1684480825133.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "where can I find a complete derivation of the formula z=z0 + a(x-x0) + b(y-y0) using parametric equations as he suggested at 8:38? I tried to do what he said but no luck!" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk0.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..ac68763fe33c1f44f762715814b1785413f6cbec --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 12, + "timestamp": 1684510931819.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "6:34, how is that z=z0 + dz/dx(x-x0) a equation of straight line. y=mx+c is a eqaution of straight line in 2D space. and x = x0 + st is vector form of equaiton in higher dimension. how is the above euqation realted to this? Thanks in advance" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk1.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..ac68763fe33c1f44f762715814b1785413f6cbec --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 12, + "timestamp": 1684510931819.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "6:34, how is that z=z0 + dz/dx(x-x0) a equation of straight line. y=mx+c is a eqaution of straight line in 2D space. and x = x0 + st is vector form of equaiton in higher dimension. how is the above euqation realted to this? Thanks in advance" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk10.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..ac68763fe33c1f44f762715814b1785413f6cbec --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 12, + "timestamp": 1684510931819.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "6:34, how is that z=z0 + dz/dx(x-x0) a equation of straight line. y=mx+c is a eqaution of straight line in 2D space. and x = x0 + st is vector form of equaiton in higher dimension. how is the above euqation realted to this? Thanks in advance" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk11.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..ac68763fe33c1f44f762715814b1785413f6cbec --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 12, + "timestamp": 1684510931819.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "6:34, how is that z=z0 + dz/dx(x-x0) a equation of straight line. y=mx+c is a eqaution of straight line in 2D space. and x = x0 + st is vector form of equaiton in higher dimension. how is the above euqation realted to this? Thanks in advance" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk12.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..ac68763fe33c1f44f762715814b1785413f6cbec --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 12, + "timestamp": 1684510931819.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "6:34, how is that z=z0 + dz/dx(x-x0) a equation of straight line. y=mx+c is a eqaution of straight line in 2D space. and x = x0 + st is vector form of equaiton in higher dimension. how is the above euqation realted to this? Thanks in advance" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk13.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..ac68763fe33c1f44f762715814b1785413f6cbec --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 12, + "timestamp": 1684510931819.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "6:34, how is that z=z0 + dz/dx(x-x0) a equation of straight line. y=mx+c is a eqaution of straight line in 2D space. and x = x0 + st is vector form of equaiton in higher dimension. how is the above euqation realted to this? Thanks in advance" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk14.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..ac68763fe33c1f44f762715814b1785413f6cbec --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 12, + "timestamp": 1684510931819.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "6:34, how is that z=z0 + dz/dx(x-x0) a equation of straight line. y=mx+c is a eqaution of straight line in 2D space. and x = x0 + st is vector form of equaiton in higher dimension. how is the above euqation realted to this? Thanks in advance" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk15.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..ac68763fe33c1f44f762715814b1785413f6cbec --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 12, + "timestamp": 1684510931819.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "6:34, how is that z=z0 + dz/dx(x-x0) a equation of straight line. y=mx+c is a eqaution of straight line in 2D space. and x = x0 + st is vector form of equaiton in higher dimension. how is the above euqation realted to this? Thanks in advance" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk16.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..ac68763fe33c1f44f762715814b1785413f6cbec --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 12, + "timestamp": 1684510931819.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "6:34, how is that z=z0 + dz/dx(x-x0) a equation of straight line. y=mx+c is a eqaution of straight line in 2D space. and x = x0 + st is vector form of equaiton in higher dimension. how is the above euqation realted to this? Thanks in advance" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk17.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..ac68763fe33c1f44f762715814b1785413f6cbec --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 12, + "timestamp": 1684510931819.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "6:34, how is that z=z0 + dz/dx(x-x0) a equation of straight line. y=mx+c is a eqaution of straight line in 2D space. and x = x0 + st is vector form of equaiton in higher dimension. how is the above euqation realted to this? Thanks in advance" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk18.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..ac68763fe33c1f44f762715814b1785413f6cbec --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 12, + "timestamp": 1684510931819.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "6:34, how is that z=z0 + dz/dx(x-x0) a equation of straight line. y=mx+c is a eqaution of straight line in 2D space. and x = x0 + st is vector form of equaiton in higher dimension. how is the above euqation realted to this? Thanks in advance" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk19.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..ac68763fe33c1f44f762715814b1785413f6cbec --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 12, + "timestamp": 1684510931819.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "6:34, how is that z=z0 + dz/dx(x-x0) a equation of straight line. y=mx+c is a eqaution of straight line in 2D space. and x = x0 + st is vector form of equaiton in higher dimension. how is the above euqation realted to this? Thanks in advance" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk2.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..23277ac8a5884a51072ecc07d9cda3ebc9817b38 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk2.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 12, + "timestamp": 1684510931819.0, + "annotatedSourceSentencesIndices": [ + 3 + ], + "names": [ + "annotator1" + ], + "text": "6:34, how is that z=z0 + dz/dx(x-x0) a equation of straight line. y=mx+c is a eqaution of straight line in 2D space. and x = x0 + st is vector form of equaiton in higher dimension. how is the above euqation realted to this? Thanks in advance" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk3.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..ac68763fe33c1f44f762715814b1785413f6cbec --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 12, + "timestamp": 1684510931819.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "6:34, how is that z=z0 + dz/dx(x-x0) a equation of straight line. y=mx+c is a eqaution of straight line in 2D space. and x = x0 + st is vector form of equaiton in higher dimension. how is the above euqation realted to this? Thanks in advance" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk4.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..ac68763fe33c1f44f762715814b1785413f6cbec --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 12, + "timestamp": 1684510931819.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "6:34, how is that z=z0 + dz/dx(x-x0) a equation of straight line. y=mx+c is a eqaution of straight line in 2D space. and x = x0 + st is vector form of equaiton in higher dimension. how is the above euqation realted to this? Thanks in advance" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk5.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..ac68763fe33c1f44f762715814b1785413f6cbec --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 12, + "timestamp": 1684510931819.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "6:34, how is that z=z0 + dz/dx(x-x0) a equation of straight line. y=mx+c is a eqaution of straight line in 2D space. and x = x0 + st is vector form of equaiton in higher dimension. how is the above euqation realted to this? Thanks in advance" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk6.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..ac68763fe33c1f44f762715814b1785413f6cbec --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 12, + "timestamp": 1684510931819.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "6:34, how is that z=z0 + dz/dx(x-x0) a equation of straight line. y=mx+c is a eqaution of straight line in 2D space. and x = x0 + st is vector form of equaiton in higher dimension. how is the above euqation realted to this? Thanks in advance" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk7.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..ac68763fe33c1f44f762715814b1785413f6cbec --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 12, + "timestamp": 1684510931819.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "6:34, how is that z=z0 + dz/dx(x-x0) a equation of straight line. y=mx+c is a eqaution of straight line in 2D space. and x = x0 + st is vector form of equaiton in higher dimension. how is the above euqation realted to this? Thanks in advance" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk8.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..ac68763fe33c1f44f762715814b1785413f6cbec --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 12, + "timestamp": 1684510931819.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "6:34, how is that z=z0 + dz/dx(x-x0) a equation of straight line. y=mx+c is a eqaution of straight line in 2D space. and x = x0 + st is vector form of equaiton in higher dimension. how is the above euqation realted to this? Thanks in advance" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk9.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..ac68763fe33c1f44f762715814b1785413f6cbec --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_12_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 12, + "timestamp": 1684510931819.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "6:34, how is that z=z0 + dz/dx(x-x0) a equation of straight line. y=mx+c is a eqaution of straight line in 2D space. and x = x0 + st is vector form of equaiton in higher dimension. how is the above euqation realted to this? Thanks in advance" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_1_chunk0.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_1_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..b4fee994c69ba48465bd11b071bf7492a1794383 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_1_chunk0.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 1, + "timestamp": 1684191408602.0, + "annotatedSourceSentencesIndices": [ + 0 + ], + "names": [ + "annotator1" + ], + "text": "Would any one please explain what did the professor mean between 13:13 and 13:44?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_1_chunk1.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_1_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..f317160fcad81ef92e31f6de104b2f3227eccdf2 --- /dev/null +++ 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at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_1_chunk11.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_1_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..f317160fcad81ef92e31f6de104b2f3227eccdf2 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_1_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 1, + "timestamp": 1684191408602.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Would any one please explain what did the professor mean between 13:13 and 13:44?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_1_chunk12.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_1_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..f317160fcad81ef92e31f6de104b2f3227eccdf2 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_1_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 1, + "timestamp": 1684191408602.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Would any one please explain what did the professor mean between 13:13 and 13:44?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_1_chunk13.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_1_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..f317160fcad81ef92e31f6de104b2f3227eccdf2 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_1_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 1, + "timestamp": 1684191408602.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Would any one please explain what did the professor mean between 13:13 and 13:44?" + } +] \ No newline at end of file diff --git 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" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk0.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..5fc4bc869e266b21c4cbc1ef789c90cc5f02c27e --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 3, + "timestamp": 1684510062486.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why is it the the deviation formula is squared? i know it must be equal to zero." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk1.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..5fc4bc869e266b21c4cbc1ef789c90cc5f02c27e --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 3, + "timestamp": 1684510062486.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why is it the the deviation formula is squared? i know it must be equal to zero." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk10.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..5fc4bc869e266b21c4cbc1ef789c90cc5f02c27e --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 3, + "timestamp": 1684510062486.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why is it the the deviation formula is squared? i know it must be equal to zero." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk11.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..5fc4bc869e266b21c4cbc1ef789c90cc5f02c27e --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 3, + "timestamp": 1684510062486.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why is it the the deviation formula is squared? i know it must be equal to zero." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk12.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..5fc4bc869e266b21c4cbc1ef789c90cc5f02c27e --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 3, + "timestamp": 1684510062486.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why is it the the deviation formula is squared? i know it must be equal to zero." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk13.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..5fc4bc869e266b21c4cbc1ef789c90cc5f02c27e --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 3, + "timestamp": 1684510062486.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why is it the the deviation formula is squared? i know it must be equal to zero." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk14.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..9cb94c5fc4c4e2d16c8681b231bb6f42536a80d6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk14.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 3, + "timestamp": 1684510062486.0, + "annotatedSourceSentencesIndices": [ + 13 + ], + "names": [ + "annotator1" + ], + "text": "why is it the the deviation formula is squared? i know it must be equal to zero." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk15.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..5fc4bc869e266b21c4cbc1ef789c90cc5f02c27e --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 3, + "timestamp": 1684510062486.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why is it the the deviation formula is squared? i know it must be equal to zero." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk16.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..5fc4bc869e266b21c4cbc1ef789c90cc5f02c27e --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 3, + "timestamp": 1684510062486.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why is it the the deviation formula is squared? i know it must be equal to zero." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk17.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..5fc4bc869e266b21c4cbc1ef789c90cc5f02c27e --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 3, + "timestamp": 1684510062486.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why is it the the deviation formula is squared? i know it must be equal to zero." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk18.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..5fc4bc869e266b21c4cbc1ef789c90cc5f02c27e --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 3, + "timestamp": 1684510062486.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why is it the the deviation formula is squared? i know it must be equal to zero." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk19.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..5fc4bc869e266b21c4cbc1ef789c90cc5f02c27e --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 3, + "timestamp": 1684510062486.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why is it the the deviation formula is squared? i know it must be equal to zero." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk2.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..5fc4bc869e266b21c4cbc1ef789c90cc5f02c27e --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 3, + "timestamp": 1684510062486.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why is it the the deviation formula is squared? i know it must be equal to zero." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk3.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..5fc4bc869e266b21c4cbc1ef789c90cc5f02c27e --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 3, + "timestamp": 1684510062486.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why is it the the deviation formula is squared? i know it must be equal to zero." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk4.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..5fc4bc869e266b21c4cbc1ef789c90cc5f02c27e --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 3, + "timestamp": 1684510062486.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why is it the the deviation formula is squared? i know it must be equal to zero." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk5.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5fc4bc869e266b21c4cbc1ef789c90cc5f02c27e --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 3, + "timestamp": 1684510062486.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why is it the the deviation formula is squared? i know it must be equal to zero." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk6.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..5fc4bc869e266b21c4cbc1ef789c90cc5f02c27e --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 3, + "timestamp": 1684510062486.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why is it the the deviation formula is squared? i know it must be equal to zero." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk7.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..5fc4bc869e266b21c4cbc1ef789c90cc5f02c27e --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 3, + "timestamp": 1684510062486.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why is it the the deviation formula is squared? i know it must be equal to zero." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk8.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..5fc4bc869e266b21c4cbc1ef789c90cc5f02c27e --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 3, + "timestamp": 1684510062486.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why is it the the deviation formula is squared? i know it must be equal to zero." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk9.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..5fc4bc869e266b21c4cbc1ef789c90cc5f02c27e --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_3_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 3, + "timestamp": 1684510062486.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why is it the the deviation formula is squared? i know it must be equal to zero." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk0.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..f71fd2160b2263c1686d947348f828100ad7987d --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 4, + "timestamp": 1684510080674.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why do we do square deviation, but not ordinary one? I don`t understand the precondition for squares. If anyone can explain, do it, please." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk1.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..f71fd2160b2263c1686d947348f828100ad7987d --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 4, + "timestamp": 1684510080674.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why do we do square deviation, but not ordinary one? I don`t understand the precondition for squares. If anyone can explain, do it, please." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk10.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..f71fd2160b2263c1686d947348f828100ad7987d --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 4, + "timestamp": 1684510080674.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why do we do square deviation, but not ordinary one? I don`t understand the precondition for squares. If anyone can explain, do it, please." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk11.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..f71fd2160b2263c1686d947348f828100ad7987d --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 4, + "timestamp": 1684510080674.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why do we do square deviation, but not ordinary one? I don`t understand the precondition for squares. If anyone can explain, do it, please." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk12.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..f71fd2160b2263c1686d947348f828100ad7987d --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 4, + "timestamp": 1684510080674.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why do we do square deviation, but not ordinary one? I don`t understand the precondition for squares. If anyone can explain, do it, please." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk13.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..f71fd2160b2263c1686d947348f828100ad7987d --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 4, + "timestamp": 1684510080674.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why do we do square deviation, but not ordinary one? I don`t understand the precondition for squares. If anyone can explain, do it, please." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk14.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..77946167cfc07266fe638597571d71ef1e5c84e8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk14.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 4, + "timestamp": 1684510080674.0, + "annotatedSourceSentencesIndices": [ + 13 + ], + "names": [ + "annotator1" + ], + "text": "Why do we do square deviation, but not ordinary one? I don`t understand the precondition for squares. If anyone can explain, do it, please." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk15.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..f71fd2160b2263c1686d947348f828100ad7987d --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 4, + "timestamp": 1684510080674.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why do we do square deviation, but not ordinary one? I don`t understand the precondition for squares. If anyone can explain, do it, please." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk16.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f71fd2160b2263c1686d947348f828100ad7987d --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 4, + "timestamp": 1684510080674.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why do we do square deviation, but not ordinary one? I don`t understand the precondition for squares. If anyone can explain, do it, please." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk17.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..f71fd2160b2263c1686d947348f828100ad7987d --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 4, + "timestamp": 1684510080674.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why do we do square deviation, but not ordinary one? I don`t understand the precondition for squares. If anyone can explain, do it, please." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk18.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..f71fd2160b2263c1686d947348f828100ad7987d --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 4, + "timestamp": 1684510080674.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why do we do square deviation, but not ordinary one? I don`t understand the precondition for squares. If anyone can explain, do it, please." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk19.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..f71fd2160b2263c1686d947348f828100ad7987d --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 4, + "timestamp": 1684510080674.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why do we do square deviation, but not ordinary one? I don`t understand the precondition for squares. If anyone can explain, do it, please." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk2.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..f71fd2160b2263c1686d947348f828100ad7987d --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 4, + "timestamp": 1684510080674.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why do we do square deviation, but not ordinary one? I don`t understand the precondition for squares. If anyone can explain, do it, please." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk3.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..f71fd2160b2263c1686d947348f828100ad7987d --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 4, + "timestamp": 1684510080674.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why do we do square deviation, but not ordinary one? I don`t understand the precondition for squares. If anyone can explain, do it, please." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk4.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..f71fd2160b2263c1686d947348f828100ad7987d --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 4, + "timestamp": 1684510080674.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why do we do square deviation, but not ordinary one? I don`t understand the precondition for squares. If anyone can explain, do it, please." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk5.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..f71fd2160b2263c1686d947348f828100ad7987d --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 4, + "timestamp": 1684510080674.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why do we do square deviation, but not ordinary one? I don`t understand the precondition for squares. If anyone can explain, do it, please." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk6.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..f71fd2160b2263c1686d947348f828100ad7987d --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 4, + "timestamp": 1684510080674.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why do we do square deviation, but not ordinary one? I don`t understand the precondition for squares. If anyone can explain, do it, please." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk7.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..f71fd2160b2263c1686d947348f828100ad7987d --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 4, + "timestamp": 1684510080674.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why do we do square deviation, but not ordinary one? I don`t understand the precondition for squares. If anyone can explain, do it, please." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk8.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f71fd2160b2263c1686d947348f828100ad7987d --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 4, + "timestamp": 1684510080674.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why do we do square deviation, but not ordinary one? I don`t understand the precondition for squares. If anyone can explain, do it, please." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk9.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..f71fd2160b2263c1686d947348f828100ad7987d --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_4_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 4, + "timestamp": 1684510080674.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Why do we do square deviation, but not ordinary one? I don`t understand the precondition for squares. If anyone can explain, do it, please." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_5_chunk0.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_5_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..cb44a7b0cd1b7ddd927597289fcc678a2ac67791 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_5_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 5, + "timestamp": 1684510172054.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "25:57\nWhy he wrote f(-1,0)?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_5_chunk1.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_5_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..cb44a7b0cd1b7ddd927597289fcc678a2ac67791 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_5_chunk1.json 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file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_5_chunk5.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_5_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..cb44a7b0cd1b7ddd927597289fcc678a2ac67791 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_5_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 5, + "timestamp": 1684510172054.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "25:57\nWhy he wrote f(-1,0)?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_5_chunk6.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_5_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..cb44a7b0cd1b7ddd927597289fcc678a2ac67791 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_5_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 5, + "timestamp": 1684510172054.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "25:57\nWhy he wrote f(-1,0)?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_5_chunk7.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_5_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..cb44a7b0cd1b7ddd927597289fcc678a2ac67791 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_5_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 5, + "timestamp": 1684510172054.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "25:57\nWhy he wrote f(-1,0)?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_5_chunk8.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_5_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..cb44a7b0cd1b7ddd927597289fcc678a2ac67791 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_5_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 5, + "timestamp": 1684510172054.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "25:57\nWhy he wrote f(-1,0)?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_5_chunk9.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_5_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..9c3812928eb38c9aa1067b1f702be9b8502634f5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_5_chunk9.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 5, + "timestamp": 1684510172054.0, + "annotatedSourceSentencesIndices": [ + 18 + ], + "names": [ + "annotator1" + ], + "text": "25:57\nWhy he wrote f(-1,0)?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk0.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..88683fed5ea92a43dae1423a8356e9222a57b873 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 7, + "timestamp": 1684510713476.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For z = z0 + a(x-x0) + b(y-y0),\nwouldn't that mean:\n-1(z-z0) + a(x-x0) + b(y-y0) = 0\nso from lecture 4 the normal vector for any f(x,y) tangent plane is <-1, a, b> ?\nI'm missing something about the -1 I'm sure" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk1.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..88683fed5ea92a43dae1423a8356e9222a57b873 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 7, + "timestamp": 1684510713476.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For z = z0 + a(x-x0) + b(y-y0),\nwouldn't that mean:\n-1(z-z0) + a(x-x0) + b(y-y0) = 0\nso from lecture 4 the normal vector for any f(x,y) tangent plane is <-1, a, b> ?\nI'm missing something about the -1 I'm sure" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk10.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..88683fed5ea92a43dae1423a8356e9222a57b873 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 7, + "timestamp": 1684510713476.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For z = z0 + a(x-x0) + b(y-y0),\nwouldn't that mean:\n-1(z-z0) + a(x-x0) + b(y-y0) = 0\nso from lecture 4 the normal vector for any f(x,y) tangent plane is <-1, a, b> ?\nI'm missing something about the -1 I'm sure" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk11.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..88683fed5ea92a43dae1423a8356e9222a57b873 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 7, + "timestamp": 1684510713476.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For z = z0 + a(x-x0) + b(y-y0),\nwouldn't that mean:\n-1(z-z0) + a(x-x0) + b(y-y0) = 0\nso from lecture 4 the normal vector for any f(x,y) tangent plane is <-1, a, b> ?\nI'm missing something about the -1 I'm sure" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk12.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..88683fed5ea92a43dae1423a8356e9222a57b873 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 7, + "timestamp": 1684510713476.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For z = z0 + a(x-x0) + b(y-y0),\nwouldn't that mean:\n-1(z-z0) + a(x-x0) + b(y-y0) = 0\nso from lecture 4 the normal vector for any f(x,y) tangent plane is <-1, a, b> ?\nI'm missing something about the -1 I'm sure" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk13.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..88683fed5ea92a43dae1423a8356e9222a57b873 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 7, + "timestamp": 1684510713476.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For z = z0 + a(x-x0) + b(y-y0),\nwouldn't that mean:\n-1(z-z0) + a(x-x0) + b(y-y0) = 0\nso from lecture 4 the normal vector for any f(x,y) tangent plane is <-1, a, b> ?\nI'm missing something about the -1 I'm sure" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk14.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..88683fed5ea92a43dae1423a8356e9222a57b873 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 7, + "timestamp": 1684510713476.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For z = z0 + a(x-x0) + b(y-y0),\nwouldn't that mean:\n-1(z-z0) + a(x-x0) + b(y-y0) = 0\nso from lecture 4 the normal vector for any f(x,y) tangent plane is <-1, a, b> ?\nI'm missing something about the -1 I'm sure" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk15.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..88683fed5ea92a43dae1423a8356e9222a57b873 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 7, + "timestamp": 1684510713476.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For z = z0 + a(x-x0) + b(y-y0),\nwouldn't that mean:\n-1(z-z0) + a(x-x0) + b(y-y0) = 0\nso from lecture 4 the normal vector for any f(x,y) tangent plane is <-1, a, b> ?\nI'm missing something about the -1 I'm sure" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk16.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..88683fed5ea92a43dae1423a8356e9222a57b873 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 7, + "timestamp": 1684510713476.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For z = z0 + a(x-x0) + b(y-y0),\nwouldn't that mean:\n-1(z-z0) + a(x-x0) + b(y-y0) = 0\nso from lecture 4 the normal vector for any f(x,y) tangent plane is <-1, a, b> ?\nI'm missing something about the -1 I'm sure" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk17.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..88683fed5ea92a43dae1423a8356e9222a57b873 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 7, + "timestamp": 1684510713476.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For z = z0 + a(x-x0) + b(y-y0),\nwouldn't that mean:\n-1(z-z0) + a(x-x0) + b(y-y0) = 0\nso from lecture 4 the normal vector for any f(x,y) tangent plane is <-1, a, b> ?\nI'm missing something about the -1 I'm sure" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk18.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..88683fed5ea92a43dae1423a8356e9222a57b873 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 7, + "timestamp": 1684510713476.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For z = z0 + a(x-x0) + b(y-y0),\nwouldn't that mean:\n-1(z-z0) + a(x-x0) + b(y-y0) = 0\nso from lecture 4 the normal vector for any f(x,y) tangent plane is <-1, a, b> ?\nI'm missing something about the -1 I'm sure" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk19.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..88683fed5ea92a43dae1423a8356e9222a57b873 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 7, + "timestamp": 1684510713476.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For z = z0 + a(x-x0) + b(y-y0),\nwouldn't that mean:\n-1(z-z0) + a(x-x0) + b(y-y0) = 0\nso from lecture 4 the normal vector for any f(x,y) tangent plane is <-1, a, b> ?\nI'm missing something about the -1 I'm sure" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk2.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6552fd83e5a3951f2ac7d0a6ed28ac40d1a62526 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk2.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 7, + "timestamp": 1684510713476.0, + "annotatedSourceSentencesIndices": [ + 11 + ], + "names": [ + "annotator1" + ], + "text": "For z = z0 + a(x-x0) + b(y-y0),\nwouldn't that mean:\n-1(z-z0) + a(x-x0) + b(y-y0) = 0\nso from lecture 4 the normal vector for any f(x,y) tangent plane is <-1, a, b> ?\nI'm missing something about the -1 I'm sure" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk3.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..88683fed5ea92a43dae1423a8356e9222a57b873 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 7, + "timestamp": 1684510713476.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For z = z0 + a(x-x0) + b(y-y0),\nwouldn't that mean:\n-1(z-z0) + a(x-x0) + b(y-y0) = 0\nso from lecture 4 the normal vector for any f(x,y) tangent plane is <-1, a, b> ?\nI'm missing something about the -1 I'm sure" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk4.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..88683fed5ea92a43dae1423a8356e9222a57b873 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 7, + "timestamp": 1684510713476.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For z = z0 + a(x-x0) + b(y-y0),\nwouldn't that mean:\n-1(z-z0) + a(x-x0) + b(y-y0) = 0\nso from lecture 4 the normal vector for any f(x,y) tangent plane is <-1, a, b> ?\nI'm missing something about the -1 I'm sure" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk5.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..88683fed5ea92a43dae1423a8356e9222a57b873 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 7, + "timestamp": 1684510713476.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For z = z0 + a(x-x0) + b(y-y0),\nwouldn't that mean:\n-1(z-z0) + a(x-x0) + b(y-y0) = 0\nso from lecture 4 the normal vector for any f(x,y) tangent plane is <-1, a, b> ?\nI'm missing something about the -1 I'm sure" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk6.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..88683fed5ea92a43dae1423a8356e9222a57b873 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 7, + "timestamp": 1684510713476.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For z = z0 + a(x-x0) + b(y-y0),\nwouldn't that mean:\n-1(z-z0) + a(x-x0) + b(y-y0) = 0\nso from lecture 4 the normal vector for any f(x,y) tangent plane is <-1, a, b> ?\nI'm missing something about the -1 I'm sure" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk7.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..88683fed5ea92a43dae1423a8356e9222a57b873 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 7, + "timestamp": 1684510713476.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For z = z0 + a(x-x0) + b(y-y0),\nwouldn't that mean:\n-1(z-z0) + a(x-x0) + b(y-y0) = 0\nso from lecture 4 the normal vector for any f(x,y) tangent plane is <-1, a, b> ?\nI'm missing something about the -1 I'm sure" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk8.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..88683fed5ea92a43dae1423a8356e9222a57b873 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 7, + "timestamp": 1684510713476.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For z = z0 + a(x-x0) + b(y-y0),\nwouldn't that mean:\n-1(z-z0) + a(x-x0) + b(y-y0) = 0\nso from lecture 4 the normal vector for any f(x,y) tangent plane is <-1, a, b> ?\nI'm missing something about the -1 I'm sure" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk9.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..88683fed5ea92a43dae1423a8356e9222a57b873 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_7_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 7, + "timestamp": 1684510713476.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For z = z0 + a(x-x0) + b(y-y0),\nwouldn't that mean:\n-1(z-z0) + a(x-x0) + b(y-y0) = 0\nso from lecture 4 the normal vector for any f(x,y) tangent plane is <-1, a, b> ?\nI'm missing something about the -1 I'm sure" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_9_chunk0.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_9_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..3ba8d4b0d1f903c360ca876b0ffc9a0b11815ec4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_9_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 9, + "timestamp": 1684510838484.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "34:58 would using perpendicular distance (instead of vertical distance) make better sense? \n" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_9_chunk1.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_9_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3ba8d4b0d1f903c360ca876b0ffc9a0b11815ec4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_9_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 9, + "timestamp": 1684510838484.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "34:58 would using perpendicular distance (instead of vertical distance) make better sense? \n" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/UYe98CcxPbs_9_chunk10.json b/sight/query/annotated_chunks_window20/UYe98CcxPbs_9_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..3ba8d4b0d1f903c360ca876b0ffc9a0b11815ec4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/UYe98CcxPbs_9_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "UYe98CcxPbs", + "query_id": 9, + "timestamp": 1684510838484.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "34:58 would using perpendicular distance (instead of vertical distance) make better sense? \n" + } +] \ No newline at end of file diff --git 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The proof contained slanted plane with an angle alpha to only one axis and not a general slant in both directions. Does this proof apply when we are considering a general slant to both x and y ? Will dA=dS Cos theta still be applicable?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk1.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..69c1df2e22607551dbcaf11f41956552285416eb --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk1.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 1, + "timestamp": 1684192120438.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "I did not understand the last step replacing dA by dxdy. The proof contained slanted plane with an angle alpha to only one axis and not a general slant in both directions. Does this proof apply when we are considering a general slant to both x and y ? Will dA=dS Cos theta still be applicable?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk10.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..69c1df2e22607551dbcaf11f41956552285416eb --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk10.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 1, + "timestamp": 1684192120438.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "I did not understand the last step replacing dA by dxdy. The proof contained slanted plane with an angle alpha to only one axis and not a general slant in both directions. Does this proof apply when we are considering a general slant to both x and y ? Will dA=dS Cos theta still be applicable?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk11.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..69c1df2e22607551dbcaf11f41956552285416eb --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk11.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 1, + "timestamp": 1684192120438.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "I did not understand the last step replacing dA by dxdy. The proof contained slanted plane with an angle alpha to only one axis and not a general slant in both directions. Does this proof apply when we are considering a general slant to both x and y ? Will dA=dS Cos theta still be applicable?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk12.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..69c1df2e22607551dbcaf11f41956552285416eb --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk12.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 1, + "timestamp": 1684192120438.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "I did not understand the last step replacing dA by dxdy. The proof contained slanted plane with an angle alpha to only one axis and not a general slant in both directions. Does this proof apply when we are considering a general slant to both x and y ? Will dA=dS Cos theta still be applicable?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk13.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..69c1df2e22607551dbcaf11f41956552285416eb --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk13.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 1, + "timestamp": 1684192120438.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "I did not understand the last step replacing dA by dxdy. The proof contained slanted plane with an angle alpha to only one axis and not a general slant in both directions. Does this proof apply when we are considering a general slant to both x and y ? Will dA=dS Cos theta still be applicable?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk14.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..69c1df2e22607551dbcaf11f41956552285416eb --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk14.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 1, + "timestamp": 1684192120438.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "I did not understand the last step replacing dA by dxdy. The proof contained slanted plane with an angle alpha to only one axis and not a general slant in both directions. Does this proof apply when we are considering a general slant to both x and y ? Will dA=dS Cos theta still be applicable?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk15.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..69c1df2e22607551dbcaf11f41956552285416eb --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk15.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 1, + "timestamp": 1684192120438.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "I did not understand the last step replacing dA by dxdy. The proof contained slanted plane with an angle alpha to only one axis and not a general slant in both directions. Does this proof apply when we are considering a general slant to both x and y ? Will dA=dS Cos theta still be applicable?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk16.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..6470d61ad43cf2fb172c3c160274c822b62bf688 --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk16.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 1, + "timestamp": 1684192120438.0, + "annotatedSourceSentencesIndices": [ + 11 + ], + "names": [ + "annotator1", + "annotator2" + ], + "text": "I did not understand the last step replacing dA by dxdy. The proof contained slanted plane with an angle alpha to only one axis and not a general slant in both directions. Does this proof apply when we are considering a general slant to both x and y ? Will dA=dS Cos theta still be applicable?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk17.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..69c1df2e22607551dbcaf11f41956552285416eb --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk17.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 1, + "timestamp": 1684192120438.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "I did not understand the last step replacing dA by dxdy. The proof contained slanted plane with an angle alpha to only one axis and not a general slant in both directions. Does this proof apply when we are considering a general slant to both x and y ? Will dA=dS Cos theta still be applicable?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk18.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..69c1df2e22607551dbcaf11f41956552285416eb --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk18.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 1, + "timestamp": 1684192120438.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "I did not understand the last step replacing dA by dxdy. The proof contained slanted plane with an angle alpha to only one axis and not a general slant in both directions. Does this proof apply when we are considering a general slant to both x and y ? Will dA=dS Cos theta still be applicable?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk19.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..69c1df2e22607551dbcaf11f41956552285416eb --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk19.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 1, + "timestamp": 1684192120438.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "I did not understand the last step replacing dA by dxdy. The proof contained slanted plane with an angle alpha to only one axis and not a general slant in both directions. Does this proof apply when we are considering a general slant to both x and y ? Will dA=dS Cos theta still be applicable?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk2.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..69c1df2e22607551dbcaf11f41956552285416eb --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk2.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 1, + "timestamp": 1684192120438.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "I did not understand the last step replacing dA by dxdy. The proof contained slanted plane with an angle alpha to only one axis and not a general slant in both directions. Does this proof apply when we are considering a general slant to both x and y ? Will dA=dS Cos theta still be applicable?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk20.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..69c1df2e22607551dbcaf11f41956552285416eb --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk20.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 1, + "timestamp": 1684192120438.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "I did not understand the last step replacing dA by dxdy. The proof contained slanted plane with an angle alpha to only one axis and not a general slant in both directions. Does this proof apply when we are considering a general slant to both x and y ? 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Will dA=dS Cos theta still be applicable?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk4.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..69c1df2e22607551dbcaf11f41956552285416eb --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk4.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 1, + "timestamp": 1684192120438.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "I did not understand the last step replacing dA by dxdy. The proof contained slanted plane with an angle alpha to only one axis and not a general slant in both directions. Does this proof apply when we are considering a general slant to both x and y ? Will dA=dS Cos theta still be applicable?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk5.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..69c1df2e22607551dbcaf11f41956552285416eb --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_1_chunk5.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 1, + "timestamp": 1684192120438.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "I did not understand the last step replacing dA by dxdy. The proof contained slanted plane with an angle alpha to only one axis and not a general slant in both directions. Does this proof apply when we are considering a general slant to both x and y ? 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file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_3_chunk5.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_3_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..9a98a7db10dbd7e020d75e1a0e3eb2369d09e0ea --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_3_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 3, + "timestamp": 1684511496045.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Do maths/science/engineering students take this class or some other multivariable calculus course like 18.024?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_3_chunk6.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_3_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9a98a7db10dbd7e020d75e1a0e3eb2369d09e0ea --- /dev/null +++ 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multivariable calculus course like 18.024?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_3_chunk8.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_3_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..9a98a7db10dbd7e020d75e1a0e3eb2369d09e0ea --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_3_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 3, + "timestamp": 1684511496045.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Do maths/science/engineering students take this class or some other multivariable calculus course like 18.024?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_3_chunk9.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_3_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..df9f7418001b69b67975148b0d1407e76d268dad --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_3_chunk9.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 3, + "timestamp": 1684511496045.0, + "annotatedSourceSentencesIndices": [ + 16, + 17 + ], + "names": [ + "annotator1" + ], + "text": "Do maths/science/engineering students take this class or some other multivariable calculus course like 18.024?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk0.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..e87f2ebd3696ff13ee1f942ae8a6eef604f0eca8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 5, + "timestamp": 1684511772657.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "18:09 why the range of r goes from 0 to 1? I think the definition of S in this problem needs further clarification. S should be a paraboloid of z = x^2 + y^2 between z=0 and z=1. It is a little confusing by justing saying \"above the unit disk\". " + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk1.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..e87f2ebd3696ff13ee1f942ae8a6eef604f0eca8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 5, + "timestamp": 1684511772657.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "18:09 why the range of r goes from 0 to 1? I think the definition of S in this problem needs further clarification. S should be a paraboloid of z = x^2 + y^2 between z=0 and z=1. It is a little confusing by justing saying \"above the unit disk\". " + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk10.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..e87f2ebd3696ff13ee1f942ae8a6eef604f0eca8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 5, + "timestamp": 1684511772657.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "18:09 why the range of r goes from 0 to 1? I think the definition of S in this problem needs further clarification. S should be a paraboloid of z = x^2 + y^2 between z=0 and z=1. It is a little confusing by justing saying \"above the unit disk\". " + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk11.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..e87f2ebd3696ff13ee1f942ae8a6eef604f0eca8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 5, + "timestamp": 1684511772657.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "18:09 why the range of r goes from 0 to 1? I think the definition of S in this problem needs further clarification. S should be a paraboloid of z = x^2 + y^2 between z=0 and z=1. It is a little confusing by justing saying \"above the unit disk\". " + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk12.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..e87f2ebd3696ff13ee1f942ae8a6eef604f0eca8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 5, + "timestamp": 1684511772657.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "18:09 why the range of r goes from 0 to 1? I think the definition of S in this problem needs further clarification. S should be a paraboloid of z = x^2 + y^2 between z=0 and z=1. It is a little confusing by justing saying \"above the unit disk\". " + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk13.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..e87f2ebd3696ff13ee1f942ae8a6eef604f0eca8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 5, + "timestamp": 1684511772657.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "18:09 why the range of r goes from 0 to 1? I think the definition of S in this problem needs further clarification. S should be a paraboloid of z = x^2 + y^2 between z=0 and z=1. It is a little confusing by justing saying \"above the unit disk\". " + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk14.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..e87f2ebd3696ff13ee1f942ae8a6eef604f0eca8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 5, + "timestamp": 1684511772657.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "18:09 why the range of r goes from 0 to 1? I think the definition of S in this problem needs further clarification. S should be a paraboloid of z = x^2 + y^2 between z=0 and z=1. It is a little confusing by justing saying \"above the unit disk\". " + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk15.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..e87f2ebd3696ff13ee1f942ae8a6eef604f0eca8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 5, + "timestamp": 1684511772657.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "18:09 why the range of r goes from 0 to 1? I think the definition of S in this problem needs further clarification. S should be a paraboloid of z = x^2 + y^2 between z=0 and z=1. It is a little confusing by justing saying \"above the unit disk\". " + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk16.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..e87f2ebd3696ff13ee1f942ae8a6eef604f0eca8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 5, + "timestamp": 1684511772657.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "18:09 why the range of r goes from 0 to 1? I think the definition of S in this problem needs further clarification. S should be a paraboloid of z = x^2 + y^2 between z=0 and z=1. It is a little confusing by justing saying \"above the unit disk\". " + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk17.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..e87f2ebd3696ff13ee1f942ae8a6eef604f0eca8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 5, + "timestamp": 1684511772657.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "18:09 why the range of r goes from 0 to 1? I think the definition of S in this problem needs further clarification. S should be a paraboloid of z = x^2 + y^2 between z=0 and z=1. It is a little confusing by justing saying \"above the unit disk\". " + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk18.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..e87f2ebd3696ff13ee1f942ae8a6eef604f0eca8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 5, + "timestamp": 1684511772657.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "18:09 why the range of r goes from 0 to 1? I think the definition of S in this problem needs further clarification. S should be a paraboloid of z = x^2 + y^2 between z=0 and z=1. It is a little confusing by justing saying \"above the unit disk\". " + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk19.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..e87f2ebd3696ff13ee1f942ae8a6eef604f0eca8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 5, + "timestamp": 1684511772657.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "18:09 why the range of r goes from 0 to 1? I think the definition of S in this problem needs further clarification. S should be a paraboloid of z = x^2 + y^2 between z=0 and z=1. It is a little confusing by justing saying \"above the unit disk\". " + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk2.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..e87f2ebd3696ff13ee1f942ae8a6eef604f0eca8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 5, + "timestamp": 1684511772657.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "18:09 why the range of r goes from 0 to 1? I think the definition of S in this problem needs further clarification. S should be a paraboloid of z = x^2 + y^2 between z=0 and z=1. It is a little confusing by justing saying \"above the unit disk\". " + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk20.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..e87f2ebd3696ff13ee1f942ae8a6eef604f0eca8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 5, + "timestamp": 1684511772657.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "18:09 why the range of r goes from 0 to 1? I think the definition of S in this problem needs further clarification. S should be a paraboloid of z = x^2 + y^2 between z=0 and z=1. It is a little confusing by justing saying \"above the unit disk\". " + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk3.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..e87f2ebd3696ff13ee1f942ae8a6eef604f0eca8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 5, + "timestamp": 1684511772657.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "18:09 why the range of r goes from 0 to 1? I think the definition of S in this problem needs further clarification. S should be a paraboloid of z = x^2 + y^2 between z=0 and z=1. It is a little confusing by justing saying \"above the unit disk\". " + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk4.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..e87f2ebd3696ff13ee1f942ae8a6eef604f0eca8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 5, + "timestamp": 1684511772657.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "18:09 why the range of r goes from 0 to 1? I think the definition of S in this problem needs further clarification. S should be a paraboloid of z = x^2 + y^2 between z=0 and z=1. It is a little confusing by justing saying \"above the unit disk\". " + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk5.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..e87f2ebd3696ff13ee1f942ae8a6eef604f0eca8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 5, + "timestamp": 1684511772657.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "18:09 why the range of r goes from 0 to 1? I think the definition of S in this problem needs further clarification. S should be a paraboloid of z = x^2 + y^2 between z=0 and z=1. It is a little confusing by justing saying \"above the unit disk\". " + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk6.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..e87f2ebd3696ff13ee1f942ae8a6eef604f0eca8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 5, + "timestamp": 1684511772657.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "18:09 why the range of r goes from 0 to 1? I think the definition of S in this problem needs further clarification. S should be a paraboloid of z = x^2 + y^2 between z=0 and z=1. It is a little confusing by justing saying \"above the unit disk\". " + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk7.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..e87f2ebd3696ff13ee1f942ae8a6eef604f0eca8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 5, + "timestamp": 1684511772657.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "18:09 why the range of r goes from 0 to 1? I think the definition of S in this problem needs further clarification. S should be a paraboloid of z = x^2 + y^2 between z=0 and z=1. It is a little confusing by justing saying \"above the unit disk\". " + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk8.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..485f4e85be633b9e3bfda2c6f8cb5915a3b8509e --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk8.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 5, + "timestamp": 1684511772657.0, + "annotatedSourceSentencesIndices": [ + 1 + ], + "names": [ + "annotator1" + ], + "text": "18:09 why the range of r goes from 0 to 1? I think the definition of S in this problem needs further clarification. S should be a paraboloid of z = x^2 + y^2 between z=0 and z=1. It is a little confusing by justing saying \"above the unit disk\". " + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk9.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..e87f2ebd3696ff13ee1f942ae8a6eef604f0eca8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_5_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 5, + "timestamp": 1684511772657.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "18:09 why the range of r goes from 0 to 1? I think the definition of S in this problem needs further clarification. S should be a paraboloid of z = x^2 + y^2 between z=0 and z=1. It is a little confusing by justing saying \"above the unit disk\". " + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_7_chunk0.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_7_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..92c1c886303776041e97f57a2340178e1ec954c8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_7_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 7, + "timestamp": 1684511834173.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Isn't this theorem called after Ostrogradsky, since he is the first one to prove it?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_7_chunk1.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_7_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..92c1c886303776041e97f57a2340178e1ec954c8 --- /dev/null +++ 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newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_8_chunk0.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_8_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..64f8cc2ebcc9fcb055e8a5362fe19777f87bee46 --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_8_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 8, + "timestamp": 1684512043723.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Wait, did he ever account for vector N not being a unit vector? He never required that the N vector represented the area of the delta slanted plane did he?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_8_chunk1.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_8_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..64f8cc2ebcc9fcb055e8a5362fe19777f87bee46 --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_8_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 8, + "timestamp": 1684512043723.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Wait, did he ever account for vector N not being a unit vector? He never required that the N vector represented the area of the delta slanted plane did he?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_8_chunk10.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_8_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..64f8cc2ebcc9fcb055e8a5362fe19777f87bee46 --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_8_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 8, + "timestamp": 1684512043723.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Wait, did he ever account for vector N not being a unit vector? He never required that the N vector represented the area of the delta slanted plane did he?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_8_chunk11.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_8_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..edf96233e926d03e9579959ee4dc8c55195c2aad --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_8_chunk11.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 8, + "timestamp": 1684512043723.0, + "annotatedSourceSentencesIndices": [ + 6, + 7 + ], + "names": [ + "annotator1" + ], + "text": "Wait, did he ever account for vector N not being a unit vector? He never required that the N vector represented the area of the delta slanted plane did he?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_8_chunk12.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_8_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..64f8cc2ebcc9fcb055e8a5362fe19777f87bee46 --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_8_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 8, + "timestamp": 1684512043723.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Wait, did he ever account for vector N not being a unit vector? He never required that the N vector represented the area of the delta slanted plane did he?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_8_chunk13.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_8_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..23fd0c75e837942372fcbf79fc0e23cf5c322f48 --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_8_chunk13.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 8, + "timestamp": 1684512043723.0, + "annotatedSourceSentencesIndices": [ + 4 + ], + "names": [ + "annotator1" + ], + "text": "Wait, did he ever account for vector N not being a unit vector? He never required that the N vector represented the area of the delta slanted plane did he?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_8_chunk14.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_8_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..64f8cc2ebcc9fcb055e8a5362fe19777f87bee46 --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_8_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 8, + "timestamp": 1684512043723.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Wait, did he ever account for vector N not being a unit vector? He never required that the N vector represented the area of the delta slanted plane did he?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/WfEQabCGAqI_8_chunk15.json b/sight/query/annotated_chunks_window20/WfEQabCGAqI_8_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..64f8cc2ebcc9fcb055e8a5362fe19777f87bee46 --- /dev/null +++ b/sight/query/annotated_chunks_window20/WfEQabCGAqI_8_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "WfEQabCGAqI", + "query_id": 8, + "timestamp": 1684512043723.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Wait, did he ever account for vector N not being a unit vector? 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"names": [ + "annotator1" + ], + "text": "Sorry I'm having trouble keeping up, but for the Poisson example, where does that expression for mu(x) come from?\n\n\nThis is terrific by the way- thank you MIT for helping me stay even a little afloat in one of my classes." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk21.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..a2d4c69e49c3f863e567da2291074a5ca98eb5ef --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 0, + "timestamp": 1684191675943.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Sorry I'm having trouble keeping up, but for the Poisson example, where does that expression for mu(x) come from?\n\n\nThis is terrific by the way- thank you MIT for 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"names": [ + "annotator1" + ], + "text": "Sorry I'm having trouble keeping up, but for the Poisson example, where does that expression for mu(x) come from?\n\n\nThis is terrific by the way- thank you MIT for helping me stay even a little afloat in one of my classes." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk30.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk30.json new file mode 100644 index 0000000000000000000000000000000000000000..a2d4c69e49c3f863e567da2291074a5ca98eb5ef --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk30.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 0, + "timestamp": 1684191675943.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Sorry I'm having trouble keeping up, but for the Poisson example, where does that expression for mu(x) come from?\n\n\nThis is terrific by the way- thank you MIT for helping me stay even a little afloat in one of my classes." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk31.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk31.json new file mode 100644 index 0000000000000000000000000000000000000000..a2d4c69e49c3f863e567da2291074a5ca98eb5ef --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk31.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 0, + "timestamp": 1684191675943.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Sorry I'm having trouble keeping up, but for the Poisson example, where does that expression for mu(x) come from?\n\n\nThis is terrific by the way- thank you MIT for helping me stay even a little afloat in one of my classes." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk32.json 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"names": [ + "annotator1" + ], + "text": "Sorry I'm having trouble keeping up, but for the Poisson example, where does that expression for mu(x) come from?\n\n\nThis is terrific by the way- thank you MIT for helping me stay even a little afloat in one of my classes." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk35.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk35.json new file mode 100644 index 0000000000000000000000000000000000000000..a2d4c69e49c3f863e567da2291074a5ca98eb5ef --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk35.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 0, + "timestamp": 1684191675943.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Sorry I'm having trouble keeping up, but for the Poisson example, where does that expression for mu(x) come from?\n\n\nThis is terrific by the way- thank you MIT for helping me stay even a little afloat in one of my classes." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk36.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk36.json new file mode 100644 index 0000000000000000000000000000000000000000..a2d4c69e49c3f863e567da2291074a5ca98eb5ef --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk36.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 0, + "timestamp": 1684191675943.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Sorry I'm having trouble keeping up, but for the Poisson example, where does that expression for mu(x) come from?\n\n\nThis is terrific by the way- thank you MIT for helping me stay even a little afloat in one of my classes." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk37.json 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"names": [ + "annotator1" + ], + "text": "Sorry I'm having trouble keeping up, but for the Poisson example, where does that expression for mu(x) come from?\n\n\nThis is terrific by the way- thank you MIT for helping me stay even a little afloat in one of my classes." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk4.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..a2d4c69e49c3f863e567da2291074a5ca98eb5ef --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 0, + "timestamp": 1684191675943.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Sorry I'm having trouble keeping up, but for the Poisson example, where does that expression for mu(x) come from?\n\n\nThis is terrific by the way- thank you MIT for helping me stay even a little afloat in one of my classes." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk40.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk40.json new file mode 100644 index 0000000000000000000000000000000000000000..a2d4c69e49c3f863e567da2291074a5ca98eb5ef --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk40.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 0, + "timestamp": 1684191675943.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Sorry I'm having trouble keeping up, but for the Poisson example, where does that expression for mu(x) come from?\n\n\nThis is terrific by the way- thank you MIT for helping me stay even a little afloat in one of my classes." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk41.json 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"names": [ + "annotator1" + ], + "text": "Sorry I'm having trouble keeping up, but for the Poisson example, where does that expression for mu(x) come from?\n\n\nThis is terrific by the way- thank you MIT for helping me stay even a little afloat in one of my classes." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk44.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk44.json new file mode 100644 index 0000000000000000000000000000000000000000..a2d4c69e49c3f863e567da2291074a5ca98eb5ef --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk44.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 0, + "timestamp": 1684191675943.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Sorry I'm having trouble keeping up, but for the Poisson example, where does that expression for mu(x) come from?\n\n\nThis is terrific by the way- thank you MIT for helping me stay even a little afloat in one of my classes." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk5.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..a2d4c69e49c3f863e567da2291074a5ca98eb5ef --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 0, + "timestamp": 1684191675943.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Sorry I'm having trouble keeping up, but for the Poisson example, where does that expression for mu(x) come from?\n\n\nThis is terrific by the way- thank you MIT for helping me stay even a little afloat in one of my classes." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk6.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..a2d4c69e49c3f863e567da2291074a5ca98eb5ef --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 0, + "timestamp": 1684191675943.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Sorry I'm having trouble keeping up, but for the Poisson example, where does that expression for mu(x) come from?\n\n\nThis is terrific by the way- thank you MIT for helping me stay even a little afloat in one of my classes." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk7.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..a2d4c69e49c3f863e567da2291074a5ca98eb5ef --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 0, + "timestamp": 1684191675943.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Sorry I'm having trouble keeping up, but for the Poisson example, where does that expression for mu(x) come from?\n\n\nThis is terrific by the way- thank you MIT for helping me stay even a little afloat in one of my classes." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk8.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..a2d4c69e49c3f863e567da2291074a5ca98eb5ef --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 0, + "timestamp": 1684191675943.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Sorry I'm having trouble keeping up, but for the Poisson example, where does that expression for mu(x) come from?\n\n\nThis is terrific by the way- thank you MIT for helping me stay even a little afloat in one of my classes." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk9.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..d97cb879ca8957a064844c62c693c69e2feb8de6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_0_chunk9.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 0, + "timestamp": 1684191675943.0, + "annotatedSourceSentencesIndices": [ + 8 + ], + "names": [ + "annotator1" + ], + "text": "Sorry I'm having trouble keeping up, but for the Poisson example, where does that expression for mu(x) come from?\n\n\nThis is terrific by the way- thank you MIT for helping me stay even a little afloat in one of my classes." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk0.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk0.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk1.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk1.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk10.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk10.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk11.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk11.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk12.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk12.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk13.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk13.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk14.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk14.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk15.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk15.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk16.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk16.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk17.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk17.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk18.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk18.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk19.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk19.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk2.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk2.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk20.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk20.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk21.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk21.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk22.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk22.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk23.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk23.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk24.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk24.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk25.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk25.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk26.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk26.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk27.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk27.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk27.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk28.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk28.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk28.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk29.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk29.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk29.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk3.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk3.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk30.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk30.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk30.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk31.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk31.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk31.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk32.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk32.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk32.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk33.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk33.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk33.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk34.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk34.json new file mode 100644 index 0000000000000000000000000000000000000000..3d9aabe727491616fb8f337d9992a9122930f745 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk34.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [ + 17 + ], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk35.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk35.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk35.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk36.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk36.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk36.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk37.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk37.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk37.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk38.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk38.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk38.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk39.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk39.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk39.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk4.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk4.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk40.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk40.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk40.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk41.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk41.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk41.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk42.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk42.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk42.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk43.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk43.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk43.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk44.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk44.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk44.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk5.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk5.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk6.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk6.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk7.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk7.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk8.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk8.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk9.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..69100619ea4f69e2c3c493f95dfdbb26b159e49f --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_2_chunk9.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 2, + "timestamp": 1684511180783.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk0.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk1.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk10.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk11.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk12.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk13.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk14.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk15.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk16.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk17.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk18.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk19.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk2.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk20.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk21.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk22.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk23.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk24.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk25.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk26.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk27.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk27.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk27.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk28.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk28.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk28.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk29.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk29.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk29.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk3.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..cb666f7642b2a6814a698f8bd1b2e40788fbb807 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk3.json @@ -0,0 +1,16 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [ + 2, + 3, + 4 + ], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk30.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk30.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk30.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk31.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk31.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk31.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk32.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk32.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk32.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk33.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk33.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk33.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk34.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk34.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk34.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk35.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk35.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk35.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk36.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk36.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk36.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk37.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk37.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk37.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk38.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk38.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk38.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk39.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk39.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk39.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk4.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk40.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk40.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk40.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk41.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk41.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk41.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk42.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk42.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk42.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk43.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk43.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk43.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk44.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk44.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk44.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk5.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk6.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk7.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk8.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk9.json b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..103e77e60fe0cb938747a9568225861408da7a83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/X-ix97pw0xY_3_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "X-ix97pw0xY", + "query_id": 3, + "timestamp": 1684511272691.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "It is mentioned that \"phi is known positive value\" (Lecture 23: 16.28 min). I am wondering, if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk0.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..ecac1710431bb08dea108e8ac31a06cd6469850c --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 0, + "timestamp": 1684512668939.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "can anyone explain how the 5th column of w8 came out to be?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk1.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..ecac1710431bb08dea108e8ac31a06cd6469850c --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 0, + "timestamp": 1684512668939.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "can anyone explain how the 5th column of w8 came out to be?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk10.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..ecac1710431bb08dea108e8ac31a06cd6469850c --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 0, + "timestamp": 1684512668939.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "can anyone explain how the 5th column of w8 came out to be?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk11.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..ecac1710431bb08dea108e8ac31a06cd6469850c --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 0, + "timestamp": 1684512668939.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "can anyone explain how the 5th column of w8 came out to be?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk12.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..ecac1710431bb08dea108e8ac31a06cd6469850c --- /dev/null +++ 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"query_id": 0, + "timestamp": 1684512668939.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "can anyone explain how the 5th column of w8 came out to be?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk7.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..ecac1710431bb08dea108e8ac31a06cd6469850c --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 0, + "timestamp": 1684512668939.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "can anyone explain how the 5th column of w8 came out to be?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk8.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..ecac1710431bb08dea108e8ac31a06cd6469850c --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 0, + "timestamp": 1684512668939.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "can anyone explain how the 5th column of w8 came out to be?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk9.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..ecac1710431bb08dea108e8ac31a06cd6469850c --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 0, + "timestamp": 1684512668939.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "can anyone explain how the 5th column of w8 came out to be?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk0.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..b044470d1eefe37c1175151f38cfc010c97f3352 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk1.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..b044470d1eefe37c1175151f38cfc010c97f3352 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk10.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..b044470d1eefe37c1175151f38cfc010c97f3352 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk11.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b044470d1eefe37c1175151f38cfc010c97f3352 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk12.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..b044470d1eefe37c1175151f38cfc010c97f3352 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk13.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..b044470d1eefe37c1175151f38cfc010c97f3352 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk14.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..b044470d1eefe37c1175151f38cfc010c97f3352 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk15.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..59bbd565d9d2812bdc1bf66b89eed74387cecd72 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk15.json @@ -0,0 +1,17 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [ + 16, + 17, + 18, + 19 + ], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk16.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..316c63cadd588f2b80799d8b9d4bb1d2a2942f3d --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk16.json @@ -0,0 +1,18 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [ + 0, + 1, + 2, + 3, + 4 + ], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk17.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b044470d1eefe37c1175151f38cfc010c97f3352 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk18.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..b044470d1eefe37c1175151f38cfc010c97f3352 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk19.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..b044470d1eefe37c1175151f38cfc010c97f3352 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk2.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..b044470d1eefe37c1175151f38cfc010c97f3352 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk20.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..b044470d1eefe37c1175151f38cfc010c97f3352 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk21.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..b044470d1eefe37c1175151f38cfc010c97f3352 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk22.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..b044470d1eefe37c1175151f38cfc010c97f3352 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk23.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..b044470d1eefe37c1175151f38cfc010c97f3352 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk24.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..b044470d1eefe37c1175151f38cfc010c97f3352 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk25.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..b044470d1eefe37c1175151f38cfc010c97f3352 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk26.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..b044470d1eefe37c1175151f38cfc010c97f3352 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk27.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk27.json new file mode 100644 index 0000000000000000000000000000000000000000..b044470d1eefe37c1175151f38cfc010c97f3352 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk27.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk28.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk28.json new file mode 100644 index 0000000000000000000000000000000000000000..b044470d1eefe37c1175151f38cfc010c97f3352 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk28.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk29.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk29.json new file mode 100644 index 0000000000000000000000000000000000000000..b044470d1eefe37c1175151f38cfc010c97f3352 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk29.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk3.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..b044470d1eefe37c1175151f38cfc010c97f3352 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk30.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk30.json new file mode 100644 index 0000000000000000000000000000000000000000..b044470d1eefe37c1175151f38cfc010c97f3352 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk30.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk31.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk31.json new file mode 100644 index 0000000000000000000000000000000000000000..b044470d1eefe37c1175151f38cfc010c97f3352 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk31.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk32.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk32.json new file mode 100644 index 0000000000000000000000000000000000000000..b044470d1eefe37c1175151f38cfc010c97f3352 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk32.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk4.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..b044470d1eefe37c1175151f38cfc010c97f3352 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk5.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..b044470d1eefe37c1175151f38cfc010c97f3352 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk6.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..b044470d1eefe37c1175151f38cfc010c97f3352 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk7.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b044470d1eefe37c1175151f38cfc010c97f3352 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk8.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..b044470d1eefe37c1175151f38cfc010c97f3352 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk9.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..b044470d1eefe37c1175151f38cfc010c97f3352 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 1, + "timestamp": 1684512757144.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Question\n23:40 - so you have H2 and to build H4 you did H2(H2)\nTo get H8 you did H2(H4) but do H4(H2) = H8 as well?\nBecause I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk0.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3241244aa82feab206c42e4898ecc18c41f797 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 3, + "timestamp": 1684512777130.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "In 17.03, Why UU transpose is symmetric?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk1.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3241244aa82feab206c42e4898ecc18c41f797 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 3, + "timestamp": 1684512777130.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "In 17.03, Why UU transpose is symmetric?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk10.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3241244aa82feab206c42e4898ecc18c41f797 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 3, + "timestamp": 1684512777130.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "In 17.03, Why UU transpose is symmetric?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk11.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..070298316fcd7501dc0a2aed8f9fa8cb3cdad9e8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk11.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 3, + "timestamp": 1684512777130.0, + "annotatedSourceSentencesIndices": [ + 1 + ], + "names": [ + "annotator1" + ], + "text": "In 17.03, Why UU transpose is symmetric?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk12.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3241244aa82feab206c42e4898ecc18c41f797 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 3, + "timestamp": 1684512777130.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "In 17.03, Why UU transpose is symmetric?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk13.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3241244aa82feab206c42e4898ecc18c41f797 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 3, + "timestamp": 1684512777130.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "In 17.03, Why UU transpose is symmetric?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk14.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3241244aa82feab206c42e4898ecc18c41f797 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 3, + "timestamp": 1684512777130.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "In 17.03, Why UU transpose is symmetric?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk15.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3241244aa82feab206c42e4898ecc18c41f797 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 3, + "timestamp": 1684512777130.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "In 17.03, Why UU transpose is symmetric?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk16.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3241244aa82feab206c42e4898ecc18c41f797 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 3, + "timestamp": 1684512777130.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "In 17.03, Why UU transpose is symmetric?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk17.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3241244aa82feab206c42e4898ecc18c41f797 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 3, + "timestamp": 1684512777130.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "In 17.03, Why UU transpose is symmetric?" + } +] \ No newline at end of file diff --git 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hold ??? a bit confused please help" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk12.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..704d3e6e87d155337d3b85cd2aad97b06e063968 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk12.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 5, + "timestamp": 1684192613269.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "for a square matrix with orthogonal columns will ||Qx||^2 = || x ||^2 hold or the columns have to be orthonormal for this equality to hold ??? a bit confused please help" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk13.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk13.json new file mode 100644 index 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1684192613269.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "for a square matrix with orthogonal columns will ||Qx||^2 = || x ||^2 hold or the columns have to be orthonormal for this equality to hold ??? a bit confused please help" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk15.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..704d3e6e87d155337d3b85cd2aad97b06e063968 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk15.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 5, + "timestamp": 1684192613269.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "for a square matrix with orthogonal columns will ||Qx||^2 = || x ||^2 hold or the columns have to be orthonormal for this equality to hold ??? a bit confused please help" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk16.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..704d3e6e87d155337d3b85cd2aad97b06e063968 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk16.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 5, + "timestamp": 1684192613269.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "for a square matrix with orthogonal columns will ||Qx||^2 = || x ||^2 hold or the columns have to be orthonormal for this equality to hold ??? a bit confused please help" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk17.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk17.json new file mode 100644 index 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1684192613269.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "for a square matrix with orthogonal columns will ||Qx||^2 = || x ||^2 hold or the columns have to be orthonormal for this equality to hold ??? a bit confused please help" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk19.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..704d3e6e87d155337d3b85cd2aad97b06e063968 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk19.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 5, + "timestamp": 1684192613269.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "for a square matrix with orthogonal columns will ||Qx||^2 = || x ||^2 hold or the columns have to be orthonormal for this equality to hold ??? a bit confused please help" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk2.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..704d3e6e87d155337d3b85cd2aad97b06e063968 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk2.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 5, + "timestamp": 1684192613269.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "for a square matrix with orthogonal columns will ||Qx||^2 = || x ||^2 hold or the columns have to be orthonormal for this equality to hold ??? a bit confused please help" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk20.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..704d3e6e87d155337d3b85cd2aad97b06e063968 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk20.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 5, + "timestamp": 1684192613269.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "for a square matrix with orthogonal columns will ||Qx||^2 = || x ||^2 hold or the columns have to be orthonormal for this equality to hold ??? a bit confused please help" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk21.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..704d3e6e87d155337d3b85cd2aad97b06e063968 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk21.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 5, + "timestamp": 1684192613269.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "for a square matrix with orthogonal columns will ||Qx||^2 = || x ||^2 hold or the columns have to be orthonormal for this equality to hold ??? a bit confused please help" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk22.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..704d3e6e87d155337d3b85cd2aad97b06e063968 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk22.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 5, + "timestamp": 1684192613269.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "for a square matrix with orthogonal columns will ||Qx||^2 = || x ||^2 hold or the columns have to be orthonormal for this equality to hold ??? a bit confused please help" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk23.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..704d3e6e87d155337d3b85cd2aad97b06e063968 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk23.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 5, + "timestamp": 1684192613269.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "for a square matrix with orthogonal columns will ||Qx||^2 = || x ||^2 hold or the columns have to be orthonormal for this equality to hold ??? a bit confused please help" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk24.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..704d3e6e87d155337d3b85cd2aad97b06e063968 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk24.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 5, + "timestamp": 1684192613269.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "for a square matrix with orthogonal columns will ||Qx||^2 = || x ||^2 hold or the columns have to be orthonormal for this equality to hold ??? a bit confused please help" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk25.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..704d3e6e87d155337d3b85cd2aad97b06e063968 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk25.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 5, + "timestamp": 1684192613269.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "for a square matrix with orthogonal columns will ||Qx||^2 = || x ||^2 hold or the columns have to be orthonormal for this equality to hold ??? a bit confused please help" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk26.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..704d3e6e87d155337d3b85cd2aad97b06e063968 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk26.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 5, + "timestamp": 1684192613269.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "for a square matrix with orthogonal columns will ||Qx||^2 = || x ||^2 hold or the columns have to be orthonormal for this equality to hold ??? a bit confused please help" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk27.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk27.json new file mode 100644 index 0000000000000000000000000000000000000000..704d3e6e87d155337d3b85cd2aad97b06e063968 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk27.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 5, + "timestamp": 1684192613269.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "for a square matrix with orthogonal columns will ||Qx||^2 = || x ||^2 hold or the columns have to be orthonormal for this equality to hold ??? a bit confused please help" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk28.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk28.json new file mode 100644 index 0000000000000000000000000000000000000000..704d3e6e87d155337d3b85cd2aad97b06e063968 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk28.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 5, + "timestamp": 1684192613269.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "for a square matrix with orthogonal columns will ||Qx||^2 = || x ||^2 hold or the columns have to be orthonormal for this equality to hold ??? a bit confused please help" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk29.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk29.json new file mode 100644 index 0000000000000000000000000000000000000000..704d3e6e87d155337d3b85cd2aad97b06e063968 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk29.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 5, + "timestamp": 1684192613269.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "for a square matrix with orthogonal columns will ||Qx||^2 = || x ||^2 hold or the columns have to be orthonormal for this equality to hold ??? a bit confused please help" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk3.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c689d3f94085b841cbeb530bfb8e6426fee2d03f --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk3.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 5, + "timestamp": 1684192613269.0, + "annotatedSourceSentencesIndices": [ + 19 + ], + "names": [ + "annotator1", + "annotator2" + ], + "text": "for a square matrix with orthogonal columns will ||Qx||^2 = || x ||^2 hold or the columns have to be orthonormal for this equality to hold ??? a bit confused please help" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk30.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk30.json new file mode 100644 index 0000000000000000000000000000000000000000..704d3e6e87d155337d3b85cd2aad97b06e063968 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk30.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 5, + "timestamp": 1684192613269.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "for a square matrix with orthogonal columns will ||Qx||^2 = || x ||^2 hold or the columns have to be orthonormal for this equality to hold ??? a bit confused please help" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk31.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk31.json new file mode 100644 index 0000000000000000000000000000000000000000..704d3e6e87d155337d3b85cd2aad97b06e063968 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk31.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 5, + "timestamp": 1684192613269.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "for a square matrix with orthogonal columns will ||Qx||^2 = || x ||^2 hold or the columns have to be orthonormal for this equality to hold ??? a bit confused please help" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk32.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk32.json new file mode 100644 index 0000000000000000000000000000000000000000..704d3e6e87d155337d3b85cd2aad97b06e063968 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk32.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 5, + "timestamp": 1684192613269.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "for a square matrix with orthogonal columns will ||Qx||^2 = || x ||^2 hold or the columns have to be orthonormal for this equality to hold ??? a bit confused please help" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk4.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..6b6adc325576571272ccb9035feb00931a11f356 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk4.json @@ -0,0 +1,17 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 5, + "timestamp": 1684192613269.0, + "annotatedSourceSentencesIndices": [ + 1, + 2, + 13 + ], + "names": [ + "annotator1", + "annotator2" + ], + "text": "for a square matrix with orthogonal columns will ||Qx||^2 = || x ||^2 hold or the columns have to be orthonormal for this equality to hold ??? a bit confused please help" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk5.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..704d3e6e87d155337d3b85cd2aad97b06e063968 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk5.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 5, + "timestamp": 1684192613269.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "for a square matrix with orthogonal columns will ||Qx||^2 = || x ||^2 hold or the columns have to be orthonormal for this equality to hold ??? a bit confused please help" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk6.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..704d3e6e87d155337d3b85cd2aad97b06e063968 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk6.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 5, + "timestamp": 1684192613269.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "for a square matrix with orthogonal columns will ||Qx||^2 = || x ||^2 hold or the columns have to be orthonormal for this equality to hold ??? a bit confused please help" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk7.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..704d3e6e87d155337d3b85cd2aad97b06e063968 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk7.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 5, + "timestamp": 1684192613269.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "for a square matrix with orthogonal columns will ||Qx||^2 = || x ||^2 hold or the columns have to be orthonormal for this equality to hold ??? a bit confused please help" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk8.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..704d3e6e87d155337d3b85cd2aad97b06e063968 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk8.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 5, + "timestamp": 1684192613269.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "for a square matrix with orthogonal columns will ||Qx||^2 = || x ||^2 hold or the columns have to be orthonormal for this equality to hold ??? a bit confused please help" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk9.json b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..704d3e6e87d155337d3b85cd2aad97b06e063968 --- /dev/null +++ b/sight/query/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk9.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "Xa2jPbURTjQ", + "query_id": 5, + "timestamp": 1684192613269.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "for a square matrix with orthogonal columns will ||Qx||^2 = || x ||^2 hold or the columns have to be orthonormal for this equality to hold ??? a bit confused please help" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk0.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..b4a54072a18d64a1471ece2051347c5e48c8d969 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 0, + "timestamp": 1684520066474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For the Expected number of fish ( ~ 19:00 ), shouldn't he include the possibility of catching N fish during the first two hours? Is the probability of 3 or more fish in 0 < t < 2 insignificant?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk1.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..b4a54072a18d64a1471ece2051347c5e48c8d969 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 0, + "timestamp": 1684520066474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For the Expected number of fish ( ~ 19:00 ), shouldn't he include the possibility of catching N fish during the first two hours? Is the probability of 3 or more fish in 0 < t < 2 insignificant?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk10.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..b4a54072a18d64a1471ece2051347c5e48c8d969 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 0, + "timestamp": 1684520066474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For the Expected number of fish ( ~ 19:00 ), shouldn't he include the possibility of catching N fish during the first two hours? Is the probability of 3 or more fish in 0 < t < 2 insignificant?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk11.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b4a54072a18d64a1471ece2051347c5e48c8d969 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 0, + "timestamp": 1684520066474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For the Expected number of fish ( ~ 19:00 ), shouldn't he include the possibility of catching N fish during the first two hours? Is the probability of 3 or more fish in 0 < t < 2 insignificant?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk12.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..b4a54072a18d64a1471ece2051347c5e48c8d969 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 0, + "timestamp": 1684520066474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For the Expected number of fish ( ~ 19:00 ), shouldn't he include the possibility of catching N fish during the first two hours? Is the probability of 3 or more fish in 0 < t < 2 insignificant?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk13.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..b4a54072a18d64a1471ece2051347c5e48c8d969 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 0, + "timestamp": 1684520066474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For the Expected number of fish ( ~ 19:00 ), shouldn't he include the possibility of catching N fish during the first two hours? Is the probability of 3 or more fish in 0 < t < 2 insignificant?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk14.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..b4a54072a18d64a1471ece2051347c5e48c8d969 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 0, + "timestamp": 1684520066474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For the Expected number of fish ( ~ 19:00 ), shouldn't he include the possibility of catching N fish during the first two hours? Is the probability of 3 or more fish in 0 < t < 2 insignificant?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk15.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..b4a54072a18d64a1471ece2051347c5e48c8d969 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 0, + "timestamp": 1684520066474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For the Expected number of fish ( ~ 19:00 ), shouldn't he include the possibility of catching N fish during the first two hours? Is the probability of 3 or more fish in 0 < t < 2 insignificant?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk16.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..b4a54072a18d64a1471ece2051347c5e48c8d969 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 0, + "timestamp": 1684520066474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For the Expected number of fish ( ~ 19:00 ), shouldn't he include the possibility of catching N fish during the first two hours? Is the probability of 3 or more fish in 0 < t < 2 insignificant?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk17.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b4a54072a18d64a1471ece2051347c5e48c8d969 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 0, + "timestamp": 1684520066474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For the Expected number of fish ( ~ 19:00 ), shouldn't he include the possibility of catching N fish during the first two hours? Is the probability of 3 or more fish in 0 < t < 2 insignificant?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk18.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..b4a54072a18d64a1471ece2051347c5e48c8d969 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 0, + "timestamp": 1684520066474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For the Expected number of fish ( ~ 19:00 ), shouldn't he include the possibility of catching N fish during the first two hours? Is the probability of 3 or more fish in 0 < t < 2 insignificant?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk19.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..b4a54072a18d64a1471ece2051347c5e48c8d969 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 0, + "timestamp": 1684520066474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For the Expected number of fish ( ~ 19:00 ), shouldn't he include the possibility of catching N fish during the first two hours? Is the probability of 3 or more fish in 0 < t < 2 insignificant?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk2.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..b4a54072a18d64a1471ece2051347c5e48c8d969 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 0, + "timestamp": 1684520066474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For the Expected number of fish ( ~ 19:00 ), shouldn't he include the possibility of catching N fish during the first two hours? Is the probability of 3 or more fish in 0 < t < 2 insignificant?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk20.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..b4a54072a18d64a1471ece2051347c5e48c8d969 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 0, + "timestamp": 1684520066474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For the Expected number of fish ( ~ 19:00 ), shouldn't he include the possibility of catching N fish during the first two hours? Is the probability of 3 or more fish in 0 < t < 2 insignificant?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk21.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..b4a54072a18d64a1471ece2051347c5e48c8d969 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 0, + "timestamp": 1684520066474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For the Expected number of fish ( ~ 19:00 ), shouldn't he include the possibility of catching N fish during the first two hours? Is the probability of 3 or more fish in 0 < t < 2 insignificant?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk22.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..b4a54072a18d64a1471ece2051347c5e48c8d969 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 0, + "timestamp": 1684520066474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For the Expected number of fish ( ~ 19:00 ), shouldn't he include the possibility of catching N fish during the first two hours? Is the probability of 3 or more fish in 0 < t < 2 insignificant?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk23.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..b4a54072a18d64a1471ece2051347c5e48c8d969 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 0, + "timestamp": 1684520066474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For the Expected number of fish ( ~ 19:00 ), shouldn't he include the possibility of catching N fish during the first two hours? Is the probability of 3 or more fish in 0 < t < 2 insignificant?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk24.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..b4a54072a18d64a1471ece2051347c5e48c8d969 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 0, + "timestamp": 1684520066474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For the Expected number of fish ( ~ 19:00 ), shouldn't he include the possibility of catching N fish during the first two hours? Is the probability of 3 or more fish in 0 < t < 2 insignificant?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk25.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..b4a54072a18d64a1471ece2051347c5e48c8d969 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 0, + "timestamp": 1684520066474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For the Expected number of fish ( ~ 19:00 ), shouldn't he include the possibility of catching N fish during the first two hours? Is the probability of 3 or more fish in 0 < t < 2 insignificant?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk3.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..b4a54072a18d64a1471ece2051347c5e48c8d969 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 0, + "timestamp": 1684520066474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For the Expected number of fish ( ~ 19:00 ), shouldn't he include the possibility of catching N fish during the first two hours? Is the probability of 3 or more fish in 0 < t < 2 insignificant?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk4.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..b4a54072a18d64a1471ece2051347c5e48c8d969 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 0, + "timestamp": 1684520066474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For the Expected number of fish ( ~ 19:00 ), shouldn't he include the possibility of catching N fish during the first two hours? Is the probability of 3 or more fish in 0 < t < 2 insignificant?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk5.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..b4a54072a18d64a1471ece2051347c5e48c8d969 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 0, + "timestamp": 1684520066474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For the Expected number of fish ( ~ 19:00 ), shouldn't he include the possibility of catching N fish during the first two hours? Is the probability of 3 or more fish in 0 < t < 2 insignificant?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk6.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..b4a54072a18d64a1471ece2051347c5e48c8d969 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 0, + "timestamp": 1684520066474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For the Expected number of fish ( ~ 19:00 ), shouldn't he include the possibility of catching N fish during the first two hours? Is the probability of 3 or more fish in 0 < t < 2 insignificant?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk7.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b4a54072a18d64a1471ece2051347c5e48c8d969 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 0, + "timestamp": 1684520066474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For the Expected number of fish ( ~ 19:00 ), shouldn't he include the possibility of catching N fish during the first two hours? Is the probability of 3 or more fish in 0 < t < 2 insignificant?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk8.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..b4a54072a18d64a1471ece2051347c5e48c8d969 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 0, + "timestamp": 1684520066474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "For the Expected number of fish ( ~ 19:00 ), shouldn't he include the possibility of catching N fish during the first two hours? Is the probability of 3 or more fish in 0 < t < 2 insignificant?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk9.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..66761f9c8e0c9e2c389965618fbbbd69edba58cb --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_0_chunk9.json @@ -0,0 +1,16 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 0, + "timestamp": 1684520066474.0, + "annotatedSourceSentencesIndices": [ + 5, + 6, + 7 + ], + "names": [ + "annotator1" + ], + "text": "For the Expected number of fish ( ~ 19:00 ), shouldn't he include the possibility of catching N fish during the first two hours? Is the probability of 3 or more fish in 0 < t < 2 insignificant?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk0.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..52b3b39694596e8617820971c2e601cc5764bf10 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 2, + "timestamp": 1684520098328.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Shouldn't the answer to the fish question at 15:46 be equal to p(0,2)*p(1,3) instead of p(0,2)*(1-p(0,3))\nI say this because the fisherman should fish for no longer than 1 fish. In the case of 1-p(0,3), he's considering all the possibilities that he could fish 1,2,3,4,5,6,7..... any number of fishes during that interval? from hour 2....5" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk1.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..52b3b39694596e8617820971c2e601cc5764bf10 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 2, + "timestamp": 1684520098328.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Shouldn't the answer to the fish question at 15:46 be equal to p(0,2)*p(1,3) instead of p(0,2)*(1-p(0,3))\nI say this because the fisherman should fish for no longer than 1 fish. In the case of 1-p(0,3), he's considering all the possibilities that he could fish 1,2,3,4,5,6,7..... any number of fishes during that interval? from hour 2....5" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk10.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..52b3b39694596e8617820971c2e601cc5764bf10 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 2, + "timestamp": 1684520098328.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Shouldn't the answer to the fish question at 15:46 be equal to p(0,2)*p(1,3) instead of p(0,2)*(1-p(0,3))\nI say this because the fisherman should fish for no longer than 1 fish. In the case of 1-p(0,3), he's considering all the possibilities that he could fish 1,2,3,4,5,6,7..... any number of fishes during that interval? from hour 2....5" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk11.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..52b3b39694596e8617820971c2e601cc5764bf10 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 2, + "timestamp": 1684520098328.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Shouldn't the answer to the fish question at 15:46 be equal to p(0,2)*p(1,3) instead of p(0,2)*(1-p(0,3))\nI say this because the fisherman should fish for no longer than 1 fish. In the case of 1-p(0,3), he's considering all the possibilities that he could fish 1,2,3,4,5,6,7..... any number of fishes during that interval? from hour 2....5" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk12.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..52b3b39694596e8617820971c2e601cc5764bf10 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 2, + "timestamp": 1684520098328.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Shouldn't the answer to the fish question at 15:46 be equal to p(0,2)*p(1,3) instead of p(0,2)*(1-p(0,3))\nI say this because the fisherman should fish for no longer than 1 fish. In the case of 1-p(0,3), he's considering all the possibilities that he could fish 1,2,3,4,5,6,7..... any number of fishes during that interval? from hour 2....5" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk13.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..52b3b39694596e8617820971c2e601cc5764bf10 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 2, + "timestamp": 1684520098328.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Shouldn't the answer to the fish question at 15:46 be equal to p(0,2)*p(1,3) instead of p(0,2)*(1-p(0,3))\nI say this because the fisherman should fish for no longer than 1 fish. In the case of 1-p(0,3), he's considering all the possibilities that he could fish 1,2,3,4,5,6,7..... any number of fishes during that interval? from hour 2....5" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk14.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..52b3b39694596e8617820971c2e601cc5764bf10 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 2, + "timestamp": 1684520098328.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Shouldn't the answer to the fish question at 15:46 be equal to p(0,2)*p(1,3) instead of p(0,2)*(1-p(0,3))\nI say this because the fisherman should fish for no longer than 1 fish. In the case of 1-p(0,3), he's considering all the possibilities that he could fish 1,2,3,4,5,6,7..... any number of fishes during that interval? from hour 2....5" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk15.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..52b3b39694596e8617820971c2e601cc5764bf10 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 2, + "timestamp": 1684520098328.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Shouldn't the answer to the fish question at 15:46 be equal to p(0,2)*p(1,3) instead of p(0,2)*(1-p(0,3))\nI say this because the fisherman should fish for no longer than 1 fish. In the case of 1-p(0,3), he's considering all the possibilities that he could fish 1,2,3,4,5,6,7..... any number of fishes during that interval? from hour 2....5" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk16.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..52b3b39694596e8617820971c2e601cc5764bf10 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 2, + "timestamp": 1684520098328.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Shouldn't the answer to the fish question at 15:46 be equal to p(0,2)*p(1,3) instead of p(0,2)*(1-p(0,3))\nI say this because the fisherman should fish for no longer than 1 fish. In the case of 1-p(0,3), he's considering all the possibilities that he could fish 1,2,3,4,5,6,7..... any number of fishes during that interval? from hour 2....5" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk17.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..52b3b39694596e8617820971c2e601cc5764bf10 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 2, + "timestamp": 1684520098328.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Shouldn't the answer to the fish question at 15:46 be equal to p(0,2)*p(1,3) instead of p(0,2)*(1-p(0,3))\nI say this because the fisherman should fish for no longer than 1 fish. In the case of 1-p(0,3), he's considering all the possibilities that he could fish 1,2,3,4,5,6,7..... any number of fishes during that interval? from hour 2....5" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk18.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..52b3b39694596e8617820971c2e601cc5764bf10 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 2, + "timestamp": 1684520098328.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Shouldn't the answer to the fish question at 15:46 be equal to p(0,2)*p(1,3) instead of p(0,2)*(1-p(0,3))\nI say this because the fisherman should fish for no longer than 1 fish. In the case of 1-p(0,3), he's considering all the possibilities that he could fish 1,2,3,4,5,6,7..... any number of fishes during that interval? from hour 2....5" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk19.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..52b3b39694596e8617820971c2e601cc5764bf10 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 2, + "timestamp": 1684520098328.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Shouldn't the answer to the fish question at 15:46 be equal to p(0,2)*p(1,3) instead of p(0,2)*(1-p(0,3))\nI say this because the fisherman should fish for no longer than 1 fish. In the case of 1-p(0,3), he's considering all the possibilities that he could fish 1,2,3,4,5,6,7..... any number of fishes during that interval? from hour 2....5" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk2.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..52b3b39694596e8617820971c2e601cc5764bf10 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 2, + "timestamp": 1684520098328.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Shouldn't the answer to the fish question at 15:46 be equal to p(0,2)*p(1,3) instead of p(0,2)*(1-p(0,3))\nI say this because the fisherman should fish for no longer than 1 fish. In the case of 1-p(0,3), he's considering all the possibilities that he could fish 1,2,3,4,5,6,7..... any number of fishes during that interval? from hour 2....5" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk20.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..52b3b39694596e8617820971c2e601cc5764bf10 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 2, + "timestamp": 1684520098328.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Shouldn't the answer to the fish question at 15:46 be equal to p(0,2)*p(1,3) instead of p(0,2)*(1-p(0,3))\nI say this because the fisherman should fish for no longer than 1 fish. In the case of 1-p(0,3), he's considering all the possibilities that he could fish 1,2,3,4,5,6,7..... any number of fishes during that interval? from hour 2....5" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk21.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..52b3b39694596e8617820971c2e601cc5764bf10 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 2, + "timestamp": 1684520098328.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Shouldn't the answer to the fish question at 15:46 be equal to p(0,2)*p(1,3) instead of p(0,2)*(1-p(0,3))\nI say this because the fisherman should fish for no longer than 1 fish. In the case of 1-p(0,3), he's considering all the possibilities that he could fish 1,2,3,4,5,6,7..... any number of fishes during that interval? from hour 2....5" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk22.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..52b3b39694596e8617820971c2e601cc5764bf10 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 2, + "timestamp": 1684520098328.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Shouldn't the answer to the fish question at 15:46 be equal to p(0,2)*p(1,3) instead of p(0,2)*(1-p(0,3))\nI say this because the fisherman should fish for no longer than 1 fish. In the case of 1-p(0,3), he's considering all the possibilities that he could fish 1,2,3,4,5,6,7..... any number of fishes during that interval? from hour 2....5" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk23.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..52b3b39694596e8617820971c2e601cc5764bf10 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 2, + "timestamp": 1684520098328.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Shouldn't the answer to the fish question at 15:46 be equal to p(0,2)*p(1,3) instead of p(0,2)*(1-p(0,3))\nI say this because the fisherman should fish for no longer than 1 fish. In the case of 1-p(0,3), he's considering all the possibilities that he could fish 1,2,3,4,5,6,7..... any number of fishes during that interval? from hour 2....5" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk24.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..52b3b39694596e8617820971c2e601cc5764bf10 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 2, + "timestamp": 1684520098328.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Shouldn't the answer to the fish question at 15:46 be equal to p(0,2)*p(1,3) instead of p(0,2)*(1-p(0,3))\nI say this because the fisherman should fish for no longer than 1 fish. In the case of 1-p(0,3), he's considering all the possibilities that he could fish 1,2,3,4,5,6,7..... any number of fishes during that interval? from hour 2....5" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk25.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..52b3b39694596e8617820971c2e601cc5764bf10 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 2, + "timestamp": 1684520098328.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Shouldn't the answer to the fish question at 15:46 be equal to p(0,2)*p(1,3) instead of p(0,2)*(1-p(0,3))\nI say this because the fisherman should fish for no longer than 1 fish. In the case of 1-p(0,3), he's considering all the possibilities that he could fish 1,2,3,4,5,6,7..... any number of fishes during that interval? from hour 2....5" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk3.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..52b3b39694596e8617820971c2e601cc5764bf10 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 2, + "timestamp": 1684520098328.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Shouldn't the answer to the fish question at 15:46 be equal to p(0,2)*p(1,3) instead of p(0,2)*(1-p(0,3))\nI say this because the fisherman should fish for no longer than 1 fish. In the case of 1-p(0,3), he's considering all the possibilities that he could fish 1,2,3,4,5,6,7..... any number of fishes during that interval? from hour 2....5" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk4.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..52b3b39694596e8617820971c2e601cc5764bf10 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 2, + "timestamp": 1684520098328.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Shouldn't the answer to the fish question at 15:46 be equal to p(0,2)*p(1,3) instead of p(0,2)*(1-p(0,3))\nI say this because the fisherman should fish for no longer than 1 fish. In the case of 1-p(0,3), he's considering all the possibilities that he could fish 1,2,3,4,5,6,7..... any number of fishes during that interval? from hour 2....5" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk5.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..52b3b39694596e8617820971c2e601cc5764bf10 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 2, + "timestamp": 1684520098328.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Shouldn't the answer to the fish question at 15:46 be equal to p(0,2)*p(1,3) instead of p(0,2)*(1-p(0,3))\nI say this because the fisherman should fish for no longer than 1 fish. In the case of 1-p(0,3), he's considering all the possibilities that he could fish 1,2,3,4,5,6,7..... any number of fishes during that interval? from hour 2....5" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk6.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..52b3b39694596e8617820971c2e601cc5764bf10 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 2, + "timestamp": 1684520098328.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Shouldn't the answer to the fish question at 15:46 be equal to p(0,2)*p(1,3) instead of p(0,2)*(1-p(0,3))\nI say this because the fisherman should fish for no longer than 1 fish. In the case of 1-p(0,3), he's considering all the possibilities that he could fish 1,2,3,4,5,6,7..... any number of fishes during that interval? from hour 2....5" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk7.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..bd253cb012595f43cdfe4208cbc6ccfa6fa51116 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk7.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 2, + "timestamp": 1684520098328.0, + "annotatedSourceSentencesIndices": [ + 15 + ], + "names": [ + "annotator1" + ], + "text": "Shouldn't the answer to the fish question at 15:46 be equal to p(0,2)*p(1,3) instead of p(0,2)*(1-p(0,3))\nI say this because the fisherman should fish for no longer than 1 fish. In the case of 1-p(0,3), he's considering all the possibilities that he could fish 1,2,3,4,5,6,7..... any number of fishes during that interval? from hour 2....5" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk8.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..52b3b39694596e8617820971c2e601cc5764bf10 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 2, + "timestamp": 1684520098328.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Shouldn't the answer to the fish question at 15:46 be equal to p(0,2)*p(1,3) instead of p(0,2)*(1-p(0,3))\nI say this because the fisherman should fish for no longer than 1 fish. In the case of 1-p(0,3), he's considering all the possibilities that he could fish 1,2,3,4,5,6,7..... any number of fishes during that interval? from hour 2....5" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk9.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..52b3b39694596e8617820971c2e601cc5764bf10 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_2_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 2, + "timestamp": 1684520098328.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Shouldn't the answer to the fish question at 15:46 be equal to p(0,2)*p(1,3) instead of p(0,2)*(1-p(0,3))\nI say this because the fisherman should fish for no longer than 1 fish. In the case of 1-p(0,3), he's considering all the possibilities that he could fish 1,2,3,4,5,6,7..... any number of fishes during that interval? from hour 2....5" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk0.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..48c8f70169f7eff03aca9b7d571f746ad807ac79 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 3, + "timestamp": 1684520173396.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The first terms in part d and f of the examples should be weighted with the probability that scenario 1 occurs, right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk1.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..48c8f70169f7eff03aca9b7d571f746ad807ac79 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 3, + "timestamp": 1684520173396.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The first terms in part d and f of the examples should be weighted with the probability that scenario 1 occurs, right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk10.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..48c8f70169f7eff03aca9b7d571f746ad807ac79 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 3, + "timestamp": 1684520173396.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The first terms in part d and f of the examples should be weighted with the probability that scenario 1 occurs, right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk11.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..48c8f70169f7eff03aca9b7d571f746ad807ac79 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 3, + "timestamp": 1684520173396.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The first terms in part d and f of the examples should be weighted with the probability that scenario 1 occurs, right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk12.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..48c8f70169f7eff03aca9b7d571f746ad807ac79 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 3, + "timestamp": 1684520173396.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The first terms in part d and f of the examples should be weighted with the probability that scenario 1 occurs, right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk13.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..48c8f70169f7eff03aca9b7d571f746ad807ac79 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 3, + "timestamp": 1684520173396.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The first terms in part d and f of the examples should be weighted with the probability that scenario 1 occurs, right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk14.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..48c8f70169f7eff03aca9b7d571f746ad807ac79 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 3, + "timestamp": 1684520173396.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The first terms in part d and f of the examples should be weighted with the probability that scenario 1 occurs, right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk15.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..48c8f70169f7eff03aca9b7d571f746ad807ac79 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 3, + "timestamp": 1684520173396.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The first terms in part d and f of the examples should be weighted with the probability that scenario 1 occurs, right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk16.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..48c8f70169f7eff03aca9b7d571f746ad807ac79 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 3, + "timestamp": 1684520173396.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The first terms in part d and f of the examples should be weighted with the probability that scenario 1 occurs, right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk17.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..48c8f70169f7eff03aca9b7d571f746ad807ac79 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 3, + "timestamp": 1684520173396.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The first terms in part d and f of the examples should be weighted with the probability that scenario 1 occurs, right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk18.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..48c8f70169f7eff03aca9b7d571f746ad807ac79 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 3, + "timestamp": 1684520173396.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The first terms in part d and f of the examples should be weighted with the probability that scenario 1 occurs, right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk19.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..48c8f70169f7eff03aca9b7d571f746ad807ac79 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 3, + "timestamp": 1684520173396.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The first terms in part d and f of the examples should be weighted with the probability that scenario 1 occurs, right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk2.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..48c8f70169f7eff03aca9b7d571f746ad807ac79 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 3, + "timestamp": 1684520173396.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The first terms in part d and f of the examples should be weighted with the probability that scenario 1 occurs, right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk20.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..48c8f70169f7eff03aca9b7d571f746ad807ac79 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 3, + "timestamp": 1684520173396.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The first terms in part d and f of the examples should be weighted with the probability that scenario 1 occurs, right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk21.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..48c8f70169f7eff03aca9b7d571f746ad807ac79 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 3, + "timestamp": 1684520173396.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The first terms in part d and f of the examples should be weighted with the probability that scenario 1 occurs, right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk22.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..48c8f70169f7eff03aca9b7d571f746ad807ac79 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 3, + "timestamp": 1684520173396.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The first terms in part d and f of the examples should be weighted with the probability that scenario 1 occurs, right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk23.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..48c8f70169f7eff03aca9b7d571f746ad807ac79 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 3, + "timestamp": 1684520173396.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The first terms in part d and f of the examples should be weighted with the probability that scenario 1 occurs, right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk24.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..48c8f70169f7eff03aca9b7d571f746ad807ac79 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 3, + "timestamp": 1684520173396.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The first terms in part d and f of the examples should be weighted with the probability that scenario 1 occurs, right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk25.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..48c8f70169f7eff03aca9b7d571f746ad807ac79 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 3, + "timestamp": 1684520173396.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The first terms in part d and f of the examples should be weighted with the probability that scenario 1 occurs, right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk3.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..48c8f70169f7eff03aca9b7d571f746ad807ac79 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 3, + "timestamp": 1684520173396.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The first terms in part d and f of the examples should be weighted with the probability that scenario 1 occurs, right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk4.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..48c8f70169f7eff03aca9b7d571f746ad807ac79 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 3, + "timestamp": 1684520173396.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The first terms in part d and f of the examples should be weighted with the probability that scenario 1 occurs, right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk5.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..48c8f70169f7eff03aca9b7d571f746ad807ac79 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 3, + "timestamp": 1684520173396.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The first terms in part d and f of the examples should be weighted with the probability that scenario 1 occurs, right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk6.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..48c8f70169f7eff03aca9b7d571f746ad807ac79 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 3, + "timestamp": 1684520173396.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The first terms in part d and f of the examples should be weighted with the probability that scenario 1 occurs, right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk7.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..48c8f70169f7eff03aca9b7d571f746ad807ac79 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 3, + "timestamp": 1684520173396.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The first terms in part d and f of the examples should be weighted with the probability that scenario 1 occurs, right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk8.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..48c8f70169f7eff03aca9b7d571f746ad807ac79 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 3, + "timestamp": 1684520173396.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The first terms in part d and f of the examples should be weighted with the probability that scenario 1 occurs, right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk9.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..06c1da723ad425446818ace8027291847905357e --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_3_chunk9.json @@ -0,0 +1,17 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 3, + "timestamp": 1684520173396.0, + "annotatedSourceSentencesIndices": [ + 14, + 16, + 17, + 18 + ], + "names": [ + "annotator1" + ], + "text": "The first terms in part d and f of the examples should be weighted with the probability that scenario 1 occurs, right?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk0.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..dc8b6adcc111b6dd622876f5febd70118044e76d --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 5, + "timestamp": 1684520219876.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "But is the life of a light bulb actually modeled by the memoryless Poisson process? I would think the past takes it's toll on the filament." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk1.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..dc8b6adcc111b6dd622876f5febd70118044e76d --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 5, + "timestamp": 1684520219876.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "But is the life of a light bulb actually modeled by the memoryless Poisson process? I would think the past takes it's toll on the filament." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk10.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..dc8b6adcc111b6dd622876f5febd70118044e76d --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 5, + "timestamp": 1684520219876.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "But is the life of a light bulb actually modeled by the memoryless Poisson process? I would think the past takes it's toll on the filament." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk11.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..dc8b6adcc111b6dd622876f5febd70118044e76d --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 5, + "timestamp": 1684520219876.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "But is the life of a light bulb actually modeled by the memoryless Poisson process? I would think the past takes it's toll on the filament." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk12.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..dc8b6adcc111b6dd622876f5febd70118044e76d --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 5, + "timestamp": 1684520219876.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "But is the life of a light bulb actually modeled by the memoryless Poisson process? I would think the past takes it's toll on the filament." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk13.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..dc8b6adcc111b6dd622876f5febd70118044e76d --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 5, + "timestamp": 1684520219876.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "But is the life of a light bulb actually modeled by the memoryless Poisson process? I would think the past takes it's toll on the filament." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk14.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..dc8b6adcc111b6dd622876f5febd70118044e76d --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 5, + "timestamp": 1684520219876.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "But is the life of a light bulb actually modeled by the memoryless Poisson process? I would think the past takes it's toll on the filament." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk15.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..dc8b6adcc111b6dd622876f5febd70118044e76d --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 5, + "timestamp": 1684520219876.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "But is the life of a light bulb actually modeled by the memoryless Poisson process? I would think the past takes it's toll on the filament." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk16.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..dc8b6adcc111b6dd622876f5febd70118044e76d --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 5, + "timestamp": 1684520219876.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "But is the life of a light bulb actually modeled by the memoryless Poisson process? I would think the past takes it's toll on the filament." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk17.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..dc8b6adcc111b6dd622876f5febd70118044e76d --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 5, + "timestamp": 1684520219876.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "But is the life of a light bulb actually modeled by the memoryless Poisson process? I would think the past takes it's toll on the filament." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk18.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..dc8b6adcc111b6dd622876f5febd70118044e76d --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 5, + "timestamp": 1684520219876.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "But is the life of a light bulb actually modeled by the memoryless Poisson process? I would think the past takes it's toll on the filament." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk19.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..dc8b6adcc111b6dd622876f5febd70118044e76d --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 5, + "timestamp": 1684520219876.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "But is the life of a light bulb actually modeled by the memoryless Poisson process? I would think the past takes it's toll on the filament." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk2.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..dc8b6adcc111b6dd622876f5febd70118044e76d --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 5, + "timestamp": 1684520219876.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "But is the life of a light bulb actually modeled by the memoryless Poisson process? I would think the past takes it's toll on the filament." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk20.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..dc8b6adcc111b6dd622876f5febd70118044e76d --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 5, + "timestamp": 1684520219876.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "But is the life of a light bulb actually modeled by the memoryless Poisson process? I would think the past takes it's toll on the filament." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk21.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..dc8b6adcc111b6dd622876f5febd70118044e76d --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 5, + "timestamp": 1684520219876.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "But is the life of a light bulb actually modeled by the memoryless Poisson process? I would think the past takes it's toll on the filament." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk22.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..dc8b6adcc111b6dd622876f5febd70118044e76d --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 5, + "timestamp": 1684520219876.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "But is the life of a light bulb actually modeled by the memoryless Poisson process? I would think the past takes it's toll on the filament." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk23.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..dc8b6adcc111b6dd622876f5febd70118044e76d --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 5, + "timestamp": 1684520219876.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "But is the life of a light bulb actually modeled by the memoryless Poisson process? I would think the past takes it's toll on the filament." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk24.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..dc8b6adcc111b6dd622876f5febd70118044e76d --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 5, + "timestamp": 1684520219876.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "But is the life of a light bulb actually modeled by the memoryless Poisson process? I would think the past takes it's toll on the filament." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk25.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..dc8b6adcc111b6dd622876f5febd70118044e76d --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 5, + "timestamp": 1684520219876.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "But is the life of a light bulb actually modeled by the memoryless Poisson process? I would think the past takes it's toll on the filament." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk3.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..dc8b6adcc111b6dd622876f5febd70118044e76d --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 5, + "timestamp": 1684520219876.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "But is the life of a light bulb actually modeled by the memoryless Poisson process? I would think the past takes it's toll on the filament." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk4.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..d49913ddd89e46781d47ca2a96a4a00e7207cca8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk4.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 5, + "timestamp": 1684520219876.0, + "annotatedSourceSentencesIndices": [ + 19 + ], + "names": [ + "annotator1" + ], + "text": "But is the life of a light bulb actually modeled by the memoryless Poisson process? I would think the past takes it's toll on the filament." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk5.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..dc8b6adcc111b6dd622876f5febd70118044e76d --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 5, + "timestamp": 1684520219876.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "But is the life of a light bulb actually modeled by the memoryless Poisson process? I would think the past takes it's toll on the filament." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk6.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..dc8b6adcc111b6dd622876f5febd70118044e76d --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 5, + "timestamp": 1684520219876.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "But is the life of a light bulb actually modeled by the memoryless Poisson process? I would think the past takes it's toll on the filament." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk7.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..dc8b6adcc111b6dd622876f5febd70118044e76d --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 5, + "timestamp": 1684520219876.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "But is the life of a light bulb actually modeled by the memoryless Poisson process? I would think the past takes it's toll on the filament." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk8.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..dc8b6adcc111b6dd622876f5febd70118044e76d --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 5, + "timestamp": 1684520219876.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "But is the life of a light bulb actually modeled by the memoryless Poisson process? I would think the past takes it's toll on the filament." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk9.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..dc8b6adcc111b6dd622876f5febd70118044e76d --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_5_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 5, + "timestamp": 1684520219876.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "But is the life of a light bulb actually modeled by the memoryless Poisson process? I would think the past takes it's toll on the filament." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk0.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..c7f7cc2a48de0e87ea1cbe9a0a86d10d609dc321 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 6, + "timestamp": 1684520305601.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Thank you very much \nI think that there is a missing factor (1-P(0,2)) in the response to the questions d and f. Is this true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk1.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..c7f7cc2a48de0e87ea1cbe9a0a86d10d609dc321 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 6, + "timestamp": 1684520305601.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Thank you very much \nI think that there is a missing factor (1-P(0,2)) in the response to the questions d and f. Is this true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk10.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..453dec964f7f4fc7b44915f33620af4a83dc5e7c --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk10.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 6, + "timestamp": 1684520305601.0, + "annotatedSourceSentencesIndices": [ + 0, + 1 + ], + "names": [ + "annotator1" + ], + "text": "Thank you very much \nI think that there is a missing factor (1-P(0,2)) in the response to the questions d and f. Is this true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk11.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..c7f7cc2a48de0e87ea1cbe9a0a86d10d609dc321 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 6, + "timestamp": 1684520305601.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Thank you very much \nI think that there is a missing factor (1-P(0,2)) in the response to the questions d and f. Is this true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk12.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..c7f7cc2a48de0e87ea1cbe9a0a86d10d609dc321 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 6, + "timestamp": 1684520305601.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Thank you very much \nI think that there is a missing factor (1-P(0,2)) in the response to the questions d and f. Is this true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk13.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..c7f7cc2a48de0e87ea1cbe9a0a86d10d609dc321 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 6, + "timestamp": 1684520305601.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Thank you very much \nI think that there is a missing factor (1-P(0,2)) in the response to the questions d and f. Is this true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk14.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..c7f7cc2a48de0e87ea1cbe9a0a86d10d609dc321 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 6, + "timestamp": 1684520305601.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Thank you very much \nI think that there is a missing factor (1-P(0,2)) in the response to the questions d and f. Is this true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk15.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..c7f7cc2a48de0e87ea1cbe9a0a86d10d609dc321 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 6, + "timestamp": 1684520305601.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Thank you very much \nI think that there is a missing factor (1-P(0,2)) in the response to the questions d and f. Is this true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk16.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..c7f7cc2a48de0e87ea1cbe9a0a86d10d609dc321 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 6, + "timestamp": 1684520305601.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Thank you very much \nI think that there is a missing factor (1-P(0,2)) in the response to the questions d and f. Is this true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk17.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..c7f7cc2a48de0e87ea1cbe9a0a86d10d609dc321 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 6, + "timestamp": 1684520305601.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Thank you very much \nI think that there is a missing factor (1-P(0,2)) in the response to the questions d and f. Is this true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk18.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..c7f7cc2a48de0e87ea1cbe9a0a86d10d609dc321 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 6, + "timestamp": 1684520305601.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Thank you very much \nI think that there is a missing factor (1-P(0,2)) in the response to the questions d and f. Is this true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk19.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..c7f7cc2a48de0e87ea1cbe9a0a86d10d609dc321 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 6, + "timestamp": 1684520305601.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Thank you very much \nI think that there is a missing factor (1-P(0,2)) in the response to the questions d and f. Is this true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk2.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..c7f7cc2a48de0e87ea1cbe9a0a86d10d609dc321 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 6, + "timestamp": 1684520305601.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Thank you very much \nI think that there is a missing factor (1-P(0,2)) in the response to the questions d and f. Is this true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk20.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c7f7cc2a48de0e87ea1cbe9a0a86d10d609dc321 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 6, + "timestamp": 1684520305601.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Thank you very much \nI think that there is a missing factor (1-P(0,2)) in the response to the questions d and f. Is this true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk21.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..c7f7cc2a48de0e87ea1cbe9a0a86d10d609dc321 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 6, + "timestamp": 1684520305601.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Thank you very much \nI think that there is a missing factor (1-P(0,2)) in the response to the questions d and f. Is this true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk22.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..c7f7cc2a48de0e87ea1cbe9a0a86d10d609dc321 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 6, + "timestamp": 1684520305601.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Thank you very much \nI think that there is a missing factor (1-P(0,2)) in the response to the questions d and f. Is this true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk23.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..c7f7cc2a48de0e87ea1cbe9a0a86d10d609dc321 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 6, + "timestamp": 1684520305601.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Thank you very much \nI think that there is a missing factor (1-P(0,2)) in the response to the questions d and f. Is this true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk24.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..c7f7cc2a48de0e87ea1cbe9a0a86d10d609dc321 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 6, + "timestamp": 1684520305601.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Thank you very much \nI think that there is a missing factor (1-P(0,2)) in the response to the questions d and f. Is this true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk25.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..c7f7cc2a48de0e87ea1cbe9a0a86d10d609dc321 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 6, + "timestamp": 1684520305601.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Thank you very much \nI think that there is a missing factor (1-P(0,2)) in the response to the questions d and f. Is this true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk3.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c7f7cc2a48de0e87ea1cbe9a0a86d10d609dc321 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 6, + "timestamp": 1684520305601.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Thank you very much \nI think that there is a missing factor (1-P(0,2)) in the response to the questions d and f. Is this true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk4.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c7f7cc2a48de0e87ea1cbe9a0a86d10d609dc321 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 6, + "timestamp": 1684520305601.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Thank you very much \nI think that there is a missing factor (1-P(0,2)) in the response to the questions d and f. Is this true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk5.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..c7f7cc2a48de0e87ea1cbe9a0a86d10d609dc321 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 6, + "timestamp": 1684520305601.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Thank you very much \nI think that there is a missing factor (1-P(0,2)) in the response to the questions d and f. Is this true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk6.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..c7f7cc2a48de0e87ea1cbe9a0a86d10d609dc321 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 6, + "timestamp": 1684520305601.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Thank you very much \nI think that there is a missing factor (1-P(0,2)) in the response to the questions d and f. Is this true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk7.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..c7f7cc2a48de0e87ea1cbe9a0a86d10d609dc321 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 6, + "timestamp": 1684520305601.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Thank you very much \nI think that there is a missing factor (1-P(0,2)) in the response to the questions d and f. Is this true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk8.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..c7f7cc2a48de0e87ea1cbe9a0a86d10d609dc321 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 6, + "timestamp": 1684520305601.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Thank you very much \nI think that there is a missing factor (1-P(0,2)) in the response to the questions d and f. Is this true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk9.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..ffd37b1d5d72d1a6c30141b6224d903443121029 --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_6_chunk9.json @@ -0,0 +1,19 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 6, + "timestamp": 1684520305601.0, + "annotatedSourceSentencesIndices": [ + 13, + 14, + 16, + 17, + 18, + 19 + ], + "names": [ + "annotator1" + ], + "text": "Thank you very much \nI think that there is a missing factor (1-P(0,2)) in the response to the questions d and f. Is this true?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk0.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..09cf708bd41ea58b54b81d5ecf5158f3db1ae46e --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 7, + "timestamp": 1684520381503.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The bus inter-arrival time example is a bad/counteractive example. If buses are running at the rate of 4 per hour, You go at a random time for many days and your average waiting time should be 7.5 minutes. Why would the bus company foll people by saying we are running buses whose time is determined by poisson process and not a uniform/predetermined time?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk1.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..09cf708bd41ea58b54b81d5ecf5158f3db1ae46e --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 7, + "timestamp": 1684520381503.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The bus inter-arrival time example is a bad/counteractive example. If buses are running at the rate of 4 per hour, You go at a random time for many days and your average waiting time should be 7.5 minutes. Why would the bus company foll people by saying we are running buses whose time is determined by poisson process and not a uniform/predetermined time?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk10.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..09cf708bd41ea58b54b81d5ecf5158f3db1ae46e --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 7, + "timestamp": 1684520381503.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The bus inter-arrival time example is a bad/counteractive example. If buses are running at the rate of 4 per hour, You go at a random time for many days and your average waiting time should be 7.5 minutes. Why would the bus company foll people by saying we are running buses whose time is determined by poisson process and not a uniform/predetermined time?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk11.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..09cf708bd41ea58b54b81d5ecf5158f3db1ae46e --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 7, + "timestamp": 1684520381503.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The bus inter-arrival time example is a bad/counteractive example. If buses are running at the rate of 4 per hour, You go at a random time for many days and your average waiting time should be 7.5 minutes. Why would the bus company foll people by saying we are running buses whose time is determined by poisson process and not a uniform/predetermined time?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk12.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..09cf708bd41ea58b54b81d5ecf5158f3db1ae46e --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 7, + "timestamp": 1684520381503.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The bus inter-arrival time example is a bad/counteractive example. If buses are running at the rate of 4 per hour, You go at a random time for many days and your average waiting time should be 7.5 minutes. Why would the bus company foll people by saying we are running buses whose time is determined by poisson process and not a uniform/predetermined time?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk13.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..09cf708bd41ea58b54b81d5ecf5158f3db1ae46e --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 7, + "timestamp": 1684520381503.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The bus inter-arrival time example is a bad/counteractive example. If buses are running at the rate of 4 per hour, You go at a random time for many days and your average waiting time should be 7.5 minutes. Why would the bus company foll people by saying we are running buses whose time is determined by poisson process and not a uniform/predetermined time?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk14.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..09cf708bd41ea58b54b81d5ecf5158f3db1ae46e --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 7, + "timestamp": 1684520381503.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The bus inter-arrival time example is a bad/counteractive example. If buses are running at the rate of 4 per hour, You go at a random time for many days and your average waiting time should be 7.5 minutes. Why would the bus company foll people by saying we are running buses whose time is determined by poisson process and not a uniform/predetermined time?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk15.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..09cf708bd41ea58b54b81d5ecf5158f3db1ae46e --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 7, + "timestamp": 1684520381503.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The bus inter-arrival time example is a bad/counteractive example. If buses are running at the rate of 4 per hour, You go at a random time for many days and your average waiting time should be 7.5 minutes. Why would the bus company foll people by saying we are running buses whose time is determined by poisson process and not a uniform/predetermined time?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk16.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..09cf708bd41ea58b54b81d5ecf5158f3db1ae46e --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 7, + "timestamp": 1684520381503.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The bus inter-arrival time example is a bad/counteractive example. If buses are running at the rate of 4 per hour, You go at a random time for many days and your average waiting time should be 7.5 minutes. Why would the bus company foll people by saying we are running buses whose time is determined by poisson process and not a uniform/predetermined time?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk17.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..09cf708bd41ea58b54b81d5ecf5158f3db1ae46e --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 7, + "timestamp": 1684520381503.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The bus inter-arrival time example is a bad/counteractive example. If buses are running at the rate of 4 per hour, You go at a random time for many days and your average waiting time should be 7.5 minutes. Why would the bus company foll people by saying we are running buses whose time is determined by poisson process and not a uniform/predetermined time?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk18.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..8f3fb5bfcde87f7920578502d7d8db624a2d843b --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk18.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 7, + "timestamp": 1684520381503.0, + "annotatedSourceSentencesIndices": [ + 15 + ], + "names": [ + "annotator1" + ], + "text": "The bus inter-arrival time example is a bad/counteractive example. If buses are running at the rate of 4 per hour, You go at a random time for many days and your average waiting time should be 7.5 minutes. Why would the bus company foll people by saying we are running buses whose time is determined by poisson process and not a uniform/predetermined time?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk19.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..8cf32ff348063eca46c88c1653c2f15bea55df6a --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk19.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 7, + "timestamp": 1684520381503.0, + "annotatedSourceSentencesIndices": [ + 8 + ], + "names": [ + "annotator1" + ], + "text": "The bus inter-arrival time example is a bad/counteractive example. If buses are running at the rate of 4 per hour, You go at a random time for many days and your average waiting time should be 7.5 minutes. Why would the bus company foll people by saying we are running buses whose time is determined by poisson process and not a uniform/predetermined time?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk2.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..09cf708bd41ea58b54b81d5ecf5158f3db1ae46e --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 7, + "timestamp": 1684520381503.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The bus inter-arrival time example is a bad/counteractive example. If buses are running at the rate of 4 per hour, You go at a random time for many days and your average waiting time should be 7.5 minutes. Why would the bus company foll people by saying we are running buses whose time is determined by poisson process and not a uniform/predetermined time?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk20.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..09cf708bd41ea58b54b81d5ecf5158f3db1ae46e --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 7, + "timestamp": 1684520381503.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The bus inter-arrival time example is a bad/counteractive example. If buses are running at the rate of 4 per hour, You go at a random time for many days and your average waiting time should be 7.5 minutes. Why would the bus company foll people by saying we are running buses whose time is determined by poisson process and not a uniform/predetermined time?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk21.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..09cf708bd41ea58b54b81d5ecf5158f3db1ae46e --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 7, + "timestamp": 1684520381503.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The bus inter-arrival time example is a bad/counteractive example. If buses are running at the rate of 4 per hour, You go at a random time for many days and your average waiting time should be 7.5 minutes. Why would the bus company foll people by saying we are running buses whose time is determined by poisson process and not a uniform/predetermined time?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk22.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..09cf708bd41ea58b54b81d5ecf5158f3db1ae46e --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 7, + "timestamp": 1684520381503.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The bus inter-arrival time example is a bad/counteractive example. If buses are running at the rate of 4 per hour, You go at a random time for many days and your average waiting time should be 7.5 minutes. Why would the bus company foll people by saying we are running buses whose time is determined by poisson process and not a uniform/predetermined time?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk23.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..09cf708bd41ea58b54b81d5ecf5158f3db1ae46e --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 7, + "timestamp": 1684520381503.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The bus inter-arrival time example is a bad/counteractive example. If buses are running at the rate of 4 per hour, You go at a random time for many days and your average waiting time should be 7.5 minutes. Why would the bus company foll people by saying we are running buses whose time is determined by poisson process and not a uniform/predetermined time?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk24.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..09cf708bd41ea58b54b81d5ecf5158f3db1ae46e --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 7, + "timestamp": 1684520381503.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The bus inter-arrival time example is a bad/counteractive example. If buses are running at the rate of 4 per hour, You go at a random time for many days and your average waiting time should be 7.5 minutes. Why would the bus company foll people by saying we are running buses whose time is determined by poisson process and not a uniform/predetermined time?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk25.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..09cf708bd41ea58b54b81d5ecf5158f3db1ae46e --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 7, + "timestamp": 1684520381503.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The bus inter-arrival time example is a bad/counteractive example. If buses are running at the rate of 4 per hour, You go at a random time for many days and your average waiting time should be 7.5 minutes. Why would the bus company foll people by saying we are running buses whose time is determined by poisson process and not a uniform/predetermined time?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk3.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..09cf708bd41ea58b54b81d5ecf5158f3db1ae46e --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 7, + "timestamp": 1684520381503.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The bus inter-arrival time example is a bad/counteractive example. If buses are running at the rate of 4 per hour, You go at a random time for many days and your average waiting time should be 7.5 minutes. Why would the bus company foll people by saying we are running buses whose time is determined by poisson process and not a uniform/predetermined time?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk4.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..09cf708bd41ea58b54b81d5ecf5158f3db1ae46e --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 7, + "timestamp": 1684520381503.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The bus inter-arrival time example is a bad/counteractive example. If buses are running at the rate of 4 per hour, You go at a random time for many days and your average waiting time should be 7.5 minutes. Why would the bus company foll people by saying we are running buses whose time is determined by poisson process and not a uniform/predetermined time?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk5.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..09cf708bd41ea58b54b81d5ecf5158f3db1ae46e --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 7, + "timestamp": 1684520381503.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The bus inter-arrival time example is a bad/counteractive example. If buses are running at the rate of 4 per hour, You go at a random time for many days and your average waiting time should be 7.5 minutes. Why would the bus company foll people by saying we are running buses whose time is determined by poisson process and not a uniform/predetermined time?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk6.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..09cf708bd41ea58b54b81d5ecf5158f3db1ae46e --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 7, + "timestamp": 1684520381503.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The bus inter-arrival time example is a bad/counteractive example. If buses are running at the rate of 4 per hour, You go at a random time for many days and your average waiting time should be 7.5 minutes. Why would the bus company foll people by saying we are running buses whose time is determined by poisson process and not a uniform/predetermined time?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk7.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..09cf708bd41ea58b54b81d5ecf5158f3db1ae46e --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 7, + "timestamp": 1684520381503.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The bus inter-arrival time example is a bad/counteractive example. If buses are running at the rate of 4 per hour, You go at a random time for many days and your average waiting time should be 7.5 minutes. Why would the bus company foll people by saying we are running buses whose time is determined by poisson process and not a uniform/predetermined time?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk8.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..09cf708bd41ea58b54b81d5ecf5158f3db1ae46e --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 7, + "timestamp": 1684520381503.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The bus inter-arrival time example is a bad/counteractive example. If buses are running at the rate of 4 per hour, You go at a random time for many days and your average waiting time should be 7.5 minutes. Why would the bus company foll people by saying we are running buses whose time is determined by poisson process and not a uniform/predetermined time?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk9.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..09cf708bd41ea58b54b81d5ecf5158f3db1ae46e --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_7_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 7, + "timestamp": 1684520381503.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "The bus inter-arrival time example is a bad/counteractive example. If buses are running at the rate of 4 per hour, You go at a random time for many days and your average waiting time should be 7.5 minutes. Why would the bus company foll people by saying we are running buses whose time is determined by poisson process and not a uniform/predetermined time?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_8_chunk0.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_8_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..85aaf0c5c0b1d4d0eaf76bcdcacf415308587b2c --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_8_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 8, + "timestamp": 1684520433574.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "what does 1 over lambda represent in the fishing example?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_8_chunk1.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_8_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..85aaf0c5c0b1d4d0eaf76bcdcacf415308587b2c --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_8_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 8, + "timestamp": 1684520433574.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "what does 1 over lambda represent in the fishing example?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/XsYXACeIklU_8_chunk10.json b/sight/query/annotated_chunks_window20/XsYXACeIklU_8_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..3fc7fb4b0f23b5be058afdc42897b098d11e967d --- /dev/null +++ b/sight/query/annotated_chunks_window20/XsYXACeIklU_8_chunk10.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "XsYXACeIklU", + "query_id": 8, + "timestamp": 1684520433574.0, + "annotatedSourceSentencesIndices": [ + 0 + ], + "names": [ + "annotator1" + ], + "text": "what does 1 over 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take (a_i - x) if a_i and x are not adjacent nodes?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/cxTmmasBiC8_0_chunk16.json b/sight/query/annotated_chunks_window20/cxTmmasBiC8_0_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..88860c3ecf7b5671be0a91f5a023edbc80f258c0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/cxTmmasBiC8_0_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "cxTmmasBiC8", + "query_id": 0, + "timestamp": 1684191388833.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "3:08 how do you take (a_i - x) if a_i and x are not adjacent nodes?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/cxTmmasBiC8_0_chunk2.json b/sight/query/annotated_chunks_window20/cxTmmasBiC8_0_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..88860c3ecf7b5671be0a91f5a023edbc80f258c0 --- /dev/null +++ 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a/sight/query/annotated_chunks_window20/cxTmmasBiC8_0_chunk4.json b/sight/query/annotated_chunks_window20/cxTmmasBiC8_0_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..88860c3ecf7b5671be0a91f5a023edbc80f258c0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/cxTmmasBiC8_0_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "cxTmmasBiC8", + "query_id": 0, + "timestamp": 1684191388833.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "3:08 how do you take (a_i - x) if a_i and x are not adjacent nodes?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/cxTmmasBiC8_0_chunk5.json b/sight/query/annotated_chunks_window20/cxTmmasBiC8_0_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..88860c3ecf7b5671be0a91f5a023edbc80f258c0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/cxTmmasBiC8_0_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "cxTmmasBiC8", + "query_id": 0, + "timestamp": 1684191388833.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "3:08 how do you take (a_i - x) if a_i and x are not adjacent nodes?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/cxTmmasBiC8_0_chunk6.json b/sight/query/annotated_chunks_window20/cxTmmasBiC8_0_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..88860c3ecf7b5671be0a91f5a023edbc80f258c0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/cxTmmasBiC8_0_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "cxTmmasBiC8", + "query_id": 0, + "timestamp": 1684191388833.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "3:08 how do you take (a_i - x) if a_i and x are not adjacent nodes?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/cxTmmasBiC8_0_chunk7.json b/sight/query/annotated_chunks_window20/cxTmmasBiC8_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..88860c3ecf7b5671be0a91f5a023edbc80f258c0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/cxTmmasBiC8_0_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "cxTmmasBiC8", + "query_id": 0, + "timestamp": 1684191388833.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "3:08 how do you take (a_i - x) if a_i and x are not adjacent nodes?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/cxTmmasBiC8_0_chunk8.json b/sight/query/annotated_chunks_window20/cxTmmasBiC8_0_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..88860c3ecf7b5671be0a91f5a023edbc80f258c0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/cxTmmasBiC8_0_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "cxTmmasBiC8", + "query_id": 0, + "timestamp": 1684191388833.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "3:08 how do you take (a_i - x) if a_i and x are not adjacent nodes?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/cxTmmasBiC8_0_chunk9.json b/sight/query/annotated_chunks_window20/cxTmmasBiC8_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..88860c3ecf7b5671be0a91f5a023edbc80f258c0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/cxTmmasBiC8_0_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "cxTmmasBiC8", + "query_id": 0, + "timestamp": 1684191388833.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "3:08 how do you take (a_i - x) if a_i and x are not adjacent nodes?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk0.json b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..cd749ddaffe052516faaf6b6d8d3ef15ad4690c0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk0.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "cxTmmasBiC8", + "query_id": 1, + "timestamp": 1684480753122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "The first two eigenvalues are 0 and 2 which correspond to the eigenvectors (1,1,1,1), (0,0,-1,1). He says some of the components in this second eigenvectors are positive and some are negative which tells you which cluster each node is in. But he never carries it out and explain the 0 components? See wolfram-alpha https://tinyurl.com/y7vdkhua for decomposition." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk1.json b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..cd749ddaffe052516faaf6b6d8d3ef15ad4690c0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk1.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "cxTmmasBiC8", + "query_id": 1, + "timestamp": 1684480753122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "The first two eigenvalues are 0 and 2 which correspond to the eigenvectors (1,1,1,1), (0,0,-1,1). He says some of the components in this second eigenvectors are positive and some are negative which tells you which cluster each node is in. But he never carries it out and explain the 0 components? See wolfram-alpha https://tinyurl.com/y7vdkhua for decomposition." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk10.json b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..cd749ddaffe052516faaf6b6d8d3ef15ad4690c0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk10.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "cxTmmasBiC8", + "query_id": 1, + "timestamp": 1684480753122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "The first two eigenvalues are 0 and 2 which correspond to the eigenvectors (1,1,1,1), (0,0,-1,1). He says some of the components in this second eigenvectors are positive and some are negative which tells you which cluster each node is in. But he never carries it out and explain the 0 components? See wolfram-alpha https://tinyurl.com/y7vdkhua for decomposition." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk11.json b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..cd749ddaffe052516faaf6b6d8d3ef15ad4690c0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk11.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "cxTmmasBiC8", + "query_id": 1, + "timestamp": 1684480753122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "The first two eigenvalues are 0 and 2 which correspond to the eigenvectors (1,1,1,1), (0,0,-1,1). He says some of the components in this second eigenvectors are positive and some are negative which tells you which cluster each node is in. But he never carries it out and explain the 0 components? See wolfram-alpha https://tinyurl.com/y7vdkhua for decomposition." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk12.json b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..cd749ddaffe052516faaf6b6d8d3ef15ad4690c0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk12.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "cxTmmasBiC8", + "query_id": 1, + "timestamp": 1684480753122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "The first two eigenvalues are 0 and 2 which correspond to the eigenvectors (1,1,1,1), (0,0,-1,1). He says some of the components in this second eigenvectors are positive and some are negative which tells you which cluster each node is in. But he never carries it out and explain the 0 components? See wolfram-alpha https://tinyurl.com/y7vdkhua for decomposition." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk13.json b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..bb50f100ef6a33a783c4e0b8cfb630bb8c71675e --- /dev/null +++ b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk13.json @@ -0,0 +1,19 @@ +[ + { + "file_id": "cxTmmasBiC8", + "query_id": 1, + "timestamp": 1684480753122.0, + "annotatedSourceSentencesIndices": [ + 5, + 6, + 7, + 9, + 10 + ], + "names": [ + "annotator1", + "annotator2" + ], + "text": "The first two eigenvalues are 0 and 2 which correspond to the eigenvectors (1,1,1,1), (0,0,-1,1). He says some of the components in this second eigenvectors are positive and some are negative which tells you which cluster each node is in. But he never carries it out and explain the 0 components? See wolfram-alpha https://tinyurl.com/y7vdkhua for decomposition." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk14.json b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..5718e36c4ac3a0528713a84d41347c4442e684cb --- /dev/null +++ b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk14.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "cxTmmasBiC8", + "query_id": 1, + "timestamp": 1684480753122.0, + "annotatedSourceSentencesIndices": [ + 11 + ], + "names": [ + "annotator1", + "annotator2" + ], + "text": "The first two eigenvalues are 0 and 2 which correspond to the eigenvectors (1,1,1,1), (0,0,-1,1). He says some of the components in this second eigenvectors are positive and some are negative which tells you which cluster each node is in. But he never carries it out and explain the 0 components? See wolfram-alpha https://tinyurl.com/y7vdkhua for decomposition." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk15.json b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..cd749ddaffe052516faaf6b6d8d3ef15ad4690c0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk15.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "cxTmmasBiC8", + "query_id": 1, + "timestamp": 1684480753122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "The first two eigenvalues are 0 and 2 which correspond to the eigenvectors (1,1,1,1), (0,0,-1,1). He says some of the components in this second eigenvectors are positive and some are negative which tells you which cluster each node is in. But he never carries it out and explain the 0 components? See wolfram-alpha https://tinyurl.com/y7vdkhua for decomposition." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk16.json b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..cd749ddaffe052516faaf6b6d8d3ef15ad4690c0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk16.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "cxTmmasBiC8", + "query_id": 1, + "timestamp": 1684480753122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "The first two eigenvalues are 0 and 2 which correspond to the eigenvectors (1,1,1,1), (0,0,-1,1). He says some of the components in this second eigenvectors are positive and some are negative which tells you which cluster each node is in. But he never carries it out and explain the 0 components? See wolfram-alpha https://tinyurl.com/y7vdkhua for decomposition." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk2.json b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..cd749ddaffe052516faaf6b6d8d3ef15ad4690c0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk2.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "cxTmmasBiC8", + "query_id": 1, + "timestamp": 1684480753122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "The first two eigenvalues are 0 and 2 which correspond to the eigenvectors (1,1,1,1), (0,0,-1,1). He says some of the components in this second eigenvectors are positive and some are negative which tells you which cluster each node is in. But he never carries it out and explain the 0 components? See wolfram-alpha https://tinyurl.com/y7vdkhua for decomposition." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk3.json b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..cd749ddaffe052516faaf6b6d8d3ef15ad4690c0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk3.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "cxTmmasBiC8", + "query_id": 1, + "timestamp": 1684480753122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "The first two eigenvalues are 0 and 2 which correspond to the eigenvectors (1,1,1,1), (0,0,-1,1). He says some of the components in this second eigenvectors are positive and some are negative which tells you which cluster each node is in. But he never carries it out and explain the 0 components? See wolfram-alpha https://tinyurl.com/y7vdkhua for decomposition." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk4.json b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..cd749ddaffe052516faaf6b6d8d3ef15ad4690c0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk4.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "cxTmmasBiC8", + "query_id": 1, + "timestamp": 1684480753122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "The first two eigenvalues are 0 and 2 which correspond to the eigenvectors (1,1,1,1), (0,0,-1,1). He says some of the components in this second eigenvectors are positive and some are negative which tells you which cluster each node is in. But he never carries it out and explain the 0 components? See wolfram-alpha https://tinyurl.com/y7vdkhua for decomposition." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk5.json b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..cd749ddaffe052516faaf6b6d8d3ef15ad4690c0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk5.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "cxTmmasBiC8", + "query_id": 1, + "timestamp": 1684480753122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "The first two eigenvalues are 0 and 2 which correspond to the eigenvectors (1,1,1,1), (0,0,-1,1). He says some of the components in this second eigenvectors are positive and some are negative which tells you which cluster each node is in. But he never carries it out and explain the 0 components? See wolfram-alpha https://tinyurl.com/y7vdkhua for decomposition." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk6.json b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..cd749ddaffe052516faaf6b6d8d3ef15ad4690c0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk6.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "cxTmmasBiC8", + "query_id": 1, + "timestamp": 1684480753122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "The first two eigenvalues are 0 and 2 which correspond to the eigenvectors (1,1,1,1), (0,0,-1,1). He says some of the components in this second eigenvectors are positive and some are negative which tells you which cluster each node is in. But he never carries it out and explain the 0 components? See wolfram-alpha https://tinyurl.com/y7vdkhua for decomposition." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk7.json b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..cd749ddaffe052516faaf6b6d8d3ef15ad4690c0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk7.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "cxTmmasBiC8", + "query_id": 1, + "timestamp": 1684480753122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "The first two eigenvalues are 0 and 2 which correspond to the eigenvectors (1,1,1,1), (0,0,-1,1). He says some of the components in this second eigenvectors are positive and some are negative which tells you which cluster each node is in. But he never carries it out and explain the 0 components? See wolfram-alpha https://tinyurl.com/y7vdkhua for decomposition." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk8.json b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..cd749ddaffe052516faaf6b6d8d3ef15ad4690c0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk8.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "cxTmmasBiC8", + "query_id": 1, + "timestamp": 1684480753122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "The first two eigenvalues are 0 and 2 which correspond to the eigenvectors (1,1,1,1), (0,0,-1,1). He says some of the components in this second eigenvectors are positive and some are negative which tells you which cluster each node is in. But he never carries it out and explain the 0 components? See wolfram-alpha https://tinyurl.com/y7vdkhua for decomposition." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk9.json b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..cd749ddaffe052516faaf6b6d8d3ef15ad4690c0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/cxTmmasBiC8_1_chunk9.json @@ -0,0 +1,13 @@ +[ + { + "file_id": "cxTmmasBiC8", + "query_id": 1, + "timestamp": 1684480753122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1", + "annotator2" + ], + "text": "The first two eigenvalues are 0 and 2 which correspond to the eigenvectors (1,1,1,1), (0,0,-1,1). He says some of the components in this second eigenvectors are positive and some are negative which tells you which cluster each node is in. But he never carries it out and explain the 0 components? See wolfram-alpha https://tinyurl.com/y7vdkhua for decomposition." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_0_chunk0.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_0_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..e727e7acfbc5daf5f3b8e27a1203be86503ce2b6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_0_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 0, + "timestamp": 1684518790918.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "so...how to find the proper \"shift\"?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_0_chunk1.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_0_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..e727e7acfbc5daf5f3b8e27a1203be86503ce2b6 --- /dev/null +++ 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+] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_0_chunk16.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_0_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..e727e7acfbc5daf5f3b8e27a1203be86503ce2b6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_0_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 0, + "timestamp": 1684518790918.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "so...how to find the proper \"shift\"?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_0_chunk17.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_0_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..e727e7acfbc5daf5f3b8e27a1203be86503ce2b6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_0_chunk17.json @@ -0,0 +1,12 @@ +[ + { + 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\"shift\"?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_0_chunk20.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_0_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..e727e7acfbc5daf5f3b8e27a1203be86503ce2b6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_0_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 0, + "timestamp": 1684518790918.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "so...how to find the proper \"shift\"?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_0_chunk21.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_0_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..e727e7acfbc5daf5f3b8e27a1203be86503ce2b6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_0_chunk21.json @@ -0,0 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the proper \"shift\"?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_0_chunk25.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_0_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..e727e7acfbc5daf5f3b8e27a1203be86503ce2b6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_0_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 0, + "timestamp": 1684518790918.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "so...how to find the proper \"shift\"?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_0_chunk26.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_0_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..e727e7acfbc5daf5f3b8e27a1203be86503ce2b6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_0_chunk26.json 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+ "names": [ + "annotator1" + ], + "text": "so...how to find the proper \"shift\"?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_0_chunk6.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_0_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..e727e7acfbc5daf5f3b8e27a1203be86503ce2b6 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_0_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 0, + "timestamp": 1684518790918.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "so...how to find the proper \"shift\"?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_0_chunk7.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..e727e7acfbc5daf5f3b8e27a1203be86503ce2b6 --- /dev/null +++ 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"timestamp": 1684518968338.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "How do we get A2 from A1 ??" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_1_chunk1.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_1_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..0605591b2f85b9aa3b2960b7572df2317ed34138 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_1_chunk1.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 1, + "timestamp": 1684518968338.0, + "annotatedSourceSentencesIndices": [ + 15 + ], + "names": [ + "annotator1" + ], + "text": "How do we get A2 from A1 ??" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_1_chunk10.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_1_chunk10.json new file mode 100644 index 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1, + "timestamp": 1684518968338.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "How do we get A2 from A1 ??" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_1_chunk4.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_1_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..e0b6bb9f16b67b7f187bcc9a7c04699e1c3b4df7 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_1_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 1, + "timestamp": 1684518968338.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "How do we get A2 from A1 ??" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_1_chunk5.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_1_chunk5.json new file mode 100644 index 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file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_1_chunk7.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_1_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..e0b6bb9f16b67b7f187bcc9a7c04699e1c3b4df7 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_1_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 1, + "timestamp": 1684518968338.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "How do we get A2 from A1 ??" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_1_chunk8.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_1_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..e0b6bb9f16b67b7f187bcc9a7c04699e1c3b4df7 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_1_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 1, + "timestamp": 1684518968338.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "How do we get A2 from A1 ??" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_1_chunk9.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_1_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..e0b6bb9f16b67b7f187bcc9a7c04699e1c3b4df7 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_1_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 1, + "timestamp": 1684518968338.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "How do we get A2 from A1 ??" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk0.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6343d006e5c70af2c86a1247cf04953991f7968c --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 2, + "timestamp": 1684519128837.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Should we not use A0 = QR , A1=RQ => A0 = QRQ^-1 since we know Q is orthogonal and hence invertible? Where as R is not invertible unless A is?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk1.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..6343d006e5c70af2c86a1247cf04953991f7968c --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 2, + "timestamp": 1684519128837.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Should we not use A0 = QR , A1=RQ => A0 = QRQ^-1 since we know Q is orthogonal and hence invertible? Where as R is not invertible unless A is?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk10.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..6343d006e5c70af2c86a1247cf04953991f7968c --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 2, + "timestamp": 1684519128837.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Should we not use A0 = QR , A1=RQ => A0 = QRQ^-1 since we know Q is orthogonal and hence invertible? Where as R is not invertible unless A is?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk11.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..6343d006e5c70af2c86a1247cf04953991f7968c --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 2, + "timestamp": 1684519128837.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Should we not use A0 = QR , A1=RQ => A0 = QRQ^-1 since we know Q is orthogonal and hence invertible? Where as R is not invertible unless A is?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk12.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..6343d006e5c70af2c86a1247cf04953991f7968c --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 2, + "timestamp": 1684519128837.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Should we not use A0 = QR , A1=RQ => A0 = QRQ^-1 since we know Q is orthogonal and hence invertible? Where as R is not invertible unless A is?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk13.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..6343d006e5c70af2c86a1247cf04953991f7968c --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 2, + "timestamp": 1684519128837.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Should we not use A0 = QR , A1=RQ => A0 = QRQ^-1 since we know Q is orthogonal and hence invertible? Where as R is not invertible unless A is?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk14.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..6343d006e5c70af2c86a1247cf04953991f7968c --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 2, + "timestamp": 1684519128837.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Should we not use A0 = QR , A1=RQ => A0 = QRQ^-1 since we know Q is orthogonal and hence invertible? Where as R is not invertible unless A is?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk15.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..6343d006e5c70af2c86a1247cf04953991f7968c --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 2, + "timestamp": 1684519128837.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Should we not use A0 = QR , A1=RQ => A0 = QRQ^-1 since we know Q is orthogonal and hence invertible? Where as R is not invertible unless A is?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk16.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..6343d006e5c70af2c86a1247cf04953991f7968c --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 2, + "timestamp": 1684519128837.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Should we not use A0 = QR , A1=RQ => A0 = QRQ^-1 since we know Q is orthogonal and hence invertible? Where as R is not invertible unless A is?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk17.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..6343d006e5c70af2c86a1247cf04953991f7968c --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 2, + "timestamp": 1684519128837.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Should we not use A0 = QR , A1=RQ => A0 = QRQ^-1 since we know Q is orthogonal and hence invertible? Where as R is not invertible unless A is?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk18.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..6343d006e5c70af2c86a1247cf04953991f7968c --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 2, + "timestamp": 1684519128837.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Should we not use A0 = QR , A1=RQ => A0 = QRQ^-1 since we know Q is orthogonal and hence invertible? Where as R is not invertible unless A is?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk19.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..6343d006e5c70af2c86a1247cf04953991f7968c --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 2, + "timestamp": 1684519128837.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Should we not use A0 = QR , A1=RQ => A0 = QRQ^-1 since we know Q is orthogonal and hence invertible? Where as R is not invertible unless A is?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk2.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6343d006e5c70af2c86a1247cf04953991f7968c --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 2, + "timestamp": 1684519128837.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Should we not use A0 = QR , A1=RQ => A0 = QRQ^-1 since we know Q is orthogonal and hence invertible? Where as R is not invertible unless A is?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk20.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6343d006e5c70af2c86a1247cf04953991f7968c --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 2, + "timestamp": 1684519128837.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Should we not use A0 = QR , A1=RQ => A0 = QRQ^-1 since we know Q is orthogonal and hence invertible? Where as R is not invertible unless A is?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk21.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..6343d006e5c70af2c86a1247cf04953991f7968c --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 2, + "timestamp": 1684519128837.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Should we not use A0 = QR , A1=RQ => A0 = QRQ^-1 since we know Q is orthogonal and hence invertible? Where as R is not invertible unless A is?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk22.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..6343d006e5c70af2c86a1247cf04953991f7968c --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 2, + "timestamp": 1684519128837.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Should we not use A0 = QR , A1=RQ => A0 = QRQ^-1 since we know Q is orthogonal and hence invertible? Where as R is not invertible unless A is?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk23.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..6343d006e5c70af2c86a1247cf04953991f7968c --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 2, + "timestamp": 1684519128837.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Should we not use A0 = QR , A1=RQ => A0 = QRQ^-1 since we know Q is orthogonal and hence invertible? Where as R is not invertible unless A is?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk24.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..6343d006e5c70af2c86a1247cf04953991f7968c --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 2, + "timestamp": 1684519128837.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Should we not use A0 = QR , A1=RQ => A0 = QRQ^-1 since we know Q is orthogonal and hence invertible? Where as R is not invertible unless A is?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk25.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..6343d006e5c70af2c86a1247cf04953991f7968c --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 2, + "timestamp": 1684519128837.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Should we not use A0 = QR , A1=RQ => A0 = QRQ^-1 since we know Q is orthogonal and hence invertible? Where as R is not invertible unless A is?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk26.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..6343d006e5c70af2c86a1247cf04953991f7968c --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 2, + "timestamp": 1684519128837.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Should we not use A0 = QR , A1=RQ => A0 = QRQ^-1 since we know Q is orthogonal and hence invertible? Where as R is not invertible unless A is?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk3.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..62cbd0e0398f126ea44c613fa62bf6dab2fe6fde --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk3.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 2, + "timestamp": 1684519128837.0, + "annotatedSourceSentencesIndices": [ + 5 + ], + "names": [ + "annotator1" + ], + "text": "Should we not use A0 = QR , A1=RQ => A0 = QRQ^-1 since we know Q is orthogonal and hence invertible? Where as R is not invertible unless A is?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk4.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..6343d006e5c70af2c86a1247cf04953991f7968c --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 2, + "timestamp": 1684519128837.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Should we not use A0 = QR , A1=RQ => A0 = QRQ^-1 since we know Q is orthogonal and hence invertible? Where as R is not invertible unless A is?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk5.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..6343d006e5c70af2c86a1247cf04953991f7968c --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 2, + "timestamp": 1684519128837.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Should we not use A0 = QR , A1=RQ => A0 = QRQ^-1 since we know Q is orthogonal and hence invertible? Where as R is not invertible unless A is?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk6.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..6343d006e5c70af2c86a1247cf04953991f7968c --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 2, + "timestamp": 1684519128837.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Should we not use A0 = QR , A1=RQ => A0 = QRQ^-1 since we know Q is orthogonal and hence invertible? Where as R is not invertible unless A is?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk7.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..6343d006e5c70af2c86a1247cf04953991f7968c --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 2, + "timestamp": 1684519128837.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Should we not use A0 = QR , A1=RQ => A0 = QRQ^-1 since we know Q is orthogonal and hence invertible? Where as R is not invertible unless A is?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk8.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..6343d006e5c70af2c86a1247cf04953991f7968c --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 2, + "timestamp": 1684519128837.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Should we not use A0 = QR , A1=RQ => A0 = QRQ^-1 since we know Q is orthogonal and hence invertible? Where as R is not invertible unless A is?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk9.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..6343d006e5c70af2c86a1247cf04953991f7968c --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_2_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 2, + "timestamp": 1684519128837.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Should we not use A0 = QR , A1=RQ => A0 = QRQ^-1 since we know Q is orthogonal and hence invertible? Where as R is not invertible unless A is?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk0.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..e14518744174b57f943ea3571eb002b7ffdc7a9f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 3, + "timestamp": 1684519167076.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is he talking about Galois or Abel?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk1.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..e14518744174b57f943ea3571eb002b7ffdc7a9f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 3, + "timestamp": 1684519167076.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is he talking about Galois or Abel?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk10.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..e14518744174b57f943ea3571eb002b7ffdc7a9f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 3, + "timestamp": 1684519167076.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is he talking about Galois or Abel?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk11.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..e14518744174b57f943ea3571eb002b7ffdc7a9f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 3, + "timestamp": 1684519167076.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is he talking about Galois or Abel?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk12.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..e14518744174b57f943ea3571eb002b7ffdc7a9f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 3, + "timestamp": 1684519167076.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is he talking about Galois or Abel?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk13.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..e14518744174b57f943ea3571eb002b7ffdc7a9f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 3, + "timestamp": 1684519167076.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is he talking about Galois or Abel?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk14.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..e14518744174b57f943ea3571eb002b7ffdc7a9f --- /dev/null +++ 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newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk25.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..e14518744174b57f943ea3571eb002b7ffdc7a9f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 3, + "timestamp": 1684519167076.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is he talking about Galois or Abel?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk26.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..e14518744174b57f943ea3571eb002b7ffdc7a9f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": 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newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk6.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..e14518744174b57f943ea3571eb002b7ffdc7a9f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 3, + "timestamp": 1684519167076.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "Is he talking about Galois or Abel?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk7.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..e14518744174b57f943ea3571eb002b7ffdc7a9f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_3_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": 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don't get it from this lecture" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk1.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..b1edc7a73d162c72911ec5fd6d1322ecc81dd410 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 4, + "timestamp": 1684519760474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why cannot simple steps to get upper triangle? still don't get it from this lecture" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk10.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..b1edc7a73d162c72911ec5fd6d1322ecc81dd410 --- /dev/null +++ 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newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk12.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..7129af10f358ab13554e21f49164e0b73409a94d --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk12.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 4, + "timestamp": 1684519760474.0, + "annotatedSourceSentencesIndices": [ + 10 + ], + "names": [ + "annotator1" + ], + "text": "why cannot simple steps to get upper triangle? still don't get it from this lecture" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk13.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..b1edc7a73d162c72911ec5fd6d1322ecc81dd410 --- /dev/null +++ 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newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk15.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..b1edc7a73d162c72911ec5fd6d1322ecc81dd410 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 4, + "timestamp": 1684519760474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why cannot simple steps to get upper triangle? still don't get it from this lecture" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk16.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..b1edc7a73d162c72911ec5fd6d1322ecc81dd410 --- /dev/null +++ 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newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk18.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..b1edc7a73d162c72911ec5fd6d1322ecc81dd410 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 4, + "timestamp": 1684519760474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why cannot simple steps to get upper triangle? still don't get it from this lecture" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk19.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..b1edc7a73d162c72911ec5fd6d1322ecc81dd410 --- /dev/null +++ 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at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk20.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..b1edc7a73d162c72911ec5fd6d1322ecc81dd410 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 4, + "timestamp": 1684519760474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why cannot simple steps to get upper triangle? still don't get it from this lecture" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk21.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..b1edc7a73d162c72911ec5fd6d1322ecc81dd410 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 4, + "timestamp": 1684519760474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why cannot simple steps to get upper triangle? still don't get it from this lecture" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk22.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..b1edc7a73d162c72911ec5fd6d1322ecc81dd410 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 4, + "timestamp": 1684519760474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why cannot simple steps to get upper triangle? still don't get it from this lecture" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk23.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..b1edc7a73d162c72911ec5fd6d1322ecc81dd410 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 4, + "timestamp": 1684519760474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why cannot simple steps to get upper triangle? still don't get it from this lecture" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk24.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..b1edc7a73d162c72911ec5fd6d1322ecc81dd410 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 4, + "timestamp": 1684519760474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why cannot simple steps to get upper triangle? still don't get it from this lecture" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk25.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..b1edc7a73d162c72911ec5fd6d1322ecc81dd410 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 4, + "timestamp": 1684519760474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why cannot simple steps to get upper triangle? still don't get it from this lecture" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk26.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..b1edc7a73d162c72911ec5fd6d1322ecc81dd410 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 4, + "timestamp": 1684519760474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why cannot simple steps to get upper triangle? still don't get it from this lecture" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk3.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..b1edc7a73d162c72911ec5fd6d1322ecc81dd410 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 4, + "timestamp": 1684519760474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why cannot simple steps to get upper triangle? still don't get it from this lecture" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk4.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..b1edc7a73d162c72911ec5fd6d1322ecc81dd410 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 4, + "timestamp": 1684519760474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why cannot simple steps to get upper triangle? still don't get it from this lecture" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk5.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..b1edc7a73d162c72911ec5fd6d1322ecc81dd410 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 4, + "timestamp": 1684519760474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why cannot simple steps to get upper triangle? still don't get it from this lecture" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk6.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..b1edc7a73d162c72911ec5fd6d1322ecc81dd410 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 4, + "timestamp": 1684519760474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why cannot simple steps to get upper triangle? still don't get it from this lecture" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk7.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b1edc7a73d162c72911ec5fd6d1322ecc81dd410 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 4, + "timestamp": 1684519760474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why cannot simple steps to get upper triangle? still don't get it from this lecture" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk8.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..b1edc7a73d162c72911ec5fd6d1322ecc81dd410 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 4, + "timestamp": 1684519760474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why cannot simple steps to get upper triangle? still don't get it from this lecture" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk9.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..b1edc7a73d162c72911ec5fd6d1322ecc81dd410 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_4_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 4, + "timestamp": 1684519760474.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "why cannot simple steps to get upper triangle? still don't get it from this lecture" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk0.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..420489a6b1e5bf9a10054878075c925237abdfd8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 6, + "timestamp": 1684519784891.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around the 21 minute mark, he says that it\u2019s too much to hope for to reduce the matrix A0 to an upper triangular matrix. He immediately follows up with a statement that it\u2019s impossible to solve a 5x5 system with simple steps. And this is why you instead reduce A0 to an upper Hessenberg matrix instead.\n\nI got lost trying to follow this argument, so I did a bit of research. Can someone tell me if I've got it right:\n1) The eigenvalues of a triangular matrix are just its diagonal elements.\n2) The Abel-Ruffini theorem says that's impossible, using radicals, to find the roots of a 5th order polynomial.\n3) If you were to try to solve det(A - lambda I) = 0 for a 5x5 triangular matrix, you'd be trying to find the roots of a 5th order polynomial. Though doesn't it automatically come perfectly factored for you to read off the eigenvalues?\n\nCombining all of these, does the Abel-Ruffini theorem imply that you can't transform a 5x5 matrix into triangular form via orthogonal transformations (e.g. Householder reflections) which preserve the eigenvalues? This doesn't sit right with me, so I'm thinking that can't be it." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk1.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..420489a6b1e5bf9a10054878075c925237abdfd8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 6, + "timestamp": 1684519784891.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around the 21 minute mark, he says that it\u2019s too much to hope for to reduce the matrix A0 to an upper triangular matrix. He immediately follows up with a statement that it\u2019s impossible to solve a 5x5 system with simple steps. And this is why you instead reduce A0 to an upper Hessenberg matrix instead.\n\nI got lost trying to follow this argument, so I did a bit of research. Can someone tell me if I've got it right:\n1) The eigenvalues of a triangular matrix are just its diagonal elements.\n2) The Abel-Ruffini theorem says that's impossible, using radicals, to find the roots of a 5th order polynomial.\n3) If you were to try to solve det(A - lambda I) = 0 for a 5x5 triangular matrix, you'd be trying to find the roots of a 5th order polynomial. Though doesn't it automatically come perfectly factored for you to read off the eigenvalues?\n\nCombining all of these, does the Abel-Ruffini theorem imply that you can't transform a 5x5 matrix into triangular form via orthogonal transformations (e.g. Householder reflections) which preserve the eigenvalues? This doesn't sit right with me, so I'm thinking that can't be it." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk10.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..420489a6b1e5bf9a10054878075c925237abdfd8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 6, + "timestamp": 1684519784891.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around the 21 minute mark, he says that it\u2019s too much to hope for to reduce the matrix A0 to an upper triangular matrix. He immediately follows up with a statement that it\u2019s impossible to solve a 5x5 system with simple steps. And this is why you instead reduce A0 to an upper Hessenberg matrix instead.\n\nI got lost trying to follow this argument, so I did a bit of research. Can someone tell me if I've got it right:\n1) The eigenvalues of a triangular matrix are just its diagonal elements.\n2) The Abel-Ruffini theorem says that's impossible, using radicals, to find the roots of a 5th order polynomial.\n3) If you were to try to solve det(A - lambda I) = 0 for a 5x5 triangular matrix, you'd be trying to find the roots of a 5th order polynomial. Though doesn't it automatically come perfectly factored for you to read off the eigenvalues?\n\nCombining all of these, does the Abel-Ruffini theorem imply that you can't transform a 5x5 matrix into triangular form via orthogonal transformations (e.g. Householder reflections) which preserve the eigenvalues? This doesn't sit right with me, so I'm thinking that can't be it." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk11.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..420489a6b1e5bf9a10054878075c925237abdfd8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 6, + "timestamp": 1684519784891.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around the 21 minute mark, he says that it\u2019s too much to hope for to reduce the matrix A0 to an upper triangular matrix. He immediately follows up with a statement that it\u2019s impossible to solve a 5x5 system with simple steps. And this is why you instead reduce A0 to an upper Hessenberg matrix instead.\n\nI got lost trying to follow this argument, so I did a bit of research. Can someone tell me if I've got it right:\n1) The eigenvalues of a triangular matrix are just its diagonal elements.\n2) The Abel-Ruffini theorem says that's impossible, using radicals, to find the roots of a 5th order polynomial.\n3) If you were to try to solve det(A - lambda I) = 0 for a 5x5 triangular matrix, you'd be trying to find the roots of a 5th order polynomial. Though doesn't it automatically come perfectly factored for you to read off the eigenvalues?\n\nCombining all of these, does the Abel-Ruffini theorem imply that you can't transform a 5x5 matrix into triangular form via orthogonal transformations (e.g. Householder reflections) which preserve the eigenvalues? This doesn't sit right with me, so I'm thinking that can't be it." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk12.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..8a2e64fddacfad512ed79189f71648ebead62c88 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk12.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 6, + "timestamp": 1684519784891.0, + "annotatedSourceSentencesIndices": [ + 10 + ], + "names": [ + "annotator1" + ], + "text": "At around the 21 minute mark, he says that it\u2019s too much to hope for to reduce the matrix A0 to an upper triangular matrix. He immediately follows up with a statement that it\u2019s impossible to solve a 5x5 system with simple steps. And this is why you instead reduce A0 to an upper Hessenberg matrix instead.\n\nI got lost trying to follow this argument, so I did a bit of research. Can someone tell me if I've got it right:\n1) The eigenvalues of a triangular matrix are just its diagonal elements.\n2) The Abel-Ruffini theorem says that's impossible, using radicals, to find the roots of a 5th order polynomial.\n3) If you were to try to solve det(A - lambda I) = 0 for a 5x5 triangular matrix, you'd be trying to find the roots of a 5th order polynomial. Though doesn't it automatically come perfectly factored for you to read off the eigenvalues?\n\nCombining all of these, does the Abel-Ruffini theorem imply that you can't transform a 5x5 matrix into triangular form via orthogonal transformations (e.g. Householder reflections) which preserve the eigenvalues? This doesn't sit right with me, so I'm thinking that can't be it." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk13.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..420489a6b1e5bf9a10054878075c925237abdfd8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 6, + "timestamp": 1684519784891.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around the 21 minute mark, he says that it\u2019s too much to hope for to reduce the matrix A0 to an upper triangular matrix. He immediately follows up with a statement that it\u2019s impossible to solve a 5x5 system with simple steps. And this is why you instead reduce A0 to an upper Hessenberg matrix instead.\n\nI got lost trying to follow this argument, so I did a bit of research. Can someone tell me if I've got it right:\n1) The eigenvalues of a triangular matrix are just its diagonal elements.\n2) The Abel-Ruffini theorem says that's impossible, using radicals, to find the roots of a 5th order polynomial.\n3) If you were to try to solve det(A - lambda I) = 0 for a 5x5 triangular matrix, you'd be trying to find the roots of a 5th order polynomial. Though doesn't it automatically come perfectly factored for you to read off the eigenvalues?\n\nCombining all of these, does the Abel-Ruffini theorem imply that you can't transform a 5x5 matrix into triangular form via orthogonal transformations (e.g. Householder reflections) which preserve the eigenvalues? This doesn't sit right with me, so I'm thinking that can't be it." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk14.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..420489a6b1e5bf9a10054878075c925237abdfd8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 6, + "timestamp": 1684519784891.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around the 21 minute mark, he says that it\u2019s too much to hope for to reduce the matrix A0 to an upper triangular matrix. He immediately follows up with a statement that it\u2019s impossible to solve a 5x5 system with simple steps. And this is why you instead reduce A0 to an upper Hessenberg matrix instead.\n\nI got lost trying to follow this argument, so I did a bit of research. Can someone tell me if I've got it right:\n1) The eigenvalues of a triangular matrix are just its diagonal elements.\n2) The Abel-Ruffini theorem says that's impossible, using radicals, to find the roots of a 5th order polynomial.\n3) If you were to try to solve det(A - lambda I) = 0 for a 5x5 triangular matrix, you'd be trying to find the roots of a 5th order polynomial. Though doesn't it automatically come perfectly factored for you to read off the eigenvalues?\n\nCombining all of these, does the Abel-Ruffini theorem imply that you can't transform a 5x5 matrix into triangular form via orthogonal transformations (e.g. Householder reflections) which preserve the eigenvalues? This doesn't sit right with me, so I'm thinking that can't be it." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk15.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..420489a6b1e5bf9a10054878075c925237abdfd8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 6, + "timestamp": 1684519784891.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around the 21 minute mark, he says that it\u2019s too much to hope for to reduce the matrix A0 to an upper triangular matrix. He immediately follows up with a statement that it\u2019s impossible to solve a 5x5 system with simple steps. And this is why you instead reduce A0 to an upper Hessenberg matrix instead.\n\nI got lost trying to follow this argument, so I did a bit of research. Can someone tell me if I've got it right:\n1) The eigenvalues of a triangular matrix are just its diagonal elements.\n2) The Abel-Ruffini theorem says that's impossible, using radicals, to find the roots of a 5th order polynomial.\n3) If you were to try to solve det(A - lambda I) = 0 for a 5x5 triangular matrix, you'd be trying to find the roots of a 5th order polynomial. Though doesn't it automatically come perfectly factored for you to read off the eigenvalues?\n\nCombining all of these, does the Abel-Ruffini theorem imply that you can't transform a 5x5 matrix into triangular form via orthogonal transformations (e.g. Householder reflections) which preserve the eigenvalues? This doesn't sit right with me, so I'm thinking that can't be it." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk16.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..420489a6b1e5bf9a10054878075c925237abdfd8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 6, + "timestamp": 1684519784891.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around the 21 minute mark, he says that it\u2019s too much to hope for to reduce the matrix A0 to an upper triangular matrix. He immediately follows up with a statement that it\u2019s impossible to solve a 5x5 system with simple steps. And this is why you instead reduce A0 to an upper Hessenberg matrix instead.\n\nI got lost trying to follow this argument, so I did a bit of research. Can someone tell me if I've got it right:\n1) The eigenvalues of a triangular matrix are just its diagonal elements.\n2) The Abel-Ruffini theorem says that's impossible, using radicals, to find the roots of a 5th order polynomial.\n3) If you were to try to solve det(A - lambda I) = 0 for a 5x5 triangular matrix, you'd be trying to find the roots of a 5th order polynomial. Though doesn't it automatically come perfectly factored for you to read off the eigenvalues?\n\nCombining all of these, does the Abel-Ruffini theorem imply that you can't transform a 5x5 matrix into triangular form via orthogonal transformations (e.g. Householder reflections) which preserve the eigenvalues? This doesn't sit right with me, so I'm thinking that can't be it." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk17.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..420489a6b1e5bf9a10054878075c925237abdfd8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 6, + "timestamp": 1684519784891.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around the 21 minute mark, he says that it\u2019s too much to hope for to reduce the matrix A0 to an upper triangular matrix. He immediately follows up with a statement that it\u2019s impossible to solve a 5x5 system with simple steps. And this is why you instead reduce A0 to an upper Hessenberg matrix instead.\n\nI got lost trying to follow this argument, so I did a bit of research. Can someone tell me if I've got it right:\n1) The eigenvalues of a triangular matrix are just its diagonal elements.\n2) The Abel-Ruffini theorem says that's impossible, using radicals, to find the roots of a 5th order polynomial.\n3) If you were to try to solve det(A - lambda I) = 0 for a 5x5 triangular matrix, you'd be trying to find the roots of a 5th order polynomial. Though doesn't it automatically come perfectly factored for you to read off the eigenvalues?\n\nCombining all of these, does the Abel-Ruffini theorem imply that you can't transform a 5x5 matrix into triangular form via orthogonal transformations (e.g. Householder reflections) which preserve the eigenvalues? This doesn't sit right with me, so I'm thinking that can't be it." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk18.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..420489a6b1e5bf9a10054878075c925237abdfd8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 6, + "timestamp": 1684519784891.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around the 21 minute mark, he says that it\u2019s too much to hope for to reduce the matrix A0 to an upper triangular matrix. He immediately follows up with a statement that it\u2019s impossible to solve a 5x5 system with simple steps. And this is why you instead reduce A0 to an upper Hessenberg matrix instead.\n\nI got lost trying to follow this argument, so I did a bit of research. Can someone tell me if I've got it right:\n1) The eigenvalues of a triangular matrix are just its diagonal elements.\n2) The Abel-Ruffini theorem says that's impossible, using radicals, to find the roots of a 5th order polynomial.\n3) If you were to try to solve det(A - lambda I) = 0 for a 5x5 triangular matrix, you'd be trying to find the roots of a 5th order polynomial. Though doesn't it automatically come perfectly factored for you to read off the eigenvalues?\n\nCombining all of these, does the Abel-Ruffini theorem imply that you can't transform a 5x5 matrix into triangular form via orthogonal transformations (e.g. Householder reflections) which preserve the eigenvalues? This doesn't sit right with me, so I'm thinking that can't be it." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk19.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..420489a6b1e5bf9a10054878075c925237abdfd8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 6, + "timestamp": 1684519784891.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around the 21 minute mark, he says that it\u2019s too much to hope for to reduce the matrix A0 to an upper triangular matrix. He immediately follows up with a statement that it\u2019s impossible to solve a 5x5 system with simple steps. And this is why you instead reduce A0 to an upper Hessenberg matrix instead.\n\nI got lost trying to follow this argument, so I did a bit of research. Can someone tell me if I've got it right:\n1) The eigenvalues of a triangular matrix are just its diagonal elements.\n2) The Abel-Ruffini theorem says that's impossible, using radicals, to find the roots of a 5th order polynomial.\n3) If you were to try to solve det(A - lambda I) = 0 for a 5x5 triangular matrix, you'd be trying to find the roots of a 5th order polynomial. Though doesn't it automatically come perfectly factored for you to read off the eigenvalues?\n\nCombining all of these, does the Abel-Ruffini theorem imply that you can't transform a 5x5 matrix into triangular form via orthogonal transformations (e.g. Householder reflections) which preserve the eigenvalues? This doesn't sit right with me, so I'm thinking that can't be it." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk2.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..420489a6b1e5bf9a10054878075c925237abdfd8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 6, + "timestamp": 1684519784891.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around the 21 minute mark, he says that it\u2019s too much to hope for to reduce the matrix A0 to an upper triangular matrix. He immediately follows up with a statement that it\u2019s impossible to solve a 5x5 system with simple steps. And this is why you instead reduce A0 to an upper Hessenberg matrix instead.\n\nI got lost trying to follow this argument, so I did a bit of research. Can someone tell me if I've got it right:\n1) The eigenvalues of a triangular matrix are just its diagonal elements.\n2) The Abel-Ruffini theorem says that's impossible, using radicals, to find the roots of a 5th order polynomial.\n3) If you were to try to solve det(A - lambda I) = 0 for a 5x5 triangular matrix, you'd be trying to find the roots of a 5th order polynomial. Though doesn't it automatically come perfectly factored for you to read off the eigenvalues?\n\nCombining all of these, does the Abel-Ruffini theorem imply that you can't transform a 5x5 matrix into triangular form via orthogonal transformations (e.g. Householder reflections) which preserve the eigenvalues? This doesn't sit right with me, so I'm thinking that can't be it." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk20.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..420489a6b1e5bf9a10054878075c925237abdfd8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 6, + "timestamp": 1684519784891.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around the 21 minute mark, he says that it\u2019s too much to hope for to reduce the matrix A0 to an upper triangular matrix. He immediately follows up with a statement that it\u2019s impossible to solve a 5x5 system with simple steps. And this is why you instead reduce A0 to an upper Hessenberg matrix instead.\n\nI got lost trying to follow this argument, so I did a bit of research. Can someone tell me if I've got it right:\n1) The eigenvalues of a triangular matrix are just its diagonal elements.\n2) The Abel-Ruffini theorem says that's impossible, using radicals, to find the roots of a 5th order polynomial.\n3) If you were to try to solve det(A - lambda I) = 0 for a 5x5 triangular matrix, you'd be trying to find the roots of a 5th order polynomial. Though doesn't it automatically come perfectly factored for you to read off the eigenvalues?\n\nCombining all of these, does the Abel-Ruffini theorem imply that you can't transform a 5x5 matrix into triangular form via orthogonal transformations (e.g. Householder reflections) which preserve the eigenvalues? This doesn't sit right with me, so I'm thinking that can't be it." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk21.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..420489a6b1e5bf9a10054878075c925237abdfd8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 6, + "timestamp": 1684519784891.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around the 21 minute mark, he says that it\u2019s too much to hope for to reduce the matrix A0 to an upper triangular matrix. He immediately follows up with a statement that it\u2019s impossible to solve a 5x5 system with simple steps. And this is why you instead reduce A0 to an upper Hessenberg matrix instead.\n\nI got lost trying to follow this argument, so I did a bit of research. Can someone tell me if I've got it right:\n1) The eigenvalues of a triangular matrix are just its diagonal elements.\n2) The Abel-Ruffini theorem says that's impossible, using radicals, to find the roots of a 5th order polynomial.\n3) If you were to try to solve det(A - lambda I) = 0 for a 5x5 triangular matrix, you'd be trying to find the roots of a 5th order polynomial. Though doesn't it automatically come perfectly factored for you to read off the eigenvalues?\n\nCombining all of these, does the Abel-Ruffini theorem imply that you can't transform a 5x5 matrix into triangular form via orthogonal transformations (e.g. Householder reflections) which preserve the eigenvalues? This doesn't sit right with me, so I'm thinking that can't be it." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk22.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..420489a6b1e5bf9a10054878075c925237abdfd8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 6, + "timestamp": 1684519784891.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around the 21 minute mark, he says that it\u2019s too much to hope for to reduce the matrix A0 to an upper triangular matrix. He immediately follows up with a statement that it\u2019s impossible to solve a 5x5 system with simple steps. And this is why you instead reduce A0 to an upper Hessenberg matrix instead.\n\nI got lost trying to follow this argument, so I did a bit of research. Can someone tell me if I've got it right:\n1) The eigenvalues of a triangular matrix are just its diagonal elements.\n2) The Abel-Ruffini theorem says that's impossible, using radicals, to find the roots of a 5th order polynomial.\n3) If you were to try to solve det(A - lambda I) = 0 for a 5x5 triangular matrix, you'd be trying to find the roots of a 5th order polynomial. Though doesn't it automatically come perfectly factored for you to read off the eigenvalues?\n\nCombining all of these, does the Abel-Ruffini theorem imply that you can't transform a 5x5 matrix into triangular form via orthogonal transformations (e.g. Householder reflections) which preserve the eigenvalues? This doesn't sit right with me, so I'm thinking that can't be it." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk23.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..420489a6b1e5bf9a10054878075c925237abdfd8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 6, + "timestamp": 1684519784891.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around the 21 minute mark, he says that it\u2019s too much to hope for to reduce the matrix A0 to an upper triangular matrix. He immediately follows up with a statement that it\u2019s impossible to solve a 5x5 system with simple steps. And this is why you instead reduce A0 to an upper Hessenberg matrix instead.\n\nI got lost trying to follow this argument, so I did a bit of research. Can someone tell me if I've got it right:\n1) The eigenvalues of a triangular matrix are just its diagonal elements.\n2) The Abel-Ruffini theorem says that's impossible, using radicals, to find the roots of a 5th order polynomial.\n3) If you were to try to solve det(A - lambda I) = 0 for a 5x5 triangular matrix, you'd be trying to find the roots of a 5th order polynomial. Though doesn't it automatically come perfectly factored for you to read off the eigenvalues?\n\nCombining all of these, does the Abel-Ruffini theorem imply that you can't transform a 5x5 matrix into triangular form via orthogonal transformations (e.g. Householder reflections) which preserve the eigenvalues? This doesn't sit right with me, so I'm thinking that can't be it." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk24.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..420489a6b1e5bf9a10054878075c925237abdfd8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 6, + "timestamp": 1684519784891.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around the 21 minute mark, he says that it\u2019s too much to hope for to reduce the matrix A0 to an upper triangular matrix. He immediately follows up with a statement that it\u2019s impossible to solve a 5x5 system with simple steps. And this is why you instead reduce A0 to an upper Hessenberg matrix instead.\n\nI got lost trying to follow this argument, so I did a bit of research. Can someone tell me if I've got it right:\n1) The eigenvalues of a triangular matrix are just its diagonal elements.\n2) The Abel-Ruffini theorem says that's impossible, using radicals, to find the roots of a 5th order polynomial.\n3) If you were to try to solve det(A - lambda I) = 0 for a 5x5 triangular matrix, you'd be trying to find the roots of a 5th order polynomial. Though doesn't it automatically come perfectly factored for you to read off the eigenvalues?\n\nCombining all of these, does the Abel-Ruffini theorem imply that you can't transform a 5x5 matrix into triangular form via orthogonal transformations (e.g. Householder reflections) which preserve the eigenvalues? This doesn't sit right with me, so I'm thinking that can't be it." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk25.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..420489a6b1e5bf9a10054878075c925237abdfd8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 6, + "timestamp": 1684519784891.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around the 21 minute mark, he says that it\u2019s too much to hope for to reduce the matrix A0 to an upper triangular matrix. He immediately follows up with a statement that it\u2019s impossible to solve a 5x5 system with simple steps. And this is why you instead reduce A0 to an upper Hessenberg matrix instead.\n\nI got lost trying to follow this argument, so I did a bit of research. Can someone tell me if I've got it right:\n1) The eigenvalues of a triangular matrix are just its diagonal elements.\n2) The Abel-Ruffini theorem says that's impossible, using radicals, to find the roots of a 5th order polynomial.\n3) If you were to try to solve det(A - lambda I) = 0 for a 5x5 triangular matrix, you'd be trying to find the roots of a 5th order polynomial. Though doesn't it automatically come perfectly factored for you to read off the eigenvalues?\n\nCombining all of these, does the Abel-Ruffini theorem imply that you can't transform a 5x5 matrix into triangular form via orthogonal transformations (e.g. Householder reflections) which preserve the eigenvalues? This doesn't sit right with me, so I'm thinking that can't be it." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk26.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..420489a6b1e5bf9a10054878075c925237abdfd8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 6, + "timestamp": 1684519784891.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around the 21 minute mark, he says that it\u2019s too much to hope for to reduce the matrix A0 to an upper triangular matrix. He immediately follows up with a statement that it\u2019s impossible to solve a 5x5 system with simple steps. And this is why you instead reduce A0 to an upper Hessenberg matrix instead.\n\nI got lost trying to follow this argument, so I did a bit of research. Can someone tell me if I've got it right:\n1) The eigenvalues of a triangular matrix are just its diagonal elements.\n2) The Abel-Ruffini theorem says that's impossible, using radicals, to find the roots of a 5th order polynomial.\n3) If you were to try to solve det(A - lambda I) = 0 for a 5x5 triangular matrix, you'd be trying to find the roots of a 5th order polynomial. Though doesn't it automatically come perfectly factored for you to read off the eigenvalues?\n\nCombining all of these, does the Abel-Ruffini theorem imply that you can't transform a 5x5 matrix into triangular form via orthogonal transformations (e.g. Householder reflections) which preserve the eigenvalues? This doesn't sit right with me, so I'm thinking that can't be it." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk3.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..420489a6b1e5bf9a10054878075c925237abdfd8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 6, + "timestamp": 1684519784891.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around the 21 minute mark, he says that it\u2019s too much to hope for to reduce the matrix A0 to an upper triangular matrix. He immediately follows up with a statement that it\u2019s impossible to solve a 5x5 system with simple steps. And this is why you instead reduce A0 to an upper Hessenberg matrix instead.\n\nI got lost trying to follow this argument, so I did a bit of research. Can someone tell me if I've got it right:\n1) The eigenvalues of a triangular matrix are just its diagonal elements.\n2) The Abel-Ruffini theorem says that's impossible, using radicals, to find the roots of a 5th order polynomial.\n3) If you were to try to solve det(A - lambda I) = 0 for a 5x5 triangular matrix, you'd be trying to find the roots of a 5th order polynomial. Though doesn't it automatically come perfectly factored for you to read off the eigenvalues?\n\nCombining all of these, does the Abel-Ruffini theorem imply that you can't transform a 5x5 matrix into triangular form via orthogonal transformations (e.g. Householder reflections) which preserve the eigenvalues? This doesn't sit right with me, so I'm thinking that can't be it." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk4.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..420489a6b1e5bf9a10054878075c925237abdfd8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 6, + "timestamp": 1684519784891.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around the 21 minute mark, he says that it\u2019s too much to hope for to reduce the matrix A0 to an upper triangular matrix. He immediately follows up with a statement that it\u2019s impossible to solve a 5x5 system with simple steps. And this is why you instead reduce A0 to an upper Hessenberg matrix instead.\n\nI got lost trying to follow this argument, so I did a bit of research. Can someone tell me if I've got it right:\n1) The eigenvalues of a triangular matrix are just its diagonal elements.\n2) The Abel-Ruffini theorem says that's impossible, using radicals, to find the roots of a 5th order polynomial.\n3) If you were to try to solve det(A - lambda I) = 0 for a 5x5 triangular matrix, you'd be trying to find the roots of a 5th order polynomial. Though doesn't it automatically come perfectly factored for you to read off the eigenvalues?\n\nCombining all of these, does the Abel-Ruffini theorem imply that you can't transform a 5x5 matrix into triangular form via orthogonal transformations (e.g. Householder reflections) which preserve the eigenvalues? This doesn't sit right with me, so I'm thinking that can't be it." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk5.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..420489a6b1e5bf9a10054878075c925237abdfd8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 6, + "timestamp": 1684519784891.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around the 21 minute mark, he says that it\u2019s too much to hope for to reduce the matrix A0 to an upper triangular matrix. He immediately follows up with a statement that it\u2019s impossible to solve a 5x5 system with simple steps. And this is why you instead reduce A0 to an upper Hessenberg matrix instead.\n\nI got lost trying to follow this argument, so I did a bit of research. Can someone tell me if I've got it right:\n1) The eigenvalues of a triangular matrix are just its diagonal elements.\n2) The Abel-Ruffini theorem says that's impossible, using radicals, to find the roots of a 5th order polynomial.\n3) If you were to try to solve det(A - lambda I) = 0 for a 5x5 triangular matrix, you'd be trying to find the roots of a 5th order polynomial. Though doesn't it automatically come perfectly factored for you to read off the eigenvalues?\n\nCombining all of these, does the Abel-Ruffini theorem imply that you can't transform a 5x5 matrix into triangular form via orthogonal transformations (e.g. Householder reflections) which preserve the eigenvalues? This doesn't sit right with me, so I'm thinking that can't be it." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk6.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..420489a6b1e5bf9a10054878075c925237abdfd8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 6, + "timestamp": 1684519784891.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around the 21 minute mark, he says that it\u2019s too much to hope for to reduce the matrix A0 to an upper triangular matrix. He immediately follows up with a statement that it\u2019s impossible to solve a 5x5 system with simple steps. And this is why you instead reduce A0 to an upper Hessenberg matrix instead.\n\nI got lost trying to follow this argument, so I did a bit of research. Can someone tell me if I've got it right:\n1) The eigenvalues of a triangular matrix are just its diagonal elements.\n2) The Abel-Ruffini theorem says that's impossible, using radicals, to find the roots of a 5th order polynomial.\n3) If you were to try to solve det(A - lambda I) = 0 for a 5x5 triangular matrix, you'd be trying to find the roots of a 5th order polynomial. Though doesn't it automatically come perfectly factored for you to read off the eigenvalues?\n\nCombining all of these, does the Abel-Ruffini theorem imply that you can't transform a 5x5 matrix into triangular form via orthogonal transformations (e.g. Householder reflections) which preserve the eigenvalues? This doesn't sit right with me, so I'm thinking that can't be it." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk7.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..420489a6b1e5bf9a10054878075c925237abdfd8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 6, + "timestamp": 1684519784891.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around the 21 minute mark, he says that it\u2019s too much to hope for to reduce the matrix A0 to an upper triangular matrix. He immediately follows up with a statement that it\u2019s impossible to solve a 5x5 system with simple steps. And this is why you instead reduce A0 to an upper Hessenberg matrix instead.\n\nI got lost trying to follow this argument, so I did a bit of research. Can someone tell me if I've got it right:\n1) The eigenvalues of a triangular matrix are just its diagonal elements.\n2) The Abel-Ruffini theorem says that's impossible, using radicals, to find the roots of a 5th order polynomial.\n3) If you were to try to solve det(A - lambda I) = 0 for a 5x5 triangular matrix, you'd be trying to find the roots of a 5th order polynomial. Though doesn't it automatically come perfectly factored for you to read off the eigenvalues?\n\nCombining all of these, does the Abel-Ruffini theorem imply that you can't transform a 5x5 matrix into triangular form via orthogonal transformations (e.g. Householder reflections) which preserve the eigenvalues? This doesn't sit right with me, so I'm thinking that can't be it." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk8.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..420489a6b1e5bf9a10054878075c925237abdfd8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 6, + "timestamp": 1684519784891.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around the 21 minute mark, he says that it\u2019s too much to hope for to reduce the matrix A0 to an upper triangular matrix. He immediately follows up with a statement that it\u2019s impossible to solve a 5x5 system with simple steps. And this is why you instead reduce A0 to an upper Hessenberg matrix instead.\n\nI got lost trying to follow this argument, so I did a bit of research. Can someone tell me if I've got it right:\n1) The eigenvalues of a triangular matrix are just its diagonal elements.\n2) The Abel-Ruffini theorem says that's impossible, using radicals, to find the roots of a 5th order polynomial.\n3) If you were to try to solve det(A - lambda I) = 0 for a 5x5 triangular matrix, you'd be trying to find the roots of a 5th order polynomial. Though doesn't it automatically come perfectly factored for you to read off the eigenvalues?\n\nCombining all of these, does the Abel-Ruffini theorem imply that you can't transform a 5x5 matrix into triangular form via orthogonal transformations (e.g. Householder reflections) which preserve the eigenvalues? This doesn't sit right with me, so I'm thinking that can't be it." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk9.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..420489a6b1e5bf9a10054878075c925237abdfd8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_6_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 6, + "timestamp": 1684519784891.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "At around the 21 minute mark, he says that it\u2019s too much to hope for to reduce the matrix A0 to an upper triangular matrix. He immediately follows up with a statement that it\u2019s impossible to solve a 5x5 system with simple steps. And this is why you instead reduce A0 to an upper Hessenberg matrix instead.\n\nI got lost trying to follow this argument, so I did a bit of research. Can someone tell me if I've got it right:\n1) The eigenvalues of a triangular matrix are just its diagonal elements.\n2) The Abel-Ruffini theorem says that's impossible, using radicals, to find the roots of a 5th order polynomial.\n3) If you were to try to solve det(A - lambda I) = 0 for a 5x5 triangular matrix, you'd be trying to find the roots of a 5th order polynomial. Though doesn't it automatically come perfectly factored for you to read off the eigenvalues?\n\nCombining all of these, does the Abel-Ruffini theorem imply that you can't transform a 5x5 matrix into triangular form via orthogonal transformations (e.g. Householder reflections) which preserve the eigenvalues? This doesn't sit right with me, so I'm thinking that can't be it." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk0.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a4cba4f1676e0e7895c481471ed4f92b6ae4b46f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 7, + "timestamp": 1684519933908.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What happens when the eigenvalues are complex? It doesn't seem like the QR method would converge as all the numbers resulting from this method would be real." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk1.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..a4cba4f1676e0e7895c481471ed4f92b6ae4b46f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 7, + "timestamp": 1684519933908.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What happens when the eigenvalues are complex? It doesn't seem like the QR method would converge as all the numbers resulting from this method would be real." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk10.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..edf5ee06edb0d0582ec391114df49344012cac5a --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk10.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 7, + "timestamp": 1684519933908.0, + "annotatedSourceSentencesIndices": [ + 11, + 14 + ], + "names": [ + "annotator1" + ], + "text": "What happens when the eigenvalues are complex? It doesn't seem like the QR method would converge as all the numbers resulting from this method would be real." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk11.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..a4cba4f1676e0e7895c481471ed4f92b6ae4b46f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 7, + "timestamp": 1684519933908.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What happens when the eigenvalues are complex? It doesn't seem like the QR method would converge as all the numbers resulting from this method would be real." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk12.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..a4cba4f1676e0e7895c481471ed4f92b6ae4b46f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 7, + "timestamp": 1684519933908.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What happens when the eigenvalues are complex? It doesn't seem like the QR method would converge as all the numbers resulting from this method would be real." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk13.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..a4cba4f1676e0e7895c481471ed4f92b6ae4b46f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 7, + "timestamp": 1684519933908.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What happens when the eigenvalues are complex? It doesn't seem like the QR method would converge as all the numbers resulting from this method would be real." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk14.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..a4cba4f1676e0e7895c481471ed4f92b6ae4b46f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 7, + "timestamp": 1684519933908.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What happens when the eigenvalues are complex? It doesn't seem like the QR method would converge as all the numbers resulting from this method would be real." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk15.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..a4cba4f1676e0e7895c481471ed4f92b6ae4b46f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 7, + "timestamp": 1684519933908.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What happens when the eigenvalues are complex? It doesn't seem like the QR method would converge as all the numbers resulting from this method would be real." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk16.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..a4cba4f1676e0e7895c481471ed4f92b6ae4b46f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 7, + "timestamp": 1684519933908.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What happens when the eigenvalues are complex? It doesn't seem like the QR method would converge as all the numbers resulting from this method would be real." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk17.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a4cba4f1676e0e7895c481471ed4f92b6ae4b46f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 7, + "timestamp": 1684519933908.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What happens when the eigenvalues are complex? It doesn't seem like the QR method would converge as all the numbers resulting from this method would be real." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk18.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..a4cba4f1676e0e7895c481471ed4f92b6ae4b46f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 7, + "timestamp": 1684519933908.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What happens when the eigenvalues are complex? It doesn't seem like the QR method would converge as all the numbers resulting from this method would be real." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk19.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..a4cba4f1676e0e7895c481471ed4f92b6ae4b46f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 7, + "timestamp": 1684519933908.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What happens when the eigenvalues are complex? It doesn't seem like the QR method would converge as all the numbers resulting from this method would be real." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk2.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..a4cba4f1676e0e7895c481471ed4f92b6ae4b46f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 7, + "timestamp": 1684519933908.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What happens when the eigenvalues are complex? It doesn't seem like the QR method would converge as all the numbers resulting from this method would be real." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk20.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..a4cba4f1676e0e7895c481471ed4f92b6ae4b46f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 7, + "timestamp": 1684519933908.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What happens when the eigenvalues are complex? It doesn't seem like the QR method would converge as all the numbers resulting from this method would be real." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk21.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..a4cba4f1676e0e7895c481471ed4f92b6ae4b46f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 7, + "timestamp": 1684519933908.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What happens when the eigenvalues are complex? It doesn't seem like the QR method would converge as all the numbers resulting from this method would be real." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk22.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..a4cba4f1676e0e7895c481471ed4f92b6ae4b46f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 7, + "timestamp": 1684519933908.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What happens when the eigenvalues are complex? It doesn't seem like the QR method would converge as all the numbers resulting from this method would be real." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk23.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..a4cba4f1676e0e7895c481471ed4f92b6ae4b46f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 7, + "timestamp": 1684519933908.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What happens when the eigenvalues are complex? It doesn't seem like the QR method would converge as all the numbers resulting from this method would be real." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk24.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..a4cba4f1676e0e7895c481471ed4f92b6ae4b46f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 7, + "timestamp": 1684519933908.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What happens when the eigenvalues are complex? It doesn't seem like the QR method would converge as all the numbers resulting from this method would be real." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk25.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..a4cba4f1676e0e7895c481471ed4f92b6ae4b46f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 7, + "timestamp": 1684519933908.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What happens when the eigenvalues are complex? It doesn't seem like the QR method would converge as all the numbers resulting from this method would be real." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk26.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..a4cba4f1676e0e7895c481471ed4f92b6ae4b46f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 7, + "timestamp": 1684519933908.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What happens when the eigenvalues are complex? It doesn't seem like the QR method would converge as all the numbers resulting from this method would be real." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk3.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..a4cba4f1676e0e7895c481471ed4f92b6ae4b46f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 7, + "timestamp": 1684519933908.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What happens when the eigenvalues are complex? It doesn't seem like the QR method would converge as all the numbers resulting from this method would be real." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk4.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..a4cba4f1676e0e7895c481471ed4f92b6ae4b46f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 7, + "timestamp": 1684519933908.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What happens when the eigenvalues are complex? It doesn't seem like the QR method would converge as all the numbers resulting from this method would be real." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk5.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..a4cba4f1676e0e7895c481471ed4f92b6ae4b46f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 7, + "timestamp": 1684519933908.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What happens when the eigenvalues are complex? 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It doesn't seem like the QR method would converge as all the numbers resulting from this method would be real." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk7.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..a4cba4f1676e0e7895c481471ed4f92b6ae4b46f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 7, + "timestamp": 1684519933908.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What happens when the eigenvalues are complex? It doesn't seem like the QR method would converge as all the numbers resulting from this method would be real." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk8.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..a4cba4f1676e0e7895c481471ed4f92b6ae4b46f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 7, + "timestamp": 1684519933908.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What happens when the eigenvalues are complex? It doesn't seem like the QR method would converge as all the numbers resulting from this method would be real." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk9.json b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..a4cba4f1676e0e7895c481471ed4f92b6ae4b46f --- /dev/null +++ b/sight/query/annotated_chunks_window20/d32WV1rKoVk_7_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "d32WV1rKoVk", + "query_id": 7, + "timestamp": 1684519933908.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator1" + ], + "text": "What happens when the eigenvalues are complex? 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"lZrIPRnoGQQ", + "query_id": 0, + "timestamp": 1684707834591.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "but if the input nodes count in NN is lower than num. of outputs then the forward mode changes to backprop from the other side, I mean if you compute Jacobians and use them in successive computations in the right order, is that so?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk12.json b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..b1a37714a73f0a1056824d50aca7f7122fcab351 --- /dev/null +++ b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "lZrIPRnoGQQ", + "query_id": 0, + "timestamp": 1684707834591.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "but if the input nodes count in NN is lower than num. of outputs then the forward mode changes to backprop from the other side, I mean if you compute Jacobians and use them in successive computations in the right order, is that so?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk13.json b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..b1a37714a73f0a1056824d50aca7f7122fcab351 --- /dev/null +++ b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "lZrIPRnoGQQ", + "query_id": 0, + "timestamp": 1684707834591.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "but if the input nodes count in NN is lower than num. of outputs then the forward mode changes to backprop from the other side, I mean if you compute Jacobians and use them in successive computations in the right order, is that so?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk14.json b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..b1a37714a73f0a1056824d50aca7f7122fcab351 --- /dev/null +++ b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "lZrIPRnoGQQ", + "query_id": 0, + "timestamp": 1684707834591.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "but if the input nodes count in NN is lower than num. of outputs then the forward mode changes to backprop from the other side, I mean if you compute Jacobians and use them in successive computations in the right order, is that so?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk15.json b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk15.json new file mode 100644 index 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"lZrIPRnoGQQ", + "query_id": 0, + "timestamp": 1684707834591.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "but if the input nodes count in NN is lower than num. of outputs then the forward mode changes to backprop from the other side, I mean if you compute Jacobians and use them in successive computations in the right order, is that so?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk17.json b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b1a37714a73f0a1056824d50aca7f7122fcab351 --- /dev/null +++ b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "lZrIPRnoGQQ", + "query_id": 0, + "timestamp": 1684707834591.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "but if the input nodes count in NN is lower than num. of outputs then the forward mode changes to backprop from the other side, I mean if you compute Jacobians and use them in successive computations in the right order, is that so?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk18.json b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..0a4467e19c0863bfde84ece73b26d6af71f983a1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk18.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "lZrIPRnoGQQ", + "query_id": 0, + "timestamp": 1684707834591.0, + "annotatedSourceSentencesIndices": [ + 13, + 19 + ], + "names": [ + "annotator2" + ], + "text": "but if the input nodes count in NN is lower than num. of outputs then the forward mode changes to backprop from the other side, I mean if you compute Jacobians and use them in successive computations in the right order, is that so?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk19.json b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..565847bc420def0f7c492f463b57c1b4d9ced5da --- /dev/null +++ b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk19.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "lZrIPRnoGQQ", + "query_id": 0, + "timestamp": 1684707834591.0, + "annotatedSourceSentencesIndices": [ + 2 + ], + "names": [ + "annotator2" + ], + "text": "but if the input nodes count in NN is lower than num. of outputs then the forward mode changes to backprop from the other side, I mean if you compute Jacobians and use them in successive computations in the right order, is that so?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk2.json b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk2.json new file mode 100644 index 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"lZrIPRnoGQQ", + "query_id": 0, + "timestamp": 1684707834591.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "but if the input nodes count in NN is lower than num. of outputs then the forward mode changes to backprop from the other side, I mean if you compute Jacobians and use them in successive computations in the right order, is that so?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk21.json b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..dafa4559e394226c368fd59d95f152d8a5e823a5 --- /dev/null +++ b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk21.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "lZrIPRnoGQQ", + "query_id": 0, + "timestamp": 1684707834591.0, + "annotatedSourceSentencesIndices": [ + 0 + ], + "names": [ + "annotator2" + ], + "text": "but if the input nodes count in NN is lower than num. of outputs then the forward mode changes to backprop from the other side, I mean if you compute Jacobians and use them in successive computations in the right order, is that so?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk22.json b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..b1a37714a73f0a1056824d50aca7f7122fcab351 --- /dev/null +++ b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "lZrIPRnoGQQ", + "query_id": 0, + "timestamp": 1684707834591.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "but if the input nodes count in NN is lower than num. of outputs then the forward mode changes to backprop from the other side, I mean if you compute Jacobians and use them in successive computations in the right order, is that so?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk23.json b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..b1a37714a73f0a1056824d50aca7f7122fcab351 --- /dev/null +++ b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk23.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "lZrIPRnoGQQ", + "query_id": 0, + "timestamp": 1684707834591.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "but if the input nodes count in NN is lower than num. of outputs then the forward mode changes to backprop from the other side, I mean if you compute Jacobians and use them in successive computations in the right order, is that so?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk24.json b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..b1a37714a73f0a1056824d50aca7f7122fcab351 --- /dev/null +++ b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk24.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "lZrIPRnoGQQ", + "query_id": 0, + "timestamp": 1684707834591.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "but if the input nodes count in NN is lower than num. of outputs then the forward mode changes to backprop from the other side, I mean if you compute Jacobians and use them in successive computations in the right order, is that so?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk25.json b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..b1a37714a73f0a1056824d50aca7f7122fcab351 --- /dev/null +++ b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk25.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "lZrIPRnoGQQ", + "query_id": 0, + "timestamp": 1684707834591.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "but if the input nodes count in NN is lower than num. of outputs then the forward mode changes to backprop from the other side, I mean if you compute Jacobians and use them in successive computations in the right order, is that so?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk26.json b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..b1a37714a73f0a1056824d50aca7f7122fcab351 --- /dev/null +++ b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk26.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "lZrIPRnoGQQ", + "query_id": 0, + "timestamp": 1684707834591.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "but if the input nodes count in NN is lower than num. of outputs then the forward mode changes to backprop from the other side, I mean if you compute Jacobians and use them in successive computations in the right order, is that so?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk27.json b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk27.json new file mode 100644 index 0000000000000000000000000000000000000000..b1a37714a73f0a1056824d50aca7f7122fcab351 --- /dev/null +++ b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk27.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "lZrIPRnoGQQ", + "query_id": 0, + "timestamp": 1684707834591.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "but if the input nodes count in NN is lower than num. of outputs then the forward mode changes to backprop from the other side, I mean if you compute Jacobians and use them in successive computations in the right order, is that so?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk3.json b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..b1a37714a73f0a1056824d50aca7f7122fcab351 --- /dev/null +++ b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "lZrIPRnoGQQ", + "query_id": 0, + "timestamp": 1684707834591.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "but if the input nodes count in NN is lower than num. of outputs then the forward mode changes to backprop from the other side, I mean if you compute Jacobians and use them in successive computations in the right order, is that so?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk4.json b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..b1a37714a73f0a1056824d50aca7f7122fcab351 --- /dev/null +++ b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "lZrIPRnoGQQ", + "query_id": 0, + "timestamp": 1684707834591.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "but if the input nodes count in NN is lower than num. of outputs then the forward mode changes to backprop from the other side, I mean if you compute Jacobians and use them in successive computations in the right order, is that so?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk5.json b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..b1a37714a73f0a1056824d50aca7f7122fcab351 --- /dev/null +++ b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "lZrIPRnoGQQ", + "query_id": 0, + "timestamp": 1684707834591.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "but if the input nodes count in NN is lower than num. of outputs then the forward mode changes to backprop from the other side, I mean if you compute Jacobians and use them in successive computations in the right order, is that so?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk6.json b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..b1a37714a73f0a1056824d50aca7f7122fcab351 --- /dev/null +++ b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "lZrIPRnoGQQ", + "query_id": 0, + "timestamp": 1684707834591.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "but if the input nodes count in NN is lower than num. of outputs then the forward mode changes to backprop from the other side, I mean if you compute Jacobians and use them in successive computations in the right order, is that so?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk7.json b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b1a37714a73f0a1056824d50aca7f7122fcab351 --- /dev/null +++ b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "lZrIPRnoGQQ", + "query_id": 0, + "timestamp": 1684707834591.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "but if the input nodes count in NN is lower than num. of outputs then the forward mode changes to backprop from the other side, I mean if you compute Jacobians and use them in successive computations in the right order, is that so?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk8.json b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..b1a37714a73f0a1056824d50aca7f7122fcab351 --- /dev/null +++ b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "lZrIPRnoGQQ", + "query_id": 0, + "timestamp": 1684707834591.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "but if the input nodes count in NN is lower than num. of outputs then the forward mode changes to backprop from the other side, I mean if you compute Jacobians and use them in successive computations in the right order, is that so?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk9.json b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..b1a37714a73f0a1056824d50aca7f7122fcab351 --- /dev/null +++ b/sight/query/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "lZrIPRnoGQQ", + "query_id": 0, + "timestamp": 1684707834591.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "but if the input nodes count in NN is lower than num. of outputs then the forward mode changes to backprop from the other side, I mean if you compute Jacobians and use them in successive computations in the right order, is that so?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk0.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a9422c6d0faf4cba0b01ff97c258404d968505f8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 0, + "timestamp": 1684702121808.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "May I say that the vectors in R span the same space as vectors in A after row operation because you can do a reverse ROW operation and construct the same vectors in A from R? It can't be true for column space because after row operations you most likely can't reverse and reconstruct the original column vectors from R through COLUMN combinations." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk1.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..a9422c6d0faf4cba0b01ff97c258404d968505f8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 0, + "timestamp": 1684702121808.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "May I say that the vectors in R span the same space as vectors in A after row operation because you can do a reverse ROW operation and construct the same vectors in A from R? It can't be true for column space because after row operations you most likely can't reverse and reconstruct the original column vectors from R through COLUMN combinations." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk10.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..cd2ae90e7d48be67491d6e4835e755a389ab07af --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk10.json @@ -0,0 +1,16 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 0, + "timestamp": 1684702121808.0, + "annotatedSourceSentencesIndices": [ + 6, + 7, + 8 + ], + "names": [ + "annotator2" + ], + "text": "May I say that the vectors in R span the same space as vectors in A after row operation because you can do a reverse ROW operation and construct the same vectors in A from R? It can't be true for column space because after row operations you most likely can't reverse and reconstruct the original column vectors from R through COLUMN combinations." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk11.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..a9422c6d0faf4cba0b01ff97c258404d968505f8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 0, + "timestamp": 1684702121808.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "May I say that the vectors in R span the same space as vectors in A after row operation because you can do a reverse ROW operation and construct the same vectors in A from R? It can't be true for column space because after row operations you most likely can't reverse and reconstruct the original column vectors from R through COLUMN combinations." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk12.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..a9422c6d0faf4cba0b01ff97c258404d968505f8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 0, + "timestamp": 1684702121808.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "May I say that the vectors in R span the same space as vectors in A after row operation because you can do a reverse ROW operation and construct the same vectors in A from R? It can't be true for column space because after row operations you most likely can't reverse and reconstruct the original column vectors from R through COLUMN combinations." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk13.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..a9422c6d0faf4cba0b01ff97c258404d968505f8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 0, + "timestamp": 1684702121808.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "May I say that the vectors in R span the same space as vectors in A after row operation because you can do a reverse ROW operation and construct the same vectors in A from R? It can't be true for column space because after row operations you most likely can't reverse and reconstruct the original column vectors from R through COLUMN combinations." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk14.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..a9422c6d0faf4cba0b01ff97c258404d968505f8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 0, + "timestamp": 1684702121808.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "May I say that the vectors in R span the same space as vectors in A after row operation because you can do a reverse ROW operation and construct the same vectors in A from R? It can't be true for column space because after row operations you most likely can't reverse and reconstruct the original column vectors from R through COLUMN combinations." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk15.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..a9422c6d0faf4cba0b01ff97c258404d968505f8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 0, + "timestamp": 1684702121808.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "May I say that the vectors in R span the same space as vectors in A after row operation because you can do a reverse ROW operation and construct the same vectors in A from R? It can't be true for column space because after row operations you most likely can't reverse and reconstruct the original column vectors from R through COLUMN combinations." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk16.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..a9422c6d0faf4cba0b01ff97c258404d968505f8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 0, + "timestamp": 1684702121808.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "May I say that the vectors in R span the same space as vectors in A after row operation because you can do a reverse ROW operation and construct the same vectors in A from R? It can't be true for column space because after row operations you most likely can't reverse and reconstruct the original column vectors from R through COLUMN combinations." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk17.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a9422c6d0faf4cba0b01ff97c258404d968505f8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 0, + "timestamp": 1684702121808.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "May I say that the vectors in R span the same space as vectors in A after row operation because you can do a reverse ROW operation and construct the same vectors in A from R? It can't be true for column space because after row operations you most likely can't reverse and reconstruct the original column vectors from R through COLUMN combinations." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk18.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..a9422c6d0faf4cba0b01ff97c258404d968505f8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 0, + "timestamp": 1684702121808.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "May I say that the vectors in R span the same space as vectors in A after row operation because you can do a reverse ROW operation and construct the same vectors in A from R? It can't be true for column space because after row operations you most likely can't reverse and reconstruct the original column vectors from R through COLUMN combinations." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk19.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..a9422c6d0faf4cba0b01ff97c258404d968505f8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 0, + "timestamp": 1684702121808.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "May I say that the vectors in R span the same space as vectors in A after row operation because you can do a reverse ROW operation and construct the same vectors in A from R? It can't be true for column space because after row operations you most likely can't reverse and reconstruct the original column vectors from R through COLUMN combinations." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk2.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..a9422c6d0faf4cba0b01ff97c258404d968505f8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 0, + "timestamp": 1684702121808.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "May I say that the vectors in R span the same space as vectors in A after row operation because you can do a reverse ROW operation and construct the same vectors in A from R? It can't be true for column space because after row operations you most likely can't reverse and reconstruct the original column vectors from R through COLUMN combinations." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk20.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..a9422c6d0faf4cba0b01ff97c258404d968505f8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 0, + "timestamp": 1684702121808.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "May I say that the vectors in R span the same space as vectors in A after row operation because you can do a reverse ROW operation and construct the same vectors in A from R? It can't be true for column space because after row operations you most likely can't reverse and reconstruct the original column vectors from R through COLUMN combinations." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk21.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..a9422c6d0faf4cba0b01ff97c258404d968505f8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 0, + "timestamp": 1684702121808.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "May I say that the vectors in R span the same space as vectors in A after row operation because you can do a reverse ROW operation and construct the same vectors in A from R? It can't be true for column space because after row operations you most likely can't reverse and reconstruct the original column vectors from R through COLUMN combinations." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk22.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..a9422c6d0faf4cba0b01ff97c258404d968505f8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 0, + "timestamp": 1684702121808.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "May I say that the vectors in R span the same space as vectors in A after row operation because you can do a reverse ROW operation and construct the same vectors in A from R? It can't be true for column space because after row operations you most likely can't reverse and reconstruct the original column vectors from R through COLUMN combinations." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk3.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..a9422c6d0faf4cba0b01ff97c258404d968505f8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 0, + "timestamp": 1684702121808.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "May I say that the vectors in R span the same space as vectors in A after row operation because you can do a reverse ROW operation and construct the same vectors in A from R? It can't be true for column space because after row operations you most likely can't reverse and reconstruct the original column vectors from R through COLUMN combinations." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk4.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..a9422c6d0faf4cba0b01ff97c258404d968505f8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 0, + "timestamp": 1684702121808.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "May I say that the vectors in R span the same space as vectors in A after row operation because you can do a reverse ROW operation and construct the same vectors in A from R? It can't be true for column space because after row operations you most likely can't reverse and reconstruct the original column vectors from R through COLUMN combinations." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk5.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..a9422c6d0faf4cba0b01ff97c258404d968505f8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 0, + "timestamp": 1684702121808.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "May I say that the vectors in R span the same space as vectors in A after row operation because you can do a reverse ROW operation and construct the same vectors in A from R? It can't be true for column space because after row operations you most likely can't reverse and reconstruct the original column vectors from R through COLUMN combinations." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk6.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..a9422c6d0faf4cba0b01ff97c258404d968505f8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 0, + "timestamp": 1684702121808.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "May I say that the vectors in R span the same space as vectors in A after row operation because you can do a reverse ROW operation and construct the same vectors in A from R? It can't be true for column space because after row operations you most likely can't reverse and reconstruct the original column vectors from R through COLUMN combinations." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk7.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..a9422c6d0faf4cba0b01ff97c258404d968505f8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 0, + "timestamp": 1684702121808.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "May I say that the vectors in R span the same space as vectors in A after row operation because you can do a reverse ROW operation and construct the same vectors in A from R? It can't be true for column space because after row operations you most likely can't reverse and reconstruct the original column vectors from R through COLUMN combinations." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk8.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..a9422c6d0faf4cba0b01ff97c258404d968505f8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 0, + "timestamp": 1684702121808.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "May I say that the vectors in R span the same space as vectors in A after row operation because you can do a reverse ROW operation and construct the same vectors in A from R? It can't be true for column space because after row operations you most likely can't reverse and reconstruct the original column vectors from R through COLUMN combinations." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk9.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..a9422c6d0faf4cba0b01ff97c258404d968505f8 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_0_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 0, + "timestamp": 1684702121808.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "May I say that the vectors in R span the same space as vectors in A after row operation because you can do a reverse ROW operation and construct the same vectors in A from R? It can't be true for column space because after row operations you most likely can't reverse and reconstruct the original column vectors from R through COLUMN combinations." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk0.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..32896c4114938e891475fe8e88898b362773ffb1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk0.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 11, + "timestamp": 1684702962651.0, + "annotatedSourceSentencesIndices": [ + 14 + ], + "names": [ + "annotator2" + ], + "text": "Can anyone explain how \"length of the linearly independent list \u2264 length of spanning list\"?\nTY in advance." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk1.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..f7227856b0033d422f6954915700b9605c03d833 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 11, + "timestamp": 1684702962651.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain how \"length of the linearly independent list \u2264 length of spanning list\"?\nTY in advance." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk10.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..f7227856b0033d422f6954915700b9605c03d833 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 11, + "timestamp": 1684702962651.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain how \"length of the linearly independent list \u2264 length of spanning list\"?\nTY in advance." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk11.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..f7227856b0033d422f6954915700b9605c03d833 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 11, + "timestamp": 1684702962651.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain how \"length of the linearly independent list \u2264 length of spanning list\"?\nTY in advance." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk12.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..f7227856b0033d422f6954915700b9605c03d833 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 11, + "timestamp": 1684702962651.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain how \"length of the linearly independent list \u2264 length of spanning list\"?\nTY in advance." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk13.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..f7227856b0033d422f6954915700b9605c03d833 --- /dev/null +++ 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\u2264 length of spanning list\"?\nTY in advance." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk15.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..f7227856b0033d422f6954915700b9605c03d833 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 11, + "timestamp": 1684702962651.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain how \"length of the linearly independent list \u2264 length of spanning list\"?\nTY in advance." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk16.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk16.json new file mode 100644 index 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"names": [ + "annotator2" + ], + "text": "Can anyone explain how \"length of the linearly independent list \u2264 length of spanning list\"?\nTY in advance." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk18.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..f7227856b0033d422f6954915700b9605c03d833 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 11, + "timestamp": 1684702962651.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain how \"length of the linearly independent list \u2264 length of spanning list\"?\nTY in advance." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk19.json 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"query_id": 11, + "timestamp": 1684702962651.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain how \"length of the linearly independent list \u2264 length of spanning list\"?\nTY in advance." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk20.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..f7227856b0033d422f6954915700b9605c03d833 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 11, + "timestamp": 1684702962651.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain how \"length of the linearly independent list \u2264 length of spanning list\"?\nTY in advance." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk21.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..32ccc1a0d3b3296b9c7224c79f1ed9bfd03e917f --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk21.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 11, + "timestamp": 1684702962651.0, + "annotatedSourceSentencesIndices": [ + 19 + ], + "names": [ + "annotator2" + ], + "text": "Can anyone explain how \"length of the linearly independent list \u2264 length of spanning list\"?\nTY in advance." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk22.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..1d69bdfc0c45e4c59cb86254a66e5fb7354dece8 --- /dev/null +++ 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list \u2264 length of spanning list\"?\nTY in advance." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk4.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..f7227856b0033d422f6954915700b9605c03d833 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 11, + "timestamp": 1684702962651.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain how \"length of the linearly independent list \u2264 length of spanning list\"?\nTY in advance." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk5.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..f7227856b0033d422f6954915700b9605c03d833 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 11, + "timestamp": 1684702962651.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain how \"length of the linearly independent list \u2264 length of spanning list\"?\nTY in advance." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk6.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..f7227856b0033d422f6954915700b9605c03d833 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 11, + "timestamp": 1684702962651.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain how \"length of the linearly independent list \u2264 length of spanning list\"?\nTY in advance." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk7.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..f7227856b0033d422f6954915700b9605c03d833 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 11, + "timestamp": 1684702962651.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "Can anyone explain how \"length of the linearly independent list \u2264 length of spanning list\"?\nTY in advance." + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_11_chunk8.json 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"query_id": 14, + "timestamp": 1684703307354.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "how do we define vector?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk14.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..f291109c33370ecf359954cd4e734cd4562b969a --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 14, + "timestamp": 1684703307354.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "how do we define vector?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk15.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk15.json new file mode 100644 index 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of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk17.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..f291109c33370ecf359954cd4e734cd4562b969a --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 14, + "timestamp": 1684703307354.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "how do we define vector?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk18.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..f291109c33370ecf359954cd4e734cd4562b969a --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 14, + "timestamp": 1684703307354.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "how do we define vector?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk19.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..f291109c33370ecf359954cd4e734cd4562b969a --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 14, + "timestamp": 1684703307354.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "how do we define vector?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk2.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk2.json new file mode 100644 index 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of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk21.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f291109c33370ecf359954cd4e734cd4562b969a --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 14, + "timestamp": 1684703307354.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "how do we define vector?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk22.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..f291109c33370ecf359954cd4e734cd4562b969a --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 14, + "timestamp": 1684703307354.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "how do we define vector?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk3.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..67cb929db599a04c6988ce1d995f904ecbafeef0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk3.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 14, + "timestamp": 1684703307354.0, + "annotatedSourceSentencesIndices": [ + 19 + ], + "names": [ + "annotator2" + ], + "text": "how do we define vector?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk4.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk4.json new file mode 100644 index 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file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk6.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..f291109c33370ecf359954cd4e734cd4562b969a --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 14, + "timestamp": 1684703307354.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "how do we define vector?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk7.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..f291109c33370ecf359954cd4e734cd4562b969a --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 14, + "timestamp": 1684703307354.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "how do we define vector?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk8.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f291109c33370ecf359954cd4e734cd4562b969a --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 14, + "timestamp": 1684703307354.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "how do we define vector?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk9.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..f291109c33370ecf359954cd4e734cd4562b969a --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_14_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 14, + "timestamp": 1684703307354.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "how do we define vector?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk0.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..513cde848efa0158a5536b2e107b8aa1c0bfb9fd --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 16, + "timestamp": 1684703606756.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "*Question:* what is the relationship between rank(A) and rank(A^T)? Does rank(A) = rank(A^T) in general?\n\nThe professor seems to be hinting at this, but rref(A) only preserves the column space, so it doesn\u2019t seem so trivial to me. Any insight is highly appreciated.\n\nEdit: I found the answer. rank(A) = rank(A^T) by virtue of the fact that linear independence of the columns implies linear independence of the rows, even for non-square matrices. I proved this for myself this evening. The main idea for the proof (at least how I did it) is that if you have two linearly dependent rows, one above the other say, row reduction kills the lower one (reduces number of possibly independent rows). Killing off the row (making the row all zeros) also makes it so that the given row can\u2019t have a pivot. Thus, we\u2019ve reduced the number of potential pivot columns by one. That\u2019s the relationship in a nutshell. The math is only slightly more involved" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk1.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..513cde848efa0158a5536b2e107b8aa1c0bfb9fd --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 16, + "timestamp": 1684703606756.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "*Question:* what is the relationship between rank(A) and rank(A^T)? Does rank(A) = rank(A^T) in general?\n\nThe professor seems to be hinting at this, but rref(A) only preserves the column space, so it doesn\u2019t seem so trivial to me. Any insight is highly appreciated.\n\nEdit: I found the answer. rank(A) = rank(A^T) by virtue of the fact that linear independence of the columns implies linear independence of the rows, even for non-square matrices. I proved this for myself this evening. The main idea for the proof (at least how I did it) is that if you have two linearly dependent rows, one above the other say, row reduction kills the lower one (reduces number of possibly independent rows). Killing off the row (making the row all zeros) also makes it so that the given row can\u2019t have a pivot. Thus, we\u2019ve reduced the number of potential pivot columns by one. That\u2019s the relationship in a nutshell. The math is only slightly more involved" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk10.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..513cde848efa0158a5536b2e107b8aa1c0bfb9fd --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 16, + "timestamp": 1684703606756.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "*Question:* what is the relationship between rank(A) and rank(A^T)? Does rank(A) = rank(A^T) in general?\n\nThe professor seems to be hinting at this, but rref(A) only preserves the column space, so it doesn\u2019t seem so trivial to me. Any insight is highly appreciated.\n\nEdit: I found the answer. rank(A) = rank(A^T) by virtue of the fact that linear independence of the columns implies linear independence of the rows, even for non-square matrices. I proved this for myself this evening. The main idea for the proof (at least how I did it) is that if you have two linearly dependent rows, one above the other say, row reduction kills the lower one (reduces number of possibly independent rows). Killing off the row (making the row all zeros) also makes it so that the given row can\u2019t have a pivot. Thus, we\u2019ve reduced the number of potential pivot columns by one. That\u2019s the relationship in a nutshell. The math is only slightly more involved" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk11.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..513cde848efa0158a5536b2e107b8aa1c0bfb9fd --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 16, + "timestamp": 1684703606756.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "*Question:* what is the relationship between rank(A) and rank(A^T)? Does rank(A) = rank(A^T) in general?\n\nThe professor seems to be hinting at this, but rref(A) only preserves the column space, so it doesn\u2019t seem so trivial to me. Any insight is highly appreciated.\n\nEdit: I found the answer. rank(A) = rank(A^T) by virtue of the fact that linear independence of the columns implies linear independence of the rows, even for non-square matrices. I proved this for myself this evening. The main idea for the proof (at least how I did it) is that if you have two linearly dependent rows, one above the other say, row reduction kills the lower one (reduces number of possibly independent rows). Killing off the row (making the row all zeros) also makes it so that the given row can\u2019t have a pivot. Thus, we\u2019ve reduced the number of potential pivot columns by one. That\u2019s the relationship in a nutshell. The math is only slightly more involved" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk12.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..513cde848efa0158a5536b2e107b8aa1c0bfb9fd --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 16, + "timestamp": 1684703606756.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "*Question:* what is the relationship between rank(A) and rank(A^T)? Does rank(A) = rank(A^T) in general?\n\nThe professor seems to be hinting at this, but rref(A) only preserves the column space, so it doesn\u2019t seem so trivial to me. Any insight is highly appreciated.\n\nEdit: I found the answer. rank(A) = rank(A^T) by virtue of the fact that linear independence of the columns implies linear independence of the rows, even for non-square matrices. I proved this for myself this evening. The main idea for the proof (at least how I did it) is that if you have two linearly dependent rows, one above the other say, row reduction kills the lower one (reduces number of possibly independent rows). Killing off the row (making the row all zeros) also makes it so that the given row can\u2019t have a pivot. Thus, we\u2019ve reduced the number of potential pivot columns by one. That\u2019s the relationship in a nutshell. The math is only slightly more involved" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk13.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..513cde848efa0158a5536b2e107b8aa1c0bfb9fd --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 16, + "timestamp": 1684703606756.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "*Question:* what is the relationship between rank(A) and rank(A^T)? Does rank(A) = rank(A^T) in general?\n\nThe professor seems to be hinting at this, but rref(A) only preserves the column space, so it doesn\u2019t seem so trivial to me. Any insight is highly appreciated.\n\nEdit: I found the answer. rank(A) = rank(A^T) by virtue of the fact that linear independence of the columns implies linear independence of the rows, even for non-square matrices. I proved this for myself this evening. The main idea for the proof (at least how I did it) is that if you have two linearly dependent rows, one above the other say, row reduction kills the lower one (reduces number of possibly independent rows). Killing off the row (making the row all zeros) also makes it so that the given row can\u2019t have a pivot. Thus, we\u2019ve reduced the number of potential pivot columns by one. That\u2019s the relationship in a nutshell. The math is only slightly more involved" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk14.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..513cde848efa0158a5536b2e107b8aa1c0bfb9fd --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 16, + "timestamp": 1684703606756.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "*Question:* what is the relationship between rank(A) and rank(A^T)? Does rank(A) = rank(A^T) in general?\n\nThe professor seems to be hinting at this, but rref(A) only preserves the column space, so it doesn\u2019t seem so trivial to me. Any insight is highly appreciated.\n\nEdit: I found the answer. rank(A) = rank(A^T) by virtue of the fact that linear independence of the columns implies linear independence of the rows, even for non-square matrices. I proved this for myself this evening. The main idea for the proof (at least how I did it) is that if you have two linearly dependent rows, one above the other say, row reduction kills the lower one (reduces number of possibly independent rows). Killing off the row (making the row all zeros) also makes it so that the given row can\u2019t have a pivot. Thus, we\u2019ve reduced the number of potential pivot columns by one. That\u2019s the relationship in a nutshell. The math is only slightly more involved" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk15.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..513cde848efa0158a5536b2e107b8aa1c0bfb9fd --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 16, + "timestamp": 1684703606756.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "*Question:* what is the relationship between rank(A) and rank(A^T)? Does rank(A) = rank(A^T) in general?\n\nThe professor seems to be hinting at this, but rref(A) only preserves the column space, so it doesn\u2019t seem so trivial to me. Any insight is highly appreciated.\n\nEdit: I found the answer. rank(A) = rank(A^T) by virtue of the fact that linear independence of the columns implies linear independence of the rows, even for non-square matrices. I proved this for myself this evening. The main idea for the proof (at least how I did it) is that if you have two linearly dependent rows, one above the other say, row reduction kills the lower one (reduces number of possibly independent rows). Killing off the row (making the row all zeros) also makes it so that the given row can\u2019t have a pivot. Thus, we\u2019ve reduced the number of potential pivot columns by one. That\u2019s the relationship in a nutshell. The math is only slightly more involved" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk16.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..513cde848efa0158a5536b2e107b8aa1c0bfb9fd --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 16, + "timestamp": 1684703606756.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "*Question:* what is the relationship between rank(A) and rank(A^T)? Does rank(A) = rank(A^T) in general?\n\nThe professor seems to be hinting at this, but rref(A) only preserves the column space, so it doesn\u2019t seem so trivial to me. Any insight is highly appreciated.\n\nEdit: I found the answer. rank(A) = rank(A^T) by virtue of the fact that linear independence of the columns implies linear independence of the rows, even for non-square matrices. I proved this for myself this evening. The main idea for the proof (at least how I did it) is that if you have two linearly dependent rows, one above the other say, row reduction kills the lower one (reduces number of possibly independent rows). Killing off the row (making the row all zeros) also makes it so that the given row can\u2019t have a pivot. Thus, we\u2019ve reduced the number of potential pivot columns by one. That\u2019s the relationship in a nutshell. The math is only slightly more involved" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk17.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..513cde848efa0158a5536b2e107b8aa1c0bfb9fd --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 16, + "timestamp": 1684703606756.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "*Question:* what is the relationship between rank(A) and rank(A^T)? Does rank(A) = rank(A^T) in general?\n\nThe professor seems to be hinting at this, but rref(A) only preserves the column space, so it doesn\u2019t seem so trivial to me. Any insight is highly appreciated.\n\nEdit: I found the answer. rank(A) = rank(A^T) by virtue of the fact that linear independence of the columns implies linear independence of the rows, even for non-square matrices. I proved this for myself this evening. The main idea for the proof (at least how I did it) is that if you have two linearly dependent rows, one above the other say, row reduction kills the lower one (reduces number of possibly independent rows). Killing off the row (making the row all zeros) also makes it so that the given row can\u2019t have a pivot. Thus, we\u2019ve reduced the number of potential pivot columns by one. That\u2019s the relationship in a nutshell. The math is only slightly more involved" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk18.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..513cde848efa0158a5536b2e107b8aa1c0bfb9fd --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 16, + "timestamp": 1684703606756.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "*Question:* what is the relationship between rank(A) and rank(A^T)? Does rank(A) = rank(A^T) in general?\n\nThe professor seems to be hinting at this, but rref(A) only preserves the column space, so it doesn\u2019t seem so trivial to me. Any insight is highly appreciated.\n\nEdit: I found the answer. rank(A) = rank(A^T) by virtue of the fact that linear independence of the columns implies linear independence of the rows, even for non-square matrices. I proved this for myself this evening. The main idea for the proof (at least how I did it) is that if you have two linearly dependent rows, one above the other say, row reduction kills the lower one (reduces number of possibly independent rows). Killing off the row (making the row all zeros) also makes it so that the given row can\u2019t have a pivot. Thus, we\u2019ve reduced the number of potential pivot columns by one. That\u2019s the relationship in a nutshell. The math is only slightly more involved" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk19.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..513cde848efa0158a5536b2e107b8aa1c0bfb9fd --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 16, + "timestamp": 1684703606756.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "*Question:* what is the relationship between rank(A) and rank(A^T)? Does rank(A) = rank(A^T) in general?\n\nThe professor seems to be hinting at this, but rref(A) only preserves the column space, so it doesn\u2019t seem so trivial to me. Any insight is highly appreciated.\n\nEdit: I found the answer. rank(A) = rank(A^T) by virtue of the fact that linear independence of the columns implies linear independence of the rows, even for non-square matrices. I proved this for myself this evening. The main idea for the proof (at least how I did it) is that if you have two linearly dependent rows, one above the other say, row reduction kills the lower one (reduces number of possibly independent rows). Killing off the row (making the row all zeros) also makes it so that the given row can\u2019t have a pivot. Thus, we\u2019ve reduced the number of potential pivot columns by one. That\u2019s the relationship in a nutshell. The math is only slightly more involved" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk2.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..513cde848efa0158a5536b2e107b8aa1c0bfb9fd --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 16, + "timestamp": 1684703606756.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "*Question:* what is the relationship between rank(A) and rank(A^T)? Does rank(A) = rank(A^T) in general?\n\nThe professor seems to be hinting at this, but rref(A) only preserves the column space, so it doesn\u2019t seem so trivial to me. Any insight is highly appreciated.\n\nEdit: I found the answer. rank(A) = rank(A^T) by virtue of the fact that linear independence of the columns implies linear independence of the rows, even for non-square matrices. I proved this for myself this evening. The main idea for the proof (at least how I did it) is that if you have two linearly dependent rows, one above the other say, row reduction kills the lower one (reduces number of possibly independent rows). Killing off the row (making the row all zeros) also makes it so that the given row can\u2019t have a pivot. Thus, we\u2019ve reduced the number of potential pivot columns by one. That\u2019s the relationship in a nutshell. The math is only slightly more involved" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk20.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..513cde848efa0158a5536b2e107b8aa1c0bfb9fd --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 16, + "timestamp": 1684703606756.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "*Question:* what is the relationship between rank(A) and rank(A^T)? Does rank(A) = rank(A^T) in general?\n\nThe professor seems to be hinting at this, but rref(A) only preserves the column space, so it doesn\u2019t seem so trivial to me. Any insight is highly appreciated.\n\nEdit: I found the answer. rank(A) = rank(A^T) by virtue of the fact that linear independence of the columns implies linear independence of the rows, even for non-square matrices. I proved this for myself this evening. The main idea for the proof (at least how I did it) is that if you have two linearly dependent rows, one above the other say, row reduction kills the lower one (reduces number of possibly independent rows). Killing off the row (making the row all zeros) also makes it so that the given row can\u2019t have a pivot. Thus, we\u2019ve reduced the number of potential pivot columns by one. That\u2019s the relationship in a nutshell. The math is only slightly more involved" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk21.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..513cde848efa0158a5536b2e107b8aa1c0bfb9fd --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 16, + "timestamp": 1684703606756.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "*Question:* what is the relationship between rank(A) and rank(A^T)? Does rank(A) = rank(A^T) in general?\n\nThe professor seems to be hinting at this, but rref(A) only preserves the column space, so it doesn\u2019t seem so trivial to me. Any insight is highly appreciated.\n\nEdit: I found the answer. rank(A) = rank(A^T) by virtue of the fact that linear independence of the columns implies linear independence of the rows, even for non-square matrices. I proved this for myself this evening. The main idea for the proof (at least how I did it) is that if you have two linearly dependent rows, one above the other say, row reduction kills the lower one (reduces number of possibly independent rows). Killing off the row (making the row all zeros) also makes it so that the given row can\u2019t have a pivot. Thus, we\u2019ve reduced the number of potential pivot columns by one. That\u2019s the relationship in a nutshell. The math is only slightly more involved" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk22.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..513cde848efa0158a5536b2e107b8aa1c0bfb9fd --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 16, + "timestamp": 1684703606756.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "*Question:* what is the relationship between rank(A) and rank(A^T)? Does rank(A) = rank(A^T) in general?\n\nThe professor seems to be hinting at this, but rref(A) only preserves the column space, so it doesn\u2019t seem so trivial to me. Any insight is highly appreciated.\n\nEdit: I found the answer. rank(A) = rank(A^T) by virtue of the fact that linear independence of the columns implies linear independence of the rows, even for non-square matrices. I proved this for myself this evening. The main idea for the proof (at least how I did it) is that if you have two linearly dependent rows, one above the other say, row reduction kills the lower one (reduces number of possibly independent rows). Killing off the row (making the row all zeros) also makes it so that the given row can\u2019t have a pivot. Thus, we\u2019ve reduced the number of potential pivot columns by one. That\u2019s the relationship in a nutshell. The math is only slightly more involved" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk3.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..513cde848efa0158a5536b2e107b8aa1c0bfb9fd --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 16, + "timestamp": 1684703606756.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "*Question:* what is the relationship between rank(A) and rank(A^T)? Does rank(A) = rank(A^T) in general?\n\nThe professor seems to be hinting at this, but rref(A) only preserves the column space, so it doesn\u2019t seem so trivial to me. Any insight is highly appreciated.\n\nEdit: I found the answer. rank(A) = rank(A^T) by virtue of the fact that linear independence of the columns implies linear independence of the rows, even for non-square matrices. I proved this for myself this evening. The main idea for the proof (at least how I did it) is that if you have two linearly dependent rows, one above the other say, row reduction kills the lower one (reduces number of possibly independent rows). Killing off the row (making the row all zeros) also makes it so that the given row can\u2019t have a pivot. Thus, we\u2019ve reduced the number of potential pivot columns by one. That\u2019s the relationship in a nutshell. The math is only slightly more involved" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk4.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..513cde848efa0158a5536b2e107b8aa1c0bfb9fd --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 16, + "timestamp": 1684703606756.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "*Question:* what is the relationship between rank(A) and rank(A^T)? Does rank(A) = rank(A^T) in general?\n\nThe professor seems to be hinting at this, but rref(A) only preserves the column space, so it doesn\u2019t seem so trivial to me. Any insight is highly appreciated.\n\nEdit: I found the answer. rank(A) = rank(A^T) by virtue of the fact that linear independence of the columns implies linear independence of the rows, even for non-square matrices. I proved this for myself this evening. The main idea for the proof (at least how I did it) is that if you have two linearly dependent rows, one above the other say, row reduction kills the lower one (reduces number of possibly independent rows). Killing off the row (making the row all zeros) also makes it so that the given row can\u2019t have a pivot. Thus, we\u2019ve reduced the number of potential pivot columns by one. That\u2019s the relationship in a nutshell. The math is only slightly more involved" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk5.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..513cde848efa0158a5536b2e107b8aa1c0bfb9fd --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 16, + "timestamp": 1684703606756.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "*Question:* what is the relationship between rank(A) and rank(A^T)? Does rank(A) = rank(A^T) in general?\n\nThe professor seems to be hinting at this, but rref(A) only preserves the column space, so it doesn\u2019t seem so trivial to me. Any insight is highly appreciated.\n\nEdit: I found the answer. rank(A) = rank(A^T) by virtue of the fact that linear independence of the columns implies linear independence of the rows, even for non-square matrices. I proved this for myself this evening. The main idea for the proof (at least how I did it) is that if you have two linearly dependent rows, one above the other say, row reduction kills the lower one (reduces number of possibly independent rows). Killing off the row (making the row all zeros) also makes it so that the given row can\u2019t have a pivot. Thus, we\u2019ve reduced the number of potential pivot columns by one. That\u2019s the relationship in a nutshell. The math is only slightly more involved" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk6.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..513cde848efa0158a5536b2e107b8aa1c0bfb9fd --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 16, + "timestamp": 1684703606756.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "*Question:* what is the relationship between rank(A) and rank(A^T)? Does rank(A) = rank(A^T) in general?\n\nThe professor seems to be hinting at this, but rref(A) only preserves the column space, so it doesn\u2019t seem so trivial to me. Any insight is highly appreciated.\n\nEdit: I found the answer. rank(A) = rank(A^T) by virtue of the fact that linear independence of the columns implies linear independence of the rows, even for non-square matrices. I proved this for myself this evening. The main idea for the proof (at least how I did it) is that if you have two linearly dependent rows, one above the other say, row reduction kills the lower one (reduces number of possibly independent rows). Killing off the row (making the row all zeros) also makes it so that the given row can\u2019t have a pivot. Thus, we\u2019ve reduced the number of potential pivot columns by one. That\u2019s the relationship in a nutshell. The math is only slightly more involved" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk7.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..efaac888ee4f0c6d7a6aada7c88d7aec262700d2 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk7.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 16, + "timestamp": 1684703606756.0, + "annotatedSourceSentencesIndices": [ + 4 + ], + "names": [ + "annotator2" + ], + "text": "*Question:* what is the relationship between rank(A) and rank(A^T)? Does rank(A) = rank(A^T) in general?\n\nThe professor seems to be hinting at this, but rref(A) only preserves the column space, so it doesn\u2019t seem so trivial to me. Any insight is highly appreciated.\n\nEdit: I found the answer. rank(A) = rank(A^T) by virtue of the fact that linear independence of the columns implies linear independence of the rows, even for non-square matrices. I proved this for myself this evening. The main idea for the proof (at least how I did it) is that if you have two linearly dependent rows, one above the other say, row reduction kills the lower one (reduces number of possibly independent rows). Killing off the row (making the row all zeros) also makes it so that the given row can\u2019t have a pivot. Thus, we\u2019ve reduced the number of potential pivot columns by one. That\u2019s the relationship in a nutshell. The math is only slightly more involved" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk8.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..513cde848efa0158a5536b2e107b8aa1c0bfb9fd --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 16, + "timestamp": 1684703606756.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "*Question:* what is the relationship between rank(A) and rank(A^T)? Does rank(A) = rank(A^T) in general?\n\nThe professor seems to be hinting at this, but rref(A) only preserves the column space, so it doesn\u2019t seem so trivial to me. Any insight is highly appreciated.\n\nEdit: I found the answer. rank(A) = rank(A^T) by virtue of the fact that linear independence of the columns implies linear independence of the rows, even for non-square matrices. I proved this for myself this evening. The main idea for the proof (at least how I did it) is that if you have two linearly dependent rows, one above the other say, row reduction kills the lower one (reduces number of possibly independent rows). Killing off the row (making the row all zeros) also makes it so that the given row can\u2019t have a pivot. Thus, we\u2019ve reduced the number of potential pivot columns by one. That\u2019s the relationship in a nutshell. The math is only slightly more involved" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk9.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..513cde848efa0158a5536b2e107b8aa1c0bfb9fd --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_16_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 16, + "timestamp": 1684703606756.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "*Question:* what is the relationship between rank(A) and rank(A^T)? Does rank(A) = rank(A^T) in general?\n\nThe professor seems to be hinting at this, but rref(A) only preserves the column space, so it doesn\u2019t seem so trivial to me. Any insight is highly appreciated.\n\nEdit: I found the answer. rank(A) = rank(A^T) by virtue of the fact that linear independence of the columns implies linear independence of the rows, even for non-square matrices. I proved this for myself this evening. The main idea for the proof (at least how I did it) is that if you have two linearly dependent rows, one above the other say, row reduction kills the lower one (reduces number of possibly independent rows). Killing off the row (making the row all zeros) also makes it so that the given row can\u2019t have a pivot. Thus, we\u2019ve reduced the number of potential pivot columns by one. That\u2019s the relationship in a nutshell. The math is only slightly more involved" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk0.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d7d37574f96aa8a6f620bef5fd3e4c39c2a49b9c --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 17, + "timestamp": 1684703913122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "m is a number of rows, and the column space is in R^m?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk1.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..d7d37574f96aa8a6f620bef5fd3e4c39c2a49b9c --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 17, + "timestamp": 1684703913122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "m is a number of rows, and the column space is in R^m?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk10.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..d7d37574f96aa8a6f620bef5fd3e4c39c2a49b9c --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 17, + "timestamp": 1684703913122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "m is a number of rows, and the column space is in R^m?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk11.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d7d37574f96aa8a6f620bef5fd3e4c39c2a49b9c --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 17, + "timestamp": 1684703913122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "m is a number of rows, and the column space is in R^m?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk12.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..d7d37574f96aa8a6f620bef5fd3e4c39c2a49b9c --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 17, + "timestamp": 1684703913122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "m is a number of rows, and the column space is in R^m?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk13.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..d7d37574f96aa8a6f620bef5fd3e4c39c2a49b9c --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 17, + "timestamp": 1684703913122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "m is a number of rows, and the column space is in R^m?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk14.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d7d37574f96aa8a6f620bef5fd3e4c39c2a49b9c --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 17, + "timestamp": 1684703913122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "m is a number of rows, and the column space is in R^m?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk15.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..d7d37574f96aa8a6f620bef5fd3e4c39c2a49b9c --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 17, + "timestamp": 1684703913122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "m is a number of rows, and the column space is in R^m?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk16.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..d7d37574f96aa8a6f620bef5fd3e4c39c2a49b9c --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 17, + "timestamp": 1684703913122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "m is a number of rows, and the column space is in R^m?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk17.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..d7d37574f96aa8a6f620bef5fd3e4c39c2a49b9c --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 17, + "timestamp": 1684703913122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "m is a number of rows, and the column space is in R^m?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk18.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..d7d37574f96aa8a6f620bef5fd3e4c39c2a49b9c --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 17, + "timestamp": 1684703913122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "m is a number of rows, and the column space is in R^m?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk19.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..d7d37574f96aa8a6f620bef5fd3e4c39c2a49b9c --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 17, + "timestamp": 1684703913122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "m is a number of rows, and the column space is in R^m?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk2.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..d7d37574f96aa8a6f620bef5fd3e4c39c2a49b9c --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 17, + "timestamp": 1684703913122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "m is a number of rows, and the column space is in R^m?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk20.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..d7d37574f96aa8a6f620bef5fd3e4c39c2a49b9c --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 17, + "timestamp": 1684703913122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "m is a number of rows, and the column space is in R^m?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk21.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..d7d37574f96aa8a6f620bef5fd3e4c39c2a49b9c --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 17, + "timestamp": 1684703913122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "m is a number of rows, and the column space is in R^m?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk22.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..d7d37574f96aa8a6f620bef5fd3e4c39c2a49b9c --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 17, + "timestamp": 1684703913122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "m is a number of rows, and the column space is in R^m?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk3.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..d7d37574f96aa8a6f620bef5fd3e4c39c2a49b9c --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 17, + "timestamp": 1684703913122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "m is a number of rows, and the column space is in R^m?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk4.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c9a9294dd0f768ca69935aae2668cee8466a2d6a --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk4.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 17, + "timestamp": 1684703913122.0, + "annotatedSourceSentencesIndices": [ + 4, + 6 + ], + "names": [ + "annotator2" + ], + "text": "m is a number of rows, and the column space is in R^m?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk5.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..d7d37574f96aa8a6f620bef5fd3e4c39c2a49b9c --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 17, + "timestamp": 1684703913122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "m is a number of rows, and the column space is in R^m?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk6.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..d7d37574f96aa8a6f620bef5fd3e4c39c2a49b9c --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 17, + "timestamp": 1684703913122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "m is a number of rows, and the column space is in R^m?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk7.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..d7d37574f96aa8a6f620bef5fd3e4c39c2a49b9c --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 17, + "timestamp": 1684703913122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "m is a number of rows, and the column space is in R^m?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk8.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..d7d37574f96aa8a6f620bef5fd3e4c39c2a49b9c --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 17, + "timestamp": 1684703913122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "m is a number of rows, and the column space is in R^m?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk9.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..d7d37574f96aa8a6f620bef5fd3e4c39c2a49b9c --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_17_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 17, + "timestamp": 1684703913122.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "m is a number of rows, and the column space is in R^m?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_20_chunk0.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_20_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..bf55b718777a648283565e0b178feaa87761078b --- /dev/null +++ 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Any answer ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk14.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..cf5bff9de2e9e3d8780388fa74ac03da0d4173e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 21, + "timestamp": 1684704008241.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "What are 8 rule for vector space.. which he never wrote. Any answer ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk15.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..cf5bff9de2e9e3d8780388fa74ac03da0d4173e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 21, + "timestamp": 1684704008241.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "What are 8 rule for vector space.. which he never wrote. Any answer ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk16.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..cf5bff9de2e9e3d8780388fa74ac03da0d4173e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 21, + "timestamp": 1684704008241.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "What are 8 rule for vector space.. which he never wrote. Any answer ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk17.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..cf5bff9de2e9e3d8780388fa74ac03da0d4173e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 21, + "timestamp": 1684704008241.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "What are 8 rule for vector space.. which he never wrote. Any answer ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk18.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..cf5bff9de2e9e3d8780388fa74ac03da0d4173e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 21, + "timestamp": 1684704008241.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "What are 8 rule for vector space.. which he never wrote. Any answer ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk19.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9d8e057a09bf2fa8b2358a4049e62655c28241 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk19.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 21, + "timestamp": 1684704008241.0, + "annotatedSourceSentencesIndices": [ + 17 + ], + "names": [ + "annotator2" + ], + "text": "What are 8 rule for vector space.. which he never wrote. Any answer ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk2.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..cf5bff9de2e9e3d8780388fa74ac03da0d4173e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 21, + "timestamp": 1684704008241.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "What are 8 rule for vector space.. which he never wrote. Any answer ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk20.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..cf5bff9de2e9e3d8780388fa74ac03da0d4173e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 21, + "timestamp": 1684704008241.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "What are 8 rule for vector space.. which he never wrote. Any answer ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk21.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..cf5bff9de2e9e3d8780388fa74ac03da0d4173e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 21, + "timestamp": 1684704008241.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "What are 8 rule for vector space.. which he never wrote. Any answer ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk22.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..cf5bff9de2e9e3d8780388fa74ac03da0d4173e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 21, + "timestamp": 1684704008241.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "What are 8 rule for vector space.. which he never wrote. Any answer ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk3.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..cf5bff9de2e9e3d8780388fa74ac03da0d4173e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 21, + "timestamp": 1684704008241.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "What are 8 rule for vector space.. which he never wrote. Any answer ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk4.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..cf5bff9de2e9e3d8780388fa74ac03da0d4173e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 21, + "timestamp": 1684704008241.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "What are 8 rule for vector space.. which he never wrote. Any answer ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk5.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..cf5bff9de2e9e3d8780388fa74ac03da0d4173e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 21, + "timestamp": 1684704008241.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "What are 8 rule for vector space.. which he never wrote. Any answer ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk6.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..cf5bff9de2e9e3d8780388fa74ac03da0d4173e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 21, + "timestamp": 1684704008241.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "What are 8 rule for vector space.. which he never wrote. Any answer ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk7.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..cf5bff9de2e9e3d8780388fa74ac03da0d4173e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 21, + "timestamp": 1684704008241.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "What are 8 rule for vector space.. which he never wrote. Any answer ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk8.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..cf5bff9de2e9e3d8780388fa74ac03da0d4173e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 21, + "timestamp": 1684704008241.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "What are 8 rule for vector space.. which he never wrote. Any answer ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk9.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..cf5bff9de2e9e3d8780388fa74ac03da0d4173e0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_21_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 21, + "timestamp": 1684704008241.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "What are 8 rule for vector space.. which he never wrote. Any answer ???" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk0.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..7930994015777c295c5efa5b989f28da0cf06717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 22, + "timestamp": 1684704082641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 24:30 why is row operation able to preserve row space and not column space? as Prof Strang mentioned that 111 can longer be found in C(R) so column space is not preserved. However, I don't see any row in A being found in R as well?. To put my question simply, how do I know if certain space is preserved after certain operation?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk1.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..7930994015777c295c5efa5b989f28da0cf06717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 22, + "timestamp": 1684704082641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 24:30 why is row operation able to preserve row space and not column space? as Prof Strang mentioned that 111 can longer be found in C(R) so column space is not preserved. However, I don't see any row in A being found in R as well?. To put my question simply, how do I know if certain space is preserved after certain operation?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk10.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..f596f8bd00d3d649834de843840e94acaec799b9 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk10.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 22, + "timestamp": 1684704082641.0, + "annotatedSourceSentencesIndices": [ + 8 + ], + "names": [ + "annotator2" + ], + "text": "@ 24:30 why is row operation able to preserve row space and not column space? as Prof Strang mentioned that 111 can longer be found in C(R) so column space is not preserved. However, I don't see any row in A being found in R as well?. To put my question simply, how do I know if certain space is preserved after certain operation?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk11.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..7930994015777c295c5efa5b989f28da0cf06717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 22, + "timestamp": 1684704082641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 24:30 why is row operation able to preserve row space and not column space? as Prof Strang mentioned that 111 can longer be found in C(R) so column space is not preserved. However, I don't see any row in A being found in R as well?. To put my question simply, how do I know if certain space is preserved after certain operation?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk12.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..7930994015777c295c5efa5b989f28da0cf06717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 22, + "timestamp": 1684704082641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 24:30 why is row operation able to preserve row space and not column space? as Prof Strang mentioned that 111 can longer be found in C(R) so column space is not preserved. However, I don't see any row in A being found in R as well?. To put my question simply, how do I know if certain space is preserved after certain operation?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk13.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..7930994015777c295c5efa5b989f28da0cf06717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 22, + "timestamp": 1684704082641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 24:30 why is row operation able to preserve row space and not column space? as Prof Strang mentioned that 111 can longer be found in C(R) so column space is not preserved. However, I don't see any row in A being found in R as well?. To put my question simply, how do I know if certain space is preserved after certain operation?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk14.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7930994015777c295c5efa5b989f28da0cf06717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 22, + "timestamp": 1684704082641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 24:30 why is row operation able to preserve row space and not column space? as Prof Strang mentioned that 111 can longer be found in C(R) so column space is not preserved. However, I don't see any row in A being found in R as well?. To put my question simply, how do I know if certain space is preserved after certain operation?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk15.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7930994015777c295c5efa5b989f28da0cf06717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 22, + "timestamp": 1684704082641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 24:30 why is row operation able to preserve row space and not column space? as Prof Strang mentioned that 111 can longer be found in C(R) so column space is not preserved. However, I don't see any row in A being found in R as well?. To put my question simply, how do I know if certain space is preserved after certain operation?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk16.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..7930994015777c295c5efa5b989f28da0cf06717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 22, + "timestamp": 1684704082641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 24:30 why is row operation able to preserve row space and not column space? as Prof Strang mentioned that 111 can longer be found in C(R) so column space is not preserved. However, I don't see any row in A being found in R as well?. To put my question simply, how do I know if certain space is preserved after certain operation?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk17.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..7930994015777c295c5efa5b989f28da0cf06717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 22, + "timestamp": 1684704082641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 24:30 why is row operation able to preserve row space and not column space? as Prof Strang mentioned that 111 can longer be found in C(R) so column space is not preserved. However, I don't see any row in A being found in R as well?. To put my question simply, how do I know if certain space is preserved after certain operation?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk18.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..7930994015777c295c5efa5b989f28da0cf06717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 22, + "timestamp": 1684704082641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 24:30 why is row operation able to preserve row space and not column space? as Prof Strang mentioned that 111 can longer be found in C(R) so column space is not preserved. However, I don't see any row in A being found in R as well?. To put my question simply, how do I know if certain space is preserved after certain operation?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk19.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..7930994015777c295c5efa5b989f28da0cf06717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 22, + "timestamp": 1684704082641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 24:30 why is row operation able to preserve row space and not column space? as Prof Strang mentioned that 111 can longer be found in C(R) so column space is not preserved. However, I don't see any row in A being found in R as well?. To put my question simply, how do I know if certain space is preserved after certain operation?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk2.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..7930994015777c295c5efa5b989f28da0cf06717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 22, + "timestamp": 1684704082641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 24:30 why is row operation able to preserve row space and not column space? as Prof Strang mentioned that 111 can longer be found in C(R) so column space is not preserved. However, I don't see any row in A being found in R as well?. To put my question simply, how do I know if certain space is preserved after certain operation?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk20.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..7930994015777c295c5efa5b989f28da0cf06717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 22, + "timestamp": 1684704082641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 24:30 why is row operation able to preserve row space and not column space? as Prof Strang mentioned that 111 can longer be found in C(R) so column space is not preserved. However, I don't see any row in A being found in R as well?. To put my question simply, how do I know if certain space is preserved after certain operation?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk21.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7930994015777c295c5efa5b989f28da0cf06717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 22, + "timestamp": 1684704082641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 24:30 why is row operation able to preserve row space and not column space? as Prof Strang mentioned that 111 can longer be found in C(R) so column space is not preserved. However, I don't see any row in A being found in R as well?. To put my question simply, how do I know if certain space is preserved after certain operation?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk22.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..7930994015777c295c5efa5b989f28da0cf06717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 22, + "timestamp": 1684704082641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 24:30 why is row operation able to preserve row space and not column space? as Prof Strang mentioned that 111 can longer be found in C(R) so column space is not preserved. However, I don't see any row in A being found in R as well?. To put my question simply, how do I know if certain space is preserved after certain operation?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk3.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..7930994015777c295c5efa5b989f28da0cf06717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 22, + "timestamp": 1684704082641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 24:30 why is row operation able to preserve row space and not column space? as Prof Strang mentioned that 111 can longer be found in C(R) so column space is not preserved. However, I don't see any row in A being found in R as well?. To put my question simply, how do I know if certain space is preserved after certain operation?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk4.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..7930994015777c295c5efa5b989f28da0cf06717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 22, + "timestamp": 1684704082641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 24:30 why is row operation able to preserve row space and not column space? as Prof Strang mentioned that 111 can longer be found in C(R) so column space is not preserved. However, I don't see any row in A being found in R as well?. To put my question simply, how do I know if certain space is preserved after certain operation?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk5.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..7930994015777c295c5efa5b989f28da0cf06717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 22, + "timestamp": 1684704082641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 24:30 why is row operation able to preserve row space and not column space? as Prof Strang mentioned that 111 can longer be found in C(R) so column space is not preserved. However, I don't see any row in A being found in R as well?. To put my question simply, how do I know if certain space is preserved after certain operation?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk6.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..7930994015777c295c5efa5b989f28da0cf06717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 22, + "timestamp": 1684704082641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 24:30 why is row operation able to preserve row space and not column space? as Prof Strang mentioned that 111 can longer be found in C(R) so column space is not preserved. However, I don't see any row in A being found in R as well?. To put my question simply, how do I know if certain space is preserved after certain operation?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk7.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..7930994015777c295c5efa5b989f28da0cf06717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 22, + "timestamp": 1684704082641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 24:30 why is row operation able to preserve row space and not column space? as Prof Strang mentioned that 111 can longer be found in C(R) so column space is not preserved. However, I don't see any row in A being found in R as well?. To put my question simply, how do I know if certain space is preserved after certain operation?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk8.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..7930994015777c295c5efa5b989f28da0cf06717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 22, + "timestamp": 1684704082641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 24:30 why is row operation able to preserve row space and not column space? as Prof Strang mentioned that 111 can longer be found in C(R) so column space is not preserved. However, I don't see any row in A being found in R as well?. To put my question simply, how do I know if certain space is preserved after certain operation?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk9.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..7930994015777c295c5efa5b989f28da0cf06717 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_22_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 22, + "timestamp": 1684704082641.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "@ 24:30 why is row operation able to preserve row space and not column space? as Prof Strang mentioned that 111 can longer be found in C(R) so column space is not preserved. However, I don't see any row in A being found in R as well?. To put my question simply, how do I know if certain space is preserved after certain operation?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk0.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..0ed3cc7cbf2308514fcfc632aebfea589c6b99b1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 24, + "timestamp": 1684704215642.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "25:06 So performing row eliminations doesn't change the row space but changes the column space?\n\nSo to get the basis for the column space, would you have to do column elimination for matrix [A]? Or could you take the transpose, do row elimination, and just use that row basis for [A] transpose as the column basis for [A]?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk1.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..0ed3cc7cbf2308514fcfc632aebfea589c6b99b1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 24, + "timestamp": 1684704215642.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "25:06 So performing row eliminations doesn't change the row space but changes the column space?\n\nSo to get the basis for the column space, would you have to do column elimination for matrix [A]? Or could you take the transpose, do row elimination, and just use that row basis for [A] transpose as the column basis for [A]?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk10.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..77406d686dbd8ea5e31e0925bf50b2d57c110942 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk10.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 24, + "timestamp": 1684704215642.0, + "annotatedSourceSentencesIndices": [ + 8 + ], + "names": [ + "annotator2" + ], + "text": "25:06 So performing row eliminations doesn't change the row space but changes the column space?\n\nSo to get the basis for the column space, would you have to do column elimination for matrix [A]? Or could you take the transpose, do row elimination, and just use that row basis for [A] transpose as the column basis for [A]?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk11.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..0ed3cc7cbf2308514fcfc632aebfea589c6b99b1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 24, + "timestamp": 1684704215642.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "25:06 So performing row eliminations doesn't change the row space but changes the column space?\n\nSo to get the basis for the column space, would you have to do column elimination for matrix [A]? Or could you take the transpose, do row elimination, and just use that row basis for [A] transpose as the column basis for [A]?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk12.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ed3cc7cbf2308514fcfc632aebfea589c6b99b1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 24, + "timestamp": 1684704215642.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "25:06 So performing row eliminations doesn't change the row space but changes the column space?\n\nSo to get the basis for the column space, would you have to do column elimination for matrix [A]? Or could you take the transpose, do row elimination, and just use that row basis for [A] transpose as the column basis for [A]?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk13.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..0ed3cc7cbf2308514fcfc632aebfea589c6b99b1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 24, + "timestamp": 1684704215642.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "25:06 So performing row eliminations doesn't change the row space but changes the column space?\n\nSo to get the basis for the column space, would you have to do column elimination for matrix [A]? Or could you take the transpose, do row elimination, and just use that row basis for [A] transpose as the column basis for [A]?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk14.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..0ed3cc7cbf2308514fcfc632aebfea589c6b99b1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 24, + "timestamp": 1684704215642.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "25:06 So performing row eliminations doesn't change the row space but changes the column space?\n\nSo to get the basis for the column space, would you have to do column elimination for matrix [A]? Or could you take the transpose, do row elimination, and just use that row basis for [A] transpose as the column basis for [A]?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk15.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..0ed3cc7cbf2308514fcfc632aebfea589c6b99b1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 24, + "timestamp": 1684704215642.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "25:06 So performing row eliminations doesn't change the row space but changes the column space?\n\nSo to get the basis for the column space, would you have to do column elimination for matrix [A]? Or could you take the transpose, do row elimination, and just use that row basis for [A] transpose as the column basis for [A]?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk16.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..0ed3cc7cbf2308514fcfc632aebfea589c6b99b1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 24, + "timestamp": 1684704215642.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "25:06 So performing row eliminations doesn't change the row space but changes the column space?\n\nSo to get the basis for the column space, would you have to do column elimination for matrix [A]? Or could you take the transpose, do row elimination, and just use that row basis for [A] transpose as the column basis for [A]?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk17.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..0ed3cc7cbf2308514fcfc632aebfea589c6b99b1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 24, + "timestamp": 1684704215642.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "25:06 So performing row eliminations doesn't change the row space but changes the column space?\n\nSo to get the basis for the column space, would you have to do column elimination for matrix [A]? Or could you take the transpose, do row elimination, and just use that row basis for [A] transpose as the column basis for [A]?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk18.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..0ed3cc7cbf2308514fcfc632aebfea589c6b99b1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 24, + "timestamp": 1684704215642.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "25:06 So performing row eliminations doesn't change the row space but changes the column space?\n\nSo to get the basis for the column space, would you have to do column elimination for matrix [A]? Or could you take the transpose, do row elimination, and just use that row basis for [A] transpose as the column basis for [A]?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk19.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..0ed3cc7cbf2308514fcfc632aebfea589c6b99b1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 24, + "timestamp": 1684704215642.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "25:06 So performing row eliminations doesn't change the row space but changes the column space?\n\nSo to get the basis for the column space, would you have to do column elimination for matrix [A]? Or could you take the transpose, do row elimination, and just use that row basis for [A] transpose as the column basis for [A]?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk2.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..0ed3cc7cbf2308514fcfc632aebfea589c6b99b1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 24, + "timestamp": 1684704215642.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "25:06 So performing row eliminations doesn't change the row space but changes the column space?\n\nSo to get the basis for the column space, would you have to do column elimination for matrix [A]? Or could you take the transpose, do row elimination, and just use that row basis for [A] transpose as the column basis for [A]?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk20.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..0ed3cc7cbf2308514fcfc632aebfea589c6b99b1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 24, + "timestamp": 1684704215642.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "25:06 So performing row eliminations doesn't change the row space but changes the column space?\n\nSo to get the basis for the column space, would you have to do column elimination for matrix [A]? Or could you take the transpose, do row elimination, and just use that row basis for [A] transpose as the column basis for [A]?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk21.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..0ed3cc7cbf2308514fcfc632aebfea589c6b99b1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 24, + "timestamp": 1684704215642.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "25:06 So performing row eliminations doesn't change the row space but changes the column space?\n\nSo to get the basis for the column space, would you have to do column elimination for matrix [A]? Or could you take the transpose, do row elimination, and just use that row basis for [A] transpose as the column basis for [A]?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk22.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0ed3cc7cbf2308514fcfc632aebfea589c6b99b1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 24, + "timestamp": 1684704215642.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "25:06 So performing row eliminations doesn't change the row space but changes the column space?\n\nSo to get the basis for the column space, would you have to do column elimination for matrix [A]? Or could you take the transpose, do row elimination, and just use that row basis for [A] transpose as the column basis for [A]?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk3.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..0ed3cc7cbf2308514fcfc632aebfea589c6b99b1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 24, + "timestamp": 1684704215642.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "25:06 So performing row eliminations doesn't change the row space but changes the column space?\n\nSo to get the basis for the column space, would you have to do column elimination for matrix [A]? Or could you take the transpose, do row elimination, and just use that row basis for [A] transpose as the column basis for [A]?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk4.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0ed3cc7cbf2308514fcfc632aebfea589c6b99b1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 24, + "timestamp": 1684704215642.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "25:06 So performing row eliminations doesn't change the row space but changes the column space?\n\nSo to get the basis for the column space, would you have to do column elimination for matrix [A]? Or could you take the transpose, do row elimination, and just use that row basis for [A] transpose as the column basis for [A]?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk5.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..0ed3cc7cbf2308514fcfc632aebfea589c6b99b1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 24, + "timestamp": 1684704215642.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "25:06 So performing row eliminations doesn't change the row space but changes the column space?\n\nSo to get the basis for the column space, would you have to do column elimination for matrix [A]? Or could you take the transpose, do row elimination, and just use that row basis for [A] transpose as the column basis for [A]?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk6.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..0ed3cc7cbf2308514fcfc632aebfea589c6b99b1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 24, + "timestamp": 1684704215642.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "25:06 So performing row eliminations doesn't change the row space but changes the column space?\n\nSo to get the basis for the column space, would you have to do column elimination for matrix [A]? Or could you take the transpose, do row elimination, and just use that row basis for [A] transpose as the column basis for [A]?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk7.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0ed3cc7cbf2308514fcfc632aebfea589c6b99b1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 24, + "timestamp": 1684704215642.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "25:06 So performing row eliminations doesn't change the row space but changes the column space?\n\nSo to get the basis for the column space, would you have to do column elimination for matrix [A]? Or could you take the transpose, do row elimination, and just use that row basis for [A] transpose as the column basis for [A]?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk8.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..0ed3cc7cbf2308514fcfc632aebfea589c6b99b1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 24, + "timestamp": 1684704215642.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "25:06 So performing row eliminations doesn't change the row space but changes the column space?\n\nSo to get the basis for the column space, would you have to do column elimination for matrix [A]? Or could you take the transpose, do row elimination, and just use that row basis for [A] transpose as the column basis for [A]?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk9.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..0ed3cc7cbf2308514fcfc632aebfea589c6b99b1 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_24_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 24, + "timestamp": 1684704215642.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "25:06 So performing row eliminations doesn't change the row space but changes the column space?\n\nSo to get the basis for the column space, would you have to do column elimination for matrix [A]? Or could you take the transpose, do row elimination, and just use that row basis for [A] transpose as the column basis for [A]?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk0.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6a046a59a187aaf139e1e7018b1973edecde2098 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 26, + "timestamp": 1684704349825.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand how vectors of N(A) can be in R^m ! If A is a m*n matrix, we need a R^n vector to have the 0 matrix, no ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk1.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..6a046a59a187aaf139e1e7018b1973edecde2098 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 26, + "timestamp": 1684704349825.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand how vectors of N(A) can be in R^m ! If A is a m*n matrix, we need a R^n vector to have the 0 matrix, no ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk10.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..6a046a59a187aaf139e1e7018b1973edecde2098 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 26, + "timestamp": 1684704349825.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand how vectors of N(A) can be in R^m ! If A is a m*n matrix, we need a R^n vector to have the 0 matrix, no ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk11.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..6a046a59a187aaf139e1e7018b1973edecde2098 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 26, + "timestamp": 1684704349825.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand how vectors of N(A) can be in R^m ! If A is a m*n matrix, we need a R^n vector to have the 0 matrix, no ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk12.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..6a046a59a187aaf139e1e7018b1973edecde2098 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 26, + "timestamp": 1684704349825.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand how vectors of N(A) can be in R^m ! If A is a m*n matrix, we need a R^n vector to have the 0 matrix, no ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk13.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..6a046a59a187aaf139e1e7018b1973edecde2098 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 26, + "timestamp": 1684704349825.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand how vectors of N(A) can be in R^m ! If A is a m*n matrix, we need a R^n vector to have the 0 matrix, no ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk14.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..6a046a59a187aaf139e1e7018b1973edecde2098 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 26, + "timestamp": 1684704349825.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand how vectors of N(A) can be in R^m ! If A is a m*n matrix, we need a R^n vector to have the 0 matrix, no ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk15.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..6a046a59a187aaf139e1e7018b1973edecde2098 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 26, + "timestamp": 1684704349825.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand how vectors of N(A) can be in R^m ! If A is a m*n matrix, we need a R^n vector to have the 0 matrix, no ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk16.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..6a046a59a187aaf139e1e7018b1973edecde2098 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 26, + "timestamp": 1684704349825.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand how vectors of N(A) can be in R^m ! If A is a m*n matrix, we need a R^n vector to have the 0 matrix, no ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk17.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..6a046a59a187aaf139e1e7018b1973edecde2098 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 26, + "timestamp": 1684704349825.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand how vectors of N(A) can be in R^m ! If A is a m*n matrix, we need a R^n vector to have the 0 matrix, no ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk18.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..6a046a59a187aaf139e1e7018b1973edecde2098 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 26, + "timestamp": 1684704349825.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand how vectors of N(A) can be in R^m ! If A is a m*n matrix, we need a R^n vector to have the 0 matrix, no ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk19.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..6a046a59a187aaf139e1e7018b1973edecde2098 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 26, + "timestamp": 1684704349825.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand how vectors of N(A) can be in R^m ! If A is a m*n matrix, we need a R^n vector to have the 0 matrix, no ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk2.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6a046a59a187aaf139e1e7018b1973edecde2098 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 26, + "timestamp": 1684704349825.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand how vectors of N(A) can be in R^m ! If A is a m*n matrix, we need a R^n vector to have the 0 matrix, no ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk20.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6a046a59a187aaf139e1e7018b1973edecde2098 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 26, + "timestamp": 1684704349825.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand how vectors of N(A) can be in R^m ! If A is a m*n matrix, we need a R^n vector to have the 0 matrix, no ?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk21.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..6a046a59a187aaf139e1e7018b1973edecde2098 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_26_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 26, + "timestamp": 1684704349825.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "I don't understand how vectors of N(A) can be in R^m ! 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[ + 11 + ], + "names": [ + "annotator2" + ], + "text": "What did he mean by the Dimensions?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_27_chunk5.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_27_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..c30e51fd634a8e37264343ef47d66f160c215bc4 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_27_chunk5.json @@ -0,0 +1,15 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 27, + "timestamp": 1684704442760.0, + "annotatedSourceSentencesIndices": [ + 6, + 10 + ], + "names": [ + "annotator2" + ], + "text": "What did he mean by the Dimensions?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_27_chunk6.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_27_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..adea2faa924fecc97a6744f335b32901918aa520 --- 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a/sight/query/annotated_chunks_window20/nHlE7EgJFds_27_chunk8.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_27_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..adea2faa924fecc97a6744f335b32901918aa520 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_27_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 27, + "timestamp": 1684704442760.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "What did he mean by the Dimensions?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_27_chunk9.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_27_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..adea2faa924fecc97a6744f335b32901918aa520 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_27_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 27, + "timestamp": 1684704442760.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "What did he mean by the Dimensions?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk0.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..ab7c6cdfea24a4232d4e3c45fc251acd0ba7f2ea --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk0.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 28, + "timestamp": 1684705683645.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "suppose I'm in 3D if nullspace is a plane can we not simply write nullspace as an equation of that plane and every x,y,z be the possible values that give b of zeroes similarly if column space is plane and vice versa for row space and null space of A^t?\np.s I do understand we can't write any of four subspace as a line in 3D because there is no equation of a line in 3D it's just the equation of the plane" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk1.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..ab7c6cdfea24a4232d4e3c45fc251acd0ba7f2ea --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 28, + "timestamp": 1684705683645.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "suppose I'm in 3D if nullspace is a plane can we not simply write nullspace as an equation of that plane and every x,y,z be the possible values that give b of zeroes similarly if column space is plane and vice versa for row space and null space of A^t?\np.s I do understand we can't write any of four subspace as a line in 3D because there is no equation of a line in 3D it's just the equation of the plane" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk10.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..ab7c6cdfea24a4232d4e3c45fc251acd0ba7f2ea --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 28, + "timestamp": 1684705683645.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "suppose I'm in 3D if nullspace is a plane can we not simply write nullspace as an equation of that plane and every x,y,z be the possible values that give b of zeroes similarly if column space is plane and vice versa for row space and null space of A^t?\np.s I do understand we can't write any of four subspace as a line in 3D because there is no equation of a line in 3D it's just the equation of the plane" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk11.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..ab7c6cdfea24a4232d4e3c45fc251acd0ba7f2ea --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 28, + "timestamp": 1684705683645.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "suppose I'm in 3D if nullspace is a plane can we not simply write nullspace as an equation of that plane and every x,y,z be the possible values that give b of zeroes similarly if column space is plane and vice versa for row space and null space of A^t?\np.s I do understand we can't write any of four subspace as a line in 3D because there is no equation of a line in 3D it's just the equation of the plane" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk12.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..ab7c6cdfea24a4232d4e3c45fc251acd0ba7f2ea --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 28, + "timestamp": 1684705683645.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "suppose I'm in 3D if nullspace is a plane can we not simply write nullspace as an equation of that plane and every x,y,z be the possible values that give b of zeroes similarly if column space is plane and vice versa for row space and null space of A^t?\np.s I do understand we can't write any of four subspace as a line in 3D because there is no equation of a line in 3D it's just the equation of the plane" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk13.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..ab7c6cdfea24a4232d4e3c45fc251acd0ba7f2ea --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 28, + "timestamp": 1684705683645.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "suppose I'm in 3D if nullspace is a plane can we not simply write nullspace as an equation of that plane and every x,y,z be the possible values that give b of zeroes similarly if column space is plane and vice versa for row space and null space of A^t?\np.s I do understand we can't write any of four subspace as a line in 3D because there is no equation of a line in 3D it's just the equation of the plane" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk14.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..ab7c6cdfea24a4232d4e3c45fc251acd0ba7f2ea --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 28, + "timestamp": 1684705683645.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "suppose I'm in 3D if nullspace is a plane can we not simply write nullspace as an equation of that plane and every x,y,z be the possible values that give b of zeroes similarly if column space is plane and vice versa for row space and null space of A^t?\np.s I do understand we can't write any of four subspace as a line in 3D because there is no equation of a line in 3D it's just the equation of the plane" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk15.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..ab7c6cdfea24a4232d4e3c45fc251acd0ba7f2ea --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 28, + "timestamp": 1684705683645.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "suppose I'm in 3D if nullspace is a plane can we not simply write nullspace as an equation of that plane and every x,y,z be the possible values that give b of zeroes similarly if column space is plane and vice versa for row space and null space of A^t?\np.s I do understand we can't write any of four subspace as a line in 3D because there is no equation of a line in 3D it's just the equation of the plane" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk16.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..ab7c6cdfea24a4232d4e3c45fc251acd0ba7f2ea --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 28, + "timestamp": 1684705683645.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "suppose I'm in 3D if nullspace is a plane can we not simply write nullspace as an equation of that plane and every x,y,z be the possible values that give b of zeroes similarly if column space is plane and vice versa for row space and null space of A^t?\np.s I do understand we can't write any of four subspace as a line in 3D because there is no equation of a line in 3D it's just the equation of the plane" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk17.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..ab7c6cdfea24a4232d4e3c45fc251acd0ba7f2ea --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 28, + "timestamp": 1684705683645.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "suppose I'm in 3D if nullspace is a plane can we not simply write nullspace as an equation of that plane and every x,y,z be the possible values that give b of zeroes similarly if column space is plane and vice versa for row space and null space of A^t?\np.s I do understand we can't write any of four subspace as a line in 3D because there is no equation of a line in 3D it's just the equation of the plane" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk18.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..ab7c6cdfea24a4232d4e3c45fc251acd0ba7f2ea --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 28, + "timestamp": 1684705683645.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "suppose I'm in 3D if nullspace is a plane can we not simply write nullspace as an equation of that plane and every x,y,z be the possible values that give b of zeroes similarly if column space is plane and vice versa for row space and null space of A^t?\np.s I do understand we can't write any of four subspace as a line in 3D because there is no equation of a line in 3D it's just the equation of the plane" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk19.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..ab7c6cdfea24a4232d4e3c45fc251acd0ba7f2ea --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 28, + "timestamp": 1684705683645.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "suppose I'm in 3D if nullspace is a plane can we not simply write nullspace as an equation of that plane and every x,y,z be the possible values that give b of zeroes similarly if column space is plane and vice versa for row space and null space of A^t?\np.s I do understand we can't write any of four subspace as a line in 3D because there is no equation of a line in 3D it's just the equation of the plane" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk2.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..ab7c6cdfea24a4232d4e3c45fc251acd0ba7f2ea --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 28, + "timestamp": 1684705683645.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "suppose I'm in 3D if nullspace is a plane can we not simply write nullspace as an equation of that plane and every x,y,z be the possible values that give b of zeroes similarly if column space is plane and vice versa for row space and null space of A^t?\np.s I do understand we can't write any of four subspace as a line in 3D because there is no equation of a line in 3D it's just the equation of the plane" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk20.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ab7c6cdfea24a4232d4e3c45fc251acd0ba7f2ea --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 28, + "timestamp": 1684705683645.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "suppose I'm in 3D if nullspace is a plane can we not simply write nullspace as an equation of that plane and every x,y,z be the possible values that give b of zeroes similarly if column space is plane and vice versa for row space and null space of A^t?\np.s I do understand we can't write any of four subspace as a line in 3D because there is no equation of a line in 3D it's just the equation of the plane" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk21.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..ab7c6cdfea24a4232d4e3c45fc251acd0ba7f2ea --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 28, + "timestamp": 1684705683645.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "suppose I'm in 3D if nullspace is a plane can we not simply write nullspace as an equation of that plane and every x,y,z be the possible values that give b of zeroes similarly if column space is plane and vice versa for row space and null space of A^t?\np.s I do understand we can't write any of four subspace as a line in 3D because there is no equation of a line in 3D it's just the equation of the plane" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk22.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..ab7c6cdfea24a4232d4e3c45fc251acd0ba7f2ea --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 28, + "timestamp": 1684705683645.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "suppose I'm in 3D if nullspace is a plane can we not simply write nullspace as an equation of that plane and every x,y,z be the possible values that give b of zeroes similarly if column space is plane and vice versa for row space and null space of A^t?\np.s I do understand we can't write any of four subspace as a line in 3D because there is no equation of a line in 3D it's just the equation of the plane" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk3.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..ab7c6cdfea24a4232d4e3c45fc251acd0ba7f2ea --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 28, + "timestamp": 1684705683645.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "suppose I'm in 3D if nullspace is a plane can we not simply write nullspace as an equation of that plane and every x,y,z be the possible values that give b of zeroes similarly if column space is plane and vice versa for row space and null space of A^t?\np.s I do understand we can't write any of four subspace as a line in 3D because there is no equation of a line in 3D it's just the equation of the plane" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk4.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..5d51740ee160d059e176557c08cf62d39ad32d4f --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk4.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 28, + "timestamp": 1684705683645.0, + "annotatedSourceSentencesIndices": [ + 1 + ], + "names": [ + "annotator2" + ], + "text": "suppose I'm in 3D if nullspace is a plane can we not simply write nullspace as an equation of that plane and every x,y,z be the possible values that give b of zeroes similarly if column space is plane and vice versa for row space and null space of A^t?\np.s I do understand we can't write any of four subspace as a line in 3D because there is no equation of a line in 3D it's just the equation of the plane" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk5.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..ab7c6cdfea24a4232d4e3c45fc251acd0ba7f2ea --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 28, + "timestamp": 1684705683645.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "suppose I'm in 3D if nullspace is a plane can we not simply write nullspace as an equation of that plane and every x,y,z be the possible values that give b of zeroes similarly if column space is plane and vice versa for row space and null space of A^t?\np.s I do understand we can't write any of four subspace as a line in 3D because there is no equation of a line in 3D it's just the equation of the plane" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk6.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..ab7c6cdfea24a4232d4e3c45fc251acd0ba7f2ea --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 28, + "timestamp": 1684705683645.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "suppose I'm in 3D if nullspace is a plane can we not simply write nullspace as an equation of that plane and every x,y,z be the possible values that give b of zeroes similarly if column space is plane and vice versa for row space and null space of A^t?\np.s I do understand we can't write any of four subspace as a line in 3D because there is no equation of a line in 3D it's just the equation of the plane" + } +] \ No newline at end of file diff --git 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a/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk8.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..ab7c6cdfea24a4232d4e3c45fc251acd0ba7f2ea --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_28_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 28, + "timestamp": 1684705683645.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "suppose I'm in 3D if nullspace is a plane can we not simply write nullspace as an equation of that plane and every x,y,z be the possible values that give b of zeroes similarly if column space is plane and vice versa for row space and null space of A^t?\np.s I do understand we can't write any of four subspace as a line in 3D because there is no equation of a line in 3D it's just the equation of the plane" + } +] \ No newline at end of file diff --git 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minute that [third vector] is not independent...'\"\nI love it. \u00a0What other professor brings this kind of passion to linear algebra? \u00a0This is what makes real in the flesh lectures worthwhile. \u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk13.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..81eda2a4b5d65cf295bca1b36b6e3a5747ddcdca --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 2, + "timestamp": 1684702165910.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "\"But, after class - TO MY SORROW - a student tells me, 'Wait a minute that [third vector] is not independent...'\"\nI love it. \u00a0What other professor brings this kind of passion to linear algebra? \u00a0This is what makes real in the flesh lectures worthwhile. \u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk14.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..81eda2a4b5d65cf295bca1b36b6e3a5747ddcdca --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 2, + "timestamp": 1684702165910.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "\"But, after class - TO MY SORROW - a student tells me, 'Wait a minute that [third vector] is not independent...'\"\nI love it. \u00a0What other professor brings this kind of passion to linear algebra? \u00a0This is what makes real in the flesh lectures worthwhile. \u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk15.json 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0000000000000000000000000000000000000000..81eda2a4b5d65cf295bca1b36b6e3a5747ddcdca --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 2, + "timestamp": 1684702165910.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "\"But, after class - TO MY SORROW - a student tells me, 'Wait a minute that [third vector] is not independent...'\"\nI love it. \u00a0What other professor brings this kind of passion to linear algebra? \u00a0This is what makes real in the flesh lectures worthwhile. \u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk17.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..81eda2a4b5d65cf295bca1b36b6e3a5747ddcdca --- /dev/null +++ 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1684702165910.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "\"But, after class - TO MY SORROW - a student tells me, 'Wait a minute that [third vector] is not independent...'\"\nI love it. \u00a0What other professor brings this kind of passion to linear algebra? \u00a0This is what makes real in the flesh lectures worthwhile. \u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk19.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..81eda2a4b5d65cf295bca1b36b6e3a5747ddcdca --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 2, + "timestamp": 1684702165910.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "\"But, after class - TO MY SORROW - a student tells me, 'Wait a minute that [third vector] is not independent...'\"\nI love it. \u00a0What other professor brings this kind of passion to linear algebra? \u00a0This is what makes real in the flesh lectures worthwhile. \u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk2.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..81eda2a4b5d65cf295bca1b36b6e3a5747ddcdca --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 2, + "timestamp": 1684702165910.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "\"But, after class - TO MY SORROW - a student tells me, 'Wait a minute that [third vector] is not independent...'\"\nI love it. \u00a0What other professor brings this kind of passion to linear algebra? \u00a0This is what makes real in the flesh lectures worthwhile. \u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk20.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..81eda2a4b5d65cf295bca1b36b6e3a5747ddcdca --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 2, + "timestamp": 1684702165910.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "\"But, after class - TO MY SORROW - a student tells me, 'Wait a minute that [third vector] is not independent...'\"\nI love it. \u00a0What other professor brings this kind of passion to linear algebra? \u00a0This is what makes real in the flesh lectures worthwhile. \u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk21.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..81eda2a4b5d65cf295bca1b36b6e3a5747ddcdca --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 2, + "timestamp": 1684702165910.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "\"But, after class - TO MY SORROW - a student tells me, 'Wait a minute that [third vector] is not independent...'\"\nI love it. \u00a0What other professor brings this kind of passion to linear algebra? \u00a0This is what makes real in the flesh lectures worthwhile. \u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk22.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..81eda2a4b5d65cf295bca1b36b6e3a5747ddcdca --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 2, + "timestamp": 1684702165910.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "\"But, after class - TO MY SORROW - a student tells me, 'Wait a minute that [third vector] is not independent...'\"\nI love it. \u00a0What other professor brings this kind of passion to linear algebra? \u00a0This is what makes real in the flesh lectures worthwhile. \u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk3.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..81eda2a4b5d65cf295bca1b36b6e3a5747ddcdca --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 2, + "timestamp": 1684702165910.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "\"But, after class - TO MY SORROW - a student tells me, 'Wait a minute that [third vector] is not independent...'\"\nI love it. \u00a0What other professor brings this kind of passion to linear algebra? \u00a0This is what makes real in the flesh lectures worthwhile. \u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk4.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..81eda2a4b5d65cf295bca1b36b6e3a5747ddcdca --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 2, + "timestamp": 1684702165910.0, + "annotatedSourceSentencesIndices": [], + "names": [ + 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other professor brings this kind of passion to linear algebra? \u00a0This is what makes real in the flesh lectures worthwhile. \u00a0" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk6.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..81eda2a4b5d65cf295bca1b36b6e3a5747ddcdca --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_2_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 2, + "timestamp": 1684702165910.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "\"But, after class - TO MY SORROW - a student tells me, 'Wait a minute that [third vector] is not independent...'\"\nI love it. \u00a0What other professor brings this kind of passion to linear algebra? \u00a0This is what makes real in the flesh lectures worthwhile. \u00a0" + } +] \ No newline at end of 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"35:55 Size of identity matrix should be be nxn so that its conformable, shouldn't it?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_5_chunk15.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_5_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..ae6da12af294add47d2e610a9cedb440e4b7ef83 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_5_chunk15.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 5, + "timestamp": 1684702466780.0, + "annotatedSourceSentencesIndices": [ + 0 + ], + "names": [ + "annotator2" + ], + "text": "35:55 Size of identity matrix should be be nxn so that its conformable, shouldn't it?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_5_chunk16.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_5_chunk16.json new file mode 100644 index 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"35:55 Size of identity matrix should be be nxn so that its conformable, shouldn't it?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_5_chunk18.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_5_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..1e89c8842468369ef374e5e5c20e120a44cb607f --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_5_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 5, + "timestamp": 1684702466780.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "35:55 Size of identity matrix should be be nxn so that its conformable, shouldn't it?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_5_chunk19.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_5_chunk19.json new file mode 100644 index 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"35:55 Size of identity matrix should be be nxn so that its conformable, shouldn't it?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_5_chunk20.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_5_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..1e89c8842468369ef374e5e5c20e120a44cb607f --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_5_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 5, + "timestamp": 1684702466780.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "35:55 Size of identity matrix should be be nxn so that its conformable, shouldn't it?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_5_chunk21.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_5_chunk21.json new file mode 100644 index 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"35:55 Size of identity matrix should be be nxn so that its conformable, shouldn't it?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_5_chunk3.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_5_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1e89c8842468369ef374e5e5c20e120a44cb607f --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_5_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 5, + "timestamp": 1684702466780.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "35:55 Size of identity matrix should be be nxn so that its conformable, shouldn't it?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_5_chunk4.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_5_chunk4.json new file mode 100644 index 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"35:55 Size of identity matrix should be be nxn so that its conformable, shouldn't it?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_5_chunk6.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_5_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..1e89c8842468369ef374e5e5c20e120a44cb607f --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_5_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 5, + "timestamp": 1684702466780.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "35:55 Size of identity matrix should be be nxn so that its conformable, shouldn't it?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_5_chunk7.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_5_chunk7.json new file mode 100644 index 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"35:55 Size of identity matrix should be be nxn so that its conformable, shouldn't it?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_5_chunk9.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_5_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..1e89c8842468369ef374e5e5c20e120a44cb607f --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_5_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 5, + "timestamp": 1684702466780.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "35:55 Size of identity matrix should be be nxn so that its conformable, shouldn't it?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk0.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..b4558eadac637416a0569cf5206acbb2cdf88bdd --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk0.json @@ -0,0 +1,14 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 9, + "timestamp": 1684702633715.0, + "annotatedSourceSentencesIndices": [ + 2 + ], + "names": [ + "annotator2" + ], + "text": "00:00 Error from last lecture, row dependent.\n04:28 4 Fundamental subspaces.\n08:30 Where are those spaces?\n11:45 Dimension of those spaces.\n21:20 Basis for those space.\n30:00 N(A^T) \"Left nullspace\"?\n42:10 New \"matrix\" space?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk1.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..38db57860b0c6b853544f95620c283faa9a594f0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk1.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 9, + "timestamp": 1684702633715.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "00:00 Error from last lecture, row dependent.\n04:28 4 Fundamental subspaces.\n08:30 Where are those spaces?\n11:45 Dimension of those spaces.\n21:20 Basis for those space.\n30:00 N(A^T) \"Left nullspace\"?\n42:10 New \"matrix\" space?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk10.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..38db57860b0c6b853544f95620c283faa9a594f0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk10.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 9, + "timestamp": 1684702633715.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "00:00 Error from last lecture, row dependent.\n04:28 4 Fundamental subspaces.\n08:30 Where are those spaces?\n11:45 Dimension of those spaces.\n21:20 Basis for those space.\n30:00 N(A^T) \"Left nullspace\"?\n42:10 New \"matrix\" space?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk11.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..38db57860b0c6b853544f95620c283faa9a594f0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk11.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 9, + "timestamp": 1684702633715.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "00:00 Error from last lecture, row dependent.\n04:28 4 Fundamental subspaces.\n08:30 Where are those spaces?\n11:45 Dimension of those spaces.\n21:20 Basis for those space.\n30:00 N(A^T) \"Left nullspace\"?\n42:10 New \"matrix\" space?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk12.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..38db57860b0c6b853544f95620c283faa9a594f0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk12.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 9, + "timestamp": 1684702633715.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "00:00 Error from last lecture, row dependent.\n04:28 4 Fundamental subspaces.\n08:30 Where are those spaces?\n11:45 Dimension of those spaces.\n21:20 Basis for those space.\n30:00 N(A^T) \"Left nullspace\"?\n42:10 New \"matrix\" space?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk13.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..38db57860b0c6b853544f95620c283faa9a594f0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk13.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 9, + "timestamp": 1684702633715.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "00:00 Error from last lecture, row dependent.\n04:28 4 Fundamental subspaces.\n08:30 Where are those spaces?\n11:45 Dimension of those spaces.\n21:20 Basis for those space.\n30:00 N(A^T) \"Left nullspace\"?\n42:10 New \"matrix\" space?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk14.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..38db57860b0c6b853544f95620c283faa9a594f0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk14.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 9, + "timestamp": 1684702633715.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "00:00 Error from last lecture, row dependent.\n04:28 4 Fundamental subspaces.\n08:30 Where are those spaces?\n11:45 Dimension of those spaces.\n21:20 Basis for those space.\n30:00 N(A^T) \"Left nullspace\"?\n42:10 New \"matrix\" space?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk15.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..38db57860b0c6b853544f95620c283faa9a594f0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk15.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 9, + "timestamp": 1684702633715.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "00:00 Error from last lecture, row dependent.\n04:28 4 Fundamental subspaces.\n08:30 Where are those spaces?\n11:45 Dimension of those spaces.\n21:20 Basis for those space.\n30:00 N(A^T) \"Left nullspace\"?\n42:10 New \"matrix\" space?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk16.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..38db57860b0c6b853544f95620c283faa9a594f0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk16.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 9, + "timestamp": 1684702633715.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "00:00 Error from last lecture, row dependent.\n04:28 4 Fundamental subspaces.\n08:30 Where are those spaces?\n11:45 Dimension of those spaces.\n21:20 Basis for those space.\n30:00 N(A^T) \"Left nullspace\"?\n42:10 New \"matrix\" space?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk17.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..38db57860b0c6b853544f95620c283faa9a594f0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk17.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 9, + "timestamp": 1684702633715.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "00:00 Error from last lecture, row dependent.\n04:28 4 Fundamental subspaces.\n08:30 Where are those spaces?\n11:45 Dimension of those spaces.\n21:20 Basis for those space.\n30:00 N(A^T) \"Left nullspace\"?\n42:10 New \"matrix\" space?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk18.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..38db57860b0c6b853544f95620c283faa9a594f0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk18.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 9, + "timestamp": 1684702633715.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "00:00 Error from last lecture, row dependent.\n04:28 4 Fundamental subspaces.\n08:30 Where are those spaces?\n11:45 Dimension of those spaces.\n21:20 Basis for those space.\n30:00 N(A^T) \"Left nullspace\"?\n42:10 New \"matrix\" space?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk19.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..38db57860b0c6b853544f95620c283faa9a594f0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk19.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 9, + "timestamp": 1684702633715.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "00:00 Error from last lecture, row dependent.\n04:28 4 Fundamental subspaces.\n08:30 Where are those spaces?\n11:45 Dimension of those spaces.\n21:20 Basis for those space.\n30:00 N(A^T) \"Left nullspace\"?\n42:10 New \"matrix\" space?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk2.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..38db57860b0c6b853544f95620c283faa9a594f0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk2.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 9, + "timestamp": 1684702633715.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "00:00 Error from last lecture, row dependent.\n04:28 4 Fundamental subspaces.\n08:30 Where are those spaces?\n11:45 Dimension of those spaces.\n21:20 Basis for those space.\n30:00 N(A^T) \"Left nullspace\"?\n42:10 New \"matrix\" space?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk20.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..38db57860b0c6b853544f95620c283faa9a594f0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk20.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 9, + "timestamp": 1684702633715.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "00:00 Error from last lecture, row dependent.\n04:28 4 Fundamental subspaces.\n08:30 Where are those spaces?\n11:45 Dimension of those spaces.\n21:20 Basis for those space.\n30:00 N(A^T) \"Left nullspace\"?\n42:10 New \"matrix\" space?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk21.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..38db57860b0c6b853544f95620c283faa9a594f0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk21.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 9, + "timestamp": 1684702633715.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "00:00 Error from last lecture, row dependent.\n04:28 4 Fundamental subspaces.\n08:30 Where are those spaces?\n11:45 Dimension of those spaces.\n21:20 Basis for those space.\n30:00 N(A^T) \"Left nullspace\"?\n42:10 New \"matrix\" space?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk22.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..38db57860b0c6b853544f95620c283faa9a594f0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk22.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 9, + "timestamp": 1684702633715.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "00:00 Error from last lecture, row dependent.\n04:28 4 Fundamental subspaces.\n08:30 Where are those spaces?\n11:45 Dimension of those spaces.\n21:20 Basis for those space.\n30:00 N(A^T) \"Left nullspace\"?\n42:10 New \"matrix\" space?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk3.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..38db57860b0c6b853544f95620c283faa9a594f0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk3.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 9, + "timestamp": 1684702633715.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "00:00 Error from last lecture, row dependent.\n04:28 4 Fundamental subspaces.\n08:30 Where are those spaces?\n11:45 Dimension of those spaces.\n21:20 Basis for those space.\n30:00 N(A^T) \"Left nullspace\"?\n42:10 New \"matrix\" space?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk4.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..38db57860b0c6b853544f95620c283faa9a594f0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk4.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 9, + "timestamp": 1684702633715.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "00:00 Error from last lecture, row dependent.\n04:28 4 Fundamental subspaces.\n08:30 Where are those spaces?\n11:45 Dimension of those spaces.\n21:20 Basis for those space.\n30:00 N(A^T) \"Left nullspace\"?\n42:10 New \"matrix\" space?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk5.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..38db57860b0c6b853544f95620c283faa9a594f0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk5.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 9, + "timestamp": 1684702633715.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "00:00 Error from last lecture, row dependent.\n04:28 4 Fundamental subspaces.\n08:30 Where are those spaces?\n11:45 Dimension of those spaces.\n21:20 Basis for those space.\n30:00 N(A^T) \"Left nullspace\"?\n42:10 New \"matrix\" space?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk6.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..38db57860b0c6b853544f95620c283faa9a594f0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk6.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 9, + "timestamp": 1684702633715.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "00:00 Error from last lecture, row dependent.\n04:28 4 Fundamental subspaces.\n08:30 Where are those spaces?\n11:45 Dimension of those spaces.\n21:20 Basis for those space.\n30:00 N(A^T) \"Left nullspace\"?\n42:10 New \"matrix\" space?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk7.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..38db57860b0c6b853544f95620c283faa9a594f0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk7.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 9, + "timestamp": 1684702633715.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "00:00 Error from last lecture, row dependent.\n04:28 4 Fundamental subspaces.\n08:30 Where are those spaces?\n11:45 Dimension of those spaces.\n21:20 Basis for those space.\n30:00 N(A^T) \"Left nullspace\"?\n42:10 New \"matrix\" space?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk8.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..38db57860b0c6b853544f95620c283faa9a594f0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk8.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 9, + "timestamp": 1684702633715.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "00:00 Error from last lecture, row dependent.\n04:28 4 Fundamental subspaces.\n08:30 Where are those spaces?\n11:45 Dimension of those spaces.\n21:20 Basis for those space.\n30:00 N(A^T) \"Left nullspace\"?\n42:10 New \"matrix\" space?" + } +] \ No newline at end of file diff --git a/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk9.json b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..38db57860b0c6b853544f95620c283faa9a594f0 --- /dev/null +++ b/sight/query/annotated_chunks_window20/nHlE7EgJFds_9_chunk9.json @@ -0,0 +1,12 @@ +[ + { + "file_id": "nHlE7EgJFds", + "query_id": 9, + "timestamp": 1684702633715.0, + "annotatedSourceSentencesIndices": [], + "names": [ + "annotator2" + ], + "text": "00:00 Error from last lecture, row dependent.\n04:28 4 Fundamental subspaces.\n08:30 Where are those spaces?\n11:45 Dimension of those spaces.\n21:20 Basis for those space.\n30:00 N(A^T) \"Left nullspace\"?\n42:10 New \"matrix\" space?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated/0Qws8BuK3RQ.json b/sight/sources/annotated/0Qws8BuK3RQ.json new file mode 100644 index 0000000000000000000000000000000000000000..5aad8c5b93bec55fd9dcbb241d01275e15688360 --- /dev/null +++ b/sight/sources/annotated/0Qws8BuK3RQ.json @@ -0,0 +1,821 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high-quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "OK, just as we're getting started, I thought I'd add a few words about a question that came up after class." + }, + { + "text": "Suppose in that discussion last time, where you were given three, you were given a distance matrix, you were given the distance between x1 and x2, between x2 and x3, and between x1 and x3, and you wanted to find points that satisfied that." + }, + { + "text": "Well, we're going to fail on this example, because if the distance here is 1, the distance here is 1, then by the triangle inequality, the distance from x1 to x3 could not be more than 2." + }, + { + "text": "And when we square it, it could not be more than 4." + }, + { + "text": "And here it's 6." + }, + { + "text": "So what's going to happen?" + }, + { + "text": "What goes wrong in that case?" + }, + { + "text": "Yeah, I hadn't commented on that, and I'm not sure that the paper that I referenced does so." + }, + { + "text": "So I had to do a little search back in the literature, because people couldn't overlook this problem." + }, + { + "text": "So this is the triangle inequality fails." + }, + { + "text": "And it's not going to help to go into 10 dimensions, because the triangle inequalities doesn't change." + }, + { + "text": "And it's still there in 10 dimensions, and we're still failing." + }, + { + "text": "So what happens?" + }, + { + "text": "Well, what could happen?" + }, + { + "text": "Do you remember, and you'll have to remind me, the key equation." + }, + { + "text": "You remember we had an equation connecting the matrix." + }, + { + "text": "So what is the matrix D for this problem?" + }, + { + "text": "So D is a 3 by 3 matrix with these distances squared." + }, + { + "text": "And it was convenient to use distances squared, because that's what comes into the next steps." + }, + { + "text": "So of course, the distance from each x to itself is 0." + }, + { + "text": "The distance from x distance squared was that." + }, + { + "text": "This one was that, but this one is 6." + }, + { + "text": "So that's the distance matrix." + }, + { + "text": "And we would like to find, the job was to find, and I'm just going to write down, we cannot find x1, x2, and x3 to match those distances." + }, + { + "text": "So what goes wrong?" + }, + { + "text": "Well, there's only one thing that could go wrong." + }, + { + "text": "When you connect this distance matrix D to the matrix x transpose x, you remember the position matrix, maybe I called it G. This is giving, so Gij is the dot product of xi with xj." + }, + { + "text": "Oops, let's make that into a j." + }, + { + "text": "Thank you." + }, + { + "text": "So Gij is the matrix of dot products." + }, + { + "text": "And the great thing was that we can discover what that matrix, that matrix G comes directly from D, comes directly from D. And of course, what do we know about this matrix of cross products?" + }, + { + "text": "We know that it is positive semidefinite." + }, + { + "text": "So what goes wrong?" + }, + { + "text": "Well, just in a word, when we write out that equation and discover what G is, if the triangle inequality fails, we learn that G doesn't come out positive definite." + }, + { + "text": "That's really all I want to say." + }, + { + "text": "And I could push through the example." + }, + { + "text": "G will not come out positive definite if D, if that's D, because it can't." + }, + { + "text": "If it came out positive definite, then we could find an x." + }, + { + "text": "So if we had the G, then the final step, you remember, is to find an x." + }, + { + "text": "Well, we know that if G is positive semidefinite, there are multiple ways to find an x." + }, + { + "text": "This is positive semidefinite matrices is what you get out of x transpose x's." + }, + { + "text": "And we can find an x given a G. We can find G given an x." + }, + { + "text": "So it has to be that this won't be true, that the matrix G that comes out of that equation will turn out not to be positive definite." + }, + { + "text": "So it's really quite nice." + }, + { + "text": "It's a beautiful little bit of mathematics that if and only if the triangle inequality is satisfied by these numbers, if and only if, then the matrix in the D matrix, then the G matrix that comes out of this equation, which I haven't written, is positive semidefinite." + }, + { + "text": "If the triangle inequality is OK, we can find the points." + }, + { + "text": "If the triangle inequality is violated, like here, then the matrix G is not positive semidefinite, has negative eigenvalues, and we cannot find the point." + }, + { + "text": "Yeah." + }, + { + "text": "I could recall the G matrix, the G equation, but it's coming to you in the two-page section that does distance matrices." + }, + { + "text": "OK. That's just a, I should have made a point." + }, + { + "text": "It's nice to have specific numbers." + }, + { + "text": "And I could get the specific numbers for G, and we would see no way it's not positive definite." + }, + { + "text": "OK." + }, + { + "text": "So that's just tidying up last time." + }, + { + "text": "I have another small problem to talk about, and then a big question of whether deep learning actually works." + }, + { + "text": "I had an email from an expert last night, which changed my view of the world about that question, as you can imagine." + }, + { + "text": "The change in my world was I had thought the answer was yes, and I now think the answer is no." + }, + { + "text": "So that's like rather a big issue for 18.065." + }, + { + "text": "But we'll see about that later." + }, + { + "text": "OK. Now, Procrustes problem." + }, + { + "text": "So Procrustes, and it's included in the notes, that name comes from a Greek myth." + }, + { + "text": "Are you guys into Greek myths?" + }, + { + "text": "So what was the story of Procrustes?" + }, + { + "text": "He was at Procrustes who adjusted the length of his." + }, + { + "text": "So he had a special bed, Procrustes' bed, certain length." + }, + { + "text": "And then he had visitors coming." + }, + { + "text": "And instead of adjusting the length of the bed to fit the visitor, Procrustes adjusted the length of the visitor to fit the bed." + }, + { + "text": "So either stretched the visitor or chopped off part of the visitor." + }, + { + "text": "So anyway, the Greeks liked this sort of thing." + }, + { + "text": "So anyway, that's a Greek myth for 18.065." + }, + { + "text": "So the whole idea of the Procrustes problem is to make something fit something else." + }, + { + "text": "So the two things are, so suppose I'm just in three dimensions." + }, + { + "text": "I have two vectors here." + }, + { + "text": "So I have a basis for a two-dimensional space." + }, + { + "text": "And over here, I have people, space scientists might have one computation of the positions of satellites." + }, + { + "text": "Then, of course, they wouldn't be off by as much as this figure shows." + }, + { + "text": "But then they have another computation using different coordinates." + }, + { + "text": "So it's partly rotated from this picture." + }, + { + "text": "But also, it's partly got round off errors and error in it between the two." + }, + { + "text": "So the question is, what's the best orthogonal transformation?" + }, + { + "text": "So this is a bunch of vectors, x1, x2, to xn, let's say." + }, + { + "text": "And I want to multiply them by an orthogonal matrix." + }, + { + "text": "No, maybe I'd do it on the other side." + }, + { + "text": "I think I do." + }, + { + "text": "Yeah, q to be as close as possible to this other set, y1, y2, up to yn." + }, + { + "text": "So let me just say it again." + }, + { + "text": "I have two sets of vectors." + }, + { + "text": "And I'm looking, and they're different, like those two sets." + }, + { + "text": "And I'm looking for the orthogonal matrix that, as well as possible, takes this set into this one." + }, + { + "text": "Of course, if this was an orthogonal basis and this was an orthogonal basis, then we would be home free." + }, + { + "text": "Q, we could get equality." + }, + { + "text": "We could take an orthogonal basis directly into an orthogonal basis with a orthogonal matrix Q." + }, + { + "text": "In other words, if x was an orthogonal matrix and y was an orthogonal matrix, we would get the exact correct Q." + }, + { + "text": "But that's not the case." + }, + { + "text": "So we're looking for the best possible." + }, + { + "text": "So that's the problem then." + }, + { + "text": "Minimize over orthogonal matrices Q." + }, + { + "text": "And I just want to get my notation to be consistent here." + }, + { + "text": "OK. OK." + }, + { + "text": "So I see that I'm starting with the y's and mapping them to x's." + }, + { + "text": "So let me ask the question." + }, + { + "text": "What orthogonal matrix Q multiplies the y's to come as close as possible to the x's?" + }, + { + "text": "So over all orthogonal Q's, I want to minimize yq minus x in the Frobenius norm." + }, + { + "text": "And I might as well square it." + }, + { + "text": "So Frobenius, we're into the Frobenius norm." + }, + { + "text": "Remember the matrix." + }, + { + "text": "Matrix, this is a very convenient norm in data science to measure the size of a matrix." + }, + { + "text": "And we have several possible formulas for it." + }, + { + "text": "So let me call the matrix A." + }, + { + "text": "And the Frobenius norm squared." + }, + { + "text": "OK, so what's one expression in terms of the entries of the matrix, the numbers Aij in the matrix?" + }, + { + "text": "The Frobenius norm just treats it like a long vector." + }, + { + "text": "So it's A11 squared plus A12 squared, all the way along the first plus second row." + }, + { + "text": "Just I'll say NN squared." + }, + { + "text": "OK." + }, + { + "text": "Sum of all the squares, just treating it like a long vector." + }, + { + "text": "OK." + }, + { + "text": "But that's an awkward expression to write down." + }, + { + "text": "So what other ways do we have to find the Frobenius norm of a matrix?" + }, + { + "text": "Let's see." + }, + { + "text": "I can look at this as A transpose A." + }, + { + "text": "Is that right?" + }, + { + "text": "A transpose A." + }, + { + "text": "So what's happening there?" + }, + { + "text": "Remind me what." + }, + { + "text": "Yeah." + }, + { + "text": "I would get all that." + }, + { + "text": "I would get all these by taking the matrix A transpose times A." + }, + { + "text": "But what?" + }, + { + "text": "Sorry, I'm not." + }, + { + "text": "I've lost my thread of talk here." + }, + { + "text": "So here's." + }, + { + "text": "Oh, and then I take the trace, of course." + }, + { + "text": "So that first row, first column of A times that one will give me the one set of squares." + }, + { + "text": "And then that one times the other one, the next one, will give me the next set of squares." + }, + { + "text": "So this is going to, if I look at the trace." + }, + { + "text": "So I just want to look at the diagonal here." + }, + { + "text": "So it's the trace." + }, + { + "text": "Remember, the trace of a matrix M is the sum down the diagonal, M11, M22, down to MNN." + }, + { + "text": "It's the diagonal sum." + }, + { + "text": "And everybody with me here?" + }, + { + "text": "So that term on the diagonal of A transpose A gives me all of that." + }, + { + "text": "Or maybe I should be doing AA transpose." + }, + { + "text": "And the point is, it doesn't matter." + }, + { + "text": "Or the trace of AA transpose." + }, + { + "text": "Those would both give the correct Frobenius norm squared." + }, + { + "text": "So traces are going to come into this little problem." + }, + { + "text": "Now, there's another formula for the Frobenius norm, even shorter, well, certainly shorter than this one, involving a sum of squares." + }, + { + "text": "And what's that one?" + }, + { + "text": "What's the other way to get this same answer?" + }, + { + "text": "If I look at the SVD, look at singular values, I think that this is also equal to sigma 1, the sum square of all the singular values." + }, + { + "text": "So it's three nice expressions for the Frobenius norm." + }, + { + "text": "The nice ones involve A transpose A or AA transpose." + }, + { + "text": "And of course, that connects to the singular values." + }, + { + "text": "Because what's the connection between singular values and these guys, A transpose A or AA transpose?" + }, + { + "text": "The singular values are the, or the singular values squared, are the eigenvalues of A transpose A." + }, + { + "text": "And then when I add up the trace, I'm adding up the eigenvalues." + }, + { + "text": "And that gives me the Frobenius norm squared." + }, + { + "text": "So that tells us something important, which we can see in different ways." + }, + { + "text": "So to solve this problem, we're going to need various facts." + }, + { + "text": "Like the QA in the Frobenius norm is the same as A in the Frobenius norm." + }, + { + "text": "Why is that?" + }, + { + "text": "Why?" + }, + { + "text": "So here I'm multiplying every column by the matrix Q." + }, + { + "text": "What happens to the length of the column when I multiply it by Q?" + }, + { + "text": "Doesn't change." + }, + { + "text": "So I could add up the lengths of the columns all squared." + }, + { + "text": "Here I wrote it in terms of rows, but I could have reordered that and got it in terms of columns." + }, + { + "text": "That's because the length of Q times any vector squared is the same as the vector squared." + }, + { + "text": "And take these to be the columns of A." + }, + { + "text": "So for column by column, the multiplication by Q doesn't change the length." + }, + { + "text": "And then when I add up all the columns squared, I get the Frobenius norm squared." + }, + { + "text": "And another way to say it, let's make the connection between this fact that Q didn't change the Frobenius norm and this fact that the Frobenius norm is expressed in terms of the sigmas." + }, + { + "text": "So what does Q do to the sigmas?" + }, + { + "text": "I want to see in another way the answer to why." + }, + { + "text": "So if I have a matrix A with singular values, I multiply by Q, what happens to the singular values?" + }, + { + "text": "Don't change." + }, + { + "text": "Don't change." + }, + { + "text": "That's the key point about singular values." + }, + { + "text": "If I multiply, so A has an SVD U sigma V transpose." + }, + { + "text": "And QA will have the SVD QU sigma V transpose." + }, + { + "text": "So all I've changed when I multiply by Q, all I changed was the first factor, the first orthogonal factor in the SVD." + }, + { + "text": "I didn't change the sigmas." + }, + { + "text": "They're still sitting there." + }, + { + "text": "And of course, I could do also Q on the other side." + }, + { + "text": "Different Q, same Q or a different Q on the other side would show up here." + }, + { + "text": "And would not change the sigmas, and therefore would not change the Frobenius norm." + }, + { + "text": "So these are important properties of this Frobenius norm." + }, + { + "text": "It looks messy to write down in that form, but it's much nicer in these forms and in that form." + }, + { + "text": "So now if I can just, then we saw that it involves traces." + }, + { + "text": "So let me make a few observations about traces." + }, + { + "text": "So I'll just, we want to be able to play with traces, and that's something we really haven't done." + }, + { + "text": "Here's a fact, that the trace of A transpose B is equal to the trace of B transpose A." + }, + { + "text": "Of course, if B is A, it's clear." + }, + { + "text": "And it's equal to the trace of B A transpose." + }, + { + "text": "So you can do little changes in your matrix without changing the trace." + }, + { + "text": "Let's see why one of these is true." + }, + { + "text": "Why is that first statement true?" + }, + { + "text": "Huh." + }, + { + "text": "Huh." + }, + { + "text": "How is that matrix related to this matrix?" + }, + { + "text": "It's just a transpose." + }, + { + "text": "If I take the transpose of that matrix, I get that." + }, + { + "text": "So what happens to the trace?" + }, + { + "text": "I'm adding down the diagonal." + }, + { + "text": "The transpose has no effect." + }, + { + "text": "Clearly, this is just the fact that the trace doesn't change, is not changed when you transpose a matrix, because the diagonal is not changed." + }, + { + "text": "Now, what about this guy?" + }, + { + "text": "I guess we're getting back to old fashioned 18.065, remembering facts about linear algebra, because this is pure linear algebra." + }, + { + "text": "So what's this one about?" + }, + { + "text": "This says that I can reverse the order of two matrices." + }, + { + "text": "I'm now looking at the connection between those two." + }, + { + "text": "And so let me just use different letters." + }, + { + "text": "CD equals the trace of DC." + }, + { + "text": "I can flip the order." + }, + { + "text": "That's all I've done here is I've reversed B with A transpose." + }, + { + "text": "I reversed C with D. OK, so why is that true?" + }, + { + "text": "Why is that true?" + }, + { + "text": "Oh, well, how shall we see the truth of that fact?" + }, + { + "text": "So these are really convenient facts that make a lot of people use the trace more often than we have in 18.065." + }, + { + "text": "I'm not a big user of arguments based on trace, but these are identities that go a long way with many problems." + }, + { + "text": "So let's see why that's true." + }, + { + "text": "Anytime you think about trace, you've got two languages to use." + }, + { + "text": "You can use the eigenvalues." + }, + { + "text": "It's the sum of the eigenvalues." + }, + { + "text": "Or you can use the diagonal entries, because it's the sum of the diagonal entries." + }, + { + "text": "Let's use eigenvalues." + }, + { + "text": "How are the eigenvalues of CD related to the eigenvalues of DC?" + }, + { + "text": "They're the same." + }, + { + "text": "If these matrices are rectangular, then there might be some extra 0 eigenvalues, because they would have different shapes." + }, + { + "text": "But 0's are not going to affect the trace." + }, + { + "text": "So this is the same non-zero eigenvalues." + }, + { + "text": "And so on." + }, + { + "text": "Yeah." + }, + { + "text": "OK. Let me just try to tell you the steps now to get the correct cue." + }, + { + "text": "Or let me tell you the answer first." + }, + { + "text": "And I'm realizing that all-important question four, does deep learning actually work?" + }, + { + "text": "We're going to run out of time today, because we only have a few minutes left." + }, + { + "text": "I suggest we bring that question back up, because it's pretty important to a lot of people." + }, + { + "text": "I had lunch with Professor Edelman, and he said, you know, deep learning and neural nets have had a record amount of publicity and hype for a sort of computational algorithm." + }, + { + "text": "And I've had people now tell me that typical, first, if you create a network using Alex's design, for example, the chances are that it won't be successful." + }, + { + "text": "That the successful networks have been worked on and experimented with, and a good structure has emerged, but wasn't there at the start." + }, + { + "text": "So I think that's a topic for Monday." + }, + { + "text": "And I'm really just realizing from talking to people in the field that it's by no means automatic that the structure, even if you put in a whole bunch of layers, it may not be what you want." + }, + { + "text": "OK, so let me finish this argument today." + }, + { + "text": "Let me give you the answer." + }, + { + "text": "So what's the good Q?" + }, + { + "text": "I have matrices Y and X." + }, + { + "text": "And the idea is that I take its, I look at Y transpose X, so that'll be all the dot products of one set of vectors with the other set of vectors." + }, + { + "text": "That's a matrix." + }, + { + "text": "And I do its SVD, U sigma V transpose." + }, + { + "text": "So multiply this, multiply the two bases that you're given." + }, + { + "text": "Of course, if Y was the same as X, if it was an orthogonal basis, you'd have the identity." + }, + { + "text": "No questions." + }, + { + "text": "But generally, it has an SVD." + }, + { + "text": "And we're looking for a orthogonal matrix." + }, + { + "text": "So the best Q is, da-da-da-da, I mean, it's the right time for expressions of amazement." + }, + { + "text": "It is UV transpose." + }, + { + "text": "OK, so that gives us the answer." + }, + { + "text": "We're given X and Y." + }, + { + "text": "We're looking for the best Q." + }, + { + "text": "And the answer comes in the simplest possible way." + }, + { + "text": "Compute Y transpose X, compute its SVD, and use the orthogonal matrices from the SVD." + }, + { + "text": "Yeah, and I'm out of time." + }, + { + "text": "So proof, it's three line later, either to just send you the section online or to discuss it in class Monday." + }, + { + "text": "But I'm really planning Monday to start with question four." + }, + { + "text": "And meanwhile, to ask a whole lot of people, everybody I can find, about that important question is, does deep learning usually work?" + }, + { + "text": "What can you do to make sure it works or give yourself a better chance to have it work?" + }, + { + "text": "So that's up for Monday then." + }, + { + "text": "Good." + } +] \ No newline at end of file diff --git a/sight/sources/annotated/0h43aV4aH7I.json b/sight/sources/annotated/0h43aV4aH7I.json new file mode 100644 index 0000000000000000000000000000000000000000..4ff64690ad7c10be25c4f3ff3cbc16a004639ddf --- /dev/null +++ b/sight/sources/annotated/0h43aV4aH7I.json @@ -0,0 +1,1232 @@ +[ + { + "text": " Okay." + }, + { + "text": "So coming near the end of the course, this lecture will be a mixture of the linear algebra that comes with a change of basis." + }, + { + "text": "And a change of basis from one basis to another basis is something you really do in applications." + }, + { + "text": "And I would like to talk about those applications." + }, + { + "text": "I got a little bit involved with compression, compressing a signal, compressing an image, and that's exactly change of basis." + }, + { + "text": "And then the main theme in this chapter is the connection between a linear transformation, which doesn't have to have coordinates, and the matrix that tells us that transformation with respect to coordinates." + }, + { + "text": "So the matrix is the coordinate-based description of the linear transformation." + }, + { + "text": "Let me start out with the nice part, which is some, just to tell you something about image compression." + }, + { + "text": "Those of you, well, everybody's going to meet compression, because you know that the amount of data that we're getting, well, these lectures are compressed." + }, + { + "text": "So that actually, probably you see my motion as jerky, shall I use that word?" + }, + { + "text": "Have you looked on the web?" + }, + { + "text": "I should like to find a better word." + }, + { + "text": "Compressed, let's see." + }, + { + "text": "So my, the, the, the complete signal is, of course, in those video cameras and in the videotape, but that goes to the bottom of building nine, and out of that comes a jumpy motion, because it uses a standard system for compressing images." + }, + { + "text": "And, you'll notice that the stuff that sits on the board comes very clearly, but it's my motion that, that, that needs a whole lot of bits, right?" + }, + { + "text": "So, and if I were to run up and back, up there and back, that would need too many bits and they'd, I'd be compressed even more." + }, + { + "text": "So, what does compression mean?" + }, + { + "text": "Can I, let me just think of a still image." + }, + { + "text": "And, and of course, satellites, oh, there's, and, and computations of the climate, computations of combustion, the, computers and sensors of all kinds are just giving us overwhelming amounts of data." + }, + { + "text": "The web is, too." + }, + { + "text": "Now, some compression can be done with no loss." + }, + { + "text": "Lossless compression is possible just using, sort of, the fact that, there's, there are redundancies." + }, + { + "text": "But I'm talking here about lossy compression." + }, + { + "text": "So I'm talking about, here's an image." + }, + { + "text": "And what does an image consist of?" + }, + { + "text": "It consists of a lot of little pixels, right?" + }, + { + "text": "Maybe five hundred and twelve by five hundred and twelve." + }, + { + "text": "Two to the ninth by two to the ninth pixels, and each, so this is pixel number one one, so that's a pixel, and if we're in black and white, the typical pixel would tell us a grayscale from zero to two fifty five." + }, + { + "text": "So a pixel is usually a, a value of a, a, one of the x i, so this would be the i-th pixel, it, it's usually a real number on a scale from zero to two fifty five." + }, + { + "text": "In other words, two to the eighth possibilities." + }, + { + "text": "So usually, that's the, that's the standard, so, so that, that's eight, eight bits." + }, + { + "text": "But then we have that for every, every pixel, so we have five hundred and twelve squared pixels." + }, + { + "text": "We're, we're really operating, x is a vector in Rn, but what is n?" + }, + { + "text": "n is five hundred and twelve squared." + }, + { + "text": "That's, that's our problem right there." + }, + { + "text": "We're, a pixel is a vector that gives us the information about the image, I'm sorry, the image that comes through is a vector of, of that length, that, that's the information we have about the image." + }, + { + "text": "If it's a color image, we would have three times that length, because we'd have, we'd need three coordinates to get color." + }, + { + "text": "So it would be three times five hundred and twelve squared." + }, + { + "text": "It's an enormous amount of information, and we couldn't send out the image for these lectures without compressing it." + }, + { + "text": "We, we, it, it would be, it would overload the system." + }, + { + "text": "So it has to be compressed." + }, + { + "text": "The standard compression, and still used in, in the, with these lectures, is, called JPEG." + }, + { + "text": "I think that stands for a Joint Photographic Experts Group." + }, + { + "text": "They established a system of compression." + }, + { + "text": "And I just want to tell you what it's about." + }, + { + "text": "It's a change of basis." + }, + { + "text": "What, what's, what basis do we have?" + }, + { + "text": "The, the current basis we have is, you could say, the standard basis is every pixel give a value." + }, + { + "text": "So that's like, we have a vector x, which is five hundred and twelve squared long, and in the i-th position, we get a number like one twenty one or something, the next, the pixel next to it might be one twenty four, maybe where, maybe where the, where my tie, begins to end." + }, + { + "text": "So if it was mostly blue shirt, this would be a slight difference in shading, but pretty close." + }, + { + "text": "Then the tie would be a different color." + }, + { + "text": "So, so we might have quite a few pixels for the blue shirt and a whole lot more for the blackboard that are very close." + }, + { + "text": "And that's what, are very correlated." + }, + { + "text": "And that's what gives us the possibility of compression." + }, + { + "text": "For example, before the lecture starts, if we had a blank blackboard, then there's an image, but it would make no sense to take that image and tell you what it is pixel by pixel." + }, + { + "text": "I mean, there's a case in which all pixel values, all gray levels are the same, or practically the same, depending on the erasing of the board, but extremely close." + }, + { + "text": "And so that's an image where the standard basis is lousy." + }, + { + "text": "That's, that's the basic fact." + }, + { + "text": "That, that the standard basis which gives the value of every pixel makes no use of the fact that we're getting a whole lot of pixels whose gray levels, the neighboring pixels tend to have the same gray level as the, as their, as their neighbors." + }, + { + "text": "So to take, how do we take advantage of that fact?" + }, + { + "text": "Well, one basis vector that would be extremely nice to, one vector that would be extremely nice to include in the basis would be a vector of all ones." + }, + { + "text": "That's not in our standard basis." + }, + { + "text": "So our, so let me just write again." + }, + { + "text": "The standard basis would, is, is our, is our one and all the rest zeros, zero, one, and all the rest zeros, everybody knows what the standard basis is." + }, + { + "text": "Now, any other basis for our, so this is, for this very high-dimensional space, now I'm going to speak about a better basis, better basis, and let me just emphasize, one vector that would be extremely nice to have in that basis is the vector of all ones." + }, + { + "text": "Why is that?" + }, + { + "text": "Let me just say again." + }, + { + "text": "Because that vector of all ones, by itself, one vector is, is able to completely give the information on a solid image." + }, + { + "text": "Of course, our image won't be solid, it'll have a mix of, of, solid and, and signal." + }, + { + "text": "So that one vector, but that, having that one vector in the basis is, is, is going to save us a whole lot." + }, + { + "text": "Now the question is, what other vectors should be in the basis?" + }, + { + "text": "The, the extreme vector in the basis might be a vector of one minus one, one minus one, one minus one." + }, + { + "text": "That would be a vector that shows, I mean, that's like a checkerboard vector, right?" + }, + { + "text": "That's a vector that would, if, if we had, if, if the image was like a huge checkerboard of plus minus, plus minus, plus minus, that vector would carry the whole signal." + }, + { + "text": "But much more common would be maybe to have half the image, darker and the other half lighter." + }, + { + "text": "So another image, another vector that might be quite useful in here would be half ones and half minus ones." + }, + { + "text": "I'm just trying to get across the idea of, that a basis could be, that first of all, we've got, the basis is at our disposal." + }, + { + "text": "Like, we're free to choose that." + }, + { + "text": "And it's a billion dollar decision what we choose." + }, + { + "text": "So, and TV people would rather, would prefer one basis based on the way the, the signal is scanned, and movie people would prefer another." + }, + { + "text": "I mean, there's giant politics in this question that really reduces to a, to a linear algebra problem what basis to choose." + }, + { + "text": "I'll just mention the best known basis, which is, which JPEG uses, let me put that here, is the Fourier basis." + }, + { + "text": "So when you, when you use the Fourier basis, that includes, this is the constant vector, the DC vector, if we're electrical engineers, the, the, the vector of all ones, so it would include one, one, one, one." + }, + { + "text": "Often, eight by eight is a good choice." + }, + { + "text": "Eight by eight is a, is a good choice." + }, + { + "text": "So, what do I mean by this eight by eight?" + }, + { + "text": "I mean that the big signal, which is five twelve by five twelve, gets broken down, and JPEG does this, into eight by eight blocks." + }, + { + "text": "And we, sort of, this is too much to deal with at once." + }, + { + "text": "So what JPEG does is take this eight by eight block, which is sixty-four coefficients, sixty-four, pixels, and changes the basis on the, on that piece." + }, + { + "text": "And then, now, let's see, I was going to write down Fourier, so you remember Fourier is, is this vector of all ones, and then, the vector, oh, well, actually, I gave a lecture earlier about the Fourier matrix, these, this matrix whose columns are powers of a, of a, complex number w. I, I won't repeat that, because I'm not, I don't want to go into the details of the Fourier basis." + }, + { + "text": "Just to tell you how compression works." + }, + { + "text": "So what happens in JPEG?" + }, + { + "text": "What happens to the video, to a, to each image of, of, of these lectures?" + }, + { + "text": "The, it gets broken into eight by eight blocks." + }, + { + "text": "OK." + }, + { + "text": "Within each block, we have sixty-four coefficients, sixty-four basis vectors, sixty-four pixels, and we change basis in sixty-four dimensional space, using these Fourier vectors." + }, + { + "text": "Just, no, that was a lossless step." + }, + { + "text": "Let, let me, let me emphasize." + }, + { + "text": "In comes the signal." + }, + { + "text": "x." + }, + { + "text": "We change basis." + }, + { + "text": "This is the basis change." + }, + { + "text": "Change basis." + }, + { + "text": "Choose a better basis." + }, + { + "text": "So it produces, the, coefficients c. So sixty-four pixels come in, sixty-four coefficients come out." + }, + { + "text": "Now comes the compression." + }, + { + "text": "Now come, this was lossless." + }, + { + "text": "It's just, we know that R64 has plenty of basis, and we've chosen one." + }, + { + "text": "Now, in that basis, we write, we write the signal in that basis, and that's what my lecture, that's the math part of my lecture." + }, + { + "text": "Now here's the application part." + }, + { + "text": "The next part is going to be the compression step." + }, + { + "text": "And that's lossy." + }, + { + "text": "We're going to lose information." + }, + { + "text": "And what, what will actually happen at that step?" + }, + { + "text": "Well, one thing we could do is just throw away the small coefficients." + }, + { + "text": "So that would be, that's called thresholding." + }, + { + "text": "We set some threshold." + }, + { + "text": "Every coefficient, every basis vector that's not in there more than the threshold value, and we set some threshold so that our eye can't see the difference, whether we throw away that, or can hardly see the difference, whether we throw away that little bit of that basis vector or keep it." + }, + { + "text": "So this compression step produces a compressed set of coefficients." + }, + { + "text": "Let me, I'll just keep going here." + }, + { + "text": "So, so it keeps going." + }, + { + "text": "This compression step produces some coefficients c hat." + }, + { + "text": "And with lots of, with many zeros." + }, + { + "text": "So that's where the compression came." + }, + { + "text": "Probably there's enough of this vector of all ones, we very seldom throw that away." + }, + { + "text": "Usually its coefficient will be large." + }, + { + "text": "But the coefficient of something like this, that quickly alternating vector, there's probably very little of that in any smooth signal." + }, + { + "text": "I mean, that's high frequent- this is, this is low frequency, zero frequency." + }, + { + "text": "This stuff is the highest frequency we could have, and there's a, if the noise, the, the jitter is producing that sort of output, but a smooth lecture like this one is, has very little of that highest frequency." + }, + { + "text": "Very little noise in this lecture." + }, + { + "text": "OK." + }, + { + "text": "So, so we throw away whatever there is, and we, we're left with just a few coefficients, and then we reconstruct a signal using those coefficients." + }, + { + "text": "We take the, those coefficients times their basis vectors, but this sum doesn't have sixty-four terms anymore." + }, + { + "text": "Probably it has about two or three terms." + }, + { + "text": "So that, if we say it has three terms." + }, + { + "text": "From sixty-four down to three, that's compression of twenty-one to one." + }, + { + "text": "That's the kind of compression you're looking for." + }, + { + "text": "And everybody is looking for that sort of compression." + }, + { + "text": "Let's see, I guess I met the problem with the FBI and fingerprints." + }, + { + "text": "So there's a whole lot of still images." + }, + { + "text": "You know, you, with your thumb, you make these inky marks, which, go somewhere." + }, + { + "text": "You used to go to Washington and get stored in a big file." + }, + { + "text": "So Washington had a file of thirty million murderers, cheaters on quizzes, other stuff, and, and actually, there was no way to retrieve them in time." + }, + { + "text": "Like, so, so suppose you're at the police station, they say, OK, this person may have done this, check with Washington, have they got his or her fingerprints on file." + }, + { + "text": "Well, Washington won't know the answer within a week, if it's got filing cabinets full of fingerprints." + }, + { + "text": "So of course the natural step is digitize them." + }, + { + "text": "So all fingerprints are now digitized, so now it's at least electronic, but still there's too much information in each, each one." + }, + { + "text": "I mean, you can't search through that many, uh, fingerprints if you, if, if the digital image is five twelve squared by five twelve squared, if it's that many pixels." + }, + { + "text": "So you get compressed." + }, + { + "text": "So the FBI had to decide what basis to choose for compression of fingerprints, and then they built a big new facility in West Virginia and that's where fingerprints now are sent." + }, + { + "text": "So if you, I think if you get your fingerprints done now at the police station, if it's an up-to-date police station, it's, it happens digitally and the signal is sent digitally, and then in West Virginia it's compressed and indexed." + }, + { + "text": "And then, if they want to find you, they can do it within minutes, instead of within a week." + }, + { + "text": "OK." + }, + { + "text": "So this compression is, comes up for signals, for images." + }, + { + "text": "For video, which is like these lectures, uh, there's another aspect." + }, + { + "text": "You could treat the video as one still image after another one, and compress each one and then run them and make a video." + }, + { + "text": "But that misses, well, you can see why that's not optimal." + }, + { + "text": "In video, so for in a video thing, you have a sequence of images, so video is really a sequence of images, but what about one image to the next image?" + }, + { + "text": "They're extremely correlated." + }, + { + "text": "I mean, that, I'm getting an image every split second, and although I'm moving slightly, that's what's producing the, jumpy motion on the video." + }, + { + "text": "But I'm not, like, you know, each, each image in the sequence is pretty close to the one before." + }, + { + "text": "So you have to use, like, prediction and correction." + }, + { + "text": "I mean, you, my, the image of me one instant, one time step later, you would assume would be the same, and then plus a small correction." + }, + { + "text": "And you would only code and digitize the correction, and compress the correction." + }, + { + "text": "So the sequence of images that's highly correlated, and the problem in compression is always to use this correlation, this fact that in time or in space, things don't change instantly, they, they're very often smooth changes, and, you can predict one value from the previous value." + }, + { + "text": "OK." + }, + { + "text": "So that's the, those are applications, which are pure linear algebra." + }, + { + "text": "I could, maybe I'll, maybe you'll allow me to tell you the, and the book describes, the new basis that's, the competition for Fourier." + }, + { + "text": "So the competition for Fourier is called wavelets, and I can describe what that basis is like, say, in the eight by eight case." + }, + { + "text": "So that eight by eight wavelet basis is the vector of all ones, eight ones, then the vector of four ones and four minus ones, then the vector of two ones and two minus ones and four zeros, and also the vector of four zeros and two ones and two minus ones." + }, + { + "text": "So now I'm up to four, and I need four more, right, for R8?" + }, + { + "text": "So the next basis vector will be one minus one and six zeros, and then three more like that, with a one minus one there and there and there." + }, + { + "text": "So those are eight vectors in eight-dimensional space." + }, + { + "text": "Those are, those are called wavelets, and you, and it's a very simple wavelet choice." + }, + { + "text": "It's a more sophisticated choice." + }, + { + "text": "This is a little jumpy, to jump between one and minus one." + }, + { + "text": "And actually, you can see now, suppose you compare the wavelet basis with the Fourier basis above." + }, + { + "text": "How could I write this guy, which is in the Fourier basis, it's an eight, it's a vector in R8, how would I write that as a combination of the wavelet basis?" + }, + { + "text": "Do you, have I told you enough about the wavelet basis that you can see?" + }, + { + "text": "How does this very fast guy, what combination of the wavelet basis is that very fast guy?" + }, + { + "text": "It would be this one, it would be the sum of these four, right?" + }, + { + "text": "That very fast guy will be that one minus one, and the next one, and the next one, and the next one." + }, + { + "text": "So this is the sum of those last four wavelets." + }, + { + "text": "This one we've kept, and so on." + }, + { + "text": "So, each, well, every, well, that's what a basis does." + }, + { + "text": "Every vector in R8 is some combination of those, and for the linear algebra, we have, so the linear algebra is this step, find the coefficients." + }, + { + "text": "That's, that's the step we want to take." + }, + { + "text": "If I give you the basis, like this wavelet basis, and I give you the pixel, so here are the pixel values, p1, p2, down to p8." + }, + { + "text": "What's, what's the job?" + }, + { + "text": "What's the linear algebra here?" + }, + { + "text": "So this is, these are the values, this is in the standard basis, right?" + }, + { + "text": "Those are just the values at eight successive points." + }, + { + "text": "I guess I'm dropping down to one dimension instead of eight by eight, I'm just going to take eight pixel values along that first top row." + }, + { + "text": "So I, what do I want to do?" + }, + { + "text": "In the standard basis, here are the pixel values." + }, + { + "text": "I want to write that as a combination of c1 times this guy, plus c2 times this guy, plus c3, these are the coefficients, plus c4 times this one." + }, + { + "text": "Do you see what I'm doing?" + }, + { + "text": "I want to write this vector p as a combination of c1 times the first wavelet, plus c8 times the eighth wavelet." + }, + { + "text": "That's the, that's the transform step." + }, + { + "text": "That's the lossless step, that's the step from p, oh, I'm calling it p here and I called it x there, so let me, at the risk of moving and therefore making this jumpy, suppose the signal I'm now calling p, the set of pixel values and I'm looking for the coefficients." + }, + { + "text": "Okay." + }, + { + "text": "Tell me how to do it." + }, + { + "text": "How do I find the, if I give you eight basis vectors and I give you the input signal and I ask for the coefficients, what do I do?" + }, + { + "text": "What's the, what's the step?" + }, + { + "text": "I want, I'm trying to solve this, I want to know the eight coefficients, so I'm changing from the standard basis, which is just the eight grayscale values, to the wavelet basis, where this same vector is represented by eight numbers." + }, + { + "text": "It's got to take eight numbers to tell you a vector in R8, and those eight numbers are the coefficients of the basis." + }, + { + "text": "Look, we've done this thing before." + }, + { + "text": "What do we, here, there is the equation in vector notation." + }, + { + "text": "We want to see it as a matrix." + }, + { + "text": "This is a combination of columns of the wavelet matrix, right?" + }, + { + "text": "This is p equals c1, c2, down to c8, and these guys are the columns." + }, + { + "text": "I mean, this is the step that we constantly take in this course." + }, + { + "text": "The first basis vector goes in the first column, the second basis vector goes in the second column, and so on." + }, + { + "text": "The eight columns of this wavelet matrix are the eight basis vectors." + }, + { + "text": "This is a wavelet matrix W. So, the step to change basis." + }, + { + "text": "So now I'm finally coming to this change of basis." + }, + { + "text": "So the change of basis, let me stay with this board, but, well, let me just go above it here." + }, + { + "text": "So the standard basis we know, the wavelet basis we have here, and the transform is simply solve the equations p equal Wc." + }, + { + "text": "So the coefficients are W inverse p, right?" + }, + { + "text": "This shows a critical point." + }, + { + "text": "A good basis has a nice, fast inverse." + }, + { + "text": "So good means, good basis means what?" + }, + { + "text": "So this is like the billion dollar competition, and it's not over yet." + }, + { + "text": "People are going to come up with better bases than these." + }, + { + "text": "So a good basis will be, first good thing would be fast." + }, + { + "text": "I have to be able to multiply by W fast and multiply by W, by its inverse fast." + }, + { + "text": "That's, if a basis doesn't allow you to do that fast, then it's going to take so much time that you can't afford it." + }, + { + "text": "So these bases, the Fourier basis, everybody said, OK, I know how to deal quickly with the Fourier basis, because we have something called the fast Fourier transform." + }, + { + "text": "So there's a FFT that came in my earlier lecture and comes in the last chapter of the book." + }, + { + "text": "So change of basis is done, if for the Fourier basis, is done fast by the FFT and there's a fast wavelet transform." + }, + { + "text": "I can change, for this wavelet example, this matrix is easy to invert." + }, + { + "text": "It's just somebody had a smart idea in choosing that wavelet basis and inverting it, it has a nice inverse." + }, + { + "text": "Actually, you can see why it has a nice inverse." + }, + { + "text": "Do you see any property of these eight basis vectors?" + }, + { + "text": "Well, I've only written five of them, but if you see that property for those five, you'll see it for the three remaining." + }, + { + "text": "What, if I give you those eight vectors and ask, what's a nice property?" + }, + { + "text": "Well, you would say, first, they're all ones and minus ones and zeros, so every multiplication is very fast using just, in binary." + }, + { + "text": "But what's the other great property of those vectors?" + }, + { + "text": "Anybody see it?" + }, + { + "text": "So, of course, when I think about a basis, one nice property, I don't have to have it, but I'm happy if it's there, is that they're orthogonal." + }, + { + "text": "If the basis vectors are orthogonal, then I'm in good shape." + }, + { + "text": "And these are, do you see, take the dot product of that with that, you get four plus ones and four minus ones, you get zero." + }, + { + "text": "Take the dot product of that with that, you get two plus ones and two minus ones." + }, + { + "text": "Or the dot product of that with that, two plus ones and two minus ones." + }, + { + "text": "You can easily check that that's an orthogonal basis." + }, + { + "text": "It's not orthonormal." + }, + { + "text": "I could, to fix it up, I should divide by the length to make them unit vectors." + }, + { + "text": "Let's suppose I do that." + }, + { + "text": "So somewhere in here I've got to account for the fact that this has length square root of eight, that has length square root of four, that has length square root of two." + }, + { + "text": "But that's just a constant factor that's easy to --." + }, + { + "text": "So suppose we've done that." + }, + { + "text": "Then tell me what's W inverse." + }, + { + "text": "That's what chapter four, section four point four was about." + }, + { + "text": "If we have orthonormal columns, what- then the inverse is the same as the transpose." + }, + { + "text": "So if we have a fast way to multiply by W, which we do, the inverse is going to look just the same and we'll have a fast way to do W inverse." + }, + { + "text": "So that's, the wavelet basis passes this requirement for fast." + }, + { + "text": "We can use it fast." + }, + { + "text": "But there's a second requirement, is it any good?" + }, + { + "text": "Because the very fastest thing we could do would be not to change basis at all." + }, + { + "text": "Right?" + }, + { + "text": "Fastest thing would be, OK, stay with a standard basis, stay with eight pixel values." + }, + { + "text": "But that was poor from compression point of view, right?" + }, + { + "text": "Those eight pixel values, if I just took those eight numbers, I can't throw some of those away." + }, + { + "text": "If I throw away ninety percent, if I compressed ten to one, and throw away ninety percent of my pixel values, well, my picture's just gone dark." + }, + { + "text": "Whereas the basis that was good, the wavelet basis or the Fourier basis, if I throw away c5, c6, c7 and c8, all I'm throwing away is little blips that are probably there in very small amounts." + }, + { + "text": "So the second property that we need is good compression." + }, + { + "text": "So, so first it, it has to be fast, and secondly, it has to be a few basis factors should come close to the signal." + }, + { + "text": "So, so a few, few is enough." + }, + { + "text": "Can I write it that way?" + }, + { + "text": "A few basis factors are enough to reproduce the image, just exactly as on the video of these 18.06 lectures." + }, + { + "text": "I don't know what the compression rate is." + }, + { + "text": "I'll ask, David, who, who does the compression, and, by the way, I'll try to get the lectures, that are relevant for the quiz, up onto the web, in time." + }, + { + "text": "So I'll send him a message today." + }, + { + "text": "So, at the point, so he's using the Fourier basis, because the JPEG, so JPEG 2000, which will be the next standard for image compression, will include wavelets." + }, + { + "text": "So, I mean, you're, you're actually getting a kind of up to date, picture of where this big world of signal and image processing is." + }, + { + "text": "That Fourier is what everybody knew, and what people automatically used, and the new, new one is wavelets, where this is the simplest set of wavelets, and this isn't the one that the FBI uses, by the way." + }, + { + "text": "The FBI uses a more, a more, a smoother wavelet." + }, + { + "text": "Instead of jumping from one to minus one, it's a smooth, cutoff." + }, + { + "text": "And, that's what we'll be in, in JPEG 2000." + }, + { + "text": "OK, so that's that application." + }, + { + "text": "Now let me come to my, the, the math, the linear algebra part of the lecture." + }, + { + "text": "Well, we've actually seen a change of basis." + }, + { + "text": "So let, let me just review that change of basis idea, and then the, and then the transformation to a matrix." + }, + { + "text": "OK, so, so this, I hope you see that these applications are really big." + }, + { + "text": "Now I have to talk a little about change of basis and little about that, the, the matrix." + }, + { + "text": "OK. OK. OK." + }, + { + "text": "So change of basis." + }, + { + "text": "Basically, forgive that pun, OK, I have, I have, I have my vector in one basis, and I want to change to a different one." + }, + { + "text": "Actually, you saw it for the wavelet case." + }, + { + "text": "So I need the, the, let the matrix W, the columns of W, be the new basis vectors." + }, + { + "text": "Then the change of basis involves, just as it did there, W inverse." + }, + { + "text": "So we have the vector, vector, say, x in the old basis, and we, that converts to a vector, let's say, c in the new basis, and the relation is exactly what we had there, that x is Wc." + }, + { + "text": "That's the, that's the, that's the, that's the step we have to take." + }, + { + "text": "There's a matrix W that gives us a change of basis." + }, + { + "text": "OK." + }, + { + "text": "I, I, what I want to do is think about mat- transformations and matrices." + }, + { + "text": "So here's, here's the question, that, that, to complete this lecture." + }, + { + "text": "Suppose I have a linear transformation T. So it's, it's a, it's a, we, we would think of it as an A, as a n by n matrix." + }, + { + "text": "And it's computed with respect to a certain basis." + }, + { + "text": "So T, so, no, I'm sorry." + }, + { + "text": "I've got the transformation T, period." + }, + { + "text": "That's taking eight-dimensional space to eight-dimensional space." + }, + { + "text": "Now let's get matrices in there." + }, + { + "text": "OK." + }, + { + "text": "So, so with respect to, with respect to a fir- a first basis, say, V1 up to V8, it has a matrix A. I'm just setting up letters here." + }, + { + "text": "With respect to a second basis, say, I'll make it U1 up to- or W1, since I've used Ws, W1 up to W8, it has a matrix B." + }, + { + "text": "And my question is, what's the connection between A and B?" + }, + { + "text": "How is the matrix- the transformation T is settled." + }, + { + "text": "We could say it's a rotation, for example." + }, + { + "text": "So that would be one transformation of eight-dimensional space, just spin it a little." + }, + { + "text": "Or project it." + }, + { + "text": "Or, or, whatever, whatever linear transformation we've got." + }, + { + "text": "Now we have to remember, so I- so first- my first step is to remind you how you create that matrix A." + }, + { + "text": "Then my second step is, we would use the same method to create B, but because it came from the same transformation, there's got to be a relation between A and B." + }, + { + "text": "What's the- what's the relation between A and B?" + }, + { + "text": "And let me jump to the answer on that one." + }, + { + "text": "That if I have- if I have the same transformation, and I'm compute- its matrix in one basis and then I compute it in another basis, those two matrices are similar." + }, + { + "text": "So these two matrices are similar." + }, + { + "text": "Now, do you remember what similar matrices meant?" + }, + { + "text": "Similar." + }, + { + "text": "A is similar- the two matrices are similar." + }, + { + "text": "Similar." + }, + { + "text": "And what do I mean by that?" + }, + { + "text": "I mean that I take the matrix B and I can compute it from the matrix A using some similarity, some matrix M on one side and M inverse on the other." + }, + { + "text": "And this M will be the change of basis matrix." + }, + { + "text": "This part of the lecture is admittedly compressed." + }, + { + "text": "What I wanted you to- it's really the conclusion that I want you to spot." + }, + { + "text": "Now I have to go back and say, what does it mean for A to be the matrix of this transformation T?" + }, + { + "text": "So I have to remind you what that meant." + }, + { + "text": "That was in the last lecture." + }, + { + "text": "Then this is the conclusion, that if I change to a different basis, we now know- see, if I change to a different basis, two things happen." + }, + { + "text": "Every vector has new coordinates." + }, + { + "text": "There, the rule is this one, between the old coordinates and the new ones." + }, + { + "text": "Every matrix changes." + }, + { + "text": "Every transformation has a new matrix." + }, + { + "text": "And the new matrix is related this way." + }, + { + "text": "The M could be the same as the W. The M there could be the W here." + }, + { + "text": "OK." + }, + { + "text": "So can I, in the remaining minutes, recapture my lecture, the end of my lecture that was just before Thanksgiving, about the matrix?" + }, + { + "text": "OK. What's the matrix?" + }, + { + "text": "And I'll just take one basis." + }, + { + "text": "So now I'm going to- this part is going to go onto this board here." + }, + { + "text": "What is the matrix?" + }, + { + "text": "What is A?" + }, + { + "text": "OK." + }, + { + "text": "Using a basis v1 up to v8." + }, + { + "text": "OK. What's the point?" + }, + { + "text": "The point is, if I know what the transformation does to those eight basis vectors, I know it completely." + }, + { + "text": "I know T, I know everything about T, I know T completely from knowing what T does to v1, what T does to v2, what T does to v8." + }, + { + "text": "Why is that?" + }, + { + "text": "It's because T is a linear transformation." + }, + { + "text": "So that if I know what these outputs are, so these are the inputs, v1 up to v8, these are the outputs from the transformation, like every one rotated, every one projected, whatever transformation I've done, then why is it that I know everything?" + }, + { + "text": "How does linearity work?" + }, + { + "text": "Why?" + }, + { + "text": "This is because every x is some combination of these basis vectors, right?" + }, + { + "text": "c1 v1, c2 v2, c8 v8." + }, + { + "text": "That's the whole point of a basis, that every vector is a combination of the basis vectors in exactly one way." + }, + { + "text": "And then, what is T of x?" + }, + { + "text": "The point is, I claim that we know T of x completely for every x, because every x is a combination of those, and now we use the linear transformation part to say that the output from x has to be c1 times the output from v1 plus c2 times the output from v2 and so on, up through c8 times the output from v8." + }, + { + "text": "So this is like just saying, OK, we know everything when we know what T does to each basis vector." + }, + { + "text": "OK." + }, + { + "text": "So those are the eight things we need." + }, + { + "text": "Now, but we need these answers in this basis." + }, + { + "text": "So T- so this first output is some combination of the eight basis vectors." + }, + { + "text": "So write T times the first- acting on the first input, in other words, write the first output as a combination of the basis vectors." + }, + { + "text": "Say a11 v1 plus a21 v2 and so on, a81 v8." + }, + { + "text": "Write T of v2 as some combination, a12 of v1, a22 of v2 and so on." + }, + { + "text": "I'm creating the matrix A, column by column." + }, + { + "text": "Those numbers go in the first column, these numbers go in the second column." + }, + { + "text": "The matrix A that this is our matrix that represents T in this basis is these numbers." + }, + { + "text": "a11 down to a18, a21 down to a28 and so on." + }, + { + "text": "OK. That's the recipe." + }, + { + "text": "In other words, if I give you a transformation and a basis, that's what I have to give you." + }, + { + "text": "The inputs are the basis and to tell you what the transformation is." + }, + { + "text": "And then you tell me, you compute T for each basis, expand that result in the basis, and that gives you the sixty-four numbers that go into the matrix A." + }, + { + "text": "Let me suppose, let's close with the best example of all." + }, + { + "text": "Suppose v1 to v8, this basis, is the eigenvectors." + }, + { + "text": "Suppose we have an eigenvector basis." + }, + { + "text": "So that T of vi is just, is in the same direction as vi." + }, + { + "text": "Now my question is, what is A?" + }, + { + "text": "Can you carry through the steps?" + }, + { + "text": "Let's, let's do them together, because we can do it in one minute." + }, + { + "text": "So we've chosen this perfect basis." + }, + { + "text": "And actually, with signal image processing, they might look for the eigenvectors, but that would take more calculation time than just saying, OK, we'll use the wavelet basis, or OK, we'll use the Fourier basis." + }, + { + "text": "But the very best basis is the eigenvector basis." + }, + { + "text": "OK, what's the matrix?" + }, + { + "text": "So, what's the first column of the matrix?" + }, + { + "text": "How do I get the first column?" + }, + { + "text": "I take the first basis vector v1." + }, + { + "text": "I op- I look to see what does the transformation do to it." + }, + { + "text": "The output is lambda one v1." + }, + { + "text": "I express that output as a combination, so the first input is v1." + }, + { + "text": "Its output is lambda one v1." + }, + { + "text": "Now write lambda one v1 as a combination of the basis vectors." + }, + { + "text": "Well, it's already done." + }, + { + "text": "It's just lambda one times the first basis vector and zero times the others." + }, + { + "text": "So this first column will have lambda one and zeros." + }, + { + "text": "OK?" + }, + { + "text": "Second input is v2." + }, + { + "text": "Output is lambda two v2." + }, + { + "text": "OK, write that output as a combination of the v's." + }, + { + "text": "It's already done." + }, + { + "text": "It's just lambda two times the second v. So we need, in the second column, we have lambda two times the second v. Well, you see what's coming." + }, + { + "text": "That in that basis, in the eigenvector basis, the matrix is diagonal." + }, + { + "text": "So that's the perfect basis." + }, + { + "text": "That's the basis we'd love to have for image processing, but to find the eigenvectors of our pixel matrix would be too expensive." + }, + { + "text": "So we do something cheaper and close, which is to choose a good basis like, like wavelengths." + }, + { + "text": "OK, thanks." + }, + { + "text": "So quiz review on Wednesday, all day." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated/13r9QY6cmjc.json b/sight/sources/annotated/13r9QY6cmjc.json new file mode 100644 index 0000000000000000000000000000000000000000..bb3838b0bf328a26528e89e99177894e7937448d --- /dev/null +++ b/sight/sources/annotated/13r9QY6cmjc.json @@ -0,0 +1,1460 @@ +[ + { + "text": " OK, shall we start?" + }, + { + "text": "This is the second lecture on eigenvalues." + }, + { + "text": "So the first lecture was set -- reached the key equation, Ax equal lambda x. x is the eigenvector and lambda is the eigenvalue." + }, + { + "text": "Now, to use that." + }, + { + "text": "And the good way to, after we've found, so job one is to find the eigenvalues and find the eigenvectors." + }, + { + "text": "Now after we found them, what do we do with them?" + }, + { + "text": "Well, the good way to see that is diagonalize the matrix." + }, + { + "text": "So the matrix is A, and I want to show, first of all, this is like the basic fact." + }, + { + "text": "This, this formula." + }, + { + "text": "That's, that's the key to today's lecture." + }, + { + "text": "This matrix A, I put its eigenvectors in the columns of a matrix S. So S will be the eigenvector matrix, and I want to look at this magic combination S inverse A S. So can I show you how that, how that, what happens there?" + }, + { + "text": "And notice, notice, there's an S inverse." + }, + { + "text": "We have to be able to invert this eigenvector matrix S. So for that we need n independent eigenvectors." + }, + { + "text": "So that's the, that's the case." + }, + { + "text": "OK." + }, + { + "text": "So suppose we have n linearly independent eigenvectors of A." + }, + { + "text": "Put them in the columns of this matrix S. So I'm naturally going to call that the eigenvector matrix, because it's got the eigenvectors in its columns." + }, + { + "text": "And all I want to do is show you what happens when you multiply A times S. So A times S. So this is A times the matrix with the first eigenvector in its first column, the second eigenvector in its second column, the nth eigenvector in its nth column." + }, + { + "text": "And how am I going to do this matrix multiplication?" + }, + { + "text": "Well, certainly I'll do it a column at a time." + }, + { + "text": "And what do I get?" + }, + { + "text": "A times the first column gives me the first column of the answer, but what is it?" + }, + { + "text": "That's an eigenvector." + }, + { + "text": "A times x1 is equal to the lambda times the x1." + }, + { + "text": "And that lambda's we'll call lambda one, of course." + }, + { + "text": "So that's the first column, A x1 is the same as lambda one x1." + }, + { + "text": "A x2 is lambda two x2, so on, along to, in the nth column, we now have lambda n xn." + }, + { + "text": "Looking good, but the next step is even better." + }, + { + "text": "So for the next step, I want to separate out those eigenvalues, those multiplying numbers, from the x's." + }, + { + "text": "So then I'll have just what I want." + }, + { + "text": "OK, so how, how am I going to separate out?" + }, + { + "text": "So that, that number lambda one is multiplying the first column." + }, + { + "text": "So if I want to factor it out of the first column, I better put, here is going to be x1, and that's going to multiply this matrix lambda one in the first entry in all zeros." + }, + { + "text": "You see that that, that's going to come out right for the first column?" + }, + { + "text": "Because we remember how, how we're going back to that original punchline, that if I want a number to multiply x1, then I can do it by putting x1 in that column, in the first column, and putting that number there." + }, + { + "text": "What am I going to have here?" + }, + { + "text": "I'm going to have lambda one, I'm going to have x1, x2, xn." + }, + { + "text": "These are going to be my columns again." + }, + { + "text": "I'm getting s back again." + }, + { + "text": "I'm getting s back again, but now what's it multiplied by?" + }, + { + "text": "On the right, it's multiplied by, if I want, if I want lambda n xn in the last column, how do I do it?" + }, + { + "text": "Well, the last column here will be, I'll, I'll take the last column, use these coefficients, put the lambda n down there, and it will multiply that nth column and give me lambda n xn." + }, + { + "text": "There, there you see matrix multiplication just working for us." + }, + { + "text": "So I started with A s. I wrote down what it meant." + }, + { + "text": "A times each eigenvector." + }, + { + "text": "That gave me lambda times the eigenvector." + }, + { + "text": "And then when I peeled off the lambdas, they were on the right-hand side, so I've got s, my matrix back again, and this matrix, this diagonal matrix, the eigenvalue matrix, and I call it capital lambda, using capital letters for matrices, and lambda to prompt me that it's, that it's eigenvalues that are in there." + }, + { + "text": "So you see that the eigenvalues are just sitting down that diagonal?" + }, + { + "text": "If I had a column x2 here, I would want the lambda two in the two two position, in the diagonal position, to multiply that x2 and give me the lambda two x2." + }, + { + "text": "That's my formula." + }, + { + "text": "A s is s lambda." + }, + { + "text": "OK. That's, that's the, you see, it's just a calculation." + }, + { + "text": "Now, I, I mentioned, and I have to mention again, this business about n independent eigenvectors." + }, + { + "text": "As it stands, this is all fine whether, I mean, I could be repeating the same eigenvector, but I, I'm no interested in that." + }, + { + "text": "I want to be able to invert s, and that's where this comes in." + }, + { + "text": "This n independent eigenvectors business comes in to tell me that that matrix is invertible." + }, + { + "text": "So let me, on the next board, write down what I've got." + }, + { + "text": "A s equals s lambda." + }, + { + "text": "And now I'm, I can multiply on the left by s inverse." + }, + { + "text": "So this is really, I can do that provided s is invertible, provided my assumption of n independent eigenvectors is satisfied." + }, + { + "text": "And I mentioned at the end of last time, and I'll say again, that there's a small number of matrices for, that don't have n independent eigenvectors." + }, + { + "text": "So I've got to discuss that, that technical point." + }, + { + "text": "But the great, the most matrices that we see have n, n independent eigenvectors and we can diagonalize." + }, + { + "text": "This is diagonalization." + }, + { + "text": "I could also write it, and I often will, the other way round." + }, + { + "text": "If I multiply on the right by s inverse, if I took this equation at the top and multiplied on the right by s inverse, I could, I would have A left here." + }, + { + "text": "Now s inverse is coming from the right." + }, + { + "text": "So can you keep those two straight?" + }, + { + "text": "A multiplies its eigenvectors." + }, + { + "text": "That's how I keep them straight." + }, + { + "text": "So A multiplies s. A multiplies s. And then this s inverse makes the whole thing diagonal." + }, + { + "text": "And this is another way of saying the same thing, putting the s's on the other side of the equation, A is s lambda s inverse." + }, + { + "text": "So that's the, that's the new factorization." + }, + { + "text": "That's the replacement for L U from elimination or Q R from Gram-Schmidt." + }, + { + "text": "And notice that the matrix, so it's, it's a matrix times a diagonal matrix times the inverse of the first one." + }, + { + "text": "It's, that's the combination that we'll see throughout this chapter." + }, + { + "text": "This, this, combination with an s and an s inverse." + }, + { + "text": "OK. Can I just begin to use that?" + }, + { + "text": "For example, what about A squared?" + }, + { + "text": "What are the eigenvalues and eigenvectors of A squared?" + }, + { + "text": "That's a straightforward question with a, with a absolutely clean answer." + }, + { + "text": "So let me, let me consider A squared." + }, + { + "text": "So I look, I start with Ax equal lambda x." + }, + { + "text": "And I'm headed for A squared." + }, + { + "text": "So let me multiply both sides by A." + }, + { + "text": "That's one way to get A squared on the left." + }, + { + "text": "So if, I should write these ifs in here." + }, + { + "text": "If Ax equals lambda x, then I multiply by A." + }, + { + "text": "So I get A squared x equals, well, I'm multiplying by A, so that's lambda Ax." + }, + { + "text": "That lambda was a number, so I just put it on the left." + }, + { + "text": "And what do I, tell me how to make that look better." + }, + { + "text": "What have I got here?" + }, + { + "text": "For, if, if A has the eigenvalue lambda and eigenvector x, what's up with A squared?" + }, + { + "text": "A squared x, I just multiply by A, but now for Ax, I'm going to substitute lambda x, so I've got lambda squared x." + }, + { + "text": "So from that simple calculation, I, my conclusion is that the eigenvalues of A squared are lambda squared." + }, + { + "text": "And the eigenvectors, I always think about both of those." + }, + { + "text": "What can I say about the eigenvalues?" + }, + { + "text": "They're squared." + }, + { + "text": "What can I say about the eigenvectors?" + }, + { + "text": "They're the same." + }, + { + "text": "The same x as in, as for A." + }, + { + "text": "Now, let me see that also from this formula." + }, + { + "text": "How can I see what A squared is looking like from this formula?" + }, + { + "text": "So let me, that, that was one way to do it." + }, + { + "text": "Let me do it by just taking A squared from that." + }, + { + "text": "A squared is S lambda S inverse, that's A, times S lambda S inverse, that's A, which is?" + }, + { + "text": "This is the beauty of eigenvalues, eigenvectors, having that S inverse and S is the identity, so I've got S lambda squared S inverse." + }, + { + "text": "Yes." + }, + { + "text": "You see what that's telling me?" + }, + { + "text": "It's, it's telling me the same thing that I just learned here, but in the, in, in a matrix form." + }, + { + "text": "It's telling me that the S is the same, the eigenvectors are the same, but the eigenvalues are squared, because this is, what's lambda squared, that's still diagonal, it's got little lambda one squared, lambda two squared, down to lambda n squared, on that diagonal, those are the eigenvalues, as we just learned, of A squared." + }, + { + "text": "OK." + }, + { + "text": "So, somehow those eigenvalues and eigenvectors are really giving you a way to, to, to, to see what's going on inside a matrix." + }, + { + "text": "Now, of course, I can continue that for, to the k-th power." + }, + { + "text": "A to the k-th power." + }, + { + "text": "If I multiply, if I have k of these together, do you see how S inverse S will keep cancelling?" + }, + { + "text": "In the, in the inside, I'll have the S outside, at the far left, and lambda will be in there k times and S inverse." + }, + { + "text": "So what's that telling me?" + }, + { + "text": "That's telling me that the eigenvalues of A, of A to the k-th power are the k-th powers." + }, + { + "text": "The eigenvalues of A cubed are the cubes of the eigenvalues of A, and the eigenvectors are the same." + }, + { + "text": "The same." + }, + { + "text": "OK." + }, + { + "text": "In other words, eigenvalues and eigenvectors give a great way to understand the powers of a matrix." + }, + { + "text": "If I take the square of a matrix or the hundredth power of a matrix, the pivots are all over the place." + }, + { + "text": "L U, if I multiply L U times L U times L U times L U a hundred times, I've got a hundred L U's." + }, + { + "text": "I can't do anything with them." + }, + { + "text": "But when I multiply S lambda S inverse by itself, when I look at the eigenvector picture a hundred times, I get a hundred or ninety-nine of these guys cancelling out inside, and I get A to the hundredth is S lambda to the hundredth S inverse." + }, + { + "text": "I mean, eigenvalues tell you about powers of a matrix in a way that we had no, no way to approach previously." + }, + { + "text": "For example, when does, when do the powers of a matrix go to zero?" + }, + { + "text": "I would call that matrix stable, maybe." + }, + { + "text": "So, so, so I could write down a, a theorem." + }, + { + "text": "I'll, I'll write it as a theorem, just to use that word to emphasize that here I'm getting this great fact from this eigenvalue picture." + }, + { + "text": "OK. A to the k approaches zero as k goes, as k gets bigger." + }, + { + "text": "If what?" + }, + { + "text": "What's the, how can I tell for a matrix A if its powers go to zero?" + }, + { + "text": "What, what's somewhere inside that matrix is that information." + }, + { + "text": "That information is not present in the pivots." + }, + { + "text": "It's present in the eigenvalues." + }, + { + "text": "What do I need for the, to know that if I take higher and higher powers of A that this matrix gets smaller and smaller?" + }, + { + "text": "Well, S and S inverse are not moving." + }, + { + "text": "So it's this guy that has to get small, and that's easy to, easy to understand." + }, + { + "text": "The requirement is all eigenvalues, so what is the requirement?" + }, + { + "text": "The eigenvalues have to be less than one." + }, + { + "text": "Now, I have to write that absolute value, because those eigenvalues could be negative, they could be complex numbers." + }, + { + "text": "So I'm taking the absolute value if all of those are below one." + }, + { + "text": "That's, in fact, we practically see why." + }, + { + "text": "Let me just say that I, that I, I'm operating on one assumption here, and I got to keep remembering that that assumption is still present." + }, + { + "text": "That assumption was that I had a full set of, of n independent eigenvectors." + }, + { + "text": "If I don't have that, then I, I, then this approach is not working." + }, + { + "text": "So, so again, a pure eigenvalue approach, eigenvector approach, needs n independent eigenvectors." + }, + { + "text": "If we don't have n independent eigenvectors, we can't diagonalize the matrix." + }, + { + "text": "We can't get to a diagonal matrix." + }, + { + "text": "This, this, this diagonalization is only possible if S inverse makes sense." + }, + { + "text": "OK. Can I, can I follow up on that point now?" + }, + { + "text": "So, so you see why, what we get and, and why we want it, because we get information about the powers of a matrix just immediately from the eigenvalues." + }, + { + "text": "OK, now let me follow up on this, business of which matrices are diagonalizable." + }, + { + "text": "Sorry about that long word." + }, + { + "text": "So a matrix is, is sure to, so here's, here's the main point." + }, + { + "text": "A is sure to be, to have n independent eigenvectors and, and B, now here comes that word, diagonalizable, if, if, so we, we, we might as well get the, the nice case out in the open." + }, + { + "text": "The nice case is when, if all the lambdas are different." + }, + { + "text": "That means, that means no repeated eigenvalues." + }, + { + "text": "OK. That's the nice case." + }, + { + "text": "If, if my matrix and most matrix, if I do a random matrix in MATLAB and compute its eigenvalues, so if I computed, if I took I of rand of ten ten, gave, gave that MATLAB command, the, we'd get a random ten by ten matrix, we would get a list of its ten eigenvalues and they would be different." + }, + { + "text": "They would be distinct, is the best word." + }, + { + "text": "I would have a random matrix will have ten distinct, a ten by ten matrix will have ten distinct eigenvalues, and if it does, the eigenvectors are automatically independent." + }, + { + "text": "So that's a nice fact." + }, + { + "text": "I can, I'll refer you to the text for the proof." + }, + { + "text": "That, that A is sure to have n independent eigenvectors if the eigenvalues are different." + }, + { + "text": "If, if all the, if all eigenvalues are different." + }, + { + "text": "It's just, if some lambdas are repeated, then I have to look more closely." + }, + { + "text": "If an eigenvalue is repeated, I have to look, I have to count, I have to check." + }, + { + "text": "Has it got, say it's repeated three times." + }, + { + "text": "So what's a possibility for, so, so here's, here's the repeated possibility." + }, + { + "text": "And, and let me emphasize the conclusion." + }, + { + "text": "That if I have repeated eigenvalues, I may or may not, I may or may not have, have n independent eigenvectors." + }, + { + "text": "I might." + }, + { + "text": "I, I, you know, this isn't a completely negative case." + }, + { + "text": "The identity matrix." + }, + { + "text": "Well, suppose I take the ten by ten identity matrix." + }, + { + "text": "What are the eigenvalues of that matrix?" + }, + { + "text": "So just, just take the easiest matrix, the identity." + }, + { + "text": "If I look for its eigenvalues, they're all ones." + }, + { + "text": "So that eigenvalue one is repeated ten times." + }, + { + "text": "But there's no shortage of eigenvectors for the identity matrix." + }, + { + "text": "In fact, every vector is an eigenvector." + }, + { + "text": "So I can take ten independent vectors." + }, + { + "text": "Oh, well, what happens to everything if, if, if A is the identity matrix, let's just think that one through in our head." + }, + { + "text": "If A is the identity matrix, then it's got plenty of eigenvectors." + }, + { + "text": "I choose ten independent vectors, they're the columns of S, and, and what do I get from S inverse A S?" + }, + { + "text": "I get I again, right?" + }, + { + "text": "If A is the identity, and of course, that's the correct lambda." + }, + { + "text": "The, the matrix was already diagonal." + }, + { + "text": "So if the matrix is already diagonal, then the, the lambda is the same as the matrix." + }, + { + "text": "A diagonal matrix has got its eigenvalues sitting right there in front of you." + }, + { + "text": "Now if it's triangular, the eigenvalues are still sitting there, but so let's, let's take a case where, it's triangular." + }, + { + "text": "Suppose A is like, two, one, two, zero." + }, + { + "text": "So there's a case that's going to be trouble." + }, + { + "text": "There's a case that's going to be trouble." + }, + { + "text": "First of all, what are the eigen- I mean, we just, like now you, if we start with a matrix, the first thing we do practically without thinking is compute the eigenvalues and eigenvectors." + }, + { + "text": "OK." + }, + { + "text": "So what are the eigenvalues?" + }, + { + "text": "You can tell me right away what they are." + }, + { + "text": "They're two and two, right." + }, + { + "text": "It's a triangular matrix, so when I do this determinant, shall I do this determinant of A minus lambda I?" + }, + { + "text": "I'll get this two minus lambda, one, zero, two minus lambda, right?" + }, + { + "text": "I take that determinant, so I make those into vertical bars to mean determinant, and what's the determinant?" + }, + { + "text": "Two minus lambda squared." + }, + { + "text": "What are the roots?" + }, + { + "text": "Lambda equal two twice." + }, + { + "text": "So the eigenvalues are lambda equals two and two." + }, + { + "text": "OK, fine." + }, + { + "text": "Now the next step, find the eigenvectors." + }, + { + "text": "So I look for eigenvectors and what do I find for this guy?" + }, + { + "text": "Eigenvectors for this guy, when I subtract two minus the identity, so A minus two I has zeros here, and I'm looking for the null space." + }, + { + "text": "What's, what are the eigenvectors?" + }, + { + "text": "They're the, they're, they're the null space of A minus lambda I." + }, + { + "text": "The null space is only one dimension." + }, + { + "text": "This is a case where I don't have enough eigenvectors." + }, + { + "text": "My algebraic multiplicity is two." + }, + { + "text": "I, I would say when I see, when I count how often the eigenvalue is repeated, that's the algebraic multiplicity." + }, + { + "text": "That's the multiplicity." + }, + { + "text": "How many times is it the root of the polynomial?" + }, + { + "text": "My polynomial is two minus lambda squared." + }, + { + "text": "It's a double root." + }, + { + "text": "So my algebraic multiplicity is two." + }, + { + "text": "But the geometric multiplicity, which looks for vectors, looks for eigenvectors and which means the null space of this thing." + }, + { + "text": "And the only eigenvector is one zero." + }, + { + "text": "That's in the null space." + }, + { + "text": "Zero one is not in the null space." + }, + { + "text": "The null space is only one dimensional." + }, + { + "text": "So there's a matrix, my, this A or the original A, that are not diagonalizable." + }, + { + "text": "I can't, I can't find two independent eigenvectors, there's only one." + }, + { + "text": "OK." + }, + { + "text": "So that's the case that I'm, that's a case that I, I'm not really handling." + }, + { + "text": "For example, when I wrote down up here that the powers went to zero if the eigenvalues were below one, I didn't really handle that case of repeated eigenvalues because my reasoning was based on this formula." + }, + { + "text": "And this formula is based on n independent eigenvectors." + }, + { + "text": "OK." + }, + { + "text": "So just to say that." + }, + { + "text": "There are some matrices that we don't cover through diagonalization, but the great majority we do." + }, + { + "text": "OK. And we're always OK if we have different distinct eigenvalues." + }, + { + "text": "OK. That's the, like, the typical case." + }, + { + "text": "Because for each eigenvalue there's at least one eigenvector, the algebraic multiplicity here is one for every eigenvalue, and the geometric multiplicity is one." + }, + { + "text": "There's one eigenvector and they are independent." + }, + { + "text": "OK. OK. Now let me come back to the important case when we're OK." + }, + { + "text": "The important case when we are diagonalizing." + }, + { + "text": "Let me look at, so let me solve this equation." + }, + { + "text": "The equation will be each, I start with some, start with a given vector u0." + }, + { + "text": "And then my equation is that every step I multiply what I have by a." + }, + { + "text": "That equation ought to be simple to handle." + }, + { + "text": "OK. And I'd like to be able to solve it." + }, + { + "text": "How would I find, if I start with a vector u0, and I multiply by a a hundred times, what have I got?" + }, + { + "text": "Well, I can certainly write down a formula for the answer." + }, + { + "text": "So what, what, so u1 is a u0." + }, + { + "text": "And u2 is, what's u2 then?" + }, + { + "text": "U2 I multiply it, u2 I get from u1 by another, multiplying by a, so I've got a twice." + }, + { + "text": "And my formula is uk, after k steps, I've multiplied by a k times the original u0." + }, + { + "text": "You see what I'm doing?" + }, + { + "text": "The next section is going to solve systems of differential equations." + }, + { + "text": "I'm going to have derivatives." + }, + { + "text": "This, this section is the nice one." + }, + { + "text": "It solves difference equations." + }, + { + "text": "I would call that a difference equation." + }, + { + "text": "It's conne- a first order." + }, + { + "text": "I would call that a first order system, because it connects only, it only goes up one level." + }, + { + "text": "And it's a system because these are vectors and that's a matrix." + }, + { + "text": "And the solution is just that." + }, + { + "text": "OK." + }, + { + "text": "But, that's a nice formula." + }, + { + "text": "That's the, like, the most compact formula I could ever get." + }, + { + "text": "U one hundred would be a to the one hundredth u0." + }, + { + "text": "But how would I actually find u one hundred?" + }, + { + "text": "How would I find, how would I discover what u one hundred is?" + }, + { + "text": "Let me, let me show you how." + }, + { + "text": "Here, here's the idea." + }, + { + "text": "If, so, to solve, to really solve, shall I say, to really solve." + }, + { + "text": "To really solve it, I would take this initial vector, u0, and I would write it as a combination of eigenvectors." + }, + { + "text": "To really solve, write, write u0 as a combination, say, certain amount of the first eigenvector plus a certain amount of the second eigenvector plus a certain amount of the last eigenvector." + }, + { + "text": "Now multiply by a." + }, + { + "text": "You want to, you got to see the magic of eigenvectors work." + }, + { + "text": "Multiply by a." + }, + { + "text": "So a u0 is what?" + }, + { + "text": "So a times that." + }, + { + "text": "A times, so what's, I can separate it out into n separate pieces and that's the whole point." + }, + { + "text": "That each of those pieces is going in its own merry way." + }, + { + "text": "Each of those pieces is an eigenvector, and when I multiply by a, what does this piece become?" + }, + { + "text": "So that's some amount of the first, let's suppose the eigenvectors are normalized to be unit vectors." + }, + { + "text": "So that says what the eigenvector is." + }, + { + "text": "It's, and I need some multiple of it to produce u0." + }, + { + "text": "OK. Now when I multiply by a, what do I get?" + }, + { + "text": "I get c1, which is just a factor, times a x1, but a x1 is lambda one x1." + }, + { + "text": "When I multiply this by a, I get c2 lambda two x2." + }, + { + "text": "And here I get cn lambda n xn." + }, + { + "text": "And suppose I multiply by a to the hundredth power now." + }, + { + "text": "Can we, can we, having done it, multiplied by a, let's multiply by a to the hundredth." + }, + { + "text": "What happens to this first term when I multiply by a to the one hundredth?" + }, + { + "text": "It's got that factor lambda to the hundredth." + }, + { + "text": "That's the key." + }, + { + "text": "That, that's what I mean by going its own merry way." + }, + { + "text": "It, it is pure eigenvector, it's exactly in a direction where multiplication by a just brings in a scalar factor lambda one." + }, + { + "text": "So a hundred times brings in this a hundred times." + }, + { + "text": "Hundred times lambda two, hundred times lambda n. Actually, we're, what are we seeing here?" + }, + { + "text": "We're seeing, this same, lambda, capital lambda to the hundredth, as in the, as in the diagonalization, and we're seeing the S matrix, the matrix S of eigenvectors." + }, + { + "text": "That's what this has got to, this has got to amount to, a lambda to the hundredth power times an S times this vector C that's telling us how much of each one is in the original thing." + }, + { + "text": "So if, if I had to really find the hundredth power, I would take u0, I would expand it as a combination of eigenvectors, this is really S, the eigenvector matrix times C, the, the coefficient vector." + }, + { + "text": "And then I would immediately, then, by inserting these hundredth powers of eigenvalues, I'd have the answer." + }, + { + "text": "So the, the, huh, there must be, well, let's see." + }, + { + "text": "OK." + }, + { + "text": "It's, so, yeah." + }, + { + "text": "So if u100 is a to the hundredth times u0, and u0 is Sc, then you see this formula is just this formula, which is the way I would actually get hold of this, of this u100, which is, let me put it here, u100." + }, + { + "text": "The way I would actually get hold of that, see what, what the solution is after a hundred steps, would be expand the initial vector into eigenvectors and, and let each eigenvector go its own way, multiplying by a hundred at, by lambda at every step, and therefore by lambda to the hundredth power after a hundredth step." + }, + { + "text": "Can I do an example?" + }, + { + "text": "So that's, that's the, the formulas." + }, + { + "text": "Now let me take an example." + }, + { + "text": "I'll use the Fibonacci sequence as an example." + }, + { + "text": "So, so Fibonacci example." + }, + { + "text": "You remember the Fibonacci numbers?" + }, + { + "text": "If we start with one and one as F0, oh, I think I start with zero, maybe." + }, + { + "text": "Let zero and one be the first ones." + }, + { + "text": "So there's F0 and F1, the first two Fibonacci numbers." + }, + { + "text": "Then what's the rule for Fibonacci numbers?" + }, + { + "text": "They're the sum." + }, + { + "text": "The next one is the sum of those, so it's one." + }, + { + "text": "The next one is the sum of those, so it's two." + }, + { + "text": "The next one is the sum of those, so it's three." + }, + { + "text": "Well, it looks like one, two, three, four, five, but somehow it's not going to do that way." + }, + { + "text": "The next one is five, right." + }, + { + "text": "Two and three makes five." + }, + { + "text": "The next one is eight." + }, + { + "text": "The next one is thirteen." + }, + { + "text": "And the one hundredth Fibonacci number is what?" + }, + { + "text": "That's my question." + }, + { + "text": "How could I get a formula for the hundredth number and for example how could I answer the question how fast are they growing?" + }, + { + "text": "How fast are those Fibonacci numbers growing?" + }, + { + "text": "They're certainly growing." + }, + { + "text": "It's not a stable case, whatever the eigenvalues of whatever matrix it is, they're not smaller than one." + }, + { + "text": "These numbers are growing." + }, + { + "text": "But how fast are they growing?" + }, + { + "text": "The answer is lies in the eigenvalue." + }, + { + "text": "So I've got to find the matrix, so let me write down the Fibonacci rule, F k plus two is F k plus one plus F k, right?" + }, + { + "text": "Now that's not in my -- I want to write that as U k plus one and A U k. But right now what I've got is a single equation, not a system." + }, + { + "text": "And it's second order." + }, + { + "text": "It's like having a second order differential equation with second derivatives." + }, + { + "text": "I want to get first derivatives." + }, + { + "text": "Here I want to get first difference." + }, + { + "text": "So the way to do it is to introduce U k will be a vector." + }, + { + "text": "See, a small trick." + }, + { + "text": "Let U k be a vector, F k plus one and F k. So I'm going to get a two by two system, first order, instead of a one, instead of a scalar system, second order, by a simple trick." + }, + { + "text": "I'm just going to add in an equation F k plus one equals F k plus one." + }, + { + "text": "That will be my second equation." + }, + { + "text": "Then this is my system, this is my unknown, and what's my one-step equation?" + }, + { + "text": "So now U k plus one." + }, + { + "text": "That's so U k plus one is the left side, and what have I got here on the right side?" + }, + { + "text": "I've got some matrix multiplying U k. Can you see that all right?" + }, + { + "text": "If you can see it, then you can tell me what the matrix is." + }, + { + "text": "You see that I'm taking my system here, I artificially made it into a system." + }, + { + "text": "I artificially made the unknown into a vector, and now I'm ready to look at and see what the matrix is." + }, + { + "text": "So do you see the left side, U k plus one is F k plus two F k plus one, that's just what I want." + }, + { + "text": "On the right side, this, remember, this U k here, let me for the moment put it as F k plus one F k. So what's the matrix?" + }, + { + "text": "Well, that has a one and a one, and that has a one and a zero." + }, + { + "text": "There's the matrix." + }, + { + "text": "You see that that gives me the right-hand side." + }, + { + "text": "So there's the matrix A, and this is our friend U k. So we've got, so that simple trick changed the second order scalar problem to a first order system, two, with two unknowns." + }, + { + "text": "With a matrix and now what do I do?" + }, + { + "text": "Well, before I even think, I find its eigenvalues and eigenvectors." + }, + { + "text": "So what are the eigenvalues and eigenvectors of that matrix?" + }, + { + "text": "Let's see." + }, + { + "text": "I was, first let me just, like, think for a minute." + }, + { + "text": "It's two by two, so this shouldn't be impossible to do." + }, + { + "text": "Let's do it." + }, + { + "text": "OK." + }, + { + "text": "So my matrix again is one one one zero." + }, + { + "text": "It's symmetric, by the way." + }, + { + "text": "So what I will eventually know about symmetric matrices is that the eigenvalues will come out real, I won't get any complex numbers here, and the eigenvectors, once I get those, actually will be orthogonal." + }, + { + "text": "But two by two, I'm more interested in what the actual numbers are." + }, + { + "text": "What do I know about the two numbers?" + }, + { + "text": "Well, should, do you want me to find this determinant of A minus lambda I?" + }, + { + "text": "Sure." + }, + { + "text": "So it's the determinant of one minus lambda one one zero, right?" + }, + { + "text": "Minus lambda, yes, got it." + }, + { + "text": "OK. OK." + }, + { + "text": "There'll be two eigenvalues." + }, + { + "text": "Well, tell me again what I know about the two eigenvalues before I go any further." + }, + { + "text": "Tell me something about these two eigenvalues, what do they add up to?" + }, + { + "text": "Lambda one plus lambda two is the same as the trace down the diagonal of the matrix, one and zero is one." + }, + { + "text": "So lambda one plus lambda two should come out to be one, and lambda one times lambda two should come out to be the determinant, which is minus one." + }, + { + "text": "So I'm expecting the eigenvalues to add to one and to multiply to minus one." + }, + { + "text": "But let's just see it happen here." + }, + { + "text": "If I multiply this out, I get that times that'll be a lambda squared minus lambda minus one." + }, + { + "text": "Good." + }, + { + "text": "Lambda squared minus lambda minus one." + }, + { + "text": "Actually, you see the, compare that with the original equation that I started with." + }, + { + "text": "Fk plus two minus Fk plus one minus Fk is zero." + }, + { + "text": "The recurrent, the recursion that the Fibonacci number satisfy is somehow showing up directly here for the eigenvalues when we set that to zero." + }, + { + "text": "OK. Let's solve." + }, + { + "text": "Well, I would like to be able to factor that, that quadratic, but I'm better off to use the quadratic formula." + }, + { + "text": "Lambda is, let's see, minus b is one, plus or minus the square root of b squared, which is one, minus four, times that, times that, which is plus four, over two." + }, + { + "text": "So that's the square root of five." + }, + { + "text": "So the eigenvalues are lambda one is one half of one plus square root of five, and lambda two is one half of one minus square root of five." + }, + { + "text": "And sure enough, they, those add up to one, and they multiply to give minus one." + }, + { + "text": "OK. Those are the two eigenvalues." + }, + { + "text": "How, how, what are those numbers approximately?" + }, + { + "text": "Square root of five, well, it's more than two, but less than three." + }, + { + "text": "It, it'd be nice to know these numbers." + }, + { + "text": "I think, I think that that, so that number comes out bigger than one, right?" + }, + { + "text": "Yeah, that's right." + }, + { + "text": "This number comes out bigger than one." + }, + { + "text": "It's about one point six one eight or something." + }, + { + "text": "Not exactly." + }, + { + "text": "It's supposed to be one point six." + }, + { + "text": "Just, like, I think so." + }, + { + "text": "Then what's lambda two?" + }, + { + "text": "Is, is lambda two positive or negative?" + }, + { + "text": "Negative, right?" + }, + { + "text": "Because I'm, it's obviously negative, and I knew that the, so it's minus, and they add up to one, so minus point six one eight, I guess." + }, + { + "text": "OK. And some order." + }, + { + "text": "Those are the two eigenvalues." + }, + { + "text": "One eigenvalue bigger than one, one eigenvalue smaller than one." + }, + { + "text": "Actually, that's a great situation to be in." + }, + { + "text": "Of course, the eigenvalues are different, so there's no doubt whatever, is this matrix diagonalizable?" + }, + { + "text": "Is this matrix diagonalizable, that original matrix A?" + }, + { + "text": "Sure." + }, + { + "text": "We've got two distinct eigenvalues and we can find the eigenvectors in a moment." + }, + { + "text": "But they'll be independent, will be diagonalizable, and now you can already answer my very first question." + }, + { + "text": "How fast are those Fibonacci numbers increasing?" + }, + { + "text": "How, those, they're increasing, right?" + }, + { + "text": "They're not doubling at every step." + }, + { + "text": "Let's look again at these numbers." + }, + { + "text": "Five eight thirteen, it's not obvious." + }, + { + "text": "The next one would be twenty one thirty four." + }, + { + "text": "So to get some idea of what F one hundred is, can you give me any, I mean the crucial number of, so it, these, it's approximately, what's controlling the growth of these Fibonacci numbers?" + }, + { + "text": "It's the eigenvalues." + }, + { + "text": "And which eigenvalues controlling that growth?" + }, + { + "text": "The big ones." + }, + { + "text": "So F one hundred will it be approximately some constant, c one, I guess, times this lambda one, this one plus square root of five over two, to the hundredth power." + }, + { + "text": "And the two hundredth have, in other words, the eigenvalue, the Fibonacci numbers are growing by about that factor." + }, + { + "text": "You see that we've got precise information about the, about the Fibonacci numbers out of the eigenvalue." + }, + { + "text": "OK. And again, why is that true?" + }, + { + "text": "Let me go over to this board and show what I'm doing here." + }, + { + "text": "The, the original eigen, the original initial value is some combination of eigenvectors, and then when we start multiple, when we start going out the theory of Fibonacci numbers, when we start multiplying by a hundred times, it's this lambda one to the hundredth, this term is, is the one that's taken over." + }, + { + "text": "It's, I mean, that's big, like, one point six to the hundredth power." + }, + { + "text": "The second term is practically nothing, right?" + }, + { + "text": "The point six, or minus point six to the hundredth power, is an extremely small, extremely small number." + }, + { + "text": "So this is, this, this, there are only two terms, because we're two by two." + }, + { + "text": "This number is, this piece of it is there, but it's, it's disappearing." + }, + { + "text": "Where this piece is there and it's growing and controlling everything." + }, + { + "text": "So, so really the, we're doing, like, problems that are evolving." + }, + { + "text": "We're doing dynamics." + }, + { + "text": "Instead of Ax equal b, that's a static problem." + }, + { + "text": "We're now, we're doing dynamics." + }, + { + "text": "A, a squared, a cubed, things are evolving in time, and the eigenvalues are the crucial, numbers." + }, + { + "text": "OK." + }, + { + "text": "I guess to complete this, I better write down the eigenvectors." + }, + { + "text": "So we should complete the, the whole process by finding the eigenvectors." + }, + { + "text": "OK. Well, I have to, up in the corner, then I have to look at A minus lambda I." + }, + { + "text": "So A minus lambda I is this one minus lambda, one, one, and minus lambda." + }, + { + "text": "And now, can we spot an eigenvector out of that?" + }, + { + "text": "That's, for these two lambdas, this matrix is singular." + }, + { + "text": "I guess the eigenvector, two by two ought to be easy." + }, + { + "text": "So if I know that this matrix is singular, then it seems to me the eigenvector has to be lambda and one, because that multiplication will give me the zero." + }, + { + "text": "And this multiplication gives me, better give me also zero." + }, + { + "text": "Do you see why it does?" + }, + { + "text": "This is the minus lambda squared plus lambda plus one." + }, + { + "text": "It's the thing that's zero, because these lambdas are special." + }, + { + "text": "There's the eigenvector." + }, + { + "text": "X1 is lambda one, one, and x2 is lambda two, one." + }, + { + "text": "I did that as a little trick that was available in the two by two case." + }, + { + "text": "So now I finally have to, oh, I have to take the initial, u0." + }, + { + "text": "So to complete this example entirely, I have to say, OK, what was u0?" + }, + { + "text": "u0 was f1 f0." + }, + { + "text": "So u0, the starting vector, is f1 f0, and those were one and zero." + }, + { + "text": "So I have to use that vector, so I have to look for, from multiple of the first eigenvector and the second, to produce u0, the one zero vector." + }, + { + "text": "This is what will find c1 and c2, and then I'm done." + }, + { + "text": "So let me, instead of in the last five seconds grinding out a formula, let me repeat the idea." + }, + { + "text": "That really, it's the idea that's central." + }, + { + "text": "When things are evolving in time, let me come back to this board, because the ideas are here." + }, + { + "text": "When things are evolving in time by a first-order system, starting from an original u0, the key is, find the eigenvalues and eigenvectors of A." + }, + { + "text": "That will tell, those eigenvectors, the eigenvalues will already tell you what's happening." + }, + { + "text": "Is the solution blowing up?" + }, + { + "text": "Is it going to zero?" + }, + { + "text": "What's it doing?" + }, + { + "text": "And then, to find out exactly a formula, you have to take your u0 and write it as a combination of eigenvectors and then follow each eigenvector separately." + }, + { + "text": "And that's really what this formula, the formula for, that's what the formula for A to the k is doing." + }, + { + "text": "So remember that formula for A to the k is S, lambda to the k S inverse." + }, + { + "text": "OK. That's, that's difference equations, and you just have to, so the homework will give some examples different from Fibonacci to follow through." + }, + { + "text": "And next time will be differential equations." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated/1RLctDS2hUQ.json b/sight/sources/annotated/1RLctDS2hUQ.json new file mode 100644 index 0000000000000000000000000000000000000000..aabe28538def0b8bdbb47c75f80c9c62583dc52c --- /dev/null +++ b/sight/sources/annotated/1RLctDS2hUQ.json @@ -0,0 +1,1541 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "Today we're going to continue with integration." + }, + { + "text": "And we get to do probably the most important thing of this entire course, which is appropriately named." + }, + { + "text": "It's called the Fundamental Theorem of Calculus." + }, + { + "text": "And we'll be abbreviating it FTC, and occasionally I'll put in a 1 here, because there will be two versions of it." + }, + { + "text": "But this is the one that you'll be using the most in this class." + }, + { + "text": "The Fundamental Theorem of Calculus says the following." + }, + { + "text": "It says that if f' is equal to f, so f' of x is equal to f of x, is a capital F and a little f, then the integral from a to b of f of x is equal to f of b minus f of a." + }, + { + "text": "That's it." + }, + { + "text": "That's the whole theorem." + }, + { + "text": "And you may recognize it." + }, + { + "text": "Before we had the notation that f was the antiderivative." + }, + { + "text": "That is, capital F was the integral of f of x." + }, + { + "text": "We wrote it this way." + }, + { + "text": "This is the indefinite integral." + }, + { + "text": "And now we're putting in definite values." + }, + { + "text": "And we have a connection between the two uses of the integral sign." + }, + { + "text": "But with the definite values, we get real numbers out instead of a function." + }, + { + "text": "Or a function up to a constant." + }, + { + "text": "So this is it." + }, + { + "text": "This is the formula." + }, + { + "text": "And it's usually also written with another notation." + }, + { + "text": "So I want to introduce that notation to you as well." + }, + { + "text": "So there's a new notation here." + }, + { + "text": "Which you'll find very convenient." + }, + { + "text": "Because we don't always have to give a letter f to the functions involved." + }, + { + "text": "So it's an abbreviation." + }, + { + "text": "For right now, there'll be a lot of f's." + }, + { + "text": "But anyway." + }, + { + "text": "So here's the abbreviation." + }, + { + "text": "Whenever I have a difference between a function at two values, I also can write this as f of x with an a down here and a b up there." + }, + { + "text": "So that's the notation that we use." + }, + { + "text": "And you can also, for emphasis, and this sometimes turns out to be important when there's more than one variable floating around in the problem, to specify that the variable is x." + }, + { + "text": "So this is the same thing as x equals a and x equals b." + }, + { + "text": "It indicates where you want to plug in, what you want to plug in." + }, + { + "text": "And now you take the top value minus the bottom value." + }, + { + "text": "So f of b minus f of a." + }, + { + "text": "This is just a notation." + }, + { + "text": "And in that notation, of course, the theorem can be written as with this set of symbols here, equally well." + }, + { + "text": "So let's just give a couple of examples." + }, + { + "text": "The first example is the one that we did last time very laboriously." + }, + { + "text": "If you take the function F of x, which happens to be x cubed over 3, then if you differentiate it, you get, well, the factor of 3 cancels." + }, + { + "text": "So you get x squared." + }, + { + "text": "That's the derivative." + }, + { + "text": "And so by the fundamental theorem, so this implies by the fundamental theorem that the integral from, say, a to b of x squared dx, that's the derivative here." + }, + { + "text": "This is the function we're going to use as f of x here." + }, + { + "text": "Is equal to this function here, f of b minus f of a." + }, + { + "text": "That's here, this function here." + }, + { + "text": "So that's f of b minus f of a." + }, + { + "text": "And that's equal to b cubed over 3 minus a cubed over 3." + }, + { + "text": "Now, in this new notation, we usually don't have all these letters." + }, + { + "text": "All we write is the following." + }, + { + "text": "We write the integral from a to b." + }, + { + "text": "And I'm going to do the case of 0 to b, because that was the one that we actually did last time." + }, + { + "text": "So I'm going to set a equals 0 here." + }, + { + "text": "And then the problem we were faced last time was this." + }, + { + "text": "And as I said, we did it very laboriously." + }, + { + "text": "But now you can see that we can do it in 10 seconds, let's say." + }, + { + "text": "Well, the antiderivative of this is x cubed over 3." + }, + { + "text": "I'm going to evaluate it at 0 and at b and subtract." + }, + { + "text": "So that's going to be b cubed over 3 minus 0 cubed over 3." + }, + { + "text": "Which, of course, is b cubed over 3." + }, + { + "text": "And that's the end." + }, + { + "text": "That's the answer." + }, + { + "text": "So this is a lot faster than yesterday." + }, + { + "text": "I hope you'll agree." + }, + { + "text": "And we can dispense with those elaborate computations." + }, + { + "text": "Although there's a conceptual reason, a very important one, for understanding the procedure that we went through." + }, + { + "text": "Because eventually you're going to be using integrals and these quick ways of doing things to solve problems like finding the volumes of pyramids." + }, + { + "text": "In other words, we're going to reverse the process." + }, + { + "text": "And so we need to understand the connection between the two." + }, + { + "text": "I'm going to give a couple more examples." + }, + { + "text": "And then we'll go on." + }, + { + "text": "So the second example would be one that would be quite difficult to do by this Riemann sum technique that we described yesterday." + }, + { + "text": "Although it is possible." + }, + { + "text": "It uses much higher mathematics to do it." + }, + { + "text": "And that is the area under one hump of the sine curve." + }, + { + "text": "Sine x." + }, + { + "text": "Let me just draw a picture of that." + }, + { + "text": "The curve goes like this." + }, + { + "text": "And we're talking about this area here." + }, + { + "text": "It starts out at 0, it goes to pi." + }, + { + "text": "That's one hump." + }, + { + "text": "And so the answer is, it's the integral from 0 to pi of sin x, dx." + }, + { + "text": "And so I need to take the antiderivative of that." + }, + { + "text": "And that's minus cos x." + }, + { + "text": "That's the thing whose derivative is sin x." + }, + { + "text": "Evaluating it at 0 and pi." + }, + { + "text": "Now, let's do this one carefully." + }, + { + "text": "Because this is where I see a lot of arithmetic mistakes." + }, + { + "text": "Even though this is the easy part of the problem." + }, + { + "text": "It's hard to pay attention and plug in the right numbers." + }, + { + "text": "And so let's just pay very close attention." + }, + { + "text": "I'm plugging in pi." + }, + { + "text": "That's minus cos pi." + }, + { + "text": "That's the first term." + }, + { + "text": "And then I'm subtracting the value at the bottom." + }, + { + "text": "Which is minus cos 0." + }, + { + "text": "There are already five opportunities for you to make a transcription error or an arithmetic mistake in what I just did." + }, + { + "text": "And I've seen all five of them." + }, + { + "text": "So the next one is that this is minus, minus 1." + }, + { + "text": "Minus negative 1, if you like." + }, + { + "text": "And then this is minus, and here's another negative 1." + }, + { + "text": "So all together we have 2." + }, + { + "text": "So that's it." + }, + { + "text": "That's the area." + }, + { + "text": "This area, which is hard to guess, this is area 2." + }, + { + "text": "The third example is maybe superfluous, but I'm going to say it anyway." + }, + { + "text": "We can take the integral, say, from 0 to 1 of x to the 100th power." + }, + { + "text": "Any power now is within our power." + }, + { + "text": "So let's do it here." + }, + { + "text": "So here we have the antiderivative is x to the 101 divided by 101." + }, + { + "text": "Evaluated at 0 and 1." + }, + { + "text": "And that is just 1 over 101." + }, + { + "text": "So that's the fundamental theorem." + }, + { + "text": "Now, this, as I say, harnesses a lot of what we've already learned all about antiderivatives." + }, + { + "text": "Now, I want to give you an intuitive interpretation." + }, + { + "text": "So let's try that." + }, + { + "text": "We'll talk about a proof of the fundamental theorem a little bit later." + }, + { + "text": "It's not actually that hard." + }, + { + "text": "But we'll give an intuitive reason, interpretation, if you like, of the fundamental theorem." + }, + { + "text": "So this is going to be one which is not related to area, but rather to time and distance." + }, + { + "text": "So we'll consider x of t is your position at time t. And then x' of t, which is the rate of change of x with respect to t, is going to be what we know as your speed." + }, + { + "text": "And then what the theorem is telling us is the following." + }, + { + "text": "It's telling us the integral from a to b of v of t dt, so reading the relationship, is equal to x of b minus x of a." + }, + { + "text": "And so this is some kind of cumulative sum of your velocities." + }, + { + "text": "So let's interpret the right-hand side first." + }, + { + "text": "This is the distance traveled." + }, + { + "text": "And it's also what you would read on your odometer." + }, + { + "text": "From the beginning to the end of the trip." + }, + { + "text": "That's what you would read on your odometer." + }, + { + "text": "Whereas this is what you would read on your speedometer." + }, + { + "text": "So this is the interpretation." + }, + { + "text": "Now, I want to just go one step further into this interpretation to make the connection with the Riemann sums that we had yesterday." + }, + { + "text": "Because those are very complicated to understand." + }, + { + "text": "And I want you to understand them viscerally on several different levels." + }, + { + "text": "Because that's how you'll understand integration better." + }, + { + "text": "The first thing that I want to imagine, so we're going to do a thought experiment now, which is that you are extremely obsessive." + }, + { + "text": "And you're driving your car from time a to time b." + }, + { + "text": "Place q to place r, whatever." + }, + { + "text": "And you check your speedometer every second." + }, + { + "text": "So you've read your speedometer in the i-th second." + }, + { + "text": "And you've read that you're going at this speed." + }, + { + "text": "Now, how far do you go in that second?" + }, + { + "text": "Well, the answer is, you go this speed times the time interval, which in this case we're imagining is 1 second." + }, + { + "text": "So this is how far you went." + }, + { + "text": "This is the time interval." + }, + { + "text": "And this is the distance traveled in second number i, in the i-th second." + }, + { + "text": "The distance traveled in the i-th second." + }, + { + "text": "That's the total distance you traveled." + }, + { + "text": "Now, what happens if you go the whole distance?" + }, + { + "text": "Well, you travel the sum of all these distances." + }, + { + "text": "So it's some massive sum where n is some ridiculous number of seconds." + }, + { + "text": "3600 seconds or something like that, whatever it is." + }, + { + "text": "And that's going to turn out to be very similar to what you would read on your odometer." + }, + { + "text": "Because during that second, you didn't change velocity very much." + }, + { + "text": "So the approximation, the speed at one time that you spotted it, is very similar to the speed during the whole second." + }, + { + "text": "It doesn't change that much." + }, + { + "text": "So this is a pretty good approximation to how far you traveled." + }, + { + "text": "And so the sum is a very realistic approximation to the entire integral, which is denoted this way." + }, + { + "text": "Which, by the fundamental theorem, is exactly how far you traveled." + }, + { + "text": "So this is x sub b minus x sub a." + }, + { + "text": "Exactly." + }, + { + "text": "The other one is approximate." + }, + { + "text": "Again, this is called a Riemann sum." + }, + { + "text": "Alright, so that's the intro to the fundamental theorem." + }, + { + "text": "And now what I need to do is extend it just a bit." + }, + { + "text": "And the way I'm going to extend it is the following." + }, + { + "text": "I'm going to do it on this example first." + }, + { + "text": "And then we'll do it more formally." + }, + { + "text": "So here's this example where we went someplace." + }, + { + "text": "But now I just want to draw you an additional picture here." + }, + { + "text": "Imagine I start here, and I go over to there, and then I come back." + }, + { + "text": "And maybe even I do a round trip." + }, + { + "text": "I come back to the same place." + }, + { + "text": "Well, if I come back to the same place, then the position is unchanged from the beginning to the end." + }, + { + "text": "In other words, the difference is 0." + }, + { + "text": "And the velocity, technically rather than the speed, it's the speed to the right and the speed to the left maybe are the same." + }, + { + "text": "But one of them is going in the positive direction, one of them is going in the negative direction, and they cancel each other." + }, + { + "text": "So if you have this kind of situation, we want that to be reflected." + }, + { + "text": "We like that interpretation." + }, + { + "text": "And we want to preserve it even in the case when the function v is negative." + }, + { + "text": "And so I'm going to now extend our notion of integration." + }, + { + "text": "So we'll extend integration to the case f negative." + }, + { + "text": "Or positive." + }, + { + "text": "In other words, it could be any sign." + }, + { + "text": "Actually, there's no change." + }, + { + "text": "The formulas are all the same." + }, + { + "text": "We just, if this v is going to be positive, we write in a positive number." + }, + { + "text": "If it's going to be negative, we write in a negative number." + }, + { + "text": "And we just leave it alone." + }, + { + "text": "And the real, so here's, let me carry out an example." + }, + { + "text": "And show you how it works." + }, + { + "text": "I'll carry out the example on this blackboard up here of the sine function." + }, + { + "text": "But we're going to try two humps." + }, + { + "text": "We're going to try the first hump and the one that goes underneath there." + }, + { + "text": "So our example here is going to be the integral from 0 to 2pi." + }, + { + "text": "Of sin x dx." + }, + { + "text": "And now, because the fundamental theorem is so important, and so useful, and so convenient, we just assume that it be true in this case as well." + }, + { + "text": "So we insist that this is going to be minus cos x, evaluated at 0 and 2pi." + }, + { + "text": "With the difference." + }, + { + "text": "Now, when we carry out that difference, what we get here is minus cos 2pi minus minus cos 0." + }, + { + "text": "Which is negative 1 minus negative 1, which is 0." + }, + { + "text": "And the interpretation of this is the following." + }, + { + "text": "Here's our double hump." + }, + { + "text": "Here's pi and here's 2pi." + }, + { + "text": "And all that's happening is that the geometric interpretation that we had before of the area under the curve has to be taken with a grain of salt." + }, + { + "text": "In other words, I lied to you before when I said that the definite integral was the area under the curve." + }, + { + "text": "It's not." + }, + { + "text": "The definite integral is the area under the curve when it's above the curve." + }, + { + "text": "And it counts negatively when it's below the curve." + }, + { + "text": "So yesterday, my geometric interpretation was incomplete and really just a plain lie." + }, + { + "text": "So the true geometric interpretation of the definite integral is plus the area above the x-axis minus the area below the x-axis." + }, + { + "text": "As in the picture." + }, + { + "text": "I'm just writing it down in words, but you should think of it visually also." + }, + { + "text": "So that's the setup here." + }, + { + "text": "And now we have the complete definition of integrals." + }, + { + "text": "And I need to list for you a bunch of their properties and how we deal with integrals." + }, + { + "text": "Are there any questions before we go on?" + }, + { + "text": "Yeah." + }, + { + "text": "STUDENT 1 Just wanted to talk about, wouldn't this be an absolute value of the velocity function to get the sense?" + }, + { + "text": "PROFESSOR ERIC GRIMSON So the question was, wouldn't the absolute value of the velocity function be involved?" + }, + { + "text": "The answer is yes." + }, + { + "text": "That is, that's one question that you could ask." + }, + { + "text": "One question you could ask is, what's the total distance traveled?" + }, + { + "text": "And in that case, you would keep track of the absolute value of the velocity, as you said." + }, + { + "text": "Whether it's positive or negative." + }, + { + "text": "And then you get the total length of this curve here." + }, + { + "text": "That's, however, not what the definite integral measures." + }, + { + "text": "It measures the net distance traveled." + }, + { + "text": "So it's another thing." + }, + { + "text": "In other words, we can do that." + }, + { + "text": "We now have the tools to do both." + }, + { + "text": "We could also, so if you like, the total distance is equal to the integral of this, from a to b." + }, + { + "text": "But the net distance is the one without the absolute value signs." + }, + { + "text": "So that's correct." + }, + { + "text": "Other questions?" + }, + { + "text": "Alright, so now let's talk about properties of integrals." + }, + { + "text": "Well, so the properties of integrals that I want to mention to you are these." + }, + { + "text": "The first one is, doesn't bear too much comment." + }, + { + "text": "If you take the cumulative integral of a sum, you're just going to get the sum of the separate integrals here." + }, + { + "text": "And I won't say much about that." + }, + { + "text": "That's because the integral is a sum." + }, + { + "text": "Incidentally, you know, this strange symbol here, there's actually a reason for it historically." + }, + { + "text": "If you go back to old books, you'll see that it actually looks a little bit more like an S. This capital sigma is a sum." + }, + { + "text": "S for sum." + }, + { + "text": "Because everybody in those days knew Latin and Greek." + }, + { + "text": "And this one is also an S. But gradually it was such an important S that they made it bigger." + }, + { + "text": "And then they stretched it out and made it a little thinner, because it didn't fit into one typesetting space." + }, + { + "text": "And so just for typesetting reason, it got stretched and got a little bit skinny." + }, + { + "text": "Anyway, so it's really an S. And in fact, in French, they call it sum." + }, + { + "text": "Even though we call it integral." + }, + { + "text": "So it's a sum." + }, + { + "text": "So it's consistent with sums in this way." + }, + { + "text": "And similarly, we can factor constants out of sums." + }, + { + "text": "So if you have an integral like this, the constant factors out." + }, + { + "text": "But definitely don't try to get a function out of this." + }, + { + "text": "That won't happen." + }, + { + "text": "In other words, c has to be a constant." + }, + { + "text": "Doesn't depend on x." + }, + { + "text": "All right." + }, + { + "text": "The third property." + }, + { + "text": "What do I want to call the third property here?" + }, + { + "text": "I have a sort of a preliminary property, yes." + }, + { + "text": "Here." + }, + { + "text": "Which is the following." + }, + { + "text": "And I'll draw a picture of it." + }, + { + "text": "Suppose you have three points along the line." + }, + { + "text": "So then I'm going to draw a picture of that." + }, + { + "text": "And I'm going to use the interpretation above the curve." + }, + { + "text": "Even though that's not the whole thing." + }, + { + "text": "So here's a, here's b, and here's c. And you can see that the area of this piece, of the first two pieces here, is, when added together, gives you the area of the whole." + }, + { + "text": "And that's the rule that I'd like to tell you." + }, + { + "text": "So if you integrate from a to b, and you add to that the integral from b to c, you'll get the integral from a to c. This is going to be just a little preliminary, because the rule is a little better than this." + }, + { + "text": "But I will explain that in a minute." + }, + { + "text": "The fourth rule is a very simple one." + }, + { + "text": "Which is that the integral from a to a of f x dx is equal to 0." + }, + { + "text": "That you can see very obviously, because there's no area, no horizontal movement there." + }, + { + "text": "The rectangle is infinitely thin." + }, + { + "text": "And there's nothing there." + }, + { + "text": "So this is the case." + }, + { + "text": "You can also interpret it as f of a minus f of a." + }, + { + "text": "So that's also consistent with our interpretation, in terms of the fundamental theorem of calculus." + }, + { + "text": "And it's perfectly reasonable that this is the case." + }, + { + "text": "Now, the fifth property is a definition." + }, + { + "text": "It's not really a property." + }, + { + "text": "But it's very important." + }, + { + "text": "The integral from a to b of f of x dx is equal to minus the integral from b to a of f of x dx." + }, + { + "text": "Now, really, the right-hand side here is an undefined quantity so far." + }, + { + "text": "We never said that you could ever do this where the a is less than the b." + }, + { + "text": "Because this is working backwards here." + }, + { + "text": "But we just have a convention that that's the definition." + }, + { + "text": "Whenever we write down this number, it's the same as minus what that number is." + }, + { + "text": "And the reason for all of these is, again, that we want them to be consistent with the fundamental theorem of calculus." + }, + { + "text": "Which is the thing that makes all of this work." + }, + { + "text": "So if you notice, the left-hand side here is f of b minus f of a, capital F. The antiderivative of little f. On the other hand, the other side is minus, and if we just ignore that we say these are letters, if we were a machine we didn't know which one was bigger than which." + }, + { + "text": "We just plugged them in." + }, + { + "text": "We would get here f of a minus f of b over here." + }, + { + "text": "And to make these two things equal, what we want is to put that minus sign in." + }, + { + "text": "Now it's consistent." + }, + { + "text": "So again, these rules are set up so that everything is consistent." + }, + { + "text": "And now I want to improve on Rule 3 here." + }, + { + "text": "And point out to you, so let me just go back to Rule 3 for a second, that now that we can evaluate integrals regardless of the order, we don't have to have a less than b, b less than c in order to make sense out of this." + }, + { + "text": "We actually have the possibility of considering integrals where the a's and the b's and the c's are in any order you want." + }, + { + "text": "And in fact, with this definition, with this definition 5, 3 works no matter what the numbers are." + }, + { + "text": "So this is much more convenient." + }, + { + "text": "We don't, this is not necessary." + }, + { + "text": "It just works using Convention 5." + }, + { + "text": "OK, with 5." + }, + { + "text": "Again, before I go on, let me emphasize, we really want to respect the sign of this velocity." + }, + { + "text": "We really want the net change in the position." + }, + { + "text": "And we don't want this absolute value here." + }, + { + "text": "Because otherwise, all of our formulas are going to mess up." + }, + { + "text": "We won't always be able to check." + }, + { + "text": "Sometimes you have letters rather than actual numbers here, and you won't know whether a is bigger than b." + }, + { + "text": "So you'll want to know that these formulas work and are consistent in all situations." + }, + { + "text": "OK, I'm going to trade these again in order to preserve the ordering 1 through 5." + }, + { + "text": "And now I have a sixth property that I want to talk about." + }, + { + "text": "This one is called estimation." + }, + { + "text": "And it says the following." + }, + { + "text": "If f of x is less than or equal to g of x, then the integral from a to b of f of x dx is less than or equal to the integral from a to b of g of x dx." + }, + { + "text": "Now, this one says that if I'm going more slowly than you, then you go farther than I do." + }, + { + "text": "That's all it's saying." + }, + { + "text": "For this one, you'd better have a is less than b." + }, + { + "text": "You need it." + }, + { + "text": "Because we flip the signs when we flip the order of a and b." + }, + { + "text": "So this one, it's essential that the lower limit be smaller than the upper limit." + }, + { + "text": "But let me just emphasize, because we're dealing with the generalities of this, actually if one of these is negative and the other one is negative, then it also works." + }, + { + "text": "This one ends up being, if f is more negative than g, then this added up thing is more negative than that one." + }, + { + "text": "Again, under the assumption that a is less than b." + }, + { + "text": "So as I wrote it, it's in full generality." + }, + { + "text": "All right, let's illustrate this one." + }, + { + "text": "And then we have one more property to learn after that." + }, + { + "text": "So let me give you an example of estimation." + }, + { + "text": "The example is the same as one that I already gave you." + }, + { + "text": "But this time, because we have the tool of integration, we can just follow our noses and it works." + }, + { + "text": "I'll start with the inequality." + }, + { + "text": "So I'm trying to illustrate estimation, so I want to start with an inequality which is what the hypothesis is here." + }, + { + "text": "And I'm going to integrate the inequality to get this conclusion and see what conclusion it is." + }, + { + "text": "The inequality that I want to take is that e to the x is greater than or equal to 1 for x greater than or equal to 0." + }, + { + "text": "That's going to be our starting place." + }, + { + "text": "And now I'm going to integrate it, that is, I'm going to use estimation to see what that gives." + }, + { + "text": "Well, I'm going to integrate, say, from 0 to b. I can't integrate below 0 because it's only true above 0." + }, + { + "text": "This is e to the x dx greater than or equal to the integral from 0 to b of 1 dx." + }, + { + "text": "Let's work out what each of these is." + }, + { + "text": "The first one, e to the x dx, is the antiderivative is e to the x evaluated at 0 and b." + }, + { + "text": "So that's e to the b minus e to the 0, which is e to the b minus 1." + }, + { + "text": "The other one, you're supposed to be able to get by the rectangle law." + }, + { + "text": "This is one rectangle of base b and height 1." + }, + { + "text": "So the answer is b." + }, + { + "text": "Or you can do it by antiderivatives, but it's b." + }, + { + "text": "That means that our inequality says, if I just combine these two things together, that e to the b minus 1 is greater than or equal to b." + }, + { + "text": "And that's the same thing as e to the b is greater than or equal to 1 plus b." + }, + { + "text": "Again, this only works for b greater than or equal to 0." + }, + { + "text": "Notice that if b were negative, this would be a well-defined quantity." + }, + { + "text": "But this estimation would be false." + }, + { + "text": "We need that the b be bigger than 0 in order for this to make sense." + }, + { + "text": "So this was used." + }, + { + "text": "And that's a good thing, because this inequality is suspect." + }, + { + "text": "Actually, it turns out to be true when b is negative." + }, + { + "text": "We certainly didn't prove it." + }, + { + "text": "I'm going to just repeat this process." + }, + { + "text": "So let's repeat it." + }, + { + "text": "Starting from the inequality, the conclusion." + }, + { + "text": "Which is sitting right here." + }, + { + "text": "But I'll write it in the form e to the x greater than or equal to 1 plus x, for x greater than or equal to 0." + }, + { + "text": "And now if I integrate this one, I get the integral from 0 to b, e to the x dx is greater than or equal to the integral from 0 to b, 1 plus x dx." + }, + { + "text": "And I remind you that we've already calculated this one." + }, + { + "text": "This is e to the b-1." + }, + { + "text": "And the other one is not hard to calculate." + }, + { + "text": "The antiderivative is x plus x squared over 2." + }, + { + "text": "We're evaluating that at 0 and b." + }, + { + "text": "So that comes out to be b plus b squared over 2." + }, + { + "text": "And so our conclusion is that the left side, which is e to the b-1, is greater than or equal to b plus b squared over 2, and this is for b greater than or equal to 0." + }, + { + "text": "And that's the same thing as e to the b greater than or equal to 1 plus b plus b squared over 2." + }, + { + "text": "This one actually is false for b negative." + }, + { + "text": "So that's something that you have to be careful with the b positives here." + }, + { + "text": "All right, so you can keep on going with this." + }, + { + "text": "And you didn't have to think, and you'll produce a very interesting polynomial, which is a good approximation to e to the b." + }, + { + "text": "All right, so that's it for the basic properties." + }, + { + "text": "Now there's one tricky property that I need to tell you about." + }, + { + "text": "It's not that tricky, but it's a little tricky." + }, + { + "text": "And this is change of variables." + }, + { + "text": "Change of variables in integration, we've actually already done." + }, + { + "text": "We called that, the last time we talked about it, we called it substitution." + }, + { + "text": "And the idea here, if you may remember, was that if you're faced with an integral like this, you can change it to, if you put in u is equal to u of x, and you have a du, which is equal to u' of x dx, then you can change the integral." + }, + { + "text": "As follows, this is the same as g of u of x, u' of x dx." + }, + { + "text": "This was the general procedure for substitution." + }, + { + "text": "What's new today is that we're going to put in the limits." + }, + { + "text": "If you have a limit here, u1, and a limit here, u2, you want to know what the relationship is between the limits here and the limits when you change variables to the new variables." + }, + { + "text": "And it's the simplest possible thing." + }, + { + "text": "Namely, the two limits over here are in the same relationship as u of x is to this symbol u here." + }, + { + "text": "In other words, u1 is equal to u of x1." + }, + { + "text": "And u2 is equal to u of x2." + }, + { + "text": "That's what works." + }, + { + "text": "Now, there's only one danger here, there's one subtlety." + }, + { + "text": "Which is, this only works if u' does not change sign." + }, + { + "text": "I've been worrying a little bit about going backwards and forwards, and I allowed myself to reverse and do all kinds of stuff with these integrals." + }, + { + "text": "So we're sort of free to do it." + }, + { + "text": "Well, this is one case where you want to avoid it." + }, + { + "text": "Just don't do it." + }, + { + "text": "It is possible, actually, to make sense out of it." + }, + { + "text": "But it's also possible to get yourself infinitely confused." + }, + { + "text": "So just make sure that, now it's OK if u' is always negative, you're always going one way." + }, + { + "text": "It's OK if u' is always positive, you're always going the other way." + }, + { + "text": "But if you mix them up, you'll get yourself mixed up." + }, + { + "text": "Let me give you an example." + }, + { + "text": "The example will be maybe close to what we did last time, did when we first did substitution, I mean." + }, + { + "text": "Let's see." + }, + { + "text": "So the integral from 1 to 2, this time I'll put indefinite limits, of x squared plus, sorry, maybe I call this x cubed, x cubed plus 2, let's say, I don't know, to the 5th power, x squared dx." + }, + { + "text": "So this is an example of an integral that we would have tried to handle by substitution before." + }, + { + "text": "And the substitution we would have used is u equals x cubed plus 2." + }, + { + "text": "And that's exactly what we're going to do here." + }, + { + "text": "But we're just going to also take into account the limits." + }, + { + "text": "The first step, as in any substitution or change of variables, is this." + }, + { + "text": "And so we can fill in the things that we would have done previously, which is that this is the integral, and this is u to the 5th power." + }, + { + "text": "And then, because this is 3x squared, we see that this is 3, sorry, let's write it the other way." + }, + { + "text": "1 3rd du is equal to x squared dx." + }, + { + "text": "So that's what I'm going to plug in for this factor here." + }, + { + "text": "So here's 1 3rd du, which replaces that." + }, + { + "text": "But now there's the extra feature." + }, + { + "text": "The extra feature is the limits." + }, + { + "text": "So here, really in disguise, because now this is incredibly important, this is one of the reasons why we use this notation dx and du." + }, + { + "text": "We want to remind ourselves which variable is involved in the integration." + }, + { + "text": "And especially if you're the one naming the variables, you may get mixed up in this respect." + }, + { + "text": "So you must know which variable is varying between 1 and 2." + }, + { + "text": "And the answer is it's x is the one that's varying between 1 and 2." + }, + { + "text": "So in disguise, even though I didn't write it, it was contained in this little symbol here." + }, + { + "text": "This reminded us which variable." + }, + { + "text": "You'll find this amazingly important when you get to multivariable calculus." + }, + { + "text": "When there are many variables floating around." + }, + { + "text": "So this is an incredibly important distinction to make." + }, + { + "text": "So now over here, we have a limit." + }, + { + "text": "But it's of course supposed to be with respect to u now." + }, + { + "text": "So we need to calculate what those corresponding limits are." + }, + { + "text": "And indeed, it's just, I plug in here u1 is going to be equal to what I plug in for x equals 1." + }, + { + "text": "That's going to be 1 cubed plus 2, which is 3." + }, + { + "text": "And then u2 is 2 cubed plus 2, which is equal to 10." + }, + { + "text": "8 plus 2 is 10." + }, + { + "text": "So this is the integral from 3 to 10 of u5 1 3rd du." + }, + { + "text": "And now I can finish the problem." + }, + { + "text": "This is 1 18th u6, from 3 to 10." + }, + { + "text": "And this is where the most common mistake occurs in substitutions of this type." + }, + { + "text": "Which is that if you ignore this, and you plug in these 1 and 2 here, you think, oh, I should just be putting it at 1 and 2." + }, + { + "text": "But actually, it should be the u value that we're interested in, and the lower limit is u equals 3, and u equals 10 is the upper limit." + }, + { + "text": "So those are suppressed here." + }, + { + "text": "But those are the ones that we want." + }, + { + "text": "And so here we go." + }, + { + "text": "It's 1 18th times some ridiculous number, which I won't calculate, 10 to the 6th minus 3 to the 6th." + }, + { + "text": "Yes, question." + }, + { + "text": "STUDENT 1 STUDENT 1 STUDENT 1 STUDENT 1 STUDENT 1 STUDENT 1 STUDENT 1 STUDENT 1 STUDENT 1 STUDENT 1 So if you want to do things where you're worrying about the sign change, the right strategy is what you suggested works, and in fact I'm going to do an example right now on this subject." + }, + { + "text": "But the right strategy is to break it up into pieces where u' has one sign or the other." + }, + { + "text": "Let me show you an example." + }, + { + "text": "But where things go wrong." + }, + { + "text": "And I'll tell you how to handle it, roughly." + }, + { + "text": "So here's our warning." + }, + { + "text": "Suppose you're integrating from minus 1 to 1 x squared dx." + }, + { + "text": "Here's an example." + }, + { + "text": "And you had the temptation to plug in u is equal to x squared." + }, + { + "text": "Now, of course, we know how to integrate this." + }, + { + "text": "But let's just pretend we were stubborn and wanted to use substitution." + }, + { + "text": "Then we have du is equal to 2x dx." + }, + { + "text": "And now, if I try to make the correspondence, notice that the limits are u1 is negative 1 squared." + }, + { + "text": "That's the bottom limit." + }, + { + "text": "And u2 is the upper limit." + }, + { + "text": "That's 1 squared." + }, + { + "text": "That's also equal to 1." + }, + { + "text": "Both limits are 1." + }, + { + "text": "So this is going from 1 to 1." + }, + { + "text": "And no matter what it is, we know it's going to be 0." + }, + { + "text": "But we know this is not 0." + }, + { + "text": "This is the integral of a positive quantity." + }, + { + "text": "And it's the area under a curve." + }, + { + "text": "It's going to be a positive area." + }, + { + "text": "So this is a positive quantity." + }, + { + "text": "It can't be 0." + }, + { + "text": "If you actually plug it in, it looks equally strange." + }, + { + "text": "You put in here this u, and then, so that would be for the u squared." + }, + { + "text": "And then to plug in for dx, you would write dx is equal to 1 over 2x du." + }, + { + "text": "And then you might write that as this." + }, + { + "text": "And so what I should put in here is this quantity here." + }, + { + "text": "Which is a perfectly OK integral." + }, + { + "text": "And it has a value, I mean, it's what it is." + }, + { + "text": "It's 0." + }, + { + "text": "So of course, this is not true." + }, + { + "text": "And the reason is that u was equal to x squared." + }, + { + "text": "And u' of x was equal to 2x." + }, + { + "text": "Which was positive for x positive, and negative for x negative." + }, + { + "text": "And this was the sign change which causes us trouble." + }, + { + "text": "If we break it up into its two halves, then it'll be OK. And you'll be able to use this." + }, + { + "text": "Now, there was a mistake." + }, + { + "text": "And this was essentially what you were saying." + }, + { + "text": "That is, it's possible to see this happening as you're doing it, if you're very careful." + }, + { + "text": "There's a mistake in this process." + }, + { + "text": "And the mistake is, in the transition, this is a mistake here." + }, + { + "text": "Maybe I haven't used any red yet today." + }, + { + "text": "So I get to use some red here." + }, + { + "text": "Oh boy." + }, + { + "text": "This is not true here." + }, + { + "text": "This step here." + }, + { + "text": "So why isn't it true?" + }, + { + "text": "It's not true for the standard reason." + }, + { + "text": "Which is that really, x is equal to plus or minus square root of u." + }, + { + "text": "And if you stick to one side or the other, you'll have a coherent formula for it." + }, + { + "text": "One of them will be the plus and one of them will be the minus." + }, + { + "text": "And it will work out when you separate it into its pieces." + }, + { + "text": "So you could do that." + }, + { + "text": "But this is a can of worms." + }, + { + "text": "So I avoid this." + }, + { + "text": "And just do it in a place where the inverse is well-defined." + }, + { + "text": "And where the function either moves steadily up or steadily down." + } +] \ No newline at end of file diff --git a/sight/sources/annotated/4HRhg4eUiMo.json b/sight/sources/annotated/4HRhg4eUiMo.json new file mode 100644 index 0000000000000000000000000000000000000000..2024f12a40b37633b66a4d335a4dc55f4bd6e940 --- /dev/null +++ b/sight/sources/annotated/4HRhg4eUiMo.json @@ -0,0 +1,2639 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "Talking about tests, and to be fair, we spend most of our time talking about new jargon that we're using." + }, + { + "text": "But the main goal is to take a binary decision, yes and no." + }, + { + "text": "So just so that we're clear and we make sure that we all speak the same language, let me just remind you what the key words are for tests." + }, + { + "text": "So the first thing is that we split theta in theta 0 and theta 1." + }, + { + "text": "Both are included in theta, and they're disjoint." + }, + { + "text": "OK." + }, + { + "text": "So I have my set of possible parameters." + }, + { + "text": "And then I have theta 0 is here, theta 1 is here, and there might be something that I leave out." + }, + { + "text": "And so what we're doing is we have two hypotheses." + }, + { + "text": "So here's our hypothesis testing problem." + }, + { + "text": "And it's h0 theta belongs to theta 0 versus h1 theta belongs to theta 1." + }, + { + "text": "This guy was called the null, and this guy was called the alternative." + }, + { + "text": "And why we give them special names is because we saw that they have an asymmetric role." + }, + { + "text": "The null represents the status quo, and data is here to bring evidence against this guy." + }, + { + "text": "And we can really never conclude that h0 is true because all we could conclude is that h1 is not true or may not be true." + }, + { + "text": "So that was the first thing." + }, + { + "text": "The second thing was the hypothesis." + }, + { + "text": "The third thing is what is a test?" + }, + { + "text": "Well, psi, it's a statistic." + }, + { + "text": "And it takes the data, and it maps it into 0 or 1." + }, + { + "text": "And I didn't really mention it, but there's something such as called randomized tests, which is, well, if it cannot really make a decision, they might as well flip a coin." + }, + { + "text": "That tends to be biased, but that's really, I mean, think about it in practice." + }, + { + "text": "You probably don't want to make decisions based on flipping a coin." + }, + { + "text": "And so what people typically do, this is happening typically at one specific value." + }, + { + "text": "So rather than flipping a coin for this very specific value, what people typically do is they say, OK, I'm going to side with h0 because that's the most conservative choice I can make." + }, + { + "text": "So in a way, they think of flipping this coin, but always falling on heads." + }, + { + "text": "So associated to this test was something called, well, the rejection region." + }, + { + "text": "And r psi, which is just the set of data, x1, xn, such that psi of x1, xn is equal to 1." + }, + { + "text": "So that means we rejected 0 when the test is 1, and those are the set of data points that actually are going to lead me to reject the test." + }, + { + "text": "OK. Then the things that were actually slightly a little more important and really peculiar to test, specific to test, were the type 1 and type 2 error." + }, + { + "text": "So the type 1 error arises when, so type 1 error is when you reject whereas h0 is correct." + }, + { + "text": "And the type 2 error is the opposite." + }, + { + "text": "So it's failed to reject whereas h1 is correct." + }, + { + "text": "h is correct." + }, + { + "text": "So those are the two types of errors you can make, and we quantify their probability of type 1 error." + }, + { + "text": "So alpha psi is the probability." + }, + { + "text": "So that's the probability of type 1 error." + }, + { + "text": "So psi is just the probability for theta that psi rejects, and that's defined for theta and theta 0." + }, + { + "text": "So for different values of theta 0, so h0 being correct means there exists a theta in theta 0 for which that actually is the right distribution." + }, + { + "text": "So for different values of theta, I might make different errors." + }, + { + "text": "So if you think, for example, about the coin example, if I'm testing if the coin is biased towards heads or biased towards tails, so if I'm testing whether p is larger than 1 half or less than 1 half, then when the true p, let's say h0 is larger than 1 half, when p is equal to 1, it's actually very difficult for me to make a mistake, because I only see heads." + }, + { + "text": "So when p is getting closer to 1 half, I'm going to start making more and more probability there." + }, + { + "text": "And so the type 2 error, so that's the probability of type 2, is denoted by beta psi." + }, + { + "text": "And it's the function that does the opposite, and this time is defined for theta and theta 0 and theta 1." + }, + { + "text": "And finally, we define something called the power pi of psi." + }, + { + "text": "And this time, this is actually a number." + }, + { + "text": "And so this number is equal to the maximum over theta and theta 0." + }, + { + "text": "I mean, that could be a supremum, but think of it as being a maximum of p theta of psi is equal, sorry, that's in 0." + }, + { + "text": "Give me one sec." + }, + { + "text": "No, that's the min." + }, + { + "text": "So this is not making a mistake." + }, + { + "text": "Theta 0 is in theta 1." + }, + { + "text": "So theta is in theta 1, and I conclude 1." + }, + { + "text": "So this is a good thing." + }, + { + "text": "I want this number to be large, and I'm looking at the worst house, what is the smallest value this number can be." + }, + { + "text": "So what I want to show you a little bit is a picture." + }, + { + "text": "So now I'm going to take theta, and think of it as being p. So I'm going to take p for some Bernoulli experiment." + }, + { + "text": "So p can range between 0 and 1, that's for sure." + }, + { + "text": "And what I'm going to try to test is whether p is less than 1 half or larger than 1 half." + }, + { + "text": "So this is going to be, let's say, theta 0, and this guy here is theta 1." + }, + { + "text": "Just trying to give you a picture of what those guys are." + }, + { + "text": "So I have my y-axis." + }, + { + "text": "Now I'm going to start drawing numbers, all these things, this function, this function, and this number are all numbers between 0 and 1." + }, + { + "text": "So now I'm claiming that when I move from left to right, what is my probability of rejecting going to do?" + }, + { + "text": "So what I'm going to plot is the probability under theta." + }, + { + "text": "The first thing I want to plot is the probability under theta that psi is equal to 1." + }, + { + "text": "And let's say psi, think of psi as being just this indicator that square root of n xn bar minus p over square root xn bar, 1 minus xn bar, is larger than some constant c for a properly chosen c. So what we choose is that c is in such a way that at 1 half, when we're testing for 1 half, what we wanted was this number to be equal to alpha, basically." + }, + { + "text": "So we fix this alpha number so that this guy, so if I want alpha of psi of theta less than alpha, given in advance, so think of it as being equal to, say, 5%." + }, + { + "text": "So I'm fixing this number, and I want this to be controlled for all theta and theta 0." + }, + { + "text": "So if you're going to give me this budget, well, I'm actually going to make it equal where I can." + }, + { + "text": "If you're telling me you can make it equal to alpha, we know that if I increase my type 1 error, I'm going to decrease my type 2 error." + }, + { + "text": "If I start putting everyone in jail, or if I start letting everyone go free, that's what we're discussing last time." + }, + { + "text": "So since we have this trade-off, and you're giving me a budget for one guy, I'm just going to max it out." + }, + { + "text": "And where am I going to max it out?" + }, + { + "text": "Exactly at 1 half at the boundary." + }, + { + "text": "So this is going to be 5%." + }, + { + "text": "So what I know is that since alpha of theta is less than alpha for all theta and theta 0, sorry, that's for theta 0, that's where alpha is defined." + }, + { + "text": "So for theta and theta 0, I know that my function is going to look like this." + }, + { + "text": "It's going to be somewhere in this rectangle." + }, + { + "text": "Everybody agrees?" + }, + { + "text": "So this function for this guy is going to look like this." + }, + { + "text": "When I'm at 0, when p is equal to 0, which means I only observe 0's, then I know that p is going to be 0." + }, + { + "text": "And I will certainly not conclude that p is equal to 1." + }, + { + "text": "This test will never conclude that p is equal to 1." + }, + { + "text": "Sorry, that was, yeah." + }, + { + "text": "That p is equal to, that p is lower than 1 half, just because xn bar is going to be equal to 0." + }, + { + "text": "OK, well, this is actually not well-defined." + }, + { + "text": "So maybe I need to do something, put it equal to 0 if xn bar is equal to 0." + }, + { + "text": "So I guess basically I get something which is negative." + }, + { + "text": "And so it's never going to be larger than what I want." + }, + { + "text": "And so here I'm actually starting at 0." + }, + { + "text": "So now this is this function here that increases." + }, + { + "text": "I mean, it should increase smoothly." + }, + { + "text": "This function here is alpha psi of theta, or alpha psi of p, let's say, because we're talking about p. Then it reaches alpha here." + }, + { + "text": "Now when I go on the other side, I'm actually looking at beta." + }, + { + "text": "When I'm on theta 1, the function that matters is the probability of type 2 error, which is beta psi." + }, + { + "text": "And this beta psi is actually going to increase." + }, + { + "text": "So beta psi is what?" + }, + { + "text": "Well, beta psi should also, sorry, that's the probability of being equal to alpha." + }, + { + "text": "So what I'm going to do is I'm going to look at the probability of rejecting." + }, + { + "text": "So let me draw this function all the way." + }, + { + "text": "It's going to look like this." + }, + { + "text": "Now here, if I look at this function here or here, this is the probability under theta that psi is equal to 1." + }, + { + "text": "And we just said that in this region, this function is called alpha psi." + }, + { + "text": "In that region, it's not called alpha psi." + }, + { + "text": "It's not called anything." + }, + { + "text": "It's just the probability of rejection." + }, + { + "text": "So it's not an error." + }, + { + "text": "It's actually what you should be doing." + }, + { + "text": "What we're looking at in this region is 1 minus this guy." + }, + { + "text": "We're looking at the probability of not rejecting." + }, + { + "text": "So I need to actually basically look at 1 minus this thing, which here is going to be 95%." + }, + { + "text": "So I'm going to do 95%." + }, + { + "text": "And this is my probability." + }, + { + "text": "And I'm just basically drawing the symmetric of this guy." + }, + { + "text": "So this here is the probability under theta that psi is equal to 0, which is 1 minus p theta that psi is equal to 1." + }, + { + "text": "So it's just 1 minus the white curve." + }, + { + "text": "And it's actually, by definition, equal to beta psi of theta." + }, + { + "text": "Now, where do I read pi psi?" + }, + { + "text": "What is pi psi on this picture?" + }, + { + "text": "Is pi psi a number or a function?" + }, + { + "text": "It's a number, right?" + }, + { + "text": "It's the minimum of a function." + }, + { + "text": "What is this function?" + }, + { + "text": "It's the probability under theta that theta is equal to 1." + }, + { + "text": "I drew this entire function between theta 0 and theta 1." + }, + { + "text": "I drew this entire white curve." + }, + { + "text": "This is this probability." + }, + { + "text": "Now, I'm saying, look at the smallest value this probability can take on the set theta 1." + }, + { + "text": "What is this?" + }, + { + "text": "This guy." + }, + { + "text": "This is where my pi, this thing here, is pi psi." + }, + { + "text": "And so it's equal to 5%." + }, + { + "text": "So that's for this particular test, because this test is sort of a continuous curve for this psi." + }, + { + "text": "And so if I want to make sure that I'm at 5% when I come to the right of theta 0, if it touches theta 1, then I better have 5% on the other side if the function is continuous." + }, + { + "text": "So basically, if this function is increasing, which will be the case for most tests, then what's going to happen is that, and continuous, then what's going to happen is that the level of the test, which is alpha, is actually going to be equal to the power of the test." + }, + { + "text": "OK?" + }, + { + "text": "Now, there's something I didn't mention, and I'm just mentioning it, pass it by." + }, + { + "text": "Here, I define the power itself." + }, + { + "text": "This function, this entire white curve here, is actually called the power function." + }, + { + "text": "This thing, that's the entire white curve." + }, + { + "text": "And what you could have is tests that have the entire curve, which is dominated by another test." + }, + { + "text": "So here, if I look at this test, and let's assume I can build another test that has this curve." + }, + { + "text": "Let's say it's the same here." + }, + { + "text": "But then here, it looks like this." + }, + { + "text": "What is the power of this test?" + }, + { + "text": "It's the same." + }, + { + "text": "It's 5%, because this point touches here exactly at the same point." + }, + { + "text": "However, for any other value than the worst possible, this guy is doing better than this guy." + }, + { + "text": "Can you see that?" + }, + { + "text": "Having a curve higher on the right-hand side is a good thing, because it means that you tend to reject more when you're actually in H1." + }, + { + "text": "So this guy is definitely better than this guy." + }, + { + "text": "And so what we say in this case is that the test with the dashed line is uniformly more powerful than the other test." + }, + { + "text": "But we're not going to go into those details, because basically, all the tests that we will describe are already the most powerful ones." + }, + { + "text": "In particular, this guy is, there's no such thing." + }, + { + "text": "All the other guys you can come up with are going to actually be below." + }, + { + "text": "So we saw a couple tests, and we saw how to pick this threshold, and we defined those two things." + }, + { + "text": "Yes?" + }, + { + "text": "AUDIENCE 2 But in that case, the down one, if it were also higher in the region of 2 to 0, do you still consider it better?" + }, + { + "text": "PHILIPPE RIGOLLETTIS Because you're given this budget of 5%, right?" + }, + { + "text": "So in this paradigm, where you're given the, actually, if the dashed line was this dashed line, I would still be happy." + }, + { + "text": "I mean, I don't care what this thing does here, as long as it's below 5%." + }, + { + "text": "But here, I'm going to try to discover it, right?" + }, + { + "text": "Think about, again, the drug discovery example." + }, + { + "text": "You're trying to find, let's say you're a scientist, and you're trying to prove that your drug works." + }, + { + "text": "What do you want to see?" + }, + { + "text": "Well, FDA puts on you this constraint that your probability of type 1 error should never exceed 5%." + }, + { + "text": "You're going to work under this assumption." + }, + { + "text": "But what you're going to do is going to try to find a test that will make you find something as often as possible." + }, + { + "text": "And so you're going to max this constraint of 5%, and then you're going to try to make this curve, this curve that means that this is basically, this number here, for any point here, is the probability that you publish your paper." + }, + { + "text": "That's the probability that you can release to market your drug." + }, + { + "text": "That's the probability that it works, right?" + }, + { + "text": "And so you want this curve to be as high as possible." + }, + { + "text": "You want to make sure that if there's evidence in the data that H1 is the truth, you want to squeeze as much of this evidence as possible." + }, + { + "text": "And the test that has the highest possible curve is the most powerful one." + }, + { + "text": "Now, you have to also understand that having two curves that are on top of each other, completely, everywhere, is a rare phenomenon." + }, + { + "text": "It's not always the case that there is a test that's uniformly more powerful than any other test." + }, + { + "text": "It might be that you have some trade-off, that it might be better here, but then you're losing power here." + }, + { + "text": "Things like this." + }, + { + "text": "Well, actually, maybe it should not go down." + }, + { + "text": "But let's say it goes like this, and then maybe this guy goes like this." + }, + { + "text": "Then you have to basically make an educated guess whether you think that the theta you're going to find is here or it's here." + }, + { + "text": "And then you pick a test." + }, + { + "text": "OK?" + }, + { + "text": "Any other question?" + }, + { + "text": "Yes?" + }, + { + "text": "AUDIENCE 2." + }, + { + "text": "What is the derivative of the type 2 error?" + }, + { + "text": "PHILIPPE RIGOLLET." + }, + { + "text": "So the green curve is exactly right." + }, + { + "text": "So that's beta psi of theta." + }, + { + "text": "So it's really the type 2 error, and it's defined only here." + }, + { + "text": "So here, it's not a definition." + }, + { + "text": "It's really just I'm just mapping it to this point." + }, + { + "text": "So it's defined only here, and it's the probability of type 2 error." + }, + { + "text": "So here, it's pretty large, right?" + }, + { + "text": "I'm making it basically as large as I could, because I'm at the boundary." + }, + { + "text": "And that means at the boundary, since the status quo is h0, I'm always going to go for h0 if I don't have any evidence, which means that what's going to pay is the type 2 error that's going to basically pay this." + }, + { + "text": "OK?" + }, + { + "text": "Any other question?" + }, + { + "text": "All right, so let's move on." + }, + { + "text": "So did we do this?" + }, + { + "text": "No, I think we stopped here, right?" + }, + { + "text": "I didn't cover that part." + }, + { + "text": "So as I said, in this paradigm, we're going to actually fix this guy to be something." + }, + { + "text": "And this thing is actually called the level of the test." + }, + { + "text": "I'm sorry, this is again more words." + }, + { + "text": "Actually, good news is that we split it into two lectures." + }, + { + "text": "So we have, what is a test?" + }, + { + "text": "What is a hypothesis?" + }, + { + "text": "What is the null?" + }, + { + "text": "What is the alternative?" + }, + { + "text": "What is the type 1 error?" + }, + { + "text": "What is the type 2 error?" + }, + { + "text": "And now, I'm telling you there's another thing." + }, + { + "text": "So we defined the power, which was some sort of a lower bound on the, or it's 1 minus the upper bound on the type 2 error, basically." + }, + { + "text": "And so it's alternative." + }, + { + "text": "So the power is the smallest probability of rejecting when you're in the null." + }, + { + "text": "And it's alternative when you're in theta 1, right?" + }, + { + "text": "So that's my power." + }, + { + "text": "I looked here, and I looked at the smallest value." + }, + { + "text": "And I can look at this side and say, well, what is the largest probability that I make a type 1 error?" + }, + { + "text": "Again, this largest probability is the level of the test." + }, + { + "text": "OK, so this is alpha equal, by definition, to the maximum for theta and theta 0 of alpha psi of theta." + }, + { + "text": "So here, I just put the level itself." + }, + { + "text": "As you can see here, it essentially says that if I'm of level 5%, I'm also of level 10%." + }, + { + "text": "I'm also of level 15%." + }, + { + "text": "So here, it's really an upper bound." + }, + { + "text": "Whatever you guys want to take, this is what it is." + }, + { + "text": "But as we said, if this number is 4.5%, you're losing in your type 2 error." + }, + { + "text": "So if you're allowed to have, if this maximum here is 4.5%, and FDA told you you can go to 5%, you're losing in your type 2 error." + }, + { + "text": "So you actually want to make sure that this is the 5% that's given to you." + }, + { + "text": "So the way it works is that you give me the alpha." + }, + { + "text": "Then I'm going to go back, pick c that depends on alpha here, so that this thing is actually equal to 5%." + }, + { + "text": "And so, of course, in many instances, we do not know the probability." + }, + { + "text": "We do not know how to compute the probability of type 1 error." + }, + { + "text": "This is a maximum value for the probability of type 1 error." + }, + { + "text": "We don't know how to compute it." + }, + { + "text": "I mean, it might be a very complicated random variable." + }, + { + "text": "Maybe it's a weird binomial." + }, + { + "text": "We could compute it, but it would be painful." + }, + { + "text": "But what we know how to compute is its asymptotic value, which is because of the central limit theorem, convergence and distribution tells me that the probability of type 1 error is basically going towards the probability that some Gaussian is in some region." + }, + { + "text": "And so we're going to compute not the level itself, but the asymptotic level." + }, + { + "text": "So again, that's basically the limit as n goes to infinity of alpha psi of theta." + }, + { + "text": "And then I'm going to make the max here." + }, + { + "text": "OK?" + }, + { + "text": "So how am I going to compute this?" + }, + { + "text": "Well, if I take a test that has rejection region of the form Tn, because it depends on the data, right?" + }, + { + "text": "That's Tn of x1, xn, my observations, larger than some number c. OK?" + }, + { + "text": "Of course, I can almost always write tests like that, except that sometimes there's going to be an absolute value, which essentially means I'm going away from some value." + }, + { + "text": "Maybe actually I'm less than something, but I can always put a negative sign in front of everything." + }, + { + "text": "So this is not without much of generality, right?" + }, + { + "text": "So this includes something that looks like something is larger than the constant, right?" + }, + { + "text": "So that means, which is equivalent to, well, let me write it as Tq." + }, + { + "text": "OK, because then that means that, so that's Tn." + }, + { + "text": "But this actually encompasses the fact that Qn is larger than c, or Qn is less than c, then minus c. So that includes this guy." + }, + { + "text": "That also includes Qn less than c, because this is equivalent to Qn is larger than minus c. Minus Qn is, and so that's going to be my Tn." + }, + { + "text": "So I can actually encode several type of things, OK?" + }, + { + "text": "Rejection regions that, so here in this case, I have a rejection region that looks like this, or a rejection region that looks like this, or a rejection region that looks like this." + }, + { + "text": "OK, and here I don't really represent it for the whole data, but maybe for the average, for example, or the normalized average." + }, + { + "text": "OK, so if I write this, then, yeah." + }, + { + "text": "And in this case, this Tn that shows up is called test statistic." + }, + { + "text": "I mean, this is sort of a, I mean, this is not like set in stone." + }, + { + "text": "Here, for example, Q could be the test statistics." + }, + { + "text": "It doesn't have to be minus Q itself that's the test statistic, right?" + }, + { + "text": "So what is the test statistic?" + }, + { + "text": "Well, it's what you're going to build from your data and then compare to some fixed value, right?" + }, + { + "text": "So in the example we had here, what is our test statistic?" + }, + { + "text": "Well, it's this guy, right?" + }, + { + "text": "This was our test statistic." + }, + { + "text": "And is this thing a statistic?" + }, + { + "text": "What are the criteria for a statistic?" + }, + { + "text": "What is a statistic?" + }, + { + "text": "I know you know the answer." + }, + { + "text": "AUDIENCE MEMBER 2." + }, + { + "text": "Is it a measurable function?" + }, + { + "text": "PROFESSOR PHILIPPE RIGOLLET." + }, + { + "text": "Yeah, it's a measurable function of the data that does not depend on the parameter." + }, + { + "text": "Is this guy a statistic?" + }, + { + "text": "AUDIENCE MEMBER 3." + }, + { + "text": "Yes, he is." + }, + { + "text": "PROFESSOR PHILIPPE RIGOLLET." + }, + { + "text": "Let's think again." + }, + { + "text": "When I implemented the test, what did I do?" + }, + { + "text": "I was able to compute my test." + }, + { + "text": "My test did not depend on some unknown parameter." + }, + { + "text": "How did we do it?" + }, + { + "text": "We just plugged in 0.5 here." + }, + { + "text": "Remember?" + }, + { + "text": "That was the value for which we computed it, because under h0, that was the value we're seeing." + }, + { + "text": "And if theta 0 is actually an entire set, I'm just going to take the value that's the closest to h1." + }, + { + "text": "We'll see that in a second." + }, + { + "text": "I mean, I did not guarantee that to you." + }, + { + "text": "But just taking the worst type 1 error and bounding it by alpha is equivalent to taking p and taking the value of p that's the closest to theta 1, which is completely intuitive." + }, + { + "text": "The worst type 1 error is going to be attained for the p that's the closest to the alternative." + }, + { + "text": "So even if the null is actually just an entire set, it's as if it was just the point that's the closest to the alternative." + }, + { + "text": "So now we can compute this, because there's no unknown parameters that shows up." + }, + { + "text": "We replaced p by 0.5." + }, + { + "text": "And so that was our test statistic." + }, + { + "text": "So when you're building a test, you want to first build a test statistic and then see what threshold you should be getting." + }, + { + "text": "So now let's go back to our example where we have x1, xn." + }, + { + "text": "They're iid Bernoulli p. And I want to test if p is 1 half versus p not equal to 1 half, which as I said is what you want to do if you want to test if a coin is fair." + }, + { + "text": "And so here I'm going to build a test statistic." + }, + { + "text": "And we concluded last time that what do we want for this statistic?" + }, + { + "text": "We want it to have a distribution which under the null does not depend on the parameters, a distribution that I can actually compute quintiles of." + }, + { + "text": "So what we did is we said, well, if I look at the central limit theorem tells me that square root of n xn bar minus p divided by." + }, + { + "text": "So if I do central limit theorem plus Slutsky, for example, I'm going to have square root." + }, + { + "text": "And we've had this discussion whether we want to use Slutsky or not here." + }, + { + "text": "But let's assume we're taking Slutsky wherever we can." + }, + { + "text": "So this thing tells me that by the central limit theorem as n goes to infinity, this thing converges in distribution to some n 0, 1." + }, + { + "text": "Now as we said, this guy is not something we know." + }, + { + "text": "But under the null, we actually know it." + }, + { + "text": "And we can actually replace it by 1 half." + }, + { + "text": "So this thing holds under h0." + }, + { + "text": "When I write under h0, it means when this is the truth." + }, + { + "text": "So now I have something that converges to something that has no dependence on anything I don't know." + }, + { + "text": "And in particular, if you have any statistics textbook, which you don't because I didn't require one, you should be thankful because this thing costs $250." + }, + { + "text": "This thing's actually, if you look at the back, you actually have a table for a standard Gaussian." + }, + { + "text": "I could have anything else here." + }, + { + "text": "I could have an exponential distribution." + }, + { + "text": "I could have a, I don't know, a, well, we'll see the chi-square distribution in a minute." + }, + { + "text": "Any distribution from which you can actually see a table that somebody actually computed this thing for which you can actually draw the PDF and start computing whatever probability you want on them, then this is what you want to see at the right-hand side." + }, + { + "text": "This is any distribution." + }, + { + "text": "It's called pivotal." + }, + { + "text": "I think we've mentioned that before." + }, + { + "text": "Pivotal means it does not depend on anything that you don't know." + }, + { + "text": "And maybe it's easy to compute those things." + }, + { + "text": "Probably, typically, you need a computer to simulate them for you because computing probabilities for Gaussians is not an easy thing." + }, + { + "text": "We don't know how to solve those integrals exactly." + }, + { + "text": "We have to do it numerically." + }, + { + "text": "OK, so now I want to do this test." + }, + { + "text": "My test statistic will be declared to be what?" + }, + { + "text": "Well, I'm going to reject if what is larger than some number?" + }, + { + "text": "The absolute value of this guy." + }, + { + "text": "So my test statistic is going to be square root of n minus 0.5 divided by square root of xn bar 1 minus xn bar." + }, + { + "text": "That's my test statistic, absolute value of this guy, because I want to reject either when this guy is too large or when this guy is too small." + }, + { + "text": "I don't know ahead whether I'm going to see p larger than 1 half or less than 1 half." + }, + { + "text": "So now I need to compute c such that the probability that tn is lower than c. So that's what?" + }, + { + "text": "That's the probability under p, which is unknown." + }, + { + "text": "I want this probability to be less than some level alpha asymptotically." + }, + { + "text": "So I want the limit of this guy to be less than alpha, and that's the level of my test." + }, + { + "text": "So that's the given level." + }, + { + "text": "So I want this thing to happen." + }, + { + "text": "Now what I know is that this limit, actually, I should say given asymptotic level." + }, + { + "text": "So what is this thing?" + }, + { + "text": "Well, OK, that's the probability that something that looks like under p. So under p, this guy, so what I know is that tn is square root of n minus xn bar minus 0.5 divided by square root of xn bar 1 minus xn bar exceeds." + }, + { + "text": "Is this true that as n goes to infinity, this probability is the same as the probability that the absolute value of a Gaussian exceeds c of a standard Gaussian?" + }, + { + "text": "Is this true?" + }, + { + "text": "Yeah, so you're saying that this, as n becomes large enough, this should be the probability that some absolute value of n0,1 exceeds c, right?" + }, + { + "text": "So I claim that this is not correct." + }, + { + "text": "Somebody tell me why." + }, + { + "text": "Even in the limit, it's not correct?" + }, + { + "text": "Even in the limit, it's not correct." + }, + { + "text": "OK." + }, + { + "text": "So what do you see?" + }, + { + "text": "It's because at the beginning, we picked the worst possible true parameter, 0.5, right?" + }, + { + "text": "So we don't actually know that this 0.5 is the least." + }, + { + "text": "Exactly, right?" + }, + { + "text": "So we picked this 0.5 here, but this is for any p, right?" + }, + { + "text": "But what is the only p I can get?" + }, + { + "text": "So what I want is that this is true for all p in theta 0." + }, + { + "text": "But the only p that's in theta 0 is actually p is equal to 0.5." + }, + { + "text": "So yes, what you said was true, but it required to specify p to be equal to 0.5." + }, + { + "text": "So this, in general, is not true." + }, + { + "text": "But it happens to be true if p belongs to theta 0, which is strictly equivalent to p is equal to 0.5, right?" + }, + { + "text": "Theta 0 is really just this one point, 0.5." + }, + { + "text": "OK, so now this becomes true." + }, + { + "text": "And so what I need to do is to find c such that this guy is equal to what?" + }, + { + "text": "I mean, let's just follow, right?" + }, + { + "text": "So I want this to be less than alpha." + }, + { + "text": "But then we see that this was equal to this, which is equal to this." + }, + { + "text": "So all I want is that this guy is less than alpha." + }, + { + "text": "But we said we might as well just make it equal to alpha if you allow me to make it as big as I want, as long as it's less than alpha." + }, + { + "text": "So this is a true statement." + }, + { + "text": "But it's if under this condition, right?" + }, + { + "text": "So I'm going to set it equal to alpha." + }, + { + "text": "And then I'm going to try to solve for c. OK, so what I'm looking for is a c such that if I draw a standard Gaussian, so that's PDF of some n0,1, I want the probability that the absolute value of my Gaussian exceeding this guy." + }, + { + "text": "So that means being either here or here." + }, + { + "text": "So that's minus c and c. I want the sum of those two things to be equal to alpha." + }, + { + "text": "So I want the sum of these areas to equal alpha." + }, + { + "text": "So by symmetry, each of them should be equal to alpha over 2." + }, + { + "text": "And so what I'm looking for is c such that the probability that my n0,1 exceeds c, which is just this area to the right now, equals alpha, which is equivalent to taking c, which is q equals alpha over 2." + }, + { + "text": "And that's q alpha over 2 by definition of q alpha over 2." + }, + { + "text": "That's just what q alpha over 2 is." + }, + { + "text": "And that's what the tables at the back of the book give you." + }, + { + "text": "Who has already seen a table for Gaussian probabilities?" + }, + { + "text": "All right." + }, + { + "text": "What it does is just a table." + }, + { + "text": "I mean, it's pretty ancient, right?" + }, + { + "text": "I mean, of course, you can actually ask Google to do it for you now." + }, + { + "text": "It's basically standard issue." + }, + { + "text": "But back in the day, they actually had to look at tables." + }, + { + "text": "And since the values alphas were pretty standard, the values alpha that people were requesting were typically 1%, 5%, 10%." + }, + { + "text": "All you could do is to compute these different values for different values of alpha." + }, + { + "text": "That was it." + }, + { + "text": "So that's really not much to give you." + }, + { + "text": "So for the Gaussian, I can tell you that alpha is equal to, if alpha is equal to 5%, then q alpha over 2, q 2.5% is equal to 1.96%." + }, + { + "text": "So those are just fixed numbers that are functions of the Gaussian." + }, + { + "text": "All right, so everybody agrees?" + }, + { + "text": "We've done that before for our confidence intervals." + }, + { + "text": "And so now we know that if I actually plug in this guy to be q alpha over 2, then this limit is actually equal to alpha." + }, + { + "text": "And so now I've actually constrained this." + }, + { + "text": "So q alpha over 2 here is, for alpha equals 5%, as I said, is 1.96." + }, + { + "text": "So in the example 1, the number that we found was 3.54, I think, or something like that, 3.55 for t. So if we scroll back very quickly, 3.45." + }, + { + "text": "That was example 1." + }, + { + "text": "Example 2, negative 0.77." + }, + { + "text": "So if I look at t, n, in example 1, tn was just the absolute value of 3.45, which don't pull out your calculators, is equal to 3.45." + }, + { + "text": "Example 2, absolute value of negative 0.77 was equal to 0.77." + }, + { + "text": "And so all I need to check is, is this number larger or smaller than 1.96?" + }, + { + "text": "That's what my test ends up being." + }, + { + "text": "So in example 1, 3.45 being larger than 1.96, that means that I reject." + }, + { + "text": "Fairness of my coins in example 2, 0.77 being smaller than 1.96, what do I do?" + }, + { + "text": "I fail to reject." + }, + { + "text": "OK?" + }, + { + "text": "So here's a question." + }, + { + "text": "In example 1, for what level alpha would psi alpha, what is the?" + }, + { + "text": "So here, what's going to happen if I start decreasing my level?" + }, + { + "text": "When I decrease my level, I'm actually making this area smaller and smaller, which means that I push the c to the right." + }, + { + "text": "So now I'm asking, what is the smallest c I should pick so that now I actually do not reject h0?" + }, + { + "text": "What is the smallest c I should be taking?" + }, + { + "text": "Here." + }, + { + "text": "What is the smallest c?" + }, + { + "text": "So c here in the example I gave you for 5% was 1.96." + }, + { + "text": "What is the smallest c I should be taking so that now this inequality is reversed?" + }, + { + "text": "3.45." + }, + { + "text": "I ask only trivial questions." + }, + { + "text": "Don't be worried." + }, + { + "text": "So 3.45 is the smallest c that I'm actually willing to tolerate." + }, + { + "text": "So let's say this was my 5%." + }, + { + "text": "If this was 2.5, if alpha here, let's say in this picture, alpha is 5%, that means maybe I need to push here." + }, + { + "text": "And this number should be what?" + }, + { + "text": "So this is going to be 1.96." + }, + { + "text": "And this number here is going to be 3.45, clearly to scale." + }, + { + "text": "And so now what I want to ask you is, well, there's two ways I can understand this number 3.45." + }, + { + "text": "It is the number 3.45." + }, + { + "text": "But I can also try to understand, what is the area to the right of this guy?" + }, + { + "text": "And if I understand what the area to the right of this guy is, this is actually some alpha prime over 2." + }, + { + "text": "And that means that if I actually fix this level, alpha prime, that would be exactly the tipping point at which I would go from accepting to rejecting." + }, + { + "text": "So I know in terms of absolute thresholds, 3.45 is the trivial answer to the question." + }, + { + "text": "That's the tipping point, because I'm comparing a number to 3.45." + }, + { + "text": "But now if I try to map this back and understand what level would have been given me this particular tipping point, that's a number between 0 and 1." + }, + { + "text": "The smaller the number, the larger this number here, which means that the more evidence I have in my data against h0." + }, + { + "text": "And so this number is actually something called the p-value." + }, + { + "text": "And so same for example 2." + }, + { + "text": "There's the tipping point, alpha, at which I go from feeling to reject to rejecting." + }, + { + "text": "And that's exactly the number, the area under the curve, such that here I see 0.77." + }, + { + "text": "And this is this alpha prime prime over 2." + }, + { + "text": "And this number is clearly, alpha prime prime is clearly larger than 5%." + }, + { + "text": "So what's the advantage of thinking and mapping back these numbers?" + }, + { + "text": "Well, now I'm actually going to spit out some number which is between 0 and 1." + }, + { + "text": "And that should be the only scale you should have in mind." + }, + { + "text": "Remember we discussed that last time." + }, + { + "text": "Well, if I actually spit out a number which is 3.45, maybe you can try to think, is 3.45 a large number for a Gaussian?" + }, + { + "text": "That's a number." + }, + { + "text": "But if I had another random variable that was not Gaussian, maybe it was a double exponential, you would have to have another scale in your mind." + }, + { + "text": "Is 3.45 a large number for the large, so large that it's unlikely to come from a double exponential?" + }, + { + "text": "If I had a gamma distribution, I can think of any distribution." + }, + { + "text": "And then that means for each distribution, you would have to have a scale in mind." + }, + { + "text": "So of course, you can have the Gaussian scale in mind." + }, + { + "text": "I mean, I have the Gaussian scale in mind." + }, + { + "text": "But then if I map it back into this number between 0 and 1, all the distributions play the same role." + }, + { + "text": "So whether I'm talking about if my limiting distribution is normal or exponential or gamma or whatever you want, for all these guys, I'm just going to map it into one number between 0 and 1." + }, + { + "text": "Small number means lots of evidence against h1." + }, + { + "text": "Large number means lots of evidence against h0." + }, + { + "text": "Small number means very few evidence against h0." + }, + { + "text": "And this is the only number you need to keep in mind." + }, + { + "text": "And the question is, am I willing to tolerate this number between 5%, 6% or maybe 10%, 12%?" + }, + { + "text": "And this is the only scale you have to have in mind." + }, + { + "text": "And this scale is the scale of p-values." + }, + { + "text": "So the p-value is the tipping point in terms of alpha." + }, + { + "text": "In words, I can make it formal, because tipping point, as far as I know, is not a mathematical term." + }, + { + "text": "So a p-value of a test is the smallest, potentially asymptotic level, if I talk about an asymptotic p-value." + }, + { + "text": "And that's what we do when we talk about central limit theorem, at which the test rejects h0." + }, + { + "text": "If I were to go any smaller, I would fail to reject." + }, + { + "text": "The smaller the level, the less likely it is for me to reject." + }, + { + "text": "And if I were to go any smaller, I would start failing to reject." + }, + { + "text": "And so it is a random number." + }, + { + "text": "It depends on what I actually observe." + }, + { + "text": "So here, of course, I instantiated those two numbers, 3.45 and 0.77, as realizations of random variables." + }, + { + "text": "But if you think of those as being the random numbers before I see my data, this was a random number." + }, + { + "text": "And therefore, the area under the curve to the right of it is also a random area." + }, + { + "text": "If this thing fluctuates, then the area under the curve fluctuates." + }, + { + "text": "And that's what the p-value is." + }, + { + "text": "That's what John Oliver talks about when he talks about p-hacking." + }, + { + "text": "And so we talked about this in the first lecture." + }, + { + "text": "So p-hacking is, how do I do?" + }, + { + "text": "Oh, if I'm a scientist, do I want to see a small p-value or a large p-value?" + }, + { + "text": "Small, right?" + }, + { + "text": "Scientists want to see small p-values, because small p-values equals rejecting, which equals discovery, which equals publication, which equals promotion." + }, + { + "text": "So that's what people want to see." + }, + { + "text": "So people are tempted to see small p-values." + }, + { + "text": "And what's called p-hacking is, well, find a way to cheat." + }, + { + "text": "Maybe look at your data, formulate your hypothesis in such a way that you will actually have a smaller p-value than you should have." + }, + { + "text": "So here, for example, there's one thing I did not insist on, because again, this is not a particular course in statistical thinking." + }, + { + "text": "But one thing that we implicitly did was set those theta 0 and theta 1 ahead of time." + }, + { + "text": "I fixed them, and I'm trying to test this." + }, + { + "text": "This is to be contrasted with the following approach." + }, + { + "text": "I draw my data." + }, + { + "text": "So I draw." + }, + { + "text": "I run this experiment, which is probably going to get me a publication in Nature." + }, + { + "text": "I'm trying to test if a coin is fair." + }, + { + "text": "And I draw my data, and I see that there's 13 out of 30 of my observations that are heads." + }, + { + "text": "That means that from this data, it looks like p is less than 1 half." + }, + { + "text": "So if I look at this data and then decide that my alternative is not p not equal to 1 half, but rather p less than 1 half, that's p-hacking." + }, + { + "text": "I'm actually making my p-value strictly smaller by first looking at the data and then deciding what my alternative is going to be." + }, + { + "text": "And that's cheating, because all the things we did were assuming that this 0.5 or d alternative was actually a fix." + }, + { + "text": "Everything was deterministic." + }, + { + "text": "The only randomness came from the data." + }, + { + "text": "But if I start looking at the data and designing my experiment or my alternatives and null hypothesis based on the data, it's as if I started putting randomness all over the place." + }, + { + "text": "And then I cannot control it, because I don't know how it just intermingles with each other." + }, + { + "text": "All right." + }, + { + "text": "So that was for the John Oliver moment." + }, + { + "text": "So the p-value is nice." + }, + { + "text": "So maybe I mentioned that before." + }, + { + "text": "My wife works in market research." + }, + { + "text": "And maybe every two years, she seems to run into a statistician in the hallway." + }, + { + "text": "And she comes home and says, what is a p-value again?" + }, + { + "text": "And for her, a p-value is just the number is in an Excel spreadsheet." + }, + { + "text": "And actually, small equals good and large equals bad." + }, + { + "text": "And that's all she needs to know at this point." + }, + { + "text": "Actually, they do the job for her." + }, + { + "text": "Small is green." + }, + { + "text": "Large is red." + }, + { + "text": "And so for her, a p-value is just green or red." + }, + { + "text": "But so what she's really implicitly doing with this color code is just applying the golden rule." + }, + { + "text": "What the statisticians do for her in the Excel spreadsheet is that they take the numbers for the p-values that are less than some fixed level." + }, + { + "text": "So depending on the field in which she works, so she works for pharmaceutical companies, so the p-values are typically compared." + }, + { + "text": "The tests are usually performed at level 1% rather than 5%." + }, + { + "text": "So 5% is maybe your gold standard if you're doing sociology or trying to, I don't know, release a new blueberry flavor for your toothpaste, like something that's not going to change the life of people." + }, + { + "text": "Maybe you're going to run at 5%." + }, + { + "text": "It's OK to make a mistake." + }, + { + "text": "People are just going to feel gross, but that's about it." + }, + { + "text": "Whereas here, if you have this p-value which is less than 1%, it might be more important for some drug discovery, for example." + }, + { + "text": "And so let's say you run at 1%." + }, + { + "text": "And so what they do in this Excel spreadsheet is that all the numbers that are below 1% show up in green, and all the numbers that are above 1% show up in red." + }, + { + "text": "And that's it." + }, + { + "text": "That's just applying the golden rule." + }, + { + "text": "If the number is green, reject." + }, + { + "text": "If the number is red, fail to reject." + }, + { + "text": "OK?" + }, + { + "text": "Yeah?" + }, + { + "text": "So going back to the example of the previous prior example where you can achieve by looking at your data and then formulating, say, a theta 1 to be p less than 1%." + }, + { + "text": "Yeah." + }, + { + "text": "So how would you achieve your goal by changing the theta 1?" + }, + { + "text": "You mean by achieving my goal?" + }, + { + "text": "You mean letting ethics aside, right?" + }, + { + "text": "Yeah." + }, + { + "text": "You want to be published." + }, + { + "text": "So OK." + }, + { + "text": "So let me teach you how." + }, + { + "text": "Well, here, what do you do?" + }, + { + "text": "You want to, at the end of the day, a test is only telling you whether you found evidence in your data that H1 was more likely than H0, basically." + }, + { + "text": "How do you make H1 more likely?" + }, + { + "text": "Well, you just basically target H1 to be what the data is going to make it more likely to be." + }, + { + "text": "All right?" + }, + { + "text": "So if, for example, I say H1 can be on both sides, then my data is going to have to take into account fluctuations on both sides." + }, + { + "text": "And I'm going to lose a factor of 2 somewhere because things are not symmetric." + }, + { + "text": "Here is the ultimate way of making this work." + }, + { + "text": "I'm going back to my example of flipping coins." + }, + { + "text": "And now, so here, what I did is I said, oh, this number 0.43 is actually smaller than 0.5." + }, + { + "text": "So I'm just going to test whether I'm 0.5 or I'm less than 0.5." + }, + { + "text": "But here is something that I can promise you I did not make the computation will reject." + }, + { + "text": "OK, so here, this one actually, yeah, this one fails to reject, right?" + }, + { + "text": "So here is one that will certainly reject." + }, + { + "text": "H0 is 0.5. p is 0.5." + }, + { + "text": "H1, p is 0.43." + }, + { + "text": "OK?" + }, + { + "text": "Now, you can try." + }, + { + "text": "But I can promise you that your data will tell you that H1 is the right one." + }, + { + "text": "OK?" + }, + { + "text": "I mean, you can check very quickly that this is really extremely likely to happen, right?" + }, + { + "text": "And so actually, what am I?" + }, + { + "text": "No, actually, that's not true." + }, + { + "text": "OK. Because here, the test that I derive that's based on this kind of stuff, right?" + }, + { + "text": "Here, at some point, somewhere, under some layers, I assume that all our tests are going to have this form." + }, + { + "text": "But here, this is only when you're trying to test one region versus another region next to it, or one point versus a region around it, or something like this." + }, + { + "text": "Whereas for this guy, there's another test I could come up with, which is, what is the probability that I get 0.43?" + }, + { + "text": "And what is the probability that I get 0.5?" + }, + { + "text": "Now, what I'm going to do is I'm going to just conclude it's whichever has the largest probability." + }, + { + "text": "Then maybe I'm going to have to make some adjustments so that the level is actually 5%." + }, + { + "text": "But I can make this happen." + }, + { + "text": "I can make the level be 5% and always conclude this guy, but I would have to use a different test." + }, + { + "text": "Now, the test that I described, again, those t and larger than c are built in to be tests that are sort of resilient to this kind of manipulations, because they're sort of oblivious towards what the alternative looks like." + }, + { + "text": "I mean, they're just saying it's either to the left or to the right, but whether it's a point or an entire half line doesn't matter." + }, + { + "text": "So if you try to look at your data and just put the data itself into your hypothesis testing problem, then you're failing the statistical principle." + }, + { + "text": "And that's what people are doing, right?" + }, + { + "text": "I mean, how can I check?" + }, + { + "text": "I mean, of course, here it's going to be pretty blatant if you publish a paper that looks like this." + }, + { + "text": "But there's ways to do it differently, right?" + }, + { + "text": "For example, one way to do it is to just do more." + }, + { + "text": "So typically, what people do is they do multiple hypothesis testing." + }, + { + "text": "They're doing 100 tests at a time." + }, + { + "text": "Then you have random fluctuations every time." + }, + { + "text": "And so they just pick the one that has the random fluctuations that go their way." + }, + { + "text": "I mean, sometimes it's going in your way, and sometimes it's going the opposite way." + }, + { + "text": "So you just pick the one that works for you." + }, + { + "text": "We'll talk about multiple hypothesis testing soon if you want to increase your publication counts." + }, + { + "text": "There's actually papers." + }, + { + "text": "I think it was big news, there's some papers, I think it's psychology or psychometrics papers, that actually refuse to publish p-values now." + }, + { + "text": "All right, where were we?" + }, + { + "text": "OK, here's the golden rule." + }, + { + "text": "So one thing that I'd like to show is this thing, just so you know how you apply the golden rule and how you apply the standard test." + }, + { + "text": "So the standard paradigm is the following." + }, + { + "text": "You have a black box, which is your test." + }, + { + "text": "For my wife, this is the fourth floor of the building." + }, + { + "text": "That's where the statisticians sit." + }, + { + "text": "What she sends there is data, let's say x1, xn." + }, + { + "text": "And she says, well, this one is about toothpaste, so here's a level." + }, + { + "text": "Let's say 5%." + }, + { + "text": "What the fourth floor brings back is an answer, yes, no." + }, + { + "text": "Green, red, just an answer." + }, + { + "text": "So that's the standard testing." + }, + { + "text": "You just feed it the data and the level at which you want to perform the test, maybe asymptotic, and it spits out a yes, no answer." + }, + { + "text": "What p-value does, you just feed it the data itself." + }, + { + "text": "And what it spits out is the p-value." + }, + { + "text": "And now, it's just up to you." + }, + { + "text": "I mean, hopefully, your brain has the computational power of deciding whether a number is larger or smaller than 5% without having to call the statisticians for this." + }, + { + "text": "And that's what it does." + }, + { + "text": "So now, we're all on one scale." + }, + { + "text": "Now, if you actually, I see some of you nodding when I talk about p-hacking." + }, + { + "text": "So that means you've seen p-values." + }, + { + "text": "If you've seen more than 100 p-values in your life, you have an entire scale." + }, + { + "text": "A good p-value is less than 10 to the minus 4." + }, + { + "text": "That's the ultimate sweet spot." + }, + { + "text": "Actually, statistical software spit out an output which says less than 10 to the minus 4." + }, + { + "text": "But then, maybe you want a p-value." + }, + { + "text": "If I tell you my p-value was 4.65, then I will say you've been doing some p-hacking until you found a number that was below 5%." + }, + { + "text": "That's typically what people will do." + }, + { + "text": "But if you're doing the test, if you're saying, I published my result." + }, + { + "text": "My test at 5% said yes, that means that maybe your p-value was 4.99, or your p-value was 10 to the minus 4." + }, + { + "text": "I will never know." + }, + { + "text": "I will never know how much evidence you had against the null." + }, + { + "text": "But if you tell me what the p-value is, I can make my own decision." + }, + { + "text": "I don't have to tell me whether it's a yes." + }, + { + "text": "No, you tell me it's 4.99." + }, + { + "text": "I'm going to say, well, maybe yes, but I'm going to take it with a grain of salt." + }, + { + "text": "And so that's why p-values are good numbers to have in mind." + }, + { + "text": "Now, I show it as if it was an old trick that you start mastering when you're 45 years old." + }, + { + "text": "No, it's just how small is the number between 0 and 1." + }, + { + "text": "That's really what you need to know." + }, + { + "text": "Maybe on the log scale, if it's 10 to the minus 1, 10 to the minus 2, 10 to the minus 3, et cetera, that's probably the extent of the mastery here." + }, + { + "text": "So this traditional standard paradigm that I showed is actually commonly referred to as the Neyman-Pearson paradigm." + }, + { + "text": "So here it says Neyman-Pearson's theory." + }, + { + "text": "So there's an entire theory that comes with it, but it's really a paradigm." + }, + { + "text": "It's a way of thinking about hypothesis testing that says, well, if I'm not going to be able to optimize both my type 1 and type 2 error, I'm actually going to lock in my type 1 error below some level and just minimize the type 2 error under this constraint." + }, + { + "text": "That's what the Neyman-Pearson paradigm is." + }, + { + "text": "And it sort of makes sense for hypothesis testing problems." + }, + { + "text": "If you were doing some other applications with multi-objective optimization, you would maybe come up with something different." + }, + { + "text": "For example, machine learning is not performing typically under Neyman-Pearson paradigm." + }, + { + "text": "So if you do spam filtering, you could say, well, I want to constrain the probability as much as I can of taking somebody's important emails and throwing them out as spam and, under this constraint, not send too much spam to that person." + }, + { + "text": "That sort of makes sense for spams." + }, + { + "text": "Now, if you're labeling cats versus dogs, it's probably not like you want to make sure that no more than 5% of the dogs are labeled cat." + }, + { + "text": "Because it doesn't matter." + }, + { + "text": "So what you typically do is you just sum up the two types of error you can make, and you minimize the sum without putting any more weight on one or the other." + }, + { + "text": "So here's an example where doing a binary decision, one or two of the errors you can make, you don't have to actually be like that." + }, + { + "text": "So this example here, I did not." + }, + { + "text": "The trivial test, psi is equal to 0." + }, + { + "text": "What was it in the US trial court example?" + }, + { + "text": "What is psi equal to 0?" + }, + { + "text": "I was concluding all ways to the null." + }, + { + "text": "What was the null?" + }, + { + "text": "Innocent, right?" + }, + { + "text": "That's the status quo." + }, + { + "text": "So that means that this guy never rejects a 0." + }, + { + "text": "Everybody's going away free." + }, + { + "text": "So you're sure you're not actually going against the Constitution because alpha is 0%, which is certainly less than 5%." + }, + { + "text": "But the power, the fact that a lot of criminals go back outside in the free world is actually formulated in terms of low power, which in this case is actually 0." + }, + { + "text": "Again, the power is a number between 0 and 1." + }, + { + "text": "Close to 0, good." + }, + { + "text": "Close to 1, bad." + }, + { + "text": "Now, what is the definition of the p-value?" + }, + { + "text": "That's going to be something." + }, + { + "text": "Mouthful, right?" + }, + { + "text": "The definition of the p-value is a mouthful." + }, + { + "text": "It's really the tipping point." + }, + { + "text": "It is the smallest level at which blah, blah, blah, blah." + }, + { + "text": "It's complicated to remember it." + }, + { + "text": "Now, I think that by my sixth explanation, my wife, after saying, oh, so it's the probability of making an error, I said, yeah, that's the probability of making an error." + }, + { + "text": "Because of course, she can think probability of making an error, small, good, large, bad." + }, + { + "text": "So that's actually a good way to remember." + }, + { + "text": "I'm pretty sure that at least 50% of people using p-values out there think that the p-value is the probability of making an error." + }, + { + "text": "Now, for all matters of purposes, if your goal is to just threshold the p-value, this is OK to have this in mind." + }, + { + "text": "But when it comes, at least until December 22, I would recommend trying to actually memorize the right definition for the p-value." + }, + { + "text": "OK?" + }, + { + "text": "OK." + }, + { + "text": "So the idea, again, is fix the level and try to optimize the power." + }, + { + "text": "So we're going to try to compute some p-values from now on." + }, + { + "text": "How do you compute the p-value?" + }, + { + "text": "Well, you can actually see it from this picture over there." + }, + { + "text": "One thing I didn't show on this picture, here was my q alpha over 2 that had alpha here, alpha over 2 here, right?" + }, + { + "text": "That was my q alpha over 2." + }, + { + "text": "And I said, if tn is to the right of this guy, I'm going to reject." + }, + { + "text": "If tn is to the left of this guy, I'm going to fail to reject." + }, + { + "text": "OK?" + }, + { + "text": "Pictorially, you can actually represent the p-value." + }, + { + "text": "It's when I replace this guy by tn itself." + }, + { + "text": "Sorry, that's p-value over 2." + }, + { + "text": "No, actually, that's p-value." + }, + { + "text": "So let me just keep it like that and put the absolute value here." + }, + { + "text": "OK?" + }, + { + "text": "So if you replace the role of q alpha over 2 by your test statistic, this is what the area under the curve is actually the p-value itself up to scaling, because of the symmetric thing." + }, + { + "text": "OK?" + }, + { + "text": "So there's a good way to see pictorially what the p-value is." + }, + { + "text": "It's just the probability that some Gaussians, which is the probability that some absolute value of n0,1 exceeds tn." + }, + { + "text": "Right?" + }, + { + "text": "That's what the p-value is." + }, + { + "text": "Now, this guy has nothing to do with this guy." + }, + { + "text": "So this is really just 1 minus the Gaussian CDF of tn." + }, + { + "text": "And that's it." + }, + { + "text": "So that's how I would compute p-values." + }, + { + "text": "Now, as I said, the p-value is a beauty, because you don't have to understand the fact that your limiting distribution is a Gaussian." + }, + { + "text": "Right?" + }, + { + "text": "It's already factored in this construction." + }, + { + "text": "The fact that I'm actually looking at this cumulative distribution function of a standard Gaussian makes my p-value automatically adjust to what the limiting distribution is." + }, + { + "text": "And if this was the cumulative distribution function of a exponential, I would just have a different function here denoted by f, for example." + }, + { + "text": "And I would just compute a different value." + }, + { + "text": "But in the end, regardless of what the limiting value is, my p-value would still be a number between 0 and 1." + }, + { + "text": "And so to illustrate that, let's look at other weird distributions that we could get in place of the standard Gaussian." + }, + { + "text": "And we're not going to see many, but we'll see one." + }, + { + "text": "And it's not called the chi-squared distribution." + }, + { + "text": "It's actually called the student's distribution, but it involves the chi-squared distribution as a building block." + }, + { + "text": "So I don't know if my phonetics are not really right there, so I try to say, well, it's chi-squared." + }, + { + "text": "Maybe it's chi-squared in Canada." + }, + { + "text": "Who knows?" + }, + { + "text": "So for a positive integer, so there's only one parameter." + }, + { + "text": "So for the Gaussian, you have two parameters, which are mu and sigma squared." + }, + { + "text": "Those are real numbers." + }, + { + "text": "Sigma squared is positive." + }, + { + "text": "Here, I have one integer parameter." + }, + { + "text": "Then the distribution, the chi-squared distribution with d degrees of freedom." + }, + { + "text": "So the parameter is called a degree of freedom, just like mu is called the expected value, and sigma squared is called the variance." + }, + { + "text": "So it's called degrees of freedom." + }, + { + "text": "You don't have to really understand why." + }, + { + "text": "So that's the law that you would get." + }, + { + "text": "That's the random variable you would get if you were to sum d squares of independent standard Gaussians." + }, + { + "text": "So I take the square of an independent random Gaussian." + }, + { + "text": "I take another one." + }, + { + "text": "I sum them, and that's a chi-squared with two degrees of freedom." + }, + { + "text": "That's how you get it." + }, + { + "text": "Now, I could define it using its probability density function." + }, + { + "text": "After all, this is the sum of positive random variables." + }, + { + "text": "It is a positive random variable." + }, + { + "text": "It has a density on the positive real line." + }, + { + "text": "And the PDF of chi-squared, PDF of chi-squared with d degrees of freedom is what?" + }, + { + "text": "Well, it's fd of x is x to the d over 2 minus 1, e to the minus x over 2." + }, + { + "text": "And then here, I have a gamma of d over 2, and the other one is, I think, 2 to the d over 2 minus 1." + }, + { + "text": "No, 2 to the d over 2." + }, + { + "text": "That's what it is." + }, + { + "text": "That's the density." + }, + { + "text": "If you are very good at probability, you can make the change of variable and write your Jacobian and do all this stuff and actually check that this is true." + }, + { + "text": "I do not recommend doing that." + }, + { + "text": "So this is the density, but it's better understood like that, at thinking of just something that you built from standard Gaussian." + }, + { + "text": "So for example, an example of a chi-squared with two degrees of freedom is actually the following thing." + }, + { + "text": "Let's assume I have a target like this." + }, + { + "text": "And I don't aim very well, and I'm trying to hit the center." + }, + { + "text": "And I'm going to have maybe a deviation, which is standard Gaussian left-right and standard Gaussian north-south." + }, + { + "text": "So I'm throwing, and then I'm here." + }, + { + "text": "And I'm claiming that this number here, by Pythagoras' theorem, the squared distance here is the sum of this squared distance here, which is the square of a Gaussian by assumption, plus the square of this distance, which is the square of another independent Gaussian." + }, + { + "text": "I assume those are independent." + }, + { + "text": "And so the squared distance from this point to this point is the chi-squared with two degrees of freedom." + }, + { + "text": "So this guy here is n01 squared." + }, + { + "text": "This is n01 squared." + }, + { + "text": "And so this guy here, this distance here, is chi-squared with two degrees of freedom." + }, + { + "text": "I mean, the squared distance." + }, + { + "text": "I'm talking about squared distances here." + }, + { + "text": "So now you can see that actually Pythagoras is basically why chi-squared arise." + }, + { + "text": "That's why it has its own name." + }, + { + "text": "I mean, I could define this random variable." + }, + { + "text": "I mean, it's actually a gamma distribution." + }, + { + "text": "It's a special case of something called the gamma distribution." + }, + { + "text": "The fact that the special case has its own name is because there's many times where we're going to take sum of squares of independent Gaussians, because Gaussians, the sum of squares is really the norm, the Euclidean norm squared, just by Pythagoras theorem." + }, + { + "text": "If I'm in higher dimension, I can start to sum more squared coordinates, and I'm going to measure the norm squared." + }, + { + "text": "So if you want to draw this picture, it looks like this." + }, + { + "text": "Again, it's the sum of positive numbers." + }, + { + "text": "So it's going to be on 0 plus infinity." + }, + { + "text": "That's fd." + }, + { + "text": "And so for f1 looks like this." + }, + { + "text": "f2 looks like this." + }, + { + "text": "So the tails becomes heavier and heavier as d increases." + }, + { + "text": "And then at start to 3, it starts to have a different shape." + }, + { + "text": "It starts from 0, and it looks like this." + }, + { + "text": "And then as d increases, it's basically as if you were to push this thing to the right." + }, + { + "text": "It's just like, pfft." + }, + { + "text": "It's just falling like a big ball." + }, + { + "text": "Everybody sees what's going on?" + }, + { + "text": "So there's just this fat thing that's just going there." + }, + { + "text": "What is the expected value of a k squared?" + }, + { + "text": "So it's the expected value of the sum of Gaussian random variables squared." + }, + { + "text": "I don't know why I said that." + }, + { + "text": "AUDIENCE 2 It's the sum of their second norm, right?" + }, + { + "text": "Which is?" + }, + { + "text": "Those are n0, 1." + }, + { + "text": "It's like, oh, I see, 1." + }, + { + "text": "Yeah." + }, + { + "text": "So n times 1, or d times 1." + }, + { + "text": "Yeah, which is d. So one thing you can check quickly is that the expected value of a k squared is d. And so you see, that's why the mass is shifting to the right as d increases." + }, + { + "text": "It's just going there." + }, + { + "text": "Actually, the variance is also increasing." + }, + { + "text": "The variance is 2d." + }, + { + "text": "So this is one thing." + }, + { + "text": "And so why do we care about this in basic statistics?" + }, + { + "text": "It's not like we actually have statistics much about throwing darts at high dimensional boards." + }, + { + "text": "So what's happening is that if I look at the sample variance, the average of the sum of squared centered by their mean, then I can actually expend this as the sum of the squares minus the average squared." + }, + { + "text": "It's just the same trick that we have for the variance." + }, + { + "text": "Second moment minus first moment squared." + }, + { + "text": "And then I claim that Cochran's theorem, I will tell you in a second what Cochran's theorem tells me, is that this sample variance is actually, so if I had only this, so now, OK, look at those guys." + }, + { + "text": "Those guys are Gaussian with mean mu and variance sigma squared." + }, + { + "text": "Think for one second, mu being 0 and sigma squared being 1." + }, + { + "text": "Now, this part would be a chi-square with n degrees of freedom divided by n. Now, I get another thing here, which is the square of something that looks like a Gaussian as well." + }, + { + "text": "So it looks like I have something else here, which looks also like a chi-square." + }, + { + "text": "Now, Cochran's theorem is essentially telling you that those things are independent." + }, + { + "text": "And so that in a way, you can think of those guys as being here n degrees of freedom minus 1 degree of freedom." + }, + { + "text": "Now, here, as I said, this is not mean 0 and variance 1." + }, + { + "text": "The fact that it's not mean 0 is not a problem, because I can remove the mean here and remove the mean here." + }, + { + "text": "And so this thing has the same distribution, regardless of what the actual mean is." + }, + { + "text": "So without loss of generality, I can assume that mu is equal 0." + }, + { + "text": "Now, the variance I'm going to have to pay, because if I multiply all these numbers by 10, then this Sn is going to be multiplied by 100." + }, + { + "text": "So this thing is going to scale with the variance." + }, + { + "text": "And not surprisingly, it's scaling like the square of the variance." + }, + { + "text": "So if I look at Sn, it's distributed as sigma-square times the chi-square with n minus 1 degrees of freedom divided by n. And we don't really write that, because a chi-square times sigma-square divided by n is not a distribution." + }, + { + "text": "So we put everything to the left." + }, + { + "text": "And we say that this is actually a chi-square with n minus 1 degrees of freedom." + }, + { + "text": "So here, I'm actually dropping a fact on you." + }, + { + "text": "But you can sort of see the building block." + }, + { + "text": "What is the thing that's sort of fussy at this point, but the rest should be crystal clear to you?" + }, + { + "text": "The thing that's fussy is that removing this square guy here is actually removing 1 degree of freedom." + }, + { + "text": "That should be weird." + }, + { + "text": "But that's what Cochran's theorem tells me." + }, + { + "text": "It's essentially stating something about orthogonality of subspaces with the span of the constant vector, something like that." + }, + { + "text": "So you don't have to think about it too much." + }, + { + "text": "But that's what it's telling me." + }, + { + "text": "But the rest, if you plug in, so the scaling in sigma-squared and in n, that should be completely clear to you." + }, + { + "text": "So in particular, if I remove that part, it should be clear to you that this thing, if mean is 0, this thing is actually distributed." + }, + { + "text": "Well, if mu is 0, what is the distribution of this guy?" + }, + { + "text": "So I remove that part, just this part." + }, + { + "text": "So I have xi, which are n0 sigma-squared." + }, + { + "text": "And I'm asking, what is the distribution of 1 over n sum from i equal 1 to n of xi-squared?" + }, + { + "text": "So it is the sum of their iid." + }, + { + "text": "So it's the sum of independent Gaussians, but not standard." + }, + { + "text": "So the first thing to make them standard is that I divide all of them by sigma-squared." + }, + { + "text": "Now, this guy is of the form zi-squared, where zi is n0, 1." + }, + { + "text": "So now this thing here has what distribution?" + }, + { + "text": "Chi-squared n. And now sigma-squared over n times chi-squared n. So if I have sigma-squared divided by n times chi-squared, sorry, so n times n divided by sigma-squared." + }, + { + "text": "So if I take this thing and I multiply it by n divided by sigma-squared, it means I remove this term." + }, + { + "text": "And now I am left with a chi-squared with n degrees of freedom." + }, + { + "text": "Now, the effect of centering with the sample mean here is only to lose 1 degree of freedom." + }, + { + "text": "That's it." + }, + { + "text": "OK?" + }, + { + "text": "So if I want to do a test about variance, since this is supposedly a good estimator of variance, this could be my pivotal distribution." + }, + { + "text": "This could play the role of a Gaussian." + }, + { + "text": "If I want to know if my variance is equal to 1 or larger than 1, I could actually build a test based on this only statement and test if the variance is larger than 1 or not." + }, + { + "text": "Now, this is not asymptotic because I started with the very assumption that my data was Gaussian itself." + }, + { + "text": "OK?" + }, + { + "text": "Now, just a side remark, you can check that this chi-squared 2, 2 is an exponential with half degrees of freedom, which is certainly not clear from the fact that z1 squared plus z2 squared is a chi-squared with 2 degrees of freedom." + }, + { + "text": "If I give you the sum of the square of two independent Gaussians, this is actually an exponential." + }, + { + "text": "That's not super clear, right?" + }, + { + "text": "But if you look at what was here, I don't know if you took notes, but let me rewrite it for you." + }, + { + "text": "So it was x to the d over 2 minus 1 e to the minus x over 2 divided by 2 to the d over 2 gamma of d over 2." + }, + { + "text": "So if I plug in d is equal to 2, gamma of 2 over 2 is gamma of 1, which is 1, right?" + }, + { + "text": "It's factorial of 0." + }, + { + "text": "So it's 1." + }, + { + "text": "So this guy goes away." + }, + { + "text": "2 to the d over 2 is 2 to the 1." + }, + { + "text": "So that's just 1." + }, + { + "text": "No, that's just 2." + }, + { + "text": "OK?" + }, + { + "text": "Then x to the d over 2 minus 1 is x to the 0, goes away." + }, + { + "text": "And so I have x minus x over 2, 1 half, which is really, indeed, of the form lambda e to the minus lambda x for lambda is equal to 1 half, which was our exponential distribution." + }, + { + "text": "OK?" + }, + { + "text": "So well, next week is Columbus Day." + }, + { + "text": "So that's next Monday." + }, + { + "text": "So next week, we'll talk about students' distribution." + }, + { + "text": "And so that was discovered by a guy who pretended his name was student but was not student." + }, + { + "text": "And I challenge you to find why in the meantime." + }, + { + "text": "All right, so I'll see you next week." + }, + { + "text": "Your homework is going to be outside, so we can release the room." + } +] \ No newline at end of file diff --git a/sight/sources/annotated/7K1sB05pE0A.json b/sight/sources/annotated/7K1sB05pE0A.json new file mode 100644 index 0000000000000000000000000000000000000000..7dd22ca35deb4ddbd4fe6aac432616a2f840dda8 --- /dev/null +++ b/sight/sources/annotated/7K1sB05pE0A.json @@ -0,0 +1,1577 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + }, + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + }, + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + }, + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + }, + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + }, + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + }, + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + }, + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + }, + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + }, + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + }, + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + }, + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + }, + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + }, + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + }, + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + }, + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + }, + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + }, + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + }, + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + }, + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + }, + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + }, + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + }, + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + }, + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + }, + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + }, + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + }, + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated/Cx5Z-OslNWE.json b/sight/sources/annotated/Cx5Z-OslNWE.json new file mode 100644 index 0000000000000000000000000000000000000000..10d35d5c570bd8f57ab79e281a63a0410d45b22f --- /dev/null +++ b/sight/sources/annotated/Cx5Z-OslNWE.json @@ -0,0 +1,1007 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "OK, now clustering for graphs." + }, + { + "text": "So this is a topic." + }, + { + "text": "This is one of the important things you can try to do with a graph." + }, + { + "text": "So you have a large graph." + }, + { + "text": "Let me kind of divide it into two clusters." + }, + { + "text": "OK, so you get a giant graph." + }, + { + "text": "And the job is to make some sense out of it." + }, + { + "text": "And one possible step is to be able to subdivide it if, as I see here, there is a cut between two reasonably equal parts of the graph, reasonably same size." + }, + { + "text": "And therefore, that graph could be studied in two pieces." + }, + { + "text": "So the question is, how do you find such a cut by an algorithm?" + }, + { + "text": "What's an algorithm that would find that cut?" + }, + { + "text": "So that's the problem." + }, + { + "text": "Let's say we're looking for two clusters." + }, + { + "text": "We could look for more clusters." + }, + { + "text": "But let's say we want to look for two clusters." + }, + { + "text": "So what are we trying to do?" + }, + { + "text": "We're trying to minimize." + }, + { + "text": "So this is the problem, then." + }, + { + "text": "So we look for find positions x and y, let's say, two which will be the centers, so to speak, of the." + }, + { + "text": "And really, it's just these points." + }, + { + "text": "Points." + }, + { + "text": "So the data is the points and the edges, as always, the nodes and the edges." + }, + { + "text": "So the problem is to find x and y so that to minimize." + }, + { + "text": "So it's a distance of points ai from x." + }, + { + "text": "Maybe I should emphasize we're in high dimensions." + }, + { + "text": "Plus the distance of other points." + }, + { + "text": "So the ai will be these points, these nodes." + }, + { + "text": "And the bi will be these nodes plus the sum of bi minus y squared." + }, + { + "text": "And you understand the rule here." + }, + { + "text": "That together, the a's union the b's give me all nodes." + }, + { + "text": "And I guess to be complete, the a's intersect the b's is empty." + }, + { + "text": "Just what you expect." + }, + { + "text": "I'm dividing the a's and the b's into two groups." + }, + { + "text": "And I'm picking an x and a y sort of at the center of those groups." + }, + { + "text": "So that is a minimum." + }, + { + "text": "So I want to minimize." + }, + { + "text": "And also, I probably want to impose some condition that the number of a's is reasonably close to the number of b's." + }, + { + "text": "In other words, I don't want just that to be the a and all the rest to be the b's." + }, + { + "text": "That would be not a satisfactory clustering." + }, + { + "text": "I'm looking for clusters that are good sized clusters." + }, + { + "text": "So minimize that." + }, + { + "text": "So there are a lot of different algorithms to do it." + }, + { + "text": "But some are more directly attacking this problem." + }, + { + "text": "Others use matrices that we associate with the graph." + }, + { + "text": "So let me tell you about two or three of those algorithms." + }, + { + "text": "And if you've studied, had a course in graph theory, you may already have seen this problem." + }, + { + "text": "First question would be, suppose I decide these are the a's and those are the b's, or some other decision." + }, + { + "text": "Yeah, probably some other decision." + }, + { + "text": "God, I want to solve the problem before I even start." + }, + { + "text": "So some a's and some b's." + }, + { + "text": "What would be the best choice of the x once you've decided on the a's?" + }, + { + "text": "And what would be the best choice of the y once you've decided on the b's?" + }, + { + "text": "So we can answer that question." + }, + { + "text": "Just if we knew the two groups, we could see where they should be centered, where the first group centered at x, the second group centered at y." + }, + { + "text": "And what does centering mean?" + }, + { + "text": "So let's just say." + }, + { + "text": "So I think what I'm saying here is, let me bring that down a little." + }, + { + "text": "So given the a's, this is a1 up to, say, ak, what is the best?" + }, + { + "text": "Is the best x?" + }, + { + "text": "Just to make that part right." + }, + { + "text": "And the answer is, do you know geometrically what x should be here?" + }, + { + "text": "x is the." + }, + { + "text": "So if I have a bunch of points and I'm looking for the middle of those points, the point x, a good point x to say, OK, that's the middle." + }, + { + "text": "It'll make the sum of the distances, I think, squared." + }, + { + "text": "I hope I'm right about that." + }, + { + "text": "A minimum." + }, + { + "text": "What is x?" + }, + { + "text": "It is the centroid." + }, + { + "text": "Centroid is the word." + }, + { + "text": "x is the centroid of the a's." + }, + { + "text": "And what is the centroid?" + }, + { + "text": "Let's see." + }, + { + "text": "Oh, maybe I don't know if x and y were a good choice." + }, + { + "text": "But let me see what." + }, + { + "text": "I guess it's the average a." + }, + { + "text": "It's the sum of the a's, of these a's." + }, + { + "text": "Those are vectors, of course, divided by the number of a's." + }, + { + "text": "I think." + }, + { + "text": "Actually, I was just quickly reviewing this morning." + }, + { + "text": "So I'm not totally on top of this centroid." + }, + { + "text": "What I'm going to talk, the algorithm that I'm going to talk about is the k, well, k means, it's always called." + }, + { + "text": "And here, it will be the k will be 2." + }, + { + "text": "I just have two partitioning into two sets, a's and b's." + }, + { + "text": "So I just k is just 2." + }, + { + "text": "OK, what's the algorithm?" + }, + { + "text": "Well, if I've chosen a partition, the a's and the b's have separated them, then that tells me what the x and the y should be." + }, + { + "text": "But now, what do I do next?" + }, + { + "text": "So this is going to be a sort of an alternating partition." + }, + { + "text": "Now, I take those two centroids." + }, + { + "text": "So step one is, for a given a's and b's, find the centroids x and y." + }, + { + "text": "And that's elementary." + }, + { + "text": "Then the second step is, given the centroids x and y, given those positions, given x and y, they won't be centroids when you see what happens." + }, + { + "text": "Given x and y, reform the best partition, best clusters." + }, + { + "text": "OK, so step one, we had a guess at what the best clusters were." + }, + { + "text": "And we found their centroids." + }, + { + "text": "Now, we start with the centroids, and we form new clusters again." + }, + { + "text": "And if these clusters are the same as the ones we started with, then the algorithm has converged." + }, + { + "text": "But probably won't be, these clusters." + }, + { + "text": "So you'll have to tell me what I mean by the best clusters." + }, + { + "text": "If I've got the two points, x and y, I want the points, I want to separate all the points that cluster around x to the ones that cluster around y." + }, + { + "text": "And then they're probably different from my original start." + }, + { + "text": "So now I've got new." + }, + { + "text": "Now I repeat step one." + }, + { + "text": "But let's just think, how do I form the best clusters?" + }, + { + "text": "Well, I take a point, and I have to decide, does it go with x, or does it go in the x cluster, or does it go in the cluster around y?" + }, + { + "text": "So how do I decide that?" + }, + { + "text": "Just whichever one it's closer to." + }, + { + "text": "So each point goes with each node." + }, + { + "text": "I could say each node goes with the closer of x and y." + }, + { + "text": "So points that should have been that are closer to x, now we're going to put them in the cluster around x." + }, + { + "text": "And does that solve the problem?" + }, + { + "text": "No, because, well, it might, but it might not." + }, + { + "text": "We have to come back to step one." + }, + { + "text": "We've now changed the clusters." + }, + { + "text": "They'll have different centroids." + }, + { + "text": "So we repeat step one, find the centroids for the two new clusters." + }, + { + "text": "Then we come to step two, find the ones that should go with the two centroids, and back and forth." + }, + { + "text": "I don't know, I don't think there's a nice theory of convergence or rate of convergence, all the questions that this course is always asking." + }, + { + "text": "But it's a very popular algorithm, k-means." + }, + { + "text": "k would be to have k clusters." + }, + { + "text": "So that's a, I'm not going to discuss the, I'd rather discuss some other ways to do this, to solve this problem, but that's one sort of hack that works quite well." + }, + { + "text": "OK, so second approach is what's coming next, second solution method." + }, + { + "text": "And it's called the spectral clustering." + }, + { + "text": "That's the name of the method." + }, + { + "text": "And before I write down what you do, what does the word spectral mean?" + }, + { + "text": "You see spectral graph theory, spectral clustering." + }, + { + "text": "And in other parts of mathematics, you see that word, you see spectral theorem." + }, + { + "text": "I gave you the most, and I described it as the most important, perhaps, theorem in linear algebra, at least one of the top three." + }, + { + "text": "So I'll write it over here, because it's not, it doesn't, this is a, it's the same word spectral." + }, + { + "text": "Well, let me ask the question again." + }, + { + "text": "What's that word spectral about?" + }, + { + "text": "What does that mean?" + }, + { + "text": "That means that if I have a matrix and I want to talk about its spectrum, what is the spectrum of the matrix?" + }, + { + "text": "It is the eigenvalues." + }, + { + "text": "So spectral theory, spectral clustering is using the eigenvalues of some matrix." + }, + { + "text": "That's what that spectral is telling me." + }, + { + "text": "So the spectral theorem, of course, is that for a symmetric matrix S, the eigenvalues are real and the eigenvectors are orthogonal." + }, + { + "text": "And don't forget what the real full statement is here, because there could be repeated real eigenvalues." + }, + { + "text": "And what does the spectral theorem tell me?" + }, + { + "text": "For symmetric matrices, if lambda equal 5 is repeated four times, if it's a four times solution of the equation that gives eigenvalues, then what's the conclusion?" + }, + { + "text": "Then there are four independent orthogonal eigenvectors to go with it." + }, + { + "text": "We can't say that about matrices, about all matrices, but we can say it about all symmetric matrices." + }, + { + "text": "And in fact, those eigenvectors are orthogonal, so we're even saying more." + }, + { + "text": "We can find four orthogonal eigenvectors that go with a multiplicity for eigenvalue." + }, + { + "text": "OK, that's spectral theorem." + }, + { + "text": "Spectral clustering starts with the graph Laplacian matrix." + }, + { + "text": "Matrix." + }, + { + "text": "May I remember what that matrix is?" + }, + { + "text": "Because that's the key connection of linear algebra to graph theory, is the properties of this graph Laplacian matrix." + }, + { + "text": "OK, so let me say L for Laplacian." + }, + { + "text": "So that matrix, one way to describe it is as a transpose A, where A is the incidence matrix of the graph." + }, + { + "text": "Or another way we'll see is the D, the degree matrix." + }, + { + "text": "That's diagonal." + }, + { + "text": "And I'll do an example just to remind you." + }, + { + "text": "Minus the, I don't know what I'd call this one." + }, + { + "text": "Shall I call it B for the moment?" + }, + { + "text": "And what matrix is B?" + }, + { + "text": "That's the adjacency matrix." + }, + { + "text": "Really, you should know these four matrices." + }, + { + "text": "They're the key four matrices associated with any graph." + }, + { + "text": "The incidence matrix, that's m by n edges and nodes." + }, + { + "text": "Edges and nodes." + }, + { + "text": "So it's rectangular, but I'm forming A transpose A here." + }, + { + "text": "So I'm forming a symmetric positive semi-definite matrix." + }, + { + "text": "So this Laplacian is symmetric positive semi-definite." + }, + { + "text": "Yeah, let me just recall what all these matrices are for a simple graph." + }, + { + "text": "OK, so I'll just draw a graph." + }, + { + "text": "All right." + }, + { + "text": "OK, so the incidence matrix, there are 1, 2, 3, 4, 5 edges, so five rows." + }, + { + "text": "There are four nodes, 1, 2, 3, and 4, so four columns." + }, + { + "text": "And a typical row would be edge 1 going from node 1 to node 2, so it would have a minus 1 and a 1 there." + }, + { + "text": "And let me take edge 2 going from 1 to node 3, so it would have a minus 1 and a 1 there." + }, + { + "text": "So that's the incidence matrix A. OK, what's the degree matrix?" + }, + { + "text": "That's simple." + }, + { + "text": "The degree matrix, well, A transpose A, this is m by n. This is n by m, so it's n by n. OK, in this case, 4 by 4." + }, + { + "text": "So the degree matrix will be 4 by 4, n by n. And it will tell us the degree of that, which means which we just count the edges." + }, + { + "text": "So it's three edges going in, node 2, three edges going in." + }, + { + "text": "Node 3 has just two edges, and node 4 has just two edges." + }, + { + "text": "So that's the degree matrix." + }, + { + "text": "And then the adjacency matrix that I've called B is also 4 by 4." + }, + { + "text": "And what is it?" + }, + { + "text": "It tells us which node is connected to which node." + }, + { + "text": "So I don't allow nodes, edges, that connect a node to itself, so 0s on the diagonal." + }, + { + "text": "So which nodes are connected to node 1?" + }, + { + "text": "Well, all of 2 and 4 and 3 are connected to 1, so I have 1s there." + }, + { + "text": "Node 2, all three nodes are connected to node 2." + }, + { + "text": "So I'll have the second column and row will have all three 1s." + }, + { + "text": "How about node 3?" + }, + { + "text": "OK, only two edges are connected." + }, + { + "text": "Only two nodes are connected to 3, 1 and 2, but not 4." + }, + { + "text": "So 1 and 2 I have, but not 4." + }, + { + "text": "So that's the adjacency matrix." + }, + { + "text": "Is that right?" + }, + { + "text": "Think so?" + }, + { + "text": "This is the degree matrix." + }, + { + "text": "This is the incidence matrix." + }, + { + "text": "And that formula gives me the Laplacian." + }, + { + "text": "Let's write down the Laplacian." + }, + { + "text": "So if I use the degree minus b, that's easy." + }, + { + "text": "The degrees were 3, 3, 2, and 2." + }, + { + "text": "Now I have these minuses, and those were 0." + }, + { + "text": "So that's a positive semidefinite matrix." + }, + { + "text": "Is it a positive definite matrix?" + }, + { + "text": "So let me ask, is it singular or is it not singular?" + }, + { + "text": "Is there a vector in its null space or is there not a vector in its null space?" + }, + { + "text": "Can you solve dx equals all 0s?" + }, + { + "text": "And of course, you can." + }, + { + "text": "Everybody sees that the vector of all 1s will be a solution to L. I'm sorry." + }, + { + "text": "I should be saying L here." + }, + { + "text": "Lx equals 0." + }, + { + "text": "Lx equals 0 is for a whole line of a one dimensional and the null space of L has dimension 1." + }, + { + "text": "It's got one basis vector, 1, 1, 1, 1." + }, + { + "text": "And that will always happen with the graph setup that I've created." + }, + { + "text": "So that's the first fact, that this positive semidefinite matrix L has lambda 1 equals 0, and the eigenvector is constants, C, C, C, C, the one dimensional eigenspace." + }, + { + "text": "Or 1, 1, 1, 1 is a typical eigenvector." + }, + { + "text": "OK. Now back to graph clustering." + }, + { + "text": "The idea of graph clustering is to look at the Fiedler eigenvector." + }, + { + "text": "This is called x2 is the next eigenvector, is the eigenvector for the smallest positive eigenvalue for lambda min excluding 0." + }, + { + "text": "So the smallest eigenvalue of L, the smallest eigenvalue and its eigenvector, this is called the Fiedler vector, named after the Czech mathematician, a great man in linear algebra." + }, + { + "text": "And he studied this vector, this situation." + }, + { + "text": "So everybody who knows about the graph Laplacian is aware that its first eigenvalue is 0, and that the next eigenvalue is important." + }, + { + "text": "Yeah?" + }, + { + "text": "AUDIENCE 2 Is the graph Laplacian named the Laplacian because it has connections?" + }, + { + "text": "GILBERT STRANGSKI-WEISBAUMGESEN To Laplace's equation, yes." + }, + { + "text": "So yeah, that's a good question." + }, + { + "text": "So why the word, the name Laplacian?" + }, + { + "text": "So yeah, that's a good question." + }, + { + "text": "So the familiar thing, so it connects to Laplace's finite difference equation, because we're talking about matrices here and not derivatives, not functions." + }, + { + "text": "So why the word Laplacian?" + }, + { + "text": "Well, so if I have a regular, if my graph is composed of a, so there is a graph with 25 nodes and 4 times 5, 20, about 40." + }, + { + "text": "This probably has about 40 edges and 25 nodes." + }, + { + "text": "And of course, I can construct its graph, all those four matrices for it." + }, + { + "text": "Its incidence matrix, its degree matrix." + }, + { + "text": "So the degree will be 4 at all these inside points." + }, + { + "text": "The degree will be 3 at these boundary points." + }, + { + "text": "The degree will be 2 at these corner points." + }, + { + "text": "But what will the matrix L look like?" + }, + { + "text": "So what is L?" + }, + { + "text": "And that will tell you why it has this name Laplacian." + }, + { + "text": "So the matrix L will have the degree 4, right, will be on the diagonal." + }, + { + "text": "That's coming from D. The other, the minus 1's that come from B, the adjacency matrix will be associated with those nodes and otherwise all 0's." + }, + { + "text": "So this is a typical row of L. This is a typical row of L centered at that node." + }, + { + "text": "So maybe that's node number 5, 10, 13." + }, + { + "text": "That's 13 out of 25 that would show you this." + }, + { + "text": "And sorry, those are minus 1's." + }, + { + "text": "Minus 1's." + }, + { + "text": "So a 4 on the diagonal and 4 minus 1's." + }, + { + "text": "That's the model problem for when the graph is a grid, square grid." + }, + { + "text": "And you associate that with Laplace's equation." + }, + { + "text": "So this is the reason that Laplace, why Laplace gets in it." + }, + { + "text": "Because Laplace's equation, the differential equation, is second derivative with respect to x squared." + }, + { + "text": "And the second derivative with respect to y squared is 0." + }, + { + "text": "And what we have here is Lu equals 0." + }, + { + "text": "It's the discrete Laplacian, the vector Laplacian, the graph Laplacian, where the second x derivative is replaced by minus 1, 2, minus 1." + }, + { + "text": "And the second y derivative is replaced by minus 1, 2, minus 1, second differences in the x and the y directions." + }, + { + "text": "So that's the explanation for Laplace." + }, + { + "text": "It's the discrete Laplace, discrete, or the finite difference Laplace." + }, + { + "text": "OK. Now, to finish, I have to tell you what clusters, how do you decide the clusters from L?" + }, + { + "text": "How does L propose two clusters, the A's and the B's?" + }, + { + "text": "And here's the answer." + }, + { + "text": "They come from this eigenvector, the Fiedler eigenvector." + }, + { + "text": "You look at that eigenvector." + }, + { + "text": "It's got some positive and some negative components." + }, + { + "text": "The components with positive numbers of this eigenvector, so the positive components of x, of this eigenvector." + }, + { + "text": "And there are negative components of this eigenvector." + }, + { + "text": "And those are the two clusters." + }, + { + "text": "So the two clusters are decided by the eigenvector, by the signs, plus or minus signs, of the components." + }, + { + "text": "The plus signs go in one, and the minus signs go in another." + }, + { + "text": "And you have to experiment to see that that would succeed." + }, + { + "text": "I don't know what it would do on this, actually, because that's hardly splits up into two." + }, + { + "text": "I suppose maybe the split is along a line like that or something to get." + }, + { + "text": "I don't know what clustering." + }, + { + "text": "This is not a graph that is naturally clustered." + }, + { + "text": "But you could still do k-means on it." + }, + { + "text": "You could still do spectral clustering." + }, + { + "text": "And you would find this eigenvector." + }, + { + "text": "Now, what's the point about this eigenvector?" + }, + { + "text": "I'll finish in one moment." + }, + { + "text": "What do we know about that eigenvector as compared to that one?" + }, + { + "text": "So here was an eigenvector all 1's." + }, + { + "text": "Let me just make it all 1's." + }, + { + "text": "1, 1, 1, 1." + }, + { + "text": "In that picture, it's 25 1's." + }, + { + "text": "Here's the next eigenvector up." + }, + { + "text": "And what's the relation between those two eigenvectors of L?" + }, + { + "text": "They are orthogonal." + }, + { + "text": "These are eigenvectors of a symmetric matrix." + }, + { + "text": "So they're orthogonal." + }, + { + "text": "So that means to be orthogonal to this guy means that your components add to 0, right?" + }, + { + "text": "A vector is orthogonal to all 1's." + }, + { + "text": "That dot product is just add up the components." + }, + { + "text": "So we have a bunch of positive components and a bunch of negative components." + }, + { + "text": "They have the same sum because the dot product with that is 0." + }, + { + "text": "And those two components, those two sets of components, are your two, tell you the two clusters in spectral clustering." + }, + { + "text": "So it's a pretty nifty algorithm." + }, + { + "text": "It does ask you to compute an eigenvector." + }, + { + "text": "And that, of course, takes time." + }, + { + "text": "And then there's a third, more direct algorithm to do this optimization problem." + }, + { + "text": "Well, actually, there are many." + }, + { + "text": "This is an important problem." + }, + { + "text": "So there are many proposed algorithms." + }, + { + "text": "Good." + }, + { + "text": "OK, I'm closing up." + }, + { + "text": "Final question?" + }, + { + "text": "Yeah." + }, + { + "text": "AUDIENCE 1 Is it possible to do more than one eigenvector?" + }, + { + "text": "GILBERT STRANGSBERRY Well, certainly for k-means." + }, + { + "text": "Now, if I had to do three clusters with Fiedler, I would look at the first three eigenvectors." + }, + { + "text": "And, well, the first one would be nothing." + }, + { + "text": "And I would look at the next two." + }, + { + "text": "And that would be pretty successful." + }, + { + "text": "If I wanted six clusters, it probably would fall off in the quality of the clustering." + }, + { + "text": "Yeah, but certainly I would look at the lowest six eigenvectors and get somewhere." + }, + { + "text": "Yeah, right." + }, + { + "text": "So OK, so that's a topic, an important topic, a sort of standard topic in applied graph theory." + }, + { + "text": "OK, so see you Wednesday." + }, + { + "text": "I'm hoping on Wednesday." + }, + { + "text": "So Professor Edelman has told me a new and optimal way to look at the problem of back propagation." + }, + { + "text": "You remember back propagation?" + }, + { + "text": "If you remember the lecture on it, you don't want to remember the lecture on it." + }, + { + "text": "It's a tricky, messy thing to explain." + }, + { + "text": "But he says, if I explain it using Julia in linear algebra, it's clear." + }, + { + "text": "So we'll give him a chance on Wednesday to show that revolutionary approach to the explanation of back propagation." + }, + { + "text": "And I hope for, I told him he could have half an hour and projects would take some time." + }, + { + "text": "I hope now we've had two with wild applause." + }, + { + "text": "So I hope we get a couple more in our last class." + }, + { + "text": "OK, see you Wednesday." + }, + { + "text": "And if you bring, well, if you have projects ready, send them to me online and maybe a printout as well." + }, + { + "text": "That would be terrific." + }, + { + "text": "If you don't have them ready by the hour, they can go." + }, + { + "text": "The envelope outside my office would receive them." + }, + { + "text": "Good, so I'll see you Wednesday for the final class." + } +] \ No newline at end of file diff --git a/sight/sources/annotated/KAySmSEGc9U.json b/sight/sources/annotated/KAySmSEGc9U.json new file mode 100644 index 0000000000000000000000000000000000000000..eddd53780e2a4ae8e0b81f204fba312a381f8245 --- /dev/null +++ b/sight/sources/annotated/KAySmSEGc9U.json @@ -0,0 +1,2006 @@ +[ + { + "text": " Okay, folks." + }, + { + "text": "Here we are again." + }, + { + "text": "Welcome back for another episode of Theory of Computation." + }, + { + "text": "This is lecture number three." + }, + { + "text": "I am going to review what we've been doing." + }, + { + "text": "We've been looking at finite automata and regular languages." + }, + { + "text": "Those are the languages that the finite automata can recognize." + }, + { + "text": "And we talked about non-determinism." + }, + { + "text": "So we had non-deterministic finite automata and deterministic finite automata." + }, + { + "text": "We showed that they're equivalent." + }, + { + "text": "We looked at the closure properties over the regular operations, union, concatenation, and star, and showed that the regular languages, really the class of regular languages, is closed under those regular operations." + }, + { + "text": "And we used the constructions that we developed in the proof of those closure properties to show that we can give a way to convert regular expressions to finite automata." + }, + { + "text": "So that was partway toward our goal of showing that these regular expressions and finite automata are equivalent with respect to the class of languages they describe, namely the regular languages." + }, + { + "text": "So regular expressions of finite automata are interchangeable from the perspective of what kinds of languages you can do with them." + }, + { + "text": "So we're going to finish that off today." + }, + { + "text": "So let's take a look at what our next topics we're going to be covering." + }, + { + "text": "We're going to reverse the construction we gave last time, which allowed us to convert regular expressions to finite automata." + }, + { + "text": "Now we're going to go backwards." + }, + { + "text": "We're going to show how to convert finite automata back to regular expressions." + }, + { + "text": "And those two constructions together show us that the regular expressions and finite automata can be interconverted from one another." + }, + { + "text": "And they're therefore equivalent with respect to the kinds of things they can do in language recognition or generation." + }, + { + "text": "Then we're going to prove that we're going to look at how you prove certain languages are not regular." + }, + { + "text": "They're beyond the capabilities of finite automata." + }, + { + "text": "And finally, at the end, we're going to introduce a new model of computation, which is more powerful than the finite automata and regular expressions, namely the context-free grammars." + }, + { + "text": "Those can do other kinds of languages that the simpler finite automata regular expressions models can't do." + }, + { + "text": "And I would also just like to note that a lot of what we're doing is a warm-up toward the more powerful models of computation that we're going to be looking at later, well, in a week or so, which are more general purpose computation." + }, + { + "text": "But along the way, introducing these models of finite automata and context-free languages is interesting and helpful because many of those, a number of those models turn out to be useful in a number of applications, whether it's from linguistics to programming languages." + }, + { + "text": "And a variety of different parts of computer science and other fields as well use those notions." + }, + { + "text": "So they're useful notions beyond just in this course." + }, + { + "text": "So I just want a couple of administrative things to touch on." + }, + { + "text": "We are going to have additional check-ins today." + }, + { + "text": "As I mentioned to you, we're going to start counting participation, not correctness, just participation in the live check-ins." + }, + { + "text": "So with that, let us move on to today's material." + }, + { + "text": "As I mentioned, we're going to be showing how to convert finite automata to regular expressions." + }, + { + "text": "And that's going to complete our equivalence of finite automata and regular expressions." + }, + { + "text": "So just to recap what we did last time, we showed that if you have a regular expression and it describes some language, then that language is regular." + }, + { + "text": "So in other words, we have a way of, we gave a way of converting regular expressions to finite automata, as kind of shown in this diagram." + }, + { + "text": "That's what we did last time." + }, + { + "text": "Now we're going to go the other way." + }, + { + "text": "We're going to show how to convert." + }, + { + "text": "Oh, and just a reminder in case you're just getting yourself your memory to work, maybe it'll help you just to remember that we actually did an example of that conversion." + }, + { + "text": "We looked at this regular expression A union AB star." + }, + { + "text": "And we actually worked through the process of converting that." + }, + { + "text": "Oops, I need to make myself smaller so you can see all that." + }, + { + "text": "We went through the process of converting A union AB star as an example of that, of, I mean, OK, well, we went through the process of actually doing that conversion." + }, + { + "text": "And now we're going to show how to do it the other way around." + }, + { + "text": "All right?" + }, + { + "text": "So we're going to invert that and go backwards the other way." + }, + { + "text": "So today's theorem is to show that if A is regular, namely, it's the language of some finite automaton, then you can convert it to a regular expression which will describe that same language." + }, + { + "text": "So basically, we're going to give a conversion from finite automata to regular expressions." + }, + { + "text": "But before we do that, we're going to have to introduce a new concept." + }, + { + "text": "So we're not going to be able to dive right into that conversion." + }, + { + "text": "We're going to have to introduce a new model first, which is going to facilitate that conversion." + }, + { + "text": "And that new model is called, it's yet another kind of finite automaton, called a generalized nondeterministic finite automaton, or a generalized NFA, or just simply a GNFA." + }, + { + "text": "So this is yet another variant of the finite automaton model." + }, + { + "text": "And conceptually, it's very simple." + }, + { + "text": "It's similar to the NFAs." + }, + { + "text": "I'll give you, here's a picture of a GNFA named G, G1." + }, + { + "text": "Very similar to the NFAs." + }, + { + "text": "But if you look at it for a second, you'll see that the transitions have more complicated labels." + }, + { + "text": "For the NFAs, we're only allowing just single symbols or the empty string to appear on the labels." + }, + { + "text": "Now I'm actually allowing you to put full regular expressions on the labels for the automaton." + }, + { + "text": "Now, we have to understand how a GNFA processes its input." + }, + { + "text": "And the way it works is not complicated to understand." + }, + { + "text": "When you're getting an input string, feeling when a GNFA is processing an input string, it starts at the start state, just like you would imagine." + }, + { + "text": "But now, to go along a transition, instead of reading just a single symbol or the empty string, as in the case for the nondeterministic machine, it actually gets to read a whole string at one step, kind of at one byte." + }, + { + "text": "It can read an entire string and go along that transition arrow, provided that chunk of the input that it read is in the regular expression that that transition has as its label." + }, + { + "text": "So for example, you can go from Q1 to Q2 in one step in this GNFA by reading AABB off the input." + }, + { + "text": "So it reads all of those four symbols all at once, just swoops them up, and then moves from Q1 to Q2 in one step." + }, + { + "text": "And then when it's in Q2, it can read AAB and move to Q3." + }, + { + "text": "And Q3 happens, there's nowhere to go." + }, + { + "text": "So this is going to be a nondeterministic machine." + }, + { + "text": "There might be several different ways of processing the input." + }, + { + "text": "And if any one of them gets to an accepting state at the end of the input, we say the GNFA accepts." + }, + { + "text": "So it's similar to nondeterministic to NFAs in the way the acceptance criterion works." + }, + { + "text": "So you could do an example, but hopefully, the concept of how this works is reasonably, you can at least buy it, that it processes the input in chunks at a time." + }, + { + "text": "And those chunks have to be described by the regular expressions on the transition arrows as it moves along those transitions." + }, + { + "text": "So what we're going to do now is to convert not DFAs to regular expressions." + }, + { + "text": "We're going to convert GNFAs to regular expression." + }, + { + "text": "That's even harder because GNFAs allow you to do all sorts of other things besides just ordinary DFAs." + }, + { + "text": "So that's a harder job." + }, + { + "text": "Why am I making my life harder?" + }, + { + "text": "Well, you'll see in a minute that it's going to actually turn out to be helpful to be working with a more powerful model in the way this construction is going to work." + }, + { + "text": "Now, before I dive in and do the construction from GNFAs to regular expressions, I'm going to make a simplifying assumption about the GNFAs." + }, + { + "text": "I'm going to put them in a special form that's going to make it easier to do the conversion." + }, + { + "text": "And that simpler form is, first of all, I'm going to assume the GNFA has just a single accepting state." + }, + { + "text": "And that accepting state is not allowed to be the start state." + }, + { + "text": "So it has to have just a single accepting state." + }, + { + "text": "I've already violated that convenient assumption in this GNFA because I have here two accepting states." + }, + { + "text": "That's not what I want." + }, + { + "text": "I want to have just one." + }, + { + "text": "Well, the thing is, it's easy to obtain just one, just to modify the machine so that I have just one by adding a new accepting state, which is branched to from the former accepting states by empty transition." + }, + { + "text": "So I can always jump from Q2 to Q4 at any time without even reading any input, just going along this empty transition." + }, + { + "text": "And then I declassify the former accepting states as accepting." + }, + { + "text": "And now I have here just a single accepting state." + }, + { + "text": "And because it's going to be a new state that I added, it won't be the start state." + }, + { + "text": "And I have accomplished that one aspect of my assumption about the form of the GNFA." + }, + { + "text": "But there's another thing that I want to do too." + }, + { + "text": "I want to assume, as you will see, which is going to be convenient in my construction, that we will have transition arrows going from every state to every other state." + }, + { + "text": "In fact, I want transition arrows going from every state, even back to themselves." + }, + { + "text": "I want there to be all possible transition arrows should be present, with two exceptions." + }, + { + "text": "For the start state, there should be only transition arrows exiting the start state." + }, + { + "text": "And for the accepting state, there's just one now, there should be only transition arrows coming in to the start state." + }, + { + "text": "So it's kind of what you would imagine as being reasonable." + }, + { + "text": "For the other states which are not accepting or starting, there should be transition arrows leaving and coming from everywhere else." + }, + { + "text": "But for the start states, just leaving, and for the accept state, just coming in." + }, + { + "text": "And you can easily modify the machine to achieve that." + }, + { + "text": "Let's just see how to do that in one example." + }, + { + "text": "So notice that from Q3 to Q2, there is no transition right now." + }, + { + "text": "And that's not good." + }, + { + "text": "That's not what I want." + }, + { + "text": "I want there to be a transition from Q3 to Q2." + }, + { + "text": "Well, I'll just add that transition in." + }, + { + "text": "But I'm going to label it with the empty language regular expression." + }, + { + "text": "So that means, yeah, the transition is there, but you never can take it." + }, + { + "text": "So it doesn't change the language that the machine is going to be recognizing, but it fulfills my assumption, my convenient assumption, that we have all of these transition arrows being present in the machine." + }, + { + "text": "So anyway, I hope you will buy it." + }, + { + "text": "It's not going to be, if you don't quite get this, don't worry." + }, + { + "text": "It's not totally critical that you're following all of these little adjustments and modifications to the GNFA." + }, + { + "text": "But it will be helpful to understand what GNFA themselves, how they work." + }, + { + "text": "So as I mentioned, we can easily modify GNFA to have the special form that we're assuming here." + }, + { + "text": "All right, so now we're going to jump in and start doing the conversion." + }, + { + "text": "So we're going to have a lemma, which is like a theorem that really is just a local interest here." + }, + { + "text": "It's not a general interest theorem." + }, + { + "text": "It's going to be relevant just to GNFA, which are really just defined to help us do this conversion." + }, + { + "text": "They really don't have any other independent value." + }, + { + "text": "So I want to show that every GNFA has an equivalent regular expression R. That's really my goal." + }, + { + "text": "And the way we're going to prove that is by induction." + }, + { + "text": "It's going to be by induction on the number of states of the GNFA." + }, + { + "text": "Now, you really should be familiar with induction as one of the expectations for being in this course." + }, + { + "text": "But in case you're a little shaky on it, don't worry." + }, + { + "text": "I'm going to unpack it as a procedure." + }, + { + "text": "It's really just recursion." + }, + { + "text": "And a proof that uses induction is really just a proof that calls itself." + }, + { + "text": "It's just a proof that it's a recursive proof." + }, + { + "text": "That's all it is." + }, + { + "text": "So if you're comfortable with recursion, you'll be comfortable with induction." + }, + { + "text": "But anyway, I'm going to describe this as a procedure." + }, + { + "text": "So if you're a little shaky on induction, don't worry." + }, + { + "text": "So the basis is, so first, I'm going to handle the case where the GNFA has just two states." + }, + { + "text": "Now, remember, I'm assuming now my GNFAs are in the special form." + }, + { + "text": "So you can't even have a GNFA with one state because it has to have a start state, and it has to have an accept state, and they have to not be the same." + }, + { + "text": "So the smallest possible GNFA to worry about is a two-state GNFA." + }, + { + "text": "Now, if we happen to have a two-state GNFA, it turns out to be very easy to find the equivalent regular expression." + }, + { + "text": "Why?" + }, + { + "text": "Because that two-state GNFA can only look like this." + }, + { + "text": "It can have a start state, can have an accept state, and it can only have a transition going from the start to the accept because no other transitions are allowed." + }, + { + "text": "It only has outgoing from the start, only incoming to the accept." + }, + { + "text": "And so there's only one transition, and it has a label with a regular expression r. So what do you think the equivalent regular expression is for this GNFA?" + }, + { + "text": "It's just simply the one that's labeling that transition because that tells us when I can go from the start to the accept." + }, + { + "text": "And there's nothing else the machine can do." + }, + { + "text": "It just makes one step, which is to accept its input if it's described by that regular expression." + }, + { + "text": "So therefore, the equivalent regular expression that we're looking for is simply label on that single transition." + }, + { + "text": "OK, so two-state GNFAs are easy." + }, + { + "text": "But what happens if you have more states?" + }, + { + "text": "Then you're going to actually have to do some work." + }, + { + "text": "So we call that the induction step." + }, + { + "text": "That's when we have more than two states." + }, + { + "text": "And the way the induction works is we're going to assume we already know how to do it for k minus 1 states." + }, + { + "text": "And we're going to use that knowledge to show how to do it for k states." + }, + { + "text": "So in other words, we already know how to do it for two states." + }, + { + "text": "I'm going to use that fact to show how to do it for three states, and then use the fact that I can do it for three states to show how to do it for four states, and so on and so on." + }, + { + "text": "All right?" + }, + { + "text": "And the idea for how to do that is actually pretty easy to grasp." + }, + { + "text": "What we're going to do is if we have a k-state GNFA that we want to convert, we're going to change that k-state GNFA to a k minus 1-state GNFA, and then use our assumption that we already know how to do the k minus 1-state GNFA." + }, + { + "text": "All right?" + }, + { + "text": "So in terms of a picture, I'm going to take a k-state to prove that I can always convert k-state GNFAs to regular expressions." + }, + { + "text": "I'm going to show how to convert the k-state one into an equivalent k minus 1-state GNFA." + }, + { + "text": "And then if you just like to think of it this procedurally, the k minus 1 gets converted to a k minus 2, gets converted to a k minus 3, and so on and so on, until I get down to 2, which then I know how to do directly." + }, + { + "text": "OK?" + }, + { + "text": "So the whole name of the game here is figuring out how to convert a GNFA that has k states into another one that has one fewer state that does the same language." + }, + { + "text": "OK, so you have to hold that in your head." + }, + { + "text": "I mean, I wish I had more blackboard space here, but it's very limited here." + }, + { + "text": "So you have to remember what we're going to be doing on the next slide, because that's going to finish the job for us." + }, + { + "text": "As long as I can show in general how to convert a k-state GNFA to a GNFA that has one fewer state, but it still does the same language, I'm good." + }, + { + "text": "Because then I can keep iterating that until I get down to 2." + }, + { + "text": "All right, so this is the guts of the argument." + }, + { + "text": "So I have my k-state machine." + }, + { + "text": "Here's my start state." + }, + { + "text": "Here's my accept state." + }, + { + "text": "Here's my k minus 1 state, that machine that I'm going to be building for you." + }, + { + "text": "It's actually going to look almost exactly the same." + }, + { + "text": "I'm just going to remove one state from the bigger machine." + }, + { + "text": "So I'm going to pick any state, which is not the start state or the accept state." + }, + { + "text": "Here it is pictured here." + }, + { + "text": "I mean, all of the states of the k-state machine are going to appear in the k minus 1 state machine, except for one state that I'm going to rip out." + }, + { + "text": "That's the state x." + }, + { + "text": "It's now here as a ghost." + }, + { + "text": "It's been removed." + }, + { + "text": "It's not there anymore." + }, + { + "text": "But I'm just helping you to remember that it used to be there by showing a shadow." + }, + { + "text": "But it's a I have taken my original machine that had k states and basically just ripped out a state." + }, + { + "text": "And now I have one fewer state." + }, + { + "text": "So the good news is that I now have a machine with k minus 1 states." + }, + { + "text": "That's what I want." + }, + { + "text": "But the bad news is that it doesn't do the same language anymore." + }, + { + "text": "I broke the machine by rip." + }, + { + "text": "If you're just going to rip out a state, who knows what the new machine is going to do?" + }, + { + "text": "It's going to be probably not the same as what the original machine did." + }, + { + "text": "So what I need to do then is repair the damage." + }, + { + "text": "I've got to fix the damage that I caused by removing x." + }, + { + "text": "And whatever role x was playing in the original machine, I've got to make sure that the new machine that I have, which doesn't have x anymore, can still do the same things that the original machine did." + }, + { + "text": "And so the way I'm going to do that is look at all of the paths that could go through x and make sure that they're still present, even though I don't have x anymore." + }, + { + "text": "And the way I'm going to do that is I'm going to consider a part of a path that might use x." + }, + { + "text": "So let's pick two states, qi and qj, in the machine that had k states." + }, + { + "text": "Let me just see here." + }, + { + "text": "I don't know if this is." + }, + { + "text": "OK." + }, + { + "text": "So if we have, we'll pick two states, qi and qj, in the original machine." + }, + { + "text": "Now, qi might have the possibility of going to state x." + }, + { + "text": "And then x might have a self loop." + }, + { + "text": "And then it might go to qj." + }, + { + "text": "The new machine doesn't have x anymore." + }, + { + "text": "So the way I'm going to fix that is by replacing the label that goes directly from i to j with a new label that adds in all of the things I lost when I removed x. OK, that's the whole idea here." + }, + { + "text": "So here is qi to qj, but there's no x anymore." + }, + { + "text": "How could I get from qi to qj?" + }, + { + "text": "What were the inputs that could have brought us from qi to qj via x?" + }, + { + "text": "Well, they would have been an input that read a string described by R1." + }, + { + "text": "I might have self looped at x a few times." + }, + { + "text": "So I might have read several strings that are described by R2." + }, + { + "text": "And then I would have read a string that was described by R3." + }, + { + "text": "And now I'm at qj." + }, + { + "text": "OK, so the new label that I'm going to place over here is going to be the strings that I get from reading R1, reading a string that's described by R1, then multiple copies of a string, multiple strings that are possibly described by R2, which is the same as R2 star, and then a string that could be described by R3." + }, + { + "text": "So that is a new addition to the transition that takes me from qi to qj." + }, + { + "text": "Of course, I need to include the things that would have taken me from qi to qj in the first place." + }, + { + "text": "So I'm also unioning in R4, which was the direct route from qi to qj that did not transit through x." + }, + { + "text": "So by making that new regular expression on the qi to qj transition, I have compensated for the loss of x for paths that go from qi to x and then out to qj." + }, + { + "text": "Now, what I need to do is to do that same thing for every pair qi and qj that are in the original machine." + }, + { + "text": "And so if I do that for every possible pair, I'll be modifying all of the transitions in the new machine in a way that compensates for the loss of x." + }, + { + "text": "And now the new machine has been repaired from the damage that I caused by removing x, and it does the same language." + }, + { + "text": "It's the kind of thing you need to think a little bit about, I understand." + }, + { + "text": "But at least hopefully, the spirit of what I just described to you comes through, that we're going to convert this machine with k states to one with k minus 1 states by removing a state and repairing the damage." + }, + { + "text": "And now it does the same language, and then I can remove another state and do the same thing over and over again until I get down to two states." + }, + { + "text": "So that's the idea." + }, + { + "text": "And that really completes the proof." + }, + { + "text": "That shows that I can convert every GNFA to a regular expression." + }, + { + "text": "OK?" + }, + { + "text": "And that really is the end of the story for this." + }, + { + "text": "And thus, I claim that DFAs now and regular expressions are equivalent." + }, + { + "text": "So I'm going to give you a little check-in here on this, really just to see, high level, if you're following what's going on." + }, + { + "text": "All right?" + }, + { + "text": "So just take a look." + }, + { + "text": "So we just showed how to convert GNFAs to regular expression, but we really wanted to convert DFAs to regular expressions." + }, + { + "text": "So how do we go from converting GNFAs to converting DFAs?" + }, + { + "text": "It's not the same, obviously." + }, + { + "text": "So how do we finish that?" + }, + { + "text": "So there are three choices here." + }, + { + "text": "First, we have to show how to convert DFAs to GNFAs, maybe, or show how to convert GNFAs to DFAs." + }, + { + "text": "Or maybe we're already done." + }, + { + "text": "So maybe I better launch that poll while you're reading that." + }, + { + "text": "And there you go." + }, + { + "text": "Hopefully, you can." + }, + { + "text": "All right." + }, + { + "text": "Why don't I end this?" + }, + { + "text": "It's a little worrisome, because I would say we have a plurality who got the right answer, but not a majority." + }, + { + "text": "So let us share the results." + }, + { + "text": "So I sense not all of you are with me, but you're going to have to either that or you're reading your email while we're talking." + }, + { + "text": "I'm not sure." + }, + { + "text": "But whatever it is, you need to think a little bit about what's going on here, because the reason why we are done is because DFAs are a kind of GNFAs." + }, + { + "text": "They have a very simple kind of regular expression on each transition." + }, + { + "text": "They just have the regular expression, which is just a single symbol." + }, + { + "text": "So all DFAs are automatically GNFAs." + }, + { + "text": "So if I can convert GNFAs, I can certainly convert DFAs, because GNFAs include the DFAs." + }, + { + "text": "I'm done." + }, + { + "text": "It really was number C was the correct answer." + }, + { + "text": "So good thing we're not counting correctness here." + }, + { + "text": "So participation is good enough." + }, + { + "text": "But I do think you need to think about what's going on and making sure that you're following along." + }, + { + "text": "So anyway, that's a we'll carry on here, but it makes me a little concerned." + }, + { + "text": "OK, so let us now move on." + }, + { + "text": "So we're going to talk a little bit about non-regular languages." + }, + { + "text": "So somebody's asking, don't we have to still make the DFAs into the special type?" + }, + { + "text": "Yes, we do." + }, + { + "text": "We have to make them to the special type." + }, + { + "text": "But we already showed how to make GNFAs into the special type." + }, + { + "text": "And DFA, that is going to apply to DFAs as well." + }, + { + "text": "They'll become GNFAs." + }, + { + "text": "You can add the extra start, add a new start state, add a new accept state, add in all the transitions, which you didn't have before with the empty language label." + }, + { + "text": "And you'll have a GNFA from a DFA." + }, + { + "text": "But that applies to GNFAs in general." + }, + { + "text": "So it's nothing special about DFAs there." + }, + { + "text": "Anyway, I think you need to chew on that." + }, + { + "text": "And hopefully, you'll be following going forward." + }, + { + "text": "Anyway, let us look now at proving non-regularity." + }, + { + "text": "So we're finished with our goal of showing that regular languages can either come from DFAs or from regular expressions." + }, + { + "text": "Those are the same in terms of, from the perspective of our course, they're interchangeable." + }, + { + "text": "So now, as we mentioned, there are going to be some languages which are not regular, which can't be done by DFAs." + }, + { + "text": "They're actually, DFAs are actually pretty weak as a computational model." + }, + { + "text": "And so there's all sorts of very simple things that they cannot do." + }, + { + "text": "There are some fairly complicated things that they can do, surprisingly enough." + }, + { + "text": "But anyway, there are some simple things they can't do." + }, + { + "text": "And so we have to develop a method for showing that a language is not regular." + }, + { + "text": "And that's going to be useful for your homework and, in general, for just understanding the power of DFAs." + }, + { + "text": "So how do we show a language is not regular?" + }, + { + "text": "So remember, if you want to show a language is regular, basically, what you need to do is give a DFA." + }, + { + "text": "Or you can use the closure properties." + }, + { + "text": "That's another way of showing a language is regular." + }, + { + "text": "But underneath that, it's basically constructing DFAs." + }, + { + "text": "All right." + }, + { + "text": "To show a language is not regular, you have to give a proof." + }, + { + "text": "Generally, not a construction." + }, + { + "text": "It's a proof that there is no DFA or that it's just going to be impossible to make a DFA." + }, + { + "text": "And we have to develop a method." + }, + { + "text": "What is that proof method?" + }, + { + "text": "Now, there is a tempting, I've taught this course many times, and there's a kind of a tempting approach that many people have." + }, + { + "text": "It's not only going to apply for finite automata, but for other things too." + }, + { + "text": "And believe me, it's not only people in this class." + }, + { + "text": "It's for people out there who are trying to think about computation in general, which is to say, well, I have some language of trying to figure out if it's regular or not." + }, + { + "text": "And so I thought really hard how to make a DFA, and I couldn't find one." + }, + { + "text": "Therefore, it's not regular." + }, + { + "text": "That's not a proof." + }, + { + "text": "Just because you couldn't find a DFA doesn't mean there is no DFA." + }, + { + "text": "You need to prove that the language is not regular using some method." + }, + { + "text": "So I'm going to give you an example where that kind of approach can lead you wrong." + }, + { + "text": "And that is, I'll give two examples of languages where you might try to prove they're regular or not, and you could be in trouble if you just follow that kind of informal approach." + }, + { + "text": "So if you take the language B, where these are straight, but let's assume our alphabet is 0's and 1's." + }, + { + "text": "B is the language of all strings that have an equal number of 0's and 1's." + }, + { + "text": "So you want to know, if I have 1,000 0's, I need to have 1,000 1's." + }, + { + "text": "So basically, the way you test that, you'd have to count up the number of 0's, count up the number of 1's, and see if those two counts are the same." + }, + { + "text": "And that's going to be really tough to make a DFA do, because how are you going to remember that really big number of 0's that the DFA might have 50 states, but you might need to count up to 100 or a million to figure out, to count up how many 0's you've seen." + }, + { + "text": "And it seems really hard to be able to do that kind of a count when you only have 50 states." + }, + { + "text": "So whatever number of states you have, it seems hard to count when you have a finite automaton." + }, + { + "text": "So the intuition is, it's not regular, because a finite automaton can't count, which, in this case, you can convert that intuition into a real proof." + }, + { + "text": "I would say it's not a real proof yet, but it can be made into a real proof." + }, + { + "text": "But compare that case with another language, which I'll call C, which instead of looking at its input to see whether it has an equal number of 0's and 1's, I'm going to look at the input and look at the substrings of 0 1's and 1 0's, those two substrings, and count the number of occurrences of 0 1 as a substring and the number of occurrences of 1 0 as a substring." + }, + { + "text": "Just to make sure you're understanding, let's look at two examples." + }, + { + "text": "So the string 0 1 0 1 is not going to be in C, because if you count up the number of 0 1's and the number of 1 0's, not the same." + }, + { + "text": "So I'm even going to help you here, if you can see that." + }, + { + "text": "The number of 0 1's is 2, but there's only a single occurrence of 1 0." + }, + { + "text": "So those two counts are different, and so that's why this input string is not in C. Compare that with the string 0 1 1 0." + }, + { + "text": "Now, if you count up the number of 0 1 and 1 0 substrings, you're going to get the same value, because here we have a single 0 1 and a single 1 0." + }, + { + "text": "And so now the two counts of those number of substrings are the same, and so that's why you're in C. Now my question is, is C a regular language?" + }, + { + "text": "Well, it looks like it shouldn't be regular for the same reason that B isn't regular, because you have to count up two quantities and compare them." + }, + { + "text": "OK?" + }, + { + "text": "So now, so if we, so that's our intuition, that you just can't do it with a finite automaton, because you have to do the same kind of counting that you would have had to do for language B." + }, + { + "text": "But here, you would be wrong, because C, in fact, is regular." + }, + { + "text": "It has a much simpler description than the one I gave over here at the beginning." + }, + { + "text": "There's the very same language C can be described in a much, much simpler way." + }, + { + "text": "I'm not going to tell you what it is." + }, + { + "text": "You can mull that over." + }, + { + "text": "You can try some examples to figure it out, but it has a much simpler description." + }, + { + "text": "It's not a totally trivial description." + }, + { + "text": "I mean, there is some content there, but it is the kind of thing that a finite automaton can do." + }, + { + "text": "It wouldn't do the counting this way." + }, + { + "text": "So the moral is, the punchline is, that sometimes the intuition works, but it can also be wrong." + }, + { + "text": "And so the moral of the story is you need to give a proof when you're doing things like that." + }, + { + "text": "OK?" + }, + { + "text": "So what we're going to do next in the second half of the lecture is to give a method for proving languages are not regular." + }, + { + "text": "And again, you're going to need to use that on your homework, so I hope you get it." + }, + { + "text": "But first of all, oh, did I never stop sharing that poll?" + }, + { + "text": "Forgive me." + }, + { + "text": "And so with that, I think we'll take our little requested break." + }, + { + "text": "And for five minutes, and we'll be back in five minutes." + }, + { + "text": "So break time." + }, + { + "text": "All righty." + }, + { + "text": "We are done here." + }, + { + "text": "And proving languages not regular." + }, + { + "text": "OK." + }, + { + "text": "The way we're going to prove languages are not regular is by introducing a method called the pumping lemma." + }, + { + "text": "And the overarching plan at the pumping lemma, without getting into the specifics of it, is to show that that lemma says all regular languages have a certain property, which we will describe." + }, + { + "text": "And so to show a language is not regular, you simply show the language doesn't have that property." + }, + { + "text": "Because all regular languages have to have that property." + }, + { + "text": "And so by showing a language fails to have the property, it could not be regular." + }, + { + "text": "OK, that's the plan." + }, + { + "text": "OK, now the property itself is a little complicated to describe, but not too bad." + }, + { + "text": "I'll try to unpack it for you." + }, + { + "text": "But first, let's look at the statement of the lemma, which says that whenever you have a regular language, let's call it A." + }, + { + "text": "So for every regular language A, there's always a special value called the pump, a number, P we'll call it, called the pumping length." + }, + { + "text": "It's a special number." + }, + { + "text": "And that length tells you that whenever a string is in that language and it's longer than that length, then something special happens." + }, + { + "text": "You can take that string, and you can modify it, and you still stay in the language." + }, + { + "text": "So anything that's longer than that special length can be modified in a certain way, and you still stay in the language." + }, + { + "text": "So let's look at the actual statement of the lemma." + }, + { + "text": "So there is a number P such that if S is a string in the language and it's longer than P, or at least of length P, then you can take S, and you can cut it up into three pieces, x, y, and z." + }, + { + "text": "So that's just breaking S into three pieces, where you can take that middle piece, repeat it as many times as you like, and you still stay in the language." + }, + { + "text": "That's what the pumping lemma is saying." + }, + { + "text": "And there's a bunch of other conditions here too." + }, + { + "text": "But the spirit of the pumping lemma says whenever you have a regular language, there's some cutoff such that all strings longer than that cutoff can be what we call pumped." + }, + { + "text": "You can take that string, you can find a section somewhere in the middle of that string, or somewhere you cut it up into three pieces, you take that center piece, and you can repeat it." + }, + { + "text": "You can pump it up." + }, + { + "text": "And by repeating that string and repeating that piece, the string gets longer and longer, but you still stay in the language." + }, + { + "text": "That's the special property that all regular languages have." + }, + { + "text": "So kind of in an informal way, and I'll try to help you get the feeling for this, formally it says that if you have a regular language, then every long string, so long is by informal way of saying bigger than this value p, every long string in the language can be pumped." + }, + { + "text": "And this result still stays in the language." + }, + { + "text": "And by pumped means I can cut the string into three pieces and repeat that middle piece as many times as I want." + }, + { + "text": "That's what I mean by pumping a string." + }, + { + "text": "So we'll do some examples in a second." + }, + { + "text": "But first, we're going to see how to prove this." + }, + { + "text": "And hopefully, that'll give you some feeling also for why it's true." + }, + { + "text": "And actually, maybe before I actually jump into the proof, let's look at these three conditions here just to understand it a little bit more thoroughly." + }, + { + "text": "So condition one kind of says what I just was telling you." + }, + { + "text": "I can break s into three pieces, x, y, z, such that if I take xy to the iz, so that's repeating y as many times as I want." + }, + { + "text": "So here's y to the i kind of defined, if that's helpful to you, just y, i copies of y." + }, + { + "text": "So I can take xy to the iz, and I remain in the language for every value of i, even i equals 0, which means we're just removing y, which is sometimes actually a useful thing to do." + }, + { + "text": "But let's not get ahead of ourselves." + }, + { + "text": "So I'm guaranteed to be able to cut s up into x, y, z, so that the string xyyy is still in the language, or xyyyyy, it's still in the language." + }, + { + "text": "That's going to be guaranteed for every regular language." + }, + { + "text": "That's a feature that's going to be true." + }, + { + "text": "And furthermore, and this is going to be turning out to be, it's not really kind of part of the core idea of the pumping lemma, but it actually turns out to be very helpful in applying the pumping lemma, you can always cut it up in such a way that the first two pieces are not longer than that value p. So it restricts on the ways you can cut the thing up." + }, + { + "text": "And that actually turns out to be very helpful." + }, + { + "text": "But let's first just look at the proof of this, giving kind of a little bit the high level picture." + }, + { + "text": "So my job is to show if I have a string in my language, let's say it's a, think of it as a long string, really long." + }, + { + "text": "So its length is more than p. But I think intuitively, it's just a very long string." + }, + { + "text": "And I'm going to feed that string into the machine and watch what happens." + }, + { + "text": "Something special happens when I feed the string and I look at how the machine proceeds on that string." + }, + { + "text": "Because s is so long that as I wander around inside the machine, I have to end up coming back to the same place more than once." + }, + { + "text": "It's like if you have a small park and you go for a long walk, you're going to end up coming back to where you've already seen." + }, + { + "text": "You just can't keep on seeing new stuff when you have a more small area of space to explore." + }, + { + "text": "So we're guaranteed that M is going to end up repeating some state when it's reading s, because s is so long." + }, + { + "text": "So pictorially, if you imagine here this wiggly line is kind of describing the path that M follows when it's reading s, it ends up coming back to that state qj more than once." + }, + { + "text": "So it comes back here, cycles around, comes back again before it ends up accepting." + }, + { + "text": "We know it ends up accepting because we're assuming we have a string that's in the language." + }, + { + "text": "So we picked s in the language." + }, + { + "text": "So it has to be accepted by M. But the important thing is that it repeats a state." + }, + { + "text": "Now, how does that tell me I can cut s up into those three pieces?" + }, + { + "text": "Well, I'm going to get those three pieces here." + }, + { + "text": "First of all, let's observe that here is as processing s. Here is that written right on top of the string, that state repetition occurring, qj more than once." + }, + { + "text": "And now if I look inside the machine, the part of s that took me to qj I'm going to call x." + }, + { + "text": "The part that took me from qj back to itself is I'm going to call y." + }, + { + "text": "And the part that took qj to the accept state, I'm going to call z." + }, + { + "text": "And I'm going to mark those off in s. And that gives me the way to cut s up into three pieces." + }, + { + "text": "Now, if you're appreciating what's going on inside the machine, you will see why M will also accept the string x, y, y, z." + }, + { + "text": "Because every time, once you're at qj, if you go around once, you come back to qj." + }, + { + "text": "And then if you go again, you'll come back to qj." + }, + { + "text": "And as many times as you keep seeing that y, you're just going to keep coming back to qj." + }, + { + "text": "So it doesn't matter how many y's you have." + }, + { + "text": "You're going to still, if you follow it by z, which is what you will do, you'll end up accepting the string." + }, + { + "text": "And that's really the proof." + }, + { + "text": "I mean, you have to do a little bit more here just to understand." + }, + { + "text": "I should have mentioned why I want to forbid y being the empty string." + }, + { + "text": "Because if y is the empty string, it's not interesting." + }, + { + "text": "It doesn't change." + }, + { + "text": "Repeating it doesn't actually change anything." + }, + { + "text": "So I have to make sure it's not empty." + }, + { + "text": "But anyway, that's kind of a detail here." + }, + { + "text": "If you look at the string x, y, y, z, that's still going to be accepted." + }, + { + "text": "So that's the proof of the pumping lemma." + }, + { + "text": "All right?" + }, + { + "text": "So let's have a little check-in related to that." + }, + { + "text": "This is not going to be, again, not super hard, but more just a curiosity." + }, + { + "text": "So the pumping lemma depends on the fact that if M has p states and it runs for more than p steps, then it's going to enter some state twice." + }, + { + "text": "So you may have seen that before." + }, + { + "text": "It actually has a name, which some of you may have seen." + }, + { + "text": "So let's see how to just get a poll here." + }, + { + "text": "I hope not too many of you are going to pick C, as some of you are." + }, + { + "text": "Oh, well." + }, + { + "text": "Yes." + }, + { + "text": "I think this one, most of you have seen this before." + }, + { + "text": "This is, I think you pretty much all got it." + }, + { + "text": "This is what's known as the pigeonhole principle." + }, + { + "text": "So here, sharing the results." + }, + { + "text": "Obviously, I was having a little fun with this." + }, + { + "text": "And some of you are having fun back at me." + }, + { + "text": "That's OK. OK, so let's continue on." + }, + { + "text": "Let's see how to use the pumping lemma to prove a language is not regular." + }, + { + "text": "So I put the pumping lemma up here just so you can remember the statement of it." + }, + { + "text": "So let's take the language D, which is the language 0 to the k, 1 to the k for any k. So that's some number of 0's followed by an equal number of 1's." + }, + { + "text": "We're going to prove that language is not regular by using the pumping lemma." + }, + { + "text": "And this is going to be just an ironclad proof." + }, + { + "text": "It's not going to say, well, I couldn't think of how to find it a finite automaton." + }, + { + "text": "This is going to be a proof." + }, + { + "text": "So we want to show that D is not regular." + }, + { + "text": "And we're going to give a, these things always go as a proof by contradiction." + }, + { + "text": "So proof by contradiction, hopefully as a reminder to you, the way that works is you're going to assume the opposite of what you're trying to prove." + }, + { + "text": "And then from that, something crazy is going to happen, something you know is obviously false or wrong." + }, + { + "text": "And so therefore, your assumption, which is the opposite of what you're trying to prove, had to be wrong." + }, + { + "text": "And so therefore, the thing you're trying to prove has to be right." + }, + { + "text": "That's the essence of what's called proof by contradiction." + }, + { + "text": "So first of all, we're going to assume to get our contradiction that D is regular, which is what we're trying to show is not the case." + }, + { + "text": "Now, if D is regular, then we can apply the pumping limit up above here, which gives us that pumping length p, which says that any string longer than p can be pumped and you stay in the language." + }, + { + "text": "That's what the pumping limit tells you." + }, + { + "text": "So let's pick the string s, which is the string 0 to the p, 1 to the p. Here's sort of a picture of s off on the side here." + }, + { + "text": "So a bunch of 0s followed by an equal number of 1s." + }, + { + "text": "And that string is in D, because D is strings of that form." + }, + { + "text": "And it's longer than p. Obviously, it's of length 2p." + }, + { + "text": "So the pumping limit tells us there's a way to cut it up, satisfying those three conditions." + }, + { + "text": "So how in the world could we possibly cut s up?" + }, + { + "text": "Well, remember the three conditions, and especially condition 3 is going to come in handy here, say that you can cut s up into three pieces, x, y, and z, where the first two pieces lie in the first p symbols of s, at most p long." + }, + { + "text": "So x and y together are not very big." + }, + { + "text": "They don't extend beyond the first half of x and first half of s. And in particular, they're all 0s." + }, + { + "text": "x and y are going to be all 0s." + }, + { + "text": "z is going to perhaps have some 0s and will have the rest of the 1s." + }, + { + "text": "We'll have the 1s." + }, + { + "text": "Now, the pumping limit says that if you cut it up that way, you can repeat y as many times as you like, and you stay in the language." + }, + { + "text": "But that's obviously false, because if you repeat y, which now has only 0s, you're going to have too many 0s." + }, + { + "text": "And so the resulting string is no longer going to be of the form 0 to the k, 1 to the k. It's going to be lots of 0s followed by not so many 1s." + }, + { + "text": "That's not in the language." + }, + { + "text": "And that violates what the pumping limit tells you is supposed to happen." + }, + { + "text": "And that's a contradiction." + }, + { + "text": "So therefore, our assumption that D is regular is false." + }, + { + "text": "And so we conclude that D is not regular." + }, + { + "text": "So that's a fairly simple one." + }, + { + "text": "I thought I would do another couple of examples, because you have this on your homework, and I thought it might be helpful." + }, + { + "text": "So here's a second one, slightly harder, but not too much." + }, + { + "text": "Let's take the language F, which looks like the strings ww." + }, + { + "text": "These are strings that are two copies of the same string." + }, + { + "text": "For any string that might be in sigma star, so for any string at all, I'm going to have two copies of that string." + }, + { + "text": "And so F is those strings which are just two copies of the same string." + }, + { + "text": "OK. We're going to show that F is not regular." + }, + { + "text": "These things always go the same way." + }, + { + "text": "It's the same pattern." + }, + { + "text": "You prove by contradiction." + }, + { + "text": "So you assume for contradiction that D, that's bad." + }, + { + "text": "That was copied from my other slide." + }, + { + "text": "That's wrong." + }, + { + "text": "Let's see if I can actually make this work here." + }, + { + "text": "Good." + }, + { + "text": "Assume for contradiction that F is regular." + }, + { + "text": "The pumping lemma gives F is above." + }, + { + "text": "And so now we need to choose a string S that's in F to do the pumping and show that the pumping lemma is going to fail." + }, + { + "text": "You're going to pump, and you're going to get something which is not in language, which shows that something has gone wrong." + }, + { + "text": "But which S to choose?" + }, + { + "text": "And sometimes, that's where the creativity in applying the pumping lemma comes in, because you have to figure out which is the right string you're going to pump on." + }, + { + "text": "So you might try the string, well, 0 to the p, 0 to the p. That's certainly in F. It's two copies of the same string." + }, + { + "text": "Here it is I've written." + }, + { + "text": "Lots of 0's followed by the same number of 0's." + }, + { + "text": "The problem is, if you use that string, it actually is a string that you can pump." + }, + { + "text": "You can break that string up into three pieces." + }, + { + "text": "And then if you let y be the string 0, 0, actually, you have to be a little careful." + }, + { + "text": "The string just 0 doesn't work, because there's an evenness-oddness phenomenon going here." + }, + { + "text": "So you might want to just think about that." + }, + { + "text": "But if you let y be the string 0, 0, then if you have the string x, y, x, any number of y's, it's still just going to be a bunch of 0's." + }, + { + "text": "And you're going to be able to see that that string is still in the language." + }, + { + "text": "So you haven't learned anything." + }, + { + "text": "If the pumping lemma works and you're satisfying the pumping lemma, you haven't learned anything." + }, + { + "text": "So what you need to find is some other string." + }, + { + "text": "That was a bad choice for s. Find a different string." + }, + { + "text": "So here's a different choice." + }, + { + "text": "0 to the p1, 0 to the p1." + }, + { + "text": "So that's two copies of the same string." + }, + { + "text": "And we're going to show it can't be pumped." + }, + { + "text": "So here's a picture of that string here." + }, + { + "text": "So 0's followed by 1, 0's followed by 1." + }, + { + "text": "And now it's very similar to the first argument." + }, + { + "text": "If you cut it into three pieces in such a way that it satisfies the conditions, the first two pieces are going to be residing only among the 0's." + }, + { + "text": "And so therefore, when you repeat a y, you're no longer going to have two copies of the same string and so won't be in the language." + }, + { + "text": "So therefore, you've got a contradiction and f is not regular." + }, + { + "text": "So you have to play with the pumping lemma a little bit." + }, + { + "text": "If you haven't seen that before, it's going to be, it takes a little getting used to." + }, + { + "text": "But you have a few homework questions that need to be solved using the pumping lemma." + }, + { + "text": "All right." + }, + { + "text": "So now let's look at, lastly, there is another method that can come in, which is combining closure properties with the pumping lemma." + }, + { + "text": "So closure properties sometimes help you." + }, + { + "text": "So let's look at the language B, which is actually we saw earlier in the lecture, where we have an equal number of 0's and 1's." + }, + { + "text": "Now, we could prove that directly using the pumping lemma as not being regular." + }, + { + "text": "But it's actually even easier." + }, + { + "text": "What we're going to prove that it is, we're going to prove that it's not regular in a different way." + }, + { + "text": "First, we're going to assume for contradiction, as we often do, that it is regular." + }, + { + "text": "And now we're going to use something, we're going to use some other knowledge." + }, + { + "text": "We're not going to use the pumping lemma here because we're going to take advantage of an earlier case where we use the pumping lemma." + }, + { + "text": "And so now we know that the string, the language 0 star 1 star is a regular language because it's described by a regular expression." + }, + { + "text": "If you take the B, which is the equal numbers of 0's and 1's, and you intersect it with 0 star 1 star, that's going to be a regular language if B was regular using closure under intersection." + }, + { + "text": "But this language B intersects 0 star 1 star is the language of equal numbers of 0's and 1's where the 0's come first." + }, + { + "text": "And that's the language D that we showed two slides back that we already know can't be regular." + }, + { + "text": "So that intersection cannot be regular, and so it violates the closure property." + }, + { + "text": "And again, we get a contradiction." + }, + { + "text": "So that's a different way of sometimes making a shortcut to prove a language is not regular." + }, + { + "text": "So we have in our last 10 minutes or so, we're going to shift gears totally in an entirely different way and consider a new model of computation, which is more powerful, that can actually do things that we can't do with finite automata." + }, + { + "text": "And these are called context-free grammars." + }, + { + "text": "So this is really just a kind of an introduction." + }, + { + "text": "We're going to spend all of next lecture looking at context-free grammars." + }, + { + "text": "And they're associated languages." + }, + { + "text": "But let's just do kind of get a preview." + }, + { + "text": "So a context-free grammar looks like this." + }, + { + "text": "You have a bunch of these what we call substitution rules or rules sometimes, which just look like a symbol, arrow, a string of symbols." + }, + { + "text": "All right?" + }, + { + "text": "That's what a context-free grammar looks like at a high level." + }, + { + "text": "Let's define some terms." + }, + { + "text": "So a rule, as I just described, is going to be a symbol, which we're going to call a variable." + }, + { + "text": "And that's going to have an arrow to a string of possibly other variables and symbols called terminals." + }, + { + "text": "So a variable is a symbol that appears on the left-hand side of a rule." + }, + { + "text": "Anything that appears on the left-hand side is going to be considered to be a variable." + }, + { + "text": "So s and r are both variables." + }, + { + "text": "Now, other symbols that appear in the grammar, which don't appear in the left-hand side, those are going to be called terminals." + }, + { + "text": "So here, 0 and 1 are terminals." + }, + { + "text": "Now, you may think that empty string should also be a terminal, but that's not a symbol." + }, + { + "text": "Empty string is a string." + }, + { + "text": "It's just a string of length 0." + }, + { + "text": "So I'm not considering empty string to be a terminal." + }, + { + "text": "And then there's going to be a special variable, which is going to be considered the starting variable, just like we had a starting state." + }, + { + "text": "And that's typically going to be written as the top left symbol." + }, + { + "text": "So this symbol s here is going to be the starting symbol." + }, + { + "text": "And grammars can be used to define languages and to gen, well, to generate strings and to define languages." + }, + { + "text": "So first of all, let's see how a grammar using this as an illustration can generate strings." + }, + { + "text": "Actually, just to emphasize this terminology here, in this particular example, we had three rules." + }, + { + "text": "The two variables were r and s. The two terminals were 0 and 1." + }, + { + "text": "And the start variable was this top left-hand symbol, as I mentioned, the s. So grammars generate strings." + }, + { + "text": "The way they do is you follow a certain procedure, which is really pretty simple." + }, + { + "text": "You write down, first of all, the start variable." + }, + { + "text": "And I'll do an example in a second." + }, + { + "text": "You write down the start variable." + }, + { + "text": "And then you take a look at what you've written down." + }, + { + "text": "And if it has any variables in it, you can apply one of the corresponding right-hand sides of a rule as a substitution for that variable." + }, + { + "text": "And so, for example, if you have an s in the thing you've written down, you can substitute for that s a 0, s, 1." + }, + { + "text": "Or you can substitute for that s an r. Or if you have an r, you can substitute for that s an empty string." + }, + { + "text": "So you're just going to keep on doing that substitutions over and over again until there are no variables left." + }, + { + "text": "So there's nothing left to substitute." + }, + { + "text": "Only terminals remain." + }, + { + "text": "At that point, you have generated a string in the language." + }, + { + "text": "So the language, then, is the collection of all generated strings." + }, + { + "text": "OK, let's do an example." + }, + { + "text": "Here's an example of G1 generating some string." + }, + { + "text": "So as I mentioned, first of all, you're going to write down the start variable." + }, + { + "text": "And I'm just going to illustrate this in sort of two parallel tracks here." + }, + { + "text": "On the left side, I'm going to show you the tree of substitutions." + }, + { + "text": "And on the right side, I'm going to show you the resulting string that you get by applying those substitutions." + }, + { + "text": "OK?" + }, + { + "text": "So over here, I'm going to substitute for s the string 0, s1." + }, + { + "text": "So on the right-hand side, I just have 0, s1 because that's what I substituted for s. But you'll see it's going to look a little different in a second." + }, + { + "text": "Here, again, I still have a variable." + }, + { + "text": "So I'm going to substitute for s 0, s1." + }, + { + "text": "Now I have the resulting string 0, 0, s1, 1 because I've substituted 0, s1 for the previous s. But the 0 and 1 stick around from before." + }, + { + "text": "They don't go anywhere." + }, + { + "text": "So I have at this point 0, 0, s1, 1." + }, + { + "text": "Now I'm going to take a different choice." + }, + { + "text": "I'm going to substitute for s. I could have gone either way." + }, + { + "text": "There's sort of something almost like nondeterminism here because you have a choice." + }, + { + "text": "I'm going to substitute for s. Instead of 0, s1, I'm going to substitute r because that's also legitimate in terms of the rules." + }, + { + "text": "And so now I'm going to have 0, 0, r, 1, 1." + }, + { + "text": "And now r, there's no choices here." + }, + { + "text": "r can only be substituted for by an empty string." + }, + { + "text": "So I get to r becomes just empty string." + }, + { + "text": "And in terms of the string generated, empty string doesn't add anything." + }, + { + "text": "It just really is nothing." + }, + { + "text": "It's a nothing." + }, + { + "text": "So I get the string 0, 0, 1, 1." + }, + { + "text": "And this is a string just of terminal symbols." + }, + { + "text": "And so that is a string in the language of the grammar G1." + }, + { + "text": "If you think about it, G1's language is that language that we saw before, which I think we called D. 0 to the k, 1 to the k for k greater than or equal to 0." + }, + { + "text": "So this is an example of a language that a context-free grammar can do, but a finite automaton cannot do." + }, + { + "text": "So that is our little introduction to content." + }, + { + "text": "Oops, there's one more check-in here." + }, + { + "text": "Oh, yeah, so I'm asking you to actually look at, let me get myself out of this picture so you don't see me blocking things." + }, + { + "text": "And we will do one last check-in." + }, + { + "text": "Check-in, make sure you're staying around for the whole thing." + }, + { + "text": "Now there could be several of these strings that are in the language." + }, + { + "text": "You have to click them all." + }, + { + "text": "All the ones that you have found that are in the language of this grammar that can be generated by grammar G2, you have to click those." + }, + { + "text": "I'll give you a little bit more time on this one to see which ones G2 can generate." + }, + { + "text": "I'll give you a hint." + }, + { + "text": "There's more than one, but not all." + }, + { + "text": "So I see you're making some progress here." + }, + { + "text": "Interesting." + }, + { + "text": "So please, we're going to wrap this up very quickly." + }, + { + "text": "You can click, somebody's telling me you can unclick." + }, + { + "text": "Thank you, good to know." + }, + { + "text": "OK, so still things are coming in here." + }, + { + "text": "So we're running toward the end of the hour here." + }, + { + "text": "I don't want to go over." + }, + { + "text": "So I'm going to end it in five seconds." + }, + { + "text": "Click away." + }, + { + "text": "And don't forget, we're not going to charge you if you get it wrong." + }, + { + "text": "Sharing results, I don't know why it has an orange one there because there are several correct answers here." + }, + { + "text": "So it's A, B, and D are correct." + }, + { + "text": "You can get any of those." + }, + { + "text": "It's really sort of two copies of the language we had before next to one another." + }, + { + "text": "And so the only thing you cannot get is 1, 0, 1, 0." + }, + { + "text": "So I encourage you to think about that." + }, + { + "text": "And I will come to our last side of today, which is just a quick review." + }, + { + "text": "I can put myself back." + }, + { + "text": "So we showed how to convert DFAs to regular expressions." + }, + { + "text": "And the summary is that DFAs, NFAs, GNFAs even, and regular expressions are all equivalent in the class of languages they can describe." + }, + { + "text": "The second thing we did was a method for proving languages not regular by using the pumping lemma or closure properties." + }, + { + "text": "And lastly, we introduced context-free grammars." + }, + { + "text": "And we're going to see more about those on Thursday." + }, + { + "text": "So with that, I think we're out of time." + }, + { + "text": "And I'll thank you for the notes of appreciation." + }, + { + "text": "And I think we're going to end here and see you on Thursday, if not before." + } +] \ No newline at end of file diff --git a/sight/sources/annotated/MsIvs_6vC38.json b/sight/sources/annotated/MsIvs_6vC38.json new file mode 100644 index 0000000000000000000000000000000000000000..eb63654f5e19ec3b9d0d6ce592514ba57cb466a5 --- /dev/null +++ b/sight/sources/annotated/MsIvs_6vC38.json @@ -0,0 +1,1565 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + }, + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + }, + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + }, + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + }, + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + }, + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + }, + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + }, + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + }, + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + }, + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + }, + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + }, + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + }, + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + }, + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + }, + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + }, + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + }, + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + }, + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + }, + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + }, + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + }, + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + }, + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + }, + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + }, + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + }, + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + }, + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated/RD9AWDdj-Yk.json b/sight/sources/annotated/RD9AWDdj-Yk.json new file mode 100644 index 0000000000000000000000000000000000000000..b3f2d7da134535f60983dff7d005ab01f5c96c54 --- /dev/null +++ b/sight/sources/annotated/RD9AWDdj-Yk.json @@ -0,0 +1,1172 @@ +[ + { + "text": " Okay." + }, + { + "text": "This is the lecture on the singular value decomposition." + }, + { + "text": "But everybody calls it the SVD." + }, + { + "text": "So this is the final and best factorization of a matrix." + }, + { + "text": "Let me tell you what's coming." + }, + { + "text": "The factors will be orthogonal matrix, diagonal matrix, orthogonal matrix." + }, + { + "text": "So it's things that we've seen before, these special good matrices, orthogonal, diagonal." + }, + { + "text": "The new point is that we need two orthogonal matrices." + }, + { + "text": "A can be any matrix whatsoever." + }, + { + "text": "Any matrix whatsoever has this singular value decomposition." + }, + { + "text": "So a diagonal one in the middle, but I need two different, probably different, orthogonal matrices to be able to do this." + }, + { + "text": "Okay." + }, + { + "text": "And this factorization has jumped into importance and is properly, I think, maybe the bringing together of everything in this course." + }, + { + "text": "One thing we'll bring together is, like, the very good family of matrices that we just studied." + }, + { + "text": "Symmetric positive definite." + }, + { + "text": "Do you remember the story with those guys?" + }, + { + "text": "Because they were symmetric, their eigenvectors were orthogonal, so I could produce an orthogonal matrix." + }, + { + "text": "This is my usual one." + }, + { + "text": "My usual one is the eigenvectors and eigenvalues." + }, + { + "text": "In the symmetric case, the eigenvectors are orthogonal, so I've got the good, my ordinary S has become a especially good Q, and positive definite, my ordinary lambda has become a positive lambda." + }, + { + "text": "So this is, that's the singular value decomposition." + }, + { + "text": "In case our matrix is symmetric positive definite, in that case, I don't need two, u and a v, one orthogonal matrix will do for both sides." + }, + { + "text": "But, so this would be no good in general, because usually the eigenvector matrix isn't orthogonal." + }, + { + "text": "So this is not what I'm, that's not what I'm after." + }, + { + "text": "I'm looking for orthogonal times diagonal times orthogonal." + }, + { + "text": "And let me show you what that means and where it comes from." + }, + { + "text": "OK. What does it mean?" + }, + { + "text": "You remember the picture of any linear transformation." + }, + { + "text": "This was, like, the most important figure in 1806." + }, + { + "text": "And what am I looking for now?" + }, + { + "text": "A typical vector in the row space, typical vector, let me call it v1, gets taken over to some vector in the column space, say u1." + }, + { + "text": "So u1 is a v1." + }, + { + "text": "OK. Now, another vector gets taken over here somewhere." + }, + { + "text": "What am I looking for?" + }, + { + "text": "In this SVD, this singular value decomposition, what I'm looking for is an orthogonal basis here that gets knocked over into an orthogonal basis over there." + }, + { + "text": "See, that's pretty special, to have an orthogonal basis in the row space that goes over into an orthogonal basis, so this is like a right angle and this is a right angle, into an orthogonal basis in the column space." + }, + { + "text": "So that's our goal, is to find -- you see how things are coming together." + }, + { + "text": "First of all, can I find an orthogonal basis for this row space?" + }, + { + "text": "Of course." + }, + { + "text": "No big deal to find an orthogonal basis." + }, + { + "text": "Graham-Schmidt tells me how to do it." + }, + { + "text": "Start with any old basis and use- grind through Graham-Schmidt, out comes an orthogonal basis." + }, + { + "text": "But then, if I just take any old orthogonal basis, then when I multiply by A, there's no reason why it should be orthogonal over here." + }, + { + "text": "So I'm looking for this special setup where A takes these basis vectors into orthogonal vectors over there." + }, + { + "text": "Now, you might have noticed that the null space I didn't include." + }, + { + "text": "Why don't I stick that in?" + }, + { + "text": "You remember our usual figure had a little null space and a little null space." + }, + { + "text": "And, those are no problems." + }, + { + "text": "Those are- null spaces are going to show up as zeros on the diagonal of sigma, so that's not what we're- that doesn't present any difficulty." + }, + { + "text": "Our difficulty is to find the- so do you see what this will mean?" + }, + { + "text": "This will mean that A times this- these v's, v1, v2, up to- what's the dimension of this row space?" + }, + { + "text": "vr." + }, + { + "text": "Sorry, that v a little smaller." + }, + { + "text": "Up to vr." + }, + { + "text": "So that's A v1 is going to be the first column, so let me- here's what I'm- here's what I'm achieving." + }, + { + "text": "Oh, I would like- I'm not only going to make these orthogonal, but why not make them orthonormal?" + }, + { + "text": "Make them unit vectors." + }, + { + "text": "So this- maybe the unit vector is here, is the u1, and this might be a multiple of it." + }, + { + "text": "So really what's happening is A v1 is some multiple of u1, right?" + }, + { + "text": "I'm going to- these guys will be unit vectors, and they'll go over into multiples of unit vectors, and the multiple I'm not going to call lambda anymore, I'm calling it sigma." + }, + { + "text": "So that's the number- the stretching number." + }, + { + "text": "And similarly, A v2 is sigma 2 u2." + }, + { + "text": "This is what- this is my goal." + }, + { + "text": "And now I want to express that goal in matrix language." + }, + { + "text": "That's the usual step." + }, + { + "text": "Think of what you want and then express it as a matrix multiplication." + }, + { + "text": "So A v1 is sigma 1 u1." + }, + { + "text": "Actually, here we go." + }, + { + "text": "Let me pull out these u1, u2 to ur, and then a matrix with the sigmas." + }, + { + "text": "It's- everything now is going to be in this- in that, in that, little part of the blackboard." + }, + { + "text": "Do you see that this equation says what I'm trying to do with my figure?" + }, + { + "text": "A times the first basis vector should be sigma 1 times the other basis- the other first basis vector." + }, + { + "text": "These are the basis vectors in the row space, these are the basis vectors in the column space, and these are the multiplying factors." + }, + { + "text": "So A v2 is sigma 2 times u2, A vr is sigma r times ur." + }, + { + "text": "And then we've got a whole lot of zeros and maybe some zeros at the end, but this is- that's the heart of it." + }, + { + "text": "And now if I express that in- as matrices, because you knew that was coming, that's what I have." + }, + { + "text": "So this is my goal." + }, + { + "text": "To find an orthogonal basis in the rows- orthonormal, even, basis in the row space, and an orthonormal basis in the column space, so that I'm sort of diagonalized the matrix." + }, + { + "text": "The matrix A is like getting converted to this diagonal matrix sigma." + }, + { + "text": "And you notice that usually I have to do- I have to allow myself two different bases." + }, + { + "text": "My little comment about symmetric positive definite was the one case where it's A q equal q sigma, where v and u are the same q." + }, + { + "text": "But mostly, I'm going to take a matrix like, oh, let me take a matrix like four four minus three three." + }, + { + "text": "Okay." + }, + { + "text": "There's a two by two matrix." + }, + { + "text": "It's invertible, so it has rank two." + }, + { + "text": "So I'm going to look for two vectors, v1 and v2, in the row space, and u- so I'm going to look for v1 v2 in the row space, which of course is R2." + }, + { + "text": "And I'm going to look for u1 u2 in the column space, which of course is also R2." + }, + { + "text": "And I'm going to look for numbers sigma 1 and sigma 2, so that it all comes out right." + }, + { + "text": "So these guys are orthonormal." + }, + { + "text": "These guys are orthonormal, and these are the scaling factors." + }, + { + "text": "So I'll do that example as soon as I get the matrix picture straight." + }, + { + "text": "Okay." + }, + { + "text": "Do you see that this expresses what I want?" + }, + { + "text": "Can I just say two words about null spaces?" + }, + { + "text": "If we have -- if there's some null space, then we've got- we want to stick in a basis for those, for that." + }, + { + "text": "So here comes a basis for the null space, v R plus one down to vn." + }, + { + "text": "So if we only had an R-dimensional row space and the other n minus R dimensions were in the null space, okay, we'll take an orthogonal- orthonormal basis there, no problem." + }, + { + "text": "And then we'll just get zeros." + }, + { + "text": "So actually, those zeros will come out from the- on the diagonal matrix." + }, + { + "text": "So I'll complete that to, to, orthonormal basis for the whole space, Rn." + }, + { + "text": "I complete this to an orthonormal basis for the whole space, Rn, and I complete that with zeros." + }, + { + "text": "Null spaces are no problem here." + }, + { + "text": "So really, the true problem is in a matrix like that, which isn't symmetric, so I can't use its eigenvectors, they're not orthogonal, but somehow I have to get these orthogonal, in fact, orthonormal guys that make it work." + }, + { + "text": "I have to find this, these orthonormal guys, these orthonormal guys, and I want A v1 to be sigma 1 u1, and A v2 to be sigma 2 u2." + }, + { + "text": "Okay." + }, + { + "text": "That's my goal." + }, + { + "text": "Here's, here's the, matrices that are going to get me there." + }, + { + "text": "Now, these are orthogonal matrices." + }, + { + "text": "I can put that, if I multiply on both sides by v inverse, I have A equals u sigma v inverse, and of course, you know the other way I can write v inverse." + }, + { + "text": "This is one of those square orthogonal matrices, so it's the same as u sigma v transpose." + }, + { + "text": "Okay." + }, + { + "text": "Here's my problem." + }, + { + "text": "I've got two orthogonal matrices here, and I don't want to find them both at once." + }, + { + "text": "So I want to cook up some expression that will make the u's disappear." + }, + { + "text": "I would like to make the u's disappear and leave me only with the v's." + }, + { + "text": "And here's how to do it." + }, + { + "text": "It's, it's the same combination that keeps showing up whenever we have a general rectangular matrix, then it's A transpose A, that's the great matrix." + }, + { + "text": "That's the great matrix." + }, + { + "text": "That's the matrix that's symmetric." + }, + { + "text": "And, in fact, positive definite or at least positive semidefinite." + }, + { + "text": "This is the matrix with nice properties." + }, + { + "text": "So let's see what will it be." + }, + { + "text": "So if I took the transpose, then, I would have A transpose A will be what?" + }, + { + "text": "What do I have?" + }, + { + "text": "If I transpose that, I have v sigma transpose u transpose, that's, that's the A transpose." + }, + { + "text": "Now the A." + }, + { + "text": "And what have I got?" + }, + { + "text": "Looks like worse, because it's got six things now together, but it's going to collapse into something good." + }, + { + "text": "What does u transpose u collapse into?" + }, + { + "text": "I." + }, + { + "text": "The identity." + }, + { + "text": "So that's the key point." + }, + { + "text": "This is the identity and we don't have u anymore." + }, + { + "text": "And sigma transpose times sigma, those are diagonal matrices." + }, + { + "text": "So their product is just going to have sigma squareds on the diagonal." + }, + { + "text": "So do you see what we've got here?" + }, + { + "text": "This is v times this easy matrix, sigma one squared, sigma two squared, times v transpose." + }, + { + "text": "This is the A transpose A." + }, + { + "text": "This is, let me copy down, A transpose A is that." + }, + { + "text": "U's are out of the picture now." + }, + { + "text": "I'm only having to choose the v's." + }, + { + "text": "And what are these v's?" + }, + { + "text": "And what are these sigmas?" + }, + { + "text": "Do you know what the v's are?" + }, + { + "text": "They're the eigenvectors." + }, + { + "text": "See, this is a perfect eigenvector, eigenvalue, Q lambda Q transpose for the matrix A transpose A." + }, + { + "text": "A itself is like nothing special." + }, + { + "text": "But A transpose A will be special." + }, + { + "text": "It'll be symmetric, positive, definite." + }, + { + "text": "So this'll be its eigenvectors and this'll be its eigenvalues." + }, + { + "text": "And the eigenvalues will be positive because this thing's positive definite." + }, + { + "text": "Can I just now so this is my method." + }, + { + "text": "This tells me what the v's are and how am I going to find the u's?" + }, + { + "text": "Well, one way would be to look at A A transpose." + }, + { + "text": "Put, multiply A by A transpose in the opposite order." + }, + { + "text": "That will stick the v's in the middle, knock them out, and leave me with the u's." + }, + { + "text": "So here's the overall picture, then." + }, + { + "text": "The v's are the eigenvectors of A transpose A." + }, + { + "text": "The u's are the eigenvectors of A A transpose, which are different." + }, + { + "text": "And the sigmas are the square roots of these and the positive square roots, so we have positive sigmas." + }, + { + "text": "Let me do that for that example." + }, + { + "text": "This is really what you should know and be able to do for, the SVD." + }, + { + "text": "Okay." + }, + { + "text": "Let me take that matrix." + }, + { + "text": "So what's my first step?" + }, + { + "text": "Compute A transpose A, because I want its eigenvectors." + }, + { + "text": "Okay, so I have to compute A transpose A." + }, + { + "text": "So A transpose is four four minus three three, and A is four four minus three three." + }, + { + "text": "And I do that multiplication and I get sixteen, I get twenty-five, I get sixteen minus nine, is that seven?" + }, + { + "text": "And it better come out symmetric and, oh, okay, and then it comes out twenty-five." + }, + { + "text": "Okay." + }, + { + "text": "So I want its eigenvectors and its eigenvalues." + }, + { + "text": "Its eigenvectors will be the v's, its eigenvalues will be the squares of the sigmas." + }, + { + "text": "Okay." + }, + { + "text": "What are the eigenvalues and eigenvectors of this guy?" + }, + { + "text": "Have you seen that two by two example enough to recognize that the eigenvectors are, that one one is an eigenvector?" + }, + { + "text": "So this is, here is A transpose A. I'm looking for its eigenvectors." + }, + { + "text": "So its eigenvectors, I think, are one one and one minus one." + }, + { + "text": "Because if I multiply that matrix by one one, what do I get?" + }, + { + "text": "If I multiply that matrix by one one, I get thirty-two thirty-two." + }, + { + "text": "So which is thirty-two of one one." + }, + { + "text": "So there's the first eigenvector." + }, + { + "text": "And there's the eigenvalue for A transpose A, so I'm going to take its square root in the, for sigma." + }, + { + "text": "Okay." + }, + { + "text": "What's the eigenvector that goes, eigenvalue that goes with this one?" + }, + { + "text": "If I do that multiplication, what do I get?" + }, + { + "text": "I get some multiple of one minus one." + }, + { + "text": "And what is that multiple?" + }, + { + "text": "Looks like eighteen." + }, + { + "text": "Okay." + }, + { + "text": "So those are the two eigenvectors." + }, + { + "text": "But, oh, just a moment, I didn't normalize them." + }, + { + "text": "To, to make everything absolutely right, I ought to normalize these eigenvectors, divide by their length, square root of two." + }, + { + "text": "So all these guys should be true unit vectors, and, of course, that normalization didn't change the thirty-two and the eighteen." + }, + { + "text": "Okay." + }, + { + "text": "So I'm happy with the Vs, here are the Vs, so now let me put together the, the, the pieces here." + }, + { + "text": "Here's my A." + }, + { + "text": "Here's my A." + }, + { + "text": "Let me, let me write down A again." + }, + { + "text": "This should, if, if life is right, we should get U, which I don't yet know, U I don't yet know, sigma, I do now know." + }, + { + "text": "What's sigma?" + }, + { + "text": "So I'm looking for U sigma V transpose." + }, + { + "text": "U, the diagonal guy, and V transpose." + }, + { + "text": "Okay." + }, + { + "text": "Let's just see that come out right." + }, + { + "text": "So what's, what are the, what are the sigmas?" + }, + { + "text": "They're the square roots of these things." + }, + { + "text": "So square root of thirty-two and square root of eighteen." + }, + { + "text": "Zero, zero." + }, + { + "text": "Okay." + }, + { + "text": "What are the Vs?" + }, + { + "text": "They're these two." + }, + { + "text": "And I have to transpose, maybe that, maybe that just leaves me with one, with one over square root of two in that row, and the other one is one over square root of two minus one over square root of two." + }, + { + "text": "Now, finally, I've got to know the Us." + }, + { + "text": "Well, actually, one way to do, since I now know all the other pieces, I could put those together and figure out what the Us are." + }, + { + "text": "But let me do it the A A transpose way." + }, + { + "text": "Okay, find the Us now." + }, + { + "text": "U1 and U2." + }, + { + "text": "And what are they?" + }, + { + "text": "I look at A A transpose, so A is supposed to be U sigma V transpose, and then when I transpose that, I get V sigma transpose U transpose." + }, + { + "text": "So I'm just doing it in the opposite order, A times A transpose, and what's the good part here?" + }, + { + "text": "That in the middle, V transpose V is going to be the identity." + }, + { + "text": "So this is just U sigma sigma transpose, that's some diagonal matrix with sigma squareds and U transpose." + }, + { + "text": "So what am I seeing here?" + }, + { + "text": "I'm seeing here, again, a symmetric positive definite or at least semi-definite matrix, and I'm seeing its eigenvectors and its eigenvalues." + }, + { + "text": "So if I compute A A transpose, its eigenvectors will be the things that go into U." + }, + { + "text": "Okay, so I need to compute A A transpose." + }, + { + "text": "I guess I'm going to have to go -." + }, + { + "text": "Let me, can I move that up just a little, maybe a little more, and do A A transpose." + }, + { + "text": "So what's A?" + }, + { + "text": "Four, four, minus three and three." + }, + { + "text": "And what's A transpose?" + }, + { + "text": "Four, four, minus three and three." + }, + { + "text": "And when I do that multiplication, I get, what do I get?" + }, + { + "text": "Sixteen and sixteen, thirty-two." + }, + { + "text": "That one comes out zero." + }, + { + "text": "Oh, so this is a lucky case, and that one comes out eighteen." + }, + { + "text": "So this is, like, an accident, that A A transpose happens to come out diagonal, so we know easily its eigenvectors and eigenvalues." + }, + { + "text": "So its eigenvectors are, what's the first eigenvector for this A A transpose matrix?" + }, + { + "text": "It's just one zero, and when I do that multiplication, I get thirty-two times one zero." + }, + { + "text": "And the other eigenvector is just zero one, and when I multiply by that, I get eighteen." + }, + { + "text": "So this is A A transpose, multiplying that gives me the thirty-two A A transpose, multiplying this guy gives me eighteen." + }, + { + "text": "First of all, I got thirty-two and eighteen again." + }, + { + "text": "Am I surprised?" + }, + { + "text": "Yeah, it's clearly not an accident." + }, + { + "text": "The eigenvalues of A A transpose were exactly the same as the eigenvalues of this one was A transpose A." + }, + { + "text": "That's no surprise at all." + }, + { + "text": "The eigenvalues of A B are same as the eigenvalues of B A." + }, + { + "text": "The order, that's a very nice fact, that eigenvalues stay the same if I switch the order of multiplication." + }, + { + "text": "So no surprise to see thirty-two and eighteen." + }, + { + "text": "What I learned, first I checked that things were numerically correct, but now I've learned these eigenvectors, and actually they're about as nice as can be." + }, + { + "text": "They're the best orthogonal matrix, just the identity." + }, + { + "text": "Okay." + }, + { + "text": "So my claim is that it ought to all fit together." + }, + { + "text": "That this numeri- this, these numbers should come out right." + }, + { + "text": "The numbers should come out right because the, the, matrix multiplications use the properties that we want." + }, + { + "text": "Okay." + }, + { + "text": "So we just check that." + }, + { + "text": "Here's the identity, so not doing anything." + }, + { + "text": "Square root of thirty-two is multiplying that row, so that's square root of thirty-two divided by square root of two means square root of sixteen, four." + }, + { + "text": "Correct?" + }, + { + "text": "And square root of eighteen is divided by square root of two, so that leaves me square root of nine, which is three, but no, Professor Strang, you see the problem." + }, + { + "text": "Why is that?" + }, + { + "text": "Okay." + }, + { + "text": "Why am I getting minus three three here, and here I'm getting three minus three?" + }, + { + "text": "Phooey." + }, + { + "text": "I don't know why." + }, + { + "text": "It shouldn't have happened, but it did." + }, + { + "text": "Now, okay, you could say, well, just, the eigenvector there could have, I could have had the minus sign here for that eigenvector, but I'm not happy about that." + }, + { + "text": "Hm." + }, + { + "text": "Okay." + }, + { + "text": "Okay." + }, + { + "text": "So I realize there's a little catch here somewhere, and I may not see it until Wednesday, which then gives you a very important reason to come back on Wednesday, to catch that sign difference." + }, + { + "text": "So what did I do illegally?" + }, + { + "text": "I think I put the eigenvectors in that matrix V transpose." + }, + { + "text": "Okay, I'm going to have to think, why did that come out, with the opposite sign?" + }, + { + "text": "So you see, I mean, if I had a minus there, I would be all right, but I don't want that." + }, + { + "text": "I want positive entries down the diagonal of sigma squared." + }, + { + "text": "Okay." + }, + { + "text": "It'll come to me, but I'm going to leave this example to finish." + }, + { + "text": "Okay." + }, + { + "text": "And the beauty of, these sliding boards is, I can make that go away." + }, + { + "text": "Can I, let me not do it, though." + }, + { + "text": "Yes, let me take a second example." + }, + { + "text": "Let me take a second example where the matrix is singular." + }, + { + "text": "So rank one." + }, + { + "text": "Okay." + }, + { + "text": "So let me take as an example two, where my matrix A is going to be rectangular again." + }, + { + "text": "Let me just make it four three eight six." + }, + { + "text": "Okay." + }, + { + "text": "That's a rank one matrix." + }, + { + "text": "So that has a null space and only a one-dimensional row space and column space." + }, + { + "text": "So actually, my picture becomes easy for this matrix, because what's my columns, my row space for this one?" + }, + { + "text": "So this is two by two, so my pictures are both two dimensional." + }, + { + "text": "My row space is all multiples of vector four three." + }, + { + "text": "So the whole, the row space is just a line, right?" + }, + { + "text": "That's the row space." + }, + { + "text": "And the null space, of course, is the perpendicular line." + }, + { + "text": "So the row space for this matrix is multiples of four three." + }, + { + "text": "Typical row." + }, + { + "text": "Okay." + }, + { + "text": "What's the column space?" + }, + { + "text": "The columns are all multiples of four eight, three six, one two." + }, + { + "text": "The column space, then, goes in, like, this direction." + }, + { + "text": "So the column space, when I look at those columns, the column space, it was only one dimensional, because the rank is one." + }, + { + "text": "It's multiples of four eight." + }, + { + "text": "Okay." + }, + { + "text": "And what's the null space of A transpose?" + }, + { + "text": "It's the perpendicular guy." + }, + { + "text": "There's the, so this was the null space of A, and this is the null space of A transpose." + }, + { + "text": "Okay." + }, + { + "text": "What I want to say here is that the, that choosing these orthogonal bases for the row space and the column space is, like, no problem." + }, + { + "text": "They're only one dimensional." + }, + { + "text": "So what should v be?" + }, + { + "text": "v should be v1, but, yeah, v1, rather." + }, + { + "text": "v1 is supposed to be a unit vector." + }, + { + "text": "There's only one v1 to choose here, only one dimension in the row space." + }, + { + "text": "I just want to make it a unit vector." + }, + { + "text": "So v1 will be, it'll be this vector, but made into a unit vector, so four, point eight, point six." + }, + { + "text": "Four fifths, three fifths." + }, + { + "text": "And what will be u1?" + }, + { + "text": "u1 will be the unit vector there, so I want to turn four eight or one two into a unit vector, so u1 will be, let's see, if it's one two, then what multiple of one two do I want?" + }, + { + "text": "That has length square root of five, so I have to divide by square root of five." + }, + { + "text": "Let me complete the singular value decomposition for this matrix." + }, + { + "text": "So this matrix, four three eight six, is, so I know what u1, here's A, and I want to get u, the basis in the column space, and it has to start with this guy." + }, + { + "text": "One over square root of five, two over square root of five." + }, + { + "text": "Then I want the sigma." + }, + { + "text": "OK. What are we expecting now for sigma?" + }, + { + "text": "Where is, this is only a rank one matrix, we're only expecting a sigma one, which I have to find, but zero's here." + }, + { + "text": "OK, so what's sigma one?" + }, + { + "text": "We should see it, it should be the, where did these sigmas come from?" + }, + { + "text": "They came from A transpose A, so I, can I do that little calculation over here?" + }, + { + "text": "A transpose A is four three, four three eight six times four three eight six." + }, + { + "text": "This had better, this is a rank one matrix, this is going to be, the whole thing will have rank one, that's sixteen and sixty four is eighty, twelve and forty eight is sixty, twelve and forty eight is sixty, nine and thirty six is forty five." + }, + { + "text": "OK." + }, + { + "text": "It's a rank one matrix." + }, + { + "text": "Of course." + }, + { + "text": "Every row is a multiple of four three." + }, + { + "text": "And what's the eigen, what are the eigenvalues of that matrix?" + }, + { + "text": "So this is like, the calculation is like practicing now." + }, + { + "text": "What are the eigenvalues of this rank one matrix?" + }, + { + "text": "Well, tell me one eigenvalue, since the rank is only one, one eigenvalue is going to be zero." + }, + { + "text": "And then you know that the other eigenvalue is going to be a hundred and twenty five." + }, + { + "text": "So that's sigma squared, right, in A transpose A." + }, + { + "text": "So this will be the square root of a hundred and twenty five." + }, + { + "text": "And then finally, the V transpose, the Vs will be, there's V1, and what's V2?" + }, + { + "text": "What's V2 in the, what's, how do I make this into a orthonormal basis?" + }, + { + "text": "Well, V2 is in the null space direction." + }, + { + "text": "It's perpendicular to that, so point six and minus point eight." + }, + { + "text": "So those are the Vs that go in here." + }, + { + "text": "Point eight, point six, and point six minus point eight." + }, + { + "text": "OK. And I guess I better finish this guy." + }, + { + "text": "So this guy, all I want is to complete the orthonormal basis." + }, + { + "text": "It'll be coming from there, it'll be a two over square root of five and a minus one over square root of five." + }, + { + "text": "I could have take, let me take square root of five out of that matrix to make it look better." + }, + { + "text": "So one over square root of five times one, one, two, two, minus one." + }, + { + "text": "OK." + }, + { + "text": "So there I have, including the square root of five, that's an orthogonal matrix, that's an orthogonal matrix, that's a diagonal matrix, and its rank is only one." + }, + { + "text": "And now if I do that multiplication, I pray that it comes out right." + }, + { + "text": "The square root of five will cancel into that square root of one twenty-five and leave me with the square root of twenty-five, which is five, and five will multiply these numbers and I'll get whole numbers and out will come A. OK. That's a second, like, a second example showing how the null space guy, so this, this vector and the, and this one were multiplied by this zero, so they, they were easy to deal with." + }, + { + "text": "It was the key ones are the ones in the column space and the row space." + }, + { + "text": "Do you see how I'm getting columns here, diagonal here, rows here, coming together to produce A?" + }, + { + "text": "OK. That's the singular value decomposition." + }, + { + "text": "So, let, let me think what I want to add to, to complete this topic." + }, + { + "text": "Sort of what we're really doing." + }, + { + "text": "So that's two examples." + }, + { + "text": "And now let's think what we're really doing." + }, + { + "text": "We're, we're choosing the right basis for the four subspaces of linear algebra." + }, + { + "text": "Let me, let me, let me write this down." + }, + { + "text": "So V1 up to Vr is an orthonormal basis for the row space." + }, + { + "text": "U1 up to Ur is an orthonormal basis for the column space." + }, + { + "text": "And then I just finish those out by Vr plus one, the rest up to Vn is an orthonormal basis for the null space." + }, + { + "text": "And finally, Ur plus one up to Um is an orthonormal basis for the null space of A transpose." + }, + { + "text": "Do you see that we finally got the bases right?" + }, + { + "text": "They're right because they're orthonormal and also, I mean, the, again, Graham-Schmidt would have done this in chapter four." + }, + { + "text": "Here we needed eigenvalues because these bases make the matrix diagonal." + }, + { + "text": "A times Vi is a multiple of Ui." + }, + { + "text": "So I'll put and." + }, + { + "text": "The matrix has been made diagonal." + }, + { + "text": "When we choose these bases, there's no coupling between Vs and no coupling between Us." + }, + { + "text": "Each A, A times each V is in the direction of the corresponding U." + }, + { + "text": "So it's exactly the right basis for the four fundamental subspaces." + }, + { + "text": "And of course, their dimensions are what we know." + }, + { + "text": "The dimension of the row space is the rank r, and so is the dimension of the column space." + }, + { + "text": "The dimension of the null space is n minus r, that's how many vectors we need, and m minus r basis vectors for the left null space, the null space of A transpose." + }, + { + "text": "OK." + }, + { + "text": "I'm going to stop there." + }, + { + "text": "I could develop further from the SVD, but we'll see it again in the very last lectures of the course." + }, + { + "text": "There's the SVD." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated/TSkDZbGS94k.json b/sight/sources/annotated/TSkDZbGS94k.json new file mode 100644 index 0000000000000000000000000000000000000000..026278371a4595d7fb77d1c1e15f3096c3508c9a --- /dev/null +++ b/sight/sources/annotated/TSkDZbGS94k.json @@ -0,0 +1,2846 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "It doesn't run Flash Player, so I had to run them on Chrome." + }, + { + "text": "All right, so let's move on to our second chapter." + }, + { + "text": "And hopefully, in this chapter, you will feel a little better if you felt like it was going a bit fast in the first chapter." + }, + { + "text": "And the main reason why I actually went fast, especially in terms of confidence interval, some of you came and asked me, what do you mean by this is a confidence interval?" + }, + { + "text": "What does it mean that it's not happening in there with probability 95%, et cetera?" + }, + { + "text": "I just went really fast so that you could see why I didn't want to give you a first week doing probability only and without understanding what the statistical context for it was." + }, + { + "text": "So hopefully, all these things that we've done in terms of probability, you actually know why we've been doing them." + }, + { + "text": "And so we're basically going to go back to what we're doing, maybe start with some statistical setup." + }, + { + "text": "But the goal of this lecture is really going to go back again to what we've seen from a purely statistical perspective." + }, + { + "text": "So the first thing we're going to do is explain why we're doing statistical modeling." + }, + { + "text": "So in practice, if you have data, if you observe a bunch of points, and here I gave you some numbers, for example." + }, + { + "text": "So here's a partial data set with the number of siblings, including self, that were collected from college students a few years back." + }, + { + "text": "So I was teaching a class like yours, and I actually asked students to go and fill out some Google form and tell me a bunch of things." + }, + { + "text": "And one of the questions was, including yourself, how many siblings do you have?" + }, + { + "text": "And so they gave me this list of numbers." + }, + { + "text": "And there's many ways I can think of this list of numbers." + }, + { + "text": "I could think of it as being just a discrete distribution on the set of numbers between 1." + }, + { + "text": "I mean, I know there's not going to be an answer which is less than 1, unless, well, someone doesn't understand the question." + }, + { + "text": "But all the answers I should get are positive integers, 1, 2, 3, et cetera." + }, + { + "text": "And there probably is an upper bound, but I don't know it on the top of my head." + }, + { + "text": "So maybe I should say 100." + }, + { + "text": "Maybe I should say 15." + }, + { + "text": "Depends, right?" + }, + { + "text": "And so I think the largest number I got for this was 6." + }, + { + "text": "So here you can see you have pretty standard families, lots of 1's, 2's, and 3's." + }, + { + "text": "So what statistical modeling is doing is to try to compress this information that I could actually describe in a very naive way." + }, + { + "text": "So let's start with the basic usual statistical setup." + }, + { + "text": "So I will start many of the boards that look like x1, xn, random variables." + }, + { + "text": "And what I'm going to assume, as we said, typically is that those guys are iid, and they have some distribution." + }, + { + "text": "So they all share the same distribution." + }, + { + "text": "And the fact that they're iid is so that I can actually do statistics." + }, + { + "text": "Statistics means looking at the global averaging thing so that I can actually get a sense of what the global behavior is for the population." + }, + { + "text": "If I start assuming that those things are not identically distributed, they all live on their own, that my sequence of number is your number of siblings, the shoe size of this person, the depth of the Charles River, and I start measuring a bunch of stuff, there's nothing I'm going to actually get together." + }, + { + "text": "I need to have something that's cohesive." + }, + { + "text": "And so here, I collected some data that was cohesive." + }, + { + "text": "And so the goal here, the first thing is to say, what is the distribution that I actually have here?" + }, + { + "text": "So I could actually be very general." + }, + { + "text": "I could just say it's some distribution p. And let's say there are random variables, not random vectors." + }, + { + "text": "I could collect entire vectors about students." + }, + { + "text": "But let's say those are just random variables." + }, + { + "text": "And so now I can start making assumptions on this distribution p. What can I say about a distribution?" + }, + { + "text": "Well, maybe if those numbers are continuous, for example, I could assume they have a density, a probability density function." + }, + { + "text": "That's already an assumption." + }, + { + "text": "Maybe I could start to assume that their probability density function is smooth." + }, + { + "text": "That's another assumption." + }, + { + "text": "Maybe I could actually assume that it's piecewise constant." + }, + { + "text": "That's even better." + }, + { + "text": "And those things make my life simpler and simpler, because what I do by making the successive assumptions is reducing the degrees of freedom of the space in which I'm actually searching the distribution." + }, + { + "text": "And so what we actually want is to have something which is small enough so we can actually have some averaging going on." + }, + { + "text": "But we also want something which is big enough that it can actually express." + }, + { + "text": "It has chances of actually containing a distribution that makes sense for us." + }, + { + "text": "So let's start with the simplest possible example, which is when the xi's belong to 0, 1." + }, + { + "text": "And as I said here, we don't have a choice." + }, + { + "text": "The distribution of those guys has to be Bernoulli." + }, + { + "text": "And since they're iid, they all share the same p. So that's definitely the simplest possible thing I could think of." + }, + { + "text": "They're just Bernoulli p. And so all I would have to figure out in this case is p. And this is the simplest case." + }, + { + "text": "And unsurprisingly, it has the simplest answer." + }, + { + "text": "We will come back to this example when we study maximum likelihood estimators or method of moments estimators by the method of moments." + }, + { + "text": "But at the end of the day, the things that we did, the things that we will do are always the naive estimator you would come up with is, what is the proportion of 1?" + }, + { + "text": "And this will be, in pretty much all respects, the best estimator you can think of." + }, + { + "text": "So then we're going to try to assess its performance." + }, + { + "text": "And we saw how to do that in the first chapter as well." + }, + { + "text": "So this problem here somehow is completely understood." + }, + { + "text": "We'll come back to it." + }, + { + "text": "But there's nothing fancy that's going to happen." + }, + { + "text": "But now I could have some more complicated things." + }, + { + "text": "So for example, in the example of the students now, my xi's belong to the sequence of integers 1, 2, 3, et cetera, which is also denoted by n, maybe without 0 if you want to put 0 in n, so the positive integers." + }, + { + "text": "Or I could actually just maybe put some prior knowledge about how humans have time to have families." + }, + { + "text": "But maybe some people thought of their college mates as being their brothers and sisters." + }, + { + "text": "And one student would actually put 465 siblings, because we're all good friends." + }, + { + "text": "Or maybe they actually think that all their Facebook contacts are actually their siblings." + }, + { + "text": "And so you never know what's going to happen." + }, + { + "text": "So maybe you want to account for this." + }, + { + "text": "But maybe you know that people are reasonable." + }, + { + "text": "And they will actually give you something like this." + }, + { + "text": "Now, intuitively, maybe you would say, well, why would you bother doing this if you're not really sure about the 20?" + }, + { + "text": "But I think that probably all of you intuitively guess that this is probably a good idea to start putting this kind of assumption rather than allowing for any number in the first place, because this eventually will be injected into the precision of our estimator." + }, + { + "text": "If I allow anything, it's going to be more complicated for me to get an accurate estimator." + }, + { + "text": "If I know that the numbers are either 1 or 2, then I'm actually going to be slightly more accurate as well." + }, + { + "text": "Because I know that, for example, somebody put a 5, I can remove it." + }, + { + "text": "Then it's not going to actually screw up with my estimator." + }, + { + "text": "All right, so now let's say we actually agree that we have numbers." + }, + { + "text": "And here I put seven numbers." + }, + { + "text": "So I just said, well, now the numbers, let's assume that the numbers I'm going to get are going to be 1 all the way to, say, this number that I denote by larger than or equal to 7, which is a placeholder for any number larger than 7." + }, + { + "text": "Because I know maybe I don't want to distinguish between people who have 9 or 25 siblings." + }, + { + "text": "And so now, this is a distribution on seven possible values, discrete distributions." + }, + { + "text": "And you know from your probability class that the way you describe this distribution is using the probability mass function, or PMF." + }, + { + "text": "So that's how we describe a discrete distribution." + }, + { + "text": "And the PMF is just a list of numbers." + }, + { + "text": "So as I wrote here, you have a list of numbers." + }, + { + "text": "And here you wrote the possible value that your random variable can take." + }, + { + "text": "And here you write the probability that your random variable takes this value." + }, + { + "text": "So the possible values being 1, 2, 3, all the way to larger than or equal to 7." + }, + { + "text": "And then I'm trying to estimate those numbers." + }, + { + "text": "If I give you those numbers, at least up to this compression of all numbers larger than or equal to 7, you have a full description of your distribution." + }, + { + "text": "And that is the ultimate goal of statistics." + }, + { + "text": "The ultimate goal of statistics is to say what distribution your data came from, because that's basically the best you're going to be able to." + }, + { + "text": "Now admittedly, if I started looking at the fraction of 1's, and the fraction of 2's, and the fraction of 3's, et cetera, I would actually eventually get those numbers." + }, + { + "text": "Just like looking at the fraction of 1's gave me a good estimate for p in the Bernoulli case, it would do the same in this case." + }, + { + "text": "It's a pretty intuitive idea." + }, + { + "text": "It's just the law of large numbers." + }, + { + "text": "Everybody agrees with that?" + }, + { + "text": "If I look at the proportion of 1's, the proportion of 2's, the proportion of 3's, that should actually give me something that gets closer and closer as my sample size increases to what I want." + }, + { + "text": "But the problem is, if my sample size is not huge, here I have seven numbers to estimate." + }, + { + "text": "And if I have 20 observations, the ratio is not really in my favor." + }, + { + "text": "I mean, 20 observations to estimate seven parameters, some of them are going to be pretty off, typically the ones with the large values." + }, + { + "text": "If I have only 20 students, look at the list of numbers." + }, + { + "text": "I don't know how many numbers I have, but it probably is close to 20, maybe 15 or something." + }, + { + "text": "And so if you look at this list, nobody has four or more siblings in this list." + }, + { + "text": "There's no such person." + }, + { + "text": "So that means that eventually, from this data set, my estimates, so those numbers I denote by, say, p1, p2, p3, et cetera, those estimates, p4 hat would be equal to what from this data?" + }, + { + "text": "0, right?" + }, + { + "text": "And p5 hat would be equal to 0, and p6 hat would be equal to 0, and p larger than or equal to 7 hat would be equal to 0." + }, + { + "text": "That would be my estimates from this data set." + }, + { + "text": "So maybe this is not." + }, + { + "text": "Maybe I want to actually pull some information from the people who have less siblings to try to make a guess, which is probably slightly better for the larger values." + }, + { + "text": "It's pretty clear that, in average, there's more than 0." + }, + { + "text": "The proportion of the population of households that have four children or more is definitely more than 0." + }, + { + "text": "So it means that my data set is not representative." + }, + { + "text": "And what I'm going to try to do is to find a model that tries to use the data that I have for the smaller values that I can observe and just pull shit out for the other ones." + }, + { + "text": "And so what we can do is to just reduce those parameters into something that's understood." + }, + { + "text": "And this is part of the modeling that I talked about in the first place." + }, + { + "text": "Now, how do you succinctly describe a number of something?" + }, + { + "text": "Well, one thing that you do is the Poisson distribution." + }, + { + "text": "Why the Poisson?" + }, + { + "text": "I mean, there's many reasons." + }, + { + "text": "I mean, again, that's part of statistical modeling." + }, + { + "text": "But once you know that you have number of something that can be modeled by a Poisson, why not try a Poisson?" + }, + { + "text": "You could just fit a Poisson." + }, + { + "text": "And the Poisson is something that looks like this." + }, + { + "text": "And I guess you've all seen it." + }, + { + "text": "But if x follows a Poisson distribution with parameter lambda, then the probability that x is equal to little x is equal to lambda to the x over factorial x e to the minus lambda." + }, + { + "text": "And if you did the sheet that I gave you on the first day, you can check that those numbers." + }, + { + "text": "So this is, of course, for x equals 0, 1, et cetera." + }, + { + "text": "So x is in natural integers." + }, + { + "text": "And if you sum from x equals 0 to infinity, this thing, you get e to the lambda." + }, + { + "text": "And so they cancel." + }, + { + "text": "And you have a sum which is equal to 1." + }, + { + "text": "So it's indeed a PMF." + }, + { + "text": "But what's key about this PMF is that it never takes value 0." + }, + { + "text": "This thing is always strictly positive." + }, + { + "text": "So whatever value of lambda I find from this data will give me something that's certainly more interesting than just putting the value 0." + }, + { + "text": "But more importantly, rather than having to estimate seven parameters, and as a consequence, you actually have to estimate 1, 2, 3, 4 of them, and it equals to 0, I have only one parameter to estimate, which is lambda." + }, + { + "text": "The problem with doing this is that now lambda may not be just something as simple as computing the average number." + }, + { + "text": "I mean, in this case, it will." + }, + { + "text": "But in many instances, it's actually not clear that this parametrization with lambda that I chose, I'm going to be able to estimate lambda just by computing the average number that I see." + }, + { + "text": "It will be the case." + }, + { + "text": "But if it's not, remember this example of the exponential we did in the last lecture." + }, + { + "text": "We could use the delta method and things like that to estimate this." + }, + { + "text": "All right, so here's the modeling 101." + }, + { + "text": "So the purpose of modeling is to restrict the space of possible distributions to a subspace that's actually plausible, but much simpler for me to estimate." + }, + { + "text": "So we went from all distributions on seven parameters, which is a large space that's a lot of things, to something which is just one number to estimate." + }, + { + "text": "This number is positive." + }, + { + "text": "OK?" + }, + { + "text": "Any questions about the purpose of doing this?" + }, + { + "text": "OK, so we're going to have to do a little bit of formalism now." + }, + { + "text": "And so if we want to talk, this is a specific class, so I'm not going to want to talk about the Poisson model specifically every single time." + }, + { + "text": "I'm going to want to talk about generic models." + }, + { + "text": "And then you're going to be able to plug in your favorite word, no Poisson, binomial, exponential, uniform, all these words that you've seen, you're going to be able to plug in there." + }, + { + "text": "But we're just going to have some generic notation and some generic terminology for statistical models." + }, + { + "text": "So here is the formal definition." + }, + { + "text": "So I'm going to go through it with you." + }, + { + "text": "OK?" + }, + { + "text": "OK, so the definition is that of a statistical model." + }, + { + "text": "OK?" + }, + { + "text": "And so, sorry, that's a statistical experiment, I should say." + }, + { + "text": "I'm sorry." + }, + { + "text": "OK, so a statistical experiment is actually just a pair, E, and that's a set, and a family of distributions, P theta, where theta ranges in some set, capital theta." + }, + { + "text": "OK, so I hope you're up to date with your Greek letters." + }, + { + "text": "So it's a small theta, it's a capital theta." + }, + { + "text": "I know I don't have the best handwriting, so if you don't see something, just ask me." + }, + { + "text": "OK, and so this thing now, so each of this guy is a probability distribution." + }, + { + "text": "All right?" + }, + { + "text": "So for example, this could be a Poisson with parameter theta, or a Bernoulli with parameter theta." + }, + { + "text": "OK, or an exponential with parameter, I don't know, 1 over theta squared, if you want." + }, + { + "text": "OK, but they're just indexed by theta." + }, + { + "text": "For each theta, this completely describes the distribution." + }, + { + "text": "It could be more complicated." + }, + { + "text": "This theta could be a pair of mu sigma squared, and that could actually give you some n mu sigma squared." + }, + { + "text": "OK, so anything where you can actually, rather than actually giving you a full distribution, I can compress it into a parameter." + }, + { + "text": "But it could be worse." + }, + { + "text": "It could be this guy here, right?" + }, + { + "text": "Theta could be p1, p larger than or equal to 7, and my distribution could just be something that has pmf." + }, + { + "text": "p1, p larger than 7." + }, + { + "text": "That's another parameter." + }, + { + "text": "This one is seven dimensional, this one is two dimensional, and all these guys are just one dimension." + }, + { + "text": "All these guys are parameters." + }, + { + "text": "Is that clear?" + }, + { + "text": "What's important here is that once I give you theta, you know exactly all the probabilities associated to this random variable." + }, + { + "text": "You know its distribution perfectly." + }, + { + "text": "OK, so here, so this is the definition." + }, + { + "text": "Is that clear for everyone?" + }, + { + "text": "Is there a question about this distribution?" + }, + { + "text": "About this definition, sorry?" + }, + { + "text": "All right, so really, the key thing is the statistical model associated to a statistical experiment." + }, + { + "text": "OK?" + }, + { + "text": "So let's just see some examples." + }, + { + "text": "It's probably just better, because again, with formalism, it's never really clear." + }, + { + "text": "Actually, that's the next slide." + }, + { + "text": "OK, so there's two things we need to assume." + }, + { + "text": "I mean, there's, OK, so the purpose of a statistical model is to, once I estimate the parameter, I actually know exactly what distribution I have." + }, + { + "text": "OK?" + }, + { + "text": "So it means that I could potentially have several parameters that give me the same distribution that would still be fine, because I could estimate one guy, or I could estimate the other guy, and I would still recover the underlying distribution of my data." + }, + { + "text": "The problem is that this creates really annoying theoretical problems, like things don't work, the algorithms won't work, the guarantees won't work." + }, + { + "text": "And so what we typically assume is that the model is so-called well-specified." + }, + { + "text": "All right, sorry, that's not well-specified." + }, + { + "text": "I'm jumping ahead of myself." + }, + { + "text": "OK, well-specified means that your data, the distribution of your data, is actually one of those guys." + }, + { + "text": "OK, so some vocabulary." + }, + { + "text": "So well-specified means that for my observations x, there exists a theta, in capital theta, such that x follows p sub theta." + }, + { + "text": "I should put a double dot." + }, + { + "text": "OK, so that's what well-specified means." + }, + { + "text": "So that means that the distribution of your actual data is just one of those guys." + }, + { + "text": "This is a bit stronger than assumption." + }, + { + "text": "It's strong in the sense that, I don't know if you've heard of this sentence, which I don't know." + }, + { + "text": "I can tell you who it's attributed to, but that probably means that this person did not work with it." + }, + { + "text": "But it said that all models are wrong, but some of them are useful." + }, + { + "text": "So all models are wrong means that maybe it's not true that this Poisson distribution that I assume for the number of siblings for college students, maybe that's not perfectly correct." + }, + { + "text": "Maybe there's a spike at three." + }, + { + "text": "Maybe there's a spike at one, because maybe those are slightly more educated families." + }, + { + "text": "They have less children." + }, + { + "text": "Maybe this is actually not exactly perfect, but it's probably good enough for our purposes." + }, + { + "text": "And when we make this assumption, we're actually assuming that the data really comes from a Poisson model." + }, + { + "text": "There is a lot of research that goes on about misspecified models, and that tells you how well you're doing in the model that's the closest to the actual distribution." + }, + { + "text": "So that's pretty much it." + }, + { + "text": "Yeah?" + }, + { + "text": "X is, so by data, it's always the way I denote one of the generic observations." + }, + { + "text": "So my observations are x1, xn, and they're iid with distribution p, always." + }, + { + "text": "So x is just one of those guys." + }, + { + "text": "I don't want to write x5 or x4." + }, + { + "text": "They're iid, so they all have the same distribution." + }, + { + "text": "So OK. No, no, no." + }, + { + "text": "They're all iid, so they all have the same p theta." + }, + { + "text": "They'll have the same p, which means they'll have the same p theta." + }, + { + "text": "So I can pick any one of them, so I just remove the index, just where it's there." + }, + { + "text": "So when I write x, I just mean think of x1." + }, + { + "text": "They're iid." + }, + { + "text": "I can pick whichever I want." + }, + { + "text": "I'm not going to write x1." + }, + { + "text": "It's going to be weird." + }, + { + "text": "OK. Is that clear?" + }, + { + "text": "OK." + }, + { + "text": "So this particular theta is called the true parameter." + }, + { + "text": "Sometimes, since we're going to want some variable theta, we might denote it by theta star as opposed to theta hat, which is always our estimator." + }, + { + "text": "But I'll keep it to be theta for now." + }, + { + "text": "And so the aim of the statistical experiment is to estimate theta so that once I actually plug in theta in the form of my distribution, for example, I could plug in theta here." + }, + { + "text": "So theta here was actually lambda." + }, + { + "text": "So once I estimate this guy, I would plug it in." + }, + { + "text": "And I would know the probability that my random variable takes any value by just putting a lambda hat and lambda hat here." + }, + { + "text": "So my goal is going to be to estimate this guy so that I can actually compute those distributions." + }, + { + "text": "But actually, we'll see, for example, when we talk about regression, that this parameter actually has a meaning in many instances." + }, + { + "text": "And so just knowing the parameter itself intuitively or, let's say, more so than just computing probabilities will actually tell us something about the process." + }, + { + "text": "So for example, we're going to run linear regression." + }, + { + "text": "And when we do linear regression, there's going to be some coefficients in the linear regression." + }, + { + "text": "And the value of this coefficient is actually telling me what is the sensitivity of the response that I'm looking at to this particular input." + }, + { + "text": "So just knowing if this number is large or if this number is small is actually going to be useful for us to just look at this guy." + }, + { + "text": "So there's going to be some instances where it's going to be important." + }, + { + "text": "Sometimes we're going to want to know if this parameter is larger or smaller than something or if it's equal to something or not equal to something." + }, + { + "text": "And those things are also important, for example, if theta actually measures the true." + }, + { + "text": "So theta is a true unknown parameter, true efficacy of a drug." + }, + { + "text": "Let's say I want to know what the true efficacy of a drug is." + }, + { + "text": "And what I'm going to want to know is maybe it's a score." + }, + { + "text": "Maybe I'm going to want to know if theta is larger than 2." + }, + { + "text": "Maybe I want to know if theta is the average number of siblings." + }, + { + "text": "Is this true number larger than 2 or not?" + }, + { + "text": "Maybe I'm interested in knowing if college students come from a sociological perspective." + }, + { + "text": "I'm interested in knowing if college students come from a household with more than two children." + }, + { + "text": "So those can be the questions that I may ask myself." + }, + { + "text": "I'm going to want to know maybe if theta is going to be equal to 1 half or not." + }, + { + "text": "So maybe for drug efficacy, is it completely standard?" + }, + { + "text": "Maybe for elections, is the proportion of the population that is going to vote for this particular candidate equal to 0.5 or is it different from 0.5?" + }, + { + "text": "And I can think of different things." + }, + { + "text": "When I'm talking about the regression, I'm going to want to test if this coefficient is actually 0 or not." + }, + { + "text": "Because if it's 0, it means that the variable that's in front of it actually goes out." + }, + { + "text": "And so those are things we're testing." + }, + { + "text": "Actually, having this very specific yes, no answer is going to give me a huge intuition or a huge understanding of what's going on in the phenomenon that I observe." + }, + { + "text": "But actually, since the questions are so precise, I'm going to be much better at answering them rather than giving you an estimate for theta with some confidence around it." + }, + { + "text": "It's sort of the same principle as trying to reduce." + }, + { + "text": "What you're trying to do as a statistician is to inject as much knowledge about the question and about the problem that you can so that the data has to do a minimal job." + }, + { + "text": "And henceforth, you actually need less data." + }, + { + "text": "So for now on, we will always assume, and this is because this is an intro stats class, you will always assume that theta, the subset of parameters, is a subset of r to the d. That means that theta is a vector with, at most, a finite number of coordinates." + }, + { + "text": "Why do I say this?" + }, + { + "text": "Well, this is called a parametric model." + }, + { + "text": "So it's called a parametric model, or sometimes parametric statistics." + }, + { + "text": "Actually, we don't really talk about parametric statistics, but we talk a lot about nonparametric statistics or a nonparametric model." + }, + { + "text": "Can somebody think of a model which is nonparametric?" + }, + { + "text": "For example, in the siblings example, if I did not cap the number of siblings to 7, but I let this list go to infinity, I would have an infinite number of parameters to estimate." + }, + { + "text": "Very likely, the last one would be 0, but still, I would have an infinite number of parameters to estimate." + }, + { + "text": "So this would not be a parametric model if I just let this list of things to be estimated to be infinite." + }, + { + "text": "But there's other classes that are actually infinite and cannot be represented by vectors." + }, + { + "text": "For example, function." + }, + { + "text": "If I tell you my model, pf is just the distribution of x's, the probability distributions that have density f. So what I know is that the density is non-negative and that it integrates to 1." + }, + { + "text": "That's all I know about density." + }, + { + "text": "Well, f is not something you're going to be able to describe with a finite number of values." + }, + { + "text": "All possible functions, this is a huge set." + }, + { + "text": "It's certainly not representable by 10 numbers." + }, + { + "text": "And so nonparametric estimation is typically when you actually want to parameterize this by a large class of functions." + }, + { + "text": "And so for example, histograms is the prime tool of nonparametric estimation." + }, + { + "text": "Because when you fit a histogram to data, you're trying to estimate the density of your data, but you're not trying to represent it as a finite number of points, even though that's really, I mean, effectively, you have to represent it." + }, + { + "text": "So you actually truncate somewhere and just say, those things are not going to matter." + }, + { + "text": "But really, the key thing is that this is nonparametric where you have an infinite, potentially infinite number of parameters, whereas we're going to only talk about finites." + }, + { + "text": "And actually, finite in most overwhelming majority of cases is going to be 1." + }, + { + "text": "So theta is going to be a subset of R1." + }, + { + "text": "We're going to be interested in estimating one parameter, just like the parameter of a poisson or the parameter of an exponential, the parameter of Bernoulli." + }, + { + "text": "But for example, rarely we're going to be interested in estimating mu and sigma square for the normal." + }, + { + "text": "So here are some statistical models." + }, + { + "text": "So I'm going to go through them with you." + }, + { + "text": "So we start, right, so if I tell you, I observe, I'm interested in understanding the, I'm still that shallow, and I'm interested in understanding the proportion of people who kiss by bending their head to the right." + }, + { + "text": "And for that, I collected n observations and I'm interested in making some inference in this statistical model." + }, + { + "text": "My question to you is, what is the statistical model?" + }, + { + "text": "Well, if you want to write the statistical model, you're going to have to write this e. Oh, sorry, I never told you what e was." + }, + { + "text": "OK, well, actually, just go to the examples and then you'll know what e is." + }, + { + "text": "So you're going to have to write to me an e and a p theta." + }, + { + "text": "OK, so let's start with the Bernoulli trials." + }, + { + "text": "So this e here is called the sample space." + }, + { + "text": "And in normal people's words, it just means the space or the set in which x, and back to your question, x is just a generic observation, lives." + }, + { + "text": "OK, and hopefully, this is the smallest you can think of." + }, + { + "text": "OK, so for example, for Bernoulli trials, I'm going to observe a sequence of 0's and 1's." + }, + { + "text": "So my experiment is going to be, as written on the board, is going to be 1, 0, 1, and then the probability distributions are going to be, well, it's just going to be the Bernoulli distributions indexed by p. So rather than writing p sub p, I'm going to write it as Bernoulli p, because it's clear what I mean when I write that." + }, + { + "text": "Is everybody happy?" + }, + { + "text": "Actually, I need to tell you something more." + }, + { + "text": "This is a family of distributions, so I need p. And maybe I don't want to have p that takes value 0 or 1." + }, + { + "text": "I mean, it doesn't make sense." + }, + { + "text": "I would probably not look at this problem if I anticipated that everybody would kiss to the right and everybody would kiss to the left." + }, + { + "text": "So I'm going to assume that p is in 0, 1, but does not have 0 and 1." + }, + { + "text": "So that's a statistical model for Bernoulli trials." + }, + { + "text": "OK?" + }, + { + "text": "OK, now the next one, what do we have?" + }, + { + "text": "Exponential." + }, + { + "text": "OK?" + }, + { + "text": "OK, so when I have exponential distributions, what is the support of the exponential distribution?" + }, + { + "text": "What value is it going to take?" + }, + { + "text": "0 to infinity, right?" + }, + { + "text": "So what I have is that my first space is the value that my random variables can take." + }, + { + "text": "So it's, well, actually, I can remove the 0 again." + }, + { + "text": "0 to plus infinity." + }, + { + "text": "And then the family of distributions that I have are exponential with parameter lambda." + }, + { + "text": "And again, maybe you see me switching from p to lambda to theta to mu to sigma square." + }, + { + "text": "Honestly, you can do whatever you want, but it's just that it's customary to have these particular Greek letters." + }, + { + "text": "OK?" + }, + { + "text": "And so the parameters of exponential are just positive numbers." + }, + { + "text": "OK, and that's my exponential model." + }, + { + "text": "What is the third one?" + }, + { + "text": "Can somebody tell me?" + }, + { + "text": "Poisson." + }, + { + "text": "OK?" + }, + { + "text": "OK, so Poisson." + }, + { + "text": "Is Poisson random variable discrete or continuous?" + }, + { + "text": "Go back to your probability." + }, + { + "text": "All right, so the answer being the opposite of continuous." + }, + { + "text": "Good job." + }, + { + "text": "All right, so it's going to be, what values can a Poisson take?" + }, + { + "text": "All the natural integers, right?" + }, + { + "text": "So 0, 1, 2, 3, all the way to infinity." + }, + { + "text": "We don't have any control of this, so I'm going to write this as n without 0." + }, + { + "text": "I think in the slides, it's n star, maybe." + }, + { + "text": "Actually, no, you can take value 0." + }, + { + "text": "I'm sorry." + }, + { + "text": "This actually takes value 0 quite a lot." + }, + { + "text": "That's typically in many instances actually the mode." + }, + { + "text": "So it's n, and then I'm going to write it as Poisson with parameter, well, here it's again lambda as a parameter." + }, + { + "text": "And lambda can take any positive value." + }, + { + "text": "And that's where you can actually see that the model that we had for the siblings, right?" + }, + { + "text": "So let me actually just squeeze in the siblings model here." + }, + { + "text": "All right, so that was the bad model that I had in the first place." + }, + { + "text": "When I actually capped this, let's say we just capped it at 7." + }, + { + "text": "Forget about large than or equal to 7." + }, + { + "text": "We just assumed it was 7." + }, + { + "text": "What was our sample space?" + }, + { + "text": "We said 7." + }, + { + "text": "So it's 1, 2, to 7, right?" + }, + { + "text": "Those were the possible values that this thing would take." + }, + { + "text": "And then what's my parameter space?" + }, + { + "text": "So that's going to be a nightmare to write, but I'm going to write it." + }, + { + "text": "So I'm going to write it as something like probability that x is equal to k is equal to p sub k. And that's going to be for p. OK, so that's for all k's, right?" + }, + { + "text": "For k equal 1 to 7." + }, + { + "text": "And here, the index is the set of parameters p1 to pk." + }, + { + "text": "And I know a little more about those guys, right?" + }, + { + "text": "They're going to be non-negative." + }, + { + "text": "pj non-negative." + }, + { + "text": "And I know that they sum to 1." + }, + { + "text": "OK, so maybe writing this, you start seeing why we like those Poisson exponential and short notation, because I actually don't have to write the PMF of a Poisson." + }, + { + "text": "I mean, a Poisson is really just this." + }, + { + "text": "But I call it Poisson, so I don't have to rewrite this all the time." + }, + { + "text": "And so here, I did not use a particular form." + }, + { + "text": "So I just have this thing, and that's what it is." + }, + { + "text": "The set of parameters is the set of positive numbers that send of, sorry, p1 to p7, pk, and sum to 7, right?" + }, + { + "text": "And so this is just the list of numbers that are non-negative and sum up to 1." + }, + { + "text": "So that's my parameter space." + }, + { + "text": "OK, so here, that's my theta." + }, + { + "text": "This whole thing here, this is my capital theta." + }, + { + "text": "So that's just the set of parameters that theta is allowed to take." + }, + { + "text": "OK, and finally, we're going to end with the star of all, and that's the normal distribution." + }, + { + "text": "And in a normal distribution, you still have also some flexibility in terms of choices, because naturally, the normal distribution is parameterized by two parameters, mean and variance." + }, + { + "text": "So what values can a Gaussian random variable take?" + }, + { + "text": "An entire real line, right?" + }, + { + "text": "And the set of parameters that it can take, so this is going to be n mu sigma squared, and mu is going to be positive, and sigma square is going to be in R, and sigma square is going to be positive." + }, + { + "text": "OK, so again here, that's the way you're supposed to write it if you really want to identify what theta is." + }, + { + "text": "Well, theta formally is the set of mu sigma squared such that in R times 0 infinity." + }, + { + "text": "That's just to be formal, but this does the job just fine." + }, + { + "text": "You don't have to be super formal." + }, + { + "text": "OK, so that's not 3." + }, + { + "text": "That's like 5." + }, + { + "text": "Actually, I just want to write another one." + }, + { + "text": "Let's call it 5-bit." + }, + { + "text": "And 5-bit is just Gaussian with known variance." + }, + { + "text": "And this arises a lot in labs when you have measurement error, when you actually receive your measurement device." + }, + { + "text": "This thing has been tested by the manufacturer so much that it actually comes in on the side of the box." + }, + { + "text": "It says that the standard deviation of your measurements is going to be 0.23." + }, + { + "text": "OK, and actually, why do you do this is because they can brag about accuracy, right?" + }, + { + "text": "I mean, that's how they sell you this particular device." + }, + { + "text": "And so you actually know exactly what sigma square is." + }, + { + "text": "So once you actually get your data in the lab, you actually only have to estimate mu because sigma comes on the label." + }, + { + "text": "And so now, what is your statistical model?" + }, + { + "text": "Well, the numbers you're going to be collecting still are positive in r. But now, the models that I have is n mu sigma squared." + }, + { + "text": "But the parameter space is not mu in r and sigma positive." + }, + { + "text": "It's just mu in r. And to be a little more emphatic about this, this is enough to describe it, right?" + }, + { + "text": "Because if sigma is the sigma that was specified by the manufacturer, then this is the sigma you want." + }, + { + "text": "But you can actually write sigma is equal to sigma square is equal to sigma square manufacturer, right?" + }, + { + "text": "You can just fix it to be this particular value." + }, + { + "text": "Or maybe you don't want to write an index that's manufacturer." + }, + { + "text": "And so you just say, well, when I write sigma square, what I mean is the sigma square of the manufacturer." + }, + { + "text": "Yeah?" + }, + { + "text": "AUDIENCE MEMBER 2 Yeah, so you can just write sigma square and then you can write sigma square." + }, + { + "text": "So you can just write sigma square and then you can write sigma square." + }, + { + "text": "Yeah?" + }, + { + "text": "AUDIENCE MEMBER 2 Yeah." + }, + { + "text": "For a particular measuring device?" + }, + { + "text": "You're in a lab and you have some measuring device, I don't know, something that measures tensile strength of something." + }, + { + "text": "And it's just going to measure something." + }, + { + "text": "And it will naturally make errors." + }, + { + "text": "But it's been tested so much by the manufacturer that they actually, and calibrated by them, they know it's not going to be perfect." + }, + { + "text": "But they knew exactly what error it's making because they've actually tried it on things for which they exactly knew what the tensile strength was." + }, + { + "text": "OK?" + }, + { + "text": "Yeah?" + }, + { + "text": "AUDIENCE MEMBER 3 This?" + }, + { + "text": "This?" + }, + { + "text": "Oh, like 5 prime?" + }, + { + "text": "OK?" + }, + { + "text": "And we can come up with other examples, right?" + }, + { + "text": "So for example, here's another one." + }, + { + "text": "OK, so the names don't really matter, right?" + }, + { + "text": "I mean, I called it the siblings model, but you won't find the siblings model in a textbook, right?" + }, + { + "text": "So I wouldn't worry too much." + }, + { + "text": "But for example, let's say you have something, so let's call it 6." + }, + { + "text": "You have, I don't know, truncated." + }, + { + "text": "And that's the name I just came up with, but it's actually not exactly describing what I want." + }, + { + "text": "But let's say I observe y, which is the indicator of x larger than, say, 5 when x follows some exponential with parameter lambda." + }, + { + "text": "OK, this is what I get to observe." + }, + { + "text": "I only observe if my waiting time was more than 5 minutes because I see somebody coming out of the candle station being really upset, and that's all I record." + }, + { + "text": "And it's, ah, he's been waiting for more than 5 minutes." + }, + { + "text": "And that's all I get to record." + }, + { + "text": "OK, that happens a lot." + }, + { + "text": "These are called censored data." + }, + { + "text": "I should probably not call it truncated, but this should be censored." + }, + { + "text": "OK?" + }, + { + "text": "You see a lot of censored data when you ask for people how much they make." + }, + { + "text": "They say, well, more than 5 figures." + }, + { + "text": "And that's all they want to tell you." + }, + { + "text": "OK?" + }, + { + "text": "And so you see a lot of censored data in survival analysis." + }, + { + "text": "Right?" + }, + { + "text": "You're trying to understand how long your patients are going to live after some surgery." + }, + { + "text": "OK?" + }, + { + "text": "And maybe you're not going to keep people alive, and you're not going to actually have them being touched in their family every day and ask them, is the guy still alive?" + }, + { + "text": "And so what you can do is just to ask people maybe five years after your study and say, please come in." + }, + { + "text": "And you will just happen to have some people who say, well, the person is deceased." + }, + { + "text": "And you will only be able to know that the person deceased less than five years ago." + }, + { + "text": "I mean, but you only see what happens after that." + }, + { + "text": "OK?" + }, + { + "text": "And so this truncated and censored data happens all the time just because you don't have the availability to do better than that." + }, + { + "text": "So this could happen here." + }, + { + "text": "So now what is my statistical experiment?" + }, + { + "text": "Right?" + }, + { + "text": "So here I should probably write this like that, because I just told you that my observations are going to be x." + }, + { + "text": "So there's some unknown y. I will never get to see this y. I only get to see the x." + }, + { + "text": "What is my statistical experiment?" + }, + { + "text": "Please help me." + }, + { + "text": "So is it the real line?" + }, + { + "text": "My sample space, is it the real line?" + }, + { + "text": "Sorry, do you know?" + }, + { + "text": "Who does not know what this means?" + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "So this is called an indicator." + }, + { + "text": "So I write it as it's, if I wrote well, that would be 1 with a double bar." + }, + { + "text": "You can also write i if you prefer, if you don't feel like writing 1 in double bars." + }, + { + "text": "And it's 1 of, say, I'm going to write it like that." + }, + { + "text": "1 of a is equal to 1 if a is true and 0 if a is false." + }, + { + "text": "OK?" + }, + { + "text": "So that means that if y is larger than 5, this thing is 1." + }, + { + "text": "And if y is not larger than 5, this thing is 0." + }, + { + "text": "OK?" + }, + { + "text": "So that's called indicator." + }, + { + "text": "Indicator function." + }, + { + "text": "OK?" + }, + { + "text": "It's very useful to just turn anything into a 0, 1." + }, + { + "text": "So now that I'm here, what is my sample space?" + }, + { + "text": "0, 1." + }, + { + "text": "Whatever this thing I did not tell you was taking value was the thing you should have." + }, + { + "text": "If I didn't tell you that's taking value 6 or 7, that would be your sample space." + }, + { + "text": "OK, so it takes value 0, 1." + }, + { + "text": "And then what is the probability here?" + }, + { + "text": "What should I write here?" + }, + { + "text": "What should you write without even thinking?" + }, + { + "text": "Yeah, so let's assume there's two seconds before the end of the exam." + }, + { + "text": "You're going to write vernally." + }, + { + "text": "And that's where you're going to start checking if I'm going to give you extra time." + }, + { + "text": "So you write vernally without thinking, because it's taking value 0, 1." + }, + { + "text": "So you just write vernally." + }, + { + "text": "But you still have to tell me what possible parameters this thing is taking, right?" + }, + { + "text": "So I'm going to write it p, because I don't know." + }, + { + "text": "And then p takes value." + }, + { + "text": "OK, so sorry." + }, + { + "text": "I could write it like that." + }, + { + "text": "That would be perfectly valid." + }, + { + "text": "But actually, no more." + }, + { + "text": "It's not any p. The p is the probability that an exponential lambda is larger than 5." + }, + { + "text": "And maybe I want to have lambda as a parameter." + }, + { + "text": "OK, so what I need to actually compute is what is the probability that y is larger than 5 when y is this exponential lambda, which means that what I need to compute is the integral between 5 and infinity of 1 over lambda." + }, + { + "text": "Huh?" + }, + { + "text": "How did I define it in this class?" + }, + { + "text": "I changed everything." + }, + { + "text": "What?" + }, + { + "text": "AUDIENCE MEMBER 2." + }, + { + "text": "Lambda e to the minus lambda x. PHILIPPE RIGOLLET." + }, + { + "text": "Oh, yeah, right, right, right." + }, + { + "text": "You're right." + }, + { + "text": "Lambda e to the minus lambda x dx, right?" + }, + { + "text": "So that's what I need to compute." + }, + { + "text": "What is this?" + }, + { + "text": "So what is the value of this integral?" + }, + { + "text": "AUDIENCE MEMBER 3." + }, + { + "text": "5." + }, + { + "text": "5." + }, + { + "text": "5." + }, + { + "text": "You take appropriate measures." + }, + { + "text": "OK. And again, this is just a basic calculus, right?" + }, + { + "text": "So when I'm going to integrate this guy, those guys are going to cancel." + }, + { + "text": "I'm going to get 0 for infinity." + }, + { + "text": "I'm going to get a 5 for this guy." + }, + { + "text": "And well, I know it's going to be a positive number, so I'm not really going to bother with the sign, because I know that's what it should be." + }, + { + "text": "So I get e to the minus 5 lambda." + }, + { + "text": "And so that means that I can actually write this like that." + }, + { + "text": "Now, parameterize this thing by lambda positive." + }, + { + "text": "So what I did here is I changed the parameterization from p to lambda." + }, + { + "text": "Why?" + }, + { + "text": "Well, because maybe if this, I know this is happening, maybe I'm actually interested in reporting lambda to MBTA, for example." + }, + { + "text": "Maybe I'm actually trying to estimate 1 over lambda, so that I know what is the, well, lambda is actually the intensity of arrival of my Poisson process, right?" + }, + { + "text": "If I have a Poisson process, that's where how my trains are coming in." + }, + { + "text": "And so I'm interested in lambda, so I will parameterize things by lambda, so that the thing I get is lambda." + }, + { + "text": "You can play with this, right?" + }, + { + "text": "I mean, I could parameterize this by 1 over lambda or 1 over lambda here if I wanted." + }, + { + "text": "But the context of your problem will tell you exactly how to parameterize this thing." + }, + { + "text": "OK?" + }, + { + "text": "So what else do I want to tell you?" + }, + { + "text": "OK, let's do a final one." + }, + { + "text": "By the way, are you guys OK with Poisson exponential Bernoulli's, I don't know, binomial, normal, all these things?" + }, + { + "text": "I'm not going to go back to it, but I'm going to use them heavily." + }, + { + "text": "So just spend five minutes on Wikipedia if you forgot about what those things are." + }, + { + "text": "Usually, you must have seen them in your probability class, so that should not be crazy name." + }, + { + "text": "And again, I'm not expecting you." + }, + { + "text": "I mean, I don't remember what the density of an exponential is, so it would be pretty unfair of me to actually ask you to remember what it is." + }, + { + "text": "Even for the Gaussian, you're not expected to remember what it is." + }, + { + "text": "But I want you to remember that if I add 5 to a Gaussian, then I have a Gaussian with mean mu plus 5." + }, + { + "text": "If I multiply it by something, right?" + }, + { + "text": "You need to know how to operate those things." + }, + { + "text": "But knowing complicated densities is definitely not part of the game." + }, + { + "text": "So let's do a final one." + }, + { + "text": "I don't know what number I have now." + }, + { + "text": "I'm going to just do uniform." + }, + { + "text": "That's another one." + }, + { + "text": "Everybody knows what uniform is?" + }, + { + "text": "So uniform, right?" + }, + { + "text": "So I'm going to have x, which my observations are going to be uniform on the interval 0 theta, right?" + }, + { + "text": "So if I want to define a uniform distribution for a random variable, I have to tell you which interval or which set I want it to be uniform on." + }, + { + "text": "And so here, I'm telling you it's the interval 0 theta." + }, + { + "text": "And so what is going to be my sample space?" + }, + { + "text": "I'm sorry?" + }, + { + "text": "0 to theta." + }, + { + "text": "And then what is my probability distribution, my family of parameters?" + }, + { + "text": "So well, I can write it like this, right?" + }, + { + "text": "Uniform theta, right?" + }, + { + "text": "And theta, let's say, is positive." + }, + { + "text": "Can somebody tell me what's wrong with what I wrote?" + }, + { + "text": "Yeah, this makes no sense." + }, + { + "text": "Tell me why." + }, + { + "text": "Yeah?" + }, + { + "text": "Yeah, this set depends on theta." + }, + { + "text": "And why is that a problem?" + }, + { + "text": "There's no theta." + }, + { + "text": "Right now, there's the families of thetas." + }, + { + "text": "Which one did you pick here?" + }, + { + "text": "This is just something that's indexed by theta." + }, + { + "text": "But I could have very well written it as just not being Greek for a second." + }, + { + "text": "I could have just written this as t, right, rather than theta." + }, + { + "text": "OK, that would be the same thing." + }, + { + "text": "And then what the hell is theta?" + }, + { + "text": "There's no such thing as theta." + }, + { + "text": "We don't know what the parameter is." + }, + { + "text": "The parameter should move with everyone." + }, + { + "text": "And so that means that I actually am not allowed to pick this theta." + }, + { + "text": "I'm actually, just for the reason that there's no parameter to put on the left side." + }, + { + "text": "There should not be, right?" + }, + { + "text": "So you just said, well, there's a problem because the parameter is on the left-hand side." + }, + { + "text": "But there's not even a parameter." + }, + { + "text": "I'm describing the family of possible parameters." + }, + { + "text": "There's no one that you can actually plug it in." + }, + { + "text": "So this should really be one." + }, + { + "text": "And I'm going to go back to writing this as theta, because that's pretty thin." + }, + { + "text": "Is that clear for everyone?" + }, + { + "text": "I cannot just pick one and put it in there." + }, + { + "text": "I just take the, before I run my experiment, I could potentially get numbers that are all the way up to 1, because I don't know what theta is going to be ahead of time." + }, + { + "text": "Now, if somebody promised to me that theta was going to be less than 0.5, that would be, sorry, why do I put 1 here?" + }, + { + "text": "I could put theta between 0 and 1." + }, + { + "text": "But if somebody is going to promise me, for example, that theta is going to be less than 1, I could put 0, 1." + }, + { + "text": "All right?" + }, + { + "text": "Is that clear?" + }, + { + "text": "OK, so now you know how to answer the question, what is the statistical model?" + }, + { + "text": "And again, within the scope of this class, you will not be asked to just come up with a model." + }, + { + "text": "I will just tell you, Poisson would be a probably good idea here." + }, + { + "text": "And then you would just have to trust me that, indeed, it would be a good idea." + }, + { + "text": "All right, so what I started talking about about 20 minutes ago, so I was definitely ahead of myself, is the notion." + }, + { + "text": "So that's when I was talking about well-specified." + }, + { + "text": "Remember, well-specified says that the true distribution is one of the distribution in this parametric families of distribution." + }, + { + "text": "The true distribution of my siblings is actually a Poisson with some parameters." + }, + { + "text": "And all I need to figure out is what this parameter is." + }, + { + "text": "When I started saying that, I said, well, but then that could be that there are several parameters that give me the same distribution, right?" + }, + { + "text": "It could be the case that Poisson 5 and Poisson 17 are exactly the same distributions when I start putting those numbers in the formula which I rephrased." + }, + { + "text": "So it could be the case that two different numbers would give me exactly the same probabilities." + }, + { + "text": "And in this case, we see that the model is not identifiable." + }, + { + "text": "I mean, the parameter is not identifiable." + }, + { + "text": "I cannot identify the parameter, even if you actually gave me an infinite amount of data, which means that I could actually estimate exactly the PMF." + }, + { + "text": "I might not be able to go back, because there would be several candidates." + }, + { + "text": "And I would not be able to tell you which one it was in the first place." + }, + { + "text": "So what we want is that this function, theta, maps to P theta is injective." + }, + { + "text": "And that's really to be fancy." + }, + { + "text": "So what I really mean is that if theta is different from theta prime, then P of theta is different from P of theta prime." + }, + { + "text": "Or if you prefer to think about the contrapositive of this, this is the same as saying that if P theta gives me the same distribution as theta prime, then that implies that theta must be equal to theta prime." + }, + { + "text": "So in logic, those two things are equivalent." + }, + { + "text": "So this means that we say that the parameter is identifiable or identified, doesn't really matter, in this model." + }, + { + "text": "OK?" + }, + { + "text": "And this is something we're going to want." + }, + { + "text": "So in all the examples that I gave you, those parameters are completely identified." + }, + { + "text": "If I tell you, I mean, if those things are in probability books, it means that they were probably thought through." + }, + { + "text": "So when I say exponential lambda, I'm really talking about one specific distribution." + }, + { + "text": "And there's not another lambda that's going to give me exactly the same distribution." + }, + { + "text": "OK?" + }, + { + "text": "So that was the case." + }, + { + "text": "And you can check that." + }, + { + "text": "But it's a little annoying." + }, + { + "text": "So I probably would not do it." + }, + { + "text": "But rather than doing this, let me just give you some examples where it would not be the case." + }, + { + "text": "And here's an example." + }, + { + "text": "If I take xi, so now I'm back to just using this indicator function, but now for a Gaussian." + }, + { + "text": "So what I observe is x is the indicator that y is, what did we say, positive?" + }, + { + "text": "OK?" + }, + { + "text": "So this is a Bernoulli random variable, right?" + }, + { + "text": "And it has some parameter p. But p now is going to depend, sorry, in here, y is n mu sigma squared." + }, + { + "text": "So the p, the probability that this thing is positive, is actually, I don't think I put the 0." + }, + { + "text": "Oh yeah, because I have mu." + }, + { + "text": "OK." + }, + { + "text": "So this distribution, this p, the probability that it's positive, is just the probability that some Gaussian is positive." + }, + { + "text": "And it will depend on mu and sigma, right?" + }, + { + "text": "Because if I draw, if I have 0, and I draw my Gaussian around mu, then the probability of this Bernoulli being 1 is really the area under the curve here." + }, + { + "text": "Right?" + }, + { + "text": "And this thing, well, if mu is very large, it's going to become very large." + }, + { + "text": "If mu is very small, it's going to become very small." + }, + { + "text": "And if sigma changes, it's also going to affect it." + }, + { + "text": "Is that clear to everyone?" + }, + { + "text": "But we can actually compute this, right?" + }, + { + "text": "So the parameter p that I'm looking for here as a function of mu and sigma is simply the probability that some y is non-negative, which is the probability that y minus mu divided by sigma is larger than minus mu divided by sigma." + }, + { + "text": "By the way, when you studied probability, is that some operation you were used to making, removing the mean and dividing by the standard deviation?" + }, + { + "text": "What is the effect of doing that on the Gaussian random variable?" + }, + { + "text": "Yeah, so you normalize it, right?" + }, + { + "text": "You standardize it." + }, + { + "text": "You actually make it a standard Gaussian." + }, + { + "text": "You remove the mean." + }, + { + "text": "It becomes a mean 0 Gaussian." + }, + { + "text": "And you remove the variance for it to become 1." + }, + { + "text": "So when you have a Gaussian, remove the mean and divide by the standard deviation, it becomes a standard Gaussian, which this thing has n 0 1 distribution, which is the one you can read the quintiles of at the end of the book." + }, + { + "text": "And that's exactly what we did." + }, + { + "text": "OK, so now you have the probability that some standard Gaussian exceeds negative mu over sigma, which I can write in terms of the cumulative distribution function capital phi, like we did in the first lecture." + }, + { + "text": "So if I do this cumulative distribution function, what is this probability in terms of phi?" + }, + { + "text": "AUDIENCE MEMBER 1." + }, + { + "text": "Lids." + }, + { + "text": "Well, that's what your name tag says." + }, + { + "text": "1 minus?" + }, + { + "text": "1 minus mu over sigma?" + }, + { + "text": "What happened to phi in our?" + }, + { + "text": "You think I defined this for fun?" + }, + { + "text": "1 minus phi of mu over sigma, right?" + }, + { + "text": "Because this is 1 minus the probability that it's less than this, and this is exactly the definition of the cumulative distribution function." + }, + { + "text": "So in particular, this thing only depends on mu over sigma." + }, + { + "text": "Agreed?" + }, + { + "text": "So in particular, if I had 2 mu over 2 sigma, p would remain unchanged." + }, + { + "text": "If I have 12 mu over 12 sigma, this thing would remain unchanged, which means that p does not change if I scale mu and sigma by the same factor." + }, + { + "text": "So there's no way, just by observing x, even an infinite amount of time, so that I can actually get exactly what p is, I'm never going to be able to get mu and sigma separately." + }, + { + "text": "All I'm going to be able to get is mu over sigma." + }, + { + "text": "So here, we say that mu sigma, the parameter mu sigma, or actually each of them individually, those guys, they're not identifiable." + }, + { + "text": "But the parameter mu over sigma is identifiable." + }, + { + "text": "So if I wanted to write a statistical model in which the parameter is identifiable, I would write 0, 1, Bernoulli, and then I would write 1 minus phi of mu over sigma." + }, + { + "text": "And then I would take two parameters, which are mu and r and sigma squared positive." + }, + { + "text": "Well, let's write sigma positive." + }, + { + "text": "Right?" + }, + { + "text": "No." + }, + { + "text": "This is not identifiable." + }, + { + "text": "I cannot write those two guys as being two things different." + }, + { + "text": "Instead, what I want to write is 0, 1, Bernoulli, 1 minus." + }, + { + "text": "And now my parameter, yeah, I forgot this." + }, + { + "text": "My parameter is mu over sigma." + }, + { + "text": "Can somebody tell me where mu over sigma lives?" + }, + { + "text": "What values can this thing take?" + }, + { + "text": "Any real value, right?" + }, + { + "text": "OK, so now I've done this, definitely out of convenience, right?" + }, + { + "text": "Because that was the only thing I was able to identify, the ratio of mu over sigma." + }, + { + "text": "But it's still something that has some meaning." + }, + { + "text": "It's the normalized mean." + }, + { + "text": "It really tells me what the mean is compared to the standard deviation." + }, + { + "text": "So in some models, in reality, in some real applications, this actually might have a good meaning for me." + }, + { + "text": "It's just telling me how big the mean is compared to the standard fluctuations of this model." + }, + { + "text": "But I won't be able to get more than that." + }, + { + "text": "Agreed?" + }, + { + "text": "All right, so now that we've set a parametric model, let's try to see what our goals are going to be." + }, + { + "text": "OK, so now we have a sample and a statistical model." + }, + { + "text": "And we want to estimate the parameter theta." + }, + { + "text": "And I could say, well, you know what?" + }, + { + "text": "I don't have time for this analysis." + }, + { + "text": "Collecting data is going to take me a while." + }, + { + "text": "And I'm going to say that mu over sigma is 4." + }, + { + "text": "I'm just going to give it to you." + }, + { + "text": "And maybe you will tell me, eh, not very good, right?" + }, + { + "text": "So we need some measure of performance of a given parameter." + }, + { + "text": "We need to be able to evaluate if eyeballing the problem is worse than actually collecting a large amount of data." + }, + { + "text": "We need to know if, even if I come up with an estimator that actually sort of uses the data, does it make an efficient use of the data?" + }, + { + "text": "Would I actually need 10 times more observations to achieve the same accuracy?" + }, + { + "text": "So to be able to answer these questions, well, I need to define what accuracy means." + }, + { + "text": "And accuracy is something that sort of makes sense." + }, + { + "text": "It says, well, I want theta hat to be close to theta." + }, + { + "text": "But theta hat is a random variable, so I'm going to have to understand what it means for a random variable to be close to a deterministic number." + }, + { + "text": "And so what is the parameter, an estimator, right?" + }, + { + "text": "So I have an estimator." + }, + { + "text": "And I said it's a random variable." + }, + { + "text": "And the formal definition to an estimator is a measurable function of the data." + }, + { + "text": "So when I write theta hat, and that will typically be my notation for an estimator, I should really write theta hat of x1, xn." + }, + { + "text": "That's what an estimator is." + }, + { + "text": "So if you want to know what an estimator is, this is a measurable function of data." + }, + { + "text": "And it's actually also known as a statistic." + }, + { + "text": "And if you're interested in, I see every day, I think, when I have a dinner with normal people, and they say I'm a statistician." + }, + { + "text": "Oh, yeah, really?" + }, + { + "text": "Like, yeah, baseball." + }, + { + "text": "And they talk to me about batting averages." + }, + { + "text": "That's not what I do." + }, + { + "text": "But for them, that's what it is." + }, + { + "text": "And that's because, in a way, that's what a statistic is." + }, + { + "text": "A batting average is a statistic." + }, + { + "text": "And so here are some examples." + }, + { + "text": "You can take the average xn bar." + }, + { + "text": "You can take the maximum of your observation." + }, + { + "text": "That's a statistic." + }, + { + "text": "You can take the first one." + }, + { + "text": "You can take the first one plus log of 1 plus the absolute value of the last one." + }, + { + "text": "You can do whatever you want." + }, + { + "text": "That will be an estimator." + }, + { + "text": "Some of them are clearly going to be bad." + }, + { + "text": "But that's still a statistic." + }, + { + "text": "And you can do this." + }, + { + "text": "Now, when I say measurable, I always have, so graduate students sometimes ask me, like, yeah, how do I know if this estimator is measurable or not?" + }, + { + "text": "And usually, my answer is, well, if I give you data, can you compute it?" + }, + { + "text": "And they say, yeah." + }, + { + "text": "I'm like, well, then it's measurable." + }, + { + "text": "That's a very good rule to check if something is actually measurable." + }, + { + "text": "When is this thing not measurable?" + }, + { + "text": "It's when it's implicitly defined." + }, + { + "text": "And in particular, the things that can give you problems are soup or inf." + }, + { + "text": "Anybody knows what a soup or an inf is?" + }, + { + "text": "It's like a max or a min, but that's not always attained." + }, + { + "text": "So if I have x1, so if I look at the infimum of the function f of x for x on the real line, and f of x, sorry, let's say x on 1 infinity, and f of x is equal to 1 over x, then the infimum is the smallest value it can take, except that it does not really take it." + }, + { + "text": "It's 0, because 1 over x is going to 0, but it's never really getting there." + }, + { + "text": "So we just call the inf 0, but it's not the value that it ever takes." + }, + { + "text": "And these things might actually be complicated to compute, and so that's when you actually have problems, when you're not really quite reaching the limit." + }, + { + "text": "You won't have this problem in general, but just so you know that an estimator is not really anything, it has to actually be measurable." + }, + { + "text": "So the first thing we want to know, I mentioned it, is an estimator is a statistic which does not depend on data, of course." + }, + { + "text": "So if I give you the data, you have to be able to compute it, and that probably should not require not knowing an unknown parameter." + }, + { + "text": "So an estimator is said to be consistent." + }, + { + "text": "When I collect more and more data, this thing is getting closer and closer to the true parameter." + }, + { + "text": "And we said that eyeballing and saying that it's going to be 4 is not really something that's probably going to be consistent, but I can have things that are consistent but that are converging to theta at different speeds." + }, + { + "text": "And we know also that this is a random variable." + }, + { + "text": "It converges to something, and there might be some different notions of conversions that kick in, and actually, they are." + }, + { + "text": "And we say that it's weakly convergent if it converges in probability, and strongly convergent if it converges almost surely." + }, + { + "text": "And this is just vocabulary." + }, + { + "text": "It won't make a big difference." + }, + { + "text": "So we will typically say it's consistent once you say any of the two." + }, + { + "text": "So in parametric statistics, it's actually a little difficult to come up with, but in non-parametric ones, I could just say if I have yi, xi, yi, and I know that yi is f of xi plus some noise epsilon i, and I know that f belongs to some class of functions, let's say, Sybil-Liff class of smooth functions, massive." + }, + { + "text": "And now I'm going to actually find the following estimator." + }, + { + "text": "I'm going to take the average." + }, + { + "text": "So I'm going to do least squares." + }, + { + "text": "So I just check." + }, + { + "text": "I'm trying to minimize the distance of each of my f of xi to my yi." + }, + { + "text": "And now I want to find the smallest of them." + }, + { + "text": "So if I look at the infimum here, then the question is, so that could be, well, that's not really an estimator for f, but it's an estimator for the smallest possible value." + }, + { + "text": "And so for example, this is actually an estimator for the variance of sigma square." + }, + { + "text": "This might not be attained, and this might not be measurable if f is massive." + }, + { + "text": "So that's the inf of some class f of x." + }, + { + "text": "So those are always things that are defined implicitly." + }, + { + "text": "If it's an average, for example, it's completely measurable." + }, + { + "text": "Any other questions?" + }, + { + "text": "OK, so we know that the first thing we might want to check, and that's definitely something we want about an estimator, is that it's consistent, because all consistency tells us is that as I collect more and more data, my estimator is going to get closer and closer to the parameters." + }, + { + "text": "There's other things we can look at." + }, + { + "text": "For each possible value of n, now I have a finite number of observations, 25." + }, + { + "text": "And I want to know something about my estimator." + }, + { + "text": "The first thing I want to check is maybe if, in average, so this is a random variable." + }, + { + "text": "Is this random variable, in average, going to be close to theta or not?" + }, + { + "text": "And so the difference, how far I am from theta, is actually called the bias." + }, + { + "text": "So the bias of an estimator is the expectation of theta hat minus the value that I hope it gets, which is theta." + }, + { + "text": "If this thing is equal to 0, we say that theta hat is unbiased." + }, + { + "text": "And unbiased estimators are things that people are looking for in general." + }, + { + "text": "The problem is that there's lots of unbiased estimators, and so it might be misleading to look for unbiasedness when that's not really the only thing you should be looking for." + }, + { + "text": "So what does it mean to be unbiased?" + }, + { + "text": "Maybe for this particular round of data you collected, you're actually pretty far from the true estimator." + }, + { + "text": "But one thing that actually, what it means is that if I redid this experiment over and over and over again, and I averaged all the values of my estimators that I got, then this would actually be the true parameter." + }, + { + "text": "That's what it means." + }, + { + "text": "If I were to repeat this experiment, in average I would actually get the right thing." + }, + { + "text": "But you don't get to repeat an experiment." + }, + { + "text": "Just a remark about estimators." + }, + { + "text": "Look at this estimator, xn bar." + }, + { + "text": "Think of the kiss example." + }, + { + "text": "I'm looking at the average of my observations." + }, + { + "text": "And I want to know what the expectation of this thing is." + }, + { + "text": "OK?" + }, + { + "text": "Now, this guy is my linearity of the expectation." + }, + { + "text": "Is this, right?" + }, + { + "text": "But my data is identically distributed." + }, + { + "text": "So in particular, all the xi's have the same expectation, right?" + }, + { + "text": "Everybody agrees with this?" + }, + { + "text": "When it's identically distributed, they all get the same expectation?" + }, + { + "text": "So what it means is that this guy's here, they're all equal to the expectation of x1, right?" + }, + { + "text": "So what it means is that this guy's, I have the average of the same number." + }, + { + "text": "So this is actually the expectation of x1." + }, + { + "text": "OK?" + }, + { + "text": "And it's true." + }, + { + "text": "In the kiss example, this was p. And this is p. So probability of turning your head right." + }, + { + "text": "OK?" + }, + { + "text": "So those two things are the same." + }, + { + "text": "In particular, that means that xn bar and just x1 have the same bias." + }, + { + "text": "So that should probably illustrate to you that bias is not something that really is telling you the entire picture." + }, + { + "text": "Right?" + }, + { + "text": "I can take only one of my observations, Bernoulli 0, 1." + }, + { + "text": "This thing will have the same bias as if I averaged 1,000 of them." + }, + { + "text": "So the bias is really telling me where I am in the average, but it's really not telling me what fluctuations I'm getting." + }, + { + "text": "And so if you want to start having fluctuations coming into the picture, we actually have to look at the risk or the quadratic risk of an estimator." + }, + { + "text": "And so the quadratic risk is defined as the expectation of the squared distance between theta hat and theta." + }, + { + "text": "OK?" + }, + { + "text": "So let's look at this." + }, + { + "text": "So the quadratic risk, sometimes it's denoted, people call it the L2 risk of theta hat, of course." + }, + { + "text": "I'm sorry for maintaining such an ugly board." + }, + { + "text": "I keep away this stuff." + }, + { + "text": "OK, so I look at the squared distance between theta hat and theta." + }, + { + "text": "This is still the function of a random variable, so it's a random variable as well." + }, + { + "text": "And I'm looking at the expectation of this guy." + }, + { + "text": "That's the definition." + }, + { + "text": "I claim that when this thing goes to 0, then my estimator is actually going to be consistent." + }, + { + "text": "Everybody agrees with this?" + }, + { + "text": "So if it goes to 0 as n goes to infinity, and here I don't need to tell you what kind of convergence I have, because this is just a number, right?" + }, + { + "text": "It's an expectation." + }, + { + "text": "So it's a regular, usual, calculus-style convergence." + }, + { + "text": "Then that implies that theta hat is actually weakly consistent." + }, + { + "text": "What did I use to tell you this?" + }, + { + "text": "Yeah, this is the convergence in L2." + }, + { + "text": "This actually is strictly equivalent." + }, + { + "text": "This is by definition saying that theta hat converges in L2 to theta." + }, + { + "text": "And we know that convergence in L2 implies convergence in probability to theta." + }, + { + "text": "That was the picture." + }, + { + "text": "We're going up." + }, + { + "text": "And this is actually equivalent to weak consistency by definition of weak consistency." + }, + { + "text": "So this is actually telling me a little more, because this guy here, they're both unbiased." + }, + { + "text": "Xn bar is unbiased." + }, + { + "text": "X1 is unbiased, but X1 is certainly not consistent, because the more data I collect, I'm not even doing anything with it." + }, + { + "text": "I'm just taking the first data point you're giving to me." + }, + { + "text": "So they're both unbiased, but this one is not consistent." + }, + { + "text": "And this one we'll see is actually consistent." + }, + { + "text": "Xn bar is consistent, and actually, we've seen that last time." + }, + { + "text": "And that's because of the what guarantees the fact that the Xn bar is consistent?" + }, + { + "text": "Law of large numbers, right?" + }, + { + "text": "Actually, it's strongly consistent because of the strong law of large numbers." + }, + { + "text": "OK." + }, + { + "text": "So just in the last two minutes, I want to tell you a little bit about how this risk is linked to, I said quadratic risk is equal to bias squared plus variance." + }, + { + "text": "Let's see what I mean by this." + }, + { + "text": "So I'm going to forget about the absolute values." + }, + { + "text": "I have a square." + }, + { + "text": "I don't really need them." + }, + { + "text": "If theta hat was unbiased, this thing would be the expectation of theta hat." + }, + { + "text": "It might not be the case." + }, + { + "text": "So let me see how I can actually see, put the bias in there." + }, + { + "text": "Well, one way to do this is to see that this is equal to the expectation of theta hat minus expectation of theta hat plus expectation of theta hat minus theta squared." + }, + { + "text": "OK?" + }, + { + "text": "I just removed the same and added the same thing, so I didn't change anything." + }, + { + "text": "Now, this guy is my bias, right?" + }, + { + "text": "So now let me expand the square." + }, + { + "text": "So what I get is the expectation of the square of theta hat minus its expectation." + }, + { + "text": "I should put some square bracket." + }, + { + "text": "Plus 2 times the cross product." + }, + { + "text": "So the cross product is what?" + }, + { + "text": "Expectation of theta hat minus expectation of theta hat times expectation of theta hat minus theta." + }, + { + "text": "And then I have the last square, expectation of theta hat minus theta squared." + }, + { + "text": "OK?" + }, + { + "text": "So square, cross product, square." + }, + { + "text": "Everybody with me?" + }, + { + "text": "Now, this guy here, if you pay attention, this thing is the expectation of some random variable, so it's a deterministic number." + }, + { + "text": "Theta is the true parameter." + }, + { + "text": "It's a deterministic number." + }, + { + "text": "So what I can do is pull out this entire thing out of the expectation like this." + }, + { + "text": "All right?" + }, + { + "text": "And compute the expectation only with respect to that part." + }, + { + "text": "But what is the expectation of this thing?" + }, + { + "text": "It's 0, right?" + }, + { + "text": "The expectation of theta hat minus expectation of theta hat is 0." + }, + { + "text": "So this entire thing is equal to 0." + }, + { + "text": "So now when I actually collect back my quadratic terms, my two squared terms in this expansion, what I get is that the expectation of theta hat minus theta squared is equal to the expectation of theta hat minus expectation of theta hat squared plus the square of expectation of theta hat minus theta." + }, + { + "text": "Right?" + }, + { + "text": "So those are just the first and the last term of the previous equality." + }, + { + "text": "Now, here I have the expectation of the square of the difference between a random variable and its expectation." + }, + { + "text": "This is otherwise known as the variance, right?" + }, + { + "text": "So this is actually equal to the variance of theta hat." + }, + { + "text": "And this, well, this was the bias." + }, + { + "text": "We already said this there." + }, + { + "text": "So this whole thing is the bias squared." + }, + { + "text": "And hence, the quadratic term is the sum of the variance and the squared bias." + }, + { + "text": "Why squared bias?" + }, + { + "text": "Well, because otherwise you would add dollars and dollars squared, right?" + }, + { + "text": "So you need to add dollars squared and dollars squared so that this thing is actually homogeneous." + }, + { + "text": "OK, so if x is in dollars, then the bias is in dollars, but the variance is in dollars squared." + }, + { + "text": "And the square here forced you to put everything on the square scale." + }, + { + "text": "So what's nice is that if the quadratic risk goes to 0, then since I have the sum of two positive terms, both of them have to go to 0." + }, + { + "text": "That means that my variance is going to 0, very little fluctuations, and my bias is also going to 0, which means that I'm actually going to be on target once I reduce my fluctuations, because it's one thing to reduce the fluctuations." + }, + { + "text": "But if I'm not on target, it's an issue, right?" + }, + { + "text": "For example, the estimator 4, the value 4, has no variance." + }, + { + "text": "Every time I'm going to repeat the experiment, I'm going to get 4, 4, 4, 4." + }, + { + "text": "Variance is 0." + }, + { + "text": "But the bias is bad." + }, + { + "text": "The bias is 4 minus theta." + }, + { + "text": "And if theta is far from 4, that's not doing very well." + }, + { + "text": "OK, so next week, we will talk about how estimators change if they have high variance or low variance, or high bias and low bias." + }, + { + "text": "And we'll talk about confidence intervals as well." + }, + { + "text": "All right." + } +] \ No newline at end of file diff --git a/sight/sources/annotated/TX_vooSnhm8.json b/sight/sources/annotated/TX_vooSnhm8.json new file mode 100644 index 0000000000000000000000000000000000000000..b3f2d7da134535f60983dff7d005ab01f5c96c54 --- /dev/null +++ b/sight/sources/annotated/TX_vooSnhm8.json @@ -0,0 +1,1172 @@ +[ + { + "text": " Okay." + }, + { + "text": "This is the lecture on the singular value decomposition." + }, + { + "text": "But everybody calls it the SVD." + }, + { + "text": "So this is the final and best factorization of a matrix." + }, + { + "text": "Let me tell you what's coming." + }, + { + "text": "The factors will be orthogonal matrix, diagonal matrix, orthogonal matrix." + }, + { + "text": "So it's things that we've seen before, these special good matrices, orthogonal, diagonal." + }, + { + "text": "The new point is that we need two orthogonal matrices." + }, + { + "text": "A can be any matrix whatsoever." + }, + { + "text": "Any matrix whatsoever has this singular value decomposition." + }, + { + "text": "So a diagonal one in the middle, but I need two different, probably different, orthogonal matrices to be able to do this." + }, + { + "text": "Okay." + }, + { + "text": "And this factorization has jumped into importance and is properly, I think, maybe the bringing together of everything in this course." + }, + { + "text": "One thing we'll bring together is, like, the very good family of matrices that we just studied." + }, + { + "text": "Symmetric positive definite." + }, + { + "text": "Do you remember the story with those guys?" + }, + { + "text": "Because they were symmetric, their eigenvectors were orthogonal, so I could produce an orthogonal matrix." + }, + { + "text": "This is my usual one." + }, + { + "text": "My usual one is the eigenvectors and eigenvalues." + }, + { + "text": "In the symmetric case, the eigenvectors are orthogonal, so I've got the good, my ordinary S has become a especially good Q, and positive definite, my ordinary lambda has become a positive lambda." + }, + { + "text": "So this is, that's the singular value decomposition." + }, + { + "text": "In case our matrix is symmetric positive definite, in that case, I don't need two, u and a v, one orthogonal matrix will do for both sides." + }, + { + "text": "But, so this would be no good in general, because usually the eigenvector matrix isn't orthogonal." + }, + { + "text": "So this is not what I'm, that's not what I'm after." + }, + { + "text": "I'm looking for orthogonal times diagonal times orthogonal." + }, + { + "text": "And let me show you what that means and where it comes from." + }, + { + "text": "OK. What does it mean?" + }, + { + "text": "You remember the picture of any linear transformation." + }, + { + "text": "This was, like, the most important figure in 1806." + }, + { + "text": "And what am I looking for now?" + }, + { + "text": "A typical vector in the row space, typical vector, let me call it v1, gets taken over to some vector in the column space, say u1." + }, + { + "text": "So u1 is a v1." + }, + { + "text": "OK. Now, another vector gets taken over here somewhere." + }, + { + "text": "What am I looking for?" + }, + { + "text": "In this SVD, this singular value decomposition, what I'm looking for is an orthogonal basis here that gets knocked over into an orthogonal basis over there." + }, + { + "text": "See, that's pretty special, to have an orthogonal basis in the row space that goes over into an orthogonal basis, so this is like a right angle and this is a right angle, into an orthogonal basis in the column space." + }, + { + "text": "So that's our goal, is to find -- you see how things are coming together." + }, + { + "text": "First of all, can I find an orthogonal basis for this row space?" + }, + { + "text": "Of course." + }, + { + "text": "No big deal to find an orthogonal basis." + }, + { + "text": "Graham-Schmidt tells me how to do it." + }, + { + "text": "Start with any old basis and use- grind through Graham-Schmidt, out comes an orthogonal basis." + }, + { + "text": "But then, if I just take any old orthogonal basis, then when I multiply by A, there's no reason why it should be orthogonal over here." + }, + { + "text": "So I'm looking for this special setup where A takes these basis vectors into orthogonal vectors over there." + }, + { + "text": "Now, you might have noticed that the null space I didn't include." + }, + { + "text": "Why don't I stick that in?" + }, + { + "text": "You remember our usual figure had a little null space and a little null space." + }, + { + "text": "And, those are no problems." + }, + { + "text": "Those are- null spaces are going to show up as zeros on the diagonal of sigma, so that's not what we're- that doesn't present any difficulty." + }, + { + "text": "Our difficulty is to find the- so do you see what this will mean?" + }, + { + "text": "This will mean that A times this- these v's, v1, v2, up to- what's the dimension of this row space?" + }, + { + "text": "vr." + }, + { + "text": "Sorry, that v a little smaller." + }, + { + "text": "Up to vr." + }, + { + "text": "So that's A v1 is going to be the first column, so let me- here's what I'm- here's what I'm achieving." + }, + { + "text": "Oh, I would like- I'm not only going to make these orthogonal, but why not make them orthonormal?" + }, + { + "text": "Make them unit vectors." + }, + { + "text": "So this- maybe the unit vector is here, is the u1, and this might be a multiple of it." + }, + { + "text": "So really what's happening is A v1 is some multiple of u1, right?" + }, + { + "text": "I'm going to- these guys will be unit vectors, and they'll go over into multiples of unit vectors, and the multiple I'm not going to call lambda anymore, I'm calling it sigma." + }, + { + "text": "So that's the number- the stretching number." + }, + { + "text": "And similarly, A v2 is sigma 2 u2." + }, + { + "text": "This is what- this is my goal." + }, + { + "text": "And now I want to express that goal in matrix language." + }, + { + "text": "That's the usual step." + }, + { + "text": "Think of what you want and then express it as a matrix multiplication." + }, + { + "text": "So A v1 is sigma 1 u1." + }, + { + "text": "Actually, here we go." + }, + { + "text": "Let me pull out these u1, u2 to ur, and then a matrix with the sigmas." + }, + { + "text": "It's- everything now is going to be in this- in that, in that, little part of the blackboard." + }, + { + "text": "Do you see that this equation says what I'm trying to do with my figure?" + }, + { + "text": "A times the first basis vector should be sigma 1 times the other basis- the other first basis vector." + }, + { + "text": "These are the basis vectors in the row space, these are the basis vectors in the column space, and these are the multiplying factors." + }, + { + "text": "So A v2 is sigma 2 times u2, A vr is sigma r times ur." + }, + { + "text": "And then we've got a whole lot of zeros and maybe some zeros at the end, but this is- that's the heart of it." + }, + { + "text": "And now if I express that in- as matrices, because you knew that was coming, that's what I have." + }, + { + "text": "So this is my goal." + }, + { + "text": "To find an orthogonal basis in the rows- orthonormal, even, basis in the row space, and an orthonormal basis in the column space, so that I'm sort of diagonalized the matrix." + }, + { + "text": "The matrix A is like getting converted to this diagonal matrix sigma." + }, + { + "text": "And you notice that usually I have to do- I have to allow myself two different bases." + }, + { + "text": "My little comment about symmetric positive definite was the one case where it's A q equal q sigma, where v and u are the same q." + }, + { + "text": "But mostly, I'm going to take a matrix like, oh, let me take a matrix like four four minus three three." + }, + { + "text": "Okay." + }, + { + "text": "There's a two by two matrix." + }, + { + "text": "It's invertible, so it has rank two." + }, + { + "text": "So I'm going to look for two vectors, v1 and v2, in the row space, and u- so I'm going to look for v1 v2 in the row space, which of course is R2." + }, + { + "text": "And I'm going to look for u1 u2 in the column space, which of course is also R2." + }, + { + "text": "And I'm going to look for numbers sigma 1 and sigma 2, so that it all comes out right." + }, + { + "text": "So these guys are orthonormal." + }, + { + "text": "These guys are orthonormal, and these are the scaling factors." + }, + { + "text": "So I'll do that example as soon as I get the matrix picture straight." + }, + { + "text": "Okay." + }, + { + "text": "Do you see that this expresses what I want?" + }, + { + "text": "Can I just say two words about null spaces?" + }, + { + "text": "If we have -- if there's some null space, then we've got- we want to stick in a basis for those, for that." + }, + { + "text": "So here comes a basis for the null space, v R plus one down to vn." + }, + { + "text": "So if we only had an R-dimensional row space and the other n minus R dimensions were in the null space, okay, we'll take an orthogonal- orthonormal basis there, no problem." + }, + { + "text": "And then we'll just get zeros." + }, + { + "text": "So actually, those zeros will come out from the- on the diagonal matrix." + }, + { + "text": "So I'll complete that to, to, orthonormal basis for the whole space, Rn." + }, + { + "text": "I complete this to an orthonormal basis for the whole space, Rn, and I complete that with zeros." + }, + { + "text": "Null spaces are no problem here." + }, + { + "text": "So really, the true problem is in a matrix like that, which isn't symmetric, so I can't use its eigenvectors, they're not orthogonal, but somehow I have to get these orthogonal, in fact, orthonormal guys that make it work." + }, + { + "text": "I have to find this, these orthonormal guys, these orthonormal guys, and I want A v1 to be sigma 1 u1, and A v2 to be sigma 2 u2." + }, + { + "text": "Okay." + }, + { + "text": "That's my goal." + }, + { + "text": "Here's, here's the, matrices that are going to get me there." + }, + { + "text": "Now, these are orthogonal matrices." + }, + { + "text": "I can put that, if I multiply on both sides by v inverse, I have A equals u sigma v inverse, and of course, you know the other way I can write v inverse." + }, + { + "text": "This is one of those square orthogonal matrices, so it's the same as u sigma v transpose." + }, + { + "text": "Okay." + }, + { + "text": "Here's my problem." + }, + { + "text": "I've got two orthogonal matrices here, and I don't want to find them both at once." + }, + { + "text": "So I want to cook up some expression that will make the u's disappear." + }, + { + "text": "I would like to make the u's disappear and leave me only with the v's." + }, + { + "text": "And here's how to do it." + }, + { + "text": "It's, it's the same combination that keeps showing up whenever we have a general rectangular matrix, then it's A transpose A, that's the great matrix." + }, + { + "text": "That's the great matrix." + }, + { + "text": "That's the matrix that's symmetric." + }, + { + "text": "And, in fact, positive definite or at least positive semidefinite." + }, + { + "text": "This is the matrix with nice properties." + }, + { + "text": "So let's see what will it be." + }, + { + "text": "So if I took the transpose, then, I would have A transpose A will be what?" + }, + { + "text": "What do I have?" + }, + { + "text": "If I transpose that, I have v sigma transpose u transpose, that's, that's the A transpose." + }, + { + "text": "Now the A." + }, + { + "text": "And what have I got?" + }, + { + "text": "Looks like worse, because it's got six things now together, but it's going to collapse into something good." + }, + { + "text": "What does u transpose u collapse into?" + }, + { + "text": "I." + }, + { + "text": "The identity." + }, + { + "text": "So that's the key point." + }, + { + "text": "This is the identity and we don't have u anymore." + }, + { + "text": "And sigma transpose times sigma, those are diagonal matrices." + }, + { + "text": "So their product is just going to have sigma squareds on the diagonal." + }, + { + "text": "So do you see what we've got here?" + }, + { + "text": "This is v times this easy matrix, sigma one squared, sigma two squared, times v transpose." + }, + { + "text": "This is the A transpose A." + }, + { + "text": "This is, let me copy down, A transpose A is that." + }, + { + "text": "U's are out of the picture now." + }, + { + "text": "I'm only having to choose the v's." + }, + { + "text": "And what are these v's?" + }, + { + "text": "And what are these sigmas?" + }, + { + "text": "Do you know what the v's are?" + }, + { + "text": "They're the eigenvectors." + }, + { + "text": "See, this is a perfect eigenvector, eigenvalue, Q lambda Q transpose for the matrix A transpose A." + }, + { + "text": "A itself is like nothing special." + }, + { + "text": "But A transpose A will be special." + }, + { + "text": "It'll be symmetric, positive, definite." + }, + { + "text": "So this'll be its eigenvectors and this'll be its eigenvalues." + }, + { + "text": "And the eigenvalues will be positive because this thing's positive definite." + }, + { + "text": "Can I just now so this is my method." + }, + { + "text": "This tells me what the v's are and how am I going to find the u's?" + }, + { + "text": "Well, one way would be to look at A A transpose." + }, + { + "text": "Put, multiply A by A transpose in the opposite order." + }, + { + "text": "That will stick the v's in the middle, knock them out, and leave me with the u's." + }, + { + "text": "So here's the overall picture, then." + }, + { + "text": "The v's are the eigenvectors of A transpose A." + }, + { + "text": "The u's are the eigenvectors of A A transpose, which are different." + }, + { + "text": "And the sigmas are the square roots of these and the positive square roots, so we have positive sigmas." + }, + { + "text": "Let me do that for that example." + }, + { + "text": "This is really what you should know and be able to do for, the SVD." + }, + { + "text": "Okay." + }, + { + "text": "Let me take that matrix." + }, + { + "text": "So what's my first step?" + }, + { + "text": "Compute A transpose A, because I want its eigenvectors." + }, + { + "text": "Okay, so I have to compute A transpose A." + }, + { + "text": "So A transpose is four four minus three three, and A is four four minus three three." + }, + { + "text": "And I do that multiplication and I get sixteen, I get twenty-five, I get sixteen minus nine, is that seven?" + }, + { + "text": "And it better come out symmetric and, oh, okay, and then it comes out twenty-five." + }, + { + "text": "Okay." + }, + { + "text": "So I want its eigenvectors and its eigenvalues." + }, + { + "text": "Its eigenvectors will be the v's, its eigenvalues will be the squares of the sigmas." + }, + { + "text": "Okay." + }, + { + "text": "What are the eigenvalues and eigenvectors of this guy?" + }, + { + "text": "Have you seen that two by two example enough to recognize that the eigenvectors are, that one one is an eigenvector?" + }, + { + "text": "So this is, here is A transpose A. I'm looking for its eigenvectors." + }, + { + "text": "So its eigenvectors, I think, are one one and one minus one." + }, + { + "text": "Because if I multiply that matrix by one one, what do I get?" + }, + { + "text": "If I multiply that matrix by one one, I get thirty-two thirty-two." + }, + { + "text": "So which is thirty-two of one one." + }, + { + "text": "So there's the first eigenvector." + }, + { + "text": "And there's the eigenvalue for A transpose A, so I'm going to take its square root in the, for sigma." + }, + { + "text": "Okay." + }, + { + "text": "What's the eigenvector that goes, eigenvalue that goes with this one?" + }, + { + "text": "If I do that multiplication, what do I get?" + }, + { + "text": "I get some multiple of one minus one." + }, + { + "text": "And what is that multiple?" + }, + { + "text": "Looks like eighteen." + }, + { + "text": "Okay." + }, + { + "text": "So those are the two eigenvectors." + }, + { + "text": "But, oh, just a moment, I didn't normalize them." + }, + { + "text": "To, to make everything absolutely right, I ought to normalize these eigenvectors, divide by their length, square root of two." + }, + { + "text": "So all these guys should be true unit vectors, and, of course, that normalization didn't change the thirty-two and the eighteen." + }, + { + "text": "Okay." + }, + { + "text": "So I'm happy with the Vs, here are the Vs, so now let me put together the, the, the pieces here." + }, + { + "text": "Here's my A." + }, + { + "text": "Here's my A." + }, + { + "text": "Let me, let me write down A again." + }, + { + "text": "This should, if, if life is right, we should get U, which I don't yet know, U I don't yet know, sigma, I do now know." + }, + { + "text": "What's sigma?" + }, + { + "text": "So I'm looking for U sigma V transpose." + }, + { + "text": "U, the diagonal guy, and V transpose." + }, + { + "text": "Okay." + }, + { + "text": "Let's just see that come out right." + }, + { + "text": "So what's, what are the, what are the sigmas?" + }, + { + "text": "They're the square roots of these things." + }, + { + "text": "So square root of thirty-two and square root of eighteen." + }, + { + "text": "Zero, zero." + }, + { + "text": "Okay." + }, + { + "text": "What are the Vs?" + }, + { + "text": "They're these two." + }, + { + "text": "And I have to transpose, maybe that, maybe that just leaves me with one, with one over square root of two in that row, and the other one is one over square root of two minus one over square root of two." + }, + { + "text": "Now, finally, I've got to know the Us." + }, + { + "text": "Well, actually, one way to do, since I now know all the other pieces, I could put those together and figure out what the Us are." + }, + { + "text": "But let me do it the A A transpose way." + }, + { + "text": "Okay, find the Us now." + }, + { + "text": "U1 and U2." + }, + { + "text": "And what are they?" + }, + { + "text": "I look at A A transpose, so A is supposed to be U sigma V transpose, and then when I transpose that, I get V sigma transpose U transpose." + }, + { + "text": "So I'm just doing it in the opposite order, A times A transpose, and what's the good part here?" + }, + { + "text": "That in the middle, V transpose V is going to be the identity." + }, + { + "text": "So this is just U sigma sigma transpose, that's some diagonal matrix with sigma squareds and U transpose." + }, + { + "text": "So what am I seeing here?" + }, + { + "text": "I'm seeing here, again, a symmetric positive definite or at least semi-definite matrix, and I'm seeing its eigenvectors and its eigenvalues." + }, + { + "text": "So if I compute A A transpose, its eigenvectors will be the things that go into U." + }, + { + "text": "Okay, so I need to compute A A transpose." + }, + { + "text": "I guess I'm going to have to go -." + }, + { + "text": "Let me, can I move that up just a little, maybe a little more, and do A A transpose." + }, + { + "text": "So what's A?" + }, + { + "text": "Four, four, minus three and three." + }, + { + "text": "And what's A transpose?" + }, + { + "text": "Four, four, minus three and three." + }, + { + "text": "And when I do that multiplication, I get, what do I get?" + }, + { + "text": "Sixteen and sixteen, thirty-two." + }, + { + "text": "That one comes out zero." + }, + { + "text": "Oh, so this is a lucky case, and that one comes out eighteen." + }, + { + "text": "So this is, like, an accident, that A A transpose happens to come out diagonal, so we know easily its eigenvectors and eigenvalues." + }, + { + "text": "So its eigenvectors are, what's the first eigenvector for this A A transpose matrix?" + }, + { + "text": "It's just one zero, and when I do that multiplication, I get thirty-two times one zero." + }, + { + "text": "And the other eigenvector is just zero one, and when I multiply by that, I get eighteen." + }, + { + "text": "So this is A A transpose, multiplying that gives me the thirty-two A A transpose, multiplying this guy gives me eighteen." + }, + { + "text": "First of all, I got thirty-two and eighteen again." + }, + { + "text": "Am I surprised?" + }, + { + "text": "Yeah, it's clearly not an accident." + }, + { + "text": "The eigenvalues of A A transpose were exactly the same as the eigenvalues of this one was A transpose A." + }, + { + "text": "That's no surprise at all." + }, + { + "text": "The eigenvalues of A B are same as the eigenvalues of B A." + }, + { + "text": "The order, that's a very nice fact, that eigenvalues stay the same if I switch the order of multiplication." + }, + { + "text": "So no surprise to see thirty-two and eighteen." + }, + { + "text": "What I learned, first I checked that things were numerically correct, but now I've learned these eigenvectors, and actually they're about as nice as can be." + }, + { + "text": "They're the best orthogonal matrix, just the identity." + }, + { + "text": "Okay." + }, + { + "text": "So my claim is that it ought to all fit together." + }, + { + "text": "That this numeri- this, these numbers should come out right." + }, + { + "text": "The numbers should come out right because the, the, matrix multiplications use the properties that we want." + }, + { + "text": "Okay." + }, + { + "text": "So we just check that." + }, + { + "text": "Here's the identity, so not doing anything." + }, + { + "text": "Square root of thirty-two is multiplying that row, so that's square root of thirty-two divided by square root of two means square root of sixteen, four." + }, + { + "text": "Correct?" + }, + { + "text": "And square root of eighteen is divided by square root of two, so that leaves me square root of nine, which is three, but no, Professor Strang, you see the problem." + }, + { + "text": "Why is that?" + }, + { + "text": "Okay." + }, + { + "text": "Why am I getting minus three three here, and here I'm getting three minus three?" + }, + { + "text": "Phooey." + }, + { + "text": "I don't know why." + }, + { + "text": "It shouldn't have happened, but it did." + }, + { + "text": "Now, okay, you could say, well, just, the eigenvector there could have, I could have had the minus sign here for that eigenvector, but I'm not happy about that." + }, + { + "text": "Hm." + }, + { + "text": "Okay." + }, + { + "text": "Okay." + }, + { + "text": "So I realize there's a little catch here somewhere, and I may not see it until Wednesday, which then gives you a very important reason to come back on Wednesday, to catch that sign difference." + }, + { + "text": "So what did I do illegally?" + }, + { + "text": "I think I put the eigenvectors in that matrix V transpose." + }, + { + "text": "Okay, I'm going to have to think, why did that come out, with the opposite sign?" + }, + { + "text": "So you see, I mean, if I had a minus there, I would be all right, but I don't want that." + }, + { + "text": "I want positive entries down the diagonal of sigma squared." + }, + { + "text": "Okay." + }, + { + "text": "It'll come to me, but I'm going to leave this example to finish." + }, + { + "text": "Okay." + }, + { + "text": "And the beauty of, these sliding boards is, I can make that go away." + }, + { + "text": "Can I, let me not do it, though." + }, + { + "text": "Yes, let me take a second example." + }, + { + "text": "Let me take a second example where the matrix is singular." + }, + { + "text": "So rank one." + }, + { + "text": "Okay." + }, + { + "text": "So let me take as an example two, where my matrix A is going to be rectangular again." + }, + { + "text": "Let me just make it four three eight six." + }, + { + "text": "Okay." + }, + { + "text": "That's a rank one matrix." + }, + { + "text": "So that has a null space and only a one-dimensional row space and column space." + }, + { + "text": "So actually, my picture becomes easy for this matrix, because what's my columns, my row space for this one?" + }, + { + "text": "So this is two by two, so my pictures are both two dimensional." + }, + { + "text": "My row space is all multiples of vector four three." + }, + { + "text": "So the whole, the row space is just a line, right?" + }, + { + "text": "That's the row space." + }, + { + "text": "And the null space, of course, is the perpendicular line." + }, + { + "text": "So the row space for this matrix is multiples of four three." + }, + { + "text": "Typical row." + }, + { + "text": "Okay." + }, + { + "text": "What's the column space?" + }, + { + "text": "The columns are all multiples of four eight, three six, one two." + }, + { + "text": "The column space, then, goes in, like, this direction." + }, + { + "text": "So the column space, when I look at those columns, the column space, it was only one dimensional, because the rank is one." + }, + { + "text": "It's multiples of four eight." + }, + { + "text": "Okay." + }, + { + "text": "And what's the null space of A transpose?" + }, + { + "text": "It's the perpendicular guy." + }, + { + "text": "There's the, so this was the null space of A, and this is the null space of A transpose." + }, + { + "text": "Okay." + }, + { + "text": "What I want to say here is that the, that choosing these orthogonal bases for the row space and the column space is, like, no problem." + }, + { + "text": "They're only one dimensional." + }, + { + "text": "So what should v be?" + }, + { + "text": "v should be v1, but, yeah, v1, rather." + }, + { + "text": "v1 is supposed to be a unit vector." + }, + { + "text": "There's only one v1 to choose here, only one dimension in the row space." + }, + { + "text": "I just want to make it a unit vector." + }, + { + "text": "So v1 will be, it'll be this vector, but made into a unit vector, so four, point eight, point six." + }, + { + "text": "Four fifths, three fifths." + }, + { + "text": "And what will be u1?" + }, + { + "text": "u1 will be the unit vector there, so I want to turn four eight or one two into a unit vector, so u1 will be, let's see, if it's one two, then what multiple of one two do I want?" + }, + { + "text": "That has length square root of five, so I have to divide by square root of five." + }, + { + "text": "Let me complete the singular value decomposition for this matrix." + }, + { + "text": "So this matrix, four three eight six, is, so I know what u1, here's A, and I want to get u, the basis in the column space, and it has to start with this guy." + }, + { + "text": "One over square root of five, two over square root of five." + }, + { + "text": "Then I want the sigma." + }, + { + "text": "OK. What are we expecting now for sigma?" + }, + { + "text": "Where is, this is only a rank one matrix, we're only expecting a sigma one, which I have to find, but zero's here." + }, + { + "text": "OK, so what's sigma one?" + }, + { + "text": "We should see it, it should be the, where did these sigmas come from?" + }, + { + "text": "They came from A transpose A, so I, can I do that little calculation over here?" + }, + { + "text": "A transpose A is four three, four three eight six times four three eight six." + }, + { + "text": "This had better, this is a rank one matrix, this is going to be, the whole thing will have rank one, that's sixteen and sixty four is eighty, twelve and forty eight is sixty, twelve and forty eight is sixty, nine and thirty six is forty five." + }, + { + "text": "OK." + }, + { + "text": "It's a rank one matrix." + }, + { + "text": "Of course." + }, + { + "text": "Every row is a multiple of four three." + }, + { + "text": "And what's the eigen, what are the eigenvalues of that matrix?" + }, + { + "text": "So this is like, the calculation is like practicing now." + }, + { + "text": "What are the eigenvalues of this rank one matrix?" + }, + { + "text": "Well, tell me one eigenvalue, since the rank is only one, one eigenvalue is going to be zero." + }, + { + "text": "And then you know that the other eigenvalue is going to be a hundred and twenty five." + }, + { + "text": "So that's sigma squared, right, in A transpose A." + }, + { + "text": "So this will be the square root of a hundred and twenty five." + }, + { + "text": "And then finally, the V transpose, the Vs will be, there's V1, and what's V2?" + }, + { + "text": "What's V2 in the, what's, how do I make this into a orthonormal basis?" + }, + { + "text": "Well, V2 is in the null space direction." + }, + { + "text": "It's perpendicular to that, so point six and minus point eight." + }, + { + "text": "So those are the Vs that go in here." + }, + { + "text": "Point eight, point six, and point six minus point eight." + }, + { + "text": "OK. And I guess I better finish this guy." + }, + { + "text": "So this guy, all I want is to complete the orthonormal basis." + }, + { + "text": "It'll be coming from there, it'll be a two over square root of five and a minus one over square root of five." + }, + { + "text": "I could have take, let me take square root of five out of that matrix to make it look better." + }, + { + "text": "So one over square root of five times one, one, two, two, minus one." + }, + { + "text": "OK." + }, + { + "text": "So there I have, including the square root of five, that's an orthogonal matrix, that's an orthogonal matrix, that's a diagonal matrix, and its rank is only one." + }, + { + "text": "And now if I do that multiplication, I pray that it comes out right." + }, + { + "text": "The square root of five will cancel into that square root of one twenty-five and leave me with the square root of twenty-five, which is five, and five will multiply these numbers and I'll get whole numbers and out will come A. OK. That's a second, like, a second example showing how the null space guy, so this, this vector and the, and this one were multiplied by this zero, so they, they were easy to deal with." + }, + { + "text": "It was the key ones are the ones in the column space and the row space." + }, + { + "text": "Do you see how I'm getting columns here, diagonal here, rows here, coming together to produce A?" + }, + { + "text": "OK. That's the singular value decomposition." + }, + { + "text": "So, let, let me think what I want to add to, to complete this topic." + }, + { + "text": "Sort of what we're really doing." + }, + { + "text": "So that's two examples." + }, + { + "text": "And now let's think what we're really doing." + }, + { + "text": "We're, we're choosing the right basis for the four subspaces of linear algebra." + }, + { + "text": "Let me, let me, let me write this down." + }, + { + "text": "So V1 up to Vr is an orthonormal basis for the row space." + }, + { + "text": "U1 up to Ur is an orthonormal basis for the column space." + }, + { + "text": "And then I just finish those out by Vr plus one, the rest up to Vn is an orthonormal basis for the null space." + }, + { + "text": "And finally, Ur plus one up to Um is an orthonormal basis for the null space of A transpose." + }, + { + "text": "Do you see that we finally got the bases right?" + }, + { + "text": "They're right because they're orthonormal and also, I mean, the, again, Graham-Schmidt would have done this in chapter four." + }, + { + "text": "Here we needed eigenvalues because these bases make the matrix diagonal." + }, + { + "text": "A times Vi is a multiple of Ui." + }, + { + "text": "So I'll put and." + }, + { + "text": "The matrix has been made diagonal." + }, + { + "text": "When we choose these bases, there's no coupling between Vs and no coupling between Us." + }, + { + "text": "Each A, A times each V is in the direction of the corresponding U." + }, + { + "text": "So it's exactly the right basis for the four fundamental subspaces." + }, + { + "text": "And of course, their dimensions are what we know." + }, + { + "text": "The dimension of the row space is the rank r, and so is the dimension of the column space." + }, + { + "text": "The dimension of the null space is n minus r, that's how many vectors we need, and m minus r basis vectors for the left null space, the null space of A transpose." + }, + { + "text": "OK." + }, + { + "text": "I'm going to stop there." + }, + { + "text": "I could develop further from the SVD, but we'll see it again in the very last lectures of the course." + }, + { + "text": "There's the SVD." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated/UYe98CcxPbs.json b/sight/sources/annotated/UYe98CcxPbs.json new file mode 100644 index 0000000000000000000000000000000000000000..2a48e3c41b4d9d4ce1f9204928eac9e23929a27b --- /dev/null +++ b/sight/sources/annotated/UYe98CcxPbs.json @@ -0,0 +1,1193 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "Today we are going to see how to use what we saw last time about partial derivatives to handle minimization or maximization problems involving functions of several variables." + }, + { + "text": "Remember last time we said that when we have a function, say, of two variables, x and y, then we have actually two different derivatives." + }, + { + "text": "Partial f, partial x, also called f sub x, is the derivative with respect to x keeping y constant." + }, + { + "text": "And we have partial f, partial y, also called f sub y, where we vary y and we treat x as a constant." + }, + { + "text": "And now, one thing I didn't have time to tell you about, but hopefully you heard about in recitation yesterday, is the approximation formula that tells you what happens if you vary both x and y. F sub x tells us what happens if we change x a little bit by some small amount delta x. F sub y tells us how f changes if we change y by a small amount delta y." + }, + { + "text": "If we do both at the same time, then the two effects will add up with each other." + }, + { + "text": "Because you can imagine that first you will change x and then you will change y or the other way around." + }, + { + "text": "It doesn't really matter." + }, + { + "text": "If we change x by a certain amount delta x, and if we change y by the amount delta y, and let's say that we have z equals f of x, y, then that changes by an amount which is approximately f sub x times delta x plus f sub y times delta y." + }, + { + "text": "And that is one of the most important formulas about partial derivatives." + }, + { + "text": "The intuition for this, again, is just the two effects add up." + }, + { + "text": "If I change x by a small amount and then I change y, well, first changing x will modify f. How much does it modify f?" + }, + { + "text": "The answer is the rate of change." + }, + { + "text": "The rate of change is f sub x." + }, + { + "text": "And, if I change y, then the rate of change of f when I change y is f sub y." + }, + { + "text": "All together, I get this change in the value of f. And, of course, that is only an approximation formula." + }, + { + "text": "Actually, there would be higher order terms involving second and third derivatives and so on." + }, + { + "text": "One way to justify this, sorry, I was distracted by a microphone problem." + }, + { + "text": "OK, so how do we justify this formula?" + }, + { + "text": "Well, one way to think about it is in terms of tangent plane approximation." + }, + { + "text": "Let's think about the tangent plane to the graph of a function f. I have some pictures to show you." + }, + { + "text": "It will be easier if I show the pictures." + }, + { + "text": "Remember, partial f over partial x was obtained by looking at the situation where y is held constant." + }, + { + "text": "That means I am slicing the graph of f by a plane that is parallel to the xz plane." + }, + { + "text": "And then, when I change x, z changes." + }, + { + "text": "And the slope of that is going to be the derivative with respect to x." + }, + { + "text": "Now, if I do the same in the other direction, then I will have similarly the slope in a slice now parallel to the yz plane that will be partial f over partial y." + }, + { + "text": "In fact, in each case I have a line." + }, + { + "text": "And that line is tangent to the surface." + }, + { + "text": "Now, if I have two lines tangent to the surface, well, then together they determine for me the tangent plane to the surface." + }, + { + "text": "Let's try to see how that works." + }, + { + "text": "We know that f sub x and f sub y are the slopes of two tangent lines to this plane, sorry, two tangent lines to the graph." + }, + { + "text": "And let's write down the equations of these lines." + }, + { + "text": "I am not going to write parametric equations." + }, + { + "text": "I am going to write them in terms of x, y, z coordinates." + }, + { + "text": "Let's say that partial f over partial x at a given point is equal to a." + }, + { + "text": "Then that means that we have a line given by the following conditions." + }, + { + "text": "I am going to keep y constant equal to y0." + }, + { + "text": "And I am going to change x." + }, + { + "text": "And, as I change x, z will change at a rate that is equal to a." + }, + { + "text": "That would be z equals z0 plus a times the change in x, x minus x0." + }, + { + "text": "That is how you would describe the line that is, I guess, the one that is plotted in green here." + }, + { + "text": "That is the intersection with the slice parallel to the xz plane." + }, + { + "text": "I hold y constant equal to y0." + }, + { + "text": "And z is a function of x that varies with a rate of a." + }, + { + "text": "And now, if I look similarly at the other slice, let's say that the partial with respect to y is equal to b, then I get another line which is obtained by the fact that z depends on y and the rate of change with respect to y will be b while x is held constant equal to x0." + }, + { + "text": "These two lines are both going to be in the tangent plane to the surface." + }, + { + "text": "They are both tangent to the surface, f of f. And, well, together they determine a plane." + }, + { + "text": "And that plane is just given by the formula z equals z0 plus a times x minus x0 plus b times y plus b." + }, + { + "text": "If you look at what happens, this is the equation of a plane, z equals constant times x plus constant times y plus constant." + }, + { + "text": "And if you look at what happens if I hold y constant and vary x, I recover the first line." + }, + { + "text": "If I hold x constant and vary y, I get the second line." + }, + { + "text": "Another way to do it, of course, would be to write actually parametric equations of these lines, get vectors along them and then take the cross-product to get the normal vector to the plane, and then get this equation for the plane using the normal vector." + }, + { + "text": "That also works and it gives you the same formula." + }, + { + "text": "If you are curious, exercise, do it again using parametrics and using cross-product to get the plane equation." + }, + { + "text": "OK, so that is how we get the tangent plane." + }, + { + "text": "And now, what this approximation formula here says is that, in fact, the graph of a function is close to the tangent plane." + }, + { + "text": "If we were moving on the tangent plane, this would be an actual equality." + }, + { + "text": "Delta z would be a linear function of delta x and delta y." + }, + { + "text": "And the graph of a function is near the tangent plane, but it is not quite the same." + }, + { + "text": "It is only an approximation for small delta x and small delta y." + }, + { + "text": "The approximation formula says the graph of f is close to its tangent plane." + }, + { + "text": "And we can use that formula over here now to estimate how the value of f changes if I change x and y at the same time." + }, + { + "text": "Questions about that?" + }, + { + "text": "Now that we have caught up with what we were supposed to see on Tuesday, I can tell you now about max and min problems." + }, + { + "text": "Min problems." + }, + { + "text": "That is going to be an application of partial derivatives to look at optimization problems." + }, + { + "text": "Maybe ten years from now when you have a real job, your job might be to actually minimize the cost of something or maximize the profit of something or whatever." + }, + { + "text": "But typically, the function that you will have to strive to minimize or maximize will depend on several variables." + }, + { + "text": "If you have a function of one variable, you know that to find its minimum or its maximum you look at the derivative and you set that equal to zero." + }, + { + "text": "And you try to then look at what happens to the function." + }, + { + "text": "Here it is going to be kind of similar, except, of course, we have several variables." + }, + { + "text": "For today, we will think about a function of two variables." + }, + { + "text": "But it works exactly the same if you have three variables, ten variables, a million variables." + }, + { + "text": "The first observation is that if we have a local minimum or a local maximum, then both partial derivative, partial f, partial x and partial f, partial y are both zero at the same time." + }, + { + "text": "Why is that?" + }, + { + "text": "Well, let's say that f sub x is zero." + }, + { + "text": "That means when I vary x, well, to first order the function doesn't change." + }, + { + "text": "Maybe that is because it is going through." + }, + { + "text": "If I look only at the slice parallel to the x-axis, then maybe I am going through the minimum." + }, + { + "text": "But then, if partial f, partial y is not zero, then actually by changing y I could still make the value larger or smaller." + }, + { + "text": "That wouldn't be an actual maximum or minimum." + }, + { + "text": "It would only be maximum or minimum if I stay in the slice." + }, + { + "text": "But if I allow myself to change y, that doesn't work." + }, + { + "text": "I need actually to know that if I change y the value will not change either to first order." + }, + { + "text": "That is why I also need partial f, partial y to be zero." + }, + { + "text": "Now, let's say that they are both zero." + }, + { + "text": "Well, why is that enough?" + }, + { + "text": "It is essentially enough because of this formula telling me that if both of these guys are zero then to first order the function doesn't change." + }, + { + "text": "And then, of course, there will be maybe quadratic terms that will actually turn that." + }, + { + "text": "This won't really say that your function is actually constant." + }, + { + "text": "It will just tell you that maybe it will be actually quadratic or higher order in delta x and delta y." + }, + { + "text": "That is what you expect to have at a maximum or a minimum." + }, + { + "text": "That condition is the same thing as saying that the tangent plane to the graph is actually going to be horizontal." + }, + { + "text": "And that is what you want to have." + }, + { + "text": "Say you have a minimum." + }, + { + "text": "Well, see that the tangent plane at this point, at the bottom of the graph, is going to be horizontal." + }, + { + "text": "And you can see that on this equation of a tangent plane, when both these coefficients are zero, that is when the equation becomes z equals constant, the horizontal plane." + }, + { + "text": "Does that make sense?" + }, + { + "text": "We will have a name for this kind of point because actually what we will see very soon is that these conditions are necessary but they are not sufficient." + }, + { + "text": "There are actually other kinds of points where the partial derivatives are zero." + }, + { + "text": "Let's give a name to this." + }, + { + "text": "We say that x0, y0 is a critical point of F if the partial derivative with respect to x and the partial derivative with respect to y are both zero." + }, + { + "text": "More generally, you would want all the partial derivatives, no matter how many variables you have, you want all the partials to be zero." + }, + { + "text": "Let's see an example." + }, + { + "text": "Let's say I give you the function f of x, y equals x squared minus 2xy plus py squared plus 2x minus 2y." + }, + { + "text": "And let's try to figure out whether we can minimize or maximize this." + }, + { + "text": "What we start doing immediately is taking the partial derivatives." + }, + { + "text": "What is f sub x?" + }, + { + "text": "It starts with 2x minus 2y plus zero plus two." + }, + { + "text": "Remember that y is a constant so this differentiates to zero." + }, + { + "text": "Now, if we do f sub y, that is going to be zero minus 2x plus 6y minus two." + }, + { + "text": "And what we want to do is set these things equal to zero." + }, + { + "text": "And we want to solve these two equations at the same time." + }, + { + "text": "An important thing to remember, maybe I should have told you a couple of weeks ago already, if you have two equations to solve, well, it is very good to try to simplify them by adding them together or whatever." + }, + { + "text": "But you must keep two equations." + }, + { + "text": "If you have two equations, you should not end up with just one equation out of nowhere." + }, + { + "text": "For example, here we can certainly simplify things by summing them together." + }, + { + "text": "See, if we add them together, well, the x's cancel and the constants cancel." + }, + { + "text": "In fact, we are just left with 4y equals zero." + }, + { + "text": "That is pretty good." + }, + { + "text": "That tells us y should be zero." + }, + { + "text": "But then we should, of course, go back to these and see what else we know." + }, + { + "text": "Well, now it tells us, if you put y equals zero, that tells you 2x plus 2 equals zero." + }, + { + "text": "That tells you x equals minus one." + }, + { + "text": "We have one critical point." + }, + { + "text": "That is x, y equals minus one over two." + }, + { + "text": "Any questions so far?" + }, + { + "text": "Well, you should have a question." + }, + { + "text": "The question should be how do we know if it is a maximum or a minimum?" + }, + { + "text": "Well, if we had a function of one variable, we would decide things based on the second derivative." + }, + { + "text": "And, in fact, we will see tomorrow how to do things based on the second derivative." + }, + { + "text": "But that is kind of tricky because there are a lot of second derivatives." + }, + { + "text": "I mean, we already have two first derivatives." + }, + { + "text": "You can imagine that if you keep taking partials, you may end up with more and more." + }, + { + "text": "We will have to figure out carefully what the condition should be." + }, + { + "text": "We will do that tomorrow." + }, + { + "text": "For now, let's just try to look at how do we understand these things by hand." + }, + { + "text": "In fact, let me point out to you immediately that there is more than maxima and minima." + }, + { + "text": "Remember, we saw the example of x squared plus y squared that has a critical point." + }, + { + "text": "The critical point is obviously a minimum." + }, + { + "text": "And, of course, it could be a local minimum because it could be that if you have a more complicated function there is indeed a minimum here." + }, + { + "text": "But then elsewhere the function drops to a lower value." + }, + { + "text": "We call that just a local minimum to say that it is a minimum if you stick to values that are close enough to that point." + }, + { + "text": "Of course, you also have a local maximum." + }, + { + "text": "Well, I did not plot it, but it is easy to plot." + }, + { + "text": "That is a local maximum." + }, + { + "text": "But there is a third example of critical point, and that is a saddle point." + }, + { + "text": "The saddle point is a new phenomenon that you do not really see in a single variable calculus." + }, + { + "text": "It is a critical point that is neither a minimum nor a maximum because, depending on which direction you look in, it is either one or the other." + }, + { + "text": "The point in the middle at the origin is a saddle point." + }, + { + "text": "If you look at the tangent plane to this graph you will see that it is actually horizontal at the origin." + }, + { + "text": "You have this mountain pass." + }, + { + "text": "At the mountain pass the ground is horizontal." + }, + { + "text": "But, depending on which direction you go, you go up or down." + }, + { + "text": "We say that the point is a saddle point if it is neither a minimum nor a maximum." + }, + { + "text": "OK, so the possibilities could be a local min, a local max, or a saddle." + }, + { + "text": "Tomorrow we will see how to decide which one it is in general using second derivatives." + }, + { + "text": "For this time let's just try to do it by hand." + }, + { + "text": "I just want to observe." + }, + { + "text": "In fact, I can try to, you know, these examples that I have here, they are x2 y2 y2-x2." + }, + { + "text": "They are sums or differences of squares." + }, + { + "text": "And, if we know that we can put things as a sum of squares, for example, we will be done." + }, + { + "text": "Let's try to express this maybe in terms of a square." + }, + { + "text": "Well, the main problem is this 2xy." + }, + { + "text": "But, observe, we know something that starts with x2 minus 2xy that is actually the square of something else." + }, + { + "text": "It would be x2 minus 2xy, well, plus y2, not plus 3y2." + }, + { + "text": "Let's try to do that." + }, + { + "text": "We are going to complete the square." + }, + { + "text": "I am going to say it is x minus y squared." + }, + { + "text": "That gives me the first two terms and also y squared." + }, + { + "text": "Well, I still need to add two more y squares." + }, + { + "text": "And I also need to add, of course, the 2x minus 2y." + }, + { + "text": "It is simpler." + }, + { + "text": "It is still not simple enough for my taste." + }, + { + "text": "I can actually do better." + }, + { + "text": "See, I mean now what is, so these guys look like a sum of squares." + }, + { + "text": "But here I have this extra stuff." + }, + { + "text": "But, 2x minus 2y, well, that is twice x minus y." + }, + { + "text": "It looks like maybe we can simplify this and make this into another square." + }, + { + "text": "In fact, I can simplify this further to x minus y plus one squared." + }, + { + "text": "See, that would start like, maybe I should put parentheses here, that would be x minus y squared plus twice x minus y." + }, + { + "text": "And then there is a plus one." + }, + { + "text": "Well, we don't have that plus one, so let's remove it by subtracting one." + }, + { + "text": "Oh, let me find that minus one here." + }, + { + "text": "And I still have my 2y squared." + }, + { + "text": "Do you see why this is the same function as that one?" + }, + { + "text": "Again, if I expand x minus y plus one squared, I get x minus y squared plus twice x minus y, that is those guys, plus one." + }, + { + "text": "But I will have a minus one and that will cancel out." + }, + { + "text": "And then I have a plus 2y squared." + }, + { + "text": "Now what I know, see, this is a sum of two squares minus one." + }, + { + "text": "And this critical point, x, y equals minus one, zero, that is exactly when this is zero and that is zero." + }, + { + "text": "That is the smallest value." + }, + { + "text": "This is always greater or equal to zero, same with that one." + }, + { + "text": "That is always at least minus one." + }, + { + "text": "And minus one happens to be the value at the critical point." + }, + { + "text": "It is a minimum." + }, + { + "text": "Now, of course, here I was very lucky." + }, + { + "text": "In general, I could not expect things to simplify that much." + }, + { + "text": "In fact, I cheated." + }, + { + "text": "I started from that." + }, + { + "text": "I expanded." + }, + { + "text": "And then that is how I got my example." + }, + { + "text": "The general method will be a bit different, but you will see it will actually also involve completing squares." + }, + { + "text": "Just there is more to it than what we have seen." + }, + { + "text": "We will come back to this tomorrow." + }, + { + "text": "How do I know that this equals?" + }, + { + "text": "y is what negative one?" + }, + { + "text": "How do I know that that whole function is greater or equal to negative one?" + }, + { + "text": "Well, I wrote f of x, y as something squared plus 2y2 minus one." + }, + { + "text": "This squared is always a positive number, non-negative." + }, + { + "text": "It is a square." + }, + { + "text": "The square of something is always non-negative." + }, + { + "text": "Similarly, y2 is also always non-negative." + }, + { + "text": "If you add something that is at least zero plus something that is at least zero and you subtract one, you get always at least minus one." + }, + { + "text": "And, in fact, the only way that you can get minus one is if both of these guys are zero at the same time." + }, + { + "text": "That is how I get my minimum." + }, + { + "text": "More about this tomorrow." + }, + { + "text": "In fact, what I would like to tell you about now instead is a nice application of min-max problems that maybe you don't think of as a min-max problem." + }, + { + "text": "But you will see, I mean, you don't think of it that way because probably your calculator can do it for you." + }, + { + "text": "Or, if not, your computer can do it for you." + }, + { + "text": "But it is actually something where the theory is based on minimization in two variables." + }, + { + "text": "Very often in experimental sequences you have to do something called least squares interpolation." + }, + { + "text": "And what is that about?" + }, + { + "text": "Well, it is the idea that maybe you do some experiments and you record some data." + }, + { + "text": "You have some data x and some data y." + }, + { + "text": "And I don't know, maybe, for example, maybe you are measuring frogs and you are trying to measure how big the frog leg is compared to the eyes of a frog or whatever, or trying to measure something." + }, + { + "text": "And if you are doing chemistry then it could be how much you put of some reactant and how much of the output product that you wanted to synthesize is going to be the same." + }, + { + "text": "All sorts of things." + }, + { + "text": "Make up your own example." + }, + { + "text": "You measure, basically, for various values of x what the value of y ends up being." + }, + { + "text": "And then you would like to claim, oh, well, these points are kind of aligned." + }, + { + "text": "I mean, of course, to a mathematician they are not aligned, but to an experimental scientist that is evidence that there is a relation between the two." + }, + { + "text": "And so you want to claim, and in your paper you will actually draw a nice little line that says, C, these two functions depend linearly on each other." + }, + { + "text": "The question is how do we come up with that nice line that passes smack in the middle of the points?" + }, + { + "text": "The question is, given experimental data, xiyi, so maybe I should actually be more precise." + }, + { + "text": "You are given some experimental data." + }, + { + "text": "You have data points x1, y1, x2, y2, and so on, xn, yn." + }, + { + "text": "The question would be find the best fit line of the form y equals ax plus b that somehow approximates very well this data." + }, + { + "text": "You can also use that, by the way, to predict various things." + }, + { + "text": "For example, if you look at your new homework, actually the first problem asks you to predict how many iPods will be on this planet in ten years, looking at past sales and how they behave." + }, + { + "text": "One thing, by the way, before you lose all the money you don't have yet, you cannot use that to predict the stock market." + }, + { + "text": "Don't try to use that to make money." + }, + { + "text": "It doesn't work." + }, + { + "text": "One tricky thing here that I want to draw your attention to is what are the unknowns here?" + }, + { + "text": "The natural answer would be to say the unknowns are x and y." + }, + { + "text": "That is not actually the case." + }, + { + "text": "We are not trying to solve for some x and y. I mean we have some values given to us." + }, + { + "text": "And when we are looking for that line we don't really care about a particular value of x." + }, + { + "text": "What we care about is actually these coefficients a and b that will tell us what the relation between x and y is." + }, + { + "text": "In fact, we are trying to solve for a and b that will give us the nicest possible line for these points." + }, + { + "text": "The unknowns in our equations will have to be a and b, not x and y." + }, + { + "text": "The question really is find the best a and b." + }, + { + "text": "And, of course, we have to decide what we mean by best." + }, + { + "text": "Best will mean that we minimize some function of a and b that measures the total error that we are making when we are choosing this line compared to the experimental data." + }, + { + "text": "Maybe, roughly speaking, it should measure how far these points are from the line." + }, + { + "text": "But now there are various ways to do it." + }, + { + "text": "And some of them are, I mean a lot of them are valid to give you different answers." + }, + { + "text": "You have to decide what it is that you prefer." + }, + { + "text": "For example, you could measure the distance to the line by projecting perpendicularly." + }, + { + "text": "Or, you could measure instead the difference between, for a given value of x, the difference between the experimental value of y and the predicted one." + }, + { + "text": "And that is often more relevant because these guys are actually maybe expressed in different units." + }, + { + "text": "They are not the same type of quantity." + }, + { + "text": "You cannot actually combine them arbitrarily." + }, + { + "text": "Anyway, the convention is usually we measure distance in this way." + }, + { + "text": "Next, you could try to minimize the largest distance." + }, + { + "text": "Say we look at where is the largest error and we make that the smallest possible." + }, + { + "text": "The drawback of doing that is experimentally very often you have one data point that is not good because maybe you fell asleep in front of the experiment." + }, + { + "text": "And so you did not measure the right thing." + }, + { + "text": "You tend to want to not give too much importance to some data point that is far away from the others." + }, + { + "text": "Maybe instead you want to measure the average distance." + }, + { + "text": "Or maybe you want to actually give more weight to things that are further away." + }, + { + "text": "And then you do not want to do the distance but the square of the distance." + }, + { + "text": "There are various possible answers." + }, + { + "text": "But one of them gives us a particularly nice formula for a and b." + }, + { + "text": "And so that is why it is the universally used one." + }, + { + "text": "Here it says least squares." + }, + { + "text": "That is because we will measure, actually, the sum of the squares of the errors." + }, + { + "text": "And why do we do that?" + }, + { + "text": "Well, part of it is because actually it looks good." + }, + { + "text": "I mean, when you see these plots in scientific papers, they really look like the line is indeed the ideal line." + }, + { + "text": "And the second reason is because actually the minimization problem that we will get is particularly simple, well-proposed and it is easy to solve." + }, + { + "text": "We will have a nice formula for the best a and the best b." + }, + { + "text": "If you have a method that is simple and gives you a good answer then that is probably the good one." + }, + { + "text": "We have to define best." + }, + { + "text": "And here it is in the sense of defining a total square error." + }, + { + "text": "Maybe I should say total square deviation." + }, + { + "text": "What do I mean by that?" + }, + { + "text": "The deviation for each data point is the difference between what you have measured and what you are predicting by your model." + }, + { + "text": "That is the difference between the two." + }, + { + "text": "Now what we will do is try to minimize the function capital D, which is just the sum for all the data points of the square of the deviation." + }, + { + "text": "Let me emphasize again this is a function of a and b. I mean, of course, there are a lot of letters in here." + }, + { + "text": "But xi and yi in real life will be numbers given to you." + }, + { + "text": "They will be the numbers that you have measured." + }, + { + "text": "You have measured all of this data." + }, + { + "text": "They are just going to be numbers." + }, + { + "text": "You put them in there and you get the answer." + }, + { + "text": "Any questions?" + }, + { + "text": "How do we minimize this function of a and b?" + }, + { + "text": "Let's use our new knowledge." + }, + { + "text": "Let's actually look for a critical point." + }, + { + "text": "We want to solve for partial d over partial a equals zero and partial d over partial b equals zero." + }, + { + "text": "That is how we look for critical points." + }, + { + "text": "Let's take the derivative of a." + }, + { + "text": "Well, the derivative of a sum is the sum of the derivatives." + }, + { + "text": "And now we have to take the derivative of this quantity squared." + }, + { + "text": "Remember how we take the derivative of a square." + }, + { + "text": "We take twice this quantity times the derivative of what we are squaring." + }, + { + "text": "We will get two times minus y i, sorry, y i minus a xi plus b times the derivative of this with respect to a." + }, + { + "text": "What is the derivative of this with respect to a?" + }, + { + "text": "Negative xi, exactly." + }, + { + "text": "And so we will want this to be zero." + }, + { + "text": "And partial d over partial b, we do the same thing but differentiating with respect to b instead of with respect to a." + }, + { + "text": "Again, sum of squares twice y i minus a xi plus b times the derivative of this with respect to b is, I think, negative one." + }, + { + "text": "That is the equations we have to solve." + }, + { + "text": "Well, let's reorganize this a little bit." + }, + { + "text": "The first equation, see, there are a's and there are b's in these equations." + }, + { + "text": "I am going to just look at the coefficients of a and b." + }, + { + "text": "If you have good eyes, you can see probably that these are actually linear equations in a and b." + }, + { + "text": "There is a lot of clutter with all these x's and y's all over the place." + }, + { + "text": "Let's actually try to expand things and make that more apparent." + }, + { + "text": "The first thing I will do is I will actually get rid of these factors of two that are just not very important." + }, + { + "text": "I can simplify things by two." + }, + { + "text": "And next I am going to look at the coefficient of a. I will get basically a times xi squared." + }, + { + "text": "Well, let me just do it and it should be clear." + }, + { + "text": "I claim when we simplify this we get a times xi squared plus xi times b minus xi yi." + }, + { + "text": "And we set this equal to zero." + }, + { + "text": "Do you agree that this is what we get when we expand that product?" + }, + { + "text": "No?" + }, + { + "text": "OK, let's do the other one." + }, + { + "text": "We just multiply by minus one." + }, + { + "text": "We take the opposite of that." + }, + { + "text": "It will be axi plus b. I will write that as xia plus b minus yi." + }, + { + "text": "And let me just reorganize that by actually putting all the a's together." + }, + { + "text": "That means actually I will have sum of all the xi squared times xi times b minus sum of xi yi equals zero." + }, + { + "text": "If I rewrite this it becomes sum of xi squared times a plus sum of the xi's times b minus, let me move the other guys to the other side, equals sum of xi yi." + }, + { + "text": "And that one becomes sum of xi times a plus how many b's do I get from this one?" + }, + { + "text": "Well, I get one for each data point." + }, + { + "text": "When I sum them together I will get n. Very good." + }, + { + "text": "So, n times b equals sum of yi." + }, + { + "text": "Now, these quantities may look scary, but they are actually just numbers." + }, + { + "text": "For example, for this one you look at all your data points." + }, + { + "text": "For each of them you take the value of x and you just sum all these numbers together." + }, + { + "text": "What you get, actually, is a linear system in a two-by-two linear system." + }, + { + "text": "And so now we can solve this for a and b." + }, + { + "text": "In practice, of course, first you plug in the numbers for xi and yi and then you solve the system that you get." + }, + { + "text": "And we know how to solve two-by-two linear systems, I hope." + }, + { + "text": "That is how we find the best fit line." + }, + { + "text": "Now, why is that going to be the best one instead of the worst one?" + }, + { + "text": "We just solved for a critical point." + }, + { + "text": "That could actually be a maximum of this error function d. We will have the answer to that next time." + }, + { + "text": "But trust me, if you really want to go for the second derivative test that we will do tomorrow and apply it in this case, it is quite hard to check." + }, + { + "text": "But you can see it is actually a minimum." + }, + { + "text": "I will just say we can show that it is a minimum." + }, + { + "text": "Now, even for the linear case, it is the one that we are the most familiar with." + }, + { + "text": "Least squares interpolation actually works in much more general settings." + }, + { + "text": "Instead of fitting for the best line, if you think that there is a different kind of relation, then maybe you can fit in using a different kind of formula." + }, + { + "text": "Let me actually illustrate that for you." + }, + { + "text": "I don't know if you are familiar with Moore's law." + }, + { + "text": "It is something that is supposed to tell you how quickly, basically, computer chips become smarter, faster and faster over time." + }, + { + "text": "It is a law that says things about the number of transistors that you can fit onto a computer chip." + }, + { + "text": "Here I have some data about the number of transistors on a standard PC processor as a function of time." + }, + { + "text": "And, well, if you try to do the best line fit, you will see quickly that it doesn't seem to follow a linear trend." + }, + { + "text": "On the other hand, if you plot the diagram in a log scale, the log of the number of transistors as a function of time, then you get a much better line." + }, + { + "text": "And so, in fact, that means that you had an exponential relation between the number of transistors and time." + }, + { + "text": "And so, actually, that is what Moore's law says." + }, + { + "text": "It says that the number of transistors on a chip doubles, depending on the version, every 18 months or every two years." + }, + { + "text": "They keep changing the statement." + }, + { + "text": "How do we find that best exponential fit?" + }, + { + "text": "Well, an exponential fit would be something of the form y equals a constant times exponential of a times x." + }, + { + "text": "That is what we want to look at." + }, + { + "text": "Well, we could try to minimize a square error like we did earlier, but that doesn't work well at all." + }, + { + "text": "The equations that you get are very complicated." + }, + { + "text": "You cannot solve them." + }, + { + "text": "But remember what I showed you on this log plot." + }, + { + "text": "If you plot the log of y as a function of x, then suddenly it becomes a linear relation." + }, + { + "text": "Observe this is the same as ln of x equals ln of c plus ax." + }, + { + "text": "And that is a linear best fit." + }, + { + "text": "What you do is you just look for the best straight line fit for the log of y." + }, + { + "text": "That is something we already know." + }, + { + "text": "But you can also do other examples." + }, + { + "text": "For example, let's say that we have something more complicated." + }, + { + "text": "Let's say that we have actually a quadratic law." + }, + { + "text": "For example, y is of the form ax2 bx c. And, of course, you are trying to find somehow the best." + }, + { + "text": "That would mean here fitting the best parabola for your data points." + }, + { + "text": "Well, to do that you would need to find a, b and c. And now you would have actually a function of a, b and c, which would be the sum of all data points of the quadratic equation." + }, + { + "text": "And if you try to solve for critical points, now you will have three equations involving a, b and c. And, in fact, you will find a three by three linear system." + }, + { + "text": "And it works just the same way." + }, + { + "text": "Just you have a little bit more data." + }, + { + "text": "Basically, you see that these best fit problems are an example of minimization problem." + }, + { + "text": "But maybe you didn't expect to see minimization problems come in." + }, + { + "text": "But that is really the way to handle these questions." + }, + { + "text": "OK, so tomorrow we will go back to the question of how do we decide whether it is a minimum or a maximum?" + }, + { + "text": "And we will continue exploring functions of several variables." + } +] \ No newline at end of file diff --git a/sight/sources/annotated/WfEQabCGAqI.json b/sight/sources/annotated/WfEQabCGAqI.json new file mode 100644 index 0000000000000000000000000000000000000000..9d2addc24a7ef383c827d76a9a204eb3b300618c --- /dev/null +++ b/sight/sources/annotated/WfEQabCGAqI.json @@ -0,0 +1,1226 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "Yesterday we have learned about flux and we have seen the first examples of how to set up and compute integrals for flux of a vector field for a surface." + }, + { + "text": "Remember the flux of a vector field F for a surface S is defined by taking the double integral on the surface of F dot n dS where n is the unit normal to the surface and dS is the area element on the surface." + }, + { + "text": "As we have seen, for various surfaces we have various formulas telling us what the normal vector is and what the area element becomes." + }, + { + "text": "For example, on spheres we typically integrate with respect to phi theta the latitude and longitude angles." + }, + { + "text": "On a horizontal plane we would just end up integrating dx dy and so on." + }, + { + "text": "At the end of the lecture we saw a formula." + }, + { + "text": "And a lot of you asked me how did we get it." + }, + { + "text": "Well, we didn't get it yet." + }, + { + "text": "We are going to try to explain where it comes from and why it works." + }, + { + "text": "The case we want to look at is the graph of a function." + }, + { + "text": "It is given by z equals some function in terms of x and y." + }, + { + "text": "Our surface is out here." + }, + { + "text": "z is a function of x and y." + }, + { + "text": "And x and y will range over some domain in the xy plane, namely the region that is the shadow of the surface on the xy plane." + }, + { + "text": "I said that we will have a formula for n ds which will end up being plus minus, minus f sub x minus f sub y one dx dy so that we will set up and evaluate the integral in terms of x and y." + }, + { + "text": "Replacing every time we see z we will replace it by f of xy, whatever the formula for f of xy is." + }, + { + "text": "By the way, if we look at a very easy case where this is just a horizontal plane, so z equals constant, the function is just a constant, well, the partial derivatives become just zero." + }, + { + "text": "You get zero, zero, one dx dy." + }, + { + "text": "That is what you would expect for a horizontal plane just from common sense." + }, + { + "text": "This is more interesting, of course, if a function is more interesting." + }, + { + "text": "How do we get that?" + }, + { + "text": "Where does this come from?" + }, + { + "text": "We need to figure out for a small piece of our surface what will be n delta S if you want." + }, + { + "text": "Let's say that we take a small rectangle in here corresponding to the sides delta x and delta y." + }, + { + "text": "And we look at the piece of surface that is above that." + }, + { + "text": "Well, the question we have now is what is the area of this little piece of surface and what is its normal vector?" + }, + { + "text": "Observe this little piece up here." + }, + { + "text": "If it is small enough it will look like a parallelogram." + }, + { + "text": "It might be slightly curvy, but roughly it looks like a parallelogram in space." + }, + { + "text": "And so we have seen how to find the area of a parallelogram in space using cross product." + }, + { + "text": "If we can figure out what are the vectors for this side and that side, then taking the cross product will give us, and taking the magnitude of the cross product will give us the area." + }, + { + "text": "Moreover, the cross product also gives us the normal direction." + }, + { + "text": "In fact, the cross product gives us two in one." + }, + { + "text": "It gives us the normal direction and the area element." + }, + { + "text": "And that is why I said that we will have an easy formula for N dS while N and dS taken separately are more complicated because you would have to actually take the length of a direction of this guy." + }, + { + "text": "Let's carry out this problem." + }, + { + "text": "Let's say I am going to look at a small piece of the xy plane." + }, + { + "text": "Here I have delta x, here I have delta y, and I am starting at some point xy." + }, + { + "text": "Now, above that I will have a parallelogram on my surface." + }, + { + "text": "I need to figure out this point here, the point where I start." + }, + { + "text": "I know what it is." + }, + { + "text": "It is just x, y, and z is f of x, y." + }, + { + "text": "Now, what I want to find actually is what are these two vectors, let's call them u and v that correspond to moving a bit in the x direction or in the y direction." + }, + { + "text": "And then u cross v will be, well, in terms of the magnitude of this guy will just be the little piece of surface area delta S. And, in terms of direction, it will be normal to the surface." + }, + { + "text": "Actually, I will get just delta S times my normal vector." + }, + { + "text": "Well, up to sign because depending on whether I do u cross v or v cross u, I might get the normal vector in the direction I want or in the direction I want." + }, + { + "text": "But we will take care of that later." + }, + { + "text": "Up to sign." + }, + { + "text": "OK, so let's find u and v. Actually, in case you have trouble with that small picture, then I have a better one here." + }, + { + "text": "Let's keep it just in case this one gets really too cluttered." + }, + { + "text": "It really represents the same thing." + }, + { + "text": "OK, so let's try to figure out these vectors u and v. So, the vector u starts at the point x, y, f of x, y." + }, + { + "text": "And it goes to, where is its head?" + }, + { + "text": "Well, I'll have moved x by delta x." + }, + { + "text": "So, x plus delta x. y doesn't change." + }, + { + "text": "And, of course, the z coordinate has to change." + }, + { + "text": "It becomes f of x plus delta x and y." + }, + { + "text": "Now, how does f change if I change x a little bit?" + }, + { + "text": "Well, we've seen that it's given by the partial derivative f sub x." + }, + { + "text": "So, this is approximately equal to f of x, y plus delta x times f sub x at the given point x, y. I'm not going to add it because notation is already long enough." + }, + { + "text": "So, that means my vector u is, well, approximately, because I'm using this linear approximation, delta x, zero, and f sub x times delta x. OK, is that OK with everyone?" + }, + { + "text": "Good." + }, + { + "text": "Now, what about v?" + }, + { + "text": "Well, v works the same way." + }, + { + "text": "OK, so I'm not going to do all the details." + }, + { + "text": "When I move from here to here, well, x doesn't change, and y changes by delta y." + }, + { + "text": "So, x component, nothing happens." + }, + { + "text": "y component changes by delta y." + }, + { + "text": "What about the z component?" + }, + { + "text": "Well, f changes by f sub y times delta y." + }, + { + "text": "That's how f changes if I increase y by delta y. OK, so I have my two sides." + }, + { + "text": "Now, I can take the cross product." + }, + { + "text": "Well, maybe I will first, sorry, factor something out." + }, + { + "text": "See, I can rewrite this as one zero f sub x times delta x." + }, + { + "text": "And, this one I will rewrite as zero one f sub y delta y." + }, + { + "text": "And so, now the cross product, so n hat delta s up to sine is going to be u cross v. u cross v, well, so we'll have to do the cross product, and we'll have a delta x delta y coming out." + }, + { + "text": "OK, I'm just saving myself the trouble of writing a lot of delta x and delta y's." + }, + { + "text": "But, if you prefer, you can just do directly this cross product there." + }, + { + "text": "OK, so let's compute this cross product." + }, + { + "text": "Well, the i component is zero minus f sub x." + }, + { + "text": "The y component is going to be, well, f sub y minus zero, but with a minus sign in front of everything, so negative f sub y." + }, + { + "text": "And, the z component will be just one times delta x delta y. OK, does that make sense for, yes, very good." + }, + { + "text": "And so, now, when we just take, we shrink this rectangle, we shrink delta x and delta y down, so that's how we get this formula for n ds equals negative fx negative fy one dx dy." + }, + { + "text": "Well, plus minus because it's up to us to choose whether we want to take the normal vector pointing up or down." + }, + { + "text": "So, see, if you take this convention, then the z component of n ds is positive." + }, + { + "text": "So, that corresponds to normal vector pointing up." + }, + { + "text": "If you take the opposite means, then the z component will be negative." + }, + { + "text": "That means your normal vector points down." + }, + { + "text": "OK, so this one is with n pointing up." + }, + { + "text": "I mean, when I say up, of course, it's still perpendicular to the surface." + }, + { + "text": "You know, if the surface really has a big slope, then it's not really going to go all that much up, but more up than down." + }, + { + "text": "OK, so that's how we get that formula." + }, + { + "text": "Any questions?" + }, + { + "text": "No?" + }, + { + "text": "OK, so that's a really useful formula." + }, + { + "text": "So, you don't really need to remember all the details of how we got it, but please remember that formula." + }, + { + "text": "Let's do an example, actually." + }, + { + "text": "So, let's say I want to find the flux of the vector field z times k. So, it's a vertical vector point of the paraboloid z equals x squared plus y squared that lives above the unit disk." + }, + { + "text": "OK, so what does that mean?" + }, + { + "text": "z equals x squared plus y squared, well, we've seen it many times." + }, + { + "text": "OK, it's this paraboloid above the unit disk means I only care about, I don't care about this infinite surface." + }, + { + "text": "I will actually stop when I hit a radius of one away from the z axis." + }, + { + "text": "And, so now I have my vector field, which is going to point overall up because, in fact, I'm at z times k. So, the more z is positive, the more your vector field goes up." + }, + { + "text": "Of course, if z were negative, then it would point down, but we live above." + }, + { + "text": "So, actually, a quick opinion poll." + }, + { + "text": "What do you think the flux should be?" + }, + { + "text": "Should it be positive, zero, negative?" + }, + { + "text": "We don't know." + }, + { + "text": "OK, so I see some I don't know." + }, + { + "text": "I see some negative, and I see some positive." + }, + { + "text": "So, of course, I didn't tell you which way I'm orienting my paraboloid." + }, + { + "text": "So, so far, both answers are correct." + }, + { + "text": "The only one that's probably not correct is zero because no matter which way you choose to orient it, you should get something." + }, + { + "text": "It's not looking like it will be zero." + }, + { + "text": "So, let's say that I'm going to do it with a normal pointing upwards." + }, + { + "text": "Second chance." + }, + { + "text": "OK, I see some people changing back and forth between one and two." + }, + { + "text": "OK, so let's draw a picture." + }, + { + "text": "Which one is pointing upwards?" + }, + { + "text": "Well, let's look at the bottom point, the normal vector pointing up." + }, + { + "text": "Here, we know what it means." + }, + { + "text": "It's this guy." + }, + { + "text": "And so, if you continue to follow your normal vector, see, they're actually pointing up and into the paraboloid." + }, + { + "text": "OK, and I claim that the answer should be positive because the vector field is crossing our paraboloid going upwards, going from the outside out and below to the inside and up side, so in the direction that we are counting positively." + }, + { + "text": "Well, we'll see how it turns out when we do the calculation." + }, + { + "text": "OK, so we have to compute the integral for flux." + }, + { + "text": "The one integral of a surface of F dot n dS is going to be, OK, so what are we going to do?" + }, + { + "text": "Well, F, we said, is 0, 0, z." + }, + { + "text": "What is n dS?" + }, + { + "text": "Well, let's use our brand new formula." + }, + { + "text": "So, it says negative F sub x, negative F sub y, one dx dy." + }, + { + "text": "What is little f in here?" + }, + { + "text": "It's x squared plus y squared, OK?" + }, + { + "text": "So, when we're using this formula, we need to know what little f stands for is whatever the formula is for z as a function of x and y." + }, + { + "text": "So, we take x squared plus y squared, and we take the partial derivatives with minus signs." + }, + { + "text": "We get negative 2x, negative 2y, and one dx dy." + }, + { + "text": "Well, of course, here it didn't really matter because we're going to dot them with zero." + }, + { + "text": "So, actually, even if we had made a mistake, we somehow wouldn't have had to pay the price, still." + }, + { + "text": "OK, so we'll end up with double integral on S of z dx dy." + }, + { + "text": "Now, what do we do with that?" + }, + { + "text": "Well, we have too many things." + }, + { + "text": "We need to get rid of z." + }, + { + "text": "So, let's use z equals x squared plus y squared once more." + }, + { + "text": "OK, so that becomes double integral of x squared plus y squared dx dy." + }, + { + "text": "And here, see, we're using the fact that we're only looking at things that are on the surface." + }, + { + "text": "It's not like in a triple integral, you could never do that because z, x, and y are independent." + }, + { + "text": "Here, they're related by the equation of a surface." + }, + { + "text": "Sorry if I sound like I'm ranting, but I know from experience this is where one of the most sticky and tricky points is, actually." + }, + { + "text": "OK, so now, how will we actually integrate that?" + }, + { + "text": "Well, now that we have just x and y, we should figure out what's the range for x and y?" + }, + { + "text": "Well, the range for x and y is going to be the shadow of our region." + }, + { + "text": "It's going to be this unit disk." + }, + { + "text": "OK, so let me just do that for now." + }, + { + "text": "And see here, this is finally where I've left the world of surface integrals to go back to a usual double integral." + }, + { + "text": "And now, I have to set it up." + }, + { + "text": "Well, I can do it this way with dx dy, but it looks like there's a smarter thing to do." + }, + { + "text": "OK, I'm going to use, actually, polar coordinates." + }, + { + "text": "So, in fact, I'm going to say this is a double integral of r squared times r dr d theta." + }, + { + "text": "I'm on the unit disk, so r goes zero to one, theta goes zero to two pi." + }, + { + "text": "And, if you do the calculation, you'll find that this is going to be pi over two." + }, + { + "text": "OK, any questions about the example?" + }, + { + "text": "Yes?" + }, + { + "text": "OK, how do I get this negative 2x and negative 2y?" + }, + { + "text": "So, I want to use my formula for n ds." + }, + { + "text": "OK, my surface is given by the graph of a function." + }, + { + "text": "It's the graph of a function x squared plus y squared." + }, + { + "text": "So, I will use this formula that's up here." + }, + { + "text": "I will take the function x squared plus y squared, and I will take its partial derivatives." + }, + { + "text": "So, if I take the partial of f, so, f x squared plus y squared with respect to x, I get 2x." + }, + { + "text": "So, I put negative 2x, and then same thing, negative 2y, one dx dy, yes?" + }, + { + "text": "Which k hat?" + }, + { + "text": "Oh, you mean the vector field?" + }, + { + "text": "Well, so it's a different part of the story, OK?" + }, + { + "text": "So, whenever you do a surface integral for flux, you have two parts of the story." + }, + { + "text": "One is the vector field whose flux you're taking." + }, + { + "text": "The other one is the surface for which you will be taking flux." + }, + { + "text": "So, the vector field only comes as this f in the notation." + }, + { + "text": "And, everything else, the bounds of the double integral and the n ds, they all come from the surface that we are looking at." + }, + { + "text": "OK, so basically, in all of this calculation, this is coming from f equals zk." + }, + { + "text": "Everything else comes from the information paraboloid z equals x squared plus y squared above the disk." + }, + { + "text": "OK, so in particular, if we wanted to now find the flux of any other vector field for the same paraboloid, well, all we have to do is just replace this guy by whatever the new vector field is." + }, + { + "text": "We've learned how to set up flux integrals for this paraboloid." + }, + { + "text": "Not that you should remember this one by heart." + }, + { + "text": "I mean, there's many paraboloids in life and other surfaces, too, so it's better to remember the general method." + }, + { + "text": "OK, any other questions?" + }, + { + "text": "No?" + }, + { + "text": "OK, let's see more ways of tackling flux integrals." + }, + { + "text": "But, just to reassure you, at this point, we've seen the most important ones." + }, + { + "text": "You know, 90% of the problems that we'll be looking at, we can do with what we've seen so far last time and this time." + }, + { + "text": "But, let's look a little bit at a more general situation." + }, + { + "text": "Let's say that my surface is so complicated that I can't actually express z as a function of x and y." + }, + { + "text": "But, let's say that actually I know how to parametrize it." + }, + { + "text": "So, I have a parametric equation for my surface." + }, + { + "text": "That means I can express x, y, z in terms of any two parameter variables that might be relevant for me." + }, + { + "text": "So, if you want, this one here is the special case where you can parametrize things in terms of x and y as your two variables." + }, + { + "text": "So, how would you do it in the fully general case?" + }, + { + "text": "In a way, that will answer your question." + }, + { + "text": "I think one of you, I forgot, asked yesterday, how would I do it in general?" + }, + { + "text": "Is there a formula like m dx plus n dy?" + }, + { + "text": "Well, that's going to be the formula." + }, + { + "text": "And, you'll see it's a little bit too complicated." + }, + { + "text": "So, the really useful ones are actually the special ones." + }, + { + "text": "So, let's say that we are given a parametric description of a surface S. So, that means we can describe S by formulas saying x is some function of two parameter variables." + }, + { + "text": "I'm going to call them u and v. I hope you don't mind." + }, + { + "text": "You can call them t1 and t2." + }, + { + "text": "You can call them whatever you want." + }, + { + "text": "OK, so one of the basic properties of a surface is because I have only two independent directions to move on, I should be able to express x, y, and z in terms of two variables." + }, + { + "text": "So, now let's say that I know how to do that." + }, + { + "text": "Or, maybe I should instead think of it in terms of a position vector if that helps you." + }, + { + "text": "The position vector, so that's just the vector with components x, y, z is given as a function of u and v. OK, so it works like a parametric curve, but with two parameters." + }, + { + "text": "So, now, how will we actually set up a flux integral on such a surface?" + }, + { + "text": "Well, because we are locating the flux in terms of u and v, we will end up with an integral du dv." + }, + { + "text": "So, we need to figure out how to express n ds in terms of du and dv." + }, + { + "text": "OK, so n ds should be something du dv." + }, + { + "text": "How do we do that?" + }, + { + "text": "Well, we can use the same method that we've actually used over here." + }, + { + "text": "Because if you think for a second, here we used, of course, a rectangle in the x, y plane, and we lifted it to a parallelogram and so on." + }, + { + "text": "But, more generally, you can think, what happens if I change u by delta u, keeping v constant, or the other way around?" + }, + { + "text": "You will get some sort of mesh grid on your surface, and you will look at a little parallelogram that's an elementary piece of that mesh and figure out what is its area and normal vector." + }, + { + "text": "Well, that will again be given by the cross product of the two sides." + }, + { + "text": "OK, so let's think a little bit about what happens when I move a little bit on my surface." + }, + { + "text": "So, I'm taking a grid on my surface given by the u and v directions." + }, + { + "text": "And, if I take a piece of that corresponding to small changes, delta u and delta v, what's going to be going on here?" + }, + { + "text": "Well, I have to deal with two vectors, one corresponding to changing u, the other one corresponding to changing v. If I change u, how does my point change?" + }, + { + "text": "Well, that's given by the derivative of this with respect to u. OK, so this vector here I will call, so the sides are given by, let me say, partial r over partial u times delta u." + }, + { + "text": "And, if you prefer, maybe I should write it as partial x over partial u delta u partial y." + }, + { + "text": "Well, it's just too boring to write, and so on." + }, + { + "text": "OK, it means just, you know, if I change u a little bit, keep v constant, then how x changes is given by partial x over partial u times delta u." + }, + { + "text": "Same thing with y, same thing with z." + }, + { + "text": "And, I'm just using vector notation to do it this way." + }, + { + "text": "That's the analog of when I said delta r for line integrals along a curve, vector delta r is the velocity vector dr over dt times delta t. OK, now if I look at the other side, OK, so, sorry, so let me start again." + }, + { + "text": "I ran out of space." + }, + { + "text": "One side is partial r partial u times delta u, and the other one would be partial r partial v times delta v because that's how the position of your point changes if you just change u or v and not the other one." + }, + { + "text": "So, now, to find the surface element together with a normal vector, I would just take the cross product between these guys." + }, + { + "text": "So, if you prefer, that's the cross product of partial r partial u with partial r partial v delta u delta v. And so, N dS is this cross product times du dv up to sine." + }, + { + "text": "I mean, also here." + }, + { + "text": "Depends on which choice I make for my normal vector, of course." + }, + { + "text": "OK, now, if you, that, of course, is a slightly confusing equation to think of." + }, + { + "text": "So, a good exercise, if you want to really understand what's going on, try this in two good examples to look at." + }, + { + "text": "One good example to look at is the previous one." + }, + { + "text": "What is it?" + }, + { + "text": "It's when u and v are just x and y. OK, so the parametric equations are just x equals x, y equals y, and z is f of x, y." + }, + { + "text": "You should end up with the same formula that we had over there." + }, + { + "text": "And, you should see why because, see, both of them are given by a cross product." + }, + { + "text": "The other case you can look at, just to convince yourselves that it's true, so we don't need to do that because we've seen the formula before." + }, + { + "text": "But, in the case of a sphere, we've seen the formula for N and for dS separately." + }, + { + "text": "So, we know what N dS are in terms of d phi d theta." + }, + { + "text": "Well, you could parametrize a sphere in terms of phi and theta." + }, + { + "text": "Namely, the formulas would be x equals a sine phi cosine theta, y equals a sine phi sine theta, z equals a cosine phi." + }, + { + "text": "The formulas for spherical coordinates setting rho equals a." + }, + { + "text": "So, that's a parametric equation for the sphere." + }, + { + "text": "And then, if you try to use this formula here, you should end up with the same things we've already seen for N dS, just with a lot more pain to actually get there because your cross product is going to be a bit complicated." + }, + { + "text": "But, we're seeing all of these formulas, they all fit together." + }, + { + "text": "Somehow, it's always the same question, just we have different angles of attack on this general problem." + }, + { + "text": "OK, questions?" + }, + { + "text": "No?" + }, + { + "text": "OK, let's look at yet another last way of finding N dS." + }, + { + "text": "And then, I promise we'll switch to something else because I can feel that you're getting a bit overwhelmed by all these formulas for N dS." + }, + { + "text": "So, OK, so what happens very often is we don't actually know how to parametrize our surface." + }, + { + "text": "Maybe we don't know how to solve for z as a function of x and y, but our surface is given by some equation." + }, + { + "text": "And so, what that means is actually maybe what we know is not really these kinds of formulas, but maybe we know a normal vector." + }, + { + "text": "And, I'm going to call this one capital N because I don't even need it to be a unit vector, you will see." + }, + { + "text": "It can be a normal vector of the surface S. So, why would we ever know a normal vector?" + }, + { + "text": "Well, for example, if our surface is a plane, say it's a slanted plane given by some equation, Ax plus By plus Cz equals D. Well, you know the normal vector." + }, + { + "text": "It's A, B, C. Of course, you could solve for z and then go back to that case, which is why I said that that one is really useful." + }, + { + "text": "But, you can also just stay with a normal vector." + }, + { + "text": "Why else would you know a normal vector?" + }, + { + "text": "Well, let's say that you know an equation that's of a form g of x, y, z equals zero." + }, + { + "text": "Well, then you know that the gradient of g is perpendicular to the level surface." + }, + { + "text": "OK, so let me just give you two examples." + }, + { + "text": "If you have a plane, Ax plus By plus Cz equals D, then the normal vector would just be A, B, C. If you have a surface S given by an equation, g of x, y, z equals zero, then you can take the normal vector to be the gradient of g. We've seen that the gradient is perpendicular to the level surface." + }, + { + "text": "Now, of course, we don't necessarily have to follow what's going to come because if we could solve for z then we might be better off doing what we did over there." + }, + { + "text": "But, let's say that we want to do it this way." + }, + { + "text": "So, then what can we do?" + }, + { + "text": "Well, I'm going to give you a little bit of information about NDS." + }, + { + "text": "So, OK, so let's start by thinking about a slanted plane." + }, + { + "text": "OK, so let's say that my surface is just a slanted plane." + }, + { + "text": "So, my normal vector would be maybe somewhere here." + }, + { + "text": "And, let's say that I'm going to try, you know, I need, of course, some handle on how to set up my integral." + }, + { + "text": "So, maybe I'm going to express this in terms of x and y. OK, so I have my coordinates, and I'll try to use x and y." + }, + { + "text": "So, then I would like to relate delta s, ds, to the area in the xy plane." + }, + { + "text": "So, that means, you know, I want maybe to look at the projection of this guy onto a horizontal plane." + }, + { + "text": "Let's squish it horizontally." + }, + { + "text": "So, then you have here another area." + }, + { + "text": "OK, so the guy on the slanted plane, let's call that delta s, and let's call this guy down here delta a." + }, + { + "text": "So, the question, and, you know, delta a would become ultimately maybe delta x, delta y, or something like that." + }, + { + "text": "The question is, how do we find the conversion rate between these two areas?" + }, + { + "text": "See, I mean, they're not the same." + }, + { + "text": "Visually, I hope it's clear to you that if my plane is actually horizontal, then, of course, they're the same." + }, + { + "text": "But, the more slanted it becomes, the more delta a becomes smaller than delta s, right?" + }, + { + "text": "I mean, if you buy, you know, if you buy land, and it's on the side of a cliff, well, whether you look at it on a map, or whether you look at it on the actual cliff, the area is going to be very different." + }, + { + "text": "I'm not sure if that's a wise thing to do if you want to build a house there, but I've been told you can get really cheap land." + }, + { + "text": "OK, so anyway, OK, so delta s versus delta a depends on how slanted things are." + }, + { + "text": "And, let's try to make that more precise by looking at the angle that our plane makes with the horizontal direction." + }, + { + "text": "OK, so let's call this angle alpha, the angle that our plane makes with the horizontal direction." + }, + { + "text": "See, it's all coming together now." + }, + { + "text": "The first unit about cross products, normal vectors, and so on is actually useful now." + }, + { + "text": "So, I claim that the surface element is related to the area in the plane by delta a equals delta s times the cosine of alpha." + }, + { + "text": "Why is that?" + }, + { + "text": "Well, let's look at this small rectangle with one horizontal side and one slanted side." + }, + { + "text": "Well, when you project, this side doesn't change." + }, + { + "text": "But, this side gets shortened by a factor of cosine alpha." + }, + { + "text": "Whatever this length was, this length here is that one times cosine alpha." + }, + { + "text": "So, that's why the area gets shrunk by cosine alpha." + }, + { + "text": "In one direction, nothing happens." + }, + { + "text": "In the other direction, you squish by cosine alpha." + }, + { + "text": "So, what that means is that, well, OK, so we'll have to deal with this." + }, + { + "text": "And, of course, the one we'll care about actually is delta s expressed in terms of delta a." + }, + { + "text": "But, what are we going to do with this cosine?" + }, + { + "text": "It's not very convenient to have a cosine left in here." + }, + { + "text": "So, remember, the angle between two planes, it's the same thing as the angle between the normal vectors." + }, + { + "text": "So, if you want to see this angle alpha elsewhere, what you can do is you can just take the vertical direction." + }, + { + "text": "Let's take k. Then, here we have our angle alpha again." + }, + { + "text": "So, in particular, cosine of alpha, I can get, well, we know how to find the angle between two vectors." + }, + { + "text": "So, if we have our normal vector n, we'll do n dot k, and we'll divide by length n length k. Well, length k is one." + }, + { + "text": "That's one easy." + }, + { + "text": "OK, so that's how we find the angle." + }, + { + "text": "So, now I'm going to say, well, delta s is going to be one over cosine alpha delta a." + }, + { + "text": "And, I can rewrite that as length of n divided by n dot k times delta a." + }, + { + "text": "Now, let's multiply that by the unit normal vector because what I'm multiplying by is not dS, but actually n dS." + }, + { + "text": "So, n delta s will be, I'm just going to multiply by n. Well, let's think for a second." + }, + { + "text": "What happens if I take the unit normal n, and I multiply it by the length of my other normal big N?" + }, + { + "text": "Well, I get big N again, right?" + }, + { + "text": "This is a normal vector of the same length as n, well, up to sine." + }, + { + "text": "But, actually, maybe I should." + }, + { + "text": "The only thing I don't know is whether this guy will be going in the same direction as big N or in the opposite direction." + }, + { + "text": "Say that, for example, my capital N has length, I don't know, length three, for example." + }, + { + "text": "The unit normal vector might be this guy, in which case, indeed, three times little n will be big N. Or, it might be this one, in which case, three times little n will be negative big N. But, up to sine, it's N. And then, I will have N over n dot k delta a." + }, + { + "text": "And so, the final formula, the one that actually we care about in case you don't really like my explanations of how we get there, is that N dS is plus or minus N over N dot k dx dy." + }, + { + "text": "That one is actually kind of useful, so let's box it." + }, + { + "text": "Now, just in case you are wondering, of course, if you didn't want to project to x, y, you would have maybe preferred to project to, say, the plane of a blackboard, yz." + }, + { + "text": "Well, you can do the same thing." + }, + { + "text": "To express N dS in terms of dy dz, you do the same argument." + }, + { + "text": "And simply, the only thing that changes is instead of using the vertical vector k, you use the normal vector i." + }, + { + "text": "So, you would be doing N over N dot i dy dz, and same thing." + }, + { + "text": "Just keep an open mind that this also works with other variables." + }, + { + "text": "But anyway, so that's how you can basically project the vector surface area element onto the x, y plane in a way." + }, + { + "text": "OK, so let's look at the special case just to see how this fits with stuff we've seen before." + }, + { + "text": "Let's do a special example where our surface is given by the equation z minus f of x, y equals zero." + }, + { + "text": "OK, that's a strange way to write the equation z equals f of x, y that we saw before." + }, + { + "text": "But now, it looks like, well, some function of x, y, z equals zero." + }, + { + "text": "So, let's try to use this new method." + }, + { + "text": "So, let's call this guy g of x, y, z." + }, + { + "text": "Well, so now let's look at the normal vector." + }, + { + "text": "The normal vector would be the gradient of g, we said." + }, + { + "text": "What's the gradient of this function?" + }, + { + "text": "So, gradient of g, well, partial g, partial x, that's just negative partial f, partial x. Gradient g, sorry, the y component, partial g, partial y is going to be negative f sub y." + }, + { + "text": "And, g sub z is just one." + }, + { + "text": "So now, if you take n over n dot k dx dy, well, it looks like that's going to be negative f sub x, negative f sub y, one divided by, well, what's n dot k?" + }, + { + "text": "If you do that with k, you'll get just one." + }, + { + "text": "So, I'm not going to write it, dx dy." + }, + { + "text": "See, that's, again, our favorite formula." + }, + { + "text": "So, this one is actually more general because you don't need to solve for z." + }, + { + "text": "But, if you can solve for z, then it's the same as before." + }, + { + "text": "OK, I think that's enough formulas for n dS." + }, + { + "text": "So, after spending a lot of time telling you how to compute surface integrals, now I'm going to try to tell you how to avoid computing them." + }, + { + "text": "And, that is called the divergence theorem." + }, + { + "text": "And, we'll see the proof and everything and applications on Tuesday, but I want to at least state the theorem and see how it works in one example." + }, + { + "text": "It's also known as the Gauss grain theorem, or just the Gauss theorem depending on who you talk to." + }, + { + "text": "So, the grain here is the same grain as in Green's theorem, OK, because somehow that's a space version of Green's theorem." + }, + { + "text": "So, what does it say?" + }, + { + "text": "It says, so, this is the analog of grain for flux." + }, + { + "text": "What it says is if S is a closed surface, OK, so remember, it's the same as with Green's theorem, we need to have something that's completely enclosed." + }, + { + "text": "So, you have a surface, and there's somehow no gaps in it." + }, + { + "text": "There's no boundary to it." + }, + { + "text": "It's really completely enclosed." + }, + { + "text": "So, I'm choosing a region in space that I will call D. And, I need to choose my orientation." + }, + { + "text": "So, the orientation that will be chosen in this theorem is choosing the normal vector to point outwards." + }, + { + "text": "OK, so, n needs to be outwards." + }, + { + "text": "So, that's one part of the puzzle." + }, + { + "text": "The other part is a vector field." + }, + { + "text": "I need to have a vector field that is defined and differentiable everywhere in D. So, same restrictions as usual." + }, + { + "text": "Then, I don't have, actually, to compute the flux integral." + }, + { + "text": "The integral of F dot n dS of a closed surface S. I need to put a circle just to remind you it's got to be a closed surface." + }, + { + "text": "That's just notation to remind us, closed surface." + }, + { + "text": "I can replace that by the triple integral of the region inside of divergence of F dV." + }, + { + "text": "Now, I need to tell you what's the divergence of a 3D vector field." + }, + { + "text": "Well, you'll see it's not much of a difference." + }, + { + "text": "In the 2D case, what you do is just, so, say that your vector field has components P, Q, and R. Then, you will take P sub x plus Q sub y plus R sub z. OK, so that's the definition." + }, + { + "text": "It's pretty easy to remember." + }, + { + "text": "You take the x component partial respect to x plus partial respect to y of the y component plus partial respect to z of the z component." + }, + { + "text": "OK, so, for example, last time we saw that the flux of the vector field zk for a sphere of radius a was four-thirds pi a cubed by computing the surface integral." + }, + { + "text": "Well, if we do it more efficiently now by Green's theorem, so we're going to use Green's theorem for this sphere." + }, + { + "text": "Because we're doing the whole sphere, it's fine." + }, + { + "text": "It's a closed surface." + }, + { + "text": "We couldn't do it for, say, a hemisphere or something like that." + }, + { + "text": "We need to, well, I mean, for the hemisphere, we'd need to add maybe the flat face at the bottom or something like that." + }, + { + "text": "So, Green's theorem says that our flux integral can be actually replaced by the triple integral of a solid ball of radius a of the divergence of zk dv." + }, + { + "text": "But now, what's the divergence of this field?" + }, + { + "text": "Well, so you have zero, zero, z." + }, + { + "text": "So, you get zero plus zero plus one." + }, + { + "text": "It looks like it will be one." + }, + { + "text": "So, if you do the triple integral of one dv, you will get just the volume of the region inside, which is four-thirds pi a cubed." + }, + { + "text": "And, so it was no accident." + }, + { + "text": "In fact, before that, we looked at also xi yj zk, and we found three times the volume." + }, + { + "text": "That's because the divergence of that field was actually three." + }, + { + "text": "So, very quickly, let me just say what this means physically." + }, + { + "text": "Physically, see, this guy on the left is the total amount of stuff that goes out of the region per unit time." + }, + { + "text": "So, I want to figure out how much stuff comes out of there." + }, + { + "text": "What does the divergence mean?" + }, + { + "text": "The divergence means, well, it measures how much the flow is expanding things." + }, + { + "text": "It measures how much, I say probably when we understood 2D divergence, it measures the amount of sources or sinks that you have inside your fluid." + }, + { + "text": "So, now it becomes common sense." + }, + { + "text": "If you take a region of space, the total amount of water that flows out of it is the total amount of sources that you have in there minus the sinks." + }, + { + "text": "In spite of this common sense explanation, we are going to see actually how to prove this, and we'll see how it works and the hypothesis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated/X-ix97pw0xY.json b/sight/sources/annotated/X-ix97pw0xY.json new file mode 100644 index 0000000000000000000000000000000000000000..cd2cc842a0c4fb63bef4905b9ce27fab52a9642d --- /dev/null +++ b/sight/sources/annotated/X-ix97pw0xY.json @@ -0,0 +1,2651 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "Chapter is a natural capstone chapter for this entire course." + }, + { + "text": "We'll see some of the things we've seen during maximum likelihood and some of the things we've seen during linear regression, some of the things we've seen in terms of the basic modeling that we've had before." + }, + { + "text": "We're not going to go back to much inference questions." + }, + { + "text": "It's really going to be about modeling." + }, + { + "text": "And in a way, generalized linear models, as the word says, are just a generalization of linear models." + }, + { + "text": "And they're actually extremely useful." + }, + { + "text": "They're often forgotten about, and people just jump onto machine learning and sophisticated techniques." + }, + { + "text": "But those things do the job quite well." + }, + { + "text": "So let's see in what sense they are a generalization of the linear model." + }, + { + "text": "So remember, the linear model looked like this." + }, + { + "text": "We said that y was equal to x transpose beta plus epsilon." + }, + { + "text": "That was our linear regression model." + }, + { + "text": "And another way to say this is that if I, let's assume that those were, say, Gaussian with mean 0 and identity covariance matrix, then another way to say this is that the conditional distribution of y given x is a Gaussian with mean x transpose beta and variance, well, we had a sigma square, which I will forget as usual, x transpose beta and then sigma square." + }, + { + "text": "So here, we just assumed that, so what is regression?" + }, + { + "text": "It's just saying I'm trying to explain y as a function of x given x. I'm assuming a distribution for the y." + }, + { + "text": "And this x is just going to be here to help me model what the mean of this Gaussian is." + }, + { + "text": "I mean, I could have something crazy." + }, + { + "text": "I could have something that looks like y given x is n0 x transpose beta." + }, + { + "text": "And then this guy could be some other thing, which looks like, I don't know, some x transpose gamma squared times, I don't know, x x transpose plus identity, some crazy thing that depends on x here." + }, + { + "text": "And we deliberately assume that all the thing that depends on x shows up in the mean." + }, + { + "text": "And so what I have here is that y given x is a Gaussian with a mean that depends on x and covariance matrix sigma square identity." + }, + { + "text": "Now, the linear model assumed a very specific form for the mean." + }, + { + "text": "It said, I want the mean to be equal to x transpose beta, which, remember, was the sum from, say, j equals 1 to p of beta j xj, where the xj's are the coordinates of x." + }, + { + "text": "But I could do something also more complicated." + }, + { + "text": "I could have something that looks like, instead, replace this by, I don't know, sum of beta j log of x to the j divided by x to the j squared, or something like this." + }, + { + "text": "I could do this as well." + }, + { + "text": "So there's two things that we've assumed." + }, + { + "text": "The first one is that when I look at the conditional distribution of y given x, x affects only the mean." + }, + { + "text": "I also assumed that it was Gaussian, and that it affects only the mean." + }, + { + "text": "And the mean is affected in a very specific way, which is linear in x." + }, + { + "text": "So this is essentially the things we're going to try to relax." + }, + { + "text": "So the first thing that we assume, the fact that y was Gaussian and had only its mean that depended on x, is what's called the random component." + }, + { + "text": "It just says that the response variables sort of make sense to assume that they're Gaussian." + }, + { + "text": "And everything was essentially captured." + }, + { + "text": "So there's this property of Gaussians that if you tell me if the variance is known, all you need to tell me to understand exactly what the distribution of a Gaussian is, all you need to tell me is its expected value." + }, + { + "text": "So that's this mu of x." + }, + { + "text": "And the second thing is that we had this link that says, well, I need to find a way to use my x's to explain this mu." + }, + { + "text": "And the link was exactly mu of x was equal to x transpose beta." + }, + { + "text": "OK?" + }, + { + "text": "Now, we are talking about generalized linear models." + }, + { + "text": "So this part here, where mu of x is of the form, the way I want my beta, my x, to show up is linear." + }, + { + "text": "This will never be questioned." + }, + { + "text": "In principle, I could add a third point, which is just question this part, the fact that mu of x is x transpose beta." + }, + { + "text": "I could have some more complicated nonlinear function of x." + }, + { + "text": "And I will never do that, because we're talking about generalized linear model." + }, + { + "text": "The only thing with generalized are the random component, the conditional distribution of y given x, and the link that just says, well, once you actually tell me that the only thing I need to figure out is the mean, I'm just going to slap it exactly this x transpose beta thing without any transformation of x transpose beta." + }, + { + "text": "OK?" + }, + { + "text": "So those are the two things." + }, + { + "text": "It will become clearer what I mean." + }, + { + "text": "This sounds like a tautology, but let's just see how we could extend that." + }, + { + "text": "So what we're going to do in generalized linear models, so when I talk about GLMs, the first thing I'm going to do with my x is turn it into some x transpose beta." + }, + { + "text": "And that's just the L part." + }, + { + "text": "This I'm not going to be able to change." + }, + { + "text": "That's the way it works." + }, + { + "text": "I'm not going to do anything nonlinear." + }, + { + "text": "But the two things I'm going to change is this random component, which is that y, which used to be some Gaussian with mean mu of x variance sigma squared." + }, + { + "text": "So y given x, sorry." + }, + { + "text": "This is going to become y given x follows some distribution." + }, + { + "text": "And I'm not going to allow any distribution." + }, + { + "text": "I want something that comes from the exponential family." + }, + { + "text": "Who knows what the exponential family of distribution is?" + }, + { + "text": "This is not the same thing as the exponential distribution." + }, + { + "text": "It's a family of distribution." + }, + { + "text": "All right, so we'll see that." + }, + { + "text": "What can that be?" + }, + { + "text": "Oh, yeah, that's actually my." + }, + { + "text": "I'm sorry?" + }, + { + "text": "You can mute your laptop." + }, + { + "text": "OK." + }, + { + "text": "I'm in presentation mode." + }, + { + "text": "That should not happen." + }, + { + "text": "OK, so hopefully this is muted." + }, + { + "text": "So essentially, this is going to be a family of distributions." + }, + { + "text": "And what makes them exponential typically is that there's an exponential that shows up in the definition of the density." + }, + { + "text": "We'll see that the Gaussian belongs to the exponential family." + }, + { + "text": "But there are slightly less expected ones, because there's this crazy thing that a to the x is exponential x log a, which makes the exponential show up without being there." + }, + { + "text": "So if there's an exponential of some power, it's going to show up." + }, + { + "text": "But it's more than that." + }, + { + "text": "So we'll actually come to this particular family of distribution." + }, + { + "text": "Why this particular family?" + }, + { + "text": "Because in a way, everything we've done for the linear model with Gaussian is going to extend fairly naturally to this family." + }, + { + "text": "And it actually also, because it encompasses pretty much everything, all the distributions we've discussed before." + }, + { + "text": "All right, so the second thing that I want to question, so before we just said, well, mu of x was directly equal to this thing." + }, + { + "text": "Mu of x was directly x transpose beta." + }, + { + "text": "So I knew I was going to have an x transpose beta." + }, + { + "text": "And I said, well, I could do something with this x transpose beta before I used it to explain the expected value." + }, + { + "text": "But I'm actually taking it like that." + }, + { + "text": "Here we're going to say, let's extend this to some function is equal to this thing." + }, + { + "text": "Now, admittedly, this is not the most natural way to think about it." + }, + { + "text": "What you would probably feel more comfortable doing is write something like mu of x is a function." + }, + { + "text": "Let's call it f of x transpose beta." + }, + { + "text": "But here I just decide to call f g inverse." + }, + { + "text": "OK, that's just my g inverse, yes." + }, + { + "text": "Is this different than just transforming the x's?" + }, + { + "text": "Yeah." + }, + { + "text": "I mean, what transformation do you want to put on your x's?" + }, + { + "text": "Like, is this equivalent to just applying some function to each individual x component and then multiplying that beta to get the mean?" + }, + { + "text": "Oh, no, certainly not, right?" + }, + { + "text": "I mean, if I force you to work with x1 plus x2, you cannot work with any function of x1 plus any function of x2, right?" + }, + { + "text": "So yeah, this is different." + }, + { + "text": "So yeah, the transformation would be just the simple part of your linear regression problem, where you would take your x's, transform them, and then just apply another linear regression." + }, + { + "text": "This is genuinely new." + }, + { + "text": "Any other question?" + }, + { + "text": "All right, so this function g, and the reason why I sort of have to stick to this slightly less natural way of defining it is because that's g that gets a name, not g inverse that gets a name." + }, + { + "text": "And the name of g is the link function." + }, + { + "text": "So if I want to give you a generalized linear model, I need to give you two ingredients." + }, + { + "text": "The first one is the random component, which is the distribution of y given x." + }, + { + "text": "And it can be anything in what's called the exponential family of distributions." + }, + { + "text": "So for example, I could say y given x is Gaussian with mean ux sigma squared identity." + }, + { + "text": "But I could also tell you y given x is gamma with shape parameter equal to alpha of x. I could do some weird things like this." + }, + { + "text": "And the second thing is I need to give you a link function." + }, + { + "text": "And the link function is going to become very clear how you pick a link function." + }, + { + "text": "And the only reason that you actually pick a link function is because of compatibility." + }, + { + "text": "This mu of x, I call it mu because mu of x is always the conditional expectation of y given x, always, which means that let's think of y as being a Bernoulli random variable." + }, + { + "text": "Where does mu of x live?" + }, + { + "text": "AUDIENCE 2." + }, + { + "text": "0, 1." + }, + { + "text": "0, 1, right?" + }, + { + "text": "That's the expectation of a Bernoulli." + }, + { + "text": "It's just the probability that my coin flip gives me 1." + }, + { + "text": "So it's a number between 0 and 1." + }, + { + "text": "But this guy right here, if my x's are anything, think of any body measurements, plus I take linear combinations with arbitrarily large coefficients, this thing can be any real number." + }, + { + "text": "So the link function, what it's effectively going to do is make those two things compatible." + }, + { + "text": "It's going to take my number, which, for example, is constrained to be between 0 and 1, and map it into the entire real line." + }, + { + "text": "If I have mu, which is forced to be positive, for example, in an exponential distribution, the mean is positive, right?" + }, + { + "text": "That's the, say, I don't know, inter-arrival time for Poisson process." + }, + { + "text": "This thing is known to be positive for an exponential." + }, + { + "text": "I need to map something that's exponential to the entire real line." + }, + { + "text": "I need a function that takes something positive and then tickets everyone." + }, + { + "text": "So we'll see, by the end of this chapter, you will have 100 ways of doing this." + }, + { + "text": "But there are some more traditional ones than other." + }, + { + "text": "So before we go any further, I gave you this example of a Bernoulli random variable." + }, + { + "text": "Let's see a few examples that actually fit there." + }, + { + "text": "Yes?" + }, + { + "text": "AUDIENCE 1 Will it come up later if we already know why the mean distribution is increasing entirely?" + }, + { + "text": "Why can't we do it?" + }, + { + "text": "PHILIPPE RIGOLLET Well, actually, this will not come up later." + }, + { + "text": "It should be very clear from here." + }, + { + "text": "Because if I actually have a model, I just want it to be plausible, right?" + }, + { + "text": "I mean, what happens if I suddenly decide that my, so this is what's going to happen." + }, + { + "text": "You're going to have only data to fit this model." + }, + { + "text": "Let's say you actually forget about this thing here." + }, + { + "text": "You can always do this, right?" + }, + { + "text": "You can always say, I'm going to pretend my y's just happen to be the realizations of, say, Gaussians that happen to be 0 or 1 only." + }, + { + "text": "You can always stuff that in some linear model, right?" + }, + { + "text": "You will have some least squares estimator for beta." + }, + { + "text": "But what's going to happen, and it's going to be fine." + }, + { + "text": "For all the points that you see, it will definitely put some number that's actually between 0 and 1." + }, + { + "text": "So this is what your picture is going to look like." + }, + { + "text": "You're going to have a bunch of values for x." + }, + { + "text": "This is your y." + }, + { + "text": "And so these are the values of x that you will get." + }, + { + "text": "And for y, you will see either 0 or 1, right?" + }, + { + "text": "That's what your Bernoulli data set would look like with a one-dimensional x." + }, + { + "text": "Now, if you do least squares on this, you will find this." + }, + { + "text": "And for this guy, this line certainly takes values between 0 and 1." + }, + { + "text": "But let's say now you get an x here." + }, + { + "text": "You're going to actually start pretending the probability that it spits out one conditionally in x is like 1.2, and that's going to be weird." + }, + { + "text": "OK?" + }, + { + "text": "Any other questions?" + }, + { + "text": "All right, so let's start with some examples." + }, + { + "text": "Right?" + }, + { + "text": "I mean, you got so used to them throughout this course." + }, + { + "text": "So the first one is all these things are taken." + }, + { + "text": "So there's a few books on generalizing your models, generalize additive models, and there's tons of applications that you can see." + }, + { + "text": "Those are extremely versatile." + }, + { + "text": "And as soon as you want to do modeling to explain some y given x, you sort of need to do that if you want to go beyond linear models." + }, + { + "text": "So this was the disease occurring rate." + }, + { + "text": "So you have a disease epidemic, and you want to basically model the expected number of new cases given at a certain time." + }, + { + "text": "OK?" + }, + { + "text": "So you have time that progresses for each of your reservation." + }, + { + "text": "Each of your relation is a timestamp, say, I don't know, 20th day." + }, + { + "text": "And your response is the number of new cases." + }, + { + "text": "And you're going to actually put your model directly on mu, right?" + }, + { + "text": "When I looked at this, everything here was on mu itself, on the expected, right?" + }, + { + "text": "Mu of x is always the expected, the conditional expectation of y given x." + }, + { + "text": "Right?" + }, + { + "text": "So all I need to model is this expected value." + }, + { + "text": "So this mu, I'm going to actually say, so I look at some parameters, and it says, well, it increases exponentially." + }, + { + "text": "So I want to have some sort of exponential trend." + }, + { + "text": "I can parameterize that in several ways." + }, + { + "text": "And the two parameters I want to slap in is some sort of gamma, which is just the coefficient." + }, + { + "text": "And then there's some rate delta that's in the exponential." + }, + { + "text": "OK?" + }, + { + "text": "So if I tell you it's exponential, that's a nice family of functions you might want to think about." + }, + { + "text": "OK, so here, mu of x, if I want to keep the notation x, is gamma exponential delta x, right?" + }, + { + "text": "Except that here, my x are t1, t2, t3, et cetera." + }, + { + "text": "OK?" + }, + { + "text": "And I want to find what the parameters gamma and delta are because I want to be able to maybe compare different epidemics and see if they have the same parameter or maybe just do some prediction based on the data that I have to extrapolate in the future." + }, + { + "text": "OK?" + }, + { + "text": "So here, clearly, mu of x is not of the form x transpose beta." + }, + { + "text": "Right?" + }, + { + "text": "That's not x transpose beta at all." + }, + { + "text": "And it's actually not even a function of x transpose beta." + }, + { + "text": "Right?" + }, + { + "text": "There's two parameters, gamma and delta, and it's not of the form." + }, + { + "text": "So here, I have x, which is 1 and x." + }, + { + "text": "Right?" + }, + { + "text": "I have two parameters." + }, + { + "text": "So what I do here is that I say, well, first, let me transform mu in such a way that I can hope to see something that's linear." + }, + { + "text": "So if I transform mu, I'm going to have log of mu, which is log of this thing." + }, + { + "text": "Right?" + }, + { + "text": "So log of mu of x is equal to log of gamma plus log of exponential delta x, which is delta x. OK?" + }, + { + "text": "And now, this thing is actually linear in x." + }, + { + "text": "So I have that this guy is my first beta 1." + }, + { + "text": "And so that's beta 1 times 1." + }, + { + "text": "And this guy is beta 2 times, sorry, let's say beta 0 times 1." + }, + { + "text": "And this guy is beta 1 times x. OK?" + }, + { + "text": "So that looks like a linear model." + }, + { + "text": "I just have to change my parameters." + }, + { + "text": "My parameters, beta 1 becomes the log of gamma, and beta 2 becomes delta itself." + }, + { + "text": "And the reason why we do this is because, well, the way we put those gamma and those delta was just so that we have some parametrization." + }, + { + "text": "It just so happens that if we want this to be linear, we need to just change the parametrization itself." + }, + { + "text": "This is going to have some effects." + }, + { + "text": "We know that it's going to have some effect in the Fisher information." + }, + { + "text": "It's going to have a bunch of effect to change those things." + }, + { + "text": "But that's what needs to be done to have a generalized linear model." + }, + { + "text": "Now, here, the function that I took to turn it into something that's linear is simple." + }, + { + "text": "It came directly from some natural thing it would do here, which is taking the log." + }, + { + "text": "And so the function g, the link that I take, is called the log link, very creatively." + }, + { + "text": "And it's just the function that I apply to mu so that I see something that's linear and that looks like this." + }, + { + "text": "OK?" + }, + { + "text": "So now, this only tells me how to deal with the link function." + }, + { + "text": "But I still have to deal with 0.1." + }, + { + "text": "And this, again, is just some modeling." + }, + { + "text": "Given some data, some random data, what distribution do you choose to explain the randomness?" + }, + { + "text": "And this, I mean, unless there's no choice, it's just a matter of practice." + }, + { + "text": "I mean, why would it be Gaussian and not doubly exponential?" + }, + { + "text": "There's matters of convenience that come into this." + }, + { + "text": "And there's just matter of experience that come into this." + }, + { + "text": "I remember when you chat with engineers, they have a very good notion of what the distribution should be." + }, + { + "text": "They have Weibull distributions." + }, + { + "text": "They do optics and things like this." + }, + { + "text": "So there's some distributions that just come up." + }, + { + "text": "But sometimes, you just have to work." + }, + { + "text": "Now, here, what do we have?" + }, + { + "text": "The thing we're trying to measure y, as we said, so mu is the conditional expectation of y given x." + }, + { + "text": "But y is the number of new cases, right?" + }, + { + "text": "Well, it's a number of." + }, + { + "text": "And the first thing you should think of when you think about number of, if it were bounded above, you would think binomial, baby." + }, + { + "text": "But here, it's just a number." + }, + { + "text": "So you think Poisson." + }, + { + "text": "That's how insurers think." + }, + { + "text": "I have a number of claims per year." + }, + { + "text": "This is a Poisson distribution." + }, + { + "text": "And hopefully, they can model the conditional distribution of the number of claims given everything that they actually ask you in this survey that I hear you now fill in 15 minutes." + }, + { + "text": "All right, so now you have this Poisson distribution." + }, + { + "text": "And that's just a modeling assumption." + }, + { + "text": "There's no particular reason why you should do this, except that that might be a good idea." + }, + { + "text": "And the expected value of your Poisson has to be this mu i at time i." + }, + { + "text": "Any question about this slide?" + }, + { + "text": "So let's switch to another example." + }, + { + "text": "Another example is the so-called prey capture rate." + }, + { + "text": "So here, what you're interested in is the rate capture of prey's Yi for a given prey." + }, + { + "text": "And you have Xi, which is your explanation." + }, + { + "text": "And this is just the density of prey." + }, + { + "text": "So you're trying to explain the rate of captures of preys given the density of the prey." + }, + { + "text": "And so you need to find some sort of relationship between the two." + }, + { + "text": "And here again, you talk to experts." + }, + { + "text": "And what they tell you is that, well, it's going to be increasing." + }, + { + "text": "Animals, like predators, are going to just eat more if there's more preys." + }, + { + "text": "But at some point, they're just going to level off because they're just going to be completely full." + }, + { + "text": "And they're going to stop capturing those preys." + }, + { + "text": "And you're just going to have some phenomenon that looks like this." + }, + { + "text": "So here is a curve that sort of makes sense." + }, + { + "text": "As your capture rate goes from 0 to 1, you're increasing." + }, + { + "text": "And then you see you have this concave function that says that at some point, it levels off." + }, + { + "text": "So here, one way I could, I mean, there's again many ways I could just model a function that looks like this." + }, + { + "text": "But a simple one that has only two parameters is this one, where mu i is just this function of Xi, where I have some parameter alpha here and some parameter h here." + }, + { + "text": "So there's clearly, so this function, there's one that essentially tells you." + }, + { + "text": "So this thing starts at 0 for sure." + }, + { + "text": "And essentially, alpha tells you how sharp this thing is." + }, + { + "text": "And h tells you at which point you end here." + }, + { + "text": "It's not exactly what those values are equal to, but it tells you this." + }, + { + "text": "So simple." + }, + { + "text": "And well, no, OK, sorry." + }, + { + "text": "That's actually alpha, which is the maximum capture rate." + }, + { + "text": "And h represents the prey density at which the capture rate is." + }, + { + "text": "So that's the half time." + }, + { + "text": "So there's actual values for this." + }, + { + "text": "So now I have this function." + }, + { + "text": "It's certainly not a function." + }, + { + "text": "I don't see it as a function of x." + }, + { + "text": "So I need to find something that looks like a function of x. OK?" + }, + { + "text": "So now here, there's no log." + }, + { + "text": "There's no, well, I could actually take a log here." + }, + { + "text": "But I would have log of x and log of x plus h. So that would be weird." + }, + { + "text": "So what we propose to do here is to look, rather than looking at mu i, we look at 1 over mu i." + }, + { + "text": "And so since your function was mu i, when you take 1 over mu i, you get h plus xi divided by alpha xi, which is h over alpha times 1 over xi plus 1 over alpha." + }, + { + "text": "And now if I am willing to make this transformation of variables and say, actually, my x, whether it's the density of prey or the inverse density of prey, it really doesn't matter." + }, + { + "text": "I can always make the transformation when the data comes." + }, + { + "text": "Then I'm actually just going to think of this as being some linear function, beta 0 plus beta 1, which is this guy, times 1 over xi." + }, + { + "text": "And now my new variable becomes 1 over xi." + }, + { + "text": "And now it's linear." + }, + { + "text": "And the transformation I had to take was this 1 over x, which is called the reciprocal link." + }, + { + "text": "You can probably guess what the exponential link is going to be and things like this." + }, + { + "text": "So we'll talk about other links that have slightly less obvious names." + }, + { + "text": "Now, again, modeling." + }, + { + "text": "So this was the random component." + }, + { + "text": "This was the easy part." + }, + { + "text": "Now I need to just pour in some domain knowledge about how do I think this function, this y, which is the rate of capture of preys." + }, + { + "text": "I want to understand how this thing is actually changing." + }, + { + "text": "What is the randomness of the thing around its mean?" + }, + { + "text": "And something that comes from this textbook, the standard deviation of capture rate might be approximately proportional to the mean rate." + }, + { + "text": "You need to find a distribution that actually has this property." + }, + { + "text": "And it turns out that this happens for gamma distribution." + }, + { + "text": "In gamma distributions, just like, say, for Poisson distribution, for Poisson, the variance and the mean are of the same order." + }, + { + "text": "Here is the standard deviation that's of the same order as the mean for gammas." + }, + { + "text": "And it's a positive distribution as well." + }, + { + "text": "So here is a candidate." + }, + { + "text": "Now, since we're sort of constrained to work under the exponential family of distributions, then you can just go through your list and just decide which one works best for you." + }, + { + "text": "All right, third example." + }, + { + "text": "So here we have binary response." + }, + { + "text": "Here, essentially, the binary response variable indicates the presence or absence of post-covariative deforming for kyphosis on children." + }, + { + "text": "And here, rather than having one covariate, which was before, in the first example, was time, in the second example was the density, here there's three covariates." + }, + { + "text": "So you measure on children." + }, + { + "text": "The first one is age of the child." + }, + { + "text": "The second one is the number of vertebrae involved in the operation." + }, + { + "text": "And the third one is the start of the range, so where it is on the spine." + }, + { + "text": "So the response variable here is, did it work or not?" + }, + { + "text": "I mean, that's very simple." + }, + { + "text": "And so here, it's nice, because the random component is the easiest one." + }, + { + "text": "As I said, any random variable that takes only two outcomes must be a Bernoulli." + }, + { + "text": "So that's nice." + }, + { + "text": "There's no modeling going on here." + }, + { + "text": "So you know that y given x is going to be Bernoulli, but of course, all your efforts are going to try to understand what the conditional mean of your Bernoulli, what the conditional probability of being 1 is going to be." + }, + { + "text": "And so in particular, so I'm just here." + }, + { + "text": "I'm spelling it out before we close those examples." + }, + { + "text": "I cannot say that mu of x is x transpose beta for exactly this picture that I drew for you here." + }, + { + "text": "There's just no way here." + }, + { + "text": "The goal of doing this is certainly to be able to extrapolate for yet unseen children whether this is something that we should be doing, and maybe the range of x's is actually going to be slightly out." + }, + { + "text": "And so OK, I don't want to say that I have a negative probability of outcome or a positive one, sorry, or a 1 that's lower than 1, so I need to make this transformation." + }, + { + "text": "What I need to do is to transform mu, which is we know only a number, all we know is a number between 0 and 1, and we need to transform it in such a way that it maps the entire real line, or reciprocally to say that, or inversely I should say, that f of x transpose beta should be a number between 0 and 1." + }, + { + "text": "I need to find a function that takes any real number and maps it into 0 and 1, and we'll see that again, but you have an army of functions that do that for you." + }, + { + "text": "What are those functions?" + }, + { + "text": "I'm sorry?" + }, + { + "text": "AUDIENCE MEMBER 2." + }, + { + "text": "Trait function." + }, + { + "text": "PHILIPPE RIGOLLET." + }, + { + "text": "Trait?" + }, + { + "text": "AUDIENCE MEMBER 2." + }, + { + "text": "Trait, trait, trait." + }, + { + "text": "PHILIPPE RIGOLLET." + }, + { + "text": "Oh." + }, + { + "text": "Yeah, I want them to be invertible, right?" + }, + { + "text": "AUDIENCE MEMBER 2." + }, + { + "text": "Yeah." + }, + { + "text": "PHILIPPE RIGOLLET." + }, + { + "text": "Yeah." + }, + { + "text": "AUDIENCE MEMBER 2." + }, + { + "text": "Longest trait." + }, + { + "text": "PHILIPPE RIGOLLET." + }, + { + "text": "I have an army of function." + }, + { + "text": "I'm not asking for one soldier in this army." + }, + { + "text": "I want the name of this army." + }, + { + "text": "AUDIENCE MEMBER 2." + }, + { + "text": "They're invertible." + }, + { + "text": "PHILIPPE RIGOLLET." + }, + { + "text": "Well, they're not really invertible either, right?" + }, + { + "text": "So they're actually in stats textbooks, because remember, statisticians don't know how to integrate functions, but they know how to turn a function into a Gaussian integral, so we know it integrates to 1, and things like this." + }, + { + "text": "Same thing here." + }, + { + "text": "We don't know how to build functions that are invertible and map the entire real line to 0, 1, but there's all the cumulative distribution functions that do that for us." + }, + { + "text": "So I can use any of those guys, and that's what I'm going to be doing, actually." + }, + { + "text": "All right, so just to recap what I just said as we were speaking, so a normal linear model is not appropriate for those examples if only because the response variable is not necessarily Gaussian." + }, + { + "text": "So and also because the linear model has to be, the mean has to be transformed before I can actually apply a linear model for all these plausible nonlinear models that I actually came up with." + }, + { + "text": "So the family we're going to go for is the exponential family of distributions, and we're going to be able to show, so one of the nice part of this is to actually compute maximum likelihood estimators for those, right?" + }, + { + "text": "In the linear model, maximum like, in the Gaussian linear model, maximum likelihood was as nice as it gets, right?" + }, + { + "text": "This actually was the least squares estimator." + }, + { + "text": "We had a closed form, x transpose x inverse x transpose y, and that was it." + }, + { + "text": "We had to just take one derivative." + }, + { + "text": "Here, we're going to have a generally concave likelihood." + }, + { + "text": "We're not going to be able to actually solve this thing directly in closed form unless it's Gaussian, but we will have, we'll see actually how this is not just a black box optimization of a concave function." + }, + { + "text": "We have a lot of properties of this concave function, and we will be able to show some iterative algorithms." + }, + { + "text": "We'll basically see how, when you open the box of convex optimization, you will actually be able to see how things work and actually implement it using least squares." + }, + { + "text": "So each iteration of this iterative algorithm will essentially be a least square, so that's actually quite huge." + }, + { + "text": "It's also very demonstrative of statisticians being pretty ingenious so that they don't have to call in some statistical software, but just can repeatedly call their least squares oracle within a statistical software." + }, + { + "text": "OK, so what is the exponential family?" + }, + { + "text": "I promised you the exponential family." + }, + { + "text": "Before we go into this, let me just tell you something about exponential families, and what's the only thing that differentiates an exponential family from all possible distributions?" + }, + { + "text": "An exponential family has two parameters, and those are not really parameters, but there's the theta parameter of my distribution." + }, + { + "text": "So it's going to be indexed by some parameter." + }, + { + "text": "Here, I'm only talking about the distribution of, say, some random variable or some random vector." + }, + { + "text": "So here, in this slide, you see that the parameter theta that indexes those distribution is k-dimensional, and the space of the x's that I'm looking at, so that should really be y." + }, + { + "text": "So what I'm going to plug in here is the conditional distribution of y given x, and theta is going to depend on x." + }, + { + "text": "But this really is the y." + }, + { + "text": "That's the distribution of the response variable." + }, + { + "text": "And so this is on q." + }, + { + "text": "So I'm going to assume that y is q-dimensional." + }, + { + "text": "Clearly, soon q is going to be equal to 1, but I can define those things generally." + }, + { + "text": "So I have this." + }, + { + "text": "I have to tell you what this looks like, and let's assume that this is a probability density function." + }, + { + "text": "So this notation, the fact that I just put my theta in subscript, is just for me to remember that this is the variable that indicates the random variable, and this is just the parameter." + }, + { + "text": "But I could just write it as a function of theta and x." + }, + { + "text": "This is just going to be, if you were in multivariable calc, you would have two parameters, theta and x, and you would need to give me a function." + }, + { + "text": "Now, think of x and theta as being one-dimensional at this point." + }, + { + "text": "Think of all the functions that can be depending on theta and x." + }, + { + "text": "There's many of them." + }, + { + "text": "And in particular, there's many ways theta and x can interact." + }, + { + "text": "What the exponential family does for you is that it restricts the way these things can actually interact with each other." + }, + { + "text": "It's essentially saying the following." + }, + { + "text": "It's saying this is going to be of the form exponential." + }, + { + "text": "So this exponential is really not much, because I could put a log next to it." + }, + { + "text": "But what I want is that the way theta and x interact has to be of the form theta times x in an exponential." + }, + { + "text": "So that's one of the ways you can think of them interacting." + }, + { + "text": "You just take the product of the two." + }, + { + "text": "Now, clearly, this is not a very rich family." + }, + { + "text": "So what I'm allowing myself is to just slap on some terms that depend only on theta and depend only on x." + }, + { + "text": "So let's just call this thing f of x g of theta." + }, + { + "text": "So here, I've restricted the way theta and x can interact." + }, + { + "text": "So I have something that depends only on x, something that depends only on theta." + }, + { + "text": "And here, I have this very specific interaction." + }, + { + "text": "And that's all that exponential families are doing for you." + }, + { + "text": "So if we go back to this slide, this is much more general." + }, + { + "text": "If I want to go from theta and x in r to theta and x theta in r to theta in rk and x in rq, I cannot take the product of theta and x. I cannot even take the inner product between theta and x, because they're not even of compatible dimensions." + }, + { + "text": "But what I can do is to first map my theta into something and map my x into something so that I actually end up having the same dimensions." + }, + { + "text": "And then I can take the inner product." + }, + { + "text": "That's the natural generalization of this simple product." + }, + { + "text": "So what I have is if I want to go from theta to x, what I'm going to first do is I'm going to take theta eta of theta." + }, + { + "text": "So let's say eta 1 of theta to eta k of theta." + }, + { + "text": "And then I'm going to actually take x becomes t1 of x all the way to tk of x." + }, + { + "text": "And what I'm going to do is take the inner product." + }, + { + "text": "So let's call this eta." + }, + { + "text": "And let's call this t. And I'm going to take the inner product of eta and t, which is just the sum from j equal 1 to k of eta j of theta times tj of x." + }, + { + "text": "So that's just a way to say I want this simple interaction." + }, + { + "text": "But in higher dimension, the simplest way I can actually make those things happen is just by taking inner product." + }, + { + "text": "And so now what it's telling me is that the distribution, I want the exponential times something that depends only on theta and something that depends only on x." + }, + { + "text": "And so what it tells me is that when I'm going to take p of theta x, it's just going to be something which is exponential times the sum from j equal 1 to k of eta j theta tj of x." + }, + { + "text": "And then I'm going to have a function that depends only." + }, + { + "text": "So let me write it for now like c of theta." + }, + { + "text": "And then a function that depends only on x." + }, + { + "text": "Let me call it h of x." + }, + { + "text": "And for convenience, there's no particular reason why I do that." + }, + { + "text": "I'm taking this function c of theta, and I'm just actually pushing it in there." + }, + { + "text": "So I can write c of theta as exponential minus log of 1 over c of theta." + }, + { + "text": "And now I have exponential times exponential." + }, + { + "text": "So I push it in, and this thing actually looks like exponential sum from j equal 1 to k of eta j theta tj of x minus log 1 over c of theta times h of x." + }, + { + "text": "And this thing here, log 1 over c of theta, I call actually b of theta." + }, + { + "text": "Because c, I called it c, but I can actually directly call it this guy b, and I don't actually care about c itself." + }, + { + "text": "Now, why don't I put back also h of x in there?" + }, + { + "text": "Because h of x is really here to just, how to put it?" + }, + { + "text": "h of x and b of theta don't play the same role." + }, + { + "text": "b of theta, in many ways, is a normalizing constant." + }, + { + "text": "I want this density to integrate to 1." + }, + { + "text": "If I did not have this guy, I'm not guaranteed that this thing integrates to 1." + }, + { + "text": "But by tweaking this function, b of theta or c of theta, their equivalent, I can actually ensure that this thing integrates to 1." + }, + { + "text": "So b of theta is just a normalizing constant." + }, + { + "text": "h of x is something that's going to be funny for us." + }, + { + "text": "It's going to be something that allows us to be able to treat both discrete and continuous variables within the framework of exponential families." + }, + { + "text": "So for those that are familiar with this, this is essentially saying that h of x is really just a change of measure." + }, + { + "text": "When I actually look at the density of p of theta, this is with respect to some measure, the fact that I just multiply by a function of x just means that I'm not looking that this guy here, without h of theta, is not the density with respect to the original measure, but it's the density with respect to the distribution that has h as a density." + }, + { + "text": "That's all I'm saying." + }, + { + "text": "So I can first transform my x's and then take the density with respect to that." + }, + { + "text": "If you don't want to think about densities or measures, you don't have to." + }, + { + "text": "This is just the way." + }, + { + "text": "This is just the definition." + }, + { + "text": "Is there any question about this definition?" + }, + { + "text": "So it looks complicated, but it's actually essentially the simplest way you could think about it." + }, + { + "text": "You want to be able to have x and theta interact, and you just say, I want the interaction to be of the form exponential x times theta." + }, + { + "text": "And if they're higher dimensions, I'm going to take the exponential of the function of x inner product for the function of theta." + }, + { + "text": "So I claimed since the beginning that the Gaussian was such an example, so let's just do it." + }, + { + "text": "Is the interaction between theta and x in a Gaussian of the form inner product?" + }, + { + "text": "And the answer is yes." + }, + { + "text": "Actually, whether I know or not what the variance is." + }, + { + "text": "So let's start for the case where I actually do not know what the variance is." + }, + { + "text": "So here I have x is n mu sigma squared." + }, + { + "text": "This is all one dimensional." + }, + { + "text": "And here I'm going to assume that my parameter is both mu and sigma squared." + }, + { + "text": "So what I need to do is to have some function of mu, some function of sigma squared, and take the inner product of some function of x and some other function of x." + }, + { + "text": "So I want to show that p theta of x is what?" + }, + { + "text": "Well, it's 1 over square root sigma 2 pi exponential minus x minus mu squared over 2 sigma squared." + }, + { + "text": "That's just my Gaussian density." + }, + { + "text": "And I want to say that this thing here, so clearly the exponential shows up already." + }, + { + "text": "I want to show that this is something that looks like eta 1 of mu sigma squared." + }, + { + "text": "So I have only two of those guys, so I'm going to need only two etas." + }, + { + "text": "So I want it to be eta 1 of mu and sigma times t1 of x plus eta 2 mu sigma squared times t2 of x." + }, + { + "text": "So I want to have something like that that shows up, and the only things that are left, I want them to depend either only on theta or only on x." + }, + { + "text": "So to find that out, we just need to expand." + }, + { + "text": "So I'm going to first put everything into my exponential and expand this guy." + }, + { + "text": "So the first term here is going to be minus x squared over 2 sigma squared." + }, + { + "text": "The second term is going to be minus mu squared over 2 sigma squared." + }, + { + "text": "And then the cross term is going to be plus x mu divided by sigma squared." + }, + { + "text": "And then I'm going to put this guy here, so I have a minus log sigma root 2 pi." + }, + { + "text": "OK, so this term here contains an interaction between x and the parameters." + }, + { + "text": "This term here contains an interaction between x and the parameters." + }, + { + "text": "So let me try to write them in a way that I want." + }, + { + "text": "This guy only depends on the parameters." + }, + { + "text": "This guy only depends on the parameter." + }, + { + "text": "So I'm going to rearrange things." + }, + { + "text": "And so I claim that this is of the form x squared." + }, + { + "text": "Well, let's say, who's getting the minus?" + }, + { + "text": "Eta, OK." + }, + { + "text": "So it's x squared times minus 1 over 2 sigma squared plus x times mu over sigma squared." + }, + { + "text": "So that's this term here." + }, + { + "text": "That's this term here." + }, + { + "text": "Now I need to get this guy here." + }, + { + "text": "And that's minus." + }, + { + "text": "So I'm going to write it like this, minus." + }, + { + "text": "And now I have mu squared over 2 sigma squared plus log sigma square root 2 pi." + }, + { + "text": "OK?" + }, + { + "text": "And now this thing is definitely of the form t1 of x times, did I call them the right way or not?" + }, + { + "text": "Of course not." + }, + { + "text": "OK, so that's going to be t2 of x times eta 2 of x, eta 2 of theta." + }, + { + "text": "This guy is going to be t1 of x times eta 1 of theta." + }, + { + "text": "So just a function of theta times a function of x, just a function of theta times a function of x." + }, + { + "text": "And the way I combine this is just by summing them." + }, + { + "text": "And this is going to be my b of theta." + }, + { + "text": "What is h of x?" + }, + { + "text": "1." + }, + { + "text": "There's one thing I can actually play with." + }, + { + "text": "And this is something you're going to have some free choices." + }, + { + "text": "This is not actually completely determined here." + }, + { + "text": "Is that, for example, when I write the log sigma square root 2 pi, this is just log of sigma plus log square root 2 pi." + }, + { + "text": "So I have two choices here." + }, + { + "text": "Either my b becomes this guy, or so either I have b of theta, which is mu squared over 2 sigma squared plus log sigma square root 2 pi, and h of x is equal to 1." + }, + { + "text": "Or I have that b of theta is mu squared over 2 sigma squared plus log sigma, and h of x is equal to what?" + }, + { + "text": "1." + }, + { + "text": "Well, I can just push this guy out." + }, + { + "text": "I can push it out of the exponential." + }, + { + "text": "And so it's just square root of 2 pi, which is a function of x, technically." + }, + { + "text": "I mean, it's a constant function of x, but it's a function of x." + }, + { + "text": "So you can see that it's not completely clear how you're going to do the trade-off." + }, + { + "text": "So the constant terms can go either in b or in h. But why bother with tracking down b and h when you can actually stuff everything into one and just call h 1 and call it a day?" + }, + { + "text": "So you can just forget about h. It's 1, and think about the rest." + }, + { + "text": "h won't matter, actually, for estimation purposes or anything like this." + }, + { + "text": "All right, so that's basically everything that's written." + }, + { + "text": "When sigma square is known, what's happening is that this guy here is no longer a function of theta, right?" + }, + { + "text": "Agreed?" + }, + { + "text": "This is no longer a parameter." + }, + { + "text": "When sigma square is known, then theta is equal to mu only." + }, + { + "text": "There's no sigma square going on." + }, + { + "text": "So everything that depends on sigma square can be thought as a constant, think 1." + }, + { + "text": "So in particular, this term here does not belong in the interaction between x and theta." + }, + { + "text": "It belongs to h, right?" + }, + { + "text": "So if sigma is known, then this guy is only a function of h of x." + }, + { + "text": "So h of x becomes exponential x squared minus x squared over 2 sigma squared, right?" + }, + { + "text": "That's just a function of x." + }, + { + "text": "Is that clear?" + }, + { + "text": "So if you complete this computation, what you're going to get is that your new one parameter thing is that p theta p theta x is not equal to exponential x times mu over sigma squared minus, well, it's still the same thing, and then you have your h of x that comes out, x squared over 2 sigma squared." + }, + { + "text": "So that's my h of x." + }, + { + "text": "That's still my b of theta." + }, + { + "text": "And this is my t1 of x, and this is my eta 1 of theta." + }, + { + "text": "And remember, theta is just equal to mu in this case." + }, + { + "text": "So if I ask you, prove that this distribution belonged to an exponential family, you just have to work it out." + }, + { + "text": "Typically, it's expanding what's in the exponential and just write it in this term and identify all the components, right?" + }, + { + "text": "So here, notice those guys don't even get an index anymore because there's just one of them." + }, + { + "text": "So I wrote theta 1 and t1, but it's really just eta and t. Oh, sorry." + }, + { + "text": "This guy also goes." + }, + { + "text": "This is also a constant, right?" + }, + { + "text": "So it can actually just put sigma divided by sigma squared over 2 pi." + }, + { + "text": "So h of x is what, actually?" + }, + { + "text": "AUDIENCE MEMBER 2." + }, + { + "text": "It's the density of?" + }, + { + "text": "AUDIENCE MEMBER 3." + }, + { + "text": "It's centered." + }, + { + "text": "It's not standard." + }, + { + "text": "It's centered." + }, + { + "text": "It has mean 0, but it has variance sigma squared, right?" + }, + { + "text": "But it's the density of a Gaussian." + }, + { + "text": "And this is what I meant when I said h of x is really just telling you with respect to which distribution, which measure you're taking the density." + }, + { + "text": "And so this thing here is really telling you the density of my Gaussian with mean mu is equal to this with respect to a centered Gaussian is this guy, right?" + }, + { + "text": "That's what it means." + }, + { + "text": "If this thing ends up being a density, it just means that now you just have a new measure, which is this density." + }, + { + "text": "So it's just saying that the density of the Gaussian with mean mu with respect to the Gaussian with mean 0 is just this thing here." + }, + { + "text": "All right, so let's move on." + }, + { + "text": "So here is that I said you can actually do all these computations and forget about the fact that x is continuous." + }, + { + "text": "You can actually do it with PMFs and do it for x is discrete." + }, + { + "text": "This actually also tells you if you can actually get the same form for your density, which is of the form exponential times the product of the interaction between theta and x is just taking this product, and then a function only of theta and a function only of x for the PMF." + }, + { + "text": "It also works." + }, + { + "text": "So I claim that the Bernoulli belongs to this family." + }, + { + "text": "So the PMF of a Bernoulli, we say parameter p, is p to the x 1 minus p to the 1 minus x, right?" + }, + { + "text": "Because we know, so that's only for x equals 0 or 1." + }, + { + "text": "And the reason is because when x is equal to 0, this is 1 minus p. When x is equal to 1, this is p. We've seen that when we were looking at likelihoods for Bernoullis." + }, + { + "text": "This is not clear this is going to look like this at all." + }, + { + "text": "But let's do it." + }, + { + "text": "So what does this thing look like?" + }, + { + "text": "Well, the first thing I want to do is to make an exponential show up." + }, + { + "text": "So what I'm going to write is I'm going to write p to the x as exponential x log p, right?" + }, + { + "text": "And so I'm going to do that for the other one." + }, + { + "text": "So this thing here, so I'm going to get exponential x log p plus 1 minus x log 1 minus p. So what I need to do is to collect my terms in x and my terms in whatever parameters I have." + }, + { + "text": "So here, theta is equal to p. So if I do this, what I end up having is equal to exponential." + }, + { + "text": "So the term in x is log p minus log 1 minus p. So that's x times log p over 1 minus p. And then the term that stays is just 1 times log 1 minus p. But I want to see this as a minus something, right?" + }, + { + "text": "It was minus b of theta." + }, + { + "text": "So I'm going to write it as minus." + }, + { + "text": "Well, I can just keep the plus." + }, + { + "text": "And I'm going to do." + }, + { + "text": "And that's all." + }, + { + "text": "Aha." + }, + { + "text": "Well, this is of the form exponential, something that depends only on x, times something that depends only on theta, minus a function that depends only on theta." + }, + { + "text": "And then h of x is equal to 1 again." + }, + { + "text": "So let's see." + }, + { + "text": "So I have t1 of x is equal to x." + }, + { + "text": "That's this guy." + }, + { + "text": "Eta 1 of theta is equal to log p 1 minus p. And b of theta is equal to log 1 over 1 minus p. And h of x is equal to 1." + }, + { + "text": "You guys want to do Poisson, or you want to have it in homework?" + }, + { + "text": "It's a dilemma, because that's an easy homework versus no homework at all." + }, + { + "text": "That may be something more difficult." + }, + { + "text": "OK, who wants to do it now?" + }, + { + "text": "Who does not want to raise their hand now?" + }, + { + "text": "Who wants to raise their hand now?" + }, + { + "text": "All right." + }, + { + "text": "So let's move on." + }, + { + "text": "I'll just do it." + }, + { + "text": "Do you want to do the gammas instead in the homework?" + }, + { + "text": "That's going to be fun." + }, + { + "text": "I'm not even going to propose to do the gammas." + }, + { + "text": "So this is the gamma distribution." + }, + { + "text": "It's brilliantly called gamma, because it has the gamma function, just like the beta distribution was at the beta function in there." + }, + { + "text": "They look very similar." + }, + { + "text": "One is defined over r plus, the positive real line." + }, + { + "text": "And remember, the beta was defined over the interval 0, 1." + }, + { + "text": "And it's of the form x to some power times exponential minus x to some time something." + }, + { + "text": "So there's a function, a polynomial in x, where the exponent depends on the parameter." + }, + { + "text": "And then there's the exponential minus x times something depends on the parameters." + }, + { + "text": "So this is going to also look like some function of x." + }, + { + "text": "Sorry, like some exponential distribution." + }, + { + "text": "Can somebody guess what is going to be t2 of x?" + }, + { + "text": "Oh, those are the functions of x that show up in this product." + }, + { + "text": "Remember when we have this, we just need to take some transformations of x, so it looks linear in those things and not in x itself." + }, + { + "text": "Remember, we had x squared and x, for example, in the Gaussian case." + }, + { + "text": "I don't know if it's still there." + }, + { + "text": "Yeah, it's still there, right?" + }, + { + "text": "t2 was x squared." + }, + { + "text": "What do you think x is going to be?" + }, + { + "text": "t2 of x." + }, + { + "text": "So here's a hint." + }, + { + "text": "t1 is going to be x. Yeah, Arjun, what is going to be t2?" + }, + { + "text": "Yeah, you cannot." + }, + { + "text": "This one is taken." + }, + { + "text": "This one is taken." + }, + { + "text": "I don't want to take it." + }, + { + "text": "What?" + }, + { + "text": "Log x, right?" + }, + { + "text": "Because this x to the a minus 1, I'm going to write it as exponential a minus 1 log x." + }, + { + "text": "So basically, eta 1 is going to be a minus 1." + }, + { + "text": "Eta 2 is going to be minus 1 over b." + }, + { + "text": "Well, actually, the opposite." + }, + { + "text": "But this is actually not too complicated." + }, + { + "text": "All right, then those parameters get names." + }, + { + "text": "a is the shape parameter." + }, + { + "text": "b is the scale parameter." + }, + { + "text": "It doesn't really matter." + }, + { + "text": "You have other things that are called the inverse gamma distribution, which has this form." + }, + { + "text": "The difference is that the parameter alpha shows negatively there." + }, + { + "text": "And then the inverse Gaussian distribution, just densities you can come up with." + }, + { + "text": "And it just happened to fall in this family." + }, + { + "text": "And there's other ones that you can actually put it there that we've seen before." + }, + { + "text": "The chi square is actually part of this family." + }, + { + "text": "The beta distribution is part of this family." + }, + { + "text": "The binomial distribution is part of this family." + }, + { + "text": "Well, that's easy because the Bernoulli was." + }, + { + "text": "The negative binomial, which is some stopping time, the first time you hit a certain number of successes when you flip some Bernoulli coins." + }, + { + "text": "So you can check for all of those." + }, + { + "text": "And you will see that you can actually write them as part of the exponential family." + }, + { + "text": "So the main goal of this slide is to convince you that this is actually a pretty broad range of distributions, because it basically includes everything we've seen, but not anything there." + }, + { + "text": "Sorry, plus more." + }, + { + "text": "OK?" + }, + { + "text": "Yeah?" + }, + { + "text": "Is there any example of a distribution which comes up pretty often that's not in the next exponential family?" + }, + { + "text": "Yeah, like uniform." + }, + { + "text": "Oh, OK. Maybe a bit more complicated than that." + }, + { + "text": "Anything that has a support that depends on the parameter is not going to fall." + }, + { + "text": "It's not going to fit in there." + }, + { + "text": "And you can actually convince yourself why anything that has the support that depends on the parameter is not going to be part of this guy." + }, + { + "text": "It's kind of a hard thing to, if I ask you, prove that it's not, and you wouldn't prove this rule." + }, + { + "text": "It's kind of a little difficult." + }, + { + "text": "But the way you can convince yourself is that, remember, the only interaction between x and theta that I allowed was taking the product of those guys and then the exponential." + }, + { + "text": "If you have something that depends on some parameter, let's say you're going to see something that looks like this." + }, + { + "text": "For uniform, it looks like this." + }, + { + "text": "Well, this is not of the form exponential x times theta." + }, + { + "text": "There's an interaction between x and theta here, but it's actually certainly not of the form x exponential x times theta." + }, + { + "text": "So this is definitely not going to be part of the exponential family." + }, + { + "text": "And every time you start doing things like that, then it's just not going to happen." + }, + { + "text": "Actually, to be fair, I'm not even sure that all these guys, when you allow them to have all their parameters free, are actually going to be part of this." + }, + { + "text": "The beta probably is, but I'm not actually entirely convinced." + }, + { + "text": "There's books on exponential families." + }, + { + "text": "So let's go back." + }, + { + "text": "So here, we've put a lot of effort understanding how big, how much wider than the Gaussian distribution can we think of for the conditional distribution of our response y given x." + }, + { + "text": "So let's go back to the generalized linear models." + }, + { + "text": "So the generalized linear model said, OK, the random component, y, has to be part of some exponential family distribution." + }, + { + "text": "Check." + }, + { + "text": "We know what this means." + }, + { + "text": "So now I have to understand two things." + }, + { + "text": "I have to understand what is the expectation, because that's actually what I model." + }, + { + "text": "I take the expectation, the conditional expectation of y given x." + }, + { + "text": "So I need to understand, given this guy, it would be nice if it had some simple rules that would tell me exactly what the expectation is, rather than having to do it over and over again." + }, + { + "text": "If I told you, here's a Gaussian, compute the expectation." + }, + { + "text": "Every time you had to use that, it would be slightly painful." + }, + { + "text": "So hopefully, this thing being simple enough, we've actually selected a simple class that's simple enough." + }, + { + "text": "So that we can have rules, whereas as soon as I give you those parameters, t1, t2, eta 1, eta 2, b, and h, you can actually have some simple rules to compute the mean and variance and all the things." + }, + { + "text": "And so in particular, I'm interested in the mean." + }, + { + "text": "And I'm going to have to actually say, well, this mean has to be mapped into the whole real line so I can actually talk about modeling this function of the mean as x transpose beta." + }, + { + "text": "And we saw that for the Kefosis data set or whatever other data sets, you can actually do this using the log of the reciprocal." + }, + { + "text": "Or for the, actually, we didn't do it for the Bernoulli." + }, + { + "text": "We'll come to this." + }, + { + "text": "This is the most important one, and that's called the logit or logistic link." + }, + { + "text": "But before we go there, this was actually a very broad family." + }, + { + "text": "When I wrote this thing on the bottom board, it's gone now." + }, + { + "text": "But when I wrote it in the first place, the only thing that I wrote is I wanted x times theta." + }, + { + "text": "Wouldn't it be nice if I have some distribution that was just x times theta, not some function of x times some function of theta?" + }, + { + "text": "The functions seem to be here so that they actually make things a little." + }, + { + "text": "So the functions were here so that I can actually put a lot of functions there." + }, + { + "text": "But first of all, if I actually decide to reparameterize my problem, I can always assume, if I have one dimensional, I can always assume that eta 1 of theta becomes my new theta." + }, + { + "text": "So this thing here, for example, I could say, well, this is actually the parameter of my Bernoulli." + }, + { + "text": "Let me call this guy theta." + }, + { + "text": "I could do that." + }, + { + "text": "Then I could say, well, here I have x that shows up here." + }, + { + "text": "And here, since I'm talking about the response, I cannot really make any transformation." + }, + { + "text": "So here I'm going to actually talk about a specific family for which this guy is not x square or square root of x or log of x or anything I want." + }, + { + "text": "I'm just going to actually look at distributions for which this is x." + }, + { + "text": "These exponential families are called canonical exponential families." + }, + { + "text": "So in the canonical exponential family, what I have is that I have my x times theta." + }, + { + "text": "I'm going to allow myself some normalization factor phi." + }, + { + "text": "And we'll see, for example, that it's very convenient when I talk about the Gaussian." + }, + { + "text": "Because even if I know this guy, which I actually pull into my, oh, that's over here, right?" + }, + { + "text": "I know sigma squared, but I don't want to change my parameter to be mu over sigma squared." + }, + { + "text": "It's kind of painful." + }, + { + "text": "So I just take mu, and I'm going to keep this guy as being this phi over there." + }, + { + "text": "And it's called the dispersion parameter from a clear analogy with the Gaussian." + }, + { + "text": "That's the variance, and that's measuring dispersion." + }, + { + "text": "So here, what I want is I'm going to think throughout this class." + }, + { + "text": "So phi may be known or not." + }, + { + "text": "And when it's not known, this actually might turn into some exponential family, or it might not." + }, + { + "text": "And the main reason is because this b of theta over phi is not necessarily a function of theta over phi." + }, + { + "text": "If I actually have phi unknown, then y theta over phi has to be, this guy has to be my new parameter." + }, + { + "text": "And b might not be a function of this new parameter." + }, + { + "text": "So in a way, it may or may not, but this is not really a concern that we're going to have, because throughout this class, we're going to assume that phi is known." + }, + { + "text": "Phi is going to be known all the time, which means that this is always an exponential family." + }, + { + "text": "And it's just the simplest one you could think of." + }, + { + "text": "One dimensional parameter, one dimensional response, and I just have the product is just y times, or we used to call it x." + }, + { + "text": "Now I've switched to y." + }, + { + "text": "But y times theta divided by phi." + }, + { + "text": "Should I write this, or is this clear to everyone what this is?" + }, + { + "text": "Let me write it somewhere so we actually keep track of it for the 10 minutes." + }, + { + "text": "OK, so this is, we have, remember we had all the distributions." + }, + { + "text": "And then here we had the exponential family." + }, + { + "text": "And now we have the canonical exponential family." + }, + { + "text": "It's actually much, much smaller." + }, + { + "text": "Well, actually, it's probably sort of a good picture." + }, + { + "text": "And what I have is that my density, or my PMF, is just exponential y times theta minus b of theta divided by phi." + }, + { + "text": "And I have plus c of, oh, yeah, plus c of y phi, which means that this is really, if phi is known, h of y is just exponential c of y phi." + }, + { + "text": "Actually, this is the reason why it's not necessarily a canonical family." + }, + { + "text": "It might not be that this depends only on y." + }, + { + "text": "It could depend on y and phi in some annoying way, and I may not be able to break it." + }, + { + "text": "But if phi is known, this is just a function that depends on y." + }, + { + "text": "Agreed?" + }, + { + "text": "In particular, I hope you can convince yourself that this is just a subcase of everything we've seen before." + }, + { + "text": "So for example, the Gaussian, when the variance is known, is indeed of this form." + }, + { + "text": "So we still have it on the board." + }, + { + "text": "So here's my y." + }, + { + "text": "So let me write this as f theta of y." + }, + { + "text": "So every x is replaced with y. Blah, blah, blah." + }, + { + "text": "This is this guy." + }, + { + "text": "And now what I have is that this is going to be my phi." + }, + { + "text": "This is my parameter theta." + }, + { + "text": "So I'm definitely of the form y times theta divided by phi." + }, + { + "text": "And then here, I have a function b that depends only on theta over phi again." + }, + { + "text": "So b of theta is mu squared divided by 2." + }, + { + "text": "Then it's divided by sigma square." + }, + { + "text": "And then I have this extra stuff, but I really don't care what it is for now." + }, + { + "text": "It's just something that depends only on y and known stuff." + }, + { + "text": "So it's just a function of y." + }, + { + "text": "Just like my h, I stuff everything in there." + }, + { + "text": "The b, though, this thing here, this is actually what's important." + }, + { + "text": "Because in a canonical family, if you think about it, when you know phi, this is just y times theta scaled by a known constant." + }, + { + "text": "Sorry, y times theta scaled by a known constant is the first term." + }, + { + "text": "The second term is b of theta scaled by some known constant." + }, + { + "text": "But b of theta is what's going to make the difference between Gaussian and Bernoulli's and gammas and betas." + }, + { + "text": "This is all in this b of theta." + }, + { + "text": "b of theta contains everything that's idiosyncratic to this particular distribution." + }, + { + "text": "And so this is going to be important." + }, + { + "text": "And we will see that b of theta is going to capture information about the mean, about the variance, about the likelihood, about everything." + }, + { + "text": "Should I go through this computation?" + }, + { + "text": "I mean, it's the same." + }, + { + "text": "We've just done it." + }, + { + "text": "So maybe it's probably better if you can redo it on your own." + }, + { + "text": "So the canonical exponential family also has other distributions." + }, + { + "text": "So there's the Gaussian, and there's the Poisson, and there's the Bernoulli." + }, + { + "text": "But the other ones may not be part of this." + }, + { + "text": "In particular, think about the gamma distribution." + }, + { + "text": "We had this log x was one of those things that showed up." + }, + { + "text": "I mean, I cannot get rid of this log x. I mean, that's part of it, except if a is equal to 1." + }, + { + "text": "And I know it for sure." + }, + { + "text": "So if a is equal to 1, then I'm going to have a minus 1, which is equal to 0." + }, + { + "text": "So I'm going to have a minus 1 times log x, which is going to be just 0." + }, + { + "text": "So log x is going to vanish from here." + }, + { + "text": "If a is equal to 1, then this distribution is actually much nicer." + }, + { + "text": "And it actually does not even deserve the name gamma." + }, + { + "text": "What is it if a is equal to 1?" + }, + { + "text": "It's an exponential, right?" + }, + { + "text": "Gamma of 1 is equal to 1. x to the a minus 1 is equal to 1. b, so I have exponential x over b divided by b." + }, + { + "text": "So 1 over b, call it lambda." + }, + { + "text": "And this is just an exponential distribution." + }, + { + "text": "And so every time you're going to see something, so all these guys that don't make it to this table, they could be part of those guys." + }, + { + "text": "But they're just to have another name in this thing." + }, + { + "text": "So you can compute the value of theta for different values." + }, + { + "text": "So again, you still have some continuous or discrete ones." + }, + { + "text": "This is my b of theta." + }, + { + "text": "And I said this is actually really what captures my theta." + }, + { + "text": "This b is actually called cumulant generating function." + }, + { + "text": "I don't have time." + }, + { + "text": "I could write five slides to explain to you." + }, + { + "text": "But it would just only tell you why it's called cumulant generating function." + }, + { + "text": "It's also known as the log of the moment generating function." + }, + { + "text": "And the way it's called cumulant generating function is because if I start taking successive derivatives and evaluate them at 0, I get the successive cumulants of this distribution, which are some transformation of the moment." + }, + { + "text": "What is the function b?" + }, + { + "text": "The function b." + }, + { + "text": "So this is just normalization." + }, + { + "text": "So this is just to tell you I can compute this, but I really don't care." + }, + { + "text": "And obviously, I don't care about stuff that's complicated." + }, + { + "text": "This is actually cute." + }, + { + "text": "And this is what computes everything." + }, + { + "text": "And the rest is just some general description." + }, + { + "text": "You don't need me to tell you that the range of y is 0 to infinity." + }, + { + "text": "And that is essentially telling me this is going to give me some hints as to which link function I should be using." + }, + { + "text": "Because the range of y tells me what the range of expectation of y is going to be." + }, + { + "text": "Here it tells me that the range of y is between 0 and 1." + }, + { + "text": "So what I want to show you is that this captures a variety of different ranges that you can have." + }, + { + "text": "So I'm going to want to go into the likelihood." + }, + { + "text": "And the likelihood I'm actually going to use to compute the expectations." + }, + { + "text": "But since I actually don't have time to do this now, let's just go quickly through this and give you a spoiler alert to make sure that you all wake up on Thursday and really, really want to think about coming here immediately." + }, + { + "text": "So the thing I'm going to want to do, as I said, is it would be nice if, at least for this canonical family, when I give you b, you would be able to say, oh, here is a simple computation of b that would actually give me the mean and the variance." + }, + { + "text": "The mean and the variance are also known as moments." + }, + { + "text": "b is called cumulant generating function." + }, + { + "text": "So it sounds like moments being related to cumulants might have a path to finding those." + }, + { + "text": "And it might involve taking derivatives of b, as we'll see." + }, + { + "text": "The way we're going to prove this is by using this thing that we've used several times." + }, + { + "text": "So this property we use when we're computing, remember, the Fisher information." + }, + { + "text": "We had two formulas for the Fisher information." + }, + { + "text": "One was the expectation of the second derivative of the likelihood." + }, + { + "text": "And one was negative expectation of the square." + }, + { + "text": "Sorry, expectation of the square." + }, + { + "text": "And the other one was negative the expectation of the second derivative." + }, + { + "text": "The log likelihood is concave." + }, + { + "text": "So this number is negative." + }, + { + "text": "This number is positive." + }, + { + "text": "And the way we did this is by just permuting some derivative and integral here." + }, + { + "text": "And we used the fact that something that looked like this, the log likelihood is log of f theta." + }, + { + "text": "And when I take the derivative of this guy with respect to theta, then I have something that looks like the derivative divided by f theta." + }, + { + "text": "And if I start taking the integral against f theta of this thing, so the expectation of this thing, those things would cancel." + }, + { + "text": "And then I had just the integral of a derivative, which I would make a leap of faith and say that it's actually the derivative of the integral." + }, + { + "text": "But this was equal to 1." + }, + { + "text": "So this derivative was actually equal to 0." + }, + { + "text": "And so that's how you got that the expectation of the derivative of the log likelihood is equal to 0." + }, + { + "text": "And you do it once again, and you get this guy." + }, + { + "text": "There's just some nice things that happen with taking the derivative of the log." + }, + { + "text": "We've done that." + }, + { + "text": "We'll do that again." + }, + { + "text": "But once you do this, you can actually apply it." + }, + { + "text": "And missing a parenthesis over there." + }, + { + "text": "So when you write the log likelihood, it's just log of an exponential." + }, + { + "text": "That's actually pretty nice." + }, + { + "text": "Just like the least squares came naturally, the least squares criterion came naturally when we took the log likelihood of the Gaussians." + }, + { + "text": "We're going to have the same thing that happens." + }, + { + "text": "When I take the log of the density, the exponential is going to go away." + }, + { + "text": "And then I'm going to use this formula." + }, + { + "text": "But this formula is going to actually give me an equation directly." + }, + { + "text": "Oh, that's where it was." + }, + { + "text": "So that's the one that's missing it there." + }, + { + "text": "So the expectation minus this thing is going to be equal to 0, which tells me that the expectation is just the derivative." + }, + { + "text": "So it's still a function of theta, but it's just the derivative of b." + }, + { + "text": "And the variance is just going to be the second derivative of b." + }, + { + "text": "But remember, this was some sort of a scaling." + }, + { + "text": "It's called the dispersion parameter." + }, + { + "text": "So if I had a Gaussian, and the variance of the Gaussian did not depend on the sigma square, which I stuffed in this phi, that would be certainly weird." + }, + { + "text": "And it cannot depend only on mu." + }, + { + "text": "And so for the Gaussian, this is definitely going to be equal to 1." + }, + { + "text": "And this is just going to be equal to my variance." + }, + { + "text": "So this is just by taking the second derivative." + }, + { + "text": "So basically, the take-home message is that this function b captures, by taking one derivative of the expectation and by taking two derivatives, captures the variance." + }, + { + "text": "Another thing that's actually cool, and we'll come back to this and I want you to think about, is if this second derivative is the variance, what can I say about this thing?" + }, + { + "text": "What do I know about a variance?" + }, + { + "text": "Yeah, it's positive." + }, + { + "text": "So I know that this is positive." + }, + { + "text": "So what does that tell me?" + }, + { + "text": "Positive?" + }, + { + "text": "That's convex, right?" + }, + { + "text": "A function that has positive second derivative is convex." + }, + { + "text": "So we're going to use that as well." + }, + { + "text": "So yeah, I'll see you on Thursday." + }, + { + "text": "Have your homework." + } +] \ No newline at end of file diff --git a/sight/sources/annotated/Xa2jPbURTjQ.json b/sight/sources/annotated/Xa2jPbURTjQ.json new file mode 100644 index 0000000000000000000000000000000000000000..f132682581b9f7a09c83979f15c255a3174887d3 --- /dev/null +++ b/sight/sources/annotated/Xa2jPbURTjQ.json @@ -0,0 +1,1961 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So we're really moving along this review of the highlights of linear algebra." + }, + { + "text": "And today it's matrices Q." + }, + { + "text": "They get that name." + }, + { + "text": "They have orthonormal columns." + }, + { + "text": "So that's what one looks like." + }, + { + "text": "And then the key fact, orthonormal columns translates directly into that simple fact that you just keep remembering." + }, + { + "text": "Every time you see Q transpose Q, you've got the identity matrix." + }, + { + "text": "Let's just see why." + }, + { + "text": "So Q transpose would be, I'll take those columns and make them into rows." + }, + { + "text": "And then I multiply by Q with the columns." + }, + { + "text": "And what do I get?" + }, + { + "text": "Well, hopefully I get the identity matrix." + }, + { + "text": "OK, why?" + }, + { + "text": "Because, oh, yeah, the normal part tells me that the length of each vector, that's the length squared Q transpose Q." + }, + { + "text": "The length squared is 1." + }, + { + "text": "So that gives me the 1 in the identity matrix all along the diagonal." + }, + { + "text": "And then Q transpose times a different Q is 0." + }, + { + "text": "That's the ortho part." + }, + { + "text": "So that gives me the 0s." + }, + { + "text": "So that's a simple identity." + }, + { + "text": "But it translates from a lot of words into a simple expression." + }, + { + "text": "Now, does that mean that in the other order, Q Q transpose, is that the identity?" + }, + { + "text": "So that's a question to think about." + }, + { + "text": "Is Q Q transpose equal the identity?" + }, + { + "text": "Question." + }, + { + "text": "Sometimes yes, sometimes no." + }, + { + "text": "Easy to tell which." + }, + { + "text": "The answer is yes." + }, + { + "text": "Yes, when Q is square." + }, + { + "text": "The answer is yes." + }, + { + "text": "If Q is a square matrix, a square matrix, this is saying that the square matrix Q has that inverse on its left." + }, + { + "text": "But for square matrices, a left inverse, Q transpose, is also a right inverse." + }, + { + "text": "And for a square matrix, if you have an inverse that works on one side, it will work on the other side." + }, + { + "text": "So the answer is yes in that case." + }, + { + "text": "And then in that case, that's the case when we call Q is, well, we really, I don't know what the right name would be." + }, + { + "text": "But here's the name everybody uses, an orthogonal matrix." + }, + { + "text": "And that's only in the square case, square." + }, + { + "text": "Q is an orthogonal matrix." + }, + { + "text": "Right, right." + }, + { + "text": "Do you want to just see an example of how that works?" + }, + { + "text": "And it will not." + }, + { + "text": "So if Q is rectangular, let me do a rectangular Q and a square Q." + }, + { + "text": "So I think there must be a board up there somewhere." + }, + { + "text": "Here." + }, + { + "text": "OK, square." + }, + { + "text": "All right, good to see some orthogonal matrices, because my message is that they're really important in all kinds of applications." + }, + { + "text": "Let's start two by two." + }, + { + "text": "I can think of two different ways to get an orthogonal matrix that's a two by two matrix." + }, + { + "text": "And one of them you will know immediately, cos theta, sine theta." + }, + { + "text": "So that's a unit vector." + }, + { + "text": "It's normalized." + }, + { + "text": "Cos squared plus sine squared is 1." + }, + { + "text": "And this guy has to be orthogonal to it." + }, + { + "text": "So I'll make that minus sine theta and cos theta." + }, + { + "text": "OK. Those are both length 1." + }, + { + "text": "They're orthogonal." + }, + { + "text": "Then this is my Q." + }, + { + "text": "And the inverse of Q will be the transpose." + }, + { + "text": "The transpose would put the minus sign down here and would produce the inverse matrix." + }, + { + "text": "And what does that particular matrix represent?" + }, + { + "text": "Geometrically, where do we see that matrix?" + }, + { + "text": "It's a rotation." + }, + { + "text": "Thank you." + }, + { + "text": "It's a rotation of the whole plane by theta." + }, + { + "text": "Yeah." + }, + { + "text": "So if I apply that to 1, 0, for example, I get the first column, which is cos theta, sine theta." + }, + { + "text": "And that's just a row." + }, + { + "text": "Let me draw a picture." + }, + { + "text": "That vector 1, 0 has got rotated up to." + }, + { + "text": "So there is the 1, 0." + }, + { + "text": "And there it got rotated through an angle theta." + }, + { + "text": "And similarly, 0, 1 will get rotated through an angle theta to there." + }, + { + "text": "So the whole plane rotates." + }, + { + "text": "Oh, that makes me remember a highly important, very important property of Q." + }, + { + "text": "It doesn't change length." + }, + { + "text": "The length of any vector is the same after you rotate it." + }, + { + "text": "The length of any vector is the same after you multiply by Q." + }, + { + "text": "Can I just do that?" + }, + { + "text": "I claim any x, any vector x, I want to look at the length of Qx." + }, + { + "text": "And I claim that it has the same length as x." + }, + { + "text": "Actually, that's the reason in computations that orthogonal matrix are so much loved, because no overflow can happen with orthogonal matrices." + }, + { + "text": "Lengths don't change." + }, + { + "text": "I can multiply by any number of orthogonal matrices, and the lengths don't change." + }, + { + "text": "Can we just see why that's true?" + }, + { + "text": "How would you show?" + }, + { + "text": "So what do we have to go on?" + }, + { + "text": "What we have to go on is Q transpose Q equal I." + }, + { + "text": "Whatever we're going to prove, it's got to come out of that, because that's all we know." + }, + { + "text": "So how do I use that to get that one?" + }, + { + "text": "Well, we haven't said a whole lot about lengths, but you'll see it all now." + }, + { + "text": "It'll be easier to prove that the squares are the same." + }, + { + "text": "So what's the matrix expression for the length squared?" + }, + { + "text": "What's the right-hand side of that equation?" + }, + { + "text": "X transpose x, right?" + }, + { + "text": "X transpose x gives me the sum of the squares." + }, + { + "text": "Pythagoras says that's the length squared." + }, + { + "text": "So that right-hand side is x transpose x." + }, + { + "text": "What's the left side?" + }, + { + "text": "It's the length squared of this, of Qx." + }, + { + "text": "So it must be the same as Qx, transpose Qx." + }, + { + "text": "And the claim is that that equation holds." + }, + { + "text": "And do you see it?" + }, + { + "text": "Where is it?" + }, + { + "text": "So any property from Q has to just come out directly from that." + }, + { + "text": "Where is it here?" + }, + { + "text": "Do I just push away a little bit at that left-hand side and see it?" + }, + { + "text": "Qx transpose is the same as x transpose Q transpose." + }, + { + "text": "And Qx is Qx." + }, + { + "text": "And now I'm seeing, well, you might say, wait a minute." + }, + { + "text": "The parentheses were there and there." + }, + { + "text": "But I say the most important law for matrix multiplication is you can move parentheses or throw them away." + }, + { + "text": "Let's throw them away." + }, + { + "text": "So in here, I'm seeing Q transpose Q, which is the identity." + }, + { + "text": "So it's true." + }, + { + "text": "So that means that you never underflow or overflow when you're multiplying by Q." + }, + { + "text": "Every numerical algorithm is written to use orthogonal matrices wherever it can." + }, + { + "text": "And here's the first example." + }, + { + "text": "So I think it may be good for me to think of other examples or for us to think of other examples of orthogonal matrices." + }, + { + "text": "So I'm using that word orthogonal matrix." + }, + { + "text": "We should really be saying orthonormal." + }, + { + "text": "And I'm really thinking mostly of square ones." + }, + { + "text": "So in the square case, when Q transpose is Q inverse." + }, + { + "text": "Of course, that fact makes it easy to solve all equations that have Q as a coefficient matrix, because you want the inverse and you just use the transpose." + }, + { + "text": "OK, let's just take some minutes to think of examples of Qs, if they're so important there have to be interesting examples." + }, + { + "text": "And that was a first one." + }, + { + "text": "Now, there's one more 2 by 2 example that you should know." + }, + { + "text": "Do you know what that would be?" + }, + { + "text": "So this will be example 2." + }, + { + "text": "And it's also going to be only 2 by 2 and real." + }, + { + "text": "And what possibility have I got left here?" + }, + { + "text": "I'll use the same first column, cos theta, sine theta, because that's more or less any unit vector in two dimensions." + }, + { + "text": "This has got that form." + }, + { + "text": "So what do you propose for the second column?" + }, + { + "text": "Yes?" + }, + { + "text": "Yeah, put the minus sign down here." + }, + { + "text": "So you think, does that make any difference?" + }, + { + "text": "So sine theta and minus cos theta." + }, + { + "text": "I don't know if you've ever looked at that matrix." + }, + { + "text": "We're trying to collect together a few matrices that are worth knowing, are worth looking at." + }, + { + "text": "OK, now what's happened here?" + }, + { + "text": "You may say that was a trivial change, which it kind of was." + }, + { + "text": "But it's a different matrix now." + }, + { + "text": "It's not a rotation anymore." + }, + { + "text": "That's not a rotation." + }, + { + "text": "And yeah, somehow, now it's symmetric." + }, + { + "text": "And yeah, its eigenvectors must be something or other." + }, + { + "text": "We'll get to those." + }, + { + "text": "But what does that matrix do?" + }, + { + "text": "I don't know if you've seen it." + }, + { + "text": "If you haven't, it doesn't jump out." + }, + { + "text": "But it's an important case." + }, + { + "text": "This is a reflection matrix." + }, + { + "text": "Notice that it's determined it is minus 1." + }, + { + "text": "You have minus cos squared theta minus sine squared theta." + }, + { + "text": "It's determined it is minus 1." + }, + { + "text": "There's some eigenvalue coming up that's got a minus." + }, + { + "text": "Yeah." + }, + { + "text": "OK, so what do I mean by a reflection matrix?" + }, + { + "text": "Let me draw the plane." + }, + { + "text": "And I think, so 1, 0." + }, + { + "text": "Let's follow it again." + }, + { + "text": "1, 0, where does that go?" + }, + { + "text": "That gives me the first column." + }, + { + "text": "So as before, it goes to cos theta sine theta." + }, + { + "text": "And when I say reflection, let me put the mirror into the picture." + }, + { + "text": "So you see what reflection it is." + }, + { + "text": "The mirror is along here at angle theta over 2, theta over 2 line." + }, + { + "text": "So sure enough, 1, 0 at angle 0 got reflected into a unit vector at angle theta." + }, + { + "text": "And halfway between was the theta over 2 line." + }, + { + "text": "That's OK. Now, what about the other guy, 0, 1?" + }, + { + "text": "Here's 0, 1." + }, + { + "text": "OK, I multiply that." + }, + { + "text": "Can I put the 0, 1 up here so your eye does the multiplication?" + }, + { + "text": "Where is the result of 0, 1?" + }, + { + "text": "What's the output from Q applied to 0, 1?" + }, + { + "text": "Sine theta minus cos theta, right?" + }, + { + "text": "It's the second column." + }, + { + "text": "And so where is that?" + }, + { + "text": "Well, it's perpendicular to that guy." + }, + { + "text": "That's what I know, right?" + }, + { + "text": "That was the point, that the two columns are perpendicular." + }, + { + "text": "So it must go down this way, right?" + }, + { + "text": "Sine theta, cos theta." + }, + { + "text": "And it doesn't change length." + }, + { + "text": "All these facts that we just learned are key." + }, + { + "text": "So there's 0, 1, and it goes to this guy, which is whatever that second column is, sine theta minus cos theta." + }, + { + "text": "And if you check that, actually, gosh, this is like plain geometry." + }, + { + "text": "I believe, it's never occurred to me before, but I believe it, that this angle going down to there, that that goes straight through, and that the halfway one is that line." + }, + { + "text": "Yeah, I think that picture has got it, and I think it's in the notes." + }, + { + "text": "So that's a reflection matrix." + }, + { + "text": "Well, that's a 2 by 2 reflection matrix." + }, + { + "text": "Would you like to see some other matrices like this one, but larger?" + }, + { + "text": "They're named after a guy named Householder." + }, + { + "text": "So these are Householder reflections." + }, + { + "text": "What am I doing here?" + }, + { + "text": "I'm collecting together some orthogonal matrices that are useful and important." + }, + { + "text": "And Householder found a whole bunch of them, and his algorithm is a much used part of numerical linear algebra." + }, + { + "text": "So he started with a unit vector." + }, + { + "text": "Start with a unit vector, u transpose u equal 1." + }, + { + "text": "So the length of the vector is 1." + }, + { + "text": "And then he created, let's name it after him, H. He created this matrix, the identity minus 2 uu transpose." + }, + { + "text": "And I believe that that's a really useful matrix." + }, + { + "text": "So it's just like, I think this review is like going beyond 18.06 into what ones are really worth knowing individually." + }, + { + "text": "Could we just check what are the properties of Householder's reflection of that I minus 2?" + }, + { + "text": "You recognize here a column times a row." + }, + { + "text": "So that's a matrix." + }, + { + "text": "And what could you tell me about that matrix uu transpose?" + }, + { + "text": "It's, yeah." + }, + { + "text": "Or what can we say about H?" + }, + { + "text": "So I guess I'm believing that H is a orthogonal matrix." + }, + { + "text": "Otherwise, it wouldn't be here today." + }, + { + "text": "So I believe that." + }, + { + "text": "And not only is it orthogonal, it is also, have a look at it, symmetric." + }, + { + "text": "It's also symmetric." + }, + { + "text": "The identity is symmetric." + }, + { + "text": "Uu transpose is symmetric." + }, + { + "text": "So this is a family of symmetric orthogonal matrices." + }, + { + "text": "And that was one of them." + }, + { + "text": "That's a symmetric orthogonal matrix." + }, + { + "text": "These matrices are really great to have." + }, + { + "text": "You just, like in using linear algebra, you just get a collection of useful matrices that you can call on." + }, + { + "text": "And these are definitely one family." + }, + { + "text": "Well, it's obviously symmetric." + }, + { + "text": "Shall we check that it's orthogonal?" + }, + { + "text": "So to check that it's orthogonal, I just, so I'm going to check that H transpose H is the identity." + }, + { + "text": "Can I just check that?" + }, + { + "text": "Well, H transpose is the same as H, because it was symmetric." + }, + { + "text": "So I'm going to square this guy." + }, + { + "text": "This is really H times H. I'm squaring it." + }, + { + "text": "And what do I get if I square?" + }, + { + "text": "So I get, I hope I get the identity, but let's see it." + }, + { + "text": "What do I get when I square this?" + }, + { + "text": "Get little, multiply it out." + }, + { + "text": "So I times I is I." + }, + { + "text": "And then I get some number of Uu transposes." + }, + { + "text": "How many do I get from that?" + }, + { + "text": "So I'm squaring this thing, because H transpose H is the same as H times H. So I'm squaring it." + }, + { + "text": "So how many, what do I put here?" + }, + { + "text": "Four, thanks." + }, + { + "text": "And now I've got this guy squared with a plus." + }, + { + "text": "So that's four Uu transpose Uu transpose." + }, + { + "text": "Yeah, I'm totally realizing I've practiced for a lifetime doing these dinky little calculations." + }, + { + "text": "But they are dinky." + }, + { + "text": "And you'll get the hang of it quickly." + }, + { + "text": "Now, what am I hoping out of that bottom line?" + }, + { + "text": "That it is?" + }, + { + "text": "I." + }, + { + "text": "We're hoping to get I." + }, + { + "text": "Do we get I?" + }, + { + "text": "Yes." + }, + { + "text": "Who sees how to get I out of that thing?" + }, + { + "text": "Yeah." + }, + { + "text": "U transpose U in here is a number." + }, + { + "text": "That was U." + }, + { + "text": "That was column times row times column times row." + }, + { + "text": "And I look at the in the middle here is row times column." + }, + { + "text": "And that's the number 1, right?" + }, + { + "text": "Because it's there." + }, + { + "text": "So that's 1." + }, + { + "text": "And then I have minus 4 of that, plus 4 of that." + }, + { + "text": "They cancel each other." + }, + { + "text": "And I get I." + }, + { + "text": "So those are good matrices." + }, + { + "text": "We'll use them." + }, + { + "text": "We'll use them." + }, + { + "text": "Actually, they're better than Graham-Schmidt." + }, + { + "text": "So we'll use them in making things orthogonal." + }, + { + "text": "So what other orthogonal matrices?" + }, + { + "text": "Let's create some." + }, + { + "text": "Creating good orthogonal matrices, it pays off." + }, + { + "text": "Let's think." + }, + { + "text": "So there's a family named after this French guy who lived to 100." + }, + { + "text": "He was a real old timer." + }, + { + "text": "Well, MIT had a faculty member in math when I came, Professor Struik, who lived to 106." + }, + { + "text": "And I heard him give a lecture at Brown University at age 100." + }, + { + "text": "And it was like perfect." + }, + { + "text": "You could not have done it better." + }, + { + "text": "So he's my inspiration." + }, + { + "text": "I keep going." + }, + { + "text": "I only have like n more years to get there." + }, + { + "text": "And n is, well, it's too many anyway." + }, + { + "text": "OK, Adamard." + }, + { + "text": "All right, Adamard." + }, + { + "text": "So Adamard, he created, well, that's the simplest, the smallest." + }, + { + "text": "Now, the next guy is going to be 4 by 4." + }, + { + "text": "I'm going to put that." + }, + { + "text": "So where I see a 1, I'm going to put Adamard in." + }, + { + "text": "1, 1, 1 minus 1, 1, 1, 1 minus 1." + }, + { + "text": "And then when I see a minus, I'm going to put it in with a minus." + }, + { + "text": "You saw that picture?" + }, + { + "text": "It was a picture of H2, H2, H2, and minus H2." + }, + { + "text": "That's what I've got there." + }, + { + "text": "And I believe those columns are orthogonal." + }, + { + "text": "Now, what could I do?" + }, + { + "text": "Well, it's not quite an orthogonal matrix." + }, + { + "text": "What do I have to do to make it?" + }, + { + "text": "This isn't quite an orthogonal matrix either." + }, + { + "text": "What do I do to make that an orthogonal matrix?" + }, + { + "text": "Divide by square root of 2." + }, + { + "text": "I need unit vectors there." + }, + { + "text": "And here, those lengths are 1 squared, 1 squared, 4." + }, + { + "text": "Square root of 4 is 2." + }, + { + "text": "So I better divide by the 2 there." + }, + { + "text": "And now here, I'm up to, yeah, so that was that one." + }, + { + "text": "Tell me the next one up." + }, + { + "text": "What's that going to be?" + }, + { + "text": "8 by 8?" + }, + { + "text": "So this is H4 here." + }, + { + "text": "Oops, 4." + }, + { + "text": "So tell me what I should do for 8 by 8." + }, + { + "text": "You'll think this is simple." + }, + { + "text": "But that's a good thing to say about it." + }, + { + "text": "In coding theory, all sorts of places, you want matrices of 1's and minus 1's." + }, + { + "text": "OK, what's H8?" + }, + { + "text": "I'm going to build it out of H4." + }, + { + "text": "So what's it going to be?" + }, + { + "text": "I'm going to put an H4 there." + }, + { + "text": "What am I going to put here?" + }, + { + "text": "Another H4." + }, + { + "text": "And up here, another H4." + }, + { + "text": "And finally here, minus H4." + }, + { + "text": "Minus H4, and I think I've got orthogonal columns again." + }, + { + "text": "Because the columns within these, dot products with themselves, give 0 and 0." + }, + { + "text": "The dot products from these columns and these columns obviously have the minus." + }, + { + "text": "And the dot products in here are 0 from that and 0 from that." + }, + { + "text": "Yeah, it works." + }, + { + "text": "And we could keep going to 16 and 32 and 64." + }, + { + "text": "But then up comes a question." + }, + { + "text": "What about H12?" + }, + { + "text": "Is there a 1's and minus 1's matrix of size 12, 12 by 12?" + }, + { + "text": "It doesn't come directly from our little pattern, which is doubling size every time." + }, + { + "text": "But you could still hope." + }, + { + "text": "And it works." + }, + { + "text": "I don't know what it is, but there's a matrix of 1's and minus 1's, 12 orthogonal columns." + }, + { + "text": "So the answer is yes." + }, + { + "text": "OK, so we make an 18.065 conjecture." + }, + { + "text": "Every matrix size, well, not every matrix size, because 3 by 3 is not going to work." + }, + { + "text": "1 by 1 is not going to work either." + }, + { + "text": "But H12 works, H8, H16." + }, + { + "text": "What's our conjecture?" + }, + { + "text": "We won't be the first to conjecture it." + }, + { + "text": "There is a 1's and minus 1's orthogonal matrix with orthogonal columns of every size n. So always, so I'll start the conjecture." + }, + { + "text": "Always possible if n, which is the size of the matrix, let's say, what would you guess?" + }, + { + "text": "Just take a shot." + }, + { + "text": "You won't be asked for a proof, because nobody has the proof." + }, + { + "text": "Even?" + }, + { + "text": "Well, you could hope for even." + }, + { + "text": "You could look for try 6, I guess, would be the first guy there." + }, + { + "text": "And I don't think it's possible." + }, + { + "text": "I think 6 is not possible." + }, + { + "text": "So every even size is, I think, not going to work." + }, + { + "text": "But it's a natural idea to try." + }, + { + "text": "What's the next thought?" + }, + { + "text": "Every multiple of 4." + }, + { + "text": "If n over 4 is a whole number." + }, + { + "text": "But nobody has a systematic way to create these things." + }, + { + "text": "So like some of them, at this point, we're down to doing it one at a time." + }, + { + "text": "And we're up to 668." + }, + { + "text": "But we haven't got that one yet." + }, + { + "text": "Isn't that crazy?" + }, + { + "text": "So all this is coming from Wikipedia, my source of all that's good in mathematics is there on Wikipedia." + }, + { + "text": "Anyway, this is the conjecture." + }, + { + "text": "Conjecture means you don't have any damn idea of whether it's true or not." + }, + { + "text": "Is that divisible by 4?" + }, + { + "text": "Yeah, I guess it would be." + }, + { + "text": "600 certainly is, and 68 certainly is." + }, + { + "text": "So I think that's the first one." + }, + { + "text": "So anybody, if you find one of size 668, just skip the homework and tell us about that one." + }, + { + "text": "But I don't think I'll assign that." + }, + { + "text": "I guess, well, I must have searched for it online." + }, + { + "text": "But yeah, anyway, so those are the Adamard matrices." + }, + { + "text": "Now, where else do I remember orthogonal matrices coming from?" + }, + { + "text": "Well, yeah, really, the biggest source of." + }, + { + "text": "So when I'm looking for orthogonal matrices, I'm looking for a basis of orthogonal vectors." + }, + { + "text": "And where in math am I going to find vectors that come out to be orthogonal?" + }, + { + "text": "We haven't seen that." + }, + { + "text": "It's the next section of the notes, but maybe you're remembering." + }, + { + "text": "Where will we sort of like automatically show up with orthogonal vectors?" + }, + { + "text": "They could be the eigenvectors of a symmetric matrix." + }, + { + "text": "And that's where the most important ones come from." + }, + { + "text": "Oh, I could tell you about wavelets, though." + }, + { + "text": "Wavelets are more like this picture." + }, + { + "text": "They're 1's and minus 1's." + }, + { + "text": "Or the simplest wavelets are 1's and minus 1's." + }, + { + "text": "Before I go on to the eigenvector business, can I mention the wavelets matrices?" + }, + { + "text": "Yeah, these are really important, simple and important constructions." + }, + { + "text": "So wavelets, let me draw a picture." + }, + { + "text": "So I'm going to come up with four." + }, + { + "text": "I'll do the 4 by 4 case." + }, + { + "text": "And these are the orthogonal guys." + }, + { + "text": "And then the next one is up and down and 0." + }, + { + "text": "And the last one is 0 and up and down." + }, + { + "text": "So that's four things, but let me show you the matrix." + }, + { + "text": "So I'll call it W for wavelets." + }, + { + "text": "So that guy I'm thinking of as 1, 1, 1, 1." + }, + { + "text": "This guy I'm thinking of as 1, 1, minus 1, minus 1." + }, + { + "text": "It's looking sort of Adhemard way, but there's a difference here." + }, + { + "text": "This guy is 1, minus 1, 0, 0." + }, + { + "text": "So the wavelets rescale." + }, + { + "text": "That's the difference between Adhemard and wavelets." + }, + { + "text": "Wavelets are self-scaling." + }, + { + "text": "And what's the last guy here?" + }, + { + "text": "What's the fourth column from that fourth wavelet?" + }, + { + "text": "0, 0, 1, minus 1." + }, + { + "text": "So Haar came up with that." + }, + { + "text": "This is the Haar wavelet, which was many years before the word wavelets was invented." + }, + { + "text": "He came up with this construction, the Haar matrix, the Haar functions." + }, + { + "text": "So they're very simple functions, but that makes them usable, the fact that they're so simple." + }, + { + "text": "Now, I don't know if you want to see the pattern in 8 by 8, but let me start the 8 by 8 so you'll know what wavelets are about." + }, + { + "text": "You'll know what these Haar wavelets are about anyway." + }, + { + "text": "They're the ones that were kind of easy to visualize." + }, + { + "text": "So if that's W4, let's just take a minute." + }, + { + "text": "It won't take long for W8." + }, + { + "text": "OK." + }, + { + "text": "So the first column is going to be 8 1's." + }, + { + "text": "And what's the next column going to be?" + }, + { + "text": "4 1's and 4 minus 1's, like so." + }, + { + "text": "So 4 1's and 4 minus 1's." + }, + { + "text": "OK, and now the next column." + }, + { + "text": "2 1's, 2 minus 1's, and 0's." + }, + { + "text": "Right?" + }, + { + "text": "1, 1, minus 1, minus 1, and 0." + }, + { + "text": "And the fourth will be 0's and 2 1's and 2 minus 1's." + }, + { + "text": "We've got half a matrix now." + }, + { + "text": "Now, if we just tell me the fifth, what do you think?" + }, + { + "text": "What do I put in the fifth one?" + }, + { + "text": "So again, it's going to squeeze down and rescale." + }, + { + "text": "And what's the fifth column up here that's going to be 1's and minus 1's and 0's now?" + }, + { + "text": "So it's not Adamard." + }, + { + "text": "It's Haar." + }, + { + "text": "And what shall I put?" + }, + { + "text": "1, 1." + }, + { + "text": "Shall I start with 1, 1?" + }, + { + "text": "Oh, 1 minus?" + }, + { + "text": "Yeah." + }, + { + "text": "And then all 0's?" + }, + { + "text": "Oh, yeah, thanks." + }, + { + "text": "Perfect." + }, + { + "text": "1 minus 1, and then all 0's." + }, + { + "text": "And then the next three columns will have the 1 minus 1 here, and the 1 minus 1 here, and the 1 minus 1 here." + }, + { + "text": "And otherwise, all 0's." + }, + { + "text": "So you see the pattern." + }, + { + "text": "It's scaling at every step." + }, + { + "text": "So that matrix has the advantage of being quite sparse." + }, + { + "text": "This, in my mind, is a 4, 1's." + }, + { + "text": "That's involved with taking the average." + }, + { + "text": "Then this guy is like taking the differences, differences between those and those." + }, + { + "text": "And then this is like taking the difference at a smaller scale, and that also at a smaller scale." + }, + { + "text": "So that's what we keep doing." + }, + { + "text": "Yeah." + }, + { + "text": "Yeah." + }, + { + "text": "So that's wavelets." + }, + { + "text": "It looks so simple, right?" + }, + { + "text": "But just a one-minute history of wavelets, so Haar invented this in like 1910." + }, + { + "text": "I mean, along, forever." + }, + { + "text": "But then you wanted wavelets that were a little better, and not just 1's and minus 1's and 0's." + }, + { + "text": "And that took a lot of thinking." + }, + { + "text": "A lot of people were searching for it." + }, + { + "text": "And Ingrid Dovashy, so I'll just put her name, became famous for finding them." + }, + { + "text": "So in about 1988, she found a whole lot of families of wavelets." + }, + { + "text": "And when I say wavelets, she found a whole lot of orthogonal matrices that had good properties." + }, + { + "text": "So that's the wavelet picture." + }, + { + "text": "Now, to close today and to connect with the next lecture on eigenvalues, eigenvectors, positive definite matrices, we're really getting to the heart of things here." + }, + { + "text": "Let me follow through on that idea." + }, + { + "text": "Idea, so the eigenvectors of a symmetric matrix, but also of an orthogonal matrix are orthogonal." + }, + { + "text": "And that is really where people, where you can invent, because you don't have to work hard." + }, + { + "text": "You just find a symmetric matrix." + }, + { + "text": "Its eigenvectors are automatically orthogonal." + }, + { + "text": "That doesn't mean they're great for use, but some of them are really important." + }, + { + "text": "And maybe the most important of all is the Fourier." + }, + { + "text": "So you probably have seen Fourier series, sines and cosines." + }, + { + "text": "Those guys are orthogonal functions." + }, + { + "text": "But the discrete Fourier series is what everybody computes, and those are orthogonal vectors." + }, + { + "text": "So the orthogonal vectors that go into the discrete Fourier transform, and then they're done at high speed by the fast Fourier transform, those are eigenvectors of Q, eigenvectors of the right Q." + }, + { + "text": "So let me just tell you the right Q, whose eigenvectors." + }, + { + "text": "So here we go." + }, + { + "text": "Eigenvectors of Q." + }, + { + "text": "You will just be amazed by how simple this matrix is." + }, + { + "text": "It's just that matrix." + }, + { + "text": "It's called a permutation matrix." + }, + { + "text": "Those are the four Fourier discrete." + }, + { + "text": "Let me put the word discrete up here, transform." + }, + { + "text": "So I really meant to put discrete Fourier transform." + }, + { + "text": "The eigenvectors of that matrix, first of all, they are orthogonal." + }, + { + "text": "And then second and more important, they're tremendously useful." + }, + { + "text": "They're the heart of signal processing." + }, + { + "text": "In signal processing, they just take the discrete Fourier transform of a vector before they even look at it." + }, + { + "text": "I mean, that's the way to see it, is split it into its frequencies." + }, + { + "text": "And that's what the eigenvectors of this will do." + }, + { + "text": "So we're going to see the discrete Fourier transform." + }, + { + "text": "But my point here is to know that they're orthogonal just comes out of this fact that the eigenvectors are orthogonal for any Q." + }, + { + "text": "And that is certainly a Q." + }, + { + "text": "Everybody can see that those columns are orthogonal." + }, + { + "text": "The columns of a permutation matrix, right?" + }, + { + "text": "You've taken the columns of the identity, which are totally orthogonal, and you just put them in a different order." + }, + { + "text": "So a permutation matrix is a reordering of the identity matrix." + }, + { + "text": "It's got to be a Q." + }, + { + "text": "And therefore, its eigenvectors are orthogonal." + }, + { + "text": "And they're just the winners." + }, + { + "text": "I mean, the matrix of the Fourier matrix with those four eigenvectors in it, I'll show you now." + }, + { + "text": "So this is really we're finishing today by leading into Wednesday, eigenvectors and eigenvalues." + }, + { + "text": "And we happen to be doing eigenvectors and eigenvalues of a Q, not today of an S. Most of the time, it's a symmetric matrix whose eigenvectors we take." + }, + { + "text": "But here, that happens to be a Q." + }, + { + "text": "Can I show you the eigenvectors, the four eigenvectors of that?" + }, + { + "text": "Now, oh, the complex number I is going to come in." + }, + { + "text": "You have to let it in here." + }, + { + "text": "Sorry." + }, + { + "text": "If S is a real symmetric matrix, its eigenvectors are real." + }, + { + "text": "But if Q is a orthogonal matrix, its eigenvectors, even though you couldn't ask for a more real matrix than that, but its eigenvectors are at least, yeah, the good way are complex numbers." + }, + { + "text": "So can I show you the eigenvectors of?" + }, + { + "text": "OK." + }, + { + "text": "So again, overall, the point today is to see orthogonal matrices." + }, + { + "text": "So I'll just repeat now while I can." + }, + { + "text": "Rotations here, reflections, wavelets, the householder idea of reflections of large matrices that have this form I minus 2 UU transpose are orthogonal." + }, + { + "text": "And now we're going to see the big guys, the eigenvectors of Q." + }, + { + "text": "Right." + }, + { + "text": "Yes?" + }, + { + "text": "AUDIENCE 2." + }, + { + "text": "The wavelets, do you want to rescale the column?" + }, + { + "text": "GILBERT STRANG, M.D." + }, + { + "text": "Oh, yeah." + }, + { + "text": "We don't have orthonormal." + }, + { + "text": "That's right." + }, + { + "text": "We don't have orthonormal." + }, + { + "text": "I better divide by square root of 8." + }, + { + "text": "Right." + }, + { + "text": "AUDIENCE 3." + }, + { + "text": "There's different forms for different." + }, + { + "text": "GILBERT STRANG, M.D." + }, + { + "text": "Oh, yes." + }, + { + "text": "Oh, you're right." + }, + { + "text": "Sorry, I thought I'd get away with that, but I didn't." + }, + { + "text": "Yeah." + }, + { + "text": "So these guys are square roots of 8." + }, + { + "text": "So are these." + }, + { + "text": "But these guys are square roots of 4." + }, + { + "text": "And these guys are square roots of 2." + }, + { + "text": "Thank you." + }, + { + "text": "Absolutely right." + }, + { + "text": "Absolutely." + }, + { + "text": "Yeah." + }, + { + "text": "OK." + }, + { + "text": "So what are the eigenvectors of a permutation?" + }, + { + "text": "This is going to be nice to see." + }, + { + "text": "And I'll use the matrix F for the eigenvector matrix of that Q up there." + }, + { + "text": "And F is for Fourier." + }, + { + "text": "And it'd be the 4 by 4 Fourier matrix." + }, + { + "text": "OK. What are the eigenvectors of Q?" + }, + { + "text": "OK." + }, + { + "text": "So Q is a permutation." + }, + { + "text": "So I'm going to ask you for one eigenvector of every permutation matrix." + }, + { + "text": "What vector can you tell me that actually the eigenvalue will be 1?" + }, + { + "text": "What vector can you tell me where if I permute it, I don't change it?" + }, + { + "text": "1, 1, 1, 1." + }, + { + "text": "It's like it's everywhere here." + }, + { + "text": "1, 1, 1, 1." + }, + { + "text": "So that's the zero frequency Fourier vector, the constant vector, all 1's." + }, + { + "text": "Everybody sees that if I multiply by Q, it doesn't change." + }, + { + "text": "OK. Now the next one, I'll show you the 4 now." + }, + { + "text": "The next one will be 1, i, i squared, and i cubed." + }, + { + "text": "Of course, i squared, I don't know how many course 6j people are in this audience." + }, + { + "text": "But this is a math building, we paid for it." + }, + { + "text": "It's 2, 190, and it's i in this room." + }, + { + "text": "Yeah." + }, + { + "text": "So yeah." + }, + { + "text": "Anyway, i is the first letter in what?" + }, + { + "text": "Imaginary, thank you." + }, + { + "text": "The first letter in imaginary." + }, + { + "text": "You can't say jimaginary." + }, + { + "text": "So that's it." + }, + { + "text": "OK. And then the next one is 1, i squared, i fourth, i sixth." + }, + { + "text": "And the next one is 1, i cubed, i sixth, and i ninth." + }, + { + "text": "Isn't that just beautiful?" + }, + { + "text": "And you could show that every one of those four columns, if you multiply them by Q, you would get the eigenvalues." + }, + { + "text": "And you would see that it's an eigenvector." + }, + { + "text": "And this is just sort of like a discrete Fourier stuff." + }, + { + "text": "And instead of e to the ix, e to the 2ix, e to the 3ix, and so on, we just have vectors." + }, + { + "text": "So those are the four eigenvectors of that permutation." + }, + { + "text": "And those are orthogonal." + }, + { + "text": "Could I just check that?" + }, + { + "text": "How do you know that this first column and the second?" + }, + { + "text": "Well, I should really say zeroth column and first column if I'm talking frequencies." + }, + { + "text": "Do you see that that's orthogonal to that?" + }, + { + "text": "Well, y is 1 plus i plus i squared plus i cubed equals 0." + }, + { + "text": "That's the dot product." + }, + { + "text": "This is column 1 dot column 2." + }, + { + "text": "Yeah." + }, + { + "text": "You're right." + }, + { + "text": "This happens to come out 0." + }, + { + "text": "Is that right?" + }, + { + "text": "Yes, that will come out 0." + }, + { + "text": "That'll come out 0." + }, + { + "text": "But somebody mentioned that this isn't right." + }, + { + "text": "It's true that that came out 0." + }, + { + "text": "But when I have imaginary numbers anywhere around, this isn't the correct dot product to test orthogonal." + }, + { + "text": "If I have complex vectors, if I have complex numbers, complex vectors, I should test column 1 conjugate dotted with column 2." + }, + { + "text": "Column i conjugate." + }, + { + "text": "Well, let me take column." + }, + { + "text": "Let's see." + }, + { + "text": "Which one shall I take?" + }, + { + "text": "Maybe that guy and that guy." + }, + { + "text": "Many of them you luck out here." + }, + { + "text": "But really, I should be taking the conjugate." + }, + { + "text": "So these 1's." + }, + { + "text": "But the thing is the complex conjugate of 1 is 1." + }, + { + "text": "So that was OK." + }, + { + "text": "But in general, if I wanted to take column 2 dotted with column, I don't know, maybe 4 would be a little dodgy." + }, + { + "text": "Yeah, look what happens." + }, + { + "text": "Take that column and that column." + }, + { + "text": "Take their dot product." + }, + { + "text": "Do it the wrong way." + }, + { + "text": "So what's the wrong way?" + }, + { + "text": "Forget about the complex conjugate and just do it the usual way." + }, + { + "text": "So 1 times 1 is 1. i times i cube is?" + }, + { + "text": "1. i squared times i6 is?" + }, + { + "text": "1." + }, + { + "text": "I'm getting all 1's." + }, + { + "text": "I'm not getting orthogonality there." + }, + { + "text": "And that's because I forgot that I should take the complex conjugate." + }, + { + "text": "Well, of these guys, 1." + }, + { + "text": "I should take minus i." + }, + { + "text": "Minus i squared." + }, + { + "text": "Well, that's real, so it's OK." + }, + { + "text": "Minus there." + }, + { + "text": "So minus i squared is still minus 1." + }, + { + "text": "So now if I do it, it comes out 0." + }, + { + "text": "So let me repeat again." + }, + { + "text": "Let me just make this statement." + }, + { + "text": "If Q transpose Q is i, and Qx is lambda x, and Qy is a different eigenvalue y. OK." + }, + { + "text": "So I'm setting up the main fact that in the last minute, I'm just going to write down." + }, + { + "text": "So I have an orthogonal matrix." + }, + { + "text": "I have an eigenvector with eigenvalue lambda." + }, + { + "text": "I have another eigenvector with a different eigenvalue mu." + }, + { + "text": "Then the claim is that, what is the claim about the eigenvectors?" + }, + { + "text": "So here has one eigen." + }, + { + "text": "This has an eigenvalue." + }, + { + "text": "This has a different eigenvalue." + }, + { + "text": "I need them to be different to really know that the x's and the y's can't be the same." + }, + { + "text": "So what is it that I want to show?" + }, + { + "text": "AUDIENCE 1." + }, + { + "text": "Conjugated x of y minus 1." + }, + { + "text": "Yes." + }, + { + "text": "That x, and I have to remember to do that, x transpose y is 0." + }, + { + "text": "That's orthogonality." + }, + { + "text": "That's orthogonality for complex vectors." + }, + { + "text": "I have to remember to change every i to a minus i in one of the vectors." + }, + { + "text": "And I can prove that fact by playing with these, by playing with starting from here, I can get to that." + }, + { + "text": "OK, that's it." + }, + { + "text": "We've done a lot today, a lot of stuff about orthogonal matrices, important ones and the sources of important ones, eigenvectors." + }, + { + "text": "And so it'll be eigenvectors on Wednesday." + } +] \ No newline at end of file diff --git a/sight/sources/annotated/XsYXACeIklU.json b/sight/sources/annotated/XsYXACeIklU.json new file mode 100644 index 0000000000000000000000000000000000000000..1a51f1d102a77a4dc80a04161fc25da9029dade8 --- /dev/null +++ b/sight/sources/annotated/XsYXACeIklU.json @@ -0,0 +1,1523 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "JOHN TSITSIKLIS: Today we're going to finish our discussion of the Poisson process." + }, + { + "text": "We're going to see a few of its properties, do a few interesting problems, some more interesting than others." + }, + { + "text": "So go through a few examples and then we're going to talk about some quite strange things that happen with the Poisson process." + }, + { + "text": "So the first thing is to remember what the Poisson processes is." + }, + { + "text": "It's a model, let's say, of arrivals of customers that are, in some sense, quote unquote, completely random, that is a customer can arrive at any point in time." + }, + { + "text": "All points in time are equally likely." + }, + { + "text": "And different points in time are sort of independent of other points in time." + }, + { + "text": "So the fact that I got an arrival now doesn't tell me anything about whether there's going to be an arrival at some other time." + }, + { + "text": "In some sense, it's a continuous time version of the Bernoulli process." + }, + { + "text": "So the best way to think about the Poisson process is that we divide time into extremely tiny slots." + }, + { + "text": "And in each time slot, there's an independent possibility of having an arrival." + }, + { + "text": "Different time slots are independent of each other." + }, + { + "text": "On the other hand, when the slot is tiny, the probability for obtaining an arrival during that tiny slot is itself going to be tiny." + }, + { + "text": "So we capture these properties into a formal definition what the Poisson process is." + }, + { + "text": "We have a probability mass function for the number of arrivals, k, during an interval of a given length." + }, + { + "text": "So this is the sort of basic description of the distribution of the number of arrivals." + }, + { + "text": "So tau is fixed." + }, + { + "text": "And k is the parameter." + }, + { + "text": "So when we add over all k's, the sum of these probabilities has to be equal to 1." + }, + { + "text": "There's a time homogeneity assumption, which is hidden in this, namely, the only thing that matters is the duration of the time interval, not where the time interval sits on the real axis." + }, + { + "text": "Then we have an independence assumption." + }, + { + "text": "Intervals that are disjoint are statistically independent from each other." + }, + { + "text": "So any information you give me about arrivals during this time interval doesn't change my beliefs about what's going to happen during another time interval." + }, + { + "text": "So this is a generalization of the idea that we had in Bernoulli processes that different time slots are independent of each other." + }, + { + "text": "And then to specify this function, the distribution of the number of arrivals, we sort of go in stages." + }, + { + "text": "We first specify this function for the case where the time interval is very small." + }, + { + "text": "And I'm telling you what those probabilities will be." + }, + { + "text": "And based on these then, we do some calculations and to find the formula for the distribution of the number of arrivals for intervals of a general duration." + }, + { + "text": "So for a small duration, delta, the probability of obtaining 1 arrival is lambda delta." + }, + { + "text": "The remaining probability is assigned to the event that we get to no arrivals during that interval." + }, + { + "text": "The probability of obtaining more than 1 arrival in a tiny interval is essentially 0." + }, + { + "text": "And when we say essentially, it's means modular, terms that of order delta squared." + }, + { + "text": "And when delta is very small, anything which is delta squared can be ignored." + }, + { + "text": "So up to delta squared terms, that's what happened during a little interval." + }, + { + "text": "Now if we know the probability distribution for the number of arrivals in a little interval." + }, + { + "text": "We can use this to get the distribution for the number of arrivals over several intervals." + }, + { + "text": "How do we do that?" + }, + { + "text": "The big interval is composed of many little intervals." + }, + { + "text": "Each little interval is independent from any other little interval, so is it is as if we have a sequence of Bernoulli trials." + }, + { + "text": "Each Bernoulli trial is associated with a little interval and has a small probability of obtaining a success or an arrival during that mini-slot." + }, + { + "text": "On the other hand, when delta is small, and you take a big interval and chop it up, you get a large number of little intervals." + }, + { + "text": "So what we essentially have here is a Bernoulli process, in which is the number of trials is huge but the probability of success during any given trial is tiny." + }, + { + "text": "The average number of trials ends up being proportional to the length of the interval." + }, + { + "text": "If you have twice as large an interval, it's as if you're having twice as many over these mini-trials, so the expected number of arrivals will increase proportionately." + }, + { + "text": "There's also this parameter lambda, which we interpret as expected number of arrivals per unit time." + }, + { + "text": "And it comes in those probabilities here." + }, + { + "text": "When you double lambda, this means that a little interval is twice as likely to get an arrival." + }, + { + "text": "So you would expect to get twice as many arrivals as well." + }, + { + "text": "That's why the expected number of arrivals during an interval of length tau also scales proportional to this parameter lambda." + }, + { + "text": "Somewhat unexpectedly, it turns out that the variance of the number of arrivals is also the same as the mean." + }, + { + "text": "This is a peculiarity that happens in the Poisson process." + }, + { + "text": "So this is one way of thinking about Poisson process, in terms of little intervals, each one of which has a tiny probability of success." + }, + { + "text": "And we think of the distribution associated with that process as being described by this particular PMF." + }, + { + "text": "So this is the PMF for the number of arrivals during an interval of a fixed duration, tau." + }, + { + "text": "It's a PMF that extends all over the entire range of non-negative integers." + }, + { + "text": "So the number of arrivals you can get during an interval for certain length can be anything." + }, + { + "text": "You can get as many arrivals as you want." + }, + { + "text": "Of course the probability of getting a zillion arrivals is going to be tiny." + }, + { + "text": "But in principle, this is possible." + }, + { + "text": "And that's because an interval, even if it's a fixed length, consists of an infinite number of mini-slots in some sense." + }, + { + "text": "You can divide, chop it up, into as many mini-slots as you want." + }, + { + "text": "So in principle, it's possible that every mini-slot gets an arrival." + }, + { + "text": "In principle, it's possible to get an arbitrarily large number of arrivals." + }, + { + "text": "So this particular formula here is not very intuitive when you look at it." + }, + { + "text": "But it's a legitimate PMF." + }, + { + "text": "And it's called the Poisson PMF." + }, + { + "text": "It's the PMF that describes the number of arrivals." + }, + { + "text": "So that's one way of thinking about the Poisson process, where the basic object of interest would be this PMF and you try to work with it." + }, + { + "text": "There's another way of thinking about what happens in the Poisson process." + }, + { + "text": "And this has to do with letting things evolve in time." + }, + { + "text": "You start at time 0." + }, + { + "text": "There's going to be a time at which the first arrival occurs, and call that time T1." + }, + { + "text": "This time turns out to have an exponential distribution with parameter lambda." + }, + { + "text": "Once you get an arrival, it's as if the process starts fresh." + }, + { + "text": "The best way to understand why this is the case is by thinking in terms of the analogy with the Bernoulli process." + }, + { + "text": "If you believe that statement for the Bernoulli process, since this is a limiting case, it should also be true." + }, + { + "text": "So starting from this time, we're going to wait a random amount of time until we get the second arrival This random amount of time, let's call it T2." + }, + { + "text": "This time, T2 is also going to have an exponential distribution with the same parameter, lambda." + }, + { + "text": "And these two are going to be independent of each other." + }, + { + "text": "OK?" + }, + { + "text": "So the Poisson process has all the same memorylessness properties that the Bernoulli process has." + }, + { + "text": "What's another way of thinking of this property?" + }, + { + "text": "So think of a process where you have a light bulb." + }, + { + "text": "The time at the light bulb burns out, you can model it by an exponential random variable." + }, + { + "text": "And suppose that they tell you that so far, we're are sitting at some time, T. And I tell you that the light bulb has not yet burned out." + }, + { + "text": "What does this tell you about the future of the light bulb?" + }, + { + "text": "Is the fact that they didn't burn out, so far, is it good news or is it bad news?" + }, + { + "text": "Would you rather keep this light bulb that has worked for t times steps and is still OK?" + }, + { + "text": "Or would you rather use a new light bulb that starts new at that point in time?" + }, + { + "text": "Because of the memorylessness property, the past of that light bulb doesn't matter." + }, + { + "text": "So the future of this light bulb is statistically the same as the future of a new light bulb." + }, + { + "text": "For both of them, the time until they burn out is going to be described an exponential distribution." + }, + { + "text": "So one way that people described the situation is to say that used is exactly as good as a new." + }, + { + "text": "So a used on is no worse than a new one." + }, + { + "text": "A used one is no better than a new one." + }, + { + "text": "So a used light bulb that hasn't yet burnt out is exactly as good as a new light bulb." + }, + { + "text": "So that's another way of thinking about the memorylessness that we have in the Poisson process." + }, + { + "text": "Back to this picture." + }, + { + "text": "The time until the second arrival is the sum of two independent exponential random variables." + }, + { + "text": "So, in principle, you can use the convolution formula to find the distribution of T1 plus T2, and that would be what we call Y2, the time until the second arrival." + }, + { + "text": "But there's also a direct way of obtaining to the distribution of Y2, and this is the calculation that we did last time on the blackboard." + }, + { + "text": "And actually, we did it more generally." + }, + { + "text": "We found the time until the case arrival occurs." + }, + { + "text": "It has a closed form formula, which is called the Erlang distribution with k degrees of freedom." + }, + { + "text": "So let's see what's going on here." + }, + { + "text": "It's a distribution Of what kind?" + }, + { + "text": "It's a continuous distribution." + }, + { + "text": "It's a probability density function." + }, + { + "text": "This is because the time is a continuous random variable." + }, + { + "text": "Time is continuous." + }, + { + "text": "Arrivals can happen at any time." + }, + { + "text": "So we're talking about the PDF." + }, + { + "text": "This k is just the parameter of the distribution." + }, + { + "text": "We're talking about the k-th arrival, so k is a fixed number." + }, + { + "text": "Lambda is another parameter of the distribution, which is the arrival rate So it's a PDF over the Y's, whereas lambda and k are parameters of the distribution." + }, + { + "text": "OK." + }, + { + "text": "So this was what we knew from last time." + }, + { + "text": "Just to get some practice, let us do a problem that's not too difficult, but just to see how we use the various formulas that we have." + }, + { + "text": "So Poisson was a mathematician, but Poisson also means fish in French." + }, + { + "text": "So Poisson goes fishing." + }, + { + "text": "And let's assume that fish are caught according to a Poisson process." + }, + { + "text": "That's not too bad an assumption." + }, + { + "text": "At any given point in time, you have a little probability that a fish would be caught." + }, + { + "text": "And whether you catch one now is sort of independent about whether at some later time a fish will be caught or not." + }, + { + "text": "So let's just make this assumption." + }, + { + "text": "And suppose that the rules of the game are that you-- Fish are being called it the certain rate of 0.6 per hour." + }, + { + "text": "You fish for 2 hours, no matter what." + }, + { + "text": "And then there are two possibilities." + }, + { + "text": "If I have caught a fish, I stop and go home." + }, + { + "text": "So if some fish have been caught, so there's at least 1 arrival during this interval, I go home." + }, + { + "text": "Or if nothing has being caught, I continue fishing until I catch something." + }, + { + "text": "And then I go home." + }, + { + "text": "So that's the description of what is going to happen." + }, + { + "text": "And now let's starts asking questions of all sorts." + }, + { + "text": "What is the probability that I'm going to be fishing for more than 2 hours?" + }, + { + "text": "I will be fishing for more than 2 hours, if and only if no fish were caught during those 2 hours, in which case, I will have to continue." + }, + { + "text": "Therefore, this is just this quantity." + }, + { + "text": "The probability of catching 2 fish in-- of catching 0 fish in the next 2 hours, and according to the formula that we have, this is going to be e to the minus lambda times how much time we have." + }, + { + "text": "There's another way of thinking about this." + }, + { + "text": "The probability that I fish for more than 2 hours is the probability that the first catch happens after time 2, which would be the integral from 2 to infinity of the density of the first arrival time." + }, + { + "text": "And that density is an exponential." + }, + { + "text": "So you do the integral of an exponential, and, of course, you would get the same answer." + }, + { + "text": "OK. That's easy." + }, + { + "text": "So what's the probability of fishing for more than 2 but less than 5 hours?" + }, + { + "text": "What does it take for this to happen?" + }, + { + "text": "For this to happen, we need to catch 0 fish from time 0 to 2 and catch the first fish sometime between 2 and 5." + }, + { + "text": "So if you-- one way of thinking about what's happening here might be to say that there's a Poisson process that keeps going on forever." + }, + { + "text": "But as soon as I catch the first fish, instead of continuing fishing and obtaining those other fish I just go home right now." + }, + { + "text": "Now the fact that I go home before time 5 means that, if I were to stay until time 5, I would have caught at least 1 fish." + }, + { + "text": "I might have caught more than 1." + }, + { + "text": "So the event of interest here is that the first catch happens between times 2 and 5." + }, + { + "text": "So one way of calculating this quantity would be-- Its the probability that the first catch happens between times 2 and 5." + }, + { + "text": "Another way to deal with it is to say, this is the probability that I caught 0 fish in the first 2 hours and then the probability that I catch at least 1 fish during the next 3 hours." + }, + { + "text": "This." + }, + { + "text": "What is this?" + }, + { + "text": "The probability of 0 fish in the next 3 hours is the probability of 0 fish during this time." + }, + { + "text": "1 minus this is the probability of catching at least 1 fish, of having at least 1 arrival, between times 2 and 5." + }, + { + "text": "If there's at least 1 arrival between times 2 and 5, then I would have gone home by time 5." + }, + { + "text": "So both of these, if you plug-in numbers and all that, of course, are going to give you the same answer." + }, + { + "text": "Now next, what's the probability that I catch at least 2 fish?" + }, + { + "text": "In which scenario are we?" + }, + { + "text": "Under this scenario, I go home when I catch my first fish." + }, + { + "text": "So in order to catch at least 2 fish, it must be in this case." + }, + { + "text": "So this is the same as the event that I catch at least 2 fish during the first 2 time steps." + }, + { + "text": "So it's going to be the probability from 2 to infinity, the probability that I catch 2 fish, or that I catch 3 fish, or I catch more than that." + }, + { + "text": "So it's this quantity." + }, + { + "text": "k is the number of fish that I catch." + }, + { + "text": "At least 2, so k goes from 2 to infinity." + }, + { + "text": "These are the probabilities of catching a number k of fish during this interval." + }, + { + "text": "And if you want a simpler form without an infinite sum, this would be 1 minus the probability of catching 0 fish, minus the probability of catching 1 fish, during a time interval of length 2." + }, + { + "text": "Another way to think of it." + }, + { + "text": "I'm going to catch 2 fish, at least 2 fish, if and only if the second fish caught in this process happens before time 2." + }, + { + "text": "So that's another way of thinking about the same event." + }, + { + "text": "So it's going to be the probability that the random variable Y2, the arrival time over the second fish, is less than or equal to 2." + }, + { + "text": "OK." + }, + { + "text": "The next one is a little trickier." + }, + { + "text": "Here we need to do a little bit of divide and conquer." + }, + { + "text": "Overall, in this expedition, what the expected number of fish to be caught?" + }, + { + "text": "One way to think about it is to try to use the total expectations theorem." + }, + { + "text": "And think of expected number of fish, given this scenario, or expected number of fish, given this scenario." + }, + { + "text": "That's a little more complicated than the way I'm going to do it." + }, + { + "text": "The way I'm going to do is to think as follows-- Expected number of fish is the expected number of fish caught between times 0 and 2 plus expected number of fish caught after time 2." + }, + { + "text": "So what's the expected number caught between time 0 and 2?" + }, + { + "text": "This is lambda t. So lambda is 0.6 times 2." + }, + { + "text": "This is the expected number of fish that are caught between times 0 and 2." + }, + { + "text": "Now let's think about the expected number of fish caught afterwards." + }, + { + "text": "How many fish are being caught afterwards?" + }, + { + "text": "Well it depends on the scenario." + }, + { + "text": "If we're in this scenario, we've gone home and we catch 0." + }, + { + "text": "If we're in this scenario, then we continue fishing until we catch one." + }, + { + "text": "So the expected number of fish to be caught after time 2 is going to be the probability of this scenario times 1." + }, + { + "text": "And the probability of that scenario is the probability that they call it's 0 fish during the first 2 time steps times 1, which is the number of fish I'm going to catch if I continue." + }, + { + "text": "The expected total fishing time we can calculate exactly the same way." + }, + { + "text": "I'm jumping to the last one." + }, + { + "text": "My total fishing time has a period of 2 time steps." + }, + { + "text": "I'm going to fish for 2 time steps no matter what." + }, + { + "text": "And then if I caught 0 fish, which happens with this probability, my expected time is going to be the expected time from here onwards, which is the expected value of this geometric random variable with parameter lambda." + }, + { + "text": "So the expected time is 1 over lambda." + }, + { + "text": "And in our case this, is 1/0.6." + }, + { + "text": "Finally, if I tell you that I have been fishing for 4 hours and nothing has been caught so far, how much do you expect this quantity to be?" + }, + { + "text": "Here is the story that, again, that for the Poisson process used is as good as new." + }, + { + "text": "The process does not have any memory." + }, + { + "text": "Given what happens in the past doesn't matter for the future." + }, + { + "text": "It's as if the process starts new at this point in time." + }, + { + "text": "So this one is going to be, again, the same exponentially distributed random variable with the same parameter lambda." + }, + { + "text": "So expected time until an arrival comes is an exponential distribut -- has an exponential distribution with parameter lambda, no matter what has happened in the past." + }, + { + "text": "Starting from now and looking into the future, it's as if the process has just started." + }, + { + "text": "So it's going to be 1 over lambda, which is 1/0.6." + }, + { + "text": "OK. Now our next example is going to be a little more complicated or subtle." + }, + { + "text": "But before we get to the example, let's refresh our memory about what we discussed last time about merging Poisson independent Poisson processes." + }, + { + "text": "Instead of drawing the picture that way, another way we could draw it could be this." + }, + { + "text": "We have a Poisson process with rate lambda1, and a Poisson process with rate lambda2." + }, + { + "text": "They have, each one of these, have their arrivals." + }, + { + "text": "And then we form the merged process." + }, + { + "text": "And the merged process records an arrival whenever there's an arrival in either of the two processes." + }, + { + "text": "This process in that process are assumed to be independent of each other." + }, + { + "text": "Now different times in this process and that process are independent of each other." + }, + { + "text": "So what happens in these two time intervals is independent from what happens in these two time intervals." + }, + { + "text": "These two time intervals to determine what happens here." + }, + { + "text": "These two time intervals determine what happens there." + }, + { + "text": "So because these are independent from these, this means that this is also independent from that." + }, + { + "text": "So the independence assumption is satisfied for the merged process." + }, + { + "text": "And the merged process turns out to be a Poisson process." + }, + { + "text": "And if you want to find the arrival rate for that process, you argue as follows." + }, + { + "text": "During a little interval of length delta, we have probability lambda1 delta of having an arrival in this process." + }, + { + "text": "We have probability lambda2 delta of an arrival in this process, plus second order terms in delta, which we're ignoring." + }, + { + "text": "And then you do the calculation and you find that in this process, you're going to have an arrival probability, which is lambda1 plus lambda2, again ignoring second order in delta-- terms that are second order in delta." + }, + { + "text": "So the merged process is a Poisson process whose arrival rate is the sum of the arrival rates of the individual processes." + }, + { + "text": "And the calculation we did at the end of the last lecture-- If I tell you that the new arrival happened here, where did that arrival come from?" + }, + { + "text": "Did it come from here or from there?" + }, + { + "text": "If the lambda1 is equal to lambda2, then by symmetry you would say that it's equally likely to have come from here or to come from there." + }, + { + "text": "But if this lambda is much bigger than that lambda, the fact that they saw an arrival is more likely to have come from there." + }, + { + "text": "And the formula that captures this is the following." + }, + { + "text": "This is the probability that my arrival has come from this particular stream rather than that particular stream." + }, + { + "text": "So when an arrival comes and you ask, what is the origin of that arrival?" + }, + { + "text": "It's as if I'm flipping a coin with these odds." + }, + { + "text": "And depending on outcome of that coin, I'm going to tell you came from there or it came from there." + }, + { + "text": "So the origin of an arrival is either this stream or that stream." + }, + { + "text": "And this is the probability that the origin of the arrival is that one." + }, + { + "text": "Now if we look at 2 different arrivals, and we ask about their origins-- So let's think about the origin of this arrival and compare it with the origin that arrival." + }, + { + "text": "The origin of this arrival is random." + }, + { + "text": "It could be right be either this or that." + }, + { + "text": "And this is the relevant probability." + }, + { + "text": "The origin of that arrival is random." + }, + { + "text": "It could be either here or is there, and again, with the same relevant probability." + }, + { + "text": "Question." + }, + { + "text": "The origin of this arrival, is it dependent or independent from the origin that arrival?" + }, + { + "text": "And here's how the argument goes." + }, + { + "text": "Separate times are independent." + }, + { + "text": "Whatever has happened in the process during this set of times is independent from whatever happened in the process during that set of times." + }, + { + "text": "Because different times have nothing to do with each other, the origin of this, of an arrival here, has nothing to do with the origin of an arrival there." + }, + { + "text": "So the origins of different arrivals are also independent random variables." + }, + { + "text": "So if I tell you that-- yeah." + }, + { + "text": "OK." + }, + { + "text": "So it as if that each time that you have an arrival in the merge process, it's as if you're flipping a coin to determine where did that arrival came from and these coins are independent of each other." + }, + { + "text": "OK. OK. Now we're going to use this-- what we know about merged processes to solve the problem that would be harder to do, if you were not using ideas from Poisson processes." + }, + { + "text": "So the formulation of the problem has nothing to do with the Poisson process." + }, + { + "text": "The formulation is the following." + }, + { + "text": "We have 3 light-bulbs." + }, + { + "text": "And each light bulb is independent and is going to die out at the time that's exponentially distributed." + }, + { + "text": "So 3 light bulbs." + }, + { + "text": "They start their lives and then at some point they die or burn out." + }, + { + "text": "So let's think of this as X, this as Y, and this as Z." + }, + { + "text": "And we're interested in the time until the last light-bulb burns out." + }, + { + "text": "So we're interested in the maximum of the 3 random variables, X, Y, and Z." + }, + { + "text": "And in particular, we want to find the expected value of this maximum." + }, + { + "text": "OK." + }, + { + "text": "So you can do derived distribution, use the expected value rule, anything you want." + }, + { + "text": "You can get this answer using the tools that you already have in your hands." + }, + { + "text": "But now let us see how we can connect to this picture with a Poisson picture and come up with the answer in a very simple way." + }, + { + "text": "What is an exponential random variable?" + }, + { + "text": "An exponential random variable is the first act in the long play that involves a whole Poisson process." + }, + { + "text": "So an exponential random variable is the first act of a Poisson movie." + }, + { + "text": "Same thing here." + }, + { + "text": "You can think of this random variable as being part of some Poisson process that has been running." + }, + { + "text": "So it's part of this bigger picture." + }, + { + "text": "We're still interested in the maximum of the 3." + }, + { + "text": "The other arrivals are not going to affect our answers." + }, + { + "text": "It's just, conceptually speaking, we can think of the exponential random variable as being embedded in a bigger Poisson picture." + }, + { + "text": "So we have 3 Poisson process that are running in parallel." + }, + { + "text": "Let us split the expected time until the last burnout into pieces, which is time until the first burnout, time from the first until the second, and time from the second until the third." + }, + { + "text": "And find the expected values of each one of these pieces." + }, + { + "text": "What can we say about the expected value of this?" + }, + { + "text": "This is the first arrival out of all of these 3 Poisson processes." + }, + { + "text": "It's the first event that happens when you look at all of these processes simultaneously." + }, + { + "text": "So 3 Poisson processes running in parallel." + }, + { + "text": "We're interested in the time until one of them, any one of them, gets in arrival." + }, + { + "text": "Rephrase." + }, + { + "text": "We merged the 3 Poisson processes, and we ask for the time until we observe an arrival in the merged process." + }, + { + "text": "When 1 of the 3 gets an arrival for the first time, the merged process gets its first arrival." + }, + { + "text": "So what's the expected value of this time until the first burnout?" + }, + { + "text": "It's going to be the expected value of a Poisson random variable." + }, + { + "text": "So the first burnout is going to have an expected value, which is-- OK." + }, + { + "text": "It's a Poisson process." + }, + { + "text": "The merged process of the 3 has a collective arrival rate, which is 3 times lambda." + }, + { + "text": "So this is the parameter over the exponential distribution that describes the time until the first arrival in the merged process." + }, + { + "text": "And the expected value of this random variable is 1 over that." + }, + { + "text": "When you have an exponential random variable with parameter lambda, the expected value of that random variable is 1 over lambda." + }, + { + "text": "Here we're talking about the first arrival time in a process with rate 3 lambda." + }, + { + "text": "The expected time until the first arrival is 1 over (3 lambda)." + }, + { + "text": "Alright." + }, + { + "text": "So at this time, this bulb, this arrival happened, this bulb has been burned." + }, + { + "text": "So we don't care about that bulb anymore." + }, + { + "text": "We start at this time, and we look forward." + }, + { + "text": "This bulb has been burned." + }, + { + "text": "So let's just look forward from now on." + }, + { + "text": "What have we got?" + }, + { + "text": "We have two bulbs that are burning." + }, + { + "text": "We have a Poisson process that's the bigger picture of what could happen to that light bulb, if we were to keep replacing it." + }, + { + "text": "Another Poisson process." + }, + { + "text": "These two processes are, again, independent." + }, + { + "text": "From this time until that time, how long does it take?" + }, + { + "text": "It's the time until either this process records an arrival or that process records and arrival." + }, + { + "text": "That's the same as the time that the merged process of these two records an arrival." + }, + { + "text": "So we're talking about the expected time until the first arrival in a merged process." + }, + { + "text": "The merged process is Poisson." + }, + { + "text": "It's Poisson with rate 2 lambda." + }, + { + "text": "So that extra time is going to take-- the expected value is going to be 1 over the (rate of that Poisson process)." + }, + { + "text": "So 1 over (2 lambda) is the expected value of this random variable." + }, + { + "text": "So at this point, this bulb now is also burned." + }, + { + "text": "So we start looking from this time on." + }, + { + "text": "That part of the picture disappears." + }, + { + "text": "Starting from this time, what's the expected value until that remaining light-bulb burns out?" + }, + { + "text": "Well, as we said before, in a Poisson process or with exponential random variables, we have memorylessness." + }, + { + "text": "A used bulb is as good as a new one." + }, + { + "text": "So it's as if we're starting from scratch here." + }, + { + "text": "So this is going to be an exponential random variable with parameter lambda." + }, + { + "text": "And the expected value of it is going to be 1 over lambda." + }, + { + "text": "So the beauty of approaching this problem in this particular way is, of course, that we manage to do everything without any calculus at all, without striking an integral, without trying to calculate expectations in any form." + }, + { + "text": "Most of the non-trivial problems that you encounter in the Poisson world basically involve tricks of these kind." + }, + { + "text": "You have a question and you try to rephrase it, trying to think in terms of what might happen in the Poisson setting, use memorylessness, use merging, et cetera, et cetera." + }, + { + "text": "Now we talked about merging." + }, + { + "text": "It turns out that the splitting of Poisson processes also works in a nice way." + }, + { + "text": "The story here is exactly the same as for the Bernoulli process." + }, + { + "text": "So I'm having a Poisson process." + }, + { + "text": "And each time, with some rate lambda, and each time that an arrival comes, I'm going to send it to that stream and the record an arrival here with some probability P. And I'm going to send it to the other stream with some probability 1 minus P. So either of this will happen or that will happen, depending on the outcome of the coin flip that I do." + }, + { + "text": "Each time that then arrival occurs, I flip a coin and I decide whether to record it here or there." + }, + { + "text": "This is called splitting a Poisson process into two pieces." + }, + { + "text": "What kind of process do we get here?" + }, + { + "text": "If you look at the little interval for length delta, what's the probability that this little interval gets an arrival?" + }, + { + "text": "It's the probability that this one gets an arrival, which is lambda delta times the probability that after I get an arrival my coin flip came out to be that way, so that it sends me there." + }, + { + "text": "So this means that this little interval is going to have probability lambda delta P. Or maybe more suggestively, I should write it as lambda P times delta." + }, + { + "text": "So every little interval has a probability of an arrival proportional to delta." + }, + { + "text": "The proportionality factor is lambda P. So lambda P is the rate of that process." + }, + { + "text": "And then you go through the mental exercise that you went through for the Bernoulli process to argue that a different intervals here are independent and so on." + }, + { + "text": "And that completes checking that this process is going to be a Poisson process." + }, + { + "text": "So when you split a Poisson process by doing independent coin flips each time that something happens, the processes that you get is again a Poisson process, but of course with a reduced rate." + }, + { + "text": "So instead of the word splitting, sometimes people also use the words thinning-out." + }, + { + "text": "That is, out of the arrivals that came, you keep a few but throw away a few." + }, + { + "text": "OK." + }, + { + "text": "So now the last topic over this lecture is a quite curious phenomenon that goes under the name of random incidents." + }, + { + "text": "So here's the story." + }, + { + "text": "Buses have been running on Mass Ave. from time immemorial." + }, + { + "text": "And the bus company that runs the buses claims that they come as a Poisson process with some rate, let's say, of 4 buses per hour." + }, + { + "text": "So that the expected time between bus arrivals is going to be 15 minutes." + }, + { + "text": "OK. Alright." + }, + { + "text": "So people have been complaining that they have been showing up there." + }, + { + "text": "They think the buses are taking too long." + }, + { + "text": "So you are asked to investigate." + }, + { + "text": "Is the company-- Does it operate according to its promises or not." + }, + { + "text": "So you send an undercover agent to go and check the interarrival times of the buses." + }, + { + "text": "Are they 15 minutes?" + }, + { + "text": "Or are they longer?" + }, + { + "text": "So you put your dark glasses and you show up at the bus stop at some random time." + }, + { + "text": "And you go and ask the guy in the falafel truck, how long has it been since the last arrival?" + }, + { + "text": "So of course that guy works for the FBI, right?" + }, + { + "text": "So they tell you, well, it's been, let's say, 12 minutes since the last bus arrival." + }, + { + "text": "And then you say, \"Oh, 12 minutes." + }, + { + "text": "Average time is 15." + }, + { + "text": "So a bus should be coming any time now.\"" + }, + { + "text": "Is that correct?" + }, + { + "text": "No, you wouldn't think that way." + }, + { + "text": "It's a Poisson process." + }, + { + "text": "It doesn't matter how long it has been since the last bus arrival." + }, + { + "text": "So you don't go through that fallacy." + }, + { + "text": "Instead of predicting how long it's going to be, you just sit down there and wait and measure the time." + }, + { + "text": "And you find that this is, let's say, 11 minutes." + }, + { + "text": "And you go to your boss and report, \"Well, it took-- I went there and the time from the previous bus to the next one was 23 minutes." + }, + { + "text": "It's more than the 15 that they said.\"" + }, + { + "text": "So go and do that again." + }, + { + "text": "You go day after day." + }, + { + "text": "You keep these statistics of the length of this interval." + }, + { + "text": "And you tell your boss it's a lot more than 15." + }, + { + "text": "It tends to be more like 30 or so." + }, + { + "text": "So the bus company is cheating us." + }, + { + "text": "Does the bus company really run Poisson buses at the rate that they have promised?" + }, + { + "text": "Well let's analyze the situation here and figure out what the length of this interval should be, on the average." + }, + { + "text": "The naive argument is that this interval is an interarrival time." + }, + { + "text": "And interarrival times, on the average, are 15 minutes, if the company runs indeed Poisson processes with these interarrival times." + }, + { + "text": "But actually the situation is a little more subtle because this is not a typical interarrival interval." + }, + { + "text": "This interarrival interval consists of two pieces." + }, + { + "text": "Let's call them T1 and T1 prime." + }, + { + "text": "What can you tell me about those two random variables?" + }, + { + "text": "What kind of random variable is T1?" + }, + { + "text": "Starting from this time, with the Poisson process, the past doesn't matter." + }, + { + "text": "It's the time until an arrival happens." + }, + { + "text": "So T1 is going to be an exponential random variable with parameter lambda." + }, + { + "text": "So in particular, the expected value of T1 is going to be 15 by itself." + }, + { + "text": "How about the random variable T1 prime." + }, + { + "text": "What kind of random variable is it?" + }, + { + "text": "This is like the first arrival in a Poisson process that runs backwards in time." + }, + { + "text": "What kind of process is a Poisson process running backwards in time?" + }, + { + "text": "Let's think of coin flips." + }, + { + "text": "Suppose you have a movie of coin flips." + }, + { + "text": "And for some accident, that fascinating movie, you happen to watch it backwards." + }, + { + "text": "Will it look any different statistically?" + }, + { + "text": "No." + }, + { + "text": "It's going to be just the sequence of random coin flips." + }, + { + "text": "So a Bernoulli process that's runs in reverse time is statistically identical to a Bernoulli process in forward time." + }, + { + "text": "The Poisson process is a limit of the Bernoulli." + }, + { + "text": "So, same story with the Poisson process." + }, + { + "text": "If you run it backwards in time it looks the same." + }, + { + "text": "So looking backwards in time, this is a Poisson process." + }, + { + "text": "And T1 prime is the time until the first arrival in this backward process." + }, + { + "text": "So T1 prime is also going to be an exponential random variable with the same parameter, lambda." + }, + { + "text": "And the expected value of T1 prime is 15." + }, + { + "text": "Conclusion is that the expected length of this interval is going to be 30 minutes." + }, + { + "text": "And the fact that this agent found the average to be something like 30 does not contradict the claims of the bus company that they're running Poisson buses with a rate of lambda equal to 4." + }, + { + "text": "OK." + }, + { + "text": "So maybe the company can this way-- they can defend themselves in court." + }, + { + "text": "But there's something puzzling here." + }, + { + "text": "How long is the interarrival time?" + }, + { + "text": "Is it 15?" + }, + { + "text": "Or is it 30?" + }, + { + "text": "On the average." + }, + { + "text": "The issue is what do we mean by a typical interarrival time." + }, + { + "text": "When we say typical, we mean some kind of average." + }, + { + "text": "But average over what?" + }, + { + "text": "And here's two different ways of thinking about averages." + }, + { + "text": "You number the buses." + }, + { + "text": "And you have bus number 100." + }, + { + "text": "You have bus number 101, bus number 102, bus number 110, and so on." + }, + { + "text": "One way of thinking about averages is that you pick a bus number at random." + }, + { + "text": "I pick, let's say, that bus, all buses being sort of equally likely to be picked." + }, + { + "text": "And I measure this interarrival time." + }, + { + "text": "So for a typical bus." + }, + { + "text": "Then, starting from here until there, the expected time has to be 1 over lambda, for the Poisson process." + }, + { + "text": "But what we did in this experiment was something different." + }, + { + "text": "We didn't pick a bus at random." + }, + { + "text": "We picked a time at random." + }, + { + "text": "And if the picture is, let's say, this way, I'm much more likely to pick this interval and therefore this interarrival time, rather than that interval." + }, + { + "text": "Because, this interval corresponds to very few times." + }, + { + "text": "So if I'm picking a time at random and, in some sense, let's say, uniform, so that all times are equally likely, I'm much more likely to fall inside a big interval rather than a small interval." + }, + { + "text": "So a person who shows up at the bus stop at a random time." + }, + { + "text": "They're selecting an interval in a biased way, with the bias favor of longer intervals." + }, + { + "text": "And that's why what they observe is a random variable that has a larger expected value then the ordinary expected value." + }, + { + "text": "So the subtlety here is to realize that we're talking between two different kinds of experiments." + }, + { + "text": "Picking a bus number at random verses picking an interval at random with a bias in favor of longer intervals." + }, + { + "text": "Lots of paradoxes that one can cook up using Poisson processes and random processes in general often have to do with the story of this kind." + }, + { + "text": "The phenomenon that we had in this particular example also shows up in general, whenever you have other kinds of arrival processes." + }, + { + "text": "So the Poisson process is the simplest arrival process there is, where the interarrival times are exponential random variables." + }, + { + "text": "There's a larger class of models." + }, + { + "text": "They're called renewal processes, in which, again, we have a sequence of successive arrivals, interarrival times are identically distributed and independent, but they may come from a general distribution." + }, + { + "text": "So to make the same point of the previous example but in a much simpler setting, suppose that bus interarrival times are either 5 or 10 minutes apart." + }, + { + "text": "So you get some intervals that are of length 5." + }, + { + "text": "You get some that are of length 10." + }, + { + "text": "And suppose that these are equally likely." + }, + { + "text": "So we have -- not exactly -- In the long run, we have as many 5 minute intervals as we have 10 minute intervals." + }, + { + "text": "So the average interarrival time is 7 and 1/2." + }, + { + "text": "But if a person shows up at a random time, what are they going to see?" + }, + { + "text": "Do we have as many 5s as 10s?" + }, + { + "text": "But every 10 covers twice as much space." + }, + { + "text": "So if I show up at a random time, I have probability 2/3 falling inside an interval of duration 10." + }, + { + "text": "And I have one 1/3 probability of falling inside an interval of duration 5." + }, + { + "text": "That's because, out of the whole real line, 2/3 of it is covered by intervals of length 10, just because they're longer." + }, + { + "text": "1/3 is covered by the smaller intervals." + }, + { + "text": "Now if I fall inside an interval of length 10 and I measure the length of the interval that I fell into, that's going to be 10." + }, + { + "text": "But if I fall inside an interval of length 5 and I measure how long it is, I'm going to get a 5." + }, + { + "text": "And that, of course, is going to be different than 7.5." + }, + { + "text": "OK. And which number should be bigger?" + }, + { + "text": "It's the second number that's bigger because this one is biased in favor of the longer intervals." + }, + { + "text": "So that's, again, another illustration of the different results that you get when you have this random incidence phenomenon." + }, + { + "text": "So the bottom line, again, is that if you talk about a typical interarrival time, one must be very precise in specifying what we mean typical." + }, + { + "text": "So typical means sort of random." + }, + { + "text": "But to use the word random, you must specify very precisely what is the random experiment that you are using." + }, + { + "text": "And if you're not careful, you can get into apparent puzzles, such as the following." + }, + { + "text": "Suppose somebody tells you the average family size is 4, but the average person lives in a family of size 6." + }, + { + "text": "Is that compatible?" + }, + { + "text": "Family size is 4 on the average, but typical people live, on the average, in families of size 6." + }, + { + "text": "Well yes." + }, + { + "text": "There's no contradiction here." + }, + { + "text": "We're talking about two different experiments." + }, + { + "text": "In one experiment, I pick a family at random, and I tell you the average family is 4." + }, + { + "text": "In another experiment, I pick a person at random and I tell you that this person, on the average, will be in their family of size 6." + }, + { + "text": "And what is the catch here?" + }, + { + "text": "That if I pick a person at random, large families are more likely to be picked." + }, + { + "text": "So there's a bias in favor of large families." + }, + { + "text": "Or if you want to survey, let's say, are trains crowded in your city?" + }, + { + "text": "Or are buses crowded?" + }, + { + "text": "One choice is to pick a bus at random and inspect how crowded it is." + }, + { + "text": "Another choice is to pick a typical person and ask them, \"Did you ride the bus today?" + }, + { + "text": "Was it's crowded?\"" + }, + { + "text": "Well suppose that in this city there's one bus that's extremely crowded and all the other buses are completely empty." + }, + { + "text": "If you ask a person." + }, + { + "text": "\"Was your bus crowded?\"" + }, + { + "text": "They will tell you, \"Yes, my bus was crowded.\"" + }, + { + "text": "There's no witness from the empty buses to testify in their favor." + }, + { + "text": "So by sampling people instead of sampling buses, you're going to get different result." + }, + { + "text": "And in the process industry, if your job is to inspect and check cookies, you will be faced with a big dilemma." + }, + { + "text": "Do you want to find out how many chocolate chips there are on a typical cookie?" + }, + { + "text": "Are you going to interview cookies or are you going to interview chocolate chips and ask them how many other chips where there on your cookie?" + }, + { + "text": "And you're going to get different answers in these cases." + }, + { + "text": "So moral is, one has to be very precise on how you formulate the sampling procedure that you have." + }, + { + "text": "And you'll get different answers." + } +] \ No newline at end of file diff --git a/sight/sources/annotated/cxTmmasBiC8.json b/sight/sources/annotated/cxTmmasBiC8.json new file mode 100644 index 0000000000000000000000000000000000000000..10d35d5c570bd8f57ab79e281a63a0410d45b22f --- /dev/null +++ b/sight/sources/annotated/cxTmmasBiC8.json @@ -0,0 +1,1007 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "OK, now clustering for graphs." + }, + { + "text": "So this is a topic." + }, + { + "text": "This is one of the important things you can try to do with a graph." + }, + { + "text": "So you have a large graph." + }, + { + "text": "Let me kind of divide it into two clusters." + }, + { + "text": "OK, so you get a giant graph." + }, + { + "text": "And the job is to make some sense out of it." + }, + { + "text": "And one possible step is to be able to subdivide it if, as I see here, there is a cut between two reasonably equal parts of the graph, reasonably same size." + }, + { + "text": "And therefore, that graph could be studied in two pieces." + }, + { + "text": "So the question is, how do you find such a cut by an algorithm?" + }, + { + "text": "What's an algorithm that would find that cut?" + }, + { + "text": "So that's the problem." + }, + { + "text": "Let's say we're looking for two clusters." + }, + { + "text": "We could look for more clusters." + }, + { + "text": "But let's say we want to look for two clusters." + }, + { + "text": "So what are we trying to do?" + }, + { + "text": "We're trying to minimize." + }, + { + "text": "So this is the problem, then." + }, + { + "text": "So we look for find positions x and y, let's say, two which will be the centers, so to speak, of the." + }, + { + "text": "And really, it's just these points." + }, + { + "text": "Points." + }, + { + "text": "So the data is the points and the edges, as always, the nodes and the edges." + }, + { + "text": "So the problem is to find x and y so that to minimize." + }, + { + "text": "So it's a distance of points ai from x." + }, + { + "text": "Maybe I should emphasize we're in high dimensions." + }, + { + "text": "Plus the distance of other points." + }, + { + "text": "So the ai will be these points, these nodes." + }, + { + "text": "And the bi will be these nodes plus the sum of bi minus y squared." + }, + { + "text": "And you understand the rule here." + }, + { + "text": "That together, the a's union the b's give me all nodes." + }, + { + "text": "And I guess to be complete, the a's intersect the b's is empty." + }, + { + "text": "Just what you expect." + }, + { + "text": "I'm dividing the a's and the b's into two groups." + }, + { + "text": "And I'm picking an x and a y sort of at the center of those groups." + }, + { + "text": "So that is a minimum." + }, + { + "text": "So I want to minimize." + }, + { + "text": "And also, I probably want to impose some condition that the number of a's is reasonably close to the number of b's." + }, + { + "text": "In other words, I don't want just that to be the a and all the rest to be the b's." + }, + { + "text": "That would be not a satisfactory clustering." + }, + { + "text": "I'm looking for clusters that are good sized clusters." + }, + { + "text": "So minimize that." + }, + { + "text": "So there are a lot of different algorithms to do it." + }, + { + "text": "But some are more directly attacking this problem." + }, + { + "text": "Others use matrices that we associate with the graph." + }, + { + "text": "So let me tell you about two or three of those algorithms." + }, + { + "text": "And if you've studied, had a course in graph theory, you may already have seen this problem." + }, + { + "text": "First question would be, suppose I decide these are the a's and those are the b's, or some other decision." + }, + { + "text": "Yeah, probably some other decision." + }, + { + "text": "God, I want to solve the problem before I even start." + }, + { + "text": "So some a's and some b's." + }, + { + "text": "What would be the best choice of the x once you've decided on the a's?" + }, + { + "text": "And what would be the best choice of the y once you've decided on the b's?" + }, + { + "text": "So we can answer that question." + }, + { + "text": "Just if we knew the two groups, we could see where they should be centered, where the first group centered at x, the second group centered at y." + }, + { + "text": "And what does centering mean?" + }, + { + "text": "So let's just say." + }, + { + "text": "So I think what I'm saying here is, let me bring that down a little." + }, + { + "text": "So given the a's, this is a1 up to, say, ak, what is the best?" + }, + { + "text": "Is the best x?" + }, + { + "text": "Just to make that part right." + }, + { + "text": "And the answer is, do you know geometrically what x should be here?" + }, + { + "text": "x is the." + }, + { + "text": "So if I have a bunch of points and I'm looking for the middle of those points, the point x, a good point x to say, OK, that's the middle." + }, + { + "text": "It'll make the sum of the distances, I think, squared." + }, + { + "text": "I hope I'm right about that." + }, + { + "text": "A minimum." + }, + { + "text": "What is x?" + }, + { + "text": "It is the centroid." + }, + { + "text": "Centroid is the word." + }, + { + "text": "x is the centroid of the a's." + }, + { + "text": "And what is the centroid?" + }, + { + "text": "Let's see." + }, + { + "text": "Oh, maybe I don't know if x and y were a good choice." + }, + { + "text": "But let me see what." + }, + { + "text": "I guess it's the average a." + }, + { + "text": "It's the sum of the a's, of these a's." + }, + { + "text": "Those are vectors, of course, divided by the number of a's." + }, + { + "text": "I think." + }, + { + "text": "Actually, I was just quickly reviewing this morning." + }, + { + "text": "So I'm not totally on top of this centroid." + }, + { + "text": "What I'm going to talk, the algorithm that I'm going to talk about is the k, well, k means, it's always called." + }, + { + "text": "And here, it will be the k will be 2." + }, + { + "text": "I just have two partitioning into two sets, a's and b's." + }, + { + "text": "So I just k is just 2." + }, + { + "text": "OK, what's the algorithm?" + }, + { + "text": "Well, if I've chosen a partition, the a's and the b's have separated them, then that tells me what the x and the y should be." + }, + { + "text": "But now, what do I do next?" + }, + { + "text": "So this is going to be a sort of an alternating partition." + }, + { + "text": "Now, I take those two centroids." + }, + { + "text": "So step one is, for a given a's and b's, find the centroids x and y." + }, + { + "text": "And that's elementary." + }, + { + "text": "Then the second step is, given the centroids x and y, given those positions, given x and y, they won't be centroids when you see what happens." + }, + { + "text": "Given x and y, reform the best partition, best clusters." + }, + { + "text": "OK, so step one, we had a guess at what the best clusters were." + }, + { + "text": "And we found their centroids." + }, + { + "text": "Now, we start with the centroids, and we form new clusters again." + }, + { + "text": "And if these clusters are the same as the ones we started with, then the algorithm has converged." + }, + { + "text": "But probably won't be, these clusters." + }, + { + "text": "So you'll have to tell me what I mean by the best clusters." + }, + { + "text": "If I've got the two points, x and y, I want the points, I want to separate all the points that cluster around x to the ones that cluster around y." + }, + { + "text": "And then they're probably different from my original start." + }, + { + "text": "So now I've got new." + }, + { + "text": "Now I repeat step one." + }, + { + "text": "But let's just think, how do I form the best clusters?" + }, + { + "text": "Well, I take a point, and I have to decide, does it go with x, or does it go in the x cluster, or does it go in the cluster around y?" + }, + { + "text": "So how do I decide that?" + }, + { + "text": "Just whichever one it's closer to." + }, + { + "text": "So each point goes with each node." + }, + { + "text": "I could say each node goes with the closer of x and y." + }, + { + "text": "So points that should have been that are closer to x, now we're going to put them in the cluster around x." + }, + { + "text": "And does that solve the problem?" + }, + { + "text": "No, because, well, it might, but it might not." + }, + { + "text": "We have to come back to step one." + }, + { + "text": "We've now changed the clusters." + }, + { + "text": "They'll have different centroids." + }, + { + "text": "So we repeat step one, find the centroids for the two new clusters." + }, + { + "text": "Then we come to step two, find the ones that should go with the two centroids, and back and forth." + }, + { + "text": "I don't know, I don't think there's a nice theory of convergence or rate of convergence, all the questions that this course is always asking." + }, + { + "text": "But it's a very popular algorithm, k-means." + }, + { + "text": "k would be to have k clusters." + }, + { + "text": "So that's a, I'm not going to discuss the, I'd rather discuss some other ways to do this, to solve this problem, but that's one sort of hack that works quite well." + }, + { + "text": "OK, so second approach is what's coming next, second solution method." + }, + { + "text": "And it's called the spectral clustering." + }, + { + "text": "That's the name of the method." + }, + { + "text": "And before I write down what you do, what does the word spectral mean?" + }, + { + "text": "You see spectral graph theory, spectral clustering." + }, + { + "text": "And in other parts of mathematics, you see that word, you see spectral theorem." + }, + { + "text": "I gave you the most, and I described it as the most important, perhaps, theorem in linear algebra, at least one of the top three." + }, + { + "text": "So I'll write it over here, because it's not, it doesn't, this is a, it's the same word spectral." + }, + { + "text": "Well, let me ask the question again." + }, + { + "text": "What's that word spectral about?" + }, + { + "text": "What does that mean?" + }, + { + "text": "That means that if I have a matrix and I want to talk about its spectrum, what is the spectrum of the matrix?" + }, + { + "text": "It is the eigenvalues." + }, + { + "text": "So spectral theory, spectral clustering is using the eigenvalues of some matrix." + }, + { + "text": "That's what that spectral is telling me." + }, + { + "text": "So the spectral theorem, of course, is that for a symmetric matrix S, the eigenvalues are real and the eigenvectors are orthogonal." + }, + { + "text": "And don't forget what the real full statement is here, because there could be repeated real eigenvalues." + }, + { + "text": "And what does the spectral theorem tell me?" + }, + { + "text": "For symmetric matrices, if lambda equal 5 is repeated four times, if it's a four times solution of the equation that gives eigenvalues, then what's the conclusion?" + }, + { + "text": "Then there are four independent orthogonal eigenvectors to go with it." + }, + { + "text": "We can't say that about matrices, about all matrices, but we can say it about all symmetric matrices." + }, + { + "text": "And in fact, those eigenvectors are orthogonal, so we're even saying more." + }, + { + "text": "We can find four orthogonal eigenvectors that go with a multiplicity for eigenvalue." + }, + { + "text": "OK, that's spectral theorem." + }, + { + "text": "Spectral clustering starts with the graph Laplacian matrix." + }, + { + "text": "Matrix." + }, + { + "text": "May I remember what that matrix is?" + }, + { + "text": "Because that's the key connection of linear algebra to graph theory, is the properties of this graph Laplacian matrix." + }, + { + "text": "OK, so let me say L for Laplacian." + }, + { + "text": "So that matrix, one way to describe it is as a transpose A, where A is the incidence matrix of the graph." + }, + { + "text": "Or another way we'll see is the D, the degree matrix." + }, + { + "text": "That's diagonal." + }, + { + "text": "And I'll do an example just to remind you." + }, + { + "text": "Minus the, I don't know what I'd call this one." + }, + { + "text": "Shall I call it B for the moment?" + }, + { + "text": "And what matrix is B?" + }, + { + "text": "That's the adjacency matrix." + }, + { + "text": "Really, you should know these four matrices." + }, + { + "text": "They're the key four matrices associated with any graph." + }, + { + "text": "The incidence matrix, that's m by n edges and nodes." + }, + { + "text": "Edges and nodes." + }, + { + "text": "So it's rectangular, but I'm forming A transpose A here." + }, + { + "text": "So I'm forming a symmetric positive semi-definite matrix." + }, + { + "text": "So this Laplacian is symmetric positive semi-definite." + }, + { + "text": "Yeah, let me just recall what all these matrices are for a simple graph." + }, + { + "text": "OK, so I'll just draw a graph." + }, + { + "text": "All right." + }, + { + "text": "OK, so the incidence matrix, there are 1, 2, 3, 4, 5 edges, so five rows." + }, + { + "text": "There are four nodes, 1, 2, 3, and 4, so four columns." + }, + { + "text": "And a typical row would be edge 1 going from node 1 to node 2, so it would have a minus 1 and a 1 there." + }, + { + "text": "And let me take edge 2 going from 1 to node 3, so it would have a minus 1 and a 1 there." + }, + { + "text": "So that's the incidence matrix A. OK, what's the degree matrix?" + }, + { + "text": "That's simple." + }, + { + "text": "The degree matrix, well, A transpose A, this is m by n. This is n by m, so it's n by n. OK, in this case, 4 by 4." + }, + { + "text": "So the degree matrix will be 4 by 4, n by n. And it will tell us the degree of that, which means which we just count the edges." + }, + { + "text": "So it's three edges going in, node 2, three edges going in." + }, + { + "text": "Node 3 has just two edges, and node 4 has just two edges." + }, + { + "text": "So that's the degree matrix." + }, + { + "text": "And then the adjacency matrix that I've called B is also 4 by 4." + }, + { + "text": "And what is it?" + }, + { + "text": "It tells us which node is connected to which node." + }, + { + "text": "So I don't allow nodes, edges, that connect a node to itself, so 0s on the diagonal." + }, + { + "text": "So which nodes are connected to node 1?" + }, + { + "text": "Well, all of 2 and 4 and 3 are connected to 1, so I have 1s there." + }, + { + "text": "Node 2, all three nodes are connected to node 2." + }, + { + "text": "So I'll have the second column and row will have all three 1s." + }, + { + "text": "How about node 3?" + }, + { + "text": "OK, only two edges are connected." + }, + { + "text": "Only two nodes are connected to 3, 1 and 2, but not 4." + }, + { + "text": "So 1 and 2 I have, but not 4." + }, + { + "text": "So that's the adjacency matrix." + }, + { + "text": "Is that right?" + }, + { + "text": "Think so?" + }, + { + "text": "This is the degree matrix." + }, + { + "text": "This is the incidence matrix." + }, + { + "text": "And that formula gives me the Laplacian." + }, + { + "text": "Let's write down the Laplacian." + }, + { + "text": "So if I use the degree minus b, that's easy." + }, + { + "text": "The degrees were 3, 3, 2, and 2." + }, + { + "text": "Now I have these minuses, and those were 0." + }, + { + "text": "So that's a positive semidefinite matrix." + }, + { + "text": "Is it a positive definite matrix?" + }, + { + "text": "So let me ask, is it singular or is it not singular?" + }, + { + "text": "Is there a vector in its null space or is there not a vector in its null space?" + }, + { + "text": "Can you solve dx equals all 0s?" + }, + { + "text": "And of course, you can." + }, + { + "text": "Everybody sees that the vector of all 1s will be a solution to L. I'm sorry." + }, + { + "text": "I should be saying L here." + }, + { + "text": "Lx equals 0." + }, + { + "text": "Lx equals 0 is for a whole line of a one dimensional and the null space of L has dimension 1." + }, + { + "text": "It's got one basis vector, 1, 1, 1, 1." + }, + { + "text": "And that will always happen with the graph setup that I've created." + }, + { + "text": "So that's the first fact, that this positive semidefinite matrix L has lambda 1 equals 0, and the eigenvector is constants, C, C, C, C, the one dimensional eigenspace." + }, + { + "text": "Or 1, 1, 1, 1 is a typical eigenvector." + }, + { + "text": "OK. Now back to graph clustering." + }, + { + "text": "The idea of graph clustering is to look at the Fiedler eigenvector." + }, + { + "text": "This is called x2 is the next eigenvector, is the eigenvector for the smallest positive eigenvalue for lambda min excluding 0." + }, + { + "text": "So the smallest eigenvalue of L, the smallest eigenvalue and its eigenvector, this is called the Fiedler vector, named after the Czech mathematician, a great man in linear algebra." + }, + { + "text": "And he studied this vector, this situation." + }, + { + "text": "So everybody who knows about the graph Laplacian is aware that its first eigenvalue is 0, and that the next eigenvalue is important." + }, + { + "text": "Yeah?" + }, + { + "text": "AUDIENCE 2 Is the graph Laplacian named the Laplacian because it has connections?" + }, + { + "text": "GILBERT STRANGSKI-WEISBAUMGESEN To Laplace's equation, yes." + }, + { + "text": "So yeah, that's a good question." + }, + { + "text": "So why the word, the name Laplacian?" + }, + { + "text": "So yeah, that's a good question." + }, + { + "text": "So the familiar thing, so it connects to Laplace's finite difference equation, because we're talking about matrices here and not derivatives, not functions." + }, + { + "text": "So why the word Laplacian?" + }, + { + "text": "Well, so if I have a regular, if my graph is composed of a, so there is a graph with 25 nodes and 4 times 5, 20, about 40." + }, + { + "text": "This probably has about 40 edges and 25 nodes." + }, + { + "text": "And of course, I can construct its graph, all those four matrices for it." + }, + { + "text": "Its incidence matrix, its degree matrix." + }, + { + "text": "So the degree will be 4 at all these inside points." + }, + { + "text": "The degree will be 3 at these boundary points." + }, + { + "text": "The degree will be 2 at these corner points." + }, + { + "text": "But what will the matrix L look like?" + }, + { + "text": "So what is L?" + }, + { + "text": "And that will tell you why it has this name Laplacian." + }, + { + "text": "So the matrix L will have the degree 4, right, will be on the diagonal." + }, + { + "text": "That's coming from D. The other, the minus 1's that come from B, the adjacency matrix will be associated with those nodes and otherwise all 0's." + }, + { + "text": "So this is a typical row of L. This is a typical row of L centered at that node." + }, + { + "text": "So maybe that's node number 5, 10, 13." + }, + { + "text": "That's 13 out of 25 that would show you this." + }, + { + "text": "And sorry, those are minus 1's." + }, + { + "text": "Minus 1's." + }, + { + "text": "So a 4 on the diagonal and 4 minus 1's." + }, + { + "text": "That's the model problem for when the graph is a grid, square grid." + }, + { + "text": "And you associate that with Laplace's equation." + }, + { + "text": "So this is the reason that Laplace, why Laplace gets in it." + }, + { + "text": "Because Laplace's equation, the differential equation, is second derivative with respect to x squared." + }, + { + "text": "And the second derivative with respect to y squared is 0." + }, + { + "text": "And what we have here is Lu equals 0." + }, + { + "text": "It's the discrete Laplacian, the vector Laplacian, the graph Laplacian, where the second x derivative is replaced by minus 1, 2, minus 1." + }, + { + "text": "And the second y derivative is replaced by minus 1, 2, minus 1, second differences in the x and the y directions." + }, + { + "text": "So that's the explanation for Laplace." + }, + { + "text": "It's the discrete Laplace, discrete, or the finite difference Laplace." + }, + { + "text": "OK. Now, to finish, I have to tell you what clusters, how do you decide the clusters from L?" + }, + { + "text": "How does L propose two clusters, the A's and the B's?" + }, + { + "text": "And here's the answer." + }, + { + "text": "They come from this eigenvector, the Fiedler eigenvector." + }, + { + "text": "You look at that eigenvector." + }, + { + "text": "It's got some positive and some negative components." + }, + { + "text": "The components with positive numbers of this eigenvector, so the positive components of x, of this eigenvector." + }, + { + "text": "And there are negative components of this eigenvector." + }, + { + "text": "And those are the two clusters." + }, + { + "text": "So the two clusters are decided by the eigenvector, by the signs, plus or minus signs, of the components." + }, + { + "text": "The plus signs go in one, and the minus signs go in another." + }, + { + "text": "And you have to experiment to see that that would succeed." + }, + { + "text": "I don't know what it would do on this, actually, because that's hardly splits up into two." + }, + { + "text": "I suppose maybe the split is along a line like that or something to get." + }, + { + "text": "I don't know what clustering." + }, + { + "text": "This is not a graph that is naturally clustered." + }, + { + "text": "But you could still do k-means on it." + }, + { + "text": "You could still do spectral clustering." + }, + { + "text": "And you would find this eigenvector." + }, + { + "text": "Now, what's the point about this eigenvector?" + }, + { + "text": "I'll finish in one moment." + }, + { + "text": "What do we know about that eigenvector as compared to that one?" + }, + { + "text": "So here was an eigenvector all 1's." + }, + { + "text": "Let me just make it all 1's." + }, + { + "text": "1, 1, 1, 1." + }, + { + "text": "In that picture, it's 25 1's." + }, + { + "text": "Here's the next eigenvector up." + }, + { + "text": "And what's the relation between those two eigenvectors of L?" + }, + { + "text": "They are orthogonal." + }, + { + "text": "These are eigenvectors of a symmetric matrix." + }, + { + "text": "So they're orthogonal." + }, + { + "text": "So that means to be orthogonal to this guy means that your components add to 0, right?" + }, + { + "text": "A vector is orthogonal to all 1's." + }, + { + "text": "That dot product is just add up the components." + }, + { + "text": "So we have a bunch of positive components and a bunch of negative components." + }, + { + "text": "They have the same sum because the dot product with that is 0." + }, + { + "text": "And those two components, those two sets of components, are your two, tell you the two clusters in spectral clustering." + }, + { + "text": "So it's a pretty nifty algorithm." + }, + { + "text": "It does ask you to compute an eigenvector." + }, + { + "text": "And that, of course, takes time." + }, + { + "text": "And then there's a third, more direct algorithm to do this optimization problem." + }, + { + "text": "Well, actually, there are many." + }, + { + "text": "This is an important problem." + }, + { + "text": "So there are many proposed algorithms." + }, + { + "text": "Good." + }, + { + "text": "OK, I'm closing up." + }, + { + "text": "Final question?" + }, + { + "text": "Yeah." + }, + { + "text": "AUDIENCE 1 Is it possible to do more than one eigenvector?" + }, + { + "text": "GILBERT STRANGSBERRY Well, certainly for k-means." + }, + { + "text": "Now, if I had to do three clusters with Fiedler, I would look at the first three eigenvectors." + }, + { + "text": "And, well, the first one would be nothing." + }, + { + "text": "And I would look at the next two." + }, + { + "text": "And that would be pretty successful." + }, + { + "text": "If I wanted six clusters, it probably would fall off in the quality of the clustering." + }, + { + "text": "Yeah, but certainly I would look at the lowest six eigenvectors and get somewhere." + }, + { + "text": "Yeah, right." + }, + { + "text": "So OK, so that's a topic, an important topic, a sort of standard topic in applied graph theory." + }, + { + "text": "OK, so see you Wednesday." + }, + { + "text": "I'm hoping on Wednesday." + }, + { + "text": "So Professor Edelman has told me a new and optimal way to look at the problem of back propagation." + }, + { + "text": "You remember back propagation?" + }, + { + "text": "If you remember the lecture on it, you don't want to remember the lecture on it." + }, + { + "text": "It's a tricky, messy thing to explain." + }, + { + "text": "But he says, if I explain it using Julia in linear algebra, it's clear." + }, + { + "text": "So we'll give him a chance on Wednesday to show that revolutionary approach to the explanation of back propagation." + }, + { + "text": "And I hope for, I told him he could have half an hour and projects would take some time." + }, + { + "text": "I hope now we've had two with wild applause." + }, + { + "text": "So I hope we get a couple more in our last class." + }, + { + "text": "OK, see you Wednesday." + }, + { + "text": "And if you bring, well, if you have projects ready, send them to me online and maybe a printout as well." + }, + { + "text": "That would be terrific." + }, + { + "text": "If you don't have them ready by the hour, they can go." + }, + { + "text": "The envelope outside my office would receive them." + }, + { + "text": "Good, so I'll see you Wednesday for the final class." + } +] \ No newline at end of file diff --git a/sight/sources/annotated/d32WV1rKoVk.json b/sight/sources/annotated/d32WV1rKoVk.json new file mode 100644 index 0000000000000000000000000000000000000000..49fb18465093b6847227d98f68b488e41cba988e --- /dev/null +++ b/sight/sources/annotated/d32WV1rKoVk.json @@ -0,0 +1,1595 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "OK, why don't I start?" + }, + { + "text": "So I was hoping that we would have the next online assignment ready, but Julia 6, the new version, is slowing us down." + }, + { + "text": "And it'd probably be next time." + }, + { + "text": "But my lectures, of course, are, well, what I want to say perhaps is this isn't intended to be a course in numerical linear algebra." + }, + { + "text": "But I thought I couldn't let the whole semester go by without saying something about how to compute eigenvalues and singular values." + }, + { + "text": "Of course, you're going to call I or SVD or the equivalent in Python or Julia." + }, + { + "text": "But actually, the QR factorization that we spoke about, that we spoke entirely about last time is the key, unexpectedly, unexpectedly." + }, + { + "text": "You have a matrix A whose eigenvalues you want." + }, + { + "text": "So let's start with eigenvalues." + }, + { + "text": "And it might be a symmetric matrix." + }, + { + "text": "I'll stay with A rather than S because it doesn't have to be." + }, + { + "text": "But you get special always." + }, + { + "text": "You get something special if the matrix is symmetric." + }, + { + "text": "OK, so this method of computing eigenvalues, to me at least, and I think to many people, came like out of the blue a while ago, but not that long ago." + }, + { + "text": "And it worked very well." + }, + { + "text": "So here's the idea." + }, + { + "text": "It's called the QR method because you start by factoring your matrix into QR." + }, + { + "text": "So here's A." + }, + { + "text": "Can we call it A0?" + }, + { + "text": "That's the matrix we start with whose eigenvalues we want." + }, + { + "text": "And I'll call these Q0 and R0." + }, + { + "text": "And you remember what that means, what's hiding behind those letters that I've written?" + }, + { + "text": "You have the columns of A, possibly symmetric, as I said, but not orthogonal, usually." + }, + { + "text": "So you find an orthogonal basis." + }, + { + "text": "You orthogonalize them." + }, + { + "text": "You line them up perpendicular to each other." + }, + { + "text": "And then there is a matrix R, which happens to be upper triangular, that connects." + }, + { + "text": "The not orthogonal basis with the orthogonal basis." + }, + { + "text": "Right, we constructed R step by step." + }, + { + "text": "And then the idea is write these in the reverse order." + }, + { + "text": "And that will be A1, the next A. OK, and then do it again, and again, and again." + }, + { + "text": "And so we're hoping, of course, that the eigenvalues didn't change." + }, + { + "text": "We're hoping that we can forget A0, start again with A1, and produce A2, and continue." + }, + { + "text": "So we're hoping two things." + }, + { + "text": "One will not be a hope." + }, + { + "text": "We can see that the eigenvalues of A1 and A0 are the same." + }, + { + "text": "So we have not changed the eigenvalues." + }, + { + "text": "How do we see that?" + }, + { + "text": "If you had to show that two matrices had the same eigenvalues, would you compute all the eigenvalues and compare them?" + }, + { + "text": "Certainly not." + }, + { + "text": "What would you do?" + }, + { + "text": "What's the best test, the usual test, the usual thing you would want to show?" + }, + { + "text": "They're similar." + }, + { + "text": "That's right." + }, + { + "text": "So the claim would be that these two matrices are similar." + }, + { + "text": "Right." + }, + { + "text": "So maybe we should show that." + }, + { + "text": "So we want to write A1 in a different way." + }, + { + "text": "So the claim is A1 is similar to A." + }, + { + "text": "So we just have to figure out." + }, + { + "text": "We have to get A1 to A0." + }, + { + "text": "So here's A1." + }, + { + "text": "OK." + }, + { + "text": "So A1, I want to show that that's right." + }, + { + "text": "So that's R0, Q0." + }, + { + "text": "But what is Q0?" + }, + { + "text": "From here, Q0 is what we is R. Q0 is, what do I want?" + }, + { + "text": "I want to put R0 inverse over there." + }, + { + "text": "So R0." + }, + { + "text": "Now for Q0, I'm going to substitute." + }, + { + "text": "So what is Q0?" + }, + { + "text": "I multiply both sides of that equation by R0 inverse." + }, + { + "text": "So Q0 is A0 is, sorry, I said A and wrote Q. A0 R0 inverse." + }, + { + "text": "Right." + }, + { + "text": "For Q0, I've put in what it equals." + }, + { + "text": "And that's done it." + }, + { + "text": "That's exactly telling me that A1, which is this, equals this." + }, + { + "text": "And that's a similarity transformation." + }, + { + "text": "I have not changed the eigenvalues." + }, + { + "text": "So that's OK." + }, + { + "text": "The other thing, which is the, like you could say, the miracle in this thing, is that when I continue to do that for almost every matrix, the matrices begin to lose stuff off the diagonal, especially below the diagonal by the ordering that QR is done." + }, + { + "text": "So you tend to start with a matrix A0." + }, + { + "text": "You get a matrix A1, which is like a little smaller here." + }, + { + "text": "This part being not especially smaller." + }, + { + "text": "You do it again." + }, + { + "text": "This is even smaller." + }, + { + "text": "So I put even smaller A2, even smaller." + }, + { + "text": "And you keep going." + }, + { + "text": "And for most matrices, the result is that I don't know how many steps we want to think of taking, but we get quite small numbers here." + }, + { + "text": "So once we get small numbers here, little epsilons, that's everybody's shorthand for small numbers, what would you expect to see on the diagonal?" + }, + { + "text": "The eigenvalues." + }, + { + "text": "Because this has the same eigenvalues as this, as this, as this." + }, + { + "text": "And these little epsilons are not going to change the eigenvalues too much." + }, + { + "text": "So these will be, on the diagonal, will be close to the eigenvalues." + }, + { + "text": "And actually, what happens is this one comes first." + }, + { + "text": "That one is quite accurate first." + }, + { + "text": "I guess we should probably do a simple example to see this happen." + }, + { + "text": "Actually, I do an example in the notes." + }, + { + "text": "And let me say what happens." + }, + { + "text": "So I do a 2 by 2 example, which has something like cos theta, sine theta." + }, + { + "text": "I don't know what." + }, + { + "text": "I've forgotten what I took." + }, + { + "text": "And I don't have that page of notes here." + }, + { + "text": "Something here." + }, + { + "text": "Something here." + }, + { + "text": "Something here as a 0." + }, + { + "text": "And then a 1, after just one step, has sine cubed theta there." + }, + { + "text": "And numbers there that are getting much closer to the eigenvalues." + }, + { + "text": "Sorry that this isn't a full scale example." + }, + { + "text": "But the point of the example is here, that this off-diagonal entry gets cubed." + }, + { + "text": "And the next step will be its ninth power, and then the 27th power." + }, + { + "text": "So it's really quickly going to 0." + }, + { + "text": "And this happens." + }, + { + "text": "So cubic convergence is a prize." + }, + { + "text": "In numerical linear algebra." + }, + { + "text": "So that happens." + }, + { + "text": "So this arrived on the scene and quickly blew away all other methods that were being used to compute eigenvalues." + }, + { + "text": "But numerical people, being what they are, they wanted to improve it." + }, + { + "text": "Like, is there a way to make it faster?" + }, + { + "text": "And turned out there is." + }, + { + "text": "It turned out that the better way, basically the same idea, but just you're always looking for a simple change." + }, + { + "text": "And the idea of introducing a shift was tried." + }, + { + "text": "And turned out to work extremely well." + }, + { + "text": "So that's the improvement." + }, + { + "text": "So we take a1." + }, + { + "text": "No, so how does the shift work?" + }, + { + "text": "So instead of a0, have I got space here to do this?" + }, + { + "text": "Instead of a0, I take a0 minus a shift." + }, + { + "text": "So a shift is some multiple of the identity." + }, + { + "text": "If I just move a matrix by a multiple of the identity, what happens to its eigenvectors?" + }, + { + "text": "What happens to its eigenvalues?" + }, + { + "text": "Something pretty simple, right?" + }, + { + "text": "Because I'm just shifting by si." + }, + { + "text": "What happens to its eigenvectors?" + }, + { + "text": "They're the same." + }, + { + "text": "And what happens to the eigenvalues?" + }, + { + "text": "They change by s. If a0v equals lambda v, then when I multiply this by v, there will be an extra." + }, + { + "text": "It'll be lambda minus s. Because the identity times the v is just v. So it just shifts all the eigenvalues by s. And you try to shift." + }, + { + "text": "You look for a shift." + }, + { + "text": "This would be great." + }, + { + "text": "If you knew lambda n, a shift there, you would be looking for 0 then, if you shifted them all by that lambda." + }, + { + "text": "And it turns out that would speed things up." + }, + { + "text": "So you work instead with this matrix as now, again, I'm factoring in a q0, r0." + }, + { + "text": "So that's the work of the method, is in doing Gram-Schmidt at every step." + }, + { + "text": "And then there's a little work in reversing the order." + }, + { + "text": "And then I want to undo the shift." + }, + { + "text": "So I do that factorization." + }, + { + "text": "Now, let's see." + }, + { + "text": "You may have to help me to remember what I should do here." + }, + { + "text": "So I factor those." + }, + { + "text": "I reverse those." + }, + { + "text": "And then I think I add back the shift." + }, + { + "text": "And that's my A1." + }, + { + "text": "So I took A0." + }, + { + "text": "I shifted it." + }, + { + "text": "I worked with it, qr, reversed the order, rq, added back the shift to get a matrix." + }, + { + "text": "And what am I, of course, hoping about the matrix A1 and A0?" + }, + { + "text": "I'm hoping they're still similar." + }, + { + "text": "I'm hoping." + }, + { + "text": "So I did a shift." + }, + { + "text": "And I undid a shift." + }, + { + "text": "But of course, after doing a qr, I have to check, are these really still similar?" + }, + { + "text": "So let me just try to check that one again." + }, + { + "text": "Maybe I'll just, it's sitting right there." + }, + { + "text": "So let me do it again." + }, + { + "text": "I'm hoping that something, you know, where did we change?" + }, + { + "text": "Oh, yeah, here." + }, + { + "text": "We showed that A1 was similar to A0." + }, + { + "text": "And I'm hoping that's probably still true, even, you know, the shift didn't mess that up." + }, + { + "text": "Let's just try." + }, + { + "text": "So A0, that's r0, q0 plus si." + }, + { + "text": "OK. And now what am I going to do?" + }, + { + "text": "I'm going to, what did I do before?" + }, + { + "text": "I figured out what q0 was from this." + }, + { + "text": "You remember?" + }, + { + "text": "So this is r0." + }, + { + "text": "Now I have to put in q0." + }, + { + "text": "But q0 is this thing inverse times this." + }, + { + "text": "Is this going to work?" + }, + { + "text": "I'm like hoping, but I don't think I wanted to get that." + }, + { + "text": "No, it's not q0 there." + }, + { + "text": "What do I put here?" + }, + { + "text": "And if it doesn't work, we'll leave it as an exercise." + }, + { + "text": "OK." + }, + { + "text": "So yeah, because I didn't sort of start right somehow." + }, + { + "text": "OK." + }, + { + "text": "So but let me just push along to see what happens." + }, + { + "text": "So I'm plugging in for q0 here." + }, + { + "text": "I'm plugging in this matrix, so it shouldn't have inverted it, times r0 inverse." + }, + { + "text": "Who knows?" + }, + { + "text": "It might work." + }, + { + "text": "Who knows?" + }, + { + "text": "So that's the r0, q0." + }, + { + "text": "Right?" + }, + { + "text": "Is everybody with me?" + }, + { + "text": "Sorry about this." + }, + { + "text": "So r0 inverse." + }, + { + "text": "And then I have to add Si." + }, + { + "text": "So what have I done?" + }, + { + "text": "I've just pushed on, believing that this would work." + }, + { + "text": "Because it's the method that is constantly used." + }, + { + "text": "Now do I have?" + }, + { + "text": "What do I have there?" + }, + { + "text": "Is it working?" + }, + { + "text": "This is r0 A." + }, + { + "text": "That was, of course, A0." + }, + { + "text": "r0 A0 r0 inverse." + }, + { + "text": "r0 A0 r0 inverse." + }, + { + "text": "Good." + }, + { + "text": "Minus S. What have I got there?" + }, + { + "text": "From the r0 minus Si r0, what is that?" + }, + { + "text": "That's minus Si." + }, + { + "text": "Look, success." + }, + { + "text": "The r0 cancels the r0 inverse." + }, + { + "text": "So that term from that, that, that is minus Si." + }, + { + "text": "Cancels plus Si." + }, + { + "text": "I'm finished." + }, + { + "text": "And lo and behold, we have the same similarity." + }, + { + "text": "So we messed around by a multiple of the identity, and it actually makes the thing converge faster if we choose the shifts well." + }, + { + "text": "But basically, the same idea is still working." + }, + { + "text": "OK." + }, + { + "text": "So that's the QR method." + }, + { + "text": "Well, that's the method we haven't shown and won't show." + }, + { + "text": "Except for this half-completed example, I don't plan to prove that the lower triangular part begins to disappear, gets smaller and smaller and smaller, and then the eigenvalues pop up on the diagonal." + }, + { + "text": "It's amazing." + }, + { + "text": "Amazing." + }, + { + "text": "OK. Now, is there any other improvement we can make?" + }, + { + "text": "So that's the method." + }, + { + "text": "And where is the work in using that method?" + }, + { + "text": "Because that's what we always focus on." + }, + { + "text": "Where are we spending computer time?" + }, + { + "text": "Well, we're spending computer time in doing the factorization." + }, + { + "text": "So it didn't cost anything to shift by the identity, but then we had to factor that into Q0, R0." + }, + { + "text": "Then it didn't cost much to multiply them in the opposite order." + }, + { + "text": "So the work was in QR." + }, + { + "text": "So could we think of anything to improve that aspect?" + }, + { + "text": "Could we think of anything there?" + }, + { + "text": "And then we've got a really first-class method." + }, + { + "text": "Well, if the matrix A, A0, the matrix we started with, had some zeros that allowed us to skip steps in doing the QR factorization." + }, + { + "text": "So what am I going to say?" + }, + { + "text": "I'm going to say if A or A0, our original matrix, has a bunch of zeros, let's say it's got a whole lot of zeros there." + }, + { + "text": "Maybe it's, well, OK." + }, + { + "text": "I overdid it here." + }, + { + "text": "I know the eigenvalues right off." + }, + { + "text": "But so the truth is I can't, saying that if that, it's not going to happen." + }, + { + "text": "But we can get zeros with one extra diagonal." + }, + { + "text": "That turns out, so here's the main diagonal." + }, + { + "text": "Everybody's got his eye on the main diagonal." + }, + { + "text": "And one diagonal, I can get a lot of zeros." + }, + { + "text": "But I can't by simple computations." + }, + { + "text": "And I'll show you how to get one." + }, + { + "text": "But I can't get all those to be 0, because then I would have the eigenvalues right there." + }, + { + "text": "And that, well, how do I know that I can't?" + }, + { + "text": "In elimination, ordinary solving AX equal B, you really do get to an upper triangular form." + }, + { + "text": "Some operator, some elimination steps, you plug away, and your matrix becomes upper triangular U." + }, + { + "text": "And you're golden." + }, + { + "text": "But that's too much to expect here." + }, + { + "text": "In fact, we know we can't do it by simple steps." + }, + { + "text": "Because if we could do it, if we could get to a U with a whole lower triangular part 0, we would have found the eigenvalues." + }, + { + "text": "And we know that the eigenvalues solve an equation of nth degree." + }, + { + "text": "And we know somebody proved centuries or more ago that you can't solve an nth degree equation by simple little steps." + }, + { + "text": "Right?" + }, + { + "text": "Do you know who that was?" + }, + { + "text": "And you know that fact?" + }, + { + "text": "And what degree does it apply to?" + }, + { + "text": "So that's an important fact that you sort of pick up in math." + }, + { + "text": "Yeah, what do you?" + }, + { + "text": "Fifth degree, yeah." + }, + { + "text": "So 5 by 5 and up would be, this is impossible." + }, + { + "text": "Impossible." + }, + { + "text": "There's no formula to find a simple formula for the lambdas." + }, + { + "text": "And similarly for the sigmas, the singular values." + }, + { + "text": "So the eigenvalues is definitely a level of difficulty beyond Ax equal b, the inverse matrix or something, the pivots." + }, + { + "text": "All that you can do exactly if you do exact arithmetic." + }, + { + "text": "We cannot find the lambdas exactly." + }, + { + "text": "But we can get as close as we like by continuing with the QR method." + }, + { + "text": "So yeah, in other words, we have to settle for, if we want to, at the beginning, improve our matrix before we start doing that stuff." + }, + { + "text": "We can get it with one extra diagonal." + }, + { + "text": "And do you know what kind of a matrix, whose name?" + }, + { + "text": "And I don't know why." + }, + { + "text": "Yeah, say it again." + }, + { + "text": "Upper Hessenberg." + }, + { + "text": "So upper is just like upper triangular." + }, + { + "text": "It's up there." + }, + { + "text": "But the key person's name is Hessenberg." + }, + { + "text": "As I say, that's a Hessenberg matrix." + }, + { + "text": "So Hessenberg matrix is a matrix with one triangular plus one more diagonal." + }, + { + "text": "But lots of zeros." + }, + { + "text": "Order of n squared, something like almost like half n squared, not quite, but close, zeros." + }, + { + "text": "And you could show that those zeros stay zeros in QR." + }, + { + "text": "So that really pays off." + }, + { + "text": "It cuts the work down significantly." + }, + { + "text": "So the full QR method is step one, reduce A to Hessenberg form with these zeros." + }, + { + "text": "And when I say reduce, I mean find a similarity transformation, of course, because I want the eigenvalues of this to end up the same as the Hessen." + }, + { + "text": "I want to keep the same eigenvalues as I go." + }, + { + "text": "And then step two is QR on this Hessenberg matrix with shifts." + }, + { + "text": "So that's the code that would be programmed in IGAVE." + }, + { + "text": "That's what MATLAB and, well, really, MATLAB is appealing, like other matrix systems, is appealing to LAPAC and LINPAC." + }, + { + "text": "The team of professional numerical analysts really spent a lot of effort and time." + }, + { + "text": "The book LAPAC has 10 authors." + }, + { + "text": "And you can download any of these codes, like the eigenvalue code." + }, + { + "text": "So that's where MATLAB naturally, that's sort of the Bible for codes in linear algebra." + }, + { + "text": "OK, now, I think it's sort of interesting to know." + }, + { + "text": "And there is one more good thing to tell you about this method." + }, + { + "text": "And it applies if the matrix is symmetric." + }, + { + "text": "If the matrix is symmetric, then if we check all this, we could find that the matrices stayed symmetric." + }, + { + "text": "If A0 is symmetric, I can check." + }, + { + "text": "You could easily check through this, and you would discover that A1 is also symmetric." + }, + { + "text": "It turns out you could rewrite this with a Q0 and a Q0 inverse on the other side." + }, + { + "text": "But that Q0 inverse is the same as Q0 transpose, because it's an orthogonal matrix, and symmetry would fall out." + }, + { + "text": "So if it's symmetric, and it's in Hessenberg form, and it stays symmetric at every step, what can you tell me about a symmetric Hessenberg matrix?" + }, + { + "text": "It's only got, yeah, you just erase all these." + }, + { + "text": "If there are zeros there, and if the matrix is symmetric, then we can safely predict that it will only have one diagonal above, one non-zero diagonal above the main diagonal." + }, + { + "text": "In fact, it'll stay symmetric." + }, + { + "text": "So now I should write symmetric Hessenberg matrix, n equals tri-diagonal matrix." + }, + { + "text": "Yeah, three diagonals." + }, + { + "text": "So now you really have reduced the time to do QR, because you've got a tri-diagonal matrix." + }, + { + "text": "It'll stay tri-diagonal in all these steps." + }, + { + "text": "So you're working with just 3n numbers." + }, + { + "text": "Well, actually, 2n, because the diagonal above and the diagonal below are the same." + }, + { + "text": "You're working with just 2n numbers instead of order n squared, and it just goes like a bomb." + }, + { + "text": "So that's I for symmetric matrices." + }, + { + "text": "And you see that it was all based, that really the heart of the algorithm was QR." + }, + { + "text": "So that's my, it took half the class to report on the favorite way, the EIG way, to find eigenvalues." + }, + { + "text": "Oh, I should say something about singular values." + }, + { + "text": "So singular values, of course, the singular values of the matrix are the eigenvalues of A transpose A, square root of those eigenvalues." + }, + { + "text": "But you wouldn't do it that way." + }, + { + "text": "You would never form A transpose A. Oh, I didn't mention the other thing you would never, ever, ever do." + }, + { + "text": "So let me just put it here." + }, + { + "text": "This is like in disgrace to solve that equation." + }, + { + "text": "It's like, OK, back to first grade, because that's not, that's very bad." + }, + { + "text": "A determinant, first of all, it's extremely slow, extremely slow." + }, + { + "text": "And the determinant is packing all this n squared pieces of information into n coefficients, and it's hopelessly ill-conditioned." + }, + { + "text": "Yeah, you just, you lose information all the time." + }, + { + "text": "So really, if this is going on camera, it better go on camera with an x, because don't do it." + }, + { + "text": "OK. Yeah." + }, + { + "text": "So where was I?" + }, + { + "text": "Singular values." + }, + { + "text": "So A transpose A." + }, + { + "text": "So again, let's think about what you could do at the beginning before starting on QR for A transpose A, or for the matrix A." + }, + { + "text": "What could you do with orthogonal matrices?" + }, + { + "text": "So I guess, what did we say about symmetric matrices?" + }, + { + "text": "So here's what I said about symmetric matrices." + }, + { + "text": "If you give me a symmetric matrix, I can, in just a simple number of simple steps, make it tridiagonal." + }, + { + "text": "I can't make it diagonal, because then I'd be finding the eigenvalues, and Abel, who was the first person to see that that was impossible, forbids it." + }, + { + "text": "But so let me write down what I'm saying here." + }, + { + "text": "If I have a symmetric matrix S, I can find a bunch of Q's and Q transposes, and I can put them all together into one big Q, and it's transposed." + }, + { + "text": "And what do I know about the eigenvalues of that matrix?" + }, + { + "text": "Q is orthogonal always." + }, + { + "text": "So what can you tell me about the, this is the same as Q S Q inverse, and therefore, the eigenvalues are the same." + }, + { + "text": "It's similar to S. And it becomes tridiagonal after I find a good Q." + }, + { + "text": "Now, and therefore, same lambdas, tridiagonal with the same lambdas." + }, + { + "text": "Now, what am I thinking about here?" + }, + { + "text": "I'm thinking about, tell me the corresponding possibility about singular values." + }, + { + "text": "I want to do something to my matrix." + }, + { + "text": "Now, I'm always taking a general matrix A." + }, + { + "text": "And I'm looking for its singular values." + }, + { + "text": "And I'm looking to simplify it." + }, + { + "text": "And what am I allowed to do?" + }, + { + "text": "Yeah, I guess my question is, similarity transformations left the eigenvalues alone." + }, + { + "text": "What can I do that leaves the singular values alone?" + }, + { + "text": "That's a fundamental question, because it was so fundamental for eigenvalues." + }, + { + "text": "By doing this, a matrix and its inverse, I got something similar." + }, + { + "text": "And I checked even in this class that the eigenvalues, same lambdas." + }, + { + "text": "Now I want a whole line that ends up with the same sigmas." + }, + { + "text": "And I want you to tell me what I'm allowed to do to the matrix without changing the sigmas." + }, + { + "text": "So maybe don't shout it out immediately." + }, + { + "text": "Let everybody think." + }, + { + "text": "What am I allowed to do to a matrix?" + }, + { + "text": "Every matrix has got these singular values." + }, + { + "text": "And now I want to make it a better matrix with more 0's or something." + }, + { + "text": "If I do that to it, does that change the sigmas?" + }, + { + "text": "Can I do more than that to it?" + }, + { + "text": "What can I do?" + }, + { + "text": "What group of matrices will have the same sigmas as my starting matrix A?" + }, + { + "text": "So that's a basic, basic question about singular values and the SVD." + }, + { + "text": "So let's think of the answer together." + }, + { + "text": "So it's connected to the SVD." + }, + { + "text": "So let me remember the SVD." + }, + { + "text": "The SVD, I have some orthogonal matrix, then the singular value matrix, SV for singular values, and then another orthogonal matrix." + }, + { + "text": "What could I do to that equation that would not touch this guy?" + }, + { + "text": "So I'm asking what invariance, because not touching it means leaving it not varying." + }, + { + "text": "So I'm looking for under what operations are the singular values invariant?" + }, + { + "text": "When I was looking at eigenvalues, this was the operation." + }, + { + "text": "Well, it didn't have to be orthogonal." + }, + { + "text": "It's something, and it's inverse." + }, + { + "text": "But now what is it up there?" + }, + { + "text": "What could I do to that matrix A?" + }, + { + "text": "Could I multiply by Q?" + }, + { + "text": "Could I throw in a Q?" + }, + { + "text": "Maybe not even on the other end." + }, + { + "text": "If I throw in an orthogonal Q, do I change the singular values or do I not change them?" + }, + { + "text": "Fundamental question." + }, + { + "text": "The answer is no, I don't change them." + }, + { + "text": "I'm allowed to do that, because here's an orthogonal matrix, a Q times U." + }, + { + "text": "If both of those are orthogonal, then the product is." + }, + { + "text": "Everybody knows that a product of two orthogonal matrix is still orthogonal." + }, + { + "text": "Better know that." + }, + { + "text": "Better know that." + }, + { + "text": "Yeah." + }, + { + "text": "So if I have an orthogonal matrix Q and an orthogonal matrix U, I claim that this is still orthogonal." + }, + { + "text": "And how do I check it?" + }, + { + "text": "Well, I use some test for orthogonality." + }, + { + "text": "What would be the test you like to use?" + }, + { + "text": "The inverse is the same as the transpose." + }, + { + "text": "You like that test?" + }, + { + "text": "So I'll invert it." + }, + { + "text": "Q U inverse." + }, + { + "text": "Of course, for any matrix, that's U inverse Q inverse." + }, + { + "text": "But these were separately orthogonal, so that's U transpose Q transpose." + }, + { + "text": "And that is the same as Q U transpose." + }, + { + "text": "Yeah." + }, + { + "text": "So I use the orthogonality of U and the orthogonality of Q to conclude that the inverse is the transpose." + }, + { + "text": "So the answer is yes, I could do that." + }, + { + "text": "Now, with singular value, with eigenvalues, I had to multiply on the other side by Q inverse or Q transpose." + }, + { + "text": "Do I have to do that now?" + }, + { + "text": "No." + }, + { + "text": "What can I do on the right-hand side?" + }, + { + "text": "I can multiply by." + }, + { + "text": "I can leave it alone." + }, + { + "text": "Then it has the same singular values because it's the same sigma in there." + }, + { + "text": "If I have a orthogonal matrix times a diagonal times an orthogonal, that diagonal, positive diagonal, is going to be sigma." + }, + { + "text": "So what can I do on this side?" + }, + { + "text": "I could multiply by any orthogonal matrix on that side, too." + }, + { + "text": "So let's call this guy Q1 and this guy Q2." + }, + { + "text": "I still have an orthogonal matrix there, orthogonal matrix there, and the same sigma popped in the middle." + }, + { + "text": "So that's what you're allowed to do." + }, + { + "text": "That gives us more freedom." + }, + { + "text": "Before, when we had to do similarity transformations with the same guy, we got it to be tridiagonal." + }, + { + "text": "But now we're allowed to do more stuff." + }, + { + "text": "We're allowed to use different orthogonal matrices on the left and right." + }, + { + "text": "And we can reduce it even further from tridiagonal to bidiagonal." + }, + { + "text": "So the first step is getting 0." + }, + { + "text": "The step of getting 0s reduces it all the way to that with all 0s there." + }, + { + "text": "So it's easier." + }, + { + "text": "Then I work on this." + }, + { + "text": "I work on using a QR type idea, some method like that." + }, + { + "text": "So everybody's seeing that our algorithm has got two stages." + }, + { + "text": "One is get a lot of 0s and get them in places that will stay 0 as part 2 of the algorithm gets going." + }, + { + "text": "And then run part 2 of the algorithm." + }, + { + "text": "You're staying with each step is very fast now because doing a QR factorization is fast." + }, + { + "text": "Was there a question?" + }, + { + "text": "Yeah." + }, + { + "text": "So I would call this bidiagonal, of course." + }, + { + "text": "And everybody recognizes that if I have a bidiagonal matrix, call it A or A0 or whatever." + }, + { + "text": "Then what do you think about A transpose A?" + }, + { + "text": "What would A transpose A?" + }, + { + "text": "If that was A, what could you tell me about A transpose A?" + }, + { + "text": "Could you multiply matrices, like knowing where the non-zeros are, like in your head, and get an idea of where?" + }, + { + "text": "So if I have a bidiagonal matrix A, then sort of implicitly in the SVD, I'm looking at A transpose A." + }, + { + "text": "And what would be true about A transpose A?" + }, + { + "text": "It would be tridiagonal." + }, + { + "text": "So what I've done here and what I've done there just match up." + }, + { + "text": "If you don't want to change singular values, you can get all the way to here." + }, + { + "text": "But then to find those singular values, that would involve A transpose A." + }, + { + "text": "It would be symmetric and tridiagonal." + }, + { + "text": "And then you'd be in that game." + }, + { + "text": "So those are the basic facts of I and SVD." + }, + { + "text": "For matrices of order up to 1,000, say." + }, + { + "text": "I'm not enough of an expert to know where." + }, + { + "text": "Maybe higher, because in perfect math, it's going to take infinitely many steps." + }, + { + "text": "Or Abel would be very surprised." + }, + { + "text": "He would see you solving for eigenvalues and then to re-equation by a whole lot of little steps and getting them exactly right." + }, + { + "text": "That won't happen." + }, + { + "text": "But you get them within epsilon in a number of steps that's like n cubed." + }, + { + "text": "So that's pretty impressive." + }, + { + "text": "The eigenvalue problem is being solved, in quotes, by a fast method that gets you a good answer within a tolerance in n cubed steps." + }, + { + "text": "Right." + }, + { + "text": "So that's great as long as n isn't too big." + }, + { + "text": "And then when n is too big, which of course happens, you have to think again." + }, + { + "text": "So this method is a giant success up to large matrices." + }, + { + "text": "But then you have to think again." + }, + { + "text": "And what is involved in thinking again?" + }, + { + "text": "Well, I guess more thinking." + }, + { + "text": "So what do you do if the matrix is bigger?" + }, + { + "text": "I guess that Krylov would say, use my method." + }, + { + "text": "So Krylov would say, especially if your matrix is sparse." + }, + { + "text": "Can we just remember what Krylov was?" + }, + { + "text": "Krylov started with a vector b, multiplied it by a, multiplied that by a, and got up to, let's say, a to the 999b." + }, + { + "text": "So now Krylov has got 1,000 dimensional space." + }, + { + "text": "He's got a basis for it, 1,000 vectors that span 1,000 dimensional space." + }, + { + "text": "And he'll look at the matrix A only on that space." + }, + { + "text": "In other words, I won't go into detail about that." + }, + { + "text": "He restricts the matrix to this 1,000 dimensional space." + }, + { + "text": "And he hopes that it's captured." + }, + { + "text": "We hope that the eigenvector is virtually in that space." + }, + { + "text": "And actually, I wouldn't go up to, let me take a 9 out of that." + }, + { + "text": "100 dimensional would probably catch the eigenvector." + }, + { + "text": "So if the eigenvector is virtually in this space, then we can look at a matrix of order 100." + }, + { + "text": "We can bring A down to just see its action on that space." + }, + { + "text": "So I look at vectors V, which are some combination, C1b plus C2ab plus C3a squared b and C100 a to the 99th b, plus an error." + }, + { + "text": "And I'm going to ignore that error." + }, + { + "text": "Because I've gone up to dimension 100." + }, + { + "text": "I probably say it's pretty safe to ignore that error." + }, + { + "text": "And then in this space, just looking at the matrix A." + }, + { + "text": "So wherever A to the 100th comes in, forget it." + }, + { + "text": "Just think about the matrix A as multiplying vectors of this kind in this space." + }, + { + "text": "Then I have a 100 by 100 eigenvalue problem." + }, + { + "text": "And so the big matrix A is reduced to a matrix of size 100 by, do you see sort of what I'm saying, even though I'm not giving the details?" + }, + { + "text": "Think of a matrix A of size a million." + }, + { + "text": "And you apply it to Krylov vectors." + }, + { + "text": "So I call them little k for a Krylov vector in this 100-dimensional space." + }, + { + "text": "So they have a million minus 100, zero components, you could say, this k. This is in the Krylov space." + }, + { + "text": "This is A, a million, k, 100." + }, + { + "text": "It's a full, it's got a million components, but it's out of just 100-dimensional space." + }, + { + "text": "So when I multiply by A, it'll be mostly in, mostly in, partly in the Krylov space, k 100, and a piece out of k 100." + }, + { + "text": "And I just ignore that part of the matrix." + }, + { + "text": "So I have a 100 by 100 problem, and I've solved to find the eigenvalues." + }, + { + "text": "And they're a pretty good approximation to the eigenvalues, to the, hopefully, like the lowest 100 eigenvalues." + }, + { + "text": "I'd like to know that." + }, + { + "text": "But I might not be sure that this idea would give me the lowest 100, the first 100 eigenvalues of the million, of the matrix of size a million." + }, + { + "text": "I'm just taking a few minutes here to sort of wave hands about what Krylov, the Krylov idea would do." + }, + { + "text": "And I probably won't mention Krylov again this semester." + }, + { + "text": "So what it can do is look at this particular type of space, because we can get a basis for it quickly, just multiply again and again by A." + }, + { + "text": "Then we can orthogonalize that basis." + }, + { + "text": "That's Graham-Schmidt in some form." + }, + { + "text": "We're always going back to Graham-Schmidt." + }, + { + "text": "Then I have a 100 by 100." + }, + { + "text": "I have a subspace of size 100." + }, + { + "text": "I look at what the matrix does in that space." + }, + { + "text": "And I could look for, I could find eigenvalues restricted to that space." + }, + { + "text": "They wouldn't be the perfect eigenvalues, but they would be accurate." + }, + { + "text": "OK, so I didn't know it would take one class time to talk about finding eigenvalues and singular values, but we did some important things." + }, + { + "text": "We remembered that similarity is the thing to check, thing to preserve, because it doesn't change the eigenvalues." + }, + { + "text": "And then for singular values, what was the thing?" + }, + { + "text": "You could multiply left and right by different orthogonal matrices." + }, + { + "text": "And somehow, maybe that doesn't have an established name, multiplying left and right by a Q1 and a Q2 transpose." + }, + { + "text": "Yeah, but the idea is clear." + }, + { + "text": "And that doesn't change the singular values." + }, + { + "text": "We're ready to move now into maybe our next step, which we don't spend a long time on." + }, + { + "text": "We'll be like random sampling." + }, + { + "text": "What if your matrix is just way too big?" + }, + { + "text": "So that's a new, very new idea, very different idea in numerical linear algebra, is just to sample the matrix." + }, + { + "text": "Could you believe that the answer is going to come out right just for a random sample?" + }, + { + "text": "Well, the odds are in your favor." + }, + { + "text": "OK, so that'll be Wednesday, and then we have lots of new, we'll move onward after that." + }, + { + "text": "OK, see you Wednesday." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated/lZrIPRnoGQQ.json b/sight/sources/annotated/lZrIPRnoGQQ.json new file mode 100644 index 0000000000000000000000000000000000000000..468241b272d9afb70d3976d346574cdbebf2c893 --- /dev/null +++ b/sight/sources/annotated/lZrIPRnoGQQ.json @@ -0,0 +1,1634 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "OK, here we go." + }, + { + "text": "All set." + }, + { + "text": "And two topics for today." + }, + { + "text": "One is to go back to Professor Sra's lecture." + }, + { + "text": "That was last Friday." + }, + { + "text": "And he promised a theorem and proof." + }, + { + "text": "And this morning, he sent it to me." + }, + { + "text": "So it's the convergence." + }, + { + "text": "It's proving the convergence of stochastic gradient descent." + }, + { + "text": "And really, what's important, maybe, and useful is not so much the details of the proof, which I'm just learning, but the assumptions." + }, + { + "text": "You know, what's the logic here?" + }, + { + "text": "What do you have to assume about the gradient and about the algorithm to get the answer?" + }, + { + "text": "But now, I actually look back at the video of his lecture." + }, + { + "text": "And it was excellent." + }, + { + "text": "And as I looked at it, there were a couple of things later in the lecture that I thought would make good projects." + }, + { + "text": "So I don't know if anybody is still open to what to do on a project." + }, + { + "text": "But here are my two ideas." + }, + { + "text": "And if you've already finished your project, well, get an A-plus by considering one of these." + }, + { + "text": "So you remember, and this will remind you of the lecture, which is a good thing." + }, + { + "text": "So do you remember that question one was whether in the stochastic part, after you've sampled one or some mini batch, but let's just say one of the loss functions coming from one sample, you remember the whole point is that if we do all zillion samples at every iteration, we're really, really slow." + }, + { + "text": "So the stochastic idea is to randomly pick one or a mini batch of the samples and just reduce their loss, just deal with the loss, say the square loss, or later we'll see cross-entropy loss." + }, + { + "text": "But whatever the cost is, just do a few or one." + }, + { + "text": "And then the question was, after you've done that one, do you put it back in the pot and every time you sample over the whole collection, but that's expensive, or do you just make a list of random list of random order of all the samples and go through them, which is then without replacement, which is sort of semi-illegal." + }, + { + "text": "That is, the logic in the randomization asks you to replace every time, but nobody does it." + }, + { + "text": "It costs a lot, probably not worth it." + }, + { + "text": "So the project would be, suppose you take 1,000, or say just 100, 100 random numbers." + }, + { + "text": "Say you use MATLAB, just the command rand." + }, + { + "text": "So you get numbers whose average is 1 by 2 from rand." + }, + { + "text": "They're between 0 and 1." + }, + { + "text": "So we know what the average is." + }, + { + "text": "So let's compute it two ways." + }, + { + "text": "One is by not replacing, and that's the interesting one." + }, + { + "text": "So take 100 samples." + }, + { + "text": "Well, I guess we know that after we've got through the full 100, we're going to get exactly the right answer." + }, + { + "text": "But anyway, my question would be, how much difference do you see in the eventual approach?" + }, + { + "text": "So the law of large numbers, I guess, would tell us we get an average of 1 half for these numbers with uniform distribution between 0 and 1." + }, + { + "text": "Should I be writing anything here?" + }, + { + "text": "Maybe I should." + }, + { + "text": "So this is project 1." + }, + { + "text": "So you pick numbers a, k, which is rand from rand, so uniformly on 0, 1, on 0, 0, 1." + }, + { + "text": "And then my question is, what about convergence to the average is 1 half?" + }, + { + "text": "And so this may be too simple an example, but could we see what happens for the convergence of the average as you either do replacements or don't do replacements?" + }, + { + "text": "And then, in fact, I would like to see a figure that looks like those in his lecture." + }, + { + "text": "He started it somewhere." + }, + { + "text": "Start." + }, + { + "text": "And then here's the finish." + }, + { + "text": "But you remember that stochastic gradient descent was kind of pretty effective at the beginning." + }, + { + "text": "Well, the beginning, those might be 100 iterations each, one epoch, one run through the full number." + }, + { + "text": "But then when it got to here, got closer, it started oscillating." + }, + { + "text": "You remember he identified the region of confusion around the thing." + }, + { + "text": "Well, my suggestion is just I think those videos should be accessible to you on, are they on Stellar?" + }, + { + "text": "Yeah." + }, + { + "text": "So I'd love to see that behavior in some good examples of that behavior and some pictures to use." + }, + { + "text": "So that would be one idea." + }, + { + "text": "With and with." + }, + { + "text": "Oh, yeah, that's also idea two." + }, + { + "text": "Idea two is the good start and then the bad finish for stochastic gradient descent." + }, + { + "text": "And of course, the magic words in, even without this, the magic words in computations is early stopping." + }, + { + "text": "We don't overfit." + }, + { + "text": "So we wanted to stop early anyway." + }, + { + "text": "And early stopping just is like a good idea for if that's what the approach to the x star that you're looking for." + }, + { + "text": "This would be the place where the, this is where, that's x star where grad f at x star is 0." + }, + { + "text": "That's the minimum point." + }, + { + "text": "That's arg min." + }, + { + "text": "Arg min." + }, + { + "text": "Exactly what we're looking for." + }, + { + "text": "And we don't find it very well, but we get close to it fast." + }, + { + "text": "OK. Two ideas on projects." + }, + { + "text": "So just, so maybe I'll go to the main topic of today, the topic I promised, the idea of back propagation." + }, + { + "text": "To compute, this is all to compute grad f, the gradient, all the derivatives." + }, + { + "text": "This is the df dx1 to df dxm, maybe I'll say, where I have m features for the sample." + }, + { + "text": "OK." + }, + { + "text": "So that's back propagation." + }, + { + "text": "And that's the thing whose discovery or rediscovery put neural nets on the map." + }, + { + "text": "That's the key calculation, of course, to find the gradient in the steepest descent algorithm." + }, + { + "text": "Every step needs a gradient." + }, + { + "text": "And if you can't compute it quickly, you're in bad shape." + }, + { + "text": "But you can compute it quickly by this automatic differentiation in reverse mode, which is otherwise known." + }, + { + "text": "I don't think the people, maybe Hinton was the first, was the leader in developing deep neural nets, deep learning." + }, + { + "text": "And he realized, so I give him big credit for that, that back propagation would work and would give him fast gradients." + }, + { + "text": "But it actually had been studied before under the name AD, automatic differentiation." + }, + { + "text": "So may I just tell you that idea?" + }, + { + "text": "Some of you may know it, may know about it, may know more than I, and might know a good website to see this description." + }, + { + "text": "There'll be, of course, a section of the book, of the notes." + }, + { + "text": "Already, you already have it." + }, + { + "text": "This is section 7.2." + }, + { + "text": "So this is the chapter on deep learning." + }, + { + "text": "And the first section was about the structure of f of x." + }, + { + "text": "And you remember the key point about the structure of f of x is that I start with x and apply some function f1 of x." + }, + { + "text": "And to that, I apply some function f2 of x." + }, + { + "text": "And to that, I apply some function of f3 of f2 of f1 of x." + }, + { + "text": "And that's the thing whose derivative I need." + }, + { + "text": "So I'll just take ordinary derivative." + }, + { + "text": "Well, partial derivatives, really, because I better say partial derivatives." + }, + { + "text": "So suppose x is a pair xy." + }, + { + "text": "Example." + }, + { + "text": "Let me show you by example." + }, + { + "text": "So suppose f of x is, let me take a simple example, x cubed times x plus 2y." + }, + { + "text": "So I want to think of that function the way anybody would, as being built as a product of two functions." + }, + { + "text": "So there is a product rule to get into the derivative." + }, + { + "text": "And then we need the derivatives of each piece." + }, + { + "text": "So there's a power rule and a linear combination rule." + }, + { + "text": "So it's got a few of the rules that we use." + }, + { + "text": "And the point is to think about the computation of f of x and the computation of df dx and the computation of df dy." + }, + { + "text": "Those are the derivatives that we need." + }, + { + "text": "This is the function we need." + }, + { + "text": "And how to do those computations quickly." + }, + { + "text": "OK." + }, + { + "text": "So and this is section 7.2, which benefited a lot from a blog." + }, + { + "text": "I'm not a blog reader or a blog writer, but somehow I found this blog." + }, + { + "text": "So let me put." + }, + { + "text": "It's Christopher Olwa is his name." + }, + { + "text": "And he really writes clear things." + }, + { + "text": "So he contributes." + }, + { + "text": "He works for one of the big companies and does the deeper research." + }, + { + "text": "But he's also a really good expositor." + }, + { + "text": "And the website that he now uses is called distill.something." + }, + { + "text": "But I think maybe this blog was earlier before the start of distill." + }, + { + "text": "But it might be loaded onto distil." + }, + { + "text": "Anyway, that's where I got this simple description of backpropagation." + }, + { + "text": "And let's just do calculus first of all." + }, + { + "text": "If I just have a function of maybe even one variable, what's the derivative?" + }, + { + "text": "What is df dx here?" + }, + { + "text": "Just to remember what calculation we have to do." + }, + { + "text": "So df dx, this is with n equal 1, one variable." + }, + { + "text": "So I'll use ordinary derivative and not partial derivative." + }, + { + "text": "But this is then what I, that's what really has to be done." + }, + { + "text": "But just what's the derivative of that, of a chain of functions?" + }, + { + "text": "Well, of course, the chain rule." + }, + { + "text": "So what does the chain rule say?" + }, + { + "text": "I differentiate F3." + }, + { + "text": "I don't know, what do I put that it's differentiated with respect to?" + }, + { + "text": "F3, df3, df2, is that what I should put?" + }, + { + "text": "OK. And where do I evaluate that derivative?" + }, + { + "text": "So yeah, I don't evaluate it at x, right?" + }, + { + "text": "I'm differentiating with respect to F2." + }, + { + "text": "So do I evaluate it at F2 of F1 of x?" + }, + { + "text": "This is where the chain rule gets sort of a little chainy, a little." + }, + { + "text": "OK, then we know that df2, df1." + }, + { + "text": "And again, that's now evaluated at F1 of x." + }, + { + "text": "And then the final factor is df1, dx, evaluated at x." + }, + { + "text": "That's somehow what we have to do." + }, + { + "text": "And that's just for an ordinary one variable function." + }, + { + "text": "And I have here a two variable function." + }, + { + "text": "And deep learning has a million variable function." + }, + { + "text": "So let's, I think we won't go to a million, but two we could manage." + }, + { + "text": "So let's compute those." + }, + { + "text": "Let's compute the function, first of all." + }, + { + "text": "Compute F. So I'm given x equals, say, 2, and y equals, say, 3." + }, + { + "text": "And I'm going to create a computational graph." + }, + { + "text": "So this is to draw." + }, + { + "text": "So I'm actually going to draw the computational graph to compute for F. And then it'll be a variation of that graph to find the derivatives." + }, + { + "text": "So let's just start with the graph, first of all, for the function, because we're going to need that." + }, + { + "text": "So again, it's x cubed plus." + }, + { + "text": "So can I write that function again?" + }, + { + "text": "x cubed times x plus 2y." + }, + { + "text": "So I think we're going to, the first step will be to find x plus x cubed, that factor, which will be 8." + }, + { + "text": "And we have to find the other factor, x plus 2y." + }, + { + "text": "So then I'm going to, that uses y and x." + }, + { + "text": "So it's a directed graph going forward with this computation." + }, + { + "text": "So x plus 2y equals whatever it is, 2 and 6." + }, + { + "text": "Oh, 8 again, not brilliant." + }, + { + "text": "What shall I change here?" + }, + { + "text": "Make it 3y, 3y, just to get a different number here." + }, + { + "text": "So now x is 2, y is 3." + }, + { + "text": "I get 11." + }, + { + "text": "That's a good number, 11." + }, + { + "text": "OK, so far so good?" + }, + { + "text": "And now the next step on this graph will be to, I have a product of those." + }, + { + "text": "So that will go to the product." + }, + { + "text": "Product F equals 8 times 11, 88." + }, + { + "text": "OK, so we got the answer, 88." + }, + { + "text": "Which math, normally I wouldn't take that much of a book to compute F. I would have said 2 cubed times 2 plus 3 times 3." + }, + { + "text": "And I'd have simplified that to 8 times 11." + }, + { + "text": "And I would have got 88." + }, + { + "text": "So if we were just writing normally, that would do it." + }, + { + "text": "But this is the picture of the computational graph." + }, + { + "text": "OK, good, good, good." + }, + { + "text": "Now it's the derivatives, two derivatives to find, dF dx and dF dy." + }, + { + "text": "Suppose we go forward first." + }, + { + "text": "My point is going to be, or the great point is that backward is better." + }, + { + "text": "Reverse mode is better." + }, + { + "text": "But we don't know what that means until we've gone forward." + }, + { + "text": "So let me go forward." + }, + { + "text": "So now I'm going to go forward." + }, + { + "text": "Forward." + }, + { + "text": "So what do we?" + }, + { + "text": "Let's do dF dx, OK?" + }, + { + "text": "Everybody's up for dF dx, the partial derivative with respect to x." + }, + { + "text": "So here we have x equal 2 and y equal 3." + }, + { + "text": "OK?" + }, + { + "text": "And then I've got to take the derivative of that step." + }, + { + "text": "The first step was x to x cubed." + }, + { + "text": "So I need the derivative." + }, + { + "text": "The whole point of AD is that the computation, every computation of a derivative breaks down like this into very simple pieces." + }, + { + "text": "And the derivatives of those simple pieces are also simple pieces." + }, + { + "text": "So the whole point is to replace appropriately those intermediate steps with derivatives, so as to compute the x derivative." + }, + { + "text": "So I have to use the fact that the derivative of x cubed with respect to x. Oh, I better do partial derivative." + }, + { + "text": "Partial derivatives of x cubed with respect to x is 3x squared." + }, + { + "text": "So now I'll put maybe a formula and then a number, so that gives 3 times 4, 12." + }, + { + "text": "And the derivative of x cubed with respect to y gives 0." + }, + { + "text": "Clearly, that's 0." + }, + { + "text": "And then the derivative." + }, + { + "text": "So I'm doing the x derivative." + }, + { + "text": "So the derivative of y with respect to x is, you get to tell me, if I'm computing partial derivatives, is 0." + }, + { + "text": "Is 0. y and x are independent." + }, + { + "text": "And this is the reason, in my view, that the forward method is wasteful, because I'm going to have to do another whole graph for the y derivative." + }, + { + "text": "In other words, tracking the x derivatives, a whole lot of stuff never got off the ground." + }, + { + "text": "So we never should have looked at it." + }, + { + "text": "So anyway." + }, + { + "text": "But I do need, I have this x plus 3y." + }, + { + "text": "Maybe, I don't know whether to erase that." + }, + { + "text": "I think I will, just because I don't know what to do with it there." + }, + { + "text": "So now let me take the ones that I really need." + }, + { + "text": "So this is the derivative with respect to x of x plus 3y, which is 1." + }, + { + "text": "And so that gives me the answer 1 for any x, actually." + }, + { + "text": "And now what?" + }, + { + "text": "Oh, yeah." + }, + { + "text": "I'm really, I don't need these." + }, + { + "text": "This is a waste of time, isn't it?" + }, + { + "text": "Is it only x derivatives I want?" + }, + { + "text": "Anyway, let's just keep going." + }, + { + "text": "You can see this takes a little organization, and I'm not practiced with it." + }, + { + "text": "So what am I going to do?" + }, + { + "text": "I'm looking for the x derivative of, I've got to use a product rule now." + }, + { + "text": "I found the x derivative of that factor was 12." + }, + { + "text": "The x derivative of this factor is 1." + }, + { + "text": "And now the x derivative of the product." + }, + { + "text": "So now I'm going to do somehow a product rule." + }, + { + "text": "The x derivative of this product." + }, + { + "text": "I should have given these two terms a name." + }, + { + "text": "Let me call that first term x cubed and the second term x plus 3y." + }, + { + "text": "Call it s. So I'll call the two terms c and s. So I now need to get, so that's dc ds." + }, + { + "text": "This is dc dx." + }, + { + "text": "This is dc dx." + }, + { + "text": "And this one is ds dx." + }, + { + "text": "And dc dy, do I need to know that?" + }, + { + "text": "I'm sorry." + }, + { + "text": "This computational graph has thrown me." + }, + { + "text": "But now I want to use the product rule." + }, + { + "text": "And I'm taking x derivatives, right?" + }, + { + "text": "So I should have computed c and s. Yes, I see I've got to need those in the product rule." + }, + { + "text": "So I should have computed c as being 8 and s as being 5." + }, + { + "text": "Is that right?" + }, + { + "text": "2 plus 3 is 11." + }, + { + "text": "Yeah, I needed the 8 and the 11." + }, + { + "text": "Is that our?" + }, + { + "text": "What's up?" + }, + { + "text": "I've just been running along here without getting myself in the whole picture." + }, + { + "text": "Yeah, 8 and 11 is right." + }, + { + "text": "But now I'm looking for the derivatives, right?" + }, + { + "text": "So I don't multiply those." + }, + { + "text": "That's not the product rule." + }, + { + "text": "So the product rule is what?" + }, + { + "text": "s times, so this product rule, I have to do this combination of this is now the product rule for the derivative of c times s. So I want c ds dx plus s dc dx." + }, + { + "text": "I think I'm on track now." + }, + { + "text": "And now I want to put in numbers." + }, + { + "text": "So c is 8. ds dx, have we computed ds dx?" + }, + { + "text": "Yes, ds dx is 1." + }, + { + "text": "And now s itself is computed as 11." + }, + { + "text": "And dc dx, we compute it as 12." + }, + { + "text": "I don't dare look." + }, + { + "text": "Have I?" + }, + { + "text": "Am I?" + }, + { + "text": "I don't think I'm going to get." + }, + { + "text": "Oh, no, I don't know the answer yet." + }, + { + "text": "Sorry, I'm not trying to get 88, right?" + }, + { + "text": "You guys are not helping." + }, + { + "text": "You see, I'm in trouble." + }, + { + "text": "But what I imagine here is that's 8 and that's 132." + }, + { + "text": "So I'm getting 140." + }, + { + "text": "Is there any possibility that that's the right answer for df dx?" + }, + { + "text": "This is df dx I computed." + }, + { + "text": "By watching me struggle here, you're seeing the idea." + }, + { + "text": "Every step, I take the derivative of each step." + }, + { + "text": "So it was a power step, x cubed." + }, + { + "text": "So I had a 3x squared and a sum step." + }, + { + "text": "So I had a 1." + }, + { + "text": "Then the next step was a multiplication." + }, + { + "text": "So I needed the product rule for that." + }, + { + "text": "I have these separate numbers." + }, + { + "text": "So I put them in." + }, + { + "text": "And so the computational graph finished." + }, + { + "text": "We only needed two levels." + }, + { + "text": "And we got 8 and 132, 140." + }, + { + "text": "But we didn't get df dy yet." + }, + { + "text": "And for that, I'd need to redo this again." + }, + { + "text": "And I don't want to do that." + }, + { + "text": "I would rather do the reverse mode and do them both at once." + }, + { + "text": "That's the point of the reverse mode." + }, + { + "text": "It's very efficient." + }, + { + "text": "It's very efficient, actually." + }, + { + "text": "Computing the gradient after you've done the work for the function, computing first derivatives, you could compute n first derivatives with about four or five times the cost, not n times." + }, + { + "text": "That's amazing to me." + }, + { + "text": "That is amazing that I can compute the gradient very efficiently by the back prop." + }, + { + "text": "So I have to show you the backwards way." + }, + { + "text": "I'm just going to follow all the paths backwards so that I get both df dx and df dy." + }, + { + "text": "You see the idea is to take the derivative of each step, each small step." + }, + { + "text": "That's really what we do in calculus." + }, + { + "text": "If you think about the start of a calculus course, what derivatives do we actually know?" + }, + { + "text": "Do we actually use xf at x plus delta x minus f?" + }, + { + "text": "What derivatives do we grind out?" + }, + { + "text": "We do the derivatives of x to the n. Every calculus book starts with x squared and then finds the derivative of x to the n. Then you do sine x and cos x." + }, + { + "text": "Then what others?" + }, + { + "text": "Are there any more?" + }, + { + "text": "Even e to the x, good, e to the x." + }, + { + "text": "And it's the inverse function log." + }, + { + "text": "In freshman calculus, you always write ln just to be out of date." + }, + { + "text": "And now that may be the list, is it?" + }, + { + "text": "And then the chain rule." + }, + { + "text": "Are there others that you actually do a computation of?" + }, + { + "text": "Actually, e to the x is defined by the property that its derivative is e to the x." + }, + { + "text": "And then you discover what log x has to be." + }, + { + "text": "And sine x, how do you do sine of x plus delta x?" + }, + { + "text": "Well, minus sine of x, how do you find the hard way, once and for all way?" + }, + { + "text": "You draw a little unit circle and mess with some angles." + }, + { + "text": "And you discover that the derivative of the sine is the cosine." + }, + { + "text": "That's if you've defined the sine as a ratio of sides in a right triangle." + }, + { + "text": "Of course, you could define it as an infinite series." + }, + { + "text": "And then you would be back to just using that." + }, + { + "text": "OK." + }, + { + "text": "So calculus does exactly what we're doing here." + }, + { + "text": "Finds all derivatives by the chain rule applied to a few ones that it has worked out in detail." + }, + { + "text": "But tangent of x, we would use the quotient rule." + }, + { + "text": "Secant of x, we would use the quotient rule, 1 over cosine." + }, + { + "text": "And the products, we use the product rule." + }, + { + "text": "So really, calculus tends to seem fairly simple when you look back to see what actually you did." + }, + { + "text": "And then integration, what is integral calculus about?" + }, + { + "text": "More or less, guessing the answer." + }, + { + "text": "You have to integrate f of x dx." + }, + { + "text": "And so really, what you have to do is sort of think, OK, what had this derivative?" + }, + { + "text": "What function had that derivative?" + }, + { + "text": "And mess around and get it." + }, + { + "text": "So really, it's a freshman course, I guess." + }, + { + "text": "OK." + }, + { + "text": "So where am I?" + }, + { + "text": "Backward, right." + }, + { + "text": "That's the thing still to do." + }, + { + "text": "How does the backward system work?" + }, + { + "text": "OK, I'll try my best." + }, + { + "text": "OK." + }, + { + "text": "So here's the big goal." + }, + { + "text": "Back." + }, + { + "text": "So reverse mode AD." + }, + { + "text": "Right." + }, + { + "text": "And let me make myself a little note." + }, + { + "text": "The little note is to give you another example where the order that you do the computations makes a big difference." + }, + { + "text": "And that's not obvious that it will, right?" + }, + { + "text": "There are many things in math that you could do in either order." + }, + { + "text": "And it seems like logically, you've done the same thing." + }, + { + "text": "So another and simpler example, which shows how one way could be way faster than another way, is when I'm multiplying two matrices, three matrices." + }, + { + "text": "So I'm multiplying three matrices, A times B times C. And the question is, do I do BC first and then multiply by A?" + }, + { + "text": "Or do I do AB first and then multiply that by C?" + }, + { + "text": "And of course, I kept them in order, in the order ABC." + }, + { + "text": "But the order of computations can be different." + }, + { + "text": "You get the same." + }, + { + "text": "You get the right answer both ways." + }, + { + "text": "But those can be completely, completely different." + }, + { + "text": "One can be 1,000 times faster than the other." + }, + { + "text": "So that's just to show." + }, + { + "text": "Actually, it kind of connects to this." + }, + { + "text": "And there is also another." + }, + { + "text": "So I'll do that too." + }, + { + "text": "And there's also this." + }, + { + "text": "So this is example 2, where this is meant to be example 1." + }, + { + "text": "And example 3 would be, leads to something called the adjoint method in differential equations or in optimization." + }, + { + "text": "In computing optimum, in maximizing." + }, + { + "text": "And that has the same, really, the underlying reason it gives a speed up is it makes the right choice in a product of three things." + }, + { + "text": "So it'll be enough to do example 1 and example 2." + }, + { + "text": "Let me go with example 1." + }, + { + "text": "Our, this is now back propagation." + }, + { + "text": "Finally, we got to it." + }, + { + "text": "OK." + }, + { + "text": "So how do I, well, I look at my notes." + }, + { + "text": "This is how I do it." + }, + { + "text": "So the notes, this is section 7.2, does these computational graphs." + }, + { + "text": "And then here is reverse mode." + }, + { + "text": "So it starts over here with, so I'm going to use the chain rule." + }, + { + "text": "So df df is 1." + }, + { + "text": "And then I go in backwards." + }, + { + "text": "And I have to use, of course, I have to take the derivatives." + }, + { + "text": "I have to use the right rule." + }, + { + "text": "So I have to use the product rule." + }, + { + "text": "And then soon I'll have to use these power rule and linear rule." + }, + { + "text": "So of course, no change there." + }, + { + "text": "The change is that by going backwards, oh, I don't know if I completed that sentence, that I could find 100 partial derivatives if the function depended on 100 variables in about 5 times the cost of one variable, 3 to 5 times the cost of 1." + }, + { + "text": "So you would expect 100 chain rules would cost 100 times." + }, + { + "text": "But you see, we're reusing the pieces in the chain and just having a larger." + }, + { + "text": "Our chain is wider, but it's not longer and it's not repeated." + }, + { + "text": "Anyway, so here I'm going to use whatever it is, df dc, and df ds." + }, + { + "text": "And I'm remembering that." + }, + { + "text": "So df dc is s, and df ds is c. That was because f started out as c times s. It was a product." + }, + { + "text": "Then we've got to evaluate those." + }, + { + "text": "I'll look again to see that I'm hopefully writing down some of the correct things." + }, + { + "text": "So now what I've written down next is df dc is 5." + }, + { + "text": "Or no, 5 on that example." + }, + { + "text": "What is it here?" + }, + { + "text": "df dc is c is x cubed." + }, + { + "text": "So df dc, yeah, I want s. I'm looking for s here." + }, + { + "text": "I'm looking for s. So I'm looking for s, and that's x plus 3y." + }, + { + "text": "Am I doing this well?" + }, + { + "text": "No." + }, + { + "text": "I want, in the end, to get the derivatives with respect to x and y, the whole gradient." + }, + { + "text": "OK, I think we're started right." + }, + { + "text": "The first derivatives is to write c and s. And then let me leave these boxes open just to get the picture." + }, + { + "text": "Then I'm going to do, then I'll need dc dx, dc dy, ds dx, and ds dy." + }, + { + "text": "I think that's right." + }, + { + "text": "Here I had a product of c and s. So I needed two, I had two derivatives." + }, + { + "text": "Here I have c and s each to differentiate." + }, + { + "text": "So I have an x and a y derivative, x and a y derivative." + }, + { + "text": "And now it's just a matter of putting in those numbers and following the chain backwards." + }, + { + "text": "Maybe I'm not going to put those numbers in, because if I didn't reach 140, you wouldn't believe in back propagation." + }, + { + "text": "And that would be like an unhappy outcome." + }, + { + "text": "So I'll leave you to put them in, maybe." + }, + { + "text": "Or the notes have a separate example that you can see." + }, + { + "text": "But do you see the point?" + }, + { + "text": "That I'm going to find all the, in the end, I'm going to find df dx and df dy from the chain, from one chain and not from a separate chain for x and a separate chain for y." + }, + { + "text": "To me, that's the point of reverse mode." + }, + { + "text": "It's a little bit of magic." + }, + { + "text": "But you see the steps, the ingredient." + }, + { + "text": "And some of you have seen this before and maybe know a better exposition." + }, + { + "text": "I found this blog by Christopher Ola clear." + }, + { + "text": "And these very simple things you'll see are clear in the notes." + }, + { + "text": "But maybe another blog brings out other points to make here." + }, + { + "text": "It's not obvious, maybe, that I could have 100 variables and do the calculation in four or five times the cost, four or five times being instead of 100." + }, + { + "text": "But it's possible." + }, + { + "text": "So could I close today with this one?" + }, + { + "text": "No." + }, + { + "text": "How could those be different?" + }, + { + "text": "You're computing the same numbers, the same aij, bjk, ckls, and doing this sums." + }, + { + "text": "But it certainly is different." + }, + { + "text": "So let's just do that." + }, + { + "text": "OK, I'll do it here." + }, + { + "text": "And then after my time, and I guess it'll be after Professor Rao on Friday and Monday, I'll come back to Professor Sra's short proof of the convergence of stochastic gradient descent." + }, + { + "text": "The whole point is to show you what assumptions do you need." + }, + { + "text": "You need some assumptions on the gradient, some assumptions on the step size." + }, + { + "text": "And for a good proof, all the assumptions fit together, and dong, out comes the conclusion." + }, + { + "text": "And the conclusion would be how fast it converges, stochastic gradient descent." + }, + { + "text": "So there's some expected things, because it's stochastic." + }, + { + "text": "We expect some assumptions about the mean and the variance to go into the proof." + }, + { + "text": "So you'll see that, but maybe it's too much for today." + }, + { + "text": "So for today, I'll just come back to that." + }, + { + "text": "I might even put it on Stellar and just close with this." + }, + { + "text": "So suppose A is m by n, B is n by p, and C is p by q." + }, + { + "text": "How many steps does it take to find A times B times C, the product of those three matrices?" + }, + { + "text": "Well, if I go this way, I have to multiply A. I have to do BC first, so BC costs." + }, + { + "text": "How many operations to multiply that times that?" + }, + { + "text": "npq." + }, + { + "text": "Nice formula, npq." + }, + { + "text": "Why is that?" + }, + { + "text": "Well, I could say that the answer is n by q, and every number in there was an inner product of a row and column of length p. So I have nq inner product, and each one costs p multiply add." + }, + { + "text": "And then, so now I have BC, which will be now." + }, + { + "text": "So now I have m by n. And then I have m by n, which is the A, times B by C, which is now n by q." + }, + { + "text": "That's BC." + }, + { + "text": "This is ABC." + }, + { + "text": "So this one costs, what's the cost here?" + }, + { + "text": "m by n, n by q." + }, + { + "text": "By the same rule, it'll be mnq." + }, + { + "text": "Good." + }, + { + "text": "That's the first way, A times BC." + }, + { + "text": "Now, the second way is AB times C. And let me write in again, m by n, n by p, p by q." + }, + { + "text": "So now I'm doing this first." + }, + { + "text": "So AB costs." + }, + { + "text": "Tell me again now, what's the rule for the cost of a matrix multiplication?" + }, + { + "text": "Mnp, mnp." + }, + { + "text": "And then I'm multiplying m by p. That's AB times p by q." + }, + { + "text": "That's C. So I have mpq." + }, + { + "text": "So I have that together with that, or that together with that." + }, + { + "text": "That sum, those two, or these two." + }, + { + "text": "And they're different." + }, + { + "text": "And let's just recognize the most important example." + }, + { + "text": "Suppose C is a column vector." + }, + { + "text": "C for a column vector." + }, + { + "text": "So q is 1." + }, + { + "text": "There's only one column." + }, + { + "text": "So if q is 1, this way did np." + }, + { + "text": "Let's just specialize to that." + }, + { + "text": "So specialize to C equal a column vector, which means that q is 1." + }, + { + "text": "I only have one column." + }, + { + "text": "So then A times BC is versus AB times C. So let's just figure that out when q is 1." + }, + { + "text": "So npq is just np." + }, + { + "text": "And mnq is just mn, where AB is mnp." + }, + { + "text": "Oh, that's a bad one." + }, + { + "text": "Disaster already." + }, + { + "text": "Multiplying, those are potentially two big matrices." + }, + { + "text": "Multiplying a column vector." + }, + { + "text": "So here I've done a matrix multiplication." + }, + { + "text": "I never should have done that." + }, + { + "text": "This is a matrix vector." + }, + { + "text": "It gives me a vector." + }, + { + "text": "And then this is a matrix vector." + }, + { + "text": "So I get nice numbers here." + }, + { + "text": "But I get a terrible number for AB." + }, + { + "text": "And then I multiply that by C. So that's mpq." + }, + { + "text": "mpq." + }, + { + "text": "So mp is factoring out." + }, + { + "text": "So if I write it as n times m plus p versus this one is m that's factoring out times m. No." + }, + { + "text": "Yeah." + }, + { + "text": "What's up here?" + }, + { + "text": "Sorry." + }, + { + "text": "What am I doing?" + }, + { + "text": "Yeah." + }, + { + "text": "Is it p that factors out from this one?" + }, + { + "text": "OK. p times m plus n, I guess." + }, + { + "text": "Sorry." + }, + { + "text": "Anyway, the difference is." + }, + { + "text": "AUDIENCE 1." + }, + { + "text": "I think it's mp times p plus q." + }, + { + "text": "Sorry." + }, + { + "text": "Shall I go over it again or write?" + }, + { + "text": "Let me do just this thinking again." + }, + { + "text": "If q is 1, if I go this way, was that my final total when q was 1?" + }, + { + "text": "And that's this." + }, + { + "text": "That's no." + }, + { + "text": "m factors out times n plus p. Whoops." + }, + { + "text": "Let's just get that right." + }, + { + "text": "This is." + }, + { + "text": "Oh, no." + }, + { + "text": "n factors out." + }, + { + "text": "Sorry." + }, + { + "text": "n factors out times n plus p. And this way was all these things." + }, + { + "text": "Both the m and the p factor out." + }, + { + "text": "Both the m and the p factor out." + }, + { + "text": "Thanks." + }, + { + "text": "Times n plus q. n plus q was 1." + }, + { + "text": "The whole point is we've got this horrible multiplication of three big numbers." + }, + { + "text": "And this only had two big numbers." + }, + { + "text": "So this is orders of magnitude faster than that." + }, + { + "text": "And of course, you would have done the calculation that way." + }, + { + "text": "You would have multiplied the column vector by a matrix to get another column vector." + }, + { + "text": "And you would have multiplied that by a matrix to get another column vector." + }, + { + "text": "Where here, you crazily multiplied two big matrices together and then got a column vector." + }, + { + "text": "So there's the bad move." + }, + { + "text": "OK, thanks." + }, + { + "text": "So we're past the time on this ABC." + }, + { + "text": "It's just to show that on a very familiar calculation, you have to do it in the right order." + }, + { + "text": "And back propagation is the right order for partial derivatives." + }, + { + "text": "OK, thank you." + }, + { + "text": "And so bring laptops Friday." + }, + { + "text": "And look forward to Professor Rao." + }, + { + "text": "Give him a good welcome." + } +] \ No newline at end of file diff --git a/sight/sources/annotated/nHlE7EgJFds.json b/sight/sources/annotated/nHlE7EgJFds.json new file mode 100644 index 0000000000000000000000000000000000000000..e3eb7d54b346a20d43e9a3c866f71860d9694bad --- /dev/null +++ b/sight/sources/annotated/nHlE7EgJFds.json @@ -0,0 +1,1340 @@ +[ + { + "text": " Okay, here is lecture ten in linear algebra." + }, + { + "text": "Two important things to do in this lecture." + }, + { + "text": "One is to correct an error from lecture nine." + }, + { + "text": "So the blackboard with that awful error is still with us." + }, + { + "text": "And the second, the big thing to do is to tell you about the four subspaces that come with a matrix." + }, + { + "text": "We've seen two subspaces, the column space and the null space, there's two to go." + }, + { + "text": "Okay." + }, + { + "text": "First of all, and this is a great way to recap and correct the previous lecture." + }, + { + "text": "So you remember I was just doing R3." + }, + { + "text": "I couldn't have taken a simpler example than R3." + }, + { + "text": "And I wrote down the standard basis." + }, + { + "text": "That's the standard basis." + }, + { + "text": "The basis, the obvious basis for the whole three-dimensional space." + }, + { + "text": "And then I wanted to make the point that there was nothing special, nothing about that basis that another basis couldn't have." + }, + { + "text": "It could have linear independence, it could span a space, there's lots of other bases." + }, + { + "text": "So I started with these vectors one one two and two two five, and those were independent." + }, + { + "text": "And then I said three three seven wouldn't do, because three three seven is the sum of those." + }, + { + "text": "So in my innocence, I put in three three eight." + }, + { + "text": "I figured probably if three three seven is on the plane, is, which I know, it's in the plane with these two, then probably three three eight sticks a little bit out of the plane." + }, + { + "text": "And it's independent and it gives a basis." + }, + { + "text": "But after class, to my sorrow, student tells me, wait a minute, that third vector three three eight is not independent." + }, + { + "text": "And why did she say that?" + }, + { + "text": "She didn't actually take the time, didn't have to, to find what combination of this one and this one gives three three eight." + }, + { + "text": "She did something else." + }, + { + "text": "In other words, she looked ahead because she said, wait a minute, if I look at that matrix, it's not invertible." + }, + { + "text": "That third column can't be independent of the first two, because when I look at that matrix, it's got two identical rows." + }, + { + "text": "I have a square matrix." + }, + { + "text": "Its rows are obviously dependent." + }, + { + "text": "And that makes the columns dependent." + }, + { + "text": "So there's my error." + }, + { + "text": "When I look at the matrix A that has those three columns, those three columns can't be independent because that matrix is not invertible because it's got two equal rows." + }, + { + "text": "And today's lecture will reach the conclusion, the great conclusion, that connects the column space with the row space." + }, + { + "text": "So those are the row space is now going to be another one of my fundamental subspaces." + }, + { + "text": "The row space of this matrix or of this one, well, the row space of this one is okay." + }, + { + "text": "But the row space of this one, I'm looking at the rows of the matrix, oh, anyway, I'll have two equal rows and the row space will be only two-dimensional." + }, + { + "text": "The rank of the matrix with these columns will only be two, so only two of those columns can be independent too." + }, + { + "text": "The rows tell me something about the columns, in other words." + }, + { + "text": "Something that I should have noticed and I didn't." + }, + { + "text": "Okay." + }, + { + "text": "So now let me pin down these four fundamental subspaces." + }, + { + "text": "So here are the four fundamental subspaces." + }, + { + "text": "This is really the heart of this approach to linear algebra, to see these four subspaces, how they're related." + }, + { + "text": "So what are they?" + }, + { + "text": "The column space, C of A." + }, + { + "text": "The null space, N of A." + }, + { + "text": "And now comes the row space, something new." + }, + { + "text": "The row space, what's in that?" + }, + { + "text": "It's all combinations of the rows." + }, + { + "text": "That's natural." + }, + { + "text": "We want a space, so we have to take all combinations and we start with the rows." + }, + { + "text": "So the rows span the row space." + }, + { + "text": "Are the rows a basis for the row space?" + }, + { + "text": "Maybe so, maybe no." + }, + { + "text": "The rows are a basis for the row space when they're independent." + }, + { + "text": "But if they're dependent, as in this example, my error from last time, they're not, those three rows are not a basis, the row space would only be two-dimensional, I only need two rows for a basis." + }, + { + "text": "So the row space, now what's in it?" + }, + { + "text": "It's all combinations of the rows of A." + }, + { + "text": "All combinations of the rows of A." + }, + { + "text": "But I don't like working with row vectors." + }, + { + "text": "All my vectors have been column vectors." + }, + { + "text": "I'd like to stay with column vectors." + }, + { + "text": "How can I get to column vectors out of these rows?" + }, + { + "text": "I transpose the matrix." + }, + { + "text": "So if that's OK with you, I'm going to transpose the matrix, I'm going to say all combinations of the columns of A transpose." + }, + { + "text": "And that allows me to use the convenient notation, the column space of A transpose." + }, + { + "text": "Nothing, no mathematics went on there, we just got some vectors that were lying down to stand up." + }, + { + "text": "But it means that we can use this column space of A transpose, that's telling me in a nice matrix notation what the row space is." + }, + { + "text": "OK. And finally is another null space." + }, + { + "text": "The fourth fundamental space will be the null space of A transpose." + }, + { + "text": "The fourth guy is the null space of A transpose." + }, + { + "text": "And of course, my notation is N of A transpose." + }, + { + "text": "That's the null space of A transpose." + }, + { + "text": "Now, we don't have a perfect name for this space as a, as a, connecting with A, but our usual name is the left null space, and I'll show you why in a moment." + }, + { + "text": "So often I call this the, just to write that word, the left null space of A." + }, + { + "text": "So just the way we have the row space of A and we switch it to the column space of A transpose, so we have this space of guys that I call the left null space of A, but the good notation is it's the null space of A transpose." + }, + { + "text": "OK. Those are four spaces." + }, + { + "text": "Where are those spaces?" + }, + { + "text": "What big space are they in for when A is m by n?" + }, + { + "text": "In that case, the null space of A, what's in the null space of A?" + }, + { + "text": "Vectors with n components." + }, + { + "text": "Solutions to Ax equals zero." + }, + { + "text": "So the null space of A is n R n. What's in the column space of A?" + }, + { + "text": "Well, columns." + }, + { + "text": "How many components do those columns have?" + }, + { + "text": "m. So this column space is n R m. What about the column space of A transpose, which are just a disguised way of saying the rows of A?" + }, + { + "text": "The rows of A in this three by six matrix have six components, n components." + }, + { + "text": "The column space is n R n. And the null space of A transpose, I see that this fourth space is already getting second, you know, second class citizen treatment and it doesn't deserve it." + }, + { + "text": "It's, it should be there, it is there, and shouldn't be squeezed." + }, + { + "text": "The null space of A transpose, well, if the null space of A had vectors with n components, the null space of A transpose will be n R m. I want to draw a picture of the four spaces." + }, + { + "text": "OK. OK." + }, + { + "text": "Here are the four spaces." + }, + { + "text": "OK, let me put n dimensional space over on this side." + }, + { + "text": "Then which were the subspaces in R n?" + }, + { + "text": "The null space was and the row space was." + }, + { + "text": "So here we have the can I make that picture of the row space?" + }, + { + "text": "And can I make this kind of picture of the null space?" + }, + { + "text": "That's just meant to be a sketch, to remind you that they're in this which, you know, how, what type of vectors are in it?" + }, + { + "text": "Vectors with n components." + }, + { + "text": "Over here, inside consisting of vectors with m components is the column space and what I'm calling the null space of A transpose." + }, + { + "text": "Those are the ones with m components." + }, + { + "text": "OK. To understand these spaces is our job now." + }, + { + "text": "Because by understanding those spaces, we know everything about this half of linear algebra." + }, + { + "text": "What do I mean by understanding those spaces?" + }, + { + "text": "I would like to know a basis for those spaces." + }, + { + "text": "For each one of those spaces, how would I create, construct a basis?" + }, + { + "text": "What systematic way would produce a basis?" + }, + { + "text": "And what's their dimension?" + }, + { + "text": "OK." + }, + { + "text": "So for each of the four spaces, I have to answer those questions." + }, + { + "text": "How do I produce a basis?" + }, + { + "text": "And then, which has a somewhat long answer, and what's the dimension, which is just a number, so it has a real short answer?" + }, + { + "text": "Can I give you the short answer first?" + }, + { + "text": "I shouldn't do it, but here it is." + }, + { + "text": "I can tell you the dimension of the column space." + }, + { + "text": "Let me start with this guy." + }, + { + "text": "What's its dimension?" + }, + { + "text": "I have an m by n matrix." + }, + { + "text": "The dimension of the column space is the rank, R. We actually got to that at the end of the last lecture, but only for an example." + }, + { + "text": "So I really have to say, OK, what's going on there?" + }, + { + "text": "I should produce a basis, and then I just look to see how many vectors I needed in that basis, and the answer will be R. Actually, I'll do that before I get on to the others." + }, + { + "text": "What's a basis for the column space?" + }, + { + "text": "We've done all the work of row reduction, identifying the pivot columns, the ones that have pivots, the ones that end up with pivots, but now I the pivot columns I'm interested in are columns of A, the original A." + }, + { + "text": "And those pivot columns, there are R of them, the rank R counts those, those are a basis." + }, + { + "text": "So if I answer this question for the column space, the answer will be a basis is the pivot columns, and the dimension is the rank R. And there are pivot columns and everything great." + }, + { + "text": "OK, so that space we pretty well understand." + }, + { + "text": "I probably have a little going back to see that, to prove that this is a right answer, but you know it's the right answer." + }, + { + "text": "Now let me look at the row space." + }, + { + "text": "OK. Shall I tell you the dimension of the row space?" + }, + { + "text": "Yes." + }, + { + "text": "Before we do even an example, let me tell you the dimension of the row space." + }, + { + "text": "Its dimension is also R. The row space and the column space have the same dimension." + }, + { + "text": "That's a wonderful fact." + }, + { + "text": "The dimension of the column space of A transpose, that's the row space, is R. That space is R-dimensional." + }, + { + "text": "And so is this one." + }, + { + "text": "OK. That's the, that's the sort of insight that got used in this example." + }, + { + "text": "If those, if those, if those, are the three columns of a matrix, let me make them the three columns of a matrix by just erasing some brackets, OK, those are the three columns of a matrix, the rank of that matrix, if I look at the columns, it wasn't obvious to me anyway." + }, + { + "text": "But if I look at the rows, it's, now it's obvious." + }, + { + "text": "The row space of that matrix obviously is two-dimensional, because I can, I see a basis for the row space, this row and that row." + }, + { + "text": "And of course, strictly speaking, I'm supposed to transpose those guys, make them stand up." + }, + { + "text": "But the rank is two, and therefore the column space is two-dimensional by this wonderful fact that the row space and column space have the same dimension, and therefore there are only two pivot columns, not three, and, those, the three columns are dependent." + }, + { + "text": "OK. Now, let me bury that error and talk about the row space." + }, + { + "text": "Well, I'm going to give you the dimensions of all the spaces, because that's the, such a nice answer." + }, + { + "text": "OK." + }, + { + "text": "So let me come back here." + }, + { + "text": "So we have this great fact to establish, that the row space, its dimension is also the rank." + }, + { + "text": "OK. What about the null space?" + }, + { + "text": "What's a basis for the null space?" + }, + { + "text": "What's the dimension of the null space?" + }, + { + "text": "Let me, I'll put that answer up here, for the null space." + }, + { + "text": "Well, how have we constructed the null space?" + }, + { + "text": "We took the matrix A, we did those row operations to get it into a form U or even further, we got it into the reduced form R, and then we read off special solutions." + }, + { + "text": "Special solutions, and every special solution came from a free variable." + }, + { + "text": "And those special solutions are in the null space, and the great thing is, they're a basis for it." + }, + { + "text": "So for the null space, a basis will be the special solutions." + }, + { + "text": "And there's one for every free variable, right?" + }, + { + "text": "For each free variable, we give that variable the value one, the other free variable zero." + }, + { + "text": "We get the pivot variables, we get a vector in the -- we get a special solution." + }, + { + "text": "So we get all together n minus R of them, because that's the number of free variables." + }, + { + "text": "If we have R, this is, the dimension is R, is the number of pivot variables, this is the number of free variables." + }, + { + "text": "So the beauty is that those special solutions do form a basis and tell us immediately that the dimension of the null space is n -- I'd better write this well, because it's so nice, n minus R. And you see the nice thing, that the two dimensions in this n-dimensional space, one subspace is R-dimensional, to be proved, that's the row space." + }, + { + "text": "The other subspace is n minus R-dimensional, that's the null space." + }, + { + "text": "And the two dimensions, like, together, give n. The sum of R and n minus R is n. And that's just great." + }, + { + "text": "It's really copying the fact that we have n variables, R of them are pivot variables and n minus R are free variables and n all together." + }, + { + "text": "OK. And now what's the dimension of this poor misbegotten fourth subspace?" + }, + { + "text": "It's got to be m minus R. The dimension of this left null space, left out practically, is m minus R. Well, that's really just saying that this, again, the sum of that plus that is m. And m is correct." + }, + { + "text": "It's the number of columns in A transpose." + }, + { + "text": "A transpose is just as good a matrix as A." + }, + { + "text": "It just happens to be n by m. It happens to have m columns, so it will have m variables, when I go to Ax equals zero, and m of them and R of them will be pivot variables and m minus R will be free variables." + }, + { + "text": "A transpose is as good a matrix as A." + }, + { + "text": "It follows the same rule that this plus the dimension, this dimension plus this dimension adds up to the number of columns." + }, + { + "text": "And over here, A transpose has m columns." + }, + { + "text": "Okay." + }, + { + "text": "Okay, so I gave you the easy answer, the dimensions." + }, + { + "text": "Now can I go back to check on a basis?" + }, + { + "text": "We would like to think that, say, the row space." + }, + { + "text": "Because we've got a basis for the column space." + }, + { + "text": "The pivot columns give a basis for the column space." + }, + { + "text": "Now I'm asking you to look at the row space." + }, + { + "text": "And I you could say, okay, I can produce a basis for the row space by transposing my matrix, making those columns, then doing elimination, row reduction, and checking out the pivot columns in this transposed matrix." + }, + { + "text": "But that means you had to do all that row reduction on A transpose." + }, + { + "text": "It ought to be possible, if we take a matrix A, let me take the matrix, maybe we had this matrix in the last lecture, one one one, two one two, three two three, one one one." + }, + { + "text": "Okay." + }, + { + "text": "That, that matrix was so easy, we spotted its pivot columns, one and two, without actually doing row reduction." + }, + { + "text": "But now let's do the job properly." + }, + { + "text": "So I subtract this away from this to produce a zero." + }, + { + "text": "So one two three one is fine." + }, + { + "text": "Subtracting that away leaves me minus one minus one zero, right?" + }, + { + "text": "And subtracting that from the last row, oh, well, that's easy." + }, + { + "text": "Okay, I'm doing row reduction." + }, + { + "text": "Now I've, the first column is all set." + }, + { + "text": "The second column, I now see the pivot, and I can clean up, if I, actually, okay, why don't I make the pivot into a one?" + }, + { + "text": "I'll multiply that row through by minus one, and then I have one one." + }, + { + "text": "That was an elementary operation, I'm allowed." + }, + { + "text": "Multiply a row by a number." + }, + { + "text": "And now I'll do elimination." + }, + { + "text": "Two of those away from that will knock this guy out and make this into a one." + }, + { + "text": "So that's now a zero and that's a one." + }, + { + "text": "Okay." + }, + { + "text": "Done." + }, + { + "text": "That's R. I'm seeing the identity matrix here, I'm seeing zeros below, and I'm seeing F there." + }, + { + "text": "Okay." + }, + { + "text": "Okay." + }, + { + "text": "What about its row space?" + }, + { + "text": "What happened to its row space?" + }, + { + "text": "Well, what happened, let me first ask, just because this is, sometimes something does happen." + }, + { + "text": "Its column space changed." + }, + { + "text": "The column space of R is not the column space of A, right?" + }, + { + "text": "Because one one one is certainly in the column space of A and certainly not in the column space of R. I did row operations." + }, + { + "text": "Those row operations preserved the row space, so the row so the column spaces are different." + }, + { + "text": "Different column spaces." + }, + { + "text": "Different column spaces." + }, + { + "text": "But I believe that they have the same row space." + }, + { + "text": "Same row space." + }, + { + "text": "I believe that the row space of that matrix and the row space of this matrix are identical." + }, + { + "text": "They have exactly the same vectors in them." + }, + { + "text": "Those vectors are vectors with four components, right?" + }, + { + "text": "They're all combinations of those rows." + }, + { + "text": "Or I believe you get the same thing by taking all combinations of these rows." + }, + { + "text": "And if true, what's a basis?" + }, + { + "text": "What's a basis for the row space of R?" + }, + { + "text": "And it'll be a basis for the row space of the original A." + }, + { + "text": "But it's obviously a basis for the row space of R. What's a basis for the row space of that matrix?" + }, + { + "text": "The first two rows." + }, + { + "text": "So a basis for the row so a basis is for the row space of A or of R is the first R rows of R, not of A." + }, + { + "text": "Sometimes it's true for A, but not necessarily." + }, + { + "text": "But R, we definitely have a matrix here whose row space we can identify." + }, + { + "text": "The row space is spanned by the three rows." + }, + { + "text": "But if we want a basis, we want independence." + }, + { + "text": "So out goes row three." + }, + { + "text": "The row space is also spanned by the first two rows." + }, + { + "text": "This guy didn't contribute anything." + }, + { + "text": "And of course, over here, this one, two, three, one in the bottom didn't contribute anything." + }, + { + "text": "We had it already." + }, + { + "text": "So this, here's a basis, one zero one one and zero one one zero." + }, + { + "text": "I believe those are in the row space." + }, + { + "text": "I know they're independent." + }, + { + "text": "Why are they in the row space?" + }, + { + "text": "Why are those two vectors in the row space?" + }, + { + "text": "Because all those operations we did, which started with these rows and took combinations of them." + }, + { + "text": "I took this row minus this row." + }, + { + "text": "That gave me something that's still in the row space." + }, + { + "text": "That's the point." + }, + { + "text": "When I took a row minus a multiple of another row, I'm staying in the row space." + }, + { + "text": "The row space is not changing." + }, + { + "text": "My little basis for it is changing, and I've ended up with, sort of, the best basis." + }, + { + "text": "If the columns of the identity matrix are the best basis for R3 or Rn, the rows of this matrix are the best basis for the row space." + }, + { + "text": "Best in the sense of being as clean as I can make it." + }, + { + "text": "Starting off with the identity and then finishing up with whatever has to be in there." + }, + { + "text": "OK. Do you see, then, that the dimension is R?" + }, + { + "text": "For sure." + }, + { + "text": "Because we've got R pivots, R nonzero rows, we've got the right number of vectors, R. They're in the row space, they're independent, that's it." + }, + { + "text": "They are a basis for the row space." + }, + { + "text": "And we can even pin that down further." + }, + { + "text": "How do I know that every row of A is a combination?" + }, + { + "text": "How do I know they span the row space?" + }, + { + "text": "Oh, well, somebody says I've got the right number of them, so they must, but that's true." + }, + { + "text": "But let me just say, how do I know that this row is a combination of these?" + }, + { + "text": "By just reversing the steps of row reduction." + }, + { + "text": "If I just reverse the steps and go from A, from R back to A, then what do I, what am I doing?" + }, + { + "text": "I'm starting with these rows, I'm taking combinations of them, after a couple of steps, undoing the subtractions that I did before, I'm back to these rows." + }, + { + "text": "So these rows are combinations of those rows, those rows are combinations of those rows, the two row spaces are the same, the bases are the same, and the natural basis is this guy." + }, + { + "text": "Is that all right for the row space?" + }, + { + "text": "The row space is sitting there in R, in its cleanest possible form." + }, + { + "text": "OK. Now what about the fourth guy, the null space of A transpose?" + }, + { + "text": "First of all, why do I call that the left null space?" + }, + { + "text": "So let me save that and bring that down." + }, + { + "text": "OK." + }, + { + "text": "So the fourth space is the null space of A transpose." + }, + { + "text": "So it has in it vectors, let me call them y, so that A transpose y equals zero." + }, + { + "text": "If A transpose y equals zero, then y is in the null space of A transpose, of course." + }, + { + "text": "So this is a matrix times a column equaling zero." + }, + { + "text": "And now, because I want y to sit on the left, and I want A instead of A transpose, I'll just transpose that equation." + }, + { + "text": "Can I just transpose that?" + }, + { + "text": "On the right, it makes the zero vector lie down." + }, + { + "text": "And on the left, it's a product, A transpose times y." + }, + { + "text": "If I take the transpose, then they come in opposite order, right?" + }, + { + "text": "So it's y transpose times A transpose transpose, but nobody's going to leave it like that." + }, + { + "text": "That's A transpose transpose is just A, of course." + }, + { + "text": "When I transposed A transpose, I got back to A." + }, + { + "text": "Now, do you see what I have now?" + }, + { + "text": "I have a row vector, y transpose, multiplying A and multiplying from the left." + }, + { + "text": "That's why I call it the left null space." + }, + { + "text": "But by making it, putting it on the left, I had to make it into a row instead of a column vector." + }, + { + "text": "And so my convention is I usually don't do that, I usually stay with A transpose y equals zero." + }, + { + "text": "OK. And you might ask, how do we get a basis, or I might ask, how do we get a basis for this fourth space, this left null space?" + }, + { + "text": "OK." + }, + { + "text": "I'll do it the example." + }, + { + "text": "As always, ah, not that one." + }, + { + "text": "The left null space is not jumping out at me here." + }, + { + "text": "I know which are the free variables, the special solutions, but those are special solutions to Ax equals zero, and now I'm looking at A transpose and I'm not seeing it here." + }, + { + "text": "So, but somehow you feel that the work that you did, which simplified A to R, should have revealed the left null space too." + }, + { + "text": "And it's slightly less immediate, but it's there." + }, + { + "text": "So from A to R, I took some steps, and I guess I'm interested in what were those steps, or what were all of them together." + }, + { + "text": "I don't want to -- I'm not interested in what particular ones they were." + }, + { + "text": "I'm interested in what was the whole matrix that took me from A to R. How would you find that?" + }, + { + "text": "Do you remember Gauss-Jordan, where you tack on the identity matrix?" + }, + { + "text": "Let's do that again." + }, + { + "text": "So I'll do it above here." + }, + { + "text": "So this is now the idea of I take the matrix A, which is m by n. In Gauss-Jordan, when we saw him before, A was a square invertible matrix and we were finding its inverse." + }, + { + "text": "Now the matrix isn't square, it's probably rectangular." + }, + { + "text": "But I'll still tack on the identity matrix, and of course, since these have length m, it better be m by m. And now I'll do the reduced row echelon form of this matrix." + }, + { + "text": "And what do I get?" + }, + { + "text": "The reduced row echelon form starts with these columns, starts with the first columns, works like mad, and produces R. Of course, still the same size, m by n, and we did it before." + }, + { + "text": "And then whatever it did to get R, something else is going to show up here." + }, + { + "text": "Let me call it E, m by m. It's whatever you see that E is just going to contain a record of what we did." + }, + { + "text": "We did whatever it took to get A to become R. And at the same time, we were doing it to the identity matrix." + }, + { + "text": "So we started with the identity matrix, we buzzed along." + }, + { + "text": "So we took some -- all this row reduction amounted to multiplying on the left by some matrix, some series of elementary matrices that all together gave us one matrix, and that matrix is E. So all this row reduction stuff amounted to multiplying by E. How do I know that?" + }, + { + "text": "It certainly amounted to multiplying by something, and that something took I to E, so that something was E. So now look at the first part, E A is R. No big deal." + }, + { + "text": "All I've said is that the row reduction steps that we all know well, taking A to R, are in a- in some matrix, and I can find out what that matrix is by just tacking I on and seeing what comes out." + }, + { + "text": "What comes out is E. Let's just review the invertible square case." + }, + { + "text": "What happened then?" + }, + { + "text": "Because I was interested in it in chapter two also." + }, + { + "text": "When A was square and invertible, I took A I, I did row elimination, what was the R that came out?" + }, + { + "text": "It was I." + }, + { + "text": "So in chapter two, in chapter two, R was I." + }, + { + "text": "The row- the reduced row echelon form of a nice invertible square matrix is the identity." + }, + { + "text": "So if R was I in that case, then E was A inverse, because E A is I." + }, + { + "text": "Good." + }, + { + "text": "That's- that was good and easy." + }, + { + "text": "Now what I'm saying is that there still is an E, it's not A inverse anymore, because A is a rectangular, it hasn't got an inverse." + }, + { + "text": "But there is still some matrix E that connected this to this." + }, + { + "text": "Oh, I should have figured out in advance what it was." + }, + { + "text": "Shoot." + }, + { + "text": "I didn't- I did those steps and sort of erased as I went, and, I should have done them to the identity, too." + }, + { + "text": "Can I do that?" + }, + { + "text": "Can I do that?" + }, + { + "text": "I'll keep the identity matrix, like I'm supposed to do, and I'll do the same operations on it and see what I end up with." + }, + { + "text": "Okay." + }, + { + "text": "So I'm starting with the identity, which I'll write in light, light enough, but okay, what did I do?" + }, + { + "text": "I subtracted that row from that one and that row from that one." + }, + { + "text": "Okay, I'll do that to the identity." + }, + { + "text": "So I subtract that first row from row two and row three." + }, + { + "text": "Good." + }, + { + "text": "Then I think I multiply, do you remember, I multiplied row two by minus one?" + }, + { + "text": "Let me just do that." + }, + { + "text": "Then what did I do?" + }, + { + "text": "I subtracted two of row two away from row one." + }, + { + "text": "I better do that." + }, + { + "text": "Subtract two of this away from this." + }, + { + "text": "That's minus one, two of these away leaves a plus two and zero." + }, + { + "text": "I believe that's E. The way to check is to see, multiply that E by this A, just to see, did I do it right?" + }, + { + "text": "So I believe E was minus one, two, zero, one minus one, zero, and minus one, zero, one." + }, + { + "text": "Okay." + }, + { + "text": "That's my E, that's my A, and that's R. All right." + }, + { + "text": "All I'm struggling to do is write the reason I wanted this blasted E was so that I could figure out the left null space." + }, + { + "text": "Not only its dimension, which I know." + }, + { + "text": "Actually, what is the dimension of the left null space?" + }, + { + "text": "Here's my matrix." + }, + { + "text": "What's the rank of the matrix?" + }, + { + "text": "Two." + }, + { + "text": "And the dimension of the left null space is supposed to be M minus R, three minus two, one." + }, + { + "text": "I believe that the left null space is one-dimensional." + }, + { + "text": "There is one combination of those three rows that produces the zero row." + }, + { + "text": "There is a basis." + }, + { + "text": "A basis for the left null space has only got one vector in it." + }, + { + "text": "And what is that vector?" + }, + { + "text": "It's here in the last row of E. But, ah, we could have seen it earlier." + }, + { + "text": "What combination of those rows gives the zero row?" + }, + { + "text": "Minus one of that, plus one of that." + }, + { + "text": "So a basis for the left null space of this matrix, I'm looking for combinations of rows that give the zero row, if I'm looking at the left null space." + }, + { + "text": "For the null space, I'm looking at combinations of columns to get the zero column." + }, + { + "text": "Now I'm looking at combinations of these three rows to get the zero row, and of course, there is my zero row, and here is my vector that produced it." + }, + { + "text": "Minus one of that row and one of that row." + }, + { + "text": "Obvious." + }, + { + "text": "Okay." + }, + { + "text": "So in that example, and actually in all examples, we have seen how to produce a basis for the left null space." + }, + { + "text": "I won't ask you that all the time." + }, + { + "text": "Because it didn't come out immediately from R, we had to keep track of E for that left null space." + }, + { + "text": "But at least it didn't require us to transpose the matrix and start all over again." + }, + { + "text": "Okay." + }, + { + "text": "Those are the four subspaces." + }, + { + "text": "Can I review them?" + }, + { + "text": "The row space and the null space are in Rn." + }, + { + "text": "Their dimensions add to n. The column space and the left null space are in Rm, and their dimensions add to m. Okay." + }, + { + "text": "So let me close these last minutes by pushing you a little bit more to a new type of vector space." + }, + { + "text": "All our vector spaces, all the ones that we took seriously, have been subspaces of some real three- or n-dimensional space." + }, + { + "text": "Now I'm going to write down another vector space, a new vector space." + }, + { + "text": "Say all three by three matrices." + }, + { + "text": "My matrices are the vectors." + }, + { + "text": "Is that all right?" + }, + { + "text": "I'm just naming them." + }, + { + "text": "You can put quotes around vectors." + }, + { + "text": "Every three by three matrix is one of my vectors." + }, + { + "text": "Now how am I entitled to call those things vectors?" + }, + { + "text": "I mean, they look very much like matrices." + }, + { + "text": "But they're vectors in my vector space because they obey the rules." + }, + { + "text": "All I'm supposed to be able to do with vectors is add them." + }, + { + "text": "I can add matrices." + }, + { + "text": "I'm supposed to be able to multiply them by scalar numbers, like seven." + }, + { + "text": "Well, I can multiply a matrix by seven." + }, + { + "text": "And I can take combinations of matrices." + }, + { + "text": "I can take three of one matrix minus five of another matrix." + }, + { + "text": "And those combinations, there's a zero matrix, the matrix that has all zeros in it." + }, + { + "text": "If I add that to another matrix, it doesn't change it." + }, + { + "text": "All the good stuff." + }, + { + "text": "If I multiply a matrix by one, it doesn't change it." + }, + { + "text": "All those eight rules for a vector space that we never wrote down, all easily satisfied." + }, + { + "text": "So now we have a different --." + }, + { + "text": "Now, of course, you can say you can multiply those matrices." + }, + { + "text": "I don't care." + }, + { + "text": "For the moment, I'm only thinking of these matrices as forming a vector space, so I am only doing A plus B and C times A. I'm not interested in A, B for now." + }, + { + "text": "The fact that I can multiply is not relevant to a vector space." + }, + { + "text": "OK, so I have three by three matrices." + }, + { + "text": "And how about subspaces?" + }, + { + "text": "What's, tell me a subspace of this matrix space." + }, + { + "text": "Let me call this matrix space M. That's my matrix space, my space of all three by three matrices." + }, + { + "text": "Tell me a subspace of it." + }, + { + "text": "OK, what about the upper triangular matrices?" + }, + { + "text": "So subspaces, subspaces of M. All upper triangular matrices." + }, + { + "text": "Another subspace." + }, + { + "text": "All symmetric matrices." + }, + { + "text": "The intersection of two subspaces is supposed to be a subspace." + }, + { + "text": "We gave a little effort to the proof of that fact." + }, + { + "text": "If I look at the matrices that are in this subspace, they're symmetric, and they're also in this subspace, they're upper triangular." + }, + { + "text": "What do they look like?" + }, + { + "text": "Well, if they're symmetric, but they have zeros below the diagonal, they better have zeros above the diagonal." + }, + { + "text": "So the intersection would be diagonal matrices." + }, + { + "text": "That's another subspace, smaller than those." + }, + { + "text": "How can I use the word smaller?" + }, + { + "text": "Well, I'm now entitled to use the word smaller." + }, + { + "text": "I mean, well, one way to say is, OK, these are contained in those." + }, + { + "text": "These are contained in those." + }, + { + "text": "But more precisely, I could give the dimension of these spaces." + }, + { + "text": "So I could, we can compute, let's compute it next time." + }, + { + "text": "The dimension of all upper, of the subspace of upper triangular three by three matrices." + }, + { + "text": "The dimension of symmetric three by three matrices." + }, + { + "text": "The dimension of diagonal three by three matrices." + }, + { + "text": "Well, to produce dimension, that means I'm supposed to produce a basis." + }, + { + "text": "And then I just count how many I needed in the basis." + }, + { + "text": "Let me give you the answer for this one." + }, + { + "text": "What's the dimension?" + }, + { + "text": "The dimension of this, say, this subspace, let me call it D, all diagonal matrices." + }, + { + "text": "The dimension of this subspace is, as I write, you're working it out, three." + }, + { + "text": "Because here's a matrix in this, it's a diagonal matrix." + }, + { + "text": "Here's another one." + }, + { + "text": "Here's another one." + }, + { + "text": "Better make it diagonal, let me put a seven there." + }, + { + "text": "That was not a very great choice, but it's three diagonal matrices, and I believe that they're a basis." + }, + { + "text": "I believe that those three matrices are independent, and I believe that any diagonal matrix is a combination of those three." + }, + { + "text": "So they span the subspace of diagonal matrices." + }, + { + "text": "Do you see that idea?" + }, + { + "text": "It's like stretching the idea from Rn to Rn by n, three by three, but we can still add, we can still multiply by numbers, and we just ignore the fact that we can multiply two matrices together." + }, + { + "text": "Okay." + }, + { + "text": "Thank you." + }, + { + "text": "That's lecture ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk0.json b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..54ffdd862ffa76e2a043b59deb217a03b96b9c95 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high-quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "OK, just as we're getting started, I thought I'd add a few words about a question that came up after class." + }, + { + "text": "Suppose in that discussion last time, where you were given three, you were given a distance matrix, you were given the distance between x1 and x2, between x2 and x3, and between x1 and x3, and you wanted to find points that satisfied that." + }, + { + "text": "Well, we're going to fail on this example, because if the distance here is 1, the distance here is 1, then by the triangle inequality, the distance from x1 to x3 could not be more than 2." + }, + { + "text": "And when we square it, it could not be more than 4." + }, + { + "text": "And here it's 6." + }, + { + "text": "So what's going to happen?" + }, + { + "text": "What goes wrong in that case?" + }, + { + "text": "Yeah, I hadn't commented on that, and I'm not sure that the paper that I referenced does so." + }, + { + "text": "So I had to do a little search back in the literature, because people couldn't overlook this problem." + }, + { + "text": "So this is the triangle inequality fails." + }, + { + "text": "And it's not going to help to go into 10 dimensions, because the triangle inequalities doesn't change." + }, + { + "text": "And it's still there in 10 dimensions, and we're still failing." + }, + { + "text": "So what happens?" + }, + { + "text": "Well, what could happen?" + }, + { + "text": "Do you remember, and you'll have to remind me, the key equation." + }, + { + "text": "You remember we had an equation connecting the matrix." + }, + { + "text": "So what is the matrix D for this problem?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk1.json b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..ccc46852e7e38828e1335f8ff612971db3999ed2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So D is a 3 by 3 matrix with these distances squared." + }, + { + "text": "And it was convenient to use distances squared, because that's what comes into the next steps." + }, + { + "text": "So of course, the distance from each x to itself is 0." + }, + { + "text": "The distance from x distance squared was that." + }, + { + "text": "This one was that, but this one is 6." + }, + { + "text": "So that's the distance matrix." + }, + { + "text": "And we would like to find, the job was to find, and I'm just going to write down, we cannot find x1, x2, and x3 to match those distances." + }, + { + "text": "So what goes wrong?" + }, + { + "text": "Well, there's only one thing that could go wrong." + }, + { + "text": "When you connect this distance matrix D to the matrix x transpose x, you remember the position matrix, maybe I called it G. This is giving, so Gij is the dot product of xi with xj." + }, + { + "text": "Oops, let's make that into a j." + }, + { + "text": "Thank you." + }, + { + "text": "So Gij is the matrix of dot products." + }, + { + "text": "And the great thing was that we can discover what that matrix, that matrix G comes directly from D, comes directly from D. And of course, what do we know about this matrix of cross products?" + }, + { + "text": "We know that it is positive semidefinite." + }, + { + "text": "So what goes wrong?" + }, + { + "text": "Well, just in a word, when we write out that equation and discover what G is, if the triangle inequality fails, we learn that G doesn't come out positive definite." + }, + { + "text": "That's really all I want to say." + }, + { + "text": "And I could push through the example." + }, + { + "text": "G will not come out positive definite if D, if that's D, because it can't." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk10.json b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..abdb02881dc704c19617b286f1fdc02612559a72 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Why is that first statement true?" + }, + { + "text": "Huh." + }, + { + "text": "Huh." + }, + { + "text": "How is that matrix related to this matrix?" + }, + { + "text": "It's just a transpose." + }, + { + "text": "If I take the transpose of that matrix, I get that." + }, + { + "text": "So what happens to the trace?" + }, + { + "text": "I'm adding down the diagonal." + }, + { + "text": "The transpose has no effect." + }, + { + "text": "Clearly, this is just the fact that the trace doesn't change, is not changed when you transpose a matrix, because the diagonal is not changed." + }, + { + "text": "Now, what about this guy?" + }, + { + "text": "I guess we're getting back to old fashioned 18.065, remembering facts about linear algebra, because this is pure linear algebra." + }, + { + "text": "So what's this one about?" + }, + { + "text": "This says that I can reverse the order of two matrices." + }, + { + "text": "I'm now looking at the connection between those two." + }, + { + "text": "And so let me just use different letters." + }, + { + "text": "CD equals the trace of DC." + }, + { + "text": "I can flip the order." + }, + { + "text": "That's all I've done here is I've reversed B with A transpose." + }, + { + "text": "I reversed C with D. OK, so why is that true?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk11.json b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..8827985a00b27f6ab1cbd6d392a0115ce90befd2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Why is that true?" + }, + { + "text": "Oh, well, how shall we see the truth of that fact?" + }, + { + "text": "So these are really convenient facts that make a lot of people use the trace more often than we have in 18.065." + }, + { + "text": "I'm not a big user of arguments based on trace, but these are identities that go a long way with many problems." + }, + { + "text": "So let's see why that's true." + }, + { + "text": "Anytime you think about trace, you've got two languages to use." + }, + { + "text": "You can use the eigenvalues." + }, + { + "text": "It's the sum of the eigenvalues." + }, + { + "text": "Or you can use the diagonal entries, because it's the sum of the diagonal entries." + }, + { + "text": "Let's use eigenvalues." + }, + { + "text": "How are the eigenvalues of CD related to the eigenvalues of DC?" + }, + { + "text": "They're the same." + }, + { + "text": "If these matrices are rectangular, then there might be some extra 0 eigenvalues, because they would have different shapes." + }, + { + "text": "But 0's are not going to affect the trace." + }, + { + "text": "So this is the same non-zero eigenvalues." + }, + { + "text": "And so on." + }, + { + "text": "Yeah." + }, + { + "text": "OK. Let me just try to tell you the steps now to get the correct cue." + }, + { + "text": "Or let me tell you the answer first." + }, + { + "text": "And I'm realizing that all-important question four, does deep learning actually work?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk12.json b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..6cf92b2e400468168992334ed80a240b0234569e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "We're going to run out of time today, because we only have a few minutes left." + }, + { + "text": "I suggest we bring that question back up, because it's pretty important to a lot of people." + }, + { + "text": "I had lunch with Professor Edelman, and he said, you know, deep learning and neural nets have had a record amount of publicity and hype for a sort of computational algorithm." + }, + { + "text": "And I've had people now tell me that typical, first, if you create a network using Alex's design, for example, the chances are that it won't be successful." + }, + { + "text": "That the successful networks have been worked on and experimented with, and a good structure has emerged, but wasn't there at the start." + }, + { + "text": "So I think that's a topic for Monday." + }, + { + "text": "And I'm really just realizing from talking to people in the field that it's by no means automatic that the structure, even if you put in a whole bunch of layers, it may not be what you want." + }, + { + "text": "OK, so let me finish this argument today." + }, + { + "text": "Let me give you the answer." + }, + { + "text": "So what's the good Q?" + }, + { + "text": "I have matrices Y and X." + }, + { + "text": "And the idea is that I take its, I look at Y transpose X, so that'll be all the dot products of one set of vectors with the other set of vectors." + }, + { + "text": "That's a matrix." + }, + { + "text": "And I do its SVD, U sigma V transpose." + }, + { + "text": "So multiply this, multiply the two bases that you're given." + }, + { + "text": "Of course, if Y was the same as X, if it was an orthogonal basis, you'd have the identity." + }, + { + "text": "No questions." + }, + { + "text": "But generally, it has an SVD." + }, + { + "text": "And we're looking for a orthogonal matrix." + }, + { + "text": "So the best Q is, da-da-da-da, I mean, it's the right time for expressions of amazement." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk13.json b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..5ecf0f78a0f821ec464075b4c598b47a97b3e296 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk13.json @@ -0,0 +1,41 @@ +[ + { + "text": "It is UV transpose." + }, + { + "text": "OK, so that gives us the answer." + }, + { + "text": "We're given X and Y." + }, + { + "text": "We're looking for the best Q." + }, + { + "text": "And the answer comes in the simplest possible way." + }, + { + "text": "Compute Y transpose X, compute its SVD, and use the orthogonal matrices from the SVD." + }, + { + "text": "Yeah, and I'm out of time." + }, + { + "text": "So proof, it's three line later, either to just send you the section online or to discuss it in class Monday." + }, + { + "text": "But I'm really planning Monday to start with question four." + }, + { + "text": "And meanwhile, to ask a whole lot of people, everybody I can find, about that important question is, does deep learning usually work?" + }, + { + "text": "What can you do to make sure it works or give yourself a better chance to have it work?" + }, + { + "text": "So that's up for Monday then." + }, + { + "text": "Good." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk2.json b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..28ad6c58d174fc38799adaef8b2fe0c25ce4401e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "If it came out positive definite, then we could find an x." + }, + { + "text": "So if we had the G, then the final step, you remember, is to find an x." + }, + { + "text": "Well, we know that if G is positive semidefinite, there are multiple ways to find an x." + }, + { + "text": "This is positive semidefinite matrices is what you get out of x transpose x's." + }, + { + "text": "And we can find an x given a G. We can find G given an x." + }, + { + "text": "So it has to be that this won't be true, that the matrix G that comes out of that equation will turn out not to be positive definite." + }, + { + "text": "So it's really quite nice." + }, + { + "text": "It's a beautiful little bit of mathematics that if and only if the triangle inequality is satisfied by these numbers, if and only if, then the matrix in the D matrix, then the G matrix that comes out of this equation, which I haven't written, is positive semidefinite." + }, + { + "text": "If the triangle inequality is OK, we can find the points." + }, + { + "text": "If the triangle inequality is violated, like here, then the matrix G is not positive semidefinite, has negative eigenvalues, and we cannot find the point." + }, + { + "text": "Yeah." + }, + { + "text": "I could recall the G matrix, the G equation, but it's coming to you in the two-page section that does distance matrices." + }, + { + "text": "OK. That's just a, I should have made a point." + }, + { + "text": "It's nice to have specific numbers." + }, + { + "text": "And I could get the specific numbers for G, and we would see no way it's not positive definite." + }, + { + "text": "OK." + }, + { + "text": "So that's just tidying up last time." + }, + { + "text": "I have another small problem to talk about, and then a big question of whether deep learning actually works." + }, + { + "text": "I had an email from an expert last night, which changed my view of the world about that question, as you can imagine." + }, + { + "text": "The change in my world was I had thought the answer was yes, and I now think the answer is no." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk3.json b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..630144696d60a2e0ec5b8fe7a5a9ca5b2817d8bf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's like rather a big issue for 18.065." + }, + { + "text": "But we'll see about that later." + }, + { + "text": "OK. Now, Procrustes problem." + }, + { + "text": "So Procrustes, and it's included in the notes, that name comes from a Greek myth." + }, + { + "text": "Are you guys into Greek myths?" + }, + { + "text": "So what was the story of Procrustes?" + }, + { + "text": "He was at Procrustes who adjusted the length of his." + }, + { + "text": "So he had a special bed, Procrustes' bed, certain length." + }, + { + "text": "And then he had visitors coming." + }, + { + "text": "And instead of adjusting the length of the bed to fit the visitor, Procrustes adjusted the length of the visitor to fit the bed." + }, + { + "text": "So either stretched the visitor or chopped off part of the visitor." + }, + { + "text": "So anyway, the Greeks liked this sort of thing." + }, + { + "text": "So anyway, that's a Greek myth for 18.065." + }, + { + "text": "So the whole idea of the Procrustes problem is to make something fit something else." + }, + { + "text": "So the two things are, so suppose I'm just in three dimensions." + }, + { + "text": "I have two vectors here." + }, + { + "text": "So I have a basis for a two-dimensional space." + }, + { + "text": "And over here, I have people, space scientists might have one computation of the positions of satellites." + }, + { + "text": "Then, of course, they wouldn't be off by as much as this figure shows." + }, + { + "text": "But then they have another computation using different coordinates." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk4.json b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..76418bf39e55f24cc47dcf46d393af5f56b5ad84 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's partly rotated from this picture." + }, + { + "text": "But also, it's partly got round off errors and error in it between the two." + }, + { + "text": "So the question is, what's the best orthogonal transformation?" + }, + { + "text": "So this is a bunch of vectors, x1, x2, to xn, let's say." + }, + { + "text": "And I want to multiply them by an orthogonal matrix." + }, + { + "text": "No, maybe I'd do it on the other side." + }, + { + "text": "I think I do." + }, + { + "text": "Yeah, q to be as close as possible to this other set, y1, y2, up to yn." + }, + { + "text": "So let me just say it again." + }, + { + "text": "I have two sets of vectors." + }, + { + "text": "And I'm looking, and they're different, like those two sets." + }, + { + "text": "And I'm looking for the orthogonal matrix that, as well as possible, takes this set into this one." + }, + { + "text": "Of course, if this was an orthogonal basis and this was an orthogonal basis, then we would be home free." + }, + { + "text": "Q, we could get equality." + }, + { + "text": "We could take an orthogonal basis directly into an orthogonal basis with a orthogonal matrix Q." + }, + { + "text": "In other words, if x was an orthogonal matrix and y was an orthogonal matrix, we would get the exact correct Q." + }, + { + "text": "But that's not the case." + }, + { + "text": "So we're looking for the best possible." + }, + { + "text": "So that's the problem then." + }, + { + "text": "Minimize over orthogonal matrices Q." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk5.json b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..3f51ed4cc67121c2ac127b45a0c520daa53827f2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I just want to get my notation to be consistent here." + }, + { + "text": "OK. OK." + }, + { + "text": "So I see that I'm starting with the y's and mapping them to x's." + }, + { + "text": "So let me ask the question." + }, + { + "text": "What orthogonal matrix Q multiplies the y's to come as close as possible to the x's?" + }, + { + "text": "So over all orthogonal Q's, I want to minimize yq minus x in the Frobenius norm." + }, + { + "text": "And I might as well square it." + }, + { + "text": "So Frobenius, we're into the Frobenius norm." + }, + { + "text": "Remember the matrix." + }, + { + "text": "Matrix, this is a very convenient norm in data science to measure the size of a matrix." + }, + { + "text": "And we have several possible formulas for it." + }, + { + "text": "So let me call the matrix A." + }, + { + "text": "And the Frobenius norm squared." + }, + { + "text": "OK, so what's one expression in terms of the entries of the matrix, the numbers Aij in the matrix?" + }, + { + "text": "The Frobenius norm just treats it like a long vector." + }, + { + "text": "So it's A11 squared plus A12 squared, all the way along the first plus second row." + }, + { + "text": "Just I'll say NN squared." + }, + { + "text": "OK." + }, + { + "text": "Sum of all the squares, just treating it like a long vector." + }, + { + "text": "OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk6.json b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..e0fdf2e99bfbc080797e05668f36589c69104495 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "But that's an awkward expression to write down." + }, + { + "text": "So what other ways do we have to find the Frobenius norm of a matrix?" + }, + { + "text": "Let's see." + }, + { + "text": "I can look at this as A transpose A." + }, + { + "text": "Is that right?" + }, + { + "text": "A transpose A." + }, + { + "text": "So what's happening there?" + }, + { + "text": "Remind me what." + }, + { + "text": "Yeah." + }, + { + "text": "I would get all that." + }, + { + "text": "I would get all these by taking the matrix A transpose times A." + }, + { + "text": "But what?" + }, + { + "text": "Sorry, I'm not." + }, + { + "text": "I've lost my thread of talk here." + }, + { + "text": "So here's." + }, + { + "text": "Oh, and then I take the trace, of course." + }, + { + "text": "So that first row, first column of A times that one will give me the one set of squares." + }, + { + "text": "And then that one times the other one, the next one, will give me the next set of squares." + }, + { + "text": "So this is going to, if I look at the trace." + }, + { + "text": "So I just want to look at the diagonal here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk7.json b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..342f7114391d9a24c87b9b8154426778728653dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's the trace." + }, + { + "text": "Remember, the trace of a matrix M is the sum down the diagonal, M11, M22, down to MNN." + }, + { + "text": "It's the diagonal sum." + }, + { + "text": "And everybody with me here?" + }, + { + "text": "So that term on the diagonal of A transpose A gives me all of that." + }, + { + "text": "Or maybe I should be doing AA transpose." + }, + { + "text": "And the point is, it doesn't matter." + }, + { + "text": "Or the trace of AA transpose." + }, + { + "text": "Those would both give the correct Frobenius norm squared." + }, + { + "text": "So traces are going to come into this little problem." + }, + { + "text": "Now, there's another formula for the Frobenius norm, even shorter, well, certainly shorter than this one, involving a sum of squares." + }, + { + "text": "And what's that one?" + }, + { + "text": "What's the other way to get this same answer?" + }, + { + "text": "If I look at the SVD, look at singular values, I think that this is also equal to sigma 1, the sum square of all the singular values." + }, + { + "text": "So it's three nice expressions for the Frobenius norm." + }, + { + "text": "The nice ones involve A transpose A or AA transpose." + }, + { + "text": "And of course, that connects to the singular values." + }, + { + "text": "Because what's the connection between singular values and these guys, A transpose A or AA transpose?" + }, + { + "text": "The singular values are the, or the singular values squared, are the eigenvalues of A transpose A." + }, + { + "text": "And then when I add up the trace, I'm adding up the eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk8.json b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..62486918ea96825270baf5c0d420b47a6d07a68a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "And that gives me the Frobenius norm squared." + }, + { + "text": "So that tells us something important, which we can see in different ways." + }, + { + "text": "So to solve this problem, we're going to need various facts." + }, + { + "text": "Like the QA in the Frobenius norm is the same as A in the Frobenius norm." + }, + { + "text": "Why is that?" + }, + { + "text": "Why?" + }, + { + "text": "So here I'm multiplying every column by the matrix Q." + }, + { + "text": "What happens to the length of the column when I multiply it by Q?" + }, + { + "text": "Doesn't change." + }, + { + "text": "So I could add up the lengths of the columns all squared." + }, + { + "text": "Here I wrote it in terms of rows, but I could have reordered that and got it in terms of columns." + }, + { + "text": "That's because the length of Q times any vector squared is the same as the vector squared." + }, + { + "text": "And take these to be the columns of A." + }, + { + "text": "So for column by column, the multiplication by Q doesn't change the length." + }, + { + "text": "And then when I add up all the columns squared, I get the Frobenius norm squared." + }, + { + "text": "And another way to say it, let's make the connection between this fact that Q didn't change the Frobenius norm and this fact that the Frobenius norm is expressed in terms of the sigmas." + }, + { + "text": "So what does Q do to the sigmas?" + }, + { + "text": "I want to see in another way the answer to why." + }, + { + "text": "So if I have a matrix A with singular values, I multiply by Q, what happens to the singular values?" + }, + { + "text": "Don't change." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk9.json b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..0b3c23e748c0366a3505addeea0a72a65f90635c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_0_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "Don't change." + }, + { + "text": "That's the key point about singular values." + }, + { + "text": "If I multiply, so A has an SVD U sigma V transpose." + }, + { + "text": "And QA will have the SVD QU sigma V transpose." + }, + { + "text": "So all I've changed when I multiply by Q, all I changed was the first factor, the first orthogonal factor in the SVD." + }, + { + "text": "I didn't change the sigmas." + }, + { + "text": "They're still sitting there." + }, + { + "text": "And of course, I could do also Q on the other side." + }, + { + "text": "Different Q, same Q or a different Q on the other side would show up here." + }, + { + "text": "And would not change the sigmas, and therefore would not change the Frobenius norm." + }, + { + "text": "So these are important properties of this Frobenius norm." + }, + { + "text": "It looks messy to write down in that form, but it's much nicer in these forms and in that form." + }, + { + "text": "So now if I can just, then we saw that it involves traces." + }, + { + "text": "So let me make a few observations about traces." + }, + { + "text": "So I'll just, we want to be able to play with traces, and that's something we really haven't done." + }, + { + "text": "Here's a fact, that the trace of A transpose B is equal to the trace of B transpose A." + }, + { + "text": "Of course, if B is A, it's clear." + }, + { + "text": "And it's equal to the trace of B A transpose." + }, + { + "text": "So you can do little changes in your matrix without changing the trace." + }, + { + "text": "Let's see why one of these is true." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk0.json b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..54ffdd862ffa76e2a043b59deb217a03b96b9c95 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high-quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "OK, just as we're getting started, I thought I'd add a few words about a question that came up after class." + }, + { + "text": "Suppose in that discussion last time, where you were given three, you were given a distance matrix, you were given the distance between x1 and x2, between x2 and x3, and between x1 and x3, and you wanted to find points that satisfied that." + }, + { + "text": "Well, we're going to fail on this example, because if the distance here is 1, the distance here is 1, then by the triangle inequality, the distance from x1 to x3 could not be more than 2." + }, + { + "text": "And when we square it, it could not be more than 4." + }, + { + "text": "And here it's 6." + }, + { + "text": "So what's going to happen?" + }, + { + "text": "What goes wrong in that case?" + }, + { + "text": "Yeah, I hadn't commented on that, and I'm not sure that the paper that I referenced does so." + }, + { + "text": "So I had to do a little search back in the literature, because people couldn't overlook this problem." + }, + { + "text": "So this is the triangle inequality fails." + }, + { + "text": "And it's not going to help to go into 10 dimensions, because the triangle inequalities doesn't change." + }, + { + "text": "And it's still there in 10 dimensions, and we're still failing." + }, + { + "text": "So what happens?" + }, + { + "text": "Well, what could happen?" + }, + { + "text": "Do you remember, and you'll have to remind me, the key equation." + }, + { + "text": "You remember we had an equation connecting the matrix." + }, + { + "text": "So what is the matrix D for this problem?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk1.json b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..ccc46852e7e38828e1335f8ff612971db3999ed2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So D is a 3 by 3 matrix with these distances squared." + }, + { + "text": "And it was convenient to use distances squared, because that's what comes into the next steps." + }, + { + "text": "So of course, the distance from each x to itself is 0." + }, + { + "text": "The distance from x distance squared was that." + }, + { + "text": "This one was that, but this one is 6." + }, + { + "text": "So that's the distance matrix." + }, + { + "text": "And we would like to find, the job was to find, and I'm just going to write down, we cannot find x1, x2, and x3 to match those distances." + }, + { + "text": "So what goes wrong?" + }, + { + "text": "Well, there's only one thing that could go wrong." + }, + { + "text": "When you connect this distance matrix D to the matrix x transpose x, you remember the position matrix, maybe I called it G. This is giving, so Gij is the dot product of xi with xj." + }, + { + "text": "Oops, let's make that into a j." + }, + { + "text": "Thank you." + }, + { + "text": "So Gij is the matrix of dot products." + }, + { + "text": "And the great thing was that we can discover what that matrix, that matrix G comes directly from D, comes directly from D. And of course, what do we know about this matrix of cross products?" + }, + { + "text": "We know that it is positive semidefinite." + }, + { + "text": "So what goes wrong?" + }, + { + "text": "Well, just in a word, when we write out that equation and discover what G is, if the triangle inequality fails, we learn that G doesn't come out positive definite." + }, + { + "text": "That's really all I want to say." + }, + { + "text": "And I could push through the example." + }, + { + "text": "G will not come out positive definite if D, if that's D, because it can't." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk10.json b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..abdb02881dc704c19617b286f1fdc02612559a72 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Why is that first statement true?" + }, + { + "text": "Huh." + }, + { + "text": "Huh." + }, + { + "text": "How is that matrix related to this matrix?" + }, + { + "text": "It's just a transpose." + }, + { + "text": "If I take the transpose of that matrix, I get that." + }, + { + "text": "So what happens to the trace?" + }, + { + "text": "I'm adding down the diagonal." + }, + { + "text": "The transpose has no effect." + }, + { + "text": "Clearly, this is just the fact that the trace doesn't change, is not changed when you transpose a matrix, because the diagonal is not changed." + }, + { + "text": "Now, what about this guy?" + }, + { + "text": "I guess we're getting back to old fashioned 18.065, remembering facts about linear algebra, because this is pure linear algebra." + }, + { + "text": "So what's this one about?" + }, + { + "text": "This says that I can reverse the order of two matrices." + }, + { + "text": "I'm now looking at the connection between those two." + }, + { + "text": "And so let me just use different letters." + }, + { + "text": "CD equals the trace of DC." + }, + { + "text": "I can flip the order." + }, + { + "text": "That's all I've done here is I've reversed B with A transpose." + }, + { + "text": "I reversed C with D. OK, so why is that true?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk11.json b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..8827985a00b27f6ab1cbd6d392a0115ce90befd2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Why is that true?" + }, + { + "text": "Oh, well, how shall we see the truth of that fact?" + }, + { + "text": "So these are really convenient facts that make a lot of people use the trace more often than we have in 18.065." + }, + { + "text": "I'm not a big user of arguments based on trace, but these are identities that go a long way with many problems." + }, + { + "text": "So let's see why that's true." + }, + { + "text": "Anytime you think about trace, you've got two languages to use." + }, + { + "text": "You can use the eigenvalues." + }, + { + "text": "It's the sum of the eigenvalues." + }, + { + "text": "Or you can use the diagonal entries, because it's the sum of the diagonal entries." + }, + { + "text": "Let's use eigenvalues." + }, + { + "text": "How are the eigenvalues of CD related to the eigenvalues of DC?" + }, + { + "text": "They're the same." + }, + { + "text": "If these matrices are rectangular, then there might be some extra 0 eigenvalues, because they would have different shapes." + }, + { + "text": "But 0's are not going to affect the trace." + }, + { + "text": "So this is the same non-zero eigenvalues." + }, + { + "text": "And so on." + }, + { + "text": "Yeah." + }, + { + "text": "OK. Let me just try to tell you the steps now to get the correct cue." + }, + { + "text": "Or let me tell you the answer first." + }, + { + "text": "And I'm realizing that all-important question four, does deep learning actually work?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk12.json b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..6cf92b2e400468168992334ed80a240b0234569e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "We're going to run out of time today, because we only have a few minutes left." + }, + { + "text": "I suggest we bring that question back up, because it's pretty important to a lot of people." + }, + { + "text": "I had lunch with Professor Edelman, and he said, you know, deep learning and neural nets have had a record amount of publicity and hype for a sort of computational algorithm." + }, + { + "text": "And I've had people now tell me that typical, first, if you create a network using Alex's design, for example, the chances are that it won't be successful." + }, + { + "text": "That the successful networks have been worked on and experimented with, and a good structure has emerged, but wasn't there at the start." + }, + { + "text": "So I think that's a topic for Monday." + }, + { + "text": "And I'm really just realizing from talking to people in the field that it's by no means automatic that the structure, even if you put in a whole bunch of layers, it may not be what you want." + }, + { + "text": "OK, so let me finish this argument today." + }, + { + "text": "Let me give you the answer." + }, + { + "text": "So what's the good Q?" + }, + { + "text": "I have matrices Y and X." + }, + { + "text": "And the idea is that I take its, I look at Y transpose X, so that'll be all the dot products of one set of vectors with the other set of vectors." + }, + { + "text": "That's a matrix." + }, + { + "text": "And I do its SVD, U sigma V transpose." + }, + { + "text": "So multiply this, multiply the two bases that you're given." + }, + { + "text": "Of course, if Y was the same as X, if it was an orthogonal basis, you'd have the identity." + }, + { + "text": "No questions." + }, + { + "text": "But generally, it has an SVD." + }, + { + "text": "And we're looking for a orthogonal matrix." + }, + { + "text": "So the best Q is, da-da-da-da, I mean, it's the right time for expressions of amazement." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk13.json b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..5ecf0f78a0f821ec464075b4c598b47a97b3e296 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk13.json @@ -0,0 +1,41 @@ +[ + { + "text": "It is UV transpose." + }, + { + "text": "OK, so that gives us the answer." + }, + { + "text": "We're given X and Y." + }, + { + "text": "We're looking for the best Q." + }, + { + "text": "And the answer comes in the simplest possible way." + }, + { + "text": "Compute Y transpose X, compute its SVD, and use the orthogonal matrices from the SVD." + }, + { + "text": "Yeah, and I'm out of time." + }, + { + "text": "So proof, it's three line later, either to just send you the section online or to discuss it in class Monday." + }, + { + "text": "But I'm really planning Monday to start with question four." + }, + { + "text": "And meanwhile, to ask a whole lot of people, everybody I can find, about that important question is, does deep learning usually work?" + }, + { + "text": "What can you do to make sure it works or give yourself a better chance to have it work?" + }, + { + "text": "So that's up for Monday then." + }, + { + "text": "Good." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk2.json b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..28ad6c58d174fc38799adaef8b2fe0c25ce4401e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "If it came out positive definite, then we could find an x." + }, + { + "text": "So if we had the G, then the final step, you remember, is to find an x." + }, + { + "text": "Well, we know that if G is positive semidefinite, there are multiple ways to find an x." + }, + { + "text": "This is positive semidefinite matrices is what you get out of x transpose x's." + }, + { + "text": "And we can find an x given a G. We can find G given an x." + }, + { + "text": "So it has to be that this won't be true, that the matrix G that comes out of that equation will turn out not to be positive definite." + }, + { + "text": "So it's really quite nice." + }, + { + "text": "It's a beautiful little bit of mathematics that if and only if the triangle inequality is satisfied by these numbers, if and only if, then the matrix in the D matrix, then the G matrix that comes out of this equation, which I haven't written, is positive semidefinite." + }, + { + "text": "If the triangle inequality is OK, we can find the points." + }, + { + "text": "If the triangle inequality is violated, like here, then the matrix G is not positive semidefinite, has negative eigenvalues, and we cannot find the point." + }, + { + "text": "Yeah." + }, + { + "text": "I could recall the G matrix, the G equation, but it's coming to you in the two-page section that does distance matrices." + }, + { + "text": "OK. That's just a, I should have made a point." + }, + { + "text": "It's nice to have specific numbers." + }, + { + "text": "And I could get the specific numbers for G, and we would see no way it's not positive definite." + }, + { + "text": "OK." + }, + { + "text": "So that's just tidying up last time." + }, + { + "text": "I have another small problem to talk about, and then a big question of whether deep learning actually works." + }, + { + "text": "I had an email from an expert last night, which changed my view of the world about that question, as you can imagine." + }, + { + "text": "The change in my world was I had thought the answer was yes, and I now think the answer is no." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk3.json b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..630144696d60a2e0ec5b8fe7a5a9ca5b2817d8bf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's like rather a big issue for 18.065." + }, + { + "text": "But we'll see about that later." + }, + { + "text": "OK. Now, Procrustes problem." + }, + { + "text": "So Procrustes, and it's included in the notes, that name comes from a Greek myth." + }, + { + "text": "Are you guys into Greek myths?" + }, + { + "text": "So what was the story of Procrustes?" + }, + { + "text": "He was at Procrustes who adjusted the length of his." + }, + { + "text": "So he had a special bed, Procrustes' bed, certain length." + }, + { + "text": "And then he had visitors coming." + }, + { + "text": "And instead of adjusting the length of the bed to fit the visitor, Procrustes adjusted the length of the visitor to fit the bed." + }, + { + "text": "So either stretched the visitor or chopped off part of the visitor." + }, + { + "text": "So anyway, the Greeks liked this sort of thing." + }, + { + "text": "So anyway, that's a Greek myth for 18.065." + }, + { + "text": "So the whole idea of the Procrustes problem is to make something fit something else." + }, + { + "text": "So the two things are, so suppose I'm just in three dimensions." + }, + { + "text": "I have two vectors here." + }, + { + "text": "So I have a basis for a two-dimensional space." + }, + { + "text": "And over here, I have people, space scientists might have one computation of the positions of satellites." + }, + { + "text": "Then, of course, they wouldn't be off by as much as this figure shows." + }, + { + "text": "But then they have another computation using different coordinates." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk4.json b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..76418bf39e55f24cc47dcf46d393af5f56b5ad84 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's partly rotated from this picture." + }, + { + "text": "But also, it's partly got round off errors and error in it between the two." + }, + { + "text": "So the question is, what's the best orthogonal transformation?" + }, + { + "text": "So this is a bunch of vectors, x1, x2, to xn, let's say." + }, + { + "text": "And I want to multiply them by an orthogonal matrix." + }, + { + "text": "No, maybe I'd do it on the other side." + }, + { + "text": "I think I do." + }, + { + "text": "Yeah, q to be as close as possible to this other set, y1, y2, up to yn." + }, + { + "text": "So let me just say it again." + }, + { + "text": "I have two sets of vectors." + }, + { + "text": "And I'm looking, and they're different, like those two sets." + }, + { + "text": "And I'm looking for the orthogonal matrix that, as well as possible, takes this set into this one." + }, + { + "text": "Of course, if this was an orthogonal basis and this was an orthogonal basis, then we would be home free." + }, + { + "text": "Q, we could get equality." + }, + { + "text": "We could take an orthogonal basis directly into an orthogonal basis with a orthogonal matrix Q." + }, + { + "text": "In other words, if x was an orthogonal matrix and y was an orthogonal matrix, we would get the exact correct Q." + }, + { + "text": "But that's not the case." + }, + { + "text": "So we're looking for the best possible." + }, + { + "text": "So that's the problem then." + }, + { + "text": "Minimize over orthogonal matrices Q." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk5.json b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..3f51ed4cc67121c2ac127b45a0c520daa53827f2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I just want to get my notation to be consistent here." + }, + { + "text": "OK. OK." + }, + { + "text": "So I see that I'm starting with the y's and mapping them to x's." + }, + { + "text": "So let me ask the question." + }, + { + "text": "What orthogonal matrix Q multiplies the y's to come as close as possible to the x's?" + }, + { + "text": "So over all orthogonal Q's, I want to minimize yq minus x in the Frobenius norm." + }, + { + "text": "And I might as well square it." + }, + { + "text": "So Frobenius, we're into the Frobenius norm." + }, + { + "text": "Remember the matrix." + }, + { + "text": "Matrix, this is a very convenient norm in data science to measure the size of a matrix." + }, + { + "text": "And we have several possible formulas for it." + }, + { + "text": "So let me call the matrix A." + }, + { + "text": "And the Frobenius norm squared." + }, + { + "text": "OK, so what's one expression in terms of the entries of the matrix, the numbers Aij in the matrix?" + }, + { + "text": "The Frobenius norm just treats it like a long vector." + }, + { + "text": "So it's A11 squared plus A12 squared, all the way along the first plus second row." + }, + { + "text": "Just I'll say NN squared." + }, + { + "text": "OK." + }, + { + "text": "Sum of all the squares, just treating it like a long vector." + }, + { + "text": "OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk6.json b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..e0fdf2e99bfbc080797e05668f36589c69104495 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "But that's an awkward expression to write down." + }, + { + "text": "So what other ways do we have to find the Frobenius norm of a matrix?" + }, + { + "text": "Let's see." + }, + { + "text": "I can look at this as A transpose A." + }, + { + "text": "Is that right?" + }, + { + "text": "A transpose A." + }, + { + "text": "So what's happening there?" + }, + { + "text": "Remind me what." + }, + { + "text": "Yeah." + }, + { + "text": "I would get all that." + }, + { + "text": "I would get all these by taking the matrix A transpose times A." + }, + { + "text": "But what?" + }, + { + "text": "Sorry, I'm not." + }, + { + "text": "I've lost my thread of talk here." + }, + { + "text": "So here's." + }, + { + "text": "Oh, and then I take the trace, of course." + }, + { + "text": "So that first row, first column of A times that one will give me the one set of squares." + }, + { + "text": "And then that one times the other one, the next one, will give me the next set of squares." + }, + { + "text": "So this is going to, if I look at the trace." + }, + { + "text": "So I just want to look at the diagonal here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk7.json b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..342f7114391d9a24c87b9b8154426778728653dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's the trace." + }, + { + "text": "Remember, the trace of a matrix M is the sum down the diagonal, M11, M22, down to MNN." + }, + { + "text": "It's the diagonal sum." + }, + { + "text": "And everybody with me here?" + }, + { + "text": "So that term on the diagonal of A transpose A gives me all of that." + }, + { + "text": "Or maybe I should be doing AA transpose." + }, + { + "text": "And the point is, it doesn't matter." + }, + { + "text": "Or the trace of AA transpose." + }, + { + "text": "Those would both give the correct Frobenius norm squared." + }, + { + "text": "So traces are going to come into this little problem." + }, + { + "text": "Now, there's another formula for the Frobenius norm, even shorter, well, certainly shorter than this one, involving a sum of squares." + }, + { + "text": "And what's that one?" + }, + { + "text": "What's the other way to get this same answer?" + }, + { + "text": "If I look at the SVD, look at singular values, I think that this is also equal to sigma 1, the sum square of all the singular values." + }, + { + "text": "So it's three nice expressions for the Frobenius norm." + }, + { + "text": "The nice ones involve A transpose A or AA transpose." + }, + { + "text": "And of course, that connects to the singular values." + }, + { + "text": "Because what's the connection between singular values and these guys, A transpose A or AA transpose?" + }, + { + "text": "The singular values are the, or the singular values squared, are the eigenvalues of A transpose A." + }, + { + "text": "And then when I add up the trace, I'm adding up the eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk8.json b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..62486918ea96825270baf5c0d420b47a6d07a68a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "And that gives me the Frobenius norm squared." + }, + { + "text": "So that tells us something important, which we can see in different ways." + }, + { + "text": "So to solve this problem, we're going to need various facts." + }, + { + "text": "Like the QA in the Frobenius norm is the same as A in the Frobenius norm." + }, + { + "text": "Why is that?" + }, + { + "text": "Why?" + }, + { + "text": "So here I'm multiplying every column by the matrix Q." + }, + { + "text": "What happens to the length of the column when I multiply it by Q?" + }, + { + "text": "Doesn't change." + }, + { + "text": "So I could add up the lengths of the columns all squared." + }, + { + "text": "Here I wrote it in terms of rows, but I could have reordered that and got it in terms of columns." + }, + { + "text": "That's because the length of Q times any vector squared is the same as the vector squared." + }, + { + "text": "And take these to be the columns of A." + }, + { + "text": "So for column by column, the multiplication by Q doesn't change the length." + }, + { + "text": "And then when I add up all the columns squared, I get the Frobenius norm squared." + }, + { + "text": "And another way to say it, let's make the connection between this fact that Q didn't change the Frobenius norm and this fact that the Frobenius norm is expressed in terms of the sigmas." + }, + { + "text": "So what does Q do to the sigmas?" + }, + { + "text": "I want to see in another way the answer to why." + }, + { + "text": "So if I have a matrix A with singular values, I multiply by Q, what happens to the singular values?" + }, + { + "text": "Don't change." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk9.json b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..0b3c23e748c0366a3505addeea0a72a65f90635c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0Qws8BuK3RQ_1_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "Don't change." + }, + { + "text": "That's the key point about singular values." + }, + { + "text": "If I multiply, so A has an SVD U sigma V transpose." + }, + { + "text": "And QA will have the SVD QU sigma V transpose." + }, + { + "text": "So all I've changed when I multiply by Q, all I changed was the first factor, the first orthogonal factor in the SVD." + }, + { + "text": "I didn't change the sigmas." + }, + { + "text": "They're still sitting there." + }, + { + "text": "And of course, I could do also Q on the other side." + }, + { + "text": "Different Q, same Q or a different Q on the other side would show up here." + }, + { + "text": "And would not change the sigmas, and therefore would not change the Frobenius norm." + }, + { + "text": "So these are important properties of this Frobenius norm." + }, + { + "text": "It looks messy to write down in that form, but it's much nicer in these forms and in that form." + }, + { + "text": "So now if I can just, then we saw that it involves traces." + }, + { + "text": "So let me make a few observations about traces." + }, + { + "text": "So I'll just, we want to be able to play with traces, and that's something we really haven't done." + }, + { + "text": "Here's a fact, that the trace of A transpose B is equal to the trace of B transpose A." + }, + { + "text": "Of course, if B is A, it's clear." + }, + { + "text": "And it's equal to the trace of B A transpose." + }, + { + "text": "So you can do little changes in your matrix without changing the trace." + }, + { + "text": "Let's see why one of these is true." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk0.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..ed695ba203c725aa80144eb85fb8edd6706cbb8c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay." + }, + { + "text": "So coming near the end of the course, this lecture will be a mixture of the linear algebra that comes with a change of basis." + }, + { + "text": "And a change of basis from one basis to another basis is something you really do in applications." + }, + { + "text": "And I would like to talk about those applications." + }, + { + "text": "I got a little bit involved with compression, compressing a signal, compressing an image, and that's exactly change of basis." + }, + { + "text": "And then the main theme in this chapter is the connection between a linear transformation, which doesn't have to have coordinates, and the matrix that tells us that transformation with respect to coordinates." + }, + { + "text": "So the matrix is the coordinate-based description of the linear transformation." + }, + { + "text": "Let me start out with the nice part, which is some, just to tell you something about image compression." + }, + { + "text": "Those of you, well, everybody's going to meet compression, because you know that the amount of data that we're getting, well, these lectures are compressed." + }, + { + "text": "So that actually, probably you see my motion as jerky, shall I use that word?" + }, + { + "text": "Have you looked on the web?" + }, + { + "text": "I should like to find a better word." + }, + { + "text": "Compressed, let's see." + }, + { + "text": "So my, the, the, the complete signal is, of course, in those video cameras and in the videotape, but that goes to the bottom of building nine, and out of that comes a jumpy motion, because it uses a standard system for compressing images." + }, + { + "text": "And, you'll notice that the stuff that sits on the board comes very clearly, but it's my motion that, that, that needs a whole lot of bits, right?" + }, + { + "text": "So, and if I were to run up and back, up there and back, that would need too many bits and they'd, I'd be compressed even more." + }, + { + "text": "So, what does compression mean?" + }, + { + "text": "Can I, let me just think of a still image." + }, + { + "text": "And, and of course, satellites, oh, there's, and, and computations of the climate, computations of combustion, the, computers and sensors of all kinds are just giving us overwhelming amounts of data." + }, + { + "text": "The web is, too." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk1.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..276b7aacae39769ce0e1627c108ec463ccf35faa --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, some compression can be done with no loss." + }, + { + "text": "Lossless compression is possible just using, sort of, the fact that, there's, there are redundancies." + }, + { + "text": "But I'm talking here about lossy compression." + }, + { + "text": "So I'm talking about, here's an image." + }, + { + "text": "And what does an image consist of?" + }, + { + "text": "It consists of a lot of little pixels, right?" + }, + { + "text": "Maybe five hundred and twelve by five hundred and twelve." + }, + { + "text": "Two to the ninth by two to the ninth pixels, and each, so this is pixel number one one, so that's a pixel, and if we're in black and white, the typical pixel would tell us a grayscale from zero to two fifty five." + }, + { + "text": "So a pixel is usually a, a value of a, a, one of the x i, so this would be the i-th pixel, it, it's usually a real number on a scale from zero to two fifty five." + }, + { + "text": "In other words, two to the eighth possibilities." + }, + { + "text": "So usually, that's the, that's the standard, so, so that, that's eight, eight bits." + }, + { + "text": "But then we have that for every, every pixel, so we have five hundred and twelve squared pixels." + }, + { + "text": "We're, we're really operating, x is a vector in Rn, but what is n?" + }, + { + "text": "n is five hundred and twelve squared." + }, + { + "text": "That's, that's our problem right there." + }, + { + "text": "We're, a pixel is a vector that gives us the information about the image, I'm sorry, the image that comes through is a vector of, of that length, that, that's the information we have about the image." + }, + { + "text": "If it's a color image, we would have three times that length, because we'd have, we'd need three coordinates to get color." + }, + { + "text": "So it would be three times five hundred and twelve squared." + }, + { + "text": "It's an enormous amount of information, and we couldn't send out the image for these lectures without compressing it." + }, + { + "text": "We, we, it, it would be, it would overload the system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk10.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..db2f6371da88f739758d4ebae59b4fdffa270d6f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "Tell me how to do it." + }, + { + "text": "How do I find the, if I give you eight basis vectors and I give you the input signal and I ask for the coefficients, what do I do?" + }, + { + "text": "What's the, what's the step?" + }, + { + "text": "I want, I'm trying to solve this, I want to know the eight coefficients, so I'm changing from the standard basis, which is just the eight grayscale values, to the wavelet basis, where this same vector is represented by eight numbers." + }, + { + "text": "It's got to take eight numbers to tell you a vector in R8, and those eight numbers are the coefficients of the basis." + }, + { + "text": "Look, we've done this thing before." + }, + { + "text": "What do we, here, there is the equation in vector notation." + }, + { + "text": "We want to see it as a matrix." + }, + { + "text": "This is a combination of columns of the wavelet matrix, right?" + }, + { + "text": "This is p equals c1, c2, down to c8, and these guys are the columns." + }, + { + "text": "I mean, this is the step that we constantly take in this course." + }, + { + "text": "The first basis vector goes in the first column, the second basis vector goes in the second column, and so on." + }, + { + "text": "The eight columns of this wavelet matrix are the eight basis vectors." + }, + { + "text": "This is a wavelet matrix W. So, the step to change basis." + }, + { + "text": "So now I'm finally coming to this change of basis." + }, + { + "text": "So the change of basis, let me stay with this board, but, well, let me just go above it here." + }, + { + "text": "So the standard basis we know, the wavelet basis we have here, and the transform is simply solve the equations p equal Wc." + }, + { + "text": "So the coefficients are W inverse p, right?" + }, + { + "text": "This shows a critical point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk11.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..8346f1691f9a546b0252c3e0960539efff45ec1f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "A good basis has a nice, fast inverse." + }, + { + "text": "So good means, good basis means what?" + }, + { + "text": "So this is like the billion dollar competition, and it's not over yet." + }, + { + "text": "People are going to come up with better bases than these." + }, + { + "text": "So a good basis will be, first good thing would be fast." + }, + { + "text": "I have to be able to multiply by W fast and multiply by W, by its inverse fast." + }, + { + "text": "That's, if a basis doesn't allow you to do that fast, then it's going to take so much time that you can't afford it." + }, + { + "text": "So these bases, the Fourier basis, everybody said, OK, I know how to deal quickly with the Fourier basis, because we have something called the fast Fourier transform." + }, + { + "text": "So there's a FFT that came in my earlier lecture and comes in the last chapter of the book." + }, + { + "text": "So change of basis is done, if for the Fourier basis, is done fast by the FFT and there's a fast wavelet transform." + }, + { + "text": "I can change, for this wavelet example, this matrix is easy to invert." + }, + { + "text": "It's just somebody had a smart idea in choosing that wavelet basis and inverting it, it has a nice inverse." + }, + { + "text": "Actually, you can see why it has a nice inverse." + }, + { + "text": "Do you see any property of these eight basis vectors?" + }, + { + "text": "Well, I've only written five of them, but if you see that property for those five, you'll see it for the three remaining." + }, + { + "text": "What, if I give you those eight vectors and ask, what's a nice property?" + }, + { + "text": "Well, you would say, first, they're all ones and minus ones and zeros, so every multiplication is very fast using just, in binary." + }, + { + "text": "But what's the other great property of those vectors?" + }, + { + "text": "Anybody see it?" + }, + { + "text": "So, of course, when I think about a basis, one nice property, I don't have to have it, but I'm happy if it's there, is that they're orthogonal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk12.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..c0eaf69080e43e238bee148545d1b059bef72365 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "If the basis vectors are orthogonal, then I'm in good shape." + }, + { + "text": "And these are, do you see, take the dot product of that with that, you get four plus ones and four minus ones, you get zero." + }, + { + "text": "Take the dot product of that with that, you get two plus ones and two minus ones." + }, + { + "text": "Or the dot product of that with that, two plus ones and two minus ones." + }, + { + "text": "You can easily check that that's an orthogonal basis." + }, + { + "text": "It's not orthonormal." + }, + { + "text": "I could, to fix it up, I should divide by the length to make them unit vectors." + }, + { + "text": "Let's suppose I do that." + }, + { + "text": "So somewhere in here I've got to account for the fact that this has length square root of eight, that has length square root of four, that has length square root of two." + }, + { + "text": "But that's just a constant factor that's easy to --." + }, + { + "text": "So suppose we've done that." + }, + { + "text": "Then tell me what's W inverse." + }, + { + "text": "That's what chapter four, section four point four was about." + }, + { + "text": "If we have orthonormal columns, what- then the inverse is the same as the transpose." + }, + { + "text": "So if we have a fast way to multiply by W, which we do, the inverse is going to look just the same and we'll have a fast way to do W inverse." + }, + { + "text": "So that's, the wavelet basis passes this requirement for fast." + }, + { + "text": "We can use it fast." + }, + { + "text": "But there's a second requirement, is it any good?" + }, + { + "text": "Because the very fastest thing we could do would be not to change basis at all." + }, + { + "text": "Right?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk13.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..4de80b529af0604a4e0b9b0291a8822dc165b83a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Fastest thing would be, OK, stay with a standard basis, stay with eight pixel values." + }, + { + "text": "But that was poor from compression point of view, right?" + }, + { + "text": "Those eight pixel values, if I just took those eight numbers, I can't throw some of those away." + }, + { + "text": "If I throw away ninety percent, if I compressed ten to one, and throw away ninety percent of my pixel values, well, my picture's just gone dark." + }, + { + "text": "Whereas the basis that was good, the wavelet basis or the Fourier basis, if I throw away c5, c6, c7 and c8, all I'm throwing away is little blips that are probably there in very small amounts." + }, + { + "text": "So the second property that we need is good compression." + }, + { + "text": "So, so first it, it has to be fast, and secondly, it has to be a few basis factors should come close to the signal." + }, + { + "text": "So, so a few, few is enough." + }, + { + "text": "Can I write it that way?" + }, + { + "text": "A few basis factors are enough to reproduce the image, just exactly as on the video of these 18.06 lectures." + }, + { + "text": "I don't know what the compression rate is." + }, + { + "text": "I'll ask, David, who, who does the compression, and, by the way, I'll try to get the lectures, that are relevant for the quiz, up onto the web, in time." + }, + { + "text": "So I'll send him a message today." + }, + { + "text": "So, at the point, so he's using the Fourier basis, because the JPEG, so JPEG 2000, which will be the next standard for image compression, will include wavelets." + }, + { + "text": "So, I mean, you're, you're actually getting a kind of up to date, picture of where this big world of signal and image processing is." + }, + { + "text": "That Fourier is what everybody knew, and what people automatically used, and the new, new one is wavelets, where this is the simplest set of wavelets, and this isn't the one that the FBI uses, by the way." + }, + { + "text": "The FBI uses a more, a more, a smoother wavelet." + }, + { + "text": "Instead of jumping from one to minus one, it's a smooth, cutoff." + }, + { + "text": "And, that's what we'll be in, in JPEG 2000." + }, + { + "text": "OK, so that's that application." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk14.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..8f1debcca7ae641417e7ed0a630d269963c01302 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now let me come to my, the, the math, the linear algebra part of the lecture." + }, + { + "text": "Well, we've actually seen a change of basis." + }, + { + "text": "So let, let me just review that change of basis idea, and then the, and then the transformation to a matrix." + }, + { + "text": "OK, so, so this, I hope you see that these applications are really big." + }, + { + "text": "Now I have to talk a little about change of basis and little about that, the, the matrix." + }, + { + "text": "OK. OK. OK." + }, + { + "text": "So change of basis." + }, + { + "text": "Basically, forgive that pun, OK, I have, I have, I have my vector in one basis, and I want to change to a different one." + }, + { + "text": "Actually, you saw it for the wavelet case." + }, + { + "text": "So I need the, the, let the matrix W, the columns of W, be the new basis vectors." + }, + { + "text": "Then the change of basis involves, just as it did there, W inverse." + }, + { + "text": "So we have the vector, vector, say, x in the old basis, and we, that converts to a vector, let's say, c in the new basis, and the relation is exactly what we had there, that x is Wc." + }, + { + "text": "That's the, that's the, that's the, that's the step we have to take." + }, + { + "text": "There's a matrix W that gives us a change of basis." + }, + { + "text": "OK." + }, + { + "text": "I, I, what I want to do is think about mat- transformations and matrices." + }, + { + "text": "So here's, here's the question, that, that, to complete this lecture." + }, + { + "text": "Suppose I have a linear transformation T. So it's, it's a, it's a, we, we would think of it as an A, as a n by n matrix." + }, + { + "text": "And it's computed with respect to a certain basis." + }, + { + "text": "So T, so, no, I'm sorry." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk15.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..dbc5ad92f06633f3366a78c24c0c7c08b058ee63 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "I've got the transformation T, period." + }, + { + "text": "That's taking eight-dimensional space to eight-dimensional space." + }, + { + "text": "Now let's get matrices in there." + }, + { + "text": "OK." + }, + { + "text": "So, so with respect to, with respect to a fir- a first basis, say, V1 up to V8, it has a matrix A. I'm just setting up letters here." + }, + { + "text": "With respect to a second basis, say, I'll make it U1 up to- or W1, since I've used Ws, W1 up to W8, it has a matrix B." + }, + { + "text": "And my question is, what's the connection between A and B?" + }, + { + "text": "How is the matrix- the transformation T is settled." + }, + { + "text": "We could say it's a rotation, for example." + }, + { + "text": "So that would be one transformation of eight-dimensional space, just spin it a little." + }, + { + "text": "Or project it." + }, + { + "text": "Or, or, whatever, whatever linear transformation we've got." + }, + { + "text": "Now we have to remember, so I- so first- my first step is to remind you how you create that matrix A." + }, + { + "text": "Then my second step is, we would use the same method to create B, but because it came from the same transformation, there's got to be a relation between A and B." + }, + { + "text": "What's the- what's the relation between A and B?" + }, + { + "text": "And let me jump to the answer on that one." + }, + { + "text": "That if I have- if I have the same transformation, and I'm compute- its matrix in one basis and then I compute it in another basis, those two matrices are similar." + }, + { + "text": "So these two matrices are similar." + }, + { + "text": "Now, do you remember what similar matrices meant?" + }, + { + "text": "Similar." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk16.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..9d019933a190fe645eec785d8363a0940d0f76a4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "A is similar- the two matrices are similar." + }, + { + "text": "Similar." + }, + { + "text": "And what do I mean by that?" + }, + { + "text": "I mean that I take the matrix B and I can compute it from the matrix A using some similarity, some matrix M on one side and M inverse on the other." + }, + { + "text": "And this M will be the change of basis matrix." + }, + { + "text": "This part of the lecture is admittedly compressed." + }, + { + "text": "What I wanted you to- it's really the conclusion that I want you to spot." + }, + { + "text": "Now I have to go back and say, what does it mean for A to be the matrix of this transformation T?" + }, + { + "text": "So I have to remind you what that meant." + }, + { + "text": "That was in the last lecture." + }, + { + "text": "Then this is the conclusion, that if I change to a different basis, we now know- see, if I change to a different basis, two things happen." + }, + { + "text": "Every vector has new coordinates." + }, + { + "text": "There, the rule is this one, between the old coordinates and the new ones." + }, + { + "text": "Every matrix changes." + }, + { + "text": "Every transformation has a new matrix." + }, + { + "text": "And the new matrix is related this way." + }, + { + "text": "The M could be the same as the W. The M there could be the W here." + }, + { + "text": "OK." + }, + { + "text": "So can I, in the remaining minutes, recapture my lecture, the end of my lecture that was just before Thanksgiving, about the matrix?" + }, + { + "text": "OK. What's the matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk17.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..f82f2cc230f9f2720733e8b152f84f80f1341c9f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll just take one basis." + }, + { + "text": "So now I'm going to- this part is going to go onto this board here." + }, + { + "text": "What is the matrix?" + }, + { + "text": "What is A?" + }, + { + "text": "OK." + }, + { + "text": "Using a basis v1 up to v8." + }, + { + "text": "OK. What's the point?" + }, + { + "text": "The point is, if I know what the transformation does to those eight basis vectors, I know it completely." + }, + { + "text": "I know T, I know everything about T, I know T completely from knowing what T does to v1, what T does to v2, what T does to v8." + }, + { + "text": "Why is that?" + }, + { + "text": "It's because T is a linear transformation." + }, + { + "text": "So that if I know what these outputs are, so these are the inputs, v1 up to v8, these are the outputs from the transformation, like every one rotated, every one projected, whatever transformation I've done, then why is it that I know everything?" + }, + { + "text": "How does linearity work?" + }, + { + "text": "Why?" + }, + { + "text": "This is because every x is some combination of these basis vectors, right?" + }, + { + "text": "c1 v1, c2 v2, c8 v8." + }, + { + "text": "That's the whole point of a basis, that every vector is a combination of the basis vectors in exactly one way." + }, + { + "text": "And then, what is T of x?" + }, + { + "text": "The point is, I claim that we know T of x completely for every x, because every x is a combination of those, and now we use the linear transformation part to say that the output from x has to be c1 times the output from v1 plus c2 times the output from v2 and so on, up through c8 times the output from v8." + }, + { + "text": "So this is like just saying, OK, we know everything when we know what T does to each basis vector." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk18.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..d9c718592303012586f37aed3dc53271be8cef29 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "So those are the eight things we need." + }, + { + "text": "Now, but we need these answers in this basis." + }, + { + "text": "So T- so this first output is some combination of the eight basis vectors." + }, + { + "text": "So write T times the first- acting on the first input, in other words, write the first output as a combination of the basis vectors." + }, + { + "text": "Say a11 v1 plus a21 v2 and so on, a81 v8." + }, + { + "text": "Write T of v2 as some combination, a12 of v1, a22 of v2 and so on." + }, + { + "text": "I'm creating the matrix A, column by column." + }, + { + "text": "Those numbers go in the first column, these numbers go in the second column." + }, + { + "text": "The matrix A that this is our matrix that represents T in this basis is these numbers." + }, + { + "text": "a11 down to a18, a21 down to a28 and so on." + }, + { + "text": "OK. That's the recipe." + }, + { + "text": "In other words, if I give you a transformation and a basis, that's what I have to give you." + }, + { + "text": "The inputs are the basis and to tell you what the transformation is." + }, + { + "text": "And then you tell me, you compute T for each basis, expand that result in the basis, and that gives you the sixty-four numbers that go into the matrix A." + }, + { + "text": "Let me suppose, let's close with the best example of all." + }, + { + "text": "Suppose v1 to v8, this basis, is the eigenvectors." + }, + { + "text": "Suppose we have an eigenvector basis." + }, + { + "text": "So that T of vi is just, is in the same direction as vi." + }, + { + "text": "Now my question is, what is A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk19.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..4bc0bda81becbd032c626bcaab40cca8eaa39155 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Can you carry through the steps?" + }, + { + "text": "Let's, let's do them together, because we can do it in one minute." + }, + { + "text": "So we've chosen this perfect basis." + }, + { + "text": "And actually, with signal image processing, they might look for the eigenvectors, but that would take more calculation time than just saying, OK, we'll use the wavelet basis, or OK, we'll use the Fourier basis." + }, + { + "text": "But the very best basis is the eigenvector basis." + }, + { + "text": "OK, what's the matrix?" + }, + { + "text": "So, what's the first column of the matrix?" + }, + { + "text": "How do I get the first column?" + }, + { + "text": "I take the first basis vector v1." + }, + { + "text": "I op- I look to see what does the transformation do to it." + }, + { + "text": "The output is lambda one v1." + }, + { + "text": "I express that output as a combination, so the first input is v1." + }, + { + "text": "Its output is lambda one v1." + }, + { + "text": "Now write lambda one v1 as a combination of the basis vectors." + }, + { + "text": "Well, it's already done." + }, + { + "text": "It's just lambda one times the first basis vector and zero times the others." + }, + { + "text": "So this first column will have lambda one and zeros." + }, + { + "text": "OK?" + }, + { + "text": "Second input is v2." + }, + { + "text": "Output is lambda two v2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk2.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..44553739c24736b408dbd01c3688e075b25f9a15 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it has to be compressed." + }, + { + "text": "The standard compression, and still used in, in the, with these lectures, is, called JPEG." + }, + { + "text": "I think that stands for a Joint Photographic Experts Group." + }, + { + "text": "They established a system of compression." + }, + { + "text": "And I just want to tell you what it's about." + }, + { + "text": "It's a change of basis." + }, + { + "text": "What, what's, what basis do we have?" + }, + { + "text": "The, the current basis we have is, you could say, the standard basis is every pixel give a value." + }, + { + "text": "So that's like, we have a vector x, which is five hundred and twelve squared long, and in the i-th position, we get a number like one twenty one or something, the next, the pixel next to it might be one twenty four, maybe where, maybe where the, where my tie, begins to end." + }, + { + "text": "So if it was mostly blue shirt, this would be a slight difference in shading, but pretty close." + }, + { + "text": "Then the tie would be a different color." + }, + { + "text": "So, so we might have quite a few pixels for the blue shirt and a whole lot more for the blackboard that are very close." + }, + { + "text": "And that's what, are very correlated." + }, + { + "text": "And that's what gives us the possibility of compression." + }, + { + "text": "For example, before the lecture starts, if we had a blank blackboard, then there's an image, but it would make no sense to take that image and tell you what it is pixel by pixel." + }, + { + "text": "I mean, there's a case in which all pixel values, all gray levels are the same, or practically the same, depending on the erasing of the board, but extremely close." + }, + { + "text": "And so that's an image where the standard basis is lousy." + }, + { + "text": "That's, that's the basic fact." + }, + { + "text": "That, that the standard basis which gives the value of every pixel makes no use of the fact that we're getting a whole lot of pixels whose gray levels, the neighboring pixels tend to have the same gray level as the, as their, as their neighbors." + }, + { + "text": "So to take, how do we take advantage of that fact?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk20.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..57e892c1f19c9a45e5f14bb334eab942b0d796a2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk20.json @@ -0,0 +1,32 @@ +[ + { + "text": "OK, write that output as a combination of the v's." + }, + { + "text": "It's already done." + }, + { + "text": "It's just lambda two times the second v. So we need, in the second column, we have lambda two times the second v. Well, you see what's coming." + }, + { + "text": "That in that basis, in the eigenvector basis, the matrix is diagonal." + }, + { + "text": "So that's the perfect basis." + }, + { + "text": "That's the basis we'd love to have for image processing, but to find the eigenvectors of our pixel matrix would be too expensive." + }, + { + "text": "So we do something cheaper and close, which is to choose a good basis like, like wavelengths." + }, + { + "text": "OK, thanks." + }, + { + "text": "So quiz review on Wednesday, all day." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk3.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..8e246b42e71ac0ef99e39e59a7562c71f3da61b4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, one basis vector that would be extremely nice to, one vector that would be extremely nice to include in the basis would be a vector of all ones." + }, + { + "text": "That's not in our standard basis." + }, + { + "text": "So our, so let me just write again." + }, + { + "text": "The standard basis would, is, is our, is our one and all the rest zeros, zero, one, and all the rest zeros, everybody knows what the standard basis is." + }, + { + "text": "Now, any other basis for our, so this is, for this very high-dimensional space, now I'm going to speak about a better basis, better basis, and let me just emphasize, one vector that would be extremely nice to have in that basis is the vector of all ones." + }, + { + "text": "Why is that?" + }, + { + "text": "Let me just say again." + }, + { + "text": "Because that vector of all ones, by itself, one vector is, is able to completely give the information on a solid image." + }, + { + "text": "Of course, our image won't be solid, it'll have a mix of, of, solid and, and signal." + }, + { + "text": "So that one vector, but that, having that one vector in the basis is, is, is going to save us a whole lot." + }, + { + "text": "Now the question is, what other vectors should be in the basis?" + }, + { + "text": "The, the extreme vector in the basis might be a vector of one minus one, one minus one, one minus one." + }, + { + "text": "That would be a vector that shows, I mean, that's like a checkerboard vector, right?" + }, + { + "text": "That's a vector that would, if, if we had, if, if the image was like a huge checkerboard of plus minus, plus minus, plus minus, that vector would carry the whole signal." + }, + { + "text": "But much more common would be maybe to have half the image, darker and the other half lighter." + }, + { + "text": "So another image, another vector that might be quite useful in here would be half ones and half minus ones." + }, + { + "text": "I'm just trying to get across the idea of, that a basis could be, that first of all, we've got, the basis is at our disposal." + }, + { + "text": "Like, we're free to choose that." + }, + { + "text": "And it's a billion dollar decision what we choose." + }, + { + "text": "So, and TV people would rather, would prefer one basis based on the way the, the signal is scanned, and movie people would prefer another." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk4.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..811c58ffd5e28e456b42de439fa8cee4339bd2a6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "I mean, there's giant politics in this question that really reduces to a, to a linear algebra problem what basis to choose." + }, + { + "text": "I'll just mention the best known basis, which is, which JPEG uses, let me put that here, is the Fourier basis." + }, + { + "text": "So when you, when you use the Fourier basis, that includes, this is the constant vector, the DC vector, if we're electrical engineers, the, the, the vector of all ones, so it would include one, one, one, one." + }, + { + "text": "Often, eight by eight is a good choice." + }, + { + "text": "Eight by eight is a, is a good choice." + }, + { + "text": "So, what do I mean by this eight by eight?" + }, + { + "text": "I mean that the big signal, which is five twelve by five twelve, gets broken down, and JPEG does this, into eight by eight blocks." + }, + { + "text": "And we, sort of, this is too much to deal with at once." + }, + { + "text": "So what JPEG does is take this eight by eight block, which is sixty-four coefficients, sixty-four, pixels, and changes the basis on the, on that piece." + }, + { + "text": "And then, now, let's see, I was going to write down Fourier, so you remember Fourier is, is this vector of all ones, and then, the vector, oh, well, actually, I gave a lecture earlier about the Fourier matrix, these, this matrix whose columns are powers of a, of a, complex number w. I, I won't repeat that, because I'm not, I don't want to go into the details of the Fourier basis." + }, + { + "text": "Just to tell you how compression works." + }, + { + "text": "So what happens in JPEG?" + }, + { + "text": "What happens to the video, to a, to each image of, of, of these lectures?" + }, + { + "text": "The, it gets broken into eight by eight blocks." + }, + { + "text": "OK." + }, + { + "text": "Within each block, we have sixty-four coefficients, sixty-four basis vectors, sixty-four pixels, and we change basis in sixty-four dimensional space, using these Fourier vectors." + }, + { + "text": "Just, no, that was a lossless step." + }, + { + "text": "Let, let me, let me emphasize." + }, + { + "text": "In comes the signal." + }, + { + "text": "x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk5.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..7ce7441a356838f6e496da3b2d782533cfb4ad1b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "We change basis." + }, + { + "text": "This is the basis change." + }, + { + "text": "Change basis." + }, + { + "text": "Choose a better basis." + }, + { + "text": "So it produces, the, coefficients c. So sixty-four pixels come in, sixty-four coefficients come out." + }, + { + "text": "Now comes the compression." + }, + { + "text": "Now come, this was lossless." + }, + { + "text": "It's just, we know that R64 has plenty of basis, and we've chosen one." + }, + { + "text": "Now, in that basis, we write, we write the signal in that basis, and that's what my lecture, that's the math part of my lecture." + }, + { + "text": "Now here's the application part." + }, + { + "text": "The next part is going to be the compression step." + }, + { + "text": "And that's lossy." + }, + { + "text": "We're going to lose information." + }, + { + "text": "And what, what will actually happen at that step?" + }, + { + "text": "Well, one thing we could do is just throw away the small coefficients." + }, + { + "text": "So that would be, that's called thresholding." + }, + { + "text": "We set some threshold." + }, + { + "text": "Every coefficient, every basis vector that's not in there more than the threshold value, and we set some threshold so that our eye can't see the difference, whether we throw away that, or can hardly see the difference, whether we throw away that little bit of that basis vector or keep it." + }, + { + "text": "So this compression step produces a compressed set of coefficients." + }, + { + "text": "Let me, I'll just keep going here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk6.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..e51518b0b218267f8c2f0d7243d31fec00ba9b42 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, so it keeps going." + }, + { + "text": "This compression step produces some coefficients c hat." + }, + { + "text": "And with lots of, with many zeros." + }, + { + "text": "So that's where the compression came." + }, + { + "text": "Probably there's enough of this vector of all ones, we very seldom throw that away." + }, + { + "text": "Usually its coefficient will be large." + }, + { + "text": "But the coefficient of something like this, that quickly alternating vector, there's probably very little of that in any smooth signal." + }, + { + "text": "I mean, that's high frequent- this is, this is low frequency, zero frequency." + }, + { + "text": "This stuff is the highest frequency we could have, and there's a, if the noise, the, the jitter is producing that sort of output, but a smooth lecture like this one is, has very little of that highest frequency." + }, + { + "text": "Very little noise in this lecture." + }, + { + "text": "OK." + }, + { + "text": "So, so we throw away whatever there is, and we, we're left with just a few coefficients, and then we reconstruct a signal using those coefficients." + }, + { + "text": "We take the, those coefficients times their basis vectors, but this sum doesn't have sixty-four terms anymore." + }, + { + "text": "Probably it has about two or three terms." + }, + { + "text": "So that, if we say it has three terms." + }, + { + "text": "From sixty-four down to three, that's compression of twenty-one to one." + }, + { + "text": "That's the kind of compression you're looking for." + }, + { + "text": "And everybody is looking for that sort of compression." + }, + { + "text": "Let's see, I guess I met the problem with the FBI and fingerprints." + }, + { + "text": "So there's a whole lot of still images." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk7.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..4cdf43a95d584ba42202d1c77ba5f96a998319d5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "You know, you, with your thumb, you make these inky marks, which, go somewhere." + }, + { + "text": "You used to go to Washington and get stored in a big file." + }, + { + "text": "So Washington had a file of thirty million murderers, cheaters on quizzes, other stuff, and, and actually, there was no way to retrieve them in time." + }, + { + "text": "Like, so, so suppose you're at the police station, they say, OK, this person may have done this, check with Washington, have they got his or her fingerprints on file." + }, + { + "text": "Well, Washington won't know the answer within a week, if it's got filing cabinets full of fingerprints." + }, + { + "text": "So of course the natural step is digitize them." + }, + { + "text": "So all fingerprints are now digitized, so now it's at least electronic, but still there's too much information in each, each one." + }, + { + "text": "I mean, you can't search through that many, uh, fingerprints if you, if, if the digital image is five twelve squared by five twelve squared, if it's that many pixels." + }, + { + "text": "So you get compressed." + }, + { + "text": "So the FBI had to decide what basis to choose for compression of fingerprints, and then they built a big new facility in West Virginia and that's where fingerprints now are sent." + }, + { + "text": "So if you, I think if you get your fingerprints done now at the police station, if it's an up-to-date police station, it's, it happens digitally and the signal is sent digitally, and then in West Virginia it's compressed and indexed." + }, + { + "text": "And then, if they want to find you, they can do it within minutes, instead of within a week." + }, + { + "text": "OK." + }, + { + "text": "So this compression is, comes up for signals, for images." + }, + { + "text": "For video, which is like these lectures, uh, there's another aspect." + }, + { + "text": "You could treat the video as one still image after another one, and compress each one and then run them and make a video." + }, + { + "text": "But that misses, well, you can see why that's not optimal." + }, + { + "text": "In video, so for in a video thing, you have a sequence of images, so video is really a sequence of images, but what about one image to the next image?" + }, + { + "text": "They're extremely correlated." + }, + { + "text": "I mean, that, I'm getting an image every split second, and although I'm moving slightly, that's what's producing the, jumpy motion on the video." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk8.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..41f54e28ef2064485cf009d9b5e4574263d3680d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "But I'm not, like, you know, each, each image in the sequence is pretty close to the one before." + }, + { + "text": "So you have to use, like, prediction and correction." + }, + { + "text": "I mean, you, my, the image of me one instant, one time step later, you would assume would be the same, and then plus a small correction." + }, + { + "text": "And you would only code and digitize the correction, and compress the correction." + }, + { + "text": "So the sequence of images that's highly correlated, and the problem in compression is always to use this correlation, this fact that in time or in space, things don't change instantly, they, they're very often smooth changes, and, you can predict one value from the previous value." + }, + { + "text": "OK." + }, + { + "text": "So that's the, those are applications, which are pure linear algebra." + }, + { + "text": "I could, maybe I'll, maybe you'll allow me to tell you the, and the book describes, the new basis that's, the competition for Fourier." + }, + { + "text": "So the competition for Fourier is called wavelets, and I can describe what that basis is like, say, in the eight by eight case." + }, + { + "text": "So that eight by eight wavelet basis is the vector of all ones, eight ones, then the vector of four ones and four minus ones, then the vector of two ones and two minus ones and four zeros, and also the vector of four zeros and two ones and two minus ones." + }, + { + "text": "So now I'm up to four, and I need four more, right, for R8?" + }, + { + "text": "So the next basis vector will be one minus one and six zeros, and then three more like that, with a one minus one there and there and there." + }, + { + "text": "So those are eight vectors in eight-dimensional space." + }, + { + "text": "Those are, those are called wavelets, and you, and it's a very simple wavelet choice." + }, + { + "text": "It's a more sophisticated choice." + }, + { + "text": "This is a little jumpy, to jump between one and minus one." + }, + { + "text": "And actually, you can see now, suppose you compare the wavelet basis with the Fourier basis above." + }, + { + "text": "How could I write this guy, which is in the Fourier basis, it's an eight, it's a vector in R8, how would I write that as a combination of the wavelet basis?" + }, + { + "text": "Do you, have I told you enough about the wavelet basis that you can see?" + }, + { + "text": "How does this very fast guy, what combination of the wavelet basis is that very fast guy?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk9.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..2bc1d292fd925c01e44d5599863fa8cb2bcfba79 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_0_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It would be this one, it would be the sum of these four, right?" + }, + { + "text": "That very fast guy will be that one minus one, and the next one, and the next one, and the next one." + }, + { + "text": "So this is the sum of those last four wavelets." + }, + { + "text": "This one we've kept, and so on." + }, + { + "text": "So, each, well, every, well, that's what a basis does." + }, + { + "text": "Every vector in R8 is some combination of those, and for the linear algebra, we have, so the linear algebra is this step, find the coefficients." + }, + { + "text": "That's, that's the step we want to take." + }, + { + "text": "If I give you the basis, like this wavelet basis, and I give you the pixel, so here are the pixel values, p1, p2, down to p8." + }, + { + "text": "What's, what's the job?" + }, + { + "text": "What's the linear algebra here?" + }, + { + "text": "So this is, these are the values, this is in the standard basis, right?" + }, + { + "text": "Those are just the values at eight successive points." + }, + { + "text": "I guess I'm dropping down to one dimension instead of eight by eight, I'm just going to take eight pixel values along that first top row." + }, + { + "text": "So I, what do I want to do?" + }, + { + "text": "In the standard basis, here are the pixel values." + }, + { + "text": "I want to write that as a combination of c1 times this guy, plus c2 times this guy, plus c3, these are the coefficients, plus c4 times this one." + }, + { + "text": "Do you see what I'm doing?" + }, + { + "text": "I want to write this vector p as a combination of c1 times the first wavelet, plus c8 times the eighth wavelet." + }, + { + "text": "That's the, that's the transform step." + }, + { + "text": "That's the lossless step, that's the step from p, oh, I'm calling it p here and I called it x there, so let me, at the risk of moving and therefore making this jumpy, suppose the signal I'm now calling p, the set of pixel values and I'm looking for the coefficients." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk0.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..ed695ba203c725aa80144eb85fb8edd6706cbb8c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay." + }, + { + "text": "So coming near the end of the course, this lecture will be a mixture of the linear algebra that comes with a change of basis." + }, + { + "text": "And a change of basis from one basis to another basis is something you really do in applications." + }, + { + "text": "And I would like to talk about those applications." + }, + { + "text": "I got a little bit involved with compression, compressing a signal, compressing an image, and that's exactly change of basis." + }, + { + "text": "And then the main theme in this chapter is the connection between a linear transformation, which doesn't have to have coordinates, and the matrix that tells us that transformation with respect to coordinates." + }, + { + "text": "So the matrix is the coordinate-based description of the linear transformation." + }, + { + "text": "Let me start out with the nice part, which is some, just to tell you something about image compression." + }, + { + "text": "Those of you, well, everybody's going to meet compression, because you know that the amount of data that we're getting, well, these lectures are compressed." + }, + { + "text": "So that actually, probably you see my motion as jerky, shall I use that word?" + }, + { + "text": "Have you looked on the web?" + }, + { + "text": "I should like to find a better word." + }, + { + "text": "Compressed, let's see." + }, + { + "text": "So my, the, the, the complete signal is, of course, in those video cameras and in the videotape, but that goes to the bottom of building nine, and out of that comes a jumpy motion, because it uses a standard system for compressing images." + }, + { + "text": "And, you'll notice that the stuff that sits on the board comes very clearly, but it's my motion that, that, that needs a whole lot of bits, right?" + }, + { + "text": "So, and if I were to run up and back, up there and back, that would need too many bits and they'd, I'd be compressed even more." + }, + { + "text": "So, what does compression mean?" + }, + { + "text": "Can I, let me just think of a still image." + }, + { + "text": "And, and of course, satellites, oh, there's, and, and computations of the climate, computations of combustion, the, computers and sensors of all kinds are just giving us overwhelming amounts of data." + }, + { + "text": "The web is, too." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk1.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..276b7aacae39769ce0e1627c108ec463ccf35faa --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, some compression can be done with no loss." + }, + { + "text": "Lossless compression is possible just using, sort of, the fact that, there's, there are redundancies." + }, + { + "text": "But I'm talking here about lossy compression." + }, + { + "text": "So I'm talking about, here's an image." + }, + { + "text": "And what does an image consist of?" + }, + { + "text": "It consists of a lot of little pixels, right?" + }, + { + "text": "Maybe five hundred and twelve by five hundred and twelve." + }, + { + "text": "Two to the ninth by two to the ninth pixels, and each, so this is pixel number one one, so that's a pixel, and if we're in black and white, the typical pixel would tell us a grayscale from zero to two fifty five." + }, + { + "text": "So a pixel is usually a, a value of a, a, one of the x i, so this would be the i-th pixel, it, it's usually a real number on a scale from zero to two fifty five." + }, + { + "text": "In other words, two to the eighth possibilities." + }, + { + "text": "So usually, that's the, that's the standard, so, so that, that's eight, eight bits." + }, + { + "text": "But then we have that for every, every pixel, so we have five hundred and twelve squared pixels." + }, + { + "text": "We're, we're really operating, x is a vector in Rn, but what is n?" + }, + { + "text": "n is five hundred and twelve squared." + }, + { + "text": "That's, that's our problem right there." + }, + { + "text": "We're, a pixel is a vector that gives us the information about the image, I'm sorry, the image that comes through is a vector of, of that length, that, that's the information we have about the image." + }, + { + "text": "If it's a color image, we would have three times that length, because we'd have, we'd need three coordinates to get color." + }, + { + "text": "So it would be three times five hundred and twelve squared." + }, + { + "text": "It's an enormous amount of information, and we couldn't send out the image for these lectures without compressing it." + }, + { + "text": "We, we, it, it would be, it would overload the system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk10.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..db2f6371da88f739758d4ebae59b4fdffa270d6f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "Tell me how to do it." + }, + { + "text": "How do I find the, if I give you eight basis vectors and I give you the input signal and I ask for the coefficients, what do I do?" + }, + { + "text": "What's the, what's the step?" + }, + { + "text": "I want, I'm trying to solve this, I want to know the eight coefficients, so I'm changing from the standard basis, which is just the eight grayscale values, to the wavelet basis, where this same vector is represented by eight numbers." + }, + { + "text": "It's got to take eight numbers to tell you a vector in R8, and those eight numbers are the coefficients of the basis." + }, + { + "text": "Look, we've done this thing before." + }, + { + "text": "What do we, here, there is the equation in vector notation." + }, + { + "text": "We want to see it as a matrix." + }, + { + "text": "This is a combination of columns of the wavelet matrix, right?" + }, + { + "text": "This is p equals c1, c2, down to c8, and these guys are the columns." + }, + { + "text": "I mean, this is the step that we constantly take in this course." + }, + { + "text": "The first basis vector goes in the first column, the second basis vector goes in the second column, and so on." + }, + { + "text": "The eight columns of this wavelet matrix are the eight basis vectors." + }, + { + "text": "This is a wavelet matrix W. So, the step to change basis." + }, + { + "text": "So now I'm finally coming to this change of basis." + }, + { + "text": "So the change of basis, let me stay with this board, but, well, let me just go above it here." + }, + { + "text": "So the standard basis we know, the wavelet basis we have here, and the transform is simply solve the equations p equal Wc." + }, + { + "text": "So the coefficients are W inverse p, right?" + }, + { + "text": "This shows a critical point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk11.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..8346f1691f9a546b0252c3e0960539efff45ec1f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "A good basis has a nice, fast inverse." + }, + { + "text": "So good means, good basis means what?" + }, + { + "text": "So this is like the billion dollar competition, and it's not over yet." + }, + { + "text": "People are going to come up with better bases than these." + }, + { + "text": "So a good basis will be, first good thing would be fast." + }, + { + "text": "I have to be able to multiply by W fast and multiply by W, by its inverse fast." + }, + { + "text": "That's, if a basis doesn't allow you to do that fast, then it's going to take so much time that you can't afford it." + }, + { + "text": "So these bases, the Fourier basis, everybody said, OK, I know how to deal quickly with the Fourier basis, because we have something called the fast Fourier transform." + }, + { + "text": "So there's a FFT that came in my earlier lecture and comes in the last chapter of the book." + }, + { + "text": "So change of basis is done, if for the Fourier basis, is done fast by the FFT and there's a fast wavelet transform." + }, + { + "text": "I can change, for this wavelet example, this matrix is easy to invert." + }, + { + "text": "It's just somebody had a smart idea in choosing that wavelet basis and inverting it, it has a nice inverse." + }, + { + "text": "Actually, you can see why it has a nice inverse." + }, + { + "text": "Do you see any property of these eight basis vectors?" + }, + { + "text": "Well, I've only written five of them, but if you see that property for those five, you'll see it for the three remaining." + }, + { + "text": "What, if I give you those eight vectors and ask, what's a nice property?" + }, + { + "text": "Well, you would say, first, they're all ones and minus ones and zeros, so every multiplication is very fast using just, in binary." + }, + { + "text": "But what's the other great property of those vectors?" + }, + { + "text": "Anybody see it?" + }, + { + "text": "So, of course, when I think about a basis, one nice property, I don't have to have it, but I'm happy if it's there, is that they're orthogonal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk12.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..c0eaf69080e43e238bee148545d1b059bef72365 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "If the basis vectors are orthogonal, then I'm in good shape." + }, + { + "text": "And these are, do you see, take the dot product of that with that, you get four plus ones and four minus ones, you get zero." + }, + { + "text": "Take the dot product of that with that, you get two plus ones and two minus ones." + }, + { + "text": "Or the dot product of that with that, two plus ones and two minus ones." + }, + { + "text": "You can easily check that that's an orthogonal basis." + }, + { + "text": "It's not orthonormal." + }, + { + "text": "I could, to fix it up, I should divide by the length to make them unit vectors." + }, + { + "text": "Let's suppose I do that." + }, + { + "text": "So somewhere in here I've got to account for the fact that this has length square root of eight, that has length square root of four, that has length square root of two." + }, + { + "text": "But that's just a constant factor that's easy to --." + }, + { + "text": "So suppose we've done that." + }, + { + "text": "Then tell me what's W inverse." + }, + { + "text": "That's what chapter four, section four point four was about." + }, + { + "text": "If we have orthonormal columns, what- then the inverse is the same as the transpose." + }, + { + "text": "So if we have a fast way to multiply by W, which we do, the inverse is going to look just the same and we'll have a fast way to do W inverse." + }, + { + "text": "So that's, the wavelet basis passes this requirement for fast." + }, + { + "text": "We can use it fast." + }, + { + "text": "But there's a second requirement, is it any good?" + }, + { + "text": "Because the very fastest thing we could do would be not to change basis at all." + }, + { + "text": "Right?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk13.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..4de80b529af0604a4e0b9b0291a8822dc165b83a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Fastest thing would be, OK, stay with a standard basis, stay with eight pixel values." + }, + { + "text": "But that was poor from compression point of view, right?" + }, + { + "text": "Those eight pixel values, if I just took those eight numbers, I can't throw some of those away." + }, + { + "text": "If I throw away ninety percent, if I compressed ten to one, and throw away ninety percent of my pixel values, well, my picture's just gone dark." + }, + { + "text": "Whereas the basis that was good, the wavelet basis or the Fourier basis, if I throw away c5, c6, c7 and c8, all I'm throwing away is little blips that are probably there in very small amounts." + }, + { + "text": "So the second property that we need is good compression." + }, + { + "text": "So, so first it, it has to be fast, and secondly, it has to be a few basis factors should come close to the signal." + }, + { + "text": "So, so a few, few is enough." + }, + { + "text": "Can I write it that way?" + }, + { + "text": "A few basis factors are enough to reproduce the image, just exactly as on the video of these 18.06 lectures." + }, + { + "text": "I don't know what the compression rate is." + }, + { + "text": "I'll ask, David, who, who does the compression, and, by the way, I'll try to get the lectures, that are relevant for the quiz, up onto the web, in time." + }, + { + "text": "So I'll send him a message today." + }, + { + "text": "So, at the point, so he's using the Fourier basis, because the JPEG, so JPEG 2000, which will be the next standard for image compression, will include wavelets." + }, + { + "text": "So, I mean, you're, you're actually getting a kind of up to date, picture of where this big world of signal and image processing is." + }, + { + "text": "That Fourier is what everybody knew, and what people automatically used, and the new, new one is wavelets, where this is the simplest set of wavelets, and this isn't the one that the FBI uses, by the way." + }, + { + "text": "The FBI uses a more, a more, a smoother wavelet." + }, + { + "text": "Instead of jumping from one to minus one, it's a smooth, cutoff." + }, + { + "text": "And, that's what we'll be in, in JPEG 2000." + }, + { + "text": "OK, so that's that application." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk14.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..8f1debcca7ae641417e7ed0a630d269963c01302 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now let me come to my, the, the math, the linear algebra part of the lecture." + }, + { + "text": "Well, we've actually seen a change of basis." + }, + { + "text": "So let, let me just review that change of basis idea, and then the, and then the transformation to a matrix." + }, + { + "text": "OK, so, so this, I hope you see that these applications are really big." + }, + { + "text": "Now I have to talk a little about change of basis and little about that, the, the matrix." + }, + { + "text": "OK. OK. OK." + }, + { + "text": "So change of basis." + }, + { + "text": "Basically, forgive that pun, OK, I have, I have, I have my vector in one basis, and I want to change to a different one." + }, + { + "text": "Actually, you saw it for the wavelet case." + }, + { + "text": "So I need the, the, let the matrix W, the columns of W, be the new basis vectors." + }, + { + "text": "Then the change of basis involves, just as it did there, W inverse." + }, + { + "text": "So we have the vector, vector, say, x in the old basis, and we, that converts to a vector, let's say, c in the new basis, and the relation is exactly what we had there, that x is Wc." + }, + { + "text": "That's the, that's the, that's the, that's the step we have to take." + }, + { + "text": "There's a matrix W that gives us a change of basis." + }, + { + "text": "OK." + }, + { + "text": "I, I, what I want to do is think about mat- transformations and matrices." + }, + { + "text": "So here's, here's the question, that, that, to complete this lecture." + }, + { + "text": "Suppose I have a linear transformation T. So it's, it's a, it's a, we, we would think of it as an A, as a n by n matrix." + }, + { + "text": "And it's computed with respect to a certain basis." + }, + { + "text": "So T, so, no, I'm sorry." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk15.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..dbc5ad92f06633f3366a78c24c0c7c08b058ee63 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "I've got the transformation T, period." + }, + { + "text": "That's taking eight-dimensional space to eight-dimensional space." + }, + { + "text": "Now let's get matrices in there." + }, + { + "text": "OK." + }, + { + "text": "So, so with respect to, with respect to a fir- a first basis, say, V1 up to V8, it has a matrix A. I'm just setting up letters here." + }, + { + "text": "With respect to a second basis, say, I'll make it U1 up to- or W1, since I've used Ws, W1 up to W8, it has a matrix B." + }, + { + "text": "And my question is, what's the connection between A and B?" + }, + { + "text": "How is the matrix- the transformation T is settled." + }, + { + "text": "We could say it's a rotation, for example." + }, + { + "text": "So that would be one transformation of eight-dimensional space, just spin it a little." + }, + { + "text": "Or project it." + }, + { + "text": "Or, or, whatever, whatever linear transformation we've got." + }, + { + "text": "Now we have to remember, so I- so first- my first step is to remind you how you create that matrix A." + }, + { + "text": "Then my second step is, we would use the same method to create B, but because it came from the same transformation, there's got to be a relation between A and B." + }, + { + "text": "What's the- what's the relation between A and B?" + }, + { + "text": "And let me jump to the answer on that one." + }, + { + "text": "That if I have- if I have the same transformation, and I'm compute- its matrix in one basis and then I compute it in another basis, those two matrices are similar." + }, + { + "text": "So these two matrices are similar." + }, + { + "text": "Now, do you remember what similar matrices meant?" + }, + { + "text": "Similar." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk16.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..9d019933a190fe645eec785d8363a0940d0f76a4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "A is similar- the two matrices are similar." + }, + { + "text": "Similar." + }, + { + "text": "And what do I mean by that?" + }, + { + "text": "I mean that I take the matrix B and I can compute it from the matrix A using some similarity, some matrix M on one side and M inverse on the other." + }, + { + "text": "And this M will be the change of basis matrix." + }, + { + "text": "This part of the lecture is admittedly compressed." + }, + { + "text": "What I wanted you to- it's really the conclusion that I want you to spot." + }, + { + "text": "Now I have to go back and say, what does it mean for A to be the matrix of this transformation T?" + }, + { + "text": "So I have to remind you what that meant." + }, + { + "text": "That was in the last lecture." + }, + { + "text": "Then this is the conclusion, that if I change to a different basis, we now know- see, if I change to a different basis, two things happen." + }, + { + "text": "Every vector has new coordinates." + }, + { + "text": "There, the rule is this one, between the old coordinates and the new ones." + }, + { + "text": "Every matrix changes." + }, + { + "text": "Every transformation has a new matrix." + }, + { + "text": "And the new matrix is related this way." + }, + { + "text": "The M could be the same as the W. The M there could be the W here." + }, + { + "text": "OK." + }, + { + "text": "So can I, in the remaining minutes, recapture my lecture, the end of my lecture that was just before Thanksgiving, about the matrix?" + }, + { + "text": "OK. What's the matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk17.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..f82f2cc230f9f2720733e8b152f84f80f1341c9f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll just take one basis." + }, + { + "text": "So now I'm going to- this part is going to go onto this board here." + }, + { + "text": "What is the matrix?" + }, + { + "text": "What is A?" + }, + { + "text": "OK." + }, + { + "text": "Using a basis v1 up to v8." + }, + { + "text": "OK. What's the point?" + }, + { + "text": "The point is, if I know what the transformation does to those eight basis vectors, I know it completely." + }, + { + "text": "I know T, I know everything about T, I know T completely from knowing what T does to v1, what T does to v2, what T does to v8." + }, + { + "text": "Why is that?" + }, + { + "text": "It's because T is a linear transformation." + }, + { + "text": "So that if I know what these outputs are, so these are the inputs, v1 up to v8, these are the outputs from the transformation, like every one rotated, every one projected, whatever transformation I've done, then why is it that I know everything?" + }, + { + "text": "How does linearity work?" + }, + { + "text": "Why?" + }, + { + "text": "This is because every x is some combination of these basis vectors, right?" + }, + { + "text": "c1 v1, c2 v2, c8 v8." + }, + { + "text": "That's the whole point of a basis, that every vector is a combination of the basis vectors in exactly one way." + }, + { + "text": "And then, what is T of x?" + }, + { + "text": "The point is, I claim that we know T of x completely for every x, because every x is a combination of those, and now we use the linear transformation part to say that the output from x has to be c1 times the output from v1 plus c2 times the output from v2 and so on, up through c8 times the output from v8." + }, + { + "text": "So this is like just saying, OK, we know everything when we know what T does to each basis vector." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk18.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..d9c718592303012586f37aed3dc53271be8cef29 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "So those are the eight things we need." + }, + { + "text": "Now, but we need these answers in this basis." + }, + { + "text": "So T- so this first output is some combination of the eight basis vectors." + }, + { + "text": "So write T times the first- acting on the first input, in other words, write the first output as a combination of the basis vectors." + }, + { + "text": "Say a11 v1 plus a21 v2 and so on, a81 v8." + }, + { + "text": "Write T of v2 as some combination, a12 of v1, a22 of v2 and so on." + }, + { + "text": "I'm creating the matrix A, column by column." + }, + { + "text": "Those numbers go in the first column, these numbers go in the second column." + }, + { + "text": "The matrix A that this is our matrix that represents T in this basis is these numbers." + }, + { + "text": "a11 down to a18, a21 down to a28 and so on." + }, + { + "text": "OK. That's the recipe." + }, + { + "text": "In other words, if I give you a transformation and a basis, that's what I have to give you." + }, + { + "text": "The inputs are the basis and to tell you what the transformation is." + }, + { + "text": "And then you tell me, you compute T for each basis, expand that result in the basis, and that gives you the sixty-four numbers that go into the matrix A." + }, + { + "text": "Let me suppose, let's close with the best example of all." + }, + { + "text": "Suppose v1 to v8, this basis, is the eigenvectors." + }, + { + "text": "Suppose we have an eigenvector basis." + }, + { + "text": "So that T of vi is just, is in the same direction as vi." + }, + { + "text": "Now my question is, what is A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk19.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..4bc0bda81becbd032c626bcaab40cca8eaa39155 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Can you carry through the steps?" + }, + { + "text": "Let's, let's do them together, because we can do it in one minute." + }, + { + "text": "So we've chosen this perfect basis." + }, + { + "text": "And actually, with signal image processing, they might look for the eigenvectors, but that would take more calculation time than just saying, OK, we'll use the wavelet basis, or OK, we'll use the Fourier basis." + }, + { + "text": "But the very best basis is the eigenvector basis." + }, + { + "text": "OK, what's the matrix?" + }, + { + "text": "So, what's the first column of the matrix?" + }, + { + "text": "How do I get the first column?" + }, + { + "text": "I take the first basis vector v1." + }, + { + "text": "I op- I look to see what does the transformation do to it." + }, + { + "text": "The output is lambda one v1." + }, + { + "text": "I express that output as a combination, so the first input is v1." + }, + { + "text": "Its output is lambda one v1." + }, + { + "text": "Now write lambda one v1 as a combination of the basis vectors." + }, + { + "text": "Well, it's already done." + }, + { + "text": "It's just lambda one times the first basis vector and zero times the others." + }, + { + "text": "So this first column will have lambda one and zeros." + }, + { + "text": "OK?" + }, + { + "text": "Second input is v2." + }, + { + "text": "Output is lambda two v2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk2.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..44553739c24736b408dbd01c3688e075b25f9a15 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it has to be compressed." + }, + { + "text": "The standard compression, and still used in, in the, with these lectures, is, called JPEG." + }, + { + "text": "I think that stands for a Joint Photographic Experts Group." + }, + { + "text": "They established a system of compression." + }, + { + "text": "And I just want to tell you what it's about." + }, + { + "text": "It's a change of basis." + }, + { + "text": "What, what's, what basis do we have?" + }, + { + "text": "The, the current basis we have is, you could say, the standard basis is every pixel give a value." + }, + { + "text": "So that's like, we have a vector x, which is five hundred and twelve squared long, and in the i-th position, we get a number like one twenty one or something, the next, the pixel next to it might be one twenty four, maybe where, maybe where the, where my tie, begins to end." + }, + { + "text": "So if it was mostly blue shirt, this would be a slight difference in shading, but pretty close." + }, + { + "text": "Then the tie would be a different color." + }, + { + "text": "So, so we might have quite a few pixels for the blue shirt and a whole lot more for the blackboard that are very close." + }, + { + "text": "And that's what, are very correlated." + }, + { + "text": "And that's what gives us the possibility of compression." + }, + { + "text": "For example, before the lecture starts, if we had a blank blackboard, then there's an image, but it would make no sense to take that image and tell you what it is pixel by pixel." + }, + { + "text": "I mean, there's a case in which all pixel values, all gray levels are the same, or practically the same, depending on the erasing of the board, but extremely close." + }, + { + "text": "And so that's an image where the standard basis is lousy." + }, + { + "text": "That's, that's the basic fact." + }, + { + "text": "That, that the standard basis which gives the value of every pixel makes no use of the fact that we're getting a whole lot of pixels whose gray levels, the neighboring pixels tend to have the same gray level as the, as their, as their neighbors." + }, + { + "text": "So to take, how do we take advantage of that fact?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk20.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..57e892c1f19c9a45e5f14bb334eab942b0d796a2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk20.json @@ -0,0 +1,32 @@ +[ + { + "text": "OK, write that output as a combination of the v's." + }, + { + "text": "It's already done." + }, + { + "text": "It's just lambda two times the second v. So we need, in the second column, we have lambda two times the second v. Well, you see what's coming." + }, + { + "text": "That in that basis, in the eigenvector basis, the matrix is diagonal." + }, + { + "text": "So that's the perfect basis." + }, + { + "text": "That's the basis we'd love to have for image processing, but to find the eigenvectors of our pixel matrix would be too expensive." + }, + { + "text": "So we do something cheaper and close, which is to choose a good basis like, like wavelengths." + }, + { + "text": "OK, thanks." + }, + { + "text": "So quiz review on Wednesday, all day." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk3.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..8e246b42e71ac0ef99e39e59a7562c71f3da61b4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, one basis vector that would be extremely nice to, one vector that would be extremely nice to include in the basis would be a vector of all ones." + }, + { + "text": "That's not in our standard basis." + }, + { + "text": "So our, so let me just write again." + }, + { + "text": "The standard basis would, is, is our, is our one and all the rest zeros, zero, one, and all the rest zeros, everybody knows what the standard basis is." + }, + { + "text": "Now, any other basis for our, so this is, for this very high-dimensional space, now I'm going to speak about a better basis, better basis, and let me just emphasize, one vector that would be extremely nice to have in that basis is the vector of all ones." + }, + { + "text": "Why is that?" + }, + { + "text": "Let me just say again." + }, + { + "text": "Because that vector of all ones, by itself, one vector is, is able to completely give the information on a solid image." + }, + { + "text": "Of course, our image won't be solid, it'll have a mix of, of, solid and, and signal." + }, + { + "text": "So that one vector, but that, having that one vector in the basis is, is, is going to save us a whole lot." + }, + { + "text": "Now the question is, what other vectors should be in the basis?" + }, + { + "text": "The, the extreme vector in the basis might be a vector of one minus one, one minus one, one minus one." + }, + { + "text": "That would be a vector that shows, I mean, that's like a checkerboard vector, right?" + }, + { + "text": "That's a vector that would, if, if we had, if, if the image was like a huge checkerboard of plus minus, plus minus, plus minus, that vector would carry the whole signal." + }, + { + "text": "But much more common would be maybe to have half the image, darker and the other half lighter." + }, + { + "text": "So another image, another vector that might be quite useful in here would be half ones and half minus ones." + }, + { + "text": "I'm just trying to get across the idea of, that a basis could be, that first of all, we've got, the basis is at our disposal." + }, + { + "text": "Like, we're free to choose that." + }, + { + "text": "And it's a billion dollar decision what we choose." + }, + { + "text": "So, and TV people would rather, would prefer one basis based on the way the, the signal is scanned, and movie people would prefer another." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk4.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..811c58ffd5e28e456b42de439fa8cee4339bd2a6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "I mean, there's giant politics in this question that really reduces to a, to a linear algebra problem what basis to choose." + }, + { + "text": "I'll just mention the best known basis, which is, which JPEG uses, let me put that here, is the Fourier basis." + }, + { + "text": "So when you, when you use the Fourier basis, that includes, this is the constant vector, the DC vector, if we're electrical engineers, the, the, the vector of all ones, so it would include one, one, one, one." + }, + { + "text": "Often, eight by eight is a good choice." + }, + { + "text": "Eight by eight is a, is a good choice." + }, + { + "text": "So, what do I mean by this eight by eight?" + }, + { + "text": "I mean that the big signal, which is five twelve by five twelve, gets broken down, and JPEG does this, into eight by eight blocks." + }, + { + "text": "And we, sort of, this is too much to deal with at once." + }, + { + "text": "So what JPEG does is take this eight by eight block, which is sixty-four coefficients, sixty-four, pixels, and changes the basis on the, on that piece." + }, + { + "text": "And then, now, let's see, I was going to write down Fourier, so you remember Fourier is, is this vector of all ones, and then, the vector, oh, well, actually, I gave a lecture earlier about the Fourier matrix, these, this matrix whose columns are powers of a, of a, complex number w. I, I won't repeat that, because I'm not, I don't want to go into the details of the Fourier basis." + }, + { + "text": "Just to tell you how compression works." + }, + { + "text": "So what happens in JPEG?" + }, + { + "text": "What happens to the video, to a, to each image of, of, of these lectures?" + }, + { + "text": "The, it gets broken into eight by eight blocks." + }, + { + "text": "OK." + }, + { + "text": "Within each block, we have sixty-four coefficients, sixty-four basis vectors, sixty-four pixels, and we change basis in sixty-four dimensional space, using these Fourier vectors." + }, + { + "text": "Just, no, that was a lossless step." + }, + { + "text": "Let, let me, let me emphasize." + }, + { + "text": "In comes the signal." + }, + { + "text": "x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk5.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..7ce7441a356838f6e496da3b2d782533cfb4ad1b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "We change basis." + }, + { + "text": "This is the basis change." + }, + { + "text": "Change basis." + }, + { + "text": "Choose a better basis." + }, + { + "text": "So it produces, the, coefficients c. So sixty-four pixels come in, sixty-four coefficients come out." + }, + { + "text": "Now comes the compression." + }, + { + "text": "Now come, this was lossless." + }, + { + "text": "It's just, we know that R64 has plenty of basis, and we've chosen one." + }, + { + "text": "Now, in that basis, we write, we write the signal in that basis, and that's what my lecture, that's the math part of my lecture." + }, + { + "text": "Now here's the application part." + }, + { + "text": "The next part is going to be the compression step." + }, + { + "text": "And that's lossy." + }, + { + "text": "We're going to lose information." + }, + { + "text": "And what, what will actually happen at that step?" + }, + { + "text": "Well, one thing we could do is just throw away the small coefficients." + }, + { + "text": "So that would be, that's called thresholding." + }, + { + "text": "We set some threshold." + }, + { + "text": "Every coefficient, every basis vector that's not in there more than the threshold value, and we set some threshold so that our eye can't see the difference, whether we throw away that, or can hardly see the difference, whether we throw away that little bit of that basis vector or keep it." + }, + { + "text": "So this compression step produces a compressed set of coefficients." + }, + { + "text": "Let me, I'll just keep going here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk6.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..e51518b0b218267f8c2f0d7243d31fec00ba9b42 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, so it keeps going." + }, + { + "text": "This compression step produces some coefficients c hat." + }, + { + "text": "And with lots of, with many zeros." + }, + { + "text": "So that's where the compression came." + }, + { + "text": "Probably there's enough of this vector of all ones, we very seldom throw that away." + }, + { + "text": "Usually its coefficient will be large." + }, + { + "text": "But the coefficient of something like this, that quickly alternating vector, there's probably very little of that in any smooth signal." + }, + { + "text": "I mean, that's high frequent- this is, this is low frequency, zero frequency." + }, + { + "text": "This stuff is the highest frequency we could have, and there's a, if the noise, the, the jitter is producing that sort of output, but a smooth lecture like this one is, has very little of that highest frequency." + }, + { + "text": "Very little noise in this lecture." + }, + { + "text": "OK." + }, + { + "text": "So, so we throw away whatever there is, and we, we're left with just a few coefficients, and then we reconstruct a signal using those coefficients." + }, + { + "text": "We take the, those coefficients times their basis vectors, but this sum doesn't have sixty-four terms anymore." + }, + { + "text": "Probably it has about two or three terms." + }, + { + "text": "So that, if we say it has three terms." + }, + { + "text": "From sixty-four down to three, that's compression of twenty-one to one." + }, + { + "text": "That's the kind of compression you're looking for." + }, + { + "text": "And everybody is looking for that sort of compression." + }, + { + "text": "Let's see, I guess I met the problem with the FBI and fingerprints." + }, + { + "text": "So there's a whole lot of still images." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk7.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..4cdf43a95d584ba42202d1c77ba5f96a998319d5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "You know, you, with your thumb, you make these inky marks, which, go somewhere." + }, + { + "text": "You used to go to Washington and get stored in a big file." + }, + { + "text": "So Washington had a file of thirty million murderers, cheaters on quizzes, other stuff, and, and actually, there was no way to retrieve them in time." + }, + { + "text": "Like, so, so suppose you're at the police station, they say, OK, this person may have done this, check with Washington, have they got his or her fingerprints on file." + }, + { + "text": "Well, Washington won't know the answer within a week, if it's got filing cabinets full of fingerprints." + }, + { + "text": "So of course the natural step is digitize them." + }, + { + "text": "So all fingerprints are now digitized, so now it's at least electronic, but still there's too much information in each, each one." + }, + { + "text": "I mean, you can't search through that many, uh, fingerprints if you, if, if the digital image is five twelve squared by five twelve squared, if it's that many pixels." + }, + { + "text": "So you get compressed." + }, + { + "text": "So the FBI had to decide what basis to choose for compression of fingerprints, and then they built a big new facility in West Virginia and that's where fingerprints now are sent." + }, + { + "text": "So if you, I think if you get your fingerprints done now at the police station, if it's an up-to-date police station, it's, it happens digitally and the signal is sent digitally, and then in West Virginia it's compressed and indexed." + }, + { + "text": "And then, if they want to find you, they can do it within minutes, instead of within a week." + }, + { + "text": "OK." + }, + { + "text": "So this compression is, comes up for signals, for images." + }, + { + "text": "For video, which is like these lectures, uh, there's another aspect." + }, + { + "text": "You could treat the video as one still image after another one, and compress each one and then run them and make a video." + }, + { + "text": "But that misses, well, you can see why that's not optimal." + }, + { + "text": "In video, so for in a video thing, you have a sequence of images, so video is really a sequence of images, but what about one image to the next image?" + }, + { + "text": "They're extremely correlated." + }, + { + "text": "I mean, that, I'm getting an image every split second, and although I'm moving slightly, that's what's producing the, jumpy motion on the video." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk8.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..41f54e28ef2064485cf009d9b5e4574263d3680d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "But I'm not, like, you know, each, each image in the sequence is pretty close to the one before." + }, + { + "text": "So you have to use, like, prediction and correction." + }, + { + "text": "I mean, you, my, the image of me one instant, one time step later, you would assume would be the same, and then plus a small correction." + }, + { + "text": "And you would only code and digitize the correction, and compress the correction." + }, + { + "text": "So the sequence of images that's highly correlated, and the problem in compression is always to use this correlation, this fact that in time or in space, things don't change instantly, they, they're very often smooth changes, and, you can predict one value from the previous value." + }, + { + "text": "OK." + }, + { + "text": "So that's the, those are applications, which are pure linear algebra." + }, + { + "text": "I could, maybe I'll, maybe you'll allow me to tell you the, and the book describes, the new basis that's, the competition for Fourier." + }, + { + "text": "So the competition for Fourier is called wavelets, and I can describe what that basis is like, say, in the eight by eight case." + }, + { + "text": "So that eight by eight wavelet basis is the vector of all ones, eight ones, then the vector of four ones and four minus ones, then the vector of two ones and two minus ones and four zeros, and also the vector of four zeros and two ones and two minus ones." + }, + { + "text": "So now I'm up to four, and I need four more, right, for R8?" + }, + { + "text": "So the next basis vector will be one minus one and six zeros, and then three more like that, with a one minus one there and there and there." + }, + { + "text": "So those are eight vectors in eight-dimensional space." + }, + { + "text": "Those are, those are called wavelets, and you, and it's a very simple wavelet choice." + }, + { + "text": "It's a more sophisticated choice." + }, + { + "text": "This is a little jumpy, to jump between one and minus one." + }, + { + "text": "And actually, you can see now, suppose you compare the wavelet basis with the Fourier basis above." + }, + { + "text": "How could I write this guy, which is in the Fourier basis, it's an eight, it's a vector in R8, how would I write that as a combination of the wavelet basis?" + }, + { + "text": "Do you, have I told you enough about the wavelet basis that you can see?" + }, + { + "text": "How does this very fast guy, what combination of the wavelet basis is that very fast guy?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk9.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..2bc1d292fd925c01e44d5599863fa8cb2bcfba79 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_1_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It would be this one, it would be the sum of these four, right?" + }, + { + "text": "That very fast guy will be that one minus one, and the next one, and the next one, and the next one." + }, + { + "text": "So this is the sum of those last four wavelets." + }, + { + "text": "This one we've kept, and so on." + }, + { + "text": "So, each, well, every, well, that's what a basis does." + }, + { + "text": "Every vector in R8 is some combination of those, and for the linear algebra, we have, so the linear algebra is this step, find the coefficients." + }, + { + "text": "That's, that's the step we want to take." + }, + { + "text": "If I give you the basis, like this wavelet basis, and I give you the pixel, so here are the pixel values, p1, p2, down to p8." + }, + { + "text": "What's, what's the job?" + }, + { + "text": "What's the linear algebra here?" + }, + { + "text": "So this is, these are the values, this is in the standard basis, right?" + }, + { + "text": "Those are just the values at eight successive points." + }, + { + "text": "I guess I'm dropping down to one dimension instead of eight by eight, I'm just going to take eight pixel values along that first top row." + }, + { + "text": "So I, what do I want to do?" + }, + { + "text": "In the standard basis, here are the pixel values." + }, + { + "text": "I want to write that as a combination of c1 times this guy, plus c2 times this guy, plus c3, these are the coefficients, plus c4 times this one." + }, + { + "text": "Do you see what I'm doing?" + }, + { + "text": "I want to write this vector p as a combination of c1 times the first wavelet, plus c8 times the eighth wavelet." + }, + { + "text": "That's the, that's the transform step." + }, + { + "text": "That's the lossless step, that's the step from p, oh, I'm calling it p here and I called it x there, so let me, at the risk of moving and therefore making this jumpy, suppose the signal I'm now calling p, the set of pixel values and I'm looking for the coefficients." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk0.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..ed695ba203c725aa80144eb85fb8edd6706cbb8c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay." + }, + { + "text": "So coming near the end of the course, this lecture will be a mixture of the linear algebra that comes with a change of basis." + }, + { + "text": "And a change of basis from one basis to another basis is something you really do in applications." + }, + { + "text": "And I would like to talk about those applications." + }, + { + "text": "I got a little bit involved with compression, compressing a signal, compressing an image, and that's exactly change of basis." + }, + { + "text": "And then the main theme in this chapter is the connection between a linear transformation, which doesn't have to have coordinates, and the matrix that tells us that transformation with respect to coordinates." + }, + { + "text": "So the matrix is the coordinate-based description of the linear transformation." + }, + { + "text": "Let me start out with the nice part, which is some, just to tell you something about image compression." + }, + { + "text": "Those of you, well, everybody's going to meet compression, because you know that the amount of data that we're getting, well, these lectures are compressed." + }, + { + "text": "So that actually, probably you see my motion as jerky, shall I use that word?" + }, + { + "text": "Have you looked on the web?" + }, + { + "text": "I should like to find a better word." + }, + { + "text": "Compressed, let's see." + }, + { + "text": "So my, the, the, the complete signal is, of course, in those video cameras and in the videotape, but that goes to the bottom of building nine, and out of that comes a jumpy motion, because it uses a standard system for compressing images." + }, + { + "text": "And, you'll notice that the stuff that sits on the board comes very clearly, but it's my motion that, that, that needs a whole lot of bits, right?" + }, + { + "text": "So, and if I were to run up and back, up there and back, that would need too many bits and they'd, I'd be compressed even more." + }, + { + "text": "So, what does compression mean?" + }, + { + "text": "Can I, let me just think of a still image." + }, + { + "text": "And, and of course, satellites, oh, there's, and, and computations of the climate, computations of combustion, the, computers and sensors of all kinds are just giving us overwhelming amounts of data." + }, + { + "text": "The web is, too." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk1.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..276b7aacae39769ce0e1627c108ec463ccf35faa --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, some compression can be done with no loss." + }, + { + "text": "Lossless compression is possible just using, sort of, the fact that, there's, there are redundancies." + }, + { + "text": "But I'm talking here about lossy compression." + }, + { + "text": "So I'm talking about, here's an image." + }, + { + "text": "And what does an image consist of?" + }, + { + "text": "It consists of a lot of little pixels, right?" + }, + { + "text": "Maybe five hundred and twelve by five hundred and twelve." + }, + { + "text": "Two to the ninth by two to the ninth pixels, and each, so this is pixel number one one, so that's a pixel, and if we're in black and white, the typical pixel would tell us a grayscale from zero to two fifty five." + }, + { + "text": "So a pixel is usually a, a value of a, a, one of the x i, so this would be the i-th pixel, it, it's usually a real number on a scale from zero to two fifty five." + }, + { + "text": "In other words, two to the eighth possibilities." + }, + { + "text": "So usually, that's the, that's the standard, so, so that, that's eight, eight bits." + }, + { + "text": "But then we have that for every, every pixel, so we have five hundred and twelve squared pixels." + }, + { + "text": "We're, we're really operating, x is a vector in Rn, but what is n?" + }, + { + "text": "n is five hundred and twelve squared." + }, + { + "text": "That's, that's our problem right there." + }, + { + "text": "We're, a pixel is a vector that gives us the information about the image, I'm sorry, the image that comes through is a vector of, of that length, that, that's the information we have about the image." + }, + { + "text": "If it's a color image, we would have three times that length, because we'd have, we'd need three coordinates to get color." + }, + { + "text": "So it would be three times five hundred and twelve squared." + }, + { + "text": "It's an enormous amount of information, and we couldn't send out the image for these lectures without compressing it." + }, + { + "text": "We, we, it, it would be, it would overload the system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk10.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..db2f6371da88f739758d4ebae59b4fdffa270d6f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "Tell me how to do it." + }, + { + "text": "How do I find the, if I give you eight basis vectors and I give you the input signal and I ask for the coefficients, what do I do?" + }, + { + "text": "What's the, what's the step?" + }, + { + "text": "I want, I'm trying to solve this, I want to know the eight coefficients, so I'm changing from the standard basis, which is just the eight grayscale values, to the wavelet basis, where this same vector is represented by eight numbers." + }, + { + "text": "It's got to take eight numbers to tell you a vector in R8, and those eight numbers are the coefficients of the basis." + }, + { + "text": "Look, we've done this thing before." + }, + { + "text": "What do we, here, there is the equation in vector notation." + }, + { + "text": "We want to see it as a matrix." + }, + { + "text": "This is a combination of columns of the wavelet matrix, right?" + }, + { + "text": "This is p equals c1, c2, down to c8, and these guys are the columns." + }, + { + "text": "I mean, this is the step that we constantly take in this course." + }, + { + "text": "The first basis vector goes in the first column, the second basis vector goes in the second column, and so on." + }, + { + "text": "The eight columns of this wavelet matrix are the eight basis vectors." + }, + { + "text": "This is a wavelet matrix W. So, the step to change basis." + }, + { + "text": "So now I'm finally coming to this change of basis." + }, + { + "text": "So the change of basis, let me stay with this board, but, well, let me just go above it here." + }, + { + "text": "So the standard basis we know, the wavelet basis we have here, and the transform is simply solve the equations p equal Wc." + }, + { + "text": "So the coefficients are W inverse p, right?" + }, + { + "text": "This shows a critical point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk11.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..8346f1691f9a546b0252c3e0960539efff45ec1f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "A good basis has a nice, fast inverse." + }, + { + "text": "So good means, good basis means what?" + }, + { + "text": "So this is like the billion dollar competition, and it's not over yet." + }, + { + "text": "People are going to come up with better bases than these." + }, + { + "text": "So a good basis will be, first good thing would be fast." + }, + { + "text": "I have to be able to multiply by W fast and multiply by W, by its inverse fast." + }, + { + "text": "That's, if a basis doesn't allow you to do that fast, then it's going to take so much time that you can't afford it." + }, + { + "text": "So these bases, the Fourier basis, everybody said, OK, I know how to deal quickly with the Fourier basis, because we have something called the fast Fourier transform." + }, + { + "text": "So there's a FFT that came in my earlier lecture and comes in the last chapter of the book." + }, + { + "text": "So change of basis is done, if for the Fourier basis, is done fast by the FFT and there's a fast wavelet transform." + }, + { + "text": "I can change, for this wavelet example, this matrix is easy to invert." + }, + { + "text": "It's just somebody had a smart idea in choosing that wavelet basis and inverting it, it has a nice inverse." + }, + { + "text": "Actually, you can see why it has a nice inverse." + }, + { + "text": "Do you see any property of these eight basis vectors?" + }, + { + "text": "Well, I've only written five of them, but if you see that property for those five, you'll see it for the three remaining." + }, + { + "text": "What, if I give you those eight vectors and ask, what's a nice property?" + }, + { + "text": "Well, you would say, first, they're all ones and minus ones and zeros, so every multiplication is very fast using just, in binary." + }, + { + "text": "But what's the other great property of those vectors?" + }, + { + "text": "Anybody see it?" + }, + { + "text": "So, of course, when I think about a basis, one nice property, I don't have to have it, but I'm happy if it's there, is that they're orthogonal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk12.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..c0eaf69080e43e238bee148545d1b059bef72365 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "If the basis vectors are orthogonal, then I'm in good shape." + }, + { + "text": "And these are, do you see, take the dot product of that with that, you get four plus ones and four minus ones, you get zero." + }, + { + "text": "Take the dot product of that with that, you get two plus ones and two minus ones." + }, + { + "text": "Or the dot product of that with that, two plus ones and two minus ones." + }, + { + "text": "You can easily check that that's an orthogonal basis." + }, + { + "text": "It's not orthonormal." + }, + { + "text": "I could, to fix it up, I should divide by the length to make them unit vectors." + }, + { + "text": "Let's suppose I do that." + }, + { + "text": "So somewhere in here I've got to account for the fact that this has length square root of eight, that has length square root of four, that has length square root of two." + }, + { + "text": "But that's just a constant factor that's easy to --." + }, + { + "text": "So suppose we've done that." + }, + { + "text": "Then tell me what's W inverse." + }, + { + "text": "That's what chapter four, section four point four was about." + }, + { + "text": "If we have orthonormal columns, what- then the inverse is the same as the transpose." + }, + { + "text": "So if we have a fast way to multiply by W, which we do, the inverse is going to look just the same and we'll have a fast way to do W inverse." + }, + { + "text": "So that's, the wavelet basis passes this requirement for fast." + }, + { + "text": "We can use it fast." + }, + { + "text": "But there's a second requirement, is it any good?" + }, + { + "text": "Because the very fastest thing we could do would be not to change basis at all." + }, + { + "text": "Right?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk13.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..4de80b529af0604a4e0b9b0291a8822dc165b83a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Fastest thing would be, OK, stay with a standard basis, stay with eight pixel values." + }, + { + "text": "But that was poor from compression point of view, right?" + }, + { + "text": "Those eight pixel values, if I just took those eight numbers, I can't throw some of those away." + }, + { + "text": "If I throw away ninety percent, if I compressed ten to one, and throw away ninety percent of my pixel values, well, my picture's just gone dark." + }, + { + "text": "Whereas the basis that was good, the wavelet basis or the Fourier basis, if I throw away c5, c6, c7 and c8, all I'm throwing away is little blips that are probably there in very small amounts." + }, + { + "text": "So the second property that we need is good compression." + }, + { + "text": "So, so first it, it has to be fast, and secondly, it has to be a few basis factors should come close to the signal." + }, + { + "text": "So, so a few, few is enough." + }, + { + "text": "Can I write it that way?" + }, + { + "text": "A few basis factors are enough to reproduce the image, just exactly as on the video of these 18.06 lectures." + }, + { + "text": "I don't know what the compression rate is." + }, + { + "text": "I'll ask, David, who, who does the compression, and, by the way, I'll try to get the lectures, that are relevant for the quiz, up onto the web, in time." + }, + { + "text": "So I'll send him a message today." + }, + { + "text": "So, at the point, so he's using the Fourier basis, because the JPEG, so JPEG 2000, which will be the next standard for image compression, will include wavelets." + }, + { + "text": "So, I mean, you're, you're actually getting a kind of up to date, picture of where this big world of signal and image processing is." + }, + { + "text": "That Fourier is what everybody knew, and what people automatically used, and the new, new one is wavelets, where this is the simplest set of wavelets, and this isn't the one that the FBI uses, by the way." + }, + { + "text": "The FBI uses a more, a more, a smoother wavelet." + }, + { + "text": "Instead of jumping from one to minus one, it's a smooth, cutoff." + }, + { + "text": "And, that's what we'll be in, in JPEG 2000." + }, + { + "text": "OK, so that's that application." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk14.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..8f1debcca7ae641417e7ed0a630d269963c01302 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now let me come to my, the, the math, the linear algebra part of the lecture." + }, + { + "text": "Well, we've actually seen a change of basis." + }, + { + "text": "So let, let me just review that change of basis idea, and then the, and then the transformation to a matrix." + }, + { + "text": "OK, so, so this, I hope you see that these applications are really big." + }, + { + "text": "Now I have to talk a little about change of basis and little about that, the, the matrix." + }, + { + "text": "OK. OK. OK." + }, + { + "text": "So change of basis." + }, + { + "text": "Basically, forgive that pun, OK, I have, I have, I have my vector in one basis, and I want to change to a different one." + }, + { + "text": "Actually, you saw it for the wavelet case." + }, + { + "text": "So I need the, the, let the matrix W, the columns of W, be the new basis vectors." + }, + { + "text": "Then the change of basis involves, just as it did there, W inverse." + }, + { + "text": "So we have the vector, vector, say, x in the old basis, and we, that converts to a vector, let's say, c in the new basis, and the relation is exactly what we had there, that x is Wc." + }, + { + "text": "That's the, that's the, that's the, that's the step we have to take." + }, + { + "text": "There's a matrix W that gives us a change of basis." + }, + { + "text": "OK." + }, + { + "text": "I, I, what I want to do is think about mat- transformations and matrices." + }, + { + "text": "So here's, here's the question, that, that, to complete this lecture." + }, + { + "text": "Suppose I have a linear transformation T. So it's, it's a, it's a, we, we would think of it as an A, as a n by n matrix." + }, + { + "text": "And it's computed with respect to a certain basis." + }, + { + "text": "So T, so, no, I'm sorry." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk15.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..dbc5ad92f06633f3366a78c24c0c7c08b058ee63 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "I've got the transformation T, period." + }, + { + "text": "That's taking eight-dimensional space to eight-dimensional space." + }, + { + "text": "Now let's get matrices in there." + }, + { + "text": "OK." + }, + { + "text": "So, so with respect to, with respect to a fir- a first basis, say, V1 up to V8, it has a matrix A. I'm just setting up letters here." + }, + { + "text": "With respect to a second basis, say, I'll make it U1 up to- or W1, since I've used Ws, W1 up to W8, it has a matrix B." + }, + { + "text": "And my question is, what's the connection between A and B?" + }, + { + "text": "How is the matrix- the transformation T is settled." + }, + { + "text": "We could say it's a rotation, for example." + }, + { + "text": "So that would be one transformation of eight-dimensional space, just spin it a little." + }, + { + "text": "Or project it." + }, + { + "text": "Or, or, whatever, whatever linear transformation we've got." + }, + { + "text": "Now we have to remember, so I- so first- my first step is to remind you how you create that matrix A." + }, + { + "text": "Then my second step is, we would use the same method to create B, but because it came from the same transformation, there's got to be a relation between A and B." + }, + { + "text": "What's the- what's the relation between A and B?" + }, + { + "text": "And let me jump to the answer on that one." + }, + { + "text": "That if I have- if I have the same transformation, and I'm compute- its matrix in one basis and then I compute it in another basis, those two matrices are similar." + }, + { + "text": "So these two matrices are similar." + }, + { + "text": "Now, do you remember what similar matrices meant?" + }, + { + "text": "Similar." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk16.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..9d019933a190fe645eec785d8363a0940d0f76a4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "A is similar- the two matrices are similar." + }, + { + "text": "Similar." + }, + { + "text": "And what do I mean by that?" + }, + { + "text": "I mean that I take the matrix B and I can compute it from the matrix A using some similarity, some matrix M on one side and M inverse on the other." + }, + { + "text": "And this M will be the change of basis matrix." + }, + { + "text": "This part of the lecture is admittedly compressed." + }, + { + "text": "What I wanted you to- it's really the conclusion that I want you to spot." + }, + { + "text": "Now I have to go back and say, what does it mean for A to be the matrix of this transformation T?" + }, + { + "text": "So I have to remind you what that meant." + }, + { + "text": "That was in the last lecture." + }, + { + "text": "Then this is the conclusion, that if I change to a different basis, we now know- see, if I change to a different basis, two things happen." + }, + { + "text": "Every vector has new coordinates." + }, + { + "text": "There, the rule is this one, between the old coordinates and the new ones." + }, + { + "text": "Every matrix changes." + }, + { + "text": "Every transformation has a new matrix." + }, + { + "text": "And the new matrix is related this way." + }, + { + "text": "The M could be the same as the W. The M there could be the W here." + }, + { + "text": "OK." + }, + { + "text": "So can I, in the remaining minutes, recapture my lecture, the end of my lecture that was just before Thanksgiving, about the matrix?" + }, + { + "text": "OK. What's the matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk17.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..f82f2cc230f9f2720733e8b152f84f80f1341c9f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll just take one basis." + }, + { + "text": "So now I'm going to- this part is going to go onto this board here." + }, + { + "text": "What is the matrix?" + }, + { + "text": "What is A?" + }, + { + "text": "OK." + }, + { + "text": "Using a basis v1 up to v8." + }, + { + "text": "OK. What's the point?" + }, + { + "text": "The point is, if I know what the transformation does to those eight basis vectors, I know it completely." + }, + { + "text": "I know T, I know everything about T, I know T completely from knowing what T does to v1, what T does to v2, what T does to v8." + }, + { + "text": "Why is that?" + }, + { + "text": "It's because T is a linear transformation." + }, + { + "text": "So that if I know what these outputs are, so these are the inputs, v1 up to v8, these are the outputs from the transformation, like every one rotated, every one projected, whatever transformation I've done, then why is it that I know everything?" + }, + { + "text": "How does linearity work?" + }, + { + "text": "Why?" + }, + { + "text": "This is because every x is some combination of these basis vectors, right?" + }, + { + "text": "c1 v1, c2 v2, c8 v8." + }, + { + "text": "That's the whole point of a basis, that every vector is a combination of the basis vectors in exactly one way." + }, + { + "text": "And then, what is T of x?" + }, + { + "text": "The point is, I claim that we know T of x completely for every x, because every x is a combination of those, and now we use the linear transformation part to say that the output from x has to be c1 times the output from v1 plus c2 times the output from v2 and so on, up through c8 times the output from v8." + }, + { + "text": "So this is like just saying, OK, we know everything when we know what T does to each basis vector." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk18.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..d9c718592303012586f37aed3dc53271be8cef29 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "So those are the eight things we need." + }, + { + "text": "Now, but we need these answers in this basis." + }, + { + "text": "So T- so this first output is some combination of the eight basis vectors." + }, + { + "text": "So write T times the first- acting on the first input, in other words, write the first output as a combination of the basis vectors." + }, + { + "text": "Say a11 v1 plus a21 v2 and so on, a81 v8." + }, + { + "text": "Write T of v2 as some combination, a12 of v1, a22 of v2 and so on." + }, + { + "text": "I'm creating the matrix A, column by column." + }, + { + "text": "Those numbers go in the first column, these numbers go in the second column." + }, + { + "text": "The matrix A that this is our matrix that represents T in this basis is these numbers." + }, + { + "text": "a11 down to a18, a21 down to a28 and so on." + }, + { + "text": "OK. That's the recipe." + }, + { + "text": "In other words, if I give you a transformation and a basis, that's what I have to give you." + }, + { + "text": "The inputs are the basis and to tell you what the transformation is." + }, + { + "text": "And then you tell me, you compute T for each basis, expand that result in the basis, and that gives you the sixty-four numbers that go into the matrix A." + }, + { + "text": "Let me suppose, let's close with the best example of all." + }, + { + "text": "Suppose v1 to v8, this basis, is the eigenvectors." + }, + { + "text": "Suppose we have an eigenvector basis." + }, + { + "text": "So that T of vi is just, is in the same direction as vi." + }, + { + "text": "Now my question is, what is A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk19.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..4bc0bda81becbd032c626bcaab40cca8eaa39155 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Can you carry through the steps?" + }, + { + "text": "Let's, let's do them together, because we can do it in one minute." + }, + { + "text": "So we've chosen this perfect basis." + }, + { + "text": "And actually, with signal image processing, they might look for the eigenvectors, but that would take more calculation time than just saying, OK, we'll use the wavelet basis, or OK, we'll use the Fourier basis." + }, + { + "text": "But the very best basis is the eigenvector basis." + }, + { + "text": "OK, what's the matrix?" + }, + { + "text": "So, what's the first column of the matrix?" + }, + { + "text": "How do I get the first column?" + }, + { + "text": "I take the first basis vector v1." + }, + { + "text": "I op- I look to see what does the transformation do to it." + }, + { + "text": "The output is lambda one v1." + }, + { + "text": "I express that output as a combination, so the first input is v1." + }, + { + "text": "Its output is lambda one v1." + }, + { + "text": "Now write lambda one v1 as a combination of the basis vectors." + }, + { + "text": "Well, it's already done." + }, + { + "text": "It's just lambda one times the first basis vector and zero times the others." + }, + { + "text": "So this first column will have lambda one and zeros." + }, + { + "text": "OK?" + }, + { + "text": "Second input is v2." + }, + { + "text": "Output is lambda two v2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk2.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..44553739c24736b408dbd01c3688e075b25f9a15 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it has to be compressed." + }, + { + "text": "The standard compression, and still used in, in the, with these lectures, is, called JPEG." + }, + { + "text": "I think that stands for a Joint Photographic Experts Group." + }, + { + "text": "They established a system of compression." + }, + { + "text": "And I just want to tell you what it's about." + }, + { + "text": "It's a change of basis." + }, + { + "text": "What, what's, what basis do we have?" + }, + { + "text": "The, the current basis we have is, you could say, the standard basis is every pixel give a value." + }, + { + "text": "So that's like, we have a vector x, which is five hundred and twelve squared long, and in the i-th position, we get a number like one twenty one or something, the next, the pixel next to it might be one twenty four, maybe where, maybe where the, where my tie, begins to end." + }, + { + "text": "So if it was mostly blue shirt, this would be a slight difference in shading, but pretty close." + }, + { + "text": "Then the tie would be a different color." + }, + { + "text": "So, so we might have quite a few pixels for the blue shirt and a whole lot more for the blackboard that are very close." + }, + { + "text": "And that's what, are very correlated." + }, + { + "text": "And that's what gives us the possibility of compression." + }, + { + "text": "For example, before the lecture starts, if we had a blank blackboard, then there's an image, but it would make no sense to take that image and tell you what it is pixel by pixel." + }, + { + "text": "I mean, there's a case in which all pixel values, all gray levels are the same, or practically the same, depending on the erasing of the board, but extremely close." + }, + { + "text": "And so that's an image where the standard basis is lousy." + }, + { + "text": "That's, that's the basic fact." + }, + { + "text": "That, that the standard basis which gives the value of every pixel makes no use of the fact that we're getting a whole lot of pixels whose gray levels, the neighboring pixels tend to have the same gray level as the, as their, as their neighbors." + }, + { + "text": "So to take, how do we take advantage of that fact?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk20.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..57e892c1f19c9a45e5f14bb334eab942b0d796a2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk20.json @@ -0,0 +1,32 @@ +[ + { + "text": "OK, write that output as a combination of the v's." + }, + { + "text": "It's already done." + }, + { + "text": "It's just lambda two times the second v. So we need, in the second column, we have lambda two times the second v. Well, you see what's coming." + }, + { + "text": "That in that basis, in the eigenvector basis, the matrix is diagonal." + }, + { + "text": "So that's the perfect basis." + }, + { + "text": "That's the basis we'd love to have for image processing, but to find the eigenvectors of our pixel matrix would be too expensive." + }, + { + "text": "So we do something cheaper and close, which is to choose a good basis like, like wavelengths." + }, + { + "text": "OK, thanks." + }, + { + "text": "So quiz review on Wednesday, all day." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk3.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..8e246b42e71ac0ef99e39e59a7562c71f3da61b4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, one basis vector that would be extremely nice to, one vector that would be extremely nice to include in the basis would be a vector of all ones." + }, + { + "text": "That's not in our standard basis." + }, + { + "text": "So our, so let me just write again." + }, + { + "text": "The standard basis would, is, is our, is our one and all the rest zeros, zero, one, and all the rest zeros, everybody knows what the standard basis is." + }, + { + "text": "Now, any other basis for our, so this is, for this very high-dimensional space, now I'm going to speak about a better basis, better basis, and let me just emphasize, one vector that would be extremely nice to have in that basis is the vector of all ones." + }, + { + "text": "Why is that?" + }, + { + "text": "Let me just say again." + }, + { + "text": "Because that vector of all ones, by itself, one vector is, is able to completely give the information on a solid image." + }, + { + "text": "Of course, our image won't be solid, it'll have a mix of, of, solid and, and signal." + }, + { + "text": "So that one vector, but that, having that one vector in the basis is, is, is going to save us a whole lot." + }, + { + "text": "Now the question is, what other vectors should be in the basis?" + }, + { + "text": "The, the extreme vector in the basis might be a vector of one minus one, one minus one, one minus one." + }, + { + "text": "That would be a vector that shows, I mean, that's like a checkerboard vector, right?" + }, + { + "text": "That's a vector that would, if, if we had, if, if the image was like a huge checkerboard of plus minus, plus minus, plus minus, that vector would carry the whole signal." + }, + { + "text": "But much more common would be maybe to have half the image, darker and the other half lighter." + }, + { + "text": "So another image, another vector that might be quite useful in here would be half ones and half minus ones." + }, + { + "text": "I'm just trying to get across the idea of, that a basis could be, that first of all, we've got, the basis is at our disposal." + }, + { + "text": "Like, we're free to choose that." + }, + { + "text": "And it's a billion dollar decision what we choose." + }, + { + "text": "So, and TV people would rather, would prefer one basis based on the way the, the signal is scanned, and movie people would prefer another." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk4.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..811c58ffd5e28e456b42de439fa8cee4339bd2a6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "I mean, there's giant politics in this question that really reduces to a, to a linear algebra problem what basis to choose." + }, + { + "text": "I'll just mention the best known basis, which is, which JPEG uses, let me put that here, is the Fourier basis." + }, + { + "text": "So when you, when you use the Fourier basis, that includes, this is the constant vector, the DC vector, if we're electrical engineers, the, the, the vector of all ones, so it would include one, one, one, one." + }, + { + "text": "Often, eight by eight is a good choice." + }, + { + "text": "Eight by eight is a, is a good choice." + }, + { + "text": "So, what do I mean by this eight by eight?" + }, + { + "text": "I mean that the big signal, which is five twelve by five twelve, gets broken down, and JPEG does this, into eight by eight blocks." + }, + { + "text": "And we, sort of, this is too much to deal with at once." + }, + { + "text": "So what JPEG does is take this eight by eight block, which is sixty-four coefficients, sixty-four, pixels, and changes the basis on the, on that piece." + }, + { + "text": "And then, now, let's see, I was going to write down Fourier, so you remember Fourier is, is this vector of all ones, and then, the vector, oh, well, actually, I gave a lecture earlier about the Fourier matrix, these, this matrix whose columns are powers of a, of a, complex number w. I, I won't repeat that, because I'm not, I don't want to go into the details of the Fourier basis." + }, + { + "text": "Just to tell you how compression works." + }, + { + "text": "So what happens in JPEG?" + }, + { + "text": "What happens to the video, to a, to each image of, of, of these lectures?" + }, + { + "text": "The, it gets broken into eight by eight blocks." + }, + { + "text": "OK." + }, + { + "text": "Within each block, we have sixty-four coefficients, sixty-four basis vectors, sixty-four pixels, and we change basis in sixty-four dimensional space, using these Fourier vectors." + }, + { + "text": "Just, no, that was a lossless step." + }, + { + "text": "Let, let me, let me emphasize." + }, + { + "text": "In comes the signal." + }, + { + "text": "x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk5.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..7ce7441a356838f6e496da3b2d782533cfb4ad1b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "We change basis." + }, + { + "text": "This is the basis change." + }, + { + "text": "Change basis." + }, + { + "text": "Choose a better basis." + }, + { + "text": "So it produces, the, coefficients c. So sixty-four pixels come in, sixty-four coefficients come out." + }, + { + "text": "Now comes the compression." + }, + { + "text": "Now come, this was lossless." + }, + { + "text": "It's just, we know that R64 has plenty of basis, and we've chosen one." + }, + { + "text": "Now, in that basis, we write, we write the signal in that basis, and that's what my lecture, that's the math part of my lecture." + }, + { + "text": "Now here's the application part." + }, + { + "text": "The next part is going to be the compression step." + }, + { + "text": "And that's lossy." + }, + { + "text": "We're going to lose information." + }, + { + "text": "And what, what will actually happen at that step?" + }, + { + "text": "Well, one thing we could do is just throw away the small coefficients." + }, + { + "text": "So that would be, that's called thresholding." + }, + { + "text": "We set some threshold." + }, + { + "text": "Every coefficient, every basis vector that's not in there more than the threshold value, and we set some threshold so that our eye can't see the difference, whether we throw away that, or can hardly see the difference, whether we throw away that little bit of that basis vector or keep it." + }, + { + "text": "So this compression step produces a compressed set of coefficients." + }, + { + "text": "Let me, I'll just keep going here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk6.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..e51518b0b218267f8c2f0d7243d31fec00ba9b42 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, so it keeps going." + }, + { + "text": "This compression step produces some coefficients c hat." + }, + { + "text": "And with lots of, with many zeros." + }, + { + "text": "So that's where the compression came." + }, + { + "text": "Probably there's enough of this vector of all ones, we very seldom throw that away." + }, + { + "text": "Usually its coefficient will be large." + }, + { + "text": "But the coefficient of something like this, that quickly alternating vector, there's probably very little of that in any smooth signal." + }, + { + "text": "I mean, that's high frequent- this is, this is low frequency, zero frequency." + }, + { + "text": "This stuff is the highest frequency we could have, and there's a, if the noise, the, the jitter is producing that sort of output, but a smooth lecture like this one is, has very little of that highest frequency." + }, + { + "text": "Very little noise in this lecture." + }, + { + "text": "OK." + }, + { + "text": "So, so we throw away whatever there is, and we, we're left with just a few coefficients, and then we reconstruct a signal using those coefficients." + }, + { + "text": "We take the, those coefficients times their basis vectors, but this sum doesn't have sixty-four terms anymore." + }, + { + "text": "Probably it has about two or three terms." + }, + { + "text": "So that, if we say it has three terms." + }, + { + "text": "From sixty-four down to three, that's compression of twenty-one to one." + }, + { + "text": "That's the kind of compression you're looking for." + }, + { + "text": "And everybody is looking for that sort of compression." + }, + { + "text": "Let's see, I guess I met the problem with the FBI and fingerprints." + }, + { + "text": "So there's a whole lot of still images." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk7.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..4cdf43a95d584ba42202d1c77ba5f96a998319d5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "You know, you, with your thumb, you make these inky marks, which, go somewhere." + }, + { + "text": "You used to go to Washington and get stored in a big file." + }, + { + "text": "So Washington had a file of thirty million murderers, cheaters on quizzes, other stuff, and, and actually, there was no way to retrieve them in time." + }, + { + "text": "Like, so, so suppose you're at the police station, they say, OK, this person may have done this, check with Washington, have they got his or her fingerprints on file." + }, + { + "text": "Well, Washington won't know the answer within a week, if it's got filing cabinets full of fingerprints." + }, + { + "text": "So of course the natural step is digitize them." + }, + { + "text": "So all fingerprints are now digitized, so now it's at least electronic, but still there's too much information in each, each one." + }, + { + "text": "I mean, you can't search through that many, uh, fingerprints if you, if, if the digital image is five twelve squared by five twelve squared, if it's that many pixels." + }, + { + "text": "So you get compressed." + }, + { + "text": "So the FBI had to decide what basis to choose for compression of fingerprints, and then they built a big new facility in West Virginia and that's where fingerprints now are sent." + }, + { + "text": "So if you, I think if you get your fingerprints done now at the police station, if it's an up-to-date police station, it's, it happens digitally and the signal is sent digitally, and then in West Virginia it's compressed and indexed." + }, + { + "text": "And then, if they want to find you, they can do it within minutes, instead of within a week." + }, + { + "text": "OK." + }, + { + "text": "So this compression is, comes up for signals, for images." + }, + { + "text": "For video, which is like these lectures, uh, there's another aspect." + }, + { + "text": "You could treat the video as one still image after another one, and compress each one and then run them and make a video." + }, + { + "text": "But that misses, well, you can see why that's not optimal." + }, + { + "text": "In video, so for in a video thing, you have a sequence of images, so video is really a sequence of images, but what about one image to the next image?" + }, + { + "text": "They're extremely correlated." + }, + { + "text": "I mean, that, I'm getting an image every split second, and although I'm moving slightly, that's what's producing the, jumpy motion on the video." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk8.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..41f54e28ef2064485cf009d9b5e4574263d3680d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "But I'm not, like, you know, each, each image in the sequence is pretty close to the one before." + }, + { + "text": "So you have to use, like, prediction and correction." + }, + { + "text": "I mean, you, my, the image of me one instant, one time step later, you would assume would be the same, and then plus a small correction." + }, + { + "text": "And you would only code and digitize the correction, and compress the correction." + }, + { + "text": "So the sequence of images that's highly correlated, and the problem in compression is always to use this correlation, this fact that in time or in space, things don't change instantly, they, they're very often smooth changes, and, you can predict one value from the previous value." + }, + { + "text": "OK." + }, + { + "text": "So that's the, those are applications, which are pure linear algebra." + }, + { + "text": "I could, maybe I'll, maybe you'll allow me to tell you the, and the book describes, the new basis that's, the competition for Fourier." + }, + { + "text": "So the competition for Fourier is called wavelets, and I can describe what that basis is like, say, in the eight by eight case." + }, + { + "text": "So that eight by eight wavelet basis is the vector of all ones, eight ones, then the vector of four ones and four minus ones, then the vector of two ones and two minus ones and four zeros, and also the vector of four zeros and two ones and two minus ones." + }, + { + "text": "So now I'm up to four, and I need four more, right, for R8?" + }, + { + "text": "So the next basis vector will be one minus one and six zeros, and then three more like that, with a one minus one there and there and there." + }, + { + "text": "So those are eight vectors in eight-dimensional space." + }, + { + "text": "Those are, those are called wavelets, and you, and it's a very simple wavelet choice." + }, + { + "text": "It's a more sophisticated choice." + }, + { + "text": "This is a little jumpy, to jump between one and minus one." + }, + { + "text": "And actually, you can see now, suppose you compare the wavelet basis with the Fourier basis above." + }, + { + "text": "How could I write this guy, which is in the Fourier basis, it's an eight, it's a vector in R8, how would I write that as a combination of the wavelet basis?" + }, + { + "text": "Do you, have I told you enough about the wavelet basis that you can see?" + }, + { + "text": "How does this very fast guy, what combination of the wavelet basis is that very fast guy?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk9.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..2bc1d292fd925c01e44d5599863fa8cb2bcfba79 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_2_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It would be this one, it would be the sum of these four, right?" + }, + { + "text": "That very fast guy will be that one minus one, and the next one, and the next one, and the next one." + }, + { + "text": "So this is the sum of those last four wavelets." + }, + { + "text": "This one we've kept, and so on." + }, + { + "text": "So, each, well, every, well, that's what a basis does." + }, + { + "text": "Every vector in R8 is some combination of those, and for the linear algebra, we have, so the linear algebra is this step, find the coefficients." + }, + { + "text": "That's, that's the step we want to take." + }, + { + "text": "If I give you the basis, like this wavelet basis, and I give you the pixel, so here are the pixel values, p1, p2, down to p8." + }, + { + "text": "What's, what's the job?" + }, + { + "text": "What's the linear algebra here?" + }, + { + "text": "So this is, these are the values, this is in the standard basis, right?" + }, + { + "text": "Those are just the values at eight successive points." + }, + { + "text": "I guess I'm dropping down to one dimension instead of eight by eight, I'm just going to take eight pixel values along that first top row." + }, + { + "text": "So I, what do I want to do?" + }, + { + "text": "In the standard basis, here are the pixel values." + }, + { + "text": "I want to write that as a combination of c1 times this guy, plus c2 times this guy, plus c3, these are the coefficients, plus c4 times this one." + }, + { + "text": "Do you see what I'm doing?" + }, + { + "text": "I want to write this vector p as a combination of c1 times the first wavelet, plus c8 times the eighth wavelet." + }, + { + "text": "That's the, that's the transform step." + }, + { + "text": "That's the lossless step, that's the step from p, oh, I'm calling it p here and I called it x there, so let me, at the risk of moving and therefore making this jumpy, suppose the signal I'm now calling p, the set of pixel values and I'm looking for the coefficients." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk0.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..ed695ba203c725aa80144eb85fb8edd6706cbb8c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay." + }, + { + "text": "So coming near the end of the course, this lecture will be a mixture of the linear algebra that comes with a change of basis." + }, + { + "text": "And a change of basis from one basis to another basis is something you really do in applications." + }, + { + "text": "And I would like to talk about those applications." + }, + { + "text": "I got a little bit involved with compression, compressing a signal, compressing an image, and that's exactly change of basis." + }, + { + "text": "And then the main theme in this chapter is the connection between a linear transformation, which doesn't have to have coordinates, and the matrix that tells us that transformation with respect to coordinates." + }, + { + "text": "So the matrix is the coordinate-based description of the linear transformation." + }, + { + "text": "Let me start out with the nice part, which is some, just to tell you something about image compression." + }, + { + "text": "Those of you, well, everybody's going to meet compression, because you know that the amount of data that we're getting, well, these lectures are compressed." + }, + { + "text": "So that actually, probably you see my motion as jerky, shall I use that word?" + }, + { + "text": "Have you looked on the web?" + }, + { + "text": "I should like to find a better word." + }, + { + "text": "Compressed, let's see." + }, + { + "text": "So my, the, the, the complete signal is, of course, in those video cameras and in the videotape, but that goes to the bottom of building nine, and out of that comes a jumpy motion, because it uses a standard system for compressing images." + }, + { + "text": "And, you'll notice that the stuff that sits on the board comes very clearly, but it's my motion that, that, that needs a whole lot of bits, right?" + }, + { + "text": "So, and if I were to run up and back, up there and back, that would need too many bits and they'd, I'd be compressed even more." + }, + { + "text": "So, what does compression mean?" + }, + { + "text": "Can I, let me just think of a still image." + }, + { + "text": "And, and of course, satellites, oh, there's, and, and computations of the climate, computations of combustion, the, computers and sensors of all kinds are just giving us overwhelming amounts of data." + }, + { + "text": "The web is, too." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk1.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..276b7aacae39769ce0e1627c108ec463ccf35faa --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, some compression can be done with no loss." + }, + { + "text": "Lossless compression is possible just using, sort of, the fact that, there's, there are redundancies." + }, + { + "text": "But I'm talking here about lossy compression." + }, + { + "text": "So I'm talking about, here's an image." + }, + { + "text": "And what does an image consist of?" + }, + { + "text": "It consists of a lot of little pixels, right?" + }, + { + "text": "Maybe five hundred and twelve by five hundred and twelve." + }, + { + "text": "Two to the ninth by two to the ninth pixels, and each, so this is pixel number one one, so that's a pixel, and if we're in black and white, the typical pixel would tell us a grayscale from zero to two fifty five." + }, + { + "text": "So a pixel is usually a, a value of a, a, one of the x i, so this would be the i-th pixel, it, it's usually a real number on a scale from zero to two fifty five." + }, + { + "text": "In other words, two to the eighth possibilities." + }, + { + "text": "So usually, that's the, that's the standard, so, so that, that's eight, eight bits." + }, + { + "text": "But then we have that for every, every pixel, so we have five hundred and twelve squared pixels." + }, + { + "text": "We're, we're really operating, x is a vector in Rn, but what is n?" + }, + { + "text": "n is five hundred and twelve squared." + }, + { + "text": "That's, that's our problem right there." + }, + { + "text": "We're, a pixel is a vector that gives us the information about the image, I'm sorry, the image that comes through is a vector of, of that length, that, that's the information we have about the image." + }, + { + "text": "If it's a color image, we would have three times that length, because we'd have, we'd need three coordinates to get color." + }, + { + "text": "So it would be three times five hundred and twelve squared." + }, + { + "text": "It's an enormous amount of information, and we couldn't send out the image for these lectures without compressing it." + }, + { + "text": "We, we, it, it would be, it would overload the system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk10.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..db2f6371da88f739758d4ebae59b4fdffa270d6f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "Tell me how to do it." + }, + { + "text": "How do I find the, if I give you eight basis vectors and I give you the input signal and I ask for the coefficients, what do I do?" + }, + { + "text": "What's the, what's the step?" + }, + { + "text": "I want, I'm trying to solve this, I want to know the eight coefficients, so I'm changing from the standard basis, which is just the eight grayscale values, to the wavelet basis, where this same vector is represented by eight numbers." + }, + { + "text": "It's got to take eight numbers to tell you a vector in R8, and those eight numbers are the coefficients of the basis." + }, + { + "text": "Look, we've done this thing before." + }, + { + "text": "What do we, here, there is the equation in vector notation." + }, + { + "text": "We want to see it as a matrix." + }, + { + "text": "This is a combination of columns of the wavelet matrix, right?" + }, + { + "text": "This is p equals c1, c2, down to c8, and these guys are the columns." + }, + { + "text": "I mean, this is the step that we constantly take in this course." + }, + { + "text": "The first basis vector goes in the first column, the second basis vector goes in the second column, and so on." + }, + { + "text": "The eight columns of this wavelet matrix are the eight basis vectors." + }, + { + "text": "This is a wavelet matrix W. So, the step to change basis." + }, + { + "text": "So now I'm finally coming to this change of basis." + }, + { + "text": "So the change of basis, let me stay with this board, but, well, let me just go above it here." + }, + { + "text": "So the standard basis we know, the wavelet basis we have here, and the transform is simply solve the equations p equal Wc." + }, + { + "text": "So the coefficients are W inverse p, right?" + }, + { + "text": "This shows a critical point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk11.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..8346f1691f9a546b0252c3e0960539efff45ec1f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "A good basis has a nice, fast inverse." + }, + { + "text": "So good means, good basis means what?" + }, + { + "text": "So this is like the billion dollar competition, and it's not over yet." + }, + { + "text": "People are going to come up with better bases than these." + }, + { + "text": "So a good basis will be, first good thing would be fast." + }, + { + "text": "I have to be able to multiply by W fast and multiply by W, by its inverse fast." + }, + { + "text": "That's, if a basis doesn't allow you to do that fast, then it's going to take so much time that you can't afford it." + }, + { + "text": "So these bases, the Fourier basis, everybody said, OK, I know how to deal quickly with the Fourier basis, because we have something called the fast Fourier transform." + }, + { + "text": "So there's a FFT that came in my earlier lecture and comes in the last chapter of the book." + }, + { + "text": "So change of basis is done, if for the Fourier basis, is done fast by the FFT and there's a fast wavelet transform." + }, + { + "text": "I can change, for this wavelet example, this matrix is easy to invert." + }, + { + "text": "It's just somebody had a smart idea in choosing that wavelet basis and inverting it, it has a nice inverse." + }, + { + "text": "Actually, you can see why it has a nice inverse." + }, + { + "text": "Do you see any property of these eight basis vectors?" + }, + { + "text": "Well, I've only written five of them, but if you see that property for those five, you'll see it for the three remaining." + }, + { + "text": "What, if I give you those eight vectors and ask, what's a nice property?" + }, + { + "text": "Well, you would say, first, they're all ones and minus ones and zeros, so every multiplication is very fast using just, in binary." + }, + { + "text": "But what's the other great property of those vectors?" + }, + { + "text": "Anybody see it?" + }, + { + "text": "So, of course, when I think about a basis, one nice property, I don't have to have it, but I'm happy if it's there, is that they're orthogonal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk12.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..c0eaf69080e43e238bee148545d1b059bef72365 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "If the basis vectors are orthogonal, then I'm in good shape." + }, + { + "text": "And these are, do you see, take the dot product of that with that, you get four plus ones and four minus ones, you get zero." + }, + { + "text": "Take the dot product of that with that, you get two plus ones and two minus ones." + }, + { + "text": "Or the dot product of that with that, two plus ones and two minus ones." + }, + { + "text": "You can easily check that that's an orthogonal basis." + }, + { + "text": "It's not orthonormal." + }, + { + "text": "I could, to fix it up, I should divide by the length to make them unit vectors." + }, + { + "text": "Let's suppose I do that." + }, + { + "text": "So somewhere in here I've got to account for the fact that this has length square root of eight, that has length square root of four, that has length square root of two." + }, + { + "text": "But that's just a constant factor that's easy to --." + }, + { + "text": "So suppose we've done that." + }, + { + "text": "Then tell me what's W inverse." + }, + { + "text": "That's what chapter four, section four point four was about." + }, + { + "text": "If we have orthonormal columns, what- then the inverse is the same as the transpose." + }, + { + "text": "So if we have a fast way to multiply by W, which we do, the inverse is going to look just the same and we'll have a fast way to do W inverse." + }, + { + "text": "So that's, the wavelet basis passes this requirement for fast." + }, + { + "text": "We can use it fast." + }, + { + "text": "But there's a second requirement, is it any good?" + }, + { + "text": "Because the very fastest thing we could do would be not to change basis at all." + }, + { + "text": "Right?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk13.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..4de80b529af0604a4e0b9b0291a8822dc165b83a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Fastest thing would be, OK, stay with a standard basis, stay with eight pixel values." + }, + { + "text": "But that was poor from compression point of view, right?" + }, + { + "text": "Those eight pixel values, if I just took those eight numbers, I can't throw some of those away." + }, + { + "text": "If I throw away ninety percent, if I compressed ten to one, and throw away ninety percent of my pixel values, well, my picture's just gone dark." + }, + { + "text": "Whereas the basis that was good, the wavelet basis or the Fourier basis, if I throw away c5, c6, c7 and c8, all I'm throwing away is little blips that are probably there in very small amounts." + }, + { + "text": "So the second property that we need is good compression." + }, + { + "text": "So, so first it, it has to be fast, and secondly, it has to be a few basis factors should come close to the signal." + }, + { + "text": "So, so a few, few is enough." + }, + { + "text": "Can I write it that way?" + }, + { + "text": "A few basis factors are enough to reproduce the image, just exactly as on the video of these 18.06 lectures." + }, + { + "text": "I don't know what the compression rate is." + }, + { + "text": "I'll ask, David, who, who does the compression, and, by the way, I'll try to get the lectures, that are relevant for the quiz, up onto the web, in time." + }, + { + "text": "So I'll send him a message today." + }, + { + "text": "So, at the point, so he's using the Fourier basis, because the JPEG, so JPEG 2000, which will be the next standard for image compression, will include wavelets." + }, + { + "text": "So, I mean, you're, you're actually getting a kind of up to date, picture of where this big world of signal and image processing is." + }, + { + "text": "That Fourier is what everybody knew, and what people automatically used, and the new, new one is wavelets, where this is the simplest set of wavelets, and this isn't the one that the FBI uses, by the way." + }, + { + "text": "The FBI uses a more, a more, a smoother wavelet." + }, + { + "text": "Instead of jumping from one to minus one, it's a smooth, cutoff." + }, + { + "text": "And, that's what we'll be in, in JPEG 2000." + }, + { + "text": "OK, so that's that application." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk14.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..8f1debcca7ae641417e7ed0a630d269963c01302 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now let me come to my, the, the math, the linear algebra part of the lecture." + }, + { + "text": "Well, we've actually seen a change of basis." + }, + { + "text": "So let, let me just review that change of basis idea, and then the, and then the transformation to a matrix." + }, + { + "text": "OK, so, so this, I hope you see that these applications are really big." + }, + { + "text": "Now I have to talk a little about change of basis and little about that, the, the matrix." + }, + { + "text": "OK. OK. OK." + }, + { + "text": "So change of basis." + }, + { + "text": "Basically, forgive that pun, OK, I have, I have, I have my vector in one basis, and I want to change to a different one." + }, + { + "text": "Actually, you saw it for the wavelet case." + }, + { + "text": "So I need the, the, let the matrix W, the columns of W, be the new basis vectors." + }, + { + "text": "Then the change of basis involves, just as it did there, W inverse." + }, + { + "text": "So we have the vector, vector, say, x in the old basis, and we, that converts to a vector, let's say, c in the new basis, and the relation is exactly what we had there, that x is Wc." + }, + { + "text": "That's the, that's the, that's the, that's the step we have to take." + }, + { + "text": "There's a matrix W that gives us a change of basis." + }, + { + "text": "OK." + }, + { + "text": "I, I, what I want to do is think about mat- transformations and matrices." + }, + { + "text": "So here's, here's the question, that, that, to complete this lecture." + }, + { + "text": "Suppose I have a linear transformation T. So it's, it's a, it's a, we, we would think of it as an A, as a n by n matrix." + }, + { + "text": "And it's computed with respect to a certain basis." + }, + { + "text": "So T, so, no, I'm sorry." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk15.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..dbc5ad92f06633f3366a78c24c0c7c08b058ee63 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "I've got the transformation T, period." + }, + { + "text": "That's taking eight-dimensional space to eight-dimensional space." + }, + { + "text": "Now let's get matrices in there." + }, + { + "text": "OK." + }, + { + "text": "So, so with respect to, with respect to a fir- a first basis, say, V1 up to V8, it has a matrix A. I'm just setting up letters here." + }, + { + "text": "With respect to a second basis, say, I'll make it U1 up to- or W1, since I've used Ws, W1 up to W8, it has a matrix B." + }, + { + "text": "And my question is, what's the connection between A and B?" + }, + { + "text": "How is the matrix- the transformation T is settled." + }, + { + "text": "We could say it's a rotation, for example." + }, + { + "text": "So that would be one transformation of eight-dimensional space, just spin it a little." + }, + { + "text": "Or project it." + }, + { + "text": "Or, or, whatever, whatever linear transformation we've got." + }, + { + "text": "Now we have to remember, so I- so first- my first step is to remind you how you create that matrix A." + }, + { + "text": "Then my second step is, we would use the same method to create B, but because it came from the same transformation, there's got to be a relation between A and B." + }, + { + "text": "What's the- what's the relation between A and B?" + }, + { + "text": "And let me jump to the answer on that one." + }, + { + "text": "That if I have- if I have the same transformation, and I'm compute- its matrix in one basis and then I compute it in another basis, those two matrices are similar." + }, + { + "text": "So these two matrices are similar." + }, + { + "text": "Now, do you remember what similar matrices meant?" + }, + { + "text": "Similar." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk16.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..9d019933a190fe645eec785d8363a0940d0f76a4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "A is similar- the two matrices are similar." + }, + { + "text": "Similar." + }, + { + "text": "And what do I mean by that?" + }, + { + "text": "I mean that I take the matrix B and I can compute it from the matrix A using some similarity, some matrix M on one side and M inverse on the other." + }, + { + "text": "And this M will be the change of basis matrix." + }, + { + "text": "This part of the lecture is admittedly compressed." + }, + { + "text": "What I wanted you to- it's really the conclusion that I want you to spot." + }, + { + "text": "Now I have to go back and say, what does it mean for A to be the matrix of this transformation T?" + }, + { + "text": "So I have to remind you what that meant." + }, + { + "text": "That was in the last lecture." + }, + { + "text": "Then this is the conclusion, that if I change to a different basis, we now know- see, if I change to a different basis, two things happen." + }, + { + "text": "Every vector has new coordinates." + }, + { + "text": "There, the rule is this one, between the old coordinates and the new ones." + }, + { + "text": "Every matrix changes." + }, + { + "text": "Every transformation has a new matrix." + }, + { + "text": "And the new matrix is related this way." + }, + { + "text": "The M could be the same as the W. The M there could be the W here." + }, + { + "text": "OK." + }, + { + "text": "So can I, in the remaining minutes, recapture my lecture, the end of my lecture that was just before Thanksgiving, about the matrix?" + }, + { + "text": "OK. What's the matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk17.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..f82f2cc230f9f2720733e8b152f84f80f1341c9f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll just take one basis." + }, + { + "text": "So now I'm going to- this part is going to go onto this board here." + }, + { + "text": "What is the matrix?" + }, + { + "text": "What is A?" + }, + { + "text": "OK." + }, + { + "text": "Using a basis v1 up to v8." + }, + { + "text": "OK. What's the point?" + }, + { + "text": "The point is, if I know what the transformation does to those eight basis vectors, I know it completely." + }, + { + "text": "I know T, I know everything about T, I know T completely from knowing what T does to v1, what T does to v2, what T does to v8." + }, + { + "text": "Why is that?" + }, + { + "text": "It's because T is a linear transformation." + }, + { + "text": "So that if I know what these outputs are, so these are the inputs, v1 up to v8, these are the outputs from the transformation, like every one rotated, every one projected, whatever transformation I've done, then why is it that I know everything?" + }, + { + "text": "How does linearity work?" + }, + { + "text": "Why?" + }, + { + "text": "This is because every x is some combination of these basis vectors, right?" + }, + { + "text": "c1 v1, c2 v2, c8 v8." + }, + { + "text": "That's the whole point of a basis, that every vector is a combination of the basis vectors in exactly one way." + }, + { + "text": "And then, what is T of x?" + }, + { + "text": "The point is, I claim that we know T of x completely for every x, because every x is a combination of those, and now we use the linear transformation part to say that the output from x has to be c1 times the output from v1 plus c2 times the output from v2 and so on, up through c8 times the output from v8." + }, + { + "text": "So this is like just saying, OK, we know everything when we know what T does to each basis vector." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk18.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..d9c718592303012586f37aed3dc53271be8cef29 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "So those are the eight things we need." + }, + { + "text": "Now, but we need these answers in this basis." + }, + { + "text": "So T- so this first output is some combination of the eight basis vectors." + }, + { + "text": "So write T times the first- acting on the first input, in other words, write the first output as a combination of the basis vectors." + }, + { + "text": "Say a11 v1 plus a21 v2 and so on, a81 v8." + }, + { + "text": "Write T of v2 as some combination, a12 of v1, a22 of v2 and so on." + }, + { + "text": "I'm creating the matrix A, column by column." + }, + { + "text": "Those numbers go in the first column, these numbers go in the second column." + }, + { + "text": "The matrix A that this is our matrix that represents T in this basis is these numbers." + }, + { + "text": "a11 down to a18, a21 down to a28 and so on." + }, + { + "text": "OK. That's the recipe." + }, + { + "text": "In other words, if I give you a transformation and a basis, that's what I have to give you." + }, + { + "text": "The inputs are the basis and to tell you what the transformation is." + }, + { + "text": "And then you tell me, you compute T for each basis, expand that result in the basis, and that gives you the sixty-four numbers that go into the matrix A." + }, + { + "text": "Let me suppose, let's close with the best example of all." + }, + { + "text": "Suppose v1 to v8, this basis, is the eigenvectors." + }, + { + "text": "Suppose we have an eigenvector basis." + }, + { + "text": "So that T of vi is just, is in the same direction as vi." + }, + { + "text": "Now my question is, what is A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk19.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..4bc0bda81becbd032c626bcaab40cca8eaa39155 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Can you carry through the steps?" + }, + { + "text": "Let's, let's do them together, because we can do it in one minute." + }, + { + "text": "So we've chosen this perfect basis." + }, + { + "text": "And actually, with signal image processing, they might look for the eigenvectors, but that would take more calculation time than just saying, OK, we'll use the wavelet basis, or OK, we'll use the Fourier basis." + }, + { + "text": "But the very best basis is the eigenvector basis." + }, + { + "text": "OK, what's the matrix?" + }, + { + "text": "So, what's the first column of the matrix?" + }, + { + "text": "How do I get the first column?" + }, + { + "text": "I take the first basis vector v1." + }, + { + "text": "I op- I look to see what does the transformation do to it." + }, + { + "text": "The output is lambda one v1." + }, + { + "text": "I express that output as a combination, so the first input is v1." + }, + { + "text": "Its output is lambda one v1." + }, + { + "text": "Now write lambda one v1 as a combination of the basis vectors." + }, + { + "text": "Well, it's already done." + }, + { + "text": "It's just lambda one times the first basis vector and zero times the others." + }, + { + "text": "So this first column will have lambda one and zeros." + }, + { + "text": "OK?" + }, + { + "text": "Second input is v2." + }, + { + "text": "Output is lambda two v2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk2.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..44553739c24736b408dbd01c3688e075b25f9a15 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it has to be compressed." + }, + { + "text": "The standard compression, and still used in, in the, with these lectures, is, called JPEG." + }, + { + "text": "I think that stands for a Joint Photographic Experts Group." + }, + { + "text": "They established a system of compression." + }, + { + "text": "And I just want to tell you what it's about." + }, + { + "text": "It's a change of basis." + }, + { + "text": "What, what's, what basis do we have?" + }, + { + "text": "The, the current basis we have is, you could say, the standard basis is every pixel give a value." + }, + { + "text": "So that's like, we have a vector x, which is five hundred and twelve squared long, and in the i-th position, we get a number like one twenty one or something, the next, the pixel next to it might be one twenty four, maybe where, maybe where the, where my tie, begins to end." + }, + { + "text": "So if it was mostly blue shirt, this would be a slight difference in shading, but pretty close." + }, + { + "text": "Then the tie would be a different color." + }, + { + "text": "So, so we might have quite a few pixels for the blue shirt and a whole lot more for the blackboard that are very close." + }, + { + "text": "And that's what, are very correlated." + }, + { + "text": "And that's what gives us the possibility of compression." + }, + { + "text": "For example, before the lecture starts, if we had a blank blackboard, then there's an image, but it would make no sense to take that image and tell you what it is pixel by pixel." + }, + { + "text": "I mean, there's a case in which all pixel values, all gray levels are the same, or practically the same, depending on the erasing of the board, but extremely close." + }, + { + "text": "And so that's an image where the standard basis is lousy." + }, + { + "text": "That's, that's the basic fact." + }, + { + "text": "That, that the standard basis which gives the value of every pixel makes no use of the fact that we're getting a whole lot of pixels whose gray levels, the neighboring pixels tend to have the same gray level as the, as their, as their neighbors." + }, + { + "text": "So to take, how do we take advantage of that fact?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk20.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..57e892c1f19c9a45e5f14bb334eab942b0d796a2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk20.json @@ -0,0 +1,32 @@ +[ + { + "text": "OK, write that output as a combination of the v's." + }, + { + "text": "It's already done." + }, + { + "text": "It's just lambda two times the second v. So we need, in the second column, we have lambda two times the second v. Well, you see what's coming." + }, + { + "text": "That in that basis, in the eigenvector basis, the matrix is diagonal." + }, + { + "text": "So that's the perfect basis." + }, + { + "text": "That's the basis we'd love to have for image processing, but to find the eigenvectors of our pixel matrix would be too expensive." + }, + { + "text": "So we do something cheaper and close, which is to choose a good basis like, like wavelengths." + }, + { + "text": "OK, thanks." + }, + { + "text": "So quiz review on Wednesday, all day." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk3.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..8e246b42e71ac0ef99e39e59a7562c71f3da61b4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, one basis vector that would be extremely nice to, one vector that would be extremely nice to include in the basis would be a vector of all ones." + }, + { + "text": "That's not in our standard basis." + }, + { + "text": "So our, so let me just write again." + }, + { + "text": "The standard basis would, is, is our, is our one and all the rest zeros, zero, one, and all the rest zeros, everybody knows what the standard basis is." + }, + { + "text": "Now, any other basis for our, so this is, for this very high-dimensional space, now I'm going to speak about a better basis, better basis, and let me just emphasize, one vector that would be extremely nice to have in that basis is the vector of all ones." + }, + { + "text": "Why is that?" + }, + { + "text": "Let me just say again." + }, + { + "text": "Because that vector of all ones, by itself, one vector is, is able to completely give the information on a solid image." + }, + { + "text": "Of course, our image won't be solid, it'll have a mix of, of, solid and, and signal." + }, + { + "text": "So that one vector, but that, having that one vector in the basis is, is, is going to save us a whole lot." + }, + { + "text": "Now the question is, what other vectors should be in the basis?" + }, + { + "text": "The, the extreme vector in the basis might be a vector of one minus one, one minus one, one minus one." + }, + { + "text": "That would be a vector that shows, I mean, that's like a checkerboard vector, right?" + }, + { + "text": "That's a vector that would, if, if we had, if, if the image was like a huge checkerboard of plus minus, plus minus, plus minus, that vector would carry the whole signal." + }, + { + "text": "But much more common would be maybe to have half the image, darker and the other half lighter." + }, + { + "text": "So another image, another vector that might be quite useful in here would be half ones and half minus ones." + }, + { + "text": "I'm just trying to get across the idea of, that a basis could be, that first of all, we've got, the basis is at our disposal." + }, + { + "text": "Like, we're free to choose that." + }, + { + "text": "And it's a billion dollar decision what we choose." + }, + { + "text": "So, and TV people would rather, would prefer one basis based on the way the, the signal is scanned, and movie people would prefer another." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk4.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..811c58ffd5e28e456b42de439fa8cee4339bd2a6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "I mean, there's giant politics in this question that really reduces to a, to a linear algebra problem what basis to choose." + }, + { + "text": "I'll just mention the best known basis, which is, which JPEG uses, let me put that here, is the Fourier basis." + }, + { + "text": "So when you, when you use the Fourier basis, that includes, this is the constant vector, the DC vector, if we're electrical engineers, the, the, the vector of all ones, so it would include one, one, one, one." + }, + { + "text": "Often, eight by eight is a good choice." + }, + { + "text": "Eight by eight is a, is a good choice." + }, + { + "text": "So, what do I mean by this eight by eight?" + }, + { + "text": "I mean that the big signal, which is five twelve by five twelve, gets broken down, and JPEG does this, into eight by eight blocks." + }, + { + "text": "And we, sort of, this is too much to deal with at once." + }, + { + "text": "So what JPEG does is take this eight by eight block, which is sixty-four coefficients, sixty-four, pixels, and changes the basis on the, on that piece." + }, + { + "text": "And then, now, let's see, I was going to write down Fourier, so you remember Fourier is, is this vector of all ones, and then, the vector, oh, well, actually, I gave a lecture earlier about the Fourier matrix, these, this matrix whose columns are powers of a, of a, complex number w. I, I won't repeat that, because I'm not, I don't want to go into the details of the Fourier basis." + }, + { + "text": "Just to tell you how compression works." + }, + { + "text": "So what happens in JPEG?" + }, + { + "text": "What happens to the video, to a, to each image of, of, of these lectures?" + }, + { + "text": "The, it gets broken into eight by eight blocks." + }, + { + "text": "OK." + }, + { + "text": "Within each block, we have sixty-four coefficients, sixty-four basis vectors, sixty-four pixels, and we change basis in sixty-four dimensional space, using these Fourier vectors." + }, + { + "text": "Just, no, that was a lossless step." + }, + { + "text": "Let, let me, let me emphasize." + }, + { + "text": "In comes the signal." + }, + { + "text": "x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk5.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..7ce7441a356838f6e496da3b2d782533cfb4ad1b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "We change basis." + }, + { + "text": "This is the basis change." + }, + { + "text": "Change basis." + }, + { + "text": "Choose a better basis." + }, + { + "text": "So it produces, the, coefficients c. So sixty-four pixels come in, sixty-four coefficients come out." + }, + { + "text": "Now comes the compression." + }, + { + "text": "Now come, this was lossless." + }, + { + "text": "It's just, we know that R64 has plenty of basis, and we've chosen one." + }, + { + "text": "Now, in that basis, we write, we write the signal in that basis, and that's what my lecture, that's the math part of my lecture." + }, + { + "text": "Now here's the application part." + }, + { + "text": "The next part is going to be the compression step." + }, + { + "text": "And that's lossy." + }, + { + "text": "We're going to lose information." + }, + { + "text": "And what, what will actually happen at that step?" + }, + { + "text": "Well, one thing we could do is just throw away the small coefficients." + }, + { + "text": "So that would be, that's called thresholding." + }, + { + "text": "We set some threshold." + }, + { + "text": "Every coefficient, every basis vector that's not in there more than the threshold value, and we set some threshold so that our eye can't see the difference, whether we throw away that, or can hardly see the difference, whether we throw away that little bit of that basis vector or keep it." + }, + { + "text": "So this compression step produces a compressed set of coefficients." + }, + { + "text": "Let me, I'll just keep going here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk6.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..e51518b0b218267f8c2f0d7243d31fec00ba9b42 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, so it keeps going." + }, + { + "text": "This compression step produces some coefficients c hat." + }, + { + "text": "And with lots of, with many zeros." + }, + { + "text": "So that's where the compression came." + }, + { + "text": "Probably there's enough of this vector of all ones, we very seldom throw that away." + }, + { + "text": "Usually its coefficient will be large." + }, + { + "text": "But the coefficient of something like this, that quickly alternating vector, there's probably very little of that in any smooth signal." + }, + { + "text": "I mean, that's high frequent- this is, this is low frequency, zero frequency." + }, + { + "text": "This stuff is the highest frequency we could have, and there's a, if the noise, the, the jitter is producing that sort of output, but a smooth lecture like this one is, has very little of that highest frequency." + }, + { + "text": "Very little noise in this lecture." + }, + { + "text": "OK." + }, + { + "text": "So, so we throw away whatever there is, and we, we're left with just a few coefficients, and then we reconstruct a signal using those coefficients." + }, + { + "text": "We take the, those coefficients times their basis vectors, but this sum doesn't have sixty-four terms anymore." + }, + { + "text": "Probably it has about two or three terms." + }, + { + "text": "So that, if we say it has three terms." + }, + { + "text": "From sixty-four down to three, that's compression of twenty-one to one." + }, + { + "text": "That's the kind of compression you're looking for." + }, + { + "text": "And everybody is looking for that sort of compression." + }, + { + "text": "Let's see, I guess I met the problem with the FBI and fingerprints." + }, + { + "text": "So there's a whole lot of still images." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk7.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..4cdf43a95d584ba42202d1c77ba5f96a998319d5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "You know, you, with your thumb, you make these inky marks, which, go somewhere." + }, + { + "text": "You used to go to Washington and get stored in a big file." + }, + { + "text": "So Washington had a file of thirty million murderers, cheaters on quizzes, other stuff, and, and actually, there was no way to retrieve them in time." + }, + { + "text": "Like, so, so suppose you're at the police station, they say, OK, this person may have done this, check with Washington, have they got his or her fingerprints on file." + }, + { + "text": "Well, Washington won't know the answer within a week, if it's got filing cabinets full of fingerprints." + }, + { + "text": "So of course the natural step is digitize them." + }, + { + "text": "So all fingerprints are now digitized, so now it's at least electronic, but still there's too much information in each, each one." + }, + { + "text": "I mean, you can't search through that many, uh, fingerprints if you, if, if the digital image is five twelve squared by five twelve squared, if it's that many pixels." + }, + { + "text": "So you get compressed." + }, + { + "text": "So the FBI had to decide what basis to choose for compression of fingerprints, and then they built a big new facility in West Virginia and that's where fingerprints now are sent." + }, + { + "text": "So if you, I think if you get your fingerprints done now at the police station, if it's an up-to-date police station, it's, it happens digitally and the signal is sent digitally, and then in West Virginia it's compressed and indexed." + }, + { + "text": "And then, if they want to find you, they can do it within minutes, instead of within a week." + }, + { + "text": "OK." + }, + { + "text": "So this compression is, comes up for signals, for images." + }, + { + "text": "For video, which is like these lectures, uh, there's another aspect." + }, + { + "text": "You could treat the video as one still image after another one, and compress each one and then run them and make a video." + }, + { + "text": "But that misses, well, you can see why that's not optimal." + }, + { + "text": "In video, so for in a video thing, you have a sequence of images, so video is really a sequence of images, but what about one image to the next image?" + }, + { + "text": "They're extremely correlated." + }, + { + "text": "I mean, that, I'm getting an image every split second, and although I'm moving slightly, that's what's producing the, jumpy motion on the video." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk8.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..41f54e28ef2064485cf009d9b5e4574263d3680d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "But I'm not, like, you know, each, each image in the sequence is pretty close to the one before." + }, + { + "text": "So you have to use, like, prediction and correction." + }, + { + "text": "I mean, you, my, the image of me one instant, one time step later, you would assume would be the same, and then plus a small correction." + }, + { + "text": "And you would only code and digitize the correction, and compress the correction." + }, + { + "text": "So the sequence of images that's highly correlated, and the problem in compression is always to use this correlation, this fact that in time or in space, things don't change instantly, they, they're very often smooth changes, and, you can predict one value from the previous value." + }, + { + "text": "OK." + }, + { + "text": "So that's the, those are applications, which are pure linear algebra." + }, + { + "text": "I could, maybe I'll, maybe you'll allow me to tell you the, and the book describes, the new basis that's, the competition for Fourier." + }, + { + "text": "So the competition for Fourier is called wavelets, and I can describe what that basis is like, say, in the eight by eight case." + }, + { + "text": "So that eight by eight wavelet basis is the vector of all ones, eight ones, then the vector of four ones and four minus ones, then the vector of two ones and two minus ones and four zeros, and also the vector of four zeros and two ones and two minus ones." + }, + { + "text": "So now I'm up to four, and I need four more, right, for R8?" + }, + { + "text": "So the next basis vector will be one minus one and six zeros, and then three more like that, with a one minus one there and there and there." + }, + { + "text": "So those are eight vectors in eight-dimensional space." + }, + { + "text": "Those are, those are called wavelets, and you, and it's a very simple wavelet choice." + }, + { + "text": "It's a more sophisticated choice." + }, + { + "text": "This is a little jumpy, to jump between one and minus one." + }, + { + "text": "And actually, you can see now, suppose you compare the wavelet basis with the Fourier basis above." + }, + { + "text": "How could I write this guy, which is in the Fourier basis, it's an eight, it's a vector in R8, how would I write that as a combination of the wavelet basis?" + }, + { + "text": "Do you, have I told you enough about the wavelet basis that you can see?" + }, + { + "text": "How does this very fast guy, what combination of the wavelet basis is that very fast guy?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk9.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..2bc1d292fd925c01e44d5599863fa8cb2bcfba79 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_3_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It would be this one, it would be the sum of these four, right?" + }, + { + "text": "That very fast guy will be that one minus one, and the next one, and the next one, and the next one." + }, + { + "text": "So this is the sum of those last four wavelets." + }, + { + "text": "This one we've kept, and so on." + }, + { + "text": "So, each, well, every, well, that's what a basis does." + }, + { + "text": "Every vector in R8 is some combination of those, and for the linear algebra, we have, so the linear algebra is this step, find the coefficients." + }, + { + "text": "That's, that's the step we want to take." + }, + { + "text": "If I give you the basis, like this wavelet basis, and I give you the pixel, so here are the pixel values, p1, p2, down to p8." + }, + { + "text": "What's, what's the job?" + }, + { + "text": "What's the linear algebra here?" + }, + { + "text": "So this is, these are the values, this is in the standard basis, right?" + }, + { + "text": "Those are just the values at eight successive points." + }, + { + "text": "I guess I'm dropping down to one dimension instead of eight by eight, I'm just going to take eight pixel values along that first top row." + }, + { + "text": "So I, what do I want to do?" + }, + { + "text": "In the standard basis, here are the pixel values." + }, + { + "text": "I want to write that as a combination of c1 times this guy, plus c2 times this guy, plus c3, these are the coefficients, plus c4 times this one." + }, + { + "text": "Do you see what I'm doing?" + }, + { + "text": "I want to write this vector p as a combination of c1 times the first wavelet, plus c8 times the eighth wavelet." + }, + { + "text": "That's the, that's the transform step." + }, + { + "text": "That's the lossless step, that's the step from p, oh, I'm calling it p here and I called it x there, so let me, at the risk of moving and therefore making this jumpy, suppose the signal I'm now calling p, the set of pixel values and I'm looking for the coefficients." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk0.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..ed695ba203c725aa80144eb85fb8edd6706cbb8c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay." + }, + { + "text": "So coming near the end of the course, this lecture will be a mixture of the linear algebra that comes with a change of basis." + }, + { + "text": "And a change of basis from one basis to another basis is something you really do in applications." + }, + { + "text": "And I would like to talk about those applications." + }, + { + "text": "I got a little bit involved with compression, compressing a signal, compressing an image, and that's exactly change of basis." + }, + { + "text": "And then the main theme in this chapter is the connection between a linear transformation, which doesn't have to have coordinates, and the matrix that tells us that transformation with respect to coordinates." + }, + { + "text": "So the matrix is the coordinate-based description of the linear transformation." + }, + { + "text": "Let me start out with the nice part, which is some, just to tell you something about image compression." + }, + { + "text": "Those of you, well, everybody's going to meet compression, because you know that the amount of data that we're getting, well, these lectures are compressed." + }, + { + "text": "So that actually, probably you see my motion as jerky, shall I use that word?" + }, + { + "text": "Have you looked on the web?" + }, + { + "text": "I should like to find a better word." + }, + { + "text": "Compressed, let's see." + }, + { + "text": "So my, the, the, the complete signal is, of course, in those video cameras and in the videotape, but that goes to the bottom of building nine, and out of that comes a jumpy motion, because it uses a standard system for compressing images." + }, + { + "text": "And, you'll notice that the stuff that sits on the board comes very clearly, but it's my motion that, that, that needs a whole lot of bits, right?" + }, + { + "text": "So, and if I were to run up and back, up there and back, that would need too many bits and they'd, I'd be compressed even more." + }, + { + "text": "So, what does compression mean?" + }, + { + "text": "Can I, let me just think of a still image." + }, + { + "text": "And, and of course, satellites, oh, there's, and, and computations of the climate, computations of combustion, the, computers and sensors of all kinds are just giving us overwhelming amounts of data." + }, + { + "text": "The web is, too." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk1.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..276b7aacae39769ce0e1627c108ec463ccf35faa --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, some compression can be done with no loss." + }, + { + "text": "Lossless compression is possible just using, sort of, the fact that, there's, there are redundancies." + }, + { + "text": "But I'm talking here about lossy compression." + }, + { + "text": "So I'm talking about, here's an image." + }, + { + "text": "And what does an image consist of?" + }, + { + "text": "It consists of a lot of little pixels, right?" + }, + { + "text": "Maybe five hundred and twelve by five hundred and twelve." + }, + { + "text": "Two to the ninth by two to the ninth pixels, and each, so this is pixel number one one, so that's a pixel, and if we're in black and white, the typical pixel would tell us a grayscale from zero to two fifty five." + }, + { + "text": "So a pixel is usually a, a value of a, a, one of the x i, so this would be the i-th pixel, it, it's usually a real number on a scale from zero to two fifty five." + }, + { + "text": "In other words, two to the eighth possibilities." + }, + { + "text": "So usually, that's the, that's the standard, so, so that, that's eight, eight bits." + }, + { + "text": "But then we have that for every, every pixel, so we have five hundred and twelve squared pixels." + }, + { + "text": "We're, we're really operating, x is a vector in Rn, but what is n?" + }, + { + "text": "n is five hundred and twelve squared." + }, + { + "text": "That's, that's our problem right there." + }, + { + "text": "We're, a pixel is a vector that gives us the information about the image, I'm sorry, the image that comes through is a vector of, of that length, that, that's the information we have about the image." + }, + { + "text": "If it's a color image, we would have three times that length, because we'd have, we'd need three coordinates to get color." + }, + { + "text": "So it would be three times five hundred and twelve squared." + }, + { + "text": "It's an enormous amount of information, and we couldn't send out the image for these lectures without compressing it." + }, + { + "text": "We, we, it, it would be, it would overload the system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk10.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..db2f6371da88f739758d4ebae59b4fdffa270d6f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "Tell me how to do it." + }, + { + "text": "How do I find the, if I give you eight basis vectors and I give you the input signal and I ask for the coefficients, what do I do?" + }, + { + "text": "What's the, what's the step?" + }, + { + "text": "I want, I'm trying to solve this, I want to know the eight coefficients, so I'm changing from the standard basis, which is just the eight grayscale values, to the wavelet basis, where this same vector is represented by eight numbers." + }, + { + "text": "It's got to take eight numbers to tell you a vector in R8, and those eight numbers are the coefficients of the basis." + }, + { + "text": "Look, we've done this thing before." + }, + { + "text": "What do we, here, there is the equation in vector notation." + }, + { + "text": "We want to see it as a matrix." + }, + { + "text": "This is a combination of columns of the wavelet matrix, right?" + }, + { + "text": "This is p equals c1, c2, down to c8, and these guys are the columns." + }, + { + "text": "I mean, this is the step that we constantly take in this course." + }, + { + "text": "The first basis vector goes in the first column, the second basis vector goes in the second column, and so on." + }, + { + "text": "The eight columns of this wavelet matrix are the eight basis vectors." + }, + { + "text": "This is a wavelet matrix W. So, the step to change basis." + }, + { + "text": "So now I'm finally coming to this change of basis." + }, + { + "text": "So the change of basis, let me stay with this board, but, well, let me just go above it here." + }, + { + "text": "So the standard basis we know, the wavelet basis we have here, and the transform is simply solve the equations p equal Wc." + }, + { + "text": "So the coefficients are W inverse p, right?" + }, + { + "text": "This shows a critical point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk11.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..8346f1691f9a546b0252c3e0960539efff45ec1f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "A good basis has a nice, fast inverse." + }, + { + "text": "So good means, good basis means what?" + }, + { + "text": "So this is like the billion dollar competition, and it's not over yet." + }, + { + "text": "People are going to come up with better bases than these." + }, + { + "text": "So a good basis will be, first good thing would be fast." + }, + { + "text": "I have to be able to multiply by W fast and multiply by W, by its inverse fast." + }, + { + "text": "That's, if a basis doesn't allow you to do that fast, then it's going to take so much time that you can't afford it." + }, + { + "text": "So these bases, the Fourier basis, everybody said, OK, I know how to deal quickly with the Fourier basis, because we have something called the fast Fourier transform." + }, + { + "text": "So there's a FFT that came in my earlier lecture and comes in the last chapter of the book." + }, + { + "text": "So change of basis is done, if for the Fourier basis, is done fast by the FFT and there's a fast wavelet transform." + }, + { + "text": "I can change, for this wavelet example, this matrix is easy to invert." + }, + { + "text": "It's just somebody had a smart idea in choosing that wavelet basis and inverting it, it has a nice inverse." + }, + { + "text": "Actually, you can see why it has a nice inverse." + }, + { + "text": "Do you see any property of these eight basis vectors?" + }, + { + "text": "Well, I've only written five of them, but if you see that property for those five, you'll see it for the three remaining." + }, + { + "text": "What, if I give you those eight vectors and ask, what's a nice property?" + }, + { + "text": "Well, you would say, first, they're all ones and minus ones and zeros, so every multiplication is very fast using just, in binary." + }, + { + "text": "But what's the other great property of those vectors?" + }, + { + "text": "Anybody see it?" + }, + { + "text": "So, of course, when I think about a basis, one nice property, I don't have to have it, but I'm happy if it's there, is that they're orthogonal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk12.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..c0eaf69080e43e238bee148545d1b059bef72365 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "If the basis vectors are orthogonal, then I'm in good shape." + }, + { + "text": "And these are, do you see, take the dot product of that with that, you get four plus ones and four minus ones, you get zero." + }, + { + "text": "Take the dot product of that with that, you get two plus ones and two minus ones." + }, + { + "text": "Or the dot product of that with that, two plus ones and two minus ones." + }, + { + "text": "You can easily check that that's an orthogonal basis." + }, + { + "text": "It's not orthonormal." + }, + { + "text": "I could, to fix it up, I should divide by the length to make them unit vectors." + }, + { + "text": "Let's suppose I do that." + }, + { + "text": "So somewhere in here I've got to account for the fact that this has length square root of eight, that has length square root of four, that has length square root of two." + }, + { + "text": "But that's just a constant factor that's easy to --." + }, + { + "text": "So suppose we've done that." + }, + { + "text": "Then tell me what's W inverse." + }, + { + "text": "That's what chapter four, section four point four was about." + }, + { + "text": "If we have orthonormal columns, what- then the inverse is the same as the transpose." + }, + { + "text": "So if we have a fast way to multiply by W, which we do, the inverse is going to look just the same and we'll have a fast way to do W inverse." + }, + { + "text": "So that's, the wavelet basis passes this requirement for fast." + }, + { + "text": "We can use it fast." + }, + { + "text": "But there's a second requirement, is it any good?" + }, + { + "text": "Because the very fastest thing we could do would be not to change basis at all." + }, + { + "text": "Right?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk13.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..4de80b529af0604a4e0b9b0291a8822dc165b83a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Fastest thing would be, OK, stay with a standard basis, stay with eight pixel values." + }, + { + "text": "But that was poor from compression point of view, right?" + }, + { + "text": "Those eight pixel values, if I just took those eight numbers, I can't throw some of those away." + }, + { + "text": "If I throw away ninety percent, if I compressed ten to one, and throw away ninety percent of my pixel values, well, my picture's just gone dark." + }, + { + "text": "Whereas the basis that was good, the wavelet basis or the Fourier basis, if I throw away c5, c6, c7 and c8, all I'm throwing away is little blips that are probably there in very small amounts." + }, + { + "text": "So the second property that we need is good compression." + }, + { + "text": "So, so first it, it has to be fast, and secondly, it has to be a few basis factors should come close to the signal." + }, + { + "text": "So, so a few, few is enough." + }, + { + "text": "Can I write it that way?" + }, + { + "text": "A few basis factors are enough to reproduce the image, just exactly as on the video of these 18.06 lectures." + }, + { + "text": "I don't know what the compression rate is." + }, + { + "text": "I'll ask, David, who, who does the compression, and, by the way, I'll try to get the lectures, that are relevant for the quiz, up onto the web, in time." + }, + { + "text": "So I'll send him a message today." + }, + { + "text": "So, at the point, so he's using the Fourier basis, because the JPEG, so JPEG 2000, which will be the next standard for image compression, will include wavelets." + }, + { + "text": "So, I mean, you're, you're actually getting a kind of up to date, picture of where this big world of signal and image processing is." + }, + { + "text": "That Fourier is what everybody knew, and what people automatically used, and the new, new one is wavelets, where this is the simplest set of wavelets, and this isn't the one that the FBI uses, by the way." + }, + { + "text": "The FBI uses a more, a more, a smoother wavelet." + }, + { + "text": "Instead of jumping from one to minus one, it's a smooth, cutoff." + }, + { + "text": "And, that's what we'll be in, in JPEG 2000." + }, + { + "text": "OK, so that's that application." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk14.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..8f1debcca7ae641417e7ed0a630d269963c01302 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now let me come to my, the, the math, the linear algebra part of the lecture." + }, + { + "text": "Well, we've actually seen a change of basis." + }, + { + "text": "So let, let me just review that change of basis idea, and then the, and then the transformation to a matrix." + }, + { + "text": "OK, so, so this, I hope you see that these applications are really big." + }, + { + "text": "Now I have to talk a little about change of basis and little about that, the, the matrix." + }, + { + "text": "OK. OK. OK." + }, + { + "text": "So change of basis." + }, + { + "text": "Basically, forgive that pun, OK, I have, I have, I have my vector in one basis, and I want to change to a different one." + }, + { + "text": "Actually, you saw it for the wavelet case." + }, + { + "text": "So I need the, the, let the matrix W, the columns of W, be the new basis vectors." + }, + { + "text": "Then the change of basis involves, just as it did there, W inverse." + }, + { + "text": "So we have the vector, vector, say, x in the old basis, and we, that converts to a vector, let's say, c in the new basis, and the relation is exactly what we had there, that x is Wc." + }, + { + "text": "That's the, that's the, that's the, that's the step we have to take." + }, + { + "text": "There's a matrix W that gives us a change of basis." + }, + { + "text": "OK." + }, + { + "text": "I, I, what I want to do is think about mat- transformations and matrices." + }, + { + "text": "So here's, here's the question, that, that, to complete this lecture." + }, + { + "text": "Suppose I have a linear transformation T. So it's, it's a, it's a, we, we would think of it as an A, as a n by n matrix." + }, + { + "text": "And it's computed with respect to a certain basis." + }, + { + "text": "So T, so, no, I'm sorry." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk15.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..dbc5ad92f06633f3366a78c24c0c7c08b058ee63 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "I've got the transformation T, period." + }, + { + "text": "That's taking eight-dimensional space to eight-dimensional space." + }, + { + "text": "Now let's get matrices in there." + }, + { + "text": "OK." + }, + { + "text": "So, so with respect to, with respect to a fir- a first basis, say, V1 up to V8, it has a matrix A. I'm just setting up letters here." + }, + { + "text": "With respect to a second basis, say, I'll make it U1 up to- or W1, since I've used Ws, W1 up to W8, it has a matrix B." + }, + { + "text": "And my question is, what's the connection between A and B?" + }, + { + "text": "How is the matrix- the transformation T is settled." + }, + { + "text": "We could say it's a rotation, for example." + }, + { + "text": "So that would be one transformation of eight-dimensional space, just spin it a little." + }, + { + "text": "Or project it." + }, + { + "text": "Or, or, whatever, whatever linear transformation we've got." + }, + { + "text": "Now we have to remember, so I- so first- my first step is to remind you how you create that matrix A." + }, + { + "text": "Then my second step is, we would use the same method to create B, but because it came from the same transformation, there's got to be a relation between A and B." + }, + { + "text": "What's the- what's the relation between A and B?" + }, + { + "text": "And let me jump to the answer on that one." + }, + { + "text": "That if I have- if I have the same transformation, and I'm compute- its matrix in one basis and then I compute it in another basis, those two matrices are similar." + }, + { + "text": "So these two matrices are similar." + }, + { + "text": "Now, do you remember what similar matrices meant?" + }, + { + "text": "Similar." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk16.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..9d019933a190fe645eec785d8363a0940d0f76a4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "A is similar- the two matrices are similar." + }, + { + "text": "Similar." + }, + { + "text": "And what do I mean by that?" + }, + { + "text": "I mean that I take the matrix B and I can compute it from the matrix A using some similarity, some matrix M on one side and M inverse on the other." + }, + { + "text": "And this M will be the change of basis matrix." + }, + { + "text": "This part of the lecture is admittedly compressed." + }, + { + "text": "What I wanted you to- it's really the conclusion that I want you to spot." + }, + { + "text": "Now I have to go back and say, what does it mean for A to be the matrix of this transformation T?" + }, + { + "text": "So I have to remind you what that meant." + }, + { + "text": "That was in the last lecture." + }, + { + "text": "Then this is the conclusion, that if I change to a different basis, we now know- see, if I change to a different basis, two things happen." + }, + { + "text": "Every vector has new coordinates." + }, + { + "text": "There, the rule is this one, between the old coordinates and the new ones." + }, + { + "text": "Every matrix changes." + }, + { + "text": "Every transformation has a new matrix." + }, + { + "text": "And the new matrix is related this way." + }, + { + "text": "The M could be the same as the W. The M there could be the W here." + }, + { + "text": "OK." + }, + { + "text": "So can I, in the remaining minutes, recapture my lecture, the end of my lecture that was just before Thanksgiving, about the matrix?" + }, + { + "text": "OK. What's the matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk17.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..f82f2cc230f9f2720733e8b152f84f80f1341c9f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll just take one basis." + }, + { + "text": "So now I'm going to- this part is going to go onto this board here." + }, + { + "text": "What is the matrix?" + }, + { + "text": "What is A?" + }, + { + "text": "OK." + }, + { + "text": "Using a basis v1 up to v8." + }, + { + "text": "OK. What's the point?" + }, + { + "text": "The point is, if I know what the transformation does to those eight basis vectors, I know it completely." + }, + { + "text": "I know T, I know everything about T, I know T completely from knowing what T does to v1, what T does to v2, what T does to v8." + }, + { + "text": "Why is that?" + }, + { + "text": "It's because T is a linear transformation." + }, + { + "text": "So that if I know what these outputs are, so these are the inputs, v1 up to v8, these are the outputs from the transformation, like every one rotated, every one projected, whatever transformation I've done, then why is it that I know everything?" + }, + { + "text": "How does linearity work?" + }, + { + "text": "Why?" + }, + { + "text": "This is because every x is some combination of these basis vectors, right?" + }, + { + "text": "c1 v1, c2 v2, c8 v8." + }, + { + "text": "That's the whole point of a basis, that every vector is a combination of the basis vectors in exactly one way." + }, + { + "text": "And then, what is T of x?" + }, + { + "text": "The point is, I claim that we know T of x completely for every x, because every x is a combination of those, and now we use the linear transformation part to say that the output from x has to be c1 times the output from v1 plus c2 times the output from v2 and so on, up through c8 times the output from v8." + }, + { + "text": "So this is like just saying, OK, we know everything when we know what T does to each basis vector." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk18.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..d9c718592303012586f37aed3dc53271be8cef29 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "So those are the eight things we need." + }, + { + "text": "Now, but we need these answers in this basis." + }, + { + "text": "So T- so this first output is some combination of the eight basis vectors." + }, + { + "text": "So write T times the first- acting on the first input, in other words, write the first output as a combination of the basis vectors." + }, + { + "text": "Say a11 v1 plus a21 v2 and so on, a81 v8." + }, + { + "text": "Write T of v2 as some combination, a12 of v1, a22 of v2 and so on." + }, + { + "text": "I'm creating the matrix A, column by column." + }, + { + "text": "Those numbers go in the first column, these numbers go in the second column." + }, + { + "text": "The matrix A that this is our matrix that represents T in this basis is these numbers." + }, + { + "text": "a11 down to a18, a21 down to a28 and so on." + }, + { + "text": "OK. That's the recipe." + }, + { + "text": "In other words, if I give you a transformation and a basis, that's what I have to give you." + }, + { + "text": "The inputs are the basis and to tell you what the transformation is." + }, + { + "text": "And then you tell me, you compute T for each basis, expand that result in the basis, and that gives you the sixty-four numbers that go into the matrix A." + }, + { + "text": "Let me suppose, let's close with the best example of all." + }, + { + "text": "Suppose v1 to v8, this basis, is the eigenvectors." + }, + { + "text": "Suppose we have an eigenvector basis." + }, + { + "text": "So that T of vi is just, is in the same direction as vi." + }, + { + "text": "Now my question is, what is A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk19.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..4bc0bda81becbd032c626bcaab40cca8eaa39155 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Can you carry through the steps?" + }, + { + "text": "Let's, let's do them together, because we can do it in one minute." + }, + { + "text": "So we've chosen this perfect basis." + }, + { + "text": "And actually, with signal image processing, they might look for the eigenvectors, but that would take more calculation time than just saying, OK, we'll use the wavelet basis, or OK, we'll use the Fourier basis." + }, + { + "text": "But the very best basis is the eigenvector basis." + }, + { + "text": "OK, what's the matrix?" + }, + { + "text": "So, what's the first column of the matrix?" + }, + { + "text": "How do I get the first column?" + }, + { + "text": "I take the first basis vector v1." + }, + { + "text": "I op- I look to see what does the transformation do to it." + }, + { + "text": "The output is lambda one v1." + }, + { + "text": "I express that output as a combination, so the first input is v1." + }, + { + "text": "Its output is lambda one v1." + }, + { + "text": "Now write lambda one v1 as a combination of the basis vectors." + }, + { + "text": "Well, it's already done." + }, + { + "text": "It's just lambda one times the first basis vector and zero times the others." + }, + { + "text": "So this first column will have lambda one and zeros." + }, + { + "text": "OK?" + }, + { + "text": "Second input is v2." + }, + { + "text": "Output is lambda two v2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk2.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..44553739c24736b408dbd01c3688e075b25f9a15 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it has to be compressed." + }, + { + "text": "The standard compression, and still used in, in the, with these lectures, is, called JPEG." + }, + { + "text": "I think that stands for a Joint Photographic Experts Group." + }, + { + "text": "They established a system of compression." + }, + { + "text": "And I just want to tell you what it's about." + }, + { + "text": "It's a change of basis." + }, + { + "text": "What, what's, what basis do we have?" + }, + { + "text": "The, the current basis we have is, you could say, the standard basis is every pixel give a value." + }, + { + "text": "So that's like, we have a vector x, which is five hundred and twelve squared long, and in the i-th position, we get a number like one twenty one or something, the next, the pixel next to it might be one twenty four, maybe where, maybe where the, where my tie, begins to end." + }, + { + "text": "So if it was mostly blue shirt, this would be a slight difference in shading, but pretty close." + }, + { + "text": "Then the tie would be a different color." + }, + { + "text": "So, so we might have quite a few pixels for the blue shirt and a whole lot more for the blackboard that are very close." + }, + { + "text": "And that's what, are very correlated." + }, + { + "text": "And that's what gives us the possibility of compression." + }, + { + "text": "For example, before the lecture starts, if we had a blank blackboard, then there's an image, but it would make no sense to take that image and tell you what it is pixel by pixel." + }, + { + "text": "I mean, there's a case in which all pixel values, all gray levels are the same, or practically the same, depending on the erasing of the board, but extremely close." + }, + { + "text": "And so that's an image where the standard basis is lousy." + }, + { + "text": "That's, that's the basic fact." + }, + { + "text": "That, that the standard basis which gives the value of every pixel makes no use of the fact that we're getting a whole lot of pixels whose gray levels, the neighboring pixels tend to have the same gray level as the, as their, as their neighbors." + }, + { + "text": "So to take, how do we take advantage of that fact?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk20.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..57e892c1f19c9a45e5f14bb334eab942b0d796a2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk20.json @@ -0,0 +1,32 @@ +[ + { + "text": "OK, write that output as a combination of the v's." + }, + { + "text": "It's already done." + }, + { + "text": "It's just lambda two times the second v. So we need, in the second column, we have lambda two times the second v. Well, you see what's coming." + }, + { + "text": "That in that basis, in the eigenvector basis, the matrix is diagonal." + }, + { + "text": "So that's the perfect basis." + }, + { + "text": "That's the basis we'd love to have for image processing, but to find the eigenvectors of our pixel matrix would be too expensive." + }, + { + "text": "So we do something cheaper and close, which is to choose a good basis like, like wavelengths." + }, + { + "text": "OK, thanks." + }, + { + "text": "So quiz review on Wednesday, all day." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk3.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..8e246b42e71ac0ef99e39e59a7562c71f3da61b4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, one basis vector that would be extremely nice to, one vector that would be extremely nice to include in the basis would be a vector of all ones." + }, + { + "text": "That's not in our standard basis." + }, + { + "text": "So our, so let me just write again." + }, + { + "text": "The standard basis would, is, is our, is our one and all the rest zeros, zero, one, and all the rest zeros, everybody knows what the standard basis is." + }, + { + "text": "Now, any other basis for our, so this is, for this very high-dimensional space, now I'm going to speak about a better basis, better basis, and let me just emphasize, one vector that would be extremely nice to have in that basis is the vector of all ones." + }, + { + "text": "Why is that?" + }, + { + "text": "Let me just say again." + }, + { + "text": "Because that vector of all ones, by itself, one vector is, is able to completely give the information on a solid image." + }, + { + "text": "Of course, our image won't be solid, it'll have a mix of, of, solid and, and signal." + }, + { + "text": "So that one vector, but that, having that one vector in the basis is, is, is going to save us a whole lot." + }, + { + "text": "Now the question is, what other vectors should be in the basis?" + }, + { + "text": "The, the extreme vector in the basis might be a vector of one minus one, one minus one, one minus one." + }, + { + "text": "That would be a vector that shows, I mean, that's like a checkerboard vector, right?" + }, + { + "text": "That's a vector that would, if, if we had, if, if the image was like a huge checkerboard of plus minus, plus minus, plus minus, that vector would carry the whole signal." + }, + { + "text": "But much more common would be maybe to have half the image, darker and the other half lighter." + }, + { + "text": "So another image, another vector that might be quite useful in here would be half ones and half minus ones." + }, + { + "text": "I'm just trying to get across the idea of, that a basis could be, that first of all, we've got, the basis is at our disposal." + }, + { + "text": "Like, we're free to choose that." + }, + { + "text": "And it's a billion dollar decision what we choose." + }, + { + "text": "So, and TV people would rather, would prefer one basis based on the way the, the signal is scanned, and movie people would prefer another." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk4.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..811c58ffd5e28e456b42de439fa8cee4339bd2a6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "I mean, there's giant politics in this question that really reduces to a, to a linear algebra problem what basis to choose." + }, + { + "text": "I'll just mention the best known basis, which is, which JPEG uses, let me put that here, is the Fourier basis." + }, + { + "text": "So when you, when you use the Fourier basis, that includes, this is the constant vector, the DC vector, if we're electrical engineers, the, the, the vector of all ones, so it would include one, one, one, one." + }, + { + "text": "Often, eight by eight is a good choice." + }, + { + "text": "Eight by eight is a, is a good choice." + }, + { + "text": "So, what do I mean by this eight by eight?" + }, + { + "text": "I mean that the big signal, which is five twelve by five twelve, gets broken down, and JPEG does this, into eight by eight blocks." + }, + { + "text": "And we, sort of, this is too much to deal with at once." + }, + { + "text": "So what JPEG does is take this eight by eight block, which is sixty-four coefficients, sixty-four, pixels, and changes the basis on the, on that piece." + }, + { + "text": "And then, now, let's see, I was going to write down Fourier, so you remember Fourier is, is this vector of all ones, and then, the vector, oh, well, actually, I gave a lecture earlier about the Fourier matrix, these, this matrix whose columns are powers of a, of a, complex number w. I, I won't repeat that, because I'm not, I don't want to go into the details of the Fourier basis." + }, + { + "text": "Just to tell you how compression works." + }, + { + "text": "So what happens in JPEG?" + }, + { + "text": "What happens to the video, to a, to each image of, of, of these lectures?" + }, + { + "text": "The, it gets broken into eight by eight blocks." + }, + { + "text": "OK." + }, + { + "text": "Within each block, we have sixty-four coefficients, sixty-four basis vectors, sixty-four pixels, and we change basis in sixty-four dimensional space, using these Fourier vectors." + }, + { + "text": "Just, no, that was a lossless step." + }, + { + "text": "Let, let me, let me emphasize." + }, + { + "text": "In comes the signal." + }, + { + "text": "x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk5.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..7ce7441a356838f6e496da3b2d782533cfb4ad1b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "We change basis." + }, + { + "text": "This is the basis change." + }, + { + "text": "Change basis." + }, + { + "text": "Choose a better basis." + }, + { + "text": "So it produces, the, coefficients c. So sixty-four pixels come in, sixty-four coefficients come out." + }, + { + "text": "Now comes the compression." + }, + { + "text": "Now come, this was lossless." + }, + { + "text": "It's just, we know that R64 has plenty of basis, and we've chosen one." + }, + { + "text": "Now, in that basis, we write, we write the signal in that basis, and that's what my lecture, that's the math part of my lecture." + }, + { + "text": "Now here's the application part." + }, + { + "text": "The next part is going to be the compression step." + }, + { + "text": "And that's lossy." + }, + { + "text": "We're going to lose information." + }, + { + "text": "And what, what will actually happen at that step?" + }, + { + "text": "Well, one thing we could do is just throw away the small coefficients." + }, + { + "text": "So that would be, that's called thresholding." + }, + { + "text": "We set some threshold." + }, + { + "text": "Every coefficient, every basis vector that's not in there more than the threshold value, and we set some threshold so that our eye can't see the difference, whether we throw away that, or can hardly see the difference, whether we throw away that little bit of that basis vector or keep it." + }, + { + "text": "So this compression step produces a compressed set of coefficients." + }, + { + "text": "Let me, I'll just keep going here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk6.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..e51518b0b218267f8c2f0d7243d31fec00ba9b42 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, so it keeps going." + }, + { + "text": "This compression step produces some coefficients c hat." + }, + { + "text": "And with lots of, with many zeros." + }, + { + "text": "So that's where the compression came." + }, + { + "text": "Probably there's enough of this vector of all ones, we very seldom throw that away." + }, + { + "text": "Usually its coefficient will be large." + }, + { + "text": "But the coefficient of something like this, that quickly alternating vector, there's probably very little of that in any smooth signal." + }, + { + "text": "I mean, that's high frequent- this is, this is low frequency, zero frequency." + }, + { + "text": "This stuff is the highest frequency we could have, and there's a, if the noise, the, the jitter is producing that sort of output, but a smooth lecture like this one is, has very little of that highest frequency." + }, + { + "text": "Very little noise in this lecture." + }, + { + "text": "OK." + }, + { + "text": "So, so we throw away whatever there is, and we, we're left with just a few coefficients, and then we reconstruct a signal using those coefficients." + }, + { + "text": "We take the, those coefficients times their basis vectors, but this sum doesn't have sixty-four terms anymore." + }, + { + "text": "Probably it has about two or three terms." + }, + { + "text": "So that, if we say it has three terms." + }, + { + "text": "From sixty-four down to three, that's compression of twenty-one to one." + }, + { + "text": "That's the kind of compression you're looking for." + }, + { + "text": "And everybody is looking for that sort of compression." + }, + { + "text": "Let's see, I guess I met the problem with the FBI and fingerprints." + }, + { + "text": "So there's a whole lot of still images." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk7.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..4cdf43a95d584ba42202d1c77ba5f96a998319d5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "You know, you, with your thumb, you make these inky marks, which, go somewhere." + }, + { + "text": "You used to go to Washington and get stored in a big file." + }, + { + "text": "So Washington had a file of thirty million murderers, cheaters on quizzes, other stuff, and, and actually, there was no way to retrieve them in time." + }, + { + "text": "Like, so, so suppose you're at the police station, they say, OK, this person may have done this, check with Washington, have they got his or her fingerprints on file." + }, + { + "text": "Well, Washington won't know the answer within a week, if it's got filing cabinets full of fingerprints." + }, + { + "text": "So of course the natural step is digitize them." + }, + { + "text": "So all fingerprints are now digitized, so now it's at least electronic, but still there's too much information in each, each one." + }, + { + "text": "I mean, you can't search through that many, uh, fingerprints if you, if, if the digital image is five twelve squared by five twelve squared, if it's that many pixels." + }, + { + "text": "So you get compressed." + }, + { + "text": "So the FBI had to decide what basis to choose for compression of fingerprints, and then they built a big new facility in West Virginia and that's where fingerprints now are sent." + }, + { + "text": "So if you, I think if you get your fingerprints done now at the police station, if it's an up-to-date police station, it's, it happens digitally and the signal is sent digitally, and then in West Virginia it's compressed and indexed." + }, + { + "text": "And then, if they want to find you, they can do it within minutes, instead of within a week." + }, + { + "text": "OK." + }, + { + "text": "So this compression is, comes up for signals, for images." + }, + { + "text": "For video, which is like these lectures, uh, there's another aspect." + }, + { + "text": "You could treat the video as one still image after another one, and compress each one and then run them and make a video." + }, + { + "text": "But that misses, well, you can see why that's not optimal." + }, + { + "text": "In video, so for in a video thing, you have a sequence of images, so video is really a sequence of images, but what about one image to the next image?" + }, + { + "text": "They're extremely correlated." + }, + { + "text": "I mean, that, I'm getting an image every split second, and although I'm moving slightly, that's what's producing the, jumpy motion on the video." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk8.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..41f54e28ef2064485cf009d9b5e4574263d3680d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "But I'm not, like, you know, each, each image in the sequence is pretty close to the one before." + }, + { + "text": "So you have to use, like, prediction and correction." + }, + { + "text": "I mean, you, my, the image of me one instant, one time step later, you would assume would be the same, and then plus a small correction." + }, + { + "text": "And you would only code and digitize the correction, and compress the correction." + }, + { + "text": "So the sequence of images that's highly correlated, and the problem in compression is always to use this correlation, this fact that in time or in space, things don't change instantly, they, they're very often smooth changes, and, you can predict one value from the previous value." + }, + { + "text": "OK." + }, + { + "text": "So that's the, those are applications, which are pure linear algebra." + }, + { + "text": "I could, maybe I'll, maybe you'll allow me to tell you the, and the book describes, the new basis that's, the competition for Fourier." + }, + { + "text": "So the competition for Fourier is called wavelets, and I can describe what that basis is like, say, in the eight by eight case." + }, + { + "text": "So that eight by eight wavelet basis is the vector of all ones, eight ones, then the vector of four ones and four minus ones, then the vector of two ones and two minus ones and four zeros, and also the vector of four zeros and two ones and two minus ones." + }, + { + "text": "So now I'm up to four, and I need four more, right, for R8?" + }, + { + "text": "So the next basis vector will be one minus one and six zeros, and then three more like that, with a one minus one there and there and there." + }, + { + "text": "So those are eight vectors in eight-dimensional space." + }, + { + "text": "Those are, those are called wavelets, and you, and it's a very simple wavelet choice." + }, + { + "text": "It's a more sophisticated choice." + }, + { + "text": "This is a little jumpy, to jump between one and minus one." + }, + { + "text": "And actually, you can see now, suppose you compare the wavelet basis with the Fourier basis above." + }, + { + "text": "How could I write this guy, which is in the Fourier basis, it's an eight, it's a vector in R8, how would I write that as a combination of the wavelet basis?" + }, + { + "text": "Do you, have I told you enough about the wavelet basis that you can see?" + }, + { + "text": "How does this very fast guy, what combination of the wavelet basis is that very fast guy?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk9.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..2bc1d292fd925c01e44d5599863fa8cb2bcfba79 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_4_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It would be this one, it would be the sum of these four, right?" + }, + { + "text": "That very fast guy will be that one minus one, and the next one, and the next one, and the next one." + }, + { + "text": "So this is the sum of those last four wavelets." + }, + { + "text": "This one we've kept, and so on." + }, + { + "text": "So, each, well, every, well, that's what a basis does." + }, + { + "text": "Every vector in R8 is some combination of those, and for the linear algebra, we have, so the linear algebra is this step, find the coefficients." + }, + { + "text": "That's, that's the step we want to take." + }, + { + "text": "If I give you the basis, like this wavelet basis, and I give you the pixel, so here are the pixel values, p1, p2, down to p8." + }, + { + "text": "What's, what's the job?" + }, + { + "text": "What's the linear algebra here?" + }, + { + "text": "So this is, these are the values, this is in the standard basis, right?" + }, + { + "text": "Those are just the values at eight successive points." + }, + { + "text": "I guess I'm dropping down to one dimension instead of eight by eight, I'm just going to take eight pixel values along that first top row." + }, + { + "text": "So I, what do I want to do?" + }, + { + "text": "In the standard basis, here are the pixel values." + }, + { + "text": "I want to write that as a combination of c1 times this guy, plus c2 times this guy, plus c3, these are the coefficients, plus c4 times this one." + }, + { + "text": "Do you see what I'm doing?" + }, + { + "text": "I want to write this vector p as a combination of c1 times the first wavelet, plus c8 times the eighth wavelet." + }, + { + "text": "That's the, that's the transform step." + }, + { + "text": "That's the lossless step, that's the step from p, oh, I'm calling it p here and I called it x there, so let me, at the risk of moving and therefore making this jumpy, suppose the signal I'm now calling p, the set of pixel values and I'm looking for the coefficients." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk0.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..ed695ba203c725aa80144eb85fb8edd6706cbb8c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay." + }, + { + "text": "So coming near the end of the course, this lecture will be a mixture of the linear algebra that comes with a change of basis." + }, + { + "text": "And a change of basis from one basis to another basis is something you really do in applications." + }, + { + "text": "And I would like to talk about those applications." + }, + { + "text": "I got a little bit involved with compression, compressing a signal, compressing an image, and that's exactly change of basis." + }, + { + "text": "And then the main theme in this chapter is the connection between a linear transformation, which doesn't have to have coordinates, and the matrix that tells us that transformation with respect to coordinates." + }, + { + "text": "So the matrix is the coordinate-based description of the linear transformation." + }, + { + "text": "Let me start out with the nice part, which is some, just to tell you something about image compression." + }, + { + "text": "Those of you, well, everybody's going to meet compression, because you know that the amount of data that we're getting, well, these lectures are compressed." + }, + { + "text": "So that actually, probably you see my motion as jerky, shall I use that word?" + }, + { + "text": "Have you looked on the web?" + }, + { + "text": "I should like to find a better word." + }, + { + "text": "Compressed, let's see." + }, + { + "text": "So my, the, the, the complete signal is, of course, in those video cameras and in the videotape, but that goes to the bottom of building nine, and out of that comes a jumpy motion, because it uses a standard system for compressing images." + }, + { + "text": "And, you'll notice that the stuff that sits on the board comes very clearly, but it's my motion that, that, that needs a whole lot of bits, right?" + }, + { + "text": "So, and if I were to run up and back, up there and back, that would need too many bits and they'd, I'd be compressed even more." + }, + { + "text": "So, what does compression mean?" + }, + { + "text": "Can I, let me just think of a still image." + }, + { + "text": "And, and of course, satellites, oh, there's, and, and computations of the climate, computations of combustion, the, computers and sensors of all kinds are just giving us overwhelming amounts of data." + }, + { + "text": "The web is, too." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk1.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..276b7aacae39769ce0e1627c108ec463ccf35faa --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, some compression can be done with no loss." + }, + { + "text": "Lossless compression is possible just using, sort of, the fact that, there's, there are redundancies." + }, + { + "text": "But I'm talking here about lossy compression." + }, + { + "text": "So I'm talking about, here's an image." + }, + { + "text": "And what does an image consist of?" + }, + { + "text": "It consists of a lot of little pixels, right?" + }, + { + "text": "Maybe five hundred and twelve by five hundred and twelve." + }, + { + "text": "Two to the ninth by two to the ninth pixels, and each, so this is pixel number one one, so that's a pixel, and if we're in black and white, the typical pixel would tell us a grayscale from zero to two fifty five." + }, + { + "text": "So a pixel is usually a, a value of a, a, one of the x i, so this would be the i-th pixel, it, it's usually a real number on a scale from zero to two fifty five." + }, + { + "text": "In other words, two to the eighth possibilities." + }, + { + "text": "So usually, that's the, that's the standard, so, so that, that's eight, eight bits." + }, + { + "text": "But then we have that for every, every pixel, so we have five hundred and twelve squared pixels." + }, + { + "text": "We're, we're really operating, x is a vector in Rn, but what is n?" + }, + { + "text": "n is five hundred and twelve squared." + }, + { + "text": "That's, that's our problem right there." + }, + { + "text": "We're, a pixel is a vector that gives us the information about the image, I'm sorry, the image that comes through is a vector of, of that length, that, that's the information we have about the image." + }, + { + "text": "If it's a color image, we would have three times that length, because we'd have, we'd need three coordinates to get color." + }, + { + "text": "So it would be three times five hundred and twelve squared." + }, + { + "text": "It's an enormous amount of information, and we couldn't send out the image for these lectures without compressing it." + }, + { + "text": "We, we, it, it would be, it would overload the system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk10.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..db2f6371da88f739758d4ebae59b4fdffa270d6f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "Tell me how to do it." + }, + { + "text": "How do I find the, if I give you eight basis vectors and I give you the input signal and I ask for the coefficients, what do I do?" + }, + { + "text": "What's the, what's the step?" + }, + { + "text": "I want, I'm trying to solve this, I want to know the eight coefficients, so I'm changing from the standard basis, which is just the eight grayscale values, to the wavelet basis, where this same vector is represented by eight numbers." + }, + { + "text": "It's got to take eight numbers to tell you a vector in R8, and those eight numbers are the coefficients of the basis." + }, + { + "text": "Look, we've done this thing before." + }, + { + "text": "What do we, here, there is the equation in vector notation." + }, + { + "text": "We want to see it as a matrix." + }, + { + "text": "This is a combination of columns of the wavelet matrix, right?" + }, + { + "text": "This is p equals c1, c2, down to c8, and these guys are the columns." + }, + { + "text": "I mean, this is the step that we constantly take in this course." + }, + { + "text": "The first basis vector goes in the first column, the second basis vector goes in the second column, and so on." + }, + { + "text": "The eight columns of this wavelet matrix are the eight basis vectors." + }, + { + "text": "This is a wavelet matrix W. So, the step to change basis." + }, + { + "text": "So now I'm finally coming to this change of basis." + }, + { + "text": "So the change of basis, let me stay with this board, but, well, let me just go above it here." + }, + { + "text": "So the standard basis we know, the wavelet basis we have here, and the transform is simply solve the equations p equal Wc." + }, + { + "text": "So the coefficients are W inverse p, right?" + }, + { + "text": "This shows a critical point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk11.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..8346f1691f9a546b0252c3e0960539efff45ec1f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "A good basis has a nice, fast inverse." + }, + { + "text": "So good means, good basis means what?" + }, + { + "text": "So this is like the billion dollar competition, and it's not over yet." + }, + { + "text": "People are going to come up with better bases than these." + }, + { + "text": "So a good basis will be, first good thing would be fast." + }, + { + "text": "I have to be able to multiply by W fast and multiply by W, by its inverse fast." + }, + { + "text": "That's, if a basis doesn't allow you to do that fast, then it's going to take so much time that you can't afford it." + }, + { + "text": "So these bases, the Fourier basis, everybody said, OK, I know how to deal quickly with the Fourier basis, because we have something called the fast Fourier transform." + }, + { + "text": "So there's a FFT that came in my earlier lecture and comes in the last chapter of the book." + }, + { + "text": "So change of basis is done, if for the Fourier basis, is done fast by the FFT and there's a fast wavelet transform." + }, + { + "text": "I can change, for this wavelet example, this matrix is easy to invert." + }, + { + "text": "It's just somebody had a smart idea in choosing that wavelet basis and inverting it, it has a nice inverse." + }, + { + "text": "Actually, you can see why it has a nice inverse." + }, + { + "text": "Do you see any property of these eight basis vectors?" + }, + { + "text": "Well, I've only written five of them, but if you see that property for those five, you'll see it for the three remaining." + }, + { + "text": "What, if I give you those eight vectors and ask, what's a nice property?" + }, + { + "text": "Well, you would say, first, they're all ones and minus ones and zeros, so every multiplication is very fast using just, in binary." + }, + { + "text": "But what's the other great property of those vectors?" + }, + { + "text": "Anybody see it?" + }, + { + "text": "So, of course, when I think about a basis, one nice property, I don't have to have it, but I'm happy if it's there, is that they're orthogonal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk12.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..c0eaf69080e43e238bee148545d1b059bef72365 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "If the basis vectors are orthogonal, then I'm in good shape." + }, + { + "text": "And these are, do you see, take the dot product of that with that, you get four plus ones and four minus ones, you get zero." + }, + { + "text": "Take the dot product of that with that, you get two plus ones and two minus ones." + }, + { + "text": "Or the dot product of that with that, two plus ones and two minus ones." + }, + { + "text": "You can easily check that that's an orthogonal basis." + }, + { + "text": "It's not orthonormal." + }, + { + "text": "I could, to fix it up, I should divide by the length to make them unit vectors." + }, + { + "text": "Let's suppose I do that." + }, + { + "text": "So somewhere in here I've got to account for the fact that this has length square root of eight, that has length square root of four, that has length square root of two." + }, + { + "text": "But that's just a constant factor that's easy to --." + }, + { + "text": "So suppose we've done that." + }, + { + "text": "Then tell me what's W inverse." + }, + { + "text": "That's what chapter four, section four point four was about." + }, + { + "text": "If we have orthonormal columns, what- then the inverse is the same as the transpose." + }, + { + "text": "So if we have a fast way to multiply by W, which we do, the inverse is going to look just the same and we'll have a fast way to do W inverse." + }, + { + "text": "So that's, the wavelet basis passes this requirement for fast." + }, + { + "text": "We can use it fast." + }, + { + "text": "But there's a second requirement, is it any good?" + }, + { + "text": "Because the very fastest thing we could do would be not to change basis at all." + }, + { + "text": "Right?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk13.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..4de80b529af0604a4e0b9b0291a8822dc165b83a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Fastest thing would be, OK, stay with a standard basis, stay with eight pixel values." + }, + { + "text": "But that was poor from compression point of view, right?" + }, + { + "text": "Those eight pixel values, if I just took those eight numbers, I can't throw some of those away." + }, + { + "text": "If I throw away ninety percent, if I compressed ten to one, and throw away ninety percent of my pixel values, well, my picture's just gone dark." + }, + { + "text": "Whereas the basis that was good, the wavelet basis or the Fourier basis, if I throw away c5, c6, c7 and c8, all I'm throwing away is little blips that are probably there in very small amounts." + }, + { + "text": "So the second property that we need is good compression." + }, + { + "text": "So, so first it, it has to be fast, and secondly, it has to be a few basis factors should come close to the signal." + }, + { + "text": "So, so a few, few is enough." + }, + { + "text": "Can I write it that way?" + }, + { + "text": "A few basis factors are enough to reproduce the image, just exactly as on the video of these 18.06 lectures." + }, + { + "text": "I don't know what the compression rate is." + }, + { + "text": "I'll ask, David, who, who does the compression, and, by the way, I'll try to get the lectures, that are relevant for the quiz, up onto the web, in time." + }, + { + "text": "So I'll send him a message today." + }, + { + "text": "So, at the point, so he's using the Fourier basis, because the JPEG, so JPEG 2000, which will be the next standard for image compression, will include wavelets." + }, + { + "text": "So, I mean, you're, you're actually getting a kind of up to date, picture of where this big world of signal and image processing is." + }, + { + "text": "That Fourier is what everybody knew, and what people automatically used, and the new, new one is wavelets, where this is the simplest set of wavelets, and this isn't the one that the FBI uses, by the way." + }, + { + "text": "The FBI uses a more, a more, a smoother wavelet." + }, + { + "text": "Instead of jumping from one to minus one, it's a smooth, cutoff." + }, + { + "text": "And, that's what we'll be in, in JPEG 2000." + }, + { + "text": "OK, so that's that application." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk14.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..8f1debcca7ae641417e7ed0a630d269963c01302 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now let me come to my, the, the math, the linear algebra part of the lecture." + }, + { + "text": "Well, we've actually seen a change of basis." + }, + { + "text": "So let, let me just review that change of basis idea, and then the, and then the transformation to a matrix." + }, + { + "text": "OK, so, so this, I hope you see that these applications are really big." + }, + { + "text": "Now I have to talk a little about change of basis and little about that, the, the matrix." + }, + { + "text": "OK. OK. OK." + }, + { + "text": "So change of basis." + }, + { + "text": "Basically, forgive that pun, OK, I have, I have, I have my vector in one basis, and I want to change to a different one." + }, + { + "text": "Actually, you saw it for the wavelet case." + }, + { + "text": "So I need the, the, let the matrix W, the columns of W, be the new basis vectors." + }, + { + "text": "Then the change of basis involves, just as it did there, W inverse." + }, + { + "text": "So we have the vector, vector, say, x in the old basis, and we, that converts to a vector, let's say, c in the new basis, and the relation is exactly what we had there, that x is Wc." + }, + { + "text": "That's the, that's the, that's the, that's the step we have to take." + }, + { + "text": "There's a matrix W that gives us a change of basis." + }, + { + "text": "OK." + }, + { + "text": "I, I, what I want to do is think about mat- transformations and matrices." + }, + { + "text": "So here's, here's the question, that, that, to complete this lecture." + }, + { + "text": "Suppose I have a linear transformation T. So it's, it's a, it's a, we, we would think of it as an A, as a n by n matrix." + }, + { + "text": "And it's computed with respect to a certain basis." + }, + { + "text": "So T, so, no, I'm sorry." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk15.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..dbc5ad92f06633f3366a78c24c0c7c08b058ee63 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "I've got the transformation T, period." + }, + { + "text": "That's taking eight-dimensional space to eight-dimensional space." + }, + { + "text": "Now let's get matrices in there." + }, + { + "text": "OK." + }, + { + "text": "So, so with respect to, with respect to a fir- a first basis, say, V1 up to V8, it has a matrix A. I'm just setting up letters here." + }, + { + "text": "With respect to a second basis, say, I'll make it U1 up to- or W1, since I've used Ws, W1 up to W8, it has a matrix B." + }, + { + "text": "And my question is, what's the connection between A and B?" + }, + { + "text": "How is the matrix- the transformation T is settled." + }, + { + "text": "We could say it's a rotation, for example." + }, + { + "text": "So that would be one transformation of eight-dimensional space, just spin it a little." + }, + { + "text": "Or project it." + }, + { + "text": "Or, or, whatever, whatever linear transformation we've got." + }, + { + "text": "Now we have to remember, so I- so first- my first step is to remind you how you create that matrix A." + }, + { + "text": "Then my second step is, we would use the same method to create B, but because it came from the same transformation, there's got to be a relation between A and B." + }, + { + "text": "What's the- what's the relation between A and B?" + }, + { + "text": "And let me jump to the answer on that one." + }, + { + "text": "That if I have- if I have the same transformation, and I'm compute- its matrix in one basis and then I compute it in another basis, those two matrices are similar." + }, + { + "text": "So these two matrices are similar." + }, + { + "text": "Now, do you remember what similar matrices meant?" + }, + { + "text": "Similar." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk16.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..9d019933a190fe645eec785d8363a0940d0f76a4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "A is similar- the two matrices are similar." + }, + { + "text": "Similar." + }, + { + "text": "And what do I mean by that?" + }, + { + "text": "I mean that I take the matrix B and I can compute it from the matrix A using some similarity, some matrix M on one side and M inverse on the other." + }, + { + "text": "And this M will be the change of basis matrix." + }, + { + "text": "This part of the lecture is admittedly compressed." + }, + { + "text": "What I wanted you to- it's really the conclusion that I want you to spot." + }, + { + "text": "Now I have to go back and say, what does it mean for A to be the matrix of this transformation T?" + }, + { + "text": "So I have to remind you what that meant." + }, + { + "text": "That was in the last lecture." + }, + { + "text": "Then this is the conclusion, that if I change to a different basis, we now know- see, if I change to a different basis, two things happen." + }, + { + "text": "Every vector has new coordinates." + }, + { + "text": "There, the rule is this one, between the old coordinates and the new ones." + }, + { + "text": "Every matrix changes." + }, + { + "text": "Every transformation has a new matrix." + }, + { + "text": "And the new matrix is related this way." + }, + { + "text": "The M could be the same as the W. The M there could be the W here." + }, + { + "text": "OK." + }, + { + "text": "So can I, in the remaining minutes, recapture my lecture, the end of my lecture that was just before Thanksgiving, about the matrix?" + }, + { + "text": "OK. What's the matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk17.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..f82f2cc230f9f2720733e8b152f84f80f1341c9f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll just take one basis." + }, + { + "text": "So now I'm going to- this part is going to go onto this board here." + }, + { + "text": "What is the matrix?" + }, + { + "text": "What is A?" + }, + { + "text": "OK." + }, + { + "text": "Using a basis v1 up to v8." + }, + { + "text": "OK. What's the point?" + }, + { + "text": "The point is, if I know what the transformation does to those eight basis vectors, I know it completely." + }, + { + "text": "I know T, I know everything about T, I know T completely from knowing what T does to v1, what T does to v2, what T does to v8." + }, + { + "text": "Why is that?" + }, + { + "text": "It's because T is a linear transformation." + }, + { + "text": "So that if I know what these outputs are, so these are the inputs, v1 up to v8, these are the outputs from the transformation, like every one rotated, every one projected, whatever transformation I've done, then why is it that I know everything?" + }, + { + "text": "How does linearity work?" + }, + { + "text": "Why?" + }, + { + "text": "This is because every x is some combination of these basis vectors, right?" + }, + { + "text": "c1 v1, c2 v2, c8 v8." + }, + { + "text": "That's the whole point of a basis, that every vector is a combination of the basis vectors in exactly one way." + }, + { + "text": "And then, what is T of x?" + }, + { + "text": "The point is, I claim that we know T of x completely for every x, because every x is a combination of those, and now we use the linear transformation part to say that the output from x has to be c1 times the output from v1 plus c2 times the output from v2 and so on, up through c8 times the output from v8." + }, + { + "text": "So this is like just saying, OK, we know everything when we know what T does to each basis vector." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk18.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..d9c718592303012586f37aed3dc53271be8cef29 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "So those are the eight things we need." + }, + { + "text": "Now, but we need these answers in this basis." + }, + { + "text": "So T- so this first output is some combination of the eight basis vectors." + }, + { + "text": "So write T times the first- acting on the first input, in other words, write the first output as a combination of the basis vectors." + }, + { + "text": "Say a11 v1 plus a21 v2 and so on, a81 v8." + }, + { + "text": "Write T of v2 as some combination, a12 of v1, a22 of v2 and so on." + }, + { + "text": "I'm creating the matrix A, column by column." + }, + { + "text": "Those numbers go in the first column, these numbers go in the second column." + }, + { + "text": "The matrix A that this is our matrix that represents T in this basis is these numbers." + }, + { + "text": "a11 down to a18, a21 down to a28 and so on." + }, + { + "text": "OK. That's the recipe." + }, + { + "text": "In other words, if I give you a transformation and a basis, that's what I have to give you." + }, + { + "text": "The inputs are the basis and to tell you what the transformation is." + }, + { + "text": "And then you tell me, you compute T for each basis, expand that result in the basis, and that gives you the sixty-four numbers that go into the matrix A." + }, + { + "text": "Let me suppose, let's close with the best example of all." + }, + { + "text": "Suppose v1 to v8, this basis, is the eigenvectors." + }, + { + "text": "Suppose we have an eigenvector basis." + }, + { + "text": "So that T of vi is just, is in the same direction as vi." + }, + { + "text": "Now my question is, what is A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk19.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..4bc0bda81becbd032c626bcaab40cca8eaa39155 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Can you carry through the steps?" + }, + { + "text": "Let's, let's do them together, because we can do it in one minute." + }, + { + "text": "So we've chosen this perfect basis." + }, + { + "text": "And actually, with signal image processing, they might look for the eigenvectors, but that would take more calculation time than just saying, OK, we'll use the wavelet basis, or OK, we'll use the Fourier basis." + }, + { + "text": "But the very best basis is the eigenvector basis." + }, + { + "text": "OK, what's the matrix?" + }, + { + "text": "So, what's the first column of the matrix?" + }, + { + "text": "How do I get the first column?" + }, + { + "text": "I take the first basis vector v1." + }, + { + "text": "I op- I look to see what does the transformation do to it." + }, + { + "text": "The output is lambda one v1." + }, + { + "text": "I express that output as a combination, so the first input is v1." + }, + { + "text": "Its output is lambda one v1." + }, + { + "text": "Now write lambda one v1 as a combination of the basis vectors." + }, + { + "text": "Well, it's already done." + }, + { + "text": "It's just lambda one times the first basis vector and zero times the others." + }, + { + "text": "So this first column will have lambda one and zeros." + }, + { + "text": "OK?" + }, + { + "text": "Second input is v2." + }, + { + "text": "Output is lambda two v2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk2.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..44553739c24736b408dbd01c3688e075b25f9a15 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it has to be compressed." + }, + { + "text": "The standard compression, and still used in, in the, with these lectures, is, called JPEG." + }, + { + "text": "I think that stands for a Joint Photographic Experts Group." + }, + { + "text": "They established a system of compression." + }, + { + "text": "And I just want to tell you what it's about." + }, + { + "text": "It's a change of basis." + }, + { + "text": "What, what's, what basis do we have?" + }, + { + "text": "The, the current basis we have is, you could say, the standard basis is every pixel give a value." + }, + { + "text": "So that's like, we have a vector x, which is five hundred and twelve squared long, and in the i-th position, we get a number like one twenty one or something, the next, the pixel next to it might be one twenty four, maybe where, maybe where the, where my tie, begins to end." + }, + { + "text": "So if it was mostly blue shirt, this would be a slight difference in shading, but pretty close." + }, + { + "text": "Then the tie would be a different color." + }, + { + "text": "So, so we might have quite a few pixels for the blue shirt and a whole lot more for the blackboard that are very close." + }, + { + "text": "And that's what, are very correlated." + }, + { + "text": "And that's what gives us the possibility of compression." + }, + { + "text": "For example, before the lecture starts, if we had a blank blackboard, then there's an image, but it would make no sense to take that image and tell you what it is pixel by pixel." + }, + { + "text": "I mean, there's a case in which all pixel values, all gray levels are the same, or practically the same, depending on the erasing of the board, but extremely close." + }, + { + "text": "And so that's an image where the standard basis is lousy." + }, + { + "text": "That's, that's the basic fact." + }, + { + "text": "That, that the standard basis which gives the value of every pixel makes no use of the fact that we're getting a whole lot of pixels whose gray levels, the neighboring pixels tend to have the same gray level as the, as their, as their neighbors." + }, + { + "text": "So to take, how do we take advantage of that fact?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk20.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..57e892c1f19c9a45e5f14bb334eab942b0d796a2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk20.json @@ -0,0 +1,32 @@ +[ + { + "text": "OK, write that output as a combination of the v's." + }, + { + "text": "It's already done." + }, + { + "text": "It's just lambda two times the second v. So we need, in the second column, we have lambda two times the second v. Well, you see what's coming." + }, + { + "text": "That in that basis, in the eigenvector basis, the matrix is diagonal." + }, + { + "text": "So that's the perfect basis." + }, + { + "text": "That's the basis we'd love to have for image processing, but to find the eigenvectors of our pixel matrix would be too expensive." + }, + { + "text": "So we do something cheaper and close, which is to choose a good basis like, like wavelengths." + }, + { + "text": "OK, thanks." + }, + { + "text": "So quiz review on Wednesday, all day." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk3.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..8e246b42e71ac0ef99e39e59a7562c71f3da61b4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, one basis vector that would be extremely nice to, one vector that would be extremely nice to include in the basis would be a vector of all ones." + }, + { + "text": "That's not in our standard basis." + }, + { + "text": "So our, so let me just write again." + }, + { + "text": "The standard basis would, is, is our, is our one and all the rest zeros, zero, one, and all the rest zeros, everybody knows what the standard basis is." + }, + { + "text": "Now, any other basis for our, so this is, for this very high-dimensional space, now I'm going to speak about a better basis, better basis, and let me just emphasize, one vector that would be extremely nice to have in that basis is the vector of all ones." + }, + { + "text": "Why is that?" + }, + { + "text": "Let me just say again." + }, + { + "text": "Because that vector of all ones, by itself, one vector is, is able to completely give the information on a solid image." + }, + { + "text": "Of course, our image won't be solid, it'll have a mix of, of, solid and, and signal." + }, + { + "text": "So that one vector, but that, having that one vector in the basis is, is, is going to save us a whole lot." + }, + { + "text": "Now the question is, what other vectors should be in the basis?" + }, + { + "text": "The, the extreme vector in the basis might be a vector of one minus one, one minus one, one minus one." + }, + { + "text": "That would be a vector that shows, I mean, that's like a checkerboard vector, right?" + }, + { + "text": "That's a vector that would, if, if we had, if, if the image was like a huge checkerboard of plus minus, plus minus, plus minus, that vector would carry the whole signal." + }, + { + "text": "But much more common would be maybe to have half the image, darker and the other half lighter." + }, + { + "text": "So another image, another vector that might be quite useful in here would be half ones and half minus ones." + }, + { + "text": "I'm just trying to get across the idea of, that a basis could be, that first of all, we've got, the basis is at our disposal." + }, + { + "text": "Like, we're free to choose that." + }, + { + "text": "And it's a billion dollar decision what we choose." + }, + { + "text": "So, and TV people would rather, would prefer one basis based on the way the, the signal is scanned, and movie people would prefer another." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk4.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..811c58ffd5e28e456b42de439fa8cee4339bd2a6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "I mean, there's giant politics in this question that really reduces to a, to a linear algebra problem what basis to choose." + }, + { + "text": "I'll just mention the best known basis, which is, which JPEG uses, let me put that here, is the Fourier basis." + }, + { + "text": "So when you, when you use the Fourier basis, that includes, this is the constant vector, the DC vector, if we're electrical engineers, the, the, the vector of all ones, so it would include one, one, one, one." + }, + { + "text": "Often, eight by eight is a good choice." + }, + { + "text": "Eight by eight is a, is a good choice." + }, + { + "text": "So, what do I mean by this eight by eight?" + }, + { + "text": "I mean that the big signal, which is five twelve by five twelve, gets broken down, and JPEG does this, into eight by eight blocks." + }, + { + "text": "And we, sort of, this is too much to deal with at once." + }, + { + "text": "So what JPEG does is take this eight by eight block, which is sixty-four coefficients, sixty-four, pixels, and changes the basis on the, on that piece." + }, + { + "text": "And then, now, let's see, I was going to write down Fourier, so you remember Fourier is, is this vector of all ones, and then, the vector, oh, well, actually, I gave a lecture earlier about the Fourier matrix, these, this matrix whose columns are powers of a, of a, complex number w. I, I won't repeat that, because I'm not, I don't want to go into the details of the Fourier basis." + }, + { + "text": "Just to tell you how compression works." + }, + { + "text": "So what happens in JPEG?" + }, + { + "text": "What happens to the video, to a, to each image of, of, of these lectures?" + }, + { + "text": "The, it gets broken into eight by eight blocks." + }, + { + "text": "OK." + }, + { + "text": "Within each block, we have sixty-four coefficients, sixty-four basis vectors, sixty-four pixels, and we change basis in sixty-four dimensional space, using these Fourier vectors." + }, + { + "text": "Just, no, that was a lossless step." + }, + { + "text": "Let, let me, let me emphasize." + }, + { + "text": "In comes the signal." + }, + { + "text": "x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk5.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..7ce7441a356838f6e496da3b2d782533cfb4ad1b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "We change basis." + }, + { + "text": "This is the basis change." + }, + { + "text": "Change basis." + }, + { + "text": "Choose a better basis." + }, + { + "text": "So it produces, the, coefficients c. So sixty-four pixels come in, sixty-four coefficients come out." + }, + { + "text": "Now comes the compression." + }, + { + "text": "Now come, this was lossless." + }, + { + "text": "It's just, we know that R64 has plenty of basis, and we've chosen one." + }, + { + "text": "Now, in that basis, we write, we write the signal in that basis, and that's what my lecture, that's the math part of my lecture." + }, + { + "text": "Now here's the application part." + }, + { + "text": "The next part is going to be the compression step." + }, + { + "text": "And that's lossy." + }, + { + "text": "We're going to lose information." + }, + { + "text": "And what, what will actually happen at that step?" + }, + { + "text": "Well, one thing we could do is just throw away the small coefficients." + }, + { + "text": "So that would be, that's called thresholding." + }, + { + "text": "We set some threshold." + }, + { + "text": "Every coefficient, every basis vector that's not in there more than the threshold value, and we set some threshold so that our eye can't see the difference, whether we throw away that, or can hardly see the difference, whether we throw away that little bit of that basis vector or keep it." + }, + { + "text": "So this compression step produces a compressed set of coefficients." + }, + { + "text": "Let me, I'll just keep going here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk6.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..e51518b0b218267f8c2f0d7243d31fec00ba9b42 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, so it keeps going." + }, + { + "text": "This compression step produces some coefficients c hat." + }, + { + "text": "And with lots of, with many zeros." + }, + { + "text": "So that's where the compression came." + }, + { + "text": "Probably there's enough of this vector of all ones, we very seldom throw that away." + }, + { + "text": "Usually its coefficient will be large." + }, + { + "text": "But the coefficient of something like this, that quickly alternating vector, there's probably very little of that in any smooth signal." + }, + { + "text": "I mean, that's high frequent- this is, this is low frequency, zero frequency." + }, + { + "text": "This stuff is the highest frequency we could have, and there's a, if the noise, the, the jitter is producing that sort of output, but a smooth lecture like this one is, has very little of that highest frequency." + }, + { + "text": "Very little noise in this lecture." + }, + { + "text": "OK." + }, + { + "text": "So, so we throw away whatever there is, and we, we're left with just a few coefficients, and then we reconstruct a signal using those coefficients." + }, + { + "text": "We take the, those coefficients times their basis vectors, but this sum doesn't have sixty-four terms anymore." + }, + { + "text": "Probably it has about two or three terms." + }, + { + "text": "So that, if we say it has three terms." + }, + { + "text": "From sixty-four down to three, that's compression of twenty-one to one." + }, + { + "text": "That's the kind of compression you're looking for." + }, + { + "text": "And everybody is looking for that sort of compression." + }, + { + "text": "Let's see, I guess I met the problem with the FBI and fingerprints." + }, + { + "text": "So there's a whole lot of still images." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk7.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..4cdf43a95d584ba42202d1c77ba5f96a998319d5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "You know, you, with your thumb, you make these inky marks, which, go somewhere." + }, + { + "text": "You used to go to Washington and get stored in a big file." + }, + { + "text": "So Washington had a file of thirty million murderers, cheaters on quizzes, other stuff, and, and actually, there was no way to retrieve them in time." + }, + { + "text": "Like, so, so suppose you're at the police station, they say, OK, this person may have done this, check with Washington, have they got his or her fingerprints on file." + }, + { + "text": "Well, Washington won't know the answer within a week, if it's got filing cabinets full of fingerprints." + }, + { + "text": "So of course the natural step is digitize them." + }, + { + "text": "So all fingerprints are now digitized, so now it's at least electronic, but still there's too much information in each, each one." + }, + { + "text": "I mean, you can't search through that many, uh, fingerprints if you, if, if the digital image is five twelve squared by five twelve squared, if it's that many pixels." + }, + { + "text": "So you get compressed." + }, + { + "text": "So the FBI had to decide what basis to choose for compression of fingerprints, and then they built a big new facility in West Virginia and that's where fingerprints now are sent." + }, + { + "text": "So if you, I think if you get your fingerprints done now at the police station, if it's an up-to-date police station, it's, it happens digitally and the signal is sent digitally, and then in West Virginia it's compressed and indexed." + }, + { + "text": "And then, if they want to find you, they can do it within minutes, instead of within a week." + }, + { + "text": "OK." + }, + { + "text": "So this compression is, comes up for signals, for images." + }, + { + "text": "For video, which is like these lectures, uh, there's another aspect." + }, + { + "text": "You could treat the video as one still image after another one, and compress each one and then run them and make a video." + }, + { + "text": "But that misses, well, you can see why that's not optimal." + }, + { + "text": "In video, so for in a video thing, you have a sequence of images, so video is really a sequence of images, but what about one image to the next image?" + }, + { + "text": "They're extremely correlated." + }, + { + "text": "I mean, that, I'm getting an image every split second, and although I'm moving slightly, that's what's producing the, jumpy motion on the video." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk8.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..41f54e28ef2064485cf009d9b5e4574263d3680d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "But I'm not, like, you know, each, each image in the sequence is pretty close to the one before." + }, + { + "text": "So you have to use, like, prediction and correction." + }, + { + "text": "I mean, you, my, the image of me one instant, one time step later, you would assume would be the same, and then plus a small correction." + }, + { + "text": "And you would only code and digitize the correction, and compress the correction." + }, + { + "text": "So the sequence of images that's highly correlated, and the problem in compression is always to use this correlation, this fact that in time or in space, things don't change instantly, they, they're very often smooth changes, and, you can predict one value from the previous value." + }, + { + "text": "OK." + }, + { + "text": "So that's the, those are applications, which are pure linear algebra." + }, + { + "text": "I could, maybe I'll, maybe you'll allow me to tell you the, and the book describes, the new basis that's, the competition for Fourier." + }, + { + "text": "So the competition for Fourier is called wavelets, and I can describe what that basis is like, say, in the eight by eight case." + }, + { + "text": "So that eight by eight wavelet basis is the vector of all ones, eight ones, then the vector of four ones and four minus ones, then the vector of two ones and two minus ones and four zeros, and also the vector of four zeros and two ones and two minus ones." + }, + { + "text": "So now I'm up to four, and I need four more, right, for R8?" + }, + { + "text": "So the next basis vector will be one minus one and six zeros, and then three more like that, with a one minus one there and there and there." + }, + { + "text": "So those are eight vectors in eight-dimensional space." + }, + { + "text": "Those are, those are called wavelets, and you, and it's a very simple wavelet choice." + }, + { + "text": "It's a more sophisticated choice." + }, + { + "text": "This is a little jumpy, to jump between one and minus one." + }, + { + "text": "And actually, you can see now, suppose you compare the wavelet basis with the Fourier basis above." + }, + { + "text": "How could I write this guy, which is in the Fourier basis, it's an eight, it's a vector in R8, how would I write that as a combination of the wavelet basis?" + }, + { + "text": "Do you, have I told you enough about the wavelet basis that you can see?" + }, + { + "text": "How does this very fast guy, what combination of the wavelet basis is that very fast guy?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk9.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..2bc1d292fd925c01e44d5599863fa8cb2bcfba79 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_5_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It would be this one, it would be the sum of these four, right?" + }, + { + "text": "That very fast guy will be that one minus one, and the next one, and the next one, and the next one." + }, + { + "text": "So this is the sum of those last four wavelets." + }, + { + "text": "This one we've kept, and so on." + }, + { + "text": "So, each, well, every, well, that's what a basis does." + }, + { + "text": "Every vector in R8 is some combination of those, and for the linear algebra, we have, so the linear algebra is this step, find the coefficients." + }, + { + "text": "That's, that's the step we want to take." + }, + { + "text": "If I give you the basis, like this wavelet basis, and I give you the pixel, so here are the pixel values, p1, p2, down to p8." + }, + { + "text": "What's, what's the job?" + }, + { + "text": "What's the linear algebra here?" + }, + { + "text": "So this is, these are the values, this is in the standard basis, right?" + }, + { + "text": "Those are just the values at eight successive points." + }, + { + "text": "I guess I'm dropping down to one dimension instead of eight by eight, I'm just going to take eight pixel values along that first top row." + }, + { + "text": "So I, what do I want to do?" + }, + { + "text": "In the standard basis, here are the pixel values." + }, + { + "text": "I want to write that as a combination of c1 times this guy, plus c2 times this guy, plus c3, these are the coefficients, plus c4 times this one." + }, + { + "text": "Do you see what I'm doing?" + }, + { + "text": "I want to write this vector p as a combination of c1 times the first wavelet, plus c8 times the eighth wavelet." + }, + { + "text": "That's the, that's the transform step." + }, + { + "text": "That's the lossless step, that's the step from p, oh, I'm calling it p here and I called it x there, so let me, at the risk of moving and therefore making this jumpy, suppose the signal I'm now calling p, the set of pixel values and I'm looking for the coefficients." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk0.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..ed695ba203c725aa80144eb85fb8edd6706cbb8c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay." + }, + { + "text": "So coming near the end of the course, this lecture will be a mixture of the linear algebra that comes with a change of basis." + }, + { + "text": "And a change of basis from one basis to another basis is something you really do in applications." + }, + { + "text": "And I would like to talk about those applications." + }, + { + "text": "I got a little bit involved with compression, compressing a signal, compressing an image, and that's exactly change of basis." + }, + { + "text": "And then the main theme in this chapter is the connection between a linear transformation, which doesn't have to have coordinates, and the matrix that tells us that transformation with respect to coordinates." + }, + { + "text": "So the matrix is the coordinate-based description of the linear transformation." + }, + { + "text": "Let me start out with the nice part, which is some, just to tell you something about image compression." + }, + { + "text": "Those of you, well, everybody's going to meet compression, because you know that the amount of data that we're getting, well, these lectures are compressed." + }, + { + "text": "So that actually, probably you see my motion as jerky, shall I use that word?" + }, + { + "text": "Have you looked on the web?" + }, + { + "text": "I should like to find a better word." + }, + { + "text": "Compressed, let's see." + }, + { + "text": "So my, the, the, the complete signal is, of course, in those video cameras and in the videotape, but that goes to the bottom of building nine, and out of that comes a jumpy motion, because it uses a standard system for compressing images." + }, + { + "text": "And, you'll notice that the stuff that sits on the board comes very clearly, but it's my motion that, that, that needs a whole lot of bits, right?" + }, + { + "text": "So, and if I were to run up and back, up there and back, that would need too many bits and they'd, I'd be compressed even more." + }, + { + "text": "So, what does compression mean?" + }, + { + "text": "Can I, let me just think of a still image." + }, + { + "text": "And, and of course, satellites, oh, there's, and, and computations of the climate, computations of combustion, the, computers and sensors of all kinds are just giving us overwhelming amounts of data." + }, + { + "text": "The web is, too." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk1.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..276b7aacae39769ce0e1627c108ec463ccf35faa --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, some compression can be done with no loss." + }, + { + "text": "Lossless compression is possible just using, sort of, the fact that, there's, there are redundancies." + }, + { + "text": "But I'm talking here about lossy compression." + }, + { + "text": "So I'm talking about, here's an image." + }, + { + "text": "And what does an image consist of?" + }, + { + "text": "It consists of a lot of little pixels, right?" + }, + { + "text": "Maybe five hundred and twelve by five hundred and twelve." + }, + { + "text": "Two to the ninth by two to the ninth pixels, and each, so this is pixel number one one, so that's a pixel, and if we're in black and white, the typical pixel would tell us a grayscale from zero to two fifty five." + }, + { + "text": "So a pixel is usually a, a value of a, a, one of the x i, so this would be the i-th pixel, it, it's usually a real number on a scale from zero to two fifty five." + }, + { + "text": "In other words, two to the eighth possibilities." + }, + { + "text": "So usually, that's the, that's the standard, so, so that, that's eight, eight bits." + }, + { + "text": "But then we have that for every, every pixel, so we have five hundred and twelve squared pixels." + }, + { + "text": "We're, we're really operating, x is a vector in Rn, but what is n?" + }, + { + "text": "n is five hundred and twelve squared." + }, + { + "text": "That's, that's our problem right there." + }, + { + "text": "We're, a pixel is a vector that gives us the information about the image, I'm sorry, the image that comes through is a vector of, of that length, that, that's the information we have about the image." + }, + { + "text": "If it's a color image, we would have three times that length, because we'd have, we'd need three coordinates to get color." + }, + { + "text": "So it would be three times five hundred and twelve squared." + }, + { + "text": "It's an enormous amount of information, and we couldn't send out the image for these lectures without compressing it." + }, + { + "text": "We, we, it, it would be, it would overload the system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk10.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..db2f6371da88f739758d4ebae59b4fdffa270d6f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "Tell me how to do it." + }, + { + "text": "How do I find the, if I give you eight basis vectors and I give you the input signal and I ask for the coefficients, what do I do?" + }, + { + "text": "What's the, what's the step?" + }, + { + "text": "I want, I'm trying to solve this, I want to know the eight coefficients, so I'm changing from the standard basis, which is just the eight grayscale values, to the wavelet basis, where this same vector is represented by eight numbers." + }, + { + "text": "It's got to take eight numbers to tell you a vector in R8, and those eight numbers are the coefficients of the basis." + }, + { + "text": "Look, we've done this thing before." + }, + { + "text": "What do we, here, there is the equation in vector notation." + }, + { + "text": "We want to see it as a matrix." + }, + { + "text": "This is a combination of columns of the wavelet matrix, right?" + }, + { + "text": "This is p equals c1, c2, down to c8, and these guys are the columns." + }, + { + "text": "I mean, this is the step that we constantly take in this course." + }, + { + "text": "The first basis vector goes in the first column, the second basis vector goes in the second column, and so on." + }, + { + "text": "The eight columns of this wavelet matrix are the eight basis vectors." + }, + { + "text": "This is a wavelet matrix W. So, the step to change basis." + }, + { + "text": "So now I'm finally coming to this change of basis." + }, + { + "text": "So the change of basis, let me stay with this board, but, well, let me just go above it here." + }, + { + "text": "So the standard basis we know, the wavelet basis we have here, and the transform is simply solve the equations p equal Wc." + }, + { + "text": "So the coefficients are W inverse p, right?" + }, + { + "text": "This shows a critical point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk11.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..8346f1691f9a546b0252c3e0960539efff45ec1f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "A good basis has a nice, fast inverse." + }, + { + "text": "So good means, good basis means what?" + }, + { + "text": "So this is like the billion dollar competition, and it's not over yet." + }, + { + "text": "People are going to come up with better bases than these." + }, + { + "text": "So a good basis will be, first good thing would be fast." + }, + { + "text": "I have to be able to multiply by W fast and multiply by W, by its inverse fast." + }, + { + "text": "That's, if a basis doesn't allow you to do that fast, then it's going to take so much time that you can't afford it." + }, + { + "text": "So these bases, the Fourier basis, everybody said, OK, I know how to deal quickly with the Fourier basis, because we have something called the fast Fourier transform." + }, + { + "text": "So there's a FFT that came in my earlier lecture and comes in the last chapter of the book." + }, + { + "text": "So change of basis is done, if for the Fourier basis, is done fast by the FFT and there's a fast wavelet transform." + }, + { + "text": "I can change, for this wavelet example, this matrix is easy to invert." + }, + { + "text": "It's just somebody had a smart idea in choosing that wavelet basis and inverting it, it has a nice inverse." + }, + { + "text": "Actually, you can see why it has a nice inverse." + }, + { + "text": "Do you see any property of these eight basis vectors?" + }, + { + "text": "Well, I've only written five of them, but if you see that property for those five, you'll see it for the three remaining." + }, + { + "text": "What, if I give you those eight vectors and ask, what's a nice property?" + }, + { + "text": "Well, you would say, first, they're all ones and minus ones and zeros, so every multiplication is very fast using just, in binary." + }, + { + "text": "But what's the other great property of those vectors?" + }, + { + "text": "Anybody see it?" + }, + { + "text": "So, of course, when I think about a basis, one nice property, I don't have to have it, but I'm happy if it's there, is that they're orthogonal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk12.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..c0eaf69080e43e238bee148545d1b059bef72365 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "If the basis vectors are orthogonal, then I'm in good shape." + }, + { + "text": "And these are, do you see, take the dot product of that with that, you get four plus ones and four minus ones, you get zero." + }, + { + "text": "Take the dot product of that with that, you get two plus ones and two minus ones." + }, + { + "text": "Or the dot product of that with that, two plus ones and two minus ones." + }, + { + "text": "You can easily check that that's an orthogonal basis." + }, + { + "text": "It's not orthonormal." + }, + { + "text": "I could, to fix it up, I should divide by the length to make them unit vectors." + }, + { + "text": "Let's suppose I do that." + }, + { + "text": "So somewhere in here I've got to account for the fact that this has length square root of eight, that has length square root of four, that has length square root of two." + }, + { + "text": "But that's just a constant factor that's easy to --." + }, + { + "text": "So suppose we've done that." + }, + { + "text": "Then tell me what's W inverse." + }, + { + "text": "That's what chapter four, section four point four was about." + }, + { + "text": "If we have orthonormal columns, what- then the inverse is the same as the transpose." + }, + { + "text": "So if we have a fast way to multiply by W, which we do, the inverse is going to look just the same and we'll have a fast way to do W inverse." + }, + { + "text": "So that's, the wavelet basis passes this requirement for fast." + }, + { + "text": "We can use it fast." + }, + { + "text": "But there's a second requirement, is it any good?" + }, + { + "text": "Because the very fastest thing we could do would be not to change basis at all." + }, + { + "text": "Right?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk13.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..4de80b529af0604a4e0b9b0291a8822dc165b83a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Fastest thing would be, OK, stay with a standard basis, stay with eight pixel values." + }, + { + "text": "But that was poor from compression point of view, right?" + }, + { + "text": "Those eight pixel values, if I just took those eight numbers, I can't throw some of those away." + }, + { + "text": "If I throw away ninety percent, if I compressed ten to one, and throw away ninety percent of my pixel values, well, my picture's just gone dark." + }, + { + "text": "Whereas the basis that was good, the wavelet basis or the Fourier basis, if I throw away c5, c6, c7 and c8, all I'm throwing away is little blips that are probably there in very small amounts." + }, + { + "text": "So the second property that we need is good compression." + }, + { + "text": "So, so first it, it has to be fast, and secondly, it has to be a few basis factors should come close to the signal." + }, + { + "text": "So, so a few, few is enough." + }, + { + "text": "Can I write it that way?" + }, + { + "text": "A few basis factors are enough to reproduce the image, just exactly as on the video of these 18.06 lectures." + }, + { + "text": "I don't know what the compression rate is." + }, + { + "text": "I'll ask, David, who, who does the compression, and, by the way, I'll try to get the lectures, that are relevant for the quiz, up onto the web, in time." + }, + { + "text": "So I'll send him a message today." + }, + { + "text": "So, at the point, so he's using the Fourier basis, because the JPEG, so JPEG 2000, which will be the next standard for image compression, will include wavelets." + }, + { + "text": "So, I mean, you're, you're actually getting a kind of up to date, picture of where this big world of signal and image processing is." + }, + { + "text": "That Fourier is what everybody knew, and what people automatically used, and the new, new one is wavelets, where this is the simplest set of wavelets, and this isn't the one that the FBI uses, by the way." + }, + { + "text": "The FBI uses a more, a more, a smoother wavelet." + }, + { + "text": "Instead of jumping from one to minus one, it's a smooth, cutoff." + }, + { + "text": "And, that's what we'll be in, in JPEG 2000." + }, + { + "text": "OK, so that's that application." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk14.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..8f1debcca7ae641417e7ed0a630d269963c01302 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now let me come to my, the, the math, the linear algebra part of the lecture." + }, + { + "text": "Well, we've actually seen a change of basis." + }, + { + "text": "So let, let me just review that change of basis idea, and then the, and then the transformation to a matrix." + }, + { + "text": "OK, so, so this, I hope you see that these applications are really big." + }, + { + "text": "Now I have to talk a little about change of basis and little about that, the, the matrix." + }, + { + "text": "OK. OK. OK." + }, + { + "text": "So change of basis." + }, + { + "text": "Basically, forgive that pun, OK, I have, I have, I have my vector in one basis, and I want to change to a different one." + }, + { + "text": "Actually, you saw it for the wavelet case." + }, + { + "text": "So I need the, the, let the matrix W, the columns of W, be the new basis vectors." + }, + { + "text": "Then the change of basis involves, just as it did there, W inverse." + }, + { + "text": "So we have the vector, vector, say, x in the old basis, and we, that converts to a vector, let's say, c in the new basis, and the relation is exactly what we had there, that x is Wc." + }, + { + "text": "That's the, that's the, that's the, that's the step we have to take." + }, + { + "text": "There's a matrix W that gives us a change of basis." + }, + { + "text": "OK." + }, + { + "text": "I, I, what I want to do is think about mat- transformations and matrices." + }, + { + "text": "So here's, here's the question, that, that, to complete this lecture." + }, + { + "text": "Suppose I have a linear transformation T. So it's, it's a, it's a, we, we would think of it as an A, as a n by n matrix." + }, + { + "text": "And it's computed with respect to a certain basis." + }, + { + "text": "So T, so, no, I'm sorry." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk15.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..dbc5ad92f06633f3366a78c24c0c7c08b058ee63 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "I've got the transformation T, period." + }, + { + "text": "That's taking eight-dimensional space to eight-dimensional space." + }, + { + "text": "Now let's get matrices in there." + }, + { + "text": "OK." + }, + { + "text": "So, so with respect to, with respect to a fir- a first basis, say, V1 up to V8, it has a matrix A. I'm just setting up letters here." + }, + { + "text": "With respect to a second basis, say, I'll make it U1 up to- or W1, since I've used Ws, W1 up to W8, it has a matrix B." + }, + { + "text": "And my question is, what's the connection between A and B?" + }, + { + "text": "How is the matrix- the transformation T is settled." + }, + { + "text": "We could say it's a rotation, for example." + }, + { + "text": "So that would be one transformation of eight-dimensional space, just spin it a little." + }, + { + "text": "Or project it." + }, + { + "text": "Or, or, whatever, whatever linear transformation we've got." + }, + { + "text": "Now we have to remember, so I- so first- my first step is to remind you how you create that matrix A." + }, + { + "text": "Then my second step is, we would use the same method to create B, but because it came from the same transformation, there's got to be a relation between A and B." + }, + { + "text": "What's the- what's the relation between A and B?" + }, + { + "text": "And let me jump to the answer on that one." + }, + { + "text": "That if I have- if I have the same transformation, and I'm compute- its matrix in one basis and then I compute it in another basis, those two matrices are similar." + }, + { + "text": "So these two matrices are similar." + }, + { + "text": "Now, do you remember what similar matrices meant?" + }, + { + "text": "Similar." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk16.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..9d019933a190fe645eec785d8363a0940d0f76a4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "A is similar- the two matrices are similar." + }, + { + "text": "Similar." + }, + { + "text": "And what do I mean by that?" + }, + { + "text": "I mean that I take the matrix B and I can compute it from the matrix A using some similarity, some matrix M on one side and M inverse on the other." + }, + { + "text": "And this M will be the change of basis matrix." + }, + { + "text": "This part of the lecture is admittedly compressed." + }, + { + "text": "What I wanted you to- it's really the conclusion that I want you to spot." + }, + { + "text": "Now I have to go back and say, what does it mean for A to be the matrix of this transformation T?" + }, + { + "text": "So I have to remind you what that meant." + }, + { + "text": "That was in the last lecture." + }, + { + "text": "Then this is the conclusion, that if I change to a different basis, we now know- see, if I change to a different basis, two things happen." + }, + { + "text": "Every vector has new coordinates." + }, + { + "text": "There, the rule is this one, between the old coordinates and the new ones." + }, + { + "text": "Every matrix changes." + }, + { + "text": "Every transformation has a new matrix." + }, + { + "text": "And the new matrix is related this way." + }, + { + "text": "The M could be the same as the W. The M there could be the W here." + }, + { + "text": "OK." + }, + { + "text": "So can I, in the remaining minutes, recapture my lecture, the end of my lecture that was just before Thanksgiving, about the matrix?" + }, + { + "text": "OK. What's the matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk17.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..f82f2cc230f9f2720733e8b152f84f80f1341c9f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll just take one basis." + }, + { + "text": "So now I'm going to- this part is going to go onto this board here." + }, + { + "text": "What is the matrix?" + }, + { + "text": "What is A?" + }, + { + "text": "OK." + }, + { + "text": "Using a basis v1 up to v8." + }, + { + "text": "OK. What's the point?" + }, + { + "text": "The point is, if I know what the transformation does to those eight basis vectors, I know it completely." + }, + { + "text": "I know T, I know everything about T, I know T completely from knowing what T does to v1, what T does to v2, what T does to v8." + }, + { + "text": "Why is that?" + }, + { + "text": "It's because T is a linear transformation." + }, + { + "text": "So that if I know what these outputs are, so these are the inputs, v1 up to v8, these are the outputs from the transformation, like every one rotated, every one projected, whatever transformation I've done, then why is it that I know everything?" + }, + { + "text": "How does linearity work?" + }, + { + "text": "Why?" + }, + { + "text": "This is because every x is some combination of these basis vectors, right?" + }, + { + "text": "c1 v1, c2 v2, c8 v8." + }, + { + "text": "That's the whole point of a basis, that every vector is a combination of the basis vectors in exactly one way." + }, + { + "text": "And then, what is T of x?" + }, + { + "text": "The point is, I claim that we know T of x completely for every x, because every x is a combination of those, and now we use the linear transformation part to say that the output from x has to be c1 times the output from v1 plus c2 times the output from v2 and so on, up through c8 times the output from v8." + }, + { + "text": "So this is like just saying, OK, we know everything when we know what T does to each basis vector." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk18.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..d9c718592303012586f37aed3dc53271be8cef29 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "So those are the eight things we need." + }, + { + "text": "Now, but we need these answers in this basis." + }, + { + "text": "So T- so this first output is some combination of the eight basis vectors." + }, + { + "text": "So write T times the first- acting on the first input, in other words, write the first output as a combination of the basis vectors." + }, + { + "text": "Say a11 v1 plus a21 v2 and so on, a81 v8." + }, + { + "text": "Write T of v2 as some combination, a12 of v1, a22 of v2 and so on." + }, + { + "text": "I'm creating the matrix A, column by column." + }, + { + "text": "Those numbers go in the first column, these numbers go in the second column." + }, + { + "text": "The matrix A that this is our matrix that represents T in this basis is these numbers." + }, + { + "text": "a11 down to a18, a21 down to a28 and so on." + }, + { + "text": "OK. That's the recipe." + }, + { + "text": "In other words, if I give you a transformation and a basis, that's what I have to give you." + }, + { + "text": "The inputs are the basis and to tell you what the transformation is." + }, + { + "text": "And then you tell me, you compute T for each basis, expand that result in the basis, and that gives you the sixty-four numbers that go into the matrix A." + }, + { + "text": "Let me suppose, let's close with the best example of all." + }, + { + "text": "Suppose v1 to v8, this basis, is the eigenvectors." + }, + { + "text": "Suppose we have an eigenvector basis." + }, + { + "text": "So that T of vi is just, is in the same direction as vi." + }, + { + "text": "Now my question is, what is A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk19.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..4bc0bda81becbd032c626bcaab40cca8eaa39155 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Can you carry through the steps?" + }, + { + "text": "Let's, let's do them together, because we can do it in one minute." + }, + { + "text": "So we've chosen this perfect basis." + }, + { + "text": "And actually, with signal image processing, they might look for the eigenvectors, but that would take more calculation time than just saying, OK, we'll use the wavelet basis, or OK, we'll use the Fourier basis." + }, + { + "text": "But the very best basis is the eigenvector basis." + }, + { + "text": "OK, what's the matrix?" + }, + { + "text": "So, what's the first column of the matrix?" + }, + { + "text": "How do I get the first column?" + }, + { + "text": "I take the first basis vector v1." + }, + { + "text": "I op- I look to see what does the transformation do to it." + }, + { + "text": "The output is lambda one v1." + }, + { + "text": "I express that output as a combination, so the first input is v1." + }, + { + "text": "Its output is lambda one v1." + }, + { + "text": "Now write lambda one v1 as a combination of the basis vectors." + }, + { + "text": "Well, it's already done." + }, + { + "text": "It's just lambda one times the first basis vector and zero times the others." + }, + { + "text": "So this first column will have lambda one and zeros." + }, + { + "text": "OK?" + }, + { + "text": "Second input is v2." + }, + { + "text": "Output is lambda two v2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk2.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..44553739c24736b408dbd01c3688e075b25f9a15 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it has to be compressed." + }, + { + "text": "The standard compression, and still used in, in the, with these lectures, is, called JPEG." + }, + { + "text": "I think that stands for a Joint Photographic Experts Group." + }, + { + "text": "They established a system of compression." + }, + { + "text": "And I just want to tell you what it's about." + }, + { + "text": "It's a change of basis." + }, + { + "text": "What, what's, what basis do we have?" + }, + { + "text": "The, the current basis we have is, you could say, the standard basis is every pixel give a value." + }, + { + "text": "So that's like, we have a vector x, which is five hundred and twelve squared long, and in the i-th position, we get a number like one twenty one or something, the next, the pixel next to it might be one twenty four, maybe where, maybe where the, where my tie, begins to end." + }, + { + "text": "So if it was mostly blue shirt, this would be a slight difference in shading, but pretty close." + }, + { + "text": "Then the tie would be a different color." + }, + { + "text": "So, so we might have quite a few pixels for the blue shirt and a whole lot more for the blackboard that are very close." + }, + { + "text": "And that's what, are very correlated." + }, + { + "text": "And that's what gives us the possibility of compression." + }, + { + "text": "For example, before the lecture starts, if we had a blank blackboard, then there's an image, but it would make no sense to take that image and tell you what it is pixel by pixel." + }, + { + "text": "I mean, there's a case in which all pixel values, all gray levels are the same, or practically the same, depending on the erasing of the board, but extremely close." + }, + { + "text": "And so that's an image where the standard basis is lousy." + }, + { + "text": "That's, that's the basic fact." + }, + { + "text": "That, that the standard basis which gives the value of every pixel makes no use of the fact that we're getting a whole lot of pixels whose gray levels, the neighboring pixels tend to have the same gray level as the, as their, as their neighbors." + }, + { + "text": "So to take, how do we take advantage of that fact?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk20.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..57e892c1f19c9a45e5f14bb334eab942b0d796a2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk20.json @@ -0,0 +1,32 @@ +[ + { + "text": "OK, write that output as a combination of the v's." + }, + { + "text": "It's already done." + }, + { + "text": "It's just lambda two times the second v. So we need, in the second column, we have lambda two times the second v. Well, you see what's coming." + }, + { + "text": "That in that basis, in the eigenvector basis, the matrix is diagonal." + }, + { + "text": "So that's the perfect basis." + }, + { + "text": "That's the basis we'd love to have for image processing, but to find the eigenvectors of our pixel matrix would be too expensive." + }, + { + "text": "So we do something cheaper and close, which is to choose a good basis like, like wavelengths." + }, + { + "text": "OK, thanks." + }, + { + "text": "So quiz review on Wednesday, all day." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk3.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..8e246b42e71ac0ef99e39e59a7562c71f3da61b4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, one basis vector that would be extremely nice to, one vector that would be extremely nice to include in the basis would be a vector of all ones." + }, + { + "text": "That's not in our standard basis." + }, + { + "text": "So our, so let me just write again." + }, + { + "text": "The standard basis would, is, is our, is our one and all the rest zeros, zero, one, and all the rest zeros, everybody knows what the standard basis is." + }, + { + "text": "Now, any other basis for our, so this is, for this very high-dimensional space, now I'm going to speak about a better basis, better basis, and let me just emphasize, one vector that would be extremely nice to have in that basis is the vector of all ones." + }, + { + "text": "Why is that?" + }, + { + "text": "Let me just say again." + }, + { + "text": "Because that vector of all ones, by itself, one vector is, is able to completely give the information on a solid image." + }, + { + "text": "Of course, our image won't be solid, it'll have a mix of, of, solid and, and signal." + }, + { + "text": "So that one vector, but that, having that one vector in the basis is, is, is going to save us a whole lot." + }, + { + "text": "Now the question is, what other vectors should be in the basis?" + }, + { + "text": "The, the extreme vector in the basis might be a vector of one minus one, one minus one, one minus one." + }, + { + "text": "That would be a vector that shows, I mean, that's like a checkerboard vector, right?" + }, + { + "text": "That's a vector that would, if, if we had, if, if the image was like a huge checkerboard of plus minus, plus minus, plus minus, that vector would carry the whole signal." + }, + { + "text": "But much more common would be maybe to have half the image, darker and the other half lighter." + }, + { + "text": "So another image, another vector that might be quite useful in here would be half ones and half minus ones." + }, + { + "text": "I'm just trying to get across the idea of, that a basis could be, that first of all, we've got, the basis is at our disposal." + }, + { + "text": "Like, we're free to choose that." + }, + { + "text": "And it's a billion dollar decision what we choose." + }, + { + "text": "So, and TV people would rather, would prefer one basis based on the way the, the signal is scanned, and movie people would prefer another." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk4.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..811c58ffd5e28e456b42de439fa8cee4339bd2a6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "I mean, there's giant politics in this question that really reduces to a, to a linear algebra problem what basis to choose." + }, + { + "text": "I'll just mention the best known basis, which is, which JPEG uses, let me put that here, is the Fourier basis." + }, + { + "text": "So when you, when you use the Fourier basis, that includes, this is the constant vector, the DC vector, if we're electrical engineers, the, the, the vector of all ones, so it would include one, one, one, one." + }, + { + "text": "Often, eight by eight is a good choice." + }, + { + "text": "Eight by eight is a, is a good choice." + }, + { + "text": "So, what do I mean by this eight by eight?" + }, + { + "text": "I mean that the big signal, which is five twelve by five twelve, gets broken down, and JPEG does this, into eight by eight blocks." + }, + { + "text": "And we, sort of, this is too much to deal with at once." + }, + { + "text": "So what JPEG does is take this eight by eight block, which is sixty-four coefficients, sixty-four, pixels, and changes the basis on the, on that piece." + }, + { + "text": "And then, now, let's see, I was going to write down Fourier, so you remember Fourier is, is this vector of all ones, and then, the vector, oh, well, actually, I gave a lecture earlier about the Fourier matrix, these, this matrix whose columns are powers of a, of a, complex number w. I, I won't repeat that, because I'm not, I don't want to go into the details of the Fourier basis." + }, + { + "text": "Just to tell you how compression works." + }, + { + "text": "So what happens in JPEG?" + }, + { + "text": "What happens to the video, to a, to each image of, of, of these lectures?" + }, + { + "text": "The, it gets broken into eight by eight blocks." + }, + { + "text": "OK." + }, + { + "text": "Within each block, we have sixty-four coefficients, sixty-four basis vectors, sixty-four pixels, and we change basis in sixty-four dimensional space, using these Fourier vectors." + }, + { + "text": "Just, no, that was a lossless step." + }, + { + "text": "Let, let me, let me emphasize." + }, + { + "text": "In comes the signal." + }, + { + "text": "x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk5.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..7ce7441a356838f6e496da3b2d782533cfb4ad1b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "We change basis." + }, + { + "text": "This is the basis change." + }, + { + "text": "Change basis." + }, + { + "text": "Choose a better basis." + }, + { + "text": "So it produces, the, coefficients c. So sixty-four pixels come in, sixty-four coefficients come out." + }, + { + "text": "Now comes the compression." + }, + { + "text": "Now come, this was lossless." + }, + { + "text": "It's just, we know that R64 has plenty of basis, and we've chosen one." + }, + { + "text": "Now, in that basis, we write, we write the signal in that basis, and that's what my lecture, that's the math part of my lecture." + }, + { + "text": "Now here's the application part." + }, + { + "text": "The next part is going to be the compression step." + }, + { + "text": "And that's lossy." + }, + { + "text": "We're going to lose information." + }, + { + "text": "And what, what will actually happen at that step?" + }, + { + "text": "Well, one thing we could do is just throw away the small coefficients." + }, + { + "text": "So that would be, that's called thresholding." + }, + { + "text": "We set some threshold." + }, + { + "text": "Every coefficient, every basis vector that's not in there more than the threshold value, and we set some threshold so that our eye can't see the difference, whether we throw away that, or can hardly see the difference, whether we throw away that little bit of that basis vector or keep it." + }, + { + "text": "So this compression step produces a compressed set of coefficients." + }, + { + "text": "Let me, I'll just keep going here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk6.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..e51518b0b218267f8c2f0d7243d31fec00ba9b42 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, so it keeps going." + }, + { + "text": "This compression step produces some coefficients c hat." + }, + { + "text": "And with lots of, with many zeros." + }, + { + "text": "So that's where the compression came." + }, + { + "text": "Probably there's enough of this vector of all ones, we very seldom throw that away." + }, + { + "text": "Usually its coefficient will be large." + }, + { + "text": "But the coefficient of something like this, that quickly alternating vector, there's probably very little of that in any smooth signal." + }, + { + "text": "I mean, that's high frequent- this is, this is low frequency, zero frequency." + }, + { + "text": "This stuff is the highest frequency we could have, and there's a, if the noise, the, the jitter is producing that sort of output, but a smooth lecture like this one is, has very little of that highest frequency." + }, + { + "text": "Very little noise in this lecture." + }, + { + "text": "OK." + }, + { + "text": "So, so we throw away whatever there is, and we, we're left with just a few coefficients, and then we reconstruct a signal using those coefficients." + }, + { + "text": "We take the, those coefficients times their basis vectors, but this sum doesn't have sixty-four terms anymore." + }, + { + "text": "Probably it has about two or three terms." + }, + { + "text": "So that, if we say it has three terms." + }, + { + "text": "From sixty-four down to three, that's compression of twenty-one to one." + }, + { + "text": "That's the kind of compression you're looking for." + }, + { + "text": "And everybody is looking for that sort of compression." + }, + { + "text": "Let's see, I guess I met the problem with the FBI and fingerprints." + }, + { + "text": "So there's a whole lot of still images." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk7.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..4cdf43a95d584ba42202d1c77ba5f96a998319d5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "You know, you, with your thumb, you make these inky marks, which, go somewhere." + }, + { + "text": "You used to go to Washington and get stored in a big file." + }, + { + "text": "So Washington had a file of thirty million murderers, cheaters on quizzes, other stuff, and, and actually, there was no way to retrieve them in time." + }, + { + "text": "Like, so, so suppose you're at the police station, they say, OK, this person may have done this, check with Washington, have they got his or her fingerprints on file." + }, + { + "text": "Well, Washington won't know the answer within a week, if it's got filing cabinets full of fingerprints." + }, + { + "text": "So of course the natural step is digitize them." + }, + { + "text": "So all fingerprints are now digitized, so now it's at least electronic, but still there's too much information in each, each one." + }, + { + "text": "I mean, you can't search through that many, uh, fingerprints if you, if, if the digital image is five twelve squared by five twelve squared, if it's that many pixels." + }, + { + "text": "So you get compressed." + }, + { + "text": "So the FBI had to decide what basis to choose for compression of fingerprints, and then they built a big new facility in West Virginia and that's where fingerprints now are sent." + }, + { + "text": "So if you, I think if you get your fingerprints done now at the police station, if it's an up-to-date police station, it's, it happens digitally and the signal is sent digitally, and then in West Virginia it's compressed and indexed." + }, + { + "text": "And then, if they want to find you, they can do it within minutes, instead of within a week." + }, + { + "text": "OK." + }, + { + "text": "So this compression is, comes up for signals, for images." + }, + { + "text": "For video, which is like these lectures, uh, there's another aspect." + }, + { + "text": "You could treat the video as one still image after another one, and compress each one and then run them and make a video." + }, + { + "text": "But that misses, well, you can see why that's not optimal." + }, + { + "text": "In video, so for in a video thing, you have a sequence of images, so video is really a sequence of images, but what about one image to the next image?" + }, + { + "text": "They're extremely correlated." + }, + { + "text": "I mean, that, I'm getting an image every split second, and although I'm moving slightly, that's what's producing the, jumpy motion on the video." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk8.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..41f54e28ef2064485cf009d9b5e4574263d3680d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "But I'm not, like, you know, each, each image in the sequence is pretty close to the one before." + }, + { + "text": "So you have to use, like, prediction and correction." + }, + { + "text": "I mean, you, my, the image of me one instant, one time step later, you would assume would be the same, and then plus a small correction." + }, + { + "text": "And you would only code and digitize the correction, and compress the correction." + }, + { + "text": "So the sequence of images that's highly correlated, and the problem in compression is always to use this correlation, this fact that in time or in space, things don't change instantly, they, they're very often smooth changes, and, you can predict one value from the previous value." + }, + { + "text": "OK." + }, + { + "text": "So that's the, those are applications, which are pure linear algebra." + }, + { + "text": "I could, maybe I'll, maybe you'll allow me to tell you the, and the book describes, the new basis that's, the competition for Fourier." + }, + { + "text": "So the competition for Fourier is called wavelets, and I can describe what that basis is like, say, in the eight by eight case." + }, + { + "text": "So that eight by eight wavelet basis is the vector of all ones, eight ones, then the vector of four ones and four minus ones, then the vector of two ones and two minus ones and four zeros, and also the vector of four zeros and two ones and two minus ones." + }, + { + "text": "So now I'm up to four, and I need four more, right, for R8?" + }, + { + "text": "So the next basis vector will be one minus one and six zeros, and then three more like that, with a one minus one there and there and there." + }, + { + "text": "So those are eight vectors in eight-dimensional space." + }, + { + "text": "Those are, those are called wavelets, and you, and it's a very simple wavelet choice." + }, + { + "text": "It's a more sophisticated choice." + }, + { + "text": "This is a little jumpy, to jump between one and minus one." + }, + { + "text": "And actually, you can see now, suppose you compare the wavelet basis with the Fourier basis above." + }, + { + "text": "How could I write this guy, which is in the Fourier basis, it's an eight, it's a vector in R8, how would I write that as a combination of the wavelet basis?" + }, + { + "text": "Do you, have I told you enough about the wavelet basis that you can see?" + }, + { + "text": "How does this very fast guy, what combination of the wavelet basis is that very fast guy?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk9.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..2bc1d292fd925c01e44d5599863fa8cb2bcfba79 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_6_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It would be this one, it would be the sum of these four, right?" + }, + { + "text": "That very fast guy will be that one minus one, and the next one, and the next one, and the next one." + }, + { + "text": "So this is the sum of those last four wavelets." + }, + { + "text": "This one we've kept, and so on." + }, + { + "text": "So, each, well, every, well, that's what a basis does." + }, + { + "text": "Every vector in R8 is some combination of those, and for the linear algebra, we have, so the linear algebra is this step, find the coefficients." + }, + { + "text": "That's, that's the step we want to take." + }, + { + "text": "If I give you the basis, like this wavelet basis, and I give you the pixel, so here are the pixel values, p1, p2, down to p8." + }, + { + "text": "What's, what's the job?" + }, + { + "text": "What's the linear algebra here?" + }, + { + "text": "So this is, these are the values, this is in the standard basis, right?" + }, + { + "text": "Those are just the values at eight successive points." + }, + { + "text": "I guess I'm dropping down to one dimension instead of eight by eight, I'm just going to take eight pixel values along that first top row." + }, + { + "text": "So I, what do I want to do?" + }, + { + "text": "In the standard basis, here are the pixel values." + }, + { + "text": "I want to write that as a combination of c1 times this guy, plus c2 times this guy, plus c3, these are the coefficients, plus c4 times this one." + }, + { + "text": "Do you see what I'm doing?" + }, + { + "text": "I want to write this vector p as a combination of c1 times the first wavelet, plus c8 times the eighth wavelet." + }, + { + "text": "That's the, that's the transform step." + }, + { + "text": "That's the lossless step, that's the step from p, oh, I'm calling it p here and I called it x there, so let me, at the risk of moving and therefore making this jumpy, suppose the signal I'm now calling p, the set of pixel values and I'm looking for the coefficients." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk0.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..ed695ba203c725aa80144eb85fb8edd6706cbb8c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay." + }, + { + "text": "So coming near the end of the course, this lecture will be a mixture of the linear algebra that comes with a change of basis." + }, + { + "text": "And a change of basis from one basis to another basis is something you really do in applications." + }, + { + "text": "And I would like to talk about those applications." + }, + { + "text": "I got a little bit involved with compression, compressing a signal, compressing an image, and that's exactly change of basis." + }, + { + "text": "And then the main theme in this chapter is the connection between a linear transformation, which doesn't have to have coordinates, and the matrix that tells us that transformation with respect to coordinates." + }, + { + "text": "So the matrix is the coordinate-based description of the linear transformation." + }, + { + "text": "Let me start out with the nice part, which is some, just to tell you something about image compression." + }, + { + "text": "Those of you, well, everybody's going to meet compression, because you know that the amount of data that we're getting, well, these lectures are compressed." + }, + { + "text": "So that actually, probably you see my motion as jerky, shall I use that word?" + }, + { + "text": "Have you looked on the web?" + }, + { + "text": "I should like to find a better word." + }, + { + "text": "Compressed, let's see." + }, + { + "text": "So my, the, the, the complete signal is, of course, in those video cameras and in the videotape, but that goes to the bottom of building nine, and out of that comes a jumpy motion, because it uses a standard system for compressing images." + }, + { + "text": "And, you'll notice that the stuff that sits on the board comes very clearly, but it's my motion that, that, that needs a whole lot of bits, right?" + }, + { + "text": "So, and if I were to run up and back, up there and back, that would need too many bits and they'd, I'd be compressed even more." + }, + { + "text": "So, what does compression mean?" + }, + { + "text": "Can I, let me just think of a still image." + }, + { + "text": "And, and of course, satellites, oh, there's, and, and computations of the climate, computations of combustion, the, computers and sensors of all kinds are just giving us overwhelming amounts of data." + }, + { + "text": "The web is, too." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk1.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..276b7aacae39769ce0e1627c108ec463ccf35faa --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, some compression can be done with no loss." + }, + { + "text": "Lossless compression is possible just using, sort of, the fact that, there's, there are redundancies." + }, + { + "text": "But I'm talking here about lossy compression." + }, + { + "text": "So I'm talking about, here's an image." + }, + { + "text": "And what does an image consist of?" + }, + { + "text": "It consists of a lot of little pixels, right?" + }, + { + "text": "Maybe five hundred and twelve by five hundred and twelve." + }, + { + "text": "Two to the ninth by two to the ninth pixels, and each, so this is pixel number one one, so that's a pixel, and if we're in black and white, the typical pixel would tell us a grayscale from zero to two fifty five." + }, + { + "text": "So a pixel is usually a, a value of a, a, one of the x i, so this would be the i-th pixel, it, it's usually a real number on a scale from zero to two fifty five." + }, + { + "text": "In other words, two to the eighth possibilities." + }, + { + "text": "So usually, that's the, that's the standard, so, so that, that's eight, eight bits." + }, + { + "text": "But then we have that for every, every pixel, so we have five hundred and twelve squared pixels." + }, + { + "text": "We're, we're really operating, x is a vector in Rn, but what is n?" + }, + { + "text": "n is five hundred and twelve squared." + }, + { + "text": "That's, that's our problem right there." + }, + { + "text": "We're, a pixel is a vector that gives us the information about the image, I'm sorry, the image that comes through is a vector of, of that length, that, that's the information we have about the image." + }, + { + "text": "If it's a color image, we would have three times that length, because we'd have, we'd need three coordinates to get color." + }, + { + "text": "So it would be three times five hundred and twelve squared." + }, + { + "text": "It's an enormous amount of information, and we couldn't send out the image for these lectures without compressing it." + }, + { + "text": "We, we, it, it would be, it would overload the system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk10.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..db2f6371da88f739758d4ebae59b4fdffa270d6f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "Tell me how to do it." + }, + { + "text": "How do I find the, if I give you eight basis vectors and I give you the input signal and I ask for the coefficients, what do I do?" + }, + { + "text": "What's the, what's the step?" + }, + { + "text": "I want, I'm trying to solve this, I want to know the eight coefficients, so I'm changing from the standard basis, which is just the eight grayscale values, to the wavelet basis, where this same vector is represented by eight numbers." + }, + { + "text": "It's got to take eight numbers to tell you a vector in R8, and those eight numbers are the coefficients of the basis." + }, + { + "text": "Look, we've done this thing before." + }, + { + "text": "What do we, here, there is the equation in vector notation." + }, + { + "text": "We want to see it as a matrix." + }, + { + "text": "This is a combination of columns of the wavelet matrix, right?" + }, + { + "text": "This is p equals c1, c2, down to c8, and these guys are the columns." + }, + { + "text": "I mean, this is the step that we constantly take in this course." + }, + { + "text": "The first basis vector goes in the first column, the second basis vector goes in the second column, and so on." + }, + { + "text": "The eight columns of this wavelet matrix are the eight basis vectors." + }, + { + "text": "This is a wavelet matrix W. So, the step to change basis." + }, + { + "text": "So now I'm finally coming to this change of basis." + }, + { + "text": "So the change of basis, let me stay with this board, but, well, let me just go above it here." + }, + { + "text": "So the standard basis we know, the wavelet basis we have here, and the transform is simply solve the equations p equal Wc." + }, + { + "text": "So the coefficients are W inverse p, right?" + }, + { + "text": "This shows a critical point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk11.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..8346f1691f9a546b0252c3e0960539efff45ec1f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "A good basis has a nice, fast inverse." + }, + { + "text": "So good means, good basis means what?" + }, + { + "text": "So this is like the billion dollar competition, and it's not over yet." + }, + { + "text": "People are going to come up with better bases than these." + }, + { + "text": "So a good basis will be, first good thing would be fast." + }, + { + "text": "I have to be able to multiply by W fast and multiply by W, by its inverse fast." + }, + { + "text": "That's, if a basis doesn't allow you to do that fast, then it's going to take so much time that you can't afford it." + }, + { + "text": "So these bases, the Fourier basis, everybody said, OK, I know how to deal quickly with the Fourier basis, because we have something called the fast Fourier transform." + }, + { + "text": "So there's a FFT that came in my earlier lecture and comes in the last chapter of the book." + }, + { + "text": "So change of basis is done, if for the Fourier basis, is done fast by the FFT and there's a fast wavelet transform." + }, + { + "text": "I can change, for this wavelet example, this matrix is easy to invert." + }, + { + "text": "It's just somebody had a smart idea in choosing that wavelet basis and inverting it, it has a nice inverse." + }, + { + "text": "Actually, you can see why it has a nice inverse." + }, + { + "text": "Do you see any property of these eight basis vectors?" + }, + { + "text": "Well, I've only written five of them, but if you see that property for those five, you'll see it for the three remaining." + }, + { + "text": "What, if I give you those eight vectors and ask, what's a nice property?" + }, + { + "text": "Well, you would say, first, they're all ones and minus ones and zeros, so every multiplication is very fast using just, in binary." + }, + { + "text": "But what's the other great property of those vectors?" + }, + { + "text": "Anybody see it?" + }, + { + "text": "So, of course, when I think about a basis, one nice property, I don't have to have it, but I'm happy if it's there, is that they're orthogonal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk12.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..c0eaf69080e43e238bee148545d1b059bef72365 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "If the basis vectors are orthogonal, then I'm in good shape." + }, + { + "text": "And these are, do you see, take the dot product of that with that, you get four plus ones and four minus ones, you get zero." + }, + { + "text": "Take the dot product of that with that, you get two plus ones and two minus ones." + }, + { + "text": "Or the dot product of that with that, two plus ones and two minus ones." + }, + { + "text": "You can easily check that that's an orthogonal basis." + }, + { + "text": "It's not orthonormal." + }, + { + "text": "I could, to fix it up, I should divide by the length to make them unit vectors." + }, + { + "text": "Let's suppose I do that." + }, + { + "text": "So somewhere in here I've got to account for the fact that this has length square root of eight, that has length square root of four, that has length square root of two." + }, + { + "text": "But that's just a constant factor that's easy to --." + }, + { + "text": "So suppose we've done that." + }, + { + "text": "Then tell me what's W inverse." + }, + { + "text": "That's what chapter four, section four point four was about." + }, + { + "text": "If we have orthonormal columns, what- then the inverse is the same as the transpose." + }, + { + "text": "So if we have a fast way to multiply by W, which we do, the inverse is going to look just the same and we'll have a fast way to do W inverse." + }, + { + "text": "So that's, the wavelet basis passes this requirement for fast." + }, + { + "text": "We can use it fast." + }, + { + "text": "But there's a second requirement, is it any good?" + }, + { + "text": "Because the very fastest thing we could do would be not to change basis at all." + }, + { + "text": "Right?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk13.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..4de80b529af0604a4e0b9b0291a8822dc165b83a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Fastest thing would be, OK, stay with a standard basis, stay with eight pixel values." + }, + { + "text": "But that was poor from compression point of view, right?" + }, + { + "text": "Those eight pixel values, if I just took those eight numbers, I can't throw some of those away." + }, + { + "text": "If I throw away ninety percent, if I compressed ten to one, and throw away ninety percent of my pixel values, well, my picture's just gone dark." + }, + { + "text": "Whereas the basis that was good, the wavelet basis or the Fourier basis, if I throw away c5, c6, c7 and c8, all I'm throwing away is little blips that are probably there in very small amounts." + }, + { + "text": "So the second property that we need is good compression." + }, + { + "text": "So, so first it, it has to be fast, and secondly, it has to be a few basis factors should come close to the signal." + }, + { + "text": "So, so a few, few is enough." + }, + { + "text": "Can I write it that way?" + }, + { + "text": "A few basis factors are enough to reproduce the image, just exactly as on the video of these 18.06 lectures." + }, + { + "text": "I don't know what the compression rate is." + }, + { + "text": "I'll ask, David, who, who does the compression, and, by the way, I'll try to get the lectures, that are relevant for the quiz, up onto the web, in time." + }, + { + "text": "So I'll send him a message today." + }, + { + "text": "So, at the point, so he's using the Fourier basis, because the JPEG, so JPEG 2000, which will be the next standard for image compression, will include wavelets." + }, + { + "text": "So, I mean, you're, you're actually getting a kind of up to date, picture of where this big world of signal and image processing is." + }, + { + "text": "That Fourier is what everybody knew, and what people automatically used, and the new, new one is wavelets, where this is the simplest set of wavelets, and this isn't the one that the FBI uses, by the way." + }, + { + "text": "The FBI uses a more, a more, a smoother wavelet." + }, + { + "text": "Instead of jumping from one to minus one, it's a smooth, cutoff." + }, + { + "text": "And, that's what we'll be in, in JPEG 2000." + }, + { + "text": "OK, so that's that application." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk14.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..8f1debcca7ae641417e7ed0a630d269963c01302 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now let me come to my, the, the math, the linear algebra part of the lecture." + }, + { + "text": "Well, we've actually seen a change of basis." + }, + { + "text": "So let, let me just review that change of basis idea, and then the, and then the transformation to a matrix." + }, + { + "text": "OK, so, so this, I hope you see that these applications are really big." + }, + { + "text": "Now I have to talk a little about change of basis and little about that, the, the matrix." + }, + { + "text": "OK. OK. OK." + }, + { + "text": "So change of basis." + }, + { + "text": "Basically, forgive that pun, OK, I have, I have, I have my vector in one basis, and I want to change to a different one." + }, + { + "text": "Actually, you saw it for the wavelet case." + }, + { + "text": "So I need the, the, let the matrix W, the columns of W, be the new basis vectors." + }, + { + "text": "Then the change of basis involves, just as it did there, W inverse." + }, + { + "text": "So we have the vector, vector, say, x in the old basis, and we, that converts to a vector, let's say, c in the new basis, and the relation is exactly what we had there, that x is Wc." + }, + { + "text": "That's the, that's the, that's the, that's the step we have to take." + }, + { + "text": "There's a matrix W that gives us a change of basis." + }, + { + "text": "OK." + }, + { + "text": "I, I, what I want to do is think about mat- transformations and matrices." + }, + { + "text": "So here's, here's the question, that, that, to complete this lecture." + }, + { + "text": "Suppose I have a linear transformation T. So it's, it's a, it's a, we, we would think of it as an A, as a n by n matrix." + }, + { + "text": "And it's computed with respect to a certain basis." + }, + { + "text": "So T, so, no, I'm sorry." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk15.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..dbc5ad92f06633f3366a78c24c0c7c08b058ee63 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "I've got the transformation T, period." + }, + { + "text": "That's taking eight-dimensional space to eight-dimensional space." + }, + { + "text": "Now let's get matrices in there." + }, + { + "text": "OK." + }, + { + "text": "So, so with respect to, with respect to a fir- a first basis, say, V1 up to V8, it has a matrix A. I'm just setting up letters here." + }, + { + "text": "With respect to a second basis, say, I'll make it U1 up to- or W1, since I've used Ws, W1 up to W8, it has a matrix B." + }, + { + "text": "And my question is, what's the connection between A and B?" + }, + { + "text": "How is the matrix- the transformation T is settled." + }, + { + "text": "We could say it's a rotation, for example." + }, + { + "text": "So that would be one transformation of eight-dimensional space, just spin it a little." + }, + { + "text": "Or project it." + }, + { + "text": "Or, or, whatever, whatever linear transformation we've got." + }, + { + "text": "Now we have to remember, so I- so first- my first step is to remind you how you create that matrix A." + }, + { + "text": "Then my second step is, we would use the same method to create B, but because it came from the same transformation, there's got to be a relation between A and B." + }, + { + "text": "What's the- what's the relation between A and B?" + }, + { + "text": "And let me jump to the answer on that one." + }, + { + "text": "That if I have- if I have the same transformation, and I'm compute- its matrix in one basis and then I compute it in another basis, those two matrices are similar." + }, + { + "text": "So these two matrices are similar." + }, + { + "text": "Now, do you remember what similar matrices meant?" + }, + { + "text": "Similar." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk16.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..9d019933a190fe645eec785d8363a0940d0f76a4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "A is similar- the two matrices are similar." + }, + { + "text": "Similar." + }, + { + "text": "And what do I mean by that?" + }, + { + "text": "I mean that I take the matrix B and I can compute it from the matrix A using some similarity, some matrix M on one side and M inverse on the other." + }, + { + "text": "And this M will be the change of basis matrix." + }, + { + "text": "This part of the lecture is admittedly compressed." + }, + { + "text": "What I wanted you to- it's really the conclusion that I want you to spot." + }, + { + "text": "Now I have to go back and say, what does it mean for A to be the matrix of this transformation T?" + }, + { + "text": "So I have to remind you what that meant." + }, + { + "text": "That was in the last lecture." + }, + { + "text": "Then this is the conclusion, that if I change to a different basis, we now know- see, if I change to a different basis, two things happen." + }, + { + "text": "Every vector has new coordinates." + }, + { + "text": "There, the rule is this one, between the old coordinates and the new ones." + }, + { + "text": "Every matrix changes." + }, + { + "text": "Every transformation has a new matrix." + }, + { + "text": "And the new matrix is related this way." + }, + { + "text": "The M could be the same as the W. The M there could be the W here." + }, + { + "text": "OK." + }, + { + "text": "So can I, in the remaining minutes, recapture my lecture, the end of my lecture that was just before Thanksgiving, about the matrix?" + }, + { + "text": "OK. What's the matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk17.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..f82f2cc230f9f2720733e8b152f84f80f1341c9f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll just take one basis." + }, + { + "text": "So now I'm going to- this part is going to go onto this board here." + }, + { + "text": "What is the matrix?" + }, + { + "text": "What is A?" + }, + { + "text": "OK." + }, + { + "text": "Using a basis v1 up to v8." + }, + { + "text": "OK. What's the point?" + }, + { + "text": "The point is, if I know what the transformation does to those eight basis vectors, I know it completely." + }, + { + "text": "I know T, I know everything about T, I know T completely from knowing what T does to v1, what T does to v2, what T does to v8." + }, + { + "text": "Why is that?" + }, + { + "text": "It's because T is a linear transformation." + }, + { + "text": "So that if I know what these outputs are, so these are the inputs, v1 up to v8, these are the outputs from the transformation, like every one rotated, every one projected, whatever transformation I've done, then why is it that I know everything?" + }, + { + "text": "How does linearity work?" + }, + { + "text": "Why?" + }, + { + "text": "This is because every x is some combination of these basis vectors, right?" + }, + { + "text": "c1 v1, c2 v2, c8 v8." + }, + { + "text": "That's the whole point of a basis, that every vector is a combination of the basis vectors in exactly one way." + }, + { + "text": "And then, what is T of x?" + }, + { + "text": "The point is, I claim that we know T of x completely for every x, because every x is a combination of those, and now we use the linear transformation part to say that the output from x has to be c1 times the output from v1 plus c2 times the output from v2 and so on, up through c8 times the output from v8." + }, + { + "text": "So this is like just saying, OK, we know everything when we know what T does to each basis vector." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk18.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..d9c718592303012586f37aed3dc53271be8cef29 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "So those are the eight things we need." + }, + { + "text": "Now, but we need these answers in this basis." + }, + { + "text": "So T- so this first output is some combination of the eight basis vectors." + }, + { + "text": "So write T times the first- acting on the first input, in other words, write the first output as a combination of the basis vectors." + }, + { + "text": "Say a11 v1 plus a21 v2 and so on, a81 v8." + }, + { + "text": "Write T of v2 as some combination, a12 of v1, a22 of v2 and so on." + }, + { + "text": "I'm creating the matrix A, column by column." + }, + { + "text": "Those numbers go in the first column, these numbers go in the second column." + }, + { + "text": "The matrix A that this is our matrix that represents T in this basis is these numbers." + }, + { + "text": "a11 down to a18, a21 down to a28 and so on." + }, + { + "text": "OK. That's the recipe." + }, + { + "text": "In other words, if I give you a transformation and a basis, that's what I have to give you." + }, + { + "text": "The inputs are the basis and to tell you what the transformation is." + }, + { + "text": "And then you tell me, you compute T for each basis, expand that result in the basis, and that gives you the sixty-four numbers that go into the matrix A." + }, + { + "text": "Let me suppose, let's close with the best example of all." + }, + { + "text": "Suppose v1 to v8, this basis, is the eigenvectors." + }, + { + "text": "Suppose we have an eigenvector basis." + }, + { + "text": "So that T of vi is just, is in the same direction as vi." + }, + { + "text": "Now my question is, what is A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk19.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..4bc0bda81becbd032c626bcaab40cca8eaa39155 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Can you carry through the steps?" + }, + { + "text": "Let's, let's do them together, because we can do it in one minute." + }, + { + "text": "So we've chosen this perfect basis." + }, + { + "text": "And actually, with signal image processing, they might look for the eigenvectors, but that would take more calculation time than just saying, OK, we'll use the wavelet basis, or OK, we'll use the Fourier basis." + }, + { + "text": "But the very best basis is the eigenvector basis." + }, + { + "text": "OK, what's the matrix?" + }, + { + "text": "So, what's the first column of the matrix?" + }, + { + "text": "How do I get the first column?" + }, + { + "text": "I take the first basis vector v1." + }, + { + "text": "I op- I look to see what does the transformation do to it." + }, + { + "text": "The output is lambda one v1." + }, + { + "text": "I express that output as a combination, so the first input is v1." + }, + { + "text": "Its output is lambda one v1." + }, + { + "text": "Now write lambda one v1 as a combination of the basis vectors." + }, + { + "text": "Well, it's already done." + }, + { + "text": "It's just lambda one times the first basis vector and zero times the others." + }, + { + "text": "So this first column will have lambda one and zeros." + }, + { + "text": "OK?" + }, + { + "text": "Second input is v2." + }, + { + "text": "Output is lambda two v2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk2.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..44553739c24736b408dbd01c3688e075b25f9a15 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it has to be compressed." + }, + { + "text": "The standard compression, and still used in, in the, with these lectures, is, called JPEG." + }, + { + "text": "I think that stands for a Joint Photographic Experts Group." + }, + { + "text": "They established a system of compression." + }, + { + "text": "And I just want to tell you what it's about." + }, + { + "text": "It's a change of basis." + }, + { + "text": "What, what's, what basis do we have?" + }, + { + "text": "The, the current basis we have is, you could say, the standard basis is every pixel give a value." + }, + { + "text": "So that's like, we have a vector x, which is five hundred and twelve squared long, and in the i-th position, we get a number like one twenty one or something, the next, the pixel next to it might be one twenty four, maybe where, maybe where the, where my tie, begins to end." + }, + { + "text": "So if it was mostly blue shirt, this would be a slight difference in shading, but pretty close." + }, + { + "text": "Then the tie would be a different color." + }, + { + "text": "So, so we might have quite a few pixels for the blue shirt and a whole lot more for the blackboard that are very close." + }, + { + "text": "And that's what, are very correlated." + }, + { + "text": "And that's what gives us the possibility of compression." + }, + { + "text": "For example, before the lecture starts, if we had a blank blackboard, then there's an image, but it would make no sense to take that image and tell you what it is pixel by pixel." + }, + { + "text": "I mean, there's a case in which all pixel values, all gray levels are the same, or practically the same, depending on the erasing of the board, but extremely close." + }, + { + "text": "And so that's an image where the standard basis is lousy." + }, + { + "text": "That's, that's the basic fact." + }, + { + "text": "That, that the standard basis which gives the value of every pixel makes no use of the fact that we're getting a whole lot of pixels whose gray levels, the neighboring pixels tend to have the same gray level as the, as their, as their neighbors." + }, + { + "text": "So to take, how do we take advantage of that fact?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk20.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..57e892c1f19c9a45e5f14bb334eab942b0d796a2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk20.json @@ -0,0 +1,32 @@ +[ + { + "text": "OK, write that output as a combination of the v's." + }, + { + "text": "It's already done." + }, + { + "text": "It's just lambda two times the second v. So we need, in the second column, we have lambda two times the second v. Well, you see what's coming." + }, + { + "text": "That in that basis, in the eigenvector basis, the matrix is diagonal." + }, + { + "text": "So that's the perfect basis." + }, + { + "text": "That's the basis we'd love to have for image processing, but to find the eigenvectors of our pixel matrix would be too expensive." + }, + { + "text": "So we do something cheaper and close, which is to choose a good basis like, like wavelengths." + }, + { + "text": "OK, thanks." + }, + { + "text": "So quiz review on Wednesday, all day." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk3.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..8e246b42e71ac0ef99e39e59a7562c71f3da61b4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, one basis vector that would be extremely nice to, one vector that would be extremely nice to include in the basis would be a vector of all ones." + }, + { + "text": "That's not in our standard basis." + }, + { + "text": "So our, so let me just write again." + }, + { + "text": "The standard basis would, is, is our, is our one and all the rest zeros, zero, one, and all the rest zeros, everybody knows what the standard basis is." + }, + { + "text": "Now, any other basis for our, so this is, for this very high-dimensional space, now I'm going to speak about a better basis, better basis, and let me just emphasize, one vector that would be extremely nice to have in that basis is the vector of all ones." + }, + { + "text": "Why is that?" + }, + { + "text": "Let me just say again." + }, + { + "text": "Because that vector of all ones, by itself, one vector is, is able to completely give the information on a solid image." + }, + { + "text": "Of course, our image won't be solid, it'll have a mix of, of, solid and, and signal." + }, + { + "text": "So that one vector, but that, having that one vector in the basis is, is, is going to save us a whole lot." + }, + { + "text": "Now the question is, what other vectors should be in the basis?" + }, + { + "text": "The, the extreme vector in the basis might be a vector of one minus one, one minus one, one minus one." + }, + { + "text": "That would be a vector that shows, I mean, that's like a checkerboard vector, right?" + }, + { + "text": "That's a vector that would, if, if we had, if, if the image was like a huge checkerboard of plus minus, plus minus, plus minus, that vector would carry the whole signal." + }, + { + "text": "But much more common would be maybe to have half the image, darker and the other half lighter." + }, + { + "text": "So another image, another vector that might be quite useful in here would be half ones and half minus ones." + }, + { + "text": "I'm just trying to get across the idea of, that a basis could be, that first of all, we've got, the basis is at our disposal." + }, + { + "text": "Like, we're free to choose that." + }, + { + "text": "And it's a billion dollar decision what we choose." + }, + { + "text": "So, and TV people would rather, would prefer one basis based on the way the, the signal is scanned, and movie people would prefer another." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk4.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..811c58ffd5e28e456b42de439fa8cee4339bd2a6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "I mean, there's giant politics in this question that really reduces to a, to a linear algebra problem what basis to choose." + }, + { + "text": "I'll just mention the best known basis, which is, which JPEG uses, let me put that here, is the Fourier basis." + }, + { + "text": "So when you, when you use the Fourier basis, that includes, this is the constant vector, the DC vector, if we're electrical engineers, the, the, the vector of all ones, so it would include one, one, one, one." + }, + { + "text": "Often, eight by eight is a good choice." + }, + { + "text": "Eight by eight is a, is a good choice." + }, + { + "text": "So, what do I mean by this eight by eight?" + }, + { + "text": "I mean that the big signal, which is five twelve by five twelve, gets broken down, and JPEG does this, into eight by eight blocks." + }, + { + "text": "And we, sort of, this is too much to deal with at once." + }, + { + "text": "So what JPEG does is take this eight by eight block, which is sixty-four coefficients, sixty-four, pixels, and changes the basis on the, on that piece." + }, + { + "text": "And then, now, let's see, I was going to write down Fourier, so you remember Fourier is, is this vector of all ones, and then, the vector, oh, well, actually, I gave a lecture earlier about the Fourier matrix, these, this matrix whose columns are powers of a, of a, complex number w. I, I won't repeat that, because I'm not, I don't want to go into the details of the Fourier basis." + }, + { + "text": "Just to tell you how compression works." + }, + { + "text": "So what happens in JPEG?" + }, + { + "text": "What happens to the video, to a, to each image of, of, of these lectures?" + }, + { + "text": "The, it gets broken into eight by eight blocks." + }, + { + "text": "OK." + }, + { + "text": "Within each block, we have sixty-four coefficients, sixty-four basis vectors, sixty-four pixels, and we change basis in sixty-four dimensional space, using these Fourier vectors." + }, + { + "text": "Just, no, that was a lossless step." + }, + { + "text": "Let, let me, let me emphasize." + }, + { + "text": "In comes the signal." + }, + { + "text": "x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk5.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..7ce7441a356838f6e496da3b2d782533cfb4ad1b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "We change basis." + }, + { + "text": "This is the basis change." + }, + { + "text": "Change basis." + }, + { + "text": "Choose a better basis." + }, + { + "text": "So it produces, the, coefficients c. So sixty-four pixels come in, sixty-four coefficients come out." + }, + { + "text": "Now comes the compression." + }, + { + "text": "Now come, this was lossless." + }, + { + "text": "It's just, we know that R64 has plenty of basis, and we've chosen one." + }, + { + "text": "Now, in that basis, we write, we write the signal in that basis, and that's what my lecture, that's the math part of my lecture." + }, + { + "text": "Now here's the application part." + }, + { + "text": "The next part is going to be the compression step." + }, + { + "text": "And that's lossy." + }, + { + "text": "We're going to lose information." + }, + { + "text": "And what, what will actually happen at that step?" + }, + { + "text": "Well, one thing we could do is just throw away the small coefficients." + }, + { + "text": "So that would be, that's called thresholding." + }, + { + "text": "We set some threshold." + }, + { + "text": "Every coefficient, every basis vector that's not in there more than the threshold value, and we set some threshold so that our eye can't see the difference, whether we throw away that, or can hardly see the difference, whether we throw away that little bit of that basis vector or keep it." + }, + { + "text": "So this compression step produces a compressed set of coefficients." + }, + { + "text": "Let me, I'll just keep going here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk6.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..e51518b0b218267f8c2f0d7243d31fec00ba9b42 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, so it keeps going." + }, + { + "text": "This compression step produces some coefficients c hat." + }, + { + "text": "And with lots of, with many zeros." + }, + { + "text": "So that's where the compression came." + }, + { + "text": "Probably there's enough of this vector of all ones, we very seldom throw that away." + }, + { + "text": "Usually its coefficient will be large." + }, + { + "text": "But the coefficient of something like this, that quickly alternating vector, there's probably very little of that in any smooth signal." + }, + { + "text": "I mean, that's high frequent- this is, this is low frequency, zero frequency." + }, + { + "text": "This stuff is the highest frequency we could have, and there's a, if the noise, the, the jitter is producing that sort of output, but a smooth lecture like this one is, has very little of that highest frequency." + }, + { + "text": "Very little noise in this lecture." + }, + { + "text": "OK." + }, + { + "text": "So, so we throw away whatever there is, and we, we're left with just a few coefficients, and then we reconstruct a signal using those coefficients." + }, + { + "text": "We take the, those coefficients times their basis vectors, but this sum doesn't have sixty-four terms anymore." + }, + { + "text": "Probably it has about two or three terms." + }, + { + "text": "So that, if we say it has three terms." + }, + { + "text": "From sixty-four down to three, that's compression of twenty-one to one." + }, + { + "text": "That's the kind of compression you're looking for." + }, + { + "text": "And everybody is looking for that sort of compression." + }, + { + "text": "Let's see, I guess I met the problem with the FBI and fingerprints." + }, + { + "text": "So there's a whole lot of still images." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk7.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..4cdf43a95d584ba42202d1c77ba5f96a998319d5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "You know, you, with your thumb, you make these inky marks, which, go somewhere." + }, + { + "text": "You used to go to Washington and get stored in a big file." + }, + { + "text": "So Washington had a file of thirty million murderers, cheaters on quizzes, other stuff, and, and actually, there was no way to retrieve them in time." + }, + { + "text": "Like, so, so suppose you're at the police station, they say, OK, this person may have done this, check with Washington, have they got his or her fingerprints on file." + }, + { + "text": "Well, Washington won't know the answer within a week, if it's got filing cabinets full of fingerprints." + }, + { + "text": "So of course the natural step is digitize them." + }, + { + "text": "So all fingerprints are now digitized, so now it's at least electronic, but still there's too much information in each, each one." + }, + { + "text": "I mean, you can't search through that many, uh, fingerprints if you, if, if the digital image is five twelve squared by five twelve squared, if it's that many pixels." + }, + { + "text": "So you get compressed." + }, + { + "text": "So the FBI had to decide what basis to choose for compression of fingerprints, and then they built a big new facility in West Virginia and that's where fingerprints now are sent." + }, + { + "text": "So if you, I think if you get your fingerprints done now at the police station, if it's an up-to-date police station, it's, it happens digitally and the signal is sent digitally, and then in West Virginia it's compressed and indexed." + }, + { + "text": "And then, if they want to find you, they can do it within minutes, instead of within a week." + }, + { + "text": "OK." + }, + { + "text": "So this compression is, comes up for signals, for images." + }, + { + "text": "For video, which is like these lectures, uh, there's another aspect." + }, + { + "text": "You could treat the video as one still image after another one, and compress each one and then run them and make a video." + }, + { + "text": "But that misses, well, you can see why that's not optimal." + }, + { + "text": "In video, so for in a video thing, you have a sequence of images, so video is really a sequence of images, but what about one image to the next image?" + }, + { + "text": "They're extremely correlated." + }, + { + "text": "I mean, that, I'm getting an image every split second, and although I'm moving slightly, that's what's producing the, jumpy motion on the video." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk8.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..41f54e28ef2064485cf009d9b5e4574263d3680d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "But I'm not, like, you know, each, each image in the sequence is pretty close to the one before." + }, + { + "text": "So you have to use, like, prediction and correction." + }, + { + "text": "I mean, you, my, the image of me one instant, one time step later, you would assume would be the same, and then plus a small correction." + }, + { + "text": "And you would only code and digitize the correction, and compress the correction." + }, + { + "text": "So the sequence of images that's highly correlated, and the problem in compression is always to use this correlation, this fact that in time or in space, things don't change instantly, they, they're very often smooth changes, and, you can predict one value from the previous value." + }, + { + "text": "OK." + }, + { + "text": "So that's the, those are applications, which are pure linear algebra." + }, + { + "text": "I could, maybe I'll, maybe you'll allow me to tell you the, and the book describes, the new basis that's, the competition for Fourier." + }, + { + "text": "So the competition for Fourier is called wavelets, and I can describe what that basis is like, say, in the eight by eight case." + }, + { + "text": "So that eight by eight wavelet basis is the vector of all ones, eight ones, then the vector of four ones and four minus ones, then the vector of two ones and two minus ones and four zeros, and also the vector of four zeros and two ones and two minus ones." + }, + { + "text": "So now I'm up to four, and I need four more, right, for R8?" + }, + { + "text": "So the next basis vector will be one minus one and six zeros, and then three more like that, with a one minus one there and there and there." + }, + { + "text": "So those are eight vectors in eight-dimensional space." + }, + { + "text": "Those are, those are called wavelets, and you, and it's a very simple wavelet choice." + }, + { + "text": "It's a more sophisticated choice." + }, + { + "text": "This is a little jumpy, to jump between one and minus one." + }, + { + "text": "And actually, you can see now, suppose you compare the wavelet basis with the Fourier basis above." + }, + { + "text": "How could I write this guy, which is in the Fourier basis, it's an eight, it's a vector in R8, how would I write that as a combination of the wavelet basis?" + }, + { + "text": "Do you, have I told you enough about the wavelet basis that you can see?" + }, + { + "text": "How does this very fast guy, what combination of the wavelet basis is that very fast guy?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk9.json b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..2bc1d292fd925c01e44d5599863fa8cb2bcfba79 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/0h43aV4aH7I_7_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It would be this one, it would be the sum of these four, right?" + }, + { + "text": "That very fast guy will be that one minus one, and the next one, and the next one, and the next one." + }, + { + "text": "So this is the sum of those last four wavelets." + }, + { + "text": "This one we've kept, and so on." + }, + { + "text": "So, each, well, every, well, that's what a basis does." + }, + { + "text": "Every vector in R8 is some combination of those, and for the linear algebra, we have, so the linear algebra is this step, find the coefficients." + }, + { + "text": "That's, that's the step we want to take." + }, + { + "text": "If I give you the basis, like this wavelet basis, and I give you the pixel, so here are the pixel values, p1, p2, down to p8." + }, + { + "text": "What's, what's the job?" + }, + { + "text": "What's the linear algebra here?" + }, + { + "text": "So this is, these are the values, this is in the standard basis, right?" + }, + { + "text": "Those are just the values at eight successive points." + }, + { + "text": "I guess I'm dropping down to one dimension instead of eight by eight, I'm just going to take eight pixel values along that first top row." + }, + { + "text": "So I, what do I want to do?" + }, + { + "text": "In the standard basis, here are the pixel values." + }, + { + "text": "I want to write that as a combination of c1 times this guy, plus c2 times this guy, plus c3, these are the coefficients, plus c4 times this one." + }, + { + "text": "Do you see what I'm doing?" + }, + { + "text": "I want to write this vector p as a combination of c1 times the first wavelet, plus c8 times the eighth wavelet." + }, + { + "text": "That's the, that's the transform step." + }, + { + "text": "That's the lossless step, that's the step from p, oh, I'm calling it p here and I called it x there, so let me, at the risk of moving and therefore making this jumpy, suppose the signal I'm now calling p, the set of pixel values and I'm looking for the coefficients." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk0.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6898d4fe66019ef6b40d0472ea94a968e7bbde9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, shall we start?" + }, + { + "text": "This is the second lecture on eigenvalues." + }, + { + "text": "So the first lecture was set -- reached the key equation, Ax equal lambda x. x is the eigenvector and lambda is the eigenvalue." + }, + { + "text": "Now, to use that." + }, + { + "text": "And the good way to, after we've found, so job one is to find the eigenvalues and find the eigenvectors." + }, + { + "text": "Now after we found them, what do we do with them?" + }, + { + "text": "Well, the good way to see that is diagonalize the matrix." + }, + { + "text": "So the matrix is A, and I want to show, first of all, this is like the basic fact." + }, + { + "text": "This, this formula." + }, + { + "text": "That's, that's the key to today's lecture." + }, + { + "text": "This matrix A, I put its eigenvectors in the columns of a matrix S. So S will be the eigenvector matrix, and I want to look at this magic combination S inverse A S. So can I show you how that, how that, what happens there?" + }, + { + "text": "And notice, notice, there's an S inverse." + }, + { + "text": "We have to be able to invert this eigenvector matrix S. So for that we need n independent eigenvectors." + }, + { + "text": "So that's the, that's the case." + }, + { + "text": "OK." + }, + { + "text": "So suppose we have n linearly independent eigenvectors of A." + }, + { + "text": "Put them in the columns of this matrix S. So I'm naturally going to call that the eigenvector matrix, because it's got the eigenvectors in its columns." + }, + { + "text": "And all I want to do is show you what happens when you multiply A times S. So A times S. So this is A times the matrix with the first eigenvector in its first column, the second eigenvector in its second column, the nth eigenvector in its nth column." + }, + { + "text": "And how am I going to do this matrix multiplication?" + }, + { + "text": "Well, certainly I'll do it a column at a time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk1.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..fbe078217bb68baea8e0605a5d04be568c49efbf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I get?" + }, + { + "text": "A times the first column gives me the first column of the answer, but what is it?" + }, + { + "text": "That's an eigenvector." + }, + { + "text": "A times x1 is equal to the lambda times the x1." + }, + { + "text": "And that lambda's we'll call lambda one, of course." + }, + { + "text": "So that's the first column, A x1 is the same as lambda one x1." + }, + { + "text": "A x2 is lambda two x2, so on, along to, in the nth column, we now have lambda n xn." + }, + { + "text": "Looking good, but the next step is even better." + }, + { + "text": "So for the next step, I want to separate out those eigenvalues, those multiplying numbers, from the x's." + }, + { + "text": "So then I'll have just what I want." + }, + { + "text": "OK, so how, how am I going to separate out?" + }, + { + "text": "So that, that number lambda one is multiplying the first column." + }, + { + "text": "So if I want to factor it out of the first column, I better put, here is going to be x1, and that's going to multiply this matrix lambda one in the first entry in all zeros." + }, + { + "text": "You see that that, that's going to come out right for the first column?" + }, + { + "text": "Because we remember how, how we're going back to that original punchline, that if I want a number to multiply x1, then I can do it by putting x1 in that column, in the first column, and putting that number there." + }, + { + "text": "What am I going to have here?" + }, + { + "text": "I'm going to have lambda one, I'm going to have x1, x2, xn." + }, + { + "text": "These are going to be my columns again." + }, + { + "text": "I'm getting s back again." + }, + { + "text": "I'm getting s back again, but now what's it multiplied by?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk10.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c58a42edbe9567233ca7f57643a0b7d43ae6761f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what are the eigenvalues?" + }, + { + "text": "You can tell me right away what they are." + }, + { + "text": "They're two and two, right." + }, + { + "text": "It's a triangular matrix, so when I do this determinant, shall I do this determinant of A minus lambda I?" + }, + { + "text": "I'll get this two minus lambda, one, zero, two minus lambda, right?" + }, + { + "text": "I take that determinant, so I make those into vertical bars to mean determinant, and what's the determinant?" + }, + { + "text": "Two minus lambda squared." + }, + { + "text": "What are the roots?" + }, + { + "text": "Lambda equal two twice." + }, + { + "text": "So the eigenvalues are lambda equals two and two." + }, + { + "text": "OK, fine." + }, + { + "text": "Now the next step, find the eigenvectors." + }, + { + "text": "So I look for eigenvectors and what do I find for this guy?" + }, + { + "text": "Eigenvectors for this guy, when I subtract two minus the identity, so A minus two I has zeros here, and I'm looking for the null space." + }, + { + "text": "What's, what are the eigenvectors?" + }, + { + "text": "They're the, they're, they're the null space of A minus lambda I." + }, + { + "text": "The null space is only one dimension." + }, + { + "text": "This is a case where I don't have enough eigenvectors." + }, + { + "text": "My algebraic multiplicity is two." + }, + { + "text": "I, I would say when I see, when I count how often the eigenvalue is repeated, that's the algebraic multiplicity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk11.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..779c2cf904d904b761080db2671aac46394ad02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the multiplicity." + }, + { + "text": "How many times is it the root of the polynomial?" + }, + { + "text": "My polynomial is two minus lambda squared." + }, + { + "text": "It's a double root." + }, + { + "text": "So my algebraic multiplicity is two." + }, + { + "text": "But the geometric multiplicity, which looks for vectors, looks for eigenvectors and which means the null space of this thing." + }, + { + "text": "And the only eigenvector is one zero." + }, + { + "text": "That's in the null space." + }, + { + "text": "Zero one is not in the null space." + }, + { + "text": "The null space is only one dimensional." + }, + { + "text": "So there's a matrix, my, this A or the original A, that are not diagonalizable." + }, + { + "text": "I can't, I can't find two independent eigenvectors, there's only one." + }, + { + "text": "OK." + }, + { + "text": "So that's the case that I'm, that's a case that I, I'm not really handling." + }, + { + "text": "For example, when I wrote down up here that the powers went to zero if the eigenvalues were below one, I didn't really handle that case of repeated eigenvalues because my reasoning was based on this formula." + }, + { + "text": "And this formula is based on n independent eigenvectors." + }, + { + "text": "OK." + }, + { + "text": "So just to say that." + }, + { + "text": "There are some matrices that we don't cover through diagonalization, but the great majority we do." + }, + { + "text": "OK. And we're always OK if we have different distinct eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk12.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..77d090704cc298475d94416b7ecb88a2a015a913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. That's the, like, the typical case." + }, + { + "text": "Because for each eigenvalue there's at least one eigenvector, the algebraic multiplicity here is one for every eigenvalue, and the geometric multiplicity is one." + }, + { + "text": "There's one eigenvector and they are independent." + }, + { + "text": "OK. OK. Now let me come back to the important case when we're OK." + }, + { + "text": "The important case when we are diagonalizing." + }, + { + "text": "Let me look at, so let me solve this equation." + }, + { + "text": "The equation will be each, I start with some, start with a given vector u0." + }, + { + "text": "And then my equation is that every step I multiply what I have by a." + }, + { + "text": "That equation ought to be simple to handle." + }, + { + "text": "OK. And I'd like to be able to solve it." + }, + { + "text": "How would I find, if I start with a vector u0, and I multiply by a a hundred times, what have I got?" + }, + { + "text": "Well, I can certainly write down a formula for the answer." + }, + { + "text": "So what, what, so u1 is a u0." + }, + { + "text": "And u2 is, what's u2 then?" + }, + { + "text": "U2 I multiply it, u2 I get from u1 by another, multiplying by a, so I've got a twice." + }, + { + "text": "And my formula is uk, after k steps, I've multiplied by a k times the original u0." + }, + { + "text": "You see what I'm doing?" + }, + { + "text": "The next section is going to solve systems of differential equations." + }, + { + "text": "I'm going to have derivatives." + }, + { + "text": "This, this section is the nice one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk13.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..ba8214d8c636e4757a266d6617801174bc939d80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "It solves difference equations." + }, + { + "text": "I would call that a difference equation." + }, + { + "text": "It's conne- a first order." + }, + { + "text": "I would call that a first order system, because it connects only, it only goes up one level." + }, + { + "text": "And it's a system because these are vectors and that's a matrix." + }, + { + "text": "And the solution is just that." + }, + { + "text": "OK." + }, + { + "text": "But, that's a nice formula." + }, + { + "text": "That's the, like, the most compact formula I could ever get." + }, + { + "text": "U one hundred would be a to the one hundredth u0." + }, + { + "text": "But how would I actually find u one hundred?" + }, + { + "text": "How would I find, how would I discover what u one hundred is?" + }, + { + "text": "Let me, let me show you how." + }, + { + "text": "Here, here's the idea." + }, + { + "text": "If, so, to solve, to really solve, shall I say, to really solve." + }, + { + "text": "To really solve it, I would take this initial vector, u0, and I would write it as a combination of eigenvectors." + }, + { + "text": "To really solve, write, write u0 as a combination, say, certain amount of the first eigenvector plus a certain amount of the second eigenvector plus a certain amount of the last eigenvector." + }, + { + "text": "Now multiply by a." + }, + { + "text": "You want to, you got to see the magic of eigenvectors work." + }, + { + "text": "Multiply by a." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk14.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7843b2bf0cac762d1c12452cf36500ea4ad13370 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a u0 is what?" + }, + { + "text": "So a times that." + }, + { + "text": "A times, so what's, I can separate it out into n separate pieces and that's the whole point." + }, + { + "text": "That each of those pieces is going in its own merry way." + }, + { + "text": "Each of those pieces is an eigenvector, and when I multiply by a, what does this piece become?" + }, + { + "text": "So that's some amount of the first, let's suppose the eigenvectors are normalized to be unit vectors." + }, + { + "text": "So that says what the eigenvector is." + }, + { + "text": "It's, and I need some multiple of it to produce u0." + }, + { + "text": "OK. Now when I multiply by a, what do I get?" + }, + { + "text": "I get c1, which is just a factor, times a x1, but a x1 is lambda one x1." + }, + { + "text": "When I multiply this by a, I get c2 lambda two x2." + }, + { + "text": "And here I get cn lambda n xn." + }, + { + "text": "And suppose I multiply by a to the hundredth power now." + }, + { + "text": "Can we, can we, having done it, multiplied by a, let's multiply by a to the hundredth." + }, + { + "text": "What happens to this first term when I multiply by a to the one hundredth?" + }, + { + "text": "It's got that factor lambda to the hundredth." + }, + { + "text": "That's the key." + }, + { + "text": "That, that's what I mean by going its own merry way." + }, + { + "text": "It, it is pure eigenvector, it's exactly in a direction where multiplication by a just brings in a scalar factor lambda one." + }, + { + "text": "So a hundred times brings in this a hundred times." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk15.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7ee3348735378aa4049d33ec2a197d0ceb0c447c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Hundred times lambda two, hundred times lambda n. Actually, we're, what are we seeing here?" + }, + { + "text": "We're seeing, this same, lambda, capital lambda to the hundredth, as in the, as in the diagonalization, and we're seeing the S matrix, the matrix S of eigenvectors." + }, + { + "text": "That's what this has got to, this has got to amount to, a lambda to the hundredth power times an S times this vector C that's telling us how much of each one is in the original thing." + }, + { + "text": "So if, if I had to really find the hundredth power, I would take u0, I would expand it as a combination of eigenvectors, this is really S, the eigenvector matrix times C, the, the coefficient vector." + }, + { + "text": "And then I would immediately, then, by inserting these hundredth powers of eigenvalues, I'd have the answer." + }, + { + "text": "So the, the, huh, there must be, well, let's see." + }, + { + "text": "OK." + }, + { + "text": "It's, so, yeah." + }, + { + "text": "So if u100 is a to the hundredth times u0, and u0 is Sc, then you see this formula is just this formula, which is the way I would actually get hold of this, of this u100, which is, let me put it here, u100." + }, + { + "text": "The way I would actually get hold of that, see what, what the solution is after a hundred steps, would be expand the initial vector into eigenvectors and, and let each eigenvector go its own way, multiplying by a hundred at, by lambda at every step, and therefore by lambda to the hundredth power after a hundredth step." + }, + { + "text": "Can I do an example?" + }, + { + "text": "So that's, that's the, the formulas." + }, + { + "text": "Now let me take an example." + }, + { + "text": "I'll use the Fibonacci sequence as an example." + }, + { + "text": "So, so Fibonacci example." + }, + { + "text": "You remember the Fibonacci numbers?" + }, + { + "text": "If we start with one and one as F0, oh, I think I start with zero, maybe." + }, + { + "text": "Let zero and one be the first ones." + }, + { + "text": "So there's F0 and F1, the first two Fibonacci numbers." + }, + { + "text": "Then what's the rule for Fibonacci numbers?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk16.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..79c65e32781f7f304b504a6c390247abb9d26ac8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "They're the sum." + }, + { + "text": "The next one is the sum of those, so it's one." + }, + { + "text": "The next one is the sum of those, so it's two." + }, + { + "text": "The next one is the sum of those, so it's three." + }, + { + "text": "Well, it looks like one, two, three, four, five, but somehow it's not going to do that way." + }, + { + "text": "The next one is five, right." + }, + { + "text": "Two and three makes five." + }, + { + "text": "The next one is eight." + }, + { + "text": "The next one is thirteen." + }, + { + "text": "And the one hundredth Fibonacci number is what?" + }, + { + "text": "That's my question." + }, + { + "text": "How could I get a formula for the hundredth number and for example how could I answer the question how fast are they growing?" + }, + { + "text": "How fast are those Fibonacci numbers growing?" + }, + { + "text": "They're certainly growing." + }, + { + "text": "It's not a stable case, whatever the eigenvalues of whatever matrix it is, they're not smaller than one." + }, + { + "text": "These numbers are growing." + }, + { + "text": "But how fast are they growing?" + }, + { + "text": "The answer is lies in the eigenvalue." + }, + { + "text": "So I've got to find the matrix, so let me write down the Fibonacci rule, F k plus two is F k plus one plus F k, right?" + }, + { + "text": "Now that's not in my -- I want to write that as U k plus one and A U k. But right now what I've got is a single equation, not a system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk17.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b3aaa9dcee3cf27c112015659bb5a0b51a983ce1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's second order." + }, + { + "text": "It's like having a second order differential equation with second derivatives." + }, + { + "text": "I want to get first derivatives." + }, + { + "text": "Here I want to get first difference." + }, + { + "text": "So the way to do it is to introduce U k will be a vector." + }, + { + "text": "See, a small trick." + }, + { + "text": "Let U k be a vector, F k plus one and F k. So I'm going to get a two by two system, first order, instead of a one, instead of a scalar system, second order, by a simple trick." + }, + { + "text": "I'm just going to add in an equation F k plus one equals F k plus one." + }, + { + "text": "That will be my second equation." + }, + { + "text": "Then this is my system, this is my unknown, and what's my one-step equation?" + }, + { + "text": "So now U k plus one." + }, + { + "text": "That's so U k plus one is the left side, and what have I got here on the right side?" + }, + { + "text": "I've got some matrix multiplying U k. Can you see that all right?" + }, + { + "text": "If you can see it, then you can tell me what the matrix is." + }, + { + "text": "You see that I'm taking my system here, I artificially made it into a system." + }, + { + "text": "I artificially made the unknown into a vector, and now I'm ready to look at and see what the matrix is." + }, + { + "text": "So do you see the left side, U k plus one is F k plus two F k plus one, that's just what I want." + }, + { + "text": "On the right side, this, remember, this U k here, let me for the moment put it as F k plus one F k. So what's the matrix?" + }, + { + "text": "Well, that has a one and a one, and that has a one and a zero." + }, + { + "text": "There's the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk18.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..6c1b68c2cb2fde3f5dea82f3100d4da31fcce70a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "You see that that gives me the right-hand side." + }, + { + "text": "So there's the matrix A, and this is our friend U k. So we've got, so that simple trick changed the second order scalar problem to a first order system, two, with two unknowns." + }, + { + "text": "With a matrix and now what do I do?" + }, + { + "text": "Well, before I even think, I find its eigenvalues and eigenvectors." + }, + { + "text": "So what are the eigenvalues and eigenvectors of that matrix?" + }, + { + "text": "Let's see." + }, + { + "text": "I was, first let me just, like, think for a minute." + }, + { + "text": "It's two by two, so this shouldn't be impossible to do." + }, + { + "text": "Let's do it." + }, + { + "text": "OK." + }, + { + "text": "So my matrix again is one one one zero." + }, + { + "text": "It's symmetric, by the way." + }, + { + "text": "So what I will eventually know about symmetric matrices is that the eigenvalues will come out real, I won't get any complex numbers here, and the eigenvectors, once I get those, actually will be orthogonal." + }, + { + "text": "But two by two, I'm more interested in what the actual numbers are." + }, + { + "text": "What do I know about the two numbers?" + }, + { + "text": "Well, should, do you want me to find this determinant of A minus lambda I?" + }, + { + "text": "Sure." + }, + { + "text": "So it's the determinant of one minus lambda one one zero, right?" + }, + { + "text": "Minus lambda, yes, got it." + }, + { + "text": "OK. OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk19.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..a73b23e3d56b889ff49ea7f55a784fac33e13c3d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "There'll be two eigenvalues." + }, + { + "text": "Well, tell me again what I know about the two eigenvalues before I go any further." + }, + { + "text": "Tell me something about these two eigenvalues, what do they add up to?" + }, + { + "text": "Lambda one plus lambda two is the same as the trace down the diagonal of the matrix, one and zero is one." + }, + { + "text": "So lambda one plus lambda two should come out to be one, and lambda one times lambda two should come out to be the determinant, which is minus one." + }, + { + "text": "So I'm expecting the eigenvalues to add to one and to multiply to minus one." + }, + { + "text": "But let's just see it happen here." + }, + { + "text": "If I multiply this out, I get that times that'll be a lambda squared minus lambda minus one." + }, + { + "text": "Good." + }, + { + "text": "Lambda squared minus lambda minus one." + }, + { + "text": "Actually, you see the, compare that with the original equation that I started with." + }, + { + "text": "Fk plus two minus Fk plus one minus Fk is zero." + }, + { + "text": "The recurrent, the recursion that the Fibonacci number satisfy is somehow showing up directly here for the eigenvalues when we set that to zero." + }, + { + "text": "OK. Let's solve." + }, + { + "text": "Well, I would like to be able to factor that, that quadratic, but I'm better off to use the quadratic formula." + }, + { + "text": "Lambda is, let's see, minus b is one, plus or minus the square root of b squared, which is one, minus four, times that, times that, which is plus four, over two." + }, + { + "text": "So that's the square root of five." + }, + { + "text": "So the eigenvalues are lambda one is one half of one plus square root of five, and lambda two is one half of one minus square root of five." + }, + { + "text": "And sure enough, they, those add up to one, and they multiply to give minus one." + }, + { + "text": "OK. Those are the two eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk2.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..43cfb012fc04a89fc7dab94c23bfb0f50ade3782 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "On the right, it's multiplied by, if I want, if I want lambda n xn in the last column, how do I do it?" + }, + { + "text": "Well, the last column here will be, I'll, I'll take the last column, use these coefficients, put the lambda n down there, and it will multiply that nth column and give me lambda n xn." + }, + { + "text": "There, there you see matrix multiplication just working for us." + }, + { + "text": "So I started with A s. I wrote down what it meant." + }, + { + "text": "A times each eigenvector." + }, + { + "text": "That gave me lambda times the eigenvector." + }, + { + "text": "And then when I peeled off the lambdas, they were on the right-hand side, so I've got s, my matrix back again, and this matrix, this diagonal matrix, the eigenvalue matrix, and I call it capital lambda, using capital letters for matrices, and lambda to prompt me that it's, that it's eigenvalues that are in there." + }, + { + "text": "So you see that the eigenvalues are just sitting down that diagonal?" + }, + { + "text": "If I had a column x2 here, I would want the lambda two in the two two position, in the diagonal position, to multiply that x2 and give me the lambda two x2." + }, + { + "text": "That's my formula." + }, + { + "text": "A s is s lambda." + }, + { + "text": "OK. That's, that's the, you see, it's just a calculation." + }, + { + "text": "Now, I, I mentioned, and I have to mention again, this business about n independent eigenvectors." + }, + { + "text": "As it stands, this is all fine whether, I mean, I could be repeating the same eigenvector, but I, I'm no interested in that." + }, + { + "text": "I want to be able to invert s, and that's where this comes in." + }, + { + "text": "This n independent eigenvectors business comes in to tell me that that matrix is invertible." + }, + { + "text": "So let me, on the next board, write down what I've got." + }, + { + "text": "A s equals s lambda." + }, + { + "text": "And now I'm, I can multiply on the left by s inverse." + }, + { + "text": "So this is really, I can do that provided s is invertible, provided my assumption of n independent eigenvectors is satisfied." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk20.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ad5a59fa5db44ce73ff5f88190423e0404fb3d39 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "How, how, what are those numbers approximately?" + }, + { + "text": "Square root of five, well, it's more than two, but less than three." + }, + { + "text": "It, it'd be nice to know these numbers." + }, + { + "text": "I think, I think that that, so that number comes out bigger than one, right?" + }, + { + "text": "Yeah, that's right." + }, + { + "text": "This number comes out bigger than one." + }, + { + "text": "It's about one point six one eight or something." + }, + { + "text": "Not exactly." + }, + { + "text": "It's supposed to be one point six." + }, + { + "text": "Just, like, I think so." + }, + { + "text": "Then what's lambda two?" + }, + { + "text": "Is, is lambda two positive or negative?" + }, + { + "text": "Negative, right?" + }, + { + "text": "Because I'm, it's obviously negative, and I knew that the, so it's minus, and they add up to one, so minus point six one eight, I guess." + }, + { + "text": "OK. And some order." + }, + { + "text": "Those are the two eigenvalues." + }, + { + "text": "One eigenvalue bigger than one, one eigenvalue smaller than one." + }, + { + "text": "Actually, that's a great situation to be in." + }, + { + "text": "Of course, the eigenvalues are different, so there's no doubt whatever, is this matrix diagonalizable?" + }, + { + "text": "Is this matrix diagonalizable, that original matrix A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk21.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..4a034475591d371995b379b5f98783a2cfb25870 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Sure." + }, + { + "text": "We've got two distinct eigenvalues and we can find the eigenvectors in a moment." + }, + { + "text": "But they'll be independent, will be diagonalizable, and now you can already answer my very first question." + }, + { + "text": "How fast are those Fibonacci numbers increasing?" + }, + { + "text": "How, those, they're increasing, right?" + }, + { + "text": "They're not doubling at every step." + }, + { + "text": "Let's look again at these numbers." + }, + { + "text": "Five eight thirteen, it's not obvious." + }, + { + "text": "The next one would be twenty one thirty four." + }, + { + "text": "So to get some idea of what F one hundred is, can you give me any, I mean the crucial number of, so it, these, it's approximately, what's controlling the growth of these Fibonacci numbers?" + }, + { + "text": "It's the eigenvalues." + }, + { + "text": "And which eigenvalues controlling that growth?" + }, + { + "text": "The big ones." + }, + { + "text": "So F one hundred will it be approximately some constant, c one, I guess, times this lambda one, this one plus square root of five over two, to the hundredth power." + }, + { + "text": "And the two hundredth have, in other words, the eigenvalue, the Fibonacci numbers are growing by about that factor." + }, + { + "text": "You see that we've got precise information about the, about the Fibonacci numbers out of the eigenvalue." + }, + { + "text": "OK. And again, why is that true?" + }, + { + "text": "Let me go over to this board and show what I'm doing here." + }, + { + "text": "The, the original eigen, the original initial value is some combination of eigenvectors, and then when we start multiple, when we start going out the theory of Fibonacci numbers, when we start multiplying by a hundred times, it's this lambda one to the hundredth, this term is, is the one that's taken over." + }, + { + "text": "It's, I mean, that's big, like, one point six to the hundredth power." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk22.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..c13a1fc9867173c3067e46c469cfff27b9b45289 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "The second term is practically nothing, right?" + }, + { + "text": "The point six, or minus point six to the hundredth power, is an extremely small, extremely small number." + }, + { + "text": "So this is, this, this, there are only two terms, because we're two by two." + }, + { + "text": "This number is, this piece of it is there, but it's, it's disappearing." + }, + { + "text": "Where this piece is there and it's growing and controlling everything." + }, + { + "text": "So, so really the, we're doing, like, problems that are evolving." + }, + { + "text": "We're doing dynamics." + }, + { + "text": "Instead of Ax equal b, that's a static problem." + }, + { + "text": "We're now, we're doing dynamics." + }, + { + "text": "A, a squared, a cubed, things are evolving in time, and the eigenvalues are the crucial, numbers." + }, + { + "text": "OK." + }, + { + "text": "I guess to complete this, I better write down the eigenvectors." + }, + { + "text": "So we should complete the, the whole process by finding the eigenvectors." + }, + { + "text": "OK. Well, I have to, up in the corner, then I have to look at A minus lambda I." + }, + { + "text": "So A minus lambda I is this one minus lambda, one, one, and minus lambda." + }, + { + "text": "And now, can we spot an eigenvector out of that?" + }, + { + "text": "That's, for these two lambdas, this matrix is singular." + }, + { + "text": "I guess the eigenvector, two by two ought to be easy." + }, + { + "text": "So if I know that this matrix is singular, then it seems to me the eigenvector has to be lambda and one, because that multiplication will give me the zero." + }, + { + "text": "And this multiplication gives me, better give me also zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk23.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..df816eb800ce767b1475c279a24ad976bb45a785 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Do you see why it does?" + }, + { + "text": "This is the minus lambda squared plus lambda plus one." + }, + { + "text": "It's the thing that's zero, because these lambdas are special." + }, + { + "text": "There's the eigenvector." + }, + { + "text": "X1 is lambda one, one, and x2 is lambda two, one." + }, + { + "text": "I did that as a little trick that was available in the two by two case." + }, + { + "text": "So now I finally have to, oh, I have to take the initial, u0." + }, + { + "text": "So to complete this example entirely, I have to say, OK, what was u0?" + }, + { + "text": "u0 was f1 f0." + }, + { + "text": "So u0, the starting vector, is f1 f0, and those were one and zero." + }, + { + "text": "So I have to use that vector, so I have to look for, from multiple of the first eigenvector and the second, to produce u0, the one zero vector." + }, + { + "text": "This is what will find c1 and c2, and then I'm done." + }, + { + "text": "So let me, instead of in the last five seconds grinding out a formula, let me repeat the idea." + }, + { + "text": "That really, it's the idea that's central." + }, + { + "text": "When things are evolving in time, let me come back to this board, because the ideas are here." + }, + { + "text": "When things are evolving in time by a first-order system, starting from an original u0, the key is, find the eigenvalues and eigenvectors of A." + }, + { + "text": "That will tell, those eigenvectors, the eigenvalues will already tell you what's happening." + }, + { + "text": "Is the solution blowing up?" + }, + { + "text": "Is it going to zero?" + }, + { + "text": "What's it doing?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk24.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..40301cb90760e2172baa94d536cbc13288d4c31f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk24.json @@ -0,0 +1,20 @@ +[ + { + "text": "And then, to find out exactly a formula, you have to take your u0 and write it as a combination of eigenvectors and then follow each eigenvector separately." + }, + { + "text": "And that's really what this formula, the formula for, that's what the formula for A to the k is doing." + }, + { + "text": "So remember that formula for A to the k is S, lambda to the k S inverse." + }, + { + "text": "OK. That's, that's difference equations, and you just have to, so the homework will give some examples different from Fibonacci to follow through." + }, + { + "text": "And next time will be differential equations." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk3.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..9bf1bb852baadc1da7837e14180c0c2951a30882 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I mentioned at the end of last time, and I'll say again, that there's a small number of matrices for, that don't have n independent eigenvectors." + }, + { + "text": "So I've got to discuss that, that technical point." + }, + { + "text": "But the great, the most matrices that we see have n, n independent eigenvectors and we can diagonalize." + }, + { + "text": "This is diagonalization." + }, + { + "text": "I could also write it, and I often will, the other way round." + }, + { + "text": "If I multiply on the right by s inverse, if I took this equation at the top and multiplied on the right by s inverse, I could, I would have A left here." + }, + { + "text": "Now s inverse is coming from the right." + }, + { + "text": "So can you keep those two straight?" + }, + { + "text": "A multiplies its eigenvectors." + }, + { + "text": "That's how I keep them straight." + }, + { + "text": "So A multiplies s. A multiplies s. And then this s inverse makes the whole thing diagonal." + }, + { + "text": "And this is another way of saying the same thing, putting the s's on the other side of the equation, A is s lambda s inverse." + }, + { + "text": "So that's the, that's the new factorization." + }, + { + "text": "That's the replacement for L U from elimination or Q R from Gram-Schmidt." + }, + { + "text": "And notice that the matrix, so it's, it's a matrix times a diagonal matrix times the inverse of the first one." + }, + { + "text": "It's, that's the combination that we'll see throughout this chapter." + }, + { + "text": "This, this, combination with an s and an s inverse." + }, + { + "text": "OK. Can I just begin to use that?" + }, + { + "text": "For example, what about A squared?" + }, + { + "text": "What are the eigenvalues and eigenvectors of A squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk4.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c687b6948acad76de8781cb82d3eb069c9da514e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's a straightforward question with a, with a absolutely clean answer." + }, + { + "text": "So let me, let me consider A squared." + }, + { + "text": "So I look, I start with Ax equal lambda x." + }, + { + "text": "And I'm headed for A squared." + }, + { + "text": "So let me multiply both sides by A." + }, + { + "text": "That's one way to get A squared on the left." + }, + { + "text": "So if, I should write these ifs in here." + }, + { + "text": "If Ax equals lambda x, then I multiply by A." + }, + { + "text": "So I get A squared x equals, well, I'm multiplying by A, so that's lambda Ax." + }, + { + "text": "That lambda was a number, so I just put it on the left." + }, + { + "text": "And what do I, tell me how to make that look better." + }, + { + "text": "What have I got here?" + }, + { + "text": "For, if, if A has the eigenvalue lambda and eigenvector x, what's up with A squared?" + }, + { + "text": "A squared x, I just multiply by A, but now for Ax, I'm going to substitute lambda x, so I've got lambda squared x." + }, + { + "text": "So from that simple calculation, I, my conclusion is that the eigenvalues of A squared are lambda squared." + }, + { + "text": "And the eigenvectors, I always think about both of those." + }, + { + "text": "What can I say about the eigenvalues?" + }, + { + "text": "They're squared." + }, + { + "text": "What can I say about the eigenvectors?" + }, + { + "text": "They're the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk5.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5bf15e20707c156c8ae71c9c7acea41a9d9d8e46 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same x as in, as for A." + }, + { + "text": "Now, let me see that also from this formula." + }, + { + "text": "How can I see what A squared is looking like from this formula?" + }, + { + "text": "So let me, that, that was one way to do it." + }, + { + "text": "Let me do it by just taking A squared from that." + }, + { + "text": "A squared is S lambda S inverse, that's A, times S lambda S inverse, that's A, which is?" + }, + { + "text": "This is the beauty of eigenvalues, eigenvectors, having that S inverse and S is the identity, so I've got S lambda squared S inverse." + }, + { + "text": "Yes." + }, + { + "text": "You see what that's telling me?" + }, + { + "text": "It's, it's telling me the same thing that I just learned here, but in the, in, in a matrix form." + }, + { + "text": "It's telling me that the S is the same, the eigenvectors are the same, but the eigenvalues are squared, because this is, what's lambda squared, that's still diagonal, it's got little lambda one squared, lambda two squared, down to lambda n squared, on that diagonal, those are the eigenvalues, as we just learned, of A squared." + }, + { + "text": "OK." + }, + { + "text": "So, somehow those eigenvalues and eigenvectors are really giving you a way to, to, to, to see what's going on inside a matrix." + }, + { + "text": "Now, of course, I can continue that for, to the k-th power." + }, + { + "text": "A to the k-th power." + }, + { + "text": "If I multiply, if I have k of these together, do you see how S inverse S will keep cancelling?" + }, + { + "text": "In the, in the inside, I'll have the S outside, at the far left, and lambda will be in there k times and S inverse." + }, + { + "text": "So what's that telling me?" + }, + { + "text": "That's telling me that the eigenvalues of A, of A to the k-th power are the k-th powers." + }, + { + "text": "The eigenvalues of A cubed are the cubes of the eigenvalues of A, and the eigenvectors are the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk6.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..c18dddbe798022f7e68278ac002a3f5fe6ed249e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same." + }, + { + "text": "OK." + }, + { + "text": "In other words, eigenvalues and eigenvectors give a great way to understand the powers of a matrix." + }, + { + "text": "If I take the square of a matrix or the hundredth power of a matrix, the pivots are all over the place." + }, + { + "text": "L U, if I multiply L U times L U times L U times L U a hundred times, I've got a hundred L U's." + }, + { + "text": "I can't do anything with them." + }, + { + "text": "But when I multiply S lambda S inverse by itself, when I look at the eigenvector picture a hundred times, I get a hundred or ninety-nine of these guys cancelling out inside, and I get A to the hundredth is S lambda to the hundredth S inverse." + }, + { + "text": "I mean, eigenvalues tell you about powers of a matrix in a way that we had no, no way to approach previously." + }, + { + "text": "For example, when does, when do the powers of a matrix go to zero?" + }, + { + "text": "I would call that matrix stable, maybe." + }, + { + "text": "So, so, so I could write down a, a theorem." + }, + { + "text": "I'll, I'll write it as a theorem, just to use that word to emphasize that here I'm getting this great fact from this eigenvalue picture." + }, + { + "text": "OK. A to the k approaches zero as k goes, as k gets bigger." + }, + { + "text": "If what?" + }, + { + "text": "What's the, how can I tell for a matrix A if its powers go to zero?" + }, + { + "text": "What, what's somewhere inside that matrix is that information." + }, + { + "text": "That information is not present in the pivots." + }, + { + "text": "It's present in the eigenvalues." + }, + { + "text": "What do I need for the, to know that if I take higher and higher powers of A that this matrix gets smaller and smaller?" + }, + { + "text": "Well, S and S inverse are not moving." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk7.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b84a5c854a5542758e8a0107e1ff043205fe3bdb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's this guy that has to get small, and that's easy to, easy to understand." + }, + { + "text": "The requirement is all eigenvalues, so what is the requirement?" + }, + { + "text": "The eigenvalues have to be less than one." + }, + { + "text": "Now, I have to write that absolute value, because those eigenvalues could be negative, they could be complex numbers." + }, + { + "text": "So I'm taking the absolute value if all of those are below one." + }, + { + "text": "That's, in fact, we practically see why." + }, + { + "text": "Let me just say that I, that I, I'm operating on one assumption here, and I got to keep remembering that that assumption is still present." + }, + { + "text": "That assumption was that I had a full set of, of n independent eigenvectors." + }, + { + "text": "If I don't have that, then I, I, then this approach is not working." + }, + { + "text": "So, so again, a pure eigenvalue approach, eigenvector approach, needs n independent eigenvectors." + }, + { + "text": "If we don't have n independent eigenvectors, we can't diagonalize the matrix." + }, + { + "text": "We can't get to a diagonal matrix." + }, + { + "text": "This, this, this diagonalization is only possible if S inverse makes sense." + }, + { + "text": "OK. Can I, can I follow up on that point now?" + }, + { + "text": "So, so you see why, what we get and, and why we want it, because we get information about the powers of a matrix just immediately from the eigenvalues." + }, + { + "text": "OK, now let me follow up on this, business of which matrices are diagonalizable." + }, + { + "text": "Sorry about that long word." + }, + { + "text": "So a matrix is, is sure to, so here's, here's the main point." + }, + { + "text": "A is sure to be, to have n independent eigenvectors and, and B, now here comes that word, diagonalizable, if, if, so we, we, we might as well get the, the nice case out in the open." + }, + { + "text": "The nice case is when, if all the lambdas are different." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk8.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f06dcec8ffa0ee1bf19440e4ab2194db33ab353b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means, that means no repeated eigenvalues." + }, + { + "text": "OK. That's the nice case." + }, + { + "text": "If, if my matrix and most matrix, if I do a random matrix in MATLAB and compute its eigenvalues, so if I computed, if I took I of rand of ten ten, gave, gave that MATLAB command, the, we'd get a random ten by ten matrix, we would get a list of its ten eigenvalues and they would be different." + }, + { + "text": "They would be distinct, is the best word." + }, + { + "text": "I would have a random matrix will have ten distinct, a ten by ten matrix will have ten distinct eigenvalues, and if it does, the eigenvectors are automatically independent." + }, + { + "text": "So that's a nice fact." + }, + { + "text": "I can, I'll refer you to the text for the proof." + }, + { + "text": "That, that A is sure to have n independent eigenvectors if the eigenvalues are different." + }, + { + "text": "If, if all the, if all eigenvalues are different." + }, + { + "text": "It's just, if some lambdas are repeated, then I have to look more closely." + }, + { + "text": "If an eigenvalue is repeated, I have to look, I have to count, I have to check." + }, + { + "text": "Has it got, say it's repeated three times." + }, + { + "text": "So what's a possibility for, so, so here's, here's the repeated possibility." + }, + { + "text": "And, and let me emphasize the conclusion." + }, + { + "text": "That if I have repeated eigenvalues, I may or may not, I may or may not have, have n independent eigenvectors." + }, + { + "text": "I might." + }, + { + "text": "I, I, you know, this isn't a completely negative case." + }, + { + "text": "The identity matrix." + }, + { + "text": "Well, suppose I take the ten by ten identity matrix." + }, + { + "text": "What are the eigenvalues of that matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk9.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..87d2a2ae5773036cf11800e2f1962908986a0dad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_0_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So just, just take the easiest matrix, the identity." + }, + { + "text": "If I look for its eigenvalues, they're all ones." + }, + { + "text": "So that eigenvalue one is repeated ten times." + }, + { + "text": "But there's no shortage of eigenvectors for the identity matrix." + }, + { + "text": "In fact, every vector is an eigenvector." + }, + { + "text": "So I can take ten independent vectors." + }, + { + "text": "Oh, well, what happens to everything if, if, if A is the identity matrix, let's just think that one through in our head." + }, + { + "text": "If A is the identity matrix, then it's got plenty of eigenvectors." + }, + { + "text": "I choose ten independent vectors, they're the columns of S, and, and what do I get from S inverse A S?" + }, + { + "text": "I get I again, right?" + }, + { + "text": "If A is the identity, and of course, that's the correct lambda." + }, + { + "text": "The, the matrix was already diagonal." + }, + { + "text": "So if the matrix is already diagonal, then the, the lambda is the same as the matrix." + }, + { + "text": "A diagonal matrix has got its eigenvalues sitting right there in front of you." + }, + { + "text": "Now if it's triangular, the eigenvalues are still sitting there, but so let's, let's take a case where, it's triangular." + }, + { + "text": "Suppose A is like, two, one, two, zero." + }, + { + "text": "So there's a case that's going to be trouble." + }, + { + "text": "There's a case that's going to be trouble." + }, + { + "text": "First of all, what are the eigen- I mean, we just, like now you, if we start with a matrix, the first thing we do practically without thinking is compute the eigenvalues and eigenvectors." + }, + { + "text": "OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk0.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6898d4fe66019ef6b40d0472ea94a968e7bbde9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, shall we start?" + }, + { + "text": "This is the second lecture on eigenvalues." + }, + { + "text": "So the first lecture was set -- reached the key equation, Ax equal lambda x. x is the eigenvector and lambda is the eigenvalue." + }, + { + "text": "Now, to use that." + }, + { + "text": "And the good way to, after we've found, so job one is to find the eigenvalues and find the eigenvectors." + }, + { + "text": "Now after we found them, what do we do with them?" + }, + { + "text": "Well, the good way to see that is diagonalize the matrix." + }, + { + "text": "So the matrix is A, and I want to show, first of all, this is like the basic fact." + }, + { + "text": "This, this formula." + }, + { + "text": "That's, that's the key to today's lecture." + }, + { + "text": "This matrix A, I put its eigenvectors in the columns of a matrix S. So S will be the eigenvector matrix, and I want to look at this magic combination S inverse A S. So can I show you how that, how that, what happens there?" + }, + { + "text": "And notice, notice, there's an S inverse." + }, + { + "text": "We have to be able to invert this eigenvector matrix S. So for that we need n independent eigenvectors." + }, + { + "text": "So that's the, that's the case." + }, + { + "text": "OK." + }, + { + "text": "So suppose we have n linearly independent eigenvectors of A." + }, + { + "text": "Put them in the columns of this matrix S. So I'm naturally going to call that the eigenvector matrix, because it's got the eigenvectors in its columns." + }, + { + "text": "And all I want to do is show you what happens when you multiply A times S. So A times S. So this is A times the matrix with the first eigenvector in its first column, the second eigenvector in its second column, the nth eigenvector in its nth column." + }, + { + "text": "And how am I going to do this matrix multiplication?" + }, + { + "text": "Well, certainly I'll do it a column at a time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk1.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..fbe078217bb68baea8e0605a5d04be568c49efbf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I get?" + }, + { + "text": "A times the first column gives me the first column of the answer, but what is it?" + }, + { + "text": "That's an eigenvector." + }, + { + "text": "A times x1 is equal to the lambda times the x1." + }, + { + "text": "And that lambda's we'll call lambda one, of course." + }, + { + "text": "So that's the first column, A x1 is the same as lambda one x1." + }, + { + "text": "A x2 is lambda two x2, so on, along to, in the nth column, we now have lambda n xn." + }, + { + "text": "Looking good, but the next step is even better." + }, + { + "text": "So for the next step, I want to separate out those eigenvalues, those multiplying numbers, from the x's." + }, + { + "text": "So then I'll have just what I want." + }, + { + "text": "OK, so how, how am I going to separate out?" + }, + { + "text": "So that, that number lambda one is multiplying the first column." + }, + { + "text": "So if I want to factor it out of the first column, I better put, here is going to be x1, and that's going to multiply this matrix lambda one in the first entry in all zeros." + }, + { + "text": "You see that that, that's going to come out right for the first column?" + }, + { + "text": "Because we remember how, how we're going back to that original punchline, that if I want a number to multiply x1, then I can do it by putting x1 in that column, in the first column, and putting that number there." + }, + { + "text": "What am I going to have here?" + }, + { + "text": "I'm going to have lambda one, I'm going to have x1, x2, xn." + }, + { + "text": "These are going to be my columns again." + }, + { + "text": "I'm getting s back again." + }, + { + "text": "I'm getting s back again, but now what's it multiplied by?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk10.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c58a42edbe9567233ca7f57643a0b7d43ae6761f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what are the eigenvalues?" + }, + { + "text": "You can tell me right away what they are." + }, + { + "text": "They're two and two, right." + }, + { + "text": "It's a triangular matrix, so when I do this determinant, shall I do this determinant of A minus lambda I?" + }, + { + "text": "I'll get this two minus lambda, one, zero, two minus lambda, right?" + }, + { + "text": "I take that determinant, so I make those into vertical bars to mean determinant, and what's the determinant?" + }, + { + "text": "Two minus lambda squared." + }, + { + "text": "What are the roots?" + }, + { + "text": "Lambda equal two twice." + }, + { + "text": "So the eigenvalues are lambda equals two and two." + }, + { + "text": "OK, fine." + }, + { + "text": "Now the next step, find the eigenvectors." + }, + { + "text": "So I look for eigenvectors and what do I find for this guy?" + }, + { + "text": "Eigenvectors for this guy, when I subtract two minus the identity, so A minus two I has zeros here, and I'm looking for the null space." + }, + { + "text": "What's, what are the eigenvectors?" + }, + { + "text": "They're the, they're, they're the null space of A minus lambda I." + }, + { + "text": "The null space is only one dimension." + }, + { + "text": "This is a case where I don't have enough eigenvectors." + }, + { + "text": "My algebraic multiplicity is two." + }, + { + "text": "I, I would say when I see, when I count how often the eigenvalue is repeated, that's the algebraic multiplicity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk11.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..779c2cf904d904b761080db2671aac46394ad02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the multiplicity." + }, + { + "text": "How many times is it the root of the polynomial?" + }, + { + "text": "My polynomial is two minus lambda squared." + }, + { + "text": "It's a double root." + }, + { + "text": "So my algebraic multiplicity is two." + }, + { + "text": "But the geometric multiplicity, which looks for vectors, looks for eigenvectors and which means the null space of this thing." + }, + { + "text": "And the only eigenvector is one zero." + }, + { + "text": "That's in the null space." + }, + { + "text": "Zero one is not in the null space." + }, + { + "text": "The null space is only one dimensional." + }, + { + "text": "So there's a matrix, my, this A or the original A, that are not diagonalizable." + }, + { + "text": "I can't, I can't find two independent eigenvectors, there's only one." + }, + { + "text": "OK." + }, + { + "text": "So that's the case that I'm, that's a case that I, I'm not really handling." + }, + { + "text": "For example, when I wrote down up here that the powers went to zero if the eigenvalues were below one, I didn't really handle that case of repeated eigenvalues because my reasoning was based on this formula." + }, + { + "text": "And this formula is based on n independent eigenvectors." + }, + { + "text": "OK." + }, + { + "text": "So just to say that." + }, + { + "text": "There are some matrices that we don't cover through diagonalization, but the great majority we do." + }, + { + "text": "OK. And we're always OK if we have different distinct eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk12.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..77d090704cc298475d94416b7ecb88a2a015a913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. That's the, like, the typical case." + }, + { + "text": "Because for each eigenvalue there's at least one eigenvector, the algebraic multiplicity here is one for every eigenvalue, and the geometric multiplicity is one." + }, + { + "text": "There's one eigenvector and they are independent." + }, + { + "text": "OK. OK. Now let me come back to the important case when we're OK." + }, + { + "text": "The important case when we are diagonalizing." + }, + { + "text": "Let me look at, so let me solve this equation." + }, + { + "text": "The equation will be each, I start with some, start with a given vector u0." + }, + { + "text": "And then my equation is that every step I multiply what I have by a." + }, + { + "text": "That equation ought to be simple to handle." + }, + { + "text": "OK. And I'd like to be able to solve it." + }, + { + "text": "How would I find, if I start with a vector u0, and I multiply by a a hundred times, what have I got?" + }, + { + "text": "Well, I can certainly write down a formula for the answer." + }, + { + "text": "So what, what, so u1 is a u0." + }, + { + "text": "And u2 is, what's u2 then?" + }, + { + "text": "U2 I multiply it, u2 I get from u1 by another, multiplying by a, so I've got a twice." + }, + { + "text": "And my formula is uk, after k steps, I've multiplied by a k times the original u0." + }, + { + "text": "You see what I'm doing?" + }, + { + "text": "The next section is going to solve systems of differential equations." + }, + { + "text": "I'm going to have derivatives." + }, + { + "text": "This, this section is the nice one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk13.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..ba8214d8c636e4757a266d6617801174bc939d80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "It solves difference equations." + }, + { + "text": "I would call that a difference equation." + }, + { + "text": "It's conne- a first order." + }, + { + "text": "I would call that a first order system, because it connects only, it only goes up one level." + }, + { + "text": "And it's a system because these are vectors and that's a matrix." + }, + { + "text": "And the solution is just that." + }, + { + "text": "OK." + }, + { + "text": "But, that's a nice formula." + }, + { + "text": "That's the, like, the most compact formula I could ever get." + }, + { + "text": "U one hundred would be a to the one hundredth u0." + }, + { + "text": "But how would I actually find u one hundred?" + }, + { + "text": "How would I find, how would I discover what u one hundred is?" + }, + { + "text": "Let me, let me show you how." + }, + { + "text": "Here, here's the idea." + }, + { + "text": "If, so, to solve, to really solve, shall I say, to really solve." + }, + { + "text": "To really solve it, I would take this initial vector, u0, and I would write it as a combination of eigenvectors." + }, + { + "text": "To really solve, write, write u0 as a combination, say, certain amount of the first eigenvector plus a certain amount of the second eigenvector plus a certain amount of the last eigenvector." + }, + { + "text": "Now multiply by a." + }, + { + "text": "You want to, you got to see the magic of eigenvectors work." + }, + { + "text": "Multiply by a." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk14.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7843b2bf0cac762d1c12452cf36500ea4ad13370 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a u0 is what?" + }, + { + "text": "So a times that." + }, + { + "text": "A times, so what's, I can separate it out into n separate pieces and that's the whole point." + }, + { + "text": "That each of those pieces is going in its own merry way." + }, + { + "text": "Each of those pieces is an eigenvector, and when I multiply by a, what does this piece become?" + }, + { + "text": "So that's some amount of the first, let's suppose the eigenvectors are normalized to be unit vectors." + }, + { + "text": "So that says what the eigenvector is." + }, + { + "text": "It's, and I need some multiple of it to produce u0." + }, + { + "text": "OK. Now when I multiply by a, what do I get?" + }, + { + "text": "I get c1, which is just a factor, times a x1, but a x1 is lambda one x1." + }, + { + "text": "When I multiply this by a, I get c2 lambda two x2." + }, + { + "text": "And here I get cn lambda n xn." + }, + { + "text": "And suppose I multiply by a to the hundredth power now." + }, + { + "text": "Can we, can we, having done it, multiplied by a, let's multiply by a to the hundredth." + }, + { + "text": "What happens to this first term when I multiply by a to the one hundredth?" + }, + { + "text": "It's got that factor lambda to the hundredth." + }, + { + "text": "That's the key." + }, + { + "text": "That, that's what I mean by going its own merry way." + }, + { + "text": "It, it is pure eigenvector, it's exactly in a direction where multiplication by a just brings in a scalar factor lambda one." + }, + { + "text": "So a hundred times brings in this a hundred times." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk15.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7ee3348735378aa4049d33ec2a197d0ceb0c447c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Hundred times lambda two, hundred times lambda n. Actually, we're, what are we seeing here?" + }, + { + "text": "We're seeing, this same, lambda, capital lambda to the hundredth, as in the, as in the diagonalization, and we're seeing the S matrix, the matrix S of eigenvectors." + }, + { + "text": "That's what this has got to, this has got to amount to, a lambda to the hundredth power times an S times this vector C that's telling us how much of each one is in the original thing." + }, + { + "text": "So if, if I had to really find the hundredth power, I would take u0, I would expand it as a combination of eigenvectors, this is really S, the eigenvector matrix times C, the, the coefficient vector." + }, + { + "text": "And then I would immediately, then, by inserting these hundredth powers of eigenvalues, I'd have the answer." + }, + { + "text": "So the, the, huh, there must be, well, let's see." + }, + { + "text": "OK." + }, + { + "text": "It's, so, yeah." + }, + { + "text": "So if u100 is a to the hundredth times u0, and u0 is Sc, then you see this formula is just this formula, which is the way I would actually get hold of this, of this u100, which is, let me put it here, u100." + }, + { + "text": "The way I would actually get hold of that, see what, what the solution is after a hundred steps, would be expand the initial vector into eigenvectors and, and let each eigenvector go its own way, multiplying by a hundred at, by lambda at every step, and therefore by lambda to the hundredth power after a hundredth step." + }, + { + "text": "Can I do an example?" + }, + { + "text": "So that's, that's the, the formulas." + }, + { + "text": "Now let me take an example." + }, + { + "text": "I'll use the Fibonacci sequence as an example." + }, + { + "text": "So, so Fibonacci example." + }, + { + "text": "You remember the Fibonacci numbers?" + }, + { + "text": "If we start with one and one as F0, oh, I think I start with zero, maybe." + }, + { + "text": "Let zero and one be the first ones." + }, + { + "text": "So there's F0 and F1, the first two Fibonacci numbers." + }, + { + "text": "Then what's the rule for Fibonacci numbers?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk16.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..79c65e32781f7f304b504a6c390247abb9d26ac8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "They're the sum." + }, + { + "text": "The next one is the sum of those, so it's one." + }, + { + "text": "The next one is the sum of those, so it's two." + }, + { + "text": "The next one is the sum of those, so it's three." + }, + { + "text": "Well, it looks like one, two, three, four, five, but somehow it's not going to do that way." + }, + { + "text": "The next one is five, right." + }, + { + "text": "Two and three makes five." + }, + { + "text": "The next one is eight." + }, + { + "text": "The next one is thirteen." + }, + { + "text": "And the one hundredth Fibonacci number is what?" + }, + { + "text": "That's my question." + }, + { + "text": "How could I get a formula for the hundredth number and for example how could I answer the question how fast are they growing?" + }, + { + "text": "How fast are those Fibonacci numbers growing?" + }, + { + "text": "They're certainly growing." + }, + { + "text": "It's not a stable case, whatever the eigenvalues of whatever matrix it is, they're not smaller than one." + }, + { + "text": "These numbers are growing." + }, + { + "text": "But how fast are they growing?" + }, + { + "text": "The answer is lies in the eigenvalue." + }, + { + "text": "So I've got to find the matrix, so let me write down the Fibonacci rule, F k plus two is F k plus one plus F k, right?" + }, + { + "text": "Now that's not in my -- I want to write that as U k plus one and A U k. But right now what I've got is a single equation, not a system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk17.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b3aaa9dcee3cf27c112015659bb5a0b51a983ce1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's second order." + }, + { + "text": "It's like having a second order differential equation with second derivatives." + }, + { + "text": "I want to get first derivatives." + }, + { + "text": "Here I want to get first difference." + }, + { + "text": "So the way to do it is to introduce U k will be a vector." + }, + { + "text": "See, a small trick." + }, + { + "text": "Let U k be a vector, F k plus one and F k. So I'm going to get a two by two system, first order, instead of a one, instead of a scalar system, second order, by a simple trick." + }, + { + "text": "I'm just going to add in an equation F k plus one equals F k plus one." + }, + { + "text": "That will be my second equation." + }, + { + "text": "Then this is my system, this is my unknown, and what's my one-step equation?" + }, + { + "text": "So now U k plus one." + }, + { + "text": "That's so U k plus one is the left side, and what have I got here on the right side?" + }, + { + "text": "I've got some matrix multiplying U k. Can you see that all right?" + }, + { + "text": "If you can see it, then you can tell me what the matrix is." + }, + { + "text": "You see that I'm taking my system here, I artificially made it into a system." + }, + { + "text": "I artificially made the unknown into a vector, and now I'm ready to look at and see what the matrix is." + }, + { + "text": "So do you see the left side, U k plus one is F k plus two F k plus one, that's just what I want." + }, + { + "text": "On the right side, this, remember, this U k here, let me for the moment put it as F k plus one F k. So what's the matrix?" + }, + { + "text": "Well, that has a one and a one, and that has a one and a zero." + }, + { + "text": "There's the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk18.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..6c1b68c2cb2fde3f5dea82f3100d4da31fcce70a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "You see that that gives me the right-hand side." + }, + { + "text": "So there's the matrix A, and this is our friend U k. So we've got, so that simple trick changed the second order scalar problem to a first order system, two, with two unknowns." + }, + { + "text": "With a matrix and now what do I do?" + }, + { + "text": "Well, before I even think, I find its eigenvalues and eigenvectors." + }, + { + "text": "So what are the eigenvalues and eigenvectors of that matrix?" + }, + { + "text": "Let's see." + }, + { + "text": "I was, first let me just, like, think for a minute." + }, + { + "text": "It's two by two, so this shouldn't be impossible to do." + }, + { + "text": "Let's do it." + }, + { + "text": "OK." + }, + { + "text": "So my matrix again is one one one zero." + }, + { + "text": "It's symmetric, by the way." + }, + { + "text": "So what I will eventually know about symmetric matrices is that the eigenvalues will come out real, I won't get any complex numbers here, and the eigenvectors, once I get those, actually will be orthogonal." + }, + { + "text": "But two by two, I'm more interested in what the actual numbers are." + }, + { + "text": "What do I know about the two numbers?" + }, + { + "text": "Well, should, do you want me to find this determinant of A minus lambda I?" + }, + { + "text": "Sure." + }, + { + "text": "So it's the determinant of one minus lambda one one zero, right?" + }, + { + "text": "Minus lambda, yes, got it." + }, + { + "text": "OK. OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk19.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..a73b23e3d56b889ff49ea7f55a784fac33e13c3d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "There'll be two eigenvalues." + }, + { + "text": "Well, tell me again what I know about the two eigenvalues before I go any further." + }, + { + "text": "Tell me something about these two eigenvalues, what do they add up to?" + }, + { + "text": "Lambda one plus lambda two is the same as the trace down the diagonal of the matrix, one and zero is one." + }, + { + "text": "So lambda one plus lambda two should come out to be one, and lambda one times lambda two should come out to be the determinant, which is minus one." + }, + { + "text": "So I'm expecting the eigenvalues to add to one and to multiply to minus one." + }, + { + "text": "But let's just see it happen here." + }, + { + "text": "If I multiply this out, I get that times that'll be a lambda squared minus lambda minus one." + }, + { + "text": "Good." + }, + { + "text": "Lambda squared minus lambda minus one." + }, + { + "text": "Actually, you see the, compare that with the original equation that I started with." + }, + { + "text": "Fk plus two minus Fk plus one minus Fk is zero." + }, + { + "text": "The recurrent, the recursion that the Fibonacci number satisfy is somehow showing up directly here for the eigenvalues when we set that to zero." + }, + { + "text": "OK. Let's solve." + }, + { + "text": "Well, I would like to be able to factor that, that quadratic, but I'm better off to use the quadratic formula." + }, + { + "text": "Lambda is, let's see, minus b is one, plus or minus the square root of b squared, which is one, minus four, times that, times that, which is plus four, over two." + }, + { + "text": "So that's the square root of five." + }, + { + "text": "So the eigenvalues are lambda one is one half of one plus square root of five, and lambda two is one half of one minus square root of five." + }, + { + "text": "And sure enough, they, those add up to one, and they multiply to give minus one." + }, + { + "text": "OK. Those are the two eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk2.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..43cfb012fc04a89fc7dab94c23bfb0f50ade3782 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "On the right, it's multiplied by, if I want, if I want lambda n xn in the last column, how do I do it?" + }, + { + "text": "Well, the last column here will be, I'll, I'll take the last column, use these coefficients, put the lambda n down there, and it will multiply that nth column and give me lambda n xn." + }, + { + "text": "There, there you see matrix multiplication just working for us." + }, + { + "text": "So I started with A s. I wrote down what it meant." + }, + { + "text": "A times each eigenvector." + }, + { + "text": "That gave me lambda times the eigenvector." + }, + { + "text": "And then when I peeled off the lambdas, they were on the right-hand side, so I've got s, my matrix back again, and this matrix, this diagonal matrix, the eigenvalue matrix, and I call it capital lambda, using capital letters for matrices, and lambda to prompt me that it's, that it's eigenvalues that are in there." + }, + { + "text": "So you see that the eigenvalues are just sitting down that diagonal?" + }, + { + "text": "If I had a column x2 here, I would want the lambda two in the two two position, in the diagonal position, to multiply that x2 and give me the lambda two x2." + }, + { + "text": "That's my formula." + }, + { + "text": "A s is s lambda." + }, + { + "text": "OK. That's, that's the, you see, it's just a calculation." + }, + { + "text": "Now, I, I mentioned, and I have to mention again, this business about n independent eigenvectors." + }, + { + "text": "As it stands, this is all fine whether, I mean, I could be repeating the same eigenvector, but I, I'm no interested in that." + }, + { + "text": "I want to be able to invert s, and that's where this comes in." + }, + { + "text": "This n independent eigenvectors business comes in to tell me that that matrix is invertible." + }, + { + "text": "So let me, on the next board, write down what I've got." + }, + { + "text": "A s equals s lambda." + }, + { + "text": "And now I'm, I can multiply on the left by s inverse." + }, + { + "text": "So this is really, I can do that provided s is invertible, provided my assumption of n independent eigenvectors is satisfied." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk20.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ad5a59fa5db44ce73ff5f88190423e0404fb3d39 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "How, how, what are those numbers approximately?" + }, + { + "text": "Square root of five, well, it's more than two, but less than three." + }, + { + "text": "It, it'd be nice to know these numbers." + }, + { + "text": "I think, I think that that, so that number comes out bigger than one, right?" + }, + { + "text": "Yeah, that's right." + }, + { + "text": "This number comes out bigger than one." + }, + { + "text": "It's about one point six one eight or something." + }, + { + "text": "Not exactly." + }, + { + "text": "It's supposed to be one point six." + }, + { + "text": "Just, like, I think so." + }, + { + "text": "Then what's lambda two?" + }, + { + "text": "Is, is lambda two positive or negative?" + }, + { + "text": "Negative, right?" + }, + { + "text": "Because I'm, it's obviously negative, and I knew that the, so it's minus, and they add up to one, so minus point six one eight, I guess." + }, + { + "text": "OK. And some order." + }, + { + "text": "Those are the two eigenvalues." + }, + { + "text": "One eigenvalue bigger than one, one eigenvalue smaller than one." + }, + { + "text": "Actually, that's a great situation to be in." + }, + { + "text": "Of course, the eigenvalues are different, so there's no doubt whatever, is this matrix diagonalizable?" + }, + { + "text": "Is this matrix diagonalizable, that original matrix A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk21.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..4a034475591d371995b379b5f98783a2cfb25870 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Sure." + }, + { + "text": "We've got two distinct eigenvalues and we can find the eigenvectors in a moment." + }, + { + "text": "But they'll be independent, will be diagonalizable, and now you can already answer my very first question." + }, + { + "text": "How fast are those Fibonacci numbers increasing?" + }, + { + "text": "How, those, they're increasing, right?" + }, + { + "text": "They're not doubling at every step." + }, + { + "text": "Let's look again at these numbers." + }, + { + "text": "Five eight thirteen, it's not obvious." + }, + { + "text": "The next one would be twenty one thirty four." + }, + { + "text": "So to get some idea of what F one hundred is, can you give me any, I mean the crucial number of, so it, these, it's approximately, what's controlling the growth of these Fibonacci numbers?" + }, + { + "text": "It's the eigenvalues." + }, + { + "text": "And which eigenvalues controlling that growth?" + }, + { + "text": "The big ones." + }, + { + "text": "So F one hundred will it be approximately some constant, c one, I guess, times this lambda one, this one plus square root of five over two, to the hundredth power." + }, + { + "text": "And the two hundredth have, in other words, the eigenvalue, the Fibonacci numbers are growing by about that factor." + }, + { + "text": "You see that we've got precise information about the, about the Fibonacci numbers out of the eigenvalue." + }, + { + "text": "OK. And again, why is that true?" + }, + { + "text": "Let me go over to this board and show what I'm doing here." + }, + { + "text": "The, the original eigen, the original initial value is some combination of eigenvectors, and then when we start multiple, when we start going out the theory of Fibonacci numbers, when we start multiplying by a hundred times, it's this lambda one to the hundredth, this term is, is the one that's taken over." + }, + { + "text": "It's, I mean, that's big, like, one point six to the hundredth power." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk22.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..c13a1fc9867173c3067e46c469cfff27b9b45289 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "The second term is practically nothing, right?" + }, + { + "text": "The point six, or minus point six to the hundredth power, is an extremely small, extremely small number." + }, + { + "text": "So this is, this, this, there are only two terms, because we're two by two." + }, + { + "text": "This number is, this piece of it is there, but it's, it's disappearing." + }, + { + "text": "Where this piece is there and it's growing and controlling everything." + }, + { + "text": "So, so really the, we're doing, like, problems that are evolving." + }, + { + "text": "We're doing dynamics." + }, + { + "text": "Instead of Ax equal b, that's a static problem." + }, + { + "text": "We're now, we're doing dynamics." + }, + { + "text": "A, a squared, a cubed, things are evolving in time, and the eigenvalues are the crucial, numbers." + }, + { + "text": "OK." + }, + { + "text": "I guess to complete this, I better write down the eigenvectors." + }, + { + "text": "So we should complete the, the whole process by finding the eigenvectors." + }, + { + "text": "OK. Well, I have to, up in the corner, then I have to look at A minus lambda I." + }, + { + "text": "So A minus lambda I is this one minus lambda, one, one, and minus lambda." + }, + { + "text": "And now, can we spot an eigenvector out of that?" + }, + { + "text": "That's, for these two lambdas, this matrix is singular." + }, + { + "text": "I guess the eigenvector, two by two ought to be easy." + }, + { + "text": "So if I know that this matrix is singular, then it seems to me the eigenvector has to be lambda and one, because that multiplication will give me the zero." + }, + { + "text": "And this multiplication gives me, better give me also zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk23.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..df816eb800ce767b1475c279a24ad976bb45a785 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Do you see why it does?" + }, + { + "text": "This is the minus lambda squared plus lambda plus one." + }, + { + "text": "It's the thing that's zero, because these lambdas are special." + }, + { + "text": "There's the eigenvector." + }, + { + "text": "X1 is lambda one, one, and x2 is lambda two, one." + }, + { + "text": "I did that as a little trick that was available in the two by two case." + }, + { + "text": "So now I finally have to, oh, I have to take the initial, u0." + }, + { + "text": "So to complete this example entirely, I have to say, OK, what was u0?" + }, + { + "text": "u0 was f1 f0." + }, + { + "text": "So u0, the starting vector, is f1 f0, and those were one and zero." + }, + { + "text": "So I have to use that vector, so I have to look for, from multiple of the first eigenvector and the second, to produce u0, the one zero vector." + }, + { + "text": "This is what will find c1 and c2, and then I'm done." + }, + { + "text": "So let me, instead of in the last five seconds grinding out a formula, let me repeat the idea." + }, + { + "text": "That really, it's the idea that's central." + }, + { + "text": "When things are evolving in time, let me come back to this board, because the ideas are here." + }, + { + "text": "When things are evolving in time by a first-order system, starting from an original u0, the key is, find the eigenvalues and eigenvectors of A." + }, + { + "text": "That will tell, those eigenvectors, the eigenvalues will already tell you what's happening." + }, + { + "text": "Is the solution blowing up?" + }, + { + "text": "Is it going to zero?" + }, + { + "text": "What's it doing?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk24.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..40301cb90760e2172baa94d536cbc13288d4c31f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk24.json @@ -0,0 +1,20 @@ +[ + { + "text": "And then, to find out exactly a formula, you have to take your u0 and write it as a combination of eigenvectors and then follow each eigenvector separately." + }, + { + "text": "And that's really what this formula, the formula for, that's what the formula for A to the k is doing." + }, + { + "text": "So remember that formula for A to the k is S, lambda to the k S inverse." + }, + { + "text": "OK. That's, that's difference equations, and you just have to, so the homework will give some examples different from Fibonacci to follow through." + }, + { + "text": "And next time will be differential equations." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk3.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..9bf1bb852baadc1da7837e14180c0c2951a30882 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I mentioned at the end of last time, and I'll say again, that there's a small number of matrices for, that don't have n independent eigenvectors." + }, + { + "text": "So I've got to discuss that, that technical point." + }, + { + "text": "But the great, the most matrices that we see have n, n independent eigenvectors and we can diagonalize." + }, + { + "text": "This is diagonalization." + }, + { + "text": "I could also write it, and I often will, the other way round." + }, + { + "text": "If I multiply on the right by s inverse, if I took this equation at the top and multiplied on the right by s inverse, I could, I would have A left here." + }, + { + "text": "Now s inverse is coming from the right." + }, + { + "text": "So can you keep those two straight?" + }, + { + "text": "A multiplies its eigenvectors." + }, + { + "text": "That's how I keep them straight." + }, + { + "text": "So A multiplies s. A multiplies s. And then this s inverse makes the whole thing diagonal." + }, + { + "text": "And this is another way of saying the same thing, putting the s's on the other side of the equation, A is s lambda s inverse." + }, + { + "text": "So that's the, that's the new factorization." + }, + { + "text": "That's the replacement for L U from elimination or Q R from Gram-Schmidt." + }, + { + "text": "And notice that the matrix, so it's, it's a matrix times a diagonal matrix times the inverse of the first one." + }, + { + "text": "It's, that's the combination that we'll see throughout this chapter." + }, + { + "text": "This, this, combination with an s and an s inverse." + }, + { + "text": "OK. Can I just begin to use that?" + }, + { + "text": "For example, what about A squared?" + }, + { + "text": "What are the eigenvalues and eigenvectors of A squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk4.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c687b6948acad76de8781cb82d3eb069c9da514e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's a straightforward question with a, with a absolutely clean answer." + }, + { + "text": "So let me, let me consider A squared." + }, + { + "text": "So I look, I start with Ax equal lambda x." + }, + { + "text": "And I'm headed for A squared." + }, + { + "text": "So let me multiply both sides by A." + }, + { + "text": "That's one way to get A squared on the left." + }, + { + "text": "So if, I should write these ifs in here." + }, + { + "text": "If Ax equals lambda x, then I multiply by A." + }, + { + "text": "So I get A squared x equals, well, I'm multiplying by A, so that's lambda Ax." + }, + { + "text": "That lambda was a number, so I just put it on the left." + }, + { + "text": "And what do I, tell me how to make that look better." + }, + { + "text": "What have I got here?" + }, + { + "text": "For, if, if A has the eigenvalue lambda and eigenvector x, what's up with A squared?" + }, + { + "text": "A squared x, I just multiply by A, but now for Ax, I'm going to substitute lambda x, so I've got lambda squared x." + }, + { + "text": "So from that simple calculation, I, my conclusion is that the eigenvalues of A squared are lambda squared." + }, + { + "text": "And the eigenvectors, I always think about both of those." + }, + { + "text": "What can I say about the eigenvalues?" + }, + { + "text": "They're squared." + }, + { + "text": "What can I say about the eigenvectors?" + }, + { + "text": "They're the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk5.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5bf15e20707c156c8ae71c9c7acea41a9d9d8e46 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same x as in, as for A." + }, + { + "text": "Now, let me see that also from this formula." + }, + { + "text": "How can I see what A squared is looking like from this formula?" + }, + { + "text": "So let me, that, that was one way to do it." + }, + { + "text": "Let me do it by just taking A squared from that." + }, + { + "text": "A squared is S lambda S inverse, that's A, times S lambda S inverse, that's A, which is?" + }, + { + "text": "This is the beauty of eigenvalues, eigenvectors, having that S inverse and S is the identity, so I've got S lambda squared S inverse." + }, + { + "text": "Yes." + }, + { + "text": "You see what that's telling me?" + }, + { + "text": "It's, it's telling me the same thing that I just learned here, but in the, in, in a matrix form." + }, + { + "text": "It's telling me that the S is the same, the eigenvectors are the same, but the eigenvalues are squared, because this is, what's lambda squared, that's still diagonal, it's got little lambda one squared, lambda two squared, down to lambda n squared, on that diagonal, those are the eigenvalues, as we just learned, of A squared." + }, + { + "text": "OK." + }, + { + "text": "So, somehow those eigenvalues and eigenvectors are really giving you a way to, to, to, to see what's going on inside a matrix." + }, + { + "text": "Now, of course, I can continue that for, to the k-th power." + }, + { + "text": "A to the k-th power." + }, + { + "text": "If I multiply, if I have k of these together, do you see how S inverse S will keep cancelling?" + }, + { + "text": "In the, in the inside, I'll have the S outside, at the far left, and lambda will be in there k times and S inverse." + }, + { + "text": "So what's that telling me?" + }, + { + "text": "That's telling me that the eigenvalues of A, of A to the k-th power are the k-th powers." + }, + { + "text": "The eigenvalues of A cubed are the cubes of the eigenvalues of A, and the eigenvectors are the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk6.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..c18dddbe798022f7e68278ac002a3f5fe6ed249e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same." + }, + { + "text": "OK." + }, + { + "text": "In other words, eigenvalues and eigenvectors give a great way to understand the powers of a matrix." + }, + { + "text": "If I take the square of a matrix or the hundredth power of a matrix, the pivots are all over the place." + }, + { + "text": "L U, if I multiply L U times L U times L U times L U a hundred times, I've got a hundred L U's." + }, + { + "text": "I can't do anything with them." + }, + { + "text": "But when I multiply S lambda S inverse by itself, when I look at the eigenvector picture a hundred times, I get a hundred or ninety-nine of these guys cancelling out inside, and I get A to the hundredth is S lambda to the hundredth S inverse." + }, + { + "text": "I mean, eigenvalues tell you about powers of a matrix in a way that we had no, no way to approach previously." + }, + { + "text": "For example, when does, when do the powers of a matrix go to zero?" + }, + { + "text": "I would call that matrix stable, maybe." + }, + { + "text": "So, so, so I could write down a, a theorem." + }, + { + "text": "I'll, I'll write it as a theorem, just to use that word to emphasize that here I'm getting this great fact from this eigenvalue picture." + }, + { + "text": "OK. A to the k approaches zero as k goes, as k gets bigger." + }, + { + "text": "If what?" + }, + { + "text": "What's the, how can I tell for a matrix A if its powers go to zero?" + }, + { + "text": "What, what's somewhere inside that matrix is that information." + }, + { + "text": "That information is not present in the pivots." + }, + { + "text": "It's present in the eigenvalues." + }, + { + "text": "What do I need for the, to know that if I take higher and higher powers of A that this matrix gets smaller and smaller?" + }, + { + "text": "Well, S and S inverse are not moving." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk7.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b84a5c854a5542758e8a0107e1ff043205fe3bdb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's this guy that has to get small, and that's easy to, easy to understand." + }, + { + "text": "The requirement is all eigenvalues, so what is the requirement?" + }, + { + "text": "The eigenvalues have to be less than one." + }, + { + "text": "Now, I have to write that absolute value, because those eigenvalues could be negative, they could be complex numbers." + }, + { + "text": "So I'm taking the absolute value if all of those are below one." + }, + { + "text": "That's, in fact, we practically see why." + }, + { + "text": "Let me just say that I, that I, I'm operating on one assumption here, and I got to keep remembering that that assumption is still present." + }, + { + "text": "That assumption was that I had a full set of, of n independent eigenvectors." + }, + { + "text": "If I don't have that, then I, I, then this approach is not working." + }, + { + "text": "So, so again, a pure eigenvalue approach, eigenvector approach, needs n independent eigenvectors." + }, + { + "text": "If we don't have n independent eigenvectors, we can't diagonalize the matrix." + }, + { + "text": "We can't get to a diagonal matrix." + }, + { + "text": "This, this, this diagonalization is only possible if S inverse makes sense." + }, + { + "text": "OK. Can I, can I follow up on that point now?" + }, + { + "text": "So, so you see why, what we get and, and why we want it, because we get information about the powers of a matrix just immediately from the eigenvalues." + }, + { + "text": "OK, now let me follow up on this, business of which matrices are diagonalizable." + }, + { + "text": "Sorry about that long word." + }, + { + "text": "So a matrix is, is sure to, so here's, here's the main point." + }, + { + "text": "A is sure to be, to have n independent eigenvectors and, and B, now here comes that word, diagonalizable, if, if, so we, we, we might as well get the, the nice case out in the open." + }, + { + "text": "The nice case is when, if all the lambdas are different." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk8.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f06dcec8ffa0ee1bf19440e4ab2194db33ab353b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means, that means no repeated eigenvalues." + }, + { + "text": "OK. That's the nice case." + }, + { + "text": "If, if my matrix and most matrix, if I do a random matrix in MATLAB and compute its eigenvalues, so if I computed, if I took I of rand of ten ten, gave, gave that MATLAB command, the, we'd get a random ten by ten matrix, we would get a list of its ten eigenvalues and they would be different." + }, + { + "text": "They would be distinct, is the best word." + }, + { + "text": "I would have a random matrix will have ten distinct, a ten by ten matrix will have ten distinct eigenvalues, and if it does, the eigenvectors are automatically independent." + }, + { + "text": "So that's a nice fact." + }, + { + "text": "I can, I'll refer you to the text for the proof." + }, + { + "text": "That, that A is sure to have n independent eigenvectors if the eigenvalues are different." + }, + { + "text": "If, if all the, if all eigenvalues are different." + }, + { + "text": "It's just, if some lambdas are repeated, then I have to look more closely." + }, + { + "text": "If an eigenvalue is repeated, I have to look, I have to count, I have to check." + }, + { + "text": "Has it got, say it's repeated three times." + }, + { + "text": "So what's a possibility for, so, so here's, here's the repeated possibility." + }, + { + "text": "And, and let me emphasize the conclusion." + }, + { + "text": "That if I have repeated eigenvalues, I may or may not, I may or may not have, have n independent eigenvectors." + }, + { + "text": "I might." + }, + { + "text": "I, I, you know, this isn't a completely negative case." + }, + { + "text": "The identity matrix." + }, + { + "text": "Well, suppose I take the ten by ten identity matrix." + }, + { + "text": "What are the eigenvalues of that matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk9.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..87d2a2ae5773036cf11800e2f1962908986a0dad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_10_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So just, just take the easiest matrix, the identity." + }, + { + "text": "If I look for its eigenvalues, they're all ones." + }, + { + "text": "So that eigenvalue one is repeated ten times." + }, + { + "text": "But there's no shortage of eigenvectors for the identity matrix." + }, + { + "text": "In fact, every vector is an eigenvector." + }, + { + "text": "So I can take ten independent vectors." + }, + { + "text": "Oh, well, what happens to everything if, if, if A is the identity matrix, let's just think that one through in our head." + }, + { + "text": "If A is the identity matrix, then it's got plenty of eigenvectors." + }, + { + "text": "I choose ten independent vectors, they're the columns of S, and, and what do I get from S inverse A S?" + }, + { + "text": "I get I again, right?" + }, + { + "text": "If A is the identity, and of course, that's the correct lambda." + }, + { + "text": "The, the matrix was already diagonal." + }, + { + "text": "So if the matrix is already diagonal, then the, the lambda is the same as the matrix." + }, + { + "text": "A diagonal matrix has got its eigenvalues sitting right there in front of you." + }, + { + "text": "Now if it's triangular, the eigenvalues are still sitting there, but so let's, let's take a case where, it's triangular." + }, + { + "text": "Suppose A is like, two, one, two, zero." + }, + { + "text": "So there's a case that's going to be trouble." + }, + { + "text": "There's a case that's going to be trouble." + }, + { + "text": "First of all, what are the eigen- I mean, we just, like now you, if we start with a matrix, the first thing we do practically without thinking is compute the eigenvalues and eigenvectors." + }, + { + "text": "OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk0.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6898d4fe66019ef6b40d0472ea94a968e7bbde9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, shall we start?" + }, + { + "text": "This is the second lecture on eigenvalues." + }, + { + "text": "So the first lecture was set -- reached the key equation, Ax equal lambda x. x is the eigenvector and lambda is the eigenvalue." + }, + { + "text": "Now, to use that." + }, + { + "text": "And the good way to, after we've found, so job one is to find the eigenvalues and find the eigenvectors." + }, + { + "text": "Now after we found them, what do we do with them?" + }, + { + "text": "Well, the good way to see that is diagonalize the matrix." + }, + { + "text": "So the matrix is A, and I want to show, first of all, this is like the basic fact." + }, + { + "text": "This, this formula." + }, + { + "text": "That's, that's the key to today's lecture." + }, + { + "text": "This matrix A, I put its eigenvectors in the columns of a matrix S. So S will be the eigenvector matrix, and I want to look at this magic combination S inverse A S. So can I show you how that, how that, what happens there?" + }, + { + "text": "And notice, notice, there's an S inverse." + }, + { + "text": "We have to be able to invert this eigenvector matrix S. So for that we need n independent eigenvectors." + }, + { + "text": "So that's the, that's the case." + }, + { + "text": "OK." + }, + { + "text": "So suppose we have n linearly independent eigenvectors of A." + }, + { + "text": "Put them in the columns of this matrix S. So I'm naturally going to call that the eigenvector matrix, because it's got the eigenvectors in its columns." + }, + { + "text": "And all I want to do is show you what happens when you multiply A times S. So A times S. So this is A times the matrix with the first eigenvector in its first column, the second eigenvector in its second column, the nth eigenvector in its nth column." + }, + { + "text": "And how am I going to do this matrix multiplication?" + }, + { + "text": "Well, certainly I'll do it a column at a time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk1.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..fbe078217bb68baea8e0605a5d04be568c49efbf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I get?" + }, + { + "text": "A times the first column gives me the first column of the answer, but what is it?" + }, + { + "text": "That's an eigenvector." + }, + { + "text": "A times x1 is equal to the lambda times the x1." + }, + { + "text": "And that lambda's we'll call lambda one, of course." + }, + { + "text": "So that's the first column, A x1 is the same as lambda one x1." + }, + { + "text": "A x2 is lambda two x2, so on, along to, in the nth column, we now have lambda n xn." + }, + { + "text": "Looking good, but the next step is even better." + }, + { + "text": "So for the next step, I want to separate out those eigenvalues, those multiplying numbers, from the x's." + }, + { + "text": "So then I'll have just what I want." + }, + { + "text": "OK, so how, how am I going to separate out?" + }, + { + "text": "So that, that number lambda one is multiplying the first column." + }, + { + "text": "So if I want to factor it out of the first column, I better put, here is going to be x1, and that's going to multiply this matrix lambda one in the first entry in all zeros." + }, + { + "text": "You see that that, that's going to come out right for the first column?" + }, + { + "text": "Because we remember how, how we're going back to that original punchline, that if I want a number to multiply x1, then I can do it by putting x1 in that column, in the first column, and putting that number there." + }, + { + "text": "What am I going to have here?" + }, + { + "text": "I'm going to have lambda one, I'm going to have x1, x2, xn." + }, + { + "text": "These are going to be my columns again." + }, + { + "text": "I'm getting s back again." + }, + { + "text": "I'm getting s back again, but now what's it multiplied by?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk10.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c58a42edbe9567233ca7f57643a0b7d43ae6761f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what are the eigenvalues?" + }, + { + "text": "You can tell me right away what they are." + }, + { + "text": "They're two and two, right." + }, + { + "text": "It's a triangular matrix, so when I do this determinant, shall I do this determinant of A minus lambda I?" + }, + { + "text": "I'll get this two minus lambda, one, zero, two minus lambda, right?" + }, + { + "text": "I take that determinant, so I make those into vertical bars to mean determinant, and what's the determinant?" + }, + { + "text": "Two minus lambda squared." + }, + { + "text": "What are the roots?" + }, + { + "text": "Lambda equal two twice." + }, + { + "text": "So the eigenvalues are lambda equals two and two." + }, + { + "text": "OK, fine." + }, + { + "text": "Now the next step, find the eigenvectors." + }, + { + "text": "So I look for eigenvectors and what do I find for this guy?" + }, + { + "text": "Eigenvectors for this guy, when I subtract two minus the identity, so A minus two I has zeros here, and I'm looking for the null space." + }, + { + "text": "What's, what are the eigenvectors?" + }, + { + "text": "They're the, they're, they're the null space of A minus lambda I." + }, + { + "text": "The null space is only one dimension." + }, + { + "text": "This is a case where I don't have enough eigenvectors." + }, + { + "text": "My algebraic multiplicity is two." + }, + { + "text": "I, I would say when I see, when I count how often the eigenvalue is repeated, that's the algebraic multiplicity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk11.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..779c2cf904d904b761080db2671aac46394ad02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the multiplicity." + }, + { + "text": "How many times is it the root of the polynomial?" + }, + { + "text": "My polynomial is two minus lambda squared." + }, + { + "text": "It's a double root." + }, + { + "text": "So my algebraic multiplicity is two." + }, + { + "text": "But the geometric multiplicity, which looks for vectors, looks for eigenvectors and which means the null space of this thing." + }, + { + "text": "And the only eigenvector is one zero." + }, + { + "text": "That's in the null space." + }, + { + "text": "Zero one is not in the null space." + }, + { + "text": "The null space is only one dimensional." + }, + { + "text": "So there's a matrix, my, this A or the original A, that are not diagonalizable." + }, + { + "text": "I can't, I can't find two independent eigenvectors, there's only one." + }, + { + "text": "OK." + }, + { + "text": "So that's the case that I'm, that's a case that I, I'm not really handling." + }, + { + "text": "For example, when I wrote down up here that the powers went to zero if the eigenvalues were below one, I didn't really handle that case of repeated eigenvalues because my reasoning was based on this formula." + }, + { + "text": "And this formula is based on n independent eigenvectors." + }, + { + "text": "OK." + }, + { + "text": "So just to say that." + }, + { + "text": "There are some matrices that we don't cover through diagonalization, but the great majority we do." + }, + { + "text": "OK. And we're always OK if we have different distinct eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk12.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..77d090704cc298475d94416b7ecb88a2a015a913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. That's the, like, the typical case." + }, + { + "text": "Because for each eigenvalue there's at least one eigenvector, the algebraic multiplicity here is one for every eigenvalue, and the geometric multiplicity is one." + }, + { + "text": "There's one eigenvector and they are independent." + }, + { + "text": "OK. OK. Now let me come back to the important case when we're OK." + }, + { + "text": "The important case when we are diagonalizing." + }, + { + "text": "Let me look at, so let me solve this equation." + }, + { + "text": "The equation will be each, I start with some, start with a given vector u0." + }, + { + "text": "And then my equation is that every step I multiply what I have by a." + }, + { + "text": "That equation ought to be simple to handle." + }, + { + "text": "OK. And I'd like to be able to solve it." + }, + { + "text": "How would I find, if I start with a vector u0, and I multiply by a a hundred times, what have I got?" + }, + { + "text": "Well, I can certainly write down a formula for the answer." + }, + { + "text": "So what, what, so u1 is a u0." + }, + { + "text": "And u2 is, what's u2 then?" + }, + { + "text": "U2 I multiply it, u2 I get from u1 by another, multiplying by a, so I've got a twice." + }, + { + "text": "And my formula is uk, after k steps, I've multiplied by a k times the original u0." + }, + { + "text": "You see what I'm doing?" + }, + { + "text": "The next section is going to solve systems of differential equations." + }, + { + "text": "I'm going to have derivatives." + }, + { + "text": "This, this section is the nice one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk13.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..ba8214d8c636e4757a266d6617801174bc939d80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "It solves difference equations." + }, + { + "text": "I would call that a difference equation." + }, + { + "text": "It's conne- a first order." + }, + { + "text": "I would call that a first order system, because it connects only, it only goes up one level." + }, + { + "text": "And it's a system because these are vectors and that's a matrix." + }, + { + "text": "And the solution is just that." + }, + { + "text": "OK." + }, + { + "text": "But, that's a nice formula." + }, + { + "text": "That's the, like, the most compact formula I could ever get." + }, + { + "text": "U one hundred would be a to the one hundredth u0." + }, + { + "text": "But how would I actually find u one hundred?" + }, + { + "text": "How would I find, how would I discover what u one hundred is?" + }, + { + "text": "Let me, let me show you how." + }, + { + "text": "Here, here's the idea." + }, + { + "text": "If, so, to solve, to really solve, shall I say, to really solve." + }, + { + "text": "To really solve it, I would take this initial vector, u0, and I would write it as a combination of eigenvectors." + }, + { + "text": "To really solve, write, write u0 as a combination, say, certain amount of the first eigenvector plus a certain amount of the second eigenvector plus a certain amount of the last eigenvector." + }, + { + "text": "Now multiply by a." + }, + { + "text": "You want to, you got to see the magic of eigenvectors work." + }, + { + "text": "Multiply by a." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk14.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7843b2bf0cac762d1c12452cf36500ea4ad13370 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a u0 is what?" + }, + { + "text": "So a times that." + }, + { + "text": "A times, so what's, I can separate it out into n separate pieces and that's the whole point." + }, + { + "text": "That each of those pieces is going in its own merry way." + }, + { + "text": "Each of those pieces is an eigenvector, and when I multiply by a, what does this piece become?" + }, + { + "text": "So that's some amount of the first, let's suppose the eigenvectors are normalized to be unit vectors." + }, + { + "text": "So that says what the eigenvector is." + }, + { + "text": "It's, and I need some multiple of it to produce u0." + }, + { + "text": "OK. Now when I multiply by a, what do I get?" + }, + { + "text": "I get c1, which is just a factor, times a x1, but a x1 is lambda one x1." + }, + { + "text": "When I multiply this by a, I get c2 lambda two x2." + }, + { + "text": "And here I get cn lambda n xn." + }, + { + "text": "And suppose I multiply by a to the hundredth power now." + }, + { + "text": "Can we, can we, having done it, multiplied by a, let's multiply by a to the hundredth." + }, + { + "text": "What happens to this first term when I multiply by a to the one hundredth?" + }, + { + "text": "It's got that factor lambda to the hundredth." + }, + { + "text": "That's the key." + }, + { + "text": "That, that's what I mean by going its own merry way." + }, + { + "text": "It, it is pure eigenvector, it's exactly in a direction where multiplication by a just brings in a scalar factor lambda one." + }, + { + "text": "So a hundred times brings in this a hundred times." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk15.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7ee3348735378aa4049d33ec2a197d0ceb0c447c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Hundred times lambda two, hundred times lambda n. Actually, we're, what are we seeing here?" + }, + { + "text": "We're seeing, this same, lambda, capital lambda to the hundredth, as in the, as in the diagonalization, and we're seeing the S matrix, the matrix S of eigenvectors." + }, + { + "text": "That's what this has got to, this has got to amount to, a lambda to the hundredth power times an S times this vector C that's telling us how much of each one is in the original thing." + }, + { + "text": "So if, if I had to really find the hundredth power, I would take u0, I would expand it as a combination of eigenvectors, this is really S, the eigenvector matrix times C, the, the coefficient vector." + }, + { + "text": "And then I would immediately, then, by inserting these hundredth powers of eigenvalues, I'd have the answer." + }, + { + "text": "So the, the, huh, there must be, well, let's see." + }, + { + "text": "OK." + }, + { + "text": "It's, so, yeah." + }, + { + "text": "So if u100 is a to the hundredth times u0, and u0 is Sc, then you see this formula is just this formula, which is the way I would actually get hold of this, of this u100, which is, let me put it here, u100." + }, + { + "text": "The way I would actually get hold of that, see what, what the solution is after a hundred steps, would be expand the initial vector into eigenvectors and, and let each eigenvector go its own way, multiplying by a hundred at, by lambda at every step, and therefore by lambda to the hundredth power after a hundredth step." + }, + { + "text": "Can I do an example?" + }, + { + "text": "So that's, that's the, the formulas." + }, + { + "text": "Now let me take an example." + }, + { + "text": "I'll use the Fibonacci sequence as an example." + }, + { + "text": "So, so Fibonacci example." + }, + { + "text": "You remember the Fibonacci numbers?" + }, + { + "text": "If we start with one and one as F0, oh, I think I start with zero, maybe." + }, + { + "text": "Let zero and one be the first ones." + }, + { + "text": "So there's F0 and F1, the first two Fibonacci numbers." + }, + { + "text": "Then what's the rule for Fibonacci numbers?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk16.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..79c65e32781f7f304b504a6c390247abb9d26ac8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "They're the sum." + }, + { + "text": "The next one is the sum of those, so it's one." + }, + { + "text": "The next one is the sum of those, so it's two." + }, + { + "text": "The next one is the sum of those, so it's three." + }, + { + "text": "Well, it looks like one, two, three, four, five, but somehow it's not going to do that way." + }, + { + "text": "The next one is five, right." + }, + { + "text": "Two and three makes five." + }, + { + "text": "The next one is eight." + }, + { + "text": "The next one is thirteen." + }, + { + "text": "And the one hundredth Fibonacci number is what?" + }, + { + "text": "That's my question." + }, + { + "text": "How could I get a formula for the hundredth number and for example how could I answer the question how fast are they growing?" + }, + { + "text": "How fast are those Fibonacci numbers growing?" + }, + { + "text": "They're certainly growing." + }, + { + "text": "It's not a stable case, whatever the eigenvalues of whatever matrix it is, they're not smaller than one." + }, + { + "text": "These numbers are growing." + }, + { + "text": "But how fast are they growing?" + }, + { + "text": "The answer is lies in the eigenvalue." + }, + { + "text": "So I've got to find the matrix, so let me write down the Fibonacci rule, F k plus two is F k plus one plus F k, right?" + }, + { + "text": "Now that's not in my -- I want to write that as U k plus one and A U k. But right now what I've got is a single equation, not a system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk17.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b3aaa9dcee3cf27c112015659bb5a0b51a983ce1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's second order." + }, + { + "text": "It's like having a second order differential equation with second derivatives." + }, + { + "text": "I want to get first derivatives." + }, + { + "text": "Here I want to get first difference." + }, + { + "text": "So the way to do it is to introduce U k will be a vector." + }, + { + "text": "See, a small trick." + }, + { + "text": "Let U k be a vector, F k plus one and F k. So I'm going to get a two by two system, first order, instead of a one, instead of a scalar system, second order, by a simple trick." + }, + { + "text": "I'm just going to add in an equation F k plus one equals F k plus one." + }, + { + "text": "That will be my second equation." + }, + { + "text": "Then this is my system, this is my unknown, and what's my one-step equation?" + }, + { + "text": "So now U k plus one." + }, + { + "text": "That's so U k plus one is the left side, and what have I got here on the right side?" + }, + { + "text": "I've got some matrix multiplying U k. Can you see that all right?" + }, + { + "text": "If you can see it, then you can tell me what the matrix is." + }, + { + "text": "You see that I'm taking my system here, I artificially made it into a system." + }, + { + "text": "I artificially made the unknown into a vector, and now I'm ready to look at and see what the matrix is." + }, + { + "text": "So do you see the left side, U k plus one is F k plus two F k plus one, that's just what I want." + }, + { + "text": "On the right side, this, remember, this U k here, let me for the moment put it as F k plus one F k. So what's the matrix?" + }, + { + "text": "Well, that has a one and a one, and that has a one and a zero." + }, + { + "text": "There's the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk18.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..6c1b68c2cb2fde3f5dea82f3100d4da31fcce70a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "You see that that gives me the right-hand side." + }, + { + "text": "So there's the matrix A, and this is our friend U k. So we've got, so that simple trick changed the second order scalar problem to a first order system, two, with two unknowns." + }, + { + "text": "With a matrix and now what do I do?" + }, + { + "text": "Well, before I even think, I find its eigenvalues and eigenvectors." + }, + { + "text": "So what are the eigenvalues and eigenvectors of that matrix?" + }, + { + "text": "Let's see." + }, + { + "text": "I was, first let me just, like, think for a minute." + }, + { + "text": "It's two by two, so this shouldn't be impossible to do." + }, + { + "text": "Let's do it." + }, + { + "text": "OK." + }, + { + "text": "So my matrix again is one one one zero." + }, + { + "text": "It's symmetric, by the way." + }, + { + "text": "So what I will eventually know about symmetric matrices is that the eigenvalues will come out real, I won't get any complex numbers here, and the eigenvectors, once I get those, actually will be orthogonal." + }, + { + "text": "But two by two, I'm more interested in what the actual numbers are." + }, + { + "text": "What do I know about the two numbers?" + }, + { + "text": "Well, should, do you want me to find this determinant of A minus lambda I?" + }, + { + "text": "Sure." + }, + { + "text": "So it's the determinant of one minus lambda one one zero, right?" + }, + { + "text": "Minus lambda, yes, got it." + }, + { + "text": "OK. OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk19.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..a73b23e3d56b889ff49ea7f55a784fac33e13c3d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "There'll be two eigenvalues." + }, + { + "text": "Well, tell me again what I know about the two eigenvalues before I go any further." + }, + { + "text": "Tell me something about these two eigenvalues, what do they add up to?" + }, + { + "text": "Lambda one plus lambda two is the same as the trace down the diagonal of the matrix, one and zero is one." + }, + { + "text": "So lambda one plus lambda two should come out to be one, and lambda one times lambda two should come out to be the determinant, which is minus one." + }, + { + "text": "So I'm expecting the eigenvalues to add to one and to multiply to minus one." + }, + { + "text": "But let's just see it happen here." + }, + { + "text": "If I multiply this out, I get that times that'll be a lambda squared minus lambda minus one." + }, + { + "text": "Good." + }, + { + "text": "Lambda squared minus lambda minus one." + }, + { + "text": "Actually, you see the, compare that with the original equation that I started with." + }, + { + "text": "Fk plus two minus Fk plus one minus Fk is zero." + }, + { + "text": "The recurrent, the recursion that the Fibonacci number satisfy is somehow showing up directly here for the eigenvalues when we set that to zero." + }, + { + "text": "OK. Let's solve." + }, + { + "text": "Well, I would like to be able to factor that, that quadratic, but I'm better off to use the quadratic formula." + }, + { + "text": "Lambda is, let's see, minus b is one, plus or minus the square root of b squared, which is one, minus four, times that, times that, which is plus four, over two." + }, + { + "text": "So that's the square root of five." + }, + { + "text": "So the eigenvalues are lambda one is one half of one plus square root of five, and lambda two is one half of one minus square root of five." + }, + { + "text": "And sure enough, they, those add up to one, and they multiply to give minus one." + }, + { + "text": "OK. Those are the two eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk2.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..43cfb012fc04a89fc7dab94c23bfb0f50ade3782 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "On the right, it's multiplied by, if I want, if I want lambda n xn in the last column, how do I do it?" + }, + { + "text": "Well, the last column here will be, I'll, I'll take the last column, use these coefficients, put the lambda n down there, and it will multiply that nth column and give me lambda n xn." + }, + { + "text": "There, there you see matrix multiplication just working for us." + }, + { + "text": "So I started with A s. I wrote down what it meant." + }, + { + "text": "A times each eigenvector." + }, + { + "text": "That gave me lambda times the eigenvector." + }, + { + "text": "And then when I peeled off the lambdas, they were on the right-hand side, so I've got s, my matrix back again, and this matrix, this diagonal matrix, the eigenvalue matrix, and I call it capital lambda, using capital letters for matrices, and lambda to prompt me that it's, that it's eigenvalues that are in there." + }, + { + "text": "So you see that the eigenvalues are just sitting down that diagonal?" + }, + { + "text": "If I had a column x2 here, I would want the lambda two in the two two position, in the diagonal position, to multiply that x2 and give me the lambda two x2." + }, + { + "text": "That's my formula." + }, + { + "text": "A s is s lambda." + }, + { + "text": "OK. That's, that's the, you see, it's just a calculation." + }, + { + "text": "Now, I, I mentioned, and I have to mention again, this business about n independent eigenvectors." + }, + { + "text": "As it stands, this is all fine whether, I mean, I could be repeating the same eigenvector, but I, I'm no interested in that." + }, + { + "text": "I want to be able to invert s, and that's where this comes in." + }, + { + "text": "This n independent eigenvectors business comes in to tell me that that matrix is invertible." + }, + { + "text": "So let me, on the next board, write down what I've got." + }, + { + "text": "A s equals s lambda." + }, + { + "text": "And now I'm, I can multiply on the left by s inverse." + }, + { + "text": "So this is really, I can do that provided s is invertible, provided my assumption of n independent eigenvectors is satisfied." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk20.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ad5a59fa5db44ce73ff5f88190423e0404fb3d39 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "How, how, what are those numbers approximately?" + }, + { + "text": "Square root of five, well, it's more than two, but less than three." + }, + { + "text": "It, it'd be nice to know these numbers." + }, + { + "text": "I think, I think that that, so that number comes out bigger than one, right?" + }, + { + "text": "Yeah, that's right." + }, + { + "text": "This number comes out bigger than one." + }, + { + "text": "It's about one point six one eight or something." + }, + { + "text": "Not exactly." + }, + { + "text": "It's supposed to be one point six." + }, + { + "text": "Just, like, I think so." + }, + { + "text": "Then what's lambda two?" + }, + { + "text": "Is, is lambda two positive or negative?" + }, + { + "text": "Negative, right?" + }, + { + "text": "Because I'm, it's obviously negative, and I knew that the, so it's minus, and they add up to one, so minus point six one eight, I guess." + }, + { + "text": "OK. And some order." + }, + { + "text": "Those are the two eigenvalues." + }, + { + "text": "One eigenvalue bigger than one, one eigenvalue smaller than one." + }, + { + "text": "Actually, that's a great situation to be in." + }, + { + "text": "Of course, the eigenvalues are different, so there's no doubt whatever, is this matrix diagonalizable?" + }, + { + "text": "Is this matrix diagonalizable, that original matrix A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk21.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..4a034475591d371995b379b5f98783a2cfb25870 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Sure." + }, + { + "text": "We've got two distinct eigenvalues and we can find the eigenvectors in a moment." + }, + { + "text": "But they'll be independent, will be diagonalizable, and now you can already answer my very first question." + }, + { + "text": "How fast are those Fibonacci numbers increasing?" + }, + { + "text": "How, those, they're increasing, right?" + }, + { + "text": "They're not doubling at every step." + }, + { + "text": "Let's look again at these numbers." + }, + { + "text": "Five eight thirteen, it's not obvious." + }, + { + "text": "The next one would be twenty one thirty four." + }, + { + "text": "So to get some idea of what F one hundred is, can you give me any, I mean the crucial number of, so it, these, it's approximately, what's controlling the growth of these Fibonacci numbers?" + }, + { + "text": "It's the eigenvalues." + }, + { + "text": "And which eigenvalues controlling that growth?" + }, + { + "text": "The big ones." + }, + { + "text": "So F one hundred will it be approximately some constant, c one, I guess, times this lambda one, this one plus square root of five over two, to the hundredth power." + }, + { + "text": "And the two hundredth have, in other words, the eigenvalue, the Fibonacci numbers are growing by about that factor." + }, + { + "text": "You see that we've got precise information about the, about the Fibonacci numbers out of the eigenvalue." + }, + { + "text": "OK. And again, why is that true?" + }, + { + "text": "Let me go over to this board and show what I'm doing here." + }, + { + "text": "The, the original eigen, the original initial value is some combination of eigenvectors, and then when we start multiple, when we start going out the theory of Fibonacci numbers, when we start multiplying by a hundred times, it's this lambda one to the hundredth, this term is, is the one that's taken over." + }, + { + "text": "It's, I mean, that's big, like, one point six to the hundredth power." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk22.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..c13a1fc9867173c3067e46c469cfff27b9b45289 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "The second term is practically nothing, right?" + }, + { + "text": "The point six, or minus point six to the hundredth power, is an extremely small, extremely small number." + }, + { + "text": "So this is, this, this, there are only two terms, because we're two by two." + }, + { + "text": "This number is, this piece of it is there, but it's, it's disappearing." + }, + { + "text": "Where this piece is there and it's growing and controlling everything." + }, + { + "text": "So, so really the, we're doing, like, problems that are evolving." + }, + { + "text": "We're doing dynamics." + }, + { + "text": "Instead of Ax equal b, that's a static problem." + }, + { + "text": "We're now, we're doing dynamics." + }, + { + "text": "A, a squared, a cubed, things are evolving in time, and the eigenvalues are the crucial, numbers." + }, + { + "text": "OK." + }, + { + "text": "I guess to complete this, I better write down the eigenvectors." + }, + { + "text": "So we should complete the, the whole process by finding the eigenvectors." + }, + { + "text": "OK. Well, I have to, up in the corner, then I have to look at A minus lambda I." + }, + { + "text": "So A minus lambda I is this one minus lambda, one, one, and minus lambda." + }, + { + "text": "And now, can we spot an eigenvector out of that?" + }, + { + "text": "That's, for these two lambdas, this matrix is singular." + }, + { + "text": "I guess the eigenvector, two by two ought to be easy." + }, + { + "text": "So if I know that this matrix is singular, then it seems to me the eigenvector has to be lambda and one, because that multiplication will give me the zero." + }, + { + "text": "And this multiplication gives me, better give me also zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk23.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..df816eb800ce767b1475c279a24ad976bb45a785 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Do you see why it does?" + }, + { + "text": "This is the minus lambda squared plus lambda plus one." + }, + { + "text": "It's the thing that's zero, because these lambdas are special." + }, + { + "text": "There's the eigenvector." + }, + { + "text": "X1 is lambda one, one, and x2 is lambda two, one." + }, + { + "text": "I did that as a little trick that was available in the two by two case." + }, + { + "text": "So now I finally have to, oh, I have to take the initial, u0." + }, + { + "text": "So to complete this example entirely, I have to say, OK, what was u0?" + }, + { + "text": "u0 was f1 f0." + }, + { + "text": "So u0, the starting vector, is f1 f0, and those were one and zero." + }, + { + "text": "So I have to use that vector, so I have to look for, from multiple of the first eigenvector and the second, to produce u0, the one zero vector." + }, + { + "text": "This is what will find c1 and c2, and then I'm done." + }, + { + "text": "So let me, instead of in the last five seconds grinding out a formula, let me repeat the idea." + }, + { + "text": "That really, it's the idea that's central." + }, + { + "text": "When things are evolving in time, let me come back to this board, because the ideas are here." + }, + { + "text": "When things are evolving in time by a first-order system, starting from an original u0, the key is, find the eigenvalues and eigenvectors of A." + }, + { + "text": "That will tell, those eigenvectors, the eigenvalues will already tell you what's happening." + }, + { + "text": "Is the solution blowing up?" + }, + { + "text": "Is it going to zero?" + }, + { + "text": "What's it doing?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk24.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..40301cb90760e2172baa94d536cbc13288d4c31f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk24.json @@ -0,0 +1,20 @@ +[ + { + "text": "And then, to find out exactly a formula, you have to take your u0 and write it as a combination of eigenvectors and then follow each eigenvector separately." + }, + { + "text": "And that's really what this formula, the formula for, that's what the formula for A to the k is doing." + }, + { + "text": "So remember that formula for A to the k is S, lambda to the k S inverse." + }, + { + "text": "OK. That's, that's difference equations, and you just have to, so the homework will give some examples different from Fibonacci to follow through." + }, + { + "text": "And next time will be differential equations." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk3.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..9bf1bb852baadc1da7837e14180c0c2951a30882 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I mentioned at the end of last time, and I'll say again, that there's a small number of matrices for, that don't have n independent eigenvectors." + }, + { + "text": "So I've got to discuss that, that technical point." + }, + { + "text": "But the great, the most matrices that we see have n, n independent eigenvectors and we can diagonalize." + }, + { + "text": "This is diagonalization." + }, + { + "text": "I could also write it, and I often will, the other way round." + }, + { + "text": "If I multiply on the right by s inverse, if I took this equation at the top and multiplied on the right by s inverse, I could, I would have A left here." + }, + { + "text": "Now s inverse is coming from the right." + }, + { + "text": "So can you keep those two straight?" + }, + { + "text": "A multiplies its eigenvectors." + }, + { + "text": "That's how I keep them straight." + }, + { + "text": "So A multiplies s. A multiplies s. And then this s inverse makes the whole thing diagonal." + }, + { + "text": "And this is another way of saying the same thing, putting the s's on the other side of the equation, A is s lambda s inverse." + }, + { + "text": "So that's the, that's the new factorization." + }, + { + "text": "That's the replacement for L U from elimination or Q R from Gram-Schmidt." + }, + { + "text": "And notice that the matrix, so it's, it's a matrix times a diagonal matrix times the inverse of the first one." + }, + { + "text": "It's, that's the combination that we'll see throughout this chapter." + }, + { + "text": "This, this, combination with an s and an s inverse." + }, + { + "text": "OK. Can I just begin to use that?" + }, + { + "text": "For example, what about A squared?" + }, + { + "text": "What are the eigenvalues and eigenvectors of A squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk4.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c687b6948acad76de8781cb82d3eb069c9da514e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's a straightforward question with a, with a absolutely clean answer." + }, + { + "text": "So let me, let me consider A squared." + }, + { + "text": "So I look, I start with Ax equal lambda x." + }, + { + "text": "And I'm headed for A squared." + }, + { + "text": "So let me multiply both sides by A." + }, + { + "text": "That's one way to get A squared on the left." + }, + { + "text": "So if, I should write these ifs in here." + }, + { + "text": "If Ax equals lambda x, then I multiply by A." + }, + { + "text": "So I get A squared x equals, well, I'm multiplying by A, so that's lambda Ax." + }, + { + "text": "That lambda was a number, so I just put it on the left." + }, + { + "text": "And what do I, tell me how to make that look better." + }, + { + "text": "What have I got here?" + }, + { + "text": "For, if, if A has the eigenvalue lambda and eigenvector x, what's up with A squared?" + }, + { + "text": "A squared x, I just multiply by A, but now for Ax, I'm going to substitute lambda x, so I've got lambda squared x." + }, + { + "text": "So from that simple calculation, I, my conclusion is that the eigenvalues of A squared are lambda squared." + }, + { + "text": "And the eigenvectors, I always think about both of those." + }, + { + "text": "What can I say about the eigenvalues?" + }, + { + "text": "They're squared." + }, + { + "text": "What can I say about the eigenvectors?" + }, + { + "text": "They're the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk5.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5bf15e20707c156c8ae71c9c7acea41a9d9d8e46 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same x as in, as for A." + }, + { + "text": "Now, let me see that also from this formula." + }, + { + "text": "How can I see what A squared is looking like from this formula?" + }, + { + "text": "So let me, that, that was one way to do it." + }, + { + "text": "Let me do it by just taking A squared from that." + }, + { + "text": "A squared is S lambda S inverse, that's A, times S lambda S inverse, that's A, which is?" + }, + { + "text": "This is the beauty of eigenvalues, eigenvectors, having that S inverse and S is the identity, so I've got S lambda squared S inverse." + }, + { + "text": "Yes." + }, + { + "text": "You see what that's telling me?" + }, + { + "text": "It's, it's telling me the same thing that I just learned here, but in the, in, in a matrix form." + }, + { + "text": "It's telling me that the S is the same, the eigenvectors are the same, but the eigenvalues are squared, because this is, what's lambda squared, that's still diagonal, it's got little lambda one squared, lambda two squared, down to lambda n squared, on that diagonal, those are the eigenvalues, as we just learned, of A squared." + }, + { + "text": "OK." + }, + { + "text": "So, somehow those eigenvalues and eigenvectors are really giving you a way to, to, to, to see what's going on inside a matrix." + }, + { + "text": "Now, of course, I can continue that for, to the k-th power." + }, + { + "text": "A to the k-th power." + }, + { + "text": "If I multiply, if I have k of these together, do you see how S inverse S will keep cancelling?" + }, + { + "text": "In the, in the inside, I'll have the S outside, at the far left, and lambda will be in there k times and S inverse." + }, + { + "text": "So what's that telling me?" + }, + { + "text": "That's telling me that the eigenvalues of A, of A to the k-th power are the k-th powers." + }, + { + "text": "The eigenvalues of A cubed are the cubes of the eigenvalues of A, and the eigenvectors are the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk6.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..c18dddbe798022f7e68278ac002a3f5fe6ed249e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same." + }, + { + "text": "OK." + }, + { + "text": "In other words, eigenvalues and eigenvectors give a great way to understand the powers of a matrix." + }, + { + "text": "If I take the square of a matrix or the hundredth power of a matrix, the pivots are all over the place." + }, + { + "text": "L U, if I multiply L U times L U times L U times L U a hundred times, I've got a hundred L U's." + }, + { + "text": "I can't do anything with them." + }, + { + "text": "But when I multiply S lambda S inverse by itself, when I look at the eigenvector picture a hundred times, I get a hundred or ninety-nine of these guys cancelling out inside, and I get A to the hundredth is S lambda to the hundredth S inverse." + }, + { + "text": "I mean, eigenvalues tell you about powers of a matrix in a way that we had no, no way to approach previously." + }, + { + "text": "For example, when does, when do the powers of a matrix go to zero?" + }, + { + "text": "I would call that matrix stable, maybe." + }, + { + "text": "So, so, so I could write down a, a theorem." + }, + { + "text": "I'll, I'll write it as a theorem, just to use that word to emphasize that here I'm getting this great fact from this eigenvalue picture." + }, + { + "text": "OK. A to the k approaches zero as k goes, as k gets bigger." + }, + { + "text": "If what?" + }, + { + "text": "What's the, how can I tell for a matrix A if its powers go to zero?" + }, + { + "text": "What, what's somewhere inside that matrix is that information." + }, + { + "text": "That information is not present in the pivots." + }, + { + "text": "It's present in the eigenvalues." + }, + { + "text": "What do I need for the, to know that if I take higher and higher powers of A that this matrix gets smaller and smaller?" + }, + { + "text": "Well, S and S inverse are not moving." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk7.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b84a5c854a5542758e8a0107e1ff043205fe3bdb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's this guy that has to get small, and that's easy to, easy to understand." + }, + { + "text": "The requirement is all eigenvalues, so what is the requirement?" + }, + { + "text": "The eigenvalues have to be less than one." + }, + { + "text": "Now, I have to write that absolute value, because those eigenvalues could be negative, they could be complex numbers." + }, + { + "text": "So I'm taking the absolute value if all of those are below one." + }, + { + "text": "That's, in fact, we practically see why." + }, + { + "text": "Let me just say that I, that I, I'm operating on one assumption here, and I got to keep remembering that that assumption is still present." + }, + { + "text": "That assumption was that I had a full set of, of n independent eigenvectors." + }, + { + "text": "If I don't have that, then I, I, then this approach is not working." + }, + { + "text": "So, so again, a pure eigenvalue approach, eigenvector approach, needs n independent eigenvectors." + }, + { + "text": "If we don't have n independent eigenvectors, we can't diagonalize the matrix." + }, + { + "text": "We can't get to a diagonal matrix." + }, + { + "text": "This, this, this diagonalization is only possible if S inverse makes sense." + }, + { + "text": "OK. Can I, can I follow up on that point now?" + }, + { + "text": "So, so you see why, what we get and, and why we want it, because we get information about the powers of a matrix just immediately from the eigenvalues." + }, + { + "text": "OK, now let me follow up on this, business of which matrices are diagonalizable." + }, + { + "text": "Sorry about that long word." + }, + { + "text": "So a matrix is, is sure to, so here's, here's the main point." + }, + { + "text": "A is sure to be, to have n independent eigenvectors and, and B, now here comes that word, diagonalizable, if, if, so we, we, we might as well get the, the nice case out in the open." + }, + { + "text": "The nice case is when, if all the lambdas are different." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk8.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f06dcec8ffa0ee1bf19440e4ab2194db33ab353b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means, that means no repeated eigenvalues." + }, + { + "text": "OK. That's the nice case." + }, + { + "text": "If, if my matrix and most matrix, if I do a random matrix in MATLAB and compute its eigenvalues, so if I computed, if I took I of rand of ten ten, gave, gave that MATLAB command, the, we'd get a random ten by ten matrix, we would get a list of its ten eigenvalues and they would be different." + }, + { + "text": "They would be distinct, is the best word." + }, + { + "text": "I would have a random matrix will have ten distinct, a ten by ten matrix will have ten distinct eigenvalues, and if it does, the eigenvectors are automatically independent." + }, + { + "text": "So that's a nice fact." + }, + { + "text": "I can, I'll refer you to the text for the proof." + }, + { + "text": "That, that A is sure to have n independent eigenvectors if the eigenvalues are different." + }, + { + "text": "If, if all the, if all eigenvalues are different." + }, + { + "text": "It's just, if some lambdas are repeated, then I have to look more closely." + }, + { + "text": "If an eigenvalue is repeated, I have to look, I have to count, I have to check." + }, + { + "text": "Has it got, say it's repeated three times." + }, + { + "text": "So what's a possibility for, so, so here's, here's the repeated possibility." + }, + { + "text": "And, and let me emphasize the conclusion." + }, + { + "text": "That if I have repeated eigenvalues, I may or may not, I may or may not have, have n independent eigenvectors." + }, + { + "text": "I might." + }, + { + "text": "I, I, you know, this isn't a completely negative case." + }, + { + "text": "The identity matrix." + }, + { + "text": "Well, suppose I take the ten by ten identity matrix." + }, + { + "text": "What are the eigenvalues of that matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk9.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..87d2a2ae5773036cf11800e2f1962908986a0dad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_11_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So just, just take the easiest matrix, the identity." + }, + { + "text": "If I look for its eigenvalues, they're all ones." + }, + { + "text": "So that eigenvalue one is repeated ten times." + }, + { + "text": "But there's no shortage of eigenvectors for the identity matrix." + }, + { + "text": "In fact, every vector is an eigenvector." + }, + { + "text": "So I can take ten independent vectors." + }, + { + "text": "Oh, well, what happens to everything if, if, if A is the identity matrix, let's just think that one through in our head." + }, + { + "text": "If A is the identity matrix, then it's got plenty of eigenvectors." + }, + { + "text": "I choose ten independent vectors, they're the columns of S, and, and what do I get from S inverse A S?" + }, + { + "text": "I get I again, right?" + }, + { + "text": "If A is the identity, and of course, that's the correct lambda." + }, + { + "text": "The, the matrix was already diagonal." + }, + { + "text": "So if the matrix is already diagonal, then the, the lambda is the same as the matrix." + }, + { + "text": "A diagonal matrix has got its eigenvalues sitting right there in front of you." + }, + { + "text": "Now if it's triangular, the eigenvalues are still sitting there, but so let's, let's take a case where, it's triangular." + }, + { + "text": "Suppose A is like, two, one, two, zero." + }, + { + "text": "So there's a case that's going to be trouble." + }, + { + "text": "There's a case that's going to be trouble." + }, + { + "text": "First of all, what are the eigen- I mean, we just, like now you, if we start with a matrix, the first thing we do practically without thinking is compute the eigenvalues and eigenvectors." + }, + { + "text": "OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk0.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6898d4fe66019ef6b40d0472ea94a968e7bbde9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, shall we start?" + }, + { + "text": "This is the second lecture on eigenvalues." + }, + { + "text": "So the first lecture was set -- reached the key equation, Ax equal lambda x. x is the eigenvector and lambda is the eigenvalue." + }, + { + "text": "Now, to use that." + }, + { + "text": "And the good way to, after we've found, so job one is to find the eigenvalues and find the eigenvectors." + }, + { + "text": "Now after we found them, what do we do with them?" + }, + { + "text": "Well, the good way to see that is diagonalize the matrix." + }, + { + "text": "So the matrix is A, and I want to show, first of all, this is like the basic fact." + }, + { + "text": "This, this formula." + }, + { + "text": "That's, that's the key to today's lecture." + }, + { + "text": "This matrix A, I put its eigenvectors in the columns of a matrix S. So S will be the eigenvector matrix, and I want to look at this magic combination S inverse A S. So can I show you how that, how that, what happens there?" + }, + { + "text": "And notice, notice, there's an S inverse." + }, + { + "text": "We have to be able to invert this eigenvector matrix S. So for that we need n independent eigenvectors." + }, + { + "text": "So that's the, that's the case." + }, + { + "text": "OK." + }, + { + "text": "So suppose we have n linearly independent eigenvectors of A." + }, + { + "text": "Put them in the columns of this matrix S. So I'm naturally going to call that the eigenvector matrix, because it's got the eigenvectors in its columns." + }, + { + "text": "And all I want to do is show you what happens when you multiply A times S. So A times S. So this is A times the matrix with the first eigenvector in its first column, the second eigenvector in its second column, the nth eigenvector in its nth column." + }, + { + "text": "And how am I going to do this matrix multiplication?" + }, + { + "text": "Well, certainly I'll do it a column at a time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk1.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..fbe078217bb68baea8e0605a5d04be568c49efbf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I get?" + }, + { + "text": "A times the first column gives me the first column of the answer, but what is it?" + }, + { + "text": "That's an eigenvector." + }, + { + "text": "A times x1 is equal to the lambda times the x1." + }, + { + "text": "And that lambda's we'll call lambda one, of course." + }, + { + "text": "So that's the first column, A x1 is the same as lambda one x1." + }, + { + "text": "A x2 is lambda two x2, so on, along to, in the nth column, we now have lambda n xn." + }, + { + "text": "Looking good, but the next step is even better." + }, + { + "text": "So for the next step, I want to separate out those eigenvalues, those multiplying numbers, from the x's." + }, + { + "text": "So then I'll have just what I want." + }, + { + "text": "OK, so how, how am I going to separate out?" + }, + { + "text": "So that, that number lambda one is multiplying the first column." + }, + { + "text": "So if I want to factor it out of the first column, I better put, here is going to be x1, and that's going to multiply this matrix lambda one in the first entry in all zeros." + }, + { + "text": "You see that that, that's going to come out right for the first column?" + }, + { + "text": "Because we remember how, how we're going back to that original punchline, that if I want a number to multiply x1, then I can do it by putting x1 in that column, in the first column, and putting that number there." + }, + { + "text": "What am I going to have here?" + }, + { + "text": "I'm going to have lambda one, I'm going to have x1, x2, xn." + }, + { + "text": "These are going to be my columns again." + }, + { + "text": "I'm getting s back again." + }, + { + "text": "I'm getting s back again, but now what's it multiplied by?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk10.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c58a42edbe9567233ca7f57643a0b7d43ae6761f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what are the eigenvalues?" + }, + { + "text": "You can tell me right away what they are." + }, + { + "text": "They're two and two, right." + }, + { + "text": "It's a triangular matrix, so when I do this determinant, shall I do this determinant of A minus lambda I?" + }, + { + "text": "I'll get this two minus lambda, one, zero, two minus lambda, right?" + }, + { + "text": "I take that determinant, so I make those into vertical bars to mean determinant, and what's the determinant?" + }, + { + "text": "Two minus lambda squared." + }, + { + "text": "What are the roots?" + }, + { + "text": "Lambda equal two twice." + }, + { + "text": "So the eigenvalues are lambda equals two and two." + }, + { + "text": "OK, fine." + }, + { + "text": "Now the next step, find the eigenvectors." + }, + { + "text": "So I look for eigenvectors and what do I find for this guy?" + }, + { + "text": "Eigenvectors for this guy, when I subtract two minus the identity, so A minus two I has zeros here, and I'm looking for the null space." + }, + { + "text": "What's, what are the eigenvectors?" + }, + { + "text": "They're the, they're, they're the null space of A minus lambda I." + }, + { + "text": "The null space is only one dimension." + }, + { + "text": "This is a case where I don't have enough eigenvectors." + }, + { + "text": "My algebraic multiplicity is two." + }, + { + "text": "I, I would say when I see, when I count how often the eigenvalue is repeated, that's the algebraic multiplicity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk11.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..779c2cf904d904b761080db2671aac46394ad02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the multiplicity." + }, + { + "text": "How many times is it the root of the polynomial?" + }, + { + "text": "My polynomial is two minus lambda squared." + }, + { + "text": "It's a double root." + }, + { + "text": "So my algebraic multiplicity is two." + }, + { + "text": "But the geometric multiplicity, which looks for vectors, looks for eigenvectors and which means the null space of this thing." + }, + { + "text": "And the only eigenvector is one zero." + }, + { + "text": "That's in the null space." + }, + { + "text": "Zero one is not in the null space." + }, + { + "text": "The null space is only one dimensional." + }, + { + "text": "So there's a matrix, my, this A or the original A, that are not diagonalizable." + }, + { + "text": "I can't, I can't find two independent eigenvectors, there's only one." + }, + { + "text": "OK." + }, + { + "text": "So that's the case that I'm, that's a case that I, I'm not really handling." + }, + { + "text": "For example, when I wrote down up here that the powers went to zero if the eigenvalues were below one, I didn't really handle that case of repeated eigenvalues because my reasoning was based on this formula." + }, + { + "text": "And this formula is based on n independent eigenvectors." + }, + { + "text": "OK." + }, + { + "text": "So just to say that." + }, + { + "text": "There are some matrices that we don't cover through diagonalization, but the great majority we do." + }, + { + "text": "OK. And we're always OK if we have different distinct eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk12.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..77d090704cc298475d94416b7ecb88a2a015a913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. That's the, like, the typical case." + }, + { + "text": "Because for each eigenvalue there's at least one eigenvector, the algebraic multiplicity here is one for every eigenvalue, and the geometric multiplicity is one." + }, + { + "text": "There's one eigenvector and they are independent." + }, + { + "text": "OK. OK. Now let me come back to the important case when we're OK." + }, + { + "text": "The important case when we are diagonalizing." + }, + { + "text": "Let me look at, so let me solve this equation." + }, + { + "text": "The equation will be each, I start with some, start with a given vector u0." + }, + { + "text": "And then my equation is that every step I multiply what I have by a." + }, + { + "text": "That equation ought to be simple to handle." + }, + { + "text": "OK. And I'd like to be able to solve it." + }, + { + "text": "How would I find, if I start with a vector u0, and I multiply by a a hundred times, what have I got?" + }, + { + "text": "Well, I can certainly write down a formula for the answer." + }, + { + "text": "So what, what, so u1 is a u0." + }, + { + "text": "And u2 is, what's u2 then?" + }, + { + "text": "U2 I multiply it, u2 I get from u1 by another, multiplying by a, so I've got a twice." + }, + { + "text": "And my formula is uk, after k steps, I've multiplied by a k times the original u0." + }, + { + "text": "You see what I'm doing?" + }, + { + "text": "The next section is going to solve systems of differential equations." + }, + { + "text": "I'm going to have derivatives." + }, + { + "text": "This, this section is the nice one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk13.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..ba8214d8c636e4757a266d6617801174bc939d80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "It solves difference equations." + }, + { + "text": "I would call that a difference equation." + }, + { + "text": "It's conne- a first order." + }, + { + "text": "I would call that a first order system, because it connects only, it only goes up one level." + }, + { + "text": "And it's a system because these are vectors and that's a matrix." + }, + { + "text": "And the solution is just that." + }, + { + "text": "OK." + }, + { + "text": "But, that's a nice formula." + }, + { + "text": "That's the, like, the most compact formula I could ever get." + }, + { + "text": "U one hundred would be a to the one hundredth u0." + }, + { + "text": "But how would I actually find u one hundred?" + }, + { + "text": "How would I find, how would I discover what u one hundred is?" + }, + { + "text": "Let me, let me show you how." + }, + { + "text": "Here, here's the idea." + }, + { + "text": "If, so, to solve, to really solve, shall I say, to really solve." + }, + { + "text": "To really solve it, I would take this initial vector, u0, and I would write it as a combination of eigenvectors." + }, + { + "text": "To really solve, write, write u0 as a combination, say, certain amount of the first eigenvector plus a certain amount of the second eigenvector plus a certain amount of the last eigenvector." + }, + { + "text": "Now multiply by a." + }, + { + "text": "You want to, you got to see the magic of eigenvectors work." + }, + { + "text": "Multiply by a." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk14.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7843b2bf0cac762d1c12452cf36500ea4ad13370 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a u0 is what?" + }, + { + "text": "So a times that." + }, + { + "text": "A times, so what's, I can separate it out into n separate pieces and that's the whole point." + }, + { + "text": "That each of those pieces is going in its own merry way." + }, + { + "text": "Each of those pieces is an eigenvector, and when I multiply by a, what does this piece become?" + }, + { + "text": "So that's some amount of the first, let's suppose the eigenvectors are normalized to be unit vectors." + }, + { + "text": "So that says what the eigenvector is." + }, + { + "text": "It's, and I need some multiple of it to produce u0." + }, + { + "text": "OK. Now when I multiply by a, what do I get?" + }, + { + "text": "I get c1, which is just a factor, times a x1, but a x1 is lambda one x1." + }, + { + "text": "When I multiply this by a, I get c2 lambda two x2." + }, + { + "text": "And here I get cn lambda n xn." + }, + { + "text": "And suppose I multiply by a to the hundredth power now." + }, + { + "text": "Can we, can we, having done it, multiplied by a, let's multiply by a to the hundredth." + }, + { + "text": "What happens to this first term when I multiply by a to the one hundredth?" + }, + { + "text": "It's got that factor lambda to the hundredth." + }, + { + "text": "That's the key." + }, + { + "text": "That, that's what I mean by going its own merry way." + }, + { + "text": "It, it is pure eigenvector, it's exactly in a direction where multiplication by a just brings in a scalar factor lambda one." + }, + { + "text": "So a hundred times brings in this a hundred times." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk15.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7ee3348735378aa4049d33ec2a197d0ceb0c447c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Hundred times lambda two, hundred times lambda n. Actually, we're, what are we seeing here?" + }, + { + "text": "We're seeing, this same, lambda, capital lambda to the hundredth, as in the, as in the diagonalization, and we're seeing the S matrix, the matrix S of eigenvectors." + }, + { + "text": "That's what this has got to, this has got to amount to, a lambda to the hundredth power times an S times this vector C that's telling us how much of each one is in the original thing." + }, + { + "text": "So if, if I had to really find the hundredth power, I would take u0, I would expand it as a combination of eigenvectors, this is really S, the eigenvector matrix times C, the, the coefficient vector." + }, + { + "text": "And then I would immediately, then, by inserting these hundredth powers of eigenvalues, I'd have the answer." + }, + { + "text": "So the, the, huh, there must be, well, let's see." + }, + { + "text": "OK." + }, + { + "text": "It's, so, yeah." + }, + { + "text": "So if u100 is a to the hundredth times u0, and u0 is Sc, then you see this formula is just this formula, which is the way I would actually get hold of this, of this u100, which is, let me put it here, u100." + }, + { + "text": "The way I would actually get hold of that, see what, what the solution is after a hundred steps, would be expand the initial vector into eigenvectors and, and let each eigenvector go its own way, multiplying by a hundred at, by lambda at every step, and therefore by lambda to the hundredth power after a hundredth step." + }, + { + "text": "Can I do an example?" + }, + { + "text": "So that's, that's the, the formulas." + }, + { + "text": "Now let me take an example." + }, + { + "text": "I'll use the Fibonacci sequence as an example." + }, + { + "text": "So, so Fibonacci example." + }, + { + "text": "You remember the Fibonacci numbers?" + }, + { + "text": "If we start with one and one as F0, oh, I think I start with zero, maybe." + }, + { + "text": "Let zero and one be the first ones." + }, + { + "text": "So there's F0 and F1, the first two Fibonacci numbers." + }, + { + "text": "Then what's the rule for Fibonacci numbers?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk16.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..79c65e32781f7f304b504a6c390247abb9d26ac8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "They're the sum." + }, + { + "text": "The next one is the sum of those, so it's one." + }, + { + "text": "The next one is the sum of those, so it's two." + }, + { + "text": "The next one is the sum of those, so it's three." + }, + { + "text": "Well, it looks like one, two, three, four, five, but somehow it's not going to do that way." + }, + { + "text": "The next one is five, right." + }, + { + "text": "Two and three makes five." + }, + { + "text": "The next one is eight." + }, + { + "text": "The next one is thirteen." + }, + { + "text": "And the one hundredth Fibonacci number is what?" + }, + { + "text": "That's my question." + }, + { + "text": "How could I get a formula for the hundredth number and for example how could I answer the question how fast are they growing?" + }, + { + "text": "How fast are those Fibonacci numbers growing?" + }, + { + "text": "They're certainly growing." + }, + { + "text": "It's not a stable case, whatever the eigenvalues of whatever matrix it is, they're not smaller than one." + }, + { + "text": "These numbers are growing." + }, + { + "text": "But how fast are they growing?" + }, + { + "text": "The answer is lies in the eigenvalue." + }, + { + "text": "So I've got to find the matrix, so let me write down the Fibonacci rule, F k plus two is F k plus one plus F k, right?" + }, + { + "text": "Now that's not in my -- I want to write that as U k plus one and A U k. But right now what I've got is a single equation, not a system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk17.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b3aaa9dcee3cf27c112015659bb5a0b51a983ce1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's second order." + }, + { + "text": "It's like having a second order differential equation with second derivatives." + }, + { + "text": "I want to get first derivatives." + }, + { + "text": "Here I want to get first difference." + }, + { + "text": "So the way to do it is to introduce U k will be a vector." + }, + { + "text": "See, a small trick." + }, + { + "text": "Let U k be a vector, F k plus one and F k. So I'm going to get a two by two system, first order, instead of a one, instead of a scalar system, second order, by a simple trick." + }, + { + "text": "I'm just going to add in an equation F k plus one equals F k plus one." + }, + { + "text": "That will be my second equation." + }, + { + "text": "Then this is my system, this is my unknown, and what's my one-step equation?" + }, + { + "text": "So now U k plus one." + }, + { + "text": "That's so U k plus one is the left side, and what have I got here on the right side?" + }, + { + "text": "I've got some matrix multiplying U k. Can you see that all right?" + }, + { + "text": "If you can see it, then you can tell me what the matrix is." + }, + { + "text": "You see that I'm taking my system here, I artificially made it into a system." + }, + { + "text": "I artificially made the unknown into a vector, and now I'm ready to look at and see what the matrix is." + }, + { + "text": "So do you see the left side, U k plus one is F k plus two F k plus one, that's just what I want." + }, + { + "text": "On the right side, this, remember, this U k here, let me for the moment put it as F k plus one F k. So what's the matrix?" + }, + { + "text": "Well, that has a one and a one, and that has a one and a zero." + }, + { + "text": "There's the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk18.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..6c1b68c2cb2fde3f5dea82f3100d4da31fcce70a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "You see that that gives me the right-hand side." + }, + { + "text": "So there's the matrix A, and this is our friend U k. So we've got, so that simple trick changed the second order scalar problem to a first order system, two, with two unknowns." + }, + { + "text": "With a matrix and now what do I do?" + }, + { + "text": "Well, before I even think, I find its eigenvalues and eigenvectors." + }, + { + "text": "So what are the eigenvalues and eigenvectors of that matrix?" + }, + { + "text": "Let's see." + }, + { + "text": "I was, first let me just, like, think for a minute." + }, + { + "text": "It's two by two, so this shouldn't be impossible to do." + }, + { + "text": "Let's do it." + }, + { + "text": "OK." + }, + { + "text": "So my matrix again is one one one zero." + }, + { + "text": "It's symmetric, by the way." + }, + { + "text": "So what I will eventually know about symmetric matrices is that the eigenvalues will come out real, I won't get any complex numbers here, and the eigenvectors, once I get those, actually will be orthogonal." + }, + { + "text": "But two by two, I'm more interested in what the actual numbers are." + }, + { + "text": "What do I know about the two numbers?" + }, + { + "text": "Well, should, do you want me to find this determinant of A minus lambda I?" + }, + { + "text": "Sure." + }, + { + "text": "So it's the determinant of one minus lambda one one zero, right?" + }, + { + "text": "Minus lambda, yes, got it." + }, + { + "text": "OK. OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk19.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..a73b23e3d56b889ff49ea7f55a784fac33e13c3d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "There'll be two eigenvalues." + }, + { + "text": "Well, tell me again what I know about the two eigenvalues before I go any further." + }, + { + "text": "Tell me something about these two eigenvalues, what do they add up to?" + }, + { + "text": "Lambda one plus lambda two is the same as the trace down the diagonal of the matrix, one and zero is one." + }, + { + "text": "So lambda one plus lambda two should come out to be one, and lambda one times lambda two should come out to be the determinant, which is minus one." + }, + { + "text": "So I'm expecting the eigenvalues to add to one and to multiply to minus one." + }, + { + "text": "But let's just see it happen here." + }, + { + "text": "If I multiply this out, I get that times that'll be a lambda squared minus lambda minus one." + }, + { + "text": "Good." + }, + { + "text": "Lambda squared minus lambda minus one." + }, + { + "text": "Actually, you see the, compare that with the original equation that I started with." + }, + { + "text": "Fk plus two minus Fk plus one minus Fk is zero." + }, + { + "text": "The recurrent, the recursion that the Fibonacci number satisfy is somehow showing up directly here for the eigenvalues when we set that to zero." + }, + { + "text": "OK. Let's solve." + }, + { + "text": "Well, I would like to be able to factor that, that quadratic, but I'm better off to use the quadratic formula." + }, + { + "text": "Lambda is, let's see, minus b is one, plus or minus the square root of b squared, which is one, minus four, times that, times that, which is plus four, over two." + }, + { + "text": "So that's the square root of five." + }, + { + "text": "So the eigenvalues are lambda one is one half of one plus square root of five, and lambda two is one half of one minus square root of five." + }, + { + "text": "And sure enough, they, those add up to one, and they multiply to give minus one." + }, + { + "text": "OK. Those are the two eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk2.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..43cfb012fc04a89fc7dab94c23bfb0f50ade3782 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "On the right, it's multiplied by, if I want, if I want lambda n xn in the last column, how do I do it?" + }, + { + "text": "Well, the last column here will be, I'll, I'll take the last column, use these coefficients, put the lambda n down there, and it will multiply that nth column and give me lambda n xn." + }, + { + "text": "There, there you see matrix multiplication just working for us." + }, + { + "text": "So I started with A s. I wrote down what it meant." + }, + { + "text": "A times each eigenvector." + }, + { + "text": "That gave me lambda times the eigenvector." + }, + { + "text": "And then when I peeled off the lambdas, they were on the right-hand side, so I've got s, my matrix back again, and this matrix, this diagonal matrix, the eigenvalue matrix, and I call it capital lambda, using capital letters for matrices, and lambda to prompt me that it's, that it's eigenvalues that are in there." + }, + { + "text": "So you see that the eigenvalues are just sitting down that diagonal?" + }, + { + "text": "If I had a column x2 here, I would want the lambda two in the two two position, in the diagonal position, to multiply that x2 and give me the lambda two x2." + }, + { + "text": "That's my formula." + }, + { + "text": "A s is s lambda." + }, + { + "text": "OK. That's, that's the, you see, it's just a calculation." + }, + { + "text": "Now, I, I mentioned, and I have to mention again, this business about n independent eigenvectors." + }, + { + "text": "As it stands, this is all fine whether, I mean, I could be repeating the same eigenvector, but I, I'm no interested in that." + }, + { + "text": "I want to be able to invert s, and that's where this comes in." + }, + { + "text": "This n independent eigenvectors business comes in to tell me that that matrix is invertible." + }, + { + "text": "So let me, on the next board, write down what I've got." + }, + { + "text": "A s equals s lambda." + }, + { + "text": "And now I'm, I can multiply on the left by s inverse." + }, + { + "text": "So this is really, I can do that provided s is invertible, provided my assumption of n independent eigenvectors is satisfied." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk20.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ad5a59fa5db44ce73ff5f88190423e0404fb3d39 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "How, how, what are those numbers approximately?" + }, + { + "text": "Square root of five, well, it's more than two, but less than three." + }, + { + "text": "It, it'd be nice to know these numbers." + }, + { + "text": "I think, I think that that, so that number comes out bigger than one, right?" + }, + { + "text": "Yeah, that's right." + }, + { + "text": "This number comes out bigger than one." + }, + { + "text": "It's about one point six one eight or something." + }, + { + "text": "Not exactly." + }, + { + "text": "It's supposed to be one point six." + }, + { + "text": "Just, like, I think so." + }, + { + "text": "Then what's lambda two?" + }, + { + "text": "Is, is lambda two positive or negative?" + }, + { + "text": "Negative, right?" + }, + { + "text": "Because I'm, it's obviously negative, and I knew that the, so it's minus, and they add up to one, so minus point six one eight, I guess." + }, + { + "text": "OK. And some order." + }, + { + "text": "Those are the two eigenvalues." + }, + { + "text": "One eigenvalue bigger than one, one eigenvalue smaller than one." + }, + { + "text": "Actually, that's a great situation to be in." + }, + { + "text": "Of course, the eigenvalues are different, so there's no doubt whatever, is this matrix diagonalizable?" + }, + { + "text": "Is this matrix diagonalizable, that original matrix A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk21.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..4a034475591d371995b379b5f98783a2cfb25870 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Sure." + }, + { + "text": "We've got two distinct eigenvalues and we can find the eigenvectors in a moment." + }, + { + "text": "But they'll be independent, will be diagonalizable, and now you can already answer my very first question." + }, + { + "text": "How fast are those Fibonacci numbers increasing?" + }, + { + "text": "How, those, they're increasing, right?" + }, + { + "text": "They're not doubling at every step." + }, + { + "text": "Let's look again at these numbers." + }, + { + "text": "Five eight thirteen, it's not obvious." + }, + { + "text": "The next one would be twenty one thirty four." + }, + { + "text": "So to get some idea of what F one hundred is, can you give me any, I mean the crucial number of, so it, these, it's approximately, what's controlling the growth of these Fibonacci numbers?" + }, + { + "text": "It's the eigenvalues." + }, + { + "text": "And which eigenvalues controlling that growth?" + }, + { + "text": "The big ones." + }, + { + "text": "So F one hundred will it be approximately some constant, c one, I guess, times this lambda one, this one plus square root of five over two, to the hundredth power." + }, + { + "text": "And the two hundredth have, in other words, the eigenvalue, the Fibonacci numbers are growing by about that factor." + }, + { + "text": "You see that we've got precise information about the, about the Fibonacci numbers out of the eigenvalue." + }, + { + "text": "OK. And again, why is that true?" + }, + { + "text": "Let me go over to this board and show what I'm doing here." + }, + { + "text": "The, the original eigen, the original initial value is some combination of eigenvectors, and then when we start multiple, when we start going out the theory of Fibonacci numbers, when we start multiplying by a hundred times, it's this lambda one to the hundredth, this term is, is the one that's taken over." + }, + { + "text": "It's, I mean, that's big, like, one point six to the hundredth power." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk22.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..c13a1fc9867173c3067e46c469cfff27b9b45289 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "The second term is practically nothing, right?" + }, + { + "text": "The point six, or minus point six to the hundredth power, is an extremely small, extremely small number." + }, + { + "text": "So this is, this, this, there are only two terms, because we're two by two." + }, + { + "text": "This number is, this piece of it is there, but it's, it's disappearing." + }, + { + "text": "Where this piece is there and it's growing and controlling everything." + }, + { + "text": "So, so really the, we're doing, like, problems that are evolving." + }, + { + "text": "We're doing dynamics." + }, + { + "text": "Instead of Ax equal b, that's a static problem." + }, + { + "text": "We're now, we're doing dynamics." + }, + { + "text": "A, a squared, a cubed, things are evolving in time, and the eigenvalues are the crucial, numbers." + }, + { + "text": "OK." + }, + { + "text": "I guess to complete this, I better write down the eigenvectors." + }, + { + "text": "So we should complete the, the whole process by finding the eigenvectors." + }, + { + "text": "OK. Well, I have to, up in the corner, then I have to look at A minus lambda I." + }, + { + "text": "So A minus lambda I is this one minus lambda, one, one, and minus lambda." + }, + { + "text": "And now, can we spot an eigenvector out of that?" + }, + { + "text": "That's, for these two lambdas, this matrix is singular." + }, + { + "text": "I guess the eigenvector, two by two ought to be easy." + }, + { + "text": "So if I know that this matrix is singular, then it seems to me the eigenvector has to be lambda and one, because that multiplication will give me the zero." + }, + { + "text": "And this multiplication gives me, better give me also zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk23.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..df816eb800ce767b1475c279a24ad976bb45a785 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Do you see why it does?" + }, + { + "text": "This is the minus lambda squared plus lambda plus one." + }, + { + "text": "It's the thing that's zero, because these lambdas are special." + }, + { + "text": "There's the eigenvector." + }, + { + "text": "X1 is lambda one, one, and x2 is lambda two, one." + }, + { + "text": "I did that as a little trick that was available in the two by two case." + }, + { + "text": "So now I finally have to, oh, I have to take the initial, u0." + }, + { + "text": "So to complete this example entirely, I have to say, OK, what was u0?" + }, + { + "text": "u0 was f1 f0." + }, + { + "text": "So u0, the starting vector, is f1 f0, and those were one and zero." + }, + { + "text": "So I have to use that vector, so I have to look for, from multiple of the first eigenvector and the second, to produce u0, the one zero vector." + }, + { + "text": "This is what will find c1 and c2, and then I'm done." + }, + { + "text": "So let me, instead of in the last five seconds grinding out a formula, let me repeat the idea." + }, + { + "text": "That really, it's the idea that's central." + }, + { + "text": "When things are evolving in time, let me come back to this board, because the ideas are here." + }, + { + "text": "When things are evolving in time by a first-order system, starting from an original u0, the key is, find the eigenvalues and eigenvectors of A." + }, + { + "text": "That will tell, those eigenvectors, the eigenvalues will already tell you what's happening." + }, + { + "text": "Is the solution blowing up?" + }, + { + "text": "Is it going to zero?" + }, + { + "text": "What's it doing?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk24.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..40301cb90760e2172baa94d536cbc13288d4c31f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk24.json @@ -0,0 +1,20 @@ +[ + { + "text": "And then, to find out exactly a formula, you have to take your u0 and write it as a combination of eigenvectors and then follow each eigenvector separately." + }, + { + "text": "And that's really what this formula, the formula for, that's what the formula for A to the k is doing." + }, + { + "text": "So remember that formula for A to the k is S, lambda to the k S inverse." + }, + { + "text": "OK. That's, that's difference equations, and you just have to, so the homework will give some examples different from Fibonacci to follow through." + }, + { + "text": "And next time will be differential equations." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk3.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..9bf1bb852baadc1da7837e14180c0c2951a30882 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I mentioned at the end of last time, and I'll say again, that there's a small number of matrices for, that don't have n independent eigenvectors." + }, + { + "text": "So I've got to discuss that, that technical point." + }, + { + "text": "But the great, the most matrices that we see have n, n independent eigenvectors and we can diagonalize." + }, + { + "text": "This is diagonalization." + }, + { + "text": "I could also write it, and I often will, the other way round." + }, + { + "text": "If I multiply on the right by s inverse, if I took this equation at the top and multiplied on the right by s inverse, I could, I would have A left here." + }, + { + "text": "Now s inverse is coming from the right." + }, + { + "text": "So can you keep those two straight?" + }, + { + "text": "A multiplies its eigenvectors." + }, + { + "text": "That's how I keep them straight." + }, + { + "text": "So A multiplies s. A multiplies s. And then this s inverse makes the whole thing diagonal." + }, + { + "text": "And this is another way of saying the same thing, putting the s's on the other side of the equation, A is s lambda s inverse." + }, + { + "text": "So that's the, that's the new factorization." + }, + { + "text": "That's the replacement for L U from elimination or Q R from Gram-Schmidt." + }, + { + "text": "And notice that the matrix, so it's, it's a matrix times a diagonal matrix times the inverse of the first one." + }, + { + "text": "It's, that's the combination that we'll see throughout this chapter." + }, + { + "text": "This, this, combination with an s and an s inverse." + }, + { + "text": "OK. Can I just begin to use that?" + }, + { + "text": "For example, what about A squared?" + }, + { + "text": "What are the eigenvalues and eigenvectors of A squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk4.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c687b6948acad76de8781cb82d3eb069c9da514e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's a straightforward question with a, with a absolutely clean answer." + }, + { + "text": "So let me, let me consider A squared." + }, + { + "text": "So I look, I start with Ax equal lambda x." + }, + { + "text": "And I'm headed for A squared." + }, + { + "text": "So let me multiply both sides by A." + }, + { + "text": "That's one way to get A squared on the left." + }, + { + "text": "So if, I should write these ifs in here." + }, + { + "text": "If Ax equals lambda x, then I multiply by A." + }, + { + "text": "So I get A squared x equals, well, I'm multiplying by A, so that's lambda Ax." + }, + { + "text": "That lambda was a number, so I just put it on the left." + }, + { + "text": "And what do I, tell me how to make that look better." + }, + { + "text": "What have I got here?" + }, + { + "text": "For, if, if A has the eigenvalue lambda and eigenvector x, what's up with A squared?" + }, + { + "text": "A squared x, I just multiply by A, but now for Ax, I'm going to substitute lambda x, so I've got lambda squared x." + }, + { + "text": "So from that simple calculation, I, my conclusion is that the eigenvalues of A squared are lambda squared." + }, + { + "text": "And the eigenvectors, I always think about both of those." + }, + { + "text": "What can I say about the eigenvalues?" + }, + { + "text": "They're squared." + }, + { + "text": "What can I say about the eigenvectors?" + }, + { + "text": "They're the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk5.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5bf15e20707c156c8ae71c9c7acea41a9d9d8e46 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same x as in, as for A." + }, + { + "text": "Now, let me see that also from this formula." + }, + { + "text": "How can I see what A squared is looking like from this formula?" + }, + { + "text": "So let me, that, that was one way to do it." + }, + { + "text": "Let me do it by just taking A squared from that." + }, + { + "text": "A squared is S lambda S inverse, that's A, times S lambda S inverse, that's A, which is?" + }, + { + "text": "This is the beauty of eigenvalues, eigenvectors, having that S inverse and S is the identity, so I've got S lambda squared S inverse." + }, + { + "text": "Yes." + }, + { + "text": "You see what that's telling me?" + }, + { + "text": "It's, it's telling me the same thing that I just learned here, but in the, in, in a matrix form." + }, + { + "text": "It's telling me that the S is the same, the eigenvectors are the same, but the eigenvalues are squared, because this is, what's lambda squared, that's still diagonal, it's got little lambda one squared, lambda two squared, down to lambda n squared, on that diagonal, those are the eigenvalues, as we just learned, of A squared." + }, + { + "text": "OK." + }, + { + "text": "So, somehow those eigenvalues and eigenvectors are really giving you a way to, to, to, to see what's going on inside a matrix." + }, + { + "text": "Now, of course, I can continue that for, to the k-th power." + }, + { + "text": "A to the k-th power." + }, + { + "text": "If I multiply, if I have k of these together, do you see how S inverse S will keep cancelling?" + }, + { + "text": "In the, in the inside, I'll have the S outside, at the far left, and lambda will be in there k times and S inverse." + }, + { + "text": "So what's that telling me?" + }, + { + "text": "That's telling me that the eigenvalues of A, of A to the k-th power are the k-th powers." + }, + { + "text": "The eigenvalues of A cubed are the cubes of the eigenvalues of A, and the eigenvectors are the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk6.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..c18dddbe798022f7e68278ac002a3f5fe6ed249e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same." + }, + { + "text": "OK." + }, + { + "text": "In other words, eigenvalues and eigenvectors give a great way to understand the powers of a matrix." + }, + { + "text": "If I take the square of a matrix or the hundredth power of a matrix, the pivots are all over the place." + }, + { + "text": "L U, if I multiply L U times L U times L U times L U a hundred times, I've got a hundred L U's." + }, + { + "text": "I can't do anything with them." + }, + { + "text": "But when I multiply S lambda S inverse by itself, when I look at the eigenvector picture a hundred times, I get a hundred or ninety-nine of these guys cancelling out inside, and I get A to the hundredth is S lambda to the hundredth S inverse." + }, + { + "text": "I mean, eigenvalues tell you about powers of a matrix in a way that we had no, no way to approach previously." + }, + { + "text": "For example, when does, when do the powers of a matrix go to zero?" + }, + { + "text": "I would call that matrix stable, maybe." + }, + { + "text": "So, so, so I could write down a, a theorem." + }, + { + "text": "I'll, I'll write it as a theorem, just to use that word to emphasize that here I'm getting this great fact from this eigenvalue picture." + }, + { + "text": "OK. A to the k approaches zero as k goes, as k gets bigger." + }, + { + "text": "If what?" + }, + { + "text": "What's the, how can I tell for a matrix A if its powers go to zero?" + }, + { + "text": "What, what's somewhere inside that matrix is that information." + }, + { + "text": "That information is not present in the pivots." + }, + { + "text": "It's present in the eigenvalues." + }, + { + "text": "What do I need for the, to know that if I take higher and higher powers of A that this matrix gets smaller and smaller?" + }, + { + "text": "Well, S and S inverse are not moving." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk7.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b84a5c854a5542758e8a0107e1ff043205fe3bdb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's this guy that has to get small, and that's easy to, easy to understand." + }, + { + "text": "The requirement is all eigenvalues, so what is the requirement?" + }, + { + "text": "The eigenvalues have to be less than one." + }, + { + "text": "Now, I have to write that absolute value, because those eigenvalues could be negative, they could be complex numbers." + }, + { + "text": "So I'm taking the absolute value if all of those are below one." + }, + { + "text": "That's, in fact, we practically see why." + }, + { + "text": "Let me just say that I, that I, I'm operating on one assumption here, and I got to keep remembering that that assumption is still present." + }, + { + "text": "That assumption was that I had a full set of, of n independent eigenvectors." + }, + { + "text": "If I don't have that, then I, I, then this approach is not working." + }, + { + "text": "So, so again, a pure eigenvalue approach, eigenvector approach, needs n independent eigenvectors." + }, + { + "text": "If we don't have n independent eigenvectors, we can't diagonalize the matrix." + }, + { + "text": "We can't get to a diagonal matrix." + }, + { + "text": "This, this, this diagonalization is only possible if S inverse makes sense." + }, + { + "text": "OK. Can I, can I follow up on that point now?" + }, + { + "text": "So, so you see why, what we get and, and why we want it, because we get information about the powers of a matrix just immediately from the eigenvalues." + }, + { + "text": "OK, now let me follow up on this, business of which matrices are diagonalizable." + }, + { + "text": "Sorry about that long word." + }, + { + "text": "So a matrix is, is sure to, so here's, here's the main point." + }, + { + "text": "A is sure to be, to have n independent eigenvectors and, and B, now here comes that word, diagonalizable, if, if, so we, we, we might as well get the, the nice case out in the open." + }, + { + "text": "The nice case is when, if all the lambdas are different." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk8.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f06dcec8ffa0ee1bf19440e4ab2194db33ab353b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means, that means no repeated eigenvalues." + }, + { + "text": "OK. That's the nice case." + }, + { + "text": "If, if my matrix and most matrix, if I do a random matrix in MATLAB and compute its eigenvalues, so if I computed, if I took I of rand of ten ten, gave, gave that MATLAB command, the, we'd get a random ten by ten matrix, we would get a list of its ten eigenvalues and they would be different." + }, + { + "text": "They would be distinct, is the best word." + }, + { + "text": "I would have a random matrix will have ten distinct, a ten by ten matrix will have ten distinct eigenvalues, and if it does, the eigenvectors are automatically independent." + }, + { + "text": "So that's a nice fact." + }, + { + "text": "I can, I'll refer you to the text for the proof." + }, + { + "text": "That, that A is sure to have n independent eigenvectors if the eigenvalues are different." + }, + { + "text": "If, if all the, if all eigenvalues are different." + }, + { + "text": "It's just, if some lambdas are repeated, then I have to look more closely." + }, + { + "text": "If an eigenvalue is repeated, I have to look, I have to count, I have to check." + }, + { + "text": "Has it got, say it's repeated three times." + }, + { + "text": "So what's a possibility for, so, so here's, here's the repeated possibility." + }, + { + "text": "And, and let me emphasize the conclusion." + }, + { + "text": "That if I have repeated eigenvalues, I may or may not, I may or may not have, have n independent eigenvectors." + }, + { + "text": "I might." + }, + { + "text": "I, I, you know, this isn't a completely negative case." + }, + { + "text": "The identity matrix." + }, + { + "text": "Well, suppose I take the ten by ten identity matrix." + }, + { + "text": "What are the eigenvalues of that matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk9.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..87d2a2ae5773036cf11800e2f1962908986a0dad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_13_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So just, just take the easiest matrix, the identity." + }, + { + "text": "If I look for its eigenvalues, they're all ones." + }, + { + "text": "So that eigenvalue one is repeated ten times." + }, + { + "text": "But there's no shortage of eigenvectors for the identity matrix." + }, + { + "text": "In fact, every vector is an eigenvector." + }, + { + "text": "So I can take ten independent vectors." + }, + { + "text": "Oh, well, what happens to everything if, if, if A is the identity matrix, let's just think that one through in our head." + }, + { + "text": "If A is the identity matrix, then it's got plenty of eigenvectors." + }, + { + "text": "I choose ten independent vectors, they're the columns of S, and, and what do I get from S inverse A S?" + }, + { + "text": "I get I again, right?" + }, + { + "text": "If A is the identity, and of course, that's the correct lambda." + }, + { + "text": "The, the matrix was already diagonal." + }, + { + "text": "So if the matrix is already diagonal, then the, the lambda is the same as the matrix." + }, + { + "text": "A diagonal matrix has got its eigenvalues sitting right there in front of you." + }, + { + "text": "Now if it's triangular, the eigenvalues are still sitting there, but so let's, let's take a case where, it's triangular." + }, + { + "text": "Suppose A is like, two, one, two, zero." + }, + { + "text": "So there's a case that's going to be trouble." + }, + { + "text": "There's a case that's going to be trouble." + }, + { + "text": "First of all, what are the eigen- I mean, we just, like now you, if we start with a matrix, the first thing we do practically without thinking is compute the eigenvalues and eigenvectors." + }, + { + "text": "OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk0.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6898d4fe66019ef6b40d0472ea94a968e7bbde9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, shall we start?" + }, + { + "text": "This is the second lecture on eigenvalues." + }, + { + "text": "So the first lecture was set -- reached the key equation, Ax equal lambda x. x is the eigenvector and lambda is the eigenvalue." + }, + { + "text": "Now, to use that." + }, + { + "text": "And the good way to, after we've found, so job one is to find the eigenvalues and find the eigenvectors." + }, + { + "text": "Now after we found them, what do we do with them?" + }, + { + "text": "Well, the good way to see that is diagonalize the matrix." + }, + { + "text": "So the matrix is A, and I want to show, first of all, this is like the basic fact." + }, + { + "text": "This, this formula." + }, + { + "text": "That's, that's the key to today's lecture." + }, + { + "text": "This matrix A, I put its eigenvectors in the columns of a matrix S. So S will be the eigenvector matrix, and I want to look at this magic combination S inverse A S. So can I show you how that, how that, what happens there?" + }, + { + "text": "And notice, notice, there's an S inverse." + }, + { + "text": "We have to be able to invert this eigenvector matrix S. So for that we need n independent eigenvectors." + }, + { + "text": "So that's the, that's the case." + }, + { + "text": "OK." + }, + { + "text": "So suppose we have n linearly independent eigenvectors of A." + }, + { + "text": "Put them in the columns of this matrix S. So I'm naturally going to call that the eigenvector matrix, because it's got the eigenvectors in its columns." + }, + { + "text": "And all I want to do is show you what happens when you multiply A times S. So A times S. So this is A times the matrix with the first eigenvector in its first column, the second eigenvector in its second column, the nth eigenvector in its nth column." + }, + { + "text": "And how am I going to do this matrix multiplication?" + }, + { + "text": "Well, certainly I'll do it a column at a time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk1.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..fbe078217bb68baea8e0605a5d04be568c49efbf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I get?" + }, + { + "text": "A times the first column gives me the first column of the answer, but what is it?" + }, + { + "text": "That's an eigenvector." + }, + { + "text": "A times x1 is equal to the lambda times the x1." + }, + { + "text": "And that lambda's we'll call lambda one, of course." + }, + { + "text": "So that's the first column, A x1 is the same as lambda one x1." + }, + { + "text": "A x2 is lambda two x2, so on, along to, in the nth column, we now have lambda n xn." + }, + { + "text": "Looking good, but the next step is even better." + }, + { + "text": "So for the next step, I want to separate out those eigenvalues, those multiplying numbers, from the x's." + }, + { + "text": "So then I'll have just what I want." + }, + { + "text": "OK, so how, how am I going to separate out?" + }, + { + "text": "So that, that number lambda one is multiplying the first column." + }, + { + "text": "So if I want to factor it out of the first column, I better put, here is going to be x1, and that's going to multiply this matrix lambda one in the first entry in all zeros." + }, + { + "text": "You see that that, that's going to come out right for the first column?" + }, + { + "text": "Because we remember how, how we're going back to that original punchline, that if I want a number to multiply x1, then I can do it by putting x1 in that column, in the first column, and putting that number there." + }, + { + "text": "What am I going to have here?" + }, + { + "text": "I'm going to have lambda one, I'm going to have x1, x2, xn." + }, + { + "text": "These are going to be my columns again." + }, + { + "text": "I'm getting s back again." + }, + { + "text": "I'm getting s back again, but now what's it multiplied by?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk10.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c58a42edbe9567233ca7f57643a0b7d43ae6761f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what are the eigenvalues?" + }, + { + "text": "You can tell me right away what they are." + }, + { + "text": "They're two and two, right." + }, + { + "text": "It's a triangular matrix, so when I do this determinant, shall I do this determinant of A minus lambda I?" + }, + { + "text": "I'll get this two minus lambda, one, zero, two minus lambda, right?" + }, + { + "text": "I take that determinant, so I make those into vertical bars to mean determinant, and what's the determinant?" + }, + { + "text": "Two minus lambda squared." + }, + { + "text": "What are the roots?" + }, + { + "text": "Lambda equal two twice." + }, + { + "text": "So the eigenvalues are lambda equals two and two." + }, + { + "text": "OK, fine." + }, + { + "text": "Now the next step, find the eigenvectors." + }, + { + "text": "So I look for eigenvectors and what do I find for this guy?" + }, + { + "text": "Eigenvectors for this guy, when I subtract two minus the identity, so A minus two I has zeros here, and I'm looking for the null space." + }, + { + "text": "What's, what are the eigenvectors?" + }, + { + "text": "They're the, they're, they're the null space of A minus lambda I." + }, + { + "text": "The null space is only one dimension." + }, + { + "text": "This is a case where I don't have enough eigenvectors." + }, + { + "text": "My algebraic multiplicity is two." + }, + { + "text": "I, I would say when I see, when I count how often the eigenvalue is repeated, that's the algebraic multiplicity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk11.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..779c2cf904d904b761080db2671aac46394ad02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the multiplicity." + }, + { + "text": "How many times is it the root of the polynomial?" + }, + { + "text": "My polynomial is two minus lambda squared." + }, + { + "text": "It's a double root." + }, + { + "text": "So my algebraic multiplicity is two." + }, + { + "text": "But the geometric multiplicity, which looks for vectors, looks for eigenvectors and which means the null space of this thing." + }, + { + "text": "And the only eigenvector is one zero." + }, + { + "text": "That's in the null space." + }, + { + "text": "Zero one is not in the null space." + }, + { + "text": "The null space is only one dimensional." + }, + { + "text": "So there's a matrix, my, this A or the original A, that are not diagonalizable." + }, + { + "text": "I can't, I can't find two independent eigenvectors, there's only one." + }, + { + "text": "OK." + }, + { + "text": "So that's the case that I'm, that's a case that I, I'm not really handling." + }, + { + "text": "For example, when I wrote down up here that the powers went to zero if the eigenvalues were below one, I didn't really handle that case of repeated eigenvalues because my reasoning was based on this formula." + }, + { + "text": "And this formula is based on n independent eigenvectors." + }, + { + "text": "OK." + }, + { + "text": "So just to say that." + }, + { + "text": "There are some matrices that we don't cover through diagonalization, but the great majority we do." + }, + { + "text": "OK. And we're always OK if we have different distinct eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk12.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..77d090704cc298475d94416b7ecb88a2a015a913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. That's the, like, the typical case." + }, + { + "text": "Because for each eigenvalue there's at least one eigenvector, the algebraic multiplicity here is one for every eigenvalue, and the geometric multiplicity is one." + }, + { + "text": "There's one eigenvector and they are independent." + }, + { + "text": "OK. OK. Now let me come back to the important case when we're OK." + }, + { + "text": "The important case when we are diagonalizing." + }, + { + "text": "Let me look at, so let me solve this equation." + }, + { + "text": "The equation will be each, I start with some, start with a given vector u0." + }, + { + "text": "And then my equation is that every step I multiply what I have by a." + }, + { + "text": "That equation ought to be simple to handle." + }, + { + "text": "OK. And I'd like to be able to solve it." + }, + { + "text": "How would I find, if I start with a vector u0, and I multiply by a a hundred times, what have I got?" + }, + { + "text": "Well, I can certainly write down a formula for the answer." + }, + { + "text": "So what, what, so u1 is a u0." + }, + { + "text": "And u2 is, what's u2 then?" + }, + { + "text": "U2 I multiply it, u2 I get from u1 by another, multiplying by a, so I've got a twice." + }, + { + "text": "And my formula is uk, after k steps, I've multiplied by a k times the original u0." + }, + { + "text": "You see what I'm doing?" + }, + { + "text": "The next section is going to solve systems of differential equations." + }, + { + "text": "I'm going to have derivatives." + }, + { + "text": "This, this section is the nice one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk13.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..ba8214d8c636e4757a266d6617801174bc939d80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "It solves difference equations." + }, + { + "text": "I would call that a difference equation." + }, + { + "text": "It's conne- a first order." + }, + { + "text": "I would call that a first order system, because it connects only, it only goes up one level." + }, + { + "text": "And it's a system because these are vectors and that's a matrix." + }, + { + "text": "And the solution is just that." + }, + { + "text": "OK." + }, + { + "text": "But, that's a nice formula." + }, + { + "text": "That's the, like, the most compact formula I could ever get." + }, + { + "text": "U one hundred would be a to the one hundredth u0." + }, + { + "text": "But how would I actually find u one hundred?" + }, + { + "text": "How would I find, how would I discover what u one hundred is?" + }, + { + "text": "Let me, let me show you how." + }, + { + "text": "Here, here's the idea." + }, + { + "text": "If, so, to solve, to really solve, shall I say, to really solve." + }, + { + "text": "To really solve it, I would take this initial vector, u0, and I would write it as a combination of eigenvectors." + }, + { + "text": "To really solve, write, write u0 as a combination, say, certain amount of the first eigenvector plus a certain amount of the second eigenvector plus a certain amount of the last eigenvector." + }, + { + "text": "Now multiply by a." + }, + { + "text": "You want to, you got to see the magic of eigenvectors work." + }, + { + "text": "Multiply by a." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk14.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7843b2bf0cac762d1c12452cf36500ea4ad13370 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a u0 is what?" + }, + { + "text": "So a times that." + }, + { + "text": "A times, so what's, I can separate it out into n separate pieces and that's the whole point." + }, + { + "text": "That each of those pieces is going in its own merry way." + }, + { + "text": "Each of those pieces is an eigenvector, and when I multiply by a, what does this piece become?" + }, + { + "text": "So that's some amount of the first, let's suppose the eigenvectors are normalized to be unit vectors." + }, + { + "text": "So that says what the eigenvector is." + }, + { + "text": "It's, and I need some multiple of it to produce u0." + }, + { + "text": "OK. Now when I multiply by a, what do I get?" + }, + { + "text": "I get c1, which is just a factor, times a x1, but a x1 is lambda one x1." + }, + { + "text": "When I multiply this by a, I get c2 lambda two x2." + }, + { + "text": "And here I get cn lambda n xn." + }, + { + "text": "And suppose I multiply by a to the hundredth power now." + }, + { + "text": "Can we, can we, having done it, multiplied by a, let's multiply by a to the hundredth." + }, + { + "text": "What happens to this first term when I multiply by a to the one hundredth?" + }, + { + "text": "It's got that factor lambda to the hundredth." + }, + { + "text": "That's the key." + }, + { + "text": "That, that's what I mean by going its own merry way." + }, + { + "text": "It, it is pure eigenvector, it's exactly in a direction where multiplication by a just brings in a scalar factor lambda one." + }, + { + "text": "So a hundred times brings in this a hundred times." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk15.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7ee3348735378aa4049d33ec2a197d0ceb0c447c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Hundred times lambda two, hundred times lambda n. Actually, we're, what are we seeing here?" + }, + { + "text": "We're seeing, this same, lambda, capital lambda to the hundredth, as in the, as in the diagonalization, and we're seeing the S matrix, the matrix S of eigenvectors." + }, + { + "text": "That's what this has got to, this has got to amount to, a lambda to the hundredth power times an S times this vector C that's telling us how much of each one is in the original thing." + }, + { + "text": "So if, if I had to really find the hundredth power, I would take u0, I would expand it as a combination of eigenvectors, this is really S, the eigenvector matrix times C, the, the coefficient vector." + }, + { + "text": "And then I would immediately, then, by inserting these hundredth powers of eigenvalues, I'd have the answer." + }, + { + "text": "So the, the, huh, there must be, well, let's see." + }, + { + "text": "OK." + }, + { + "text": "It's, so, yeah." + }, + { + "text": "So if u100 is a to the hundredth times u0, and u0 is Sc, then you see this formula is just this formula, which is the way I would actually get hold of this, of this u100, which is, let me put it here, u100." + }, + { + "text": "The way I would actually get hold of that, see what, what the solution is after a hundred steps, would be expand the initial vector into eigenvectors and, and let each eigenvector go its own way, multiplying by a hundred at, by lambda at every step, and therefore by lambda to the hundredth power after a hundredth step." + }, + { + "text": "Can I do an example?" + }, + { + "text": "So that's, that's the, the formulas." + }, + { + "text": "Now let me take an example." + }, + { + "text": "I'll use the Fibonacci sequence as an example." + }, + { + "text": "So, so Fibonacci example." + }, + { + "text": "You remember the Fibonacci numbers?" + }, + { + "text": "If we start with one and one as F0, oh, I think I start with zero, maybe." + }, + { + "text": "Let zero and one be the first ones." + }, + { + "text": "So there's F0 and F1, the first two Fibonacci numbers." + }, + { + "text": "Then what's the rule for Fibonacci numbers?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk16.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..79c65e32781f7f304b504a6c390247abb9d26ac8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "They're the sum." + }, + { + "text": "The next one is the sum of those, so it's one." + }, + { + "text": "The next one is the sum of those, so it's two." + }, + { + "text": "The next one is the sum of those, so it's three." + }, + { + "text": "Well, it looks like one, two, three, four, five, but somehow it's not going to do that way." + }, + { + "text": "The next one is five, right." + }, + { + "text": "Two and three makes five." + }, + { + "text": "The next one is eight." + }, + { + "text": "The next one is thirteen." + }, + { + "text": "And the one hundredth Fibonacci number is what?" + }, + { + "text": "That's my question." + }, + { + "text": "How could I get a formula for the hundredth number and for example how could I answer the question how fast are they growing?" + }, + { + "text": "How fast are those Fibonacci numbers growing?" + }, + { + "text": "They're certainly growing." + }, + { + "text": "It's not a stable case, whatever the eigenvalues of whatever matrix it is, they're not smaller than one." + }, + { + "text": "These numbers are growing." + }, + { + "text": "But how fast are they growing?" + }, + { + "text": "The answer is lies in the eigenvalue." + }, + { + "text": "So I've got to find the matrix, so let me write down the Fibonacci rule, F k plus two is F k plus one plus F k, right?" + }, + { + "text": "Now that's not in my -- I want to write that as U k plus one and A U k. But right now what I've got is a single equation, not a system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk17.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b3aaa9dcee3cf27c112015659bb5a0b51a983ce1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's second order." + }, + { + "text": "It's like having a second order differential equation with second derivatives." + }, + { + "text": "I want to get first derivatives." + }, + { + "text": "Here I want to get first difference." + }, + { + "text": "So the way to do it is to introduce U k will be a vector." + }, + { + "text": "See, a small trick." + }, + { + "text": "Let U k be a vector, F k plus one and F k. So I'm going to get a two by two system, first order, instead of a one, instead of a scalar system, second order, by a simple trick." + }, + { + "text": "I'm just going to add in an equation F k plus one equals F k plus one." + }, + { + "text": "That will be my second equation." + }, + { + "text": "Then this is my system, this is my unknown, and what's my one-step equation?" + }, + { + "text": "So now U k plus one." + }, + { + "text": "That's so U k plus one is the left side, and what have I got here on the right side?" + }, + { + "text": "I've got some matrix multiplying U k. Can you see that all right?" + }, + { + "text": "If you can see it, then you can tell me what the matrix is." + }, + { + "text": "You see that I'm taking my system here, I artificially made it into a system." + }, + { + "text": "I artificially made the unknown into a vector, and now I'm ready to look at and see what the matrix is." + }, + { + "text": "So do you see the left side, U k plus one is F k plus two F k plus one, that's just what I want." + }, + { + "text": "On the right side, this, remember, this U k here, let me for the moment put it as F k plus one F k. So what's the matrix?" + }, + { + "text": "Well, that has a one and a one, and that has a one and a zero." + }, + { + "text": "There's the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk18.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..6c1b68c2cb2fde3f5dea82f3100d4da31fcce70a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "You see that that gives me the right-hand side." + }, + { + "text": "So there's the matrix A, and this is our friend U k. So we've got, so that simple trick changed the second order scalar problem to a first order system, two, with two unknowns." + }, + { + "text": "With a matrix and now what do I do?" + }, + { + "text": "Well, before I even think, I find its eigenvalues and eigenvectors." + }, + { + "text": "So what are the eigenvalues and eigenvectors of that matrix?" + }, + { + "text": "Let's see." + }, + { + "text": "I was, first let me just, like, think for a minute." + }, + { + "text": "It's two by two, so this shouldn't be impossible to do." + }, + { + "text": "Let's do it." + }, + { + "text": "OK." + }, + { + "text": "So my matrix again is one one one zero." + }, + { + "text": "It's symmetric, by the way." + }, + { + "text": "So what I will eventually know about symmetric matrices is that the eigenvalues will come out real, I won't get any complex numbers here, and the eigenvectors, once I get those, actually will be orthogonal." + }, + { + "text": "But two by two, I'm more interested in what the actual numbers are." + }, + { + "text": "What do I know about the two numbers?" + }, + { + "text": "Well, should, do you want me to find this determinant of A minus lambda I?" + }, + { + "text": "Sure." + }, + { + "text": "So it's the determinant of one minus lambda one one zero, right?" + }, + { + "text": "Minus lambda, yes, got it." + }, + { + "text": "OK. OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk19.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..a73b23e3d56b889ff49ea7f55a784fac33e13c3d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "There'll be two eigenvalues." + }, + { + "text": "Well, tell me again what I know about the two eigenvalues before I go any further." + }, + { + "text": "Tell me something about these two eigenvalues, what do they add up to?" + }, + { + "text": "Lambda one plus lambda two is the same as the trace down the diagonal of the matrix, one and zero is one." + }, + { + "text": "So lambda one plus lambda two should come out to be one, and lambda one times lambda two should come out to be the determinant, which is minus one." + }, + { + "text": "So I'm expecting the eigenvalues to add to one and to multiply to minus one." + }, + { + "text": "But let's just see it happen here." + }, + { + "text": "If I multiply this out, I get that times that'll be a lambda squared minus lambda minus one." + }, + { + "text": "Good." + }, + { + "text": "Lambda squared minus lambda minus one." + }, + { + "text": "Actually, you see the, compare that with the original equation that I started with." + }, + { + "text": "Fk plus two minus Fk plus one minus Fk is zero." + }, + { + "text": "The recurrent, the recursion that the Fibonacci number satisfy is somehow showing up directly here for the eigenvalues when we set that to zero." + }, + { + "text": "OK. Let's solve." + }, + { + "text": "Well, I would like to be able to factor that, that quadratic, but I'm better off to use the quadratic formula." + }, + { + "text": "Lambda is, let's see, minus b is one, plus or minus the square root of b squared, which is one, minus four, times that, times that, which is plus four, over two." + }, + { + "text": "So that's the square root of five." + }, + { + "text": "So the eigenvalues are lambda one is one half of one plus square root of five, and lambda two is one half of one minus square root of five." + }, + { + "text": "And sure enough, they, those add up to one, and they multiply to give minus one." + }, + { + "text": "OK. Those are the two eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk2.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..43cfb012fc04a89fc7dab94c23bfb0f50ade3782 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "On the right, it's multiplied by, if I want, if I want lambda n xn in the last column, how do I do it?" + }, + { + "text": "Well, the last column here will be, I'll, I'll take the last column, use these coefficients, put the lambda n down there, and it will multiply that nth column and give me lambda n xn." + }, + { + "text": "There, there you see matrix multiplication just working for us." + }, + { + "text": "So I started with A s. I wrote down what it meant." + }, + { + "text": "A times each eigenvector." + }, + { + "text": "That gave me lambda times the eigenvector." + }, + { + "text": "And then when I peeled off the lambdas, they were on the right-hand side, so I've got s, my matrix back again, and this matrix, this diagonal matrix, the eigenvalue matrix, and I call it capital lambda, using capital letters for matrices, and lambda to prompt me that it's, that it's eigenvalues that are in there." + }, + { + "text": "So you see that the eigenvalues are just sitting down that diagonal?" + }, + { + "text": "If I had a column x2 here, I would want the lambda two in the two two position, in the diagonal position, to multiply that x2 and give me the lambda two x2." + }, + { + "text": "That's my formula." + }, + { + "text": "A s is s lambda." + }, + { + "text": "OK. That's, that's the, you see, it's just a calculation." + }, + { + "text": "Now, I, I mentioned, and I have to mention again, this business about n independent eigenvectors." + }, + { + "text": "As it stands, this is all fine whether, I mean, I could be repeating the same eigenvector, but I, I'm no interested in that." + }, + { + "text": "I want to be able to invert s, and that's where this comes in." + }, + { + "text": "This n independent eigenvectors business comes in to tell me that that matrix is invertible." + }, + { + "text": "So let me, on the next board, write down what I've got." + }, + { + "text": "A s equals s lambda." + }, + { + "text": "And now I'm, I can multiply on the left by s inverse." + }, + { + "text": "So this is really, I can do that provided s is invertible, provided my assumption of n independent eigenvectors is satisfied." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk20.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ad5a59fa5db44ce73ff5f88190423e0404fb3d39 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "How, how, what are those numbers approximately?" + }, + { + "text": "Square root of five, well, it's more than two, but less than three." + }, + { + "text": "It, it'd be nice to know these numbers." + }, + { + "text": "I think, I think that that, so that number comes out bigger than one, right?" + }, + { + "text": "Yeah, that's right." + }, + { + "text": "This number comes out bigger than one." + }, + { + "text": "It's about one point six one eight or something." + }, + { + "text": "Not exactly." + }, + { + "text": "It's supposed to be one point six." + }, + { + "text": "Just, like, I think so." + }, + { + "text": "Then what's lambda two?" + }, + { + "text": "Is, is lambda two positive or negative?" + }, + { + "text": "Negative, right?" + }, + { + "text": "Because I'm, it's obviously negative, and I knew that the, so it's minus, and they add up to one, so minus point six one eight, I guess." + }, + { + "text": "OK. And some order." + }, + { + "text": "Those are the two eigenvalues." + }, + { + "text": "One eigenvalue bigger than one, one eigenvalue smaller than one." + }, + { + "text": "Actually, that's a great situation to be in." + }, + { + "text": "Of course, the eigenvalues are different, so there's no doubt whatever, is this matrix diagonalizable?" + }, + { + "text": "Is this matrix diagonalizable, that original matrix A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk21.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..4a034475591d371995b379b5f98783a2cfb25870 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Sure." + }, + { + "text": "We've got two distinct eigenvalues and we can find the eigenvectors in a moment." + }, + { + "text": "But they'll be independent, will be diagonalizable, and now you can already answer my very first question." + }, + { + "text": "How fast are those Fibonacci numbers increasing?" + }, + { + "text": "How, those, they're increasing, right?" + }, + { + "text": "They're not doubling at every step." + }, + { + "text": "Let's look again at these numbers." + }, + { + "text": "Five eight thirteen, it's not obvious." + }, + { + "text": "The next one would be twenty one thirty four." + }, + { + "text": "So to get some idea of what F one hundred is, can you give me any, I mean the crucial number of, so it, these, it's approximately, what's controlling the growth of these Fibonacci numbers?" + }, + { + "text": "It's the eigenvalues." + }, + { + "text": "And which eigenvalues controlling that growth?" + }, + { + "text": "The big ones." + }, + { + "text": "So F one hundred will it be approximately some constant, c one, I guess, times this lambda one, this one plus square root of five over two, to the hundredth power." + }, + { + "text": "And the two hundredth have, in other words, the eigenvalue, the Fibonacci numbers are growing by about that factor." + }, + { + "text": "You see that we've got precise information about the, about the Fibonacci numbers out of the eigenvalue." + }, + { + "text": "OK. And again, why is that true?" + }, + { + "text": "Let me go over to this board and show what I'm doing here." + }, + { + "text": "The, the original eigen, the original initial value is some combination of eigenvectors, and then when we start multiple, when we start going out the theory of Fibonacci numbers, when we start multiplying by a hundred times, it's this lambda one to the hundredth, this term is, is the one that's taken over." + }, + { + "text": "It's, I mean, that's big, like, one point six to the hundredth power." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk22.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..c13a1fc9867173c3067e46c469cfff27b9b45289 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "The second term is practically nothing, right?" + }, + { + "text": "The point six, or minus point six to the hundredth power, is an extremely small, extremely small number." + }, + { + "text": "So this is, this, this, there are only two terms, because we're two by two." + }, + { + "text": "This number is, this piece of it is there, but it's, it's disappearing." + }, + { + "text": "Where this piece is there and it's growing and controlling everything." + }, + { + "text": "So, so really the, we're doing, like, problems that are evolving." + }, + { + "text": "We're doing dynamics." + }, + { + "text": "Instead of Ax equal b, that's a static problem." + }, + { + "text": "We're now, we're doing dynamics." + }, + { + "text": "A, a squared, a cubed, things are evolving in time, and the eigenvalues are the crucial, numbers." + }, + { + "text": "OK." + }, + { + "text": "I guess to complete this, I better write down the eigenvectors." + }, + { + "text": "So we should complete the, the whole process by finding the eigenvectors." + }, + { + "text": "OK. Well, I have to, up in the corner, then I have to look at A minus lambda I." + }, + { + "text": "So A minus lambda I is this one minus lambda, one, one, and minus lambda." + }, + { + "text": "And now, can we spot an eigenvector out of that?" + }, + { + "text": "That's, for these two lambdas, this matrix is singular." + }, + { + "text": "I guess the eigenvector, two by two ought to be easy." + }, + { + "text": "So if I know that this matrix is singular, then it seems to me the eigenvector has to be lambda and one, because that multiplication will give me the zero." + }, + { + "text": "And this multiplication gives me, better give me also zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk23.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..df816eb800ce767b1475c279a24ad976bb45a785 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Do you see why it does?" + }, + { + "text": "This is the minus lambda squared plus lambda plus one." + }, + { + "text": "It's the thing that's zero, because these lambdas are special." + }, + { + "text": "There's the eigenvector." + }, + { + "text": "X1 is lambda one, one, and x2 is lambda two, one." + }, + { + "text": "I did that as a little trick that was available in the two by two case." + }, + { + "text": "So now I finally have to, oh, I have to take the initial, u0." + }, + { + "text": "So to complete this example entirely, I have to say, OK, what was u0?" + }, + { + "text": "u0 was f1 f0." + }, + { + "text": "So u0, the starting vector, is f1 f0, and those were one and zero." + }, + { + "text": "So I have to use that vector, so I have to look for, from multiple of the first eigenvector and the second, to produce u0, the one zero vector." + }, + { + "text": "This is what will find c1 and c2, and then I'm done." + }, + { + "text": "So let me, instead of in the last five seconds grinding out a formula, let me repeat the idea." + }, + { + "text": "That really, it's the idea that's central." + }, + { + "text": "When things are evolving in time, let me come back to this board, because the ideas are here." + }, + { + "text": "When things are evolving in time by a first-order system, starting from an original u0, the key is, find the eigenvalues and eigenvectors of A." + }, + { + "text": "That will tell, those eigenvectors, the eigenvalues will already tell you what's happening." + }, + { + "text": "Is the solution blowing up?" + }, + { + "text": "Is it going to zero?" + }, + { + "text": "What's it doing?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk24.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..40301cb90760e2172baa94d536cbc13288d4c31f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk24.json @@ -0,0 +1,20 @@ +[ + { + "text": "And then, to find out exactly a formula, you have to take your u0 and write it as a combination of eigenvectors and then follow each eigenvector separately." + }, + { + "text": "And that's really what this formula, the formula for, that's what the formula for A to the k is doing." + }, + { + "text": "So remember that formula for A to the k is S, lambda to the k S inverse." + }, + { + "text": "OK. That's, that's difference equations, and you just have to, so the homework will give some examples different from Fibonacci to follow through." + }, + { + "text": "And next time will be differential equations." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk3.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..9bf1bb852baadc1da7837e14180c0c2951a30882 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I mentioned at the end of last time, and I'll say again, that there's a small number of matrices for, that don't have n independent eigenvectors." + }, + { + "text": "So I've got to discuss that, that technical point." + }, + { + "text": "But the great, the most matrices that we see have n, n independent eigenvectors and we can diagonalize." + }, + { + "text": "This is diagonalization." + }, + { + "text": "I could also write it, and I often will, the other way round." + }, + { + "text": "If I multiply on the right by s inverse, if I took this equation at the top and multiplied on the right by s inverse, I could, I would have A left here." + }, + { + "text": "Now s inverse is coming from the right." + }, + { + "text": "So can you keep those two straight?" + }, + { + "text": "A multiplies its eigenvectors." + }, + { + "text": "That's how I keep them straight." + }, + { + "text": "So A multiplies s. A multiplies s. And then this s inverse makes the whole thing diagonal." + }, + { + "text": "And this is another way of saying the same thing, putting the s's on the other side of the equation, A is s lambda s inverse." + }, + { + "text": "So that's the, that's the new factorization." + }, + { + "text": "That's the replacement for L U from elimination or Q R from Gram-Schmidt." + }, + { + "text": "And notice that the matrix, so it's, it's a matrix times a diagonal matrix times the inverse of the first one." + }, + { + "text": "It's, that's the combination that we'll see throughout this chapter." + }, + { + "text": "This, this, combination with an s and an s inverse." + }, + { + "text": "OK. Can I just begin to use that?" + }, + { + "text": "For example, what about A squared?" + }, + { + "text": "What are the eigenvalues and eigenvectors of A squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk4.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c687b6948acad76de8781cb82d3eb069c9da514e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's a straightforward question with a, with a absolutely clean answer." + }, + { + "text": "So let me, let me consider A squared." + }, + { + "text": "So I look, I start with Ax equal lambda x." + }, + { + "text": "And I'm headed for A squared." + }, + { + "text": "So let me multiply both sides by A." + }, + { + "text": "That's one way to get A squared on the left." + }, + { + "text": "So if, I should write these ifs in here." + }, + { + "text": "If Ax equals lambda x, then I multiply by A." + }, + { + "text": "So I get A squared x equals, well, I'm multiplying by A, so that's lambda Ax." + }, + { + "text": "That lambda was a number, so I just put it on the left." + }, + { + "text": "And what do I, tell me how to make that look better." + }, + { + "text": "What have I got here?" + }, + { + "text": "For, if, if A has the eigenvalue lambda and eigenvector x, what's up with A squared?" + }, + { + "text": "A squared x, I just multiply by A, but now for Ax, I'm going to substitute lambda x, so I've got lambda squared x." + }, + { + "text": "So from that simple calculation, I, my conclusion is that the eigenvalues of A squared are lambda squared." + }, + { + "text": "And the eigenvectors, I always think about both of those." + }, + { + "text": "What can I say about the eigenvalues?" + }, + { + "text": "They're squared." + }, + { + "text": "What can I say about the eigenvectors?" + }, + { + "text": "They're the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk5.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5bf15e20707c156c8ae71c9c7acea41a9d9d8e46 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same x as in, as for A." + }, + { + "text": "Now, let me see that also from this formula." + }, + { + "text": "How can I see what A squared is looking like from this formula?" + }, + { + "text": "So let me, that, that was one way to do it." + }, + { + "text": "Let me do it by just taking A squared from that." + }, + { + "text": "A squared is S lambda S inverse, that's A, times S lambda S inverse, that's A, which is?" + }, + { + "text": "This is the beauty of eigenvalues, eigenvectors, having that S inverse and S is the identity, so I've got S lambda squared S inverse." + }, + { + "text": "Yes." + }, + { + "text": "You see what that's telling me?" + }, + { + "text": "It's, it's telling me the same thing that I just learned here, but in the, in, in a matrix form." + }, + { + "text": "It's telling me that the S is the same, the eigenvectors are the same, but the eigenvalues are squared, because this is, what's lambda squared, that's still diagonal, it's got little lambda one squared, lambda two squared, down to lambda n squared, on that diagonal, those are the eigenvalues, as we just learned, of A squared." + }, + { + "text": "OK." + }, + { + "text": "So, somehow those eigenvalues and eigenvectors are really giving you a way to, to, to, to see what's going on inside a matrix." + }, + { + "text": "Now, of course, I can continue that for, to the k-th power." + }, + { + "text": "A to the k-th power." + }, + { + "text": "If I multiply, if I have k of these together, do you see how S inverse S will keep cancelling?" + }, + { + "text": "In the, in the inside, I'll have the S outside, at the far left, and lambda will be in there k times and S inverse." + }, + { + "text": "So what's that telling me?" + }, + { + "text": "That's telling me that the eigenvalues of A, of A to the k-th power are the k-th powers." + }, + { + "text": "The eigenvalues of A cubed are the cubes of the eigenvalues of A, and the eigenvectors are the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk6.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..c18dddbe798022f7e68278ac002a3f5fe6ed249e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same." + }, + { + "text": "OK." + }, + { + "text": "In other words, eigenvalues and eigenvectors give a great way to understand the powers of a matrix." + }, + { + "text": "If I take the square of a matrix or the hundredth power of a matrix, the pivots are all over the place." + }, + { + "text": "L U, if I multiply L U times L U times L U times L U a hundred times, I've got a hundred L U's." + }, + { + "text": "I can't do anything with them." + }, + { + "text": "But when I multiply S lambda S inverse by itself, when I look at the eigenvector picture a hundred times, I get a hundred or ninety-nine of these guys cancelling out inside, and I get A to the hundredth is S lambda to the hundredth S inverse." + }, + { + "text": "I mean, eigenvalues tell you about powers of a matrix in a way that we had no, no way to approach previously." + }, + { + "text": "For example, when does, when do the powers of a matrix go to zero?" + }, + { + "text": "I would call that matrix stable, maybe." + }, + { + "text": "So, so, so I could write down a, a theorem." + }, + { + "text": "I'll, I'll write it as a theorem, just to use that word to emphasize that here I'm getting this great fact from this eigenvalue picture." + }, + { + "text": "OK. A to the k approaches zero as k goes, as k gets bigger." + }, + { + "text": "If what?" + }, + { + "text": "What's the, how can I tell for a matrix A if its powers go to zero?" + }, + { + "text": "What, what's somewhere inside that matrix is that information." + }, + { + "text": "That information is not present in the pivots." + }, + { + "text": "It's present in the eigenvalues." + }, + { + "text": "What do I need for the, to know that if I take higher and higher powers of A that this matrix gets smaller and smaller?" + }, + { + "text": "Well, S and S inverse are not moving." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk7.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b84a5c854a5542758e8a0107e1ff043205fe3bdb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's this guy that has to get small, and that's easy to, easy to understand." + }, + { + "text": "The requirement is all eigenvalues, so what is the requirement?" + }, + { + "text": "The eigenvalues have to be less than one." + }, + { + "text": "Now, I have to write that absolute value, because those eigenvalues could be negative, they could be complex numbers." + }, + { + "text": "So I'm taking the absolute value if all of those are below one." + }, + { + "text": "That's, in fact, we practically see why." + }, + { + "text": "Let me just say that I, that I, I'm operating on one assumption here, and I got to keep remembering that that assumption is still present." + }, + { + "text": "That assumption was that I had a full set of, of n independent eigenvectors." + }, + { + "text": "If I don't have that, then I, I, then this approach is not working." + }, + { + "text": "So, so again, a pure eigenvalue approach, eigenvector approach, needs n independent eigenvectors." + }, + { + "text": "If we don't have n independent eigenvectors, we can't diagonalize the matrix." + }, + { + "text": "We can't get to a diagonal matrix." + }, + { + "text": "This, this, this diagonalization is only possible if S inverse makes sense." + }, + { + "text": "OK. Can I, can I follow up on that point now?" + }, + { + "text": "So, so you see why, what we get and, and why we want it, because we get information about the powers of a matrix just immediately from the eigenvalues." + }, + { + "text": "OK, now let me follow up on this, business of which matrices are diagonalizable." + }, + { + "text": "Sorry about that long word." + }, + { + "text": "So a matrix is, is sure to, so here's, here's the main point." + }, + { + "text": "A is sure to be, to have n independent eigenvectors and, and B, now here comes that word, diagonalizable, if, if, so we, we, we might as well get the, the nice case out in the open." + }, + { + "text": "The nice case is when, if all the lambdas are different." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk8.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f06dcec8ffa0ee1bf19440e4ab2194db33ab353b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means, that means no repeated eigenvalues." + }, + { + "text": "OK. That's the nice case." + }, + { + "text": "If, if my matrix and most matrix, if I do a random matrix in MATLAB and compute its eigenvalues, so if I computed, if I took I of rand of ten ten, gave, gave that MATLAB command, the, we'd get a random ten by ten matrix, we would get a list of its ten eigenvalues and they would be different." + }, + { + "text": "They would be distinct, is the best word." + }, + { + "text": "I would have a random matrix will have ten distinct, a ten by ten matrix will have ten distinct eigenvalues, and if it does, the eigenvectors are automatically independent." + }, + { + "text": "So that's a nice fact." + }, + { + "text": "I can, I'll refer you to the text for the proof." + }, + { + "text": "That, that A is sure to have n independent eigenvectors if the eigenvalues are different." + }, + { + "text": "If, if all the, if all eigenvalues are different." + }, + { + "text": "It's just, if some lambdas are repeated, then I have to look more closely." + }, + { + "text": "If an eigenvalue is repeated, I have to look, I have to count, I have to check." + }, + { + "text": "Has it got, say it's repeated three times." + }, + { + "text": "So what's a possibility for, so, so here's, here's the repeated possibility." + }, + { + "text": "And, and let me emphasize the conclusion." + }, + { + "text": "That if I have repeated eigenvalues, I may or may not, I may or may not have, have n independent eigenvectors." + }, + { + "text": "I might." + }, + { + "text": "I, I, you know, this isn't a completely negative case." + }, + { + "text": "The identity matrix." + }, + { + "text": "Well, suppose I take the ten by ten identity matrix." + }, + { + "text": "What are the eigenvalues of that matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk9.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..87d2a2ae5773036cf11800e2f1962908986a0dad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_14_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So just, just take the easiest matrix, the identity." + }, + { + "text": "If I look for its eigenvalues, they're all ones." + }, + { + "text": "So that eigenvalue one is repeated ten times." + }, + { + "text": "But there's no shortage of eigenvectors for the identity matrix." + }, + { + "text": "In fact, every vector is an eigenvector." + }, + { + "text": "So I can take ten independent vectors." + }, + { + "text": "Oh, well, what happens to everything if, if, if A is the identity matrix, let's just think that one through in our head." + }, + { + "text": "If A is the identity matrix, then it's got plenty of eigenvectors." + }, + { + "text": "I choose ten independent vectors, they're the columns of S, and, and what do I get from S inverse A S?" + }, + { + "text": "I get I again, right?" + }, + { + "text": "If A is the identity, and of course, that's the correct lambda." + }, + { + "text": "The, the matrix was already diagonal." + }, + { + "text": "So if the matrix is already diagonal, then the, the lambda is the same as the matrix." + }, + { + "text": "A diagonal matrix has got its eigenvalues sitting right there in front of you." + }, + { + "text": "Now if it's triangular, the eigenvalues are still sitting there, but so let's, let's take a case where, it's triangular." + }, + { + "text": "Suppose A is like, two, one, two, zero." + }, + { + "text": "So there's a case that's going to be trouble." + }, + { + "text": "There's a case that's going to be trouble." + }, + { + "text": "First of all, what are the eigen- I mean, we just, like now you, if we start with a matrix, the first thing we do practically without thinking is compute the eigenvalues and eigenvectors." + }, + { + "text": "OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk0.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6898d4fe66019ef6b40d0472ea94a968e7bbde9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, shall we start?" + }, + { + "text": "This is the second lecture on eigenvalues." + }, + { + "text": "So the first lecture was set -- reached the key equation, Ax equal lambda x. x is the eigenvector and lambda is the eigenvalue." + }, + { + "text": "Now, to use that." + }, + { + "text": "And the good way to, after we've found, so job one is to find the eigenvalues and find the eigenvectors." + }, + { + "text": "Now after we found them, what do we do with them?" + }, + { + "text": "Well, the good way to see that is diagonalize the matrix." + }, + { + "text": "So the matrix is A, and I want to show, first of all, this is like the basic fact." + }, + { + "text": "This, this formula." + }, + { + "text": "That's, that's the key to today's lecture." + }, + { + "text": "This matrix A, I put its eigenvectors in the columns of a matrix S. So S will be the eigenvector matrix, and I want to look at this magic combination S inverse A S. So can I show you how that, how that, what happens there?" + }, + { + "text": "And notice, notice, there's an S inverse." + }, + { + "text": "We have to be able to invert this eigenvector matrix S. So for that we need n independent eigenvectors." + }, + { + "text": "So that's the, that's the case." + }, + { + "text": "OK." + }, + { + "text": "So suppose we have n linearly independent eigenvectors of A." + }, + { + "text": "Put them in the columns of this matrix S. So I'm naturally going to call that the eigenvector matrix, because it's got the eigenvectors in its columns." + }, + { + "text": "And all I want to do is show you what happens when you multiply A times S. So A times S. So this is A times the matrix with the first eigenvector in its first column, the second eigenvector in its second column, the nth eigenvector in its nth column." + }, + { + "text": "And how am I going to do this matrix multiplication?" + }, + { + "text": "Well, certainly I'll do it a column at a time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk1.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..fbe078217bb68baea8e0605a5d04be568c49efbf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I get?" + }, + { + "text": "A times the first column gives me the first column of the answer, but what is it?" + }, + { + "text": "That's an eigenvector." + }, + { + "text": "A times x1 is equal to the lambda times the x1." + }, + { + "text": "And that lambda's we'll call lambda one, of course." + }, + { + "text": "So that's the first column, A x1 is the same as lambda one x1." + }, + { + "text": "A x2 is lambda two x2, so on, along to, in the nth column, we now have lambda n xn." + }, + { + "text": "Looking good, but the next step is even better." + }, + { + "text": "So for the next step, I want to separate out those eigenvalues, those multiplying numbers, from the x's." + }, + { + "text": "So then I'll have just what I want." + }, + { + "text": "OK, so how, how am I going to separate out?" + }, + { + "text": "So that, that number lambda one is multiplying the first column." + }, + { + "text": "So if I want to factor it out of the first column, I better put, here is going to be x1, and that's going to multiply this matrix lambda one in the first entry in all zeros." + }, + { + "text": "You see that that, that's going to come out right for the first column?" + }, + { + "text": "Because we remember how, how we're going back to that original punchline, that if I want a number to multiply x1, then I can do it by putting x1 in that column, in the first column, and putting that number there." + }, + { + "text": "What am I going to have here?" + }, + { + "text": "I'm going to have lambda one, I'm going to have x1, x2, xn." + }, + { + "text": "These are going to be my columns again." + }, + { + "text": "I'm getting s back again." + }, + { + "text": "I'm getting s back again, but now what's it multiplied by?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk10.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c58a42edbe9567233ca7f57643a0b7d43ae6761f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what are the eigenvalues?" + }, + { + "text": "You can tell me right away what they are." + }, + { + "text": "They're two and two, right." + }, + { + "text": "It's a triangular matrix, so when I do this determinant, shall I do this determinant of A minus lambda I?" + }, + { + "text": "I'll get this two minus lambda, one, zero, two minus lambda, right?" + }, + { + "text": "I take that determinant, so I make those into vertical bars to mean determinant, and what's the determinant?" + }, + { + "text": "Two minus lambda squared." + }, + { + "text": "What are the roots?" + }, + { + "text": "Lambda equal two twice." + }, + { + "text": "So the eigenvalues are lambda equals two and two." + }, + { + "text": "OK, fine." + }, + { + "text": "Now the next step, find the eigenvectors." + }, + { + "text": "So I look for eigenvectors and what do I find for this guy?" + }, + { + "text": "Eigenvectors for this guy, when I subtract two minus the identity, so A minus two I has zeros here, and I'm looking for the null space." + }, + { + "text": "What's, what are the eigenvectors?" + }, + { + "text": "They're the, they're, they're the null space of A minus lambda I." + }, + { + "text": "The null space is only one dimension." + }, + { + "text": "This is a case where I don't have enough eigenvectors." + }, + { + "text": "My algebraic multiplicity is two." + }, + { + "text": "I, I would say when I see, when I count how often the eigenvalue is repeated, that's the algebraic multiplicity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk11.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..779c2cf904d904b761080db2671aac46394ad02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the multiplicity." + }, + { + "text": "How many times is it the root of the polynomial?" + }, + { + "text": "My polynomial is two minus lambda squared." + }, + { + "text": "It's a double root." + }, + { + "text": "So my algebraic multiplicity is two." + }, + { + "text": "But the geometric multiplicity, which looks for vectors, looks for eigenvectors and which means the null space of this thing." + }, + { + "text": "And the only eigenvector is one zero." + }, + { + "text": "That's in the null space." + }, + { + "text": "Zero one is not in the null space." + }, + { + "text": "The null space is only one dimensional." + }, + { + "text": "So there's a matrix, my, this A or the original A, that are not diagonalizable." + }, + { + "text": "I can't, I can't find two independent eigenvectors, there's only one." + }, + { + "text": "OK." + }, + { + "text": "So that's the case that I'm, that's a case that I, I'm not really handling." + }, + { + "text": "For example, when I wrote down up here that the powers went to zero if the eigenvalues were below one, I didn't really handle that case of repeated eigenvalues because my reasoning was based on this formula." + }, + { + "text": "And this formula is based on n independent eigenvectors." + }, + { + "text": "OK." + }, + { + "text": "So just to say that." + }, + { + "text": "There are some matrices that we don't cover through diagonalization, but the great majority we do." + }, + { + "text": "OK. And we're always OK if we have different distinct eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk12.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..77d090704cc298475d94416b7ecb88a2a015a913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. That's the, like, the typical case." + }, + { + "text": "Because for each eigenvalue there's at least one eigenvector, the algebraic multiplicity here is one for every eigenvalue, and the geometric multiplicity is one." + }, + { + "text": "There's one eigenvector and they are independent." + }, + { + "text": "OK. OK. Now let me come back to the important case when we're OK." + }, + { + "text": "The important case when we are diagonalizing." + }, + { + "text": "Let me look at, so let me solve this equation." + }, + { + "text": "The equation will be each, I start with some, start with a given vector u0." + }, + { + "text": "And then my equation is that every step I multiply what I have by a." + }, + { + "text": "That equation ought to be simple to handle." + }, + { + "text": "OK. And I'd like to be able to solve it." + }, + { + "text": "How would I find, if I start with a vector u0, and I multiply by a a hundred times, what have I got?" + }, + { + "text": "Well, I can certainly write down a formula for the answer." + }, + { + "text": "So what, what, so u1 is a u0." + }, + { + "text": "And u2 is, what's u2 then?" + }, + { + "text": "U2 I multiply it, u2 I get from u1 by another, multiplying by a, so I've got a twice." + }, + { + "text": "And my formula is uk, after k steps, I've multiplied by a k times the original u0." + }, + { + "text": "You see what I'm doing?" + }, + { + "text": "The next section is going to solve systems of differential equations." + }, + { + "text": "I'm going to have derivatives." + }, + { + "text": "This, this section is the nice one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk13.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..ba8214d8c636e4757a266d6617801174bc939d80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "It solves difference equations." + }, + { + "text": "I would call that a difference equation." + }, + { + "text": "It's conne- a first order." + }, + { + "text": "I would call that a first order system, because it connects only, it only goes up one level." + }, + { + "text": "And it's a system because these are vectors and that's a matrix." + }, + { + "text": "And the solution is just that." + }, + { + "text": "OK." + }, + { + "text": "But, that's a nice formula." + }, + { + "text": "That's the, like, the most compact formula I could ever get." + }, + { + "text": "U one hundred would be a to the one hundredth u0." + }, + { + "text": "But how would I actually find u one hundred?" + }, + { + "text": "How would I find, how would I discover what u one hundred is?" + }, + { + "text": "Let me, let me show you how." + }, + { + "text": "Here, here's the idea." + }, + { + "text": "If, so, to solve, to really solve, shall I say, to really solve." + }, + { + "text": "To really solve it, I would take this initial vector, u0, and I would write it as a combination of eigenvectors." + }, + { + "text": "To really solve, write, write u0 as a combination, say, certain amount of the first eigenvector plus a certain amount of the second eigenvector plus a certain amount of the last eigenvector." + }, + { + "text": "Now multiply by a." + }, + { + "text": "You want to, you got to see the magic of eigenvectors work." + }, + { + "text": "Multiply by a." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk14.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7843b2bf0cac762d1c12452cf36500ea4ad13370 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a u0 is what?" + }, + { + "text": "So a times that." + }, + { + "text": "A times, so what's, I can separate it out into n separate pieces and that's the whole point." + }, + { + "text": "That each of those pieces is going in its own merry way." + }, + { + "text": "Each of those pieces is an eigenvector, and when I multiply by a, what does this piece become?" + }, + { + "text": "So that's some amount of the first, let's suppose the eigenvectors are normalized to be unit vectors." + }, + { + "text": "So that says what the eigenvector is." + }, + { + "text": "It's, and I need some multiple of it to produce u0." + }, + { + "text": "OK. Now when I multiply by a, what do I get?" + }, + { + "text": "I get c1, which is just a factor, times a x1, but a x1 is lambda one x1." + }, + { + "text": "When I multiply this by a, I get c2 lambda two x2." + }, + { + "text": "And here I get cn lambda n xn." + }, + { + "text": "And suppose I multiply by a to the hundredth power now." + }, + { + "text": "Can we, can we, having done it, multiplied by a, let's multiply by a to the hundredth." + }, + { + "text": "What happens to this first term when I multiply by a to the one hundredth?" + }, + { + "text": "It's got that factor lambda to the hundredth." + }, + { + "text": "That's the key." + }, + { + "text": "That, that's what I mean by going its own merry way." + }, + { + "text": "It, it is pure eigenvector, it's exactly in a direction where multiplication by a just brings in a scalar factor lambda one." + }, + { + "text": "So a hundred times brings in this a hundred times." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk15.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7ee3348735378aa4049d33ec2a197d0ceb0c447c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Hundred times lambda two, hundred times lambda n. Actually, we're, what are we seeing here?" + }, + { + "text": "We're seeing, this same, lambda, capital lambda to the hundredth, as in the, as in the diagonalization, and we're seeing the S matrix, the matrix S of eigenvectors." + }, + { + "text": "That's what this has got to, this has got to amount to, a lambda to the hundredth power times an S times this vector C that's telling us how much of each one is in the original thing." + }, + { + "text": "So if, if I had to really find the hundredth power, I would take u0, I would expand it as a combination of eigenvectors, this is really S, the eigenvector matrix times C, the, the coefficient vector." + }, + { + "text": "And then I would immediately, then, by inserting these hundredth powers of eigenvalues, I'd have the answer." + }, + { + "text": "So the, the, huh, there must be, well, let's see." + }, + { + "text": "OK." + }, + { + "text": "It's, so, yeah." + }, + { + "text": "So if u100 is a to the hundredth times u0, and u0 is Sc, then you see this formula is just this formula, which is the way I would actually get hold of this, of this u100, which is, let me put it here, u100." + }, + { + "text": "The way I would actually get hold of that, see what, what the solution is after a hundred steps, would be expand the initial vector into eigenvectors and, and let each eigenvector go its own way, multiplying by a hundred at, by lambda at every step, and therefore by lambda to the hundredth power after a hundredth step." + }, + { + "text": "Can I do an example?" + }, + { + "text": "So that's, that's the, the formulas." + }, + { + "text": "Now let me take an example." + }, + { + "text": "I'll use the Fibonacci sequence as an example." + }, + { + "text": "So, so Fibonacci example." + }, + { + "text": "You remember the Fibonacci numbers?" + }, + { + "text": "If we start with one and one as F0, oh, I think I start with zero, maybe." + }, + { + "text": "Let zero and one be the first ones." + }, + { + "text": "So there's F0 and F1, the first two Fibonacci numbers." + }, + { + "text": "Then what's the rule for Fibonacci numbers?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk16.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..79c65e32781f7f304b504a6c390247abb9d26ac8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "They're the sum." + }, + { + "text": "The next one is the sum of those, so it's one." + }, + { + "text": "The next one is the sum of those, so it's two." + }, + { + "text": "The next one is the sum of those, so it's three." + }, + { + "text": "Well, it looks like one, two, three, four, five, but somehow it's not going to do that way." + }, + { + "text": "The next one is five, right." + }, + { + "text": "Two and three makes five." + }, + { + "text": "The next one is eight." + }, + { + "text": "The next one is thirteen." + }, + { + "text": "And the one hundredth Fibonacci number is what?" + }, + { + "text": "That's my question." + }, + { + "text": "How could I get a formula for the hundredth number and for example how could I answer the question how fast are they growing?" + }, + { + "text": "How fast are those Fibonacci numbers growing?" + }, + { + "text": "They're certainly growing." + }, + { + "text": "It's not a stable case, whatever the eigenvalues of whatever matrix it is, they're not smaller than one." + }, + { + "text": "These numbers are growing." + }, + { + "text": "But how fast are they growing?" + }, + { + "text": "The answer is lies in the eigenvalue." + }, + { + "text": "So I've got to find the matrix, so let me write down the Fibonacci rule, F k plus two is F k plus one plus F k, right?" + }, + { + "text": "Now that's not in my -- I want to write that as U k plus one and A U k. But right now what I've got is a single equation, not a system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk17.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b3aaa9dcee3cf27c112015659bb5a0b51a983ce1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's second order." + }, + { + "text": "It's like having a second order differential equation with second derivatives." + }, + { + "text": "I want to get first derivatives." + }, + { + "text": "Here I want to get first difference." + }, + { + "text": "So the way to do it is to introduce U k will be a vector." + }, + { + "text": "See, a small trick." + }, + { + "text": "Let U k be a vector, F k plus one and F k. So I'm going to get a two by two system, first order, instead of a one, instead of a scalar system, second order, by a simple trick." + }, + { + "text": "I'm just going to add in an equation F k plus one equals F k plus one." + }, + { + "text": "That will be my second equation." + }, + { + "text": "Then this is my system, this is my unknown, and what's my one-step equation?" + }, + { + "text": "So now U k plus one." + }, + { + "text": "That's so U k plus one is the left side, and what have I got here on the right side?" + }, + { + "text": "I've got some matrix multiplying U k. Can you see that all right?" + }, + { + "text": "If you can see it, then you can tell me what the matrix is." + }, + { + "text": "You see that I'm taking my system here, I artificially made it into a system." + }, + { + "text": "I artificially made the unknown into a vector, and now I'm ready to look at and see what the matrix is." + }, + { + "text": "So do you see the left side, U k plus one is F k plus two F k plus one, that's just what I want." + }, + { + "text": "On the right side, this, remember, this U k here, let me for the moment put it as F k plus one F k. So what's the matrix?" + }, + { + "text": "Well, that has a one and a one, and that has a one and a zero." + }, + { + "text": "There's the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk18.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..6c1b68c2cb2fde3f5dea82f3100d4da31fcce70a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "You see that that gives me the right-hand side." + }, + { + "text": "So there's the matrix A, and this is our friend U k. So we've got, so that simple trick changed the second order scalar problem to a first order system, two, with two unknowns." + }, + { + "text": "With a matrix and now what do I do?" + }, + { + "text": "Well, before I even think, I find its eigenvalues and eigenvectors." + }, + { + "text": "So what are the eigenvalues and eigenvectors of that matrix?" + }, + { + "text": "Let's see." + }, + { + "text": "I was, first let me just, like, think for a minute." + }, + { + "text": "It's two by two, so this shouldn't be impossible to do." + }, + { + "text": "Let's do it." + }, + { + "text": "OK." + }, + { + "text": "So my matrix again is one one one zero." + }, + { + "text": "It's symmetric, by the way." + }, + { + "text": "So what I will eventually know about symmetric matrices is that the eigenvalues will come out real, I won't get any complex numbers here, and the eigenvectors, once I get those, actually will be orthogonal." + }, + { + "text": "But two by two, I'm more interested in what the actual numbers are." + }, + { + "text": "What do I know about the two numbers?" + }, + { + "text": "Well, should, do you want me to find this determinant of A minus lambda I?" + }, + { + "text": "Sure." + }, + { + "text": "So it's the determinant of one minus lambda one one zero, right?" + }, + { + "text": "Minus lambda, yes, got it." + }, + { + "text": "OK. OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk19.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..a73b23e3d56b889ff49ea7f55a784fac33e13c3d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "There'll be two eigenvalues." + }, + { + "text": "Well, tell me again what I know about the two eigenvalues before I go any further." + }, + { + "text": "Tell me something about these two eigenvalues, what do they add up to?" + }, + { + "text": "Lambda one plus lambda two is the same as the trace down the diagonal of the matrix, one and zero is one." + }, + { + "text": "So lambda one plus lambda two should come out to be one, and lambda one times lambda two should come out to be the determinant, which is minus one." + }, + { + "text": "So I'm expecting the eigenvalues to add to one and to multiply to minus one." + }, + { + "text": "But let's just see it happen here." + }, + { + "text": "If I multiply this out, I get that times that'll be a lambda squared minus lambda minus one." + }, + { + "text": "Good." + }, + { + "text": "Lambda squared minus lambda minus one." + }, + { + "text": "Actually, you see the, compare that with the original equation that I started with." + }, + { + "text": "Fk plus two minus Fk plus one minus Fk is zero." + }, + { + "text": "The recurrent, the recursion that the Fibonacci number satisfy is somehow showing up directly here for the eigenvalues when we set that to zero." + }, + { + "text": "OK. Let's solve." + }, + { + "text": "Well, I would like to be able to factor that, that quadratic, but I'm better off to use the quadratic formula." + }, + { + "text": "Lambda is, let's see, minus b is one, plus or minus the square root of b squared, which is one, minus four, times that, times that, which is plus four, over two." + }, + { + "text": "So that's the square root of five." + }, + { + "text": "So the eigenvalues are lambda one is one half of one plus square root of five, and lambda two is one half of one minus square root of five." + }, + { + "text": "And sure enough, they, those add up to one, and they multiply to give minus one." + }, + { + "text": "OK. Those are the two eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk2.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..43cfb012fc04a89fc7dab94c23bfb0f50ade3782 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "On the right, it's multiplied by, if I want, if I want lambda n xn in the last column, how do I do it?" + }, + { + "text": "Well, the last column here will be, I'll, I'll take the last column, use these coefficients, put the lambda n down there, and it will multiply that nth column and give me lambda n xn." + }, + { + "text": "There, there you see matrix multiplication just working for us." + }, + { + "text": "So I started with A s. I wrote down what it meant." + }, + { + "text": "A times each eigenvector." + }, + { + "text": "That gave me lambda times the eigenvector." + }, + { + "text": "And then when I peeled off the lambdas, they were on the right-hand side, so I've got s, my matrix back again, and this matrix, this diagonal matrix, the eigenvalue matrix, and I call it capital lambda, using capital letters for matrices, and lambda to prompt me that it's, that it's eigenvalues that are in there." + }, + { + "text": "So you see that the eigenvalues are just sitting down that diagonal?" + }, + { + "text": "If I had a column x2 here, I would want the lambda two in the two two position, in the diagonal position, to multiply that x2 and give me the lambda two x2." + }, + { + "text": "That's my formula." + }, + { + "text": "A s is s lambda." + }, + { + "text": "OK. That's, that's the, you see, it's just a calculation." + }, + { + "text": "Now, I, I mentioned, and I have to mention again, this business about n independent eigenvectors." + }, + { + "text": "As it stands, this is all fine whether, I mean, I could be repeating the same eigenvector, but I, I'm no interested in that." + }, + { + "text": "I want to be able to invert s, and that's where this comes in." + }, + { + "text": "This n independent eigenvectors business comes in to tell me that that matrix is invertible." + }, + { + "text": "So let me, on the next board, write down what I've got." + }, + { + "text": "A s equals s lambda." + }, + { + "text": "And now I'm, I can multiply on the left by s inverse." + }, + { + "text": "So this is really, I can do that provided s is invertible, provided my assumption of n independent eigenvectors is satisfied." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk20.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ad5a59fa5db44ce73ff5f88190423e0404fb3d39 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "How, how, what are those numbers approximately?" + }, + { + "text": "Square root of five, well, it's more than two, but less than three." + }, + { + "text": "It, it'd be nice to know these numbers." + }, + { + "text": "I think, I think that that, so that number comes out bigger than one, right?" + }, + { + "text": "Yeah, that's right." + }, + { + "text": "This number comes out bigger than one." + }, + { + "text": "It's about one point six one eight or something." + }, + { + "text": "Not exactly." + }, + { + "text": "It's supposed to be one point six." + }, + { + "text": "Just, like, I think so." + }, + { + "text": "Then what's lambda two?" + }, + { + "text": "Is, is lambda two positive or negative?" + }, + { + "text": "Negative, right?" + }, + { + "text": "Because I'm, it's obviously negative, and I knew that the, so it's minus, and they add up to one, so minus point six one eight, I guess." + }, + { + "text": "OK. And some order." + }, + { + "text": "Those are the two eigenvalues." + }, + { + "text": "One eigenvalue bigger than one, one eigenvalue smaller than one." + }, + { + "text": "Actually, that's a great situation to be in." + }, + { + "text": "Of course, the eigenvalues are different, so there's no doubt whatever, is this matrix diagonalizable?" + }, + { + "text": "Is this matrix diagonalizable, that original matrix A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk21.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..4a034475591d371995b379b5f98783a2cfb25870 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Sure." + }, + { + "text": "We've got two distinct eigenvalues and we can find the eigenvectors in a moment." + }, + { + "text": "But they'll be independent, will be diagonalizable, and now you can already answer my very first question." + }, + { + "text": "How fast are those Fibonacci numbers increasing?" + }, + { + "text": "How, those, they're increasing, right?" + }, + { + "text": "They're not doubling at every step." + }, + { + "text": "Let's look again at these numbers." + }, + { + "text": "Five eight thirteen, it's not obvious." + }, + { + "text": "The next one would be twenty one thirty four." + }, + { + "text": "So to get some idea of what F one hundred is, can you give me any, I mean the crucial number of, so it, these, it's approximately, what's controlling the growth of these Fibonacci numbers?" + }, + { + "text": "It's the eigenvalues." + }, + { + "text": "And which eigenvalues controlling that growth?" + }, + { + "text": "The big ones." + }, + { + "text": "So F one hundred will it be approximately some constant, c one, I guess, times this lambda one, this one plus square root of five over two, to the hundredth power." + }, + { + "text": "And the two hundredth have, in other words, the eigenvalue, the Fibonacci numbers are growing by about that factor." + }, + { + "text": "You see that we've got precise information about the, about the Fibonacci numbers out of the eigenvalue." + }, + { + "text": "OK. And again, why is that true?" + }, + { + "text": "Let me go over to this board and show what I'm doing here." + }, + { + "text": "The, the original eigen, the original initial value is some combination of eigenvectors, and then when we start multiple, when we start going out the theory of Fibonacci numbers, when we start multiplying by a hundred times, it's this lambda one to the hundredth, this term is, is the one that's taken over." + }, + { + "text": "It's, I mean, that's big, like, one point six to the hundredth power." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk22.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..c13a1fc9867173c3067e46c469cfff27b9b45289 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "The second term is practically nothing, right?" + }, + { + "text": "The point six, or minus point six to the hundredth power, is an extremely small, extremely small number." + }, + { + "text": "So this is, this, this, there are only two terms, because we're two by two." + }, + { + "text": "This number is, this piece of it is there, but it's, it's disappearing." + }, + { + "text": "Where this piece is there and it's growing and controlling everything." + }, + { + "text": "So, so really the, we're doing, like, problems that are evolving." + }, + { + "text": "We're doing dynamics." + }, + { + "text": "Instead of Ax equal b, that's a static problem." + }, + { + "text": "We're now, we're doing dynamics." + }, + { + "text": "A, a squared, a cubed, things are evolving in time, and the eigenvalues are the crucial, numbers." + }, + { + "text": "OK." + }, + { + "text": "I guess to complete this, I better write down the eigenvectors." + }, + { + "text": "So we should complete the, the whole process by finding the eigenvectors." + }, + { + "text": "OK. Well, I have to, up in the corner, then I have to look at A minus lambda I." + }, + { + "text": "So A minus lambda I is this one minus lambda, one, one, and minus lambda." + }, + { + "text": "And now, can we spot an eigenvector out of that?" + }, + { + "text": "That's, for these two lambdas, this matrix is singular." + }, + { + "text": "I guess the eigenvector, two by two ought to be easy." + }, + { + "text": "So if I know that this matrix is singular, then it seems to me the eigenvector has to be lambda and one, because that multiplication will give me the zero." + }, + { + "text": "And this multiplication gives me, better give me also zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk23.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..df816eb800ce767b1475c279a24ad976bb45a785 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Do you see why it does?" + }, + { + "text": "This is the minus lambda squared plus lambda plus one." + }, + { + "text": "It's the thing that's zero, because these lambdas are special." + }, + { + "text": "There's the eigenvector." + }, + { + "text": "X1 is lambda one, one, and x2 is lambda two, one." + }, + { + "text": "I did that as a little trick that was available in the two by two case." + }, + { + "text": "So now I finally have to, oh, I have to take the initial, u0." + }, + { + "text": "So to complete this example entirely, I have to say, OK, what was u0?" + }, + { + "text": "u0 was f1 f0." + }, + { + "text": "So u0, the starting vector, is f1 f0, and those were one and zero." + }, + { + "text": "So I have to use that vector, so I have to look for, from multiple of the first eigenvector and the second, to produce u0, the one zero vector." + }, + { + "text": "This is what will find c1 and c2, and then I'm done." + }, + { + "text": "So let me, instead of in the last five seconds grinding out a formula, let me repeat the idea." + }, + { + "text": "That really, it's the idea that's central." + }, + { + "text": "When things are evolving in time, let me come back to this board, because the ideas are here." + }, + { + "text": "When things are evolving in time by a first-order system, starting from an original u0, the key is, find the eigenvalues and eigenvectors of A." + }, + { + "text": "That will tell, those eigenvectors, the eigenvalues will already tell you what's happening." + }, + { + "text": "Is the solution blowing up?" + }, + { + "text": "Is it going to zero?" + }, + { + "text": "What's it doing?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk24.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..40301cb90760e2172baa94d536cbc13288d4c31f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk24.json @@ -0,0 +1,20 @@ +[ + { + "text": "And then, to find out exactly a formula, you have to take your u0 and write it as a combination of eigenvectors and then follow each eigenvector separately." + }, + { + "text": "And that's really what this formula, the formula for, that's what the formula for A to the k is doing." + }, + { + "text": "So remember that formula for A to the k is S, lambda to the k S inverse." + }, + { + "text": "OK. That's, that's difference equations, and you just have to, so the homework will give some examples different from Fibonacci to follow through." + }, + { + "text": "And next time will be differential equations." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk3.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..9bf1bb852baadc1da7837e14180c0c2951a30882 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I mentioned at the end of last time, and I'll say again, that there's a small number of matrices for, that don't have n independent eigenvectors." + }, + { + "text": "So I've got to discuss that, that technical point." + }, + { + "text": "But the great, the most matrices that we see have n, n independent eigenvectors and we can diagonalize." + }, + { + "text": "This is diagonalization." + }, + { + "text": "I could also write it, and I often will, the other way round." + }, + { + "text": "If I multiply on the right by s inverse, if I took this equation at the top and multiplied on the right by s inverse, I could, I would have A left here." + }, + { + "text": "Now s inverse is coming from the right." + }, + { + "text": "So can you keep those two straight?" + }, + { + "text": "A multiplies its eigenvectors." + }, + { + "text": "That's how I keep them straight." + }, + { + "text": "So A multiplies s. A multiplies s. And then this s inverse makes the whole thing diagonal." + }, + { + "text": "And this is another way of saying the same thing, putting the s's on the other side of the equation, A is s lambda s inverse." + }, + { + "text": "So that's the, that's the new factorization." + }, + { + "text": "That's the replacement for L U from elimination or Q R from Gram-Schmidt." + }, + { + "text": "And notice that the matrix, so it's, it's a matrix times a diagonal matrix times the inverse of the first one." + }, + { + "text": "It's, that's the combination that we'll see throughout this chapter." + }, + { + "text": "This, this, combination with an s and an s inverse." + }, + { + "text": "OK. Can I just begin to use that?" + }, + { + "text": "For example, what about A squared?" + }, + { + "text": "What are the eigenvalues and eigenvectors of A squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk4.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c687b6948acad76de8781cb82d3eb069c9da514e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's a straightforward question with a, with a absolutely clean answer." + }, + { + "text": "So let me, let me consider A squared." + }, + { + "text": "So I look, I start with Ax equal lambda x." + }, + { + "text": "And I'm headed for A squared." + }, + { + "text": "So let me multiply both sides by A." + }, + { + "text": "That's one way to get A squared on the left." + }, + { + "text": "So if, I should write these ifs in here." + }, + { + "text": "If Ax equals lambda x, then I multiply by A." + }, + { + "text": "So I get A squared x equals, well, I'm multiplying by A, so that's lambda Ax." + }, + { + "text": "That lambda was a number, so I just put it on the left." + }, + { + "text": "And what do I, tell me how to make that look better." + }, + { + "text": "What have I got here?" + }, + { + "text": "For, if, if A has the eigenvalue lambda and eigenvector x, what's up with A squared?" + }, + { + "text": "A squared x, I just multiply by A, but now for Ax, I'm going to substitute lambda x, so I've got lambda squared x." + }, + { + "text": "So from that simple calculation, I, my conclusion is that the eigenvalues of A squared are lambda squared." + }, + { + "text": "And the eigenvectors, I always think about both of those." + }, + { + "text": "What can I say about the eigenvalues?" + }, + { + "text": "They're squared." + }, + { + "text": "What can I say about the eigenvectors?" + }, + { + "text": "They're the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk5.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5bf15e20707c156c8ae71c9c7acea41a9d9d8e46 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same x as in, as for A." + }, + { + "text": "Now, let me see that also from this formula." + }, + { + "text": "How can I see what A squared is looking like from this formula?" + }, + { + "text": "So let me, that, that was one way to do it." + }, + { + "text": "Let me do it by just taking A squared from that." + }, + { + "text": "A squared is S lambda S inverse, that's A, times S lambda S inverse, that's A, which is?" + }, + { + "text": "This is the beauty of eigenvalues, eigenvectors, having that S inverse and S is the identity, so I've got S lambda squared S inverse." + }, + { + "text": "Yes." + }, + { + "text": "You see what that's telling me?" + }, + { + "text": "It's, it's telling me the same thing that I just learned here, but in the, in, in a matrix form." + }, + { + "text": "It's telling me that the S is the same, the eigenvectors are the same, but the eigenvalues are squared, because this is, what's lambda squared, that's still diagonal, it's got little lambda one squared, lambda two squared, down to lambda n squared, on that diagonal, those are the eigenvalues, as we just learned, of A squared." + }, + { + "text": "OK." + }, + { + "text": "So, somehow those eigenvalues and eigenvectors are really giving you a way to, to, to, to see what's going on inside a matrix." + }, + { + "text": "Now, of course, I can continue that for, to the k-th power." + }, + { + "text": "A to the k-th power." + }, + { + "text": "If I multiply, if I have k of these together, do you see how S inverse S will keep cancelling?" + }, + { + "text": "In the, in the inside, I'll have the S outside, at the far left, and lambda will be in there k times and S inverse." + }, + { + "text": "So what's that telling me?" + }, + { + "text": "That's telling me that the eigenvalues of A, of A to the k-th power are the k-th powers." + }, + { + "text": "The eigenvalues of A cubed are the cubes of the eigenvalues of A, and the eigenvectors are the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk6.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..c18dddbe798022f7e68278ac002a3f5fe6ed249e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same." + }, + { + "text": "OK." + }, + { + "text": "In other words, eigenvalues and eigenvectors give a great way to understand the powers of a matrix." + }, + { + "text": "If I take the square of a matrix or the hundredth power of a matrix, the pivots are all over the place." + }, + { + "text": "L U, if I multiply L U times L U times L U times L U a hundred times, I've got a hundred L U's." + }, + { + "text": "I can't do anything with them." + }, + { + "text": "But when I multiply S lambda S inverse by itself, when I look at the eigenvector picture a hundred times, I get a hundred or ninety-nine of these guys cancelling out inside, and I get A to the hundredth is S lambda to the hundredth S inverse." + }, + { + "text": "I mean, eigenvalues tell you about powers of a matrix in a way that we had no, no way to approach previously." + }, + { + "text": "For example, when does, when do the powers of a matrix go to zero?" + }, + { + "text": "I would call that matrix stable, maybe." + }, + { + "text": "So, so, so I could write down a, a theorem." + }, + { + "text": "I'll, I'll write it as a theorem, just to use that word to emphasize that here I'm getting this great fact from this eigenvalue picture." + }, + { + "text": "OK. A to the k approaches zero as k goes, as k gets bigger." + }, + { + "text": "If what?" + }, + { + "text": "What's the, how can I tell for a matrix A if its powers go to zero?" + }, + { + "text": "What, what's somewhere inside that matrix is that information." + }, + { + "text": "That information is not present in the pivots." + }, + { + "text": "It's present in the eigenvalues." + }, + { + "text": "What do I need for the, to know that if I take higher and higher powers of A that this matrix gets smaller and smaller?" + }, + { + "text": "Well, S and S inverse are not moving." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk7.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b84a5c854a5542758e8a0107e1ff043205fe3bdb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's this guy that has to get small, and that's easy to, easy to understand." + }, + { + "text": "The requirement is all eigenvalues, so what is the requirement?" + }, + { + "text": "The eigenvalues have to be less than one." + }, + { + "text": "Now, I have to write that absolute value, because those eigenvalues could be negative, they could be complex numbers." + }, + { + "text": "So I'm taking the absolute value if all of those are below one." + }, + { + "text": "That's, in fact, we practically see why." + }, + { + "text": "Let me just say that I, that I, I'm operating on one assumption here, and I got to keep remembering that that assumption is still present." + }, + { + "text": "That assumption was that I had a full set of, of n independent eigenvectors." + }, + { + "text": "If I don't have that, then I, I, then this approach is not working." + }, + { + "text": "So, so again, a pure eigenvalue approach, eigenvector approach, needs n independent eigenvectors." + }, + { + "text": "If we don't have n independent eigenvectors, we can't diagonalize the matrix." + }, + { + "text": "We can't get to a diagonal matrix." + }, + { + "text": "This, this, this diagonalization is only possible if S inverse makes sense." + }, + { + "text": "OK. Can I, can I follow up on that point now?" + }, + { + "text": "So, so you see why, what we get and, and why we want it, because we get information about the powers of a matrix just immediately from the eigenvalues." + }, + { + "text": "OK, now let me follow up on this, business of which matrices are diagonalizable." + }, + { + "text": "Sorry about that long word." + }, + { + "text": "So a matrix is, is sure to, so here's, here's the main point." + }, + { + "text": "A is sure to be, to have n independent eigenvectors and, and B, now here comes that word, diagonalizable, if, if, so we, we, we might as well get the, the nice case out in the open." + }, + { + "text": "The nice case is when, if all the lambdas are different." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk8.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f06dcec8ffa0ee1bf19440e4ab2194db33ab353b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means, that means no repeated eigenvalues." + }, + { + "text": "OK. That's the nice case." + }, + { + "text": "If, if my matrix and most matrix, if I do a random matrix in MATLAB and compute its eigenvalues, so if I computed, if I took I of rand of ten ten, gave, gave that MATLAB command, the, we'd get a random ten by ten matrix, we would get a list of its ten eigenvalues and they would be different." + }, + { + "text": "They would be distinct, is the best word." + }, + { + "text": "I would have a random matrix will have ten distinct, a ten by ten matrix will have ten distinct eigenvalues, and if it does, the eigenvectors are automatically independent." + }, + { + "text": "So that's a nice fact." + }, + { + "text": "I can, I'll refer you to the text for the proof." + }, + { + "text": "That, that A is sure to have n independent eigenvectors if the eigenvalues are different." + }, + { + "text": "If, if all the, if all eigenvalues are different." + }, + { + "text": "It's just, if some lambdas are repeated, then I have to look more closely." + }, + { + "text": "If an eigenvalue is repeated, I have to look, I have to count, I have to check." + }, + { + "text": "Has it got, say it's repeated three times." + }, + { + "text": "So what's a possibility for, so, so here's, here's the repeated possibility." + }, + { + "text": "And, and let me emphasize the conclusion." + }, + { + "text": "That if I have repeated eigenvalues, I may or may not, I may or may not have, have n independent eigenvectors." + }, + { + "text": "I might." + }, + { + "text": "I, I, you know, this isn't a completely negative case." + }, + { + "text": "The identity matrix." + }, + { + "text": "Well, suppose I take the ten by ten identity matrix." + }, + { + "text": "What are the eigenvalues of that matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk9.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..87d2a2ae5773036cf11800e2f1962908986a0dad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_15_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So just, just take the easiest matrix, the identity." + }, + { + "text": "If I look for its eigenvalues, they're all ones." + }, + { + "text": "So that eigenvalue one is repeated ten times." + }, + { + "text": "But there's no shortage of eigenvectors for the identity matrix." + }, + { + "text": "In fact, every vector is an eigenvector." + }, + { + "text": "So I can take ten independent vectors." + }, + { + "text": "Oh, well, what happens to everything if, if, if A is the identity matrix, let's just think that one through in our head." + }, + { + "text": "If A is the identity matrix, then it's got plenty of eigenvectors." + }, + { + "text": "I choose ten independent vectors, they're the columns of S, and, and what do I get from S inverse A S?" + }, + { + "text": "I get I again, right?" + }, + { + "text": "If A is the identity, and of course, that's the correct lambda." + }, + { + "text": "The, the matrix was already diagonal." + }, + { + "text": "So if the matrix is already diagonal, then the, the lambda is the same as the matrix." + }, + { + "text": "A diagonal matrix has got its eigenvalues sitting right there in front of you." + }, + { + "text": "Now if it's triangular, the eigenvalues are still sitting there, but so let's, let's take a case where, it's triangular." + }, + { + "text": "Suppose A is like, two, one, two, zero." + }, + { + "text": "So there's a case that's going to be trouble." + }, + { + "text": "There's a case that's going to be trouble." + }, + { + "text": "First of all, what are the eigen- I mean, we just, like now you, if we start with a matrix, the first thing we do practically without thinking is compute the eigenvalues and eigenvectors." + }, + { + "text": "OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk0.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6898d4fe66019ef6b40d0472ea94a968e7bbde9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, shall we start?" + }, + { + "text": "This is the second lecture on eigenvalues." + }, + { + "text": "So the first lecture was set -- reached the key equation, Ax equal lambda x. x is the eigenvector and lambda is the eigenvalue." + }, + { + "text": "Now, to use that." + }, + { + "text": "And the good way to, after we've found, so job one is to find the eigenvalues and find the eigenvectors." + }, + { + "text": "Now after we found them, what do we do with them?" + }, + { + "text": "Well, the good way to see that is diagonalize the matrix." + }, + { + "text": "So the matrix is A, and I want to show, first of all, this is like the basic fact." + }, + { + "text": "This, this formula." + }, + { + "text": "That's, that's the key to today's lecture." + }, + { + "text": "This matrix A, I put its eigenvectors in the columns of a matrix S. So S will be the eigenvector matrix, and I want to look at this magic combination S inverse A S. So can I show you how that, how that, what happens there?" + }, + { + "text": "And notice, notice, there's an S inverse." + }, + { + "text": "We have to be able to invert this eigenvector matrix S. So for that we need n independent eigenvectors." + }, + { + "text": "So that's the, that's the case." + }, + { + "text": "OK." + }, + { + "text": "So suppose we have n linearly independent eigenvectors of A." + }, + { + "text": "Put them in the columns of this matrix S. So I'm naturally going to call that the eigenvector matrix, because it's got the eigenvectors in its columns." + }, + { + "text": "And all I want to do is show you what happens when you multiply A times S. So A times S. So this is A times the matrix with the first eigenvector in its first column, the second eigenvector in its second column, the nth eigenvector in its nth column." + }, + { + "text": "And how am I going to do this matrix multiplication?" + }, + { + "text": "Well, certainly I'll do it a column at a time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk1.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..fbe078217bb68baea8e0605a5d04be568c49efbf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I get?" + }, + { + "text": "A times the first column gives me the first column of the answer, but what is it?" + }, + { + "text": "That's an eigenvector." + }, + { + "text": "A times x1 is equal to the lambda times the x1." + }, + { + "text": "And that lambda's we'll call lambda one, of course." + }, + { + "text": "So that's the first column, A x1 is the same as lambda one x1." + }, + { + "text": "A x2 is lambda two x2, so on, along to, in the nth column, we now have lambda n xn." + }, + { + "text": "Looking good, but the next step is even better." + }, + { + "text": "So for the next step, I want to separate out those eigenvalues, those multiplying numbers, from the x's." + }, + { + "text": "So then I'll have just what I want." + }, + { + "text": "OK, so how, how am I going to separate out?" + }, + { + "text": "So that, that number lambda one is multiplying the first column." + }, + { + "text": "So if I want to factor it out of the first column, I better put, here is going to be x1, and that's going to multiply this matrix lambda one in the first entry in all zeros." + }, + { + "text": "You see that that, that's going to come out right for the first column?" + }, + { + "text": "Because we remember how, how we're going back to that original punchline, that if I want a number to multiply x1, then I can do it by putting x1 in that column, in the first column, and putting that number there." + }, + { + "text": "What am I going to have here?" + }, + { + "text": "I'm going to have lambda one, I'm going to have x1, x2, xn." + }, + { + "text": "These are going to be my columns again." + }, + { + "text": "I'm getting s back again." + }, + { + "text": "I'm getting s back again, but now what's it multiplied by?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk10.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c58a42edbe9567233ca7f57643a0b7d43ae6761f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what are the eigenvalues?" + }, + { + "text": "You can tell me right away what they are." + }, + { + "text": "They're two and two, right." + }, + { + "text": "It's a triangular matrix, so when I do this determinant, shall I do this determinant of A minus lambda I?" + }, + { + "text": "I'll get this two minus lambda, one, zero, two minus lambda, right?" + }, + { + "text": "I take that determinant, so I make those into vertical bars to mean determinant, and what's the determinant?" + }, + { + "text": "Two minus lambda squared." + }, + { + "text": "What are the roots?" + }, + { + "text": "Lambda equal two twice." + }, + { + "text": "So the eigenvalues are lambda equals two and two." + }, + { + "text": "OK, fine." + }, + { + "text": "Now the next step, find the eigenvectors." + }, + { + "text": "So I look for eigenvectors and what do I find for this guy?" + }, + { + "text": "Eigenvectors for this guy, when I subtract two minus the identity, so A minus two I has zeros here, and I'm looking for the null space." + }, + { + "text": "What's, what are the eigenvectors?" + }, + { + "text": "They're the, they're, they're the null space of A minus lambda I." + }, + { + "text": "The null space is only one dimension." + }, + { + "text": "This is a case where I don't have enough eigenvectors." + }, + { + "text": "My algebraic multiplicity is two." + }, + { + "text": "I, I would say when I see, when I count how often the eigenvalue is repeated, that's the algebraic multiplicity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk11.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..779c2cf904d904b761080db2671aac46394ad02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the multiplicity." + }, + { + "text": "How many times is it the root of the polynomial?" + }, + { + "text": "My polynomial is two minus lambda squared." + }, + { + "text": "It's a double root." + }, + { + "text": "So my algebraic multiplicity is two." + }, + { + "text": "But the geometric multiplicity, which looks for vectors, looks for eigenvectors and which means the null space of this thing." + }, + { + "text": "And the only eigenvector is one zero." + }, + { + "text": "That's in the null space." + }, + { + "text": "Zero one is not in the null space." + }, + { + "text": "The null space is only one dimensional." + }, + { + "text": "So there's a matrix, my, this A or the original A, that are not diagonalizable." + }, + { + "text": "I can't, I can't find two independent eigenvectors, there's only one." + }, + { + "text": "OK." + }, + { + "text": "So that's the case that I'm, that's a case that I, I'm not really handling." + }, + { + "text": "For example, when I wrote down up here that the powers went to zero if the eigenvalues were below one, I didn't really handle that case of repeated eigenvalues because my reasoning was based on this formula." + }, + { + "text": "And this formula is based on n independent eigenvectors." + }, + { + "text": "OK." + }, + { + "text": "So just to say that." + }, + { + "text": "There are some matrices that we don't cover through diagonalization, but the great majority we do." + }, + { + "text": "OK. And we're always OK if we have different distinct eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk12.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..77d090704cc298475d94416b7ecb88a2a015a913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. That's the, like, the typical case." + }, + { + "text": "Because for each eigenvalue there's at least one eigenvector, the algebraic multiplicity here is one for every eigenvalue, and the geometric multiplicity is one." + }, + { + "text": "There's one eigenvector and they are independent." + }, + { + "text": "OK. OK. Now let me come back to the important case when we're OK." + }, + { + "text": "The important case when we are diagonalizing." + }, + { + "text": "Let me look at, so let me solve this equation." + }, + { + "text": "The equation will be each, I start with some, start with a given vector u0." + }, + { + "text": "And then my equation is that every step I multiply what I have by a." + }, + { + "text": "That equation ought to be simple to handle." + }, + { + "text": "OK. And I'd like to be able to solve it." + }, + { + "text": "How would I find, if I start with a vector u0, and I multiply by a a hundred times, what have I got?" + }, + { + "text": "Well, I can certainly write down a formula for the answer." + }, + { + "text": "So what, what, so u1 is a u0." + }, + { + "text": "And u2 is, what's u2 then?" + }, + { + "text": "U2 I multiply it, u2 I get from u1 by another, multiplying by a, so I've got a twice." + }, + { + "text": "And my formula is uk, after k steps, I've multiplied by a k times the original u0." + }, + { + "text": "You see what I'm doing?" + }, + { + "text": "The next section is going to solve systems of differential equations." + }, + { + "text": "I'm going to have derivatives." + }, + { + "text": "This, this section is the nice one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk13.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..ba8214d8c636e4757a266d6617801174bc939d80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "It solves difference equations." + }, + { + "text": "I would call that a difference equation." + }, + { + "text": "It's conne- a first order." + }, + { + "text": "I would call that a first order system, because it connects only, it only goes up one level." + }, + { + "text": "And it's a system because these are vectors and that's a matrix." + }, + { + "text": "And the solution is just that." + }, + { + "text": "OK." + }, + { + "text": "But, that's a nice formula." + }, + { + "text": "That's the, like, the most compact formula I could ever get." + }, + { + "text": "U one hundred would be a to the one hundredth u0." + }, + { + "text": "But how would I actually find u one hundred?" + }, + { + "text": "How would I find, how would I discover what u one hundred is?" + }, + { + "text": "Let me, let me show you how." + }, + { + "text": "Here, here's the idea." + }, + { + "text": "If, so, to solve, to really solve, shall I say, to really solve." + }, + { + "text": "To really solve it, I would take this initial vector, u0, and I would write it as a combination of eigenvectors." + }, + { + "text": "To really solve, write, write u0 as a combination, say, certain amount of the first eigenvector plus a certain amount of the second eigenvector plus a certain amount of the last eigenvector." + }, + { + "text": "Now multiply by a." + }, + { + "text": "You want to, you got to see the magic of eigenvectors work." + }, + { + "text": "Multiply by a." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk14.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7843b2bf0cac762d1c12452cf36500ea4ad13370 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a u0 is what?" + }, + { + "text": "So a times that." + }, + { + "text": "A times, so what's, I can separate it out into n separate pieces and that's the whole point." + }, + { + "text": "That each of those pieces is going in its own merry way." + }, + { + "text": "Each of those pieces is an eigenvector, and when I multiply by a, what does this piece become?" + }, + { + "text": "So that's some amount of the first, let's suppose the eigenvectors are normalized to be unit vectors." + }, + { + "text": "So that says what the eigenvector is." + }, + { + "text": "It's, and I need some multiple of it to produce u0." + }, + { + "text": "OK. Now when I multiply by a, what do I get?" + }, + { + "text": "I get c1, which is just a factor, times a x1, but a x1 is lambda one x1." + }, + { + "text": "When I multiply this by a, I get c2 lambda two x2." + }, + { + "text": "And here I get cn lambda n xn." + }, + { + "text": "And suppose I multiply by a to the hundredth power now." + }, + { + "text": "Can we, can we, having done it, multiplied by a, let's multiply by a to the hundredth." + }, + { + "text": "What happens to this first term when I multiply by a to the one hundredth?" + }, + { + "text": "It's got that factor lambda to the hundredth." + }, + { + "text": "That's the key." + }, + { + "text": "That, that's what I mean by going its own merry way." + }, + { + "text": "It, it is pure eigenvector, it's exactly in a direction where multiplication by a just brings in a scalar factor lambda one." + }, + { + "text": "So a hundred times brings in this a hundred times." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk15.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7ee3348735378aa4049d33ec2a197d0ceb0c447c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Hundred times lambda two, hundred times lambda n. Actually, we're, what are we seeing here?" + }, + { + "text": "We're seeing, this same, lambda, capital lambda to the hundredth, as in the, as in the diagonalization, and we're seeing the S matrix, the matrix S of eigenvectors." + }, + { + "text": "That's what this has got to, this has got to amount to, a lambda to the hundredth power times an S times this vector C that's telling us how much of each one is in the original thing." + }, + { + "text": "So if, if I had to really find the hundredth power, I would take u0, I would expand it as a combination of eigenvectors, this is really S, the eigenvector matrix times C, the, the coefficient vector." + }, + { + "text": "And then I would immediately, then, by inserting these hundredth powers of eigenvalues, I'd have the answer." + }, + { + "text": "So the, the, huh, there must be, well, let's see." + }, + { + "text": "OK." + }, + { + "text": "It's, so, yeah." + }, + { + "text": "So if u100 is a to the hundredth times u0, and u0 is Sc, then you see this formula is just this formula, which is the way I would actually get hold of this, of this u100, which is, let me put it here, u100." + }, + { + "text": "The way I would actually get hold of that, see what, what the solution is after a hundred steps, would be expand the initial vector into eigenvectors and, and let each eigenvector go its own way, multiplying by a hundred at, by lambda at every step, and therefore by lambda to the hundredth power after a hundredth step." + }, + { + "text": "Can I do an example?" + }, + { + "text": "So that's, that's the, the formulas." + }, + { + "text": "Now let me take an example." + }, + { + "text": "I'll use the Fibonacci sequence as an example." + }, + { + "text": "So, so Fibonacci example." + }, + { + "text": "You remember the Fibonacci numbers?" + }, + { + "text": "If we start with one and one as F0, oh, I think I start with zero, maybe." + }, + { + "text": "Let zero and one be the first ones." + }, + { + "text": "So there's F0 and F1, the first two Fibonacci numbers." + }, + { + "text": "Then what's the rule for Fibonacci numbers?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk16.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..79c65e32781f7f304b504a6c390247abb9d26ac8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "They're the sum." + }, + { + "text": "The next one is the sum of those, so it's one." + }, + { + "text": "The next one is the sum of those, so it's two." + }, + { + "text": "The next one is the sum of those, so it's three." + }, + { + "text": "Well, it looks like one, two, three, four, five, but somehow it's not going to do that way." + }, + { + "text": "The next one is five, right." + }, + { + "text": "Two and three makes five." + }, + { + "text": "The next one is eight." + }, + { + "text": "The next one is thirteen." + }, + { + "text": "And the one hundredth Fibonacci number is what?" + }, + { + "text": "That's my question." + }, + { + "text": "How could I get a formula for the hundredth number and for example how could I answer the question how fast are they growing?" + }, + { + "text": "How fast are those Fibonacci numbers growing?" + }, + { + "text": "They're certainly growing." + }, + { + "text": "It's not a stable case, whatever the eigenvalues of whatever matrix it is, they're not smaller than one." + }, + { + "text": "These numbers are growing." + }, + { + "text": "But how fast are they growing?" + }, + { + "text": "The answer is lies in the eigenvalue." + }, + { + "text": "So I've got to find the matrix, so let me write down the Fibonacci rule, F k plus two is F k plus one plus F k, right?" + }, + { + "text": "Now that's not in my -- I want to write that as U k plus one and A U k. But right now what I've got is a single equation, not a system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk17.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b3aaa9dcee3cf27c112015659bb5a0b51a983ce1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's second order." + }, + { + "text": "It's like having a second order differential equation with second derivatives." + }, + { + "text": "I want to get first derivatives." + }, + { + "text": "Here I want to get first difference." + }, + { + "text": "So the way to do it is to introduce U k will be a vector." + }, + { + "text": "See, a small trick." + }, + { + "text": "Let U k be a vector, F k plus one and F k. So I'm going to get a two by two system, first order, instead of a one, instead of a scalar system, second order, by a simple trick." + }, + { + "text": "I'm just going to add in an equation F k plus one equals F k plus one." + }, + { + "text": "That will be my second equation." + }, + { + "text": "Then this is my system, this is my unknown, and what's my one-step equation?" + }, + { + "text": "So now U k plus one." + }, + { + "text": "That's so U k plus one is the left side, and what have I got here on the right side?" + }, + { + "text": "I've got some matrix multiplying U k. Can you see that all right?" + }, + { + "text": "If you can see it, then you can tell me what the matrix is." + }, + { + "text": "You see that I'm taking my system here, I artificially made it into a system." + }, + { + "text": "I artificially made the unknown into a vector, and now I'm ready to look at and see what the matrix is." + }, + { + "text": "So do you see the left side, U k plus one is F k plus two F k plus one, that's just what I want." + }, + { + "text": "On the right side, this, remember, this U k here, let me for the moment put it as F k plus one F k. So what's the matrix?" + }, + { + "text": "Well, that has a one and a one, and that has a one and a zero." + }, + { + "text": "There's the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk18.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..6c1b68c2cb2fde3f5dea82f3100d4da31fcce70a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "You see that that gives me the right-hand side." + }, + { + "text": "So there's the matrix A, and this is our friend U k. So we've got, so that simple trick changed the second order scalar problem to a first order system, two, with two unknowns." + }, + { + "text": "With a matrix and now what do I do?" + }, + { + "text": "Well, before I even think, I find its eigenvalues and eigenvectors." + }, + { + "text": "So what are the eigenvalues and eigenvectors of that matrix?" + }, + { + "text": "Let's see." + }, + { + "text": "I was, first let me just, like, think for a minute." + }, + { + "text": "It's two by two, so this shouldn't be impossible to do." + }, + { + "text": "Let's do it." + }, + { + "text": "OK." + }, + { + "text": "So my matrix again is one one one zero." + }, + { + "text": "It's symmetric, by the way." + }, + { + "text": "So what I will eventually know about symmetric matrices is that the eigenvalues will come out real, I won't get any complex numbers here, and the eigenvectors, once I get those, actually will be orthogonal." + }, + { + "text": "But two by two, I'm more interested in what the actual numbers are." + }, + { + "text": "What do I know about the two numbers?" + }, + { + "text": "Well, should, do you want me to find this determinant of A minus lambda I?" + }, + { + "text": "Sure." + }, + { + "text": "So it's the determinant of one minus lambda one one zero, right?" + }, + { + "text": "Minus lambda, yes, got it." + }, + { + "text": "OK. OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk19.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..a73b23e3d56b889ff49ea7f55a784fac33e13c3d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "There'll be two eigenvalues." + }, + { + "text": "Well, tell me again what I know about the two eigenvalues before I go any further." + }, + { + "text": "Tell me something about these two eigenvalues, what do they add up to?" + }, + { + "text": "Lambda one plus lambda two is the same as the trace down the diagonal of the matrix, one and zero is one." + }, + { + "text": "So lambda one plus lambda two should come out to be one, and lambda one times lambda two should come out to be the determinant, which is minus one." + }, + { + "text": "So I'm expecting the eigenvalues to add to one and to multiply to minus one." + }, + { + "text": "But let's just see it happen here." + }, + { + "text": "If I multiply this out, I get that times that'll be a lambda squared minus lambda minus one." + }, + { + "text": "Good." + }, + { + "text": "Lambda squared minus lambda minus one." + }, + { + "text": "Actually, you see the, compare that with the original equation that I started with." + }, + { + "text": "Fk plus two minus Fk plus one minus Fk is zero." + }, + { + "text": "The recurrent, the recursion that the Fibonacci number satisfy is somehow showing up directly here for the eigenvalues when we set that to zero." + }, + { + "text": "OK. Let's solve." + }, + { + "text": "Well, I would like to be able to factor that, that quadratic, but I'm better off to use the quadratic formula." + }, + { + "text": "Lambda is, let's see, minus b is one, plus or minus the square root of b squared, which is one, minus four, times that, times that, which is plus four, over two." + }, + { + "text": "So that's the square root of five." + }, + { + "text": "So the eigenvalues are lambda one is one half of one plus square root of five, and lambda two is one half of one minus square root of five." + }, + { + "text": "And sure enough, they, those add up to one, and they multiply to give minus one." + }, + { + "text": "OK. Those are the two eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk2.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..43cfb012fc04a89fc7dab94c23bfb0f50ade3782 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "On the right, it's multiplied by, if I want, if I want lambda n xn in the last column, how do I do it?" + }, + { + "text": "Well, the last column here will be, I'll, I'll take the last column, use these coefficients, put the lambda n down there, and it will multiply that nth column and give me lambda n xn." + }, + { + "text": "There, there you see matrix multiplication just working for us." + }, + { + "text": "So I started with A s. I wrote down what it meant." + }, + { + "text": "A times each eigenvector." + }, + { + "text": "That gave me lambda times the eigenvector." + }, + { + "text": "And then when I peeled off the lambdas, they were on the right-hand side, so I've got s, my matrix back again, and this matrix, this diagonal matrix, the eigenvalue matrix, and I call it capital lambda, using capital letters for matrices, and lambda to prompt me that it's, that it's eigenvalues that are in there." + }, + { + "text": "So you see that the eigenvalues are just sitting down that diagonal?" + }, + { + "text": "If I had a column x2 here, I would want the lambda two in the two two position, in the diagonal position, to multiply that x2 and give me the lambda two x2." + }, + { + "text": "That's my formula." + }, + { + "text": "A s is s lambda." + }, + { + "text": "OK. That's, that's the, you see, it's just a calculation." + }, + { + "text": "Now, I, I mentioned, and I have to mention again, this business about n independent eigenvectors." + }, + { + "text": "As it stands, this is all fine whether, I mean, I could be repeating the same eigenvector, but I, I'm no interested in that." + }, + { + "text": "I want to be able to invert s, and that's where this comes in." + }, + { + "text": "This n independent eigenvectors business comes in to tell me that that matrix is invertible." + }, + { + "text": "So let me, on the next board, write down what I've got." + }, + { + "text": "A s equals s lambda." + }, + { + "text": "And now I'm, I can multiply on the left by s inverse." + }, + { + "text": "So this is really, I can do that provided s is invertible, provided my assumption of n independent eigenvectors is satisfied." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk20.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ad5a59fa5db44ce73ff5f88190423e0404fb3d39 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "How, how, what are those numbers approximately?" + }, + { + "text": "Square root of five, well, it's more than two, but less than three." + }, + { + "text": "It, it'd be nice to know these numbers." + }, + { + "text": "I think, I think that that, so that number comes out bigger than one, right?" + }, + { + "text": "Yeah, that's right." + }, + { + "text": "This number comes out bigger than one." + }, + { + "text": "It's about one point six one eight or something." + }, + { + "text": "Not exactly." + }, + { + "text": "It's supposed to be one point six." + }, + { + "text": "Just, like, I think so." + }, + { + "text": "Then what's lambda two?" + }, + { + "text": "Is, is lambda two positive or negative?" + }, + { + "text": "Negative, right?" + }, + { + "text": "Because I'm, it's obviously negative, and I knew that the, so it's minus, and they add up to one, so minus point six one eight, I guess." + }, + { + "text": "OK. And some order." + }, + { + "text": "Those are the two eigenvalues." + }, + { + "text": "One eigenvalue bigger than one, one eigenvalue smaller than one." + }, + { + "text": "Actually, that's a great situation to be in." + }, + { + "text": "Of course, the eigenvalues are different, so there's no doubt whatever, is this matrix diagonalizable?" + }, + { + "text": "Is this matrix diagonalizable, that original matrix A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk21.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..4a034475591d371995b379b5f98783a2cfb25870 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Sure." + }, + { + "text": "We've got two distinct eigenvalues and we can find the eigenvectors in a moment." + }, + { + "text": "But they'll be independent, will be diagonalizable, and now you can already answer my very first question." + }, + { + "text": "How fast are those Fibonacci numbers increasing?" + }, + { + "text": "How, those, they're increasing, right?" + }, + { + "text": "They're not doubling at every step." + }, + { + "text": "Let's look again at these numbers." + }, + { + "text": "Five eight thirteen, it's not obvious." + }, + { + "text": "The next one would be twenty one thirty four." + }, + { + "text": "So to get some idea of what F one hundred is, can you give me any, I mean the crucial number of, so it, these, it's approximately, what's controlling the growth of these Fibonacci numbers?" + }, + { + "text": "It's the eigenvalues." + }, + { + "text": "And which eigenvalues controlling that growth?" + }, + { + "text": "The big ones." + }, + { + "text": "So F one hundred will it be approximately some constant, c one, I guess, times this lambda one, this one plus square root of five over two, to the hundredth power." + }, + { + "text": "And the two hundredth have, in other words, the eigenvalue, the Fibonacci numbers are growing by about that factor." + }, + { + "text": "You see that we've got precise information about the, about the Fibonacci numbers out of the eigenvalue." + }, + { + "text": "OK. And again, why is that true?" + }, + { + "text": "Let me go over to this board and show what I'm doing here." + }, + { + "text": "The, the original eigen, the original initial value is some combination of eigenvectors, and then when we start multiple, when we start going out the theory of Fibonacci numbers, when we start multiplying by a hundred times, it's this lambda one to the hundredth, this term is, is the one that's taken over." + }, + { + "text": "It's, I mean, that's big, like, one point six to the hundredth power." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk22.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..c13a1fc9867173c3067e46c469cfff27b9b45289 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "The second term is practically nothing, right?" + }, + { + "text": "The point six, or minus point six to the hundredth power, is an extremely small, extremely small number." + }, + { + "text": "So this is, this, this, there are only two terms, because we're two by two." + }, + { + "text": "This number is, this piece of it is there, but it's, it's disappearing." + }, + { + "text": "Where this piece is there and it's growing and controlling everything." + }, + { + "text": "So, so really the, we're doing, like, problems that are evolving." + }, + { + "text": "We're doing dynamics." + }, + { + "text": "Instead of Ax equal b, that's a static problem." + }, + { + "text": "We're now, we're doing dynamics." + }, + { + "text": "A, a squared, a cubed, things are evolving in time, and the eigenvalues are the crucial, numbers." + }, + { + "text": "OK." + }, + { + "text": "I guess to complete this, I better write down the eigenvectors." + }, + { + "text": "So we should complete the, the whole process by finding the eigenvectors." + }, + { + "text": "OK. Well, I have to, up in the corner, then I have to look at A minus lambda I." + }, + { + "text": "So A minus lambda I is this one minus lambda, one, one, and minus lambda." + }, + { + "text": "And now, can we spot an eigenvector out of that?" + }, + { + "text": "That's, for these two lambdas, this matrix is singular." + }, + { + "text": "I guess the eigenvector, two by two ought to be easy." + }, + { + "text": "So if I know that this matrix is singular, then it seems to me the eigenvector has to be lambda and one, because that multiplication will give me the zero." + }, + { + "text": "And this multiplication gives me, better give me also zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk23.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..df816eb800ce767b1475c279a24ad976bb45a785 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Do you see why it does?" + }, + { + "text": "This is the minus lambda squared plus lambda plus one." + }, + { + "text": "It's the thing that's zero, because these lambdas are special." + }, + { + "text": "There's the eigenvector." + }, + { + "text": "X1 is lambda one, one, and x2 is lambda two, one." + }, + { + "text": "I did that as a little trick that was available in the two by two case." + }, + { + "text": "So now I finally have to, oh, I have to take the initial, u0." + }, + { + "text": "So to complete this example entirely, I have to say, OK, what was u0?" + }, + { + "text": "u0 was f1 f0." + }, + { + "text": "So u0, the starting vector, is f1 f0, and those were one and zero." + }, + { + "text": "So I have to use that vector, so I have to look for, from multiple of the first eigenvector and the second, to produce u0, the one zero vector." + }, + { + "text": "This is what will find c1 and c2, and then I'm done." + }, + { + "text": "So let me, instead of in the last five seconds grinding out a formula, let me repeat the idea." + }, + { + "text": "That really, it's the idea that's central." + }, + { + "text": "When things are evolving in time, let me come back to this board, because the ideas are here." + }, + { + "text": "When things are evolving in time by a first-order system, starting from an original u0, the key is, find the eigenvalues and eigenvectors of A." + }, + { + "text": "That will tell, those eigenvectors, the eigenvalues will already tell you what's happening." + }, + { + "text": "Is the solution blowing up?" + }, + { + "text": "Is it going to zero?" + }, + { + "text": "What's it doing?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk24.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..40301cb90760e2172baa94d536cbc13288d4c31f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk24.json @@ -0,0 +1,20 @@ +[ + { + "text": "And then, to find out exactly a formula, you have to take your u0 and write it as a combination of eigenvectors and then follow each eigenvector separately." + }, + { + "text": "And that's really what this formula, the formula for, that's what the formula for A to the k is doing." + }, + { + "text": "So remember that formula for A to the k is S, lambda to the k S inverse." + }, + { + "text": "OK. That's, that's difference equations, and you just have to, so the homework will give some examples different from Fibonacci to follow through." + }, + { + "text": "And next time will be differential equations." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk3.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..9bf1bb852baadc1da7837e14180c0c2951a30882 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I mentioned at the end of last time, and I'll say again, that there's a small number of matrices for, that don't have n independent eigenvectors." + }, + { + "text": "So I've got to discuss that, that technical point." + }, + { + "text": "But the great, the most matrices that we see have n, n independent eigenvectors and we can diagonalize." + }, + { + "text": "This is diagonalization." + }, + { + "text": "I could also write it, and I often will, the other way round." + }, + { + "text": "If I multiply on the right by s inverse, if I took this equation at the top and multiplied on the right by s inverse, I could, I would have A left here." + }, + { + "text": "Now s inverse is coming from the right." + }, + { + "text": "So can you keep those two straight?" + }, + { + "text": "A multiplies its eigenvectors." + }, + { + "text": "That's how I keep them straight." + }, + { + "text": "So A multiplies s. A multiplies s. And then this s inverse makes the whole thing diagonal." + }, + { + "text": "And this is another way of saying the same thing, putting the s's on the other side of the equation, A is s lambda s inverse." + }, + { + "text": "So that's the, that's the new factorization." + }, + { + "text": "That's the replacement for L U from elimination or Q R from Gram-Schmidt." + }, + { + "text": "And notice that the matrix, so it's, it's a matrix times a diagonal matrix times the inverse of the first one." + }, + { + "text": "It's, that's the combination that we'll see throughout this chapter." + }, + { + "text": "This, this, combination with an s and an s inverse." + }, + { + "text": "OK. Can I just begin to use that?" + }, + { + "text": "For example, what about A squared?" + }, + { + "text": "What are the eigenvalues and eigenvectors of A squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk4.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c687b6948acad76de8781cb82d3eb069c9da514e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's a straightforward question with a, with a absolutely clean answer." + }, + { + "text": "So let me, let me consider A squared." + }, + { + "text": "So I look, I start with Ax equal lambda x." + }, + { + "text": "And I'm headed for A squared." + }, + { + "text": "So let me multiply both sides by A." + }, + { + "text": "That's one way to get A squared on the left." + }, + { + "text": "So if, I should write these ifs in here." + }, + { + "text": "If Ax equals lambda x, then I multiply by A." + }, + { + "text": "So I get A squared x equals, well, I'm multiplying by A, so that's lambda Ax." + }, + { + "text": "That lambda was a number, so I just put it on the left." + }, + { + "text": "And what do I, tell me how to make that look better." + }, + { + "text": "What have I got here?" + }, + { + "text": "For, if, if A has the eigenvalue lambda and eigenvector x, what's up with A squared?" + }, + { + "text": "A squared x, I just multiply by A, but now for Ax, I'm going to substitute lambda x, so I've got lambda squared x." + }, + { + "text": "So from that simple calculation, I, my conclusion is that the eigenvalues of A squared are lambda squared." + }, + { + "text": "And the eigenvectors, I always think about both of those." + }, + { + "text": "What can I say about the eigenvalues?" + }, + { + "text": "They're squared." + }, + { + "text": "What can I say about the eigenvectors?" + }, + { + "text": "They're the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk5.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5bf15e20707c156c8ae71c9c7acea41a9d9d8e46 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same x as in, as for A." + }, + { + "text": "Now, let me see that also from this formula." + }, + { + "text": "How can I see what A squared is looking like from this formula?" + }, + { + "text": "So let me, that, that was one way to do it." + }, + { + "text": "Let me do it by just taking A squared from that." + }, + { + "text": "A squared is S lambda S inverse, that's A, times S lambda S inverse, that's A, which is?" + }, + { + "text": "This is the beauty of eigenvalues, eigenvectors, having that S inverse and S is the identity, so I've got S lambda squared S inverse." + }, + { + "text": "Yes." + }, + { + "text": "You see what that's telling me?" + }, + { + "text": "It's, it's telling me the same thing that I just learned here, but in the, in, in a matrix form." + }, + { + "text": "It's telling me that the S is the same, the eigenvectors are the same, but the eigenvalues are squared, because this is, what's lambda squared, that's still diagonal, it's got little lambda one squared, lambda two squared, down to lambda n squared, on that diagonal, those are the eigenvalues, as we just learned, of A squared." + }, + { + "text": "OK." + }, + { + "text": "So, somehow those eigenvalues and eigenvectors are really giving you a way to, to, to, to see what's going on inside a matrix." + }, + { + "text": "Now, of course, I can continue that for, to the k-th power." + }, + { + "text": "A to the k-th power." + }, + { + "text": "If I multiply, if I have k of these together, do you see how S inverse S will keep cancelling?" + }, + { + "text": "In the, in the inside, I'll have the S outside, at the far left, and lambda will be in there k times and S inverse." + }, + { + "text": "So what's that telling me?" + }, + { + "text": "That's telling me that the eigenvalues of A, of A to the k-th power are the k-th powers." + }, + { + "text": "The eigenvalues of A cubed are the cubes of the eigenvalues of A, and the eigenvectors are the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk6.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..c18dddbe798022f7e68278ac002a3f5fe6ed249e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same." + }, + { + "text": "OK." + }, + { + "text": "In other words, eigenvalues and eigenvectors give a great way to understand the powers of a matrix." + }, + { + "text": "If I take the square of a matrix or the hundredth power of a matrix, the pivots are all over the place." + }, + { + "text": "L U, if I multiply L U times L U times L U times L U a hundred times, I've got a hundred L U's." + }, + { + "text": "I can't do anything with them." + }, + { + "text": "But when I multiply S lambda S inverse by itself, when I look at the eigenvector picture a hundred times, I get a hundred or ninety-nine of these guys cancelling out inside, and I get A to the hundredth is S lambda to the hundredth S inverse." + }, + { + "text": "I mean, eigenvalues tell you about powers of a matrix in a way that we had no, no way to approach previously." + }, + { + "text": "For example, when does, when do the powers of a matrix go to zero?" + }, + { + "text": "I would call that matrix stable, maybe." + }, + { + "text": "So, so, so I could write down a, a theorem." + }, + { + "text": "I'll, I'll write it as a theorem, just to use that word to emphasize that here I'm getting this great fact from this eigenvalue picture." + }, + { + "text": "OK. A to the k approaches zero as k goes, as k gets bigger." + }, + { + "text": "If what?" + }, + { + "text": "What's the, how can I tell for a matrix A if its powers go to zero?" + }, + { + "text": "What, what's somewhere inside that matrix is that information." + }, + { + "text": "That information is not present in the pivots." + }, + { + "text": "It's present in the eigenvalues." + }, + { + "text": "What do I need for the, to know that if I take higher and higher powers of A that this matrix gets smaller and smaller?" + }, + { + "text": "Well, S and S inverse are not moving." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk7.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b84a5c854a5542758e8a0107e1ff043205fe3bdb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's this guy that has to get small, and that's easy to, easy to understand." + }, + { + "text": "The requirement is all eigenvalues, so what is the requirement?" + }, + { + "text": "The eigenvalues have to be less than one." + }, + { + "text": "Now, I have to write that absolute value, because those eigenvalues could be negative, they could be complex numbers." + }, + { + "text": "So I'm taking the absolute value if all of those are below one." + }, + { + "text": "That's, in fact, we practically see why." + }, + { + "text": "Let me just say that I, that I, I'm operating on one assumption here, and I got to keep remembering that that assumption is still present." + }, + { + "text": "That assumption was that I had a full set of, of n independent eigenvectors." + }, + { + "text": "If I don't have that, then I, I, then this approach is not working." + }, + { + "text": "So, so again, a pure eigenvalue approach, eigenvector approach, needs n independent eigenvectors." + }, + { + "text": "If we don't have n independent eigenvectors, we can't diagonalize the matrix." + }, + { + "text": "We can't get to a diagonal matrix." + }, + { + "text": "This, this, this diagonalization is only possible if S inverse makes sense." + }, + { + "text": "OK. Can I, can I follow up on that point now?" + }, + { + "text": "So, so you see why, what we get and, and why we want it, because we get information about the powers of a matrix just immediately from the eigenvalues." + }, + { + "text": "OK, now let me follow up on this, business of which matrices are diagonalizable." + }, + { + "text": "Sorry about that long word." + }, + { + "text": "So a matrix is, is sure to, so here's, here's the main point." + }, + { + "text": "A is sure to be, to have n independent eigenvectors and, and B, now here comes that word, diagonalizable, if, if, so we, we, we might as well get the, the nice case out in the open." + }, + { + "text": "The nice case is when, if all the lambdas are different." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk8.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f06dcec8ffa0ee1bf19440e4ab2194db33ab353b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means, that means no repeated eigenvalues." + }, + { + "text": "OK. That's the nice case." + }, + { + "text": "If, if my matrix and most matrix, if I do a random matrix in MATLAB and compute its eigenvalues, so if I computed, if I took I of rand of ten ten, gave, gave that MATLAB command, the, we'd get a random ten by ten matrix, we would get a list of its ten eigenvalues and they would be different." + }, + { + "text": "They would be distinct, is the best word." + }, + { + "text": "I would have a random matrix will have ten distinct, a ten by ten matrix will have ten distinct eigenvalues, and if it does, the eigenvectors are automatically independent." + }, + { + "text": "So that's a nice fact." + }, + { + "text": "I can, I'll refer you to the text for the proof." + }, + { + "text": "That, that A is sure to have n independent eigenvectors if the eigenvalues are different." + }, + { + "text": "If, if all the, if all eigenvalues are different." + }, + { + "text": "It's just, if some lambdas are repeated, then I have to look more closely." + }, + { + "text": "If an eigenvalue is repeated, I have to look, I have to count, I have to check." + }, + { + "text": "Has it got, say it's repeated three times." + }, + { + "text": "So what's a possibility for, so, so here's, here's the repeated possibility." + }, + { + "text": "And, and let me emphasize the conclusion." + }, + { + "text": "That if I have repeated eigenvalues, I may or may not, I may or may not have, have n independent eigenvectors." + }, + { + "text": "I might." + }, + { + "text": "I, I, you know, this isn't a completely negative case." + }, + { + "text": "The identity matrix." + }, + { + "text": "Well, suppose I take the ten by ten identity matrix." + }, + { + "text": "What are the eigenvalues of that matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk9.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..87d2a2ae5773036cf11800e2f1962908986a0dad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_17_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So just, just take the easiest matrix, the identity." + }, + { + "text": "If I look for its eigenvalues, they're all ones." + }, + { + "text": "So that eigenvalue one is repeated ten times." + }, + { + "text": "But there's no shortage of eigenvectors for the identity matrix." + }, + { + "text": "In fact, every vector is an eigenvector." + }, + { + "text": "So I can take ten independent vectors." + }, + { + "text": "Oh, well, what happens to everything if, if, if A is the identity matrix, let's just think that one through in our head." + }, + { + "text": "If A is the identity matrix, then it's got plenty of eigenvectors." + }, + { + "text": "I choose ten independent vectors, they're the columns of S, and, and what do I get from S inverse A S?" + }, + { + "text": "I get I again, right?" + }, + { + "text": "If A is the identity, and of course, that's the correct lambda." + }, + { + "text": "The, the matrix was already diagonal." + }, + { + "text": "So if the matrix is already diagonal, then the, the lambda is the same as the matrix." + }, + { + "text": "A diagonal matrix has got its eigenvalues sitting right there in front of you." + }, + { + "text": "Now if it's triangular, the eigenvalues are still sitting there, but so let's, let's take a case where, it's triangular." + }, + { + "text": "Suppose A is like, two, one, two, zero." + }, + { + "text": "So there's a case that's going to be trouble." + }, + { + "text": "There's a case that's going to be trouble." + }, + { + "text": "First of all, what are the eigen- I mean, we just, like now you, if we start with a matrix, the first thing we do practically without thinking is compute the eigenvalues and eigenvectors." + }, + { + "text": "OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk0.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6898d4fe66019ef6b40d0472ea94a968e7bbde9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, shall we start?" + }, + { + "text": "This is the second lecture on eigenvalues." + }, + { + "text": "So the first lecture was set -- reached the key equation, Ax equal lambda x. x is the eigenvector and lambda is the eigenvalue." + }, + { + "text": "Now, to use that." + }, + { + "text": "And the good way to, after we've found, so job one is to find the eigenvalues and find the eigenvectors." + }, + { + "text": "Now after we found them, what do we do with them?" + }, + { + "text": "Well, the good way to see that is diagonalize the matrix." + }, + { + "text": "So the matrix is A, and I want to show, first of all, this is like the basic fact." + }, + { + "text": "This, this formula." + }, + { + "text": "That's, that's the key to today's lecture." + }, + { + "text": "This matrix A, I put its eigenvectors in the columns of a matrix S. So S will be the eigenvector matrix, and I want to look at this magic combination S inverse A S. So can I show you how that, how that, what happens there?" + }, + { + "text": "And notice, notice, there's an S inverse." + }, + { + "text": "We have to be able to invert this eigenvector matrix S. So for that we need n independent eigenvectors." + }, + { + "text": "So that's the, that's the case." + }, + { + "text": "OK." + }, + { + "text": "So suppose we have n linearly independent eigenvectors of A." + }, + { + "text": "Put them in the columns of this matrix S. So I'm naturally going to call that the eigenvector matrix, because it's got the eigenvectors in its columns." + }, + { + "text": "And all I want to do is show you what happens when you multiply A times S. So A times S. So this is A times the matrix with the first eigenvector in its first column, the second eigenvector in its second column, the nth eigenvector in its nth column." + }, + { + "text": "And how am I going to do this matrix multiplication?" + }, + { + "text": "Well, certainly I'll do it a column at a time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk1.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..fbe078217bb68baea8e0605a5d04be568c49efbf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I get?" + }, + { + "text": "A times the first column gives me the first column of the answer, but what is it?" + }, + { + "text": "That's an eigenvector." + }, + { + "text": "A times x1 is equal to the lambda times the x1." + }, + { + "text": "And that lambda's we'll call lambda one, of course." + }, + { + "text": "So that's the first column, A x1 is the same as lambda one x1." + }, + { + "text": "A x2 is lambda two x2, so on, along to, in the nth column, we now have lambda n xn." + }, + { + "text": "Looking good, but the next step is even better." + }, + { + "text": "So for the next step, I want to separate out those eigenvalues, those multiplying numbers, from the x's." + }, + { + "text": "So then I'll have just what I want." + }, + { + "text": "OK, so how, how am I going to separate out?" + }, + { + "text": "So that, that number lambda one is multiplying the first column." + }, + { + "text": "So if I want to factor it out of the first column, I better put, here is going to be x1, and that's going to multiply this matrix lambda one in the first entry in all zeros." + }, + { + "text": "You see that that, that's going to come out right for the first column?" + }, + { + "text": "Because we remember how, how we're going back to that original punchline, that if I want a number to multiply x1, then I can do it by putting x1 in that column, in the first column, and putting that number there." + }, + { + "text": "What am I going to have here?" + }, + { + "text": "I'm going to have lambda one, I'm going to have x1, x2, xn." + }, + { + "text": "These are going to be my columns again." + }, + { + "text": "I'm getting s back again." + }, + { + "text": "I'm getting s back again, but now what's it multiplied by?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk10.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c58a42edbe9567233ca7f57643a0b7d43ae6761f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what are the eigenvalues?" + }, + { + "text": "You can tell me right away what they are." + }, + { + "text": "They're two and two, right." + }, + { + "text": "It's a triangular matrix, so when I do this determinant, shall I do this determinant of A minus lambda I?" + }, + { + "text": "I'll get this two minus lambda, one, zero, two minus lambda, right?" + }, + { + "text": "I take that determinant, so I make those into vertical bars to mean determinant, and what's the determinant?" + }, + { + "text": "Two minus lambda squared." + }, + { + "text": "What are the roots?" + }, + { + "text": "Lambda equal two twice." + }, + { + "text": "So the eigenvalues are lambda equals two and two." + }, + { + "text": "OK, fine." + }, + { + "text": "Now the next step, find the eigenvectors." + }, + { + "text": "So I look for eigenvectors and what do I find for this guy?" + }, + { + "text": "Eigenvectors for this guy, when I subtract two minus the identity, so A minus two I has zeros here, and I'm looking for the null space." + }, + { + "text": "What's, what are the eigenvectors?" + }, + { + "text": "They're the, they're, they're the null space of A minus lambda I." + }, + { + "text": "The null space is only one dimension." + }, + { + "text": "This is a case where I don't have enough eigenvectors." + }, + { + "text": "My algebraic multiplicity is two." + }, + { + "text": "I, I would say when I see, when I count how often the eigenvalue is repeated, that's the algebraic multiplicity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk11.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..779c2cf904d904b761080db2671aac46394ad02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the multiplicity." + }, + { + "text": "How many times is it the root of the polynomial?" + }, + { + "text": "My polynomial is two minus lambda squared." + }, + { + "text": "It's a double root." + }, + { + "text": "So my algebraic multiplicity is two." + }, + { + "text": "But the geometric multiplicity, which looks for vectors, looks for eigenvectors and which means the null space of this thing." + }, + { + "text": "And the only eigenvector is one zero." + }, + { + "text": "That's in the null space." + }, + { + "text": "Zero one is not in the null space." + }, + { + "text": "The null space is only one dimensional." + }, + { + "text": "So there's a matrix, my, this A or the original A, that are not diagonalizable." + }, + { + "text": "I can't, I can't find two independent eigenvectors, there's only one." + }, + { + "text": "OK." + }, + { + "text": "So that's the case that I'm, that's a case that I, I'm not really handling." + }, + { + "text": "For example, when I wrote down up here that the powers went to zero if the eigenvalues were below one, I didn't really handle that case of repeated eigenvalues because my reasoning was based on this formula." + }, + { + "text": "And this formula is based on n independent eigenvectors." + }, + { + "text": "OK." + }, + { + "text": "So just to say that." + }, + { + "text": "There are some matrices that we don't cover through diagonalization, but the great majority we do." + }, + { + "text": "OK. And we're always OK if we have different distinct eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk12.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..77d090704cc298475d94416b7ecb88a2a015a913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. That's the, like, the typical case." + }, + { + "text": "Because for each eigenvalue there's at least one eigenvector, the algebraic multiplicity here is one for every eigenvalue, and the geometric multiplicity is one." + }, + { + "text": "There's one eigenvector and they are independent." + }, + { + "text": "OK. OK. Now let me come back to the important case when we're OK." + }, + { + "text": "The important case when we are diagonalizing." + }, + { + "text": "Let me look at, so let me solve this equation." + }, + { + "text": "The equation will be each, I start with some, start with a given vector u0." + }, + { + "text": "And then my equation is that every step I multiply what I have by a." + }, + { + "text": "That equation ought to be simple to handle." + }, + { + "text": "OK. And I'd like to be able to solve it." + }, + { + "text": "How would I find, if I start with a vector u0, and I multiply by a a hundred times, what have I got?" + }, + { + "text": "Well, I can certainly write down a formula for the answer." + }, + { + "text": "So what, what, so u1 is a u0." + }, + { + "text": "And u2 is, what's u2 then?" + }, + { + "text": "U2 I multiply it, u2 I get from u1 by another, multiplying by a, so I've got a twice." + }, + { + "text": "And my formula is uk, after k steps, I've multiplied by a k times the original u0." + }, + { + "text": "You see what I'm doing?" + }, + { + "text": "The next section is going to solve systems of differential equations." + }, + { + "text": "I'm going to have derivatives." + }, + { + "text": "This, this section is the nice one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk13.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..ba8214d8c636e4757a266d6617801174bc939d80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "It solves difference equations." + }, + { + "text": "I would call that a difference equation." + }, + { + "text": "It's conne- a first order." + }, + { + "text": "I would call that a first order system, because it connects only, it only goes up one level." + }, + { + "text": "And it's a system because these are vectors and that's a matrix." + }, + { + "text": "And the solution is just that." + }, + { + "text": "OK." + }, + { + "text": "But, that's a nice formula." + }, + { + "text": "That's the, like, the most compact formula I could ever get." + }, + { + "text": "U one hundred would be a to the one hundredth u0." + }, + { + "text": "But how would I actually find u one hundred?" + }, + { + "text": "How would I find, how would I discover what u one hundred is?" + }, + { + "text": "Let me, let me show you how." + }, + { + "text": "Here, here's the idea." + }, + { + "text": "If, so, to solve, to really solve, shall I say, to really solve." + }, + { + "text": "To really solve it, I would take this initial vector, u0, and I would write it as a combination of eigenvectors." + }, + { + "text": "To really solve, write, write u0 as a combination, say, certain amount of the first eigenvector plus a certain amount of the second eigenvector plus a certain amount of the last eigenvector." + }, + { + "text": "Now multiply by a." + }, + { + "text": "You want to, you got to see the magic of eigenvectors work." + }, + { + "text": "Multiply by a." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk14.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7843b2bf0cac762d1c12452cf36500ea4ad13370 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a u0 is what?" + }, + { + "text": "So a times that." + }, + { + "text": "A times, so what's, I can separate it out into n separate pieces and that's the whole point." + }, + { + "text": "That each of those pieces is going in its own merry way." + }, + { + "text": "Each of those pieces is an eigenvector, and when I multiply by a, what does this piece become?" + }, + { + "text": "So that's some amount of the first, let's suppose the eigenvectors are normalized to be unit vectors." + }, + { + "text": "So that says what the eigenvector is." + }, + { + "text": "It's, and I need some multiple of it to produce u0." + }, + { + "text": "OK. Now when I multiply by a, what do I get?" + }, + { + "text": "I get c1, which is just a factor, times a x1, but a x1 is lambda one x1." + }, + { + "text": "When I multiply this by a, I get c2 lambda two x2." + }, + { + "text": "And here I get cn lambda n xn." + }, + { + "text": "And suppose I multiply by a to the hundredth power now." + }, + { + "text": "Can we, can we, having done it, multiplied by a, let's multiply by a to the hundredth." + }, + { + "text": "What happens to this first term when I multiply by a to the one hundredth?" + }, + { + "text": "It's got that factor lambda to the hundredth." + }, + { + "text": "That's the key." + }, + { + "text": "That, that's what I mean by going its own merry way." + }, + { + "text": "It, it is pure eigenvector, it's exactly in a direction where multiplication by a just brings in a scalar factor lambda one." + }, + { + "text": "So a hundred times brings in this a hundred times." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk15.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7ee3348735378aa4049d33ec2a197d0ceb0c447c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Hundred times lambda two, hundred times lambda n. Actually, we're, what are we seeing here?" + }, + { + "text": "We're seeing, this same, lambda, capital lambda to the hundredth, as in the, as in the diagonalization, and we're seeing the S matrix, the matrix S of eigenvectors." + }, + { + "text": "That's what this has got to, this has got to amount to, a lambda to the hundredth power times an S times this vector C that's telling us how much of each one is in the original thing." + }, + { + "text": "So if, if I had to really find the hundredth power, I would take u0, I would expand it as a combination of eigenvectors, this is really S, the eigenvector matrix times C, the, the coefficient vector." + }, + { + "text": "And then I would immediately, then, by inserting these hundredth powers of eigenvalues, I'd have the answer." + }, + { + "text": "So the, the, huh, there must be, well, let's see." + }, + { + "text": "OK." + }, + { + "text": "It's, so, yeah." + }, + { + "text": "So if u100 is a to the hundredth times u0, and u0 is Sc, then you see this formula is just this formula, which is the way I would actually get hold of this, of this u100, which is, let me put it here, u100." + }, + { + "text": "The way I would actually get hold of that, see what, what the solution is after a hundred steps, would be expand the initial vector into eigenvectors and, and let each eigenvector go its own way, multiplying by a hundred at, by lambda at every step, and therefore by lambda to the hundredth power after a hundredth step." + }, + { + "text": "Can I do an example?" + }, + { + "text": "So that's, that's the, the formulas." + }, + { + "text": "Now let me take an example." + }, + { + "text": "I'll use the Fibonacci sequence as an example." + }, + { + "text": "So, so Fibonacci example." + }, + { + "text": "You remember the Fibonacci numbers?" + }, + { + "text": "If we start with one and one as F0, oh, I think I start with zero, maybe." + }, + { + "text": "Let zero and one be the first ones." + }, + { + "text": "So there's F0 and F1, the first two Fibonacci numbers." + }, + { + "text": "Then what's the rule for Fibonacci numbers?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk16.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..79c65e32781f7f304b504a6c390247abb9d26ac8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "They're the sum." + }, + { + "text": "The next one is the sum of those, so it's one." + }, + { + "text": "The next one is the sum of those, so it's two." + }, + { + "text": "The next one is the sum of those, so it's three." + }, + { + "text": "Well, it looks like one, two, three, four, five, but somehow it's not going to do that way." + }, + { + "text": "The next one is five, right." + }, + { + "text": "Two and three makes five." + }, + { + "text": "The next one is eight." + }, + { + "text": "The next one is thirteen." + }, + { + "text": "And the one hundredth Fibonacci number is what?" + }, + { + "text": "That's my question." + }, + { + "text": "How could I get a formula for the hundredth number and for example how could I answer the question how fast are they growing?" + }, + { + "text": "How fast are those Fibonacci numbers growing?" + }, + { + "text": "They're certainly growing." + }, + { + "text": "It's not a stable case, whatever the eigenvalues of whatever matrix it is, they're not smaller than one." + }, + { + "text": "These numbers are growing." + }, + { + "text": "But how fast are they growing?" + }, + { + "text": "The answer is lies in the eigenvalue." + }, + { + "text": "So I've got to find the matrix, so let me write down the Fibonacci rule, F k plus two is F k plus one plus F k, right?" + }, + { + "text": "Now that's not in my -- I want to write that as U k plus one and A U k. But right now what I've got is a single equation, not a system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk17.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b3aaa9dcee3cf27c112015659bb5a0b51a983ce1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's second order." + }, + { + "text": "It's like having a second order differential equation with second derivatives." + }, + { + "text": "I want to get first derivatives." + }, + { + "text": "Here I want to get first difference." + }, + { + "text": "So the way to do it is to introduce U k will be a vector." + }, + { + "text": "See, a small trick." + }, + { + "text": "Let U k be a vector, F k plus one and F k. So I'm going to get a two by two system, first order, instead of a one, instead of a scalar system, second order, by a simple trick." + }, + { + "text": "I'm just going to add in an equation F k plus one equals F k plus one." + }, + { + "text": "That will be my second equation." + }, + { + "text": "Then this is my system, this is my unknown, and what's my one-step equation?" + }, + { + "text": "So now U k plus one." + }, + { + "text": "That's so U k plus one is the left side, and what have I got here on the right side?" + }, + { + "text": "I've got some matrix multiplying U k. Can you see that all right?" + }, + { + "text": "If you can see it, then you can tell me what the matrix is." + }, + { + "text": "You see that I'm taking my system here, I artificially made it into a system." + }, + { + "text": "I artificially made the unknown into a vector, and now I'm ready to look at and see what the matrix is." + }, + { + "text": "So do you see the left side, U k plus one is F k plus two F k plus one, that's just what I want." + }, + { + "text": "On the right side, this, remember, this U k here, let me for the moment put it as F k plus one F k. So what's the matrix?" + }, + { + "text": "Well, that has a one and a one, and that has a one and a zero." + }, + { + "text": "There's the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk18.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..6c1b68c2cb2fde3f5dea82f3100d4da31fcce70a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "You see that that gives me the right-hand side." + }, + { + "text": "So there's the matrix A, and this is our friend U k. So we've got, so that simple trick changed the second order scalar problem to a first order system, two, with two unknowns." + }, + { + "text": "With a matrix and now what do I do?" + }, + { + "text": "Well, before I even think, I find its eigenvalues and eigenvectors." + }, + { + "text": "So what are the eigenvalues and eigenvectors of that matrix?" + }, + { + "text": "Let's see." + }, + { + "text": "I was, first let me just, like, think for a minute." + }, + { + "text": "It's two by two, so this shouldn't be impossible to do." + }, + { + "text": "Let's do it." + }, + { + "text": "OK." + }, + { + "text": "So my matrix again is one one one zero." + }, + { + "text": "It's symmetric, by the way." + }, + { + "text": "So what I will eventually know about symmetric matrices is that the eigenvalues will come out real, I won't get any complex numbers here, and the eigenvectors, once I get those, actually will be orthogonal." + }, + { + "text": "But two by two, I'm more interested in what the actual numbers are." + }, + { + "text": "What do I know about the two numbers?" + }, + { + "text": "Well, should, do you want me to find this determinant of A minus lambda I?" + }, + { + "text": "Sure." + }, + { + "text": "So it's the determinant of one minus lambda one one zero, right?" + }, + { + "text": "Minus lambda, yes, got it." + }, + { + "text": "OK. OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk19.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..a73b23e3d56b889ff49ea7f55a784fac33e13c3d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "There'll be two eigenvalues." + }, + { + "text": "Well, tell me again what I know about the two eigenvalues before I go any further." + }, + { + "text": "Tell me something about these two eigenvalues, what do they add up to?" + }, + { + "text": "Lambda one plus lambda two is the same as the trace down the diagonal of the matrix, one and zero is one." + }, + { + "text": "So lambda one plus lambda two should come out to be one, and lambda one times lambda two should come out to be the determinant, which is minus one." + }, + { + "text": "So I'm expecting the eigenvalues to add to one and to multiply to minus one." + }, + { + "text": "But let's just see it happen here." + }, + { + "text": "If I multiply this out, I get that times that'll be a lambda squared minus lambda minus one." + }, + { + "text": "Good." + }, + { + "text": "Lambda squared minus lambda minus one." + }, + { + "text": "Actually, you see the, compare that with the original equation that I started with." + }, + { + "text": "Fk plus two minus Fk plus one minus Fk is zero." + }, + { + "text": "The recurrent, the recursion that the Fibonacci number satisfy is somehow showing up directly here for the eigenvalues when we set that to zero." + }, + { + "text": "OK. Let's solve." + }, + { + "text": "Well, I would like to be able to factor that, that quadratic, but I'm better off to use the quadratic formula." + }, + { + "text": "Lambda is, let's see, minus b is one, plus or minus the square root of b squared, which is one, minus four, times that, times that, which is plus four, over two." + }, + { + "text": "So that's the square root of five." + }, + { + "text": "So the eigenvalues are lambda one is one half of one plus square root of five, and lambda two is one half of one minus square root of five." + }, + { + "text": "And sure enough, they, those add up to one, and they multiply to give minus one." + }, + { + "text": "OK. Those are the two eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk2.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..43cfb012fc04a89fc7dab94c23bfb0f50ade3782 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "On the right, it's multiplied by, if I want, if I want lambda n xn in the last column, how do I do it?" + }, + { + "text": "Well, the last column here will be, I'll, I'll take the last column, use these coefficients, put the lambda n down there, and it will multiply that nth column and give me lambda n xn." + }, + { + "text": "There, there you see matrix multiplication just working for us." + }, + { + "text": "So I started with A s. I wrote down what it meant." + }, + { + "text": "A times each eigenvector." + }, + { + "text": "That gave me lambda times the eigenvector." + }, + { + "text": "And then when I peeled off the lambdas, they were on the right-hand side, so I've got s, my matrix back again, and this matrix, this diagonal matrix, the eigenvalue matrix, and I call it capital lambda, using capital letters for matrices, and lambda to prompt me that it's, that it's eigenvalues that are in there." + }, + { + "text": "So you see that the eigenvalues are just sitting down that diagonal?" + }, + { + "text": "If I had a column x2 here, I would want the lambda two in the two two position, in the diagonal position, to multiply that x2 and give me the lambda two x2." + }, + { + "text": "That's my formula." + }, + { + "text": "A s is s lambda." + }, + { + "text": "OK. That's, that's the, you see, it's just a calculation." + }, + { + "text": "Now, I, I mentioned, and I have to mention again, this business about n independent eigenvectors." + }, + { + "text": "As it stands, this is all fine whether, I mean, I could be repeating the same eigenvector, but I, I'm no interested in that." + }, + { + "text": "I want to be able to invert s, and that's where this comes in." + }, + { + "text": "This n independent eigenvectors business comes in to tell me that that matrix is invertible." + }, + { + "text": "So let me, on the next board, write down what I've got." + }, + { + "text": "A s equals s lambda." + }, + { + "text": "And now I'm, I can multiply on the left by s inverse." + }, + { + "text": "So this is really, I can do that provided s is invertible, provided my assumption of n independent eigenvectors is satisfied." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk20.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ad5a59fa5db44ce73ff5f88190423e0404fb3d39 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "How, how, what are those numbers approximately?" + }, + { + "text": "Square root of five, well, it's more than two, but less than three." + }, + { + "text": "It, it'd be nice to know these numbers." + }, + { + "text": "I think, I think that that, so that number comes out bigger than one, right?" + }, + { + "text": "Yeah, that's right." + }, + { + "text": "This number comes out bigger than one." + }, + { + "text": "It's about one point six one eight or something." + }, + { + "text": "Not exactly." + }, + { + "text": "It's supposed to be one point six." + }, + { + "text": "Just, like, I think so." + }, + { + "text": "Then what's lambda two?" + }, + { + "text": "Is, is lambda two positive or negative?" + }, + { + "text": "Negative, right?" + }, + { + "text": "Because I'm, it's obviously negative, and I knew that the, so it's minus, and they add up to one, so minus point six one eight, I guess." + }, + { + "text": "OK. And some order." + }, + { + "text": "Those are the two eigenvalues." + }, + { + "text": "One eigenvalue bigger than one, one eigenvalue smaller than one." + }, + { + "text": "Actually, that's a great situation to be in." + }, + { + "text": "Of course, the eigenvalues are different, so there's no doubt whatever, is this matrix diagonalizable?" + }, + { + "text": "Is this matrix diagonalizable, that original matrix A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk21.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..4a034475591d371995b379b5f98783a2cfb25870 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Sure." + }, + { + "text": "We've got two distinct eigenvalues and we can find the eigenvectors in a moment." + }, + { + "text": "But they'll be independent, will be diagonalizable, and now you can already answer my very first question." + }, + { + "text": "How fast are those Fibonacci numbers increasing?" + }, + { + "text": "How, those, they're increasing, right?" + }, + { + "text": "They're not doubling at every step." + }, + { + "text": "Let's look again at these numbers." + }, + { + "text": "Five eight thirteen, it's not obvious." + }, + { + "text": "The next one would be twenty one thirty four." + }, + { + "text": "So to get some idea of what F one hundred is, can you give me any, I mean the crucial number of, so it, these, it's approximately, what's controlling the growth of these Fibonacci numbers?" + }, + { + "text": "It's the eigenvalues." + }, + { + "text": "And which eigenvalues controlling that growth?" + }, + { + "text": "The big ones." + }, + { + "text": "So F one hundred will it be approximately some constant, c one, I guess, times this lambda one, this one plus square root of five over two, to the hundredth power." + }, + { + "text": "And the two hundredth have, in other words, the eigenvalue, the Fibonacci numbers are growing by about that factor." + }, + { + "text": "You see that we've got precise information about the, about the Fibonacci numbers out of the eigenvalue." + }, + { + "text": "OK. And again, why is that true?" + }, + { + "text": "Let me go over to this board and show what I'm doing here." + }, + { + "text": "The, the original eigen, the original initial value is some combination of eigenvectors, and then when we start multiple, when we start going out the theory of Fibonacci numbers, when we start multiplying by a hundred times, it's this lambda one to the hundredth, this term is, is the one that's taken over." + }, + { + "text": "It's, I mean, that's big, like, one point six to the hundredth power." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk22.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..c13a1fc9867173c3067e46c469cfff27b9b45289 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "The second term is practically nothing, right?" + }, + { + "text": "The point six, or minus point six to the hundredth power, is an extremely small, extremely small number." + }, + { + "text": "So this is, this, this, there are only two terms, because we're two by two." + }, + { + "text": "This number is, this piece of it is there, but it's, it's disappearing." + }, + { + "text": "Where this piece is there and it's growing and controlling everything." + }, + { + "text": "So, so really the, we're doing, like, problems that are evolving." + }, + { + "text": "We're doing dynamics." + }, + { + "text": "Instead of Ax equal b, that's a static problem." + }, + { + "text": "We're now, we're doing dynamics." + }, + { + "text": "A, a squared, a cubed, things are evolving in time, and the eigenvalues are the crucial, numbers." + }, + { + "text": "OK." + }, + { + "text": "I guess to complete this, I better write down the eigenvectors." + }, + { + "text": "So we should complete the, the whole process by finding the eigenvectors." + }, + { + "text": "OK. Well, I have to, up in the corner, then I have to look at A minus lambda I." + }, + { + "text": "So A minus lambda I is this one minus lambda, one, one, and minus lambda." + }, + { + "text": "And now, can we spot an eigenvector out of that?" + }, + { + "text": "That's, for these two lambdas, this matrix is singular." + }, + { + "text": "I guess the eigenvector, two by two ought to be easy." + }, + { + "text": "So if I know that this matrix is singular, then it seems to me the eigenvector has to be lambda and one, because that multiplication will give me the zero." + }, + { + "text": "And this multiplication gives me, better give me also zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk23.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..df816eb800ce767b1475c279a24ad976bb45a785 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Do you see why it does?" + }, + { + "text": "This is the minus lambda squared plus lambda plus one." + }, + { + "text": "It's the thing that's zero, because these lambdas are special." + }, + { + "text": "There's the eigenvector." + }, + { + "text": "X1 is lambda one, one, and x2 is lambda two, one." + }, + { + "text": "I did that as a little trick that was available in the two by two case." + }, + { + "text": "So now I finally have to, oh, I have to take the initial, u0." + }, + { + "text": "So to complete this example entirely, I have to say, OK, what was u0?" + }, + { + "text": "u0 was f1 f0." + }, + { + "text": "So u0, the starting vector, is f1 f0, and those were one and zero." + }, + { + "text": "So I have to use that vector, so I have to look for, from multiple of the first eigenvector and the second, to produce u0, the one zero vector." + }, + { + "text": "This is what will find c1 and c2, and then I'm done." + }, + { + "text": "So let me, instead of in the last five seconds grinding out a formula, let me repeat the idea." + }, + { + "text": "That really, it's the idea that's central." + }, + { + "text": "When things are evolving in time, let me come back to this board, because the ideas are here." + }, + { + "text": "When things are evolving in time by a first-order system, starting from an original u0, the key is, find the eigenvalues and eigenvectors of A." + }, + { + "text": "That will tell, those eigenvectors, the eigenvalues will already tell you what's happening." + }, + { + "text": "Is the solution blowing up?" + }, + { + "text": "Is it going to zero?" + }, + { + "text": "What's it doing?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk24.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..40301cb90760e2172baa94d536cbc13288d4c31f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk24.json @@ -0,0 +1,20 @@ +[ + { + "text": "And then, to find out exactly a formula, you have to take your u0 and write it as a combination of eigenvectors and then follow each eigenvector separately." + }, + { + "text": "And that's really what this formula, the formula for, that's what the formula for A to the k is doing." + }, + { + "text": "So remember that formula for A to the k is S, lambda to the k S inverse." + }, + { + "text": "OK. That's, that's difference equations, and you just have to, so the homework will give some examples different from Fibonacci to follow through." + }, + { + "text": "And next time will be differential equations." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk3.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..9bf1bb852baadc1da7837e14180c0c2951a30882 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I mentioned at the end of last time, and I'll say again, that there's a small number of matrices for, that don't have n independent eigenvectors." + }, + { + "text": "So I've got to discuss that, that technical point." + }, + { + "text": "But the great, the most matrices that we see have n, n independent eigenvectors and we can diagonalize." + }, + { + "text": "This is diagonalization." + }, + { + "text": "I could also write it, and I often will, the other way round." + }, + { + "text": "If I multiply on the right by s inverse, if I took this equation at the top and multiplied on the right by s inverse, I could, I would have A left here." + }, + { + "text": "Now s inverse is coming from the right." + }, + { + "text": "So can you keep those two straight?" + }, + { + "text": "A multiplies its eigenvectors." + }, + { + "text": "That's how I keep them straight." + }, + { + "text": "So A multiplies s. A multiplies s. And then this s inverse makes the whole thing diagonal." + }, + { + "text": "And this is another way of saying the same thing, putting the s's on the other side of the equation, A is s lambda s inverse." + }, + { + "text": "So that's the, that's the new factorization." + }, + { + "text": "That's the replacement for L U from elimination or Q R from Gram-Schmidt." + }, + { + "text": "And notice that the matrix, so it's, it's a matrix times a diagonal matrix times the inverse of the first one." + }, + { + "text": "It's, that's the combination that we'll see throughout this chapter." + }, + { + "text": "This, this, combination with an s and an s inverse." + }, + { + "text": "OK. Can I just begin to use that?" + }, + { + "text": "For example, what about A squared?" + }, + { + "text": "What are the eigenvalues and eigenvectors of A squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk4.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c687b6948acad76de8781cb82d3eb069c9da514e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's a straightforward question with a, with a absolutely clean answer." + }, + { + "text": "So let me, let me consider A squared." + }, + { + "text": "So I look, I start with Ax equal lambda x." + }, + { + "text": "And I'm headed for A squared." + }, + { + "text": "So let me multiply both sides by A." + }, + { + "text": "That's one way to get A squared on the left." + }, + { + "text": "So if, I should write these ifs in here." + }, + { + "text": "If Ax equals lambda x, then I multiply by A." + }, + { + "text": "So I get A squared x equals, well, I'm multiplying by A, so that's lambda Ax." + }, + { + "text": "That lambda was a number, so I just put it on the left." + }, + { + "text": "And what do I, tell me how to make that look better." + }, + { + "text": "What have I got here?" + }, + { + "text": "For, if, if A has the eigenvalue lambda and eigenvector x, what's up with A squared?" + }, + { + "text": "A squared x, I just multiply by A, but now for Ax, I'm going to substitute lambda x, so I've got lambda squared x." + }, + { + "text": "So from that simple calculation, I, my conclusion is that the eigenvalues of A squared are lambda squared." + }, + { + "text": "And the eigenvectors, I always think about both of those." + }, + { + "text": "What can I say about the eigenvalues?" + }, + { + "text": "They're squared." + }, + { + "text": "What can I say about the eigenvectors?" + }, + { + "text": "They're the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk5.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5bf15e20707c156c8ae71c9c7acea41a9d9d8e46 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same x as in, as for A." + }, + { + "text": "Now, let me see that also from this formula." + }, + { + "text": "How can I see what A squared is looking like from this formula?" + }, + { + "text": "So let me, that, that was one way to do it." + }, + { + "text": "Let me do it by just taking A squared from that." + }, + { + "text": "A squared is S lambda S inverse, that's A, times S lambda S inverse, that's A, which is?" + }, + { + "text": "This is the beauty of eigenvalues, eigenvectors, having that S inverse and S is the identity, so I've got S lambda squared S inverse." + }, + { + "text": "Yes." + }, + { + "text": "You see what that's telling me?" + }, + { + "text": "It's, it's telling me the same thing that I just learned here, but in the, in, in a matrix form." + }, + { + "text": "It's telling me that the S is the same, the eigenvectors are the same, but the eigenvalues are squared, because this is, what's lambda squared, that's still diagonal, it's got little lambda one squared, lambda two squared, down to lambda n squared, on that diagonal, those are the eigenvalues, as we just learned, of A squared." + }, + { + "text": "OK." + }, + { + "text": "So, somehow those eigenvalues and eigenvectors are really giving you a way to, to, to, to see what's going on inside a matrix." + }, + { + "text": "Now, of course, I can continue that for, to the k-th power." + }, + { + "text": "A to the k-th power." + }, + { + "text": "If I multiply, if I have k of these together, do you see how S inverse S will keep cancelling?" + }, + { + "text": "In the, in the inside, I'll have the S outside, at the far left, and lambda will be in there k times and S inverse." + }, + { + "text": "So what's that telling me?" + }, + { + "text": "That's telling me that the eigenvalues of A, of A to the k-th power are the k-th powers." + }, + { + "text": "The eigenvalues of A cubed are the cubes of the eigenvalues of A, and the eigenvectors are the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk6.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..c18dddbe798022f7e68278ac002a3f5fe6ed249e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same." + }, + { + "text": "OK." + }, + { + "text": "In other words, eigenvalues and eigenvectors give a great way to understand the powers of a matrix." + }, + { + "text": "If I take the square of a matrix or the hundredth power of a matrix, the pivots are all over the place." + }, + { + "text": "L U, if I multiply L U times L U times L U times L U a hundred times, I've got a hundred L U's." + }, + { + "text": "I can't do anything with them." + }, + { + "text": "But when I multiply S lambda S inverse by itself, when I look at the eigenvector picture a hundred times, I get a hundred or ninety-nine of these guys cancelling out inside, and I get A to the hundredth is S lambda to the hundredth S inverse." + }, + { + "text": "I mean, eigenvalues tell you about powers of a matrix in a way that we had no, no way to approach previously." + }, + { + "text": "For example, when does, when do the powers of a matrix go to zero?" + }, + { + "text": "I would call that matrix stable, maybe." + }, + { + "text": "So, so, so I could write down a, a theorem." + }, + { + "text": "I'll, I'll write it as a theorem, just to use that word to emphasize that here I'm getting this great fact from this eigenvalue picture." + }, + { + "text": "OK. A to the k approaches zero as k goes, as k gets bigger." + }, + { + "text": "If what?" + }, + { + "text": "What's the, how can I tell for a matrix A if its powers go to zero?" + }, + { + "text": "What, what's somewhere inside that matrix is that information." + }, + { + "text": "That information is not present in the pivots." + }, + { + "text": "It's present in the eigenvalues." + }, + { + "text": "What do I need for the, to know that if I take higher and higher powers of A that this matrix gets smaller and smaller?" + }, + { + "text": "Well, S and S inverse are not moving." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk7.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b84a5c854a5542758e8a0107e1ff043205fe3bdb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's this guy that has to get small, and that's easy to, easy to understand." + }, + { + "text": "The requirement is all eigenvalues, so what is the requirement?" + }, + { + "text": "The eigenvalues have to be less than one." + }, + { + "text": "Now, I have to write that absolute value, because those eigenvalues could be negative, they could be complex numbers." + }, + { + "text": "So I'm taking the absolute value if all of those are below one." + }, + { + "text": "That's, in fact, we practically see why." + }, + { + "text": "Let me just say that I, that I, I'm operating on one assumption here, and I got to keep remembering that that assumption is still present." + }, + { + "text": "That assumption was that I had a full set of, of n independent eigenvectors." + }, + { + "text": "If I don't have that, then I, I, then this approach is not working." + }, + { + "text": "So, so again, a pure eigenvalue approach, eigenvector approach, needs n independent eigenvectors." + }, + { + "text": "If we don't have n independent eigenvectors, we can't diagonalize the matrix." + }, + { + "text": "We can't get to a diagonal matrix." + }, + { + "text": "This, this, this diagonalization is only possible if S inverse makes sense." + }, + { + "text": "OK. Can I, can I follow up on that point now?" + }, + { + "text": "So, so you see why, what we get and, and why we want it, because we get information about the powers of a matrix just immediately from the eigenvalues." + }, + { + "text": "OK, now let me follow up on this, business of which matrices are diagonalizable." + }, + { + "text": "Sorry about that long word." + }, + { + "text": "So a matrix is, is sure to, so here's, here's the main point." + }, + { + "text": "A is sure to be, to have n independent eigenvectors and, and B, now here comes that word, diagonalizable, if, if, so we, we, we might as well get the, the nice case out in the open." + }, + { + "text": "The nice case is when, if all the lambdas are different." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk8.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f06dcec8ffa0ee1bf19440e4ab2194db33ab353b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means, that means no repeated eigenvalues." + }, + { + "text": "OK. That's the nice case." + }, + { + "text": "If, if my matrix and most matrix, if I do a random matrix in MATLAB and compute its eigenvalues, so if I computed, if I took I of rand of ten ten, gave, gave that MATLAB command, the, we'd get a random ten by ten matrix, we would get a list of its ten eigenvalues and they would be different." + }, + { + "text": "They would be distinct, is the best word." + }, + { + "text": "I would have a random matrix will have ten distinct, a ten by ten matrix will have ten distinct eigenvalues, and if it does, the eigenvectors are automatically independent." + }, + { + "text": "So that's a nice fact." + }, + { + "text": "I can, I'll refer you to the text for the proof." + }, + { + "text": "That, that A is sure to have n independent eigenvectors if the eigenvalues are different." + }, + { + "text": "If, if all the, if all eigenvalues are different." + }, + { + "text": "It's just, if some lambdas are repeated, then I have to look more closely." + }, + { + "text": "If an eigenvalue is repeated, I have to look, I have to count, I have to check." + }, + { + "text": "Has it got, say it's repeated three times." + }, + { + "text": "So what's a possibility for, so, so here's, here's the repeated possibility." + }, + { + "text": "And, and let me emphasize the conclusion." + }, + { + "text": "That if I have repeated eigenvalues, I may or may not, I may or may not have, have n independent eigenvectors." + }, + { + "text": "I might." + }, + { + "text": "I, I, you know, this isn't a completely negative case." + }, + { + "text": "The identity matrix." + }, + { + "text": "Well, suppose I take the ten by ten identity matrix." + }, + { + "text": "What are the eigenvalues of that matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk9.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..87d2a2ae5773036cf11800e2f1962908986a0dad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_18_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So just, just take the easiest matrix, the identity." + }, + { + "text": "If I look for its eigenvalues, they're all ones." + }, + { + "text": "So that eigenvalue one is repeated ten times." + }, + { + "text": "But there's no shortage of eigenvectors for the identity matrix." + }, + { + "text": "In fact, every vector is an eigenvector." + }, + { + "text": "So I can take ten independent vectors." + }, + { + "text": "Oh, well, what happens to everything if, if, if A is the identity matrix, let's just think that one through in our head." + }, + { + "text": "If A is the identity matrix, then it's got plenty of eigenvectors." + }, + { + "text": "I choose ten independent vectors, they're the columns of S, and, and what do I get from S inverse A S?" + }, + { + "text": "I get I again, right?" + }, + { + "text": "If A is the identity, and of course, that's the correct lambda." + }, + { + "text": "The, the matrix was already diagonal." + }, + { + "text": "So if the matrix is already diagonal, then the, the lambda is the same as the matrix." + }, + { + "text": "A diagonal matrix has got its eigenvalues sitting right there in front of you." + }, + { + "text": "Now if it's triangular, the eigenvalues are still sitting there, but so let's, let's take a case where, it's triangular." + }, + { + "text": "Suppose A is like, two, one, two, zero." + }, + { + "text": "So there's a case that's going to be trouble." + }, + { + "text": "There's a case that's going to be trouble." + }, + { + "text": "First of all, what are the eigen- I mean, we just, like now you, if we start with a matrix, the first thing we do practically without thinking is compute the eigenvalues and eigenvectors." + }, + { + "text": "OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk0.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6898d4fe66019ef6b40d0472ea94a968e7bbde9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, shall we start?" + }, + { + "text": "This is the second lecture on eigenvalues." + }, + { + "text": "So the first lecture was set -- reached the key equation, Ax equal lambda x. x is the eigenvector and lambda is the eigenvalue." + }, + { + "text": "Now, to use that." + }, + { + "text": "And the good way to, after we've found, so job one is to find the eigenvalues and find the eigenvectors." + }, + { + "text": "Now after we found them, what do we do with them?" + }, + { + "text": "Well, the good way to see that is diagonalize the matrix." + }, + { + "text": "So the matrix is A, and I want to show, first of all, this is like the basic fact." + }, + { + "text": "This, this formula." + }, + { + "text": "That's, that's the key to today's lecture." + }, + { + "text": "This matrix A, I put its eigenvectors in the columns of a matrix S. So S will be the eigenvector matrix, and I want to look at this magic combination S inverse A S. So can I show you how that, how that, what happens there?" + }, + { + "text": "And notice, notice, there's an S inverse." + }, + { + "text": "We have to be able to invert this eigenvector matrix S. So for that we need n independent eigenvectors." + }, + { + "text": "So that's the, that's the case." + }, + { + "text": "OK." + }, + { + "text": "So suppose we have n linearly independent eigenvectors of A." + }, + { + "text": "Put them in the columns of this matrix S. So I'm naturally going to call that the eigenvector matrix, because it's got the eigenvectors in its columns." + }, + { + "text": "And all I want to do is show you what happens when you multiply A times S. So A times S. So this is A times the matrix with the first eigenvector in its first column, the second eigenvector in its second column, the nth eigenvector in its nth column." + }, + { + "text": "And how am I going to do this matrix multiplication?" + }, + { + "text": "Well, certainly I'll do it a column at a time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk1.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..fbe078217bb68baea8e0605a5d04be568c49efbf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I get?" + }, + { + "text": "A times the first column gives me the first column of the answer, but what is it?" + }, + { + "text": "That's an eigenvector." + }, + { + "text": "A times x1 is equal to the lambda times the x1." + }, + { + "text": "And that lambda's we'll call lambda one, of course." + }, + { + "text": "So that's the first column, A x1 is the same as lambda one x1." + }, + { + "text": "A x2 is lambda two x2, so on, along to, in the nth column, we now have lambda n xn." + }, + { + "text": "Looking good, but the next step is even better." + }, + { + "text": "So for the next step, I want to separate out those eigenvalues, those multiplying numbers, from the x's." + }, + { + "text": "So then I'll have just what I want." + }, + { + "text": "OK, so how, how am I going to separate out?" + }, + { + "text": "So that, that number lambda one is multiplying the first column." + }, + { + "text": "So if I want to factor it out of the first column, I better put, here is going to be x1, and that's going to multiply this matrix lambda one in the first entry in all zeros." + }, + { + "text": "You see that that, that's going to come out right for the first column?" + }, + { + "text": "Because we remember how, how we're going back to that original punchline, that if I want a number to multiply x1, then I can do it by putting x1 in that column, in the first column, and putting that number there." + }, + { + "text": "What am I going to have here?" + }, + { + "text": "I'm going to have lambda one, I'm going to have x1, x2, xn." + }, + { + "text": "These are going to be my columns again." + }, + { + "text": "I'm getting s back again." + }, + { + "text": "I'm getting s back again, but now what's it multiplied by?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk10.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c58a42edbe9567233ca7f57643a0b7d43ae6761f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what are the eigenvalues?" + }, + { + "text": "You can tell me right away what they are." + }, + { + "text": "They're two and two, right." + }, + { + "text": "It's a triangular matrix, so when I do this determinant, shall I do this determinant of A minus lambda I?" + }, + { + "text": "I'll get this two minus lambda, one, zero, two minus lambda, right?" + }, + { + "text": "I take that determinant, so I make those into vertical bars to mean determinant, and what's the determinant?" + }, + { + "text": "Two minus lambda squared." + }, + { + "text": "What are the roots?" + }, + { + "text": "Lambda equal two twice." + }, + { + "text": "So the eigenvalues are lambda equals two and two." + }, + { + "text": "OK, fine." + }, + { + "text": "Now the next step, find the eigenvectors." + }, + { + "text": "So I look for eigenvectors and what do I find for this guy?" + }, + { + "text": "Eigenvectors for this guy, when I subtract two minus the identity, so A minus two I has zeros here, and I'm looking for the null space." + }, + { + "text": "What's, what are the eigenvectors?" + }, + { + "text": "They're the, they're, they're the null space of A minus lambda I." + }, + { + "text": "The null space is only one dimension." + }, + { + "text": "This is a case where I don't have enough eigenvectors." + }, + { + "text": "My algebraic multiplicity is two." + }, + { + "text": "I, I would say when I see, when I count how often the eigenvalue is repeated, that's the algebraic multiplicity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk11.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..779c2cf904d904b761080db2671aac46394ad02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the multiplicity." + }, + { + "text": "How many times is it the root of the polynomial?" + }, + { + "text": "My polynomial is two minus lambda squared." + }, + { + "text": "It's a double root." + }, + { + "text": "So my algebraic multiplicity is two." + }, + { + "text": "But the geometric multiplicity, which looks for vectors, looks for eigenvectors and which means the null space of this thing." + }, + { + "text": "And the only eigenvector is one zero." + }, + { + "text": "That's in the null space." + }, + { + "text": "Zero one is not in the null space." + }, + { + "text": "The null space is only one dimensional." + }, + { + "text": "So there's a matrix, my, this A or the original A, that are not diagonalizable." + }, + { + "text": "I can't, I can't find two independent eigenvectors, there's only one." + }, + { + "text": "OK." + }, + { + "text": "So that's the case that I'm, that's a case that I, I'm not really handling." + }, + { + "text": "For example, when I wrote down up here that the powers went to zero if the eigenvalues were below one, I didn't really handle that case of repeated eigenvalues because my reasoning was based on this formula." + }, + { + "text": "And this formula is based on n independent eigenvectors." + }, + { + "text": "OK." + }, + { + "text": "So just to say that." + }, + { + "text": "There are some matrices that we don't cover through diagonalization, but the great majority we do." + }, + { + "text": "OK. And we're always OK if we have different distinct eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk12.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..77d090704cc298475d94416b7ecb88a2a015a913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. That's the, like, the typical case." + }, + { + "text": "Because for each eigenvalue there's at least one eigenvector, the algebraic multiplicity here is one for every eigenvalue, and the geometric multiplicity is one." + }, + { + "text": "There's one eigenvector and they are independent." + }, + { + "text": "OK. OK. Now let me come back to the important case when we're OK." + }, + { + "text": "The important case when we are diagonalizing." + }, + { + "text": "Let me look at, so let me solve this equation." + }, + { + "text": "The equation will be each, I start with some, start with a given vector u0." + }, + { + "text": "And then my equation is that every step I multiply what I have by a." + }, + { + "text": "That equation ought to be simple to handle." + }, + { + "text": "OK. And I'd like to be able to solve it." + }, + { + "text": "How would I find, if I start with a vector u0, and I multiply by a a hundred times, what have I got?" + }, + { + "text": "Well, I can certainly write down a formula for the answer." + }, + { + "text": "So what, what, so u1 is a u0." + }, + { + "text": "And u2 is, what's u2 then?" + }, + { + "text": "U2 I multiply it, u2 I get from u1 by another, multiplying by a, so I've got a twice." + }, + { + "text": "And my formula is uk, after k steps, I've multiplied by a k times the original u0." + }, + { + "text": "You see what I'm doing?" + }, + { + "text": "The next section is going to solve systems of differential equations." + }, + { + "text": "I'm going to have derivatives." + }, + { + "text": "This, this section is the nice one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk13.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..ba8214d8c636e4757a266d6617801174bc939d80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "It solves difference equations." + }, + { + "text": "I would call that a difference equation." + }, + { + "text": "It's conne- a first order." + }, + { + "text": "I would call that a first order system, because it connects only, it only goes up one level." + }, + { + "text": "And it's a system because these are vectors and that's a matrix." + }, + { + "text": "And the solution is just that." + }, + { + "text": "OK." + }, + { + "text": "But, that's a nice formula." + }, + { + "text": "That's the, like, the most compact formula I could ever get." + }, + { + "text": "U one hundred would be a to the one hundredth u0." + }, + { + "text": "But how would I actually find u one hundred?" + }, + { + "text": "How would I find, how would I discover what u one hundred is?" + }, + { + "text": "Let me, let me show you how." + }, + { + "text": "Here, here's the idea." + }, + { + "text": "If, so, to solve, to really solve, shall I say, to really solve." + }, + { + "text": "To really solve it, I would take this initial vector, u0, and I would write it as a combination of eigenvectors." + }, + { + "text": "To really solve, write, write u0 as a combination, say, certain amount of the first eigenvector plus a certain amount of the second eigenvector plus a certain amount of the last eigenvector." + }, + { + "text": "Now multiply by a." + }, + { + "text": "You want to, you got to see the magic of eigenvectors work." + }, + { + "text": "Multiply by a." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk14.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7843b2bf0cac762d1c12452cf36500ea4ad13370 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a u0 is what?" + }, + { + "text": "So a times that." + }, + { + "text": "A times, so what's, I can separate it out into n separate pieces and that's the whole point." + }, + { + "text": "That each of those pieces is going in its own merry way." + }, + { + "text": "Each of those pieces is an eigenvector, and when I multiply by a, what does this piece become?" + }, + { + "text": "So that's some amount of the first, let's suppose the eigenvectors are normalized to be unit vectors." + }, + { + "text": "So that says what the eigenvector is." + }, + { + "text": "It's, and I need some multiple of it to produce u0." + }, + { + "text": "OK. Now when I multiply by a, what do I get?" + }, + { + "text": "I get c1, which is just a factor, times a x1, but a x1 is lambda one x1." + }, + { + "text": "When I multiply this by a, I get c2 lambda two x2." + }, + { + "text": "And here I get cn lambda n xn." + }, + { + "text": "And suppose I multiply by a to the hundredth power now." + }, + { + "text": "Can we, can we, having done it, multiplied by a, let's multiply by a to the hundredth." + }, + { + "text": "What happens to this first term when I multiply by a to the one hundredth?" + }, + { + "text": "It's got that factor lambda to the hundredth." + }, + { + "text": "That's the key." + }, + { + "text": "That, that's what I mean by going its own merry way." + }, + { + "text": "It, it is pure eigenvector, it's exactly in a direction where multiplication by a just brings in a scalar factor lambda one." + }, + { + "text": "So a hundred times brings in this a hundred times." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk15.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7ee3348735378aa4049d33ec2a197d0ceb0c447c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Hundred times lambda two, hundred times lambda n. Actually, we're, what are we seeing here?" + }, + { + "text": "We're seeing, this same, lambda, capital lambda to the hundredth, as in the, as in the diagonalization, and we're seeing the S matrix, the matrix S of eigenvectors." + }, + { + "text": "That's what this has got to, this has got to amount to, a lambda to the hundredth power times an S times this vector C that's telling us how much of each one is in the original thing." + }, + { + "text": "So if, if I had to really find the hundredth power, I would take u0, I would expand it as a combination of eigenvectors, this is really S, the eigenvector matrix times C, the, the coefficient vector." + }, + { + "text": "And then I would immediately, then, by inserting these hundredth powers of eigenvalues, I'd have the answer." + }, + { + "text": "So the, the, huh, there must be, well, let's see." + }, + { + "text": "OK." + }, + { + "text": "It's, so, yeah." + }, + { + "text": "So if u100 is a to the hundredth times u0, and u0 is Sc, then you see this formula is just this formula, which is the way I would actually get hold of this, of this u100, which is, let me put it here, u100." + }, + { + "text": "The way I would actually get hold of that, see what, what the solution is after a hundred steps, would be expand the initial vector into eigenvectors and, and let each eigenvector go its own way, multiplying by a hundred at, by lambda at every step, and therefore by lambda to the hundredth power after a hundredth step." + }, + { + "text": "Can I do an example?" + }, + { + "text": "So that's, that's the, the formulas." + }, + { + "text": "Now let me take an example." + }, + { + "text": "I'll use the Fibonacci sequence as an example." + }, + { + "text": "So, so Fibonacci example." + }, + { + "text": "You remember the Fibonacci numbers?" + }, + { + "text": "If we start with one and one as F0, oh, I think I start with zero, maybe." + }, + { + "text": "Let zero and one be the first ones." + }, + { + "text": "So there's F0 and F1, the first two Fibonacci numbers." + }, + { + "text": "Then what's the rule for Fibonacci numbers?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk16.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..79c65e32781f7f304b504a6c390247abb9d26ac8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "They're the sum." + }, + { + "text": "The next one is the sum of those, so it's one." + }, + { + "text": "The next one is the sum of those, so it's two." + }, + { + "text": "The next one is the sum of those, so it's three." + }, + { + "text": "Well, it looks like one, two, three, four, five, but somehow it's not going to do that way." + }, + { + "text": "The next one is five, right." + }, + { + "text": "Two and three makes five." + }, + { + "text": "The next one is eight." + }, + { + "text": "The next one is thirteen." + }, + { + "text": "And the one hundredth Fibonacci number is what?" + }, + { + "text": "That's my question." + }, + { + "text": "How could I get a formula for the hundredth number and for example how could I answer the question how fast are they growing?" + }, + { + "text": "How fast are those Fibonacci numbers growing?" + }, + { + "text": "They're certainly growing." + }, + { + "text": "It's not a stable case, whatever the eigenvalues of whatever matrix it is, they're not smaller than one." + }, + { + "text": "These numbers are growing." + }, + { + "text": "But how fast are they growing?" + }, + { + "text": "The answer is lies in the eigenvalue." + }, + { + "text": "So I've got to find the matrix, so let me write down the Fibonacci rule, F k plus two is F k plus one plus F k, right?" + }, + { + "text": "Now that's not in my -- I want to write that as U k plus one and A U k. But right now what I've got is a single equation, not a system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk17.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b3aaa9dcee3cf27c112015659bb5a0b51a983ce1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's second order." + }, + { + "text": "It's like having a second order differential equation with second derivatives." + }, + { + "text": "I want to get first derivatives." + }, + { + "text": "Here I want to get first difference." + }, + { + "text": "So the way to do it is to introduce U k will be a vector." + }, + { + "text": "See, a small trick." + }, + { + "text": "Let U k be a vector, F k plus one and F k. So I'm going to get a two by two system, first order, instead of a one, instead of a scalar system, second order, by a simple trick." + }, + { + "text": "I'm just going to add in an equation F k plus one equals F k plus one." + }, + { + "text": "That will be my second equation." + }, + { + "text": "Then this is my system, this is my unknown, and what's my one-step equation?" + }, + { + "text": "So now U k plus one." + }, + { + "text": "That's so U k plus one is the left side, and what have I got here on the right side?" + }, + { + "text": "I've got some matrix multiplying U k. Can you see that all right?" + }, + { + "text": "If you can see it, then you can tell me what the matrix is." + }, + { + "text": "You see that I'm taking my system here, I artificially made it into a system." + }, + { + "text": "I artificially made the unknown into a vector, and now I'm ready to look at and see what the matrix is." + }, + { + "text": "So do you see the left side, U k plus one is F k plus two F k plus one, that's just what I want." + }, + { + "text": "On the right side, this, remember, this U k here, let me for the moment put it as F k plus one F k. So what's the matrix?" + }, + { + "text": "Well, that has a one and a one, and that has a one and a zero." + }, + { + "text": "There's the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk18.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..6c1b68c2cb2fde3f5dea82f3100d4da31fcce70a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "You see that that gives me the right-hand side." + }, + { + "text": "So there's the matrix A, and this is our friend U k. So we've got, so that simple trick changed the second order scalar problem to a first order system, two, with two unknowns." + }, + { + "text": "With a matrix and now what do I do?" + }, + { + "text": "Well, before I even think, I find its eigenvalues and eigenvectors." + }, + { + "text": "So what are the eigenvalues and eigenvectors of that matrix?" + }, + { + "text": "Let's see." + }, + { + "text": "I was, first let me just, like, think for a minute." + }, + { + "text": "It's two by two, so this shouldn't be impossible to do." + }, + { + "text": "Let's do it." + }, + { + "text": "OK." + }, + { + "text": "So my matrix again is one one one zero." + }, + { + "text": "It's symmetric, by the way." + }, + { + "text": "So what I will eventually know about symmetric matrices is that the eigenvalues will come out real, I won't get any complex numbers here, and the eigenvectors, once I get those, actually will be orthogonal." + }, + { + "text": "But two by two, I'm more interested in what the actual numbers are." + }, + { + "text": "What do I know about the two numbers?" + }, + { + "text": "Well, should, do you want me to find this determinant of A minus lambda I?" + }, + { + "text": "Sure." + }, + { + "text": "So it's the determinant of one minus lambda one one zero, right?" + }, + { + "text": "Minus lambda, yes, got it." + }, + { + "text": "OK. OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk19.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..a73b23e3d56b889ff49ea7f55a784fac33e13c3d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "There'll be two eigenvalues." + }, + { + "text": "Well, tell me again what I know about the two eigenvalues before I go any further." + }, + { + "text": "Tell me something about these two eigenvalues, what do they add up to?" + }, + { + "text": "Lambda one plus lambda two is the same as the trace down the diagonal of the matrix, one and zero is one." + }, + { + "text": "So lambda one plus lambda two should come out to be one, and lambda one times lambda two should come out to be the determinant, which is minus one." + }, + { + "text": "So I'm expecting the eigenvalues to add to one and to multiply to minus one." + }, + { + "text": "But let's just see it happen here." + }, + { + "text": "If I multiply this out, I get that times that'll be a lambda squared minus lambda minus one." + }, + { + "text": "Good." + }, + { + "text": "Lambda squared minus lambda minus one." + }, + { + "text": "Actually, you see the, compare that with the original equation that I started with." + }, + { + "text": "Fk plus two minus Fk plus one minus Fk is zero." + }, + { + "text": "The recurrent, the recursion that the Fibonacci number satisfy is somehow showing up directly here for the eigenvalues when we set that to zero." + }, + { + "text": "OK. Let's solve." + }, + { + "text": "Well, I would like to be able to factor that, that quadratic, but I'm better off to use the quadratic formula." + }, + { + "text": "Lambda is, let's see, minus b is one, plus or minus the square root of b squared, which is one, minus four, times that, times that, which is plus four, over two." + }, + { + "text": "So that's the square root of five." + }, + { + "text": "So the eigenvalues are lambda one is one half of one plus square root of five, and lambda two is one half of one minus square root of five." + }, + { + "text": "And sure enough, they, those add up to one, and they multiply to give minus one." + }, + { + "text": "OK. Those are the two eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk2.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..43cfb012fc04a89fc7dab94c23bfb0f50ade3782 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "On the right, it's multiplied by, if I want, if I want lambda n xn in the last column, how do I do it?" + }, + { + "text": "Well, the last column here will be, I'll, I'll take the last column, use these coefficients, put the lambda n down there, and it will multiply that nth column and give me lambda n xn." + }, + { + "text": "There, there you see matrix multiplication just working for us." + }, + { + "text": "So I started with A s. I wrote down what it meant." + }, + { + "text": "A times each eigenvector." + }, + { + "text": "That gave me lambda times the eigenvector." + }, + { + "text": "And then when I peeled off the lambdas, they were on the right-hand side, so I've got s, my matrix back again, and this matrix, this diagonal matrix, the eigenvalue matrix, and I call it capital lambda, using capital letters for matrices, and lambda to prompt me that it's, that it's eigenvalues that are in there." + }, + { + "text": "So you see that the eigenvalues are just sitting down that diagonal?" + }, + { + "text": "If I had a column x2 here, I would want the lambda two in the two two position, in the diagonal position, to multiply that x2 and give me the lambda two x2." + }, + { + "text": "That's my formula." + }, + { + "text": "A s is s lambda." + }, + { + "text": "OK. That's, that's the, you see, it's just a calculation." + }, + { + "text": "Now, I, I mentioned, and I have to mention again, this business about n independent eigenvectors." + }, + { + "text": "As it stands, this is all fine whether, I mean, I could be repeating the same eigenvector, but I, I'm no interested in that." + }, + { + "text": "I want to be able to invert s, and that's where this comes in." + }, + { + "text": "This n independent eigenvectors business comes in to tell me that that matrix is invertible." + }, + { + "text": "So let me, on the next board, write down what I've got." + }, + { + "text": "A s equals s lambda." + }, + { + "text": "And now I'm, I can multiply on the left by s inverse." + }, + { + "text": "So this is really, I can do that provided s is invertible, provided my assumption of n independent eigenvectors is satisfied." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk20.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ad5a59fa5db44ce73ff5f88190423e0404fb3d39 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "How, how, what are those numbers approximately?" + }, + { + "text": "Square root of five, well, it's more than two, but less than three." + }, + { + "text": "It, it'd be nice to know these numbers." + }, + { + "text": "I think, I think that that, so that number comes out bigger than one, right?" + }, + { + "text": "Yeah, that's right." + }, + { + "text": "This number comes out bigger than one." + }, + { + "text": "It's about one point six one eight or something." + }, + { + "text": "Not exactly." + }, + { + "text": "It's supposed to be one point six." + }, + { + "text": "Just, like, I think so." + }, + { + "text": "Then what's lambda two?" + }, + { + "text": "Is, is lambda two positive or negative?" + }, + { + "text": "Negative, right?" + }, + { + "text": "Because I'm, it's obviously negative, and I knew that the, so it's minus, and they add up to one, so minus point six one eight, I guess." + }, + { + "text": "OK. And some order." + }, + { + "text": "Those are the two eigenvalues." + }, + { + "text": "One eigenvalue bigger than one, one eigenvalue smaller than one." + }, + { + "text": "Actually, that's a great situation to be in." + }, + { + "text": "Of course, the eigenvalues are different, so there's no doubt whatever, is this matrix diagonalizable?" + }, + { + "text": "Is this matrix diagonalizable, that original matrix A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk21.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..4a034475591d371995b379b5f98783a2cfb25870 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Sure." + }, + { + "text": "We've got two distinct eigenvalues and we can find the eigenvectors in a moment." + }, + { + "text": "But they'll be independent, will be diagonalizable, and now you can already answer my very first question." + }, + { + "text": "How fast are those Fibonacci numbers increasing?" + }, + { + "text": "How, those, they're increasing, right?" + }, + { + "text": "They're not doubling at every step." + }, + { + "text": "Let's look again at these numbers." + }, + { + "text": "Five eight thirteen, it's not obvious." + }, + { + "text": "The next one would be twenty one thirty four." + }, + { + "text": "So to get some idea of what F one hundred is, can you give me any, I mean the crucial number of, so it, these, it's approximately, what's controlling the growth of these Fibonacci numbers?" + }, + { + "text": "It's the eigenvalues." + }, + { + "text": "And which eigenvalues controlling that growth?" + }, + { + "text": "The big ones." + }, + { + "text": "So F one hundred will it be approximately some constant, c one, I guess, times this lambda one, this one plus square root of five over two, to the hundredth power." + }, + { + "text": "And the two hundredth have, in other words, the eigenvalue, the Fibonacci numbers are growing by about that factor." + }, + { + "text": "You see that we've got precise information about the, about the Fibonacci numbers out of the eigenvalue." + }, + { + "text": "OK. And again, why is that true?" + }, + { + "text": "Let me go over to this board and show what I'm doing here." + }, + { + "text": "The, the original eigen, the original initial value is some combination of eigenvectors, and then when we start multiple, when we start going out the theory of Fibonacci numbers, when we start multiplying by a hundred times, it's this lambda one to the hundredth, this term is, is the one that's taken over." + }, + { + "text": "It's, I mean, that's big, like, one point six to the hundredth power." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk22.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..c13a1fc9867173c3067e46c469cfff27b9b45289 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "The second term is practically nothing, right?" + }, + { + "text": "The point six, or minus point six to the hundredth power, is an extremely small, extremely small number." + }, + { + "text": "So this is, this, this, there are only two terms, because we're two by two." + }, + { + "text": "This number is, this piece of it is there, but it's, it's disappearing." + }, + { + "text": "Where this piece is there and it's growing and controlling everything." + }, + { + "text": "So, so really the, we're doing, like, problems that are evolving." + }, + { + "text": "We're doing dynamics." + }, + { + "text": "Instead of Ax equal b, that's a static problem." + }, + { + "text": "We're now, we're doing dynamics." + }, + { + "text": "A, a squared, a cubed, things are evolving in time, and the eigenvalues are the crucial, numbers." + }, + { + "text": "OK." + }, + { + "text": "I guess to complete this, I better write down the eigenvectors." + }, + { + "text": "So we should complete the, the whole process by finding the eigenvectors." + }, + { + "text": "OK. Well, I have to, up in the corner, then I have to look at A minus lambda I." + }, + { + "text": "So A minus lambda I is this one minus lambda, one, one, and minus lambda." + }, + { + "text": "And now, can we spot an eigenvector out of that?" + }, + { + "text": "That's, for these two lambdas, this matrix is singular." + }, + { + "text": "I guess the eigenvector, two by two ought to be easy." + }, + { + "text": "So if I know that this matrix is singular, then it seems to me the eigenvector has to be lambda and one, because that multiplication will give me the zero." + }, + { + "text": "And this multiplication gives me, better give me also zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk23.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..df816eb800ce767b1475c279a24ad976bb45a785 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Do you see why it does?" + }, + { + "text": "This is the minus lambda squared plus lambda plus one." + }, + { + "text": "It's the thing that's zero, because these lambdas are special." + }, + { + "text": "There's the eigenvector." + }, + { + "text": "X1 is lambda one, one, and x2 is lambda two, one." + }, + { + "text": "I did that as a little trick that was available in the two by two case." + }, + { + "text": "So now I finally have to, oh, I have to take the initial, u0." + }, + { + "text": "So to complete this example entirely, I have to say, OK, what was u0?" + }, + { + "text": "u0 was f1 f0." + }, + { + "text": "So u0, the starting vector, is f1 f0, and those were one and zero." + }, + { + "text": "So I have to use that vector, so I have to look for, from multiple of the first eigenvector and the second, to produce u0, the one zero vector." + }, + { + "text": "This is what will find c1 and c2, and then I'm done." + }, + { + "text": "So let me, instead of in the last five seconds grinding out a formula, let me repeat the idea." + }, + { + "text": "That really, it's the idea that's central." + }, + { + "text": "When things are evolving in time, let me come back to this board, because the ideas are here." + }, + { + "text": "When things are evolving in time by a first-order system, starting from an original u0, the key is, find the eigenvalues and eigenvectors of A." + }, + { + "text": "That will tell, those eigenvectors, the eigenvalues will already tell you what's happening." + }, + { + "text": "Is the solution blowing up?" + }, + { + "text": "Is it going to zero?" + }, + { + "text": "What's it doing?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk24.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..40301cb90760e2172baa94d536cbc13288d4c31f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk24.json @@ -0,0 +1,20 @@ +[ + { + "text": "And then, to find out exactly a formula, you have to take your u0 and write it as a combination of eigenvectors and then follow each eigenvector separately." + }, + { + "text": "And that's really what this formula, the formula for, that's what the formula for A to the k is doing." + }, + { + "text": "So remember that formula for A to the k is S, lambda to the k S inverse." + }, + { + "text": "OK. That's, that's difference equations, and you just have to, so the homework will give some examples different from Fibonacci to follow through." + }, + { + "text": "And next time will be differential equations." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk3.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..9bf1bb852baadc1da7837e14180c0c2951a30882 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I mentioned at the end of last time, and I'll say again, that there's a small number of matrices for, that don't have n independent eigenvectors." + }, + { + "text": "So I've got to discuss that, that technical point." + }, + { + "text": "But the great, the most matrices that we see have n, n independent eigenvectors and we can diagonalize." + }, + { + "text": "This is diagonalization." + }, + { + "text": "I could also write it, and I often will, the other way round." + }, + { + "text": "If I multiply on the right by s inverse, if I took this equation at the top and multiplied on the right by s inverse, I could, I would have A left here." + }, + { + "text": "Now s inverse is coming from the right." + }, + { + "text": "So can you keep those two straight?" + }, + { + "text": "A multiplies its eigenvectors." + }, + { + "text": "That's how I keep them straight." + }, + { + "text": "So A multiplies s. A multiplies s. And then this s inverse makes the whole thing diagonal." + }, + { + "text": "And this is another way of saying the same thing, putting the s's on the other side of the equation, A is s lambda s inverse." + }, + { + "text": "So that's the, that's the new factorization." + }, + { + "text": "That's the replacement for L U from elimination or Q R from Gram-Schmidt." + }, + { + "text": "And notice that the matrix, so it's, it's a matrix times a diagonal matrix times the inverse of the first one." + }, + { + "text": "It's, that's the combination that we'll see throughout this chapter." + }, + { + "text": "This, this, combination with an s and an s inverse." + }, + { + "text": "OK. Can I just begin to use that?" + }, + { + "text": "For example, what about A squared?" + }, + { + "text": "What are the eigenvalues and eigenvectors of A squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk4.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c687b6948acad76de8781cb82d3eb069c9da514e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's a straightforward question with a, with a absolutely clean answer." + }, + { + "text": "So let me, let me consider A squared." + }, + { + "text": "So I look, I start with Ax equal lambda x." + }, + { + "text": "And I'm headed for A squared." + }, + { + "text": "So let me multiply both sides by A." + }, + { + "text": "That's one way to get A squared on the left." + }, + { + "text": "So if, I should write these ifs in here." + }, + { + "text": "If Ax equals lambda x, then I multiply by A." + }, + { + "text": "So I get A squared x equals, well, I'm multiplying by A, so that's lambda Ax." + }, + { + "text": "That lambda was a number, so I just put it on the left." + }, + { + "text": "And what do I, tell me how to make that look better." + }, + { + "text": "What have I got here?" + }, + { + "text": "For, if, if A has the eigenvalue lambda and eigenvector x, what's up with A squared?" + }, + { + "text": "A squared x, I just multiply by A, but now for Ax, I'm going to substitute lambda x, so I've got lambda squared x." + }, + { + "text": "So from that simple calculation, I, my conclusion is that the eigenvalues of A squared are lambda squared." + }, + { + "text": "And the eigenvectors, I always think about both of those." + }, + { + "text": "What can I say about the eigenvalues?" + }, + { + "text": "They're squared." + }, + { + "text": "What can I say about the eigenvectors?" + }, + { + "text": "They're the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk5.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5bf15e20707c156c8ae71c9c7acea41a9d9d8e46 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same x as in, as for A." + }, + { + "text": "Now, let me see that also from this formula." + }, + { + "text": "How can I see what A squared is looking like from this formula?" + }, + { + "text": "So let me, that, that was one way to do it." + }, + { + "text": "Let me do it by just taking A squared from that." + }, + { + "text": "A squared is S lambda S inverse, that's A, times S lambda S inverse, that's A, which is?" + }, + { + "text": "This is the beauty of eigenvalues, eigenvectors, having that S inverse and S is the identity, so I've got S lambda squared S inverse." + }, + { + "text": "Yes." + }, + { + "text": "You see what that's telling me?" + }, + { + "text": "It's, it's telling me the same thing that I just learned here, but in the, in, in a matrix form." + }, + { + "text": "It's telling me that the S is the same, the eigenvectors are the same, but the eigenvalues are squared, because this is, what's lambda squared, that's still diagonal, it's got little lambda one squared, lambda two squared, down to lambda n squared, on that diagonal, those are the eigenvalues, as we just learned, of A squared." + }, + { + "text": "OK." + }, + { + "text": "So, somehow those eigenvalues and eigenvectors are really giving you a way to, to, to, to see what's going on inside a matrix." + }, + { + "text": "Now, of course, I can continue that for, to the k-th power." + }, + { + "text": "A to the k-th power." + }, + { + "text": "If I multiply, if I have k of these together, do you see how S inverse S will keep cancelling?" + }, + { + "text": "In the, in the inside, I'll have the S outside, at the far left, and lambda will be in there k times and S inverse." + }, + { + "text": "So what's that telling me?" + }, + { + "text": "That's telling me that the eigenvalues of A, of A to the k-th power are the k-th powers." + }, + { + "text": "The eigenvalues of A cubed are the cubes of the eigenvalues of A, and the eigenvectors are the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk6.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..c18dddbe798022f7e68278ac002a3f5fe6ed249e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same." + }, + { + "text": "OK." + }, + { + "text": "In other words, eigenvalues and eigenvectors give a great way to understand the powers of a matrix." + }, + { + "text": "If I take the square of a matrix or the hundredth power of a matrix, the pivots are all over the place." + }, + { + "text": "L U, if I multiply L U times L U times L U times L U a hundred times, I've got a hundred L U's." + }, + { + "text": "I can't do anything with them." + }, + { + "text": "But when I multiply S lambda S inverse by itself, when I look at the eigenvector picture a hundred times, I get a hundred or ninety-nine of these guys cancelling out inside, and I get A to the hundredth is S lambda to the hundredth S inverse." + }, + { + "text": "I mean, eigenvalues tell you about powers of a matrix in a way that we had no, no way to approach previously." + }, + { + "text": "For example, when does, when do the powers of a matrix go to zero?" + }, + { + "text": "I would call that matrix stable, maybe." + }, + { + "text": "So, so, so I could write down a, a theorem." + }, + { + "text": "I'll, I'll write it as a theorem, just to use that word to emphasize that here I'm getting this great fact from this eigenvalue picture." + }, + { + "text": "OK. A to the k approaches zero as k goes, as k gets bigger." + }, + { + "text": "If what?" + }, + { + "text": "What's the, how can I tell for a matrix A if its powers go to zero?" + }, + { + "text": "What, what's somewhere inside that matrix is that information." + }, + { + "text": "That information is not present in the pivots." + }, + { + "text": "It's present in the eigenvalues." + }, + { + "text": "What do I need for the, to know that if I take higher and higher powers of A that this matrix gets smaller and smaller?" + }, + { + "text": "Well, S and S inverse are not moving." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk7.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b84a5c854a5542758e8a0107e1ff043205fe3bdb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's this guy that has to get small, and that's easy to, easy to understand." + }, + { + "text": "The requirement is all eigenvalues, so what is the requirement?" + }, + { + "text": "The eigenvalues have to be less than one." + }, + { + "text": "Now, I have to write that absolute value, because those eigenvalues could be negative, they could be complex numbers." + }, + { + "text": "So I'm taking the absolute value if all of those are below one." + }, + { + "text": "That's, in fact, we practically see why." + }, + { + "text": "Let me just say that I, that I, I'm operating on one assumption here, and I got to keep remembering that that assumption is still present." + }, + { + "text": "That assumption was that I had a full set of, of n independent eigenvectors." + }, + { + "text": "If I don't have that, then I, I, then this approach is not working." + }, + { + "text": "So, so again, a pure eigenvalue approach, eigenvector approach, needs n independent eigenvectors." + }, + { + "text": "If we don't have n independent eigenvectors, we can't diagonalize the matrix." + }, + { + "text": "We can't get to a diagonal matrix." + }, + { + "text": "This, this, this diagonalization is only possible if S inverse makes sense." + }, + { + "text": "OK. Can I, can I follow up on that point now?" + }, + { + "text": "So, so you see why, what we get and, and why we want it, because we get information about the powers of a matrix just immediately from the eigenvalues." + }, + { + "text": "OK, now let me follow up on this, business of which matrices are diagonalizable." + }, + { + "text": "Sorry about that long word." + }, + { + "text": "So a matrix is, is sure to, so here's, here's the main point." + }, + { + "text": "A is sure to be, to have n independent eigenvectors and, and B, now here comes that word, diagonalizable, if, if, so we, we, we might as well get the, the nice case out in the open." + }, + { + "text": "The nice case is when, if all the lambdas are different." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk8.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f06dcec8ffa0ee1bf19440e4ab2194db33ab353b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means, that means no repeated eigenvalues." + }, + { + "text": "OK. That's the nice case." + }, + { + "text": "If, if my matrix and most matrix, if I do a random matrix in MATLAB and compute its eigenvalues, so if I computed, if I took I of rand of ten ten, gave, gave that MATLAB command, the, we'd get a random ten by ten matrix, we would get a list of its ten eigenvalues and they would be different." + }, + { + "text": "They would be distinct, is the best word." + }, + { + "text": "I would have a random matrix will have ten distinct, a ten by ten matrix will have ten distinct eigenvalues, and if it does, the eigenvectors are automatically independent." + }, + { + "text": "So that's a nice fact." + }, + { + "text": "I can, I'll refer you to the text for the proof." + }, + { + "text": "That, that A is sure to have n independent eigenvectors if the eigenvalues are different." + }, + { + "text": "If, if all the, if all eigenvalues are different." + }, + { + "text": "It's just, if some lambdas are repeated, then I have to look more closely." + }, + { + "text": "If an eigenvalue is repeated, I have to look, I have to count, I have to check." + }, + { + "text": "Has it got, say it's repeated three times." + }, + { + "text": "So what's a possibility for, so, so here's, here's the repeated possibility." + }, + { + "text": "And, and let me emphasize the conclusion." + }, + { + "text": "That if I have repeated eigenvalues, I may or may not, I may or may not have, have n independent eigenvectors." + }, + { + "text": "I might." + }, + { + "text": "I, I, you know, this isn't a completely negative case." + }, + { + "text": "The identity matrix." + }, + { + "text": "Well, suppose I take the ten by ten identity matrix." + }, + { + "text": "What are the eigenvalues of that matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk9.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..87d2a2ae5773036cf11800e2f1962908986a0dad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_1_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So just, just take the easiest matrix, the identity." + }, + { + "text": "If I look for its eigenvalues, they're all ones." + }, + { + "text": "So that eigenvalue one is repeated ten times." + }, + { + "text": "But there's no shortage of eigenvectors for the identity matrix." + }, + { + "text": "In fact, every vector is an eigenvector." + }, + { + "text": "So I can take ten independent vectors." + }, + { + "text": "Oh, well, what happens to everything if, if, if A is the identity matrix, let's just think that one through in our head." + }, + { + "text": "If A is the identity matrix, then it's got plenty of eigenvectors." + }, + { + "text": "I choose ten independent vectors, they're the columns of S, and, and what do I get from S inverse A S?" + }, + { + "text": "I get I again, right?" + }, + { + "text": "If A is the identity, and of course, that's the correct lambda." + }, + { + "text": "The, the matrix was already diagonal." + }, + { + "text": "So if the matrix is already diagonal, then the, the lambda is the same as the matrix." + }, + { + "text": "A diagonal matrix has got its eigenvalues sitting right there in front of you." + }, + { + "text": "Now if it's triangular, the eigenvalues are still sitting there, but so let's, let's take a case where, it's triangular." + }, + { + "text": "Suppose A is like, two, one, two, zero." + }, + { + "text": "So there's a case that's going to be trouble." + }, + { + "text": "There's a case that's going to be trouble." + }, + { + "text": "First of all, what are the eigen- I mean, we just, like now you, if we start with a matrix, the first thing we do practically without thinking is compute the eigenvalues and eigenvectors." + }, + { + "text": "OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk0.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6898d4fe66019ef6b40d0472ea94a968e7bbde9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, shall we start?" + }, + { + "text": "This is the second lecture on eigenvalues." + }, + { + "text": "So the first lecture was set -- reached the key equation, Ax equal lambda x. x is the eigenvector and lambda is the eigenvalue." + }, + { + "text": "Now, to use that." + }, + { + "text": "And the good way to, after we've found, so job one is to find the eigenvalues and find the eigenvectors." + }, + { + "text": "Now after we found them, what do we do with them?" + }, + { + "text": "Well, the good way to see that is diagonalize the matrix." + }, + { + "text": "So the matrix is A, and I want to show, first of all, this is like the basic fact." + }, + { + "text": "This, this formula." + }, + { + "text": "That's, that's the key to today's lecture." + }, + { + "text": "This matrix A, I put its eigenvectors in the columns of a matrix S. So S will be the eigenvector matrix, and I want to look at this magic combination S inverse A S. So can I show you how that, how that, what happens there?" + }, + { + "text": "And notice, notice, there's an S inverse." + }, + { + "text": "We have to be able to invert this eigenvector matrix S. So for that we need n independent eigenvectors." + }, + { + "text": "So that's the, that's the case." + }, + { + "text": "OK." + }, + { + "text": "So suppose we have n linearly independent eigenvectors of A." + }, + { + "text": "Put them in the columns of this matrix S. So I'm naturally going to call that the eigenvector matrix, because it's got the eigenvectors in its columns." + }, + { + "text": "And all I want to do is show you what happens when you multiply A times S. So A times S. So this is A times the matrix with the first eigenvector in its first column, the second eigenvector in its second column, the nth eigenvector in its nth column." + }, + { + "text": "And how am I going to do this matrix multiplication?" + }, + { + "text": "Well, certainly I'll do it a column at a time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk1.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..fbe078217bb68baea8e0605a5d04be568c49efbf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I get?" + }, + { + "text": "A times the first column gives me the first column of the answer, but what is it?" + }, + { + "text": "That's an eigenvector." + }, + { + "text": "A times x1 is equal to the lambda times the x1." + }, + { + "text": "And that lambda's we'll call lambda one, of course." + }, + { + "text": "So that's the first column, A x1 is the same as lambda one x1." + }, + { + "text": "A x2 is lambda two x2, so on, along to, in the nth column, we now have lambda n xn." + }, + { + "text": "Looking good, but the next step is even better." + }, + { + "text": "So for the next step, I want to separate out those eigenvalues, those multiplying numbers, from the x's." + }, + { + "text": "So then I'll have just what I want." + }, + { + "text": "OK, so how, how am I going to separate out?" + }, + { + "text": "So that, that number lambda one is multiplying the first column." + }, + { + "text": "So if I want to factor it out of the first column, I better put, here is going to be x1, and that's going to multiply this matrix lambda one in the first entry in all zeros." + }, + { + "text": "You see that that, that's going to come out right for the first column?" + }, + { + "text": "Because we remember how, how we're going back to that original punchline, that if I want a number to multiply x1, then I can do it by putting x1 in that column, in the first column, and putting that number there." + }, + { + "text": "What am I going to have here?" + }, + { + "text": "I'm going to have lambda one, I'm going to have x1, x2, xn." + }, + { + "text": "These are going to be my columns again." + }, + { + "text": "I'm getting s back again." + }, + { + "text": "I'm getting s back again, but now what's it multiplied by?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk10.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c58a42edbe9567233ca7f57643a0b7d43ae6761f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what are the eigenvalues?" + }, + { + "text": "You can tell me right away what they are." + }, + { + "text": "They're two and two, right." + }, + { + "text": "It's a triangular matrix, so when I do this determinant, shall I do this determinant of A minus lambda I?" + }, + { + "text": "I'll get this two minus lambda, one, zero, two minus lambda, right?" + }, + { + "text": "I take that determinant, so I make those into vertical bars to mean determinant, and what's the determinant?" + }, + { + "text": "Two minus lambda squared." + }, + { + "text": "What are the roots?" + }, + { + "text": "Lambda equal two twice." + }, + { + "text": "So the eigenvalues are lambda equals two and two." + }, + { + "text": "OK, fine." + }, + { + "text": "Now the next step, find the eigenvectors." + }, + { + "text": "So I look for eigenvectors and what do I find for this guy?" + }, + { + "text": "Eigenvectors for this guy, when I subtract two minus the identity, so A minus two I has zeros here, and I'm looking for the null space." + }, + { + "text": "What's, what are the eigenvectors?" + }, + { + "text": "They're the, they're, they're the null space of A minus lambda I." + }, + { + "text": "The null space is only one dimension." + }, + { + "text": "This is a case where I don't have enough eigenvectors." + }, + { + "text": "My algebraic multiplicity is two." + }, + { + "text": "I, I would say when I see, when I count how often the eigenvalue is repeated, that's the algebraic multiplicity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk11.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..779c2cf904d904b761080db2671aac46394ad02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the multiplicity." + }, + { + "text": "How many times is it the root of the polynomial?" + }, + { + "text": "My polynomial is two minus lambda squared." + }, + { + "text": "It's a double root." + }, + { + "text": "So my algebraic multiplicity is two." + }, + { + "text": "But the geometric multiplicity, which looks for vectors, looks for eigenvectors and which means the null space of this thing." + }, + { + "text": "And the only eigenvector is one zero." + }, + { + "text": "That's in the null space." + }, + { + "text": "Zero one is not in the null space." + }, + { + "text": "The null space is only one dimensional." + }, + { + "text": "So there's a matrix, my, this A or the original A, that are not diagonalizable." + }, + { + "text": "I can't, I can't find two independent eigenvectors, there's only one." + }, + { + "text": "OK." + }, + { + "text": "So that's the case that I'm, that's a case that I, I'm not really handling." + }, + { + "text": "For example, when I wrote down up here that the powers went to zero if the eigenvalues were below one, I didn't really handle that case of repeated eigenvalues because my reasoning was based on this formula." + }, + { + "text": "And this formula is based on n independent eigenvectors." + }, + { + "text": "OK." + }, + { + "text": "So just to say that." + }, + { + "text": "There are some matrices that we don't cover through diagonalization, but the great majority we do." + }, + { + "text": "OK. And we're always OK if we have different distinct eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk12.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..77d090704cc298475d94416b7ecb88a2a015a913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. That's the, like, the typical case." + }, + { + "text": "Because for each eigenvalue there's at least one eigenvector, the algebraic multiplicity here is one for every eigenvalue, and the geometric multiplicity is one." + }, + { + "text": "There's one eigenvector and they are independent." + }, + { + "text": "OK. OK. Now let me come back to the important case when we're OK." + }, + { + "text": "The important case when we are diagonalizing." + }, + { + "text": "Let me look at, so let me solve this equation." + }, + { + "text": "The equation will be each, I start with some, start with a given vector u0." + }, + { + "text": "And then my equation is that every step I multiply what I have by a." + }, + { + "text": "That equation ought to be simple to handle." + }, + { + "text": "OK. And I'd like to be able to solve it." + }, + { + "text": "How would I find, if I start with a vector u0, and I multiply by a a hundred times, what have I got?" + }, + { + "text": "Well, I can certainly write down a formula for the answer." + }, + { + "text": "So what, what, so u1 is a u0." + }, + { + "text": "And u2 is, what's u2 then?" + }, + { + "text": "U2 I multiply it, u2 I get from u1 by another, multiplying by a, so I've got a twice." + }, + { + "text": "And my formula is uk, after k steps, I've multiplied by a k times the original u0." + }, + { + "text": "You see what I'm doing?" + }, + { + "text": "The next section is going to solve systems of differential equations." + }, + { + "text": "I'm going to have derivatives." + }, + { + "text": "This, this section is the nice one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk13.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..ba8214d8c636e4757a266d6617801174bc939d80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "It solves difference equations." + }, + { + "text": "I would call that a difference equation." + }, + { + "text": "It's conne- a first order." + }, + { + "text": "I would call that a first order system, because it connects only, it only goes up one level." + }, + { + "text": "And it's a system because these are vectors and that's a matrix." + }, + { + "text": "And the solution is just that." + }, + { + "text": "OK." + }, + { + "text": "But, that's a nice formula." + }, + { + "text": "That's the, like, the most compact formula I could ever get." + }, + { + "text": "U one hundred would be a to the one hundredth u0." + }, + { + "text": "But how would I actually find u one hundred?" + }, + { + "text": "How would I find, how would I discover what u one hundred is?" + }, + { + "text": "Let me, let me show you how." + }, + { + "text": "Here, here's the idea." + }, + { + "text": "If, so, to solve, to really solve, shall I say, to really solve." + }, + { + "text": "To really solve it, I would take this initial vector, u0, and I would write it as a combination of eigenvectors." + }, + { + "text": "To really solve, write, write u0 as a combination, say, certain amount of the first eigenvector plus a certain amount of the second eigenvector plus a certain amount of the last eigenvector." + }, + { + "text": "Now multiply by a." + }, + { + "text": "You want to, you got to see the magic of eigenvectors work." + }, + { + "text": "Multiply by a." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk14.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7843b2bf0cac762d1c12452cf36500ea4ad13370 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a u0 is what?" + }, + { + "text": "So a times that." + }, + { + "text": "A times, so what's, I can separate it out into n separate pieces and that's the whole point." + }, + { + "text": "That each of those pieces is going in its own merry way." + }, + { + "text": "Each of those pieces is an eigenvector, and when I multiply by a, what does this piece become?" + }, + { + "text": "So that's some amount of the first, let's suppose the eigenvectors are normalized to be unit vectors." + }, + { + "text": "So that says what the eigenvector is." + }, + { + "text": "It's, and I need some multiple of it to produce u0." + }, + { + "text": "OK. Now when I multiply by a, what do I get?" + }, + { + "text": "I get c1, which is just a factor, times a x1, but a x1 is lambda one x1." + }, + { + "text": "When I multiply this by a, I get c2 lambda two x2." + }, + { + "text": "And here I get cn lambda n xn." + }, + { + "text": "And suppose I multiply by a to the hundredth power now." + }, + { + "text": "Can we, can we, having done it, multiplied by a, let's multiply by a to the hundredth." + }, + { + "text": "What happens to this first term when I multiply by a to the one hundredth?" + }, + { + "text": "It's got that factor lambda to the hundredth." + }, + { + "text": "That's the key." + }, + { + "text": "That, that's what I mean by going its own merry way." + }, + { + "text": "It, it is pure eigenvector, it's exactly in a direction where multiplication by a just brings in a scalar factor lambda one." + }, + { + "text": "So a hundred times brings in this a hundred times." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk15.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7ee3348735378aa4049d33ec2a197d0ceb0c447c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Hundred times lambda two, hundred times lambda n. Actually, we're, what are we seeing here?" + }, + { + "text": "We're seeing, this same, lambda, capital lambda to the hundredth, as in the, as in the diagonalization, and we're seeing the S matrix, the matrix S of eigenvectors." + }, + { + "text": "That's what this has got to, this has got to amount to, a lambda to the hundredth power times an S times this vector C that's telling us how much of each one is in the original thing." + }, + { + "text": "So if, if I had to really find the hundredth power, I would take u0, I would expand it as a combination of eigenvectors, this is really S, the eigenvector matrix times C, the, the coefficient vector." + }, + { + "text": "And then I would immediately, then, by inserting these hundredth powers of eigenvalues, I'd have the answer." + }, + { + "text": "So the, the, huh, there must be, well, let's see." + }, + { + "text": "OK." + }, + { + "text": "It's, so, yeah." + }, + { + "text": "So if u100 is a to the hundredth times u0, and u0 is Sc, then you see this formula is just this formula, which is the way I would actually get hold of this, of this u100, which is, let me put it here, u100." + }, + { + "text": "The way I would actually get hold of that, see what, what the solution is after a hundred steps, would be expand the initial vector into eigenvectors and, and let each eigenvector go its own way, multiplying by a hundred at, by lambda at every step, and therefore by lambda to the hundredth power after a hundredth step." + }, + { + "text": "Can I do an example?" + }, + { + "text": "So that's, that's the, the formulas." + }, + { + "text": "Now let me take an example." + }, + { + "text": "I'll use the Fibonacci sequence as an example." + }, + { + "text": "So, so Fibonacci example." + }, + { + "text": "You remember the Fibonacci numbers?" + }, + { + "text": "If we start with one and one as F0, oh, I think I start with zero, maybe." + }, + { + "text": "Let zero and one be the first ones." + }, + { + "text": "So there's F0 and F1, the first two Fibonacci numbers." + }, + { + "text": "Then what's the rule for Fibonacci numbers?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk16.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..79c65e32781f7f304b504a6c390247abb9d26ac8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "They're the sum." + }, + { + "text": "The next one is the sum of those, so it's one." + }, + { + "text": "The next one is the sum of those, so it's two." + }, + { + "text": "The next one is the sum of those, so it's three." + }, + { + "text": "Well, it looks like one, two, three, four, five, but somehow it's not going to do that way." + }, + { + "text": "The next one is five, right." + }, + { + "text": "Two and three makes five." + }, + { + "text": "The next one is eight." + }, + { + "text": "The next one is thirteen." + }, + { + "text": "And the one hundredth Fibonacci number is what?" + }, + { + "text": "That's my question." + }, + { + "text": "How could I get a formula for the hundredth number and for example how could I answer the question how fast are they growing?" + }, + { + "text": "How fast are those Fibonacci numbers growing?" + }, + { + "text": "They're certainly growing." + }, + { + "text": "It's not a stable case, whatever the eigenvalues of whatever matrix it is, they're not smaller than one." + }, + { + "text": "These numbers are growing." + }, + { + "text": "But how fast are they growing?" + }, + { + "text": "The answer is lies in the eigenvalue." + }, + { + "text": "So I've got to find the matrix, so let me write down the Fibonacci rule, F k plus two is F k plus one plus F k, right?" + }, + { + "text": "Now that's not in my -- I want to write that as U k plus one and A U k. But right now what I've got is a single equation, not a system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk17.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b3aaa9dcee3cf27c112015659bb5a0b51a983ce1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's second order." + }, + { + "text": "It's like having a second order differential equation with second derivatives." + }, + { + "text": "I want to get first derivatives." + }, + { + "text": "Here I want to get first difference." + }, + { + "text": "So the way to do it is to introduce U k will be a vector." + }, + { + "text": "See, a small trick." + }, + { + "text": "Let U k be a vector, F k plus one and F k. So I'm going to get a two by two system, first order, instead of a one, instead of a scalar system, second order, by a simple trick." + }, + { + "text": "I'm just going to add in an equation F k plus one equals F k plus one." + }, + { + "text": "That will be my second equation." + }, + { + "text": "Then this is my system, this is my unknown, and what's my one-step equation?" + }, + { + "text": "So now U k plus one." + }, + { + "text": "That's so U k plus one is the left side, and what have I got here on the right side?" + }, + { + "text": "I've got some matrix multiplying U k. Can you see that all right?" + }, + { + "text": "If you can see it, then you can tell me what the matrix is." + }, + { + "text": "You see that I'm taking my system here, I artificially made it into a system." + }, + { + "text": "I artificially made the unknown into a vector, and now I'm ready to look at and see what the matrix is." + }, + { + "text": "So do you see the left side, U k plus one is F k plus two F k plus one, that's just what I want." + }, + { + "text": "On the right side, this, remember, this U k here, let me for the moment put it as F k plus one F k. So what's the matrix?" + }, + { + "text": "Well, that has a one and a one, and that has a one and a zero." + }, + { + "text": "There's the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk18.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..6c1b68c2cb2fde3f5dea82f3100d4da31fcce70a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "You see that that gives me the right-hand side." + }, + { + "text": "So there's the matrix A, and this is our friend U k. So we've got, so that simple trick changed the second order scalar problem to a first order system, two, with two unknowns." + }, + { + "text": "With a matrix and now what do I do?" + }, + { + "text": "Well, before I even think, I find its eigenvalues and eigenvectors." + }, + { + "text": "So what are the eigenvalues and eigenvectors of that matrix?" + }, + { + "text": "Let's see." + }, + { + "text": "I was, first let me just, like, think for a minute." + }, + { + "text": "It's two by two, so this shouldn't be impossible to do." + }, + { + "text": "Let's do it." + }, + { + "text": "OK." + }, + { + "text": "So my matrix again is one one one zero." + }, + { + "text": "It's symmetric, by the way." + }, + { + "text": "So what I will eventually know about symmetric matrices is that the eigenvalues will come out real, I won't get any complex numbers here, and the eigenvectors, once I get those, actually will be orthogonal." + }, + { + "text": "But two by two, I'm more interested in what the actual numbers are." + }, + { + "text": "What do I know about the two numbers?" + }, + { + "text": "Well, should, do you want me to find this determinant of A minus lambda I?" + }, + { + "text": "Sure." + }, + { + "text": "So it's the determinant of one minus lambda one one zero, right?" + }, + { + "text": "Minus lambda, yes, got it." + }, + { + "text": "OK. OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk19.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..a73b23e3d56b889ff49ea7f55a784fac33e13c3d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "There'll be two eigenvalues." + }, + { + "text": "Well, tell me again what I know about the two eigenvalues before I go any further." + }, + { + "text": "Tell me something about these two eigenvalues, what do they add up to?" + }, + { + "text": "Lambda one plus lambda two is the same as the trace down the diagonal of the matrix, one and zero is one." + }, + { + "text": "So lambda one plus lambda two should come out to be one, and lambda one times lambda two should come out to be the determinant, which is minus one." + }, + { + "text": "So I'm expecting the eigenvalues to add to one and to multiply to minus one." + }, + { + "text": "But let's just see it happen here." + }, + { + "text": "If I multiply this out, I get that times that'll be a lambda squared minus lambda minus one." + }, + { + "text": "Good." + }, + { + "text": "Lambda squared minus lambda minus one." + }, + { + "text": "Actually, you see the, compare that with the original equation that I started with." + }, + { + "text": "Fk plus two minus Fk plus one minus Fk is zero." + }, + { + "text": "The recurrent, the recursion that the Fibonacci number satisfy is somehow showing up directly here for the eigenvalues when we set that to zero." + }, + { + "text": "OK. Let's solve." + }, + { + "text": "Well, I would like to be able to factor that, that quadratic, but I'm better off to use the quadratic formula." + }, + { + "text": "Lambda is, let's see, minus b is one, plus or minus the square root of b squared, which is one, minus four, times that, times that, which is plus four, over two." + }, + { + "text": "So that's the square root of five." + }, + { + "text": "So the eigenvalues are lambda one is one half of one plus square root of five, and lambda two is one half of one minus square root of five." + }, + { + "text": "And sure enough, they, those add up to one, and they multiply to give minus one." + }, + { + "text": "OK. Those are the two eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk2.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..43cfb012fc04a89fc7dab94c23bfb0f50ade3782 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "On the right, it's multiplied by, if I want, if I want lambda n xn in the last column, how do I do it?" + }, + { + "text": "Well, the last column here will be, I'll, I'll take the last column, use these coefficients, put the lambda n down there, and it will multiply that nth column and give me lambda n xn." + }, + { + "text": "There, there you see matrix multiplication just working for us." + }, + { + "text": "So I started with A s. I wrote down what it meant." + }, + { + "text": "A times each eigenvector." + }, + { + "text": "That gave me lambda times the eigenvector." + }, + { + "text": "And then when I peeled off the lambdas, they were on the right-hand side, so I've got s, my matrix back again, and this matrix, this diagonal matrix, the eigenvalue matrix, and I call it capital lambda, using capital letters for matrices, and lambda to prompt me that it's, that it's eigenvalues that are in there." + }, + { + "text": "So you see that the eigenvalues are just sitting down that diagonal?" + }, + { + "text": "If I had a column x2 here, I would want the lambda two in the two two position, in the diagonal position, to multiply that x2 and give me the lambda two x2." + }, + { + "text": "That's my formula." + }, + { + "text": "A s is s lambda." + }, + { + "text": "OK. That's, that's the, you see, it's just a calculation." + }, + { + "text": "Now, I, I mentioned, and I have to mention again, this business about n independent eigenvectors." + }, + { + "text": "As it stands, this is all fine whether, I mean, I could be repeating the same eigenvector, but I, I'm no interested in that." + }, + { + "text": "I want to be able to invert s, and that's where this comes in." + }, + { + "text": "This n independent eigenvectors business comes in to tell me that that matrix is invertible." + }, + { + "text": "So let me, on the next board, write down what I've got." + }, + { + "text": "A s equals s lambda." + }, + { + "text": "And now I'm, I can multiply on the left by s inverse." + }, + { + "text": "So this is really, I can do that provided s is invertible, provided my assumption of n independent eigenvectors is satisfied." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk20.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ad5a59fa5db44ce73ff5f88190423e0404fb3d39 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "How, how, what are those numbers approximately?" + }, + { + "text": "Square root of five, well, it's more than two, but less than three." + }, + { + "text": "It, it'd be nice to know these numbers." + }, + { + "text": "I think, I think that that, so that number comes out bigger than one, right?" + }, + { + "text": "Yeah, that's right." + }, + { + "text": "This number comes out bigger than one." + }, + { + "text": "It's about one point six one eight or something." + }, + { + "text": "Not exactly." + }, + { + "text": "It's supposed to be one point six." + }, + { + "text": "Just, like, I think so." + }, + { + "text": "Then what's lambda two?" + }, + { + "text": "Is, is lambda two positive or negative?" + }, + { + "text": "Negative, right?" + }, + { + "text": "Because I'm, it's obviously negative, and I knew that the, so it's minus, and they add up to one, so minus point six one eight, I guess." + }, + { + "text": "OK. And some order." + }, + { + "text": "Those are the two eigenvalues." + }, + { + "text": "One eigenvalue bigger than one, one eigenvalue smaller than one." + }, + { + "text": "Actually, that's a great situation to be in." + }, + { + "text": "Of course, the eigenvalues are different, so there's no doubt whatever, is this matrix diagonalizable?" + }, + { + "text": "Is this matrix diagonalizable, that original matrix A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk21.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..4a034475591d371995b379b5f98783a2cfb25870 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Sure." + }, + { + "text": "We've got two distinct eigenvalues and we can find the eigenvectors in a moment." + }, + { + "text": "But they'll be independent, will be diagonalizable, and now you can already answer my very first question." + }, + { + "text": "How fast are those Fibonacci numbers increasing?" + }, + { + "text": "How, those, they're increasing, right?" + }, + { + "text": "They're not doubling at every step." + }, + { + "text": "Let's look again at these numbers." + }, + { + "text": "Five eight thirteen, it's not obvious." + }, + { + "text": "The next one would be twenty one thirty four." + }, + { + "text": "So to get some idea of what F one hundred is, can you give me any, I mean the crucial number of, so it, these, it's approximately, what's controlling the growth of these Fibonacci numbers?" + }, + { + "text": "It's the eigenvalues." + }, + { + "text": "And which eigenvalues controlling that growth?" + }, + { + "text": "The big ones." + }, + { + "text": "So F one hundred will it be approximately some constant, c one, I guess, times this lambda one, this one plus square root of five over two, to the hundredth power." + }, + { + "text": "And the two hundredth have, in other words, the eigenvalue, the Fibonacci numbers are growing by about that factor." + }, + { + "text": "You see that we've got precise information about the, about the Fibonacci numbers out of the eigenvalue." + }, + { + "text": "OK. And again, why is that true?" + }, + { + "text": "Let me go over to this board and show what I'm doing here." + }, + { + "text": "The, the original eigen, the original initial value is some combination of eigenvectors, and then when we start multiple, when we start going out the theory of Fibonacci numbers, when we start multiplying by a hundred times, it's this lambda one to the hundredth, this term is, is the one that's taken over." + }, + { + "text": "It's, I mean, that's big, like, one point six to the hundredth power." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk22.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..c13a1fc9867173c3067e46c469cfff27b9b45289 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "The second term is practically nothing, right?" + }, + { + "text": "The point six, or minus point six to the hundredth power, is an extremely small, extremely small number." + }, + { + "text": "So this is, this, this, there are only two terms, because we're two by two." + }, + { + "text": "This number is, this piece of it is there, but it's, it's disappearing." + }, + { + "text": "Where this piece is there and it's growing and controlling everything." + }, + { + "text": "So, so really the, we're doing, like, problems that are evolving." + }, + { + "text": "We're doing dynamics." + }, + { + "text": "Instead of Ax equal b, that's a static problem." + }, + { + "text": "We're now, we're doing dynamics." + }, + { + "text": "A, a squared, a cubed, things are evolving in time, and the eigenvalues are the crucial, numbers." + }, + { + "text": "OK." + }, + { + "text": "I guess to complete this, I better write down the eigenvectors." + }, + { + "text": "So we should complete the, the whole process by finding the eigenvectors." + }, + { + "text": "OK. Well, I have to, up in the corner, then I have to look at A minus lambda I." + }, + { + "text": "So A minus lambda I is this one minus lambda, one, one, and minus lambda." + }, + { + "text": "And now, can we spot an eigenvector out of that?" + }, + { + "text": "That's, for these two lambdas, this matrix is singular." + }, + { + "text": "I guess the eigenvector, two by two ought to be easy." + }, + { + "text": "So if I know that this matrix is singular, then it seems to me the eigenvector has to be lambda and one, because that multiplication will give me the zero." + }, + { + "text": "And this multiplication gives me, better give me also zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk23.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..df816eb800ce767b1475c279a24ad976bb45a785 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Do you see why it does?" + }, + { + "text": "This is the minus lambda squared plus lambda plus one." + }, + { + "text": "It's the thing that's zero, because these lambdas are special." + }, + { + "text": "There's the eigenvector." + }, + { + "text": "X1 is lambda one, one, and x2 is lambda two, one." + }, + { + "text": "I did that as a little trick that was available in the two by two case." + }, + { + "text": "So now I finally have to, oh, I have to take the initial, u0." + }, + { + "text": "So to complete this example entirely, I have to say, OK, what was u0?" + }, + { + "text": "u0 was f1 f0." + }, + { + "text": "So u0, the starting vector, is f1 f0, and those were one and zero." + }, + { + "text": "So I have to use that vector, so I have to look for, from multiple of the first eigenvector and the second, to produce u0, the one zero vector." + }, + { + "text": "This is what will find c1 and c2, and then I'm done." + }, + { + "text": "So let me, instead of in the last five seconds grinding out a formula, let me repeat the idea." + }, + { + "text": "That really, it's the idea that's central." + }, + { + "text": "When things are evolving in time, let me come back to this board, because the ideas are here." + }, + { + "text": "When things are evolving in time by a first-order system, starting from an original u0, the key is, find the eigenvalues and eigenvectors of A." + }, + { + "text": "That will tell, those eigenvectors, the eigenvalues will already tell you what's happening." + }, + { + "text": "Is the solution blowing up?" + }, + { + "text": "Is it going to zero?" + }, + { + "text": "What's it doing?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk24.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..40301cb90760e2172baa94d536cbc13288d4c31f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk24.json @@ -0,0 +1,20 @@ +[ + { + "text": "And then, to find out exactly a formula, you have to take your u0 and write it as a combination of eigenvectors and then follow each eigenvector separately." + }, + { + "text": "And that's really what this formula, the formula for, that's what the formula for A to the k is doing." + }, + { + "text": "So remember that formula for A to the k is S, lambda to the k S inverse." + }, + { + "text": "OK. That's, that's difference equations, and you just have to, so the homework will give some examples different from Fibonacci to follow through." + }, + { + "text": "And next time will be differential equations." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk3.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..9bf1bb852baadc1da7837e14180c0c2951a30882 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I mentioned at the end of last time, and I'll say again, that there's a small number of matrices for, that don't have n independent eigenvectors." + }, + { + "text": "So I've got to discuss that, that technical point." + }, + { + "text": "But the great, the most matrices that we see have n, n independent eigenvectors and we can diagonalize." + }, + { + "text": "This is diagonalization." + }, + { + "text": "I could also write it, and I often will, the other way round." + }, + { + "text": "If I multiply on the right by s inverse, if I took this equation at the top and multiplied on the right by s inverse, I could, I would have A left here." + }, + { + "text": "Now s inverse is coming from the right." + }, + { + "text": "So can you keep those two straight?" + }, + { + "text": "A multiplies its eigenvectors." + }, + { + "text": "That's how I keep them straight." + }, + { + "text": "So A multiplies s. A multiplies s. And then this s inverse makes the whole thing diagonal." + }, + { + "text": "And this is another way of saying the same thing, putting the s's on the other side of the equation, A is s lambda s inverse." + }, + { + "text": "So that's the, that's the new factorization." + }, + { + "text": "That's the replacement for L U from elimination or Q R from Gram-Schmidt." + }, + { + "text": "And notice that the matrix, so it's, it's a matrix times a diagonal matrix times the inverse of the first one." + }, + { + "text": "It's, that's the combination that we'll see throughout this chapter." + }, + { + "text": "This, this, combination with an s and an s inverse." + }, + { + "text": "OK. Can I just begin to use that?" + }, + { + "text": "For example, what about A squared?" + }, + { + "text": "What are the eigenvalues and eigenvectors of A squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk4.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c687b6948acad76de8781cb82d3eb069c9da514e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's a straightforward question with a, with a absolutely clean answer." + }, + { + "text": "So let me, let me consider A squared." + }, + { + "text": "So I look, I start with Ax equal lambda x." + }, + { + "text": "And I'm headed for A squared." + }, + { + "text": "So let me multiply both sides by A." + }, + { + "text": "That's one way to get A squared on the left." + }, + { + "text": "So if, I should write these ifs in here." + }, + { + "text": "If Ax equals lambda x, then I multiply by A." + }, + { + "text": "So I get A squared x equals, well, I'm multiplying by A, so that's lambda Ax." + }, + { + "text": "That lambda was a number, so I just put it on the left." + }, + { + "text": "And what do I, tell me how to make that look better." + }, + { + "text": "What have I got here?" + }, + { + "text": "For, if, if A has the eigenvalue lambda and eigenvector x, what's up with A squared?" + }, + { + "text": "A squared x, I just multiply by A, but now for Ax, I'm going to substitute lambda x, so I've got lambda squared x." + }, + { + "text": "So from that simple calculation, I, my conclusion is that the eigenvalues of A squared are lambda squared." + }, + { + "text": "And the eigenvectors, I always think about both of those." + }, + { + "text": "What can I say about the eigenvalues?" + }, + { + "text": "They're squared." + }, + { + "text": "What can I say about the eigenvectors?" + }, + { + "text": "They're the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk5.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5bf15e20707c156c8ae71c9c7acea41a9d9d8e46 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same x as in, as for A." + }, + { + "text": "Now, let me see that also from this formula." + }, + { + "text": "How can I see what A squared is looking like from this formula?" + }, + { + "text": "So let me, that, that was one way to do it." + }, + { + "text": "Let me do it by just taking A squared from that." + }, + { + "text": "A squared is S lambda S inverse, that's A, times S lambda S inverse, that's A, which is?" + }, + { + "text": "This is the beauty of eigenvalues, eigenvectors, having that S inverse and S is the identity, so I've got S lambda squared S inverse." + }, + { + "text": "Yes." + }, + { + "text": "You see what that's telling me?" + }, + { + "text": "It's, it's telling me the same thing that I just learned here, but in the, in, in a matrix form." + }, + { + "text": "It's telling me that the S is the same, the eigenvectors are the same, but the eigenvalues are squared, because this is, what's lambda squared, that's still diagonal, it's got little lambda one squared, lambda two squared, down to lambda n squared, on that diagonal, those are the eigenvalues, as we just learned, of A squared." + }, + { + "text": "OK." + }, + { + "text": "So, somehow those eigenvalues and eigenvectors are really giving you a way to, to, to, to see what's going on inside a matrix." + }, + { + "text": "Now, of course, I can continue that for, to the k-th power." + }, + { + "text": "A to the k-th power." + }, + { + "text": "If I multiply, if I have k of these together, do you see how S inverse S will keep cancelling?" + }, + { + "text": "In the, in the inside, I'll have the S outside, at the far left, and lambda will be in there k times and S inverse." + }, + { + "text": "So what's that telling me?" + }, + { + "text": "That's telling me that the eigenvalues of A, of A to the k-th power are the k-th powers." + }, + { + "text": "The eigenvalues of A cubed are the cubes of the eigenvalues of A, and the eigenvectors are the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk6.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..c18dddbe798022f7e68278ac002a3f5fe6ed249e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same." + }, + { + "text": "OK." + }, + { + "text": "In other words, eigenvalues and eigenvectors give a great way to understand the powers of a matrix." + }, + { + "text": "If I take the square of a matrix or the hundredth power of a matrix, the pivots are all over the place." + }, + { + "text": "L U, if I multiply L U times L U times L U times L U a hundred times, I've got a hundred L U's." + }, + { + "text": "I can't do anything with them." + }, + { + "text": "But when I multiply S lambda S inverse by itself, when I look at the eigenvector picture a hundred times, I get a hundred or ninety-nine of these guys cancelling out inside, and I get A to the hundredth is S lambda to the hundredth S inverse." + }, + { + "text": "I mean, eigenvalues tell you about powers of a matrix in a way that we had no, no way to approach previously." + }, + { + "text": "For example, when does, when do the powers of a matrix go to zero?" + }, + { + "text": "I would call that matrix stable, maybe." + }, + { + "text": "So, so, so I could write down a, a theorem." + }, + { + "text": "I'll, I'll write it as a theorem, just to use that word to emphasize that here I'm getting this great fact from this eigenvalue picture." + }, + { + "text": "OK. A to the k approaches zero as k goes, as k gets bigger." + }, + { + "text": "If what?" + }, + { + "text": "What's the, how can I tell for a matrix A if its powers go to zero?" + }, + { + "text": "What, what's somewhere inside that matrix is that information." + }, + { + "text": "That information is not present in the pivots." + }, + { + "text": "It's present in the eigenvalues." + }, + { + "text": "What do I need for the, to know that if I take higher and higher powers of A that this matrix gets smaller and smaller?" + }, + { + "text": "Well, S and S inverse are not moving." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk7.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b84a5c854a5542758e8a0107e1ff043205fe3bdb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's this guy that has to get small, and that's easy to, easy to understand." + }, + { + "text": "The requirement is all eigenvalues, so what is the requirement?" + }, + { + "text": "The eigenvalues have to be less than one." + }, + { + "text": "Now, I have to write that absolute value, because those eigenvalues could be negative, they could be complex numbers." + }, + { + "text": "So I'm taking the absolute value if all of those are below one." + }, + { + "text": "That's, in fact, we practically see why." + }, + { + "text": "Let me just say that I, that I, I'm operating on one assumption here, and I got to keep remembering that that assumption is still present." + }, + { + "text": "That assumption was that I had a full set of, of n independent eigenvectors." + }, + { + "text": "If I don't have that, then I, I, then this approach is not working." + }, + { + "text": "So, so again, a pure eigenvalue approach, eigenvector approach, needs n independent eigenvectors." + }, + { + "text": "If we don't have n independent eigenvectors, we can't diagonalize the matrix." + }, + { + "text": "We can't get to a diagonal matrix." + }, + { + "text": "This, this, this diagonalization is only possible if S inverse makes sense." + }, + { + "text": "OK. Can I, can I follow up on that point now?" + }, + { + "text": "So, so you see why, what we get and, and why we want it, because we get information about the powers of a matrix just immediately from the eigenvalues." + }, + { + "text": "OK, now let me follow up on this, business of which matrices are diagonalizable." + }, + { + "text": "Sorry about that long word." + }, + { + "text": "So a matrix is, is sure to, so here's, here's the main point." + }, + { + "text": "A is sure to be, to have n independent eigenvectors and, and B, now here comes that word, diagonalizable, if, if, so we, we, we might as well get the, the nice case out in the open." + }, + { + "text": "The nice case is when, if all the lambdas are different." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk8.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f06dcec8ffa0ee1bf19440e4ab2194db33ab353b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means, that means no repeated eigenvalues." + }, + { + "text": "OK. That's the nice case." + }, + { + "text": "If, if my matrix and most matrix, if I do a random matrix in MATLAB and compute its eigenvalues, so if I computed, if I took I of rand of ten ten, gave, gave that MATLAB command, the, we'd get a random ten by ten matrix, we would get a list of its ten eigenvalues and they would be different." + }, + { + "text": "They would be distinct, is the best word." + }, + { + "text": "I would have a random matrix will have ten distinct, a ten by ten matrix will have ten distinct eigenvalues, and if it does, the eigenvectors are automatically independent." + }, + { + "text": "So that's a nice fact." + }, + { + "text": "I can, I'll refer you to the text for the proof." + }, + { + "text": "That, that A is sure to have n independent eigenvectors if the eigenvalues are different." + }, + { + "text": "If, if all the, if all eigenvalues are different." + }, + { + "text": "It's just, if some lambdas are repeated, then I have to look more closely." + }, + { + "text": "If an eigenvalue is repeated, I have to look, I have to count, I have to check." + }, + { + "text": "Has it got, say it's repeated three times." + }, + { + "text": "So what's a possibility for, so, so here's, here's the repeated possibility." + }, + { + "text": "And, and let me emphasize the conclusion." + }, + { + "text": "That if I have repeated eigenvalues, I may or may not, I may or may not have, have n independent eigenvectors." + }, + { + "text": "I might." + }, + { + "text": "I, I, you know, this isn't a completely negative case." + }, + { + "text": "The identity matrix." + }, + { + "text": "Well, suppose I take the ten by ten identity matrix." + }, + { + "text": "What are the eigenvalues of that matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk9.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..87d2a2ae5773036cf11800e2f1962908986a0dad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_21_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So just, just take the easiest matrix, the identity." + }, + { + "text": "If I look for its eigenvalues, they're all ones." + }, + { + "text": "So that eigenvalue one is repeated ten times." + }, + { + "text": "But there's no shortage of eigenvectors for the identity matrix." + }, + { + "text": "In fact, every vector is an eigenvector." + }, + { + "text": "So I can take ten independent vectors." + }, + { + "text": "Oh, well, what happens to everything if, if, if A is the identity matrix, let's just think that one through in our head." + }, + { + "text": "If A is the identity matrix, then it's got plenty of eigenvectors." + }, + { + "text": "I choose ten independent vectors, they're the columns of S, and, and what do I get from S inverse A S?" + }, + { + "text": "I get I again, right?" + }, + { + "text": "If A is the identity, and of course, that's the correct lambda." + }, + { + "text": "The, the matrix was already diagonal." + }, + { + "text": "So if the matrix is already diagonal, then the, the lambda is the same as the matrix." + }, + { + "text": "A diagonal matrix has got its eigenvalues sitting right there in front of you." + }, + { + "text": "Now if it's triangular, the eigenvalues are still sitting there, but so let's, let's take a case where, it's triangular." + }, + { + "text": "Suppose A is like, two, one, two, zero." + }, + { + "text": "So there's a case that's going to be trouble." + }, + { + "text": "There's a case that's going to be trouble." + }, + { + "text": "First of all, what are the eigen- I mean, we just, like now you, if we start with a matrix, the first thing we do practically without thinking is compute the eigenvalues and eigenvectors." + }, + { + "text": "OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk0.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6898d4fe66019ef6b40d0472ea94a968e7bbde9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, shall we start?" + }, + { + "text": "This is the second lecture on eigenvalues." + }, + { + "text": "So the first lecture was set -- reached the key equation, Ax equal lambda x. x is the eigenvector and lambda is the eigenvalue." + }, + { + "text": "Now, to use that." + }, + { + "text": "And the good way to, after we've found, so job one is to find the eigenvalues and find the eigenvectors." + }, + { + "text": "Now after we found them, what do we do with them?" + }, + { + "text": "Well, the good way to see that is diagonalize the matrix." + }, + { + "text": "So the matrix is A, and I want to show, first of all, this is like the basic fact." + }, + { + "text": "This, this formula." + }, + { + "text": "That's, that's the key to today's lecture." + }, + { + "text": "This matrix A, I put its eigenvectors in the columns of a matrix S. So S will be the eigenvector matrix, and I want to look at this magic combination S inverse A S. So can I show you how that, how that, what happens there?" + }, + { + "text": "And notice, notice, there's an S inverse." + }, + { + "text": "We have to be able to invert this eigenvector matrix S. So for that we need n independent eigenvectors." + }, + { + "text": "So that's the, that's the case." + }, + { + "text": "OK." + }, + { + "text": "So suppose we have n linearly independent eigenvectors of A." + }, + { + "text": "Put them in the columns of this matrix S. So I'm naturally going to call that the eigenvector matrix, because it's got the eigenvectors in its columns." + }, + { + "text": "And all I want to do is show you what happens when you multiply A times S. So A times S. So this is A times the matrix with the first eigenvector in its first column, the second eigenvector in its second column, the nth eigenvector in its nth column." + }, + { + "text": "And how am I going to do this matrix multiplication?" + }, + { + "text": "Well, certainly I'll do it a column at a time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk1.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..fbe078217bb68baea8e0605a5d04be568c49efbf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I get?" + }, + { + "text": "A times the first column gives me the first column of the answer, but what is it?" + }, + { + "text": "That's an eigenvector." + }, + { + "text": "A times x1 is equal to the lambda times the x1." + }, + { + "text": "And that lambda's we'll call lambda one, of course." + }, + { + "text": "So that's the first column, A x1 is the same as lambda one x1." + }, + { + "text": "A x2 is lambda two x2, so on, along to, in the nth column, we now have lambda n xn." + }, + { + "text": "Looking good, but the next step is even better." + }, + { + "text": "So for the next step, I want to separate out those eigenvalues, those multiplying numbers, from the x's." + }, + { + "text": "So then I'll have just what I want." + }, + { + "text": "OK, so how, how am I going to separate out?" + }, + { + "text": "So that, that number lambda one is multiplying the first column." + }, + { + "text": "So if I want to factor it out of the first column, I better put, here is going to be x1, and that's going to multiply this matrix lambda one in the first entry in all zeros." + }, + { + "text": "You see that that, that's going to come out right for the first column?" + }, + { + "text": "Because we remember how, how we're going back to that original punchline, that if I want a number to multiply x1, then I can do it by putting x1 in that column, in the first column, and putting that number there." + }, + { + "text": "What am I going to have here?" + }, + { + "text": "I'm going to have lambda one, I'm going to have x1, x2, xn." + }, + { + "text": "These are going to be my columns again." + }, + { + "text": "I'm getting s back again." + }, + { + "text": "I'm getting s back again, but now what's it multiplied by?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk10.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c58a42edbe9567233ca7f57643a0b7d43ae6761f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what are the eigenvalues?" + }, + { + "text": "You can tell me right away what they are." + }, + { + "text": "They're two and two, right." + }, + { + "text": "It's a triangular matrix, so when I do this determinant, shall I do this determinant of A minus lambda I?" + }, + { + "text": "I'll get this two minus lambda, one, zero, two minus lambda, right?" + }, + { + "text": "I take that determinant, so I make those into vertical bars to mean determinant, and what's the determinant?" + }, + { + "text": "Two minus lambda squared." + }, + { + "text": "What are the roots?" + }, + { + "text": "Lambda equal two twice." + }, + { + "text": "So the eigenvalues are lambda equals two and two." + }, + { + "text": "OK, fine." + }, + { + "text": "Now the next step, find the eigenvectors." + }, + { + "text": "So I look for eigenvectors and what do I find for this guy?" + }, + { + "text": "Eigenvectors for this guy, when I subtract two minus the identity, so A minus two I has zeros here, and I'm looking for the null space." + }, + { + "text": "What's, what are the eigenvectors?" + }, + { + "text": "They're the, they're, they're the null space of A minus lambda I." + }, + { + "text": "The null space is only one dimension." + }, + { + "text": "This is a case where I don't have enough eigenvectors." + }, + { + "text": "My algebraic multiplicity is two." + }, + { + "text": "I, I would say when I see, when I count how often the eigenvalue is repeated, that's the algebraic multiplicity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk11.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..779c2cf904d904b761080db2671aac46394ad02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the multiplicity." + }, + { + "text": "How many times is it the root of the polynomial?" + }, + { + "text": "My polynomial is two minus lambda squared." + }, + { + "text": "It's a double root." + }, + { + "text": "So my algebraic multiplicity is two." + }, + { + "text": "But the geometric multiplicity, which looks for vectors, looks for eigenvectors and which means the null space of this thing." + }, + { + "text": "And the only eigenvector is one zero." + }, + { + "text": "That's in the null space." + }, + { + "text": "Zero one is not in the null space." + }, + { + "text": "The null space is only one dimensional." + }, + { + "text": "So there's a matrix, my, this A or the original A, that are not diagonalizable." + }, + { + "text": "I can't, I can't find two independent eigenvectors, there's only one." + }, + { + "text": "OK." + }, + { + "text": "So that's the case that I'm, that's a case that I, I'm not really handling." + }, + { + "text": "For example, when I wrote down up here that the powers went to zero if the eigenvalues were below one, I didn't really handle that case of repeated eigenvalues because my reasoning was based on this formula." + }, + { + "text": "And this formula is based on n independent eigenvectors." + }, + { + "text": "OK." + }, + { + "text": "So just to say that." + }, + { + "text": "There are some matrices that we don't cover through diagonalization, but the great majority we do." + }, + { + "text": "OK. And we're always OK if we have different distinct eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk12.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..77d090704cc298475d94416b7ecb88a2a015a913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. That's the, like, the typical case." + }, + { + "text": "Because for each eigenvalue there's at least one eigenvector, the algebraic multiplicity here is one for every eigenvalue, and the geometric multiplicity is one." + }, + { + "text": "There's one eigenvector and they are independent." + }, + { + "text": "OK. OK. Now let me come back to the important case when we're OK." + }, + { + "text": "The important case when we are diagonalizing." + }, + { + "text": "Let me look at, so let me solve this equation." + }, + { + "text": "The equation will be each, I start with some, start with a given vector u0." + }, + { + "text": "And then my equation is that every step I multiply what I have by a." + }, + { + "text": "That equation ought to be simple to handle." + }, + { + "text": "OK. And I'd like to be able to solve it." + }, + { + "text": "How would I find, if I start with a vector u0, and I multiply by a a hundred times, what have I got?" + }, + { + "text": "Well, I can certainly write down a formula for the answer." + }, + { + "text": "So what, what, so u1 is a u0." + }, + { + "text": "And u2 is, what's u2 then?" + }, + { + "text": "U2 I multiply it, u2 I get from u1 by another, multiplying by a, so I've got a twice." + }, + { + "text": "And my formula is uk, after k steps, I've multiplied by a k times the original u0." + }, + { + "text": "You see what I'm doing?" + }, + { + "text": "The next section is going to solve systems of differential equations." + }, + { + "text": "I'm going to have derivatives." + }, + { + "text": "This, this section is the nice one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk13.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..ba8214d8c636e4757a266d6617801174bc939d80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "It solves difference equations." + }, + { + "text": "I would call that a difference equation." + }, + { + "text": "It's conne- a first order." + }, + { + "text": "I would call that a first order system, because it connects only, it only goes up one level." + }, + { + "text": "And it's a system because these are vectors and that's a matrix." + }, + { + "text": "And the solution is just that." + }, + { + "text": "OK." + }, + { + "text": "But, that's a nice formula." + }, + { + "text": "That's the, like, the most compact formula I could ever get." + }, + { + "text": "U one hundred would be a to the one hundredth u0." + }, + { + "text": "But how would I actually find u one hundred?" + }, + { + "text": "How would I find, how would I discover what u one hundred is?" + }, + { + "text": "Let me, let me show you how." + }, + { + "text": "Here, here's the idea." + }, + { + "text": "If, so, to solve, to really solve, shall I say, to really solve." + }, + { + "text": "To really solve it, I would take this initial vector, u0, and I would write it as a combination of eigenvectors." + }, + { + "text": "To really solve, write, write u0 as a combination, say, certain amount of the first eigenvector plus a certain amount of the second eigenvector plus a certain amount of the last eigenvector." + }, + { + "text": "Now multiply by a." + }, + { + "text": "You want to, you got to see the magic of eigenvectors work." + }, + { + "text": "Multiply by a." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk14.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7843b2bf0cac762d1c12452cf36500ea4ad13370 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a u0 is what?" + }, + { + "text": "So a times that." + }, + { + "text": "A times, so what's, I can separate it out into n separate pieces and that's the whole point." + }, + { + "text": "That each of those pieces is going in its own merry way." + }, + { + "text": "Each of those pieces is an eigenvector, and when I multiply by a, what does this piece become?" + }, + { + "text": "So that's some amount of the first, let's suppose the eigenvectors are normalized to be unit vectors." + }, + { + "text": "So that says what the eigenvector is." + }, + { + "text": "It's, and I need some multiple of it to produce u0." + }, + { + "text": "OK. Now when I multiply by a, what do I get?" + }, + { + "text": "I get c1, which is just a factor, times a x1, but a x1 is lambda one x1." + }, + { + "text": "When I multiply this by a, I get c2 lambda two x2." + }, + { + "text": "And here I get cn lambda n xn." + }, + { + "text": "And suppose I multiply by a to the hundredth power now." + }, + { + "text": "Can we, can we, having done it, multiplied by a, let's multiply by a to the hundredth." + }, + { + "text": "What happens to this first term when I multiply by a to the one hundredth?" + }, + { + "text": "It's got that factor lambda to the hundredth." + }, + { + "text": "That's the key." + }, + { + "text": "That, that's what I mean by going its own merry way." + }, + { + "text": "It, it is pure eigenvector, it's exactly in a direction where multiplication by a just brings in a scalar factor lambda one." + }, + { + "text": "So a hundred times brings in this a hundred times." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk15.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7ee3348735378aa4049d33ec2a197d0ceb0c447c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Hundred times lambda two, hundred times lambda n. Actually, we're, what are we seeing here?" + }, + { + "text": "We're seeing, this same, lambda, capital lambda to the hundredth, as in the, as in the diagonalization, and we're seeing the S matrix, the matrix S of eigenvectors." + }, + { + "text": "That's what this has got to, this has got to amount to, a lambda to the hundredth power times an S times this vector C that's telling us how much of each one is in the original thing." + }, + { + "text": "So if, if I had to really find the hundredth power, I would take u0, I would expand it as a combination of eigenvectors, this is really S, the eigenvector matrix times C, the, the coefficient vector." + }, + { + "text": "And then I would immediately, then, by inserting these hundredth powers of eigenvalues, I'd have the answer." + }, + { + "text": "So the, the, huh, there must be, well, let's see." + }, + { + "text": "OK." + }, + { + "text": "It's, so, yeah." + }, + { + "text": "So if u100 is a to the hundredth times u0, and u0 is Sc, then you see this formula is just this formula, which is the way I would actually get hold of this, of this u100, which is, let me put it here, u100." + }, + { + "text": "The way I would actually get hold of that, see what, what the solution is after a hundred steps, would be expand the initial vector into eigenvectors and, and let each eigenvector go its own way, multiplying by a hundred at, by lambda at every step, and therefore by lambda to the hundredth power after a hundredth step." + }, + { + "text": "Can I do an example?" + }, + { + "text": "So that's, that's the, the formulas." + }, + { + "text": "Now let me take an example." + }, + { + "text": "I'll use the Fibonacci sequence as an example." + }, + { + "text": "So, so Fibonacci example." + }, + { + "text": "You remember the Fibonacci numbers?" + }, + { + "text": "If we start with one and one as F0, oh, I think I start with zero, maybe." + }, + { + "text": "Let zero and one be the first ones." + }, + { + "text": "So there's F0 and F1, the first two Fibonacci numbers." + }, + { + "text": "Then what's the rule for Fibonacci numbers?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk16.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..79c65e32781f7f304b504a6c390247abb9d26ac8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "They're the sum." + }, + { + "text": "The next one is the sum of those, so it's one." + }, + { + "text": "The next one is the sum of those, so it's two." + }, + { + "text": "The next one is the sum of those, so it's three." + }, + { + "text": "Well, it looks like one, two, three, four, five, but somehow it's not going to do that way." + }, + { + "text": "The next one is five, right." + }, + { + "text": "Two and three makes five." + }, + { + "text": "The next one is eight." + }, + { + "text": "The next one is thirteen." + }, + { + "text": "And the one hundredth Fibonacci number is what?" + }, + { + "text": "That's my question." + }, + { + "text": "How could I get a formula for the hundredth number and for example how could I answer the question how fast are they growing?" + }, + { + "text": "How fast are those Fibonacci numbers growing?" + }, + { + "text": "They're certainly growing." + }, + { + "text": "It's not a stable case, whatever the eigenvalues of whatever matrix it is, they're not smaller than one." + }, + { + "text": "These numbers are growing." + }, + { + "text": "But how fast are they growing?" + }, + { + "text": "The answer is lies in the eigenvalue." + }, + { + "text": "So I've got to find the matrix, so let me write down the Fibonacci rule, F k plus two is F k plus one plus F k, right?" + }, + { + "text": "Now that's not in my -- I want to write that as U k plus one and A U k. But right now what I've got is a single equation, not a system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk17.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b3aaa9dcee3cf27c112015659bb5a0b51a983ce1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's second order." + }, + { + "text": "It's like having a second order differential equation with second derivatives." + }, + { + "text": "I want to get first derivatives." + }, + { + "text": "Here I want to get first difference." + }, + { + "text": "So the way to do it is to introduce U k will be a vector." + }, + { + "text": "See, a small trick." + }, + { + "text": "Let U k be a vector, F k plus one and F k. So I'm going to get a two by two system, first order, instead of a one, instead of a scalar system, second order, by a simple trick." + }, + { + "text": "I'm just going to add in an equation F k plus one equals F k plus one." + }, + { + "text": "That will be my second equation." + }, + { + "text": "Then this is my system, this is my unknown, and what's my one-step equation?" + }, + { + "text": "So now U k plus one." + }, + { + "text": "That's so U k plus one is the left side, and what have I got here on the right side?" + }, + { + "text": "I've got some matrix multiplying U k. Can you see that all right?" + }, + { + "text": "If you can see it, then you can tell me what the matrix is." + }, + { + "text": "You see that I'm taking my system here, I artificially made it into a system." + }, + { + "text": "I artificially made the unknown into a vector, and now I'm ready to look at and see what the matrix is." + }, + { + "text": "So do you see the left side, U k plus one is F k plus two F k plus one, that's just what I want." + }, + { + "text": "On the right side, this, remember, this U k here, let me for the moment put it as F k plus one F k. So what's the matrix?" + }, + { + "text": "Well, that has a one and a one, and that has a one and a zero." + }, + { + "text": "There's the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk18.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..6c1b68c2cb2fde3f5dea82f3100d4da31fcce70a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "You see that that gives me the right-hand side." + }, + { + "text": "So there's the matrix A, and this is our friend U k. So we've got, so that simple trick changed the second order scalar problem to a first order system, two, with two unknowns." + }, + { + "text": "With a matrix and now what do I do?" + }, + { + "text": "Well, before I even think, I find its eigenvalues and eigenvectors." + }, + { + "text": "So what are the eigenvalues and eigenvectors of that matrix?" + }, + { + "text": "Let's see." + }, + { + "text": "I was, first let me just, like, think for a minute." + }, + { + "text": "It's two by two, so this shouldn't be impossible to do." + }, + { + "text": "Let's do it." + }, + { + "text": "OK." + }, + { + "text": "So my matrix again is one one one zero." + }, + { + "text": "It's symmetric, by the way." + }, + { + "text": "So what I will eventually know about symmetric matrices is that the eigenvalues will come out real, I won't get any complex numbers here, and the eigenvectors, once I get those, actually will be orthogonal." + }, + { + "text": "But two by two, I'm more interested in what the actual numbers are." + }, + { + "text": "What do I know about the two numbers?" + }, + { + "text": "Well, should, do you want me to find this determinant of A minus lambda I?" + }, + { + "text": "Sure." + }, + { + "text": "So it's the determinant of one minus lambda one one zero, right?" + }, + { + "text": "Minus lambda, yes, got it." + }, + { + "text": "OK. OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk19.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..a73b23e3d56b889ff49ea7f55a784fac33e13c3d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "There'll be two eigenvalues." + }, + { + "text": "Well, tell me again what I know about the two eigenvalues before I go any further." + }, + { + "text": "Tell me something about these two eigenvalues, what do they add up to?" + }, + { + "text": "Lambda one plus lambda two is the same as the trace down the diagonal of the matrix, one and zero is one." + }, + { + "text": "So lambda one plus lambda two should come out to be one, and lambda one times lambda two should come out to be the determinant, which is minus one." + }, + { + "text": "So I'm expecting the eigenvalues to add to one and to multiply to minus one." + }, + { + "text": "But let's just see it happen here." + }, + { + "text": "If I multiply this out, I get that times that'll be a lambda squared minus lambda minus one." + }, + { + "text": "Good." + }, + { + "text": "Lambda squared minus lambda minus one." + }, + { + "text": "Actually, you see the, compare that with the original equation that I started with." + }, + { + "text": "Fk plus two minus Fk plus one minus Fk is zero." + }, + { + "text": "The recurrent, the recursion that the Fibonacci number satisfy is somehow showing up directly here for the eigenvalues when we set that to zero." + }, + { + "text": "OK. Let's solve." + }, + { + "text": "Well, I would like to be able to factor that, that quadratic, but I'm better off to use the quadratic formula." + }, + { + "text": "Lambda is, let's see, minus b is one, plus or minus the square root of b squared, which is one, minus four, times that, times that, which is plus four, over two." + }, + { + "text": "So that's the square root of five." + }, + { + "text": "So the eigenvalues are lambda one is one half of one plus square root of five, and lambda two is one half of one minus square root of five." + }, + { + "text": "And sure enough, they, those add up to one, and they multiply to give minus one." + }, + { + "text": "OK. Those are the two eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk2.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..43cfb012fc04a89fc7dab94c23bfb0f50ade3782 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "On the right, it's multiplied by, if I want, if I want lambda n xn in the last column, how do I do it?" + }, + { + "text": "Well, the last column here will be, I'll, I'll take the last column, use these coefficients, put the lambda n down there, and it will multiply that nth column and give me lambda n xn." + }, + { + "text": "There, there you see matrix multiplication just working for us." + }, + { + "text": "So I started with A s. I wrote down what it meant." + }, + { + "text": "A times each eigenvector." + }, + { + "text": "That gave me lambda times the eigenvector." + }, + { + "text": "And then when I peeled off the lambdas, they were on the right-hand side, so I've got s, my matrix back again, and this matrix, this diagonal matrix, the eigenvalue matrix, and I call it capital lambda, using capital letters for matrices, and lambda to prompt me that it's, that it's eigenvalues that are in there." + }, + { + "text": "So you see that the eigenvalues are just sitting down that diagonal?" + }, + { + "text": "If I had a column x2 here, I would want the lambda two in the two two position, in the diagonal position, to multiply that x2 and give me the lambda two x2." + }, + { + "text": "That's my formula." + }, + { + "text": "A s is s lambda." + }, + { + "text": "OK. That's, that's the, you see, it's just a calculation." + }, + { + "text": "Now, I, I mentioned, and I have to mention again, this business about n independent eigenvectors." + }, + { + "text": "As it stands, this is all fine whether, I mean, I could be repeating the same eigenvector, but I, I'm no interested in that." + }, + { + "text": "I want to be able to invert s, and that's where this comes in." + }, + { + "text": "This n independent eigenvectors business comes in to tell me that that matrix is invertible." + }, + { + "text": "So let me, on the next board, write down what I've got." + }, + { + "text": "A s equals s lambda." + }, + { + "text": "And now I'm, I can multiply on the left by s inverse." + }, + { + "text": "So this is really, I can do that provided s is invertible, provided my assumption of n independent eigenvectors is satisfied." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk20.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ad5a59fa5db44ce73ff5f88190423e0404fb3d39 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "How, how, what are those numbers approximately?" + }, + { + "text": "Square root of five, well, it's more than two, but less than three." + }, + { + "text": "It, it'd be nice to know these numbers." + }, + { + "text": "I think, I think that that, so that number comes out bigger than one, right?" + }, + { + "text": "Yeah, that's right." + }, + { + "text": "This number comes out bigger than one." + }, + { + "text": "It's about one point six one eight or something." + }, + { + "text": "Not exactly." + }, + { + "text": "It's supposed to be one point six." + }, + { + "text": "Just, like, I think so." + }, + { + "text": "Then what's lambda two?" + }, + { + "text": "Is, is lambda two positive or negative?" + }, + { + "text": "Negative, right?" + }, + { + "text": "Because I'm, it's obviously negative, and I knew that the, so it's minus, and they add up to one, so minus point six one eight, I guess." + }, + { + "text": "OK. And some order." + }, + { + "text": "Those are the two eigenvalues." + }, + { + "text": "One eigenvalue bigger than one, one eigenvalue smaller than one." + }, + { + "text": "Actually, that's a great situation to be in." + }, + { + "text": "Of course, the eigenvalues are different, so there's no doubt whatever, is this matrix diagonalizable?" + }, + { + "text": "Is this matrix diagonalizable, that original matrix A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk21.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..4a034475591d371995b379b5f98783a2cfb25870 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Sure." + }, + { + "text": "We've got two distinct eigenvalues and we can find the eigenvectors in a moment." + }, + { + "text": "But they'll be independent, will be diagonalizable, and now you can already answer my very first question." + }, + { + "text": "How fast are those Fibonacci numbers increasing?" + }, + { + "text": "How, those, they're increasing, right?" + }, + { + "text": "They're not doubling at every step." + }, + { + "text": "Let's look again at these numbers." + }, + { + "text": "Five eight thirteen, it's not obvious." + }, + { + "text": "The next one would be twenty one thirty four." + }, + { + "text": "So to get some idea of what F one hundred is, can you give me any, I mean the crucial number of, so it, these, it's approximately, what's controlling the growth of these Fibonacci numbers?" + }, + { + "text": "It's the eigenvalues." + }, + { + "text": "And which eigenvalues controlling that growth?" + }, + { + "text": "The big ones." + }, + { + "text": "So F one hundred will it be approximately some constant, c one, I guess, times this lambda one, this one plus square root of five over two, to the hundredth power." + }, + { + "text": "And the two hundredth have, in other words, the eigenvalue, the Fibonacci numbers are growing by about that factor." + }, + { + "text": "You see that we've got precise information about the, about the Fibonacci numbers out of the eigenvalue." + }, + { + "text": "OK. And again, why is that true?" + }, + { + "text": "Let me go over to this board and show what I'm doing here." + }, + { + "text": "The, the original eigen, the original initial value is some combination of eigenvectors, and then when we start multiple, when we start going out the theory of Fibonacci numbers, when we start multiplying by a hundred times, it's this lambda one to the hundredth, this term is, is the one that's taken over." + }, + { + "text": "It's, I mean, that's big, like, one point six to the hundredth power." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk22.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..c13a1fc9867173c3067e46c469cfff27b9b45289 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "The second term is practically nothing, right?" + }, + { + "text": "The point six, or minus point six to the hundredth power, is an extremely small, extremely small number." + }, + { + "text": "So this is, this, this, there are only two terms, because we're two by two." + }, + { + "text": "This number is, this piece of it is there, but it's, it's disappearing." + }, + { + "text": "Where this piece is there and it's growing and controlling everything." + }, + { + "text": "So, so really the, we're doing, like, problems that are evolving." + }, + { + "text": "We're doing dynamics." + }, + { + "text": "Instead of Ax equal b, that's a static problem." + }, + { + "text": "We're now, we're doing dynamics." + }, + { + "text": "A, a squared, a cubed, things are evolving in time, and the eigenvalues are the crucial, numbers." + }, + { + "text": "OK." + }, + { + "text": "I guess to complete this, I better write down the eigenvectors." + }, + { + "text": "So we should complete the, the whole process by finding the eigenvectors." + }, + { + "text": "OK. Well, I have to, up in the corner, then I have to look at A minus lambda I." + }, + { + "text": "So A minus lambda I is this one minus lambda, one, one, and minus lambda." + }, + { + "text": "And now, can we spot an eigenvector out of that?" + }, + { + "text": "That's, for these two lambdas, this matrix is singular." + }, + { + "text": "I guess the eigenvector, two by two ought to be easy." + }, + { + "text": "So if I know that this matrix is singular, then it seems to me the eigenvector has to be lambda and one, because that multiplication will give me the zero." + }, + { + "text": "And this multiplication gives me, better give me also zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk23.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..df816eb800ce767b1475c279a24ad976bb45a785 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Do you see why it does?" + }, + { + "text": "This is the minus lambda squared plus lambda plus one." + }, + { + "text": "It's the thing that's zero, because these lambdas are special." + }, + { + "text": "There's the eigenvector." + }, + { + "text": "X1 is lambda one, one, and x2 is lambda two, one." + }, + { + "text": "I did that as a little trick that was available in the two by two case." + }, + { + "text": "So now I finally have to, oh, I have to take the initial, u0." + }, + { + "text": "So to complete this example entirely, I have to say, OK, what was u0?" + }, + { + "text": "u0 was f1 f0." + }, + { + "text": "So u0, the starting vector, is f1 f0, and those were one and zero." + }, + { + "text": "So I have to use that vector, so I have to look for, from multiple of the first eigenvector and the second, to produce u0, the one zero vector." + }, + { + "text": "This is what will find c1 and c2, and then I'm done." + }, + { + "text": "So let me, instead of in the last five seconds grinding out a formula, let me repeat the idea." + }, + { + "text": "That really, it's the idea that's central." + }, + { + "text": "When things are evolving in time, let me come back to this board, because the ideas are here." + }, + { + "text": "When things are evolving in time by a first-order system, starting from an original u0, the key is, find the eigenvalues and eigenvectors of A." + }, + { + "text": "That will tell, those eigenvectors, the eigenvalues will already tell you what's happening." + }, + { + "text": "Is the solution blowing up?" + }, + { + "text": "Is it going to zero?" + }, + { + "text": "What's it doing?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk24.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..40301cb90760e2172baa94d536cbc13288d4c31f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk24.json @@ -0,0 +1,20 @@ +[ + { + "text": "And then, to find out exactly a formula, you have to take your u0 and write it as a combination of eigenvectors and then follow each eigenvector separately." + }, + { + "text": "And that's really what this formula, the formula for, that's what the formula for A to the k is doing." + }, + { + "text": "So remember that formula for A to the k is S, lambda to the k S inverse." + }, + { + "text": "OK. That's, that's difference equations, and you just have to, so the homework will give some examples different from Fibonacci to follow through." + }, + { + "text": "And next time will be differential equations." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk3.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..9bf1bb852baadc1da7837e14180c0c2951a30882 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I mentioned at the end of last time, and I'll say again, that there's a small number of matrices for, that don't have n independent eigenvectors." + }, + { + "text": "So I've got to discuss that, that technical point." + }, + { + "text": "But the great, the most matrices that we see have n, n independent eigenvectors and we can diagonalize." + }, + { + "text": "This is diagonalization." + }, + { + "text": "I could also write it, and I often will, the other way round." + }, + { + "text": "If I multiply on the right by s inverse, if I took this equation at the top and multiplied on the right by s inverse, I could, I would have A left here." + }, + { + "text": "Now s inverse is coming from the right." + }, + { + "text": "So can you keep those two straight?" + }, + { + "text": "A multiplies its eigenvectors." + }, + { + "text": "That's how I keep them straight." + }, + { + "text": "So A multiplies s. A multiplies s. And then this s inverse makes the whole thing diagonal." + }, + { + "text": "And this is another way of saying the same thing, putting the s's on the other side of the equation, A is s lambda s inverse." + }, + { + "text": "So that's the, that's the new factorization." + }, + { + "text": "That's the replacement for L U from elimination or Q R from Gram-Schmidt." + }, + { + "text": "And notice that the matrix, so it's, it's a matrix times a diagonal matrix times the inverse of the first one." + }, + { + "text": "It's, that's the combination that we'll see throughout this chapter." + }, + { + "text": "This, this, combination with an s and an s inverse." + }, + { + "text": "OK. Can I just begin to use that?" + }, + { + "text": "For example, what about A squared?" + }, + { + "text": "What are the eigenvalues and eigenvectors of A squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk4.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c687b6948acad76de8781cb82d3eb069c9da514e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's a straightforward question with a, with a absolutely clean answer." + }, + { + "text": "So let me, let me consider A squared." + }, + { + "text": "So I look, I start with Ax equal lambda x." + }, + { + "text": "And I'm headed for A squared." + }, + { + "text": "So let me multiply both sides by A." + }, + { + "text": "That's one way to get A squared on the left." + }, + { + "text": "So if, I should write these ifs in here." + }, + { + "text": "If Ax equals lambda x, then I multiply by A." + }, + { + "text": "So I get A squared x equals, well, I'm multiplying by A, so that's lambda Ax." + }, + { + "text": "That lambda was a number, so I just put it on the left." + }, + { + "text": "And what do I, tell me how to make that look better." + }, + { + "text": "What have I got here?" + }, + { + "text": "For, if, if A has the eigenvalue lambda and eigenvector x, what's up with A squared?" + }, + { + "text": "A squared x, I just multiply by A, but now for Ax, I'm going to substitute lambda x, so I've got lambda squared x." + }, + { + "text": "So from that simple calculation, I, my conclusion is that the eigenvalues of A squared are lambda squared." + }, + { + "text": "And the eigenvectors, I always think about both of those." + }, + { + "text": "What can I say about the eigenvalues?" + }, + { + "text": "They're squared." + }, + { + "text": "What can I say about the eigenvectors?" + }, + { + "text": "They're the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk5.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5bf15e20707c156c8ae71c9c7acea41a9d9d8e46 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same x as in, as for A." + }, + { + "text": "Now, let me see that also from this formula." + }, + { + "text": "How can I see what A squared is looking like from this formula?" + }, + { + "text": "So let me, that, that was one way to do it." + }, + { + "text": "Let me do it by just taking A squared from that." + }, + { + "text": "A squared is S lambda S inverse, that's A, times S lambda S inverse, that's A, which is?" + }, + { + "text": "This is the beauty of eigenvalues, eigenvectors, having that S inverse and S is the identity, so I've got S lambda squared S inverse." + }, + { + "text": "Yes." + }, + { + "text": "You see what that's telling me?" + }, + { + "text": "It's, it's telling me the same thing that I just learned here, but in the, in, in a matrix form." + }, + { + "text": "It's telling me that the S is the same, the eigenvectors are the same, but the eigenvalues are squared, because this is, what's lambda squared, that's still diagonal, it's got little lambda one squared, lambda two squared, down to lambda n squared, on that diagonal, those are the eigenvalues, as we just learned, of A squared." + }, + { + "text": "OK." + }, + { + "text": "So, somehow those eigenvalues and eigenvectors are really giving you a way to, to, to, to see what's going on inside a matrix." + }, + { + "text": "Now, of course, I can continue that for, to the k-th power." + }, + { + "text": "A to the k-th power." + }, + { + "text": "If I multiply, if I have k of these together, do you see how S inverse S will keep cancelling?" + }, + { + "text": "In the, in the inside, I'll have the S outside, at the far left, and lambda will be in there k times and S inverse." + }, + { + "text": "So what's that telling me?" + }, + { + "text": "That's telling me that the eigenvalues of A, of A to the k-th power are the k-th powers." + }, + { + "text": "The eigenvalues of A cubed are the cubes of the eigenvalues of A, and the eigenvectors are the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk6.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..c18dddbe798022f7e68278ac002a3f5fe6ed249e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same." + }, + { + "text": "OK." + }, + { + "text": "In other words, eigenvalues and eigenvectors give a great way to understand the powers of a matrix." + }, + { + "text": "If I take the square of a matrix or the hundredth power of a matrix, the pivots are all over the place." + }, + { + "text": "L U, if I multiply L U times L U times L U times L U a hundred times, I've got a hundred L U's." + }, + { + "text": "I can't do anything with them." + }, + { + "text": "But when I multiply S lambda S inverse by itself, when I look at the eigenvector picture a hundred times, I get a hundred or ninety-nine of these guys cancelling out inside, and I get A to the hundredth is S lambda to the hundredth S inverse." + }, + { + "text": "I mean, eigenvalues tell you about powers of a matrix in a way that we had no, no way to approach previously." + }, + { + "text": "For example, when does, when do the powers of a matrix go to zero?" + }, + { + "text": "I would call that matrix stable, maybe." + }, + { + "text": "So, so, so I could write down a, a theorem." + }, + { + "text": "I'll, I'll write it as a theorem, just to use that word to emphasize that here I'm getting this great fact from this eigenvalue picture." + }, + { + "text": "OK. A to the k approaches zero as k goes, as k gets bigger." + }, + { + "text": "If what?" + }, + { + "text": "What's the, how can I tell for a matrix A if its powers go to zero?" + }, + { + "text": "What, what's somewhere inside that matrix is that information." + }, + { + "text": "That information is not present in the pivots." + }, + { + "text": "It's present in the eigenvalues." + }, + { + "text": "What do I need for the, to know that if I take higher and higher powers of A that this matrix gets smaller and smaller?" + }, + { + "text": "Well, S and S inverse are not moving." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk7.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b84a5c854a5542758e8a0107e1ff043205fe3bdb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's this guy that has to get small, and that's easy to, easy to understand." + }, + { + "text": "The requirement is all eigenvalues, so what is the requirement?" + }, + { + "text": "The eigenvalues have to be less than one." + }, + { + "text": "Now, I have to write that absolute value, because those eigenvalues could be negative, they could be complex numbers." + }, + { + "text": "So I'm taking the absolute value if all of those are below one." + }, + { + "text": "That's, in fact, we practically see why." + }, + { + "text": "Let me just say that I, that I, I'm operating on one assumption here, and I got to keep remembering that that assumption is still present." + }, + { + "text": "That assumption was that I had a full set of, of n independent eigenvectors." + }, + { + "text": "If I don't have that, then I, I, then this approach is not working." + }, + { + "text": "So, so again, a pure eigenvalue approach, eigenvector approach, needs n independent eigenvectors." + }, + { + "text": "If we don't have n independent eigenvectors, we can't diagonalize the matrix." + }, + { + "text": "We can't get to a diagonal matrix." + }, + { + "text": "This, this, this diagonalization is only possible if S inverse makes sense." + }, + { + "text": "OK. Can I, can I follow up on that point now?" + }, + { + "text": "So, so you see why, what we get and, and why we want it, because we get information about the powers of a matrix just immediately from the eigenvalues." + }, + { + "text": "OK, now let me follow up on this, business of which matrices are diagonalizable." + }, + { + "text": "Sorry about that long word." + }, + { + "text": "So a matrix is, is sure to, so here's, here's the main point." + }, + { + "text": "A is sure to be, to have n independent eigenvectors and, and B, now here comes that word, diagonalizable, if, if, so we, we, we might as well get the, the nice case out in the open." + }, + { + "text": "The nice case is when, if all the lambdas are different." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk8.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f06dcec8ffa0ee1bf19440e4ab2194db33ab353b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means, that means no repeated eigenvalues." + }, + { + "text": "OK. That's the nice case." + }, + { + "text": "If, if my matrix and most matrix, if I do a random matrix in MATLAB and compute its eigenvalues, so if I computed, if I took I of rand of ten ten, gave, gave that MATLAB command, the, we'd get a random ten by ten matrix, we would get a list of its ten eigenvalues and they would be different." + }, + { + "text": "They would be distinct, is the best word." + }, + { + "text": "I would have a random matrix will have ten distinct, a ten by ten matrix will have ten distinct eigenvalues, and if it does, the eigenvectors are automatically independent." + }, + { + "text": "So that's a nice fact." + }, + { + "text": "I can, I'll refer you to the text for the proof." + }, + { + "text": "That, that A is sure to have n independent eigenvectors if the eigenvalues are different." + }, + { + "text": "If, if all the, if all eigenvalues are different." + }, + { + "text": "It's just, if some lambdas are repeated, then I have to look more closely." + }, + { + "text": "If an eigenvalue is repeated, I have to look, I have to count, I have to check." + }, + { + "text": "Has it got, say it's repeated three times." + }, + { + "text": "So what's a possibility for, so, so here's, here's the repeated possibility." + }, + { + "text": "And, and let me emphasize the conclusion." + }, + { + "text": "That if I have repeated eigenvalues, I may or may not, I may or may not have, have n independent eigenvectors." + }, + { + "text": "I might." + }, + { + "text": "I, I, you know, this isn't a completely negative case." + }, + { + "text": "The identity matrix." + }, + { + "text": "Well, suppose I take the ten by ten identity matrix." + }, + { + "text": "What are the eigenvalues of that matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk9.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..87d2a2ae5773036cf11800e2f1962908986a0dad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_22_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So just, just take the easiest matrix, the identity." + }, + { + "text": "If I look for its eigenvalues, they're all ones." + }, + { + "text": "So that eigenvalue one is repeated ten times." + }, + { + "text": "But there's no shortage of eigenvectors for the identity matrix." + }, + { + "text": "In fact, every vector is an eigenvector." + }, + { + "text": "So I can take ten independent vectors." + }, + { + "text": "Oh, well, what happens to everything if, if, if A is the identity matrix, let's just think that one through in our head." + }, + { + "text": "If A is the identity matrix, then it's got plenty of eigenvectors." + }, + { + "text": "I choose ten independent vectors, they're the columns of S, and, and what do I get from S inverse A S?" + }, + { + "text": "I get I again, right?" + }, + { + "text": "If A is the identity, and of course, that's the correct lambda." + }, + { + "text": "The, the matrix was already diagonal." + }, + { + "text": "So if the matrix is already diagonal, then the, the lambda is the same as the matrix." + }, + { + "text": "A diagonal matrix has got its eigenvalues sitting right there in front of you." + }, + { + "text": "Now if it's triangular, the eigenvalues are still sitting there, but so let's, let's take a case where, it's triangular." + }, + { + "text": "Suppose A is like, two, one, two, zero." + }, + { + "text": "So there's a case that's going to be trouble." + }, + { + "text": "There's a case that's going to be trouble." + }, + { + "text": "First of all, what are the eigen- I mean, we just, like now you, if we start with a matrix, the first thing we do practically without thinking is compute the eigenvalues and eigenvectors." + }, + { + "text": "OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk0.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6898d4fe66019ef6b40d0472ea94a968e7bbde9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, shall we start?" + }, + { + "text": "This is the second lecture on eigenvalues." + }, + { + "text": "So the first lecture was set -- reached the key equation, Ax equal lambda x. x is the eigenvector and lambda is the eigenvalue." + }, + { + "text": "Now, to use that." + }, + { + "text": "And the good way to, after we've found, so job one is to find the eigenvalues and find the eigenvectors." + }, + { + "text": "Now after we found them, what do we do with them?" + }, + { + "text": "Well, the good way to see that is diagonalize the matrix." + }, + { + "text": "So the matrix is A, and I want to show, first of all, this is like the basic fact." + }, + { + "text": "This, this formula." + }, + { + "text": "That's, that's the key to today's lecture." + }, + { + "text": "This matrix A, I put its eigenvectors in the columns of a matrix S. So S will be the eigenvector matrix, and I want to look at this magic combination S inverse A S. So can I show you how that, how that, what happens there?" + }, + { + "text": "And notice, notice, there's an S inverse." + }, + { + "text": "We have to be able to invert this eigenvector matrix S. So for that we need n independent eigenvectors." + }, + { + "text": "So that's the, that's the case." + }, + { + "text": "OK." + }, + { + "text": "So suppose we have n linearly independent eigenvectors of A." + }, + { + "text": "Put them in the columns of this matrix S. So I'm naturally going to call that the eigenvector matrix, because it's got the eigenvectors in its columns." + }, + { + "text": "And all I want to do is show you what happens when you multiply A times S. So A times S. So this is A times the matrix with the first eigenvector in its first column, the second eigenvector in its second column, the nth eigenvector in its nth column." + }, + { + "text": "And how am I going to do this matrix multiplication?" + }, + { + "text": "Well, certainly I'll do it a column at a time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk1.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..fbe078217bb68baea8e0605a5d04be568c49efbf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I get?" + }, + { + "text": "A times the first column gives me the first column of the answer, but what is it?" + }, + { + "text": "That's an eigenvector." + }, + { + "text": "A times x1 is equal to the lambda times the x1." + }, + { + "text": "And that lambda's we'll call lambda one, of course." + }, + { + "text": "So that's the first column, A x1 is the same as lambda one x1." + }, + { + "text": "A x2 is lambda two x2, so on, along to, in the nth column, we now have lambda n xn." + }, + { + "text": "Looking good, but the next step is even better." + }, + { + "text": "So for the next step, I want to separate out those eigenvalues, those multiplying numbers, from the x's." + }, + { + "text": "So then I'll have just what I want." + }, + { + "text": "OK, so how, how am I going to separate out?" + }, + { + "text": "So that, that number lambda one is multiplying the first column." + }, + { + "text": "So if I want to factor it out of the first column, I better put, here is going to be x1, and that's going to multiply this matrix lambda one in the first entry in all zeros." + }, + { + "text": "You see that that, that's going to come out right for the first column?" + }, + { + "text": "Because we remember how, how we're going back to that original punchline, that if I want a number to multiply x1, then I can do it by putting x1 in that column, in the first column, and putting that number there." + }, + { + "text": "What am I going to have here?" + }, + { + "text": "I'm going to have lambda one, I'm going to have x1, x2, xn." + }, + { + "text": "These are going to be my columns again." + }, + { + "text": "I'm getting s back again." + }, + { + "text": "I'm getting s back again, but now what's it multiplied by?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk10.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c58a42edbe9567233ca7f57643a0b7d43ae6761f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what are the eigenvalues?" + }, + { + "text": "You can tell me right away what they are." + }, + { + "text": "They're two and two, right." + }, + { + "text": "It's a triangular matrix, so when I do this determinant, shall I do this determinant of A minus lambda I?" + }, + { + "text": "I'll get this two minus lambda, one, zero, two minus lambda, right?" + }, + { + "text": "I take that determinant, so I make those into vertical bars to mean determinant, and what's the determinant?" + }, + { + "text": "Two minus lambda squared." + }, + { + "text": "What are the roots?" + }, + { + "text": "Lambda equal two twice." + }, + { + "text": "So the eigenvalues are lambda equals two and two." + }, + { + "text": "OK, fine." + }, + { + "text": "Now the next step, find the eigenvectors." + }, + { + "text": "So I look for eigenvectors and what do I find for this guy?" + }, + { + "text": "Eigenvectors for this guy, when I subtract two minus the identity, so A minus two I has zeros here, and I'm looking for the null space." + }, + { + "text": "What's, what are the eigenvectors?" + }, + { + "text": "They're the, they're, they're the null space of A minus lambda I." + }, + { + "text": "The null space is only one dimension." + }, + { + "text": "This is a case where I don't have enough eigenvectors." + }, + { + "text": "My algebraic multiplicity is two." + }, + { + "text": "I, I would say when I see, when I count how often the eigenvalue is repeated, that's the algebraic multiplicity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk11.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..779c2cf904d904b761080db2671aac46394ad02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the multiplicity." + }, + { + "text": "How many times is it the root of the polynomial?" + }, + { + "text": "My polynomial is two minus lambda squared." + }, + { + "text": "It's a double root." + }, + { + "text": "So my algebraic multiplicity is two." + }, + { + "text": "But the geometric multiplicity, which looks for vectors, looks for eigenvectors and which means the null space of this thing." + }, + { + "text": "And the only eigenvector is one zero." + }, + { + "text": "That's in the null space." + }, + { + "text": "Zero one is not in the null space." + }, + { + "text": "The null space is only one dimensional." + }, + { + "text": "So there's a matrix, my, this A or the original A, that are not diagonalizable." + }, + { + "text": "I can't, I can't find two independent eigenvectors, there's only one." + }, + { + "text": "OK." + }, + { + "text": "So that's the case that I'm, that's a case that I, I'm not really handling." + }, + { + "text": "For example, when I wrote down up here that the powers went to zero if the eigenvalues were below one, I didn't really handle that case of repeated eigenvalues because my reasoning was based on this formula." + }, + { + "text": "And this formula is based on n independent eigenvectors." + }, + { + "text": "OK." + }, + { + "text": "So just to say that." + }, + { + "text": "There are some matrices that we don't cover through diagonalization, but the great majority we do." + }, + { + "text": "OK. And we're always OK if we have different distinct eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk12.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..77d090704cc298475d94416b7ecb88a2a015a913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. That's the, like, the typical case." + }, + { + "text": "Because for each eigenvalue there's at least one eigenvector, the algebraic multiplicity here is one for every eigenvalue, and the geometric multiplicity is one." + }, + { + "text": "There's one eigenvector and they are independent." + }, + { + "text": "OK. OK. Now let me come back to the important case when we're OK." + }, + { + "text": "The important case when we are diagonalizing." + }, + { + "text": "Let me look at, so let me solve this equation." + }, + { + "text": "The equation will be each, I start with some, start with a given vector u0." + }, + { + "text": "And then my equation is that every step I multiply what I have by a." + }, + { + "text": "That equation ought to be simple to handle." + }, + { + "text": "OK. And I'd like to be able to solve it." + }, + { + "text": "How would I find, if I start with a vector u0, and I multiply by a a hundred times, what have I got?" + }, + { + "text": "Well, I can certainly write down a formula for the answer." + }, + { + "text": "So what, what, so u1 is a u0." + }, + { + "text": "And u2 is, what's u2 then?" + }, + { + "text": "U2 I multiply it, u2 I get from u1 by another, multiplying by a, so I've got a twice." + }, + { + "text": "And my formula is uk, after k steps, I've multiplied by a k times the original u0." + }, + { + "text": "You see what I'm doing?" + }, + { + "text": "The next section is going to solve systems of differential equations." + }, + { + "text": "I'm going to have derivatives." + }, + { + "text": "This, this section is the nice one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk13.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..ba8214d8c636e4757a266d6617801174bc939d80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "It solves difference equations." + }, + { + "text": "I would call that a difference equation." + }, + { + "text": "It's conne- a first order." + }, + { + "text": "I would call that a first order system, because it connects only, it only goes up one level." + }, + { + "text": "And it's a system because these are vectors and that's a matrix." + }, + { + "text": "And the solution is just that." + }, + { + "text": "OK." + }, + { + "text": "But, that's a nice formula." + }, + { + "text": "That's the, like, the most compact formula I could ever get." + }, + { + "text": "U one hundred would be a to the one hundredth u0." + }, + { + "text": "But how would I actually find u one hundred?" + }, + { + "text": "How would I find, how would I discover what u one hundred is?" + }, + { + "text": "Let me, let me show you how." + }, + { + "text": "Here, here's the idea." + }, + { + "text": "If, so, to solve, to really solve, shall I say, to really solve." + }, + { + "text": "To really solve it, I would take this initial vector, u0, and I would write it as a combination of eigenvectors." + }, + { + "text": "To really solve, write, write u0 as a combination, say, certain amount of the first eigenvector plus a certain amount of the second eigenvector plus a certain amount of the last eigenvector." + }, + { + "text": "Now multiply by a." + }, + { + "text": "You want to, you got to see the magic of eigenvectors work." + }, + { + "text": "Multiply by a." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk14.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7843b2bf0cac762d1c12452cf36500ea4ad13370 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a u0 is what?" + }, + { + "text": "So a times that." + }, + { + "text": "A times, so what's, I can separate it out into n separate pieces and that's the whole point." + }, + { + "text": "That each of those pieces is going in its own merry way." + }, + { + "text": "Each of those pieces is an eigenvector, and when I multiply by a, what does this piece become?" + }, + { + "text": "So that's some amount of the first, let's suppose the eigenvectors are normalized to be unit vectors." + }, + { + "text": "So that says what the eigenvector is." + }, + { + "text": "It's, and I need some multiple of it to produce u0." + }, + { + "text": "OK. Now when I multiply by a, what do I get?" + }, + { + "text": "I get c1, which is just a factor, times a x1, but a x1 is lambda one x1." + }, + { + "text": "When I multiply this by a, I get c2 lambda two x2." + }, + { + "text": "And here I get cn lambda n xn." + }, + { + "text": "And suppose I multiply by a to the hundredth power now." + }, + { + "text": "Can we, can we, having done it, multiplied by a, let's multiply by a to the hundredth." + }, + { + "text": "What happens to this first term when I multiply by a to the one hundredth?" + }, + { + "text": "It's got that factor lambda to the hundredth." + }, + { + "text": "That's the key." + }, + { + "text": "That, that's what I mean by going its own merry way." + }, + { + "text": "It, it is pure eigenvector, it's exactly in a direction where multiplication by a just brings in a scalar factor lambda one." + }, + { + "text": "So a hundred times brings in this a hundred times." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk15.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7ee3348735378aa4049d33ec2a197d0ceb0c447c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Hundred times lambda two, hundred times lambda n. Actually, we're, what are we seeing here?" + }, + { + "text": "We're seeing, this same, lambda, capital lambda to the hundredth, as in the, as in the diagonalization, and we're seeing the S matrix, the matrix S of eigenvectors." + }, + { + "text": "That's what this has got to, this has got to amount to, a lambda to the hundredth power times an S times this vector C that's telling us how much of each one is in the original thing." + }, + { + "text": "So if, if I had to really find the hundredth power, I would take u0, I would expand it as a combination of eigenvectors, this is really S, the eigenvector matrix times C, the, the coefficient vector." + }, + { + "text": "And then I would immediately, then, by inserting these hundredth powers of eigenvalues, I'd have the answer." + }, + { + "text": "So the, the, huh, there must be, well, let's see." + }, + { + "text": "OK." + }, + { + "text": "It's, so, yeah." + }, + { + "text": "So if u100 is a to the hundredth times u0, and u0 is Sc, then you see this formula is just this formula, which is the way I would actually get hold of this, of this u100, which is, let me put it here, u100." + }, + { + "text": "The way I would actually get hold of that, see what, what the solution is after a hundred steps, would be expand the initial vector into eigenvectors and, and let each eigenvector go its own way, multiplying by a hundred at, by lambda at every step, and therefore by lambda to the hundredth power after a hundredth step." + }, + { + "text": "Can I do an example?" + }, + { + "text": "So that's, that's the, the formulas." + }, + { + "text": "Now let me take an example." + }, + { + "text": "I'll use the Fibonacci sequence as an example." + }, + { + "text": "So, so Fibonacci example." + }, + { + "text": "You remember the Fibonacci numbers?" + }, + { + "text": "If we start with one and one as F0, oh, I think I start with zero, maybe." + }, + { + "text": "Let zero and one be the first ones." + }, + { + "text": "So there's F0 and F1, the first two Fibonacci numbers." + }, + { + "text": "Then what's the rule for Fibonacci numbers?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk16.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..79c65e32781f7f304b504a6c390247abb9d26ac8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "They're the sum." + }, + { + "text": "The next one is the sum of those, so it's one." + }, + { + "text": "The next one is the sum of those, so it's two." + }, + { + "text": "The next one is the sum of those, so it's three." + }, + { + "text": "Well, it looks like one, two, three, four, five, but somehow it's not going to do that way." + }, + { + "text": "The next one is five, right." + }, + { + "text": "Two and three makes five." + }, + { + "text": "The next one is eight." + }, + { + "text": "The next one is thirteen." + }, + { + "text": "And the one hundredth Fibonacci number is what?" + }, + { + "text": "That's my question." + }, + { + "text": "How could I get a formula for the hundredth number and for example how could I answer the question how fast are they growing?" + }, + { + "text": "How fast are those Fibonacci numbers growing?" + }, + { + "text": "They're certainly growing." + }, + { + "text": "It's not a stable case, whatever the eigenvalues of whatever matrix it is, they're not smaller than one." + }, + { + "text": "These numbers are growing." + }, + { + "text": "But how fast are they growing?" + }, + { + "text": "The answer is lies in the eigenvalue." + }, + { + "text": "So I've got to find the matrix, so let me write down the Fibonacci rule, F k plus two is F k plus one plus F k, right?" + }, + { + "text": "Now that's not in my -- I want to write that as U k plus one and A U k. But right now what I've got is a single equation, not a system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk17.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b3aaa9dcee3cf27c112015659bb5a0b51a983ce1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's second order." + }, + { + "text": "It's like having a second order differential equation with second derivatives." + }, + { + "text": "I want to get first derivatives." + }, + { + "text": "Here I want to get first difference." + }, + { + "text": "So the way to do it is to introduce U k will be a vector." + }, + { + "text": "See, a small trick." + }, + { + "text": "Let U k be a vector, F k plus one and F k. So I'm going to get a two by two system, first order, instead of a one, instead of a scalar system, second order, by a simple trick." + }, + { + "text": "I'm just going to add in an equation F k plus one equals F k plus one." + }, + { + "text": "That will be my second equation." + }, + { + "text": "Then this is my system, this is my unknown, and what's my one-step equation?" + }, + { + "text": "So now U k plus one." + }, + { + "text": "That's so U k plus one is the left side, and what have I got here on the right side?" + }, + { + "text": "I've got some matrix multiplying U k. Can you see that all right?" + }, + { + "text": "If you can see it, then you can tell me what the matrix is." + }, + { + "text": "You see that I'm taking my system here, I artificially made it into a system." + }, + { + "text": "I artificially made the unknown into a vector, and now I'm ready to look at and see what the matrix is." + }, + { + "text": "So do you see the left side, U k plus one is F k plus two F k plus one, that's just what I want." + }, + { + "text": "On the right side, this, remember, this U k here, let me for the moment put it as F k plus one F k. So what's the matrix?" + }, + { + "text": "Well, that has a one and a one, and that has a one and a zero." + }, + { + "text": "There's the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk18.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..6c1b68c2cb2fde3f5dea82f3100d4da31fcce70a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "You see that that gives me the right-hand side." + }, + { + "text": "So there's the matrix A, and this is our friend U k. So we've got, so that simple trick changed the second order scalar problem to a first order system, two, with two unknowns." + }, + { + "text": "With a matrix and now what do I do?" + }, + { + "text": "Well, before I even think, I find its eigenvalues and eigenvectors." + }, + { + "text": "So what are the eigenvalues and eigenvectors of that matrix?" + }, + { + "text": "Let's see." + }, + { + "text": "I was, first let me just, like, think for a minute." + }, + { + "text": "It's two by two, so this shouldn't be impossible to do." + }, + { + "text": "Let's do it." + }, + { + "text": "OK." + }, + { + "text": "So my matrix again is one one one zero." + }, + { + "text": "It's symmetric, by the way." + }, + { + "text": "So what I will eventually know about symmetric matrices is that the eigenvalues will come out real, I won't get any complex numbers here, and the eigenvectors, once I get those, actually will be orthogonal." + }, + { + "text": "But two by two, I'm more interested in what the actual numbers are." + }, + { + "text": "What do I know about the two numbers?" + }, + { + "text": "Well, should, do you want me to find this determinant of A minus lambda I?" + }, + { + "text": "Sure." + }, + { + "text": "So it's the determinant of one minus lambda one one zero, right?" + }, + { + "text": "Minus lambda, yes, got it." + }, + { + "text": "OK. OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk19.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..a73b23e3d56b889ff49ea7f55a784fac33e13c3d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "There'll be two eigenvalues." + }, + { + "text": "Well, tell me again what I know about the two eigenvalues before I go any further." + }, + { + "text": "Tell me something about these two eigenvalues, what do they add up to?" + }, + { + "text": "Lambda one plus lambda two is the same as the trace down the diagonal of the matrix, one and zero is one." + }, + { + "text": "So lambda one plus lambda two should come out to be one, and lambda one times lambda two should come out to be the determinant, which is minus one." + }, + { + "text": "So I'm expecting the eigenvalues to add to one and to multiply to minus one." + }, + { + "text": "But let's just see it happen here." + }, + { + "text": "If I multiply this out, I get that times that'll be a lambda squared minus lambda minus one." + }, + { + "text": "Good." + }, + { + "text": "Lambda squared minus lambda minus one." + }, + { + "text": "Actually, you see the, compare that with the original equation that I started with." + }, + { + "text": "Fk plus two minus Fk plus one minus Fk is zero." + }, + { + "text": "The recurrent, the recursion that the Fibonacci number satisfy is somehow showing up directly here for the eigenvalues when we set that to zero." + }, + { + "text": "OK. Let's solve." + }, + { + "text": "Well, I would like to be able to factor that, that quadratic, but I'm better off to use the quadratic formula." + }, + { + "text": "Lambda is, let's see, minus b is one, plus or minus the square root of b squared, which is one, minus four, times that, times that, which is plus four, over two." + }, + { + "text": "So that's the square root of five." + }, + { + "text": "So the eigenvalues are lambda one is one half of one plus square root of five, and lambda two is one half of one minus square root of five." + }, + { + "text": "And sure enough, they, those add up to one, and they multiply to give minus one." + }, + { + "text": "OK. Those are the two eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk2.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..43cfb012fc04a89fc7dab94c23bfb0f50ade3782 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "On the right, it's multiplied by, if I want, if I want lambda n xn in the last column, how do I do it?" + }, + { + "text": "Well, the last column here will be, I'll, I'll take the last column, use these coefficients, put the lambda n down there, and it will multiply that nth column and give me lambda n xn." + }, + { + "text": "There, there you see matrix multiplication just working for us." + }, + { + "text": "So I started with A s. I wrote down what it meant." + }, + { + "text": "A times each eigenvector." + }, + { + "text": "That gave me lambda times the eigenvector." + }, + { + "text": "And then when I peeled off the lambdas, they were on the right-hand side, so I've got s, my matrix back again, and this matrix, this diagonal matrix, the eigenvalue matrix, and I call it capital lambda, using capital letters for matrices, and lambda to prompt me that it's, that it's eigenvalues that are in there." + }, + { + "text": "So you see that the eigenvalues are just sitting down that diagonal?" + }, + { + "text": "If I had a column x2 here, I would want the lambda two in the two two position, in the diagonal position, to multiply that x2 and give me the lambda two x2." + }, + { + "text": "That's my formula." + }, + { + "text": "A s is s lambda." + }, + { + "text": "OK. That's, that's the, you see, it's just a calculation." + }, + { + "text": "Now, I, I mentioned, and I have to mention again, this business about n independent eigenvectors." + }, + { + "text": "As it stands, this is all fine whether, I mean, I could be repeating the same eigenvector, but I, I'm no interested in that." + }, + { + "text": "I want to be able to invert s, and that's where this comes in." + }, + { + "text": "This n independent eigenvectors business comes in to tell me that that matrix is invertible." + }, + { + "text": "So let me, on the next board, write down what I've got." + }, + { + "text": "A s equals s lambda." + }, + { + "text": "And now I'm, I can multiply on the left by s inverse." + }, + { + "text": "So this is really, I can do that provided s is invertible, provided my assumption of n independent eigenvectors is satisfied." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk20.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ad5a59fa5db44ce73ff5f88190423e0404fb3d39 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "How, how, what are those numbers approximately?" + }, + { + "text": "Square root of five, well, it's more than two, but less than three." + }, + { + "text": "It, it'd be nice to know these numbers." + }, + { + "text": "I think, I think that that, so that number comes out bigger than one, right?" + }, + { + "text": "Yeah, that's right." + }, + { + "text": "This number comes out bigger than one." + }, + { + "text": "It's about one point six one eight or something." + }, + { + "text": "Not exactly." + }, + { + "text": "It's supposed to be one point six." + }, + { + "text": "Just, like, I think so." + }, + { + "text": "Then what's lambda two?" + }, + { + "text": "Is, is lambda two positive or negative?" + }, + { + "text": "Negative, right?" + }, + { + "text": "Because I'm, it's obviously negative, and I knew that the, so it's minus, and they add up to one, so minus point six one eight, I guess." + }, + { + "text": "OK. And some order." + }, + { + "text": "Those are the two eigenvalues." + }, + { + "text": "One eigenvalue bigger than one, one eigenvalue smaller than one." + }, + { + "text": "Actually, that's a great situation to be in." + }, + { + "text": "Of course, the eigenvalues are different, so there's no doubt whatever, is this matrix diagonalizable?" + }, + { + "text": "Is this matrix diagonalizable, that original matrix A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk21.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..4a034475591d371995b379b5f98783a2cfb25870 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Sure." + }, + { + "text": "We've got two distinct eigenvalues and we can find the eigenvectors in a moment." + }, + { + "text": "But they'll be independent, will be diagonalizable, and now you can already answer my very first question." + }, + { + "text": "How fast are those Fibonacci numbers increasing?" + }, + { + "text": "How, those, they're increasing, right?" + }, + { + "text": "They're not doubling at every step." + }, + { + "text": "Let's look again at these numbers." + }, + { + "text": "Five eight thirteen, it's not obvious." + }, + { + "text": "The next one would be twenty one thirty four." + }, + { + "text": "So to get some idea of what F one hundred is, can you give me any, I mean the crucial number of, so it, these, it's approximately, what's controlling the growth of these Fibonacci numbers?" + }, + { + "text": "It's the eigenvalues." + }, + { + "text": "And which eigenvalues controlling that growth?" + }, + { + "text": "The big ones." + }, + { + "text": "So F one hundred will it be approximately some constant, c one, I guess, times this lambda one, this one plus square root of five over two, to the hundredth power." + }, + { + "text": "And the two hundredth have, in other words, the eigenvalue, the Fibonacci numbers are growing by about that factor." + }, + { + "text": "You see that we've got precise information about the, about the Fibonacci numbers out of the eigenvalue." + }, + { + "text": "OK. And again, why is that true?" + }, + { + "text": "Let me go over to this board and show what I'm doing here." + }, + { + "text": "The, the original eigen, the original initial value is some combination of eigenvectors, and then when we start multiple, when we start going out the theory of Fibonacci numbers, when we start multiplying by a hundred times, it's this lambda one to the hundredth, this term is, is the one that's taken over." + }, + { + "text": "It's, I mean, that's big, like, one point six to the hundredth power." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk22.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..c13a1fc9867173c3067e46c469cfff27b9b45289 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "The second term is practically nothing, right?" + }, + { + "text": "The point six, or minus point six to the hundredth power, is an extremely small, extremely small number." + }, + { + "text": "So this is, this, this, there are only two terms, because we're two by two." + }, + { + "text": "This number is, this piece of it is there, but it's, it's disappearing." + }, + { + "text": "Where this piece is there and it's growing and controlling everything." + }, + { + "text": "So, so really the, we're doing, like, problems that are evolving." + }, + { + "text": "We're doing dynamics." + }, + { + "text": "Instead of Ax equal b, that's a static problem." + }, + { + "text": "We're now, we're doing dynamics." + }, + { + "text": "A, a squared, a cubed, things are evolving in time, and the eigenvalues are the crucial, numbers." + }, + { + "text": "OK." + }, + { + "text": "I guess to complete this, I better write down the eigenvectors." + }, + { + "text": "So we should complete the, the whole process by finding the eigenvectors." + }, + { + "text": "OK. Well, I have to, up in the corner, then I have to look at A minus lambda I." + }, + { + "text": "So A minus lambda I is this one minus lambda, one, one, and minus lambda." + }, + { + "text": "And now, can we spot an eigenvector out of that?" + }, + { + "text": "That's, for these two lambdas, this matrix is singular." + }, + { + "text": "I guess the eigenvector, two by two ought to be easy." + }, + { + "text": "So if I know that this matrix is singular, then it seems to me the eigenvector has to be lambda and one, because that multiplication will give me the zero." + }, + { + "text": "And this multiplication gives me, better give me also zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk23.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..df816eb800ce767b1475c279a24ad976bb45a785 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Do you see why it does?" + }, + { + "text": "This is the minus lambda squared plus lambda plus one." + }, + { + "text": "It's the thing that's zero, because these lambdas are special." + }, + { + "text": "There's the eigenvector." + }, + { + "text": "X1 is lambda one, one, and x2 is lambda two, one." + }, + { + "text": "I did that as a little trick that was available in the two by two case." + }, + { + "text": "So now I finally have to, oh, I have to take the initial, u0." + }, + { + "text": "So to complete this example entirely, I have to say, OK, what was u0?" + }, + { + "text": "u0 was f1 f0." + }, + { + "text": "So u0, the starting vector, is f1 f0, and those were one and zero." + }, + { + "text": "So I have to use that vector, so I have to look for, from multiple of the first eigenvector and the second, to produce u0, the one zero vector." + }, + { + "text": "This is what will find c1 and c2, and then I'm done." + }, + { + "text": "So let me, instead of in the last five seconds grinding out a formula, let me repeat the idea." + }, + { + "text": "That really, it's the idea that's central." + }, + { + "text": "When things are evolving in time, let me come back to this board, because the ideas are here." + }, + { + "text": "When things are evolving in time by a first-order system, starting from an original u0, the key is, find the eigenvalues and eigenvectors of A." + }, + { + "text": "That will tell, those eigenvectors, the eigenvalues will already tell you what's happening." + }, + { + "text": "Is the solution blowing up?" + }, + { + "text": "Is it going to zero?" + }, + { + "text": "What's it doing?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk24.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..40301cb90760e2172baa94d536cbc13288d4c31f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk24.json @@ -0,0 +1,20 @@ +[ + { + "text": "And then, to find out exactly a formula, you have to take your u0 and write it as a combination of eigenvectors and then follow each eigenvector separately." + }, + { + "text": "And that's really what this formula, the formula for, that's what the formula for A to the k is doing." + }, + { + "text": "So remember that formula for A to the k is S, lambda to the k S inverse." + }, + { + "text": "OK. That's, that's difference equations, and you just have to, so the homework will give some examples different from Fibonacci to follow through." + }, + { + "text": "And next time will be differential equations." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk3.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..9bf1bb852baadc1da7837e14180c0c2951a30882 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I mentioned at the end of last time, and I'll say again, that there's a small number of matrices for, that don't have n independent eigenvectors." + }, + { + "text": "So I've got to discuss that, that technical point." + }, + { + "text": "But the great, the most matrices that we see have n, n independent eigenvectors and we can diagonalize." + }, + { + "text": "This is diagonalization." + }, + { + "text": "I could also write it, and I often will, the other way round." + }, + { + "text": "If I multiply on the right by s inverse, if I took this equation at the top and multiplied on the right by s inverse, I could, I would have A left here." + }, + { + "text": "Now s inverse is coming from the right." + }, + { + "text": "So can you keep those two straight?" + }, + { + "text": "A multiplies its eigenvectors." + }, + { + "text": "That's how I keep them straight." + }, + { + "text": "So A multiplies s. A multiplies s. And then this s inverse makes the whole thing diagonal." + }, + { + "text": "And this is another way of saying the same thing, putting the s's on the other side of the equation, A is s lambda s inverse." + }, + { + "text": "So that's the, that's the new factorization." + }, + { + "text": "That's the replacement for L U from elimination or Q R from Gram-Schmidt." + }, + { + "text": "And notice that the matrix, so it's, it's a matrix times a diagonal matrix times the inverse of the first one." + }, + { + "text": "It's, that's the combination that we'll see throughout this chapter." + }, + { + "text": "This, this, combination with an s and an s inverse." + }, + { + "text": "OK. Can I just begin to use that?" + }, + { + "text": "For example, what about A squared?" + }, + { + "text": "What are the eigenvalues and eigenvectors of A squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk4.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c687b6948acad76de8781cb82d3eb069c9da514e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's a straightforward question with a, with a absolutely clean answer." + }, + { + "text": "So let me, let me consider A squared." + }, + { + "text": "So I look, I start with Ax equal lambda x." + }, + { + "text": "And I'm headed for A squared." + }, + { + "text": "So let me multiply both sides by A." + }, + { + "text": "That's one way to get A squared on the left." + }, + { + "text": "So if, I should write these ifs in here." + }, + { + "text": "If Ax equals lambda x, then I multiply by A." + }, + { + "text": "So I get A squared x equals, well, I'm multiplying by A, so that's lambda Ax." + }, + { + "text": "That lambda was a number, so I just put it on the left." + }, + { + "text": "And what do I, tell me how to make that look better." + }, + { + "text": "What have I got here?" + }, + { + "text": "For, if, if A has the eigenvalue lambda and eigenvector x, what's up with A squared?" + }, + { + "text": "A squared x, I just multiply by A, but now for Ax, I'm going to substitute lambda x, so I've got lambda squared x." + }, + { + "text": "So from that simple calculation, I, my conclusion is that the eigenvalues of A squared are lambda squared." + }, + { + "text": "And the eigenvectors, I always think about both of those." + }, + { + "text": "What can I say about the eigenvalues?" + }, + { + "text": "They're squared." + }, + { + "text": "What can I say about the eigenvectors?" + }, + { + "text": "They're the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk5.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5bf15e20707c156c8ae71c9c7acea41a9d9d8e46 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same x as in, as for A." + }, + { + "text": "Now, let me see that also from this formula." + }, + { + "text": "How can I see what A squared is looking like from this formula?" + }, + { + "text": "So let me, that, that was one way to do it." + }, + { + "text": "Let me do it by just taking A squared from that." + }, + { + "text": "A squared is S lambda S inverse, that's A, times S lambda S inverse, that's A, which is?" + }, + { + "text": "This is the beauty of eigenvalues, eigenvectors, having that S inverse and S is the identity, so I've got S lambda squared S inverse." + }, + { + "text": "Yes." + }, + { + "text": "You see what that's telling me?" + }, + { + "text": "It's, it's telling me the same thing that I just learned here, but in the, in, in a matrix form." + }, + { + "text": "It's telling me that the S is the same, the eigenvectors are the same, but the eigenvalues are squared, because this is, what's lambda squared, that's still diagonal, it's got little lambda one squared, lambda two squared, down to lambda n squared, on that diagonal, those are the eigenvalues, as we just learned, of A squared." + }, + { + "text": "OK." + }, + { + "text": "So, somehow those eigenvalues and eigenvectors are really giving you a way to, to, to, to see what's going on inside a matrix." + }, + { + "text": "Now, of course, I can continue that for, to the k-th power." + }, + { + "text": "A to the k-th power." + }, + { + "text": "If I multiply, if I have k of these together, do you see how S inverse S will keep cancelling?" + }, + { + "text": "In the, in the inside, I'll have the S outside, at the far left, and lambda will be in there k times and S inverse." + }, + { + "text": "So what's that telling me?" + }, + { + "text": "That's telling me that the eigenvalues of A, of A to the k-th power are the k-th powers." + }, + { + "text": "The eigenvalues of A cubed are the cubes of the eigenvalues of A, and the eigenvectors are the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk6.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..c18dddbe798022f7e68278ac002a3f5fe6ed249e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same." + }, + { + "text": "OK." + }, + { + "text": "In other words, eigenvalues and eigenvectors give a great way to understand the powers of a matrix." + }, + { + "text": "If I take the square of a matrix or the hundredth power of a matrix, the pivots are all over the place." + }, + { + "text": "L U, if I multiply L U times L U times L U times L U a hundred times, I've got a hundred L U's." + }, + { + "text": "I can't do anything with them." + }, + { + "text": "But when I multiply S lambda S inverse by itself, when I look at the eigenvector picture a hundred times, I get a hundred or ninety-nine of these guys cancelling out inside, and I get A to the hundredth is S lambda to the hundredth S inverse." + }, + { + "text": "I mean, eigenvalues tell you about powers of a matrix in a way that we had no, no way to approach previously." + }, + { + "text": "For example, when does, when do the powers of a matrix go to zero?" + }, + { + "text": "I would call that matrix stable, maybe." + }, + { + "text": "So, so, so I could write down a, a theorem." + }, + { + "text": "I'll, I'll write it as a theorem, just to use that word to emphasize that here I'm getting this great fact from this eigenvalue picture." + }, + { + "text": "OK. A to the k approaches zero as k goes, as k gets bigger." + }, + { + "text": "If what?" + }, + { + "text": "What's the, how can I tell for a matrix A if its powers go to zero?" + }, + { + "text": "What, what's somewhere inside that matrix is that information." + }, + { + "text": "That information is not present in the pivots." + }, + { + "text": "It's present in the eigenvalues." + }, + { + "text": "What do I need for the, to know that if I take higher and higher powers of A that this matrix gets smaller and smaller?" + }, + { + "text": "Well, S and S inverse are not moving." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk7.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b84a5c854a5542758e8a0107e1ff043205fe3bdb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's this guy that has to get small, and that's easy to, easy to understand." + }, + { + "text": "The requirement is all eigenvalues, so what is the requirement?" + }, + { + "text": "The eigenvalues have to be less than one." + }, + { + "text": "Now, I have to write that absolute value, because those eigenvalues could be negative, they could be complex numbers." + }, + { + "text": "So I'm taking the absolute value if all of those are below one." + }, + { + "text": "That's, in fact, we practically see why." + }, + { + "text": "Let me just say that I, that I, I'm operating on one assumption here, and I got to keep remembering that that assumption is still present." + }, + { + "text": "That assumption was that I had a full set of, of n independent eigenvectors." + }, + { + "text": "If I don't have that, then I, I, then this approach is not working." + }, + { + "text": "So, so again, a pure eigenvalue approach, eigenvector approach, needs n independent eigenvectors." + }, + { + "text": "If we don't have n independent eigenvectors, we can't diagonalize the matrix." + }, + { + "text": "We can't get to a diagonal matrix." + }, + { + "text": "This, this, this diagonalization is only possible if S inverse makes sense." + }, + { + "text": "OK. Can I, can I follow up on that point now?" + }, + { + "text": "So, so you see why, what we get and, and why we want it, because we get information about the powers of a matrix just immediately from the eigenvalues." + }, + { + "text": "OK, now let me follow up on this, business of which matrices are diagonalizable." + }, + { + "text": "Sorry about that long word." + }, + { + "text": "So a matrix is, is sure to, so here's, here's the main point." + }, + { + "text": "A is sure to be, to have n independent eigenvectors and, and B, now here comes that word, diagonalizable, if, if, so we, we, we might as well get the, the nice case out in the open." + }, + { + "text": "The nice case is when, if all the lambdas are different." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk8.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f06dcec8ffa0ee1bf19440e4ab2194db33ab353b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means, that means no repeated eigenvalues." + }, + { + "text": "OK. That's the nice case." + }, + { + "text": "If, if my matrix and most matrix, if I do a random matrix in MATLAB and compute its eigenvalues, so if I computed, if I took I of rand of ten ten, gave, gave that MATLAB command, the, we'd get a random ten by ten matrix, we would get a list of its ten eigenvalues and they would be different." + }, + { + "text": "They would be distinct, is the best word." + }, + { + "text": "I would have a random matrix will have ten distinct, a ten by ten matrix will have ten distinct eigenvalues, and if it does, the eigenvectors are automatically independent." + }, + { + "text": "So that's a nice fact." + }, + { + "text": "I can, I'll refer you to the text for the proof." + }, + { + "text": "That, that A is sure to have n independent eigenvectors if the eigenvalues are different." + }, + { + "text": "If, if all the, if all eigenvalues are different." + }, + { + "text": "It's just, if some lambdas are repeated, then I have to look more closely." + }, + { + "text": "If an eigenvalue is repeated, I have to look, I have to count, I have to check." + }, + { + "text": "Has it got, say it's repeated three times." + }, + { + "text": "So what's a possibility for, so, so here's, here's the repeated possibility." + }, + { + "text": "And, and let me emphasize the conclusion." + }, + { + "text": "That if I have repeated eigenvalues, I may or may not, I may or may not have, have n independent eigenvectors." + }, + { + "text": "I might." + }, + { + "text": "I, I, you know, this isn't a completely negative case." + }, + { + "text": "The identity matrix." + }, + { + "text": "Well, suppose I take the ten by ten identity matrix." + }, + { + "text": "What are the eigenvalues of that matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk9.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..87d2a2ae5773036cf11800e2f1962908986a0dad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_23_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So just, just take the easiest matrix, the identity." + }, + { + "text": "If I look for its eigenvalues, they're all ones." + }, + { + "text": "So that eigenvalue one is repeated ten times." + }, + { + "text": "But there's no shortage of eigenvectors for the identity matrix." + }, + { + "text": "In fact, every vector is an eigenvector." + }, + { + "text": "So I can take ten independent vectors." + }, + { + "text": "Oh, well, what happens to everything if, if, if A is the identity matrix, let's just think that one through in our head." + }, + { + "text": "If A is the identity matrix, then it's got plenty of eigenvectors." + }, + { + "text": "I choose ten independent vectors, they're the columns of S, and, and what do I get from S inverse A S?" + }, + { + "text": "I get I again, right?" + }, + { + "text": "If A is the identity, and of course, that's the correct lambda." + }, + { + "text": "The, the matrix was already diagonal." + }, + { + "text": "So if the matrix is already diagonal, then the, the lambda is the same as the matrix." + }, + { + "text": "A diagonal matrix has got its eigenvalues sitting right there in front of you." + }, + { + "text": "Now if it's triangular, the eigenvalues are still sitting there, but so let's, let's take a case where, it's triangular." + }, + { + "text": "Suppose A is like, two, one, two, zero." + }, + { + "text": "So there's a case that's going to be trouble." + }, + { + "text": "There's a case that's going to be trouble." + }, + { + "text": "First of all, what are the eigen- I mean, we just, like now you, if we start with a matrix, the first thing we do practically without thinking is compute the eigenvalues and eigenvectors." + }, + { + "text": "OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk0.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6898d4fe66019ef6b40d0472ea94a968e7bbde9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, shall we start?" + }, + { + "text": "This is the second lecture on eigenvalues." + }, + { + "text": "So the first lecture was set -- reached the key equation, Ax equal lambda x. x is the eigenvector and lambda is the eigenvalue." + }, + { + "text": "Now, to use that." + }, + { + "text": "And the good way to, after we've found, so job one is to find the eigenvalues and find the eigenvectors." + }, + { + "text": "Now after we found them, what do we do with them?" + }, + { + "text": "Well, the good way to see that is diagonalize the matrix." + }, + { + "text": "So the matrix is A, and I want to show, first of all, this is like the basic fact." + }, + { + "text": "This, this formula." + }, + { + "text": "That's, that's the key to today's lecture." + }, + { + "text": "This matrix A, I put its eigenvectors in the columns of a matrix S. So S will be the eigenvector matrix, and I want to look at this magic combination S inverse A S. So can I show you how that, how that, what happens there?" + }, + { + "text": "And notice, notice, there's an S inverse." + }, + { + "text": "We have to be able to invert this eigenvector matrix S. So for that we need n independent eigenvectors." + }, + { + "text": "So that's the, that's the case." + }, + { + "text": "OK." + }, + { + "text": "So suppose we have n linearly independent eigenvectors of A." + }, + { + "text": "Put them in the columns of this matrix S. So I'm naturally going to call that the eigenvector matrix, because it's got the eigenvectors in its columns." + }, + { + "text": "And all I want to do is show you what happens when you multiply A times S. So A times S. So this is A times the matrix with the first eigenvector in its first column, the second eigenvector in its second column, the nth eigenvector in its nth column." + }, + { + "text": "And how am I going to do this matrix multiplication?" + }, + { + "text": "Well, certainly I'll do it a column at a time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk1.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..fbe078217bb68baea8e0605a5d04be568c49efbf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I get?" + }, + { + "text": "A times the first column gives me the first column of the answer, but what is it?" + }, + { + "text": "That's an eigenvector." + }, + { + "text": "A times x1 is equal to the lambda times the x1." + }, + { + "text": "And that lambda's we'll call lambda one, of course." + }, + { + "text": "So that's the first column, A x1 is the same as lambda one x1." + }, + { + "text": "A x2 is lambda two x2, so on, along to, in the nth column, we now have lambda n xn." + }, + { + "text": "Looking good, but the next step is even better." + }, + { + "text": "So for the next step, I want to separate out those eigenvalues, those multiplying numbers, from the x's." + }, + { + "text": "So then I'll have just what I want." + }, + { + "text": "OK, so how, how am I going to separate out?" + }, + { + "text": "So that, that number lambda one is multiplying the first column." + }, + { + "text": "So if I want to factor it out of the first column, I better put, here is going to be x1, and that's going to multiply this matrix lambda one in the first entry in all zeros." + }, + { + "text": "You see that that, that's going to come out right for the first column?" + }, + { + "text": "Because we remember how, how we're going back to that original punchline, that if I want a number to multiply x1, then I can do it by putting x1 in that column, in the first column, and putting that number there." + }, + { + "text": "What am I going to have here?" + }, + { + "text": "I'm going to have lambda one, I'm going to have x1, x2, xn." + }, + { + "text": "These are going to be my columns again." + }, + { + "text": "I'm getting s back again." + }, + { + "text": "I'm getting s back again, but now what's it multiplied by?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk10.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c58a42edbe9567233ca7f57643a0b7d43ae6761f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what are the eigenvalues?" + }, + { + "text": "You can tell me right away what they are." + }, + { + "text": "They're two and two, right." + }, + { + "text": "It's a triangular matrix, so when I do this determinant, shall I do this determinant of A minus lambda I?" + }, + { + "text": "I'll get this two minus lambda, one, zero, two minus lambda, right?" + }, + { + "text": "I take that determinant, so I make those into vertical bars to mean determinant, and what's the determinant?" + }, + { + "text": "Two minus lambda squared." + }, + { + "text": "What are the roots?" + }, + { + "text": "Lambda equal two twice." + }, + { + "text": "So the eigenvalues are lambda equals two and two." + }, + { + "text": "OK, fine." + }, + { + "text": "Now the next step, find the eigenvectors." + }, + { + "text": "So I look for eigenvectors and what do I find for this guy?" + }, + { + "text": "Eigenvectors for this guy, when I subtract two minus the identity, so A minus two I has zeros here, and I'm looking for the null space." + }, + { + "text": "What's, what are the eigenvectors?" + }, + { + "text": "They're the, they're, they're the null space of A minus lambda I." + }, + { + "text": "The null space is only one dimension." + }, + { + "text": "This is a case where I don't have enough eigenvectors." + }, + { + "text": "My algebraic multiplicity is two." + }, + { + "text": "I, I would say when I see, when I count how often the eigenvalue is repeated, that's the algebraic multiplicity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk11.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..779c2cf904d904b761080db2671aac46394ad02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the multiplicity." + }, + { + "text": "How many times is it the root of the polynomial?" + }, + { + "text": "My polynomial is two minus lambda squared." + }, + { + "text": "It's a double root." + }, + { + "text": "So my algebraic multiplicity is two." + }, + { + "text": "But the geometric multiplicity, which looks for vectors, looks for eigenvectors and which means the null space of this thing." + }, + { + "text": "And the only eigenvector is one zero." + }, + { + "text": "That's in the null space." + }, + { + "text": "Zero one is not in the null space." + }, + { + "text": "The null space is only one dimensional." + }, + { + "text": "So there's a matrix, my, this A or the original A, that are not diagonalizable." + }, + { + "text": "I can't, I can't find two independent eigenvectors, there's only one." + }, + { + "text": "OK." + }, + { + "text": "So that's the case that I'm, that's a case that I, I'm not really handling." + }, + { + "text": "For example, when I wrote down up here that the powers went to zero if the eigenvalues were below one, I didn't really handle that case of repeated eigenvalues because my reasoning was based on this formula." + }, + { + "text": "And this formula is based on n independent eigenvectors." + }, + { + "text": "OK." + }, + { + "text": "So just to say that." + }, + { + "text": "There are some matrices that we don't cover through diagonalization, but the great majority we do." + }, + { + "text": "OK. And we're always OK if we have different distinct eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk12.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..77d090704cc298475d94416b7ecb88a2a015a913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. That's the, like, the typical case." + }, + { + "text": "Because for each eigenvalue there's at least one eigenvector, the algebraic multiplicity here is one for every eigenvalue, and the geometric multiplicity is one." + }, + { + "text": "There's one eigenvector and they are independent." + }, + { + "text": "OK. OK. Now let me come back to the important case when we're OK." + }, + { + "text": "The important case when we are diagonalizing." + }, + { + "text": "Let me look at, so let me solve this equation." + }, + { + "text": "The equation will be each, I start with some, start with a given vector u0." + }, + { + "text": "And then my equation is that every step I multiply what I have by a." + }, + { + "text": "That equation ought to be simple to handle." + }, + { + "text": "OK. And I'd like to be able to solve it." + }, + { + "text": "How would I find, if I start with a vector u0, and I multiply by a a hundred times, what have I got?" + }, + { + "text": "Well, I can certainly write down a formula for the answer." + }, + { + "text": "So what, what, so u1 is a u0." + }, + { + "text": "And u2 is, what's u2 then?" + }, + { + "text": "U2 I multiply it, u2 I get from u1 by another, multiplying by a, so I've got a twice." + }, + { + "text": "And my formula is uk, after k steps, I've multiplied by a k times the original u0." + }, + { + "text": "You see what I'm doing?" + }, + { + "text": "The next section is going to solve systems of differential equations." + }, + { + "text": "I'm going to have derivatives." + }, + { + "text": "This, this section is the nice one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk13.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..ba8214d8c636e4757a266d6617801174bc939d80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "It solves difference equations." + }, + { + "text": "I would call that a difference equation." + }, + { + "text": "It's conne- a first order." + }, + { + "text": "I would call that a first order system, because it connects only, it only goes up one level." + }, + { + "text": "And it's a system because these are vectors and that's a matrix." + }, + { + "text": "And the solution is just that." + }, + { + "text": "OK." + }, + { + "text": "But, that's a nice formula." + }, + { + "text": "That's the, like, the most compact formula I could ever get." + }, + { + "text": "U one hundred would be a to the one hundredth u0." + }, + { + "text": "But how would I actually find u one hundred?" + }, + { + "text": "How would I find, how would I discover what u one hundred is?" + }, + { + "text": "Let me, let me show you how." + }, + { + "text": "Here, here's the idea." + }, + { + "text": "If, so, to solve, to really solve, shall I say, to really solve." + }, + { + "text": "To really solve it, I would take this initial vector, u0, and I would write it as a combination of eigenvectors." + }, + { + "text": "To really solve, write, write u0 as a combination, say, certain amount of the first eigenvector plus a certain amount of the second eigenvector plus a certain amount of the last eigenvector." + }, + { + "text": "Now multiply by a." + }, + { + "text": "You want to, you got to see the magic of eigenvectors work." + }, + { + "text": "Multiply by a." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk14.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7843b2bf0cac762d1c12452cf36500ea4ad13370 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a u0 is what?" + }, + { + "text": "So a times that." + }, + { + "text": "A times, so what's, I can separate it out into n separate pieces and that's the whole point." + }, + { + "text": "That each of those pieces is going in its own merry way." + }, + { + "text": "Each of those pieces is an eigenvector, and when I multiply by a, what does this piece become?" + }, + { + "text": "So that's some amount of the first, let's suppose the eigenvectors are normalized to be unit vectors." + }, + { + "text": "So that says what the eigenvector is." + }, + { + "text": "It's, and I need some multiple of it to produce u0." + }, + { + "text": "OK. Now when I multiply by a, what do I get?" + }, + { + "text": "I get c1, which is just a factor, times a x1, but a x1 is lambda one x1." + }, + { + "text": "When I multiply this by a, I get c2 lambda two x2." + }, + { + "text": "And here I get cn lambda n xn." + }, + { + "text": "And suppose I multiply by a to the hundredth power now." + }, + { + "text": "Can we, can we, having done it, multiplied by a, let's multiply by a to the hundredth." + }, + { + "text": "What happens to this first term when I multiply by a to the one hundredth?" + }, + { + "text": "It's got that factor lambda to the hundredth." + }, + { + "text": "That's the key." + }, + { + "text": "That, that's what I mean by going its own merry way." + }, + { + "text": "It, it is pure eigenvector, it's exactly in a direction where multiplication by a just brings in a scalar factor lambda one." + }, + { + "text": "So a hundred times brings in this a hundred times." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk15.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7ee3348735378aa4049d33ec2a197d0ceb0c447c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Hundred times lambda two, hundred times lambda n. Actually, we're, what are we seeing here?" + }, + { + "text": "We're seeing, this same, lambda, capital lambda to the hundredth, as in the, as in the diagonalization, and we're seeing the S matrix, the matrix S of eigenvectors." + }, + { + "text": "That's what this has got to, this has got to amount to, a lambda to the hundredth power times an S times this vector C that's telling us how much of each one is in the original thing." + }, + { + "text": "So if, if I had to really find the hundredth power, I would take u0, I would expand it as a combination of eigenvectors, this is really S, the eigenvector matrix times C, the, the coefficient vector." + }, + { + "text": "And then I would immediately, then, by inserting these hundredth powers of eigenvalues, I'd have the answer." + }, + { + "text": "So the, the, huh, there must be, well, let's see." + }, + { + "text": "OK." + }, + { + "text": "It's, so, yeah." + }, + { + "text": "So if u100 is a to the hundredth times u0, and u0 is Sc, then you see this formula is just this formula, which is the way I would actually get hold of this, of this u100, which is, let me put it here, u100." + }, + { + "text": "The way I would actually get hold of that, see what, what the solution is after a hundred steps, would be expand the initial vector into eigenvectors and, and let each eigenvector go its own way, multiplying by a hundred at, by lambda at every step, and therefore by lambda to the hundredth power after a hundredth step." + }, + { + "text": "Can I do an example?" + }, + { + "text": "So that's, that's the, the formulas." + }, + { + "text": "Now let me take an example." + }, + { + "text": "I'll use the Fibonacci sequence as an example." + }, + { + "text": "So, so Fibonacci example." + }, + { + "text": "You remember the Fibonacci numbers?" + }, + { + "text": "If we start with one and one as F0, oh, I think I start with zero, maybe." + }, + { + "text": "Let zero and one be the first ones." + }, + { + "text": "So there's F0 and F1, the first two Fibonacci numbers." + }, + { + "text": "Then what's the rule for Fibonacci numbers?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk16.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..79c65e32781f7f304b504a6c390247abb9d26ac8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "They're the sum." + }, + { + "text": "The next one is the sum of those, so it's one." + }, + { + "text": "The next one is the sum of those, so it's two." + }, + { + "text": "The next one is the sum of those, so it's three." + }, + { + "text": "Well, it looks like one, two, three, four, five, but somehow it's not going to do that way." + }, + { + "text": "The next one is five, right." + }, + { + "text": "Two and three makes five." + }, + { + "text": "The next one is eight." + }, + { + "text": "The next one is thirteen." + }, + { + "text": "And the one hundredth Fibonacci number is what?" + }, + { + "text": "That's my question." + }, + { + "text": "How could I get a formula for the hundredth number and for example how could I answer the question how fast are they growing?" + }, + { + "text": "How fast are those Fibonacci numbers growing?" + }, + { + "text": "They're certainly growing." + }, + { + "text": "It's not a stable case, whatever the eigenvalues of whatever matrix it is, they're not smaller than one." + }, + { + "text": "These numbers are growing." + }, + { + "text": "But how fast are they growing?" + }, + { + "text": "The answer is lies in the eigenvalue." + }, + { + "text": "So I've got to find the matrix, so let me write down the Fibonacci rule, F k plus two is F k plus one plus F k, right?" + }, + { + "text": "Now that's not in my -- I want to write that as U k plus one and A U k. But right now what I've got is a single equation, not a system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk17.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b3aaa9dcee3cf27c112015659bb5a0b51a983ce1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's second order." + }, + { + "text": "It's like having a second order differential equation with second derivatives." + }, + { + "text": "I want to get first derivatives." + }, + { + "text": "Here I want to get first difference." + }, + { + "text": "So the way to do it is to introduce U k will be a vector." + }, + { + "text": "See, a small trick." + }, + { + "text": "Let U k be a vector, F k plus one and F k. So I'm going to get a two by two system, first order, instead of a one, instead of a scalar system, second order, by a simple trick." + }, + { + "text": "I'm just going to add in an equation F k plus one equals F k plus one." + }, + { + "text": "That will be my second equation." + }, + { + "text": "Then this is my system, this is my unknown, and what's my one-step equation?" + }, + { + "text": "So now U k plus one." + }, + { + "text": "That's so U k plus one is the left side, and what have I got here on the right side?" + }, + { + "text": "I've got some matrix multiplying U k. Can you see that all right?" + }, + { + "text": "If you can see it, then you can tell me what the matrix is." + }, + { + "text": "You see that I'm taking my system here, I artificially made it into a system." + }, + { + "text": "I artificially made the unknown into a vector, and now I'm ready to look at and see what the matrix is." + }, + { + "text": "So do you see the left side, U k plus one is F k plus two F k plus one, that's just what I want." + }, + { + "text": "On the right side, this, remember, this U k here, let me for the moment put it as F k plus one F k. So what's the matrix?" + }, + { + "text": "Well, that has a one and a one, and that has a one and a zero." + }, + { + "text": "There's the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk18.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..6c1b68c2cb2fde3f5dea82f3100d4da31fcce70a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "You see that that gives me the right-hand side." + }, + { + "text": "So there's the matrix A, and this is our friend U k. So we've got, so that simple trick changed the second order scalar problem to a first order system, two, with two unknowns." + }, + { + "text": "With a matrix and now what do I do?" + }, + { + "text": "Well, before I even think, I find its eigenvalues and eigenvectors." + }, + { + "text": "So what are the eigenvalues and eigenvectors of that matrix?" + }, + { + "text": "Let's see." + }, + { + "text": "I was, first let me just, like, think for a minute." + }, + { + "text": "It's two by two, so this shouldn't be impossible to do." + }, + { + "text": "Let's do it." + }, + { + "text": "OK." + }, + { + "text": "So my matrix again is one one one zero." + }, + { + "text": "It's symmetric, by the way." + }, + { + "text": "So what I will eventually know about symmetric matrices is that the eigenvalues will come out real, I won't get any complex numbers here, and the eigenvectors, once I get those, actually will be orthogonal." + }, + { + "text": "But two by two, I'm more interested in what the actual numbers are." + }, + { + "text": "What do I know about the two numbers?" + }, + { + "text": "Well, should, do you want me to find this determinant of A minus lambda I?" + }, + { + "text": "Sure." + }, + { + "text": "So it's the determinant of one minus lambda one one zero, right?" + }, + { + "text": "Minus lambda, yes, got it." + }, + { + "text": "OK. OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk19.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..a73b23e3d56b889ff49ea7f55a784fac33e13c3d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "There'll be two eigenvalues." + }, + { + "text": "Well, tell me again what I know about the two eigenvalues before I go any further." + }, + { + "text": "Tell me something about these two eigenvalues, what do they add up to?" + }, + { + "text": "Lambda one plus lambda two is the same as the trace down the diagonal of the matrix, one and zero is one." + }, + { + "text": "So lambda one plus lambda two should come out to be one, and lambda one times lambda two should come out to be the determinant, which is minus one." + }, + { + "text": "So I'm expecting the eigenvalues to add to one and to multiply to minus one." + }, + { + "text": "But let's just see it happen here." + }, + { + "text": "If I multiply this out, I get that times that'll be a lambda squared minus lambda minus one." + }, + { + "text": "Good." + }, + { + "text": "Lambda squared minus lambda minus one." + }, + { + "text": "Actually, you see the, compare that with the original equation that I started with." + }, + { + "text": "Fk plus two minus Fk plus one minus Fk is zero." + }, + { + "text": "The recurrent, the recursion that the Fibonacci number satisfy is somehow showing up directly here for the eigenvalues when we set that to zero." + }, + { + "text": "OK. Let's solve." + }, + { + "text": "Well, I would like to be able to factor that, that quadratic, but I'm better off to use the quadratic formula." + }, + { + "text": "Lambda is, let's see, minus b is one, plus or minus the square root of b squared, which is one, minus four, times that, times that, which is plus four, over two." + }, + { + "text": "So that's the square root of five." + }, + { + "text": "So the eigenvalues are lambda one is one half of one plus square root of five, and lambda two is one half of one minus square root of five." + }, + { + "text": "And sure enough, they, those add up to one, and they multiply to give minus one." + }, + { + "text": "OK. Those are the two eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk2.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..43cfb012fc04a89fc7dab94c23bfb0f50ade3782 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "On the right, it's multiplied by, if I want, if I want lambda n xn in the last column, how do I do it?" + }, + { + "text": "Well, the last column here will be, I'll, I'll take the last column, use these coefficients, put the lambda n down there, and it will multiply that nth column and give me lambda n xn." + }, + { + "text": "There, there you see matrix multiplication just working for us." + }, + { + "text": "So I started with A s. I wrote down what it meant." + }, + { + "text": "A times each eigenvector." + }, + { + "text": "That gave me lambda times the eigenvector." + }, + { + "text": "And then when I peeled off the lambdas, they were on the right-hand side, so I've got s, my matrix back again, and this matrix, this diagonal matrix, the eigenvalue matrix, and I call it capital lambda, using capital letters for matrices, and lambda to prompt me that it's, that it's eigenvalues that are in there." + }, + { + "text": "So you see that the eigenvalues are just sitting down that diagonal?" + }, + { + "text": "If I had a column x2 here, I would want the lambda two in the two two position, in the diagonal position, to multiply that x2 and give me the lambda two x2." + }, + { + "text": "That's my formula." + }, + { + "text": "A s is s lambda." + }, + { + "text": "OK. That's, that's the, you see, it's just a calculation." + }, + { + "text": "Now, I, I mentioned, and I have to mention again, this business about n independent eigenvectors." + }, + { + "text": "As it stands, this is all fine whether, I mean, I could be repeating the same eigenvector, but I, I'm no interested in that." + }, + { + "text": "I want to be able to invert s, and that's where this comes in." + }, + { + "text": "This n independent eigenvectors business comes in to tell me that that matrix is invertible." + }, + { + "text": "So let me, on the next board, write down what I've got." + }, + { + "text": "A s equals s lambda." + }, + { + "text": "And now I'm, I can multiply on the left by s inverse." + }, + { + "text": "So this is really, I can do that provided s is invertible, provided my assumption of n independent eigenvectors is satisfied." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk20.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ad5a59fa5db44ce73ff5f88190423e0404fb3d39 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "How, how, what are those numbers approximately?" + }, + { + "text": "Square root of five, well, it's more than two, but less than three." + }, + { + "text": "It, it'd be nice to know these numbers." + }, + { + "text": "I think, I think that that, so that number comes out bigger than one, right?" + }, + { + "text": "Yeah, that's right." + }, + { + "text": "This number comes out bigger than one." + }, + { + "text": "It's about one point six one eight or something." + }, + { + "text": "Not exactly." + }, + { + "text": "It's supposed to be one point six." + }, + { + "text": "Just, like, I think so." + }, + { + "text": "Then what's lambda two?" + }, + { + "text": "Is, is lambda two positive or negative?" + }, + { + "text": "Negative, right?" + }, + { + "text": "Because I'm, it's obviously negative, and I knew that the, so it's minus, and they add up to one, so minus point six one eight, I guess." + }, + { + "text": "OK. And some order." + }, + { + "text": "Those are the two eigenvalues." + }, + { + "text": "One eigenvalue bigger than one, one eigenvalue smaller than one." + }, + { + "text": "Actually, that's a great situation to be in." + }, + { + "text": "Of course, the eigenvalues are different, so there's no doubt whatever, is this matrix diagonalizable?" + }, + { + "text": "Is this matrix diagonalizable, that original matrix A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk21.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..4a034475591d371995b379b5f98783a2cfb25870 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Sure." + }, + { + "text": "We've got two distinct eigenvalues and we can find the eigenvectors in a moment." + }, + { + "text": "But they'll be independent, will be diagonalizable, and now you can already answer my very first question." + }, + { + "text": "How fast are those Fibonacci numbers increasing?" + }, + { + "text": "How, those, they're increasing, right?" + }, + { + "text": "They're not doubling at every step." + }, + { + "text": "Let's look again at these numbers." + }, + { + "text": "Five eight thirteen, it's not obvious." + }, + { + "text": "The next one would be twenty one thirty four." + }, + { + "text": "So to get some idea of what F one hundred is, can you give me any, I mean the crucial number of, so it, these, it's approximately, what's controlling the growth of these Fibonacci numbers?" + }, + { + "text": "It's the eigenvalues." + }, + { + "text": "And which eigenvalues controlling that growth?" + }, + { + "text": "The big ones." + }, + { + "text": "So F one hundred will it be approximately some constant, c one, I guess, times this lambda one, this one plus square root of five over two, to the hundredth power." + }, + { + "text": "And the two hundredth have, in other words, the eigenvalue, the Fibonacci numbers are growing by about that factor." + }, + { + "text": "You see that we've got precise information about the, about the Fibonacci numbers out of the eigenvalue." + }, + { + "text": "OK. And again, why is that true?" + }, + { + "text": "Let me go over to this board and show what I'm doing here." + }, + { + "text": "The, the original eigen, the original initial value is some combination of eigenvectors, and then when we start multiple, when we start going out the theory of Fibonacci numbers, when we start multiplying by a hundred times, it's this lambda one to the hundredth, this term is, is the one that's taken over." + }, + { + "text": "It's, I mean, that's big, like, one point six to the hundredth power." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk22.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..c13a1fc9867173c3067e46c469cfff27b9b45289 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "The second term is practically nothing, right?" + }, + { + "text": "The point six, or minus point six to the hundredth power, is an extremely small, extremely small number." + }, + { + "text": "So this is, this, this, there are only two terms, because we're two by two." + }, + { + "text": "This number is, this piece of it is there, but it's, it's disappearing." + }, + { + "text": "Where this piece is there and it's growing and controlling everything." + }, + { + "text": "So, so really the, we're doing, like, problems that are evolving." + }, + { + "text": "We're doing dynamics." + }, + { + "text": "Instead of Ax equal b, that's a static problem." + }, + { + "text": "We're now, we're doing dynamics." + }, + { + "text": "A, a squared, a cubed, things are evolving in time, and the eigenvalues are the crucial, numbers." + }, + { + "text": "OK." + }, + { + "text": "I guess to complete this, I better write down the eigenvectors." + }, + { + "text": "So we should complete the, the whole process by finding the eigenvectors." + }, + { + "text": "OK. Well, I have to, up in the corner, then I have to look at A minus lambda I." + }, + { + "text": "So A minus lambda I is this one minus lambda, one, one, and minus lambda." + }, + { + "text": "And now, can we spot an eigenvector out of that?" + }, + { + "text": "That's, for these two lambdas, this matrix is singular." + }, + { + "text": "I guess the eigenvector, two by two ought to be easy." + }, + { + "text": "So if I know that this matrix is singular, then it seems to me the eigenvector has to be lambda and one, because that multiplication will give me the zero." + }, + { + "text": "And this multiplication gives me, better give me also zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk23.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..df816eb800ce767b1475c279a24ad976bb45a785 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Do you see why it does?" + }, + { + "text": "This is the minus lambda squared plus lambda plus one." + }, + { + "text": "It's the thing that's zero, because these lambdas are special." + }, + { + "text": "There's the eigenvector." + }, + { + "text": "X1 is lambda one, one, and x2 is lambda two, one." + }, + { + "text": "I did that as a little trick that was available in the two by two case." + }, + { + "text": "So now I finally have to, oh, I have to take the initial, u0." + }, + { + "text": "So to complete this example entirely, I have to say, OK, what was u0?" + }, + { + "text": "u0 was f1 f0." + }, + { + "text": "So u0, the starting vector, is f1 f0, and those were one and zero." + }, + { + "text": "So I have to use that vector, so I have to look for, from multiple of the first eigenvector and the second, to produce u0, the one zero vector." + }, + { + "text": "This is what will find c1 and c2, and then I'm done." + }, + { + "text": "So let me, instead of in the last five seconds grinding out a formula, let me repeat the idea." + }, + { + "text": "That really, it's the idea that's central." + }, + { + "text": "When things are evolving in time, let me come back to this board, because the ideas are here." + }, + { + "text": "When things are evolving in time by a first-order system, starting from an original u0, the key is, find the eigenvalues and eigenvectors of A." + }, + { + "text": "That will tell, those eigenvectors, the eigenvalues will already tell you what's happening." + }, + { + "text": "Is the solution blowing up?" + }, + { + "text": "Is it going to zero?" + }, + { + "text": "What's it doing?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk24.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..40301cb90760e2172baa94d536cbc13288d4c31f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk24.json @@ -0,0 +1,20 @@ +[ + { + "text": "And then, to find out exactly a formula, you have to take your u0 and write it as a combination of eigenvectors and then follow each eigenvector separately." + }, + { + "text": "And that's really what this formula, the formula for, that's what the formula for A to the k is doing." + }, + { + "text": "So remember that formula for A to the k is S, lambda to the k S inverse." + }, + { + "text": "OK. That's, that's difference equations, and you just have to, so the homework will give some examples different from Fibonacci to follow through." + }, + { + "text": "And next time will be differential equations." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk3.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..9bf1bb852baadc1da7837e14180c0c2951a30882 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I mentioned at the end of last time, and I'll say again, that there's a small number of matrices for, that don't have n independent eigenvectors." + }, + { + "text": "So I've got to discuss that, that technical point." + }, + { + "text": "But the great, the most matrices that we see have n, n independent eigenvectors and we can diagonalize." + }, + { + "text": "This is diagonalization." + }, + { + "text": "I could also write it, and I often will, the other way round." + }, + { + "text": "If I multiply on the right by s inverse, if I took this equation at the top and multiplied on the right by s inverse, I could, I would have A left here." + }, + { + "text": "Now s inverse is coming from the right." + }, + { + "text": "So can you keep those two straight?" + }, + { + "text": "A multiplies its eigenvectors." + }, + { + "text": "That's how I keep them straight." + }, + { + "text": "So A multiplies s. A multiplies s. And then this s inverse makes the whole thing diagonal." + }, + { + "text": "And this is another way of saying the same thing, putting the s's on the other side of the equation, A is s lambda s inverse." + }, + { + "text": "So that's the, that's the new factorization." + }, + { + "text": "That's the replacement for L U from elimination or Q R from Gram-Schmidt." + }, + { + "text": "And notice that the matrix, so it's, it's a matrix times a diagonal matrix times the inverse of the first one." + }, + { + "text": "It's, that's the combination that we'll see throughout this chapter." + }, + { + "text": "This, this, combination with an s and an s inverse." + }, + { + "text": "OK. Can I just begin to use that?" + }, + { + "text": "For example, what about A squared?" + }, + { + "text": "What are the eigenvalues and eigenvectors of A squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk4.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c687b6948acad76de8781cb82d3eb069c9da514e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's a straightforward question with a, with a absolutely clean answer." + }, + { + "text": "So let me, let me consider A squared." + }, + { + "text": "So I look, I start with Ax equal lambda x." + }, + { + "text": "And I'm headed for A squared." + }, + { + "text": "So let me multiply both sides by A." + }, + { + "text": "That's one way to get A squared on the left." + }, + { + "text": "So if, I should write these ifs in here." + }, + { + "text": "If Ax equals lambda x, then I multiply by A." + }, + { + "text": "So I get A squared x equals, well, I'm multiplying by A, so that's lambda Ax." + }, + { + "text": "That lambda was a number, so I just put it on the left." + }, + { + "text": "And what do I, tell me how to make that look better." + }, + { + "text": "What have I got here?" + }, + { + "text": "For, if, if A has the eigenvalue lambda and eigenvector x, what's up with A squared?" + }, + { + "text": "A squared x, I just multiply by A, but now for Ax, I'm going to substitute lambda x, so I've got lambda squared x." + }, + { + "text": "So from that simple calculation, I, my conclusion is that the eigenvalues of A squared are lambda squared." + }, + { + "text": "And the eigenvectors, I always think about both of those." + }, + { + "text": "What can I say about the eigenvalues?" + }, + { + "text": "They're squared." + }, + { + "text": "What can I say about the eigenvectors?" + }, + { + "text": "They're the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk5.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5bf15e20707c156c8ae71c9c7acea41a9d9d8e46 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same x as in, as for A." + }, + { + "text": "Now, let me see that also from this formula." + }, + { + "text": "How can I see what A squared is looking like from this formula?" + }, + { + "text": "So let me, that, that was one way to do it." + }, + { + "text": "Let me do it by just taking A squared from that." + }, + { + "text": "A squared is S lambda S inverse, that's A, times S lambda S inverse, that's A, which is?" + }, + { + "text": "This is the beauty of eigenvalues, eigenvectors, having that S inverse and S is the identity, so I've got S lambda squared S inverse." + }, + { + "text": "Yes." + }, + { + "text": "You see what that's telling me?" + }, + { + "text": "It's, it's telling me the same thing that I just learned here, but in the, in, in a matrix form." + }, + { + "text": "It's telling me that the S is the same, the eigenvectors are the same, but the eigenvalues are squared, because this is, what's lambda squared, that's still diagonal, it's got little lambda one squared, lambda two squared, down to lambda n squared, on that diagonal, those are the eigenvalues, as we just learned, of A squared." + }, + { + "text": "OK." + }, + { + "text": "So, somehow those eigenvalues and eigenvectors are really giving you a way to, to, to, to see what's going on inside a matrix." + }, + { + "text": "Now, of course, I can continue that for, to the k-th power." + }, + { + "text": "A to the k-th power." + }, + { + "text": "If I multiply, if I have k of these together, do you see how S inverse S will keep cancelling?" + }, + { + "text": "In the, in the inside, I'll have the S outside, at the far left, and lambda will be in there k times and S inverse." + }, + { + "text": "So what's that telling me?" + }, + { + "text": "That's telling me that the eigenvalues of A, of A to the k-th power are the k-th powers." + }, + { + "text": "The eigenvalues of A cubed are the cubes of the eigenvalues of A, and the eigenvectors are the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk6.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..c18dddbe798022f7e68278ac002a3f5fe6ed249e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same." + }, + { + "text": "OK." + }, + { + "text": "In other words, eigenvalues and eigenvectors give a great way to understand the powers of a matrix." + }, + { + "text": "If I take the square of a matrix or the hundredth power of a matrix, the pivots are all over the place." + }, + { + "text": "L U, if I multiply L U times L U times L U times L U a hundred times, I've got a hundred L U's." + }, + { + "text": "I can't do anything with them." + }, + { + "text": "But when I multiply S lambda S inverse by itself, when I look at the eigenvector picture a hundred times, I get a hundred or ninety-nine of these guys cancelling out inside, and I get A to the hundredth is S lambda to the hundredth S inverse." + }, + { + "text": "I mean, eigenvalues tell you about powers of a matrix in a way that we had no, no way to approach previously." + }, + { + "text": "For example, when does, when do the powers of a matrix go to zero?" + }, + { + "text": "I would call that matrix stable, maybe." + }, + { + "text": "So, so, so I could write down a, a theorem." + }, + { + "text": "I'll, I'll write it as a theorem, just to use that word to emphasize that here I'm getting this great fact from this eigenvalue picture." + }, + { + "text": "OK. A to the k approaches zero as k goes, as k gets bigger." + }, + { + "text": "If what?" + }, + { + "text": "What's the, how can I tell for a matrix A if its powers go to zero?" + }, + { + "text": "What, what's somewhere inside that matrix is that information." + }, + { + "text": "That information is not present in the pivots." + }, + { + "text": "It's present in the eigenvalues." + }, + { + "text": "What do I need for the, to know that if I take higher and higher powers of A that this matrix gets smaller and smaller?" + }, + { + "text": "Well, S and S inverse are not moving." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk7.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b84a5c854a5542758e8a0107e1ff043205fe3bdb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's this guy that has to get small, and that's easy to, easy to understand." + }, + { + "text": "The requirement is all eigenvalues, so what is the requirement?" + }, + { + "text": "The eigenvalues have to be less than one." + }, + { + "text": "Now, I have to write that absolute value, because those eigenvalues could be negative, they could be complex numbers." + }, + { + "text": "So I'm taking the absolute value if all of those are below one." + }, + { + "text": "That's, in fact, we practically see why." + }, + { + "text": "Let me just say that I, that I, I'm operating on one assumption here, and I got to keep remembering that that assumption is still present." + }, + { + "text": "That assumption was that I had a full set of, of n independent eigenvectors." + }, + { + "text": "If I don't have that, then I, I, then this approach is not working." + }, + { + "text": "So, so again, a pure eigenvalue approach, eigenvector approach, needs n independent eigenvectors." + }, + { + "text": "If we don't have n independent eigenvectors, we can't diagonalize the matrix." + }, + { + "text": "We can't get to a diagonal matrix." + }, + { + "text": "This, this, this diagonalization is only possible if S inverse makes sense." + }, + { + "text": "OK. Can I, can I follow up on that point now?" + }, + { + "text": "So, so you see why, what we get and, and why we want it, because we get information about the powers of a matrix just immediately from the eigenvalues." + }, + { + "text": "OK, now let me follow up on this, business of which matrices are diagonalizable." + }, + { + "text": "Sorry about that long word." + }, + { + "text": "So a matrix is, is sure to, so here's, here's the main point." + }, + { + "text": "A is sure to be, to have n independent eigenvectors and, and B, now here comes that word, diagonalizable, if, if, so we, we, we might as well get the, the nice case out in the open." + }, + { + "text": "The nice case is when, if all the lambdas are different." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk8.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f06dcec8ffa0ee1bf19440e4ab2194db33ab353b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means, that means no repeated eigenvalues." + }, + { + "text": "OK. That's the nice case." + }, + { + "text": "If, if my matrix and most matrix, if I do a random matrix in MATLAB and compute its eigenvalues, so if I computed, if I took I of rand of ten ten, gave, gave that MATLAB command, the, we'd get a random ten by ten matrix, we would get a list of its ten eigenvalues and they would be different." + }, + { + "text": "They would be distinct, is the best word." + }, + { + "text": "I would have a random matrix will have ten distinct, a ten by ten matrix will have ten distinct eigenvalues, and if it does, the eigenvectors are automatically independent." + }, + { + "text": "So that's a nice fact." + }, + { + "text": "I can, I'll refer you to the text for the proof." + }, + { + "text": "That, that A is sure to have n independent eigenvectors if the eigenvalues are different." + }, + { + "text": "If, if all the, if all eigenvalues are different." + }, + { + "text": "It's just, if some lambdas are repeated, then I have to look more closely." + }, + { + "text": "If an eigenvalue is repeated, I have to look, I have to count, I have to check." + }, + { + "text": "Has it got, say it's repeated three times." + }, + { + "text": "So what's a possibility for, so, so here's, here's the repeated possibility." + }, + { + "text": "And, and let me emphasize the conclusion." + }, + { + "text": "That if I have repeated eigenvalues, I may or may not, I may or may not have, have n independent eigenvectors." + }, + { + "text": "I might." + }, + { + "text": "I, I, you know, this isn't a completely negative case." + }, + { + "text": "The identity matrix." + }, + { + "text": "Well, suppose I take the ten by ten identity matrix." + }, + { + "text": "What are the eigenvalues of that matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk9.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..87d2a2ae5773036cf11800e2f1962908986a0dad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_25_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So just, just take the easiest matrix, the identity." + }, + { + "text": "If I look for its eigenvalues, they're all ones." + }, + { + "text": "So that eigenvalue one is repeated ten times." + }, + { + "text": "But there's no shortage of eigenvectors for the identity matrix." + }, + { + "text": "In fact, every vector is an eigenvector." + }, + { + "text": "So I can take ten independent vectors." + }, + { + "text": "Oh, well, what happens to everything if, if, if A is the identity matrix, let's just think that one through in our head." + }, + { + "text": "If A is the identity matrix, then it's got plenty of eigenvectors." + }, + { + "text": "I choose ten independent vectors, they're the columns of S, and, and what do I get from S inverse A S?" + }, + { + "text": "I get I again, right?" + }, + { + "text": "If A is the identity, and of course, that's the correct lambda." + }, + { + "text": "The, the matrix was already diagonal." + }, + { + "text": "So if the matrix is already diagonal, then the, the lambda is the same as the matrix." + }, + { + "text": "A diagonal matrix has got its eigenvalues sitting right there in front of you." + }, + { + "text": "Now if it's triangular, the eigenvalues are still sitting there, but so let's, let's take a case where, it's triangular." + }, + { + "text": "Suppose A is like, two, one, two, zero." + }, + { + "text": "So there's a case that's going to be trouble." + }, + { + "text": "There's a case that's going to be trouble." + }, + { + "text": "First of all, what are the eigen- I mean, we just, like now you, if we start with a matrix, the first thing we do practically without thinking is compute the eigenvalues and eigenvectors." + }, + { + "text": "OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk0.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6898d4fe66019ef6b40d0472ea94a968e7bbde9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, shall we start?" + }, + { + "text": "This is the second lecture on eigenvalues." + }, + { + "text": "So the first lecture was set -- reached the key equation, Ax equal lambda x. x is the eigenvector and lambda is the eigenvalue." + }, + { + "text": "Now, to use that." + }, + { + "text": "And the good way to, after we've found, so job one is to find the eigenvalues and find the eigenvectors." + }, + { + "text": "Now after we found them, what do we do with them?" + }, + { + "text": "Well, the good way to see that is diagonalize the matrix." + }, + { + "text": "So the matrix is A, and I want to show, first of all, this is like the basic fact." + }, + { + "text": "This, this formula." + }, + { + "text": "That's, that's the key to today's lecture." + }, + { + "text": "This matrix A, I put its eigenvectors in the columns of a matrix S. So S will be the eigenvector matrix, and I want to look at this magic combination S inverse A S. So can I show you how that, how that, what happens there?" + }, + { + "text": "And notice, notice, there's an S inverse." + }, + { + "text": "We have to be able to invert this eigenvector matrix S. So for that we need n independent eigenvectors." + }, + { + "text": "So that's the, that's the case." + }, + { + "text": "OK." + }, + { + "text": "So suppose we have n linearly independent eigenvectors of A." + }, + { + "text": "Put them in the columns of this matrix S. So I'm naturally going to call that the eigenvector matrix, because it's got the eigenvectors in its columns." + }, + { + "text": "And all I want to do is show you what happens when you multiply A times S. So A times S. So this is A times the matrix with the first eigenvector in its first column, the second eigenvector in its second column, the nth eigenvector in its nth column." + }, + { + "text": "And how am I going to do this matrix multiplication?" + }, + { + "text": "Well, certainly I'll do it a column at a time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk1.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..fbe078217bb68baea8e0605a5d04be568c49efbf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I get?" + }, + { + "text": "A times the first column gives me the first column of the answer, but what is it?" + }, + { + "text": "That's an eigenvector." + }, + { + "text": "A times x1 is equal to the lambda times the x1." + }, + { + "text": "And that lambda's we'll call lambda one, of course." + }, + { + "text": "So that's the first column, A x1 is the same as lambda one x1." + }, + { + "text": "A x2 is lambda two x2, so on, along to, in the nth column, we now have lambda n xn." + }, + { + "text": "Looking good, but the next step is even better." + }, + { + "text": "So for the next step, I want to separate out those eigenvalues, those multiplying numbers, from the x's." + }, + { + "text": "So then I'll have just what I want." + }, + { + "text": "OK, so how, how am I going to separate out?" + }, + { + "text": "So that, that number lambda one is multiplying the first column." + }, + { + "text": "So if I want to factor it out of the first column, I better put, here is going to be x1, and that's going to multiply this matrix lambda one in the first entry in all zeros." + }, + { + "text": "You see that that, that's going to come out right for the first column?" + }, + { + "text": "Because we remember how, how we're going back to that original punchline, that if I want a number to multiply x1, then I can do it by putting x1 in that column, in the first column, and putting that number there." + }, + { + "text": "What am I going to have here?" + }, + { + "text": "I'm going to have lambda one, I'm going to have x1, x2, xn." + }, + { + "text": "These are going to be my columns again." + }, + { + "text": "I'm getting s back again." + }, + { + "text": "I'm getting s back again, but now what's it multiplied by?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk10.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c58a42edbe9567233ca7f57643a0b7d43ae6761f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what are the eigenvalues?" + }, + { + "text": "You can tell me right away what they are." + }, + { + "text": "They're two and two, right." + }, + { + "text": "It's a triangular matrix, so when I do this determinant, shall I do this determinant of A minus lambda I?" + }, + { + "text": "I'll get this two minus lambda, one, zero, two minus lambda, right?" + }, + { + "text": "I take that determinant, so I make those into vertical bars to mean determinant, and what's the determinant?" + }, + { + "text": "Two minus lambda squared." + }, + { + "text": "What are the roots?" + }, + { + "text": "Lambda equal two twice." + }, + { + "text": "So the eigenvalues are lambda equals two and two." + }, + { + "text": "OK, fine." + }, + { + "text": "Now the next step, find the eigenvectors." + }, + { + "text": "So I look for eigenvectors and what do I find for this guy?" + }, + { + "text": "Eigenvectors for this guy, when I subtract two minus the identity, so A minus two I has zeros here, and I'm looking for the null space." + }, + { + "text": "What's, what are the eigenvectors?" + }, + { + "text": "They're the, they're, they're the null space of A minus lambda I." + }, + { + "text": "The null space is only one dimension." + }, + { + "text": "This is a case where I don't have enough eigenvectors." + }, + { + "text": "My algebraic multiplicity is two." + }, + { + "text": "I, I would say when I see, when I count how often the eigenvalue is repeated, that's the algebraic multiplicity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk11.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..779c2cf904d904b761080db2671aac46394ad02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the multiplicity." + }, + { + "text": "How many times is it the root of the polynomial?" + }, + { + "text": "My polynomial is two minus lambda squared." + }, + { + "text": "It's a double root." + }, + { + "text": "So my algebraic multiplicity is two." + }, + { + "text": "But the geometric multiplicity, which looks for vectors, looks for eigenvectors and which means the null space of this thing." + }, + { + "text": "And the only eigenvector is one zero." + }, + { + "text": "That's in the null space." + }, + { + "text": "Zero one is not in the null space." + }, + { + "text": "The null space is only one dimensional." + }, + { + "text": "So there's a matrix, my, this A or the original A, that are not diagonalizable." + }, + { + "text": "I can't, I can't find two independent eigenvectors, there's only one." + }, + { + "text": "OK." + }, + { + "text": "So that's the case that I'm, that's a case that I, I'm not really handling." + }, + { + "text": "For example, when I wrote down up here that the powers went to zero if the eigenvalues were below one, I didn't really handle that case of repeated eigenvalues because my reasoning was based on this formula." + }, + { + "text": "And this formula is based on n independent eigenvectors." + }, + { + "text": "OK." + }, + { + "text": "So just to say that." + }, + { + "text": "There are some matrices that we don't cover through diagonalization, but the great majority we do." + }, + { + "text": "OK. And we're always OK if we have different distinct eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk12.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..77d090704cc298475d94416b7ecb88a2a015a913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. That's the, like, the typical case." + }, + { + "text": "Because for each eigenvalue there's at least one eigenvector, the algebraic multiplicity here is one for every eigenvalue, and the geometric multiplicity is one." + }, + { + "text": "There's one eigenvector and they are independent." + }, + { + "text": "OK. OK. Now let me come back to the important case when we're OK." + }, + { + "text": "The important case when we are diagonalizing." + }, + { + "text": "Let me look at, so let me solve this equation." + }, + { + "text": "The equation will be each, I start with some, start with a given vector u0." + }, + { + "text": "And then my equation is that every step I multiply what I have by a." + }, + { + "text": "That equation ought to be simple to handle." + }, + { + "text": "OK. And I'd like to be able to solve it." + }, + { + "text": "How would I find, if I start with a vector u0, and I multiply by a a hundred times, what have I got?" + }, + { + "text": "Well, I can certainly write down a formula for the answer." + }, + { + "text": "So what, what, so u1 is a u0." + }, + { + "text": "And u2 is, what's u2 then?" + }, + { + "text": "U2 I multiply it, u2 I get from u1 by another, multiplying by a, so I've got a twice." + }, + { + "text": "And my formula is uk, after k steps, I've multiplied by a k times the original u0." + }, + { + "text": "You see what I'm doing?" + }, + { + "text": "The next section is going to solve systems of differential equations." + }, + { + "text": "I'm going to have derivatives." + }, + { + "text": "This, this section is the nice one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk13.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..ba8214d8c636e4757a266d6617801174bc939d80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "It solves difference equations." + }, + { + "text": "I would call that a difference equation." + }, + { + "text": "It's conne- a first order." + }, + { + "text": "I would call that a first order system, because it connects only, it only goes up one level." + }, + { + "text": "And it's a system because these are vectors and that's a matrix." + }, + { + "text": "And the solution is just that." + }, + { + "text": "OK." + }, + { + "text": "But, that's a nice formula." + }, + { + "text": "That's the, like, the most compact formula I could ever get." + }, + { + "text": "U one hundred would be a to the one hundredth u0." + }, + { + "text": "But how would I actually find u one hundred?" + }, + { + "text": "How would I find, how would I discover what u one hundred is?" + }, + { + "text": "Let me, let me show you how." + }, + { + "text": "Here, here's the idea." + }, + { + "text": "If, so, to solve, to really solve, shall I say, to really solve." + }, + { + "text": "To really solve it, I would take this initial vector, u0, and I would write it as a combination of eigenvectors." + }, + { + "text": "To really solve, write, write u0 as a combination, say, certain amount of the first eigenvector plus a certain amount of the second eigenvector plus a certain amount of the last eigenvector." + }, + { + "text": "Now multiply by a." + }, + { + "text": "You want to, you got to see the magic of eigenvectors work." + }, + { + "text": "Multiply by a." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk14.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7843b2bf0cac762d1c12452cf36500ea4ad13370 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a u0 is what?" + }, + { + "text": "So a times that." + }, + { + "text": "A times, so what's, I can separate it out into n separate pieces and that's the whole point." + }, + { + "text": "That each of those pieces is going in its own merry way." + }, + { + "text": "Each of those pieces is an eigenvector, and when I multiply by a, what does this piece become?" + }, + { + "text": "So that's some amount of the first, let's suppose the eigenvectors are normalized to be unit vectors." + }, + { + "text": "So that says what the eigenvector is." + }, + { + "text": "It's, and I need some multiple of it to produce u0." + }, + { + "text": "OK. Now when I multiply by a, what do I get?" + }, + { + "text": "I get c1, which is just a factor, times a x1, but a x1 is lambda one x1." + }, + { + "text": "When I multiply this by a, I get c2 lambda two x2." + }, + { + "text": "And here I get cn lambda n xn." + }, + { + "text": "And suppose I multiply by a to the hundredth power now." + }, + { + "text": "Can we, can we, having done it, multiplied by a, let's multiply by a to the hundredth." + }, + { + "text": "What happens to this first term when I multiply by a to the one hundredth?" + }, + { + "text": "It's got that factor lambda to the hundredth." + }, + { + "text": "That's the key." + }, + { + "text": "That, that's what I mean by going its own merry way." + }, + { + "text": "It, it is pure eigenvector, it's exactly in a direction where multiplication by a just brings in a scalar factor lambda one." + }, + { + "text": "So a hundred times brings in this a hundred times." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk15.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7ee3348735378aa4049d33ec2a197d0ceb0c447c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Hundred times lambda two, hundred times lambda n. Actually, we're, what are we seeing here?" + }, + { + "text": "We're seeing, this same, lambda, capital lambda to the hundredth, as in the, as in the diagonalization, and we're seeing the S matrix, the matrix S of eigenvectors." + }, + { + "text": "That's what this has got to, this has got to amount to, a lambda to the hundredth power times an S times this vector C that's telling us how much of each one is in the original thing." + }, + { + "text": "So if, if I had to really find the hundredth power, I would take u0, I would expand it as a combination of eigenvectors, this is really S, the eigenvector matrix times C, the, the coefficient vector." + }, + { + "text": "And then I would immediately, then, by inserting these hundredth powers of eigenvalues, I'd have the answer." + }, + { + "text": "So the, the, huh, there must be, well, let's see." + }, + { + "text": "OK." + }, + { + "text": "It's, so, yeah." + }, + { + "text": "So if u100 is a to the hundredth times u0, and u0 is Sc, then you see this formula is just this formula, which is the way I would actually get hold of this, of this u100, which is, let me put it here, u100." + }, + { + "text": "The way I would actually get hold of that, see what, what the solution is after a hundred steps, would be expand the initial vector into eigenvectors and, and let each eigenvector go its own way, multiplying by a hundred at, by lambda at every step, and therefore by lambda to the hundredth power after a hundredth step." + }, + { + "text": "Can I do an example?" + }, + { + "text": "So that's, that's the, the formulas." + }, + { + "text": "Now let me take an example." + }, + { + "text": "I'll use the Fibonacci sequence as an example." + }, + { + "text": "So, so Fibonacci example." + }, + { + "text": "You remember the Fibonacci numbers?" + }, + { + "text": "If we start with one and one as F0, oh, I think I start with zero, maybe." + }, + { + "text": "Let zero and one be the first ones." + }, + { + "text": "So there's F0 and F1, the first two Fibonacci numbers." + }, + { + "text": "Then what's the rule for Fibonacci numbers?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk16.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..79c65e32781f7f304b504a6c390247abb9d26ac8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "They're the sum." + }, + { + "text": "The next one is the sum of those, so it's one." + }, + { + "text": "The next one is the sum of those, so it's two." + }, + { + "text": "The next one is the sum of those, so it's three." + }, + { + "text": "Well, it looks like one, two, three, four, five, but somehow it's not going to do that way." + }, + { + "text": "The next one is five, right." + }, + { + "text": "Two and three makes five." + }, + { + "text": "The next one is eight." + }, + { + "text": "The next one is thirteen." + }, + { + "text": "And the one hundredth Fibonacci number is what?" + }, + { + "text": "That's my question." + }, + { + "text": "How could I get a formula for the hundredth number and for example how could I answer the question how fast are they growing?" + }, + { + "text": "How fast are those Fibonacci numbers growing?" + }, + { + "text": "They're certainly growing." + }, + { + "text": "It's not a stable case, whatever the eigenvalues of whatever matrix it is, they're not smaller than one." + }, + { + "text": "These numbers are growing." + }, + { + "text": "But how fast are they growing?" + }, + { + "text": "The answer is lies in the eigenvalue." + }, + { + "text": "So I've got to find the matrix, so let me write down the Fibonacci rule, F k plus two is F k plus one plus F k, right?" + }, + { + "text": "Now that's not in my -- I want to write that as U k plus one and A U k. But right now what I've got is a single equation, not a system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk17.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b3aaa9dcee3cf27c112015659bb5a0b51a983ce1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's second order." + }, + { + "text": "It's like having a second order differential equation with second derivatives." + }, + { + "text": "I want to get first derivatives." + }, + { + "text": "Here I want to get first difference." + }, + { + "text": "So the way to do it is to introduce U k will be a vector." + }, + { + "text": "See, a small trick." + }, + { + "text": "Let U k be a vector, F k plus one and F k. So I'm going to get a two by two system, first order, instead of a one, instead of a scalar system, second order, by a simple trick." + }, + { + "text": "I'm just going to add in an equation F k plus one equals F k plus one." + }, + { + "text": "That will be my second equation." + }, + { + "text": "Then this is my system, this is my unknown, and what's my one-step equation?" + }, + { + "text": "So now U k plus one." + }, + { + "text": "That's so U k plus one is the left side, and what have I got here on the right side?" + }, + { + "text": "I've got some matrix multiplying U k. Can you see that all right?" + }, + { + "text": "If you can see it, then you can tell me what the matrix is." + }, + { + "text": "You see that I'm taking my system here, I artificially made it into a system." + }, + { + "text": "I artificially made the unknown into a vector, and now I'm ready to look at and see what the matrix is." + }, + { + "text": "So do you see the left side, U k plus one is F k plus two F k plus one, that's just what I want." + }, + { + "text": "On the right side, this, remember, this U k here, let me for the moment put it as F k plus one F k. So what's the matrix?" + }, + { + "text": "Well, that has a one and a one, and that has a one and a zero." + }, + { + "text": "There's the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk18.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..6c1b68c2cb2fde3f5dea82f3100d4da31fcce70a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "You see that that gives me the right-hand side." + }, + { + "text": "So there's the matrix A, and this is our friend U k. So we've got, so that simple trick changed the second order scalar problem to a first order system, two, with two unknowns." + }, + { + "text": "With a matrix and now what do I do?" + }, + { + "text": "Well, before I even think, I find its eigenvalues and eigenvectors." + }, + { + "text": "So what are the eigenvalues and eigenvectors of that matrix?" + }, + { + "text": "Let's see." + }, + { + "text": "I was, first let me just, like, think for a minute." + }, + { + "text": "It's two by two, so this shouldn't be impossible to do." + }, + { + "text": "Let's do it." + }, + { + "text": "OK." + }, + { + "text": "So my matrix again is one one one zero." + }, + { + "text": "It's symmetric, by the way." + }, + { + "text": "So what I will eventually know about symmetric matrices is that the eigenvalues will come out real, I won't get any complex numbers here, and the eigenvectors, once I get those, actually will be orthogonal." + }, + { + "text": "But two by two, I'm more interested in what the actual numbers are." + }, + { + "text": "What do I know about the two numbers?" + }, + { + "text": "Well, should, do you want me to find this determinant of A minus lambda I?" + }, + { + "text": "Sure." + }, + { + "text": "So it's the determinant of one minus lambda one one zero, right?" + }, + { + "text": "Minus lambda, yes, got it." + }, + { + "text": "OK. OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk19.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..a73b23e3d56b889ff49ea7f55a784fac33e13c3d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "There'll be two eigenvalues." + }, + { + "text": "Well, tell me again what I know about the two eigenvalues before I go any further." + }, + { + "text": "Tell me something about these two eigenvalues, what do they add up to?" + }, + { + "text": "Lambda one plus lambda two is the same as the trace down the diagonal of the matrix, one and zero is one." + }, + { + "text": "So lambda one plus lambda two should come out to be one, and lambda one times lambda two should come out to be the determinant, which is minus one." + }, + { + "text": "So I'm expecting the eigenvalues to add to one and to multiply to minus one." + }, + { + "text": "But let's just see it happen here." + }, + { + "text": "If I multiply this out, I get that times that'll be a lambda squared minus lambda minus one." + }, + { + "text": "Good." + }, + { + "text": "Lambda squared minus lambda minus one." + }, + { + "text": "Actually, you see the, compare that with the original equation that I started with." + }, + { + "text": "Fk plus two minus Fk plus one minus Fk is zero." + }, + { + "text": "The recurrent, the recursion that the Fibonacci number satisfy is somehow showing up directly here for the eigenvalues when we set that to zero." + }, + { + "text": "OK. Let's solve." + }, + { + "text": "Well, I would like to be able to factor that, that quadratic, but I'm better off to use the quadratic formula." + }, + { + "text": "Lambda is, let's see, minus b is one, plus or minus the square root of b squared, which is one, minus four, times that, times that, which is plus four, over two." + }, + { + "text": "So that's the square root of five." + }, + { + "text": "So the eigenvalues are lambda one is one half of one plus square root of five, and lambda two is one half of one minus square root of five." + }, + { + "text": "And sure enough, they, those add up to one, and they multiply to give minus one." + }, + { + "text": "OK. Those are the two eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk2.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..43cfb012fc04a89fc7dab94c23bfb0f50ade3782 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "On the right, it's multiplied by, if I want, if I want lambda n xn in the last column, how do I do it?" + }, + { + "text": "Well, the last column here will be, I'll, I'll take the last column, use these coefficients, put the lambda n down there, and it will multiply that nth column and give me lambda n xn." + }, + { + "text": "There, there you see matrix multiplication just working for us." + }, + { + "text": "So I started with A s. I wrote down what it meant." + }, + { + "text": "A times each eigenvector." + }, + { + "text": "That gave me lambda times the eigenvector." + }, + { + "text": "And then when I peeled off the lambdas, they were on the right-hand side, so I've got s, my matrix back again, and this matrix, this diagonal matrix, the eigenvalue matrix, and I call it capital lambda, using capital letters for matrices, and lambda to prompt me that it's, that it's eigenvalues that are in there." + }, + { + "text": "So you see that the eigenvalues are just sitting down that diagonal?" + }, + { + "text": "If I had a column x2 here, I would want the lambda two in the two two position, in the diagonal position, to multiply that x2 and give me the lambda two x2." + }, + { + "text": "That's my formula." + }, + { + "text": "A s is s lambda." + }, + { + "text": "OK. That's, that's the, you see, it's just a calculation." + }, + { + "text": "Now, I, I mentioned, and I have to mention again, this business about n independent eigenvectors." + }, + { + "text": "As it stands, this is all fine whether, I mean, I could be repeating the same eigenvector, but I, I'm no interested in that." + }, + { + "text": "I want to be able to invert s, and that's where this comes in." + }, + { + "text": "This n independent eigenvectors business comes in to tell me that that matrix is invertible." + }, + { + "text": "So let me, on the next board, write down what I've got." + }, + { + "text": "A s equals s lambda." + }, + { + "text": "And now I'm, I can multiply on the left by s inverse." + }, + { + "text": "So this is really, I can do that provided s is invertible, provided my assumption of n independent eigenvectors is satisfied." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk20.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ad5a59fa5db44ce73ff5f88190423e0404fb3d39 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "How, how, what are those numbers approximately?" + }, + { + "text": "Square root of five, well, it's more than two, but less than three." + }, + { + "text": "It, it'd be nice to know these numbers." + }, + { + "text": "I think, I think that that, so that number comes out bigger than one, right?" + }, + { + "text": "Yeah, that's right." + }, + { + "text": "This number comes out bigger than one." + }, + { + "text": "It's about one point six one eight or something." + }, + { + "text": "Not exactly." + }, + { + "text": "It's supposed to be one point six." + }, + { + "text": "Just, like, I think so." + }, + { + "text": "Then what's lambda two?" + }, + { + "text": "Is, is lambda two positive or negative?" + }, + { + "text": "Negative, right?" + }, + { + "text": "Because I'm, it's obviously negative, and I knew that the, so it's minus, and they add up to one, so minus point six one eight, I guess." + }, + { + "text": "OK. And some order." + }, + { + "text": "Those are the two eigenvalues." + }, + { + "text": "One eigenvalue bigger than one, one eigenvalue smaller than one." + }, + { + "text": "Actually, that's a great situation to be in." + }, + { + "text": "Of course, the eigenvalues are different, so there's no doubt whatever, is this matrix diagonalizable?" + }, + { + "text": "Is this matrix diagonalizable, that original matrix A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk21.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..4a034475591d371995b379b5f98783a2cfb25870 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Sure." + }, + { + "text": "We've got two distinct eigenvalues and we can find the eigenvectors in a moment." + }, + { + "text": "But they'll be independent, will be diagonalizable, and now you can already answer my very first question." + }, + { + "text": "How fast are those Fibonacci numbers increasing?" + }, + { + "text": "How, those, they're increasing, right?" + }, + { + "text": "They're not doubling at every step." + }, + { + "text": "Let's look again at these numbers." + }, + { + "text": "Five eight thirteen, it's not obvious." + }, + { + "text": "The next one would be twenty one thirty four." + }, + { + "text": "So to get some idea of what F one hundred is, can you give me any, I mean the crucial number of, so it, these, it's approximately, what's controlling the growth of these Fibonacci numbers?" + }, + { + "text": "It's the eigenvalues." + }, + { + "text": "And which eigenvalues controlling that growth?" + }, + { + "text": "The big ones." + }, + { + "text": "So F one hundred will it be approximately some constant, c one, I guess, times this lambda one, this one plus square root of five over two, to the hundredth power." + }, + { + "text": "And the two hundredth have, in other words, the eigenvalue, the Fibonacci numbers are growing by about that factor." + }, + { + "text": "You see that we've got precise information about the, about the Fibonacci numbers out of the eigenvalue." + }, + { + "text": "OK. And again, why is that true?" + }, + { + "text": "Let me go over to this board and show what I'm doing here." + }, + { + "text": "The, the original eigen, the original initial value is some combination of eigenvectors, and then when we start multiple, when we start going out the theory of Fibonacci numbers, when we start multiplying by a hundred times, it's this lambda one to the hundredth, this term is, is the one that's taken over." + }, + { + "text": "It's, I mean, that's big, like, one point six to the hundredth power." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk22.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..c13a1fc9867173c3067e46c469cfff27b9b45289 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "The second term is practically nothing, right?" + }, + { + "text": "The point six, or minus point six to the hundredth power, is an extremely small, extremely small number." + }, + { + "text": "So this is, this, this, there are only two terms, because we're two by two." + }, + { + "text": "This number is, this piece of it is there, but it's, it's disappearing." + }, + { + "text": "Where this piece is there and it's growing and controlling everything." + }, + { + "text": "So, so really the, we're doing, like, problems that are evolving." + }, + { + "text": "We're doing dynamics." + }, + { + "text": "Instead of Ax equal b, that's a static problem." + }, + { + "text": "We're now, we're doing dynamics." + }, + { + "text": "A, a squared, a cubed, things are evolving in time, and the eigenvalues are the crucial, numbers." + }, + { + "text": "OK." + }, + { + "text": "I guess to complete this, I better write down the eigenvectors." + }, + { + "text": "So we should complete the, the whole process by finding the eigenvectors." + }, + { + "text": "OK. Well, I have to, up in the corner, then I have to look at A minus lambda I." + }, + { + "text": "So A minus lambda I is this one minus lambda, one, one, and minus lambda." + }, + { + "text": "And now, can we spot an eigenvector out of that?" + }, + { + "text": "That's, for these two lambdas, this matrix is singular." + }, + { + "text": "I guess the eigenvector, two by two ought to be easy." + }, + { + "text": "So if I know that this matrix is singular, then it seems to me the eigenvector has to be lambda and one, because that multiplication will give me the zero." + }, + { + "text": "And this multiplication gives me, better give me also zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk23.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..df816eb800ce767b1475c279a24ad976bb45a785 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Do you see why it does?" + }, + { + "text": "This is the minus lambda squared plus lambda plus one." + }, + { + "text": "It's the thing that's zero, because these lambdas are special." + }, + { + "text": "There's the eigenvector." + }, + { + "text": "X1 is lambda one, one, and x2 is lambda two, one." + }, + { + "text": "I did that as a little trick that was available in the two by two case." + }, + { + "text": "So now I finally have to, oh, I have to take the initial, u0." + }, + { + "text": "So to complete this example entirely, I have to say, OK, what was u0?" + }, + { + "text": "u0 was f1 f0." + }, + { + "text": "So u0, the starting vector, is f1 f0, and those were one and zero." + }, + { + "text": "So I have to use that vector, so I have to look for, from multiple of the first eigenvector and the second, to produce u0, the one zero vector." + }, + { + "text": "This is what will find c1 and c2, and then I'm done." + }, + { + "text": "So let me, instead of in the last five seconds grinding out a formula, let me repeat the idea." + }, + { + "text": "That really, it's the idea that's central." + }, + { + "text": "When things are evolving in time, let me come back to this board, because the ideas are here." + }, + { + "text": "When things are evolving in time by a first-order system, starting from an original u0, the key is, find the eigenvalues and eigenvectors of A." + }, + { + "text": "That will tell, those eigenvectors, the eigenvalues will already tell you what's happening." + }, + { + "text": "Is the solution blowing up?" + }, + { + "text": "Is it going to zero?" + }, + { + "text": "What's it doing?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk24.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..40301cb90760e2172baa94d536cbc13288d4c31f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk24.json @@ -0,0 +1,20 @@ +[ + { + "text": "And then, to find out exactly a formula, you have to take your u0 and write it as a combination of eigenvectors and then follow each eigenvector separately." + }, + { + "text": "And that's really what this formula, the formula for, that's what the formula for A to the k is doing." + }, + { + "text": "So remember that formula for A to the k is S, lambda to the k S inverse." + }, + { + "text": "OK. That's, that's difference equations, and you just have to, so the homework will give some examples different from Fibonacci to follow through." + }, + { + "text": "And next time will be differential equations." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk3.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..9bf1bb852baadc1da7837e14180c0c2951a30882 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I mentioned at the end of last time, and I'll say again, that there's a small number of matrices for, that don't have n independent eigenvectors." + }, + { + "text": "So I've got to discuss that, that technical point." + }, + { + "text": "But the great, the most matrices that we see have n, n independent eigenvectors and we can diagonalize." + }, + { + "text": "This is diagonalization." + }, + { + "text": "I could also write it, and I often will, the other way round." + }, + { + "text": "If I multiply on the right by s inverse, if I took this equation at the top and multiplied on the right by s inverse, I could, I would have A left here." + }, + { + "text": "Now s inverse is coming from the right." + }, + { + "text": "So can you keep those two straight?" + }, + { + "text": "A multiplies its eigenvectors." + }, + { + "text": "That's how I keep them straight." + }, + { + "text": "So A multiplies s. A multiplies s. And then this s inverse makes the whole thing diagonal." + }, + { + "text": "And this is another way of saying the same thing, putting the s's on the other side of the equation, A is s lambda s inverse." + }, + { + "text": "So that's the, that's the new factorization." + }, + { + "text": "That's the replacement for L U from elimination or Q R from Gram-Schmidt." + }, + { + "text": "And notice that the matrix, so it's, it's a matrix times a diagonal matrix times the inverse of the first one." + }, + { + "text": "It's, that's the combination that we'll see throughout this chapter." + }, + { + "text": "This, this, combination with an s and an s inverse." + }, + { + "text": "OK. Can I just begin to use that?" + }, + { + "text": "For example, what about A squared?" + }, + { + "text": "What are the eigenvalues and eigenvectors of A squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk4.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c687b6948acad76de8781cb82d3eb069c9da514e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's a straightforward question with a, with a absolutely clean answer." + }, + { + "text": "So let me, let me consider A squared." + }, + { + "text": "So I look, I start with Ax equal lambda x." + }, + { + "text": "And I'm headed for A squared." + }, + { + "text": "So let me multiply both sides by A." + }, + { + "text": "That's one way to get A squared on the left." + }, + { + "text": "So if, I should write these ifs in here." + }, + { + "text": "If Ax equals lambda x, then I multiply by A." + }, + { + "text": "So I get A squared x equals, well, I'm multiplying by A, so that's lambda Ax." + }, + { + "text": "That lambda was a number, so I just put it on the left." + }, + { + "text": "And what do I, tell me how to make that look better." + }, + { + "text": "What have I got here?" + }, + { + "text": "For, if, if A has the eigenvalue lambda and eigenvector x, what's up with A squared?" + }, + { + "text": "A squared x, I just multiply by A, but now for Ax, I'm going to substitute lambda x, so I've got lambda squared x." + }, + { + "text": "So from that simple calculation, I, my conclusion is that the eigenvalues of A squared are lambda squared." + }, + { + "text": "And the eigenvectors, I always think about both of those." + }, + { + "text": "What can I say about the eigenvalues?" + }, + { + "text": "They're squared." + }, + { + "text": "What can I say about the eigenvectors?" + }, + { + "text": "They're the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk5.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5bf15e20707c156c8ae71c9c7acea41a9d9d8e46 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same x as in, as for A." + }, + { + "text": "Now, let me see that also from this formula." + }, + { + "text": "How can I see what A squared is looking like from this formula?" + }, + { + "text": "So let me, that, that was one way to do it." + }, + { + "text": "Let me do it by just taking A squared from that." + }, + { + "text": "A squared is S lambda S inverse, that's A, times S lambda S inverse, that's A, which is?" + }, + { + "text": "This is the beauty of eigenvalues, eigenvectors, having that S inverse and S is the identity, so I've got S lambda squared S inverse." + }, + { + "text": "Yes." + }, + { + "text": "You see what that's telling me?" + }, + { + "text": "It's, it's telling me the same thing that I just learned here, but in the, in, in a matrix form." + }, + { + "text": "It's telling me that the S is the same, the eigenvectors are the same, but the eigenvalues are squared, because this is, what's lambda squared, that's still diagonal, it's got little lambda one squared, lambda two squared, down to lambda n squared, on that diagonal, those are the eigenvalues, as we just learned, of A squared." + }, + { + "text": "OK." + }, + { + "text": "So, somehow those eigenvalues and eigenvectors are really giving you a way to, to, to, to see what's going on inside a matrix." + }, + { + "text": "Now, of course, I can continue that for, to the k-th power." + }, + { + "text": "A to the k-th power." + }, + { + "text": "If I multiply, if I have k of these together, do you see how S inverse S will keep cancelling?" + }, + { + "text": "In the, in the inside, I'll have the S outside, at the far left, and lambda will be in there k times and S inverse." + }, + { + "text": "So what's that telling me?" + }, + { + "text": "That's telling me that the eigenvalues of A, of A to the k-th power are the k-th powers." + }, + { + "text": "The eigenvalues of A cubed are the cubes of the eigenvalues of A, and the eigenvectors are the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk6.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..c18dddbe798022f7e68278ac002a3f5fe6ed249e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same." + }, + { + "text": "OK." + }, + { + "text": "In other words, eigenvalues and eigenvectors give a great way to understand the powers of a matrix." + }, + { + "text": "If I take the square of a matrix or the hundredth power of a matrix, the pivots are all over the place." + }, + { + "text": "L U, if I multiply L U times L U times L U times L U a hundred times, I've got a hundred L U's." + }, + { + "text": "I can't do anything with them." + }, + { + "text": "But when I multiply S lambda S inverse by itself, when I look at the eigenvector picture a hundred times, I get a hundred or ninety-nine of these guys cancelling out inside, and I get A to the hundredth is S lambda to the hundredth S inverse." + }, + { + "text": "I mean, eigenvalues tell you about powers of a matrix in a way that we had no, no way to approach previously." + }, + { + "text": "For example, when does, when do the powers of a matrix go to zero?" + }, + { + "text": "I would call that matrix stable, maybe." + }, + { + "text": "So, so, so I could write down a, a theorem." + }, + { + "text": "I'll, I'll write it as a theorem, just to use that word to emphasize that here I'm getting this great fact from this eigenvalue picture." + }, + { + "text": "OK. A to the k approaches zero as k goes, as k gets bigger." + }, + { + "text": "If what?" + }, + { + "text": "What's the, how can I tell for a matrix A if its powers go to zero?" + }, + { + "text": "What, what's somewhere inside that matrix is that information." + }, + { + "text": "That information is not present in the pivots." + }, + { + "text": "It's present in the eigenvalues." + }, + { + "text": "What do I need for the, to know that if I take higher and higher powers of A that this matrix gets smaller and smaller?" + }, + { + "text": "Well, S and S inverse are not moving." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk7.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b84a5c854a5542758e8a0107e1ff043205fe3bdb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's this guy that has to get small, and that's easy to, easy to understand." + }, + { + "text": "The requirement is all eigenvalues, so what is the requirement?" + }, + { + "text": "The eigenvalues have to be less than one." + }, + { + "text": "Now, I have to write that absolute value, because those eigenvalues could be negative, they could be complex numbers." + }, + { + "text": "So I'm taking the absolute value if all of those are below one." + }, + { + "text": "That's, in fact, we practically see why." + }, + { + "text": "Let me just say that I, that I, I'm operating on one assumption here, and I got to keep remembering that that assumption is still present." + }, + { + "text": "That assumption was that I had a full set of, of n independent eigenvectors." + }, + { + "text": "If I don't have that, then I, I, then this approach is not working." + }, + { + "text": "So, so again, a pure eigenvalue approach, eigenvector approach, needs n independent eigenvectors." + }, + { + "text": "If we don't have n independent eigenvectors, we can't diagonalize the matrix." + }, + { + "text": "We can't get to a diagonal matrix." + }, + { + "text": "This, this, this diagonalization is only possible if S inverse makes sense." + }, + { + "text": "OK. Can I, can I follow up on that point now?" + }, + { + "text": "So, so you see why, what we get and, and why we want it, because we get information about the powers of a matrix just immediately from the eigenvalues." + }, + { + "text": "OK, now let me follow up on this, business of which matrices are diagonalizable." + }, + { + "text": "Sorry about that long word." + }, + { + "text": "So a matrix is, is sure to, so here's, here's the main point." + }, + { + "text": "A is sure to be, to have n independent eigenvectors and, and B, now here comes that word, diagonalizable, if, if, so we, we, we might as well get the, the nice case out in the open." + }, + { + "text": "The nice case is when, if all the lambdas are different." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk8.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f06dcec8ffa0ee1bf19440e4ab2194db33ab353b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means, that means no repeated eigenvalues." + }, + { + "text": "OK. That's the nice case." + }, + { + "text": "If, if my matrix and most matrix, if I do a random matrix in MATLAB and compute its eigenvalues, so if I computed, if I took I of rand of ten ten, gave, gave that MATLAB command, the, we'd get a random ten by ten matrix, we would get a list of its ten eigenvalues and they would be different." + }, + { + "text": "They would be distinct, is the best word." + }, + { + "text": "I would have a random matrix will have ten distinct, a ten by ten matrix will have ten distinct eigenvalues, and if it does, the eigenvectors are automatically independent." + }, + { + "text": "So that's a nice fact." + }, + { + "text": "I can, I'll refer you to the text for the proof." + }, + { + "text": "That, that A is sure to have n independent eigenvectors if the eigenvalues are different." + }, + { + "text": "If, if all the, if all eigenvalues are different." + }, + { + "text": "It's just, if some lambdas are repeated, then I have to look more closely." + }, + { + "text": "If an eigenvalue is repeated, I have to look, I have to count, I have to check." + }, + { + "text": "Has it got, say it's repeated three times." + }, + { + "text": "So what's a possibility for, so, so here's, here's the repeated possibility." + }, + { + "text": "And, and let me emphasize the conclusion." + }, + { + "text": "That if I have repeated eigenvalues, I may or may not, I may or may not have, have n independent eigenvectors." + }, + { + "text": "I might." + }, + { + "text": "I, I, you know, this isn't a completely negative case." + }, + { + "text": "The identity matrix." + }, + { + "text": "Well, suppose I take the ten by ten identity matrix." + }, + { + "text": "What are the eigenvalues of that matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk9.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..87d2a2ae5773036cf11800e2f1962908986a0dad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_26_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So just, just take the easiest matrix, the identity." + }, + { + "text": "If I look for its eigenvalues, they're all ones." + }, + { + "text": "So that eigenvalue one is repeated ten times." + }, + { + "text": "But there's no shortage of eigenvectors for the identity matrix." + }, + { + "text": "In fact, every vector is an eigenvector." + }, + { + "text": "So I can take ten independent vectors." + }, + { + "text": "Oh, well, what happens to everything if, if, if A is the identity matrix, let's just think that one through in our head." + }, + { + "text": "If A is the identity matrix, then it's got plenty of eigenvectors." + }, + { + "text": "I choose ten independent vectors, they're the columns of S, and, and what do I get from S inverse A S?" + }, + { + "text": "I get I again, right?" + }, + { + "text": "If A is the identity, and of course, that's the correct lambda." + }, + { + "text": "The, the matrix was already diagonal." + }, + { + "text": "So if the matrix is already diagonal, then the, the lambda is the same as the matrix." + }, + { + "text": "A diagonal matrix has got its eigenvalues sitting right there in front of you." + }, + { + "text": "Now if it's triangular, the eigenvalues are still sitting there, but so let's, let's take a case where, it's triangular." + }, + { + "text": "Suppose A is like, two, one, two, zero." + }, + { + "text": "So there's a case that's going to be trouble." + }, + { + "text": "There's a case that's going to be trouble." + }, + { + "text": "First of all, what are the eigen- I mean, we just, like now you, if we start with a matrix, the first thing we do practically without thinking is compute the eigenvalues and eigenvectors." + }, + { + "text": "OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk0.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6898d4fe66019ef6b40d0472ea94a968e7bbde9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, shall we start?" + }, + { + "text": "This is the second lecture on eigenvalues." + }, + { + "text": "So the first lecture was set -- reached the key equation, Ax equal lambda x. x is the eigenvector and lambda is the eigenvalue." + }, + { + "text": "Now, to use that." + }, + { + "text": "And the good way to, after we've found, so job one is to find the eigenvalues and find the eigenvectors." + }, + { + "text": "Now after we found them, what do we do with them?" + }, + { + "text": "Well, the good way to see that is diagonalize the matrix." + }, + { + "text": "So the matrix is A, and I want to show, first of all, this is like the basic fact." + }, + { + "text": "This, this formula." + }, + { + "text": "That's, that's the key to today's lecture." + }, + { + "text": "This matrix A, I put its eigenvectors in the columns of a matrix S. So S will be the eigenvector matrix, and I want to look at this magic combination S inverse A S. So can I show you how that, how that, what happens there?" + }, + { + "text": "And notice, notice, there's an S inverse." + }, + { + "text": "We have to be able to invert this eigenvector matrix S. So for that we need n independent eigenvectors." + }, + { + "text": "So that's the, that's the case." + }, + { + "text": "OK." + }, + { + "text": "So suppose we have n linearly independent eigenvectors of A." + }, + { + "text": "Put them in the columns of this matrix S. So I'm naturally going to call that the eigenvector matrix, because it's got the eigenvectors in its columns." + }, + { + "text": "And all I want to do is show you what happens when you multiply A times S. So A times S. So this is A times the matrix with the first eigenvector in its first column, the second eigenvector in its second column, the nth eigenvector in its nth column." + }, + { + "text": "And how am I going to do this matrix multiplication?" + }, + { + "text": "Well, certainly I'll do it a column at a time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk1.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..fbe078217bb68baea8e0605a5d04be568c49efbf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I get?" + }, + { + "text": "A times the first column gives me the first column of the answer, but what is it?" + }, + { + "text": "That's an eigenvector." + }, + { + "text": "A times x1 is equal to the lambda times the x1." + }, + { + "text": "And that lambda's we'll call lambda one, of course." + }, + { + "text": "So that's the first column, A x1 is the same as lambda one x1." + }, + { + "text": "A x2 is lambda two x2, so on, along to, in the nth column, we now have lambda n xn." + }, + { + "text": "Looking good, but the next step is even better." + }, + { + "text": "So for the next step, I want to separate out those eigenvalues, those multiplying numbers, from the x's." + }, + { + "text": "So then I'll have just what I want." + }, + { + "text": "OK, so how, how am I going to separate out?" + }, + { + "text": "So that, that number lambda one is multiplying the first column." + }, + { + "text": "So if I want to factor it out of the first column, I better put, here is going to be x1, and that's going to multiply this matrix lambda one in the first entry in all zeros." + }, + { + "text": "You see that that, that's going to come out right for the first column?" + }, + { + "text": "Because we remember how, how we're going back to that original punchline, that if I want a number to multiply x1, then I can do it by putting x1 in that column, in the first column, and putting that number there." + }, + { + "text": "What am I going to have here?" + }, + { + "text": "I'm going to have lambda one, I'm going to have x1, x2, xn." + }, + { + "text": "These are going to be my columns again." + }, + { + "text": "I'm getting s back again." + }, + { + "text": "I'm getting s back again, but now what's it multiplied by?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk10.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c58a42edbe9567233ca7f57643a0b7d43ae6761f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what are the eigenvalues?" + }, + { + "text": "You can tell me right away what they are." + }, + { + "text": "They're two and two, right." + }, + { + "text": "It's a triangular matrix, so when I do this determinant, shall I do this determinant of A minus lambda I?" + }, + { + "text": "I'll get this two minus lambda, one, zero, two minus lambda, right?" + }, + { + "text": "I take that determinant, so I make those into vertical bars to mean determinant, and what's the determinant?" + }, + { + "text": "Two minus lambda squared." + }, + { + "text": "What are the roots?" + }, + { + "text": "Lambda equal two twice." + }, + { + "text": "So the eigenvalues are lambda equals two and two." + }, + { + "text": "OK, fine." + }, + { + "text": "Now the next step, find the eigenvectors." + }, + { + "text": "So I look for eigenvectors and what do I find for this guy?" + }, + { + "text": "Eigenvectors for this guy, when I subtract two minus the identity, so A minus two I has zeros here, and I'm looking for the null space." + }, + { + "text": "What's, what are the eigenvectors?" + }, + { + "text": "They're the, they're, they're the null space of A minus lambda I." + }, + { + "text": "The null space is only one dimension." + }, + { + "text": "This is a case where I don't have enough eigenvectors." + }, + { + "text": "My algebraic multiplicity is two." + }, + { + "text": "I, I would say when I see, when I count how often the eigenvalue is repeated, that's the algebraic multiplicity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk11.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..779c2cf904d904b761080db2671aac46394ad02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the multiplicity." + }, + { + "text": "How many times is it the root of the polynomial?" + }, + { + "text": "My polynomial is two minus lambda squared." + }, + { + "text": "It's a double root." + }, + { + "text": "So my algebraic multiplicity is two." + }, + { + "text": "But the geometric multiplicity, which looks for vectors, looks for eigenvectors and which means the null space of this thing." + }, + { + "text": "And the only eigenvector is one zero." + }, + { + "text": "That's in the null space." + }, + { + "text": "Zero one is not in the null space." + }, + { + "text": "The null space is only one dimensional." + }, + { + "text": "So there's a matrix, my, this A or the original A, that are not diagonalizable." + }, + { + "text": "I can't, I can't find two independent eigenvectors, there's only one." + }, + { + "text": "OK." + }, + { + "text": "So that's the case that I'm, that's a case that I, I'm not really handling." + }, + { + "text": "For example, when I wrote down up here that the powers went to zero if the eigenvalues were below one, I didn't really handle that case of repeated eigenvalues because my reasoning was based on this formula." + }, + { + "text": "And this formula is based on n independent eigenvectors." + }, + { + "text": "OK." + }, + { + "text": "So just to say that." + }, + { + "text": "There are some matrices that we don't cover through diagonalization, but the great majority we do." + }, + { + "text": "OK. And we're always OK if we have different distinct eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk12.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..77d090704cc298475d94416b7ecb88a2a015a913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. That's the, like, the typical case." + }, + { + "text": "Because for each eigenvalue there's at least one eigenvector, the algebraic multiplicity here is one for every eigenvalue, and the geometric multiplicity is one." + }, + { + "text": "There's one eigenvector and they are independent." + }, + { + "text": "OK. OK. Now let me come back to the important case when we're OK." + }, + { + "text": "The important case when we are diagonalizing." + }, + { + "text": "Let me look at, so let me solve this equation." + }, + { + "text": "The equation will be each, I start with some, start with a given vector u0." + }, + { + "text": "And then my equation is that every step I multiply what I have by a." + }, + { + "text": "That equation ought to be simple to handle." + }, + { + "text": "OK. And I'd like to be able to solve it." + }, + { + "text": "How would I find, if I start with a vector u0, and I multiply by a a hundred times, what have I got?" + }, + { + "text": "Well, I can certainly write down a formula for the answer." + }, + { + "text": "So what, what, so u1 is a u0." + }, + { + "text": "And u2 is, what's u2 then?" + }, + { + "text": "U2 I multiply it, u2 I get from u1 by another, multiplying by a, so I've got a twice." + }, + { + "text": "And my formula is uk, after k steps, I've multiplied by a k times the original u0." + }, + { + "text": "You see what I'm doing?" + }, + { + "text": "The next section is going to solve systems of differential equations." + }, + { + "text": "I'm going to have derivatives." + }, + { + "text": "This, this section is the nice one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk13.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..ba8214d8c636e4757a266d6617801174bc939d80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "It solves difference equations." + }, + { + "text": "I would call that a difference equation." + }, + { + "text": "It's conne- a first order." + }, + { + "text": "I would call that a first order system, because it connects only, it only goes up one level." + }, + { + "text": "And it's a system because these are vectors and that's a matrix." + }, + { + "text": "And the solution is just that." + }, + { + "text": "OK." + }, + { + "text": "But, that's a nice formula." + }, + { + "text": "That's the, like, the most compact formula I could ever get." + }, + { + "text": "U one hundred would be a to the one hundredth u0." + }, + { + "text": "But how would I actually find u one hundred?" + }, + { + "text": "How would I find, how would I discover what u one hundred is?" + }, + { + "text": "Let me, let me show you how." + }, + { + "text": "Here, here's the idea." + }, + { + "text": "If, so, to solve, to really solve, shall I say, to really solve." + }, + { + "text": "To really solve it, I would take this initial vector, u0, and I would write it as a combination of eigenvectors." + }, + { + "text": "To really solve, write, write u0 as a combination, say, certain amount of the first eigenvector plus a certain amount of the second eigenvector plus a certain amount of the last eigenvector." + }, + { + "text": "Now multiply by a." + }, + { + "text": "You want to, you got to see the magic of eigenvectors work." + }, + { + "text": "Multiply by a." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk14.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7843b2bf0cac762d1c12452cf36500ea4ad13370 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a u0 is what?" + }, + { + "text": "So a times that." + }, + { + "text": "A times, so what's, I can separate it out into n separate pieces and that's the whole point." + }, + { + "text": "That each of those pieces is going in its own merry way." + }, + { + "text": "Each of those pieces is an eigenvector, and when I multiply by a, what does this piece become?" + }, + { + "text": "So that's some amount of the first, let's suppose the eigenvectors are normalized to be unit vectors." + }, + { + "text": "So that says what the eigenvector is." + }, + { + "text": "It's, and I need some multiple of it to produce u0." + }, + { + "text": "OK. Now when I multiply by a, what do I get?" + }, + { + "text": "I get c1, which is just a factor, times a x1, but a x1 is lambda one x1." + }, + { + "text": "When I multiply this by a, I get c2 lambda two x2." + }, + { + "text": "And here I get cn lambda n xn." + }, + { + "text": "And suppose I multiply by a to the hundredth power now." + }, + { + "text": "Can we, can we, having done it, multiplied by a, let's multiply by a to the hundredth." + }, + { + "text": "What happens to this first term when I multiply by a to the one hundredth?" + }, + { + "text": "It's got that factor lambda to the hundredth." + }, + { + "text": "That's the key." + }, + { + "text": "That, that's what I mean by going its own merry way." + }, + { + "text": "It, it is pure eigenvector, it's exactly in a direction where multiplication by a just brings in a scalar factor lambda one." + }, + { + "text": "So a hundred times brings in this a hundred times." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk15.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7ee3348735378aa4049d33ec2a197d0ceb0c447c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Hundred times lambda two, hundred times lambda n. Actually, we're, what are we seeing here?" + }, + { + "text": "We're seeing, this same, lambda, capital lambda to the hundredth, as in the, as in the diagonalization, and we're seeing the S matrix, the matrix S of eigenvectors." + }, + { + "text": "That's what this has got to, this has got to amount to, a lambda to the hundredth power times an S times this vector C that's telling us how much of each one is in the original thing." + }, + { + "text": "So if, if I had to really find the hundredth power, I would take u0, I would expand it as a combination of eigenvectors, this is really S, the eigenvector matrix times C, the, the coefficient vector." + }, + { + "text": "And then I would immediately, then, by inserting these hundredth powers of eigenvalues, I'd have the answer." + }, + { + "text": "So the, the, huh, there must be, well, let's see." + }, + { + "text": "OK." + }, + { + "text": "It's, so, yeah." + }, + { + "text": "So if u100 is a to the hundredth times u0, and u0 is Sc, then you see this formula is just this formula, which is the way I would actually get hold of this, of this u100, which is, let me put it here, u100." + }, + { + "text": "The way I would actually get hold of that, see what, what the solution is after a hundred steps, would be expand the initial vector into eigenvectors and, and let each eigenvector go its own way, multiplying by a hundred at, by lambda at every step, and therefore by lambda to the hundredth power after a hundredth step." + }, + { + "text": "Can I do an example?" + }, + { + "text": "So that's, that's the, the formulas." + }, + { + "text": "Now let me take an example." + }, + { + "text": "I'll use the Fibonacci sequence as an example." + }, + { + "text": "So, so Fibonacci example." + }, + { + "text": "You remember the Fibonacci numbers?" + }, + { + "text": "If we start with one and one as F0, oh, I think I start with zero, maybe." + }, + { + "text": "Let zero and one be the first ones." + }, + { + "text": "So there's F0 and F1, the first two Fibonacci numbers." + }, + { + "text": "Then what's the rule for Fibonacci numbers?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk16.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..79c65e32781f7f304b504a6c390247abb9d26ac8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "They're the sum." + }, + { + "text": "The next one is the sum of those, so it's one." + }, + { + "text": "The next one is the sum of those, so it's two." + }, + { + "text": "The next one is the sum of those, so it's three." + }, + { + "text": "Well, it looks like one, two, three, four, five, but somehow it's not going to do that way." + }, + { + "text": "The next one is five, right." + }, + { + "text": "Two and three makes five." + }, + { + "text": "The next one is eight." + }, + { + "text": "The next one is thirteen." + }, + { + "text": "And the one hundredth Fibonacci number is what?" + }, + { + "text": "That's my question." + }, + { + "text": "How could I get a formula for the hundredth number and for example how could I answer the question how fast are they growing?" + }, + { + "text": "How fast are those Fibonacci numbers growing?" + }, + { + "text": "They're certainly growing." + }, + { + "text": "It's not a stable case, whatever the eigenvalues of whatever matrix it is, they're not smaller than one." + }, + { + "text": "These numbers are growing." + }, + { + "text": "But how fast are they growing?" + }, + { + "text": "The answer is lies in the eigenvalue." + }, + { + "text": "So I've got to find the matrix, so let me write down the Fibonacci rule, F k plus two is F k plus one plus F k, right?" + }, + { + "text": "Now that's not in my -- I want to write that as U k plus one and A U k. But right now what I've got is a single equation, not a system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk17.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b3aaa9dcee3cf27c112015659bb5a0b51a983ce1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's second order." + }, + { + "text": "It's like having a second order differential equation with second derivatives." + }, + { + "text": "I want to get first derivatives." + }, + { + "text": "Here I want to get first difference." + }, + { + "text": "So the way to do it is to introduce U k will be a vector." + }, + { + "text": "See, a small trick." + }, + { + "text": "Let U k be a vector, F k plus one and F k. So I'm going to get a two by two system, first order, instead of a one, instead of a scalar system, second order, by a simple trick." + }, + { + "text": "I'm just going to add in an equation F k plus one equals F k plus one." + }, + { + "text": "That will be my second equation." + }, + { + "text": "Then this is my system, this is my unknown, and what's my one-step equation?" + }, + { + "text": "So now U k plus one." + }, + { + "text": "That's so U k plus one is the left side, and what have I got here on the right side?" + }, + { + "text": "I've got some matrix multiplying U k. Can you see that all right?" + }, + { + "text": "If you can see it, then you can tell me what the matrix is." + }, + { + "text": "You see that I'm taking my system here, I artificially made it into a system." + }, + { + "text": "I artificially made the unknown into a vector, and now I'm ready to look at and see what the matrix is." + }, + { + "text": "So do you see the left side, U k plus one is F k plus two F k plus one, that's just what I want." + }, + { + "text": "On the right side, this, remember, this U k here, let me for the moment put it as F k plus one F k. So what's the matrix?" + }, + { + "text": "Well, that has a one and a one, and that has a one and a zero." + }, + { + "text": "There's the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk18.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..6c1b68c2cb2fde3f5dea82f3100d4da31fcce70a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "You see that that gives me the right-hand side." + }, + { + "text": "So there's the matrix A, and this is our friend U k. So we've got, so that simple trick changed the second order scalar problem to a first order system, two, with two unknowns." + }, + { + "text": "With a matrix and now what do I do?" + }, + { + "text": "Well, before I even think, I find its eigenvalues and eigenvectors." + }, + { + "text": "So what are the eigenvalues and eigenvectors of that matrix?" + }, + { + "text": "Let's see." + }, + { + "text": "I was, first let me just, like, think for a minute." + }, + { + "text": "It's two by two, so this shouldn't be impossible to do." + }, + { + "text": "Let's do it." + }, + { + "text": "OK." + }, + { + "text": "So my matrix again is one one one zero." + }, + { + "text": "It's symmetric, by the way." + }, + { + "text": "So what I will eventually know about symmetric matrices is that the eigenvalues will come out real, I won't get any complex numbers here, and the eigenvectors, once I get those, actually will be orthogonal." + }, + { + "text": "But two by two, I'm more interested in what the actual numbers are." + }, + { + "text": "What do I know about the two numbers?" + }, + { + "text": "Well, should, do you want me to find this determinant of A minus lambda I?" + }, + { + "text": "Sure." + }, + { + "text": "So it's the determinant of one minus lambda one one zero, right?" + }, + { + "text": "Minus lambda, yes, got it." + }, + { + "text": "OK. OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk19.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..a73b23e3d56b889ff49ea7f55a784fac33e13c3d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "There'll be two eigenvalues." + }, + { + "text": "Well, tell me again what I know about the two eigenvalues before I go any further." + }, + { + "text": "Tell me something about these two eigenvalues, what do they add up to?" + }, + { + "text": "Lambda one plus lambda two is the same as the trace down the diagonal of the matrix, one and zero is one." + }, + { + "text": "So lambda one plus lambda two should come out to be one, and lambda one times lambda two should come out to be the determinant, which is minus one." + }, + { + "text": "So I'm expecting the eigenvalues to add to one and to multiply to minus one." + }, + { + "text": "But let's just see it happen here." + }, + { + "text": "If I multiply this out, I get that times that'll be a lambda squared minus lambda minus one." + }, + { + "text": "Good." + }, + { + "text": "Lambda squared minus lambda minus one." + }, + { + "text": "Actually, you see the, compare that with the original equation that I started with." + }, + { + "text": "Fk plus two minus Fk plus one minus Fk is zero." + }, + { + "text": "The recurrent, the recursion that the Fibonacci number satisfy is somehow showing up directly here for the eigenvalues when we set that to zero." + }, + { + "text": "OK. Let's solve." + }, + { + "text": "Well, I would like to be able to factor that, that quadratic, but I'm better off to use the quadratic formula." + }, + { + "text": "Lambda is, let's see, minus b is one, plus or minus the square root of b squared, which is one, minus four, times that, times that, which is plus four, over two." + }, + { + "text": "So that's the square root of five." + }, + { + "text": "So the eigenvalues are lambda one is one half of one plus square root of five, and lambda two is one half of one minus square root of five." + }, + { + "text": "And sure enough, they, those add up to one, and they multiply to give minus one." + }, + { + "text": "OK. Those are the two eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk2.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..43cfb012fc04a89fc7dab94c23bfb0f50ade3782 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "On the right, it's multiplied by, if I want, if I want lambda n xn in the last column, how do I do it?" + }, + { + "text": "Well, the last column here will be, I'll, I'll take the last column, use these coefficients, put the lambda n down there, and it will multiply that nth column and give me lambda n xn." + }, + { + "text": "There, there you see matrix multiplication just working for us." + }, + { + "text": "So I started with A s. I wrote down what it meant." + }, + { + "text": "A times each eigenvector." + }, + { + "text": "That gave me lambda times the eigenvector." + }, + { + "text": "And then when I peeled off the lambdas, they were on the right-hand side, so I've got s, my matrix back again, and this matrix, this diagonal matrix, the eigenvalue matrix, and I call it capital lambda, using capital letters for matrices, and lambda to prompt me that it's, that it's eigenvalues that are in there." + }, + { + "text": "So you see that the eigenvalues are just sitting down that diagonal?" + }, + { + "text": "If I had a column x2 here, I would want the lambda two in the two two position, in the diagonal position, to multiply that x2 and give me the lambda two x2." + }, + { + "text": "That's my formula." + }, + { + "text": "A s is s lambda." + }, + { + "text": "OK. That's, that's the, you see, it's just a calculation." + }, + { + "text": "Now, I, I mentioned, and I have to mention again, this business about n independent eigenvectors." + }, + { + "text": "As it stands, this is all fine whether, I mean, I could be repeating the same eigenvector, but I, I'm no interested in that." + }, + { + "text": "I want to be able to invert s, and that's where this comes in." + }, + { + "text": "This n independent eigenvectors business comes in to tell me that that matrix is invertible." + }, + { + "text": "So let me, on the next board, write down what I've got." + }, + { + "text": "A s equals s lambda." + }, + { + "text": "And now I'm, I can multiply on the left by s inverse." + }, + { + "text": "So this is really, I can do that provided s is invertible, provided my assumption of n independent eigenvectors is satisfied." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk20.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ad5a59fa5db44ce73ff5f88190423e0404fb3d39 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "How, how, what are those numbers approximately?" + }, + { + "text": "Square root of five, well, it's more than two, but less than three." + }, + { + "text": "It, it'd be nice to know these numbers." + }, + { + "text": "I think, I think that that, so that number comes out bigger than one, right?" + }, + { + "text": "Yeah, that's right." + }, + { + "text": "This number comes out bigger than one." + }, + { + "text": "It's about one point six one eight or something." + }, + { + "text": "Not exactly." + }, + { + "text": "It's supposed to be one point six." + }, + { + "text": "Just, like, I think so." + }, + { + "text": "Then what's lambda two?" + }, + { + "text": "Is, is lambda two positive or negative?" + }, + { + "text": "Negative, right?" + }, + { + "text": "Because I'm, it's obviously negative, and I knew that the, so it's minus, and they add up to one, so minus point six one eight, I guess." + }, + { + "text": "OK. And some order." + }, + { + "text": "Those are the two eigenvalues." + }, + { + "text": "One eigenvalue bigger than one, one eigenvalue smaller than one." + }, + { + "text": "Actually, that's a great situation to be in." + }, + { + "text": "Of course, the eigenvalues are different, so there's no doubt whatever, is this matrix diagonalizable?" + }, + { + "text": "Is this matrix diagonalizable, that original matrix A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk21.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..4a034475591d371995b379b5f98783a2cfb25870 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Sure." + }, + { + "text": "We've got two distinct eigenvalues and we can find the eigenvectors in a moment." + }, + { + "text": "But they'll be independent, will be diagonalizable, and now you can already answer my very first question." + }, + { + "text": "How fast are those Fibonacci numbers increasing?" + }, + { + "text": "How, those, they're increasing, right?" + }, + { + "text": "They're not doubling at every step." + }, + { + "text": "Let's look again at these numbers." + }, + { + "text": "Five eight thirteen, it's not obvious." + }, + { + "text": "The next one would be twenty one thirty four." + }, + { + "text": "So to get some idea of what F one hundred is, can you give me any, I mean the crucial number of, so it, these, it's approximately, what's controlling the growth of these Fibonacci numbers?" + }, + { + "text": "It's the eigenvalues." + }, + { + "text": "And which eigenvalues controlling that growth?" + }, + { + "text": "The big ones." + }, + { + "text": "So F one hundred will it be approximately some constant, c one, I guess, times this lambda one, this one plus square root of five over two, to the hundredth power." + }, + { + "text": "And the two hundredth have, in other words, the eigenvalue, the Fibonacci numbers are growing by about that factor." + }, + { + "text": "You see that we've got precise information about the, about the Fibonacci numbers out of the eigenvalue." + }, + { + "text": "OK. And again, why is that true?" + }, + { + "text": "Let me go over to this board and show what I'm doing here." + }, + { + "text": "The, the original eigen, the original initial value is some combination of eigenvectors, and then when we start multiple, when we start going out the theory of Fibonacci numbers, when we start multiplying by a hundred times, it's this lambda one to the hundredth, this term is, is the one that's taken over." + }, + { + "text": "It's, I mean, that's big, like, one point six to the hundredth power." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk22.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..c13a1fc9867173c3067e46c469cfff27b9b45289 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "The second term is practically nothing, right?" + }, + { + "text": "The point six, or minus point six to the hundredth power, is an extremely small, extremely small number." + }, + { + "text": "So this is, this, this, there are only two terms, because we're two by two." + }, + { + "text": "This number is, this piece of it is there, but it's, it's disappearing." + }, + { + "text": "Where this piece is there and it's growing and controlling everything." + }, + { + "text": "So, so really the, we're doing, like, problems that are evolving." + }, + { + "text": "We're doing dynamics." + }, + { + "text": "Instead of Ax equal b, that's a static problem." + }, + { + "text": "We're now, we're doing dynamics." + }, + { + "text": "A, a squared, a cubed, things are evolving in time, and the eigenvalues are the crucial, numbers." + }, + { + "text": "OK." + }, + { + "text": "I guess to complete this, I better write down the eigenvectors." + }, + { + "text": "So we should complete the, the whole process by finding the eigenvectors." + }, + { + "text": "OK. Well, I have to, up in the corner, then I have to look at A minus lambda I." + }, + { + "text": "So A minus lambda I is this one minus lambda, one, one, and minus lambda." + }, + { + "text": "And now, can we spot an eigenvector out of that?" + }, + { + "text": "That's, for these two lambdas, this matrix is singular." + }, + { + "text": "I guess the eigenvector, two by two ought to be easy." + }, + { + "text": "So if I know that this matrix is singular, then it seems to me the eigenvector has to be lambda and one, because that multiplication will give me the zero." + }, + { + "text": "And this multiplication gives me, better give me also zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk23.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..df816eb800ce767b1475c279a24ad976bb45a785 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Do you see why it does?" + }, + { + "text": "This is the minus lambda squared plus lambda plus one." + }, + { + "text": "It's the thing that's zero, because these lambdas are special." + }, + { + "text": "There's the eigenvector." + }, + { + "text": "X1 is lambda one, one, and x2 is lambda two, one." + }, + { + "text": "I did that as a little trick that was available in the two by two case." + }, + { + "text": "So now I finally have to, oh, I have to take the initial, u0." + }, + { + "text": "So to complete this example entirely, I have to say, OK, what was u0?" + }, + { + "text": "u0 was f1 f0." + }, + { + "text": "So u0, the starting vector, is f1 f0, and those were one and zero." + }, + { + "text": "So I have to use that vector, so I have to look for, from multiple of the first eigenvector and the second, to produce u0, the one zero vector." + }, + { + "text": "This is what will find c1 and c2, and then I'm done." + }, + { + "text": "So let me, instead of in the last five seconds grinding out a formula, let me repeat the idea." + }, + { + "text": "That really, it's the idea that's central." + }, + { + "text": "When things are evolving in time, let me come back to this board, because the ideas are here." + }, + { + "text": "When things are evolving in time by a first-order system, starting from an original u0, the key is, find the eigenvalues and eigenvectors of A." + }, + { + "text": "That will tell, those eigenvectors, the eigenvalues will already tell you what's happening." + }, + { + "text": "Is the solution blowing up?" + }, + { + "text": "Is it going to zero?" + }, + { + "text": "What's it doing?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk24.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..40301cb90760e2172baa94d536cbc13288d4c31f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk24.json @@ -0,0 +1,20 @@ +[ + { + "text": "And then, to find out exactly a formula, you have to take your u0 and write it as a combination of eigenvectors and then follow each eigenvector separately." + }, + { + "text": "And that's really what this formula, the formula for, that's what the formula for A to the k is doing." + }, + { + "text": "So remember that formula for A to the k is S, lambda to the k S inverse." + }, + { + "text": "OK. That's, that's difference equations, and you just have to, so the homework will give some examples different from Fibonacci to follow through." + }, + { + "text": "And next time will be differential equations." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk3.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..9bf1bb852baadc1da7837e14180c0c2951a30882 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I mentioned at the end of last time, and I'll say again, that there's a small number of matrices for, that don't have n independent eigenvectors." + }, + { + "text": "So I've got to discuss that, that technical point." + }, + { + "text": "But the great, the most matrices that we see have n, n independent eigenvectors and we can diagonalize." + }, + { + "text": "This is diagonalization." + }, + { + "text": "I could also write it, and I often will, the other way round." + }, + { + "text": "If I multiply on the right by s inverse, if I took this equation at the top and multiplied on the right by s inverse, I could, I would have A left here." + }, + { + "text": "Now s inverse is coming from the right." + }, + { + "text": "So can you keep those two straight?" + }, + { + "text": "A multiplies its eigenvectors." + }, + { + "text": "That's how I keep them straight." + }, + { + "text": "So A multiplies s. A multiplies s. And then this s inverse makes the whole thing diagonal." + }, + { + "text": "And this is another way of saying the same thing, putting the s's on the other side of the equation, A is s lambda s inverse." + }, + { + "text": "So that's the, that's the new factorization." + }, + { + "text": "That's the replacement for L U from elimination or Q R from Gram-Schmidt." + }, + { + "text": "And notice that the matrix, so it's, it's a matrix times a diagonal matrix times the inverse of the first one." + }, + { + "text": "It's, that's the combination that we'll see throughout this chapter." + }, + { + "text": "This, this, combination with an s and an s inverse." + }, + { + "text": "OK. Can I just begin to use that?" + }, + { + "text": "For example, what about A squared?" + }, + { + "text": "What are the eigenvalues and eigenvectors of A squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk4.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c687b6948acad76de8781cb82d3eb069c9da514e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's a straightforward question with a, with a absolutely clean answer." + }, + { + "text": "So let me, let me consider A squared." + }, + { + "text": "So I look, I start with Ax equal lambda x." + }, + { + "text": "And I'm headed for A squared." + }, + { + "text": "So let me multiply both sides by A." + }, + { + "text": "That's one way to get A squared on the left." + }, + { + "text": "So if, I should write these ifs in here." + }, + { + "text": "If Ax equals lambda x, then I multiply by A." + }, + { + "text": "So I get A squared x equals, well, I'm multiplying by A, so that's lambda Ax." + }, + { + "text": "That lambda was a number, so I just put it on the left." + }, + { + "text": "And what do I, tell me how to make that look better." + }, + { + "text": "What have I got here?" + }, + { + "text": "For, if, if A has the eigenvalue lambda and eigenvector x, what's up with A squared?" + }, + { + "text": "A squared x, I just multiply by A, but now for Ax, I'm going to substitute lambda x, so I've got lambda squared x." + }, + { + "text": "So from that simple calculation, I, my conclusion is that the eigenvalues of A squared are lambda squared." + }, + { + "text": "And the eigenvectors, I always think about both of those." + }, + { + "text": "What can I say about the eigenvalues?" + }, + { + "text": "They're squared." + }, + { + "text": "What can I say about the eigenvectors?" + }, + { + "text": "They're the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk5.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5bf15e20707c156c8ae71c9c7acea41a9d9d8e46 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same x as in, as for A." + }, + { + "text": "Now, let me see that also from this formula." + }, + { + "text": "How can I see what A squared is looking like from this formula?" + }, + { + "text": "So let me, that, that was one way to do it." + }, + { + "text": "Let me do it by just taking A squared from that." + }, + { + "text": "A squared is S lambda S inverse, that's A, times S lambda S inverse, that's A, which is?" + }, + { + "text": "This is the beauty of eigenvalues, eigenvectors, having that S inverse and S is the identity, so I've got S lambda squared S inverse." + }, + { + "text": "Yes." + }, + { + "text": "You see what that's telling me?" + }, + { + "text": "It's, it's telling me the same thing that I just learned here, but in the, in, in a matrix form." + }, + { + "text": "It's telling me that the S is the same, the eigenvectors are the same, but the eigenvalues are squared, because this is, what's lambda squared, that's still diagonal, it's got little lambda one squared, lambda two squared, down to lambda n squared, on that diagonal, those are the eigenvalues, as we just learned, of A squared." + }, + { + "text": "OK." + }, + { + "text": "So, somehow those eigenvalues and eigenvectors are really giving you a way to, to, to, to see what's going on inside a matrix." + }, + { + "text": "Now, of course, I can continue that for, to the k-th power." + }, + { + "text": "A to the k-th power." + }, + { + "text": "If I multiply, if I have k of these together, do you see how S inverse S will keep cancelling?" + }, + { + "text": "In the, in the inside, I'll have the S outside, at the far left, and lambda will be in there k times and S inverse." + }, + { + "text": "So what's that telling me?" + }, + { + "text": "That's telling me that the eigenvalues of A, of A to the k-th power are the k-th powers." + }, + { + "text": "The eigenvalues of A cubed are the cubes of the eigenvalues of A, and the eigenvectors are the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk6.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..c18dddbe798022f7e68278ac002a3f5fe6ed249e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same." + }, + { + "text": "OK." + }, + { + "text": "In other words, eigenvalues and eigenvectors give a great way to understand the powers of a matrix." + }, + { + "text": "If I take the square of a matrix or the hundredth power of a matrix, the pivots are all over the place." + }, + { + "text": "L U, if I multiply L U times L U times L U times L U a hundred times, I've got a hundred L U's." + }, + { + "text": "I can't do anything with them." + }, + { + "text": "But when I multiply S lambda S inverse by itself, when I look at the eigenvector picture a hundred times, I get a hundred or ninety-nine of these guys cancelling out inside, and I get A to the hundredth is S lambda to the hundredth S inverse." + }, + { + "text": "I mean, eigenvalues tell you about powers of a matrix in a way that we had no, no way to approach previously." + }, + { + "text": "For example, when does, when do the powers of a matrix go to zero?" + }, + { + "text": "I would call that matrix stable, maybe." + }, + { + "text": "So, so, so I could write down a, a theorem." + }, + { + "text": "I'll, I'll write it as a theorem, just to use that word to emphasize that here I'm getting this great fact from this eigenvalue picture." + }, + { + "text": "OK. A to the k approaches zero as k goes, as k gets bigger." + }, + { + "text": "If what?" + }, + { + "text": "What's the, how can I tell for a matrix A if its powers go to zero?" + }, + { + "text": "What, what's somewhere inside that matrix is that information." + }, + { + "text": "That information is not present in the pivots." + }, + { + "text": "It's present in the eigenvalues." + }, + { + "text": "What do I need for the, to know that if I take higher and higher powers of A that this matrix gets smaller and smaller?" + }, + { + "text": "Well, S and S inverse are not moving." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk7.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b84a5c854a5542758e8a0107e1ff043205fe3bdb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's this guy that has to get small, and that's easy to, easy to understand." + }, + { + "text": "The requirement is all eigenvalues, so what is the requirement?" + }, + { + "text": "The eigenvalues have to be less than one." + }, + { + "text": "Now, I have to write that absolute value, because those eigenvalues could be negative, they could be complex numbers." + }, + { + "text": "So I'm taking the absolute value if all of those are below one." + }, + { + "text": "That's, in fact, we practically see why." + }, + { + "text": "Let me just say that I, that I, I'm operating on one assumption here, and I got to keep remembering that that assumption is still present." + }, + { + "text": "That assumption was that I had a full set of, of n independent eigenvectors." + }, + { + "text": "If I don't have that, then I, I, then this approach is not working." + }, + { + "text": "So, so again, a pure eigenvalue approach, eigenvector approach, needs n independent eigenvectors." + }, + { + "text": "If we don't have n independent eigenvectors, we can't diagonalize the matrix." + }, + { + "text": "We can't get to a diagonal matrix." + }, + { + "text": "This, this, this diagonalization is only possible if S inverse makes sense." + }, + { + "text": "OK. Can I, can I follow up on that point now?" + }, + { + "text": "So, so you see why, what we get and, and why we want it, because we get information about the powers of a matrix just immediately from the eigenvalues." + }, + { + "text": "OK, now let me follow up on this, business of which matrices are diagonalizable." + }, + { + "text": "Sorry about that long word." + }, + { + "text": "So a matrix is, is sure to, so here's, here's the main point." + }, + { + "text": "A is sure to be, to have n independent eigenvectors and, and B, now here comes that word, diagonalizable, if, if, so we, we, we might as well get the, the nice case out in the open." + }, + { + "text": "The nice case is when, if all the lambdas are different." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk8.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f06dcec8ffa0ee1bf19440e4ab2194db33ab353b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means, that means no repeated eigenvalues." + }, + { + "text": "OK. That's the nice case." + }, + { + "text": "If, if my matrix and most matrix, if I do a random matrix in MATLAB and compute its eigenvalues, so if I computed, if I took I of rand of ten ten, gave, gave that MATLAB command, the, we'd get a random ten by ten matrix, we would get a list of its ten eigenvalues and they would be different." + }, + { + "text": "They would be distinct, is the best word." + }, + { + "text": "I would have a random matrix will have ten distinct, a ten by ten matrix will have ten distinct eigenvalues, and if it does, the eigenvectors are automatically independent." + }, + { + "text": "So that's a nice fact." + }, + { + "text": "I can, I'll refer you to the text for the proof." + }, + { + "text": "That, that A is sure to have n independent eigenvectors if the eigenvalues are different." + }, + { + "text": "If, if all the, if all eigenvalues are different." + }, + { + "text": "It's just, if some lambdas are repeated, then I have to look more closely." + }, + { + "text": "If an eigenvalue is repeated, I have to look, I have to count, I have to check." + }, + { + "text": "Has it got, say it's repeated three times." + }, + { + "text": "So what's a possibility for, so, so here's, here's the repeated possibility." + }, + { + "text": "And, and let me emphasize the conclusion." + }, + { + "text": "That if I have repeated eigenvalues, I may or may not, I may or may not have, have n independent eigenvectors." + }, + { + "text": "I might." + }, + { + "text": "I, I, you know, this isn't a completely negative case." + }, + { + "text": "The identity matrix." + }, + { + "text": "Well, suppose I take the ten by ten identity matrix." + }, + { + "text": "What are the eigenvalues of that matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk9.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..87d2a2ae5773036cf11800e2f1962908986a0dad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_27_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So just, just take the easiest matrix, the identity." + }, + { + "text": "If I look for its eigenvalues, they're all ones." + }, + { + "text": "So that eigenvalue one is repeated ten times." + }, + { + "text": "But there's no shortage of eigenvectors for the identity matrix." + }, + { + "text": "In fact, every vector is an eigenvector." + }, + { + "text": "So I can take ten independent vectors." + }, + { + "text": "Oh, well, what happens to everything if, if, if A is the identity matrix, let's just think that one through in our head." + }, + { + "text": "If A is the identity matrix, then it's got plenty of eigenvectors." + }, + { + "text": "I choose ten independent vectors, they're the columns of S, and, and what do I get from S inverse A S?" + }, + { + "text": "I get I again, right?" + }, + { + "text": "If A is the identity, and of course, that's the correct lambda." + }, + { + "text": "The, the matrix was already diagonal." + }, + { + "text": "So if the matrix is already diagonal, then the, the lambda is the same as the matrix." + }, + { + "text": "A diagonal matrix has got its eigenvalues sitting right there in front of you." + }, + { + "text": "Now if it's triangular, the eigenvalues are still sitting there, but so let's, let's take a case where, it's triangular." + }, + { + "text": "Suppose A is like, two, one, two, zero." + }, + { + "text": "So there's a case that's going to be trouble." + }, + { + "text": "There's a case that's going to be trouble." + }, + { + "text": "First of all, what are the eigen- I mean, we just, like now you, if we start with a matrix, the first thing we do practically without thinking is compute the eigenvalues and eigenvectors." + }, + { + "text": "OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk0.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6898d4fe66019ef6b40d0472ea94a968e7bbde9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, shall we start?" + }, + { + "text": "This is the second lecture on eigenvalues." + }, + { + "text": "So the first lecture was set -- reached the key equation, Ax equal lambda x. x is the eigenvector and lambda is the eigenvalue." + }, + { + "text": "Now, to use that." + }, + { + "text": "And the good way to, after we've found, so job one is to find the eigenvalues and find the eigenvectors." + }, + { + "text": "Now after we found them, what do we do with them?" + }, + { + "text": "Well, the good way to see that is diagonalize the matrix." + }, + { + "text": "So the matrix is A, and I want to show, first of all, this is like the basic fact." + }, + { + "text": "This, this formula." + }, + { + "text": "That's, that's the key to today's lecture." + }, + { + "text": "This matrix A, I put its eigenvectors in the columns of a matrix S. So S will be the eigenvector matrix, and I want to look at this magic combination S inverse A S. So can I show you how that, how that, what happens there?" + }, + { + "text": "And notice, notice, there's an S inverse." + }, + { + "text": "We have to be able to invert this eigenvector matrix S. So for that we need n independent eigenvectors." + }, + { + "text": "So that's the, that's the case." + }, + { + "text": "OK." + }, + { + "text": "So suppose we have n linearly independent eigenvectors of A." + }, + { + "text": "Put them in the columns of this matrix S. So I'm naturally going to call that the eigenvector matrix, because it's got the eigenvectors in its columns." + }, + { + "text": "And all I want to do is show you what happens when you multiply A times S. So A times S. So this is A times the matrix with the first eigenvector in its first column, the second eigenvector in its second column, the nth eigenvector in its nth column." + }, + { + "text": "And how am I going to do this matrix multiplication?" + }, + { + "text": "Well, certainly I'll do it a column at a time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk1.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..fbe078217bb68baea8e0605a5d04be568c49efbf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I get?" + }, + { + "text": "A times the first column gives me the first column of the answer, but what is it?" + }, + { + "text": "That's an eigenvector." + }, + { + "text": "A times x1 is equal to the lambda times the x1." + }, + { + "text": "And that lambda's we'll call lambda one, of course." + }, + { + "text": "So that's the first column, A x1 is the same as lambda one x1." + }, + { + "text": "A x2 is lambda two x2, so on, along to, in the nth column, we now have lambda n xn." + }, + { + "text": "Looking good, but the next step is even better." + }, + { + "text": "So for the next step, I want to separate out those eigenvalues, those multiplying numbers, from the x's." + }, + { + "text": "So then I'll have just what I want." + }, + { + "text": "OK, so how, how am I going to separate out?" + }, + { + "text": "So that, that number lambda one is multiplying the first column." + }, + { + "text": "So if I want to factor it out of the first column, I better put, here is going to be x1, and that's going to multiply this matrix lambda one in the first entry in all zeros." + }, + { + "text": "You see that that, that's going to come out right for the first column?" + }, + { + "text": "Because we remember how, how we're going back to that original punchline, that if I want a number to multiply x1, then I can do it by putting x1 in that column, in the first column, and putting that number there." + }, + { + "text": "What am I going to have here?" + }, + { + "text": "I'm going to have lambda one, I'm going to have x1, x2, xn." + }, + { + "text": "These are going to be my columns again." + }, + { + "text": "I'm getting s back again." + }, + { + "text": "I'm getting s back again, but now what's it multiplied by?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk10.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c58a42edbe9567233ca7f57643a0b7d43ae6761f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what are the eigenvalues?" + }, + { + "text": "You can tell me right away what they are." + }, + { + "text": "They're two and two, right." + }, + { + "text": "It's a triangular matrix, so when I do this determinant, shall I do this determinant of A minus lambda I?" + }, + { + "text": "I'll get this two minus lambda, one, zero, two minus lambda, right?" + }, + { + "text": "I take that determinant, so I make those into vertical bars to mean determinant, and what's the determinant?" + }, + { + "text": "Two minus lambda squared." + }, + { + "text": "What are the roots?" + }, + { + "text": "Lambda equal two twice." + }, + { + "text": "So the eigenvalues are lambda equals two and two." + }, + { + "text": "OK, fine." + }, + { + "text": "Now the next step, find the eigenvectors." + }, + { + "text": "So I look for eigenvectors and what do I find for this guy?" + }, + { + "text": "Eigenvectors for this guy, when I subtract two minus the identity, so A minus two I has zeros here, and I'm looking for the null space." + }, + { + "text": "What's, what are the eigenvectors?" + }, + { + "text": "They're the, they're, they're the null space of A minus lambda I." + }, + { + "text": "The null space is only one dimension." + }, + { + "text": "This is a case where I don't have enough eigenvectors." + }, + { + "text": "My algebraic multiplicity is two." + }, + { + "text": "I, I would say when I see, when I count how often the eigenvalue is repeated, that's the algebraic multiplicity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk11.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..779c2cf904d904b761080db2671aac46394ad02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the multiplicity." + }, + { + "text": "How many times is it the root of the polynomial?" + }, + { + "text": "My polynomial is two minus lambda squared." + }, + { + "text": "It's a double root." + }, + { + "text": "So my algebraic multiplicity is two." + }, + { + "text": "But the geometric multiplicity, which looks for vectors, looks for eigenvectors and which means the null space of this thing." + }, + { + "text": "And the only eigenvector is one zero." + }, + { + "text": "That's in the null space." + }, + { + "text": "Zero one is not in the null space." + }, + { + "text": "The null space is only one dimensional." + }, + { + "text": "So there's a matrix, my, this A or the original A, that are not diagonalizable." + }, + { + "text": "I can't, I can't find two independent eigenvectors, there's only one." + }, + { + "text": "OK." + }, + { + "text": "So that's the case that I'm, that's a case that I, I'm not really handling." + }, + { + "text": "For example, when I wrote down up here that the powers went to zero if the eigenvalues were below one, I didn't really handle that case of repeated eigenvalues because my reasoning was based on this formula." + }, + { + "text": "And this formula is based on n independent eigenvectors." + }, + { + "text": "OK." + }, + { + "text": "So just to say that." + }, + { + "text": "There are some matrices that we don't cover through diagonalization, but the great majority we do." + }, + { + "text": "OK. And we're always OK if we have different distinct eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk12.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..77d090704cc298475d94416b7ecb88a2a015a913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. That's the, like, the typical case." + }, + { + "text": "Because for each eigenvalue there's at least one eigenvector, the algebraic multiplicity here is one for every eigenvalue, and the geometric multiplicity is one." + }, + { + "text": "There's one eigenvector and they are independent." + }, + { + "text": "OK. OK. Now let me come back to the important case when we're OK." + }, + { + "text": "The important case when we are diagonalizing." + }, + { + "text": "Let me look at, so let me solve this equation." + }, + { + "text": "The equation will be each, I start with some, start with a given vector u0." + }, + { + "text": "And then my equation is that every step I multiply what I have by a." + }, + { + "text": "That equation ought to be simple to handle." + }, + { + "text": "OK. And I'd like to be able to solve it." + }, + { + "text": "How would I find, if I start with a vector u0, and I multiply by a a hundred times, what have I got?" + }, + { + "text": "Well, I can certainly write down a formula for the answer." + }, + { + "text": "So what, what, so u1 is a u0." + }, + { + "text": "And u2 is, what's u2 then?" + }, + { + "text": "U2 I multiply it, u2 I get from u1 by another, multiplying by a, so I've got a twice." + }, + { + "text": "And my formula is uk, after k steps, I've multiplied by a k times the original u0." + }, + { + "text": "You see what I'm doing?" + }, + { + "text": "The next section is going to solve systems of differential equations." + }, + { + "text": "I'm going to have derivatives." + }, + { + "text": "This, this section is the nice one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk13.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..ba8214d8c636e4757a266d6617801174bc939d80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "It solves difference equations." + }, + { + "text": "I would call that a difference equation." + }, + { + "text": "It's conne- a first order." + }, + { + "text": "I would call that a first order system, because it connects only, it only goes up one level." + }, + { + "text": "And it's a system because these are vectors and that's a matrix." + }, + { + "text": "And the solution is just that." + }, + { + "text": "OK." + }, + { + "text": "But, that's a nice formula." + }, + { + "text": "That's the, like, the most compact formula I could ever get." + }, + { + "text": "U one hundred would be a to the one hundredth u0." + }, + { + "text": "But how would I actually find u one hundred?" + }, + { + "text": "How would I find, how would I discover what u one hundred is?" + }, + { + "text": "Let me, let me show you how." + }, + { + "text": "Here, here's the idea." + }, + { + "text": "If, so, to solve, to really solve, shall I say, to really solve." + }, + { + "text": "To really solve it, I would take this initial vector, u0, and I would write it as a combination of eigenvectors." + }, + { + "text": "To really solve, write, write u0 as a combination, say, certain amount of the first eigenvector plus a certain amount of the second eigenvector plus a certain amount of the last eigenvector." + }, + { + "text": "Now multiply by a." + }, + { + "text": "You want to, you got to see the magic of eigenvectors work." + }, + { + "text": "Multiply by a." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk14.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7843b2bf0cac762d1c12452cf36500ea4ad13370 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a u0 is what?" + }, + { + "text": "So a times that." + }, + { + "text": "A times, so what's, I can separate it out into n separate pieces and that's the whole point." + }, + { + "text": "That each of those pieces is going in its own merry way." + }, + { + "text": "Each of those pieces is an eigenvector, and when I multiply by a, what does this piece become?" + }, + { + "text": "So that's some amount of the first, let's suppose the eigenvectors are normalized to be unit vectors." + }, + { + "text": "So that says what the eigenvector is." + }, + { + "text": "It's, and I need some multiple of it to produce u0." + }, + { + "text": "OK. Now when I multiply by a, what do I get?" + }, + { + "text": "I get c1, which is just a factor, times a x1, but a x1 is lambda one x1." + }, + { + "text": "When I multiply this by a, I get c2 lambda two x2." + }, + { + "text": "And here I get cn lambda n xn." + }, + { + "text": "And suppose I multiply by a to the hundredth power now." + }, + { + "text": "Can we, can we, having done it, multiplied by a, let's multiply by a to the hundredth." + }, + { + "text": "What happens to this first term when I multiply by a to the one hundredth?" + }, + { + "text": "It's got that factor lambda to the hundredth." + }, + { + "text": "That's the key." + }, + { + "text": "That, that's what I mean by going its own merry way." + }, + { + "text": "It, it is pure eigenvector, it's exactly in a direction where multiplication by a just brings in a scalar factor lambda one." + }, + { + "text": "So a hundred times brings in this a hundred times." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk15.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7ee3348735378aa4049d33ec2a197d0ceb0c447c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Hundred times lambda two, hundred times lambda n. Actually, we're, what are we seeing here?" + }, + { + "text": "We're seeing, this same, lambda, capital lambda to the hundredth, as in the, as in the diagonalization, and we're seeing the S matrix, the matrix S of eigenvectors." + }, + { + "text": "That's what this has got to, this has got to amount to, a lambda to the hundredth power times an S times this vector C that's telling us how much of each one is in the original thing." + }, + { + "text": "So if, if I had to really find the hundredth power, I would take u0, I would expand it as a combination of eigenvectors, this is really S, the eigenvector matrix times C, the, the coefficient vector." + }, + { + "text": "And then I would immediately, then, by inserting these hundredth powers of eigenvalues, I'd have the answer." + }, + { + "text": "So the, the, huh, there must be, well, let's see." + }, + { + "text": "OK." + }, + { + "text": "It's, so, yeah." + }, + { + "text": "So if u100 is a to the hundredth times u0, and u0 is Sc, then you see this formula is just this formula, which is the way I would actually get hold of this, of this u100, which is, let me put it here, u100." + }, + { + "text": "The way I would actually get hold of that, see what, what the solution is after a hundred steps, would be expand the initial vector into eigenvectors and, and let each eigenvector go its own way, multiplying by a hundred at, by lambda at every step, and therefore by lambda to the hundredth power after a hundredth step." + }, + { + "text": "Can I do an example?" + }, + { + "text": "So that's, that's the, the formulas." + }, + { + "text": "Now let me take an example." + }, + { + "text": "I'll use the Fibonacci sequence as an example." + }, + { + "text": "So, so Fibonacci example." + }, + { + "text": "You remember the Fibonacci numbers?" + }, + { + "text": "If we start with one and one as F0, oh, I think I start with zero, maybe." + }, + { + "text": "Let zero and one be the first ones." + }, + { + "text": "So there's F0 and F1, the first two Fibonacci numbers." + }, + { + "text": "Then what's the rule for Fibonacci numbers?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk16.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..79c65e32781f7f304b504a6c390247abb9d26ac8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "They're the sum." + }, + { + "text": "The next one is the sum of those, so it's one." + }, + { + "text": "The next one is the sum of those, so it's two." + }, + { + "text": "The next one is the sum of those, so it's three." + }, + { + "text": "Well, it looks like one, two, three, four, five, but somehow it's not going to do that way." + }, + { + "text": "The next one is five, right." + }, + { + "text": "Two and three makes five." + }, + { + "text": "The next one is eight." + }, + { + "text": "The next one is thirteen." + }, + { + "text": "And the one hundredth Fibonacci number is what?" + }, + { + "text": "That's my question." + }, + { + "text": "How could I get a formula for the hundredth number and for example how could I answer the question how fast are they growing?" + }, + { + "text": "How fast are those Fibonacci numbers growing?" + }, + { + "text": "They're certainly growing." + }, + { + "text": "It's not a stable case, whatever the eigenvalues of whatever matrix it is, they're not smaller than one." + }, + { + "text": "These numbers are growing." + }, + { + "text": "But how fast are they growing?" + }, + { + "text": "The answer is lies in the eigenvalue." + }, + { + "text": "So I've got to find the matrix, so let me write down the Fibonacci rule, F k plus two is F k plus one plus F k, right?" + }, + { + "text": "Now that's not in my -- I want to write that as U k plus one and A U k. But right now what I've got is a single equation, not a system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk17.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b3aaa9dcee3cf27c112015659bb5a0b51a983ce1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's second order." + }, + { + "text": "It's like having a second order differential equation with second derivatives." + }, + { + "text": "I want to get first derivatives." + }, + { + "text": "Here I want to get first difference." + }, + { + "text": "So the way to do it is to introduce U k will be a vector." + }, + { + "text": "See, a small trick." + }, + { + "text": "Let U k be a vector, F k plus one and F k. So I'm going to get a two by two system, first order, instead of a one, instead of a scalar system, second order, by a simple trick." + }, + { + "text": "I'm just going to add in an equation F k plus one equals F k plus one." + }, + { + "text": "That will be my second equation." + }, + { + "text": "Then this is my system, this is my unknown, and what's my one-step equation?" + }, + { + "text": "So now U k plus one." + }, + { + "text": "That's so U k plus one is the left side, and what have I got here on the right side?" + }, + { + "text": "I've got some matrix multiplying U k. Can you see that all right?" + }, + { + "text": "If you can see it, then you can tell me what the matrix is." + }, + { + "text": "You see that I'm taking my system here, I artificially made it into a system." + }, + { + "text": "I artificially made the unknown into a vector, and now I'm ready to look at and see what the matrix is." + }, + { + "text": "So do you see the left side, U k plus one is F k plus two F k plus one, that's just what I want." + }, + { + "text": "On the right side, this, remember, this U k here, let me for the moment put it as F k plus one F k. So what's the matrix?" + }, + { + "text": "Well, that has a one and a one, and that has a one and a zero." + }, + { + "text": "There's the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk18.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..6c1b68c2cb2fde3f5dea82f3100d4da31fcce70a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "You see that that gives me the right-hand side." + }, + { + "text": "So there's the matrix A, and this is our friend U k. So we've got, so that simple trick changed the second order scalar problem to a first order system, two, with two unknowns." + }, + { + "text": "With a matrix and now what do I do?" + }, + { + "text": "Well, before I even think, I find its eigenvalues and eigenvectors." + }, + { + "text": "So what are the eigenvalues and eigenvectors of that matrix?" + }, + { + "text": "Let's see." + }, + { + "text": "I was, first let me just, like, think for a minute." + }, + { + "text": "It's two by two, so this shouldn't be impossible to do." + }, + { + "text": "Let's do it." + }, + { + "text": "OK." + }, + { + "text": "So my matrix again is one one one zero." + }, + { + "text": "It's symmetric, by the way." + }, + { + "text": "So what I will eventually know about symmetric matrices is that the eigenvalues will come out real, I won't get any complex numbers here, and the eigenvectors, once I get those, actually will be orthogonal." + }, + { + "text": "But two by two, I'm more interested in what the actual numbers are." + }, + { + "text": "What do I know about the two numbers?" + }, + { + "text": "Well, should, do you want me to find this determinant of A minus lambda I?" + }, + { + "text": "Sure." + }, + { + "text": "So it's the determinant of one minus lambda one one zero, right?" + }, + { + "text": "Minus lambda, yes, got it." + }, + { + "text": "OK. OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk19.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..a73b23e3d56b889ff49ea7f55a784fac33e13c3d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "There'll be two eigenvalues." + }, + { + "text": "Well, tell me again what I know about the two eigenvalues before I go any further." + }, + { + "text": "Tell me something about these two eigenvalues, what do they add up to?" + }, + { + "text": "Lambda one plus lambda two is the same as the trace down the diagonal of the matrix, one and zero is one." + }, + { + "text": "So lambda one plus lambda two should come out to be one, and lambda one times lambda two should come out to be the determinant, which is minus one." + }, + { + "text": "So I'm expecting the eigenvalues to add to one and to multiply to minus one." + }, + { + "text": "But let's just see it happen here." + }, + { + "text": "If I multiply this out, I get that times that'll be a lambda squared minus lambda minus one." + }, + { + "text": "Good." + }, + { + "text": "Lambda squared minus lambda minus one." + }, + { + "text": "Actually, you see the, compare that with the original equation that I started with." + }, + { + "text": "Fk plus two minus Fk plus one minus Fk is zero." + }, + { + "text": "The recurrent, the recursion that the Fibonacci number satisfy is somehow showing up directly here for the eigenvalues when we set that to zero." + }, + { + "text": "OK. Let's solve." + }, + { + "text": "Well, I would like to be able to factor that, that quadratic, but I'm better off to use the quadratic formula." + }, + { + "text": "Lambda is, let's see, minus b is one, plus or minus the square root of b squared, which is one, minus four, times that, times that, which is plus four, over two." + }, + { + "text": "So that's the square root of five." + }, + { + "text": "So the eigenvalues are lambda one is one half of one plus square root of five, and lambda two is one half of one minus square root of five." + }, + { + "text": "And sure enough, they, those add up to one, and they multiply to give minus one." + }, + { + "text": "OK. Those are the two eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk2.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..43cfb012fc04a89fc7dab94c23bfb0f50ade3782 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "On the right, it's multiplied by, if I want, if I want lambda n xn in the last column, how do I do it?" + }, + { + "text": "Well, the last column here will be, I'll, I'll take the last column, use these coefficients, put the lambda n down there, and it will multiply that nth column and give me lambda n xn." + }, + { + "text": "There, there you see matrix multiplication just working for us." + }, + { + "text": "So I started with A s. I wrote down what it meant." + }, + { + "text": "A times each eigenvector." + }, + { + "text": "That gave me lambda times the eigenvector." + }, + { + "text": "And then when I peeled off the lambdas, they were on the right-hand side, so I've got s, my matrix back again, and this matrix, this diagonal matrix, the eigenvalue matrix, and I call it capital lambda, using capital letters for matrices, and lambda to prompt me that it's, that it's eigenvalues that are in there." + }, + { + "text": "So you see that the eigenvalues are just sitting down that diagonal?" + }, + { + "text": "If I had a column x2 here, I would want the lambda two in the two two position, in the diagonal position, to multiply that x2 and give me the lambda two x2." + }, + { + "text": "That's my formula." + }, + { + "text": "A s is s lambda." + }, + { + "text": "OK. That's, that's the, you see, it's just a calculation." + }, + { + "text": "Now, I, I mentioned, and I have to mention again, this business about n independent eigenvectors." + }, + { + "text": "As it stands, this is all fine whether, I mean, I could be repeating the same eigenvector, but I, I'm no interested in that." + }, + { + "text": "I want to be able to invert s, and that's where this comes in." + }, + { + "text": "This n independent eigenvectors business comes in to tell me that that matrix is invertible." + }, + { + "text": "So let me, on the next board, write down what I've got." + }, + { + "text": "A s equals s lambda." + }, + { + "text": "And now I'm, I can multiply on the left by s inverse." + }, + { + "text": "So this is really, I can do that provided s is invertible, provided my assumption of n independent eigenvectors is satisfied." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk20.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ad5a59fa5db44ce73ff5f88190423e0404fb3d39 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "How, how, what are those numbers approximately?" + }, + { + "text": "Square root of five, well, it's more than two, but less than three." + }, + { + "text": "It, it'd be nice to know these numbers." + }, + { + "text": "I think, I think that that, so that number comes out bigger than one, right?" + }, + { + "text": "Yeah, that's right." + }, + { + "text": "This number comes out bigger than one." + }, + { + "text": "It's about one point six one eight or something." + }, + { + "text": "Not exactly." + }, + { + "text": "It's supposed to be one point six." + }, + { + "text": "Just, like, I think so." + }, + { + "text": "Then what's lambda two?" + }, + { + "text": "Is, is lambda two positive or negative?" + }, + { + "text": "Negative, right?" + }, + { + "text": "Because I'm, it's obviously negative, and I knew that the, so it's minus, and they add up to one, so minus point six one eight, I guess." + }, + { + "text": "OK. And some order." + }, + { + "text": "Those are the two eigenvalues." + }, + { + "text": "One eigenvalue bigger than one, one eigenvalue smaller than one." + }, + { + "text": "Actually, that's a great situation to be in." + }, + { + "text": "Of course, the eigenvalues are different, so there's no doubt whatever, is this matrix diagonalizable?" + }, + { + "text": "Is this matrix diagonalizable, that original matrix A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk21.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..4a034475591d371995b379b5f98783a2cfb25870 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Sure." + }, + { + "text": "We've got two distinct eigenvalues and we can find the eigenvectors in a moment." + }, + { + "text": "But they'll be independent, will be diagonalizable, and now you can already answer my very first question." + }, + { + "text": "How fast are those Fibonacci numbers increasing?" + }, + { + "text": "How, those, they're increasing, right?" + }, + { + "text": "They're not doubling at every step." + }, + { + "text": "Let's look again at these numbers." + }, + { + "text": "Five eight thirteen, it's not obvious." + }, + { + "text": "The next one would be twenty one thirty four." + }, + { + "text": "So to get some idea of what F one hundred is, can you give me any, I mean the crucial number of, so it, these, it's approximately, what's controlling the growth of these Fibonacci numbers?" + }, + { + "text": "It's the eigenvalues." + }, + { + "text": "And which eigenvalues controlling that growth?" + }, + { + "text": "The big ones." + }, + { + "text": "So F one hundred will it be approximately some constant, c one, I guess, times this lambda one, this one plus square root of five over two, to the hundredth power." + }, + { + "text": "And the two hundredth have, in other words, the eigenvalue, the Fibonacci numbers are growing by about that factor." + }, + { + "text": "You see that we've got precise information about the, about the Fibonacci numbers out of the eigenvalue." + }, + { + "text": "OK. And again, why is that true?" + }, + { + "text": "Let me go over to this board and show what I'm doing here." + }, + { + "text": "The, the original eigen, the original initial value is some combination of eigenvectors, and then when we start multiple, when we start going out the theory of Fibonacci numbers, when we start multiplying by a hundred times, it's this lambda one to the hundredth, this term is, is the one that's taken over." + }, + { + "text": "It's, I mean, that's big, like, one point six to the hundredth power." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk22.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..c13a1fc9867173c3067e46c469cfff27b9b45289 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "The second term is practically nothing, right?" + }, + { + "text": "The point six, or minus point six to the hundredth power, is an extremely small, extremely small number." + }, + { + "text": "So this is, this, this, there are only two terms, because we're two by two." + }, + { + "text": "This number is, this piece of it is there, but it's, it's disappearing." + }, + { + "text": "Where this piece is there and it's growing and controlling everything." + }, + { + "text": "So, so really the, we're doing, like, problems that are evolving." + }, + { + "text": "We're doing dynamics." + }, + { + "text": "Instead of Ax equal b, that's a static problem." + }, + { + "text": "We're now, we're doing dynamics." + }, + { + "text": "A, a squared, a cubed, things are evolving in time, and the eigenvalues are the crucial, numbers." + }, + { + "text": "OK." + }, + { + "text": "I guess to complete this, I better write down the eigenvectors." + }, + { + "text": "So we should complete the, the whole process by finding the eigenvectors." + }, + { + "text": "OK. Well, I have to, up in the corner, then I have to look at A minus lambda I." + }, + { + "text": "So A minus lambda I is this one minus lambda, one, one, and minus lambda." + }, + { + "text": "And now, can we spot an eigenvector out of that?" + }, + { + "text": "That's, for these two lambdas, this matrix is singular." + }, + { + "text": "I guess the eigenvector, two by two ought to be easy." + }, + { + "text": "So if I know that this matrix is singular, then it seems to me the eigenvector has to be lambda and one, because that multiplication will give me the zero." + }, + { + "text": "And this multiplication gives me, better give me also zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk23.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..df816eb800ce767b1475c279a24ad976bb45a785 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Do you see why it does?" + }, + { + "text": "This is the minus lambda squared plus lambda plus one." + }, + { + "text": "It's the thing that's zero, because these lambdas are special." + }, + { + "text": "There's the eigenvector." + }, + { + "text": "X1 is lambda one, one, and x2 is lambda two, one." + }, + { + "text": "I did that as a little trick that was available in the two by two case." + }, + { + "text": "So now I finally have to, oh, I have to take the initial, u0." + }, + { + "text": "So to complete this example entirely, I have to say, OK, what was u0?" + }, + { + "text": "u0 was f1 f0." + }, + { + "text": "So u0, the starting vector, is f1 f0, and those were one and zero." + }, + { + "text": "So I have to use that vector, so I have to look for, from multiple of the first eigenvector and the second, to produce u0, the one zero vector." + }, + { + "text": "This is what will find c1 and c2, and then I'm done." + }, + { + "text": "So let me, instead of in the last five seconds grinding out a formula, let me repeat the idea." + }, + { + "text": "That really, it's the idea that's central." + }, + { + "text": "When things are evolving in time, let me come back to this board, because the ideas are here." + }, + { + "text": "When things are evolving in time by a first-order system, starting from an original u0, the key is, find the eigenvalues and eigenvectors of A." + }, + { + "text": "That will tell, those eigenvectors, the eigenvalues will already tell you what's happening." + }, + { + "text": "Is the solution blowing up?" + }, + { + "text": "Is it going to zero?" + }, + { + "text": "What's it doing?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk24.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..40301cb90760e2172baa94d536cbc13288d4c31f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk24.json @@ -0,0 +1,20 @@ +[ + { + "text": "And then, to find out exactly a formula, you have to take your u0 and write it as a combination of eigenvectors and then follow each eigenvector separately." + }, + { + "text": "And that's really what this formula, the formula for, that's what the formula for A to the k is doing." + }, + { + "text": "So remember that formula for A to the k is S, lambda to the k S inverse." + }, + { + "text": "OK. That's, that's difference equations, and you just have to, so the homework will give some examples different from Fibonacci to follow through." + }, + { + "text": "And next time will be differential equations." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk3.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..9bf1bb852baadc1da7837e14180c0c2951a30882 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I mentioned at the end of last time, and I'll say again, that there's a small number of matrices for, that don't have n independent eigenvectors." + }, + { + "text": "So I've got to discuss that, that technical point." + }, + { + "text": "But the great, the most matrices that we see have n, n independent eigenvectors and we can diagonalize." + }, + { + "text": "This is diagonalization." + }, + { + "text": "I could also write it, and I often will, the other way round." + }, + { + "text": "If I multiply on the right by s inverse, if I took this equation at the top and multiplied on the right by s inverse, I could, I would have A left here." + }, + { + "text": "Now s inverse is coming from the right." + }, + { + "text": "So can you keep those two straight?" + }, + { + "text": "A multiplies its eigenvectors." + }, + { + "text": "That's how I keep them straight." + }, + { + "text": "So A multiplies s. A multiplies s. And then this s inverse makes the whole thing diagonal." + }, + { + "text": "And this is another way of saying the same thing, putting the s's on the other side of the equation, A is s lambda s inverse." + }, + { + "text": "So that's the, that's the new factorization." + }, + { + "text": "That's the replacement for L U from elimination or Q R from Gram-Schmidt." + }, + { + "text": "And notice that the matrix, so it's, it's a matrix times a diagonal matrix times the inverse of the first one." + }, + { + "text": "It's, that's the combination that we'll see throughout this chapter." + }, + { + "text": "This, this, combination with an s and an s inverse." + }, + { + "text": "OK. Can I just begin to use that?" + }, + { + "text": "For example, what about A squared?" + }, + { + "text": "What are the eigenvalues and eigenvectors of A squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk4.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c687b6948acad76de8781cb82d3eb069c9da514e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's a straightforward question with a, with a absolutely clean answer." + }, + { + "text": "So let me, let me consider A squared." + }, + { + "text": "So I look, I start with Ax equal lambda x." + }, + { + "text": "And I'm headed for A squared." + }, + { + "text": "So let me multiply both sides by A." + }, + { + "text": "That's one way to get A squared on the left." + }, + { + "text": "So if, I should write these ifs in here." + }, + { + "text": "If Ax equals lambda x, then I multiply by A." + }, + { + "text": "So I get A squared x equals, well, I'm multiplying by A, so that's lambda Ax." + }, + { + "text": "That lambda was a number, so I just put it on the left." + }, + { + "text": "And what do I, tell me how to make that look better." + }, + { + "text": "What have I got here?" + }, + { + "text": "For, if, if A has the eigenvalue lambda and eigenvector x, what's up with A squared?" + }, + { + "text": "A squared x, I just multiply by A, but now for Ax, I'm going to substitute lambda x, so I've got lambda squared x." + }, + { + "text": "So from that simple calculation, I, my conclusion is that the eigenvalues of A squared are lambda squared." + }, + { + "text": "And the eigenvectors, I always think about both of those." + }, + { + "text": "What can I say about the eigenvalues?" + }, + { + "text": "They're squared." + }, + { + "text": "What can I say about the eigenvectors?" + }, + { + "text": "They're the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk5.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5bf15e20707c156c8ae71c9c7acea41a9d9d8e46 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same x as in, as for A." + }, + { + "text": "Now, let me see that also from this formula." + }, + { + "text": "How can I see what A squared is looking like from this formula?" + }, + { + "text": "So let me, that, that was one way to do it." + }, + { + "text": "Let me do it by just taking A squared from that." + }, + { + "text": "A squared is S lambda S inverse, that's A, times S lambda S inverse, that's A, which is?" + }, + { + "text": "This is the beauty of eigenvalues, eigenvectors, having that S inverse and S is the identity, so I've got S lambda squared S inverse." + }, + { + "text": "Yes." + }, + { + "text": "You see what that's telling me?" + }, + { + "text": "It's, it's telling me the same thing that I just learned here, but in the, in, in a matrix form." + }, + { + "text": "It's telling me that the S is the same, the eigenvectors are the same, but the eigenvalues are squared, because this is, what's lambda squared, that's still diagonal, it's got little lambda one squared, lambda two squared, down to lambda n squared, on that diagonal, those are the eigenvalues, as we just learned, of A squared." + }, + { + "text": "OK." + }, + { + "text": "So, somehow those eigenvalues and eigenvectors are really giving you a way to, to, to, to see what's going on inside a matrix." + }, + { + "text": "Now, of course, I can continue that for, to the k-th power." + }, + { + "text": "A to the k-th power." + }, + { + "text": "If I multiply, if I have k of these together, do you see how S inverse S will keep cancelling?" + }, + { + "text": "In the, in the inside, I'll have the S outside, at the far left, and lambda will be in there k times and S inverse." + }, + { + "text": "So what's that telling me?" + }, + { + "text": "That's telling me that the eigenvalues of A, of A to the k-th power are the k-th powers." + }, + { + "text": "The eigenvalues of A cubed are the cubes of the eigenvalues of A, and the eigenvectors are the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk6.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..c18dddbe798022f7e68278ac002a3f5fe6ed249e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same." + }, + { + "text": "OK." + }, + { + "text": "In other words, eigenvalues and eigenvectors give a great way to understand the powers of a matrix." + }, + { + "text": "If I take the square of a matrix or the hundredth power of a matrix, the pivots are all over the place." + }, + { + "text": "L U, if I multiply L U times L U times L U times L U a hundred times, I've got a hundred L U's." + }, + { + "text": "I can't do anything with them." + }, + { + "text": "But when I multiply S lambda S inverse by itself, when I look at the eigenvector picture a hundred times, I get a hundred or ninety-nine of these guys cancelling out inside, and I get A to the hundredth is S lambda to the hundredth S inverse." + }, + { + "text": "I mean, eigenvalues tell you about powers of a matrix in a way that we had no, no way to approach previously." + }, + { + "text": "For example, when does, when do the powers of a matrix go to zero?" + }, + { + "text": "I would call that matrix stable, maybe." + }, + { + "text": "So, so, so I could write down a, a theorem." + }, + { + "text": "I'll, I'll write it as a theorem, just to use that word to emphasize that here I'm getting this great fact from this eigenvalue picture." + }, + { + "text": "OK. A to the k approaches zero as k goes, as k gets bigger." + }, + { + "text": "If what?" + }, + { + "text": "What's the, how can I tell for a matrix A if its powers go to zero?" + }, + { + "text": "What, what's somewhere inside that matrix is that information." + }, + { + "text": "That information is not present in the pivots." + }, + { + "text": "It's present in the eigenvalues." + }, + { + "text": "What do I need for the, to know that if I take higher and higher powers of A that this matrix gets smaller and smaller?" + }, + { + "text": "Well, S and S inverse are not moving." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk7.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b84a5c854a5542758e8a0107e1ff043205fe3bdb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's this guy that has to get small, and that's easy to, easy to understand." + }, + { + "text": "The requirement is all eigenvalues, so what is the requirement?" + }, + { + "text": "The eigenvalues have to be less than one." + }, + { + "text": "Now, I have to write that absolute value, because those eigenvalues could be negative, they could be complex numbers." + }, + { + "text": "So I'm taking the absolute value if all of those are below one." + }, + { + "text": "That's, in fact, we practically see why." + }, + { + "text": "Let me just say that I, that I, I'm operating on one assumption here, and I got to keep remembering that that assumption is still present." + }, + { + "text": "That assumption was that I had a full set of, of n independent eigenvectors." + }, + { + "text": "If I don't have that, then I, I, then this approach is not working." + }, + { + "text": "So, so again, a pure eigenvalue approach, eigenvector approach, needs n independent eigenvectors." + }, + { + "text": "If we don't have n independent eigenvectors, we can't diagonalize the matrix." + }, + { + "text": "We can't get to a diagonal matrix." + }, + { + "text": "This, this, this diagonalization is only possible if S inverse makes sense." + }, + { + "text": "OK. Can I, can I follow up on that point now?" + }, + { + "text": "So, so you see why, what we get and, and why we want it, because we get information about the powers of a matrix just immediately from the eigenvalues." + }, + { + "text": "OK, now let me follow up on this, business of which matrices are diagonalizable." + }, + { + "text": "Sorry about that long word." + }, + { + "text": "So a matrix is, is sure to, so here's, here's the main point." + }, + { + "text": "A is sure to be, to have n independent eigenvectors and, and B, now here comes that word, diagonalizable, if, if, so we, we, we might as well get the, the nice case out in the open." + }, + { + "text": "The nice case is when, if all the lambdas are different." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk8.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f06dcec8ffa0ee1bf19440e4ab2194db33ab353b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means, that means no repeated eigenvalues." + }, + { + "text": "OK. That's the nice case." + }, + { + "text": "If, if my matrix and most matrix, if I do a random matrix in MATLAB and compute its eigenvalues, so if I computed, if I took I of rand of ten ten, gave, gave that MATLAB command, the, we'd get a random ten by ten matrix, we would get a list of its ten eigenvalues and they would be different." + }, + { + "text": "They would be distinct, is the best word." + }, + { + "text": "I would have a random matrix will have ten distinct, a ten by ten matrix will have ten distinct eigenvalues, and if it does, the eigenvectors are automatically independent." + }, + { + "text": "So that's a nice fact." + }, + { + "text": "I can, I'll refer you to the text for the proof." + }, + { + "text": "That, that A is sure to have n independent eigenvectors if the eigenvalues are different." + }, + { + "text": "If, if all the, if all eigenvalues are different." + }, + { + "text": "It's just, if some lambdas are repeated, then I have to look more closely." + }, + { + "text": "If an eigenvalue is repeated, I have to look, I have to count, I have to check." + }, + { + "text": "Has it got, say it's repeated three times." + }, + { + "text": "So what's a possibility for, so, so here's, here's the repeated possibility." + }, + { + "text": "And, and let me emphasize the conclusion." + }, + { + "text": "That if I have repeated eigenvalues, I may or may not, I may or may not have, have n independent eigenvectors." + }, + { + "text": "I might." + }, + { + "text": "I, I, you know, this isn't a completely negative case." + }, + { + "text": "The identity matrix." + }, + { + "text": "Well, suppose I take the ten by ten identity matrix." + }, + { + "text": "What are the eigenvalues of that matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk9.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..87d2a2ae5773036cf11800e2f1962908986a0dad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_2_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So just, just take the easiest matrix, the identity." + }, + { + "text": "If I look for its eigenvalues, they're all ones." + }, + { + "text": "So that eigenvalue one is repeated ten times." + }, + { + "text": "But there's no shortage of eigenvectors for the identity matrix." + }, + { + "text": "In fact, every vector is an eigenvector." + }, + { + "text": "So I can take ten independent vectors." + }, + { + "text": "Oh, well, what happens to everything if, if, if A is the identity matrix, let's just think that one through in our head." + }, + { + "text": "If A is the identity matrix, then it's got plenty of eigenvectors." + }, + { + "text": "I choose ten independent vectors, they're the columns of S, and, and what do I get from S inverse A S?" + }, + { + "text": "I get I again, right?" + }, + { + "text": "If A is the identity, and of course, that's the correct lambda." + }, + { + "text": "The, the matrix was already diagonal." + }, + { + "text": "So if the matrix is already diagonal, then the, the lambda is the same as the matrix." + }, + { + "text": "A diagonal matrix has got its eigenvalues sitting right there in front of you." + }, + { + "text": "Now if it's triangular, the eigenvalues are still sitting there, but so let's, let's take a case where, it's triangular." + }, + { + "text": "Suppose A is like, two, one, two, zero." + }, + { + "text": "So there's a case that's going to be trouble." + }, + { + "text": "There's a case that's going to be trouble." + }, + { + "text": "First of all, what are the eigen- I mean, we just, like now you, if we start with a matrix, the first thing we do practically without thinking is compute the eigenvalues and eigenvectors." + }, + { + "text": "OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk0.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6898d4fe66019ef6b40d0472ea94a968e7bbde9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, shall we start?" + }, + { + "text": "This is the second lecture on eigenvalues." + }, + { + "text": "So the first lecture was set -- reached the key equation, Ax equal lambda x. x is the eigenvector and lambda is the eigenvalue." + }, + { + "text": "Now, to use that." + }, + { + "text": "And the good way to, after we've found, so job one is to find the eigenvalues and find the eigenvectors." + }, + { + "text": "Now after we found them, what do we do with them?" + }, + { + "text": "Well, the good way to see that is diagonalize the matrix." + }, + { + "text": "So the matrix is A, and I want to show, first of all, this is like the basic fact." + }, + { + "text": "This, this formula." + }, + { + "text": "That's, that's the key to today's lecture." + }, + { + "text": "This matrix A, I put its eigenvectors in the columns of a matrix S. So S will be the eigenvector matrix, and I want to look at this magic combination S inverse A S. So can I show you how that, how that, what happens there?" + }, + { + "text": "And notice, notice, there's an S inverse." + }, + { + "text": "We have to be able to invert this eigenvector matrix S. So for that we need n independent eigenvectors." + }, + { + "text": "So that's the, that's the case." + }, + { + "text": "OK." + }, + { + "text": "So suppose we have n linearly independent eigenvectors of A." + }, + { + "text": "Put them in the columns of this matrix S. So I'm naturally going to call that the eigenvector matrix, because it's got the eigenvectors in its columns." + }, + { + "text": "And all I want to do is show you what happens when you multiply A times S. So A times S. So this is A times the matrix with the first eigenvector in its first column, the second eigenvector in its second column, the nth eigenvector in its nth column." + }, + { + "text": "And how am I going to do this matrix multiplication?" + }, + { + "text": "Well, certainly I'll do it a column at a time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk1.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..fbe078217bb68baea8e0605a5d04be568c49efbf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I get?" + }, + { + "text": "A times the first column gives me the first column of the answer, but what is it?" + }, + { + "text": "That's an eigenvector." + }, + { + "text": "A times x1 is equal to the lambda times the x1." + }, + { + "text": "And that lambda's we'll call lambda one, of course." + }, + { + "text": "So that's the first column, A x1 is the same as lambda one x1." + }, + { + "text": "A x2 is lambda two x2, so on, along to, in the nth column, we now have lambda n xn." + }, + { + "text": "Looking good, but the next step is even better." + }, + { + "text": "So for the next step, I want to separate out those eigenvalues, those multiplying numbers, from the x's." + }, + { + "text": "So then I'll have just what I want." + }, + { + "text": "OK, so how, how am I going to separate out?" + }, + { + "text": "So that, that number lambda one is multiplying the first column." + }, + { + "text": "So if I want to factor it out of the first column, I better put, here is going to be x1, and that's going to multiply this matrix lambda one in the first entry in all zeros." + }, + { + "text": "You see that that, that's going to come out right for the first column?" + }, + { + "text": "Because we remember how, how we're going back to that original punchline, that if I want a number to multiply x1, then I can do it by putting x1 in that column, in the first column, and putting that number there." + }, + { + "text": "What am I going to have here?" + }, + { + "text": "I'm going to have lambda one, I'm going to have x1, x2, xn." + }, + { + "text": "These are going to be my columns again." + }, + { + "text": "I'm getting s back again." + }, + { + "text": "I'm getting s back again, but now what's it multiplied by?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk10.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c58a42edbe9567233ca7f57643a0b7d43ae6761f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what are the eigenvalues?" + }, + { + "text": "You can tell me right away what they are." + }, + { + "text": "They're two and two, right." + }, + { + "text": "It's a triangular matrix, so when I do this determinant, shall I do this determinant of A minus lambda I?" + }, + { + "text": "I'll get this two minus lambda, one, zero, two minus lambda, right?" + }, + { + "text": "I take that determinant, so I make those into vertical bars to mean determinant, and what's the determinant?" + }, + { + "text": "Two minus lambda squared." + }, + { + "text": "What are the roots?" + }, + { + "text": "Lambda equal two twice." + }, + { + "text": "So the eigenvalues are lambda equals two and two." + }, + { + "text": "OK, fine." + }, + { + "text": "Now the next step, find the eigenvectors." + }, + { + "text": "So I look for eigenvectors and what do I find for this guy?" + }, + { + "text": "Eigenvectors for this guy, when I subtract two minus the identity, so A minus two I has zeros here, and I'm looking for the null space." + }, + { + "text": "What's, what are the eigenvectors?" + }, + { + "text": "They're the, they're, they're the null space of A minus lambda I." + }, + { + "text": "The null space is only one dimension." + }, + { + "text": "This is a case where I don't have enough eigenvectors." + }, + { + "text": "My algebraic multiplicity is two." + }, + { + "text": "I, I would say when I see, when I count how often the eigenvalue is repeated, that's the algebraic multiplicity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk11.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..779c2cf904d904b761080db2671aac46394ad02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the multiplicity." + }, + { + "text": "How many times is it the root of the polynomial?" + }, + { + "text": "My polynomial is two minus lambda squared." + }, + { + "text": "It's a double root." + }, + { + "text": "So my algebraic multiplicity is two." + }, + { + "text": "But the geometric multiplicity, which looks for vectors, looks for eigenvectors and which means the null space of this thing." + }, + { + "text": "And the only eigenvector is one zero." + }, + { + "text": "That's in the null space." + }, + { + "text": "Zero one is not in the null space." + }, + { + "text": "The null space is only one dimensional." + }, + { + "text": "So there's a matrix, my, this A or the original A, that are not diagonalizable." + }, + { + "text": "I can't, I can't find two independent eigenvectors, there's only one." + }, + { + "text": "OK." + }, + { + "text": "So that's the case that I'm, that's a case that I, I'm not really handling." + }, + { + "text": "For example, when I wrote down up here that the powers went to zero if the eigenvalues were below one, I didn't really handle that case of repeated eigenvalues because my reasoning was based on this formula." + }, + { + "text": "And this formula is based on n independent eigenvectors." + }, + { + "text": "OK." + }, + { + "text": "So just to say that." + }, + { + "text": "There are some matrices that we don't cover through diagonalization, but the great majority we do." + }, + { + "text": "OK. And we're always OK if we have different distinct eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk12.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..77d090704cc298475d94416b7ecb88a2a015a913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. That's the, like, the typical case." + }, + { + "text": "Because for each eigenvalue there's at least one eigenvector, the algebraic multiplicity here is one for every eigenvalue, and the geometric multiplicity is one." + }, + { + "text": "There's one eigenvector and they are independent." + }, + { + "text": "OK. OK. Now let me come back to the important case when we're OK." + }, + { + "text": "The important case when we are diagonalizing." + }, + { + "text": "Let me look at, so let me solve this equation." + }, + { + "text": "The equation will be each, I start with some, start with a given vector u0." + }, + { + "text": "And then my equation is that every step I multiply what I have by a." + }, + { + "text": "That equation ought to be simple to handle." + }, + { + "text": "OK. And I'd like to be able to solve it." + }, + { + "text": "How would I find, if I start with a vector u0, and I multiply by a a hundred times, what have I got?" + }, + { + "text": "Well, I can certainly write down a formula for the answer." + }, + { + "text": "So what, what, so u1 is a u0." + }, + { + "text": "And u2 is, what's u2 then?" + }, + { + "text": "U2 I multiply it, u2 I get from u1 by another, multiplying by a, so I've got a twice." + }, + { + "text": "And my formula is uk, after k steps, I've multiplied by a k times the original u0." + }, + { + "text": "You see what I'm doing?" + }, + { + "text": "The next section is going to solve systems of differential equations." + }, + { + "text": "I'm going to have derivatives." + }, + { + "text": "This, this section is the nice one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk13.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..ba8214d8c636e4757a266d6617801174bc939d80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "It solves difference equations." + }, + { + "text": "I would call that a difference equation." + }, + { + "text": "It's conne- a first order." + }, + { + "text": "I would call that a first order system, because it connects only, it only goes up one level." + }, + { + "text": "And it's a system because these are vectors and that's a matrix." + }, + { + "text": "And the solution is just that." + }, + { + "text": "OK." + }, + { + "text": "But, that's a nice formula." + }, + { + "text": "That's the, like, the most compact formula I could ever get." + }, + { + "text": "U one hundred would be a to the one hundredth u0." + }, + { + "text": "But how would I actually find u one hundred?" + }, + { + "text": "How would I find, how would I discover what u one hundred is?" + }, + { + "text": "Let me, let me show you how." + }, + { + "text": "Here, here's the idea." + }, + { + "text": "If, so, to solve, to really solve, shall I say, to really solve." + }, + { + "text": "To really solve it, I would take this initial vector, u0, and I would write it as a combination of eigenvectors." + }, + { + "text": "To really solve, write, write u0 as a combination, say, certain amount of the first eigenvector plus a certain amount of the second eigenvector plus a certain amount of the last eigenvector." + }, + { + "text": "Now multiply by a." + }, + { + "text": "You want to, you got to see the magic of eigenvectors work." + }, + { + "text": "Multiply by a." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk14.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7843b2bf0cac762d1c12452cf36500ea4ad13370 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a u0 is what?" + }, + { + "text": "So a times that." + }, + { + "text": "A times, so what's, I can separate it out into n separate pieces and that's the whole point." + }, + { + "text": "That each of those pieces is going in its own merry way." + }, + { + "text": "Each of those pieces is an eigenvector, and when I multiply by a, what does this piece become?" + }, + { + "text": "So that's some amount of the first, let's suppose the eigenvectors are normalized to be unit vectors." + }, + { + "text": "So that says what the eigenvector is." + }, + { + "text": "It's, and I need some multiple of it to produce u0." + }, + { + "text": "OK. Now when I multiply by a, what do I get?" + }, + { + "text": "I get c1, which is just a factor, times a x1, but a x1 is lambda one x1." + }, + { + "text": "When I multiply this by a, I get c2 lambda two x2." + }, + { + "text": "And here I get cn lambda n xn." + }, + { + "text": "And suppose I multiply by a to the hundredth power now." + }, + { + "text": "Can we, can we, having done it, multiplied by a, let's multiply by a to the hundredth." + }, + { + "text": "What happens to this first term when I multiply by a to the one hundredth?" + }, + { + "text": "It's got that factor lambda to the hundredth." + }, + { + "text": "That's the key." + }, + { + "text": "That, that's what I mean by going its own merry way." + }, + { + "text": "It, it is pure eigenvector, it's exactly in a direction where multiplication by a just brings in a scalar factor lambda one." + }, + { + "text": "So a hundred times brings in this a hundred times." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk15.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7ee3348735378aa4049d33ec2a197d0ceb0c447c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Hundred times lambda two, hundred times lambda n. Actually, we're, what are we seeing here?" + }, + { + "text": "We're seeing, this same, lambda, capital lambda to the hundredth, as in the, as in the diagonalization, and we're seeing the S matrix, the matrix S of eigenvectors." + }, + { + "text": "That's what this has got to, this has got to amount to, a lambda to the hundredth power times an S times this vector C that's telling us how much of each one is in the original thing." + }, + { + "text": "So if, if I had to really find the hundredth power, I would take u0, I would expand it as a combination of eigenvectors, this is really S, the eigenvector matrix times C, the, the coefficient vector." + }, + { + "text": "And then I would immediately, then, by inserting these hundredth powers of eigenvalues, I'd have the answer." + }, + { + "text": "So the, the, huh, there must be, well, let's see." + }, + { + "text": "OK." + }, + { + "text": "It's, so, yeah." + }, + { + "text": "So if u100 is a to the hundredth times u0, and u0 is Sc, then you see this formula is just this formula, which is the way I would actually get hold of this, of this u100, which is, let me put it here, u100." + }, + { + "text": "The way I would actually get hold of that, see what, what the solution is after a hundred steps, would be expand the initial vector into eigenvectors and, and let each eigenvector go its own way, multiplying by a hundred at, by lambda at every step, and therefore by lambda to the hundredth power after a hundredth step." + }, + { + "text": "Can I do an example?" + }, + { + "text": "So that's, that's the, the formulas." + }, + { + "text": "Now let me take an example." + }, + { + "text": "I'll use the Fibonacci sequence as an example." + }, + { + "text": "So, so Fibonacci example." + }, + { + "text": "You remember the Fibonacci numbers?" + }, + { + "text": "If we start with one and one as F0, oh, I think I start with zero, maybe." + }, + { + "text": "Let zero and one be the first ones." + }, + { + "text": "So there's F0 and F1, the first two Fibonacci numbers." + }, + { + "text": "Then what's the rule for Fibonacci numbers?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk16.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..79c65e32781f7f304b504a6c390247abb9d26ac8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "They're the sum." + }, + { + "text": "The next one is the sum of those, so it's one." + }, + { + "text": "The next one is the sum of those, so it's two." + }, + { + "text": "The next one is the sum of those, so it's three." + }, + { + "text": "Well, it looks like one, two, three, four, five, but somehow it's not going to do that way." + }, + { + "text": "The next one is five, right." + }, + { + "text": "Two and three makes five." + }, + { + "text": "The next one is eight." + }, + { + "text": "The next one is thirteen." + }, + { + "text": "And the one hundredth Fibonacci number is what?" + }, + { + "text": "That's my question." + }, + { + "text": "How could I get a formula for the hundredth number and for example how could I answer the question how fast are they growing?" + }, + { + "text": "How fast are those Fibonacci numbers growing?" + }, + { + "text": "They're certainly growing." + }, + { + "text": "It's not a stable case, whatever the eigenvalues of whatever matrix it is, they're not smaller than one." + }, + { + "text": "These numbers are growing." + }, + { + "text": "But how fast are they growing?" + }, + { + "text": "The answer is lies in the eigenvalue." + }, + { + "text": "So I've got to find the matrix, so let me write down the Fibonacci rule, F k plus two is F k plus one plus F k, right?" + }, + { + "text": "Now that's not in my -- I want to write that as U k plus one and A U k. But right now what I've got is a single equation, not a system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk17.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b3aaa9dcee3cf27c112015659bb5a0b51a983ce1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's second order." + }, + { + "text": "It's like having a second order differential equation with second derivatives." + }, + { + "text": "I want to get first derivatives." + }, + { + "text": "Here I want to get first difference." + }, + { + "text": "So the way to do it is to introduce U k will be a vector." + }, + { + "text": "See, a small trick." + }, + { + "text": "Let U k be a vector, F k plus one and F k. So I'm going to get a two by two system, first order, instead of a one, instead of a scalar system, second order, by a simple trick." + }, + { + "text": "I'm just going to add in an equation F k plus one equals F k plus one." + }, + { + "text": "That will be my second equation." + }, + { + "text": "Then this is my system, this is my unknown, and what's my one-step equation?" + }, + { + "text": "So now U k plus one." + }, + { + "text": "That's so U k plus one is the left side, and what have I got here on the right side?" + }, + { + "text": "I've got some matrix multiplying U k. Can you see that all right?" + }, + { + "text": "If you can see it, then you can tell me what the matrix is." + }, + { + "text": "You see that I'm taking my system here, I artificially made it into a system." + }, + { + "text": "I artificially made the unknown into a vector, and now I'm ready to look at and see what the matrix is." + }, + { + "text": "So do you see the left side, U k plus one is F k plus two F k plus one, that's just what I want." + }, + { + "text": "On the right side, this, remember, this U k here, let me for the moment put it as F k plus one F k. So what's the matrix?" + }, + { + "text": "Well, that has a one and a one, and that has a one and a zero." + }, + { + "text": "There's the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk18.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..6c1b68c2cb2fde3f5dea82f3100d4da31fcce70a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "You see that that gives me the right-hand side." + }, + { + "text": "So there's the matrix A, and this is our friend U k. So we've got, so that simple trick changed the second order scalar problem to a first order system, two, with two unknowns." + }, + { + "text": "With a matrix and now what do I do?" + }, + { + "text": "Well, before I even think, I find its eigenvalues and eigenvectors." + }, + { + "text": "So what are the eigenvalues and eigenvectors of that matrix?" + }, + { + "text": "Let's see." + }, + { + "text": "I was, first let me just, like, think for a minute." + }, + { + "text": "It's two by two, so this shouldn't be impossible to do." + }, + { + "text": "Let's do it." + }, + { + "text": "OK." + }, + { + "text": "So my matrix again is one one one zero." + }, + { + "text": "It's symmetric, by the way." + }, + { + "text": "So what I will eventually know about symmetric matrices is that the eigenvalues will come out real, I won't get any complex numbers here, and the eigenvectors, once I get those, actually will be orthogonal." + }, + { + "text": "But two by two, I'm more interested in what the actual numbers are." + }, + { + "text": "What do I know about the two numbers?" + }, + { + "text": "Well, should, do you want me to find this determinant of A minus lambda I?" + }, + { + "text": "Sure." + }, + { + "text": "So it's the determinant of one minus lambda one one zero, right?" + }, + { + "text": "Minus lambda, yes, got it." + }, + { + "text": "OK. OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk19.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..a73b23e3d56b889ff49ea7f55a784fac33e13c3d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "There'll be two eigenvalues." + }, + { + "text": "Well, tell me again what I know about the two eigenvalues before I go any further." + }, + { + "text": "Tell me something about these two eigenvalues, what do they add up to?" + }, + { + "text": "Lambda one plus lambda two is the same as the trace down the diagonal of the matrix, one and zero is one." + }, + { + "text": "So lambda one plus lambda two should come out to be one, and lambda one times lambda two should come out to be the determinant, which is minus one." + }, + { + "text": "So I'm expecting the eigenvalues to add to one and to multiply to minus one." + }, + { + "text": "But let's just see it happen here." + }, + { + "text": "If I multiply this out, I get that times that'll be a lambda squared minus lambda minus one." + }, + { + "text": "Good." + }, + { + "text": "Lambda squared minus lambda minus one." + }, + { + "text": "Actually, you see the, compare that with the original equation that I started with." + }, + { + "text": "Fk plus two minus Fk plus one minus Fk is zero." + }, + { + "text": "The recurrent, the recursion that the Fibonacci number satisfy is somehow showing up directly here for the eigenvalues when we set that to zero." + }, + { + "text": "OK. Let's solve." + }, + { + "text": "Well, I would like to be able to factor that, that quadratic, but I'm better off to use the quadratic formula." + }, + { + "text": "Lambda is, let's see, minus b is one, plus or minus the square root of b squared, which is one, minus four, times that, times that, which is plus four, over two." + }, + { + "text": "So that's the square root of five." + }, + { + "text": "So the eigenvalues are lambda one is one half of one plus square root of five, and lambda two is one half of one minus square root of five." + }, + { + "text": "And sure enough, they, those add up to one, and they multiply to give minus one." + }, + { + "text": "OK. Those are the two eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk2.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..43cfb012fc04a89fc7dab94c23bfb0f50ade3782 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "On the right, it's multiplied by, if I want, if I want lambda n xn in the last column, how do I do it?" + }, + { + "text": "Well, the last column here will be, I'll, I'll take the last column, use these coefficients, put the lambda n down there, and it will multiply that nth column and give me lambda n xn." + }, + { + "text": "There, there you see matrix multiplication just working for us." + }, + { + "text": "So I started with A s. I wrote down what it meant." + }, + { + "text": "A times each eigenvector." + }, + { + "text": "That gave me lambda times the eigenvector." + }, + { + "text": "And then when I peeled off the lambdas, they were on the right-hand side, so I've got s, my matrix back again, and this matrix, this diagonal matrix, the eigenvalue matrix, and I call it capital lambda, using capital letters for matrices, and lambda to prompt me that it's, that it's eigenvalues that are in there." + }, + { + "text": "So you see that the eigenvalues are just sitting down that diagonal?" + }, + { + "text": "If I had a column x2 here, I would want the lambda two in the two two position, in the diagonal position, to multiply that x2 and give me the lambda two x2." + }, + { + "text": "That's my formula." + }, + { + "text": "A s is s lambda." + }, + { + "text": "OK. That's, that's the, you see, it's just a calculation." + }, + { + "text": "Now, I, I mentioned, and I have to mention again, this business about n independent eigenvectors." + }, + { + "text": "As it stands, this is all fine whether, I mean, I could be repeating the same eigenvector, but I, I'm no interested in that." + }, + { + "text": "I want to be able to invert s, and that's where this comes in." + }, + { + "text": "This n independent eigenvectors business comes in to tell me that that matrix is invertible." + }, + { + "text": "So let me, on the next board, write down what I've got." + }, + { + "text": "A s equals s lambda." + }, + { + "text": "And now I'm, I can multiply on the left by s inverse." + }, + { + "text": "So this is really, I can do that provided s is invertible, provided my assumption of n independent eigenvectors is satisfied." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk20.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ad5a59fa5db44ce73ff5f88190423e0404fb3d39 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "How, how, what are those numbers approximately?" + }, + { + "text": "Square root of five, well, it's more than two, but less than three." + }, + { + "text": "It, it'd be nice to know these numbers." + }, + { + "text": "I think, I think that that, so that number comes out bigger than one, right?" + }, + { + "text": "Yeah, that's right." + }, + { + "text": "This number comes out bigger than one." + }, + { + "text": "It's about one point six one eight or something." + }, + { + "text": "Not exactly." + }, + { + "text": "It's supposed to be one point six." + }, + { + "text": "Just, like, I think so." + }, + { + "text": "Then what's lambda two?" + }, + { + "text": "Is, is lambda two positive or negative?" + }, + { + "text": "Negative, right?" + }, + { + "text": "Because I'm, it's obviously negative, and I knew that the, so it's minus, and they add up to one, so minus point six one eight, I guess." + }, + { + "text": "OK. And some order." + }, + { + "text": "Those are the two eigenvalues." + }, + { + "text": "One eigenvalue bigger than one, one eigenvalue smaller than one." + }, + { + "text": "Actually, that's a great situation to be in." + }, + { + "text": "Of course, the eigenvalues are different, so there's no doubt whatever, is this matrix diagonalizable?" + }, + { + "text": "Is this matrix diagonalizable, that original matrix A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk21.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..4a034475591d371995b379b5f98783a2cfb25870 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Sure." + }, + { + "text": "We've got two distinct eigenvalues and we can find the eigenvectors in a moment." + }, + { + "text": "But they'll be independent, will be diagonalizable, and now you can already answer my very first question." + }, + { + "text": "How fast are those Fibonacci numbers increasing?" + }, + { + "text": "How, those, they're increasing, right?" + }, + { + "text": "They're not doubling at every step." + }, + { + "text": "Let's look again at these numbers." + }, + { + "text": "Five eight thirteen, it's not obvious." + }, + { + "text": "The next one would be twenty one thirty four." + }, + { + "text": "So to get some idea of what F one hundred is, can you give me any, I mean the crucial number of, so it, these, it's approximately, what's controlling the growth of these Fibonacci numbers?" + }, + { + "text": "It's the eigenvalues." + }, + { + "text": "And which eigenvalues controlling that growth?" + }, + { + "text": "The big ones." + }, + { + "text": "So F one hundred will it be approximately some constant, c one, I guess, times this lambda one, this one plus square root of five over two, to the hundredth power." + }, + { + "text": "And the two hundredth have, in other words, the eigenvalue, the Fibonacci numbers are growing by about that factor." + }, + { + "text": "You see that we've got precise information about the, about the Fibonacci numbers out of the eigenvalue." + }, + { + "text": "OK. And again, why is that true?" + }, + { + "text": "Let me go over to this board and show what I'm doing here." + }, + { + "text": "The, the original eigen, the original initial value is some combination of eigenvectors, and then when we start multiple, when we start going out the theory of Fibonacci numbers, when we start multiplying by a hundred times, it's this lambda one to the hundredth, this term is, is the one that's taken over." + }, + { + "text": "It's, I mean, that's big, like, one point six to the hundredth power." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk22.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..c13a1fc9867173c3067e46c469cfff27b9b45289 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "The second term is practically nothing, right?" + }, + { + "text": "The point six, or minus point six to the hundredth power, is an extremely small, extremely small number." + }, + { + "text": "So this is, this, this, there are only two terms, because we're two by two." + }, + { + "text": "This number is, this piece of it is there, but it's, it's disappearing." + }, + { + "text": "Where this piece is there and it's growing and controlling everything." + }, + { + "text": "So, so really the, we're doing, like, problems that are evolving." + }, + { + "text": "We're doing dynamics." + }, + { + "text": "Instead of Ax equal b, that's a static problem." + }, + { + "text": "We're now, we're doing dynamics." + }, + { + "text": "A, a squared, a cubed, things are evolving in time, and the eigenvalues are the crucial, numbers." + }, + { + "text": "OK." + }, + { + "text": "I guess to complete this, I better write down the eigenvectors." + }, + { + "text": "So we should complete the, the whole process by finding the eigenvectors." + }, + { + "text": "OK. Well, I have to, up in the corner, then I have to look at A minus lambda I." + }, + { + "text": "So A minus lambda I is this one minus lambda, one, one, and minus lambda." + }, + { + "text": "And now, can we spot an eigenvector out of that?" + }, + { + "text": "That's, for these two lambdas, this matrix is singular." + }, + { + "text": "I guess the eigenvector, two by two ought to be easy." + }, + { + "text": "So if I know that this matrix is singular, then it seems to me the eigenvector has to be lambda and one, because that multiplication will give me the zero." + }, + { + "text": "And this multiplication gives me, better give me also zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk23.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..df816eb800ce767b1475c279a24ad976bb45a785 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Do you see why it does?" + }, + { + "text": "This is the minus lambda squared plus lambda plus one." + }, + { + "text": "It's the thing that's zero, because these lambdas are special." + }, + { + "text": "There's the eigenvector." + }, + { + "text": "X1 is lambda one, one, and x2 is lambda two, one." + }, + { + "text": "I did that as a little trick that was available in the two by two case." + }, + { + "text": "So now I finally have to, oh, I have to take the initial, u0." + }, + { + "text": "So to complete this example entirely, I have to say, OK, what was u0?" + }, + { + "text": "u0 was f1 f0." + }, + { + "text": "So u0, the starting vector, is f1 f0, and those were one and zero." + }, + { + "text": "So I have to use that vector, so I have to look for, from multiple of the first eigenvector and the second, to produce u0, the one zero vector." + }, + { + "text": "This is what will find c1 and c2, and then I'm done." + }, + { + "text": "So let me, instead of in the last five seconds grinding out a formula, let me repeat the idea." + }, + { + "text": "That really, it's the idea that's central." + }, + { + "text": "When things are evolving in time, let me come back to this board, because the ideas are here." + }, + { + "text": "When things are evolving in time by a first-order system, starting from an original u0, the key is, find the eigenvalues and eigenvectors of A." + }, + { + "text": "That will tell, those eigenvectors, the eigenvalues will already tell you what's happening." + }, + { + "text": "Is the solution blowing up?" + }, + { + "text": "Is it going to zero?" + }, + { + "text": "What's it doing?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk24.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..40301cb90760e2172baa94d536cbc13288d4c31f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk24.json @@ -0,0 +1,20 @@ +[ + { + "text": "And then, to find out exactly a formula, you have to take your u0 and write it as a combination of eigenvectors and then follow each eigenvector separately." + }, + { + "text": "And that's really what this formula, the formula for, that's what the formula for A to the k is doing." + }, + { + "text": "So remember that formula for A to the k is S, lambda to the k S inverse." + }, + { + "text": "OK. That's, that's difference equations, and you just have to, so the homework will give some examples different from Fibonacci to follow through." + }, + { + "text": "And next time will be differential equations." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk3.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..9bf1bb852baadc1da7837e14180c0c2951a30882 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I mentioned at the end of last time, and I'll say again, that there's a small number of matrices for, that don't have n independent eigenvectors." + }, + { + "text": "So I've got to discuss that, that technical point." + }, + { + "text": "But the great, the most matrices that we see have n, n independent eigenvectors and we can diagonalize." + }, + { + "text": "This is diagonalization." + }, + { + "text": "I could also write it, and I often will, the other way round." + }, + { + "text": "If I multiply on the right by s inverse, if I took this equation at the top and multiplied on the right by s inverse, I could, I would have A left here." + }, + { + "text": "Now s inverse is coming from the right." + }, + { + "text": "So can you keep those two straight?" + }, + { + "text": "A multiplies its eigenvectors." + }, + { + "text": "That's how I keep them straight." + }, + { + "text": "So A multiplies s. A multiplies s. And then this s inverse makes the whole thing diagonal." + }, + { + "text": "And this is another way of saying the same thing, putting the s's on the other side of the equation, A is s lambda s inverse." + }, + { + "text": "So that's the, that's the new factorization." + }, + { + "text": "That's the replacement for L U from elimination or Q R from Gram-Schmidt." + }, + { + "text": "And notice that the matrix, so it's, it's a matrix times a diagonal matrix times the inverse of the first one." + }, + { + "text": "It's, that's the combination that we'll see throughout this chapter." + }, + { + "text": "This, this, combination with an s and an s inverse." + }, + { + "text": "OK. Can I just begin to use that?" + }, + { + "text": "For example, what about A squared?" + }, + { + "text": "What are the eigenvalues and eigenvectors of A squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk4.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c687b6948acad76de8781cb82d3eb069c9da514e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's a straightforward question with a, with a absolutely clean answer." + }, + { + "text": "So let me, let me consider A squared." + }, + { + "text": "So I look, I start with Ax equal lambda x." + }, + { + "text": "And I'm headed for A squared." + }, + { + "text": "So let me multiply both sides by A." + }, + { + "text": "That's one way to get A squared on the left." + }, + { + "text": "So if, I should write these ifs in here." + }, + { + "text": "If Ax equals lambda x, then I multiply by A." + }, + { + "text": "So I get A squared x equals, well, I'm multiplying by A, so that's lambda Ax." + }, + { + "text": "That lambda was a number, so I just put it on the left." + }, + { + "text": "And what do I, tell me how to make that look better." + }, + { + "text": "What have I got here?" + }, + { + "text": "For, if, if A has the eigenvalue lambda and eigenvector x, what's up with A squared?" + }, + { + "text": "A squared x, I just multiply by A, but now for Ax, I'm going to substitute lambda x, so I've got lambda squared x." + }, + { + "text": "So from that simple calculation, I, my conclusion is that the eigenvalues of A squared are lambda squared." + }, + { + "text": "And the eigenvectors, I always think about both of those." + }, + { + "text": "What can I say about the eigenvalues?" + }, + { + "text": "They're squared." + }, + { + "text": "What can I say about the eigenvectors?" + }, + { + "text": "They're the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk5.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5bf15e20707c156c8ae71c9c7acea41a9d9d8e46 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same x as in, as for A." + }, + { + "text": "Now, let me see that also from this formula." + }, + { + "text": "How can I see what A squared is looking like from this formula?" + }, + { + "text": "So let me, that, that was one way to do it." + }, + { + "text": "Let me do it by just taking A squared from that." + }, + { + "text": "A squared is S lambda S inverse, that's A, times S lambda S inverse, that's A, which is?" + }, + { + "text": "This is the beauty of eigenvalues, eigenvectors, having that S inverse and S is the identity, so I've got S lambda squared S inverse." + }, + { + "text": "Yes." + }, + { + "text": "You see what that's telling me?" + }, + { + "text": "It's, it's telling me the same thing that I just learned here, but in the, in, in a matrix form." + }, + { + "text": "It's telling me that the S is the same, the eigenvectors are the same, but the eigenvalues are squared, because this is, what's lambda squared, that's still diagonal, it's got little lambda one squared, lambda two squared, down to lambda n squared, on that diagonal, those are the eigenvalues, as we just learned, of A squared." + }, + { + "text": "OK." + }, + { + "text": "So, somehow those eigenvalues and eigenvectors are really giving you a way to, to, to, to see what's going on inside a matrix." + }, + { + "text": "Now, of course, I can continue that for, to the k-th power." + }, + { + "text": "A to the k-th power." + }, + { + "text": "If I multiply, if I have k of these together, do you see how S inverse S will keep cancelling?" + }, + { + "text": "In the, in the inside, I'll have the S outside, at the far left, and lambda will be in there k times and S inverse." + }, + { + "text": "So what's that telling me?" + }, + { + "text": "That's telling me that the eigenvalues of A, of A to the k-th power are the k-th powers." + }, + { + "text": "The eigenvalues of A cubed are the cubes of the eigenvalues of A, and the eigenvectors are the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk6.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..c18dddbe798022f7e68278ac002a3f5fe6ed249e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same." + }, + { + "text": "OK." + }, + { + "text": "In other words, eigenvalues and eigenvectors give a great way to understand the powers of a matrix." + }, + { + "text": "If I take the square of a matrix or the hundredth power of a matrix, the pivots are all over the place." + }, + { + "text": "L U, if I multiply L U times L U times L U times L U a hundred times, I've got a hundred L U's." + }, + { + "text": "I can't do anything with them." + }, + { + "text": "But when I multiply S lambda S inverse by itself, when I look at the eigenvector picture a hundred times, I get a hundred or ninety-nine of these guys cancelling out inside, and I get A to the hundredth is S lambda to the hundredth S inverse." + }, + { + "text": "I mean, eigenvalues tell you about powers of a matrix in a way that we had no, no way to approach previously." + }, + { + "text": "For example, when does, when do the powers of a matrix go to zero?" + }, + { + "text": "I would call that matrix stable, maybe." + }, + { + "text": "So, so, so I could write down a, a theorem." + }, + { + "text": "I'll, I'll write it as a theorem, just to use that word to emphasize that here I'm getting this great fact from this eigenvalue picture." + }, + { + "text": "OK. A to the k approaches zero as k goes, as k gets bigger." + }, + { + "text": "If what?" + }, + { + "text": "What's the, how can I tell for a matrix A if its powers go to zero?" + }, + { + "text": "What, what's somewhere inside that matrix is that information." + }, + { + "text": "That information is not present in the pivots." + }, + { + "text": "It's present in the eigenvalues." + }, + { + "text": "What do I need for the, to know that if I take higher and higher powers of A that this matrix gets smaller and smaller?" + }, + { + "text": "Well, S and S inverse are not moving." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk7.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b84a5c854a5542758e8a0107e1ff043205fe3bdb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's this guy that has to get small, and that's easy to, easy to understand." + }, + { + "text": "The requirement is all eigenvalues, so what is the requirement?" + }, + { + "text": "The eigenvalues have to be less than one." + }, + { + "text": "Now, I have to write that absolute value, because those eigenvalues could be negative, they could be complex numbers." + }, + { + "text": "So I'm taking the absolute value if all of those are below one." + }, + { + "text": "That's, in fact, we practically see why." + }, + { + "text": "Let me just say that I, that I, I'm operating on one assumption here, and I got to keep remembering that that assumption is still present." + }, + { + "text": "That assumption was that I had a full set of, of n independent eigenvectors." + }, + { + "text": "If I don't have that, then I, I, then this approach is not working." + }, + { + "text": "So, so again, a pure eigenvalue approach, eigenvector approach, needs n independent eigenvectors." + }, + { + "text": "If we don't have n independent eigenvectors, we can't diagonalize the matrix." + }, + { + "text": "We can't get to a diagonal matrix." + }, + { + "text": "This, this, this diagonalization is only possible if S inverse makes sense." + }, + { + "text": "OK. Can I, can I follow up on that point now?" + }, + { + "text": "So, so you see why, what we get and, and why we want it, because we get information about the powers of a matrix just immediately from the eigenvalues." + }, + { + "text": "OK, now let me follow up on this, business of which matrices are diagonalizable." + }, + { + "text": "Sorry about that long word." + }, + { + "text": "So a matrix is, is sure to, so here's, here's the main point." + }, + { + "text": "A is sure to be, to have n independent eigenvectors and, and B, now here comes that word, diagonalizable, if, if, so we, we, we might as well get the, the nice case out in the open." + }, + { + "text": "The nice case is when, if all the lambdas are different." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk8.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f06dcec8ffa0ee1bf19440e4ab2194db33ab353b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means, that means no repeated eigenvalues." + }, + { + "text": "OK. That's the nice case." + }, + { + "text": "If, if my matrix and most matrix, if I do a random matrix in MATLAB and compute its eigenvalues, so if I computed, if I took I of rand of ten ten, gave, gave that MATLAB command, the, we'd get a random ten by ten matrix, we would get a list of its ten eigenvalues and they would be different." + }, + { + "text": "They would be distinct, is the best word." + }, + { + "text": "I would have a random matrix will have ten distinct, a ten by ten matrix will have ten distinct eigenvalues, and if it does, the eigenvectors are automatically independent." + }, + { + "text": "So that's a nice fact." + }, + { + "text": "I can, I'll refer you to the text for the proof." + }, + { + "text": "That, that A is sure to have n independent eigenvectors if the eigenvalues are different." + }, + { + "text": "If, if all the, if all eigenvalues are different." + }, + { + "text": "It's just, if some lambdas are repeated, then I have to look more closely." + }, + { + "text": "If an eigenvalue is repeated, I have to look, I have to count, I have to check." + }, + { + "text": "Has it got, say it's repeated three times." + }, + { + "text": "So what's a possibility for, so, so here's, here's the repeated possibility." + }, + { + "text": "And, and let me emphasize the conclusion." + }, + { + "text": "That if I have repeated eigenvalues, I may or may not, I may or may not have, have n independent eigenvectors." + }, + { + "text": "I might." + }, + { + "text": "I, I, you know, this isn't a completely negative case." + }, + { + "text": "The identity matrix." + }, + { + "text": "Well, suppose I take the ten by ten identity matrix." + }, + { + "text": "What are the eigenvalues of that matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk9.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..87d2a2ae5773036cf11800e2f1962908986a0dad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_30_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So just, just take the easiest matrix, the identity." + }, + { + "text": "If I look for its eigenvalues, they're all ones." + }, + { + "text": "So that eigenvalue one is repeated ten times." + }, + { + "text": "But there's no shortage of eigenvectors for the identity matrix." + }, + { + "text": "In fact, every vector is an eigenvector." + }, + { + "text": "So I can take ten independent vectors." + }, + { + "text": "Oh, well, what happens to everything if, if, if A is the identity matrix, let's just think that one through in our head." + }, + { + "text": "If A is the identity matrix, then it's got plenty of eigenvectors." + }, + { + "text": "I choose ten independent vectors, they're the columns of S, and, and what do I get from S inverse A S?" + }, + { + "text": "I get I again, right?" + }, + { + "text": "If A is the identity, and of course, that's the correct lambda." + }, + { + "text": "The, the matrix was already diagonal." + }, + { + "text": "So if the matrix is already diagonal, then the, the lambda is the same as the matrix." + }, + { + "text": "A diagonal matrix has got its eigenvalues sitting right there in front of you." + }, + { + "text": "Now if it's triangular, the eigenvalues are still sitting there, but so let's, let's take a case where, it's triangular." + }, + { + "text": "Suppose A is like, two, one, two, zero." + }, + { + "text": "So there's a case that's going to be trouble." + }, + { + "text": "There's a case that's going to be trouble." + }, + { + "text": "First of all, what are the eigen- I mean, we just, like now you, if we start with a matrix, the first thing we do practically without thinking is compute the eigenvalues and eigenvectors." + }, + { + "text": "OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk0.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6898d4fe66019ef6b40d0472ea94a968e7bbde9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, shall we start?" + }, + { + "text": "This is the second lecture on eigenvalues." + }, + { + "text": "So the first lecture was set -- reached the key equation, Ax equal lambda x. x is the eigenvector and lambda is the eigenvalue." + }, + { + "text": "Now, to use that." + }, + { + "text": "And the good way to, after we've found, so job one is to find the eigenvalues and find the eigenvectors." + }, + { + "text": "Now after we found them, what do we do with them?" + }, + { + "text": "Well, the good way to see that is diagonalize the matrix." + }, + { + "text": "So the matrix is A, and I want to show, first of all, this is like the basic fact." + }, + { + "text": "This, this formula." + }, + { + "text": "That's, that's the key to today's lecture." + }, + { + "text": "This matrix A, I put its eigenvectors in the columns of a matrix S. So S will be the eigenvector matrix, and I want to look at this magic combination S inverse A S. So can I show you how that, how that, what happens there?" + }, + { + "text": "And notice, notice, there's an S inverse." + }, + { + "text": "We have to be able to invert this eigenvector matrix S. So for that we need n independent eigenvectors." + }, + { + "text": "So that's the, that's the case." + }, + { + "text": "OK." + }, + { + "text": "So suppose we have n linearly independent eigenvectors of A." + }, + { + "text": "Put them in the columns of this matrix S. So I'm naturally going to call that the eigenvector matrix, because it's got the eigenvectors in its columns." + }, + { + "text": "And all I want to do is show you what happens when you multiply A times S. So A times S. So this is A times the matrix with the first eigenvector in its first column, the second eigenvector in its second column, the nth eigenvector in its nth column." + }, + { + "text": "And how am I going to do this matrix multiplication?" + }, + { + "text": "Well, certainly I'll do it a column at a time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk1.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..fbe078217bb68baea8e0605a5d04be568c49efbf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I get?" + }, + { + "text": "A times the first column gives me the first column of the answer, but what is it?" + }, + { + "text": "That's an eigenvector." + }, + { + "text": "A times x1 is equal to the lambda times the x1." + }, + { + "text": "And that lambda's we'll call lambda one, of course." + }, + { + "text": "So that's the first column, A x1 is the same as lambda one x1." + }, + { + "text": "A x2 is lambda two x2, so on, along to, in the nth column, we now have lambda n xn." + }, + { + "text": "Looking good, but the next step is even better." + }, + { + "text": "So for the next step, I want to separate out those eigenvalues, those multiplying numbers, from the x's." + }, + { + "text": "So then I'll have just what I want." + }, + { + "text": "OK, so how, how am I going to separate out?" + }, + { + "text": "So that, that number lambda one is multiplying the first column." + }, + { + "text": "So if I want to factor it out of the first column, I better put, here is going to be x1, and that's going to multiply this matrix lambda one in the first entry in all zeros." + }, + { + "text": "You see that that, that's going to come out right for the first column?" + }, + { + "text": "Because we remember how, how we're going back to that original punchline, that if I want a number to multiply x1, then I can do it by putting x1 in that column, in the first column, and putting that number there." + }, + { + "text": "What am I going to have here?" + }, + { + "text": "I'm going to have lambda one, I'm going to have x1, x2, xn." + }, + { + "text": "These are going to be my columns again." + }, + { + "text": "I'm getting s back again." + }, + { + "text": "I'm getting s back again, but now what's it multiplied by?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk10.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c58a42edbe9567233ca7f57643a0b7d43ae6761f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what are the eigenvalues?" + }, + { + "text": "You can tell me right away what they are." + }, + { + "text": "They're two and two, right." + }, + { + "text": "It's a triangular matrix, so when I do this determinant, shall I do this determinant of A minus lambda I?" + }, + { + "text": "I'll get this two minus lambda, one, zero, two minus lambda, right?" + }, + { + "text": "I take that determinant, so I make those into vertical bars to mean determinant, and what's the determinant?" + }, + { + "text": "Two minus lambda squared." + }, + { + "text": "What are the roots?" + }, + { + "text": "Lambda equal two twice." + }, + { + "text": "So the eigenvalues are lambda equals two and two." + }, + { + "text": "OK, fine." + }, + { + "text": "Now the next step, find the eigenvectors." + }, + { + "text": "So I look for eigenvectors and what do I find for this guy?" + }, + { + "text": "Eigenvectors for this guy, when I subtract two minus the identity, so A minus two I has zeros here, and I'm looking for the null space." + }, + { + "text": "What's, what are the eigenvectors?" + }, + { + "text": "They're the, they're, they're the null space of A minus lambda I." + }, + { + "text": "The null space is only one dimension." + }, + { + "text": "This is a case where I don't have enough eigenvectors." + }, + { + "text": "My algebraic multiplicity is two." + }, + { + "text": "I, I would say when I see, when I count how often the eigenvalue is repeated, that's the algebraic multiplicity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk11.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..779c2cf904d904b761080db2671aac46394ad02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the multiplicity." + }, + { + "text": "How many times is it the root of the polynomial?" + }, + { + "text": "My polynomial is two minus lambda squared." + }, + { + "text": "It's a double root." + }, + { + "text": "So my algebraic multiplicity is two." + }, + { + "text": "But the geometric multiplicity, which looks for vectors, looks for eigenvectors and which means the null space of this thing." + }, + { + "text": "And the only eigenvector is one zero." + }, + { + "text": "That's in the null space." + }, + { + "text": "Zero one is not in the null space." + }, + { + "text": "The null space is only one dimensional." + }, + { + "text": "So there's a matrix, my, this A or the original A, that are not diagonalizable." + }, + { + "text": "I can't, I can't find two independent eigenvectors, there's only one." + }, + { + "text": "OK." + }, + { + "text": "So that's the case that I'm, that's a case that I, I'm not really handling." + }, + { + "text": "For example, when I wrote down up here that the powers went to zero if the eigenvalues were below one, I didn't really handle that case of repeated eigenvalues because my reasoning was based on this formula." + }, + { + "text": "And this formula is based on n independent eigenvectors." + }, + { + "text": "OK." + }, + { + "text": "So just to say that." + }, + { + "text": "There are some matrices that we don't cover through diagonalization, but the great majority we do." + }, + { + "text": "OK. And we're always OK if we have different distinct eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk12.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..77d090704cc298475d94416b7ecb88a2a015a913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. That's the, like, the typical case." + }, + { + "text": "Because for each eigenvalue there's at least one eigenvector, the algebraic multiplicity here is one for every eigenvalue, and the geometric multiplicity is one." + }, + { + "text": "There's one eigenvector and they are independent." + }, + { + "text": "OK. OK. Now let me come back to the important case when we're OK." + }, + { + "text": "The important case when we are diagonalizing." + }, + { + "text": "Let me look at, so let me solve this equation." + }, + { + "text": "The equation will be each, I start with some, start with a given vector u0." + }, + { + "text": "And then my equation is that every step I multiply what I have by a." + }, + { + "text": "That equation ought to be simple to handle." + }, + { + "text": "OK. And I'd like to be able to solve it." + }, + { + "text": "How would I find, if I start with a vector u0, and I multiply by a a hundred times, what have I got?" + }, + { + "text": "Well, I can certainly write down a formula for the answer." + }, + { + "text": "So what, what, so u1 is a u0." + }, + { + "text": "And u2 is, what's u2 then?" + }, + { + "text": "U2 I multiply it, u2 I get from u1 by another, multiplying by a, so I've got a twice." + }, + { + "text": "And my formula is uk, after k steps, I've multiplied by a k times the original u0." + }, + { + "text": "You see what I'm doing?" + }, + { + "text": "The next section is going to solve systems of differential equations." + }, + { + "text": "I'm going to have derivatives." + }, + { + "text": "This, this section is the nice one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk13.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..ba8214d8c636e4757a266d6617801174bc939d80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "It solves difference equations." + }, + { + "text": "I would call that a difference equation." + }, + { + "text": "It's conne- a first order." + }, + { + "text": "I would call that a first order system, because it connects only, it only goes up one level." + }, + { + "text": "And it's a system because these are vectors and that's a matrix." + }, + { + "text": "And the solution is just that." + }, + { + "text": "OK." + }, + { + "text": "But, that's a nice formula." + }, + { + "text": "That's the, like, the most compact formula I could ever get." + }, + { + "text": "U one hundred would be a to the one hundredth u0." + }, + { + "text": "But how would I actually find u one hundred?" + }, + { + "text": "How would I find, how would I discover what u one hundred is?" + }, + { + "text": "Let me, let me show you how." + }, + { + "text": "Here, here's the idea." + }, + { + "text": "If, so, to solve, to really solve, shall I say, to really solve." + }, + { + "text": "To really solve it, I would take this initial vector, u0, and I would write it as a combination of eigenvectors." + }, + { + "text": "To really solve, write, write u0 as a combination, say, certain amount of the first eigenvector plus a certain amount of the second eigenvector plus a certain amount of the last eigenvector." + }, + { + "text": "Now multiply by a." + }, + { + "text": "You want to, you got to see the magic of eigenvectors work." + }, + { + "text": "Multiply by a." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk14.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7843b2bf0cac762d1c12452cf36500ea4ad13370 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a u0 is what?" + }, + { + "text": "So a times that." + }, + { + "text": "A times, so what's, I can separate it out into n separate pieces and that's the whole point." + }, + { + "text": "That each of those pieces is going in its own merry way." + }, + { + "text": "Each of those pieces is an eigenvector, and when I multiply by a, what does this piece become?" + }, + { + "text": "So that's some amount of the first, let's suppose the eigenvectors are normalized to be unit vectors." + }, + { + "text": "So that says what the eigenvector is." + }, + { + "text": "It's, and I need some multiple of it to produce u0." + }, + { + "text": "OK. Now when I multiply by a, what do I get?" + }, + { + "text": "I get c1, which is just a factor, times a x1, but a x1 is lambda one x1." + }, + { + "text": "When I multiply this by a, I get c2 lambda two x2." + }, + { + "text": "And here I get cn lambda n xn." + }, + { + "text": "And suppose I multiply by a to the hundredth power now." + }, + { + "text": "Can we, can we, having done it, multiplied by a, let's multiply by a to the hundredth." + }, + { + "text": "What happens to this first term when I multiply by a to the one hundredth?" + }, + { + "text": "It's got that factor lambda to the hundredth." + }, + { + "text": "That's the key." + }, + { + "text": "That, that's what I mean by going its own merry way." + }, + { + "text": "It, it is pure eigenvector, it's exactly in a direction where multiplication by a just brings in a scalar factor lambda one." + }, + { + "text": "So a hundred times brings in this a hundred times." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk15.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7ee3348735378aa4049d33ec2a197d0ceb0c447c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Hundred times lambda two, hundred times lambda n. Actually, we're, what are we seeing here?" + }, + { + "text": "We're seeing, this same, lambda, capital lambda to the hundredth, as in the, as in the diagonalization, and we're seeing the S matrix, the matrix S of eigenvectors." + }, + { + "text": "That's what this has got to, this has got to amount to, a lambda to the hundredth power times an S times this vector C that's telling us how much of each one is in the original thing." + }, + { + "text": "So if, if I had to really find the hundredth power, I would take u0, I would expand it as a combination of eigenvectors, this is really S, the eigenvector matrix times C, the, the coefficient vector." + }, + { + "text": "And then I would immediately, then, by inserting these hundredth powers of eigenvalues, I'd have the answer." + }, + { + "text": "So the, the, huh, there must be, well, let's see." + }, + { + "text": "OK." + }, + { + "text": "It's, so, yeah." + }, + { + "text": "So if u100 is a to the hundredth times u0, and u0 is Sc, then you see this formula is just this formula, which is the way I would actually get hold of this, of this u100, which is, let me put it here, u100." + }, + { + "text": "The way I would actually get hold of that, see what, what the solution is after a hundred steps, would be expand the initial vector into eigenvectors and, and let each eigenvector go its own way, multiplying by a hundred at, by lambda at every step, and therefore by lambda to the hundredth power after a hundredth step." + }, + { + "text": "Can I do an example?" + }, + { + "text": "So that's, that's the, the formulas." + }, + { + "text": "Now let me take an example." + }, + { + "text": "I'll use the Fibonacci sequence as an example." + }, + { + "text": "So, so Fibonacci example." + }, + { + "text": "You remember the Fibonacci numbers?" + }, + { + "text": "If we start with one and one as F0, oh, I think I start with zero, maybe." + }, + { + "text": "Let zero and one be the first ones." + }, + { + "text": "So there's F0 and F1, the first two Fibonacci numbers." + }, + { + "text": "Then what's the rule for Fibonacci numbers?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk16.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..79c65e32781f7f304b504a6c390247abb9d26ac8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "They're the sum." + }, + { + "text": "The next one is the sum of those, so it's one." + }, + { + "text": "The next one is the sum of those, so it's two." + }, + { + "text": "The next one is the sum of those, so it's three." + }, + { + "text": "Well, it looks like one, two, three, four, five, but somehow it's not going to do that way." + }, + { + "text": "The next one is five, right." + }, + { + "text": "Two and three makes five." + }, + { + "text": "The next one is eight." + }, + { + "text": "The next one is thirteen." + }, + { + "text": "And the one hundredth Fibonacci number is what?" + }, + { + "text": "That's my question." + }, + { + "text": "How could I get a formula for the hundredth number and for example how could I answer the question how fast are they growing?" + }, + { + "text": "How fast are those Fibonacci numbers growing?" + }, + { + "text": "They're certainly growing." + }, + { + "text": "It's not a stable case, whatever the eigenvalues of whatever matrix it is, they're not smaller than one." + }, + { + "text": "These numbers are growing." + }, + { + "text": "But how fast are they growing?" + }, + { + "text": "The answer is lies in the eigenvalue." + }, + { + "text": "So I've got to find the matrix, so let me write down the Fibonacci rule, F k plus two is F k plus one plus F k, right?" + }, + { + "text": "Now that's not in my -- I want to write that as U k plus one and A U k. But right now what I've got is a single equation, not a system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk17.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b3aaa9dcee3cf27c112015659bb5a0b51a983ce1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's second order." + }, + { + "text": "It's like having a second order differential equation with second derivatives." + }, + { + "text": "I want to get first derivatives." + }, + { + "text": "Here I want to get first difference." + }, + { + "text": "So the way to do it is to introduce U k will be a vector." + }, + { + "text": "See, a small trick." + }, + { + "text": "Let U k be a vector, F k plus one and F k. So I'm going to get a two by two system, first order, instead of a one, instead of a scalar system, second order, by a simple trick." + }, + { + "text": "I'm just going to add in an equation F k plus one equals F k plus one." + }, + { + "text": "That will be my second equation." + }, + { + "text": "Then this is my system, this is my unknown, and what's my one-step equation?" + }, + { + "text": "So now U k plus one." + }, + { + "text": "That's so U k plus one is the left side, and what have I got here on the right side?" + }, + { + "text": "I've got some matrix multiplying U k. Can you see that all right?" + }, + { + "text": "If you can see it, then you can tell me what the matrix is." + }, + { + "text": "You see that I'm taking my system here, I artificially made it into a system." + }, + { + "text": "I artificially made the unknown into a vector, and now I'm ready to look at and see what the matrix is." + }, + { + "text": "So do you see the left side, U k plus one is F k plus two F k plus one, that's just what I want." + }, + { + "text": "On the right side, this, remember, this U k here, let me for the moment put it as F k plus one F k. So what's the matrix?" + }, + { + "text": "Well, that has a one and a one, and that has a one and a zero." + }, + { + "text": "There's the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk18.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..6c1b68c2cb2fde3f5dea82f3100d4da31fcce70a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "You see that that gives me the right-hand side." + }, + { + "text": "So there's the matrix A, and this is our friend U k. So we've got, so that simple trick changed the second order scalar problem to a first order system, two, with two unknowns." + }, + { + "text": "With a matrix and now what do I do?" + }, + { + "text": "Well, before I even think, I find its eigenvalues and eigenvectors." + }, + { + "text": "So what are the eigenvalues and eigenvectors of that matrix?" + }, + { + "text": "Let's see." + }, + { + "text": "I was, first let me just, like, think for a minute." + }, + { + "text": "It's two by two, so this shouldn't be impossible to do." + }, + { + "text": "Let's do it." + }, + { + "text": "OK." + }, + { + "text": "So my matrix again is one one one zero." + }, + { + "text": "It's symmetric, by the way." + }, + { + "text": "So what I will eventually know about symmetric matrices is that the eigenvalues will come out real, I won't get any complex numbers here, and the eigenvectors, once I get those, actually will be orthogonal." + }, + { + "text": "But two by two, I'm more interested in what the actual numbers are." + }, + { + "text": "What do I know about the two numbers?" + }, + { + "text": "Well, should, do you want me to find this determinant of A minus lambda I?" + }, + { + "text": "Sure." + }, + { + "text": "So it's the determinant of one minus lambda one one zero, right?" + }, + { + "text": "Minus lambda, yes, got it." + }, + { + "text": "OK. OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk19.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..a73b23e3d56b889ff49ea7f55a784fac33e13c3d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "There'll be two eigenvalues." + }, + { + "text": "Well, tell me again what I know about the two eigenvalues before I go any further." + }, + { + "text": "Tell me something about these two eigenvalues, what do they add up to?" + }, + { + "text": "Lambda one plus lambda two is the same as the trace down the diagonal of the matrix, one and zero is one." + }, + { + "text": "So lambda one plus lambda two should come out to be one, and lambda one times lambda two should come out to be the determinant, which is minus one." + }, + { + "text": "So I'm expecting the eigenvalues to add to one and to multiply to minus one." + }, + { + "text": "But let's just see it happen here." + }, + { + "text": "If I multiply this out, I get that times that'll be a lambda squared minus lambda minus one." + }, + { + "text": "Good." + }, + { + "text": "Lambda squared minus lambda minus one." + }, + { + "text": "Actually, you see the, compare that with the original equation that I started with." + }, + { + "text": "Fk plus two minus Fk plus one minus Fk is zero." + }, + { + "text": "The recurrent, the recursion that the Fibonacci number satisfy is somehow showing up directly here for the eigenvalues when we set that to zero." + }, + { + "text": "OK. Let's solve." + }, + { + "text": "Well, I would like to be able to factor that, that quadratic, but I'm better off to use the quadratic formula." + }, + { + "text": "Lambda is, let's see, minus b is one, plus or minus the square root of b squared, which is one, minus four, times that, times that, which is plus four, over two." + }, + { + "text": "So that's the square root of five." + }, + { + "text": "So the eigenvalues are lambda one is one half of one plus square root of five, and lambda two is one half of one minus square root of five." + }, + { + "text": "And sure enough, they, those add up to one, and they multiply to give minus one." + }, + { + "text": "OK. Those are the two eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk2.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..43cfb012fc04a89fc7dab94c23bfb0f50ade3782 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "On the right, it's multiplied by, if I want, if I want lambda n xn in the last column, how do I do it?" + }, + { + "text": "Well, the last column here will be, I'll, I'll take the last column, use these coefficients, put the lambda n down there, and it will multiply that nth column and give me lambda n xn." + }, + { + "text": "There, there you see matrix multiplication just working for us." + }, + { + "text": "So I started with A s. I wrote down what it meant." + }, + { + "text": "A times each eigenvector." + }, + { + "text": "That gave me lambda times the eigenvector." + }, + { + "text": "And then when I peeled off the lambdas, they were on the right-hand side, so I've got s, my matrix back again, and this matrix, this diagonal matrix, the eigenvalue matrix, and I call it capital lambda, using capital letters for matrices, and lambda to prompt me that it's, that it's eigenvalues that are in there." + }, + { + "text": "So you see that the eigenvalues are just sitting down that diagonal?" + }, + { + "text": "If I had a column x2 here, I would want the lambda two in the two two position, in the diagonal position, to multiply that x2 and give me the lambda two x2." + }, + { + "text": "That's my formula." + }, + { + "text": "A s is s lambda." + }, + { + "text": "OK. That's, that's the, you see, it's just a calculation." + }, + { + "text": "Now, I, I mentioned, and I have to mention again, this business about n independent eigenvectors." + }, + { + "text": "As it stands, this is all fine whether, I mean, I could be repeating the same eigenvector, but I, I'm no interested in that." + }, + { + "text": "I want to be able to invert s, and that's where this comes in." + }, + { + "text": "This n independent eigenvectors business comes in to tell me that that matrix is invertible." + }, + { + "text": "So let me, on the next board, write down what I've got." + }, + { + "text": "A s equals s lambda." + }, + { + "text": "And now I'm, I can multiply on the left by s inverse." + }, + { + "text": "So this is really, I can do that provided s is invertible, provided my assumption of n independent eigenvectors is satisfied." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk20.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ad5a59fa5db44ce73ff5f88190423e0404fb3d39 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "How, how, what are those numbers approximately?" + }, + { + "text": "Square root of five, well, it's more than two, but less than three." + }, + { + "text": "It, it'd be nice to know these numbers." + }, + { + "text": "I think, I think that that, so that number comes out bigger than one, right?" + }, + { + "text": "Yeah, that's right." + }, + { + "text": "This number comes out bigger than one." + }, + { + "text": "It's about one point six one eight or something." + }, + { + "text": "Not exactly." + }, + { + "text": "It's supposed to be one point six." + }, + { + "text": "Just, like, I think so." + }, + { + "text": "Then what's lambda two?" + }, + { + "text": "Is, is lambda two positive or negative?" + }, + { + "text": "Negative, right?" + }, + { + "text": "Because I'm, it's obviously negative, and I knew that the, so it's minus, and they add up to one, so minus point six one eight, I guess." + }, + { + "text": "OK. And some order." + }, + { + "text": "Those are the two eigenvalues." + }, + { + "text": "One eigenvalue bigger than one, one eigenvalue smaller than one." + }, + { + "text": "Actually, that's a great situation to be in." + }, + { + "text": "Of course, the eigenvalues are different, so there's no doubt whatever, is this matrix diagonalizable?" + }, + { + "text": "Is this matrix diagonalizable, that original matrix A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk21.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..4a034475591d371995b379b5f98783a2cfb25870 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Sure." + }, + { + "text": "We've got two distinct eigenvalues and we can find the eigenvectors in a moment." + }, + { + "text": "But they'll be independent, will be diagonalizable, and now you can already answer my very first question." + }, + { + "text": "How fast are those Fibonacci numbers increasing?" + }, + { + "text": "How, those, they're increasing, right?" + }, + { + "text": "They're not doubling at every step." + }, + { + "text": "Let's look again at these numbers." + }, + { + "text": "Five eight thirteen, it's not obvious." + }, + { + "text": "The next one would be twenty one thirty four." + }, + { + "text": "So to get some idea of what F one hundred is, can you give me any, I mean the crucial number of, so it, these, it's approximately, what's controlling the growth of these Fibonacci numbers?" + }, + { + "text": "It's the eigenvalues." + }, + { + "text": "And which eigenvalues controlling that growth?" + }, + { + "text": "The big ones." + }, + { + "text": "So F one hundred will it be approximately some constant, c one, I guess, times this lambda one, this one plus square root of five over two, to the hundredth power." + }, + { + "text": "And the two hundredth have, in other words, the eigenvalue, the Fibonacci numbers are growing by about that factor." + }, + { + "text": "You see that we've got precise information about the, about the Fibonacci numbers out of the eigenvalue." + }, + { + "text": "OK. And again, why is that true?" + }, + { + "text": "Let me go over to this board and show what I'm doing here." + }, + { + "text": "The, the original eigen, the original initial value is some combination of eigenvectors, and then when we start multiple, when we start going out the theory of Fibonacci numbers, when we start multiplying by a hundred times, it's this lambda one to the hundredth, this term is, is the one that's taken over." + }, + { + "text": "It's, I mean, that's big, like, one point six to the hundredth power." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk22.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..c13a1fc9867173c3067e46c469cfff27b9b45289 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "The second term is practically nothing, right?" + }, + { + "text": "The point six, or minus point six to the hundredth power, is an extremely small, extremely small number." + }, + { + "text": "So this is, this, this, there are only two terms, because we're two by two." + }, + { + "text": "This number is, this piece of it is there, but it's, it's disappearing." + }, + { + "text": "Where this piece is there and it's growing and controlling everything." + }, + { + "text": "So, so really the, we're doing, like, problems that are evolving." + }, + { + "text": "We're doing dynamics." + }, + { + "text": "Instead of Ax equal b, that's a static problem." + }, + { + "text": "We're now, we're doing dynamics." + }, + { + "text": "A, a squared, a cubed, things are evolving in time, and the eigenvalues are the crucial, numbers." + }, + { + "text": "OK." + }, + { + "text": "I guess to complete this, I better write down the eigenvectors." + }, + { + "text": "So we should complete the, the whole process by finding the eigenvectors." + }, + { + "text": "OK. Well, I have to, up in the corner, then I have to look at A minus lambda I." + }, + { + "text": "So A minus lambda I is this one minus lambda, one, one, and minus lambda." + }, + { + "text": "And now, can we spot an eigenvector out of that?" + }, + { + "text": "That's, for these two lambdas, this matrix is singular." + }, + { + "text": "I guess the eigenvector, two by two ought to be easy." + }, + { + "text": "So if I know that this matrix is singular, then it seems to me the eigenvector has to be lambda and one, because that multiplication will give me the zero." + }, + { + "text": "And this multiplication gives me, better give me also zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk23.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..df816eb800ce767b1475c279a24ad976bb45a785 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Do you see why it does?" + }, + { + "text": "This is the minus lambda squared plus lambda plus one." + }, + { + "text": "It's the thing that's zero, because these lambdas are special." + }, + { + "text": "There's the eigenvector." + }, + { + "text": "X1 is lambda one, one, and x2 is lambda two, one." + }, + { + "text": "I did that as a little trick that was available in the two by two case." + }, + { + "text": "So now I finally have to, oh, I have to take the initial, u0." + }, + { + "text": "So to complete this example entirely, I have to say, OK, what was u0?" + }, + { + "text": "u0 was f1 f0." + }, + { + "text": "So u0, the starting vector, is f1 f0, and those were one and zero." + }, + { + "text": "So I have to use that vector, so I have to look for, from multiple of the first eigenvector and the second, to produce u0, the one zero vector." + }, + { + "text": "This is what will find c1 and c2, and then I'm done." + }, + { + "text": "So let me, instead of in the last five seconds grinding out a formula, let me repeat the idea." + }, + { + "text": "That really, it's the idea that's central." + }, + { + "text": "When things are evolving in time, let me come back to this board, because the ideas are here." + }, + { + "text": "When things are evolving in time by a first-order system, starting from an original u0, the key is, find the eigenvalues and eigenvectors of A." + }, + { + "text": "That will tell, those eigenvectors, the eigenvalues will already tell you what's happening." + }, + { + "text": "Is the solution blowing up?" + }, + { + "text": "Is it going to zero?" + }, + { + "text": "What's it doing?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk24.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..40301cb90760e2172baa94d536cbc13288d4c31f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk24.json @@ -0,0 +1,20 @@ +[ + { + "text": "And then, to find out exactly a formula, you have to take your u0 and write it as a combination of eigenvectors and then follow each eigenvector separately." + }, + { + "text": "And that's really what this formula, the formula for, that's what the formula for A to the k is doing." + }, + { + "text": "So remember that formula for A to the k is S, lambda to the k S inverse." + }, + { + "text": "OK. That's, that's difference equations, and you just have to, so the homework will give some examples different from Fibonacci to follow through." + }, + { + "text": "And next time will be differential equations." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk3.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..9bf1bb852baadc1da7837e14180c0c2951a30882 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I mentioned at the end of last time, and I'll say again, that there's a small number of matrices for, that don't have n independent eigenvectors." + }, + { + "text": "So I've got to discuss that, that technical point." + }, + { + "text": "But the great, the most matrices that we see have n, n independent eigenvectors and we can diagonalize." + }, + { + "text": "This is diagonalization." + }, + { + "text": "I could also write it, and I often will, the other way round." + }, + { + "text": "If I multiply on the right by s inverse, if I took this equation at the top and multiplied on the right by s inverse, I could, I would have A left here." + }, + { + "text": "Now s inverse is coming from the right." + }, + { + "text": "So can you keep those two straight?" + }, + { + "text": "A multiplies its eigenvectors." + }, + { + "text": "That's how I keep them straight." + }, + { + "text": "So A multiplies s. A multiplies s. And then this s inverse makes the whole thing diagonal." + }, + { + "text": "And this is another way of saying the same thing, putting the s's on the other side of the equation, A is s lambda s inverse." + }, + { + "text": "So that's the, that's the new factorization." + }, + { + "text": "That's the replacement for L U from elimination or Q R from Gram-Schmidt." + }, + { + "text": "And notice that the matrix, so it's, it's a matrix times a diagonal matrix times the inverse of the first one." + }, + { + "text": "It's, that's the combination that we'll see throughout this chapter." + }, + { + "text": "This, this, combination with an s and an s inverse." + }, + { + "text": "OK. Can I just begin to use that?" + }, + { + "text": "For example, what about A squared?" + }, + { + "text": "What are the eigenvalues and eigenvectors of A squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk4.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c687b6948acad76de8781cb82d3eb069c9da514e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's a straightforward question with a, with a absolutely clean answer." + }, + { + "text": "So let me, let me consider A squared." + }, + { + "text": "So I look, I start with Ax equal lambda x." + }, + { + "text": "And I'm headed for A squared." + }, + { + "text": "So let me multiply both sides by A." + }, + { + "text": "That's one way to get A squared on the left." + }, + { + "text": "So if, I should write these ifs in here." + }, + { + "text": "If Ax equals lambda x, then I multiply by A." + }, + { + "text": "So I get A squared x equals, well, I'm multiplying by A, so that's lambda Ax." + }, + { + "text": "That lambda was a number, so I just put it on the left." + }, + { + "text": "And what do I, tell me how to make that look better." + }, + { + "text": "What have I got here?" + }, + { + "text": "For, if, if A has the eigenvalue lambda and eigenvector x, what's up with A squared?" + }, + { + "text": "A squared x, I just multiply by A, but now for Ax, I'm going to substitute lambda x, so I've got lambda squared x." + }, + { + "text": "So from that simple calculation, I, my conclusion is that the eigenvalues of A squared are lambda squared." + }, + { + "text": "And the eigenvectors, I always think about both of those." + }, + { + "text": "What can I say about the eigenvalues?" + }, + { + "text": "They're squared." + }, + { + "text": "What can I say about the eigenvectors?" + }, + { + "text": "They're the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk5.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5bf15e20707c156c8ae71c9c7acea41a9d9d8e46 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same x as in, as for A." + }, + { + "text": "Now, let me see that also from this formula." + }, + { + "text": "How can I see what A squared is looking like from this formula?" + }, + { + "text": "So let me, that, that was one way to do it." + }, + { + "text": "Let me do it by just taking A squared from that." + }, + { + "text": "A squared is S lambda S inverse, that's A, times S lambda S inverse, that's A, which is?" + }, + { + "text": "This is the beauty of eigenvalues, eigenvectors, having that S inverse and S is the identity, so I've got S lambda squared S inverse." + }, + { + "text": "Yes." + }, + { + "text": "You see what that's telling me?" + }, + { + "text": "It's, it's telling me the same thing that I just learned here, but in the, in, in a matrix form." + }, + { + "text": "It's telling me that the S is the same, the eigenvectors are the same, but the eigenvalues are squared, because this is, what's lambda squared, that's still diagonal, it's got little lambda one squared, lambda two squared, down to lambda n squared, on that diagonal, those are the eigenvalues, as we just learned, of A squared." + }, + { + "text": "OK." + }, + { + "text": "So, somehow those eigenvalues and eigenvectors are really giving you a way to, to, to, to see what's going on inside a matrix." + }, + { + "text": "Now, of course, I can continue that for, to the k-th power." + }, + { + "text": "A to the k-th power." + }, + { + "text": "If I multiply, if I have k of these together, do you see how S inverse S will keep cancelling?" + }, + { + "text": "In the, in the inside, I'll have the S outside, at the far left, and lambda will be in there k times and S inverse." + }, + { + "text": "So what's that telling me?" + }, + { + "text": "That's telling me that the eigenvalues of A, of A to the k-th power are the k-th powers." + }, + { + "text": "The eigenvalues of A cubed are the cubes of the eigenvalues of A, and the eigenvectors are the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk6.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..c18dddbe798022f7e68278ac002a3f5fe6ed249e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same." + }, + { + "text": "OK." + }, + { + "text": "In other words, eigenvalues and eigenvectors give a great way to understand the powers of a matrix." + }, + { + "text": "If I take the square of a matrix or the hundredth power of a matrix, the pivots are all over the place." + }, + { + "text": "L U, if I multiply L U times L U times L U times L U a hundred times, I've got a hundred L U's." + }, + { + "text": "I can't do anything with them." + }, + { + "text": "But when I multiply S lambda S inverse by itself, when I look at the eigenvector picture a hundred times, I get a hundred or ninety-nine of these guys cancelling out inside, and I get A to the hundredth is S lambda to the hundredth S inverse." + }, + { + "text": "I mean, eigenvalues tell you about powers of a matrix in a way that we had no, no way to approach previously." + }, + { + "text": "For example, when does, when do the powers of a matrix go to zero?" + }, + { + "text": "I would call that matrix stable, maybe." + }, + { + "text": "So, so, so I could write down a, a theorem." + }, + { + "text": "I'll, I'll write it as a theorem, just to use that word to emphasize that here I'm getting this great fact from this eigenvalue picture." + }, + { + "text": "OK. A to the k approaches zero as k goes, as k gets bigger." + }, + { + "text": "If what?" + }, + { + "text": "What's the, how can I tell for a matrix A if its powers go to zero?" + }, + { + "text": "What, what's somewhere inside that matrix is that information." + }, + { + "text": "That information is not present in the pivots." + }, + { + "text": "It's present in the eigenvalues." + }, + { + "text": "What do I need for the, to know that if I take higher and higher powers of A that this matrix gets smaller and smaller?" + }, + { + "text": "Well, S and S inverse are not moving." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk7.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b84a5c854a5542758e8a0107e1ff043205fe3bdb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's this guy that has to get small, and that's easy to, easy to understand." + }, + { + "text": "The requirement is all eigenvalues, so what is the requirement?" + }, + { + "text": "The eigenvalues have to be less than one." + }, + { + "text": "Now, I have to write that absolute value, because those eigenvalues could be negative, they could be complex numbers." + }, + { + "text": "So I'm taking the absolute value if all of those are below one." + }, + { + "text": "That's, in fact, we practically see why." + }, + { + "text": "Let me just say that I, that I, I'm operating on one assumption here, and I got to keep remembering that that assumption is still present." + }, + { + "text": "That assumption was that I had a full set of, of n independent eigenvectors." + }, + { + "text": "If I don't have that, then I, I, then this approach is not working." + }, + { + "text": "So, so again, a pure eigenvalue approach, eigenvector approach, needs n independent eigenvectors." + }, + { + "text": "If we don't have n independent eigenvectors, we can't diagonalize the matrix." + }, + { + "text": "We can't get to a diagonal matrix." + }, + { + "text": "This, this, this diagonalization is only possible if S inverse makes sense." + }, + { + "text": "OK. Can I, can I follow up on that point now?" + }, + { + "text": "So, so you see why, what we get and, and why we want it, because we get information about the powers of a matrix just immediately from the eigenvalues." + }, + { + "text": "OK, now let me follow up on this, business of which matrices are diagonalizable." + }, + { + "text": "Sorry about that long word." + }, + { + "text": "So a matrix is, is sure to, so here's, here's the main point." + }, + { + "text": "A is sure to be, to have n independent eigenvectors and, and B, now here comes that word, diagonalizable, if, if, so we, we, we might as well get the, the nice case out in the open." + }, + { + "text": "The nice case is when, if all the lambdas are different." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk8.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f06dcec8ffa0ee1bf19440e4ab2194db33ab353b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means, that means no repeated eigenvalues." + }, + { + "text": "OK. That's the nice case." + }, + { + "text": "If, if my matrix and most matrix, if I do a random matrix in MATLAB and compute its eigenvalues, so if I computed, if I took I of rand of ten ten, gave, gave that MATLAB command, the, we'd get a random ten by ten matrix, we would get a list of its ten eigenvalues and they would be different." + }, + { + "text": "They would be distinct, is the best word." + }, + { + "text": "I would have a random matrix will have ten distinct, a ten by ten matrix will have ten distinct eigenvalues, and if it does, the eigenvectors are automatically independent." + }, + { + "text": "So that's a nice fact." + }, + { + "text": "I can, I'll refer you to the text for the proof." + }, + { + "text": "That, that A is sure to have n independent eigenvectors if the eigenvalues are different." + }, + { + "text": "If, if all the, if all eigenvalues are different." + }, + { + "text": "It's just, if some lambdas are repeated, then I have to look more closely." + }, + { + "text": "If an eigenvalue is repeated, I have to look, I have to count, I have to check." + }, + { + "text": "Has it got, say it's repeated three times." + }, + { + "text": "So what's a possibility for, so, so here's, here's the repeated possibility." + }, + { + "text": "And, and let me emphasize the conclusion." + }, + { + "text": "That if I have repeated eigenvalues, I may or may not, I may or may not have, have n independent eigenvectors." + }, + { + "text": "I might." + }, + { + "text": "I, I, you know, this isn't a completely negative case." + }, + { + "text": "The identity matrix." + }, + { + "text": "Well, suppose I take the ten by ten identity matrix." + }, + { + "text": "What are the eigenvalues of that matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk9.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..87d2a2ae5773036cf11800e2f1962908986a0dad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_31_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So just, just take the easiest matrix, the identity." + }, + { + "text": "If I look for its eigenvalues, they're all ones." + }, + { + "text": "So that eigenvalue one is repeated ten times." + }, + { + "text": "But there's no shortage of eigenvectors for the identity matrix." + }, + { + "text": "In fact, every vector is an eigenvector." + }, + { + "text": "So I can take ten independent vectors." + }, + { + "text": "Oh, well, what happens to everything if, if, if A is the identity matrix, let's just think that one through in our head." + }, + { + "text": "If A is the identity matrix, then it's got plenty of eigenvectors." + }, + { + "text": "I choose ten independent vectors, they're the columns of S, and, and what do I get from S inverse A S?" + }, + { + "text": "I get I again, right?" + }, + { + "text": "If A is the identity, and of course, that's the correct lambda." + }, + { + "text": "The, the matrix was already diagonal." + }, + { + "text": "So if the matrix is already diagonal, then the, the lambda is the same as the matrix." + }, + { + "text": "A diagonal matrix has got its eigenvalues sitting right there in front of you." + }, + { + "text": "Now if it's triangular, the eigenvalues are still sitting there, but so let's, let's take a case where, it's triangular." + }, + { + "text": "Suppose A is like, two, one, two, zero." + }, + { + "text": "So there's a case that's going to be trouble." + }, + { + "text": "There's a case that's going to be trouble." + }, + { + "text": "First of all, what are the eigen- I mean, we just, like now you, if we start with a matrix, the first thing we do practically without thinking is compute the eigenvalues and eigenvectors." + }, + { + "text": "OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk0.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6898d4fe66019ef6b40d0472ea94a968e7bbde9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, shall we start?" + }, + { + "text": "This is the second lecture on eigenvalues." + }, + { + "text": "So the first lecture was set -- reached the key equation, Ax equal lambda x. x is the eigenvector and lambda is the eigenvalue." + }, + { + "text": "Now, to use that." + }, + { + "text": "And the good way to, after we've found, so job one is to find the eigenvalues and find the eigenvectors." + }, + { + "text": "Now after we found them, what do we do with them?" + }, + { + "text": "Well, the good way to see that is diagonalize the matrix." + }, + { + "text": "So the matrix is A, and I want to show, first of all, this is like the basic fact." + }, + { + "text": "This, this formula." + }, + { + "text": "That's, that's the key to today's lecture." + }, + { + "text": "This matrix A, I put its eigenvectors in the columns of a matrix S. So S will be the eigenvector matrix, and I want to look at this magic combination S inverse A S. So can I show you how that, how that, what happens there?" + }, + { + "text": "And notice, notice, there's an S inverse." + }, + { + "text": "We have to be able to invert this eigenvector matrix S. So for that we need n independent eigenvectors." + }, + { + "text": "So that's the, that's the case." + }, + { + "text": "OK." + }, + { + "text": "So suppose we have n linearly independent eigenvectors of A." + }, + { + "text": "Put them in the columns of this matrix S. So I'm naturally going to call that the eigenvector matrix, because it's got the eigenvectors in its columns." + }, + { + "text": "And all I want to do is show you what happens when you multiply A times S. So A times S. So this is A times the matrix with the first eigenvector in its first column, the second eigenvector in its second column, the nth eigenvector in its nth column." + }, + { + "text": "And how am I going to do this matrix multiplication?" + }, + { + "text": "Well, certainly I'll do it a column at a time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk1.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..fbe078217bb68baea8e0605a5d04be568c49efbf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I get?" + }, + { + "text": "A times the first column gives me the first column of the answer, but what is it?" + }, + { + "text": "That's an eigenvector." + }, + { + "text": "A times x1 is equal to the lambda times the x1." + }, + { + "text": "And that lambda's we'll call lambda one, of course." + }, + { + "text": "So that's the first column, A x1 is the same as lambda one x1." + }, + { + "text": "A x2 is lambda two x2, so on, along to, in the nth column, we now have lambda n xn." + }, + { + "text": "Looking good, but the next step is even better." + }, + { + "text": "So for the next step, I want to separate out those eigenvalues, those multiplying numbers, from the x's." + }, + { + "text": "So then I'll have just what I want." + }, + { + "text": "OK, so how, how am I going to separate out?" + }, + { + "text": "So that, that number lambda one is multiplying the first column." + }, + { + "text": "So if I want to factor it out of the first column, I better put, here is going to be x1, and that's going to multiply this matrix lambda one in the first entry in all zeros." + }, + { + "text": "You see that that, that's going to come out right for the first column?" + }, + { + "text": "Because we remember how, how we're going back to that original punchline, that if I want a number to multiply x1, then I can do it by putting x1 in that column, in the first column, and putting that number there." + }, + { + "text": "What am I going to have here?" + }, + { + "text": "I'm going to have lambda one, I'm going to have x1, x2, xn." + }, + { + "text": "These are going to be my columns again." + }, + { + "text": "I'm getting s back again." + }, + { + "text": "I'm getting s back again, but now what's it multiplied by?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk10.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c58a42edbe9567233ca7f57643a0b7d43ae6761f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what are the eigenvalues?" + }, + { + "text": "You can tell me right away what they are." + }, + { + "text": "They're two and two, right." + }, + { + "text": "It's a triangular matrix, so when I do this determinant, shall I do this determinant of A minus lambda I?" + }, + { + "text": "I'll get this two minus lambda, one, zero, two minus lambda, right?" + }, + { + "text": "I take that determinant, so I make those into vertical bars to mean determinant, and what's the determinant?" + }, + { + "text": "Two minus lambda squared." + }, + { + "text": "What are the roots?" + }, + { + "text": "Lambda equal two twice." + }, + { + "text": "So the eigenvalues are lambda equals two and two." + }, + { + "text": "OK, fine." + }, + { + "text": "Now the next step, find the eigenvectors." + }, + { + "text": "So I look for eigenvectors and what do I find for this guy?" + }, + { + "text": "Eigenvectors for this guy, when I subtract two minus the identity, so A minus two I has zeros here, and I'm looking for the null space." + }, + { + "text": "What's, what are the eigenvectors?" + }, + { + "text": "They're the, they're, they're the null space of A minus lambda I." + }, + { + "text": "The null space is only one dimension." + }, + { + "text": "This is a case where I don't have enough eigenvectors." + }, + { + "text": "My algebraic multiplicity is two." + }, + { + "text": "I, I would say when I see, when I count how often the eigenvalue is repeated, that's the algebraic multiplicity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk11.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..779c2cf904d904b761080db2671aac46394ad02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the multiplicity." + }, + { + "text": "How many times is it the root of the polynomial?" + }, + { + "text": "My polynomial is two minus lambda squared." + }, + { + "text": "It's a double root." + }, + { + "text": "So my algebraic multiplicity is two." + }, + { + "text": "But the geometric multiplicity, which looks for vectors, looks for eigenvectors and which means the null space of this thing." + }, + { + "text": "And the only eigenvector is one zero." + }, + { + "text": "That's in the null space." + }, + { + "text": "Zero one is not in the null space." + }, + { + "text": "The null space is only one dimensional." + }, + { + "text": "So there's a matrix, my, this A or the original A, that are not diagonalizable." + }, + { + "text": "I can't, I can't find two independent eigenvectors, there's only one." + }, + { + "text": "OK." + }, + { + "text": "So that's the case that I'm, that's a case that I, I'm not really handling." + }, + { + "text": "For example, when I wrote down up here that the powers went to zero if the eigenvalues were below one, I didn't really handle that case of repeated eigenvalues because my reasoning was based on this formula." + }, + { + "text": "And this formula is based on n independent eigenvectors." + }, + { + "text": "OK." + }, + { + "text": "So just to say that." + }, + { + "text": "There are some matrices that we don't cover through diagonalization, but the great majority we do." + }, + { + "text": "OK. And we're always OK if we have different distinct eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk12.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..77d090704cc298475d94416b7ecb88a2a015a913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. That's the, like, the typical case." + }, + { + "text": "Because for each eigenvalue there's at least one eigenvector, the algebraic multiplicity here is one for every eigenvalue, and the geometric multiplicity is one." + }, + { + "text": "There's one eigenvector and they are independent." + }, + { + "text": "OK. OK. Now let me come back to the important case when we're OK." + }, + { + "text": "The important case when we are diagonalizing." + }, + { + "text": "Let me look at, so let me solve this equation." + }, + { + "text": "The equation will be each, I start with some, start with a given vector u0." + }, + { + "text": "And then my equation is that every step I multiply what I have by a." + }, + { + "text": "That equation ought to be simple to handle." + }, + { + "text": "OK. And I'd like to be able to solve it." + }, + { + "text": "How would I find, if I start with a vector u0, and I multiply by a a hundred times, what have I got?" + }, + { + "text": "Well, I can certainly write down a formula for the answer." + }, + { + "text": "So what, what, so u1 is a u0." + }, + { + "text": "And u2 is, what's u2 then?" + }, + { + "text": "U2 I multiply it, u2 I get from u1 by another, multiplying by a, so I've got a twice." + }, + { + "text": "And my formula is uk, after k steps, I've multiplied by a k times the original u0." + }, + { + "text": "You see what I'm doing?" + }, + { + "text": "The next section is going to solve systems of differential equations." + }, + { + "text": "I'm going to have derivatives." + }, + { + "text": "This, this section is the nice one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk13.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..ba8214d8c636e4757a266d6617801174bc939d80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "It solves difference equations." + }, + { + "text": "I would call that a difference equation." + }, + { + "text": "It's conne- a first order." + }, + { + "text": "I would call that a first order system, because it connects only, it only goes up one level." + }, + { + "text": "And it's a system because these are vectors and that's a matrix." + }, + { + "text": "And the solution is just that." + }, + { + "text": "OK." + }, + { + "text": "But, that's a nice formula." + }, + { + "text": "That's the, like, the most compact formula I could ever get." + }, + { + "text": "U one hundred would be a to the one hundredth u0." + }, + { + "text": "But how would I actually find u one hundred?" + }, + { + "text": "How would I find, how would I discover what u one hundred is?" + }, + { + "text": "Let me, let me show you how." + }, + { + "text": "Here, here's the idea." + }, + { + "text": "If, so, to solve, to really solve, shall I say, to really solve." + }, + { + "text": "To really solve it, I would take this initial vector, u0, and I would write it as a combination of eigenvectors." + }, + { + "text": "To really solve, write, write u0 as a combination, say, certain amount of the first eigenvector plus a certain amount of the second eigenvector plus a certain amount of the last eigenvector." + }, + { + "text": "Now multiply by a." + }, + { + "text": "You want to, you got to see the magic of eigenvectors work." + }, + { + "text": "Multiply by a." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk14.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7843b2bf0cac762d1c12452cf36500ea4ad13370 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a u0 is what?" + }, + { + "text": "So a times that." + }, + { + "text": "A times, so what's, I can separate it out into n separate pieces and that's the whole point." + }, + { + "text": "That each of those pieces is going in its own merry way." + }, + { + "text": "Each of those pieces is an eigenvector, and when I multiply by a, what does this piece become?" + }, + { + "text": "So that's some amount of the first, let's suppose the eigenvectors are normalized to be unit vectors." + }, + { + "text": "So that says what the eigenvector is." + }, + { + "text": "It's, and I need some multiple of it to produce u0." + }, + { + "text": "OK. Now when I multiply by a, what do I get?" + }, + { + "text": "I get c1, which is just a factor, times a x1, but a x1 is lambda one x1." + }, + { + "text": "When I multiply this by a, I get c2 lambda two x2." + }, + { + "text": "And here I get cn lambda n xn." + }, + { + "text": "And suppose I multiply by a to the hundredth power now." + }, + { + "text": "Can we, can we, having done it, multiplied by a, let's multiply by a to the hundredth." + }, + { + "text": "What happens to this first term when I multiply by a to the one hundredth?" + }, + { + "text": "It's got that factor lambda to the hundredth." + }, + { + "text": "That's the key." + }, + { + "text": "That, that's what I mean by going its own merry way." + }, + { + "text": "It, it is pure eigenvector, it's exactly in a direction where multiplication by a just brings in a scalar factor lambda one." + }, + { + "text": "So a hundred times brings in this a hundred times." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk15.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7ee3348735378aa4049d33ec2a197d0ceb0c447c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Hundred times lambda two, hundred times lambda n. Actually, we're, what are we seeing here?" + }, + { + "text": "We're seeing, this same, lambda, capital lambda to the hundredth, as in the, as in the diagonalization, and we're seeing the S matrix, the matrix S of eigenvectors." + }, + { + "text": "That's what this has got to, this has got to amount to, a lambda to the hundredth power times an S times this vector C that's telling us how much of each one is in the original thing." + }, + { + "text": "So if, if I had to really find the hundredth power, I would take u0, I would expand it as a combination of eigenvectors, this is really S, the eigenvector matrix times C, the, the coefficient vector." + }, + { + "text": "And then I would immediately, then, by inserting these hundredth powers of eigenvalues, I'd have the answer." + }, + { + "text": "So the, the, huh, there must be, well, let's see." + }, + { + "text": "OK." + }, + { + "text": "It's, so, yeah." + }, + { + "text": "So if u100 is a to the hundredth times u0, and u0 is Sc, then you see this formula is just this formula, which is the way I would actually get hold of this, of this u100, which is, let me put it here, u100." + }, + { + "text": "The way I would actually get hold of that, see what, what the solution is after a hundred steps, would be expand the initial vector into eigenvectors and, and let each eigenvector go its own way, multiplying by a hundred at, by lambda at every step, and therefore by lambda to the hundredth power after a hundredth step." + }, + { + "text": "Can I do an example?" + }, + { + "text": "So that's, that's the, the formulas." + }, + { + "text": "Now let me take an example." + }, + { + "text": "I'll use the Fibonacci sequence as an example." + }, + { + "text": "So, so Fibonacci example." + }, + { + "text": "You remember the Fibonacci numbers?" + }, + { + "text": "If we start with one and one as F0, oh, I think I start with zero, maybe." + }, + { + "text": "Let zero and one be the first ones." + }, + { + "text": "So there's F0 and F1, the first two Fibonacci numbers." + }, + { + "text": "Then what's the rule for Fibonacci numbers?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk16.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..79c65e32781f7f304b504a6c390247abb9d26ac8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "They're the sum." + }, + { + "text": "The next one is the sum of those, so it's one." + }, + { + "text": "The next one is the sum of those, so it's two." + }, + { + "text": "The next one is the sum of those, so it's three." + }, + { + "text": "Well, it looks like one, two, three, four, five, but somehow it's not going to do that way." + }, + { + "text": "The next one is five, right." + }, + { + "text": "Two and three makes five." + }, + { + "text": "The next one is eight." + }, + { + "text": "The next one is thirteen." + }, + { + "text": "And the one hundredth Fibonacci number is what?" + }, + { + "text": "That's my question." + }, + { + "text": "How could I get a formula for the hundredth number and for example how could I answer the question how fast are they growing?" + }, + { + "text": "How fast are those Fibonacci numbers growing?" + }, + { + "text": "They're certainly growing." + }, + { + "text": "It's not a stable case, whatever the eigenvalues of whatever matrix it is, they're not smaller than one." + }, + { + "text": "These numbers are growing." + }, + { + "text": "But how fast are they growing?" + }, + { + "text": "The answer is lies in the eigenvalue." + }, + { + "text": "So I've got to find the matrix, so let me write down the Fibonacci rule, F k plus two is F k plus one plus F k, right?" + }, + { + "text": "Now that's not in my -- I want to write that as U k plus one and A U k. But right now what I've got is a single equation, not a system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk17.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b3aaa9dcee3cf27c112015659bb5a0b51a983ce1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's second order." + }, + { + "text": "It's like having a second order differential equation with second derivatives." + }, + { + "text": "I want to get first derivatives." + }, + { + "text": "Here I want to get first difference." + }, + { + "text": "So the way to do it is to introduce U k will be a vector." + }, + { + "text": "See, a small trick." + }, + { + "text": "Let U k be a vector, F k plus one and F k. So I'm going to get a two by two system, first order, instead of a one, instead of a scalar system, second order, by a simple trick." + }, + { + "text": "I'm just going to add in an equation F k plus one equals F k plus one." + }, + { + "text": "That will be my second equation." + }, + { + "text": "Then this is my system, this is my unknown, and what's my one-step equation?" + }, + { + "text": "So now U k plus one." + }, + { + "text": "That's so U k plus one is the left side, and what have I got here on the right side?" + }, + { + "text": "I've got some matrix multiplying U k. Can you see that all right?" + }, + { + "text": "If you can see it, then you can tell me what the matrix is." + }, + { + "text": "You see that I'm taking my system here, I artificially made it into a system." + }, + { + "text": "I artificially made the unknown into a vector, and now I'm ready to look at and see what the matrix is." + }, + { + "text": "So do you see the left side, U k plus one is F k plus two F k plus one, that's just what I want." + }, + { + "text": "On the right side, this, remember, this U k here, let me for the moment put it as F k plus one F k. So what's the matrix?" + }, + { + "text": "Well, that has a one and a one, and that has a one and a zero." + }, + { + "text": "There's the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk18.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..6c1b68c2cb2fde3f5dea82f3100d4da31fcce70a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "You see that that gives me the right-hand side." + }, + { + "text": "So there's the matrix A, and this is our friend U k. So we've got, so that simple trick changed the second order scalar problem to a first order system, two, with two unknowns." + }, + { + "text": "With a matrix and now what do I do?" + }, + { + "text": "Well, before I even think, I find its eigenvalues and eigenvectors." + }, + { + "text": "So what are the eigenvalues and eigenvectors of that matrix?" + }, + { + "text": "Let's see." + }, + { + "text": "I was, first let me just, like, think for a minute." + }, + { + "text": "It's two by two, so this shouldn't be impossible to do." + }, + { + "text": "Let's do it." + }, + { + "text": "OK." + }, + { + "text": "So my matrix again is one one one zero." + }, + { + "text": "It's symmetric, by the way." + }, + { + "text": "So what I will eventually know about symmetric matrices is that the eigenvalues will come out real, I won't get any complex numbers here, and the eigenvectors, once I get those, actually will be orthogonal." + }, + { + "text": "But two by two, I'm more interested in what the actual numbers are." + }, + { + "text": "What do I know about the two numbers?" + }, + { + "text": "Well, should, do you want me to find this determinant of A minus lambda I?" + }, + { + "text": "Sure." + }, + { + "text": "So it's the determinant of one minus lambda one one zero, right?" + }, + { + "text": "Minus lambda, yes, got it." + }, + { + "text": "OK. OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk19.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..a73b23e3d56b889ff49ea7f55a784fac33e13c3d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "There'll be two eigenvalues." + }, + { + "text": "Well, tell me again what I know about the two eigenvalues before I go any further." + }, + { + "text": "Tell me something about these two eigenvalues, what do they add up to?" + }, + { + "text": "Lambda one plus lambda two is the same as the trace down the diagonal of the matrix, one and zero is one." + }, + { + "text": "So lambda one plus lambda two should come out to be one, and lambda one times lambda two should come out to be the determinant, which is minus one." + }, + { + "text": "So I'm expecting the eigenvalues to add to one and to multiply to minus one." + }, + { + "text": "But let's just see it happen here." + }, + { + "text": "If I multiply this out, I get that times that'll be a lambda squared minus lambda minus one." + }, + { + "text": "Good." + }, + { + "text": "Lambda squared minus lambda minus one." + }, + { + "text": "Actually, you see the, compare that with the original equation that I started with." + }, + { + "text": "Fk plus two minus Fk plus one minus Fk is zero." + }, + { + "text": "The recurrent, the recursion that the Fibonacci number satisfy is somehow showing up directly here for the eigenvalues when we set that to zero." + }, + { + "text": "OK. Let's solve." + }, + { + "text": "Well, I would like to be able to factor that, that quadratic, but I'm better off to use the quadratic formula." + }, + { + "text": "Lambda is, let's see, minus b is one, plus or minus the square root of b squared, which is one, minus four, times that, times that, which is plus four, over two." + }, + { + "text": "So that's the square root of five." + }, + { + "text": "So the eigenvalues are lambda one is one half of one plus square root of five, and lambda two is one half of one minus square root of five." + }, + { + "text": "And sure enough, they, those add up to one, and they multiply to give minus one." + }, + { + "text": "OK. Those are the two eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk2.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..43cfb012fc04a89fc7dab94c23bfb0f50ade3782 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "On the right, it's multiplied by, if I want, if I want lambda n xn in the last column, how do I do it?" + }, + { + "text": "Well, the last column here will be, I'll, I'll take the last column, use these coefficients, put the lambda n down there, and it will multiply that nth column and give me lambda n xn." + }, + { + "text": "There, there you see matrix multiplication just working for us." + }, + { + "text": "So I started with A s. I wrote down what it meant." + }, + { + "text": "A times each eigenvector." + }, + { + "text": "That gave me lambda times the eigenvector." + }, + { + "text": "And then when I peeled off the lambdas, they were on the right-hand side, so I've got s, my matrix back again, and this matrix, this diagonal matrix, the eigenvalue matrix, and I call it capital lambda, using capital letters for matrices, and lambda to prompt me that it's, that it's eigenvalues that are in there." + }, + { + "text": "So you see that the eigenvalues are just sitting down that diagonal?" + }, + { + "text": "If I had a column x2 here, I would want the lambda two in the two two position, in the diagonal position, to multiply that x2 and give me the lambda two x2." + }, + { + "text": "That's my formula." + }, + { + "text": "A s is s lambda." + }, + { + "text": "OK. That's, that's the, you see, it's just a calculation." + }, + { + "text": "Now, I, I mentioned, and I have to mention again, this business about n independent eigenvectors." + }, + { + "text": "As it stands, this is all fine whether, I mean, I could be repeating the same eigenvector, but I, I'm no interested in that." + }, + { + "text": "I want to be able to invert s, and that's where this comes in." + }, + { + "text": "This n independent eigenvectors business comes in to tell me that that matrix is invertible." + }, + { + "text": "So let me, on the next board, write down what I've got." + }, + { + "text": "A s equals s lambda." + }, + { + "text": "And now I'm, I can multiply on the left by s inverse." + }, + { + "text": "So this is really, I can do that provided s is invertible, provided my assumption of n independent eigenvectors is satisfied." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk20.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ad5a59fa5db44ce73ff5f88190423e0404fb3d39 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "How, how, what are those numbers approximately?" + }, + { + "text": "Square root of five, well, it's more than two, but less than three." + }, + { + "text": "It, it'd be nice to know these numbers." + }, + { + "text": "I think, I think that that, so that number comes out bigger than one, right?" + }, + { + "text": "Yeah, that's right." + }, + { + "text": "This number comes out bigger than one." + }, + { + "text": "It's about one point six one eight or something." + }, + { + "text": "Not exactly." + }, + { + "text": "It's supposed to be one point six." + }, + { + "text": "Just, like, I think so." + }, + { + "text": "Then what's lambda two?" + }, + { + "text": "Is, is lambda two positive or negative?" + }, + { + "text": "Negative, right?" + }, + { + "text": "Because I'm, it's obviously negative, and I knew that the, so it's minus, and they add up to one, so minus point six one eight, I guess." + }, + { + "text": "OK. And some order." + }, + { + "text": "Those are the two eigenvalues." + }, + { + "text": "One eigenvalue bigger than one, one eigenvalue smaller than one." + }, + { + "text": "Actually, that's a great situation to be in." + }, + { + "text": "Of course, the eigenvalues are different, so there's no doubt whatever, is this matrix diagonalizable?" + }, + { + "text": "Is this matrix diagonalizable, that original matrix A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk21.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..4a034475591d371995b379b5f98783a2cfb25870 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Sure." + }, + { + "text": "We've got two distinct eigenvalues and we can find the eigenvectors in a moment." + }, + { + "text": "But they'll be independent, will be diagonalizable, and now you can already answer my very first question." + }, + { + "text": "How fast are those Fibonacci numbers increasing?" + }, + { + "text": "How, those, they're increasing, right?" + }, + { + "text": "They're not doubling at every step." + }, + { + "text": "Let's look again at these numbers." + }, + { + "text": "Five eight thirteen, it's not obvious." + }, + { + "text": "The next one would be twenty one thirty four." + }, + { + "text": "So to get some idea of what F one hundred is, can you give me any, I mean the crucial number of, so it, these, it's approximately, what's controlling the growth of these Fibonacci numbers?" + }, + { + "text": "It's the eigenvalues." + }, + { + "text": "And which eigenvalues controlling that growth?" + }, + { + "text": "The big ones." + }, + { + "text": "So F one hundred will it be approximately some constant, c one, I guess, times this lambda one, this one plus square root of five over two, to the hundredth power." + }, + { + "text": "And the two hundredth have, in other words, the eigenvalue, the Fibonacci numbers are growing by about that factor." + }, + { + "text": "You see that we've got precise information about the, about the Fibonacci numbers out of the eigenvalue." + }, + { + "text": "OK. And again, why is that true?" + }, + { + "text": "Let me go over to this board and show what I'm doing here." + }, + { + "text": "The, the original eigen, the original initial value is some combination of eigenvectors, and then when we start multiple, when we start going out the theory of Fibonacci numbers, when we start multiplying by a hundred times, it's this lambda one to the hundredth, this term is, is the one that's taken over." + }, + { + "text": "It's, I mean, that's big, like, one point six to the hundredth power." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk22.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..c13a1fc9867173c3067e46c469cfff27b9b45289 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "The second term is practically nothing, right?" + }, + { + "text": "The point six, or minus point six to the hundredth power, is an extremely small, extremely small number." + }, + { + "text": "So this is, this, this, there are only two terms, because we're two by two." + }, + { + "text": "This number is, this piece of it is there, but it's, it's disappearing." + }, + { + "text": "Where this piece is there and it's growing and controlling everything." + }, + { + "text": "So, so really the, we're doing, like, problems that are evolving." + }, + { + "text": "We're doing dynamics." + }, + { + "text": "Instead of Ax equal b, that's a static problem." + }, + { + "text": "We're now, we're doing dynamics." + }, + { + "text": "A, a squared, a cubed, things are evolving in time, and the eigenvalues are the crucial, numbers." + }, + { + "text": "OK." + }, + { + "text": "I guess to complete this, I better write down the eigenvectors." + }, + { + "text": "So we should complete the, the whole process by finding the eigenvectors." + }, + { + "text": "OK. Well, I have to, up in the corner, then I have to look at A minus lambda I." + }, + { + "text": "So A minus lambda I is this one minus lambda, one, one, and minus lambda." + }, + { + "text": "And now, can we spot an eigenvector out of that?" + }, + { + "text": "That's, for these two lambdas, this matrix is singular." + }, + { + "text": "I guess the eigenvector, two by two ought to be easy." + }, + { + "text": "So if I know that this matrix is singular, then it seems to me the eigenvector has to be lambda and one, because that multiplication will give me the zero." + }, + { + "text": "And this multiplication gives me, better give me also zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk23.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..df816eb800ce767b1475c279a24ad976bb45a785 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Do you see why it does?" + }, + { + "text": "This is the minus lambda squared plus lambda plus one." + }, + { + "text": "It's the thing that's zero, because these lambdas are special." + }, + { + "text": "There's the eigenvector." + }, + { + "text": "X1 is lambda one, one, and x2 is lambda two, one." + }, + { + "text": "I did that as a little trick that was available in the two by two case." + }, + { + "text": "So now I finally have to, oh, I have to take the initial, u0." + }, + { + "text": "So to complete this example entirely, I have to say, OK, what was u0?" + }, + { + "text": "u0 was f1 f0." + }, + { + "text": "So u0, the starting vector, is f1 f0, and those were one and zero." + }, + { + "text": "So I have to use that vector, so I have to look for, from multiple of the first eigenvector and the second, to produce u0, the one zero vector." + }, + { + "text": "This is what will find c1 and c2, and then I'm done." + }, + { + "text": "So let me, instead of in the last five seconds grinding out a formula, let me repeat the idea." + }, + { + "text": "That really, it's the idea that's central." + }, + { + "text": "When things are evolving in time, let me come back to this board, because the ideas are here." + }, + { + "text": "When things are evolving in time by a first-order system, starting from an original u0, the key is, find the eigenvalues and eigenvectors of A." + }, + { + "text": "That will tell, those eigenvectors, the eigenvalues will already tell you what's happening." + }, + { + "text": "Is the solution blowing up?" + }, + { + "text": "Is it going to zero?" + }, + { + "text": "What's it doing?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk24.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..40301cb90760e2172baa94d536cbc13288d4c31f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk24.json @@ -0,0 +1,20 @@ +[ + { + "text": "And then, to find out exactly a formula, you have to take your u0 and write it as a combination of eigenvectors and then follow each eigenvector separately." + }, + { + "text": "And that's really what this formula, the formula for, that's what the formula for A to the k is doing." + }, + { + "text": "So remember that formula for A to the k is S, lambda to the k S inverse." + }, + { + "text": "OK. That's, that's difference equations, and you just have to, so the homework will give some examples different from Fibonacci to follow through." + }, + { + "text": "And next time will be differential equations." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk3.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..9bf1bb852baadc1da7837e14180c0c2951a30882 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I mentioned at the end of last time, and I'll say again, that there's a small number of matrices for, that don't have n independent eigenvectors." + }, + { + "text": "So I've got to discuss that, that technical point." + }, + { + "text": "But the great, the most matrices that we see have n, n independent eigenvectors and we can diagonalize." + }, + { + "text": "This is diagonalization." + }, + { + "text": "I could also write it, and I often will, the other way round." + }, + { + "text": "If I multiply on the right by s inverse, if I took this equation at the top and multiplied on the right by s inverse, I could, I would have A left here." + }, + { + "text": "Now s inverse is coming from the right." + }, + { + "text": "So can you keep those two straight?" + }, + { + "text": "A multiplies its eigenvectors." + }, + { + "text": "That's how I keep them straight." + }, + { + "text": "So A multiplies s. A multiplies s. And then this s inverse makes the whole thing diagonal." + }, + { + "text": "And this is another way of saying the same thing, putting the s's on the other side of the equation, A is s lambda s inverse." + }, + { + "text": "So that's the, that's the new factorization." + }, + { + "text": "That's the replacement for L U from elimination or Q R from Gram-Schmidt." + }, + { + "text": "And notice that the matrix, so it's, it's a matrix times a diagonal matrix times the inverse of the first one." + }, + { + "text": "It's, that's the combination that we'll see throughout this chapter." + }, + { + "text": "This, this, combination with an s and an s inverse." + }, + { + "text": "OK. Can I just begin to use that?" + }, + { + "text": "For example, what about A squared?" + }, + { + "text": "What are the eigenvalues and eigenvectors of A squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk4.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c687b6948acad76de8781cb82d3eb069c9da514e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's a straightforward question with a, with a absolutely clean answer." + }, + { + "text": "So let me, let me consider A squared." + }, + { + "text": "So I look, I start with Ax equal lambda x." + }, + { + "text": "And I'm headed for A squared." + }, + { + "text": "So let me multiply both sides by A." + }, + { + "text": "That's one way to get A squared on the left." + }, + { + "text": "So if, I should write these ifs in here." + }, + { + "text": "If Ax equals lambda x, then I multiply by A." + }, + { + "text": "So I get A squared x equals, well, I'm multiplying by A, so that's lambda Ax." + }, + { + "text": "That lambda was a number, so I just put it on the left." + }, + { + "text": "And what do I, tell me how to make that look better." + }, + { + "text": "What have I got here?" + }, + { + "text": "For, if, if A has the eigenvalue lambda and eigenvector x, what's up with A squared?" + }, + { + "text": "A squared x, I just multiply by A, but now for Ax, I'm going to substitute lambda x, so I've got lambda squared x." + }, + { + "text": "So from that simple calculation, I, my conclusion is that the eigenvalues of A squared are lambda squared." + }, + { + "text": "And the eigenvectors, I always think about both of those." + }, + { + "text": "What can I say about the eigenvalues?" + }, + { + "text": "They're squared." + }, + { + "text": "What can I say about the eigenvectors?" + }, + { + "text": "They're the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk5.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5bf15e20707c156c8ae71c9c7acea41a9d9d8e46 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same x as in, as for A." + }, + { + "text": "Now, let me see that also from this formula." + }, + { + "text": "How can I see what A squared is looking like from this formula?" + }, + { + "text": "So let me, that, that was one way to do it." + }, + { + "text": "Let me do it by just taking A squared from that." + }, + { + "text": "A squared is S lambda S inverse, that's A, times S lambda S inverse, that's A, which is?" + }, + { + "text": "This is the beauty of eigenvalues, eigenvectors, having that S inverse and S is the identity, so I've got S lambda squared S inverse." + }, + { + "text": "Yes." + }, + { + "text": "You see what that's telling me?" + }, + { + "text": "It's, it's telling me the same thing that I just learned here, but in the, in, in a matrix form." + }, + { + "text": "It's telling me that the S is the same, the eigenvectors are the same, but the eigenvalues are squared, because this is, what's lambda squared, that's still diagonal, it's got little lambda one squared, lambda two squared, down to lambda n squared, on that diagonal, those are the eigenvalues, as we just learned, of A squared." + }, + { + "text": "OK." + }, + { + "text": "So, somehow those eigenvalues and eigenvectors are really giving you a way to, to, to, to see what's going on inside a matrix." + }, + { + "text": "Now, of course, I can continue that for, to the k-th power." + }, + { + "text": "A to the k-th power." + }, + { + "text": "If I multiply, if I have k of these together, do you see how S inverse S will keep cancelling?" + }, + { + "text": "In the, in the inside, I'll have the S outside, at the far left, and lambda will be in there k times and S inverse." + }, + { + "text": "So what's that telling me?" + }, + { + "text": "That's telling me that the eigenvalues of A, of A to the k-th power are the k-th powers." + }, + { + "text": "The eigenvalues of A cubed are the cubes of the eigenvalues of A, and the eigenvectors are the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk6.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..c18dddbe798022f7e68278ac002a3f5fe6ed249e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same." + }, + { + "text": "OK." + }, + { + "text": "In other words, eigenvalues and eigenvectors give a great way to understand the powers of a matrix." + }, + { + "text": "If I take the square of a matrix or the hundredth power of a matrix, the pivots are all over the place." + }, + { + "text": "L U, if I multiply L U times L U times L U times L U a hundred times, I've got a hundred L U's." + }, + { + "text": "I can't do anything with them." + }, + { + "text": "But when I multiply S lambda S inverse by itself, when I look at the eigenvector picture a hundred times, I get a hundred or ninety-nine of these guys cancelling out inside, and I get A to the hundredth is S lambda to the hundredth S inverse." + }, + { + "text": "I mean, eigenvalues tell you about powers of a matrix in a way that we had no, no way to approach previously." + }, + { + "text": "For example, when does, when do the powers of a matrix go to zero?" + }, + { + "text": "I would call that matrix stable, maybe." + }, + { + "text": "So, so, so I could write down a, a theorem." + }, + { + "text": "I'll, I'll write it as a theorem, just to use that word to emphasize that here I'm getting this great fact from this eigenvalue picture." + }, + { + "text": "OK. A to the k approaches zero as k goes, as k gets bigger." + }, + { + "text": "If what?" + }, + { + "text": "What's the, how can I tell for a matrix A if its powers go to zero?" + }, + { + "text": "What, what's somewhere inside that matrix is that information." + }, + { + "text": "That information is not present in the pivots." + }, + { + "text": "It's present in the eigenvalues." + }, + { + "text": "What do I need for the, to know that if I take higher and higher powers of A that this matrix gets smaller and smaller?" + }, + { + "text": "Well, S and S inverse are not moving." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk7.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b84a5c854a5542758e8a0107e1ff043205fe3bdb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's this guy that has to get small, and that's easy to, easy to understand." + }, + { + "text": "The requirement is all eigenvalues, so what is the requirement?" + }, + { + "text": "The eigenvalues have to be less than one." + }, + { + "text": "Now, I have to write that absolute value, because those eigenvalues could be negative, they could be complex numbers." + }, + { + "text": "So I'm taking the absolute value if all of those are below one." + }, + { + "text": "That's, in fact, we practically see why." + }, + { + "text": "Let me just say that I, that I, I'm operating on one assumption here, and I got to keep remembering that that assumption is still present." + }, + { + "text": "That assumption was that I had a full set of, of n independent eigenvectors." + }, + { + "text": "If I don't have that, then I, I, then this approach is not working." + }, + { + "text": "So, so again, a pure eigenvalue approach, eigenvector approach, needs n independent eigenvectors." + }, + { + "text": "If we don't have n independent eigenvectors, we can't diagonalize the matrix." + }, + { + "text": "We can't get to a diagonal matrix." + }, + { + "text": "This, this, this diagonalization is only possible if S inverse makes sense." + }, + { + "text": "OK. Can I, can I follow up on that point now?" + }, + { + "text": "So, so you see why, what we get and, and why we want it, because we get information about the powers of a matrix just immediately from the eigenvalues." + }, + { + "text": "OK, now let me follow up on this, business of which matrices are diagonalizable." + }, + { + "text": "Sorry about that long word." + }, + { + "text": "So a matrix is, is sure to, so here's, here's the main point." + }, + { + "text": "A is sure to be, to have n independent eigenvectors and, and B, now here comes that word, diagonalizable, if, if, so we, we, we might as well get the, the nice case out in the open." + }, + { + "text": "The nice case is when, if all the lambdas are different." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk8.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f06dcec8ffa0ee1bf19440e4ab2194db33ab353b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means, that means no repeated eigenvalues." + }, + { + "text": "OK. That's the nice case." + }, + { + "text": "If, if my matrix and most matrix, if I do a random matrix in MATLAB and compute its eigenvalues, so if I computed, if I took I of rand of ten ten, gave, gave that MATLAB command, the, we'd get a random ten by ten matrix, we would get a list of its ten eigenvalues and they would be different." + }, + { + "text": "They would be distinct, is the best word." + }, + { + "text": "I would have a random matrix will have ten distinct, a ten by ten matrix will have ten distinct eigenvalues, and if it does, the eigenvectors are automatically independent." + }, + { + "text": "So that's a nice fact." + }, + { + "text": "I can, I'll refer you to the text for the proof." + }, + { + "text": "That, that A is sure to have n independent eigenvectors if the eigenvalues are different." + }, + { + "text": "If, if all the, if all eigenvalues are different." + }, + { + "text": "It's just, if some lambdas are repeated, then I have to look more closely." + }, + { + "text": "If an eigenvalue is repeated, I have to look, I have to count, I have to check." + }, + { + "text": "Has it got, say it's repeated three times." + }, + { + "text": "So what's a possibility for, so, so here's, here's the repeated possibility." + }, + { + "text": "And, and let me emphasize the conclusion." + }, + { + "text": "That if I have repeated eigenvalues, I may or may not, I may or may not have, have n independent eigenvectors." + }, + { + "text": "I might." + }, + { + "text": "I, I, you know, this isn't a completely negative case." + }, + { + "text": "The identity matrix." + }, + { + "text": "Well, suppose I take the ten by ten identity matrix." + }, + { + "text": "What are the eigenvalues of that matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk9.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..87d2a2ae5773036cf11800e2f1962908986a0dad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_32_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So just, just take the easiest matrix, the identity." + }, + { + "text": "If I look for its eigenvalues, they're all ones." + }, + { + "text": "So that eigenvalue one is repeated ten times." + }, + { + "text": "But there's no shortage of eigenvectors for the identity matrix." + }, + { + "text": "In fact, every vector is an eigenvector." + }, + { + "text": "So I can take ten independent vectors." + }, + { + "text": "Oh, well, what happens to everything if, if, if A is the identity matrix, let's just think that one through in our head." + }, + { + "text": "If A is the identity matrix, then it's got plenty of eigenvectors." + }, + { + "text": "I choose ten independent vectors, they're the columns of S, and, and what do I get from S inverse A S?" + }, + { + "text": "I get I again, right?" + }, + { + "text": "If A is the identity, and of course, that's the correct lambda." + }, + { + "text": "The, the matrix was already diagonal." + }, + { + "text": "So if the matrix is already diagonal, then the, the lambda is the same as the matrix." + }, + { + "text": "A diagonal matrix has got its eigenvalues sitting right there in front of you." + }, + { + "text": "Now if it's triangular, the eigenvalues are still sitting there, but so let's, let's take a case where, it's triangular." + }, + { + "text": "Suppose A is like, two, one, two, zero." + }, + { + "text": "So there's a case that's going to be trouble." + }, + { + "text": "There's a case that's going to be trouble." + }, + { + "text": "First of all, what are the eigen- I mean, we just, like now you, if we start with a matrix, the first thing we do practically without thinking is compute the eigenvalues and eigenvectors." + }, + { + "text": "OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk0.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6898d4fe66019ef6b40d0472ea94a968e7bbde9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, shall we start?" + }, + { + "text": "This is the second lecture on eigenvalues." + }, + { + "text": "So the first lecture was set -- reached the key equation, Ax equal lambda x. x is the eigenvector and lambda is the eigenvalue." + }, + { + "text": "Now, to use that." + }, + { + "text": "And the good way to, after we've found, so job one is to find the eigenvalues and find the eigenvectors." + }, + { + "text": "Now after we found them, what do we do with them?" + }, + { + "text": "Well, the good way to see that is diagonalize the matrix." + }, + { + "text": "So the matrix is A, and I want to show, first of all, this is like the basic fact." + }, + { + "text": "This, this formula." + }, + { + "text": "That's, that's the key to today's lecture." + }, + { + "text": "This matrix A, I put its eigenvectors in the columns of a matrix S. So S will be the eigenvector matrix, and I want to look at this magic combination S inverse A S. So can I show you how that, how that, what happens there?" + }, + { + "text": "And notice, notice, there's an S inverse." + }, + { + "text": "We have to be able to invert this eigenvector matrix S. So for that we need n independent eigenvectors." + }, + { + "text": "So that's the, that's the case." + }, + { + "text": "OK." + }, + { + "text": "So suppose we have n linearly independent eigenvectors of A." + }, + { + "text": "Put them in the columns of this matrix S. So I'm naturally going to call that the eigenvector matrix, because it's got the eigenvectors in its columns." + }, + { + "text": "And all I want to do is show you what happens when you multiply A times S. So A times S. So this is A times the matrix with the first eigenvector in its first column, the second eigenvector in its second column, the nth eigenvector in its nth column." + }, + { + "text": "And how am I going to do this matrix multiplication?" + }, + { + "text": "Well, certainly I'll do it a column at a time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk1.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..fbe078217bb68baea8e0605a5d04be568c49efbf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I get?" + }, + { + "text": "A times the first column gives me the first column of the answer, but what is it?" + }, + { + "text": "That's an eigenvector." + }, + { + "text": "A times x1 is equal to the lambda times the x1." + }, + { + "text": "And that lambda's we'll call lambda one, of course." + }, + { + "text": "So that's the first column, A x1 is the same as lambda one x1." + }, + { + "text": "A x2 is lambda two x2, so on, along to, in the nth column, we now have lambda n xn." + }, + { + "text": "Looking good, but the next step is even better." + }, + { + "text": "So for the next step, I want to separate out those eigenvalues, those multiplying numbers, from the x's." + }, + { + "text": "So then I'll have just what I want." + }, + { + "text": "OK, so how, how am I going to separate out?" + }, + { + "text": "So that, that number lambda one is multiplying the first column." + }, + { + "text": "So if I want to factor it out of the first column, I better put, here is going to be x1, and that's going to multiply this matrix lambda one in the first entry in all zeros." + }, + { + "text": "You see that that, that's going to come out right for the first column?" + }, + { + "text": "Because we remember how, how we're going back to that original punchline, that if I want a number to multiply x1, then I can do it by putting x1 in that column, in the first column, and putting that number there." + }, + { + "text": "What am I going to have here?" + }, + { + "text": "I'm going to have lambda one, I'm going to have x1, x2, xn." + }, + { + "text": "These are going to be my columns again." + }, + { + "text": "I'm getting s back again." + }, + { + "text": "I'm getting s back again, but now what's it multiplied by?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk10.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c58a42edbe9567233ca7f57643a0b7d43ae6761f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what are the eigenvalues?" + }, + { + "text": "You can tell me right away what they are." + }, + { + "text": "They're two and two, right." + }, + { + "text": "It's a triangular matrix, so when I do this determinant, shall I do this determinant of A minus lambda I?" + }, + { + "text": "I'll get this two minus lambda, one, zero, two minus lambda, right?" + }, + { + "text": "I take that determinant, so I make those into vertical bars to mean determinant, and what's the determinant?" + }, + { + "text": "Two minus lambda squared." + }, + { + "text": "What are the roots?" + }, + { + "text": "Lambda equal two twice." + }, + { + "text": "So the eigenvalues are lambda equals two and two." + }, + { + "text": "OK, fine." + }, + { + "text": "Now the next step, find the eigenvectors." + }, + { + "text": "So I look for eigenvectors and what do I find for this guy?" + }, + { + "text": "Eigenvectors for this guy, when I subtract two minus the identity, so A minus two I has zeros here, and I'm looking for the null space." + }, + { + "text": "What's, what are the eigenvectors?" + }, + { + "text": "They're the, they're, they're the null space of A minus lambda I." + }, + { + "text": "The null space is only one dimension." + }, + { + "text": "This is a case where I don't have enough eigenvectors." + }, + { + "text": "My algebraic multiplicity is two." + }, + { + "text": "I, I would say when I see, when I count how often the eigenvalue is repeated, that's the algebraic multiplicity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk11.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..779c2cf904d904b761080db2671aac46394ad02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the multiplicity." + }, + { + "text": "How many times is it the root of the polynomial?" + }, + { + "text": "My polynomial is two minus lambda squared." + }, + { + "text": "It's a double root." + }, + { + "text": "So my algebraic multiplicity is two." + }, + { + "text": "But the geometric multiplicity, which looks for vectors, looks for eigenvectors and which means the null space of this thing." + }, + { + "text": "And the only eigenvector is one zero." + }, + { + "text": "That's in the null space." + }, + { + "text": "Zero one is not in the null space." + }, + { + "text": "The null space is only one dimensional." + }, + { + "text": "So there's a matrix, my, this A or the original A, that are not diagonalizable." + }, + { + "text": "I can't, I can't find two independent eigenvectors, there's only one." + }, + { + "text": "OK." + }, + { + "text": "So that's the case that I'm, that's a case that I, I'm not really handling." + }, + { + "text": "For example, when I wrote down up here that the powers went to zero if the eigenvalues were below one, I didn't really handle that case of repeated eigenvalues because my reasoning was based on this formula." + }, + { + "text": "And this formula is based on n independent eigenvectors." + }, + { + "text": "OK." + }, + { + "text": "So just to say that." + }, + { + "text": "There are some matrices that we don't cover through diagonalization, but the great majority we do." + }, + { + "text": "OK. And we're always OK if we have different distinct eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk12.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..77d090704cc298475d94416b7ecb88a2a015a913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. That's the, like, the typical case." + }, + { + "text": "Because for each eigenvalue there's at least one eigenvector, the algebraic multiplicity here is one for every eigenvalue, and the geometric multiplicity is one." + }, + { + "text": "There's one eigenvector and they are independent." + }, + { + "text": "OK. OK. Now let me come back to the important case when we're OK." + }, + { + "text": "The important case when we are diagonalizing." + }, + { + "text": "Let me look at, so let me solve this equation." + }, + { + "text": "The equation will be each, I start with some, start with a given vector u0." + }, + { + "text": "And then my equation is that every step I multiply what I have by a." + }, + { + "text": "That equation ought to be simple to handle." + }, + { + "text": "OK. And I'd like to be able to solve it." + }, + { + "text": "How would I find, if I start with a vector u0, and I multiply by a a hundred times, what have I got?" + }, + { + "text": "Well, I can certainly write down a formula for the answer." + }, + { + "text": "So what, what, so u1 is a u0." + }, + { + "text": "And u2 is, what's u2 then?" + }, + { + "text": "U2 I multiply it, u2 I get from u1 by another, multiplying by a, so I've got a twice." + }, + { + "text": "And my formula is uk, after k steps, I've multiplied by a k times the original u0." + }, + { + "text": "You see what I'm doing?" + }, + { + "text": "The next section is going to solve systems of differential equations." + }, + { + "text": "I'm going to have derivatives." + }, + { + "text": "This, this section is the nice one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk13.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..ba8214d8c636e4757a266d6617801174bc939d80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "It solves difference equations." + }, + { + "text": "I would call that a difference equation." + }, + { + "text": "It's conne- a first order." + }, + { + "text": "I would call that a first order system, because it connects only, it only goes up one level." + }, + { + "text": "And it's a system because these are vectors and that's a matrix." + }, + { + "text": "And the solution is just that." + }, + { + "text": "OK." + }, + { + "text": "But, that's a nice formula." + }, + { + "text": "That's the, like, the most compact formula I could ever get." + }, + { + "text": "U one hundred would be a to the one hundredth u0." + }, + { + "text": "But how would I actually find u one hundred?" + }, + { + "text": "How would I find, how would I discover what u one hundred is?" + }, + { + "text": "Let me, let me show you how." + }, + { + "text": "Here, here's the idea." + }, + { + "text": "If, so, to solve, to really solve, shall I say, to really solve." + }, + { + "text": "To really solve it, I would take this initial vector, u0, and I would write it as a combination of eigenvectors." + }, + { + "text": "To really solve, write, write u0 as a combination, say, certain amount of the first eigenvector plus a certain amount of the second eigenvector plus a certain amount of the last eigenvector." + }, + { + "text": "Now multiply by a." + }, + { + "text": "You want to, you got to see the magic of eigenvectors work." + }, + { + "text": "Multiply by a." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk14.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7843b2bf0cac762d1c12452cf36500ea4ad13370 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a u0 is what?" + }, + { + "text": "So a times that." + }, + { + "text": "A times, so what's, I can separate it out into n separate pieces and that's the whole point." + }, + { + "text": "That each of those pieces is going in its own merry way." + }, + { + "text": "Each of those pieces is an eigenvector, and when I multiply by a, what does this piece become?" + }, + { + "text": "So that's some amount of the first, let's suppose the eigenvectors are normalized to be unit vectors." + }, + { + "text": "So that says what the eigenvector is." + }, + { + "text": "It's, and I need some multiple of it to produce u0." + }, + { + "text": "OK. Now when I multiply by a, what do I get?" + }, + { + "text": "I get c1, which is just a factor, times a x1, but a x1 is lambda one x1." + }, + { + "text": "When I multiply this by a, I get c2 lambda two x2." + }, + { + "text": "And here I get cn lambda n xn." + }, + { + "text": "And suppose I multiply by a to the hundredth power now." + }, + { + "text": "Can we, can we, having done it, multiplied by a, let's multiply by a to the hundredth." + }, + { + "text": "What happens to this first term when I multiply by a to the one hundredth?" + }, + { + "text": "It's got that factor lambda to the hundredth." + }, + { + "text": "That's the key." + }, + { + "text": "That, that's what I mean by going its own merry way." + }, + { + "text": "It, it is pure eigenvector, it's exactly in a direction where multiplication by a just brings in a scalar factor lambda one." + }, + { + "text": "So a hundred times brings in this a hundred times." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk15.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7ee3348735378aa4049d33ec2a197d0ceb0c447c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Hundred times lambda two, hundred times lambda n. Actually, we're, what are we seeing here?" + }, + { + "text": "We're seeing, this same, lambda, capital lambda to the hundredth, as in the, as in the diagonalization, and we're seeing the S matrix, the matrix S of eigenvectors." + }, + { + "text": "That's what this has got to, this has got to amount to, a lambda to the hundredth power times an S times this vector C that's telling us how much of each one is in the original thing." + }, + { + "text": "So if, if I had to really find the hundredth power, I would take u0, I would expand it as a combination of eigenvectors, this is really S, the eigenvector matrix times C, the, the coefficient vector." + }, + { + "text": "And then I would immediately, then, by inserting these hundredth powers of eigenvalues, I'd have the answer." + }, + { + "text": "So the, the, huh, there must be, well, let's see." + }, + { + "text": "OK." + }, + { + "text": "It's, so, yeah." + }, + { + "text": "So if u100 is a to the hundredth times u0, and u0 is Sc, then you see this formula is just this formula, which is the way I would actually get hold of this, of this u100, which is, let me put it here, u100." + }, + { + "text": "The way I would actually get hold of that, see what, what the solution is after a hundred steps, would be expand the initial vector into eigenvectors and, and let each eigenvector go its own way, multiplying by a hundred at, by lambda at every step, and therefore by lambda to the hundredth power after a hundredth step." + }, + { + "text": "Can I do an example?" + }, + { + "text": "So that's, that's the, the formulas." + }, + { + "text": "Now let me take an example." + }, + { + "text": "I'll use the Fibonacci sequence as an example." + }, + { + "text": "So, so Fibonacci example." + }, + { + "text": "You remember the Fibonacci numbers?" + }, + { + "text": "If we start with one and one as F0, oh, I think I start with zero, maybe." + }, + { + "text": "Let zero and one be the first ones." + }, + { + "text": "So there's F0 and F1, the first two Fibonacci numbers." + }, + { + "text": "Then what's the rule for Fibonacci numbers?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk16.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..79c65e32781f7f304b504a6c390247abb9d26ac8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "They're the sum." + }, + { + "text": "The next one is the sum of those, so it's one." + }, + { + "text": "The next one is the sum of those, so it's two." + }, + { + "text": "The next one is the sum of those, so it's three." + }, + { + "text": "Well, it looks like one, two, three, four, five, but somehow it's not going to do that way." + }, + { + "text": "The next one is five, right." + }, + { + "text": "Two and three makes five." + }, + { + "text": "The next one is eight." + }, + { + "text": "The next one is thirteen." + }, + { + "text": "And the one hundredth Fibonacci number is what?" + }, + { + "text": "That's my question." + }, + { + "text": "How could I get a formula for the hundredth number and for example how could I answer the question how fast are they growing?" + }, + { + "text": "How fast are those Fibonacci numbers growing?" + }, + { + "text": "They're certainly growing." + }, + { + "text": "It's not a stable case, whatever the eigenvalues of whatever matrix it is, they're not smaller than one." + }, + { + "text": "These numbers are growing." + }, + { + "text": "But how fast are they growing?" + }, + { + "text": "The answer is lies in the eigenvalue." + }, + { + "text": "So I've got to find the matrix, so let me write down the Fibonacci rule, F k plus two is F k plus one plus F k, right?" + }, + { + "text": "Now that's not in my -- I want to write that as U k plus one and A U k. But right now what I've got is a single equation, not a system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk17.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b3aaa9dcee3cf27c112015659bb5a0b51a983ce1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's second order." + }, + { + "text": "It's like having a second order differential equation with second derivatives." + }, + { + "text": "I want to get first derivatives." + }, + { + "text": "Here I want to get first difference." + }, + { + "text": "So the way to do it is to introduce U k will be a vector." + }, + { + "text": "See, a small trick." + }, + { + "text": "Let U k be a vector, F k plus one and F k. So I'm going to get a two by two system, first order, instead of a one, instead of a scalar system, second order, by a simple trick." + }, + { + "text": "I'm just going to add in an equation F k plus one equals F k plus one." + }, + { + "text": "That will be my second equation." + }, + { + "text": "Then this is my system, this is my unknown, and what's my one-step equation?" + }, + { + "text": "So now U k plus one." + }, + { + "text": "That's so U k plus one is the left side, and what have I got here on the right side?" + }, + { + "text": "I've got some matrix multiplying U k. Can you see that all right?" + }, + { + "text": "If you can see it, then you can tell me what the matrix is." + }, + { + "text": "You see that I'm taking my system here, I artificially made it into a system." + }, + { + "text": "I artificially made the unknown into a vector, and now I'm ready to look at and see what the matrix is." + }, + { + "text": "So do you see the left side, U k plus one is F k plus two F k plus one, that's just what I want." + }, + { + "text": "On the right side, this, remember, this U k here, let me for the moment put it as F k plus one F k. So what's the matrix?" + }, + { + "text": "Well, that has a one and a one, and that has a one and a zero." + }, + { + "text": "There's the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk18.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..6c1b68c2cb2fde3f5dea82f3100d4da31fcce70a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "You see that that gives me the right-hand side." + }, + { + "text": "So there's the matrix A, and this is our friend U k. So we've got, so that simple trick changed the second order scalar problem to a first order system, two, with two unknowns." + }, + { + "text": "With a matrix and now what do I do?" + }, + { + "text": "Well, before I even think, I find its eigenvalues and eigenvectors." + }, + { + "text": "So what are the eigenvalues and eigenvectors of that matrix?" + }, + { + "text": "Let's see." + }, + { + "text": "I was, first let me just, like, think for a minute." + }, + { + "text": "It's two by two, so this shouldn't be impossible to do." + }, + { + "text": "Let's do it." + }, + { + "text": "OK." + }, + { + "text": "So my matrix again is one one one zero." + }, + { + "text": "It's symmetric, by the way." + }, + { + "text": "So what I will eventually know about symmetric matrices is that the eigenvalues will come out real, I won't get any complex numbers here, and the eigenvectors, once I get those, actually will be orthogonal." + }, + { + "text": "But two by two, I'm more interested in what the actual numbers are." + }, + { + "text": "What do I know about the two numbers?" + }, + { + "text": "Well, should, do you want me to find this determinant of A minus lambda I?" + }, + { + "text": "Sure." + }, + { + "text": "So it's the determinant of one minus lambda one one zero, right?" + }, + { + "text": "Minus lambda, yes, got it." + }, + { + "text": "OK. OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk19.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..a73b23e3d56b889ff49ea7f55a784fac33e13c3d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "There'll be two eigenvalues." + }, + { + "text": "Well, tell me again what I know about the two eigenvalues before I go any further." + }, + { + "text": "Tell me something about these two eigenvalues, what do they add up to?" + }, + { + "text": "Lambda one plus lambda two is the same as the trace down the diagonal of the matrix, one and zero is one." + }, + { + "text": "So lambda one plus lambda two should come out to be one, and lambda one times lambda two should come out to be the determinant, which is minus one." + }, + { + "text": "So I'm expecting the eigenvalues to add to one and to multiply to minus one." + }, + { + "text": "But let's just see it happen here." + }, + { + "text": "If I multiply this out, I get that times that'll be a lambda squared minus lambda minus one." + }, + { + "text": "Good." + }, + { + "text": "Lambda squared minus lambda minus one." + }, + { + "text": "Actually, you see the, compare that with the original equation that I started with." + }, + { + "text": "Fk plus two minus Fk plus one minus Fk is zero." + }, + { + "text": "The recurrent, the recursion that the Fibonacci number satisfy is somehow showing up directly here for the eigenvalues when we set that to zero." + }, + { + "text": "OK. Let's solve." + }, + { + "text": "Well, I would like to be able to factor that, that quadratic, but I'm better off to use the quadratic formula." + }, + { + "text": "Lambda is, let's see, minus b is one, plus or minus the square root of b squared, which is one, minus four, times that, times that, which is plus four, over two." + }, + { + "text": "So that's the square root of five." + }, + { + "text": "So the eigenvalues are lambda one is one half of one plus square root of five, and lambda two is one half of one minus square root of five." + }, + { + "text": "And sure enough, they, those add up to one, and they multiply to give minus one." + }, + { + "text": "OK. Those are the two eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk2.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..43cfb012fc04a89fc7dab94c23bfb0f50ade3782 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "On the right, it's multiplied by, if I want, if I want lambda n xn in the last column, how do I do it?" + }, + { + "text": "Well, the last column here will be, I'll, I'll take the last column, use these coefficients, put the lambda n down there, and it will multiply that nth column and give me lambda n xn." + }, + { + "text": "There, there you see matrix multiplication just working for us." + }, + { + "text": "So I started with A s. I wrote down what it meant." + }, + { + "text": "A times each eigenvector." + }, + { + "text": "That gave me lambda times the eigenvector." + }, + { + "text": "And then when I peeled off the lambdas, they were on the right-hand side, so I've got s, my matrix back again, and this matrix, this diagonal matrix, the eigenvalue matrix, and I call it capital lambda, using capital letters for matrices, and lambda to prompt me that it's, that it's eigenvalues that are in there." + }, + { + "text": "So you see that the eigenvalues are just sitting down that diagonal?" + }, + { + "text": "If I had a column x2 here, I would want the lambda two in the two two position, in the diagonal position, to multiply that x2 and give me the lambda two x2." + }, + { + "text": "That's my formula." + }, + { + "text": "A s is s lambda." + }, + { + "text": "OK. That's, that's the, you see, it's just a calculation." + }, + { + "text": "Now, I, I mentioned, and I have to mention again, this business about n independent eigenvectors." + }, + { + "text": "As it stands, this is all fine whether, I mean, I could be repeating the same eigenvector, but I, I'm no interested in that." + }, + { + "text": "I want to be able to invert s, and that's where this comes in." + }, + { + "text": "This n independent eigenvectors business comes in to tell me that that matrix is invertible." + }, + { + "text": "So let me, on the next board, write down what I've got." + }, + { + "text": "A s equals s lambda." + }, + { + "text": "And now I'm, I can multiply on the left by s inverse." + }, + { + "text": "So this is really, I can do that provided s is invertible, provided my assumption of n independent eigenvectors is satisfied." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk20.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ad5a59fa5db44ce73ff5f88190423e0404fb3d39 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "How, how, what are those numbers approximately?" + }, + { + "text": "Square root of five, well, it's more than two, but less than three." + }, + { + "text": "It, it'd be nice to know these numbers." + }, + { + "text": "I think, I think that that, so that number comes out bigger than one, right?" + }, + { + "text": "Yeah, that's right." + }, + { + "text": "This number comes out bigger than one." + }, + { + "text": "It's about one point six one eight or something." + }, + { + "text": "Not exactly." + }, + { + "text": "It's supposed to be one point six." + }, + { + "text": "Just, like, I think so." + }, + { + "text": "Then what's lambda two?" + }, + { + "text": "Is, is lambda two positive or negative?" + }, + { + "text": "Negative, right?" + }, + { + "text": "Because I'm, it's obviously negative, and I knew that the, so it's minus, and they add up to one, so minus point six one eight, I guess." + }, + { + "text": "OK. And some order." + }, + { + "text": "Those are the two eigenvalues." + }, + { + "text": "One eigenvalue bigger than one, one eigenvalue smaller than one." + }, + { + "text": "Actually, that's a great situation to be in." + }, + { + "text": "Of course, the eigenvalues are different, so there's no doubt whatever, is this matrix diagonalizable?" + }, + { + "text": "Is this matrix diagonalizable, that original matrix A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk21.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..4a034475591d371995b379b5f98783a2cfb25870 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Sure." + }, + { + "text": "We've got two distinct eigenvalues and we can find the eigenvectors in a moment." + }, + { + "text": "But they'll be independent, will be diagonalizable, and now you can already answer my very first question." + }, + { + "text": "How fast are those Fibonacci numbers increasing?" + }, + { + "text": "How, those, they're increasing, right?" + }, + { + "text": "They're not doubling at every step." + }, + { + "text": "Let's look again at these numbers." + }, + { + "text": "Five eight thirteen, it's not obvious." + }, + { + "text": "The next one would be twenty one thirty four." + }, + { + "text": "So to get some idea of what F one hundred is, can you give me any, I mean the crucial number of, so it, these, it's approximately, what's controlling the growth of these Fibonacci numbers?" + }, + { + "text": "It's the eigenvalues." + }, + { + "text": "And which eigenvalues controlling that growth?" + }, + { + "text": "The big ones." + }, + { + "text": "So F one hundred will it be approximately some constant, c one, I guess, times this lambda one, this one plus square root of five over two, to the hundredth power." + }, + { + "text": "And the two hundredth have, in other words, the eigenvalue, the Fibonacci numbers are growing by about that factor." + }, + { + "text": "You see that we've got precise information about the, about the Fibonacci numbers out of the eigenvalue." + }, + { + "text": "OK. And again, why is that true?" + }, + { + "text": "Let me go over to this board and show what I'm doing here." + }, + { + "text": "The, the original eigen, the original initial value is some combination of eigenvectors, and then when we start multiple, when we start going out the theory of Fibonacci numbers, when we start multiplying by a hundred times, it's this lambda one to the hundredth, this term is, is the one that's taken over." + }, + { + "text": "It's, I mean, that's big, like, one point six to the hundredth power." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk22.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..c13a1fc9867173c3067e46c469cfff27b9b45289 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "The second term is practically nothing, right?" + }, + { + "text": "The point six, or minus point six to the hundredth power, is an extremely small, extremely small number." + }, + { + "text": "So this is, this, this, there are only two terms, because we're two by two." + }, + { + "text": "This number is, this piece of it is there, but it's, it's disappearing." + }, + { + "text": "Where this piece is there and it's growing and controlling everything." + }, + { + "text": "So, so really the, we're doing, like, problems that are evolving." + }, + { + "text": "We're doing dynamics." + }, + { + "text": "Instead of Ax equal b, that's a static problem." + }, + { + "text": "We're now, we're doing dynamics." + }, + { + "text": "A, a squared, a cubed, things are evolving in time, and the eigenvalues are the crucial, numbers." + }, + { + "text": "OK." + }, + { + "text": "I guess to complete this, I better write down the eigenvectors." + }, + { + "text": "So we should complete the, the whole process by finding the eigenvectors." + }, + { + "text": "OK. Well, I have to, up in the corner, then I have to look at A minus lambda I." + }, + { + "text": "So A minus lambda I is this one minus lambda, one, one, and minus lambda." + }, + { + "text": "And now, can we spot an eigenvector out of that?" + }, + { + "text": "That's, for these two lambdas, this matrix is singular." + }, + { + "text": "I guess the eigenvector, two by two ought to be easy." + }, + { + "text": "So if I know that this matrix is singular, then it seems to me the eigenvector has to be lambda and one, because that multiplication will give me the zero." + }, + { + "text": "And this multiplication gives me, better give me also zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk23.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..df816eb800ce767b1475c279a24ad976bb45a785 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Do you see why it does?" + }, + { + "text": "This is the minus lambda squared plus lambda plus one." + }, + { + "text": "It's the thing that's zero, because these lambdas are special." + }, + { + "text": "There's the eigenvector." + }, + { + "text": "X1 is lambda one, one, and x2 is lambda two, one." + }, + { + "text": "I did that as a little trick that was available in the two by two case." + }, + { + "text": "So now I finally have to, oh, I have to take the initial, u0." + }, + { + "text": "So to complete this example entirely, I have to say, OK, what was u0?" + }, + { + "text": "u0 was f1 f0." + }, + { + "text": "So u0, the starting vector, is f1 f0, and those were one and zero." + }, + { + "text": "So I have to use that vector, so I have to look for, from multiple of the first eigenvector and the second, to produce u0, the one zero vector." + }, + { + "text": "This is what will find c1 and c2, and then I'm done." + }, + { + "text": "So let me, instead of in the last five seconds grinding out a formula, let me repeat the idea." + }, + { + "text": "That really, it's the idea that's central." + }, + { + "text": "When things are evolving in time, let me come back to this board, because the ideas are here." + }, + { + "text": "When things are evolving in time by a first-order system, starting from an original u0, the key is, find the eigenvalues and eigenvectors of A." + }, + { + "text": "That will tell, those eigenvectors, the eigenvalues will already tell you what's happening." + }, + { + "text": "Is the solution blowing up?" + }, + { + "text": "Is it going to zero?" + }, + { + "text": "What's it doing?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk24.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..40301cb90760e2172baa94d536cbc13288d4c31f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk24.json @@ -0,0 +1,20 @@ +[ + { + "text": "And then, to find out exactly a formula, you have to take your u0 and write it as a combination of eigenvectors and then follow each eigenvector separately." + }, + { + "text": "And that's really what this formula, the formula for, that's what the formula for A to the k is doing." + }, + { + "text": "So remember that formula for A to the k is S, lambda to the k S inverse." + }, + { + "text": "OK. That's, that's difference equations, and you just have to, so the homework will give some examples different from Fibonacci to follow through." + }, + { + "text": "And next time will be differential equations." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk3.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..9bf1bb852baadc1da7837e14180c0c2951a30882 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I mentioned at the end of last time, and I'll say again, that there's a small number of matrices for, that don't have n independent eigenvectors." + }, + { + "text": "So I've got to discuss that, that technical point." + }, + { + "text": "But the great, the most matrices that we see have n, n independent eigenvectors and we can diagonalize." + }, + { + "text": "This is diagonalization." + }, + { + "text": "I could also write it, and I often will, the other way round." + }, + { + "text": "If I multiply on the right by s inverse, if I took this equation at the top and multiplied on the right by s inverse, I could, I would have A left here." + }, + { + "text": "Now s inverse is coming from the right." + }, + { + "text": "So can you keep those two straight?" + }, + { + "text": "A multiplies its eigenvectors." + }, + { + "text": "That's how I keep them straight." + }, + { + "text": "So A multiplies s. A multiplies s. And then this s inverse makes the whole thing diagonal." + }, + { + "text": "And this is another way of saying the same thing, putting the s's on the other side of the equation, A is s lambda s inverse." + }, + { + "text": "So that's the, that's the new factorization." + }, + { + "text": "That's the replacement for L U from elimination or Q R from Gram-Schmidt." + }, + { + "text": "And notice that the matrix, so it's, it's a matrix times a diagonal matrix times the inverse of the first one." + }, + { + "text": "It's, that's the combination that we'll see throughout this chapter." + }, + { + "text": "This, this, combination with an s and an s inverse." + }, + { + "text": "OK. Can I just begin to use that?" + }, + { + "text": "For example, what about A squared?" + }, + { + "text": "What are the eigenvalues and eigenvectors of A squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk4.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c687b6948acad76de8781cb82d3eb069c9da514e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's a straightforward question with a, with a absolutely clean answer." + }, + { + "text": "So let me, let me consider A squared." + }, + { + "text": "So I look, I start with Ax equal lambda x." + }, + { + "text": "And I'm headed for A squared." + }, + { + "text": "So let me multiply both sides by A." + }, + { + "text": "That's one way to get A squared on the left." + }, + { + "text": "So if, I should write these ifs in here." + }, + { + "text": "If Ax equals lambda x, then I multiply by A." + }, + { + "text": "So I get A squared x equals, well, I'm multiplying by A, so that's lambda Ax." + }, + { + "text": "That lambda was a number, so I just put it on the left." + }, + { + "text": "And what do I, tell me how to make that look better." + }, + { + "text": "What have I got here?" + }, + { + "text": "For, if, if A has the eigenvalue lambda and eigenvector x, what's up with A squared?" + }, + { + "text": "A squared x, I just multiply by A, but now for Ax, I'm going to substitute lambda x, so I've got lambda squared x." + }, + { + "text": "So from that simple calculation, I, my conclusion is that the eigenvalues of A squared are lambda squared." + }, + { + "text": "And the eigenvectors, I always think about both of those." + }, + { + "text": "What can I say about the eigenvalues?" + }, + { + "text": "They're squared." + }, + { + "text": "What can I say about the eigenvectors?" + }, + { + "text": "They're the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk5.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5bf15e20707c156c8ae71c9c7acea41a9d9d8e46 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same x as in, as for A." + }, + { + "text": "Now, let me see that also from this formula." + }, + { + "text": "How can I see what A squared is looking like from this formula?" + }, + { + "text": "So let me, that, that was one way to do it." + }, + { + "text": "Let me do it by just taking A squared from that." + }, + { + "text": "A squared is S lambda S inverse, that's A, times S lambda S inverse, that's A, which is?" + }, + { + "text": "This is the beauty of eigenvalues, eigenvectors, having that S inverse and S is the identity, so I've got S lambda squared S inverse." + }, + { + "text": "Yes." + }, + { + "text": "You see what that's telling me?" + }, + { + "text": "It's, it's telling me the same thing that I just learned here, but in the, in, in a matrix form." + }, + { + "text": "It's telling me that the S is the same, the eigenvectors are the same, but the eigenvalues are squared, because this is, what's lambda squared, that's still diagonal, it's got little lambda one squared, lambda two squared, down to lambda n squared, on that diagonal, those are the eigenvalues, as we just learned, of A squared." + }, + { + "text": "OK." + }, + { + "text": "So, somehow those eigenvalues and eigenvectors are really giving you a way to, to, to, to see what's going on inside a matrix." + }, + { + "text": "Now, of course, I can continue that for, to the k-th power." + }, + { + "text": "A to the k-th power." + }, + { + "text": "If I multiply, if I have k of these together, do you see how S inverse S will keep cancelling?" + }, + { + "text": "In the, in the inside, I'll have the S outside, at the far left, and lambda will be in there k times and S inverse." + }, + { + "text": "So what's that telling me?" + }, + { + "text": "That's telling me that the eigenvalues of A, of A to the k-th power are the k-th powers." + }, + { + "text": "The eigenvalues of A cubed are the cubes of the eigenvalues of A, and the eigenvectors are the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk6.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..c18dddbe798022f7e68278ac002a3f5fe6ed249e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same." + }, + { + "text": "OK." + }, + { + "text": "In other words, eigenvalues and eigenvectors give a great way to understand the powers of a matrix." + }, + { + "text": "If I take the square of a matrix or the hundredth power of a matrix, the pivots are all over the place." + }, + { + "text": "L U, if I multiply L U times L U times L U times L U a hundred times, I've got a hundred L U's." + }, + { + "text": "I can't do anything with them." + }, + { + "text": "But when I multiply S lambda S inverse by itself, when I look at the eigenvector picture a hundred times, I get a hundred or ninety-nine of these guys cancelling out inside, and I get A to the hundredth is S lambda to the hundredth S inverse." + }, + { + "text": "I mean, eigenvalues tell you about powers of a matrix in a way that we had no, no way to approach previously." + }, + { + "text": "For example, when does, when do the powers of a matrix go to zero?" + }, + { + "text": "I would call that matrix stable, maybe." + }, + { + "text": "So, so, so I could write down a, a theorem." + }, + { + "text": "I'll, I'll write it as a theorem, just to use that word to emphasize that here I'm getting this great fact from this eigenvalue picture." + }, + { + "text": "OK. A to the k approaches zero as k goes, as k gets bigger." + }, + { + "text": "If what?" + }, + { + "text": "What's the, how can I tell for a matrix A if its powers go to zero?" + }, + { + "text": "What, what's somewhere inside that matrix is that information." + }, + { + "text": "That information is not present in the pivots." + }, + { + "text": "It's present in the eigenvalues." + }, + { + "text": "What do I need for the, to know that if I take higher and higher powers of A that this matrix gets smaller and smaller?" + }, + { + "text": "Well, S and S inverse are not moving." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk7.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b84a5c854a5542758e8a0107e1ff043205fe3bdb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's this guy that has to get small, and that's easy to, easy to understand." + }, + { + "text": "The requirement is all eigenvalues, so what is the requirement?" + }, + { + "text": "The eigenvalues have to be less than one." + }, + { + "text": "Now, I have to write that absolute value, because those eigenvalues could be negative, they could be complex numbers." + }, + { + "text": "So I'm taking the absolute value if all of those are below one." + }, + { + "text": "That's, in fact, we practically see why." + }, + { + "text": "Let me just say that I, that I, I'm operating on one assumption here, and I got to keep remembering that that assumption is still present." + }, + { + "text": "That assumption was that I had a full set of, of n independent eigenvectors." + }, + { + "text": "If I don't have that, then I, I, then this approach is not working." + }, + { + "text": "So, so again, a pure eigenvalue approach, eigenvector approach, needs n independent eigenvectors." + }, + { + "text": "If we don't have n independent eigenvectors, we can't diagonalize the matrix." + }, + { + "text": "We can't get to a diagonal matrix." + }, + { + "text": "This, this, this diagonalization is only possible if S inverse makes sense." + }, + { + "text": "OK. Can I, can I follow up on that point now?" + }, + { + "text": "So, so you see why, what we get and, and why we want it, because we get information about the powers of a matrix just immediately from the eigenvalues." + }, + { + "text": "OK, now let me follow up on this, business of which matrices are diagonalizable." + }, + { + "text": "Sorry about that long word." + }, + { + "text": "So a matrix is, is sure to, so here's, here's the main point." + }, + { + "text": "A is sure to be, to have n independent eigenvectors and, and B, now here comes that word, diagonalizable, if, if, so we, we, we might as well get the, the nice case out in the open." + }, + { + "text": "The nice case is when, if all the lambdas are different." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk8.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f06dcec8ffa0ee1bf19440e4ab2194db33ab353b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means, that means no repeated eigenvalues." + }, + { + "text": "OK. That's the nice case." + }, + { + "text": "If, if my matrix and most matrix, if I do a random matrix in MATLAB and compute its eigenvalues, so if I computed, if I took I of rand of ten ten, gave, gave that MATLAB command, the, we'd get a random ten by ten matrix, we would get a list of its ten eigenvalues and they would be different." + }, + { + "text": "They would be distinct, is the best word." + }, + { + "text": "I would have a random matrix will have ten distinct, a ten by ten matrix will have ten distinct eigenvalues, and if it does, the eigenvectors are automatically independent." + }, + { + "text": "So that's a nice fact." + }, + { + "text": "I can, I'll refer you to the text for the proof." + }, + { + "text": "That, that A is sure to have n independent eigenvectors if the eigenvalues are different." + }, + { + "text": "If, if all the, if all eigenvalues are different." + }, + { + "text": "It's just, if some lambdas are repeated, then I have to look more closely." + }, + { + "text": "If an eigenvalue is repeated, I have to look, I have to count, I have to check." + }, + { + "text": "Has it got, say it's repeated three times." + }, + { + "text": "So what's a possibility for, so, so here's, here's the repeated possibility." + }, + { + "text": "And, and let me emphasize the conclusion." + }, + { + "text": "That if I have repeated eigenvalues, I may or may not, I may or may not have, have n independent eigenvectors." + }, + { + "text": "I might." + }, + { + "text": "I, I, you know, this isn't a completely negative case." + }, + { + "text": "The identity matrix." + }, + { + "text": "Well, suppose I take the ten by ten identity matrix." + }, + { + "text": "What are the eigenvalues of that matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk9.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..87d2a2ae5773036cf11800e2f1962908986a0dad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_36_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So just, just take the easiest matrix, the identity." + }, + { + "text": "If I look for its eigenvalues, they're all ones." + }, + { + "text": "So that eigenvalue one is repeated ten times." + }, + { + "text": "But there's no shortage of eigenvectors for the identity matrix." + }, + { + "text": "In fact, every vector is an eigenvector." + }, + { + "text": "So I can take ten independent vectors." + }, + { + "text": "Oh, well, what happens to everything if, if, if A is the identity matrix, let's just think that one through in our head." + }, + { + "text": "If A is the identity matrix, then it's got plenty of eigenvectors." + }, + { + "text": "I choose ten independent vectors, they're the columns of S, and, and what do I get from S inverse A S?" + }, + { + "text": "I get I again, right?" + }, + { + "text": "If A is the identity, and of course, that's the correct lambda." + }, + { + "text": "The, the matrix was already diagonal." + }, + { + "text": "So if the matrix is already diagonal, then the, the lambda is the same as the matrix." + }, + { + "text": "A diagonal matrix has got its eigenvalues sitting right there in front of you." + }, + { + "text": "Now if it's triangular, the eigenvalues are still sitting there, but so let's, let's take a case where, it's triangular." + }, + { + "text": "Suppose A is like, two, one, two, zero." + }, + { + "text": "So there's a case that's going to be trouble." + }, + { + "text": "There's a case that's going to be trouble." + }, + { + "text": "First of all, what are the eigen- I mean, we just, like now you, if we start with a matrix, the first thing we do practically without thinking is compute the eigenvalues and eigenvectors." + }, + { + "text": "OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk0.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6898d4fe66019ef6b40d0472ea94a968e7bbde9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, shall we start?" + }, + { + "text": "This is the second lecture on eigenvalues." + }, + { + "text": "So the first lecture was set -- reached the key equation, Ax equal lambda x. x is the eigenvector and lambda is the eigenvalue." + }, + { + "text": "Now, to use that." + }, + { + "text": "And the good way to, after we've found, so job one is to find the eigenvalues and find the eigenvectors." + }, + { + "text": "Now after we found them, what do we do with them?" + }, + { + "text": "Well, the good way to see that is diagonalize the matrix." + }, + { + "text": "So the matrix is A, and I want to show, first of all, this is like the basic fact." + }, + { + "text": "This, this formula." + }, + { + "text": "That's, that's the key to today's lecture." + }, + { + "text": "This matrix A, I put its eigenvectors in the columns of a matrix S. So S will be the eigenvector matrix, and I want to look at this magic combination S inverse A S. So can I show you how that, how that, what happens there?" + }, + { + "text": "And notice, notice, there's an S inverse." + }, + { + "text": "We have to be able to invert this eigenvector matrix S. So for that we need n independent eigenvectors." + }, + { + "text": "So that's the, that's the case." + }, + { + "text": "OK." + }, + { + "text": "So suppose we have n linearly independent eigenvectors of A." + }, + { + "text": "Put them in the columns of this matrix S. So I'm naturally going to call that the eigenvector matrix, because it's got the eigenvectors in its columns." + }, + { + "text": "And all I want to do is show you what happens when you multiply A times S. So A times S. So this is A times the matrix with the first eigenvector in its first column, the second eigenvector in its second column, the nth eigenvector in its nth column." + }, + { + "text": "And how am I going to do this matrix multiplication?" + }, + { + "text": "Well, certainly I'll do it a column at a time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk1.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..fbe078217bb68baea8e0605a5d04be568c49efbf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I get?" + }, + { + "text": "A times the first column gives me the first column of the answer, but what is it?" + }, + { + "text": "That's an eigenvector." + }, + { + "text": "A times x1 is equal to the lambda times the x1." + }, + { + "text": "And that lambda's we'll call lambda one, of course." + }, + { + "text": "So that's the first column, A x1 is the same as lambda one x1." + }, + { + "text": "A x2 is lambda two x2, so on, along to, in the nth column, we now have lambda n xn." + }, + { + "text": "Looking good, but the next step is even better." + }, + { + "text": "So for the next step, I want to separate out those eigenvalues, those multiplying numbers, from the x's." + }, + { + "text": "So then I'll have just what I want." + }, + { + "text": "OK, so how, how am I going to separate out?" + }, + { + "text": "So that, that number lambda one is multiplying the first column." + }, + { + "text": "So if I want to factor it out of the first column, I better put, here is going to be x1, and that's going to multiply this matrix lambda one in the first entry in all zeros." + }, + { + "text": "You see that that, that's going to come out right for the first column?" + }, + { + "text": "Because we remember how, how we're going back to that original punchline, that if I want a number to multiply x1, then I can do it by putting x1 in that column, in the first column, and putting that number there." + }, + { + "text": "What am I going to have here?" + }, + { + "text": "I'm going to have lambda one, I'm going to have x1, x2, xn." + }, + { + "text": "These are going to be my columns again." + }, + { + "text": "I'm getting s back again." + }, + { + "text": "I'm getting s back again, but now what's it multiplied by?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk10.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c58a42edbe9567233ca7f57643a0b7d43ae6761f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what are the eigenvalues?" + }, + { + "text": "You can tell me right away what they are." + }, + { + "text": "They're two and two, right." + }, + { + "text": "It's a triangular matrix, so when I do this determinant, shall I do this determinant of A minus lambda I?" + }, + { + "text": "I'll get this two minus lambda, one, zero, two minus lambda, right?" + }, + { + "text": "I take that determinant, so I make those into vertical bars to mean determinant, and what's the determinant?" + }, + { + "text": "Two minus lambda squared." + }, + { + "text": "What are the roots?" + }, + { + "text": "Lambda equal two twice." + }, + { + "text": "So the eigenvalues are lambda equals two and two." + }, + { + "text": "OK, fine." + }, + { + "text": "Now the next step, find the eigenvectors." + }, + { + "text": "So I look for eigenvectors and what do I find for this guy?" + }, + { + "text": "Eigenvectors for this guy, when I subtract two minus the identity, so A minus two I has zeros here, and I'm looking for the null space." + }, + { + "text": "What's, what are the eigenvectors?" + }, + { + "text": "They're the, they're, they're the null space of A minus lambda I." + }, + { + "text": "The null space is only one dimension." + }, + { + "text": "This is a case where I don't have enough eigenvectors." + }, + { + "text": "My algebraic multiplicity is two." + }, + { + "text": "I, I would say when I see, when I count how often the eigenvalue is repeated, that's the algebraic multiplicity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk11.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..779c2cf904d904b761080db2671aac46394ad02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the multiplicity." + }, + { + "text": "How many times is it the root of the polynomial?" + }, + { + "text": "My polynomial is two minus lambda squared." + }, + { + "text": "It's a double root." + }, + { + "text": "So my algebraic multiplicity is two." + }, + { + "text": "But the geometric multiplicity, which looks for vectors, looks for eigenvectors and which means the null space of this thing." + }, + { + "text": "And the only eigenvector is one zero." + }, + { + "text": "That's in the null space." + }, + { + "text": "Zero one is not in the null space." + }, + { + "text": "The null space is only one dimensional." + }, + { + "text": "So there's a matrix, my, this A or the original A, that are not diagonalizable." + }, + { + "text": "I can't, I can't find two independent eigenvectors, there's only one." + }, + { + "text": "OK." + }, + { + "text": "So that's the case that I'm, that's a case that I, I'm not really handling." + }, + { + "text": "For example, when I wrote down up here that the powers went to zero if the eigenvalues were below one, I didn't really handle that case of repeated eigenvalues because my reasoning was based on this formula." + }, + { + "text": "And this formula is based on n independent eigenvectors." + }, + { + "text": "OK." + }, + { + "text": "So just to say that." + }, + { + "text": "There are some matrices that we don't cover through diagonalization, but the great majority we do." + }, + { + "text": "OK. And we're always OK if we have different distinct eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk12.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..77d090704cc298475d94416b7ecb88a2a015a913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. That's the, like, the typical case." + }, + { + "text": "Because for each eigenvalue there's at least one eigenvector, the algebraic multiplicity here is one for every eigenvalue, and the geometric multiplicity is one." + }, + { + "text": "There's one eigenvector and they are independent." + }, + { + "text": "OK. OK. Now let me come back to the important case when we're OK." + }, + { + "text": "The important case when we are diagonalizing." + }, + { + "text": "Let me look at, so let me solve this equation." + }, + { + "text": "The equation will be each, I start with some, start with a given vector u0." + }, + { + "text": "And then my equation is that every step I multiply what I have by a." + }, + { + "text": "That equation ought to be simple to handle." + }, + { + "text": "OK. And I'd like to be able to solve it." + }, + { + "text": "How would I find, if I start with a vector u0, and I multiply by a a hundred times, what have I got?" + }, + { + "text": "Well, I can certainly write down a formula for the answer." + }, + { + "text": "So what, what, so u1 is a u0." + }, + { + "text": "And u2 is, what's u2 then?" + }, + { + "text": "U2 I multiply it, u2 I get from u1 by another, multiplying by a, so I've got a twice." + }, + { + "text": "And my formula is uk, after k steps, I've multiplied by a k times the original u0." + }, + { + "text": "You see what I'm doing?" + }, + { + "text": "The next section is going to solve systems of differential equations." + }, + { + "text": "I'm going to have derivatives." + }, + { + "text": "This, this section is the nice one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk13.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..ba8214d8c636e4757a266d6617801174bc939d80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "It solves difference equations." + }, + { + "text": "I would call that a difference equation." + }, + { + "text": "It's conne- a first order." + }, + { + "text": "I would call that a first order system, because it connects only, it only goes up one level." + }, + { + "text": "And it's a system because these are vectors and that's a matrix." + }, + { + "text": "And the solution is just that." + }, + { + "text": "OK." + }, + { + "text": "But, that's a nice formula." + }, + { + "text": "That's the, like, the most compact formula I could ever get." + }, + { + "text": "U one hundred would be a to the one hundredth u0." + }, + { + "text": "But how would I actually find u one hundred?" + }, + { + "text": "How would I find, how would I discover what u one hundred is?" + }, + { + "text": "Let me, let me show you how." + }, + { + "text": "Here, here's the idea." + }, + { + "text": "If, so, to solve, to really solve, shall I say, to really solve." + }, + { + "text": "To really solve it, I would take this initial vector, u0, and I would write it as a combination of eigenvectors." + }, + { + "text": "To really solve, write, write u0 as a combination, say, certain amount of the first eigenvector plus a certain amount of the second eigenvector plus a certain amount of the last eigenvector." + }, + { + "text": "Now multiply by a." + }, + { + "text": "You want to, you got to see the magic of eigenvectors work." + }, + { + "text": "Multiply by a." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk14.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7843b2bf0cac762d1c12452cf36500ea4ad13370 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a u0 is what?" + }, + { + "text": "So a times that." + }, + { + "text": "A times, so what's, I can separate it out into n separate pieces and that's the whole point." + }, + { + "text": "That each of those pieces is going in its own merry way." + }, + { + "text": "Each of those pieces is an eigenvector, and when I multiply by a, what does this piece become?" + }, + { + "text": "So that's some amount of the first, let's suppose the eigenvectors are normalized to be unit vectors." + }, + { + "text": "So that says what the eigenvector is." + }, + { + "text": "It's, and I need some multiple of it to produce u0." + }, + { + "text": "OK. Now when I multiply by a, what do I get?" + }, + { + "text": "I get c1, which is just a factor, times a x1, but a x1 is lambda one x1." + }, + { + "text": "When I multiply this by a, I get c2 lambda two x2." + }, + { + "text": "And here I get cn lambda n xn." + }, + { + "text": "And suppose I multiply by a to the hundredth power now." + }, + { + "text": "Can we, can we, having done it, multiplied by a, let's multiply by a to the hundredth." + }, + { + "text": "What happens to this first term when I multiply by a to the one hundredth?" + }, + { + "text": "It's got that factor lambda to the hundredth." + }, + { + "text": "That's the key." + }, + { + "text": "That, that's what I mean by going its own merry way." + }, + { + "text": "It, it is pure eigenvector, it's exactly in a direction where multiplication by a just brings in a scalar factor lambda one." + }, + { + "text": "So a hundred times brings in this a hundred times." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk15.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7ee3348735378aa4049d33ec2a197d0ceb0c447c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Hundred times lambda two, hundred times lambda n. Actually, we're, what are we seeing here?" + }, + { + "text": "We're seeing, this same, lambda, capital lambda to the hundredth, as in the, as in the diagonalization, and we're seeing the S matrix, the matrix S of eigenvectors." + }, + { + "text": "That's what this has got to, this has got to amount to, a lambda to the hundredth power times an S times this vector C that's telling us how much of each one is in the original thing." + }, + { + "text": "So if, if I had to really find the hundredth power, I would take u0, I would expand it as a combination of eigenvectors, this is really S, the eigenvector matrix times C, the, the coefficient vector." + }, + { + "text": "And then I would immediately, then, by inserting these hundredth powers of eigenvalues, I'd have the answer." + }, + { + "text": "So the, the, huh, there must be, well, let's see." + }, + { + "text": "OK." + }, + { + "text": "It's, so, yeah." + }, + { + "text": "So if u100 is a to the hundredth times u0, and u0 is Sc, then you see this formula is just this formula, which is the way I would actually get hold of this, of this u100, which is, let me put it here, u100." + }, + { + "text": "The way I would actually get hold of that, see what, what the solution is after a hundred steps, would be expand the initial vector into eigenvectors and, and let each eigenvector go its own way, multiplying by a hundred at, by lambda at every step, and therefore by lambda to the hundredth power after a hundredth step." + }, + { + "text": "Can I do an example?" + }, + { + "text": "So that's, that's the, the formulas." + }, + { + "text": "Now let me take an example." + }, + { + "text": "I'll use the Fibonacci sequence as an example." + }, + { + "text": "So, so Fibonacci example." + }, + { + "text": "You remember the Fibonacci numbers?" + }, + { + "text": "If we start with one and one as F0, oh, I think I start with zero, maybe." + }, + { + "text": "Let zero and one be the first ones." + }, + { + "text": "So there's F0 and F1, the first two Fibonacci numbers." + }, + { + "text": "Then what's the rule for Fibonacci numbers?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk16.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..79c65e32781f7f304b504a6c390247abb9d26ac8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "They're the sum." + }, + { + "text": "The next one is the sum of those, so it's one." + }, + { + "text": "The next one is the sum of those, so it's two." + }, + { + "text": "The next one is the sum of those, so it's three." + }, + { + "text": "Well, it looks like one, two, three, four, five, but somehow it's not going to do that way." + }, + { + "text": "The next one is five, right." + }, + { + "text": "Two and three makes five." + }, + { + "text": "The next one is eight." + }, + { + "text": "The next one is thirteen." + }, + { + "text": "And the one hundredth Fibonacci number is what?" + }, + { + "text": "That's my question." + }, + { + "text": "How could I get a formula for the hundredth number and for example how could I answer the question how fast are they growing?" + }, + { + "text": "How fast are those Fibonacci numbers growing?" + }, + { + "text": "They're certainly growing." + }, + { + "text": "It's not a stable case, whatever the eigenvalues of whatever matrix it is, they're not smaller than one." + }, + { + "text": "These numbers are growing." + }, + { + "text": "But how fast are they growing?" + }, + { + "text": "The answer is lies in the eigenvalue." + }, + { + "text": "So I've got to find the matrix, so let me write down the Fibonacci rule, F k plus two is F k plus one plus F k, right?" + }, + { + "text": "Now that's not in my -- I want to write that as U k plus one and A U k. But right now what I've got is a single equation, not a system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk17.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b3aaa9dcee3cf27c112015659bb5a0b51a983ce1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's second order." + }, + { + "text": "It's like having a second order differential equation with second derivatives." + }, + { + "text": "I want to get first derivatives." + }, + { + "text": "Here I want to get first difference." + }, + { + "text": "So the way to do it is to introduce U k will be a vector." + }, + { + "text": "See, a small trick." + }, + { + "text": "Let U k be a vector, F k plus one and F k. So I'm going to get a two by two system, first order, instead of a one, instead of a scalar system, second order, by a simple trick." + }, + { + "text": "I'm just going to add in an equation F k plus one equals F k plus one." + }, + { + "text": "That will be my second equation." + }, + { + "text": "Then this is my system, this is my unknown, and what's my one-step equation?" + }, + { + "text": "So now U k plus one." + }, + { + "text": "That's so U k plus one is the left side, and what have I got here on the right side?" + }, + { + "text": "I've got some matrix multiplying U k. Can you see that all right?" + }, + { + "text": "If you can see it, then you can tell me what the matrix is." + }, + { + "text": "You see that I'm taking my system here, I artificially made it into a system." + }, + { + "text": "I artificially made the unknown into a vector, and now I'm ready to look at and see what the matrix is." + }, + { + "text": "So do you see the left side, U k plus one is F k plus two F k plus one, that's just what I want." + }, + { + "text": "On the right side, this, remember, this U k here, let me for the moment put it as F k plus one F k. So what's the matrix?" + }, + { + "text": "Well, that has a one and a one, and that has a one and a zero." + }, + { + "text": "There's the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk18.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..6c1b68c2cb2fde3f5dea82f3100d4da31fcce70a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "You see that that gives me the right-hand side." + }, + { + "text": "So there's the matrix A, and this is our friend U k. So we've got, so that simple trick changed the second order scalar problem to a first order system, two, with two unknowns." + }, + { + "text": "With a matrix and now what do I do?" + }, + { + "text": "Well, before I even think, I find its eigenvalues and eigenvectors." + }, + { + "text": "So what are the eigenvalues and eigenvectors of that matrix?" + }, + { + "text": "Let's see." + }, + { + "text": "I was, first let me just, like, think for a minute." + }, + { + "text": "It's two by two, so this shouldn't be impossible to do." + }, + { + "text": "Let's do it." + }, + { + "text": "OK." + }, + { + "text": "So my matrix again is one one one zero." + }, + { + "text": "It's symmetric, by the way." + }, + { + "text": "So what I will eventually know about symmetric matrices is that the eigenvalues will come out real, I won't get any complex numbers here, and the eigenvectors, once I get those, actually will be orthogonal." + }, + { + "text": "But two by two, I'm more interested in what the actual numbers are." + }, + { + "text": "What do I know about the two numbers?" + }, + { + "text": "Well, should, do you want me to find this determinant of A minus lambda I?" + }, + { + "text": "Sure." + }, + { + "text": "So it's the determinant of one minus lambda one one zero, right?" + }, + { + "text": "Minus lambda, yes, got it." + }, + { + "text": "OK. OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk19.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..a73b23e3d56b889ff49ea7f55a784fac33e13c3d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "There'll be two eigenvalues." + }, + { + "text": "Well, tell me again what I know about the two eigenvalues before I go any further." + }, + { + "text": "Tell me something about these two eigenvalues, what do they add up to?" + }, + { + "text": "Lambda one plus lambda two is the same as the trace down the diagonal of the matrix, one and zero is one." + }, + { + "text": "So lambda one plus lambda two should come out to be one, and lambda one times lambda two should come out to be the determinant, which is minus one." + }, + { + "text": "So I'm expecting the eigenvalues to add to one and to multiply to minus one." + }, + { + "text": "But let's just see it happen here." + }, + { + "text": "If I multiply this out, I get that times that'll be a lambda squared minus lambda minus one." + }, + { + "text": "Good." + }, + { + "text": "Lambda squared minus lambda minus one." + }, + { + "text": "Actually, you see the, compare that with the original equation that I started with." + }, + { + "text": "Fk plus two minus Fk plus one minus Fk is zero." + }, + { + "text": "The recurrent, the recursion that the Fibonacci number satisfy is somehow showing up directly here for the eigenvalues when we set that to zero." + }, + { + "text": "OK. Let's solve." + }, + { + "text": "Well, I would like to be able to factor that, that quadratic, but I'm better off to use the quadratic formula." + }, + { + "text": "Lambda is, let's see, minus b is one, plus or minus the square root of b squared, which is one, minus four, times that, times that, which is plus four, over two." + }, + { + "text": "So that's the square root of five." + }, + { + "text": "So the eigenvalues are lambda one is one half of one plus square root of five, and lambda two is one half of one minus square root of five." + }, + { + "text": "And sure enough, they, those add up to one, and they multiply to give minus one." + }, + { + "text": "OK. Those are the two eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk2.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..43cfb012fc04a89fc7dab94c23bfb0f50ade3782 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "On the right, it's multiplied by, if I want, if I want lambda n xn in the last column, how do I do it?" + }, + { + "text": "Well, the last column here will be, I'll, I'll take the last column, use these coefficients, put the lambda n down there, and it will multiply that nth column and give me lambda n xn." + }, + { + "text": "There, there you see matrix multiplication just working for us." + }, + { + "text": "So I started with A s. I wrote down what it meant." + }, + { + "text": "A times each eigenvector." + }, + { + "text": "That gave me lambda times the eigenvector." + }, + { + "text": "And then when I peeled off the lambdas, they were on the right-hand side, so I've got s, my matrix back again, and this matrix, this diagonal matrix, the eigenvalue matrix, and I call it capital lambda, using capital letters for matrices, and lambda to prompt me that it's, that it's eigenvalues that are in there." + }, + { + "text": "So you see that the eigenvalues are just sitting down that diagonal?" + }, + { + "text": "If I had a column x2 here, I would want the lambda two in the two two position, in the diagonal position, to multiply that x2 and give me the lambda two x2." + }, + { + "text": "That's my formula." + }, + { + "text": "A s is s lambda." + }, + { + "text": "OK. That's, that's the, you see, it's just a calculation." + }, + { + "text": "Now, I, I mentioned, and I have to mention again, this business about n independent eigenvectors." + }, + { + "text": "As it stands, this is all fine whether, I mean, I could be repeating the same eigenvector, but I, I'm no interested in that." + }, + { + "text": "I want to be able to invert s, and that's where this comes in." + }, + { + "text": "This n independent eigenvectors business comes in to tell me that that matrix is invertible." + }, + { + "text": "So let me, on the next board, write down what I've got." + }, + { + "text": "A s equals s lambda." + }, + { + "text": "And now I'm, I can multiply on the left by s inverse." + }, + { + "text": "So this is really, I can do that provided s is invertible, provided my assumption of n independent eigenvectors is satisfied." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk20.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ad5a59fa5db44ce73ff5f88190423e0404fb3d39 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "How, how, what are those numbers approximately?" + }, + { + "text": "Square root of five, well, it's more than two, but less than three." + }, + { + "text": "It, it'd be nice to know these numbers." + }, + { + "text": "I think, I think that that, so that number comes out bigger than one, right?" + }, + { + "text": "Yeah, that's right." + }, + { + "text": "This number comes out bigger than one." + }, + { + "text": "It's about one point six one eight or something." + }, + { + "text": "Not exactly." + }, + { + "text": "It's supposed to be one point six." + }, + { + "text": "Just, like, I think so." + }, + { + "text": "Then what's lambda two?" + }, + { + "text": "Is, is lambda two positive or negative?" + }, + { + "text": "Negative, right?" + }, + { + "text": "Because I'm, it's obviously negative, and I knew that the, so it's minus, and they add up to one, so minus point six one eight, I guess." + }, + { + "text": "OK. And some order." + }, + { + "text": "Those are the two eigenvalues." + }, + { + "text": "One eigenvalue bigger than one, one eigenvalue smaller than one." + }, + { + "text": "Actually, that's a great situation to be in." + }, + { + "text": "Of course, the eigenvalues are different, so there's no doubt whatever, is this matrix diagonalizable?" + }, + { + "text": "Is this matrix diagonalizable, that original matrix A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk21.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..4a034475591d371995b379b5f98783a2cfb25870 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Sure." + }, + { + "text": "We've got two distinct eigenvalues and we can find the eigenvectors in a moment." + }, + { + "text": "But they'll be independent, will be diagonalizable, and now you can already answer my very first question." + }, + { + "text": "How fast are those Fibonacci numbers increasing?" + }, + { + "text": "How, those, they're increasing, right?" + }, + { + "text": "They're not doubling at every step." + }, + { + "text": "Let's look again at these numbers." + }, + { + "text": "Five eight thirteen, it's not obvious." + }, + { + "text": "The next one would be twenty one thirty four." + }, + { + "text": "So to get some idea of what F one hundred is, can you give me any, I mean the crucial number of, so it, these, it's approximately, what's controlling the growth of these Fibonacci numbers?" + }, + { + "text": "It's the eigenvalues." + }, + { + "text": "And which eigenvalues controlling that growth?" + }, + { + "text": "The big ones." + }, + { + "text": "So F one hundred will it be approximately some constant, c one, I guess, times this lambda one, this one plus square root of five over two, to the hundredth power." + }, + { + "text": "And the two hundredth have, in other words, the eigenvalue, the Fibonacci numbers are growing by about that factor." + }, + { + "text": "You see that we've got precise information about the, about the Fibonacci numbers out of the eigenvalue." + }, + { + "text": "OK. And again, why is that true?" + }, + { + "text": "Let me go over to this board and show what I'm doing here." + }, + { + "text": "The, the original eigen, the original initial value is some combination of eigenvectors, and then when we start multiple, when we start going out the theory of Fibonacci numbers, when we start multiplying by a hundred times, it's this lambda one to the hundredth, this term is, is the one that's taken over." + }, + { + "text": "It's, I mean, that's big, like, one point six to the hundredth power." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk22.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..c13a1fc9867173c3067e46c469cfff27b9b45289 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "The second term is practically nothing, right?" + }, + { + "text": "The point six, or minus point six to the hundredth power, is an extremely small, extremely small number." + }, + { + "text": "So this is, this, this, there are only two terms, because we're two by two." + }, + { + "text": "This number is, this piece of it is there, but it's, it's disappearing." + }, + { + "text": "Where this piece is there and it's growing and controlling everything." + }, + { + "text": "So, so really the, we're doing, like, problems that are evolving." + }, + { + "text": "We're doing dynamics." + }, + { + "text": "Instead of Ax equal b, that's a static problem." + }, + { + "text": "We're now, we're doing dynamics." + }, + { + "text": "A, a squared, a cubed, things are evolving in time, and the eigenvalues are the crucial, numbers." + }, + { + "text": "OK." + }, + { + "text": "I guess to complete this, I better write down the eigenvectors." + }, + { + "text": "So we should complete the, the whole process by finding the eigenvectors." + }, + { + "text": "OK. Well, I have to, up in the corner, then I have to look at A minus lambda I." + }, + { + "text": "So A minus lambda I is this one minus lambda, one, one, and minus lambda." + }, + { + "text": "And now, can we spot an eigenvector out of that?" + }, + { + "text": "That's, for these two lambdas, this matrix is singular." + }, + { + "text": "I guess the eigenvector, two by two ought to be easy." + }, + { + "text": "So if I know that this matrix is singular, then it seems to me the eigenvector has to be lambda and one, because that multiplication will give me the zero." + }, + { + "text": "And this multiplication gives me, better give me also zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk23.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..df816eb800ce767b1475c279a24ad976bb45a785 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Do you see why it does?" + }, + { + "text": "This is the minus lambda squared plus lambda plus one." + }, + { + "text": "It's the thing that's zero, because these lambdas are special." + }, + { + "text": "There's the eigenvector." + }, + { + "text": "X1 is lambda one, one, and x2 is lambda two, one." + }, + { + "text": "I did that as a little trick that was available in the two by two case." + }, + { + "text": "So now I finally have to, oh, I have to take the initial, u0." + }, + { + "text": "So to complete this example entirely, I have to say, OK, what was u0?" + }, + { + "text": "u0 was f1 f0." + }, + { + "text": "So u0, the starting vector, is f1 f0, and those were one and zero." + }, + { + "text": "So I have to use that vector, so I have to look for, from multiple of the first eigenvector and the second, to produce u0, the one zero vector." + }, + { + "text": "This is what will find c1 and c2, and then I'm done." + }, + { + "text": "So let me, instead of in the last five seconds grinding out a formula, let me repeat the idea." + }, + { + "text": "That really, it's the idea that's central." + }, + { + "text": "When things are evolving in time, let me come back to this board, because the ideas are here." + }, + { + "text": "When things are evolving in time by a first-order system, starting from an original u0, the key is, find the eigenvalues and eigenvectors of A." + }, + { + "text": "That will tell, those eigenvectors, the eigenvalues will already tell you what's happening." + }, + { + "text": "Is the solution blowing up?" + }, + { + "text": "Is it going to zero?" + }, + { + "text": "What's it doing?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk24.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..40301cb90760e2172baa94d536cbc13288d4c31f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk24.json @@ -0,0 +1,20 @@ +[ + { + "text": "And then, to find out exactly a formula, you have to take your u0 and write it as a combination of eigenvectors and then follow each eigenvector separately." + }, + { + "text": "And that's really what this formula, the formula for, that's what the formula for A to the k is doing." + }, + { + "text": "So remember that formula for A to the k is S, lambda to the k S inverse." + }, + { + "text": "OK. That's, that's difference equations, and you just have to, so the homework will give some examples different from Fibonacci to follow through." + }, + { + "text": "And next time will be differential equations." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk3.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..9bf1bb852baadc1da7837e14180c0c2951a30882 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I mentioned at the end of last time, and I'll say again, that there's a small number of matrices for, that don't have n independent eigenvectors." + }, + { + "text": "So I've got to discuss that, that technical point." + }, + { + "text": "But the great, the most matrices that we see have n, n independent eigenvectors and we can diagonalize." + }, + { + "text": "This is diagonalization." + }, + { + "text": "I could also write it, and I often will, the other way round." + }, + { + "text": "If I multiply on the right by s inverse, if I took this equation at the top and multiplied on the right by s inverse, I could, I would have A left here." + }, + { + "text": "Now s inverse is coming from the right." + }, + { + "text": "So can you keep those two straight?" + }, + { + "text": "A multiplies its eigenvectors." + }, + { + "text": "That's how I keep them straight." + }, + { + "text": "So A multiplies s. A multiplies s. And then this s inverse makes the whole thing diagonal." + }, + { + "text": "And this is another way of saying the same thing, putting the s's on the other side of the equation, A is s lambda s inverse." + }, + { + "text": "So that's the, that's the new factorization." + }, + { + "text": "That's the replacement for L U from elimination or Q R from Gram-Schmidt." + }, + { + "text": "And notice that the matrix, so it's, it's a matrix times a diagonal matrix times the inverse of the first one." + }, + { + "text": "It's, that's the combination that we'll see throughout this chapter." + }, + { + "text": "This, this, combination with an s and an s inverse." + }, + { + "text": "OK. Can I just begin to use that?" + }, + { + "text": "For example, what about A squared?" + }, + { + "text": "What are the eigenvalues and eigenvectors of A squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk4.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c687b6948acad76de8781cb82d3eb069c9da514e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's a straightforward question with a, with a absolutely clean answer." + }, + { + "text": "So let me, let me consider A squared." + }, + { + "text": "So I look, I start with Ax equal lambda x." + }, + { + "text": "And I'm headed for A squared." + }, + { + "text": "So let me multiply both sides by A." + }, + { + "text": "That's one way to get A squared on the left." + }, + { + "text": "So if, I should write these ifs in here." + }, + { + "text": "If Ax equals lambda x, then I multiply by A." + }, + { + "text": "So I get A squared x equals, well, I'm multiplying by A, so that's lambda Ax." + }, + { + "text": "That lambda was a number, so I just put it on the left." + }, + { + "text": "And what do I, tell me how to make that look better." + }, + { + "text": "What have I got here?" + }, + { + "text": "For, if, if A has the eigenvalue lambda and eigenvector x, what's up with A squared?" + }, + { + "text": "A squared x, I just multiply by A, but now for Ax, I'm going to substitute lambda x, so I've got lambda squared x." + }, + { + "text": "So from that simple calculation, I, my conclusion is that the eigenvalues of A squared are lambda squared." + }, + { + "text": "And the eigenvectors, I always think about both of those." + }, + { + "text": "What can I say about the eigenvalues?" + }, + { + "text": "They're squared." + }, + { + "text": "What can I say about the eigenvectors?" + }, + { + "text": "They're the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk5.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5bf15e20707c156c8ae71c9c7acea41a9d9d8e46 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same x as in, as for A." + }, + { + "text": "Now, let me see that also from this formula." + }, + { + "text": "How can I see what A squared is looking like from this formula?" + }, + { + "text": "So let me, that, that was one way to do it." + }, + { + "text": "Let me do it by just taking A squared from that." + }, + { + "text": "A squared is S lambda S inverse, that's A, times S lambda S inverse, that's A, which is?" + }, + { + "text": "This is the beauty of eigenvalues, eigenvectors, having that S inverse and S is the identity, so I've got S lambda squared S inverse." + }, + { + "text": "Yes." + }, + { + "text": "You see what that's telling me?" + }, + { + "text": "It's, it's telling me the same thing that I just learned here, but in the, in, in a matrix form." + }, + { + "text": "It's telling me that the S is the same, the eigenvectors are the same, but the eigenvalues are squared, because this is, what's lambda squared, that's still diagonal, it's got little lambda one squared, lambda two squared, down to lambda n squared, on that diagonal, those are the eigenvalues, as we just learned, of A squared." + }, + { + "text": "OK." + }, + { + "text": "So, somehow those eigenvalues and eigenvectors are really giving you a way to, to, to, to see what's going on inside a matrix." + }, + { + "text": "Now, of course, I can continue that for, to the k-th power." + }, + { + "text": "A to the k-th power." + }, + { + "text": "If I multiply, if I have k of these together, do you see how S inverse S will keep cancelling?" + }, + { + "text": "In the, in the inside, I'll have the S outside, at the far left, and lambda will be in there k times and S inverse." + }, + { + "text": "So what's that telling me?" + }, + { + "text": "That's telling me that the eigenvalues of A, of A to the k-th power are the k-th powers." + }, + { + "text": "The eigenvalues of A cubed are the cubes of the eigenvalues of A, and the eigenvectors are the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk6.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..c18dddbe798022f7e68278ac002a3f5fe6ed249e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same." + }, + { + "text": "OK." + }, + { + "text": "In other words, eigenvalues and eigenvectors give a great way to understand the powers of a matrix." + }, + { + "text": "If I take the square of a matrix or the hundredth power of a matrix, the pivots are all over the place." + }, + { + "text": "L U, if I multiply L U times L U times L U times L U a hundred times, I've got a hundred L U's." + }, + { + "text": "I can't do anything with them." + }, + { + "text": "But when I multiply S lambda S inverse by itself, when I look at the eigenvector picture a hundred times, I get a hundred or ninety-nine of these guys cancelling out inside, and I get A to the hundredth is S lambda to the hundredth S inverse." + }, + { + "text": "I mean, eigenvalues tell you about powers of a matrix in a way that we had no, no way to approach previously." + }, + { + "text": "For example, when does, when do the powers of a matrix go to zero?" + }, + { + "text": "I would call that matrix stable, maybe." + }, + { + "text": "So, so, so I could write down a, a theorem." + }, + { + "text": "I'll, I'll write it as a theorem, just to use that word to emphasize that here I'm getting this great fact from this eigenvalue picture." + }, + { + "text": "OK. A to the k approaches zero as k goes, as k gets bigger." + }, + { + "text": "If what?" + }, + { + "text": "What's the, how can I tell for a matrix A if its powers go to zero?" + }, + { + "text": "What, what's somewhere inside that matrix is that information." + }, + { + "text": "That information is not present in the pivots." + }, + { + "text": "It's present in the eigenvalues." + }, + { + "text": "What do I need for the, to know that if I take higher and higher powers of A that this matrix gets smaller and smaller?" + }, + { + "text": "Well, S and S inverse are not moving." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk7.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b84a5c854a5542758e8a0107e1ff043205fe3bdb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's this guy that has to get small, and that's easy to, easy to understand." + }, + { + "text": "The requirement is all eigenvalues, so what is the requirement?" + }, + { + "text": "The eigenvalues have to be less than one." + }, + { + "text": "Now, I have to write that absolute value, because those eigenvalues could be negative, they could be complex numbers." + }, + { + "text": "So I'm taking the absolute value if all of those are below one." + }, + { + "text": "That's, in fact, we practically see why." + }, + { + "text": "Let me just say that I, that I, I'm operating on one assumption here, and I got to keep remembering that that assumption is still present." + }, + { + "text": "That assumption was that I had a full set of, of n independent eigenvectors." + }, + { + "text": "If I don't have that, then I, I, then this approach is not working." + }, + { + "text": "So, so again, a pure eigenvalue approach, eigenvector approach, needs n independent eigenvectors." + }, + { + "text": "If we don't have n independent eigenvectors, we can't diagonalize the matrix." + }, + { + "text": "We can't get to a diagonal matrix." + }, + { + "text": "This, this, this diagonalization is only possible if S inverse makes sense." + }, + { + "text": "OK. Can I, can I follow up on that point now?" + }, + { + "text": "So, so you see why, what we get and, and why we want it, because we get information about the powers of a matrix just immediately from the eigenvalues." + }, + { + "text": "OK, now let me follow up on this, business of which matrices are diagonalizable." + }, + { + "text": "Sorry about that long word." + }, + { + "text": "So a matrix is, is sure to, so here's, here's the main point." + }, + { + "text": "A is sure to be, to have n independent eigenvectors and, and B, now here comes that word, diagonalizable, if, if, so we, we, we might as well get the, the nice case out in the open." + }, + { + "text": "The nice case is when, if all the lambdas are different." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk8.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f06dcec8ffa0ee1bf19440e4ab2194db33ab353b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means, that means no repeated eigenvalues." + }, + { + "text": "OK. That's the nice case." + }, + { + "text": "If, if my matrix and most matrix, if I do a random matrix in MATLAB and compute its eigenvalues, so if I computed, if I took I of rand of ten ten, gave, gave that MATLAB command, the, we'd get a random ten by ten matrix, we would get a list of its ten eigenvalues and they would be different." + }, + { + "text": "They would be distinct, is the best word." + }, + { + "text": "I would have a random matrix will have ten distinct, a ten by ten matrix will have ten distinct eigenvalues, and if it does, the eigenvectors are automatically independent." + }, + { + "text": "So that's a nice fact." + }, + { + "text": "I can, I'll refer you to the text for the proof." + }, + { + "text": "That, that A is sure to have n independent eigenvectors if the eigenvalues are different." + }, + { + "text": "If, if all the, if all eigenvalues are different." + }, + { + "text": "It's just, if some lambdas are repeated, then I have to look more closely." + }, + { + "text": "If an eigenvalue is repeated, I have to look, I have to count, I have to check." + }, + { + "text": "Has it got, say it's repeated three times." + }, + { + "text": "So what's a possibility for, so, so here's, here's the repeated possibility." + }, + { + "text": "And, and let me emphasize the conclusion." + }, + { + "text": "That if I have repeated eigenvalues, I may or may not, I may or may not have, have n independent eigenvectors." + }, + { + "text": "I might." + }, + { + "text": "I, I, you know, this isn't a completely negative case." + }, + { + "text": "The identity matrix." + }, + { + "text": "Well, suppose I take the ten by ten identity matrix." + }, + { + "text": "What are the eigenvalues of that matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk9.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..87d2a2ae5773036cf11800e2f1962908986a0dad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_37_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So just, just take the easiest matrix, the identity." + }, + { + "text": "If I look for its eigenvalues, they're all ones." + }, + { + "text": "So that eigenvalue one is repeated ten times." + }, + { + "text": "But there's no shortage of eigenvectors for the identity matrix." + }, + { + "text": "In fact, every vector is an eigenvector." + }, + { + "text": "So I can take ten independent vectors." + }, + { + "text": "Oh, well, what happens to everything if, if, if A is the identity matrix, let's just think that one through in our head." + }, + { + "text": "If A is the identity matrix, then it's got plenty of eigenvectors." + }, + { + "text": "I choose ten independent vectors, they're the columns of S, and, and what do I get from S inverse A S?" + }, + { + "text": "I get I again, right?" + }, + { + "text": "If A is the identity, and of course, that's the correct lambda." + }, + { + "text": "The, the matrix was already diagonal." + }, + { + "text": "So if the matrix is already diagonal, then the, the lambda is the same as the matrix." + }, + { + "text": "A diagonal matrix has got its eigenvalues sitting right there in front of you." + }, + { + "text": "Now if it's triangular, the eigenvalues are still sitting there, but so let's, let's take a case where, it's triangular." + }, + { + "text": "Suppose A is like, two, one, two, zero." + }, + { + "text": "So there's a case that's going to be trouble." + }, + { + "text": "There's a case that's going to be trouble." + }, + { + "text": "First of all, what are the eigen- I mean, we just, like now you, if we start with a matrix, the first thing we do practically without thinking is compute the eigenvalues and eigenvectors." + }, + { + "text": "OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk0.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6898d4fe66019ef6b40d0472ea94a968e7bbde9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, shall we start?" + }, + { + "text": "This is the second lecture on eigenvalues." + }, + { + "text": "So the first lecture was set -- reached the key equation, Ax equal lambda x. x is the eigenvector and lambda is the eigenvalue." + }, + { + "text": "Now, to use that." + }, + { + "text": "And the good way to, after we've found, so job one is to find the eigenvalues and find the eigenvectors." + }, + { + "text": "Now after we found them, what do we do with them?" + }, + { + "text": "Well, the good way to see that is diagonalize the matrix." + }, + { + "text": "So the matrix is A, and I want to show, first of all, this is like the basic fact." + }, + { + "text": "This, this formula." + }, + { + "text": "That's, that's the key to today's lecture." + }, + { + "text": "This matrix A, I put its eigenvectors in the columns of a matrix S. So S will be the eigenvector matrix, and I want to look at this magic combination S inverse A S. So can I show you how that, how that, what happens there?" + }, + { + "text": "And notice, notice, there's an S inverse." + }, + { + "text": "We have to be able to invert this eigenvector matrix S. So for that we need n independent eigenvectors." + }, + { + "text": "So that's the, that's the case." + }, + { + "text": "OK." + }, + { + "text": "So suppose we have n linearly independent eigenvectors of A." + }, + { + "text": "Put them in the columns of this matrix S. So I'm naturally going to call that the eigenvector matrix, because it's got the eigenvectors in its columns." + }, + { + "text": "And all I want to do is show you what happens when you multiply A times S. So A times S. So this is A times the matrix with the first eigenvector in its first column, the second eigenvector in its second column, the nth eigenvector in its nth column." + }, + { + "text": "And how am I going to do this matrix multiplication?" + }, + { + "text": "Well, certainly I'll do it a column at a time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk1.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..fbe078217bb68baea8e0605a5d04be568c49efbf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I get?" + }, + { + "text": "A times the first column gives me the first column of the answer, but what is it?" + }, + { + "text": "That's an eigenvector." + }, + { + "text": "A times x1 is equal to the lambda times the x1." + }, + { + "text": "And that lambda's we'll call lambda one, of course." + }, + { + "text": "So that's the first column, A x1 is the same as lambda one x1." + }, + { + "text": "A x2 is lambda two x2, so on, along to, in the nth column, we now have lambda n xn." + }, + { + "text": "Looking good, but the next step is even better." + }, + { + "text": "So for the next step, I want to separate out those eigenvalues, those multiplying numbers, from the x's." + }, + { + "text": "So then I'll have just what I want." + }, + { + "text": "OK, so how, how am I going to separate out?" + }, + { + "text": "So that, that number lambda one is multiplying the first column." + }, + { + "text": "So if I want to factor it out of the first column, I better put, here is going to be x1, and that's going to multiply this matrix lambda one in the first entry in all zeros." + }, + { + "text": "You see that that, that's going to come out right for the first column?" + }, + { + "text": "Because we remember how, how we're going back to that original punchline, that if I want a number to multiply x1, then I can do it by putting x1 in that column, in the first column, and putting that number there." + }, + { + "text": "What am I going to have here?" + }, + { + "text": "I'm going to have lambda one, I'm going to have x1, x2, xn." + }, + { + "text": "These are going to be my columns again." + }, + { + "text": "I'm getting s back again." + }, + { + "text": "I'm getting s back again, but now what's it multiplied by?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk10.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c58a42edbe9567233ca7f57643a0b7d43ae6761f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what are the eigenvalues?" + }, + { + "text": "You can tell me right away what they are." + }, + { + "text": "They're two and two, right." + }, + { + "text": "It's a triangular matrix, so when I do this determinant, shall I do this determinant of A minus lambda I?" + }, + { + "text": "I'll get this two minus lambda, one, zero, two minus lambda, right?" + }, + { + "text": "I take that determinant, so I make those into vertical bars to mean determinant, and what's the determinant?" + }, + { + "text": "Two minus lambda squared." + }, + { + "text": "What are the roots?" + }, + { + "text": "Lambda equal two twice." + }, + { + "text": "So the eigenvalues are lambda equals two and two." + }, + { + "text": "OK, fine." + }, + { + "text": "Now the next step, find the eigenvectors." + }, + { + "text": "So I look for eigenvectors and what do I find for this guy?" + }, + { + "text": "Eigenvectors for this guy, when I subtract two minus the identity, so A minus two I has zeros here, and I'm looking for the null space." + }, + { + "text": "What's, what are the eigenvectors?" + }, + { + "text": "They're the, they're, they're the null space of A minus lambda I." + }, + { + "text": "The null space is only one dimension." + }, + { + "text": "This is a case where I don't have enough eigenvectors." + }, + { + "text": "My algebraic multiplicity is two." + }, + { + "text": "I, I would say when I see, when I count how often the eigenvalue is repeated, that's the algebraic multiplicity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk11.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..779c2cf904d904b761080db2671aac46394ad02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the multiplicity." + }, + { + "text": "How many times is it the root of the polynomial?" + }, + { + "text": "My polynomial is two minus lambda squared." + }, + { + "text": "It's a double root." + }, + { + "text": "So my algebraic multiplicity is two." + }, + { + "text": "But the geometric multiplicity, which looks for vectors, looks for eigenvectors and which means the null space of this thing." + }, + { + "text": "And the only eigenvector is one zero." + }, + { + "text": "That's in the null space." + }, + { + "text": "Zero one is not in the null space." + }, + { + "text": "The null space is only one dimensional." + }, + { + "text": "So there's a matrix, my, this A or the original A, that are not diagonalizable." + }, + { + "text": "I can't, I can't find two independent eigenvectors, there's only one." + }, + { + "text": "OK." + }, + { + "text": "So that's the case that I'm, that's a case that I, I'm not really handling." + }, + { + "text": "For example, when I wrote down up here that the powers went to zero if the eigenvalues were below one, I didn't really handle that case of repeated eigenvalues because my reasoning was based on this formula." + }, + { + "text": "And this formula is based on n independent eigenvectors." + }, + { + "text": "OK." + }, + { + "text": "So just to say that." + }, + { + "text": "There are some matrices that we don't cover through diagonalization, but the great majority we do." + }, + { + "text": "OK. And we're always OK if we have different distinct eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk12.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..77d090704cc298475d94416b7ecb88a2a015a913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. That's the, like, the typical case." + }, + { + "text": "Because for each eigenvalue there's at least one eigenvector, the algebraic multiplicity here is one for every eigenvalue, and the geometric multiplicity is one." + }, + { + "text": "There's one eigenvector and they are independent." + }, + { + "text": "OK. OK. Now let me come back to the important case when we're OK." + }, + { + "text": "The important case when we are diagonalizing." + }, + { + "text": "Let me look at, so let me solve this equation." + }, + { + "text": "The equation will be each, I start with some, start with a given vector u0." + }, + { + "text": "And then my equation is that every step I multiply what I have by a." + }, + { + "text": "That equation ought to be simple to handle." + }, + { + "text": "OK. And I'd like to be able to solve it." + }, + { + "text": "How would I find, if I start with a vector u0, and I multiply by a a hundred times, what have I got?" + }, + { + "text": "Well, I can certainly write down a formula for the answer." + }, + { + "text": "So what, what, so u1 is a u0." + }, + { + "text": "And u2 is, what's u2 then?" + }, + { + "text": "U2 I multiply it, u2 I get from u1 by another, multiplying by a, so I've got a twice." + }, + { + "text": "And my formula is uk, after k steps, I've multiplied by a k times the original u0." + }, + { + "text": "You see what I'm doing?" + }, + { + "text": "The next section is going to solve systems of differential equations." + }, + { + "text": "I'm going to have derivatives." + }, + { + "text": "This, this section is the nice one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk13.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..ba8214d8c636e4757a266d6617801174bc939d80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "It solves difference equations." + }, + { + "text": "I would call that a difference equation." + }, + { + "text": "It's conne- a first order." + }, + { + "text": "I would call that a first order system, because it connects only, it only goes up one level." + }, + { + "text": "And it's a system because these are vectors and that's a matrix." + }, + { + "text": "And the solution is just that." + }, + { + "text": "OK." + }, + { + "text": "But, that's a nice formula." + }, + { + "text": "That's the, like, the most compact formula I could ever get." + }, + { + "text": "U one hundred would be a to the one hundredth u0." + }, + { + "text": "But how would I actually find u one hundred?" + }, + { + "text": "How would I find, how would I discover what u one hundred is?" + }, + { + "text": "Let me, let me show you how." + }, + { + "text": "Here, here's the idea." + }, + { + "text": "If, so, to solve, to really solve, shall I say, to really solve." + }, + { + "text": "To really solve it, I would take this initial vector, u0, and I would write it as a combination of eigenvectors." + }, + { + "text": "To really solve, write, write u0 as a combination, say, certain amount of the first eigenvector plus a certain amount of the second eigenvector plus a certain amount of the last eigenvector." + }, + { + "text": "Now multiply by a." + }, + { + "text": "You want to, you got to see the magic of eigenvectors work." + }, + { + "text": "Multiply by a." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk14.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7843b2bf0cac762d1c12452cf36500ea4ad13370 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a u0 is what?" + }, + { + "text": "So a times that." + }, + { + "text": "A times, so what's, I can separate it out into n separate pieces and that's the whole point." + }, + { + "text": "That each of those pieces is going in its own merry way." + }, + { + "text": "Each of those pieces is an eigenvector, and when I multiply by a, what does this piece become?" + }, + { + "text": "So that's some amount of the first, let's suppose the eigenvectors are normalized to be unit vectors." + }, + { + "text": "So that says what the eigenvector is." + }, + { + "text": "It's, and I need some multiple of it to produce u0." + }, + { + "text": "OK. Now when I multiply by a, what do I get?" + }, + { + "text": "I get c1, which is just a factor, times a x1, but a x1 is lambda one x1." + }, + { + "text": "When I multiply this by a, I get c2 lambda two x2." + }, + { + "text": "And here I get cn lambda n xn." + }, + { + "text": "And suppose I multiply by a to the hundredth power now." + }, + { + "text": "Can we, can we, having done it, multiplied by a, let's multiply by a to the hundredth." + }, + { + "text": "What happens to this first term when I multiply by a to the one hundredth?" + }, + { + "text": "It's got that factor lambda to the hundredth." + }, + { + "text": "That's the key." + }, + { + "text": "That, that's what I mean by going its own merry way." + }, + { + "text": "It, it is pure eigenvector, it's exactly in a direction where multiplication by a just brings in a scalar factor lambda one." + }, + { + "text": "So a hundred times brings in this a hundred times." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk15.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7ee3348735378aa4049d33ec2a197d0ceb0c447c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Hundred times lambda two, hundred times lambda n. Actually, we're, what are we seeing here?" + }, + { + "text": "We're seeing, this same, lambda, capital lambda to the hundredth, as in the, as in the diagonalization, and we're seeing the S matrix, the matrix S of eigenvectors." + }, + { + "text": "That's what this has got to, this has got to amount to, a lambda to the hundredth power times an S times this vector C that's telling us how much of each one is in the original thing." + }, + { + "text": "So if, if I had to really find the hundredth power, I would take u0, I would expand it as a combination of eigenvectors, this is really S, the eigenvector matrix times C, the, the coefficient vector." + }, + { + "text": "And then I would immediately, then, by inserting these hundredth powers of eigenvalues, I'd have the answer." + }, + { + "text": "So the, the, huh, there must be, well, let's see." + }, + { + "text": "OK." + }, + { + "text": "It's, so, yeah." + }, + { + "text": "So if u100 is a to the hundredth times u0, and u0 is Sc, then you see this formula is just this formula, which is the way I would actually get hold of this, of this u100, which is, let me put it here, u100." + }, + { + "text": "The way I would actually get hold of that, see what, what the solution is after a hundred steps, would be expand the initial vector into eigenvectors and, and let each eigenvector go its own way, multiplying by a hundred at, by lambda at every step, and therefore by lambda to the hundredth power after a hundredth step." + }, + { + "text": "Can I do an example?" + }, + { + "text": "So that's, that's the, the formulas." + }, + { + "text": "Now let me take an example." + }, + { + "text": "I'll use the Fibonacci sequence as an example." + }, + { + "text": "So, so Fibonacci example." + }, + { + "text": "You remember the Fibonacci numbers?" + }, + { + "text": "If we start with one and one as F0, oh, I think I start with zero, maybe." + }, + { + "text": "Let zero and one be the first ones." + }, + { + "text": "So there's F0 and F1, the first two Fibonacci numbers." + }, + { + "text": "Then what's the rule for Fibonacci numbers?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk16.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..79c65e32781f7f304b504a6c390247abb9d26ac8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "They're the sum." + }, + { + "text": "The next one is the sum of those, so it's one." + }, + { + "text": "The next one is the sum of those, so it's two." + }, + { + "text": "The next one is the sum of those, so it's three." + }, + { + "text": "Well, it looks like one, two, three, four, five, but somehow it's not going to do that way." + }, + { + "text": "The next one is five, right." + }, + { + "text": "Two and three makes five." + }, + { + "text": "The next one is eight." + }, + { + "text": "The next one is thirteen." + }, + { + "text": "And the one hundredth Fibonacci number is what?" + }, + { + "text": "That's my question." + }, + { + "text": "How could I get a formula for the hundredth number and for example how could I answer the question how fast are they growing?" + }, + { + "text": "How fast are those Fibonacci numbers growing?" + }, + { + "text": "They're certainly growing." + }, + { + "text": "It's not a stable case, whatever the eigenvalues of whatever matrix it is, they're not smaller than one." + }, + { + "text": "These numbers are growing." + }, + { + "text": "But how fast are they growing?" + }, + { + "text": "The answer is lies in the eigenvalue." + }, + { + "text": "So I've got to find the matrix, so let me write down the Fibonacci rule, F k plus two is F k plus one plus F k, right?" + }, + { + "text": "Now that's not in my -- I want to write that as U k plus one and A U k. But right now what I've got is a single equation, not a system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk17.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b3aaa9dcee3cf27c112015659bb5a0b51a983ce1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's second order." + }, + { + "text": "It's like having a second order differential equation with second derivatives." + }, + { + "text": "I want to get first derivatives." + }, + { + "text": "Here I want to get first difference." + }, + { + "text": "So the way to do it is to introduce U k will be a vector." + }, + { + "text": "See, a small trick." + }, + { + "text": "Let U k be a vector, F k plus one and F k. So I'm going to get a two by two system, first order, instead of a one, instead of a scalar system, second order, by a simple trick." + }, + { + "text": "I'm just going to add in an equation F k plus one equals F k plus one." + }, + { + "text": "That will be my second equation." + }, + { + "text": "Then this is my system, this is my unknown, and what's my one-step equation?" + }, + { + "text": "So now U k plus one." + }, + { + "text": "That's so U k plus one is the left side, and what have I got here on the right side?" + }, + { + "text": "I've got some matrix multiplying U k. Can you see that all right?" + }, + { + "text": "If you can see it, then you can tell me what the matrix is." + }, + { + "text": "You see that I'm taking my system here, I artificially made it into a system." + }, + { + "text": "I artificially made the unknown into a vector, and now I'm ready to look at and see what the matrix is." + }, + { + "text": "So do you see the left side, U k plus one is F k plus two F k plus one, that's just what I want." + }, + { + "text": "On the right side, this, remember, this U k here, let me for the moment put it as F k plus one F k. So what's the matrix?" + }, + { + "text": "Well, that has a one and a one, and that has a one and a zero." + }, + { + "text": "There's the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk18.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..6c1b68c2cb2fde3f5dea82f3100d4da31fcce70a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "You see that that gives me the right-hand side." + }, + { + "text": "So there's the matrix A, and this is our friend U k. So we've got, so that simple trick changed the second order scalar problem to a first order system, two, with two unknowns." + }, + { + "text": "With a matrix and now what do I do?" + }, + { + "text": "Well, before I even think, I find its eigenvalues and eigenvectors." + }, + { + "text": "So what are the eigenvalues and eigenvectors of that matrix?" + }, + { + "text": "Let's see." + }, + { + "text": "I was, first let me just, like, think for a minute." + }, + { + "text": "It's two by two, so this shouldn't be impossible to do." + }, + { + "text": "Let's do it." + }, + { + "text": "OK." + }, + { + "text": "So my matrix again is one one one zero." + }, + { + "text": "It's symmetric, by the way." + }, + { + "text": "So what I will eventually know about symmetric matrices is that the eigenvalues will come out real, I won't get any complex numbers here, and the eigenvectors, once I get those, actually will be orthogonal." + }, + { + "text": "But two by two, I'm more interested in what the actual numbers are." + }, + { + "text": "What do I know about the two numbers?" + }, + { + "text": "Well, should, do you want me to find this determinant of A minus lambda I?" + }, + { + "text": "Sure." + }, + { + "text": "So it's the determinant of one minus lambda one one zero, right?" + }, + { + "text": "Minus lambda, yes, got it." + }, + { + "text": "OK. OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk19.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..a73b23e3d56b889ff49ea7f55a784fac33e13c3d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "There'll be two eigenvalues." + }, + { + "text": "Well, tell me again what I know about the two eigenvalues before I go any further." + }, + { + "text": "Tell me something about these two eigenvalues, what do they add up to?" + }, + { + "text": "Lambda one plus lambda two is the same as the trace down the diagonal of the matrix, one and zero is one." + }, + { + "text": "So lambda one plus lambda two should come out to be one, and lambda one times lambda two should come out to be the determinant, which is minus one." + }, + { + "text": "So I'm expecting the eigenvalues to add to one and to multiply to minus one." + }, + { + "text": "But let's just see it happen here." + }, + { + "text": "If I multiply this out, I get that times that'll be a lambda squared minus lambda minus one." + }, + { + "text": "Good." + }, + { + "text": "Lambda squared minus lambda minus one." + }, + { + "text": "Actually, you see the, compare that with the original equation that I started with." + }, + { + "text": "Fk plus two minus Fk plus one minus Fk is zero." + }, + { + "text": "The recurrent, the recursion that the Fibonacci number satisfy is somehow showing up directly here for the eigenvalues when we set that to zero." + }, + { + "text": "OK. Let's solve." + }, + { + "text": "Well, I would like to be able to factor that, that quadratic, but I'm better off to use the quadratic formula." + }, + { + "text": "Lambda is, let's see, minus b is one, plus or minus the square root of b squared, which is one, minus four, times that, times that, which is plus four, over two." + }, + { + "text": "So that's the square root of five." + }, + { + "text": "So the eigenvalues are lambda one is one half of one plus square root of five, and lambda two is one half of one minus square root of five." + }, + { + "text": "And sure enough, they, those add up to one, and they multiply to give minus one." + }, + { + "text": "OK. Those are the two eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk2.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..43cfb012fc04a89fc7dab94c23bfb0f50ade3782 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "On the right, it's multiplied by, if I want, if I want lambda n xn in the last column, how do I do it?" + }, + { + "text": "Well, the last column here will be, I'll, I'll take the last column, use these coefficients, put the lambda n down there, and it will multiply that nth column and give me lambda n xn." + }, + { + "text": "There, there you see matrix multiplication just working for us." + }, + { + "text": "So I started with A s. I wrote down what it meant." + }, + { + "text": "A times each eigenvector." + }, + { + "text": "That gave me lambda times the eigenvector." + }, + { + "text": "And then when I peeled off the lambdas, they were on the right-hand side, so I've got s, my matrix back again, and this matrix, this diagonal matrix, the eigenvalue matrix, and I call it capital lambda, using capital letters for matrices, and lambda to prompt me that it's, that it's eigenvalues that are in there." + }, + { + "text": "So you see that the eigenvalues are just sitting down that diagonal?" + }, + { + "text": "If I had a column x2 here, I would want the lambda two in the two two position, in the diagonal position, to multiply that x2 and give me the lambda two x2." + }, + { + "text": "That's my formula." + }, + { + "text": "A s is s lambda." + }, + { + "text": "OK. That's, that's the, you see, it's just a calculation." + }, + { + "text": "Now, I, I mentioned, and I have to mention again, this business about n independent eigenvectors." + }, + { + "text": "As it stands, this is all fine whether, I mean, I could be repeating the same eigenvector, but I, I'm no interested in that." + }, + { + "text": "I want to be able to invert s, and that's where this comes in." + }, + { + "text": "This n independent eigenvectors business comes in to tell me that that matrix is invertible." + }, + { + "text": "So let me, on the next board, write down what I've got." + }, + { + "text": "A s equals s lambda." + }, + { + "text": "And now I'm, I can multiply on the left by s inverse." + }, + { + "text": "So this is really, I can do that provided s is invertible, provided my assumption of n independent eigenvectors is satisfied." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk20.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ad5a59fa5db44ce73ff5f88190423e0404fb3d39 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "How, how, what are those numbers approximately?" + }, + { + "text": "Square root of five, well, it's more than two, but less than three." + }, + { + "text": "It, it'd be nice to know these numbers." + }, + { + "text": "I think, I think that that, so that number comes out bigger than one, right?" + }, + { + "text": "Yeah, that's right." + }, + { + "text": "This number comes out bigger than one." + }, + { + "text": "It's about one point six one eight or something." + }, + { + "text": "Not exactly." + }, + { + "text": "It's supposed to be one point six." + }, + { + "text": "Just, like, I think so." + }, + { + "text": "Then what's lambda two?" + }, + { + "text": "Is, is lambda two positive or negative?" + }, + { + "text": "Negative, right?" + }, + { + "text": "Because I'm, it's obviously negative, and I knew that the, so it's minus, and they add up to one, so minus point six one eight, I guess." + }, + { + "text": "OK. And some order." + }, + { + "text": "Those are the two eigenvalues." + }, + { + "text": "One eigenvalue bigger than one, one eigenvalue smaller than one." + }, + { + "text": "Actually, that's a great situation to be in." + }, + { + "text": "Of course, the eigenvalues are different, so there's no doubt whatever, is this matrix diagonalizable?" + }, + { + "text": "Is this matrix diagonalizable, that original matrix A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk21.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..4a034475591d371995b379b5f98783a2cfb25870 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Sure." + }, + { + "text": "We've got two distinct eigenvalues and we can find the eigenvectors in a moment." + }, + { + "text": "But they'll be independent, will be diagonalizable, and now you can already answer my very first question." + }, + { + "text": "How fast are those Fibonacci numbers increasing?" + }, + { + "text": "How, those, they're increasing, right?" + }, + { + "text": "They're not doubling at every step." + }, + { + "text": "Let's look again at these numbers." + }, + { + "text": "Five eight thirteen, it's not obvious." + }, + { + "text": "The next one would be twenty one thirty four." + }, + { + "text": "So to get some idea of what F one hundred is, can you give me any, I mean the crucial number of, so it, these, it's approximately, what's controlling the growth of these Fibonacci numbers?" + }, + { + "text": "It's the eigenvalues." + }, + { + "text": "And which eigenvalues controlling that growth?" + }, + { + "text": "The big ones." + }, + { + "text": "So F one hundred will it be approximately some constant, c one, I guess, times this lambda one, this one plus square root of five over two, to the hundredth power." + }, + { + "text": "And the two hundredth have, in other words, the eigenvalue, the Fibonacci numbers are growing by about that factor." + }, + { + "text": "You see that we've got precise information about the, about the Fibonacci numbers out of the eigenvalue." + }, + { + "text": "OK. And again, why is that true?" + }, + { + "text": "Let me go over to this board and show what I'm doing here." + }, + { + "text": "The, the original eigen, the original initial value is some combination of eigenvectors, and then when we start multiple, when we start going out the theory of Fibonacci numbers, when we start multiplying by a hundred times, it's this lambda one to the hundredth, this term is, is the one that's taken over." + }, + { + "text": "It's, I mean, that's big, like, one point six to the hundredth power." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk22.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..c13a1fc9867173c3067e46c469cfff27b9b45289 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "The second term is practically nothing, right?" + }, + { + "text": "The point six, or minus point six to the hundredth power, is an extremely small, extremely small number." + }, + { + "text": "So this is, this, this, there are only two terms, because we're two by two." + }, + { + "text": "This number is, this piece of it is there, but it's, it's disappearing." + }, + { + "text": "Where this piece is there and it's growing and controlling everything." + }, + { + "text": "So, so really the, we're doing, like, problems that are evolving." + }, + { + "text": "We're doing dynamics." + }, + { + "text": "Instead of Ax equal b, that's a static problem." + }, + { + "text": "We're now, we're doing dynamics." + }, + { + "text": "A, a squared, a cubed, things are evolving in time, and the eigenvalues are the crucial, numbers." + }, + { + "text": "OK." + }, + { + "text": "I guess to complete this, I better write down the eigenvectors." + }, + { + "text": "So we should complete the, the whole process by finding the eigenvectors." + }, + { + "text": "OK. Well, I have to, up in the corner, then I have to look at A minus lambda I." + }, + { + "text": "So A minus lambda I is this one minus lambda, one, one, and minus lambda." + }, + { + "text": "And now, can we spot an eigenvector out of that?" + }, + { + "text": "That's, for these two lambdas, this matrix is singular." + }, + { + "text": "I guess the eigenvector, two by two ought to be easy." + }, + { + "text": "So if I know that this matrix is singular, then it seems to me the eigenvector has to be lambda and one, because that multiplication will give me the zero." + }, + { + "text": "And this multiplication gives me, better give me also zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk23.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..df816eb800ce767b1475c279a24ad976bb45a785 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Do you see why it does?" + }, + { + "text": "This is the minus lambda squared plus lambda plus one." + }, + { + "text": "It's the thing that's zero, because these lambdas are special." + }, + { + "text": "There's the eigenvector." + }, + { + "text": "X1 is lambda one, one, and x2 is lambda two, one." + }, + { + "text": "I did that as a little trick that was available in the two by two case." + }, + { + "text": "So now I finally have to, oh, I have to take the initial, u0." + }, + { + "text": "So to complete this example entirely, I have to say, OK, what was u0?" + }, + { + "text": "u0 was f1 f0." + }, + { + "text": "So u0, the starting vector, is f1 f0, and those were one and zero." + }, + { + "text": "So I have to use that vector, so I have to look for, from multiple of the first eigenvector and the second, to produce u0, the one zero vector." + }, + { + "text": "This is what will find c1 and c2, and then I'm done." + }, + { + "text": "So let me, instead of in the last five seconds grinding out a formula, let me repeat the idea." + }, + { + "text": "That really, it's the idea that's central." + }, + { + "text": "When things are evolving in time, let me come back to this board, because the ideas are here." + }, + { + "text": "When things are evolving in time by a first-order system, starting from an original u0, the key is, find the eigenvalues and eigenvectors of A." + }, + { + "text": "That will tell, those eigenvectors, the eigenvalues will already tell you what's happening." + }, + { + "text": "Is the solution blowing up?" + }, + { + "text": "Is it going to zero?" + }, + { + "text": "What's it doing?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk24.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..40301cb90760e2172baa94d536cbc13288d4c31f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk24.json @@ -0,0 +1,20 @@ +[ + { + "text": "And then, to find out exactly a formula, you have to take your u0 and write it as a combination of eigenvectors and then follow each eigenvector separately." + }, + { + "text": "And that's really what this formula, the formula for, that's what the formula for A to the k is doing." + }, + { + "text": "So remember that formula for A to the k is S, lambda to the k S inverse." + }, + { + "text": "OK. That's, that's difference equations, and you just have to, so the homework will give some examples different from Fibonacci to follow through." + }, + { + "text": "And next time will be differential equations." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk3.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..9bf1bb852baadc1da7837e14180c0c2951a30882 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I mentioned at the end of last time, and I'll say again, that there's a small number of matrices for, that don't have n independent eigenvectors." + }, + { + "text": "So I've got to discuss that, that technical point." + }, + { + "text": "But the great, the most matrices that we see have n, n independent eigenvectors and we can diagonalize." + }, + { + "text": "This is diagonalization." + }, + { + "text": "I could also write it, and I often will, the other way round." + }, + { + "text": "If I multiply on the right by s inverse, if I took this equation at the top and multiplied on the right by s inverse, I could, I would have A left here." + }, + { + "text": "Now s inverse is coming from the right." + }, + { + "text": "So can you keep those two straight?" + }, + { + "text": "A multiplies its eigenvectors." + }, + { + "text": "That's how I keep them straight." + }, + { + "text": "So A multiplies s. A multiplies s. And then this s inverse makes the whole thing diagonal." + }, + { + "text": "And this is another way of saying the same thing, putting the s's on the other side of the equation, A is s lambda s inverse." + }, + { + "text": "So that's the, that's the new factorization." + }, + { + "text": "That's the replacement for L U from elimination or Q R from Gram-Schmidt." + }, + { + "text": "And notice that the matrix, so it's, it's a matrix times a diagonal matrix times the inverse of the first one." + }, + { + "text": "It's, that's the combination that we'll see throughout this chapter." + }, + { + "text": "This, this, combination with an s and an s inverse." + }, + { + "text": "OK. Can I just begin to use that?" + }, + { + "text": "For example, what about A squared?" + }, + { + "text": "What are the eigenvalues and eigenvectors of A squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk4.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c687b6948acad76de8781cb82d3eb069c9da514e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's a straightforward question with a, with a absolutely clean answer." + }, + { + "text": "So let me, let me consider A squared." + }, + { + "text": "So I look, I start with Ax equal lambda x." + }, + { + "text": "And I'm headed for A squared." + }, + { + "text": "So let me multiply both sides by A." + }, + { + "text": "That's one way to get A squared on the left." + }, + { + "text": "So if, I should write these ifs in here." + }, + { + "text": "If Ax equals lambda x, then I multiply by A." + }, + { + "text": "So I get A squared x equals, well, I'm multiplying by A, so that's lambda Ax." + }, + { + "text": "That lambda was a number, so I just put it on the left." + }, + { + "text": "And what do I, tell me how to make that look better." + }, + { + "text": "What have I got here?" + }, + { + "text": "For, if, if A has the eigenvalue lambda and eigenvector x, what's up with A squared?" + }, + { + "text": "A squared x, I just multiply by A, but now for Ax, I'm going to substitute lambda x, so I've got lambda squared x." + }, + { + "text": "So from that simple calculation, I, my conclusion is that the eigenvalues of A squared are lambda squared." + }, + { + "text": "And the eigenvectors, I always think about both of those." + }, + { + "text": "What can I say about the eigenvalues?" + }, + { + "text": "They're squared." + }, + { + "text": "What can I say about the eigenvectors?" + }, + { + "text": "They're the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk5.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5bf15e20707c156c8ae71c9c7acea41a9d9d8e46 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same x as in, as for A." + }, + { + "text": "Now, let me see that also from this formula." + }, + { + "text": "How can I see what A squared is looking like from this formula?" + }, + { + "text": "So let me, that, that was one way to do it." + }, + { + "text": "Let me do it by just taking A squared from that." + }, + { + "text": "A squared is S lambda S inverse, that's A, times S lambda S inverse, that's A, which is?" + }, + { + "text": "This is the beauty of eigenvalues, eigenvectors, having that S inverse and S is the identity, so I've got S lambda squared S inverse." + }, + { + "text": "Yes." + }, + { + "text": "You see what that's telling me?" + }, + { + "text": "It's, it's telling me the same thing that I just learned here, but in the, in, in a matrix form." + }, + { + "text": "It's telling me that the S is the same, the eigenvectors are the same, but the eigenvalues are squared, because this is, what's lambda squared, that's still diagonal, it's got little lambda one squared, lambda two squared, down to lambda n squared, on that diagonal, those are the eigenvalues, as we just learned, of A squared." + }, + { + "text": "OK." + }, + { + "text": "So, somehow those eigenvalues and eigenvectors are really giving you a way to, to, to, to see what's going on inside a matrix." + }, + { + "text": "Now, of course, I can continue that for, to the k-th power." + }, + { + "text": "A to the k-th power." + }, + { + "text": "If I multiply, if I have k of these together, do you see how S inverse S will keep cancelling?" + }, + { + "text": "In the, in the inside, I'll have the S outside, at the far left, and lambda will be in there k times and S inverse." + }, + { + "text": "So what's that telling me?" + }, + { + "text": "That's telling me that the eigenvalues of A, of A to the k-th power are the k-th powers." + }, + { + "text": "The eigenvalues of A cubed are the cubes of the eigenvalues of A, and the eigenvectors are the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk6.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..c18dddbe798022f7e68278ac002a3f5fe6ed249e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same." + }, + { + "text": "OK." + }, + { + "text": "In other words, eigenvalues and eigenvectors give a great way to understand the powers of a matrix." + }, + { + "text": "If I take the square of a matrix or the hundredth power of a matrix, the pivots are all over the place." + }, + { + "text": "L U, if I multiply L U times L U times L U times L U a hundred times, I've got a hundred L U's." + }, + { + "text": "I can't do anything with them." + }, + { + "text": "But when I multiply S lambda S inverse by itself, when I look at the eigenvector picture a hundred times, I get a hundred or ninety-nine of these guys cancelling out inside, and I get A to the hundredth is S lambda to the hundredth S inverse." + }, + { + "text": "I mean, eigenvalues tell you about powers of a matrix in a way that we had no, no way to approach previously." + }, + { + "text": "For example, when does, when do the powers of a matrix go to zero?" + }, + { + "text": "I would call that matrix stable, maybe." + }, + { + "text": "So, so, so I could write down a, a theorem." + }, + { + "text": "I'll, I'll write it as a theorem, just to use that word to emphasize that here I'm getting this great fact from this eigenvalue picture." + }, + { + "text": "OK. A to the k approaches zero as k goes, as k gets bigger." + }, + { + "text": "If what?" + }, + { + "text": "What's the, how can I tell for a matrix A if its powers go to zero?" + }, + { + "text": "What, what's somewhere inside that matrix is that information." + }, + { + "text": "That information is not present in the pivots." + }, + { + "text": "It's present in the eigenvalues." + }, + { + "text": "What do I need for the, to know that if I take higher and higher powers of A that this matrix gets smaller and smaller?" + }, + { + "text": "Well, S and S inverse are not moving." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk7.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b84a5c854a5542758e8a0107e1ff043205fe3bdb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's this guy that has to get small, and that's easy to, easy to understand." + }, + { + "text": "The requirement is all eigenvalues, so what is the requirement?" + }, + { + "text": "The eigenvalues have to be less than one." + }, + { + "text": "Now, I have to write that absolute value, because those eigenvalues could be negative, they could be complex numbers." + }, + { + "text": "So I'm taking the absolute value if all of those are below one." + }, + { + "text": "That's, in fact, we practically see why." + }, + { + "text": "Let me just say that I, that I, I'm operating on one assumption here, and I got to keep remembering that that assumption is still present." + }, + { + "text": "That assumption was that I had a full set of, of n independent eigenvectors." + }, + { + "text": "If I don't have that, then I, I, then this approach is not working." + }, + { + "text": "So, so again, a pure eigenvalue approach, eigenvector approach, needs n independent eigenvectors." + }, + { + "text": "If we don't have n independent eigenvectors, we can't diagonalize the matrix." + }, + { + "text": "We can't get to a diagonal matrix." + }, + { + "text": "This, this, this diagonalization is only possible if S inverse makes sense." + }, + { + "text": "OK. Can I, can I follow up on that point now?" + }, + { + "text": "So, so you see why, what we get and, and why we want it, because we get information about the powers of a matrix just immediately from the eigenvalues." + }, + { + "text": "OK, now let me follow up on this, business of which matrices are diagonalizable." + }, + { + "text": "Sorry about that long word." + }, + { + "text": "So a matrix is, is sure to, so here's, here's the main point." + }, + { + "text": "A is sure to be, to have n independent eigenvectors and, and B, now here comes that word, diagonalizable, if, if, so we, we, we might as well get the, the nice case out in the open." + }, + { + "text": "The nice case is when, if all the lambdas are different." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk8.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f06dcec8ffa0ee1bf19440e4ab2194db33ab353b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means, that means no repeated eigenvalues." + }, + { + "text": "OK. That's the nice case." + }, + { + "text": "If, if my matrix and most matrix, if I do a random matrix in MATLAB and compute its eigenvalues, so if I computed, if I took I of rand of ten ten, gave, gave that MATLAB command, the, we'd get a random ten by ten matrix, we would get a list of its ten eigenvalues and they would be different." + }, + { + "text": "They would be distinct, is the best word." + }, + { + "text": "I would have a random matrix will have ten distinct, a ten by ten matrix will have ten distinct eigenvalues, and if it does, the eigenvectors are automatically independent." + }, + { + "text": "So that's a nice fact." + }, + { + "text": "I can, I'll refer you to the text for the proof." + }, + { + "text": "That, that A is sure to have n independent eigenvectors if the eigenvalues are different." + }, + { + "text": "If, if all the, if all eigenvalues are different." + }, + { + "text": "It's just, if some lambdas are repeated, then I have to look more closely." + }, + { + "text": "If an eigenvalue is repeated, I have to look, I have to count, I have to check." + }, + { + "text": "Has it got, say it's repeated three times." + }, + { + "text": "So what's a possibility for, so, so here's, here's the repeated possibility." + }, + { + "text": "And, and let me emphasize the conclusion." + }, + { + "text": "That if I have repeated eigenvalues, I may or may not, I may or may not have, have n independent eigenvectors." + }, + { + "text": "I might." + }, + { + "text": "I, I, you know, this isn't a completely negative case." + }, + { + "text": "The identity matrix." + }, + { + "text": "Well, suppose I take the ten by ten identity matrix." + }, + { + "text": "What are the eigenvalues of that matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk9.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..87d2a2ae5773036cf11800e2f1962908986a0dad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_38_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So just, just take the easiest matrix, the identity." + }, + { + "text": "If I look for its eigenvalues, they're all ones." + }, + { + "text": "So that eigenvalue one is repeated ten times." + }, + { + "text": "But there's no shortage of eigenvectors for the identity matrix." + }, + { + "text": "In fact, every vector is an eigenvector." + }, + { + "text": "So I can take ten independent vectors." + }, + { + "text": "Oh, well, what happens to everything if, if, if A is the identity matrix, let's just think that one through in our head." + }, + { + "text": "If A is the identity matrix, then it's got plenty of eigenvectors." + }, + { + "text": "I choose ten independent vectors, they're the columns of S, and, and what do I get from S inverse A S?" + }, + { + "text": "I get I again, right?" + }, + { + "text": "If A is the identity, and of course, that's the correct lambda." + }, + { + "text": "The, the matrix was already diagonal." + }, + { + "text": "So if the matrix is already diagonal, then the, the lambda is the same as the matrix." + }, + { + "text": "A diagonal matrix has got its eigenvalues sitting right there in front of you." + }, + { + "text": "Now if it's triangular, the eigenvalues are still sitting there, but so let's, let's take a case where, it's triangular." + }, + { + "text": "Suppose A is like, two, one, two, zero." + }, + { + "text": "So there's a case that's going to be trouble." + }, + { + "text": "There's a case that's going to be trouble." + }, + { + "text": "First of all, what are the eigen- I mean, we just, like now you, if we start with a matrix, the first thing we do practically without thinking is compute the eigenvalues and eigenvectors." + }, + { + "text": "OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk0.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6898d4fe66019ef6b40d0472ea94a968e7bbde9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, shall we start?" + }, + { + "text": "This is the second lecture on eigenvalues." + }, + { + "text": "So the first lecture was set -- reached the key equation, Ax equal lambda x. x is the eigenvector and lambda is the eigenvalue." + }, + { + "text": "Now, to use that." + }, + { + "text": "And the good way to, after we've found, so job one is to find the eigenvalues and find the eigenvectors." + }, + { + "text": "Now after we found them, what do we do with them?" + }, + { + "text": "Well, the good way to see that is diagonalize the matrix." + }, + { + "text": "So the matrix is A, and I want to show, first of all, this is like the basic fact." + }, + { + "text": "This, this formula." + }, + { + "text": "That's, that's the key to today's lecture." + }, + { + "text": "This matrix A, I put its eigenvectors in the columns of a matrix S. So S will be the eigenvector matrix, and I want to look at this magic combination S inverse A S. So can I show you how that, how that, what happens there?" + }, + { + "text": "And notice, notice, there's an S inverse." + }, + { + "text": "We have to be able to invert this eigenvector matrix S. So for that we need n independent eigenvectors." + }, + { + "text": "So that's the, that's the case." + }, + { + "text": "OK." + }, + { + "text": "So suppose we have n linearly independent eigenvectors of A." + }, + { + "text": "Put them in the columns of this matrix S. So I'm naturally going to call that the eigenvector matrix, because it's got the eigenvectors in its columns." + }, + { + "text": "And all I want to do is show you what happens when you multiply A times S. So A times S. So this is A times the matrix with the first eigenvector in its first column, the second eigenvector in its second column, the nth eigenvector in its nth column." + }, + { + "text": "And how am I going to do this matrix multiplication?" + }, + { + "text": "Well, certainly I'll do it a column at a time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk1.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..fbe078217bb68baea8e0605a5d04be568c49efbf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I get?" + }, + { + "text": "A times the first column gives me the first column of the answer, but what is it?" + }, + { + "text": "That's an eigenvector." + }, + { + "text": "A times x1 is equal to the lambda times the x1." + }, + { + "text": "And that lambda's we'll call lambda one, of course." + }, + { + "text": "So that's the first column, A x1 is the same as lambda one x1." + }, + { + "text": "A x2 is lambda two x2, so on, along to, in the nth column, we now have lambda n xn." + }, + { + "text": "Looking good, but the next step is even better." + }, + { + "text": "So for the next step, I want to separate out those eigenvalues, those multiplying numbers, from the x's." + }, + { + "text": "So then I'll have just what I want." + }, + { + "text": "OK, so how, how am I going to separate out?" + }, + { + "text": "So that, that number lambda one is multiplying the first column." + }, + { + "text": "So if I want to factor it out of the first column, I better put, here is going to be x1, and that's going to multiply this matrix lambda one in the first entry in all zeros." + }, + { + "text": "You see that that, that's going to come out right for the first column?" + }, + { + "text": "Because we remember how, how we're going back to that original punchline, that if I want a number to multiply x1, then I can do it by putting x1 in that column, in the first column, and putting that number there." + }, + { + "text": "What am I going to have here?" + }, + { + "text": "I'm going to have lambda one, I'm going to have x1, x2, xn." + }, + { + "text": "These are going to be my columns again." + }, + { + "text": "I'm getting s back again." + }, + { + "text": "I'm getting s back again, but now what's it multiplied by?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk10.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c58a42edbe9567233ca7f57643a0b7d43ae6761f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what are the eigenvalues?" + }, + { + "text": "You can tell me right away what they are." + }, + { + "text": "They're two and two, right." + }, + { + "text": "It's a triangular matrix, so when I do this determinant, shall I do this determinant of A minus lambda I?" + }, + { + "text": "I'll get this two minus lambda, one, zero, two minus lambda, right?" + }, + { + "text": "I take that determinant, so I make those into vertical bars to mean determinant, and what's the determinant?" + }, + { + "text": "Two minus lambda squared." + }, + { + "text": "What are the roots?" + }, + { + "text": "Lambda equal two twice." + }, + { + "text": "So the eigenvalues are lambda equals two and two." + }, + { + "text": "OK, fine." + }, + { + "text": "Now the next step, find the eigenvectors." + }, + { + "text": "So I look for eigenvectors and what do I find for this guy?" + }, + { + "text": "Eigenvectors for this guy, when I subtract two minus the identity, so A minus two I has zeros here, and I'm looking for the null space." + }, + { + "text": "What's, what are the eigenvectors?" + }, + { + "text": "They're the, they're, they're the null space of A minus lambda I." + }, + { + "text": "The null space is only one dimension." + }, + { + "text": "This is a case where I don't have enough eigenvectors." + }, + { + "text": "My algebraic multiplicity is two." + }, + { + "text": "I, I would say when I see, when I count how often the eigenvalue is repeated, that's the algebraic multiplicity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk11.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..779c2cf904d904b761080db2671aac46394ad02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the multiplicity." + }, + { + "text": "How many times is it the root of the polynomial?" + }, + { + "text": "My polynomial is two minus lambda squared." + }, + { + "text": "It's a double root." + }, + { + "text": "So my algebraic multiplicity is two." + }, + { + "text": "But the geometric multiplicity, which looks for vectors, looks for eigenvectors and which means the null space of this thing." + }, + { + "text": "And the only eigenvector is one zero." + }, + { + "text": "That's in the null space." + }, + { + "text": "Zero one is not in the null space." + }, + { + "text": "The null space is only one dimensional." + }, + { + "text": "So there's a matrix, my, this A or the original A, that are not diagonalizable." + }, + { + "text": "I can't, I can't find two independent eigenvectors, there's only one." + }, + { + "text": "OK." + }, + { + "text": "So that's the case that I'm, that's a case that I, I'm not really handling." + }, + { + "text": "For example, when I wrote down up here that the powers went to zero if the eigenvalues were below one, I didn't really handle that case of repeated eigenvalues because my reasoning was based on this formula." + }, + { + "text": "And this formula is based on n independent eigenvectors." + }, + { + "text": "OK." + }, + { + "text": "So just to say that." + }, + { + "text": "There are some matrices that we don't cover through diagonalization, but the great majority we do." + }, + { + "text": "OK. And we're always OK if we have different distinct eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk12.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..77d090704cc298475d94416b7ecb88a2a015a913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. That's the, like, the typical case." + }, + { + "text": "Because for each eigenvalue there's at least one eigenvector, the algebraic multiplicity here is one for every eigenvalue, and the geometric multiplicity is one." + }, + { + "text": "There's one eigenvector and they are independent." + }, + { + "text": "OK. OK. Now let me come back to the important case when we're OK." + }, + { + "text": "The important case when we are diagonalizing." + }, + { + "text": "Let me look at, so let me solve this equation." + }, + { + "text": "The equation will be each, I start with some, start with a given vector u0." + }, + { + "text": "And then my equation is that every step I multiply what I have by a." + }, + { + "text": "That equation ought to be simple to handle." + }, + { + "text": "OK. And I'd like to be able to solve it." + }, + { + "text": "How would I find, if I start with a vector u0, and I multiply by a a hundred times, what have I got?" + }, + { + "text": "Well, I can certainly write down a formula for the answer." + }, + { + "text": "So what, what, so u1 is a u0." + }, + { + "text": "And u2 is, what's u2 then?" + }, + { + "text": "U2 I multiply it, u2 I get from u1 by another, multiplying by a, so I've got a twice." + }, + { + "text": "And my formula is uk, after k steps, I've multiplied by a k times the original u0." + }, + { + "text": "You see what I'm doing?" + }, + { + "text": "The next section is going to solve systems of differential equations." + }, + { + "text": "I'm going to have derivatives." + }, + { + "text": "This, this section is the nice one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk13.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..ba8214d8c636e4757a266d6617801174bc939d80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "It solves difference equations." + }, + { + "text": "I would call that a difference equation." + }, + { + "text": "It's conne- a first order." + }, + { + "text": "I would call that a first order system, because it connects only, it only goes up one level." + }, + { + "text": "And it's a system because these are vectors and that's a matrix." + }, + { + "text": "And the solution is just that." + }, + { + "text": "OK." + }, + { + "text": "But, that's a nice formula." + }, + { + "text": "That's the, like, the most compact formula I could ever get." + }, + { + "text": "U one hundred would be a to the one hundredth u0." + }, + { + "text": "But how would I actually find u one hundred?" + }, + { + "text": "How would I find, how would I discover what u one hundred is?" + }, + { + "text": "Let me, let me show you how." + }, + { + "text": "Here, here's the idea." + }, + { + "text": "If, so, to solve, to really solve, shall I say, to really solve." + }, + { + "text": "To really solve it, I would take this initial vector, u0, and I would write it as a combination of eigenvectors." + }, + { + "text": "To really solve, write, write u0 as a combination, say, certain amount of the first eigenvector plus a certain amount of the second eigenvector plus a certain amount of the last eigenvector." + }, + { + "text": "Now multiply by a." + }, + { + "text": "You want to, you got to see the magic of eigenvectors work." + }, + { + "text": "Multiply by a." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk14.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7843b2bf0cac762d1c12452cf36500ea4ad13370 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a u0 is what?" + }, + { + "text": "So a times that." + }, + { + "text": "A times, so what's, I can separate it out into n separate pieces and that's the whole point." + }, + { + "text": "That each of those pieces is going in its own merry way." + }, + { + "text": "Each of those pieces is an eigenvector, and when I multiply by a, what does this piece become?" + }, + { + "text": "So that's some amount of the first, let's suppose the eigenvectors are normalized to be unit vectors." + }, + { + "text": "So that says what the eigenvector is." + }, + { + "text": "It's, and I need some multiple of it to produce u0." + }, + { + "text": "OK. Now when I multiply by a, what do I get?" + }, + { + "text": "I get c1, which is just a factor, times a x1, but a x1 is lambda one x1." + }, + { + "text": "When I multiply this by a, I get c2 lambda two x2." + }, + { + "text": "And here I get cn lambda n xn." + }, + { + "text": "And suppose I multiply by a to the hundredth power now." + }, + { + "text": "Can we, can we, having done it, multiplied by a, let's multiply by a to the hundredth." + }, + { + "text": "What happens to this first term when I multiply by a to the one hundredth?" + }, + { + "text": "It's got that factor lambda to the hundredth." + }, + { + "text": "That's the key." + }, + { + "text": "That, that's what I mean by going its own merry way." + }, + { + "text": "It, it is pure eigenvector, it's exactly in a direction where multiplication by a just brings in a scalar factor lambda one." + }, + { + "text": "So a hundred times brings in this a hundred times." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk15.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7ee3348735378aa4049d33ec2a197d0ceb0c447c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Hundred times lambda two, hundred times lambda n. Actually, we're, what are we seeing here?" + }, + { + "text": "We're seeing, this same, lambda, capital lambda to the hundredth, as in the, as in the diagonalization, and we're seeing the S matrix, the matrix S of eigenvectors." + }, + { + "text": "That's what this has got to, this has got to amount to, a lambda to the hundredth power times an S times this vector C that's telling us how much of each one is in the original thing." + }, + { + "text": "So if, if I had to really find the hundredth power, I would take u0, I would expand it as a combination of eigenvectors, this is really S, the eigenvector matrix times C, the, the coefficient vector." + }, + { + "text": "And then I would immediately, then, by inserting these hundredth powers of eigenvalues, I'd have the answer." + }, + { + "text": "So the, the, huh, there must be, well, let's see." + }, + { + "text": "OK." + }, + { + "text": "It's, so, yeah." + }, + { + "text": "So if u100 is a to the hundredth times u0, and u0 is Sc, then you see this formula is just this formula, which is the way I would actually get hold of this, of this u100, which is, let me put it here, u100." + }, + { + "text": "The way I would actually get hold of that, see what, what the solution is after a hundred steps, would be expand the initial vector into eigenvectors and, and let each eigenvector go its own way, multiplying by a hundred at, by lambda at every step, and therefore by lambda to the hundredth power after a hundredth step." + }, + { + "text": "Can I do an example?" + }, + { + "text": "So that's, that's the, the formulas." + }, + { + "text": "Now let me take an example." + }, + { + "text": "I'll use the Fibonacci sequence as an example." + }, + { + "text": "So, so Fibonacci example." + }, + { + "text": "You remember the Fibonacci numbers?" + }, + { + "text": "If we start with one and one as F0, oh, I think I start with zero, maybe." + }, + { + "text": "Let zero and one be the first ones." + }, + { + "text": "So there's F0 and F1, the first two Fibonacci numbers." + }, + { + "text": "Then what's the rule for Fibonacci numbers?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk16.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..79c65e32781f7f304b504a6c390247abb9d26ac8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "They're the sum." + }, + { + "text": "The next one is the sum of those, so it's one." + }, + { + "text": "The next one is the sum of those, so it's two." + }, + { + "text": "The next one is the sum of those, so it's three." + }, + { + "text": "Well, it looks like one, two, three, four, five, but somehow it's not going to do that way." + }, + { + "text": "The next one is five, right." + }, + { + "text": "Two and three makes five." + }, + { + "text": "The next one is eight." + }, + { + "text": "The next one is thirteen." + }, + { + "text": "And the one hundredth Fibonacci number is what?" + }, + { + "text": "That's my question." + }, + { + "text": "How could I get a formula for the hundredth number and for example how could I answer the question how fast are they growing?" + }, + { + "text": "How fast are those Fibonacci numbers growing?" + }, + { + "text": "They're certainly growing." + }, + { + "text": "It's not a stable case, whatever the eigenvalues of whatever matrix it is, they're not smaller than one." + }, + { + "text": "These numbers are growing." + }, + { + "text": "But how fast are they growing?" + }, + { + "text": "The answer is lies in the eigenvalue." + }, + { + "text": "So I've got to find the matrix, so let me write down the Fibonacci rule, F k plus two is F k plus one plus F k, right?" + }, + { + "text": "Now that's not in my -- I want to write that as U k plus one and A U k. But right now what I've got is a single equation, not a system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk17.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b3aaa9dcee3cf27c112015659bb5a0b51a983ce1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's second order." + }, + { + "text": "It's like having a second order differential equation with second derivatives." + }, + { + "text": "I want to get first derivatives." + }, + { + "text": "Here I want to get first difference." + }, + { + "text": "So the way to do it is to introduce U k will be a vector." + }, + { + "text": "See, a small trick." + }, + { + "text": "Let U k be a vector, F k plus one and F k. So I'm going to get a two by two system, first order, instead of a one, instead of a scalar system, second order, by a simple trick." + }, + { + "text": "I'm just going to add in an equation F k plus one equals F k plus one." + }, + { + "text": "That will be my second equation." + }, + { + "text": "Then this is my system, this is my unknown, and what's my one-step equation?" + }, + { + "text": "So now U k plus one." + }, + { + "text": "That's so U k plus one is the left side, and what have I got here on the right side?" + }, + { + "text": "I've got some matrix multiplying U k. Can you see that all right?" + }, + { + "text": "If you can see it, then you can tell me what the matrix is." + }, + { + "text": "You see that I'm taking my system here, I artificially made it into a system." + }, + { + "text": "I artificially made the unknown into a vector, and now I'm ready to look at and see what the matrix is." + }, + { + "text": "So do you see the left side, U k plus one is F k plus two F k plus one, that's just what I want." + }, + { + "text": "On the right side, this, remember, this U k here, let me for the moment put it as F k plus one F k. So what's the matrix?" + }, + { + "text": "Well, that has a one and a one, and that has a one and a zero." + }, + { + "text": "There's the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk18.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..6c1b68c2cb2fde3f5dea82f3100d4da31fcce70a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "You see that that gives me the right-hand side." + }, + { + "text": "So there's the matrix A, and this is our friend U k. So we've got, so that simple trick changed the second order scalar problem to a first order system, two, with two unknowns." + }, + { + "text": "With a matrix and now what do I do?" + }, + { + "text": "Well, before I even think, I find its eigenvalues and eigenvectors." + }, + { + "text": "So what are the eigenvalues and eigenvectors of that matrix?" + }, + { + "text": "Let's see." + }, + { + "text": "I was, first let me just, like, think for a minute." + }, + { + "text": "It's two by two, so this shouldn't be impossible to do." + }, + { + "text": "Let's do it." + }, + { + "text": "OK." + }, + { + "text": "So my matrix again is one one one zero." + }, + { + "text": "It's symmetric, by the way." + }, + { + "text": "So what I will eventually know about symmetric matrices is that the eigenvalues will come out real, I won't get any complex numbers here, and the eigenvectors, once I get those, actually will be orthogonal." + }, + { + "text": "But two by two, I'm more interested in what the actual numbers are." + }, + { + "text": "What do I know about the two numbers?" + }, + { + "text": "Well, should, do you want me to find this determinant of A minus lambda I?" + }, + { + "text": "Sure." + }, + { + "text": "So it's the determinant of one minus lambda one one zero, right?" + }, + { + "text": "Minus lambda, yes, got it." + }, + { + "text": "OK. OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk19.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..a73b23e3d56b889ff49ea7f55a784fac33e13c3d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "There'll be two eigenvalues." + }, + { + "text": "Well, tell me again what I know about the two eigenvalues before I go any further." + }, + { + "text": "Tell me something about these two eigenvalues, what do they add up to?" + }, + { + "text": "Lambda one plus lambda two is the same as the trace down the diagonal of the matrix, one and zero is one." + }, + { + "text": "So lambda one plus lambda two should come out to be one, and lambda one times lambda two should come out to be the determinant, which is minus one." + }, + { + "text": "So I'm expecting the eigenvalues to add to one and to multiply to minus one." + }, + { + "text": "But let's just see it happen here." + }, + { + "text": "If I multiply this out, I get that times that'll be a lambda squared minus lambda minus one." + }, + { + "text": "Good." + }, + { + "text": "Lambda squared minus lambda minus one." + }, + { + "text": "Actually, you see the, compare that with the original equation that I started with." + }, + { + "text": "Fk plus two minus Fk plus one minus Fk is zero." + }, + { + "text": "The recurrent, the recursion that the Fibonacci number satisfy is somehow showing up directly here for the eigenvalues when we set that to zero." + }, + { + "text": "OK. Let's solve." + }, + { + "text": "Well, I would like to be able to factor that, that quadratic, but I'm better off to use the quadratic formula." + }, + { + "text": "Lambda is, let's see, minus b is one, plus or minus the square root of b squared, which is one, minus four, times that, times that, which is plus four, over two." + }, + { + "text": "So that's the square root of five." + }, + { + "text": "So the eigenvalues are lambda one is one half of one plus square root of five, and lambda two is one half of one minus square root of five." + }, + { + "text": "And sure enough, they, those add up to one, and they multiply to give minus one." + }, + { + "text": "OK. Those are the two eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk2.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..43cfb012fc04a89fc7dab94c23bfb0f50ade3782 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "On the right, it's multiplied by, if I want, if I want lambda n xn in the last column, how do I do it?" + }, + { + "text": "Well, the last column here will be, I'll, I'll take the last column, use these coefficients, put the lambda n down there, and it will multiply that nth column and give me lambda n xn." + }, + { + "text": "There, there you see matrix multiplication just working for us." + }, + { + "text": "So I started with A s. I wrote down what it meant." + }, + { + "text": "A times each eigenvector." + }, + { + "text": "That gave me lambda times the eigenvector." + }, + { + "text": "And then when I peeled off the lambdas, they were on the right-hand side, so I've got s, my matrix back again, and this matrix, this diagonal matrix, the eigenvalue matrix, and I call it capital lambda, using capital letters for matrices, and lambda to prompt me that it's, that it's eigenvalues that are in there." + }, + { + "text": "So you see that the eigenvalues are just sitting down that diagonal?" + }, + { + "text": "If I had a column x2 here, I would want the lambda two in the two two position, in the diagonal position, to multiply that x2 and give me the lambda two x2." + }, + { + "text": "That's my formula." + }, + { + "text": "A s is s lambda." + }, + { + "text": "OK. That's, that's the, you see, it's just a calculation." + }, + { + "text": "Now, I, I mentioned, and I have to mention again, this business about n independent eigenvectors." + }, + { + "text": "As it stands, this is all fine whether, I mean, I could be repeating the same eigenvector, but I, I'm no interested in that." + }, + { + "text": "I want to be able to invert s, and that's where this comes in." + }, + { + "text": "This n independent eigenvectors business comes in to tell me that that matrix is invertible." + }, + { + "text": "So let me, on the next board, write down what I've got." + }, + { + "text": "A s equals s lambda." + }, + { + "text": "And now I'm, I can multiply on the left by s inverse." + }, + { + "text": "So this is really, I can do that provided s is invertible, provided my assumption of n independent eigenvectors is satisfied." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk20.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ad5a59fa5db44ce73ff5f88190423e0404fb3d39 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "How, how, what are those numbers approximately?" + }, + { + "text": "Square root of five, well, it's more than two, but less than three." + }, + { + "text": "It, it'd be nice to know these numbers." + }, + { + "text": "I think, I think that that, so that number comes out bigger than one, right?" + }, + { + "text": "Yeah, that's right." + }, + { + "text": "This number comes out bigger than one." + }, + { + "text": "It's about one point six one eight or something." + }, + { + "text": "Not exactly." + }, + { + "text": "It's supposed to be one point six." + }, + { + "text": "Just, like, I think so." + }, + { + "text": "Then what's lambda two?" + }, + { + "text": "Is, is lambda two positive or negative?" + }, + { + "text": "Negative, right?" + }, + { + "text": "Because I'm, it's obviously negative, and I knew that the, so it's minus, and they add up to one, so minus point six one eight, I guess." + }, + { + "text": "OK. And some order." + }, + { + "text": "Those are the two eigenvalues." + }, + { + "text": "One eigenvalue bigger than one, one eigenvalue smaller than one." + }, + { + "text": "Actually, that's a great situation to be in." + }, + { + "text": "Of course, the eigenvalues are different, so there's no doubt whatever, is this matrix diagonalizable?" + }, + { + "text": "Is this matrix diagonalizable, that original matrix A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk21.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..4a034475591d371995b379b5f98783a2cfb25870 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Sure." + }, + { + "text": "We've got two distinct eigenvalues and we can find the eigenvectors in a moment." + }, + { + "text": "But they'll be independent, will be diagonalizable, and now you can already answer my very first question." + }, + { + "text": "How fast are those Fibonacci numbers increasing?" + }, + { + "text": "How, those, they're increasing, right?" + }, + { + "text": "They're not doubling at every step." + }, + { + "text": "Let's look again at these numbers." + }, + { + "text": "Five eight thirteen, it's not obvious." + }, + { + "text": "The next one would be twenty one thirty four." + }, + { + "text": "So to get some idea of what F one hundred is, can you give me any, I mean the crucial number of, so it, these, it's approximately, what's controlling the growth of these Fibonacci numbers?" + }, + { + "text": "It's the eigenvalues." + }, + { + "text": "And which eigenvalues controlling that growth?" + }, + { + "text": "The big ones." + }, + { + "text": "So F one hundred will it be approximately some constant, c one, I guess, times this lambda one, this one plus square root of five over two, to the hundredth power." + }, + { + "text": "And the two hundredth have, in other words, the eigenvalue, the Fibonacci numbers are growing by about that factor." + }, + { + "text": "You see that we've got precise information about the, about the Fibonacci numbers out of the eigenvalue." + }, + { + "text": "OK. And again, why is that true?" + }, + { + "text": "Let me go over to this board and show what I'm doing here." + }, + { + "text": "The, the original eigen, the original initial value is some combination of eigenvectors, and then when we start multiple, when we start going out the theory of Fibonacci numbers, when we start multiplying by a hundred times, it's this lambda one to the hundredth, this term is, is the one that's taken over." + }, + { + "text": "It's, I mean, that's big, like, one point six to the hundredth power." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk22.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..c13a1fc9867173c3067e46c469cfff27b9b45289 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "The second term is practically nothing, right?" + }, + { + "text": "The point six, or minus point six to the hundredth power, is an extremely small, extremely small number." + }, + { + "text": "So this is, this, this, there are only two terms, because we're two by two." + }, + { + "text": "This number is, this piece of it is there, but it's, it's disappearing." + }, + { + "text": "Where this piece is there and it's growing and controlling everything." + }, + { + "text": "So, so really the, we're doing, like, problems that are evolving." + }, + { + "text": "We're doing dynamics." + }, + { + "text": "Instead of Ax equal b, that's a static problem." + }, + { + "text": "We're now, we're doing dynamics." + }, + { + "text": "A, a squared, a cubed, things are evolving in time, and the eigenvalues are the crucial, numbers." + }, + { + "text": "OK." + }, + { + "text": "I guess to complete this, I better write down the eigenvectors." + }, + { + "text": "So we should complete the, the whole process by finding the eigenvectors." + }, + { + "text": "OK. Well, I have to, up in the corner, then I have to look at A minus lambda I." + }, + { + "text": "So A minus lambda I is this one minus lambda, one, one, and minus lambda." + }, + { + "text": "And now, can we spot an eigenvector out of that?" + }, + { + "text": "That's, for these two lambdas, this matrix is singular." + }, + { + "text": "I guess the eigenvector, two by two ought to be easy." + }, + { + "text": "So if I know that this matrix is singular, then it seems to me the eigenvector has to be lambda and one, because that multiplication will give me the zero." + }, + { + "text": "And this multiplication gives me, better give me also zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk23.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..df816eb800ce767b1475c279a24ad976bb45a785 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Do you see why it does?" + }, + { + "text": "This is the minus lambda squared plus lambda plus one." + }, + { + "text": "It's the thing that's zero, because these lambdas are special." + }, + { + "text": "There's the eigenvector." + }, + { + "text": "X1 is lambda one, one, and x2 is lambda two, one." + }, + { + "text": "I did that as a little trick that was available in the two by two case." + }, + { + "text": "So now I finally have to, oh, I have to take the initial, u0." + }, + { + "text": "So to complete this example entirely, I have to say, OK, what was u0?" + }, + { + "text": "u0 was f1 f0." + }, + { + "text": "So u0, the starting vector, is f1 f0, and those were one and zero." + }, + { + "text": "So I have to use that vector, so I have to look for, from multiple of the first eigenvector and the second, to produce u0, the one zero vector." + }, + { + "text": "This is what will find c1 and c2, and then I'm done." + }, + { + "text": "So let me, instead of in the last five seconds grinding out a formula, let me repeat the idea." + }, + { + "text": "That really, it's the idea that's central." + }, + { + "text": "When things are evolving in time, let me come back to this board, because the ideas are here." + }, + { + "text": "When things are evolving in time by a first-order system, starting from an original u0, the key is, find the eigenvalues and eigenvectors of A." + }, + { + "text": "That will tell, those eigenvectors, the eigenvalues will already tell you what's happening." + }, + { + "text": "Is the solution blowing up?" + }, + { + "text": "Is it going to zero?" + }, + { + "text": "What's it doing?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk24.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..40301cb90760e2172baa94d536cbc13288d4c31f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk24.json @@ -0,0 +1,20 @@ +[ + { + "text": "And then, to find out exactly a formula, you have to take your u0 and write it as a combination of eigenvectors and then follow each eigenvector separately." + }, + { + "text": "And that's really what this formula, the formula for, that's what the formula for A to the k is doing." + }, + { + "text": "So remember that formula for A to the k is S, lambda to the k S inverse." + }, + { + "text": "OK. That's, that's difference equations, and you just have to, so the homework will give some examples different from Fibonacci to follow through." + }, + { + "text": "And next time will be differential equations." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk3.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..9bf1bb852baadc1da7837e14180c0c2951a30882 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I mentioned at the end of last time, and I'll say again, that there's a small number of matrices for, that don't have n independent eigenvectors." + }, + { + "text": "So I've got to discuss that, that technical point." + }, + { + "text": "But the great, the most matrices that we see have n, n independent eigenvectors and we can diagonalize." + }, + { + "text": "This is diagonalization." + }, + { + "text": "I could also write it, and I often will, the other way round." + }, + { + "text": "If I multiply on the right by s inverse, if I took this equation at the top and multiplied on the right by s inverse, I could, I would have A left here." + }, + { + "text": "Now s inverse is coming from the right." + }, + { + "text": "So can you keep those two straight?" + }, + { + "text": "A multiplies its eigenvectors." + }, + { + "text": "That's how I keep them straight." + }, + { + "text": "So A multiplies s. A multiplies s. And then this s inverse makes the whole thing diagonal." + }, + { + "text": "And this is another way of saying the same thing, putting the s's on the other side of the equation, A is s lambda s inverse." + }, + { + "text": "So that's the, that's the new factorization." + }, + { + "text": "That's the replacement for L U from elimination or Q R from Gram-Schmidt." + }, + { + "text": "And notice that the matrix, so it's, it's a matrix times a diagonal matrix times the inverse of the first one." + }, + { + "text": "It's, that's the combination that we'll see throughout this chapter." + }, + { + "text": "This, this, combination with an s and an s inverse." + }, + { + "text": "OK. Can I just begin to use that?" + }, + { + "text": "For example, what about A squared?" + }, + { + "text": "What are the eigenvalues and eigenvectors of A squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk4.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c687b6948acad76de8781cb82d3eb069c9da514e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's a straightforward question with a, with a absolutely clean answer." + }, + { + "text": "So let me, let me consider A squared." + }, + { + "text": "So I look, I start with Ax equal lambda x." + }, + { + "text": "And I'm headed for A squared." + }, + { + "text": "So let me multiply both sides by A." + }, + { + "text": "That's one way to get A squared on the left." + }, + { + "text": "So if, I should write these ifs in here." + }, + { + "text": "If Ax equals lambda x, then I multiply by A." + }, + { + "text": "So I get A squared x equals, well, I'm multiplying by A, so that's lambda Ax." + }, + { + "text": "That lambda was a number, so I just put it on the left." + }, + { + "text": "And what do I, tell me how to make that look better." + }, + { + "text": "What have I got here?" + }, + { + "text": "For, if, if A has the eigenvalue lambda and eigenvector x, what's up with A squared?" + }, + { + "text": "A squared x, I just multiply by A, but now for Ax, I'm going to substitute lambda x, so I've got lambda squared x." + }, + { + "text": "So from that simple calculation, I, my conclusion is that the eigenvalues of A squared are lambda squared." + }, + { + "text": "And the eigenvectors, I always think about both of those." + }, + { + "text": "What can I say about the eigenvalues?" + }, + { + "text": "They're squared." + }, + { + "text": "What can I say about the eigenvectors?" + }, + { + "text": "They're the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk5.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5bf15e20707c156c8ae71c9c7acea41a9d9d8e46 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same x as in, as for A." + }, + { + "text": "Now, let me see that also from this formula." + }, + { + "text": "How can I see what A squared is looking like from this formula?" + }, + { + "text": "So let me, that, that was one way to do it." + }, + { + "text": "Let me do it by just taking A squared from that." + }, + { + "text": "A squared is S lambda S inverse, that's A, times S lambda S inverse, that's A, which is?" + }, + { + "text": "This is the beauty of eigenvalues, eigenvectors, having that S inverse and S is the identity, so I've got S lambda squared S inverse." + }, + { + "text": "Yes." + }, + { + "text": "You see what that's telling me?" + }, + { + "text": "It's, it's telling me the same thing that I just learned here, but in the, in, in a matrix form." + }, + { + "text": "It's telling me that the S is the same, the eigenvectors are the same, but the eigenvalues are squared, because this is, what's lambda squared, that's still diagonal, it's got little lambda one squared, lambda two squared, down to lambda n squared, on that diagonal, those are the eigenvalues, as we just learned, of A squared." + }, + { + "text": "OK." + }, + { + "text": "So, somehow those eigenvalues and eigenvectors are really giving you a way to, to, to, to see what's going on inside a matrix." + }, + { + "text": "Now, of course, I can continue that for, to the k-th power." + }, + { + "text": "A to the k-th power." + }, + { + "text": "If I multiply, if I have k of these together, do you see how S inverse S will keep cancelling?" + }, + { + "text": "In the, in the inside, I'll have the S outside, at the far left, and lambda will be in there k times and S inverse." + }, + { + "text": "So what's that telling me?" + }, + { + "text": "That's telling me that the eigenvalues of A, of A to the k-th power are the k-th powers." + }, + { + "text": "The eigenvalues of A cubed are the cubes of the eigenvalues of A, and the eigenvectors are the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk6.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..c18dddbe798022f7e68278ac002a3f5fe6ed249e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same." + }, + { + "text": "OK." + }, + { + "text": "In other words, eigenvalues and eigenvectors give a great way to understand the powers of a matrix." + }, + { + "text": "If I take the square of a matrix or the hundredth power of a matrix, the pivots are all over the place." + }, + { + "text": "L U, if I multiply L U times L U times L U times L U a hundred times, I've got a hundred L U's." + }, + { + "text": "I can't do anything with them." + }, + { + "text": "But when I multiply S lambda S inverse by itself, when I look at the eigenvector picture a hundred times, I get a hundred or ninety-nine of these guys cancelling out inside, and I get A to the hundredth is S lambda to the hundredth S inverse." + }, + { + "text": "I mean, eigenvalues tell you about powers of a matrix in a way that we had no, no way to approach previously." + }, + { + "text": "For example, when does, when do the powers of a matrix go to zero?" + }, + { + "text": "I would call that matrix stable, maybe." + }, + { + "text": "So, so, so I could write down a, a theorem." + }, + { + "text": "I'll, I'll write it as a theorem, just to use that word to emphasize that here I'm getting this great fact from this eigenvalue picture." + }, + { + "text": "OK. A to the k approaches zero as k goes, as k gets bigger." + }, + { + "text": "If what?" + }, + { + "text": "What's the, how can I tell for a matrix A if its powers go to zero?" + }, + { + "text": "What, what's somewhere inside that matrix is that information." + }, + { + "text": "That information is not present in the pivots." + }, + { + "text": "It's present in the eigenvalues." + }, + { + "text": "What do I need for the, to know that if I take higher and higher powers of A that this matrix gets smaller and smaller?" + }, + { + "text": "Well, S and S inverse are not moving." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk7.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b84a5c854a5542758e8a0107e1ff043205fe3bdb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's this guy that has to get small, and that's easy to, easy to understand." + }, + { + "text": "The requirement is all eigenvalues, so what is the requirement?" + }, + { + "text": "The eigenvalues have to be less than one." + }, + { + "text": "Now, I have to write that absolute value, because those eigenvalues could be negative, they could be complex numbers." + }, + { + "text": "So I'm taking the absolute value if all of those are below one." + }, + { + "text": "That's, in fact, we practically see why." + }, + { + "text": "Let me just say that I, that I, I'm operating on one assumption here, and I got to keep remembering that that assumption is still present." + }, + { + "text": "That assumption was that I had a full set of, of n independent eigenvectors." + }, + { + "text": "If I don't have that, then I, I, then this approach is not working." + }, + { + "text": "So, so again, a pure eigenvalue approach, eigenvector approach, needs n independent eigenvectors." + }, + { + "text": "If we don't have n independent eigenvectors, we can't diagonalize the matrix." + }, + { + "text": "We can't get to a diagonal matrix." + }, + { + "text": "This, this, this diagonalization is only possible if S inverse makes sense." + }, + { + "text": "OK. Can I, can I follow up on that point now?" + }, + { + "text": "So, so you see why, what we get and, and why we want it, because we get information about the powers of a matrix just immediately from the eigenvalues." + }, + { + "text": "OK, now let me follow up on this, business of which matrices are diagonalizable." + }, + { + "text": "Sorry about that long word." + }, + { + "text": "So a matrix is, is sure to, so here's, here's the main point." + }, + { + "text": "A is sure to be, to have n independent eigenvectors and, and B, now here comes that word, diagonalizable, if, if, so we, we, we might as well get the, the nice case out in the open." + }, + { + "text": "The nice case is when, if all the lambdas are different." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk8.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f06dcec8ffa0ee1bf19440e4ab2194db33ab353b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means, that means no repeated eigenvalues." + }, + { + "text": "OK. That's the nice case." + }, + { + "text": "If, if my matrix and most matrix, if I do a random matrix in MATLAB and compute its eigenvalues, so if I computed, if I took I of rand of ten ten, gave, gave that MATLAB command, the, we'd get a random ten by ten matrix, we would get a list of its ten eigenvalues and they would be different." + }, + { + "text": "They would be distinct, is the best word." + }, + { + "text": "I would have a random matrix will have ten distinct, a ten by ten matrix will have ten distinct eigenvalues, and if it does, the eigenvectors are automatically independent." + }, + { + "text": "So that's a nice fact." + }, + { + "text": "I can, I'll refer you to the text for the proof." + }, + { + "text": "That, that A is sure to have n independent eigenvectors if the eigenvalues are different." + }, + { + "text": "If, if all the, if all eigenvalues are different." + }, + { + "text": "It's just, if some lambdas are repeated, then I have to look more closely." + }, + { + "text": "If an eigenvalue is repeated, I have to look, I have to count, I have to check." + }, + { + "text": "Has it got, say it's repeated three times." + }, + { + "text": "So what's a possibility for, so, so here's, here's the repeated possibility." + }, + { + "text": "And, and let me emphasize the conclusion." + }, + { + "text": "That if I have repeated eigenvalues, I may or may not, I may or may not have, have n independent eigenvectors." + }, + { + "text": "I might." + }, + { + "text": "I, I, you know, this isn't a completely negative case." + }, + { + "text": "The identity matrix." + }, + { + "text": "Well, suppose I take the ten by ten identity matrix." + }, + { + "text": "What are the eigenvalues of that matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk9.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..87d2a2ae5773036cf11800e2f1962908986a0dad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_5_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So just, just take the easiest matrix, the identity." + }, + { + "text": "If I look for its eigenvalues, they're all ones." + }, + { + "text": "So that eigenvalue one is repeated ten times." + }, + { + "text": "But there's no shortage of eigenvectors for the identity matrix." + }, + { + "text": "In fact, every vector is an eigenvector." + }, + { + "text": "So I can take ten independent vectors." + }, + { + "text": "Oh, well, what happens to everything if, if, if A is the identity matrix, let's just think that one through in our head." + }, + { + "text": "If A is the identity matrix, then it's got plenty of eigenvectors." + }, + { + "text": "I choose ten independent vectors, they're the columns of S, and, and what do I get from S inverse A S?" + }, + { + "text": "I get I again, right?" + }, + { + "text": "If A is the identity, and of course, that's the correct lambda." + }, + { + "text": "The, the matrix was already diagonal." + }, + { + "text": "So if the matrix is already diagonal, then the, the lambda is the same as the matrix." + }, + { + "text": "A diagonal matrix has got its eigenvalues sitting right there in front of you." + }, + { + "text": "Now if it's triangular, the eigenvalues are still sitting there, but so let's, let's take a case where, it's triangular." + }, + { + "text": "Suppose A is like, two, one, two, zero." + }, + { + "text": "So there's a case that's going to be trouble." + }, + { + "text": "There's a case that's going to be trouble." + }, + { + "text": "First of all, what are the eigen- I mean, we just, like now you, if we start with a matrix, the first thing we do practically without thinking is compute the eigenvalues and eigenvectors." + }, + { + "text": "OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk0.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6898d4fe66019ef6b40d0472ea94a968e7bbde9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, shall we start?" + }, + { + "text": "This is the second lecture on eigenvalues." + }, + { + "text": "So the first lecture was set -- reached the key equation, Ax equal lambda x. x is the eigenvector and lambda is the eigenvalue." + }, + { + "text": "Now, to use that." + }, + { + "text": "And the good way to, after we've found, so job one is to find the eigenvalues and find the eigenvectors." + }, + { + "text": "Now after we found them, what do we do with them?" + }, + { + "text": "Well, the good way to see that is diagonalize the matrix." + }, + { + "text": "So the matrix is A, and I want to show, first of all, this is like the basic fact." + }, + { + "text": "This, this formula." + }, + { + "text": "That's, that's the key to today's lecture." + }, + { + "text": "This matrix A, I put its eigenvectors in the columns of a matrix S. So S will be the eigenvector matrix, and I want to look at this magic combination S inverse A S. So can I show you how that, how that, what happens there?" + }, + { + "text": "And notice, notice, there's an S inverse." + }, + { + "text": "We have to be able to invert this eigenvector matrix S. So for that we need n independent eigenvectors." + }, + { + "text": "So that's the, that's the case." + }, + { + "text": "OK." + }, + { + "text": "So suppose we have n linearly independent eigenvectors of A." + }, + { + "text": "Put them in the columns of this matrix S. So I'm naturally going to call that the eigenvector matrix, because it's got the eigenvectors in its columns." + }, + { + "text": "And all I want to do is show you what happens when you multiply A times S. So A times S. So this is A times the matrix with the first eigenvector in its first column, the second eigenvector in its second column, the nth eigenvector in its nth column." + }, + { + "text": "And how am I going to do this matrix multiplication?" + }, + { + "text": "Well, certainly I'll do it a column at a time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk1.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..fbe078217bb68baea8e0605a5d04be568c49efbf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I get?" + }, + { + "text": "A times the first column gives me the first column of the answer, but what is it?" + }, + { + "text": "That's an eigenvector." + }, + { + "text": "A times x1 is equal to the lambda times the x1." + }, + { + "text": "And that lambda's we'll call lambda one, of course." + }, + { + "text": "So that's the first column, A x1 is the same as lambda one x1." + }, + { + "text": "A x2 is lambda two x2, so on, along to, in the nth column, we now have lambda n xn." + }, + { + "text": "Looking good, but the next step is even better." + }, + { + "text": "So for the next step, I want to separate out those eigenvalues, those multiplying numbers, from the x's." + }, + { + "text": "So then I'll have just what I want." + }, + { + "text": "OK, so how, how am I going to separate out?" + }, + { + "text": "So that, that number lambda one is multiplying the first column." + }, + { + "text": "So if I want to factor it out of the first column, I better put, here is going to be x1, and that's going to multiply this matrix lambda one in the first entry in all zeros." + }, + { + "text": "You see that that, that's going to come out right for the first column?" + }, + { + "text": "Because we remember how, how we're going back to that original punchline, that if I want a number to multiply x1, then I can do it by putting x1 in that column, in the first column, and putting that number there." + }, + { + "text": "What am I going to have here?" + }, + { + "text": "I'm going to have lambda one, I'm going to have x1, x2, xn." + }, + { + "text": "These are going to be my columns again." + }, + { + "text": "I'm getting s back again." + }, + { + "text": "I'm getting s back again, but now what's it multiplied by?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk10.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c58a42edbe9567233ca7f57643a0b7d43ae6761f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what are the eigenvalues?" + }, + { + "text": "You can tell me right away what they are." + }, + { + "text": "They're two and two, right." + }, + { + "text": "It's a triangular matrix, so when I do this determinant, shall I do this determinant of A minus lambda I?" + }, + { + "text": "I'll get this two minus lambda, one, zero, two minus lambda, right?" + }, + { + "text": "I take that determinant, so I make those into vertical bars to mean determinant, and what's the determinant?" + }, + { + "text": "Two minus lambda squared." + }, + { + "text": "What are the roots?" + }, + { + "text": "Lambda equal two twice." + }, + { + "text": "So the eigenvalues are lambda equals two and two." + }, + { + "text": "OK, fine." + }, + { + "text": "Now the next step, find the eigenvectors." + }, + { + "text": "So I look for eigenvectors and what do I find for this guy?" + }, + { + "text": "Eigenvectors for this guy, when I subtract two minus the identity, so A minus two I has zeros here, and I'm looking for the null space." + }, + { + "text": "What's, what are the eigenvectors?" + }, + { + "text": "They're the, they're, they're the null space of A minus lambda I." + }, + { + "text": "The null space is only one dimension." + }, + { + "text": "This is a case where I don't have enough eigenvectors." + }, + { + "text": "My algebraic multiplicity is two." + }, + { + "text": "I, I would say when I see, when I count how often the eigenvalue is repeated, that's the algebraic multiplicity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk11.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..779c2cf904d904b761080db2671aac46394ad02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the multiplicity." + }, + { + "text": "How many times is it the root of the polynomial?" + }, + { + "text": "My polynomial is two minus lambda squared." + }, + { + "text": "It's a double root." + }, + { + "text": "So my algebraic multiplicity is two." + }, + { + "text": "But the geometric multiplicity, which looks for vectors, looks for eigenvectors and which means the null space of this thing." + }, + { + "text": "And the only eigenvector is one zero." + }, + { + "text": "That's in the null space." + }, + { + "text": "Zero one is not in the null space." + }, + { + "text": "The null space is only one dimensional." + }, + { + "text": "So there's a matrix, my, this A or the original A, that are not diagonalizable." + }, + { + "text": "I can't, I can't find two independent eigenvectors, there's only one." + }, + { + "text": "OK." + }, + { + "text": "So that's the case that I'm, that's a case that I, I'm not really handling." + }, + { + "text": "For example, when I wrote down up here that the powers went to zero if the eigenvalues were below one, I didn't really handle that case of repeated eigenvalues because my reasoning was based on this formula." + }, + { + "text": "And this formula is based on n independent eigenvectors." + }, + { + "text": "OK." + }, + { + "text": "So just to say that." + }, + { + "text": "There are some matrices that we don't cover through diagonalization, but the great majority we do." + }, + { + "text": "OK. And we're always OK if we have different distinct eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk12.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..77d090704cc298475d94416b7ecb88a2a015a913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. That's the, like, the typical case." + }, + { + "text": "Because for each eigenvalue there's at least one eigenvector, the algebraic multiplicity here is one for every eigenvalue, and the geometric multiplicity is one." + }, + { + "text": "There's one eigenvector and they are independent." + }, + { + "text": "OK. OK. Now let me come back to the important case when we're OK." + }, + { + "text": "The important case when we are diagonalizing." + }, + { + "text": "Let me look at, so let me solve this equation." + }, + { + "text": "The equation will be each, I start with some, start with a given vector u0." + }, + { + "text": "And then my equation is that every step I multiply what I have by a." + }, + { + "text": "That equation ought to be simple to handle." + }, + { + "text": "OK. And I'd like to be able to solve it." + }, + { + "text": "How would I find, if I start with a vector u0, and I multiply by a a hundred times, what have I got?" + }, + { + "text": "Well, I can certainly write down a formula for the answer." + }, + { + "text": "So what, what, so u1 is a u0." + }, + { + "text": "And u2 is, what's u2 then?" + }, + { + "text": "U2 I multiply it, u2 I get from u1 by another, multiplying by a, so I've got a twice." + }, + { + "text": "And my formula is uk, after k steps, I've multiplied by a k times the original u0." + }, + { + "text": "You see what I'm doing?" + }, + { + "text": "The next section is going to solve systems of differential equations." + }, + { + "text": "I'm going to have derivatives." + }, + { + "text": "This, this section is the nice one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk13.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..ba8214d8c636e4757a266d6617801174bc939d80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "It solves difference equations." + }, + { + "text": "I would call that a difference equation." + }, + { + "text": "It's conne- a first order." + }, + { + "text": "I would call that a first order system, because it connects only, it only goes up one level." + }, + { + "text": "And it's a system because these are vectors and that's a matrix." + }, + { + "text": "And the solution is just that." + }, + { + "text": "OK." + }, + { + "text": "But, that's a nice formula." + }, + { + "text": "That's the, like, the most compact formula I could ever get." + }, + { + "text": "U one hundred would be a to the one hundredth u0." + }, + { + "text": "But how would I actually find u one hundred?" + }, + { + "text": "How would I find, how would I discover what u one hundred is?" + }, + { + "text": "Let me, let me show you how." + }, + { + "text": "Here, here's the idea." + }, + { + "text": "If, so, to solve, to really solve, shall I say, to really solve." + }, + { + "text": "To really solve it, I would take this initial vector, u0, and I would write it as a combination of eigenvectors." + }, + { + "text": "To really solve, write, write u0 as a combination, say, certain amount of the first eigenvector plus a certain amount of the second eigenvector plus a certain amount of the last eigenvector." + }, + { + "text": "Now multiply by a." + }, + { + "text": "You want to, you got to see the magic of eigenvectors work." + }, + { + "text": "Multiply by a." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk14.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7843b2bf0cac762d1c12452cf36500ea4ad13370 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a u0 is what?" + }, + { + "text": "So a times that." + }, + { + "text": "A times, so what's, I can separate it out into n separate pieces and that's the whole point." + }, + { + "text": "That each of those pieces is going in its own merry way." + }, + { + "text": "Each of those pieces is an eigenvector, and when I multiply by a, what does this piece become?" + }, + { + "text": "So that's some amount of the first, let's suppose the eigenvectors are normalized to be unit vectors." + }, + { + "text": "So that says what the eigenvector is." + }, + { + "text": "It's, and I need some multiple of it to produce u0." + }, + { + "text": "OK. Now when I multiply by a, what do I get?" + }, + { + "text": "I get c1, which is just a factor, times a x1, but a x1 is lambda one x1." + }, + { + "text": "When I multiply this by a, I get c2 lambda two x2." + }, + { + "text": "And here I get cn lambda n xn." + }, + { + "text": "And suppose I multiply by a to the hundredth power now." + }, + { + "text": "Can we, can we, having done it, multiplied by a, let's multiply by a to the hundredth." + }, + { + "text": "What happens to this first term when I multiply by a to the one hundredth?" + }, + { + "text": "It's got that factor lambda to the hundredth." + }, + { + "text": "That's the key." + }, + { + "text": "That, that's what I mean by going its own merry way." + }, + { + "text": "It, it is pure eigenvector, it's exactly in a direction where multiplication by a just brings in a scalar factor lambda one." + }, + { + "text": "So a hundred times brings in this a hundred times." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk15.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7ee3348735378aa4049d33ec2a197d0ceb0c447c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Hundred times lambda two, hundred times lambda n. Actually, we're, what are we seeing here?" + }, + { + "text": "We're seeing, this same, lambda, capital lambda to the hundredth, as in the, as in the diagonalization, and we're seeing the S matrix, the matrix S of eigenvectors." + }, + { + "text": "That's what this has got to, this has got to amount to, a lambda to the hundredth power times an S times this vector C that's telling us how much of each one is in the original thing." + }, + { + "text": "So if, if I had to really find the hundredth power, I would take u0, I would expand it as a combination of eigenvectors, this is really S, the eigenvector matrix times C, the, the coefficient vector." + }, + { + "text": "And then I would immediately, then, by inserting these hundredth powers of eigenvalues, I'd have the answer." + }, + { + "text": "So the, the, huh, there must be, well, let's see." + }, + { + "text": "OK." + }, + { + "text": "It's, so, yeah." + }, + { + "text": "So if u100 is a to the hundredth times u0, and u0 is Sc, then you see this formula is just this formula, which is the way I would actually get hold of this, of this u100, which is, let me put it here, u100." + }, + { + "text": "The way I would actually get hold of that, see what, what the solution is after a hundred steps, would be expand the initial vector into eigenvectors and, and let each eigenvector go its own way, multiplying by a hundred at, by lambda at every step, and therefore by lambda to the hundredth power after a hundredth step." + }, + { + "text": "Can I do an example?" + }, + { + "text": "So that's, that's the, the formulas." + }, + { + "text": "Now let me take an example." + }, + { + "text": "I'll use the Fibonacci sequence as an example." + }, + { + "text": "So, so Fibonacci example." + }, + { + "text": "You remember the Fibonacci numbers?" + }, + { + "text": "If we start with one and one as F0, oh, I think I start with zero, maybe." + }, + { + "text": "Let zero and one be the first ones." + }, + { + "text": "So there's F0 and F1, the first two Fibonacci numbers." + }, + { + "text": "Then what's the rule for Fibonacci numbers?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk16.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..79c65e32781f7f304b504a6c390247abb9d26ac8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "They're the sum." + }, + { + "text": "The next one is the sum of those, so it's one." + }, + { + "text": "The next one is the sum of those, so it's two." + }, + { + "text": "The next one is the sum of those, so it's three." + }, + { + "text": "Well, it looks like one, two, three, four, five, but somehow it's not going to do that way." + }, + { + "text": "The next one is five, right." + }, + { + "text": "Two and three makes five." + }, + { + "text": "The next one is eight." + }, + { + "text": "The next one is thirteen." + }, + { + "text": "And the one hundredth Fibonacci number is what?" + }, + { + "text": "That's my question." + }, + { + "text": "How could I get a formula for the hundredth number and for example how could I answer the question how fast are they growing?" + }, + { + "text": "How fast are those Fibonacci numbers growing?" + }, + { + "text": "They're certainly growing." + }, + { + "text": "It's not a stable case, whatever the eigenvalues of whatever matrix it is, they're not smaller than one." + }, + { + "text": "These numbers are growing." + }, + { + "text": "But how fast are they growing?" + }, + { + "text": "The answer is lies in the eigenvalue." + }, + { + "text": "So I've got to find the matrix, so let me write down the Fibonacci rule, F k plus two is F k plus one plus F k, right?" + }, + { + "text": "Now that's not in my -- I want to write that as U k plus one and A U k. But right now what I've got is a single equation, not a system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk17.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b3aaa9dcee3cf27c112015659bb5a0b51a983ce1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's second order." + }, + { + "text": "It's like having a second order differential equation with second derivatives." + }, + { + "text": "I want to get first derivatives." + }, + { + "text": "Here I want to get first difference." + }, + { + "text": "So the way to do it is to introduce U k will be a vector." + }, + { + "text": "See, a small trick." + }, + { + "text": "Let U k be a vector, F k plus one and F k. So I'm going to get a two by two system, first order, instead of a one, instead of a scalar system, second order, by a simple trick." + }, + { + "text": "I'm just going to add in an equation F k plus one equals F k plus one." + }, + { + "text": "That will be my second equation." + }, + { + "text": "Then this is my system, this is my unknown, and what's my one-step equation?" + }, + { + "text": "So now U k plus one." + }, + { + "text": "That's so U k plus one is the left side, and what have I got here on the right side?" + }, + { + "text": "I've got some matrix multiplying U k. Can you see that all right?" + }, + { + "text": "If you can see it, then you can tell me what the matrix is." + }, + { + "text": "You see that I'm taking my system here, I artificially made it into a system." + }, + { + "text": "I artificially made the unknown into a vector, and now I'm ready to look at and see what the matrix is." + }, + { + "text": "So do you see the left side, U k plus one is F k plus two F k plus one, that's just what I want." + }, + { + "text": "On the right side, this, remember, this U k here, let me for the moment put it as F k plus one F k. So what's the matrix?" + }, + { + "text": "Well, that has a one and a one, and that has a one and a zero." + }, + { + "text": "There's the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk18.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..6c1b68c2cb2fde3f5dea82f3100d4da31fcce70a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "You see that that gives me the right-hand side." + }, + { + "text": "So there's the matrix A, and this is our friend U k. So we've got, so that simple trick changed the second order scalar problem to a first order system, two, with two unknowns." + }, + { + "text": "With a matrix and now what do I do?" + }, + { + "text": "Well, before I even think, I find its eigenvalues and eigenvectors." + }, + { + "text": "So what are the eigenvalues and eigenvectors of that matrix?" + }, + { + "text": "Let's see." + }, + { + "text": "I was, first let me just, like, think for a minute." + }, + { + "text": "It's two by two, so this shouldn't be impossible to do." + }, + { + "text": "Let's do it." + }, + { + "text": "OK." + }, + { + "text": "So my matrix again is one one one zero." + }, + { + "text": "It's symmetric, by the way." + }, + { + "text": "So what I will eventually know about symmetric matrices is that the eigenvalues will come out real, I won't get any complex numbers here, and the eigenvectors, once I get those, actually will be orthogonal." + }, + { + "text": "But two by two, I'm more interested in what the actual numbers are." + }, + { + "text": "What do I know about the two numbers?" + }, + { + "text": "Well, should, do you want me to find this determinant of A minus lambda I?" + }, + { + "text": "Sure." + }, + { + "text": "So it's the determinant of one minus lambda one one zero, right?" + }, + { + "text": "Minus lambda, yes, got it." + }, + { + "text": "OK. OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk19.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..a73b23e3d56b889ff49ea7f55a784fac33e13c3d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "There'll be two eigenvalues." + }, + { + "text": "Well, tell me again what I know about the two eigenvalues before I go any further." + }, + { + "text": "Tell me something about these two eigenvalues, what do they add up to?" + }, + { + "text": "Lambda one plus lambda two is the same as the trace down the diagonal of the matrix, one and zero is one." + }, + { + "text": "So lambda one plus lambda two should come out to be one, and lambda one times lambda two should come out to be the determinant, which is minus one." + }, + { + "text": "So I'm expecting the eigenvalues to add to one and to multiply to minus one." + }, + { + "text": "But let's just see it happen here." + }, + { + "text": "If I multiply this out, I get that times that'll be a lambda squared minus lambda minus one." + }, + { + "text": "Good." + }, + { + "text": "Lambda squared minus lambda minus one." + }, + { + "text": "Actually, you see the, compare that with the original equation that I started with." + }, + { + "text": "Fk plus two minus Fk plus one minus Fk is zero." + }, + { + "text": "The recurrent, the recursion that the Fibonacci number satisfy is somehow showing up directly here for the eigenvalues when we set that to zero." + }, + { + "text": "OK. Let's solve." + }, + { + "text": "Well, I would like to be able to factor that, that quadratic, but I'm better off to use the quadratic formula." + }, + { + "text": "Lambda is, let's see, minus b is one, plus or minus the square root of b squared, which is one, minus four, times that, times that, which is plus four, over two." + }, + { + "text": "So that's the square root of five." + }, + { + "text": "So the eigenvalues are lambda one is one half of one plus square root of five, and lambda two is one half of one minus square root of five." + }, + { + "text": "And sure enough, they, those add up to one, and they multiply to give minus one." + }, + { + "text": "OK. Those are the two eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk2.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..43cfb012fc04a89fc7dab94c23bfb0f50ade3782 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "On the right, it's multiplied by, if I want, if I want lambda n xn in the last column, how do I do it?" + }, + { + "text": "Well, the last column here will be, I'll, I'll take the last column, use these coefficients, put the lambda n down there, and it will multiply that nth column and give me lambda n xn." + }, + { + "text": "There, there you see matrix multiplication just working for us." + }, + { + "text": "So I started with A s. I wrote down what it meant." + }, + { + "text": "A times each eigenvector." + }, + { + "text": "That gave me lambda times the eigenvector." + }, + { + "text": "And then when I peeled off the lambdas, they were on the right-hand side, so I've got s, my matrix back again, and this matrix, this diagonal matrix, the eigenvalue matrix, and I call it capital lambda, using capital letters for matrices, and lambda to prompt me that it's, that it's eigenvalues that are in there." + }, + { + "text": "So you see that the eigenvalues are just sitting down that diagonal?" + }, + { + "text": "If I had a column x2 here, I would want the lambda two in the two two position, in the diagonal position, to multiply that x2 and give me the lambda two x2." + }, + { + "text": "That's my formula." + }, + { + "text": "A s is s lambda." + }, + { + "text": "OK. That's, that's the, you see, it's just a calculation." + }, + { + "text": "Now, I, I mentioned, and I have to mention again, this business about n independent eigenvectors." + }, + { + "text": "As it stands, this is all fine whether, I mean, I could be repeating the same eigenvector, but I, I'm no interested in that." + }, + { + "text": "I want to be able to invert s, and that's where this comes in." + }, + { + "text": "This n independent eigenvectors business comes in to tell me that that matrix is invertible." + }, + { + "text": "So let me, on the next board, write down what I've got." + }, + { + "text": "A s equals s lambda." + }, + { + "text": "And now I'm, I can multiply on the left by s inverse." + }, + { + "text": "So this is really, I can do that provided s is invertible, provided my assumption of n independent eigenvectors is satisfied." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk20.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ad5a59fa5db44ce73ff5f88190423e0404fb3d39 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "How, how, what are those numbers approximately?" + }, + { + "text": "Square root of five, well, it's more than two, but less than three." + }, + { + "text": "It, it'd be nice to know these numbers." + }, + { + "text": "I think, I think that that, so that number comes out bigger than one, right?" + }, + { + "text": "Yeah, that's right." + }, + { + "text": "This number comes out bigger than one." + }, + { + "text": "It's about one point six one eight or something." + }, + { + "text": "Not exactly." + }, + { + "text": "It's supposed to be one point six." + }, + { + "text": "Just, like, I think so." + }, + { + "text": "Then what's lambda two?" + }, + { + "text": "Is, is lambda two positive or negative?" + }, + { + "text": "Negative, right?" + }, + { + "text": "Because I'm, it's obviously negative, and I knew that the, so it's minus, and they add up to one, so minus point six one eight, I guess." + }, + { + "text": "OK. And some order." + }, + { + "text": "Those are the two eigenvalues." + }, + { + "text": "One eigenvalue bigger than one, one eigenvalue smaller than one." + }, + { + "text": "Actually, that's a great situation to be in." + }, + { + "text": "Of course, the eigenvalues are different, so there's no doubt whatever, is this matrix diagonalizable?" + }, + { + "text": "Is this matrix diagonalizable, that original matrix A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk21.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..4a034475591d371995b379b5f98783a2cfb25870 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Sure." + }, + { + "text": "We've got two distinct eigenvalues and we can find the eigenvectors in a moment." + }, + { + "text": "But they'll be independent, will be diagonalizable, and now you can already answer my very first question." + }, + { + "text": "How fast are those Fibonacci numbers increasing?" + }, + { + "text": "How, those, they're increasing, right?" + }, + { + "text": "They're not doubling at every step." + }, + { + "text": "Let's look again at these numbers." + }, + { + "text": "Five eight thirteen, it's not obvious." + }, + { + "text": "The next one would be twenty one thirty four." + }, + { + "text": "So to get some idea of what F one hundred is, can you give me any, I mean the crucial number of, so it, these, it's approximately, what's controlling the growth of these Fibonacci numbers?" + }, + { + "text": "It's the eigenvalues." + }, + { + "text": "And which eigenvalues controlling that growth?" + }, + { + "text": "The big ones." + }, + { + "text": "So F one hundred will it be approximately some constant, c one, I guess, times this lambda one, this one plus square root of five over two, to the hundredth power." + }, + { + "text": "And the two hundredth have, in other words, the eigenvalue, the Fibonacci numbers are growing by about that factor." + }, + { + "text": "You see that we've got precise information about the, about the Fibonacci numbers out of the eigenvalue." + }, + { + "text": "OK. And again, why is that true?" + }, + { + "text": "Let me go over to this board and show what I'm doing here." + }, + { + "text": "The, the original eigen, the original initial value is some combination of eigenvectors, and then when we start multiple, when we start going out the theory of Fibonacci numbers, when we start multiplying by a hundred times, it's this lambda one to the hundredth, this term is, is the one that's taken over." + }, + { + "text": "It's, I mean, that's big, like, one point six to the hundredth power." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk22.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..c13a1fc9867173c3067e46c469cfff27b9b45289 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "The second term is practically nothing, right?" + }, + { + "text": "The point six, or minus point six to the hundredth power, is an extremely small, extremely small number." + }, + { + "text": "So this is, this, this, there are only two terms, because we're two by two." + }, + { + "text": "This number is, this piece of it is there, but it's, it's disappearing." + }, + { + "text": "Where this piece is there and it's growing and controlling everything." + }, + { + "text": "So, so really the, we're doing, like, problems that are evolving." + }, + { + "text": "We're doing dynamics." + }, + { + "text": "Instead of Ax equal b, that's a static problem." + }, + { + "text": "We're now, we're doing dynamics." + }, + { + "text": "A, a squared, a cubed, things are evolving in time, and the eigenvalues are the crucial, numbers." + }, + { + "text": "OK." + }, + { + "text": "I guess to complete this, I better write down the eigenvectors." + }, + { + "text": "So we should complete the, the whole process by finding the eigenvectors." + }, + { + "text": "OK. Well, I have to, up in the corner, then I have to look at A minus lambda I." + }, + { + "text": "So A minus lambda I is this one minus lambda, one, one, and minus lambda." + }, + { + "text": "And now, can we spot an eigenvector out of that?" + }, + { + "text": "That's, for these two lambdas, this matrix is singular." + }, + { + "text": "I guess the eigenvector, two by two ought to be easy." + }, + { + "text": "So if I know that this matrix is singular, then it seems to me the eigenvector has to be lambda and one, because that multiplication will give me the zero." + }, + { + "text": "And this multiplication gives me, better give me also zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk23.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..df816eb800ce767b1475c279a24ad976bb45a785 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Do you see why it does?" + }, + { + "text": "This is the minus lambda squared plus lambda plus one." + }, + { + "text": "It's the thing that's zero, because these lambdas are special." + }, + { + "text": "There's the eigenvector." + }, + { + "text": "X1 is lambda one, one, and x2 is lambda two, one." + }, + { + "text": "I did that as a little trick that was available in the two by two case." + }, + { + "text": "So now I finally have to, oh, I have to take the initial, u0." + }, + { + "text": "So to complete this example entirely, I have to say, OK, what was u0?" + }, + { + "text": "u0 was f1 f0." + }, + { + "text": "So u0, the starting vector, is f1 f0, and those were one and zero." + }, + { + "text": "So I have to use that vector, so I have to look for, from multiple of the first eigenvector and the second, to produce u0, the one zero vector." + }, + { + "text": "This is what will find c1 and c2, and then I'm done." + }, + { + "text": "So let me, instead of in the last five seconds grinding out a formula, let me repeat the idea." + }, + { + "text": "That really, it's the idea that's central." + }, + { + "text": "When things are evolving in time, let me come back to this board, because the ideas are here." + }, + { + "text": "When things are evolving in time by a first-order system, starting from an original u0, the key is, find the eigenvalues and eigenvectors of A." + }, + { + "text": "That will tell, those eigenvectors, the eigenvalues will already tell you what's happening." + }, + { + "text": "Is the solution blowing up?" + }, + { + "text": "Is it going to zero?" + }, + { + "text": "What's it doing?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk24.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..40301cb90760e2172baa94d536cbc13288d4c31f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk24.json @@ -0,0 +1,20 @@ +[ + { + "text": "And then, to find out exactly a formula, you have to take your u0 and write it as a combination of eigenvectors and then follow each eigenvector separately." + }, + { + "text": "And that's really what this formula, the formula for, that's what the formula for A to the k is doing." + }, + { + "text": "So remember that formula for A to the k is S, lambda to the k S inverse." + }, + { + "text": "OK. That's, that's difference equations, and you just have to, so the homework will give some examples different from Fibonacci to follow through." + }, + { + "text": "And next time will be differential equations." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk3.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..9bf1bb852baadc1da7837e14180c0c2951a30882 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I mentioned at the end of last time, and I'll say again, that there's a small number of matrices for, that don't have n independent eigenvectors." + }, + { + "text": "So I've got to discuss that, that technical point." + }, + { + "text": "But the great, the most matrices that we see have n, n independent eigenvectors and we can diagonalize." + }, + { + "text": "This is diagonalization." + }, + { + "text": "I could also write it, and I often will, the other way round." + }, + { + "text": "If I multiply on the right by s inverse, if I took this equation at the top and multiplied on the right by s inverse, I could, I would have A left here." + }, + { + "text": "Now s inverse is coming from the right." + }, + { + "text": "So can you keep those two straight?" + }, + { + "text": "A multiplies its eigenvectors." + }, + { + "text": "That's how I keep them straight." + }, + { + "text": "So A multiplies s. A multiplies s. And then this s inverse makes the whole thing diagonal." + }, + { + "text": "And this is another way of saying the same thing, putting the s's on the other side of the equation, A is s lambda s inverse." + }, + { + "text": "So that's the, that's the new factorization." + }, + { + "text": "That's the replacement for L U from elimination or Q R from Gram-Schmidt." + }, + { + "text": "And notice that the matrix, so it's, it's a matrix times a diagonal matrix times the inverse of the first one." + }, + { + "text": "It's, that's the combination that we'll see throughout this chapter." + }, + { + "text": "This, this, combination with an s and an s inverse." + }, + { + "text": "OK. Can I just begin to use that?" + }, + { + "text": "For example, what about A squared?" + }, + { + "text": "What are the eigenvalues and eigenvectors of A squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk4.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c687b6948acad76de8781cb82d3eb069c9da514e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's a straightforward question with a, with a absolutely clean answer." + }, + { + "text": "So let me, let me consider A squared." + }, + { + "text": "So I look, I start with Ax equal lambda x." + }, + { + "text": "And I'm headed for A squared." + }, + { + "text": "So let me multiply both sides by A." + }, + { + "text": "That's one way to get A squared on the left." + }, + { + "text": "So if, I should write these ifs in here." + }, + { + "text": "If Ax equals lambda x, then I multiply by A." + }, + { + "text": "So I get A squared x equals, well, I'm multiplying by A, so that's lambda Ax." + }, + { + "text": "That lambda was a number, so I just put it on the left." + }, + { + "text": "And what do I, tell me how to make that look better." + }, + { + "text": "What have I got here?" + }, + { + "text": "For, if, if A has the eigenvalue lambda and eigenvector x, what's up with A squared?" + }, + { + "text": "A squared x, I just multiply by A, but now for Ax, I'm going to substitute lambda x, so I've got lambda squared x." + }, + { + "text": "So from that simple calculation, I, my conclusion is that the eigenvalues of A squared are lambda squared." + }, + { + "text": "And the eigenvectors, I always think about both of those." + }, + { + "text": "What can I say about the eigenvalues?" + }, + { + "text": "They're squared." + }, + { + "text": "What can I say about the eigenvectors?" + }, + { + "text": "They're the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk5.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5bf15e20707c156c8ae71c9c7acea41a9d9d8e46 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same x as in, as for A." + }, + { + "text": "Now, let me see that also from this formula." + }, + { + "text": "How can I see what A squared is looking like from this formula?" + }, + { + "text": "So let me, that, that was one way to do it." + }, + { + "text": "Let me do it by just taking A squared from that." + }, + { + "text": "A squared is S lambda S inverse, that's A, times S lambda S inverse, that's A, which is?" + }, + { + "text": "This is the beauty of eigenvalues, eigenvectors, having that S inverse and S is the identity, so I've got S lambda squared S inverse." + }, + { + "text": "Yes." + }, + { + "text": "You see what that's telling me?" + }, + { + "text": "It's, it's telling me the same thing that I just learned here, but in the, in, in a matrix form." + }, + { + "text": "It's telling me that the S is the same, the eigenvectors are the same, but the eigenvalues are squared, because this is, what's lambda squared, that's still diagonal, it's got little lambda one squared, lambda two squared, down to lambda n squared, on that diagonal, those are the eigenvalues, as we just learned, of A squared." + }, + { + "text": "OK." + }, + { + "text": "So, somehow those eigenvalues and eigenvectors are really giving you a way to, to, to, to see what's going on inside a matrix." + }, + { + "text": "Now, of course, I can continue that for, to the k-th power." + }, + { + "text": "A to the k-th power." + }, + { + "text": "If I multiply, if I have k of these together, do you see how S inverse S will keep cancelling?" + }, + { + "text": "In the, in the inside, I'll have the S outside, at the far left, and lambda will be in there k times and S inverse." + }, + { + "text": "So what's that telling me?" + }, + { + "text": "That's telling me that the eigenvalues of A, of A to the k-th power are the k-th powers." + }, + { + "text": "The eigenvalues of A cubed are the cubes of the eigenvalues of A, and the eigenvectors are the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk6.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..c18dddbe798022f7e68278ac002a3f5fe6ed249e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same." + }, + { + "text": "OK." + }, + { + "text": "In other words, eigenvalues and eigenvectors give a great way to understand the powers of a matrix." + }, + { + "text": "If I take the square of a matrix or the hundredth power of a matrix, the pivots are all over the place." + }, + { + "text": "L U, if I multiply L U times L U times L U times L U a hundred times, I've got a hundred L U's." + }, + { + "text": "I can't do anything with them." + }, + { + "text": "But when I multiply S lambda S inverse by itself, when I look at the eigenvector picture a hundred times, I get a hundred or ninety-nine of these guys cancelling out inside, and I get A to the hundredth is S lambda to the hundredth S inverse." + }, + { + "text": "I mean, eigenvalues tell you about powers of a matrix in a way that we had no, no way to approach previously." + }, + { + "text": "For example, when does, when do the powers of a matrix go to zero?" + }, + { + "text": "I would call that matrix stable, maybe." + }, + { + "text": "So, so, so I could write down a, a theorem." + }, + { + "text": "I'll, I'll write it as a theorem, just to use that word to emphasize that here I'm getting this great fact from this eigenvalue picture." + }, + { + "text": "OK. A to the k approaches zero as k goes, as k gets bigger." + }, + { + "text": "If what?" + }, + { + "text": "What's the, how can I tell for a matrix A if its powers go to zero?" + }, + { + "text": "What, what's somewhere inside that matrix is that information." + }, + { + "text": "That information is not present in the pivots." + }, + { + "text": "It's present in the eigenvalues." + }, + { + "text": "What do I need for the, to know that if I take higher and higher powers of A that this matrix gets smaller and smaller?" + }, + { + "text": "Well, S and S inverse are not moving." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk7.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b84a5c854a5542758e8a0107e1ff043205fe3bdb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's this guy that has to get small, and that's easy to, easy to understand." + }, + { + "text": "The requirement is all eigenvalues, so what is the requirement?" + }, + { + "text": "The eigenvalues have to be less than one." + }, + { + "text": "Now, I have to write that absolute value, because those eigenvalues could be negative, they could be complex numbers." + }, + { + "text": "So I'm taking the absolute value if all of those are below one." + }, + { + "text": "That's, in fact, we practically see why." + }, + { + "text": "Let me just say that I, that I, I'm operating on one assumption here, and I got to keep remembering that that assumption is still present." + }, + { + "text": "That assumption was that I had a full set of, of n independent eigenvectors." + }, + { + "text": "If I don't have that, then I, I, then this approach is not working." + }, + { + "text": "So, so again, a pure eigenvalue approach, eigenvector approach, needs n independent eigenvectors." + }, + { + "text": "If we don't have n independent eigenvectors, we can't diagonalize the matrix." + }, + { + "text": "We can't get to a diagonal matrix." + }, + { + "text": "This, this, this diagonalization is only possible if S inverse makes sense." + }, + { + "text": "OK. Can I, can I follow up on that point now?" + }, + { + "text": "So, so you see why, what we get and, and why we want it, because we get information about the powers of a matrix just immediately from the eigenvalues." + }, + { + "text": "OK, now let me follow up on this, business of which matrices are diagonalizable." + }, + { + "text": "Sorry about that long word." + }, + { + "text": "So a matrix is, is sure to, so here's, here's the main point." + }, + { + "text": "A is sure to be, to have n independent eigenvectors and, and B, now here comes that word, diagonalizable, if, if, so we, we, we might as well get the, the nice case out in the open." + }, + { + "text": "The nice case is when, if all the lambdas are different." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk8.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f06dcec8ffa0ee1bf19440e4ab2194db33ab353b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means, that means no repeated eigenvalues." + }, + { + "text": "OK. That's the nice case." + }, + { + "text": "If, if my matrix and most matrix, if I do a random matrix in MATLAB and compute its eigenvalues, so if I computed, if I took I of rand of ten ten, gave, gave that MATLAB command, the, we'd get a random ten by ten matrix, we would get a list of its ten eigenvalues and they would be different." + }, + { + "text": "They would be distinct, is the best word." + }, + { + "text": "I would have a random matrix will have ten distinct, a ten by ten matrix will have ten distinct eigenvalues, and if it does, the eigenvectors are automatically independent." + }, + { + "text": "So that's a nice fact." + }, + { + "text": "I can, I'll refer you to the text for the proof." + }, + { + "text": "That, that A is sure to have n independent eigenvectors if the eigenvalues are different." + }, + { + "text": "If, if all the, if all eigenvalues are different." + }, + { + "text": "It's just, if some lambdas are repeated, then I have to look more closely." + }, + { + "text": "If an eigenvalue is repeated, I have to look, I have to count, I have to check." + }, + { + "text": "Has it got, say it's repeated three times." + }, + { + "text": "So what's a possibility for, so, so here's, here's the repeated possibility." + }, + { + "text": "And, and let me emphasize the conclusion." + }, + { + "text": "That if I have repeated eigenvalues, I may or may not, I may or may not have, have n independent eigenvectors." + }, + { + "text": "I might." + }, + { + "text": "I, I, you know, this isn't a completely negative case." + }, + { + "text": "The identity matrix." + }, + { + "text": "Well, suppose I take the ten by ten identity matrix." + }, + { + "text": "What are the eigenvalues of that matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk9.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..87d2a2ae5773036cf11800e2f1962908986a0dad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_6_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So just, just take the easiest matrix, the identity." + }, + { + "text": "If I look for its eigenvalues, they're all ones." + }, + { + "text": "So that eigenvalue one is repeated ten times." + }, + { + "text": "But there's no shortage of eigenvectors for the identity matrix." + }, + { + "text": "In fact, every vector is an eigenvector." + }, + { + "text": "So I can take ten independent vectors." + }, + { + "text": "Oh, well, what happens to everything if, if, if A is the identity matrix, let's just think that one through in our head." + }, + { + "text": "If A is the identity matrix, then it's got plenty of eigenvectors." + }, + { + "text": "I choose ten independent vectors, they're the columns of S, and, and what do I get from S inverse A S?" + }, + { + "text": "I get I again, right?" + }, + { + "text": "If A is the identity, and of course, that's the correct lambda." + }, + { + "text": "The, the matrix was already diagonal." + }, + { + "text": "So if the matrix is already diagonal, then the, the lambda is the same as the matrix." + }, + { + "text": "A diagonal matrix has got its eigenvalues sitting right there in front of you." + }, + { + "text": "Now if it's triangular, the eigenvalues are still sitting there, but so let's, let's take a case where, it's triangular." + }, + { + "text": "Suppose A is like, two, one, two, zero." + }, + { + "text": "So there's a case that's going to be trouble." + }, + { + "text": "There's a case that's going to be trouble." + }, + { + "text": "First of all, what are the eigen- I mean, we just, like now you, if we start with a matrix, the first thing we do practically without thinking is compute the eigenvalues and eigenvectors." + }, + { + "text": "OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk0.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6898d4fe66019ef6b40d0472ea94a968e7bbde9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, shall we start?" + }, + { + "text": "This is the second lecture on eigenvalues." + }, + { + "text": "So the first lecture was set -- reached the key equation, Ax equal lambda x. x is the eigenvector and lambda is the eigenvalue." + }, + { + "text": "Now, to use that." + }, + { + "text": "And the good way to, after we've found, so job one is to find the eigenvalues and find the eigenvectors." + }, + { + "text": "Now after we found them, what do we do with them?" + }, + { + "text": "Well, the good way to see that is diagonalize the matrix." + }, + { + "text": "So the matrix is A, and I want to show, first of all, this is like the basic fact." + }, + { + "text": "This, this formula." + }, + { + "text": "That's, that's the key to today's lecture." + }, + { + "text": "This matrix A, I put its eigenvectors in the columns of a matrix S. So S will be the eigenvector matrix, and I want to look at this magic combination S inverse A S. So can I show you how that, how that, what happens there?" + }, + { + "text": "And notice, notice, there's an S inverse." + }, + { + "text": "We have to be able to invert this eigenvector matrix S. So for that we need n independent eigenvectors." + }, + { + "text": "So that's the, that's the case." + }, + { + "text": "OK." + }, + { + "text": "So suppose we have n linearly independent eigenvectors of A." + }, + { + "text": "Put them in the columns of this matrix S. So I'm naturally going to call that the eigenvector matrix, because it's got the eigenvectors in its columns." + }, + { + "text": "And all I want to do is show you what happens when you multiply A times S. So A times S. So this is A times the matrix with the first eigenvector in its first column, the second eigenvector in its second column, the nth eigenvector in its nth column." + }, + { + "text": "And how am I going to do this matrix multiplication?" + }, + { + "text": "Well, certainly I'll do it a column at a time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk1.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..fbe078217bb68baea8e0605a5d04be568c49efbf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I get?" + }, + { + "text": "A times the first column gives me the first column of the answer, but what is it?" + }, + { + "text": "That's an eigenvector." + }, + { + "text": "A times x1 is equal to the lambda times the x1." + }, + { + "text": "And that lambda's we'll call lambda one, of course." + }, + { + "text": "So that's the first column, A x1 is the same as lambda one x1." + }, + { + "text": "A x2 is lambda two x2, so on, along to, in the nth column, we now have lambda n xn." + }, + { + "text": "Looking good, but the next step is even better." + }, + { + "text": "So for the next step, I want to separate out those eigenvalues, those multiplying numbers, from the x's." + }, + { + "text": "So then I'll have just what I want." + }, + { + "text": "OK, so how, how am I going to separate out?" + }, + { + "text": "So that, that number lambda one is multiplying the first column." + }, + { + "text": "So if I want to factor it out of the first column, I better put, here is going to be x1, and that's going to multiply this matrix lambda one in the first entry in all zeros." + }, + { + "text": "You see that that, that's going to come out right for the first column?" + }, + { + "text": "Because we remember how, how we're going back to that original punchline, that if I want a number to multiply x1, then I can do it by putting x1 in that column, in the first column, and putting that number there." + }, + { + "text": "What am I going to have here?" + }, + { + "text": "I'm going to have lambda one, I'm going to have x1, x2, xn." + }, + { + "text": "These are going to be my columns again." + }, + { + "text": "I'm getting s back again." + }, + { + "text": "I'm getting s back again, but now what's it multiplied by?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk10.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c58a42edbe9567233ca7f57643a0b7d43ae6761f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what are the eigenvalues?" + }, + { + "text": "You can tell me right away what they are." + }, + { + "text": "They're two and two, right." + }, + { + "text": "It's a triangular matrix, so when I do this determinant, shall I do this determinant of A minus lambda I?" + }, + { + "text": "I'll get this two minus lambda, one, zero, two minus lambda, right?" + }, + { + "text": "I take that determinant, so I make those into vertical bars to mean determinant, and what's the determinant?" + }, + { + "text": "Two minus lambda squared." + }, + { + "text": "What are the roots?" + }, + { + "text": "Lambda equal two twice." + }, + { + "text": "So the eigenvalues are lambda equals two and two." + }, + { + "text": "OK, fine." + }, + { + "text": "Now the next step, find the eigenvectors." + }, + { + "text": "So I look for eigenvectors and what do I find for this guy?" + }, + { + "text": "Eigenvectors for this guy, when I subtract two minus the identity, so A minus two I has zeros here, and I'm looking for the null space." + }, + { + "text": "What's, what are the eigenvectors?" + }, + { + "text": "They're the, they're, they're the null space of A minus lambda I." + }, + { + "text": "The null space is only one dimension." + }, + { + "text": "This is a case where I don't have enough eigenvectors." + }, + { + "text": "My algebraic multiplicity is two." + }, + { + "text": "I, I would say when I see, when I count how often the eigenvalue is repeated, that's the algebraic multiplicity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk11.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..779c2cf904d904b761080db2671aac46394ad02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the multiplicity." + }, + { + "text": "How many times is it the root of the polynomial?" + }, + { + "text": "My polynomial is two minus lambda squared." + }, + { + "text": "It's a double root." + }, + { + "text": "So my algebraic multiplicity is two." + }, + { + "text": "But the geometric multiplicity, which looks for vectors, looks for eigenvectors and which means the null space of this thing." + }, + { + "text": "And the only eigenvector is one zero." + }, + { + "text": "That's in the null space." + }, + { + "text": "Zero one is not in the null space." + }, + { + "text": "The null space is only one dimensional." + }, + { + "text": "So there's a matrix, my, this A or the original A, that are not diagonalizable." + }, + { + "text": "I can't, I can't find two independent eigenvectors, there's only one." + }, + { + "text": "OK." + }, + { + "text": "So that's the case that I'm, that's a case that I, I'm not really handling." + }, + { + "text": "For example, when I wrote down up here that the powers went to zero if the eigenvalues were below one, I didn't really handle that case of repeated eigenvalues because my reasoning was based on this formula." + }, + { + "text": "And this formula is based on n independent eigenvectors." + }, + { + "text": "OK." + }, + { + "text": "So just to say that." + }, + { + "text": "There are some matrices that we don't cover through diagonalization, but the great majority we do." + }, + { + "text": "OK. And we're always OK if we have different distinct eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk12.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..77d090704cc298475d94416b7ecb88a2a015a913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. That's the, like, the typical case." + }, + { + "text": "Because for each eigenvalue there's at least one eigenvector, the algebraic multiplicity here is one for every eigenvalue, and the geometric multiplicity is one." + }, + { + "text": "There's one eigenvector and they are independent." + }, + { + "text": "OK. OK. Now let me come back to the important case when we're OK." + }, + { + "text": "The important case when we are diagonalizing." + }, + { + "text": "Let me look at, so let me solve this equation." + }, + { + "text": "The equation will be each, I start with some, start with a given vector u0." + }, + { + "text": "And then my equation is that every step I multiply what I have by a." + }, + { + "text": "That equation ought to be simple to handle." + }, + { + "text": "OK. And I'd like to be able to solve it." + }, + { + "text": "How would I find, if I start with a vector u0, and I multiply by a a hundred times, what have I got?" + }, + { + "text": "Well, I can certainly write down a formula for the answer." + }, + { + "text": "So what, what, so u1 is a u0." + }, + { + "text": "And u2 is, what's u2 then?" + }, + { + "text": "U2 I multiply it, u2 I get from u1 by another, multiplying by a, so I've got a twice." + }, + { + "text": "And my formula is uk, after k steps, I've multiplied by a k times the original u0." + }, + { + "text": "You see what I'm doing?" + }, + { + "text": "The next section is going to solve systems of differential equations." + }, + { + "text": "I'm going to have derivatives." + }, + { + "text": "This, this section is the nice one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk13.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..ba8214d8c636e4757a266d6617801174bc939d80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "It solves difference equations." + }, + { + "text": "I would call that a difference equation." + }, + { + "text": "It's conne- a first order." + }, + { + "text": "I would call that a first order system, because it connects only, it only goes up one level." + }, + { + "text": "And it's a system because these are vectors and that's a matrix." + }, + { + "text": "And the solution is just that." + }, + { + "text": "OK." + }, + { + "text": "But, that's a nice formula." + }, + { + "text": "That's the, like, the most compact formula I could ever get." + }, + { + "text": "U one hundred would be a to the one hundredth u0." + }, + { + "text": "But how would I actually find u one hundred?" + }, + { + "text": "How would I find, how would I discover what u one hundred is?" + }, + { + "text": "Let me, let me show you how." + }, + { + "text": "Here, here's the idea." + }, + { + "text": "If, so, to solve, to really solve, shall I say, to really solve." + }, + { + "text": "To really solve it, I would take this initial vector, u0, and I would write it as a combination of eigenvectors." + }, + { + "text": "To really solve, write, write u0 as a combination, say, certain amount of the first eigenvector plus a certain amount of the second eigenvector plus a certain amount of the last eigenvector." + }, + { + "text": "Now multiply by a." + }, + { + "text": "You want to, you got to see the magic of eigenvectors work." + }, + { + "text": "Multiply by a." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk14.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7843b2bf0cac762d1c12452cf36500ea4ad13370 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a u0 is what?" + }, + { + "text": "So a times that." + }, + { + "text": "A times, so what's, I can separate it out into n separate pieces and that's the whole point." + }, + { + "text": "That each of those pieces is going in its own merry way." + }, + { + "text": "Each of those pieces is an eigenvector, and when I multiply by a, what does this piece become?" + }, + { + "text": "So that's some amount of the first, let's suppose the eigenvectors are normalized to be unit vectors." + }, + { + "text": "So that says what the eigenvector is." + }, + { + "text": "It's, and I need some multiple of it to produce u0." + }, + { + "text": "OK. Now when I multiply by a, what do I get?" + }, + { + "text": "I get c1, which is just a factor, times a x1, but a x1 is lambda one x1." + }, + { + "text": "When I multiply this by a, I get c2 lambda two x2." + }, + { + "text": "And here I get cn lambda n xn." + }, + { + "text": "And suppose I multiply by a to the hundredth power now." + }, + { + "text": "Can we, can we, having done it, multiplied by a, let's multiply by a to the hundredth." + }, + { + "text": "What happens to this first term when I multiply by a to the one hundredth?" + }, + { + "text": "It's got that factor lambda to the hundredth." + }, + { + "text": "That's the key." + }, + { + "text": "That, that's what I mean by going its own merry way." + }, + { + "text": "It, it is pure eigenvector, it's exactly in a direction where multiplication by a just brings in a scalar factor lambda one." + }, + { + "text": "So a hundred times brings in this a hundred times." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk15.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7ee3348735378aa4049d33ec2a197d0ceb0c447c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Hundred times lambda two, hundred times lambda n. Actually, we're, what are we seeing here?" + }, + { + "text": "We're seeing, this same, lambda, capital lambda to the hundredth, as in the, as in the diagonalization, and we're seeing the S matrix, the matrix S of eigenvectors." + }, + { + "text": "That's what this has got to, this has got to amount to, a lambda to the hundredth power times an S times this vector C that's telling us how much of each one is in the original thing." + }, + { + "text": "So if, if I had to really find the hundredth power, I would take u0, I would expand it as a combination of eigenvectors, this is really S, the eigenvector matrix times C, the, the coefficient vector." + }, + { + "text": "And then I would immediately, then, by inserting these hundredth powers of eigenvalues, I'd have the answer." + }, + { + "text": "So the, the, huh, there must be, well, let's see." + }, + { + "text": "OK." + }, + { + "text": "It's, so, yeah." + }, + { + "text": "So if u100 is a to the hundredth times u0, and u0 is Sc, then you see this formula is just this formula, which is the way I would actually get hold of this, of this u100, which is, let me put it here, u100." + }, + { + "text": "The way I would actually get hold of that, see what, what the solution is after a hundred steps, would be expand the initial vector into eigenvectors and, and let each eigenvector go its own way, multiplying by a hundred at, by lambda at every step, and therefore by lambda to the hundredth power after a hundredth step." + }, + { + "text": "Can I do an example?" + }, + { + "text": "So that's, that's the, the formulas." + }, + { + "text": "Now let me take an example." + }, + { + "text": "I'll use the Fibonacci sequence as an example." + }, + { + "text": "So, so Fibonacci example." + }, + { + "text": "You remember the Fibonacci numbers?" + }, + { + "text": "If we start with one and one as F0, oh, I think I start with zero, maybe." + }, + { + "text": "Let zero and one be the first ones." + }, + { + "text": "So there's F0 and F1, the first two Fibonacci numbers." + }, + { + "text": "Then what's the rule for Fibonacci numbers?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk16.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..79c65e32781f7f304b504a6c390247abb9d26ac8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "They're the sum." + }, + { + "text": "The next one is the sum of those, so it's one." + }, + { + "text": "The next one is the sum of those, so it's two." + }, + { + "text": "The next one is the sum of those, so it's three." + }, + { + "text": "Well, it looks like one, two, three, four, five, but somehow it's not going to do that way." + }, + { + "text": "The next one is five, right." + }, + { + "text": "Two and three makes five." + }, + { + "text": "The next one is eight." + }, + { + "text": "The next one is thirteen." + }, + { + "text": "And the one hundredth Fibonacci number is what?" + }, + { + "text": "That's my question." + }, + { + "text": "How could I get a formula for the hundredth number and for example how could I answer the question how fast are they growing?" + }, + { + "text": "How fast are those Fibonacci numbers growing?" + }, + { + "text": "They're certainly growing." + }, + { + "text": "It's not a stable case, whatever the eigenvalues of whatever matrix it is, they're not smaller than one." + }, + { + "text": "These numbers are growing." + }, + { + "text": "But how fast are they growing?" + }, + { + "text": "The answer is lies in the eigenvalue." + }, + { + "text": "So I've got to find the matrix, so let me write down the Fibonacci rule, F k plus two is F k plus one plus F k, right?" + }, + { + "text": "Now that's not in my -- I want to write that as U k plus one and A U k. But right now what I've got is a single equation, not a system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk17.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b3aaa9dcee3cf27c112015659bb5a0b51a983ce1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's second order." + }, + { + "text": "It's like having a second order differential equation with second derivatives." + }, + { + "text": "I want to get first derivatives." + }, + { + "text": "Here I want to get first difference." + }, + { + "text": "So the way to do it is to introduce U k will be a vector." + }, + { + "text": "See, a small trick." + }, + { + "text": "Let U k be a vector, F k plus one and F k. So I'm going to get a two by two system, first order, instead of a one, instead of a scalar system, second order, by a simple trick." + }, + { + "text": "I'm just going to add in an equation F k plus one equals F k plus one." + }, + { + "text": "That will be my second equation." + }, + { + "text": "Then this is my system, this is my unknown, and what's my one-step equation?" + }, + { + "text": "So now U k plus one." + }, + { + "text": "That's so U k plus one is the left side, and what have I got here on the right side?" + }, + { + "text": "I've got some matrix multiplying U k. Can you see that all right?" + }, + { + "text": "If you can see it, then you can tell me what the matrix is." + }, + { + "text": "You see that I'm taking my system here, I artificially made it into a system." + }, + { + "text": "I artificially made the unknown into a vector, and now I'm ready to look at and see what the matrix is." + }, + { + "text": "So do you see the left side, U k plus one is F k plus two F k plus one, that's just what I want." + }, + { + "text": "On the right side, this, remember, this U k here, let me for the moment put it as F k plus one F k. So what's the matrix?" + }, + { + "text": "Well, that has a one and a one, and that has a one and a zero." + }, + { + "text": "There's the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk18.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..6c1b68c2cb2fde3f5dea82f3100d4da31fcce70a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "You see that that gives me the right-hand side." + }, + { + "text": "So there's the matrix A, and this is our friend U k. So we've got, so that simple trick changed the second order scalar problem to a first order system, two, with two unknowns." + }, + { + "text": "With a matrix and now what do I do?" + }, + { + "text": "Well, before I even think, I find its eigenvalues and eigenvectors." + }, + { + "text": "So what are the eigenvalues and eigenvectors of that matrix?" + }, + { + "text": "Let's see." + }, + { + "text": "I was, first let me just, like, think for a minute." + }, + { + "text": "It's two by two, so this shouldn't be impossible to do." + }, + { + "text": "Let's do it." + }, + { + "text": "OK." + }, + { + "text": "So my matrix again is one one one zero." + }, + { + "text": "It's symmetric, by the way." + }, + { + "text": "So what I will eventually know about symmetric matrices is that the eigenvalues will come out real, I won't get any complex numbers here, and the eigenvectors, once I get those, actually will be orthogonal." + }, + { + "text": "But two by two, I'm more interested in what the actual numbers are." + }, + { + "text": "What do I know about the two numbers?" + }, + { + "text": "Well, should, do you want me to find this determinant of A minus lambda I?" + }, + { + "text": "Sure." + }, + { + "text": "So it's the determinant of one minus lambda one one zero, right?" + }, + { + "text": "Minus lambda, yes, got it." + }, + { + "text": "OK. OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk19.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..a73b23e3d56b889ff49ea7f55a784fac33e13c3d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "There'll be two eigenvalues." + }, + { + "text": "Well, tell me again what I know about the two eigenvalues before I go any further." + }, + { + "text": "Tell me something about these two eigenvalues, what do they add up to?" + }, + { + "text": "Lambda one plus lambda two is the same as the trace down the diagonal of the matrix, one and zero is one." + }, + { + "text": "So lambda one plus lambda two should come out to be one, and lambda one times lambda two should come out to be the determinant, which is minus one." + }, + { + "text": "So I'm expecting the eigenvalues to add to one and to multiply to minus one." + }, + { + "text": "But let's just see it happen here." + }, + { + "text": "If I multiply this out, I get that times that'll be a lambda squared minus lambda minus one." + }, + { + "text": "Good." + }, + { + "text": "Lambda squared minus lambda minus one." + }, + { + "text": "Actually, you see the, compare that with the original equation that I started with." + }, + { + "text": "Fk plus two minus Fk plus one minus Fk is zero." + }, + { + "text": "The recurrent, the recursion that the Fibonacci number satisfy is somehow showing up directly here for the eigenvalues when we set that to zero." + }, + { + "text": "OK. Let's solve." + }, + { + "text": "Well, I would like to be able to factor that, that quadratic, but I'm better off to use the quadratic formula." + }, + { + "text": "Lambda is, let's see, minus b is one, plus or minus the square root of b squared, which is one, minus four, times that, times that, which is plus four, over two." + }, + { + "text": "So that's the square root of five." + }, + { + "text": "So the eigenvalues are lambda one is one half of one plus square root of five, and lambda two is one half of one minus square root of five." + }, + { + "text": "And sure enough, they, those add up to one, and they multiply to give minus one." + }, + { + "text": "OK. Those are the two eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk2.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..43cfb012fc04a89fc7dab94c23bfb0f50ade3782 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "On the right, it's multiplied by, if I want, if I want lambda n xn in the last column, how do I do it?" + }, + { + "text": "Well, the last column here will be, I'll, I'll take the last column, use these coefficients, put the lambda n down there, and it will multiply that nth column and give me lambda n xn." + }, + { + "text": "There, there you see matrix multiplication just working for us." + }, + { + "text": "So I started with A s. I wrote down what it meant." + }, + { + "text": "A times each eigenvector." + }, + { + "text": "That gave me lambda times the eigenvector." + }, + { + "text": "And then when I peeled off the lambdas, they were on the right-hand side, so I've got s, my matrix back again, and this matrix, this diagonal matrix, the eigenvalue matrix, and I call it capital lambda, using capital letters for matrices, and lambda to prompt me that it's, that it's eigenvalues that are in there." + }, + { + "text": "So you see that the eigenvalues are just sitting down that diagonal?" + }, + { + "text": "If I had a column x2 here, I would want the lambda two in the two two position, in the diagonal position, to multiply that x2 and give me the lambda two x2." + }, + { + "text": "That's my formula." + }, + { + "text": "A s is s lambda." + }, + { + "text": "OK. That's, that's the, you see, it's just a calculation." + }, + { + "text": "Now, I, I mentioned, and I have to mention again, this business about n independent eigenvectors." + }, + { + "text": "As it stands, this is all fine whether, I mean, I could be repeating the same eigenvector, but I, I'm no interested in that." + }, + { + "text": "I want to be able to invert s, and that's where this comes in." + }, + { + "text": "This n independent eigenvectors business comes in to tell me that that matrix is invertible." + }, + { + "text": "So let me, on the next board, write down what I've got." + }, + { + "text": "A s equals s lambda." + }, + { + "text": "And now I'm, I can multiply on the left by s inverse." + }, + { + "text": "So this is really, I can do that provided s is invertible, provided my assumption of n independent eigenvectors is satisfied." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk20.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ad5a59fa5db44ce73ff5f88190423e0404fb3d39 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "How, how, what are those numbers approximately?" + }, + { + "text": "Square root of five, well, it's more than two, but less than three." + }, + { + "text": "It, it'd be nice to know these numbers." + }, + { + "text": "I think, I think that that, so that number comes out bigger than one, right?" + }, + { + "text": "Yeah, that's right." + }, + { + "text": "This number comes out bigger than one." + }, + { + "text": "It's about one point six one eight or something." + }, + { + "text": "Not exactly." + }, + { + "text": "It's supposed to be one point six." + }, + { + "text": "Just, like, I think so." + }, + { + "text": "Then what's lambda two?" + }, + { + "text": "Is, is lambda two positive or negative?" + }, + { + "text": "Negative, right?" + }, + { + "text": "Because I'm, it's obviously negative, and I knew that the, so it's minus, and they add up to one, so minus point six one eight, I guess." + }, + { + "text": "OK. And some order." + }, + { + "text": "Those are the two eigenvalues." + }, + { + "text": "One eigenvalue bigger than one, one eigenvalue smaller than one." + }, + { + "text": "Actually, that's a great situation to be in." + }, + { + "text": "Of course, the eigenvalues are different, so there's no doubt whatever, is this matrix diagonalizable?" + }, + { + "text": "Is this matrix diagonalizable, that original matrix A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk21.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..4a034475591d371995b379b5f98783a2cfb25870 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Sure." + }, + { + "text": "We've got two distinct eigenvalues and we can find the eigenvectors in a moment." + }, + { + "text": "But they'll be independent, will be diagonalizable, and now you can already answer my very first question." + }, + { + "text": "How fast are those Fibonacci numbers increasing?" + }, + { + "text": "How, those, they're increasing, right?" + }, + { + "text": "They're not doubling at every step." + }, + { + "text": "Let's look again at these numbers." + }, + { + "text": "Five eight thirteen, it's not obvious." + }, + { + "text": "The next one would be twenty one thirty four." + }, + { + "text": "So to get some idea of what F one hundred is, can you give me any, I mean the crucial number of, so it, these, it's approximately, what's controlling the growth of these Fibonacci numbers?" + }, + { + "text": "It's the eigenvalues." + }, + { + "text": "And which eigenvalues controlling that growth?" + }, + { + "text": "The big ones." + }, + { + "text": "So F one hundred will it be approximately some constant, c one, I guess, times this lambda one, this one plus square root of five over two, to the hundredth power." + }, + { + "text": "And the two hundredth have, in other words, the eigenvalue, the Fibonacci numbers are growing by about that factor." + }, + { + "text": "You see that we've got precise information about the, about the Fibonacci numbers out of the eigenvalue." + }, + { + "text": "OK. And again, why is that true?" + }, + { + "text": "Let me go over to this board and show what I'm doing here." + }, + { + "text": "The, the original eigen, the original initial value is some combination of eigenvectors, and then when we start multiple, when we start going out the theory of Fibonacci numbers, when we start multiplying by a hundred times, it's this lambda one to the hundredth, this term is, is the one that's taken over." + }, + { + "text": "It's, I mean, that's big, like, one point six to the hundredth power." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk22.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..c13a1fc9867173c3067e46c469cfff27b9b45289 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "The second term is practically nothing, right?" + }, + { + "text": "The point six, or minus point six to the hundredth power, is an extremely small, extremely small number." + }, + { + "text": "So this is, this, this, there are only two terms, because we're two by two." + }, + { + "text": "This number is, this piece of it is there, but it's, it's disappearing." + }, + { + "text": "Where this piece is there and it's growing and controlling everything." + }, + { + "text": "So, so really the, we're doing, like, problems that are evolving." + }, + { + "text": "We're doing dynamics." + }, + { + "text": "Instead of Ax equal b, that's a static problem." + }, + { + "text": "We're now, we're doing dynamics." + }, + { + "text": "A, a squared, a cubed, things are evolving in time, and the eigenvalues are the crucial, numbers." + }, + { + "text": "OK." + }, + { + "text": "I guess to complete this, I better write down the eigenvectors." + }, + { + "text": "So we should complete the, the whole process by finding the eigenvectors." + }, + { + "text": "OK. Well, I have to, up in the corner, then I have to look at A minus lambda I." + }, + { + "text": "So A minus lambda I is this one minus lambda, one, one, and minus lambda." + }, + { + "text": "And now, can we spot an eigenvector out of that?" + }, + { + "text": "That's, for these two lambdas, this matrix is singular." + }, + { + "text": "I guess the eigenvector, two by two ought to be easy." + }, + { + "text": "So if I know that this matrix is singular, then it seems to me the eigenvector has to be lambda and one, because that multiplication will give me the zero." + }, + { + "text": "And this multiplication gives me, better give me also zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk23.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..df816eb800ce767b1475c279a24ad976bb45a785 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Do you see why it does?" + }, + { + "text": "This is the minus lambda squared plus lambda plus one." + }, + { + "text": "It's the thing that's zero, because these lambdas are special." + }, + { + "text": "There's the eigenvector." + }, + { + "text": "X1 is lambda one, one, and x2 is lambda two, one." + }, + { + "text": "I did that as a little trick that was available in the two by two case." + }, + { + "text": "So now I finally have to, oh, I have to take the initial, u0." + }, + { + "text": "So to complete this example entirely, I have to say, OK, what was u0?" + }, + { + "text": "u0 was f1 f0." + }, + { + "text": "So u0, the starting vector, is f1 f0, and those were one and zero." + }, + { + "text": "So I have to use that vector, so I have to look for, from multiple of the first eigenvector and the second, to produce u0, the one zero vector." + }, + { + "text": "This is what will find c1 and c2, and then I'm done." + }, + { + "text": "So let me, instead of in the last five seconds grinding out a formula, let me repeat the idea." + }, + { + "text": "That really, it's the idea that's central." + }, + { + "text": "When things are evolving in time, let me come back to this board, because the ideas are here." + }, + { + "text": "When things are evolving in time by a first-order system, starting from an original u0, the key is, find the eigenvalues and eigenvectors of A." + }, + { + "text": "That will tell, those eigenvectors, the eigenvalues will already tell you what's happening." + }, + { + "text": "Is the solution blowing up?" + }, + { + "text": "Is it going to zero?" + }, + { + "text": "What's it doing?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk24.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..40301cb90760e2172baa94d536cbc13288d4c31f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk24.json @@ -0,0 +1,20 @@ +[ + { + "text": "And then, to find out exactly a formula, you have to take your u0 and write it as a combination of eigenvectors and then follow each eigenvector separately." + }, + { + "text": "And that's really what this formula, the formula for, that's what the formula for A to the k is doing." + }, + { + "text": "So remember that formula for A to the k is S, lambda to the k S inverse." + }, + { + "text": "OK. That's, that's difference equations, and you just have to, so the homework will give some examples different from Fibonacci to follow through." + }, + { + "text": "And next time will be differential equations." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk3.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..9bf1bb852baadc1da7837e14180c0c2951a30882 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I mentioned at the end of last time, and I'll say again, that there's a small number of matrices for, that don't have n independent eigenvectors." + }, + { + "text": "So I've got to discuss that, that technical point." + }, + { + "text": "But the great, the most matrices that we see have n, n independent eigenvectors and we can diagonalize." + }, + { + "text": "This is diagonalization." + }, + { + "text": "I could also write it, and I often will, the other way round." + }, + { + "text": "If I multiply on the right by s inverse, if I took this equation at the top and multiplied on the right by s inverse, I could, I would have A left here." + }, + { + "text": "Now s inverse is coming from the right." + }, + { + "text": "So can you keep those two straight?" + }, + { + "text": "A multiplies its eigenvectors." + }, + { + "text": "That's how I keep them straight." + }, + { + "text": "So A multiplies s. A multiplies s. And then this s inverse makes the whole thing diagonal." + }, + { + "text": "And this is another way of saying the same thing, putting the s's on the other side of the equation, A is s lambda s inverse." + }, + { + "text": "So that's the, that's the new factorization." + }, + { + "text": "That's the replacement for L U from elimination or Q R from Gram-Schmidt." + }, + { + "text": "And notice that the matrix, so it's, it's a matrix times a diagonal matrix times the inverse of the first one." + }, + { + "text": "It's, that's the combination that we'll see throughout this chapter." + }, + { + "text": "This, this, combination with an s and an s inverse." + }, + { + "text": "OK. Can I just begin to use that?" + }, + { + "text": "For example, what about A squared?" + }, + { + "text": "What are the eigenvalues and eigenvectors of A squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk4.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c687b6948acad76de8781cb82d3eb069c9da514e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's a straightforward question with a, with a absolutely clean answer." + }, + { + "text": "So let me, let me consider A squared." + }, + { + "text": "So I look, I start with Ax equal lambda x." + }, + { + "text": "And I'm headed for A squared." + }, + { + "text": "So let me multiply both sides by A." + }, + { + "text": "That's one way to get A squared on the left." + }, + { + "text": "So if, I should write these ifs in here." + }, + { + "text": "If Ax equals lambda x, then I multiply by A." + }, + { + "text": "So I get A squared x equals, well, I'm multiplying by A, so that's lambda Ax." + }, + { + "text": "That lambda was a number, so I just put it on the left." + }, + { + "text": "And what do I, tell me how to make that look better." + }, + { + "text": "What have I got here?" + }, + { + "text": "For, if, if A has the eigenvalue lambda and eigenvector x, what's up with A squared?" + }, + { + "text": "A squared x, I just multiply by A, but now for Ax, I'm going to substitute lambda x, so I've got lambda squared x." + }, + { + "text": "So from that simple calculation, I, my conclusion is that the eigenvalues of A squared are lambda squared." + }, + { + "text": "And the eigenvectors, I always think about both of those." + }, + { + "text": "What can I say about the eigenvalues?" + }, + { + "text": "They're squared." + }, + { + "text": "What can I say about the eigenvectors?" + }, + { + "text": "They're the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk5.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5bf15e20707c156c8ae71c9c7acea41a9d9d8e46 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same x as in, as for A." + }, + { + "text": "Now, let me see that also from this formula." + }, + { + "text": "How can I see what A squared is looking like from this formula?" + }, + { + "text": "So let me, that, that was one way to do it." + }, + { + "text": "Let me do it by just taking A squared from that." + }, + { + "text": "A squared is S lambda S inverse, that's A, times S lambda S inverse, that's A, which is?" + }, + { + "text": "This is the beauty of eigenvalues, eigenvectors, having that S inverse and S is the identity, so I've got S lambda squared S inverse." + }, + { + "text": "Yes." + }, + { + "text": "You see what that's telling me?" + }, + { + "text": "It's, it's telling me the same thing that I just learned here, but in the, in, in a matrix form." + }, + { + "text": "It's telling me that the S is the same, the eigenvectors are the same, but the eigenvalues are squared, because this is, what's lambda squared, that's still diagonal, it's got little lambda one squared, lambda two squared, down to lambda n squared, on that diagonal, those are the eigenvalues, as we just learned, of A squared." + }, + { + "text": "OK." + }, + { + "text": "So, somehow those eigenvalues and eigenvectors are really giving you a way to, to, to, to see what's going on inside a matrix." + }, + { + "text": "Now, of course, I can continue that for, to the k-th power." + }, + { + "text": "A to the k-th power." + }, + { + "text": "If I multiply, if I have k of these together, do you see how S inverse S will keep cancelling?" + }, + { + "text": "In the, in the inside, I'll have the S outside, at the far left, and lambda will be in there k times and S inverse." + }, + { + "text": "So what's that telling me?" + }, + { + "text": "That's telling me that the eigenvalues of A, of A to the k-th power are the k-th powers." + }, + { + "text": "The eigenvalues of A cubed are the cubes of the eigenvalues of A, and the eigenvectors are the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk6.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..c18dddbe798022f7e68278ac002a3f5fe6ed249e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same." + }, + { + "text": "OK." + }, + { + "text": "In other words, eigenvalues and eigenvectors give a great way to understand the powers of a matrix." + }, + { + "text": "If I take the square of a matrix or the hundredth power of a matrix, the pivots are all over the place." + }, + { + "text": "L U, if I multiply L U times L U times L U times L U a hundred times, I've got a hundred L U's." + }, + { + "text": "I can't do anything with them." + }, + { + "text": "But when I multiply S lambda S inverse by itself, when I look at the eigenvector picture a hundred times, I get a hundred or ninety-nine of these guys cancelling out inside, and I get A to the hundredth is S lambda to the hundredth S inverse." + }, + { + "text": "I mean, eigenvalues tell you about powers of a matrix in a way that we had no, no way to approach previously." + }, + { + "text": "For example, when does, when do the powers of a matrix go to zero?" + }, + { + "text": "I would call that matrix stable, maybe." + }, + { + "text": "So, so, so I could write down a, a theorem." + }, + { + "text": "I'll, I'll write it as a theorem, just to use that word to emphasize that here I'm getting this great fact from this eigenvalue picture." + }, + { + "text": "OK. A to the k approaches zero as k goes, as k gets bigger." + }, + { + "text": "If what?" + }, + { + "text": "What's the, how can I tell for a matrix A if its powers go to zero?" + }, + { + "text": "What, what's somewhere inside that matrix is that information." + }, + { + "text": "That information is not present in the pivots." + }, + { + "text": "It's present in the eigenvalues." + }, + { + "text": "What do I need for the, to know that if I take higher and higher powers of A that this matrix gets smaller and smaller?" + }, + { + "text": "Well, S and S inverse are not moving." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk7.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b84a5c854a5542758e8a0107e1ff043205fe3bdb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's this guy that has to get small, and that's easy to, easy to understand." + }, + { + "text": "The requirement is all eigenvalues, so what is the requirement?" + }, + { + "text": "The eigenvalues have to be less than one." + }, + { + "text": "Now, I have to write that absolute value, because those eigenvalues could be negative, they could be complex numbers." + }, + { + "text": "So I'm taking the absolute value if all of those are below one." + }, + { + "text": "That's, in fact, we practically see why." + }, + { + "text": "Let me just say that I, that I, I'm operating on one assumption here, and I got to keep remembering that that assumption is still present." + }, + { + "text": "That assumption was that I had a full set of, of n independent eigenvectors." + }, + { + "text": "If I don't have that, then I, I, then this approach is not working." + }, + { + "text": "So, so again, a pure eigenvalue approach, eigenvector approach, needs n independent eigenvectors." + }, + { + "text": "If we don't have n independent eigenvectors, we can't diagonalize the matrix." + }, + { + "text": "We can't get to a diagonal matrix." + }, + { + "text": "This, this, this diagonalization is only possible if S inverse makes sense." + }, + { + "text": "OK. Can I, can I follow up on that point now?" + }, + { + "text": "So, so you see why, what we get and, and why we want it, because we get information about the powers of a matrix just immediately from the eigenvalues." + }, + { + "text": "OK, now let me follow up on this, business of which matrices are diagonalizable." + }, + { + "text": "Sorry about that long word." + }, + { + "text": "So a matrix is, is sure to, so here's, here's the main point." + }, + { + "text": "A is sure to be, to have n independent eigenvectors and, and B, now here comes that word, diagonalizable, if, if, so we, we, we might as well get the, the nice case out in the open." + }, + { + "text": "The nice case is when, if all the lambdas are different." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk8.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f06dcec8ffa0ee1bf19440e4ab2194db33ab353b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means, that means no repeated eigenvalues." + }, + { + "text": "OK. That's the nice case." + }, + { + "text": "If, if my matrix and most matrix, if I do a random matrix in MATLAB and compute its eigenvalues, so if I computed, if I took I of rand of ten ten, gave, gave that MATLAB command, the, we'd get a random ten by ten matrix, we would get a list of its ten eigenvalues and they would be different." + }, + { + "text": "They would be distinct, is the best word." + }, + { + "text": "I would have a random matrix will have ten distinct, a ten by ten matrix will have ten distinct eigenvalues, and if it does, the eigenvectors are automatically independent." + }, + { + "text": "So that's a nice fact." + }, + { + "text": "I can, I'll refer you to the text for the proof." + }, + { + "text": "That, that A is sure to have n independent eigenvectors if the eigenvalues are different." + }, + { + "text": "If, if all the, if all eigenvalues are different." + }, + { + "text": "It's just, if some lambdas are repeated, then I have to look more closely." + }, + { + "text": "If an eigenvalue is repeated, I have to look, I have to count, I have to check." + }, + { + "text": "Has it got, say it's repeated three times." + }, + { + "text": "So what's a possibility for, so, so here's, here's the repeated possibility." + }, + { + "text": "And, and let me emphasize the conclusion." + }, + { + "text": "That if I have repeated eigenvalues, I may or may not, I may or may not have, have n independent eigenvectors." + }, + { + "text": "I might." + }, + { + "text": "I, I, you know, this isn't a completely negative case." + }, + { + "text": "The identity matrix." + }, + { + "text": "Well, suppose I take the ten by ten identity matrix." + }, + { + "text": "What are the eigenvalues of that matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk9.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..87d2a2ae5773036cf11800e2f1962908986a0dad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_7_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So just, just take the easiest matrix, the identity." + }, + { + "text": "If I look for its eigenvalues, they're all ones." + }, + { + "text": "So that eigenvalue one is repeated ten times." + }, + { + "text": "But there's no shortage of eigenvectors for the identity matrix." + }, + { + "text": "In fact, every vector is an eigenvector." + }, + { + "text": "So I can take ten independent vectors." + }, + { + "text": "Oh, well, what happens to everything if, if, if A is the identity matrix, let's just think that one through in our head." + }, + { + "text": "If A is the identity matrix, then it's got plenty of eigenvectors." + }, + { + "text": "I choose ten independent vectors, they're the columns of S, and, and what do I get from S inverse A S?" + }, + { + "text": "I get I again, right?" + }, + { + "text": "If A is the identity, and of course, that's the correct lambda." + }, + { + "text": "The, the matrix was already diagonal." + }, + { + "text": "So if the matrix is already diagonal, then the, the lambda is the same as the matrix." + }, + { + "text": "A diagonal matrix has got its eigenvalues sitting right there in front of you." + }, + { + "text": "Now if it's triangular, the eigenvalues are still sitting there, but so let's, let's take a case where, it's triangular." + }, + { + "text": "Suppose A is like, two, one, two, zero." + }, + { + "text": "So there's a case that's going to be trouble." + }, + { + "text": "There's a case that's going to be trouble." + }, + { + "text": "First of all, what are the eigen- I mean, we just, like now you, if we start with a matrix, the first thing we do practically without thinking is compute the eigenvalues and eigenvectors." + }, + { + "text": "OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk0.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6898d4fe66019ef6b40d0472ea94a968e7bbde9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, shall we start?" + }, + { + "text": "This is the second lecture on eigenvalues." + }, + { + "text": "So the first lecture was set -- reached the key equation, Ax equal lambda x. x is the eigenvector and lambda is the eigenvalue." + }, + { + "text": "Now, to use that." + }, + { + "text": "And the good way to, after we've found, so job one is to find the eigenvalues and find the eigenvectors." + }, + { + "text": "Now after we found them, what do we do with them?" + }, + { + "text": "Well, the good way to see that is diagonalize the matrix." + }, + { + "text": "So the matrix is A, and I want to show, first of all, this is like the basic fact." + }, + { + "text": "This, this formula." + }, + { + "text": "That's, that's the key to today's lecture." + }, + { + "text": "This matrix A, I put its eigenvectors in the columns of a matrix S. So S will be the eigenvector matrix, and I want to look at this magic combination S inverse A S. So can I show you how that, how that, what happens there?" + }, + { + "text": "And notice, notice, there's an S inverse." + }, + { + "text": "We have to be able to invert this eigenvector matrix S. So for that we need n independent eigenvectors." + }, + { + "text": "So that's the, that's the case." + }, + { + "text": "OK." + }, + { + "text": "So suppose we have n linearly independent eigenvectors of A." + }, + { + "text": "Put them in the columns of this matrix S. So I'm naturally going to call that the eigenvector matrix, because it's got the eigenvectors in its columns." + }, + { + "text": "And all I want to do is show you what happens when you multiply A times S. So A times S. So this is A times the matrix with the first eigenvector in its first column, the second eigenvector in its second column, the nth eigenvector in its nth column." + }, + { + "text": "And how am I going to do this matrix multiplication?" + }, + { + "text": "Well, certainly I'll do it a column at a time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk1.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..fbe078217bb68baea8e0605a5d04be568c49efbf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I get?" + }, + { + "text": "A times the first column gives me the first column of the answer, but what is it?" + }, + { + "text": "That's an eigenvector." + }, + { + "text": "A times x1 is equal to the lambda times the x1." + }, + { + "text": "And that lambda's we'll call lambda one, of course." + }, + { + "text": "So that's the first column, A x1 is the same as lambda one x1." + }, + { + "text": "A x2 is lambda two x2, so on, along to, in the nth column, we now have lambda n xn." + }, + { + "text": "Looking good, but the next step is even better." + }, + { + "text": "So for the next step, I want to separate out those eigenvalues, those multiplying numbers, from the x's." + }, + { + "text": "So then I'll have just what I want." + }, + { + "text": "OK, so how, how am I going to separate out?" + }, + { + "text": "So that, that number lambda one is multiplying the first column." + }, + { + "text": "So if I want to factor it out of the first column, I better put, here is going to be x1, and that's going to multiply this matrix lambda one in the first entry in all zeros." + }, + { + "text": "You see that that, that's going to come out right for the first column?" + }, + { + "text": "Because we remember how, how we're going back to that original punchline, that if I want a number to multiply x1, then I can do it by putting x1 in that column, in the first column, and putting that number there." + }, + { + "text": "What am I going to have here?" + }, + { + "text": "I'm going to have lambda one, I'm going to have x1, x2, xn." + }, + { + "text": "These are going to be my columns again." + }, + { + "text": "I'm getting s back again." + }, + { + "text": "I'm getting s back again, but now what's it multiplied by?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk10.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c58a42edbe9567233ca7f57643a0b7d43ae6761f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what are the eigenvalues?" + }, + { + "text": "You can tell me right away what they are." + }, + { + "text": "They're two and two, right." + }, + { + "text": "It's a triangular matrix, so when I do this determinant, shall I do this determinant of A minus lambda I?" + }, + { + "text": "I'll get this two minus lambda, one, zero, two minus lambda, right?" + }, + { + "text": "I take that determinant, so I make those into vertical bars to mean determinant, and what's the determinant?" + }, + { + "text": "Two minus lambda squared." + }, + { + "text": "What are the roots?" + }, + { + "text": "Lambda equal two twice." + }, + { + "text": "So the eigenvalues are lambda equals two and two." + }, + { + "text": "OK, fine." + }, + { + "text": "Now the next step, find the eigenvectors." + }, + { + "text": "So I look for eigenvectors and what do I find for this guy?" + }, + { + "text": "Eigenvectors for this guy, when I subtract two minus the identity, so A minus two I has zeros here, and I'm looking for the null space." + }, + { + "text": "What's, what are the eigenvectors?" + }, + { + "text": "They're the, they're, they're the null space of A minus lambda I." + }, + { + "text": "The null space is only one dimension." + }, + { + "text": "This is a case where I don't have enough eigenvectors." + }, + { + "text": "My algebraic multiplicity is two." + }, + { + "text": "I, I would say when I see, when I count how often the eigenvalue is repeated, that's the algebraic multiplicity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk11.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..779c2cf904d904b761080db2671aac46394ad02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the multiplicity." + }, + { + "text": "How many times is it the root of the polynomial?" + }, + { + "text": "My polynomial is two minus lambda squared." + }, + { + "text": "It's a double root." + }, + { + "text": "So my algebraic multiplicity is two." + }, + { + "text": "But the geometric multiplicity, which looks for vectors, looks for eigenvectors and which means the null space of this thing." + }, + { + "text": "And the only eigenvector is one zero." + }, + { + "text": "That's in the null space." + }, + { + "text": "Zero one is not in the null space." + }, + { + "text": "The null space is only one dimensional." + }, + { + "text": "So there's a matrix, my, this A or the original A, that are not diagonalizable." + }, + { + "text": "I can't, I can't find two independent eigenvectors, there's only one." + }, + { + "text": "OK." + }, + { + "text": "So that's the case that I'm, that's a case that I, I'm not really handling." + }, + { + "text": "For example, when I wrote down up here that the powers went to zero if the eigenvalues were below one, I didn't really handle that case of repeated eigenvalues because my reasoning was based on this formula." + }, + { + "text": "And this formula is based on n independent eigenvectors." + }, + { + "text": "OK." + }, + { + "text": "So just to say that." + }, + { + "text": "There are some matrices that we don't cover through diagonalization, but the great majority we do." + }, + { + "text": "OK. And we're always OK if we have different distinct eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk12.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..77d090704cc298475d94416b7ecb88a2a015a913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. That's the, like, the typical case." + }, + { + "text": "Because for each eigenvalue there's at least one eigenvector, the algebraic multiplicity here is one for every eigenvalue, and the geometric multiplicity is one." + }, + { + "text": "There's one eigenvector and they are independent." + }, + { + "text": "OK. OK. Now let me come back to the important case when we're OK." + }, + { + "text": "The important case when we are diagonalizing." + }, + { + "text": "Let me look at, so let me solve this equation." + }, + { + "text": "The equation will be each, I start with some, start with a given vector u0." + }, + { + "text": "And then my equation is that every step I multiply what I have by a." + }, + { + "text": "That equation ought to be simple to handle." + }, + { + "text": "OK. And I'd like to be able to solve it." + }, + { + "text": "How would I find, if I start with a vector u0, and I multiply by a a hundred times, what have I got?" + }, + { + "text": "Well, I can certainly write down a formula for the answer." + }, + { + "text": "So what, what, so u1 is a u0." + }, + { + "text": "And u2 is, what's u2 then?" + }, + { + "text": "U2 I multiply it, u2 I get from u1 by another, multiplying by a, so I've got a twice." + }, + { + "text": "And my formula is uk, after k steps, I've multiplied by a k times the original u0." + }, + { + "text": "You see what I'm doing?" + }, + { + "text": "The next section is going to solve systems of differential equations." + }, + { + "text": "I'm going to have derivatives." + }, + { + "text": "This, this section is the nice one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk13.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..ba8214d8c636e4757a266d6617801174bc939d80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "It solves difference equations." + }, + { + "text": "I would call that a difference equation." + }, + { + "text": "It's conne- a first order." + }, + { + "text": "I would call that a first order system, because it connects only, it only goes up one level." + }, + { + "text": "And it's a system because these are vectors and that's a matrix." + }, + { + "text": "And the solution is just that." + }, + { + "text": "OK." + }, + { + "text": "But, that's a nice formula." + }, + { + "text": "That's the, like, the most compact formula I could ever get." + }, + { + "text": "U one hundred would be a to the one hundredth u0." + }, + { + "text": "But how would I actually find u one hundred?" + }, + { + "text": "How would I find, how would I discover what u one hundred is?" + }, + { + "text": "Let me, let me show you how." + }, + { + "text": "Here, here's the idea." + }, + { + "text": "If, so, to solve, to really solve, shall I say, to really solve." + }, + { + "text": "To really solve it, I would take this initial vector, u0, and I would write it as a combination of eigenvectors." + }, + { + "text": "To really solve, write, write u0 as a combination, say, certain amount of the first eigenvector plus a certain amount of the second eigenvector plus a certain amount of the last eigenvector." + }, + { + "text": "Now multiply by a." + }, + { + "text": "You want to, you got to see the magic of eigenvectors work." + }, + { + "text": "Multiply by a." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk14.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7843b2bf0cac762d1c12452cf36500ea4ad13370 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a u0 is what?" + }, + { + "text": "So a times that." + }, + { + "text": "A times, so what's, I can separate it out into n separate pieces and that's the whole point." + }, + { + "text": "That each of those pieces is going in its own merry way." + }, + { + "text": "Each of those pieces is an eigenvector, and when I multiply by a, what does this piece become?" + }, + { + "text": "So that's some amount of the first, let's suppose the eigenvectors are normalized to be unit vectors." + }, + { + "text": "So that says what the eigenvector is." + }, + { + "text": "It's, and I need some multiple of it to produce u0." + }, + { + "text": "OK. Now when I multiply by a, what do I get?" + }, + { + "text": "I get c1, which is just a factor, times a x1, but a x1 is lambda one x1." + }, + { + "text": "When I multiply this by a, I get c2 lambda two x2." + }, + { + "text": "And here I get cn lambda n xn." + }, + { + "text": "And suppose I multiply by a to the hundredth power now." + }, + { + "text": "Can we, can we, having done it, multiplied by a, let's multiply by a to the hundredth." + }, + { + "text": "What happens to this first term when I multiply by a to the one hundredth?" + }, + { + "text": "It's got that factor lambda to the hundredth." + }, + { + "text": "That's the key." + }, + { + "text": "That, that's what I mean by going its own merry way." + }, + { + "text": "It, it is pure eigenvector, it's exactly in a direction where multiplication by a just brings in a scalar factor lambda one." + }, + { + "text": "So a hundred times brings in this a hundred times." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk15.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7ee3348735378aa4049d33ec2a197d0ceb0c447c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Hundred times lambda two, hundred times lambda n. Actually, we're, what are we seeing here?" + }, + { + "text": "We're seeing, this same, lambda, capital lambda to the hundredth, as in the, as in the diagonalization, and we're seeing the S matrix, the matrix S of eigenvectors." + }, + { + "text": "That's what this has got to, this has got to amount to, a lambda to the hundredth power times an S times this vector C that's telling us how much of each one is in the original thing." + }, + { + "text": "So if, if I had to really find the hundredth power, I would take u0, I would expand it as a combination of eigenvectors, this is really S, the eigenvector matrix times C, the, the coefficient vector." + }, + { + "text": "And then I would immediately, then, by inserting these hundredth powers of eigenvalues, I'd have the answer." + }, + { + "text": "So the, the, huh, there must be, well, let's see." + }, + { + "text": "OK." + }, + { + "text": "It's, so, yeah." + }, + { + "text": "So if u100 is a to the hundredth times u0, and u0 is Sc, then you see this formula is just this formula, which is the way I would actually get hold of this, of this u100, which is, let me put it here, u100." + }, + { + "text": "The way I would actually get hold of that, see what, what the solution is after a hundred steps, would be expand the initial vector into eigenvectors and, and let each eigenvector go its own way, multiplying by a hundred at, by lambda at every step, and therefore by lambda to the hundredth power after a hundredth step." + }, + { + "text": "Can I do an example?" + }, + { + "text": "So that's, that's the, the formulas." + }, + { + "text": "Now let me take an example." + }, + { + "text": "I'll use the Fibonacci sequence as an example." + }, + { + "text": "So, so Fibonacci example." + }, + { + "text": "You remember the Fibonacci numbers?" + }, + { + "text": "If we start with one and one as F0, oh, I think I start with zero, maybe." + }, + { + "text": "Let zero and one be the first ones." + }, + { + "text": "So there's F0 and F1, the first two Fibonacci numbers." + }, + { + "text": "Then what's the rule for Fibonacci numbers?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk16.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..79c65e32781f7f304b504a6c390247abb9d26ac8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "They're the sum." + }, + { + "text": "The next one is the sum of those, so it's one." + }, + { + "text": "The next one is the sum of those, so it's two." + }, + { + "text": "The next one is the sum of those, so it's three." + }, + { + "text": "Well, it looks like one, two, three, four, five, but somehow it's not going to do that way." + }, + { + "text": "The next one is five, right." + }, + { + "text": "Two and three makes five." + }, + { + "text": "The next one is eight." + }, + { + "text": "The next one is thirteen." + }, + { + "text": "And the one hundredth Fibonacci number is what?" + }, + { + "text": "That's my question." + }, + { + "text": "How could I get a formula for the hundredth number and for example how could I answer the question how fast are they growing?" + }, + { + "text": "How fast are those Fibonacci numbers growing?" + }, + { + "text": "They're certainly growing." + }, + { + "text": "It's not a stable case, whatever the eigenvalues of whatever matrix it is, they're not smaller than one." + }, + { + "text": "These numbers are growing." + }, + { + "text": "But how fast are they growing?" + }, + { + "text": "The answer is lies in the eigenvalue." + }, + { + "text": "So I've got to find the matrix, so let me write down the Fibonacci rule, F k plus two is F k plus one plus F k, right?" + }, + { + "text": "Now that's not in my -- I want to write that as U k plus one and A U k. But right now what I've got is a single equation, not a system." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk17.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b3aaa9dcee3cf27c112015659bb5a0b51a983ce1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's second order." + }, + { + "text": "It's like having a second order differential equation with second derivatives." + }, + { + "text": "I want to get first derivatives." + }, + { + "text": "Here I want to get first difference." + }, + { + "text": "So the way to do it is to introduce U k will be a vector." + }, + { + "text": "See, a small trick." + }, + { + "text": "Let U k be a vector, F k plus one and F k. So I'm going to get a two by two system, first order, instead of a one, instead of a scalar system, second order, by a simple trick." + }, + { + "text": "I'm just going to add in an equation F k plus one equals F k plus one." + }, + { + "text": "That will be my second equation." + }, + { + "text": "Then this is my system, this is my unknown, and what's my one-step equation?" + }, + { + "text": "So now U k plus one." + }, + { + "text": "That's so U k plus one is the left side, and what have I got here on the right side?" + }, + { + "text": "I've got some matrix multiplying U k. Can you see that all right?" + }, + { + "text": "If you can see it, then you can tell me what the matrix is." + }, + { + "text": "You see that I'm taking my system here, I artificially made it into a system." + }, + { + "text": "I artificially made the unknown into a vector, and now I'm ready to look at and see what the matrix is." + }, + { + "text": "So do you see the left side, U k plus one is F k plus two F k plus one, that's just what I want." + }, + { + "text": "On the right side, this, remember, this U k here, let me for the moment put it as F k plus one F k. So what's the matrix?" + }, + { + "text": "Well, that has a one and a one, and that has a one and a zero." + }, + { + "text": "There's the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk18.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..6c1b68c2cb2fde3f5dea82f3100d4da31fcce70a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "You see that that gives me the right-hand side." + }, + { + "text": "So there's the matrix A, and this is our friend U k. So we've got, so that simple trick changed the second order scalar problem to a first order system, two, with two unknowns." + }, + { + "text": "With a matrix and now what do I do?" + }, + { + "text": "Well, before I even think, I find its eigenvalues and eigenvectors." + }, + { + "text": "So what are the eigenvalues and eigenvectors of that matrix?" + }, + { + "text": "Let's see." + }, + { + "text": "I was, first let me just, like, think for a minute." + }, + { + "text": "It's two by two, so this shouldn't be impossible to do." + }, + { + "text": "Let's do it." + }, + { + "text": "OK." + }, + { + "text": "So my matrix again is one one one zero." + }, + { + "text": "It's symmetric, by the way." + }, + { + "text": "So what I will eventually know about symmetric matrices is that the eigenvalues will come out real, I won't get any complex numbers here, and the eigenvectors, once I get those, actually will be orthogonal." + }, + { + "text": "But two by two, I'm more interested in what the actual numbers are." + }, + { + "text": "What do I know about the two numbers?" + }, + { + "text": "Well, should, do you want me to find this determinant of A minus lambda I?" + }, + { + "text": "Sure." + }, + { + "text": "So it's the determinant of one minus lambda one one zero, right?" + }, + { + "text": "Minus lambda, yes, got it." + }, + { + "text": "OK. OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk19.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..a73b23e3d56b889ff49ea7f55a784fac33e13c3d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "There'll be two eigenvalues." + }, + { + "text": "Well, tell me again what I know about the two eigenvalues before I go any further." + }, + { + "text": "Tell me something about these two eigenvalues, what do they add up to?" + }, + { + "text": "Lambda one plus lambda two is the same as the trace down the diagonal of the matrix, one and zero is one." + }, + { + "text": "So lambda one plus lambda two should come out to be one, and lambda one times lambda two should come out to be the determinant, which is minus one." + }, + { + "text": "So I'm expecting the eigenvalues to add to one and to multiply to minus one." + }, + { + "text": "But let's just see it happen here." + }, + { + "text": "If I multiply this out, I get that times that'll be a lambda squared minus lambda minus one." + }, + { + "text": "Good." + }, + { + "text": "Lambda squared minus lambda minus one." + }, + { + "text": "Actually, you see the, compare that with the original equation that I started with." + }, + { + "text": "Fk plus two minus Fk plus one minus Fk is zero." + }, + { + "text": "The recurrent, the recursion that the Fibonacci number satisfy is somehow showing up directly here for the eigenvalues when we set that to zero." + }, + { + "text": "OK. Let's solve." + }, + { + "text": "Well, I would like to be able to factor that, that quadratic, but I'm better off to use the quadratic formula." + }, + { + "text": "Lambda is, let's see, minus b is one, plus or minus the square root of b squared, which is one, minus four, times that, times that, which is plus four, over two." + }, + { + "text": "So that's the square root of five." + }, + { + "text": "So the eigenvalues are lambda one is one half of one plus square root of five, and lambda two is one half of one minus square root of five." + }, + { + "text": "And sure enough, they, those add up to one, and they multiply to give minus one." + }, + { + "text": "OK. Those are the two eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk2.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..43cfb012fc04a89fc7dab94c23bfb0f50ade3782 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "On the right, it's multiplied by, if I want, if I want lambda n xn in the last column, how do I do it?" + }, + { + "text": "Well, the last column here will be, I'll, I'll take the last column, use these coefficients, put the lambda n down there, and it will multiply that nth column and give me lambda n xn." + }, + { + "text": "There, there you see matrix multiplication just working for us." + }, + { + "text": "So I started with A s. I wrote down what it meant." + }, + { + "text": "A times each eigenvector." + }, + { + "text": "That gave me lambda times the eigenvector." + }, + { + "text": "And then when I peeled off the lambdas, they were on the right-hand side, so I've got s, my matrix back again, and this matrix, this diagonal matrix, the eigenvalue matrix, and I call it capital lambda, using capital letters for matrices, and lambda to prompt me that it's, that it's eigenvalues that are in there." + }, + { + "text": "So you see that the eigenvalues are just sitting down that diagonal?" + }, + { + "text": "If I had a column x2 here, I would want the lambda two in the two two position, in the diagonal position, to multiply that x2 and give me the lambda two x2." + }, + { + "text": "That's my formula." + }, + { + "text": "A s is s lambda." + }, + { + "text": "OK. That's, that's the, you see, it's just a calculation." + }, + { + "text": "Now, I, I mentioned, and I have to mention again, this business about n independent eigenvectors." + }, + { + "text": "As it stands, this is all fine whether, I mean, I could be repeating the same eigenvector, but I, I'm no interested in that." + }, + { + "text": "I want to be able to invert s, and that's where this comes in." + }, + { + "text": "This n independent eigenvectors business comes in to tell me that that matrix is invertible." + }, + { + "text": "So let me, on the next board, write down what I've got." + }, + { + "text": "A s equals s lambda." + }, + { + "text": "And now I'm, I can multiply on the left by s inverse." + }, + { + "text": "So this is really, I can do that provided s is invertible, provided my assumption of n independent eigenvectors is satisfied." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk20.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ad5a59fa5db44ce73ff5f88190423e0404fb3d39 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "How, how, what are those numbers approximately?" + }, + { + "text": "Square root of five, well, it's more than two, but less than three." + }, + { + "text": "It, it'd be nice to know these numbers." + }, + { + "text": "I think, I think that that, so that number comes out bigger than one, right?" + }, + { + "text": "Yeah, that's right." + }, + { + "text": "This number comes out bigger than one." + }, + { + "text": "It's about one point six one eight or something." + }, + { + "text": "Not exactly." + }, + { + "text": "It's supposed to be one point six." + }, + { + "text": "Just, like, I think so." + }, + { + "text": "Then what's lambda two?" + }, + { + "text": "Is, is lambda two positive or negative?" + }, + { + "text": "Negative, right?" + }, + { + "text": "Because I'm, it's obviously negative, and I knew that the, so it's minus, and they add up to one, so minus point six one eight, I guess." + }, + { + "text": "OK. And some order." + }, + { + "text": "Those are the two eigenvalues." + }, + { + "text": "One eigenvalue bigger than one, one eigenvalue smaller than one." + }, + { + "text": "Actually, that's a great situation to be in." + }, + { + "text": "Of course, the eigenvalues are different, so there's no doubt whatever, is this matrix diagonalizable?" + }, + { + "text": "Is this matrix diagonalizable, that original matrix A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk21.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..4a034475591d371995b379b5f98783a2cfb25870 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Sure." + }, + { + "text": "We've got two distinct eigenvalues and we can find the eigenvectors in a moment." + }, + { + "text": "But they'll be independent, will be diagonalizable, and now you can already answer my very first question." + }, + { + "text": "How fast are those Fibonacci numbers increasing?" + }, + { + "text": "How, those, they're increasing, right?" + }, + { + "text": "They're not doubling at every step." + }, + { + "text": "Let's look again at these numbers." + }, + { + "text": "Five eight thirteen, it's not obvious." + }, + { + "text": "The next one would be twenty one thirty four." + }, + { + "text": "So to get some idea of what F one hundred is, can you give me any, I mean the crucial number of, so it, these, it's approximately, what's controlling the growth of these Fibonacci numbers?" + }, + { + "text": "It's the eigenvalues." + }, + { + "text": "And which eigenvalues controlling that growth?" + }, + { + "text": "The big ones." + }, + { + "text": "So F one hundred will it be approximately some constant, c one, I guess, times this lambda one, this one plus square root of five over two, to the hundredth power." + }, + { + "text": "And the two hundredth have, in other words, the eigenvalue, the Fibonacci numbers are growing by about that factor." + }, + { + "text": "You see that we've got precise information about the, about the Fibonacci numbers out of the eigenvalue." + }, + { + "text": "OK. And again, why is that true?" + }, + { + "text": "Let me go over to this board and show what I'm doing here." + }, + { + "text": "The, the original eigen, the original initial value is some combination of eigenvectors, and then when we start multiple, when we start going out the theory of Fibonacci numbers, when we start multiplying by a hundred times, it's this lambda one to the hundredth, this term is, is the one that's taken over." + }, + { + "text": "It's, I mean, that's big, like, one point six to the hundredth power." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk22.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..c13a1fc9867173c3067e46c469cfff27b9b45289 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "The second term is practically nothing, right?" + }, + { + "text": "The point six, or minus point six to the hundredth power, is an extremely small, extremely small number." + }, + { + "text": "So this is, this, this, there are only two terms, because we're two by two." + }, + { + "text": "This number is, this piece of it is there, but it's, it's disappearing." + }, + { + "text": "Where this piece is there and it's growing and controlling everything." + }, + { + "text": "So, so really the, we're doing, like, problems that are evolving." + }, + { + "text": "We're doing dynamics." + }, + { + "text": "Instead of Ax equal b, that's a static problem." + }, + { + "text": "We're now, we're doing dynamics." + }, + { + "text": "A, a squared, a cubed, things are evolving in time, and the eigenvalues are the crucial, numbers." + }, + { + "text": "OK." + }, + { + "text": "I guess to complete this, I better write down the eigenvectors." + }, + { + "text": "So we should complete the, the whole process by finding the eigenvectors." + }, + { + "text": "OK. Well, I have to, up in the corner, then I have to look at A minus lambda I." + }, + { + "text": "So A minus lambda I is this one minus lambda, one, one, and minus lambda." + }, + { + "text": "And now, can we spot an eigenvector out of that?" + }, + { + "text": "That's, for these two lambdas, this matrix is singular." + }, + { + "text": "I guess the eigenvector, two by two ought to be easy." + }, + { + "text": "So if I know that this matrix is singular, then it seems to me the eigenvector has to be lambda and one, because that multiplication will give me the zero." + }, + { + "text": "And this multiplication gives me, better give me also zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk23.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..df816eb800ce767b1475c279a24ad976bb45a785 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Do you see why it does?" + }, + { + "text": "This is the minus lambda squared plus lambda plus one." + }, + { + "text": "It's the thing that's zero, because these lambdas are special." + }, + { + "text": "There's the eigenvector." + }, + { + "text": "X1 is lambda one, one, and x2 is lambda two, one." + }, + { + "text": "I did that as a little trick that was available in the two by two case." + }, + { + "text": "So now I finally have to, oh, I have to take the initial, u0." + }, + { + "text": "So to complete this example entirely, I have to say, OK, what was u0?" + }, + { + "text": "u0 was f1 f0." + }, + { + "text": "So u0, the starting vector, is f1 f0, and those were one and zero." + }, + { + "text": "So I have to use that vector, so I have to look for, from multiple of the first eigenvector and the second, to produce u0, the one zero vector." + }, + { + "text": "This is what will find c1 and c2, and then I'm done." + }, + { + "text": "So let me, instead of in the last five seconds grinding out a formula, let me repeat the idea." + }, + { + "text": "That really, it's the idea that's central." + }, + { + "text": "When things are evolving in time, let me come back to this board, because the ideas are here." + }, + { + "text": "When things are evolving in time by a first-order system, starting from an original u0, the key is, find the eigenvalues and eigenvectors of A." + }, + { + "text": "That will tell, those eigenvectors, the eigenvalues will already tell you what's happening." + }, + { + "text": "Is the solution blowing up?" + }, + { + "text": "Is it going to zero?" + }, + { + "text": "What's it doing?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk24.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..40301cb90760e2172baa94d536cbc13288d4c31f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk24.json @@ -0,0 +1,20 @@ +[ + { + "text": "And then, to find out exactly a formula, you have to take your u0 and write it as a combination of eigenvectors and then follow each eigenvector separately." + }, + { + "text": "And that's really what this formula, the formula for, that's what the formula for A to the k is doing." + }, + { + "text": "So remember that formula for A to the k is S, lambda to the k S inverse." + }, + { + "text": "OK. That's, that's difference equations, and you just have to, so the homework will give some examples different from Fibonacci to follow through." + }, + { + "text": "And next time will be differential equations." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk3.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..9bf1bb852baadc1da7837e14180c0c2951a30882 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I mentioned at the end of last time, and I'll say again, that there's a small number of matrices for, that don't have n independent eigenvectors." + }, + { + "text": "So I've got to discuss that, that technical point." + }, + { + "text": "But the great, the most matrices that we see have n, n independent eigenvectors and we can diagonalize." + }, + { + "text": "This is diagonalization." + }, + { + "text": "I could also write it, and I often will, the other way round." + }, + { + "text": "If I multiply on the right by s inverse, if I took this equation at the top and multiplied on the right by s inverse, I could, I would have A left here." + }, + { + "text": "Now s inverse is coming from the right." + }, + { + "text": "So can you keep those two straight?" + }, + { + "text": "A multiplies its eigenvectors." + }, + { + "text": "That's how I keep them straight." + }, + { + "text": "So A multiplies s. A multiplies s. And then this s inverse makes the whole thing diagonal." + }, + { + "text": "And this is another way of saying the same thing, putting the s's on the other side of the equation, A is s lambda s inverse." + }, + { + "text": "So that's the, that's the new factorization." + }, + { + "text": "That's the replacement for L U from elimination or Q R from Gram-Schmidt." + }, + { + "text": "And notice that the matrix, so it's, it's a matrix times a diagonal matrix times the inverse of the first one." + }, + { + "text": "It's, that's the combination that we'll see throughout this chapter." + }, + { + "text": "This, this, combination with an s and an s inverse." + }, + { + "text": "OK. Can I just begin to use that?" + }, + { + "text": "For example, what about A squared?" + }, + { + "text": "What are the eigenvalues and eigenvectors of A squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk4.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c687b6948acad76de8781cb82d3eb069c9da514e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's a straightforward question with a, with a absolutely clean answer." + }, + { + "text": "So let me, let me consider A squared." + }, + { + "text": "So I look, I start with Ax equal lambda x." + }, + { + "text": "And I'm headed for A squared." + }, + { + "text": "So let me multiply both sides by A." + }, + { + "text": "That's one way to get A squared on the left." + }, + { + "text": "So if, I should write these ifs in here." + }, + { + "text": "If Ax equals lambda x, then I multiply by A." + }, + { + "text": "So I get A squared x equals, well, I'm multiplying by A, so that's lambda Ax." + }, + { + "text": "That lambda was a number, so I just put it on the left." + }, + { + "text": "And what do I, tell me how to make that look better." + }, + { + "text": "What have I got here?" + }, + { + "text": "For, if, if A has the eigenvalue lambda and eigenvector x, what's up with A squared?" + }, + { + "text": "A squared x, I just multiply by A, but now for Ax, I'm going to substitute lambda x, so I've got lambda squared x." + }, + { + "text": "So from that simple calculation, I, my conclusion is that the eigenvalues of A squared are lambda squared." + }, + { + "text": "And the eigenvectors, I always think about both of those." + }, + { + "text": "What can I say about the eigenvalues?" + }, + { + "text": "They're squared." + }, + { + "text": "What can I say about the eigenvectors?" + }, + { + "text": "They're the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk5.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5bf15e20707c156c8ae71c9c7acea41a9d9d8e46 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same x as in, as for A." + }, + { + "text": "Now, let me see that also from this formula." + }, + { + "text": "How can I see what A squared is looking like from this formula?" + }, + { + "text": "So let me, that, that was one way to do it." + }, + { + "text": "Let me do it by just taking A squared from that." + }, + { + "text": "A squared is S lambda S inverse, that's A, times S lambda S inverse, that's A, which is?" + }, + { + "text": "This is the beauty of eigenvalues, eigenvectors, having that S inverse and S is the identity, so I've got S lambda squared S inverse." + }, + { + "text": "Yes." + }, + { + "text": "You see what that's telling me?" + }, + { + "text": "It's, it's telling me the same thing that I just learned here, but in the, in, in a matrix form." + }, + { + "text": "It's telling me that the S is the same, the eigenvectors are the same, but the eigenvalues are squared, because this is, what's lambda squared, that's still diagonal, it's got little lambda one squared, lambda two squared, down to lambda n squared, on that diagonal, those are the eigenvalues, as we just learned, of A squared." + }, + { + "text": "OK." + }, + { + "text": "So, somehow those eigenvalues and eigenvectors are really giving you a way to, to, to, to see what's going on inside a matrix." + }, + { + "text": "Now, of course, I can continue that for, to the k-th power." + }, + { + "text": "A to the k-th power." + }, + { + "text": "If I multiply, if I have k of these together, do you see how S inverse S will keep cancelling?" + }, + { + "text": "In the, in the inside, I'll have the S outside, at the far left, and lambda will be in there k times and S inverse." + }, + { + "text": "So what's that telling me?" + }, + { + "text": "That's telling me that the eigenvalues of A, of A to the k-th power are the k-th powers." + }, + { + "text": "The eigenvalues of A cubed are the cubes of the eigenvalues of A, and the eigenvectors are the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk6.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..c18dddbe798022f7e68278ac002a3f5fe6ed249e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "The same." + }, + { + "text": "OK." + }, + { + "text": "In other words, eigenvalues and eigenvectors give a great way to understand the powers of a matrix." + }, + { + "text": "If I take the square of a matrix or the hundredth power of a matrix, the pivots are all over the place." + }, + { + "text": "L U, if I multiply L U times L U times L U times L U a hundred times, I've got a hundred L U's." + }, + { + "text": "I can't do anything with them." + }, + { + "text": "But when I multiply S lambda S inverse by itself, when I look at the eigenvector picture a hundred times, I get a hundred or ninety-nine of these guys cancelling out inside, and I get A to the hundredth is S lambda to the hundredth S inverse." + }, + { + "text": "I mean, eigenvalues tell you about powers of a matrix in a way that we had no, no way to approach previously." + }, + { + "text": "For example, when does, when do the powers of a matrix go to zero?" + }, + { + "text": "I would call that matrix stable, maybe." + }, + { + "text": "So, so, so I could write down a, a theorem." + }, + { + "text": "I'll, I'll write it as a theorem, just to use that word to emphasize that here I'm getting this great fact from this eigenvalue picture." + }, + { + "text": "OK. A to the k approaches zero as k goes, as k gets bigger." + }, + { + "text": "If what?" + }, + { + "text": "What's the, how can I tell for a matrix A if its powers go to zero?" + }, + { + "text": "What, what's somewhere inside that matrix is that information." + }, + { + "text": "That information is not present in the pivots." + }, + { + "text": "It's present in the eigenvalues." + }, + { + "text": "What do I need for the, to know that if I take higher and higher powers of A that this matrix gets smaller and smaller?" + }, + { + "text": "Well, S and S inverse are not moving." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk7.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..b84a5c854a5542758e8a0107e1ff043205fe3bdb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's this guy that has to get small, and that's easy to, easy to understand." + }, + { + "text": "The requirement is all eigenvalues, so what is the requirement?" + }, + { + "text": "The eigenvalues have to be less than one." + }, + { + "text": "Now, I have to write that absolute value, because those eigenvalues could be negative, they could be complex numbers." + }, + { + "text": "So I'm taking the absolute value if all of those are below one." + }, + { + "text": "That's, in fact, we practically see why." + }, + { + "text": "Let me just say that I, that I, I'm operating on one assumption here, and I got to keep remembering that that assumption is still present." + }, + { + "text": "That assumption was that I had a full set of, of n independent eigenvectors." + }, + { + "text": "If I don't have that, then I, I, then this approach is not working." + }, + { + "text": "So, so again, a pure eigenvalue approach, eigenvector approach, needs n independent eigenvectors." + }, + { + "text": "If we don't have n independent eigenvectors, we can't diagonalize the matrix." + }, + { + "text": "We can't get to a diagonal matrix." + }, + { + "text": "This, this, this diagonalization is only possible if S inverse makes sense." + }, + { + "text": "OK. Can I, can I follow up on that point now?" + }, + { + "text": "So, so you see why, what we get and, and why we want it, because we get information about the powers of a matrix just immediately from the eigenvalues." + }, + { + "text": "OK, now let me follow up on this, business of which matrices are diagonalizable." + }, + { + "text": "Sorry about that long word." + }, + { + "text": "So a matrix is, is sure to, so here's, here's the main point." + }, + { + "text": "A is sure to be, to have n independent eigenvectors and, and B, now here comes that word, diagonalizable, if, if, so we, we, we might as well get the, the nice case out in the open." + }, + { + "text": "The nice case is when, if all the lambdas are different." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk8.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f06dcec8ffa0ee1bf19440e4ab2194db33ab353b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means, that means no repeated eigenvalues." + }, + { + "text": "OK. That's the nice case." + }, + { + "text": "If, if my matrix and most matrix, if I do a random matrix in MATLAB and compute its eigenvalues, so if I computed, if I took I of rand of ten ten, gave, gave that MATLAB command, the, we'd get a random ten by ten matrix, we would get a list of its ten eigenvalues and they would be different." + }, + { + "text": "They would be distinct, is the best word." + }, + { + "text": "I would have a random matrix will have ten distinct, a ten by ten matrix will have ten distinct eigenvalues, and if it does, the eigenvectors are automatically independent." + }, + { + "text": "So that's a nice fact." + }, + { + "text": "I can, I'll refer you to the text for the proof." + }, + { + "text": "That, that A is sure to have n independent eigenvectors if the eigenvalues are different." + }, + { + "text": "If, if all the, if all eigenvalues are different." + }, + { + "text": "It's just, if some lambdas are repeated, then I have to look more closely." + }, + { + "text": "If an eigenvalue is repeated, I have to look, I have to count, I have to check." + }, + { + "text": "Has it got, say it's repeated three times." + }, + { + "text": "So what's a possibility for, so, so here's, here's the repeated possibility." + }, + { + "text": "And, and let me emphasize the conclusion." + }, + { + "text": "That if I have repeated eigenvalues, I may or may not, I may or may not have, have n independent eigenvectors." + }, + { + "text": "I might." + }, + { + "text": "I, I, you know, this isn't a completely negative case." + }, + { + "text": "The identity matrix." + }, + { + "text": "Well, suppose I take the ten by ten identity matrix." + }, + { + "text": "What are the eigenvalues of that matrix?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk9.json b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..87d2a2ae5773036cf11800e2f1962908986a0dad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/13r9QY6cmjc_9_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So just, just take the easiest matrix, the identity." + }, + { + "text": "If I look for its eigenvalues, they're all ones." + }, + { + "text": "So that eigenvalue one is repeated ten times." + }, + { + "text": "But there's no shortage of eigenvectors for the identity matrix." + }, + { + "text": "In fact, every vector is an eigenvector." + }, + { + "text": "So I can take ten independent vectors." + }, + { + "text": "Oh, well, what happens to everything if, if, if A is the identity matrix, let's just think that one through in our head." + }, + { + "text": "If A is the identity matrix, then it's got plenty of eigenvectors." + }, + { + "text": "I choose ten independent vectors, they're the columns of S, and, and what do I get from S inverse A S?" + }, + { + "text": "I get I again, right?" + }, + { + "text": "If A is the identity, and of course, that's the correct lambda." + }, + { + "text": "The, the matrix was already diagonal." + }, + { + "text": "So if the matrix is already diagonal, then the, the lambda is the same as the matrix." + }, + { + "text": "A diagonal matrix has got its eigenvalues sitting right there in front of you." + }, + { + "text": "Now if it's triangular, the eigenvalues are still sitting there, but so let's, let's take a case where, it's triangular." + }, + { + "text": "Suppose A is like, two, one, two, zero." + }, + { + "text": "So there's a case that's going to be trouble." + }, + { + "text": "There's a case that's going to be trouble." + }, + { + "text": "First of all, what are the eigen- I mean, we just, like now you, if we start with a matrix, the first thing we do practically without thinking is compute the eigenvalues and eigenvectors." + }, + { + "text": "OK." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk0.json b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..aedaade07875409e9cf5122cf6d7f3b8888695fa --- /dev/null +++ b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "Today we're going to continue with integration." + }, + { + "text": "And we get to do probably the most important thing of this entire course, which is appropriately named." + }, + { + "text": "It's called the Fundamental Theorem of Calculus." + }, + { + "text": "And we'll be abbreviating it FTC, and occasionally I'll put in a 1 here, because there will be two versions of it." + }, + { + "text": "But this is the one that you'll be using the most in this class." + }, + { + "text": "The Fundamental Theorem of Calculus says the following." + }, + { + "text": "It says that if f' is equal to f, so f' of x is equal to f of x, is a capital F and a little f, then the integral from a to b of f of x is equal to f of b minus f of a." + }, + { + "text": "That's it." + }, + { + "text": "That's the whole theorem." + }, + { + "text": "And you may recognize it." + }, + { + "text": "Before we had the notation that f was the antiderivative." + }, + { + "text": "That is, capital F was the integral of f of x." + }, + { + "text": "We wrote it this way." + }, + { + "text": "This is the indefinite integral." + }, + { + "text": "And now we're putting in definite values." + }, + { + "text": "And we have a connection between the two uses of the integral sign." + }, + { + "text": "But with the definite values, we get real numbers out instead of a function." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk1.json b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..cdc9b02e5ed9198b4eaf9cb420528344fc94f3db --- /dev/null +++ b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "Or a function up to a constant." + }, + { + "text": "So this is it." + }, + { + "text": "This is the formula." + }, + { + "text": "And it's usually also written with another notation." + }, + { + "text": "So I want to introduce that notation to you as well." + }, + { + "text": "So there's a new notation here." + }, + { + "text": "Which you'll find very convenient." + }, + { + "text": "Because we don't always have to give a letter f to the functions involved." + }, + { + "text": "So it's an abbreviation." + }, + { + "text": "For right now, there'll be a lot of f's." + }, + { + "text": "But anyway." + }, + { + "text": "So here's the abbreviation." + }, + { + "text": "Whenever I have a difference between a function at two values, I also can write this as f of x with an a down here and a b up there." + }, + { + "text": "So that's the notation that we use." + }, + { + "text": "And you can also, for emphasis, and this sometimes turns out to be important when there's more than one variable floating around in the problem, to specify that the variable is x." + }, + { + "text": "So this is the same thing as x equals a and x equals b." + }, + { + "text": "It indicates where you want to plug in, what you want to plug in." + }, + { + "text": "And now you take the top value minus the bottom value." + }, + { + "text": "So f of b minus f of a." + }, + { + "text": "This is just a notation." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk10.json b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..d13588e3003ee33ffd9fab0d161dc27df0f54526 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now, because the fundamental theorem is so important, and so useful, and so convenient, we just assume that it be true in this case as well." + }, + { + "text": "So we insist that this is going to be minus cos x, evaluated at 0 and 2pi." + }, + { + "text": "With the difference." + }, + { + "text": "Now, when we carry out that difference, what we get here is minus cos 2pi minus minus cos 0." + }, + { + "text": "Which is negative 1 minus negative 1, which is 0." + }, + { + "text": "And the interpretation of this is the following." + }, + { + "text": "Here's our double hump." + }, + { + "text": "Here's pi and here's 2pi." + }, + { + "text": "And all that's happening is that the geometric interpretation that we had before of the area under the curve has to be taken with a grain of salt." + }, + { + "text": "In other words, I lied to you before when I said that the definite integral was the area under the curve." + }, + { + "text": "It's not." + }, + { + "text": "The definite integral is the area under the curve when it's above the curve." + }, + { + "text": "And it counts negatively when it's below the curve." + }, + { + "text": "So yesterday, my geometric interpretation was incomplete and really just a plain lie." + }, + { + "text": "So the true geometric interpretation of the definite integral is plus the area above the x-axis minus the area below the x-axis." + }, + { + "text": "As in the picture." + }, + { + "text": "I'm just writing it down in words, but you should think of it visually also." + }, + { + "text": "So that's the setup here." + }, + { + "text": "And now we have the complete definition of integrals." + }, + { + "text": "And I need to list for you a bunch of their properties and how we deal with integrals." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk11.json b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..fc1f06986d61b7e3f7c3514d7d4d19f5e33cea3d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Are there any questions before we go on?" + }, + { + "text": "Yeah." + }, + { + "text": "STUDENT 1 Just wanted to talk about, wouldn't this be an absolute value of the velocity function to get the sense?" + }, + { + "text": "PROFESSOR ERIC GRIMSON So the question was, wouldn't the absolute value of the velocity function be involved?" + }, + { + "text": "The answer is yes." + }, + { + "text": "That is, that's one question that you could ask." + }, + { + "text": "One question you could ask is, what's the total distance traveled?" + }, + { + "text": "And in that case, you would keep track of the absolute value of the velocity, as you said." + }, + { + "text": "Whether it's positive or negative." + }, + { + "text": "And then you get the total length of this curve here." + }, + { + "text": "That's, however, not what the definite integral measures." + }, + { + "text": "It measures the net distance traveled." + }, + { + "text": "So it's another thing." + }, + { + "text": "In other words, we can do that." + }, + { + "text": "We now have the tools to do both." + }, + { + "text": "We could also, so if you like, the total distance is equal to the integral of this, from a to b." + }, + { + "text": "But the net distance is the one without the absolute value signs." + }, + { + "text": "So that's correct." + }, + { + "text": "Other questions?" + }, + { + "text": "Alright, so now let's talk about properties of integrals." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk12.json b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..ee301e05c5131728f2c06d01255dfc8f2b520e30 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so the properties of integrals that I want to mention to you are these." + }, + { + "text": "The first one is, doesn't bear too much comment." + }, + { + "text": "If you take the cumulative integral of a sum, you're just going to get the sum of the separate integrals here." + }, + { + "text": "And I won't say much about that." + }, + { + "text": "That's because the integral is a sum." + }, + { + "text": "Incidentally, you know, this strange symbol here, there's actually a reason for it historically." + }, + { + "text": "If you go back to old books, you'll see that it actually looks a little bit more like an S. This capital sigma is a sum." + }, + { + "text": "S for sum." + }, + { + "text": "Because everybody in those days knew Latin and Greek." + }, + { + "text": "And this one is also an S. But gradually it was such an important S that they made it bigger." + }, + { + "text": "And then they stretched it out and made it a little thinner, because it didn't fit into one typesetting space." + }, + { + "text": "And so just for typesetting reason, it got stretched and got a little bit skinny." + }, + { + "text": "Anyway, so it's really an S. And in fact, in French, they call it sum." + }, + { + "text": "Even though we call it integral." + }, + { + "text": "So it's a sum." + }, + { + "text": "So it's consistent with sums in this way." + }, + { + "text": "And similarly, we can factor constants out of sums." + }, + { + "text": "So if you have an integral like this, the constant factors out." + }, + { + "text": "But definitely don't try to get a function out of this." + }, + { + "text": "That won't happen." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk13.json b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..16eac683b6747a656bba511d6d26d20bb78f9ef2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "In other words, c has to be a constant." + }, + { + "text": "Doesn't depend on x." + }, + { + "text": "All right." + }, + { + "text": "The third property." + }, + { + "text": "What do I want to call the third property here?" + }, + { + "text": "I have a sort of a preliminary property, yes." + }, + { + "text": "Here." + }, + { + "text": "Which is the following." + }, + { + "text": "And I'll draw a picture of it." + }, + { + "text": "Suppose you have three points along the line." + }, + { + "text": "So then I'm going to draw a picture of that." + }, + { + "text": "And I'm going to use the interpretation above the curve." + }, + { + "text": "Even though that's not the whole thing." + }, + { + "text": "So here's a, here's b, and here's c. And you can see that the area of this piece, of the first two pieces here, is, when added together, gives you the area of the whole." + }, + { + "text": "And that's the rule that I'd like to tell you." + }, + { + "text": "So if you integrate from a to b, and you add to that the integral from b to c, you'll get the integral from a to c. This is going to be just a little preliminary, because the rule is a little better than this." + }, + { + "text": "But I will explain that in a minute." + }, + { + "text": "The fourth rule is a very simple one." + }, + { + "text": "Which is that the integral from a to a of f x dx is equal to 0." + }, + { + "text": "That you can see very obviously, because there's no area, no horizontal movement there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk14.json b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..05ac822c67f78951448242ed646be38917cef800 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "The rectangle is infinitely thin." + }, + { + "text": "And there's nothing there." + }, + { + "text": "So this is the case." + }, + { + "text": "You can also interpret it as f of a minus f of a." + }, + { + "text": "So that's also consistent with our interpretation, in terms of the fundamental theorem of calculus." + }, + { + "text": "And it's perfectly reasonable that this is the case." + }, + { + "text": "Now, the fifth property is a definition." + }, + { + "text": "It's not really a property." + }, + { + "text": "But it's very important." + }, + { + "text": "The integral from a to b of f of x dx is equal to minus the integral from b to a of f of x dx." + }, + { + "text": "Now, really, the right-hand side here is an undefined quantity so far." + }, + { + "text": "We never said that you could ever do this where the a is less than the b." + }, + { + "text": "Because this is working backwards here." + }, + { + "text": "But we just have a convention that that's the definition." + }, + { + "text": "Whenever we write down this number, it's the same as minus what that number is." + }, + { + "text": "And the reason for all of these is, again, that we want them to be consistent with the fundamental theorem of calculus." + }, + { + "text": "Which is the thing that makes all of this work." + }, + { + "text": "So if you notice, the left-hand side here is f of b minus f of a, capital F. The antiderivative of little f. On the other hand, the other side is minus, and if we just ignore that we say these are letters, if we were a machine we didn't know which one was bigger than which." + }, + { + "text": "We just plugged them in." + }, + { + "text": "We would get here f of a minus f of b over here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk15.json b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..dbebef3944bd2aaf89417dea7c7fc0ea7bdb383f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "And to make these two things equal, what we want is to put that minus sign in." + }, + { + "text": "Now it's consistent." + }, + { + "text": "So again, these rules are set up so that everything is consistent." + }, + { + "text": "And now I want to improve on Rule 3 here." + }, + { + "text": "And point out to you, so let me just go back to Rule 3 for a second, that now that we can evaluate integrals regardless of the order, we don't have to have a less than b, b less than c in order to make sense out of this." + }, + { + "text": "We actually have the possibility of considering integrals where the a's and the b's and the c's are in any order you want." + }, + { + "text": "And in fact, with this definition, with this definition 5, 3 works no matter what the numbers are." + }, + { + "text": "So this is much more convenient." + }, + { + "text": "We don't, this is not necessary." + }, + { + "text": "It just works using Convention 5." + }, + { + "text": "OK, with 5." + }, + { + "text": "Again, before I go on, let me emphasize, we really want to respect the sign of this velocity." + }, + { + "text": "We really want the net change in the position." + }, + { + "text": "And we don't want this absolute value here." + }, + { + "text": "Because otherwise, all of our formulas are going to mess up." + }, + { + "text": "We won't always be able to check." + }, + { + "text": "Sometimes you have letters rather than actual numbers here, and you won't know whether a is bigger than b." + }, + { + "text": "So you'll want to know that these formulas work and are consistent in all situations." + }, + { + "text": "OK, I'm going to trade these again in order to preserve the ordering 1 through 5." + }, + { + "text": "And now I have a sixth property that I want to talk about." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk16.json b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..ab51088f9e4bebbc9c56b9ad394b06ba3c122182 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "This one is called estimation." + }, + { + "text": "And it says the following." + }, + { + "text": "If f of x is less than or equal to g of x, then the integral from a to b of f of x dx is less than or equal to the integral from a to b of g of x dx." + }, + { + "text": "Now, this one says that if I'm going more slowly than you, then you go farther than I do." + }, + { + "text": "That's all it's saying." + }, + { + "text": "For this one, you'd better have a is less than b." + }, + { + "text": "You need it." + }, + { + "text": "Because we flip the signs when we flip the order of a and b." + }, + { + "text": "So this one, it's essential that the lower limit be smaller than the upper limit." + }, + { + "text": "But let me just emphasize, because we're dealing with the generalities of this, actually if one of these is negative and the other one is negative, then it also works." + }, + { + "text": "This one ends up being, if f is more negative than g, then this added up thing is more negative than that one." + }, + { + "text": "Again, under the assumption that a is less than b." + }, + { + "text": "So as I wrote it, it's in full generality." + }, + { + "text": "All right, let's illustrate this one." + }, + { + "text": "And then we have one more property to learn after that." + }, + { + "text": "So let me give you an example of estimation." + }, + { + "text": "The example is the same as one that I already gave you." + }, + { + "text": "But this time, because we have the tool of integration, we can just follow our noses and it works." + }, + { + "text": "I'll start with the inequality." + }, + { + "text": "So I'm trying to illustrate estimation, so I want to start with an inequality which is what the hypothesis is here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk17.json b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..3c4d99704c104ab597ac05fe0d0bdb35d4e7bc52 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'm going to integrate the inequality to get this conclusion and see what conclusion it is." + }, + { + "text": "The inequality that I want to take is that e to the x is greater than or equal to 1 for x greater than or equal to 0." + }, + { + "text": "That's going to be our starting place." + }, + { + "text": "And now I'm going to integrate it, that is, I'm going to use estimation to see what that gives." + }, + { + "text": "Well, I'm going to integrate, say, from 0 to b. I can't integrate below 0 because it's only true above 0." + }, + { + "text": "This is e to the x dx greater than or equal to the integral from 0 to b of 1 dx." + }, + { + "text": "Let's work out what each of these is." + }, + { + "text": "The first one, e to the x dx, is the antiderivative is e to the x evaluated at 0 and b." + }, + { + "text": "So that's e to the b minus e to the 0, which is e to the b minus 1." + }, + { + "text": "The other one, you're supposed to be able to get by the rectangle law." + }, + { + "text": "This is one rectangle of base b and height 1." + }, + { + "text": "So the answer is b." + }, + { + "text": "Or you can do it by antiderivatives, but it's b." + }, + { + "text": "That means that our inequality says, if I just combine these two things together, that e to the b minus 1 is greater than or equal to b." + }, + { + "text": "And that's the same thing as e to the b is greater than or equal to 1 plus b." + }, + { + "text": "Again, this only works for b greater than or equal to 0." + }, + { + "text": "Notice that if b were negative, this would be a well-defined quantity." + }, + { + "text": "But this estimation would be false." + }, + { + "text": "We need that the b be bigger than 0 in order for this to make sense." + }, + { + "text": "So this was used." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk18.json b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..898ba9d4188263e684f29b35313a5dab3c45b2cc --- /dev/null +++ b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And that's a good thing, because this inequality is suspect." + }, + { + "text": "Actually, it turns out to be true when b is negative." + }, + { + "text": "We certainly didn't prove it." + }, + { + "text": "I'm going to just repeat this process." + }, + { + "text": "So let's repeat it." + }, + { + "text": "Starting from the inequality, the conclusion." + }, + { + "text": "Which is sitting right here." + }, + { + "text": "But I'll write it in the form e to the x greater than or equal to 1 plus x, for x greater than or equal to 0." + }, + { + "text": "And now if I integrate this one, I get the integral from 0 to b, e to the x dx is greater than or equal to the integral from 0 to b, 1 plus x dx." + }, + { + "text": "And I remind you that we've already calculated this one." + }, + { + "text": "This is e to the b-1." + }, + { + "text": "And the other one is not hard to calculate." + }, + { + "text": "The antiderivative is x plus x squared over 2." + }, + { + "text": "We're evaluating that at 0 and b." + }, + { + "text": "So that comes out to be b plus b squared over 2." + }, + { + "text": "And so our conclusion is that the left side, which is e to the b-1, is greater than or equal to b plus b squared over 2, and this is for b greater than or equal to 0." + }, + { + "text": "And that's the same thing as e to the b greater than or equal to 1 plus b plus b squared over 2." + }, + { + "text": "This one actually is false for b negative." + }, + { + "text": "So that's something that you have to be careful with the b positives here." + }, + { + "text": "All right, so you can keep on going with this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk19.json b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..045398bbd655a1da3f7914eb3bf951ae3e27d6ff --- /dev/null +++ b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you didn't have to think, and you'll produce a very interesting polynomial, which is a good approximation to e to the b." + }, + { + "text": "All right, so that's it for the basic properties." + }, + { + "text": "Now there's one tricky property that I need to tell you about." + }, + { + "text": "It's not that tricky, but it's a little tricky." + }, + { + "text": "And this is change of variables." + }, + { + "text": "Change of variables in integration, we've actually already done." + }, + { + "text": "We called that, the last time we talked about it, we called it substitution." + }, + { + "text": "And the idea here, if you may remember, was that if you're faced with an integral like this, you can change it to, if you put in u is equal to u of x, and you have a du, which is equal to u' of x dx, then you can change the integral." + }, + { + "text": "As follows, this is the same as g of u of x, u' of x dx." + }, + { + "text": "This was the general procedure for substitution." + }, + { + "text": "What's new today is that we're going to put in the limits." + }, + { + "text": "If you have a limit here, u1, and a limit here, u2, you want to know what the relationship is between the limits here and the limits when you change variables to the new variables." + }, + { + "text": "And it's the simplest possible thing." + }, + { + "text": "Namely, the two limits over here are in the same relationship as u of x is to this symbol u here." + }, + { + "text": "In other words, u1 is equal to u of x1." + }, + { + "text": "And u2 is equal to u of x2." + }, + { + "text": "That's what works." + }, + { + "text": "Now, there's only one danger here, there's one subtlety." + }, + { + "text": "Which is, this only works if u' does not change sign." + }, + { + "text": "I've been worrying a little bit about going backwards and forwards, and I allowed myself to reverse and do all kinds of stuff with these integrals." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk2.json b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..450c5c2459c0b0028ffd1407e81c7584e8bc389f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "And in that notation, of course, the theorem can be written as with this set of symbols here, equally well." + }, + { + "text": "So let's just give a couple of examples." + }, + { + "text": "The first example is the one that we did last time very laboriously." + }, + { + "text": "If you take the function F of x, which happens to be x cubed over 3, then if you differentiate it, you get, well, the factor of 3 cancels." + }, + { + "text": "So you get x squared." + }, + { + "text": "That's the derivative." + }, + { + "text": "And so by the fundamental theorem, so this implies by the fundamental theorem that the integral from, say, a to b of x squared dx, that's the derivative here." + }, + { + "text": "This is the function we're going to use as f of x here." + }, + { + "text": "Is equal to this function here, f of b minus f of a." + }, + { + "text": "That's here, this function here." + }, + { + "text": "So that's f of b minus f of a." + }, + { + "text": "And that's equal to b cubed over 3 minus a cubed over 3." + }, + { + "text": "Now, in this new notation, we usually don't have all these letters." + }, + { + "text": "All we write is the following." + }, + { + "text": "We write the integral from a to b." + }, + { + "text": "And I'm going to do the case of 0 to b, because that was the one that we actually did last time." + }, + { + "text": "So I'm going to set a equals 0 here." + }, + { + "text": "And then the problem we were faced last time was this." + }, + { + "text": "And as I said, we did it very laboriously." + }, + { + "text": "But now you can see that we can do it in 10 seconds, let's say." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk20.json b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..ffec796890e1e8392efcf938754c711a1cf3df1a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "So we're sort of free to do it." + }, + { + "text": "Well, this is one case where you want to avoid it." + }, + { + "text": "Just don't do it." + }, + { + "text": "It is possible, actually, to make sense out of it." + }, + { + "text": "But it's also possible to get yourself infinitely confused." + }, + { + "text": "So just make sure that, now it's OK if u' is always negative, you're always going one way." + }, + { + "text": "It's OK if u' is always positive, you're always going the other way." + }, + { + "text": "But if you mix them up, you'll get yourself mixed up." + }, + { + "text": "Let me give you an example." + }, + { + "text": "The example will be maybe close to what we did last time, did when we first did substitution, I mean." + }, + { + "text": "Let's see." + }, + { + "text": "So the integral from 1 to 2, this time I'll put indefinite limits, of x squared plus, sorry, maybe I call this x cubed, x cubed plus 2, let's say, I don't know, to the 5th power, x squared dx." + }, + { + "text": "So this is an example of an integral that we would have tried to handle by substitution before." + }, + { + "text": "And the substitution we would have used is u equals x cubed plus 2." + }, + { + "text": "And that's exactly what we're going to do here." + }, + { + "text": "But we're just going to also take into account the limits." + }, + { + "text": "The first step, as in any substitution or change of variables, is this." + }, + { + "text": "And so we can fill in the things that we would have done previously, which is that this is the integral, and this is u to the 5th power." + }, + { + "text": "And then, because this is 3x squared, we see that this is 3, sorry, let's write it the other way." + }, + { + "text": "1 3rd du is equal to x squared dx." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk21.json b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..c5d43bae73646d99959cd9bd5553c4492878df5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what I'm going to plug in for this factor here." + }, + { + "text": "So here's 1 3rd du, which replaces that." + }, + { + "text": "But now there's the extra feature." + }, + { + "text": "The extra feature is the limits." + }, + { + "text": "So here, really in disguise, because now this is incredibly important, this is one of the reasons why we use this notation dx and du." + }, + { + "text": "We want to remind ourselves which variable is involved in the integration." + }, + { + "text": "And especially if you're the one naming the variables, you may get mixed up in this respect." + }, + { + "text": "So you must know which variable is varying between 1 and 2." + }, + { + "text": "And the answer is it's x is the one that's varying between 1 and 2." + }, + { + "text": "So in disguise, even though I didn't write it, it was contained in this little symbol here." + }, + { + "text": "This reminded us which variable." + }, + { + "text": "You'll find this amazingly important when you get to multivariable calculus." + }, + { + "text": "When there are many variables floating around." + }, + { + "text": "So this is an incredibly important distinction to make." + }, + { + "text": "So now over here, we have a limit." + }, + { + "text": "But it's of course supposed to be with respect to u now." + }, + { + "text": "So we need to calculate what those corresponding limits are." + }, + { + "text": "And indeed, it's just, I plug in here u1 is going to be equal to what I plug in for x equals 1." + }, + { + "text": "That's going to be 1 cubed plus 2, which is 3." + }, + { + "text": "And then u2 is 2 cubed plus 2, which is equal to 10." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk22.json b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..06fba8956381664006717a06146196480368da38 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "8 plus 2 is 10." + }, + { + "text": "So this is the integral from 3 to 10 of u5 1 3rd du." + }, + { + "text": "And now I can finish the problem." + }, + { + "text": "This is 1 18th u6, from 3 to 10." + }, + { + "text": "And this is where the most common mistake occurs in substitutions of this type." + }, + { + "text": "Which is that if you ignore this, and you plug in these 1 and 2 here, you think, oh, I should just be putting it at 1 and 2." + }, + { + "text": "But actually, it should be the u value that we're interested in, and the lower limit is u equals 3, and u equals 10 is the upper limit." + }, + { + "text": "So those are suppressed here." + }, + { + "text": "But those are the ones that we want." + }, + { + "text": "And so here we go." + }, + { + "text": "It's 1 18th times some ridiculous number, which I won't calculate, 10 to the 6th minus 3 to the 6th." + }, + { + "text": "Yes, question." + }, + { + "text": "STUDENT 1 STUDENT 1 STUDENT 1 STUDENT 1 STUDENT 1 STUDENT 1 STUDENT 1 STUDENT 1 STUDENT 1 STUDENT 1 So if you want to do things where you're worrying about the sign change, the right strategy is what you suggested works, and in fact I'm going to do an example right now on this subject." + }, + { + "text": "But the right strategy is to break it up into pieces where u' has one sign or the other." + }, + { + "text": "Let me show you an example." + }, + { + "text": "But where things go wrong." + }, + { + "text": "And I'll tell you how to handle it, roughly." + }, + { + "text": "So here's our warning." + }, + { + "text": "Suppose you're integrating from minus 1 to 1 x squared dx." + }, + { + "text": "Here's an example." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk23.json b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..314d44c50adf51492c82d57ba2bb9fa80060462e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you had the temptation to plug in u is equal to x squared." + }, + { + "text": "Now, of course, we know how to integrate this." + }, + { + "text": "But let's just pretend we were stubborn and wanted to use substitution." + }, + { + "text": "Then we have du is equal to 2x dx." + }, + { + "text": "And now, if I try to make the correspondence, notice that the limits are u1 is negative 1 squared." + }, + { + "text": "That's the bottom limit." + }, + { + "text": "And u2 is the upper limit." + }, + { + "text": "That's 1 squared." + }, + { + "text": "That's also equal to 1." + }, + { + "text": "Both limits are 1." + }, + { + "text": "So this is going from 1 to 1." + }, + { + "text": "And no matter what it is, we know it's going to be 0." + }, + { + "text": "But we know this is not 0." + }, + { + "text": "This is the integral of a positive quantity." + }, + { + "text": "And it's the area under a curve." + }, + { + "text": "It's going to be a positive area." + }, + { + "text": "So this is a positive quantity." + }, + { + "text": "It can't be 0." + }, + { + "text": "If you actually plug it in, it looks equally strange." + }, + { + "text": "You put in here this u, and then, so that would be for the u squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk24.json b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..19f4ef23fc9ed2f4028c10de28ec6eb1b13f0821 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then to plug in for dx, you would write dx is equal to 1 over 2x du." + }, + { + "text": "And then you might write that as this." + }, + { + "text": "And so what I should put in here is this quantity here." + }, + { + "text": "Which is a perfectly OK integral." + }, + { + "text": "And it has a value, I mean, it's what it is." + }, + { + "text": "It's 0." + }, + { + "text": "So of course, this is not true." + }, + { + "text": "And the reason is that u was equal to x squared." + }, + { + "text": "And u' of x was equal to 2x." + }, + { + "text": "Which was positive for x positive, and negative for x negative." + }, + { + "text": "And this was the sign change which causes us trouble." + }, + { + "text": "If we break it up into its two halves, then it'll be OK. And you'll be able to use this." + }, + { + "text": "Now, there was a mistake." + }, + { + "text": "And this was essentially what you were saying." + }, + { + "text": "That is, it's possible to see this happening as you're doing it, if you're very careful." + }, + { + "text": "There's a mistake in this process." + }, + { + "text": "And the mistake is, in the transition, this is a mistake here." + }, + { + "text": "Maybe I haven't used any red yet today." + }, + { + "text": "So I get to use some red here." + }, + { + "text": "Oh boy." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk25.json b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..3977e1624680272f0b1638a263756d39c8ef0d86 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk25.json @@ -0,0 +1,41 @@ +[ + { + "text": "This is not true here." + }, + { + "text": "This step here." + }, + { + "text": "So why isn't it true?" + }, + { + "text": "It's not true for the standard reason." + }, + { + "text": "Which is that really, x is equal to plus or minus square root of u." + }, + { + "text": "And if you stick to one side or the other, you'll have a coherent formula for it." + }, + { + "text": "One of them will be the plus and one of them will be the minus." + }, + { + "text": "And it will work out when you separate it into its pieces." + }, + { + "text": "So you could do that." + }, + { + "text": "But this is a can of worms." + }, + { + "text": "So I avoid this." + }, + { + "text": "And just do it in a place where the inverse is well-defined." + }, + { + "text": "And where the function either moves steadily up or steadily down." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk3.json b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..5bc68a47e26d6af4448db3a238a9cb357bee1119 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, the antiderivative of this is x cubed over 3." + }, + { + "text": "I'm going to evaluate it at 0 and at b and subtract." + }, + { + "text": "So that's going to be b cubed over 3 minus 0 cubed over 3." + }, + { + "text": "Which, of course, is b cubed over 3." + }, + { + "text": "And that's the end." + }, + { + "text": "That's the answer." + }, + { + "text": "So this is a lot faster than yesterday." + }, + { + "text": "I hope you'll agree." + }, + { + "text": "And we can dispense with those elaborate computations." + }, + { + "text": "Although there's a conceptual reason, a very important one, for understanding the procedure that we went through." + }, + { + "text": "Because eventually you're going to be using integrals and these quick ways of doing things to solve problems like finding the volumes of pyramids." + }, + { + "text": "In other words, we're going to reverse the process." + }, + { + "text": "And so we need to understand the connection between the two." + }, + { + "text": "I'm going to give a couple more examples." + }, + { + "text": "And then we'll go on." + }, + { + "text": "So the second example would be one that would be quite difficult to do by this Riemann sum technique that we described yesterday." + }, + { + "text": "Although it is possible." + }, + { + "text": "It uses much higher mathematics to do it." + }, + { + "text": "And that is the area under one hump of the sine curve." + }, + { + "text": "Sine x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk4.json b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..d5844f70fea8c7f2bd4ebe592eccb468733e64ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me just draw a picture of that." + }, + { + "text": "The curve goes like this." + }, + { + "text": "And we're talking about this area here." + }, + { + "text": "It starts out at 0, it goes to pi." + }, + { + "text": "That's one hump." + }, + { + "text": "And so the answer is, it's the integral from 0 to pi of sin x, dx." + }, + { + "text": "And so I need to take the antiderivative of that." + }, + { + "text": "And that's minus cos x." + }, + { + "text": "That's the thing whose derivative is sin x." + }, + { + "text": "Evaluating it at 0 and pi." + }, + { + "text": "Now, let's do this one carefully." + }, + { + "text": "Because this is where I see a lot of arithmetic mistakes." + }, + { + "text": "Even though this is the easy part of the problem." + }, + { + "text": "It's hard to pay attention and plug in the right numbers." + }, + { + "text": "And so let's just pay very close attention." + }, + { + "text": "I'm plugging in pi." + }, + { + "text": "That's minus cos pi." + }, + { + "text": "That's the first term." + }, + { + "text": "And then I'm subtracting the value at the bottom." + }, + { + "text": "Which is minus cos 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk5.json b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..8b64c96eafcf2d6bc6d8e12da5296996038cd485 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "There are already five opportunities for you to make a transcription error or an arithmetic mistake in what I just did." + }, + { + "text": "And I've seen all five of them." + }, + { + "text": "So the next one is that this is minus, minus 1." + }, + { + "text": "Minus negative 1, if you like." + }, + { + "text": "And then this is minus, and here's another negative 1." + }, + { + "text": "So all together we have 2." + }, + { + "text": "So that's it." + }, + { + "text": "That's the area." + }, + { + "text": "This area, which is hard to guess, this is area 2." + }, + { + "text": "The third example is maybe superfluous, but I'm going to say it anyway." + }, + { + "text": "We can take the integral, say, from 0 to 1 of x to the 100th power." + }, + { + "text": "Any power now is within our power." + }, + { + "text": "So let's do it here." + }, + { + "text": "So here we have the antiderivative is x to the 101 divided by 101." + }, + { + "text": "Evaluated at 0 and 1." + }, + { + "text": "And that is just 1 over 101." + }, + { + "text": "So that's the fundamental theorem." + }, + { + "text": "Now, this, as I say, harnesses a lot of what we've already learned all about antiderivatives." + }, + { + "text": "Now, I want to give you an intuitive interpretation." + }, + { + "text": "So let's try that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk6.json b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..25cb0926cf5c57eb478a921c6a1c9a858e7dce97 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll talk about a proof of the fundamental theorem a little bit later." + }, + { + "text": "It's not actually that hard." + }, + { + "text": "But we'll give an intuitive reason, interpretation, if you like, of the fundamental theorem." + }, + { + "text": "So this is going to be one which is not related to area, but rather to time and distance." + }, + { + "text": "So we'll consider x of t is your position at time t. And then x' of t, which is the rate of change of x with respect to t, is going to be what we know as your speed." + }, + { + "text": "And then what the theorem is telling us is the following." + }, + { + "text": "It's telling us the integral from a to b of v of t dt, so reading the relationship, is equal to x of b minus x of a." + }, + { + "text": "And so this is some kind of cumulative sum of your velocities." + }, + { + "text": "So let's interpret the right-hand side first." + }, + { + "text": "This is the distance traveled." + }, + { + "text": "And it's also what you would read on your odometer." + }, + { + "text": "From the beginning to the end of the trip." + }, + { + "text": "That's what you would read on your odometer." + }, + { + "text": "Whereas this is what you would read on your speedometer." + }, + { + "text": "So this is the interpretation." + }, + { + "text": "Now, I want to just go one step further into this interpretation to make the connection with the Riemann sums that we had yesterday." + }, + { + "text": "Because those are very complicated to understand." + }, + { + "text": "And I want you to understand them viscerally on several different levels." + }, + { + "text": "Because that's how you'll understand integration better." + }, + { + "text": "The first thing that I want to imagine, so we're going to do a thought experiment now, which is that you are extremely obsessive." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk7.json b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..68a8a9325c28e92ced083920eb23bdef5e6f6069 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you're driving your car from time a to time b." + }, + { + "text": "Place q to place r, whatever." + }, + { + "text": "And you check your speedometer every second." + }, + { + "text": "So you've read your speedometer in the i-th second." + }, + { + "text": "And you've read that you're going at this speed." + }, + { + "text": "Now, how far do you go in that second?" + }, + { + "text": "Well, the answer is, you go this speed times the time interval, which in this case we're imagining is 1 second." + }, + { + "text": "So this is how far you went." + }, + { + "text": "This is the time interval." + }, + { + "text": "And this is the distance traveled in second number i, in the i-th second." + }, + { + "text": "The distance traveled in the i-th second." + }, + { + "text": "That's the total distance you traveled." + }, + { + "text": "Now, what happens if you go the whole distance?" + }, + { + "text": "Well, you travel the sum of all these distances." + }, + { + "text": "So it's some massive sum where n is some ridiculous number of seconds." + }, + { + "text": "3600 seconds or something like that, whatever it is." + }, + { + "text": "And that's going to turn out to be very similar to what you would read on your odometer." + }, + { + "text": "Because during that second, you didn't change velocity very much." + }, + { + "text": "So the approximation, the speed at one time that you spotted it, is very similar to the speed during the whole second." + }, + { + "text": "It doesn't change that much." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk8.json b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..2482b04ff0278d77d456b2f0c2b8760300968a23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "So this is a pretty good approximation to how far you traveled." + }, + { + "text": "And so the sum is a very realistic approximation to the entire integral, which is denoted this way." + }, + { + "text": "Which, by the fundamental theorem, is exactly how far you traveled." + }, + { + "text": "So this is x sub b minus x sub a." + }, + { + "text": "Exactly." + }, + { + "text": "The other one is approximate." + }, + { + "text": "Again, this is called a Riemann sum." + }, + { + "text": "Alright, so that's the intro to the fundamental theorem." + }, + { + "text": "And now what I need to do is extend it just a bit." + }, + { + "text": "And the way I'm going to extend it is the following." + }, + { + "text": "I'm going to do it on this example first." + }, + { + "text": "And then we'll do it more formally." + }, + { + "text": "So here's this example where we went someplace." + }, + { + "text": "But now I just want to draw you an additional picture here." + }, + { + "text": "Imagine I start here, and I go over to there, and then I come back." + }, + { + "text": "And maybe even I do a round trip." + }, + { + "text": "I come back to the same place." + }, + { + "text": "Well, if I come back to the same place, then the position is unchanged from the beginning to the end." + }, + { + "text": "In other words, the difference is 0." + }, + { + "text": "And the velocity, technically rather than the speed, it's the speed to the right and the speed to the left maybe are the same." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk9.json b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..03cd57e53da1550c3979830a62077d9274f95e57 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/1RLctDS2hUQ_0_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "But one of them is going in the positive direction, one of them is going in the negative direction, and they cancel each other." + }, + { + "text": "So if you have this kind of situation, we want that to be reflected." + }, + { + "text": "We like that interpretation." + }, + { + "text": "And we want to preserve it even in the case when the function v is negative." + }, + { + "text": "And so I'm going to now extend our notion of integration." + }, + { + "text": "So we'll extend integration to the case f negative." + }, + { + "text": "Or positive." + }, + { + "text": "In other words, it could be any sign." + }, + { + "text": "Actually, there's no change." + }, + { + "text": "The formulas are all the same." + }, + { + "text": "We just, if this v is going to be positive, we write in a positive number." + }, + { + "text": "If it's going to be negative, we write in a negative number." + }, + { + "text": "And we just leave it alone." + }, + { + "text": "And the real, so here's, let me carry out an example." + }, + { + "text": "And show you how it works." + }, + { + "text": "I'll carry out the example on this blackboard up here of the sine function." + }, + { + "text": "But we're going to try two humps." + }, + { + "text": "We're going to try the first hump and the one that goes underneath there." + }, + { + "text": "So our example here is going to be the integral from 0 to 2pi." + }, + { + "text": "Of sin x dx." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk0.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..65c23c5cab5e2c4f1a8f872964a31edc5dd21493 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "Talking about tests, and to be fair, we spend most of our time talking about new jargon that we're using." + }, + { + "text": "But the main goal is to take a binary decision, yes and no." + }, + { + "text": "So just so that we're clear and we make sure that we all speak the same language, let me just remind you what the key words are for tests." + }, + { + "text": "So the first thing is that we split theta in theta 0 and theta 1." + }, + { + "text": "Both are included in theta, and they're disjoint." + }, + { + "text": "OK." + }, + { + "text": "So I have my set of possible parameters." + }, + { + "text": "And then I have theta 0 is here, theta 1 is here, and there might be something that I leave out." + }, + { + "text": "And so what we're doing is we have two hypotheses." + }, + { + "text": "So here's our hypothesis testing problem." + }, + { + "text": "And it's h0 theta belongs to theta 0 versus h1 theta belongs to theta 1." + }, + { + "text": "This guy was called the null, and this guy was called the alternative." + }, + { + "text": "And why we give them special names is because we saw that they have an asymmetric role." + }, + { + "text": "The null represents the status quo, and data is here to bring evidence against this guy." + }, + { + "text": "And we can really never conclude that h0 is true because all we could conclude is that h1 is not true or may not be true." + }, + { + "text": "So that was the first thing." + }, + { + "text": "The second thing was the hypothesis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk1.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3b72e60009f76e8f81d23cb396a309bf7d70b355 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "The third thing is what is a test?" + }, + { + "text": "Well, psi, it's a statistic." + }, + { + "text": "And it takes the data, and it maps it into 0 or 1." + }, + { + "text": "And I didn't really mention it, but there's something such as called randomized tests, which is, well, if it cannot really make a decision, they might as well flip a coin." + }, + { + "text": "That tends to be biased, but that's really, I mean, think about it in practice." + }, + { + "text": "You probably don't want to make decisions based on flipping a coin." + }, + { + "text": "And so what people typically do, this is happening typically at one specific value." + }, + { + "text": "So rather than flipping a coin for this very specific value, what people typically do is they say, OK, I'm going to side with h0 because that's the most conservative choice I can make." + }, + { + "text": "So in a way, they think of flipping this coin, but always falling on heads." + }, + { + "text": "So associated to this test was something called, well, the rejection region." + }, + { + "text": "And r psi, which is just the set of data, x1, xn, such that psi of x1, xn is equal to 1." + }, + { + "text": "So that means we rejected 0 when the test is 1, and those are the set of data points that actually are going to lead me to reject the test." + }, + { + "text": "OK. Then the things that were actually slightly a little more important and really peculiar to test, specific to test, were the type 1 and type 2 error." + }, + { + "text": "So the type 1 error arises when, so type 1 error is when you reject whereas h0 is correct." + }, + { + "text": "And the type 2 error is the opposite." + }, + { + "text": "So it's failed to reject whereas h1 is correct." + }, + { + "text": "h is correct." + }, + { + "text": "So those are the two types of errors you can make, and we quantify their probability of type 1 error." + }, + { + "text": "So alpha psi is the probability." + }, + { + "text": "So that's the probability of type 1 error." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk10.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c19b0d21dee98686b07f25081871711f112710fa --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "And that means at the boundary, since the status quo is h0, I'm always going to go for h0 if I don't have any evidence, which means that what's going to pay is the type 2 error that's going to basically pay this." + }, + { + "text": "OK?" + }, + { + "text": "Any other question?" + }, + { + "text": "All right, so let's move on." + }, + { + "text": "So did we do this?" + }, + { + "text": "No, I think we stopped here, right?" + }, + { + "text": "I didn't cover that part." + }, + { + "text": "So as I said, in this paradigm, we're going to actually fix this guy to be something." + }, + { + "text": "And this thing is actually called the level of the test." + }, + { + "text": "I'm sorry, this is again more words." + }, + { + "text": "Actually, good news is that we split it into two lectures." + }, + { + "text": "So we have, what is a test?" + }, + { + "text": "What is a hypothesis?" + }, + { + "text": "What is the null?" + }, + { + "text": "What is the alternative?" + }, + { + "text": "What is the type 1 error?" + }, + { + "text": "What is the type 2 error?" + }, + { + "text": "And now, I'm telling you there's another thing." + }, + { + "text": "So we defined the power, which was some sort of a lower bound on the, or it's 1 minus the upper bound on the type 2 error, basically." + }, + { + "text": "And so it's alternative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk11.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..815ec78c1b831dd92a2b3f1d68a91dd8df86f618 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "So the power is the smallest probability of rejecting when you're in the null." + }, + { + "text": "And it's alternative when you're in theta 1, right?" + }, + { + "text": "So that's my power." + }, + { + "text": "I looked here, and I looked at the smallest value." + }, + { + "text": "And I can look at this side and say, well, what is the largest probability that I make a type 1 error?" + }, + { + "text": "Again, this largest probability is the level of the test." + }, + { + "text": "OK, so this is alpha equal, by definition, to the maximum for theta and theta 0 of alpha psi of theta." + }, + { + "text": "So here, I just put the level itself." + }, + { + "text": "As you can see here, it essentially says that if I'm of level 5%, I'm also of level 10%." + }, + { + "text": "I'm also of level 15%." + }, + { + "text": "So here, it's really an upper bound." + }, + { + "text": "Whatever you guys want to take, this is what it is." + }, + { + "text": "But as we said, if this number is 4.5%, you're losing in your type 2 error." + }, + { + "text": "So if you're allowed to have, if this maximum here is 4.5%, and FDA told you you can go to 5%, you're losing in your type 2 error." + }, + { + "text": "So you actually want to make sure that this is the 5% that's given to you." + }, + { + "text": "So the way it works is that you give me the alpha." + }, + { + "text": "Then I'm going to go back, pick c that depends on alpha here, so that this thing is actually equal to 5%." + }, + { + "text": "And so, of course, in many instances, we do not know the probability." + }, + { + "text": "We do not know how to compute the probability of type 1 error." + }, + { + "text": "This is a maximum value for the probability of type 1 error." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk12.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..4bd3834b631a0a7c734e2b14c2fe32eaf6f601e6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "We don't know how to compute it." + }, + { + "text": "I mean, it might be a very complicated random variable." + }, + { + "text": "Maybe it's a weird binomial." + }, + { + "text": "We could compute it, but it would be painful." + }, + { + "text": "But what we know how to compute is its asymptotic value, which is because of the central limit theorem, convergence and distribution tells me that the probability of type 1 error is basically going towards the probability that some Gaussian is in some region." + }, + { + "text": "And so we're going to compute not the level itself, but the asymptotic level." + }, + { + "text": "So again, that's basically the limit as n goes to infinity of alpha psi of theta." + }, + { + "text": "And then I'm going to make the max here." + }, + { + "text": "OK?" + }, + { + "text": "So how am I going to compute this?" + }, + { + "text": "Well, if I take a test that has rejection region of the form Tn, because it depends on the data, right?" + }, + { + "text": "That's Tn of x1, xn, my observations, larger than some number c. OK?" + }, + { + "text": "Of course, I can almost always write tests like that, except that sometimes there's going to be an absolute value, which essentially means I'm going away from some value." + }, + { + "text": "Maybe actually I'm less than something, but I can always put a negative sign in front of everything." + }, + { + "text": "So this is not without much of generality, right?" + }, + { + "text": "So this includes something that looks like something is larger than the constant, right?" + }, + { + "text": "So that means, which is equivalent to, well, let me write it as Tq." + }, + { + "text": "OK, because then that means that, so that's Tn." + }, + { + "text": "But this actually encompasses the fact that Qn is larger than c, or Qn is less than c, then minus c. So that includes this guy." + }, + { + "text": "That also includes Qn less than c, because this is equivalent to Qn is larger than minus c. Minus Qn is, and so that's going to be my Tn." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk13.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..d0fc40d7fea49cc51a82242971122ccb04ee2caf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I can actually encode several type of things, OK?" + }, + { + "text": "Rejection regions that, so here in this case, I have a rejection region that looks like this, or a rejection region that looks like this, or a rejection region that looks like this." + }, + { + "text": "OK, and here I don't really represent it for the whole data, but maybe for the average, for example, or the normalized average." + }, + { + "text": "OK, so if I write this, then, yeah." + }, + { + "text": "And in this case, this Tn that shows up is called test statistic." + }, + { + "text": "I mean, this is sort of a, I mean, this is not like set in stone." + }, + { + "text": "Here, for example, Q could be the test statistics." + }, + { + "text": "It doesn't have to be minus Q itself that's the test statistic, right?" + }, + { + "text": "So what is the test statistic?" + }, + { + "text": "Well, it's what you're going to build from your data and then compare to some fixed value, right?" + }, + { + "text": "So in the example we had here, what is our test statistic?" + }, + { + "text": "Well, it's this guy, right?" + }, + { + "text": "This was our test statistic." + }, + { + "text": "And is this thing a statistic?" + }, + { + "text": "What are the criteria for a statistic?" + }, + { + "text": "What is a statistic?" + }, + { + "text": "I know you know the answer." + }, + { + "text": "AUDIENCE MEMBER 2." + }, + { + "text": "Is it a measurable function?" + }, + { + "text": "PROFESSOR PHILIPPE RIGOLLET." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk14.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..deb918611779af5e70f1e976f45cfc296740fc0a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "Yeah, it's a measurable function of the data that does not depend on the parameter." + }, + { + "text": "Is this guy a statistic?" + }, + { + "text": "AUDIENCE MEMBER 3." + }, + { + "text": "Yes, he is." + }, + { + "text": "PROFESSOR PHILIPPE RIGOLLET." + }, + { + "text": "Let's think again." + }, + { + "text": "When I implemented the test, what did I do?" + }, + { + "text": "I was able to compute my test." + }, + { + "text": "My test did not depend on some unknown parameter." + }, + { + "text": "How did we do it?" + }, + { + "text": "We just plugged in 0.5 here." + }, + { + "text": "Remember?" + }, + { + "text": "That was the value for which we computed it, because under h0, that was the value we're seeing." + }, + { + "text": "And if theta 0 is actually an entire set, I'm just going to take the value that's the closest to h1." + }, + { + "text": "We'll see that in a second." + }, + { + "text": "I mean, I did not guarantee that to you." + }, + { + "text": "But just taking the worst type 1 error and bounding it by alpha is equivalent to taking p and taking the value of p that's the closest to theta 1, which is completely intuitive." + }, + { + "text": "The worst type 1 error is going to be attained for the p that's the closest to the alternative." + }, + { + "text": "So even if the null is actually just an entire set, it's as if it was just the point that's the closest to the alternative." + }, + { + "text": "So now we can compute this, because there's no unknown parameters that shows up." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk15.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..0bc365016096bbbfd9f7a60ab9c2724dec760020 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "We replaced p by 0.5." + }, + { + "text": "And so that was our test statistic." + }, + { + "text": "So when you're building a test, you want to first build a test statistic and then see what threshold you should be getting." + }, + { + "text": "So now let's go back to our example where we have x1, xn." + }, + { + "text": "They're iid Bernoulli p. And I want to test if p is 1 half versus p not equal to 1 half, which as I said is what you want to do if you want to test if a coin is fair." + }, + { + "text": "And so here I'm going to build a test statistic." + }, + { + "text": "And we concluded last time that what do we want for this statistic?" + }, + { + "text": "We want it to have a distribution which under the null does not depend on the parameters, a distribution that I can actually compute quintiles of." + }, + { + "text": "So what we did is we said, well, if I look at the central limit theorem tells me that square root of n xn bar minus p divided by." + }, + { + "text": "So if I do central limit theorem plus Slutsky, for example, I'm going to have square root." + }, + { + "text": "And we've had this discussion whether we want to use Slutsky or not here." + }, + { + "text": "But let's assume we're taking Slutsky wherever we can." + }, + { + "text": "So this thing tells me that by the central limit theorem as n goes to infinity, this thing converges in distribution to some n 0, 1." + }, + { + "text": "Now as we said, this guy is not something we know." + }, + { + "text": "But under the null, we actually know it." + }, + { + "text": "And we can actually replace it by 1 half." + }, + { + "text": "So this thing holds under h0." + }, + { + "text": "When I write under h0, it means when this is the truth." + }, + { + "text": "So now I have something that converges to something that has no dependence on anything I don't know." + }, + { + "text": "And in particular, if you have any statistics textbook, which you don't because I didn't require one, you should be thankful because this thing costs $250." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk16.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..298b0fb997de98b972702f498d96cfa89d4e4b7d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "This thing's actually, if you look at the back, you actually have a table for a standard Gaussian." + }, + { + "text": "I could have anything else here." + }, + { + "text": "I could have an exponential distribution." + }, + { + "text": "I could have a, I don't know, a, well, we'll see the chi-square distribution in a minute." + }, + { + "text": "Any distribution from which you can actually see a table that somebody actually computed this thing for which you can actually draw the PDF and start computing whatever probability you want on them, then this is what you want to see at the right-hand side." + }, + { + "text": "This is any distribution." + }, + { + "text": "It's called pivotal." + }, + { + "text": "I think we've mentioned that before." + }, + { + "text": "Pivotal means it does not depend on anything that you don't know." + }, + { + "text": "And maybe it's easy to compute those things." + }, + { + "text": "Probably, typically, you need a computer to simulate them for you because computing probabilities for Gaussians is not an easy thing." + }, + { + "text": "We don't know how to solve those integrals exactly." + }, + { + "text": "We have to do it numerically." + }, + { + "text": "OK, so now I want to do this test." + }, + { + "text": "My test statistic will be declared to be what?" + }, + { + "text": "Well, I'm going to reject if what is larger than some number?" + }, + { + "text": "The absolute value of this guy." + }, + { + "text": "So my test statistic is going to be square root of n minus 0.5 divided by square root of xn bar 1 minus xn bar." + }, + { + "text": "That's my test statistic, absolute value of this guy, because I want to reject either when this guy is too large or when this guy is too small." + }, + { + "text": "I don't know ahead whether I'm going to see p larger than 1 half or less than 1 half." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk17.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..c16a8c6be2149a29434fcd2457ee0fdbf0606f2d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "So now I need to compute c such that the probability that tn is lower than c. So that's what?" + }, + { + "text": "That's the probability under p, which is unknown." + }, + { + "text": "I want this probability to be less than some level alpha asymptotically." + }, + { + "text": "So I want the limit of this guy to be less than alpha, and that's the level of my test." + }, + { + "text": "So that's the given level." + }, + { + "text": "So I want this thing to happen." + }, + { + "text": "Now what I know is that this limit, actually, I should say given asymptotic level." + }, + { + "text": "So what is this thing?" + }, + { + "text": "Well, OK, that's the probability that something that looks like under p. So under p, this guy, so what I know is that tn is square root of n minus xn bar minus 0.5 divided by square root of xn bar 1 minus xn bar exceeds." + }, + { + "text": "Is this true that as n goes to infinity, this probability is the same as the probability that the absolute value of a Gaussian exceeds c of a standard Gaussian?" + }, + { + "text": "Is this true?" + }, + { + "text": "Yeah, so you're saying that this, as n becomes large enough, this should be the probability that some absolute value of n0,1 exceeds c, right?" + }, + { + "text": "So I claim that this is not correct." + }, + { + "text": "Somebody tell me why." + }, + { + "text": "Even in the limit, it's not correct?" + }, + { + "text": "Even in the limit, it's not correct." + }, + { + "text": "OK." + }, + { + "text": "So what do you see?" + }, + { + "text": "It's because at the beginning, we picked the worst possible true parameter, 0.5, right?" + }, + { + "text": "So we don't actually know that this 0.5 is the least." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk18.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..21ff2eaef450e95222ef4c4c025a1ccb1a883204 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Exactly, right?" + }, + { + "text": "So we picked this 0.5 here, but this is for any p, right?" + }, + { + "text": "But what is the only p I can get?" + }, + { + "text": "So what I want is that this is true for all p in theta 0." + }, + { + "text": "But the only p that's in theta 0 is actually p is equal to 0.5." + }, + { + "text": "So yes, what you said was true, but it required to specify p to be equal to 0.5." + }, + { + "text": "So this, in general, is not true." + }, + { + "text": "But it happens to be true if p belongs to theta 0, which is strictly equivalent to p is equal to 0.5, right?" + }, + { + "text": "Theta 0 is really just this one point, 0.5." + }, + { + "text": "OK, so now this becomes true." + }, + { + "text": "And so what I need to do is to find c such that this guy is equal to what?" + }, + { + "text": "I mean, let's just follow, right?" + }, + { + "text": "So I want this to be less than alpha." + }, + { + "text": "But then we see that this was equal to this, which is equal to this." + }, + { + "text": "So all I want is that this guy is less than alpha." + }, + { + "text": "But we said we might as well just make it equal to alpha if you allow me to make it as big as I want, as long as it's less than alpha." + }, + { + "text": "So this is a true statement." + }, + { + "text": "But it's if under this condition, right?" + }, + { + "text": "So I'm going to set it equal to alpha." + }, + { + "text": "And then I'm going to try to solve for c. OK, so what I'm looking for is a c such that if I draw a standard Gaussian, so that's PDF of some n0,1, I want the probability that the absolute value of my Gaussian exceeding this guy." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk19.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..b610ab510e065f845cbac3e680352a281a5977db --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that means being either here or here." + }, + { + "text": "So that's minus c and c. I want the sum of those two things to be equal to alpha." + }, + { + "text": "So I want the sum of these areas to equal alpha." + }, + { + "text": "So by symmetry, each of them should be equal to alpha over 2." + }, + { + "text": "And so what I'm looking for is c such that the probability that my n0,1 exceeds c, which is just this area to the right now, equals alpha, which is equivalent to taking c, which is q equals alpha over 2." + }, + { + "text": "And that's q alpha over 2 by definition of q alpha over 2." + }, + { + "text": "That's just what q alpha over 2 is." + }, + { + "text": "And that's what the tables at the back of the book give you." + }, + { + "text": "Who has already seen a table for Gaussian probabilities?" + }, + { + "text": "All right." + }, + { + "text": "What it does is just a table." + }, + { + "text": "I mean, it's pretty ancient, right?" + }, + { + "text": "I mean, of course, you can actually ask Google to do it for you now." + }, + { + "text": "It's basically standard issue." + }, + { + "text": "But back in the day, they actually had to look at tables." + }, + { + "text": "And since the values alphas were pretty standard, the values alpha that people were requesting were typically 1%, 5%, 10%." + }, + { + "text": "All you could do is to compute these different values for different values of alpha." + }, + { + "text": "That was it." + }, + { + "text": "So that's really not much to give you." + }, + { + "text": "So for the Gaussian, I can tell you that alpha is equal to, if alpha is equal to 5%, then q alpha over 2, q 2.5% is equal to 1.96%." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk2.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..d35a9367292f43552ea9e2c936629f0062774757 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So psi is just the probability for theta that psi rejects, and that's defined for theta and theta 0." + }, + { + "text": "So for different values of theta 0, so h0 being correct means there exists a theta in theta 0 for which that actually is the right distribution." + }, + { + "text": "So for different values of theta, I might make different errors." + }, + { + "text": "So if you think, for example, about the coin example, if I'm testing if the coin is biased towards heads or biased towards tails, so if I'm testing whether p is larger than 1 half or less than 1 half, then when the true p, let's say h0 is larger than 1 half, when p is equal to 1, it's actually very difficult for me to make a mistake, because I only see heads." + }, + { + "text": "So when p is getting closer to 1 half, I'm going to start making more and more probability there." + }, + { + "text": "And so the type 2 error, so that's the probability of type 2, is denoted by beta psi." + }, + { + "text": "And it's the function that does the opposite, and this time is defined for theta and theta 0 and theta 1." + }, + { + "text": "And finally, we define something called the power pi of psi." + }, + { + "text": "And this time, this is actually a number." + }, + { + "text": "And so this number is equal to the maximum over theta and theta 0." + }, + { + "text": "I mean, that could be a supremum, but think of it as being a maximum of p theta of psi is equal, sorry, that's in 0." + }, + { + "text": "Give me one sec." + }, + { + "text": "No, that's the min." + }, + { + "text": "So this is not making a mistake." + }, + { + "text": "Theta 0 is in theta 1." + }, + { + "text": "So theta is in theta 1, and I conclude 1." + }, + { + "text": "So this is a good thing." + }, + { + "text": "I want this number to be large, and I'm looking at the worst house, what is the smallest value this number can be." + }, + { + "text": "So what I want to show you a little bit is a picture." + }, + { + "text": "So now I'm going to take theta, and think of it as being p. So I'm going to take p for some Bernoulli experiment." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk20.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..20ad1dac1f1c76cdb383bd9a41a5521bfc8e8f80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "So those are just fixed numbers that are functions of the Gaussian." + }, + { + "text": "All right, so everybody agrees?" + }, + { + "text": "We've done that before for our confidence intervals." + }, + { + "text": "And so now we know that if I actually plug in this guy to be q alpha over 2, then this limit is actually equal to alpha." + }, + { + "text": "And so now I've actually constrained this." + }, + { + "text": "So q alpha over 2 here is, for alpha equals 5%, as I said, is 1.96." + }, + { + "text": "So in the example 1, the number that we found was 3.54, I think, or something like that, 3.55 for t. So if we scroll back very quickly, 3.45." + }, + { + "text": "That was example 1." + }, + { + "text": "Example 2, negative 0.77." + }, + { + "text": "So if I look at t, n, in example 1, tn was just the absolute value of 3.45, which don't pull out your calculators, is equal to 3.45." + }, + { + "text": "Example 2, absolute value of negative 0.77 was equal to 0.77." + }, + { + "text": "And so all I need to check is, is this number larger or smaller than 1.96?" + }, + { + "text": "That's what my test ends up being." + }, + { + "text": "So in example 1, 3.45 being larger than 1.96, that means that I reject." + }, + { + "text": "Fairness of my coins in example 2, 0.77 being smaller than 1.96, what do I do?" + }, + { + "text": "I fail to reject." + }, + { + "text": "OK?" + }, + { + "text": "So here's a question." + }, + { + "text": "In example 1, for what level alpha would psi alpha, what is the?" + }, + { + "text": "So here, what's going to happen if I start decreasing my level?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk21.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..8a92eddc8e39673740ca195fad03c2d25a729273 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "When I decrease my level, I'm actually making this area smaller and smaller, which means that I push the c to the right." + }, + { + "text": "So now I'm asking, what is the smallest c I should pick so that now I actually do not reject h0?" + }, + { + "text": "What is the smallest c I should be taking?" + }, + { + "text": "Here." + }, + { + "text": "What is the smallest c?" + }, + { + "text": "So c here in the example I gave you for 5% was 1.96." + }, + { + "text": "What is the smallest c I should be taking so that now this inequality is reversed?" + }, + { + "text": "3.45." + }, + { + "text": "I ask only trivial questions." + }, + { + "text": "Don't be worried." + }, + { + "text": "So 3.45 is the smallest c that I'm actually willing to tolerate." + }, + { + "text": "So let's say this was my 5%." + }, + { + "text": "If this was 2.5, if alpha here, let's say in this picture, alpha is 5%, that means maybe I need to push here." + }, + { + "text": "And this number should be what?" + }, + { + "text": "So this is going to be 1.96." + }, + { + "text": "And this number here is going to be 3.45, clearly to scale." + }, + { + "text": "And so now what I want to ask you is, well, there's two ways I can understand this number 3.45." + }, + { + "text": "It is the number 3.45." + }, + { + "text": "But I can also try to understand, what is the area to the right of this guy?" + }, + { + "text": "And if I understand what the area to the right of this guy is, this is actually some alpha prime over 2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk22.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..7503edb72bbc4e9db22fe8e956729e7f3881d675 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "And that means that if I actually fix this level, alpha prime, that would be exactly the tipping point at which I would go from accepting to rejecting." + }, + { + "text": "So I know in terms of absolute thresholds, 3.45 is the trivial answer to the question." + }, + { + "text": "That's the tipping point, because I'm comparing a number to 3.45." + }, + { + "text": "But now if I try to map this back and understand what level would have been given me this particular tipping point, that's a number between 0 and 1." + }, + { + "text": "The smaller the number, the larger this number here, which means that the more evidence I have in my data against h0." + }, + { + "text": "And so this number is actually something called the p-value." + }, + { + "text": "And so same for example 2." + }, + { + "text": "There's the tipping point, alpha, at which I go from feeling to reject to rejecting." + }, + { + "text": "And that's exactly the number, the area under the curve, such that here I see 0.77." + }, + { + "text": "And this is this alpha prime prime over 2." + }, + { + "text": "And this number is clearly, alpha prime prime is clearly larger than 5%." + }, + { + "text": "So what's the advantage of thinking and mapping back these numbers?" + }, + { + "text": "Well, now I'm actually going to spit out some number which is between 0 and 1." + }, + { + "text": "And that should be the only scale you should have in mind." + }, + { + "text": "Remember we discussed that last time." + }, + { + "text": "Well, if I actually spit out a number which is 3.45, maybe you can try to think, is 3.45 a large number for a Gaussian?" + }, + { + "text": "That's a number." + }, + { + "text": "But if I had another random variable that was not Gaussian, maybe it was a double exponential, you would have to have another scale in your mind." + }, + { + "text": "Is 3.45 a large number for the large, so large that it's unlikely to come from a double exponential?" + }, + { + "text": "If I had a gamma distribution, I can think of any distribution." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk23.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..d0d0fdec57ad2cc7e2dadb707abb6df87bdbb70b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then that means for each distribution, you would have to have a scale in mind." + }, + { + "text": "So of course, you can have the Gaussian scale in mind." + }, + { + "text": "I mean, I have the Gaussian scale in mind." + }, + { + "text": "But then if I map it back into this number between 0 and 1, all the distributions play the same role." + }, + { + "text": "So whether I'm talking about if my limiting distribution is normal or exponential or gamma or whatever you want, for all these guys, I'm just going to map it into one number between 0 and 1." + }, + { + "text": "Small number means lots of evidence against h1." + }, + { + "text": "Large number means lots of evidence against h0." + }, + { + "text": "Small number means very few evidence against h0." + }, + { + "text": "And this is the only number you need to keep in mind." + }, + { + "text": "And the question is, am I willing to tolerate this number between 5%, 6% or maybe 10%, 12%?" + }, + { + "text": "And this is the only scale you have to have in mind." + }, + { + "text": "And this scale is the scale of p-values." + }, + { + "text": "So the p-value is the tipping point in terms of alpha." + }, + { + "text": "In words, I can make it formal, because tipping point, as far as I know, is not a mathematical term." + }, + { + "text": "So a p-value of a test is the smallest, potentially asymptotic level, if I talk about an asymptotic p-value." + }, + { + "text": "And that's what we do when we talk about central limit theorem, at which the test rejects h0." + }, + { + "text": "If I were to go any smaller, I would fail to reject." + }, + { + "text": "The smaller the level, the less likely it is for me to reject." + }, + { + "text": "And if I were to go any smaller, I would start failing to reject." + }, + { + "text": "And so it is a random number." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk24.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..70790440238c22e23b0b77fc5e658fdf89d62e44 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "It depends on what I actually observe." + }, + { + "text": "So here, of course, I instantiated those two numbers, 3.45 and 0.77, as realizations of random variables." + }, + { + "text": "But if you think of those as being the random numbers before I see my data, this was a random number." + }, + { + "text": "And therefore, the area under the curve to the right of it is also a random area." + }, + { + "text": "If this thing fluctuates, then the area under the curve fluctuates." + }, + { + "text": "And that's what the p-value is." + }, + { + "text": "That's what John Oliver talks about when he talks about p-hacking." + }, + { + "text": "And so we talked about this in the first lecture." + }, + { + "text": "So p-hacking is, how do I do?" + }, + { + "text": "Oh, if I'm a scientist, do I want to see a small p-value or a large p-value?" + }, + { + "text": "Small, right?" + }, + { + "text": "Scientists want to see small p-values, because small p-values equals rejecting, which equals discovery, which equals publication, which equals promotion." + }, + { + "text": "So that's what people want to see." + }, + { + "text": "So people are tempted to see small p-values." + }, + { + "text": "And what's called p-hacking is, well, find a way to cheat." + }, + { + "text": "Maybe look at your data, formulate your hypothesis in such a way that you will actually have a smaller p-value than you should have." + }, + { + "text": "So here, for example, there's one thing I did not insist on, because again, this is not a particular course in statistical thinking." + }, + { + "text": "But one thing that we implicitly did was set those theta 0 and theta 1 ahead of time." + }, + { + "text": "I fixed them, and I'm trying to test this." + }, + { + "text": "This is to be contrasted with the following approach." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk25.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..ae5989051a3c9ad74dd6e26eac906c8e26ce8535 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "I draw my data." + }, + { + "text": "So I draw." + }, + { + "text": "I run this experiment, which is probably going to get me a publication in Nature." + }, + { + "text": "I'm trying to test if a coin is fair." + }, + { + "text": "And I draw my data, and I see that there's 13 out of 30 of my observations that are heads." + }, + { + "text": "That means that from this data, it looks like p is less than 1 half." + }, + { + "text": "So if I look at this data and then decide that my alternative is not p not equal to 1 half, but rather p less than 1 half, that's p-hacking." + }, + { + "text": "I'm actually making my p-value strictly smaller by first looking at the data and then deciding what my alternative is going to be." + }, + { + "text": "And that's cheating, because all the things we did were assuming that this 0.5 or d alternative was actually a fix." + }, + { + "text": "Everything was deterministic." + }, + { + "text": "The only randomness came from the data." + }, + { + "text": "But if I start looking at the data and designing my experiment or my alternatives and null hypothesis based on the data, it's as if I started putting randomness all over the place." + }, + { + "text": "And then I cannot control it, because I don't know how it just intermingles with each other." + }, + { + "text": "All right." + }, + { + "text": "So that was for the John Oliver moment." + }, + { + "text": "So the p-value is nice." + }, + { + "text": "So maybe I mentioned that before." + }, + { + "text": "My wife works in market research." + }, + { + "text": "And maybe every two years, she seems to run into a statistician in the hallway." + }, + { + "text": "And she comes home and says, what is a p-value again?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk26.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..582b81ac1a78246b0f187a4c706af274ba689dbe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk26.json @@ -0,0 +1,62 @@ +[ + { + "text": "And for her, a p-value is just the number is in an Excel spreadsheet." + }, + { + "text": "And actually, small equals good and large equals bad." + }, + { + "text": "And that's all she needs to know at this point." + }, + { + "text": "Actually, they do the job for her." + }, + { + "text": "Small is green." + }, + { + "text": "Large is red." + }, + { + "text": "And so for her, a p-value is just green or red." + }, + { + "text": "But so what she's really implicitly doing with this color code is just applying the golden rule." + }, + { + "text": "What the statisticians do for her in the Excel spreadsheet is that they take the numbers for the p-values that are less than some fixed level." + }, + { + "text": "So depending on the field in which she works, so she works for pharmaceutical companies, so the p-values are typically compared." + }, + { + "text": "The tests are usually performed at level 1% rather than 5%." + }, + { + "text": "So 5% is maybe your gold standard if you're doing sociology or trying to, I don't know, release a new blueberry flavor for your toothpaste, like something that's not going to change the life of people." + }, + { + "text": "Maybe you're going to run at 5%." + }, + { + "text": "It's OK to make a mistake." + }, + { + "text": "People are just going to feel gross, but that's about it." + }, + { + "text": "Whereas here, if you have this p-value which is less than 1%, it might be more important for some drug discovery, for example." + }, + { + "text": "And so let's say you run at 1%." + }, + { + "text": "And so what they do in this Excel spreadsheet is that all the numbers that are below 1% show up in green, and all the numbers that are above 1% show up in red." + }, + { + "text": "And that's it." + }, + { + "text": "That's just applying the golden rule." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk27.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk27.json new file mode 100644 index 0000000000000000000000000000000000000000..6d2b3e73a1f2bfb3d007d43a22bc17095a5878f8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk27.json @@ -0,0 +1,62 @@ +[ + { + "text": "If the number is green, reject." + }, + { + "text": "If the number is red, fail to reject." + }, + { + "text": "OK?" + }, + { + "text": "Yeah?" + }, + { + "text": "So going back to the example of the previous prior example where you can achieve by looking at your data and then formulating, say, a theta 1 to be p less than 1%." + }, + { + "text": "Yeah." + }, + { + "text": "So how would you achieve your goal by changing the theta 1?" + }, + { + "text": "You mean by achieving my goal?" + }, + { + "text": "You mean letting ethics aside, right?" + }, + { + "text": "Yeah." + }, + { + "text": "You want to be published." + }, + { + "text": "So OK." + }, + { + "text": "So let me teach you how." + }, + { + "text": "Well, here, what do you do?" + }, + { + "text": "You want to, at the end of the day, a test is only telling you whether you found evidence in your data that H1 was more likely than H0, basically." + }, + { + "text": "How do you make H1 more likely?" + }, + { + "text": "Well, you just basically target H1 to be what the data is going to make it more likely to be." + }, + { + "text": "All right?" + }, + { + "text": "So if, for example, I say H1 can be on both sides, then my data is going to have to take into account fluctuations on both sides." + }, + { + "text": "And I'm going to lose a factor of 2 somewhere because things are not symmetric." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk28.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk28.json new file mode 100644 index 0000000000000000000000000000000000000000..b6a2e04f21d17d3f9d8f51277fef4b6bd544ea8c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk28.json @@ -0,0 +1,62 @@ +[ + { + "text": "Here is the ultimate way of making this work." + }, + { + "text": "I'm going back to my example of flipping coins." + }, + { + "text": "And now, so here, what I did is I said, oh, this number 0.43 is actually smaller than 0.5." + }, + { + "text": "So I'm just going to test whether I'm 0.5 or I'm less than 0.5." + }, + { + "text": "But here is something that I can promise you I did not make the computation will reject." + }, + { + "text": "OK, so here, this one actually, yeah, this one fails to reject, right?" + }, + { + "text": "So here is one that will certainly reject." + }, + { + "text": "H0 is 0.5. p is 0.5." + }, + { + "text": "H1, p is 0.43." + }, + { + "text": "OK?" + }, + { + "text": "Now, you can try." + }, + { + "text": "But I can promise you that your data will tell you that H1 is the right one." + }, + { + "text": "OK?" + }, + { + "text": "I mean, you can check very quickly that this is really extremely likely to happen, right?" + }, + { + "text": "And so actually, what am I?" + }, + { + "text": "No, actually, that's not true." + }, + { + "text": "OK. Because here, the test that I derive that's based on this kind of stuff, right?" + }, + { + "text": "Here, at some point, somewhere, under some layers, I assume that all our tests are going to have this form." + }, + { + "text": "But here, this is only when you're trying to test one region versus another region next to it, or one point versus a region around it, or something like this." + }, + { + "text": "Whereas for this guy, there's another test I could come up with, which is, what is the probability that I get 0.43?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk29.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk29.json new file mode 100644 index 0000000000000000000000000000000000000000..7c83fb4d5133113ff729308f195ed934ccaaacb9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk29.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what is the probability that I get 0.5?" + }, + { + "text": "Now, what I'm going to do is I'm going to just conclude it's whichever has the largest probability." + }, + { + "text": "Then maybe I'm going to have to make some adjustments so that the level is actually 5%." + }, + { + "text": "But I can make this happen." + }, + { + "text": "I can make the level be 5% and always conclude this guy, but I would have to use a different test." + }, + { + "text": "Now, the test that I described, again, those t and larger than c are built in to be tests that are sort of resilient to this kind of manipulations, because they're sort of oblivious towards what the alternative looks like." + }, + { + "text": "I mean, they're just saying it's either to the left or to the right, but whether it's a point or an entire half line doesn't matter." + }, + { + "text": "So if you try to look at your data and just put the data itself into your hypothesis testing problem, then you're failing the statistical principle." + }, + { + "text": "And that's what people are doing, right?" + }, + { + "text": "I mean, how can I check?" + }, + { + "text": "I mean, of course, here it's going to be pretty blatant if you publish a paper that looks like this." + }, + { + "text": "But there's ways to do it differently, right?" + }, + { + "text": "For example, one way to do it is to just do more." + }, + { + "text": "So typically, what people do is they do multiple hypothesis testing." + }, + { + "text": "They're doing 100 tests at a time." + }, + { + "text": "Then you have random fluctuations every time." + }, + { + "text": "And so they just pick the one that has the random fluctuations that go their way." + }, + { + "text": "I mean, sometimes it's going in your way, and sometimes it's going the opposite way." + }, + { + "text": "So you just pick the one that works for you." + }, + { + "text": "We'll talk about multiple hypothesis testing soon if you want to increase your publication counts." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk3.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..82298a0911f771c50c0c0e31234286bcbe2ed969 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "So p can range between 0 and 1, that's for sure." + }, + { + "text": "And what I'm going to try to test is whether p is less than 1 half or larger than 1 half." + }, + { + "text": "So this is going to be, let's say, theta 0, and this guy here is theta 1." + }, + { + "text": "Just trying to give you a picture of what those guys are." + }, + { + "text": "So I have my y-axis." + }, + { + "text": "Now I'm going to start drawing numbers, all these things, this function, this function, and this number are all numbers between 0 and 1." + }, + { + "text": "So now I'm claiming that when I move from left to right, what is my probability of rejecting going to do?" + }, + { + "text": "So what I'm going to plot is the probability under theta." + }, + { + "text": "The first thing I want to plot is the probability under theta that psi is equal to 1." + }, + { + "text": "And let's say psi, think of psi as being just this indicator that square root of n xn bar minus p over square root xn bar, 1 minus xn bar, is larger than some constant c for a properly chosen c. So what we choose is that c is in such a way that at 1 half, when we're testing for 1 half, what we wanted was this number to be equal to alpha, basically." + }, + { + "text": "So we fix this alpha number so that this guy, so if I want alpha of psi of theta less than alpha, given in advance, so think of it as being equal to, say, 5%." + }, + { + "text": "So I'm fixing this number, and I want this to be controlled for all theta and theta 0." + }, + { + "text": "So if you're going to give me this budget, well, I'm actually going to make it equal where I can." + }, + { + "text": "If you're telling me you can make it equal to alpha, we know that if I increase my type 1 error, I'm going to decrease my type 2 error." + }, + { + "text": "If I start putting everyone in jail, or if I start letting everyone go free, that's what we're discussing last time." + }, + { + "text": "So since we have this trade-off, and you're giving me a budget for one guy, I'm just going to max it out." + }, + { + "text": "And where am I going to max it out?" + }, + { + "text": "Exactly at 1 half at the boundary." + }, + { + "text": "So this is going to be 5%." + }, + { + "text": "So what I know is that since alpha of theta is less than alpha for all theta and theta 0, sorry, that's for theta 0, that's where alpha is defined." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk30.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk30.json new file mode 100644 index 0000000000000000000000000000000000000000..a8e80051fb683b419557b2b36ba8c95a3d50cf00 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk30.json @@ -0,0 +1,62 @@ +[ + { + "text": "There's actually papers." + }, + { + "text": "I think it was big news, there's some papers, I think it's psychology or psychometrics papers, that actually refuse to publish p-values now." + }, + { + "text": "All right, where were we?" + }, + { + "text": "OK, here's the golden rule." + }, + { + "text": "So one thing that I'd like to show is this thing, just so you know how you apply the golden rule and how you apply the standard test." + }, + { + "text": "So the standard paradigm is the following." + }, + { + "text": "You have a black box, which is your test." + }, + { + "text": "For my wife, this is the fourth floor of the building." + }, + { + "text": "That's where the statisticians sit." + }, + { + "text": "What she sends there is data, let's say x1, xn." + }, + { + "text": "And she says, well, this one is about toothpaste, so here's a level." + }, + { + "text": "Let's say 5%." + }, + { + "text": "What the fourth floor brings back is an answer, yes, no." + }, + { + "text": "Green, red, just an answer." + }, + { + "text": "So that's the standard testing." + }, + { + "text": "You just feed it the data and the level at which you want to perform the test, maybe asymptotic, and it spits out a yes, no answer." + }, + { + "text": "What p-value does, you just feed it the data itself." + }, + { + "text": "And what it spits out is the p-value." + }, + { + "text": "And now, it's just up to you." + }, + { + "text": "I mean, hopefully, your brain has the computational power of deciding whether a number is larger or smaller than 5% without having to call the statisticians for this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk31.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk31.json new file mode 100644 index 0000000000000000000000000000000000000000..9fb2296acde7c40202805ca4f7e73e4c07f68e6a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk31.json @@ -0,0 +1,62 @@ +[ + { + "text": "And that's what it does." + }, + { + "text": "So now, we're all on one scale." + }, + { + "text": "Now, if you actually, I see some of you nodding when I talk about p-hacking." + }, + { + "text": "So that means you've seen p-values." + }, + { + "text": "If you've seen more than 100 p-values in your life, you have an entire scale." + }, + { + "text": "A good p-value is less than 10 to the minus 4." + }, + { + "text": "That's the ultimate sweet spot." + }, + { + "text": "Actually, statistical software spit out an output which says less than 10 to the minus 4." + }, + { + "text": "But then, maybe you want a p-value." + }, + { + "text": "If I tell you my p-value was 4.65, then I will say you've been doing some p-hacking until you found a number that was below 5%." + }, + { + "text": "That's typically what people will do." + }, + { + "text": "But if you're doing the test, if you're saying, I published my result." + }, + { + "text": "My test at 5% said yes, that means that maybe your p-value was 4.99, or your p-value was 10 to the minus 4." + }, + { + "text": "I will never know." + }, + { + "text": "I will never know how much evidence you had against the null." + }, + { + "text": "But if you tell me what the p-value is, I can make my own decision." + }, + { + "text": "I don't have to tell me whether it's a yes." + }, + { + "text": "No, you tell me it's 4.99." + }, + { + "text": "I'm going to say, well, maybe yes, but I'm going to take it with a grain of salt." + }, + { + "text": "And so that's why p-values are good numbers to have in mind." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk32.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk32.json new file mode 100644 index 0000000000000000000000000000000000000000..96ed5fb80473cde620f1dcbaecbdda179310c37c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk32.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, I show it as if it was an old trick that you start mastering when you're 45 years old." + }, + { + "text": "No, it's just how small is the number between 0 and 1." + }, + { + "text": "That's really what you need to know." + }, + { + "text": "Maybe on the log scale, if it's 10 to the minus 1, 10 to the minus 2, 10 to the minus 3, et cetera, that's probably the extent of the mastery here." + }, + { + "text": "So this traditional standard paradigm that I showed is actually commonly referred to as the Neyman-Pearson paradigm." + }, + { + "text": "So here it says Neyman-Pearson's theory." + }, + { + "text": "So there's an entire theory that comes with it, but it's really a paradigm." + }, + { + "text": "It's a way of thinking about hypothesis testing that says, well, if I'm not going to be able to optimize both my type 1 and type 2 error, I'm actually going to lock in my type 1 error below some level and just minimize the type 2 error under this constraint." + }, + { + "text": "That's what the Neyman-Pearson paradigm is." + }, + { + "text": "And it sort of makes sense for hypothesis testing problems." + }, + { + "text": "If you were doing some other applications with multi-objective optimization, you would maybe come up with something different." + }, + { + "text": "For example, machine learning is not performing typically under Neyman-Pearson paradigm." + }, + { + "text": "So if you do spam filtering, you could say, well, I want to constrain the probability as much as I can of taking somebody's important emails and throwing them out as spam and, under this constraint, not send too much spam to that person." + }, + { + "text": "That sort of makes sense for spams." + }, + { + "text": "Now, if you're labeling cats versus dogs, it's probably not like you want to make sure that no more than 5% of the dogs are labeled cat." + }, + { + "text": "Because it doesn't matter." + }, + { + "text": "So what you typically do is you just sum up the two types of error you can make, and you minimize the sum without putting any more weight on one or the other." + }, + { + "text": "So here's an example where doing a binary decision, one or two of the errors you can make, you don't have to actually be like that." + }, + { + "text": "So this example here, I did not." + }, + { + "text": "The trivial test, psi is equal to 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk33.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk33.json new file mode 100644 index 0000000000000000000000000000000000000000..0c2da6bcc636025ed6d047d161fdfe68e3b68329 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk33.json @@ -0,0 +1,62 @@ +[ + { + "text": "What was it in the US trial court example?" + }, + { + "text": "What is psi equal to 0?" + }, + { + "text": "I was concluding all ways to the null." + }, + { + "text": "What was the null?" + }, + { + "text": "Innocent, right?" + }, + { + "text": "That's the status quo." + }, + { + "text": "So that means that this guy never rejects a 0." + }, + { + "text": "Everybody's going away free." + }, + { + "text": "So you're sure you're not actually going against the Constitution because alpha is 0%, which is certainly less than 5%." + }, + { + "text": "But the power, the fact that a lot of criminals go back outside in the free world is actually formulated in terms of low power, which in this case is actually 0." + }, + { + "text": "Again, the power is a number between 0 and 1." + }, + { + "text": "Close to 0, good." + }, + { + "text": "Close to 1, bad." + }, + { + "text": "Now, what is the definition of the p-value?" + }, + { + "text": "That's going to be something." + }, + { + "text": "Mouthful, right?" + }, + { + "text": "The definition of the p-value is a mouthful." + }, + { + "text": "It's really the tipping point." + }, + { + "text": "It is the smallest level at which blah, blah, blah, blah." + }, + { + "text": "It's complicated to remember it." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk34.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk34.json new file mode 100644 index 0000000000000000000000000000000000000000..074297c2186646a83b698c991607273c1d143e1c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk34.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, I think that by my sixth explanation, my wife, after saying, oh, so it's the probability of making an error, I said, yeah, that's the probability of making an error." + }, + { + "text": "Because of course, she can think probability of making an error, small, good, large, bad." + }, + { + "text": "So that's actually a good way to remember." + }, + { + "text": "I'm pretty sure that at least 50% of people using p-values out there think that the p-value is the probability of making an error." + }, + { + "text": "Now, for all matters of purposes, if your goal is to just threshold the p-value, this is OK to have this in mind." + }, + { + "text": "But when it comes, at least until December 22, I would recommend trying to actually memorize the right definition for the p-value." + }, + { + "text": "OK?" + }, + { + "text": "OK." + }, + { + "text": "So the idea, again, is fix the level and try to optimize the power." + }, + { + "text": "So we're going to try to compute some p-values from now on." + }, + { + "text": "How do you compute the p-value?" + }, + { + "text": "Well, you can actually see it from this picture over there." + }, + { + "text": "One thing I didn't show on this picture, here was my q alpha over 2 that had alpha here, alpha over 2 here, right?" + }, + { + "text": "That was my q alpha over 2." + }, + { + "text": "And I said, if tn is to the right of this guy, I'm going to reject." + }, + { + "text": "If tn is to the left of this guy, I'm going to fail to reject." + }, + { + "text": "OK?" + }, + { + "text": "Pictorially, you can actually represent the p-value." + }, + { + "text": "It's when I replace this guy by tn itself." + }, + { + "text": "Sorry, that's p-value over 2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk35.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk35.json new file mode 100644 index 0000000000000000000000000000000000000000..9f1a7b89f2d43b53944bbf516e37f98c7cf70618 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk35.json @@ -0,0 +1,62 @@ +[ + { + "text": "No, actually, that's p-value." + }, + { + "text": "So let me just keep it like that and put the absolute value here." + }, + { + "text": "OK?" + }, + { + "text": "So if you replace the role of q alpha over 2 by your test statistic, this is what the area under the curve is actually the p-value itself up to scaling, because of the symmetric thing." + }, + { + "text": "OK?" + }, + { + "text": "So there's a good way to see pictorially what the p-value is." + }, + { + "text": "It's just the probability that some Gaussians, which is the probability that some absolute value of n0,1 exceeds tn." + }, + { + "text": "Right?" + }, + { + "text": "That's what the p-value is." + }, + { + "text": "Now, this guy has nothing to do with this guy." + }, + { + "text": "So this is really just 1 minus the Gaussian CDF of tn." + }, + { + "text": "And that's it." + }, + { + "text": "So that's how I would compute p-values." + }, + { + "text": "Now, as I said, the p-value is a beauty, because you don't have to understand the fact that your limiting distribution is a Gaussian." + }, + { + "text": "Right?" + }, + { + "text": "It's already factored in this construction." + }, + { + "text": "The fact that I'm actually looking at this cumulative distribution function of a standard Gaussian makes my p-value automatically adjust to what the limiting distribution is." + }, + { + "text": "And if this was the cumulative distribution function of a exponential, I would just have a different function here denoted by f, for example." + }, + { + "text": "And I would just compute a different value." + }, + { + "text": "But in the end, regardless of what the limiting value is, my p-value would still be a number between 0 and 1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk36.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk36.json new file mode 100644 index 0000000000000000000000000000000000000000..2d4547dd85e8e54b4a9640f590a534ed56d0306a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk36.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so to illustrate that, let's look at other weird distributions that we could get in place of the standard Gaussian." + }, + { + "text": "And we're not going to see many, but we'll see one." + }, + { + "text": "And it's not called the chi-squared distribution." + }, + { + "text": "It's actually called the student's distribution, but it involves the chi-squared distribution as a building block." + }, + { + "text": "So I don't know if my phonetics are not really right there, so I try to say, well, it's chi-squared." + }, + { + "text": "Maybe it's chi-squared in Canada." + }, + { + "text": "Who knows?" + }, + { + "text": "So for a positive integer, so there's only one parameter." + }, + { + "text": "So for the Gaussian, you have two parameters, which are mu and sigma squared." + }, + { + "text": "Those are real numbers." + }, + { + "text": "Sigma squared is positive." + }, + { + "text": "Here, I have one integer parameter." + }, + { + "text": "Then the distribution, the chi-squared distribution with d degrees of freedom." + }, + { + "text": "So the parameter is called a degree of freedom, just like mu is called the expected value, and sigma squared is called the variance." + }, + { + "text": "So it's called degrees of freedom." + }, + { + "text": "You don't have to really understand why." + }, + { + "text": "So that's the law that you would get." + }, + { + "text": "That's the random variable you would get if you were to sum d squares of independent standard Gaussians." + }, + { + "text": "So I take the square of an independent random Gaussian." + }, + { + "text": "I take another one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk37.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk37.json new file mode 100644 index 0000000000000000000000000000000000000000..6fa169cd52b7910e64c667064ab385a1dc476da0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk37.json @@ -0,0 +1,62 @@ +[ + { + "text": "I sum them, and that's a chi-squared with two degrees of freedom." + }, + { + "text": "That's how you get it." + }, + { + "text": "Now, I could define it using its probability density function." + }, + { + "text": "After all, this is the sum of positive random variables." + }, + { + "text": "It is a positive random variable." + }, + { + "text": "It has a density on the positive real line." + }, + { + "text": "And the PDF of chi-squared, PDF of chi-squared with d degrees of freedom is what?" + }, + { + "text": "Well, it's fd of x is x to the d over 2 minus 1, e to the minus x over 2." + }, + { + "text": "And then here, I have a gamma of d over 2, and the other one is, I think, 2 to the d over 2 minus 1." + }, + { + "text": "No, 2 to the d over 2." + }, + { + "text": "That's what it is." + }, + { + "text": "That's the density." + }, + { + "text": "If you are very good at probability, you can make the change of variable and write your Jacobian and do all this stuff and actually check that this is true." + }, + { + "text": "I do not recommend doing that." + }, + { + "text": "So this is the density, but it's better understood like that, at thinking of just something that you built from standard Gaussian." + }, + { + "text": "So for example, an example of a chi-squared with two degrees of freedom is actually the following thing." + }, + { + "text": "Let's assume I have a target like this." + }, + { + "text": "And I don't aim very well, and I'm trying to hit the center." + }, + { + "text": "And I'm going to have maybe a deviation, which is standard Gaussian left-right and standard Gaussian north-south." + }, + { + "text": "So I'm throwing, and then I'm here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk38.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk38.json new file mode 100644 index 0000000000000000000000000000000000000000..e9321d18ef5daa35196a20db9f6bb7680045ede5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk38.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'm claiming that this number here, by Pythagoras' theorem, the squared distance here is the sum of this squared distance here, which is the square of a Gaussian by assumption, plus the square of this distance, which is the square of another independent Gaussian." + }, + { + "text": "I assume those are independent." + }, + { + "text": "And so the squared distance from this point to this point is the chi-squared with two degrees of freedom." + }, + { + "text": "So this guy here is n01 squared." + }, + { + "text": "This is n01 squared." + }, + { + "text": "And so this guy here, this distance here, is chi-squared with two degrees of freedom." + }, + { + "text": "I mean, the squared distance." + }, + { + "text": "I'm talking about squared distances here." + }, + { + "text": "So now you can see that actually Pythagoras is basically why chi-squared arise." + }, + { + "text": "That's why it has its own name." + }, + { + "text": "I mean, I could define this random variable." + }, + { + "text": "I mean, it's actually a gamma distribution." + }, + { + "text": "It's a special case of something called the gamma distribution." + }, + { + "text": "The fact that the special case has its own name is because there's many times where we're going to take sum of squares of independent Gaussians, because Gaussians, the sum of squares is really the norm, the Euclidean norm squared, just by Pythagoras theorem." + }, + { + "text": "If I'm in higher dimension, I can start to sum more squared coordinates, and I'm going to measure the norm squared." + }, + { + "text": "So if you want to draw this picture, it looks like this." + }, + { + "text": "Again, it's the sum of positive numbers." + }, + { + "text": "So it's going to be on 0 plus infinity." + }, + { + "text": "That's fd." + }, + { + "text": "And so for f1 looks like this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk39.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk39.json new file mode 100644 index 0000000000000000000000000000000000000000..530fa0ac2ba5f7380bf835d6fd19c3b55d8a53a3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk39.json @@ -0,0 +1,62 @@ +[ + { + "text": "f2 looks like this." + }, + { + "text": "So the tails becomes heavier and heavier as d increases." + }, + { + "text": "And then at start to 3, it starts to have a different shape." + }, + { + "text": "It starts from 0, and it looks like this." + }, + { + "text": "And then as d increases, it's basically as if you were to push this thing to the right." + }, + { + "text": "It's just like, pfft." + }, + { + "text": "It's just falling like a big ball." + }, + { + "text": "Everybody sees what's going on?" + }, + { + "text": "So there's just this fat thing that's just going there." + }, + { + "text": "What is the expected value of a k squared?" + }, + { + "text": "So it's the expected value of the sum of Gaussian random variables squared." + }, + { + "text": "I don't know why I said that." + }, + { + "text": "AUDIENCE 2 It's the sum of their second norm, right?" + }, + { + "text": "Which is?" + }, + { + "text": "Those are n0, 1." + }, + { + "text": "It's like, oh, I see, 1." + }, + { + "text": "Yeah." + }, + { + "text": "So n times 1, or d times 1." + }, + { + "text": "Yeah, which is d. So one thing you can check quickly is that the expected value of a k squared is d. And so you see, that's why the mass is shifting to the right as d increases." + }, + { + "text": "It's just going there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk4.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..07e0b7e52902074c6ec8439999a1046b4b977809 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "So for theta and theta 0, I know that my function is going to look like this." + }, + { + "text": "It's going to be somewhere in this rectangle." + }, + { + "text": "Everybody agrees?" + }, + { + "text": "So this function for this guy is going to look like this." + }, + { + "text": "When I'm at 0, when p is equal to 0, which means I only observe 0's, then I know that p is going to be 0." + }, + { + "text": "And I will certainly not conclude that p is equal to 1." + }, + { + "text": "This test will never conclude that p is equal to 1." + }, + { + "text": "Sorry, that was, yeah." + }, + { + "text": "That p is equal to, that p is lower than 1 half, just because xn bar is going to be equal to 0." + }, + { + "text": "OK, well, this is actually not well-defined." + }, + { + "text": "So maybe I need to do something, put it equal to 0 if xn bar is equal to 0." + }, + { + "text": "So I guess basically I get something which is negative." + }, + { + "text": "And so it's never going to be larger than what I want." + }, + { + "text": "And so here I'm actually starting at 0." + }, + { + "text": "So now this is this function here that increases." + }, + { + "text": "I mean, it should increase smoothly." + }, + { + "text": "This function here is alpha psi of theta, or alpha psi of p, let's say, because we're talking about p. Then it reaches alpha here." + }, + { + "text": "Now when I go on the other side, I'm actually looking at beta." + }, + { + "text": "When I'm on theta 1, the function that matters is the probability of type 2 error, which is beta psi." + }, + { + "text": "And this beta psi is actually going to increase." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk40.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk40.json new file mode 100644 index 0000000000000000000000000000000000000000..cf303c16babeea5b89d0924caa36f4dde58e6495 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk40.json @@ -0,0 +1,62 @@ +[ + { + "text": "Actually, the variance is also increasing." + }, + { + "text": "The variance is 2d." + }, + { + "text": "So this is one thing." + }, + { + "text": "And so why do we care about this in basic statistics?" + }, + { + "text": "It's not like we actually have statistics much about throwing darts at high dimensional boards." + }, + { + "text": "So what's happening is that if I look at the sample variance, the average of the sum of squared centered by their mean, then I can actually expend this as the sum of the squares minus the average squared." + }, + { + "text": "It's just the same trick that we have for the variance." + }, + { + "text": "Second moment minus first moment squared." + }, + { + "text": "And then I claim that Cochran's theorem, I will tell you in a second what Cochran's theorem tells me, is that this sample variance is actually, so if I had only this, so now, OK, look at those guys." + }, + { + "text": "Those guys are Gaussian with mean mu and variance sigma squared." + }, + { + "text": "Think for one second, mu being 0 and sigma squared being 1." + }, + { + "text": "Now, this part would be a chi-square with n degrees of freedom divided by n. Now, I get another thing here, which is the square of something that looks like a Gaussian as well." + }, + { + "text": "So it looks like I have something else here, which looks also like a chi-square." + }, + { + "text": "Now, Cochran's theorem is essentially telling you that those things are independent." + }, + { + "text": "And so that in a way, you can think of those guys as being here n degrees of freedom minus 1 degree of freedom." + }, + { + "text": "Now, here, as I said, this is not mean 0 and variance 1." + }, + { + "text": "The fact that it's not mean 0 is not a problem, because I can remove the mean here and remove the mean here." + }, + { + "text": "And so this thing has the same distribution, regardless of what the actual mean is." + }, + { + "text": "So without loss of generality, I can assume that mu is equal 0." + }, + { + "text": "Now, the variance I'm going to have to pay, because if I multiply all these numbers by 10, then this Sn is going to be multiplied by 100." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk41.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk41.json new file mode 100644 index 0000000000000000000000000000000000000000..be699853a1170afd439414bc8f189e87e84b0b94 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk41.json @@ -0,0 +1,62 @@ +[ + { + "text": "So this thing is going to scale with the variance." + }, + { + "text": "And not surprisingly, it's scaling like the square of the variance." + }, + { + "text": "So if I look at Sn, it's distributed as sigma-square times the chi-square with n minus 1 degrees of freedom divided by n. And we don't really write that, because a chi-square times sigma-square divided by n is not a distribution." + }, + { + "text": "So we put everything to the left." + }, + { + "text": "And we say that this is actually a chi-square with n minus 1 degrees of freedom." + }, + { + "text": "So here, I'm actually dropping a fact on you." + }, + { + "text": "But you can sort of see the building block." + }, + { + "text": "What is the thing that's sort of fussy at this point, but the rest should be crystal clear to you?" + }, + { + "text": "The thing that's fussy is that removing this square guy here is actually removing 1 degree of freedom." + }, + { + "text": "That should be weird." + }, + { + "text": "But that's what Cochran's theorem tells me." + }, + { + "text": "It's essentially stating something about orthogonality of subspaces with the span of the constant vector, something like that." + }, + { + "text": "So you don't have to think about it too much." + }, + { + "text": "But that's what it's telling me." + }, + { + "text": "But the rest, if you plug in, so the scaling in sigma-squared and in n, that should be completely clear to you." + }, + { + "text": "So in particular, if I remove that part, it should be clear to you that this thing, if mean is 0, this thing is actually distributed." + }, + { + "text": "Well, if mu is 0, what is the distribution of this guy?" + }, + { + "text": "So I remove that part, just this part." + }, + { + "text": "So I have xi, which are n0 sigma-squared." + }, + { + "text": "And I'm asking, what is the distribution of 1 over n sum from i equal 1 to n of xi-squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk42.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk42.json new file mode 100644 index 0000000000000000000000000000000000000000..3596e452514719b86b744b50b7402e7dd02b9ace --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk42.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it is the sum of their iid." + }, + { + "text": "So it's the sum of independent Gaussians, but not standard." + }, + { + "text": "So the first thing to make them standard is that I divide all of them by sigma-squared." + }, + { + "text": "Now, this guy is of the form zi-squared, where zi is n0, 1." + }, + { + "text": "So now this thing here has what distribution?" + }, + { + "text": "Chi-squared n. And now sigma-squared over n times chi-squared n. So if I have sigma-squared divided by n times chi-squared, sorry, so n times n divided by sigma-squared." + }, + { + "text": "So if I take this thing and I multiply it by n divided by sigma-squared, it means I remove this term." + }, + { + "text": "And now I am left with a chi-squared with n degrees of freedom." + }, + { + "text": "Now, the effect of centering with the sample mean here is only to lose 1 degree of freedom." + }, + { + "text": "That's it." + }, + { + "text": "OK?" + }, + { + "text": "So if I want to do a test about variance, since this is supposedly a good estimator of variance, this could be my pivotal distribution." + }, + { + "text": "This could play the role of a Gaussian." + }, + { + "text": "If I want to know if my variance is equal to 1 or larger than 1, I could actually build a test based on this only statement and test if the variance is larger than 1 or not." + }, + { + "text": "Now, this is not asymptotic because I started with the very assumption that my data was Gaussian itself." + }, + { + "text": "OK?" + }, + { + "text": "Now, just a side remark, you can check that this chi-squared 2, 2 is an exponential with half degrees of freedom, which is certainly not clear from the fact that z1 squared plus z2 squared is a chi-squared with 2 degrees of freedom." + }, + { + "text": "If I give you the sum of the square of two independent Gaussians, this is actually an exponential." + }, + { + "text": "That's not super clear, right?" + }, + { + "text": "But if you look at what was here, I don't know if you took notes, but let me rewrite it for you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk43.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk43.json new file mode 100644 index 0000000000000000000000000000000000000000..c1c4ce2a1e88dbaf6e313e0235a0fa58a881a709 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk43.json @@ -0,0 +1,59 @@ +[ + { + "text": "So it was x to the d over 2 minus 1 e to the minus x over 2 divided by 2 to the d over 2 gamma of d over 2." + }, + { + "text": "So if I plug in d is equal to 2, gamma of 2 over 2 is gamma of 1, which is 1, right?" + }, + { + "text": "It's factorial of 0." + }, + { + "text": "So it's 1." + }, + { + "text": "So this guy goes away." + }, + { + "text": "2 to the d over 2 is 2 to the 1." + }, + { + "text": "So that's just 1." + }, + { + "text": "No, that's just 2." + }, + { + "text": "OK?" + }, + { + "text": "Then x to the d over 2 minus 1 is x to the 0, goes away." + }, + { + "text": "And so I have x minus x over 2, 1 half, which is really, indeed, of the form lambda e to the minus lambda x for lambda is equal to 1 half, which was our exponential distribution." + }, + { + "text": "OK?" + }, + { + "text": "So well, next week is Columbus Day." + }, + { + "text": "So that's next Monday." + }, + { + "text": "So next week, we'll talk about students' distribution." + }, + { + "text": "And so that was discovered by a guy who pretended his name was student but was not student." + }, + { + "text": "And I challenge you to find why in the meantime." + }, + { + "text": "All right, so I'll see you next week." + }, + { + "text": "Your homework is going to be outside, so we can release the room." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk5.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..89ec03ee891688f8ef72df5ae36dcaada4844313 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "So beta psi is what?" + }, + { + "text": "Well, beta psi should also, sorry, that's the probability of being equal to alpha." + }, + { + "text": "So what I'm going to do is I'm going to look at the probability of rejecting." + }, + { + "text": "So let me draw this function all the way." + }, + { + "text": "It's going to look like this." + }, + { + "text": "Now here, if I look at this function here or here, this is the probability under theta that psi is equal to 1." + }, + { + "text": "And we just said that in this region, this function is called alpha psi." + }, + { + "text": "In that region, it's not called alpha psi." + }, + { + "text": "It's not called anything." + }, + { + "text": "It's just the probability of rejection." + }, + { + "text": "So it's not an error." + }, + { + "text": "It's actually what you should be doing." + }, + { + "text": "What we're looking at in this region is 1 minus this guy." + }, + { + "text": "We're looking at the probability of not rejecting." + }, + { + "text": "So I need to actually basically look at 1 minus this thing, which here is going to be 95%." + }, + { + "text": "So I'm going to do 95%." + }, + { + "text": "And this is my probability." + }, + { + "text": "And I'm just basically drawing the symmetric of this guy." + }, + { + "text": "So this here is the probability under theta that psi is equal to 0, which is 1 minus p theta that psi is equal to 1." + }, + { + "text": "So it's just 1 minus the white curve." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk6.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..2ba3f3f31acb2d89e2bd57110d90b292f5959fce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's actually, by definition, equal to beta psi of theta." + }, + { + "text": "Now, where do I read pi psi?" + }, + { + "text": "What is pi psi on this picture?" + }, + { + "text": "Is pi psi a number or a function?" + }, + { + "text": "It's a number, right?" + }, + { + "text": "It's the minimum of a function." + }, + { + "text": "What is this function?" + }, + { + "text": "It's the probability under theta that theta is equal to 1." + }, + { + "text": "I drew this entire function between theta 0 and theta 1." + }, + { + "text": "I drew this entire white curve." + }, + { + "text": "This is this probability." + }, + { + "text": "Now, I'm saying, look at the smallest value this probability can take on the set theta 1." + }, + { + "text": "What is this?" + }, + { + "text": "This guy." + }, + { + "text": "This is where my pi, this thing here, is pi psi." + }, + { + "text": "And so it's equal to 5%." + }, + { + "text": "So that's for this particular test, because this test is sort of a continuous curve for this psi." + }, + { + "text": "And so if I want to make sure that I'm at 5% when I come to the right of theta 0, if it touches theta 1, then I better have 5% on the other side if the function is continuous." + }, + { + "text": "So basically, if this function is increasing, which will be the case for most tests, then what's going to happen is that, and continuous, then what's going to happen is that the level of the test, which is alpha, is actually going to be equal to the power of the test." + }, + { + "text": "OK?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk7.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..4f5cdee6b6891b45c5f7794aece5ce2b8c13dc7a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, there's something I didn't mention, and I'm just mentioning it, pass it by." + }, + { + "text": "Here, I define the power itself." + }, + { + "text": "This function, this entire white curve here, is actually called the power function." + }, + { + "text": "This thing, that's the entire white curve." + }, + { + "text": "And what you could have is tests that have the entire curve, which is dominated by another test." + }, + { + "text": "So here, if I look at this test, and let's assume I can build another test that has this curve." + }, + { + "text": "Let's say it's the same here." + }, + { + "text": "But then here, it looks like this." + }, + { + "text": "What is the power of this test?" + }, + { + "text": "It's the same." + }, + { + "text": "It's 5%, because this point touches here exactly at the same point." + }, + { + "text": "However, for any other value than the worst possible, this guy is doing better than this guy." + }, + { + "text": "Can you see that?" + }, + { + "text": "Having a curve higher on the right-hand side is a good thing, because it means that you tend to reject more when you're actually in H1." + }, + { + "text": "So this guy is definitely better than this guy." + }, + { + "text": "And so what we say in this case is that the test with the dashed line is uniformly more powerful than the other test." + }, + { + "text": "But we're not going to go into those details, because basically, all the tests that we will describe are already the most powerful ones." + }, + { + "text": "In particular, this guy is, there's no such thing." + }, + { + "text": "All the other guys you can come up with are going to actually be below." + }, + { + "text": "So we saw a couple tests, and we saw how to pick this threshold, and we defined those two things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk8.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8b9449415f7337b53908d8098f0293899e0ba86e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "Yes?" + }, + { + "text": "AUDIENCE 2 But in that case, the down one, if it were also higher in the region of 2 to 0, do you still consider it better?" + }, + { + "text": "PHILIPPE RIGOLLETTIS Because you're given this budget of 5%, right?" + }, + { + "text": "So in this paradigm, where you're given the, actually, if the dashed line was this dashed line, I would still be happy." + }, + { + "text": "I mean, I don't care what this thing does here, as long as it's below 5%." + }, + { + "text": "But here, I'm going to try to discover it, right?" + }, + { + "text": "Think about, again, the drug discovery example." + }, + { + "text": "You're trying to find, let's say you're a scientist, and you're trying to prove that your drug works." + }, + { + "text": "What do you want to see?" + }, + { + "text": "Well, FDA puts on you this constraint that your probability of type 1 error should never exceed 5%." + }, + { + "text": "You're going to work under this assumption." + }, + { + "text": "But what you're going to do is going to try to find a test that will make you find something as often as possible." + }, + { + "text": "And so you're going to max this constraint of 5%, and then you're going to try to make this curve, this curve that means that this is basically, this number here, for any point here, is the probability that you publish your paper." + }, + { + "text": "That's the probability that you can release to market your drug." + }, + { + "text": "That's the probability that it works, right?" + }, + { + "text": "And so you want this curve to be as high as possible." + }, + { + "text": "You want to make sure that if there's evidence in the data that H1 is the truth, you want to squeeze as much of this evidence as possible." + }, + { + "text": "And the test that has the highest possible curve is the most powerful one." + }, + { + "text": "Now, you have to also understand that having two curves that are on top of each other, completely, everywhere, is a rare phenomenon." + }, + { + "text": "It's not always the case that there is a test that's uniformly more powerful than any other test." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk9.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bbad3ae05fbb39d9ef76b7b89aa0fada7d5adc3e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_0_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It might be that you have some trade-off, that it might be better here, but then you're losing power here." + }, + { + "text": "Things like this." + }, + { + "text": "Well, actually, maybe it should not go down." + }, + { + "text": "But let's say it goes like this, and then maybe this guy goes like this." + }, + { + "text": "Then you have to basically make an educated guess whether you think that the theta you're going to find is here or it's here." + }, + { + "text": "And then you pick a test." + }, + { + "text": "OK?" + }, + { + "text": "Any other question?" + }, + { + "text": "Yes?" + }, + { + "text": "AUDIENCE 2." + }, + { + "text": "What is the derivative of the type 2 error?" + }, + { + "text": "PHILIPPE RIGOLLET." + }, + { + "text": "So the green curve is exactly right." + }, + { + "text": "So that's beta psi of theta." + }, + { + "text": "So it's really the type 2 error, and it's defined only here." + }, + { + "text": "So here, it's not a definition." + }, + { + "text": "It's really just I'm just mapping it to this point." + }, + { + "text": "So it's defined only here, and it's the probability of type 2 error." + }, + { + "text": "So here, it's pretty large, right?" + }, + { + "text": "I'm making it basically as large as I could, because I'm at the boundary." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk0.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..65c23c5cab5e2c4f1a8f872964a31edc5dd21493 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "Talking about tests, and to be fair, we spend most of our time talking about new jargon that we're using." + }, + { + "text": "But the main goal is to take a binary decision, yes and no." + }, + { + "text": "So just so that we're clear and we make sure that we all speak the same language, let me just remind you what the key words are for tests." + }, + { + "text": "So the first thing is that we split theta in theta 0 and theta 1." + }, + { + "text": "Both are included in theta, and they're disjoint." + }, + { + "text": "OK." + }, + { + "text": "So I have my set of possible parameters." + }, + { + "text": "And then I have theta 0 is here, theta 1 is here, and there might be something that I leave out." + }, + { + "text": "And so what we're doing is we have two hypotheses." + }, + { + "text": "So here's our hypothesis testing problem." + }, + { + "text": "And it's h0 theta belongs to theta 0 versus h1 theta belongs to theta 1." + }, + { + "text": "This guy was called the null, and this guy was called the alternative." + }, + { + "text": "And why we give them special names is because we saw that they have an asymmetric role." + }, + { + "text": "The null represents the status quo, and data is here to bring evidence against this guy." + }, + { + "text": "And we can really never conclude that h0 is true because all we could conclude is that h1 is not true or may not be true." + }, + { + "text": "So that was the first thing." + }, + { + "text": "The second thing was the hypothesis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk1.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3b72e60009f76e8f81d23cb396a309bf7d70b355 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "The third thing is what is a test?" + }, + { + "text": "Well, psi, it's a statistic." + }, + { + "text": "And it takes the data, and it maps it into 0 or 1." + }, + { + "text": "And I didn't really mention it, but there's something such as called randomized tests, which is, well, if it cannot really make a decision, they might as well flip a coin." + }, + { + "text": "That tends to be biased, but that's really, I mean, think about it in practice." + }, + { + "text": "You probably don't want to make decisions based on flipping a coin." + }, + { + "text": "And so what people typically do, this is happening typically at one specific value." + }, + { + "text": "So rather than flipping a coin for this very specific value, what people typically do is they say, OK, I'm going to side with h0 because that's the most conservative choice I can make." + }, + { + "text": "So in a way, they think of flipping this coin, but always falling on heads." + }, + { + "text": "So associated to this test was something called, well, the rejection region." + }, + { + "text": "And r psi, which is just the set of data, x1, xn, such that psi of x1, xn is equal to 1." + }, + { + "text": "So that means we rejected 0 when the test is 1, and those are the set of data points that actually are going to lead me to reject the test." + }, + { + "text": "OK. Then the things that were actually slightly a little more important and really peculiar to test, specific to test, were the type 1 and type 2 error." + }, + { + "text": "So the type 1 error arises when, so type 1 error is when you reject whereas h0 is correct." + }, + { + "text": "And the type 2 error is the opposite." + }, + { + "text": "So it's failed to reject whereas h1 is correct." + }, + { + "text": "h is correct." + }, + { + "text": "So those are the two types of errors you can make, and we quantify their probability of type 1 error." + }, + { + "text": "So alpha psi is the probability." + }, + { + "text": "So that's the probability of type 1 error." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk10.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c19b0d21dee98686b07f25081871711f112710fa --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "And that means at the boundary, since the status quo is h0, I'm always going to go for h0 if I don't have any evidence, which means that what's going to pay is the type 2 error that's going to basically pay this." + }, + { + "text": "OK?" + }, + { + "text": "Any other question?" + }, + { + "text": "All right, so let's move on." + }, + { + "text": "So did we do this?" + }, + { + "text": "No, I think we stopped here, right?" + }, + { + "text": "I didn't cover that part." + }, + { + "text": "So as I said, in this paradigm, we're going to actually fix this guy to be something." + }, + { + "text": "And this thing is actually called the level of the test." + }, + { + "text": "I'm sorry, this is again more words." + }, + { + "text": "Actually, good news is that we split it into two lectures." + }, + { + "text": "So we have, what is a test?" + }, + { + "text": "What is a hypothesis?" + }, + { + "text": "What is the null?" + }, + { + "text": "What is the alternative?" + }, + { + "text": "What is the type 1 error?" + }, + { + "text": "What is the type 2 error?" + }, + { + "text": "And now, I'm telling you there's another thing." + }, + { + "text": "So we defined the power, which was some sort of a lower bound on the, or it's 1 minus the upper bound on the type 2 error, basically." + }, + { + "text": "And so it's alternative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk11.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..815ec78c1b831dd92a2b3f1d68a91dd8df86f618 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "So the power is the smallest probability of rejecting when you're in the null." + }, + { + "text": "And it's alternative when you're in theta 1, right?" + }, + { + "text": "So that's my power." + }, + { + "text": "I looked here, and I looked at the smallest value." + }, + { + "text": "And I can look at this side and say, well, what is the largest probability that I make a type 1 error?" + }, + { + "text": "Again, this largest probability is the level of the test." + }, + { + "text": "OK, so this is alpha equal, by definition, to the maximum for theta and theta 0 of alpha psi of theta." + }, + { + "text": "So here, I just put the level itself." + }, + { + "text": "As you can see here, it essentially says that if I'm of level 5%, I'm also of level 10%." + }, + { + "text": "I'm also of level 15%." + }, + { + "text": "So here, it's really an upper bound." + }, + { + "text": "Whatever you guys want to take, this is what it is." + }, + { + "text": "But as we said, if this number is 4.5%, you're losing in your type 2 error." + }, + { + "text": "So if you're allowed to have, if this maximum here is 4.5%, and FDA told you you can go to 5%, you're losing in your type 2 error." + }, + { + "text": "So you actually want to make sure that this is the 5% that's given to you." + }, + { + "text": "So the way it works is that you give me the alpha." + }, + { + "text": "Then I'm going to go back, pick c that depends on alpha here, so that this thing is actually equal to 5%." + }, + { + "text": "And so, of course, in many instances, we do not know the probability." + }, + { + "text": "We do not know how to compute the probability of type 1 error." + }, + { + "text": "This is a maximum value for the probability of type 1 error." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk12.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..4bd3834b631a0a7c734e2b14c2fe32eaf6f601e6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "We don't know how to compute it." + }, + { + "text": "I mean, it might be a very complicated random variable." + }, + { + "text": "Maybe it's a weird binomial." + }, + { + "text": "We could compute it, but it would be painful." + }, + { + "text": "But what we know how to compute is its asymptotic value, which is because of the central limit theorem, convergence and distribution tells me that the probability of type 1 error is basically going towards the probability that some Gaussian is in some region." + }, + { + "text": "And so we're going to compute not the level itself, but the asymptotic level." + }, + { + "text": "So again, that's basically the limit as n goes to infinity of alpha psi of theta." + }, + { + "text": "And then I'm going to make the max here." + }, + { + "text": "OK?" + }, + { + "text": "So how am I going to compute this?" + }, + { + "text": "Well, if I take a test that has rejection region of the form Tn, because it depends on the data, right?" + }, + { + "text": "That's Tn of x1, xn, my observations, larger than some number c. OK?" + }, + { + "text": "Of course, I can almost always write tests like that, except that sometimes there's going to be an absolute value, which essentially means I'm going away from some value." + }, + { + "text": "Maybe actually I'm less than something, but I can always put a negative sign in front of everything." + }, + { + "text": "So this is not without much of generality, right?" + }, + { + "text": "So this includes something that looks like something is larger than the constant, right?" + }, + { + "text": "So that means, which is equivalent to, well, let me write it as Tq." + }, + { + "text": "OK, because then that means that, so that's Tn." + }, + { + "text": "But this actually encompasses the fact that Qn is larger than c, or Qn is less than c, then minus c. So that includes this guy." + }, + { + "text": "That also includes Qn less than c, because this is equivalent to Qn is larger than minus c. Minus Qn is, and so that's going to be my Tn." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk13.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..d0fc40d7fea49cc51a82242971122ccb04ee2caf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I can actually encode several type of things, OK?" + }, + { + "text": "Rejection regions that, so here in this case, I have a rejection region that looks like this, or a rejection region that looks like this, or a rejection region that looks like this." + }, + { + "text": "OK, and here I don't really represent it for the whole data, but maybe for the average, for example, or the normalized average." + }, + { + "text": "OK, so if I write this, then, yeah." + }, + { + "text": "And in this case, this Tn that shows up is called test statistic." + }, + { + "text": "I mean, this is sort of a, I mean, this is not like set in stone." + }, + { + "text": "Here, for example, Q could be the test statistics." + }, + { + "text": "It doesn't have to be minus Q itself that's the test statistic, right?" + }, + { + "text": "So what is the test statistic?" + }, + { + "text": "Well, it's what you're going to build from your data and then compare to some fixed value, right?" + }, + { + "text": "So in the example we had here, what is our test statistic?" + }, + { + "text": "Well, it's this guy, right?" + }, + { + "text": "This was our test statistic." + }, + { + "text": "And is this thing a statistic?" + }, + { + "text": "What are the criteria for a statistic?" + }, + { + "text": "What is a statistic?" + }, + { + "text": "I know you know the answer." + }, + { + "text": "AUDIENCE MEMBER 2." + }, + { + "text": "Is it a measurable function?" + }, + { + "text": "PROFESSOR PHILIPPE RIGOLLET." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk14.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..deb918611779af5e70f1e976f45cfc296740fc0a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "Yeah, it's a measurable function of the data that does not depend on the parameter." + }, + { + "text": "Is this guy a statistic?" + }, + { + "text": "AUDIENCE MEMBER 3." + }, + { + "text": "Yes, he is." + }, + { + "text": "PROFESSOR PHILIPPE RIGOLLET." + }, + { + "text": "Let's think again." + }, + { + "text": "When I implemented the test, what did I do?" + }, + { + "text": "I was able to compute my test." + }, + { + "text": "My test did not depend on some unknown parameter." + }, + { + "text": "How did we do it?" + }, + { + "text": "We just plugged in 0.5 here." + }, + { + "text": "Remember?" + }, + { + "text": "That was the value for which we computed it, because under h0, that was the value we're seeing." + }, + { + "text": "And if theta 0 is actually an entire set, I'm just going to take the value that's the closest to h1." + }, + { + "text": "We'll see that in a second." + }, + { + "text": "I mean, I did not guarantee that to you." + }, + { + "text": "But just taking the worst type 1 error and bounding it by alpha is equivalent to taking p and taking the value of p that's the closest to theta 1, which is completely intuitive." + }, + { + "text": "The worst type 1 error is going to be attained for the p that's the closest to the alternative." + }, + { + "text": "So even if the null is actually just an entire set, it's as if it was just the point that's the closest to the alternative." + }, + { + "text": "So now we can compute this, because there's no unknown parameters that shows up." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk15.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..0bc365016096bbbfd9f7a60ab9c2724dec760020 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "We replaced p by 0.5." + }, + { + "text": "And so that was our test statistic." + }, + { + "text": "So when you're building a test, you want to first build a test statistic and then see what threshold you should be getting." + }, + { + "text": "So now let's go back to our example where we have x1, xn." + }, + { + "text": "They're iid Bernoulli p. And I want to test if p is 1 half versus p not equal to 1 half, which as I said is what you want to do if you want to test if a coin is fair." + }, + { + "text": "And so here I'm going to build a test statistic." + }, + { + "text": "And we concluded last time that what do we want for this statistic?" + }, + { + "text": "We want it to have a distribution which under the null does not depend on the parameters, a distribution that I can actually compute quintiles of." + }, + { + "text": "So what we did is we said, well, if I look at the central limit theorem tells me that square root of n xn bar minus p divided by." + }, + { + "text": "So if I do central limit theorem plus Slutsky, for example, I'm going to have square root." + }, + { + "text": "And we've had this discussion whether we want to use Slutsky or not here." + }, + { + "text": "But let's assume we're taking Slutsky wherever we can." + }, + { + "text": "So this thing tells me that by the central limit theorem as n goes to infinity, this thing converges in distribution to some n 0, 1." + }, + { + "text": "Now as we said, this guy is not something we know." + }, + { + "text": "But under the null, we actually know it." + }, + { + "text": "And we can actually replace it by 1 half." + }, + { + "text": "So this thing holds under h0." + }, + { + "text": "When I write under h0, it means when this is the truth." + }, + { + "text": "So now I have something that converges to something that has no dependence on anything I don't know." + }, + { + "text": "And in particular, if you have any statistics textbook, which you don't because I didn't require one, you should be thankful because this thing costs $250." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk16.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..298b0fb997de98b972702f498d96cfa89d4e4b7d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "This thing's actually, if you look at the back, you actually have a table for a standard Gaussian." + }, + { + "text": "I could have anything else here." + }, + { + "text": "I could have an exponential distribution." + }, + { + "text": "I could have a, I don't know, a, well, we'll see the chi-square distribution in a minute." + }, + { + "text": "Any distribution from which you can actually see a table that somebody actually computed this thing for which you can actually draw the PDF and start computing whatever probability you want on them, then this is what you want to see at the right-hand side." + }, + { + "text": "This is any distribution." + }, + { + "text": "It's called pivotal." + }, + { + "text": "I think we've mentioned that before." + }, + { + "text": "Pivotal means it does not depend on anything that you don't know." + }, + { + "text": "And maybe it's easy to compute those things." + }, + { + "text": "Probably, typically, you need a computer to simulate them for you because computing probabilities for Gaussians is not an easy thing." + }, + { + "text": "We don't know how to solve those integrals exactly." + }, + { + "text": "We have to do it numerically." + }, + { + "text": "OK, so now I want to do this test." + }, + { + "text": "My test statistic will be declared to be what?" + }, + { + "text": "Well, I'm going to reject if what is larger than some number?" + }, + { + "text": "The absolute value of this guy." + }, + { + "text": "So my test statistic is going to be square root of n minus 0.5 divided by square root of xn bar 1 minus xn bar." + }, + { + "text": "That's my test statistic, absolute value of this guy, because I want to reject either when this guy is too large or when this guy is too small." + }, + { + "text": "I don't know ahead whether I'm going to see p larger than 1 half or less than 1 half." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk17.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..c16a8c6be2149a29434fcd2457ee0fdbf0606f2d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "So now I need to compute c such that the probability that tn is lower than c. So that's what?" + }, + { + "text": "That's the probability under p, which is unknown." + }, + { + "text": "I want this probability to be less than some level alpha asymptotically." + }, + { + "text": "So I want the limit of this guy to be less than alpha, and that's the level of my test." + }, + { + "text": "So that's the given level." + }, + { + "text": "So I want this thing to happen." + }, + { + "text": "Now what I know is that this limit, actually, I should say given asymptotic level." + }, + { + "text": "So what is this thing?" + }, + { + "text": "Well, OK, that's the probability that something that looks like under p. So under p, this guy, so what I know is that tn is square root of n minus xn bar minus 0.5 divided by square root of xn bar 1 minus xn bar exceeds." + }, + { + "text": "Is this true that as n goes to infinity, this probability is the same as the probability that the absolute value of a Gaussian exceeds c of a standard Gaussian?" + }, + { + "text": "Is this true?" + }, + { + "text": "Yeah, so you're saying that this, as n becomes large enough, this should be the probability that some absolute value of n0,1 exceeds c, right?" + }, + { + "text": "So I claim that this is not correct." + }, + { + "text": "Somebody tell me why." + }, + { + "text": "Even in the limit, it's not correct?" + }, + { + "text": "Even in the limit, it's not correct." + }, + { + "text": "OK." + }, + { + "text": "So what do you see?" + }, + { + "text": "It's because at the beginning, we picked the worst possible true parameter, 0.5, right?" + }, + { + "text": "So we don't actually know that this 0.5 is the least." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk18.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..21ff2eaef450e95222ef4c4c025a1ccb1a883204 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Exactly, right?" + }, + { + "text": "So we picked this 0.5 here, but this is for any p, right?" + }, + { + "text": "But what is the only p I can get?" + }, + { + "text": "So what I want is that this is true for all p in theta 0." + }, + { + "text": "But the only p that's in theta 0 is actually p is equal to 0.5." + }, + { + "text": "So yes, what you said was true, but it required to specify p to be equal to 0.5." + }, + { + "text": "So this, in general, is not true." + }, + { + "text": "But it happens to be true if p belongs to theta 0, which is strictly equivalent to p is equal to 0.5, right?" + }, + { + "text": "Theta 0 is really just this one point, 0.5." + }, + { + "text": "OK, so now this becomes true." + }, + { + "text": "And so what I need to do is to find c such that this guy is equal to what?" + }, + { + "text": "I mean, let's just follow, right?" + }, + { + "text": "So I want this to be less than alpha." + }, + { + "text": "But then we see that this was equal to this, which is equal to this." + }, + { + "text": "So all I want is that this guy is less than alpha." + }, + { + "text": "But we said we might as well just make it equal to alpha if you allow me to make it as big as I want, as long as it's less than alpha." + }, + { + "text": "So this is a true statement." + }, + { + "text": "But it's if under this condition, right?" + }, + { + "text": "So I'm going to set it equal to alpha." + }, + { + "text": "And then I'm going to try to solve for c. OK, so what I'm looking for is a c such that if I draw a standard Gaussian, so that's PDF of some n0,1, I want the probability that the absolute value of my Gaussian exceeding this guy." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk19.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..b610ab510e065f845cbac3e680352a281a5977db --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that means being either here or here." + }, + { + "text": "So that's minus c and c. I want the sum of those two things to be equal to alpha." + }, + { + "text": "So I want the sum of these areas to equal alpha." + }, + { + "text": "So by symmetry, each of them should be equal to alpha over 2." + }, + { + "text": "And so what I'm looking for is c such that the probability that my n0,1 exceeds c, which is just this area to the right now, equals alpha, which is equivalent to taking c, which is q equals alpha over 2." + }, + { + "text": "And that's q alpha over 2 by definition of q alpha over 2." + }, + { + "text": "That's just what q alpha over 2 is." + }, + { + "text": "And that's what the tables at the back of the book give you." + }, + { + "text": "Who has already seen a table for Gaussian probabilities?" + }, + { + "text": "All right." + }, + { + "text": "What it does is just a table." + }, + { + "text": "I mean, it's pretty ancient, right?" + }, + { + "text": "I mean, of course, you can actually ask Google to do it for you now." + }, + { + "text": "It's basically standard issue." + }, + { + "text": "But back in the day, they actually had to look at tables." + }, + { + "text": "And since the values alphas were pretty standard, the values alpha that people were requesting were typically 1%, 5%, 10%." + }, + { + "text": "All you could do is to compute these different values for different values of alpha." + }, + { + "text": "That was it." + }, + { + "text": "So that's really not much to give you." + }, + { + "text": "So for the Gaussian, I can tell you that alpha is equal to, if alpha is equal to 5%, then q alpha over 2, q 2.5% is equal to 1.96%." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk2.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..d35a9367292f43552ea9e2c936629f0062774757 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So psi is just the probability for theta that psi rejects, and that's defined for theta and theta 0." + }, + { + "text": "So for different values of theta 0, so h0 being correct means there exists a theta in theta 0 for which that actually is the right distribution." + }, + { + "text": "So for different values of theta, I might make different errors." + }, + { + "text": "So if you think, for example, about the coin example, if I'm testing if the coin is biased towards heads or biased towards tails, so if I'm testing whether p is larger than 1 half or less than 1 half, then when the true p, let's say h0 is larger than 1 half, when p is equal to 1, it's actually very difficult for me to make a mistake, because I only see heads." + }, + { + "text": "So when p is getting closer to 1 half, I'm going to start making more and more probability there." + }, + { + "text": "And so the type 2 error, so that's the probability of type 2, is denoted by beta psi." + }, + { + "text": "And it's the function that does the opposite, and this time is defined for theta and theta 0 and theta 1." + }, + { + "text": "And finally, we define something called the power pi of psi." + }, + { + "text": "And this time, this is actually a number." + }, + { + "text": "And so this number is equal to the maximum over theta and theta 0." + }, + { + "text": "I mean, that could be a supremum, but think of it as being a maximum of p theta of psi is equal, sorry, that's in 0." + }, + { + "text": "Give me one sec." + }, + { + "text": "No, that's the min." + }, + { + "text": "So this is not making a mistake." + }, + { + "text": "Theta 0 is in theta 1." + }, + { + "text": "So theta is in theta 1, and I conclude 1." + }, + { + "text": "So this is a good thing." + }, + { + "text": "I want this number to be large, and I'm looking at the worst house, what is the smallest value this number can be." + }, + { + "text": "So what I want to show you a little bit is a picture." + }, + { + "text": "So now I'm going to take theta, and think of it as being p. So I'm going to take p for some Bernoulli experiment." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk20.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..20ad1dac1f1c76cdb383bd9a41a5521bfc8e8f80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "So those are just fixed numbers that are functions of the Gaussian." + }, + { + "text": "All right, so everybody agrees?" + }, + { + "text": "We've done that before for our confidence intervals." + }, + { + "text": "And so now we know that if I actually plug in this guy to be q alpha over 2, then this limit is actually equal to alpha." + }, + { + "text": "And so now I've actually constrained this." + }, + { + "text": "So q alpha over 2 here is, for alpha equals 5%, as I said, is 1.96." + }, + { + "text": "So in the example 1, the number that we found was 3.54, I think, or something like that, 3.55 for t. So if we scroll back very quickly, 3.45." + }, + { + "text": "That was example 1." + }, + { + "text": "Example 2, negative 0.77." + }, + { + "text": "So if I look at t, n, in example 1, tn was just the absolute value of 3.45, which don't pull out your calculators, is equal to 3.45." + }, + { + "text": "Example 2, absolute value of negative 0.77 was equal to 0.77." + }, + { + "text": "And so all I need to check is, is this number larger or smaller than 1.96?" + }, + { + "text": "That's what my test ends up being." + }, + { + "text": "So in example 1, 3.45 being larger than 1.96, that means that I reject." + }, + { + "text": "Fairness of my coins in example 2, 0.77 being smaller than 1.96, what do I do?" + }, + { + "text": "I fail to reject." + }, + { + "text": "OK?" + }, + { + "text": "So here's a question." + }, + { + "text": "In example 1, for what level alpha would psi alpha, what is the?" + }, + { + "text": "So here, what's going to happen if I start decreasing my level?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk21.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..8a92eddc8e39673740ca195fad03c2d25a729273 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "When I decrease my level, I'm actually making this area smaller and smaller, which means that I push the c to the right." + }, + { + "text": "So now I'm asking, what is the smallest c I should pick so that now I actually do not reject h0?" + }, + { + "text": "What is the smallest c I should be taking?" + }, + { + "text": "Here." + }, + { + "text": "What is the smallest c?" + }, + { + "text": "So c here in the example I gave you for 5% was 1.96." + }, + { + "text": "What is the smallest c I should be taking so that now this inequality is reversed?" + }, + { + "text": "3.45." + }, + { + "text": "I ask only trivial questions." + }, + { + "text": "Don't be worried." + }, + { + "text": "So 3.45 is the smallest c that I'm actually willing to tolerate." + }, + { + "text": "So let's say this was my 5%." + }, + { + "text": "If this was 2.5, if alpha here, let's say in this picture, alpha is 5%, that means maybe I need to push here." + }, + { + "text": "And this number should be what?" + }, + { + "text": "So this is going to be 1.96." + }, + { + "text": "And this number here is going to be 3.45, clearly to scale." + }, + { + "text": "And so now what I want to ask you is, well, there's two ways I can understand this number 3.45." + }, + { + "text": "It is the number 3.45." + }, + { + "text": "But I can also try to understand, what is the area to the right of this guy?" + }, + { + "text": "And if I understand what the area to the right of this guy is, this is actually some alpha prime over 2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk22.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..7503edb72bbc4e9db22fe8e956729e7f3881d675 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "And that means that if I actually fix this level, alpha prime, that would be exactly the tipping point at which I would go from accepting to rejecting." + }, + { + "text": "So I know in terms of absolute thresholds, 3.45 is the trivial answer to the question." + }, + { + "text": "That's the tipping point, because I'm comparing a number to 3.45." + }, + { + "text": "But now if I try to map this back and understand what level would have been given me this particular tipping point, that's a number between 0 and 1." + }, + { + "text": "The smaller the number, the larger this number here, which means that the more evidence I have in my data against h0." + }, + { + "text": "And so this number is actually something called the p-value." + }, + { + "text": "And so same for example 2." + }, + { + "text": "There's the tipping point, alpha, at which I go from feeling to reject to rejecting." + }, + { + "text": "And that's exactly the number, the area under the curve, such that here I see 0.77." + }, + { + "text": "And this is this alpha prime prime over 2." + }, + { + "text": "And this number is clearly, alpha prime prime is clearly larger than 5%." + }, + { + "text": "So what's the advantage of thinking and mapping back these numbers?" + }, + { + "text": "Well, now I'm actually going to spit out some number which is between 0 and 1." + }, + { + "text": "And that should be the only scale you should have in mind." + }, + { + "text": "Remember we discussed that last time." + }, + { + "text": "Well, if I actually spit out a number which is 3.45, maybe you can try to think, is 3.45 a large number for a Gaussian?" + }, + { + "text": "That's a number." + }, + { + "text": "But if I had another random variable that was not Gaussian, maybe it was a double exponential, you would have to have another scale in your mind." + }, + { + "text": "Is 3.45 a large number for the large, so large that it's unlikely to come from a double exponential?" + }, + { + "text": "If I had a gamma distribution, I can think of any distribution." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk23.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..d0d0fdec57ad2cc7e2dadb707abb6df87bdbb70b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then that means for each distribution, you would have to have a scale in mind." + }, + { + "text": "So of course, you can have the Gaussian scale in mind." + }, + { + "text": "I mean, I have the Gaussian scale in mind." + }, + { + "text": "But then if I map it back into this number between 0 and 1, all the distributions play the same role." + }, + { + "text": "So whether I'm talking about if my limiting distribution is normal or exponential or gamma or whatever you want, for all these guys, I'm just going to map it into one number between 0 and 1." + }, + { + "text": "Small number means lots of evidence against h1." + }, + { + "text": "Large number means lots of evidence against h0." + }, + { + "text": "Small number means very few evidence against h0." + }, + { + "text": "And this is the only number you need to keep in mind." + }, + { + "text": "And the question is, am I willing to tolerate this number between 5%, 6% or maybe 10%, 12%?" + }, + { + "text": "And this is the only scale you have to have in mind." + }, + { + "text": "And this scale is the scale of p-values." + }, + { + "text": "So the p-value is the tipping point in terms of alpha." + }, + { + "text": "In words, I can make it formal, because tipping point, as far as I know, is not a mathematical term." + }, + { + "text": "So a p-value of a test is the smallest, potentially asymptotic level, if I talk about an asymptotic p-value." + }, + { + "text": "And that's what we do when we talk about central limit theorem, at which the test rejects h0." + }, + { + "text": "If I were to go any smaller, I would fail to reject." + }, + { + "text": "The smaller the level, the less likely it is for me to reject." + }, + { + "text": "And if I were to go any smaller, I would start failing to reject." + }, + { + "text": "And so it is a random number." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk24.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..70790440238c22e23b0b77fc5e658fdf89d62e44 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "It depends on what I actually observe." + }, + { + "text": "So here, of course, I instantiated those two numbers, 3.45 and 0.77, as realizations of random variables." + }, + { + "text": "But if you think of those as being the random numbers before I see my data, this was a random number." + }, + { + "text": "And therefore, the area under the curve to the right of it is also a random area." + }, + { + "text": "If this thing fluctuates, then the area under the curve fluctuates." + }, + { + "text": "And that's what the p-value is." + }, + { + "text": "That's what John Oliver talks about when he talks about p-hacking." + }, + { + "text": "And so we talked about this in the first lecture." + }, + { + "text": "So p-hacking is, how do I do?" + }, + { + "text": "Oh, if I'm a scientist, do I want to see a small p-value or a large p-value?" + }, + { + "text": "Small, right?" + }, + { + "text": "Scientists want to see small p-values, because small p-values equals rejecting, which equals discovery, which equals publication, which equals promotion." + }, + { + "text": "So that's what people want to see." + }, + { + "text": "So people are tempted to see small p-values." + }, + { + "text": "And what's called p-hacking is, well, find a way to cheat." + }, + { + "text": "Maybe look at your data, formulate your hypothesis in such a way that you will actually have a smaller p-value than you should have." + }, + { + "text": "So here, for example, there's one thing I did not insist on, because again, this is not a particular course in statistical thinking." + }, + { + "text": "But one thing that we implicitly did was set those theta 0 and theta 1 ahead of time." + }, + { + "text": "I fixed them, and I'm trying to test this." + }, + { + "text": "This is to be contrasted with the following approach." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk25.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..ae5989051a3c9ad74dd6e26eac906c8e26ce8535 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "I draw my data." + }, + { + "text": "So I draw." + }, + { + "text": "I run this experiment, which is probably going to get me a publication in Nature." + }, + { + "text": "I'm trying to test if a coin is fair." + }, + { + "text": "And I draw my data, and I see that there's 13 out of 30 of my observations that are heads." + }, + { + "text": "That means that from this data, it looks like p is less than 1 half." + }, + { + "text": "So if I look at this data and then decide that my alternative is not p not equal to 1 half, but rather p less than 1 half, that's p-hacking." + }, + { + "text": "I'm actually making my p-value strictly smaller by first looking at the data and then deciding what my alternative is going to be." + }, + { + "text": "And that's cheating, because all the things we did were assuming that this 0.5 or d alternative was actually a fix." + }, + { + "text": "Everything was deterministic." + }, + { + "text": "The only randomness came from the data." + }, + { + "text": "But if I start looking at the data and designing my experiment or my alternatives and null hypothesis based on the data, it's as if I started putting randomness all over the place." + }, + { + "text": "And then I cannot control it, because I don't know how it just intermingles with each other." + }, + { + "text": "All right." + }, + { + "text": "So that was for the John Oliver moment." + }, + { + "text": "So the p-value is nice." + }, + { + "text": "So maybe I mentioned that before." + }, + { + "text": "My wife works in market research." + }, + { + "text": "And maybe every two years, she seems to run into a statistician in the hallway." + }, + { + "text": "And she comes home and says, what is a p-value again?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk26.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..582b81ac1a78246b0f187a4c706af274ba689dbe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk26.json @@ -0,0 +1,62 @@ +[ + { + "text": "And for her, a p-value is just the number is in an Excel spreadsheet." + }, + { + "text": "And actually, small equals good and large equals bad." + }, + { + "text": "And that's all she needs to know at this point." + }, + { + "text": "Actually, they do the job for her." + }, + { + "text": "Small is green." + }, + { + "text": "Large is red." + }, + { + "text": "And so for her, a p-value is just green or red." + }, + { + "text": "But so what she's really implicitly doing with this color code is just applying the golden rule." + }, + { + "text": "What the statisticians do for her in the Excel spreadsheet is that they take the numbers for the p-values that are less than some fixed level." + }, + { + "text": "So depending on the field in which she works, so she works for pharmaceutical companies, so the p-values are typically compared." + }, + { + "text": "The tests are usually performed at level 1% rather than 5%." + }, + { + "text": "So 5% is maybe your gold standard if you're doing sociology or trying to, I don't know, release a new blueberry flavor for your toothpaste, like something that's not going to change the life of people." + }, + { + "text": "Maybe you're going to run at 5%." + }, + { + "text": "It's OK to make a mistake." + }, + { + "text": "People are just going to feel gross, but that's about it." + }, + { + "text": "Whereas here, if you have this p-value which is less than 1%, it might be more important for some drug discovery, for example." + }, + { + "text": "And so let's say you run at 1%." + }, + { + "text": "And so what they do in this Excel spreadsheet is that all the numbers that are below 1% show up in green, and all the numbers that are above 1% show up in red." + }, + { + "text": "And that's it." + }, + { + "text": "That's just applying the golden rule." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk27.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk27.json new file mode 100644 index 0000000000000000000000000000000000000000..6d2b3e73a1f2bfb3d007d43a22bc17095a5878f8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk27.json @@ -0,0 +1,62 @@ +[ + { + "text": "If the number is green, reject." + }, + { + "text": "If the number is red, fail to reject." + }, + { + "text": "OK?" + }, + { + "text": "Yeah?" + }, + { + "text": "So going back to the example of the previous prior example where you can achieve by looking at your data and then formulating, say, a theta 1 to be p less than 1%." + }, + { + "text": "Yeah." + }, + { + "text": "So how would you achieve your goal by changing the theta 1?" + }, + { + "text": "You mean by achieving my goal?" + }, + { + "text": "You mean letting ethics aside, right?" + }, + { + "text": "Yeah." + }, + { + "text": "You want to be published." + }, + { + "text": "So OK." + }, + { + "text": "So let me teach you how." + }, + { + "text": "Well, here, what do you do?" + }, + { + "text": "You want to, at the end of the day, a test is only telling you whether you found evidence in your data that H1 was more likely than H0, basically." + }, + { + "text": "How do you make H1 more likely?" + }, + { + "text": "Well, you just basically target H1 to be what the data is going to make it more likely to be." + }, + { + "text": "All right?" + }, + { + "text": "So if, for example, I say H1 can be on both sides, then my data is going to have to take into account fluctuations on both sides." + }, + { + "text": "And I'm going to lose a factor of 2 somewhere because things are not symmetric." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk28.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk28.json new file mode 100644 index 0000000000000000000000000000000000000000..b6a2e04f21d17d3f9d8f51277fef4b6bd544ea8c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk28.json @@ -0,0 +1,62 @@ +[ + { + "text": "Here is the ultimate way of making this work." + }, + { + "text": "I'm going back to my example of flipping coins." + }, + { + "text": "And now, so here, what I did is I said, oh, this number 0.43 is actually smaller than 0.5." + }, + { + "text": "So I'm just going to test whether I'm 0.5 or I'm less than 0.5." + }, + { + "text": "But here is something that I can promise you I did not make the computation will reject." + }, + { + "text": "OK, so here, this one actually, yeah, this one fails to reject, right?" + }, + { + "text": "So here is one that will certainly reject." + }, + { + "text": "H0 is 0.5. p is 0.5." + }, + { + "text": "H1, p is 0.43." + }, + { + "text": "OK?" + }, + { + "text": "Now, you can try." + }, + { + "text": "But I can promise you that your data will tell you that H1 is the right one." + }, + { + "text": "OK?" + }, + { + "text": "I mean, you can check very quickly that this is really extremely likely to happen, right?" + }, + { + "text": "And so actually, what am I?" + }, + { + "text": "No, actually, that's not true." + }, + { + "text": "OK. Because here, the test that I derive that's based on this kind of stuff, right?" + }, + { + "text": "Here, at some point, somewhere, under some layers, I assume that all our tests are going to have this form." + }, + { + "text": "But here, this is only when you're trying to test one region versus another region next to it, or one point versus a region around it, or something like this." + }, + { + "text": "Whereas for this guy, there's another test I could come up with, which is, what is the probability that I get 0.43?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk29.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk29.json new file mode 100644 index 0000000000000000000000000000000000000000..7c83fb4d5133113ff729308f195ed934ccaaacb9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk29.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what is the probability that I get 0.5?" + }, + { + "text": "Now, what I'm going to do is I'm going to just conclude it's whichever has the largest probability." + }, + { + "text": "Then maybe I'm going to have to make some adjustments so that the level is actually 5%." + }, + { + "text": "But I can make this happen." + }, + { + "text": "I can make the level be 5% and always conclude this guy, but I would have to use a different test." + }, + { + "text": "Now, the test that I described, again, those t and larger than c are built in to be tests that are sort of resilient to this kind of manipulations, because they're sort of oblivious towards what the alternative looks like." + }, + { + "text": "I mean, they're just saying it's either to the left or to the right, but whether it's a point or an entire half line doesn't matter." + }, + { + "text": "So if you try to look at your data and just put the data itself into your hypothesis testing problem, then you're failing the statistical principle." + }, + { + "text": "And that's what people are doing, right?" + }, + { + "text": "I mean, how can I check?" + }, + { + "text": "I mean, of course, here it's going to be pretty blatant if you publish a paper that looks like this." + }, + { + "text": "But there's ways to do it differently, right?" + }, + { + "text": "For example, one way to do it is to just do more." + }, + { + "text": "So typically, what people do is they do multiple hypothesis testing." + }, + { + "text": "They're doing 100 tests at a time." + }, + { + "text": "Then you have random fluctuations every time." + }, + { + "text": "And so they just pick the one that has the random fluctuations that go their way." + }, + { + "text": "I mean, sometimes it's going in your way, and sometimes it's going the opposite way." + }, + { + "text": "So you just pick the one that works for you." + }, + { + "text": "We'll talk about multiple hypothesis testing soon if you want to increase your publication counts." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk3.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..82298a0911f771c50c0c0e31234286bcbe2ed969 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "So p can range between 0 and 1, that's for sure." + }, + { + "text": "And what I'm going to try to test is whether p is less than 1 half or larger than 1 half." + }, + { + "text": "So this is going to be, let's say, theta 0, and this guy here is theta 1." + }, + { + "text": "Just trying to give you a picture of what those guys are." + }, + { + "text": "So I have my y-axis." + }, + { + "text": "Now I'm going to start drawing numbers, all these things, this function, this function, and this number are all numbers between 0 and 1." + }, + { + "text": "So now I'm claiming that when I move from left to right, what is my probability of rejecting going to do?" + }, + { + "text": "So what I'm going to plot is the probability under theta." + }, + { + "text": "The first thing I want to plot is the probability under theta that psi is equal to 1." + }, + { + "text": "And let's say psi, think of psi as being just this indicator that square root of n xn bar minus p over square root xn bar, 1 minus xn bar, is larger than some constant c for a properly chosen c. So what we choose is that c is in such a way that at 1 half, when we're testing for 1 half, what we wanted was this number to be equal to alpha, basically." + }, + { + "text": "So we fix this alpha number so that this guy, so if I want alpha of psi of theta less than alpha, given in advance, so think of it as being equal to, say, 5%." + }, + { + "text": "So I'm fixing this number, and I want this to be controlled for all theta and theta 0." + }, + { + "text": "So if you're going to give me this budget, well, I'm actually going to make it equal where I can." + }, + { + "text": "If you're telling me you can make it equal to alpha, we know that if I increase my type 1 error, I'm going to decrease my type 2 error." + }, + { + "text": "If I start putting everyone in jail, or if I start letting everyone go free, that's what we're discussing last time." + }, + { + "text": "So since we have this trade-off, and you're giving me a budget for one guy, I'm just going to max it out." + }, + { + "text": "And where am I going to max it out?" + }, + { + "text": "Exactly at 1 half at the boundary." + }, + { + "text": "So this is going to be 5%." + }, + { + "text": "So what I know is that since alpha of theta is less than alpha for all theta and theta 0, sorry, that's for theta 0, that's where alpha is defined." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk30.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk30.json new file mode 100644 index 0000000000000000000000000000000000000000..a8e80051fb683b419557b2b36ba8c95a3d50cf00 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk30.json @@ -0,0 +1,62 @@ +[ + { + "text": "There's actually papers." + }, + { + "text": "I think it was big news, there's some papers, I think it's psychology or psychometrics papers, that actually refuse to publish p-values now." + }, + { + "text": "All right, where were we?" + }, + { + "text": "OK, here's the golden rule." + }, + { + "text": "So one thing that I'd like to show is this thing, just so you know how you apply the golden rule and how you apply the standard test." + }, + { + "text": "So the standard paradigm is the following." + }, + { + "text": "You have a black box, which is your test." + }, + { + "text": "For my wife, this is the fourth floor of the building." + }, + { + "text": "That's where the statisticians sit." + }, + { + "text": "What she sends there is data, let's say x1, xn." + }, + { + "text": "And she says, well, this one is about toothpaste, so here's a level." + }, + { + "text": "Let's say 5%." + }, + { + "text": "What the fourth floor brings back is an answer, yes, no." + }, + { + "text": "Green, red, just an answer." + }, + { + "text": "So that's the standard testing." + }, + { + "text": "You just feed it the data and the level at which you want to perform the test, maybe asymptotic, and it spits out a yes, no answer." + }, + { + "text": "What p-value does, you just feed it the data itself." + }, + { + "text": "And what it spits out is the p-value." + }, + { + "text": "And now, it's just up to you." + }, + { + "text": "I mean, hopefully, your brain has the computational power of deciding whether a number is larger or smaller than 5% without having to call the statisticians for this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk31.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk31.json new file mode 100644 index 0000000000000000000000000000000000000000..9fb2296acde7c40202805ca4f7e73e4c07f68e6a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk31.json @@ -0,0 +1,62 @@ +[ + { + "text": "And that's what it does." + }, + { + "text": "So now, we're all on one scale." + }, + { + "text": "Now, if you actually, I see some of you nodding when I talk about p-hacking." + }, + { + "text": "So that means you've seen p-values." + }, + { + "text": "If you've seen more than 100 p-values in your life, you have an entire scale." + }, + { + "text": "A good p-value is less than 10 to the minus 4." + }, + { + "text": "That's the ultimate sweet spot." + }, + { + "text": "Actually, statistical software spit out an output which says less than 10 to the minus 4." + }, + { + "text": "But then, maybe you want a p-value." + }, + { + "text": "If I tell you my p-value was 4.65, then I will say you've been doing some p-hacking until you found a number that was below 5%." + }, + { + "text": "That's typically what people will do." + }, + { + "text": "But if you're doing the test, if you're saying, I published my result." + }, + { + "text": "My test at 5% said yes, that means that maybe your p-value was 4.99, or your p-value was 10 to the minus 4." + }, + { + "text": "I will never know." + }, + { + "text": "I will never know how much evidence you had against the null." + }, + { + "text": "But if you tell me what the p-value is, I can make my own decision." + }, + { + "text": "I don't have to tell me whether it's a yes." + }, + { + "text": "No, you tell me it's 4.99." + }, + { + "text": "I'm going to say, well, maybe yes, but I'm going to take it with a grain of salt." + }, + { + "text": "And so that's why p-values are good numbers to have in mind." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk32.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk32.json new file mode 100644 index 0000000000000000000000000000000000000000..96ed5fb80473cde620f1dcbaecbdda179310c37c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk32.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, I show it as if it was an old trick that you start mastering when you're 45 years old." + }, + { + "text": "No, it's just how small is the number between 0 and 1." + }, + { + "text": "That's really what you need to know." + }, + { + "text": "Maybe on the log scale, if it's 10 to the minus 1, 10 to the minus 2, 10 to the minus 3, et cetera, that's probably the extent of the mastery here." + }, + { + "text": "So this traditional standard paradigm that I showed is actually commonly referred to as the Neyman-Pearson paradigm." + }, + { + "text": "So here it says Neyman-Pearson's theory." + }, + { + "text": "So there's an entire theory that comes with it, but it's really a paradigm." + }, + { + "text": "It's a way of thinking about hypothesis testing that says, well, if I'm not going to be able to optimize both my type 1 and type 2 error, I'm actually going to lock in my type 1 error below some level and just minimize the type 2 error under this constraint." + }, + { + "text": "That's what the Neyman-Pearson paradigm is." + }, + { + "text": "And it sort of makes sense for hypothesis testing problems." + }, + { + "text": "If you were doing some other applications with multi-objective optimization, you would maybe come up with something different." + }, + { + "text": "For example, machine learning is not performing typically under Neyman-Pearson paradigm." + }, + { + "text": "So if you do spam filtering, you could say, well, I want to constrain the probability as much as I can of taking somebody's important emails and throwing them out as spam and, under this constraint, not send too much spam to that person." + }, + { + "text": "That sort of makes sense for spams." + }, + { + "text": "Now, if you're labeling cats versus dogs, it's probably not like you want to make sure that no more than 5% of the dogs are labeled cat." + }, + { + "text": "Because it doesn't matter." + }, + { + "text": "So what you typically do is you just sum up the two types of error you can make, and you minimize the sum without putting any more weight on one or the other." + }, + { + "text": "So here's an example where doing a binary decision, one or two of the errors you can make, you don't have to actually be like that." + }, + { + "text": "So this example here, I did not." + }, + { + "text": "The trivial test, psi is equal to 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk33.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk33.json new file mode 100644 index 0000000000000000000000000000000000000000..0c2da6bcc636025ed6d047d161fdfe68e3b68329 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk33.json @@ -0,0 +1,62 @@ +[ + { + "text": "What was it in the US trial court example?" + }, + { + "text": "What is psi equal to 0?" + }, + { + "text": "I was concluding all ways to the null." + }, + { + "text": "What was the null?" + }, + { + "text": "Innocent, right?" + }, + { + "text": "That's the status quo." + }, + { + "text": "So that means that this guy never rejects a 0." + }, + { + "text": "Everybody's going away free." + }, + { + "text": "So you're sure you're not actually going against the Constitution because alpha is 0%, which is certainly less than 5%." + }, + { + "text": "But the power, the fact that a lot of criminals go back outside in the free world is actually formulated in terms of low power, which in this case is actually 0." + }, + { + "text": "Again, the power is a number between 0 and 1." + }, + { + "text": "Close to 0, good." + }, + { + "text": "Close to 1, bad." + }, + { + "text": "Now, what is the definition of the p-value?" + }, + { + "text": "That's going to be something." + }, + { + "text": "Mouthful, right?" + }, + { + "text": "The definition of the p-value is a mouthful." + }, + { + "text": "It's really the tipping point." + }, + { + "text": "It is the smallest level at which blah, blah, blah, blah." + }, + { + "text": "It's complicated to remember it." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk34.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk34.json new file mode 100644 index 0000000000000000000000000000000000000000..074297c2186646a83b698c991607273c1d143e1c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk34.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, I think that by my sixth explanation, my wife, after saying, oh, so it's the probability of making an error, I said, yeah, that's the probability of making an error." + }, + { + "text": "Because of course, she can think probability of making an error, small, good, large, bad." + }, + { + "text": "So that's actually a good way to remember." + }, + { + "text": "I'm pretty sure that at least 50% of people using p-values out there think that the p-value is the probability of making an error." + }, + { + "text": "Now, for all matters of purposes, if your goal is to just threshold the p-value, this is OK to have this in mind." + }, + { + "text": "But when it comes, at least until December 22, I would recommend trying to actually memorize the right definition for the p-value." + }, + { + "text": "OK?" + }, + { + "text": "OK." + }, + { + "text": "So the idea, again, is fix the level and try to optimize the power." + }, + { + "text": "So we're going to try to compute some p-values from now on." + }, + { + "text": "How do you compute the p-value?" + }, + { + "text": "Well, you can actually see it from this picture over there." + }, + { + "text": "One thing I didn't show on this picture, here was my q alpha over 2 that had alpha here, alpha over 2 here, right?" + }, + { + "text": "That was my q alpha over 2." + }, + { + "text": "And I said, if tn is to the right of this guy, I'm going to reject." + }, + { + "text": "If tn is to the left of this guy, I'm going to fail to reject." + }, + { + "text": "OK?" + }, + { + "text": "Pictorially, you can actually represent the p-value." + }, + { + "text": "It's when I replace this guy by tn itself." + }, + { + "text": "Sorry, that's p-value over 2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk35.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk35.json new file mode 100644 index 0000000000000000000000000000000000000000..9f1a7b89f2d43b53944bbf516e37f98c7cf70618 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk35.json @@ -0,0 +1,62 @@ +[ + { + "text": "No, actually, that's p-value." + }, + { + "text": "So let me just keep it like that and put the absolute value here." + }, + { + "text": "OK?" + }, + { + "text": "So if you replace the role of q alpha over 2 by your test statistic, this is what the area under the curve is actually the p-value itself up to scaling, because of the symmetric thing." + }, + { + "text": "OK?" + }, + { + "text": "So there's a good way to see pictorially what the p-value is." + }, + { + "text": "It's just the probability that some Gaussians, which is the probability that some absolute value of n0,1 exceeds tn." + }, + { + "text": "Right?" + }, + { + "text": "That's what the p-value is." + }, + { + "text": "Now, this guy has nothing to do with this guy." + }, + { + "text": "So this is really just 1 minus the Gaussian CDF of tn." + }, + { + "text": "And that's it." + }, + { + "text": "So that's how I would compute p-values." + }, + { + "text": "Now, as I said, the p-value is a beauty, because you don't have to understand the fact that your limiting distribution is a Gaussian." + }, + { + "text": "Right?" + }, + { + "text": "It's already factored in this construction." + }, + { + "text": "The fact that I'm actually looking at this cumulative distribution function of a standard Gaussian makes my p-value automatically adjust to what the limiting distribution is." + }, + { + "text": "And if this was the cumulative distribution function of a exponential, I would just have a different function here denoted by f, for example." + }, + { + "text": "And I would just compute a different value." + }, + { + "text": "But in the end, regardless of what the limiting value is, my p-value would still be a number between 0 and 1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk36.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk36.json new file mode 100644 index 0000000000000000000000000000000000000000..2d4547dd85e8e54b4a9640f590a534ed56d0306a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk36.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so to illustrate that, let's look at other weird distributions that we could get in place of the standard Gaussian." + }, + { + "text": "And we're not going to see many, but we'll see one." + }, + { + "text": "And it's not called the chi-squared distribution." + }, + { + "text": "It's actually called the student's distribution, but it involves the chi-squared distribution as a building block." + }, + { + "text": "So I don't know if my phonetics are not really right there, so I try to say, well, it's chi-squared." + }, + { + "text": "Maybe it's chi-squared in Canada." + }, + { + "text": "Who knows?" + }, + { + "text": "So for a positive integer, so there's only one parameter." + }, + { + "text": "So for the Gaussian, you have two parameters, which are mu and sigma squared." + }, + { + "text": "Those are real numbers." + }, + { + "text": "Sigma squared is positive." + }, + { + "text": "Here, I have one integer parameter." + }, + { + "text": "Then the distribution, the chi-squared distribution with d degrees of freedom." + }, + { + "text": "So the parameter is called a degree of freedom, just like mu is called the expected value, and sigma squared is called the variance." + }, + { + "text": "So it's called degrees of freedom." + }, + { + "text": "You don't have to really understand why." + }, + { + "text": "So that's the law that you would get." + }, + { + "text": "That's the random variable you would get if you were to sum d squares of independent standard Gaussians." + }, + { + "text": "So I take the square of an independent random Gaussian." + }, + { + "text": "I take another one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk37.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk37.json new file mode 100644 index 0000000000000000000000000000000000000000..6fa169cd52b7910e64c667064ab385a1dc476da0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk37.json @@ -0,0 +1,62 @@ +[ + { + "text": "I sum them, and that's a chi-squared with two degrees of freedom." + }, + { + "text": "That's how you get it." + }, + { + "text": "Now, I could define it using its probability density function." + }, + { + "text": "After all, this is the sum of positive random variables." + }, + { + "text": "It is a positive random variable." + }, + { + "text": "It has a density on the positive real line." + }, + { + "text": "And the PDF of chi-squared, PDF of chi-squared with d degrees of freedom is what?" + }, + { + "text": "Well, it's fd of x is x to the d over 2 minus 1, e to the minus x over 2." + }, + { + "text": "And then here, I have a gamma of d over 2, and the other one is, I think, 2 to the d over 2 minus 1." + }, + { + "text": "No, 2 to the d over 2." + }, + { + "text": "That's what it is." + }, + { + "text": "That's the density." + }, + { + "text": "If you are very good at probability, you can make the change of variable and write your Jacobian and do all this stuff and actually check that this is true." + }, + { + "text": "I do not recommend doing that." + }, + { + "text": "So this is the density, but it's better understood like that, at thinking of just something that you built from standard Gaussian." + }, + { + "text": "So for example, an example of a chi-squared with two degrees of freedom is actually the following thing." + }, + { + "text": "Let's assume I have a target like this." + }, + { + "text": "And I don't aim very well, and I'm trying to hit the center." + }, + { + "text": "And I'm going to have maybe a deviation, which is standard Gaussian left-right and standard Gaussian north-south." + }, + { + "text": "So I'm throwing, and then I'm here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk38.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk38.json new file mode 100644 index 0000000000000000000000000000000000000000..e9321d18ef5daa35196a20db9f6bb7680045ede5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk38.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'm claiming that this number here, by Pythagoras' theorem, the squared distance here is the sum of this squared distance here, which is the square of a Gaussian by assumption, plus the square of this distance, which is the square of another independent Gaussian." + }, + { + "text": "I assume those are independent." + }, + { + "text": "And so the squared distance from this point to this point is the chi-squared with two degrees of freedom." + }, + { + "text": "So this guy here is n01 squared." + }, + { + "text": "This is n01 squared." + }, + { + "text": "And so this guy here, this distance here, is chi-squared with two degrees of freedom." + }, + { + "text": "I mean, the squared distance." + }, + { + "text": "I'm talking about squared distances here." + }, + { + "text": "So now you can see that actually Pythagoras is basically why chi-squared arise." + }, + { + "text": "That's why it has its own name." + }, + { + "text": "I mean, I could define this random variable." + }, + { + "text": "I mean, it's actually a gamma distribution." + }, + { + "text": "It's a special case of something called the gamma distribution." + }, + { + "text": "The fact that the special case has its own name is because there's many times where we're going to take sum of squares of independent Gaussians, because Gaussians, the sum of squares is really the norm, the Euclidean norm squared, just by Pythagoras theorem." + }, + { + "text": "If I'm in higher dimension, I can start to sum more squared coordinates, and I'm going to measure the norm squared." + }, + { + "text": "So if you want to draw this picture, it looks like this." + }, + { + "text": "Again, it's the sum of positive numbers." + }, + { + "text": "So it's going to be on 0 plus infinity." + }, + { + "text": "That's fd." + }, + { + "text": "And so for f1 looks like this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk39.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk39.json new file mode 100644 index 0000000000000000000000000000000000000000..530fa0ac2ba5f7380bf835d6fd19c3b55d8a53a3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk39.json @@ -0,0 +1,62 @@ +[ + { + "text": "f2 looks like this." + }, + { + "text": "So the tails becomes heavier and heavier as d increases." + }, + { + "text": "And then at start to 3, it starts to have a different shape." + }, + { + "text": "It starts from 0, and it looks like this." + }, + { + "text": "And then as d increases, it's basically as if you were to push this thing to the right." + }, + { + "text": "It's just like, pfft." + }, + { + "text": "It's just falling like a big ball." + }, + { + "text": "Everybody sees what's going on?" + }, + { + "text": "So there's just this fat thing that's just going there." + }, + { + "text": "What is the expected value of a k squared?" + }, + { + "text": "So it's the expected value of the sum of Gaussian random variables squared." + }, + { + "text": "I don't know why I said that." + }, + { + "text": "AUDIENCE 2 It's the sum of their second norm, right?" + }, + { + "text": "Which is?" + }, + { + "text": "Those are n0, 1." + }, + { + "text": "It's like, oh, I see, 1." + }, + { + "text": "Yeah." + }, + { + "text": "So n times 1, or d times 1." + }, + { + "text": "Yeah, which is d. So one thing you can check quickly is that the expected value of a k squared is d. And so you see, that's why the mass is shifting to the right as d increases." + }, + { + "text": "It's just going there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk4.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..07e0b7e52902074c6ec8439999a1046b4b977809 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "So for theta and theta 0, I know that my function is going to look like this." + }, + { + "text": "It's going to be somewhere in this rectangle." + }, + { + "text": "Everybody agrees?" + }, + { + "text": "So this function for this guy is going to look like this." + }, + { + "text": "When I'm at 0, when p is equal to 0, which means I only observe 0's, then I know that p is going to be 0." + }, + { + "text": "And I will certainly not conclude that p is equal to 1." + }, + { + "text": "This test will never conclude that p is equal to 1." + }, + { + "text": "Sorry, that was, yeah." + }, + { + "text": "That p is equal to, that p is lower than 1 half, just because xn bar is going to be equal to 0." + }, + { + "text": "OK, well, this is actually not well-defined." + }, + { + "text": "So maybe I need to do something, put it equal to 0 if xn bar is equal to 0." + }, + { + "text": "So I guess basically I get something which is negative." + }, + { + "text": "And so it's never going to be larger than what I want." + }, + { + "text": "And so here I'm actually starting at 0." + }, + { + "text": "So now this is this function here that increases." + }, + { + "text": "I mean, it should increase smoothly." + }, + { + "text": "This function here is alpha psi of theta, or alpha psi of p, let's say, because we're talking about p. Then it reaches alpha here." + }, + { + "text": "Now when I go on the other side, I'm actually looking at beta." + }, + { + "text": "When I'm on theta 1, the function that matters is the probability of type 2 error, which is beta psi." + }, + { + "text": "And this beta psi is actually going to increase." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk40.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk40.json new file mode 100644 index 0000000000000000000000000000000000000000..cf303c16babeea5b89d0924caa36f4dde58e6495 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk40.json @@ -0,0 +1,62 @@ +[ + { + "text": "Actually, the variance is also increasing." + }, + { + "text": "The variance is 2d." + }, + { + "text": "So this is one thing." + }, + { + "text": "And so why do we care about this in basic statistics?" + }, + { + "text": "It's not like we actually have statistics much about throwing darts at high dimensional boards." + }, + { + "text": "So what's happening is that if I look at the sample variance, the average of the sum of squared centered by their mean, then I can actually expend this as the sum of the squares minus the average squared." + }, + { + "text": "It's just the same trick that we have for the variance." + }, + { + "text": "Second moment minus first moment squared." + }, + { + "text": "And then I claim that Cochran's theorem, I will tell you in a second what Cochran's theorem tells me, is that this sample variance is actually, so if I had only this, so now, OK, look at those guys." + }, + { + "text": "Those guys are Gaussian with mean mu and variance sigma squared." + }, + { + "text": "Think for one second, mu being 0 and sigma squared being 1." + }, + { + "text": "Now, this part would be a chi-square with n degrees of freedom divided by n. Now, I get another thing here, which is the square of something that looks like a Gaussian as well." + }, + { + "text": "So it looks like I have something else here, which looks also like a chi-square." + }, + { + "text": "Now, Cochran's theorem is essentially telling you that those things are independent." + }, + { + "text": "And so that in a way, you can think of those guys as being here n degrees of freedom minus 1 degree of freedom." + }, + { + "text": "Now, here, as I said, this is not mean 0 and variance 1." + }, + { + "text": "The fact that it's not mean 0 is not a problem, because I can remove the mean here and remove the mean here." + }, + { + "text": "And so this thing has the same distribution, regardless of what the actual mean is." + }, + { + "text": "So without loss of generality, I can assume that mu is equal 0." + }, + { + "text": "Now, the variance I'm going to have to pay, because if I multiply all these numbers by 10, then this Sn is going to be multiplied by 100." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk41.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk41.json new file mode 100644 index 0000000000000000000000000000000000000000..be699853a1170afd439414bc8f189e87e84b0b94 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk41.json @@ -0,0 +1,62 @@ +[ + { + "text": "So this thing is going to scale with the variance." + }, + { + "text": "And not surprisingly, it's scaling like the square of the variance." + }, + { + "text": "So if I look at Sn, it's distributed as sigma-square times the chi-square with n minus 1 degrees of freedom divided by n. And we don't really write that, because a chi-square times sigma-square divided by n is not a distribution." + }, + { + "text": "So we put everything to the left." + }, + { + "text": "And we say that this is actually a chi-square with n minus 1 degrees of freedom." + }, + { + "text": "So here, I'm actually dropping a fact on you." + }, + { + "text": "But you can sort of see the building block." + }, + { + "text": "What is the thing that's sort of fussy at this point, but the rest should be crystal clear to you?" + }, + { + "text": "The thing that's fussy is that removing this square guy here is actually removing 1 degree of freedom." + }, + { + "text": "That should be weird." + }, + { + "text": "But that's what Cochran's theorem tells me." + }, + { + "text": "It's essentially stating something about orthogonality of subspaces with the span of the constant vector, something like that." + }, + { + "text": "So you don't have to think about it too much." + }, + { + "text": "But that's what it's telling me." + }, + { + "text": "But the rest, if you plug in, so the scaling in sigma-squared and in n, that should be completely clear to you." + }, + { + "text": "So in particular, if I remove that part, it should be clear to you that this thing, if mean is 0, this thing is actually distributed." + }, + { + "text": "Well, if mu is 0, what is the distribution of this guy?" + }, + { + "text": "So I remove that part, just this part." + }, + { + "text": "So I have xi, which are n0 sigma-squared." + }, + { + "text": "And I'm asking, what is the distribution of 1 over n sum from i equal 1 to n of xi-squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk42.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk42.json new file mode 100644 index 0000000000000000000000000000000000000000..3596e452514719b86b744b50b7402e7dd02b9ace --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk42.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it is the sum of their iid." + }, + { + "text": "So it's the sum of independent Gaussians, but not standard." + }, + { + "text": "So the first thing to make them standard is that I divide all of them by sigma-squared." + }, + { + "text": "Now, this guy is of the form zi-squared, where zi is n0, 1." + }, + { + "text": "So now this thing here has what distribution?" + }, + { + "text": "Chi-squared n. And now sigma-squared over n times chi-squared n. So if I have sigma-squared divided by n times chi-squared, sorry, so n times n divided by sigma-squared." + }, + { + "text": "So if I take this thing and I multiply it by n divided by sigma-squared, it means I remove this term." + }, + { + "text": "And now I am left with a chi-squared with n degrees of freedom." + }, + { + "text": "Now, the effect of centering with the sample mean here is only to lose 1 degree of freedom." + }, + { + "text": "That's it." + }, + { + "text": "OK?" + }, + { + "text": "So if I want to do a test about variance, since this is supposedly a good estimator of variance, this could be my pivotal distribution." + }, + { + "text": "This could play the role of a Gaussian." + }, + { + "text": "If I want to know if my variance is equal to 1 or larger than 1, I could actually build a test based on this only statement and test if the variance is larger than 1 or not." + }, + { + "text": "Now, this is not asymptotic because I started with the very assumption that my data was Gaussian itself." + }, + { + "text": "OK?" + }, + { + "text": "Now, just a side remark, you can check that this chi-squared 2, 2 is an exponential with half degrees of freedom, which is certainly not clear from the fact that z1 squared plus z2 squared is a chi-squared with 2 degrees of freedom." + }, + { + "text": "If I give you the sum of the square of two independent Gaussians, this is actually an exponential." + }, + { + "text": "That's not super clear, right?" + }, + { + "text": "But if you look at what was here, I don't know if you took notes, but let me rewrite it for you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk43.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk43.json new file mode 100644 index 0000000000000000000000000000000000000000..c1c4ce2a1e88dbaf6e313e0235a0fa58a881a709 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk43.json @@ -0,0 +1,59 @@ +[ + { + "text": "So it was x to the d over 2 minus 1 e to the minus x over 2 divided by 2 to the d over 2 gamma of d over 2." + }, + { + "text": "So if I plug in d is equal to 2, gamma of 2 over 2 is gamma of 1, which is 1, right?" + }, + { + "text": "It's factorial of 0." + }, + { + "text": "So it's 1." + }, + { + "text": "So this guy goes away." + }, + { + "text": "2 to the d over 2 is 2 to the 1." + }, + { + "text": "So that's just 1." + }, + { + "text": "No, that's just 2." + }, + { + "text": "OK?" + }, + { + "text": "Then x to the d over 2 minus 1 is x to the 0, goes away." + }, + { + "text": "And so I have x minus x over 2, 1 half, which is really, indeed, of the form lambda e to the minus lambda x for lambda is equal to 1 half, which was our exponential distribution." + }, + { + "text": "OK?" + }, + { + "text": "So well, next week is Columbus Day." + }, + { + "text": "So that's next Monday." + }, + { + "text": "So next week, we'll talk about students' distribution." + }, + { + "text": "And so that was discovered by a guy who pretended his name was student but was not student." + }, + { + "text": "And I challenge you to find why in the meantime." + }, + { + "text": "All right, so I'll see you next week." + }, + { + "text": "Your homework is going to be outside, so we can release the room." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk5.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..89ec03ee891688f8ef72df5ae36dcaada4844313 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "So beta psi is what?" + }, + { + "text": "Well, beta psi should also, sorry, that's the probability of being equal to alpha." + }, + { + "text": "So what I'm going to do is I'm going to look at the probability of rejecting." + }, + { + "text": "So let me draw this function all the way." + }, + { + "text": "It's going to look like this." + }, + { + "text": "Now here, if I look at this function here or here, this is the probability under theta that psi is equal to 1." + }, + { + "text": "And we just said that in this region, this function is called alpha psi." + }, + { + "text": "In that region, it's not called alpha psi." + }, + { + "text": "It's not called anything." + }, + { + "text": "It's just the probability of rejection." + }, + { + "text": "So it's not an error." + }, + { + "text": "It's actually what you should be doing." + }, + { + "text": "What we're looking at in this region is 1 minus this guy." + }, + { + "text": "We're looking at the probability of not rejecting." + }, + { + "text": "So I need to actually basically look at 1 minus this thing, which here is going to be 95%." + }, + { + "text": "So I'm going to do 95%." + }, + { + "text": "And this is my probability." + }, + { + "text": "And I'm just basically drawing the symmetric of this guy." + }, + { + "text": "So this here is the probability under theta that psi is equal to 0, which is 1 minus p theta that psi is equal to 1." + }, + { + "text": "So it's just 1 minus the white curve." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk6.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..2ba3f3f31acb2d89e2bd57110d90b292f5959fce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's actually, by definition, equal to beta psi of theta." + }, + { + "text": "Now, where do I read pi psi?" + }, + { + "text": "What is pi psi on this picture?" + }, + { + "text": "Is pi psi a number or a function?" + }, + { + "text": "It's a number, right?" + }, + { + "text": "It's the minimum of a function." + }, + { + "text": "What is this function?" + }, + { + "text": "It's the probability under theta that theta is equal to 1." + }, + { + "text": "I drew this entire function between theta 0 and theta 1." + }, + { + "text": "I drew this entire white curve." + }, + { + "text": "This is this probability." + }, + { + "text": "Now, I'm saying, look at the smallest value this probability can take on the set theta 1." + }, + { + "text": "What is this?" + }, + { + "text": "This guy." + }, + { + "text": "This is where my pi, this thing here, is pi psi." + }, + { + "text": "And so it's equal to 5%." + }, + { + "text": "So that's for this particular test, because this test is sort of a continuous curve for this psi." + }, + { + "text": "And so if I want to make sure that I'm at 5% when I come to the right of theta 0, if it touches theta 1, then I better have 5% on the other side if the function is continuous." + }, + { + "text": "So basically, if this function is increasing, which will be the case for most tests, then what's going to happen is that, and continuous, then what's going to happen is that the level of the test, which is alpha, is actually going to be equal to the power of the test." + }, + { + "text": "OK?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk7.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..4f5cdee6b6891b45c5f7794aece5ce2b8c13dc7a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, there's something I didn't mention, and I'm just mentioning it, pass it by." + }, + { + "text": "Here, I define the power itself." + }, + { + "text": "This function, this entire white curve here, is actually called the power function." + }, + { + "text": "This thing, that's the entire white curve." + }, + { + "text": "And what you could have is tests that have the entire curve, which is dominated by another test." + }, + { + "text": "So here, if I look at this test, and let's assume I can build another test that has this curve." + }, + { + "text": "Let's say it's the same here." + }, + { + "text": "But then here, it looks like this." + }, + { + "text": "What is the power of this test?" + }, + { + "text": "It's the same." + }, + { + "text": "It's 5%, because this point touches here exactly at the same point." + }, + { + "text": "However, for any other value than the worst possible, this guy is doing better than this guy." + }, + { + "text": "Can you see that?" + }, + { + "text": "Having a curve higher on the right-hand side is a good thing, because it means that you tend to reject more when you're actually in H1." + }, + { + "text": "So this guy is definitely better than this guy." + }, + { + "text": "And so what we say in this case is that the test with the dashed line is uniformly more powerful than the other test." + }, + { + "text": "But we're not going to go into those details, because basically, all the tests that we will describe are already the most powerful ones." + }, + { + "text": "In particular, this guy is, there's no such thing." + }, + { + "text": "All the other guys you can come up with are going to actually be below." + }, + { + "text": "So we saw a couple tests, and we saw how to pick this threshold, and we defined those two things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk8.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8b9449415f7337b53908d8098f0293899e0ba86e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "Yes?" + }, + { + "text": "AUDIENCE 2 But in that case, the down one, if it were also higher in the region of 2 to 0, do you still consider it better?" + }, + { + "text": "PHILIPPE RIGOLLETTIS Because you're given this budget of 5%, right?" + }, + { + "text": "So in this paradigm, where you're given the, actually, if the dashed line was this dashed line, I would still be happy." + }, + { + "text": "I mean, I don't care what this thing does here, as long as it's below 5%." + }, + { + "text": "But here, I'm going to try to discover it, right?" + }, + { + "text": "Think about, again, the drug discovery example." + }, + { + "text": "You're trying to find, let's say you're a scientist, and you're trying to prove that your drug works." + }, + { + "text": "What do you want to see?" + }, + { + "text": "Well, FDA puts on you this constraint that your probability of type 1 error should never exceed 5%." + }, + { + "text": "You're going to work under this assumption." + }, + { + "text": "But what you're going to do is going to try to find a test that will make you find something as often as possible." + }, + { + "text": "And so you're going to max this constraint of 5%, and then you're going to try to make this curve, this curve that means that this is basically, this number here, for any point here, is the probability that you publish your paper." + }, + { + "text": "That's the probability that you can release to market your drug." + }, + { + "text": "That's the probability that it works, right?" + }, + { + "text": "And so you want this curve to be as high as possible." + }, + { + "text": "You want to make sure that if there's evidence in the data that H1 is the truth, you want to squeeze as much of this evidence as possible." + }, + { + "text": "And the test that has the highest possible curve is the most powerful one." + }, + { + "text": "Now, you have to also understand that having two curves that are on top of each other, completely, everywhere, is a rare phenomenon." + }, + { + "text": "It's not always the case that there is a test that's uniformly more powerful than any other test." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk9.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bbad3ae05fbb39d9ef76b7b89aa0fada7d5adc3e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_1_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It might be that you have some trade-off, that it might be better here, but then you're losing power here." + }, + { + "text": "Things like this." + }, + { + "text": "Well, actually, maybe it should not go down." + }, + { + "text": "But let's say it goes like this, and then maybe this guy goes like this." + }, + { + "text": "Then you have to basically make an educated guess whether you think that the theta you're going to find is here or it's here." + }, + { + "text": "And then you pick a test." + }, + { + "text": "OK?" + }, + { + "text": "Any other question?" + }, + { + "text": "Yes?" + }, + { + "text": "AUDIENCE 2." + }, + { + "text": "What is the derivative of the type 2 error?" + }, + { + "text": "PHILIPPE RIGOLLET." + }, + { + "text": "So the green curve is exactly right." + }, + { + "text": "So that's beta psi of theta." + }, + { + "text": "So it's really the type 2 error, and it's defined only here." + }, + { + "text": "So here, it's not a definition." + }, + { + "text": "It's really just I'm just mapping it to this point." + }, + { + "text": "So it's defined only here, and it's the probability of type 2 error." + }, + { + "text": "So here, it's pretty large, right?" + }, + { + "text": "I'm making it basically as large as I could, because I'm at the boundary." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk0.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..65c23c5cab5e2c4f1a8f872964a31edc5dd21493 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "Talking about tests, and to be fair, we spend most of our time talking about new jargon that we're using." + }, + { + "text": "But the main goal is to take a binary decision, yes and no." + }, + { + "text": "So just so that we're clear and we make sure that we all speak the same language, let me just remind you what the key words are for tests." + }, + { + "text": "So the first thing is that we split theta in theta 0 and theta 1." + }, + { + "text": "Both are included in theta, and they're disjoint." + }, + { + "text": "OK." + }, + { + "text": "So I have my set of possible parameters." + }, + { + "text": "And then I have theta 0 is here, theta 1 is here, and there might be something that I leave out." + }, + { + "text": "And so what we're doing is we have two hypotheses." + }, + { + "text": "So here's our hypothesis testing problem." + }, + { + "text": "And it's h0 theta belongs to theta 0 versus h1 theta belongs to theta 1." + }, + { + "text": "This guy was called the null, and this guy was called the alternative." + }, + { + "text": "And why we give them special names is because we saw that they have an asymmetric role." + }, + { + "text": "The null represents the status quo, and data is here to bring evidence against this guy." + }, + { + "text": "And we can really never conclude that h0 is true because all we could conclude is that h1 is not true or may not be true." + }, + { + "text": "So that was the first thing." + }, + { + "text": "The second thing was the hypothesis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk1.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3b72e60009f76e8f81d23cb396a309bf7d70b355 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "The third thing is what is a test?" + }, + { + "text": "Well, psi, it's a statistic." + }, + { + "text": "And it takes the data, and it maps it into 0 or 1." + }, + { + "text": "And I didn't really mention it, but there's something such as called randomized tests, which is, well, if it cannot really make a decision, they might as well flip a coin." + }, + { + "text": "That tends to be biased, but that's really, I mean, think about it in practice." + }, + { + "text": "You probably don't want to make decisions based on flipping a coin." + }, + { + "text": "And so what people typically do, this is happening typically at one specific value." + }, + { + "text": "So rather than flipping a coin for this very specific value, what people typically do is they say, OK, I'm going to side with h0 because that's the most conservative choice I can make." + }, + { + "text": "So in a way, they think of flipping this coin, but always falling on heads." + }, + { + "text": "So associated to this test was something called, well, the rejection region." + }, + { + "text": "And r psi, which is just the set of data, x1, xn, such that psi of x1, xn is equal to 1." + }, + { + "text": "So that means we rejected 0 when the test is 1, and those are the set of data points that actually are going to lead me to reject the test." + }, + { + "text": "OK. Then the things that were actually slightly a little more important and really peculiar to test, specific to test, were the type 1 and type 2 error." + }, + { + "text": "So the type 1 error arises when, so type 1 error is when you reject whereas h0 is correct." + }, + { + "text": "And the type 2 error is the opposite." + }, + { + "text": "So it's failed to reject whereas h1 is correct." + }, + { + "text": "h is correct." + }, + { + "text": "So those are the two types of errors you can make, and we quantify their probability of type 1 error." + }, + { + "text": "So alpha psi is the probability." + }, + { + "text": "So that's the probability of type 1 error." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk10.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c19b0d21dee98686b07f25081871711f112710fa --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "And that means at the boundary, since the status quo is h0, I'm always going to go for h0 if I don't have any evidence, which means that what's going to pay is the type 2 error that's going to basically pay this." + }, + { + "text": "OK?" + }, + { + "text": "Any other question?" + }, + { + "text": "All right, so let's move on." + }, + { + "text": "So did we do this?" + }, + { + "text": "No, I think we stopped here, right?" + }, + { + "text": "I didn't cover that part." + }, + { + "text": "So as I said, in this paradigm, we're going to actually fix this guy to be something." + }, + { + "text": "And this thing is actually called the level of the test." + }, + { + "text": "I'm sorry, this is again more words." + }, + { + "text": "Actually, good news is that we split it into two lectures." + }, + { + "text": "So we have, what is a test?" + }, + { + "text": "What is a hypothesis?" + }, + { + "text": "What is the null?" + }, + { + "text": "What is the alternative?" + }, + { + "text": "What is the type 1 error?" + }, + { + "text": "What is the type 2 error?" + }, + { + "text": "And now, I'm telling you there's another thing." + }, + { + "text": "So we defined the power, which was some sort of a lower bound on the, or it's 1 minus the upper bound on the type 2 error, basically." + }, + { + "text": "And so it's alternative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk11.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..815ec78c1b831dd92a2b3f1d68a91dd8df86f618 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "So the power is the smallest probability of rejecting when you're in the null." + }, + { + "text": "And it's alternative when you're in theta 1, right?" + }, + { + "text": "So that's my power." + }, + { + "text": "I looked here, and I looked at the smallest value." + }, + { + "text": "And I can look at this side and say, well, what is the largest probability that I make a type 1 error?" + }, + { + "text": "Again, this largest probability is the level of the test." + }, + { + "text": "OK, so this is alpha equal, by definition, to the maximum for theta and theta 0 of alpha psi of theta." + }, + { + "text": "So here, I just put the level itself." + }, + { + "text": "As you can see here, it essentially says that if I'm of level 5%, I'm also of level 10%." + }, + { + "text": "I'm also of level 15%." + }, + { + "text": "So here, it's really an upper bound." + }, + { + "text": "Whatever you guys want to take, this is what it is." + }, + { + "text": "But as we said, if this number is 4.5%, you're losing in your type 2 error." + }, + { + "text": "So if you're allowed to have, if this maximum here is 4.5%, and FDA told you you can go to 5%, you're losing in your type 2 error." + }, + { + "text": "So you actually want to make sure that this is the 5% that's given to you." + }, + { + "text": "So the way it works is that you give me the alpha." + }, + { + "text": "Then I'm going to go back, pick c that depends on alpha here, so that this thing is actually equal to 5%." + }, + { + "text": "And so, of course, in many instances, we do not know the probability." + }, + { + "text": "We do not know how to compute the probability of type 1 error." + }, + { + "text": "This is a maximum value for the probability of type 1 error." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk12.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..4bd3834b631a0a7c734e2b14c2fe32eaf6f601e6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "We don't know how to compute it." + }, + { + "text": "I mean, it might be a very complicated random variable." + }, + { + "text": "Maybe it's a weird binomial." + }, + { + "text": "We could compute it, but it would be painful." + }, + { + "text": "But what we know how to compute is its asymptotic value, which is because of the central limit theorem, convergence and distribution tells me that the probability of type 1 error is basically going towards the probability that some Gaussian is in some region." + }, + { + "text": "And so we're going to compute not the level itself, but the asymptotic level." + }, + { + "text": "So again, that's basically the limit as n goes to infinity of alpha psi of theta." + }, + { + "text": "And then I'm going to make the max here." + }, + { + "text": "OK?" + }, + { + "text": "So how am I going to compute this?" + }, + { + "text": "Well, if I take a test that has rejection region of the form Tn, because it depends on the data, right?" + }, + { + "text": "That's Tn of x1, xn, my observations, larger than some number c. OK?" + }, + { + "text": "Of course, I can almost always write tests like that, except that sometimes there's going to be an absolute value, which essentially means I'm going away from some value." + }, + { + "text": "Maybe actually I'm less than something, but I can always put a negative sign in front of everything." + }, + { + "text": "So this is not without much of generality, right?" + }, + { + "text": "So this includes something that looks like something is larger than the constant, right?" + }, + { + "text": "So that means, which is equivalent to, well, let me write it as Tq." + }, + { + "text": "OK, because then that means that, so that's Tn." + }, + { + "text": "But this actually encompasses the fact that Qn is larger than c, or Qn is less than c, then minus c. So that includes this guy." + }, + { + "text": "That also includes Qn less than c, because this is equivalent to Qn is larger than minus c. Minus Qn is, and so that's going to be my Tn." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk13.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..d0fc40d7fea49cc51a82242971122ccb04ee2caf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I can actually encode several type of things, OK?" + }, + { + "text": "Rejection regions that, so here in this case, I have a rejection region that looks like this, or a rejection region that looks like this, or a rejection region that looks like this." + }, + { + "text": "OK, and here I don't really represent it for the whole data, but maybe for the average, for example, or the normalized average." + }, + { + "text": "OK, so if I write this, then, yeah." + }, + { + "text": "And in this case, this Tn that shows up is called test statistic." + }, + { + "text": "I mean, this is sort of a, I mean, this is not like set in stone." + }, + { + "text": "Here, for example, Q could be the test statistics." + }, + { + "text": "It doesn't have to be minus Q itself that's the test statistic, right?" + }, + { + "text": "So what is the test statistic?" + }, + { + "text": "Well, it's what you're going to build from your data and then compare to some fixed value, right?" + }, + { + "text": "So in the example we had here, what is our test statistic?" + }, + { + "text": "Well, it's this guy, right?" + }, + { + "text": "This was our test statistic." + }, + { + "text": "And is this thing a statistic?" + }, + { + "text": "What are the criteria for a statistic?" + }, + { + "text": "What is a statistic?" + }, + { + "text": "I know you know the answer." + }, + { + "text": "AUDIENCE MEMBER 2." + }, + { + "text": "Is it a measurable function?" + }, + { + "text": "PROFESSOR PHILIPPE RIGOLLET." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk14.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..deb918611779af5e70f1e976f45cfc296740fc0a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "Yeah, it's a measurable function of the data that does not depend on the parameter." + }, + { + "text": "Is this guy a statistic?" + }, + { + "text": "AUDIENCE MEMBER 3." + }, + { + "text": "Yes, he is." + }, + { + "text": "PROFESSOR PHILIPPE RIGOLLET." + }, + { + "text": "Let's think again." + }, + { + "text": "When I implemented the test, what did I do?" + }, + { + "text": "I was able to compute my test." + }, + { + "text": "My test did not depend on some unknown parameter." + }, + { + "text": "How did we do it?" + }, + { + "text": "We just plugged in 0.5 here." + }, + { + "text": "Remember?" + }, + { + "text": "That was the value for which we computed it, because under h0, that was the value we're seeing." + }, + { + "text": "And if theta 0 is actually an entire set, I'm just going to take the value that's the closest to h1." + }, + { + "text": "We'll see that in a second." + }, + { + "text": "I mean, I did not guarantee that to you." + }, + { + "text": "But just taking the worst type 1 error and bounding it by alpha is equivalent to taking p and taking the value of p that's the closest to theta 1, which is completely intuitive." + }, + { + "text": "The worst type 1 error is going to be attained for the p that's the closest to the alternative." + }, + { + "text": "So even if the null is actually just an entire set, it's as if it was just the point that's the closest to the alternative." + }, + { + "text": "So now we can compute this, because there's no unknown parameters that shows up." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk15.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..0bc365016096bbbfd9f7a60ab9c2724dec760020 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "We replaced p by 0.5." + }, + { + "text": "And so that was our test statistic." + }, + { + "text": "So when you're building a test, you want to first build a test statistic and then see what threshold you should be getting." + }, + { + "text": "So now let's go back to our example where we have x1, xn." + }, + { + "text": "They're iid Bernoulli p. And I want to test if p is 1 half versus p not equal to 1 half, which as I said is what you want to do if you want to test if a coin is fair." + }, + { + "text": "And so here I'm going to build a test statistic." + }, + { + "text": "And we concluded last time that what do we want for this statistic?" + }, + { + "text": "We want it to have a distribution which under the null does not depend on the parameters, a distribution that I can actually compute quintiles of." + }, + { + "text": "So what we did is we said, well, if I look at the central limit theorem tells me that square root of n xn bar minus p divided by." + }, + { + "text": "So if I do central limit theorem plus Slutsky, for example, I'm going to have square root." + }, + { + "text": "And we've had this discussion whether we want to use Slutsky or not here." + }, + { + "text": "But let's assume we're taking Slutsky wherever we can." + }, + { + "text": "So this thing tells me that by the central limit theorem as n goes to infinity, this thing converges in distribution to some n 0, 1." + }, + { + "text": "Now as we said, this guy is not something we know." + }, + { + "text": "But under the null, we actually know it." + }, + { + "text": "And we can actually replace it by 1 half." + }, + { + "text": "So this thing holds under h0." + }, + { + "text": "When I write under h0, it means when this is the truth." + }, + { + "text": "So now I have something that converges to something that has no dependence on anything I don't know." + }, + { + "text": "And in particular, if you have any statistics textbook, which you don't because I didn't require one, you should be thankful because this thing costs $250." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk16.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..298b0fb997de98b972702f498d96cfa89d4e4b7d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "This thing's actually, if you look at the back, you actually have a table for a standard Gaussian." + }, + { + "text": "I could have anything else here." + }, + { + "text": "I could have an exponential distribution." + }, + { + "text": "I could have a, I don't know, a, well, we'll see the chi-square distribution in a minute." + }, + { + "text": "Any distribution from which you can actually see a table that somebody actually computed this thing for which you can actually draw the PDF and start computing whatever probability you want on them, then this is what you want to see at the right-hand side." + }, + { + "text": "This is any distribution." + }, + { + "text": "It's called pivotal." + }, + { + "text": "I think we've mentioned that before." + }, + { + "text": "Pivotal means it does not depend on anything that you don't know." + }, + { + "text": "And maybe it's easy to compute those things." + }, + { + "text": "Probably, typically, you need a computer to simulate them for you because computing probabilities for Gaussians is not an easy thing." + }, + { + "text": "We don't know how to solve those integrals exactly." + }, + { + "text": "We have to do it numerically." + }, + { + "text": "OK, so now I want to do this test." + }, + { + "text": "My test statistic will be declared to be what?" + }, + { + "text": "Well, I'm going to reject if what is larger than some number?" + }, + { + "text": "The absolute value of this guy." + }, + { + "text": "So my test statistic is going to be square root of n minus 0.5 divided by square root of xn bar 1 minus xn bar." + }, + { + "text": "That's my test statistic, absolute value of this guy, because I want to reject either when this guy is too large or when this guy is too small." + }, + { + "text": "I don't know ahead whether I'm going to see p larger than 1 half or less than 1 half." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk17.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..c16a8c6be2149a29434fcd2457ee0fdbf0606f2d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "So now I need to compute c such that the probability that tn is lower than c. So that's what?" + }, + { + "text": "That's the probability under p, which is unknown." + }, + { + "text": "I want this probability to be less than some level alpha asymptotically." + }, + { + "text": "So I want the limit of this guy to be less than alpha, and that's the level of my test." + }, + { + "text": "So that's the given level." + }, + { + "text": "So I want this thing to happen." + }, + { + "text": "Now what I know is that this limit, actually, I should say given asymptotic level." + }, + { + "text": "So what is this thing?" + }, + { + "text": "Well, OK, that's the probability that something that looks like under p. So under p, this guy, so what I know is that tn is square root of n minus xn bar minus 0.5 divided by square root of xn bar 1 minus xn bar exceeds." + }, + { + "text": "Is this true that as n goes to infinity, this probability is the same as the probability that the absolute value of a Gaussian exceeds c of a standard Gaussian?" + }, + { + "text": "Is this true?" + }, + { + "text": "Yeah, so you're saying that this, as n becomes large enough, this should be the probability that some absolute value of n0,1 exceeds c, right?" + }, + { + "text": "So I claim that this is not correct." + }, + { + "text": "Somebody tell me why." + }, + { + "text": "Even in the limit, it's not correct?" + }, + { + "text": "Even in the limit, it's not correct." + }, + { + "text": "OK." + }, + { + "text": "So what do you see?" + }, + { + "text": "It's because at the beginning, we picked the worst possible true parameter, 0.5, right?" + }, + { + "text": "So we don't actually know that this 0.5 is the least." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk18.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..21ff2eaef450e95222ef4c4c025a1ccb1a883204 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Exactly, right?" + }, + { + "text": "So we picked this 0.5 here, but this is for any p, right?" + }, + { + "text": "But what is the only p I can get?" + }, + { + "text": "So what I want is that this is true for all p in theta 0." + }, + { + "text": "But the only p that's in theta 0 is actually p is equal to 0.5." + }, + { + "text": "So yes, what you said was true, but it required to specify p to be equal to 0.5." + }, + { + "text": "So this, in general, is not true." + }, + { + "text": "But it happens to be true if p belongs to theta 0, which is strictly equivalent to p is equal to 0.5, right?" + }, + { + "text": "Theta 0 is really just this one point, 0.5." + }, + { + "text": "OK, so now this becomes true." + }, + { + "text": "And so what I need to do is to find c such that this guy is equal to what?" + }, + { + "text": "I mean, let's just follow, right?" + }, + { + "text": "So I want this to be less than alpha." + }, + { + "text": "But then we see that this was equal to this, which is equal to this." + }, + { + "text": "So all I want is that this guy is less than alpha." + }, + { + "text": "But we said we might as well just make it equal to alpha if you allow me to make it as big as I want, as long as it's less than alpha." + }, + { + "text": "So this is a true statement." + }, + { + "text": "But it's if under this condition, right?" + }, + { + "text": "So I'm going to set it equal to alpha." + }, + { + "text": "And then I'm going to try to solve for c. OK, so what I'm looking for is a c such that if I draw a standard Gaussian, so that's PDF of some n0,1, I want the probability that the absolute value of my Gaussian exceeding this guy." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk19.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..b610ab510e065f845cbac3e680352a281a5977db --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that means being either here or here." + }, + { + "text": "So that's minus c and c. I want the sum of those two things to be equal to alpha." + }, + { + "text": "So I want the sum of these areas to equal alpha." + }, + { + "text": "So by symmetry, each of them should be equal to alpha over 2." + }, + { + "text": "And so what I'm looking for is c such that the probability that my n0,1 exceeds c, which is just this area to the right now, equals alpha, which is equivalent to taking c, which is q equals alpha over 2." + }, + { + "text": "And that's q alpha over 2 by definition of q alpha over 2." + }, + { + "text": "That's just what q alpha over 2 is." + }, + { + "text": "And that's what the tables at the back of the book give you." + }, + { + "text": "Who has already seen a table for Gaussian probabilities?" + }, + { + "text": "All right." + }, + { + "text": "What it does is just a table." + }, + { + "text": "I mean, it's pretty ancient, right?" + }, + { + "text": "I mean, of course, you can actually ask Google to do it for you now." + }, + { + "text": "It's basically standard issue." + }, + { + "text": "But back in the day, they actually had to look at tables." + }, + { + "text": "And since the values alphas were pretty standard, the values alpha that people were requesting were typically 1%, 5%, 10%." + }, + { + "text": "All you could do is to compute these different values for different values of alpha." + }, + { + "text": "That was it." + }, + { + "text": "So that's really not much to give you." + }, + { + "text": "So for the Gaussian, I can tell you that alpha is equal to, if alpha is equal to 5%, then q alpha over 2, q 2.5% is equal to 1.96%." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk2.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..d35a9367292f43552ea9e2c936629f0062774757 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So psi is just the probability for theta that psi rejects, and that's defined for theta and theta 0." + }, + { + "text": "So for different values of theta 0, so h0 being correct means there exists a theta in theta 0 for which that actually is the right distribution." + }, + { + "text": "So for different values of theta, I might make different errors." + }, + { + "text": "So if you think, for example, about the coin example, if I'm testing if the coin is biased towards heads or biased towards tails, so if I'm testing whether p is larger than 1 half or less than 1 half, then when the true p, let's say h0 is larger than 1 half, when p is equal to 1, it's actually very difficult for me to make a mistake, because I only see heads." + }, + { + "text": "So when p is getting closer to 1 half, I'm going to start making more and more probability there." + }, + { + "text": "And so the type 2 error, so that's the probability of type 2, is denoted by beta psi." + }, + { + "text": "And it's the function that does the opposite, and this time is defined for theta and theta 0 and theta 1." + }, + { + "text": "And finally, we define something called the power pi of psi." + }, + { + "text": "And this time, this is actually a number." + }, + { + "text": "And so this number is equal to the maximum over theta and theta 0." + }, + { + "text": "I mean, that could be a supremum, but think of it as being a maximum of p theta of psi is equal, sorry, that's in 0." + }, + { + "text": "Give me one sec." + }, + { + "text": "No, that's the min." + }, + { + "text": "So this is not making a mistake." + }, + { + "text": "Theta 0 is in theta 1." + }, + { + "text": "So theta is in theta 1, and I conclude 1." + }, + { + "text": "So this is a good thing." + }, + { + "text": "I want this number to be large, and I'm looking at the worst house, what is the smallest value this number can be." + }, + { + "text": "So what I want to show you a little bit is a picture." + }, + { + "text": "So now I'm going to take theta, and think of it as being p. So I'm going to take p for some Bernoulli experiment." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk20.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..20ad1dac1f1c76cdb383bd9a41a5521bfc8e8f80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "So those are just fixed numbers that are functions of the Gaussian." + }, + { + "text": "All right, so everybody agrees?" + }, + { + "text": "We've done that before for our confidence intervals." + }, + { + "text": "And so now we know that if I actually plug in this guy to be q alpha over 2, then this limit is actually equal to alpha." + }, + { + "text": "And so now I've actually constrained this." + }, + { + "text": "So q alpha over 2 here is, for alpha equals 5%, as I said, is 1.96." + }, + { + "text": "So in the example 1, the number that we found was 3.54, I think, or something like that, 3.55 for t. So if we scroll back very quickly, 3.45." + }, + { + "text": "That was example 1." + }, + { + "text": "Example 2, negative 0.77." + }, + { + "text": "So if I look at t, n, in example 1, tn was just the absolute value of 3.45, which don't pull out your calculators, is equal to 3.45." + }, + { + "text": "Example 2, absolute value of negative 0.77 was equal to 0.77." + }, + { + "text": "And so all I need to check is, is this number larger or smaller than 1.96?" + }, + { + "text": "That's what my test ends up being." + }, + { + "text": "So in example 1, 3.45 being larger than 1.96, that means that I reject." + }, + { + "text": "Fairness of my coins in example 2, 0.77 being smaller than 1.96, what do I do?" + }, + { + "text": "I fail to reject." + }, + { + "text": "OK?" + }, + { + "text": "So here's a question." + }, + { + "text": "In example 1, for what level alpha would psi alpha, what is the?" + }, + { + "text": "So here, what's going to happen if I start decreasing my level?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk21.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..8a92eddc8e39673740ca195fad03c2d25a729273 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "When I decrease my level, I'm actually making this area smaller and smaller, which means that I push the c to the right." + }, + { + "text": "So now I'm asking, what is the smallest c I should pick so that now I actually do not reject h0?" + }, + { + "text": "What is the smallest c I should be taking?" + }, + { + "text": "Here." + }, + { + "text": "What is the smallest c?" + }, + { + "text": "So c here in the example I gave you for 5% was 1.96." + }, + { + "text": "What is the smallest c I should be taking so that now this inequality is reversed?" + }, + { + "text": "3.45." + }, + { + "text": "I ask only trivial questions." + }, + { + "text": "Don't be worried." + }, + { + "text": "So 3.45 is the smallest c that I'm actually willing to tolerate." + }, + { + "text": "So let's say this was my 5%." + }, + { + "text": "If this was 2.5, if alpha here, let's say in this picture, alpha is 5%, that means maybe I need to push here." + }, + { + "text": "And this number should be what?" + }, + { + "text": "So this is going to be 1.96." + }, + { + "text": "And this number here is going to be 3.45, clearly to scale." + }, + { + "text": "And so now what I want to ask you is, well, there's two ways I can understand this number 3.45." + }, + { + "text": "It is the number 3.45." + }, + { + "text": "But I can also try to understand, what is the area to the right of this guy?" + }, + { + "text": "And if I understand what the area to the right of this guy is, this is actually some alpha prime over 2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk22.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..7503edb72bbc4e9db22fe8e956729e7f3881d675 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "And that means that if I actually fix this level, alpha prime, that would be exactly the tipping point at which I would go from accepting to rejecting." + }, + { + "text": "So I know in terms of absolute thresholds, 3.45 is the trivial answer to the question." + }, + { + "text": "That's the tipping point, because I'm comparing a number to 3.45." + }, + { + "text": "But now if I try to map this back and understand what level would have been given me this particular tipping point, that's a number between 0 and 1." + }, + { + "text": "The smaller the number, the larger this number here, which means that the more evidence I have in my data against h0." + }, + { + "text": "And so this number is actually something called the p-value." + }, + { + "text": "And so same for example 2." + }, + { + "text": "There's the tipping point, alpha, at which I go from feeling to reject to rejecting." + }, + { + "text": "And that's exactly the number, the area under the curve, such that here I see 0.77." + }, + { + "text": "And this is this alpha prime prime over 2." + }, + { + "text": "And this number is clearly, alpha prime prime is clearly larger than 5%." + }, + { + "text": "So what's the advantage of thinking and mapping back these numbers?" + }, + { + "text": "Well, now I'm actually going to spit out some number which is between 0 and 1." + }, + { + "text": "And that should be the only scale you should have in mind." + }, + { + "text": "Remember we discussed that last time." + }, + { + "text": "Well, if I actually spit out a number which is 3.45, maybe you can try to think, is 3.45 a large number for a Gaussian?" + }, + { + "text": "That's a number." + }, + { + "text": "But if I had another random variable that was not Gaussian, maybe it was a double exponential, you would have to have another scale in your mind." + }, + { + "text": "Is 3.45 a large number for the large, so large that it's unlikely to come from a double exponential?" + }, + { + "text": "If I had a gamma distribution, I can think of any distribution." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk23.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..d0d0fdec57ad2cc7e2dadb707abb6df87bdbb70b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then that means for each distribution, you would have to have a scale in mind." + }, + { + "text": "So of course, you can have the Gaussian scale in mind." + }, + { + "text": "I mean, I have the Gaussian scale in mind." + }, + { + "text": "But then if I map it back into this number between 0 and 1, all the distributions play the same role." + }, + { + "text": "So whether I'm talking about if my limiting distribution is normal or exponential or gamma or whatever you want, for all these guys, I'm just going to map it into one number between 0 and 1." + }, + { + "text": "Small number means lots of evidence against h1." + }, + { + "text": "Large number means lots of evidence against h0." + }, + { + "text": "Small number means very few evidence against h0." + }, + { + "text": "And this is the only number you need to keep in mind." + }, + { + "text": "And the question is, am I willing to tolerate this number between 5%, 6% or maybe 10%, 12%?" + }, + { + "text": "And this is the only scale you have to have in mind." + }, + { + "text": "And this scale is the scale of p-values." + }, + { + "text": "So the p-value is the tipping point in terms of alpha." + }, + { + "text": "In words, I can make it formal, because tipping point, as far as I know, is not a mathematical term." + }, + { + "text": "So a p-value of a test is the smallest, potentially asymptotic level, if I talk about an asymptotic p-value." + }, + { + "text": "And that's what we do when we talk about central limit theorem, at which the test rejects h0." + }, + { + "text": "If I were to go any smaller, I would fail to reject." + }, + { + "text": "The smaller the level, the less likely it is for me to reject." + }, + { + "text": "And if I were to go any smaller, I would start failing to reject." + }, + { + "text": "And so it is a random number." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk24.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..70790440238c22e23b0b77fc5e658fdf89d62e44 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "It depends on what I actually observe." + }, + { + "text": "So here, of course, I instantiated those two numbers, 3.45 and 0.77, as realizations of random variables." + }, + { + "text": "But if you think of those as being the random numbers before I see my data, this was a random number." + }, + { + "text": "And therefore, the area under the curve to the right of it is also a random area." + }, + { + "text": "If this thing fluctuates, then the area under the curve fluctuates." + }, + { + "text": "And that's what the p-value is." + }, + { + "text": "That's what John Oliver talks about when he talks about p-hacking." + }, + { + "text": "And so we talked about this in the first lecture." + }, + { + "text": "So p-hacking is, how do I do?" + }, + { + "text": "Oh, if I'm a scientist, do I want to see a small p-value or a large p-value?" + }, + { + "text": "Small, right?" + }, + { + "text": "Scientists want to see small p-values, because small p-values equals rejecting, which equals discovery, which equals publication, which equals promotion." + }, + { + "text": "So that's what people want to see." + }, + { + "text": "So people are tempted to see small p-values." + }, + { + "text": "And what's called p-hacking is, well, find a way to cheat." + }, + { + "text": "Maybe look at your data, formulate your hypothesis in such a way that you will actually have a smaller p-value than you should have." + }, + { + "text": "So here, for example, there's one thing I did not insist on, because again, this is not a particular course in statistical thinking." + }, + { + "text": "But one thing that we implicitly did was set those theta 0 and theta 1 ahead of time." + }, + { + "text": "I fixed them, and I'm trying to test this." + }, + { + "text": "This is to be contrasted with the following approach." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk25.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..ae5989051a3c9ad74dd6e26eac906c8e26ce8535 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "I draw my data." + }, + { + "text": "So I draw." + }, + { + "text": "I run this experiment, which is probably going to get me a publication in Nature." + }, + { + "text": "I'm trying to test if a coin is fair." + }, + { + "text": "And I draw my data, and I see that there's 13 out of 30 of my observations that are heads." + }, + { + "text": "That means that from this data, it looks like p is less than 1 half." + }, + { + "text": "So if I look at this data and then decide that my alternative is not p not equal to 1 half, but rather p less than 1 half, that's p-hacking." + }, + { + "text": "I'm actually making my p-value strictly smaller by first looking at the data and then deciding what my alternative is going to be." + }, + { + "text": "And that's cheating, because all the things we did were assuming that this 0.5 or d alternative was actually a fix." + }, + { + "text": "Everything was deterministic." + }, + { + "text": "The only randomness came from the data." + }, + { + "text": "But if I start looking at the data and designing my experiment or my alternatives and null hypothesis based on the data, it's as if I started putting randomness all over the place." + }, + { + "text": "And then I cannot control it, because I don't know how it just intermingles with each other." + }, + { + "text": "All right." + }, + { + "text": "So that was for the John Oliver moment." + }, + { + "text": "So the p-value is nice." + }, + { + "text": "So maybe I mentioned that before." + }, + { + "text": "My wife works in market research." + }, + { + "text": "And maybe every two years, she seems to run into a statistician in the hallway." + }, + { + "text": "And she comes home and says, what is a p-value again?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk26.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..582b81ac1a78246b0f187a4c706af274ba689dbe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk26.json @@ -0,0 +1,62 @@ +[ + { + "text": "And for her, a p-value is just the number is in an Excel spreadsheet." + }, + { + "text": "And actually, small equals good and large equals bad." + }, + { + "text": "And that's all she needs to know at this point." + }, + { + "text": "Actually, they do the job for her." + }, + { + "text": "Small is green." + }, + { + "text": "Large is red." + }, + { + "text": "And so for her, a p-value is just green or red." + }, + { + "text": "But so what she's really implicitly doing with this color code is just applying the golden rule." + }, + { + "text": "What the statisticians do for her in the Excel spreadsheet is that they take the numbers for the p-values that are less than some fixed level." + }, + { + "text": "So depending on the field in which she works, so she works for pharmaceutical companies, so the p-values are typically compared." + }, + { + "text": "The tests are usually performed at level 1% rather than 5%." + }, + { + "text": "So 5% is maybe your gold standard if you're doing sociology or trying to, I don't know, release a new blueberry flavor for your toothpaste, like something that's not going to change the life of people." + }, + { + "text": "Maybe you're going to run at 5%." + }, + { + "text": "It's OK to make a mistake." + }, + { + "text": "People are just going to feel gross, but that's about it." + }, + { + "text": "Whereas here, if you have this p-value which is less than 1%, it might be more important for some drug discovery, for example." + }, + { + "text": "And so let's say you run at 1%." + }, + { + "text": "And so what they do in this Excel spreadsheet is that all the numbers that are below 1% show up in green, and all the numbers that are above 1% show up in red." + }, + { + "text": "And that's it." + }, + { + "text": "That's just applying the golden rule." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk27.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk27.json new file mode 100644 index 0000000000000000000000000000000000000000..6d2b3e73a1f2bfb3d007d43a22bc17095a5878f8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk27.json @@ -0,0 +1,62 @@ +[ + { + "text": "If the number is green, reject." + }, + { + "text": "If the number is red, fail to reject." + }, + { + "text": "OK?" + }, + { + "text": "Yeah?" + }, + { + "text": "So going back to the example of the previous prior example where you can achieve by looking at your data and then formulating, say, a theta 1 to be p less than 1%." + }, + { + "text": "Yeah." + }, + { + "text": "So how would you achieve your goal by changing the theta 1?" + }, + { + "text": "You mean by achieving my goal?" + }, + { + "text": "You mean letting ethics aside, right?" + }, + { + "text": "Yeah." + }, + { + "text": "You want to be published." + }, + { + "text": "So OK." + }, + { + "text": "So let me teach you how." + }, + { + "text": "Well, here, what do you do?" + }, + { + "text": "You want to, at the end of the day, a test is only telling you whether you found evidence in your data that H1 was more likely than H0, basically." + }, + { + "text": "How do you make H1 more likely?" + }, + { + "text": "Well, you just basically target H1 to be what the data is going to make it more likely to be." + }, + { + "text": "All right?" + }, + { + "text": "So if, for example, I say H1 can be on both sides, then my data is going to have to take into account fluctuations on both sides." + }, + { + "text": "And I'm going to lose a factor of 2 somewhere because things are not symmetric." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk28.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk28.json new file mode 100644 index 0000000000000000000000000000000000000000..b6a2e04f21d17d3f9d8f51277fef4b6bd544ea8c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk28.json @@ -0,0 +1,62 @@ +[ + { + "text": "Here is the ultimate way of making this work." + }, + { + "text": "I'm going back to my example of flipping coins." + }, + { + "text": "And now, so here, what I did is I said, oh, this number 0.43 is actually smaller than 0.5." + }, + { + "text": "So I'm just going to test whether I'm 0.5 or I'm less than 0.5." + }, + { + "text": "But here is something that I can promise you I did not make the computation will reject." + }, + { + "text": "OK, so here, this one actually, yeah, this one fails to reject, right?" + }, + { + "text": "So here is one that will certainly reject." + }, + { + "text": "H0 is 0.5. p is 0.5." + }, + { + "text": "H1, p is 0.43." + }, + { + "text": "OK?" + }, + { + "text": "Now, you can try." + }, + { + "text": "But I can promise you that your data will tell you that H1 is the right one." + }, + { + "text": "OK?" + }, + { + "text": "I mean, you can check very quickly that this is really extremely likely to happen, right?" + }, + { + "text": "And so actually, what am I?" + }, + { + "text": "No, actually, that's not true." + }, + { + "text": "OK. Because here, the test that I derive that's based on this kind of stuff, right?" + }, + { + "text": "Here, at some point, somewhere, under some layers, I assume that all our tests are going to have this form." + }, + { + "text": "But here, this is only when you're trying to test one region versus another region next to it, or one point versus a region around it, or something like this." + }, + { + "text": "Whereas for this guy, there's another test I could come up with, which is, what is the probability that I get 0.43?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk29.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk29.json new file mode 100644 index 0000000000000000000000000000000000000000..7c83fb4d5133113ff729308f195ed934ccaaacb9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk29.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what is the probability that I get 0.5?" + }, + { + "text": "Now, what I'm going to do is I'm going to just conclude it's whichever has the largest probability." + }, + { + "text": "Then maybe I'm going to have to make some adjustments so that the level is actually 5%." + }, + { + "text": "But I can make this happen." + }, + { + "text": "I can make the level be 5% and always conclude this guy, but I would have to use a different test." + }, + { + "text": "Now, the test that I described, again, those t and larger than c are built in to be tests that are sort of resilient to this kind of manipulations, because they're sort of oblivious towards what the alternative looks like." + }, + { + "text": "I mean, they're just saying it's either to the left or to the right, but whether it's a point or an entire half line doesn't matter." + }, + { + "text": "So if you try to look at your data and just put the data itself into your hypothesis testing problem, then you're failing the statistical principle." + }, + { + "text": "And that's what people are doing, right?" + }, + { + "text": "I mean, how can I check?" + }, + { + "text": "I mean, of course, here it's going to be pretty blatant if you publish a paper that looks like this." + }, + { + "text": "But there's ways to do it differently, right?" + }, + { + "text": "For example, one way to do it is to just do more." + }, + { + "text": "So typically, what people do is they do multiple hypothesis testing." + }, + { + "text": "They're doing 100 tests at a time." + }, + { + "text": "Then you have random fluctuations every time." + }, + { + "text": "And so they just pick the one that has the random fluctuations that go their way." + }, + { + "text": "I mean, sometimes it's going in your way, and sometimes it's going the opposite way." + }, + { + "text": "So you just pick the one that works for you." + }, + { + "text": "We'll talk about multiple hypothesis testing soon if you want to increase your publication counts." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk3.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..82298a0911f771c50c0c0e31234286bcbe2ed969 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "So p can range between 0 and 1, that's for sure." + }, + { + "text": "And what I'm going to try to test is whether p is less than 1 half or larger than 1 half." + }, + { + "text": "So this is going to be, let's say, theta 0, and this guy here is theta 1." + }, + { + "text": "Just trying to give you a picture of what those guys are." + }, + { + "text": "So I have my y-axis." + }, + { + "text": "Now I'm going to start drawing numbers, all these things, this function, this function, and this number are all numbers between 0 and 1." + }, + { + "text": "So now I'm claiming that when I move from left to right, what is my probability of rejecting going to do?" + }, + { + "text": "So what I'm going to plot is the probability under theta." + }, + { + "text": "The first thing I want to plot is the probability under theta that psi is equal to 1." + }, + { + "text": "And let's say psi, think of psi as being just this indicator that square root of n xn bar minus p over square root xn bar, 1 minus xn bar, is larger than some constant c for a properly chosen c. So what we choose is that c is in such a way that at 1 half, when we're testing for 1 half, what we wanted was this number to be equal to alpha, basically." + }, + { + "text": "So we fix this alpha number so that this guy, so if I want alpha of psi of theta less than alpha, given in advance, so think of it as being equal to, say, 5%." + }, + { + "text": "So I'm fixing this number, and I want this to be controlled for all theta and theta 0." + }, + { + "text": "So if you're going to give me this budget, well, I'm actually going to make it equal where I can." + }, + { + "text": "If you're telling me you can make it equal to alpha, we know that if I increase my type 1 error, I'm going to decrease my type 2 error." + }, + { + "text": "If I start putting everyone in jail, or if I start letting everyone go free, that's what we're discussing last time." + }, + { + "text": "So since we have this trade-off, and you're giving me a budget for one guy, I'm just going to max it out." + }, + { + "text": "And where am I going to max it out?" + }, + { + "text": "Exactly at 1 half at the boundary." + }, + { + "text": "So this is going to be 5%." + }, + { + "text": "So what I know is that since alpha of theta is less than alpha for all theta and theta 0, sorry, that's for theta 0, that's where alpha is defined." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk30.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk30.json new file mode 100644 index 0000000000000000000000000000000000000000..a8e80051fb683b419557b2b36ba8c95a3d50cf00 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk30.json @@ -0,0 +1,62 @@ +[ + { + "text": "There's actually papers." + }, + { + "text": "I think it was big news, there's some papers, I think it's psychology or psychometrics papers, that actually refuse to publish p-values now." + }, + { + "text": "All right, where were we?" + }, + { + "text": "OK, here's the golden rule." + }, + { + "text": "So one thing that I'd like to show is this thing, just so you know how you apply the golden rule and how you apply the standard test." + }, + { + "text": "So the standard paradigm is the following." + }, + { + "text": "You have a black box, which is your test." + }, + { + "text": "For my wife, this is the fourth floor of the building." + }, + { + "text": "That's where the statisticians sit." + }, + { + "text": "What she sends there is data, let's say x1, xn." + }, + { + "text": "And she says, well, this one is about toothpaste, so here's a level." + }, + { + "text": "Let's say 5%." + }, + { + "text": "What the fourth floor brings back is an answer, yes, no." + }, + { + "text": "Green, red, just an answer." + }, + { + "text": "So that's the standard testing." + }, + { + "text": "You just feed it the data and the level at which you want to perform the test, maybe asymptotic, and it spits out a yes, no answer." + }, + { + "text": "What p-value does, you just feed it the data itself." + }, + { + "text": "And what it spits out is the p-value." + }, + { + "text": "And now, it's just up to you." + }, + { + "text": "I mean, hopefully, your brain has the computational power of deciding whether a number is larger or smaller than 5% without having to call the statisticians for this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk31.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk31.json new file mode 100644 index 0000000000000000000000000000000000000000..9fb2296acde7c40202805ca4f7e73e4c07f68e6a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk31.json @@ -0,0 +1,62 @@ +[ + { + "text": "And that's what it does." + }, + { + "text": "So now, we're all on one scale." + }, + { + "text": "Now, if you actually, I see some of you nodding when I talk about p-hacking." + }, + { + "text": "So that means you've seen p-values." + }, + { + "text": "If you've seen more than 100 p-values in your life, you have an entire scale." + }, + { + "text": "A good p-value is less than 10 to the minus 4." + }, + { + "text": "That's the ultimate sweet spot." + }, + { + "text": "Actually, statistical software spit out an output which says less than 10 to the minus 4." + }, + { + "text": "But then, maybe you want a p-value." + }, + { + "text": "If I tell you my p-value was 4.65, then I will say you've been doing some p-hacking until you found a number that was below 5%." + }, + { + "text": "That's typically what people will do." + }, + { + "text": "But if you're doing the test, if you're saying, I published my result." + }, + { + "text": "My test at 5% said yes, that means that maybe your p-value was 4.99, or your p-value was 10 to the minus 4." + }, + { + "text": "I will never know." + }, + { + "text": "I will never know how much evidence you had against the null." + }, + { + "text": "But if you tell me what the p-value is, I can make my own decision." + }, + { + "text": "I don't have to tell me whether it's a yes." + }, + { + "text": "No, you tell me it's 4.99." + }, + { + "text": "I'm going to say, well, maybe yes, but I'm going to take it with a grain of salt." + }, + { + "text": "And so that's why p-values are good numbers to have in mind." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk32.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk32.json new file mode 100644 index 0000000000000000000000000000000000000000..96ed5fb80473cde620f1dcbaecbdda179310c37c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk32.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, I show it as if it was an old trick that you start mastering when you're 45 years old." + }, + { + "text": "No, it's just how small is the number between 0 and 1." + }, + { + "text": "That's really what you need to know." + }, + { + "text": "Maybe on the log scale, if it's 10 to the minus 1, 10 to the minus 2, 10 to the minus 3, et cetera, that's probably the extent of the mastery here." + }, + { + "text": "So this traditional standard paradigm that I showed is actually commonly referred to as the Neyman-Pearson paradigm." + }, + { + "text": "So here it says Neyman-Pearson's theory." + }, + { + "text": "So there's an entire theory that comes with it, but it's really a paradigm." + }, + { + "text": "It's a way of thinking about hypothesis testing that says, well, if I'm not going to be able to optimize both my type 1 and type 2 error, I'm actually going to lock in my type 1 error below some level and just minimize the type 2 error under this constraint." + }, + { + "text": "That's what the Neyman-Pearson paradigm is." + }, + { + "text": "And it sort of makes sense for hypothesis testing problems." + }, + { + "text": "If you were doing some other applications with multi-objective optimization, you would maybe come up with something different." + }, + { + "text": "For example, machine learning is not performing typically under Neyman-Pearson paradigm." + }, + { + "text": "So if you do spam filtering, you could say, well, I want to constrain the probability as much as I can of taking somebody's important emails and throwing them out as spam and, under this constraint, not send too much spam to that person." + }, + { + "text": "That sort of makes sense for spams." + }, + { + "text": "Now, if you're labeling cats versus dogs, it's probably not like you want to make sure that no more than 5% of the dogs are labeled cat." + }, + { + "text": "Because it doesn't matter." + }, + { + "text": "So what you typically do is you just sum up the two types of error you can make, and you minimize the sum without putting any more weight on one or the other." + }, + { + "text": "So here's an example where doing a binary decision, one or two of the errors you can make, you don't have to actually be like that." + }, + { + "text": "So this example here, I did not." + }, + { + "text": "The trivial test, psi is equal to 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk33.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk33.json new file mode 100644 index 0000000000000000000000000000000000000000..0c2da6bcc636025ed6d047d161fdfe68e3b68329 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk33.json @@ -0,0 +1,62 @@ +[ + { + "text": "What was it in the US trial court example?" + }, + { + "text": "What is psi equal to 0?" + }, + { + "text": "I was concluding all ways to the null." + }, + { + "text": "What was the null?" + }, + { + "text": "Innocent, right?" + }, + { + "text": "That's the status quo." + }, + { + "text": "So that means that this guy never rejects a 0." + }, + { + "text": "Everybody's going away free." + }, + { + "text": "So you're sure you're not actually going against the Constitution because alpha is 0%, which is certainly less than 5%." + }, + { + "text": "But the power, the fact that a lot of criminals go back outside in the free world is actually formulated in terms of low power, which in this case is actually 0." + }, + { + "text": "Again, the power is a number between 0 and 1." + }, + { + "text": "Close to 0, good." + }, + { + "text": "Close to 1, bad." + }, + { + "text": "Now, what is the definition of the p-value?" + }, + { + "text": "That's going to be something." + }, + { + "text": "Mouthful, right?" + }, + { + "text": "The definition of the p-value is a mouthful." + }, + { + "text": "It's really the tipping point." + }, + { + "text": "It is the smallest level at which blah, blah, blah, blah." + }, + { + "text": "It's complicated to remember it." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk34.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk34.json new file mode 100644 index 0000000000000000000000000000000000000000..074297c2186646a83b698c991607273c1d143e1c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk34.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, I think that by my sixth explanation, my wife, after saying, oh, so it's the probability of making an error, I said, yeah, that's the probability of making an error." + }, + { + "text": "Because of course, she can think probability of making an error, small, good, large, bad." + }, + { + "text": "So that's actually a good way to remember." + }, + { + "text": "I'm pretty sure that at least 50% of people using p-values out there think that the p-value is the probability of making an error." + }, + { + "text": "Now, for all matters of purposes, if your goal is to just threshold the p-value, this is OK to have this in mind." + }, + { + "text": "But when it comes, at least until December 22, I would recommend trying to actually memorize the right definition for the p-value." + }, + { + "text": "OK?" + }, + { + "text": "OK." + }, + { + "text": "So the idea, again, is fix the level and try to optimize the power." + }, + { + "text": "So we're going to try to compute some p-values from now on." + }, + { + "text": "How do you compute the p-value?" + }, + { + "text": "Well, you can actually see it from this picture over there." + }, + { + "text": "One thing I didn't show on this picture, here was my q alpha over 2 that had alpha here, alpha over 2 here, right?" + }, + { + "text": "That was my q alpha over 2." + }, + { + "text": "And I said, if tn is to the right of this guy, I'm going to reject." + }, + { + "text": "If tn is to the left of this guy, I'm going to fail to reject." + }, + { + "text": "OK?" + }, + { + "text": "Pictorially, you can actually represent the p-value." + }, + { + "text": "It's when I replace this guy by tn itself." + }, + { + "text": "Sorry, that's p-value over 2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk35.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk35.json new file mode 100644 index 0000000000000000000000000000000000000000..9f1a7b89f2d43b53944bbf516e37f98c7cf70618 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk35.json @@ -0,0 +1,62 @@ +[ + { + "text": "No, actually, that's p-value." + }, + { + "text": "So let me just keep it like that and put the absolute value here." + }, + { + "text": "OK?" + }, + { + "text": "So if you replace the role of q alpha over 2 by your test statistic, this is what the area under the curve is actually the p-value itself up to scaling, because of the symmetric thing." + }, + { + "text": "OK?" + }, + { + "text": "So there's a good way to see pictorially what the p-value is." + }, + { + "text": "It's just the probability that some Gaussians, which is the probability that some absolute value of n0,1 exceeds tn." + }, + { + "text": "Right?" + }, + { + "text": "That's what the p-value is." + }, + { + "text": "Now, this guy has nothing to do with this guy." + }, + { + "text": "So this is really just 1 minus the Gaussian CDF of tn." + }, + { + "text": "And that's it." + }, + { + "text": "So that's how I would compute p-values." + }, + { + "text": "Now, as I said, the p-value is a beauty, because you don't have to understand the fact that your limiting distribution is a Gaussian." + }, + { + "text": "Right?" + }, + { + "text": "It's already factored in this construction." + }, + { + "text": "The fact that I'm actually looking at this cumulative distribution function of a standard Gaussian makes my p-value automatically adjust to what the limiting distribution is." + }, + { + "text": "And if this was the cumulative distribution function of a exponential, I would just have a different function here denoted by f, for example." + }, + { + "text": "And I would just compute a different value." + }, + { + "text": "But in the end, regardless of what the limiting value is, my p-value would still be a number between 0 and 1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk36.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk36.json new file mode 100644 index 0000000000000000000000000000000000000000..2d4547dd85e8e54b4a9640f590a534ed56d0306a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk36.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so to illustrate that, let's look at other weird distributions that we could get in place of the standard Gaussian." + }, + { + "text": "And we're not going to see many, but we'll see one." + }, + { + "text": "And it's not called the chi-squared distribution." + }, + { + "text": "It's actually called the student's distribution, but it involves the chi-squared distribution as a building block." + }, + { + "text": "So I don't know if my phonetics are not really right there, so I try to say, well, it's chi-squared." + }, + { + "text": "Maybe it's chi-squared in Canada." + }, + { + "text": "Who knows?" + }, + { + "text": "So for a positive integer, so there's only one parameter." + }, + { + "text": "So for the Gaussian, you have two parameters, which are mu and sigma squared." + }, + { + "text": "Those are real numbers." + }, + { + "text": "Sigma squared is positive." + }, + { + "text": "Here, I have one integer parameter." + }, + { + "text": "Then the distribution, the chi-squared distribution with d degrees of freedom." + }, + { + "text": "So the parameter is called a degree of freedom, just like mu is called the expected value, and sigma squared is called the variance." + }, + { + "text": "So it's called degrees of freedom." + }, + { + "text": "You don't have to really understand why." + }, + { + "text": "So that's the law that you would get." + }, + { + "text": "That's the random variable you would get if you were to sum d squares of independent standard Gaussians." + }, + { + "text": "So I take the square of an independent random Gaussian." + }, + { + "text": "I take another one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk37.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk37.json new file mode 100644 index 0000000000000000000000000000000000000000..6fa169cd52b7910e64c667064ab385a1dc476da0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk37.json @@ -0,0 +1,62 @@ +[ + { + "text": "I sum them, and that's a chi-squared with two degrees of freedom." + }, + { + "text": "That's how you get it." + }, + { + "text": "Now, I could define it using its probability density function." + }, + { + "text": "After all, this is the sum of positive random variables." + }, + { + "text": "It is a positive random variable." + }, + { + "text": "It has a density on the positive real line." + }, + { + "text": "And the PDF of chi-squared, PDF of chi-squared with d degrees of freedom is what?" + }, + { + "text": "Well, it's fd of x is x to the d over 2 minus 1, e to the minus x over 2." + }, + { + "text": "And then here, I have a gamma of d over 2, and the other one is, I think, 2 to the d over 2 minus 1." + }, + { + "text": "No, 2 to the d over 2." + }, + { + "text": "That's what it is." + }, + { + "text": "That's the density." + }, + { + "text": "If you are very good at probability, you can make the change of variable and write your Jacobian and do all this stuff and actually check that this is true." + }, + { + "text": "I do not recommend doing that." + }, + { + "text": "So this is the density, but it's better understood like that, at thinking of just something that you built from standard Gaussian." + }, + { + "text": "So for example, an example of a chi-squared with two degrees of freedom is actually the following thing." + }, + { + "text": "Let's assume I have a target like this." + }, + { + "text": "And I don't aim very well, and I'm trying to hit the center." + }, + { + "text": "And I'm going to have maybe a deviation, which is standard Gaussian left-right and standard Gaussian north-south." + }, + { + "text": "So I'm throwing, and then I'm here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk38.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk38.json new file mode 100644 index 0000000000000000000000000000000000000000..e9321d18ef5daa35196a20db9f6bb7680045ede5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk38.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'm claiming that this number here, by Pythagoras' theorem, the squared distance here is the sum of this squared distance here, which is the square of a Gaussian by assumption, plus the square of this distance, which is the square of another independent Gaussian." + }, + { + "text": "I assume those are independent." + }, + { + "text": "And so the squared distance from this point to this point is the chi-squared with two degrees of freedom." + }, + { + "text": "So this guy here is n01 squared." + }, + { + "text": "This is n01 squared." + }, + { + "text": "And so this guy here, this distance here, is chi-squared with two degrees of freedom." + }, + { + "text": "I mean, the squared distance." + }, + { + "text": "I'm talking about squared distances here." + }, + { + "text": "So now you can see that actually Pythagoras is basically why chi-squared arise." + }, + { + "text": "That's why it has its own name." + }, + { + "text": "I mean, I could define this random variable." + }, + { + "text": "I mean, it's actually a gamma distribution." + }, + { + "text": "It's a special case of something called the gamma distribution." + }, + { + "text": "The fact that the special case has its own name is because there's many times where we're going to take sum of squares of independent Gaussians, because Gaussians, the sum of squares is really the norm, the Euclidean norm squared, just by Pythagoras theorem." + }, + { + "text": "If I'm in higher dimension, I can start to sum more squared coordinates, and I'm going to measure the norm squared." + }, + { + "text": "So if you want to draw this picture, it looks like this." + }, + { + "text": "Again, it's the sum of positive numbers." + }, + { + "text": "So it's going to be on 0 plus infinity." + }, + { + "text": "That's fd." + }, + { + "text": "And so for f1 looks like this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk39.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk39.json new file mode 100644 index 0000000000000000000000000000000000000000..530fa0ac2ba5f7380bf835d6fd19c3b55d8a53a3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk39.json @@ -0,0 +1,62 @@ +[ + { + "text": "f2 looks like this." + }, + { + "text": "So the tails becomes heavier and heavier as d increases." + }, + { + "text": "And then at start to 3, it starts to have a different shape." + }, + { + "text": "It starts from 0, and it looks like this." + }, + { + "text": "And then as d increases, it's basically as if you were to push this thing to the right." + }, + { + "text": "It's just like, pfft." + }, + { + "text": "It's just falling like a big ball." + }, + { + "text": "Everybody sees what's going on?" + }, + { + "text": "So there's just this fat thing that's just going there." + }, + { + "text": "What is the expected value of a k squared?" + }, + { + "text": "So it's the expected value of the sum of Gaussian random variables squared." + }, + { + "text": "I don't know why I said that." + }, + { + "text": "AUDIENCE 2 It's the sum of their second norm, right?" + }, + { + "text": "Which is?" + }, + { + "text": "Those are n0, 1." + }, + { + "text": "It's like, oh, I see, 1." + }, + { + "text": "Yeah." + }, + { + "text": "So n times 1, or d times 1." + }, + { + "text": "Yeah, which is d. So one thing you can check quickly is that the expected value of a k squared is d. And so you see, that's why the mass is shifting to the right as d increases." + }, + { + "text": "It's just going there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk4.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..07e0b7e52902074c6ec8439999a1046b4b977809 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "So for theta and theta 0, I know that my function is going to look like this." + }, + { + "text": "It's going to be somewhere in this rectangle." + }, + { + "text": "Everybody agrees?" + }, + { + "text": "So this function for this guy is going to look like this." + }, + { + "text": "When I'm at 0, when p is equal to 0, which means I only observe 0's, then I know that p is going to be 0." + }, + { + "text": "And I will certainly not conclude that p is equal to 1." + }, + { + "text": "This test will never conclude that p is equal to 1." + }, + { + "text": "Sorry, that was, yeah." + }, + { + "text": "That p is equal to, that p is lower than 1 half, just because xn bar is going to be equal to 0." + }, + { + "text": "OK, well, this is actually not well-defined." + }, + { + "text": "So maybe I need to do something, put it equal to 0 if xn bar is equal to 0." + }, + { + "text": "So I guess basically I get something which is negative." + }, + { + "text": "And so it's never going to be larger than what I want." + }, + { + "text": "And so here I'm actually starting at 0." + }, + { + "text": "So now this is this function here that increases." + }, + { + "text": "I mean, it should increase smoothly." + }, + { + "text": "This function here is alpha psi of theta, or alpha psi of p, let's say, because we're talking about p. Then it reaches alpha here." + }, + { + "text": "Now when I go on the other side, I'm actually looking at beta." + }, + { + "text": "When I'm on theta 1, the function that matters is the probability of type 2 error, which is beta psi." + }, + { + "text": "And this beta psi is actually going to increase." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk40.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk40.json new file mode 100644 index 0000000000000000000000000000000000000000..cf303c16babeea5b89d0924caa36f4dde58e6495 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk40.json @@ -0,0 +1,62 @@ +[ + { + "text": "Actually, the variance is also increasing." + }, + { + "text": "The variance is 2d." + }, + { + "text": "So this is one thing." + }, + { + "text": "And so why do we care about this in basic statistics?" + }, + { + "text": "It's not like we actually have statistics much about throwing darts at high dimensional boards." + }, + { + "text": "So what's happening is that if I look at the sample variance, the average of the sum of squared centered by their mean, then I can actually expend this as the sum of the squares minus the average squared." + }, + { + "text": "It's just the same trick that we have for the variance." + }, + { + "text": "Second moment minus first moment squared." + }, + { + "text": "And then I claim that Cochran's theorem, I will tell you in a second what Cochran's theorem tells me, is that this sample variance is actually, so if I had only this, so now, OK, look at those guys." + }, + { + "text": "Those guys are Gaussian with mean mu and variance sigma squared." + }, + { + "text": "Think for one second, mu being 0 and sigma squared being 1." + }, + { + "text": "Now, this part would be a chi-square with n degrees of freedom divided by n. Now, I get another thing here, which is the square of something that looks like a Gaussian as well." + }, + { + "text": "So it looks like I have something else here, which looks also like a chi-square." + }, + { + "text": "Now, Cochran's theorem is essentially telling you that those things are independent." + }, + { + "text": "And so that in a way, you can think of those guys as being here n degrees of freedom minus 1 degree of freedom." + }, + { + "text": "Now, here, as I said, this is not mean 0 and variance 1." + }, + { + "text": "The fact that it's not mean 0 is not a problem, because I can remove the mean here and remove the mean here." + }, + { + "text": "And so this thing has the same distribution, regardless of what the actual mean is." + }, + { + "text": "So without loss of generality, I can assume that mu is equal 0." + }, + { + "text": "Now, the variance I'm going to have to pay, because if I multiply all these numbers by 10, then this Sn is going to be multiplied by 100." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk41.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk41.json new file mode 100644 index 0000000000000000000000000000000000000000..be699853a1170afd439414bc8f189e87e84b0b94 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk41.json @@ -0,0 +1,62 @@ +[ + { + "text": "So this thing is going to scale with the variance." + }, + { + "text": "And not surprisingly, it's scaling like the square of the variance." + }, + { + "text": "So if I look at Sn, it's distributed as sigma-square times the chi-square with n minus 1 degrees of freedom divided by n. And we don't really write that, because a chi-square times sigma-square divided by n is not a distribution." + }, + { + "text": "So we put everything to the left." + }, + { + "text": "And we say that this is actually a chi-square with n minus 1 degrees of freedom." + }, + { + "text": "So here, I'm actually dropping a fact on you." + }, + { + "text": "But you can sort of see the building block." + }, + { + "text": "What is the thing that's sort of fussy at this point, but the rest should be crystal clear to you?" + }, + { + "text": "The thing that's fussy is that removing this square guy here is actually removing 1 degree of freedom." + }, + { + "text": "That should be weird." + }, + { + "text": "But that's what Cochran's theorem tells me." + }, + { + "text": "It's essentially stating something about orthogonality of subspaces with the span of the constant vector, something like that." + }, + { + "text": "So you don't have to think about it too much." + }, + { + "text": "But that's what it's telling me." + }, + { + "text": "But the rest, if you plug in, so the scaling in sigma-squared and in n, that should be completely clear to you." + }, + { + "text": "So in particular, if I remove that part, it should be clear to you that this thing, if mean is 0, this thing is actually distributed." + }, + { + "text": "Well, if mu is 0, what is the distribution of this guy?" + }, + { + "text": "So I remove that part, just this part." + }, + { + "text": "So I have xi, which are n0 sigma-squared." + }, + { + "text": "And I'm asking, what is the distribution of 1 over n sum from i equal 1 to n of xi-squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk42.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk42.json new file mode 100644 index 0000000000000000000000000000000000000000..3596e452514719b86b744b50b7402e7dd02b9ace --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk42.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it is the sum of their iid." + }, + { + "text": "So it's the sum of independent Gaussians, but not standard." + }, + { + "text": "So the first thing to make them standard is that I divide all of them by sigma-squared." + }, + { + "text": "Now, this guy is of the form zi-squared, where zi is n0, 1." + }, + { + "text": "So now this thing here has what distribution?" + }, + { + "text": "Chi-squared n. And now sigma-squared over n times chi-squared n. So if I have sigma-squared divided by n times chi-squared, sorry, so n times n divided by sigma-squared." + }, + { + "text": "So if I take this thing and I multiply it by n divided by sigma-squared, it means I remove this term." + }, + { + "text": "And now I am left with a chi-squared with n degrees of freedom." + }, + { + "text": "Now, the effect of centering with the sample mean here is only to lose 1 degree of freedom." + }, + { + "text": "That's it." + }, + { + "text": "OK?" + }, + { + "text": "So if I want to do a test about variance, since this is supposedly a good estimator of variance, this could be my pivotal distribution." + }, + { + "text": "This could play the role of a Gaussian." + }, + { + "text": "If I want to know if my variance is equal to 1 or larger than 1, I could actually build a test based on this only statement and test if the variance is larger than 1 or not." + }, + { + "text": "Now, this is not asymptotic because I started with the very assumption that my data was Gaussian itself." + }, + { + "text": "OK?" + }, + { + "text": "Now, just a side remark, you can check that this chi-squared 2, 2 is an exponential with half degrees of freedom, which is certainly not clear from the fact that z1 squared plus z2 squared is a chi-squared with 2 degrees of freedom." + }, + { + "text": "If I give you the sum of the square of two independent Gaussians, this is actually an exponential." + }, + { + "text": "That's not super clear, right?" + }, + { + "text": "But if you look at what was here, I don't know if you took notes, but let me rewrite it for you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk43.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk43.json new file mode 100644 index 0000000000000000000000000000000000000000..c1c4ce2a1e88dbaf6e313e0235a0fa58a881a709 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk43.json @@ -0,0 +1,59 @@ +[ + { + "text": "So it was x to the d over 2 minus 1 e to the minus x over 2 divided by 2 to the d over 2 gamma of d over 2." + }, + { + "text": "So if I plug in d is equal to 2, gamma of 2 over 2 is gamma of 1, which is 1, right?" + }, + { + "text": "It's factorial of 0." + }, + { + "text": "So it's 1." + }, + { + "text": "So this guy goes away." + }, + { + "text": "2 to the d over 2 is 2 to the 1." + }, + { + "text": "So that's just 1." + }, + { + "text": "No, that's just 2." + }, + { + "text": "OK?" + }, + { + "text": "Then x to the d over 2 minus 1 is x to the 0, goes away." + }, + { + "text": "And so I have x minus x over 2, 1 half, which is really, indeed, of the form lambda e to the minus lambda x for lambda is equal to 1 half, which was our exponential distribution." + }, + { + "text": "OK?" + }, + { + "text": "So well, next week is Columbus Day." + }, + { + "text": "So that's next Monday." + }, + { + "text": "So next week, we'll talk about students' distribution." + }, + { + "text": "And so that was discovered by a guy who pretended his name was student but was not student." + }, + { + "text": "And I challenge you to find why in the meantime." + }, + { + "text": "All right, so I'll see you next week." + }, + { + "text": "Your homework is going to be outside, so we can release the room." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk5.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..89ec03ee891688f8ef72df5ae36dcaada4844313 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "So beta psi is what?" + }, + { + "text": "Well, beta psi should also, sorry, that's the probability of being equal to alpha." + }, + { + "text": "So what I'm going to do is I'm going to look at the probability of rejecting." + }, + { + "text": "So let me draw this function all the way." + }, + { + "text": "It's going to look like this." + }, + { + "text": "Now here, if I look at this function here or here, this is the probability under theta that psi is equal to 1." + }, + { + "text": "And we just said that in this region, this function is called alpha psi." + }, + { + "text": "In that region, it's not called alpha psi." + }, + { + "text": "It's not called anything." + }, + { + "text": "It's just the probability of rejection." + }, + { + "text": "So it's not an error." + }, + { + "text": "It's actually what you should be doing." + }, + { + "text": "What we're looking at in this region is 1 minus this guy." + }, + { + "text": "We're looking at the probability of not rejecting." + }, + { + "text": "So I need to actually basically look at 1 minus this thing, which here is going to be 95%." + }, + { + "text": "So I'm going to do 95%." + }, + { + "text": "And this is my probability." + }, + { + "text": "And I'm just basically drawing the symmetric of this guy." + }, + { + "text": "So this here is the probability under theta that psi is equal to 0, which is 1 minus p theta that psi is equal to 1." + }, + { + "text": "So it's just 1 minus the white curve." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk6.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..2ba3f3f31acb2d89e2bd57110d90b292f5959fce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's actually, by definition, equal to beta psi of theta." + }, + { + "text": "Now, where do I read pi psi?" + }, + { + "text": "What is pi psi on this picture?" + }, + { + "text": "Is pi psi a number or a function?" + }, + { + "text": "It's a number, right?" + }, + { + "text": "It's the minimum of a function." + }, + { + "text": "What is this function?" + }, + { + "text": "It's the probability under theta that theta is equal to 1." + }, + { + "text": "I drew this entire function between theta 0 and theta 1." + }, + { + "text": "I drew this entire white curve." + }, + { + "text": "This is this probability." + }, + { + "text": "Now, I'm saying, look at the smallest value this probability can take on the set theta 1." + }, + { + "text": "What is this?" + }, + { + "text": "This guy." + }, + { + "text": "This is where my pi, this thing here, is pi psi." + }, + { + "text": "And so it's equal to 5%." + }, + { + "text": "So that's for this particular test, because this test is sort of a continuous curve for this psi." + }, + { + "text": "And so if I want to make sure that I'm at 5% when I come to the right of theta 0, if it touches theta 1, then I better have 5% on the other side if the function is continuous." + }, + { + "text": "So basically, if this function is increasing, which will be the case for most tests, then what's going to happen is that, and continuous, then what's going to happen is that the level of the test, which is alpha, is actually going to be equal to the power of the test." + }, + { + "text": "OK?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk7.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..4f5cdee6b6891b45c5f7794aece5ce2b8c13dc7a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, there's something I didn't mention, and I'm just mentioning it, pass it by." + }, + { + "text": "Here, I define the power itself." + }, + { + "text": "This function, this entire white curve here, is actually called the power function." + }, + { + "text": "This thing, that's the entire white curve." + }, + { + "text": "And what you could have is tests that have the entire curve, which is dominated by another test." + }, + { + "text": "So here, if I look at this test, and let's assume I can build another test that has this curve." + }, + { + "text": "Let's say it's the same here." + }, + { + "text": "But then here, it looks like this." + }, + { + "text": "What is the power of this test?" + }, + { + "text": "It's the same." + }, + { + "text": "It's 5%, because this point touches here exactly at the same point." + }, + { + "text": "However, for any other value than the worst possible, this guy is doing better than this guy." + }, + { + "text": "Can you see that?" + }, + { + "text": "Having a curve higher on the right-hand side is a good thing, because it means that you tend to reject more when you're actually in H1." + }, + { + "text": "So this guy is definitely better than this guy." + }, + { + "text": "And so what we say in this case is that the test with the dashed line is uniformly more powerful than the other test." + }, + { + "text": "But we're not going to go into those details, because basically, all the tests that we will describe are already the most powerful ones." + }, + { + "text": "In particular, this guy is, there's no such thing." + }, + { + "text": "All the other guys you can come up with are going to actually be below." + }, + { + "text": "So we saw a couple tests, and we saw how to pick this threshold, and we defined those two things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk8.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8b9449415f7337b53908d8098f0293899e0ba86e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "Yes?" + }, + { + "text": "AUDIENCE 2 But in that case, the down one, if it were also higher in the region of 2 to 0, do you still consider it better?" + }, + { + "text": "PHILIPPE RIGOLLETTIS Because you're given this budget of 5%, right?" + }, + { + "text": "So in this paradigm, where you're given the, actually, if the dashed line was this dashed line, I would still be happy." + }, + { + "text": "I mean, I don't care what this thing does here, as long as it's below 5%." + }, + { + "text": "But here, I'm going to try to discover it, right?" + }, + { + "text": "Think about, again, the drug discovery example." + }, + { + "text": "You're trying to find, let's say you're a scientist, and you're trying to prove that your drug works." + }, + { + "text": "What do you want to see?" + }, + { + "text": "Well, FDA puts on you this constraint that your probability of type 1 error should never exceed 5%." + }, + { + "text": "You're going to work under this assumption." + }, + { + "text": "But what you're going to do is going to try to find a test that will make you find something as often as possible." + }, + { + "text": "And so you're going to max this constraint of 5%, and then you're going to try to make this curve, this curve that means that this is basically, this number here, for any point here, is the probability that you publish your paper." + }, + { + "text": "That's the probability that you can release to market your drug." + }, + { + "text": "That's the probability that it works, right?" + }, + { + "text": "And so you want this curve to be as high as possible." + }, + { + "text": "You want to make sure that if there's evidence in the data that H1 is the truth, you want to squeeze as much of this evidence as possible." + }, + { + "text": "And the test that has the highest possible curve is the most powerful one." + }, + { + "text": "Now, you have to also understand that having two curves that are on top of each other, completely, everywhere, is a rare phenomenon." + }, + { + "text": "It's not always the case that there is a test that's uniformly more powerful than any other test." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk9.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bbad3ae05fbb39d9ef76b7b89aa0fada7d5adc3e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_2_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It might be that you have some trade-off, that it might be better here, but then you're losing power here." + }, + { + "text": "Things like this." + }, + { + "text": "Well, actually, maybe it should not go down." + }, + { + "text": "But let's say it goes like this, and then maybe this guy goes like this." + }, + { + "text": "Then you have to basically make an educated guess whether you think that the theta you're going to find is here or it's here." + }, + { + "text": "And then you pick a test." + }, + { + "text": "OK?" + }, + { + "text": "Any other question?" + }, + { + "text": "Yes?" + }, + { + "text": "AUDIENCE 2." + }, + { + "text": "What is the derivative of the type 2 error?" + }, + { + "text": "PHILIPPE RIGOLLET." + }, + { + "text": "So the green curve is exactly right." + }, + { + "text": "So that's beta psi of theta." + }, + { + "text": "So it's really the type 2 error, and it's defined only here." + }, + { + "text": "So here, it's not a definition." + }, + { + "text": "It's really just I'm just mapping it to this point." + }, + { + "text": "So it's defined only here, and it's the probability of type 2 error." + }, + { + "text": "So here, it's pretty large, right?" + }, + { + "text": "I'm making it basically as large as I could, because I'm at the boundary." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk0.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..65c23c5cab5e2c4f1a8f872964a31edc5dd21493 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "Talking about tests, and to be fair, we spend most of our time talking about new jargon that we're using." + }, + { + "text": "But the main goal is to take a binary decision, yes and no." + }, + { + "text": "So just so that we're clear and we make sure that we all speak the same language, let me just remind you what the key words are for tests." + }, + { + "text": "So the first thing is that we split theta in theta 0 and theta 1." + }, + { + "text": "Both are included in theta, and they're disjoint." + }, + { + "text": "OK." + }, + { + "text": "So I have my set of possible parameters." + }, + { + "text": "And then I have theta 0 is here, theta 1 is here, and there might be something that I leave out." + }, + { + "text": "And so what we're doing is we have two hypotheses." + }, + { + "text": "So here's our hypothesis testing problem." + }, + { + "text": "And it's h0 theta belongs to theta 0 versus h1 theta belongs to theta 1." + }, + { + "text": "This guy was called the null, and this guy was called the alternative." + }, + { + "text": "And why we give them special names is because we saw that they have an asymmetric role." + }, + { + "text": "The null represents the status quo, and data is here to bring evidence against this guy." + }, + { + "text": "And we can really never conclude that h0 is true because all we could conclude is that h1 is not true or may not be true." + }, + { + "text": "So that was the first thing." + }, + { + "text": "The second thing was the hypothesis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk1.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3b72e60009f76e8f81d23cb396a309bf7d70b355 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "The third thing is what is a test?" + }, + { + "text": "Well, psi, it's a statistic." + }, + { + "text": "And it takes the data, and it maps it into 0 or 1." + }, + { + "text": "And I didn't really mention it, but there's something such as called randomized tests, which is, well, if it cannot really make a decision, they might as well flip a coin." + }, + { + "text": "That tends to be biased, but that's really, I mean, think about it in practice." + }, + { + "text": "You probably don't want to make decisions based on flipping a coin." + }, + { + "text": "And so what people typically do, this is happening typically at one specific value." + }, + { + "text": "So rather than flipping a coin for this very specific value, what people typically do is they say, OK, I'm going to side with h0 because that's the most conservative choice I can make." + }, + { + "text": "So in a way, they think of flipping this coin, but always falling on heads." + }, + { + "text": "So associated to this test was something called, well, the rejection region." + }, + { + "text": "And r psi, which is just the set of data, x1, xn, such that psi of x1, xn is equal to 1." + }, + { + "text": "So that means we rejected 0 when the test is 1, and those are the set of data points that actually are going to lead me to reject the test." + }, + { + "text": "OK. Then the things that were actually slightly a little more important and really peculiar to test, specific to test, were the type 1 and type 2 error." + }, + { + "text": "So the type 1 error arises when, so type 1 error is when you reject whereas h0 is correct." + }, + { + "text": "And the type 2 error is the opposite." + }, + { + "text": "So it's failed to reject whereas h1 is correct." + }, + { + "text": "h is correct." + }, + { + "text": "So those are the two types of errors you can make, and we quantify their probability of type 1 error." + }, + { + "text": "So alpha psi is the probability." + }, + { + "text": "So that's the probability of type 1 error." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk10.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c19b0d21dee98686b07f25081871711f112710fa --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "And that means at the boundary, since the status quo is h0, I'm always going to go for h0 if I don't have any evidence, which means that what's going to pay is the type 2 error that's going to basically pay this." + }, + { + "text": "OK?" + }, + { + "text": "Any other question?" + }, + { + "text": "All right, so let's move on." + }, + { + "text": "So did we do this?" + }, + { + "text": "No, I think we stopped here, right?" + }, + { + "text": "I didn't cover that part." + }, + { + "text": "So as I said, in this paradigm, we're going to actually fix this guy to be something." + }, + { + "text": "And this thing is actually called the level of the test." + }, + { + "text": "I'm sorry, this is again more words." + }, + { + "text": "Actually, good news is that we split it into two lectures." + }, + { + "text": "So we have, what is a test?" + }, + { + "text": "What is a hypothesis?" + }, + { + "text": "What is the null?" + }, + { + "text": "What is the alternative?" + }, + { + "text": "What is the type 1 error?" + }, + { + "text": "What is the type 2 error?" + }, + { + "text": "And now, I'm telling you there's another thing." + }, + { + "text": "So we defined the power, which was some sort of a lower bound on the, or it's 1 minus the upper bound on the type 2 error, basically." + }, + { + "text": "And so it's alternative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk11.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..815ec78c1b831dd92a2b3f1d68a91dd8df86f618 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "So the power is the smallest probability of rejecting when you're in the null." + }, + { + "text": "And it's alternative when you're in theta 1, right?" + }, + { + "text": "So that's my power." + }, + { + "text": "I looked here, and I looked at the smallest value." + }, + { + "text": "And I can look at this side and say, well, what is the largest probability that I make a type 1 error?" + }, + { + "text": "Again, this largest probability is the level of the test." + }, + { + "text": "OK, so this is alpha equal, by definition, to the maximum for theta and theta 0 of alpha psi of theta." + }, + { + "text": "So here, I just put the level itself." + }, + { + "text": "As you can see here, it essentially says that if I'm of level 5%, I'm also of level 10%." + }, + { + "text": "I'm also of level 15%." + }, + { + "text": "So here, it's really an upper bound." + }, + { + "text": "Whatever you guys want to take, this is what it is." + }, + { + "text": "But as we said, if this number is 4.5%, you're losing in your type 2 error." + }, + { + "text": "So if you're allowed to have, if this maximum here is 4.5%, and FDA told you you can go to 5%, you're losing in your type 2 error." + }, + { + "text": "So you actually want to make sure that this is the 5% that's given to you." + }, + { + "text": "So the way it works is that you give me the alpha." + }, + { + "text": "Then I'm going to go back, pick c that depends on alpha here, so that this thing is actually equal to 5%." + }, + { + "text": "And so, of course, in many instances, we do not know the probability." + }, + { + "text": "We do not know how to compute the probability of type 1 error." + }, + { + "text": "This is a maximum value for the probability of type 1 error." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk12.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..4bd3834b631a0a7c734e2b14c2fe32eaf6f601e6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "We don't know how to compute it." + }, + { + "text": "I mean, it might be a very complicated random variable." + }, + { + "text": "Maybe it's a weird binomial." + }, + { + "text": "We could compute it, but it would be painful." + }, + { + "text": "But what we know how to compute is its asymptotic value, which is because of the central limit theorem, convergence and distribution tells me that the probability of type 1 error is basically going towards the probability that some Gaussian is in some region." + }, + { + "text": "And so we're going to compute not the level itself, but the asymptotic level." + }, + { + "text": "So again, that's basically the limit as n goes to infinity of alpha psi of theta." + }, + { + "text": "And then I'm going to make the max here." + }, + { + "text": "OK?" + }, + { + "text": "So how am I going to compute this?" + }, + { + "text": "Well, if I take a test that has rejection region of the form Tn, because it depends on the data, right?" + }, + { + "text": "That's Tn of x1, xn, my observations, larger than some number c. OK?" + }, + { + "text": "Of course, I can almost always write tests like that, except that sometimes there's going to be an absolute value, which essentially means I'm going away from some value." + }, + { + "text": "Maybe actually I'm less than something, but I can always put a negative sign in front of everything." + }, + { + "text": "So this is not without much of generality, right?" + }, + { + "text": "So this includes something that looks like something is larger than the constant, right?" + }, + { + "text": "So that means, which is equivalent to, well, let me write it as Tq." + }, + { + "text": "OK, because then that means that, so that's Tn." + }, + { + "text": "But this actually encompasses the fact that Qn is larger than c, or Qn is less than c, then minus c. So that includes this guy." + }, + { + "text": "That also includes Qn less than c, because this is equivalent to Qn is larger than minus c. Minus Qn is, and so that's going to be my Tn." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk13.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..d0fc40d7fea49cc51a82242971122ccb04ee2caf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I can actually encode several type of things, OK?" + }, + { + "text": "Rejection regions that, so here in this case, I have a rejection region that looks like this, or a rejection region that looks like this, or a rejection region that looks like this." + }, + { + "text": "OK, and here I don't really represent it for the whole data, but maybe for the average, for example, or the normalized average." + }, + { + "text": "OK, so if I write this, then, yeah." + }, + { + "text": "And in this case, this Tn that shows up is called test statistic." + }, + { + "text": "I mean, this is sort of a, I mean, this is not like set in stone." + }, + { + "text": "Here, for example, Q could be the test statistics." + }, + { + "text": "It doesn't have to be minus Q itself that's the test statistic, right?" + }, + { + "text": "So what is the test statistic?" + }, + { + "text": "Well, it's what you're going to build from your data and then compare to some fixed value, right?" + }, + { + "text": "So in the example we had here, what is our test statistic?" + }, + { + "text": "Well, it's this guy, right?" + }, + { + "text": "This was our test statistic." + }, + { + "text": "And is this thing a statistic?" + }, + { + "text": "What are the criteria for a statistic?" + }, + { + "text": "What is a statistic?" + }, + { + "text": "I know you know the answer." + }, + { + "text": "AUDIENCE MEMBER 2." + }, + { + "text": "Is it a measurable function?" + }, + { + "text": "PROFESSOR PHILIPPE RIGOLLET." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk14.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..deb918611779af5e70f1e976f45cfc296740fc0a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "Yeah, it's a measurable function of the data that does not depend on the parameter." + }, + { + "text": "Is this guy a statistic?" + }, + { + "text": "AUDIENCE MEMBER 3." + }, + { + "text": "Yes, he is." + }, + { + "text": "PROFESSOR PHILIPPE RIGOLLET." + }, + { + "text": "Let's think again." + }, + { + "text": "When I implemented the test, what did I do?" + }, + { + "text": "I was able to compute my test." + }, + { + "text": "My test did not depend on some unknown parameter." + }, + { + "text": "How did we do it?" + }, + { + "text": "We just plugged in 0.5 here." + }, + { + "text": "Remember?" + }, + { + "text": "That was the value for which we computed it, because under h0, that was the value we're seeing." + }, + { + "text": "And if theta 0 is actually an entire set, I'm just going to take the value that's the closest to h1." + }, + { + "text": "We'll see that in a second." + }, + { + "text": "I mean, I did not guarantee that to you." + }, + { + "text": "But just taking the worst type 1 error and bounding it by alpha is equivalent to taking p and taking the value of p that's the closest to theta 1, which is completely intuitive." + }, + { + "text": "The worst type 1 error is going to be attained for the p that's the closest to the alternative." + }, + { + "text": "So even if the null is actually just an entire set, it's as if it was just the point that's the closest to the alternative." + }, + { + "text": "So now we can compute this, because there's no unknown parameters that shows up." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk15.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..0bc365016096bbbfd9f7a60ab9c2724dec760020 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "We replaced p by 0.5." + }, + { + "text": "And so that was our test statistic." + }, + { + "text": "So when you're building a test, you want to first build a test statistic and then see what threshold you should be getting." + }, + { + "text": "So now let's go back to our example where we have x1, xn." + }, + { + "text": "They're iid Bernoulli p. And I want to test if p is 1 half versus p not equal to 1 half, which as I said is what you want to do if you want to test if a coin is fair." + }, + { + "text": "And so here I'm going to build a test statistic." + }, + { + "text": "And we concluded last time that what do we want for this statistic?" + }, + { + "text": "We want it to have a distribution which under the null does not depend on the parameters, a distribution that I can actually compute quintiles of." + }, + { + "text": "So what we did is we said, well, if I look at the central limit theorem tells me that square root of n xn bar minus p divided by." + }, + { + "text": "So if I do central limit theorem plus Slutsky, for example, I'm going to have square root." + }, + { + "text": "And we've had this discussion whether we want to use Slutsky or not here." + }, + { + "text": "But let's assume we're taking Slutsky wherever we can." + }, + { + "text": "So this thing tells me that by the central limit theorem as n goes to infinity, this thing converges in distribution to some n 0, 1." + }, + { + "text": "Now as we said, this guy is not something we know." + }, + { + "text": "But under the null, we actually know it." + }, + { + "text": "And we can actually replace it by 1 half." + }, + { + "text": "So this thing holds under h0." + }, + { + "text": "When I write under h0, it means when this is the truth." + }, + { + "text": "So now I have something that converges to something that has no dependence on anything I don't know." + }, + { + "text": "And in particular, if you have any statistics textbook, which you don't because I didn't require one, you should be thankful because this thing costs $250." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk16.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..298b0fb997de98b972702f498d96cfa89d4e4b7d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "This thing's actually, if you look at the back, you actually have a table for a standard Gaussian." + }, + { + "text": "I could have anything else here." + }, + { + "text": "I could have an exponential distribution." + }, + { + "text": "I could have a, I don't know, a, well, we'll see the chi-square distribution in a minute." + }, + { + "text": "Any distribution from which you can actually see a table that somebody actually computed this thing for which you can actually draw the PDF and start computing whatever probability you want on them, then this is what you want to see at the right-hand side." + }, + { + "text": "This is any distribution." + }, + { + "text": "It's called pivotal." + }, + { + "text": "I think we've mentioned that before." + }, + { + "text": "Pivotal means it does not depend on anything that you don't know." + }, + { + "text": "And maybe it's easy to compute those things." + }, + { + "text": "Probably, typically, you need a computer to simulate them for you because computing probabilities for Gaussians is not an easy thing." + }, + { + "text": "We don't know how to solve those integrals exactly." + }, + { + "text": "We have to do it numerically." + }, + { + "text": "OK, so now I want to do this test." + }, + { + "text": "My test statistic will be declared to be what?" + }, + { + "text": "Well, I'm going to reject if what is larger than some number?" + }, + { + "text": "The absolute value of this guy." + }, + { + "text": "So my test statistic is going to be square root of n minus 0.5 divided by square root of xn bar 1 minus xn bar." + }, + { + "text": "That's my test statistic, absolute value of this guy, because I want to reject either when this guy is too large or when this guy is too small." + }, + { + "text": "I don't know ahead whether I'm going to see p larger than 1 half or less than 1 half." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk17.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..c16a8c6be2149a29434fcd2457ee0fdbf0606f2d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "So now I need to compute c such that the probability that tn is lower than c. So that's what?" + }, + { + "text": "That's the probability under p, which is unknown." + }, + { + "text": "I want this probability to be less than some level alpha asymptotically." + }, + { + "text": "So I want the limit of this guy to be less than alpha, and that's the level of my test." + }, + { + "text": "So that's the given level." + }, + { + "text": "So I want this thing to happen." + }, + { + "text": "Now what I know is that this limit, actually, I should say given asymptotic level." + }, + { + "text": "So what is this thing?" + }, + { + "text": "Well, OK, that's the probability that something that looks like under p. So under p, this guy, so what I know is that tn is square root of n minus xn bar minus 0.5 divided by square root of xn bar 1 minus xn bar exceeds." + }, + { + "text": "Is this true that as n goes to infinity, this probability is the same as the probability that the absolute value of a Gaussian exceeds c of a standard Gaussian?" + }, + { + "text": "Is this true?" + }, + { + "text": "Yeah, so you're saying that this, as n becomes large enough, this should be the probability that some absolute value of n0,1 exceeds c, right?" + }, + { + "text": "So I claim that this is not correct." + }, + { + "text": "Somebody tell me why." + }, + { + "text": "Even in the limit, it's not correct?" + }, + { + "text": "Even in the limit, it's not correct." + }, + { + "text": "OK." + }, + { + "text": "So what do you see?" + }, + { + "text": "It's because at the beginning, we picked the worst possible true parameter, 0.5, right?" + }, + { + "text": "So we don't actually know that this 0.5 is the least." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk18.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..21ff2eaef450e95222ef4c4c025a1ccb1a883204 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Exactly, right?" + }, + { + "text": "So we picked this 0.5 here, but this is for any p, right?" + }, + { + "text": "But what is the only p I can get?" + }, + { + "text": "So what I want is that this is true for all p in theta 0." + }, + { + "text": "But the only p that's in theta 0 is actually p is equal to 0.5." + }, + { + "text": "So yes, what you said was true, but it required to specify p to be equal to 0.5." + }, + { + "text": "So this, in general, is not true." + }, + { + "text": "But it happens to be true if p belongs to theta 0, which is strictly equivalent to p is equal to 0.5, right?" + }, + { + "text": "Theta 0 is really just this one point, 0.5." + }, + { + "text": "OK, so now this becomes true." + }, + { + "text": "And so what I need to do is to find c such that this guy is equal to what?" + }, + { + "text": "I mean, let's just follow, right?" + }, + { + "text": "So I want this to be less than alpha." + }, + { + "text": "But then we see that this was equal to this, which is equal to this." + }, + { + "text": "So all I want is that this guy is less than alpha." + }, + { + "text": "But we said we might as well just make it equal to alpha if you allow me to make it as big as I want, as long as it's less than alpha." + }, + { + "text": "So this is a true statement." + }, + { + "text": "But it's if under this condition, right?" + }, + { + "text": "So I'm going to set it equal to alpha." + }, + { + "text": "And then I'm going to try to solve for c. OK, so what I'm looking for is a c such that if I draw a standard Gaussian, so that's PDF of some n0,1, I want the probability that the absolute value of my Gaussian exceeding this guy." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk19.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..b610ab510e065f845cbac3e680352a281a5977db --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that means being either here or here." + }, + { + "text": "So that's minus c and c. I want the sum of those two things to be equal to alpha." + }, + { + "text": "So I want the sum of these areas to equal alpha." + }, + { + "text": "So by symmetry, each of them should be equal to alpha over 2." + }, + { + "text": "And so what I'm looking for is c such that the probability that my n0,1 exceeds c, which is just this area to the right now, equals alpha, which is equivalent to taking c, which is q equals alpha over 2." + }, + { + "text": "And that's q alpha over 2 by definition of q alpha over 2." + }, + { + "text": "That's just what q alpha over 2 is." + }, + { + "text": "And that's what the tables at the back of the book give you." + }, + { + "text": "Who has already seen a table for Gaussian probabilities?" + }, + { + "text": "All right." + }, + { + "text": "What it does is just a table." + }, + { + "text": "I mean, it's pretty ancient, right?" + }, + { + "text": "I mean, of course, you can actually ask Google to do it for you now." + }, + { + "text": "It's basically standard issue." + }, + { + "text": "But back in the day, they actually had to look at tables." + }, + { + "text": "And since the values alphas were pretty standard, the values alpha that people were requesting were typically 1%, 5%, 10%." + }, + { + "text": "All you could do is to compute these different values for different values of alpha." + }, + { + "text": "That was it." + }, + { + "text": "So that's really not much to give you." + }, + { + "text": "So for the Gaussian, I can tell you that alpha is equal to, if alpha is equal to 5%, then q alpha over 2, q 2.5% is equal to 1.96%." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk2.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..d35a9367292f43552ea9e2c936629f0062774757 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So psi is just the probability for theta that psi rejects, and that's defined for theta and theta 0." + }, + { + "text": "So for different values of theta 0, so h0 being correct means there exists a theta in theta 0 for which that actually is the right distribution." + }, + { + "text": "So for different values of theta, I might make different errors." + }, + { + "text": "So if you think, for example, about the coin example, if I'm testing if the coin is biased towards heads or biased towards tails, so if I'm testing whether p is larger than 1 half or less than 1 half, then when the true p, let's say h0 is larger than 1 half, when p is equal to 1, it's actually very difficult for me to make a mistake, because I only see heads." + }, + { + "text": "So when p is getting closer to 1 half, I'm going to start making more and more probability there." + }, + { + "text": "And so the type 2 error, so that's the probability of type 2, is denoted by beta psi." + }, + { + "text": "And it's the function that does the opposite, and this time is defined for theta and theta 0 and theta 1." + }, + { + "text": "And finally, we define something called the power pi of psi." + }, + { + "text": "And this time, this is actually a number." + }, + { + "text": "And so this number is equal to the maximum over theta and theta 0." + }, + { + "text": "I mean, that could be a supremum, but think of it as being a maximum of p theta of psi is equal, sorry, that's in 0." + }, + { + "text": "Give me one sec." + }, + { + "text": "No, that's the min." + }, + { + "text": "So this is not making a mistake." + }, + { + "text": "Theta 0 is in theta 1." + }, + { + "text": "So theta is in theta 1, and I conclude 1." + }, + { + "text": "So this is a good thing." + }, + { + "text": "I want this number to be large, and I'm looking at the worst house, what is the smallest value this number can be." + }, + { + "text": "So what I want to show you a little bit is a picture." + }, + { + "text": "So now I'm going to take theta, and think of it as being p. So I'm going to take p for some Bernoulli experiment." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk20.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..20ad1dac1f1c76cdb383bd9a41a5521bfc8e8f80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "So those are just fixed numbers that are functions of the Gaussian." + }, + { + "text": "All right, so everybody agrees?" + }, + { + "text": "We've done that before for our confidence intervals." + }, + { + "text": "And so now we know that if I actually plug in this guy to be q alpha over 2, then this limit is actually equal to alpha." + }, + { + "text": "And so now I've actually constrained this." + }, + { + "text": "So q alpha over 2 here is, for alpha equals 5%, as I said, is 1.96." + }, + { + "text": "So in the example 1, the number that we found was 3.54, I think, or something like that, 3.55 for t. So if we scroll back very quickly, 3.45." + }, + { + "text": "That was example 1." + }, + { + "text": "Example 2, negative 0.77." + }, + { + "text": "So if I look at t, n, in example 1, tn was just the absolute value of 3.45, which don't pull out your calculators, is equal to 3.45." + }, + { + "text": "Example 2, absolute value of negative 0.77 was equal to 0.77." + }, + { + "text": "And so all I need to check is, is this number larger or smaller than 1.96?" + }, + { + "text": "That's what my test ends up being." + }, + { + "text": "So in example 1, 3.45 being larger than 1.96, that means that I reject." + }, + { + "text": "Fairness of my coins in example 2, 0.77 being smaller than 1.96, what do I do?" + }, + { + "text": "I fail to reject." + }, + { + "text": "OK?" + }, + { + "text": "So here's a question." + }, + { + "text": "In example 1, for what level alpha would psi alpha, what is the?" + }, + { + "text": "So here, what's going to happen if I start decreasing my level?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk21.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..8a92eddc8e39673740ca195fad03c2d25a729273 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "When I decrease my level, I'm actually making this area smaller and smaller, which means that I push the c to the right." + }, + { + "text": "So now I'm asking, what is the smallest c I should pick so that now I actually do not reject h0?" + }, + { + "text": "What is the smallest c I should be taking?" + }, + { + "text": "Here." + }, + { + "text": "What is the smallest c?" + }, + { + "text": "So c here in the example I gave you for 5% was 1.96." + }, + { + "text": "What is the smallest c I should be taking so that now this inequality is reversed?" + }, + { + "text": "3.45." + }, + { + "text": "I ask only trivial questions." + }, + { + "text": "Don't be worried." + }, + { + "text": "So 3.45 is the smallest c that I'm actually willing to tolerate." + }, + { + "text": "So let's say this was my 5%." + }, + { + "text": "If this was 2.5, if alpha here, let's say in this picture, alpha is 5%, that means maybe I need to push here." + }, + { + "text": "And this number should be what?" + }, + { + "text": "So this is going to be 1.96." + }, + { + "text": "And this number here is going to be 3.45, clearly to scale." + }, + { + "text": "And so now what I want to ask you is, well, there's two ways I can understand this number 3.45." + }, + { + "text": "It is the number 3.45." + }, + { + "text": "But I can also try to understand, what is the area to the right of this guy?" + }, + { + "text": "And if I understand what the area to the right of this guy is, this is actually some alpha prime over 2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk22.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..7503edb72bbc4e9db22fe8e956729e7f3881d675 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "And that means that if I actually fix this level, alpha prime, that would be exactly the tipping point at which I would go from accepting to rejecting." + }, + { + "text": "So I know in terms of absolute thresholds, 3.45 is the trivial answer to the question." + }, + { + "text": "That's the tipping point, because I'm comparing a number to 3.45." + }, + { + "text": "But now if I try to map this back and understand what level would have been given me this particular tipping point, that's a number between 0 and 1." + }, + { + "text": "The smaller the number, the larger this number here, which means that the more evidence I have in my data against h0." + }, + { + "text": "And so this number is actually something called the p-value." + }, + { + "text": "And so same for example 2." + }, + { + "text": "There's the tipping point, alpha, at which I go from feeling to reject to rejecting." + }, + { + "text": "And that's exactly the number, the area under the curve, such that here I see 0.77." + }, + { + "text": "And this is this alpha prime prime over 2." + }, + { + "text": "And this number is clearly, alpha prime prime is clearly larger than 5%." + }, + { + "text": "So what's the advantage of thinking and mapping back these numbers?" + }, + { + "text": "Well, now I'm actually going to spit out some number which is between 0 and 1." + }, + { + "text": "And that should be the only scale you should have in mind." + }, + { + "text": "Remember we discussed that last time." + }, + { + "text": "Well, if I actually spit out a number which is 3.45, maybe you can try to think, is 3.45 a large number for a Gaussian?" + }, + { + "text": "That's a number." + }, + { + "text": "But if I had another random variable that was not Gaussian, maybe it was a double exponential, you would have to have another scale in your mind." + }, + { + "text": "Is 3.45 a large number for the large, so large that it's unlikely to come from a double exponential?" + }, + { + "text": "If I had a gamma distribution, I can think of any distribution." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk23.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..d0d0fdec57ad2cc7e2dadb707abb6df87bdbb70b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then that means for each distribution, you would have to have a scale in mind." + }, + { + "text": "So of course, you can have the Gaussian scale in mind." + }, + { + "text": "I mean, I have the Gaussian scale in mind." + }, + { + "text": "But then if I map it back into this number between 0 and 1, all the distributions play the same role." + }, + { + "text": "So whether I'm talking about if my limiting distribution is normal or exponential or gamma or whatever you want, for all these guys, I'm just going to map it into one number between 0 and 1." + }, + { + "text": "Small number means lots of evidence against h1." + }, + { + "text": "Large number means lots of evidence against h0." + }, + { + "text": "Small number means very few evidence against h0." + }, + { + "text": "And this is the only number you need to keep in mind." + }, + { + "text": "And the question is, am I willing to tolerate this number between 5%, 6% or maybe 10%, 12%?" + }, + { + "text": "And this is the only scale you have to have in mind." + }, + { + "text": "And this scale is the scale of p-values." + }, + { + "text": "So the p-value is the tipping point in terms of alpha." + }, + { + "text": "In words, I can make it formal, because tipping point, as far as I know, is not a mathematical term." + }, + { + "text": "So a p-value of a test is the smallest, potentially asymptotic level, if I talk about an asymptotic p-value." + }, + { + "text": "And that's what we do when we talk about central limit theorem, at which the test rejects h0." + }, + { + "text": "If I were to go any smaller, I would fail to reject." + }, + { + "text": "The smaller the level, the less likely it is for me to reject." + }, + { + "text": "And if I were to go any smaller, I would start failing to reject." + }, + { + "text": "And so it is a random number." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk24.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..70790440238c22e23b0b77fc5e658fdf89d62e44 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "It depends on what I actually observe." + }, + { + "text": "So here, of course, I instantiated those two numbers, 3.45 and 0.77, as realizations of random variables." + }, + { + "text": "But if you think of those as being the random numbers before I see my data, this was a random number." + }, + { + "text": "And therefore, the area under the curve to the right of it is also a random area." + }, + { + "text": "If this thing fluctuates, then the area under the curve fluctuates." + }, + { + "text": "And that's what the p-value is." + }, + { + "text": "That's what John Oliver talks about when he talks about p-hacking." + }, + { + "text": "And so we talked about this in the first lecture." + }, + { + "text": "So p-hacking is, how do I do?" + }, + { + "text": "Oh, if I'm a scientist, do I want to see a small p-value or a large p-value?" + }, + { + "text": "Small, right?" + }, + { + "text": "Scientists want to see small p-values, because small p-values equals rejecting, which equals discovery, which equals publication, which equals promotion." + }, + { + "text": "So that's what people want to see." + }, + { + "text": "So people are tempted to see small p-values." + }, + { + "text": "And what's called p-hacking is, well, find a way to cheat." + }, + { + "text": "Maybe look at your data, formulate your hypothesis in such a way that you will actually have a smaller p-value than you should have." + }, + { + "text": "So here, for example, there's one thing I did not insist on, because again, this is not a particular course in statistical thinking." + }, + { + "text": "But one thing that we implicitly did was set those theta 0 and theta 1 ahead of time." + }, + { + "text": "I fixed them, and I'm trying to test this." + }, + { + "text": "This is to be contrasted with the following approach." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk25.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..ae5989051a3c9ad74dd6e26eac906c8e26ce8535 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "I draw my data." + }, + { + "text": "So I draw." + }, + { + "text": "I run this experiment, which is probably going to get me a publication in Nature." + }, + { + "text": "I'm trying to test if a coin is fair." + }, + { + "text": "And I draw my data, and I see that there's 13 out of 30 of my observations that are heads." + }, + { + "text": "That means that from this data, it looks like p is less than 1 half." + }, + { + "text": "So if I look at this data and then decide that my alternative is not p not equal to 1 half, but rather p less than 1 half, that's p-hacking." + }, + { + "text": "I'm actually making my p-value strictly smaller by first looking at the data and then deciding what my alternative is going to be." + }, + { + "text": "And that's cheating, because all the things we did were assuming that this 0.5 or d alternative was actually a fix." + }, + { + "text": "Everything was deterministic." + }, + { + "text": "The only randomness came from the data." + }, + { + "text": "But if I start looking at the data and designing my experiment or my alternatives and null hypothesis based on the data, it's as if I started putting randomness all over the place." + }, + { + "text": "And then I cannot control it, because I don't know how it just intermingles with each other." + }, + { + "text": "All right." + }, + { + "text": "So that was for the John Oliver moment." + }, + { + "text": "So the p-value is nice." + }, + { + "text": "So maybe I mentioned that before." + }, + { + "text": "My wife works in market research." + }, + { + "text": "And maybe every two years, she seems to run into a statistician in the hallway." + }, + { + "text": "And she comes home and says, what is a p-value again?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk26.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..582b81ac1a78246b0f187a4c706af274ba689dbe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk26.json @@ -0,0 +1,62 @@ +[ + { + "text": "And for her, a p-value is just the number is in an Excel spreadsheet." + }, + { + "text": "And actually, small equals good and large equals bad." + }, + { + "text": "And that's all she needs to know at this point." + }, + { + "text": "Actually, they do the job for her." + }, + { + "text": "Small is green." + }, + { + "text": "Large is red." + }, + { + "text": "And so for her, a p-value is just green or red." + }, + { + "text": "But so what she's really implicitly doing with this color code is just applying the golden rule." + }, + { + "text": "What the statisticians do for her in the Excel spreadsheet is that they take the numbers for the p-values that are less than some fixed level." + }, + { + "text": "So depending on the field in which she works, so she works for pharmaceutical companies, so the p-values are typically compared." + }, + { + "text": "The tests are usually performed at level 1% rather than 5%." + }, + { + "text": "So 5% is maybe your gold standard if you're doing sociology or trying to, I don't know, release a new blueberry flavor for your toothpaste, like something that's not going to change the life of people." + }, + { + "text": "Maybe you're going to run at 5%." + }, + { + "text": "It's OK to make a mistake." + }, + { + "text": "People are just going to feel gross, but that's about it." + }, + { + "text": "Whereas here, if you have this p-value which is less than 1%, it might be more important for some drug discovery, for example." + }, + { + "text": "And so let's say you run at 1%." + }, + { + "text": "And so what they do in this Excel spreadsheet is that all the numbers that are below 1% show up in green, and all the numbers that are above 1% show up in red." + }, + { + "text": "And that's it." + }, + { + "text": "That's just applying the golden rule." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk27.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk27.json new file mode 100644 index 0000000000000000000000000000000000000000..6d2b3e73a1f2bfb3d007d43a22bc17095a5878f8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk27.json @@ -0,0 +1,62 @@ +[ + { + "text": "If the number is green, reject." + }, + { + "text": "If the number is red, fail to reject." + }, + { + "text": "OK?" + }, + { + "text": "Yeah?" + }, + { + "text": "So going back to the example of the previous prior example where you can achieve by looking at your data and then formulating, say, a theta 1 to be p less than 1%." + }, + { + "text": "Yeah." + }, + { + "text": "So how would you achieve your goal by changing the theta 1?" + }, + { + "text": "You mean by achieving my goal?" + }, + { + "text": "You mean letting ethics aside, right?" + }, + { + "text": "Yeah." + }, + { + "text": "You want to be published." + }, + { + "text": "So OK." + }, + { + "text": "So let me teach you how." + }, + { + "text": "Well, here, what do you do?" + }, + { + "text": "You want to, at the end of the day, a test is only telling you whether you found evidence in your data that H1 was more likely than H0, basically." + }, + { + "text": "How do you make H1 more likely?" + }, + { + "text": "Well, you just basically target H1 to be what the data is going to make it more likely to be." + }, + { + "text": "All right?" + }, + { + "text": "So if, for example, I say H1 can be on both sides, then my data is going to have to take into account fluctuations on both sides." + }, + { + "text": "And I'm going to lose a factor of 2 somewhere because things are not symmetric." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk28.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk28.json new file mode 100644 index 0000000000000000000000000000000000000000..b6a2e04f21d17d3f9d8f51277fef4b6bd544ea8c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk28.json @@ -0,0 +1,62 @@ +[ + { + "text": "Here is the ultimate way of making this work." + }, + { + "text": "I'm going back to my example of flipping coins." + }, + { + "text": "And now, so here, what I did is I said, oh, this number 0.43 is actually smaller than 0.5." + }, + { + "text": "So I'm just going to test whether I'm 0.5 or I'm less than 0.5." + }, + { + "text": "But here is something that I can promise you I did not make the computation will reject." + }, + { + "text": "OK, so here, this one actually, yeah, this one fails to reject, right?" + }, + { + "text": "So here is one that will certainly reject." + }, + { + "text": "H0 is 0.5. p is 0.5." + }, + { + "text": "H1, p is 0.43." + }, + { + "text": "OK?" + }, + { + "text": "Now, you can try." + }, + { + "text": "But I can promise you that your data will tell you that H1 is the right one." + }, + { + "text": "OK?" + }, + { + "text": "I mean, you can check very quickly that this is really extremely likely to happen, right?" + }, + { + "text": "And so actually, what am I?" + }, + { + "text": "No, actually, that's not true." + }, + { + "text": "OK. Because here, the test that I derive that's based on this kind of stuff, right?" + }, + { + "text": "Here, at some point, somewhere, under some layers, I assume that all our tests are going to have this form." + }, + { + "text": "But here, this is only when you're trying to test one region versus another region next to it, or one point versus a region around it, or something like this." + }, + { + "text": "Whereas for this guy, there's another test I could come up with, which is, what is the probability that I get 0.43?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk29.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk29.json new file mode 100644 index 0000000000000000000000000000000000000000..7c83fb4d5133113ff729308f195ed934ccaaacb9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk29.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what is the probability that I get 0.5?" + }, + { + "text": "Now, what I'm going to do is I'm going to just conclude it's whichever has the largest probability." + }, + { + "text": "Then maybe I'm going to have to make some adjustments so that the level is actually 5%." + }, + { + "text": "But I can make this happen." + }, + { + "text": "I can make the level be 5% and always conclude this guy, but I would have to use a different test." + }, + { + "text": "Now, the test that I described, again, those t and larger than c are built in to be tests that are sort of resilient to this kind of manipulations, because they're sort of oblivious towards what the alternative looks like." + }, + { + "text": "I mean, they're just saying it's either to the left or to the right, but whether it's a point or an entire half line doesn't matter." + }, + { + "text": "So if you try to look at your data and just put the data itself into your hypothesis testing problem, then you're failing the statistical principle." + }, + { + "text": "And that's what people are doing, right?" + }, + { + "text": "I mean, how can I check?" + }, + { + "text": "I mean, of course, here it's going to be pretty blatant if you publish a paper that looks like this." + }, + { + "text": "But there's ways to do it differently, right?" + }, + { + "text": "For example, one way to do it is to just do more." + }, + { + "text": "So typically, what people do is they do multiple hypothesis testing." + }, + { + "text": "They're doing 100 tests at a time." + }, + { + "text": "Then you have random fluctuations every time." + }, + { + "text": "And so they just pick the one that has the random fluctuations that go their way." + }, + { + "text": "I mean, sometimes it's going in your way, and sometimes it's going the opposite way." + }, + { + "text": "So you just pick the one that works for you." + }, + { + "text": "We'll talk about multiple hypothesis testing soon if you want to increase your publication counts." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk3.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..82298a0911f771c50c0c0e31234286bcbe2ed969 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "So p can range between 0 and 1, that's for sure." + }, + { + "text": "And what I'm going to try to test is whether p is less than 1 half or larger than 1 half." + }, + { + "text": "So this is going to be, let's say, theta 0, and this guy here is theta 1." + }, + { + "text": "Just trying to give you a picture of what those guys are." + }, + { + "text": "So I have my y-axis." + }, + { + "text": "Now I'm going to start drawing numbers, all these things, this function, this function, and this number are all numbers between 0 and 1." + }, + { + "text": "So now I'm claiming that when I move from left to right, what is my probability of rejecting going to do?" + }, + { + "text": "So what I'm going to plot is the probability under theta." + }, + { + "text": "The first thing I want to plot is the probability under theta that psi is equal to 1." + }, + { + "text": "And let's say psi, think of psi as being just this indicator that square root of n xn bar minus p over square root xn bar, 1 minus xn bar, is larger than some constant c for a properly chosen c. So what we choose is that c is in such a way that at 1 half, when we're testing for 1 half, what we wanted was this number to be equal to alpha, basically." + }, + { + "text": "So we fix this alpha number so that this guy, so if I want alpha of psi of theta less than alpha, given in advance, so think of it as being equal to, say, 5%." + }, + { + "text": "So I'm fixing this number, and I want this to be controlled for all theta and theta 0." + }, + { + "text": "So if you're going to give me this budget, well, I'm actually going to make it equal where I can." + }, + { + "text": "If you're telling me you can make it equal to alpha, we know that if I increase my type 1 error, I'm going to decrease my type 2 error." + }, + { + "text": "If I start putting everyone in jail, or if I start letting everyone go free, that's what we're discussing last time." + }, + { + "text": "So since we have this trade-off, and you're giving me a budget for one guy, I'm just going to max it out." + }, + { + "text": "And where am I going to max it out?" + }, + { + "text": "Exactly at 1 half at the boundary." + }, + { + "text": "So this is going to be 5%." + }, + { + "text": "So what I know is that since alpha of theta is less than alpha for all theta and theta 0, sorry, that's for theta 0, that's where alpha is defined." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk30.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk30.json new file mode 100644 index 0000000000000000000000000000000000000000..a8e80051fb683b419557b2b36ba8c95a3d50cf00 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk30.json @@ -0,0 +1,62 @@ +[ + { + "text": "There's actually papers." + }, + { + "text": "I think it was big news, there's some papers, I think it's psychology or psychometrics papers, that actually refuse to publish p-values now." + }, + { + "text": "All right, where were we?" + }, + { + "text": "OK, here's the golden rule." + }, + { + "text": "So one thing that I'd like to show is this thing, just so you know how you apply the golden rule and how you apply the standard test." + }, + { + "text": "So the standard paradigm is the following." + }, + { + "text": "You have a black box, which is your test." + }, + { + "text": "For my wife, this is the fourth floor of the building." + }, + { + "text": "That's where the statisticians sit." + }, + { + "text": "What she sends there is data, let's say x1, xn." + }, + { + "text": "And she says, well, this one is about toothpaste, so here's a level." + }, + { + "text": "Let's say 5%." + }, + { + "text": "What the fourth floor brings back is an answer, yes, no." + }, + { + "text": "Green, red, just an answer." + }, + { + "text": "So that's the standard testing." + }, + { + "text": "You just feed it the data and the level at which you want to perform the test, maybe asymptotic, and it spits out a yes, no answer." + }, + { + "text": "What p-value does, you just feed it the data itself." + }, + { + "text": "And what it spits out is the p-value." + }, + { + "text": "And now, it's just up to you." + }, + { + "text": "I mean, hopefully, your brain has the computational power of deciding whether a number is larger or smaller than 5% without having to call the statisticians for this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk31.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk31.json new file mode 100644 index 0000000000000000000000000000000000000000..9fb2296acde7c40202805ca4f7e73e4c07f68e6a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk31.json @@ -0,0 +1,62 @@ +[ + { + "text": "And that's what it does." + }, + { + "text": "So now, we're all on one scale." + }, + { + "text": "Now, if you actually, I see some of you nodding when I talk about p-hacking." + }, + { + "text": "So that means you've seen p-values." + }, + { + "text": "If you've seen more than 100 p-values in your life, you have an entire scale." + }, + { + "text": "A good p-value is less than 10 to the minus 4." + }, + { + "text": "That's the ultimate sweet spot." + }, + { + "text": "Actually, statistical software spit out an output which says less than 10 to the minus 4." + }, + { + "text": "But then, maybe you want a p-value." + }, + { + "text": "If I tell you my p-value was 4.65, then I will say you've been doing some p-hacking until you found a number that was below 5%." + }, + { + "text": "That's typically what people will do." + }, + { + "text": "But if you're doing the test, if you're saying, I published my result." + }, + { + "text": "My test at 5% said yes, that means that maybe your p-value was 4.99, or your p-value was 10 to the minus 4." + }, + { + "text": "I will never know." + }, + { + "text": "I will never know how much evidence you had against the null." + }, + { + "text": "But if you tell me what the p-value is, I can make my own decision." + }, + { + "text": "I don't have to tell me whether it's a yes." + }, + { + "text": "No, you tell me it's 4.99." + }, + { + "text": "I'm going to say, well, maybe yes, but I'm going to take it with a grain of salt." + }, + { + "text": "And so that's why p-values are good numbers to have in mind." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk32.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk32.json new file mode 100644 index 0000000000000000000000000000000000000000..96ed5fb80473cde620f1dcbaecbdda179310c37c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk32.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, I show it as if it was an old trick that you start mastering when you're 45 years old." + }, + { + "text": "No, it's just how small is the number between 0 and 1." + }, + { + "text": "That's really what you need to know." + }, + { + "text": "Maybe on the log scale, if it's 10 to the minus 1, 10 to the minus 2, 10 to the minus 3, et cetera, that's probably the extent of the mastery here." + }, + { + "text": "So this traditional standard paradigm that I showed is actually commonly referred to as the Neyman-Pearson paradigm." + }, + { + "text": "So here it says Neyman-Pearson's theory." + }, + { + "text": "So there's an entire theory that comes with it, but it's really a paradigm." + }, + { + "text": "It's a way of thinking about hypothesis testing that says, well, if I'm not going to be able to optimize both my type 1 and type 2 error, I'm actually going to lock in my type 1 error below some level and just minimize the type 2 error under this constraint." + }, + { + "text": "That's what the Neyman-Pearson paradigm is." + }, + { + "text": "And it sort of makes sense for hypothesis testing problems." + }, + { + "text": "If you were doing some other applications with multi-objective optimization, you would maybe come up with something different." + }, + { + "text": "For example, machine learning is not performing typically under Neyman-Pearson paradigm." + }, + { + "text": "So if you do spam filtering, you could say, well, I want to constrain the probability as much as I can of taking somebody's important emails and throwing them out as spam and, under this constraint, not send too much spam to that person." + }, + { + "text": "That sort of makes sense for spams." + }, + { + "text": "Now, if you're labeling cats versus dogs, it's probably not like you want to make sure that no more than 5% of the dogs are labeled cat." + }, + { + "text": "Because it doesn't matter." + }, + { + "text": "So what you typically do is you just sum up the two types of error you can make, and you minimize the sum without putting any more weight on one or the other." + }, + { + "text": "So here's an example where doing a binary decision, one or two of the errors you can make, you don't have to actually be like that." + }, + { + "text": "So this example here, I did not." + }, + { + "text": "The trivial test, psi is equal to 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk33.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk33.json new file mode 100644 index 0000000000000000000000000000000000000000..0c2da6bcc636025ed6d047d161fdfe68e3b68329 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk33.json @@ -0,0 +1,62 @@ +[ + { + "text": "What was it in the US trial court example?" + }, + { + "text": "What is psi equal to 0?" + }, + { + "text": "I was concluding all ways to the null." + }, + { + "text": "What was the null?" + }, + { + "text": "Innocent, right?" + }, + { + "text": "That's the status quo." + }, + { + "text": "So that means that this guy never rejects a 0." + }, + { + "text": "Everybody's going away free." + }, + { + "text": "So you're sure you're not actually going against the Constitution because alpha is 0%, which is certainly less than 5%." + }, + { + "text": "But the power, the fact that a lot of criminals go back outside in the free world is actually formulated in terms of low power, which in this case is actually 0." + }, + { + "text": "Again, the power is a number between 0 and 1." + }, + { + "text": "Close to 0, good." + }, + { + "text": "Close to 1, bad." + }, + { + "text": "Now, what is the definition of the p-value?" + }, + { + "text": "That's going to be something." + }, + { + "text": "Mouthful, right?" + }, + { + "text": "The definition of the p-value is a mouthful." + }, + { + "text": "It's really the tipping point." + }, + { + "text": "It is the smallest level at which blah, blah, blah, blah." + }, + { + "text": "It's complicated to remember it." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk34.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk34.json new file mode 100644 index 0000000000000000000000000000000000000000..074297c2186646a83b698c991607273c1d143e1c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk34.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, I think that by my sixth explanation, my wife, after saying, oh, so it's the probability of making an error, I said, yeah, that's the probability of making an error." + }, + { + "text": "Because of course, she can think probability of making an error, small, good, large, bad." + }, + { + "text": "So that's actually a good way to remember." + }, + { + "text": "I'm pretty sure that at least 50% of people using p-values out there think that the p-value is the probability of making an error." + }, + { + "text": "Now, for all matters of purposes, if your goal is to just threshold the p-value, this is OK to have this in mind." + }, + { + "text": "But when it comes, at least until December 22, I would recommend trying to actually memorize the right definition for the p-value." + }, + { + "text": "OK?" + }, + { + "text": "OK." + }, + { + "text": "So the idea, again, is fix the level and try to optimize the power." + }, + { + "text": "So we're going to try to compute some p-values from now on." + }, + { + "text": "How do you compute the p-value?" + }, + { + "text": "Well, you can actually see it from this picture over there." + }, + { + "text": "One thing I didn't show on this picture, here was my q alpha over 2 that had alpha here, alpha over 2 here, right?" + }, + { + "text": "That was my q alpha over 2." + }, + { + "text": "And I said, if tn is to the right of this guy, I'm going to reject." + }, + { + "text": "If tn is to the left of this guy, I'm going to fail to reject." + }, + { + "text": "OK?" + }, + { + "text": "Pictorially, you can actually represent the p-value." + }, + { + "text": "It's when I replace this guy by tn itself." + }, + { + "text": "Sorry, that's p-value over 2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk35.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk35.json new file mode 100644 index 0000000000000000000000000000000000000000..9f1a7b89f2d43b53944bbf516e37f98c7cf70618 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk35.json @@ -0,0 +1,62 @@ +[ + { + "text": "No, actually, that's p-value." + }, + { + "text": "So let me just keep it like that and put the absolute value here." + }, + { + "text": "OK?" + }, + { + "text": "So if you replace the role of q alpha over 2 by your test statistic, this is what the area under the curve is actually the p-value itself up to scaling, because of the symmetric thing." + }, + { + "text": "OK?" + }, + { + "text": "So there's a good way to see pictorially what the p-value is." + }, + { + "text": "It's just the probability that some Gaussians, which is the probability that some absolute value of n0,1 exceeds tn." + }, + { + "text": "Right?" + }, + { + "text": "That's what the p-value is." + }, + { + "text": "Now, this guy has nothing to do with this guy." + }, + { + "text": "So this is really just 1 minus the Gaussian CDF of tn." + }, + { + "text": "And that's it." + }, + { + "text": "So that's how I would compute p-values." + }, + { + "text": "Now, as I said, the p-value is a beauty, because you don't have to understand the fact that your limiting distribution is a Gaussian." + }, + { + "text": "Right?" + }, + { + "text": "It's already factored in this construction." + }, + { + "text": "The fact that I'm actually looking at this cumulative distribution function of a standard Gaussian makes my p-value automatically adjust to what the limiting distribution is." + }, + { + "text": "And if this was the cumulative distribution function of a exponential, I would just have a different function here denoted by f, for example." + }, + { + "text": "And I would just compute a different value." + }, + { + "text": "But in the end, regardless of what the limiting value is, my p-value would still be a number between 0 and 1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk36.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk36.json new file mode 100644 index 0000000000000000000000000000000000000000..2d4547dd85e8e54b4a9640f590a534ed56d0306a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk36.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so to illustrate that, let's look at other weird distributions that we could get in place of the standard Gaussian." + }, + { + "text": "And we're not going to see many, but we'll see one." + }, + { + "text": "And it's not called the chi-squared distribution." + }, + { + "text": "It's actually called the student's distribution, but it involves the chi-squared distribution as a building block." + }, + { + "text": "So I don't know if my phonetics are not really right there, so I try to say, well, it's chi-squared." + }, + { + "text": "Maybe it's chi-squared in Canada." + }, + { + "text": "Who knows?" + }, + { + "text": "So for a positive integer, so there's only one parameter." + }, + { + "text": "So for the Gaussian, you have two parameters, which are mu and sigma squared." + }, + { + "text": "Those are real numbers." + }, + { + "text": "Sigma squared is positive." + }, + { + "text": "Here, I have one integer parameter." + }, + { + "text": "Then the distribution, the chi-squared distribution with d degrees of freedom." + }, + { + "text": "So the parameter is called a degree of freedom, just like mu is called the expected value, and sigma squared is called the variance." + }, + { + "text": "So it's called degrees of freedom." + }, + { + "text": "You don't have to really understand why." + }, + { + "text": "So that's the law that you would get." + }, + { + "text": "That's the random variable you would get if you were to sum d squares of independent standard Gaussians." + }, + { + "text": "So I take the square of an independent random Gaussian." + }, + { + "text": "I take another one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk37.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk37.json new file mode 100644 index 0000000000000000000000000000000000000000..6fa169cd52b7910e64c667064ab385a1dc476da0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk37.json @@ -0,0 +1,62 @@ +[ + { + "text": "I sum them, and that's a chi-squared with two degrees of freedom." + }, + { + "text": "That's how you get it." + }, + { + "text": "Now, I could define it using its probability density function." + }, + { + "text": "After all, this is the sum of positive random variables." + }, + { + "text": "It is a positive random variable." + }, + { + "text": "It has a density on the positive real line." + }, + { + "text": "And the PDF of chi-squared, PDF of chi-squared with d degrees of freedom is what?" + }, + { + "text": "Well, it's fd of x is x to the d over 2 minus 1, e to the minus x over 2." + }, + { + "text": "And then here, I have a gamma of d over 2, and the other one is, I think, 2 to the d over 2 minus 1." + }, + { + "text": "No, 2 to the d over 2." + }, + { + "text": "That's what it is." + }, + { + "text": "That's the density." + }, + { + "text": "If you are very good at probability, you can make the change of variable and write your Jacobian and do all this stuff and actually check that this is true." + }, + { + "text": "I do not recommend doing that." + }, + { + "text": "So this is the density, but it's better understood like that, at thinking of just something that you built from standard Gaussian." + }, + { + "text": "So for example, an example of a chi-squared with two degrees of freedom is actually the following thing." + }, + { + "text": "Let's assume I have a target like this." + }, + { + "text": "And I don't aim very well, and I'm trying to hit the center." + }, + { + "text": "And I'm going to have maybe a deviation, which is standard Gaussian left-right and standard Gaussian north-south." + }, + { + "text": "So I'm throwing, and then I'm here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk38.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk38.json new file mode 100644 index 0000000000000000000000000000000000000000..e9321d18ef5daa35196a20db9f6bb7680045ede5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk38.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'm claiming that this number here, by Pythagoras' theorem, the squared distance here is the sum of this squared distance here, which is the square of a Gaussian by assumption, plus the square of this distance, which is the square of another independent Gaussian." + }, + { + "text": "I assume those are independent." + }, + { + "text": "And so the squared distance from this point to this point is the chi-squared with two degrees of freedom." + }, + { + "text": "So this guy here is n01 squared." + }, + { + "text": "This is n01 squared." + }, + { + "text": "And so this guy here, this distance here, is chi-squared with two degrees of freedom." + }, + { + "text": "I mean, the squared distance." + }, + { + "text": "I'm talking about squared distances here." + }, + { + "text": "So now you can see that actually Pythagoras is basically why chi-squared arise." + }, + { + "text": "That's why it has its own name." + }, + { + "text": "I mean, I could define this random variable." + }, + { + "text": "I mean, it's actually a gamma distribution." + }, + { + "text": "It's a special case of something called the gamma distribution." + }, + { + "text": "The fact that the special case has its own name is because there's many times where we're going to take sum of squares of independent Gaussians, because Gaussians, the sum of squares is really the norm, the Euclidean norm squared, just by Pythagoras theorem." + }, + { + "text": "If I'm in higher dimension, I can start to sum more squared coordinates, and I'm going to measure the norm squared." + }, + { + "text": "So if you want to draw this picture, it looks like this." + }, + { + "text": "Again, it's the sum of positive numbers." + }, + { + "text": "So it's going to be on 0 plus infinity." + }, + { + "text": "That's fd." + }, + { + "text": "And so for f1 looks like this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk39.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk39.json new file mode 100644 index 0000000000000000000000000000000000000000..530fa0ac2ba5f7380bf835d6fd19c3b55d8a53a3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk39.json @@ -0,0 +1,62 @@ +[ + { + "text": "f2 looks like this." + }, + { + "text": "So the tails becomes heavier and heavier as d increases." + }, + { + "text": "And then at start to 3, it starts to have a different shape." + }, + { + "text": "It starts from 0, and it looks like this." + }, + { + "text": "And then as d increases, it's basically as if you were to push this thing to the right." + }, + { + "text": "It's just like, pfft." + }, + { + "text": "It's just falling like a big ball." + }, + { + "text": "Everybody sees what's going on?" + }, + { + "text": "So there's just this fat thing that's just going there." + }, + { + "text": "What is the expected value of a k squared?" + }, + { + "text": "So it's the expected value of the sum of Gaussian random variables squared." + }, + { + "text": "I don't know why I said that." + }, + { + "text": "AUDIENCE 2 It's the sum of their second norm, right?" + }, + { + "text": "Which is?" + }, + { + "text": "Those are n0, 1." + }, + { + "text": "It's like, oh, I see, 1." + }, + { + "text": "Yeah." + }, + { + "text": "So n times 1, or d times 1." + }, + { + "text": "Yeah, which is d. So one thing you can check quickly is that the expected value of a k squared is d. And so you see, that's why the mass is shifting to the right as d increases." + }, + { + "text": "It's just going there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk4.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..07e0b7e52902074c6ec8439999a1046b4b977809 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "So for theta and theta 0, I know that my function is going to look like this." + }, + { + "text": "It's going to be somewhere in this rectangle." + }, + { + "text": "Everybody agrees?" + }, + { + "text": "So this function for this guy is going to look like this." + }, + { + "text": "When I'm at 0, when p is equal to 0, which means I only observe 0's, then I know that p is going to be 0." + }, + { + "text": "And I will certainly not conclude that p is equal to 1." + }, + { + "text": "This test will never conclude that p is equal to 1." + }, + { + "text": "Sorry, that was, yeah." + }, + { + "text": "That p is equal to, that p is lower than 1 half, just because xn bar is going to be equal to 0." + }, + { + "text": "OK, well, this is actually not well-defined." + }, + { + "text": "So maybe I need to do something, put it equal to 0 if xn bar is equal to 0." + }, + { + "text": "So I guess basically I get something which is negative." + }, + { + "text": "And so it's never going to be larger than what I want." + }, + { + "text": "And so here I'm actually starting at 0." + }, + { + "text": "So now this is this function here that increases." + }, + { + "text": "I mean, it should increase smoothly." + }, + { + "text": "This function here is alpha psi of theta, or alpha psi of p, let's say, because we're talking about p. Then it reaches alpha here." + }, + { + "text": "Now when I go on the other side, I'm actually looking at beta." + }, + { + "text": "When I'm on theta 1, the function that matters is the probability of type 2 error, which is beta psi." + }, + { + "text": "And this beta psi is actually going to increase." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk40.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk40.json new file mode 100644 index 0000000000000000000000000000000000000000..cf303c16babeea5b89d0924caa36f4dde58e6495 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk40.json @@ -0,0 +1,62 @@ +[ + { + "text": "Actually, the variance is also increasing." + }, + { + "text": "The variance is 2d." + }, + { + "text": "So this is one thing." + }, + { + "text": "And so why do we care about this in basic statistics?" + }, + { + "text": "It's not like we actually have statistics much about throwing darts at high dimensional boards." + }, + { + "text": "So what's happening is that if I look at the sample variance, the average of the sum of squared centered by their mean, then I can actually expend this as the sum of the squares minus the average squared." + }, + { + "text": "It's just the same trick that we have for the variance." + }, + { + "text": "Second moment minus first moment squared." + }, + { + "text": "And then I claim that Cochran's theorem, I will tell you in a second what Cochran's theorem tells me, is that this sample variance is actually, so if I had only this, so now, OK, look at those guys." + }, + { + "text": "Those guys are Gaussian with mean mu and variance sigma squared." + }, + { + "text": "Think for one second, mu being 0 and sigma squared being 1." + }, + { + "text": "Now, this part would be a chi-square with n degrees of freedom divided by n. Now, I get another thing here, which is the square of something that looks like a Gaussian as well." + }, + { + "text": "So it looks like I have something else here, which looks also like a chi-square." + }, + { + "text": "Now, Cochran's theorem is essentially telling you that those things are independent." + }, + { + "text": "And so that in a way, you can think of those guys as being here n degrees of freedom minus 1 degree of freedom." + }, + { + "text": "Now, here, as I said, this is not mean 0 and variance 1." + }, + { + "text": "The fact that it's not mean 0 is not a problem, because I can remove the mean here and remove the mean here." + }, + { + "text": "And so this thing has the same distribution, regardless of what the actual mean is." + }, + { + "text": "So without loss of generality, I can assume that mu is equal 0." + }, + { + "text": "Now, the variance I'm going to have to pay, because if I multiply all these numbers by 10, then this Sn is going to be multiplied by 100." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk41.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk41.json new file mode 100644 index 0000000000000000000000000000000000000000..be699853a1170afd439414bc8f189e87e84b0b94 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk41.json @@ -0,0 +1,62 @@ +[ + { + "text": "So this thing is going to scale with the variance." + }, + { + "text": "And not surprisingly, it's scaling like the square of the variance." + }, + { + "text": "So if I look at Sn, it's distributed as sigma-square times the chi-square with n minus 1 degrees of freedom divided by n. And we don't really write that, because a chi-square times sigma-square divided by n is not a distribution." + }, + { + "text": "So we put everything to the left." + }, + { + "text": "And we say that this is actually a chi-square with n minus 1 degrees of freedom." + }, + { + "text": "So here, I'm actually dropping a fact on you." + }, + { + "text": "But you can sort of see the building block." + }, + { + "text": "What is the thing that's sort of fussy at this point, but the rest should be crystal clear to you?" + }, + { + "text": "The thing that's fussy is that removing this square guy here is actually removing 1 degree of freedom." + }, + { + "text": "That should be weird." + }, + { + "text": "But that's what Cochran's theorem tells me." + }, + { + "text": "It's essentially stating something about orthogonality of subspaces with the span of the constant vector, something like that." + }, + { + "text": "So you don't have to think about it too much." + }, + { + "text": "But that's what it's telling me." + }, + { + "text": "But the rest, if you plug in, so the scaling in sigma-squared and in n, that should be completely clear to you." + }, + { + "text": "So in particular, if I remove that part, it should be clear to you that this thing, if mean is 0, this thing is actually distributed." + }, + { + "text": "Well, if mu is 0, what is the distribution of this guy?" + }, + { + "text": "So I remove that part, just this part." + }, + { + "text": "So I have xi, which are n0 sigma-squared." + }, + { + "text": "And I'm asking, what is the distribution of 1 over n sum from i equal 1 to n of xi-squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk42.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk42.json new file mode 100644 index 0000000000000000000000000000000000000000..3596e452514719b86b744b50b7402e7dd02b9ace --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk42.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it is the sum of their iid." + }, + { + "text": "So it's the sum of independent Gaussians, but not standard." + }, + { + "text": "So the first thing to make them standard is that I divide all of them by sigma-squared." + }, + { + "text": "Now, this guy is of the form zi-squared, where zi is n0, 1." + }, + { + "text": "So now this thing here has what distribution?" + }, + { + "text": "Chi-squared n. And now sigma-squared over n times chi-squared n. So if I have sigma-squared divided by n times chi-squared, sorry, so n times n divided by sigma-squared." + }, + { + "text": "So if I take this thing and I multiply it by n divided by sigma-squared, it means I remove this term." + }, + { + "text": "And now I am left with a chi-squared with n degrees of freedom." + }, + { + "text": "Now, the effect of centering with the sample mean here is only to lose 1 degree of freedom." + }, + { + "text": "That's it." + }, + { + "text": "OK?" + }, + { + "text": "So if I want to do a test about variance, since this is supposedly a good estimator of variance, this could be my pivotal distribution." + }, + { + "text": "This could play the role of a Gaussian." + }, + { + "text": "If I want to know if my variance is equal to 1 or larger than 1, I could actually build a test based on this only statement and test if the variance is larger than 1 or not." + }, + { + "text": "Now, this is not asymptotic because I started with the very assumption that my data was Gaussian itself." + }, + { + "text": "OK?" + }, + { + "text": "Now, just a side remark, you can check that this chi-squared 2, 2 is an exponential with half degrees of freedom, which is certainly not clear from the fact that z1 squared plus z2 squared is a chi-squared with 2 degrees of freedom." + }, + { + "text": "If I give you the sum of the square of two independent Gaussians, this is actually an exponential." + }, + { + "text": "That's not super clear, right?" + }, + { + "text": "But if you look at what was here, I don't know if you took notes, but let me rewrite it for you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk43.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk43.json new file mode 100644 index 0000000000000000000000000000000000000000..c1c4ce2a1e88dbaf6e313e0235a0fa58a881a709 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk43.json @@ -0,0 +1,59 @@ +[ + { + "text": "So it was x to the d over 2 minus 1 e to the minus x over 2 divided by 2 to the d over 2 gamma of d over 2." + }, + { + "text": "So if I plug in d is equal to 2, gamma of 2 over 2 is gamma of 1, which is 1, right?" + }, + { + "text": "It's factorial of 0." + }, + { + "text": "So it's 1." + }, + { + "text": "So this guy goes away." + }, + { + "text": "2 to the d over 2 is 2 to the 1." + }, + { + "text": "So that's just 1." + }, + { + "text": "No, that's just 2." + }, + { + "text": "OK?" + }, + { + "text": "Then x to the d over 2 minus 1 is x to the 0, goes away." + }, + { + "text": "And so I have x minus x over 2, 1 half, which is really, indeed, of the form lambda e to the minus lambda x for lambda is equal to 1 half, which was our exponential distribution." + }, + { + "text": "OK?" + }, + { + "text": "So well, next week is Columbus Day." + }, + { + "text": "So that's next Monday." + }, + { + "text": "So next week, we'll talk about students' distribution." + }, + { + "text": "And so that was discovered by a guy who pretended his name was student but was not student." + }, + { + "text": "And I challenge you to find why in the meantime." + }, + { + "text": "All right, so I'll see you next week." + }, + { + "text": "Your homework is going to be outside, so we can release the room." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk5.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..89ec03ee891688f8ef72df5ae36dcaada4844313 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "So beta psi is what?" + }, + { + "text": "Well, beta psi should also, sorry, that's the probability of being equal to alpha." + }, + { + "text": "So what I'm going to do is I'm going to look at the probability of rejecting." + }, + { + "text": "So let me draw this function all the way." + }, + { + "text": "It's going to look like this." + }, + { + "text": "Now here, if I look at this function here or here, this is the probability under theta that psi is equal to 1." + }, + { + "text": "And we just said that in this region, this function is called alpha psi." + }, + { + "text": "In that region, it's not called alpha psi." + }, + { + "text": "It's not called anything." + }, + { + "text": "It's just the probability of rejection." + }, + { + "text": "So it's not an error." + }, + { + "text": "It's actually what you should be doing." + }, + { + "text": "What we're looking at in this region is 1 minus this guy." + }, + { + "text": "We're looking at the probability of not rejecting." + }, + { + "text": "So I need to actually basically look at 1 minus this thing, which here is going to be 95%." + }, + { + "text": "So I'm going to do 95%." + }, + { + "text": "And this is my probability." + }, + { + "text": "And I'm just basically drawing the symmetric of this guy." + }, + { + "text": "So this here is the probability under theta that psi is equal to 0, which is 1 minus p theta that psi is equal to 1." + }, + { + "text": "So it's just 1 minus the white curve." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk6.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..2ba3f3f31acb2d89e2bd57110d90b292f5959fce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's actually, by definition, equal to beta psi of theta." + }, + { + "text": "Now, where do I read pi psi?" + }, + { + "text": "What is pi psi on this picture?" + }, + { + "text": "Is pi psi a number or a function?" + }, + { + "text": "It's a number, right?" + }, + { + "text": "It's the minimum of a function." + }, + { + "text": "What is this function?" + }, + { + "text": "It's the probability under theta that theta is equal to 1." + }, + { + "text": "I drew this entire function between theta 0 and theta 1." + }, + { + "text": "I drew this entire white curve." + }, + { + "text": "This is this probability." + }, + { + "text": "Now, I'm saying, look at the smallest value this probability can take on the set theta 1." + }, + { + "text": "What is this?" + }, + { + "text": "This guy." + }, + { + "text": "This is where my pi, this thing here, is pi psi." + }, + { + "text": "And so it's equal to 5%." + }, + { + "text": "So that's for this particular test, because this test is sort of a continuous curve for this psi." + }, + { + "text": "And so if I want to make sure that I'm at 5% when I come to the right of theta 0, if it touches theta 1, then I better have 5% on the other side if the function is continuous." + }, + { + "text": "So basically, if this function is increasing, which will be the case for most tests, then what's going to happen is that, and continuous, then what's going to happen is that the level of the test, which is alpha, is actually going to be equal to the power of the test." + }, + { + "text": "OK?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk7.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..4f5cdee6b6891b45c5f7794aece5ce2b8c13dc7a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, there's something I didn't mention, and I'm just mentioning it, pass it by." + }, + { + "text": "Here, I define the power itself." + }, + { + "text": "This function, this entire white curve here, is actually called the power function." + }, + { + "text": "This thing, that's the entire white curve." + }, + { + "text": "And what you could have is tests that have the entire curve, which is dominated by another test." + }, + { + "text": "So here, if I look at this test, and let's assume I can build another test that has this curve." + }, + { + "text": "Let's say it's the same here." + }, + { + "text": "But then here, it looks like this." + }, + { + "text": "What is the power of this test?" + }, + { + "text": "It's the same." + }, + { + "text": "It's 5%, because this point touches here exactly at the same point." + }, + { + "text": "However, for any other value than the worst possible, this guy is doing better than this guy." + }, + { + "text": "Can you see that?" + }, + { + "text": "Having a curve higher on the right-hand side is a good thing, because it means that you tend to reject more when you're actually in H1." + }, + { + "text": "So this guy is definitely better than this guy." + }, + { + "text": "And so what we say in this case is that the test with the dashed line is uniformly more powerful than the other test." + }, + { + "text": "But we're not going to go into those details, because basically, all the tests that we will describe are already the most powerful ones." + }, + { + "text": "In particular, this guy is, there's no such thing." + }, + { + "text": "All the other guys you can come up with are going to actually be below." + }, + { + "text": "So we saw a couple tests, and we saw how to pick this threshold, and we defined those two things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk8.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8b9449415f7337b53908d8098f0293899e0ba86e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "Yes?" + }, + { + "text": "AUDIENCE 2 But in that case, the down one, if it were also higher in the region of 2 to 0, do you still consider it better?" + }, + { + "text": "PHILIPPE RIGOLLETTIS Because you're given this budget of 5%, right?" + }, + { + "text": "So in this paradigm, where you're given the, actually, if the dashed line was this dashed line, I would still be happy." + }, + { + "text": "I mean, I don't care what this thing does here, as long as it's below 5%." + }, + { + "text": "But here, I'm going to try to discover it, right?" + }, + { + "text": "Think about, again, the drug discovery example." + }, + { + "text": "You're trying to find, let's say you're a scientist, and you're trying to prove that your drug works." + }, + { + "text": "What do you want to see?" + }, + { + "text": "Well, FDA puts on you this constraint that your probability of type 1 error should never exceed 5%." + }, + { + "text": "You're going to work under this assumption." + }, + { + "text": "But what you're going to do is going to try to find a test that will make you find something as often as possible." + }, + { + "text": "And so you're going to max this constraint of 5%, and then you're going to try to make this curve, this curve that means that this is basically, this number here, for any point here, is the probability that you publish your paper." + }, + { + "text": "That's the probability that you can release to market your drug." + }, + { + "text": "That's the probability that it works, right?" + }, + { + "text": "And so you want this curve to be as high as possible." + }, + { + "text": "You want to make sure that if there's evidence in the data that H1 is the truth, you want to squeeze as much of this evidence as possible." + }, + { + "text": "And the test that has the highest possible curve is the most powerful one." + }, + { + "text": "Now, you have to also understand that having two curves that are on top of each other, completely, everywhere, is a rare phenomenon." + }, + { + "text": "It's not always the case that there is a test that's uniformly more powerful than any other test." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk9.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bbad3ae05fbb39d9ef76b7b89aa0fada7d5adc3e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_3_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It might be that you have some trade-off, that it might be better here, but then you're losing power here." + }, + { + "text": "Things like this." + }, + { + "text": "Well, actually, maybe it should not go down." + }, + { + "text": "But let's say it goes like this, and then maybe this guy goes like this." + }, + { + "text": "Then you have to basically make an educated guess whether you think that the theta you're going to find is here or it's here." + }, + { + "text": "And then you pick a test." + }, + { + "text": "OK?" + }, + { + "text": "Any other question?" + }, + { + "text": "Yes?" + }, + { + "text": "AUDIENCE 2." + }, + { + "text": "What is the derivative of the type 2 error?" + }, + { + "text": "PHILIPPE RIGOLLET." + }, + { + "text": "So the green curve is exactly right." + }, + { + "text": "So that's beta psi of theta." + }, + { + "text": "So it's really the type 2 error, and it's defined only here." + }, + { + "text": "So here, it's not a definition." + }, + { + "text": "It's really just I'm just mapping it to this point." + }, + { + "text": "So it's defined only here, and it's the probability of type 2 error." + }, + { + "text": "So here, it's pretty large, right?" + }, + { + "text": "I'm making it basically as large as I could, because I'm at the boundary." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk0.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..65c23c5cab5e2c4f1a8f872964a31edc5dd21493 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "Talking about tests, and to be fair, we spend most of our time talking about new jargon that we're using." + }, + { + "text": "But the main goal is to take a binary decision, yes and no." + }, + { + "text": "So just so that we're clear and we make sure that we all speak the same language, let me just remind you what the key words are for tests." + }, + { + "text": "So the first thing is that we split theta in theta 0 and theta 1." + }, + { + "text": "Both are included in theta, and they're disjoint." + }, + { + "text": "OK." + }, + { + "text": "So I have my set of possible parameters." + }, + { + "text": "And then I have theta 0 is here, theta 1 is here, and there might be something that I leave out." + }, + { + "text": "And so what we're doing is we have two hypotheses." + }, + { + "text": "So here's our hypothesis testing problem." + }, + { + "text": "And it's h0 theta belongs to theta 0 versus h1 theta belongs to theta 1." + }, + { + "text": "This guy was called the null, and this guy was called the alternative." + }, + { + "text": "And why we give them special names is because we saw that they have an asymmetric role." + }, + { + "text": "The null represents the status quo, and data is here to bring evidence against this guy." + }, + { + "text": "And we can really never conclude that h0 is true because all we could conclude is that h1 is not true or may not be true." + }, + { + "text": "So that was the first thing." + }, + { + "text": "The second thing was the hypothesis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk1.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3b72e60009f76e8f81d23cb396a309bf7d70b355 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "The third thing is what is a test?" + }, + { + "text": "Well, psi, it's a statistic." + }, + { + "text": "And it takes the data, and it maps it into 0 or 1." + }, + { + "text": "And I didn't really mention it, but there's something such as called randomized tests, which is, well, if it cannot really make a decision, they might as well flip a coin." + }, + { + "text": "That tends to be biased, but that's really, I mean, think about it in practice." + }, + { + "text": "You probably don't want to make decisions based on flipping a coin." + }, + { + "text": "And so what people typically do, this is happening typically at one specific value." + }, + { + "text": "So rather than flipping a coin for this very specific value, what people typically do is they say, OK, I'm going to side with h0 because that's the most conservative choice I can make." + }, + { + "text": "So in a way, they think of flipping this coin, but always falling on heads." + }, + { + "text": "So associated to this test was something called, well, the rejection region." + }, + { + "text": "And r psi, which is just the set of data, x1, xn, such that psi of x1, xn is equal to 1." + }, + { + "text": "So that means we rejected 0 when the test is 1, and those are the set of data points that actually are going to lead me to reject the test." + }, + { + "text": "OK. Then the things that were actually slightly a little more important and really peculiar to test, specific to test, were the type 1 and type 2 error." + }, + { + "text": "So the type 1 error arises when, so type 1 error is when you reject whereas h0 is correct." + }, + { + "text": "And the type 2 error is the opposite." + }, + { + "text": "So it's failed to reject whereas h1 is correct." + }, + { + "text": "h is correct." + }, + { + "text": "So those are the two types of errors you can make, and we quantify their probability of type 1 error." + }, + { + "text": "So alpha psi is the probability." + }, + { + "text": "So that's the probability of type 1 error." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk10.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c19b0d21dee98686b07f25081871711f112710fa --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "And that means at the boundary, since the status quo is h0, I'm always going to go for h0 if I don't have any evidence, which means that what's going to pay is the type 2 error that's going to basically pay this." + }, + { + "text": "OK?" + }, + { + "text": "Any other question?" + }, + { + "text": "All right, so let's move on." + }, + { + "text": "So did we do this?" + }, + { + "text": "No, I think we stopped here, right?" + }, + { + "text": "I didn't cover that part." + }, + { + "text": "So as I said, in this paradigm, we're going to actually fix this guy to be something." + }, + { + "text": "And this thing is actually called the level of the test." + }, + { + "text": "I'm sorry, this is again more words." + }, + { + "text": "Actually, good news is that we split it into two lectures." + }, + { + "text": "So we have, what is a test?" + }, + { + "text": "What is a hypothesis?" + }, + { + "text": "What is the null?" + }, + { + "text": "What is the alternative?" + }, + { + "text": "What is the type 1 error?" + }, + { + "text": "What is the type 2 error?" + }, + { + "text": "And now, I'm telling you there's another thing." + }, + { + "text": "So we defined the power, which was some sort of a lower bound on the, or it's 1 minus the upper bound on the type 2 error, basically." + }, + { + "text": "And so it's alternative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk11.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..815ec78c1b831dd92a2b3f1d68a91dd8df86f618 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "So the power is the smallest probability of rejecting when you're in the null." + }, + { + "text": "And it's alternative when you're in theta 1, right?" + }, + { + "text": "So that's my power." + }, + { + "text": "I looked here, and I looked at the smallest value." + }, + { + "text": "And I can look at this side and say, well, what is the largest probability that I make a type 1 error?" + }, + { + "text": "Again, this largest probability is the level of the test." + }, + { + "text": "OK, so this is alpha equal, by definition, to the maximum for theta and theta 0 of alpha psi of theta." + }, + { + "text": "So here, I just put the level itself." + }, + { + "text": "As you can see here, it essentially says that if I'm of level 5%, I'm also of level 10%." + }, + { + "text": "I'm also of level 15%." + }, + { + "text": "So here, it's really an upper bound." + }, + { + "text": "Whatever you guys want to take, this is what it is." + }, + { + "text": "But as we said, if this number is 4.5%, you're losing in your type 2 error." + }, + { + "text": "So if you're allowed to have, if this maximum here is 4.5%, and FDA told you you can go to 5%, you're losing in your type 2 error." + }, + { + "text": "So you actually want to make sure that this is the 5% that's given to you." + }, + { + "text": "So the way it works is that you give me the alpha." + }, + { + "text": "Then I'm going to go back, pick c that depends on alpha here, so that this thing is actually equal to 5%." + }, + { + "text": "And so, of course, in many instances, we do not know the probability." + }, + { + "text": "We do not know how to compute the probability of type 1 error." + }, + { + "text": "This is a maximum value for the probability of type 1 error." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk12.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..4bd3834b631a0a7c734e2b14c2fe32eaf6f601e6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "We don't know how to compute it." + }, + { + "text": "I mean, it might be a very complicated random variable." + }, + { + "text": "Maybe it's a weird binomial." + }, + { + "text": "We could compute it, but it would be painful." + }, + { + "text": "But what we know how to compute is its asymptotic value, which is because of the central limit theorem, convergence and distribution tells me that the probability of type 1 error is basically going towards the probability that some Gaussian is in some region." + }, + { + "text": "And so we're going to compute not the level itself, but the asymptotic level." + }, + { + "text": "So again, that's basically the limit as n goes to infinity of alpha psi of theta." + }, + { + "text": "And then I'm going to make the max here." + }, + { + "text": "OK?" + }, + { + "text": "So how am I going to compute this?" + }, + { + "text": "Well, if I take a test that has rejection region of the form Tn, because it depends on the data, right?" + }, + { + "text": "That's Tn of x1, xn, my observations, larger than some number c. OK?" + }, + { + "text": "Of course, I can almost always write tests like that, except that sometimes there's going to be an absolute value, which essentially means I'm going away from some value." + }, + { + "text": "Maybe actually I'm less than something, but I can always put a negative sign in front of everything." + }, + { + "text": "So this is not without much of generality, right?" + }, + { + "text": "So this includes something that looks like something is larger than the constant, right?" + }, + { + "text": "So that means, which is equivalent to, well, let me write it as Tq." + }, + { + "text": "OK, because then that means that, so that's Tn." + }, + { + "text": "But this actually encompasses the fact that Qn is larger than c, or Qn is less than c, then minus c. So that includes this guy." + }, + { + "text": "That also includes Qn less than c, because this is equivalent to Qn is larger than minus c. Minus Qn is, and so that's going to be my Tn." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk13.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..d0fc40d7fea49cc51a82242971122ccb04ee2caf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I can actually encode several type of things, OK?" + }, + { + "text": "Rejection regions that, so here in this case, I have a rejection region that looks like this, or a rejection region that looks like this, or a rejection region that looks like this." + }, + { + "text": "OK, and here I don't really represent it for the whole data, but maybe for the average, for example, or the normalized average." + }, + { + "text": "OK, so if I write this, then, yeah." + }, + { + "text": "And in this case, this Tn that shows up is called test statistic." + }, + { + "text": "I mean, this is sort of a, I mean, this is not like set in stone." + }, + { + "text": "Here, for example, Q could be the test statistics." + }, + { + "text": "It doesn't have to be minus Q itself that's the test statistic, right?" + }, + { + "text": "So what is the test statistic?" + }, + { + "text": "Well, it's what you're going to build from your data and then compare to some fixed value, right?" + }, + { + "text": "So in the example we had here, what is our test statistic?" + }, + { + "text": "Well, it's this guy, right?" + }, + { + "text": "This was our test statistic." + }, + { + "text": "And is this thing a statistic?" + }, + { + "text": "What are the criteria for a statistic?" + }, + { + "text": "What is a statistic?" + }, + { + "text": "I know you know the answer." + }, + { + "text": "AUDIENCE MEMBER 2." + }, + { + "text": "Is it a measurable function?" + }, + { + "text": "PROFESSOR PHILIPPE RIGOLLET." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk14.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..deb918611779af5e70f1e976f45cfc296740fc0a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "Yeah, it's a measurable function of the data that does not depend on the parameter." + }, + { + "text": "Is this guy a statistic?" + }, + { + "text": "AUDIENCE MEMBER 3." + }, + { + "text": "Yes, he is." + }, + { + "text": "PROFESSOR PHILIPPE RIGOLLET." + }, + { + "text": "Let's think again." + }, + { + "text": "When I implemented the test, what did I do?" + }, + { + "text": "I was able to compute my test." + }, + { + "text": "My test did not depend on some unknown parameter." + }, + { + "text": "How did we do it?" + }, + { + "text": "We just plugged in 0.5 here." + }, + { + "text": "Remember?" + }, + { + "text": "That was the value for which we computed it, because under h0, that was the value we're seeing." + }, + { + "text": "And if theta 0 is actually an entire set, I'm just going to take the value that's the closest to h1." + }, + { + "text": "We'll see that in a second." + }, + { + "text": "I mean, I did not guarantee that to you." + }, + { + "text": "But just taking the worst type 1 error and bounding it by alpha is equivalent to taking p and taking the value of p that's the closest to theta 1, which is completely intuitive." + }, + { + "text": "The worst type 1 error is going to be attained for the p that's the closest to the alternative." + }, + { + "text": "So even if the null is actually just an entire set, it's as if it was just the point that's the closest to the alternative." + }, + { + "text": "So now we can compute this, because there's no unknown parameters that shows up." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk15.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..0bc365016096bbbfd9f7a60ab9c2724dec760020 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "We replaced p by 0.5." + }, + { + "text": "And so that was our test statistic." + }, + { + "text": "So when you're building a test, you want to first build a test statistic and then see what threshold you should be getting." + }, + { + "text": "So now let's go back to our example where we have x1, xn." + }, + { + "text": "They're iid Bernoulli p. And I want to test if p is 1 half versus p not equal to 1 half, which as I said is what you want to do if you want to test if a coin is fair." + }, + { + "text": "And so here I'm going to build a test statistic." + }, + { + "text": "And we concluded last time that what do we want for this statistic?" + }, + { + "text": "We want it to have a distribution which under the null does not depend on the parameters, a distribution that I can actually compute quintiles of." + }, + { + "text": "So what we did is we said, well, if I look at the central limit theorem tells me that square root of n xn bar minus p divided by." + }, + { + "text": "So if I do central limit theorem plus Slutsky, for example, I'm going to have square root." + }, + { + "text": "And we've had this discussion whether we want to use Slutsky or not here." + }, + { + "text": "But let's assume we're taking Slutsky wherever we can." + }, + { + "text": "So this thing tells me that by the central limit theorem as n goes to infinity, this thing converges in distribution to some n 0, 1." + }, + { + "text": "Now as we said, this guy is not something we know." + }, + { + "text": "But under the null, we actually know it." + }, + { + "text": "And we can actually replace it by 1 half." + }, + { + "text": "So this thing holds under h0." + }, + { + "text": "When I write under h0, it means when this is the truth." + }, + { + "text": "So now I have something that converges to something that has no dependence on anything I don't know." + }, + { + "text": "And in particular, if you have any statistics textbook, which you don't because I didn't require one, you should be thankful because this thing costs $250." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk16.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..298b0fb997de98b972702f498d96cfa89d4e4b7d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "This thing's actually, if you look at the back, you actually have a table for a standard Gaussian." + }, + { + "text": "I could have anything else here." + }, + { + "text": "I could have an exponential distribution." + }, + { + "text": "I could have a, I don't know, a, well, we'll see the chi-square distribution in a minute." + }, + { + "text": "Any distribution from which you can actually see a table that somebody actually computed this thing for which you can actually draw the PDF and start computing whatever probability you want on them, then this is what you want to see at the right-hand side." + }, + { + "text": "This is any distribution." + }, + { + "text": "It's called pivotal." + }, + { + "text": "I think we've mentioned that before." + }, + { + "text": "Pivotal means it does not depend on anything that you don't know." + }, + { + "text": "And maybe it's easy to compute those things." + }, + { + "text": "Probably, typically, you need a computer to simulate them for you because computing probabilities for Gaussians is not an easy thing." + }, + { + "text": "We don't know how to solve those integrals exactly." + }, + { + "text": "We have to do it numerically." + }, + { + "text": "OK, so now I want to do this test." + }, + { + "text": "My test statistic will be declared to be what?" + }, + { + "text": "Well, I'm going to reject if what is larger than some number?" + }, + { + "text": "The absolute value of this guy." + }, + { + "text": "So my test statistic is going to be square root of n minus 0.5 divided by square root of xn bar 1 minus xn bar." + }, + { + "text": "That's my test statistic, absolute value of this guy, because I want to reject either when this guy is too large or when this guy is too small." + }, + { + "text": "I don't know ahead whether I'm going to see p larger than 1 half or less than 1 half." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk17.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..c16a8c6be2149a29434fcd2457ee0fdbf0606f2d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "So now I need to compute c such that the probability that tn is lower than c. So that's what?" + }, + { + "text": "That's the probability under p, which is unknown." + }, + { + "text": "I want this probability to be less than some level alpha asymptotically." + }, + { + "text": "So I want the limit of this guy to be less than alpha, and that's the level of my test." + }, + { + "text": "So that's the given level." + }, + { + "text": "So I want this thing to happen." + }, + { + "text": "Now what I know is that this limit, actually, I should say given asymptotic level." + }, + { + "text": "So what is this thing?" + }, + { + "text": "Well, OK, that's the probability that something that looks like under p. So under p, this guy, so what I know is that tn is square root of n minus xn bar minus 0.5 divided by square root of xn bar 1 minus xn bar exceeds." + }, + { + "text": "Is this true that as n goes to infinity, this probability is the same as the probability that the absolute value of a Gaussian exceeds c of a standard Gaussian?" + }, + { + "text": "Is this true?" + }, + { + "text": "Yeah, so you're saying that this, as n becomes large enough, this should be the probability that some absolute value of n0,1 exceeds c, right?" + }, + { + "text": "So I claim that this is not correct." + }, + { + "text": "Somebody tell me why." + }, + { + "text": "Even in the limit, it's not correct?" + }, + { + "text": "Even in the limit, it's not correct." + }, + { + "text": "OK." + }, + { + "text": "So what do you see?" + }, + { + "text": "It's because at the beginning, we picked the worst possible true parameter, 0.5, right?" + }, + { + "text": "So we don't actually know that this 0.5 is the least." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk18.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..21ff2eaef450e95222ef4c4c025a1ccb1a883204 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Exactly, right?" + }, + { + "text": "So we picked this 0.5 here, but this is for any p, right?" + }, + { + "text": "But what is the only p I can get?" + }, + { + "text": "So what I want is that this is true for all p in theta 0." + }, + { + "text": "But the only p that's in theta 0 is actually p is equal to 0.5." + }, + { + "text": "So yes, what you said was true, but it required to specify p to be equal to 0.5." + }, + { + "text": "So this, in general, is not true." + }, + { + "text": "But it happens to be true if p belongs to theta 0, which is strictly equivalent to p is equal to 0.5, right?" + }, + { + "text": "Theta 0 is really just this one point, 0.5." + }, + { + "text": "OK, so now this becomes true." + }, + { + "text": "And so what I need to do is to find c such that this guy is equal to what?" + }, + { + "text": "I mean, let's just follow, right?" + }, + { + "text": "So I want this to be less than alpha." + }, + { + "text": "But then we see that this was equal to this, which is equal to this." + }, + { + "text": "So all I want is that this guy is less than alpha." + }, + { + "text": "But we said we might as well just make it equal to alpha if you allow me to make it as big as I want, as long as it's less than alpha." + }, + { + "text": "So this is a true statement." + }, + { + "text": "But it's if under this condition, right?" + }, + { + "text": "So I'm going to set it equal to alpha." + }, + { + "text": "And then I'm going to try to solve for c. OK, so what I'm looking for is a c such that if I draw a standard Gaussian, so that's PDF of some n0,1, I want the probability that the absolute value of my Gaussian exceeding this guy." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk19.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..b610ab510e065f845cbac3e680352a281a5977db --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that means being either here or here." + }, + { + "text": "So that's minus c and c. I want the sum of those two things to be equal to alpha." + }, + { + "text": "So I want the sum of these areas to equal alpha." + }, + { + "text": "So by symmetry, each of them should be equal to alpha over 2." + }, + { + "text": "And so what I'm looking for is c such that the probability that my n0,1 exceeds c, which is just this area to the right now, equals alpha, which is equivalent to taking c, which is q equals alpha over 2." + }, + { + "text": "And that's q alpha over 2 by definition of q alpha over 2." + }, + { + "text": "That's just what q alpha over 2 is." + }, + { + "text": "And that's what the tables at the back of the book give you." + }, + { + "text": "Who has already seen a table for Gaussian probabilities?" + }, + { + "text": "All right." + }, + { + "text": "What it does is just a table." + }, + { + "text": "I mean, it's pretty ancient, right?" + }, + { + "text": "I mean, of course, you can actually ask Google to do it for you now." + }, + { + "text": "It's basically standard issue." + }, + { + "text": "But back in the day, they actually had to look at tables." + }, + { + "text": "And since the values alphas were pretty standard, the values alpha that people were requesting were typically 1%, 5%, 10%." + }, + { + "text": "All you could do is to compute these different values for different values of alpha." + }, + { + "text": "That was it." + }, + { + "text": "So that's really not much to give you." + }, + { + "text": "So for the Gaussian, I can tell you that alpha is equal to, if alpha is equal to 5%, then q alpha over 2, q 2.5% is equal to 1.96%." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk2.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..d35a9367292f43552ea9e2c936629f0062774757 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So psi is just the probability for theta that psi rejects, and that's defined for theta and theta 0." + }, + { + "text": "So for different values of theta 0, so h0 being correct means there exists a theta in theta 0 for which that actually is the right distribution." + }, + { + "text": "So for different values of theta, I might make different errors." + }, + { + "text": "So if you think, for example, about the coin example, if I'm testing if the coin is biased towards heads or biased towards tails, so if I'm testing whether p is larger than 1 half or less than 1 half, then when the true p, let's say h0 is larger than 1 half, when p is equal to 1, it's actually very difficult for me to make a mistake, because I only see heads." + }, + { + "text": "So when p is getting closer to 1 half, I'm going to start making more and more probability there." + }, + { + "text": "And so the type 2 error, so that's the probability of type 2, is denoted by beta psi." + }, + { + "text": "And it's the function that does the opposite, and this time is defined for theta and theta 0 and theta 1." + }, + { + "text": "And finally, we define something called the power pi of psi." + }, + { + "text": "And this time, this is actually a number." + }, + { + "text": "And so this number is equal to the maximum over theta and theta 0." + }, + { + "text": "I mean, that could be a supremum, but think of it as being a maximum of p theta of psi is equal, sorry, that's in 0." + }, + { + "text": "Give me one sec." + }, + { + "text": "No, that's the min." + }, + { + "text": "So this is not making a mistake." + }, + { + "text": "Theta 0 is in theta 1." + }, + { + "text": "So theta is in theta 1, and I conclude 1." + }, + { + "text": "So this is a good thing." + }, + { + "text": "I want this number to be large, and I'm looking at the worst house, what is the smallest value this number can be." + }, + { + "text": "So what I want to show you a little bit is a picture." + }, + { + "text": "So now I'm going to take theta, and think of it as being p. So I'm going to take p for some Bernoulli experiment." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk20.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..20ad1dac1f1c76cdb383bd9a41a5521bfc8e8f80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "So those are just fixed numbers that are functions of the Gaussian." + }, + { + "text": "All right, so everybody agrees?" + }, + { + "text": "We've done that before for our confidence intervals." + }, + { + "text": "And so now we know that if I actually plug in this guy to be q alpha over 2, then this limit is actually equal to alpha." + }, + { + "text": "And so now I've actually constrained this." + }, + { + "text": "So q alpha over 2 here is, for alpha equals 5%, as I said, is 1.96." + }, + { + "text": "So in the example 1, the number that we found was 3.54, I think, or something like that, 3.55 for t. So if we scroll back very quickly, 3.45." + }, + { + "text": "That was example 1." + }, + { + "text": "Example 2, negative 0.77." + }, + { + "text": "So if I look at t, n, in example 1, tn was just the absolute value of 3.45, which don't pull out your calculators, is equal to 3.45." + }, + { + "text": "Example 2, absolute value of negative 0.77 was equal to 0.77." + }, + { + "text": "And so all I need to check is, is this number larger or smaller than 1.96?" + }, + { + "text": "That's what my test ends up being." + }, + { + "text": "So in example 1, 3.45 being larger than 1.96, that means that I reject." + }, + { + "text": "Fairness of my coins in example 2, 0.77 being smaller than 1.96, what do I do?" + }, + { + "text": "I fail to reject." + }, + { + "text": "OK?" + }, + { + "text": "So here's a question." + }, + { + "text": "In example 1, for what level alpha would psi alpha, what is the?" + }, + { + "text": "So here, what's going to happen if I start decreasing my level?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk21.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..8a92eddc8e39673740ca195fad03c2d25a729273 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "When I decrease my level, I'm actually making this area smaller and smaller, which means that I push the c to the right." + }, + { + "text": "So now I'm asking, what is the smallest c I should pick so that now I actually do not reject h0?" + }, + { + "text": "What is the smallest c I should be taking?" + }, + { + "text": "Here." + }, + { + "text": "What is the smallest c?" + }, + { + "text": "So c here in the example I gave you for 5% was 1.96." + }, + { + "text": "What is the smallest c I should be taking so that now this inequality is reversed?" + }, + { + "text": "3.45." + }, + { + "text": "I ask only trivial questions." + }, + { + "text": "Don't be worried." + }, + { + "text": "So 3.45 is the smallest c that I'm actually willing to tolerate." + }, + { + "text": "So let's say this was my 5%." + }, + { + "text": "If this was 2.5, if alpha here, let's say in this picture, alpha is 5%, that means maybe I need to push here." + }, + { + "text": "And this number should be what?" + }, + { + "text": "So this is going to be 1.96." + }, + { + "text": "And this number here is going to be 3.45, clearly to scale." + }, + { + "text": "And so now what I want to ask you is, well, there's two ways I can understand this number 3.45." + }, + { + "text": "It is the number 3.45." + }, + { + "text": "But I can also try to understand, what is the area to the right of this guy?" + }, + { + "text": "And if I understand what the area to the right of this guy is, this is actually some alpha prime over 2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk22.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..7503edb72bbc4e9db22fe8e956729e7f3881d675 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "And that means that if I actually fix this level, alpha prime, that would be exactly the tipping point at which I would go from accepting to rejecting." + }, + { + "text": "So I know in terms of absolute thresholds, 3.45 is the trivial answer to the question." + }, + { + "text": "That's the tipping point, because I'm comparing a number to 3.45." + }, + { + "text": "But now if I try to map this back and understand what level would have been given me this particular tipping point, that's a number between 0 and 1." + }, + { + "text": "The smaller the number, the larger this number here, which means that the more evidence I have in my data against h0." + }, + { + "text": "And so this number is actually something called the p-value." + }, + { + "text": "And so same for example 2." + }, + { + "text": "There's the tipping point, alpha, at which I go from feeling to reject to rejecting." + }, + { + "text": "And that's exactly the number, the area under the curve, such that here I see 0.77." + }, + { + "text": "And this is this alpha prime prime over 2." + }, + { + "text": "And this number is clearly, alpha prime prime is clearly larger than 5%." + }, + { + "text": "So what's the advantage of thinking and mapping back these numbers?" + }, + { + "text": "Well, now I'm actually going to spit out some number which is between 0 and 1." + }, + { + "text": "And that should be the only scale you should have in mind." + }, + { + "text": "Remember we discussed that last time." + }, + { + "text": "Well, if I actually spit out a number which is 3.45, maybe you can try to think, is 3.45 a large number for a Gaussian?" + }, + { + "text": "That's a number." + }, + { + "text": "But if I had another random variable that was not Gaussian, maybe it was a double exponential, you would have to have another scale in your mind." + }, + { + "text": "Is 3.45 a large number for the large, so large that it's unlikely to come from a double exponential?" + }, + { + "text": "If I had a gamma distribution, I can think of any distribution." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk23.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..d0d0fdec57ad2cc7e2dadb707abb6df87bdbb70b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then that means for each distribution, you would have to have a scale in mind." + }, + { + "text": "So of course, you can have the Gaussian scale in mind." + }, + { + "text": "I mean, I have the Gaussian scale in mind." + }, + { + "text": "But then if I map it back into this number between 0 and 1, all the distributions play the same role." + }, + { + "text": "So whether I'm talking about if my limiting distribution is normal or exponential or gamma or whatever you want, for all these guys, I'm just going to map it into one number between 0 and 1." + }, + { + "text": "Small number means lots of evidence against h1." + }, + { + "text": "Large number means lots of evidence against h0." + }, + { + "text": "Small number means very few evidence against h0." + }, + { + "text": "And this is the only number you need to keep in mind." + }, + { + "text": "And the question is, am I willing to tolerate this number between 5%, 6% or maybe 10%, 12%?" + }, + { + "text": "And this is the only scale you have to have in mind." + }, + { + "text": "And this scale is the scale of p-values." + }, + { + "text": "So the p-value is the tipping point in terms of alpha." + }, + { + "text": "In words, I can make it formal, because tipping point, as far as I know, is not a mathematical term." + }, + { + "text": "So a p-value of a test is the smallest, potentially asymptotic level, if I talk about an asymptotic p-value." + }, + { + "text": "And that's what we do when we talk about central limit theorem, at which the test rejects h0." + }, + { + "text": "If I were to go any smaller, I would fail to reject." + }, + { + "text": "The smaller the level, the less likely it is for me to reject." + }, + { + "text": "And if I were to go any smaller, I would start failing to reject." + }, + { + "text": "And so it is a random number." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk24.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..70790440238c22e23b0b77fc5e658fdf89d62e44 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "It depends on what I actually observe." + }, + { + "text": "So here, of course, I instantiated those two numbers, 3.45 and 0.77, as realizations of random variables." + }, + { + "text": "But if you think of those as being the random numbers before I see my data, this was a random number." + }, + { + "text": "And therefore, the area under the curve to the right of it is also a random area." + }, + { + "text": "If this thing fluctuates, then the area under the curve fluctuates." + }, + { + "text": "And that's what the p-value is." + }, + { + "text": "That's what John Oliver talks about when he talks about p-hacking." + }, + { + "text": "And so we talked about this in the first lecture." + }, + { + "text": "So p-hacking is, how do I do?" + }, + { + "text": "Oh, if I'm a scientist, do I want to see a small p-value or a large p-value?" + }, + { + "text": "Small, right?" + }, + { + "text": "Scientists want to see small p-values, because small p-values equals rejecting, which equals discovery, which equals publication, which equals promotion." + }, + { + "text": "So that's what people want to see." + }, + { + "text": "So people are tempted to see small p-values." + }, + { + "text": "And what's called p-hacking is, well, find a way to cheat." + }, + { + "text": "Maybe look at your data, formulate your hypothesis in such a way that you will actually have a smaller p-value than you should have." + }, + { + "text": "So here, for example, there's one thing I did not insist on, because again, this is not a particular course in statistical thinking." + }, + { + "text": "But one thing that we implicitly did was set those theta 0 and theta 1 ahead of time." + }, + { + "text": "I fixed them, and I'm trying to test this." + }, + { + "text": "This is to be contrasted with the following approach." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk25.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..ae5989051a3c9ad74dd6e26eac906c8e26ce8535 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "I draw my data." + }, + { + "text": "So I draw." + }, + { + "text": "I run this experiment, which is probably going to get me a publication in Nature." + }, + { + "text": "I'm trying to test if a coin is fair." + }, + { + "text": "And I draw my data, and I see that there's 13 out of 30 of my observations that are heads." + }, + { + "text": "That means that from this data, it looks like p is less than 1 half." + }, + { + "text": "So if I look at this data and then decide that my alternative is not p not equal to 1 half, but rather p less than 1 half, that's p-hacking." + }, + { + "text": "I'm actually making my p-value strictly smaller by first looking at the data and then deciding what my alternative is going to be." + }, + { + "text": "And that's cheating, because all the things we did were assuming that this 0.5 or d alternative was actually a fix." + }, + { + "text": "Everything was deterministic." + }, + { + "text": "The only randomness came from the data." + }, + { + "text": "But if I start looking at the data and designing my experiment or my alternatives and null hypothesis based on the data, it's as if I started putting randomness all over the place." + }, + { + "text": "And then I cannot control it, because I don't know how it just intermingles with each other." + }, + { + "text": "All right." + }, + { + "text": "So that was for the John Oliver moment." + }, + { + "text": "So the p-value is nice." + }, + { + "text": "So maybe I mentioned that before." + }, + { + "text": "My wife works in market research." + }, + { + "text": "And maybe every two years, she seems to run into a statistician in the hallway." + }, + { + "text": "And she comes home and says, what is a p-value again?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk26.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..582b81ac1a78246b0f187a4c706af274ba689dbe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk26.json @@ -0,0 +1,62 @@ +[ + { + "text": "And for her, a p-value is just the number is in an Excel spreadsheet." + }, + { + "text": "And actually, small equals good and large equals bad." + }, + { + "text": "And that's all she needs to know at this point." + }, + { + "text": "Actually, they do the job for her." + }, + { + "text": "Small is green." + }, + { + "text": "Large is red." + }, + { + "text": "And so for her, a p-value is just green or red." + }, + { + "text": "But so what she's really implicitly doing with this color code is just applying the golden rule." + }, + { + "text": "What the statisticians do for her in the Excel spreadsheet is that they take the numbers for the p-values that are less than some fixed level." + }, + { + "text": "So depending on the field in which she works, so she works for pharmaceutical companies, so the p-values are typically compared." + }, + { + "text": "The tests are usually performed at level 1% rather than 5%." + }, + { + "text": "So 5% is maybe your gold standard if you're doing sociology or trying to, I don't know, release a new blueberry flavor for your toothpaste, like something that's not going to change the life of people." + }, + { + "text": "Maybe you're going to run at 5%." + }, + { + "text": "It's OK to make a mistake." + }, + { + "text": "People are just going to feel gross, but that's about it." + }, + { + "text": "Whereas here, if you have this p-value which is less than 1%, it might be more important for some drug discovery, for example." + }, + { + "text": "And so let's say you run at 1%." + }, + { + "text": "And so what they do in this Excel spreadsheet is that all the numbers that are below 1% show up in green, and all the numbers that are above 1% show up in red." + }, + { + "text": "And that's it." + }, + { + "text": "That's just applying the golden rule." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk27.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk27.json new file mode 100644 index 0000000000000000000000000000000000000000..6d2b3e73a1f2bfb3d007d43a22bc17095a5878f8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk27.json @@ -0,0 +1,62 @@ +[ + { + "text": "If the number is green, reject." + }, + { + "text": "If the number is red, fail to reject." + }, + { + "text": "OK?" + }, + { + "text": "Yeah?" + }, + { + "text": "So going back to the example of the previous prior example where you can achieve by looking at your data and then formulating, say, a theta 1 to be p less than 1%." + }, + { + "text": "Yeah." + }, + { + "text": "So how would you achieve your goal by changing the theta 1?" + }, + { + "text": "You mean by achieving my goal?" + }, + { + "text": "You mean letting ethics aside, right?" + }, + { + "text": "Yeah." + }, + { + "text": "You want to be published." + }, + { + "text": "So OK." + }, + { + "text": "So let me teach you how." + }, + { + "text": "Well, here, what do you do?" + }, + { + "text": "You want to, at the end of the day, a test is only telling you whether you found evidence in your data that H1 was more likely than H0, basically." + }, + { + "text": "How do you make H1 more likely?" + }, + { + "text": "Well, you just basically target H1 to be what the data is going to make it more likely to be." + }, + { + "text": "All right?" + }, + { + "text": "So if, for example, I say H1 can be on both sides, then my data is going to have to take into account fluctuations on both sides." + }, + { + "text": "And I'm going to lose a factor of 2 somewhere because things are not symmetric." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk28.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk28.json new file mode 100644 index 0000000000000000000000000000000000000000..b6a2e04f21d17d3f9d8f51277fef4b6bd544ea8c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk28.json @@ -0,0 +1,62 @@ +[ + { + "text": "Here is the ultimate way of making this work." + }, + { + "text": "I'm going back to my example of flipping coins." + }, + { + "text": "And now, so here, what I did is I said, oh, this number 0.43 is actually smaller than 0.5." + }, + { + "text": "So I'm just going to test whether I'm 0.5 or I'm less than 0.5." + }, + { + "text": "But here is something that I can promise you I did not make the computation will reject." + }, + { + "text": "OK, so here, this one actually, yeah, this one fails to reject, right?" + }, + { + "text": "So here is one that will certainly reject." + }, + { + "text": "H0 is 0.5. p is 0.5." + }, + { + "text": "H1, p is 0.43." + }, + { + "text": "OK?" + }, + { + "text": "Now, you can try." + }, + { + "text": "But I can promise you that your data will tell you that H1 is the right one." + }, + { + "text": "OK?" + }, + { + "text": "I mean, you can check very quickly that this is really extremely likely to happen, right?" + }, + { + "text": "And so actually, what am I?" + }, + { + "text": "No, actually, that's not true." + }, + { + "text": "OK. Because here, the test that I derive that's based on this kind of stuff, right?" + }, + { + "text": "Here, at some point, somewhere, under some layers, I assume that all our tests are going to have this form." + }, + { + "text": "But here, this is only when you're trying to test one region versus another region next to it, or one point versus a region around it, or something like this." + }, + { + "text": "Whereas for this guy, there's another test I could come up with, which is, what is the probability that I get 0.43?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk29.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk29.json new file mode 100644 index 0000000000000000000000000000000000000000..7c83fb4d5133113ff729308f195ed934ccaaacb9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk29.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what is the probability that I get 0.5?" + }, + { + "text": "Now, what I'm going to do is I'm going to just conclude it's whichever has the largest probability." + }, + { + "text": "Then maybe I'm going to have to make some adjustments so that the level is actually 5%." + }, + { + "text": "But I can make this happen." + }, + { + "text": "I can make the level be 5% and always conclude this guy, but I would have to use a different test." + }, + { + "text": "Now, the test that I described, again, those t and larger than c are built in to be tests that are sort of resilient to this kind of manipulations, because they're sort of oblivious towards what the alternative looks like." + }, + { + "text": "I mean, they're just saying it's either to the left or to the right, but whether it's a point or an entire half line doesn't matter." + }, + { + "text": "So if you try to look at your data and just put the data itself into your hypothesis testing problem, then you're failing the statistical principle." + }, + { + "text": "And that's what people are doing, right?" + }, + { + "text": "I mean, how can I check?" + }, + { + "text": "I mean, of course, here it's going to be pretty blatant if you publish a paper that looks like this." + }, + { + "text": "But there's ways to do it differently, right?" + }, + { + "text": "For example, one way to do it is to just do more." + }, + { + "text": "So typically, what people do is they do multiple hypothesis testing." + }, + { + "text": "They're doing 100 tests at a time." + }, + { + "text": "Then you have random fluctuations every time." + }, + { + "text": "And so they just pick the one that has the random fluctuations that go their way." + }, + { + "text": "I mean, sometimes it's going in your way, and sometimes it's going the opposite way." + }, + { + "text": "So you just pick the one that works for you." + }, + { + "text": "We'll talk about multiple hypothesis testing soon if you want to increase your publication counts." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk3.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..82298a0911f771c50c0c0e31234286bcbe2ed969 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "So p can range between 0 and 1, that's for sure." + }, + { + "text": "And what I'm going to try to test is whether p is less than 1 half or larger than 1 half." + }, + { + "text": "So this is going to be, let's say, theta 0, and this guy here is theta 1." + }, + { + "text": "Just trying to give you a picture of what those guys are." + }, + { + "text": "So I have my y-axis." + }, + { + "text": "Now I'm going to start drawing numbers, all these things, this function, this function, and this number are all numbers between 0 and 1." + }, + { + "text": "So now I'm claiming that when I move from left to right, what is my probability of rejecting going to do?" + }, + { + "text": "So what I'm going to plot is the probability under theta." + }, + { + "text": "The first thing I want to plot is the probability under theta that psi is equal to 1." + }, + { + "text": "And let's say psi, think of psi as being just this indicator that square root of n xn bar minus p over square root xn bar, 1 minus xn bar, is larger than some constant c for a properly chosen c. So what we choose is that c is in such a way that at 1 half, when we're testing for 1 half, what we wanted was this number to be equal to alpha, basically." + }, + { + "text": "So we fix this alpha number so that this guy, so if I want alpha of psi of theta less than alpha, given in advance, so think of it as being equal to, say, 5%." + }, + { + "text": "So I'm fixing this number, and I want this to be controlled for all theta and theta 0." + }, + { + "text": "So if you're going to give me this budget, well, I'm actually going to make it equal where I can." + }, + { + "text": "If you're telling me you can make it equal to alpha, we know that if I increase my type 1 error, I'm going to decrease my type 2 error." + }, + { + "text": "If I start putting everyone in jail, or if I start letting everyone go free, that's what we're discussing last time." + }, + { + "text": "So since we have this trade-off, and you're giving me a budget for one guy, I'm just going to max it out." + }, + { + "text": "And where am I going to max it out?" + }, + { + "text": "Exactly at 1 half at the boundary." + }, + { + "text": "So this is going to be 5%." + }, + { + "text": "So what I know is that since alpha of theta is less than alpha for all theta and theta 0, sorry, that's for theta 0, that's where alpha is defined." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk30.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk30.json new file mode 100644 index 0000000000000000000000000000000000000000..a8e80051fb683b419557b2b36ba8c95a3d50cf00 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk30.json @@ -0,0 +1,62 @@ +[ + { + "text": "There's actually papers." + }, + { + "text": "I think it was big news, there's some papers, I think it's psychology or psychometrics papers, that actually refuse to publish p-values now." + }, + { + "text": "All right, where were we?" + }, + { + "text": "OK, here's the golden rule." + }, + { + "text": "So one thing that I'd like to show is this thing, just so you know how you apply the golden rule and how you apply the standard test." + }, + { + "text": "So the standard paradigm is the following." + }, + { + "text": "You have a black box, which is your test." + }, + { + "text": "For my wife, this is the fourth floor of the building." + }, + { + "text": "That's where the statisticians sit." + }, + { + "text": "What she sends there is data, let's say x1, xn." + }, + { + "text": "And she says, well, this one is about toothpaste, so here's a level." + }, + { + "text": "Let's say 5%." + }, + { + "text": "What the fourth floor brings back is an answer, yes, no." + }, + { + "text": "Green, red, just an answer." + }, + { + "text": "So that's the standard testing." + }, + { + "text": "You just feed it the data and the level at which you want to perform the test, maybe asymptotic, and it spits out a yes, no answer." + }, + { + "text": "What p-value does, you just feed it the data itself." + }, + { + "text": "And what it spits out is the p-value." + }, + { + "text": "And now, it's just up to you." + }, + { + "text": "I mean, hopefully, your brain has the computational power of deciding whether a number is larger or smaller than 5% without having to call the statisticians for this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk31.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk31.json new file mode 100644 index 0000000000000000000000000000000000000000..9fb2296acde7c40202805ca4f7e73e4c07f68e6a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk31.json @@ -0,0 +1,62 @@ +[ + { + "text": "And that's what it does." + }, + { + "text": "So now, we're all on one scale." + }, + { + "text": "Now, if you actually, I see some of you nodding when I talk about p-hacking." + }, + { + "text": "So that means you've seen p-values." + }, + { + "text": "If you've seen more than 100 p-values in your life, you have an entire scale." + }, + { + "text": "A good p-value is less than 10 to the minus 4." + }, + { + "text": "That's the ultimate sweet spot." + }, + { + "text": "Actually, statistical software spit out an output which says less than 10 to the minus 4." + }, + { + "text": "But then, maybe you want a p-value." + }, + { + "text": "If I tell you my p-value was 4.65, then I will say you've been doing some p-hacking until you found a number that was below 5%." + }, + { + "text": "That's typically what people will do." + }, + { + "text": "But if you're doing the test, if you're saying, I published my result." + }, + { + "text": "My test at 5% said yes, that means that maybe your p-value was 4.99, or your p-value was 10 to the minus 4." + }, + { + "text": "I will never know." + }, + { + "text": "I will never know how much evidence you had against the null." + }, + { + "text": "But if you tell me what the p-value is, I can make my own decision." + }, + { + "text": "I don't have to tell me whether it's a yes." + }, + { + "text": "No, you tell me it's 4.99." + }, + { + "text": "I'm going to say, well, maybe yes, but I'm going to take it with a grain of salt." + }, + { + "text": "And so that's why p-values are good numbers to have in mind." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk32.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk32.json new file mode 100644 index 0000000000000000000000000000000000000000..96ed5fb80473cde620f1dcbaecbdda179310c37c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk32.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, I show it as if it was an old trick that you start mastering when you're 45 years old." + }, + { + "text": "No, it's just how small is the number between 0 and 1." + }, + { + "text": "That's really what you need to know." + }, + { + "text": "Maybe on the log scale, if it's 10 to the minus 1, 10 to the minus 2, 10 to the minus 3, et cetera, that's probably the extent of the mastery here." + }, + { + "text": "So this traditional standard paradigm that I showed is actually commonly referred to as the Neyman-Pearson paradigm." + }, + { + "text": "So here it says Neyman-Pearson's theory." + }, + { + "text": "So there's an entire theory that comes with it, but it's really a paradigm." + }, + { + "text": "It's a way of thinking about hypothesis testing that says, well, if I'm not going to be able to optimize both my type 1 and type 2 error, I'm actually going to lock in my type 1 error below some level and just minimize the type 2 error under this constraint." + }, + { + "text": "That's what the Neyman-Pearson paradigm is." + }, + { + "text": "And it sort of makes sense for hypothesis testing problems." + }, + { + "text": "If you were doing some other applications with multi-objective optimization, you would maybe come up with something different." + }, + { + "text": "For example, machine learning is not performing typically under Neyman-Pearson paradigm." + }, + { + "text": "So if you do spam filtering, you could say, well, I want to constrain the probability as much as I can of taking somebody's important emails and throwing them out as spam and, under this constraint, not send too much spam to that person." + }, + { + "text": "That sort of makes sense for spams." + }, + { + "text": "Now, if you're labeling cats versus dogs, it's probably not like you want to make sure that no more than 5% of the dogs are labeled cat." + }, + { + "text": "Because it doesn't matter." + }, + { + "text": "So what you typically do is you just sum up the two types of error you can make, and you minimize the sum without putting any more weight on one or the other." + }, + { + "text": "So here's an example where doing a binary decision, one or two of the errors you can make, you don't have to actually be like that." + }, + { + "text": "So this example here, I did not." + }, + { + "text": "The trivial test, psi is equal to 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk33.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk33.json new file mode 100644 index 0000000000000000000000000000000000000000..0c2da6bcc636025ed6d047d161fdfe68e3b68329 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk33.json @@ -0,0 +1,62 @@ +[ + { + "text": "What was it in the US trial court example?" + }, + { + "text": "What is psi equal to 0?" + }, + { + "text": "I was concluding all ways to the null." + }, + { + "text": "What was the null?" + }, + { + "text": "Innocent, right?" + }, + { + "text": "That's the status quo." + }, + { + "text": "So that means that this guy never rejects a 0." + }, + { + "text": "Everybody's going away free." + }, + { + "text": "So you're sure you're not actually going against the Constitution because alpha is 0%, which is certainly less than 5%." + }, + { + "text": "But the power, the fact that a lot of criminals go back outside in the free world is actually formulated in terms of low power, which in this case is actually 0." + }, + { + "text": "Again, the power is a number between 0 and 1." + }, + { + "text": "Close to 0, good." + }, + { + "text": "Close to 1, bad." + }, + { + "text": "Now, what is the definition of the p-value?" + }, + { + "text": "That's going to be something." + }, + { + "text": "Mouthful, right?" + }, + { + "text": "The definition of the p-value is a mouthful." + }, + { + "text": "It's really the tipping point." + }, + { + "text": "It is the smallest level at which blah, blah, blah, blah." + }, + { + "text": "It's complicated to remember it." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk34.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk34.json new file mode 100644 index 0000000000000000000000000000000000000000..074297c2186646a83b698c991607273c1d143e1c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk34.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, I think that by my sixth explanation, my wife, after saying, oh, so it's the probability of making an error, I said, yeah, that's the probability of making an error." + }, + { + "text": "Because of course, she can think probability of making an error, small, good, large, bad." + }, + { + "text": "So that's actually a good way to remember." + }, + { + "text": "I'm pretty sure that at least 50% of people using p-values out there think that the p-value is the probability of making an error." + }, + { + "text": "Now, for all matters of purposes, if your goal is to just threshold the p-value, this is OK to have this in mind." + }, + { + "text": "But when it comes, at least until December 22, I would recommend trying to actually memorize the right definition for the p-value." + }, + { + "text": "OK?" + }, + { + "text": "OK." + }, + { + "text": "So the idea, again, is fix the level and try to optimize the power." + }, + { + "text": "So we're going to try to compute some p-values from now on." + }, + { + "text": "How do you compute the p-value?" + }, + { + "text": "Well, you can actually see it from this picture over there." + }, + { + "text": "One thing I didn't show on this picture, here was my q alpha over 2 that had alpha here, alpha over 2 here, right?" + }, + { + "text": "That was my q alpha over 2." + }, + { + "text": "And I said, if tn is to the right of this guy, I'm going to reject." + }, + { + "text": "If tn is to the left of this guy, I'm going to fail to reject." + }, + { + "text": "OK?" + }, + { + "text": "Pictorially, you can actually represent the p-value." + }, + { + "text": "It's when I replace this guy by tn itself." + }, + { + "text": "Sorry, that's p-value over 2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk35.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk35.json new file mode 100644 index 0000000000000000000000000000000000000000..9f1a7b89f2d43b53944bbf516e37f98c7cf70618 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk35.json @@ -0,0 +1,62 @@ +[ + { + "text": "No, actually, that's p-value." + }, + { + "text": "So let me just keep it like that and put the absolute value here." + }, + { + "text": "OK?" + }, + { + "text": "So if you replace the role of q alpha over 2 by your test statistic, this is what the area under the curve is actually the p-value itself up to scaling, because of the symmetric thing." + }, + { + "text": "OK?" + }, + { + "text": "So there's a good way to see pictorially what the p-value is." + }, + { + "text": "It's just the probability that some Gaussians, which is the probability that some absolute value of n0,1 exceeds tn." + }, + { + "text": "Right?" + }, + { + "text": "That's what the p-value is." + }, + { + "text": "Now, this guy has nothing to do with this guy." + }, + { + "text": "So this is really just 1 minus the Gaussian CDF of tn." + }, + { + "text": "And that's it." + }, + { + "text": "So that's how I would compute p-values." + }, + { + "text": "Now, as I said, the p-value is a beauty, because you don't have to understand the fact that your limiting distribution is a Gaussian." + }, + { + "text": "Right?" + }, + { + "text": "It's already factored in this construction." + }, + { + "text": "The fact that I'm actually looking at this cumulative distribution function of a standard Gaussian makes my p-value automatically adjust to what the limiting distribution is." + }, + { + "text": "And if this was the cumulative distribution function of a exponential, I would just have a different function here denoted by f, for example." + }, + { + "text": "And I would just compute a different value." + }, + { + "text": "But in the end, regardless of what the limiting value is, my p-value would still be a number between 0 and 1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk36.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk36.json new file mode 100644 index 0000000000000000000000000000000000000000..2d4547dd85e8e54b4a9640f590a534ed56d0306a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk36.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so to illustrate that, let's look at other weird distributions that we could get in place of the standard Gaussian." + }, + { + "text": "And we're not going to see many, but we'll see one." + }, + { + "text": "And it's not called the chi-squared distribution." + }, + { + "text": "It's actually called the student's distribution, but it involves the chi-squared distribution as a building block." + }, + { + "text": "So I don't know if my phonetics are not really right there, so I try to say, well, it's chi-squared." + }, + { + "text": "Maybe it's chi-squared in Canada." + }, + { + "text": "Who knows?" + }, + { + "text": "So for a positive integer, so there's only one parameter." + }, + { + "text": "So for the Gaussian, you have two parameters, which are mu and sigma squared." + }, + { + "text": "Those are real numbers." + }, + { + "text": "Sigma squared is positive." + }, + { + "text": "Here, I have one integer parameter." + }, + { + "text": "Then the distribution, the chi-squared distribution with d degrees of freedom." + }, + { + "text": "So the parameter is called a degree of freedom, just like mu is called the expected value, and sigma squared is called the variance." + }, + { + "text": "So it's called degrees of freedom." + }, + { + "text": "You don't have to really understand why." + }, + { + "text": "So that's the law that you would get." + }, + { + "text": "That's the random variable you would get if you were to sum d squares of independent standard Gaussians." + }, + { + "text": "So I take the square of an independent random Gaussian." + }, + { + "text": "I take another one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk37.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk37.json new file mode 100644 index 0000000000000000000000000000000000000000..6fa169cd52b7910e64c667064ab385a1dc476da0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk37.json @@ -0,0 +1,62 @@ +[ + { + "text": "I sum them, and that's a chi-squared with two degrees of freedom." + }, + { + "text": "That's how you get it." + }, + { + "text": "Now, I could define it using its probability density function." + }, + { + "text": "After all, this is the sum of positive random variables." + }, + { + "text": "It is a positive random variable." + }, + { + "text": "It has a density on the positive real line." + }, + { + "text": "And the PDF of chi-squared, PDF of chi-squared with d degrees of freedom is what?" + }, + { + "text": "Well, it's fd of x is x to the d over 2 minus 1, e to the minus x over 2." + }, + { + "text": "And then here, I have a gamma of d over 2, and the other one is, I think, 2 to the d over 2 minus 1." + }, + { + "text": "No, 2 to the d over 2." + }, + { + "text": "That's what it is." + }, + { + "text": "That's the density." + }, + { + "text": "If you are very good at probability, you can make the change of variable and write your Jacobian and do all this stuff and actually check that this is true." + }, + { + "text": "I do not recommend doing that." + }, + { + "text": "So this is the density, but it's better understood like that, at thinking of just something that you built from standard Gaussian." + }, + { + "text": "So for example, an example of a chi-squared with two degrees of freedom is actually the following thing." + }, + { + "text": "Let's assume I have a target like this." + }, + { + "text": "And I don't aim very well, and I'm trying to hit the center." + }, + { + "text": "And I'm going to have maybe a deviation, which is standard Gaussian left-right and standard Gaussian north-south." + }, + { + "text": "So I'm throwing, and then I'm here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk38.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk38.json new file mode 100644 index 0000000000000000000000000000000000000000..e9321d18ef5daa35196a20db9f6bb7680045ede5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk38.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'm claiming that this number here, by Pythagoras' theorem, the squared distance here is the sum of this squared distance here, which is the square of a Gaussian by assumption, plus the square of this distance, which is the square of another independent Gaussian." + }, + { + "text": "I assume those are independent." + }, + { + "text": "And so the squared distance from this point to this point is the chi-squared with two degrees of freedom." + }, + { + "text": "So this guy here is n01 squared." + }, + { + "text": "This is n01 squared." + }, + { + "text": "And so this guy here, this distance here, is chi-squared with two degrees of freedom." + }, + { + "text": "I mean, the squared distance." + }, + { + "text": "I'm talking about squared distances here." + }, + { + "text": "So now you can see that actually Pythagoras is basically why chi-squared arise." + }, + { + "text": "That's why it has its own name." + }, + { + "text": "I mean, I could define this random variable." + }, + { + "text": "I mean, it's actually a gamma distribution." + }, + { + "text": "It's a special case of something called the gamma distribution." + }, + { + "text": "The fact that the special case has its own name is because there's many times where we're going to take sum of squares of independent Gaussians, because Gaussians, the sum of squares is really the norm, the Euclidean norm squared, just by Pythagoras theorem." + }, + { + "text": "If I'm in higher dimension, I can start to sum more squared coordinates, and I'm going to measure the norm squared." + }, + { + "text": "So if you want to draw this picture, it looks like this." + }, + { + "text": "Again, it's the sum of positive numbers." + }, + { + "text": "So it's going to be on 0 plus infinity." + }, + { + "text": "That's fd." + }, + { + "text": "And so for f1 looks like this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk39.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk39.json new file mode 100644 index 0000000000000000000000000000000000000000..530fa0ac2ba5f7380bf835d6fd19c3b55d8a53a3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk39.json @@ -0,0 +1,62 @@ +[ + { + "text": "f2 looks like this." + }, + { + "text": "So the tails becomes heavier and heavier as d increases." + }, + { + "text": "And then at start to 3, it starts to have a different shape." + }, + { + "text": "It starts from 0, and it looks like this." + }, + { + "text": "And then as d increases, it's basically as if you were to push this thing to the right." + }, + { + "text": "It's just like, pfft." + }, + { + "text": "It's just falling like a big ball." + }, + { + "text": "Everybody sees what's going on?" + }, + { + "text": "So there's just this fat thing that's just going there." + }, + { + "text": "What is the expected value of a k squared?" + }, + { + "text": "So it's the expected value of the sum of Gaussian random variables squared." + }, + { + "text": "I don't know why I said that." + }, + { + "text": "AUDIENCE 2 It's the sum of their second norm, right?" + }, + { + "text": "Which is?" + }, + { + "text": "Those are n0, 1." + }, + { + "text": "It's like, oh, I see, 1." + }, + { + "text": "Yeah." + }, + { + "text": "So n times 1, or d times 1." + }, + { + "text": "Yeah, which is d. So one thing you can check quickly is that the expected value of a k squared is d. And so you see, that's why the mass is shifting to the right as d increases." + }, + { + "text": "It's just going there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk4.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..07e0b7e52902074c6ec8439999a1046b4b977809 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "So for theta and theta 0, I know that my function is going to look like this." + }, + { + "text": "It's going to be somewhere in this rectangle." + }, + { + "text": "Everybody agrees?" + }, + { + "text": "So this function for this guy is going to look like this." + }, + { + "text": "When I'm at 0, when p is equal to 0, which means I only observe 0's, then I know that p is going to be 0." + }, + { + "text": "And I will certainly not conclude that p is equal to 1." + }, + { + "text": "This test will never conclude that p is equal to 1." + }, + { + "text": "Sorry, that was, yeah." + }, + { + "text": "That p is equal to, that p is lower than 1 half, just because xn bar is going to be equal to 0." + }, + { + "text": "OK, well, this is actually not well-defined." + }, + { + "text": "So maybe I need to do something, put it equal to 0 if xn bar is equal to 0." + }, + { + "text": "So I guess basically I get something which is negative." + }, + { + "text": "And so it's never going to be larger than what I want." + }, + { + "text": "And so here I'm actually starting at 0." + }, + { + "text": "So now this is this function here that increases." + }, + { + "text": "I mean, it should increase smoothly." + }, + { + "text": "This function here is alpha psi of theta, or alpha psi of p, let's say, because we're talking about p. Then it reaches alpha here." + }, + { + "text": "Now when I go on the other side, I'm actually looking at beta." + }, + { + "text": "When I'm on theta 1, the function that matters is the probability of type 2 error, which is beta psi." + }, + { + "text": "And this beta psi is actually going to increase." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk40.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk40.json new file mode 100644 index 0000000000000000000000000000000000000000..cf303c16babeea5b89d0924caa36f4dde58e6495 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk40.json @@ -0,0 +1,62 @@ +[ + { + "text": "Actually, the variance is also increasing." + }, + { + "text": "The variance is 2d." + }, + { + "text": "So this is one thing." + }, + { + "text": "And so why do we care about this in basic statistics?" + }, + { + "text": "It's not like we actually have statistics much about throwing darts at high dimensional boards." + }, + { + "text": "So what's happening is that if I look at the sample variance, the average of the sum of squared centered by their mean, then I can actually expend this as the sum of the squares minus the average squared." + }, + { + "text": "It's just the same trick that we have for the variance." + }, + { + "text": "Second moment minus first moment squared." + }, + { + "text": "And then I claim that Cochran's theorem, I will tell you in a second what Cochran's theorem tells me, is that this sample variance is actually, so if I had only this, so now, OK, look at those guys." + }, + { + "text": "Those guys are Gaussian with mean mu and variance sigma squared." + }, + { + "text": "Think for one second, mu being 0 and sigma squared being 1." + }, + { + "text": "Now, this part would be a chi-square with n degrees of freedom divided by n. Now, I get another thing here, which is the square of something that looks like a Gaussian as well." + }, + { + "text": "So it looks like I have something else here, which looks also like a chi-square." + }, + { + "text": "Now, Cochran's theorem is essentially telling you that those things are independent." + }, + { + "text": "And so that in a way, you can think of those guys as being here n degrees of freedom minus 1 degree of freedom." + }, + { + "text": "Now, here, as I said, this is not mean 0 and variance 1." + }, + { + "text": "The fact that it's not mean 0 is not a problem, because I can remove the mean here and remove the mean here." + }, + { + "text": "And so this thing has the same distribution, regardless of what the actual mean is." + }, + { + "text": "So without loss of generality, I can assume that mu is equal 0." + }, + { + "text": "Now, the variance I'm going to have to pay, because if I multiply all these numbers by 10, then this Sn is going to be multiplied by 100." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk41.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk41.json new file mode 100644 index 0000000000000000000000000000000000000000..be699853a1170afd439414bc8f189e87e84b0b94 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk41.json @@ -0,0 +1,62 @@ +[ + { + "text": "So this thing is going to scale with the variance." + }, + { + "text": "And not surprisingly, it's scaling like the square of the variance." + }, + { + "text": "So if I look at Sn, it's distributed as sigma-square times the chi-square with n minus 1 degrees of freedom divided by n. And we don't really write that, because a chi-square times sigma-square divided by n is not a distribution." + }, + { + "text": "So we put everything to the left." + }, + { + "text": "And we say that this is actually a chi-square with n minus 1 degrees of freedom." + }, + { + "text": "So here, I'm actually dropping a fact on you." + }, + { + "text": "But you can sort of see the building block." + }, + { + "text": "What is the thing that's sort of fussy at this point, but the rest should be crystal clear to you?" + }, + { + "text": "The thing that's fussy is that removing this square guy here is actually removing 1 degree of freedom." + }, + { + "text": "That should be weird." + }, + { + "text": "But that's what Cochran's theorem tells me." + }, + { + "text": "It's essentially stating something about orthogonality of subspaces with the span of the constant vector, something like that." + }, + { + "text": "So you don't have to think about it too much." + }, + { + "text": "But that's what it's telling me." + }, + { + "text": "But the rest, if you plug in, so the scaling in sigma-squared and in n, that should be completely clear to you." + }, + { + "text": "So in particular, if I remove that part, it should be clear to you that this thing, if mean is 0, this thing is actually distributed." + }, + { + "text": "Well, if mu is 0, what is the distribution of this guy?" + }, + { + "text": "So I remove that part, just this part." + }, + { + "text": "So I have xi, which are n0 sigma-squared." + }, + { + "text": "And I'm asking, what is the distribution of 1 over n sum from i equal 1 to n of xi-squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk42.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk42.json new file mode 100644 index 0000000000000000000000000000000000000000..3596e452514719b86b744b50b7402e7dd02b9ace --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk42.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it is the sum of their iid." + }, + { + "text": "So it's the sum of independent Gaussians, but not standard." + }, + { + "text": "So the first thing to make them standard is that I divide all of them by sigma-squared." + }, + { + "text": "Now, this guy is of the form zi-squared, where zi is n0, 1." + }, + { + "text": "So now this thing here has what distribution?" + }, + { + "text": "Chi-squared n. And now sigma-squared over n times chi-squared n. So if I have sigma-squared divided by n times chi-squared, sorry, so n times n divided by sigma-squared." + }, + { + "text": "So if I take this thing and I multiply it by n divided by sigma-squared, it means I remove this term." + }, + { + "text": "And now I am left with a chi-squared with n degrees of freedom." + }, + { + "text": "Now, the effect of centering with the sample mean here is only to lose 1 degree of freedom." + }, + { + "text": "That's it." + }, + { + "text": "OK?" + }, + { + "text": "So if I want to do a test about variance, since this is supposedly a good estimator of variance, this could be my pivotal distribution." + }, + { + "text": "This could play the role of a Gaussian." + }, + { + "text": "If I want to know if my variance is equal to 1 or larger than 1, I could actually build a test based on this only statement and test if the variance is larger than 1 or not." + }, + { + "text": "Now, this is not asymptotic because I started with the very assumption that my data was Gaussian itself." + }, + { + "text": "OK?" + }, + { + "text": "Now, just a side remark, you can check that this chi-squared 2, 2 is an exponential with half degrees of freedom, which is certainly not clear from the fact that z1 squared plus z2 squared is a chi-squared with 2 degrees of freedom." + }, + { + "text": "If I give you the sum of the square of two independent Gaussians, this is actually an exponential." + }, + { + "text": "That's not super clear, right?" + }, + { + "text": "But if you look at what was here, I don't know if you took notes, but let me rewrite it for you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk43.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk43.json new file mode 100644 index 0000000000000000000000000000000000000000..c1c4ce2a1e88dbaf6e313e0235a0fa58a881a709 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk43.json @@ -0,0 +1,59 @@ +[ + { + "text": "So it was x to the d over 2 minus 1 e to the minus x over 2 divided by 2 to the d over 2 gamma of d over 2." + }, + { + "text": "So if I plug in d is equal to 2, gamma of 2 over 2 is gamma of 1, which is 1, right?" + }, + { + "text": "It's factorial of 0." + }, + { + "text": "So it's 1." + }, + { + "text": "So this guy goes away." + }, + { + "text": "2 to the d over 2 is 2 to the 1." + }, + { + "text": "So that's just 1." + }, + { + "text": "No, that's just 2." + }, + { + "text": "OK?" + }, + { + "text": "Then x to the d over 2 minus 1 is x to the 0, goes away." + }, + { + "text": "And so I have x minus x over 2, 1 half, which is really, indeed, of the form lambda e to the minus lambda x for lambda is equal to 1 half, which was our exponential distribution." + }, + { + "text": "OK?" + }, + { + "text": "So well, next week is Columbus Day." + }, + { + "text": "So that's next Monday." + }, + { + "text": "So next week, we'll talk about students' distribution." + }, + { + "text": "And so that was discovered by a guy who pretended his name was student but was not student." + }, + { + "text": "And I challenge you to find why in the meantime." + }, + { + "text": "All right, so I'll see you next week." + }, + { + "text": "Your homework is going to be outside, so we can release the room." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk5.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..89ec03ee891688f8ef72df5ae36dcaada4844313 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "So beta psi is what?" + }, + { + "text": "Well, beta psi should also, sorry, that's the probability of being equal to alpha." + }, + { + "text": "So what I'm going to do is I'm going to look at the probability of rejecting." + }, + { + "text": "So let me draw this function all the way." + }, + { + "text": "It's going to look like this." + }, + { + "text": "Now here, if I look at this function here or here, this is the probability under theta that psi is equal to 1." + }, + { + "text": "And we just said that in this region, this function is called alpha psi." + }, + { + "text": "In that region, it's not called alpha psi." + }, + { + "text": "It's not called anything." + }, + { + "text": "It's just the probability of rejection." + }, + { + "text": "So it's not an error." + }, + { + "text": "It's actually what you should be doing." + }, + { + "text": "What we're looking at in this region is 1 minus this guy." + }, + { + "text": "We're looking at the probability of not rejecting." + }, + { + "text": "So I need to actually basically look at 1 minus this thing, which here is going to be 95%." + }, + { + "text": "So I'm going to do 95%." + }, + { + "text": "And this is my probability." + }, + { + "text": "And I'm just basically drawing the symmetric of this guy." + }, + { + "text": "So this here is the probability under theta that psi is equal to 0, which is 1 minus p theta that psi is equal to 1." + }, + { + "text": "So it's just 1 minus the white curve." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk6.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..2ba3f3f31acb2d89e2bd57110d90b292f5959fce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's actually, by definition, equal to beta psi of theta." + }, + { + "text": "Now, where do I read pi psi?" + }, + { + "text": "What is pi psi on this picture?" + }, + { + "text": "Is pi psi a number or a function?" + }, + { + "text": "It's a number, right?" + }, + { + "text": "It's the minimum of a function." + }, + { + "text": "What is this function?" + }, + { + "text": "It's the probability under theta that theta is equal to 1." + }, + { + "text": "I drew this entire function between theta 0 and theta 1." + }, + { + "text": "I drew this entire white curve." + }, + { + "text": "This is this probability." + }, + { + "text": "Now, I'm saying, look at the smallest value this probability can take on the set theta 1." + }, + { + "text": "What is this?" + }, + { + "text": "This guy." + }, + { + "text": "This is where my pi, this thing here, is pi psi." + }, + { + "text": "And so it's equal to 5%." + }, + { + "text": "So that's for this particular test, because this test is sort of a continuous curve for this psi." + }, + { + "text": "And so if I want to make sure that I'm at 5% when I come to the right of theta 0, if it touches theta 1, then I better have 5% on the other side if the function is continuous." + }, + { + "text": "So basically, if this function is increasing, which will be the case for most tests, then what's going to happen is that, and continuous, then what's going to happen is that the level of the test, which is alpha, is actually going to be equal to the power of the test." + }, + { + "text": "OK?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk7.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..4f5cdee6b6891b45c5f7794aece5ce2b8c13dc7a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, there's something I didn't mention, and I'm just mentioning it, pass it by." + }, + { + "text": "Here, I define the power itself." + }, + { + "text": "This function, this entire white curve here, is actually called the power function." + }, + { + "text": "This thing, that's the entire white curve." + }, + { + "text": "And what you could have is tests that have the entire curve, which is dominated by another test." + }, + { + "text": "So here, if I look at this test, and let's assume I can build another test that has this curve." + }, + { + "text": "Let's say it's the same here." + }, + { + "text": "But then here, it looks like this." + }, + { + "text": "What is the power of this test?" + }, + { + "text": "It's the same." + }, + { + "text": "It's 5%, because this point touches here exactly at the same point." + }, + { + "text": "However, for any other value than the worst possible, this guy is doing better than this guy." + }, + { + "text": "Can you see that?" + }, + { + "text": "Having a curve higher on the right-hand side is a good thing, because it means that you tend to reject more when you're actually in H1." + }, + { + "text": "So this guy is definitely better than this guy." + }, + { + "text": "And so what we say in this case is that the test with the dashed line is uniformly more powerful than the other test." + }, + { + "text": "But we're not going to go into those details, because basically, all the tests that we will describe are already the most powerful ones." + }, + { + "text": "In particular, this guy is, there's no such thing." + }, + { + "text": "All the other guys you can come up with are going to actually be below." + }, + { + "text": "So we saw a couple tests, and we saw how to pick this threshold, and we defined those two things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk8.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8b9449415f7337b53908d8098f0293899e0ba86e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "Yes?" + }, + { + "text": "AUDIENCE 2 But in that case, the down one, if it were also higher in the region of 2 to 0, do you still consider it better?" + }, + { + "text": "PHILIPPE RIGOLLETTIS Because you're given this budget of 5%, right?" + }, + { + "text": "So in this paradigm, where you're given the, actually, if the dashed line was this dashed line, I would still be happy." + }, + { + "text": "I mean, I don't care what this thing does here, as long as it's below 5%." + }, + { + "text": "But here, I'm going to try to discover it, right?" + }, + { + "text": "Think about, again, the drug discovery example." + }, + { + "text": "You're trying to find, let's say you're a scientist, and you're trying to prove that your drug works." + }, + { + "text": "What do you want to see?" + }, + { + "text": "Well, FDA puts on you this constraint that your probability of type 1 error should never exceed 5%." + }, + { + "text": "You're going to work under this assumption." + }, + { + "text": "But what you're going to do is going to try to find a test that will make you find something as often as possible." + }, + { + "text": "And so you're going to max this constraint of 5%, and then you're going to try to make this curve, this curve that means that this is basically, this number here, for any point here, is the probability that you publish your paper." + }, + { + "text": "That's the probability that you can release to market your drug." + }, + { + "text": "That's the probability that it works, right?" + }, + { + "text": "And so you want this curve to be as high as possible." + }, + { + "text": "You want to make sure that if there's evidence in the data that H1 is the truth, you want to squeeze as much of this evidence as possible." + }, + { + "text": "And the test that has the highest possible curve is the most powerful one." + }, + { + "text": "Now, you have to also understand that having two curves that are on top of each other, completely, everywhere, is a rare phenomenon." + }, + { + "text": "It's not always the case that there is a test that's uniformly more powerful than any other test." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk9.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bbad3ae05fbb39d9ef76b7b89aa0fada7d5adc3e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_4_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It might be that you have some trade-off, that it might be better here, but then you're losing power here." + }, + { + "text": "Things like this." + }, + { + "text": "Well, actually, maybe it should not go down." + }, + { + "text": "But let's say it goes like this, and then maybe this guy goes like this." + }, + { + "text": "Then you have to basically make an educated guess whether you think that the theta you're going to find is here or it's here." + }, + { + "text": "And then you pick a test." + }, + { + "text": "OK?" + }, + { + "text": "Any other question?" + }, + { + "text": "Yes?" + }, + { + "text": "AUDIENCE 2." + }, + { + "text": "What is the derivative of the type 2 error?" + }, + { + "text": "PHILIPPE RIGOLLET." + }, + { + "text": "So the green curve is exactly right." + }, + { + "text": "So that's beta psi of theta." + }, + { + "text": "So it's really the type 2 error, and it's defined only here." + }, + { + "text": "So here, it's not a definition." + }, + { + "text": "It's really just I'm just mapping it to this point." + }, + { + "text": "So it's defined only here, and it's the probability of type 2 error." + }, + { + "text": "So here, it's pretty large, right?" + }, + { + "text": "I'm making it basically as large as I could, because I'm at the boundary." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk0.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..65c23c5cab5e2c4f1a8f872964a31edc5dd21493 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "Talking about tests, and to be fair, we spend most of our time talking about new jargon that we're using." + }, + { + "text": "But the main goal is to take a binary decision, yes and no." + }, + { + "text": "So just so that we're clear and we make sure that we all speak the same language, let me just remind you what the key words are for tests." + }, + { + "text": "So the first thing is that we split theta in theta 0 and theta 1." + }, + { + "text": "Both are included in theta, and they're disjoint." + }, + { + "text": "OK." + }, + { + "text": "So I have my set of possible parameters." + }, + { + "text": "And then I have theta 0 is here, theta 1 is here, and there might be something that I leave out." + }, + { + "text": "And so what we're doing is we have two hypotheses." + }, + { + "text": "So here's our hypothesis testing problem." + }, + { + "text": "And it's h0 theta belongs to theta 0 versus h1 theta belongs to theta 1." + }, + { + "text": "This guy was called the null, and this guy was called the alternative." + }, + { + "text": "And why we give them special names is because we saw that they have an asymmetric role." + }, + { + "text": "The null represents the status quo, and data is here to bring evidence against this guy." + }, + { + "text": "And we can really never conclude that h0 is true because all we could conclude is that h1 is not true or may not be true." + }, + { + "text": "So that was the first thing." + }, + { + "text": "The second thing was the hypothesis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk1.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3b72e60009f76e8f81d23cb396a309bf7d70b355 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "The third thing is what is a test?" + }, + { + "text": "Well, psi, it's a statistic." + }, + { + "text": "And it takes the data, and it maps it into 0 or 1." + }, + { + "text": "And I didn't really mention it, but there's something such as called randomized tests, which is, well, if it cannot really make a decision, they might as well flip a coin." + }, + { + "text": "That tends to be biased, but that's really, I mean, think about it in practice." + }, + { + "text": "You probably don't want to make decisions based on flipping a coin." + }, + { + "text": "And so what people typically do, this is happening typically at one specific value." + }, + { + "text": "So rather than flipping a coin for this very specific value, what people typically do is they say, OK, I'm going to side with h0 because that's the most conservative choice I can make." + }, + { + "text": "So in a way, they think of flipping this coin, but always falling on heads." + }, + { + "text": "So associated to this test was something called, well, the rejection region." + }, + { + "text": "And r psi, which is just the set of data, x1, xn, such that psi of x1, xn is equal to 1." + }, + { + "text": "So that means we rejected 0 when the test is 1, and those are the set of data points that actually are going to lead me to reject the test." + }, + { + "text": "OK. Then the things that were actually slightly a little more important and really peculiar to test, specific to test, were the type 1 and type 2 error." + }, + { + "text": "So the type 1 error arises when, so type 1 error is when you reject whereas h0 is correct." + }, + { + "text": "And the type 2 error is the opposite." + }, + { + "text": "So it's failed to reject whereas h1 is correct." + }, + { + "text": "h is correct." + }, + { + "text": "So those are the two types of errors you can make, and we quantify their probability of type 1 error." + }, + { + "text": "So alpha psi is the probability." + }, + { + "text": "So that's the probability of type 1 error." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk10.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c19b0d21dee98686b07f25081871711f112710fa --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "And that means at the boundary, since the status quo is h0, I'm always going to go for h0 if I don't have any evidence, which means that what's going to pay is the type 2 error that's going to basically pay this." + }, + { + "text": "OK?" + }, + { + "text": "Any other question?" + }, + { + "text": "All right, so let's move on." + }, + { + "text": "So did we do this?" + }, + { + "text": "No, I think we stopped here, right?" + }, + { + "text": "I didn't cover that part." + }, + { + "text": "So as I said, in this paradigm, we're going to actually fix this guy to be something." + }, + { + "text": "And this thing is actually called the level of the test." + }, + { + "text": "I'm sorry, this is again more words." + }, + { + "text": "Actually, good news is that we split it into two lectures." + }, + { + "text": "So we have, what is a test?" + }, + { + "text": "What is a hypothesis?" + }, + { + "text": "What is the null?" + }, + { + "text": "What is the alternative?" + }, + { + "text": "What is the type 1 error?" + }, + { + "text": "What is the type 2 error?" + }, + { + "text": "And now, I'm telling you there's another thing." + }, + { + "text": "So we defined the power, which was some sort of a lower bound on the, or it's 1 minus the upper bound on the type 2 error, basically." + }, + { + "text": "And so it's alternative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk11.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..815ec78c1b831dd92a2b3f1d68a91dd8df86f618 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "So the power is the smallest probability of rejecting when you're in the null." + }, + { + "text": "And it's alternative when you're in theta 1, right?" + }, + { + "text": "So that's my power." + }, + { + "text": "I looked here, and I looked at the smallest value." + }, + { + "text": "And I can look at this side and say, well, what is the largest probability that I make a type 1 error?" + }, + { + "text": "Again, this largest probability is the level of the test." + }, + { + "text": "OK, so this is alpha equal, by definition, to the maximum for theta and theta 0 of alpha psi of theta." + }, + { + "text": "So here, I just put the level itself." + }, + { + "text": "As you can see here, it essentially says that if I'm of level 5%, I'm also of level 10%." + }, + { + "text": "I'm also of level 15%." + }, + { + "text": "So here, it's really an upper bound." + }, + { + "text": "Whatever you guys want to take, this is what it is." + }, + { + "text": "But as we said, if this number is 4.5%, you're losing in your type 2 error." + }, + { + "text": "So if you're allowed to have, if this maximum here is 4.5%, and FDA told you you can go to 5%, you're losing in your type 2 error." + }, + { + "text": "So you actually want to make sure that this is the 5% that's given to you." + }, + { + "text": "So the way it works is that you give me the alpha." + }, + { + "text": "Then I'm going to go back, pick c that depends on alpha here, so that this thing is actually equal to 5%." + }, + { + "text": "And so, of course, in many instances, we do not know the probability." + }, + { + "text": "We do not know how to compute the probability of type 1 error." + }, + { + "text": "This is a maximum value for the probability of type 1 error." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk12.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..4bd3834b631a0a7c734e2b14c2fe32eaf6f601e6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "We don't know how to compute it." + }, + { + "text": "I mean, it might be a very complicated random variable." + }, + { + "text": "Maybe it's a weird binomial." + }, + { + "text": "We could compute it, but it would be painful." + }, + { + "text": "But what we know how to compute is its asymptotic value, which is because of the central limit theorem, convergence and distribution tells me that the probability of type 1 error is basically going towards the probability that some Gaussian is in some region." + }, + { + "text": "And so we're going to compute not the level itself, but the asymptotic level." + }, + { + "text": "So again, that's basically the limit as n goes to infinity of alpha psi of theta." + }, + { + "text": "And then I'm going to make the max here." + }, + { + "text": "OK?" + }, + { + "text": "So how am I going to compute this?" + }, + { + "text": "Well, if I take a test that has rejection region of the form Tn, because it depends on the data, right?" + }, + { + "text": "That's Tn of x1, xn, my observations, larger than some number c. OK?" + }, + { + "text": "Of course, I can almost always write tests like that, except that sometimes there's going to be an absolute value, which essentially means I'm going away from some value." + }, + { + "text": "Maybe actually I'm less than something, but I can always put a negative sign in front of everything." + }, + { + "text": "So this is not without much of generality, right?" + }, + { + "text": "So this includes something that looks like something is larger than the constant, right?" + }, + { + "text": "So that means, which is equivalent to, well, let me write it as Tq." + }, + { + "text": "OK, because then that means that, so that's Tn." + }, + { + "text": "But this actually encompasses the fact that Qn is larger than c, or Qn is less than c, then minus c. So that includes this guy." + }, + { + "text": "That also includes Qn less than c, because this is equivalent to Qn is larger than minus c. Minus Qn is, and so that's going to be my Tn." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk13.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..d0fc40d7fea49cc51a82242971122ccb04ee2caf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I can actually encode several type of things, OK?" + }, + { + "text": "Rejection regions that, so here in this case, I have a rejection region that looks like this, or a rejection region that looks like this, or a rejection region that looks like this." + }, + { + "text": "OK, and here I don't really represent it for the whole data, but maybe for the average, for example, or the normalized average." + }, + { + "text": "OK, so if I write this, then, yeah." + }, + { + "text": "And in this case, this Tn that shows up is called test statistic." + }, + { + "text": "I mean, this is sort of a, I mean, this is not like set in stone." + }, + { + "text": "Here, for example, Q could be the test statistics." + }, + { + "text": "It doesn't have to be minus Q itself that's the test statistic, right?" + }, + { + "text": "So what is the test statistic?" + }, + { + "text": "Well, it's what you're going to build from your data and then compare to some fixed value, right?" + }, + { + "text": "So in the example we had here, what is our test statistic?" + }, + { + "text": "Well, it's this guy, right?" + }, + { + "text": "This was our test statistic." + }, + { + "text": "And is this thing a statistic?" + }, + { + "text": "What are the criteria for a statistic?" + }, + { + "text": "What is a statistic?" + }, + { + "text": "I know you know the answer." + }, + { + "text": "AUDIENCE MEMBER 2." + }, + { + "text": "Is it a measurable function?" + }, + { + "text": "PROFESSOR PHILIPPE RIGOLLET." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk14.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..deb918611779af5e70f1e976f45cfc296740fc0a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "Yeah, it's a measurable function of the data that does not depend on the parameter." + }, + { + "text": "Is this guy a statistic?" + }, + { + "text": "AUDIENCE MEMBER 3." + }, + { + "text": "Yes, he is." + }, + { + "text": "PROFESSOR PHILIPPE RIGOLLET." + }, + { + "text": "Let's think again." + }, + { + "text": "When I implemented the test, what did I do?" + }, + { + "text": "I was able to compute my test." + }, + { + "text": "My test did not depend on some unknown parameter." + }, + { + "text": "How did we do it?" + }, + { + "text": "We just plugged in 0.5 here." + }, + { + "text": "Remember?" + }, + { + "text": "That was the value for which we computed it, because under h0, that was the value we're seeing." + }, + { + "text": "And if theta 0 is actually an entire set, I'm just going to take the value that's the closest to h1." + }, + { + "text": "We'll see that in a second." + }, + { + "text": "I mean, I did not guarantee that to you." + }, + { + "text": "But just taking the worst type 1 error and bounding it by alpha is equivalent to taking p and taking the value of p that's the closest to theta 1, which is completely intuitive." + }, + { + "text": "The worst type 1 error is going to be attained for the p that's the closest to the alternative." + }, + { + "text": "So even if the null is actually just an entire set, it's as if it was just the point that's the closest to the alternative." + }, + { + "text": "So now we can compute this, because there's no unknown parameters that shows up." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk15.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..0bc365016096bbbfd9f7a60ab9c2724dec760020 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "We replaced p by 0.5." + }, + { + "text": "And so that was our test statistic." + }, + { + "text": "So when you're building a test, you want to first build a test statistic and then see what threshold you should be getting." + }, + { + "text": "So now let's go back to our example where we have x1, xn." + }, + { + "text": "They're iid Bernoulli p. And I want to test if p is 1 half versus p not equal to 1 half, which as I said is what you want to do if you want to test if a coin is fair." + }, + { + "text": "And so here I'm going to build a test statistic." + }, + { + "text": "And we concluded last time that what do we want for this statistic?" + }, + { + "text": "We want it to have a distribution which under the null does not depend on the parameters, a distribution that I can actually compute quintiles of." + }, + { + "text": "So what we did is we said, well, if I look at the central limit theorem tells me that square root of n xn bar minus p divided by." + }, + { + "text": "So if I do central limit theorem plus Slutsky, for example, I'm going to have square root." + }, + { + "text": "And we've had this discussion whether we want to use Slutsky or not here." + }, + { + "text": "But let's assume we're taking Slutsky wherever we can." + }, + { + "text": "So this thing tells me that by the central limit theorem as n goes to infinity, this thing converges in distribution to some n 0, 1." + }, + { + "text": "Now as we said, this guy is not something we know." + }, + { + "text": "But under the null, we actually know it." + }, + { + "text": "And we can actually replace it by 1 half." + }, + { + "text": "So this thing holds under h0." + }, + { + "text": "When I write under h0, it means when this is the truth." + }, + { + "text": "So now I have something that converges to something that has no dependence on anything I don't know." + }, + { + "text": "And in particular, if you have any statistics textbook, which you don't because I didn't require one, you should be thankful because this thing costs $250." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk16.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..298b0fb997de98b972702f498d96cfa89d4e4b7d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "This thing's actually, if you look at the back, you actually have a table for a standard Gaussian." + }, + { + "text": "I could have anything else here." + }, + { + "text": "I could have an exponential distribution." + }, + { + "text": "I could have a, I don't know, a, well, we'll see the chi-square distribution in a minute." + }, + { + "text": "Any distribution from which you can actually see a table that somebody actually computed this thing for which you can actually draw the PDF and start computing whatever probability you want on them, then this is what you want to see at the right-hand side." + }, + { + "text": "This is any distribution." + }, + { + "text": "It's called pivotal." + }, + { + "text": "I think we've mentioned that before." + }, + { + "text": "Pivotal means it does not depend on anything that you don't know." + }, + { + "text": "And maybe it's easy to compute those things." + }, + { + "text": "Probably, typically, you need a computer to simulate them for you because computing probabilities for Gaussians is not an easy thing." + }, + { + "text": "We don't know how to solve those integrals exactly." + }, + { + "text": "We have to do it numerically." + }, + { + "text": "OK, so now I want to do this test." + }, + { + "text": "My test statistic will be declared to be what?" + }, + { + "text": "Well, I'm going to reject if what is larger than some number?" + }, + { + "text": "The absolute value of this guy." + }, + { + "text": "So my test statistic is going to be square root of n minus 0.5 divided by square root of xn bar 1 minus xn bar." + }, + { + "text": "That's my test statistic, absolute value of this guy, because I want to reject either when this guy is too large or when this guy is too small." + }, + { + "text": "I don't know ahead whether I'm going to see p larger than 1 half or less than 1 half." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk17.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..c16a8c6be2149a29434fcd2457ee0fdbf0606f2d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "So now I need to compute c such that the probability that tn is lower than c. So that's what?" + }, + { + "text": "That's the probability under p, which is unknown." + }, + { + "text": "I want this probability to be less than some level alpha asymptotically." + }, + { + "text": "So I want the limit of this guy to be less than alpha, and that's the level of my test." + }, + { + "text": "So that's the given level." + }, + { + "text": "So I want this thing to happen." + }, + { + "text": "Now what I know is that this limit, actually, I should say given asymptotic level." + }, + { + "text": "So what is this thing?" + }, + { + "text": "Well, OK, that's the probability that something that looks like under p. So under p, this guy, so what I know is that tn is square root of n minus xn bar minus 0.5 divided by square root of xn bar 1 minus xn bar exceeds." + }, + { + "text": "Is this true that as n goes to infinity, this probability is the same as the probability that the absolute value of a Gaussian exceeds c of a standard Gaussian?" + }, + { + "text": "Is this true?" + }, + { + "text": "Yeah, so you're saying that this, as n becomes large enough, this should be the probability that some absolute value of n0,1 exceeds c, right?" + }, + { + "text": "So I claim that this is not correct." + }, + { + "text": "Somebody tell me why." + }, + { + "text": "Even in the limit, it's not correct?" + }, + { + "text": "Even in the limit, it's not correct." + }, + { + "text": "OK." + }, + { + "text": "So what do you see?" + }, + { + "text": "It's because at the beginning, we picked the worst possible true parameter, 0.5, right?" + }, + { + "text": "So we don't actually know that this 0.5 is the least." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk18.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..21ff2eaef450e95222ef4c4c025a1ccb1a883204 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Exactly, right?" + }, + { + "text": "So we picked this 0.5 here, but this is for any p, right?" + }, + { + "text": "But what is the only p I can get?" + }, + { + "text": "So what I want is that this is true for all p in theta 0." + }, + { + "text": "But the only p that's in theta 0 is actually p is equal to 0.5." + }, + { + "text": "So yes, what you said was true, but it required to specify p to be equal to 0.5." + }, + { + "text": "So this, in general, is not true." + }, + { + "text": "But it happens to be true if p belongs to theta 0, which is strictly equivalent to p is equal to 0.5, right?" + }, + { + "text": "Theta 0 is really just this one point, 0.5." + }, + { + "text": "OK, so now this becomes true." + }, + { + "text": "And so what I need to do is to find c such that this guy is equal to what?" + }, + { + "text": "I mean, let's just follow, right?" + }, + { + "text": "So I want this to be less than alpha." + }, + { + "text": "But then we see that this was equal to this, which is equal to this." + }, + { + "text": "So all I want is that this guy is less than alpha." + }, + { + "text": "But we said we might as well just make it equal to alpha if you allow me to make it as big as I want, as long as it's less than alpha." + }, + { + "text": "So this is a true statement." + }, + { + "text": "But it's if under this condition, right?" + }, + { + "text": "So I'm going to set it equal to alpha." + }, + { + "text": "And then I'm going to try to solve for c. OK, so what I'm looking for is a c such that if I draw a standard Gaussian, so that's PDF of some n0,1, I want the probability that the absolute value of my Gaussian exceeding this guy." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk19.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..b610ab510e065f845cbac3e680352a281a5977db --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that means being either here or here." + }, + { + "text": "So that's minus c and c. I want the sum of those two things to be equal to alpha." + }, + { + "text": "So I want the sum of these areas to equal alpha." + }, + { + "text": "So by symmetry, each of them should be equal to alpha over 2." + }, + { + "text": "And so what I'm looking for is c such that the probability that my n0,1 exceeds c, which is just this area to the right now, equals alpha, which is equivalent to taking c, which is q equals alpha over 2." + }, + { + "text": "And that's q alpha over 2 by definition of q alpha over 2." + }, + { + "text": "That's just what q alpha over 2 is." + }, + { + "text": "And that's what the tables at the back of the book give you." + }, + { + "text": "Who has already seen a table for Gaussian probabilities?" + }, + { + "text": "All right." + }, + { + "text": "What it does is just a table." + }, + { + "text": "I mean, it's pretty ancient, right?" + }, + { + "text": "I mean, of course, you can actually ask Google to do it for you now." + }, + { + "text": "It's basically standard issue." + }, + { + "text": "But back in the day, they actually had to look at tables." + }, + { + "text": "And since the values alphas were pretty standard, the values alpha that people were requesting were typically 1%, 5%, 10%." + }, + { + "text": "All you could do is to compute these different values for different values of alpha." + }, + { + "text": "That was it." + }, + { + "text": "So that's really not much to give you." + }, + { + "text": "So for the Gaussian, I can tell you that alpha is equal to, if alpha is equal to 5%, then q alpha over 2, q 2.5% is equal to 1.96%." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk2.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..d35a9367292f43552ea9e2c936629f0062774757 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So psi is just the probability for theta that psi rejects, and that's defined for theta and theta 0." + }, + { + "text": "So for different values of theta 0, so h0 being correct means there exists a theta in theta 0 for which that actually is the right distribution." + }, + { + "text": "So for different values of theta, I might make different errors." + }, + { + "text": "So if you think, for example, about the coin example, if I'm testing if the coin is biased towards heads or biased towards tails, so if I'm testing whether p is larger than 1 half or less than 1 half, then when the true p, let's say h0 is larger than 1 half, when p is equal to 1, it's actually very difficult for me to make a mistake, because I only see heads." + }, + { + "text": "So when p is getting closer to 1 half, I'm going to start making more and more probability there." + }, + { + "text": "And so the type 2 error, so that's the probability of type 2, is denoted by beta psi." + }, + { + "text": "And it's the function that does the opposite, and this time is defined for theta and theta 0 and theta 1." + }, + { + "text": "And finally, we define something called the power pi of psi." + }, + { + "text": "And this time, this is actually a number." + }, + { + "text": "And so this number is equal to the maximum over theta and theta 0." + }, + { + "text": "I mean, that could be a supremum, but think of it as being a maximum of p theta of psi is equal, sorry, that's in 0." + }, + { + "text": "Give me one sec." + }, + { + "text": "No, that's the min." + }, + { + "text": "So this is not making a mistake." + }, + { + "text": "Theta 0 is in theta 1." + }, + { + "text": "So theta is in theta 1, and I conclude 1." + }, + { + "text": "So this is a good thing." + }, + { + "text": "I want this number to be large, and I'm looking at the worst house, what is the smallest value this number can be." + }, + { + "text": "So what I want to show you a little bit is a picture." + }, + { + "text": "So now I'm going to take theta, and think of it as being p. So I'm going to take p for some Bernoulli experiment." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk20.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..20ad1dac1f1c76cdb383bd9a41a5521bfc8e8f80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "So those are just fixed numbers that are functions of the Gaussian." + }, + { + "text": "All right, so everybody agrees?" + }, + { + "text": "We've done that before for our confidence intervals." + }, + { + "text": "And so now we know that if I actually plug in this guy to be q alpha over 2, then this limit is actually equal to alpha." + }, + { + "text": "And so now I've actually constrained this." + }, + { + "text": "So q alpha over 2 here is, for alpha equals 5%, as I said, is 1.96." + }, + { + "text": "So in the example 1, the number that we found was 3.54, I think, or something like that, 3.55 for t. So if we scroll back very quickly, 3.45." + }, + { + "text": "That was example 1." + }, + { + "text": "Example 2, negative 0.77." + }, + { + "text": "So if I look at t, n, in example 1, tn was just the absolute value of 3.45, which don't pull out your calculators, is equal to 3.45." + }, + { + "text": "Example 2, absolute value of negative 0.77 was equal to 0.77." + }, + { + "text": "And so all I need to check is, is this number larger or smaller than 1.96?" + }, + { + "text": "That's what my test ends up being." + }, + { + "text": "So in example 1, 3.45 being larger than 1.96, that means that I reject." + }, + { + "text": "Fairness of my coins in example 2, 0.77 being smaller than 1.96, what do I do?" + }, + { + "text": "I fail to reject." + }, + { + "text": "OK?" + }, + { + "text": "So here's a question." + }, + { + "text": "In example 1, for what level alpha would psi alpha, what is the?" + }, + { + "text": "So here, what's going to happen if I start decreasing my level?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk21.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..8a92eddc8e39673740ca195fad03c2d25a729273 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "When I decrease my level, I'm actually making this area smaller and smaller, which means that I push the c to the right." + }, + { + "text": "So now I'm asking, what is the smallest c I should pick so that now I actually do not reject h0?" + }, + { + "text": "What is the smallest c I should be taking?" + }, + { + "text": "Here." + }, + { + "text": "What is the smallest c?" + }, + { + "text": "So c here in the example I gave you for 5% was 1.96." + }, + { + "text": "What is the smallest c I should be taking so that now this inequality is reversed?" + }, + { + "text": "3.45." + }, + { + "text": "I ask only trivial questions." + }, + { + "text": "Don't be worried." + }, + { + "text": "So 3.45 is the smallest c that I'm actually willing to tolerate." + }, + { + "text": "So let's say this was my 5%." + }, + { + "text": "If this was 2.5, if alpha here, let's say in this picture, alpha is 5%, that means maybe I need to push here." + }, + { + "text": "And this number should be what?" + }, + { + "text": "So this is going to be 1.96." + }, + { + "text": "And this number here is going to be 3.45, clearly to scale." + }, + { + "text": "And so now what I want to ask you is, well, there's two ways I can understand this number 3.45." + }, + { + "text": "It is the number 3.45." + }, + { + "text": "But I can also try to understand, what is the area to the right of this guy?" + }, + { + "text": "And if I understand what the area to the right of this guy is, this is actually some alpha prime over 2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk22.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..7503edb72bbc4e9db22fe8e956729e7f3881d675 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "And that means that if I actually fix this level, alpha prime, that would be exactly the tipping point at which I would go from accepting to rejecting." + }, + { + "text": "So I know in terms of absolute thresholds, 3.45 is the trivial answer to the question." + }, + { + "text": "That's the tipping point, because I'm comparing a number to 3.45." + }, + { + "text": "But now if I try to map this back and understand what level would have been given me this particular tipping point, that's a number between 0 and 1." + }, + { + "text": "The smaller the number, the larger this number here, which means that the more evidence I have in my data against h0." + }, + { + "text": "And so this number is actually something called the p-value." + }, + { + "text": "And so same for example 2." + }, + { + "text": "There's the tipping point, alpha, at which I go from feeling to reject to rejecting." + }, + { + "text": "And that's exactly the number, the area under the curve, such that here I see 0.77." + }, + { + "text": "And this is this alpha prime prime over 2." + }, + { + "text": "And this number is clearly, alpha prime prime is clearly larger than 5%." + }, + { + "text": "So what's the advantage of thinking and mapping back these numbers?" + }, + { + "text": "Well, now I'm actually going to spit out some number which is between 0 and 1." + }, + { + "text": "And that should be the only scale you should have in mind." + }, + { + "text": "Remember we discussed that last time." + }, + { + "text": "Well, if I actually spit out a number which is 3.45, maybe you can try to think, is 3.45 a large number for a Gaussian?" + }, + { + "text": "That's a number." + }, + { + "text": "But if I had another random variable that was not Gaussian, maybe it was a double exponential, you would have to have another scale in your mind." + }, + { + "text": "Is 3.45 a large number for the large, so large that it's unlikely to come from a double exponential?" + }, + { + "text": "If I had a gamma distribution, I can think of any distribution." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk23.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..d0d0fdec57ad2cc7e2dadb707abb6df87bdbb70b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then that means for each distribution, you would have to have a scale in mind." + }, + { + "text": "So of course, you can have the Gaussian scale in mind." + }, + { + "text": "I mean, I have the Gaussian scale in mind." + }, + { + "text": "But then if I map it back into this number between 0 and 1, all the distributions play the same role." + }, + { + "text": "So whether I'm talking about if my limiting distribution is normal or exponential or gamma or whatever you want, for all these guys, I'm just going to map it into one number between 0 and 1." + }, + { + "text": "Small number means lots of evidence against h1." + }, + { + "text": "Large number means lots of evidence against h0." + }, + { + "text": "Small number means very few evidence against h0." + }, + { + "text": "And this is the only number you need to keep in mind." + }, + { + "text": "And the question is, am I willing to tolerate this number between 5%, 6% or maybe 10%, 12%?" + }, + { + "text": "And this is the only scale you have to have in mind." + }, + { + "text": "And this scale is the scale of p-values." + }, + { + "text": "So the p-value is the tipping point in terms of alpha." + }, + { + "text": "In words, I can make it formal, because tipping point, as far as I know, is not a mathematical term." + }, + { + "text": "So a p-value of a test is the smallest, potentially asymptotic level, if I talk about an asymptotic p-value." + }, + { + "text": "And that's what we do when we talk about central limit theorem, at which the test rejects h0." + }, + { + "text": "If I were to go any smaller, I would fail to reject." + }, + { + "text": "The smaller the level, the less likely it is for me to reject." + }, + { + "text": "And if I were to go any smaller, I would start failing to reject." + }, + { + "text": "And so it is a random number." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk24.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..70790440238c22e23b0b77fc5e658fdf89d62e44 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "It depends on what I actually observe." + }, + { + "text": "So here, of course, I instantiated those two numbers, 3.45 and 0.77, as realizations of random variables." + }, + { + "text": "But if you think of those as being the random numbers before I see my data, this was a random number." + }, + { + "text": "And therefore, the area under the curve to the right of it is also a random area." + }, + { + "text": "If this thing fluctuates, then the area under the curve fluctuates." + }, + { + "text": "And that's what the p-value is." + }, + { + "text": "That's what John Oliver talks about when he talks about p-hacking." + }, + { + "text": "And so we talked about this in the first lecture." + }, + { + "text": "So p-hacking is, how do I do?" + }, + { + "text": "Oh, if I'm a scientist, do I want to see a small p-value or a large p-value?" + }, + { + "text": "Small, right?" + }, + { + "text": "Scientists want to see small p-values, because small p-values equals rejecting, which equals discovery, which equals publication, which equals promotion." + }, + { + "text": "So that's what people want to see." + }, + { + "text": "So people are tempted to see small p-values." + }, + { + "text": "And what's called p-hacking is, well, find a way to cheat." + }, + { + "text": "Maybe look at your data, formulate your hypothesis in such a way that you will actually have a smaller p-value than you should have." + }, + { + "text": "So here, for example, there's one thing I did not insist on, because again, this is not a particular course in statistical thinking." + }, + { + "text": "But one thing that we implicitly did was set those theta 0 and theta 1 ahead of time." + }, + { + "text": "I fixed them, and I'm trying to test this." + }, + { + "text": "This is to be contrasted with the following approach." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk25.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..ae5989051a3c9ad74dd6e26eac906c8e26ce8535 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "I draw my data." + }, + { + "text": "So I draw." + }, + { + "text": "I run this experiment, which is probably going to get me a publication in Nature." + }, + { + "text": "I'm trying to test if a coin is fair." + }, + { + "text": "And I draw my data, and I see that there's 13 out of 30 of my observations that are heads." + }, + { + "text": "That means that from this data, it looks like p is less than 1 half." + }, + { + "text": "So if I look at this data and then decide that my alternative is not p not equal to 1 half, but rather p less than 1 half, that's p-hacking." + }, + { + "text": "I'm actually making my p-value strictly smaller by first looking at the data and then deciding what my alternative is going to be." + }, + { + "text": "And that's cheating, because all the things we did were assuming that this 0.5 or d alternative was actually a fix." + }, + { + "text": "Everything was deterministic." + }, + { + "text": "The only randomness came from the data." + }, + { + "text": "But if I start looking at the data and designing my experiment or my alternatives and null hypothesis based on the data, it's as if I started putting randomness all over the place." + }, + { + "text": "And then I cannot control it, because I don't know how it just intermingles with each other." + }, + { + "text": "All right." + }, + { + "text": "So that was for the John Oliver moment." + }, + { + "text": "So the p-value is nice." + }, + { + "text": "So maybe I mentioned that before." + }, + { + "text": "My wife works in market research." + }, + { + "text": "And maybe every two years, she seems to run into a statistician in the hallway." + }, + { + "text": "And she comes home and says, what is a p-value again?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk26.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..582b81ac1a78246b0f187a4c706af274ba689dbe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk26.json @@ -0,0 +1,62 @@ +[ + { + "text": "And for her, a p-value is just the number is in an Excel spreadsheet." + }, + { + "text": "And actually, small equals good and large equals bad." + }, + { + "text": "And that's all she needs to know at this point." + }, + { + "text": "Actually, they do the job for her." + }, + { + "text": "Small is green." + }, + { + "text": "Large is red." + }, + { + "text": "And so for her, a p-value is just green or red." + }, + { + "text": "But so what she's really implicitly doing with this color code is just applying the golden rule." + }, + { + "text": "What the statisticians do for her in the Excel spreadsheet is that they take the numbers for the p-values that are less than some fixed level." + }, + { + "text": "So depending on the field in which she works, so she works for pharmaceutical companies, so the p-values are typically compared." + }, + { + "text": "The tests are usually performed at level 1% rather than 5%." + }, + { + "text": "So 5% is maybe your gold standard if you're doing sociology or trying to, I don't know, release a new blueberry flavor for your toothpaste, like something that's not going to change the life of people." + }, + { + "text": "Maybe you're going to run at 5%." + }, + { + "text": "It's OK to make a mistake." + }, + { + "text": "People are just going to feel gross, but that's about it." + }, + { + "text": "Whereas here, if you have this p-value which is less than 1%, it might be more important for some drug discovery, for example." + }, + { + "text": "And so let's say you run at 1%." + }, + { + "text": "And so what they do in this Excel spreadsheet is that all the numbers that are below 1% show up in green, and all the numbers that are above 1% show up in red." + }, + { + "text": "And that's it." + }, + { + "text": "That's just applying the golden rule." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk27.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk27.json new file mode 100644 index 0000000000000000000000000000000000000000..6d2b3e73a1f2bfb3d007d43a22bc17095a5878f8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk27.json @@ -0,0 +1,62 @@ +[ + { + "text": "If the number is green, reject." + }, + { + "text": "If the number is red, fail to reject." + }, + { + "text": "OK?" + }, + { + "text": "Yeah?" + }, + { + "text": "So going back to the example of the previous prior example where you can achieve by looking at your data and then formulating, say, a theta 1 to be p less than 1%." + }, + { + "text": "Yeah." + }, + { + "text": "So how would you achieve your goal by changing the theta 1?" + }, + { + "text": "You mean by achieving my goal?" + }, + { + "text": "You mean letting ethics aside, right?" + }, + { + "text": "Yeah." + }, + { + "text": "You want to be published." + }, + { + "text": "So OK." + }, + { + "text": "So let me teach you how." + }, + { + "text": "Well, here, what do you do?" + }, + { + "text": "You want to, at the end of the day, a test is only telling you whether you found evidence in your data that H1 was more likely than H0, basically." + }, + { + "text": "How do you make H1 more likely?" + }, + { + "text": "Well, you just basically target H1 to be what the data is going to make it more likely to be." + }, + { + "text": "All right?" + }, + { + "text": "So if, for example, I say H1 can be on both sides, then my data is going to have to take into account fluctuations on both sides." + }, + { + "text": "And I'm going to lose a factor of 2 somewhere because things are not symmetric." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk28.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk28.json new file mode 100644 index 0000000000000000000000000000000000000000..b6a2e04f21d17d3f9d8f51277fef4b6bd544ea8c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk28.json @@ -0,0 +1,62 @@ +[ + { + "text": "Here is the ultimate way of making this work." + }, + { + "text": "I'm going back to my example of flipping coins." + }, + { + "text": "And now, so here, what I did is I said, oh, this number 0.43 is actually smaller than 0.5." + }, + { + "text": "So I'm just going to test whether I'm 0.5 or I'm less than 0.5." + }, + { + "text": "But here is something that I can promise you I did not make the computation will reject." + }, + { + "text": "OK, so here, this one actually, yeah, this one fails to reject, right?" + }, + { + "text": "So here is one that will certainly reject." + }, + { + "text": "H0 is 0.5. p is 0.5." + }, + { + "text": "H1, p is 0.43." + }, + { + "text": "OK?" + }, + { + "text": "Now, you can try." + }, + { + "text": "But I can promise you that your data will tell you that H1 is the right one." + }, + { + "text": "OK?" + }, + { + "text": "I mean, you can check very quickly that this is really extremely likely to happen, right?" + }, + { + "text": "And so actually, what am I?" + }, + { + "text": "No, actually, that's not true." + }, + { + "text": "OK. Because here, the test that I derive that's based on this kind of stuff, right?" + }, + { + "text": "Here, at some point, somewhere, under some layers, I assume that all our tests are going to have this form." + }, + { + "text": "But here, this is only when you're trying to test one region versus another region next to it, or one point versus a region around it, or something like this." + }, + { + "text": "Whereas for this guy, there's another test I could come up with, which is, what is the probability that I get 0.43?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk29.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk29.json new file mode 100644 index 0000000000000000000000000000000000000000..7c83fb4d5133113ff729308f195ed934ccaaacb9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk29.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what is the probability that I get 0.5?" + }, + { + "text": "Now, what I'm going to do is I'm going to just conclude it's whichever has the largest probability." + }, + { + "text": "Then maybe I'm going to have to make some adjustments so that the level is actually 5%." + }, + { + "text": "But I can make this happen." + }, + { + "text": "I can make the level be 5% and always conclude this guy, but I would have to use a different test." + }, + { + "text": "Now, the test that I described, again, those t and larger than c are built in to be tests that are sort of resilient to this kind of manipulations, because they're sort of oblivious towards what the alternative looks like." + }, + { + "text": "I mean, they're just saying it's either to the left or to the right, but whether it's a point or an entire half line doesn't matter." + }, + { + "text": "So if you try to look at your data and just put the data itself into your hypothesis testing problem, then you're failing the statistical principle." + }, + { + "text": "And that's what people are doing, right?" + }, + { + "text": "I mean, how can I check?" + }, + { + "text": "I mean, of course, here it's going to be pretty blatant if you publish a paper that looks like this." + }, + { + "text": "But there's ways to do it differently, right?" + }, + { + "text": "For example, one way to do it is to just do more." + }, + { + "text": "So typically, what people do is they do multiple hypothesis testing." + }, + { + "text": "They're doing 100 tests at a time." + }, + { + "text": "Then you have random fluctuations every time." + }, + { + "text": "And so they just pick the one that has the random fluctuations that go their way." + }, + { + "text": "I mean, sometimes it's going in your way, and sometimes it's going the opposite way." + }, + { + "text": "So you just pick the one that works for you." + }, + { + "text": "We'll talk about multiple hypothesis testing soon if you want to increase your publication counts." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk3.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..82298a0911f771c50c0c0e31234286bcbe2ed969 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "So p can range between 0 and 1, that's for sure." + }, + { + "text": "And what I'm going to try to test is whether p is less than 1 half or larger than 1 half." + }, + { + "text": "So this is going to be, let's say, theta 0, and this guy here is theta 1." + }, + { + "text": "Just trying to give you a picture of what those guys are." + }, + { + "text": "So I have my y-axis." + }, + { + "text": "Now I'm going to start drawing numbers, all these things, this function, this function, and this number are all numbers between 0 and 1." + }, + { + "text": "So now I'm claiming that when I move from left to right, what is my probability of rejecting going to do?" + }, + { + "text": "So what I'm going to plot is the probability under theta." + }, + { + "text": "The first thing I want to plot is the probability under theta that psi is equal to 1." + }, + { + "text": "And let's say psi, think of psi as being just this indicator that square root of n xn bar minus p over square root xn bar, 1 minus xn bar, is larger than some constant c for a properly chosen c. So what we choose is that c is in such a way that at 1 half, when we're testing for 1 half, what we wanted was this number to be equal to alpha, basically." + }, + { + "text": "So we fix this alpha number so that this guy, so if I want alpha of psi of theta less than alpha, given in advance, so think of it as being equal to, say, 5%." + }, + { + "text": "So I'm fixing this number, and I want this to be controlled for all theta and theta 0." + }, + { + "text": "So if you're going to give me this budget, well, I'm actually going to make it equal where I can." + }, + { + "text": "If you're telling me you can make it equal to alpha, we know that if I increase my type 1 error, I'm going to decrease my type 2 error." + }, + { + "text": "If I start putting everyone in jail, or if I start letting everyone go free, that's what we're discussing last time." + }, + { + "text": "So since we have this trade-off, and you're giving me a budget for one guy, I'm just going to max it out." + }, + { + "text": "And where am I going to max it out?" + }, + { + "text": "Exactly at 1 half at the boundary." + }, + { + "text": "So this is going to be 5%." + }, + { + "text": "So what I know is that since alpha of theta is less than alpha for all theta and theta 0, sorry, that's for theta 0, that's where alpha is defined." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk30.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk30.json new file mode 100644 index 0000000000000000000000000000000000000000..a8e80051fb683b419557b2b36ba8c95a3d50cf00 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk30.json @@ -0,0 +1,62 @@ +[ + { + "text": "There's actually papers." + }, + { + "text": "I think it was big news, there's some papers, I think it's psychology or psychometrics papers, that actually refuse to publish p-values now." + }, + { + "text": "All right, where were we?" + }, + { + "text": "OK, here's the golden rule." + }, + { + "text": "So one thing that I'd like to show is this thing, just so you know how you apply the golden rule and how you apply the standard test." + }, + { + "text": "So the standard paradigm is the following." + }, + { + "text": "You have a black box, which is your test." + }, + { + "text": "For my wife, this is the fourth floor of the building." + }, + { + "text": "That's where the statisticians sit." + }, + { + "text": "What she sends there is data, let's say x1, xn." + }, + { + "text": "And she says, well, this one is about toothpaste, so here's a level." + }, + { + "text": "Let's say 5%." + }, + { + "text": "What the fourth floor brings back is an answer, yes, no." + }, + { + "text": "Green, red, just an answer." + }, + { + "text": "So that's the standard testing." + }, + { + "text": "You just feed it the data and the level at which you want to perform the test, maybe asymptotic, and it spits out a yes, no answer." + }, + { + "text": "What p-value does, you just feed it the data itself." + }, + { + "text": "And what it spits out is the p-value." + }, + { + "text": "And now, it's just up to you." + }, + { + "text": "I mean, hopefully, your brain has the computational power of deciding whether a number is larger or smaller than 5% without having to call the statisticians for this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk31.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk31.json new file mode 100644 index 0000000000000000000000000000000000000000..9fb2296acde7c40202805ca4f7e73e4c07f68e6a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk31.json @@ -0,0 +1,62 @@ +[ + { + "text": "And that's what it does." + }, + { + "text": "So now, we're all on one scale." + }, + { + "text": "Now, if you actually, I see some of you nodding when I talk about p-hacking." + }, + { + "text": "So that means you've seen p-values." + }, + { + "text": "If you've seen more than 100 p-values in your life, you have an entire scale." + }, + { + "text": "A good p-value is less than 10 to the minus 4." + }, + { + "text": "That's the ultimate sweet spot." + }, + { + "text": "Actually, statistical software spit out an output which says less than 10 to the minus 4." + }, + { + "text": "But then, maybe you want a p-value." + }, + { + "text": "If I tell you my p-value was 4.65, then I will say you've been doing some p-hacking until you found a number that was below 5%." + }, + { + "text": "That's typically what people will do." + }, + { + "text": "But if you're doing the test, if you're saying, I published my result." + }, + { + "text": "My test at 5% said yes, that means that maybe your p-value was 4.99, or your p-value was 10 to the minus 4." + }, + { + "text": "I will never know." + }, + { + "text": "I will never know how much evidence you had against the null." + }, + { + "text": "But if you tell me what the p-value is, I can make my own decision." + }, + { + "text": "I don't have to tell me whether it's a yes." + }, + { + "text": "No, you tell me it's 4.99." + }, + { + "text": "I'm going to say, well, maybe yes, but I'm going to take it with a grain of salt." + }, + { + "text": "And so that's why p-values are good numbers to have in mind." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk32.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk32.json new file mode 100644 index 0000000000000000000000000000000000000000..96ed5fb80473cde620f1dcbaecbdda179310c37c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk32.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, I show it as if it was an old trick that you start mastering when you're 45 years old." + }, + { + "text": "No, it's just how small is the number between 0 and 1." + }, + { + "text": "That's really what you need to know." + }, + { + "text": "Maybe on the log scale, if it's 10 to the minus 1, 10 to the minus 2, 10 to the minus 3, et cetera, that's probably the extent of the mastery here." + }, + { + "text": "So this traditional standard paradigm that I showed is actually commonly referred to as the Neyman-Pearson paradigm." + }, + { + "text": "So here it says Neyman-Pearson's theory." + }, + { + "text": "So there's an entire theory that comes with it, but it's really a paradigm." + }, + { + "text": "It's a way of thinking about hypothesis testing that says, well, if I'm not going to be able to optimize both my type 1 and type 2 error, I'm actually going to lock in my type 1 error below some level and just minimize the type 2 error under this constraint." + }, + { + "text": "That's what the Neyman-Pearson paradigm is." + }, + { + "text": "And it sort of makes sense for hypothesis testing problems." + }, + { + "text": "If you were doing some other applications with multi-objective optimization, you would maybe come up with something different." + }, + { + "text": "For example, machine learning is not performing typically under Neyman-Pearson paradigm." + }, + { + "text": "So if you do spam filtering, you could say, well, I want to constrain the probability as much as I can of taking somebody's important emails and throwing them out as spam and, under this constraint, not send too much spam to that person." + }, + { + "text": "That sort of makes sense for spams." + }, + { + "text": "Now, if you're labeling cats versus dogs, it's probably not like you want to make sure that no more than 5% of the dogs are labeled cat." + }, + { + "text": "Because it doesn't matter." + }, + { + "text": "So what you typically do is you just sum up the two types of error you can make, and you minimize the sum without putting any more weight on one or the other." + }, + { + "text": "So here's an example where doing a binary decision, one or two of the errors you can make, you don't have to actually be like that." + }, + { + "text": "So this example here, I did not." + }, + { + "text": "The trivial test, psi is equal to 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk33.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk33.json new file mode 100644 index 0000000000000000000000000000000000000000..0c2da6bcc636025ed6d047d161fdfe68e3b68329 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk33.json @@ -0,0 +1,62 @@ +[ + { + "text": "What was it in the US trial court example?" + }, + { + "text": "What is psi equal to 0?" + }, + { + "text": "I was concluding all ways to the null." + }, + { + "text": "What was the null?" + }, + { + "text": "Innocent, right?" + }, + { + "text": "That's the status quo." + }, + { + "text": "So that means that this guy never rejects a 0." + }, + { + "text": "Everybody's going away free." + }, + { + "text": "So you're sure you're not actually going against the Constitution because alpha is 0%, which is certainly less than 5%." + }, + { + "text": "But the power, the fact that a lot of criminals go back outside in the free world is actually formulated in terms of low power, which in this case is actually 0." + }, + { + "text": "Again, the power is a number between 0 and 1." + }, + { + "text": "Close to 0, good." + }, + { + "text": "Close to 1, bad." + }, + { + "text": "Now, what is the definition of the p-value?" + }, + { + "text": "That's going to be something." + }, + { + "text": "Mouthful, right?" + }, + { + "text": "The definition of the p-value is a mouthful." + }, + { + "text": "It's really the tipping point." + }, + { + "text": "It is the smallest level at which blah, blah, blah, blah." + }, + { + "text": "It's complicated to remember it." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk34.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk34.json new file mode 100644 index 0000000000000000000000000000000000000000..074297c2186646a83b698c991607273c1d143e1c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk34.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, I think that by my sixth explanation, my wife, after saying, oh, so it's the probability of making an error, I said, yeah, that's the probability of making an error." + }, + { + "text": "Because of course, she can think probability of making an error, small, good, large, bad." + }, + { + "text": "So that's actually a good way to remember." + }, + { + "text": "I'm pretty sure that at least 50% of people using p-values out there think that the p-value is the probability of making an error." + }, + { + "text": "Now, for all matters of purposes, if your goal is to just threshold the p-value, this is OK to have this in mind." + }, + { + "text": "But when it comes, at least until December 22, I would recommend trying to actually memorize the right definition for the p-value." + }, + { + "text": "OK?" + }, + { + "text": "OK." + }, + { + "text": "So the idea, again, is fix the level and try to optimize the power." + }, + { + "text": "So we're going to try to compute some p-values from now on." + }, + { + "text": "How do you compute the p-value?" + }, + { + "text": "Well, you can actually see it from this picture over there." + }, + { + "text": "One thing I didn't show on this picture, here was my q alpha over 2 that had alpha here, alpha over 2 here, right?" + }, + { + "text": "That was my q alpha over 2." + }, + { + "text": "And I said, if tn is to the right of this guy, I'm going to reject." + }, + { + "text": "If tn is to the left of this guy, I'm going to fail to reject." + }, + { + "text": "OK?" + }, + { + "text": "Pictorially, you can actually represent the p-value." + }, + { + "text": "It's when I replace this guy by tn itself." + }, + { + "text": "Sorry, that's p-value over 2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk35.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk35.json new file mode 100644 index 0000000000000000000000000000000000000000..9f1a7b89f2d43b53944bbf516e37f98c7cf70618 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk35.json @@ -0,0 +1,62 @@ +[ + { + "text": "No, actually, that's p-value." + }, + { + "text": "So let me just keep it like that and put the absolute value here." + }, + { + "text": "OK?" + }, + { + "text": "So if you replace the role of q alpha over 2 by your test statistic, this is what the area under the curve is actually the p-value itself up to scaling, because of the symmetric thing." + }, + { + "text": "OK?" + }, + { + "text": "So there's a good way to see pictorially what the p-value is." + }, + { + "text": "It's just the probability that some Gaussians, which is the probability that some absolute value of n0,1 exceeds tn." + }, + { + "text": "Right?" + }, + { + "text": "That's what the p-value is." + }, + { + "text": "Now, this guy has nothing to do with this guy." + }, + { + "text": "So this is really just 1 minus the Gaussian CDF of tn." + }, + { + "text": "And that's it." + }, + { + "text": "So that's how I would compute p-values." + }, + { + "text": "Now, as I said, the p-value is a beauty, because you don't have to understand the fact that your limiting distribution is a Gaussian." + }, + { + "text": "Right?" + }, + { + "text": "It's already factored in this construction." + }, + { + "text": "The fact that I'm actually looking at this cumulative distribution function of a standard Gaussian makes my p-value automatically adjust to what the limiting distribution is." + }, + { + "text": "And if this was the cumulative distribution function of a exponential, I would just have a different function here denoted by f, for example." + }, + { + "text": "And I would just compute a different value." + }, + { + "text": "But in the end, regardless of what the limiting value is, my p-value would still be a number between 0 and 1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk36.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk36.json new file mode 100644 index 0000000000000000000000000000000000000000..2d4547dd85e8e54b4a9640f590a534ed56d0306a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk36.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so to illustrate that, let's look at other weird distributions that we could get in place of the standard Gaussian." + }, + { + "text": "And we're not going to see many, but we'll see one." + }, + { + "text": "And it's not called the chi-squared distribution." + }, + { + "text": "It's actually called the student's distribution, but it involves the chi-squared distribution as a building block." + }, + { + "text": "So I don't know if my phonetics are not really right there, so I try to say, well, it's chi-squared." + }, + { + "text": "Maybe it's chi-squared in Canada." + }, + { + "text": "Who knows?" + }, + { + "text": "So for a positive integer, so there's only one parameter." + }, + { + "text": "So for the Gaussian, you have two parameters, which are mu and sigma squared." + }, + { + "text": "Those are real numbers." + }, + { + "text": "Sigma squared is positive." + }, + { + "text": "Here, I have one integer parameter." + }, + { + "text": "Then the distribution, the chi-squared distribution with d degrees of freedom." + }, + { + "text": "So the parameter is called a degree of freedom, just like mu is called the expected value, and sigma squared is called the variance." + }, + { + "text": "So it's called degrees of freedom." + }, + { + "text": "You don't have to really understand why." + }, + { + "text": "So that's the law that you would get." + }, + { + "text": "That's the random variable you would get if you were to sum d squares of independent standard Gaussians." + }, + { + "text": "So I take the square of an independent random Gaussian." + }, + { + "text": "I take another one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk37.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk37.json new file mode 100644 index 0000000000000000000000000000000000000000..6fa169cd52b7910e64c667064ab385a1dc476da0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk37.json @@ -0,0 +1,62 @@ +[ + { + "text": "I sum them, and that's a chi-squared with two degrees of freedom." + }, + { + "text": "That's how you get it." + }, + { + "text": "Now, I could define it using its probability density function." + }, + { + "text": "After all, this is the sum of positive random variables." + }, + { + "text": "It is a positive random variable." + }, + { + "text": "It has a density on the positive real line." + }, + { + "text": "And the PDF of chi-squared, PDF of chi-squared with d degrees of freedom is what?" + }, + { + "text": "Well, it's fd of x is x to the d over 2 minus 1, e to the minus x over 2." + }, + { + "text": "And then here, I have a gamma of d over 2, and the other one is, I think, 2 to the d over 2 minus 1." + }, + { + "text": "No, 2 to the d over 2." + }, + { + "text": "That's what it is." + }, + { + "text": "That's the density." + }, + { + "text": "If you are very good at probability, you can make the change of variable and write your Jacobian and do all this stuff and actually check that this is true." + }, + { + "text": "I do not recommend doing that." + }, + { + "text": "So this is the density, but it's better understood like that, at thinking of just something that you built from standard Gaussian." + }, + { + "text": "So for example, an example of a chi-squared with two degrees of freedom is actually the following thing." + }, + { + "text": "Let's assume I have a target like this." + }, + { + "text": "And I don't aim very well, and I'm trying to hit the center." + }, + { + "text": "And I'm going to have maybe a deviation, which is standard Gaussian left-right and standard Gaussian north-south." + }, + { + "text": "So I'm throwing, and then I'm here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk38.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk38.json new file mode 100644 index 0000000000000000000000000000000000000000..e9321d18ef5daa35196a20db9f6bb7680045ede5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk38.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'm claiming that this number here, by Pythagoras' theorem, the squared distance here is the sum of this squared distance here, which is the square of a Gaussian by assumption, plus the square of this distance, which is the square of another independent Gaussian." + }, + { + "text": "I assume those are independent." + }, + { + "text": "And so the squared distance from this point to this point is the chi-squared with two degrees of freedom." + }, + { + "text": "So this guy here is n01 squared." + }, + { + "text": "This is n01 squared." + }, + { + "text": "And so this guy here, this distance here, is chi-squared with two degrees of freedom." + }, + { + "text": "I mean, the squared distance." + }, + { + "text": "I'm talking about squared distances here." + }, + { + "text": "So now you can see that actually Pythagoras is basically why chi-squared arise." + }, + { + "text": "That's why it has its own name." + }, + { + "text": "I mean, I could define this random variable." + }, + { + "text": "I mean, it's actually a gamma distribution." + }, + { + "text": "It's a special case of something called the gamma distribution." + }, + { + "text": "The fact that the special case has its own name is because there's many times where we're going to take sum of squares of independent Gaussians, because Gaussians, the sum of squares is really the norm, the Euclidean norm squared, just by Pythagoras theorem." + }, + { + "text": "If I'm in higher dimension, I can start to sum more squared coordinates, and I'm going to measure the norm squared." + }, + { + "text": "So if you want to draw this picture, it looks like this." + }, + { + "text": "Again, it's the sum of positive numbers." + }, + { + "text": "So it's going to be on 0 plus infinity." + }, + { + "text": "That's fd." + }, + { + "text": "And so for f1 looks like this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk39.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk39.json new file mode 100644 index 0000000000000000000000000000000000000000..530fa0ac2ba5f7380bf835d6fd19c3b55d8a53a3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk39.json @@ -0,0 +1,62 @@ +[ + { + "text": "f2 looks like this." + }, + { + "text": "So the tails becomes heavier and heavier as d increases." + }, + { + "text": "And then at start to 3, it starts to have a different shape." + }, + { + "text": "It starts from 0, and it looks like this." + }, + { + "text": "And then as d increases, it's basically as if you were to push this thing to the right." + }, + { + "text": "It's just like, pfft." + }, + { + "text": "It's just falling like a big ball." + }, + { + "text": "Everybody sees what's going on?" + }, + { + "text": "So there's just this fat thing that's just going there." + }, + { + "text": "What is the expected value of a k squared?" + }, + { + "text": "So it's the expected value of the sum of Gaussian random variables squared." + }, + { + "text": "I don't know why I said that." + }, + { + "text": "AUDIENCE 2 It's the sum of their second norm, right?" + }, + { + "text": "Which is?" + }, + { + "text": "Those are n0, 1." + }, + { + "text": "It's like, oh, I see, 1." + }, + { + "text": "Yeah." + }, + { + "text": "So n times 1, or d times 1." + }, + { + "text": "Yeah, which is d. So one thing you can check quickly is that the expected value of a k squared is d. And so you see, that's why the mass is shifting to the right as d increases." + }, + { + "text": "It's just going there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk4.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..07e0b7e52902074c6ec8439999a1046b4b977809 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "So for theta and theta 0, I know that my function is going to look like this." + }, + { + "text": "It's going to be somewhere in this rectangle." + }, + { + "text": "Everybody agrees?" + }, + { + "text": "So this function for this guy is going to look like this." + }, + { + "text": "When I'm at 0, when p is equal to 0, which means I only observe 0's, then I know that p is going to be 0." + }, + { + "text": "And I will certainly not conclude that p is equal to 1." + }, + { + "text": "This test will never conclude that p is equal to 1." + }, + { + "text": "Sorry, that was, yeah." + }, + { + "text": "That p is equal to, that p is lower than 1 half, just because xn bar is going to be equal to 0." + }, + { + "text": "OK, well, this is actually not well-defined." + }, + { + "text": "So maybe I need to do something, put it equal to 0 if xn bar is equal to 0." + }, + { + "text": "So I guess basically I get something which is negative." + }, + { + "text": "And so it's never going to be larger than what I want." + }, + { + "text": "And so here I'm actually starting at 0." + }, + { + "text": "So now this is this function here that increases." + }, + { + "text": "I mean, it should increase smoothly." + }, + { + "text": "This function here is alpha psi of theta, or alpha psi of p, let's say, because we're talking about p. Then it reaches alpha here." + }, + { + "text": "Now when I go on the other side, I'm actually looking at beta." + }, + { + "text": "When I'm on theta 1, the function that matters is the probability of type 2 error, which is beta psi." + }, + { + "text": "And this beta psi is actually going to increase." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk40.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk40.json new file mode 100644 index 0000000000000000000000000000000000000000..cf303c16babeea5b89d0924caa36f4dde58e6495 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk40.json @@ -0,0 +1,62 @@ +[ + { + "text": "Actually, the variance is also increasing." + }, + { + "text": "The variance is 2d." + }, + { + "text": "So this is one thing." + }, + { + "text": "And so why do we care about this in basic statistics?" + }, + { + "text": "It's not like we actually have statistics much about throwing darts at high dimensional boards." + }, + { + "text": "So what's happening is that if I look at the sample variance, the average of the sum of squared centered by their mean, then I can actually expend this as the sum of the squares minus the average squared." + }, + { + "text": "It's just the same trick that we have for the variance." + }, + { + "text": "Second moment minus first moment squared." + }, + { + "text": "And then I claim that Cochran's theorem, I will tell you in a second what Cochran's theorem tells me, is that this sample variance is actually, so if I had only this, so now, OK, look at those guys." + }, + { + "text": "Those guys are Gaussian with mean mu and variance sigma squared." + }, + { + "text": "Think for one second, mu being 0 and sigma squared being 1." + }, + { + "text": "Now, this part would be a chi-square with n degrees of freedom divided by n. Now, I get another thing here, which is the square of something that looks like a Gaussian as well." + }, + { + "text": "So it looks like I have something else here, which looks also like a chi-square." + }, + { + "text": "Now, Cochran's theorem is essentially telling you that those things are independent." + }, + { + "text": "And so that in a way, you can think of those guys as being here n degrees of freedom minus 1 degree of freedom." + }, + { + "text": "Now, here, as I said, this is not mean 0 and variance 1." + }, + { + "text": "The fact that it's not mean 0 is not a problem, because I can remove the mean here and remove the mean here." + }, + { + "text": "And so this thing has the same distribution, regardless of what the actual mean is." + }, + { + "text": "So without loss of generality, I can assume that mu is equal 0." + }, + { + "text": "Now, the variance I'm going to have to pay, because if I multiply all these numbers by 10, then this Sn is going to be multiplied by 100." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk41.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk41.json new file mode 100644 index 0000000000000000000000000000000000000000..be699853a1170afd439414bc8f189e87e84b0b94 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk41.json @@ -0,0 +1,62 @@ +[ + { + "text": "So this thing is going to scale with the variance." + }, + { + "text": "And not surprisingly, it's scaling like the square of the variance." + }, + { + "text": "So if I look at Sn, it's distributed as sigma-square times the chi-square with n minus 1 degrees of freedom divided by n. And we don't really write that, because a chi-square times sigma-square divided by n is not a distribution." + }, + { + "text": "So we put everything to the left." + }, + { + "text": "And we say that this is actually a chi-square with n minus 1 degrees of freedom." + }, + { + "text": "So here, I'm actually dropping a fact on you." + }, + { + "text": "But you can sort of see the building block." + }, + { + "text": "What is the thing that's sort of fussy at this point, but the rest should be crystal clear to you?" + }, + { + "text": "The thing that's fussy is that removing this square guy here is actually removing 1 degree of freedom." + }, + { + "text": "That should be weird." + }, + { + "text": "But that's what Cochran's theorem tells me." + }, + { + "text": "It's essentially stating something about orthogonality of subspaces with the span of the constant vector, something like that." + }, + { + "text": "So you don't have to think about it too much." + }, + { + "text": "But that's what it's telling me." + }, + { + "text": "But the rest, if you plug in, so the scaling in sigma-squared and in n, that should be completely clear to you." + }, + { + "text": "So in particular, if I remove that part, it should be clear to you that this thing, if mean is 0, this thing is actually distributed." + }, + { + "text": "Well, if mu is 0, what is the distribution of this guy?" + }, + { + "text": "So I remove that part, just this part." + }, + { + "text": "So I have xi, which are n0 sigma-squared." + }, + { + "text": "And I'm asking, what is the distribution of 1 over n sum from i equal 1 to n of xi-squared?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk42.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk42.json new file mode 100644 index 0000000000000000000000000000000000000000..3596e452514719b86b744b50b7402e7dd02b9ace --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk42.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it is the sum of their iid." + }, + { + "text": "So it's the sum of independent Gaussians, but not standard." + }, + { + "text": "So the first thing to make them standard is that I divide all of them by sigma-squared." + }, + { + "text": "Now, this guy is of the form zi-squared, where zi is n0, 1." + }, + { + "text": "So now this thing here has what distribution?" + }, + { + "text": "Chi-squared n. And now sigma-squared over n times chi-squared n. So if I have sigma-squared divided by n times chi-squared, sorry, so n times n divided by sigma-squared." + }, + { + "text": "So if I take this thing and I multiply it by n divided by sigma-squared, it means I remove this term." + }, + { + "text": "And now I am left with a chi-squared with n degrees of freedom." + }, + { + "text": "Now, the effect of centering with the sample mean here is only to lose 1 degree of freedom." + }, + { + "text": "That's it." + }, + { + "text": "OK?" + }, + { + "text": "So if I want to do a test about variance, since this is supposedly a good estimator of variance, this could be my pivotal distribution." + }, + { + "text": "This could play the role of a Gaussian." + }, + { + "text": "If I want to know if my variance is equal to 1 or larger than 1, I could actually build a test based on this only statement and test if the variance is larger than 1 or not." + }, + { + "text": "Now, this is not asymptotic because I started with the very assumption that my data was Gaussian itself." + }, + { + "text": "OK?" + }, + { + "text": "Now, just a side remark, you can check that this chi-squared 2, 2 is an exponential with half degrees of freedom, which is certainly not clear from the fact that z1 squared plus z2 squared is a chi-squared with 2 degrees of freedom." + }, + { + "text": "If I give you the sum of the square of two independent Gaussians, this is actually an exponential." + }, + { + "text": "That's not super clear, right?" + }, + { + "text": "But if you look at what was here, I don't know if you took notes, but let me rewrite it for you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk43.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk43.json new file mode 100644 index 0000000000000000000000000000000000000000..c1c4ce2a1e88dbaf6e313e0235a0fa58a881a709 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk43.json @@ -0,0 +1,59 @@ +[ + { + "text": "So it was x to the d over 2 minus 1 e to the minus x over 2 divided by 2 to the d over 2 gamma of d over 2." + }, + { + "text": "So if I plug in d is equal to 2, gamma of 2 over 2 is gamma of 1, which is 1, right?" + }, + { + "text": "It's factorial of 0." + }, + { + "text": "So it's 1." + }, + { + "text": "So this guy goes away." + }, + { + "text": "2 to the d over 2 is 2 to the 1." + }, + { + "text": "So that's just 1." + }, + { + "text": "No, that's just 2." + }, + { + "text": "OK?" + }, + { + "text": "Then x to the d over 2 minus 1 is x to the 0, goes away." + }, + { + "text": "And so I have x minus x over 2, 1 half, which is really, indeed, of the form lambda e to the minus lambda x for lambda is equal to 1 half, which was our exponential distribution." + }, + { + "text": "OK?" + }, + { + "text": "So well, next week is Columbus Day." + }, + { + "text": "So that's next Monday." + }, + { + "text": "So next week, we'll talk about students' distribution." + }, + { + "text": "And so that was discovered by a guy who pretended his name was student but was not student." + }, + { + "text": "And I challenge you to find why in the meantime." + }, + { + "text": "All right, so I'll see you next week." + }, + { + "text": "Your homework is going to be outside, so we can release the room." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk5.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..89ec03ee891688f8ef72df5ae36dcaada4844313 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "So beta psi is what?" + }, + { + "text": "Well, beta psi should also, sorry, that's the probability of being equal to alpha." + }, + { + "text": "So what I'm going to do is I'm going to look at the probability of rejecting." + }, + { + "text": "So let me draw this function all the way." + }, + { + "text": "It's going to look like this." + }, + { + "text": "Now here, if I look at this function here or here, this is the probability under theta that psi is equal to 1." + }, + { + "text": "And we just said that in this region, this function is called alpha psi." + }, + { + "text": "In that region, it's not called alpha psi." + }, + { + "text": "It's not called anything." + }, + { + "text": "It's just the probability of rejection." + }, + { + "text": "So it's not an error." + }, + { + "text": "It's actually what you should be doing." + }, + { + "text": "What we're looking at in this region is 1 minus this guy." + }, + { + "text": "We're looking at the probability of not rejecting." + }, + { + "text": "So I need to actually basically look at 1 minus this thing, which here is going to be 95%." + }, + { + "text": "So I'm going to do 95%." + }, + { + "text": "And this is my probability." + }, + { + "text": "And I'm just basically drawing the symmetric of this guy." + }, + { + "text": "So this here is the probability under theta that psi is equal to 0, which is 1 minus p theta that psi is equal to 1." + }, + { + "text": "So it's just 1 minus the white curve." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk6.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..2ba3f3f31acb2d89e2bd57110d90b292f5959fce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's actually, by definition, equal to beta psi of theta." + }, + { + "text": "Now, where do I read pi psi?" + }, + { + "text": "What is pi psi on this picture?" + }, + { + "text": "Is pi psi a number or a function?" + }, + { + "text": "It's a number, right?" + }, + { + "text": "It's the minimum of a function." + }, + { + "text": "What is this function?" + }, + { + "text": "It's the probability under theta that theta is equal to 1." + }, + { + "text": "I drew this entire function between theta 0 and theta 1." + }, + { + "text": "I drew this entire white curve." + }, + { + "text": "This is this probability." + }, + { + "text": "Now, I'm saying, look at the smallest value this probability can take on the set theta 1." + }, + { + "text": "What is this?" + }, + { + "text": "This guy." + }, + { + "text": "This is where my pi, this thing here, is pi psi." + }, + { + "text": "And so it's equal to 5%." + }, + { + "text": "So that's for this particular test, because this test is sort of a continuous curve for this psi." + }, + { + "text": "And so if I want to make sure that I'm at 5% when I come to the right of theta 0, if it touches theta 1, then I better have 5% on the other side if the function is continuous." + }, + { + "text": "So basically, if this function is increasing, which will be the case for most tests, then what's going to happen is that, and continuous, then what's going to happen is that the level of the test, which is alpha, is actually going to be equal to the power of the test." + }, + { + "text": "OK?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk7.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..4f5cdee6b6891b45c5f7794aece5ce2b8c13dc7a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, there's something I didn't mention, and I'm just mentioning it, pass it by." + }, + { + "text": "Here, I define the power itself." + }, + { + "text": "This function, this entire white curve here, is actually called the power function." + }, + { + "text": "This thing, that's the entire white curve." + }, + { + "text": "And what you could have is tests that have the entire curve, which is dominated by another test." + }, + { + "text": "So here, if I look at this test, and let's assume I can build another test that has this curve." + }, + { + "text": "Let's say it's the same here." + }, + { + "text": "But then here, it looks like this." + }, + { + "text": "What is the power of this test?" + }, + { + "text": "It's the same." + }, + { + "text": "It's 5%, because this point touches here exactly at the same point." + }, + { + "text": "However, for any other value than the worst possible, this guy is doing better than this guy." + }, + { + "text": "Can you see that?" + }, + { + "text": "Having a curve higher on the right-hand side is a good thing, because it means that you tend to reject more when you're actually in H1." + }, + { + "text": "So this guy is definitely better than this guy." + }, + { + "text": "And so what we say in this case is that the test with the dashed line is uniformly more powerful than the other test." + }, + { + "text": "But we're not going to go into those details, because basically, all the tests that we will describe are already the most powerful ones." + }, + { + "text": "In particular, this guy is, there's no such thing." + }, + { + "text": "All the other guys you can come up with are going to actually be below." + }, + { + "text": "So we saw a couple tests, and we saw how to pick this threshold, and we defined those two things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk8.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8b9449415f7337b53908d8098f0293899e0ba86e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "Yes?" + }, + { + "text": "AUDIENCE 2 But in that case, the down one, if it were also higher in the region of 2 to 0, do you still consider it better?" + }, + { + "text": "PHILIPPE RIGOLLETTIS Because you're given this budget of 5%, right?" + }, + { + "text": "So in this paradigm, where you're given the, actually, if the dashed line was this dashed line, I would still be happy." + }, + { + "text": "I mean, I don't care what this thing does here, as long as it's below 5%." + }, + { + "text": "But here, I'm going to try to discover it, right?" + }, + { + "text": "Think about, again, the drug discovery example." + }, + { + "text": "You're trying to find, let's say you're a scientist, and you're trying to prove that your drug works." + }, + { + "text": "What do you want to see?" + }, + { + "text": "Well, FDA puts on you this constraint that your probability of type 1 error should never exceed 5%." + }, + { + "text": "You're going to work under this assumption." + }, + { + "text": "But what you're going to do is going to try to find a test that will make you find something as often as possible." + }, + { + "text": "And so you're going to max this constraint of 5%, and then you're going to try to make this curve, this curve that means that this is basically, this number here, for any point here, is the probability that you publish your paper." + }, + { + "text": "That's the probability that you can release to market your drug." + }, + { + "text": "That's the probability that it works, right?" + }, + { + "text": "And so you want this curve to be as high as possible." + }, + { + "text": "You want to make sure that if there's evidence in the data that H1 is the truth, you want to squeeze as much of this evidence as possible." + }, + { + "text": "And the test that has the highest possible curve is the most powerful one." + }, + { + "text": "Now, you have to also understand that having two curves that are on top of each other, completely, everywhere, is a rare phenomenon." + }, + { + "text": "It's not always the case that there is a test that's uniformly more powerful than any other test." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk9.json b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bbad3ae05fbb39d9ef76b7b89aa0fada7d5adc3e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/4HRhg4eUiMo_5_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It might be that you have some trade-off, that it might be better here, but then you're losing power here." + }, + { + "text": "Things like this." + }, + { + "text": "Well, actually, maybe it should not go down." + }, + { + "text": "But let's say it goes like this, and then maybe this guy goes like this." + }, + { + "text": "Then you have to basically make an educated guess whether you think that the theta you're going to find is here or it's here." + }, + { + "text": "And then you pick a test." + }, + { + "text": "OK?" + }, + { + "text": "Any other question?" + }, + { + "text": "Yes?" + }, + { + "text": "AUDIENCE 2." + }, + { + "text": "What is the derivative of the type 2 error?" + }, + { + "text": "PHILIPPE RIGOLLET." + }, + { + "text": "So the green curve is exactly right." + }, + { + "text": "So that's beta psi of theta." + }, + { + "text": "So it's really the type 2 error, and it's defined only here." + }, + { + "text": "So here, it's not a definition." + }, + { + "text": "It's really just I'm just mapping it to this point." + }, + { + "text": "So it's defined only here, and it's the probability of type 2 error." + }, + { + "text": "So here, it's pretty large, right?" + }, + { + "text": "I'm making it basically as large as I could, because I'm at the boundary." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_10_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_11_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_14_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_15_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_16_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_17_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_20_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_21_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_22_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_24_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_26_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_27_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_28_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_29_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_2_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_30_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_31_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_32_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_33_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_36_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_38_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_3_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_42_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_43_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_47_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_48_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_49_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_52_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_55_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_58_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_5_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_60_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_63_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_64_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_65_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_66_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_67_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_6_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_70_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_72_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_73_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_74_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_75_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_76_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_77_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_78_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_79_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_80_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_82_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_83_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_84_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk0.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d168c54e8211f4c66cabb0c81bf4c018d35ffeee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So again, welcome to 18.01." + }, + { + "text": "We're getting started today with what we're calling Unit 1, highly imaginative topic, highly imaginative title." + }, + { + "text": "And it's differentiation." + }, + { + "text": "So let me first tell you briefly what's in store in the next couple of weeks." + }, + { + "text": "The main topic today is what is a derivative." + }, + { + "text": "And we're going to look at this from several different points of view." + }, + { + "text": "And the first one is the geometric interpretation." + }, + { + "text": "And that's what we'll spend most of today on." + }, + { + "text": "And then we'll also talk about a physical interpretation of what a derivative is." + }, + { + "text": "And then there's going to be something else, which I guess is maybe the reason why calculus is so fundamental and why we always start with it in most science and engineering schools, which is the importance of derivatives, of this, to all measurements." + }, + { + "text": "So that means pretty much every place." + }, + { + "text": "That means in science, in engineering, in economics, in political science, etc." + }, + { + "text": "Polling, lots of commercial applications." + }, + { + "text": "Just about everything." + }, + { + "text": "Now, so that's what we'll be getting started with." + }, + { + "text": "And then there's another thing that we're going to do in this unit." + }, + { + "text": "Which is, we're going to explain how to differentiate anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk1.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..3c9f2a295725dda6c025fb6ea95f12be7e4cad11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how to differentiate any function you know." + }, + { + "text": "And that's kind of a tall order." + }, + { + "text": "But let me just give you an example." + }, + { + "text": "If you want to take the derivative, this we'll see today as the notation for the derivative of something, of some messy function like e to the x arctan of x, we'll work this out by the end of this unit." + }, + { + "text": "So anything you can think of, anything you can write down, we can differentiate it." + }, + { + "text": "So that's what we're going to do." + }, + { + "text": "And today, as I said, we're going to spend most of our time on this geometric interpretation." + }, + { + "text": "So let's begin with that." + }, + { + "text": "So here we go with the geometric interpretation of derivatives." + }, + { + "text": "And what we're going to do is just ask the geometric problem of finding the tangent line to some graph of some function at some point." + }, + { + "text": "Which is, say, x0, y0." + }, + { + "text": "So that's the problem that we're addressing here." + }, + { + "text": "Guess I should probably turn this off." + }, + { + "text": "All right." + }, + { + "text": "So here's our problem." + }, + { + "text": "And now let me show you the solution." + }, + { + "text": "So, well, let's graph the function." + }, + { + "text": "So let's say here's its graph." + }, + { + "text": "And here's some point." + }, + { + "text": "Maybe I should draw it just a bit lower so that I don't..." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk10.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..53b1c4969e0cbfa6b9cd0f600feb985165be6739 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is a good thing." + }, + { + "text": "You see that slope there is negative." + }, + { + "text": "That's the simplest check that you could make." + }, + { + "text": "And the second thing that I would just like to point out is that as x goes to infinity, that is, as we go farther to the right, it gets less and less steep." + }, + { + "text": "So less." + }, + { + "text": "And whoops, as x0 goes to infinity, not 0." + }, + { + "text": "As x0 goes to infinity, less and less steep." + }, + { + "text": "So that's also consistent here." + }, + { + "text": "When x0 is very large, this is a smaller and smaller number in magnitude." + }, + { + "text": "Although it's always negative." + }, + { + "text": "It's always sloping down." + }, + { + "text": "So I've managed to fill the boards, so maybe I should stop for a question or two." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "Can you explain why it's 2, 2, and 0, and why it's 2, 1, 1, and 0?" + }, + { + "text": "PROFESSOR CELESTE GRAYSON So the question is to explain again this limiting process." + }, + { + "text": "So the formula here is, we have basically two numbers." + }, + { + "text": "So in other words, why is it that this expression, when delta x tends to 0, is equal to minus 1 over x0 squared?" + }, + { + "text": "Let me illustrate it by sticking in a number for x0 to make it more explicit." + }, + { + "text": "So for instance, let me stick in here for x0 the number 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk11.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d37e5d7f909abc8c7b0e16c9fee027ab94868e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's minus 1 over 3 plus delta x times 3." + }, + { + "text": "That's the situation that we've got." + }, + { + "text": "And now the question is, what happens as this number gets smaller and smaller and smaller and gets to be practically 0?" + }, + { + "text": "Well, literally what we can do is just plug in 0 there." + }, + { + "text": "Then you get 3 plus 0 times 3 in the denominator." + }, + { + "text": "Minus 1 in the numerator." + }, + { + "text": "So this tends to minus 1 over 9, over 3 squared." + }, + { + "text": "And that's what I'm saying in general with this extra number here." + }, + { + "text": "Other questions?" + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 2 How do you simplify from delta f over delta x?" + }, + { + "text": "How do you simplify from your equation to 1 over delta x factor of?" + }, + { + "text": "So the question is, what happened between this step and this step?" + }, + { + "text": "Explain this step here." + }, + { + "text": "So there were two parts to that." + }, + { + "text": "The first is, this delta x which was sitting in the denominator, I factored all the way out front." + }, + { + "text": "And so what's in the parentheses is supposed to be the same as what's in the numerator of this other expression." + }, + { + "text": "And then, at the same time as doing that, I put that expression, which is the difference of two fractions, I expressed it with a common denominator." + }, + { + "text": "So in the denominator here, you see the product of the denominators of the two fractions." + }, + { + "text": "And then I just figured out what the numerator had to be." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk12.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..086d9ca2fecb9cef806d9277cc9755f79a1588ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Without really, yeah." + }, + { + "text": "Other questions?" + }, + { + "text": "OK." + }, + { + "text": "So now, so I claim that on the whole, calculus gets a bad rap." + }, + { + "text": "That it's actually easier than most things." + }, + { + "text": "But there's a perception that it's harder." + }, + { + "text": "And so I really have a duty to give you the calculus made harder story here." + }, + { + "text": "So we have to make things harder, because that's our job." + }, + { + "text": "And this is actually what most people do in calculus." + }, + { + "text": "And it's the reason why calculus has a bad reputation." + }, + { + "text": "So the secret is that when people ask problems in calculus, they generally ask them in context." + }, + { + "text": "And there are many, many other things going on." + }, + { + "text": "And so the little piece of the problem, which is calculus, is actually fairly routine." + }, + { + "text": "And has to be isolated and gotten through." + }, + { + "text": "But all the rest of it relies on everything else you learned in mathematics up to this stage." + }, + { + "text": "From grade school through high school." + }, + { + "text": "So that's the complication." + }, + { + "text": "So now we're going to do a little bit of calculus made hard." + }, + { + "text": "By talking about a word problem." + }, + { + "text": "Now, we only have one sort of word problem that we can pose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk13.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2ecb3985df76a83cfd84b2b270b388b237e188fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because all we've talked about is this geometry point of view." + }, + { + "text": "So so far those are the only kinds of word problems we can pose." + }, + { + "text": "So what we're going to do is just pose such a problem." + }, + { + "text": "So find the areas of triangles enclosed by the axes and the tangent to y equals 1 over x." + }, + { + "text": "So that's a geometry problem." + }, + { + "text": "And let me draw a picture of it." + }, + { + "text": "It's practically the same as the picture for example 1, of course." + }, + { + "text": "So here's, we'll only consider the first quadrant." + }, + { + "text": "Here's our shape." + }, + { + "text": "It's the hyperbola." + }, + { + "text": "And here's maybe one of our tangent lines, which is coming in like this." + }, + { + "text": "And then we're trying to find this area here." + }, + { + "text": "So there's our problem." + }, + { + "text": "So why does it have to do with calculus?" + }, + { + "text": "It has to do with calculus because there's a tangent line in it." + }, + { + "text": "And so we're going to need to do some calculus to answer this question." + }, + { + "text": "But as you'll see, the calculus is the easy part." + }, + { + "text": "So let's get started with this problem." + }, + { + "text": "First of all, I'm going to label a few things." + }, + { + "text": "And one important thing to remember, of course, is that the curve is y equals 1 over x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk14.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d76e1ed4c265a434d1e964110861f1447f47c84e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's perfectly reasonable to do." + }, + { + "text": "And also, we're going to calculate the areas of the triangles." + }, + { + "text": "And you could ask yourself, in terms of what?" + }, + { + "text": "Well, we're going to have to pick a point and give it a name." + }, + { + "text": "And since we need a number, we're going to have to do more than geometry." + }, + { + "text": "We're going to have to do some of this analysis, just as we've done before." + }, + { + "text": "So I'm going to pick a point." + }, + { + "text": "And consistent with the labeling we've done before, I'm going to call it x0, y0." + }, + { + "text": "So that's almost half the battle." + }, + { + "text": "Having notations, x and y for the variables, and x0 and y0 for the specific point." + }, + { + "text": "Now, once you see that you have these labelings, I hope it's reasonable to do the following." + }, + { + "text": "So first of all, this is the point x0." + }, + { + "text": "And over here is the point y0." + }, + { + "text": "That's something that we're used to in graphs." + }, + { + "text": "And in order to figure out the area of this triangle, it's pretty clear that we should find the base." + }, + { + "text": "Which is that we should find this location here." + }, + { + "text": "And we should find the height." + }, + { + "text": "So we need to find that value there." + }, + { + "text": "So let's go ahead and do it." + }, + { + "text": "So how are we going to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk15.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3b60485d77769d4c0e75a4796cce6276c7bc60bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, so let's just take a look." + }, + { + "text": "So what is it that we need to do?" + }, + { + "text": "I claim that there's only one calculus step." + }, + { + "text": "And I'm going to put a star here for this tangent line." + }, + { + "text": "I have to understand what the tangent line is." + }, + { + "text": "And once I figure out what the tangent line is, the rest of the problem is no longer calculus." + }, + { + "text": "It's just that slope that we need." + }, + { + "text": "So what's the formula for the tangent line?" + }, + { + "text": "Put that over here." + }, + { + "text": "It's going to be y minus y0 is equal to, and here's the magic number, we already calculated it." + }, + { + "text": "It's in the box over there." + }, + { + "text": "It's minus 1 over x0 squared." + }, + { + "text": "x minus x0." + }, + { + "text": "So this is the only bit of calculus in this problem." + }, + { + "text": "But now we're not done." + }, + { + "text": "We have to finish it." + }, + { + "text": "We have to figure out all the rest of these quantities so we can figure out the area." + }, + { + "text": "So how do we do that?" + }, + { + "text": "Well, to find this point, this has a name." + }, + { + "text": "We're going to find the so-called x-intercept." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk16.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..f2204643a150f121237881920c05bb6270725ac2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the first thing we're going to do." + }, + { + "text": "So to do that, what we need to do is to find where this horizontal line meets that diagonal line." + }, + { + "text": "And the equation for the x-intercept is y equals 0." + }, + { + "text": "So we plug in y equals 0, that's this horizontal line, and we find this point." + }, + { + "text": "So let's do that into star." + }, + { + "text": "So we get 0 minus, oh, one other thing we need to know." + }, + { + "text": "We know that y0 is f x0, and f x is 1 over x." + }, + { + "text": "So this thing is 1 over x0." + }, + { + "text": "And that's equal to minus 1 over x0 squared." + }, + { + "text": "And here's x, and here's x0." + }, + { + "text": "So in order to find this x value, I have to plug in one equation into the other." + }, + { + "text": "So this simplifies a bit." + }, + { + "text": "Let's put, let's see, this is minus x over x0 squared." + }, + { + "text": "And this is plus 1 over x0, because the x0 and x0 squared cancel somewhat." + }, + { + "text": "And so if I put this on the other side, I get x divided by x0 squared is equal to 2 over x0." + }, + { + "text": "And if I then multiply through, so that's what this implies." + }, + { + "text": "And if I multiply through by x0 squared, I get x is equal to 2x0." + }, + { + "text": "So I claim at this point, we've just calculated, it's 2x0." + }, + { + "text": "Now, I'm almost done." + }, + { + "text": "I need to get the other one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk17.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..50c443f1223e24993e890d17b19e3199b41300bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "I need to get this one up here." + }, + { + "text": "Now, I'm going to use a very big shortcut to do that." + }, + { + "text": "So the shortcut to the y-intercept is to use symmetry." + }, + { + "text": "I claim I can stare at this, and I can look at that, and I know the formula for the y-intercept." + }, + { + "text": "It's equal to 2y0." + }, + { + "text": "That's what that one is." + }, + { + "text": "So this one is 2y0." + }, + { + "text": "And the reason I know this is the following." + }, + { + "text": "So here's the symmetry of the situation, which is not completely direct." + }, + { + "text": "It's a kind of mirror symmetry around the diagonal." + }, + { + "text": "It involves the exchange of x, y with y, x." + }, + { + "text": "So it's trading the roles of x and y." + }, + { + "text": "So the symmetry that I'm using is that any formula I get that involves x's and y's, if I trade all the x's and replace them by y's, and trade all the y's and replace them by x's, then I'll have a correct formula on the other way." + }, + { + "text": "So everywhere I see a y, I make it an x." + }, + { + "text": "And everywhere I see an x, I make it a y." + }, + { + "text": "The switch will take place." + }, + { + "text": "So why is that?" + }, + { + "text": "That's because the, that's just an accident of this equation." + }, + { + "text": "That's because, so the symmetry explained is that the equation is y equals 1 over x." + }, + { + "text": "But that's the same thing as xy equals 1, if I multiply through by x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk18.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..4ec32f867586c1f1965c57c500fbd40fe76b88a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the same thing as x equals 1 over y." + }, + { + "text": "So here's where the x and the y get reversed." + }, + { + "text": "Now, if you don't trust this explanation, you can also get the y-intercept by plugging x equals 0 into the equation star." + }, + { + "text": "We plugged y equals 0 in, and we got the x value." + }, + { + "text": "And you could do the same thing analogously the other way." + }, + { + "text": "So I'm almost done with the geometry problem." + }, + { + "text": "And let's finish it off now." + }, + { + "text": "Well, let me hold off for one second before I finish it off." + }, + { + "text": "What I'd like to say is just make one more tiny remark." + }, + { + "text": "And this is the hardest part of calculus, in my opinion." + }, + { + "text": "So the hardest part of calculus is that we call it one-variable calculus." + }, + { + "text": "But we're perfectly happy to deal with four variables at a time." + }, + { + "text": "Or five." + }, + { + "text": "Or any number." + }, + { + "text": "In this problem, I had an x, a y, an x0, and a y0." + }, + { + "text": "That's already four different things." + }, + { + "text": "They have various interrelationships between them." + }, + { + "text": "So of course, the manipulations we do with them are algebraic." + }, + { + "text": "And when we're doing the derivatives, we just consider what's known as one-variable calculus." + }, + { + "text": "But really, there are millions of variables floating around, potentially." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk19.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..823206ea1fcd1fdbd97652e4c402e4908f1a4f96 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's what makes things complicated." + }, + { + "text": "And that's something that you have to get used to." + }, + { + "text": "Now, there's something else which is more subtle in that I think many people who teach the subject, or use the subject, aren't aware because they've already entered into the language." + }, + { + "text": "And they're so comfortable with it that they don't even notice this confusion." + }, + { + "text": "There's something deliberately sloppy about the way we deal with these variables." + }, + { + "text": "The reason is very simple." + }, + { + "text": "There are already four variables here." + }, + { + "text": "I don't want to create six names for variables, or eight names for variables." + }, + { + "text": "But really, in this problem, there were about eight." + }, + { + "text": "I just slipped them by you." + }, + { + "text": "So why is that?" + }, + { + "text": "Well, notice that the first time that I got a formula for y0 here, it was this point." + }, + { + "text": "And so the formula for y0, which I plugged in right here, was from the equation of the curve, y0 equals 1 over x0." + }, + { + "text": "The second time I did it, I did not use y equals 1 over x. I used this equation here." + }, + { + "text": "So this is not y equals 1 over x." + }, + { + "text": "That's the wrong thing to do." + }, + { + "text": "That's an easy mistake to make if the formulas are all a blur to you, and you're not paying attention to where they are on the diagram." + }, + { + "text": "You see, that y-intercept, that x-intercept calculation there, involved where this horizontal line met this diagonal line." + }, + { + "text": "And y equals 0 represented this line here." + }, + { + "text": "So the sloppiness is that y means two different things." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk2.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..1d308a0dd3c0d3feb4363984c75f1b52572a012b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's a point P. Maybe it's above the point x0." + }, + { + "text": "x0, by the way, this was supposed to be an x0." + }, + { + "text": "That was some fixed place on the x-axis." + }, + { + "text": "And now, in order to perform this mighty feat, I will use another color of chalk." + }, + { + "text": "How about red?" + }, + { + "text": "OK." + }, + { + "text": "So here it is." + }, + { + "text": "There's the tangent line." + }, + { + "text": "Well, not quite straight." + }, + { + "text": "Close enough." + }, + { + "text": "I did it." + }, + { + "text": "That's the end." + }, + { + "text": "That's the geometric problem." + }, + { + "text": "I achieved what I wanted to do." + }, + { + "text": "And it's kind of an interesting question, which unfortunately I can't solve for you in this class." + }, + { + "text": "Which is, how did I do that?" + }, + { + "text": "That is, how physically did I manage to know what to do to draw this tangent line?" + }, + { + "text": "But that's what geometric problems are like." + }, + { + "text": "We visualize it, we can figure it out." + }, + { + "text": "Somewhere in our brains it happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk20.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..6e6699b0c9a211ff0133a15447bfe686497cfb37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we do this constantly because it's way, way more complicated not to do it." + }, + { + "text": "It's much more convenient for us to allow ourselves the flexibility to change the role that this letter plays in the middle of the computation." + }, + { + "text": "And similarly, later on, if I had done this by this more straightforward method for the y-intercept, I would have set x equal to 0." + }, + { + "text": "That would have been this vertical line, which is x equals 0." + }, + { + "text": "But I didn't change the letter x when I did that." + }, + { + "text": "Because that would be a waste for us." + }, + { + "text": "So this is one of the main confusions that happens." + }, + { + "text": "If you can keep yourself straight, you're a lot better off." + }, + { + "text": "And as I say, this is one of the complexities." + }, + { + "text": "So now let's finish off the problem." + }, + { + "text": "Let me finally get this area here." + }, + { + "text": "So actually, I'll just finish it off right here." + }, + { + "text": "So the area of the triangle is, well, it's the base times the height." + }, + { + "text": "The base is 2x0, the height is 2y0, and a half of that." + }, + { + "text": "So it's 1 by 2x0 times 2y0, which is 2x0y0, which is, lo and behold, 2." + }, + { + "text": "So the amusing thing in this case is it actually didn't matter what x0 and y0 are." + }, + { + "text": "We get the same answer every time." + }, + { + "text": "That's just an accident of the function 1 over x." + }, + { + "text": "Happens to be the function with that property." + }, + { + "text": "So we still have more business today." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk21.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..7c1effb55785c865bddee3b4785287ea3ad8f3df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Serious business." + }, + { + "text": "So let me continue." + }, + { + "text": "So first of all, I want to give you a few more notations." + }, + { + "text": "And these are just other ways that people refer, notations that people use to refer to derivatives." + }, + { + "text": "And the first one is the following." + }, + { + "text": "We already wrote y is equal to f x." + }, + { + "text": "And so when we write delta y, that means the same thing as delta f. That's a typical notation." + }, + { + "text": "And previously, we wrote f' for the derivative." + }, + { + "text": "So this is Newton's notation for the derivative." + }, + { + "text": "But there are other notations." + }, + { + "text": "And one of them is df dx." + }, + { + "text": "And another one is dy dx, meaning exactly the same thing." + }, + { + "text": "And sometimes we let the function slip down below." + }, + { + "text": "So that becomes d by dx of f, or d by dx of y." + }, + { + "text": "So these are all notations that are used for the derivative, and these were initiated by Leibniz." + }, + { + "text": "And these notations are used interchangeably, sometimes practically together." + }, + { + "text": "They both turn out to be extremely useful." + }, + { + "text": "This one omits, notice that this thing omits the underlying base point x0." + }, + { + "text": "That's one of the nuisances." + }, + { + "text": "It doesn't give you all the information." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk22.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..0f2f74ec57267ae3a628aef0ded955b05fb30d66 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But there are lots of situations like that where people leave out some of the important information." + }, + { + "text": "You have to fill it in from context." + }, + { + "text": "So that's another couple of notations." + }, + { + "text": "So now I have one more calculation for you today." + }, + { + "text": "I carried out this calculation of the derivative of the function 1 over x. I want to take care of some other powers." + }, + { + "text": "So let's do that." + }, + { + "text": "So Example 2 is going to be the function f x is x n. n equals 1, 2, 3." + }, + { + "text": "One of these guys." + }, + { + "text": "And now what we're trying to figure out is the derivative with respect to x of x n in our new notation." + }, + { + "text": "What this is equal to." + }, + { + "text": "So again, we're going to form this expression, delta f delta x, and we're going to make some algebraic simplification." + }, + { + "text": "So what we plug in for delta f is x delta x to the n minus x to the n divided by delta x." + }, + { + "text": "Now, before, let me just stick this in and I'm going to erase it." + }, + { + "text": "Before, I wrote x0 here and x0 there." + }, + { + "text": "But now I'm going to get rid of it." + }, + { + "text": "Because in this particular calculation, it's a nuisance." + }, + { + "text": "I don't have an x floating around, which means something different from the x0." + }, + { + "text": "And I just don't want to have to keep on writing all those symbols." + }, + { + "text": "It's a waste of blackboard energy." + }, + { + "text": "There's a total amount of energy that I'm, you know, I've already filled up so many blackboards that it's just a limited amount of, plus I'm trying to conserve chalk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk23.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..e87c2cb20ee545162310a7db1eb3fadf01988cdf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, anyway, no 0's." + }, + { + "text": "So think of x as fixed." + }, + { + "text": "Again, in this case, delta x moves and x is fixed." + }, + { + "text": "In this calculation." + }, + { + "text": "Now, in order to simplify this, in order to understand algebraically what's going on, I need to understand what the nth power of a sum is." + }, + { + "text": "And that's a famous formula." + }, + { + "text": "We only need a little tiny bit of it." + }, + { + "text": "Called the binomial theorem." + }, + { + "text": "So the binomial theorem, which is in your text and explained in an exercise, says, in an appendix, sorry, says that if you take the sum of two guys and you take them to the nth power, that of course is x delta x multiplied by itself n times." + }, + { + "text": "And so the first term is x n. That's when all of the n factors come in." + }, + { + "text": "And then you could have this factor of delta x and all the rest x's." + }, + { + "text": "So at least one term of the form x n-1 times delta x." + }, + { + "text": "And how many times does that happen?" + }, + { + "text": "Well, it happens when there's a factor from here, from the next factor, and so on and so on and so on." + }, + { + "text": "There's a total of n possible times that that happens." + }, + { + "text": "And now, the great thing is that with this alone, all the rest of the terms are junk." + }, + { + "text": "That we won't have to worry about." + }, + { + "text": "So to be more specific, the junk, there's a very careful notation for the junk." + }, + { + "text": "The junk is what's called big O of delta x squared." + }, + { + "text": "What that means is that these are terms of order, so with, delta x squared, delta x cubed, or higher." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk24.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..ed7b21847f51c348c73d087276edf42d6bd389b6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's how." + }, + { + "text": "Very exciting, higher order terms." + }, + { + "text": "So this is the only algebra that we need to do." + }, + { + "text": "And now we just need to combine it together to get our result." + }, + { + "text": "So now I'm going to just carry out the cancellations that we need." + }, + { + "text": "So here we go." + }, + { + "text": "We have delta f over delta x, which remember was 1 over delta x times this." + }, + { + "text": "Which is this times, now this is x to the n, plus n x to the n-1 delta x, plus this junk term, minus x to the n. So that's what we have so far, based on our previous calculations." + }, + { + "text": "Now I'm going to do the main cancellation, which is this." + }, + { + "text": "So that's 1 over delta x times n x to the n-1 delta x." + }, + { + "text": "Plus this term here." + }, + { + "text": "And now I can divide in by delta x." + }, + { + "text": "So I get n x to the n-1 plus, now it's O of delta x." + }, + { + "text": "There's at least one factor of delta x, not two factors of delta x, because I have to cancel one of them." + }, + { + "text": "And now I can just take the limit." + }, + { + "text": "And the limit this term is going to be 0." + }, + { + "text": "That's why I called it junk originally." + }, + { + "text": "Because it disappears." + }, + { + "text": "And in math, junk is something that goes away." + }, + { + "text": "So this tends to, as delta x goes to 0, n x to the n-1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk25.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..d0f8df6873003da5fa64ab04eddf54dd769778f5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what I've shown you is that d by dx of x to the n minus, sorry, n, is equal to n x to the n-1." + }, + { + "text": "So now this is going to be super important to you, right on your problem set in every possible way." + }, + { + "text": "And I want to tell you one thing, one way in which it's very important." + }, + { + "text": "And one way that extends it immediately." + }, + { + "text": "So this thing extends to polynomials." + }, + { + "text": "We get quite a lot out of this one calculation." + }, + { + "text": "Namely, if I take d by dx of something like x cubed plus 5x to the 10th power, that's going to be equal to 3x squared." + }, + { + "text": "That's applying this rule to x cubed." + }, + { + "text": "And then here I'll get 5 times 10." + }, + { + "text": "So 50 x to the 9th." + }, + { + "text": "So this is the type of thing that we get out of it." + }, + { + "text": "And we're going to make more hay with that next time." + }, + { + "text": "Question." + }, + { + "text": "I turned myself off." + }, + { + "text": "Yes." + }, + { + "text": "STUDENT 1." + }, + { + "text": "The binomial theorem only works when delta x goes to 0." + }, + { + "text": "PROFESSOR ERIK DEMAINER The question was, the binomial theorem only works when delta x goes to 0." + }, + { + "text": "No, the binomial theorem is a general formula which also specifies exactly what the junk is." + }, + { + "text": "It's very much more detailed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk26.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..f9010f3210fcad1dc6ece944a525ec1e99ea8910 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk26.json @@ -0,0 +1,17 @@ +[ + { + "text": "But we only needed this part." + }, + { + "text": "We didn't care what all these crazy terms were." + }, + { + "text": "It's junk for our purposes now, because we don't happen to need any more than those first two terms." + }, + { + "text": "Yes, because the delta x goes to 0." + }, + { + "text": "OK, see you next time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk3.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c32c3cc60c13097dbf48db61cd15804c14fd3623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the task that we have now is to figure out how to do it analytically." + }, + { + "text": "To do it in a way that a machine could do just as well as I did." + }, + { + "text": "In drawing this tangent line." + }, + { + "text": "So what did we learn in high school about what a tangent line is?" + }, + { + "text": "Well, a tangent line has an equation." + }, + { + "text": "And any line through a point has the equation y minus y0 is equal to m, the slope, times x minus x0." + }, + { + "text": "So here's the equation for that line." + }, + { + "text": "And now there are two pieces of information that we're going to need to work out what the line is." + }, + { + "text": "The first one is the point." + }, + { + "text": "That's that point P there." + }, + { + "text": "And to specify P, given x, we need to know the level of y, which is of course just f of x0." + }, + { + "text": "Now, that's not a calculus problem, but anyway that's a very important part of the process." + }, + { + "text": "So that's the first thing we need to know." + }, + { + "text": "And the second thing we need to know is the slope." + }, + { + "text": "And that's this number m. And in calculus, we have another name for it." + }, + { + "text": "We call it f' of x0." + }, + { + "text": "Namely, the derivative of f. So that's the calculus part." + }, + { + "text": "That's the tricky part." + }, + { + "text": "And that's the part that we have to discuss now." + }, + { + "text": "So just to make that explicit here, I'm going to make a definition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk4.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..414f8a4a15814cbb200852d03ff10738032db3a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is that f' of x0, which is known as the derivative of f, at x0, is the slope of the tangent line to y equals f of x at the point, let's just call it P. So that's what it is." + }, + { + "text": "But still I haven't made any progress in figuring out any better how I drew that line." + }, + { + "text": "So I have to say something that's more concrete." + }, + { + "text": "Because I want to be able to cook up what these numbers are." + }, + { + "text": "I have to figure out what this number m is." + }, + { + "text": "And one way of thinking about that, let me just try it, is, so I certainly am taking for granted the sort of non-calculus part." + }, + { + "text": "That I know what a line through a point is." + }, + { + "text": "So I know this equation." + }, + { + "text": "But another possibility might be this line here." + }, + { + "text": "How do I know, well, unfortunately I didn't draw it quite straight, but there it is." + }, + { + "text": "How do I know that this orange line is not a tangent line, but this other line is a tangent line?" + }, + { + "text": "Well, it's actually not so obvious." + }, + { + "text": "But I'm going to describe it a little bit." + }, + { + "text": "It's not really the fact, this thing crosses at some other place." + }, + { + "text": "Which is this point q." + }, + { + "text": "But it's not really the fact that the thing crosses at two places." + }, + { + "text": "Because the line could be wiggly, the curve could be wiggly." + }, + { + "text": "And it could cross back and forth a number of times." + }, + { + "text": "That's not what distinguishes the tangent line." + }, + { + "text": "So I'm going to have to somehow grasp this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk5.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..eb512a1d1ca8cda96617ac7c8aa94656b25c7e76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'll first do it in language." + }, + { + "text": "And it's the following idea." + }, + { + "text": "It's that if you take this orange line, which is called a secant line, and you think of the q, the point q is getting closer and closer to p, then the slope of that line will get closer and closer to the slope of the red line." + }, + { + "text": "And if we draw it close enough, then that's going to be the correct line." + }, + { + "text": "So that's really what I did, sort of in my brain, when I drew that first line." + }, + { + "text": "And so that's the way I'm going to articulate it first now." + }, + { + "text": "So the tangent line is equal to the limit of what's so-called secant lines, pq, as q tends to p. And here we're thinking of p as being fixed." + }, + { + "text": "And q as varying." + }, + { + "text": "Alright, so that's the, again this is still a geometric discussion." + }, + { + "text": "But now we're going to be able to put symbols and formulas to this computation." + }, + { + "text": "And we'll be able to work out formulas in any example." + }, + { + "text": "So let's do that." + }, + { + "text": "So first of all, I'm going to write out these points p and q again." + }, + { + "text": "So maybe we'll put p here and q here." + }, + { + "text": "And I'm thinking of this line through them." + }, + { + "text": "I guess it was orange, so we'll leave it as orange." + }, + { + "text": "And now I want to compute its slope." + }, + { + "text": "And so this gradually, we'll do this in two steps." + }, + { + "text": "And these steps will introduce us to the basic notations which are used throughout calculus, including multivariable calculus, across the board." + }, + { + "text": "So the first notation that's used is, you imagine, here's the x-axis underneath, and here's the x0, the location directly below the point p. And we're traveling here a horizontal distance, which is denoted by delta x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk6.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9af12055ebf57cb71aebe91c71be33d106ae07ce --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's delta x, so-called." + }, + { + "text": "And we could also call it the change in x." + }, + { + "text": "So that's one thing we want to measure in order to get the slope of this line p, q." + }, + { + "text": "And the other thing is this height." + }, + { + "text": "So that's this distance here, which we denote delta f, which is the change in f. And then the slope is just the ratio delta f over delta x." + }, + { + "text": "So this is the slope of the secant." + }, + { + "text": "And the process I just described over here with this limit applies not just to the whole line itself, but also in particular to its slope." + }, + { + "text": "And the way we write that is the limit as delta x goes to 0." + }, + { + "text": "And that's going to be our slope." + }, + { + "text": "So this is the slope of the tangent line." + }, + { + "text": "OK, now this is still a little general, and I want to work out a more usable form here." + }, + { + "text": "I want to work out a better formula for this." + }, + { + "text": "And in order to do that, I'm going to write delta f, the numerator, more explicitly here." + }, + { + "text": "The change in f. So remember that the point p is the point x0, f of x0." + }, + { + "text": "That's what we got from our formula for the point." + }, + { + "text": "And in order to compute these distances, and in particular the vertical distance here, I'm going to have to get a formula for q as well." + }, + { + "text": "So if this horizontal distance is delta x, then this location is x0 plus delta x." + }, + { + "text": "And so the point above that point has a formula which is x0 plus delta x, f of, and this is a mouthful, x0 plus delta x." + }, + { + "text": "So there's the formula for the point q." + }, + { + "text": "Here's the formula for the point p. And now I can write a different formula for the derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk7.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..929b8037a81cd31002d7b2123eb318ec868efc9e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Which is the following." + }, + { + "text": "So this f' of x0, which is the same as m, is going to be the limit as delta x goes to 0 of the change in f. Well, the change in f is the value of f at the upper point here, which is x0 plus delta x." + }, + { + "text": "And minus its value at the lower point, p, which is f of x0, divided by delta x." + }, + { + "text": "So this is the formula." + }, + { + "text": "I'm going to put this in a little box, because this is by far the most important formula today, which we use to derive pretty much everything else." + }, + { + "text": "And this is the way that we're going to be able to compute these numbers." + }, + { + "text": "So let's do an example." + }, + { + "text": "This example, so we'll call this example 1." + }, + { + "text": "We'll take the function f of x, which is 1 over x." + }, + { + "text": "That's sufficiently complicated to have an interesting answer." + }, + { + "text": "And sufficiently straightforward that we can compute the derivative fairly quickly." + }, + { + "text": "So what is it that we're going to do here?" + }, + { + "text": "All we're going to do is we're going to plug in this formula here for that function." + }, + { + "text": "That's all we're going to do." + }, + { + "text": "And visually, what we're accomplishing is somehow to take the hyperbola, and take a point on the hyperbola, and figure out some tangent line." + }, + { + "text": "That's what we're accomplishing when we do that." + }, + { + "text": "So we're accomplishing this geometrically, but we'll be doing it algebraically." + }, + { + "text": "So first, we consider this difference, delta f over delta x." + }, + { + "text": "And write out its formula." + }, + { + "text": "So I have to have a place, so I'm going to make it again above this point x0, which is a general point." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk8.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8f81015132847a3cd86ba2f3e1e859b82f4677f0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We'll make the general calculation." + }, + { + "text": "So the value of f at the top, when we move to the right by f of x, so I just read off from this, read off from here the formula." + }, + { + "text": "The first thing I get here is 1 over x0 plus delta x." + }, + { + "text": "That's the left-hand term." + }, + { + "text": "Minus 1 over x0." + }, + { + "text": "That's the right-hand term." + }, + { + "text": "And then I have to divide that by delta x." + }, + { + "text": "So here's our expression." + }, + { + "text": "And by the way, this has a name." + }, + { + "text": "This thing is called a difference quotient." + }, + { + "text": "It's pretty complicated because there's always a difference in the numerator." + }, + { + "text": "And in disguise, the denominator is a difference because it's the difference between the value on the right side and the value on the left side here." + }, + { + "text": "So now we're going to simplify it by some algebra." + }, + { + "text": "So let's just take a look." + }, + { + "text": "So this is equal to, let's continue on the next level here, this is equal to 1 over delta x times, now all I'm going to do is put it over a common denominator." + }, + { + "text": "So the common denominator is x0 plus delta x times x0." + }, + { + "text": "And so in the numerator, for the first expression, I have x0." + }, + { + "text": "And for the second expression, I have x0 plus delta x." + }, + { + "text": "So this is the same thing as I had in the numerator before." + }, + { + "text": "Factoring out this denominator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk9.json b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..4f0ac6146749aefc860b778b684fa2e52267672e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/7K1sB05pE0A_8_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And here I put that numerator into this more amenable form." + }, + { + "text": "And now there are two basic cancellations." + }, + { + "text": "The first one is that x0 and x0 cancel." + }, + { + "text": "So we have this." + }, + { + "text": "And then the second step is that these two expressions cancel." + }, + { + "text": "The numerator and denominator, now we have a cancellation that we can make use of." + }, + { + "text": "So we'll write that under here." + }, + { + "text": "And this is equals minus 1 over x0 plus delta x times x0." + }, + { + "text": "And then the very last step is to take the limit as delta x tends to 0." + }, + { + "text": "And now we can do it." + }, + { + "text": "Before we couldn't do it." + }, + { + "text": "Why?" + }, + { + "text": "Because the numerator and the denominator gave us 0 over 0." + }, + { + "text": "But now that I've made this cancellation, I can pass to the limit." + }, + { + "text": "And all that happens is I set this delta x equal to 0, and I get minus 1 over x0 squared." + }, + { + "text": "So that's the answer." + }, + { + "text": "So in other words, what I've shown, let me put it up here, is that f' x0 is minus 1 over x0 squared." + }, + { + "text": "Now, let's look at the graph just a little bit to check this for plausibility." + }, + { + "text": "What's happening here is, first of all, it's negative." + }, + { + "text": "It's less than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk0.json b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..510df1089fd21a6784687fd45af97c7fb5509dfd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "OK, now clustering for graphs." + }, + { + "text": "So this is a topic." + }, + { + "text": "This is one of the important things you can try to do with a graph." + }, + { + "text": "So you have a large graph." + }, + { + "text": "Let me kind of divide it into two clusters." + }, + { + "text": "OK, so you get a giant graph." + }, + { + "text": "And the job is to make some sense out of it." + }, + { + "text": "And one possible step is to be able to subdivide it if, as I see here, there is a cut between two reasonably equal parts of the graph, reasonably same size." + }, + { + "text": "And therefore, that graph could be studied in two pieces." + }, + { + "text": "So the question is, how do you find such a cut by an algorithm?" + }, + { + "text": "What's an algorithm that would find that cut?" + }, + { + "text": "So that's the problem." + }, + { + "text": "Let's say we're looking for two clusters." + }, + { + "text": "We could look for more clusters." + }, + { + "text": "But let's say we want to look for two clusters." + }, + { + "text": "So what are we trying to do?" + }, + { + "text": "We're trying to minimize." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk1.json b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..b0b4cd43a0d0410163047924f80e639cc1985a55 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So this is the problem, then." + }, + { + "text": "So we look for find positions x and y, let's say, two which will be the centers, so to speak, of the." + }, + { + "text": "And really, it's just these points." + }, + { + "text": "Points." + }, + { + "text": "So the data is the points and the edges, as always, the nodes and the edges." + }, + { + "text": "So the problem is to find x and y so that to minimize." + }, + { + "text": "So it's a distance of points ai from x." + }, + { + "text": "Maybe I should emphasize we're in high dimensions." + }, + { + "text": "Plus the distance of other points." + }, + { + "text": "So the ai will be these points, these nodes." + }, + { + "text": "And the bi will be these nodes plus the sum of bi minus y squared." + }, + { + "text": "And you understand the rule here." + }, + { + "text": "That together, the a's union the b's give me all nodes." + }, + { + "text": "And I guess to be complete, the a's intersect the b's is empty." + }, + { + "text": "Just what you expect." + }, + { + "text": "I'm dividing the a's and the b's into two groups." + }, + { + "text": "And I'm picking an x and a y sort of at the center of those groups." + }, + { + "text": "So that is a minimum." + }, + { + "text": "So I want to minimize." + }, + { + "text": "And also, I probably want to impose some condition that the number of a's is reasonably close to the number of b's." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk10.json b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..1357e7a698b8cc04b2307b38f9835b26b26cf65d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let's write down the Laplacian." + }, + { + "text": "So if I use the degree minus b, that's easy." + }, + { + "text": "The degrees were 3, 3, 2, and 2." + }, + { + "text": "Now I have these minuses, and those were 0." + }, + { + "text": "So that's a positive semidefinite matrix." + }, + { + "text": "Is it a positive definite matrix?" + }, + { + "text": "So let me ask, is it singular or is it not singular?" + }, + { + "text": "Is there a vector in its null space or is there not a vector in its null space?" + }, + { + "text": "Can you solve dx equals all 0s?" + }, + { + "text": "And of course, you can." + }, + { + "text": "Everybody sees that the vector of all 1s will be a solution to L. I'm sorry." + }, + { + "text": "I should be saying L here." + }, + { + "text": "Lx equals 0." + }, + { + "text": "Lx equals 0 is for a whole line of a one dimensional and the null space of L has dimension 1." + }, + { + "text": "It's got one basis vector, 1, 1, 1, 1." + }, + { + "text": "And that will always happen with the graph setup that I've created." + }, + { + "text": "So that's the first fact, that this positive semidefinite matrix L has lambda 1 equals 0, and the eigenvector is constants, C, C, C, C, the one dimensional eigenspace." + }, + { + "text": "Or 1, 1, 1, 1 is a typical eigenvector." + }, + { + "text": "OK. Now back to graph clustering." + }, + { + "text": "The idea of graph clustering is to look at the Fiedler eigenvector." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk11.json b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..281caddddde4055024d281f54754cc7d51c84615 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "This is called x2 is the next eigenvector, is the eigenvector for the smallest positive eigenvalue for lambda min excluding 0." + }, + { + "text": "So the smallest eigenvalue of L, the smallest eigenvalue and its eigenvector, this is called the Fiedler vector, named after the Czech mathematician, a great man in linear algebra." + }, + { + "text": "And he studied this vector, this situation." + }, + { + "text": "So everybody who knows about the graph Laplacian is aware that its first eigenvalue is 0, and that the next eigenvalue is important." + }, + { + "text": "Yeah?" + }, + { + "text": "AUDIENCE 2 Is the graph Laplacian named the Laplacian because it has connections?" + }, + { + "text": "GILBERT STRANGSKI-WEISBAUMGESEN To Laplace's equation, yes." + }, + { + "text": "So yeah, that's a good question." + }, + { + "text": "So why the word, the name Laplacian?" + }, + { + "text": "So yeah, that's a good question." + }, + { + "text": "So the familiar thing, so it connects to Laplace's finite difference equation, because we're talking about matrices here and not derivatives, not functions." + }, + { + "text": "So why the word Laplacian?" + }, + { + "text": "Well, so if I have a regular, if my graph is composed of a, so there is a graph with 25 nodes and 4 times 5, 20, about 40." + }, + { + "text": "This probably has about 40 edges and 25 nodes." + }, + { + "text": "And of course, I can construct its graph, all those four matrices for it." + }, + { + "text": "Its incidence matrix, its degree matrix." + }, + { + "text": "So the degree will be 4 at all these inside points." + }, + { + "text": "The degree will be 3 at these boundary points." + }, + { + "text": "The degree will be 2 at these corner points." + }, + { + "text": "But what will the matrix L look like?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk12.json b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..12daa4372923d18ded725df528b5481880269763 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what is L?" + }, + { + "text": "And that will tell you why it has this name Laplacian." + }, + { + "text": "So the matrix L will have the degree 4, right, will be on the diagonal." + }, + { + "text": "That's coming from D. The other, the minus 1's that come from B, the adjacency matrix will be associated with those nodes and otherwise all 0's." + }, + { + "text": "So this is a typical row of L. This is a typical row of L centered at that node." + }, + { + "text": "So maybe that's node number 5, 10, 13." + }, + { + "text": "That's 13 out of 25 that would show you this." + }, + { + "text": "And sorry, those are minus 1's." + }, + { + "text": "Minus 1's." + }, + { + "text": "So a 4 on the diagonal and 4 minus 1's." + }, + { + "text": "That's the model problem for when the graph is a grid, square grid." + }, + { + "text": "And you associate that with Laplace's equation." + }, + { + "text": "So this is the reason that Laplace, why Laplace gets in it." + }, + { + "text": "Because Laplace's equation, the differential equation, is second derivative with respect to x squared." + }, + { + "text": "And the second derivative with respect to y squared is 0." + }, + { + "text": "And what we have here is Lu equals 0." + }, + { + "text": "It's the discrete Laplacian, the vector Laplacian, the graph Laplacian, where the second x derivative is replaced by minus 1, 2, minus 1." + }, + { + "text": "And the second y derivative is replaced by minus 1, 2, minus 1, second differences in the x and the y directions." + }, + { + "text": "So that's the explanation for Laplace." + }, + { + "text": "It's the discrete Laplace, discrete, or the finite difference Laplace." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk13.json b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..735b134e5903367fe066cd16a7e4f76a605a7890 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, to finish, I have to tell you what clusters, how do you decide the clusters from L?" + }, + { + "text": "How does L propose two clusters, the A's and the B's?" + }, + { + "text": "And here's the answer." + }, + { + "text": "They come from this eigenvector, the Fiedler eigenvector." + }, + { + "text": "You look at that eigenvector." + }, + { + "text": "It's got some positive and some negative components." + }, + { + "text": "The components with positive numbers of this eigenvector, so the positive components of x, of this eigenvector." + }, + { + "text": "And there are negative components of this eigenvector." + }, + { + "text": "And those are the two clusters." + }, + { + "text": "So the two clusters are decided by the eigenvector, by the signs, plus or minus signs, of the components." + }, + { + "text": "The plus signs go in one, and the minus signs go in another." + }, + { + "text": "And you have to experiment to see that that would succeed." + }, + { + "text": "I don't know what it would do on this, actually, because that's hardly splits up into two." + }, + { + "text": "I suppose maybe the split is along a line like that or something to get." + }, + { + "text": "I don't know what clustering." + }, + { + "text": "This is not a graph that is naturally clustered." + }, + { + "text": "But you could still do k-means on it." + }, + { + "text": "You could still do spectral clustering." + }, + { + "text": "And you would find this eigenvector." + }, + { + "text": "Now, what's the point about this eigenvector?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk14.json b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d82fbf2e485ffc2071dd7965af955b9488bb4fd3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'll finish in one moment." + }, + { + "text": "What do we know about that eigenvector as compared to that one?" + }, + { + "text": "So here was an eigenvector all 1's." + }, + { + "text": "Let me just make it all 1's." + }, + { + "text": "1, 1, 1, 1." + }, + { + "text": "In that picture, it's 25 1's." + }, + { + "text": "Here's the next eigenvector up." + }, + { + "text": "And what's the relation between those two eigenvectors of L?" + }, + { + "text": "They are orthogonal." + }, + { + "text": "These are eigenvectors of a symmetric matrix." + }, + { + "text": "So they're orthogonal." + }, + { + "text": "So that means to be orthogonal to this guy means that your components add to 0, right?" + }, + { + "text": "A vector is orthogonal to all 1's." + }, + { + "text": "That dot product is just add up the components." + }, + { + "text": "So we have a bunch of positive components and a bunch of negative components." + }, + { + "text": "They have the same sum because the dot product with that is 0." + }, + { + "text": "And those two components, those two sets of components, are your two, tell you the two clusters in spectral clustering." + }, + { + "text": "So it's a pretty nifty algorithm." + }, + { + "text": "It does ask you to compute an eigenvector." + }, + { + "text": "And that, of course, takes time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk15.json b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..33b314de4bcbf9001b168559a42a59434408ceb9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then there's a third, more direct algorithm to do this optimization problem." + }, + { + "text": "Well, actually, there are many." + }, + { + "text": "This is an important problem." + }, + { + "text": "So there are many proposed algorithms." + }, + { + "text": "Good." + }, + { + "text": "OK, I'm closing up." + }, + { + "text": "Final question?" + }, + { + "text": "Yeah." + }, + { + "text": "AUDIENCE 1 Is it possible to do more than one eigenvector?" + }, + { + "text": "GILBERT STRANGSBERRY Well, certainly for k-means." + }, + { + "text": "Now, if I had to do three clusters with Fiedler, I would look at the first three eigenvectors." + }, + { + "text": "And, well, the first one would be nothing." + }, + { + "text": "And I would look at the next two." + }, + { + "text": "And that would be pretty successful." + }, + { + "text": "If I wanted six clusters, it probably would fall off in the quality of the clustering." + }, + { + "text": "Yeah, but certainly I would look at the lowest six eigenvectors and get somewhere." + }, + { + "text": "Yeah, right." + }, + { + "text": "So OK, so that's a topic, an important topic, a sort of standard topic in applied graph theory." + }, + { + "text": "OK, so see you Wednesday." + }, + { + "text": "I'm hoping on Wednesday." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk16.json b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..369303b0fe81782847fe72a1f77fa9546a3fe220 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk16.json @@ -0,0 +1,47 @@ +[ + { + "text": "So Professor Edelman has told me a new and optimal way to look at the problem of back propagation." + }, + { + "text": "You remember back propagation?" + }, + { + "text": "If you remember the lecture on it, you don't want to remember the lecture on it." + }, + { + "text": "It's a tricky, messy thing to explain." + }, + { + "text": "But he says, if I explain it using Julia in linear algebra, it's clear." + }, + { + "text": "So we'll give him a chance on Wednesday to show that revolutionary approach to the explanation of back propagation." + }, + { + "text": "And I hope for, I told him he could have half an hour and projects would take some time." + }, + { + "text": "I hope now we've had two with wild applause." + }, + { + "text": "So I hope we get a couple more in our last class." + }, + { + "text": "OK, see you Wednesday." + }, + { + "text": "And if you bring, well, if you have projects ready, send them to me online and maybe a printout as well." + }, + { + "text": "That would be terrific." + }, + { + "text": "If you don't have them ready by the hour, they can go." + }, + { + "text": "The envelope outside my office would receive them." + }, + { + "text": "Good, so I'll see you Wednesday for the final class." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk2.json b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..33767a0a3dad583cc8f7063e11d58f516d9e5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "In other words, I don't want just that to be the a and all the rest to be the b's." + }, + { + "text": "That would be not a satisfactory clustering." + }, + { + "text": "I'm looking for clusters that are good sized clusters." + }, + { + "text": "So minimize that." + }, + { + "text": "So there are a lot of different algorithms to do it." + }, + { + "text": "But some are more directly attacking this problem." + }, + { + "text": "Others use matrices that we associate with the graph." + }, + { + "text": "So let me tell you about two or three of those algorithms." + }, + { + "text": "And if you've studied, had a course in graph theory, you may already have seen this problem." + }, + { + "text": "First question would be, suppose I decide these are the a's and those are the b's, or some other decision." + }, + { + "text": "Yeah, probably some other decision." + }, + { + "text": "God, I want to solve the problem before I even start." + }, + { + "text": "So some a's and some b's." + }, + { + "text": "What would be the best choice of the x once you've decided on the a's?" + }, + { + "text": "And what would be the best choice of the y once you've decided on the b's?" + }, + { + "text": "So we can answer that question." + }, + { + "text": "Just if we knew the two groups, we could see where they should be centered, where the first group centered at x, the second group centered at y." + }, + { + "text": "And what does centering mean?" + }, + { + "text": "So let's just say." + }, + { + "text": "So I think what I'm saying here is, let me bring that down a little." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk3.json b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..d50ee5c51dc35b55941a75d0e1fa8771e11923e2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "So given the a's, this is a1 up to, say, ak, what is the best?" + }, + { + "text": "Is the best x?" + }, + { + "text": "Just to make that part right." + }, + { + "text": "And the answer is, do you know geometrically what x should be here?" + }, + { + "text": "x is the." + }, + { + "text": "So if I have a bunch of points and I'm looking for the middle of those points, the point x, a good point x to say, OK, that's the middle." + }, + { + "text": "It'll make the sum of the distances, I think, squared." + }, + { + "text": "I hope I'm right about that." + }, + { + "text": "A minimum." + }, + { + "text": "What is x?" + }, + { + "text": "It is the centroid." + }, + { + "text": "Centroid is the word." + }, + { + "text": "x is the centroid of the a's." + }, + { + "text": "And what is the centroid?" + }, + { + "text": "Let's see." + }, + { + "text": "Oh, maybe I don't know if x and y were a good choice." + }, + { + "text": "But let me see what." + }, + { + "text": "I guess it's the average a." + }, + { + "text": "It's the sum of the a's, of these a's." + }, + { + "text": "Those are vectors, of course, divided by the number of a's." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk4.json b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..1e80e6b52d8909b62ebd123fe6561cc5be464fc3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "I think." + }, + { + "text": "Actually, I was just quickly reviewing this morning." + }, + { + "text": "So I'm not totally on top of this centroid." + }, + { + "text": "What I'm going to talk, the algorithm that I'm going to talk about is the k, well, k means, it's always called." + }, + { + "text": "And here, it will be the k will be 2." + }, + { + "text": "I just have two partitioning into two sets, a's and b's." + }, + { + "text": "So I just k is just 2." + }, + { + "text": "OK, what's the algorithm?" + }, + { + "text": "Well, if I've chosen a partition, the a's and the b's have separated them, then that tells me what the x and the y should be." + }, + { + "text": "But now, what do I do next?" + }, + { + "text": "So this is going to be a sort of an alternating partition." + }, + { + "text": "Now, I take those two centroids." + }, + { + "text": "So step one is, for a given a's and b's, find the centroids x and y." + }, + { + "text": "And that's elementary." + }, + { + "text": "Then the second step is, given the centroids x and y, given those positions, given x and y, they won't be centroids when you see what happens." + }, + { + "text": "Given x and y, reform the best partition, best clusters." + }, + { + "text": "OK, so step one, we had a guess at what the best clusters were." + }, + { + "text": "And we found their centroids." + }, + { + "text": "Now, we start with the centroids, and we form new clusters again." + }, + { + "text": "And if these clusters are the same as the ones we started with, then the algorithm has converged." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk5.json b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..7b33825ec164ef11eec503e9bdcbf59f77aba79e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "But probably won't be, these clusters." + }, + { + "text": "So you'll have to tell me what I mean by the best clusters." + }, + { + "text": "If I've got the two points, x and y, I want the points, I want to separate all the points that cluster around x to the ones that cluster around y." + }, + { + "text": "And then they're probably different from my original start." + }, + { + "text": "So now I've got new." + }, + { + "text": "Now I repeat step one." + }, + { + "text": "But let's just think, how do I form the best clusters?" + }, + { + "text": "Well, I take a point, and I have to decide, does it go with x, or does it go in the x cluster, or does it go in the cluster around y?" + }, + { + "text": "So how do I decide that?" + }, + { + "text": "Just whichever one it's closer to." + }, + { + "text": "So each point goes with each node." + }, + { + "text": "I could say each node goes with the closer of x and y." + }, + { + "text": "So points that should have been that are closer to x, now we're going to put them in the cluster around x." + }, + { + "text": "And does that solve the problem?" + }, + { + "text": "No, because, well, it might, but it might not." + }, + { + "text": "We have to come back to step one." + }, + { + "text": "We've now changed the clusters." + }, + { + "text": "They'll have different centroids." + }, + { + "text": "So we repeat step one, find the centroids for the two new clusters." + }, + { + "text": "Then we come to step two, find the ones that should go with the two centroids, and back and forth." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk6.json b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..c9703db94287ed7629f6d5a0547a4da9b7a456ac --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "I don't know, I don't think there's a nice theory of convergence or rate of convergence, all the questions that this course is always asking." + }, + { + "text": "But it's a very popular algorithm, k-means." + }, + { + "text": "k would be to have k clusters." + }, + { + "text": "So that's a, I'm not going to discuss the, I'd rather discuss some other ways to do this, to solve this problem, but that's one sort of hack that works quite well." + }, + { + "text": "OK, so second approach is what's coming next, second solution method." + }, + { + "text": "And it's called the spectral clustering." + }, + { + "text": "That's the name of the method." + }, + { + "text": "And before I write down what you do, what does the word spectral mean?" + }, + { + "text": "You see spectral graph theory, spectral clustering." + }, + { + "text": "And in other parts of mathematics, you see that word, you see spectral theorem." + }, + { + "text": "I gave you the most, and I described it as the most important, perhaps, theorem in linear algebra, at least one of the top three." + }, + { + "text": "So I'll write it over here, because it's not, it doesn't, this is a, it's the same word spectral." + }, + { + "text": "Well, let me ask the question again." + }, + { + "text": "What's that word spectral about?" + }, + { + "text": "What does that mean?" + }, + { + "text": "That means that if I have a matrix and I want to talk about its spectrum, what is the spectrum of the matrix?" + }, + { + "text": "It is the eigenvalues." + }, + { + "text": "So spectral theory, spectral clustering is using the eigenvalues of some matrix." + }, + { + "text": "That's what that spectral is telling me." + }, + { + "text": "So the spectral theorem, of course, is that for a symmetric matrix S, the eigenvalues are real and the eigenvectors are orthogonal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk7.json b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..d86e9f9bbdd7d9404d7723410ffb138f3e4560c3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And don't forget what the real full statement is here, because there could be repeated real eigenvalues." + }, + { + "text": "And what does the spectral theorem tell me?" + }, + { + "text": "For symmetric matrices, if lambda equal 5 is repeated four times, if it's a four times solution of the equation that gives eigenvalues, then what's the conclusion?" + }, + { + "text": "Then there are four independent orthogonal eigenvectors to go with it." + }, + { + "text": "We can't say that about matrices, about all matrices, but we can say it about all symmetric matrices." + }, + { + "text": "And in fact, those eigenvectors are orthogonal, so we're even saying more." + }, + { + "text": "We can find four orthogonal eigenvectors that go with a multiplicity for eigenvalue." + }, + { + "text": "OK, that's spectral theorem." + }, + { + "text": "Spectral clustering starts with the graph Laplacian matrix." + }, + { + "text": "Matrix." + }, + { + "text": "May I remember what that matrix is?" + }, + { + "text": "Because that's the key connection of linear algebra to graph theory, is the properties of this graph Laplacian matrix." + }, + { + "text": "OK, so let me say L for Laplacian." + }, + { + "text": "So that matrix, one way to describe it is as a transpose A, where A is the incidence matrix of the graph." + }, + { + "text": "Or another way we'll see is the D, the degree matrix." + }, + { + "text": "That's diagonal." + }, + { + "text": "And I'll do an example just to remind you." + }, + { + "text": "Minus the, I don't know what I'd call this one." + }, + { + "text": "Shall I call it B for the moment?" + }, + { + "text": "And what matrix is B?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk8.json b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..67236625f07a70f0d7d710097a866d77120c4a81 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the adjacency matrix." + }, + { + "text": "Really, you should know these four matrices." + }, + { + "text": "They're the key four matrices associated with any graph." + }, + { + "text": "The incidence matrix, that's m by n edges and nodes." + }, + { + "text": "Edges and nodes." + }, + { + "text": "So it's rectangular, but I'm forming A transpose A here." + }, + { + "text": "So I'm forming a symmetric positive semi-definite matrix." + }, + { + "text": "So this Laplacian is symmetric positive semi-definite." + }, + { + "text": "Yeah, let me just recall what all these matrices are for a simple graph." + }, + { + "text": "OK, so I'll just draw a graph." + }, + { + "text": "All right." + }, + { + "text": "OK, so the incidence matrix, there are 1, 2, 3, 4, 5 edges, so five rows." + }, + { + "text": "There are four nodes, 1, 2, 3, and 4, so four columns." + }, + { + "text": "And a typical row would be edge 1 going from node 1 to node 2, so it would have a minus 1 and a 1 there." + }, + { + "text": "And let me take edge 2 going from 1 to node 3, so it would have a minus 1 and a 1 there." + }, + { + "text": "So that's the incidence matrix A. OK, what's the degree matrix?" + }, + { + "text": "That's simple." + }, + { + "text": "The degree matrix, well, A transpose A, this is m by n. This is n by m, so it's n by n. OK, in this case, 4 by 4." + }, + { + "text": "So the degree matrix will be 4 by 4, n by n. And it will tell us the degree of that, which means which we just count the edges." + }, + { + "text": "So it's three edges going in, node 2, three edges going in." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk9.json b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..0b60f0d528f2e4ce2779436b0c9941475e9da813 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Cx5Z-OslNWE_0_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "Node 3 has just two edges, and node 4 has just two edges." + }, + { + "text": "So that's the degree matrix." + }, + { + "text": "And then the adjacency matrix that I've called B is also 4 by 4." + }, + { + "text": "And what is it?" + }, + { + "text": "It tells us which node is connected to which node." + }, + { + "text": "So I don't allow nodes, edges, that connect a node to itself, so 0s on the diagonal." + }, + { + "text": "So which nodes are connected to node 1?" + }, + { + "text": "Well, all of 2 and 4 and 3 are connected to 1, so I have 1s there." + }, + { + "text": "Node 2, all three nodes are connected to node 2." + }, + { + "text": "So I'll have the second column and row will have all three 1s." + }, + { + "text": "How about node 3?" + }, + { + "text": "OK, only two edges are connected." + }, + { + "text": "Only two nodes are connected to 3, 1 and 2, but not 4." + }, + { + "text": "So 1 and 2 I have, but not 4." + }, + { + "text": "So that's the adjacency matrix." + }, + { + "text": "Is that right?" + }, + { + "text": "Think so?" + }, + { + "text": "This is the degree matrix." + }, + { + "text": "This is the incidence matrix." + }, + { + "text": "And that formula gives me the Laplacian." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk0.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..9286debb4969f2ab2aefd848d4fffac039ca6f55 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay, folks." + }, + { + "text": "Here we are again." + }, + { + "text": "Welcome back for another episode of Theory of Computation." + }, + { + "text": "This is lecture number three." + }, + { + "text": "I am going to review what we've been doing." + }, + { + "text": "We've been looking at finite automata and regular languages." + }, + { + "text": "Those are the languages that the finite automata can recognize." + }, + { + "text": "And we talked about non-determinism." + }, + { + "text": "So we had non-deterministic finite automata and deterministic finite automata." + }, + { + "text": "We showed that they're equivalent." + }, + { + "text": "We looked at the closure properties over the regular operations, union, concatenation, and star, and showed that the regular languages, really the class of regular languages, is closed under those regular operations." + }, + { + "text": "And we used the constructions that we developed in the proof of those closure properties to show that we can give a way to convert regular expressions to finite automata." + }, + { + "text": "So that was partway toward our goal of showing that these regular expressions and finite automata are equivalent with respect to the class of languages they describe, namely the regular languages." + }, + { + "text": "So regular expressions of finite automata are interchangeable from the perspective of what kinds of languages you can do with them." + }, + { + "text": "So we're going to finish that off today." + }, + { + "text": "So let's take a look at what our next topics we're going to be covering." + }, + { + "text": "We're going to reverse the construction we gave last time, which allowed us to convert regular expressions to finite automata." + }, + { + "text": "Now we're going to go backwards." + }, + { + "text": "We're going to show how to convert finite automata back to regular expressions." + }, + { + "text": "And those two constructions together show us that the regular expressions and finite automata can be interconverted from one another." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk1.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..83e2e7e646f6e7885e4c8cce2c717ec347478ab1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And they're therefore equivalent with respect to the kinds of things they can do in language recognition or generation." + }, + { + "text": "Then we're going to prove that we're going to look at how you prove certain languages are not regular." + }, + { + "text": "They're beyond the capabilities of finite automata." + }, + { + "text": "And finally, at the end, we're going to introduce a new model of computation, which is more powerful than the finite automata and regular expressions, namely the context-free grammars." + }, + { + "text": "Those can do other kinds of languages that the simpler finite automata regular expressions models can't do." + }, + { + "text": "And I would also just like to note that a lot of what we're doing is a warm-up toward the more powerful models of computation that we're going to be looking at later, well, in a week or so, which are more general purpose computation." + }, + { + "text": "But along the way, introducing these models of finite automata and context-free languages is interesting and helpful because many of those, a number of those models turn out to be useful in a number of applications, whether it's from linguistics to programming languages." + }, + { + "text": "And a variety of different parts of computer science and other fields as well use those notions." + }, + { + "text": "So they're useful notions beyond just in this course." + }, + { + "text": "So I just want a couple of administrative things to touch on." + }, + { + "text": "We are going to have additional check-ins today." + }, + { + "text": "As I mentioned to you, we're going to start counting participation, not correctness, just participation in the live check-ins." + }, + { + "text": "So with that, let us move on to today's material." + }, + { + "text": "As I mentioned, we're going to be showing how to convert finite automata to regular expressions." + }, + { + "text": "And that's going to complete our equivalence of finite automata and regular expressions." + }, + { + "text": "So just to recap what we did last time, we showed that if you have a regular expression and it describes some language, then that language is regular." + }, + { + "text": "So in other words, we have a way of, we gave a way of converting regular expressions to finite automata, as kind of shown in this diagram." + }, + { + "text": "That's what we did last time." + }, + { + "text": "Now we're going to go the other way." + }, + { + "text": "We're going to show how to convert." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk10.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..252369997cbaf6cb940707c8eac940076c4ff217 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "I've got to fix the damage that I caused by removing x." + }, + { + "text": "And whatever role x was playing in the original machine, I've got to make sure that the new machine that I have, which doesn't have x anymore, can still do the same things that the original machine did." + }, + { + "text": "And so the way I'm going to do that is look at all of the paths that could go through x and make sure that they're still present, even though I don't have x anymore." + }, + { + "text": "And the way I'm going to do that is I'm going to consider a part of a path that might use x." + }, + { + "text": "So let's pick two states, qi and qj, in the machine that had k states." + }, + { + "text": "Let me just see here." + }, + { + "text": "I don't know if this is." + }, + { + "text": "OK." + }, + { + "text": "So if we have, we'll pick two states, qi and qj, in the original machine." + }, + { + "text": "Now, qi might have the possibility of going to state x." + }, + { + "text": "And then x might have a self loop." + }, + { + "text": "And then it might go to qj." + }, + { + "text": "The new machine doesn't have x anymore." + }, + { + "text": "So the way I'm going to fix that is by replacing the label that goes directly from i to j with a new label that adds in all of the things I lost when I removed x. OK, that's the whole idea here." + }, + { + "text": "So here is qi to qj, but there's no x anymore." + }, + { + "text": "How could I get from qi to qj?" + }, + { + "text": "What were the inputs that could have brought us from qi to qj via x?" + }, + { + "text": "Well, they would have been an input that read a string described by R1." + }, + { + "text": "I might have self looped at x a few times." + }, + { + "text": "So I might have read several strings that are described by R2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk11.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..568360bc5f2588be674edcfcb746eadb5c2f9fe8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I would have read a string that was described by R3." + }, + { + "text": "And now I'm at qj." + }, + { + "text": "OK, so the new label that I'm going to place over here is going to be the strings that I get from reading R1, reading a string that's described by R1, then multiple copies of a string, multiple strings that are possibly described by R2, which is the same as R2 star, and then a string that could be described by R3." + }, + { + "text": "So that is a new addition to the transition that takes me from qi to qj." + }, + { + "text": "Of course, I need to include the things that would have taken me from qi to qj in the first place." + }, + { + "text": "So I'm also unioning in R4, which was the direct route from qi to qj that did not transit through x." + }, + { + "text": "So by making that new regular expression on the qi to qj transition, I have compensated for the loss of x for paths that go from qi to x and then out to qj." + }, + { + "text": "Now, what I need to do is to do that same thing for every pair qi and qj that are in the original machine." + }, + { + "text": "And so if I do that for every possible pair, I'll be modifying all of the transitions in the new machine in a way that compensates for the loss of x." + }, + { + "text": "And now the new machine has been repaired from the damage that I caused by removing x, and it does the same language." + }, + { + "text": "It's the kind of thing you need to think a little bit about, I understand." + }, + { + "text": "But at least hopefully, the spirit of what I just described to you comes through, that we're going to convert this machine with k states to one with k minus 1 states by removing a state and repairing the damage." + }, + { + "text": "And now it does the same language, and then I can remove another state and do the same thing over and over again until I get down to two states." + }, + { + "text": "So that's the idea." + }, + { + "text": "And that really completes the proof." + }, + { + "text": "That shows that I can convert every GNFA to a regular expression." + }, + { + "text": "OK?" + }, + { + "text": "And that really is the end of the story for this." + }, + { + "text": "And thus, I claim that DFAs now and regular expressions are equivalent." + }, + { + "text": "So I'm going to give you a little check-in here on this, really just to see, high level, if you're following what's going on." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk12.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..dbe5caad5cce0bc2bc69d4c6d06bb18a987d24fc --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "All right?" + }, + { + "text": "So just take a look." + }, + { + "text": "So we just showed how to convert GNFAs to regular expression, but we really wanted to convert DFAs to regular expressions." + }, + { + "text": "So how do we go from converting GNFAs to converting DFAs?" + }, + { + "text": "It's not the same, obviously." + }, + { + "text": "So how do we finish that?" + }, + { + "text": "So there are three choices here." + }, + { + "text": "First, we have to show how to convert DFAs to GNFAs, maybe, or show how to convert GNFAs to DFAs." + }, + { + "text": "Or maybe we're already done." + }, + { + "text": "So maybe I better launch that poll while you're reading that." + }, + { + "text": "And there you go." + }, + { + "text": "Hopefully, you can." + }, + { + "text": "All right." + }, + { + "text": "Why don't I end this?" + }, + { + "text": "It's a little worrisome, because I would say we have a plurality who got the right answer, but not a majority." + }, + { + "text": "So let us share the results." + }, + { + "text": "So I sense not all of you are with me, but you're going to have to either that or you're reading your email while we're talking." + }, + { + "text": "I'm not sure." + }, + { + "text": "But whatever it is, you need to think a little bit about what's going on here, because the reason why we are done is because DFAs are a kind of GNFAs." + }, + { + "text": "They have a very simple kind of regular expression on each transition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk13.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..dca0ba4b63bf044c3e170fa5966aafd47c578e59 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "They just have the regular expression, which is just a single symbol." + }, + { + "text": "So all DFAs are automatically GNFAs." + }, + { + "text": "So if I can convert GNFAs, I can certainly convert DFAs, because GNFAs include the DFAs." + }, + { + "text": "I'm done." + }, + { + "text": "It really was number C was the correct answer." + }, + { + "text": "So good thing we're not counting correctness here." + }, + { + "text": "So participation is good enough." + }, + { + "text": "But I do think you need to think about what's going on and making sure that you're following along." + }, + { + "text": "So anyway, that's a we'll carry on here, but it makes me a little concerned." + }, + { + "text": "OK, so let us now move on." + }, + { + "text": "So we're going to talk a little bit about non-regular languages." + }, + { + "text": "So somebody's asking, don't we have to still make the DFAs into the special type?" + }, + { + "text": "Yes, we do." + }, + { + "text": "We have to make them to the special type." + }, + { + "text": "But we already showed how to make GNFAs into the special type." + }, + { + "text": "And DFA, that is going to apply to DFAs as well." + }, + { + "text": "They'll become GNFAs." + }, + { + "text": "You can add the extra start, add a new start state, add a new accept state, add in all the transitions, which you didn't have before with the empty language label." + }, + { + "text": "And you'll have a GNFA from a DFA." + }, + { + "text": "But that applies to GNFAs in general." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk14.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..01ae4c50774a06079ffb3aa23520bf0e5e1d63af --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's nothing special about DFAs there." + }, + { + "text": "Anyway, I think you need to chew on that." + }, + { + "text": "And hopefully, you'll be following going forward." + }, + { + "text": "Anyway, let us look now at proving non-regularity." + }, + { + "text": "So we're finished with our goal of showing that regular languages can either come from DFAs or from regular expressions." + }, + { + "text": "Those are the same in terms of, from the perspective of our course, they're interchangeable." + }, + { + "text": "So now, as we mentioned, there are going to be some languages which are not regular, which can't be done by DFAs." + }, + { + "text": "They're actually, DFAs are actually pretty weak as a computational model." + }, + { + "text": "And so there's all sorts of very simple things that they cannot do." + }, + { + "text": "There are some fairly complicated things that they can do, surprisingly enough." + }, + { + "text": "But anyway, there are some simple things they can't do." + }, + { + "text": "And so we have to develop a method for showing that a language is not regular." + }, + { + "text": "And that's going to be useful for your homework and, in general, for just understanding the power of DFAs." + }, + { + "text": "So how do we show a language is not regular?" + }, + { + "text": "So remember, if you want to show a language is regular, basically, what you need to do is give a DFA." + }, + { + "text": "Or you can use the closure properties." + }, + { + "text": "That's another way of showing a language is regular." + }, + { + "text": "But underneath that, it's basically constructing DFAs." + }, + { + "text": "All right." + }, + { + "text": "To show a language is not regular, you have to give a proof." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk15.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..be42fee89e7bfab24c0f41195c67f09c15259d03 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Generally, not a construction." + }, + { + "text": "It's a proof that there is no DFA or that it's just going to be impossible to make a DFA." + }, + { + "text": "And we have to develop a method." + }, + { + "text": "What is that proof method?" + }, + { + "text": "Now, there is a tempting, I've taught this course many times, and there's a kind of a tempting approach that many people have." + }, + { + "text": "It's not only going to apply for finite automata, but for other things too." + }, + { + "text": "And believe me, it's not only people in this class." + }, + { + "text": "It's for people out there who are trying to think about computation in general, which is to say, well, I have some language of trying to figure out if it's regular or not." + }, + { + "text": "And so I thought really hard how to make a DFA, and I couldn't find one." + }, + { + "text": "Therefore, it's not regular." + }, + { + "text": "That's not a proof." + }, + { + "text": "Just because you couldn't find a DFA doesn't mean there is no DFA." + }, + { + "text": "You need to prove that the language is not regular using some method." + }, + { + "text": "So I'm going to give you an example where that kind of approach can lead you wrong." + }, + { + "text": "And that is, I'll give two examples of languages where you might try to prove they're regular or not, and you could be in trouble if you just follow that kind of informal approach." + }, + { + "text": "So if you take the language B, where these are straight, but let's assume our alphabet is 0's and 1's." + }, + { + "text": "B is the language of all strings that have an equal number of 0's and 1's." + }, + { + "text": "So you want to know, if I have 1,000 0's, I need to have 1,000 1's." + }, + { + "text": "So basically, the way you test that, you'd have to count up the number of 0's, count up the number of 1's, and see if those two counts are the same." + }, + { + "text": "And that's going to be really tough to make a DFA do, because how are you going to remember that really big number of 0's that the DFA might have 50 states, but you might need to count up to 100 or a million to figure out, to count up how many 0's you've seen." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk16.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..869d18fb7ad9c2c13594508db2fb7931a3946a56 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it seems really hard to be able to do that kind of a count when you only have 50 states." + }, + { + "text": "So whatever number of states you have, it seems hard to count when you have a finite automaton." + }, + { + "text": "So the intuition is, it's not regular, because a finite automaton can't count, which, in this case, you can convert that intuition into a real proof." + }, + { + "text": "I would say it's not a real proof yet, but it can be made into a real proof." + }, + { + "text": "But compare that case with another language, which I'll call C, which instead of looking at its input to see whether it has an equal number of 0's and 1's, I'm going to look at the input and look at the substrings of 0 1's and 1 0's, those two substrings, and count the number of occurrences of 0 1 as a substring and the number of occurrences of 1 0 as a substring." + }, + { + "text": "Just to make sure you're understanding, let's look at two examples." + }, + { + "text": "So the string 0 1 0 1 is not going to be in C, because if you count up the number of 0 1's and the number of 1 0's, not the same." + }, + { + "text": "So I'm even going to help you here, if you can see that." + }, + { + "text": "The number of 0 1's is 2, but there's only a single occurrence of 1 0." + }, + { + "text": "So those two counts are different, and so that's why this input string is not in C. Compare that with the string 0 1 1 0." + }, + { + "text": "Now, if you count up the number of 0 1 and 1 0 substrings, you're going to get the same value, because here we have a single 0 1 and a single 1 0." + }, + { + "text": "And so now the two counts of those number of substrings are the same, and so that's why you're in C. Now my question is, is C a regular language?" + }, + { + "text": "Well, it looks like it shouldn't be regular for the same reason that B isn't regular, because you have to count up two quantities and compare them." + }, + { + "text": "OK?" + }, + { + "text": "So now, so if we, so that's our intuition, that you just can't do it with a finite automaton, because you have to do the same kind of counting that you would have had to do for language B." + }, + { + "text": "But here, you would be wrong, because C, in fact, is regular." + }, + { + "text": "It has a much simpler description than the one I gave over here at the beginning." + }, + { + "text": "There's the very same language C can be described in a much, much simpler way." + }, + { + "text": "I'm not going to tell you what it is." + }, + { + "text": "You can mull that over." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk17.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..4a3dcc0d97e5c9491cfeabfbca0fb80b79bb39fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "You can try some examples to figure it out, but it has a much simpler description." + }, + { + "text": "It's not a totally trivial description." + }, + { + "text": "I mean, there is some content there, but it is the kind of thing that a finite automaton can do." + }, + { + "text": "It wouldn't do the counting this way." + }, + { + "text": "So the moral is, the punchline is, that sometimes the intuition works, but it can also be wrong." + }, + { + "text": "And so the moral of the story is you need to give a proof when you're doing things like that." + }, + { + "text": "OK?" + }, + { + "text": "So what we're going to do next in the second half of the lecture is to give a method for proving languages are not regular." + }, + { + "text": "And again, you're going to need to use that on your homework, so I hope you get it." + }, + { + "text": "But first of all, oh, did I never stop sharing that poll?" + }, + { + "text": "Forgive me." + }, + { + "text": "And so with that, I think we'll take our little requested break." + }, + { + "text": "And for five minutes, and we'll be back in five minutes." + }, + { + "text": "So break time." + }, + { + "text": "All righty." + }, + { + "text": "We are done here." + }, + { + "text": "And proving languages not regular." + }, + { + "text": "OK." + }, + { + "text": "The way we're going to prove languages are not regular is by introducing a method called the pumping lemma." + }, + { + "text": "And the overarching plan at the pumping lemma, without getting into the specifics of it, is to show that that lemma says all regular languages have a certain property, which we will describe." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk18.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..3a7cdaf962dbe23e26a82d78bd238821d23c9d4f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so to show a language is not regular, you simply show the language doesn't have that property." + }, + { + "text": "Because all regular languages have to have that property." + }, + { + "text": "And so by showing a language fails to have the property, it could not be regular." + }, + { + "text": "OK, that's the plan." + }, + { + "text": "OK, now the property itself is a little complicated to describe, but not too bad." + }, + { + "text": "I'll try to unpack it for you." + }, + { + "text": "But first, let's look at the statement of the lemma, which says that whenever you have a regular language, let's call it A." + }, + { + "text": "So for every regular language A, there's always a special value called the pump, a number, P we'll call it, called the pumping length." + }, + { + "text": "It's a special number." + }, + { + "text": "And that length tells you that whenever a string is in that language and it's longer than that length, then something special happens." + }, + { + "text": "You can take that string, and you can modify it, and you still stay in the language." + }, + { + "text": "So anything that's longer than that special length can be modified in a certain way, and you still stay in the language." + }, + { + "text": "So let's look at the actual statement of the lemma." + }, + { + "text": "So there is a number P such that if S is a string in the language and it's longer than P, or at least of length P, then you can take S, and you can cut it up into three pieces, x, y, and z." + }, + { + "text": "So that's just breaking S into three pieces, where you can take that middle piece, repeat it as many times as you like, and you still stay in the language." + }, + { + "text": "That's what the pumping lemma is saying." + }, + { + "text": "And there's a bunch of other conditions here too." + }, + { + "text": "But the spirit of the pumping lemma says whenever you have a regular language, there's some cutoff such that all strings longer than that cutoff can be what we call pumped." + }, + { + "text": "You can take that string, you can find a section somewhere in the middle of that string, or somewhere you cut it up into three pieces, you take that center piece, and you can repeat it." + }, + { + "text": "You can pump it up." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk19.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..8403cf67b9b11571a56211adc8dbe40022202c75 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "And by repeating that string and repeating that piece, the string gets longer and longer, but you still stay in the language." + }, + { + "text": "That's the special property that all regular languages have." + }, + { + "text": "So kind of in an informal way, and I'll try to help you get the feeling for this, formally it says that if you have a regular language, then every long string, so long is by informal way of saying bigger than this value p, every long string in the language can be pumped." + }, + { + "text": "And this result still stays in the language." + }, + { + "text": "And by pumped means I can cut the string into three pieces and repeat that middle piece as many times as I want." + }, + { + "text": "That's what I mean by pumping a string." + }, + { + "text": "So we'll do some examples in a second." + }, + { + "text": "But first, we're going to see how to prove this." + }, + { + "text": "And hopefully, that'll give you some feeling also for why it's true." + }, + { + "text": "And actually, maybe before I actually jump into the proof, let's look at these three conditions here just to understand it a little bit more thoroughly." + }, + { + "text": "So condition one kind of says what I just was telling you." + }, + { + "text": "I can break s into three pieces, x, y, z, such that if I take xy to the iz, so that's repeating y as many times as I want." + }, + { + "text": "So here's y to the i kind of defined, if that's helpful to you, just y, i copies of y." + }, + { + "text": "So I can take xy to the iz, and I remain in the language for every value of i, even i equals 0, which means we're just removing y, which is sometimes actually a useful thing to do." + }, + { + "text": "But let's not get ahead of ourselves." + }, + { + "text": "So I'm guaranteed to be able to cut s up into x, y, z, so that the string xyyy is still in the language, or xyyyyy, it's still in the language." + }, + { + "text": "That's going to be guaranteed for every regular language." + }, + { + "text": "That's a feature that's going to be true." + }, + { + "text": "And furthermore, and this is going to be turning out to be, it's not really kind of part of the core idea of the pumping lemma, but it actually turns out to be very helpful in applying the pumping lemma, you can always cut it up in such a way that the first two pieces are not longer than that value p. So it restricts on the ways you can cut the thing up." + }, + { + "text": "And that actually turns out to be very helpful." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk2.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..c3b8b03523aaa28deab6d17770cb0f2a52dd0df2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Oh, and just a reminder in case you're just getting yourself your memory to work, maybe it'll help you just to remember that we actually did an example of that conversion." + }, + { + "text": "We looked at this regular expression A union AB star." + }, + { + "text": "And we actually worked through the process of converting that." + }, + { + "text": "Oops, I need to make myself smaller so you can see all that." + }, + { + "text": "We went through the process of converting A union AB star as an example of that, of, I mean, OK, well, we went through the process of actually doing that conversion." + }, + { + "text": "And now we're going to show how to do it the other way around." + }, + { + "text": "All right?" + }, + { + "text": "So we're going to invert that and go backwards the other way." + }, + { + "text": "So today's theorem is to show that if A is regular, namely, it's the language of some finite automaton, then you can convert it to a regular expression which will describe that same language." + }, + { + "text": "So basically, we're going to give a conversion from finite automata to regular expressions." + }, + { + "text": "But before we do that, we're going to have to introduce a new concept." + }, + { + "text": "So we're not going to be able to dive right into that conversion." + }, + { + "text": "We're going to have to introduce a new model first, which is going to facilitate that conversion." + }, + { + "text": "And that new model is called, it's yet another kind of finite automaton, called a generalized nondeterministic finite automaton, or a generalized NFA, or just simply a GNFA." + }, + { + "text": "So this is yet another variant of the finite automaton model." + }, + { + "text": "And conceptually, it's very simple." + }, + { + "text": "It's similar to the NFAs." + }, + { + "text": "I'll give you, here's a picture of a GNFA named G, G1." + }, + { + "text": "Very similar to the NFAs." + }, + { + "text": "But if you look at it for a second, you'll see that the transitions have more complicated labels." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk20.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..49e4439744e11671b889cab994b48437311d0b43 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "But let's first just look at the proof of this, giving kind of a little bit the high level picture." + }, + { + "text": "So my job is to show if I have a string in my language, let's say it's a, think of it as a long string, really long." + }, + { + "text": "So its length is more than p. But I think intuitively, it's just a very long string." + }, + { + "text": "And I'm going to feed that string into the machine and watch what happens." + }, + { + "text": "Something special happens when I feed the string and I look at how the machine proceeds on that string." + }, + { + "text": "Because s is so long that as I wander around inside the machine, I have to end up coming back to the same place more than once." + }, + { + "text": "It's like if you have a small park and you go for a long walk, you're going to end up coming back to where you've already seen." + }, + { + "text": "You just can't keep on seeing new stuff when you have a more small area of space to explore." + }, + { + "text": "So we're guaranteed that M is going to end up repeating some state when it's reading s, because s is so long." + }, + { + "text": "So pictorially, if you imagine here this wiggly line is kind of describing the path that M follows when it's reading s, it ends up coming back to that state qj more than once." + }, + { + "text": "So it comes back here, cycles around, comes back again before it ends up accepting." + }, + { + "text": "We know it ends up accepting because we're assuming we have a string that's in the language." + }, + { + "text": "So we picked s in the language." + }, + { + "text": "So it has to be accepted by M. But the important thing is that it repeats a state." + }, + { + "text": "Now, how does that tell me I can cut s up into those three pieces?" + }, + { + "text": "Well, I'm going to get those three pieces here." + }, + { + "text": "First of all, let's observe that here is as processing s. Here is that written right on top of the string, that state repetition occurring, qj more than once." + }, + { + "text": "And now if I look inside the machine, the part of s that took me to qj I'm going to call x." + }, + { + "text": "The part that took me from qj back to itself is I'm going to call y." + }, + { + "text": "And the part that took qj to the accept state, I'm going to call z." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk21.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..b4f87b7d241103ee7f11c3784b2529abdb28305a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'm going to mark those off in s. And that gives me the way to cut s up into three pieces." + }, + { + "text": "Now, if you're appreciating what's going on inside the machine, you will see why M will also accept the string x, y, y, z." + }, + { + "text": "Because every time, once you're at qj, if you go around once, you come back to qj." + }, + { + "text": "And then if you go again, you'll come back to qj." + }, + { + "text": "And as many times as you keep seeing that y, you're just going to keep coming back to qj." + }, + { + "text": "So it doesn't matter how many y's you have." + }, + { + "text": "You're going to still, if you follow it by z, which is what you will do, you'll end up accepting the string." + }, + { + "text": "And that's really the proof." + }, + { + "text": "I mean, you have to do a little bit more here just to understand." + }, + { + "text": "I should have mentioned why I want to forbid y being the empty string." + }, + { + "text": "Because if y is the empty string, it's not interesting." + }, + { + "text": "It doesn't change." + }, + { + "text": "Repeating it doesn't actually change anything." + }, + { + "text": "So I have to make sure it's not empty." + }, + { + "text": "But anyway, that's kind of a detail here." + }, + { + "text": "If you look at the string x, y, y, z, that's still going to be accepted." + }, + { + "text": "So that's the proof of the pumping lemma." + }, + { + "text": "All right?" + }, + { + "text": "So let's have a little check-in related to that." + }, + { + "text": "This is not going to be, again, not super hard, but more just a curiosity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk22.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..8f1447a06a268817402bd9ef6444e19235d9d813 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "So the pumping lemma depends on the fact that if M has p states and it runs for more than p steps, then it's going to enter some state twice." + }, + { + "text": "So you may have seen that before." + }, + { + "text": "It actually has a name, which some of you may have seen." + }, + { + "text": "So let's see how to just get a poll here." + }, + { + "text": "I hope not too many of you are going to pick C, as some of you are." + }, + { + "text": "Oh, well." + }, + { + "text": "Yes." + }, + { + "text": "I think this one, most of you have seen this before." + }, + { + "text": "This is, I think you pretty much all got it." + }, + { + "text": "This is what's known as the pigeonhole principle." + }, + { + "text": "So here, sharing the results." + }, + { + "text": "Obviously, I was having a little fun with this." + }, + { + "text": "And some of you are having fun back at me." + }, + { + "text": "That's OK. OK, so let's continue on." + }, + { + "text": "Let's see how to use the pumping lemma to prove a language is not regular." + }, + { + "text": "So I put the pumping lemma up here just so you can remember the statement of it." + }, + { + "text": "So let's take the language D, which is the language 0 to the k, 1 to the k for any k. So that's some number of 0's followed by an equal number of 1's." + }, + { + "text": "We're going to prove that language is not regular by using the pumping lemma." + }, + { + "text": "And this is going to be just an ironclad proof." + }, + { + "text": "It's not going to say, well, I couldn't think of how to find it a finite automaton." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk23.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..15139d54352e8d5182294ce05941ccf15bfd881d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "This is going to be a proof." + }, + { + "text": "So we want to show that D is not regular." + }, + { + "text": "And we're going to give a, these things always go as a proof by contradiction." + }, + { + "text": "So proof by contradiction, hopefully as a reminder to you, the way that works is you're going to assume the opposite of what you're trying to prove." + }, + { + "text": "And then from that, something crazy is going to happen, something you know is obviously false or wrong." + }, + { + "text": "And so therefore, your assumption, which is the opposite of what you're trying to prove, had to be wrong." + }, + { + "text": "And so therefore, the thing you're trying to prove has to be right." + }, + { + "text": "That's the essence of what's called proof by contradiction." + }, + { + "text": "So first of all, we're going to assume to get our contradiction that D is regular, which is what we're trying to show is not the case." + }, + { + "text": "Now, if D is regular, then we can apply the pumping limit up above here, which gives us that pumping length p, which says that any string longer than p can be pumped and you stay in the language." + }, + { + "text": "That's what the pumping limit tells you." + }, + { + "text": "So let's pick the string s, which is the string 0 to the p, 1 to the p. Here's sort of a picture of s off on the side here." + }, + { + "text": "So a bunch of 0s followed by an equal number of 1s." + }, + { + "text": "And that string is in D, because D is strings of that form." + }, + { + "text": "And it's longer than p. Obviously, it's of length 2p." + }, + { + "text": "So the pumping limit tells us there's a way to cut it up, satisfying those three conditions." + }, + { + "text": "So how in the world could we possibly cut s up?" + }, + { + "text": "Well, remember the three conditions, and especially condition 3 is going to come in handy here, say that you can cut s up into three pieces, x, y, and z, where the first two pieces lie in the first p symbols of s, at most p long." + }, + { + "text": "So x and y together are not very big." + }, + { + "text": "They don't extend beyond the first half of x and first half of s. And in particular, they're all 0s." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk24.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..74f127a7fff9f07a8fee72071dc2d799c1fbdbfe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "x and y are going to be all 0s." + }, + { + "text": "z is going to perhaps have some 0s and will have the rest of the 1s." + }, + { + "text": "We'll have the 1s." + }, + { + "text": "Now, the pumping limit says that if you cut it up that way, you can repeat y as many times as you like, and you stay in the language." + }, + { + "text": "But that's obviously false, because if you repeat y, which now has only 0s, you're going to have too many 0s." + }, + { + "text": "And so the resulting string is no longer going to be of the form 0 to the k, 1 to the k. It's going to be lots of 0s followed by not so many 1s." + }, + { + "text": "That's not in the language." + }, + { + "text": "And that violates what the pumping limit tells you is supposed to happen." + }, + { + "text": "And that's a contradiction." + }, + { + "text": "So therefore, our assumption that D is regular is false." + }, + { + "text": "And so we conclude that D is not regular." + }, + { + "text": "So that's a fairly simple one." + }, + { + "text": "I thought I would do another couple of examples, because you have this on your homework, and I thought it might be helpful." + }, + { + "text": "So here's a second one, slightly harder, but not too much." + }, + { + "text": "Let's take the language F, which looks like the strings ww." + }, + { + "text": "These are strings that are two copies of the same string." + }, + { + "text": "For any string that might be in sigma star, so for any string at all, I'm going to have two copies of that string." + }, + { + "text": "And so F is those strings which are just two copies of the same string." + }, + { + "text": "OK. We're going to show that F is not regular." + }, + { + "text": "These things always go the same way." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk25.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..abe9c80e62aa87a66a61bd402ba07ed83a5bc6c5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the same pattern." + }, + { + "text": "You prove by contradiction." + }, + { + "text": "So you assume for contradiction that D, that's bad." + }, + { + "text": "That was copied from my other slide." + }, + { + "text": "That's wrong." + }, + { + "text": "Let's see if I can actually make this work here." + }, + { + "text": "Good." + }, + { + "text": "Assume for contradiction that F is regular." + }, + { + "text": "The pumping lemma gives F is above." + }, + { + "text": "And so now we need to choose a string S that's in F to do the pumping and show that the pumping lemma is going to fail." + }, + { + "text": "You're going to pump, and you're going to get something which is not in language, which shows that something has gone wrong." + }, + { + "text": "But which S to choose?" + }, + { + "text": "And sometimes, that's where the creativity in applying the pumping lemma comes in, because you have to figure out which is the right string you're going to pump on." + }, + { + "text": "So you might try the string, well, 0 to the p, 0 to the p. That's certainly in F. It's two copies of the same string." + }, + { + "text": "Here it is I've written." + }, + { + "text": "Lots of 0's followed by the same number of 0's." + }, + { + "text": "The problem is, if you use that string, it actually is a string that you can pump." + }, + { + "text": "You can break that string up into three pieces." + }, + { + "text": "And then if you let y be the string 0, 0, actually, you have to be a little careful." + }, + { + "text": "The string just 0 doesn't work, because there's an evenness-oddness phenomenon going here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk26.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..c93dce28015b5b124095b8bed4df964430437405 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk26.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you might want to just think about that." + }, + { + "text": "But if you let y be the string 0, 0, then if you have the string x, y, x, any number of y's, it's still just going to be a bunch of 0's." + }, + { + "text": "And you're going to be able to see that that string is still in the language." + }, + { + "text": "So you haven't learned anything." + }, + { + "text": "If the pumping lemma works and you're satisfying the pumping lemma, you haven't learned anything." + }, + { + "text": "So what you need to find is some other string." + }, + { + "text": "That was a bad choice for s. Find a different string." + }, + { + "text": "So here's a different choice." + }, + { + "text": "0 to the p1, 0 to the p1." + }, + { + "text": "So that's two copies of the same string." + }, + { + "text": "And we're going to show it can't be pumped." + }, + { + "text": "So here's a picture of that string here." + }, + { + "text": "So 0's followed by 1, 0's followed by 1." + }, + { + "text": "And now it's very similar to the first argument." + }, + { + "text": "If you cut it into three pieces in such a way that it satisfies the conditions, the first two pieces are going to be residing only among the 0's." + }, + { + "text": "And so therefore, when you repeat a y, you're no longer going to have two copies of the same string and so won't be in the language." + }, + { + "text": "So therefore, you've got a contradiction and f is not regular." + }, + { + "text": "So you have to play with the pumping lemma a little bit." + }, + { + "text": "If you haven't seen that before, it's going to be, it takes a little getting used to." + }, + { + "text": "But you have a few homework questions that need to be solved using the pumping lemma." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk27.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk27.json new file mode 100644 index 0000000000000000000000000000000000000000..4a6822eab5b9a3a8ebaf98bf8cf56da7dd0beaf3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk27.json @@ -0,0 +1,62 @@ +[ + { + "text": "All right." + }, + { + "text": "So now let's look at, lastly, there is another method that can come in, which is combining closure properties with the pumping lemma." + }, + { + "text": "So closure properties sometimes help you." + }, + { + "text": "So let's look at the language B, which is actually we saw earlier in the lecture, where we have an equal number of 0's and 1's." + }, + { + "text": "Now, we could prove that directly using the pumping lemma as not being regular." + }, + { + "text": "But it's actually even easier." + }, + { + "text": "What we're going to prove that it is, we're going to prove that it's not regular in a different way." + }, + { + "text": "First, we're going to assume for contradiction, as we often do, that it is regular." + }, + { + "text": "And now we're going to use something, we're going to use some other knowledge." + }, + { + "text": "We're not going to use the pumping lemma here because we're going to take advantage of an earlier case where we use the pumping lemma." + }, + { + "text": "And so now we know that the string, the language 0 star 1 star is a regular language because it's described by a regular expression." + }, + { + "text": "If you take the B, which is the equal numbers of 0's and 1's, and you intersect it with 0 star 1 star, that's going to be a regular language if B was regular using closure under intersection." + }, + { + "text": "But this language B intersects 0 star 1 star is the language of equal numbers of 0's and 1's where the 0's come first." + }, + { + "text": "And that's the language D that we showed two slides back that we already know can't be regular." + }, + { + "text": "So that intersection cannot be regular, and so it violates the closure property." + }, + { + "text": "And again, we get a contradiction." + }, + { + "text": "So that's a different way of sometimes making a shortcut to prove a language is not regular." + }, + { + "text": "So we have in our last 10 minutes or so, we're going to shift gears totally in an entirely different way and consider a new model of computation, which is more powerful, that can actually do things that we can't do with finite automata." + }, + { + "text": "And these are called context-free grammars." + }, + { + "text": "So this is really just a kind of an introduction." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk28.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk28.json new file mode 100644 index 0000000000000000000000000000000000000000..135abf63d4f4fe4563d349e8585ba20f755f4900 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk28.json @@ -0,0 +1,62 @@ +[ + { + "text": "We're going to spend all of next lecture looking at context-free grammars." + }, + { + "text": "And they're associated languages." + }, + { + "text": "But let's just do kind of get a preview." + }, + { + "text": "So a context-free grammar looks like this." + }, + { + "text": "You have a bunch of these what we call substitution rules or rules sometimes, which just look like a symbol, arrow, a string of symbols." + }, + { + "text": "All right?" + }, + { + "text": "That's what a context-free grammar looks like at a high level." + }, + { + "text": "Let's define some terms." + }, + { + "text": "So a rule, as I just described, is going to be a symbol, which we're going to call a variable." + }, + { + "text": "And that's going to have an arrow to a string of possibly other variables and symbols called terminals." + }, + { + "text": "So a variable is a symbol that appears on the left-hand side of a rule." + }, + { + "text": "Anything that appears on the left-hand side is going to be considered to be a variable." + }, + { + "text": "So s and r are both variables." + }, + { + "text": "Now, other symbols that appear in the grammar, which don't appear in the left-hand side, those are going to be called terminals." + }, + { + "text": "So here, 0 and 1 are terminals." + }, + { + "text": "Now, you may think that empty string should also be a terminal, but that's not a symbol." + }, + { + "text": "Empty string is a string." + }, + { + "text": "It's just a string of length 0." + }, + { + "text": "So I'm not considering empty string to be a terminal." + }, + { + "text": "And then there's going to be a special variable, which is going to be considered the starting variable, just like we had a starting state." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk29.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk29.json new file mode 100644 index 0000000000000000000000000000000000000000..efafd54bf5686f35914d2bbf6828c3e31e557613 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk29.json @@ -0,0 +1,62 @@ +[ + { + "text": "And that's typically going to be written as the top left symbol." + }, + { + "text": "So this symbol s here is going to be the starting symbol." + }, + { + "text": "And grammars can be used to define languages and to gen, well, to generate strings and to define languages." + }, + { + "text": "So first of all, let's see how a grammar using this as an illustration can generate strings." + }, + { + "text": "Actually, just to emphasize this terminology here, in this particular example, we had three rules." + }, + { + "text": "The two variables were r and s. The two terminals were 0 and 1." + }, + { + "text": "And the start variable was this top left-hand symbol, as I mentioned, the s. So grammars generate strings." + }, + { + "text": "The way they do is you follow a certain procedure, which is really pretty simple." + }, + { + "text": "You write down, first of all, the start variable." + }, + { + "text": "And I'll do an example in a second." + }, + { + "text": "You write down the start variable." + }, + { + "text": "And then you take a look at what you've written down." + }, + { + "text": "And if it has any variables in it, you can apply one of the corresponding right-hand sides of a rule as a substitution for that variable." + }, + { + "text": "And so, for example, if you have an s in the thing you've written down, you can substitute for that s a 0, s, 1." + }, + { + "text": "Or you can substitute for that s an r. Or if you have an r, you can substitute for that s an empty string." + }, + { + "text": "So you're just going to keep on doing that substitutions over and over again until there are no variables left." + }, + { + "text": "So there's nothing left to substitute." + }, + { + "text": "Only terminals remain." + }, + { + "text": "At that point, you have generated a string in the language." + }, + { + "text": "So the language, then, is the collection of all generated strings." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk3.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..156859044caea8ac8df8b834513914788227dd74 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "For the NFAs, we're only allowing just single symbols or the empty string to appear on the labels." + }, + { + "text": "Now I'm actually allowing you to put full regular expressions on the labels for the automaton." + }, + { + "text": "Now, we have to understand how a GNFA processes its input." + }, + { + "text": "And the way it works is not complicated to understand." + }, + { + "text": "When you're getting an input string, feeling when a GNFA is processing an input string, it starts at the start state, just like you would imagine." + }, + { + "text": "But now, to go along a transition, instead of reading just a single symbol or the empty string, as in the case for the nondeterministic machine, it actually gets to read a whole string at one step, kind of at one byte." + }, + { + "text": "It can read an entire string and go along that transition arrow, provided that chunk of the input that it read is in the regular expression that that transition has as its label." + }, + { + "text": "So for example, you can go from Q1 to Q2 in one step in this GNFA by reading AABB off the input." + }, + { + "text": "So it reads all of those four symbols all at once, just swoops them up, and then moves from Q1 to Q2 in one step." + }, + { + "text": "And then when it's in Q2, it can read AAB and move to Q3." + }, + { + "text": "And Q3 happens, there's nowhere to go." + }, + { + "text": "So this is going to be a nondeterministic machine." + }, + { + "text": "There might be several different ways of processing the input." + }, + { + "text": "And if any one of them gets to an accepting state at the end of the input, we say the GNFA accepts." + }, + { + "text": "So it's similar to nondeterministic to NFAs in the way the acceptance criterion works." + }, + { + "text": "So you could do an example, but hopefully, the concept of how this works is reasonably, you can at least buy it, that it processes the input in chunks at a time." + }, + { + "text": "And those chunks have to be described by the regular expressions on the transition arrows as it moves along those transitions." + }, + { + "text": "So what we're going to do now is to convert not DFAs to regular expressions." + }, + { + "text": "We're going to convert GNFAs to regular expression." + }, + { + "text": "That's even harder because GNFAs allow you to do all sorts of other things besides just ordinary DFAs." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk30.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk30.json new file mode 100644 index 0000000000000000000000000000000000000000..7e2faf8e26e344cd085bac4e39d6887fdb9b80e4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk30.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, let's do an example." + }, + { + "text": "Here's an example of G1 generating some string." + }, + { + "text": "So as I mentioned, first of all, you're going to write down the start variable." + }, + { + "text": "And I'm just going to illustrate this in sort of two parallel tracks here." + }, + { + "text": "On the left side, I'm going to show you the tree of substitutions." + }, + { + "text": "And on the right side, I'm going to show you the resulting string that you get by applying those substitutions." + }, + { + "text": "OK?" + }, + { + "text": "So over here, I'm going to substitute for s the string 0, s1." + }, + { + "text": "So on the right-hand side, I just have 0, s1 because that's what I substituted for s. But you'll see it's going to look a little different in a second." + }, + { + "text": "Here, again, I still have a variable." + }, + { + "text": "So I'm going to substitute for s 0, s1." + }, + { + "text": "Now I have the resulting string 0, 0, s1, 1 because I've substituted 0, s1 for the previous s. But the 0 and 1 stick around from before." + }, + { + "text": "They don't go anywhere." + }, + { + "text": "So I have at this point 0, 0, s1, 1." + }, + { + "text": "Now I'm going to take a different choice." + }, + { + "text": "I'm going to substitute for s. I could have gone either way." + }, + { + "text": "There's sort of something almost like nondeterminism here because you have a choice." + }, + { + "text": "I'm going to substitute for s. Instead of 0, s1, I'm going to substitute r because that's also legitimate in terms of the rules." + }, + { + "text": "And so now I'm going to have 0, 0, r, 1, 1." + }, + { + "text": "And now r, there's no choices here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk31.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk31.json new file mode 100644 index 0000000000000000000000000000000000000000..a6b30a611a3de96bd126a4f9a480709882e3cb76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk31.json @@ -0,0 +1,62 @@ +[ + { + "text": "r can only be substituted for by an empty string." + }, + { + "text": "So I get to r becomes just empty string." + }, + { + "text": "And in terms of the string generated, empty string doesn't add anything." + }, + { + "text": "It just really is nothing." + }, + { + "text": "It's a nothing." + }, + { + "text": "So I get the string 0, 0, 1, 1." + }, + { + "text": "And this is a string just of terminal symbols." + }, + { + "text": "And so that is a string in the language of the grammar G1." + }, + { + "text": "If you think about it, G1's language is that language that we saw before, which I think we called D. 0 to the k, 1 to the k for k greater than or equal to 0." + }, + { + "text": "So this is an example of a language that a context-free grammar can do, but a finite automaton cannot do." + }, + { + "text": "So that is our little introduction to content." + }, + { + "text": "Oops, there's one more check-in here." + }, + { + "text": "Oh, yeah, so I'm asking you to actually look at, let me get myself out of this picture so you don't see me blocking things." + }, + { + "text": "And we will do one last check-in." + }, + { + "text": "Check-in, make sure you're staying around for the whole thing." + }, + { + "text": "Now there could be several of these strings that are in the language." + }, + { + "text": "You have to click them all." + }, + { + "text": "All the ones that you have found that are in the language of this grammar that can be generated by grammar G2, you have to click those." + }, + { + "text": "I'll give you a little bit more time on this one to see which ones G2 can generate." + }, + { + "text": "I'll give you a hint." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk32.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk32.json new file mode 100644 index 0000000000000000000000000000000000000000..29c334ff719f29048a591810bb2423b8d296f883 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk32.json @@ -0,0 +1,62 @@ +[ + { + "text": "There's more than one, but not all." + }, + { + "text": "So I see you're making some progress here." + }, + { + "text": "Interesting." + }, + { + "text": "So please, we're going to wrap this up very quickly." + }, + { + "text": "You can click, somebody's telling me you can unclick." + }, + { + "text": "Thank you, good to know." + }, + { + "text": "OK, so still things are coming in here." + }, + { + "text": "So we're running toward the end of the hour here." + }, + { + "text": "I don't want to go over." + }, + { + "text": "So I'm going to end it in five seconds." + }, + { + "text": "Click away." + }, + { + "text": "And don't forget, we're not going to charge you if you get it wrong." + }, + { + "text": "Sharing results, I don't know why it has an orange one there because there are several correct answers here." + }, + { + "text": "So it's A, B, and D are correct." + }, + { + "text": "You can get any of those." + }, + { + "text": "It's really sort of two copies of the language we had before next to one another." + }, + { + "text": "And so the only thing you cannot get is 1, 0, 1, 0." + }, + { + "text": "So I encourage you to think about that." + }, + { + "text": "And I will come to our last side of today, which is just a quick review." + }, + { + "text": "I can put myself back." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk33.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk33.json new file mode 100644 index 0000000000000000000000000000000000000000..c9acb271e5df7aa61fe9639e258eaf0c493b6aa0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk33.json @@ -0,0 +1,26 @@ +[ + { + "text": "So we showed how to convert DFAs to regular expressions." + }, + { + "text": "And the summary is that DFAs, NFAs, GNFAs even, and regular expressions are all equivalent in the class of languages they can describe." + }, + { + "text": "The second thing we did was a method for proving languages not regular by using the pumping lemma or closure properties." + }, + { + "text": "And lastly, we introduced context-free grammars." + }, + { + "text": "And we're going to see more about those on Thursday." + }, + { + "text": "So with that, I think we're out of time." + }, + { + "text": "And I'll thank you for the notes of appreciation." + }, + { + "text": "And I think we're going to end here and see you on Thursday, if not before." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk4.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..1abb85ffc0c9fe28dfd0e54212e5b201e25c69fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's a harder job." + }, + { + "text": "Why am I making my life harder?" + }, + { + "text": "Well, you'll see in a minute that it's going to actually turn out to be helpful to be working with a more powerful model in the way this construction is going to work." + }, + { + "text": "Now, before I dive in and do the construction from GNFAs to regular expressions, I'm going to make a simplifying assumption about the GNFAs." + }, + { + "text": "I'm going to put them in a special form that's going to make it easier to do the conversion." + }, + { + "text": "And that simpler form is, first of all, I'm going to assume the GNFA has just a single accepting state." + }, + { + "text": "And that accepting state is not allowed to be the start state." + }, + { + "text": "So it has to have just a single accepting state." + }, + { + "text": "I've already violated that convenient assumption in this GNFA because I have here two accepting states." + }, + { + "text": "That's not what I want." + }, + { + "text": "I want to have just one." + }, + { + "text": "Well, the thing is, it's easy to obtain just one, just to modify the machine so that I have just one by adding a new accepting state, which is branched to from the former accepting states by empty transition." + }, + { + "text": "So I can always jump from Q2 to Q4 at any time without even reading any input, just going along this empty transition." + }, + { + "text": "And then I declassify the former accepting states as accepting." + }, + { + "text": "And now I have here just a single accepting state." + }, + { + "text": "And because it's going to be a new state that I added, it won't be the start state." + }, + { + "text": "And I have accomplished that one aspect of my assumption about the form of the GNFA." + }, + { + "text": "But there's another thing that I want to do too." + }, + { + "text": "I want to assume, as you will see, which is going to be convenient in my construction, that we will have transition arrows going from every state to every other state." + }, + { + "text": "In fact, I want transition arrows going from every state, even back to themselves." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk5.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..521d4ba36192f0be34911067bb4275e288e25a4a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "I want there to be all possible transition arrows should be present, with two exceptions." + }, + { + "text": "For the start state, there should be only transition arrows exiting the start state." + }, + { + "text": "And for the accepting state, there's just one now, there should be only transition arrows coming in to the start state." + }, + { + "text": "So it's kind of what you would imagine as being reasonable." + }, + { + "text": "For the other states which are not accepting or starting, there should be transition arrows leaving and coming from everywhere else." + }, + { + "text": "But for the start states, just leaving, and for the accept state, just coming in." + }, + { + "text": "And you can easily modify the machine to achieve that." + }, + { + "text": "Let's just see how to do that in one example." + }, + { + "text": "So notice that from Q3 to Q2, there is no transition right now." + }, + { + "text": "And that's not good." + }, + { + "text": "That's not what I want." + }, + { + "text": "I want there to be a transition from Q3 to Q2." + }, + { + "text": "Well, I'll just add that transition in." + }, + { + "text": "But I'm going to label it with the empty language regular expression." + }, + { + "text": "So that means, yeah, the transition is there, but you never can take it." + }, + { + "text": "So it doesn't change the language that the machine is going to be recognizing, but it fulfills my assumption, my convenient assumption, that we have all of these transition arrows being present in the machine." + }, + { + "text": "So anyway, I hope you will buy it." + }, + { + "text": "It's not going to be, if you don't quite get this, don't worry." + }, + { + "text": "It's not totally critical that you're following all of these little adjustments and modifications to the GNFA." + }, + { + "text": "But it will be helpful to understand what GNFA themselves, how they work." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk6.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..67174286045cf45ee03934650fbbd6cd17fcf8db --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So as I mentioned, we can easily modify GNFA to have the special form that we're assuming here." + }, + { + "text": "All right, so now we're going to jump in and start doing the conversion." + }, + { + "text": "So we're going to have a lemma, which is like a theorem that really is just a local interest here." + }, + { + "text": "It's not a general interest theorem." + }, + { + "text": "It's going to be relevant just to GNFA, which are really just defined to help us do this conversion." + }, + { + "text": "They really don't have any other independent value." + }, + { + "text": "So I want to show that every GNFA has an equivalent regular expression R. That's really my goal." + }, + { + "text": "And the way we're going to prove that is by induction." + }, + { + "text": "It's going to be by induction on the number of states of the GNFA." + }, + { + "text": "Now, you really should be familiar with induction as one of the expectations for being in this course." + }, + { + "text": "But in case you're a little shaky on it, don't worry." + }, + { + "text": "I'm going to unpack it as a procedure." + }, + { + "text": "It's really just recursion." + }, + { + "text": "And a proof that uses induction is really just a proof that calls itself." + }, + { + "text": "It's just a proof that it's a recursive proof." + }, + { + "text": "That's all it is." + }, + { + "text": "So if you're comfortable with recursion, you'll be comfortable with induction." + }, + { + "text": "But anyway, I'm going to describe this as a procedure." + }, + { + "text": "So if you're a little shaky on induction, don't worry." + }, + { + "text": "So the basis is, so first, I'm going to handle the case where the GNFA has just two states." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk7.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..2ae3a210649fe25ab767d4daea72fa1940be0890 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, remember, I'm assuming now my GNFAs are in the special form." + }, + { + "text": "So you can't even have a GNFA with one state because it has to have a start state, and it has to have an accept state, and they have to not be the same." + }, + { + "text": "So the smallest possible GNFA to worry about is a two-state GNFA." + }, + { + "text": "Now, if we happen to have a two-state GNFA, it turns out to be very easy to find the equivalent regular expression." + }, + { + "text": "Why?" + }, + { + "text": "Because that two-state GNFA can only look like this." + }, + { + "text": "It can have a start state, can have an accept state, and it can only have a transition going from the start to the accept because no other transitions are allowed." + }, + { + "text": "It only has outgoing from the start, only incoming to the accept." + }, + { + "text": "And so there's only one transition, and it has a label with a regular expression r. So what do you think the equivalent regular expression is for this GNFA?" + }, + { + "text": "It's just simply the one that's labeling that transition because that tells us when I can go from the start to the accept." + }, + { + "text": "And there's nothing else the machine can do." + }, + { + "text": "It just makes one step, which is to accept its input if it's described by that regular expression." + }, + { + "text": "So therefore, the equivalent regular expression that we're looking for is simply label on that single transition." + }, + { + "text": "OK, so two-state GNFAs are easy." + }, + { + "text": "But what happens if you have more states?" + }, + { + "text": "Then you're going to actually have to do some work." + }, + { + "text": "So we call that the induction step." + }, + { + "text": "That's when we have more than two states." + }, + { + "text": "And the way the induction works is we're going to assume we already know how to do it for k minus 1 states." + }, + { + "text": "And we're going to use that knowledge to show how to do it for k states." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk8.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..b9f7d5f3fe171ffef6f4721c917566ae0b7d2241 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "So in other words, we already know how to do it for two states." + }, + { + "text": "I'm going to use that fact to show how to do it for three states, and then use the fact that I can do it for three states to show how to do it for four states, and so on and so on." + }, + { + "text": "All right?" + }, + { + "text": "And the idea for how to do that is actually pretty easy to grasp." + }, + { + "text": "What we're going to do is if we have a k-state GNFA that we want to convert, we're going to change that k-state GNFA to a k minus 1-state GNFA, and then use our assumption that we already know how to do the k minus 1-state GNFA." + }, + { + "text": "All right?" + }, + { + "text": "So in terms of a picture, I'm going to take a k-state to prove that I can always convert k-state GNFAs to regular expressions." + }, + { + "text": "I'm going to show how to convert the k-state one into an equivalent k minus 1-state GNFA." + }, + { + "text": "And then if you just like to think of it this procedurally, the k minus 1 gets converted to a k minus 2, gets converted to a k minus 3, and so on and so on, until I get down to 2, which then I know how to do directly." + }, + { + "text": "OK?" + }, + { + "text": "So the whole name of the game here is figuring out how to convert a GNFA that has k states into another one that has one fewer state that does the same language." + }, + { + "text": "OK, so you have to hold that in your head." + }, + { + "text": "I mean, I wish I had more blackboard space here, but it's very limited here." + }, + { + "text": "So you have to remember what we're going to be doing on the next slide, because that's going to finish the job for us." + }, + { + "text": "As long as I can show in general how to convert a k-state GNFA to a GNFA that has one fewer state, but it still does the same language, I'm good." + }, + { + "text": "Because then I can keep iterating that until I get down to 2." + }, + { + "text": "All right, so this is the guts of the argument." + }, + { + "text": "So I have my k-state machine." + }, + { + "text": "Here's my start state." + }, + { + "text": "Here's my accept state." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk9.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..5e87a17d5f39b11dc10ac74dbf5bb68324bb160e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_0_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "Here's my k minus 1 state, that machine that I'm going to be building for you." + }, + { + "text": "It's actually going to look almost exactly the same." + }, + { + "text": "I'm just going to remove one state from the bigger machine." + }, + { + "text": "So I'm going to pick any state, which is not the start state or the accept state." + }, + { + "text": "Here it is pictured here." + }, + { + "text": "I mean, all of the states of the k-state machine are going to appear in the k minus 1 state machine, except for one state that I'm going to rip out." + }, + { + "text": "That's the state x." + }, + { + "text": "It's now here as a ghost." + }, + { + "text": "It's been removed." + }, + { + "text": "It's not there anymore." + }, + { + "text": "But I'm just helping you to remember that it used to be there by showing a shadow." + }, + { + "text": "But it's a I have taken my original machine that had k states and basically just ripped out a state." + }, + { + "text": "And now I have one fewer state." + }, + { + "text": "So the good news is that I now have a machine with k minus 1 states." + }, + { + "text": "That's what I want." + }, + { + "text": "But the bad news is that it doesn't do the same language anymore." + }, + { + "text": "I broke the machine by rip." + }, + { + "text": "If you're just going to rip out a state, who knows what the new machine is going to do?" + }, + { + "text": "It's going to be probably not the same as what the original machine did." + }, + { + "text": "So what I need to do then is repair the damage." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk0.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..9286debb4969f2ab2aefd848d4fffac039ca6f55 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay, folks." + }, + { + "text": "Here we are again." + }, + { + "text": "Welcome back for another episode of Theory of Computation." + }, + { + "text": "This is lecture number three." + }, + { + "text": "I am going to review what we've been doing." + }, + { + "text": "We've been looking at finite automata and regular languages." + }, + { + "text": "Those are the languages that the finite automata can recognize." + }, + { + "text": "And we talked about non-determinism." + }, + { + "text": "So we had non-deterministic finite automata and deterministic finite automata." + }, + { + "text": "We showed that they're equivalent." + }, + { + "text": "We looked at the closure properties over the regular operations, union, concatenation, and star, and showed that the regular languages, really the class of regular languages, is closed under those regular operations." + }, + { + "text": "And we used the constructions that we developed in the proof of those closure properties to show that we can give a way to convert regular expressions to finite automata." + }, + { + "text": "So that was partway toward our goal of showing that these regular expressions and finite automata are equivalent with respect to the class of languages they describe, namely the regular languages." + }, + { + "text": "So regular expressions of finite automata are interchangeable from the perspective of what kinds of languages you can do with them." + }, + { + "text": "So we're going to finish that off today." + }, + { + "text": "So let's take a look at what our next topics we're going to be covering." + }, + { + "text": "We're going to reverse the construction we gave last time, which allowed us to convert regular expressions to finite automata." + }, + { + "text": "Now we're going to go backwards." + }, + { + "text": "We're going to show how to convert finite automata back to regular expressions." + }, + { + "text": "And those two constructions together show us that the regular expressions and finite automata can be interconverted from one another." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk1.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..83e2e7e646f6e7885e4c8cce2c717ec347478ab1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And they're therefore equivalent with respect to the kinds of things they can do in language recognition or generation." + }, + { + "text": "Then we're going to prove that we're going to look at how you prove certain languages are not regular." + }, + { + "text": "They're beyond the capabilities of finite automata." + }, + { + "text": "And finally, at the end, we're going to introduce a new model of computation, which is more powerful than the finite automata and regular expressions, namely the context-free grammars." + }, + { + "text": "Those can do other kinds of languages that the simpler finite automata regular expressions models can't do." + }, + { + "text": "And I would also just like to note that a lot of what we're doing is a warm-up toward the more powerful models of computation that we're going to be looking at later, well, in a week or so, which are more general purpose computation." + }, + { + "text": "But along the way, introducing these models of finite automata and context-free languages is interesting and helpful because many of those, a number of those models turn out to be useful in a number of applications, whether it's from linguistics to programming languages." + }, + { + "text": "And a variety of different parts of computer science and other fields as well use those notions." + }, + { + "text": "So they're useful notions beyond just in this course." + }, + { + "text": "So I just want a couple of administrative things to touch on." + }, + { + "text": "We are going to have additional check-ins today." + }, + { + "text": "As I mentioned to you, we're going to start counting participation, not correctness, just participation in the live check-ins." + }, + { + "text": "So with that, let us move on to today's material." + }, + { + "text": "As I mentioned, we're going to be showing how to convert finite automata to regular expressions." + }, + { + "text": "And that's going to complete our equivalence of finite automata and regular expressions." + }, + { + "text": "So just to recap what we did last time, we showed that if you have a regular expression and it describes some language, then that language is regular." + }, + { + "text": "So in other words, we have a way of, we gave a way of converting regular expressions to finite automata, as kind of shown in this diagram." + }, + { + "text": "That's what we did last time." + }, + { + "text": "Now we're going to go the other way." + }, + { + "text": "We're going to show how to convert." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk10.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..252369997cbaf6cb940707c8eac940076c4ff217 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "I've got to fix the damage that I caused by removing x." + }, + { + "text": "And whatever role x was playing in the original machine, I've got to make sure that the new machine that I have, which doesn't have x anymore, can still do the same things that the original machine did." + }, + { + "text": "And so the way I'm going to do that is look at all of the paths that could go through x and make sure that they're still present, even though I don't have x anymore." + }, + { + "text": "And the way I'm going to do that is I'm going to consider a part of a path that might use x." + }, + { + "text": "So let's pick two states, qi and qj, in the machine that had k states." + }, + { + "text": "Let me just see here." + }, + { + "text": "I don't know if this is." + }, + { + "text": "OK." + }, + { + "text": "So if we have, we'll pick two states, qi and qj, in the original machine." + }, + { + "text": "Now, qi might have the possibility of going to state x." + }, + { + "text": "And then x might have a self loop." + }, + { + "text": "And then it might go to qj." + }, + { + "text": "The new machine doesn't have x anymore." + }, + { + "text": "So the way I'm going to fix that is by replacing the label that goes directly from i to j with a new label that adds in all of the things I lost when I removed x. OK, that's the whole idea here." + }, + { + "text": "So here is qi to qj, but there's no x anymore." + }, + { + "text": "How could I get from qi to qj?" + }, + { + "text": "What were the inputs that could have brought us from qi to qj via x?" + }, + { + "text": "Well, they would have been an input that read a string described by R1." + }, + { + "text": "I might have self looped at x a few times." + }, + { + "text": "So I might have read several strings that are described by R2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk11.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..568360bc5f2588be674edcfcb746eadb5c2f9fe8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I would have read a string that was described by R3." + }, + { + "text": "And now I'm at qj." + }, + { + "text": "OK, so the new label that I'm going to place over here is going to be the strings that I get from reading R1, reading a string that's described by R1, then multiple copies of a string, multiple strings that are possibly described by R2, which is the same as R2 star, and then a string that could be described by R3." + }, + { + "text": "So that is a new addition to the transition that takes me from qi to qj." + }, + { + "text": "Of course, I need to include the things that would have taken me from qi to qj in the first place." + }, + { + "text": "So I'm also unioning in R4, which was the direct route from qi to qj that did not transit through x." + }, + { + "text": "So by making that new regular expression on the qi to qj transition, I have compensated for the loss of x for paths that go from qi to x and then out to qj." + }, + { + "text": "Now, what I need to do is to do that same thing for every pair qi and qj that are in the original machine." + }, + { + "text": "And so if I do that for every possible pair, I'll be modifying all of the transitions in the new machine in a way that compensates for the loss of x." + }, + { + "text": "And now the new machine has been repaired from the damage that I caused by removing x, and it does the same language." + }, + { + "text": "It's the kind of thing you need to think a little bit about, I understand." + }, + { + "text": "But at least hopefully, the spirit of what I just described to you comes through, that we're going to convert this machine with k states to one with k minus 1 states by removing a state and repairing the damage." + }, + { + "text": "And now it does the same language, and then I can remove another state and do the same thing over and over again until I get down to two states." + }, + { + "text": "So that's the idea." + }, + { + "text": "And that really completes the proof." + }, + { + "text": "That shows that I can convert every GNFA to a regular expression." + }, + { + "text": "OK?" + }, + { + "text": "And that really is the end of the story for this." + }, + { + "text": "And thus, I claim that DFAs now and regular expressions are equivalent." + }, + { + "text": "So I'm going to give you a little check-in here on this, really just to see, high level, if you're following what's going on." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk12.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..dbe5caad5cce0bc2bc69d4c6d06bb18a987d24fc --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "All right?" + }, + { + "text": "So just take a look." + }, + { + "text": "So we just showed how to convert GNFAs to regular expression, but we really wanted to convert DFAs to regular expressions." + }, + { + "text": "So how do we go from converting GNFAs to converting DFAs?" + }, + { + "text": "It's not the same, obviously." + }, + { + "text": "So how do we finish that?" + }, + { + "text": "So there are three choices here." + }, + { + "text": "First, we have to show how to convert DFAs to GNFAs, maybe, or show how to convert GNFAs to DFAs." + }, + { + "text": "Or maybe we're already done." + }, + { + "text": "So maybe I better launch that poll while you're reading that." + }, + { + "text": "And there you go." + }, + { + "text": "Hopefully, you can." + }, + { + "text": "All right." + }, + { + "text": "Why don't I end this?" + }, + { + "text": "It's a little worrisome, because I would say we have a plurality who got the right answer, but not a majority." + }, + { + "text": "So let us share the results." + }, + { + "text": "So I sense not all of you are with me, but you're going to have to either that or you're reading your email while we're talking." + }, + { + "text": "I'm not sure." + }, + { + "text": "But whatever it is, you need to think a little bit about what's going on here, because the reason why we are done is because DFAs are a kind of GNFAs." + }, + { + "text": "They have a very simple kind of regular expression on each transition." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk13.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..dca0ba4b63bf044c3e170fa5966aafd47c578e59 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "They just have the regular expression, which is just a single symbol." + }, + { + "text": "So all DFAs are automatically GNFAs." + }, + { + "text": "So if I can convert GNFAs, I can certainly convert DFAs, because GNFAs include the DFAs." + }, + { + "text": "I'm done." + }, + { + "text": "It really was number C was the correct answer." + }, + { + "text": "So good thing we're not counting correctness here." + }, + { + "text": "So participation is good enough." + }, + { + "text": "But I do think you need to think about what's going on and making sure that you're following along." + }, + { + "text": "So anyway, that's a we'll carry on here, but it makes me a little concerned." + }, + { + "text": "OK, so let us now move on." + }, + { + "text": "So we're going to talk a little bit about non-regular languages." + }, + { + "text": "So somebody's asking, don't we have to still make the DFAs into the special type?" + }, + { + "text": "Yes, we do." + }, + { + "text": "We have to make them to the special type." + }, + { + "text": "But we already showed how to make GNFAs into the special type." + }, + { + "text": "And DFA, that is going to apply to DFAs as well." + }, + { + "text": "They'll become GNFAs." + }, + { + "text": "You can add the extra start, add a new start state, add a new accept state, add in all the transitions, which you didn't have before with the empty language label." + }, + { + "text": "And you'll have a GNFA from a DFA." + }, + { + "text": "But that applies to GNFAs in general." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk14.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..01ae4c50774a06079ffb3aa23520bf0e5e1d63af --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it's nothing special about DFAs there." + }, + { + "text": "Anyway, I think you need to chew on that." + }, + { + "text": "And hopefully, you'll be following going forward." + }, + { + "text": "Anyway, let us look now at proving non-regularity." + }, + { + "text": "So we're finished with our goal of showing that regular languages can either come from DFAs or from regular expressions." + }, + { + "text": "Those are the same in terms of, from the perspective of our course, they're interchangeable." + }, + { + "text": "So now, as we mentioned, there are going to be some languages which are not regular, which can't be done by DFAs." + }, + { + "text": "They're actually, DFAs are actually pretty weak as a computational model." + }, + { + "text": "And so there's all sorts of very simple things that they cannot do." + }, + { + "text": "There are some fairly complicated things that they can do, surprisingly enough." + }, + { + "text": "But anyway, there are some simple things they can't do." + }, + { + "text": "And so we have to develop a method for showing that a language is not regular." + }, + { + "text": "And that's going to be useful for your homework and, in general, for just understanding the power of DFAs." + }, + { + "text": "So how do we show a language is not regular?" + }, + { + "text": "So remember, if you want to show a language is regular, basically, what you need to do is give a DFA." + }, + { + "text": "Or you can use the closure properties." + }, + { + "text": "That's another way of showing a language is regular." + }, + { + "text": "But underneath that, it's basically constructing DFAs." + }, + { + "text": "All right." + }, + { + "text": "To show a language is not regular, you have to give a proof." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk15.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..be42fee89e7bfab24c0f41195c67f09c15259d03 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Generally, not a construction." + }, + { + "text": "It's a proof that there is no DFA or that it's just going to be impossible to make a DFA." + }, + { + "text": "And we have to develop a method." + }, + { + "text": "What is that proof method?" + }, + { + "text": "Now, there is a tempting, I've taught this course many times, and there's a kind of a tempting approach that many people have." + }, + { + "text": "It's not only going to apply for finite automata, but for other things too." + }, + { + "text": "And believe me, it's not only people in this class." + }, + { + "text": "It's for people out there who are trying to think about computation in general, which is to say, well, I have some language of trying to figure out if it's regular or not." + }, + { + "text": "And so I thought really hard how to make a DFA, and I couldn't find one." + }, + { + "text": "Therefore, it's not regular." + }, + { + "text": "That's not a proof." + }, + { + "text": "Just because you couldn't find a DFA doesn't mean there is no DFA." + }, + { + "text": "You need to prove that the language is not regular using some method." + }, + { + "text": "So I'm going to give you an example where that kind of approach can lead you wrong." + }, + { + "text": "And that is, I'll give two examples of languages where you might try to prove they're regular or not, and you could be in trouble if you just follow that kind of informal approach." + }, + { + "text": "So if you take the language B, where these are straight, but let's assume our alphabet is 0's and 1's." + }, + { + "text": "B is the language of all strings that have an equal number of 0's and 1's." + }, + { + "text": "So you want to know, if I have 1,000 0's, I need to have 1,000 1's." + }, + { + "text": "So basically, the way you test that, you'd have to count up the number of 0's, count up the number of 1's, and see if those two counts are the same." + }, + { + "text": "And that's going to be really tough to make a DFA do, because how are you going to remember that really big number of 0's that the DFA might have 50 states, but you might need to count up to 100 or a million to figure out, to count up how many 0's you've seen." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk16.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..869d18fb7ad9c2c13594508db2fb7931a3946a56 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it seems really hard to be able to do that kind of a count when you only have 50 states." + }, + { + "text": "So whatever number of states you have, it seems hard to count when you have a finite automaton." + }, + { + "text": "So the intuition is, it's not regular, because a finite automaton can't count, which, in this case, you can convert that intuition into a real proof." + }, + { + "text": "I would say it's not a real proof yet, but it can be made into a real proof." + }, + { + "text": "But compare that case with another language, which I'll call C, which instead of looking at its input to see whether it has an equal number of 0's and 1's, I'm going to look at the input and look at the substrings of 0 1's and 1 0's, those two substrings, and count the number of occurrences of 0 1 as a substring and the number of occurrences of 1 0 as a substring." + }, + { + "text": "Just to make sure you're understanding, let's look at two examples." + }, + { + "text": "So the string 0 1 0 1 is not going to be in C, because if you count up the number of 0 1's and the number of 1 0's, not the same." + }, + { + "text": "So I'm even going to help you here, if you can see that." + }, + { + "text": "The number of 0 1's is 2, but there's only a single occurrence of 1 0." + }, + { + "text": "So those two counts are different, and so that's why this input string is not in C. Compare that with the string 0 1 1 0." + }, + { + "text": "Now, if you count up the number of 0 1 and 1 0 substrings, you're going to get the same value, because here we have a single 0 1 and a single 1 0." + }, + { + "text": "And so now the two counts of those number of substrings are the same, and so that's why you're in C. Now my question is, is C a regular language?" + }, + { + "text": "Well, it looks like it shouldn't be regular for the same reason that B isn't regular, because you have to count up two quantities and compare them." + }, + { + "text": "OK?" + }, + { + "text": "So now, so if we, so that's our intuition, that you just can't do it with a finite automaton, because you have to do the same kind of counting that you would have had to do for language B." + }, + { + "text": "But here, you would be wrong, because C, in fact, is regular." + }, + { + "text": "It has a much simpler description than the one I gave over here at the beginning." + }, + { + "text": "There's the very same language C can be described in a much, much simpler way." + }, + { + "text": "I'm not going to tell you what it is." + }, + { + "text": "You can mull that over." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk17.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..4a3dcc0d97e5c9491cfeabfbca0fb80b79bb39fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "You can try some examples to figure it out, but it has a much simpler description." + }, + { + "text": "It's not a totally trivial description." + }, + { + "text": "I mean, there is some content there, but it is the kind of thing that a finite automaton can do." + }, + { + "text": "It wouldn't do the counting this way." + }, + { + "text": "So the moral is, the punchline is, that sometimes the intuition works, but it can also be wrong." + }, + { + "text": "And so the moral of the story is you need to give a proof when you're doing things like that." + }, + { + "text": "OK?" + }, + { + "text": "So what we're going to do next in the second half of the lecture is to give a method for proving languages are not regular." + }, + { + "text": "And again, you're going to need to use that on your homework, so I hope you get it." + }, + { + "text": "But first of all, oh, did I never stop sharing that poll?" + }, + { + "text": "Forgive me." + }, + { + "text": "And so with that, I think we'll take our little requested break." + }, + { + "text": "And for five minutes, and we'll be back in five minutes." + }, + { + "text": "So break time." + }, + { + "text": "All righty." + }, + { + "text": "We are done here." + }, + { + "text": "And proving languages not regular." + }, + { + "text": "OK." + }, + { + "text": "The way we're going to prove languages are not regular is by introducing a method called the pumping lemma." + }, + { + "text": "And the overarching plan at the pumping lemma, without getting into the specifics of it, is to show that that lemma says all regular languages have a certain property, which we will describe." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk18.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..3a7cdaf962dbe23e26a82d78bd238821d23c9d4f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so to show a language is not regular, you simply show the language doesn't have that property." + }, + { + "text": "Because all regular languages have to have that property." + }, + { + "text": "And so by showing a language fails to have the property, it could not be regular." + }, + { + "text": "OK, that's the plan." + }, + { + "text": "OK, now the property itself is a little complicated to describe, but not too bad." + }, + { + "text": "I'll try to unpack it for you." + }, + { + "text": "But first, let's look at the statement of the lemma, which says that whenever you have a regular language, let's call it A." + }, + { + "text": "So for every regular language A, there's always a special value called the pump, a number, P we'll call it, called the pumping length." + }, + { + "text": "It's a special number." + }, + { + "text": "And that length tells you that whenever a string is in that language and it's longer than that length, then something special happens." + }, + { + "text": "You can take that string, and you can modify it, and you still stay in the language." + }, + { + "text": "So anything that's longer than that special length can be modified in a certain way, and you still stay in the language." + }, + { + "text": "So let's look at the actual statement of the lemma." + }, + { + "text": "So there is a number P such that if S is a string in the language and it's longer than P, or at least of length P, then you can take S, and you can cut it up into three pieces, x, y, and z." + }, + { + "text": "So that's just breaking S into three pieces, where you can take that middle piece, repeat it as many times as you like, and you still stay in the language." + }, + { + "text": "That's what the pumping lemma is saying." + }, + { + "text": "And there's a bunch of other conditions here too." + }, + { + "text": "But the spirit of the pumping lemma says whenever you have a regular language, there's some cutoff such that all strings longer than that cutoff can be what we call pumped." + }, + { + "text": "You can take that string, you can find a section somewhere in the middle of that string, or somewhere you cut it up into three pieces, you take that center piece, and you can repeat it." + }, + { + "text": "You can pump it up." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk19.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..8403cf67b9b11571a56211adc8dbe40022202c75 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "And by repeating that string and repeating that piece, the string gets longer and longer, but you still stay in the language." + }, + { + "text": "That's the special property that all regular languages have." + }, + { + "text": "So kind of in an informal way, and I'll try to help you get the feeling for this, formally it says that if you have a regular language, then every long string, so long is by informal way of saying bigger than this value p, every long string in the language can be pumped." + }, + { + "text": "And this result still stays in the language." + }, + { + "text": "And by pumped means I can cut the string into three pieces and repeat that middle piece as many times as I want." + }, + { + "text": "That's what I mean by pumping a string." + }, + { + "text": "So we'll do some examples in a second." + }, + { + "text": "But first, we're going to see how to prove this." + }, + { + "text": "And hopefully, that'll give you some feeling also for why it's true." + }, + { + "text": "And actually, maybe before I actually jump into the proof, let's look at these three conditions here just to understand it a little bit more thoroughly." + }, + { + "text": "So condition one kind of says what I just was telling you." + }, + { + "text": "I can break s into three pieces, x, y, z, such that if I take xy to the iz, so that's repeating y as many times as I want." + }, + { + "text": "So here's y to the i kind of defined, if that's helpful to you, just y, i copies of y." + }, + { + "text": "So I can take xy to the iz, and I remain in the language for every value of i, even i equals 0, which means we're just removing y, which is sometimes actually a useful thing to do." + }, + { + "text": "But let's not get ahead of ourselves." + }, + { + "text": "So I'm guaranteed to be able to cut s up into x, y, z, so that the string xyyy is still in the language, or xyyyyy, it's still in the language." + }, + { + "text": "That's going to be guaranteed for every regular language." + }, + { + "text": "That's a feature that's going to be true." + }, + { + "text": "And furthermore, and this is going to be turning out to be, it's not really kind of part of the core idea of the pumping lemma, but it actually turns out to be very helpful in applying the pumping lemma, you can always cut it up in such a way that the first two pieces are not longer than that value p. So it restricts on the ways you can cut the thing up." + }, + { + "text": "And that actually turns out to be very helpful." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk2.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..c3b8b03523aaa28deab6d17770cb0f2a52dd0df2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Oh, and just a reminder in case you're just getting yourself your memory to work, maybe it'll help you just to remember that we actually did an example of that conversion." + }, + { + "text": "We looked at this regular expression A union AB star." + }, + { + "text": "And we actually worked through the process of converting that." + }, + { + "text": "Oops, I need to make myself smaller so you can see all that." + }, + { + "text": "We went through the process of converting A union AB star as an example of that, of, I mean, OK, well, we went through the process of actually doing that conversion." + }, + { + "text": "And now we're going to show how to do it the other way around." + }, + { + "text": "All right?" + }, + { + "text": "So we're going to invert that and go backwards the other way." + }, + { + "text": "So today's theorem is to show that if A is regular, namely, it's the language of some finite automaton, then you can convert it to a regular expression which will describe that same language." + }, + { + "text": "So basically, we're going to give a conversion from finite automata to regular expressions." + }, + { + "text": "But before we do that, we're going to have to introduce a new concept." + }, + { + "text": "So we're not going to be able to dive right into that conversion." + }, + { + "text": "We're going to have to introduce a new model first, which is going to facilitate that conversion." + }, + { + "text": "And that new model is called, it's yet another kind of finite automaton, called a generalized nondeterministic finite automaton, or a generalized NFA, or just simply a GNFA." + }, + { + "text": "So this is yet another variant of the finite automaton model." + }, + { + "text": "And conceptually, it's very simple." + }, + { + "text": "It's similar to the NFAs." + }, + { + "text": "I'll give you, here's a picture of a GNFA named G, G1." + }, + { + "text": "Very similar to the NFAs." + }, + { + "text": "But if you look at it for a second, you'll see that the transitions have more complicated labels." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk20.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..49e4439744e11671b889cab994b48437311d0b43 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "But let's first just look at the proof of this, giving kind of a little bit the high level picture." + }, + { + "text": "So my job is to show if I have a string in my language, let's say it's a, think of it as a long string, really long." + }, + { + "text": "So its length is more than p. But I think intuitively, it's just a very long string." + }, + { + "text": "And I'm going to feed that string into the machine and watch what happens." + }, + { + "text": "Something special happens when I feed the string and I look at how the machine proceeds on that string." + }, + { + "text": "Because s is so long that as I wander around inside the machine, I have to end up coming back to the same place more than once." + }, + { + "text": "It's like if you have a small park and you go for a long walk, you're going to end up coming back to where you've already seen." + }, + { + "text": "You just can't keep on seeing new stuff when you have a more small area of space to explore." + }, + { + "text": "So we're guaranteed that M is going to end up repeating some state when it's reading s, because s is so long." + }, + { + "text": "So pictorially, if you imagine here this wiggly line is kind of describing the path that M follows when it's reading s, it ends up coming back to that state qj more than once." + }, + { + "text": "So it comes back here, cycles around, comes back again before it ends up accepting." + }, + { + "text": "We know it ends up accepting because we're assuming we have a string that's in the language." + }, + { + "text": "So we picked s in the language." + }, + { + "text": "So it has to be accepted by M. But the important thing is that it repeats a state." + }, + { + "text": "Now, how does that tell me I can cut s up into those three pieces?" + }, + { + "text": "Well, I'm going to get those three pieces here." + }, + { + "text": "First of all, let's observe that here is as processing s. Here is that written right on top of the string, that state repetition occurring, qj more than once." + }, + { + "text": "And now if I look inside the machine, the part of s that took me to qj I'm going to call x." + }, + { + "text": "The part that took me from qj back to itself is I'm going to call y." + }, + { + "text": "And the part that took qj to the accept state, I'm going to call z." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk21.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..b4f87b7d241103ee7f11c3784b2529abdb28305a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I'm going to mark those off in s. And that gives me the way to cut s up into three pieces." + }, + { + "text": "Now, if you're appreciating what's going on inside the machine, you will see why M will also accept the string x, y, y, z." + }, + { + "text": "Because every time, once you're at qj, if you go around once, you come back to qj." + }, + { + "text": "And then if you go again, you'll come back to qj." + }, + { + "text": "And as many times as you keep seeing that y, you're just going to keep coming back to qj." + }, + { + "text": "So it doesn't matter how many y's you have." + }, + { + "text": "You're going to still, if you follow it by z, which is what you will do, you'll end up accepting the string." + }, + { + "text": "And that's really the proof." + }, + { + "text": "I mean, you have to do a little bit more here just to understand." + }, + { + "text": "I should have mentioned why I want to forbid y being the empty string." + }, + { + "text": "Because if y is the empty string, it's not interesting." + }, + { + "text": "It doesn't change." + }, + { + "text": "Repeating it doesn't actually change anything." + }, + { + "text": "So I have to make sure it's not empty." + }, + { + "text": "But anyway, that's kind of a detail here." + }, + { + "text": "If you look at the string x, y, y, z, that's still going to be accepted." + }, + { + "text": "So that's the proof of the pumping lemma." + }, + { + "text": "All right?" + }, + { + "text": "So let's have a little check-in related to that." + }, + { + "text": "This is not going to be, again, not super hard, but more just a curiosity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk22.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..8f1447a06a268817402bd9ef6444e19235d9d813 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "So the pumping lemma depends on the fact that if M has p states and it runs for more than p steps, then it's going to enter some state twice." + }, + { + "text": "So you may have seen that before." + }, + { + "text": "It actually has a name, which some of you may have seen." + }, + { + "text": "So let's see how to just get a poll here." + }, + { + "text": "I hope not too many of you are going to pick C, as some of you are." + }, + { + "text": "Oh, well." + }, + { + "text": "Yes." + }, + { + "text": "I think this one, most of you have seen this before." + }, + { + "text": "This is, I think you pretty much all got it." + }, + { + "text": "This is what's known as the pigeonhole principle." + }, + { + "text": "So here, sharing the results." + }, + { + "text": "Obviously, I was having a little fun with this." + }, + { + "text": "And some of you are having fun back at me." + }, + { + "text": "That's OK. OK, so let's continue on." + }, + { + "text": "Let's see how to use the pumping lemma to prove a language is not regular." + }, + { + "text": "So I put the pumping lemma up here just so you can remember the statement of it." + }, + { + "text": "So let's take the language D, which is the language 0 to the k, 1 to the k for any k. So that's some number of 0's followed by an equal number of 1's." + }, + { + "text": "We're going to prove that language is not regular by using the pumping lemma." + }, + { + "text": "And this is going to be just an ironclad proof." + }, + { + "text": "It's not going to say, well, I couldn't think of how to find it a finite automaton." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk23.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..15139d54352e8d5182294ce05941ccf15bfd881d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "This is going to be a proof." + }, + { + "text": "So we want to show that D is not regular." + }, + { + "text": "And we're going to give a, these things always go as a proof by contradiction." + }, + { + "text": "So proof by contradiction, hopefully as a reminder to you, the way that works is you're going to assume the opposite of what you're trying to prove." + }, + { + "text": "And then from that, something crazy is going to happen, something you know is obviously false or wrong." + }, + { + "text": "And so therefore, your assumption, which is the opposite of what you're trying to prove, had to be wrong." + }, + { + "text": "And so therefore, the thing you're trying to prove has to be right." + }, + { + "text": "That's the essence of what's called proof by contradiction." + }, + { + "text": "So first of all, we're going to assume to get our contradiction that D is regular, which is what we're trying to show is not the case." + }, + { + "text": "Now, if D is regular, then we can apply the pumping limit up above here, which gives us that pumping length p, which says that any string longer than p can be pumped and you stay in the language." + }, + { + "text": "That's what the pumping limit tells you." + }, + { + "text": "So let's pick the string s, which is the string 0 to the p, 1 to the p. Here's sort of a picture of s off on the side here." + }, + { + "text": "So a bunch of 0s followed by an equal number of 1s." + }, + { + "text": "And that string is in D, because D is strings of that form." + }, + { + "text": "And it's longer than p. Obviously, it's of length 2p." + }, + { + "text": "So the pumping limit tells us there's a way to cut it up, satisfying those three conditions." + }, + { + "text": "So how in the world could we possibly cut s up?" + }, + { + "text": "Well, remember the three conditions, and especially condition 3 is going to come in handy here, say that you can cut s up into three pieces, x, y, and z, where the first two pieces lie in the first p symbols of s, at most p long." + }, + { + "text": "So x and y together are not very big." + }, + { + "text": "They don't extend beyond the first half of x and first half of s. And in particular, they're all 0s." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk24.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..74f127a7fff9f07a8fee72071dc2d799c1fbdbfe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "x and y are going to be all 0s." + }, + { + "text": "z is going to perhaps have some 0s and will have the rest of the 1s." + }, + { + "text": "We'll have the 1s." + }, + { + "text": "Now, the pumping limit says that if you cut it up that way, you can repeat y as many times as you like, and you stay in the language." + }, + { + "text": "But that's obviously false, because if you repeat y, which now has only 0s, you're going to have too many 0s." + }, + { + "text": "And so the resulting string is no longer going to be of the form 0 to the k, 1 to the k. It's going to be lots of 0s followed by not so many 1s." + }, + { + "text": "That's not in the language." + }, + { + "text": "And that violates what the pumping limit tells you is supposed to happen." + }, + { + "text": "And that's a contradiction." + }, + { + "text": "So therefore, our assumption that D is regular is false." + }, + { + "text": "And so we conclude that D is not regular." + }, + { + "text": "So that's a fairly simple one." + }, + { + "text": "I thought I would do another couple of examples, because you have this on your homework, and I thought it might be helpful." + }, + { + "text": "So here's a second one, slightly harder, but not too much." + }, + { + "text": "Let's take the language F, which looks like the strings ww." + }, + { + "text": "These are strings that are two copies of the same string." + }, + { + "text": "For any string that might be in sigma star, so for any string at all, I'm going to have two copies of that string." + }, + { + "text": "And so F is those strings which are just two copies of the same string." + }, + { + "text": "OK. We're going to show that F is not regular." + }, + { + "text": "These things always go the same way." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk25.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..abe9c80e62aa87a66a61bd402ba07ed83a5bc6c5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the same pattern." + }, + { + "text": "You prove by contradiction." + }, + { + "text": "So you assume for contradiction that D, that's bad." + }, + { + "text": "That was copied from my other slide." + }, + { + "text": "That's wrong." + }, + { + "text": "Let's see if I can actually make this work here." + }, + { + "text": "Good." + }, + { + "text": "Assume for contradiction that F is regular." + }, + { + "text": "The pumping lemma gives F is above." + }, + { + "text": "And so now we need to choose a string S that's in F to do the pumping and show that the pumping lemma is going to fail." + }, + { + "text": "You're going to pump, and you're going to get something which is not in language, which shows that something has gone wrong." + }, + { + "text": "But which S to choose?" + }, + { + "text": "And sometimes, that's where the creativity in applying the pumping lemma comes in, because you have to figure out which is the right string you're going to pump on." + }, + { + "text": "So you might try the string, well, 0 to the p, 0 to the p. That's certainly in F. It's two copies of the same string." + }, + { + "text": "Here it is I've written." + }, + { + "text": "Lots of 0's followed by the same number of 0's." + }, + { + "text": "The problem is, if you use that string, it actually is a string that you can pump." + }, + { + "text": "You can break that string up into three pieces." + }, + { + "text": "And then if you let y be the string 0, 0, actually, you have to be a little careful." + }, + { + "text": "The string just 0 doesn't work, because there's an evenness-oddness phenomenon going here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk26.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..c93dce28015b5b124095b8bed4df964430437405 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk26.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you might want to just think about that." + }, + { + "text": "But if you let y be the string 0, 0, then if you have the string x, y, x, any number of y's, it's still just going to be a bunch of 0's." + }, + { + "text": "And you're going to be able to see that that string is still in the language." + }, + { + "text": "So you haven't learned anything." + }, + { + "text": "If the pumping lemma works and you're satisfying the pumping lemma, you haven't learned anything." + }, + { + "text": "So what you need to find is some other string." + }, + { + "text": "That was a bad choice for s. Find a different string." + }, + { + "text": "So here's a different choice." + }, + { + "text": "0 to the p1, 0 to the p1." + }, + { + "text": "So that's two copies of the same string." + }, + { + "text": "And we're going to show it can't be pumped." + }, + { + "text": "So here's a picture of that string here." + }, + { + "text": "So 0's followed by 1, 0's followed by 1." + }, + { + "text": "And now it's very similar to the first argument." + }, + { + "text": "If you cut it into three pieces in such a way that it satisfies the conditions, the first two pieces are going to be residing only among the 0's." + }, + { + "text": "And so therefore, when you repeat a y, you're no longer going to have two copies of the same string and so won't be in the language." + }, + { + "text": "So therefore, you've got a contradiction and f is not regular." + }, + { + "text": "So you have to play with the pumping lemma a little bit." + }, + { + "text": "If you haven't seen that before, it's going to be, it takes a little getting used to." + }, + { + "text": "But you have a few homework questions that need to be solved using the pumping lemma." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk27.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk27.json new file mode 100644 index 0000000000000000000000000000000000000000..4a6822eab5b9a3a8ebaf98bf8cf56da7dd0beaf3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk27.json @@ -0,0 +1,62 @@ +[ + { + "text": "All right." + }, + { + "text": "So now let's look at, lastly, there is another method that can come in, which is combining closure properties with the pumping lemma." + }, + { + "text": "So closure properties sometimes help you." + }, + { + "text": "So let's look at the language B, which is actually we saw earlier in the lecture, where we have an equal number of 0's and 1's." + }, + { + "text": "Now, we could prove that directly using the pumping lemma as not being regular." + }, + { + "text": "But it's actually even easier." + }, + { + "text": "What we're going to prove that it is, we're going to prove that it's not regular in a different way." + }, + { + "text": "First, we're going to assume for contradiction, as we often do, that it is regular." + }, + { + "text": "And now we're going to use something, we're going to use some other knowledge." + }, + { + "text": "We're not going to use the pumping lemma here because we're going to take advantage of an earlier case where we use the pumping lemma." + }, + { + "text": "And so now we know that the string, the language 0 star 1 star is a regular language because it's described by a regular expression." + }, + { + "text": "If you take the B, which is the equal numbers of 0's and 1's, and you intersect it with 0 star 1 star, that's going to be a regular language if B was regular using closure under intersection." + }, + { + "text": "But this language B intersects 0 star 1 star is the language of equal numbers of 0's and 1's where the 0's come first." + }, + { + "text": "And that's the language D that we showed two slides back that we already know can't be regular." + }, + { + "text": "So that intersection cannot be regular, and so it violates the closure property." + }, + { + "text": "And again, we get a contradiction." + }, + { + "text": "So that's a different way of sometimes making a shortcut to prove a language is not regular." + }, + { + "text": "So we have in our last 10 minutes or so, we're going to shift gears totally in an entirely different way and consider a new model of computation, which is more powerful, that can actually do things that we can't do with finite automata." + }, + { + "text": "And these are called context-free grammars." + }, + { + "text": "So this is really just a kind of an introduction." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk28.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk28.json new file mode 100644 index 0000000000000000000000000000000000000000..135abf63d4f4fe4563d349e8585ba20f755f4900 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk28.json @@ -0,0 +1,62 @@ +[ + { + "text": "We're going to spend all of next lecture looking at context-free grammars." + }, + { + "text": "And they're associated languages." + }, + { + "text": "But let's just do kind of get a preview." + }, + { + "text": "So a context-free grammar looks like this." + }, + { + "text": "You have a bunch of these what we call substitution rules or rules sometimes, which just look like a symbol, arrow, a string of symbols." + }, + { + "text": "All right?" + }, + { + "text": "That's what a context-free grammar looks like at a high level." + }, + { + "text": "Let's define some terms." + }, + { + "text": "So a rule, as I just described, is going to be a symbol, which we're going to call a variable." + }, + { + "text": "And that's going to have an arrow to a string of possibly other variables and symbols called terminals." + }, + { + "text": "So a variable is a symbol that appears on the left-hand side of a rule." + }, + { + "text": "Anything that appears on the left-hand side is going to be considered to be a variable." + }, + { + "text": "So s and r are both variables." + }, + { + "text": "Now, other symbols that appear in the grammar, which don't appear in the left-hand side, those are going to be called terminals." + }, + { + "text": "So here, 0 and 1 are terminals." + }, + { + "text": "Now, you may think that empty string should also be a terminal, but that's not a symbol." + }, + { + "text": "Empty string is a string." + }, + { + "text": "It's just a string of length 0." + }, + { + "text": "So I'm not considering empty string to be a terminal." + }, + { + "text": "And then there's going to be a special variable, which is going to be considered the starting variable, just like we had a starting state." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk29.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk29.json new file mode 100644 index 0000000000000000000000000000000000000000..efafd54bf5686f35914d2bbf6828c3e31e557613 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk29.json @@ -0,0 +1,62 @@ +[ + { + "text": "And that's typically going to be written as the top left symbol." + }, + { + "text": "So this symbol s here is going to be the starting symbol." + }, + { + "text": "And grammars can be used to define languages and to gen, well, to generate strings and to define languages." + }, + { + "text": "So first of all, let's see how a grammar using this as an illustration can generate strings." + }, + { + "text": "Actually, just to emphasize this terminology here, in this particular example, we had three rules." + }, + { + "text": "The two variables were r and s. The two terminals were 0 and 1." + }, + { + "text": "And the start variable was this top left-hand symbol, as I mentioned, the s. So grammars generate strings." + }, + { + "text": "The way they do is you follow a certain procedure, which is really pretty simple." + }, + { + "text": "You write down, first of all, the start variable." + }, + { + "text": "And I'll do an example in a second." + }, + { + "text": "You write down the start variable." + }, + { + "text": "And then you take a look at what you've written down." + }, + { + "text": "And if it has any variables in it, you can apply one of the corresponding right-hand sides of a rule as a substitution for that variable." + }, + { + "text": "And so, for example, if you have an s in the thing you've written down, you can substitute for that s a 0, s, 1." + }, + { + "text": "Or you can substitute for that s an r. Or if you have an r, you can substitute for that s an empty string." + }, + { + "text": "So you're just going to keep on doing that substitutions over and over again until there are no variables left." + }, + { + "text": "So there's nothing left to substitute." + }, + { + "text": "Only terminals remain." + }, + { + "text": "At that point, you have generated a string in the language." + }, + { + "text": "So the language, then, is the collection of all generated strings." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk3.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..156859044caea8ac8df8b834513914788227dd74 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "For the NFAs, we're only allowing just single symbols or the empty string to appear on the labels." + }, + { + "text": "Now I'm actually allowing you to put full regular expressions on the labels for the automaton." + }, + { + "text": "Now, we have to understand how a GNFA processes its input." + }, + { + "text": "And the way it works is not complicated to understand." + }, + { + "text": "When you're getting an input string, feeling when a GNFA is processing an input string, it starts at the start state, just like you would imagine." + }, + { + "text": "But now, to go along a transition, instead of reading just a single symbol or the empty string, as in the case for the nondeterministic machine, it actually gets to read a whole string at one step, kind of at one byte." + }, + { + "text": "It can read an entire string and go along that transition arrow, provided that chunk of the input that it read is in the regular expression that that transition has as its label." + }, + { + "text": "So for example, you can go from Q1 to Q2 in one step in this GNFA by reading AABB off the input." + }, + { + "text": "So it reads all of those four symbols all at once, just swoops them up, and then moves from Q1 to Q2 in one step." + }, + { + "text": "And then when it's in Q2, it can read AAB and move to Q3." + }, + { + "text": "And Q3 happens, there's nowhere to go." + }, + { + "text": "So this is going to be a nondeterministic machine." + }, + { + "text": "There might be several different ways of processing the input." + }, + { + "text": "And if any one of them gets to an accepting state at the end of the input, we say the GNFA accepts." + }, + { + "text": "So it's similar to nondeterministic to NFAs in the way the acceptance criterion works." + }, + { + "text": "So you could do an example, but hopefully, the concept of how this works is reasonably, you can at least buy it, that it processes the input in chunks at a time." + }, + { + "text": "And those chunks have to be described by the regular expressions on the transition arrows as it moves along those transitions." + }, + { + "text": "So what we're going to do now is to convert not DFAs to regular expressions." + }, + { + "text": "We're going to convert GNFAs to regular expression." + }, + { + "text": "That's even harder because GNFAs allow you to do all sorts of other things besides just ordinary DFAs." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk30.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk30.json new file mode 100644 index 0000000000000000000000000000000000000000..7e2faf8e26e344cd085bac4e39d6887fdb9b80e4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk30.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, let's do an example." + }, + { + "text": "Here's an example of G1 generating some string." + }, + { + "text": "So as I mentioned, first of all, you're going to write down the start variable." + }, + { + "text": "And I'm just going to illustrate this in sort of two parallel tracks here." + }, + { + "text": "On the left side, I'm going to show you the tree of substitutions." + }, + { + "text": "And on the right side, I'm going to show you the resulting string that you get by applying those substitutions." + }, + { + "text": "OK?" + }, + { + "text": "So over here, I'm going to substitute for s the string 0, s1." + }, + { + "text": "So on the right-hand side, I just have 0, s1 because that's what I substituted for s. But you'll see it's going to look a little different in a second." + }, + { + "text": "Here, again, I still have a variable." + }, + { + "text": "So I'm going to substitute for s 0, s1." + }, + { + "text": "Now I have the resulting string 0, 0, s1, 1 because I've substituted 0, s1 for the previous s. But the 0 and 1 stick around from before." + }, + { + "text": "They don't go anywhere." + }, + { + "text": "So I have at this point 0, 0, s1, 1." + }, + { + "text": "Now I'm going to take a different choice." + }, + { + "text": "I'm going to substitute for s. I could have gone either way." + }, + { + "text": "There's sort of something almost like nondeterminism here because you have a choice." + }, + { + "text": "I'm going to substitute for s. Instead of 0, s1, I'm going to substitute r because that's also legitimate in terms of the rules." + }, + { + "text": "And so now I'm going to have 0, 0, r, 1, 1." + }, + { + "text": "And now r, there's no choices here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk31.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk31.json new file mode 100644 index 0000000000000000000000000000000000000000..a6b30a611a3de96bd126a4f9a480709882e3cb76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk31.json @@ -0,0 +1,62 @@ +[ + { + "text": "r can only be substituted for by an empty string." + }, + { + "text": "So I get to r becomes just empty string." + }, + { + "text": "And in terms of the string generated, empty string doesn't add anything." + }, + { + "text": "It just really is nothing." + }, + { + "text": "It's a nothing." + }, + { + "text": "So I get the string 0, 0, 1, 1." + }, + { + "text": "And this is a string just of terminal symbols." + }, + { + "text": "And so that is a string in the language of the grammar G1." + }, + { + "text": "If you think about it, G1's language is that language that we saw before, which I think we called D. 0 to the k, 1 to the k for k greater than or equal to 0." + }, + { + "text": "So this is an example of a language that a context-free grammar can do, but a finite automaton cannot do." + }, + { + "text": "So that is our little introduction to content." + }, + { + "text": "Oops, there's one more check-in here." + }, + { + "text": "Oh, yeah, so I'm asking you to actually look at, let me get myself out of this picture so you don't see me blocking things." + }, + { + "text": "And we will do one last check-in." + }, + { + "text": "Check-in, make sure you're staying around for the whole thing." + }, + { + "text": "Now there could be several of these strings that are in the language." + }, + { + "text": "You have to click them all." + }, + { + "text": "All the ones that you have found that are in the language of this grammar that can be generated by grammar G2, you have to click those." + }, + { + "text": "I'll give you a little bit more time on this one to see which ones G2 can generate." + }, + { + "text": "I'll give you a hint." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk32.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk32.json new file mode 100644 index 0000000000000000000000000000000000000000..29c334ff719f29048a591810bb2423b8d296f883 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk32.json @@ -0,0 +1,62 @@ +[ + { + "text": "There's more than one, but not all." + }, + { + "text": "So I see you're making some progress here." + }, + { + "text": "Interesting." + }, + { + "text": "So please, we're going to wrap this up very quickly." + }, + { + "text": "You can click, somebody's telling me you can unclick." + }, + { + "text": "Thank you, good to know." + }, + { + "text": "OK, so still things are coming in here." + }, + { + "text": "So we're running toward the end of the hour here." + }, + { + "text": "I don't want to go over." + }, + { + "text": "So I'm going to end it in five seconds." + }, + { + "text": "Click away." + }, + { + "text": "And don't forget, we're not going to charge you if you get it wrong." + }, + { + "text": "Sharing results, I don't know why it has an orange one there because there are several correct answers here." + }, + { + "text": "So it's A, B, and D are correct." + }, + { + "text": "You can get any of those." + }, + { + "text": "It's really sort of two copies of the language we had before next to one another." + }, + { + "text": "And so the only thing you cannot get is 1, 0, 1, 0." + }, + { + "text": "So I encourage you to think about that." + }, + { + "text": "And I will come to our last side of today, which is just a quick review." + }, + { + "text": "I can put myself back." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk33.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk33.json new file mode 100644 index 0000000000000000000000000000000000000000..c9acb271e5df7aa61fe9639e258eaf0c493b6aa0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk33.json @@ -0,0 +1,26 @@ +[ + { + "text": "So we showed how to convert DFAs to regular expressions." + }, + { + "text": "And the summary is that DFAs, NFAs, GNFAs even, and regular expressions are all equivalent in the class of languages they can describe." + }, + { + "text": "The second thing we did was a method for proving languages not regular by using the pumping lemma or closure properties." + }, + { + "text": "And lastly, we introduced context-free grammars." + }, + { + "text": "And we're going to see more about those on Thursday." + }, + { + "text": "So with that, I think we're out of time." + }, + { + "text": "And I'll thank you for the notes of appreciation." + }, + { + "text": "And I think we're going to end here and see you on Thursday, if not before." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk4.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..1abb85ffc0c9fe28dfd0e54212e5b201e25c69fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's a harder job." + }, + { + "text": "Why am I making my life harder?" + }, + { + "text": "Well, you'll see in a minute that it's going to actually turn out to be helpful to be working with a more powerful model in the way this construction is going to work." + }, + { + "text": "Now, before I dive in and do the construction from GNFAs to regular expressions, I'm going to make a simplifying assumption about the GNFAs." + }, + { + "text": "I'm going to put them in a special form that's going to make it easier to do the conversion." + }, + { + "text": "And that simpler form is, first of all, I'm going to assume the GNFA has just a single accepting state." + }, + { + "text": "And that accepting state is not allowed to be the start state." + }, + { + "text": "So it has to have just a single accepting state." + }, + { + "text": "I've already violated that convenient assumption in this GNFA because I have here two accepting states." + }, + { + "text": "That's not what I want." + }, + { + "text": "I want to have just one." + }, + { + "text": "Well, the thing is, it's easy to obtain just one, just to modify the machine so that I have just one by adding a new accepting state, which is branched to from the former accepting states by empty transition." + }, + { + "text": "So I can always jump from Q2 to Q4 at any time without even reading any input, just going along this empty transition." + }, + { + "text": "And then I declassify the former accepting states as accepting." + }, + { + "text": "And now I have here just a single accepting state." + }, + { + "text": "And because it's going to be a new state that I added, it won't be the start state." + }, + { + "text": "And I have accomplished that one aspect of my assumption about the form of the GNFA." + }, + { + "text": "But there's another thing that I want to do too." + }, + { + "text": "I want to assume, as you will see, which is going to be convenient in my construction, that we will have transition arrows going from every state to every other state." + }, + { + "text": "In fact, I want transition arrows going from every state, even back to themselves." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk5.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..521d4ba36192f0be34911067bb4275e288e25a4a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "I want there to be all possible transition arrows should be present, with two exceptions." + }, + { + "text": "For the start state, there should be only transition arrows exiting the start state." + }, + { + "text": "And for the accepting state, there's just one now, there should be only transition arrows coming in to the start state." + }, + { + "text": "So it's kind of what you would imagine as being reasonable." + }, + { + "text": "For the other states which are not accepting or starting, there should be transition arrows leaving and coming from everywhere else." + }, + { + "text": "But for the start states, just leaving, and for the accept state, just coming in." + }, + { + "text": "And you can easily modify the machine to achieve that." + }, + { + "text": "Let's just see how to do that in one example." + }, + { + "text": "So notice that from Q3 to Q2, there is no transition right now." + }, + { + "text": "And that's not good." + }, + { + "text": "That's not what I want." + }, + { + "text": "I want there to be a transition from Q3 to Q2." + }, + { + "text": "Well, I'll just add that transition in." + }, + { + "text": "But I'm going to label it with the empty language regular expression." + }, + { + "text": "So that means, yeah, the transition is there, but you never can take it." + }, + { + "text": "So it doesn't change the language that the machine is going to be recognizing, but it fulfills my assumption, my convenient assumption, that we have all of these transition arrows being present in the machine." + }, + { + "text": "So anyway, I hope you will buy it." + }, + { + "text": "It's not going to be, if you don't quite get this, don't worry." + }, + { + "text": "It's not totally critical that you're following all of these little adjustments and modifications to the GNFA." + }, + { + "text": "But it will be helpful to understand what GNFA themselves, how they work." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk6.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..67174286045cf45ee03934650fbbd6cd17fcf8db --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So as I mentioned, we can easily modify GNFA to have the special form that we're assuming here." + }, + { + "text": "All right, so now we're going to jump in and start doing the conversion." + }, + { + "text": "So we're going to have a lemma, which is like a theorem that really is just a local interest here." + }, + { + "text": "It's not a general interest theorem." + }, + { + "text": "It's going to be relevant just to GNFA, which are really just defined to help us do this conversion." + }, + { + "text": "They really don't have any other independent value." + }, + { + "text": "So I want to show that every GNFA has an equivalent regular expression R. That's really my goal." + }, + { + "text": "And the way we're going to prove that is by induction." + }, + { + "text": "It's going to be by induction on the number of states of the GNFA." + }, + { + "text": "Now, you really should be familiar with induction as one of the expectations for being in this course." + }, + { + "text": "But in case you're a little shaky on it, don't worry." + }, + { + "text": "I'm going to unpack it as a procedure." + }, + { + "text": "It's really just recursion." + }, + { + "text": "And a proof that uses induction is really just a proof that calls itself." + }, + { + "text": "It's just a proof that it's a recursive proof." + }, + { + "text": "That's all it is." + }, + { + "text": "So if you're comfortable with recursion, you'll be comfortable with induction." + }, + { + "text": "But anyway, I'm going to describe this as a procedure." + }, + { + "text": "So if you're a little shaky on induction, don't worry." + }, + { + "text": "So the basis is, so first, I'm going to handle the case where the GNFA has just two states." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk7.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..2ae3a210649fe25ab767d4daea72fa1940be0890 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, remember, I'm assuming now my GNFAs are in the special form." + }, + { + "text": "So you can't even have a GNFA with one state because it has to have a start state, and it has to have an accept state, and they have to not be the same." + }, + { + "text": "So the smallest possible GNFA to worry about is a two-state GNFA." + }, + { + "text": "Now, if we happen to have a two-state GNFA, it turns out to be very easy to find the equivalent regular expression." + }, + { + "text": "Why?" + }, + { + "text": "Because that two-state GNFA can only look like this." + }, + { + "text": "It can have a start state, can have an accept state, and it can only have a transition going from the start to the accept because no other transitions are allowed." + }, + { + "text": "It only has outgoing from the start, only incoming to the accept." + }, + { + "text": "And so there's only one transition, and it has a label with a regular expression r. So what do you think the equivalent regular expression is for this GNFA?" + }, + { + "text": "It's just simply the one that's labeling that transition because that tells us when I can go from the start to the accept." + }, + { + "text": "And there's nothing else the machine can do." + }, + { + "text": "It just makes one step, which is to accept its input if it's described by that regular expression." + }, + { + "text": "So therefore, the equivalent regular expression that we're looking for is simply label on that single transition." + }, + { + "text": "OK, so two-state GNFAs are easy." + }, + { + "text": "But what happens if you have more states?" + }, + { + "text": "Then you're going to actually have to do some work." + }, + { + "text": "So we call that the induction step." + }, + { + "text": "That's when we have more than two states." + }, + { + "text": "And the way the induction works is we're going to assume we already know how to do it for k minus 1 states." + }, + { + "text": "And we're going to use that knowledge to show how to do it for k states." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk8.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..b9f7d5f3fe171ffef6f4721c917566ae0b7d2241 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "So in other words, we already know how to do it for two states." + }, + { + "text": "I'm going to use that fact to show how to do it for three states, and then use the fact that I can do it for three states to show how to do it for four states, and so on and so on." + }, + { + "text": "All right?" + }, + { + "text": "And the idea for how to do that is actually pretty easy to grasp." + }, + { + "text": "What we're going to do is if we have a k-state GNFA that we want to convert, we're going to change that k-state GNFA to a k minus 1-state GNFA, and then use our assumption that we already know how to do the k minus 1-state GNFA." + }, + { + "text": "All right?" + }, + { + "text": "So in terms of a picture, I'm going to take a k-state to prove that I can always convert k-state GNFAs to regular expressions." + }, + { + "text": "I'm going to show how to convert the k-state one into an equivalent k minus 1-state GNFA." + }, + { + "text": "And then if you just like to think of it this procedurally, the k minus 1 gets converted to a k minus 2, gets converted to a k minus 3, and so on and so on, until I get down to 2, which then I know how to do directly." + }, + { + "text": "OK?" + }, + { + "text": "So the whole name of the game here is figuring out how to convert a GNFA that has k states into another one that has one fewer state that does the same language." + }, + { + "text": "OK, so you have to hold that in your head." + }, + { + "text": "I mean, I wish I had more blackboard space here, but it's very limited here." + }, + { + "text": "So you have to remember what we're going to be doing on the next slide, because that's going to finish the job for us." + }, + { + "text": "As long as I can show in general how to convert a k-state GNFA to a GNFA that has one fewer state, but it still does the same language, I'm good." + }, + { + "text": "Because then I can keep iterating that until I get down to 2." + }, + { + "text": "All right, so this is the guts of the argument." + }, + { + "text": "So I have my k-state machine." + }, + { + "text": "Here's my start state." + }, + { + "text": "Here's my accept state." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk9.json b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..5e87a17d5f39b11dc10ac74dbf5bb68324bb160e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/KAySmSEGc9U_1_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "Here's my k minus 1 state, that machine that I'm going to be building for you." + }, + { + "text": "It's actually going to look almost exactly the same." + }, + { + "text": "I'm just going to remove one state from the bigger machine." + }, + { + "text": "So I'm going to pick any state, which is not the start state or the accept state." + }, + { + "text": "Here it is pictured here." + }, + { + "text": "I mean, all of the states of the k-state machine are going to appear in the k minus 1 state machine, except for one state that I'm going to rip out." + }, + { + "text": "That's the state x." + }, + { + "text": "It's now here as a ghost." + }, + { + "text": "It's been removed." + }, + { + "text": "It's not there anymore." + }, + { + "text": "But I'm just helping you to remember that it used to be there by showing a shadow." + }, + { + "text": "But it's a I have taken my original machine that had k states and basically just ripped out a state." + }, + { + "text": "And now I have one fewer state." + }, + { + "text": "So the good news is that I now have a machine with k minus 1 states." + }, + { + "text": "That's what I want." + }, + { + "text": "But the bad news is that it doesn't do the same language anymore." + }, + { + "text": "I broke the machine by rip." + }, + { + "text": "If you're just going to rip out a state, who knows what the new machine is going to do?" + }, + { + "text": "It's going to be probably not the same as what the original machine did." + }, + { + "text": "So what I need to do then is repair the damage." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_0_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_10_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_12_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_13_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_14_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_15_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_16_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_17_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_18_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_20_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_21_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_22_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_23_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_24_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_28_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_2_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_30_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_31_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_32_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_34_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_36_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_39_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_3_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_40_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_42_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_43_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_44_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_4_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_5_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_6_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_7_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_8_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk0.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..a0e3b22b725801451b3b8ca12161c99680d17ad9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " OK, this is linear algebra lecture four, and the first thing I have to do is something that was on the list for last time, but here it is now." + }, + { + "text": "What's the inverse of a product?" + }, + { + "text": "If I multiply two matrices together and I know their inverses, how do I get the inverse of A times B?" + }, + { + "text": "So I know what inverses mean for a single matrix A and for a matrix B." + }, + { + "text": "What matrix do I multiply by to get the identity if I have A here?" + }, + { + "text": "OK, that'll be simple but so basic." + }, + { + "text": "Then I'm going to use that to -." + }, + { + "text": "I will have a product of matrices, and the product that we'll meet will be these elimination matrices, and the net result of today's lecture is the Bayes formula for elimination." + }, + { + "text": "So the net result of today's lecture is this great way to look at Gaussian elimination." + }, + { + "text": "We know that we get from A to U by elimination." + }, + { + "text": "We know the steps, but now we get the right way to look at it, A equal LU." + }, + { + "text": "So that's the high point for today." + }, + { + "text": "OK. Can I take the easy part, the first step first?" + }, + { + "text": "So suppose A is invertible, and of course, it's going to be a big question, when is the matrix invertible, but let's say A is invertible and B is invertible, then what matrix gives me the inverse of AB?" + }, + { + "text": "So that's the direct question." + }, + { + "text": "What's the inverse of AB?" + }, + { + "text": "Do I multiply those separate inverses?" + }, + { + "text": "Yes." + }, + { + "text": "I multiply the two matrices A inverse and B inverse, but what order do I multiply?" + }, + { + "text": "In reverse order." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk1.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..46b87a2193173c68b5a503ffec3f6e37e9cd18a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you see why, so that the right thing to put here is B inverse A inverse." + }, + { + "text": "That's the inverse I'm after." + }, + { + "text": "We can just check that AB times that matrix gives the identity." + }, + { + "text": "OK." + }, + { + "text": "So why?" + }, + { + "text": "Once again, it's this fact that I can move parentheses around." + }, + { + "text": "I can, actually, I can just erase them all and do the multiplications any way I want to." + }, + { + "text": "So what's the right multiplication to do first?" + }, + { + "text": "B times B inverse." + }, + { + "text": "This product here is the identity." + }, + { + "text": "Then A times the identity is the identity, and then finally A times A inverse gives the identity." + }, + { + "text": "So forgive the dumb example in the book, it's just why do you do the inverse things in reverse order, it's just like taking, you take off your shoes, you take off your socks, then the good way to invert that process is socks back on first, then shoes." + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "I'm sorry that's on tape, but all right." + }, + { + "text": "And of course, on the other side, we should really just check on the other side, I have B inverse A inverse, that does multiply AB, and this time it's these guys that give the identity, squeeze down, they give the identity, we're in shape." + }, + { + "text": "OK." + }, + { + "text": "So there's the inverse." + }, + { + "text": "Good." + }, + { + "text": "While we're at it, let me do a transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk10.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..93bf10ce1465f31cb2247c4a37feffd7a2a08592 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK." + }, + { + "text": "There's a typical." + }, + { + "text": "That's a typical case in which we didn't need an E three one." + }, + { + "text": "Maybe we already had a zero in that three one position." + }, + { + "text": "OK. Let me see if that, is that going to be enough to show my point." + }, + { + "text": "Let's, let me do that multiplication." + }, + { + "text": "OK, so if I do that multiplication, this is, it's like good practice to multiply these matrices." + }, + { + "text": "Tell me what's above the diagonal when I do this multiplication." + }, + { + "text": "All zeros." + }, + { + "text": "When I do this multiplication, I'm going to get ones on the diagonal and zeros above." + }, + { + "text": "Because, what does that say?" + }, + { + "text": "That says that I'm subtracting rows from lower rows." + }, + { + "text": "So nothing is moving upwards as it did last time in Gauss-Jordan." + }, + { + "text": "OK. Now, so really, what I have to do is check this, minus two one zero." + }, + { + "text": "Now this is, so what am I, what's that number?" + }, + { + "text": "That, this is the number that I'm really have in mind." + }, + { + "text": "That number is ten." + }, + { + "text": "And this one is, what goes here?" + }, + { + "text": "Row three against column two looks like the minus five." + }, + { + "text": "What, it's that ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk11.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b34e9d162b8366835a2c5f9fa39d52c346788913 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "How did that ten get in there?" + }, + { + "text": "I don't like that ten." + }, + { + "text": "I mean, of course, I don't want to erase it, because it's right, but I don't want it there." + }, + { + "text": "It's because the ten got in there, because I subtracted two of row one from row two, and then I subtracted five of that new row two from row three." + }, + { + "text": "So doing it in that order, how did row one affect row three?" + }, + { + "text": "Well, it did, because two of it got removed from row two, and then five of those got removed from row three." + }, + { + "text": "So altogether, ten of row one got thrown into row three." + }, + { + "text": "Now my point is in the reverse direction." + }, + { + "text": "So now I can do, now I'll do, below it I'll do the inverse." + }, + { + "text": "OK. And of course, opposite order." + }, + { + "text": "Reverse order." + }, + { + "text": "Reverse order." + }, + { + "text": "OK." + }, + { + "text": "So now this is going to, this is the E that goes on the left side." + }, + { + "text": "Left of A." + }, + { + "text": "Now I'm going to do the inverses in the opposite order, so what's the, so the opposite order means I put this inverse first, and what is its inverse?" + }, + { + "text": "What's the inverse of E two one?" + }, + { + "text": "Same thing with a plus sign, right?" + }, + { + "text": "For the individual matrices, instead of taking away two, I add back two of row one to row two." + }, + { + "text": "So, no problem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk12.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..0ba3a88b964e8859c9daa0e651cd5374991185ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now in reverse order, I want to invert that." + }, + { + "text": "Just, right, I'm doing just this, this." + }, + { + "text": "So now the inverse is, again, the same thing, but add in the five." + }, + { + "text": "And now I'll do that multiplication, and I'll get a happy result." + }, + { + "text": "I hope." + }, + { + "text": "Did I do it right so far?" + }, + { + "text": "Yes?" + }, + { + "text": "OK. Let me do the multiplication." + }, + { + "text": "I believe this comes out." + }, + { + "text": "So row one of the answer is one zero zero." + }, + { + "text": "Oh, I know that all this is going to be that, right?" + }, + { + "text": "Then I have two one zero." + }, + { + "text": "So I get two one zero there, right?" + }, + { + "text": "And what's the third row?" + }, + { + "text": "What's the third row in this product?" + }, + { + "text": "Just read it out to me, the third row." + }, + { + "text": "Zero five one." + }, + { + "text": "Because I, one way to say is, this is saying take one of the last row and there it is." + }, + { + "text": "And this is my matrix L, and it's the one that goes to the left, it goes on the left of U." + }, + { + "text": "It goes into, this is, what do I mean here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk13.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3b934133bc2b7b48b71b995db3ee1a27894a6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe rather than saying left of A, left of U, let me write down again what I mean." + }, + { + "text": "EA is U, whereas A is LU." + }, + { + "text": "OK. Let me make the point now in words." + }, + { + "text": "The order that the matrices come for L is the right order." + }, + { + "text": "The two and the five don't sort of interfere to produce this ten." + }, + { + "text": "In the right order, the multipliers just sit in the matrix L. That's the point." + }, + { + "text": "That the, so that if I want to know L, I've no work to do." + }, + { + "text": "I just keep a record of what those multipliers were." + }, + { + "text": "And that gives me L. So I'll draw the, so what's the order?" + }, + { + "text": "So let me state it." + }, + { + "text": "So this is the A equal LU." + }, + { + "text": "So if no row exchanges, the multipliers, those numbers that we multiplied rows by and subtracted when we did an elimination step, the multipliers go directly into L. OK." + }, + { + "text": "So L is, this is the way to look at elimination." + }, + { + "text": "That the, you go through the elimination steps, and actually, if you do it right, you can throw away A as you create L and U." + }, + { + "text": "If you think about it, those steps of elimination, as you, when you've done, when you've finished with row two of A, you've created a new row two of U, which you have to save, and you've created the multipliers that you used, which you have to save, and then you can forget A." + }, + { + "text": "So the, because it's all there in L and U." + }, + { + "text": "So that's, that's like, I mean, this may, this moment is maybe the, the new insight in elimination that comes from matrix, doing it in matrix form." + }, + { + "text": "So it was, the product of, of Es is, we can't see what that product of Es is." + }, + { + "text": "The matrix E is not particularly attractive." + }, + { + "text": "What's great is when we put them on the other side, they're inverses in the opposite order, there the L comes out just fine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk14.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..22bb94f8faa56945eeb30256161c3ed839e8f000 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, oh gosh, so today is a sort of like practical day." + }, + { + "text": "Can I, can we think together how expensive is elimination?" + }, + { + "text": "How much, how many operations do we do?" + }, + { + "text": "So I, so this is now a kind of new topic, which I didn't list as on the program, but here it came." + }, + { + "text": "Here it comes." + }, + { + "text": "How many operations on an n by n matrix A?" + }, + { + "text": "I mean, it's a very practical question." + }, + { + "text": "Can we, can we solve systems of order a thousand in a second or a minute or a week?" + }, + { + "text": "Can we solve systems of order a million in a second or an hour or a week?" + }, + { + "text": "I mean, what's the, if it's n by n, we, we often want to take n bigger." + }, + { + "text": "I mean, we put in more information." + }, + { + "text": "We make the, the whole thing is more accurate for the bigger matrix." + }, + { + "text": "But it's more expensive, too, and the question is, how much more expensive?" + }, + { + "text": "If I go, if I have, matrices of order a hundred." + }, + { + "text": "Let's say a hundred by a hundred." + }, + { + "text": "Let me, let me take n to be a hundred." + }, + { + "text": "Say n equal a hundred." + }, + { + "text": "How many steps are we doing?" + }, + { + "text": "How many operations are we actually doing that we, that we're, or not we." + }, + { + "text": "The, and let's suppose there aren't any zeros." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk15.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..eaa5c29da6a30492fa4b0d58fab149c5b7d242c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because of course if the, if the matrix has got a lot of zeros in good places, we don't have to do those operations, and it'll be much faster." + }, + { + "text": "But, so just think for a moment about the first step." + }, + { + "text": "So here's our matrix A, hundred by a hundred, and the first step will be that column has got zeros down here." + }, + { + "text": "So it's, it's down to ninety-nine by ninety-nine." + }, + { + "text": "Right?" + }, + { + "text": "That, that, that's really like the first, stage of elimination." + }, + { + "text": "To get from this hundred by hundred non-zero matrix to this stage where the first pivot is sitting up here and the first row's okay and the first column is okay." + }, + { + "text": "So, essentially, I, what the, how many steps did that take?" + }, + { + "text": "You see, I'm, I'm trying to get an idea." + }, + { + "text": "Is the answer proportional to n?" + }, + { + "text": "Is the, is the total number of steps in elimination, the total number, is it proportional to n?" + }, + { + "text": "In which case if I double n from a hundred to two hundred, does it take me twice as long?" + }, + { + "text": "Does it square, so it would take me four times as long?" + }, + { + "text": "Does it cube, so it would take me eight times as long?" + }, + { + "text": "Or is it n factorial, so it would take me a hundred times as long?" + }, + { + "text": "I, I think, you know, from a practical point of view, we have to have some idea of the cost here." + }, + { + "text": "So, so these are the questions." + }, + { + "text": "So let me ask those questions again." + }, + { + "text": "Is it proportional, does it go like n, like n squared, like n cubed, like some higher power of n, like n factorial, where, where every step up multiplies by a hundred and then by a hundred and one and then by a hundred and two, which is it?" + }, + { + "text": "Okay, so that's the only way I know to answer that is to, is to think through what we actually had to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk16.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..32e1c1b6d4dff24fb0912892b0dd6e3a883d7c85 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "So how much, what was the cost here?" + }, + { + "text": "Well, let's see, what do I mean by an operation?" + }, + { + "text": "I guess I mean, well, an addition or, yeah, no big deal." + }, + { + "text": "I guess I mean an addition or a subtraction or a multiplication or a division." + }, + { + "text": "Okay." + }, + { + "text": "And actually, what operation am I doing all the time?" + }, + { + "text": "I'm, when I multiply row one by a multiplier L and I subtract from row six, what's happening there individually?" + }, + { + "text": "What's the, what's going on?" + }, + { + "text": "If I multiply, I do a multiplication by L and then a subtraction." + }, + { + "text": "So I guess operation, can I count that for the moment as, like, one operation or you may want to count them separately." + }, + { + "text": "The typical operation is multiply plus subtract." + }, + { + "text": "So if I count those together, my answer's going to come out half as many as if, if I count them separately, I'd have a certain number of multiplies, certain number of subtracts." + }, + { + "text": "That's really what I want to do." + }, + { + "text": "Okay." + }, + { + "text": "How many have I got here?" + }, + { + "text": "So I think, let's see." + }, + { + "text": "It's about, well, how many roughly?" + }, + { + "text": "How many operations to get from here to here?" + }, + { + "text": "Well, maybe one way to look at it is all these numbers had to get changed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk17.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..a087e5c0eebc67b58bd3bc6ad89e777d94d850ec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "The first row didn't get changed, but all the other rows got changed at this step." + }, + { + "text": "So this step, well, I guess maybe, shall I say, it cost about, this cost about a hundred squared." + }, + { + "text": "I mean, if I had changed the first row, then it would have been exactly a hundred squared, because that's how many numbers are here." + }, + { + "text": "A hundred squared numbers is the total count of the entries, and all but this insignificant first row got changed." + }, + { + "text": "So I would say about a hundred squared." + }, + { + "text": "Okay." + }, + { + "text": "Now what about the next step?" + }, + { + "text": "So now the first row is fine." + }, + { + "text": "The second row is fine." + }, + { + "text": "And I'm changing, and these zeros are all fine." + }, + { + "text": "So what's up at the second step?" + }, + { + "text": "And then you're with me." + }, + { + "text": "Roughly what's the cost?" + }, + { + "text": "If this first step cost a hundred squared, about, operations, then this one, which is really working on this guy to produce this, cost about what?" + }, + { + "text": "How many operations to fix?" + }, + { + "text": "About ninety-nine squared." + }, + { + "text": "Or ninety-nine times ninety-eight." + }, + { + "text": "But less, right?" + }, + { + "text": "Less, because our problem's getting smaller." + }, + { + "text": "About ninety-nine squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk18.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..2f3c60ea7f37d902fe976e4812dd275b4034a57d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then I go down and down, and the next one will be ninety-eight squared, the next ninety-seven squared, and finally I'm down around one squared, or where?" + }, + { + "text": "It's just like, just little numbers." + }, + { + "text": "The big numbers are here." + }, + { + "text": "So the number of operations is about n squared plus that was n, right?" + }, + { + "text": "n was a hundred." + }, + { + "text": "It n squared for the first step, then n minus one squared, then n minus two squared, finally down to three squared and two squared and even one squared." + }, + { + "text": "No way I should have written that, squeezed that in." + }, + { + "text": "Let me try it." + }, + { + "text": "So the count is n squared plus n minus one squared plus all the way down to one squared." + }, + { + "text": "That's a pretty decent count." + }, + { + "text": "Admittedly, we didn't catch every single tiny operation, but we got the right leading term here." + }, + { + "text": "And what do those add up to?" + }, + { + "text": "Okay, so now we're at, we're coming to the punch of this question, this operation count." + }, + { + "text": "So this is the operations on the left side, on the matrix A, to finally get to U." + }, + { + "text": "And anybody, so which of, which of these quantities is the right ballpark for that count?" + }, + { + "text": "If I add a hundred squared to ninety-nine squared to ninety-eight squared, ninety-seven squared, all the way down to two squared and one squared, what, what, what am I, what have I got about?" + }, + { + "text": "It's one of these, so count, let's identify it first." + }, + { + "text": "Is it n?" + }, + { + "text": "Certainly not." + }, + { + "text": "Is it n factorial?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk19.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1aefb75fdfb98813426faf3e7f40d4f21cdfe721 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "No." + }, + { + "text": "If it was n factorial, we would, with determinants it is n factorial." + }, + { + "text": "I'll put in a bad mark against determinants, because that, that, okay, so what is it?" + }, + { + "text": "It's n, well, this is the answer." + }, + { + "text": "It's, it's, it's, it's this order, n cubed." + }, + { + "text": "It's like I have n terms, right?" + }, + { + "text": "I've got n terms in this sum, and the biggest one is n squared, so the, the worst it could be would be n cubed, but it's not as bad as, it's n cubed times, there's a, it's about one third of n cubed." + }, + { + "text": "That's the, that's the magic, operation, okay." + }, + { + "text": "Somehow that one third takes account of the fact that the, the numbers are getting smaller." + }, + { + "text": "If they weren't getting smaller, we would have n terms times n squared would be exactly n cubed." + }, + { + "text": "But our numbers are getting smaller." + }, + { + "text": "Actually, do you remember where, where does one third come in this, I'll, I'll even allow a mention of calculus." + }, + { + "text": "So calculus can be mentioned, integration can be mentioned now in the next minute and, and not again for weeks." + }, + { + "text": "It's not that I don't like eighteen oh one, but eighteen oh six is better." + }, + { + "text": "Okay." + }, + { + "text": "So, so what's, what's the calculus formula that that looks like?" + }, + { + "text": "It looks like a sum is like, if we were in calculus, instead of summing stuff, we would integrate, so I would integrate x squared and I would get one third x cubed." + }, + { + "text": "So, so if that was like an integral from one to n of x squared dx, it, the answer would be one third n cubed." + }, + { + "text": "And it's correct for the sum also, because that's like the whole point of calculus." + }, + { + "text": "The whole point of calculus is, oh, I don't want to tell you, I mean, you know the whole point of calculus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk2.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6587cf4696f96e65d20c8b248f95e9931328a8dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because the next lecture has got a lot to do, it involves transposes." + }, + { + "text": "So how do I, if I transpose a matrix, I'm talking about square invertible matrices right now, if I transpose one, what's its inverse?" + }, + { + "text": "Well, the nice formula is, let's see, let me start from A A inverse equal the identity." + }, + { + "text": "And let me transpose both sides." + }, + { + "text": "That will bring a transpose into the picture." + }, + { + "text": "So if I transpose the identity matrix, what do I have?" + }, + { + "text": "The identity, right?" + }, + { + "text": "If I exchange rows and columns, the identity is a symmetric matrix that doesn't know the difference." + }, + { + "text": "If I transpose these guys, that product, then again, it turns out that I have to reverse the order." + }, + { + "text": "I can transpose them separately, but when I multiply, those transposes come in the opposite order." + }, + { + "text": "So it's A inverse transpose times A transpose, giving the identity." + }, + { + "text": "So that's this equation, it just comes directly from that one." + }, + { + "text": "But this equation tells me what I wanted to know." + }, + { + "text": "Namely, what is the inverse of this guy A transpose?" + }, + { + "text": "What's the inverse of that, if I transpose a matrix, what's the inverse of the result?" + }, + { + "text": "And this equation tells me that here it is." + }, + { + "text": "This is." + }, + { + "text": "This is the inverse, this is the inverse of A transpose." + }, + { + "text": "Inverse of A transpose." + }, + { + "text": "Of A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk20.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..c583136cb76ba36e38afda7b7da6cde8ef62bb13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Calculus is like sums except it's continuous." + }, + { + "text": "Okay." + }, + { + "text": "And we're, and algebra is discrete." + }, + { + "text": "Okay." + }, + { + "text": "So the answer is one third n cubed." + }, + { + "text": "Now I'll just, let me, let me say one more thing about operations." + }, + { + "text": "What about the right-hand side?" + }, + { + "text": "This was what it cost on the left side." + }, + { + "text": "Count." + }, + { + "text": "This is on A." + }, + { + "text": "Because this is A that we're working with." + }, + { + "text": "But what's the cost on the extra column vector B that we're hanging around here?" + }, + { + "text": "So B, B costs a lot less, obviously." + }, + { + "text": "Because it's just one column." + }, + { + "text": "We carry it through elimination and then actually we do back substitution." + }, + { + "text": "Let me just tell you the answer there." + }, + { + "text": "It's n squared." + }, + { + "text": "So the cost for every right-hand side is n squared." + }, + { + "text": "So let me, I'll just fit that in here." + }, + { + "text": "For the right, for the cost of B, of B, turns out to be n squared." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk21.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..f2675d6368061e895cb63e5d25c02056180ac44c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So you see, if we have, as we often have, a matrix A and several right-hand sides, then we pay the price on A, the higher price on A, to get it split up into L and U, to do elimination on A, but then we can process every right-hand side at low cost." + }, + { + "text": "Okay." + }, + { + "text": "So the, that's, we really have discussed the most fundamental algorithm of, of, for a system of equations." + }, + { + "text": "Okay." + }, + { + "text": "So, I'm ready to allow row exchanges." + }, + { + "text": "Ready to allow, now, what happens to this whole today's lecture if there are row exchanges?" + }, + { + "text": "When would there be row exchanges?" + }, + { + "text": "There are row, we need to do row exchanges if a zero shows up in the pivot position." + }, + { + "text": "So I'm, I'm moving then into the final section of this chapter, which is about transposes." + }, + { + "text": "Well, we've already seen some transposes." + }, + { + "text": "And, so what's the, the title of this section is?" + }, + { + "text": "Transposes and permutations." + }, + { + "text": "Okay." + }, + { + "text": "So can I say now where does a permutation come in?" + }, + { + "text": "Let me talk a little about permutations." + }, + { + "text": "So that'll be up here, permutations." + }, + { + "text": "So these are the matrices that I need to do row exchanges." + }, + { + "text": "And I may have to do two row exchanges." + }, + { + "text": "Is it, can you invent a matrix where I would have to do two row exchanges and then it would come out fine?" + }, + { + "text": "Yeah, let's just, for the heck of it, so I'll put it here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk22.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..e1668b91472eeb9189cb4afd3c31860e32e6e4fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do three by threes." + }, + { + "text": "Actually, why don't I just plain list all the three by three permutation matrices?" + }, + { + "text": "They're a nice little group of them." + }, + { + "text": "What are all the matrices that exchange no rows at all?" + }, + { + "text": "Well, I'll include the identity." + }, + { + "text": "So that's a permutation matrix that doesn't do anything." + }, + { + "text": "Now what's the permutation matrix that exchanges, what is P one two?" + }, + { + "text": "The permutation matrix that exchanges rows one and two would be zero one zero one zero zero, right?" + }, + { + "text": "I just exchanged those rows of the identity and I've got it." + }, + { + "text": "Okay." + }, + { + "text": "Actually, I'll, yeah." + }, + { + "text": "Let me not clutter this up." + }, + { + "text": "Okay." + }, + { + "text": "Give me a complete list of all the row exchange matrices." + }, + { + "text": "So what are they?" + }, + { + "text": "They're all the ways I can take the identity matrix and rearrange its rows." + }, + { + "text": "How many will there be?" + }, + { + "text": "How many three by three permutation matrices?" + }, + { + "text": "Shall we keep going and get the answer?" + }, + { + "text": "So tell me some more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk23.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..4c9095a112a5a86fd8598e316dd75525a6d9c7a5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero, okay, what are you going to do now?" + }, + { + "text": "Switch row one and three." + }, + { + "text": "One and three, okay." + }, + { + "text": "One and three." + }, + { + "text": "Leaving two alone." + }, + { + "text": "Okay." + }, + { + "text": "Now what else?" + }, + { + "text": "Switch, what will be the next easy one is switch two and three." + }, + { + "text": "Good." + }, + { + "text": "So I'll leave one zero zero alone and I'll switch, I'll move number three up and number two down." + }, + { + "text": "Okay." + }, + { + "text": "Those are the ones that just exchange single, a pair of rows." + }, + { + "text": "This guy, this guy and this guy exchanges a pair of rows." + }, + { + "text": "But now there are more possibilities." + }, + { + "text": "What are the, what's left?" + }, + { + "text": "So tell me, there is another one here." + }, + { + "text": "What's that?" + }, + { + "text": "It's going to move, it's going to change all rows, right?" + }, + { + "text": "Where shall we put them?" + }, + { + "text": "So give me a first row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk24.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b9f4b416392c5b35b81e3d702b0d52111fa65d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Zero one zero." + }, + { + "text": "Okay, now a second row, say zero zero one and the third guy one zero zero." + }, + { + "text": "So that is like a cycle." + }, + { + "text": "That puts row two moves up to row one, row three moves up to row two, and row one moves down to row three." + }, + { + "text": "And there's one more, which is, let's see, what's left?" + }, + { + "text": "Is it zero zero one, okay." + }, + { + "text": "One zero zero, okay." + }, + { + "text": "Zero one zero, okay." + }, + { + "text": "Great." + }, + { + "text": "Six." + }, + { + "text": "Six of them." + }, + { + "text": "Six P. L. And they're sort of nice, because what happens if I like multiply two of them together?" + }, + { + "text": "If I multiply two of these matrices together, what can you tell me about the answer?" + }, + { + "text": "It's on the list." + }, + { + "text": "If I do some row exchanges and then I do some more row exchanges, then all together I've done row exchanges." + }, + { + "text": "So if I multiply, but I don't know." + }, + { + "text": "And if I invert, then I'm just doing row exchanges to get back again, so the inverses are all there." + }, + { + "text": "It's a little family of matrices that, like, they've got their own, if I multiply, I'm still inside this group, if I invert, I'm inside this group." + }, + { + "text": "Actually, group is the right name for this." + }, + { + "text": "It's a group of six matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk25.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..4fe0550a66f8e128ca71678686955bc4e7dae115 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what about the inverses?" + }, + { + "text": "What's the inverse of this guy, for example?" + }, + { + "text": "What's the inverse, if I exchange rows one and two, what's the inverse matrix?" + }, + { + "text": "Just tell me fast." + }, + { + "text": "The inverse of that matrix is, if I exchange rows one and two, then what I should do to get back to where I started is?" + }, + { + "text": "The same thing." + }, + { + "text": "So this thing is its own inverse." + }, + { + "text": "This is, that's probably its own inverse." + }, + { + "text": "This is probably not, actually, I think these are inverses of each other." + }, + { + "text": "Oh yeah, actually, the inverse is the transpose." + }, + { + "text": "There's a curious fact about permutation matrices, that the inverses are the transpose." + }, + { + "text": "And final moment, how many are there if I, how many four by four permutations?" + }, + { + "text": "So let me take four by four, how many P's?" + }, + { + "text": "Well, okay." + }, + { + "text": "Make a good guess." + }, + { + "text": "Twenty-four, right." + }, + { + "text": "Twenty-four P's." + }, + { + "text": "Okay." + }, + { + "text": "So we've got these permutation matrices, and in the next lecture we use them." + }, + { + "text": "So the next lecture finishes Chapter Two and moves to Chapter Three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk26.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..ab2c850d4d4e5a4195063177b0d9878f4b1e02ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk26.json @@ -0,0 +1,5 @@ +[ + { + "text": "Thank you." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk3.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1ff779167d14db134dbdff41d6757d5a11f52b5d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I just, so I'll put a big circle around that, because that's the answer, that's the best answer we can hope for." + }, + { + "text": "That if you want to know the inverse of A transpose, and you know the inverse of A, then you just transpose that." + }, + { + "text": "So in a, to put it another way, transposing and inversing, you can do in either order, for a single thing." + }, + { + "text": "OK." + }, + { + "text": "So that, these are like basic facts that we can now use." + }, + { + "text": "All right." + }, + { + "text": "So now I put it to use." + }, + { + "text": "I put it to use by thinking we're really completing the subject of elimination." + }, + { + "text": "Actually, I, the thing about elimination is it's the right way to understand what the matrix has got." + }, + { + "text": "This A equal LU is the most basic factorization of a matrix." + }, + { + "text": "I always worry that you will think this course is just, is all elimination." + }, + { + "text": "It's just row operations." + }, + { + "text": "And please don't." + }, + { + "text": "It's, it will be beyond that." + }, + { + "text": "But it's the right, it's the right algebra to do first." + }, + { + "text": "OK." + }, + { + "text": "So now I'm coming near the end of it, but I want to get it in a decent form." + }, + { + "text": "So my decent form is matrix form." + }, + { + "text": "I have a matrix A." + }, + { + "text": "Let's suppose it's a good matrix, I can do elimination, no row exchanges, so no row exchanges for now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk4.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..0771c901bb9a49c49e2cc60575c1d0ff508f215d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Pivots all fine, nothing zero in the pivot position, I get to the very end, which is U." + }, + { + "text": "So I get from A to U." + }, + { + "text": "And I want to know what's the connection." + }, + { + "text": "How is A related to U?" + }, + { + "text": "And this is going to tell me that there's a matrix L that connects them." + }, + { + "text": "OK. Can I do it for a two by two first?" + }, + { + "text": "OK. Two by two, elimination." + }, + { + "text": "OK." + }, + { + "text": "So I'll do it under D. So let my matrix A be, let's just, we'll keep it simple." + }, + { + "text": "Say two and an eight, so we know that the first pivot is a two, and the multiplier is going to be a four, and then let me put a one here, and what number do I not want to put there?" + }, + { + "text": "Four." + }, + { + "text": "I don't want a four there because in that case, the second pivot would not, we wouldn't have a second pivot, the matrix would be singular, general, screw up." + }, + { + "text": "OK." + }, + { + "text": "So let me put some other number here like seven." + }, + { + "text": "OK. OK. Now I want to operate on that with my elementary matrix." + }, + { + "text": "So what's the elementary matrix?" + }, + { + "text": "Strictly speaking, it's E two one, because it's the guy that's going to produce a zero in that position." + }, + { + "text": "And it's going to produce U in one shot, because it's just a two by two matrix." + }, + { + "text": "So two one, and I'm going to take four of those away from those, produce that zero, and leave a three there." + }, + { + "text": "And that's U." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk5.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..60e149006db9034e8189291d21f1148f4c7f5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what's the matrix that did it?" + }, + { + "text": "Quick review, then." + }, + { + "text": "What's the elimination elementary matrix E two one?" + }, + { + "text": "It's one zero, thanks, and negative four one." + }, + { + "text": "Right." + }, + { + "text": "Good." + }, + { + "text": "OK." + }, + { + "text": "So that's, I, I, you see the difference between this and what I'm shooting for." + }, + { + "text": "I'm shooting for A on one side and the other matrices on the other side of the equation." + }, + { + "text": "OK." + }, + { + "text": "So I can do that right away." + }, + { + "text": "Now I'm, now here's going to be my A equal LU." + }, + { + "text": "And you won't have any trouble telling me what, so A is still two one eight seven." + }, + { + "text": "L is what you're going to tell me." + }, + { + "text": "And U is still two one zero three." + }, + { + "text": "OK." + }, + { + "text": "So what's L in this case?" + }, + { + "text": "Well, first, so how is L related to this E guy?" + }, + { + "text": "It's the inverse." + }, + { + "text": "Because I want to multiply through by the inverse of this, which will put the identity here, and the inverse will show up there and I'll call it L. So what is the inverse of this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk6.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9c88408f1a375101ce756775f11aaacc64696ff6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember that those elimination matrices are easy to invert." + }, + { + "text": "The inverse matrix for this one is one zero four one." + }, + { + "text": "It's, it has the plus sign because it adds back what this removes." + }, + { + "text": "OK. Do you want, so if we did the numbers right, we must, this should be correct." + }, + { + "text": "OK. And, of course it is." + }, + { + "text": "That says the first row is right, four times the first row plus the second row is eight seven." + }, + { + "text": "Good." + }, + { + "text": "OK. That's simple." + }, + { + "text": "Two by two." + }, + { + "text": "But it already shows the form that we're headed for." + }, + { + "text": "It shows, so what's the L stand for?" + }, + { + "text": "Why the letter L?" + }, + { + "text": "If U stood for upper triangular, then, of course, L stands for lower triangular." + }, + { + "text": "And actually it has ones on the diagonal." + }, + { + "text": "Where this thing has the pivots on the diagonal." + }, + { + "text": "Oh, sometimes we may want to separate out the pivots." + }, + { + "text": "So can I just mention that sometimes we could also write this as, we could have this one zero four one." + }, + { + "text": "I'll just show you how I would divide out this matrix of pivots." + }, + { + "text": "Two three." + }, + { + "text": "There's a diagonal matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk7.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..0e89d94d0093569bb297f75ab37e9197144bdb23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I've just, whatever is left is here." + }, + { + "text": "Now what's left?" + }, + { + "text": "If I divide this first row by two to pull out the two, then I have a one and a one half." + }, + { + "text": "And if I divide the second row by three to pull out the three, then I have a one." + }, + { + "text": "So that's the, if this is L U, this is maybe called L D for pivot U." + }, + { + "text": "And now it's a little more balanced because we have ones on the diagonal here and here." + }, + { + "text": "And the diagonal matrix in the middle." + }, + { + "text": "So both of those, Matlab would produce either one." + }, + { + "text": "I'll basically stay with L U." + }, + { + "text": "Okay." + }, + { + "text": "Now I have to think about bigger than two by two." + }, + { + "text": "Right now this was just like an easy exercise." + }, + { + "text": "And to tell the truth, that this one with the minus sign and this one with the plus sign, I mean, that's the only difference." + }, + { + "text": "But with three by three, there's a more significant difference." + }, + { + "text": "Let me show you how that works." + }, + { + "text": "Let me move up to a three by three, let's say, some matrix A." + }, + { + "text": "Okay." + }, + { + "text": "And just imagine it's three by three." + }, + { + "text": "I won't write numbers down for now." + }, + { + "text": "So what's the first elimination step that I do, the first matrix I multiply it by, what letter will I use for that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk8.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..01780d57756c436662ae172a4236d4a3b7b8d83e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the, it'll be E two one." + }, + { + "text": "Because it's the first step will be to get a zero in that two one position." + }, + { + "text": "And then the next step will be to get a zero in the three one position." + }, + { + "text": "And the final step will be to get a zero in the three two position." + }, + { + "text": "That's what elimination is, and it produces U." + }, + { + "text": "And again, no row exchanges." + }, + { + "text": "We will, I'm taking the nice case now, the typical case, too, when I don't have to do any row exchange, all I do is these elimination steps." + }, + { + "text": "Okay." + }, + { + "text": "Now, suppose I want that stuff over on the right-hand side, as I really do." + }, + { + "text": "That's, like, my point here." + }, + { + "text": "I can multiply these together to get a matrix E, but I want it over on the right." + }, + { + "text": "I want its inverse over there." + }, + { + "text": "So what's the right expression now?" + }, + { + "text": "If I write A and U, what goes there?" + }, + { + "text": "Okay." + }, + { + "text": "So I've got the inverse of this, I've got three matrices in a row now." + }, + { + "text": "And it's their inverses that are going to show up, because each one is easy to invert." + }, + { + "text": "Question is, what about the whole bunch?" + }, + { + "text": "How easy is it to invert the whole bunch?" + }, + { + "text": "So that's what we know how to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk9.json b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..bea074f4d8e6696f3d74bacbb167ef224f67f8ee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/MsIvs_6vC38_9_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "We know how to invert, we should take the separate inverses, but they go in the opposite order." + }, + { + "text": "So what goes here?" + }, + { + "text": "E three two inverse, right, because I multiply from the left by E three two inverse, that'll pop it up next to U." + }, + { + "text": "And then will come E three one inverse." + }, + { + "text": "And then this'll be the only guy left standing, and that's gone when I do an E two one inverse." + }, + { + "text": "So there is L. That's L U. L is this product of inverses." + }, + { + "text": "Now you still can ask why is this guy preferring inverses?" + }, + { + "text": "And let me explain why." + }, + { + "text": "Let me explain why is this product nicer than this one?" + }, + { + "text": "This product turns out to be better than this one." + }, + { + "text": "Let me take a typical case here." + }, + { + "text": "Let me take a typical case." + }, + { + "text": "So let me, I have to do three by three for you to see the improvement." + }, + { + "text": "Two by two, there was just one E, no problem." + }, + { + "text": "But let me go up to this case." + }, + { + "text": "Suppose my matrices E two one, suppose E two one has a minus two in there." + }, + { + "text": "Suppose that, and now suppose, oh, I'll even suppose E three one is the identity." + }, + { + "text": "So I'll just, I'm just going to, I'm going to make the point with just a couple of these." + }, + { + "text": "OK, now this guy will have do something, now let's suppose minus five." + }, + { + "text": "What?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk0.json b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..fd25ea0818dacffdd5bd1cff722aaf7d067f8f16 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay." + }, + { + "text": "This is the lecture on the singular value decomposition." + }, + { + "text": "But everybody calls it the SVD." + }, + { + "text": "So this is the final and best factorization of a matrix." + }, + { + "text": "Let me tell you what's coming." + }, + { + "text": "The factors will be orthogonal matrix, diagonal matrix, orthogonal matrix." + }, + { + "text": "So it's things that we've seen before, these special good matrices, orthogonal, diagonal." + }, + { + "text": "The new point is that we need two orthogonal matrices." + }, + { + "text": "A can be any matrix whatsoever." + }, + { + "text": "Any matrix whatsoever has this singular value decomposition." + }, + { + "text": "So a diagonal one in the middle, but I need two different, probably different, orthogonal matrices to be able to do this." + }, + { + "text": "Okay." + }, + { + "text": "And this factorization has jumped into importance and is properly, I think, maybe the bringing together of everything in this course." + }, + { + "text": "One thing we'll bring together is, like, the very good family of matrices that we just studied." + }, + { + "text": "Symmetric positive definite." + }, + { + "text": "Do you remember the story with those guys?" + }, + { + "text": "Because they were symmetric, their eigenvectors were orthogonal, so I could produce an orthogonal matrix." + }, + { + "text": "This is my usual one." + }, + { + "text": "My usual one is the eigenvectors and eigenvalues." + }, + { + "text": "In the symmetric case, the eigenvectors are orthogonal, so I've got the good, my ordinary S has become a especially good Q, and positive definite, my ordinary lambda has become a positive lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk1.json b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..7e27d1aa155a8c107e4e8383a665af50464268d3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So this is, that's the singular value decomposition." + }, + { + "text": "In case our matrix is symmetric positive definite, in that case, I don't need two, u and a v, one orthogonal matrix will do for both sides." + }, + { + "text": "But, so this would be no good in general, because usually the eigenvector matrix isn't orthogonal." + }, + { + "text": "So this is not what I'm, that's not what I'm after." + }, + { + "text": "I'm looking for orthogonal times diagonal times orthogonal." + }, + { + "text": "And let me show you what that means and where it comes from." + }, + { + "text": "OK. What does it mean?" + }, + { + "text": "You remember the picture of any linear transformation." + }, + { + "text": "This was, like, the most important figure in 1806." + }, + { + "text": "And what am I looking for now?" + }, + { + "text": "A typical vector in the row space, typical vector, let me call it v1, gets taken over to some vector in the column space, say u1." + }, + { + "text": "So u1 is a v1." + }, + { + "text": "OK. Now, another vector gets taken over here somewhere." + }, + { + "text": "What am I looking for?" + }, + { + "text": "In this SVD, this singular value decomposition, what I'm looking for is an orthogonal basis here that gets knocked over into an orthogonal basis over there." + }, + { + "text": "See, that's pretty special, to have an orthogonal basis in the row space that goes over into an orthogonal basis, so this is like a right angle and this is a right angle, into an orthogonal basis in the column space." + }, + { + "text": "So that's our goal, is to find -- you see how things are coming together." + }, + { + "text": "First of all, can I find an orthogonal basis for this row space?" + }, + { + "text": "Of course." + }, + { + "text": "No big deal to find an orthogonal basis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk10.json b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..0179b0117bf00f95a1b04b6b86a542ce8f0c3b70 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "What's sigma?" + }, + { + "text": "So I'm looking for U sigma V transpose." + }, + { + "text": "U, the diagonal guy, and V transpose." + }, + { + "text": "Okay." + }, + { + "text": "Let's just see that come out right." + }, + { + "text": "So what's, what are the, what are the sigmas?" + }, + { + "text": "They're the square roots of these things." + }, + { + "text": "So square root of thirty-two and square root of eighteen." + }, + { + "text": "Zero, zero." + }, + { + "text": "Okay." + }, + { + "text": "What are the Vs?" + }, + { + "text": "They're these two." + }, + { + "text": "And I have to transpose, maybe that, maybe that just leaves me with one, with one over square root of two in that row, and the other one is one over square root of two minus one over square root of two." + }, + { + "text": "Now, finally, I've got to know the Us." + }, + { + "text": "Well, actually, one way to do, since I now know all the other pieces, I could put those together and figure out what the Us are." + }, + { + "text": "But let me do it the A A transpose way." + }, + { + "text": "Okay, find the Us now." + }, + { + "text": "U1 and U2." + }, + { + "text": "And what are they?" + }, + { + "text": "I look at A A transpose, so A is supposed to be U sigma V transpose, and then when I transpose that, I get V sigma transpose U transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk11.json b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..96d6a665ffcc93fda55a75d250402ff8f7417df8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I'm just doing it in the opposite order, A times A transpose, and what's the good part here?" + }, + { + "text": "That in the middle, V transpose V is going to be the identity." + }, + { + "text": "So this is just U sigma sigma transpose, that's some diagonal matrix with sigma squareds and U transpose." + }, + { + "text": "So what am I seeing here?" + }, + { + "text": "I'm seeing here, again, a symmetric positive definite or at least semi-definite matrix, and I'm seeing its eigenvectors and its eigenvalues." + }, + { + "text": "So if I compute A A transpose, its eigenvectors will be the things that go into U." + }, + { + "text": "Okay, so I need to compute A A transpose." + }, + { + "text": "I guess I'm going to have to go -." + }, + { + "text": "Let me, can I move that up just a little, maybe a little more, and do A A transpose." + }, + { + "text": "So what's A?" + }, + { + "text": "Four, four, minus three and three." + }, + { + "text": "And what's A transpose?" + }, + { + "text": "Four, four, minus three and three." + }, + { + "text": "And when I do that multiplication, I get, what do I get?" + }, + { + "text": "Sixteen and sixteen, thirty-two." + }, + { + "text": "That one comes out zero." + }, + { + "text": "Oh, so this is a lucky case, and that one comes out eighteen." + }, + { + "text": "So this is, like, an accident, that A A transpose happens to come out diagonal, so we know easily its eigenvectors and eigenvalues." + }, + { + "text": "So its eigenvectors are, what's the first eigenvector for this A A transpose matrix?" + }, + { + "text": "It's just one zero, and when I do that multiplication, I get thirty-two times one zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk12.json b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..3bea51beac69b154780aa5b76ef1f4e76eb0490c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the other eigenvector is just zero one, and when I multiply by that, I get eighteen." + }, + { + "text": "So this is A A transpose, multiplying that gives me the thirty-two A A transpose, multiplying this guy gives me eighteen." + }, + { + "text": "First of all, I got thirty-two and eighteen again." + }, + { + "text": "Am I surprised?" + }, + { + "text": "Yeah, it's clearly not an accident." + }, + { + "text": "The eigenvalues of A A transpose were exactly the same as the eigenvalues of this one was A transpose A." + }, + { + "text": "That's no surprise at all." + }, + { + "text": "The eigenvalues of A B are same as the eigenvalues of B A." + }, + { + "text": "The order, that's a very nice fact, that eigenvalues stay the same if I switch the order of multiplication." + }, + { + "text": "So no surprise to see thirty-two and eighteen." + }, + { + "text": "What I learned, first I checked that things were numerically correct, but now I've learned these eigenvectors, and actually they're about as nice as can be." + }, + { + "text": "They're the best orthogonal matrix, just the identity." + }, + { + "text": "Okay." + }, + { + "text": "So my claim is that it ought to all fit together." + }, + { + "text": "That this numeri- this, these numbers should come out right." + }, + { + "text": "The numbers should come out right because the, the, matrix multiplications use the properties that we want." + }, + { + "text": "Okay." + }, + { + "text": "So we just check that." + }, + { + "text": "Here's the identity, so not doing anything." + }, + { + "text": "Square root of thirty-two is multiplying that row, so that's square root of thirty-two divided by square root of two means square root of sixteen, four." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk13.json b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..a104483771ba144bbf5e80f6d0432de06fbabe37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Correct?" + }, + { + "text": "And square root of eighteen is divided by square root of two, so that leaves me square root of nine, which is three, but no, Professor Strang, you see the problem." + }, + { + "text": "Why is that?" + }, + { + "text": "Okay." + }, + { + "text": "Why am I getting minus three three here, and here I'm getting three minus three?" + }, + { + "text": "Phooey." + }, + { + "text": "I don't know why." + }, + { + "text": "It shouldn't have happened, but it did." + }, + { + "text": "Now, okay, you could say, well, just, the eigenvector there could have, I could have had the minus sign here for that eigenvector, but I'm not happy about that." + }, + { + "text": "Hm." + }, + { + "text": "Okay." + }, + { + "text": "Okay." + }, + { + "text": "So I realize there's a little catch here somewhere, and I may not see it until Wednesday, which then gives you a very important reason to come back on Wednesday, to catch that sign difference." + }, + { + "text": "So what did I do illegally?" + }, + { + "text": "I think I put the eigenvectors in that matrix V transpose." + }, + { + "text": "Okay, I'm going to have to think, why did that come out, with the opposite sign?" + }, + { + "text": "So you see, I mean, if I had a minus there, I would be all right, but I don't want that." + }, + { + "text": "I want positive entries down the diagonal of sigma squared." + }, + { + "text": "Okay." + }, + { + "text": "It'll come to me, but I'm going to leave this example to finish." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk14.json b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..6271feb6ec2eed0c67666d8fdac07717f2b70521 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "And the beauty of, these sliding boards is, I can make that go away." + }, + { + "text": "Can I, let me not do it, though." + }, + { + "text": "Yes, let me take a second example." + }, + { + "text": "Let me take a second example where the matrix is singular." + }, + { + "text": "So rank one." + }, + { + "text": "Okay." + }, + { + "text": "So let me take as an example two, where my matrix A is going to be rectangular again." + }, + { + "text": "Let me just make it four three eight six." + }, + { + "text": "Okay." + }, + { + "text": "That's a rank one matrix." + }, + { + "text": "So that has a null space and only a one-dimensional row space and column space." + }, + { + "text": "So actually, my picture becomes easy for this matrix, because what's my columns, my row space for this one?" + }, + { + "text": "So this is two by two, so my pictures are both two dimensional." + }, + { + "text": "My row space is all multiples of vector four three." + }, + { + "text": "So the whole, the row space is just a line, right?" + }, + { + "text": "That's the row space." + }, + { + "text": "And the null space, of course, is the perpendicular line." + }, + { + "text": "So the row space for this matrix is multiples of four three." + }, + { + "text": "Typical row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk15.json b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..247a2fb607840b5c46901a1736533537c0de9d60 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "What's the column space?" + }, + { + "text": "The columns are all multiples of four eight, three six, one two." + }, + { + "text": "The column space, then, goes in, like, this direction." + }, + { + "text": "So the column space, when I look at those columns, the column space, it was only one dimensional, because the rank is one." + }, + { + "text": "It's multiples of four eight." + }, + { + "text": "Okay." + }, + { + "text": "And what's the null space of A transpose?" + }, + { + "text": "It's the perpendicular guy." + }, + { + "text": "There's the, so this was the null space of A, and this is the null space of A transpose." + }, + { + "text": "Okay." + }, + { + "text": "What I want to say here is that the, that choosing these orthogonal bases for the row space and the column space is, like, no problem." + }, + { + "text": "They're only one dimensional." + }, + { + "text": "So what should v be?" + }, + { + "text": "v should be v1, but, yeah, v1, rather." + }, + { + "text": "v1 is supposed to be a unit vector." + }, + { + "text": "There's only one v1 to choose here, only one dimension in the row space." + }, + { + "text": "I just want to make it a unit vector." + }, + { + "text": "So v1 will be, it'll be this vector, but made into a unit vector, so four, point eight, point six." + }, + { + "text": "Four fifths, three fifths." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk16.json b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..9ebd9d5b85dc5cf2ad0e297580201c57ae64e6f6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what will be u1?" + }, + { + "text": "u1 will be the unit vector there, so I want to turn four eight or one two into a unit vector, so u1 will be, let's see, if it's one two, then what multiple of one two do I want?" + }, + { + "text": "That has length square root of five, so I have to divide by square root of five." + }, + { + "text": "Let me complete the singular value decomposition for this matrix." + }, + { + "text": "So this matrix, four three eight six, is, so I know what u1, here's A, and I want to get u, the basis in the column space, and it has to start with this guy." + }, + { + "text": "One over square root of five, two over square root of five." + }, + { + "text": "Then I want the sigma." + }, + { + "text": "OK. What are we expecting now for sigma?" + }, + { + "text": "Where is, this is only a rank one matrix, we're only expecting a sigma one, which I have to find, but zero's here." + }, + { + "text": "OK, so what's sigma one?" + }, + { + "text": "We should see it, it should be the, where did these sigmas come from?" + }, + { + "text": "They came from A transpose A, so I, can I do that little calculation over here?" + }, + { + "text": "A transpose A is four three, four three eight six times four three eight six." + }, + { + "text": "This had better, this is a rank one matrix, this is going to be, the whole thing will have rank one, that's sixteen and sixty four is eighty, twelve and forty eight is sixty, twelve and forty eight is sixty, nine and thirty six is forty five." + }, + { + "text": "OK." + }, + { + "text": "It's a rank one matrix." + }, + { + "text": "Of course." + }, + { + "text": "Every row is a multiple of four three." + }, + { + "text": "And what's the eigen, what are the eigenvalues of that matrix?" + }, + { + "text": "So this is like, the calculation is like practicing now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk17.json b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b48a4d8f19e69f562ef2b2b5013cd6a113ef2e4d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "What are the eigenvalues of this rank one matrix?" + }, + { + "text": "Well, tell me one eigenvalue, since the rank is only one, one eigenvalue is going to be zero." + }, + { + "text": "And then you know that the other eigenvalue is going to be a hundred and twenty five." + }, + { + "text": "So that's sigma squared, right, in A transpose A." + }, + { + "text": "So this will be the square root of a hundred and twenty five." + }, + { + "text": "And then finally, the V transpose, the Vs will be, there's V1, and what's V2?" + }, + { + "text": "What's V2 in the, what's, how do I make this into a orthonormal basis?" + }, + { + "text": "Well, V2 is in the null space direction." + }, + { + "text": "It's perpendicular to that, so point six and minus point eight." + }, + { + "text": "So those are the Vs that go in here." + }, + { + "text": "Point eight, point six, and point six minus point eight." + }, + { + "text": "OK. And I guess I better finish this guy." + }, + { + "text": "So this guy, all I want is to complete the orthonormal basis." + }, + { + "text": "It'll be coming from there, it'll be a two over square root of five and a minus one over square root of five." + }, + { + "text": "I could have take, let me take square root of five out of that matrix to make it look better." + }, + { + "text": "So one over square root of five times one, one, two, two, minus one." + }, + { + "text": "OK." + }, + { + "text": "So there I have, including the square root of five, that's an orthogonal matrix, that's an orthogonal matrix, that's a diagonal matrix, and its rank is only one." + }, + { + "text": "And now if I do that multiplication, I pray that it comes out right." + }, + { + "text": "The square root of five will cancel into that square root of one twenty-five and leave me with the square root of twenty-five, which is five, and five will multiply these numbers and I'll get whole numbers and out will come A. OK. That's a second, like, a second example showing how the null space guy, so this, this vector and the, and this one were multiplied by this zero, so they, they were easy to deal with." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk18.json b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..fe0c1e2162590b6461e7e5aa30c5f31ab402b16a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "It was the key ones are the ones in the column space and the row space." + }, + { + "text": "Do you see how I'm getting columns here, diagonal here, rows here, coming together to produce A?" + }, + { + "text": "OK. That's the singular value decomposition." + }, + { + "text": "So, let, let me think what I want to add to, to complete this topic." + }, + { + "text": "Sort of what we're really doing." + }, + { + "text": "So that's two examples." + }, + { + "text": "And now let's think what we're really doing." + }, + { + "text": "We're, we're choosing the right basis for the four subspaces of linear algebra." + }, + { + "text": "Let me, let me, let me write this down." + }, + { + "text": "So V1 up to Vr is an orthonormal basis for the row space." + }, + { + "text": "U1 up to Ur is an orthonormal basis for the column space." + }, + { + "text": "And then I just finish those out by Vr plus one, the rest up to Vn is an orthonormal basis for the null space." + }, + { + "text": "And finally, Ur plus one up to Um is an orthonormal basis for the null space of A transpose." + }, + { + "text": "Do you see that we finally got the bases right?" + }, + { + "text": "They're right because they're orthonormal and also, I mean, the, again, Graham-Schmidt would have done this in chapter four." + }, + { + "text": "Here we needed eigenvalues because these bases make the matrix diagonal." + }, + { + "text": "A times Vi is a multiple of Ui." + }, + { + "text": "So I'll put and." + }, + { + "text": "The matrix has been made diagonal." + }, + { + "text": "When we choose these bases, there's no coupling between Vs and no coupling between Us." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk19.json b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..ef84969ea528bd698a227de6c8007d53a10c135a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk19.json @@ -0,0 +1,32 @@ +[ + { + "text": "Each A, A times each V is in the direction of the corresponding U." + }, + { + "text": "So it's exactly the right basis for the four fundamental subspaces." + }, + { + "text": "And of course, their dimensions are what we know." + }, + { + "text": "The dimension of the row space is the rank r, and so is the dimension of the column space." + }, + { + "text": "The dimension of the null space is n minus r, that's how many vectors we need, and m minus r basis vectors for the left null space, the null space of A transpose." + }, + { + "text": "OK." + }, + { + "text": "I'm going to stop there." + }, + { + "text": "I could develop further from the SVD, but we'll see it again in the very last lectures of the course." + }, + { + "text": "There's the SVD." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk2.json b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6e336773d56df67c43cd476ce2fda66a297e1c38 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Graham-Schmidt tells me how to do it." + }, + { + "text": "Start with any old basis and use- grind through Graham-Schmidt, out comes an orthogonal basis." + }, + { + "text": "But then, if I just take any old orthogonal basis, then when I multiply by A, there's no reason why it should be orthogonal over here." + }, + { + "text": "So I'm looking for this special setup where A takes these basis vectors into orthogonal vectors over there." + }, + { + "text": "Now, you might have noticed that the null space I didn't include." + }, + { + "text": "Why don't I stick that in?" + }, + { + "text": "You remember our usual figure had a little null space and a little null space." + }, + { + "text": "And, those are no problems." + }, + { + "text": "Those are- null spaces are going to show up as zeros on the diagonal of sigma, so that's not what we're- that doesn't present any difficulty." + }, + { + "text": "Our difficulty is to find the- so do you see what this will mean?" + }, + { + "text": "This will mean that A times this- these v's, v1, v2, up to- what's the dimension of this row space?" + }, + { + "text": "vr." + }, + { + "text": "Sorry, that v a little smaller." + }, + { + "text": "Up to vr." + }, + { + "text": "So that's A v1 is going to be the first column, so let me- here's what I'm- here's what I'm achieving." + }, + { + "text": "Oh, I would like- I'm not only going to make these orthogonal, but why not make them orthonormal?" + }, + { + "text": "Make them unit vectors." + }, + { + "text": "So this- maybe the unit vector is here, is the u1, and this might be a multiple of it." + }, + { + "text": "So really what's happening is A v1 is some multiple of u1, right?" + }, + { + "text": "I'm going to- these guys will be unit vectors, and they'll go over into multiples of unit vectors, and the multiple I'm not going to call lambda anymore, I'm calling it sigma." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk3.json b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c34819f1e56e21a93db616f1627e90900e7c35b8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's the number- the stretching number." + }, + { + "text": "And similarly, A v2 is sigma 2 u2." + }, + { + "text": "This is what- this is my goal." + }, + { + "text": "And now I want to express that goal in matrix language." + }, + { + "text": "That's the usual step." + }, + { + "text": "Think of what you want and then express it as a matrix multiplication." + }, + { + "text": "So A v1 is sigma 1 u1." + }, + { + "text": "Actually, here we go." + }, + { + "text": "Let me pull out these u1, u2 to ur, and then a matrix with the sigmas." + }, + { + "text": "It's- everything now is going to be in this- in that, in that, little part of the blackboard." + }, + { + "text": "Do you see that this equation says what I'm trying to do with my figure?" + }, + { + "text": "A times the first basis vector should be sigma 1 times the other basis- the other first basis vector." + }, + { + "text": "These are the basis vectors in the row space, these are the basis vectors in the column space, and these are the multiplying factors." + }, + { + "text": "So A v2 is sigma 2 times u2, A vr is sigma r times ur." + }, + { + "text": "And then we've got a whole lot of zeros and maybe some zeros at the end, but this is- that's the heart of it." + }, + { + "text": "And now if I express that in- as matrices, because you knew that was coming, that's what I have." + }, + { + "text": "So this is my goal." + }, + { + "text": "To find an orthogonal basis in the rows- orthonormal, even, basis in the row space, and an orthonormal basis in the column space, so that I'm sort of diagonalized the matrix." + }, + { + "text": "The matrix A is like getting converted to this diagonal matrix sigma." + }, + { + "text": "And you notice that usually I have to do- I have to allow myself two different bases." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk4.json b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..191e383650177ee1c7a8b51ce0359c195d9afdec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "My little comment about symmetric positive definite was the one case where it's A q equal q sigma, where v and u are the same q." + }, + { + "text": "But mostly, I'm going to take a matrix like, oh, let me take a matrix like four four minus three three." + }, + { + "text": "Okay." + }, + { + "text": "There's a two by two matrix." + }, + { + "text": "It's invertible, so it has rank two." + }, + { + "text": "So I'm going to look for two vectors, v1 and v2, in the row space, and u- so I'm going to look for v1 v2 in the row space, which of course is R2." + }, + { + "text": "And I'm going to look for u1 u2 in the column space, which of course is also R2." + }, + { + "text": "And I'm going to look for numbers sigma 1 and sigma 2, so that it all comes out right." + }, + { + "text": "So these guys are orthonormal." + }, + { + "text": "These guys are orthonormal, and these are the scaling factors." + }, + { + "text": "So I'll do that example as soon as I get the matrix picture straight." + }, + { + "text": "Okay." + }, + { + "text": "Do you see that this expresses what I want?" + }, + { + "text": "Can I just say two words about null spaces?" + }, + { + "text": "If we have -- if there's some null space, then we've got- we want to stick in a basis for those, for that." + }, + { + "text": "So here comes a basis for the null space, v R plus one down to vn." + }, + { + "text": "So if we only had an R-dimensional row space and the other n minus R dimensions were in the null space, okay, we'll take an orthogonal- orthonormal basis there, no problem." + }, + { + "text": "And then we'll just get zeros." + }, + { + "text": "So actually, those zeros will come out from the- on the diagonal matrix." + }, + { + "text": "So I'll complete that to, to, orthonormal basis for the whole space, Rn." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk5.json b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..8d6aafa6aa98e697236b4b5cd884684c97d6a470 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "I complete this to an orthonormal basis for the whole space, Rn, and I complete that with zeros." + }, + { + "text": "Null spaces are no problem here." + }, + { + "text": "So really, the true problem is in a matrix like that, which isn't symmetric, so I can't use its eigenvectors, they're not orthogonal, but somehow I have to get these orthogonal, in fact, orthonormal guys that make it work." + }, + { + "text": "I have to find this, these orthonormal guys, these orthonormal guys, and I want A v1 to be sigma 1 u1, and A v2 to be sigma 2 u2." + }, + { + "text": "Okay." + }, + { + "text": "That's my goal." + }, + { + "text": "Here's, here's the, matrices that are going to get me there." + }, + { + "text": "Now, these are orthogonal matrices." + }, + { + "text": "I can put that, if I multiply on both sides by v inverse, I have A equals u sigma v inverse, and of course, you know the other way I can write v inverse." + }, + { + "text": "This is one of those square orthogonal matrices, so it's the same as u sigma v transpose." + }, + { + "text": "Okay." + }, + { + "text": "Here's my problem." + }, + { + "text": "I've got two orthogonal matrices here, and I don't want to find them both at once." + }, + { + "text": "So I want to cook up some expression that will make the u's disappear." + }, + { + "text": "I would like to make the u's disappear and leave me only with the v's." + }, + { + "text": "And here's how to do it." + }, + { + "text": "It's, it's the same combination that keeps showing up whenever we have a general rectangular matrix, then it's A transpose A, that's the great matrix." + }, + { + "text": "That's the great matrix." + }, + { + "text": "That's the matrix that's symmetric." + }, + { + "text": "And, in fact, positive definite or at least positive semidefinite." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk6.json b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..df7b3f09adc2388b2ce3ad477bb1b91bf8d74d84 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "This is the matrix with nice properties." + }, + { + "text": "So let's see what will it be." + }, + { + "text": "So if I took the transpose, then, I would have A transpose A will be what?" + }, + { + "text": "What do I have?" + }, + { + "text": "If I transpose that, I have v sigma transpose u transpose, that's, that's the A transpose." + }, + { + "text": "Now the A." + }, + { + "text": "And what have I got?" + }, + { + "text": "Looks like worse, because it's got six things now together, but it's going to collapse into something good." + }, + { + "text": "What does u transpose u collapse into?" + }, + { + "text": "I." + }, + { + "text": "The identity." + }, + { + "text": "So that's the key point." + }, + { + "text": "This is the identity and we don't have u anymore." + }, + { + "text": "And sigma transpose times sigma, those are diagonal matrices." + }, + { + "text": "So their product is just going to have sigma squareds on the diagonal." + }, + { + "text": "So do you see what we've got here?" + }, + { + "text": "This is v times this easy matrix, sigma one squared, sigma two squared, times v transpose." + }, + { + "text": "This is the A transpose A." + }, + { + "text": "This is, let me copy down, A transpose A is that." + }, + { + "text": "U's are out of the picture now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk7.json b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..bff98ae0a99f2983b0755af21ee925990c6fab2c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'm only having to choose the v's." + }, + { + "text": "And what are these v's?" + }, + { + "text": "And what are these sigmas?" + }, + { + "text": "Do you know what the v's are?" + }, + { + "text": "They're the eigenvectors." + }, + { + "text": "See, this is a perfect eigenvector, eigenvalue, Q lambda Q transpose for the matrix A transpose A." + }, + { + "text": "A itself is like nothing special." + }, + { + "text": "But A transpose A will be special." + }, + { + "text": "It'll be symmetric, positive, definite." + }, + { + "text": "So this'll be its eigenvectors and this'll be its eigenvalues." + }, + { + "text": "And the eigenvalues will be positive because this thing's positive definite." + }, + { + "text": "Can I just now so this is my method." + }, + { + "text": "This tells me what the v's are and how am I going to find the u's?" + }, + { + "text": "Well, one way would be to look at A A transpose." + }, + { + "text": "Put, multiply A by A transpose in the opposite order." + }, + { + "text": "That will stick the v's in the middle, knock them out, and leave me with the u's." + }, + { + "text": "So here's the overall picture, then." + }, + { + "text": "The v's are the eigenvectors of A transpose A." + }, + { + "text": "The u's are the eigenvectors of A A transpose, which are different." + }, + { + "text": "And the sigmas are the square roots of these and the positive square roots, so we have positive sigmas." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk8.json b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..cb5b25b4a97f60e6bc1aa3c42941190d5c2e5b99 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do that for that example." + }, + { + "text": "This is really what you should know and be able to do for, the SVD." + }, + { + "text": "Okay." + }, + { + "text": "Let me take that matrix." + }, + { + "text": "So what's my first step?" + }, + { + "text": "Compute A transpose A, because I want its eigenvectors." + }, + { + "text": "Okay, so I have to compute A transpose A." + }, + { + "text": "So A transpose is four four minus three three, and A is four four minus three three." + }, + { + "text": "And I do that multiplication and I get sixteen, I get twenty-five, I get sixteen minus nine, is that seven?" + }, + { + "text": "And it better come out symmetric and, oh, okay, and then it comes out twenty-five." + }, + { + "text": "Okay." + }, + { + "text": "So I want its eigenvectors and its eigenvalues." + }, + { + "text": "Its eigenvectors will be the v's, its eigenvalues will be the squares of the sigmas." + }, + { + "text": "Okay." + }, + { + "text": "What are the eigenvalues and eigenvectors of this guy?" + }, + { + "text": "Have you seen that two by two example enough to recognize that the eigenvectors are, that one one is an eigenvector?" + }, + { + "text": "So this is, here is A transpose A. I'm looking for its eigenvectors." + }, + { + "text": "So its eigenvectors, I think, are one one and one minus one." + }, + { + "text": "Because if I multiply that matrix by one one, what do I get?" + }, + { + "text": "If I multiply that matrix by one one, I get thirty-two thirty-two." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk9.json b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..15f3f793471c1b5693d2cfa38e670c0a75251236 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/RD9AWDdj-Yk_0_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So which is thirty-two of one one." + }, + { + "text": "So there's the first eigenvector." + }, + { + "text": "And there's the eigenvalue for A transpose A, so I'm going to take its square root in the, for sigma." + }, + { + "text": "Okay." + }, + { + "text": "What's the eigenvector that goes, eigenvalue that goes with this one?" + }, + { + "text": "If I do that multiplication, what do I get?" + }, + { + "text": "I get some multiple of one minus one." + }, + { + "text": "And what is that multiple?" + }, + { + "text": "Looks like eighteen." + }, + { + "text": "Okay." + }, + { + "text": "So those are the two eigenvectors." + }, + { + "text": "But, oh, just a moment, I didn't normalize them." + }, + { + "text": "To, to make everything absolutely right, I ought to normalize these eigenvectors, divide by their length, square root of two." + }, + { + "text": "So all these guys should be true unit vectors, and, of course, that normalization didn't change the thirty-two and the eighteen." + }, + { + "text": "Okay." + }, + { + "text": "So I'm happy with the Vs, here are the Vs, so now let me put together the, the, the pieces here." + }, + { + "text": "Here's my A." + }, + { + "text": "Here's my A." + }, + { + "text": "Let me, let me write down A again." + }, + { + "text": "This should, if, if life is right, we should get U, which I don't yet know, U I don't yet know, sigma, I do now know." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk0.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6e60456bfd56c49876fbdca713bb6c3b371b0f9c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "It doesn't run Flash Player, so I had to run them on Chrome." + }, + { + "text": "All right, so let's move on to our second chapter." + }, + { + "text": "And hopefully, in this chapter, you will feel a little better if you felt like it was going a bit fast in the first chapter." + }, + { + "text": "And the main reason why I actually went fast, especially in terms of confidence interval, some of you came and asked me, what do you mean by this is a confidence interval?" + }, + { + "text": "What does it mean that it's not happening in there with probability 95%, et cetera?" + }, + { + "text": "I just went really fast so that you could see why I didn't want to give you a first week doing probability only and without understanding what the statistical context for it was." + }, + { + "text": "So hopefully, all these things that we've done in terms of probability, you actually know why we've been doing them." + }, + { + "text": "And so we're basically going to go back to what we're doing, maybe start with some statistical setup." + }, + { + "text": "But the goal of this lecture is really going to go back again to what we've seen from a purely statistical perspective." + }, + { + "text": "So the first thing we're going to do is explain why we're doing statistical modeling." + }, + { + "text": "So in practice, if you have data, if you observe a bunch of points, and here I gave you some numbers, for example." + }, + { + "text": "So here's a partial data set with the number of siblings, including self, that were collected from college students a few years back." + }, + { + "text": "So I was teaching a class like yours, and I actually asked students to go and fill out some Google form and tell me a bunch of things." + }, + { + "text": "And one of the questions was, including yourself, how many siblings do you have?" + }, + { + "text": "And so they gave me this list of numbers." + }, + { + "text": "And there's many ways I can think of this list of numbers." + }, + { + "text": "I could think of it as being just a discrete distribution on the set of numbers between 1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk1.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..7f3c348a69d1db34cdf09a02c51f6df5de35b497 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "I mean, I know there's not going to be an answer which is less than 1, unless, well, someone doesn't understand the question." + }, + { + "text": "But all the answers I should get are positive integers, 1, 2, 3, et cetera." + }, + { + "text": "And there probably is an upper bound, but I don't know it on the top of my head." + }, + { + "text": "So maybe I should say 100." + }, + { + "text": "Maybe I should say 15." + }, + { + "text": "Depends, right?" + }, + { + "text": "And so I think the largest number I got for this was 6." + }, + { + "text": "So here you can see you have pretty standard families, lots of 1's, 2's, and 3's." + }, + { + "text": "So what statistical modeling is doing is to try to compress this information that I could actually describe in a very naive way." + }, + { + "text": "So let's start with the basic usual statistical setup." + }, + { + "text": "So I will start many of the boards that look like x1, xn, random variables." + }, + { + "text": "And what I'm going to assume, as we said, typically is that those guys are iid, and they have some distribution." + }, + { + "text": "So they all share the same distribution." + }, + { + "text": "And the fact that they're iid is so that I can actually do statistics." + }, + { + "text": "Statistics means looking at the global averaging thing so that I can actually get a sense of what the global behavior is for the population." + }, + { + "text": "If I start assuming that those things are not identically distributed, they all live on their own, that my sequence of number is your number of siblings, the shoe size of this person, the depth of the Charles River, and I start measuring a bunch of stuff, there's nothing I'm going to actually get together." + }, + { + "text": "I need to have something that's cohesive." + }, + { + "text": "And so here, I collected some data that was cohesive." + }, + { + "text": "And so the goal here, the first thing is to say, what is the distribution that I actually have here?" + }, + { + "text": "So I could actually be very general." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk10.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..ea49da809c2586659f138352b75f093c41fe5360 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's probably just better, because again, with formalism, it's never really clear." + }, + { + "text": "Actually, that's the next slide." + }, + { + "text": "OK, so there's two things we need to assume." + }, + { + "text": "I mean, there's, OK, so the purpose of a statistical model is to, once I estimate the parameter, I actually know exactly what distribution I have." + }, + { + "text": "OK?" + }, + { + "text": "So it means that I could potentially have several parameters that give me the same distribution that would still be fine, because I could estimate one guy, or I could estimate the other guy, and I would still recover the underlying distribution of my data." + }, + { + "text": "The problem is that this creates really annoying theoretical problems, like things don't work, the algorithms won't work, the guarantees won't work." + }, + { + "text": "And so what we typically assume is that the model is so-called well-specified." + }, + { + "text": "All right, sorry, that's not well-specified." + }, + { + "text": "I'm jumping ahead of myself." + }, + { + "text": "OK, well-specified means that your data, the distribution of your data, is actually one of those guys." + }, + { + "text": "OK, so some vocabulary." + }, + { + "text": "So well-specified means that for my observations x, there exists a theta, in capital theta, such that x follows p sub theta." + }, + { + "text": "I should put a double dot." + }, + { + "text": "OK, so that's what well-specified means." + }, + { + "text": "So that means that the distribution of your actual data is just one of those guys." + }, + { + "text": "This is a bit stronger than assumption." + }, + { + "text": "It's strong in the sense that, I don't know if you've heard of this sentence, which I don't know." + }, + { + "text": "I can tell you who it's attributed to, but that probably means that this person did not work with it." + }, + { + "text": "But it said that all models are wrong, but some of them are useful." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk11.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..f231d416482991329585fa315977e99c9d1d6f06 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "So all models are wrong means that maybe it's not true that this Poisson distribution that I assume for the number of siblings for college students, maybe that's not perfectly correct." + }, + { + "text": "Maybe there's a spike at three." + }, + { + "text": "Maybe there's a spike at one, because maybe those are slightly more educated families." + }, + { + "text": "They have less children." + }, + { + "text": "Maybe this is actually not exactly perfect, but it's probably good enough for our purposes." + }, + { + "text": "And when we make this assumption, we're actually assuming that the data really comes from a Poisson model." + }, + { + "text": "There is a lot of research that goes on about misspecified models, and that tells you how well you're doing in the model that's the closest to the actual distribution." + }, + { + "text": "So that's pretty much it." + }, + { + "text": "Yeah?" + }, + { + "text": "X is, so by data, it's always the way I denote one of the generic observations." + }, + { + "text": "So my observations are x1, xn, and they're iid with distribution p, always." + }, + { + "text": "So x is just one of those guys." + }, + { + "text": "I don't want to write x5 or x4." + }, + { + "text": "They're iid, so they all have the same distribution." + }, + { + "text": "So OK. No, no, no." + }, + { + "text": "They're all iid, so they all have the same p theta." + }, + { + "text": "They'll have the same p, which means they'll have the same p theta." + }, + { + "text": "So I can pick any one of them, so I just remove the index, just where it's there." + }, + { + "text": "So when I write x, I just mean think of x1." + }, + { + "text": "They're iid." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk12.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..2d79e83794e0663dbc06e48155908b4cd7f2ec95 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "I can pick whichever I want." + }, + { + "text": "I'm not going to write x1." + }, + { + "text": "It's going to be weird." + }, + { + "text": "OK. Is that clear?" + }, + { + "text": "OK." + }, + { + "text": "So this particular theta is called the true parameter." + }, + { + "text": "Sometimes, since we're going to want some variable theta, we might denote it by theta star as opposed to theta hat, which is always our estimator." + }, + { + "text": "But I'll keep it to be theta for now." + }, + { + "text": "And so the aim of the statistical experiment is to estimate theta so that once I actually plug in theta in the form of my distribution, for example, I could plug in theta here." + }, + { + "text": "So theta here was actually lambda." + }, + { + "text": "So once I estimate this guy, I would plug it in." + }, + { + "text": "And I would know the probability that my random variable takes any value by just putting a lambda hat and lambda hat here." + }, + { + "text": "So my goal is going to be to estimate this guy so that I can actually compute those distributions." + }, + { + "text": "But actually, we'll see, for example, when we talk about regression, that this parameter actually has a meaning in many instances." + }, + { + "text": "And so just knowing the parameter itself intuitively or, let's say, more so than just computing probabilities will actually tell us something about the process." + }, + { + "text": "So for example, we're going to run linear regression." + }, + { + "text": "And when we do linear regression, there's going to be some coefficients in the linear regression." + }, + { + "text": "And the value of this coefficient is actually telling me what is the sensitivity of the response that I'm looking at to this particular input." + }, + { + "text": "So just knowing if this number is large or if this number is small is actually going to be useful for us to just look at this guy." + }, + { + "text": "So there's going to be some instances where it's going to be important." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk13.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..5f008079960a43c6ec63d1f9f4c2f3806b503962 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Sometimes we're going to want to know if this parameter is larger or smaller than something or if it's equal to something or not equal to something." + }, + { + "text": "And those things are also important, for example, if theta actually measures the true." + }, + { + "text": "So theta is a true unknown parameter, true efficacy of a drug." + }, + { + "text": "Let's say I want to know what the true efficacy of a drug is." + }, + { + "text": "And what I'm going to want to know is maybe it's a score." + }, + { + "text": "Maybe I'm going to want to know if theta is larger than 2." + }, + { + "text": "Maybe I want to know if theta is the average number of siblings." + }, + { + "text": "Is this true number larger than 2 or not?" + }, + { + "text": "Maybe I'm interested in knowing if college students come from a sociological perspective." + }, + { + "text": "I'm interested in knowing if college students come from a household with more than two children." + }, + { + "text": "So those can be the questions that I may ask myself." + }, + { + "text": "I'm going to want to know maybe if theta is going to be equal to 1 half or not." + }, + { + "text": "So maybe for drug efficacy, is it completely standard?" + }, + { + "text": "Maybe for elections, is the proportion of the population that is going to vote for this particular candidate equal to 0.5 or is it different from 0.5?" + }, + { + "text": "And I can think of different things." + }, + { + "text": "When I'm talking about the regression, I'm going to want to test if this coefficient is actually 0 or not." + }, + { + "text": "Because if it's 0, it means that the variable that's in front of it actually goes out." + }, + { + "text": "And so those are things we're testing." + }, + { + "text": "Actually, having this very specific yes, no answer is going to give me a huge intuition or a huge understanding of what's going on in the phenomenon that I observe." + }, + { + "text": "But actually, since the questions are so precise, I'm going to be much better at answering them rather than giving you an estimate for theta with some confidence around it." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk14.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..03faa4278f01a482f8bea61bbb70111f5a1b6d92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's sort of the same principle as trying to reduce." + }, + { + "text": "What you're trying to do as a statistician is to inject as much knowledge about the question and about the problem that you can so that the data has to do a minimal job." + }, + { + "text": "And henceforth, you actually need less data." + }, + { + "text": "So for now on, we will always assume, and this is because this is an intro stats class, you will always assume that theta, the subset of parameters, is a subset of r to the d. That means that theta is a vector with, at most, a finite number of coordinates." + }, + { + "text": "Why do I say this?" + }, + { + "text": "Well, this is called a parametric model." + }, + { + "text": "So it's called a parametric model, or sometimes parametric statistics." + }, + { + "text": "Actually, we don't really talk about parametric statistics, but we talk a lot about nonparametric statistics or a nonparametric model." + }, + { + "text": "Can somebody think of a model which is nonparametric?" + }, + { + "text": "For example, in the siblings example, if I did not cap the number of siblings to 7, but I let this list go to infinity, I would have an infinite number of parameters to estimate." + }, + { + "text": "Very likely, the last one would be 0, but still, I would have an infinite number of parameters to estimate." + }, + { + "text": "So this would not be a parametric model if I just let this list of things to be estimated to be infinite." + }, + { + "text": "But there's other classes that are actually infinite and cannot be represented by vectors." + }, + { + "text": "For example, function." + }, + { + "text": "If I tell you my model, pf is just the distribution of x's, the probability distributions that have density f. So what I know is that the density is non-negative and that it integrates to 1." + }, + { + "text": "That's all I know about density." + }, + { + "text": "Well, f is not something you're going to be able to describe with a finite number of values." + }, + { + "text": "All possible functions, this is a huge set." + }, + { + "text": "It's certainly not representable by 10 numbers." + }, + { + "text": "And so nonparametric estimation is typically when you actually want to parameterize this by a large class of functions." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk15.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..6b1a11de42dbf8b404db2e3e7aa427e647d335d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so for example, histograms is the prime tool of nonparametric estimation." + }, + { + "text": "Because when you fit a histogram to data, you're trying to estimate the density of your data, but you're not trying to represent it as a finite number of points, even though that's really, I mean, effectively, you have to represent it." + }, + { + "text": "So you actually truncate somewhere and just say, those things are not going to matter." + }, + { + "text": "But really, the key thing is that this is nonparametric where you have an infinite, potentially infinite number of parameters, whereas we're going to only talk about finites." + }, + { + "text": "And actually, finite in most overwhelming majority of cases is going to be 1." + }, + { + "text": "So theta is going to be a subset of R1." + }, + { + "text": "We're going to be interested in estimating one parameter, just like the parameter of a poisson or the parameter of an exponential, the parameter of Bernoulli." + }, + { + "text": "But for example, rarely we're going to be interested in estimating mu and sigma square for the normal." + }, + { + "text": "So here are some statistical models." + }, + { + "text": "So I'm going to go through them with you." + }, + { + "text": "So we start, right, so if I tell you, I observe, I'm interested in understanding the, I'm still that shallow, and I'm interested in understanding the proportion of people who kiss by bending their head to the right." + }, + { + "text": "And for that, I collected n observations and I'm interested in making some inference in this statistical model." + }, + { + "text": "My question to you is, what is the statistical model?" + }, + { + "text": "Well, if you want to write the statistical model, you're going to have to write this e. Oh, sorry, I never told you what e was." + }, + { + "text": "OK, well, actually, just go to the examples and then you'll know what e is." + }, + { + "text": "So you're going to have to write to me an e and a p theta." + }, + { + "text": "OK, so let's start with the Bernoulli trials." + }, + { + "text": "So this e here is called the sample space." + }, + { + "text": "And in normal people's words, it just means the space or the set in which x, and back to your question, x is just a generic observation, lives." + }, + { + "text": "OK, and hopefully, this is the smallest you can think of." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk16.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..edf4f42d2d3f2f33f737eb935785bce345703366 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, so for example, for Bernoulli trials, I'm going to observe a sequence of 0's and 1's." + }, + { + "text": "So my experiment is going to be, as written on the board, is going to be 1, 0, 1, and then the probability distributions are going to be, well, it's just going to be the Bernoulli distributions indexed by p. So rather than writing p sub p, I'm going to write it as Bernoulli p, because it's clear what I mean when I write that." + }, + { + "text": "Is everybody happy?" + }, + { + "text": "Actually, I need to tell you something more." + }, + { + "text": "This is a family of distributions, so I need p. And maybe I don't want to have p that takes value 0 or 1." + }, + { + "text": "I mean, it doesn't make sense." + }, + { + "text": "I would probably not look at this problem if I anticipated that everybody would kiss to the right and everybody would kiss to the left." + }, + { + "text": "So I'm going to assume that p is in 0, 1, but does not have 0 and 1." + }, + { + "text": "So that's a statistical model for Bernoulli trials." + }, + { + "text": "OK?" + }, + { + "text": "OK, now the next one, what do we have?" + }, + { + "text": "Exponential." + }, + { + "text": "OK?" + }, + { + "text": "OK, so when I have exponential distributions, what is the support of the exponential distribution?" + }, + { + "text": "What value is it going to take?" + }, + { + "text": "0 to infinity, right?" + }, + { + "text": "So what I have is that my first space is the value that my random variables can take." + }, + { + "text": "So it's, well, actually, I can remove the 0 again." + }, + { + "text": "0 to plus infinity." + }, + { + "text": "And then the family of distributions that I have are exponential with parameter lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk17.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..cbd8fc46b4a15560899f1af7a6ee93705af68053 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And again, maybe you see me switching from p to lambda to theta to mu to sigma square." + }, + { + "text": "Honestly, you can do whatever you want, but it's just that it's customary to have these particular Greek letters." + }, + { + "text": "OK?" + }, + { + "text": "And so the parameters of exponential are just positive numbers." + }, + { + "text": "OK, and that's my exponential model." + }, + { + "text": "What is the third one?" + }, + { + "text": "Can somebody tell me?" + }, + { + "text": "Poisson." + }, + { + "text": "OK?" + }, + { + "text": "OK, so Poisson." + }, + { + "text": "Is Poisson random variable discrete or continuous?" + }, + { + "text": "Go back to your probability." + }, + { + "text": "All right, so the answer being the opposite of continuous." + }, + { + "text": "Good job." + }, + { + "text": "All right, so it's going to be, what values can a Poisson take?" + }, + { + "text": "All the natural integers, right?" + }, + { + "text": "So 0, 1, 2, 3, all the way to infinity." + }, + { + "text": "We don't have any control of this, so I'm going to write this as n without 0." + }, + { + "text": "I think in the slides, it's n star, maybe." + }, + { + "text": "Actually, no, you can take value 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk18.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..02bf0c1dc7d72cffdd5bb08348058c7b53c6f5c4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'm sorry." + }, + { + "text": "This actually takes value 0 quite a lot." + }, + { + "text": "That's typically in many instances actually the mode." + }, + { + "text": "So it's n, and then I'm going to write it as Poisson with parameter, well, here it's again lambda as a parameter." + }, + { + "text": "And lambda can take any positive value." + }, + { + "text": "And that's where you can actually see that the model that we had for the siblings, right?" + }, + { + "text": "So let me actually just squeeze in the siblings model here." + }, + { + "text": "All right, so that was the bad model that I had in the first place." + }, + { + "text": "When I actually capped this, let's say we just capped it at 7." + }, + { + "text": "Forget about large than or equal to 7." + }, + { + "text": "We just assumed it was 7." + }, + { + "text": "What was our sample space?" + }, + { + "text": "We said 7." + }, + { + "text": "So it's 1, 2, to 7, right?" + }, + { + "text": "Those were the possible values that this thing would take." + }, + { + "text": "And then what's my parameter space?" + }, + { + "text": "So that's going to be a nightmare to write, but I'm going to write it." + }, + { + "text": "So I'm going to write it as something like probability that x is equal to k is equal to p sub k. And that's going to be for p. OK, so that's for all k's, right?" + }, + { + "text": "For k equal 1 to 7." + }, + { + "text": "And here, the index is the set of parameters p1 to pk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk19.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..9fd8a1df68a8c4055a93ba8048e796f2221fd9d2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I know a little more about those guys, right?" + }, + { + "text": "They're going to be non-negative." + }, + { + "text": "pj non-negative." + }, + { + "text": "And I know that they sum to 1." + }, + { + "text": "OK, so maybe writing this, you start seeing why we like those Poisson exponential and short notation, because I actually don't have to write the PMF of a Poisson." + }, + { + "text": "I mean, a Poisson is really just this." + }, + { + "text": "But I call it Poisson, so I don't have to rewrite this all the time." + }, + { + "text": "And so here, I did not use a particular form." + }, + { + "text": "So I just have this thing, and that's what it is." + }, + { + "text": "The set of parameters is the set of positive numbers that send of, sorry, p1 to p7, pk, and sum to 7, right?" + }, + { + "text": "And so this is just the list of numbers that are non-negative and sum up to 1." + }, + { + "text": "So that's my parameter space." + }, + { + "text": "OK, so here, that's my theta." + }, + { + "text": "This whole thing here, this is my capital theta." + }, + { + "text": "So that's just the set of parameters that theta is allowed to take." + }, + { + "text": "OK, and finally, we're going to end with the star of all, and that's the normal distribution." + }, + { + "text": "And in a normal distribution, you still have also some flexibility in terms of choices, because naturally, the normal distribution is parameterized by two parameters, mean and variance." + }, + { + "text": "So what values can a Gaussian random variable take?" + }, + { + "text": "An entire real line, right?" + }, + { + "text": "And the set of parameters that it can take, so this is going to be n mu sigma squared, and mu is going to be positive, and sigma square is going to be in R, and sigma square is going to be positive." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk2.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..f945073162153b33cc99758bcf9316f0711decf1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "I could just say it's some distribution p. And let's say there are random variables, not random vectors." + }, + { + "text": "I could collect entire vectors about students." + }, + { + "text": "But let's say those are just random variables." + }, + { + "text": "And so now I can start making assumptions on this distribution p. What can I say about a distribution?" + }, + { + "text": "Well, maybe if those numbers are continuous, for example, I could assume they have a density, a probability density function." + }, + { + "text": "That's already an assumption." + }, + { + "text": "Maybe I could start to assume that their probability density function is smooth." + }, + { + "text": "That's another assumption." + }, + { + "text": "Maybe I could actually assume that it's piecewise constant." + }, + { + "text": "That's even better." + }, + { + "text": "And those things make my life simpler and simpler, because what I do by making the successive assumptions is reducing the degrees of freedom of the space in which I'm actually searching the distribution." + }, + { + "text": "And so what we actually want is to have something which is small enough so we can actually have some averaging going on." + }, + { + "text": "But we also want something which is big enough that it can actually express." + }, + { + "text": "It has chances of actually containing a distribution that makes sense for us." + }, + { + "text": "So let's start with the simplest possible example, which is when the xi's belong to 0, 1." + }, + { + "text": "And as I said here, we don't have a choice." + }, + { + "text": "The distribution of those guys has to be Bernoulli." + }, + { + "text": "And since they're iid, they all share the same p. So that's definitely the simplest possible thing I could think of." + }, + { + "text": "They're just Bernoulli p. And so all I would have to figure out in this case is p. And this is the simplest case." + }, + { + "text": "And unsurprisingly, it has the simplest answer." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk20.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..5ab5b9b62a8b77934383e3a12ce71b88d9b78b42 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, so again here, that's the way you're supposed to write it if you really want to identify what theta is." + }, + { + "text": "Well, theta formally is the set of mu sigma squared such that in R times 0 infinity." + }, + { + "text": "That's just to be formal, but this does the job just fine." + }, + { + "text": "You don't have to be super formal." + }, + { + "text": "OK, so that's not 3." + }, + { + "text": "That's like 5." + }, + { + "text": "Actually, I just want to write another one." + }, + { + "text": "Let's call it 5-bit." + }, + { + "text": "And 5-bit is just Gaussian with known variance." + }, + { + "text": "And this arises a lot in labs when you have measurement error, when you actually receive your measurement device." + }, + { + "text": "This thing has been tested by the manufacturer so much that it actually comes in on the side of the box." + }, + { + "text": "It says that the standard deviation of your measurements is going to be 0.23." + }, + { + "text": "OK, and actually, why do you do this is because they can brag about accuracy, right?" + }, + { + "text": "I mean, that's how they sell you this particular device." + }, + { + "text": "And so you actually know exactly what sigma square is." + }, + { + "text": "So once you actually get your data in the lab, you actually only have to estimate mu because sigma comes on the label." + }, + { + "text": "And so now, what is your statistical model?" + }, + { + "text": "Well, the numbers you're going to be collecting still are positive in r. But now, the models that I have is n mu sigma squared." + }, + { + "text": "But the parameter space is not mu in r and sigma positive." + }, + { + "text": "It's just mu in r. And to be a little more emphatic about this, this is enough to describe it, right?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk21.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..4d5546c82c9ebd4988001ae951b41ff89ffbd2ef --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because if sigma is the sigma that was specified by the manufacturer, then this is the sigma you want." + }, + { + "text": "But you can actually write sigma is equal to sigma square is equal to sigma square manufacturer, right?" + }, + { + "text": "You can just fix it to be this particular value." + }, + { + "text": "Or maybe you don't want to write an index that's manufacturer." + }, + { + "text": "And so you just say, well, when I write sigma square, what I mean is the sigma square of the manufacturer." + }, + { + "text": "Yeah?" + }, + { + "text": "AUDIENCE MEMBER 2 Yeah, so you can just write sigma square and then you can write sigma square." + }, + { + "text": "So you can just write sigma square and then you can write sigma square." + }, + { + "text": "Yeah?" + }, + { + "text": "AUDIENCE MEMBER 2 Yeah." + }, + { + "text": "For a particular measuring device?" + }, + { + "text": "You're in a lab and you have some measuring device, I don't know, something that measures tensile strength of something." + }, + { + "text": "And it's just going to measure something." + }, + { + "text": "And it will naturally make errors." + }, + { + "text": "But it's been tested so much by the manufacturer that they actually, and calibrated by them, they know it's not going to be perfect." + }, + { + "text": "But they knew exactly what error it's making because they've actually tried it on things for which they exactly knew what the tensile strength was." + }, + { + "text": "OK?" + }, + { + "text": "Yeah?" + }, + { + "text": "AUDIENCE MEMBER 3 This?" + }, + { + "text": "This?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk22.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..aaa3080d68eddd7bca2e68fa61f1ea4fd1c74199 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Oh, like 5 prime?" + }, + { + "text": "OK?" + }, + { + "text": "And we can come up with other examples, right?" + }, + { + "text": "So for example, here's another one." + }, + { + "text": "OK, so the names don't really matter, right?" + }, + { + "text": "I mean, I called it the siblings model, but you won't find the siblings model in a textbook, right?" + }, + { + "text": "So I wouldn't worry too much." + }, + { + "text": "But for example, let's say you have something, so let's call it 6." + }, + { + "text": "You have, I don't know, truncated." + }, + { + "text": "And that's the name I just came up with, but it's actually not exactly describing what I want." + }, + { + "text": "But let's say I observe y, which is the indicator of x larger than, say, 5 when x follows some exponential with parameter lambda." + }, + { + "text": "OK, this is what I get to observe." + }, + { + "text": "I only observe if my waiting time was more than 5 minutes because I see somebody coming out of the candle station being really upset, and that's all I record." + }, + { + "text": "And it's, ah, he's been waiting for more than 5 minutes." + }, + { + "text": "And that's all I get to record." + }, + { + "text": "OK, that happens a lot." + }, + { + "text": "These are called censored data." + }, + { + "text": "I should probably not call it truncated, but this should be censored." + }, + { + "text": "OK?" + }, + { + "text": "You see a lot of censored data when you ask for people how much they make." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk23.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..eb2e7c38cf564ea687eef46c1e43627d3f08face --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "They say, well, more than 5 figures." + }, + { + "text": "And that's all they want to tell you." + }, + { + "text": "OK?" + }, + { + "text": "And so you see a lot of censored data in survival analysis." + }, + { + "text": "Right?" + }, + { + "text": "You're trying to understand how long your patients are going to live after some surgery." + }, + { + "text": "OK?" + }, + { + "text": "And maybe you're not going to keep people alive, and you're not going to actually have them being touched in their family every day and ask them, is the guy still alive?" + }, + { + "text": "And so what you can do is just to ask people maybe five years after your study and say, please come in." + }, + { + "text": "And you will just happen to have some people who say, well, the person is deceased." + }, + { + "text": "And you will only be able to know that the person deceased less than five years ago." + }, + { + "text": "I mean, but you only see what happens after that." + }, + { + "text": "OK?" + }, + { + "text": "And so this truncated and censored data happens all the time just because you don't have the availability to do better than that." + }, + { + "text": "So this could happen here." + }, + { + "text": "So now what is my statistical experiment?" + }, + { + "text": "Right?" + }, + { + "text": "So here I should probably write this like that, because I just told you that my observations are going to be x." + }, + { + "text": "So there's some unknown y. I will never get to see this y. I only get to see the x." + }, + { + "text": "What is my statistical experiment?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk24.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..a89e8843ea33b0bc151e9dc34f00dd5408f36cb5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Please help me." + }, + { + "text": "So is it the real line?" + }, + { + "text": "My sample space, is it the real line?" + }, + { + "text": "Sorry, do you know?" + }, + { + "text": "Who does not know what this means?" + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "So this is called an indicator." + }, + { + "text": "So I write it as it's, if I wrote well, that would be 1 with a double bar." + }, + { + "text": "You can also write i if you prefer, if you don't feel like writing 1 in double bars." + }, + { + "text": "And it's 1 of, say, I'm going to write it like that." + }, + { + "text": "1 of a is equal to 1 if a is true and 0 if a is false." + }, + { + "text": "OK?" + }, + { + "text": "So that means that if y is larger than 5, this thing is 1." + }, + { + "text": "And if y is not larger than 5, this thing is 0." + }, + { + "text": "OK?" + }, + { + "text": "So that's called indicator." + }, + { + "text": "Indicator function." + }, + { + "text": "OK?" + }, + { + "text": "It's very useful to just turn anything into a 0, 1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk25.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..830960597ae73417cc9360a1563f9acb794668fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "So now that I'm here, what is my sample space?" + }, + { + "text": "0, 1." + }, + { + "text": "Whatever this thing I did not tell you was taking value was the thing you should have." + }, + { + "text": "If I didn't tell you that's taking value 6 or 7, that would be your sample space." + }, + { + "text": "OK, so it takes value 0, 1." + }, + { + "text": "And then what is the probability here?" + }, + { + "text": "What should I write here?" + }, + { + "text": "What should you write without even thinking?" + }, + { + "text": "Yeah, so let's assume there's two seconds before the end of the exam." + }, + { + "text": "You're going to write vernally." + }, + { + "text": "And that's where you're going to start checking if I'm going to give you extra time." + }, + { + "text": "So you write vernally without thinking, because it's taking value 0, 1." + }, + { + "text": "So you just write vernally." + }, + { + "text": "But you still have to tell me what possible parameters this thing is taking, right?" + }, + { + "text": "So I'm going to write it p, because I don't know." + }, + { + "text": "And then p takes value." + }, + { + "text": "OK, so sorry." + }, + { + "text": "I could write it like that." + }, + { + "text": "That would be perfectly valid." + }, + { + "text": "But actually, no more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk26.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..381a402c50c4922d06a56cf8b1a2b2befa976393 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk26.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's not any p. The p is the probability that an exponential lambda is larger than 5." + }, + { + "text": "And maybe I want to have lambda as a parameter." + }, + { + "text": "OK, so what I need to actually compute is what is the probability that y is larger than 5 when y is this exponential lambda, which means that what I need to compute is the integral between 5 and infinity of 1 over lambda." + }, + { + "text": "Huh?" + }, + { + "text": "How did I define it in this class?" + }, + { + "text": "I changed everything." + }, + { + "text": "What?" + }, + { + "text": "AUDIENCE MEMBER 2." + }, + { + "text": "Lambda e to the minus lambda x. PHILIPPE RIGOLLET." + }, + { + "text": "Oh, yeah, right, right, right." + }, + { + "text": "You're right." + }, + { + "text": "Lambda e to the minus lambda x dx, right?" + }, + { + "text": "So that's what I need to compute." + }, + { + "text": "What is this?" + }, + { + "text": "So what is the value of this integral?" + }, + { + "text": "AUDIENCE MEMBER 3." + }, + { + "text": "5." + }, + { + "text": "5." + }, + { + "text": "5." + }, + { + "text": "You take appropriate measures." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk27.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk27.json new file mode 100644 index 0000000000000000000000000000000000000000..bb780078a148ac9d9c350287dc074e09f2c6fccc --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk27.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. And again, this is just a basic calculus, right?" + }, + { + "text": "So when I'm going to integrate this guy, those guys are going to cancel." + }, + { + "text": "I'm going to get 0 for infinity." + }, + { + "text": "I'm going to get a 5 for this guy." + }, + { + "text": "And well, I know it's going to be a positive number, so I'm not really going to bother with the sign, because I know that's what it should be." + }, + { + "text": "So I get e to the minus 5 lambda." + }, + { + "text": "And so that means that I can actually write this like that." + }, + { + "text": "Now, parameterize this thing by lambda positive." + }, + { + "text": "So what I did here is I changed the parameterization from p to lambda." + }, + { + "text": "Why?" + }, + { + "text": "Well, because maybe if this, I know this is happening, maybe I'm actually interested in reporting lambda to MBTA, for example." + }, + { + "text": "Maybe I'm actually trying to estimate 1 over lambda, so that I know what is the, well, lambda is actually the intensity of arrival of my Poisson process, right?" + }, + { + "text": "If I have a Poisson process, that's where how my trains are coming in." + }, + { + "text": "And so I'm interested in lambda, so I will parameterize things by lambda, so that the thing I get is lambda." + }, + { + "text": "You can play with this, right?" + }, + { + "text": "I mean, I could parameterize this by 1 over lambda or 1 over lambda here if I wanted." + }, + { + "text": "But the context of your problem will tell you exactly how to parameterize this thing." + }, + { + "text": "OK?" + }, + { + "text": "So what else do I want to tell you?" + }, + { + "text": "OK, let's do a final one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk28.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk28.json new file mode 100644 index 0000000000000000000000000000000000000000..d0d13da48cddff744dc922d480aba326032e5cf5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk28.json @@ -0,0 +1,62 @@ +[ + { + "text": "By the way, are you guys OK with Poisson exponential Bernoulli's, I don't know, binomial, normal, all these things?" + }, + { + "text": "I'm not going to go back to it, but I'm going to use them heavily." + }, + { + "text": "So just spend five minutes on Wikipedia if you forgot about what those things are." + }, + { + "text": "Usually, you must have seen them in your probability class, so that should not be crazy name." + }, + { + "text": "And again, I'm not expecting you." + }, + { + "text": "I mean, I don't remember what the density of an exponential is, so it would be pretty unfair of me to actually ask you to remember what it is." + }, + { + "text": "Even for the Gaussian, you're not expected to remember what it is." + }, + { + "text": "But I want you to remember that if I add 5 to a Gaussian, then I have a Gaussian with mean mu plus 5." + }, + { + "text": "If I multiply it by something, right?" + }, + { + "text": "You need to know how to operate those things." + }, + { + "text": "But knowing complicated densities is definitely not part of the game." + }, + { + "text": "So let's do a final one." + }, + { + "text": "I don't know what number I have now." + }, + { + "text": "I'm going to just do uniform." + }, + { + "text": "That's another one." + }, + { + "text": "Everybody knows what uniform is?" + }, + { + "text": "So uniform, right?" + }, + { + "text": "So I'm going to have x, which my observations are going to be uniform on the interval 0 theta, right?" + }, + { + "text": "So if I want to define a uniform distribution for a random variable, I have to tell you which interval or which set I want it to be uniform on." + }, + { + "text": "And so here, I'm telling you it's the interval 0 theta." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk29.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk29.json new file mode 100644 index 0000000000000000000000000000000000000000..92b9ca99f9d549d54aed14a7dc495c09293d5428 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk29.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what is going to be my sample space?" + }, + { + "text": "I'm sorry?" + }, + { + "text": "0 to theta." + }, + { + "text": "And then what is my probability distribution, my family of parameters?" + }, + { + "text": "So well, I can write it like this, right?" + }, + { + "text": "Uniform theta, right?" + }, + { + "text": "And theta, let's say, is positive." + }, + { + "text": "Can somebody tell me what's wrong with what I wrote?" + }, + { + "text": "Yeah, this makes no sense." + }, + { + "text": "Tell me why." + }, + { + "text": "Yeah?" + }, + { + "text": "Yeah, this set depends on theta." + }, + { + "text": "And why is that a problem?" + }, + { + "text": "There's no theta." + }, + { + "text": "Right now, there's the families of thetas." + }, + { + "text": "Which one did you pick here?" + }, + { + "text": "This is just something that's indexed by theta." + }, + { + "text": "But I could have very well written it as just not being Greek for a second." + }, + { + "text": "I could have just written this as t, right, rather than theta." + }, + { + "text": "OK, that would be the same thing." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk3.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..b4f72390451e86d7c7344367d84606de62f2f9ba --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "We will come back to this example when we study maximum likelihood estimators or method of moments estimators by the method of moments." + }, + { + "text": "But at the end of the day, the things that we did, the things that we will do are always the naive estimator you would come up with is, what is the proportion of 1?" + }, + { + "text": "And this will be, in pretty much all respects, the best estimator you can think of." + }, + { + "text": "So then we're going to try to assess its performance." + }, + { + "text": "And we saw how to do that in the first chapter as well." + }, + { + "text": "So this problem here somehow is completely understood." + }, + { + "text": "We'll come back to it." + }, + { + "text": "But there's nothing fancy that's going to happen." + }, + { + "text": "But now I could have some more complicated things." + }, + { + "text": "So for example, in the example of the students now, my xi's belong to the sequence of integers 1, 2, 3, et cetera, which is also denoted by n, maybe without 0 if you want to put 0 in n, so the positive integers." + }, + { + "text": "Or I could actually just maybe put some prior knowledge about how humans have time to have families." + }, + { + "text": "But maybe some people thought of their college mates as being their brothers and sisters." + }, + { + "text": "And one student would actually put 465 siblings, because we're all good friends." + }, + { + "text": "Or maybe they actually think that all their Facebook contacts are actually their siblings." + }, + { + "text": "And so you never know what's going to happen." + }, + { + "text": "So maybe you want to account for this." + }, + { + "text": "But maybe you know that people are reasonable." + }, + { + "text": "And they will actually give you something like this." + }, + { + "text": "Now, intuitively, maybe you would say, well, why would you bother doing this if you're not really sure about the 20?" + }, + { + "text": "But I think that probably all of you intuitively guess that this is probably a good idea to start putting this kind of assumption rather than allowing for any number in the first place, because this eventually will be injected into the precision of our estimator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk30.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk30.json new file mode 100644 index 0000000000000000000000000000000000000000..2b74866121a17dca1506a42a9b9e62b4429a13c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk30.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then what the hell is theta?" + }, + { + "text": "There's no such thing as theta." + }, + { + "text": "We don't know what the parameter is." + }, + { + "text": "The parameter should move with everyone." + }, + { + "text": "And so that means that I actually am not allowed to pick this theta." + }, + { + "text": "I'm actually, just for the reason that there's no parameter to put on the left side." + }, + { + "text": "There should not be, right?" + }, + { + "text": "So you just said, well, there's a problem because the parameter is on the left-hand side." + }, + { + "text": "But there's not even a parameter." + }, + { + "text": "I'm describing the family of possible parameters." + }, + { + "text": "There's no one that you can actually plug it in." + }, + { + "text": "So this should really be one." + }, + { + "text": "And I'm going to go back to writing this as theta, because that's pretty thin." + }, + { + "text": "Is that clear for everyone?" + }, + { + "text": "I cannot just pick one and put it in there." + }, + { + "text": "I just take the, before I run my experiment, I could potentially get numbers that are all the way up to 1, because I don't know what theta is going to be ahead of time." + }, + { + "text": "Now, if somebody promised to me that theta was going to be less than 0.5, that would be, sorry, why do I put 1 here?" + }, + { + "text": "I could put theta between 0 and 1." + }, + { + "text": "But if somebody is going to promise me, for example, that theta is going to be less than 1, I could put 0, 1." + }, + { + "text": "All right?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk31.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk31.json new file mode 100644 index 0000000000000000000000000000000000000000..b954a90d701dde628ee923be06886cfd0919da3e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk31.json @@ -0,0 +1,62 @@ +[ + { + "text": "Is that clear?" + }, + { + "text": "OK, so now you know how to answer the question, what is the statistical model?" + }, + { + "text": "And again, within the scope of this class, you will not be asked to just come up with a model." + }, + { + "text": "I will just tell you, Poisson would be a probably good idea here." + }, + { + "text": "And then you would just have to trust me that, indeed, it would be a good idea." + }, + { + "text": "All right, so what I started talking about about 20 minutes ago, so I was definitely ahead of myself, is the notion." + }, + { + "text": "So that's when I was talking about well-specified." + }, + { + "text": "Remember, well-specified says that the true distribution is one of the distribution in this parametric families of distribution." + }, + { + "text": "The true distribution of my siblings is actually a Poisson with some parameters." + }, + { + "text": "And all I need to figure out is what this parameter is." + }, + { + "text": "When I started saying that, I said, well, but then that could be that there are several parameters that give me the same distribution, right?" + }, + { + "text": "It could be the case that Poisson 5 and Poisson 17 are exactly the same distributions when I start putting those numbers in the formula which I rephrased." + }, + { + "text": "So it could be the case that two different numbers would give me exactly the same probabilities." + }, + { + "text": "And in this case, we see that the model is not identifiable." + }, + { + "text": "I mean, the parameter is not identifiable." + }, + { + "text": "I cannot identify the parameter, even if you actually gave me an infinite amount of data, which means that I could actually estimate exactly the PMF." + }, + { + "text": "I might not be able to go back, because there would be several candidates." + }, + { + "text": "And I would not be able to tell you which one it was in the first place." + }, + { + "text": "So what we want is that this function, theta, maps to P theta is injective." + }, + { + "text": "And that's really to be fancy." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk32.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk32.json new file mode 100644 index 0000000000000000000000000000000000000000..82f9323ce7b2101d9fef6e2588d0e9665b6956d7 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk32.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what I really mean is that if theta is different from theta prime, then P of theta is different from P of theta prime." + }, + { + "text": "Or if you prefer to think about the contrapositive of this, this is the same as saying that if P theta gives me the same distribution as theta prime, then that implies that theta must be equal to theta prime." + }, + { + "text": "So in logic, those two things are equivalent." + }, + { + "text": "So this means that we say that the parameter is identifiable or identified, doesn't really matter, in this model." + }, + { + "text": "OK?" + }, + { + "text": "And this is something we're going to want." + }, + { + "text": "So in all the examples that I gave you, those parameters are completely identified." + }, + { + "text": "If I tell you, I mean, if those things are in probability books, it means that they were probably thought through." + }, + { + "text": "So when I say exponential lambda, I'm really talking about one specific distribution." + }, + { + "text": "And there's not another lambda that's going to give me exactly the same distribution." + }, + { + "text": "OK?" + }, + { + "text": "So that was the case." + }, + { + "text": "And you can check that." + }, + { + "text": "But it's a little annoying." + }, + { + "text": "So I probably would not do it." + }, + { + "text": "But rather than doing this, let me just give you some examples where it would not be the case." + }, + { + "text": "And here's an example." + }, + { + "text": "If I take xi, so now I'm back to just using this indicator function, but now for a Gaussian." + }, + { + "text": "So what I observe is x is the indicator that y is, what did we say, positive?" + }, + { + "text": "OK?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk33.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk33.json new file mode 100644 index 0000000000000000000000000000000000000000..1d58d09e3350f128163563ffa59db82f8635d40b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk33.json @@ -0,0 +1,62 @@ +[ + { + "text": "So this is a Bernoulli random variable, right?" + }, + { + "text": "And it has some parameter p. But p now is going to depend, sorry, in here, y is n mu sigma squared." + }, + { + "text": "So the p, the probability that this thing is positive, is actually, I don't think I put the 0." + }, + { + "text": "Oh yeah, because I have mu." + }, + { + "text": "OK." + }, + { + "text": "So this distribution, this p, the probability that it's positive, is just the probability that some Gaussian is positive." + }, + { + "text": "And it will depend on mu and sigma, right?" + }, + { + "text": "Because if I draw, if I have 0, and I draw my Gaussian around mu, then the probability of this Bernoulli being 1 is really the area under the curve here." + }, + { + "text": "Right?" + }, + { + "text": "And this thing, well, if mu is very large, it's going to become very large." + }, + { + "text": "If mu is very small, it's going to become very small." + }, + { + "text": "And if sigma changes, it's also going to affect it." + }, + { + "text": "Is that clear to everyone?" + }, + { + "text": "But we can actually compute this, right?" + }, + { + "text": "So the parameter p that I'm looking for here as a function of mu and sigma is simply the probability that some y is non-negative, which is the probability that y minus mu divided by sigma is larger than minus mu divided by sigma." + }, + { + "text": "By the way, when you studied probability, is that some operation you were used to making, removing the mean and dividing by the standard deviation?" + }, + { + "text": "What is the effect of doing that on the Gaussian random variable?" + }, + { + "text": "Yeah, so you normalize it, right?" + }, + { + "text": "You standardize it." + }, + { + "text": "You actually make it a standard Gaussian." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk34.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk34.json new file mode 100644 index 0000000000000000000000000000000000000000..6c78cb86e4595e4cfbb1c3ad587dd6e981044623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk34.json @@ -0,0 +1,62 @@ +[ + { + "text": "You remove the mean." + }, + { + "text": "It becomes a mean 0 Gaussian." + }, + { + "text": "And you remove the variance for it to become 1." + }, + { + "text": "So when you have a Gaussian, remove the mean and divide by the standard deviation, it becomes a standard Gaussian, which this thing has n 0 1 distribution, which is the one you can read the quintiles of at the end of the book." + }, + { + "text": "And that's exactly what we did." + }, + { + "text": "OK, so now you have the probability that some standard Gaussian exceeds negative mu over sigma, which I can write in terms of the cumulative distribution function capital phi, like we did in the first lecture." + }, + { + "text": "So if I do this cumulative distribution function, what is this probability in terms of phi?" + }, + { + "text": "AUDIENCE MEMBER 1." + }, + { + "text": "Lids." + }, + { + "text": "Well, that's what your name tag says." + }, + { + "text": "1 minus?" + }, + { + "text": "1 minus mu over sigma?" + }, + { + "text": "What happened to phi in our?" + }, + { + "text": "You think I defined this for fun?" + }, + { + "text": "1 minus phi of mu over sigma, right?" + }, + { + "text": "Because this is 1 minus the probability that it's less than this, and this is exactly the definition of the cumulative distribution function." + }, + { + "text": "So in particular, this thing only depends on mu over sigma." + }, + { + "text": "Agreed?" + }, + { + "text": "So in particular, if I had 2 mu over 2 sigma, p would remain unchanged." + }, + { + "text": "If I have 12 mu over 12 sigma, this thing would remain unchanged, which means that p does not change if I scale mu and sigma by the same factor." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk35.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk35.json new file mode 100644 index 0000000000000000000000000000000000000000..90828def788683ef3c7c3aaa3039a3c357adbe7e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk35.json @@ -0,0 +1,62 @@ +[ + { + "text": "So there's no way, just by observing x, even an infinite amount of time, so that I can actually get exactly what p is, I'm never going to be able to get mu and sigma separately." + }, + { + "text": "All I'm going to be able to get is mu over sigma." + }, + { + "text": "So here, we say that mu sigma, the parameter mu sigma, or actually each of them individually, those guys, they're not identifiable." + }, + { + "text": "But the parameter mu over sigma is identifiable." + }, + { + "text": "So if I wanted to write a statistical model in which the parameter is identifiable, I would write 0, 1, Bernoulli, and then I would write 1 minus phi of mu over sigma." + }, + { + "text": "And then I would take two parameters, which are mu and r and sigma squared positive." + }, + { + "text": "Well, let's write sigma positive." + }, + { + "text": "Right?" + }, + { + "text": "No." + }, + { + "text": "This is not identifiable." + }, + { + "text": "I cannot write those two guys as being two things different." + }, + { + "text": "Instead, what I want to write is 0, 1, Bernoulli, 1 minus." + }, + { + "text": "And now my parameter, yeah, I forgot this." + }, + { + "text": "My parameter is mu over sigma." + }, + { + "text": "Can somebody tell me where mu over sigma lives?" + }, + { + "text": "What values can this thing take?" + }, + { + "text": "Any real value, right?" + }, + { + "text": "OK, so now I've done this, definitely out of convenience, right?" + }, + { + "text": "Because that was the only thing I was able to identify, the ratio of mu over sigma." + }, + { + "text": "But it's still something that has some meaning." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk36.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk36.json new file mode 100644 index 0000000000000000000000000000000000000000..d78b58041de678db8abde68f3cefeabe5fa17f3a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk36.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the normalized mean." + }, + { + "text": "It really tells me what the mean is compared to the standard deviation." + }, + { + "text": "So in some models, in reality, in some real applications, this actually might have a good meaning for me." + }, + { + "text": "It's just telling me how big the mean is compared to the standard fluctuations of this model." + }, + { + "text": "But I won't be able to get more than that." + }, + { + "text": "Agreed?" + }, + { + "text": "All right, so now that we've set a parametric model, let's try to see what our goals are going to be." + }, + { + "text": "OK, so now we have a sample and a statistical model." + }, + { + "text": "And we want to estimate the parameter theta." + }, + { + "text": "And I could say, well, you know what?" + }, + { + "text": "I don't have time for this analysis." + }, + { + "text": "Collecting data is going to take me a while." + }, + { + "text": "And I'm going to say that mu over sigma is 4." + }, + { + "text": "I'm just going to give it to you." + }, + { + "text": "And maybe you will tell me, eh, not very good, right?" + }, + { + "text": "So we need some measure of performance of a given parameter." + }, + { + "text": "We need to be able to evaluate if eyeballing the problem is worse than actually collecting a large amount of data." + }, + { + "text": "We need to know if, even if I come up with an estimator that actually sort of uses the data, does it make an efficient use of the data?" + }, + { + "text": "Would I actually need 10 times more observations to achieve the same accuracy?" + }, + { + "text": "So to be able to answer these questions, well, I need to define what accuracy means." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk37.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk37.json new file mode 100644 index 0000000000000000000000000000000000000000..d1ad8aa2be51b6eac448741dba14e985c21c9523 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk37.json @@ -0,0 +1,62 @@ +[ + { + "text": "And accuracy is something that sort of makes sense." + }, + { + "text": "It says, well, I want theta hat to be close to theta." + }, + { + "text": "But theta hat is a random variable, so I'm going to have to understand what it means for a random variable to be close to a deterministic number." + }, + { + "text": "And so what is the parameter, an estimator, right?" + }, + { + "text": "So I have an estimator." + }, + { + "text": "And I said it's a random variable." + }, + { + "text": "And the formal definition to an estimator is a measurable function of the data." + }, + { + "text": "So when I write theta hat, and that will typically be my notation for an estimator, I should really write theta hat of x1, xn." + }, + { + "text": "That's what an estimator is." + }, + { + "text": "So if you want to know what an estimator is, this is a measurable function of data." + }, + { + "text": "And it's actually also known as a statistic." + }, + { + "text": "And if you're interested in, I see every day, I think, when I have a dinner with normal people, and they say I'm a statistician." + }, + { + "text": "Oh, yeah, really?" + }, + { + "text": "Like, yeah, baseball." + }, + { + "text": "And they talk to me about batting averages." + }, + { + "text": "That's not what I do." + }, + { + "text": "But for them, that's what it is." + }, + { + "text": "And that's because, in a way, that's what a statistic is." + }, + { + "text": "A batting average is a statistic." + }, + { + "text": "And so here are some examples." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk38.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk38.json new file mode 100644 index 0000000000000000000000000000000000000000..b068d8c10a4d3f99d897f848076b0ed604acd1b4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk38.json @@ -0,0 +1,62 @@ +[ + { + "text": "You can take the average xn bar." + }, + { + "text": "You can take the maximum of your observation." + }, + { + "text": "That's a statistic." + }, + { + "text": "You can take the first one." + }, + { + "text": "You can take the first one plus log of 1 plus the absolute value of the last one." + }, + { + "text": "You can do whatever you want." + }, + { + "text": "That will be an estimator." + }, + { + "text": "Some of them are clearly going to be bad." + }, + { + "text": "But that's still a statistic." + }, + { + "text": "And you can do this." + }, + { + "text": "Now, when I say measurable, I always have, so graduate students sometimes ask me, like, yeah, how do I know if this estimator is measurable or not?" + }, + { + "text": "And usually, my answer is, well, if I give you data, can you compute it?" + }, + { + "text": "And they say, yeah." + }, + { + "text": "I'm like, well, then it's measurable." + }, + { + "text": "That's a very good rule to check if something is actually measurable." + }, + { + "text": "When is this thing not measurable?" + }, + { + "text": "It's when it's implicitly defined." + }, + { + "text": "And in particular, the things that can give you problems are soup or inf." + }, + { + "text": "Anybody knows what a soup or an inf is?" + }, + { + "text": "It's like a max or a min, but that's not always attained." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk39.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk39.json new file mode 100644 index 0000000000000000000000000000000000000000..333de3218861fe0fbc392413ba3aa06b25513e38 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk39.json @@ -0,0 +1,62 @@ +[ + { + "text": "So if I have x1, so if I look at the infimum of the function f of x for x on the real line, and f of x, sorry, let's say x on 1 infinity, and f of x is equal to 1 over x, then the infimum is the smallest value it can take, except that it does not really take it." + }, + { + "text": "It's 0, because 1 over x is going to 0, but it's never really getting there." + }, + { + "text": "So we just call the inf 0, but it's not the value that it ever takes." + }, + { + "text": "And these things might actually be complicated to compute, and so that's when you actually have problems, when you're not really quite reaching the limit." + }, + { + "text": "You won't have this problem in general, but just so you know that an estimator is not really anything, it has to actually be measurable." + }, + { + "text": "So the first thing we want to know, I mentioned it, is an estimator is a statistic which does not depend on data, of course." + }, + { + "text": "So if I give you the data, you have to be able to compute it, and that probably should not require not knowing an unknown parameter." + }, + { + "text": "So an estimator is said to be consistent." + }, + { + "text": "When I collect more and more data, this thing is getting closer and closer to the true parameter." + }, + { + "text": "And we said that eyeballing and saying that it's going to be 4 is not really something that's probably going to be consistent, but I can have things that are consistent but that are converging to theta at different speeds." + }, + { + "text": "And we know also that this is a random variable." + }, + { + "text": "It converges to something, and there might be some different notions of conversions that kick in, and actually, they are." + }, + { + "text": "And we say that it's weakly convergent if it converges in probability, and strongly convergent if it converges almost surely." + }, + { + "text": "And this is just vocabulary." + }, + { + "text": "It won't make a big difference." + }, + { + "text": "So we will typically say it's consistent once you say any of the two." + }, + { + "text": "So in parametric statistics, it's actually a little difficult to come up with, but in non-parametric ones, I could just say if I have yi, xi, yi, and I know that yi is f of xi plus some noise epsilon i, and I know that f belongs to some class of functions, let's say, Sybil-Liff class of smooth functions, massive." + }, + { + "text": "And now I'm going to actually find the following estimator." + }, + { + "text": "I'm going to take the average." + }, + { + "text": "So I'm going to do least squares." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk4.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..af9945cf9fde8f2e1076eb57f0e492ebedb19c45 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "If I allow anything, it's going to be more complicated for me to get an accurate estimator." + }, + { + "text": "If I know that the numbers are either 1 or 2, then I'm actually going to be slightly more accurate as well." + }, + { + "text": "Because I know that, for example, somebody put a 5, I can remove it." + }, + { + "text": "Then it's not going to actually screw up with my estimator." + }, + { + "text": "All right, so now let's say we actually agree that we have numbers." + }, + { + "text": "And here I put seven numbers." + }, + { + "text": "So I just said, well, now the numbers, let's assume that the numbers I'm going to get are going to be 1 all the way to, say, this number that I denote by larger than or equal to 7, which is a placeholder for any number larger than 7." + }, + { + "text": "Because I know maybe I don't want to distinguish between people who have 9 or 25 siblings." + }, + { + "text": "And so now, this is a distribution on seven possible values, discrete distributions." + }, + { + "text": "And you know from your probability class that the way you describe this distribution is using the probability mass function, or PMF." + }, + { + "text": "So that's how we describe a discrete distribution." + }, + { + "text": "And the PMF is just a list of numbers." + }, + { + "text": "So as I wrote here, you have a list of numbers." + }, + { + "text": "And here you wrote the possible value that your random variable can take." + }, + { + "text": "And here you write the probability that your random variable takes this value." + }, + { + "text": "So the possible values being 1, 2, 3, all the way to larger than or equal to 7." + }, + { + "text": "And then I'm trying to estimate those numbers." + }, + { + "text": "If I give you those numbers, at least up to this compression of all numbers larger than or equal to 7, you have a full description of your distribution." + }, + { + "text": "And that is the ultimate goal of statistics." + }, + { + "text": "The ultimate goal of statistics is to say what distribution your data came from, because that's basically the best you're going to be able to." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk40.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk40.json new file mode 100644 index 0000000000000000000000000000000000000000..3d8db4ffb09272df056c54676f4946bbec2f1f76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk40.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I just check." + }, + { + "text": "I'm trying to minimize the distance of each of my f of xi to my yi." + }, + { + "text": "And now I want to find the smallest of them." + }, + { + "text": "So if I look at the infimum here, then the question is, so that could be, well, that's not really an estimator for f, but it's an estimator for the smallest possible value." + }, + { + "text": "And so for example, this is actually an estimator for the variance of sigma square." + }, + { + "text": "This might not be attained, and this might not be measurable if f is massive." + }, + { + "text": "So that's the inf of some class f of x." + }, + { + "text": "So those are always things that are defined implicitly." + }, + { + "text": "If it's an average, for example, it's completely measurable." + }, + { + "text": "Any other questions?" + }, + { + "text": "OK, so we know that the first thing we might want to check, and that's definitely something we want about an estimator, is that it's consistent, because all consistency tells us is that as I collect more and more data, my estimator is going to get closer and closer to the parameters." + }, + { + "text": "There's other things we can look at." + }, + { + "text": "For each possible value of n, now I have a finite number of observations, 25." + }, + { + "text": "And I want to know something about my estimator." + }, + { + "text": "The first thing I want to check is maybe if, in average, so this is a random variable." + }, + { + "text": "Is this random variable, in average, going to be close to theta or not?" + }, + { + "text": "And so the difference, how far I am from theta, is actually called the bias." + }, + { + "text": "So the bias of an estimator is the expectation of theta hat minus the value that I hope it gets, which is theta." + }, + { + "text": "If this thing is equal to 0, we say that theta hat is unbiased." + }, + { + "text": "And unbiased estimators are things that people are looking for in general." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk41.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk41.json new file mode 100644 index 0000000000000000000000000000000000000000..1690a8a499d54f5a021d192b47468606eaca1c01 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk41.json @@ -0,0 +1,62 @@ +[ + { + "text": "The problem is that there's lots of unbiased estimators, and so it might be misleading to look for unbiasedness when that's not really the only thing you should be looking for." + }, + { + "text": "So what does it mean to be unbiased?" + }, + { + "text": "Maybe for this particular round of data you collected, you're actually pretty far from the true estimator." + }, + { + "text": "But one thing that actually, what it means is that if I redid this experiment over and over and over again, and I averaged all the values of my estimators that I got, then this would actually be the true parameter." + }, + { + "text": "That's what it means." + }, + { + "text": "If I were to repeat this experiment, in average I would actually get the right thing." + }, + { + "text": "But you don't get to repeat an experiment." + }, + { + "text": "Just a remark about estimators." + }, + { + "text": "Look at this estimator, xn bar." + }, + { + "text": "Think of the kiss example." + }, + { + "text": "I'm looking at the average of my observations." + }, + { + "text": "And I want to know what the expectation of this thing is." + }, + { + "text": "OK?" + }, + { + "text": "Now, this guy is my linearity of the expectation." + }, + { + "text": "Is this, right?" + }, + { + "text": "But my data is identically distributed." + }, + { + "text": "So in particular, all the xi's have the same expectation, right?" + }, + { + "text": "Everybody agrees with this?" + }, + { + "text": "When it's identically distributed, they all get the same expectation?" + }, + { + "text": "So what it means is that this guy's here, they're all equal to the expectation of x1, right?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk42.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk42.json new file mode 100644 index 0000000000000000000000000000000000000000..710ba984fa10bb1d5ca29d4eea5e3b9ee9b71d93 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk42.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what it means is that this guy's, I have the average of the same number." + }, + { + "text": "So this is actually the expectation of x1." + }, + { + "text": "OK?" + }, + { + "text": "And it's true." + }, + { + "text": "In the kiss example, this was p. And this is p. So probability of turning your head right." + }, + { + "text": "OK?" + }, + { + "text": "So those two things are the same." + }, + { + "text": "In particular, that means that xn bar and just x1 have the same bias." + }, + { + "text": "So that should probably illustrate to you that bias is not something that really is telling you the entire picture." + }, + { + "text": "Right?" + }, + { + "text": "I can take only one of my observations, Bernoulli 0, 1." + }, + { + "text": "This thing will have the same bias as if I averaged 1,000 of them." + }, + { + "text": "So the bias is really telling me where I am in the average, but it's really not telling me what fluctuations I'm getting." + }, + { + "text": "And so if you want to start having fluctuations coming into the picture, we actually have to look at the risk or the quadratic risk of an estimator." + }, + { + "text": "And so the quadratic risk is defined as the expectation of the squared distance between theta hat and theta." + }, + { + "text": "OK?" + }, + { + "text": "So let's look at this." + }, + { + "text": "So the quadratic risk, sometimes it's denoted, people call it the L2 risk of theta hat, of course." + }, + { + "text": "I'm sorry for maintaining such an ugly board." + }, + { + "text": "I keep away this stuff." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk43.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk43.json new file mode 100644 index 0000000000000000000000000000000000000000..7045c106b5b63772bb7925e82252e103b8cbb333 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk43.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, so I look at the squared distance between theta hat and theta." + }, + { + "text": "This is still the function of a random variable, so it's a random variable as well." + }, + { + "text": "And I'm looking at the expectation of this guy." + }, + { + "text": "That's the definition." + }, + { + "text": "I claim that when this thing goes to 0, then my estimator is actually going to be consistent." + }, + { + "text": "Everybody agrees with this?" + }, + { + "text": "So if it goes to 0 as n goes to infinity, and here I don't need to tell you what kind of convergence I have, because this is just a number, right?" + }, + { + "text": "It's an expectation." + }, + { + "text": "So it's a regular, usual, calculus-style convergence." + }, + { + "text": "Then that implies that theta hat is actually weakly consistent." + }, + { + "text": "What did I use to tell you this?" + }, + { + "text": "Yeah, this is the convergence in L2." + }, + { + "text": "This actually is strictly equivalent." + }, + { + "text": "This is by definition saying that theta hat converges in L2 to theta." + }, + { + "text": "And we know that convergence in L2 implies convergence in probability to theta." + }, + { + "text": "That was the picture." + }, + { + "text": "We're going up." + }, + { + "text": "And this is actually equivalent to weak consistency by definition of weak consistency." + }, + { + "text": "So this is actually telling me a little more, because this guy here, they're both unbiased." + }, + { + "text": "Xn bar is unbiased." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk44.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk44.json new file mode 100644 index 0000000000000000000000000000000000000000..15e49ae14c37e70b0067958879db7096b0b62f6f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk44.json @@ -0,0 +1,62 @@ +[ + { + "text": "X1 is unbiased, but X1 is certainly not consistent, because the more data I collect, I'm not even doing anything with it." + }, + { + "text": "I'm just taking the first data point you're giving to me." + }, + { + "text": "So they're both unbiased, but this one is not consistent." + }, + { + "text": "And this one we'll see is actually consistent." + }, + { + "text": "Xn bar is consistent, and actually, we've seen that last time." + }, + { + "text": "And that's because of the what guarantees the fact that the Xn bar is consistent?" + }, + { + "text": "Law of large numbers, right?" + }, + { + "text": "Actually, it's strongly consistent because of the strong law of large numbers." + }, + { + "text": "OK." + }, + { + "text": "So just in the last two minutes, I want to tell you a little bit about how this risk is linked to, I said quadratic risk is equal to bias squared plus variance." + }, + { + "text": "Let's see what I mean by this." + }, + { + "text": "So I'm going to forget about the absolute values." + }, + { + "text": "I have a square." + }, + { + "text": "I don't really need them." + }, + { + "text": "If theta hat was unbiased, this thing would be the expectation of theta hat." + }, + { + "text": "It might not be the case." + }, + { + "text": "So let me see how I can actually see, put the bias in there." + }, + { + "text": "Well, one way to do this is to see that this is equal to the expectation of theta hat minus expectation of theta hat plus expectation of theta hat minus theta squared." + }, + { + "text": "OK?" + }, + { + "text": "I just removed the same and added the same thing, so I didn't change anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk45.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk45.json new file mode 100644 index 0000000000000000000000000000000000000000..4c2c5c39325cf6077d66a18711d2177d807042b4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk45.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, this guy is my bias, right?" + }, + { + "text": "So now let me expand the square." + }, + { + "text": "So what I get is the expectation of the square of theta hat minus its expectation." + }, + { + "text": "I should put some square bracket." + }, + { + "text": "Plus 2 times the cross product." + }, + { + "text": "So the cross product is what?" + }, + { + "text": "Expectation of theta hat minus expectation of theta hat times expectation of theta hat minus theta." + }, + { + "text": "And then I have the last square, expectation of theta hat minus theta squared." + }, + { + "text": "OK?" + }, + { + "text": "So square, cross product, square." + }, + { + "text": "Everybody with me?" + }, + { + "text": "Now, this guy here, if you pay attention, this thing is the expectation of some random variable, so it's a deterministic number." + }, + { + "text": "Theta is the true parameter." + }, + { + "text": "It's a deterministic number." + }, + { + "text": "So what I can do is pull out this entire thing out of the expectation like this." + }, + { + "text": "All right?" + }, + { + "text": "And compute the expectation only with respect to that part." + }, + { + "text": "But what is the expectation of this thing?" + }, + { + "text": "It's 0, right?" + }, + { + "text": "The expectation of theta hat minus expectation of theta hat is 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk46.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk46.json new file mode 100644 index 0000000000000000000000000000000000000000..58670cc783eb53d4ef2b37e2ce0a850c49922ea1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk46.json @@ -0,0 +1,62 @@ +[ + { + "text": "So this entire thing is equal to 0." + }, + { + "text": "So now when I actually collect back my quadratic terms, my two squared terms in this expansion, what I get is that the expectation of theta hat minus theta squared is equal to the expectation of theta hat minus expectation of theta hat squared plus the square of expectation of theta hat minus theta." + }, + { + "text": "Right?" + }, + { + "text": "So those are just the first and the last term of the previous equality." + }, + { + "text": "Now, here I have the expectation of the square of the difference between a random variable and its expectation." + }, + { + "text": "This is otherwise known as the variance, right?" + }, + { + "text": "So this is actually equal to the variance of theta hat." + }, + { + "text": "And this, well, this was the bias." + }, + { + "text": "We already said this there." + }, + { + "text": "So this whole thing is the bias squared." + }, + { + "text": "And hence, the quadratic term is the sum of the variance and the squared bias." + }, + { + "text": "Why squared bias?" + }, + { + "text": "Well, because otherwise you would add dollars and dollars squared, right?" + }, + { + "text": "So you need to add dollars squared and dollars squared so that this thing is actually homogeneous." + }, + { + "text": "OK, so if x is in dollars, then the bias is in dollars, but the variance is in dollars squared." + }, + { + "text": "And the square here forced you to put everything on the square scale." + }, + { + "text": "So what's nice is that if the quadratic risk goes to 0, then since I have the sum of two positive terms, both of them have to go to 0." + }, + { + "text": "That means that my variance is going to 0, very little fluctuations, and my bias is also going to 0, which means that I'm actually going to be on target once I reduce my fluctuations, because it's one thing to reduce the fluctuations." + }, + { + "text": "But if I'm not on target, it's an issue, right?" + }, + { + "text": "For example, the estimator 4, the value 4, has no variance." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk47.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk47.json new file mode 100644 index 0000000000000000000000000000000000000000..7e775eaa9d8586ae46e452748a723da24310d0c3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk47.json @@ -0,0 +1,26 @@ +[ + { + "text": "Every time I'm going to repeat the experiment, I'm going to get 4, 4, 4, 4." + }, + { + "text": "Variance is 0." + }, + { + "text": "But the bias is bad." + }, + { + "text": "The bias is 4 minus theta." + }, + { + "text": "And if theta is far from 4, that's not doing very well." + }, + { + "text": "OK, so next week, we will talk about how estimators change if they have high variance or low variance, or high bias and low bias." + }, + { + "text": "And we'll talk about confidence intervals as well." + }, + { + "text": "All right." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk5.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..2b213e6f1200eca1d7893bb18a8d4aa8470ed89f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now admittedly, if I started looking at the fraction of 1's, and the fraction of 2's, and the fraction of 3's, et cetera, I would actually eventually get those numbers." + }, + { + "text": "Just like looking at the fraction of 1's gave me a good estimate for p in the Bernoulli case, it would do the same in this case." + }, + { + "text": "It's a pretty intuitive idea." + }, + { + "text": "It's just the law of large numbers." + }, + { + "text": "Everybody agrees with that?" + }, + { + "text": "If I look at the proportion of 1's, the proportion of 2's, the proportion of 3's, that should actually give me something that gets closer and closer as my sample size increases to what I want." + }, + { + "text": "But the problem is, if my sample size is not huge, here I have seven numbers to estimate." + }, + { + "text": "And if I have 20 observations, the ratio is not really in my favor." + }, + { + "text": "I mean, 20 observations to estimate seven parameters, some of them are going to be pretty off, typically the ones with the large values." + }, + { + "text": "If I have only 20 students, look at the list of numbers." + }, + { + "text": "I don't know how many numbers I have, but it probably is close to 20, maybe 15 or something." + }, + { + "text": "And so if you look at this list, nobody has four or more siblings in this list." + }, + { + "text": "There's no such person." + }, + { + "text": "So that means that eventually, from this data set, my estimates, so those numbers I denote by, say, p1, p2, p3, et cetera, those estimates, p4 hat would be equal to what from this data?" + }, + { + "text": "0, right?" + }, + { + "text": "And p5 hat would be equal to 0, and p6 hat would be equal to 0, and p larger than or equal to 7 hat would be equal to 0." + }, + { + "text": "That would be my estimates from this data set." + }, + { + "text": "So maybe this is not." + }, + { + "text": "Maybe I want to actually pull some information from the people who have less siblings to try to make a guess, which is probably slightly better for the larger values." + }, + { + "text": "It's pretty clear that, in average, there's more than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk6.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..d3c38ba2593e85f08f8208f44c7601d118dd0df2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "The proportion of the population of households that have four children or more is definitely more than 0." + }, + { + "text": "So it means that my data set is not representative." + }, + { + "text": "And what I'm going to try to do is to find a model that tries to use the data that I have for the smaller values that I can observe and just pull shit out for the other ones." + }, + { + "text": "And so what we can do is to just reduce those parameters into something that's understood." + }, + { + "text": "And this is part of the modeling that I talked about in the first place." + }, + { + "text": "Now, how do you succinctly describe a number of something?" + }, + { + "text": "Well, one thing that you do is the Poisson distribution." + }, + { + "text": "Why the Poisson?" + }, + { + "text": "I mean, there's many reasons." + }, + { + "text": "I mean, again, that's part of statistical modeling." + }, + { + "text": "But once you know that you have number of something that can be modeled by a Poisson, why not try a Poisson?" + }, + { + "text": "You could just fit a Poisson." + }, + { + "text": "And the Poisson is something that looks like this." + }, + { + "text": "And I guess you've all seen it." + }, + { + "text": "But if x follows a Poisson distribution with parameter lambda, then the probability that x is equal to little x is equal to lambda to the x over factorial x e to the minus lambda." + }, + { + "text": "And if you did the sheet that I gave you on the first day, you can check that those numbers." + }, + { + "text": "So this is, of course, for x equals 0, 1, et cetera." + }, + { + "text": "So x is in natural integers." + }, + { + "text": "And if you sum from x equals 0 to infinity, this thing, you get e to the lambda." + }, + { + "text": "And so they cancel." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk7.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..d0dbf008c5822fe33350f4ea444434acd2b8712a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you have a sum which is equal to 1." + }, + { + "text": "So it's indeed a PMF." + }, + { + "text": "But what's key about this PMF is that it never takes value 0." + }, + { + "text": "This thing is always strictly positive." + }, + { + "text": "So whatever value of lambda I find from this data will give me something that's certainly more interesting than just putting the value 0." + }, + { + "text": "But more importantly, rather than having to estimate seven parameters, and as a consequence, you actually have to estimate 1, 2, 3, 4 of them, and it equals to 0, I have only one parameter to estimate, which is lambda." + }, + { + "text": "The problem with doing this is that now lambda may not be just something as simple as computing the average number." + }, + { + "text": "I mean, in this case, it will." + }, + { + "text": "But in many instances, it's actually not clear that this parametrization with lambda that I chose, I'm going to be able to estimate lambda just by computing the average number that I see." + }, + { + "text": "It will be the case." + }, + { + "text": "But if it's not, remember this example of the exponential we did in the last lecture." + }, + { + "text": "We could use the delta method and things like that to estimate this." + }, + { + "text": "All right, so here's the modeling 101." + }, + { + "text": "So the purpose of modeling is to restrict the space of possible distributions to a subspace that's actually plausible, but much simpler for me to estimate." + }, + { + "text": "So we went from all distributions on seven parameters, which is a large space that's a lot of things, to something which is just one number to estimate." + }, + { + "text": "This number is positive." + }, + { + "text": "OK?" + }, + { + "text": "Any questions about the purpose of doing this?" + }, + { + "text": "OK, so we're going to have to do a little bit of formalism now." + }, + { + "text": "And so if we want to talk, this is a specific class, so I'm not going to want to talk about the Poisson model specifically every single time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk8.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..87fc8b22abffc95ade364e887ef6306998bfeacf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'm going to want to talk about generic models." + }, + { + "text": "And then you're going to be able to plug in your favorite word, no Poisson, binomial, exponential, uniform, all these words that you've seen, you're going to be able to plug in there." + }, + { + "text": "But we're just going to have some generic notation and some generic terminology for statistical models." + }, + { + "text": "So here is the formal definition." + }, + { + "text": "So I'm going to go through it with you." + }, + { + "text": "OK?" + }, + { + "text": "OK, so the definition is that of a statistical model." + }, + { + "text": "OK?" + }, + { + "text": "And so, sorry, that's a statistical experiment, I should say." + }, + { + "text": "I'm sorry." + }, + { + "text": "OK, so a statistical experiment is actually just a pair, E, and that's a set, and a family of distributions, P theta, where theta ranges in some set, capital theta." + }, + { + "text": "OK, so I hope you're up to date with your Greek letters." + }, + { + "text": "So it's a small theta, it's a capital theta." + }, + { + "text": "I know I don't have the best handwriting, so if you don't see something, just ask me." + }, + { + "text": "OK, and so this thing now, so each of this guy is a probability distribution." + }, + { + "text": "All right?" + }, + { + "text": "So for example, this could be a Poisson with parameter theta, or a Bernoulli with parameter theta." + }, + { + "text": "OK, or an exponential with parameter, I don't know, 1 over theta squared, if you want." + }, + { + "text": "OK, but they're just indexed by theta." + }, + { + "text": "For each theta, this completely describes the distribution." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk9.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..332c4c3ada7371741c1a08a5615c45d79d625879 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_0_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It could be more complicated." + }, + { + "text": "This theta could be a pair of mu sigma squared, and that could actually give you some n mu sigma squared." + }, + { + "text": "OK, so anything where you can actually, rather than actually giving you a full distribution, I can compress it into a parameter." + }, + { + "text": "But it could be worse." + }, + { + "text": "It could be this guy here, right?" + }, + { + "text": "Theta could be p1, p larger than or equal to 7, and my distribution could just be something that has pmf." + }, + { + "text": "p1, p larger than 7." + }, + { + "text": "That's another parameter." + }, + { + "text": "This one is seven dimensional, this one is two dimensional, and all these guys are just one dimension." + }, + { + "text": "All these guys are parameters." + }, + { + "text": "Is that clear?" + }, + { + "text": "What's important here is that once I give you theta, you know exactly all the probabilities associated to this random variable." + }, + { + "text": "You know its distribution perfectly." + }, + { + "text": "OK, so here, so this is the definition." + }, + { + "text": "Is that clear for everyone?" + }, + { + "text": "Is there a question about this distribution?" + }, + { + "text": "About this definition, sorry?" + }, + { + "text": "All right, so really, the key thing is the statistical model associated to a statistical experiment." + }, + { + "text": "OK?" + }, + { + "text": "So let's just see some examples." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk0.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6e60456bfd56c49876fbdca713bb6c3b371b0f9c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "It doesn't run Flash Player, so I had to run them on Chrome." + }, + { + "text": "All right, so let's move on to our second chapter." + }, + { + "text": "And hopefully, in this chapter, you will feel a little better if you felt like it was going a bit fast in the first chapter." + }, + { + "text": "And the main reason why I actually went fast, especially in terms of confidence interval, some of you came and asked me, what do you mean by this is a confidence interval?" + }, + { + "text": "What does it mean that it's not happening in there with probability 95%, et cetera?" + }, + { + "text": "I just went really fast so that you could see why I didn't want to give you a first week doing probability only and without understanding what the statistical context for it was." + }, + { + "text": "So hopefully, all these things that we've done in terms of probability, you actually know why we've been doing them." + }, + { + "text": "And so we're basically going to go back to what we're doing, maybe start with some statistical setup." + }, + { + "text": "But the goal of this lecture is really going to go back again to what we've seen from a purely statistical perspective." + }, + { + "text": "So the first thing we're going to do is explain why we're doing statistical modeling." + }, + { + "text": "So in practice, if you have data, if you observe a bunch of points, and here I gave you some numbers, for example." + }, + { + "text": "So here's a partial data set with the number of siblings, including self, that were collected from college students a few years back." + }, + { + "text": "So I was teaching a class like yours, and I actually asked students to go and fill out some Google form and tell me a bunch of things." + }, + { + "text": "And one of the questions was, including yourself, how many siblings do you have?" + }, + { + "text": "And so they gave me this list of numbers." + }, + { + "text": "And there's many ways I can think of this list of numbers." + }, + { + "text": "I could think of it as being just a discrete distribution on the set of numbers between 1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk1.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..7f3c348a69d1db34cdf09a02c51f6df5de35b497 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "I mean, I know there's not going to be an answer which is less than 1, unless, well, someone doesn't understand the question." + }, + { + "text": "But all the answers I should get are positive integers, 1, 2, 3, et cetera." + }, + { + "text": "And there probably is an upper bound, but I don't know it on the top of my head." + }, + { + "text": "So maybe I should say 100." + }, + { + "text": "Maybe I should say 15." + }, + { + "text": "Depends, right?" + }, + { + "text": "And so I think the largest number I got for this was 6." + }, + { + "text": "So here you can see you have pretty standard families, lots of 1's, 2's, and 3's." + }, + { + "text": "So what statistical modeling is doing is to try to compress this information that I could actually describe in a very naive way." + }, + { + "text": "So let's start with the basic usual statistical setup." + }, + { + "text": "So I will start many of the boards that look like x1, xn, random variables." + }, + { + "text": "And what I'm going to assume, as we said, typically is that those guys are iid, and they have some distribution." + }, + { + "text": "So they all share the same distribution." + }, + { + "text": "And the fact that they're iid is so that I can actually do statistics." + }, + { + "text": "Statistics means looking at the global averaging thing so that I can actually get a sense of what the global behavior is for the population." + }, + { + "text": "If I start assuming that those things are not identically distributed, they all live on their own, that my sequence of number is your number of siblings, the shoe size of this person, the depth of the Charles River, and I start measuring a bunch of stuff, there's nothing I'm going to actually get together." + }, + { + "text": "I need to have something that's cohesive." + }, + { + "text": "And so here, I collected some data that was cohesive." + }, + { + "text": "And so the goal here, the first thing is to say, what is the distribution that I actually have here?" + }, + { + "text": "So I could actually be very general." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk10.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..ea49da809c2586659f138352b75f093c41fe5360 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's probably just better, because again, with formalism, it's never really clear." + }, + { + "text": "Actually, that's the next slide." + }, + { + "text": "OK, so there's two things we need to assume." + }, + { + "text": "I mean, there's, OK, so the purpose of a statistical model is to, once I estimate the parameter, I actually know exactly what distribution I have." + }, + { + "text": "OK?" + }, + { + "text": "So it means that I could potentially have several parameters that give me the same distribution that would still be fine, because I could estimate one guy, or I could estimate the other guy, and I would still recover the underlying distribution of my data." + }, + { + "text": "The problem is that this creates really annoying theoretical problems, like things don't work, the algorithms won't work, the guarantees won't work." + }, + { + "text": "And so what we typically assume is that the model is so-called well-specified." + }, + { + "text": "All right, sorry, that's not well-specified." + }, + { + "text": "I'm jumping ahead of myself." + }, + { + "text": "OK, well-specified means that your data, the distribution of your data, is actually one of those guys." + }, + { + "text": "OK, so some vocabulary." + }, + { + "text": "So well-specified means that for my observations x, there exists a theta, in capital theta, such that x follows p sub theta." + }, + { + "text": "I should put a double dot." + }, + { + "text": "OK, so that's what well-specified means." + }, + { + "text": "So that means that the distribution of your actual data is just one of those guys." + }, + { + "text": "This is a bit stronger than assumption." + }, + { + "text": "It's strong in the sense that, I don't know if you've heard of this sentence, which I don't know." + }, + { + "text": "I can tell you who it's attributed to, but that probably means that this person did not work with it." + }, + { + "text": "But it said that all models are wrong, but some of them are useful." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk11.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..f231d416482991329585fa315977e99c9d1d6f06 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "So all models are wrong means that maybe it's not true that this Poisson distribution that I assume for the number of siblings for college students, maybe that's not perfectly correct." + }, + { + "text": "Maybe there's a spike at three." + }, + { + "text": "Maybe there's a spike at one, because maybe those are slightly more educated families." + }, + { + "text": "They have less children." + }, + { + "text": "Maybe this is actually not exactly perfect, but it's probably good enough for our purposes." + }, + { + "text": "And when we make this assumption, we're actually assuming that the data really comes from a Poisson model." + }, + { + "text": "There is a lot of research that goes on about misspecified models, and that tells you how well you're doing in the model that's the closest to the actual distribution." + }, + { + "text": "So that's pretty much it." + }, + { + "text": "Yeah?" + }, + { + "text": "X is, so by data, it's always the way I denote one of the generic observations." + }, + { + "text": "So my observations are x1, xn, and they're iid with distribution p, always." + }, + { + "text": "So x is just one of those guys." + }, + { + "text": "I don't want to write x5 or x4." + }, + { + "text": "They're iid, so they all have the same distribution." + }, + { + "text": "So OK. No, no, no." + }, + { + "text": "They're all iid, so they all have the same p theta." + }, + { + "text": "They'll have the same p, which means they'll have the same p theta." + }, + { + "text": "So I can pick any one of them, so I just remove the index, just where it's there." + }, + { + "text": "So when I write x, I just mean think of x1." + }, + { + "text": "They're iid." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk12.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..2d79e83794e0663dbc06e48155908b4cd7f2ec95 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "I can pick whichever I want." + }, + { + "text": "I'm not going to write x1." + }, + { + "text": "It's going to be weird." + }, + { + "text": "OK. Is that clear?" + }, + { + "text": "OK." + }, + { + "text": "So this particular theta is called the true parameter." + }, + { + "text": "Sometimes, since we're going to want some variable theta, we might denote it by theta star as opposed to theta hat, which is always our estimator." + }, + { + "text": "But I'll keep it to be theta for now." + }, + { + "text": "And so the aim of the statistical experiment is to estimate theta so that once I actually plug in theta in the form of my distribution, for example, I could plug in theta here." + }, + { + "text": "So theta here was actually lambda." + }, + { + "text": "So once I estimate this guy, I would plug it in." + }, + { + "text": "And I would know the probability that my random variable takes any value by just putting a lambda hat and lambda hat here." + }, + { + "text": "So my goal is going to be to estimate this guy so that I can actually compute those distributions." + }, + { + "text": "But actually, we'll see, for example, when we talk about regression, that this parameter actually has a meaning in many instances." + }, + { + "text": "And so just knowing the parameter itself intuitively or, let's say, more so than just computing probabilities will actually tell us something about the process." + }, + { + "text": "So for example, we're going to run linear regression." + }, + { + "text": "And when we do linear regression, there's going to be some coefficients in the linear regression." + }, + { + "text": "And the value of this coefficient is actually telling me what is the sensitivity of the response that I'm looking at to this particular input." + }, + { + "text": "So just knowing if this number is large or if this number is small is actually going to be useful for us to just look at this guy." + }, + { + "text": "So there's going to be some instances where it's going to be important." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk13.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..5f008079960a43c6ec63d1f9f4c2f3806b503962 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Sometimes we're going to want to know if this parameter is larger or smaller than something or if it's equal to something or not equal to something." + }, + { + "text": "And those things are also important, for example, if theta actually measures the true." + }, + { + "text": "So theta is a true unknown parameter, true efficacy of a drug." + }, + { + "text": "Let's say I want to know what the true efficacy of a drug is." + }, + { + "text": "And what I'm going to want to know is maybe it's a score." + }, + { + "text": "Maybe I'm going to want to know if theta is larger than 2." + }, + { + "text": "Maybe I want to know if theta is the average number of siblings." + }, + { + "text": "Is this true number larger than 2 or not?" + }, + { + "text": "Maybe I'm interested in knowing if college students come from a sociological perspective." + }, + { + "text": "I'm interested in knowing if college students come from a household with more than two children." + }, + { + "text": "So those can be the questions that I may ask myself." + }, + { + "text": "I'm going to want to know maybe if theta is going to be equal to 1 half or not." + }, + { + "text": "So maybe for drug efficacy, is it completely standard?" + }, + { + "text": "Maybe for elections, is the proportion of the population that is going to vote for this particular candidate equal to 0.5 or is it different from 0.5?" + }, + { + "text": "And I can think of different things." + }, + { + "text": "When I'm talking about the regression, I'm going to want to test if this coefficient is actually 0 or not." + }, + { + "text": "Because if it's 0, it means that the variable that's in front of it actually goes out." + }, + { + "text": "And so those are things we're testing." + }, + { + "text": "Actually, having this very specific yes, no answer is going to give me a huge intuition or a huge understanding of what's going on in the phenomenon that I observe." + }, + { + "text": "But actually, since the questions are so precise, I'm going to be much better at answering them rather than giving you an estimate for theta with some confidence around it." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk14.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..03faa4278f01a482f8bea61bbb70111f5a1b6d92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's sort of the same principle as trying to reduce." + }, + { + "text": "What you're trying to do as a statistician is to inject as much knowledge about the question and about the problem that you can so that the data has to do a minimal job." + }, + { + "text": "And henceforth, you actually need less data." + }, + { + "text": "So for now on, we will always assume, and this is because this is an intro stats class, you will always assume that theta, the subset of parameters, is a subset of r to the d. That means that theta is a vector with, at most, a finite number of coordinates." + }, + { + "text": "Why do I say this?" + }, + { + "text": "Well, this is called a parametric model." + }, + { + "text": "So it's called a parametric model, or sometimes parametric statistics." + }, + { + "text": "Actually, we don't really talk about parametric statistics, but we talk a lot about nonparametric statistics or a nonparametric model." + }, + { + "text": "Can somebody think of a model which is nonparametric?" + }, + { + "text": "For example, in the siblings example, if I did not cap the number of siblings to 7, but I let this list go to infinity, I would have an infinite number of parameters to estimate." + }, + { + "text": "Very likely, the last one would be 0, but still, I would have an infinite number of parameters to estimate." + }, + { + "text": "So this would not be a parametric model if I just let this list of things to be estimated to be infinite." + }, + { + "text": "But there's other classes that are actually infinite and cannot be represented by vectors." + }, + { + "text": "For example, function." + }, + { + "text": "If I tell you my model, pf is just the distribution of x's, the probability distributions that have density f. So what I know is that the density is non-negative and that it integrates to 1." + }, + { + "text": "That's all I know about density." + }, + { + "text": "Well, f is not something you're going to be able to describe with a finite number of values." + }, + { + "text": "All possible functions, this is a huge set." + }, + { + "text": "It's certainly not representable by 10 numbers." + }, + { + "text": "And so nonparametric estimation is typically when you actually want to parameterize this by a large class of functions." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk15.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..6b1a11de42dbf8b404db2e3e7aa427e647d335d4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so for example, histograms is the prime tool of nonparametric estimation." + }, + { + "text": "Because when you fit a histogram to data, you're trying to estimate the density of your data, but you're not trying to represent it as a finite number of points, even though that's really, I mean, effectively, you have to represent it." + }, + { + "text": "So you actually truncate somewhere and just say, those things are not going to matter." + }, + { + "text": "But really, the key thing is that this is nonparametric where you have an infinite, potentially infinite number of parameters, whereas we're going to only talk about finites." + }, + { + "text": "And actually, finite in most overwhelming majority of cases is going to be 1." + }, + { + "text": "So theta is going to be a subset of R1." + }, + { + "text": "We're going to be interested in estimating one parameter, just like the parameter of a poisson or the parameter of an exponential, the parameter of Bernoulli." + }, + { + "text": "But for example, rarely we're going to be interested in estimating mu and sigma square for the normal." + }, + { + "text": "So here are some statistical models." + }, + { + "text": "So I'm going to go through them with you." + }, + { + "text": "So we start, right, so if I tell you, I observe, I'm interested in understanding the, I'm still that shallow, and I'm interested in understanding the proportion of people who kiss by bending their head to the right." + }, + { + "text": "And for that, I collected n observations and I'm interested in making some inference in this statistical model." + }, + { + "text": "My question to you is, what is the statistical model?" + }, + { + "text": "Well, if you want to write the statistical model, you're going to have to write this e. Oh, sorry, I never told you what e was." + }, + { + "text": "OK, well, actually, just go to the examples and then you'll know what e is." + }, + { + "text": "So you're going to have to write to me an e and a p theta." + }, + { + "text": "OK, so let's start with the Bernoulli trials." + }, + { + "text": "So this e here is called the sample space." + }, + { + "text": "And in normal people's words, it just means the space or the set in which x, and back to your question, x is just a generic observation, lives." + }, + { + "text": "OK, and hopefully, this is the smallest you can think of." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk16.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..edf4f42d2d3f2f33f737eb935785bce345703366 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, so for example, for Bernoulli trials, I'm going to observe a sequence of 0's and 1's." + }, + { + "text": "So my experiment is going to be, as written on the board, is going to be 1, 0, 1, and then the probability distributions are going to be, well, it's just going to be the Bernoulli distributions indexed by p. So rather than writing p sub p, I'm going to write it as Bernoulli p, because it's clear what I mean when I write that." + }, + { + "text": "Is everybody happy?" + }, + { + "text": "Actually, I need to tell you something more." + }, + { + "text": "This is a family of distributions, so I need p. And maybe I don't want to have p that takes value 0 or 1." + }, + { + "text": "I mean, it doesn't make sense." + }, + { + "text": "I would probably not look at this problem if I anticipated that everybody would kiss to the right and everybody would kiss to the left." + }, + { + "text": "So I'm going to assume that p is in 0, 1, but does not have 0 and 1." + }, + { + "text": "So that's a statistical model for Bernoulli trials." + }, + { + "text": "OK?" + }, + { + "text": "OK, now the next one, what do we have?" + }, + { + "text": "Exponential." + }, + { + "text": "OK?" + }, + { + "text": "OK, so when I have exponential distributions, what is the support of the exponential distribution?" + }, + { + "text": "What value is it going to take?" + }, + { + "text": "0 to infinity, right?" + }, + { + "text": "So what I have is that my first space is the value that my random variables can take." + }, + { + "text": "So it's, well, actually, I can remove the 0 again." + }, + { + "text": "0 to plus infinity." + }, + { + "text": "And then the family of distributions that I have are exponential with parameter lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk17.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..cbd8fc46b4a15560899f1af7a6ee93705af68053 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And again, maybe you see me switching from p to lambda to theta to mu to sigma square." + }, + { + "text": "Honestly, you can do whatever you want, but it's just that it's customary to have these particular Greek letters." + }, + { + "text": "OK?" + }, + { + "text": "And so the parameters of exponential are just positive numbers." + }, + { + "text": "OK, and that's my exponential model." + }, + { + "text": "What is the third one?" + }, + { + "text": "Can somebody tell me?" + }, + { + "text": "Poisson." + }, + { + "text": "OK?" + }, + { + "text": "OK, so Poisson." + }, + { + "text": "Is Poisson random variable discrete or continuous?" + }, + { + "text": "Go back to your probability." + }, + { + "text": "All right, so the answer being the opposite of continuous." + }, + { + "text": "Good job." + }, + { + "text": "All right, so it's going to be, what values can a Poisson take?" + }, + { + "text": "All the natural integers, right?" + }, + { + "text": "So 0, 1, 2, 3, all the way to infinity." + }, + { + "text": "We don't have any control of this, so I'm going to write this as n without 0." + }, + { + "text": "I think in the slides, it's n star, maybe." + }, + { + "text": "Actually, no, you can take value 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk18.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..02bf0c1dc7d72cffdd5bb08348058c7b53c6f5c4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'm sorry." + }, + { + "text": "This actually takes value 0 quite a lot." + }, + { + "text": "That's typically in many instances actually the mode." + }, + { + "text": "So it's n, and then I'm going to write it as Poisson with parameter, well, here it's again lambda as a parameter." + }, + { + "text": "And lambda can take any positive value." + }, + { + "text": "And that's where you can actually see that the model that we had for the siblings, right?" + }, + { + "text": "So let me actually just squeeze in the siblings model here." + }, + { + "text": "All right, so that was the bad model that I had in the first place." + }, + { + "text": "When I actually capped this, let's say we just capped it at 7." + }, + { + "text": "Forget about large than or equal to 7." + }, + { + "text": "We just assumed it was 7." + }, + { + "text": "What was our sample space?" + }, + { + "text": "We said 7." + }, + { + "text": "So it's 1, 2, to 7, right?" + }, + { + "text": "Those were the possible values that this thing would take." + }, + { + "text": "And then what's my parameter space?" + }, + { + "text": "So that's going to be a nightmare to write, but I'm going to write it." + }, + { + "text": "So I'm going to write it as something like probability that x is equal to k is equal to p sub k. And that's going to be for p. OK, so that's for all k's, right?" + }, + { + "text": "For k equal 1 to 7." + }, + { + "text": "And here, the index is the set of parameters p1 to pk." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk19.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..9fd8a1df68a8c4055a93ba8048e796f2221fd9d2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I know a little more about those guys, right?" + }, + { + "text": "They're going to be non-negative." + }, + { + "text": "pj non-negative." + }, + { + "text": "And I know that they sum to 1." + }, + { + "text": "OK, so maybe writing this, you start seeing why we like those Poisson exponential and short notation, because I actually don't have to write the PMF of a Poisson." + }, + { + "text": "I mean, a Poisson is really just this." + }, + { + "text": "But I call it Poisson, so I don't have to rewrite this all the time." + }, + { + "text": "And so here, I did not use a particular form." + }, + { + "text": "So I just have this thing, and that's what it is." + }, + { + "text": "The set of parameters is the set of positive numbers that send of, sorry, p1 to p7, pk, and sum to 7, right?" + }, + { + "text": "And so this is just the list of numbers that are non-negative and sum up to 1." + }, + { + "text": "So that's my parameter space." + }, + { + "text": "OK, so here, that's my theta." + }, + { + "text": "This whole thing here, this is my capital theta." + }, + { + "text": "So that's just the set of parameters that theta is allowed to take." + }, + { + "text": "OK, and finally, we're going to end with the star of all, and that's the normal distribution." + }, + { + "text": "And in a normal distribution, you still have also some flexibility in terms of choices, because naturally, the normal distribution is parameterized by two parameters, mean and variance." + }, + { + "text": "So what values can a Gaussian random variable take?" + }, + { + "text": "An entire real line, right?" + }, + { + "text": "And the set of parameters that it can take, so this is going to be n mu sigma squared, and mu is going to be positive, and sigma square is going to be in R, and sigma square is going to be positive." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk2.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..f945073162153b33cc99758bcf9316f0711decf1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "I could just say it's some distribution p. And let's say there are random variables, not random vectors." + }, + { + "text": "I could collect entire vectors about students." + }, + { + "text": "But let's say those are just random variables." + }, + { + "text": "And so now I can start making assumptions on this distribution p. What can I say about a distribution?" + }, + { + "text": "Well, maybe if those numbers are continuous, for example, I could assume they have a density, a probability density function." + }, + { + "text": "That's already an assumption." + }, + { + "text": "Maybe I could start to assume that their probability density function is smooth." + }, + { + "text": "That's another assumption." + }, + { + "text": "Maybe I could actually assume that it's piecewise constant." + }, + { + "text": "That's even better." + }, + { + "text": "And those things make my life simpler and simpler, because what I do by making the successive assumptions is reducing the degrees of freedom of the space in which I'm actually searching the distribution." + }, + { + "text": "And so what we actually want is to have something which is small enough so we can actually have some averaging going on." + }, + { + "text": "But we also want something which is big enough that it can actually express." + }, + { + "text": "It has chances of actually containing a distribution that makes sense for us." + }, + { + "text": "So let's start with the simplest possible example, which is when the xi's belong to 0, 1." + }, + { + "text": "And as I said here, we don't have a choice." + }, + { + "text": "The distribution of those guys has to be Bernoulli." + }, + { + "text": "And since they're iid, they all share the same p. So that's definitely the simplest possible thing I could think of." + }, + { + "text": "They're just Bernoulli p. And so all I would have to figure out in this case is p. And this is the simplest case." + }, + { + "text": "And unsurprisingly, it has the simplest answer." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk20.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..5ab5b9b62a8b77934383e3a12ce71b88d9b78b42 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, so again here, that's the way you're supposed to write it if you really want to identify what theta is." + }, + { + "text": "Well, theta formally is the set of mu sigma squared such that in R times 0 infinity." + }, + { + "text": "That's just to be formal, but this does the job just fine." + }, + { + "text": "You don't have to be super formal." + }, + { + "text": "OK, so that's not 3." + }, + { + "text": "That's like 5." + }, + { + "text": "Actually, I just want to write another one." + }, + { + "text": "Let's call it 5-bit." + }, + { + "text": "And 5-bit is just Gaussian with known variance." + }, + { + "text": "And this arises a lot in labs when you have measurement error, when you actually receive your measurement device." + }, + { + "text": "This thing has been tested by the manufacturer so much that it actually comes in on the side of the box." + }, + { + "text": "It says that the standard deviation of your measurements is going to be 0.23." + }, + { + "text": "OK, and actually, why do you do this is because they can brag about accuracy, right?" + }, + { + "text": "I mean, that's how they sell you this particular device." + }, + { + "text": "And so you actually know exactly what sigma square is." + }, + { + "text": "So once you actually get your data in the lab, you actually only have to estimate mu because sigma comes on the label." + }, + { + "text": "And so now, what is your statistical model?" + }, + { + "text": "Well, the numbers you're going to be collecting still are positive in r. But now, the models that I have is n mu sigma squared." + }, + { + "text": "But the parameter space is not mu in r and sigma positive." + }, + { + "text": "It's just mu in r. And to be a little more emphatic about this, this is enough to describe it, right?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk21.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..4d5546c82c9ebd4988001ae951b41ff89ffbd2ef --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because if sigma is the sigma that was specified by the manufacturer, then this is the sigma you want." + }, + { + "text": "But you can actually write sigma is equal to sigma square is equal to sigma square manufacturer, right?" + }, + { + "text": "You can just fix it to be this particular value." + }, + { + "text": "Or maybe you don't want to write an index that's manufacturer." + }, + { + "text": "And so you just say, well, when I write sigma square, what I mean is the sigma square of the manufacturer." + }, + { + "text": "Yeah?" + }, + { + "text": "AUDIENCE MEMBER 2 Yeah, so you can just write sigma square and then you can write sigma square." + }, + { + "text": "So you can just write sigma square and then you can write sigma square." + }, + { + "text": "Yeah?" + }, + { + "text": "AUDIENCE MEMBER 2 Yeah." + }, + { + "text": "For a particular measuring device?" + }, + { + "text": "You're in a lab and you have some measuring device, I don't know, something that measures tensile strength of something." + }, + { + "text": "And it's just going to measure something." + }, + { + "text": "And it will naturally make errors." + }, + { + "text": "But it's been tested so much by the manufacturer that they actually, and calibrated by them, they know it's not going to be perfect." + }, + { + "text": "But they knew exactly what error it's making because they've actually tried it on things for which they exactly knew what the tensile strength was." + }, + { + "text": "OK?" + }, + { + "text": "Yeah?" + }, + { + "text": "AUDIENCE MEMBER 3 This?" + }, + { + "text": "This?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk22.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..aaa3080d68eddd7bca2e68fa61f1ea4fd1c74199 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Oh, like 5 prime?" + }, + { + "text": "OK?" + }, + { + "text": "And we can come up with other examples, right?" + }, + { + "text": "So for example, here's another one." + }, + { + "text": "OK, so the names don't really matter, right?" + }, + { + "text": "I mean, I called it the siblings model, but you won't find the siblings model in a textbook, right?" + }, + { + "text": "So I wouldn't worry too much." + }, + { + "text": "But for example, let's say you have something, so let's call it 6." + }, + { + "text": "You have, I don't know, truncated." + }, + { + "text": "And that's the name I just came up with, but it's actually not exactly describing what I want." + }, + { + "text": "But let's say I observe y, which is the indicator of x larger than, say, 5 when x follows some exponential with parameter lambda." + }, + { + "text": "OK, this is what I get to observe." + }, + { + "text": "I only observe if my waiting time was more than 5 minutes because I see somebody coming out of the candle station being really upset, and that's all I record." + }, + { + "text": "And it's, ah, he's been waiting for more than 5 minutes." + }, + { + "text": "And that's all I get to record." + }, + { + "text": "OK, that happens a lot." + }, + { + "text": "These are called censored data." + }, + { + "text": "I should probably not call it truncated, but this should be censored." + }, + { + "text": "OK?" + }, + { + "text": "You see a lot of censored data when you ask for people how much they make." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk23.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..eb2e7c38cf564ea687eef46c1e43627d3f08face --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "They say, well, more than 5 figures." + }, + { + "text": "And that's all they want to tell you." + }, + { + "text": "OK?" + }, + { + "text": "And so you see a lot of censored data in survival analysis." + }, + { + "text": "Right?" + }, + { + "text": "You're trying to understand how long your patients are going to live after some surgery." + }, + { + "text": "OK?" + }, + { + "text": "And maybe you're not going to keep people alive, and you're not going to actually have them being touched in their family every day and ask them, is the guy still alive?" + }, + { + "text": "And so what you can do is just to ask people maybe five years after your study and say, please come in." + }, + { + "text": "And you will just happen to have some people who say, well, the person is deceased." + }, + { + "text": "And you will only be able to know that the person deceased less than five years ago." + }, + { + "text": "I mean, but you only see what happens after that." + }, + { + "text": "OK?" + }, + { + "text": "And so this truncated and censored data happens all the time just because you don't have the availability to do better than that." + }, + { + "text": "So this could happen here." + }, + { + "text": "So now what is my statistical experiment?" + }, + { + "text": "Right?" + }, + { + "text": "So here I should probably write this like that, because I just told you that my observations are going to be x." + }, + { + "text": "So there's some unknown y. I will never get to see this y. I only get to see the x." + }, + { + "text": "What is my statistical experiment?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk24.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..a89e8843ea33b0bc151e9dc34f00dd5408f36cb5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Please help me." + }, + { + "text": "So is it the real line?" + }, + { + "text": "My sample space, is it the real line?" + }, + { + "text": "Sorry, do you know?" + }, + { + "text": "Who does not know what this means?" + }, + { + "text": "Sorry." + }, + { + "text": "OK." + }, + { + "text": "So this is called an indicator." + }, + { + "text": "So I write it as it's, if I wrote well, that would be 1 with a double bar." + }, + { + "text": "You can also write i if you prefer, if you don't feel like writing 1 in double bars." + }, + { + "text": "And it's 1 of, say, I'm going to write it like that." + }, + { + "text": "1 of a is equal to 1 if a is true and 0 if a is false." + }, + { + "text": "OK?" + }, + { + "text": "So that means that if y is larger than 5, this thing is 1." + }, + { + "text": "And if y is not larger than 5, this thing is 0." + }, + { + "text": "OK?" + }, + { + "text": "So that's called indicator." + }, + { + "text": "Indicator function." + }, + { + "text": "OK?" + }, + { + "text": "It's very useful to just turn anything into a 0, 1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk25.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..830960597ae73417cc9360a1563f9acb794668fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "So now that I'm here, what is my sample space?" + }, + { + "text": "0, 1." + }, + { + "text": "Whatever this thing I did not tell you was taking value was the thing you should have." + }, + { + "text": "If I didn't tell you that's taking value 6 or 7, that would be your sample space." + }, + { + "text": "OK, so it takes value 0, 1." + }, + { + "text": "And then what is the probability here?" + }, + { + "text": "What should I write here?" + }, + { + "text": "What should you write without even thinking?" + }, + { + "text": "Yeah, so let's assume there's two seconds before the end of the exam." + }, + { + "text": "You're going to write vernally." + }, + { + "text": "And that's where you're going to start checking if I'm going to give you extra time." + }, + { + "text": "So you write vernally without thinking, because it's taking value 0, 1." + }, + { + "text": "So you just write vernally." + }, + { + "text": "But you still have to tell me what possible parameters this thing is taking, right?" + }, + { + "text": "So I'm going to write it p, because I don't know." + }, + { + "text": "And then p takes value." + }, + { + "text": "OK, so sorry." + }, + { + "text": "I could write it like that." + }, + { + "text": "That would be perfectly valid." + }, + { + "text": "But actually, no more." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk26.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..381a402c50c4922d06a56cf8b1a2b2befa976393 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk26.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's not any p. The p is the probability that an exponential lambda is larger than 5." + }, + { + "text": "And maybe I want to have lambda as a parameter." + }, + { + "text": "OK, so what I need to actually compute is what is the probability that y is larger than 5 when y is this exponential lambda, which means that what I need to compute is the integral between 5 and infinity of 1 over lambda." + }, + { + "text": "Huh?" + }, + { + "text": "How did I define it in this class?" + }, + { + "text": "I changed everything." + }, + { + "text": "What?" + }, + { + "text": "AUDIENCE MEMBER 2." + }, + { + "text": "Lambda e to the minus lambda x. PHILIPPE RIGOLLET." + }, + { + "text": "Oh, yeah, right, right, right." + }, + { + "text": "You're right." + }, + { + "text": "Lambda e to the minus lambda x dx, right?" + }, + { + "text": "So that's what I need to compute." + }, + { + "text": "What is this?" + }, + { + "text": "So what is the value of this integral?" + }, + { + "text": "AUDIENCE MEMBER 3." + }, + { + "text": "5." + }, + { + "text": "5." + }, + { + "text": "5." + }, + { + "text": "You take appropriate measures." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk27.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk27.json new file mode 100644 index 0000000000000000000000000000000000000000..bb780078a148ac9d9c350287dc074e09f2c6fccc --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk27.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. And again, this is just a basic calculus, right?" + }, + { + "text": "So when I'm going to integrate this guy, those guys are going to cancel." + }, + { + "text": "I'm going to get 0 for infinity." + }, + { + "text": "I'm going to get a 5 for this guy." + }, + { + "text": "And well, I know it's going to be a positive number, so I'm not really going to bother with the sign, because I know that's what it should be." + }, + { + "text": "So I get e to the minus 5 lambda." + }, + { + "text": "And so that means that I can actually write this like that." + }, + { + "text": "Now, parameterize this thing by lambda positive." + }, + { + "text": "So what I did here is I changed the parameterization from p to lambda." + }, + { + "text": "Why?" + }, + { + "text": "Well, because maybe if this, I know this is happening, maybe I'm actually interested in reporting lambda to MBTA, for example." + }, + { + "text": "Maybe I'm actually trying to estimate 1 over lambda, so that I know what is the, well, lambda is actually the intensity of arrival of my Poisson process, right?" + }, + { + "text": "If I have a Poisson process, that's where how my trains are coming in." + }, + { + "text": "And so I'm interested in lambda, so I will parameterize things by lambda, so that the thing I get is lambda." + }, + { + "text": "You can play with this, right?" + }, + { + "text": "I mean, I could parameterize this by 1 over lambda or 1 over lambda here if I wanted." + }, + { + "text": "But the context of your problem will tell you exactly how to parameterize this thing." + }, + { + "text": "OK?" + }, + { + "text": "So what else do I want to tell you?" + }, + { + "text": "OK, let's do a final one." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk28.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk28.json new file mode 100644 index 0000000000000000000000000000000000000000..d0d13da48cddff744dc922d480aba326032e5cf5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk28.json @@ -0,0 +1,62 @@ +[ + { + "text": "By the way, are you guys OK with Poisson exponential Bernoulli's, I don't know, binomial, normal, all these things?" + }, + { + "text": "I'm not going to go back to it, but I'm going to use them heavily." + }, + { + "text": "So just spend five minutes on Wikipedia if you forgot about what those things are." + }, + { + "text": "Usually, you must have seen them in your probability class, so that should not be crazy name." + }, + { + "text": "And again, I'm not expecting you." + }, + { + "text": "I mean, I don't remember what the density of an exponential is, so it would be pretty unfair of me to actually ask you to remember what it is." + }, + { + "text": "Even for the Gaussian, you're not expected to remember what it is." + }, + { + "text": "But I want you to remember that if I add 5 to a Gaussian, then I have a Gaussian with mean mu plus 5." + }, + { + "text": "If I multiply it by something, right?" + }, + { + "text": "You need to know how to operate those things." + }, + { + "text": "But knowing complicated densities is definitely not part of the game." + }, + { + "text": "So let's do a final one." + }, + { + "text": "I don't know what number I have now." + }, + { + "text": "I'm going to just do uniform." + }, + { + "text": "That's another one." + }, + { + "text": "Everybody knows what uniform is?" + }, + { + "text": "So uniform, right?" + }, + { + "text": "So I'm going to have x, which my observations are going to be uniform on the interval 0 theta, right?" + }, + { + "text": "So if I want to define a uniform distribution for a random variable, I have to tell you which interval or which set I want it to be uniform on." + }, + { + "text": "And so here, I'm telling you it's the interval 0 theta." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk29.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk29.json new file mode 100644 index 0000000000000000000000000000000000000000..92b9ca99f9d549d54aed14a7dc495c09293d5428 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk29.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so what is going to be my sample space?" + }, + { + "text": "I'm sorry?" + }, + { + "text": "0 to theta." + }, + { + "text": "And then what is my probability distribution, my family of parameters?" + }, + { + "text": "So well, I can write it like this, right?" + }, + { + "text": "Uniform theta, right?" + }, + { + "text": "And theta, let's say, is positive." + }, + { + "text": "Can somebody tell me what's wrong with what I wrote?" + }, + { + "text": "Yeah, this makes no sense." + }, + { + "text": "Tell me why." + }, + { + "text": "Yeah?" + }, + { + "text": "Yeah, this set depends on theta." + }, + { + "text": "And why is that a problem?" + }, + { + "text": "There's no theta." + }, + { + "text": "Right now, there's the families of thetas." + }, + { + "text": "Which one did you pick here?" + }, + { + "text": "This is just something that's indexed by theta." + }, + { + "text": "But I could have very well written it as just not being Greek for a second." + }, + { + "text": "I could have just written this as t, right, rather than theta." + }, + { + "text": "OK, that would be the same thing." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk3.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..b4f72390451e86d7c7344367d84606de62f2f9ba --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "We will come back to this example when we study maximum likelihood estimators or method of moments estimators by the method of moments." + }, + { + "text": "But at the end of the day, the things that we did, the things that we will do are always the naive estimator you would come up with is, what is the proportion of 1?" + }, + { + "text": "And this will be, in pretty much all respects, the best estimator you can think of." + }, + { + "text": "So then we're going to try to assess its performance." + }, + { + "text": "And we saw how to do that in the first chapter as well." + }, + { + "text": "So this problem here somehow is completely understood." + }, + { + "text": "We'll come back to it." + }, + { + "text": "But there's nothing fancy that's going to happen." + }, + { + "text": "But now I could have some more complicated things." + }, + { + "text": "So for example, in the example of the students now, my xi's belong to the sequence of integers 1, 2, 3, et cetera, which is also denoted by n, maybe without 0 if you want to put 0 in n, so the positive integers." + }, + { + "text": "Or I could actually just maybe put some prior knowledge about how humans have time to have families." + }, + { + "text": "But maybe some people thought of their college mates as being their brothers and sisters." + }, + { + "text": "And one student would actually put 465 siblings, because we're all good friends." + }, + { + "text": "Or maybe they actually think that all their Facebook contacts are actually their siblings." + }, + { + "text": "And so you never know what's going to happen." + }, + { + "text": "So maybe you want to account for this." + }, + { + "text": "But maybe you know that people are reasonable." + }, + { + "text": "And they will actually give you something like this." + }, + { + "text": "Now, intuitively, maybe you would say, well, why would you bother doing this if you're not really sure about the 20?" + }, + { + "text": "But I think that probably all of you intuitively guess that this is probably a good idea to start putting this kind of assumption rather than allowing for any number in the first place, because this eventually will be injected into the precision of our estimator." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk30.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk30.json new file mode 100644 index 0000000000000000000000000000000000000000..2b74866121a17dca1506a42a9b9e62b4429a13c2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk30.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then what the hell is theta?" + }, + { + "text": "There's no such thing as theta." + }, + { + "text": "We don't know what the parameter is." + }, + { + "text": "The parameter should move with everyone." + }, + { + "text": "And so that means that I actually am not allowed to pick this theta." + }, + { + "text": "I'm actually, just for the reason that there's no parameter to put on the left side." + }, + { + "text": "There should not be, right?" + }, + { + "text": "So you just said, well, there's a problem because the parameter is on the left-hand side." + }, + { + "text": "But there's not even a parameter." + }, + { + "text": "I'm describing the family of possible parameters." + }, + { + "text": "There's no one that you can actually plug it in." + }, + { + "text": "So this should really be one." + }, + { + "text": "And I'm going to go back to writing this as theta, because that's pretty thin." + }, + { + "text": "Is that clear for everyone?" + }, + { + "text": "I cannot just pick one and put it in there." + }, + { + "text": "I just take the, before I run my experiment, I could potentially get numbers that are all the way up to 1, because I don't know what theta is going to be ahead of time." + }, + { + "text": "Now, if somebody promised to me that theta was going to be less than 0.5, that would be, sorry, why do I put 1 here?" + }, + { + "text": "I could put theta between 0 and 1." + }, + { + "text": "But if somebody is going to promise me, for example, that theta is going to be less than 1, I could put 0, 1." + }, + { + "text": "All right?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk31.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk31.json new file mode 100644 index 0000000000000000000000000000000000000000..b954a90d701dde628ee923be06886cfd0919da3e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk31.json @@ -0,0 +1,62 @@ +[ + { + "text": "Is that clear?" + }, + { + "text": "OK, so now you know how to answer the question, what is the statistical model?" + }, + { + "text": "And again, within the scope of this class, you will not be asked to just come up with a model." + }, + { + "text": "I will just tell you, Poisson would be a probably good idea here." + }, + { + "text": "And then you would just have to trust me that, indeed, it would be a good idea." + }, + { + "text": "All right, so what I started talking about about 20 minutes ago, so I was definitely ahead of myself, is the notion." + }, + { + "text": "So that's when I was talking about well-specified." + }, + { + "text": "Remember, well-specified says that the true distribution is one of the distribution in this parametric families of distribution." + }, + { + "text": "The true distribution of my siblings is actually a Poisson with some parameters." + }, + { + "text": "And all I need to figure out is what this parameter is." + }, + { + "text": "When I started saying that, I said, well, but then that could be that there are several parameters that give me the same distribution, right?" + }, + { + "text": "It could be the case that Poisson 5 and Poisson 17 are exactly the same distributions when I start putting those numbers in the formula which I rephrased." + }, + { + "text": "So it could be the case that two different numbers would give me exactly the same probabilities." + }, + { + "text": "And in this case, we see that the model is not identifiable." + }, + { + "text": "I mean, the parameter is not identifiable." + }, + { + "text": "I cannot identify the parameter, even if you actually gave me an infinite amount of data, which means that I could actually estimate exactly the PMF." + }, + { + "text": "I might not be able to go back, because there would be several candidates." + }, + { + "text": "And I would not be able to tell you which one it was in the first place." + }, + { + "text": "So what we want is that this function, theta, maps to P theta is injective." + }, + { + "text": "And that's really to be fancy." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk32.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk32.json new file mode 100644 index 0000000000000000000000000000000000000000..82f9323ce7b2101d9fef6e2588d0e9665b6956d7 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk32.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what I really mean is that if theta is different from theta prime, then P of theta is different from P of theta prime." + }, + { + "text": "Or if you prefer to think about the contrapositive of this, this is the same as saying that if P theta gives me the same distribution as theta prime, then that implies that theta must be equal to theta prime." + }, + { + "text": "So in logic, those two things are equivalent." + }, + { + "text": "So this means that we say that the parameter is identifiable or identified, doesn't really matter, in this model." + }, + { + "text": "OK?" + }, + { + "text": "And this is something we're going to want." + }, + { + "text": "So in all the examples that I gave you, those parameters are completely identified." + }, + { + "text": "If I tell you, I mean, if those things are in probability books, it means that they were probably thought through." + }, + { + "text": "So when I say exponential lambda, I'm really talking about one specific distribution." + }, + { + "text": "And there's not another lambda that's going to give me exactly the same distribution." + }, + { + "text": "OK?" + }, + { + "text": "So that was the case." + }, + { + "text": "And you can check that." + }, + { + "text": "But it's a little annoying." + }, + { + "text": "So I probably would not do it." + }, + { + "text": "But rather than doing this, let me just give you some examples where it would not be the case." + }, + { + "text": "And here's an example." + }, + { + "text": "If I take xi, so now I'm back to just using this indicator function, but now for a Gaussian." + }, + { + "text": "So what I observe is x is the indicator that y is, what did we say, positive?" + }, + { + "text": "OK?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk33.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk33.json new file mode 100644 index 0000000000000000000000000000000000000000..1d58d09e3350f128163563ffa59db82f8635d40b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk33.json @@ -0,0 +1,62 @@ +[ + { + "text": "So this is a Bernoulli random variable, right?" + }, + { + "text": "And it has some parameter p. But p now is going to depend, sorry, in here, y is n mu sigma squared." + }, + { + "text": "So the p, the probability that this thing is positive, is actually, I don't think I put the 0." + }, + { + "text": "Oh yeah, because I have mu." + }, + { + "text": "OK." + }, + { + "text": "So this distribution, this p, the probability that it's positive, is just the probability that some Gaussian is positive." + }, + { + "text": "And it will depend on mu and sigma, right?" + }, + { + "text": "Because if I draw, if I have 0, and I draw my Gaussian around mu, then the probability of this Bernoulli being 1 is really the area under the curve here." + }, + { + "text": "Right?" + }, + { + "text": "And this thing, well, if mu is very large, it's going to become very large." + }, + { + "text": "If mu is very small, it's going to become very small." + }, + { + "text": "And if sigma changes, it's also going to affect it." + }, + { + "text": "Is that clear to everyone?" + }, + { + "text": "But we can actually compute this, right?" + }, + { + "text": "So the parameter p that I'm looking for here as a function of mu and sigma is simply the probability that some y is non-negative, which is the probability that y minus mu divided by sigma is larger than minus mu divided by sigma." + }, + { + "text": "By the way, when you studied probability, is that some operation you were used to making, removing the mean and dividing by the standard deviation?" + }, + { + "text": "What is the effect of doing that on the Gaussian random variable?" + }, + { + "text": "Yeah, so you normalize it, right?" + }, + { + "text": "You standardize it." + }, + { + "text": "You actually make it a standard Gaussian." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk34.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk34.json new file mode 100644 index 0000000000000000000000000000000000000000..6c78cb86e4595e4cfbb1c3ad587dd6e981044623 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk34.json @@ -0,0 +1,62 @@ +[ + { + "text": "You remove the mean." + }, + { + "text": "It becomes a mean 0 Gaussian." + }, + { + "text": "And you remove the variance for it to become 1." + }, + { + "text": "So when you have a Gaussian, remove the mean and divide by the standard deviation, it becomes a standard Gaussian, which this thing has n 0 1 distribution, which is the one you can read the quintiles of at the end of the book." + }, + { + "text": "And that's exactly what we did." + }, + { + "text": "OK, so now you have the probability that some standard Gaussian exceeds negative mu over sigma, which I can write in terms of the cumulative distribution function capital phi, like we did in the first lecture." + }, + { + "text": "So if I do this cumulative distribution function, what is this probability in terms of phi?" + }, + { + "text": "AUDIENCE MEMBER 1." + }, + { + "text": "Lids." + }, + { + "text": "Well, that's what your name tag says." + }, + { + "text": "1 minus?" + }, + { + "text": "1 minus mu over sigma?" + }, + { + "text": "What happened to phi in our?" + }, + { + "text": "You think I defined this for fun?" + }, + { + "text": "1 minus phi of mu over sigma, right?" + }, + { + "text": "Because this is 1 minus the probability that it's less than this, and this is exactly the definition of the cumulative distribution function." + }, + { + "text": "So in particular, this thing only depends on mu over sigma." + }, + { + "text": "Agreed?" + }, + { + "text": "So in particular, if I had 2 mu over 2 sigma, p would remain unchanged." + }, + { + "text": "If I have 12 mu over 12 sigma, this thing would remain unchanged, which means that p does not change if I scale mu and sigma by the same factor." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk35.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk35.json new file mode 100644 index 0000000000000000000000000000000000000000..90828def788683ef3c7c3aaa3039a3c357adbe7e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk35.json @@ -0,0 +1,62 @@ +[ + { + "text": "So there's no way, just by observing x, even an infinite amount of time, so that I can actually get exactly what p is, I'm never going to be able to get mu and sigma separately." + }, + { + "text": "All I'm going to be able to get is mu over sigma." + }, + { + "text": "So here, we say that mu sigma, the parameter mu sigma, or actually each of them individually, those guys, they're not identifiable." + }, + { + "text": "But the parameter mu over sigma is identifiable." + }, + { + "text": "So if I wanted to write a statistical model in which the parameter is identifiable, I would write 0, 1, Bernoulli, and then I would write 1 minus phi of mu over sigma." + }, + { + "text": "And then I would take two parameters, which are mu and r and sigma squared positive." + }, + { + "text": "Well, let's write sigma positive." + }, + { + "text": "Right?" + }, + { + "text": "No." + }, + { + "text": "This is not identifiable." + }, + { + "text": "I cannot write those two guys as being two things different." + }, + { + "text": "Instead, what I want to write is 0, 1, Bernoulli, 1 minus." + }, + { + "text": "And now my parameter, yeah, I forgot this." + }, + { + "text": "My parameter is mu over sigma." + }, + { + "text": "Can somebody tell me where mu over sigma lives?" + }, + { + "text": "What values can this thing take?" + }, + { + "text": "Any real value, right?" + }, + { + "text": "OK, so now I've done this, definitely out of convenience, right?" + }, + { + "text": "Because that was the only thing I was able to identify, the ratio of mu over sigma." + }, + { + "text": "But it's still something that has some meaning." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk36.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk36.json new file mode 100644 index 0000000000000000000000000000000000000000..d78b58041de678db8abde68f3cefeabe5fa17f3a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk36.json @@ -0,0 +1,62 @@ +[ + { + "text": "It's the normalized mean." + }, + { + "text": "It really tells me what the mean is compared to the standard deviation." + }, + { + "text": "So in some models, in reality, in some real applications, this actually might have a good meaning for me." + }, + { + "text": "It's just telling me how big the mean is compared to the standard fluctuations of this model." + }, + { + "text": "But I won't be able to get more than that." + }, + { + "text": "Agreed?" + }, + { + "text": "All right, so now that we've set a parametric model, let's try to see what our goals are going to be." + }, + { + "text": "OK, so now we have a sample and a statistical model." + }, + { + "text": "And we want to estimate the parameter theta." + }, + { + "text": "And I could say, well, you know what?" + }, + { + "text": "I don't have time for this analysis." + }, + { + "text": "Collecting data is going to take me a while." + }, + { + "text": "And I'm going to say that mu over sigma is 4." + }, + { + "text": "I'm just going to give it to you." + }, + { + "text": "And maybe you will tell me, eh, not very good, right?" + }, + { + "text": "So we need some measure of performance of a given parameter." + }, + { + "text": "We need to be able to evaluate if eyeballing the problem is worse than actually collecting a large amount of data." + }, + { + "text": "We need to know if, even if I come up with an estimator that actually sort of uses the data, does it make an efficient use of the data?" + }, + { + "text": "Would I actually need 10 times more observations to achieve the same accuracy?" + }, + { + "text": "So to be able to answer these questions, well, I need to define what accuracy means." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk37.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk37.json new file mode 100644 index 0000000000000000000000000000000000000000..d1ad8aa2be51b6eac448741dba14e985c21c9523 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk37.json @@ -0,0 +1,62 @@ +[ + { + "text": "And accuracy is something that sort of makes sense." + }, + { + "text": "It says, well, I want theta hat to be close to theta." + }, + { + "text": "But theta hat is a random variable, so I'm going to have to understand what it means for a random variable to be close to a deterministic number." + }, + { + "text": "And so what is the parameter, an estimator, right?" + }, + { + "text": "So I have an estimator." + }, + { + "text": "And I said it's a random variable." + }, + { + "text": "And the formal definition to an estimator is a measurable function of the data." + }, + { + "text": "So when I write theta hat, and that will typically be my notation for an estimator, I should really write theta hat of x1, xn." + }, + { + "text": "That's what an estimator is." + }, + { + "text": "So if you want to know what an estimator is, this is a measurable function of data." + }, + { + "text": "And it's actually also known as a statistic." + }, + { + "text": "And if you're interested in, I see every day, I think, when I have a dinner with normal people, and they say I'm a statistician." + }, + { + "text": "Oh, yeah, really?" + }, + { + "text": "Like, yeah, baseball." + }, + { + "text": "And they talk to me about batting averages." + }, + { + "text": "That's not what I do." + }, + { + "text": "But for them, that's what it is." + }, + { + "text": "And that's because, in a way, that's what a statistic is." + }, + { + "text": "A batting average is a statistic." + }, + { + "text": "And so here are some examples." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk38.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk38.json new file mode 100644 index 0000000000000000000000000000000000000000..b068d8c10a4d3f99d897f848076b0ed604acd1b4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk38.json @@ -0,0 +1,62 @@ +[ + { + "text": "You can take the average xn bar." + }, + { + "text": "You can take the maximum of your observation." + }, + { + "text": "That's a statistic." + }, + { + "text": "You can take the first one." + }, + { + "text": "You can take the first one plus log of 1 plus the absolute value of the last one." + }, + { + "text": "You can do whatever you want." + }, + { + "text": "That will be an estimator." + }, + { + "text": "Some of them are clearly going to be bad." + }, + { + "text": "But that's still a statistic." + }, + { + "text": "And you can do this." + }, + { + "text": "Now, when I say measurable, I always have, so graduate students sometimes ask me, like, yeah, how do I know if this estimator is measurable or not?" + }, + { + "text": "And usually, my answer is, well, if I give you data, can you compute it?" + }, + { + "text": "And they say, yeah." + }, + { + "text": "I'm like, well, then it's measurable." + }, + { + "text": "That's a very good rule to check if something is actually measurable." + }, + { + "text": "When is this thing not measurable?" + }, + { + "text": "It's when it's implicitly defined." + }, + { + "text": "And in particular, the things that can give you problems are soup or inf." + }, + { + "text": "Anybody knows what a soup or an inf is?" + }, + { + "text": "It's like a max or a min, but that's not always attained." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk39.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk39.json new file mode 100644 index 0000000000000000000000000000000000000000..333de3218861fe0fbc392413ba3aa06b25513e38 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk39.json @@ -0,0 +1,62 @@ +[ + { + "text": "So if I have x1, so if I look at the infimum of the function f of x for x on the real line, and f of x, sorry, let's say x on 1 infinity, and f of x is equal to 1 over x, then the infimum is the smallest value it can take, except that it does not really take it." + }, + { + "text": "It's 0, because 1 over x is going to 0, but it's never really getting there." + }, + { + "text": "So we just call the inf 0, but it's not the value that it ever takes." + }, + { + "text": "And these things might actually be complicated to compute, and so that's when you actually have problems, when you're not really quite reaching the limit." + }, + { + "text": "You won't have this problem in general, but just so you know that an estimator is not really anything, it has to actually be measurable." + }, + { + "text": "So the first thing we want to know, I mentioned it, is an estimator is a statistic which does not depend on data, of course." + }, + { + "text": "So if I give you the data, you have to be able to compute it, and that probably should not require not knowing an unknown parameter." + }, + { + "text": "So an estimator is said to be consistent." + }, + { + "text": "When I collect more and more data, this thing is getting closer and closer to the true parameter." + }, + { + "text": "And we said that eyeballing and saying that it's going to be 4 is not really something that's probably going to be consistent, but I can have things that are consistent but that are converging to theta at different speeds." + }, + { + "text": "And we know also that this is a random variable." + }, + { + "text": "It converges to something, and there might be some different notions of conversions that kick in, and actually, they are." + }, + { + "text": "And we say that it's weakly convergent if it converges in probability, and strongly convergent if it converges almost surely." + }, + { + "text": "And this is just vocabulary." + }, + { + "text": "It won't make a big difference." + }, + { + "text": "So we will typically say it's consistent once you say any of the two." + }, + { + "text": "So in parametric statistics, it's actually a little difficult to come up with, but in non-parametric ones, I could just say if I have yi, xi, yi, and I know that yi is f of xi plus some noise epsilon i, and I know that f belongs to some class of functions, let's say, Sybil-Liff class of smooth functions, massive." + }, + { + "text": "And now I'm going to actually find the following estimator." + }, + { + "text": "I'm going to take the average." + }, + { + "text": "So I'm going to do least squares." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk4.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..af9945cf9fde8f2e1076eb57f0e492ebedb19c45 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "If I allow anything, it's going to be more complicated for me to get an accurate estimator." + }, + { + "text": "If I know that the numbers are either 1 or 2, then I'm actually going to be slightly more accurate as well." + }, + { + "text": "Because I know that, for example, somebody put a 5, I can remove it." + }, + { + "text": "Then it's not going to actually screw up with my estimator." + }, + { + "text": "All right, so now let's say we actually agree that we have numbers." + }, + { + "text": "And here I put seven numbers." + }, + { + "text": "So I just said, well, now the numbers, let's assume that the numbers I'm going to get are going to be 1 all the way to, say, this number that I denote by larger than or equal to 7, which is a placeholder for any number larger than 7." + }, + { + "text": "Because I know maybe I don't want to distinguish between people who have 9 or 25 siblings." + }, + { + "text": "And so now, this is a distribution on seven possible values, discrete distributions." + }, + { + "text": "And you know from your probability class that the way you describe this distribution is using the probability mass function, or PMF." + }, + { + "text": "So that's how we describe a discrete distribution." + }, + { + "text": "And the PMF is just a list of numbers." + }, + { + "text": "So as I wrote here, you have a list of numbers." + }, + { + "text": "And here you wrote the possible value that your random variable can take." + }, + { + "text": "And here you write the probability that your random variable takes this value." + }, + { + "text": "So the possible values being 1, 2, 3, all the way to larger than or equal to 7." + }, + { + "text": "And then I'm trying to estimate those numbers." + }, + { + "text": "If I give you those numbers, at least up to this compression of all numbers larger than or equal to 7, you have a full description of your distribution." + }, + { + "text": "And that is the ultimate goal of statistics." + }, + { + "text": "The ultimate goal of statistics is to say what distribution your data came from, because that's basically the best you're going to be able to." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk40.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk40.json new file mode 100644 index 0000000000000000000000000000000000000000..3d8db4ffb09272df056c54676f4946bbec2f1f76 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk40.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I just check." + }, + { + "text": "I'm trying to minimize the distance of each of my f of xi to my yi." + }, + { + "text": "And now I want to find the smallest of them." + }, + { + "text": "So if I look at the infimum here, then the question is, so that could be, well, that's not really an estimator for f, but it's an estimator for the smallest possible value." + }, + { + "text": "And so for example, this is actually an estimator for the variance of sigma square." + }, + { + "text": "This might not be attained, and this might not be measurable if f is massive." + }, + { + "text": "So that's the inf of some class f of x." + }, + { + "text": "So those are always things that are defined implicitly." + }, + { + "text": "If it's an average, for example, it's completely measurable." + }, + { + "text": "Any other questions?" + }, + { + "text": "OK, so we know that the first thing we might want to check, and that's definitely something we want about an estimator, is that it's consistent, because all consistency tells us is that as I collect more and more data, my estimator is going to get closer and closer to the parameters." + }, + { + "text": "There's other things we can look at." + }, + { + "text": "For each possible value of n, now I have a finite number of observations, 25." + }, + { + "text": "And I want to know something about my estimator." + }, + { + "text": "The first thing I want to check is maybe if, in average, so this is a random variable." + }, + { + "text": "Is this random variable, in average, going to be close to theta or not?" + }, + { + "text": "And so the difference, how far I am from theta, is actually called the bias." + }, + { + "text": "So the bias of an estimator is the expectation of theta hat minus the value that I hope it gets, which is theta." + }, + { + "text": "If this thing is equal to 0, we say that theta hat is unbiased." + }, + { + "text": "And unbiased estimators are things that people are looking for in general." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk41.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk41.json new file mode 100644 index 0000000000000000000000000000000000000000..1690a8a499d54f5a021d192b47468606eaca1c01 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk41.json @@ -0,0 +1,62 @@ +[ + { + "text": "The problem is that there's lots of unbiased estimators, and so it might be misleading to look for unbiasedness when that's not really the only thing you should be looking for." + }, + { + "text": "So what does it mean to be unbiased?" + }, + { + "text": "Maybe for this particular round of data you collected, you're actually pretty far from the true estimator." + }, + { + "text": "But one thing that actually, what it means is that if I redid this experiment over and over and over again, and I averaged all the values of my estimators that I got, then this would actually be the true parameter." + }, + { + "text": "That's what it means." + }, + { + "text": "If I were to repeat this experiment, in average I would actually get the right thing." + }, + { + "text": "But you don't get to repeat an experiment." + }, + { + "text": "Just a remark about estimators." + }, + { + "text": "Look at this estimator, xn bar." + }, + { + "text": "Think of the kiss example." + }, + { + "text": "I'm looking at the average of my observations." + }, + { + "text": "And I want to know what the expectation of this thing is." + }, + { + "text": "OK?" + }, + { + "text": "Now, this guy is my linearity of the expectation." + }, + { + "text": "Is this, right?" + }, + { + "text": "But my data is identically distributed." + }, + { + "text": "So in particular, all the xi's have the same expectation, right?" + }, + { + "text": "Everybody agrees with this?" + }, + { + "text": "When it's identically distributed, they all get the same expectation?" + }, + { + "text": "So what it means is that this guy's here, they're all equal to the expectation of x1, right?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk42.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk42.json new file mode 100644 index 0000000000000000000000000000000000000000..710ba984fa10bb1d5ca29d4eea5e3b9ee9b71d93 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk42.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what it means is that this guy's, I have the average of the same number." + }, + { + "text": "So this is actually the expectation of x1." + }, + { + "text": "OK?" + }, + { + "text": "And it's true." + }, + { + "text": "In the kiss example, this was p. And this is p. So probability of turning your head right." + }, + { + "text": "OK?" + }, + { + "text": "So those two things are the same." + }, + { + "text": "In particular, that means that xn bar and just x1 have the same bias." + }, + { + "text": "So that should probably illustrate to you that bias is not something that really is telling you the entire picture." + }, + { + "text": "Right?" + }, + { + "text": "I can take only one of my observations, Bernoulli 0, 1." + }, + { + "text": "This thing will have the same bias as if I averaged 1,000 of them." + }, + { + "text": "So the bias is really telling me where I am in the average, but it's really not telling me what fluctuations I'm getting." + }, + { + "text": "And so if you want to start having fluctuations coming into the picture, we actually have to look at the risk or the quadratic risk of an estimator." + }, + { + "text": "And so the quadratic risk is defined as the expectation of the squared distance between theta hat and theta." + }, + { + "text": "OK?" + }, + { + "text": "So let's look at this." + }, + { + "text": "So the quadratic risk, sometimes it's denoted, people call it the L2 risk of theta hat, of course." + }, + { + "text": "I'm sorry for maintaining such an ugly board." + }, + { + "text": "I keep away this stuff." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk43.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk43.json new file mode 100644 index 0000000000000000000000000000000000000000..7045c106b5b63772bb7925e82252e103b8cbb333 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk43.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, so I look at the squared distance between theta hat and theta." + }, + { + "text": "This is still the function of a random variable, so it's a random variable as well." + }, + { + "text": "And I'm looking at the expectation of this guy." + }, + { + "text": "That's the definition." + }, + { + "text": "I claim that when this thing goes to 0, then my estimator is actually going to be consistent." + }, + { + "text": "Everybody agrees with this?" + }, + { + "text": "So if it goes to 0 as n goes to infinity, and here I don't need to tell you what kind of convergence I have, because this is just a number, right?" + }, + { + "text": "It's an expectation." + }, + { + "text": "So it's a regular, usual, calculus-style convergence." + }, + { + "text": "Then that implies that theta hat is actually weakly consistent." + }, + { + "text": "What did I use to tell you this?" + }, + { + "text": "Yeah, this is the convergence in L2." + }, + { + "text": "This actually is strictly equivalent." + }, + { + "text": "This is by definition saying that theta hat converges in L2 to theta." + }, + { + "text": "And we know that convergence in L2 implies convergence in probability to theta." + }, + { + "text": "That was the picture." + }, + { + "text": "We're going up." + }, + { + "text": "And this is actually equivalent to weak consistency by definition of weak consistency." + }, + { + "text": "So this is actually telling me a little more, because this guy here, they're both unbiased." + }, + { + "text": "Xn bar is unbiased." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk44.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk44.json new file mode 100644 index 0000000000000000000000000000000000000000..15e49ae14c37e70b0067958879db7096b0b62f6f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk44.json @@ -0,0 +1,62 @@ +[ + { + "text": "X1 is unbiased, but X1 is certainly not consistent, because the more data I collect, I'm not even doing anything with it." + }, + { + "text": "I'm just taking the first data point you're giving to me." + }, + { + "text": "So they're both unbiased, but this one is not consistent." + }, + { + "text": "And this one we'll see is actually consistent." + }, + { + "text": "Xn bar is consistent, and actually, we've seen that last time." + }, + { + "text": "And that's because of the what guarantees the fact that the Xn bar is consistent?" + }, + { + "text": "Law of large numbers, right?" + }, + { + "text": "Actually, it's strongly consistent because of the strong law of large numbers." + }, + { + "text": "OK." + }, + { + "text": "So just in the last two minutes, I want to tell you a little bit about how this risk is linked to, I said quadratic risk is equal to bias squared plus variance." + }, + { + "text": "Let's see what I mean by this." + }, + { + "text": "So I'm going to forget about the absolute values." + }, + { + "text": "I have a square." + }, + { + "text": "I don't really need them." + }, + { + "text": "If theta hat was unbiased, this thing would be the expectation of theta hat." + }, + { + "text": "It might not be the case." + }, + { + "text": "So let me see how I can actually see, put the bias in there." + }, + { + "text": "Well, one way to do this is to see that this is equal to the expectation of theta hat minus expectation of theta hat plus expectation of theta hat minus theta squared." + }, + { + "text": "OK?" + }, + { + "text": "I just removed the same and added the same thing, so I didn't change anything." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk45.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk45.json new file mode 100644 index 0000000000000000000000000000000000000000..4c2c5c39325cf6077d66a18711d2177d807042b4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk45.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, this guy is my bias, right?" + }, + { + "text": "So now let me expand the square." + }, + { + "text": "So what I get is the expectation of the square of theta hat minus its expectation." + }, + { + "text": "I should put some square bracket." + }, + { + "text": "Plus 2 times the cross product." + }, + { + "text": "So the cross product is what?" + }, + { + "text": "Expectation of theta hat minus expectation of theta hat times expectation of theta hat minus theta." + }, + { + "text": "And then I have the last square, expectation of theta hat minus theta squared." + }, + { + "text": "OK?" + }, + { + "text": "So square, cross product, square." + }, + { + "text": "Everybody with me?" + }, + { + "text": "Now, this guy here, if you pay attention, this thing is the expectation of some random variable, so it's a deterministic number." + }, + { + "text": "Theta is the true parameter." + }, + { + "text": "It's a deterministic number." + }, + { + "text": "So what I can do is pull out this entire thing out of the expectation like this." + }, + { + "text": "All right?" + }, + { + "text": "And compute the expectation only with respect to that part." + }, + { + "text": "But what is the expectation of this thing?" + }, + { + "text": "It's 0, right?" + }, + { + "text": "The expectation of theta hat minus expectation of theta hat is 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk46.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk46.json new file mode 100644 index 0000000000000000000000000000000000000000..58670cc783eb53d4ef2b37e2ce0a850c49922ea1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk46.json @@ -0,0 +1,62 @@ +[ + { + "text": "So this entire thing is equal to 0." + }, + { + "text": "So now when I actually collect back my quadratic terms, my two squared terms in this expansion, what I get is that the expectation of theta hat minus theta squared is equal to the expectation of theta hat minus expectation of theta hat squared plus the square of expectation of theta hat minus theta." + }, + { + "text": "Right?" + }, + { + "text": "So those are just the first and the last term of the previous equality." + }, + { + "text": "Now, here I have the expectation of the square of the difference between a random variable and its expectation." + }, + { + "text": "This is otherwise known as the variance, right?" + }, + { + "text": "So this is actually equal to the variance of theta hat." + }, + { + "text": "And this, well, this was the bias." + }, + { + "text": "We already said this there." + }, + { + "text": "So this whole thing is the bias squared." + }, + { + "text": "And hence, the quadratic term is the sum of the variance and the squared bias." + }, + { + "text": "Why squared bias?" + }, + { + "text": "Well, because otherwise you would add dollars and dollars squared, right?" + }, + { + "text": "So you need to add dollars squared and dollars squared so that this thing is actually homogeneous." + }, + { + "text": "OK, so if x is in dollars, then the bias is in dollars, but the variance is in dollars squared." + }, + { + "text": "And the square here forced you to put everything on the square scale." + }, + { + "text": "So what's nice is that if the quadratic risk goes to 0, then since I have the sum of two positive terms, both of them have to go to 0." + }, + { + "text": "That means that my variance is going to 0, very little fluctuations, and my bias is also going to 0, which means that I'm actually going to be on target once I reduce my fluctuations, because it's one thing to reduce the fluctuations." + }, + { + "text": "But if I'm not on target, it's an issue, right?" + }, + { + "text": "For example, the estimator 4, the value 4, has no variance." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk47.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk47.json new file mode 100644 index 0000000000000000000000000000000000000000..7e775eaa9d8586ae46e452748a723da24310d0c3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk47.json @@ -0,0 +1,26 @@ +[ + { + "text": "Every time I'm going to repeat the experiment, I'm going to get 4, 4, 4, 4." + }, + { + "text": "Variance is 0." + }, + { + "text": "But the bias is bad." + }, + { + "text": "The bias is 4 minus theta." + }, + { + "text": "And if theta is far from 4, that's not doing very well." + }, + { + "text": "OK, so next week, we will talk about how estimators change if they have high variance or low variance, or high bias and low bias." + }, + { + "text": "And we'll talk about confidence intervals as well." + }, + { + "text": "All right." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk5.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..2b213e6f1200eca1d7893bb18a8d4aa8470ed89f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now admittedly, if I started looking at the fraction of 1's, and the fraction of 2's, and the fraction of 3's, et cetera, I would actually eventually get those numbers." + }, + { + "text": "Just like looking at the fraction of 1's gave me a good estimate for p in the Bernoulli case, it would do the same in this case." + }, + { + "text": "It's a pretty intuitive idea." + }, + { + "text": "It's just the law of large numbers." + }, + { + "text": "Everybody agrees with that?" + }, + { + "text": "If I look at the proportion of 1's, the proportion of 2's, the proportion of 3's, that should actually give me something that gets closer and closer as my sample size increases to what I want." + }, + { + "text": "But the problem is, if my sample size is not huge, here I have seven numbers to estimate." + }, + { + "text": "And if I have 20 observations, the ratio is not really in my favor." + }, + { + "text": "I mean, 20 observations to estimate seven parameters, some of them are going to be pretty off, typically the ones with the large values." + }, + { + "text": "If I have only 20 students, look at the list of numbers." + }, + { + "text": "I don't know how many numbers I have, but it probably is close to 20, maybe 15 or something." + }, + { + "text": "And so if you look at this list, nobody has four or more siblings in this list." + }, + { + "text": "There's no such person." + }, + { + "text": "So that means that eventually, from this data set, my estimates, so those numbers I denote by, say, p1, p2, p3, et cetera, those estimates, p4 hat would be equal to what from this data?" + }, + { + "text": "0, right?" + }, + { + "text": "And p5 hat would be equal to 0, and p6 hat would be equal to 0, and p larger than or equal to 7 hat would be equal to 0." + }, + { + "text": "That would be my estimates from this data set." + }, + { + "text": "So maybe this is not." + }, + { + "text": "Maybe I want to actually pull some information from the people who have less siblings to try to make a guess, which is probably slightly better for the larger values." + }, + { + "text": "It's pretty clear that, in average, there's more than 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk6.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..d3c38ba2593e85f08f8208f44c7601d118dd0df2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "The proportion of the population of households that have four children or more is definitely more than 0." + }, + { + "text": "So it means that my data set is not representative." + }, + { + "text": "And what I'm going to try to do is to find a model that tries to use the data that I have for the smaller values that I can observe and just pull shit out for the other ones." + }, + { + "text": "And so what we can do is to just reduce those parameters into something that's understood." + }, + { + "text": "And this is part of the modeling that I talked about in the first place." + }, + { + "text": "Now, how do you succinctly describe a number of something?" + }, + { + "text": "Well, one thing that you do is the Poisson distribution." + }, + { + "text": "Why the Poisson?" + }, + { + "text": "I mean, there's many reasons." + }, + { + "text": "I mean, again, that's part of statistical modeling." + }, + { + "text": "But once you know that you have number of something that can be modeled by a Poisson, why not try a Poisson?" + }, + { + "text": "You could just fit a Poisson." + }, + { + "text": "And the Poisson is something that looks like this." + }, + { + "text": "And I guess you've all seen it." + }, + { + "text": "But if x follows a Poisson distribution with parameter lambda, then the probability that x is equal to little x is equal to lambda to the x over factorial x e to the minus lambda." + }, + { + "text": "And if you did the sheet that I gave you on the first day, you can check that those numbers." + }, + { + "text": "So this is, of course, for x equals 0, 1, et cetera." + }, + { + "text": "So x is in natural integers." + }, + { + "text": "And if you sum from x equals 0 to infinity, this thing, you get e to the lambda." + }, + { + "text": "And so they cancel." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk7.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..d0dbf008c5822fe33350f4ea444434acd2b8712a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you have a sum which is equal to 1." + }, + { + "text": "So it's indeed a PMF." + }, + { + "text": "But what's key about this PMF is that it never takes value 0." + }, + { + "text": "This thing is always strictly positive." + }, + { + "text": "So whatever value of lambda I find from this data will give me something that's certainly more interesting than just putting the value 0." + }, + { + "text": "But more importantly, rather than having to estimate seven parameters, and as a consequence, you actually have to estimate 1, 2, 3, 4 of them, and it equals to 0, I have only one parameter to estimate, which is lambda." + }, + { + "text": "The problem with doing this is that now lambda may not be just something as simple as computing the average number." + }, + { + "text": "I mean, in this case, it will." + }, + { + "text": "But in many instances, it's actually not clear that this parametrization with lambda that I chose, I'm going to be able to estimate lambda just by computing the average number that I see." + }, + { + "text": "It will be the case." + }, + { + "text": "But if it's not, remember this example of the exponential we did in the last lecture." + }, + { + "text": "We could use the delta method and things like that to estimate this." + }, + { + "text": "All right, so here's the modeling 101." + }, + { + "text": "So the purpose of modeling is to restrict the space of possible distributions to a subspace that's actually plausible, but much simpler for me to estimate." + }, + { + "text": "So we went from all distributions on seven parameters, which is a large space that's a lot of things, to something which is just one number to estimate." + }, + { + "text": "This number is positive." + }, + { + "text": "OK?" + }, + { + "text": "Any questions about the purpose of doing this?" + }, + { + "text": "OK, so we're going to have to do a little bit of formalism now." + }, + { + "text": "And so if we want to talk, this is a specific class, so I'm not going to want to talk about the Poisson model specifically every single time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk8.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..87fc8b22abffc95ade364e887ef6306998bfeacf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'm going to want to talk about generic models." + }, + { + "text": "And then you're going to be able to plug in your favorite word, no Poisson, binomial, exponential, uniform, all these words that you've seen, you're going to be able to plug in there." + }, + { + "text": "But we're just going to have some generic notation and some generic terminology for statistical models." + }, + { + "text": "So here is the formal definition." + }, + { + "text": "So I'm going to go through it with you." + }, + { + "text": "OK?" + }, + { + "text": "OK, so the definition is that of a statistical model." + }, + { + "text": "OK?" + }, + { + "text": "And so, sorry, that's a statistical experiment, I should say." + }, + { + "text": "I'm sorry." + }, + { + "text": "OK, so a statistical experiment is actually just a pair, E, and that's a set, and a family of distributions, P theta, where theta ranges in some set, capital theta." + }, + { + "text": "OK, so I hope you're up to date with your Greek letters." + }, + { + "text": "So it's a small theta, it's a capital theta." + }, + { + "text": "I know I don't have the best handwriting, so if you don't see something, just ask me." + }, + { + "text": "OK, and so this thing now, so each of this guy is a probability distribution." + }, + { + "text": "All right?" + }, + { + "text": "So for example, this could be a Poisson with parameter theta, or a Bernoulli with parameter theta." + }, + { + "text": "OK, or an exponential with parameter, I don't know, 1 over theta squared, if you want." + }, + { + "text": "OK, but they're just indexed by theta." + }, + { + "text": "For each theta, this completely describes the distribution." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk9.json b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..332c4c3ada7371741c1a08a5615c45d79d625879 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TSkDZbGS94k_1_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It could be more complicated." + }, + { + "text": "This theta could be a pair of mu sigma squared, and that could actually give you some n mu sigma squared." + }, + { + "text": "OK, so anything where you can actually, rather than actually giving you a full distribution, I can compress it into a parameter." + }, + { + "text": "But it could be worse." + }, + { + "text": "It could be this guy here, right?" + }, + { + "text": "Theta could be p1, p larger than or equal to 7, and my distribution could just be something that has pmf." + }, + { + "text": "p1, p larger than 7." + }, + { + "text": "That's another parameter." + }, + { + "text": "This one is seven dimensional, this one is two dimensional, and all these guys are just one dimension." + }, + { + "text": "All these guys are parameters." + }, + { + "text": "Is that clear?" + }, + { + "text": "What's important here is that once I give you theta, you know exactly all the probabilities associated to this random variable." + }, + { + "text": "You know its distribution perfectly." + }, + { + "text": "OK, so here, so this is the definition." + }, + { + "text": "Is that clear for everyone?" + }, + { + "text": "Is there a question about this distribution?" + }, + { + "text": "About this definition, sorry?" + }, + { + "text": "All right, so really, the key thing is the statistical model associated to a statistical experiment." + }, + { + "text": "OK?" + }, + { + "text": "So let's just see some examples." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk0.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..fd25ea0818dacffdd5bd1cff722aaf7d067f8f16 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay." + }, + { + "text": "This is the lecture on the singular value decomposition." + }, + { + "text": "But everybody calls it the SVD." + }, + { + "text": "So this is the final and best factorization of a matrix." + }, + { + "text": "Let me tell you what's coming." + }, + { + "text": "The factors will be orthogonal matrix, diagonal matrix, orthogonal matrix." + }, + { + "text": "So it's things that we've seen before, these special good matrices, orthogonal, diagonal." + }, + { + "text": "The new point is that we need two orthogonal matrices." + }, + { + "text": "A can be any matrix whatsoever." + }, + { + "text": "Any matrix whatsoever has this singular value decomposition." + }, + { + "text": "So a diagonal one in the middle, but I need two different, probably different, orthogonal matrices to be able to do this." + }, + { + "text": "Okay." + }, + { + "text": "And this factorization has jumped into importance and is properly, I think, maybe the bringing together of everything in this course." + }, + { + "text": "One thing we'll bring together is, like, the very good family of matrices that we just studied." + }, + { + "text": "Symmetric positive definite." + }, + { + "text": "Do you remember the story with those guys?" + }, + { + "text": "Because they were symmetric, their eigenvectors were orthogonal, so I could produce an orthogonal matrix." + }, + { + "text": "This is my usual one." + }, + { + "text": "My usual one is the eigenvectors and eigenvalues." + }, + { + "text": "In the symmetric case, the eigenvectors are orthogonal, so I've got the good, my ordinary S has become a especially good Q, and positive definite, my ordinary lambda has become a positive lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk1.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..7e27d1aa155a8c107e4e8383a665af50464268d3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So this is, that's the singular value decomposition." + }, + { + "text": "In case our matrix is symmetric positive definite, in that case, I don't need two, u and a v, one orthogonal matrix will do for both sides." + }, + { + "text": "But, so this would be no good in general, because usually the eigenvector matrix isn't orthogonal." + }, + { + "text": "So this is not what I'm, that's not what I'm after." + }, + { + "text": "I'm looking for orthogonal times diagonal times orthogonal." + }, + { + "text": "And let me show you what that means and where it comes from." + }, + { + "text": "OK. What does it mean?" + }, + { + "text": "You remember the picture of any linear transformation." + }, + { + "text": "This was, like, the most important figure in 1806." + }, + { + "text": "And what am I looking for now?" + }, + { + "text": "A typical vector in the row space, typical vector, let me call it v1, gets taken over to some vector in the column space, say u1." + }, + { + "text": "So u1 is a v1." + }, + { + "text": "OK. Now, another vector gets taken over here somewhere." + }, + { + "text": "What am I looking for?" + }, + { + "text": "In this SVD, this singular value decomposition, what I'm looking for is an orthogonal basis here that gets knocked over into an orthogonal basis over there." + }, + { + "text": "See, that's pretty special, to have an orthogonal basis in the row space that goes over into an orthogonal basis, so this is like a right angle and this is a right angle, into an orthogonal basis in the column space." + }, + { + "text": "So that's our goal, is to find -- you see how things are coming together." + }, + { + "text": "First of all, can I find an orthogonal basis for this row space?" + }, + { + "text": "Of course." + }, + { + "text": "No big deal to find an orthogonal basis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk10.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..0179b0117bf00f95a1b04b6b86a542ce8f0c3b70 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "What's sigma?" + }, + { + "text": "So I'm looking for U sigma V transpose." + }, + { + "text": "U, the diagonal guy, and V transpose." + }, + { + "text": "Okay." + }, + { + "text": "Let's just see that come out right." + }, + { + "text": "So what's, what are the, what are the sigmas?" + }, + { + "text": "They're the square roots of these things." + }, + { + "text": "So square root of thirty-two and square root of eighteen." + }, + { + "text": "Zero, zero." + }, + { + "text": "Okay." + }, + { + "text": "What are the Vs?" + }, + { + "text": "They're these two." + }, + { + "text": "And I have to transpose, maybe that, maybe that just leaves me with one, with one over square root of two in that row, and the other one is one over square root of two minus one over square root of two." + }, + { + "text": "Now, finally, I've got to know the Us." + }, + { + "text": "Well, actually, one way to do, since I now know all the other pieces, I could put those together and figure out what the Us are." + }, + { + "text": "But let me do it the A A transpose way." + }, + { + "text": "Okay, find the Us now." + }, + { + "text": "U1 and U2." + }, + { + "text": "And what are they?" + }, + { + "text": "I look at A A transpose, so A is supposed to be U sigma V transpose, and then when I transpose that, I get V sigma transpose U transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk11.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..96d6a665ffcc93fda55a75d250402ff8f7417df8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I'm just doing it in the opposite order, A times A transpose, and what's the good part here?" + }, + { + "text": "That in the middle, V transpose V is going to be the identity." + }, + { + "text": "So this is just U sigma sigma transpose, that's some diagonal matrix with sigma squareds and U transpose." + }, + { + "text": "So what am I seeing here?" + }, + { + "text": "I'm seeing here, again, a symmetric positive definite or at least semi-definite matrix, and I'm seeing its eigenvectors and its eigenvalues." + }, + { + "text": "So if I compute A A transpose, its eigenvectors will be the things that go into U." + }, + { + "text": "Okay, so I need to compute A A transpose." + }, + { + "text": "I guess I'm going to have to go -." + }, + { + "text": "Let me, can I move that up just a little, maybe a little more, and do A A transpose." + }, + { + "text": "So what's A?" + }, + { + "text": "Four, four, minus three and three." + }, + { + "text": "And what's A transpose?" + }, + { + "text": "Four, four, minus three and three." + }, + { + "text": "And when I do that multiplication, I get, what do I get?" + }, + { + "text": "Sixteen and sixteen, thirty-two." + }, + { + "text": "That one comes out zero." + }, + { + "text": "Oh, so this is a lucky case, and that one comes out eighteen." + }, + { + "text": "So this is, like, an accident, that A A transpose happens to come out diagonal, so we know easily its eigenvectors and eigenvalues." + }, + { + "text": "So its eigenvectors are, what's the first eigenvector for this A A transpose matrix?" + }, + { + "text": "It's just one zero, and when I do that multiplication, I get thirty-two times one zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk12.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..3bea51beac69b154780aa5b76ef1f4e76eb0490c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the other eigenvector is just zero one, and when I multiply by that, I get eighteen." + }, + { + "text": "So this is A A transpose, multiplying that gives me the thirty-two A A transpose, multiplying this guy gives me eighteen." + }, + { + "text": "First of all, I got thirty-two and eighteen again." + }, + { + "text": "Am I surprised?" + }, + { + "text": "Yeah, it's clearly not an accident." + }, + { + "text": "The eigenvalues of A A transpose were exactly the same as the eigenvalues of this one was A transpose A." + }, + { + "text": "That's no surprise at all." + }, + { + "text": "The eigenvalues of A B are same as the eigenvalues of B A." + }, + { + "text": "The order, that's a very nice fact, that eigenvalues stay the same if I switch the order of multiplication." + }, + { + "text": "So no surprise to see thirty-two and eighteen." + }, + { + "text": "What I learned, first I checked that things were numerically correct, but now I've learned these eigenvectors, and actually they're about as nice as can be." + }, + { + "text": "They're the best orthogonal matrix, just the identity." + }, + { + "text": "Okay." + }, + { + "text": "So my claim is that it ought to all fit together." + }, + { + "text": "That this numeri- this, these numbers should come out right." + }, + { + "text": "The numbers should come out right because the, the, matrix multiplications use the properties that we want." + }, + { + "text": "Okay." + }, + { + "text": "So we just check that." + }, + { + "text": "Here's the identity, so not doing anything." + }, + { + "text": "Square root of thirty-two is multiplying that row, so that's square root of thirty-two divided by square root of two means square root of sixteen, four." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk13.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..a104483771ba144bbf5e80f6d0432de06fbabe37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Correct?" + }, + { + "text": "And square root of eighteen is divided by square root of two, so that leaves me square root of nine, which is three, but no, Professor Strang, you see the problem." + }, + { + "text": "Why is that?" + }, + { + "text": "Okay." + }, + { + "text": "Why am I getting minus three three here, and here I'm getting three minus three?" + }, + { + "text": "Phooey." + }, + { + "text": "I don't know why." + }, + { + "text": "It shouldn't have happened, but it did." + }, + { + "text": "Now, okay, you could say, well, just, the eigenvector there could have, I could have had the minus sign here for that eigenvector, but I'm not happy about that." + }, + { + "text": "Hm." + }, + { + "text": "Okay." + }, + { + "text": "Okay." + }, + { + "text": "So I realize there's a little catch here somewhere, and I may not see it until Wednesday, which then gives you a very important reason to come back on Wednesday, to catch that sign difference." + }, + { + "text": "So what did I do illegally?" + }, + { + "text": "I think I put the eigenvectors in that matrix V transpose." + }, + { + "text": "Okay, I'm going to have to think, why did that come out, with the opposite sign?" + }, + { + "text": "So you see, I mean, if I had a minus there, I would be all right, but I don't want that." + }, + { + "text": "I want positive entries down the diagonal of sigma squared." + }, + { + "text": "Okay." + }, + { + "text": "It'll come to me, but I'm going to leave this example to finish." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk14.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..6271feb6ec2eed0c67666d8fdac07717f2b70521 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "And the beauty of, these sliding boards is, I can make that go away." + }, + { + "text": "Can I, let me not do it, though." + }, + { + "text": "Yes, let me take a second example." + }, + { + "text": "Let me take a second example where the matrix is singular." + }, + { + "text": "So rank one." + }, + { + "text": "Okay." + }, + { + "text": "So let me take as an example two, where my matrix A is going to be rectangular again." + }, + { + "text": "Let me just make it four three eight six." + }, + { + "text": "Okay." + }, + { + "text": "That's a rank one matrix." + }, + { + "text": "So that has a null space and only a one-dimensional row space and column space." + }, + { + "text": "So actually, my picture becomes easy for this matrix, because what's my columns, my row space for this one?" + }, + { + "text": "So this is two by two, so my pictures are both two dimensional." + }, + { + "text": "My row space is all multiples of vector four three." + }, + { + "text": "So the whole, the row space is just a line, right?" + }, + { + "text": "That's the row space." + }, + { + "text": "And the null space, of course, is the perpendicular line." + }, + { + "text": "So the row space for this matrix is multiples of four three." + }, + { + "text": "Typical row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk15.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..247a2fb607840b5c46901a1736533537c0de9d60 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "What's the column space?" + }, + { + "text": "The columns are all multiples of four eight, three six, one two." + }, + { + "text": "The column space, then, goes in, like, this direction." + }, + { + "text": "So the column space, when I look at those columns, the column space, it was only one dimensional, because the rank is one." + }, + { + "text": "It's multiples of four eight." + }, + { + "text": "Okay." + }, + { + "text": "And what's the null space of A transpose?" + }, + { + "text": "It's the perpendicular guy." + }, + { + "text": "There's the, so this was the null space of A, and this is the null space of A transpose." + }, + { + "text": "Okay." + }, + { + "text": "What I want to say here is that the, that choosing these orthogonal bases for the row space and the column space is, like, no problem." + }, + { + "text": "They're only one dimensional." + }, + { + "text": "So what should v be?" + }, + { + "text": "v should be v1, but, yeah, v1, rather." + }, + { + "text": "v1 is supposed to be a unit vector." + }, + { + "text": "There's only one v1 to choose here, only one dimension in the row space." + }, + { + "text": "I just want to make it a unit vector." + }, + { + "text": "So v1 will be, it'll be this vector, but made into a unit vector, so four, point eight, point six." + }, + { + "text": "Four fifths, three fifths." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk16.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..9ebd9d5b85dc5cf2ad0e297580201c57ae64e6f6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what will be u1?" + }, + { + "text": "u1 will be the unit vector there, so I want to turn four eight or one two into a unit vector, so u1 will be, let's see, if it's one two, then what multiple of one two do I want?" + }, + { + "text": "That has length square root of five, so I have to divide by square root of five." + }, + { + "text": "Let me complete the singular value decomposition for this matrix." + }, + { + "text": "So this matrix, four three eight six, is, so I know what u1, here's A, and I want to get u, the basis in the column space, and it has to start with this guy." + }, + { + "text": "One over square root of five, two over square root of five." + }, + { + "text": "Then I want the sigma." + }, + { + "text": "OK. What are we expecting now for sigma?" + }, + { + "text": "Where is, this is only a rank one matrix, we're only expecting a sigma one, which I have to find, but zero's here." + }, + { + "text": "OK, so what's sigma one?" + }, + { + "text": "We should see it, it should be the, where did these sigmas come from?" + }, + { + "text": "They came from A transpose A, so I, can I do that little calculation over here?" + }, + { + "text": "A transpose A is four three, four three eight six times four three eight six." + }, + { + "text": "This had better, this is a rank one matrix, this is going to be, the whole thing will have rank one, that's sixteen and sixty four is eighty, twelve and forty eight is sixty, twelve and forty eight is sixty, nine and thirty six is forty five." + }, + { + "text": "OK." + }, + { + "text": "It's a rank one matrix." + }, + { + "text": "Of course." + }, + { + "text": "Every row is a multiple of four three." + }, + { + "text": "And what's the eigen, what are the eigenvalues of that matrix?" + }, + { + "text": "So this is like, the calculation is like practicing now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk17.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b48a4d8f19e69f562ef2b2b5013cd6a113ef2e4d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "What are the eigenvalues of this rank one matrix?" + }, + { + "text": "Well, tell me one eigenvalue, since the rank is only one, one eigenvalue is going to be zero." + }, + { + "text": "And then you know that the other eigenvalue is going to be a hundred and twenty five." + }, + { + "text": "So that's sigma squared, right, in A transpose A." + }, + { + "text": "So this will be the square root of a hundred and twenty five." + }, + { + "text": "And then finally, the V transpose, the Vs will be, there's V1, and what's V2?" + }, + { + "text": "What's V2 in the, what's, how do I make this into a orthonormal basis?" + }, + { + "text": "Well, V2 is in the null space direction." + }, + { + "text": "It's perpendicular to that, so point six and minus point eight." + }, + { + "text": "So those are the Vs that go in here." + }, + { + "text": "Point eight, point six, and point six minus point eight." + }, + { + "text": "OK. And I guess I better finish this guy." + }, + { + "text": "So this guy, all I want is to complete the orthonormal basis." + }, + { + "text": "It'll be coming from there, it'll be a two over square root of five and a minus one over square root of five." + }, + { + "text": "I could have take, let me take square root of five out of that matrix to make it look better." + }, + { + "text": "So one over square root of five times one, one, two, two, minus one." + }, + { + "text": "OK." + }, + { + "text": "So there I have, including the square root of five, that's an orthogonal matrix, that's an orthogonal matrix, that's a diagonal matrix, and its rank is only one." + }, + { + "text": "And now if I do that multiplication, I pray that it comes out right." + }, + { + "text": "The square root of five will cancel into that square root of one twenty-five and leave me with the square root of twenty-five, which is five, and five will multiply these numbers and I'll get whole numbers and out will come A. OK. That's a second, like, a second example showing how the null space guy, so this, this vector and the, and this one were multiplied by this zero, so they, they were easy to deal with." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk18.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..fe0c1e2162590b6461e7e5aa30c5f31ab402b16a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "It was the key ones are the ones in the column space and the row space." + }, + { + "text": "Do you see how I'm getting columns here, diagonal here, rows here, coming together to produce A?" + }, + { + "text": "OK. That's the singular value decomposition." + }, + { + "text": "So, let, let me think what I want to add to, to complete this topic." + }, + { + "text": "Sort of what we're really doing." + }, + { + "text": "So that's two examples." + }, + { + "text": "And now let's think what we're really doing." + }, + { + "text": "We're, we're choosing the right basis for the four subspaces of linear algebra." + }, + { + "text": "Let me, let me, let me write this down." + }, + { + "text": "So V1 up to Vr is an orthonormal basis for the row space." + }, + { + "text": "U1 up to Ur is an orthonormal basis for the column space." + }, + { + "text": "And then I just finish those out by Vr plus one, the rest up to Vn is an orthonormal basis for the null space." + }, + { + "text": "And finally, Ur plus one up to Um is an orthonormal basis for the null space of A transpose." + }, + { + "text": "Do you see that we finally got the bases right?" + }, + { + "text": "They're right because they're orthonormal and also, I mean, the, again, Graham-Schmidt would have done this in chapter four." + }, + { + "text": "Here we needed eigenvalues because these bases make the matrix diagonal." + }, + { + "text": "A times Vi is a multiple of Ui." + }, + { + "text": "So I'll put and." + }, + { + "text": "The matrix has been made diagonal." + }, + { + "text": "When we choose these bases, there's no coupling between Vs and no coupling between Us." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk19.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..ef84969ea528bd698a227de6c8007d53a10c135a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk19.json @@ -0,0 +1,32 @@ +[ + { + "text": "Each A, A times each V is in the direction of the corresponding U." + }, + { + "text": "So it's exactly the right basis for the four fundamental subspaces." + }, + { + "text": "And of course, their dimensions are what we know." + }, + { + "text": "The dimension of the row space is the rank r, and so is the dimension of the column space." + }, + { + "text": "The dimension of the null space is n minus r, that's how many vectors we need, and m minus r basis vectors for the left null space, the null space of A transpose." + }, + { + "text": "OK." + }, + { + "text": "I'm going to stop there." + }, + { + "text": "I could develop further from the SVD, but we'll see it again in the very last lectures of the course." + }, + { + "text": "There's the SVD." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk2.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6e336773d56df67c43cd476ce2fda66a297e1c38 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Graham-Schmidt tells me how to do it." + }, + { + "text": "Start with any old basis and use- grind through Graham-Schmidt, out comes an orthogonal basis." + }, + { + "text": "But then, if I just take any old orthogonal basis, then when I multiply by A, there's no reason why it should be orthogonal over here." + }, + { + "text": "So I'm looking for this special setup where A takes these basis vectors into orthogonal vectors over there." + }, + { + "text": "Now, you might have noticed that the null space I didn't include." + }, + { + "text": "Why don't I stick that in?" + }, + { + "text": "You remember our usual figure had a little null space and a little null space." + }, + { + "text": "And, those are no problems." + }, + { + "text": "Those are- null spaces are going to show up as zeros on the diagonal of sigma, so that's not what we're- that doesn't present any difficulty." + }, + { + "text": "Our difficulty is to find the- so do you see what this will mean?" + }, + { + "text": "This will mean that A times this- these v's, v1, v2, up to- what's the dimension of this row space?" + }, + { + "text": "vr." + }, + { + "text": "Sorry, that v a little smaller." + }, + { + "text": "Up to vr." + }, + { + "text": "So that's A v1 is going to be the first column, so let me- here's what I'm- here's what I'm achieving." + }, + { + "text": "Oh, I would like- I'm not only going to make these orthogonal, but why not make them orthonormal?" + }, + { + "text": "Make them unit vectors." + }, + { + "text": "So this- maybe the unit vector is here, is the u1, and this might be a multiple of it." + }, + { + "text": "So really what's happening is A v1 is some multiple of u1, right?" + }, + { + "text": "I'm going to- these guys will be unit vectors, and they'll go over into multiples of unit vectors, and the multiple I'm not going to call lambda anymore, I'm calling it sigma." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk3.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c34819f1e56e21a93db616f1627e90900e7c35b8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's the number- the stretching number." + }, + { + "text": "And similarly, A v2 is sigma 2 u2." + }, + { + "text": "This is what- this is my goal." + }, + { + "text": "And now I want to express that goal in matrix language." + }, + { + "text": "That's the usual step." + }, + { + "text": "Think of what you want and then express it as a matrix multiplication." + }, + { + "text": "So A v1 is sigma 1 u1." + }, + { + "text": "Actually, here we go." + }, + { + "text": "Let me pull out these u1, u2 to ur, and then a matrix with the sigmas." + }, + { + "text": "It's- everything now is going to be in this- in that, in that, little part of the blackboard." + }, + { + "text": "Do you see that this equation says what I'm trying to do with my figure?" + }, + { + "text": "A times the first basis vector should be sigma 1 times the other basis- the other first basis vector." + }, + { + "text": "These are the basis vectors in the row space, these are the basis vectors in the column space, and these are the multiplying factors." + }, + { + "text": "So A v2 is sigma 2 times u2, A vr is sigma r times ur." + }, + { + "text": "And then we've got a whole lot of zeros and maybe some zeros at the end, but this is- that's the heart of it." + }, + { + "text": "And now if I express that in- as matrices, because you knew that was coming, that's what I have." + }, + { + "text": "So this is my goal." + }, + { + "text": "To find an orthogonal basis in the rows- orthonormal, even, basis in the row space, and an orthonormal basis in the column space, so that I'm sort of diagonalized the matrix." + }, + { + "text": "The matrix A is like getting converted to this diagonal matrix sigma." + }, + { + "text": "And you notice that usually I have to do- I have to allow myself two different bases." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk4.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..191e383650177ee1c7a8b51ce0359c195d9afdec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "My little comment about symmetric positive definite was the one case where it's A q equal q sigma, where v and u are the same q." + }, + { + "text": "But mostly, I'm going to take a matrix like, oh, let me take a matrix like four four minus three three." + }, + { + "text": "Okay." + }, + { + "text": "There's a two by two matrix." + }, + { + "text": "It's invertible, so it has rank two." + }, + { + "text": "So I'm going to look for two vectors, v1 and v2, in the row space, and u- so I'm going to look for v1 v2 in the row space, which of course is R2." + }, + { + "text": "And I'm going to look for u1 u2 in the column space, which of course is also R2." + }, + { + "text": "And I'm going to look for numbers sigma 1 and sigma 2, so that it all comes out right." + }, + { + "text": "So these guys are orthonormal." + }, + { + "text": "These guys are orthonormal, and these are the scaling factors." + }, + { + "text": "So I'll do that example as soon as I get the matrix picture straight." + }, + { + "text": "Okay." + }, + { + "text": "Do you see that this expresses what I want?" + }, + { + "text": "Can I just say two words about null spaces?" + }, + { + "text": "If we have -- if there's some null space, then we've got- we want to stick in a basis for those, for that." + }, + { + "text": "So here comes a basis for the null space, v R plus one down to vn." + }, + { + "text": "So if we only had an R-dimensional row space and the other n minus R dimensions were in the null space, okay, we'll take an orthogonal- orthonormal basis there, no problem." + }, + { + "text": "And then we'll just get zeros." + }, + { + "text": "So actually, those zeros will come out from the- on the diagonal matrix." + }, + { + "text": "So I'll complete that to, to, orthonormal basis for the whole space, Rn." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk5.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..8d6aafa6aa98e697236b4b5cd884684c97d6a470 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "I complete this to an orthonormal basis for the whole space, Rn, and I complete that with zeros." + }, + { + "text": "Null spaces are no problem here." + }, + { + "text": "So really, the true problem is in a matrix like that, which isn't symmetric, so I can't use its eigenvectors, they're not orthogonal, but somehow I have to get these orthogonal, in fact, orthonormal guys that make it work." + }, + { + "text": "I have to find this, these orthonormal guys, these orthonormal guys, and I want A v1 to be sigma 1 u1, and A v2 to be sigma 2 u2." + }, + { + "text": "Okay." + }, + { + "text": "That's my goal." + }, + { + "text": "Here's, here's the, matrices that are going to get me there." + }, + { + "text": "Now, these are orthogonal matrices." + }, + { + "text": "I can put that, if I multiply on both sides by v inverse, I have A equals u sigma v inverse, and of course, you know the other way I can write v inverse." + }, + { + "text": "This is one of those square orthogonal matrices, so it's the same as u sigma v transpose." + }, + { + "text": "Okay." + }, + { + "text": "Here's my problem." + }, + { + "text": "I've got two orthogonal matrices here, and I don't want to find them both at once." + }, + { + "text": "So I want to cook up some expression that will make the u's disappear." + }, + { + "text": "I would like to make the u's disappear and leave me only with the v's." + }, + { + "text": "And here's how to do it." + }, + { + "text": "It's, it's the same combination that keeps showing up whenever we have a general rectangular matrix, then it's A transpose A, that's the great matrix." + }, + { + "text": "That's the great matrix." + }, + { + "text": "That's the matrix that's symmetric." + }, + { + "text": "And, in fact, positive definite or at least positive semidefinite." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk6.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..df7b3f09adc2388b2ce3ad477bb1b91bf8d74d84 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "This is the matrix with nice properties." + }, + { + "text": "So let's see what will it be." + }, + { + "text": "So if I took the transpose, then, I would have A transpose A will be what?" + }, + { + "text": "What do I have?" + }, + { + "text": "If I transpose that, I have v sigma transpose u transpose, that's, that's the A transpose." + }, + { + "text": "Now the A." + }, + { + "text": "And what have I got?" + }, + { + "text": "Looks like worse, because it's got six things now together, but it's going to collapse into something good." + }, + { + "text": "What does u transpose u collapse into?" + }, + { + "text": "I." + }, + { + "text": "The identity." + }, + { + "text": "So that's the key point." + }, + { + "text": "This is the identity and we don't have u anymore." + }, + { + "text": "And sigma transpose times sigma, those are diagonal matrices." + }, + { + "text": "So their product is just going to have sigma squareds on the diagonal." + }, + { + "text": "So do you see what we've got here?" + }, + { + "text": "This is v times this easy matrix, sigma one squared, sigma two squared, times v transpose." + }, + { + "text": "This is the A transpose A." + }, + { + "text": "This is, let me copy down, A transpose A is that." + }, + { + "text": "U's are out of the picture now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk7.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..bff98ae0a99f2983b0755af21ee925990c6fab2c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'm only having to choose the v's." + }, + { + "text": "And what are these v's?" + }, + { + "text": "And what are these sigmas?" + }, + { + "text": "Do you know what the v's are?" + }, + { + "text": "They're the eigenvectors." + }, + { + "text": "See, this is a perfect eigenvector, eigenvalue, Q lambda Q transpose for the matrix A transpose A." + }, + { + "text": "A itself is like nothing special." + }, + { + "text": "But A transpose A will be special." + }, + { + "text": "It'll be symmetric, positive, definite." + }, + { + "text": "So this'll be its eigenvectors and this'll be its eigenvalues." + }, + { + "text": "And the eigenvalues will be positive because this thing's positive definite." + }, + { + "text": "Can I just now so this is my method." + }, + { + "text": "This tells me what the v's are and how am I going to find the u's?" + }, + { + "text": "Well, one way would be to look at A A transpose." + }, + { + "text": "Put, multiply A by A transpose in the opposite order." + }, + { + "text": "That will stick the v's in the middle, knock them out, and leave me with the u's." + }, + { + "text": "So here's the overall picture, then." + }, + { + "text": "The v's are the eigenvectors of A transpose A." + }, + { + "text": "The u's are the eigenvectors of A A transpose, which are different." + }, + { + "text": "And the sigmas are the square roots of these and the positive square roots, so we have positive sigmas." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk8.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..cb5b25b4a97f60e6bc1aa3c42941190d5c2e5b99 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do that for that example." + }, + { + "text": "This is really what you should know and be able to do for, the SVD." + }, + { + "text": "Okay." + }, + { + "text": "Let me take that matrix." + }, + { + "text": "So what's my first step?" + }, + { + "text": "Compute A transpose A, because I want its eigenvectors." + }, + { + "text": "Okay, so I have to compute A transpose A." + }, + { + "text": "So A transpose is four four minus three three, and A is four four minus three three." + }, + { + "text": "And I do that multiplication and I get sixteen, I get twenty-five, I get sixteen minus nine, is that seven?" + }, + { + "text": "And it better come out symmetric and, oh, okay, and then it comes out twenty-five." + }, + { + "text": "Okay." + }, + { + "text": "So I want its eigenvectors and its eigenvalues." + }, + { + "text": "Its eigenvectors will be the v's, its eigenvalues will be the squares of the sigmas." + }, + { + "text": "Okay." + }, + { + "text": "What are the eigenvalues and eigenvectors of this guy?" + }, + { + "text": "Have you seen that two by two example enough to recognize that the eigenvectors are, that one one is an eigenvector?" + }, + { + "text": "So this is, here is A transpose A. I'm looking for its eigenvectors." + }, + { + "text": "So its eigenvectors, I think, are one one and one minus one." + }, + { + "text": "Because if I multiply that matrix by one one, what do I get?" + }, + { + "text": "If I multiply that matrix by one one, I get thirty-two thirty-two." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk9.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..15f3f793471c1b5693d2cfa38e670c0a75251236 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_10_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So which is thirty-two of one one." + }, + { + "text": "So there's the first eigenvector." + }, + { + "text": "And there's the eigenvalue for A transpose A, so I'm going to take its square root in the, for sigma." + }, + { + "text": "Okay." + }, + { + "text": "What's the eigenvector that goes, eigenvalue that goes with this one?" + }, + { + "text": "If I do that multiplication, what do I get?" + }, + { + "text": "I get some multiple of one minus one." + }, + { + "text": "And what is that multiple?" + }, + { + "text": "Looks like eighteen." + }, + { + "text": "Okay." + }, + { + "text": "So those are the two eigenvectors." + }, + { + "text": "But, oh, just a moment, I didn't normalize them." + }, + { + "text": "To, to make everything absolutely right, I ought to normalize these eigenvectors, divide by their length, square root of two." + }, + { + "text": "So all these guys should be true unit vectors, and, of course, that normalization didn't change the thirty-two and the eighteen." + }, + { + "text": "Okay." + }, + { + "text": "So I'm happy with the Vs, here are the Vs, so now let me put together the, the, the pieces here." + }, + { + "text": "Here's my A." + }, + { + "text": "Here's my A." + }, + { + "text": "Let me, let me write down A again." + }, + { + "text": "This should, if, if life is right, we should get U, which I don't yet know, U I don't yet know, sigma, I do now know." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk0.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..fd25ea0818dacffdd5bd1cff722aaf7d067f8f16 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay." + }, + { + "text": "This is the lecture on the singular value decomposition." + }, + { + "text": "But everybody calls it the SVD." + }, + { + "text": "So this is the final and best factorization of a matrix." + }, + { + "text": "Let me tell you what's coming." + }, + { + "text": "The factors will be orthogonal matrix, diagonal matrix, orthogonal matrix." + }, + { + "text": "So it's things that we've seen before, these special good matrices, orthogonal, diagonal." + }, + { + "text": "The new point is that we need two orthogonal matrices." + }, + { + "text": "A can be any matrix whatsoever." + }, + { + "text": "Any matrix whatsoever has this singular value decomposition." + }, + { + "text": "So a diagonal one in the middle, but I need two different, probably different, orthogonal matrices to be able to do this." + }, + { + "text": "Okay." + }, + { + "text": "And this factorization has jumped into importance and is properly, I think, maybe the bringing together of everything in this course." + }, + { + "text": "One thing we'll bring together is, like, the very good family of matrices that we just studied." + }, + { + "text": "Symmetric positive definite." + }, + { + "text": "Do you remember the story with those guys?" + }, + { + "text": "Because they were symmetric, their eigenvectors were orthogonal, so I could produce an orthogonal matrix." + }, + { + "text": "This is my usual one." + }, + { + "text": "My usual one is the eigenvectors and eigenvalues." + }, + { + "text": "In the symmetric case, the eigenvectors are orthogonal, so I've got the good, my ordinary S has become a especially good Q, and positive definite, my ordinary lambda has become a positive lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk1.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..7e27d1aa155a8c107e4e8383a665af50464268d3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So this is, that's the singular value decomposition." + }, + { + "text": "In case our matrix is symmetric positive definite, in that case, I don't need two, u and a v, one orthogonal matrix will do for both sides." + }, + { + "text": "But, so this would be no good in general, because usually the eigenvector matrix isn't orthogonal." + }, + { + "text": "So this is not what I'm, that's not what I'm after." + }, + { + "text": "I'm looking for orthogonal times diagonal times orthogonal." + }, + { + "text": "And let me show you what that means and where it comes from." + }, + { + "text": "OK. What does it mean?" + }, + { + "text": "You remember the picture of any linear transformation." + }, + { + "text": "This was, like, the most important figure in 1806." + }, + { + "text": "And what am I looking for now?" + }, + { + "text": "A typical vector in the row space, typical vector, let me call it v1, gets taken over to some vector in the column space, say u1." + }, + { + "text": "So u1 is a v1." + }, + { + "text": "OK. Now, another vector gets taken over here somewhere." + }, + { + "text": "What am I looking for?" + }, + { + "text": "In this SVD, this singular value decomposition, what I'm looking for is an orthogonal basis here that gets knocked over into an orthogonal basis over there." + }, + { + "text": "See, that's pretty special, to have an orthogonal basis in the row space that goes over into an orthogonal basis, so this is like a right angle and this is a right angle, into an orthogonal basis in the column space." + }, + { + "text": "So that's our goal, is to find -- you see how things are coming together." + }, + { + "text": "First of all, can I find an orthogonal basis for this row space?" + }, + { + "text": "Of course." + }, + { + "text": "No big deal to find an orthogonal basis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk10.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..0179b0117bf00f95a1b04b6b86a542ce8f0c3b70 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "What's sigma?" + }, + { + "text": "So I'm looking for U sigma V transpose." + }, + { + "text": "U, the diagonal guy, and V transpose." + }, + { + "text": "Okay." + }, + { + "text": "Let's just see that come out right." + }, + { + "text": "So what's, what are the, what are the sigmas?" + }, + { + "text": "They're the square roots of these things." + }, + { + "text": "So square root of thirty-two and square root of eighteen." + }, + { + "text": "Zero, zero." + }, + { + "text": "Okay." + }, + { + "text": "What are the Vs?" + }, + { + "text": "They're these two." + }, + { + "text": "And I have to transpose, maybe that, maybe that just leaves me with one, with one over square root of two in that row, and the other one is one over square root of two minus one over square root of two." + }, + { + "text": "Now, finally, I've got to know the Us." + }, + { + "text": "Well, actually, one way to do, since I now know all the other pieces, I could put those together and figure out what the Us are." + }, + { + "text": "But let me do it the A A transpose way." + }, + { + "text": "Okay, find the Us now." + }, + { + "text": "U1 and U2." + }, + { + "text": "And what are they?" + }, + { + "text": "I look at A A transpose, so A is supposed to be U sigma V transpose, and then when I transpose that, I get V sigma transpose U transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk11.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..96d6a665ffcc93fda55a75d250402ff8f7417df8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I'm just doing it in the opposite order, A times A transpose, and what's the good part here?" + }, + { + "text": "That in the middle, V transpose V is going to be the identity." + }, + { + "text": "So this is just U sigma sigma transpose, that's some diagonal matrix with sigma squareds and U transpose." + }, + { + "text": "So what am I seeing here?" + }, + { + "text": "I'm seeing here, again, a symmetric positive definite or at least semi-definite matrix, and I'm seeing its eigenvectors and its eigenvalues." + }, + { + "text": "So if I compute A A transpose, its eigenvectors will be the things that go into U." + }, + { + "text": "Okay, so I need to compute A A transpose." + }, + { + "text": "I guess I'm going to have to go -." + }, + { + "text": "Let me, can I move that up just a little, maybe a little more, and do A A transpose." + }, + { + "text": "So what's A?" + }, + { + "text": "Four, four, minus three and three." + }, + { + "text": "And what's A transpose?" + }, + { + "text": "Four, four, minus three and three." + }, + { + "text": "And when I do that multiplication, I get, what do I get?" + }, + { + "text": "Sixteen and sixteen, thirty-two." + }, + { + "text": "That one comes out zero." + }, + { + "text": "Oh, so this is a lucky case, and that one comes out eighteen." + }, + { + "text": "So this is, like, an accident, that A A transpose happens to come out diagonal, so we know easily its eigenvectors and eigenvalues." + }, + { + "text": "So its eigenvectors are, what's the first eigenvector for this A A transpose matrix?" + }, + { + "text": "It's just one zero, and when I do that multiplication, I get thirty-two times one zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk12.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..3bea51beac69b154780aa5b76ef1f4e76eb0490c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the other eigenvector is just zero one, and when I multiply by that, I get eighteen." + }, + { + "text": "So this is A A transpose, multiplying that gives me the thirty-two A A transpose, multiplying this guy gives me eighteen." + }, + { + "text": "First of all, I got thirty-two and eighteen again." + }, + { + "text": "Am I surprised?" + }, + { + "text": "Yeah, it's clearly not an accident." + }, + { + "text": "The eigenvalues of A A transpose were exactly the same as the eigenvalues of this one was A transpose A." + }, + { + "text": "That's no surprise at all." + }, + { + "text": "The eigenvalues of A B are same as the eigenvalues of B A." + }, + { + "text": "The order, that's a very nice fact, that eigenvalues stay the same if I switch the order of multiplication." + }, + { + "text": "So no surprise to see thirty-two and eighteen." + }, + { + "text": "What I learned, first I checked that things were numerically correct, but now I've learned these eigenvectors, and actually they're about as nice as can be." + }, + { + "text": "They're the best orthogonal matrix, just the identity." + }, + { + "text": "Okay." + }, + { + "text": "So my claim is that it ought to all fit together." + }, + { + "text": "That this numeri- this, these numbers should come out right." + }, + { + "text": "The numbers should come out right because the, the, matrix multiplications use the properties that we want." + }, + { + "text": "Okay." + }, + { + "text": "So we just check that." + }, + { + "text": "Here's the identity, so not doing anything." + }, + { + "text": "Square root of thirty-two is multiplying that row, so that's square root of thirty-two divided by square root of two means square root of sixteen, four." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk13.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..a104483771ba144bbf5e80f6d0432de06fbabe37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Correct?" + }, + { + "text": "And square root of eighteen is divided by square root of two, so that leaves me square root of nine, which is three, but no, Professor Strang, you see the problem." + }, + { + "text": "Why is that?" + }, + { + "text": "Okay." + }, + { + "text": "Why am I getting minus three three here, and here I'm getting three minus three?" + }, + { + "text": "Phooey." + }, + { + "text": "I don't know why." + }, + { + "text": "It shouldn't have happened, but it did." + }, + { + "text": "Now, okay, you could say, well, just, the eigenvector there could have, I could have had the minus sign here for that eigenvector, but I'm not happy about that." + }, + { + "text": "Hm." + }, + { + "text": "Okay." + }, + { + "text": "Okay." + }, + { + "text": "So I realize there's a little catch here somewhere, and I may not see it until Wednesday, which then gives you a very important reason to come back on Wednesday, to catch that sign difference." + }, + { + "text": "So what did I do illegally?" + }, + { + "text": "I think I put the eigenvectors in that matrix V transpose." + }, + { + "text": "Okay, I'm going to have to think, why did that come out, with the opposite sign?" + }, + { + "text": "So you see, I mean, if I had a minus there, I would be all right, but I don't want that." + }, + { + "text": "I want positive entries down the diagonal of sigma squared." + }, + { + "text": "Okay." + }, + { + "text": "It'll come to me, but I'm going to leave this example to finish." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk14.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..6271feb6ec2eed0c67666d8fdac07717f2b70521 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "And the beauty of, these sliding boards is, I can make that go away." + }, + { + "text": "Can I, let me not do it, though." + }, + { + "text": "Yes, let me take a second example." + }, + { + "text": "Let me take a second example where the matrix is singular." + }, + { + "text": "So rank one." + }, + { + "text": "Okay." + }, + { + "text": "So let me take as an example two, where my matrix A is going to be rectangular again." + }, + { + "text": "Let me just make it four three eight six." + }, + { + "text": "Okay." + }, + { + "text": "That's a rank one matrix." + }, + { + "text": "So that has a null space and only a one-dimensional row space and column space." + }, + { + "text": "So actually, my picture becomes easy for this matrix, because what's my columns, my row space for this one?" + }, + { + "text": "So this is two by two, so my pictures are both two dimensional." + }, + { + "text": "My row space is all multiples of vector four three." + }, + { + "text": "So the whole, the row space is just a line, right?" + }, + { + "text": "That's the row space." + }, + { + "text": "And the null space, of course, is the perpendicular line." + }, + { + "text": "So the row space for this matrix is multiples of four three." + }, + { + "text": "Typical row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk15.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..247a2fb607840b5c46901a1736533537c0de9d60 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "What's the column space?" + }, + { + "text": "The columns are all multiples of four eight, three six, one two." + }, + { + "text": "The column space, then, goes in, like, this direction." + }, + { + "text": "So the column space, when I look at those columns, the column space, it was only one dimensional, because the rank is one." + }, + { + "text": "It's multiples of four eight." + }, + { + "text": "Okay." + }, + { + "text": "And what's the null space of A transpose?" + }, + { + "text": "It's the perpendicular guy." + }, + { + "text": "There's the, so this was the null space of A, and this is the null space of A transpose." + }, + { + "text": "Okay." + }, + { + "text": "What I want to say here is that the, that choosing these orthogonal bases for the row space and the column space is, like, no problem." + }, + { + "text": "They're only one dimensional." + }, + { + "text": "So what should v be?" + }, + { + "text": "v should be v1, but, yeah, v1, rather." + }, + { + "text": "v1 is supposed to be a unit vector." + }, + { + "text": "There's only one v1 to choose here, only one dimension in the row space." + }, + { + "text": "I just want to make it a unit vector." + }, + { + "text": "So v1 will be, it'll be this vector, but made into a unit vector, so four, point eight, point six." + }, + { + "text": "Four fifths, three fifths." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk16.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..9ebd9d5b85dc5cf2ad0e297580201c57ae64e6f6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what will be u1?" + }, + { + "text": "u1 will be the unit vector there, so I want to turn four eight or one two into a unit vector, so u1 will be, let's see, if it's one two, then what multiple of one two do I want?" + }, + { + "text": "That has length square root of five, so I have to divide by square root of five." + }, + { + "text": "Let me complete the singular value decomposition for this matrix." + }, + { + "text": "So this matrix, four three eight six, is, so I know what u1, here's A, and I want to get u, the basis in the column space, and it has to start with this guy." + }, + { + "text": "One over square root of five, two over square root of five." + }, + { + "text": "Then I want the sigma." + }, + { + "text": "OK. What are we expecting now for sigma?" + }, + { + "text": "Where is, this is only a rank one matrix, we're only expecting a sigma one, which I have to find, but zero's here." + }, + { + "text": "OK, so what's sigma one?" + }, + { + "text": "We should see it, it should be the, where did these sigmas come from?" + }, + { + "text": "They came from A transpose A, so I, can I do that little calculation over here?" + }, + { + "text": "A transpose A is four three, four three eight six times four three eight six." + }, + { + "text": "This had better, this is a rank one matrix, this is going to be, the whole thing will have rank one, that's sixteen and sixty four is eighty, twelve and forty eight is sixty, twelve and forty eight is sixty, nine and thirty six is forty five." + }, + { + "text": "OK." + }, + { + "text": "It's a rank one matrix." + }, + { + "text": "Of course." + }, + { + "text": "Every row is a multiple of four three." + }, + { + "text": "And what's the eigen, what are the eigenvalues of that matrix?" + }, + { + "text": "So this is like, the calculation is like practicing now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk17.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b48a4d8f19e69f562ef2b2b5013cd6a113ef2e4d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "What are the eigenvalues of this rank one matrix?" + }, + { + "text": "Well, tell me one eigenvalue, since the rank is only one, one eigenvalue is going to be zero." + }, + { + "text": "And then you know that the other eigenvalue is going to be a hundred and twenty five." + }, + { + "text": "So that's sigma squared, right, in A transpose A." + }, + { + "text": "So this will be the square root of a hundred and twenty five." + }, + { + "text": "And then finally, the V transpose, the Vs will be, there's V1, and what's V2?" + }, + { + "text": "What's V2 in the, what's, how do I make this into a orthonormal basis?" + }, + { + "text": "Well, V2 is in the null space direction." + }, + { + "text": "It's perpendicular to that, so point six and minus point eight." + }, + { + "text": "So those are the Vs that go in here." + }, + { + "text": "Point eight, point six, and point six minus point eight." + }, + { + "text": "OK. And I guess I better finish this guy." + }, + { + "text": "So this guy, all I want is to complete the orthonormal basis." + }, + { + "text": "It'll be coming from there, it'll be a two over square root of five and a minus one over square root of five." + }, + { + "text": "I could have take, let me take square root of five out of that matrix to make it look better." + }, + { + "text": "So one over square root of five times one, one, two, two, minus one." + }, + { + "text": "OK." + }, + { + "text": "So there I have, including the square root of five, that's an orthogonal matrix, that's an orthogonal matrix, that's a diagonal matrix, and its rank is only one." + }, + { + "text": "And now if I do that multiplication, I pray that it comes out right." + }, + { + "text": "The square root of five will cancel into that square root of one twenty-five and leave me with the square root of twenty-five, which is five, and five will multiply these numbers and I'll get whole numbers and out will come A. OK. That's a second, like, a second example showing how the null space guy, so this, this vector and the, and this one were multiplied by this zero, so they, they were easy to deal with." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk18.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..fe0c1e2162590b6461e7e5aa30c5f31ab402b16a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "It was the key ones are the ones in the column space and the row space." + }, + { + "text": "Do you see how I'm getting columns here, diagonal here, rows here, coming together to produce A?" + }, + { + "text": "OK. That's the singular value decomposition." + }, + { + "text": "So, let, let me think what I want to add to, to complete this topic." + }, + { + "text": "Sort of what we're really doing." + }, + { + "text": "So that's two examples." + }, + { + "text": "And now let's think what we're really doing." + }, + { + "text": "We're, we're choosing the right basis for the four subspaces of linear algebra." + }, + { + "text": "Let me, let me, let me write this down." + }, + { + "text": "So V1 up to Vr is an orthonormal basis for the row space." + }, + { + "text": "U1 up to Ur is an orthonormal basis for the column space." + }, + { + "text": "And then I just finish those out by Vr plus one, the rest up to Vn is an orthonormal basis for the null space." + }, + { + "text": "And finally, Ur plus one up to Um is an orthonormal basis for the null space of A transpose." + }, + { + "text": "Do you see that we finally got the bases right?" + }, + { + "text": "They're right because they're orthonormal and also, I mean, the, again, Graham-Schmidt would have done this in chapter four." + }, + { + "text": "Here we needed eigenvalues because these bases make the matrix diagonal." + }, + { + "text": "A times Vi is a multiple of Ui." + }, + { + "text": "So I'll put and." + }, + { + "text": "The matrix has been made diagonal." + }, + { + "text": "When we choose these bases, there's no coupling between Vs and no coupling between Us." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk19.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..ef84969ea528bd698a227de6c8007d53a10c135a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk19.json @@ -0,0 +1,32 @@ +[ + { + "text": "Each A, A times each V is in the direction of the corresponding U." + }, + { + "text": "So it's exactly the right basis for the four fundamental subspaces." + }, + { + "text": "And of course, their dimensions are what we know." + }, + { + "text": "The dimension of the row space is the rank r, and so is the dimension of the column space." + }, + { + "text": "The dimension of the null space is n minus r, that's how many vectors we need, and m minus r basis vectors for the left null space, the null space of A transpose." + }, + { + "text": "OK." + }, + { + "text": "I'm going to stop there." + }, + { + "text": "I could develop further from the SVD, but we'll see it again in the very last lectures of the course." + }, + { + "text": "There's the SVD." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk2.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6e336773d56df67c43cd476ce2fda66a297e1c38 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Graham-Schmidt tells me how to do it." + }, + { + "text": "Start with any old basis and use- grind through Graham-Schmidt, out comes an orthogonal basis." + }, + { + "text": "But then, if I just take any old orthogonal basis, then when I multiply by A, there's no reason why it should be orthogonal over here." + }, + { + "text": "So I'm looking for this special setup where A takes these basis vectors into orthogonal vectors over there." + }, + { + "text": "Now, you might have noticed that the null space I didn't include." + }, + { + "text": "Why don't I stick that in?" + }, + { + "text": "You remember our usual figure had a little null space and a little null space." + }, + { + "text": "And, those are no problems." + }, + { + "text": "Those are- null spaces are going to show up as zeros on the diagonal of sigma, so that's not what we're- that doesn't present any difficulty." + }, + { + "text": "Our difficulty is to find the- so do you see what this will mean?" + }, + { + "text": "This will mean that A times this- these v's, v1, v2, up to- what's the dimension of this row space?" + }, + { + "text": "vr." + }, + { + "text": "Sorry, that v a little smaller." + }, + { + "text": "Up to vr." + }, + { + "text": "So that's A v1 is going to be the first column, so let me- here's what I'm- here's what I'm achieving." + }, + { + "text": "Oh, I would like- I'm not only going to make these orthogonal, but why not make them orthonormal?" + }, + { + "text": "Make them unit vectors." + }, + { + "text": "So this- maybe the unit vector is here, is the u1, and this might be a multiple of it." + }, + { + "text": "So really what's happening is A v1 is some multiple of u1, right?" + }, + { + "text": "I'm going to- these guys will be unit vectors, and they'll go over into multiples of unit vectors, and the multiple I'm not going to call lambda anymore, I'm calling it sigma." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk3.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c34819f1e56e21a93db616f1627e90900e7c35b8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's the number- the stretching number." + }, + { + "text": "And similarly, A v2 is sigma 2 u2." + }, + { + "text": "This is what- this is my goal." + }, + { + "text": "And now I want to express that goal in matrix language." + }, + { + "text": "That's the usual step." + }, + { + "text": "Think of what you want and then express it as a matrix multiplication." + }, + { + "text": "So A v1 is sigma 1 u1." + }, + { + "text": "Actually, here we go." + }, + { + "text": "Let me pull out these u1, u2 to ur, and then a matrix with the sigmas." + }, + { + "text": "It's- everything now is going to be in this- in that, in that, little part of the blackboard." + }, + { + "text": "Do you see that this equation says what I'm trying to do with my figure?" + }, + { + "text": "A times the first basis vector should be sigma 1 times the other basis- the other first basis vector." + }, + { + "text": "These are the basis vectors in the row space, these are the basis vectors in the column space, and these are the multiplying factors." + }, + { + "text": "So A v2 is sigma 2 times u2, A vr is sigma r times ur." + }, + { + "text": "And then we've got a whole lot of zeros and maybe some zeros at the end, but this is- that's the heart of it." + }, + { + "text": "And now if I express that in- as matrices, because you knew that was coming, that's what I have." + }, + { + "text": "So this is my goal." + }, + { + "text": "To find an orthogonal basis in the rows- orthonormal, even, basis in the row space, and an orthonormal basis in the column space, so that I'm sort of diagonalized the matrix." + }, + { + "text": "The matrix A is like getting converted to this diagonal matrix sigma." + }, + { + "text": "And you notice that usually I have to do- I have to allow myself two different bases." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk4.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..191e383650177ee1c7a8b51ce0359c195d9afdec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "My little comment about symmetric positive definite was the one case where it's A q equal q sigma, where v and u are the same q." + }, + { + "text": "But mostly, I'm going to take a matrix like, oh, let me take a matrix like four four minus three three." + }, + { + "text": "Okay." + }, + { + "text": "There's a two by two matrix." + }, + { + "text": "It's invertible, so it has rank two." + }, + { + "text": "So I'm going to look for two vectors, v1 and v2, in the row space, and u- so I'm going to look for v1 v2 in the row space, which of course is R2." + }, + { + "text": "And I'm going to look for u1 u2 in the column space, which of course is also R2." + }, + { + "text": "And I'm going to look for numbers sigma 1 and sigma 2, so that it all comes out right." + }, + { + "text": "So these guys are orthonormal." + }, + { + "text": "These guys are orthonormal, and these are the scaling factors." + }, + { + "text": "So I'll do that example as soon as I get the matrix picture straight." + }, + { + "text": "Okay." + }, + { + "text": "Do you see that this expresses what I want?" + }, + { + "text": "Can I just say two words about null spaces?" + }, + { + "text": "If we have -- if there's some null space, then we've got- we want to stick in a basis for those, for that." + }, + { + "text": "So here comes a basis for the null space, v R plus one down to vn." + }, + { + "text": "So if we only had an R-dimensional row space and the other n minus R dimensions were in the null space, okay, we'll take an orthogonal- orthonormal basis there, no problem." + }, + { + "text": "And then we'll just get zeros." + }, + { + "text": "So actually, those zeros will come out from the- on the diagonal matrix." + }, + { + "text": "So I'll complete that to, to, orthonormal basis for the whole space, Rn." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk5.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..8d6aafa6aa98e697236b4b5cd884684c97d6a470 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "I complete this to an orthonormal basis for the whole space, Rn, and I complete that with zeros." + }, + { + "text": "Null spaces are no problem here." + }, + { + "text": "So really, the true problem is in a matrix like that, which isn't symmetric, so I can't use its eigenvectors, they're not orthogonal, but somehow I have to get these orthogonal, in fact, orthonormal guys that make it work." + }, + { + "text": "I have to find this, these orthonormal guys, these orthonormal guys, and I want A v1 to be sigma 1 u1, and A v2 to be sigma 2 u2." + }, + { + "text": "Okay." + }, + { + "text": "That's my goal." + }, + { + "text": "Here's, here's the, matrices that are going to get me there." + }, + { + "text": "Now, these are orthogonal matrices." + }, + { + "text": "I can put that, if I multiply on both sides by v inverse, I have A equals u sigma v inverse, and of course, you know the other way I can write v inverse." + }, + { + "text": "This is one of those square orthogonal matrices, so it's the same as u sigma v transpose." + }, + { + "text": "Okay." + }, + { + "text": "Here's my problem." + }, + { + "text": "I've got two orthogonal matrices here, and I don't want to find them both at once." + }, + { + "text": "So I want to cook up some expression that will make the u's disappear." + }, + { + "text": "I would like to make the u's disappear and leave me only with the v's." + }, + { + "text": "And here's how to do it." + }, + { + "text": "It's, it's the same combination that keeps showing up whenever we have a general rectangular matrix, then it's A transpose A, that's the great matrix." + }, + { + "text": "That's the great matrix." + }, + { + "text": "That's the matrix that's symmetric." + }, + { + "text": "And, in fact, positive definite or at least positive semidefinite." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk6.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..df7b3f09adc2388b2ce3ad477bb1b91bf8d74d84 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "This is the matrix with nice properties." + }, + { + "text": "So let's see what will it be." + }, + { + "text": "So if I took the transpose, then, I would have A transpose A will be what?" + }, + { + "text": "What do I have?" + }, + { + "text": "If I transpose that, I have v sigma transpose u transpose, that's, that's the A transpose." + }, + { + "text": "Now the A." + }, + { + "text": "And what have I got?" + }, + { + "text": "Looks like worse, because it's got six things now together, but it's going to collapse into something good." + }, + { + "text": "What does u transpose u collapse into?" + }, + { + "text": "I." + }, + { + "text": "The identity." + }, + { + "text": "So that's the key point." + }, + { + "text": "This is the identity and we don't have u anymore." + }, + { + "text": "And sigma transpose times sigma, those are diagonal matrices." + }, + { + "text": "So their product is just going to have sigma squareds on the diagonal." + }, + { + "text": "So do you see what we've got here?" + }, + { + "text": "This is v times this easy matrix, sigma one squared, sigma two squared, times v transpose." + }, + { + "text": "This is the A transpose A." + }, + { + "text": "This is, let me copy down, A transpose A is that." + }, + { + "text": "U's are out of the picture now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk7.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..bff98ae0a99f2983b0755af21ee925990c6fab2c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'm only having to choose the v's." + }, + { + "text": "And what are these v's?" + }, + { + "text": "And what are these sigmas?" + }, + { + "text": "Do you know what the v's are?" + }, + { + "text": "They're the eigenvectors." + }, + { + "text": "See, this is a perfect eigenvector, eigenvalue, Q lambda Q transpose for the matrix A transpose A." + }, + { + "text": "A itself is like nothing special." + }, + { + "text": "But A transpose A will be special." + }, + { + "text": "It'll be symmetric, positive, definite." + }, + { + "text": "So this'll be its eigenvectors and this'll be its eigenvalues." + }, + { + "text": "And the eigenvalues will be positive because this thing's positive definite." + }, + { + "text": "Can I just now so this is my method." + }, + { + "text": "This tells me what the v's are and how am I going to find the u's?" + }, + { + "text": "Well, one way would be to look at A A transpose." + }, + { + "text": "Put, multiply A by A transpose in the opposite order." + }, + { + "text": "That will stick the v's in the middle, knock them out, and leave me with the u's." + }, + { + "text": "So here's the overall picture, then." + }, + { + "text": "The v's are the eigenvectors of A transpose A." + }, + { + "text": "The u's are the eigenvectors of A A transpose, which are different." + }, + { + "text": "And the sigmas are the square roots of these and the positive square roots, so we have positive sigmas." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk8.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..cb5b25b4a97f60e6bc1aa3c42941190d5c2e5b99 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do that for that example." + }, + { + "text": "This is really what you should know and be able to do for, the SVD." + }, + { + "text": "Okay." + }, + { + "text": "Let me take that matrix." + }, + { + "text": "So what's my first step?" + }, + { + "text": "Compute A transpose A, because I want its eigenvectors." + }, + { + "text": "Okay, so I have to compute A transpose A." + }, + { + "text": "So A transpose is four four minus three three, and A is four four minus three three." + }, + { + "text": "And I do that multiplication and I get sixteen, I get twenty-five, I get sixteen minus nine, is that seven?" + }, + { + "text": "And it better come out symmetric and, oh, okay, and then it comes out twenty-five." + }, + { + "text": "Okay." + }, + { + "text": "So I want its eigenvectors and its eigenvalues." + }, + { + "text": "Its eigenvectors will be the v's, its eigenvalues will be the squares of the sigmas." + }, + { + "text": "Okay." + }, + { + "text": "What are the eigenvalues and eigenvectors of this guy?" + }, + { + "text": "Have you seen that two by two example enough to recognize that the eigenvectors are, that one one is an eigenvector?" + }, + { + "text": "So this is, here is A transpose A. I'm looking for its eigenvectors." + }, + { + "text": "So its eigenvectors, I think, are one one and one minus one." + }, + { + "text": "Because if I multiply that matrix by one one, what do I get?" + }, + { + "text": "If I multiply that matrix by one one, I get thirty-two thirty-two." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk9.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..15f3f793471c1b5693d2cfa38e670c0a75251236 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_1_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So which is thirty-two of one one." + }, + { + "text": "So there's the first eigenvector." + }, + { + "text": "And there's the eigenvalue for A transpose A, so I'm going to take its square root in the, for sigma." + }, + { + "text": "Okay." + }, + { + "text": "What's the eigenvector that goes, eigenvalue that goes with this one?" + }, + { + "text": "If I do that multiplication, what do I get?" + }, + { + "text": "I get some multiple of one minus one." + }, + { + "text": "And what is that multiple?" + }, + { + "text": "Looks like eighteen." + }, + { + "text": "Okay." + }, + { + "text": "So those are the two eigenvectors." + }, + { + "text": "But, oh, just a moment, I didn't normalize them." + }, + { + "text": "To, to make everything absolutely right, I ought to normalize these eigenvectors, divide by their length, square root of two." + }, + { + "text": "So all these guys should be true unit vectors, and, of course, that normalization didn't change the thirty-two and the eighteen." + }, + { + "text": "Okay." + }, + { + "text": "So I'm happy with the Vs, here are the Vs, so now let me put together the, the, the pieces here." + }, + { + "text": "Here's my A." + }, + { + "text": "Here's my A." + }, + { + "text": "Let me, let me write down A again." + }, + { + "text": "This should, if, if life is right, we should get U, which I don't yet know, U I don't yet know, sigma, I do now know." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk0.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..fd25ea0818dacffdd5bd1cff722aaf7d067f8f16 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay." + }, + { + "text": "This is the lecture on the singular value decomposition." + }, + { + "text": "But everybody calls it the SVD." + }, + { + "text": "So this is the final and best factorization of a matrix." + }, + { + "text": "Let me tell you what's coming." + }, + { + "text": "The factors will be orthogonal matrix, diagonal matrix, orthogonal matrix." + }, + { + "text": "So it's things that we've seen before, these special good matrices, orthogonal, diagonal." + }, + { + "text": "The new point is that we need two orthogonal matrices." + }, + { + "text": "A can be any matrix whatsoever." + }, + { + "text": "Any matrix whatsoever has this singular value decomposition." + }, + { + "text": "So a diagonal one in the middle, but I need two different, probably different, orthogonal matrices to be able to do this." + }, + { + "text": "Okay." + }, + { + "text": "And this factorization has jumped into importance and is properly, I think, maybe the bringing together of everything in this course." + }, + { + "text": "One thing we'll bring together is, like, the very good family of matrices that we just studied." + }, + { + "text": "Symmetric positive definite." + }, + { + "text": "Do you remember the story with those guys?" + }, + { + "text": "Because they were symmetric, their eigenvectors were orthogonal, so I could produce an orthogonal matrix." + }, + { + "text": "This is my usual one." + }, + { + "text": "My usual one is the eigenvectors and eigenvalues." + }, + { + "text": "In the symmetric case, the eigenvectors are orthogonal, so I've got the good, my ordinary S has become a especially good Q, and positive definite, my ordinary lambda has become a positive lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk1.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..7e27d1aa155a8c107e4e8383a665af50464268d3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So this is, that's the singular value decomposition." + }, + { + "text": "In case our matrix is symmetric positive definite, in that case, I don't need two, u and a v, one orthogonal matrix will do for both sides." + }, + { + "text": "But, so this would be no good in general, because usually the eigenvector matrix isn't orthogonal." + }, + { + "text": "So this is not what I'm, that's not what I'm after." + }, + { + "text": "I'm looking for orthogonal times diagonal times orthogonal." + }, + { + "text": "And let me show you what that means and where it comes from." + }, + { + "text": "OK. What does it mean?" + }, + { + "text": "You remember the picture of any linear transformation." + }, + { + "text": "This was, like, the most important figure in 1806." + }, + { + "text": "And what am I looking for now?" + }, + { + "text": "A typical vector in the row space, typical vector, let me call it v1, gets taken over to some vector in the column space, say u1." + }, + { + "text": "So u1 is a v1." + }, + { + "text": "OK. Now, another vector gets taken over here somewhere." + }, + { + "text": "What am I looking for?" + }, + { + "text": "In this SVD, this singular value decomposition, what I'm looking for is an orthogonal basis here that gets knocked over into an orthogonal basis over there." + }, + { + "text": "See, that's pretty special, to have an orthogonal basis in the row space that goes over into an orthogonal basis, so this is like a right angle and this is a right angle, into an orthogonal basis in the column space." + }, + { + "text": "So that's our goal, is to find -- you see how things are coming together." + }, + { + "text": "First of all, can I find an orthogonal basis for this row space?" + }, + { + "text": "Of course." + }, + { + "text": "No big deal to find an orthogonal basis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk10.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..0179b0117bf00f95a1b04b6b86a542ce8f0c3b70 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "What's sigma?" + }, + { + "text": "So I'm looking for U sigma V transpose." + }, + { + "text": "U, the diagonal guy, and V transpose." + }, + { + "text": "Okay." + }, + { + "text": "Let's just see that come out right." + }, + { + "text": "So what's, what are the, what are the sigmas?" + }, + { + "text": "They're the square roots of these things." + }, + { + "text": "So square root of thirty-two and square root of eighteen." + }, + { + "text": "Zero, zero." + }, + { + "text": "Okay." + }, + { + "text": "What are the Vs?" + }, + { + "text": "They're these two." + }, + { + "text": "And I have to transpose, maybe that, maybe that just leaves me with one, with one over square root of two in that row, and the other one is one over square root of two minus one over square root of two." + }, + { + "text": "Now, finally, I've got to know the Us." + }, + { + "text": "Well, actually, one way to do, since I now know all the other pieces, I could put those together and figure out what the Us are." + }, + { + "text": "But let me do it the A A transpose way." + }, + { + "text": "Okay, find the Us now." + }, + { + "text": "U1 and U2." + }, + { + "text": "And what are they?" + }, + { + "text": "I look at A A transpose, so A is supposed to be U sigma V transpose, and then when I transpose that, I get V sigma transpose U transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk11.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..96d6a665ffcc93fda55a75d250402ff8f7417df8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I'm just doing it in the opposite order, A times A transpose, and what's the good part here?" + }, + { + "text": "That in the middle, V transpose V is going to be the identity." + }, + { + "text": "So this is just U sigma sigma transpose, that's some diagonal matrix with sigma squareds and U transpose." + }, + { + "text": "So what am I seeing here?" + }, + { + "text": "I'm seeing here, again, a symmetric positive definite or at least semi-definite matrix, and I'm seeing its eigenvectors and its eigenvalues." + }, + { + "text": "So if I compute A A transpose, its eigenvectors will be the things that go into U." + }, + { + "text": "Okay, so I need to compute A A transpose." + }, + { + "text": "I guess I'm going to have to go -." + }, + { + "text": "Let me, can I move that up just a little, maybe a little more, and do A A transpose." + }, + { + "text": "So what's A?" + }, + { + "text": "Four, four, minus three and three." + }, + { + "text": "And what's A transpose?" + }, + { + "text": "Four, four, minus three and three." + }, + { + "text": "And when I do that multiplication, I get, what do I get?" + }, + { + "text": "Sixteen and sixteen, thirty-two." + }, + { + "text": "That one comes out zero." + }, + { + "text": "Oh, so this is a lucky case, and that one comes out eighteen." + }, + { + "text": "So this is, like, an accident, that A A transpose happens to come out diagonal, so we know easily its eigenvectors and eigenvalues." + }, + { + "text": "So its eigenvectors are, what's the first eigenvector for this A A transpose matrix?" + }, + { + "text": "It's just one zero, and when I do that multiplication, I get thirty-two times one zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk12.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..3bea51beac69b154780aa5b76ef1f4e76eb0490c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the other eigenvector is just zero one, and when I multiply by that, I get eighteen." + }, + { + "text": "So this is A A transpose, multiplying that gives me the thirty-two A A transpose, multiplying this guy gives me eighteen." + }, + { + "text": "First of all, I got thirty-two and eighteen again." + }, + { + "text": "Am I surprised?" + }, + { + "text": "Yeah, it's clearly not an accident." + }, + { + "text": "The eigenvalues of A A transpose were exactly the same as the eigenvalues of this one was A transpose A." + }, + { + "text": "That's no surprise at all." + }, + { + "text": "The eigenvalues of A B are same as the eigenvalues of B A." + }, + { + "text": "The order, that's a very nice fact, that eigenvalues stay the same if I switch the order of multiplication." + }, + { + "text": "So no surprise to see thirty-two and eighteen." + }, + { + "text": "What I learned, first I checked that things were numerically correct, but now I've learned these eigenvectors, and actually they're about as nice as can be." + }, + { + "text": "They're the best orthogonal matrix, just the identity." + }, + { + "text": "Okay." + }, + { + "text": "So my claim is that it ought to all fit together." + }, + { + "text": "That this numeri- this, these numbers should come out right." + }, + { + "text": "The numbers should come out right because the, the, matrix multiplications use the properties that we want." + }, + { + "text": "Okay." + }, + { + "text": "So we just check that." + }, + { + "text": "Here's the identity, so not doing anything." + }, + { + "text": "Square root of thirty-two is multiplying that row, so that's square root of thirty-two divided by square root of two means square root of sixteen, four." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk13.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..a104483771ba144bbf5e80f6d0432de06fbabe37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Correct?" + }, + { + "text": "And square root of eighteen is divided by square root of two, so that leaves me square root of nine, which is three, but no, Professor Strang, you see the problem." + }, + { + "text": "Why is that?" + }, + { + "text": "Okay." + }, + { + "text": "Why am I getting minus three three here, and here I'm getting three minus three?" + }, + { + "text": "Phooey." + }, + { + "text": "I don't know why." + }, + { + "text": "It shouldn't have happened, but it did." + }, + { + "text": "Now, okay, you could say, well, just, the eigenvector there could have, I could have had the minus sign here for that eigenvector, but I'm not happy about that." + }, + { + "text": "Hm." + }, + { + "text": "Okay." + }, + { + "text": "Okay." + }, + { + "text": "So I realize there's a little catch here somewhere, and I may not see it until Wednesday, which then gives you a very important reason to come back on Wednesday, to catch that sign difference." + }, + { + "text": "So what did I do illegally?" + }, + { + "text": "I think I put the eigenvectors in that matrix V transpose." + }, + { + "text": "Okay, I'm going to have to think, why did that come out, with the opposite sign?" + }, + { + "text": "So you see, I mean, if I had a minus there, I would be all right, but I don't want that." + }, + { + "text": "I want positive entries down the diagonal of sigma squared." + }, + { + "text": "Okay." + }, + { + "text": "It'll come to me, but I'm going to leave this example to finish." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk14.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..6271feb6ec2eed0c67666d8fdac07717f2b70521 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "And the beauty of, these sliding boards is, I can make that go away." + }, + { + "text": "Can I, let me not do it, though." + }, + { + "text": "Yes, let me take a second example." + }, + { + "text": "Let me take a second example where the matrix is singular." + }, + { + "text": "So rank one." + }, + { + "text": "Okay." + }, + { + "text": "So let me take as an example two, where my matrix A is going to be rectangular again." + }, + { + "text": "Let me just make it four three eight six." + }, + { + "text": "Okay." + }, + { + "text": "That's a rank one matrix." + }, + { + "text": "So that has a null space and only a one-dimensional row space and column space." + }, + { + "text": "So actually, my picture becomes easy for this matrix, because what's my columns, my row space for this one?" + }, + { + "text": "So this is two by two, so my pictures are both two dimensional." + }, + { + "text": "My row space is all multiples of vector four three." + }, + { + "text": "So the whole, the row space is just a line, right?" + }, + { + "text": "That's the row space." + }, + { + "text": "And the null space, of course, is the perpendicular line." + }, + { + "text": "So the row space for this matrix is multiples of four three." + }, + { + "text": "Typical row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk15.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..247a2fb607840b5c46901a1736533537c0de9d60 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "What's the column space?" + }, + { + "text": "The columns are all multiples of four eight, three six, one two." + }, + { + "text": "The column space, then, goes in, like, this direction." + }, + { + "text": "So the column space, when I look at those columns, the column space, it was only one dimensional, because the rank is one." + }, + { + "text": "It's multiples of four eight." + }, + { + "text": "Okay." + }, + { + "text": "And what's the null space of A transpose?" + }, + { + "text": "It's the perpendicular guy." + }, + { + "text": "There's the, so this was the null space of A, and this is the null space of A transpose." + }, + { + "text": "Okay." + }, + { + "text": "What I want to say here is that the, that choosing these orthogonal bases for the row space and the column space is, like, no problem." + }, + { + "text": "They're only one dimensional." + }, + { + "text": "So what should v be?" + }, + { + "text": "v should be v1, but, yeah, v1, rather." + }, + { + "text": "v1 is supposed to be a unit vector." + }, + { + "text": "There's only one v1 to choose here, only one dimension in the row space." + }, + { + "text": "I just want to make it a unit vector." + }, + { + "text": "So v1 will be, it'll be this vector, but made into a unit vector, so four, point eight, point six." + }, + { + "text": "Four fifths, three fifths." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk16.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..9ebd9d5b85dc5cf2ad0e297580201c57ae64e6f6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what will be u1?" + }, + { + "text": "u1 will be the unit vector there, so I want to turn four eight or one two into a unit vector, so u1 will be, let's see, if it's one two, then what multiple of one two do I want?" + }, + { + "text": "That has length square root of five, so I have to divide by square root of five." + }, + { + "text": "Let me complete the singular value decomposition for this matrix." + }, + { + "text": "So this matrix, four three eight six, is, so I know what u1, here's A, and I want to get u, the basis in the column space, and it has to start with this guy." + }, + { + "text": "One over square root of five, two over square root of five." + }, + { + "text": "Then I want the sigma." + }, + { + "text": "OK. What are we expecting now for sigma?" + }, + { + "text": "Where is, this is only a rank one matrix, we're only expecting a sigma one, which I have to find, but zero's here." + }, + { + "text": "OK, so what's sigma one?" + }, + { + "text": "We should see it, it should be the, where did these sigmas come from?" + }, + { + "text": "They came from A transpose A, so I, can I do that little calculation over here?" + }, + { + "text": "A transpose A is four three, four three eight six times four three eight six." + }, + { + "text": "This had better, this is a rank one matrix, this is going to be, the whole thing will have rank one, that's sixteen and sixty four is eighty, twelve and forty eight is sixty, twelve and forty eight is sixty, nine and thirty six is forty five." + }, + { + "text": "OK." + }, + { + "text": "It's a rank one matrix." + }, + { + "text": "Of course." + }, + { + "text": "Every row is a multiple of four three." + }, + { + "text": "And what's the eigen, what are the eigenvalues of that matrix?" + }, + { + "text": "So this is like, the calculation is like practicing now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk17.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b48a4d8f19e69f562ef2b2b5013cd6a113ef2e4d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "What are the eigenvalues of this rank one matrix?" + }, + { + "text": "Well, tell me one eigenvalue, since the rank is only one, one eigenvalue is going to be zero." + }, + { + "text": "And then you know that the other eigenvalue is going to be a hundred and twenty five." + }, + { + "text": "So that's sigma squared, right, in A transpose A." + }, + { + "text": "So this will be the square root of a hundred and twenty five." + }, + { + "text": "And then finally, the V transpose, the Vs will be, there's V1, and what's V2?" + }, + { + "text": "What's V2 in the, what's, how do I make this into a orthonormal basis?" + }, + { + "text": "Well, V2 is in the null space direction." + }, + { + "text": "It's perpendicular to that, so point six and minus point eight." + }, + { + "text": "So those are the Vs that go in here." + }, + { + "text": "Point eight, point six, and point six minus point eight." + }, + { + "text": "OK. And I guess I better finish this guy." + }, + { + "text": "So this guy, all I want is to complete the orthonormal basis." + }, + { + "text": "It'll be coming from there, it'll be a two over square root of five and a minus one over square root of five." + }, + { + "text": "I could have take, let me take square root of five out of that matrix to make it look better." + }, + { + "text": "So one over square root of five times one, one, two, two, minus one." + }, + { + "text": "OK." + }, + { + "text": "So there I have, including the square root of five, that's an orthogonal matrix, that's an orthogonal matrix, that's a diagonal matrix, and its rank is only one." + }, + { + "text": "And now if I do that multiplication, I pray that it comes out right." + }, + { + "text": "The square root of five will cancel into that square root of one twenty-five and leave me with the square root of twenty-five, which is five, and five will multiply these numbers and I'll get whole numbers and out will come A. OK. That's a second, like, a second example showing how the null space guy, so this, this vector and the, and this one were multiplied by this zero, so they, they were easy to deal with." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk18.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..fe0c1e2162590b6461e7e5aa30c5f31ab402b16a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "It was the key ones are the ones in the column space and the row space." + }, + { + "text": "Do you see how I'm getting columns here, diagonal here, rows here, coming together to produce A?" + }, + { + "text": "OK. That's the singular value decomposition." + }, + { + "text": "So, let, let me think what I want to add to, to complete this topic." + }, + { + "text": "Sort of what we're really doing." + }, + { + "text": "So that's two examples." + }, + { + "text": "And now let's think what we're really doing." + }, + { + "text": "We're, we're choosing the right basis for the four subspaces of linear algebra." + }, + { + "text": "Let me, let me, let me write this down." + }, + { + "text": "So V1 up to Vr is an orthonormal basis for the row space." + }, + { + "text": "U1 up to Ur is an orthonormal basis for the column space." + }, + { + "text": "And then I just finish those out by Vr plus one, the rest up to Vn is an orthonormal basis for the null space." + }, + { + "text": "And finally, Ur plus one up to Um is an orthonormal basis for the null space of A transpose." + }, + { + "text": "Do you see that we finally got the bases right?" + }, + { + "text": "They're right because they're orthonormal and also, I mean, the, again, Graham-Schmidt would have done this in chapter four." + }, + { + "text": "Here we needed eigenvalues because these bases make the matrix diagonal." + }, + { + "text": "A times Vi is a multiple of Ui." + }, + { + "text": "So I'll put and." + }, + { + "text": "The matrix has been made diagonal." + }, + { + "text": "When we choose these bases, there's no coupling between Vs and no coupling between Us." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk19.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..ef84969ea528bd698a227de6c8007d53a10c135a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk19.json @@ -0,0 +1,32 @@ +[ + { + "text": "Each A, A times each V is in the direction of the corresponding U." + }, + { + "text": "So it's exactly the right basis for the four fundamental subspaces." + }, + { + "text": "And of course, their dimensions are what we know." + }, + { + "text": "The dimension of the row space is the rank r, and so is the dimension of the column space." + }, + { + "text": "The dimension of the null space is n minus r, that's how many vectors we need, and m minus r basis vectors for the left null space, the null space of A transpose." + }, + { + "text": "OK." + }, + { + "text": "I'm going to stop there." + }, + { + "text": "I could develop further from the SVD, but we'll see it again in the very last lectures of the course." + }, + { + "text": "There's the SVD." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk2.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6e336773d56df67c43cd476ce2fda66a297e1c38 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Graham-Schmidt tells me how to do it." + }, + { + "text": "Start with any old basis and use- grind through Graham-Schmidt, out comes an orthogonal basis." + }, + { + "text": "But then, if I just take any old orthogonal basis, then when I multiply by A, there's no reason why it should be orthogonal over here." + }, + { + "text": "So I'm looking for this special setup where A takes these basis vectors into orthogonal vectors over there." + }, + { + "text": "Now, you might have noticed that the null space I didn't include." + }, + { + "text": "Why don't I stick that in?" + }, + { + "text": "You remember our usual figure had a little null space and a little null space." + }, + { + "text": "And, those are no problems." + }, + { + "text": "Those are- null spaces are going to show up as zeros on the diagonal of sigma, so that's not what we're- that doesn't present any difficulty." + }, + { + "text": "Our difficulty is to find the- so do you see what this will mean?" + }, + { + "text": "This will mean that A times this- these v's, v1, v2, up to- what's the dimension of this row space?" + }, + { + "text": "vr." + }, + { + "text": "Sorry, that v a little smaller." + }, + { + "text": "Up to vr." + }, + { + "text": "So that's A v1 is going to be the first column, so let me- here's what I'm- here's what I'm achieving." + }, + { + "text": "Oh, I would like- I'm not only going to make these orthogonal, but why not make them orthonormal?" + }, + { + "text": "Make them unit vectors." + }, + { + "text": "So this- maybe the unit vector is here, is the u1, and this might be a multiple of it." + }, + { + "text": "So really what's happening is A v1 is some multiple of u1, right?" + }, + { + "text": "I'm going to- these guys will be unit vectors, and they'll go over into multiples of unit vectors, and the multiple I'm not going to call lambda anymore, I'm calling it sigma." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk3.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c34819f1e56e21a93db616f1627e90900e7c35b8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's the number- the stretching number." + }, + { + "text": "And similarly, A v2 is sigma 2 u2." + }, + { + "text": "This is what- this is my goal." + }, + { + "text": "And now I want to express that goal in matrix language." + }, + { + "text": "That's the usual step." + }, + { + "text": "Think of what you want and then express it as a matrix multiplication." + }, + { + "text": "So A v1 is sigma 1 u1." + }, + { + "text": "Actually, here we go." + }, + { + "text": "Let me pull out these u1, u2 to ur, and then a matrix with the sigmas." + }, + { + "text": "It's- everything now is going to be in this- in that, in that, little part of the blackboard." + }, + { + "text": "Do you see that this equation says what I'm trying to do with my figure?" + }, + { + "text": "A times the first basis vector should be sigma 1 times the other basis- the other first basis vector." + }, + { + "text": "These are the basis vectors in the row space, these are the basis vectors in the column space, and these are the multiplying factors." + }, + { + "text": "So A v2 is sigma 2 times u2, A vr is sigma r times ur." + }, + { + "text": "And then we've got a whole lot of zeros and maybe some zeros at the end, but this is- that's the heart of it." + }, + { + "text": "And now if I express that in- as matrices, because you knew that was coming, that's what I have." + }, + { + "text": "So this is my goal." + }, + { + "text": "To find an orthogonal basis in the rows- orthonormal, even, basis in the row space, and an orthonormal basis in the column space, so that I'm sort of diagonalized the matrix." + }, + { + "text": "The matrix A is like getting converted to this diagonal matrix sigma." + }, + { + "text": "And you notice that usually I have to do- I have to allow myself two different bases." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk4.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..191e383650177ee1c7a8b51ce0359c195d9afdec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "My little comment about symmetric positive definite was the one case where it's A q equal q sigma, where v and u are the same q." + }, + { + "text": "But mostly, I'm going to take a matrix like, oh, let me take a matrix like four four minus three three." + }, + { + "text": "Okay." + }, + { + "text": "There's a two by two matrix." + }, + { + "text": "It's invertible, so it has rank two." + }, + { + "text": "So I'm going to look for two vectors, v1 and v2, in the row space, and u- so I'm going to look for v1 v2 in the row space, which of course is R2." + }, + { + "text": "And I'm going to look for u1 u2 in the column space, which of course is also R2." + }, + { + "text": "And I'm going to look for numbers sigma 1 and sigma 2, so that it all comes out right." + }, + { + "text": "So these guys are orthonormal." + }, + { + "text": "These guys are orthonormal, and these are the scaling factors." + }, + { + "text": "So I'll do that example as soon as I get the matrix picture straight." + }, + { + "text": "Okay." + }, + { + "text": "Do you see that this expresses what I want?" + }, + { + "text": "Can I just say two words about null spaces?" + }, + { + "text": "If we have -- if there's some null space, then we've got- we want to stick in a basis for those, for that." + }, + { + "text": "So here comes a basis for the null space, v R plus one down to vn." + }, + { + "text": "So if we only had an R-dimensional row space and the other n minus R dimensions were in the null space, okay, we'll take an orthogonal- orthonormal basis there, no problem." + }, + { + "text": "And then we'll just get zeros." + }, + { + "text": "So actually, those zeros will come out from the- on the diagonal matrix." + }, + { + "text": "So I'll complete that to, to, orthonormal basis for the whole space, Rn." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk5.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..8d6aafa6aa98e697236b4b5cd884684c97d6a470 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "I complete this to an orthonormal basis for the whole space, Rn, and I complete that with zeros." + }, + { + "text": "Null spaces are no problem here." + }, + { + "text": "So really, the true problem is in a matrix like that, which isn't symmetric, so I can't use its eigenvectors, they're not orthogonal, but somehow I have to get these orthogonal, in fact, orthonormal guys that make it work." + }, + { + "text": "I have to find this, these orthonormal guys, these orthonormal guys, and I want A v1 to be sigma 1 u1, and A v2 to be sigma 2 u2." + }, + { + "text": "Okay." + }, + { + "text": "That's my goal." + }, + { + "text": "Here's, here's the, matrices that are going to get me there." + }, + { + "text": "Now, these are orthogonal matrices." + }, + { + "text": "I can put that, if I multiply on both sides by v inverse, I have A equals u sigma v inverse, and of course, you know the other way I can write v inverse." + }, + { + "text": "This is one of those square orthogonal matrices, so it's the same as u sigma v transpose." + }, + { + "text": "Okay." + }, + { + "text": "Here's my problem." + }, + { + "text": "I've got two orthogonal matrices here, and I don't want to find them both at once." + }, + { + "text": "So I want to cook up some expression that will make the u's disappear." + }, + { + "text": "I would like to make the u's disappear and leave me only with the v's." + }, + { + "text": "And here's how to do it." + }, + { + "text": "It's, it's the same combination that keeps showing up whenever we have a general rectangular matrix, then it's A transpose A, that's the great matrix." + }, + { + "text": "That's the great matrix." + }, + { + "text": "That's the matrix that's symmetric." + }, + { + "text": "And, in fact, positive definite or at least positive semidefinite." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk6.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..df7b3f09adc2388b2ce3ad477bb1b91bf8d74d84 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "This is the matrix with nice properties." + }, + { + "text": "So let's see what will it be." + }, + { + "text": "So if I took the transpose, then, I would have A transpose A will be what?" + }, + { + "text": "What do I have?" + }, + { + "text": "If I transpose that, I have v sigma transpose u transpose, that's, that's the A transpose." + }, + { + "text": "Now the A." + }, + { + "text": "And what have I got?" + }, + { + "text": "Looks like worse, because it's got six things now together, but it's going to collapse into something good." + }, + { + "text": "What does u transpose u collapse into?" + }, + { + "text": "I." + }, + { + "text": "The identity." + }, + { + "text": "So that's the key point." + }, + { + "text": "This is the identity and we don't have u anymore." + }, + { + "text": "And sigma transpose times sigma, those are diagonal matrices." + }, + { + "text": "So their product is just going to have sigma squareds on the diagonal." + }, + { + "text": "So do you see what we've got here?" + }, + { + "text": "This is v times this easy matrix, sigma one squared, sigma two squared, times v transpose." + }, + { + "text": "This is the A transpose A." + }, + { + "text": "This is, let me copy down, A transpose A is that." + }, + { + "text": "U's are out of the picture now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk7.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..bff98ae0a99f2983b0755af21ee925990c6fab2c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'm only having to choose the v's." + }, + { + "text": "And what are these v's?" + }, + { + "text": "And what are these sigmas?" + }, + { + "text": "Do you know what the v's are?" + }, + { + "text": "They're the eigenvectors." + }, + { + "text": "See, this is a perfect eigenvector, eigenvalue, Q lambda Q transpose for the matrix A transpose A." + }, + { + "text": "A itself is like nothing special." + }, + { + "text": "But A transpose A will be special." + }, + { + "text": "It'll be symmetric, positive, definite." + }, + { + "text": "So this'll be its eigenvectors and this'll be its eigenvalues." + }, + { + "text": "And the eigenvalues will be positive because this thing's positive definite." + }, + { + "text": "Can I just now so this is my method." + }, + { + "text": "This tells me what the v's are and how am I going to find the u's?" + }, + { + "text": "Well, one way would be to look at A A transpose." + }, + { + "text": "Put, multiply A by A transpose in the opposite order." + }, + { + "text": "That will stick the v's in the middle, knock them out, and leave me with the u's." + }, + { + "text": "So here's the overall picture, then." + }, + { + "text": "The v's are the eigenvectors of A transpose A." + }, + { + "text": "The u's are the eigenvectors of A A transpose, which are different." + }, + { + "text": "And the sigmas are the square roots of these and the positive square roots, so we have positive sigmas." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk8.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..cb5b25b4a97f60e6bc1aa3c42941190d5c2e5b99 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do that for that example." + }, + { + "text": "This is really what you should know and be able to do for, the SVD." + }, + { + "text": "Okay." + }, + { + "text": "Let me take that matrix." + }, + { + "text": "So what's my first step?" + }, + { + "text": "Compute A transpose A, because I want its eigenvectors." + }, + { + "text": "Okay, so I have to compute A transpose A." + }, + { + "text": "So A transpose is four four minus three three, and A is four four minus three three." + }, + { + "text": "And I do that multiplication and I get sixteen, I get twenty-five, I get sixteen minus nine, is that seven?" + }, + { + "text": "And it better come out symmetric and, oh, okay, and then it comes out twenty-five." + }, + { + "text": "Okay." + }, + { + "text": "So I want its eigenvectors and its eigenvalues." + }, + { + "text": "Its eigenvectors will be the v's, its eigenvalues will be the squares of the sigmas." + }, + { + "text": "Okay." + }, + { + "text": "What are the eigenvalues and eigenvectors of this guy?" + }, + { + "text": "Have you seen that two by two example enough to recognize that the eigenvectors are, that one one is an eigenvector?" + }, + { + "text": "So this is, here is A transpose A. I'm looking for its eigenvectors." + }, + { + "text": "So its eigenvectors, I think, are one one and one minus one." + }, + { + "text": "Because if I multiply that matrix by one one, what do I get?" + }, + { + "text": "If I multiply that matrix by one one, I get thirty-two thirty-two." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk9.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..15f3f793471c1b5693d2cfa38e670c0a75251236 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_2_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So which is thirty-two of one one." + }, + { + "text": "So there's the first eigenvector." + }, + { + "text": "And there's the eigenvalue for A transpose A, so I'm going to take its square root in the, for sigma." + }, + { + "text": "Okay." + }, + { + "text": "What's the eigenvector that goes, eigenvalue that goes with this one?" + }, + { + "text": "If I do that multiplication, what do I get?" + }, + { + "text": "I get some multiple of one minus one." + }, + { + "text": "And what is that multiple?" + }, + { + "text": "Looks like eighteen." + }, + { + "text": "Okay." + }, + { + "text": "So those are the two eigenvectors." + }, + { + "text": "But, oh, just a moment, I didn't normalize them." + }, + { + "text": "To, to make everything absolutely right, I ought to normalize these eigenvectors, divide by their length, square root of two." + }, + { + "text": "So all these guys should be true unit vectors, and, of course, that normalization didn't change the thirty-two and the eighteen." + }, + { + "text": "Okay." + }, + { + "text": "So I'm happy with the Vs, here are the Vs, so now let me put together the, the, the pieces here." + }, + { + "text": "Here's my A." + }, + { + "text": "Here's my A." + }, + { + "text": "Let me, let me write down A again." + }, + { + "text": "This should, if, if life is right, we should get U, which I don't yet know, U I don't yet know, sigma, I do now know." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk0.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..fd25ea0818dacffdd5bd1cff722aaf7d067f8f16 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay." + }, + { + "text": "This is the lecture on the singular value decomposition." + }, + { + "text": "But everybody calls it the SVD." + }, + { + "text": "So this is the final and best factorization of a matrix." + }, + { + "text": "Let me tell you what's coming." + }, + { + "text": "The factors will be orthogonal matrix, diagonal matrix, orthogonal matrix." + }, + { + "text": "So it's things that we've seen before, these special good matrices, orthogonal, diagonal." + }, + { + "text": "The new point is that we need two orthogonal matrices." + }, + { + "text": "A can be any matrix whatsoever." + }, + { + "text": "Any matrix whatsoever has this singular value decomposition." + }, + { + "text": "So a diagonal one in the middle, but I need two different, probably different, orthogonal matrices to be able to do this." + }, + { + "text": "Okay." + }, + { + "text": "And this factorization has jumped into importance and is properly, I think, maybe the bringing together of everything in this course." + }, + { + "text": "One thing we'll bring together is, like, the very good family of matrices that we just studied." + }, + { + "text": "Symmetric positive definite." + }, + { + "text": "Do you remember the story with those guys?" + }, + { + "text": "Because they were symmetric, their eigenvectors were orthogonal, so I could produce an orthogonal matrix." + }, + { + "text": "This is my usual one." + }, + { + "text": "My usual one is the eigenvectors and eigenvalues." + }, + { + "text": "In the symmetric case, the eigenvectors are orthogonal, so I've got the good, my ordinary S has become a especially good Q, and positive definite, my ordinary lambda has become a positive lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk1.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..7e27d1aa155a8c107e4e8383a665af50464268d3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So this is, that's the singular value decomposition." + }, + { + "text": "In case our matrix is symmetric positive definite, in that case, I don't need two, u and a v, one orthogonal matrix will do for both sides." + }, + { + "text": "But, so this would be no good in general, because usually the eigenvector matrix isn't orthogonal." + }, + { + "text": "So this is not what I'm, that's not what I'm after." + }, + { + "text": "I'm looking for orthogonal times diagonal times orthogonal." + }, + { + "text": "And let me show you what that means and where it comes from." + }, + { + "text": "OK. What does it mean?" + }, + { + "text": "You remember the picture of any linear transformation." + }, + { + "text": "This was, like, the most important figure in 1806." + }, + { + "text": "And what am I looking for now?" + }, + { + "text": "A typical vector in the row space, typical vector, let me call it v1, gets taken over to some vector in the column space, say u1." + }, + { + "text": "So u1 is a v1." + }, + { + "text": "OK. Now, another vector gets taken over here somewhere." + }, + { + "text": "What am I looking for?" + }, + { + "text": "In this SVD, this singular value decomposition, what I'm looking for is an orthogonal basis here that gets knocked over into an orthogonal basis over there." + }, + { + "text": "See, that's pretty special, to have an orthogonal basis in the row space that goes over into an orthogonal basis, so this is like a right angle and this is a right angle, into an orthogonal basis in the column space." + }, + { + "text": "So that's our goal, is to find -- you see how things are coming together." + }, + { + "text": "First of all, can I find an orthogonal basis for this row space?" + }, + { + "text": "Of course." + }, + { + "text": "No big deal to find an orthogonal basis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk10.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..0179b0117bf00f95a1b04b6b86a542ce8f0c3b70 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "What's sigma?" + }, + { + "text": "So I'm looking for U sigma V transpose." + }, + { + "text": "U, the diagonal guy, and V transpose." + }, + { + "text": "Okay." + }, + { + "text": "Let's just see that come out right." + }, + { + "text": "So what's, what are the, what are the sigmas?" + }, + { + "text": "They're the square roots of these things." + }, + { + "text": "So square root of thirty-two and square root of eighteen." + }, + { + "text": "Zero, zero." + }, + { + "text": "Okay." + }, + { + "text": "What are the Vs?" + }, + { + "text": "They're these two." + }, + { + "text": "And I have to transpose, maybe that, maybe that just leaves me with one, with one over square root of two in that row, and the other one is one over square root of two minus one over square root of two." + }, + { + "text": "Now, finally, I've got to know the Us." + }, + { + "text": "Well, actually, one way to do, since I now know all the other pieces, I could put those together and figure out what the Us are." + }, + { + "text": "But let me do it the A A transpose way." + }, + { + "text": "Okay, find the Us now." + }, + { + "text": "U1 and U2." + }, + { + "text": "And what are they?" + }, + { + "text": "I look at A A transpose, so A is supposed to be U sigma V transpose, and then when I transpose that, I get V sigma transpose U transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk11.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..96d6a665ffcc93fda55a75d250402ff8f7417df8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I'm just doing it in the opposite order, A times A transpose, and what's the good part here?" + }, + { + "text": "That in the middle, V transpose V is going to be the identity." + }, + { + "text": "So this is just U sigma sigma transpose, that's some diagonal matrix with sigma squareds and U transpose." + }, + { + "text": "So what am I seeing here?" + }, + { + "text": "I'm seeing here, again, a symmetric positive definite or at least semi-definite matrix, and I'm seeing its eigenvectors and its eigenvalues." + }, + { + "text": "So if I compute A A transpose, its eigenvectors will be the things that go into U." + }, + { + "text": "Okay, so I need to compute A A transpose." + }, + { + "text": "I guess I'm going to have to go -." + }, + { + "text": "Let me, can I move that up just a little, maybe a little more, and do A A transpose." + }, + { + "text": "So what's A?" + }, + { + "text": "Four, four, minus three and three." + }, + { + "text": "And what's A transpose?" + }, + { + "text": "Four, four, minus three and three." + }, + { + "text": "And when I do that multiplication, I get, what do I get?" + }, + { + "text": "Sixteen and sixteen, thirty-two." + }, + { + "text": "That one comes out zero." + }, + { + "text": "Oh, so this is a lucky case, and that one comes out eighteen." + }, + { + "text": "So this is, like, an accident, that A A transpose happens to come out diagonal, so we know easily its eigenvectors and eigenvalues." + }, + { + "text": "So its eigenvectors are, what's the first eigenvector for this A A transpose matrix?" + }, + { + "text": "It's just one zero, and when I do that multiplication, I get thirty-two times one zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk12.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..3bea51beac69b154780aa5b76ef1f4e76eb0490c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the other eigenvector is just zero one, and when I multiply by that, I get eighteen." + }, + { + "text": "So this is A A transpose, multiplying that gives me the thirty-two A A transpose, multiplying this guy gives me eighteen." + }, + { + "text": "First of all, I got thirty-two and eighteen again." + }, + { + "text": "Am I surprised?" + }, + { + "text": "Yeah, it's clearly not an accident." + }, + { + "text": "The eigenvalues of A A transpose were exactly the same as the eigenvalues of this one was A transpose A." + }, + { + "text": "That's no surprise at all." + }, + { + "text": "The eigenvalues of A B are same as the eigenvalues of B A." + }, + { + "text": "The order, that's a very nice fact, that eigenvalues stay the same if I switch the order of multiplication." + }, + { + "text": "So no surprise to see thirty-two and eighteen." + }, + { + "text": "What I learned, first I checked that things were numerically correct, but now I've learned these eigenvectors, and actually they're about as nice as can be." + }, + { + "text": "They're the best orthogonal matrix, just the identity." + }, + { + "text": "Okay." + }, + { + "text": "So my claim is that it ought to all fit together." + }, + { + "text": "That this numeri- this, these numbers should come out right." + }, + { + "text": "The numbers should come out right because the, the, matrix multiplications use the properties that we want." + }, + { + "text": "Okay." + }, + { + "text": "So we just check that." + }, + { + "text": "Here's the identity, so not doing anything." + }, + { + "text": "Square root of thirty-two is multiplying that row, so that's square root of thirty-two divided by square root of two means square root of sixteen, four." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk13.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..a104483771ba144bbf5e80f6d0432de06fbabe37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Correct?" + }, + { + "text": "And square root of eighteen is divided by square root of two, so that leaves me square root of nine, which is three, but no, Professor Strang, you see the problem." + }, + { + "text": "Why is that?" + }, + { + "text": "Okay." + }, + { + "text": "Why am I getting minus three three here, and here I'm getting three minus three?" + }, + { + "text": "Phooey." + }, + { + "text": "I don't know why." + }, + { + "text": "It shouldn't have happened, but it did." + }, + { + "text": "Now, okay, you could say, well, just, the eigenvector there could have, I could have had the minus sign here for that eigenvector, but I'm not happy about that." + }, + { + "text": "Hm." + }, + { + "text": "Okay." + }, + { + "text": "Okay." + }, + { + "text": "So I realize there's a little catch here somewhere, and I may not see it until Wednesday, which then gives you a very important reason to come back on Wednesday, to catch that sign difference." + }, + { + "text": "So what did I do illegally?" + }, + { + "text": "I think I put the eigenvectors in that matrix V transpose." + }, + { + "text": "Okay, I'm going to have to think, why did that come out, with the opposite sign?" + }, + { + "text": "So you see, I mean, if I had a minus there, I would be all right, but I don't want that." + }, + { + "text": "I want positive entries down the diagonal of sigma squared." + }, + { + "text": "Okay." + }, + { + "text": "It'll come to me, but I'm going to leave this example to finish." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk14.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..6271feb6ec2eed0c67666d8fdac07717f2b70521 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "And the beauty of, these sliding boards is, I can make that go away." + }, + { + "text": "Can I, let me not do it, though." + }, + { + "text": "Yes, let me take a second example." + }, + { + "text": "Let me take a second example where the matrix is singular." + }, + { + "text": "So rank one." + }, + { + "text": "Okay." + }, + { + "text": "So let me take as an example two, where my matrix A is going to be rectangular again." + }, + { + "text": "Let me just make it four three eight six." + }, + { + "text": "Okay." + }, + { + "text": "That's a rank one matrix." + }, + { + "text": "So that has a null space and only a one-dimensional row space and column space." + }, + { + "text": "So actually, my picture becomes easy for this matrix, because what's my columns, my row space for this one?" + }, + { + "text": "So this is two by two, so my pictures are both two dimensional." + }, + { + "text": "My row space is all multiples of vector four three." + }, + { + "text": "So the whole, the row space is just a line, right?" + }, + { + "text": "That's the row space." + }, + { + "text": "And the null space, of course, is the perpendicular line." + }, + { + "text": "So the row space for this matrix is multiples of four three." + }, + { + "text": "Typical row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk15.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..247a2fb607840b5c46901a1736533537c0de9d60 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "What's the column space?" + }, + { + "text": "The columns are all multiples of four eight, three six, one two." + }, + { + "text": "The column space, then, goes in, like, this direction." + }, + { + "text": "So the column space, when I look at those columns, the column space, it was only one dimensional, because the rank is one." + }, + { + "text": "It's multiples of four eight." + }, + { + "text": "Okay." + }, + { + "text": "And what's the null space of A transpose?" + }, + { + "text": "It's the perpendicular guy." + }, + { + "text": "There's the, so this was the null space of A, and this is the null space of A transpose." + }, + { + "text": "Okay." + }, + { + "text": "What I want to say here is that the, that choosing these orthogonal bases for the row space and the column space is, like, no problem." + }, + { + "text": "They're only one dimensional." + }, + { + "text": "So what should v be?" + }, + { + "text": "v should be v1, but, yeah, v1, rather." + }, + { + "text": "v1 is supposed to be a unit vector." + }, + { + "text": "There's only one v1 to choose here, only one dimension in the row space." + }, + { + "text": "I just want to make it a unit vector." + }, + { + "text": "So v1 will be, it'll be this vector, but made into a unit vector, so four, point eight, point six." + }, + { + "text": "Four fifths, three fifths." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk16.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..9ebd9d5b85dc5cf2ad0e297580201c57ae64e6f6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what will be u1?" + }, + { + "text": "u1 will be the unit vector there, so I want to turn four eight or one two into a unit vector, so u1 will be, let's see, if it's one two, then what multiple of one two do I want?" + }, + { + "text": "That has length square root of five, so I have to divide by square root of five." + }, + { + "text": "Let me complete the singular value decomposition for this matrix." + }, + { + "text": "So this matrix, four three eight six, is, so I know what u1, here's A, and I want to get u, the basis in the column space, and it has to start with this guy." + }, + { + "text": "One over square root of five, two over square root of five." + }, + { + "text": "Then I want the sigma." + }, + { + "text": "OK. What are we expecting now for sigma?" + }, + { + "text": "Where is, this is only a rank one matrix, we're only expecting a sigma one, which I have to find, but zero's here." + }, + { + "text": "OK, so what's sigma one?" + }, + { + "text": "We should see it, it should be the, where did these sigmas come from?" + }, + { + "text": "They came from A transpose A, so I, can I do that little calculation over here?" + }, + { + "text": "A transpose A is four three, four three eight six times four three eight six." + }, + { + "text": "This had better, this is a rank one matrix, this is going to be, the whole thing will have rank one, that's sixteen and sixty four is eighty, twelve and forty eight is sixty, twelve and forty eight is sixty, nine and thirty six is forty five." + }, + { + "text": "OK." + }, + { + "text": "It's a rank one matrix." + }, + { + "text": "Of course." + }, + { + "text": "Every row is a multiple of four three." + }, + { + "text": "And what's the eigen, what are the eigenvalues of that matrix?" + }, + { + "text": "So this is like, the calculation is like practicing now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk17.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b48a4d8f19e69f562ef2b2b5013cd6a113ef2e4d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "What are the eigenvalues of this rank one matrix?" + }, + { + "text": "Well, tell me one eigenvalue, since the rank is only one, one eigenvalue is going to be zero." + }, + { + "text": "And then you know that the other eigenvalue is going to be a hundred and twenty five." + }, + { + "text": "So that's sigma squared, right, in A transpose A." + }, + { + "text": "So this will be the square root of a hundred and twenty five." + }, + { + "text": "And then finally, the V transpose, the Vs will be, there's V1, and what's V2?" + }, + { + "text": "What's V2 in the, what's, how do I make this into a orthonormal basis?" + }, + { + "text": "Well, V2 is in the null space direction." + }, + { + "text": "It's perpendicular to that, so point six and minus point eight." + }, + { + "text": "So those are the Vs that go in here." + }, + { + "text": "Point eight, point six, and point six minus point eight." + }, + { + "text": "OK. And I guess I better finish this guy." + }, + { + "text": "So this guy, all I want is to complete the orthonormal basis." + }, + { + "text": "It'll be coming from there, it'll be a two over square root of five and a minus one over square root of five." + }, + { + "text": "I could have take, let me take square root of five out of that matrix to make it look better." + }, + { + "text": "So one over square root of five times one, one, two, two, minus one." + }, + { + "text": "OK." + }, + { + "text": "So there I have, including the square root of five, that's an orthogonal matrix, that's an orthogonal matrix, that's a diagonal matrix, and its rank is only one." + }, + { + "text": "And now if I do that multiplication, I pray that it comes out right." + }, + { + "text": "The square root of five will cancel into that square root of one twenty-five and leave me with the square root of twenty-five, which is five, and five will multiply these numbers and I'll get whole numbers and out will come A. OK. That's a second, like, a second example showing how the null space guy, so this, this vector and the, and this one were multiplied by this zero, so they, they were easy to deal with." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk18.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..fe0c1e2162590b6461e7e5aa30c5f31ab402b16a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "It was the key ones are the ones in the column space and the row space." + }, + { + "text": "Do you see how I'm getting columns here, diagonal here, rows here, coming together to produce A?" + }, + { + "text": "OK. That's the singular value decomposition." + }, + { + "text": "So, let, let me think what I want to add to, to complete this topic." + }, + { + "text": "Sort of what we're really doing." + }, + { + "text": "So that's two examples." + }, + { + "text": "And now let's think what we're really doing." + }, + { + "text": "We're, we're choosing the right basis for the four subspaces of linear algebra." + }, + { + "text": "Let me, let me, let me write this down." + }, + { + "text": "So V1 up to Vr is an orthonormal basis for the row space." + }, + { + "text": "U1 up to Ur is an orthonormal basis for the column space." + }, + { + "text": "And then I just finish those out by Vr plus one, the rest up to Vn is an orthonormal basis for the null space." + }, + { + "text": "And finally, Ur plus one up to Um is an orthonormal basis for the null space of A transpose." + }, + { + "text": "Do you see that we finally got the bases right?" + }, + { + "text": "They're right because they're orthonormal and also, I mean, the, again, Graham-Schmidt would have done this in chapter four." + }, + { + "text": "Here we needed eigenvalues because these bases make the matrix diagonal." + }, + { + "text": "A times Vi is a multiple of Ui." + }, + { + "text": "So I'll put and." + }, + { + "text": "The matrix has been made diagonal." + }, + { + "text": "When we choose these bases, there's no coupling between Vs and no coupling between Us." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk19.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..ef84969ea528bd698a227de6c8007d53a10c135a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk19.json @@ -0,0 +1,32 @@ +[ + { + "text": "Each A, A times each V is in the direction of the corresponding U." + }, + { + "text": "So it's exactly the right basis for the four fundamental subspaces." + }, + { + "text": "And of course, their dimensions are what we know." + }, + { + "text": "The dimension of the row space is the rank r, and so is the dimension of the column space." + }, + { + "text": "The dimension of the null space is n minus r, that's how many vectors we need, and m minus r basis vectors for the left null space, the null space of A transpose." + }, + { + "text": "OK." + }, + { + "text": "I'm going to stop there." + }, + { + "text": "I could develop further from the SVD, but we'll see it again in the very last lectures of the course." + }, + { + "text": "There's the SVD." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk2.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6e336773d56df67c43cd476ce2fda66a297e1c38 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Graham-Schmidt tells me how to do it." + }, + { + "text": "Start with any old basis and use- grind through Graham-Schmidt, out comes an orthogonal basis." + }, + { + "text": "But then, if I just take any old orthogonal basis, then when I multiply by A, there's no reason why it should be orthogonal over here." + }, + { + "text": "So I'm looking for this special setup where A takes these basis vectors into orthogonal vectors over there." + }, + { + "text": "Now, you might have noticed that the null space I didn't include." + }, + { + "text": "Why don't I stick that in?" + }, + { + "text": "You remember our usual figure had a little null space and a little null space." + }, + { + "text": "And, those are no problems." + }, + { + "text": "Those are- null spaces are going to show up as zeros on the diagonal of sigma, so that's not what we're- that doesn't present any difficulty." + }, + { + "text": "Our difficulty is to find the- so do you see what this will mean?" + }, + { + "text": "This will mean that A times this- these v's, v1, v2, up to- what's the dimension of this row space?" + }, + { + "text": "vr." + }, + { + "text": "Sorry, that v a little smaller." + }, + { + "text": "Up to vr." + }, + { + "text": "So that's A v1 is going to be the first column, so let me- here's what I'm- here's what I'm achieving." + }, + { + "text": "Oh, I would like- I'm not only going to make these orthogonal, but why not make them orthonormal?" + }, + { + "text": "Make them unit vectors." + }, + { + "text": "So this- maybe the unit vector is here, is the u1, and this might be a multiple of it." + }, + { + "text": "So really what's happening is A v1 is some multiple of u1, right?" + }, + { + "text": "I'm going to- these guys will be unit vectors, and they'll go over into multiples of unit vectors, and the multiple I'm not going to call lambda anymore, I'm calling it sigma." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk3.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c34819f1e56e21a93db616f1627e90900e7c35b8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's the number- the stretching number." + }, + { + "text": "And similarly, A v2 is sigma 2 u2." + }, + { + "text": "This is what- this is my goal." + }, + { + "text": "And now I want to express that goal in matrix language." + }, + { + "text": "That's the usual step." + }, + { + "text": "Think of what you want and then express it as a matrix multiplication." + }, + { + "text": "So A v1 is sigma 1 u1." + }, + { + "text": "Actually, here we go." + }, + { + "text": "Let me pull out these u1, u2 to ur, and then a matrix with the sigmas." + }, + { + "text": "It's- everything now is going to be in this- in that, in that, little part of the blackboard." + }, + { + "text": "Do you see that this equation says what I'm trying to do with my figure?" + }, + { + "text": "A times the first basis vector should be sigma 1 times the other basis- the other first basis vector." + }, + { + "text": "These are the basis vectors in the row space, these are the basis vectors in the column space, and these are the multiplying factors." + }, + { + "text": "So A v2 is sigma 2 times u2, A vr is sigma r times ur." + }, + { + "text": "And then we've got a whole lot of zeros and maybe some zeros at the end, but this is- that's the heart of it." + }, + { + "text": "And now if I express that in- as matrices, because you knew that was coming, that's what I have." + }, + { + "text": "So this is my goal." + }, + { + "text": "To find an orthogonal basis in the rows- orthonormal, even, basis in the row space, and an orthonormal basis in the column space, so that I'm sort of diagonalized the matrix." + }, + { + "text": "The matrix A is like getting converted to this diagonal matrix sigma." + }, + { + "text": "And you notice that usually I have to do- I have to allow myself two different bases." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk4.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..191e383650177ee1c7a8b51ce0359c195d9afdec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "My little comment about symmetric positive definite was the one case where it's A q equal q sigma, where v and u are the same q." + }, + { + "text": "But mostly, I'm going to take a matrix like, oh, let me take a matrix like four four minus three three." + }, + { + "text": "Okay." + }, + { + "text": "There's a two by two matrix." + }, + { + "text": "It's invertible, so it has rank two." + }, + { + "text": "So I'm going to look for two vectors, v1 and v2, in the row space, and u- so I'm going to look for v1 v2 in the row space, which of course is R2." + }, + { + "text": "And I'm going to look for u1 u2 in the column space, which of course is also R2." + }, + { + "text": "And I'm going to look for numbers sigma 1 and sigma 2, so that it all comes out right." + }, + { + "text": "So these guys are orthonormal." + }, + { + "text": "These guys are orthonormal, and these are the scaling factors." + }, + { + "text": "So I'll do that example as soon as I get the matrix picture straight." + }, + { + "text": "Okay." + }, + { + "text": "Do you see that this expresses what I want?" + }, + { + "text": "Can I just say two words about null spaces?" + }, + { + "text": "If we have -- if there's some null space, then we've got- we want to stick in a basis for those, for that." + }, + { + "text": "So here comes a basis for the null space, v R plus one down to vn." + }, + { + "text": "So if we only had an R-dimensional row space and the other n minus R dimensions were in the null space, okay, we'll take an orthogonal- orthonormal basis there, no problem." + }, + { + "text": "And then we'll just get zeros." + }, + { + "text": "So actually, those zeros will come out from the- on the diagonal matrix." + }, + { + "text": "So I'll complete that to, to, orthonormal basis for the whole space, Rn." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk5.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..8d6aafa6aa98e697236b4b5cd884684c97d6a470 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "I complete this to an orthonormal basis for the whole space, Rn, and I complete that with zeros." + }, + { + "text": "Null spaces are no problem here." + }, + { + "text": "So really, the true problem is in a matrix like that, which isn't symmetric, so I can't use its eigenvectors, they're not orthogonal, but somehow I have to get these orthogonal, in fact, orthonormal guys that make it work." + }, + { + "text": "I have to find this, these orthonormal guys, these orthonormal guys, and I want A v1 to be sigma 1 u1, and A v2 to be sigma 2 u2." + }, + { + "text": "Okay." + }, + { + "text": "That's my goal." + }, + { + "text": "Here's, here's the, matrices that are going to get me there." + }, + { + "text": "Now, these are orthogonal matrices." + }, + { + "text": "I can put that, if I multiply on both sides by v inverse, I have A equals u sigma v inverse, and of course, you know the other way I can write v inverse." + }, + { + "text": "This is one of those square orthogonal matrices, so it's the same as u sigma v transpose." + }, + { + "text": "Okay." + }, + { + "text": "Here's my problem." + }, + { + "text": "I've got two orthogonal matrices here, and I don't want to find them both at once." + }, + { + "text": "So I want to cook up some expression that will make the u's disappear." + }, + { + "text": "I would like to make the u's disappear and leave me only with the v's." + }, + { + "text": "And here's how to do it." + }, + { + "text": "It's, it's the same combination that keeps showing up whenever we have a general rectangular matrix, then it's A transpose A, that's the great matrix." + }, + { + "text": "That's the great matrix." + }, + { + "text": "That's the matrix that's symmetric." + }, + { + "text": "And, in fact, positive definite or at least positive semidefinite." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk6.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..df7b3f09adc2388b2ce3ad477bb1b91bf8d74d84 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "This is the matrix with nice properties." + }, + { + "text": "So let's see what will it be." + }, + { + "text": "So if I took the transpose, then, I would have A transpose A will be what?" + }, + { + "text": "What do I have?" + }, + { + "text": "If I transpose that, I have v sigma transpose u transpose, that's, that's the A transpose." + }, + { + "text": "Now the A." + }, + { + "text": "And what have I got?" + }, + { + "text": "Looks like worse, because it's got six things now together, but it's going to collapse into something good." + }, + { + "text": "What does u transpose u collapse into?" + }, + { + "text": "I." + }, + { + "text": "The identity." + }, + { + "text": "So that's the key point." + }, + { + "text": "This is the identity and we don't have u anymore." + }, + { + "text": "And sigma transpose times sigma, those are diagonal matrices." + }, + { + "text": "So their product is just going to have sigma squareds on the diagonal." + }, + { + "text": "So do you see what we've got here?" + }, + { + "text": "This is v times this easy matrix, sigma one squared, sigma two squared, times v transpose." + }, + { + "text": "This is the A transpose A." + }, + { + "text": "This is, let me copy down, A transpose A is that." + }, + { + "text": "U's are out of the picture now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk7.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..bff98ae0a99f2983b0755af21ee925990c6fab2c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'm only having to choose the v's." + }, + { + "text": "And what are these v's?" + }, + { + "text": "And what are these sigmas?" + }, + { + "text": "Do you know what the v's are?" + }, + { + "text": "They're the eigenvectors." + }, + { + "text": "See, this is a perfect eigenvector, eigenvalue, Q lambda Q transpose for the matrix A transpose A." + }, + { + "text": "A itself is like nothing special." + }, + { + "text": "But A transpose A will be special." + }, + { + "text": "It'll be symmetric, positive, definite." + }, + { + "text": "So this'll be its eigenvectors and this'll be its eigenvalues." + }, + { + "text": "And the eigenvalues will be positive because this thing's positive definite." + }, + { + "text": "Can I just now so this is my method." + }, + { + "text": "This tells me what the v's are and how am I going to find the u's?" + }, + { + "text": "Well, one way would be to look at A A transpose." + }, + { + "text": "Put, multiply A by A transpose in the opposite order." + }, + { + "text": "That will stick the v's in the middle, knock them out, and leave me with the u's." + }, + { + "text": "So here's the overall picture, then." + }, + { + "text": "The v's are the eigenvectors of A transpose A." + }, + { + "text": "The u's are the eigenvectors of A A transpose, which are different." + }, + { + "text": "And the sigmas are the square roots of these and the positive square roots, so we have positive sigmas." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk8.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..cb5b25b4a97f60e6bc1aa3c42941190d5c2e5b99 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do that for that example." + }, + { + "text": "This is really what you should know and be able to do for, the SVD." + }, + { + "text": "Okay." + }, + { + "text": "Let me take that matrix." + }, + { + "text": "So what's my first step?" + }, + { + "text": "Compute A transpose A, because I want its eigenvectors." + }, + { + "text": "Okay, so I have to compute A transpose A." + }, + { + "text": "So A transpose is four four minus three three, and A is four four minus three three." + }, + { + "text": "And I do that multiplication and I get sixteen, I get twenty-five, I get sixteen minus nine, is that seven?" + }, + { + "text": "And it better come out symmetric and, oh, okay, and then it comes out twenty-five." + }, + { + "text": "Okay." + }, + { + "text": "So I want its eigenvectors and its eigenvalues." + }, + { + "text": "Its eigenvectors will be the v's, its eigenvalues will be the squares of the sigmas." + }, + { + "text": "Okay." + }, + { + "text": "What are the eigenvalues and eigenvectors of this guy?" + }, + { + "text": "Have you seen that two by two example enough to recognize that the eigenvectors are, that one one is an eigenvector?" + }, + { + "text": "So this is, here is A transpose A. I'm looking for its eigenvectors." + }, + { + "text": "So its eigenvectors, I think, are one one and one minus one." + }, + { + "text": "Because if I multiply that matrix by one one, what do I get?" + }, + { + "text": "If I multiply that matrix by one one, I get thirty-two thirty-two." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk9.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..15f3f793471c1b5693d2cfa38e670c0a75251236 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_4_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So which is thirty-two of one one." + }, + { + "text": "So there's the first eigenvector." + }, + { + "text": "And there's the eigenvalue for A transpose A, so I'm going to take its square root in the, for sigma." + }, + { + "text": "Okay." + }, + { + "text": "What's the eigenvector that goes, eigenvalue that goes with this one?" + }, + { + "text": "If I do that multiplication, what do I get?" + }, + { + "text": "I get some multiple of one minus one." + }, + { + "text": "And what is that multiple?" + }, + { + "text": "Looks like eighteen." + }, + { + "text": "Okay." + }, + { + "text": "So those are the two eigenvectors." + }, + { + "text": "But, oh, just a moment, I didn't normalize them." + }, + { + "text": "To, to make everything absolutely right, I ought to normalize these eigenvectors, divide by their length, square root of two." + }, + { + "text": "So all these guys should be true unit vectors, and, of course, that normalization didn't change the thirty-two and the eighteen." + }, + { + "text": "Okay." + }, + { + "text": "So I'm happy with the Vs, here are the Vs, so now let me put together the, the, the pieces here." + }, + { + "text": "Here's my A." + }, + { + "text": "Here's my A." + }, + { + "text": "Let me, let me write down A again." + }, + { + "text": "This should, if, if life is right, we should get U, which I don't yet know, U I don't yet know, sigma, I do now know." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk0.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..fd25ea0818dacffdd5bd1cff722aaf7d067f8f16 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay." + }, + { + "text": "This is the lecture on the singular value decomposition." + }, + { + "text": "But everybody calls it the SVD." + }, + { + "text": "So this is the final and best factorization of a matrix." + }, + { + "text": "Let me tell you what's coming." + }, + { + "text": "The factors will be orthogonal matrix, diagonal matrix, orthogonal matrix." + }, + { + "text": "So it's things that we've seen before, these special good matrices, orthogonal, diagonal." + }, + { + "text": "The new point is that we need two orthogonal matrices." + }, + { + "text": "A can be any matrix whatsoever." + }, + { + "text": "Any matrix whatsoever has this singular value decomposition." + }, + { + "text": "So a diagonal one in the middle, but I need two different, probably different, orthogonal matrices to be able to do this." + }, + { + "text": "Okay." + }, + { + "text": "And this factorization has jumped into importance and is properly, I think, maybe the bringing together of everything in this course." + }, + { + "text": "One thing we'll bring together is, like, the very good family of matrices that we just studied." + }, + { + "text": "Symmetric positive definite." + }, + { + "text": "Do you remember the story with those guys?" + }, + { + "text": "Because they were symmetric, their eigenvectors were orthogonal, so I could produce an orthogonal matrix." + }, + { + "text": "This is my usual one." + }, + { + "text": "My usual one is the eigenvectors and eigenvalues." + }, + { + "text": "In the symmetric case, the eigenvectors are orthogonal, so I've got the good, my ordinary S has become a especially good Q, and positive definite, my ordinary lambda has become a positive lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk1.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..7e27d1aa155a8c107e4e8383a665af50464268d3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So this is, that's the singular value decomposition." + }, + { + "text": "In case our matrix is symmetric positive definite, in that case, I don't need two, u and a v, one orthogonal matrix will do for both sides." + }, + { + "text": "But, so this would be no good in general, because usually the eigenvector matrix isn't orthogonal." + }, + { + "text": "So this is not what I'm, that's not what I'm after." + }, + { + "text": "I'm looking for orthogonal times diagonal times orthogonal." + }, + { + "text": "And let me show you what that means and where it comes from." + }, + { + "text": "OK. What does it mean?" + }, + { + "text": "You remember the picture of any linear transformation." + }, + { + "text": "This was, like, the most important figure in 1806." + }, + { + "text": "And what am I looking for now?" + }, + { + "text": "A typical vector in the row space, typical vector, let me call it v1, gets taken over to some vector in the column space, say u1." + }, + { + "text": "So u1 is a v1." + }, + { + "text": "OK. Now, another vector gets taken over here somewhere." + }, + { + "text": "What am I looking for?" + }, + { + "text": "In this SVD, this singular value decomposition, what I'm looking for is an orthogonal basis here that gets knocked over into an orthogonal basis over there." + }, + { + "text": "See, that's pretty special, to have an orthogonal basis in the row space that goes over into an orthogonal basis, so this is like a right angle and this is a right angle, into an orthogonal basis in the column space." + }, + { + "text": "So that's our goal, is to find -- you see how things are coming together." + }, + { + "text": "First of all, can I find an orthogonal basis for this row space?" + }, + { + "text": "Of course." + }, + { + "text": "No big deal to find an orthogonal basis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk10.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..0179b0117bf00f95a1b04b6b86a542ce8f0c3b70 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "What's sigma?" + }, + { + "text": "So I'm looking for U sigma V transpose." + }, + { + "text": "U, the diagonal guy, and V transpose." + }, + { + "text": "Okay." + }, + { + "text": "Let's just see that come out right." + }, + { + "text": "So what's, what are the, what are the sigmas?" + }, + { + "text": "They're the square roots of these things." + }, + { + "text": "So square root of thirty-two and square root of eighteen." + }, + { + "text": "Zero, zero." + }, + { + "text": "Okay." + }, + { + "text": "What are the Vs?" + }, + { + "text": "They're these two." + }, + { + "text": "And I have to transpose, maybe that, maybe that just leaves me with one, with one over square root of two in that row, and the other one is one over square root of two minus one over square root of two." + }, + { + "text": "Now, finally, I've got to know the Us." + }, + { + "text": "Well, actually, one way to do, since I now know all the other pieces, I could put those together and figure out what the Us are." + }, + { + "text": "But let me do it the A A transpose way." + }, + { + "text": "Okay, find the Us now." + }, + { + "text": "U1 and U2." + }, + { + "text": "And what are they?" + }, + { + "text": "I look at A A transpose, so A is supposed to be U sigma V transpose, and then when I transpose that, I get V sigma transpose U transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk11.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..96d6a665ffcc93fda55a75d250402ff8f7417df8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I'm just doing it in the opposite order, A times A transpose, and what's the good part here?" + }, + { + "text": "That in the middle, V transpose V is going to be the identity." + }, + { + "text": "So this is just U sigma sigma transpose, that's some diagonal matrix with sigma squareds and U transpose." + }, + { + "text": "So what am I seeing here?" + }, + { + "text": "I'm seeing here, again, a symmetric positive definite or at least semi-definite matrix, and I'm seeing its eigenvectors and its eigenvalues." + }, + { + "text": "So if I compute A A transpose, its eigenvectors will be the things that go into U." + }, + { + "text": "Okay, so I need to compute A A transpose." + }, + { + "text": "I guess I'm going to have to go -." + }, + { + "text": "Let me, can I move that up just a little, maybe a little more, and do A A transpose." + }, + { + "text": "So what's A?" + }, + { + "text": "Four, four, minus three and three." + }, + { + "text": "And what's A transpose?" + }, + { + "text": "Four, four, minus three and three." + }, + { + "text": "And when I do that multiplication, I get, what do I get?" + }, + { + "text": "Sixteen and sixteen, thirty-two." + }, + { + "text": "That one comes out zero." + }, + { + "text": "Oh, so this is a lucky case, and that one comes out eighteen." + }, + { + "text": "So this is, like, an accident, that A A transpose happens to come out diagonal, so we know easily its eigenvectors and eigenvalues." + }, + { + "text": "So its eigenvectors are, what's the first eigenvector for this A A transpose matrix?" + }, + { + "text": "It's just one zero, and when I do that multiplication, I get thirty-two times one zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk12.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..3bea51beac69b154780aa5b76ef1f4e76eb0490c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the other eigenvector is just zero one, and when I multiply by that, I get eighteen." + }, + { + "text": "So this is A A transpose, multiplying that gives me the thirty-two A A transpose, multiplying this guy gives me eighteen." + }, + { + "text": "First of all, I got thirty-two and eighteen again." + }, + { + "text": "Am I surprised?" + }, + { + "text": "Yeah, it's clearly not an accident." + }, + { + "text": "The eigenvalues of A A transpose were exactly the same as the eigenvalues of this one was A transpose A." + }, + { + "text": "That's no surprise at all." + }, + { + "text": "The eigenvalues of A B are same as the eigenvalues of B A." + }, + { + "text": "The order, that's a very nice fact, that eigenvalues stay the same if I switch the order of multiplication." + }, + { + "text": "So no surprise to see thirty-two and eighteen." + }, + { + "text": "What I learned, first I checked that things were numerically correct, but now I've learned these eigenvectors, and actually they're about as nice as can be." + }, + { + "text": "They're the best orthogonal matrix, just the identity." + }, + { + "text": "Okay." + }, + { + "text": "So my claim is that it ought to all fit together." + }, + { + "text": "That this numeri- this, these numbers should come out right." + }, + { + "text": "The numbers should come out right because the, the, matrix multiplications use the properties that we want." + }, + { + "text": "Okay." + }, + { + "text": "So we just check that." + }, + { + "text": "Here's the identity, so not doing anything." + }, + { + "text": "Square root of thirty-two is multiplying that row, so that's square root of thirty-two divided by square root of two means square root of sixteen, four." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk13.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..a104483771ba144bbf5e80f6d0432de06fbabe37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Correct?" + }, + { + "text": "And square root of eighteen is divided by square root of two, so that leaves me square root of nine, which is three, but no, Professor Strang, you see the problem." + }, + { + "text": "Why is that?" + }, + { + "text": "Okay." + }, + { + "text": "Why am I getting minus three three here, and here I'm getting three minus three?" + }, + { + "text": "Phooey." + }, + { + "text": "I don't know why." + }, + { + "text": "It shouldn't have happened, but it did." + }, + { + "text": "Now, okay, you could say, well, just, the eigenvector there could have, I could have had the minus sign here for that eigenvector, but I'm not happy about that." + }, + { + "text": "Hm." + }, + { + "text": "Okay." + }, + { + "text": "Okay." + }, + { + "text": "So I realize there's a little catch here somewhere, and I may not see it until Wednesday, which then gives you a very important reason to come back on Wednesday, to catch that sign difference." + }, + { + "text": "So what did I do illegally?" + }, + { + "text": "I think I put the eigenvectors in that matrix V transpose." + }, + { + "text": "Okay, I'm going to have to think, why did that come out, with the opposite sign?" + }, + { + "text": "So you see, I mean, if I had a minus there, I would be all right, but I don't want that." + }, + { + "text": "I want positive entries down the diagonal of sigma squared." + }, + { + "text": "Okay." + }, + { + "text": "It'll come to me, but I'm going to leave this example to finish." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk14.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..6271feb6ec2eed0c67666d8fdac07717f2b70521 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "And the beauty of, these sliding boards is, I can make that go away." + }, + { + "text": "Can I, let me not do it, though." + }, + { + "text": "Yes, let me take a second example." + }, + { + "text": "Let me take a second example where the matrix is singular." + }, + { + "text": "So rank one." + }, + { + "text": "Okay." + }, + { + "text": "So let me take as an example two, where my matrix A is going to be rectangular again." + }, + { + "text": "Let me just make it four three eight six." + }, + { + "text": "Okay." + }, + { + "text": "That's a rank one matrix." + }, + { + "text": "So that has a null space and only a one-dimensional row space and column space." + }, + { + "text": "So actually, my picture becomes easy for this matrix, because what's my columns, my row space for this one?" + }, + { + "text": "So this is two by two, so my pictures are both two dimensional." + }, + { + "text": "My row space is all multiples of vector four three." + }, + { + "text": "So the whole, the row space is just a line, right?" + }, + { + "text": "That's the row space." + }, + { + "text": "And the null space, of course, is the perpendicular line." + }, + { + "text": "So the row space for this matrix is multiples of four three." + }, + { + "text": "Typical row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk15.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..247a2fb607840b5c46901a1736533537c0de9d60 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "What's the column space?" + }, + { + "text": "The columns are all multiples of four eight, three six, one two." + }, + { + "text": "The column space, then, goes in, like, this direction." + }, + { + "text": "So the column space, when I look at those columns, the column space, it was only one dimensional, because the rank is one." + }, + { + "text": "It's multiples of four eight." + }, + { + "text": "Okay." + }, + { + "text": "And what's the null space of A transpose?" + }, + { + "text": "It's the perpendicular guy." + }, + { + "text": "There's the, so this was the null space of A, and this is the null space of A transpose." + }, + { + "text": "Okay." + }, + { + "text": "What I want to say here is that the, that choosing these orthogonal bases for the row space and the column space is, like, no problem." + }, + { + "text": "They're only one dimensional." + }, + { + "text": "So what should v be?" + }, + { + "text": "v should be v1, but, yeah, v1, rather." + }, + { + "text": "v1 is supposed to be a unit vector." + }, + { + "text": "There's only one v1 to choose here, only one dimension in the row space." + }, + { + "text": "I just want to make it a unit vector." + }, + { + "text": "So v1 will be, it'll be this vector, but made into a unit vector, so four, point eight, point six." + }, + { + "text": "Four fifths, three fifths." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk16.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..9ebd9d5b85dc5cf2ad0e297580201c57ae64e6f6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what will be u1?" + }, + { + "text": "u1 will be the unit vector there, so I want to turn four eight or one two into a unit vector, so u1 will be, let's see, if it's one two, then what multiple of one two do I want?" + }, + { + "text": "That has length square root of five, so I have to divide by square root of five." + }, + { + "text": "Let me complete the singular value decomposition for this matrix." + }, + { + "text": "So this matrix, four three eight six, is, so I know what u1, here's A, and I want to get u, the basis in the column space, and it has to start with this guy." + }, + { + "text": "One over square root of five, two over square root of five." + }, + { + "text": "Then I want the sigma." + }, + { + "text": "OK. What are we expecting now for sigma?" + }, + { + "text": "Where is, this is only a rank one matrix, we're only expecting a sigma one, which I have to find, but zero's here." + }, + { + "text": "OK, so what's sigma one?" + }, + { + "text": "We should see it, it should be the, where did these sigmas come from?" + }, + { + "text": "They came from A transpose A, so I, can I do that little calculation over here?" + }, + { + "text": "A transpose A is four three, four three eight six times four three eight six." + }, + { + "text": "This had better, this is a rank one matrix, this is going to be, the whole thing will have rank one, that's sixteen and sixty four is eighty, twelve and forty eight is sixty, twelve and forty eight is sixty, nine and thirty six is forty five." + }, + { + "text": "OK." + }, + { + "text": "It's a rank one matrix." + }, + { + "text": "Of course." + }, + { + "text": "Every row is a multiple of four three." + }, + { + "text": "And what's the eigen, what are the eigenvalues of that matrix?" + }, + { + "text": "So this is like, the calculation is like practicing now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk17.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b48a4d8f19e69f562ef2b2b5013cd6a113ef2e4d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "What are the eigenvalues of this rank one matrix?" + }, + { + "text": "Well, tell me one eigenvalue, since the rank is only one, one eigenvalue is going to be zero." + }, + { + "text": "And then you know that the other eigenvalue is going to be a hundred and twenty five." + }, + { + "text": "So that's sigma squared, right, in A transpose A." + }, + { + "text": "So this will be the square root of a hundred and twenty five." + }, + { + "text": "And then finally, the V transpose, the Vs will be, there's V1, and what's V2?" + }, + { + "text": "What's V2 in the, what's, how do I make this into a orthonormal basis?" + }, + { + "text": "Well, V2 is in the null space direction." + }, + { + "text": "It's perpendicular to that, so point six and minus point eight." + }, + { + "text": "So those are the Vs that go in here." + }, + { + "text": "Point eight, point six, and point six minus point eight." + }, + { + "text": "OK. And I guess I better finish this guy." + }, + { + "text": "So this guy, all I want is to complete the orthonormal basis." + }, + { + "text": "It'll be coming from there, it'll be a two over square root of five and a minus one over square root of five." + }, + { + "text": "I could have take, let me take square root of five out of that matrix to make it look better." + }, + { + "text": "So one over square root of five times one, one, two, two, minus one." + }, + { + "text": "OK." + }, + { + "text": "So there I have, including the square root of five, that's an orthogonal matrix, that's an orthogonal matrix, that's a diagonal matrix, and its rank is only one." + }, + { + "text": "And now if I do that multiplication, I pray that it comes out right." + }, + { + "text": "The square root of five will cancel into that square root of one twenty-five and leave me with the square root of twenty-five, which is five, and five will multiply these numbers and I'll get whole numbers and out will come A. OK. That's a second, like, a second example showing how the null space guy, so this, this vector and the, and this one were multiplied by this zero, so they, they were easy to deal with." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk18.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..fe0c1e2162590b6461e7e5aa30c5f31ab402b16a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "It was the key ones are the ones in the column space and the row space." + }, + { + "text": "Do you see how I'm getting columns here, diagonal here, rows here, coming together to produce A?" + }, + { + "text": "OK. That's the singular value decomposition." + }, + { + "text": "So, let, let me think what I want to add to, to complete this topic." + }, + { + "text": "Sort of what we're really doing." + }, + { + "text": "So that's two examples." + }, + { + "text": "And now let's think what we're really doing." + }, + { + "text": "We're, we're choosing the right basis for the four subspaces of linear algebra." + }, + { + "text": "Let me, let me, let me write this down." + }, + { + "text": "So V1 up to Vr is an orthonormal basis for the row space." + }, + { + "text": "U1 up to Ur is an orthonormal basis for the column space." + }, + { + "text": "And then I just finish those out by Vr plus one, the rest up to Vn is an orthonormal basis for the null space." + }, + { + "text": "And finally, Ur plus one up to Um is an orthonormal basis for the null space of A transpose." + }, + { + "text": "Do you see that we finally got the bases right?" + }, + { + "text": "They're right because they're orthonormal and also, I mean, the, again, Graham-Schmidt would have done this in chapter four." + }, + { + "text": "Here we needed eigenvalues because these bases make the matrix diagonal." + }, + { + "text": "A times Vi is a multiple of Ui." + }, + { + "text": "So I'll put and." + }, + { + "text": "The matrix has been made diagonal." + }, + { + "text": "When we choose these bases, there's no coupling between Vs and no coupling between Us." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk19.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..ef84969ea528bd698a227de6c8007d53a10c135a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk19.json @@ -0,0 +1,32 @@ +[ + { + "text": "Each A, A times each V is in the direction of the corresponding U." + }, + { + "text": "So it's exactly the right basis for the four fundamental subspaces." + }, + { + "text": "And of course, their dimensions are what we know." + }, + { + "text": "The dimension of the row space is the rank r, and so is the dimension of the column space." + }, + { + "text": "The dimension of the null space is n minus r, that's how many vectors we need, and m minus r basis vectors for the left null space, the null space of A transpose." + }, + { + "text": "OK." + }, + { + "text": "I'm going to stop there." + }, + { + "text": "I could develop further from the SVD, but we'll see it again in the very last lectures of the course." + }, + { + "text": "There's the SVD." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk2.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6e336773d56df67c43cd476ce2fda66a297e1c38 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Graham-Schmidt tells me how to do it." + }, + { + "text": "Start with any old basis and use- grind through Graham-Schmidt, out comes an orthogonal basis." + }, + { + "text": "But then, if I just take any old orthogonal basis, then when I multiply by A, there's no reason why it should be orthogonal over here." + }, + { + "text": "So I'm looking for this special setup where A takes these basis vectors into orthogonal vectors over there." + }, + { + "text": "Now, you might have noticed that the null space I didn't include." + }, + { + "text": "Why don't I stick that in?" + }, + { + "text": "You remember our usual figure had a little null space and a little null space." + }, + { + "text": "And, those are no problems." + }, + { + "text": "Those are- null spaces are going to show up as zeros on the diagonal of sigma, so that's not what we're- that doesn't present any difficulty." + }, + { + "text": "Our difficulty is to find the- so do you see what this will mean?" + }, + { + "text": "This will mean that A times this- these v's, v1, v2, up to- what's the dimension of this row space?" + }, + { + "text": "vr." + }, + { + "text": "Sorry, that v a little smaller." + }, + { + "text": "Up to vr." + }, + { + "text": "So that's A v1 is going to be the first column, so let me- here's what I'm- here's what I'm achieving." + }, + { + "text": "Oh, I would like- I'm not only going to make these orthogonal, but why not make them orthonormal?" + }, + { + "text": "Make them unit vectors." + }, + { + "text": "So this- maybe the unit vector is here, is the u1, and this might be a multiple of it." + }, + { + "text": "So really what's happening is A v1 is some multiple of u1, right?" + }, + { + "text": "I'm going to- these guys will be unit vectors, and they'll go over into multiples of unit vectors, and the multiple I'm not going to call lambda anymore, I'm calling it sigma." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk3.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c34819f1e56e21a93db616f1627e90900e7c35b8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's the number- the stretching number." + }, + { + "text": "And similarly, A v2 is sigma 2 u2." + }, + { + "text": "This is what- this is my goal." + }, + { + "text": "And now I want to express that goal in matrix language." + }, + { + "text": "That's the usual step." + }, + { + "text": "Think of what you want and then express it as a matrix multiplication." + }, + { + "text": "So A v1 is sigma 1 u1." + }, + { + "text": "Actually, here we go." + }, + { + "text": "Let me pull out these u1, u2 to ur, and then a matrix with the sigmas." + }, + { + "text": "It's- everything now is going to be in this- in that, in that, little part of the blackboard." + }, + { + "text": "Do you see that this equation says what I'm trying to do with my figure?" + }, + { + "text": "A times the first basis vector should be sigma 1 times the other basis- the other first basis vector." + }, + { + "text": "These are the basis vectors in the row space, these are the basis vectors in the column space, and these are the multiplying factors." + }, + { + "text": "So A v2 is sigma 2 times u2, A vr is sigma r times ur." + }, + { + "text": "And then we've got a whole lot of zeros and maybe some zeros at the end, but this is- that's the heart of it." + }, + { + "text": "And now if I express that in- as matrices, because you knew that was coming, that's what I have." + }, + { + "text": "So this is my goal." + }, + { + "text": "To find an orthogonal basis in the rows- orthonormal, even, basis in the row space, and an orthonormal basis in the column space, so that I'm sort of diagonalized the matrix." + }, + { + "text": "The matrix A is like getting converted to this diagonal matrix sigma." + }, + { + "text": "And you notice that usually I have to do- I have to allow myself two different bases." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk4.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..191e383650177ee1c7a8b51ce0359c195d9afdec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "My little comment about symmetric positive definite was the one case where it's A q equal q sigma, where v and u are the same q." + }, + { + "text": "But mostly, I'm going to take a matrix like, oh, let me take a matrix like four four minus three three." + }, + { + "text": "Okay." + }, + { + "text": "There's a two by two matrix." + }, + { + "text": "It's invertible, so it has rank two." + }, + { + "text": "So I'm going to look for two vectors, v1 and v2, in the row space, and u- so I'm going to look for v1 v2 in the row space, which of course is R2." + }, + { + "text": "And I'm going to look for u1 u2 in the column space, which of course is also R2." + }, + { + "text": "And I'm going to look for numbers sigma 1 and sigma 2, so that it all comes out right." + }, + { + "text": "So these guys are orthonormal." + }, + { + "text": "These guys are orthonormal, and these are the scaling factors." + }, + { + "text": "So I'll do that example as soon as I get the matrix picture straight." + }, + { + "text": "Okay." + }, + { + "text": "Do you see that this expresses what I want?" + }, + { + "text": "Can I just say two words about null spaces?" + }, + { + "text": "If we have -- if there's some null space, then we've got- we want to stick in a basis for those, for that." + }, + { + "text": "So here comes a basis for the null space, v R plus one down to vn." + }, + { + "text": "So if we only had an R-dimensional row space and the other n minus R dimensions were in the null space, okay, we'll take an orthogonal- orthonormal basis there, no problem." + }, + { + "text": "And then we'll just get zeros." + }, + { + "text": "So actually, those zeros will come out from the- on the diagonal matrix." + }, + { + "text": "So I'll complete that to, to, orthonormal basis for the whole space, Rn." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk5.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..8d6aafa6aa98e697236b4b5cd884684c97d6a470 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "I complete this to an orthonormal basis for the whole space, Rn, and I complete that with zeros." + }, + { + "text": "Null spaces are no problem here." + }, + { + "text": "So really, the true problem is in a matrix like that, which isn't symmetric, so I can't use its eigenvectors, they're not orthogonal, but somehow I have to get these orthogonal, in fact, orthonormal guys that make it work." + }, + { + "text": "I have to find this, these orthonormal guys, these orthonormal guys, and I want A v1 to be sigma 1 u1, and A v2 to be sigma 2 u2." + }, + { + "text": "Okay." + }, + { + "text": "That's my goal." + }, + { + "text": "Here's, here's the, matrices that are going to get me there." + }, + { + "text": "Now, these are orthogonal matrices." + }, + { + "text": "I can put that, if I multiply on both sides by v inverse, I have A equals u sigma v inverse, and of course, you know the other way I can write v inverse." + }, + { + "text": "This is one of those square orthogonal matrices, so it's the same as u sigma v transpose." + }, + { + "text": "Okay." + }, + { + "text": "Here's my problem." + }, + { + "text": "I've got two orthogonal matrices here, and I don't want to find them both at once." + }, + { + "text": "So I want to cook up some expression that will make the u's disappear." + }, + { + "text": "I would like to make the u's disappear and leave me only with the v's." + }, + { + "text": "And here's how to do it." + }, + { + "text": "It's, it's the same combination that keeps showing up whenever we have a general rectangular matrix, then it's A transpose A, that's the great matrix." + }, + { + "text": "That's the great matrix." + }, + { + "text": "That's the matrix that's symmetric." + }, + { + "text": "And, in fact, positive definite or at least positive semidefinite." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk6.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..df7b3f09adc2388b2ce3ad477bb1b91bf8d74d84 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "This is the matrix with nice properties." + }, + { + "text": "So let's see what will it be." + }, + { + "text": "So if I took the transpose, then, I would have A transpose A will be what?" + }, + { + "text": "What do I have?" + }, + { + "text": "If I transpose that, I have v sigma transpose u transpose, that's, that's the A transpose." + }, + { + "text": "Now the A." + }, + { + "text": "And what have I got?" + }, + { + "text": "Looks like worse, because it's got six things now together, but it's going to collapse into something good." + }, + { + "text": "What does u transpose u collapse into?" + }, + { + "text": "I." + }, + { + "text": "The identity." + }, + { + "text": "So that's the key point." + }, + { + "text": "This is the identity and we don't have u anymore." + }, + { + "text": "And sigma transpose times sigma, those are diagonal matrices." + }, + { + "text": "So their product is just going to have sigma squareds on the diagonal." + }, + { + "text": "So do you see what we've got here?" + }, + { + "text": "This is v times this easy matrix, sigma one squared, sigma two squared, times v transpose." + }, + { + "text": "This is the A transpose A." + }, + { + "text": "This is, let me copy down, A transpose A is that." + }, + { + "text": "U's are out of the picture now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk7.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..bff98ae0a99f2983b0755af21ee925990c6fab2c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'm only having to choose the v's." + }, + { + "text": "And what are these v's?" + }, + { + "text": "And what are these sigmas?" + }, + { + "text": "Do you know what the v's are?" + }, + { + "text": "They're the eigenvectors." + }, + { + "text": "See, this is a perfect eigenvector, eigenvalue, Q lambda Q transpose for the matrix A transpose A." + }, + { + "text": "A itself is like nothing special." + }, + { + "text": "But A transpose A will be special." + }, + { + "text": "It'll be symmetric, positive, definite." + }, + { + "text": "So this'll be its eigenvectors and this'll be its eigenvalues." + }, + { + "text": "And the eigenvalues will be positive because this thing's positive definite." + }, + { + "text": "Can I just now so this is my method." + }, + { + "text": "This tells me what the v's are and how am I going to find the u's?" + }, + { + "text": "Well, one way would be to look at A A transpose." + }, + { + "text": "Put, multiply A by A transpose in the opposite order." + }, + { + "text": "That will stick the v's in the middle, knock them out, and leave me with the u's." + }, + { + "text": "So here's the overall picture, then." + }, + { + "text": "The v's are the eigenvectors of A transpose A." + }, + { + "text": "The u's are the eigenvectors of A A transpose, which are different." + }, + { + "text": "And the sigmas are the square roots of these and the positive square roots, so we have positive sigmas." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk8.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..cb5b25b4a97f60e6bc1aa3c42941190d5c2e5b99 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do that for that example." + }, + { + "text": "This is really what you should know and be able to do for, the SVD." + }, + { + "text": "Okay." + }, + { + "text": "Let me take that matrix." + }, + { + "text": "So what's my first step?" + }, + { + "text": "Compute A transpose A, because I want its eigenvectors." + }, + { + "text": "Okay, so I have to compute A transpose A." + }, + { + "text": "So A transpose is four four minus three three, and A is four four minus three three." + }, + { + "text": "And I do that multiplication and I get sixteen, I get twenty-five, I get sixteen minus nine, is that seven?" + }, + { + "text": "And it better come out symmetric and, oh, okay, and then it comes out twenty-five." + }, + { + "text": "Okay." + }, + { + "text": "So I want its eigenvectors and its eigenvalues." + }, + { + "text": "Its eigenvectors will be the v's, its eigenvalues will be the squares of the sigmas." + }, + { + "text": "Okay." + }, + { + "text": "What are the eigenvalues and eigenvectors of this guy?" + }, + { + "text": "Have you seen that two by two example enough to recognize that the eigenvectors are, that one one is an eigenvector?" + }, + { + "text": "So this is, here is A transpose A. I'm looking for its eigenvectors." + }, + { + "text": "So its eigenvectors, I think, are one one and one minus one." + }, + { + "text": "Because if I multiply that matrix by one one, what do I get?" + }, + { + "text": "If I multiply that matrix by one one, I get thirty-two thirty-two." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk9.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..15f3f793471c1b5693d2cfa38e670c0a75251236 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_7_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So which is thirty-two of one one." + }, + { + "text": "So there's the first eigenvector." + }, + { + "text": "And there's the eigenvalue for A transpose A, so I'm going to take its square root in the, for sigma." + }, + { + "text": "Okay." + }, + { + "text": "What's the eigenvector that goes, eigenvalue that goes with this one?" + }, + { + "text": "If I do that multiplication, what do I get?" + }, + { + "text": "I get some multiple of one minus one." + }, + { + "text": "And what is that multiple?" + }, + { + "text": "Looks like eighteen." + }, + { + "text": "Okay." + }, + { + "text": "So those are the two eigenvectors." + }, + { + "text": "But, oh, just a moment, I didn't normalize them." + }, + { + "text": "To, to make everything absolutely right, I ought to normalize these eigenvectors, divide by their length, square root of two." + }, + { + "text": "So all these guys should be true unit vectors, and, of course, that normalization didn't change the thirty-two and the eighteen." + }, + { + "text": "Okay." + }, + { + "text": "So I'm happy with the Vs, here are the Vs, so now let me put together the, the, the pieces here." + }, + { + "text": "Here's my A." + }, + { + "text": "Here's my A." + }, + { + "text": "Let me, let me write down A again." + }, + { + "text": "This should, if, if life is right, we should get U, which I don't yet know, U I don't yet know, sigma, I do now know." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk0.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..fd25ea0818dacffdd5bd1cff722aaf7d067f8f16 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay." + }, + { + "text": "This is the lecture on the singular value decomposition." + }, + { + "text": "But everybody calls it the SVD." + }, + { + "text": "So this is the final and best factorization of a matrix." + }, + { + "text": "Let me tell you what's coming." + }, + { + "text": "The factors will be orthogonal matrix, diagonal matrix, orthogonal matrix." + }, + { + "text": "So it's things that we've seen before, these special good matrices, orthogonal, diagonal." + }, + { + "text": "The new point is that we need two orthogonal matrices." + }, + { + "text": "A can be any matrix whatsoever." + }, + { + "text": "Any matrix whatsoever has this singular value decomposition." + }, + { + "text": "So a diagonal one in the middle, but I need two different, probably different, orthogonal matrices to be able to do this." + }, + { + "text": "Okay." + }, + { + "text": "And this factorization has jumped into importance and is properly, I think, maybe the bringing together of everything in this course." + }, + { + "text": "One thing we'll bring together is, like, the very good family of matrices that we just studied." + }, + { + "text": "Symmetric positive definite." + }, + { + "text": "Do you remember the story with those guys?" + }, + { + "text": "Because they were symmetric, their eigenvectors were orthogonal, so I could produce an orthogonal matrix." + }, + { + "text": "This is my usual one." + }, + { + "text": "My usual one is the eigenvectors and eigenvalues." + }, + { + "text": "In the symmetric case, the eigenvectors are orthogonal, so I've got the good, my ordinary S has become a especially good Q, and positive definite, my ordinary lambda has become a positive lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk1.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..7e27d1aa155a8c107e4e8383a665af50464268d3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So this is, that's the singular value decomposition." + }, + { + "text": "In case our matrix is symmetric positive definite, in that case, I don't need two, u and a v, one orthogonal matrix will do for both sides." + }, + { + "text": "But, so this would be no good in general, because usually the eigenvector matrix isn't orthogonal." + }, + { + "text": "So this is not what I'm, that's not what I'm after." + }, + { + "text": "I'm looking for orthogonal times diagonal times orthogonal." + }, + { + "text": "And let me show you what that means and where it comes from." + }, + { + "text": "OK. What does it mean?" + }, + { + "text": "You remember the picture of any linear transformation." + }, + { + "text": "This was, like, the most important figure in 1806." + }, + { + "text": "And what am I looking for now?" + }, + { + "text": "A typical vector in the row space, typical vector, let me call it v1, gets taken over to some vector in the column space, say u1." + }, + { + "text": "So u1 is a v1." + }, + { + "text": "OK. Now, another vector gets taken over here somewhere." + }, + { + "text": "What am I looking for?" + }, + { + "text": "In this SVD, this singular value decomposition, what I'm looking for is an orthogonal basis here that gets knocked over into an orthogonal basis over there." + }, + { + "text": "See, that's pretty special, to have an orthogonal basis in the row space that goes over into an orthogonal basis, so this is like a right angle and this is a right angle, into an orthogonal basis in the column space." + }, + { + "text": "So that's our goal, is to find -- you see how things are coming together." + }, + { + "text": "First of all, can I find an orthogonal basis for this row space?" + }, + { + "text": "Of course." + }, + { + "text": "No big deal to find an orthogonal basis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk10.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..0179b0117bf00f95a1b04b6b86a542ce8f0c3b70 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "What's sigma?" + }, + { + "text": "So I'm looking for U sigma V transpose." + }, + { + "text": "U, the diagonal guy, and V transpose." + }, + { + "text": "Okay." + }, + { + "text": "Let's just see that come out right." + }, + { + "text": "So what's, what are the, what are the sigmas?" + }, + { + "text": "They're the square roots of these things." + }, + { + "text": "So square root of thirty-two and square root of eighteen." + }, + { + "text": "Zero, zero." + }, + { + "text": "Okay." + }, + { + "text": "What are the Vs?" + }, + { + "text": "They're these two." + }, + { + "text": "And I have to transpose, maybe that, maybe that just leaves me with one, with one over square root of two in that row, and the other one is one over square root of two minus one over square root of two." + }, + { + "text": "Now, finally, I've got to know the Us." + }, + { + "text": "Well, actually, one way to do, since I now know all the other pieces, I could put those together and figure out what the Us are." + }, + { + "text": "But let me do it the A A transpose way." + }, + { + "text": "Okay, find the Us now." + }, + { + "text": "U1 and U2." + }, + { + "text": "And what are they?" + }, + { + "text": "I look at A A transpose, so A is supposed to be U sigma V transpose, and then when I transpose that, I get V sigma transpose U transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk11.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..96d6a665ffcc93fda55a75d250402ff8f7417df8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I'm just doing it in the opposite order, A times A transpose, and what's the good part here?" + }, + { + "text": "That in the middle, V transpose V is going to be the identity." + }, + { + "text": "So this is just U sigma sigma transpose, that's some diagonal matrix with sigma squareds and U transpose." + }, + { + "text": "So what am I seeing here?" + }, + { + "text": "I'm seeing here, again, a symmetric positive definite or at least semi-definite matrix, and I'm seeing its eigenvectors and its eigenvalues." + }, + { + "text": "So if I compute A A transpose, its eigenvectors will be the things that go into U." + }, + { + "text": "Okay, so I need to compute A A transpose." + }, + { + "text": "I guess I'm going to have to go -." + }, + { + "text": "Let me, can I move that up just a little, maybe a little more, and do A A transpose." + }, + { + "text": "So what's A?" + }, + { + "text": "Four, four, minus three and three." + }, + { + "text": "And what's A transpose?" + }, + { + "text": "Four, four, minus three and three." + }, + { + "text": "And when I do that multiplication, I get, what do I get?" + }, + { + "text": "Sixteen and sixteen, thirty-two." + }, + { + "text": "That one comes out zero." + }, + { + "text": "Oh, so this is a lucky case, and that one comes out eighteen." + }, + { + "text": "So this is, like, an accident, that A A transpose happens to come out diagonal, so we know easily its eigenvectors and eigenvalues." + }, + { + "text": "So its eigenvectors are, what's the first eigenvector for this A A transpose matrix?" + }, + { + "text": "It's just one zero, and when I do that multiplication, I get thirty-two times one zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk12.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..3bea51beac69b154780aa5b76ef1f4e76eb0490c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the other eigenvector is just zero one, and when I multiply by that, I get eighteen." + }, + { + "text": "So this is A A transpose, multiplying that gives me the thirty-two A A transpose, multiplying this guy gives me eighteen." + }, + { + "text": "First of all, I got thirty-two and eighteen again." + }, + { + "text": "Am I surprised?" + }, + { + "text": "Yeah, it's clearly not an accident." + }, + { + "text": "The eigenvalues of A A transpose were exactly the same as the eigenvalues of this one was A transpose A." + }, + { + "text": "That's no surprise at all." + }, + { + "text": "The eigenvalues of A B are same as the eigenvalues of B A." + }, + { + "text": "The order, that's a very nice fact, that eigenvalues stay the same if I switch the order of multiplication." + }, + { + "text": "So no surprise to see thirty-two and eighteen." + }, + { + "text": "What I learned, first I checked that things were numerically correct, but now I've learned these eigenvectors, and actually they're about as nice as can be." + }, + { + "text": "They're the best orthogonal matrix, just the identity." + }, + { + "text": "Okay." + }, + { + "text": "So my claim is that it ought to all fit together." + }, + { + "text": "That this numeri- this, these numbers should come out right." + }, + { + "text": "The numbers should come out right because the, the, matrix multiplications use the properties that we want." + }, + { + "text": "Okay." + }, + { + "text": "So we just check that." + }, + { + "text": "Here's the identity, so not doing anything." + }, + { + "text": "Square root of thirty-two is multiplying that row, so that's square root of thirty-two divided by square root of two means square root of sixteen, four." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk13.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..a104483771ba144bbf5e80f6d0432de06fbabe37 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Correct?" + }, + { + "text": "And square root of eighteen is divided by square root of two, so that leaves me square root of nine, which is three, but no, Professor Strang, you see the problem." + }, + { + "text": "Why is that?" + }, + { + "text": "Okay." + }, + { + "text": "Why am I getting minus three three here, and here I'm getting three minus three?" + }, + { + "text": "Phooey." + }, + { + "text": "I don't know why." + }, + { + "text": "It shouldn't have happened, but it did." + }, + { + "text": "Now, okay, you could say, well, just, the eigenvector there could have, I could have had the minus sign here for that eigenvector, but I'm not happy about that." + }, + { + "text": "Hm." + }, + { + "text": "Okay." + }, + { + "text": "Okay." + }, + { + "text": "So I realize there's a little catch here somewhere, and I may not see it until Wednesday, which then gives you a very important reason to come back on Wednesday, to catch that sign difference." + }, + { + "text": "So what did I do illegally?" + }, + { + "text": "I think I put the eigenvectors in that matrix V transpose." + }, + { + "text": "Okay, I'm going to have to think, why did that come out, with the opposite sign?" + }, + { + "text": "So you see, I mean, if I had a minus there, I would be all right, but I don't want that." + }, + { + "text": "I want positive entries down the diagonal of sigma squared." + }, + { + "text": "Okay." + }, + { + "text": "It'll come to me, but I'm going to leave this example to finish." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk14.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..6271feb6ec2eed0c67666d8fdac07717f2b70521 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "And the beauty of, these sliding boards is, I can make that go away." + }, + { + "text": "Can I, let me not do it, though." + }, + { + "text": "Yes, let me take a second example." + }, + { + "text": "Let me take a second example where the matrix is singular." + }, + { + "text": "So rank one." + }, + { + "text": "Okay." + }, + { + "text": "So let me take as an example two, where my matrix A is going to be rectangular again." + }, + { + "text": "Let me just make it four three eight six." + }, + { + "text": "Okay." + }, + { + "text": "That's a rank one matrix." + }, + { + "text": "So that has a null space and only a one-dimensional row space and column space." + }, + { + "text": "So actually, my picture becomes easy for this matrix, because what's my columns, my row space for this one?" + }, + { + "text": "So this is two by two, so my pictures are both two dimensional." + }, + { + "text": "My row space is all multiples of vector four three." + }, + { + "text": "So the whole, the row space is just a line, right?" + }, + { + "text": "That's the row space." + }, + { + "text": "And the null space, of course, is the perpendicular line." + }, + { + "text": "So the row space for this matrix is multiples of four three." + }, + { + "text": "Typical row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk15.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..247a2fb607840b5c46901a1736533537c0de9d60 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "What's the column space?" + }, + { + "text": "The columns are all multiples of four eight, three six, one two." + }, + { + "text": "The column space, then, goes in, like, this direction." + }, + { + "text": "So the column space, when I look at those columns, the column space, it was only one dimensional, because the rank is one." + }, + { + "text": "It's multiples of four eight." + }, + { + "text": "Okay." + }, + { + "text": "And what's the null space of A transpose?" + }, + { + "text": "It's the perpendicular guy." + }, + { + "text": "There's the, so this was the null space of A, and this is the null space of A transpose." + }, + { + "text": "Okay." + }, + { + "text": "What I want to say here is that the, that choosing these orthogonal bases for the row space and the column space is, like, no problem." + }, + { + "text": "They're only one dimensional." + }, + { + "text": "So what should v be?" + }, + { + "text": "v should be v1, but, yeah, v1, rather." + }, + { + "text": "v1 is supposed to be a unit vector." + }, + { + "text": "There's only one v1 to choose here, only one dimension in the row space." + }, + { + "text": "I just want to make it a unit vector." + }, + { + "text": "So v1 will be, it'll be this vector, but made into a unit vector, so four, point eight, point six." + }, + { + "text": "Four fifths, three fifths." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk16.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..9ebd9d5b85dc5cf2ad0e297580201c57ae64e6f6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what will be u1?" + }, + { + "text": "u1 will be the unit vector there, so I want to turn four eight or one two into a unit vector, so u1 will be, let's see, if it's one two, then what multiple of one two do I want?" + }, + { + "text": "That has length square root of five, so I have to divide by square root of five." + }, + { + "text": "Let me complete the singular value decomposition for this matrix." + }, + { + "text": "So this matrix, four three eight six, is, so I know what u1, here's A, and I want to get u, the basis in the column space, and it has to start with this guy." + }, + { + "text": "One over square root of five, two over square root of five." + }, + { + "text": "Then I want the sigma." + }, + { + "text": "OK. What are we expecting now for sigma?" + }, + { + "text": "Where is, this is only a rank one matrix, we're only expecting a sigma one, which I have to find, but zero's here." + }, + { + "text": "OK, so what's sigma one?" + }, + { + "text": "We should see it, it should be the, where did these sigmas come from?" + }, + { + "text": "They came from A transpose A, so I, can I do that little calculation over here?" + }, + { + "text": "A transpose A is four three, four three eight six times four three eight six." + }, + { + "text": "This had better, this is a rank one matrix, this is going to be, the whole thing will have rank one, that's sixteen and sixty four is eighty, twelve and forty eight is sixty, twelve and forty eight is sixty, nine and thirty six is forty five." + }, + { + "text": "OK." + }, + { + "text": "It's a rank one matrix." + }, + { + "text": "Of course." + }, + { + "text": "Every row is a multiple of four three." + }, + { + "text": "And what's the eigen, what are the eigenvalues of that matrix?" + }, + { + "text": "So this is like, the calculation is like practicing now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk17.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..b48a4d8f19e69f562ef2b2b5013cd6a113ef2e4d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "What are the eigenvalues of this rank one matrix?" + }, + { + "text": "Well, tell me one eigenvalue, since the rank is only one, one eigenvalue is going to be zero." + }, + { + "text": "And then you know that the other eigenvalue is going to be a hundred and twenty five." + }, + { + "text": "So that's sigma squared, right, in A transpose A." + }, + { + "text": "So this will be the square root of a hundred and twenty five." + }, + { + "text": "And then finally, the V transpose, the Vs will be, there's V1, and what's V2?" + }, + { + "text": "What's V2 in the, what's, how do I make this into a orthonormal basis?" + }, + { + "text": "Well, V2 is in the null space direction." + }, + { + "text": "It's perpendicular to that, so point six and minus point eight." + }, + { + "text": "So those are the Vs that go in here." + }, + { + "text": "Point eight, point six, and point six minus point eight." + }, + { + "text": "OK. And I guess I better finish this guy." + }, + { + "text": "So this guy, all I want is to complete the orthonormal basis." + }, + { + "text": "It'll be coming from there, it'll be a two over square root of five and a minus one over square root of five." + }, + { + "text": "I could have take, let me take square root of five out of that matrix to make it look better." + }, + { + "text": "So one over square root of five times one, one, two, two, minus one." + }, + { + "text": "OK." + }, + { + "text": "So there I have, including the square root of five, that's an orthogonal matrix, that's an orthogonal matrix, that's a diagonal matrix, and its rank is only one." + }, + { + "text": "And now if I do that multiplication, I pray that it comes out right." + }, + { + "text": "The square root of five will cancel into that square root of one twenty-five and leave me with the square root of twenty-five, which is five, and five will multiply these numbers and I'll get whole numbers and out will come A. OK. That's a second, like, a second example showing how the null space guy, so this, this vector and the, and this one were multiplied by this zero, so they, they were easy to deal with." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk18.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..fe0c1e2162590b6461e7e5aa30c5f31ab402b16a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "It was the key ones are the ones in the column space and the row space." + }, + { + "text": "Do you see how I'm getting columns here, diagonal here, rows here, coming together to produce A?" + }, + { + "text": "OK. That's the singular value decomposition." + }, + { + "text": "So, let, let me think what I want to add to, to complete this topic." + }, + { + "text": "Sort of what we're really doing." + }, + { + "text": "So that's two examples." + }, + { + "text": "And now let's think what we're really doing." + }, + { + "text": "We're, we're choosing the right basis for the four subspaces of linear algebra." + }, + { + "text": "Let me, let me, let me write this down." + }, + { + "text": "So V1 up to Vr is an orthonormal basis for the row space." + }, + { + "text": "U1 up to Ur is an orthonormal basis for the column space." + }, + { + "text": "And then I just finish those out by Vr plus one, the rest up to Vn is an orthonormal basis for the null space." + }, + { + "text": "And finally, Ur plus one up to Um is an orthonormal basis for the null space of A transpose." + }, + { + "text": "Do you see that we finally got the bases right?" + }, + { + "text": "They're right because they're orthonormal and also, I mean, the, again, Graham-Schmidt would have done this in chapter four." + }, + { + "text": "Here we needed eigenvalues because these bases make the matrix diagonal." + }, + { + "text": "A times Vi is a multiple of Ui." + }, + { + "text": "So I'll put and." + }, + { + "text": "The matrix has been made diagonal." + }, + { + "text": "When we choose these bases, there's no coupling between Vs and no coupling between Us." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk19.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..ef84969ea528bd698a227de6c8007d53a10c135a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk19.json @@ -0,0 +1,32 @@ +[ + { + "text": "Each A, A times each V is in the direction of the corresponding U." + }, + { + "text": "So it's exactly the right basis for the four fundamental subspaces." + }, + { + "text": "And of course, their dimensions are what we know." + }, + { + "text": "The dimension of the row space is the rank r, and so is the dimension of the column space." + }, + { + "text": "The dimension of the null space is n minus r, that's how many vectors we need, and m minus r basis vectors for the left null space, the null space of A transpose." + }, + { + "text": "OK." + }, + { + "text": "I'm going to stop there." + }, + { + "text": "I could develop further from the SVD, but we'll see it again in the very last lectures of the course." + }, + { + "text": "There's the SVD." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk2.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..6e336773d56df67c43cd476ce2fda66a297e1c38 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Graham-Schmidt tells me how to do it." + }, + { + "text": "Start with any old basis and use- grind through Graham-Schmidt, out comes an orthogonal basis." + }, + { + "text": "But then, if I just take any old orthogonal basis, then when I multiply by A, there's no reason why it should be orthogonal over here." + }, + { + "text": "So I'm looking for this special setup where A takes these basis vectors into orthogonal vectors over there." + }, + { + "text": "Now, you might have noticed that the null space I didn't include." + }, + { + "text": "Why don't I stick that in?" + }, + { + "text": "You remember our usual figure had a little null space and a little null space." + }, + { + "text": "And, those are no problems." + }, + { + "text": "Those are- null spaces are going to show up as zeros on the diagonal of sigma, so that's not what we're- that doesn't present any difficulty." + }, + { + "text": "Our difficulty is to find the- so do you see what this will mean?" + }, + { + "text": "This will mean that A times this- these v's, v1, v2, up to- what's the dimension of this row space?" + }, + { + "text": "vr." + }, + { + "text": "Sorry, that v a little smaller." + }, + { + "text": "Up to vr." + }, + { + "text": "So that's A v1 is going to be the first column, so let me- here's what I'm- here's what I'm achieving." + }, + { + "text": "Oh, I would like- I'm not only going to make these orthogonal, but why not make them orthonormal?" + }, + { + "text": "Make them unit vectors." + }, + { + "text": "So this- maybe the unit vector is here, is the u1, and this might be a multiple of it." + }, + { + "text": "So really what's happening is A v1 is some multiple of u1, right?" + }, + { + "text": "I'm going to- these guys will be unit vectors, and they'll go over into multiples of unit vectors, and the multiple I'm not going to call lambda anymore, I'm calling it sigma." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk3.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..c34819f1e56e21a93db616f1627e90900e7c35b8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's the number- the stretching number." + }, + { + "text": "And similarly, A v2 is sigma 2 u2." + }, + { + "text": "This is what- this is my goal." + }, + { + "text": "And now I want to express that goal in matrix language." + }, + { + "text": "That's the usual step." + }, + { + "text": "Think of what you want and then express it as a matrix multiplication." + }, + { + "text": "So A v1 is sigma 1 u1." + }, + { + "text": "Actually, here we go." + }, + { + "text": "Let me pull out these u1, u2 to ur, and then a matrix with the sigmas." + }, + { + "text": "It's- everything now is going to be in this- in that, in that, little part of the blackboard." + }, + { + "text": "Do you see that this equation says what I'm trying to do with my figure?" + }, + { + "text": "A times the first basis vector should be sigma 1 times the other basis- the other first basis vector." + }, + { + "text": "These are the basis vectors in the row space, these are the basis vectors in the column space, and these are the multiplying factors." + }, + { + "text": "So A v2 is sigma 2 times u2, A vr is sigma r times ur." + }, + { + "text": "And then we've got a whole lot of zeros and maybe some zeros at the end, but this is- that's the heart of it." + }, + { + "text": "And now if I express that in- as matrices, because you knew that was coming, that's what I have." + }, + { + "text": "So this is my goal." + }, + { + "text": "To find an orthogonal basis in the rows- orthonormal, even, basis in the row space, and an orthonormal basis in the column space, so that I'm sort of diagonalized the matrix." + }, + { + "text": "The matrix A is like getting converted to this diagonal matrix sigma." + }, + { + "text": "And you notice that usually I have to do- I have to allow myself two different bases." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk4.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..191e383650177ee1c7a8b51ce0359c195d9afdec --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "My little comment about symmetric positive definite was the one case where it's A q equal q sigma, where v and u are the same q." + }, + { + "text": "But mostly, I'm going to take a matrix like, oh, let me take a matrix like four four minus three three." + }, + { + "text": "Okay." + }, + { + "text": "There's a two by two matrix." + }, + { + "text": "It's invertible, so it has rank two." + }, + { + "text": "So I'm going to look for two vectors, v1 and v2, in the row space, and u- so I'm going to look for v1 v2 in the row space, which of course is R2." + }, + { + "text": "And I'm going to look for u1 u2 in the column space, which of course is also R2." + }, + { + "text": "And I'm going to look for numbers sigma 1 and sigma 2, so that it all comes out right." + }, + { + "text": "So these guys are orthonormal." + }, + { + "text": "These guys are orthonormal, and these are the scaling factors." + }, + { + "text": "So I'll do that example as soon as I get the matrix picture straight." + }, + { + "text": "Okay." + }, + { + "text": "Do you see that this expresses what I want?" + }, + { + "text": "Can I just say two words about null spaces?" + }, + { + "text": "If we have -- if there's some null space, then we've got- we want to stick in a basis for those, for that." + }, + { + "text": "So here comes a basis for the null space, v R plus one down to vn." + }, + { + "text": "So if we only had an R-dimensional row space and the other n minus R dimensions were in the null space, okay, we'll take an orthogonal- orthonormal basis there, no problem." + }, + { + "text": "And then we'll just get zeros." + }, + { + "text": "So actually, those zeros will come out from the- on the diagonal matrix." + }, + { + "text": "So I'll complete that to, to, orthonormal basis for the whole space, Rn." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk5.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..8d6aafa6aa98e697236b4b5cd884684c97d6a470 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "I complete this to an orthonormal basis for the whole space, Rn, and I complete that with zeros." + }, + { + "text": "Null spaces are no problem here." + }, + { + "text": "So really, the true problem is in a matrix like that, which isn't symmetric, so I can't use its eigenvectors, they're not orthogonal, but somehow I have to get these orthogonal, in fact, orthonormal guys that make it work." + }, + { + "text": "I have to find this, these orthonormal guys, these orthonormal guys, and I want A v1 to be sigma 1 u1, and A v2 to be sigma 2 u2." + }, + { + "text": "Okay." + }, + { + "text": "That's my goal." + }, + { + "text": "Here's, here's the, matrices that are going to get me there." + }, + { + "text": "Now, these are orthogonal matrices." + }, + { + "text": "I can put that, if I multiply on both sides by v inverse, I have A equals u sigma v inverse, and of course, you know the other way I can write v inverse." + }, + { + "text": "This is one of those square orthogonal matrices, so it's the same as u sigma v transpose." + }, + { + "text": "Okay." + }, + { + "text": "Here's my problem." + }, + { + "text": "I've got two orthogonal matrices here, and I don't want to find them both at once." + }, + { + "text": "So I want to cook up some expression that will make the u's disappear." + }, + { + "text": "I would like to make the u's disappear and leave me only with the v's." + }, + { + "text": "And here's how to do it." + }, + { + "text": "It's, it's the same combination that keeps showing up whenever we have a general rectangular matrix, then it's A transpose A, that's the great matrix." + }, + { + "text": "That's the great matrix." + }, + { + "text": "That's the matrix that's symmetric." + }, + { + "text": "And, in fact, positive definite or at least positive semidefinite." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk6.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..df7b3f09adc2388b2ce3ad477bb1b91bf8d74d84 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "This is the matrix with nice properties." + }, + { + "text": "So let's see what will it be." + }, + { + "text": "So if I took the transpose, then, I would have A transpose A will be what?" + }, + { + "text": "What do I have?" + }, + { + "text": "If I transpose that, I have v sigma transpose u transpose, that's, that's the A transpose." + }, + { + "text": "Now the A." + }, + { + "text": "And what have I got?" + }, + { + "text": "Looks like worse, because it's got six things now together, but it's going to collapse into something good." + }, + { + "text": "What does u transpose u collapse into?" + }, + { + "text": "I." + }, + { + "text": "The identity." + }, + { + "text": "So that's the key point." + }, + { + "text": "This is the identity and we don't have u anymore." + }, + { + "text": "And sigma transpose times sigma, those are diagonal matrices." + }, + { + "text": "So their product is just going to have sigma squareds on the diagonal." + }, + { + "text": "So do you see what we've got here?" + }, + { + "text": "This is v times this easy matrix, sigma one squared, sigma two squared, times v transpose." + }, + { + "text": "This is the A transpose A." + }, + { + "text": "This is, let me copy down, A transpose A is that." + }, + { + "text": "U's are out of the picture now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk7.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..bff98ae0a99f2983b0755af21ee925990c6fab2c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'm only having to choose the v's." + }, + { + "text": "And what are these v's?" + }, + { + "text": "And what are these sigmas?" + }, + { + "text": "Do you know what the v's are?" + }, + { + "text": "They're the eigenvectors." + }, + { + "text": "See, this is a perfect eigenvector, eigenvalue, Q lambda Q transpose for the matrix A transpose A." + }, + { + "text": "A itself is like nothing special." + }, + { + "text": "But A transpose A will be special." + }, + { + "text": "It'll be symmetric, positive, definite." + }, + { + "text": "So this'll be its eigenvectors and this'll be its eigenvalues." + }, + { + "text": "And the eigenvalues will be positive because this thing's positive definite." + }, + { + "text": "Can I just now so this is my method." + }, + { + "text": "This tells me what the v's are and how am I going to find the u's?" + }, + { + "text": "Well, one way would be to look at A A transpose." + }, + { + "text": "Put, multiply A by A transpose in the opposite order." + }, + { + "text": "That will stick the v's in the middle, knock them out, and leave me with the u's." + }, + { + "text": "So here's the overall picture, then." + }, + { + "text": "The v's are the eigenvectors of A transpose A." + }, + { + "text": "The u's are the eigenvectors of A A transpose, which are different." + }, + { + "text": "And the sigmas are the square roots of these and the positive square roots, so we have positive sigmas." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk8.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..cb5b25b4a97f60e6bc1aa3c42941190d5c2e5b99 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me do that for that example." + }, + { + "text": "This is really what you should know and be able to do for, the SVD." + }, + { + "text": "Okay." + }, + { + "text": "Let me take that matrix." + }, + { + "text": "So what's my first step?" + }, + { + "text": "Compute A transpose A, because I want its eigenvectors." + }, + { + "text": "Okay, so I have to compute A transpose A." + }, + { + "text": "So A transpose is four four minus three three, and A is four four minus three three." + }, + { + "text": "And I do that multiplication and I get sixteen, I get twenty-five, I get sixteen minus nine, is that seven?" + }, + { + "text": "And it better come out symmetric and, oh, okay, and then it comes out twenty-five." + }, + { + "text": "Okay." + }, + { + "text": "So I want its eigenvectors and its eigenvalues." + }, + { + "text": "Its eigenvectors will be the v's, its eigenvalues will be the squares of the sigmas." + }, + { + "text": "Okay." + }, + { + "text": "What are the eigenvalues and eigenvectors of this guy?" + }, + { + "text": "Have you seen that two by two example enough to recognize that the eigenvectors are, that one one is an eigenvector?" + }, + { + "text": "So this is, here is A transpose A. I'm looking for its eigenvectors." + }, + { + "text": "So its eigenvectors, I think, are one one and one minus one." + }, + { + "text": "Because if I multiply that matrix by one one, what do I get?" + }, + { + "text": "If I multiply that matrix by one one, I get thirty-two thirty-two." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk9.json b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..15f3f793471c1b5693d2cfa38e670c0a75251236 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/TX_vooSnhm8_8_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So which is thirty-two of one one." + }, + { + "text": "So there's the first eigenvector." + }, + { + "text": "And there's the eigenvalue for A transpose A, so I'm going to take its square root in the, for sigma." + }, + { + "text": "Okay." + }, + { + "text": "What's the eigenvector that goes, eigenvalue that goes with this one?" + }, + { + "text": "If I do that multiplication, what do I get?" + }, + { + "text": "I get some multiple of one minus one." + }, + { + "text": "And what is that multiple?" + }, + { + "text": "Looks like eighteen." + }, + { + "text": "Okay." + }, + { + "text": "So those are the two eigenvectors." + }, + { + "text": "But, oh, just a moment, I didn't normalize them." + }, + { + "text": "To, to make everything absolutely right, I ought to normalize these eigenvectors, divide by their length, square root of two." + }, + { + "text": "So all these guys should be true unit vectors, and, of course, that normalization didn't change the thirty-two and the eighteen." + }, + { + "text": "Okay." + }, + { + "text": "So I'm happy with the Vs, here are the Vs, so now let me put together the, the, the pieces here." + }, + { + "text": "Here's my A." + }, + { + "text": "Here's my A." + }, + { + "text": "Let me, let me write down A again." + }, + { + "text": "This should, if, if life is right, we should get U, which I don't yet know, U I don't yet know, sigma, I do now know." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk0.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..e6499639a2dd486fc34915743508e989029de764 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "Today we are going to see how to use what we saw last time about partial derivatives to handle minimization or maximization problems involving functions of several variables." + }, + { + "text": "Remember last time we said that when we have a function, say, of two variables, x and y, then we have actually two different derivatives." + }, + { + "text": "Partial f, partial x, also called f sub x, is the derivative with respect to x keeping y constant." + }, + { + "text": "And we have partial f, partial y, also called f sub y, where we vary y and we treat x as a constant." + }, + { + "text": "And now, one thing I didn't have time to tell you about, but hopefully you heard about in recitation yesterday, is the approximation formula that tells you what happens if you vary both x and y. F sub x tells us what happens if we change x a little bit by some small amount delta x. F sub y tells us how f changes if we change y by a small amount delta y." + }, + { + "text": "If we do both at the same time, then the two effects will add up with each other." + }, + { + "text": "Because you can imagine that first you will change x and then you will change y or the other way around." + }, + { + "text": "It doesn't really matter." + }, + { + "text": "If we change x by a certain amount delta x, and if we change y by the amount delta y, and let's say that we have z equals f of x, y, then that changes by an amount which is approximately f sub x times delta x plus f sub y times delta y." + }, + { + "text": "And that is one of the most important formulas about partial derivatives." + }, + { + "text": "The intuition for this, again, is just the two effects add up." + }, + { + "text": "If I change x by a small amount and then I change y, well, first changing x will modify f. How much does it modify f?" + }, + { + "text": "The answer is the rate of change." + }, + { + "text": "The rate of change is f sub x." + }, + { + "text": "And, if I change y, then the rate of change of f when I change y is f sub y." + }, + { + "text": "All together, I get this change in the value of f. And, of course, that is only an approximation formula." + }, + { + "text": "Actually, there would be higher order terms involving second and third derivatives and so on." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk1.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..24332c5f071c389023f7abaf7259fb1a63c23f92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "One way to justify this, sorry, I was distracted by a microphone problem." + }, + { + "text": "OK, so how do we justify this formula?" + }, + { + "text": "Well, one way to think about it is in terms of tangent plane approximation." + }, + { + "text": "Let's think about the tangent plane to the graph of a function f. I have some pictures to show you." + }, + { + "text": "It will be easier if I show the pictures." + }, + { + "text": "Remember, partial f over partial x was obtained by looking at the situation where y is held constant." + }, + { + "text": "That means I am slicing the graph of f by a plane that is parallel to the xz plane." + }, + { + "text": "And then, when I change x, z changes." + }, + { + "text": "And the slope of that is going to be the derivative with respect to x." + }, + { + "text": "Now, if I do the same in the other direction, then I will have similarly the slope in a slice now parallel to the yz plane that will be partial f over partial y." + }, + { + "text": "In fact, in each case I have a line." + }, + { + "text": "And that line is tangent to the surface." + }, + { + "text": "Now, if I have two lines tangent to the surface, well, then together they determine for me the tangent plane to the surface." + }, + { + "text": "Let's try to see how that works." + }, + { + "text": "We know that f sub x and f sub y are the slopes of two tangent lines to this plane, sorry, two tangent lines to the graph." + }, + { + "text": "And let's write down the equations of these lines." + }, + { + "text": "I am not going to write parametric equations." + }, + { + "text": "I am going to write them in terms of x, y, z coordinates." + }, + { + "text": "Let's say that partial f over partial x at a given point is equal to a." + }, + { + "text": "Then that means that we have a line given by the following conditions." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk10.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..04a9beb08f73a15fd9091546cca18b48afb0c0c0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, of course, here I was very lucky." + }, + { + "text": "In general, I could not expect things to simplify that much." + }, + { + "text": "In fact, I cheated." + }, + { + "text": "I started from that." + }, + { + "text": "I expanded." + }, + { + "text": "And then that is how I got my example." + }, + { + "text": "The general method will be a bit different, but you will see it will actually also involve completing squares." + }, + { + "text": "Just there is more to it than what we have seen." + }, + { + "text": "We will come back to this tomorrow." + }, + { + "text": "How do I know that this equals?" + }, + { + "text": "y is what negative one?" + }, + { + "text": "How do I know that that whole function is greater or equal to negative one?" + }, + { + "text": "Well, I wrote f of x, y as something squared plus 2y2 minus one." + }, + { + "text": "This squared is always a positive number, non-negative." + }, + { + "text": "It is a square." + }, + { + "text": "The square of something is always non-negative." + }, + { + "text": "Similarly, y2 is also always non-negative." + }, + { + "text": "If you add something that is at least zero plus something that is at least zero and you subtract one, you get always at least minus one." + }, + { + "text": "And, in fact, the only way that you can get minus one is if both of these guys are zero at the same time." + }, + { + "text": "That is how I get my minimum." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk11.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..f4eced0dcd7ffc5bdcf9cd95cd7f63aa34e4a4ac --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "More about this tomorrow." + }, + { + "text": "In fact, what I would like to tell you about now instead is a nice application of min-max problems that maybe you don't think of as a min-max problem." + }, + { + "text": "But you will see, I mean, you don't think of it that way because probably your calculator can do it for you." + }, + { + "text": "Or, if not, your computer can do it for you." + }, + { + "text": "But it is actually something where the theory is based on minimization in two variables." + }, + { + "text": "Very often in experimental sequences you have to do something called least squares interpolation." + }, + { + "text": "And what is that about?" + }, + { + "text": "Well, it is the idea that maybe you do some experiments and you record some data." + }, + { + "text": "You have some data x and some data y." + }, + { + "text": "And I don't know, maybe, for example, maybe you are measuring frogs and you are trying to measure how big the frog leg is compared to the eyes of a frog or whatever, or trying to measure something." + }, + { + "text": "And if you are doing chemistry then it could be how much you put of some reactant and how much of the output product that you wanted to synthesize is going to be the same." + }, + { + "text": "All sorts of things." + }, + { + "text": "Make up your own example." + }, + { + "text": "You measure, basically, for various values of x what the value of y ends up being." + }, + { + "text": "And then you would like to claim, oh, well, these points are kind of aligned." + }, + { + "text": "I mean, of course, to a mathematician they are not aligned, but to an experimental scientist that is evidence that there is a relation between the two." + }, + { + "text": "And so you want to claim, and in your paper you will actually draw a nice little line that says, C, these two functions depend linearly on each other." + }, + { + "text": "The question is how do we come up with that nice line that passes smack in the middle of the points?" + }, + { + "text": "The question is, given experimental data, xiyi, so maybe I should actually be more precise." + }, + { + "text": "You are given some experimental data." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk12.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..ec058dcefcf28c0e3655b8df350c1a7550b31989 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "You have data points x1, y1, x2, y2, and so on, xn, yn." + }, + { + "text": "The question would be find the best fit line of the form y equals ax plus b that somehow approximates very well this data." + }, + { + "text": "You can also use that, by the way, to predict various things." + }, + { + "text": "For example, if you look at your new homework, actually the first problem asks you to predict how many iPods will be on this planet in ten years, looking at past sales and how they behave." + }, + { + "text": "One thing, by the way, before you lose all the money you don't have yet, you cannot use that to predict the stock market." + }, + { + "text": "Don't try to use that to make money." + }, + { + "text": "It doesn't work." + }, + { + "text": "One tricky thing here that I want to draw your attention to is what are the unknowns here?" + }, + { + "text": "The natural answer would be to say the unknowns are x and y." + }, + { + "text": "That is not actually the case." + }, + { + "text": "We are not trying to solve for some x and y. I mean we have some values given to us." + }, + { + "text": "And when we are looking for that line we don't really care about a particular value of x." + }, + { + "text": "What we care about is actually these coefficients a and b that will tell us what the relation between x and y is." + }, + { + "text": "In fact, we are trying to solve for a and b that will give us the nicest possible line for these points." + }, + { + "text": "The unknowns in our equations will have to be a and b, not x and y." + }, + { + "text": "The question really is find the best a and b." + }, + { + "text": "And, of course, we have to decide what we mean by best." + }, + { + "text": "Best will mean that we minimize some function of a and b that measures the total error that we are making when we are choosing this line compared to the experimental data." + }, + { + "text": "Maybe, roughly speaking, it should measure how far these points are from the line." + }, + { + "text": "But now there are various ways to do it." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk13.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..5d2475feee1af92e7e44b93eafd8ef1a1aeab556 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "And some of them are, I mean a lot of them are valid to give you different answers." + }, + { + "text": "You have to decide what it is that you prefer." + }, + { + "text": "For example, you could measure the distance to the line by projecting perpendicularly." + }, + { + "text": "Or, you could measure instead the difference between, for a given value of x, the difference between the experimental value of y and the predicted one." + }, + { + "text": "And that is often more relevant because these guys are actually maybe expressed in different units." + }, + { + "text": "They are not the same type of quantity." + }, + { + "text": "You cannot actually combine them arbitrarily." + }, + { + "text": "Anyway, the convention is usually we measure distance in this way." + }, + { + "text": "Next, you could try to minimize the largest distance." + }, + { + "text": "Say we look at where is the largest error and we make that the smallest possible." + }, + { + "text": "The drawback of doing that is experimentally very often you have one data point that is not good because maybe you fell asleep in front of the experiment." + }, + { + "text": "And so you did not measure the right thing." + }, + { + "text": "You tend to want to not give too much importance to some data point that is far away from the others." + }, + { + "text": "Maybe instead you want to measure the average distance." + }, + { + "text": "Or maybe you want to actually give more weight to things that are further away." + }, + { + "text": "And then you do not want to do the distance but the square of the distance." + }, + { + "text": "There are various possible answers." + }, + { + "text": "But one of them gives us a particularly nice formula for a and b." + }, + { + "text": "And so that is why it is the universally used one." + }, + { + "text": "Here it says least squares." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk14.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..03f389ad03cba30ec35302a03113c11b9ae12887 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That is because we will measure, actually, the sum of the squares of the errors." + }, + { + "text": "And why do we do that?" + }, + { + "text": "Well, part of it is because actually it looks good." + }, + { + "text": "I mean, when you see these plots in scientific papers, they really look like the line is indeed the ideal line." + }, + { + "text": "And the second reason is because actually the minimization problem that we will get is particularly simple, well-proposed and it is easy to solve." + }, + { + "text": "We will have a nice formula for the best a and the best b." + }, + { + "text": "If you have a method that is simple and gives you a good answer then that is probably the good one." + }, + { + "text": "We have to define best." + }, + { + "text": "And here it is in the sense of defining a total square error." + }, + { + "text": "Maybe I should say total square deviation." + }, + { + "text": "What do I mean by that?" + }, + { + "text": "The deviation for each data point is the difference between what you have measured and what you are predicting by your model." + }, + { + "text": "That is the difference between the two." + }, + { + "text": "Now what we will do is try to minimize the function capital D, which is just the sum for all the data points of the square of the deviation." + }, + { + "text": "Let me emphasize again this is a function of a and b. I mean, of course, there are a lot of letters in here." + }, + { + "text": "But xi and yi in real life will be numbers given to you." + }, + { + "text": "They will be the numbers that you have measured." + }, + { + "text": "You have measured all of this data." + }, + { + "text": "They are just going to be numbers." + }, + { + "text": "You put them in there and you get the answer." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk15.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..574ce46fe50beb8d2adc71dc4ba061053cadb260 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Any questions?" + }, + { + "text": "How do we minimize this function of a and b?" + }, + { + "text": "Let's use our new knowledge." + }, + { + "text": "Let's actually look for a critical point." + }, + { + "text": "We want to solve for partial d over partial a equals zero and partial d over partial b equals zero." + }, + { + "text": "That is how we look for critical points." + }, + { + "text": "Let's take the derivative of a." + }, + { + "text": "Well, the derivative of a sum is the sum of the derivatives." + }, + { + "text": "And now we have to take the derivative of this quantity squared." + }, + { + "text": "Remember how we take the derivative of a square." + }, + { + "text": "We take twice this quantity times the derivative of what we are squaring." + }, + { + "text": "We will get two times minus y i, sorry, y i minus a xi plus b times the derivative of this with respect to a." + }, + { + "text": "What is the derivative of this with respect to a?" + }, + { + "text": "Negative xi, exactly." + }, + { + "text": "And so we will want this to be zero." + }, + { + "text": "And partial d over partial b, we do the same thing but differentiating with respect to b instead of with respect to a." + }, + { + "text": "Again, sum of squares twice y i minus a xi plus b times the derivative of this with respect to b is, I think, negative one." + }, + { + "text": "That is the equations we have to solve." + }, + { + "text": "Well, let's reorganize this a little bit." + }, + { + "text": "The first equation, see, there are a's and there are b's in these equations." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk16.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..6dbbcdfd1a44915f775e513934285605a93fde83 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "I am going to just look at the coefficients of a and b." + }, + { + "text": "If you have good eyes, you can see probably that these are actually linear equations in a and b." + }, + { + "text": "There is a lot of clutter with all these x's and y's all over the place." + }, + { + "text": "Let's actually try to expand things and make that more apparent." + }, + { + "text": "The first thing I will do is I will actually get rid of these factors of two that are just not very important." + }, + { + "text": "I can simplify things by two." + }, + { + "text": "And next I am going to look at the coefficient of a. I will get basically a times xi squared." + }, + { + "text": "Well, let me just do it and it should be clear." + }, + { + "text": "I claim when we simplify this we get a times xi squared plus xi times b minus xi yi." + }, + { + "text": "And we set this equal to zero." + }, + { + "text": "Do you agree that this is what we get when we expand that product?" + }, + { + "text": "No?" + }, + { + "text": "OK, let's do the other one." + }, + { + "text": "We just multiply by minus one." + }, + { + "text": "We take the opposite of that." + }, + { + "text": "It will be axi plus b. I will write that as xia plus b minus yi." + }, + { + "text": "And let me just reorganize that by actually putting all the a's together." + }, + { + "text": "That means actually I will have sum of all the xi squared times xi times b minus sum of xi yi equals zero." + }, + { + "text": "If I rewrite this it becomes sum of xi squared times a plus sum of the xi's times b minus, let me move the other guys to the other side, equals sum of xi yi." + }, + { + "text": "And that one becomes sum of xi times a plus how many b's do I get from this one?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk17.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..46c92ceb193fbddba6ccd0128c8434e1fa895b6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, I get one for each data point." + }, + { + "text": "When I sum them together I will get n. Very good." + }, + { + "text": "So, n times b equals sum of yi." + }, + { + "text": "Now, these quantities may look scary, but they are actually just numbers." + }, + { + "text": "For example, for this one you look at all your data points." + }, + { + "text": "For each of them you take the value of x and you just sum all these numbers together." + }, + { + "text": "What you get, actually, is a linear system in a two-by-two linear system." + }, + { + "text": "And so now we can solve this for a and b." + }, + { + "text": "In practice, of course, first you plug in the numbers for xi and yi and then you solve the system that you get." + }, + { + "text": "And we know how to solve two-by-two linear systems, I hope." + }, + { + "text": "That is how we find the best fit line." + }, + { + "text": "Now, why is that going to be the best one instead of the worst one?" + }, + { + "text": "We just solved for a critical point." + }, + { + "text": "That could actually be a maximum of this error function d. We will have the answer to that next time." + }, + { + "text": "But trust me, if you really want to go for the second derivative test that we will do tomorrow and apply it in this case, it is quite hard to check." + }, + { + "text": "But you can see it is actually a minimum." + }, + { + "text": "I will just say we can show that it is a minimum." + }, + { + "text": "Now, even for the linear case, it is the one that we are the most familiar with." + }, + { + "text": "Least squares interpolation actually works in much more general settings." + }, + { + "text": "Instead of fitting for the best line, if you think that there is a different kind of relation, then maybe you can fit in using a different kind of formula." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk18.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..fa2ca36c0d134e6b3372da5aa353386c01a4066b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me actually illustrate that for you." + }, + { + "text": "I don't know if you are familiar with Moore's law." + }, + { + "text": "It is something that is supposed to tell you how quickly, basically, computer chips become smarter, faster and faster over time." + }, + { + "text": "It is a law that says things about the number of transistors that you can fit onto a computer chip." + }, + { + "text": "Here I have some data about the number of transistors on a standard PC processor as a function of time." + }, + { + "text": "And, well, if you try to do the best line fit, you will see quickly that it doesn't seem to follow a linear trend." + }, + { + "text": "On the other hand, if you plot the diagram in a log scale, the log of the number of transistors as a function of time, then you get a much better line." + }, + { + "text": "And so, in fact, that means that you had an exponential relation between the number of transistors and time." + }, + { + "text": "And so, actually, that is what Moore's law says." + }, + { + "text": "It says that the number of transistors on a chip doubles, depending on the version, every 18 months or every two years." + }, + { + "text": "They keep changing the statement." + }, + { + "text": "How do we find that best exponential fit?" + }, + { + "text": "Well, an exponential fit would be something of the form y equals a constant times exponential of a times x." + }, + { + "text": "That is what we want to look at." + }, + { + "text": "Well, we could try to minimize a square error like we did earlier, but that doesn't work well at all." + }, + { + "text": "The equations that you get are very complicated." + }, + { + "text": "You cannot solve them." + }, + { + "text": "But remember what I showed you on this log plot." + }, + { + "text": "If you plot the log of y as a function of x, then suddenly it becomes a linear relation." + }, + { + "text": "Observe this is the same as ln of x equals ln of c plus ax." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk19.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..55b8384a00899de02bdae34fca68d10a37a51f56 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk19.json @@ -0,0 +1,53 @@ +[ + { + "text": "And that is a linear best fit." + }, + { + "text": "What you do is you just look for the best straight line fit for the log of y." + }, + { + "text": "That is something we already know." + }, + { + "text": "But you can also do other examples." + }, + { + "text": "For example, let's say that we have something more complicated." + }, + { + "text": "Let's say that we have actually a quadratic law." + }, + { + "text": "For example, y is of the form ax2 bx c. And, of course, you are trying to find somehow the best." + }, + { + "text": "That would mean here fitting the best parabola for your data points." + }, + { + "text": "Well, to do that you would need to find a, b and c. And now you would have actually a function of a, b and c, which would be the sum of all data points of the quadratic equation." + }, + { + "text": "And if you try to solve for critical points, now you will have three equations involving a, b and c. And, in fact, you will find a three by three linear system." + }, + { + "text": "And it works just the same way." + }, + { + "text": "Just you have a little bit more data." + }, + { + "text": "Basically, you see that these best fit problems are an example of minimization problem." + }, + { + "text": "But maybe you didn't expect to see minimization problems come in." + }, + { + "text": "But that is really the way to handle these questions." + }, + { + "text": "OK, so tomorrow we will go back to the question of how do we decide whether it is a minimum or a maximum?" + }, + { + "text": "And we will continue exploring functions of several variables." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk2.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..cbdde5612839d21f7df1c4e4a177c22a02adffc6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "I am going to keep y constant equal to y0." + }, + { + "text": "And I am going to change x." + }, + { + "text": "And, as I change x, z will change at a rate that is equal to a." + }, + { + "text": "That would be z equals z0 plus a times the change in x, x minus x0." + }, + { + "text": "That is how you would describe the line that is, I guess, the one that is plotted in green here." + }, + { + "text": "That is the intersection with the slice parallel to the xz plane." + }, + { + "text": "I hold y constant equal to y0." + }, + { + "text": "And z is a function of x that varies with a rate of a." + }, + { + "text": "And now, if I look similarly at the other slice, let's say that the partial with respect to y is equal to b, then I get another line which is obtained by the fact that z depends on y and the rate of change with respect to y will be b while x is held constant equal to x0." + }, + { + "text": "These two lines are both going to be in the tangent plane to the surface." + }, + { + "text": "They are both tangent to the surface, f of f. And, well, together they determine a plane." + }, + { + "text": "And that plane is just given by the formula z equals z0 plus a times x minus x0 plus b times y plus b." + }, + { + "text": "If you look at what happens, this is the equation of a plane, z equals constant times x plus constant times y plus constant." + }, + { + "text": "And if you look at what happens if I hold y constant and vary x, I recover the first line." + }, + { + "text": "If I hold x constant and vary y, I get the second line." + }, + { + "text": "Another way to do it, of course, would be to write actually parametric equations of these lines, get vectors along them and then take the cross-product to get the normal vector to the plane, and then get this equation for the plane using the normal vector." + }, + { + "text": "That also works and it gives you the same formula." + }, + { + "text": "If you are curious, exercise, do it again using parametrics and using cross-product to get the plane equation." + }, + { + "text": "OK, so that is how we get the tangent plane." + }, + { + "text": "And now, what this approximation formula here says is that, in fact, the graph of a function is close to the tangent plane." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk3.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..db670d552209553a73abe7a57967ebd9528e07b0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "If we were moving on the tangent plane, this would be an actual equality." + }, + { + "text": "Delta z would be a linear function of delta x and delta y." + }, + { + "text": "And the graph of a function is near the tangent plane, but it is not quite the same." + }, + { + "text": "It is only an approximation for small delta x and small delta y." + }, + { + "text": "The approximation formula says the graph of f is close to its tangent plane." + }, + { + "text": "And we can use that formula over here now to estimate how the value of f changes if I change x and y at the same time." + }, + { + "text": "Questions about that?" + }, + { + "text": "Now that we have caught up with what we were supposed to see on Tuesday, I can tell you now about max and min problems." + }, + { + "text": "Min problems." + }, + { + "text": "That is going to be an application of partial derivatives to look at optimization problems." + }, + { + "text": "Maybe ten years from now when you have a real job, your job might be to actually minimize the cost of something or maximize the profit of something or whatever." + }, + { + "text": "But typically, the function that you will have to strive to minimize or maximize will depend on several variables." + }, + { + "text": "If you have a function of one variable, you know that to find its minimum or its maximum you look at the derivative and you set that equal to zero." + }, + { + "text": "And you try to then look at what happens to the function." + }, + { + "text": "Here it is going to be kind of similar, except, of course, we have several variables." + }, + { + "text": "For today, we will think about a function of two variables." + }, + { + "text": "But it works exactly the same if you have three variables, ten variables, a million variables." + }, + { + "text": "The first observation is that if we have a local minimum or a local maximum, then both partial derivative, partial f, partial x and partial f, partial y are both zero at the same time." + }, + { + "text": "Why is that?" + }, + { + "text": "Well, let's say that f sub x is zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk4.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..6a4752d759dedab56f0865629de49a11db927b62 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means when I vary x, well, to first order the function doesn't change." + }, + { + "text": "Maybe that is because it is going through." + }, + { + "text": "If I look only at the slice parallel to the x-axis, then maybe I am going through the minimum." + }, + { + "text": "But then, if partial f, partial y is not zero, then actually by changing y I could still make the value larger or smaller." + }, + { + "text": "That wouldn't be an actual maximum or minimum." + }, + { + "text": "It would only be maximum or minimum if I stay in the slice." + }, + { + "text": "But if I allow myself to change y, that doesn't work." + }, + { + "text": "I need actually to know that if I change y the value will not change either to first order." + }, + { + "text": "That is why I also need partial f, partial y to be zero." + }, + { + "text": "Now, let's say that they are both zero." + }, + { + "text": "Well, why is that enough?" + }, + { + "text": "It is essentially enough because of this formula telling me that if both of these guys are zero then to first order the function doesn't change." + }, + { + "text": "And then, of course, there will be maybe quadratic terms that will actually turn that." + }, + { + "text": "This won't really say that your function is actually constant." + }, + { + "text": "It will just tell you that maybe it will be actually quadratic or higher order in delta x and delta y." + }, + { + "text": "That is what you expect to have at a maximum or a minimum." + }, + { + "text": "That condition is the same thing as saying that the tangent plane to the graph is actually going to be horizontal." + }, + { + "text": "And that is what you want to have." + }, + { + "text": "Say you have a minimum." + }, + { + "text": "Well, see that the tangent plane at this point, at the bottom of the graph, is going to be horizontal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk5.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..7e48c199e023a813f11acd0a96e5d01eb8971e00 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you can see that on this equation of a tangent plane, when both these coefficients are zero, that is when the equation becomes z equals constant, the horizontal plane." + }, + { + "text": "Does that make sense?" + }, + { + "text": "We will have a name for this kind of point because actually what we will see very soon is that these conditions are necessary but they are not sufficient." + }, + { + "text": "There are actually other kinds of points where the partial derivatives are zero." + }, + { + "text": "Let's give a name to this." + }, + { + "text": "We say that x0, y0 is a critical point of F if the partial derivative with respect to x and the partial derivative with respect to y are both zero." + }, + { + "text": "More generally, you would want all the partial derivatives, no matter how many variables you have, you want all the partials to be zero." + }, + { + "text": "Let's see an example." + }, + { + "text": "Let's say I give you the function f of x, y equals x squared minus 2xy plus py squared plus 2x minus 2y." + }, + { + "text": "And let's try to figure out whether we can minimize or maximize this." + }, + { + "text": "What we start doing immediately is taking the partial derivatives." + }, + { + "text": "What is f sub x?" + }, + { + "text": "It starts with 2x minus 2y plus zero plus two." + }, + { + "text": "Remember that y is a constant so this differentiates to zero." + }, + { + "text": "Now, if we do f sub y, that is going to be zero minus 2x plus 6y minus two." + }, + { + "text": "And what we want to do is set these things equal to zero." + }, + { + "text": "And we want to solve these two equations at the same time." + }, + { + "text": "An important thing to remember, maybe I should have told you a couple of weeks ago already, if you have two equations to solve, well, it is very good to try to simplify them by adding them together or whatever." + }, + { + "text": "But you must keep two equations." + }, + { + "text": "If you have two equations, you should not end up with just one equation out of nowhere." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk6.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9395a90268474c96a0037bb843bc6e78e8145fe5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "For example, here we can certainly simplify things by summing them together." + }, + { + "text": "See, if we add them together, well, the x's cancel and the constants cancel." + }, + { + "text": "In fact, we are just left with 4y equals zero." + }, + { + "text": "That is pretty good." + }, + { + "text": "That tells us y should be zero." + }, + { + "text": "But then we should, of course, go back to these and see what else we know." + }, + { + "text": "Well, now it tells us, if you put y equals zero, that tells you 2x plus 2 equals zero." + }, + { + "text": "That tells you x equals minus one." + }, + { + "text": "We have one critical point." + }, + { + "text": "That is x, y equals minus one over two." + }, + { + "text": "Any questions so far?" + }, + { + "text": "Well, you should have a question." + }, + { + "text": "The question should be how do we know if it is a maximum or a minimum?" + }, + { + "text": "Well, if we had a function of one variable, we would decide things based on the second derivative." + }, + { + "text": "And, in fact, we will see tomorrow how to do things based on the second derivative." + }, + { + "text": "But that is kind of tricky because there are a lot of second derivatives." + }, + { + "text": "I mean, we already have two first derivatives." + }, + { + "text": "You can imagine that if you keep taking partials, you may end up with more and more." + }, + { + "text": "We will have to figure out carefully what the condition should be." + }, + { + "text": "We will do that tomorrow." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk7.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..4bcbbf6b2197e00d7483dbd1b1319f8d7b454496 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "For now, let's just try to look at how do we understand these things by hand." + }, + { + "text": "In fact, let me point out to you immediately that there is more than maxima and minima." + }, + { + "text": "Remember, we saw the example of x squared plus y squared that has a critical point." + }, + { + "text": "The critical point is obviously a minimum." + }, + { + "text": "And, of course, it could be a local minimum because it could be that if you have a more complicated function there is indeed a minimum here." + }, + { + "text": "But then elsewhere the function drops to a lower value." + }, + { + "text": "We call that just a local minimum to say that it is a minimum if you stick to values that are close enough to that point." + }, + { + "text": "Of course, you also have a local maximum." + }, + { + "text": "Well, I did not plot it, but it is easy to plot." + }, + { + "text": "That is a local maximum." + }, + { + "text": "But there is a third example of critical point, and that is a saddle point." + }, + { + "text": "The saddle point is a new phenomenon that you do not really see in a single variable calculus." + }, + { + "text": "It is a critical point that is neither a minimum nor a maximum because, depending on which direction you look in, it is either one or the other." + }, + { + "text": "The point in the middle at the origin is a saddle point." + }, + { + "text": "If you look at the tangent plane to this graph you will see that it is actually horizontal at the origin." + }, + { + "text": "You have this mountain pass." + }, + { + "text": "At the mountain pass the ground is horizontal." + }, + { + "text": "But, depending on which direction you go, you go up or down." + }, + { + "text": "We say that the point is a saddle point if it is neither a minimum nor a maximum." + }, + { + "text": "OK, so the possibilities could be a local min, a local max, or a saddle." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk8.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8eebe5d35e57a9bb443552331906178033fbb172 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "Tomorrow we will see how to decide which one it is in general using second derivatives." + }, + { + "text": "For this time let's just try to do it by hand." + }, + { + "text": "I just want to observe." + }, + { + "text": "In fact, I can try to, you know, these examples that I have here, they are x2 y2 y2-x2." + }, + { + "text": "They are sums or differences of squares." + }, + { + "text": "And, if we know that we can put things as a sum of squares, for example, we will be done." + }, + { + "text": "Let's try to express this maybe in terms of a square." + }, + { + "text": "Well, the main problem is this 2xy." + }, + { + "text": "But, observe, we know something that starts with x2 minus 2xy that is actually the square of something else." + }, + { + "text": "It would be x2 minus 2xy, well, plus y2, not plus 3y2." + }, + { + "text": "Let's try to do that." + }, + { + "text": "We are going to complete the square." + }, + { + "text": "I am going to say it is x minus y squared." + }, + { + "text": "That gives me the first two terms and also y squared." + }, + { + "text": "Well, I still need to add two more y squares." + }, + { + "text": "And I also need to add, of course, the 2x minus 2y." + }, + { + "text": "It is simpler." + }, + { + "text": "It is still not simple enough for my taste." + }, + { + "text": "I can actually do better." + }, + { + "text": "See, I mean now what is, so these guys look like a sum of squares." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk9.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..2ebab68b48ed9108ed215c21106e93056b697b19 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_0_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "But here I have this extra stuff." + }, + { + "text": "But, 2x minus 2y, well, that is twice x minus y." + }, + { + "text": "It looks like maybe we can simplify this and make this into another square." + }, + { + "text": "In fact, I can simplify this further to x minus y plus one squared." + }, + { + "text": "See, that would start like, maybe I should put parentheses here, that would be x minus y squared plus twice x minus y." + }, + { + "text": "And then there is a plus one." + }, + { + "text": "Well, we don't have that plus one, so let's remove it by subtracting one." + }, + { + "text": "Oh, let me find that minus one here." + }, + { + "text": "And I still have my 2y squared." + }, + { + "text": "Do you see why this is the same function as that one?" + }, + { + "text": "Again, if I expand x minus y plus one squared, I get x minus y squared plus twice x minus y, that is those guys, plus one." + }, + { + "text": "But I will have a minus one and that will cancel out." + }, + { + "text": "And then I have a plus 2y squared." + }, + { + "text": "Now what I know, see, this is a sum of two squares minus one." + }, + { + "text": "And this critical point, x, y equals minus one, zero, that is exactly when this is zero and that is zero." + }, + { + "text": "That is the smallest value." + }, + { + "text": "This is always greater or equal to zero, same with that one." + }, + { + "text": "That is always at least minus one." + }, + { + "text": "And minus one happens to be the value at the critical point." + }, + { + "text": "It is a minimum." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk0.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..e6499639a2dd486fc34915743508e989029de764 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "Today we are going to see how to use what we saw last time about partial derivatives to handle minimization or maximization problems involving functions of several variables." + }, + { + "text": "Remember last time we said that when we have a function, say, of two variables, x and y, then we have actually two different derivatives." + }, + { + "text": "Partial f, partial x, also called f sub x, is the derivative with respect to x keeping y constant." + }, + { + "text": "And we have partial f, partial y, also called f sub y, where we vary y and we treat x as a constant." + }, + { + "text": "And now, one thing I didn't have time to tell you about, but hopefully you heard about in recitation yesterday, is the approximation formula that tells you what happens if you vary both x and y. F sub x tells us what happens if we change x a little bit by some small amount delta x. F sub y tells us how f changes if we change y by a small amount delta y." + }, + { + "text": "If we do both at the same time, then the two effects will add up with each other." + }, + { + "text": "Because you can imagine that first you will change x and then you will change y or the other way around." + }, + { + "text": "It doesn't really matter." + }, + { + "text": "If we change x by a certain amount delta x, and if we change y by the amount delta y, and let's say that we have z equals f of x, y, then that changes by an amount which is approximately f sub x times delta x plus f sub y times delta y." + }, + { + "text": "And that is one of the most important formulas about partial derivatives." + }, + { + "text": "The intuition for this, again, is just the two effects add up." + }, + { + "text": "If I change x by a small amount and then I change y, well, first changing x will modify f. How much does it modify f?" + }, + { + "text": "The answer is the rate of change." + }, + { + "text": "The rate of change is f sub x." + }, + { + "text": "And, if I change y, then the rate of change of f when I change y is f sub y." + }, + { + "text": "All together, I get this change in the value of f. And, of course, that is only an approximation formula." + }, + { + "text": "Actually, there would be higher order terms involving second and third derivatives and so on." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk1.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..24332c5f071c389023f7abaf7259fb1a63c23f92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "One way to justify this, sorry, I was distracted by a microphone problem." + }, + { + "text": "OK, so how do we justify this formula?" + }, + { + "text": "Well, one way to think about it is in terms of tangent plane approximation." + }, + { + "text": "Let's think about the tangent plane to the graph of a function f. I have some pictures to show you." + }, + { + "text": "It will be easier if I show the pictures." + }, + { + "text": "Remember, partial f over partial x was obtained by looking at the situation where y is held constant." + }, + { + "text": "That means I am slicing the graph of f by a plane that is parallel to the xz plane." + }, + { + "text": "And then, when I change x, z changes." + }, + { + "text": "And the slope of that is going to be the derivative with respect to x." + }, + { + "text": "Now, if I do the same in the other direction, then I will have similarly the slope in a slice now parallel to the yz plane that will be partial f over partial y." + }, + { + "text": "In fact, in each case I have a line." + }, + { + "text": "And that line is tangent to the surface." + }, + { + "text": "Now, if I have two lines tangent to the surface, well, then together they determine for me the tangent plane to the surface." + }, + { + "text": "Let's try to see how that works." + }, + { + "text": "We know that f sub x and f sub y are the slopes of two tangent lines to this plane, sorry, two tangent lines to the graph." + }, + { + "text": "And let's write down the equations of these lines." + }, + { + "text": "I am not going to write parametric equations." + }, + { + "text": "I am going to write them in terms of x, y, z coordinates." + }, + { + "text": "Let's say that partial f over partial x at a given point is equal to a." + }, + { + "text": "Then that means that we have a line given by the following conditions." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk10.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..04a9beb08f73a15fd9091546cca18b48afb0c0c0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, of course, here I was very lucky." + }, + { + "text": "In general, I could not expect things to simplify that much." + }, + { + "text": "In fact, I cheated." + }, + { + "text": "I started from that." + }, + { + "text": "I expanded." + }, + { + "text": "And then that is how I got my example." + }, + { + "text": "The general method will be a bit different, but you will see it will actually also involve completing squares." + }, + { + "text": "Just there is more to it than what we have seen." + }, + { + "text": "We will come back to this tomorrow." + }, + { + "text": "How do I know that this equals?" + }, + { + "text": "y is what negative one?" + }, + { + "text": "How do I know that that whole function is greater or equal to negative one?" + }, + { + "text": "Well, I wrote f of x, y as something squared plus 2y2 minus one." + }, + { + "text": "This squared is always a positive number, non-negative." + }, + { + "text": "It is a square." + }, + { + "text": "The square of something is always non-negative." + }, + { + "text": "Similarly, y2 is also always non-negative." + }, + { + "text": "If you add something that is at least zero plus something that is at least zero and you subtract one, you get always at least minus one." + }, + { + "text": "And, in fact, the only way that you can get minus one is if both of these guys are zero at the same time." + }, + { + "text": "That is how I get my minimum." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk11.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..f4eced0dcd7ffc5bdcf9cd95cd7f63aa34e4a4ac --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "More about this tomorrow." + }, + { + "text": "In fact, what I would like to tell you about now instead is a nice application of min-max problems that maybe you don't think of as a min-max problem." + }, + { + "text": "But you will see, I mean, you don't think of it that way because probably your calculator can do it for you." + }, + { + "text": "Or, if not, your computer can do it for you." + }, + { + "text": "But it is actually something where the theory is based on minimization in two variables." + }, + { + "text": "Very often in experimental sequences you have to do something called least squares interpolation." + }, + { + "text": "And what is that about?" + }, + { + "text": "Well, it is the idea that maybe you do some experiments and you record some data." + }, + { + "text": "You have some data x and some data y." + }, + { + "text": "And I don't know, maybe, for example, maybe you are measuring frogs and you are trying to measure how big the frog leg is compared to the eyes of a frog or whatever, or trying to measure something." + }, + { + "text": "And if you are doing chemistry then it could be how much you put of some reactant and how much of the output product that you wanted to synthesize is going to be the same." + }, + { + "text": "All sorts of things." + }, + { + "text": "Make up your own example." + }, + { + "text": "You measure, basically, for various values of x what the value of y ends up being." + }, + { + "text": "And then you would like to claim, oh, well, these points are kind of aligned." + }, + { + "text": "I mean, of course, to a mathematician they are not aligned, but to an experimental scientist that is evidence that there is a relation between the two." + }, + { + "text": "And so you want to claim, and in your paper you will actually draw a nice little line that says, C, these two functions depend linearly on each other." + }, + { + "text": "The question is how do we come up with that nice line that passes smack in the middle of the points?" + }, + { + "text": "The question is, given experimental data, xiyi, so maybe I should actually be more precise." + }, + { + "text": "You are given some experimental data." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk12.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..ec058dcefcf28c0e3655b8df350c1a7550b31989 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "You have data points x1, y1, x2, y2, and so on, xn, yn." + }, + { + "text": "The question would be find the best fit line of the form y equals ax plus b that somehow approximates very well this data." + }, + { + "text": "You can also use that, by the way, to predict various things." + }, + { + "text": "For example, if you look at your new homework, actually the first problem asks you to predict how many iPods will be on this planet in ten years, looking at past sales and how they behave." + }, + { + "text": "One thing, by the way, before you lose all the money you don't have yet, you cannot use that to predict the stock market." + }, + { + "text": "Don't try to use that to make money." + }, + { + "text": "It doesn't work." + }, + { + "text": "One tricky thing here that I want to draw your attention to is what are the unknowns here?" + }, + { + "text": "The natural answer would be to say the unknowns are x and y." + }, + { + "text": "That is not actually the case." + }, + { + "text": "We are not trying to solve for some x and y. I mean we have some values given to us." + }, + { + "text": "And when we are looking for that line we don't really care about a particular value of x." + }, + { + "text": "What we care about is actually these coefficients a and b that will tell us what the relation between x and y is." + }, + { + "text": "In fact, we are trying to solve for a and b that will give us the nicest possible line for these points." + }, + { + "text": "The unknowns in our equations will have to be a and b, not x and y." + }, + { + "text": "The question really is find the best a and b." + }, + { + "text": "And, of course, we have to decide what we mean by best." + }, + { + "text": "Best will mean that we minimize some function of a and b that measures the total error that we are making when we are choosing this line compared to the experimental data." + }, + { + "text": "Maybe, roughly speaking, it should measure how far these points are from the line." + }, + { + "text": "But now there are various ways to do it." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk13.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..5d2475feee1af92e7e44b93eafd8ef1a1aeab556 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "And some of them are, I mean a lot of them are valid to give you different answers." + }, + { + "text": "You have to decide what it is that you prefer." + }, + { + "text": "For example, you could measure the distance to the line by projecting perpendicularly." + }, + { + "text": "Or, you could measure instead the difference between, for a given value of x, the difference between the experimental value of y and the predicted one." + }, + { + "text": "And that is often more relevant because these guys are actually maybe expressed in different units." + }, + { + "text": "They are not the same type of quantity." + }, + { + "text": "You cannot actually combine them arbitrarily." + }, + { + "text": "Anyway, the convention is usually we measure distance in this way." + }, + { + "text": "Next, you could try to minimize the largest distance." + }, + { + "text": "Say we look at where is the largest error and we make that the smallest possible." + }, + { + "text": "The drawback of doing that is experimentally very often you have one data point that is not good because maybe you fell asleep in front of the experiment." + }, + { + "text": "And so you did not measure the right thing." + }, + { + "text": "You tend to want to not give too much importance to some data point that is far away from the others." + }, + { + "text": "Maybe instead you want to measure the average distance." + }, + { + "text": "Or maybe you want to actually give more weight to things that are further away." + }, + { + "text": "And then you do not want to do the distance but the square of the distance." + }, + { + "text": "There are various possible answers." + }, + { + "text": "But one of them gives us a particularly nice formula for a and b." + }, + { + "text": "And so that is why it is the universally used one." + }, + { + "text": "Here it says least squares." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk14.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..03f389ad03cba30ec35302a03113c11b9ae12887 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That is because we will measure, actually, the sum of the squares of the errors." + }, + { + "text": "And why do we do that?" + }, + { + "text": "Well, part of it is because actually it looks good." + }, + { + "text": "I mean, when you see these plots in scientific papers, they really look like the line is indeed the ideal line." + }, + { + "text": "And the second reason is because actually the minimization problem that we will get is particularly simple, well-proposed and it is easy to solve." + }, + { + "text": "We will have a nice formula for the best a and the best b." + }, + { + "text": "If you have a method that is simple and gives you a good answer then that is probably the good one." + }, + { + "text": "We have to define best." + }, + { + "text": "And here it is in the sense of defining a total square error." + }, + { + "text": "Maybe I should say total square deviation." + }, + { + "text": "What do I mean by that?" + }, + { + "text": "The deviation for each data point is the difference between what you have measured and what you are predicting by your model." + }, + { + "text": "That is the difference between the two." + }, + { + "text": "Now what we will do is try to minimize the function capital D, which is just the sum for all the data points of the square of the deviation." + }, + { + "text": "Let me emphasize again this is a function of a and b. I mean, of course, there are a lot of letters in here." + }, + { + "text": "But xi and yi in real life will be numbers given to you." + }, + { + "text": "They will be the numbers that you have measured." + }, + { + "text": "You have measured all of this data." + }, + { + "text": "They are just going to be numbers." + }, + { + "text": "You put them in there and you get the answer." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk15.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..574ce46fe50beb8d2adc71dc4ba061053cadb260 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Any questions?" + }, + { + "text": "How do we minimize this function of a and b?" + }, + { + "text": "Let's use our new knowledge." + }, + { + "text": "Let's actually look for a critical point." + }, + { + "text": "We want to solve for partial d over partial a equals zero and partial d over partial b equals zero." + }, + { + "text": "That is how we look for critical points." + }, + { + "text": "Let's take the derivative of a." + }, + { + "text": "Well, the derivative of a sum is the sum of the derivatives." + }, + { + "text": "And now we have to take the derivative of this quantity squared." + }, + { + "text": "Remember how we take the derivative of a square." + }, + { + "text": "We take twice this quantity times the derivative of what we are squaring." + }, + { + "text": "We will get two times minus y i, sorry, y i minus a xi plus b times the derivative of this with respect to a." + }, + { + "text": "What is the derivative of this with respect to a?" + }, + { + "text": "Negative xi, exactly." + }, + { + "text": "And so we will want this to be zero." + }, + { + "text": "And partial d over partial b, we do the same thing but differentiating with respect to b instead of with respect to a." + }, + { + "text": "Again, sum of squares twice y i minus a xi plus b times the derivative of this with respect to b is, I think, negative one." + }, + { + "text": "That is the equations we have to solve." + }, + { + "text": "Well, let's reorganize this a little bit." + }, + { + "text": "The first equation, see, there are a's and there are b's in these equations." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk16.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..6dbbcdfd1a44915f775e513934285605a93fde83 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "I am going to just look at the coefficients of a and b." + }, + { + "text": "If you have good eyes, you can see probably that these are actually linear equations in a and b." + }, + { + "text": "There is a lot of clutter with all these x's and y's all over the place." + }, + { + "text": "Let's actually try to expand things and make that more apparent." + }, + { + "text": "The first thing I will do is I will actually get rid of these factors of two that are just not very important." + }, + { + "text": "I can simplify things by two." + }, + { + "text": "And next I am going to look at the coefficient of a. I will get basically a times xi squared." + }, + { + "text": "Well, let me just do it and it should be clear." + }, + { + "text": "I claim when we simplify this we get a times xi squared plus xi times b minus xi yi." + }, + { + "text": "And we set this equal to zero." + }, + { + "text": "Do you agree that this is what we get when we expand that product?" + }, + { + "text": "No?" + }, + { + "text": "OK, let's do the other one." + }, + { + "text": "We just multiply by minus one." + }, + { + "text": "We take the opposite of that." + }, + { + "text": "It will be axi plus b. I will write that as xia plus b minus yi." + }, + { + "text": "And let me just reorganize that by actually putting all the a's together." + }, + { + "text": "That means actually I will have sum of all the xi squared times xi times b minus sum of xi yi equals zero." + }, + { + "text": "If I rewrite this it becomes sum of xi squared times a plus sum of the xi's times b minus, let me move the other guys to the other side, equals sum of xi yi." + }, + { + "text": "And that one becomes sum of xi times a plus how many b's do I get from this one?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk17.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..46c92ceb193fbddba6ccd0128c8434e1fa895b6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, I get one for each data point." + }, + { + "text": "When I sum them together I will get n. Very good." + }, + { + "text": "So, n times b equals sum of yi." + }, + { + "text": "Now, these quantities may look scary, but they are actually just numbers." + }, + { + "text": "For example, for this one you look at all your data points." + }, + { + "text": "For each of them you take the value of x and you just sum all these numbers together." + }, + { + "text": "What you get, actually, is a linear system in a two-by-two linear system." + }, + { + "text": "And so now we can solve this for a and b." + }, + { + "text": "In practice, of course, first you plug in the numbers for xi and yi and then you solve the system that you get." + }, + { + "text": "And we know how to solve two-by-two linear systems, I hope." + }, + { + "text": "That is how we find the best fit line." + }, + { + "text": "Now, why is that going to be the best one instead of the worst one?" + }, + { + "text": "We just solved for a critical point." + }, + { + "text": "That could actually be a maximum of this error function d. We will have the answer to that next time." + }, + { + "text": "But trust me, if you really want to go for the second derivative test that we will do tomorrow and apply it in this case, it is quite hard to check." + }, + { + "text": "But you can see it is actually a minimum." + }, + { + "text": "I will just say we can show that it is a minimum." + }, + { + "text": "Now, even for the linear case, it is the one that we are the most familiar with." + }, + { + "text": "Least squares interpolation actually works in much more general settings." + }, + { + "text": "Instead of fitting for the best line, if you think that there is a different kind of relation, then maybe you can fit in using a different kind of formula." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk18.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..fa2ca36c0d134e6b3372da5aa353386c01a4066b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me actually illustrate that for you." + }, + { + "text": "I don't know if you are familiar with Moore's law." + }, + { + "text": "It is something that is supposed to tell you how quickly, basically, computer chips become smarter, faster and faster over time." + }, + { + "text": "It is a law that says things about the number of transistors that you can fit onto a computer chip." + }, + { + "text": "Here I have some data about the number of transistors on a standard PC processor as a function of time." + }, + { + "text": "And, well, if you try to do the best line fit, you will see quickly that it doesn't seem to follow a linear trend." + }, + { + "text": "On the other hand, if you plot the diagram in a log scale, the log of the number of transistors as a function of time, then you get a much better line." + }, + { + "text": "And so, in fact, that means that you had an exponential relation between the number of transistors and time." + }, + { + "text": "And so, actually, that is what Moore's law says." + }, + { + "text": "It says that the number of transistors on a chip doubles, depending on the version, every 18 months or every two years." + }, + { + "text": "They keep changing the statement." + }, + { + "text": "How do we find that best exponential fit?" + }, + { + "text": "Well, an exponential fit would be something of the form y equals a constant times exponential of a times x." + }, + { + "text": "That is what we want to look at." + }, + { + "text": "Well, we could try to minimize a square error like we did earlier, but that doesn't work well at all." + }, + { + "text": "The equations that you get are very complicated." + }, + { + "text": "You cannot solve them." + }, + { + "text": "But remember what I showed you on this log plot." + }, + { + "text": "If you plot the log of y as a function of x, then suddenly it becomes a linear relation." + }, + { + "text": "Observe this is the same as ln of x equals ln of c plus ax." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk19.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..55b8384a00899de02bdae34fca68d10a37a51f56 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk19.json @@ -0,0 +1,53 @@ +[ + { + "text": "And that is a linear best fit." + }, + { + "text": "What you do is you just look for the best straight line fit for the log of y." + }, + { + "text": "That is something we already know." + }, + { + "text": "But you can also do other examples." + }, + { + "text": "For example, let's say that we have something more complicated." + }, + { + "text": "Let's say that we have actually a quadratic law." + }, + { + "text": "For example, y is of the form ax2 bx c. And, of course, you are trying to find somehow the best." + }, + { + "text": "That would mean here fitting the best parabola for your data points." + }, + { + "text": "Well, to do that you would need to find a, b and c. And now you would have actually a function of a, b and c, which would be the sum of all data points of the quadratic equation." + }, + { + "text": "And if you try to solve for critical points, now you will have three equations involving a, b and c. And, in fact, you will find a three by three linear system." + }, + { + "text": "And it works just the same way." + }, + { + "text": "Just you have a little bit more data." + }, + { + "text": "Basically, you see that these best fit problems are an example of minimization problem." + }, + { + "text": "But maybe you didn't expect to see minimization problems come in." + }, + { + "text": "But that is really the way to handle these questions." + }, + { + "text": "OK, so tomorrow we will go back to the question of how do we decide whether it is a minimum or a maximum?" + }, + { + "text": "And we will continue exploring functions of several variables." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk2.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..cbdde5612839d21f7df1c4e4a177c22a02adffc6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "I am going to keep y constant equal to y0." + }, + { + "text": "And I am going to change x." + }, + { + "text": "And, as I change x, z will change at a rate that is equal to a." + }, + { + "text": "That would be z equals z0 plus a times the change in x, x minus x0." + }, + { + "text": "That is how you would describe the line that is, I guess, the one that is plotted in green here." + }, + { + "text": "That is the intersection with the slice parallel to the xz plane." + }, + { + "text": "I hold y constant equal to y0." + }, + { + "text": "And z is a function of x that varies with a rate of a." + }, + { + "text": "And now, if I look similarly at the other slice, let's say that the partial with respect to y is equal to b, then I get another line which is obtained by the fact that z depends on y and the rate of change with respect to y will be b while x is held constant equal to x0." + }, + { + "text": "These two lines are both going to be in the tangent plane to the surface." + }, + { + "text": "They are both tangent to the surface, f of f. And, well, together they determine a plane." + }, + { + "text": "And that plane is just given by the formula z equals z0 plus a times x minus x0 plus b times y plus b." + }, + { + "text": "If you look at what happens, this is the equation of a plane, z equals constant times x plus constant times y plus constant." + }, + { + "text": "And if you look at what happens if I hold y constant and vary x, I recover the first line." + }, + { + "text": "If I hold x constant and vary y, I get the second line." + }, + { + "text": "Another way to do it, of course, would be to write actually parametric equations of these lines, get vectors along them and then take the cross-product to get the normal vector to the plane, and then get this equation for the plane using the normal vector." + }, + { + "text": "That also works and it gives you the same formula." + }, + { + "text": "If you are curious, exercise, do it again using parametrics and using cross-product to get the plane equation." + }, + { + "text": "OK, so that is how we get the tangent plane." + }, + { + "text": "And now, what this approximation formula here says is that, in fact, the graph of a function is close to the tangent plane." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk3.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..db670d552209553a73abe7a57967ebd9528e07b0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "If we were moving on the tangent plane, this would be an actual equality." + }, + { + "text": "Delta z would be a linear function of delta x and delta y." + }, + { + "text": "And the graph of a function is near the tangent plane, but it is not quite the same." + }, + { + "text": "It is only an approximation for small delta x and small delta y." + }, + { + "text": "The approximation formula says the graph of f is close to its tangent plane." + }, + { + "text": "And we can use that formula over here now to estimate how the value of f changes if I change x and y at the same time." + }, + { + "text": "Questions about that?" + }, + { + "text": "Now that we have caught up with what we were supposed to see on Tuesday, I can tell you now about max and min problems." + }, + { + "text": "Min problems." + }, + { + "text": "That is going to be an application of partial derivatives to look at optimization problems." + }, + { + "text": "Maybe ten years from now when you have a real job, your job might be to actually minimize the cost of something or maximize the profit of something or whatever." + }, + { + "text": "But typically, the function that you will have to strive to minimize or maximize will depend on several variables." + }, + { + "text": "If you have a function of one variable, you know that to find its minimum or its maximum you look at the derivative and you set that equal to zero." + }, + { + "text": "And you try to then look at what happens to the function." + }, + { + "text": "Here it is going to be kind of similar, except, of course, we have several variables." + }, + { + "text": "For today, we will think about a function of two variables." + }, + { + "text": "But it works exactly the same if you have three variables, ten variables, a million variables." + }, + { + "text": "The first observation is that if we have a local minimum or a local maximum, then both partial derivative, partial f, partial x and partial f, partial y are both zero at the same time." + }, + { + "text": "Why is that?" + }, + { + "text": "Well, let's say that f sub x is zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk4.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..6a4752d759dedab56f0865629de49a11db927b62 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means when I vary x, well, to first order the function doesn't change." + }, + { + "text": "Maybe that is because it is going through." + }, + { + "text": "If I look only at the slice parallel to the x-axis, then maybe I am going through the minimum." + }, + { + "text": "But then, if partial f, partial y is not zero, then actually by changing y I could still make the value larger or smaller." + }, + { + "text": "That wouldn't be an actual maximum or minimum." + }, + { + "text": "It would only be maximum or minimum if I stay in the slice." + }, + { + "text": "But if I allow myself to change y, that doesn't work." + }, + { + "text": "I need actually to know that if I change y the value will not change either to first order." + }, + { + "text": "That is why I also need partial f, partial y to be zero." + }, + { + "text": "Now, let's say that they are both zero." + }, + { + "text": "Well, why is that enough?" + }, + { + "text": "It is essentially enough because of this formula telling me that if both of these guys are zero then to first order the function doesn't change." + }, + { + "text": "And then, of course, there will be maybe quadratic terms that will actually turn that." + }, + { + "text": "This won't really say that your function is actually constant." + }, + { + "text": "It will just tell you that maybe it will be actually quadratic or higher order in delta x and delta y." + }, + { + "text": "That is what you expect to have at a maximum or a minimum." + }, + { + "text": "That condition is the same thing as saying that the tangent plane to the graph is actually going to be horizontal." + }, + { + "text": "And that is what you want to have." + }, + { + "text": "Say you have a minimum." + }, + { + "text": "Well, see that the tangent plane at this point, at the bottom of the graph, is going to be horizontal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk5.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..7e48c199e023a813f11acd0a96e5d01eb8971e00 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you can see that on this equation of a tangent plane, when both these coefficients are zero, that is when the equation becomes z equals constant, the horizontal plane." + }, + { + "text": "Does that make sense?" + }, + { + "text": "We will have a name for this kind of point because actually what we will see very soon is that these conditions are necessary but they are not sufficient." + }, + { + "text": "There are actually other kinds of points where the partial derivatives are zero." + }, + { + "text": "Let's give a name to this." + }, + { + "text": "We say that x0, y0 is a critical point of F if the partial derivative with respect to x and the partial derivative with respect to y are both zero." + }, + { + "text": "More generally, you would want all the partial derivatives, no matter how many variables you have, you want all the partials to be zero." + }, + { + "text": "Let's see an example." + }, + { + "text": "Let's say I give you the function f of x, y equals x squared minus 2xy plus py squared plus 2x minus 2y." + }, + { + "text": "And let's try to figure out whether we can minimize or maximize this." + }, + { + "text": "What we start doing immediately is taking the partial derivatives." + }, + { + "text": "What is f sub x?" + }, + { + "text": "It starts with 2x minus 2y plus zero plus two." + }, + { + "text": "Remember that y is a constant so this differentiates to zero." + }, + { + "text": "Now, if we do f sub y, that is going to be zero minus 2x plus 6y minus two." + }, + { + "text": "And what we want to do is set these things equal to zero." + }, + { + "text": "And we want to solve these two equations at the same time." + }, + { + "text": "An important thing to remember, maybe I should have told you a couple of weeks ago already, if you have two equations to solve, well, it is very good to try to simplify them by adding them together or whatever." + }, + { + "text": "But you must keep two equations." + }, + { + "text": "If you have two equations, you should not end up with just one equation out of nowhere." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk6.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9395a90268474c96a0037bb843bc6e78e8145fe5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "For example, here we can certainly simplify things by summing them together." + }, + { + "text": "See, if we add them together, well, the x's cancel and the constants cancel." + }, + { + "text": "In fact, we are just left with 4y equals zero." + }, + { + "text": "That is pretty good." + }, + { + "text": "That tells us y should be zero." + }, + { + "text": "But then we should, of course, go back to these and see what else we know." + }, + { + "text": "Well, now it tells us, if you put y equals zero, that tells you 2x plus 2 equals zero." + }, + { + "text": "That tells you x equals minus one." + }, + { + "text": "We have one critical point." + }, + { + "text": "That is x, y equals minus one over two." + }, + { + "text": "Any questions so far?" + }, + { + "text": "Well, you should have a question." + }, + { + "text": "The question should be how do we know if it is a maximum or a minimum?" + }, + { + "text": "Well, if we had a function of one variable, we would decide things based on the second derivative." + }, + { + "text": "And, in fact, we will see tomorrow how to do things based on the second derivative." + }, + { + "text": "But that is kind of tricky because there are a lot of second derivatives." + }, + { + "text": "I mean, we already have two first derivatives." + }, + { + "text": "You can imagine that if you keep taking partials, you may end up with more and more." + }, + { + "text": "We will have to figure out carefully what the condition should be." + }, + { + "text": "We will do that tomorrow." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk7.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..4bcbbf6b2197e00d7483dbd1b1319f8d7b454496 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "For now, let's just try to look at how do we understand these things by hand." + }, + { + "text": "In fact, let me point out to you immediately that there is more than maxima and minima." + }, + { + "text": "Remember, we saw the example of x squared plus y squared that has a critical point." + }, + { + "text": "The critical point is obviously a minimum." + }, + { + "text": "And, of course, it could be a local minimum because it could be that if you have a more complicated function there is indeed a minimum here." + }, + { + "text": "But then elsewhere the function drops to a lower value." + }, + { + "text": "We call that just a local minimum to say that it is a minimum if you stick to values that are close enough to that point." + }, + { + "text": "Of course, you also have a local maximum." + }, + { + "text": "Well, I did not plot it, but it is easy to plot." + }, + { + "text": "That is a local maximum." + }, + { + "text": "But there is a third example of critical point, and that is a saddle point." + }, + { + "text": "The saddle point is a new phenomenon that you do not really see in a single variable calculus." + }, + { + "text": "It is a critical point that is neither a minimum nor a maximum because, depending on which direction you look in, it is either one or the other." + }, + { + "text": "The point in the middle at the origin is a saddle point." + }, + { + "text": "If you look at the tangent plane to this graph you will see that it is actually horizontal at the origin." + }, + { + "text": "You have this mountain pass." + }, + { + "text": "At the mountain pass the ground is horizontal." + }, + { + "text": "But, depending on which direction you go, you go up or down." + }, + { + "text": "We say that the point is a saddle point if it is neither a minimum nor a maximum." + }, + { + "text": "OK, so the possibilities could be a local min, a local max, or a saddle." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk8.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8eebe5d35e57a9bb443552331906178033fbb172 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "Tomorrow we will see how to decide which one it is in general using second derivatives." + }, + { + "text": "For this time let's just try to do it by hand." + }, + { + "text": "I just want to observe." + }, + { + "text": "In fact, I can try to, you know, these examples that I have here, they are x2 y2 y2-x2." + }, + { + "text": "They are sums or differences of squares." + }, + { + "text": "And, if we know that we can put things as a sum of squares, for example, we will be done." + }, + { + "text": "Let's try to express this maybe in terms of a square." + }, + { + "text": "Well, the main problem is this 2xy." + }, + { + "text": "But, observe, we know something that starts with x2 minus 2xy that is actually the square of something else." + }, + { + "text": "It would be x2 minus 2xy, well, plus y2, not plus 3y2." + }, + { + "text": "Let's try to do that." + }, + { + "text": "We are going to complete the square." + }, + { + "text": "I am going to say it is x minus y squared." + }, + { + "text": "That gives me the first two terms and also y squared." + }, + { + "text": "Well, I still need to add two more y squares." + }, + { + "text": "And I also need to add, of course, the 2x minus 2y." + }, + { + "text": "It is simpler." + }, + { + "text": "It is still not simple enough for my taste." + }, + { + "text": "I can actually do better." + }, + { + "text": "See, I mean now what is, so these guys look like a sum of squares." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk9.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..2ebab68b48ed9108ed215c21106e93056b697b19 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_12_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "But here I have this extra stuff." + }, + { + "text": "But, 2x minus 2y, well, that is twice x minus y." + }, + { + "text": "It looks like maybe we can simplify this and make this into another square." + }, + { + "text": "In fact, I can simplify this further to x minus y plus one squared." + }, + { + "text": "See, that would start like, maybe I should put parentheses here, that would be x minus y squared plus twice x minus y." + }, + { + "text": "And then there is a plus one." + }, + { + "text": "Well, we don't have that plus one, so let's remove it by subtracting one." + }, + { + "text": "Oh, let me find that minus one here." + }, + { + "text": "And I still have my 2y squared." + }, + { + "text": "Do you see why this is the same function as that one?" + }, + { + "text": "Again, if I expand x minus y plus one squared, I get x minus y squared plus twice x minus y, that is those guys, plus one." + }, + { + "text": "But I will have a minus one and that will cancel out." + }, + { + "text": "And then I have a plus 2y squared." + }, + { + "text": "Now what I know, see, this is a sum of two squares minus one." + }, + { + "text": "And this critical point, x, y equals minus one, zero, that is exactly when this is zero and that is zero." + }, + { + "text": "That is the smallest value." + }, + { + "text": "This is always greater or equal to zero, same with that one." + }, + { + "text": "That is always at least minus one." + }, + { + "text": "And minus one happens to be the value at the critical point." + }, + { + "text": "It is a minimum." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk0.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..e6499639a2dd486fc34915743508e989029de764 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "Today we are going to see how to use what we saw last time about partial derivatives to handle minimization or maximization problems involving functions of several variables." + }, + { + "text": "Remember last time we said that when we have a function, say, of two variables, x and y, then we have actually two different derivatives." + }, + { + "text": "Partial f, partial x, also called f sub x, is the derivative with respect to x keeping y constant." + }, + { + "text": "And we have partial f, partial y, also called f sub y, where we vary y and we treat x as a constant." + }, + { + "text": "And now, one thing I didn't have time to tell you about, but hopefully you heard about in recitation yesterday, is the approximation formula that tells you what happens if you vary both x and y. F sub x tells us what happens if we change x a little bit by some small amount delta x. F sub y tells us how f changes if we change y by a small amount delta y." + }, + { + "text": "If we do both at the same time, then the two effects will add up with each other." + }, + { + "text": "Because you can imagine that first you will change x and then you will change y or the other way around." + }, + { + "text": "It doesn't really matter." + }, + { + "text": "If we change x by a certain amount delta x, and if we change y by the amount delta y, and let's say that we have z equals f of x, y, then that changes by an amount which is approximately f sub x times delta x plus f sub y times delta y." + }, + { + "text": "And that is one of the most important formulas about partial derivatives." + }, + { + "text": "The intuition for this, again, is just the two effects add up." + }, + { + "text": "If I change x by a small amount and then I change y, well, first changing x will modify f. How much does it modify f?" + }, + { + "text": "The answer is the rate of change." + }, + { + "text": "The rate of change is f sub x." + }, + { + "text": "And, if I change y, then the rate of change of f when I change y is f sub y." + }, + { + "text": "All together, I get this change in the value of f. And, of course, that is only an approximation formula." + }, + { + "text": "Actually, there would be higher order terms involving second and third derivatives and so on." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk1.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..24332c5f071c389023f7abaf7259fb1a63c23f92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "One way to justify this, sorry, I was distracted by a microphone problem." + }, + { + "text": "OK, so how do we justify this formula?" + }, + { + "text": "Well, one way to think about it is in terms of tangent plane approximation." + }, + { + "text": "Let's think about the tangent plane to the graph of a function f. I have some pictures to show you." + }, + { + "text": "It will be easier if I show the pictures." + }, + { + "text": "Remember, partial f over partial x was obtained by looking at the situation where y is held constant." + }, + { + "text": "That means I am slicing the graph of f by a plane that is parallel to the xz plane." + }, + { + "text": "And then, when I change x, z changes." + }, + { + "text": "And the slope of that is going to be the derivative with respect to x." + }, + { + "text": "Now, if I do the same in the other direction, then I will have similarly the slope in a slice now parallel to the yz plane that will be partial f over partial y." + }, + { + "text": "In fact, in each case I have a line." + }, + { + "text": "And that line is tangent to the surface." + }, + { + "text": "Now, if I have two lines tangent to the surface, well, then together they determine for me the tangent plane to the surface." + }, + { + "text": "Let's try to see how that works." + }, + { + "text": "We know that f sub x and f sub y are the slopes of two tangent lines to this plane, sorry, two tangent lines to the graph." + }, + { + "text": "And let's write down the equations of these lines." + }, + { + "text": "I am not going to write parametric equations." + }, + { + "text": "I am going to write them in terms of x, y, z coordinates." + }, + { + "text": "Let's say that partial f over partial x at a given point is equal to a." + }, + { + "text": "Then that means that we have a line given by the following conditions." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk10.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..04a9beb08f73a15fd9091546cca18b48afb0c0c0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, of course, here I was very lucky." + }, + { + "text": "In general, I could not expect things to simplify that much." + }, + { + "text": "In fact, I cheated." + }, + { + "text": "I started from that." + }, + { + "text": "I expanded." + }, + { + "text": "And then that is how I got my example." + }, + { + "text": "The general method will be a bit different, but you will see it will actually also involve completing squares." + }, + { + "text": "Just there is more to it than what we have seen." + }, + { + "text": "We will come back to this tomorrow." + }, + { + "text": "How do I know that this equals?" + }, + { + "text": "y is what negative one?" + }, + { + "text": "How do I know that that whole function is greater or equal to negative one?" + }, + { + "text": "Well, I wrote f of x, y as something squared plus 2y2 minus one." + }, + { + "text": "This squared is always a positive number, non-negative." + }, + { + "text": "It is a square." + }, + { + "text": "The square of something is always non-negative." + }, + { + "text": "Similarly, y2 is also always non-negative." + }, + { + "text": "If you add something that is at least zero plus something that is at least zero and you subtract one, you get always at least minus one." + }, + { + "text": "And, in fact, the only way that you can get minus one is if both of these guys are zero at the same time." + }, + { + "text": "That is how I get my minimum." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk11.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..f4eced0dcd7ffc5bdcf9cd95cd7f63aa34e4a4ac --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "More about this tomorrow." + }, + { + "text": "In fact, what I would like to tell you about now instead is a nice application of min-max problems that maybe you don't think of as a min-max problem." + }, + { + "text": "But you will see, I mean, you don't think of it that way because probably your calculator can do it for you." + }, + { + "text": "Or, if not, your computer can do it for you." + }, + { + "text": "But it is actually something where the theory is based on minimization in two variables." + }, + { + "text": "Very often in experimental sequences you have to do something called least squares interpolation." + }, + { + "text": "And what is that about?" + }, + { + "text": "Well, it is the idea that maybe you do some experiments and you record some data." + }, + { + "text": "You have some data x and some data y." + }, + { + "text": "And I don't know, maybe, for example, maybe you are measuring frogs and you are trying to measure how big the frog leg is compared to the eyes of a frog or whatever, or trying to measure something." + }, + { + "text": "And if you are doing chemistry then it could be how much you put of some reactant and how much of the output product that you wanted to synthesize is going to be the same." + }, + { + "text": "All sorts of things." + }, + { + "text": "Make up your own example." + }, + { + "text": "You measure, basically, for various values of x what the value of y ends up being." + }, + { + "text": "And then you would like to claim, oh, well, these points are kind of aligned." + }, + { + "text": "I mean, of course, to a mathematician they are not aligned, but to an experimental scientist that is evidence that there is a relation between the two." + }, + { + "text": "And so you want to claim, and in your paper you will actually draw a nice little line that says, C, these two functions depend linearly on each other." + }, + { + "text": "The question is how do we come up with that nice line that passes smack in the middle of the points?" + }, + { + "text": "The question is, given experimental data, xiyi, so maybe I should actually be more precise." + }, + { + "text": "You are given some experimental data." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk12.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..ec058dcefcf28c0e3655b8df350c1a7550b31989 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "You have data points x1, y1, x2, y2, and so on, xn, yn." + }, + { + "text": "The question would be find the best fit line of the form y equals ax plus b that somehow approximates very well this data." + }, + { + "text": "You can also use that, by the way, to predict various things." + }, + { + "text": "For example, if you look at your new homework, actually the first problem asks you to predict how many iPods will be on this planet in ten years, looking at past sales and how they behave." + }, + { + "text": "One thing, by the way, before you lose all the money you don't have yet, you cannot use that to predict the stock market." + }, + { + "text": "Don't try to use that to make money." + }, + { + "text": "It doesn't work." + }, + { + "text": "One tricky thing here that I want to draw your attention to is what are the unknowns here?" + }, + { + "text": "The natural answer would be to say the unknowns are x and y." + }, + { + "text": "That is not actually the case." + }, + { + "text": "We are not trying to solve for some x and y. I mean we have some values given to us." + }, + { + "text": "And when we are looking for that line we don't really care about a particular value of x." + }, + { + "text": "What we care about is actually these coefficients a and b that will tell us what the relation between x and y is." + }, + { + "text": "In fact, we are trying to solve for a and b that will give us the nicest possible line for these points." + }, + { + "text": "The unknowns in our equations will have to be a and b, not x and y." + }, + { + "text": "The question really is find the best a and b." + }, + { + "text": "And, of course, we have to decide what we mean by best." + }, + { + "text": "Best will mean that we minimize some function of a and b that measures the total error that we are making when we are choosing this line compared to the experimental data." + }, + { + "text": "Maybe, roughly speaking, it should measure how far these points are from the line." + }, + { + "text": "But now there are various ways to do it." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk13.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..5d2475feee1af92e7e44b93eafd8ef1a1aeab556 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "And some of them are, I mean a lot of them are valid to give you different answers." + }, + { + "text": "You have to decide what it is that you prefer." + }, + { + "text": "For example, you could measure the distance to the line by projecting perpendicularly." + }, + { + "text": "Or, you could measure instead the difference between, for a given value of x, the difference between the experimental value of y and the predicted one." + }, + { + "text": "And that is often more relevant because these guys are actually maybe expressed in different units." + }, + { + "text": "They are not the same type of quantity." + }, + { + "text": "You cannot actually combine them arbitrarily." + }, + { + "text": "Anyway, the convention is usually we measure distance in this way." + }, + { + "text": "Next, you could try to minimize the largest distance." + }, + { + "text": "Say we look at where is the largest error and we make that the smallest possible." + }, + { + "text": "The drawback of doing that is experimentally very often you have one data point that is not good because maybe you fell asleep in front of the experiment." + }, + { + "text": "And so you did not measure the right thing." + }, + { + "text": "You tend to want to not give too much importance to some data point that is far away from the others." + }, + { + "text": "Maybe instead you want to measure the average distance." + }, + { + "text": "Or maybe you want to actually give more weight to things that are further away." + }, + { + "text": "And then you do not want to do the distance but the square of the distance." + }, + { + "text": "There are various possible answers." + }, + { + "text": "But one of them gives us a particularly nice formula for a and b." + }, + { + "text": "And so that is why it is the universally used one." + }, + { + "text": "Here it says least squares." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk14.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..03f389ad03cba30ec35302a03113c11b9ae12887 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That is because we will measure, actually, the sum of the squares of the errors." + }, + { + "text": "And why do we do that?" + }, + { + "text": "Well, part of it is because actually it looks good." + }, + { + "text": "I mean, when you see these plots in scientific papers, they really look like the line is indeed the ideal line." + }, + { + "text": "And the second reason is because actually the minimization problem that we will get is particularly simple, well-proposed and it is easy to solve." + }, + { + "text": "We will have a nice formula for the best a and the best b." + }, + { + "text": "If you have a method that is simple and gives you a good answer then that is probably the good one." + }, + { + "text": "We have to define best." + }, + { + "text": "And here it is in the sense of defining a total square error." + }, + { + "text": "Maybe I should say total square deviation." + }, + { + "text": "What do I mean by that?" + }, + { + "text": "The deviation for each data point is the difference between what you have measured and what you are predicting by your model." + }, + { + "text": "That is the difference between the two." + }, + { + "text": "Now what we will do is try to minimize the function capital D, which is just the sum for all the data points of the square of the deviation." + }, + { + "text": "Let me emphasize again this is a function of a and b. I mean, of course, there are a lot of letters in here." + }, + { + "text": "But xi and yi in real life will be numbers given to you." + }, + { + "text": "They will be the numbers that you have measured." + }, + { + "text": "You have measured all of this data." + }, + { + "text": "They are just going to be numbers." + }, + { + "text": "You put them in there and you get the answer." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk15.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..574ce46fe50beb8d2adc71dc4ba061053cadb260 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Any questions?" + }, + { + "text": "How do we minimize this function of a and b?" + }, + { + "text": "Let's use our new knowledge." + }, + { + "text": "Let's actually look for a critical point." + }, + { + "text": "We want to solve for partial d over partial a equals zero and partial d over partial b equals zero." + }, + { + "text": "That is how we look for critical points." + }, + { + "text": "Let's take the derivative of a." + }, + { + "text": "Well, the derivative of a sum is the sum of the derivatives." + }, + { + "text": "And now we have to take the derivative of this quantity squared." + }, + { + "text": "Remember how we take the derivative of a square." + }, + { + "text": "We take twice this quantity times the derivative of what we are squaring." + }, + { + "text": "We will get two times minus y i, sorry, y i minus a xi plus b times the derivative of this with respect to a." + }, + { + "text": "What is the derivative of this with respect to a?" + }, + { + "text": "Negative xi, exactly." + }, + { + "text": "And so we will want this to be zero." + }, + { + "text": "And partial d over partial b, we do the same thing but differentiating with respect to b instead of with respect to a." + }, + { + "text": "Again, sum of squares twice y i minus a xi plus b times the derivative of this with respect to b is, I think, negative one." + }, + { + "text": "That is the equations we have to solve." + }, + { + "text": "Well, let's reorganize this a little bit." + }, + { + "text": "The first equation, see, there are a's and there are b's in these equations." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk16.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..6dbbcdfd1a44915f775e513934285605a93fde83 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "I am going to just look at the coefficients of a and b." + }, + { + "text": "If you have good eyes, you can see probably that these are actually linear equations in a and b." + }, + { + "text": "There is a lot of clutter with all these x's and y's all over the place." + }, + { + "text": "Let's actually try to expand things and make that more apparent." + }, + { + "text": "The first thing I will do is I will actually get rid of these factors of two that are just not very important." + }, + { + "text": "I can simplify things by two." + }, + { + "text": "And next I am going to look at the coefficient of a. I will get basically a times xi squared." + }, + { + "text": "Well, let me just do it and it should be clear." + }, + { + "text": "I claim when we simplify this we get a times xi squared plus xi times b minus xi yi." + }, + { + "text": "And we set this equal to zero." + }, + { + "text": "Do you agree that this is what we get when we expand that product?" + }, + { + "text": "No?" + }, + { + "text": "OK, let's do the other one." + }, + { + "text": "We just multiply by minus one." + }, + { + "text": "We take the opposite of that." + }, + { + "text": "It will be axi plus b. I will write that as xia plus b minus yi." + }, + { + "text": "And let me just reorganize that by actually putting all the a's together." + }, + { + "text": "That means actually I will have sum of all the xi squared times xi times b minus sum of xi yi equals zero." + }, + { + "text": "If I rewrite this it becomes sum of xi squared times a plus sum of the xi's times b minus, let me move the other guys to the other side, equals sum of xi yi." + }, + { + "text": "And that one becomes sum of xi times a plus how many b's do I get from this one?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk17.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..46c92ceb193fbddba6ccd0128c8434e1fa895b6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, I get one for each data point." + }, + { + "text": "When I sum them together I will get n. Very good." + }, + { + "text": "So, n times b equals sum of yi." + }, + { + "text": "Now, these quantities may look scary, but they are actually just numbers." + }, + { + "text": "For example, for this one you look at all your data points." + }, + { + "text": "For each of them you take the value of x and you just sum all these numbers together." + }, + { + "text": "What you get, actually, is a linear system in a two-by-two linear system." + }, + { + "text": "And so now we can solve this for a and b." + }, + { + "text": "In practice, of course, first you plug in the numbers for xi and yi and then you solve the system that you get." + }, + { + "text": "And we know how to solve two-by-two linear systems, I hope." + }, + { + "text": "That is how we find the best fit line." + }, + { + "text": "Now, why is that going to be the best one instead of the worst one?" + }, + { + "text": "We just solved for a critical point." + }, + { + "text": "That could actually be a maximum of this error function d. We will have the answer to that next time." + }, + { + "text": "But trust me, if you really want to go for the second derivative test that we will do tomorrow and apply it in this case, it is quite hard to check." + }, + { + "text": "But you can see it is actually a minimum." + }, + { + "text": "I will just say we can show that it is a minimum." + }, + { + "text": "Now, even for the linear case, it is the one that we are the most familiar with." + }, + { + "text": "Least squares interpolation actually works in much more general settings." + }, + { + "text": "Instead of fitting for the best line, if you think that there is a different kind of relation, then maybe you can fit in using a different kind of formula." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk18.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..fa2ca36c0d134e6b3372da5aa353386c01a4066b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me actually illustrate that for you." + }, + { + "text": "I don't know if you are familiar with Moore's law." + }, + { + "text": "It is something that is supposed to tell you how quickly, basically, computer chips become smarter, faster and faster over time." + }, + { + "text": "It is a law that says things about the number of transistors that you can fit onto a computer chip." + }, + { + "text": "Here I have some data about the number of transistors on a standard PC processor as a function of time." + }, + { + "text": "And, well, if you try to do the best line fit, you will see quickly that it doesn't seem to follow a linear trend." + }, + { + "text": "On the other hand, if you plot the diagram in a log scale, the log of the number of transistors as a function of time, then you get a much better line." + }, + { + "text": "And so, in fact, that means that you had an exponential relation between the number of transistors and time." + }, + { + "text": "And so, actually, that is what Moore's law says." + }, + { + "text": "It says that the number of transistors on a chip doubles, depending on the version, every 18 months or every two years." + }, + { + "text": "They keep changing the statement." + }, + { + "text": "How do we find that best exponential fit?" + }, + { + "text": "Well, an exponential fit would be something of the form y equals a constant times exponential of a times x." + }, + { + "text": "That is what we want to look at." + }, + { + "text": "Well, we could try to minimize a square error like we did earlier, but that doesn't work well at all." + }, + { + "text": "The equations that you get are very complicated." + }, + { + "text": "You cannot solve them." + }, + { + "text": "But remember what I showed you on this log plot." + }, + { + "text": "If you plot the log of y as a function of x, then suddenly it becomes a linear relation." + }, + { + "text": "Observe this is the same as ln of x equals ln of c plus ax." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk19.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..55b8384a00899de02bdae34fca68d10a37a51f56 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk19.json @@ -0,0 +1,53 @@ +[ + { + "text": "And that is a linear best fit." + }, + { + "text": "What you do is you just look for the best straight line fit for the log of y." + }, + { + "text": "That is something we already know." + }, + { + "text": "But you can also do other examples." + }, + { + "text": "For example, let's say that we have something more complicated." + }, + { + "text": "Let's say that we have actually a quadratic law." + }, + { + "text": "For example, y is of the form ax2 bx c. And, of course, you are trying to find somehow the best." + }, + { + "text": "That would mean here fitting the best parabola for your data points." + }, + { + "text": "Well, to do that you would need to find a, b and c. And now you would have actually a function of a, b and c, which would be the sum of all data points of the quadratic equation." + }, + { + "text": "And if you try to solve for critical points, now you will have three equations involving a, b and c. And, in fact, you will find a three by three linear system." + }, + { + "text": "And it works just the same way." + }, + { + "text": "Just you have a little bit more data." + }, + { + "text": "Basically, you see that these best fit problems are an example of minimization problem." + }, + { + "text": "But maybe you didn't expect to see minimization problems come in." + }, + { + "text": "But that is really the way to handle these questions." + }, + { + "text": "OK, so tomorrow we will go back to the question of how do we decide whether it is a minimum or a maximum?" + }, + { + "text": "And we will continue exploring functions of several variables." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk2.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..cbdde5612839d21f7df1c4e4a177c22a02adffc6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "I am going to keep y constant equal to y0." + }, + { + "text": "And I am going to change x." + }, + { + "text": "And, as I change x, z will change at a rate that is equal to a." + }, + { + "text": "That would be z equals z0 plus a times the change in x, x minus x0." + }, + { + "text": "That is how you would describe the line that is, I guess, the one that is plotted in green here." + }, + { + "text": "That is the intersection with the slice parallel to the xz plane." + }, + { + "text": "I hold y constant equal to y0." + }, + { + "text": "And z is a function of x that varies with a rate of a." + }, + { + "text": "And now, if I look similarly at the other slice, let's say that the partial with respect to y is equal to b, then I get another line which is obtained by the fact that z depends on y and the rate of change with respect to y will be b while x is held constant equal to x0." + }, + { + "text": "These two lines are both going to be in the tangent plane to the surface." + }, + { + "text": "They are both tangent to the surface, f of f. And, well, together they determine a plane." + }, + { + "text": "And that plane is just given by the formula z equals z0 plus a times x minus x0 plus b times y plus b." + }, + { + "text": "If you look at what happens, this is the equation of a plane, z equals constant times x plus constant times y plus constant." + }, + { + "text": "And if you look at what happens if I hold y constant and vary x, I recover the first line." + }, + { + "text": "If I hold x constant and vary y, I get the second line." + }, + { + "text": "Another way to do it, of course, would be to write actually parametric equations of these lines, get vectors along them and then take the cross-product to get the normal vector to the plane, and then get this equation for the plane using the normal vector." + }, + { + "text": "That also works and it gives you the same formula." + }, + { + "text": "If you are curious, exercise, do it again using parametrics and using cross-product to get the plane equation." + }, + { + "text": "OK, so that is how we get the tangent plane." + }, + { + "text": "And now, what this approximation formula here says is that, in fact, the graph of a function is close to the tangent plane." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk3.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..db670d552209553a73abe7a57967ebd9528e07b0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "If we were moving on the tangent plane, this would be an actual equality." + }, + { + "text": "Delta z would be a linear function of delta x and delta y." + }, + { + "text": "And the graph of a function is near the tangent plane, but it is not quite the same." + }, + { + "text": "It is only an approximation for small delta x and small delta y." + }, + { + "text": "The approximation formula says the graph of f is close to its tangent plane." + }, + { + "text": "And we can use that formula over here now to estimate how the value of f changes if I change x and y at the same time." + }, + { + "text": "Questions about that?" + }, + { + "text": "Now that we have caught up with what we were supposed to see on Tuesday, I can tell you now about max and min problems." + }, + { + "text": "Min problems." + }, + { + "text": "That is going to be an application of partial derivatives to look at optimization problems." + }, + { + "text": "Maybe ten years from now when you have a real job, your job might be to actually minimize the cost of something or maximize the profit of something or whatever." + }, + { + "text": "But typically, the function that you will have to strive to minimize or maximize will depend on several variables." + }, + { + "text": "If you have a function of one variable, you know that to find its minimum or its maximum you look at the derivative and you set that equal to zero." + }, + { + "text": "And you try to then look at what happens to the function." + }, + { + "text": "Here it is going to be kind of similar, except, of course, we have several variables." + }, + { + "text": "For today, we will think about a function of two variables." + }, + { + "text": "But it works exactly the same if you have three variables, ten variables, a million variables." + }, + { + "text": "The first observation is that if we have a local minimum or a local maximum, then both partial derivative, partial f, partial x and partial f, partial y are both zero at the same time." + }, + { + "text": "Why is that?" + }, + { + "text": "Well, let's say that f sub x is zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk4.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..6a4752d759dedab56f0865629de49a11db927b62 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means when I vary x, well, to first order the function doesn't change." + }, + { + "text": "Maybe that is because it is going through." + }, + { + "text": "If I look only at the slice parallel to the x-axis, then maybe I am going through the minimum." + }, + { + "text": "But then, if partial f, partial y is not zero, then actually by changing y I could still make the value larger or smaller." + }, + { + "text": "That wouldn't be an actual maximum or minimum." + }, + { + "text": "It would only be maximum or minimum if I stay in the slice." + }, + { + "text": "But if I allow myself to change y, that doesn't work." + }, + { + "text": "I need actually to know that if I change y the value will not change either to first order." + }, + { + "text": "That is why I also need partial f, partial y to be zero." + }, + { + "text": "Now, let's say that they are both zero." + }, + { + "text": "Well, why is that enough?" + }, + { + "text": "It is essentially enough because of this formula telling me that if both of these guys are zero then to first order the function doesn't change." + }, + { + "text": "And then, of course, there will be maybe quadratic terms that will actually turn that." + }, + { + "text": "This won't really say that your function is actually constant." + }, + { + "text": "It will just tell you that maybe it will be actually quadratic or higher order in delta x and delta y." + }, + { + "text": "That is what you expect to have at a maximum or a minimum." + }, + { + "text": "That condition is the same thing as saying that the tangent plane to the graph is actually going to be horizontal." + }, + { + "text": "And that is what you want to have." + }, + { + "text": "Say you have a minimum." + }, + { + "text": "Well, see that the tangent plane at this point, at the bottom of the graph, is going to be horizontal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk5.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..7e48c199e023a813f11acd0a96e5d01eb8971e00 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you can see that on this equation of a tangent plane, when both these coefficients are zero, that is when the equation becomes z equals constant, the horizontal plane." + }, + { + "text": "Does that make sense?" + }, + { + "text": "We will have a name for this kind of point because actually what we will see very soon is that these conditions are necessary but they are not sufficient." + }, + { + "text": "There are actually other kinds of points where the partial derivatives are zero." + }, + { + "text": "Let's give a name to this." + }, + { + "text": "We say that x0, y0 is a critical point of F if the partial derivative with respect to x and the partial derivative with respect to y are both zero." + }, + { + "text": "More generally, you would want all the partial derivatives, no matter how many variables you have, you want all the partials to be zero." + }, + { + "text": "Let's see an example." + }, + { + "text": "Let's say I give you the function f of x, y equals x squared minus 2xy plus py squared plus 2x minus 2y." + }, + { + "text": "And let's try to figure out whether we can minimize or maximize this." + }, + { + "text": "What we start doing immediately is taking the partial derivatives." + }, + { + "text": "What is f sub x?" + }, + { + "text": "It starts with 2x minus 2y plus zero plus two." + }, + { + "text": "Remember that y is a constant so this differentiates to zero." + }, + { + "text": "Now, if we do f sub y, that is going to be zero minus 2x plus 6y minus two." + }, + { + "text": "And what we want to do is set these things equal to zero." + }, + { + "text": "And we want to solve these two equations at the same time." + }, + { + "text": "An important thing to remember, maybe I should have told you a couple of weeks ago already, if you have two equations to solve, well, it is very good to try to simplify them by adding them together or whatever." + }, + { + "text": "But you must keep two equations." + }, + { + "text": "If you have two equations, you should not end up with just one equation out of nowhere." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk6.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9395a90268474c96a0037bb843bc6e78e8145fe5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "For example, here we can certainly simplify things by summing them together." + }, + { + "text": "See, if we add them together, well, the x's cancel and the constants cancel." + }, + { + "text": "In fact, we are just left with 4y equals zero." + }, + { + "text": "That is pretty good." + }, + { + "text": "That tells us y should be zero." + }, + { + "text": "But then we should, of course, go back to these and see what else we know." + }, + { + "text": "Well, now it tells us, if you put y equals zero, that tells you 2x plus 2 equals zero." + }, + { + "text": "That tells you x equals minus one." + }, + { + "text": "We have one critical point." + }, + { + "text": "That is x, y equals minus one over two." + }, + { + "text": "Any questions so far?" + }, + { + "text": "Well, you should have a question." + }, + { + "text": "The question should be how do we know if it is a maximum or a minimum?" + }, + { + "text": "Well, if we had a function of one variable, we would decide things based on the second derivative." + }, + { + "text": "And, in fact, we will see tomorrow how to do things based on the second derivative." + }, + { + "text": "But that is kind of tricky because there are a lot of second derivatives." + }, + { + "text": "I mean, we already have two first derivatives." + }, + { + "text": "You can imagine that if you keep taking partials, you may end up with more and more." + }, + { + "text": "We will have to figure out carefully what the condition should be." + }, + { + "text": "We will do that tomorrow." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk7.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..4bcbbf6b2197e00d7483dbd1b1319f8d7b454496 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "For now, let's just try to look at how do we understand these things by hand." + }, + { + "text": "In fact, let me point out to you immediately that there is more than maxima and minima." + }, + { + "text": "Remember, we saw the example of x squared plus y squared that has a critical point." + }, + { + "text": "The critical point is obviously a minimum." + }, + { + "text": "And, of course, it could be a local minimum because it could be that if you have a more complicated function there is indeed a minimum here." + }, + { + "text": "But then elsewhere the function drops to a lower value." + }, + { + "text": "We call that just a local minimum to say that it is a minimum if you stick to values that are close enough to that point." + }, + { + "text": "Of course, you also have a local maximum." + }, + { + "text": "Well, I did not plot it, but it is easy to plot." + }, + { + "text": "That is a local maximum." + }, + { + "text": "But there is a third example of critical point, and that is a saddle point." + }, + { + "text": "The saddle point is a new phenomenon that you do not really see in a single variable calculus." + }, + { + "text": "It is a critical point that is neither a minimum nor a maximum because, depending on which direction you look in, it is either one or the other." + }, + { + "text": "The point in the middle at the origin is a saddle point." + }, + { + "text": "If you look at the tangent plane to this graph you will see that it is actually horizontal at the origin." + }, + { + "text": "You have this mountain pass." + }, + { + "text": "At the mountain pass the ground is horizontal." + }, + { + "text": "But, depending on which direction you go, you go up or down." + }, + { + "text": "We say that the point is a saddle point if it is neither a minimum nor a maximum." + }, + { + "text": "OK, so the possibilities could be a local min, a local max, or a saddle." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk8.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8eebe5d35e57a9bb443552331906178033fbb172 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "Tomorrow we will see how to decide which one it is in general using second derivatives." + }, + { + "text": "For this time let's just try to do it by hand." + }, + { + "text": "I just want to observe." + }, + { + "text": "In fact, I can try to, you know, these examples that I have here, they are x2 y2 y2-x2." + }, + { + "text": "They are sums or differences of squares." + }, + { + "text": "And, if we know that we can put things as a sum of squares, for example, we will be done." + }, + { + "text": "Let's try to express this maybe in terms of a square." + }, + { + "text": "Well, the main problem is this 2xy." + }, + { + "text": "But, observe, we know something that starts with x2 minus 2xy that is actually the square of something else." + }, + { + "text": "It would be x2 minus 2xy, well, plus y2, not plus 3y2." + }, + { + "text": "Let's try to do that." + }, + { + "text": "We are going to complete the square." + }, + { + "text": "I am going to say it is x minus y squared." + }, + { + "text": "That gives me the first two terms and also y squared." + }, + { + "text": "Well, I still need to add two more y squares." + }, + { + "text": "And I also need to add, of course, the 2x minus 2y." + }, + { + "text": "It is simpler." + }, + { + "text": "It is still not simple enough for my taste." + }, + { + "text": "I can actually do better." + }, + { + "text": "See, I mean now what is, so these guys look like a sum of squares." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk9.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..2ebab68b48ed9108ed215c21106e93056b697b19 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_1_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "But here I have this extra stuff." + }, + { + "text": "But, 2x minus 2y, well, that is twice x minus y." + }, + { + "text": "It looks like maybe we can simplify this and make this into another square." + }, + { + "text": "In fact, I can simplify this further to x minus y plus one squared." + }, + { + "text": "See, that would start like, maybe I should put parentheses here, that would be x minus y squared plus twice x minus y." + }, + { + "text": "And then there is a plus one." + }, + { + "text": "Well, we don't have that plus one, so let's remove it by subtracting one." + }, + { + "text": "Oh, let me find that minus one here." + }, + { + "text": "And I still have my 2y squared." + }, + { + "text": "Do you see why this is the same function as that one?" + }, + { + "text": "Again, if I expand x minus y plus one squared, I get x minus y squared plus twice x minus y, that is those guys, plus one." + }, + { + "text": "But I will have a minus one and that will cancel out." + }, + { + "text": "And then I have a plus 2y squared." + }, + { + "text": "Now what I know, see, this is a sum of two squares minus one." + }, + { + "text": "And this critical point, x, y equals minus one, zero, that is exactly when this is zero and that is zero." + }, + { + "text": "That is the smallest value." + }, + { + "text": "This is always greater or equal to zero, same with that one." + }, + { + "text": "That is always at least minus one." + }, + { + "text": "And minus one happens to be the value at the critical point." + }, + { + "text": "It is a minimum." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk0.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..e6499639a2dd486fc34915743508e989029de764 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "Today we are going to see how to use what we saw last time about partial derivatives to handle minimization or maximization problems involving functions of several variables." + }, + { + "text": "Remember last time we said that when we have a function, say, of two variables, x and y, then we have actually two different derivatives." + }, + { + "text": "Partial f, partial x, also called f sub x, is the derivative with respect to x keeping y constant." + }, + { + "text": "And we have partial f, partial y, also called f sub y, where we vary y and we treat x as a constant." + }, + { + "text": "And now, one thing I didn't have time to tell you about, but hopefully you heard about in recitation yesterday, is the approximation formula that tells you what happens if you vary both x and y. F sub x tells us what happens if we change x a little bit by some small amount delta x. F sub y tells us how f changes if we change y by a small amount delta y." + }, + { + "text": "If we do both at the same time, then the two effects will add up with each other." + }, + { + "text": "Because you can imagine that first you will change x and then you will change y or the other way around." + }, + { + "text": "It doesn't really matter." + }, + { + "text": "If we change x by a certain amount delta x, and if we change y by the amount delta y, and let's say that we have z equals f of x, y, then that changes by an amount which is approximately f sub x times delta x plus f sub y times delta y." + }, + { + "text": "And that is one of the most important formulas about partial derivatives." + }, + { + "text": "The intuition for this, again, is just the two effects add up." + }, + { + "text": "If I change x by a small amount and then I change y, well, first changing x will modify f. How much does it modify f?" + }, + { + "text": "The answer is the rate of change." + }, + { + "text": "The rate of change is f sub x." + }, + { + "text": "And, if I change y, then the rate of change of f when I change y is f sub y." + }, + { + "text": "All together, I get this change in the value of f. And, of course, that is only an approximation formula." + }, + { + "text": "Actually, there would be higher order terms involving second and third derivatives and so on." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk1.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..24332c5f071c389023f7abaf7259fb1a63c23f92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "One way to justify this, sorry, I was distracted by a microphone problem." + }, + { + "text": "OK, so how do we justify this formula?" + }, + { + "text": "Well, one way to think about it is in terms of tangent plane approximation." + }, + { + "text": "Let's think about the tangent plane to the graph of a function f. I have some pictures to show you." + }, + { + "text": "It will be easier if I show the pictures." + }, + { + "text": "Remember, partial f over partial x was obtained by looking at the situation where y is held constant." + }, + { + "text": "That means I am slicing the graph of f by a plane that is parallel to the xz plane." + }, + { + "text": "And then, when I change x, z changes." + }, + { + "text": "And the slope of that is going to be the derivative with respect to x." + }, + { + "text": "Now, if I do the same in the other direction, then I will have similarly the slope in a slice now parallel to the yz plane that will be partial f over partial y." + }, + { + "text": "In fact, in each case I have a line." + }, + { + "text": "And that line is tangent to the surface." + }, + { + "text": "Now, if I have two lines tangent to the surface, well, then together they determine for me the tangent plane to the surface." + }, + { + "text": "Let's try to see how that works." + }, + { + "text": "We know that f sub x and f sub y are the slopes of two tangent lines to this plane, sorry, two tangent lines to the graph." + }, + { + "text": "And let's write down the equations of these lines." + }, + { + "text": "I am not going to write parametric equations." + }, + { + "text": "I am going to write them in terms of x, y, z coordinates." + }, + { + "text": "Let's say that partial f over partial x at a given point is equal to a." + }, + { + "text": "Then that means that we have a line given by the following conditions." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk10.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..04a9beb08f73a15fd9091546cca18b48afb0c0c0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, of course, here I was very lucky." + }, + { + "text": "In general, I could not expect things to simplify that much." + }, + { + "text": "In fact, I cheated." + }, + { + "text": "I started from that." + }, + { + "text": "I expanded." + }, + { + "text": "And then that is how I got my example." + }, + { + "text": "The general method will be a bit different, but you will see it will actually also involve completing squares." + }, + { + "text": "Just there is more to it than what we have seen." + }, + { + "text": "We will come back to this tomorrow." + }, + { + "text": "How do I know that this equals?" + }, + { + "text": "y is what negative one?" + }, + { + "text": "How do I know that that whole function is greater or equal to negative one?" + }, + { + "text": "Well, I wrote f of x, y as something squared plus 2y2 minus one." + }, + { + "text": "This squared is always a positive number, non-negative." + }, + { + "text": "It is a square." + }, + { + "text": "The square of something is always non-negative." + }, + { + "text": "Similarly, y2 is also always non-negative." + }, + { + "text": "If you add something that is at least zero plus something that is at least zero and you subtract one, you get always at least minus one." + }, + { + "text": "And, in fact, the only way that you can get minus one is if both of these guys are zero at the same time." + }, + { + "text": "That is how I get my minimum." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk11.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..f4eced0dcd7ffc5bdcf9cd95cd7f63aa34e4a4ac --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "More about this tomorrow." + }, + { + "text": "In fact, what I would like to tell you about now instead is a nice application of min-max problems that maybe you don't think of as a min-max problem." + }, + { + "text": "But you will see, I mean, you don't think of it that way because probably your calculator can do it for you." + }, + { + "text": "Or, if not, your computer can do it for you." + }, + { + "text": "But it is actually something where the theory is based on minimization in two variables." + }, + { + "text": "Very often in experimental sequences you have to do something called least squares interpolation." + }, + { + "text": "And what is that about?" + }, + { + "text": "Well, it is the idea that maybe you do some experiments and you record some data." + }, + { + "text": "You have some data x and some data y." + }, + { + "text": "And I don't know, maybe, for example, maybe you are measuring frogs and you are trying to measure how big the frog leg is compared to the eyes of a frog or whatever, or trying to measure something." + }, + { + "text": "And if you are doing chemistry then it could be how much you put of some reactant and how much of the output product that you wanted to synthesize is going to be the same." + }, + { + "text": "All sorts of things." + }, + { + "text": "Make up your own example." + }, + { + "text": "You measure, basically, for various values of x what the value of y ends up being." + }, + { + "text": "And then you would like to claim, oh, well, these points are kind of aligned." + }, + { + "text": "I mean, of course, to a mathematician they are not aligned, but to an experimental scientist that is evidence that there is a relation between the two." + }, + { + "text": "And so you want to claim, and in your paper you will actually draw a nice little line that says, C, these two functions depend linearly on each other." + }, + { + "text": "The question is how do we come up with that nice line that passes smack in the middle of the points?" + }, + { + "text": "The question is, given experimental data, xiyi, so maybe I should actually be more precise." + }, + { + "text": "You are given some experimental data." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk12.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..ec058dcefcf28c0e3655b8df350c1a7550b31989 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "You have data points x1, y1, x2, y2, and so on, xn, yn." + }, + { + "text": "The question would be find the best fit line of the form y equals ax plus b that somehow approximates very well this data." + }, + { + "text": "You can also use that, by the way, to predict various things." + }, + { + "text": "For example, if you look at your new homework, actually the first problem asks you to predict how many iPods will be on this planet in ten years, looking at past sales and how they behave." + }, + { + "text": "One thing, by the way, before you lose all the money you don't have yet, you cannot use that to predict the stock market." + }, + { + "text": "Don't try to use that to make money." + }, + { + "text": "It doesn't work." + }, + { + "text": "One tricky thing here that I want to draw your attention to is what are the unknowns here?" + }, + { + "text": "The natural answer would be to say the unknowns are x and y." + }, + { + "text": "That is not actually the case." + }, + { + "text": "We are not trying to solve for some x and y. I mean we have some values given to us." + }, + { + "text": "And when we are looking for that line we don't really care about a particular value of x." + }, + { + "text": "What we care about is actually these coefficients a and b that will tell us what the relation between x and y is." + }, + { + "text": "In fact, we are trying to solve for a and b that will give us the nicest possible line for these points." + }, + { + "text": "The unknowns in our equations will have to be a and b, not x and y." + }, + { + "text": "The question really is find the best a and b." + }, + { + "text": "And, of course, we have to decide what we mean by best." + }, + { + "text": "Best will mean that we minimize some function of a and b that measures the total error that we are making when we are choosing this line compared to the experimental data." + }, + { + "text": "Maybe, roughly speaking, it should measure how far these points are from the line." + }, + { + "text": "But now there are various ways to do it." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk13.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..5d2475feee1af92e7e44b93eafd8ef1a1aeab556 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "And some of them are, I mean a lot of them are valid to give you different answers." + }, + { + "text": "You have to decide what it is that you prefer." + }, + { + "text": "For example, you could measure the distance to the line by projecting perpendicularly." + }, + { + "text": "Or, you could measure instead the difference between, for a given value of x, the difference between the experimental value of y and the predicted one." + }, + { + "text": "And that is often more relevant because these guys are actually maybe expressed in different units." + }, + { + "text": "They are not the same type of quantity." + }, + { + "text": "You cannot actually combine them arbitrarily." + }, + { + "text": "Anyway, the convention is usually we measure distance in this way." + }, + { + "text": "Next, you could try to minimize the largest distance." + }, + { + "text": "Say we look at where is the largest error and we make that the smallest possible." + }, + { + "text": "The drawback of doing that is experimentally very often you have one data point that is not good because maybe you fell asleep in front of the experiment." + }, + { + "text": "And so you did not measure the right thing." + }, + { + "text": "You tend to want to not give too much importance to some data point that is far away from the others." + }, + { + "text": "Maybe instead you want to measure the average distance." + }, + { + "text": "Or maybe you want to actually give more weight to things that are further away." + }, + { + "text": "And then you do not want to do the distance but the square of the distance." + }, + { + "text": "There are various possible answers." + }, + { + "text": "But one of them gives us a particularly nice formula for a and b." + }, + { + "text": "And so that is why it is the universally used one." + }, + { + "text": "Here it says least squares." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk14.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..03f389ad03cba30ec35302a03113c11b9ae12887 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That is because we will measure, actually, the sum of the squares of the errors." + }, + { + "text": "And why do we do that?" + }, + { + "text": "Well, part of it is because actually it looks good." + }, + { + "text": "I mean, when you see these plots in scientific papers, they really look like the line is indeed the ideal line." + }, + { + "text": "And the second reason is because actually the minimization problem that we will get is particularly simple, well-proposed and it is easy to solve." + }, + { + "text": "We will have a nice formula for the best a and the best b." + }, + { + "text": "If you have a method that is simple and gives you a good answer then that is probably the good one." + }, + { + "text": "We have to define best." + }, + { + "text": "And here it is in the sense of defining a total square error." + }, + { + "text": "Maybe I should say total square deviation." + }, + { + "text": "What do I mean by that?" + }, + { + "text": "The deviation for each data point is the difference between what you have measured and what you are predicting by your model." + }, + { + "text": "That is the difference between the two." + }, + { + "text": "Now what we will do is try to minimize the function capital D, which is just the sum for all the data points of the square of the deviation." + }, + { + "text": "Let me emphasize again this is a function of a and b. I mean, of course, there are a lot of letters in here." + }, + { + "text": "But xi and yi in real life will be numbers given to you." + }, + { + "text": "They will be the numbers that you have measured." + }, + { + "text": "You have measured all of this data." + }, + { + "text": "They are just going to be numbers." + }, + { + "text": "You put them in there and you get the answer." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk15.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..574ce46fe50beb8d2adc71dc4ba061053cadb260 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Any questions?" + }, + { + "text": "How do we minimize this function of a and b?" + }, + { + "text": "Let's use our new knowledge." + }, + { + "text": "Let's actually look for a critical point." + }, + { + "text": "We want to solve for partial d over partial a equals zero and partial d over partial b equals zero." + }, + { + "text": "That is how we look for critical points." + }, + { + "text": "Let's take the derivative of a." + }, + { + "text": "Well, the derivative of a sum is the sum of the derivatives." + }, + { + "text": "And now we have to take the derivative of this quantity squared." + }, + { + "text": "Remember how we take the derivative of a square." + }, + { + "text": "We take twice this quantity times the derivative of what we are squaring." + }, + { + "text": "We will get two times minus y i, sorry, y i minus a xi plus b times the derivative of this with respect to a." + }, + { + "text": "What is the derivative of this with respect to a?" + }, + { + "text": "Negative xi, exactly." + }, + { + "text": "And so we will want this to be zero." + }, + { + "text": "And partial d over partial b, we do the same thing but differentiating with respect to b instead of with respect to a." + }, + { + "text": "Again, sum of squares twice y i minus a xi plus b times the derivative of this with respect to b is, I think, negative one." + }, + { + "text": "That is the equations we have to solve." + }, + { + "text": "Well, let's reorganize this a little bit." + }, + { + "text": "The first equation, see, there are a's and there are b's in these equations." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk16.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..6dbbcdfd1a44915f775e513934285605a93fde83 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "I am going to just look at the coefficients of a and b." + }, + { + "text": "If you have good eyes, you can see probably that these are actually linear equations in a and b." + }, + { + "text": "There is a lot of clutter with all these x's and y's all over the place." + }, + { + "text": "Let's actually try to expand things and make that more apparent." + }, + { + "text": "The first thing I will do is I will actually get rid of these factors of two that are just not very important." + }, + { + "text": "I can simplify things by two." + }, + { + "text": "And next I am going to look at the coefficient of a. I will get basically a times xi squared." + }, + { + "text": "Well, let me just do it and it should be clear." + }, + { + "text": "I claim when we simplify this we get a times xi squared plus xi times b minus xi yi." + }, + { + "text": "And we set this equal to zero." + }, + { + "text": "Do you agree that this is what we get when we expand that product?" + }, + { + "text": "No?" + }, + { + "text": "OK, let's do the other one." + }, + { + "text": "We just multiply by minus one." + }, + { + "text": "We take the opposite of that." + }, + { + "text": "It will be axi plus b. I will write that as xia plus b minus yi." + }, + { + "text": "And let me just reorganize that by actually putting all the a's together." + }, + { + "text": "That means actually I will have sum of all the xi squared times xi times b minus sum of xi yi equals zero." + }, + { + "text": "If I rewrite this it becomes sum of xi squared times a plus sum of the xi's times b minus, let me move the other guys to the other side, equals sum of xi yi." + }, + { + "text": "And that one becomes sum of xi times a plus how many b's do I get from this one?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk17.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..46c92ceb193fbddba6ccd0128c8434e1fa895b6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, I get one for each data point." + }, + { + "text": "When I sum them together I will get n. Very good." + }, + { + "text": "So, n times b equals sum of yi." + }, + { + "text": "Now, these quantities may look scary, but they are actually just numbers." + }, + { + "text": "For example, for this one you look at all your data points." + }, + { + "text": "For each of them you take the value of x and you just sum all these numbers together." + }, + { + "text": "What you get, actually, is a linear system in a two-by-two linear system." + }, + { + "text": "And so now we can solve this for a and b." + }, + { + "text": "In practice, of course, first you plug in the numbers for xi and yi and then you solve the system that you get." + }, + { + "text": "And we know how to solve two-by-two linear systems, I hope." + }, + { + "text": "That is how we find the best fit line." + }, + { + "text": "Now, why is that going to be the best one instead of the worst one?" + }, + { + "text": "We just solved for a critical point." + }, + { + "text": "That could actually be a maximum of this error function d. We will have the answer to that next time." + }, + { + "text": "But trust me, if you really want to go for the second derivative test that we will do tomorrow and apply it in this case, it is quite hard to check." + }, + { + "text": "But you can see it is actually a minimum." + }, + { + "text": "I will just say we can show that it is a minimum." + }, + { + "text": "Now, even for the linear case, it is the one that we are the most familiar with." + }, + { + "text": "Least squares interpolation actually works in much more general settings." + }, + { + "text": "Instead of fitting for the best line, if you think that there is a different kind of relation, then maybe you can fit in using a different kind of formula." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk18.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..fa2ca36c0d134e6b3372da5aa353386c01a4066b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me actually illustrate that for you." + }, + { + "text": "I don't know if you are familiar with Moore's law." + }, + { + "text": "It is something that is supposed to tell you how quickly, basically, computer chips become smarter, faster and faster over time." + }, + { + "text": "It is a law that says things about the number of transistors that you can fit onto a computer chip." + }, + { + "text": "Here I have some data about the number of transistors on a standard PC processor as a function of time." + }, + { + "text": "And, well, if you try to do the best line fit, you will see quickly that it doesn't seem to follow a linear trend." + }, + { + "text": "On the other hand, if you plot the diagram in a log scale, the log of the number of transistors as a function of time, then you get a much better line." + }, + { + "text": "And so, in fact, that means that you had an exponential relation between the number of transistors and time." + }, + { + "text": "And so, actually, that is what Moore's law says." + }, + { + "text": "It says that the number of transistors on a chip doubles, depending on the version, every 18 months or every two years." + }, + { + "text": "They keep changing the statement." + }, + { + "text": "How do we find that best exponential fit?" + }, + { + "text": "Well, an exponential fit would be something of the form y equals a constant times exponential of a times x." + }, + { + "text": "That is what we want to look at." + }, + { + "text": "Well, we could try to minimize a square error like we did earlier, but that doesn't work well at all." + }, + { + "text": "The equations that you get are very complicated." + }, + { + "text": "You cannot solve them." + }, + { + "text": "But remember what I showed you on this log plot." + }, + { + "text": "If you plot the log of y as a function of x, then suddenly it becomes a linear relation." + }, + { + "text": "Observe this is the same as ln of x equals ln of c plus ax." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk19.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..55b8384a00899de02bdae34fca68d10a37a51f56 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk19.json @@ -0,0 +1,53 @@ +[ + { + "text": "And that is a linear best fit." + }, + { + "text": "What you do is you just look for the best straight line fit for the log of y." + }, + { + "text": "That is something we already know." + }, + { + "text": "But you can also do other examples." + }, + { + "text": "For example, let's say that we have something more complicated." + }, + { + "text": "Let's say that we have actually a quadratic law." + }, + { + "text": "For example, y is of the form ax2 bx c. And, of course, you are trying to find somehow the best." + }, + { + "text": "That would mean here fitting the best parabola for your data points." + }, + { + "text": "Well, to do that you would need to find a, b and c. And now you would have actually a function of a, b and c, which would be the sum of all data points of the quadratic equation." + }, + { + "text": "And if you try to solve for critical points, now you will have three equations involving a, b and c. And, in fact, you will find a three by three linear system." + }, + { + "text": "And it works just the same way." + }, + { + "text": "Just you have a little bit more data." + }, + { + "text": "Basically, you see that these best fit problems are an example of minimization problem." + }, + { + "text": "But maybe you didn't expect to see minimization problems come in." + }, + { + "text": "But that is really the way to handle these questions." + }, + { + "text": "OK, so tomorrow we will go back to the question of how do we decide whether it is a minimum or a maximum?" + }, + { + "text": "And we will continue exploring functions of several variables." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk2.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..cbdde5612839d21f7df1c4e4a177c22a02adffc6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "I am going to keep y constant equal to y0." + }, + { + "text": "And I am going to change x." + }, + { + "text": "And, as I change x, z will change at a rate that is equal to a." + }, + { + "text": "That would be z equals z0 plus a times the change in x, x minus x0." + }, + { + "text": "That is how you would describe the line that is, I guess, the one that is plotted in green here." + }, + { + "text": "That is the intersection with the slice parallel to the xz plane." + }, + { + "text": "I hold y constant equal to y0." + }, + { + "text": "And z is a function of x that varies with a rate of a." + }, + { + "text": "And now, if I look similarly at the other slice, let's say that the partial with respect to y is equal to b, then I get another line which is obtained by the fact that z depends on y and the rate of change with respect to y will be b while x is held constant equal to x0." + }, + { + "text": "These two lines are both going to be in the tangent plane to the surface." + }, + { + "text": "They are both tangent to the surface, f of f. And, well, together they determine a plane." + }, + { + "text": "And that plane is just given by the formula z equals z0 plus a times x minus x0 plus b times y plus b." + }, + { + "text": "If you look at what happens, this is the equation of a plane, z equals constant times x plus constant times y plus constant." + }, + { + "text": "And if you look at what happens if I hold y constant and vary x, I recover the first line." + }, + { + "text": "If I hold x constant and vary y, I get the second line." + }, + { + "text": "Another way to do it, of course, would be to write actually parametric equations of these lines, get vectors along them and then take the cross-product to get the normal vector to the plane, and then get this equation for the plane using the normal vector." + }, + { + "text": "That also works and it gives you the same formula." + }, + { + "text": "If you are curious, exercise, do it again using parametrics and using cross-product to get the plane equation." + }, + { + "text": "OK, so that is how we get the tangent plane." + }, + { + "text": "And now, what this approximation formula here says is that, in fact, the graph of a function is close to the tangent plane." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk3.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..db670d552209553a73abe7a57967ebd9528e07b0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "If we were moving on the tangent plane, this would be an actual equality." + }, + { + "text": "Delta z would be a linear function of delta x and delta y." + }, + { + "text": "And the graph of a function is near the tangent plane, but it is not quite the same." + }, + { + "text": "It is only an approximation for small delta x and small delta y." + }, + { + "text": "The approximation formula says the graph of f is close to its tangent plane." + }, + { + "text": "And we can use that formula over here now to estimate how the value of f changes if I change x and y at the same time." + }, + { + "text": "Questions about that?" + }, + { + "text": "Now that we have caught up with what we were supposed to see on Tuesday, I can tell you now about max and min problems." + }, + { + "text": "Min problems." + }, + { + "text": "That is going to be an application of partial derivatives to look at optimization problems." + }, + { + "text": "Maybe ten years from now when you have a real job, your job might be to actually minimize the cost of something or maximize the profit of something or whatever." + }, + { + "text": "But typically, the function that you will have to strive to minimize or maximize will depend on several variables." + }, + { + "text": "If you have a function of one variable, you know that to find its minimum or its maximum you look at the derivative and you set that equal to zero." + }, + { + "text": "And you try to then look at what happens to the function." + }, + { + "text": "Here it is going to be kind of similar, except, of course, we have several variables." + }, + { + "text": "For today, we will think about a function of two variables." + }, + { + "text": "But it works exactly the same if you have three variables, ten variables, a million variables." + }, + { + "text": "The first observation is that if we have a local minimum or a local maximum, then both partial derivative, partial f, partial x and partial f, partial y are both zero at the same time." + }, + { + "text": "Why is that?" + }, + { + "text": "Well, let's say that f sub x is zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk4.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..6a4752d759dedab56f0865629de49a11db927b62 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means when I vary x, well, to first order the function doesn't change." + }, + { + "text": "Maybe that is because it is going through." + }, + { + "text": "If I look only at the slice parallel to the x-axis, then maybe I am going through the minimum." + }, + { + "text": "But then, if partial f, partial y is not zero, then actually by changing y I could still make the value larger or smaller." + }, + { + "text": "That wouldn't be an actual maximum or minimum." + }, + { + "text": "It would only be maximum or minimum if I stay in the slice." + }, + { + "text": "But if I allow myself to change y, that doesn't work." + }, + { + "text": "I need actually to know that if I change y the value will not change either to first order." + }, + { + "text": "That is why I also need partial f, partial y to be zero." + }, + { + "text": "Now, let's say that they are both zero." + }, + { + "text": "Well, why is that enough?" + }, + { + "text": "It is essentially enough because of this formula telling me that if both of these guys are zero then to first order the function doesn't change." + }, + { + "text": "And then, of course, there will be maybe quadratic terms that will actually turn that." + }, + { + "text": "This won't really say that your function is actually constant." + }, + { + "text": "It will just tell you that maybe it will be actually quadratic or higher order in delta x and delta y." + }, + { + "text": "That is what you expect to have at a maximum or a minimum." + }, + { + "text": "That condition is the same thing as saying that the tangent plane to the graph is actually going to be horizontal." + }, + { + "text": "And that is what you want to have." + }, + { + "text": "Say you have a minimum." + }, + { + "text": "Well, see that the tangent plane at this point, at the bottom of the graph, is going to be horizontal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk5.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..7e48c199e023a813f11acd0a96e5d01eb8971e00 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you can see that on this equation of a tangent plane, when both these coefficients are zero, that is when the equation becomes z equals constant, the horizontal plane." + }, + { + "text": "Does that make sense?" + }, + { + "text": "We will have a name for this kind of point because actually what we will see very soon is that these conditions are necessary but they are not sufficient." + }, + { + "text": "There are actually other kinds of points where the partial derivatives are zero." + }, + { + "text": "Let's give a name to this." + }, + { + "text": "We say that x0, y0 is a critical point of F if the partial derivative with respect to x and the partial derivative with respect to y are both zero." + }, + { + "text": "More generally, you would want all the partial derivatives, no matter how many variables you have, you want all the partials to be zero." + }, + { + "text": "Let's see an example." + }, + { + "text": "Let's say I give you the function f of x, y equals x squared minus 2xy plus py squared plus 2x minus 2y." + }, + { + "text": "And let's try to figure out whether we can minimize or maximize this." + }, + { + "text": "What we start doing immediately is taking the partial derivatives." + }, + { + "text": "What is f sub x?" + }, + { + "text": "It starts with 2x minus 2y plus zero plus two." + }, + { + "text": "Remember that y is a constant so this differentiates to zero." + }, + { + "text": "Now, if we do f sub y, that is going to be zero minus 2x plus 6y minus two." + }, + { + "text": "And what we want to do is set these things equal to zero." + }, + { + "text": "And we want to solve these two equations at the same time." + }, + { + "text": "An important thing to remember, maybe I should have told you a couple of weeks ago already, if you have two equations to solve, well, it is very good to try to simplify them by adding them together or whatever." + }, + { + "text": "But you must keep two equations." + }, + { + "text": "If you have two equations, you should not end up with just one equation out of nowhere." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk6.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9395a90268474c96a0037bb843bc6e78e8145fe5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "For example, here we can certainly simplify things by summing them together." + }, + { + "text": "See, if we add them together, well, the x's cancel and the constants cancel." + }, + { + "text": "In fact, we are just left with 4y equals zero." + }, + { + "text": "That is pretty good." + }, + { + "text": "That tells us y should be zero." + }, + { + "text": "But then we should, of course, go back to these and see what else we know." + }, + { + "text": "Well, now it tells us, if you put y equals zero, that tells you 2x plus 2 equals zero." + }, + { + "text": "That tells you x equals minus one." + }, + { + "text": "We have one critical point." + }, + { + "text": "That is x, y equals minus one over two." + }, + { + "text": "Any questions so far?" + }, + { + "text": "Well, you should have a question." + }, + { + "text": "The question should be how do we know if it is a maximum or a minimum?" + }, + { + "text": "Well, if we had a function of one variable, we would decide things based on the second derivative." + }, + { + "text": "And, in fact, we will see tomorrow how to do things based on the second derivative." + }, + { + "text": "But that is kind of tricky because there are a lot of second derivatives." + }, + { + "text": "I mean, we already have two first derivatives." + }, + { + "text": "You can imagine that if you keep taking partials, you may end up with more and more." + }, + { + "text": "We will have to figure out carefully what the condition should be." + }, + { + "text": "We will do that tomorrow." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk7.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..4bcbbf6b2197e00d7483dbd1b1319f8d7b454496 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "For now, let's just try to look at how do we understand these things by hand." + }, + { + "text": "In fact, let me point out to you immediately that there is more than maxima and minima." + }, + { + "text": "Remember, we saw the example of x squared plus y squared that has a critical point." + }, + { + "text": "The critical point is obviously a minimum." + }, + { + "text": "And, of course, it could be a local minimum because it could be that if you have a more complicated function there is indeed a minimum here." + }, + { + "text": "But then elsewhere the function drops to a lower value." + }, + { + "text": "We call that just a local minimum to say that it is a minimum if you stick to values that are close enough to that point." + }, + { + "text": "Of course, you also have a local maximum." + }, + { + "text": "Well, I did not plot it, but it is easy to plot." + }, + { + "text": "That is a local maximum." + }, + { + "text": "But there is a third example of critical point, and that is a saddle point." + }, + { + "text": "The saddle point is a new phenomenon that you do not really see in a single variable calculus." + }, + { + "text": "It is a critical point that is neither a minimum nor a maximum because, depending on which direction you look in, it is either one or the other." + }, + { + "text": "The point in the middle at the origin is a saddle point." + }, + { + "text": "If you look at the tangent plane to this graph you will see that it is actually horizontal at the origin." + }, + { + "text": "You have this mountain pass." + }, + { + "text": "At the mountain pass the ground is horizontal." + }, + { + "text": "But, depending on which direction you go, you go up or down." + }, + { + "text": "We say that the point is a saddle point if it is neither a minimum nor a maximum." + }, + { + "text": "OK, so the possibilities could be a local min, a local max, or a saddle." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk8.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8eebe5d35e57a9bb443552331906178033fbb172 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "Tomorrow we will see how to decide which one it is in general using second derivatives." + }, + { + "text": "For this time let's just try to do it by hand." + }, + { + "text": "I just want to observe." + }, + { + "text": "In fact, I can try to, you know, these examples that I have here, they are x2 y2 y2-x2." + }, + { + "text": "They are sums or differences of squares." + }, + { + "text": "And, if we know that we can put things as a sum of squares, for example, we will be done." + }, + { + "text": "Let's try to express this maybe in terms of a square." + }, + { + "text": "Well, the main problem is this 2xy." + }, + { + "text": "But, observe, we know something that starts with x2 minus 2xy that is actually the square of something else." + }, + { + "text": "It would be x2 minus 2xy, well, plus y2, not plus 3y2." + }, + { + "text": "Let's try to do that." + }, + { + "text": "We are going to complete the square." + }, + { + "text": "I am going to say it is x minus y squared." + }, + { + "text": "That gives me the first two terms and also y squared." + }, + { + "text": "Well, I still need to add two more y squares." + }, + { + "text": "And I also need to add, of course, the 2x minus 2y." + }, + { + "text": "It is simpler." + }, + { + "text": "It is still not simple enough for my taste." + }, + { + "text": "I can actually do better." + }, + { + "text": "See, I mean now what is, so these guys look like a sum of squares." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk9.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..2ebab68b48ed9108ed215c21106e93056b697b19 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_2_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "But here I have this extra stuff." + }, + { + "text": "But, 2x minus 2y, well, that is twice x minus y." + }, + { + "text": "It looks like maybe we can simplify this and make this into another square." + }, + { + "text": "In fact, I can simplify this further to x minus y plus one squared." + }, + { + "text": "See, that would start like, maybe I should put parentheses here, that would be x minus y squared plus twice x minus y." + }, + { + "text": "And then there is a plus one." + }, + { + "text": "Well, we don't have that plus one, so let's remove it by subtracting one." + }, + { + "text": "Oh, let me find that minus one here." + }, + { + "text": "And I still have my 2y squared." + }, + { + "text": "Do you see why this is the same function as that one?" + }, + { + "text": "Again, if I expand x minus y plus one squared, I get x minus y squared plus twice x minus y, that is those guys, plus one." + }, + { + "text": "But I will have a minus one and that will cancel out." + }, + { + "text": "And then I have a plus 2y squared." + }, + { + "text": "Now what I know, see, this is a sum of two squares minus one." + }, + { + "text": "And this critical point, x, y equals minus one, zero, that is exactly when this is zero and that is zero." + }, + { + "text": "That is the smallest value." + }, + { + "text": "This is always greater or equal to zero, same with that one." + }, + { + "text": "That is always at least minus one." + }, + { + "text": "And minus one happens to be the value at the critical point." + }, + { + "text": "It is a minimum." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk0.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..e6499639a2dd486fc34915743508e989029de764 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "Today we are going to see how to use what we saw last time about partial derivatives to handle minimization or maximization problems involving functions of several variables." + }, + { + "text": "Remember last time we said that when we have a function, say, of two variables, x and y, then we have actually two different derivatives." + }, + { + "text": "Partial f, partial x, also called f sub x, is the derivative with respect to x keeping y constant." + }, + { + "text": "And we have partial f, partial y, also called f sub y, where we vary y and we treat x as a constant." + }, + { + "text": "And now, one thing I didn't have time to tell you about, but hopefully you heard about in recitation yesterday, is the approximation formula that tells you what happens if you vary both x and y. F sub x tells us what happens if we change x a little bit by some small amount delta x. F sub y tells us how f changes if we change y by a small amount delta y." + }, + { + "text": "If we do both at the same time, then the two effects will add up with each other." + }, + { + "text": "Because you can imagine that first you will change x and then you will change y or the other way around." + }, + { + "text": "It doesn't really matter." + }, + { + "text": "If we change x by a certain amount delta x, and if we change y by the amount delta y, and let's say that we have z equals f of x, y, then that changes by an amount which is approximately f sub x times delta x plus f sub y times delta y." + }, + { + "text": "And that is one of the most important formulas about partial derivatives." + }, + { + "text": "The intuition for this, again, is just the two effects add up." + }, + { + "text": "If I change x by a small amount and then I change y, well, first changing x will modify f. How much does it modify f?" + }, + { + "text": "The answer is the rate of change." + }, + { + "text": "The rate of change is f sub x." + }, + { + "text": "And, if I change y, then the rate of change of f when I change y is f sub y." + }, + { + "text": "All together, I get this change in the value of f. And, of course, that is only an approximation formula." + }, + { + "text": "Actually, there would be higher order terms involving second and third derivatives and so on." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk1.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..24332c5f071c389023f7abaf7259fb1a63c23f92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "One way to justify this, sorry, I was distracted by a microphone problem." + }, + { + "text": "OK, so how do we justify this formula?" + }, + { + "text": "Well, one way to think about it is in terms of tangent plane approximation." + }, + { + "text": "Let's think about the tangent plane to the graph of a function f. I have some pictures to show you." + }, + { + "text": "It will be easier if I show the pictures." + }, + { + "text": "Remember, partial f over partial x was obtained by looking at the situation where y is held constant." + }, + { + "text": "That means I am slicing the graph of f by a plane that is parallel to the xz plane." + }, + { + "text": "And then, when I change x, z changes." + }, + { + "text": "And the slope of that is going to be the derivative with respect to x." + }, + { + "text": "Now, if I do the same in the other direction, then I will have similarly the slope in a slice now parallel to the yz plane that will be partial f over partial y." + }, + { + "text": "In fact, in each case I have a line." + }, + { + "text": "And that line is tangent to the surface." + }, + { + "text": "Now, if I have two lines tangent to the surface, well, then together they determine for me the tangent plane to the surface." + }, + { + "text": "Let's try to see how that works." + }, + { + "text": "We know that f sub x and f sub y are the slopes of two tangent lines to this plane, sorry, two tangent lines to the graph." + }, + { + "text": "And let's write down the equations of these lines." + }, + { + "text": "I am not going to write parametric equations." + }, + { + "text": "I am going to write them in terms of x, y, z coordinates." + }, + { + "text": "Let's say that partial f over partial x at a given point is equal to a." + }, + { + "text": "Then that means that we have a line given by the following conditions." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk10.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..04a9beb08f73a15fd9091546cca18b48afb0c0c0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, of course, here I was very lucky." + }, + { + "text": "In general, I could not expect things to simplify that much." + }, + { + "text": "In fact, I cheated." + }, + { + "text": "I started from that." + }, + { + "text": "I expanded." + }, + { + "text": "And then that is how I got my example." + }, + { + "text": "The general method will be a bit different, but you will see it will actually also involve completing squares." + }, + { + "text": "Just there is more to it than what we have seen." + }, + { + "text": "We will come back to this tomorrow." + }, + { + "text": "How do I know that this equals?" + }, + { + "text": "y is what negative one?" + }, + { + "text": "How do I know that that whole function is greater or equal to negative one?" + }, + { + "text": "Well, I wrote f of x, y as something squared plus 2y2 minus one." + }, + { + "text": "This squared is always a positive number, non-negative." + }, + { + "text": "It is a square." + }, + { + "text": "The square of something is always non-negative." + }, + { + "text": "Similarly, y2 is also always non-negative." + }, + { + "text": "If you add something that is at least zero plus something that is at least zero and you subtract one, you get always at least minus one." + }, + { + "text": "And, in fact, the only way that you can get minus one is if both of these guys are zero at the same time." + }, + { + "text": "That is how I get my minimum." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk11.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..f4eced0dcd7ffc5bdcf9cd95cd7f63aa34e4a4ac --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "More about this tomorrow." + }, + { + "text": "In fact, what I would like to tell you about now instead is a nice application of min-max problems that maybe you don't think of as a min-max problem." + }, + { + "text": "But you will see, I mean, you don't think of it that way because probably your calculator can do it for you." + }, + { + "text": "Or, if not, your computer can do it for you." + }, + { + "text": "But it is actually something where the theory is based on minimization in two variables." + }, + { + "text": "Very often in experimental sequences you have to do something called least squares interpolation." + }, + { + "text": "And what is that about?" + }, + { + "text": "Well, it is the idea that maybe you do some experiments and you record some data." + }, + { + "text": "You have some data x and some data y." + }, + { + "text": "And I don't know, maybe, for example, maybe you are measuring frogs and you are trying to measure how big the frog leg is compared to the eyes of a frog or whatever, or trying to measure something." + }, + { + "text": "And if you are doing chemistry then it could be how much you put of some reactant and how much of the output product that you wanted to synthesize is going to be the same." + }, + { + "text": "All sorts of things." + }, + { + "text": "Make up your own example." + }, + { + "text": "You measure, basically, for various values of x what the value of y ends up being." + }, + { + "text": "And then you would like to claim, oh, well, these points are kind of aligned." + }, + { + "text": "I mean, of course, to a mathematician they are not aligned, but to an experimental scientist that is evidence that there is a relation between the two." + }, + { + "text": "And so you want to claim, and in your paper you will actually draw a nice little line that says, C, these two functions depend linearly on each other." + }, + { + "text": "The question is how do we come up with that nice line that passes smack in the middle of the points?" + }, + { + "text": "The question is, given experimental data, xiyi, so maybe I should actually be more precise." + }, + { + "text": "You are given some experimental data." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk12.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..ec058dcefcf28c0e3655b8df350c1a7550b31989 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "You have data points x1, y1, x2, y2, and so on, xn, yn." + }, + { + "text": "The question would be find the best fit line of the form y equals ax plus b that somehow approximates very well this data." + }, + { + "text": "You can also use that, by the way, to predict various things." + }, + { + "text": "For example, if you look at your new homework, actually the first problem asks you to predict how many iPods will be on this planet in ten years, looking at past sales and how they behave." + }, + { + "text": "One thing, by the way, before you lose all the money you don't have yet, you cannot use that to predict the stock market." + }, + { + "text": "Don't try to use that to make money." + }, + { + "text": "It doesn't work." + }, + { + "text": "One tricky thing here that I want to draw your attention to is what are the unknowns here?" + }, + { + "text": "The natural answer would be to say the unknowns are x and y." + }, + { + "text": "That is not actually the case." + }, + { + "text": "We are not trying to solve for some x and y. I mean we have some values given to us." + }, + { + "text": "And when we are looking for that line we don't really care about a particular value of x." + }, + { + "text": "What we care about is actually these coefficients a and b that will tell us what the relation between x and y is." + }, + { + "text": "In fact, we are trying to solve for a and b that will give us the nicest possible line for these points." + }, + { + "text": "The unknowns in our equations will have to be a and b, not x and y." + }, + { + "text": "The question really is find the best a and b." + }, + { + "text": "And, of course, we have to decide what we mean by best." + }, + { + "text": "Best will mean that we minimize some function of a and b that measures the total error that we are making when we are choosing this line compared to the experimental data." + }, + { + "text": "Maybe, roughly speaking, it should measure how far these points are from the line." + }, + { + "text": "But now there are various ways to do it." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk13.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..5d2475feee1af92e7e44b93eafd8ef1a1aeab556 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "And some of them are, I mean a lot of them are valid to give you different answers." + }, + { + "text": "You have to decide what it is that you prefer." + }, + { + "text": "For example, you could measure the distance to the line by projecting perpendicularly." + }, + { + "text": "Or, you could measure instead the difference between, for a given value of x, the difference between the experimental value of y and the predicted one." + }, + { + "text": "And that is often more relevant because these guys are actually maybe expressed in different units." + }, + { + "text": "They are not the same type of quantity." + }, + { + "text": "You cannot actually combine them arbitrarily." + }, + { + "text": "Anyway, the convention is usually we measure distance in this way." + }, + { + "text": "Next, you could try to minimize the largest distance." + }, + { + "text": "Say we look at where is the largest error and we make that the smallest possible." + }, + { + "text": "The drawback of doing that is experimentally very often you have one data point that is not good because maybe you fell asleep in front of the experiment." + }, + { + "text": "And so you did not measure the right thing." + }, + { + "text": "You tend to want to not give too much importance to some data point that is far away from the others." + }, + { + "text": "Maybe instead you want to measure the average distance." + }, + { + "text": "Or maybe you want to actually give more weight to things that are further away." + }, + { + "text": "And then you do not want to do the distance but the square of the distance." + }, + { + "text": "There are various possible answers." + }, + { + "text": "But one of them gives us a particularly nice formula for a and b." + }, + { + "text": "And so that is why it is the universally used one." + }, + { + "text": "Here it says least squares." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk14.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..03f389ad03cba30ec35302a03113c11b9ae12887 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That is because we will measure, actually, the sum of the squares of the errors." + }, + { + "text": "And why do we do that?" + }, + { + "text": "Well, part of it is because actually it looks good." + }, + { + "text": "I mean, when you see these plots in scientific papers, they really look like the line is indeed the ideal line." + }, + { + "text": "And the second reason is because actually the minimization problem that we will get is particularly simple, well-proposed and it is easy to solve." + }, + { + "text": "We will have a nice formula for the best a and the best b." + }, + { + "text": "If you have a method that is simple and gives you a good answer then that is probably the good one." + }, + { + "text": "We have to define best." + }, + { + "text": "And here it is in the sense of defining a total square error." + }, + { + "text": "Maybe I should say total square deviation." + }, + { + "text": "What do I mean by that?" + }, + { + "text": "The deviation for each data point is the difference between what you have measured and what you are predicting by your model." + }, + { + "text": "That is the difference between the two." + }, + { + "text": "Now what we will do is try to minimize the function capital D, which is just the sum for all the data points of the square of the deviation." + }, + { + "text": "Let me emphasize again this is a function of a and b. I mean, of course, there are a lot of letters in here." + }, + { + "text": "But xi and yi in real life will be numbers given to you." + }, + { + "text": "They will be the numbers that you have measured." + }, + { + "text": "You have measured all of this data." + }, + { + "text": "They are just going to be numbers." + }, + { + "text": "You put them in there and you get the answer." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk15.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..574ce46fe50beb8d2adc71dc4ba061053cadb260 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Any questions?" + }, + { + "text": "How do we minimize this function of a and b?" + }, + { + "text": "Let's use our new knowledge." + }, + { + "text": "Let's actually look for a critical point." + }, + { + "text": "We want to solve for partial d over partial a equals zero and partial d over partial b equals zero." + }, + { + "text": "That is how we look for critical points." + }, + { + "text": "Let's take the derivative of a." + }, + { + "text": "Well, the derivative of a sum is the sum of the derivatives." + }, + { + "text": "And now we have to take the derivative of this quantity squared." + }, + { + "text": "Remember how we take the derivative of a square." + }, + { + "text": "We take twice this quantity times the derivative of what we are squaring." + }, + { + "text": "We will get two times minus y i, sorry, y i minus a xi plus b times the derivative of this with respect to a." + }, + { + "text": "What is the derivative of this with respect to a?" + }, + { + "text": "Negative xi, exactly." + }, + { + "text": "And so we will want this to be zero." + }, + { + "text": "And partial d over partial b, we do the same thing but differentiating with respect to b instead of with respect to a." + }, + { + "text": "Again, sum of squares twice y i minus a xi plus b times the derivative of this with respect to b is, I think, negative one." + }, + { + "text": "That is the equations we have to solve." + }, + { + "text": "Well, let's reorganize this a little bit." + }, + { + "text": "The first equation, see, there are a's and there are b's in these equations." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk16.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..6dbbcdfd1a44915f775e513934285605a93fde83 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "I am going to just look at the coefficients of a and b." + }, + { + "text": "If you have good eyes, you can see probably that these are actually linear equations in a and b." + }, + { + "text": "There is a lot of clutter with all these x's and y's all over the place." + }, + { + "text": "Let's actually try to expand things and make that more apparent." + }, + { + "text": "The first thing I will do is I will actually get rid of these factors of two that are just not very important." + }, + { + "text": "I can simplify things by two." + }, + { + "text": "And next I am going to look at the coefficient of a. I will get basically a times xi squared." + }, + { + "text": "Well, let me just do it and it should be clear." + }, + { + "text": "I claim when we simplify this we get a times xi squared plus xi times b minus xi yi." + }, + { + "text": "And we set this equal to zero." + }, + { + "text": "Do you agree that this is what we get when we expand that product?" + }, + { + "text": "No?" + }, + { + "text": "OK, let's do the other one." + }, + { + "text": "We just multiply by minus one." + }, + { + "text": "We take the opposite of that." + }, + { + "text": "It will be axi plus b. I will write that as xia plus b minus yi." + }, + { + "text": "And let me just reorganize that by actually putting all the a's together." + }, + { + "text": "That means actually I will have sum of all the xi squared times xi times b minus sum of xi yi equals zero." + }, + { + "text": "If I rewrite this it becomes sum of xi squared times a plus sum of the xi's times b minus, let me move the other guys to the other side, equals sum of xi yi." + }, + { + "text": "And that one becomes sum of xi times a plus how many b's do I get from this one?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk17.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..46c92ceb193fbddba6ccd0128c8434e1fa895b6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, I get one for each data point." + }, + { + "text": "When I sum them together I will get n. Very good." + }, + { + "text": "So, n times b equals sum of yi." + }, + { + "text": "Now, these quantities may look scary, but they are actually just numbers." + }, + { + "text": "For example, for this one you look at all your data points." + }, + { + "text": "For each of them you take the value of x and you just sum all these numbers together." + }, + { + "text": "What you get, actually, is a linear system in a two-by-two linear system." + }, + { + "text": "And so now we can solve this for a and b." + }, + { + "text": "In practice, of course, first you plug in the numbers for xi and yi and then you solve the system that you get." + }, + { + "text": "And we know how to solve two-by-two linear systems, I hope." + }, + { + "text": "That is how we find the best fit line." + }, + { + "text": "Now, why is that going to be the best one instead of the worst one?" + }, + { + "text": "We just solved for a critical point." + }, + { + "text": "That could actually be a maximum of this error function d. We will have the answer to that next time." + }, + { + "text": "But trust me, if you really want to go for the second derivative test that we will do tomorrow and apply it in this case, it is quite hard to check." + }, + { + "text": "But you can see it is actually a minimum." + }, + { + "text": "I will just say we can show that it is a minimum." + }, + { + "text": "Now, even for the linear case, it is the one that we are the most familiar with." + }, + { + "text": "Least squares interpolation actually works in much more general settings." + }, + { + "text": "Instead of fitting for the best line, if you think that there is a different kind of relation, then maybe you can fit in using a different kind of formula." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk18.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..fa2ca36c0d134e6b3372da5aa353386c01a4066b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me actually illustrate that for you." + }, + { + "text": "I don't know if you are familiar with Moore's law." + }, + { + "text": "It is something that is supposed to tell you how quickly, basically, computer chips become smarter, faster and faster over time." + }, + { + "text": "It is a law that says things about the number of transistors that you can fit onto a computer chip." + }, + { + "text": "Here I have some data about the number of transistors on a standard PC processor as a function of time." + }, + { + "text": "And, well, if you try to do the best line fit, you will see quickly that it doesn't seem to follow a linear trend." + }, + { + "text": "On the other hand, if you plot the diagram in a log scale, the log of the number of transistors as a function of time, then you get a much better line." + }, + { + "text": "And so, in fact, that means that you had an exponential relation between the number of transistors and time." + }, + { + "text": "And so, actually, that is what Moore's law says." + }, + { + "text": "It says that the number of transistors on a chip doubles, depending on the version, every 18 months or every two years." + }, + { + "text": "They keep changing the statement." + }, + { + "text": "How do we find that best exponential fit?" + }, + { + "text": "Well, an exponential fit would be something of the form y equals a constant times exponential of a times x." + }, + { + "text": "That is what we want to look at." + }, + { + "text": "Well, we could try to minimize a square error like we did earlier, but that doesn't work well at all." + }, + { + "text": "The equations that you get are very complicated." + }, + { + "text": "You cannot solve them." + }, + { + "text": "But remember what I showed you on this log plot." + }, + { + "text": "If you plot the log of y as a function of x, then suddenly it becomes a linear relation." + }, + { + "text": "Observe this is the same as ln of x equals ln of c plus ax." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk19.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..55b8384a00899de02bdae34fca68d10a37a51f56 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk19.json @@ -0,0 +1,53 @@ +[ + { + "text": "And that is a linear best fit." + }, + { + "text": "What you do is you just look for the best straight line fit for the log of y." + }, + { + "text": "That is something we already know." + }, + { + "text": "But you can also do other examples." + }, + { + "text": "For example, let's say that we have something more complicated." + }, + { + "text": "Let's say that we have actually a quadratic law." + }, + { + "text": "For example, y is of the form ax2 bx c. And, of course, you are trying to find somehow the best." + }, + { + "text": "That would mean here fitting the best parabola for your data points." + }, + { + "text": "Well, to do that you would need to find a, b and c. And now you would have actually a function of a, b and c, which would be the sum of all data points of the quadratic equation." + }, + { + "text": "And if you try to solve for critical points, now you will have three equations involving a, b and c. And, in fact, you will find a three by three linear system." + }, + { + "text": "And it works just the same way." + }, + { + "text": "Just you have a little bit more data." + }, + { + "text": "Basically, you see that these best fit problems are an example of minimization problem." + }, + { + "text": "But maybe you didn't expect to see minimization problems come in." + }, + { + "text": "But that is really the way to handle these questions." + }, + { + "text": "OK, so tomorrow we will go back to the question of how do we decide whether it is a minimum or a maximum?" + }, + { + "text": "And we will continue exploring functions of several variables." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk2.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..cbdde5612839d21f7df1c4e4a177c22a02adffc6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "I am going to keep y constant equal to y0." + }, + { + "text": "And I am going to change x." + }, + { + "text": "And, as I change x, z will change at a rate that is equal to a." + }, + { + "text": "That would be z equals z0 plus a times the change in x, x minus x0." + }, + { + "text": "That is how you would describe the line that is, I guess, the one that is plotted in green here." + }, + { + "text": "That is the intersection with the slice parallel to the xz plane." + }, + { + "text": "I hold y constant equal to y0." + }, + { + "text": "And z is a function of x that varies with a rate of a." + }, + { + "text": "And now, if I look similarly at the other slice, let's say that the partial with respect to y is equal to b, then I get another line which is obtained by the fact that z depends on y and the rate of change with respect to y will be b while x is held constant equal to x0." + }, + { + "text": "These two lines are both going to be in the tangent plane to the surface." + }, + { + "text": "They are both tangent to the surface, f of f. And, well, together they determine a plane." + }, + { + "text": "And that plane is just given by the formula z equals z0 plus a times x minus x0 plus b times y plus b." + }, + { + "text": "If you look at what happens, this is the equation of a plane, z equals constant times x plus constant times y plus constant." + }, + { + "text": "And if you look at what happens if I hold y constant and vary x, I recover the first line." + }, + { + "text": "If I hold x constant and vary y, I get the second line." + }, + { + "text": "Another way to do it, of course, would be to write actually parametric equations of these lines, get vectors along them and then take the cross-product to get the normal vector to the plane, and then get this equation for the plane using the normal vector." + }, + { + "text": "That also works and it gives you the same formula." + }, + { + "text": "If you are curious, exercise, do it again using parametrics and using cross-product to get the plane equation." + }, + { + "text": "OK, so that is how we get the tangent plane." + }, + { + "text": "And now, what this approximation formula here says is that, in fact, the graph of a function is close to the tangent plane." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk3.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..db670d552209553a73abe7a57967ebd9528e07b0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "If we were moving on the tangent plane, this would be an actual equality." + }, + { + "text": "Delta z would be a linear function of delta x and delta y." + }, + { + "text": "And the graph of a function is near the tangent plane, but it is not quite the same." + }, + { + "text": "It is only an approximation for small delta x and small delta y." + }, + { + "text": "The approximation formula says the graph of f is close to its tangent plane." + }, + { + "text": "And we can use that formula over here now to estimate how the value of f changes if I change x and y at the same time." + }, + { + "text": "Questions about that?" + }, + { + "text": "Now that we have caught up with what we were supposed to see on Tuesday, I can tell you now about max and min problems." + }, + { + "text": "Min problems." + }, + { + "text": "That is going to be an application of partial derivatives to look at optimization problems." + }, + { + "text": "Maybe ten years from now when you have a real job, your job might be to actually minimize the cost of something or maximize the profit of something or whatever." + }, + { + "text": "But typically, the function that you will have to strive to minimize or maximize will depend on several variables." + }, + { + "text": "If you have a function of one variable, you know that to find its minimum or its maximum you look at the derivative and you set that equal to zero." + }, + { + "text": "And you try to then look at what happens to the function." + }, + { + "text": "Here it is going to be kind of similar, except, of course, we have several variables." + }, + { + "text": "For today, we will think about a function of two variables." + }, + { + "text": "But it works exactly the same if you have three variables, ten variables, a million variables." + }, + { + "text": "The first observation is that if we have a local minimum or a local maximum, then both partial derivative, partial f, partial x and partial f, partial y are both zero at the same time." + }, + { + "text": "Why is that?" + }, + { + "text": "Well, let's say that f sub x is zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk4.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..6a4752d759dedab56f0865629de49a11db927b62 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means when I vary x, well, to first order the function doesn't change." + }, + { + "text": "Maybe that is because it is going through." + }, + { + "text": "If I look only at the slice parallel to the x-axis, then maybe I am going through the minimum." + }, + { + "text": "But then, if partial f, partial y is not zero, then actually by changing y I could still make the value larger or smaller." + }, + { + "text": "That wouldn't be an actual maximum or minimum." + }, + { + "text": "It would only be maximum or minimum if I stay in the slice." + }, + { + "text": "But if I allow myself to change y, that doesn't work." + }, + { + "text": "I need actually to know that if I change y the value will not change either to first order." + }, + { + "text": "That is why I also need partial f, partial y to be zero." + }, + { + "text": "Now, let's say that they are both zero." + }, + { + "text": "Well, why is that enough?" + }, + { + "text": "It is essentially enough because of this formula telling me that if both of these guys are zero then to first order the function doesn't change." + }, + { + "text": "And then, of course, there will be maybe quadratic terms that will actually turn that." + }, + { + "text": "This won't really say that your function is actually constant." + }, + { + "text": "It will just tell you that maybe it will be actually quadratic or higher order in delta x and delta y." + }, + { + "text": "That is what you expect to have at a maximum or a minimum." + }, + { + "text": "That condition is the same thing as saying that the tangent plane to the graph is actually going to be horizontal." + }, + { + "text": "And that is what you want to have." + }, + { + "text": "Say you have a minimum." + }, + { + "text": "Well, see that the tangent plane at this point, at the bottom of the graph, is going to be horizontal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk5.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..7e48c199e023a813f11acd0a96e5d01eb8971e00 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you can see that on this equation of a tangent plane, when both these coefficients are zero, that is when the equation becomes z equals constant, the horizontal plane." + }, + { + "text": "Does that make sense?" + }, + { + "text": "We will have a name for this kind of point because actually what we will see very soon is that these conditions are necessary but they are not sufficient." + }, + { + "text": "There are actually other kinds of points where the partial derivatives are zero." + }, + { + "text": "Let's give a name to this." + }, + { + "text": "We say that x0, y0 is a critical point of F if the partial derivative with respect to x and the partial derivative with respect to y are both zero." + }, + { + "text": "More generally, you would want all the partial derivatives, no matter how many variables you have, you want all the partials to be zero." + }, + { + "text": "Let's see an example." + }, + { + "text": "Let's say I give you the function f of x, y equals x squared minus 2xy plus py squared plus 2x minus 2y." + }, + { + "text": "And let's try to figure out whether we can minimize or maximize this." + }, + { + "text": "What we start doing immediately is taking the partial derivatives." + }, + { + "text": "What is f sub x?" + }, + { + "text": "It starts with 2x minus 2y plus zero plus two." + }, + { + "text": "Remember that y is a constant so this differentiates to zero." + }, + { + "text": "Now, if we do f sub y, that is going to be zero minus 2x plus 6y minus two." + }, + { + "text": "And what we want to do is set these things equal to zero." + }, + { + "text": "And we want to solve these two equations at the same time." + }, + { + "text": "An important thing to remember, maybe I should have told you a couple of weeks ago already, if you have two equations to solve, well, it is very good to try to simplify them by adding them together or whatever." + }, + { + "text": "But you must keep two equations." + }, + { + "text": "If you have two equations, you should not end up with just one equation out of nowhere." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk6.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9395a90268474c96a0037bb843bc6e78e8145fe5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "For example, here we can certainly simplify things by summing them together." + }, + { + "text": "See, if we add them together, well, the x's cancel and the constants cancel." + }, + { + "text": "In fact, we are just left with 4y equals zero." + }, + { + "text": "That is pretty good." + }, + { + "text": "That tells us y should be zero." + }, + { + "text": "But then we should, of course, go back to these and see what else we know." + }, + { + "text": "Well, now it tells us, if you put y equals zero, that tells you 2x plus 2 equals zero." + }, + { + "text": "That tells you x equals minus one." + }, + { + "text": "We have one critical point." + }, + { + "text": "That is x, y equals minus one over two." + }, + { + "text": "Any questions so far?" + }, + { + "text": "Well, you should have a question." + }, + { + "text": "The question should be how do we know if it is a maximum or a minimum?" + }, + { + "text": "Well, if we had a function of one variable, we would decide things based on the second derivative." + }, + { + "text": "And, in fact, we will see tomorrow how to do things based on the second derivative." + }, + { + "text": "But that is kind of tricky because there are a lot of second derivatives." + }, + { + "text": "I mean, we already have two first derivatives." + }, + { + "text": "You can imagine that if you keep taking partials, you may end up with more and more." + }, + { + "text": "We will have to figure out carefully what the condition should be." + }, + { + "text": "We will do that tomorrow." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk7.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..4bcbbf6b2197e00d7483dbd1b1319f8d7b454496 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "For now, let's just try to look at how do we understand these things by hand." + }, + { + "text": "In fact, let me point out to you immediately that there is more than maxima and minima." + }, + { + "text": "Remember, we saw the example of x squared plus y squared that has a critical point." + }, + { + "text": "The critical point is obviously a minimum." + }, + { + "text": "And, of course, it could be a local minimum because it could be that if you have a more complicated function there is indeed a minimum here." + }, + { + "text": "But then elsewhere the function drops to a lower value." + }, + { + "text": "We call that just a local minimum to say that it is a minimum if you stick to values that are close enough to that point." + }, + { + "text": "Of course, you also have a local maximum." + }, + { + "text": "Well, I did not plot it, but it is easy to plot." + }, + { + "text": "That is a local maximum." + }, + { + "text": "But there is a third example of critical point, and that is a saddle point." + }, + { + "text": "The saddle point is a new phenomenon that you do not really see in a single variable calculus." + }, + { + "text": "It is a critical point that is neither a minimum nor a maximum because, depending on which direction you look in, it is either one or the other." + }, + { + "text": "The point in the middle at the origin is a saddle point." + }, + { + "text": "If you look at the tangent plane to this graph you will see that it is actually horizontal at the origin." + }, + { + "text": "You have this mountain pass." + }, + { + "text": "At the mountain pass the ground is horizontal." + }, + { + "text": "But, depending on which direction you go, you go up or down." + }, + { + "text": "We say that the point is a saddle point if it is neither a minimum nor a maximum." + }, + { + "text": "OK, so the possibilities could be a local min, a local max, or a saddle." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk8.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8eebe5d35e57a9bb443552331906178033fbb172 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "Tomorrow we will see how to decide which one it is in general using second derivatives." + }, + { + "text": "For this time let's just try to do it by hand." + }, + { + "text": "I just want to observe." + }, + { + "text": "In fact, I can try to, you know, these examples that I have here, they are x2 y2 y2-x2." + }, + { + "text": "They are sums or differences of squares." + }, + { + "text": "And, if we know that we can put things as a sum of squares, for example, we will be done." + }, + { + "text": "Let's try to express this maybe in terms of a square." + }, + { + "text": "Well, the main problem is this 2xy." + }, + { + "text": "But, observe, we know something that starts with x2 minus 2xy that is actually the square of something else." + }, + { + "text": "It would be x2 minus 2xy, well, plus y2, not plus 3y2." + }, + { + "text": "Let's try to do that." + }, + { + "text": "We are going to complete the square." + }, + { + "text": "I am going to say it is x minus y squared." + }, + { + "text": "That gives me the first two terms and also y squared." + }, + { + "text": "Well, I still need to add two more y squares." + }, + { + "text": "And I also need to add, of course, the 2x minus 2y." + }, + { + "text": "It is simpler." + }, + { + "text": "It is still not simple enough for my taste." + }, + { + "text": "I can actually do better." + }, + { + "text": "See, I mean now what is, so these guys look like a sum of squares." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk9.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..2ebab68b48ed9108ed215c21106e93056b697b19 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_3_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "But here I have this extra stuff." + }, + { + "text": "But, 2x minus 2y, well, that is twice x minus y." + }, + { + "text": "It looks like maybe we can simplify this and make this into another square." + }, + { + "text": "In fact, I can simplify this further to x minus y plus one squared." + }, + { + "text": "See, that would start like, maybe I should put parentheses here, that would be x minus y squared plus twice x minus y." + }, + { + "text": "And then there is a plus one." + }, + { + "text": "Well, we don't have that plus one, so let's remove it by subtracting one." + }, + { + "text": "Oh, let me find that minus one here." + }, + { + "text": "And I still have my 2y squared." + }, + { + "text": "Do you see why this is the same function as that one?" + }, + { + "text": "Again, if I expand x minus y plus one squared, I get x minus y squared plus twice x minus y, that is those guys, plus one." + }, + { + "text": "But I will have a minus one and that will cancel out." + }, + { + "text": "And then I have a plus 2y squared." + }, + { + "text": "Now what I know, see, this is a sum of two squares minus one." + }, + { + "text": "And this critical point, x, y equals minus one, zero, that is exactly when this is zero and that is zero." + }, + { + "text": "That is the smallest value." + }, + { + "text": "This is always greater or equal to zero, same with that one." + }, + { + "text": "That is always at least minus one." + }, + { + "text": "And minus one happens to be the value at the critical point." + }, + { + "text": "It is a minimum." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk0.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..e6499639a2dd486fc34915743508e989029de764 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "Today we are going to see how to use what we saw last time about partial derivatives to handle minimization or maximization problems involving functions of several variables." + }, + { + "text": "Remember last time we said that when we have a function, say, of two variables, x and y, then we have actually two different derivatives." + }, + { + "text": "Partial f, partial x, also called f sub x, is the derivative with respect to x keeping y constant." + }, + { + "text": "And we have partial f, partial y, also called f sub y, where we vary y and we treat x as a constant." + }, + { + "text": "And now, one thing I didn't have time to tell you about, but hopefully you heard about in recitation yesterday, is the approximation formula that tells you what happens if you vary both x and y. F sub x tells us what happens if we change x a little bit by some small amount delta x. F sub y tells us how f changes if we change y by a small amount delta y." + }, + { + "text": "If we do both at the same time, then the two effects will add up with each other." + }, + { + "text": "Because you can imagine that first you will change x and then you will change y or the other way around." + }, + { + "text": "It doesn't really matter." + }, + { + "text": "If we change x by a certain amount delta x, and if we change y by the amount delta y, and let's say that we have z equals f of x, y, then that changes by an amount which is approximately f sub x times delta x plus f sub y times delta y." + }, + { + "text": "And that is one of the most important formulas about partial derivatives." + }, + { + "text": "The intuition for this, again, is just the two effects add up." + }, + { + "text": "If I change x by a small amount and then I change y, well, first changing x will modify f. How much does it modify f?" + }, + { + "text": "The answer is the rate of change." + }, + { + "text": "The rate of change is f sub x." + }, + { + "text": "And, if I change y, then the rate of change of f when I change y is f sub y." + }, + { + "text": "All together, I get this change in the value of f. And, of course, that is only an approximation formula." + }, + { + "text": "Actually, there would be higher order terms involving second and third derivatives and so on." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk1.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..24332c5f071c389023f7abaf7259fb1a63c23f92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "One way to justify this, sorry, I was distracted by a microphone problem." + }, + { + "text": "OK, so how do we justify this formula?" + }, + { + "text": "Well, one way to think about it is in terms of tangent plane approximation." + }, + { + "text": "Let's think about the tangent plane to the graph of a function f. I have some pictures to show you." + }, + { + "text": "It will be easier if I show the pictures." + }, + { + "text": "Remember, partial f over partial x was obtained by looking at the situation where y is held constant." + }, + { + "text": "That means I am slicing the graph of f by a plane that is parallel to the xz plane." + }, + { + "text": "And then, when I change x, z changes." + }, + { + "text": "And the slope of that is going to be the derivative with respect to x." + }, + { + "text": "Now, if I do the same in the other direction, then I will have similarly the slope in a slice now parallel to the yz plane that will be partial f over partial y." + }, + { + "text": "In fact, in each case I have a line." + }, + { + "text": "And that line is tangent to the surface." + }, + { + "text": "Now, if I have two lines tangent to the surface, well, then together they determine for me the tangent plane to the surface." + }, + { + "text": "Let's try to see how that works." + }, + { + "text": "We know that f sub x and f sub y are the slopes of two tangent lines to this plane, sorry, two tangent lines to the graph." + }, + { + "text": "And let's write down the equations of these lines." + }, + { + "text": "I am not going to write parametric equations." + }, + { + "text": "I am going to write them in terms of x, y, z coordinates." + }, + { + "text": "Let's say that partial f over partial x at a given point is equal to a." + }, + { + "text": "Then that means that we have a line given by the following conditions." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk10.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..04a9beb08f73a15fd9091546cca18b48afb0c0c0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, of course, here I was very lucky." + }, + { + "text": "In general, I could not expect things to simplify that much." + }, + { + "text": "In fact, I cheated." + }, + { + "text": "I started from that." + }, + { + "text": "I expanded." + }, + { + "text": "And then that is how I got my example." + }, + { + "text": "The general method will be a bit different, but you will see it will actually also involve completing squares." + }, + { + "text": "Just there is more to it than what we have seen." + }, + { + "text": "We will come back to this tomorrow." + }, + { + "text": "How do I know that this equals?" + }, + { + "text": "y is what negative one?" + }, + { + "text": "How do I know that that whole function is greater or equal to negative one?" + }, + { + "text": "Well, I wrote f of x, y as something squared plus 2y2 minus one." + }, + { + "text": "This squared is always a positive number, non-negative." + }, + { + "text": "It is a square." + }, + { + "text": "The square of something is always non-negative." + }, + { + "text": "Similarly, y2 is also always non-negative." + }, + { + "text": "If you add something that is at least zero plus something that is at least zero and you subtract one, you get always at least minus one." + }, + { + "text": "And, in fact, the only way that you can get minus one is if both of these guys are zero at the same time." + }, + { + "text": "That is how I get my minimum." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk11.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..f4eced0dcd7ffc5bdcf9cd95cd7f63aa34e4a4ac --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "More about this tomorrow." + }, + { + "text": "In fact, what I would like to tell you about now instead is a nice application of min-max problems that maybe you don't think of as a min-max problem." + }, + { + "text": "But you will see, I mean, you don't think of it that way because probably your calculator can do it for you." + }, + { + "text": "Or, if not, your computer can do it for you." + }, + { + "text": "But it is actually something where the theory is based on minimization in two variables." + }, + { + "text": "Very often in experimental sequences you have to do something called least squares interpolation." + }, + { + "text": "And what is that about?" + }, + { + "text": "Well, it is the idea that maybe you do some experiments and you record some data." + }, + { + "text": "You have some data x and some data y." + }, + { + "text": "And I don't know, maybe, for example, maybe you are measuring frogs and you are trying to measure how big the frog leg is compared to the eyes of a frog or whatever, or trying to measure something." + }, + { + "text": "And if you are doing chemistry then it could be how much you put of some reactant and how much of the output product that you wanted to synthesize is going to be the same." + }, + { + "text": "All sorts of things." + }, + { + "text": "Make up your own example." + }, + { + "text": "You measure, basically, for various values of x what the value of y ends up being." + }, + { + "text": "And then you would like to claim, oh, well, these points are kind of aligned." + }, + { + "text": "I mean, of course, to a mathematician they are not aligned, but to an experimental scientist that is evidence that there is a relation between the two." + }, + { + "text": "And so you want to claim, and in your paper you will actually draw a nice little line that says, C, these two functions depend linearly on each other." + }, + { + "text": "The question is how do we come up with that nice line that passes smack in the middle of the points?" + }, + { + "text": "The question is, given experimental data, xiyi, so maybe I should actually be more precise." + }, + { + "text": "You are given some experimental data." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk12.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..ec058dcefcf28c0e3655b8df350c1a7550b31989 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "You have data points x1, y1, x2, y2, and so on, xn, yn." + }, + { + "text": "The question would be find the best fit line of the form y equals ax plus b that somehow approximates very well this data." + }, + { + "text": "You can also use that, by the way, to predict various things." + }, + { + "text": "For example, if you look at your new homework, actually the first problem asks you to predict how many iPods will be on this planet in ten years, looking at past sales and how they behave." + }, + { + "text": "One thing, by the way, before you lose all the money you don't have yet, you cannot use that to predict the stock market." + }, + { + "text": "Don't try to use that to make money." + }, + { + "text": "It doesn't work." + }, + { + "text": "One tricky thing here that I want to draw your attention to is what are the unknowns here?" + }, + { + "text": "The natural answer would be to say the unknowns are x and y." + }, + { + "text": "That is not actually the case." + }, + { + "text": "We are not trying to solve for some x and y. I mean we have some values given to us." + }, + { + "text": "And when we are looking for that line we don't really care about a particular value of x." + }, + { + "text": "What we care about is actually these coefficients a and b that will tell us what the relation between x and y is." + }, + { + "text": "In fact, we are trying to solve for a and b that will give us the nicest possible line for these points." + }, + { + "text": "The unknowns in our equations will have to be a and b, not x and y." + }, + { + "text": "The question really is find the best a and b." + }, + { + "text": "And, of course, we have to decide what we mean by best." + }, + { + "text": "Best will mean that we minimize some function of a and b that measures the total error that we are making when we are choosing this line compared to the experimental data." + }, + { + "text": "Maybe, roughly speaking, it should measure how far these points are from the line." + }, + { + "text": "But now there are various ways to do it." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk13.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..5d2475feee1af92e7e44b93eafd8ef1a1aeab556 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "And some of them are, I mean a lot of them are valid to give you different answers." + }, + { + "text": "You have to decide what it is that you prefer." + }, + { + "text": "For example, you could measure the distance to the line by projecting perpendicularly." + }, + { + "text": "Or, you could measure instead the difference between, for a given value of x, the difference between the experimental value of y and the predicted one." + }, + { + "text": "And that is often more relevant because these guys are actually maybe expressed in different units." + }, + { + "text": "They are not the same type of quantity." + }, + { + "text": "You cannot actually combine them arbitrarily." + }, + { + "text": "Anyway, the convention is usually we measure distance in this way." + }, + { + "text": "Next, you could try to minimize the largest distance." + }, + { + "text": "Say we look at where is the largest error and we make that the smallest possible." + }, + { + "text": "The drawback of doing that is experimentally very often you have one data point that is not good because maybe you fell asleep in front of the experiment." + }, + { + "text": "And so you did not measure the right thing." + }, + { + "text": "You tend to want to not give too much importance to some data point that is far away from the others." + }, + { + "text": "Maybe instead you want to measure the average distance." + }, + { + "text": "Or maybe you want to actually give more weight to things that are further away." + }, + { + "text": "And then you do not want to do the distance but the square of the distance." + }, + { + "text": "There are various possible answers." + }, + { + "text": "But one of them gives us a particularly nice formula for a and b." + }, + { + "text": "And so that is why it is the universally used one." + }, + { + "text": "Here it says least squares." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk14.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..03f389ad03cba30ec35302a03113c11b9ae12887 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That is because we will measure, actually, the sum of the squares of the errors." + }, + { + "text": "And why do we do that?" + }, + { + "text": "Well, part of it is because actually it looks good." + }, + { + "text": "I mean, when you see these plots in scientific papers, they really look like the line is indeed the ideal line." + }, + { + "text": "And the second reason is because actually the minimization problem that we will get is particularly simple, well-proposed and it is easy to solve." + }, + { + "text": "We will have a nice formula for the best a and the best b." + }, + { + "text": "If you have a method that is simple and gives you a good answer then that is probably the good one." + }, + { + "text": "We have to define best." + }, + { + "text": "And here it is in the sense of defining a total square error." + }, + { + "text": "Maybe I should say total square deviation." + }, + { + "text": "What do I mean by that?" + }, + { + "text": "The deviation for each data point is the difference between what you have measured and what you are predicting by your model." + }, + { + "text": "That is the difference between the two." + }, + { + "text": "Now what we will do is try to minimize the function capital D, which is just the sum for all the data points of the square of the deviation." + }, + { + "text": "Let me emphasize again this is a function of a and b. I mean, of course, there are a lot of letters in here." + }, + { + "text": "But xi and yi in real life will be numbers given to you." + }, + { + "text": "They will be the numbers that you have measured." + }, + { + "text": "You have measured all of this data." + }, + { + "text": "They are just going to be numbers." + }, + { + "text": "You put them in there and you get the answer." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk15.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..574ce46fe50beb8d2adc71dc4ba061053cadb260 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Any questions?" + }, + { + "text": "How do we minimize this function of a and b?" + }, + { + "text": "Let's use our new knowledge." + }, + { + "text": "Let's actually look for a critical point." + }, + { + "text": "We want to solve for partial d over partial a equals zero and partial d over partial b equals zero." + }, + { + "text": "That is how we look for critical points." + }, + { + "text": "Let's take the derivative of a." + }, + { + "text": "Well, the derivative of a sum is the sum of the derivatives." + }, + { + "text": "And now we have to take the derivative of this quantity squared." + }, + { + "text": "Remember how we take the derivative of a square." + }, + { + "text": "We take twice this quantity times the derivative of what we are squaring." + }, + { + "text": "We will get two times minus y i, sorry, y i minus a xi plus b times the derivative of this with respect to a." + }, + { + "text": "What is the derivative of this with respect to a?" + }, + { + "text": "Negative xi, exactly." + }, + { + "text": "And so we will want this to be zero." + }, + { + "text": "And partial d over partial b, we do the same thing but differentiating with respect to b instead of with respect to a." + }, + { + "text": "Again, sum of squares twice y i minus a xi plus b times the derivative of this with respect to b is, I think, negative one." + }, + { + "text": "That is the equations we have to solve." + }, + { + "text": "Well, let's reorganize this a little bit." + }, + { + "text": "The first equation, see, there are a's and there are b's in these equations." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk16.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..6dbbcdfd1a44915f775e513934285605a93fde83 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "I am going to just look at the coefficients of a and b." + }, + { + "text": "If you have good eyes, you can see probably that these are actually linear equations in a and b." + }, + { + "text": "There is a lot of clutter with all these x's and y's all over the place." + }, + { + "text": "Let's actually try to expand things and make that more apparent." + }, + { + "text": "The first thing I will do is I will actually get rid of these factors of two that are just not very important." + }, + { + "text": "I can simplify things by two." + }, + { + "text": "And next I am going to look at the coefficient of a. I will get basically a times xi squared." + }, + { + "text": "Well, let me just do it and it should be clear." + }, + { + "text": "I claim when we simplify this we get a times xi squared plus xi times b minus xi yi." + }, + { + "text": "And we set this equal to zero." + }, + { + "text": "Do you agree that this is what we get when we expand that product?" + }, + { + "text": "No?" + }, + { + "text": "OK, let's do the other one." + }, + { + "text": "We just multiply by minus one." + }, + { + "text": "We take the opposite of that." + }, + { + "text": "It will be axi plus b. I will write that as xia plus b minus yi." + }, + { + "text": "And let me just reorganize that by actually putting all the a's together." + }, + { + "text": "That means actually I will have sum of all the xi squared times xi times b minus sum of xi yi equals zero." + }, + { + "text": "If I rewrite this it becomes sum of xi squared times a plus sum of the xi's times b minus, let me move the other guys to the other side, equals sum of xi yi." + }, + { + "text": "And that one becomes sum of xi times a plus how many b's do I get from this one?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk17.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..46c92ceb193fbddba6ccd0128c8434e1fa895b6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, I get one for each data point." + }, + { + "text": "When I sum them together I will get n. Very good." + }, + { + "text": "So, n times b equals sum of yi." + }, + { + "text": "Now, these quantities may look scary, but they are actually just numbers." + }, + { + "text": "For example, for this one you look at all your data points." + }, + { + "text": "For each of them you take the value of x and you just sum all these numbers together." + }, + { + "text": "What you get, actually, is a linear system in a two-by-two linear system." + }, + { + "text": "And so now we can solve this for a and b." + }, + { + "text": "In practice, of course, first you plug in the numbers for xi and yi and then you solve the system that you get." + }, + { + "text": "And we know how to solve two-by-two linear systems, I hope." + }, + { + "text": "That is how we find the best fit line." + }, + { + "text": "Now, why is that going to be the best one instead of the worst one?" + }, + { + "text": "We just solved for a critical point." + }, + { + "text": "That could actually be a maximum of this error function d. We will have the answer to that next time." + }, + { + "text": "But trust me, if you really want to go for the second derivative test that we will do tomorrow and apply it in this case, it is quite hard to check." + }, + { + "text": "But you can see it is actually a minimum." + }, + { + "text": "I will just say we can show that it is a minimum." + }, + { + "text": "Now, even for the linear case, it is the one that we are the most familiar with." + }, + { + "text": "Least squares interpolation actually works in much more general settings." + }, + { + "text": "Instead of fitting for the best line, if you think that there is a different kind of relation, then maybe you can fit in using a different kind of formula." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk18.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..fa2ca36c0d134e6b3372da5aa353386c01a4066b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me actually illustrate that for you." + }, + { + "text": "I don't know if you are familiar with Moore's law." + }, + { + "text": "It is something that is supposed to tell you how quickly, basically, computer chips become smarter, faster and faster over time." + }, + { + "text": "It is a law that says things about the number of transistors that you can fit onto a computer chip." + }, + { + "text": "Here I have some data about the number of transistors on a standard PC processor as a function of time." + }, + { + "text": "And, well, if you try to do the best line fit, you will see quickly that it doesn't seem to follow a linear trend." + }, + { + "text": "On the other hand, if you plot the diagram in a log scale, the log of the number of transistors as a function of time, then you get a much better line." + }, + { + "text": "And so, in fact, that means that you had an exponential relation between the number of transistors and time." + }, + { + "text": "And so, actually, that is what Moore's law says." + }, + { + "text": "It says that the number of transistors on a chip doubles, depending on the version, every 18 months or every two years." + }, + { + "text": "They keep changing the statement." + }, + { + "text": "How do we find that best exponential fit?" + }, + { + "text": "Well, an exponential fit would be something of the form y equals a constant times exponential of a times x." + }, + { + "text": "That is what we want to look at." + }, + { + "text": "Well, we could try to minimize a square error like we did earlier, but that doesn't work well at all." + }, + { + "text": "The equations that you get are very complicated." + }, + { + "text": "You cannot solve them." + }, + { + "text": "But remember what I showed you on this log plot." + }, + { + "text": "If you plot the log of y as a function of x, then suddenly it becomes a linear relation." + }, + { + "text": "Observe this is the same as ln of x equals ln of c plus ax." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk19.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..55b8384a00899de02bdae34fca68d10a37a51f56 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk19.json @@ -0,0 +1,53 @@ +[ + { + "text": "And that is a linear best fit." + }, + { + "text": "What you do is you just look for the best straight line fit for the log of y." + }, + { + "text": "That is something we already know." + }, + { + "text": "But you can also do other examples." + }, + { + "text": "For example, let's say that we have something more complicated." + }, + { + "text": "Let's say that we have actually a quadratic law." + }, + { + "text": "For example, y is of the form ax2 bx c. And, of course, you are trying to find somehow the best." + }, + { + "text": "That would mean here fitting the best parabola for your data points." + }, + { + "text": "Well, to do that you would need to find a, b and c. And now you would have actually a function of a, b and c, which would be the sum of all data points of the quadratic equation." + }, + { + "text": "And if you try to solve for critical points, now you will have three equations involving a, b and c. And, in fact, you will find a three by three linear system." + }, + { + "text": "And it works just the same way." + }, + { + "text": "Just you have a little bit more data." + }, + { + "text": "Basically, you see that these best fit problems are an example of minimization problem." + }, + { + "text": "But maybe you didn't expect to see minimization problems come in." + }, + { + "text": "But that is really the way to handle these questions." + }, + { + "text": "OK, so tomorrow we will go back to the question of how do we decide whether it is a minimum or a maximum?" + }, + { + "text": "And we will continue exploring functions of several variables." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk2.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..cbdde5612839d21f7df1c4e4a177c22a02adffc6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "I am going to keep y constant equal to y0." + }, + { + "text": "And I am going to change x." + }, + { + "text": "And, as I change x, z will change at a rate that is equal to a." + }, + { + "text": "That would be z equals z0 plus a times the change in x, x minus x0." + }, + { + "text": "That is how you would describe the line that is, I guess, the one that is plotted in green here." + }, + { + "text": "That is the intersection with the slice parallel to the xz plane." + }, + { + "text": "I hold y constant equal to y0." + }, + { + "text": "And z is a function of x that varies with a rate of a." + }, + { + "text": "And now, if I look similarly at the other slice, let's say that the partial with respect to y is equal to b, then I get another line which is obtained by the fact that z depends on y and the rate of change with respect to y will be b while x is held constant equal to x0." + }, + { + "text": "These two lines are both going to be in the tangent plane to the surface." + }, + { + "text": "They are both tangent to the surface, f of f. And, well, together they determine a plane." + }, + { + "text": "And that plane is just given by the formula z equals z0 plus a times x minus x0 plus b times y plus b." + }, + { + "text": "If you look at what happens, this is the equation of a plane, z equals constant times x plus constant times y plus constant." + }, + { + "text": "And if you look at what happens if I hold y constant and vary x, I recover the first line." + }, + { + "text": "If I hold x constant and vary y, I get the second line." + }, + { + "text": "Another way to do it, of course, would be to write actually parametric equations of these lines, get vectors along them and then take the cross-product to get the normal vector to the plane, and then get this equation for the plane using the normal vector." + }, + { + "text": "That also works and it gives you the same formula." + }, + { + "text": "If you are curious, exercise, do it again using parametrics and using cross-product to get the plane equation." + }, + { + "text": "OK, so that is how we get the tangent plane." + }, + { + "text": "And now, what this approximation formula here says is that, in fact, the graph of a function is close to the tangent plane." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk3.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..db670d552209553a73abe7a57967ebd9528e07b0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "If we were moving on the tangent plane, this would be an actual equality." + }, + { + "text": "Delta z would be a linear function of delta x and delta y." + }, + { + "text": "And the graph of a function is near the tangent plane, but it is not quite the same." + }, + { + "text": "It is only an approximation for small delta x and small delta y." + }, + { + "text": "The approximation formula says the graph of f is close to its tangent plane." + }, + { + "text": "And we can use that formula over here now to estimate how the value of f changes if I change x and y at the same time." + }, + { + "text": "Questions about that?" + }, + { + "text": "Now that we have caught up with what we were supposed to see on Tuesday, I can tell you now about max and min problems." + }, + { + "text": "Min problems." + }, + { + "text": "That is going to be an application of partial derivatives to look at optimization problems." + }, + { + "text": "Maybe ten years from now when you have a real job, your job might be to actually minimize the cost of something or maximize the profit of something or whatever." + }, + { + "text": "But typically, the function that you will have to strive to minimize or maximize will depend on several variables." + }, + { + "text": "If you have a function of one variable, you know that to find its minimum or its maximum you look at the derivative and you set that equal to zero." + }, + { + "text": "And you try to then look at what happens to the function." + }, + { + "text": "Here it is going to be kind of similar, except, of course, we have several variables." + }, + { + "text": "For today, we will think about a function of two variables." + }, + { + "text": "But it works exactly the same if you have three variables, ten variables, a million variables." + }, + { + "text": "The first observation is that if we have a local minimum or a local maximum, then both partial derivative, partial f, partial x and partial f, partial y are both zero at the same time." + }, + { + "text": "Why is that?" + }, + { + "text": "Well, let's say that f sub x is zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk4.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..6a4752d759dedab56f0865629de49a11db927b62 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means when I vary x, well, to first order the function doesn't change." + }, + { + "text": "Maybe that is because it is going through." + }, + { + "text": "If I look only at the slice parallel to the x-axis, then maybe I am going through the minimum." + }, + { + "text": "But then, if partial f, partial y is not zero, then actually by changing y I could still make the value larger or smaller." + }, + { + "text": "That wouldn't be an actual maximum or minimum." + }, + { + "text": "It would only be maximum or minimum if I stay in the slice." + }, + { + "text": "But if I allow myself to change y, that doesn't work." + }, + { + "text": "I need actually to know that if I change y the value will not change either to first order." + }, + { + "text": "That is why I also need partial f, partial y to be zero." + }, + { + "text": "Now, let's say that they are both zero." + }, + { + "text": "Well, why is that enough?" + }, + { + "text": "It is essentially enough because of this formula telling me that if both of these guys are zero then to first order the function doesn't change." + }, + { + "text": "And then, of course, there will be maybe quadratic terms that will actually turn that." + }, + { + "text": "This won't really say that your function is actually constant." + }, + { + "text": "It will just tell you that maybe it will be actually quadratic or higher order in delta x and delta y." + }, + { + "text": "That is what you expect to have at a maximum or a minimum." + }, + { + "text": "That condition is the same thing as saying that the tangent plane to the graph is actually going to be horizontal." + }, + { + "text": "And that is what you want to have." + }, + { + "text": "Say you have a minimum." + }, + { + "text": "Well, see that the tangent plane at this point, at the bottom of the graph, is going to be horizontal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk5.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..7e48c199e023a813f11acd0a96e5d01eb8971e00 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you can see that on this equation of a tangent plane, when both these coefficients are zero, that is when the equation becomes z equals constant, the horizontal plane." + }, + { + "text": "Does that make sense?" + }, + { + "text": "We will have a name for this kind of point because actually what we will see very soon is that these conditions are necessary but they are not sufficient." + }, + { + "text": "There are actually other kinds of points where the partial derivatives are zero." + }, + { + "text": "Let's give a name to this." + }, + { + "text": "We say that x0, y0 is a critical point of F if the partial derivative with respect to x and the partial derivative with respect to y are both zero." + }, + { + "text": "More generally, you would want all the partial derivatives, no matter how many variables you have, you want all the partials to be zero." + }, + { + "text": "Let's see an example." + }, + { + "text": "Let's say I give you the function f of x, y equals x squared minus 2xy plus py squared plus 2x minus 2y." + }, + { + "text": "And let's try to figure out whether we can minimize or maximize this." + }, + { + "text": "What we start doing immediately is taking the partial derivatives." + }, + { + "text": "What is f sub x?" + }, + { + "text": "It starts with 2x minus 2y plus zero plus two." + }, + { + "text": "Remember that y is a constant so this differentiates to zero." + }, + { + "text": "Now, if we do f sub y, that is going to be zero minus 2x plus 6y minus two." + }, + { + "text": "And what we want to do is set these things equal to zero." + }, + { + "text": "And we want to solve these two equations at the same time." + }, + { + "text": "An important thing to remember, maybe I should have told you a couple of weeks ago already, if you have two equations to solve, well, it is very good to try to simplify them by adding them together or whatever." + }, + { + "text": "But you must keep two equations." + }, + { + "text": "If you have two equations, you should not end up with just one equation out of nowhere." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk6.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9395a90268474c96a0037bb843bc6e78e8145fe5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "For example, here we can certainly simplify things by summing them together." + }, + { + "text": "See, if we add them together, well, the x's cancel and the constants cancel." + }, + { + "text": "In fact, we are just left with 4y equals zero." + }, + { + "text": "That is pretty good." + }, + { + "text": "That tells us y should be zero." + }, + { + "text": "But then we should, of course, go back to these and see what else we know." + }, + { + "text": "Well, now it tells us, if you put y equals zero, that tells you 2x plus 2 equals zero." + }, + { + "text": "That tells you x equals minus one." + }, + { + "text": "We have one critical point." + }, + { + "text": "That is x, y equals minus one over two." + }, + { + "text": "Any questions so far?" + }, + { + "text": "Well, you should have a question." + }, + { + "text": "The question should be how do we know if it is a maximum or a minimum?" + }, + { + "text": "Well, if we had a function of one variable, we would decide things based on the second derivative." + }, + { + "text": "And, in fact, we will see tomorrow how to do things based on the second derivative." + }, + { + "text": "But that is kind of tricky because there are a lot of second derivatives." + }, + { + "text": "I mean, we already have two first derivatives." + }, + { + "text": "You can imagine that if you keep taking partials, you may end up with more and more." + }, + { + "text": "We will have to figure out carefully what the condition should be." + }, + { + "text": "We will do that tomorrow." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk7.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..4bcbbf6b2197e00d7483dbd1b1319f8d7b454496 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "For now, let's just try to look at how do we understand these things by hand." + }, + { + "text": "In fact, let me point out to you immediately that there is more than maxima and minima." + }, + { + "text": "Remember, we saw the example of x squared plus y squared that has a critical point." + }, + { + "text": "The critical point is obviously a minimum." + }, + { + "text": "And, of course, it could be a local minimum because it could be that if you have a more complicated function there is indeed a minimum here." + }, + { + "text": "But then elsewhere the function drops to a lower value." + }, + { + "text": "We call that just a local minimum to say that it is a minimum if you stick to values that are close enough to that point." + }, + { + "text": "Of course, you also have a local maximum." + }, + { + "text": "Well, I did not plot it, but it is easy to plot." + }, + { + "text": "That is a local maximum." + }, + { + "text": "But there is a third example of critical point, and that is a saddle point." + }, + { + "text": "The saddle point is a new phenomenon that you do not really see in a single variable calculus." + }, + { + "text": "It is a critical point that is neither a minimum nor a maximum because, depending on which direction you look in, it is either one or the other." + }, + { + "text": "The point in the middle at the origin is a saddle point." + }, + { + "text": "If you look at the tangent plane to this graph you will see that it is actually horizontal at the origin." + }, + { + "text": "You have this mountain pass." + }, + { + "text": "At the mountain pass the ground is horizontal." + }, + { + "text": "But, depending on which direction you go, you go up or down." + }, + { + "text": "We say that the point is a saddle point if it is neither a minimum nor a maximum." + }, + { + "text": "OK, so the possibilities could be a local min, a local max, or a saddle." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk8.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8eebe5d35e57a9bb443552331906178033fbb172 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "Tomorrow we will see how to decide which one it is in general using second derivatives." + }, + { + "text": "For this time let's just try to do it by hand." + }, + { + "text": "I just want to observe." + }, + { + "text": "In fact, I can try to, you know, these examples that I have here, they are x2 y2 y2-x2." + }, + { + "text": "They are sums or differences of squares." + }, + { + "text": "And, if we know that we can put things as a sum of squares, for example, we will be done." + }, + { + "text": "Let's try to express this maybe in terms of a square." + }, + { + "text": "Well, the main problem is this 2xy." + }, + { + "text": "But, observe, we know something that starts with x2 minus 2xy that is actually the square of something else." + }, + { + "text": "It would be x2 minus 2xy, well, plus y2, not plus 3y2." + }, + { + "text": "Let's try to do that." + }, + { + "text": "We are going to complete the square." + }, + { + "text": "I am going to say it is x minus y squared." + }, + { + "text": "That gives me the first two terms and also y squared." + }, + { + "text": "Well, I still need to add two more y squares." + }, + { + "text": "And I also need to add, of course, the 2x minus 2y." + }, + { + "text": "It is simpler." + }, + { + "text": "It is still not simple enough for my taste." + }, + { + "text": "I can actually do better." + }, + { + "text": "See, I mean now what is, so these guys look like a sum of squares." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk9.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..2ebab68b48ed9108ed215c21106e93056b697b19 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_4_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "But here I have this extra stuff." + }, + { + "text": "But, 2x minus 2y, well, that is twice x minus y." + }, + { + "text": "It looks like maybe we can simplify this and make this into another square." + }, + { + "text": "In fact, I can simplify this further to x minus y plus one squared." + }, + { + "text": "See, that would start like, maybe I should put parentheses here, that would be x minus y squared plus twice x minus y." + }, + { + "text": "And then there is a plus one." + }, + { + "text": "Well, we don't have that plus one, so let's remove it by subtracting one." + }, + { + "text": "Oh, let me find that minus one here." + }, + { + "text": "And I still have my 2y squared." + }, + { + "text": "Do you see why this is the same function as that one?" + }, + { + "text": "Again, if I expand x minus y plus one squared, I get x minus y squared plus twice x minus y, that is those guys, plus one." + }, + { + "text": "But I will have a minus one and that will cancel out." + }, + { + "text": "And then I have a plus 2y squared." + }, + { + "text": "Now what I know, see, this is a sum of two squares minus one." + }, + { + "text": "And this critical point, x, y equals minus one, zero, that is exactly when this is zero and that is zero." + }, + { + "text": "That is the smallest value." + }, + { + "text": "This is always greater or equal to zero, same with that one." + }, + { + "text": "That is always at least minus one." + }, + { + "text": "And minus one happens to be the value at the critical point." + }, + { + "text": "It is a minimum." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk0.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..e6499639a2dd486fc34915743508e989029de764 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "Today we are going to see how to use what we saw last time about partial derivatives to handle minimization or maximization problems involving functions of several variables." + }, + { + "text": "Remember last time we said that when we have a function, say, of two variables, x and y, then we have actually two different derivatives." + }, + { + "text": "Partial f, partial x, also called f sub x, is the derivative with respect to x keeping y constant." + }, + { + "text": "And we have partial f, partial y, also called f sub y, where we vary y and we treat x as a constant." + }, + { + "text": "And now, one thing I didn't have time to tell you about, but hopefully you heard about in recitation yesterday, is the approximation formula that tells you what happens if you vary both x and y. F sub x tells us what happens if we change x a little bit by some small amount delta x. F sub y tells us how f changes if we change y by a small amount delta y." + }, + { + "text": "If we do both at the same time, then the two effects will add up with each other." + }, + { + "text": "Because you can imagine that first you will change x and then you will change y or the other way around." + }, + { + "text": "It doesn't really matter." + }, + { + "text": "If we change x by a certain amount delta x, and if we change y by the amount delta y, and let's say that we have z equals f of x, y, then that changes by an amount which is approximately f sub x times delta x plus f sub y times delta y." + }, + { + "text": "And that is one of the most important formulas about partial derivatives." + }, + { + "text": "The intuition for this, again, is just the two effects add up." + }, + { + "text": "If I change x by a small amount and then I change y, well, first changing x will modify f. How much does it modify f?" + }, + { + "text": "The answer is the rate of change." + }, + { + "text": "The rate of change is f sub x." + }, + { + "text": "And, if I change y, then the rate of change of f when I change y is f sub y." + }, + { + "text": "All together, I get this change in the value of f. And, of course, that is only an approximation formula." + }, + { + "text": "Actually, there would be higher order terms involving second and third derivatives and so on." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk1.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..24332c5f071c389023f7abaf7259fb1a63c23f92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "One way to justify this, sorry, I was distracted by a microphone problem." + }, + { + "text": "OK, so how do we justify this formula?" + }, + { + "text": "Well, one way to think about it is in terms of tangent plane approximation." + }, + { + "text": "Let's think about the tangent plane to the graph of a function f. I have some pictures to show you." + }, + { + "text": "It will be easier if I show the pictures." + }, + { + "text": "Remember, partial f over partial x was obtained by looking at the situation where y is held constant." + }, + { + "text": "That means I am slicing the graph of f by a plane that is parallel to the xz plane." + }, + { + "text": "And then, when I change x, z changes." + }, + { + "text": "And the slope of that is going to be the derivative with respect to x." + }, + { + "text": "Now, if I do the same in the other direction, then I will have similarly the slope in a slice now parallel to the yz plane that will be partial f over partial y." + }, + { + "text": "In fact, in each case I have a line." + }, + { + "text": "And that line is tangent to the surface." + }, + { + "text": "Now, if I have two lines tangent to the surface, well, then together they determine for me the tangent plane to the surface." + }, + { + "text": "Let's try to see how that works." + }, + { + "text": "We know that f sub x and f sub y are the slopes of two tangent lines to this plane, sorry, two tangent lines to the graph." + }, + { + "text": "And let's write down the equations of these lines." + }, + { + "text": "I am not going to write parametric equations." + }, + { + "text": "I am going to write them in terms of x, y, z coordinates." + }, + { + "text": "Let's say that partial f over partial x at a given point is equal to a." + }, + { + "text": "Then that means that we have a line given by the following conditions." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk10.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..04a9beb08f73a15fd9091546cca18b48afb0c0c0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, of course, here I was very lucky." + }, + { + "text": "In general, I could not expect things to simplify that much." + }, + { + "text": "In fact, I cheated." + }, + { + "text": "I started from that." + }, + { + "text": "I expanded." + }, + { + "text": "And then that is how I got my example." + }, + { + "text": "The general method will be a bit different, but you will see it will actually also involve completing squares." + }, + { + "text": "Just there is more to it than what we have seen." + }, + { + "text": "We will come back to this tomorrow." + }, + { + "text": "How do I know that this equals?" + }, + { + "text": "y is what negative one?" + }, + { + "text": "How do I know that that whole function is greater or equal to negative one?" + }, + { + "text": "Well, I wrote f of x, y as something squared plus 2y2 minus one." + }, + { + "text": "This squared is always a positive number, non-negative." + }, + { + "text": "It is a square." + }, + { + "text": "The square of something is always non-negative." + }, + { + "text": "Similarly, y2 is also always non-negative." + }, + { + "text": "If you add something that is at least zero plus something that is at least zero and you subtract one, you get always at least minus one." + }, + { + "text": "And, in fact, the only way that you can get minus one is if both of these guys are zero at the same time." + }, + { + "text": "That is how I get my minimum." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk11.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..f4eced0dcd7ffc5bdcf9cd95cd7f63aa34e4a4ac --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "More about this tomorrow." + }, + { + "text": "In fact, what I would like to tell you about now instead is a nice application of min-max problems that maybe you don't think of as a min-max problem." + }, + { + "text": "But you will see, I mean, you don't think of it that way because probably your calculator can do it for you." + }, + { + "text": "Or, if not, your computer can do it for you." + }, + { + "text": "But it is actually something where the theory is based on minimization in two variables." + }, + { + "text": "Very often in experimental sequences you have to do something called least squares interpolation." + }, + { + "text": "And what is that about?" + }, + { + "text": "Well, it is the idea that maybe you do some experiments and you record some data." + }, + { + "text": "You have some data x and some data y." + }, + { + "text": "And I don't know, maybe, for example, maybe you are measuring frogs and you are trying to measure how big the frog leg is compared to the eyes of a frog or whatever, or trying to measure something." + }, + { + "text": "And if you are doing chemistry then it could be how much you put of some reactant and how much of the output product that you wanted to synthesize is going to be the same." + }, + { + "text": "All sorts of things." + }, + { + "text": "Make up your own example." + }, + { + "text": "You measure, basically, for various values of x what the value of y ends up being." + }, + { + "text": "And then you would like to claim, oh, well, these points are kind of aligned." + }, + { + "text": "I mean, of course, to a mathematician they are not aligned, but to an experimental scientist that is evidence that there is a relation between the two." + }, + { + "text": "And so you want to claim, and in your paper you will actually draw a nice little line that says, C, these two functions depend linearly on each other." + }, + { + "text": "The question is how do we come up with that nice line that passes smack in the middle of the points?" + }, + { + "text": "The question is, given experimental data, xiyi, so maybe I should actually be more precise." + }, + { + "text": "You are given some experimental data." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk12.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..ec058dcefcf28c0e3655b8df350c1a7550b31989 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "You have data points x1, y1, x2, y2, and so on, xn, yn." + }, + { + "text": "The question would be find the best fit line of the form y equals ax plus b that somehow approximates very well this data." + }, + { + "text": "You can also use that, by the way, to predict various things." + }, + { + "text": "For example, if you look at your new homework, actually the first problem asks you to predict how many iPods will be on this planet in ten years, looking at past sales and how they behave." + }, + { + "text": "One thing, by the way, before you lose all the money you don't have yet, you cannot use that to predict the stock market." + }, + { + "text": "Don't try to use that to make money." + }, + { + "text": "It doesn't work." + }, + { + "text": "One tricky thing here that I want to draw your attention to is what are the unknowns here?" + }, + { + "text": "The natural answer would be to say the unknowns are x and y." + }, + { + "text": "That is not actually the case." + }, + { + "text": "We are not trying to solve for some x and y. I mean we have some values given to us." + }, + { + "text": "And when we are looking for that line we don't really care about a particular value of x." + }, + { + "text": "What we care about is actually these coefficients a and b that will tell us what the relation between x and y is." + }, + { + "text": "In fact, we are trying to solve for a and b that will give us the nicest possible line for these points." + }, + { + "text": "The unknowns in our equations will have to be a and b, not x and y." + }, + { + "text": "The question really is find the best a and b." + }, + { + "text": "And, of course, we have to decide what we mean by best." + }, + { + "text": "Best will mean that we minimize some function of a and b that measures the total error that we are making when we are choosing this line compared to the experimental data." + }, + { + "text": "Maybe, roughly speaking, it should measure how far these points are from the line." + }, + { + "text": "But now there are various ways to do it." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk13.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..5d2475feee1af92e7e44b93eafd8ef1a1aeab556 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "And some of them are, I mean a lot of them are valid to give you different answers." + }, + { + "text": "You have to decide what it is that you prefer." + }, + { + "text": "For example, you could measure the distance to the line by projecting perpendicularly." + }, + { + "text": "Or, you could measure instead the difference between, for a given value of x, the difference between the experimental value of y and the predicted one." + }, + { + "text": "And that is often more relevant because these guys are actually maybe expressed in different units." + }, + { + "text": "They are not the same type of quantity." + }, + { + "text": "You cannot actually combine them arbitrarily." + }, + { + "text": "Anyway, the convention is usually we measure distance in this way." + }, + { + "text": "Next, you could try to minimize the largest distance." + }, + { + "text": "Say we look at where is the largest error and we make that the smallest possible." + }, + { + "text": "The drawback of doing that is experimentally very often you have one data point that is not good because maybe you fell asleep in front of the experiment." + }, + { + "text": "And so you did not measure the right thing." + }, + { + "text": "You tend to want to not give too much importance to some data point that is far away from the others." + }, + { + "text": "Maybe instead you want to measure the average distance." + }, + { + "text": "Or maybe you want to actually give more weight to things that are further away." + }, + { + "text": "And then you do not want to do the distance but the square of the distance." + }, + { + "text": "There are various possible answers." + }, + { + "text": "But one of them gives us a particularly nice formula for a and b." + }, + { + "text": "And so that is why it is the universally used one." + }, + { + "text": "Here it says least squares." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk14.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..03f389ad03cba30ec35302a03113c11b9ae12887 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That is because we will measure, actually, the sum of the squares of the errors." + }, + { + "text": "And why do we do that?" + }, + { + "text": "Well, part of it is because actually it looks good." + }, + { + "text": "I mean, when you see these plots in scientific papers, they really look like the line is indeed the ideal line." + }, + { + "text": "And the second reason is because actually the minimization problem that we will get is particularly simple, well-proposed and it is easy to solve." + }, + { + "text": "We will have a nice formula for the best a and the best b." + }, + { + "text": "If you have a method that is simple and gives you a good answer then that is probably the good one." + }, + { + "text": "We have to define best." + }, + { + "text": "And here it is in the sense of defining a total square error." + }, + { + "text": "Maybe I should say total square deviation." + }, + { + "text": "What do I mean by that?" + }, + { + "text": "The deviation for each data point is the difference between what you have measured and what you are predicting by your model." + }, + { + "text": "That is the difference between the two." + }, + { + "text": "Now what we will do is try to minimize the function capital D, which is just the sum for all the data points of the square of the deviation." + }, + { + "text": "Let me emphasize again this is a function of a and b. I mean, of course, there are a lot of letters in here." + }, + { + "text": "But xi and yi in real life will be numbers given to you." + }, + { + "text": "They will be the numbers that you have measured." + }, + { + "text": "You have measured all of this data." + }, + { + "text": "They are just going to be numbers." + }, + { + "text": "You put them in there and you get the answer." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk15.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..574ce46fe50beb8d2adc71dc4ba061053cadb260 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Any questions?" + }, + { + "text": "How do we minimize this function of a and b?" + }, + { + "text": "Let's use our new knowledge." + }, + { + "text": "Let's actually look for a critical point." + }, + { + "text": "We want to solve for partial d over partial a equals zero and partial d over partial b equals zero." + }, + { + "text": "That is how we look for critical points." + }, + { + "text": "Let's take the derivative of a." + }, + { + "text": "Well, the derivative of a sum is the sum of the derivatives." + }, + { + "text": "And now we have to take the derivative of this quantity squared." + }, + { + "text": "Remember how we take the derivative of a square." + }, + { + "text": "We take twice this quantity times the derivative of what we are squaring." + }, + { + "text": "We will get two times minus y i, sorry, y i minus a xi plus b times the derivative of this with respect to a." + }, + { + "text": "What is the derivative of this with respect to a?" + }, + { + "text": "Negative xi, exactly." + }, + { + "text": "And so we will want this to be zero." + }, + { + "text": "And partial d over partial b, we do the same thing but differentiating with respect to b instead of with respect to a." + }, + { + "text": "Again, sum of squares twice y i minus a xi plus b times the derivative of this with respect to b is, I think, negative one." + }, + { + "text": "That is the equations we have to solve." + }, + { + "text": "Well, let's reorganize this a little bit." + }, + { + "text": "The first equation, see, there are a's and there are b's in these equations." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk16.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..6dbbcdfd1a44915f775e513934285605a93fde83 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "I am going to just look at the coefficients of a and b." + }, + { + "text": "If you have good eyes, you can see probably that these are actually linear equations in a and b." + }, + { + "text": "There is a lot of clutter with all these x's and y's all over the place." + }, + { + "text": "Let's actually try to expand things and make that more apparent." + }, + { + "text": "The first thing I will do is I will actually get rid of these factors of two that are just not very important." + }, + { + "text": "I can simplify things by two." + }, + { + "text": "And next I am going to look at the coefficient of a. I will get basically a times xi squared." + }, + { + "text": "Well, let me just do it and it should be clear." + }, + { + "text": "I claim when we simplify this we get a times xi squared plus xi times b minus xi yi." + }, + { + "text": "And we set this equal to zero." + }, + { + "text": "Do you agree that this is what we get when we expand that product?" + }, + { + "text": "No?" + }, + { + "text": "OK, let's do the other one." + }, + { + "text": "We just multiply by minus one." + }, + { + "text": "We take the opposite of that." + }, + { + "text": "It will be axi plus b. I will write that as xia plus b minus yi." + }, + { + "text": "And let me just reorganize that by actually putting all the a's together." + }, + { + "text": "That means actually I will have sum of all the xi squared times xi times b minus sum of xi yi equals zero." + }, + { + "text": "If I rewrite this it becomes sum of xi squared times a plus sum of the xi's times b minus, let me move the other guys to the other side, equals sum of xi yi." + }, + { + "text": "And that one becomes sum of xi times a plus how many b's do I get from this one?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk17.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..46c92ceb193fbddba6ccd0128c8434e1fa895b6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, I get one for each data point." + }, + { + "text": "When I sum them together I will get n. Very good." + }, + { + "text": "So, n times b equals sum of yi." + }, + { + "text": "Now, these quantities may look scary, but they are actually just numbers." + }, + { + "text": "For example, for this one you look at all your data points." + }, + { + "text": "For each of them you take the value of x and you just sum all these numbers together." + }, + { + "text": "What you get, actually, is a linear system in a two-by-two linear system." + }, + { + "text": "And so now we can solve this for a and b." + }, + { + "text": "In practice, of course, first you plug in the numbers for xi and yi and then you solve the system that you get." + }, + { + "text": "And we know how to solve two-by-two linear systems, I hope." + }, + { + "text": "That is how we find the best fit line." + }, + { + "text": "Now, why is that going to be the best one instead of the worst one?" + }, + { + "text": "We just solved for a critical point." + }, + { + "text": "That could actually be a maximum of this error function d. We will have the answer to that next time." + }, + { + "text": "But trust me, if you really want to go for the second derivative test that we will do tomorrow and apply it in this case, it is quite hard to check." + }, + { + "text": "But you can see it is actually a minimum." + }, + { + "text": "I will just say we can show that it is a minimum." + }, + { + "text": "Now, even for the linear case, it is the one that we are the most familiar with." + }, + { + "text": "Least squares interpolation actually works in much more general settings." + }, + { + "text": "Instead of fitting for the best line, if you think that there is a different kind of relation, then maybe you can fit in using a different kind of formula." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk18.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..fa2ca36c0d134e6b3372da5aa353386c01a4066b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me actually illustrate that for you." + }, + { + "text": "I don't know if you are familiar with Moore's law." + }, + { + "text": "It is something that is supposed to tell you how quickly, basically, computer chips become smarter, faster and faster over time." + }, + { + "text": "It is a law that says things about the number of transistors that you can fit onto a computer chip." + }, + { + "text": "Here I have some data about the number of transistors on a standard PC processor as a function of time." + }, + { + "text": "And, well, if you try to do the best line fit, you will see quickly that it doesn't seem to follow a linear trend." + }, + { + "text": "On the other hand, if you plot the diagram in a log scale, the log of the number of transistors as a function of time, then you get a much better line." + }, + { + "text": "And so, in fact, that means that you had an exponential relation between the number of transistors and time." + }, + { + "text": "And so, actually, that is what Moore's law says." + }, + { + "text": "It says that the number of transistors on a chip doubles, depending on the version, every 18 months or every two years." + }, + { + "text": "They keep changing the statement." + }, + { + "text": "How do we find that best exponential fit?" + }, + { + "text": "Well, an exponential fit would be something of the form y equals a constant times exponential of a times x." + }, + { + "text": "That is what we want to look at." + }, + { + "text": "Well, we could try to minimize a square error like we did earlier, but that doesn't work well at all." + }, + { + "text": "The equations that you get are very complicated." + }, + { + "text": "You cannot solve them." + }, + { + "text": "But remember what I showed you on this log plot." + }, + { + "text": "If you plot the log of y as a function of x, then suddenly it becomes a linear relation." + }, + { + "text": "Observe this is the same as ln of x equals ln of c plus ax." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk19.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..55b8384a00899de02bdae34fca68d10a37a51f56 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk19.json @@ -0,0 +1,53 @@ +[ + { + "text": "And that is a linear best fit." + }, + { + "text": "What you do is you just look for the best straight line fit for the log of y." + }, + { + "text": "That is something we already know." + }, + { + "text": "But you can also do other examples." + }, + { + "text": "For example, let's say that we have something more complicated." + }, + { + "text": "Let's say that we have actually a quadratic law." + }, + { + "text": "For example, y is of the form ax2 bx c. And, of course, you are trying to find somehow the best." + }, + { + "text": "That would mean here fitting the best parabola for your data points." + }, + { + "text": "Well, to do that you would need to find a, b and c. And now you would have actually a function of a, b and c, which would be the sum of all data points of the quadratic equation." + }, + { + "text": "And if you try to solve for critical points, now you will have three equations involving a, b and c. And, in fact, you will find a three by three linear system." + }, + { + "text": "And it works just the same way." + }, + { + "text": "Just you have a little bit more data." + }, + { + "text": "Basically, you see that these best fit problems are an example of minimization problem." + }, + { + "text": "But maybe you didn't expect to see minimization problems come in." + }, + { + "text": "But that is really the way to handle these questions." + }, + { + "text": "OK, so tomorrow we will go back to the question of how do we decide whether it is a minimum or a maximum?" + }, + { + "text": "And we will continue exploring functions of several variables." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk2.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..cbdde5612839d21f7df1c4e4a177c22a02adffc6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "I am going to keep y constant equal to y0." + }, + { + "text": "And I am going to change x." + }, + { + "text": "And, as I change x, z will change at a rate that is equal to a." + }, + { + "text": "That would be z equals z0 plus a times the change in x, x minus x0." + }, + { + "text": "That is how you would describe the line that is, I guess, the one that is plotted in green here." + }, + { + "text": "That is the intersection with the slice parallel to the xz plane." + }, + { + "text": "I hold y constant equal to y0." + }, + { + "text": "And z is a function of x that varies with a rate of a." + }, + { + "text": "And now, if I look similarly at the other slice, let's say that the partial with respect to y is equal to b, then I get another line which is obtained by the fact that z depends on y and the rate of change with respect to y will be b while x is held constant equal to x0." + }, + { + "text": "These two lines are both going to be in the tangent plane to the surface." + }, + { + "text": "They are both tangent to the surface, f of f. And, well, together they determine a plane." + }, + { + "text": "And that plane is just given by the formula z equals z0 plus a times x minus x0 plus b times y plus b." + }, + { + "text": "If you look at what happens, this is the equation of a plane, z equals constant times x plus constant times y plus constant." + }, + { + "text": "And if you look at what happens if I hold y constant and vary x, I recover the first line." + }, + { + "text": "If I hold x constant and vary y, I get the second line." + }, + { + "text": "Another way to do it, of course, would be to write actually parametric equations of these lines, get vectors along them and then take the cross-product to get the normal vector to the plane, and then get this equation for the plane using the normal vector." + }, + { + "text": "That also works and it gives you the same formula." + }, + { + "text": "If you are curious, exercise, do it again using parametrics and using cross-product to get the plane equation." + }, + { + "text": "OK, so that is how we get the tangent plane." + }, + { + "text": "And now, what this approximation formula here says is that, in fact, the graph of a function is close to the tangent plane." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk3.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..db670d552209553a73abe7a57967ebd9528e07b0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "If we were moving on the tangent plane, this would be an actual equality." + }, + { + "text": "Delta z would be a linear function of delta x and delta y." + }, + { + "text": "And the graph of a function is near the tangent plane, but it is not quite the same." + }, + { + "text": "It is only an approximation for small delta x and small delta y." + }, + { + "text": "The approximation formula says the graph of f is close to its tangent plane." + }, + { + "text": "And we can use that formula over here now to estimate how the value of f changes if I change x and y at the same time." + }, + { + "text": "Questions about that?" + }, + { + "text": "Now that we have caught up with what we were supposed to see on Tuesday, I can tell you now about max and min problems." + }, + { + "text": "Min problems." + }, + { + "text": "That is going to be an application of partial derivatives to look at optimization problems." + }, + { + "text": "Maybe ten years from now when you have a real job, your job might be to actually minimize the cost of something or maximize the profit of something or whatever." + }, + { + "text": "But typically, the function that you will have to strive to minimize or maximize will depend on several variables." + }, + { + "text": "If you have a function of one variable, you know that to find its minimum or its maximum you look at the derivative and you set that equal to zero." + }, + { + "text": "And you try to then look at what happens to the function." + }, + { + "text": "Here it is going to be kind of similar, except, of course, we have several variables." + }, + { + "text": "For today, we will think about a function of two variables." + }, + { + "text": "But it works exactly the same if you have three variables, ten variables, a million variables." + }, + { + "text": "The first observation is that if we have a local minimum or a local maximum, then both partial derivative, partial f, partial x and partial f, partial y are both zero at the same time." + }, + { + "text": "Why is that?" + }, + { + "text": "Well, let's say that f sub x is zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk4.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..6a4752d759dedab56f0865629de49a11db927b62 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means when I vary x, well, to first order the function doesn't change." + }, + { + "text": "Maybe that is because it is going through." + }, + { + "text": "If I look only at the slice parallel to the x-axis, then maybe I am going through the minimum." + }, + { + "text": "But then, if partial f, partial y is not zero, then actually by changing y I could still make the value larger or smaller." + }, + { + "text": "That wouldn't be an actual maximum or minimum." + }, + { + "text": "It would only be maximum or minimum if I stay in the slice." + }, + { + "text": "But if I allow myself to change y, that doesn't work." + }, + { + "text": "I need actually to know that if I change y the value will not change either to first order." + }, + { + "text": "That is why I also need partial f, partial y to be zero." + }, + { + "text": "Now, let's say that they are both zero." + }, + { + "text": "Well, why is that enough?" + }, + { + "text": "It is essentially enough because of this formula telling me that if both of these guys are zero then to first order the function doesn't change." + }, + { + "text": "And then, of course, there will be maybe quadratic terms that will actually turn that." + }, + { + "text": "This won't really say that your function is actually constant." + }, + { + "text": "It will just tell you that maybe it will be actually quadratic or higher order in delta x and delta y." + }, + { + "text": "That is what you expect to have at a maximum or a minimum." + }, + { + "text": "That condition is the same thing as saying that the tangent plane to the graph is actually going to be horizontal." + }, + { + "text": "And that is what you want to have." + }, + { + "text": "Say you have a minimum." + }, + { + "text": "Well, see that the tangent plane at this point, at the bottom of the graph, is going to be horizontal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk5.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..7e48c199e023a813f11acd0a96e5d01eb8971e00 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you can see that on this equation of a tangent plane, when both these coefficients are zero, that is when the equation becomes z equals constant, the horizontal plane." + }, + { + "text": "Does that make sense?" + }, + { + "text": "We will have a name for this kind of point because actually what we will see very soon is that these conditions are necessary but they are not sufficient." + }, + { + "text": "There are actually other kinds of points where the partial derivatives are zero." + }, + { + "text": "Let's give a name to this." + }, + { + "text": "We say that x0, y0 is a critical point of F if the partial derivative with respect to x and the partial derivative with respect to y are both zero." + }, + { + "text": "More generally, you would want all the partial derivatives, no matter how many variables you have, you want all the partials to be zero." + }, + { + "text": "Let's see an example." + }, + { + "text": "Let's say I give you the function f of x, y equals x squared minus 2xy plus py squared plus 2x minus 2y." + }, + { + "text": "And let's try to figure out whether we can minimize or maximize this." + }, + { + "text": "What we start doing immediately is taking the partial derivatives." + }, + { + "text": "What is f sub x?" + }, + { + "text": "It starts with 2x minus 2y plus zero plus two." + }, + { + "text": "Remember that y is a constant so this differentiates to zero." + }, + { + "text": "Now, if we do f sub y, that is going to be zero minus 2x plus 6y minus two." + }, + { + "text": "And what we want to do is set these things equal to zero." + }, + { + "text": "And we want to solve these two equations at the same time." + }, + { + "text": "An important thing to remember, maybe I should have told you a couple of weeks ago already, if you have two equations to solve, well, it is very good to try to simplify them by adding them together or whatever." + }, + { + "text": "But you must keep two equations." + }, + { + "text": "If you have two equations, you should not end up with just one equation out of nowhere." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk6.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9395a90268474c96a0037bb843bc6e78e8145fe5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "For example, here we can certainly simplify things by summing them together." + }, + { + "text": "See, if we add them together, well, the x's cancel and the constants cancel." + }, + { + "text": "In fact, we are just left with 4y equals zero." + }, + { + "text": "That is pretty good." + }, + { + "text": "That tells us y should be zero." + }, + { + "text": "But then we should, of course, go back to these and see what else we know." + }, + { + "text": "Well, now it tells us, if you put y equals zero, that tells you 2x plus 2 equals zero." + }, + { + "text": "That tells you x equals minus one." + }, + { + "text": "We have one critical point." + }, + { + "text": "That is x, y equals minus one over two." + }, + { + "text": "Any questions so far?" + }, + { + "text": "Well, you should have a question." + }, + { + "text": "The question should be how do we know if it is a maximum or a minimum?" + }, + { + "text": "Well, if we had a function of one variable, we would decide things based on the second derivative." + }, + { + "text": "And, in fact, we will see tomorrow how to do things based on the second derivative." + }, + { + "text": "But that is kind of tricky because there are a lot of second derivatives." + }, + { + "text": "I mean, we already have two first derivatives." + }, + { + "text": "You can imagine that if you keep taking partials, you may end up with more and more." + }, + { + "text": "We will have to figure out carefully what the condition should be." + }, + { + "text": "We will do that tomorrow." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk7.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..4bcbbf6b2197e00d7483dbd1b1319f8d7b454496 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "For now, let's just try to look at how do we understand these things by hand." + }, + { + "text": "In fact, let me point out to you immediately that there is more than maxima and minima." + }, + { + "text": "Remember, we saw the example of x squared plus y squared that has a critical point." + }, + { + "text": "The critical point is obviously a minimum." + }, + { + "text": "And, of course, it could be a local minimum because it could be that if you have a more complicated function there is indeed a minimum here." + }, + { + "text": "But then elsewhere the function drops to a lower value." + }, + { + "text": "We call that just a local minimum to say that it is a minimum if you stick to values that are close enough to that point." + }, + { + "text": "Of course, you also have a local maximum." + }, + { + "text": "Well, I did not plot it, but it is easy to plot." + }, + { + "text": "That is a local maximum." + }, + { + "text": "But there is a third example of critical point, and that is a saddle point." + }, + { + "text": "The saddle point is a new phenomenon that you do not really see in a single variable calculus." + }, + { + "text": "It is a critical point that is neither a minimum nor a maximum because, depending on which direction you look in, it is either one or the other." + }, + { + "text": "The point in the middle at the origin is a saddle point." + }, + { + "text": "If you look at the tangent plane to this graph you will see that it is actually horizontal at the origin." + }, + { + "text": "You have this mountain pass." + }, + { + "text": "At the mountain pass the ground is horizontal." + }, + { + "text": "But, depending on which direction you go, you go up or down." + }, + { + "text": "We say that the point is a saddle point if it is neither a minimum nor a maximum." + }, + { + "text": "OK, so the possibilities could be a local min, a local max, or a saddle." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk8.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8eebe5d35e57a9bb443552331906178033fbb172 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "Tomorrow we will see how to decide which one it is in general using second derivatives." + }, + { + "text": "For this time let's just try to do it by hand." + }, + { + "text": "I just want to observe." + }, + { + "text": "In fact, I can try to, you know, these examples that I have here, they are x2 y2 y2-x2." + }, + { + "text": "They are sums or differences of squares." + }, + { + "text": "And, if we know that we can put things as a sum of squares, for example, we will be done." + }, + { + "text": "Let's try to express this maybe in terms of a square." + }, + { + "text": "Well, the main problem is this 2xy." + }, + { + "text": "But, observe, we know something that starts with x2 minus 2xy that is actually the square of something else." + }, + { + "text": "It would be x2 minus 2xy, well, plus y2, not plus 3y2." + }, + { + "text": "Let's try to do that." + }, + { + "text": "We are going to complete the square." + }, + { + "text": "I am going to say it is x minus y squared." + }, + { + "text": "That gives me the first two terms and also y squared." + }, + { + "text": "Well, I still need to add two more y squares." + }, + { + "text": "And I also need to add, of course, the 2x minus 2y." + }, + { + "text": "It is simpler." + }, + { + "text": "It is still not simple enough for my taste." + }, + { + "text": "I can actually do better." + }, + { + "text": "See, I mean now what is, so these guys look like a sum of squares." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk9.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..2ebab68b48ed9108ed215c21106e93056b697b19 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_5_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "But here I have this extra stuff." + }, + { + "text": "But, 2x minus 2y, well, that is twice x minus y." + }, + { + "text": "It looks like maybe we can simplify this and make this into another square." + }, + { + "text": "In fact, I can simplify this further to x minus y plus one squared." + }, + { + "text": "See, that would start like, maybe I should put parentheses here, that would be x minus y squared plus twice x minus y." + }, + { + "text": "And then there is a plus one." + }, + { + "text": "Well, we don't have that plus one, so let's remove it by subtracting one." + }, + { + "text": "Oh, let me find that minus one here." + }, + { + "text": "And I still have my 2y squared." + }, + { + "text": "Do you see why this is the same function as that one?" + }, + { + "text": "Again, if I expand x minus y plus one squared, I get x minus y squared plus twice x minus y, that is those guys, plus one." + }, + { + "text": "But I will have a minus one and that will cancel out." + }, + { + "text": "And then I have a plus 2y squared." + }, + { + "text": "Now what I know, see, this is a sum of two squares minus one." + }, + { + "text": "And this critical point, x, y equals minus one, zero, that is exactly when this is zero and that is zero." + }, + { + "text": "That is the smallest value." + }, + { + "text": "This is always greater or equal to zero, same with that one." + }, + { + "text": "That is always at least minus one." + }, + { + "text": "And minus one happens to be the value at the critical point." + }, + { + "text": "It is a minimum." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk0.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..e6499639a2dd486fc34915743508e989029de764 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "Today we are going to see how to use what we saw last time about partial derivatives to handle minimization or maximization problems involving functions of several variables." + }, + { + "text": "Remember last time we said that when we have a function, say, of two variables, x and y, then we have actually two different derivatives." + }, + { + "text": "Partial f, partial x, also called f sub x, is the derivative with respect to x keeping y constant." + }, + { + "text": "And we have partial f, partial y, also called f sub y, where we vary y and we treat x as a constant." + }, + { + "text": "And now, one thing I didn't have time to tell you about, but hopefully you heard about in recitation yesterday, is the approximation formula that tells you what happens if you vary both x and y. F sub x tells us what happens if we change x a little bit by some small amount delta x. F sub y tells us how f changes if we change y by a small amount delta y." + }, + { + "text": "If we do both at the same time, then the two effects will add up with each other." + }, + { + "text": "Because you can imagine that first you will change x and then you will change y or the other way around." + }, + { + "text": "It doesn't really matter." + }, + { + "text": "If we change x by a certain amount delta x, and if we change y by the amount delta y, and let's say that we have z equals f of x, y, then that changes by an amount which is approximately f sub x times delta x plus f sub y times delta y." + }, + { + "text": "And that is one of the most important formulas about partial derivatives." + }, + { + "text": "The intuition for this, again, is just the two effects add up." + }, + { + "text": "If I change x by a small amount and then I change y, well, first changing x will modify f. How much does it modify f?" + }, + { + "text": "The answer is the rate of change." + }, + { + "text": "The rate of change is f sub x." + }, + { + "text": "And, if I change y, then the rate of change of f when I change y is f sub y." + }, + { + "text": "All together, I get this change in the value of f. And, of course, that is only an approximation formula." + }, + { + "text": "Actually, there would be higher order terms involving second and third derivatives and so on." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk1.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..24332c5f071c389023f7abaf7259fb1a63c23f92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "One way to justify this, sorry, I was distracted by a microphone problem." + }, + { + "text": "OK, so how do we justify this formula?" + }, + { + "text": "Well, one way to think about it is in terms of tangent plane approximation." + }, + { + "text": "Let's think about the tangent plane to the graph of a function f. I have some pictures to show you." + }, + { + "text": "It will be easier if I show the pictures." + }, + { + "text": "Remember, partial f over partial x was obtained by looking at the situation where y is held constant." + }, + { + "text": "That means I am slicing the graph of f by a plane that is parallel to the xz plane." + }, + { + "text": "And then, when I change x, z changes." + }, + { + "text": "And the slope of that is going to be the derivative with respect to x." + }, + { + "text": "Now, if I do the same in the other direction, then I will have similarly the slope in a slice now parallel to the yz plane that will be partial f over partial y." + }, + { + "text": "In fact, in each case I have a line." + }, + { + "text": "And that line is tangent to the surface." + }, + { + "text": "Now, if I have two lines tangent to the surface, well, then together they determine for me the tangent plane to the surface." + }, + { + "text": "Let's try to see how that works." + }, + { + "text": "We know that f sub x and f sub y are the slopes of two tangent lines to this plane, sorry, two tangent lines to the graph." + }, + { + "text": "And let's write down the equations of these lines." + }, + { + "text": "I am not going to write parametric equations." + }, + { + "text": "I am going to write them in terms of x, y, z coordinates." + }, + { + "text": "Let's say that partial f over partial x at a given point is equal to a." + }, + { + "text": "Then that means that we have a line given by the following conditions." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk10.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..04a9beb08f73a15fd9091546cca18b48afb0c0c0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, of course, here I was very lucky." + }, + { + "text": "In general, I could not expect things to simplify that much." + }, + { + "text": "In fact, I cheated." + }, + { + "text": "I started from that." + }, + { + "text": "I expanded." + }, + { + "text": "And then that is how I got my example." + }, + { + "text": "The general method will be a bit different, but you will see it will actually also involve completing squares." + }, + { + "text": "Just there is more to it than what we have seen." + }, + { + "text": "We will come back to this tomorrow." + }, + { + "text": "How do I know that this equals?" + }, + { + "text": "y is what negative one?" + }, + { + "text": "How do I know that that whole function is greater or equal to negative one?" + }, + { + "text": "Well, I wrote f of x, y as something squared plus 2y2 minus one." + }, + { + "text": "This squared is always a positive number, non-negative." + }, + { + "text": "It is a square." + }, + { + "text": "The square of something is always non-negative." + }, + { + "text": "Similarly, y2 is also always non-negative." + }, + { + "text": "If you add something that is at least zero plus something that is at least zero and you subtract one, you get always at least minus one." + }, + { + "text": "And, in fact, the only way that you can get minus one is if both of these guys are zero at the same time." + }, + { + "text": "That is how I get my minimum." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk11.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..f4eced0dcd7ffc5bdcf9cd95cd7f63aa34e4a4ac --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "More about this tomorrow." + }, + { + "text": "In fact, what I would like to tell you about now instead is a nice application of min-max problems that maybe you don't think of as a min-max problem." + }, + { + "text": "But you will see, I mean, you don't think of it that way because probably your calculator can do it for you." + }, + { + "text": "Or, if not, your computer can do it for you." + }, + { + "text": "But it is actually something where the theory is based on minimization in two variables." + }, + { + "text": "Very often in experimental sequences you have to do something called least squares interpolation." + }, + { + "text": "And what is that about?" + }, + { + "text": "Well, it is the idea that maybe you do some experiments and you record some data." + }, + { + "text": "You have some data x and some data y." + }, + { + "text": "And I don't know, maybe, for example, maybe you are measuring frogs and you are trying to measure how big the frog leg is compared to the eyes of a frog or whatever, or trying to measure something." + }, + { + "text": "And if you are doing chemistry then it could be how much you put of some reactant and how much of the output product that you wanted to synthesize is going to be the same." + }, + { + "text": "All sorts of things." + }, + { + "text": "Make up your own example." + }, + { + "text": "You measure, basically, for various values of x what the value of y ends up being." + }, + { + "text": "And then you would like to claim, oh, well, these points are kind of aligned." + }, + { + "text": "I mean, of course, to a mathematician they are not aligned, but to an experimental scientist that is evidence that there is a relation between the two." + }, + { + "text": "And so you want to claim, and in your paper you will actually draw a nice little line that says, C, these two functions depend linearly on each other." + }, + { + "text": "The question is how do we come up with that nice line that passes smack in the middle of the points?" + }, + { + "text": "The question is, given experimental data, xiyi, so maybe I should actually be more precise." + }, + { + "text": "You are given some experimental data." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk12.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..ec058dcefcf28c0e3655b8df350c1a7550b31989 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "You have data points x1, y1, x2, y2, and so on, xn, yn." + }, + { + "text": "The question would be find the best fit line of the form y equals ax plus b that somehow approximates very well this data." + }, + { + "text": "You can also use that, by the way, to predict various things." + }, + { + "text": "For example, if you look at your new homework, actually the first problem asks you to predict how many iPods will be on this planet in ten years, looking at past sales and how they behave." + }, + { + "text": "One thing, by the way, before you lose all the money you don't have yet, you cannot use that to predict the stock market." + }, + { + "text": "Don't try to use that to make money." + }, + { + "text": "It doesn't work." + }, + { + "text": "One tricky thing here that I want to draw your attention to is what are the unknowns here?" + }, + { + "text": "The natural answer would be to say the unknowns are x and y." + }, + { + "text": "That is not actually the case." + }, + { + "text": "We are not trying to solve for some x and y. I mean we have some values given to us." + }, + { + "text": "And when we are looking for that line we don't really care about a particular value of x." + }, + { + "text": "What we care about is actually these coefficients a and b that will tell us what the relation between x and y is." + }, + { + "text": "In fact, we are trying to solve for a and b that will give us the nicest possible line for these points." + }, + { + "text": "The unknowns in our equations will have to be a and b, not x and y." + }, + { + "text": "The question really is find the best a and b." + }, + { + "text": "And, of course, we have to decide what we mean by best." + }, + { + "text": "Best will mean that we minimize some function of a and b that measures the total error that we are making when we are choosing this line compared to the experimental data." + }, + { + "text": "Maybe, roughly speaking, it should measure how far these points are from the line." + }, + { + "text": "But now there are various ways to do it." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk13.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..5d2475feee1af92e7e44b93eafd8ef1a1aeab556 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "And some of them are, I mean a lot of them are valid to give you different answers." + }, + { + "text": "You have to decide what it is that you prefer." + }, + { + "text": "For example, you could measure the distance to the line by projecting perpendicularly." + }, + { + "text": "Or, you could measure instead the difference between, for a given value of x, the difference between the experimental value of y and the predicted one." + }, + { + "text": "And that is often more relevant because these guys are actually maybe expressed in different units." + }, + { + "text": "They are not the same type of quantity." + }, + { + "text": "You cannot actually combine them arbitrarily." + }, + { + "text": "Anyway, the convention is usually we measure distance in this way." + }, + { + "text": "Next, you could try to minimize the largest distance." + }, + { + "text": "Say we look at where is the largest error and we make that the smallest possible." + }, + { + "text": "The drawback of doing that is experimentally very often you have one data point that is not good because maybe you fell asleep in front of the experiment." + }, + { + "text": "And so you did not measure the right thing." + }, + { + "text": "You tend to want to not give too much importance to some data point that is far away from the others." + }, + { + "text": "Maybe instead you want to measure the average distance." + }, + { + "text": "Or maybe you want to actually give more weight to things that are further away." + }, + { + "text": "And then you do not want to do the distance but the square of the distance." + }, + { + "text": "There are various possible answers." + }, + { + "text": "But one of them gives us a particularly nice formula for a and b." + }, + { + "text": "And so that is why it is the universally used one." + }, + { + "text": "Here it says least squares." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk14.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..03f389ad03cba30ec35302a03113c11b9ae12887 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That is because we will measure, actually, the sum of the squares of the errors." + }, + { + "text": "And why do we do that?" + }, + { + "text": "Well, part of it is because actually it looks good." + }, + { + "text": "I mean, when you see these plots in scientific papers, they really look like the line is indeed the ideal line." + }, + { + "text": "And the second reason is because actually the minimization problem that we will get is particularly simple, well-proposed and it is easy to solve." + }, + { + "text": "We will have a nice formula for the best a and the best b." + }, + { + "text": "If you have a method that is simple and gives you a good answer then that is probably the good one." + }, + { + "text": "We have to define best." + }, + { + "text": "And here it is in the sense of defining a total square error." + }, + { + "text": "Maybe I should say total square deviation." + }, + { + "text": "What do I mean by that?" + }, + { + "text": "The deviation for each data point is the difference between what you have measured and what you are predicting by your model." + }, + { + "text": "That is the difference between the two." + }, + { + "text": "Now what we will do is try to minimize the function capital D, which is just the sum for all the data points of the square of the deviation." + }, + { + "text": "Let me emphasize again this is a function of a and b. I mean, of course, there are a lot of letters in here." + }, + { + "text": "But xi and yi in real life will be numbers given to you." + }, + { + "text": "They will be the numbers that you have measured." + }, + { + "text": "You have measured all of this data." + }, + { + "text": "They are just going to be numbers." + }, + { + "text": "You put them in there and you get the answer." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk15.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..574ce46fe50beb8d2adc71dc4ba061053cadb260 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Any questions?" + }, + { + "text": "How do we minimize this function of a and b?" + }, + { + "text": "Let's use our new knowledge." + }, + { + "text": "Let's actually look for a critical point." + }, + { + "text": "We want to solve for partial d over partial a equals zero and partial d over partial b equals zero." + }, + { + "text": "That is how we look for critical points." + }, + { + "text": "Let's take the derivative of a." + }, + { + "text": "Well, the derivative of a sum is the sum of the derivatives." + }, + { + "text": "And now we have to take the derivative of this quantity squared." + }, + { + "text": "Remember how we take the derivative of a square." + }, + { + "text": "We take twice this quantity times the derivative of what we are squaring." + }, + { + "text": "We will get two times minus y i, sorry, y i minus a xi plus b times the derivative of this with respect to a." + }, + { + "text": "What is the derivative of this with respect to a?" + }, + { + "text": "Negative xi, exactly." + }, + { + "text": "And so we will want this to be zero." + }, + { + "text": "And partial d over partial b, we do the same thing but differentiating with respect to b instead of with respect to a." + }, + { + "text": "Again, sum of squares twice y i minus a xi plus b times the derivative of this with respect to b is, I think, negative one." + }, + { + "text": "That is the equations we have to solve." + }, + { + "text": "Well, let's reorganize this a little bit." + }, + { + "text": "The first equation, see, there are a's and there are b's in these equations." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk16.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..6dbbcdfd1a44915f775e513934285605a93fde83 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "I am going to just look at the coefficients of a and b." + }, + { + "text": "If you have good eyes, you can see probably that these are actually linear equations in a and b." + }, + { + "text": "There is a lot of clutter with all these x's and y's all over the place." + }, + { + "text": "Let's actually try to expand things and make that more apparent." + }, + { + "text": "The first thing I will do is I will actually get rid of these factors of two that are just not very important." + }, + { + "text": "I can simplify things by two." + }, + { + "text": "And next I am going to look at the coefficient of a. I will get basically a times xi squared." + }, + { + "text": "Well, let me just do it and it should be clear." + }, + { + "text": "I claim when we simplify this we get a times xi squared plus xi times b minus xi yi." + }, + { + "text": "And we set this equal to zero." + }, + { + "text": "Do you agree that this is what we get when we expand that product?" + }, + { + "text": "No?" + }, + { + "text": "OK, let's do the other one." + }, + { + "text": "We just multiply by minus one." + }, + { + "text": "We take the opposite of that." + }, + { + "text": "It will be axi plus b. I will write that as xia plus b minus yi." + }, + { + "text": "And let me just reorganize that by actually putting all the a's together." + }, + { + "text": "That means actually I will have sum of all the xi squared times xi times b minus sum of xi yi equals zero." + }, + { + "text": "If I rewrite this it becomes sum of xi squared times a plus sum of the xi's times b minus, let me move the other guys to the other side, equals sum of xi yi." + }, + { + "text": "And that one becomes sum of xi times a plus how many b's do I get from this one?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk17.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..46c92ceb193fbddba6ccd0128c8434e1fa895b6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, I get one for each data point." + }, + { + "text": "When I sum them together I will get n. Very good." + }, + { + "text": "So, n times b equals sum of yi." + }, + { + "text": "Now, these quantities may look scary, but they are actually just numbers." + }, + { + "text": "For example, for this one you look at all your data points." + }, + { + "text": "For each of them you take the value of x and you just sum all these numbers together." + }, + { + "text": "What you get, actually, is a linear system in a two-by-two linear system." + }, + { + "text": "And so now we can solve this for a and b." + }, + { + "text": "In practice, of course, first you plug in the numbers for xi and yi and then you solve the system that you get." + }, + { + "text": "And we know how to solve two-by-two linear systems, I hope." + }, + { + "text": "That is how we find the best fit line." + }, + { + "text": "Now, why is that going to be the best one instead of the worst one?" + }, + { + "text": "We just solved for a critical point." + }, + { + "text": "That could actually be a maximum of this error function d. We will have the answer to that next time." + }, + { + "text": "But trust me, if you really want to go for the second derivative test that we will do tomorrow and apply it in this case, it is quite hard to check." + }, + { + "text": "But you can see it is actually a minimum." + }, + { + "text": "I will just say we can show that it is a minimum." + }, + { + "text": "Now, even for the linear case, it is the one that we are the most familiar with." + }, + { + "text": "Least squares interpolation actually works in much more general settings." + }, + { + "text": "Instead of fitting for the best line, if you think that there is a different kind of relation, then maybe you can fit in using a different kind of formula." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk18.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..fa2ca36c0d134e6b3372da5aa353386c01a4066b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me actually illustrate that for you." + }, + { + "text": "I don't know if you are familiar with Moore's law." + }, + { + "text": "It is something that is supposed to tell you how quickly, basically, computer chips become smarter, faster and faster over time." + }, + { + "text": "It is a law that says things about the number of transistors that you can fit onto a computer chip." + }, + { + "text": "Here I have some data about the number of transistors on a standard PC processor as a function of time." + }, + { + "text": "And, well, if you try to do the best line fit, you will see quickly that it doesn't seem to follow a linear trend." + }, + { + "text": "On the other hand, if you plot the diagram in a log scale, the log of the number of transistors as a function of time, then you get a much better line." + }, + { + "text": "And so, in fact, that means that you had an exponential relation between the number of transistors and time." + }, + { + "text": "And so, actually, that is what Moore's law says." + }, + { + "text": "It says that the number of transistors on a chip doubles, depending on the version, every 18 months or every two years." + }, + { + "text": "They keep changing the statement." + }, + { + "text": "How do we find that best exponential fit?" + }, + { + "text": "Well, an exponential fit would be something of the form y equals a constant times exponential of a times x." + }, + { + "text": "That is what we want to look at." + }, + { + "text": "Well, we could try to minimize a square error like we did earlier, but that doesn't work well at all." + }, + { + "text": "The equations that you get are very complicated." + }, + { + "text": "You cannot solve them." + }, + { + "text": "But remember what I showed you on this log plot." + }, + { + "text": "If you plot the log of y as a function of x, then suddenly it becomes a linear relation." + }, + { + "text": "Observe this is the same as ln of x equals ln of c plus ax." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk19.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..55b8384a00899de02bdae34fca68d10a37a51f56 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk19.json @@ -0,0 +1,53 @@ +[ + { + "text": "And that is a linear best fit." + }, + { + "text": "What you do is you just look for the best straight line fit for the log of y." + }, + { + "text": "That is something we already know." + }, + { + "text": "But you can also do other examples." + }, + { + "text": "For example, let's say that we have something more complicated." + }, + { + "text": "Let's say that we have actually a quadratic law." + }, + { + "text": "For example, y is of the form ax2 bx c. And, of course, you are trying to find somehow the best." + }, + { + "text": "That would mean here fitting the best parabola for your data points." + }, + { + "text": "Well, to do that you would need to find a, b and c. And now you would have actually a function of a, b and c, which would be the sum of all data points of the quadratic equation." + }, + { + "text": "And if you try to solve for critical points, now you will have three equations involving a, b and c. And, in fact, you will find a three by three linear system." + }, + { + "text": "And it works just the same way." + }, + { + "text": "Just you have a little bit more data." + }, + { + "text": "Basically, you see that these best fit problems are an example of minimization problem." + }, + { + "text": "But maybe you didn't expect to see minimization problems come in." + }, + { + "text": "But that is really the way to handle these questions." + }, + { + "text": "OK, so tomorrow we will go back to the question of how do we decide whether it is a minimum or a maximum?" + }, + { + "text": "And we will continue exploring functions of several variables." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk2.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..cbdde5612839d21f7df1c4e4a177c22a02adffc6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "I am going to keep y constant equal to y0." + }, + { + "text": "And I am going to change x." + }, + { + "text": "And, as I change x, z will change at a rate that is equal to a." + }, + { + "text": "That would be z equals z0 plus a times the change in x, x minus x0." + }, + { + "text": "That is how you would describe the line that is, I guess, the one that is plotted in green here." + }, + { + "text": "That is the intersection with the slice parallel to the xz plane." + }, + { + "text": "I hold y constant equal to y0." + }, + { + "text": "And z is a function of x that varies with a rate of a." + }, + { + "text": "And now, if I look similarly at the other slice, let's say that the partial with respect to y is equal to b, then I get another line which is obtained by the fact that z depends on y and the rate of change with respect to y will be b while x is held constant equal to x0." + }, + { + "text": "These two lines are both going to be in the tangent plane to the surface." + }, + { + "text": "They are both tangent to the surface, f of f. And, well, together they determine a plane." + }, + { + "text": "And that plane is just given by the formula z equals z0 plus a times x minus x0 plus b times y plus b." + }, + { + "text": "If you look at what happens, this is the equation of a plane, z equals constant times x plus constant times y plus constant." + }, + { + "text": "And if you look at what happens if I hold y constant and vary x, I recover the first line." + }, + { + "text": "If I hold x constant and vary y, I get the second line." + }, + { + "text": "Another way to do it, of course, would be to write actually parametric equations of these lines, get vectors along them and then take the cross-product to get the normal vector to the plane, and then get this equation for the plane using the normal vector." + }, + { + "text": "That also works and it gives you the same formula." + }, + { + "text": "If you are curious, exercise, do it again using parametrics and using cross-product to get the plane equation." + }, + { + "text": "OK, so that is how we get the tangent plane." + }, + { + "text": "And now, what this approximation formula here says is that, in fact, the graph of a function is close to the tangent plane." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk3.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..db670d552209553a73abe7a57967ebd9528e07b0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "If we were moving on the tangent plane, this would be an actual equality." + }, + { + "text": "Delta z would be a linear function of delta x and delta y." + }, + { + "text": "And the graph of a function is near the tangent plane, but it is not quite the same." + }, + { + "text": "It is only an approximation for small delta x and small delta y." + }, + { + "text": "The approximation formula says the graph of f is close to its tangent plane." + }, + { + "text": "And we can use that formula over here now to estimate how the value of f changes if I change x and y at the same time." + }, + { + "text": "Questions about that?" + }, + { + "text": "Now that we have caught up with what we were supposed to see on Tuesday, I can tell you now about max and min problems." + }, + { + "text": "Min problems." + }, + { + "text": "That is going to be an application of partial derivatives to look at optimization problems." + }, + { + "text": "Maybe ten years from now when you have a real job, your job might be to actually minimize the cost of something or maximize the profit of something or whatever." + }, + { + "text": "But typically, the function that you will have to strive to minimize or maximize will depend on several variables." + }, + { + "text": "If you have a function of one variable, you know that to find its minimum or its maximum you look at the derivative and you set that equal to zero." + }, + { + "text": "And you try to then look at what happens to the function." + }, + { + "text": "Here it is going to be kind of similar, except, of course, we have several variables." + }, + { + "text": "For today, we will think about a function of two variables." + }, + { + "text": "But it works exactly the same if you have three variables, ten variables, a million variables." + }, + { + "text": "The first observation is that if we have a local minimum or a local maximum, then both partial derivative, partial f, partial x and partial f, partial y are both zero at the same time." + }, + { + "text": "Why is that?" + }, + { + "text": "Well, let's say that f sub x is zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk4.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..6a4752d759dedab56f0865629de49a11db927b62 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means when I vary x, well, to first order the function doesn't change." + }, + { + "text": "Maybe that is because it is going through." + }, + { + "text": "If I look only at the slice parallel to the x-axis, then maybe I am going through the minimum." + }, + { + "text": "But then, if partial f, partial y is not zero, then actually by changing y I could still make the value larger or smaller." + }, + { + "text": "That wouldn't be an actual maximum or minimum." + }, + { + "text": "It would only be maximum or minimum if I stay in the slice." + }, + { + "text": "But if I allow myself to change y, that doesn't work." + }, + { + "text": "I need actually to know that if I change y the value will not change either to first order." + }, + { + "text": "That is why I also need partial f, partial y to be zero." + }, + { + "text": "Now, let's say that they are both zero." + }, + { + "text": "Well, why is that enough?" + }, + { + "text": "It is essentially enough because of this formula telling me that if both of these guys are zero then to first order the function doesn't change." + }, + { + "text": "And then, of course, there will be maybe quadratic terms that will actually turn that." + }, + { + "text": "This won't really say that your function is actually constant." + }, + { + "text": "It will just tell you that maybe it will be actually quadratic or higher order in delta x and delta y." + }, + { + "text": "That is what you expect to have at a maximum or a minimum." + }, + { + "text": "That condition is the same thing as saying that the tangent plane to the graph is actually going to be horizontal." + }, + { + "text": "And that is what you want to have." + }, + { + "text": "Say you have a minimum." + }, + { + "text": "Well, see that the tangent plane at this point, at the bottom of the graph, is going to be horizontal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk5.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..7e48c199e023a813f11acd0a96e5d01eb8971e00 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you can see that on this equation of a tangent plane, when both these coefficients are zero, that is when the equation becomes z equals constant, the horizontal plane." + }, + { + "text": "Does that make sense?" + }, + { + "text": "We will have a name for this kind of point because actually what we will see very soon is that these conditions are necessary but they are not sufficient." + }, + { + "text": "There are actually other kinds of points where the partial derivatives are zero." + }, + { + "text": "Let's give a name to this." + }, + { + "text": "We say that x0, y0 is a critical point of F if the partial derivative with respect to x and the partial derivative with respect to y are both zero." + }, + { + "text": "More generally, you would want all the partial derivatives, no matter how many variables you have, you want all the partials to be zero." + }, + { + "text": "Let's see an example." + }, + { + "text": "Let's say I give you the function f of x, y equals x squared minus 2xy plus py squared plus 2x minus 2y." + }, + { + "text": "And let's try to figure out whether we can minimize or maximize this." + }, + { + "text": "What we start doing immediately is taking the partial derivatives." + }, + { + "text": "What is f sub x?" + }, + { + "text": "It starts with 2x minus 2y plus zero plus two." + }, + { + "text": "Remember that y is a constant so this differentiates to zero." + }, + { + "text": "Now, if we do f sub y, that is going to be zero minus 2x plus 6y minus two." + }, + { + "text": "And what we want to do is set these things equal to zero." + }, + { + "text": "And we want to solve these two equations at the same time." + }, + { + "text": "An important thing to remember, maybe I should have told you a couple of weeks ago already, if you have two equations to solve, well, it is very good to try to simplify them by adding them together or whatever." + }, + { + "text": "But you must keep two equations." + }, + { + "text": "If you have two equations, you should not end up with just one equation out of nowhere." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk6.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9395a90268474c96a0037bb843bc6e78e8145fe5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "For example, here we can certainly simplify things by summing them together." + }, + { + "text": "See, if we add them together, well, the x's cancel and the constants cancel." + }, + { + "text": "In fact, we are just left with 4y equals zero." + }, + { + "text": "That is pretty good." + }, + { + "text": "That tells us y should be zero." + }, + { + "text": "But then we should, of course, go back to these and see what else we know." + }, + { + "text": "Well, now it tells us, if you put y equals zero, that tells you 2x plus 2 equals zero." + }, + { + "text": "That tells you x equals minus one." + }, + { + "text": "We have one critical point." + }, + { + "text": "That is x, y equals minus one over two." + }, + { + "text": "Any questions so far?" + }, + { + "text": "Well, you should have a question." + }, + { + "text": "The question should be how do we know if it is a maximum or a minimum?" + }, + { + "text": "Well, if we had a function of one variable, we would decide things based on the second derivative." + }, + { + "text": "And, in fact, we will see tomorrow how to do things based on the second derivative." + }, + { + "text": "But that is kind of tricky because there are a lot of second derivatives." + }, + { + "text": "I mean, we already have two first derivatives." + }, + { + "text": "You can imagine that if you keep taking partials, you may end up with more and more." + }, + { + "text": "We will have to figure out carefully what the condition should be." + }, + { + "text": "We will do that tomorrow." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk7.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..4bcbbf6b2197e00d7483dbd1b1319f8d7b454496 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "For now, let's just try to look at how do we understand these things by hand." + }, + { + "text": "In fact, let me point out to you immediately that there is more than maxima and minima." + }, + { + "text": "Remember, we saw the example of x squared plus y squared that has a critical point." + }, + { + "text": "The critical point is obviously a minimum." + }, + { + "text": "And, of course, it could be a local minimum because it could be that if you have a more complicated function there is indeed a minimum here." + }, + { + "text": "But then elsewhere the function drops to a lower value." + }, + { + "text": "We call that just a local minimum to say that it is a minimum if you stick to values that are close enough to that point." + }, + { + "text": "Of course, you also have a local maximum." + }, + { + "text": "Well, I did not plot it, but it is easy to plot." + }, + { + "text": "That is a local maximum." + }, + { + "text": "But there is a third example of critical point, and that is a saddle point." + }, + { + "text": "The saddle point is a new phenomenon that you do not really see in a single variable calculus." + }, + { + "text": "It is a critical point that is neither a minimum nor a maximum because, depending on which direction you look in, it is either one or the other." + }, + { + "text": "The point in the middle at the origin is a saddle point." + }, + { + "text": "If you look at the tangent plane to this graph you will see that it is actually horizontal at the origin." + }, + { + "text": "You have this mountain pass." + }, + { + "text": "At the mountain pass the ground is horizontal." + }, + { + "text": "But, depending on which direction you go, you go up or down." + }, + { + "text": "We say that the point is a saddle point if it is neither a minimum nor a maximum." + }, + { + "text": "OK, so the possibilities could be a local min, a local max, or a saddle." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk8.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8eebe5d35e57a9bb443552331906178033fbb172 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "Tomorrow we will see how to decide which one it is in general using second derivatives." + }, + { + "text": "For this time let's just try to do it by hand." + }, + { + "text": "I just want to observe." + }, + { + "text": "In fact, I can try to, you know, these examples that I have here, they are x2 y2 y2-x2." + }, + { + "text": "They are sums or differences of squares." + }, + { + "text": "And, if we know that we can put things as a sum of squares, for example, we will be done." + }, + { + "text": "Let's try to express this maybe in terms of a square." + }, + { + "text": "Well, the main problem is this 2xy." + }, + { + "text": "But, observe, we know something that starts with x2 minus 2xy that is actually the square of something else." + }, + { + "text": "It would be x2 minus 2xy, well, plus y2, not plus 3y2." + }, + { + "text": "Let's try to do that." + }, + { + "text": "We are going to complete the square." + }, + { + "text": "I am going to say it is x minus y squared." + }, + { + "text": "That gives me the first two terms and also y squared." + }, + { + "text": "Well, I still need to add two more y squares." + }, + { + "text": "And I also need to add, of course, the 2x minus 2y." + }, + { + "text": "It is simpler." + }, + { + "text": "It is still not simple enough for my taste." + }, + { + "text": "I can actually do better." + }, + { + "text": "See, I mean now what is, so these guys look like a sum of squares." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk9.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..2ebab68b48ed9108ed215c21106e93056b697b19 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_7_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "But here I have this extra stuff." + }, + { + "text": "But, 2x minus 2y, well, that is twice x minus y." + }, + { + "text": "It looks like maybe we can simplify this and make this into another square." + }, + { + "text": "In fact, I can simplify this further to x minus y plus one squared." + }, + { + "text": "See, that would start like, maybe I should put parentheses here, that would be x minus y squared plus twice x minus y." + }, + { + "text": "And then there is a plus one." + }, + { + "text": "Well, we don't have that plus one, so let's remove it by subtracting one." + }, + { + "text": "Oh, let me find that minus one here." + }, + { + "text": "And I still have my 2y squared." + }, + { + "text": "Do you see why this is the same function as that one?" + }, + { + "text": "Again, if I expand x minus y plus one squared, I get x minus y squared plus twice x minus y, that is those guys, plus one." + }, + { + "text": "But I will have a minus one and that will cancel out." + }, + { + "text": "And then I have a plus 2y squared." + }, + { + "text": "Now what I know, see, this is a sum of two squares minus one." + }, + { + "text": "And this critical point, x, y equals minus one, zero, that is exactly when this is zero and that is zero." + }, + { + "text": "That is the smallest value." + }, + { + "text": "This is always greater or equal to zero, same with that one." + }, + { + "text": "That is always at least minus one." + }, + { + "text": "And minus one happens to be the value at the critical point." + }, + { + "text": "It is a minimum." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk0.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..e6499639a2dd486fc34915743508e989029de764 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "Today we are going to see how to use what we saw last time about partial derivatives to handle minimization or maximization problems involving functions of several variables." + }, + { + "text": "Remember last time we said that when we have a function, say, of two variables, x and y, then we have actually two different derivatives." + }, + { + "text": "Partial f, partial x, also called f sub x, is the derivative with respect to x keeping y constant." + }, + { + "text": "And we have partial f, partial y, also called f sub y, where we vary y and we treat x as a constant." + }, + { + "text": "And now, one thing I didn't have time to tell you about, but hopefully you heard about in recitation yesterday, is the approximation formula that tells you what happens if you vary both x and y. F sub x tells us what happens if we change x a little bit by some small amount delta x. F sub y tells us how f changes if we change y by a small amount delta y." + }, + { + "text": "If we do both at the same time, then the two effects will add up with each other." + }, + { + "text": "Because you can imagine that first you will change x and then you will change y or the other way around." + }, + { + "text": "It doesn't really matter." + }, + { + "text": "If we change x by a certain amount delta x, and if we change y by the amount delta y, and let's say that we have z equals f of x, y, then that changes by an amount which is approximately f sub x times delta x plus f sub y times delta y." + }, + { + "text": "And that is one of the most important formulas about partial derivatives." + }, + { + "text": "The intuition for this, again, is just the two effects add up." + }, + { + "text": "If I change x by a small amount and then I change y, well, first changing x will modify f. How much does it modify f?" + }, + { + "text": "The answer is the rate of change." + }, + { + "text": "The rate of change is f sub x." + }, + { + "text": "And, if I change y, then the rate of change of f when I change y is f sub y." + }, + { + "text": "All together, I get this change in the value of f. And, of course, that is only an approximation formula." + }, + { + "text": "Actually, there would be higher order terms involving second and third derivatives and so on." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk1.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..24332c5f071c389023f7abaf7259fb1a63c23f92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "One way to justify this, sorry, I was distracted by a microphone problem." + }, + { + "text": "OK, so how do we justify this formula?" + }, + { + "text": "Well, one way to think about it is in terms of tangent plane approximation." + }, + { + "text": "Let's think about the tangent plane to the graph of a function f. I have some pictures to show you." + }, + { + "text": "It will be easier if I show the pictures." + }, + { + "text": "Remember, partial f over partial x was obtained by looking at the situation where y is held constant." + }, + { + "text": "That means I am slicing the graph of f by a plane that is parallel to the xz plane." + }, + { + "text": "And then, when I change x, z changes." + }, + { + "text": "And the slope of that is going to be the derivative with respect to x." + }, + { + "text": "Now, if I do the same in the other direction, then I will have similarly the slope in a slice now parallel to the yz plane that will be partial f over partial y." + }, + { + "text": "In fact, in each case I have a line." + }, + { + "text": "And that line is tangent to the surface." + }, + { + "text": "Now, if I have two lines tangent to the surface, well, then together they determine for me the tangent plane to the surface." + }, + { + "text": "Let's try to see how that works." + }, + { + "text": "We know that f sub x and f sub y are the slopes of two tangent lines to this plane, sorry, two tangent lines to the graph." + }, + { + "text": "And let's write down the equations of these lines." + }, + { + "text": "I am not going to write parametric equations." + }, + { + "text": "I am going to write them in terms of x, y, z coordinates." + }, + { + "text": "Let's say that partial f over partial x at a given point is equal to a." + }, + { + "text": "Then that means that we have a line given by the following conditions." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk10.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..04a9beb08f73a15fd9091546cca18b48afb0c0c0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, of course, here I was very lucky." + }, + { + "text": "In general, I could not expect things to simplify that much." + }, + { + "text": "In fact, I cheated." + }, + { + "text": "I started from that." + }, + { + "text": "I expanded." + }, + { + "text": "And then that is how I got my example." + }, + { + "text": "The general method will be a bit different, but you will see it will actually also involve completing squares." + }, + { + "text": "Just there is more to it than what we have seen." + }, + { + "text": "We will come back to this tomorrow." + }, + { + "text": "How do I know that this equals?" + }, + { + "text": "y is what negative one?" + }, + { + "text": "How do I know that that whole function is greater or equal to negative one?" + }, + { + "text": "Well, I wrote f of x, y as something squared plus 2y2 minus one." + }, + { + "text": "This squared is always a positive number, non-negative." + }, + { + "text": "It is a square." + }, + { + "text": "The square of something is always non-negative." + }, + { + "text": "Similarly, y2 is also always non-negative." + }, + { + "text": "If you add something that is at least zero plus something that is at least zero and you subtract one, you get always at least minus one." + }, + { + "text": "And, in fact, the only way that you can get minus one is if both of these guys are zero at the same time." + }, + { + "text": "That is how I get my minimum." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk11.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..f4eced0dcd7ffc5bdcf9cd95cd7f63aa34e4a4ac --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "More about this tomorrow." + }, + { + "text": "In fact, what I would like to tell you about now instead is a nice application of min-max problems that maybe you don't think of as a min-max problem." + }, + { + "text": "But you will see, I mean, you don't think of it that way because probably your calculator can do it for you." + }, + { + "text": "Or, if not, your computer can do it for you." + }, + { + "text": "But it is actually something where the theory is based on minimization in two variables." + }, + { + "text": "Very often in experimental sequences you have to do something called least squares interpolation." + }, + { + "text": "And what is that about?" + }, + { + "text": "Well, it is the idea that maybe you do some experiments and you record some data." + }, + { + "text": "You have some data x and some data y." + }, + { + "text": "And I don't know, maybe, for example, maybe you are measuring frogs and you are trying to measure how big the frog leg is compared to the eyes of a frog or whatever, or trying to measure something." + }, + { + "text": "And if you are doing chemistry then it could be how much you put of some reactant and how much of the output product that you wanted to synthesize is going to be the same." + }, + { + "text": "All sorts of things." + }, + { + "text": "Make up your own example." + }, + { + "text": "You measure, basically, for various values of x what the value of y ends up being." + }, + { + "text": "And then you would like to claim, oh, well, these points are kind of aligned." + }, + { + "text": "I mean, of course, to a mathematician they are not aligned, but to an experimental scientist that is evidence that there is a relation between the two." + }, + { + "text": "And so you want to claim, and in your paper you will actually draw a nice little line that says, C, these two functions depend linearly on each other." + }, + { + "text": "The question is how do we come up with that nice line that passes smack in the middle of the points?" + }, + { + "text": "The question is, given experimental data, xiyi, so maybe I should actually be more precise." + }, + { + "text": "You are given some experimental data." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk12.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..ec058dcefcf28c0e3655b8df350c1a7550b31989 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "You have data points x1, y1, x2, y2, and so on, xn, yn." + }, + { + "text": "The question would be find the best fit line of the form y equals ax plus b that somehow approximates very well this data." + }, + { + "text": "You can also use that, by the way, to predict various things." + }, + { + "text": "For example, if you look at your new homework, actually the first problem asks you to predict how many iPods will be on this planet in ten years, looking at past sales and how they behave." + }, + { + "text": "One thing, by the way, before you lose all the money you don't have yet, you cannot use that to predict the stock market." + }, + { + "text": "Don't try to use that to make money." + }, + { + "text": "It doesn't work." + }, + { + "text": "One tricky thing here that I want to draw your attention to is what are the unknowns here?" + }, + { + "text": "The natural answer would be to say the unknowns are x and y." + }, + { + "text": "That is not actually the case." + }, + { + "text": "We are not trying to solve for some x and y. I mean we have some values given to us." + }, + { + "text": "And when we are looking for that line we don't really care about a particular value of x." + }, + { + "text": "What we care about is actually these coefficients a and b that will tell us what the relation between x and y is." + }, + { + "text": "In fact, we are trying to solve for a and b that will give us the nicest possible line for these points." + }, + { + "text": "The unknowns in our equations will have to be a and b, not x and y." + }, + { + "text": "The question really is find the best a and b." + }, + { + "text": "And, of course, we have to decide what we mean by best." + }, + { + "text": "Best will mean that we minimize some function of a and b that measures the total error that we are making when we are choosing this line compared to the experimental data." + }, + { + "text": "Maybe, roughly speaking, it should measure how far these points are from the line." + }, + { + "text": "But now there are various ways to do it." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk13.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..5d2475feee1af92e7e44b93eafd8ef1a1aeab556 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "And some of them are, I mean a lot of them are valid to give you different answers." + }, + { + "text": "You have to decide what it is that you prefer." + }, + { + "text": "For example, you could measure the distance to the line by projecting perpendicularly." + }, + { + "text": "Or, you could measure instead the difference between, for a given value of x, the difference between the experimental value of y and the predicted one." + }, + { + "text": "And that is often more relevant because these guys are actually maybe expressed in different units." + }, + { + "text": "They are not the same type of quantity." + }, + { + "text": "You cannot actually combine them arbitrarily." + }, + { + "text": "Anyway, the convention is usually we measure distance in this way." + }, + { + "text": "Next, you could try to minimize the largest distance." + }, + { + "text": "Say we look at where is the largest error and we make that the smallest possible." + }, + { + "text": "The drawback of doing that is experimentally very often you have one data point that is not good because maybe you fell asleep in front of the experiment." + }, + { + "text": "And so you did not measure the right thing." + }, + { + "text": "You tend to want to not give too much importance to some data point that is far away from the others." + }, + { + "text": "Maybe instead you want to measure the average distance." + }, + { + "text": "Or maybe you want to actually give more weight to things that are further away." + }, + { + "text": "And then you do not want to do the distance but the square of the distance." + }, + { + "text": "There are various possible answers." + }, + { + "text": "But one of them gives us a particularly nice formula for a and b." + }, + { + "text": "And so that is why it is the universally used one." + }, + { + "text": "Here it says least squares." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk14.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..03f389ad03cba30ec35302a03113c11b9ae12887 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "That is because we will measure, actually, the sum of the squares of the errors." + }, + { + "text": "And why do we do that?" + }, + { + "text": "Well, part of it is because actually it looks good." + }, + { + "text": "I mean, when you see these plots in scientific papers, they really look like the line is indeed the ideal line." + }, + { + "text": "And the second reason is because actually the minimization problem that we will get is particularly simple, well-proposed and it is easy to solve." + }, + { + "text": "We will have a nice formula for the best a and the best b." + }, + { + "text": "If you have a method that is simple and gives you a good answer then that is probably the good one." + }, + { + "text": "We have to define best." + }, + { + "text": "And here it is in the sense of defining a total square error." + }, + { + "text": "Maybe I should say total square deviation." + }, + { + "text": "What do I mean by that?" + }, + { + "text": "The deviation for each data point is the difference between what you have measured and what you are predicting by your model." + }, + { + "text": "That is the difference between the two." + }, + { + "text": "Now what we will do is try to minimize the function capital D, which is just the sum for all the data points of the square of the deviation." + }, + { + "text": "Let me emphasize again this is a function of a and b. I mean, of course, there are a lot of letters in here." + }, + { + "text": "But xi and yi in real life will be numbers given to you." + }, + { + "text": "They will be the numbers that you have measured." + }, + { + "text": "You have measured all of this data." + }, + { + "text": "They are just going to be numbers." + }, + { + "text": "You put them in there and you get the answer." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk15.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..574ce46fe50beb8d2adc71dc4ba061053cadb260 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Any questions?" + }, + { + "text": "How do we minimize this function of a and b?" + }, + { + "text": "Let's use our new knowledge." + }, + { + "text": "Let's actually look for a critical point." + }, + { + "text": "We want to solve for partial d over partial a equals zero and partial d over partial b equals zero." + }, + { + "text": "That is how we look for critical points." + }, + { + "text": "Let's take the derivative of a." + }, + { + "text": "Well, the derivative of a sum is the sum of the derivatives." + }, + { + "text": "And now we have to take the derivative of this quantity squared." + }, + { + "text": "Remember how we take the derivative of a square." + }, + { + "text": "We take twice this quantity times the derivative of what we are squaring." + }, + { + "text": "We will get two times minus y i, sorry, y i minus a xi plus b times the derivative of this with respect to a." + }, + { + "text": "What is the derivative of this with respect to a?" + }, + { + "text": "Negative xi, exactly." + }, + { + "text": "And so we will want this to be zero." + }, + { + "text": "And partial d over partial b, we do the same thing but differentiating with respect to b instead of with respect to a." + }, + { + "text": "Again, sum of squares twice y i minus a xi plus b times the derivative of this with respect to b is, I think, negative one." + }, + { + "text": "That is the equations we have to solve." + }, + { + "text": "Well, let's reorganize this a little bit." + }, + { + "text": "The first equation, see, there are a's and there are b's in these equations." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk16.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..6dbbcdfd1a44915f775e513934285605a93fde83 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "I am going to just look at the coefficients of a and b." + }, + { + "text": "If you have good eyes, you can see probably that these are actually linear equations in a and b." + }, + { + "text": "There is a lot of clutter with all these x's and y's all over the place." + }, + { + "text": "Let's actually try to expand things and make that more apparent." + }, + { + "text": "The first thing I will do is I will actually get rid of these factors of two that are just not very important." + }, + { + "text": "I can simplify things by two." + }, + { + "text": "And next I am going to look at the coefficient of a. I will get basically a times xi squared." + }, + { + "text": "Well, let me just do it and it should be clear." + }, + { + "text": "I claim when we simplify this we get a times xi squared plus xi times b minus xi yi." + }, + { + "text": "And we set this equal to zero." + }, + { + "text": "Do you agree that this is what we get when we expand that product?" + }, + { + "text": "No?" + }, + { + "text": "OK, let's do the other one." + }, + { + "text": "We just multiply by minus one." + }, + { + "text": "We take the opposite of that." + }, + { + "text": "It will be axi plus b. I will write that as xia plus b minus yi." + }, + { + "text": "And let me just reorganize that by actually putting all the a's together." + }, + { + "text": "That means actually I will have sum of all the xi squared times xi times b minus sum of xi yi equals zero." + }, + { + "text": "If I rewrite this it becomes sum of xi squared times a plus sum of the xi's times b minus, let me move the other guys to the other side, equals sum of xi yi." + }, + { + "text": "And that one becomes sum of xi times a plus how many b's do I get from this one?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk17.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..46c92ceb193fbddba6ccd0128c8434e1fa895b6b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, I get one for each data point." + }, + { + "text": "When I sum them together I will get n. Very good." + }, + { + "text": "So, n times b equals sum of yi." + }, + { + "text": "Now, these quantities may look scary, but they are actually just numbers." + }, + { + "text": "For example, for this one you look at all your data points." + }, + { + "text": "For each of them you take the value of x and you just sum all these numbers together." + }, + { + "text": "What you get, actually, is a linear system in a two-by-two linear system." + }, + { + "text": "And so now we can solve this for a and b." + }, + { + "text": "In practice, of course, first you plug in the numbers for xi and yi and then you solve the system that you get." + }, + { + "text": "And we know how to solve two-by-two linear systems, I hope." + }, + { + "text": "That is how we find the best fit line." + }, + { + "text": "Now, why is that going to be the best one instead of the worst one?" + }, + { + "text": "We just solved for a critical point." + }, + { + "text": "That could actually be a maximum of this error function d. We will have the answer to that next time." + }, + { + "text": "But trust me, if you really want to go for the second derivative test that we will do tomorrow and apply it in this case, it is quite hard to check." + }, + { + "text": "But you can see it is actually a minimum." + }, + { + "text": "I will just say we can show that it is a minimum." + }, + { + "text": "Now, even for the linear case, it is the one that we are the most familiar with." + }, + { + "text": "Least squares interpolation actually works in much more general settings." + }, + { + "text": "Instead of fitting for the best line, if you think that there is a different kind of relation, then maybe you can fit in using a different kind of formula." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk18.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..fa2ca36c0d134e6b3372da5aa353386c01a4066b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let me actually illustrate that for you." + }, + { + "text": "I don't know if you are familiar with Moore's law." + }, + { + "text": "It is something that is supposed to tell you how quickly, basically, computer chips become smarter, faster and faster over time." + }, + { + "text": "It is a law that says things about the number of transistors that you can fit onto a computer chip." + }, + { + "text": "Here I have some data about the number of transistors on a standard PC processor as a function of time." + }, + { + "text": "And, well, if you try to do the best line fit, you will see quickly that it doesn't seem to follow a linear trend." + }, + { + "text": "On the other hand, if you plot the diagram in a log scale, the log of the number of transistors as a function of time, then you get a much better line." + }, + { + "text": "And so, in fact, that means that you had an exponential relation between the number of transistors and time." + }, + { + "text": "And so, actually, that is what Moore's law says." + }, + { + "text": "It says that the number of transistors on a chip doubles, depending on the version, every 18 months or every two years." + }, + { + "text": "They keep changing the statement." + }, + { + "text": "How do we find that best exponential fit?" + }, + { + "text": "Well, an exponential fit would be something of the form y equals a constant times exponential of a times x." + }, + { + "text": "That is what we want to look at." + }, + { + "text": "Well, we could try to minimize a square error like we did earlier, but that doesn't work well at all." + }, + { + "text": "The equations that you get are very complicated." + }, + { + "text": "You cannot solve them." + }, + { + "text": "But remember what I showed you on this log plot." + }, + { + "text": "If you plot the log of y as a function of x, then suddenly it becomes a linear relation." + }, + { + "text": "Observe this is the same as ln of x equals ln of c plus ax." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk19.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..55b8384a00899de02bdae34fca68d10a37a51f56 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk19.json @@ -0,0 +1,53 @@ +[ + { + "text": "And that is a linear best fit." + }, + { + "text": "What you do is you just look for the best straight line fit for the log of y." + }, + { + "text": "That is something we already know." + }, + { + "text": "But you can also do other examples." + }, + { + "text": "For example, let's say that we have something more complicated." + }, + { + "text": "Let's say that we have actually a quadratic law." + }, + { + "text": "For example, y is of the form ax2 bx c. And, of course, you are trying to find somehow the best." + }, + { + "text": "That would mean here fitting the best parabola for your data points." + }, + { + "text": "Well, to do that you would need to find a, b and c. And now you would have actually a function of a, b and c, which would be the sum of all data points of the quadratic equation." + }, + { + "text": "And if you try to solve for critical points, now you will have three equations involving a, b and c. And, in fact, you will find a three by three linear system." + }, + { + "text": "And it works just the same way." + }, + { + "text": "Just you have a little bit more data." + }, + { + "text": "Basically, you see that these best fit problems are an example of minimization problem." + }, + { + "text": "But maybe you didn't expect to see minimization problems come in." + }, + { + "text": "But that is really the way to handle these questions." + }, + { + "text": "OK, so tomorrow we will go back to the question of how do we decide whether it is a minimum or a maximum?" + }, + { + "text": "And we will continue exploring functions of several variables." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk2.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..cbdde5612839d21f7df1c4e4a177c22a02adffc6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "I am going to keep y constant equal to y0." + }, + { + "text": "And I am going to change x." + }, + { + "text": "And, as I change x, z will change at a rate that is equal to a." + }, + { + "text": "That would be z equals z0 plus a times the change in x, x minus x0." + }, + { + "text": "That is how you would describe the line that is, I guess, the one that is plotted in green here." + }, + { + "text": "That is the intersection with the slice parallel to the xz plane." + }, + { + "text": "I hold y constant equal to y0." + }, + { + "text": "And z is a function of x that varies with a rate of a." + }, + { + "text": "And now, if I look similarly at the other slice, let's say that the partial with respect to y is equal to b, then I get another line which is obtained by the fact that z depends on y and the rate of change with respect to y will be b while x is held constant equal to x0." + }, + { + "text": "These two lines are both going to be in the tangent plane to the surface." + }, + { + "text": "They are both tangent to the surface, f of f. And, well, together they determine a plane." + }, + { + "text": "And that plane is just given by the formula z equals z0 plus a times x minus x0 plus b times y plus b." + }, + { + "text": "If you look at what happens, this is the equation of a plane, z equals constant times x plus constant times y plus constant." + }, + { + "text": "And if you look at what happens if I hold y constant and vary x, I recover the first line." + }, + { + "text": "If I hold x constant and vary y, I get the second line." + }, + { + "text": "Another way to do it, of course, would be to write actually parametric equations of these lines, get vectors along them and then take the cross-product to get the normal vector to the plane, and then get this equation for the plane using the normal vector." + }, + { + "text": "That also works and it gives you the same formula." + }, + { + "text": "If you are curious, exercise, do it again using parametrics and using cross-product to get the plane equation." + }, + { + "text": "OK, so that is how we get the tangent plane." + }, + { + "text": "And now, what this approximation formula here says is that, in fact, the graph of a function is close to the tangent plane." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk3.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..db670d552209553a73abe7a57967ebd9528e07b0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "If we were moving on the tangent plane, this would be an actual equality." + }, + { + "text": "Delta z would be a linear function of delta x and delta y." + }, + { + "text": "And the graph of a function is near the tangent plane, but it is not quite the same." + }, + { + "text": "It is only an approximation for small delta x and small delta y." + }, + { + "text": "The approximation formula says the graph of f is close to its tangent plane." + }, + { + "text": "And we can use that formula over here now to estimate how the value of f changes if I change x and y at the same time." + }, + { + "text": "Questions about that?" + }, + { + "text": "Now that we have caught up with what we were supposed to see on Tuesday, I can tell you now about max and min problems." + }, + { + "text": "Min problems." + }, + { + "text": "That is going to be an application of partial derivatives to look at optimization problems." + }, + { + "text": "Maybe ten years from now when you have a real job, your job might be to actually minimize the cost of something or maximize the profit of something or whatever." + }, + { + "text": "But typically, the function that you will have to strive to minimize or maximize will depend on several variables." + }, + { + "text": "If you have a function of one variable, you know that to find its minimum or its maximum you look at the derivative and you set that equal to zero." + }, + { + "text": "And you try to then look at what happens to the function." + }, + { + "text": "Here it is going to be kind of similar, except, of course, we have several variables." + }, + { + "text": "For today, we will think about a function of two variables." + }, + { + "text": "But it works exactly the same if you have three variables, ten variables, a million variables." + }, + { + "text": "The first observation is that if we have a local minimum or a local maximum, then both partial derivative, partial f, partial x and partial f, partial y are both zero at the same time." + }, + { + "text": "Why is that?" + }, + { + "text": "Well, let's say that f sub x is zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk4.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..6a4752d759dedab56f0865629de49a11db927b62 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "That means when I vary x, well, to first order the function doesn't change." + }, + { + "text": "Maybe that is because it is going through." + }, + { + "text": "If I look only at the slice parallel to the x-axis, then maybe I am going through the minimum." + }, + { + "text": "But then, if partial f, partial y is not zero, then actually by changing y I could still make the value larger or smaller." + }, + { + "text": "That wouldn't be an actual maximum or minimum." + }, + { + "text": "It would only be maximum or minimum if I stay in the slice." + }, + { + "text": "But if I allow myself to change y, that doesn't work." + }, + { + "text": "I need actually to know that if I change y the value will not change either to first order." + }, + { + "text": "That is why I also need partial f, partial y to be zero." + }, + { + "text": "Now, let's say that they are both zero." + }, + { + "text": "Well, why is that enough?" + }, + { + "text": "It is essentially enough because of this formula telling me that if both of these guys are zero then to first order the function doesn't change." + }, + { + "text": "And then, of course, there will be maybe quadratic terms that will actually turn that." + }, + { + "text": "This won't really say that your function is actually constant." + }, + { + "text": "It will just tell you that maybe it will be actually quadratic or higher order in delta x and delta y." + }, + { + "text": "That is what you expect to have at a maximum or a minimum." + }, + { + "text": "That condition is the same thing as saying that the tangent plane to the graph is actually going to be horizontal." + }, + { + "text": "And that is what you want to have." + }, + { + "text": "Say you have a minimum." + }, + { + "text": "Well, see that the tangent plane at this point, at the bottom of the graph, is going to be horizontal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk5.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..7e48c199e023a813f11acd0a96e5d01eb8971e00 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you can see that on this equation of a tangent plane, when both these coefficients are zero, that is when the equation becomes z equals constant, the horizontal plane." + }, + { + "text": "Does that make sense?" + }, + { + "text": "We will have a name for this kind of point because actually what we will see very soon is that these conditions are necessary but they are not sufficient." + }, + { + "text": "There are actually other kinds of points where the partial derivatives are zero." + }, + { + "text": "Let's give a name to this." + }, + { + "text": "We say that x0, y0 is a critical point of F if the partial derivative with respect to x and the partial derivative with respect to y are both zero." + }, + { + "text": "More generally, you would want all the partial derivatives, no matter how many variables you have, you want all the partials to be zero." + }, + { + "text": "Let's see an example." + }, + { + "text": "Let's say I give you the function f of x, y equals x squared minus 2xy plus py squared plus 2x minus 2y." + }, + { + "text": "And let's try to figure out whether we can minimize or maximize this." + }, + { + "text": "What we start doing immediately is taking the partial derivatives." + }, + { + "text": "What is f sub x?" + }, + { + "text": "It starts with 2x minus 2y plus zero plus two." + }, + { + "text": "Remember that y is a constant so this differentiates to zero." + }, + { + "text": "Now, if we do f sub y, that is going to be zero minus 2x plus 6y minus two." + }, + { + "text": "And what we want to do is set these things equal to zero." + }, + { + "text": "And we want to solve these two equations at the same time." + }, + { + "text": "An important thing to remember, maybe I should have told you a couple of weeks ago already, if you have two equations to solve, well, it is very good to try to simplify them by adding them together or whatever." + }, + { + "text": "But you must keep two equations." + }, + { + "text": "If you have two equations, you should not end up with just one equation out of nowhere." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk6.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..9395a90268474c96a0037bb843bc6e78e8145fe5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "For example, here we can certainly simplify things by summing them together." + }, + { + "text": "See, if we add them together, well, the x's cancel and the constants cancel." + }, + { + "text": "In fact, we are just left with 4y equals zero." + }, + { + "text": "That is pretty good." + }, + { + "text": "That tells us y should be zero." + }, + { + "text": "But then we should, of course, go back to these and see what else we know." + }, + { + "text": "Well, now it tells us, if you put y equals zero, that tells you 2x plus 2 equals zero." + }, + { + "text": "That tells you x equals minus one." + }, + { + "text": "We have one critical point." + }, + { + "text": "That is x, y equals minus one over two." + }, + { + "text": "Any questions so far?" + }, + { + "text": "Well, you should have a question." + }, + { + "text": "The question should be how do we know if it is a maximum or a minimum?" + }, + { + "text": "Well, if we had a function of one variable, we would decide things based on the second derivative." + }, + { + "text": "And, in fact, we will see tomorrow how to do things based on the second derivative." + }, + { + "text": "But that is kind of tricky because there are a lot of second derivatives." + }, + { + "text": "I mean, we already have two first derivatives." + }, + { + "text": "You can imagine that if you keep taking partials, you may end up with more and more." + }, + { + "text": "We will have to figure out carefully what the condition should be." + }, + { + "text": "We will do that tomorrow." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk7.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..4bcbbf6b2197e00d7483dbd1b1319f8d7b454496 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "For now, let's just try to look at how do we understand these things by hand." + }, + { + "text": "In fact, let me point out to you immediately that there is more than maxima and minima." + }, + { + "text": "Remember, we saw the example of x squared plus y squared that has a critical point." + }, + { + "text": "The critical point is obviously a minimum." + }, + { + "text": "And, of course, it could be a local minimum because it could be that if you have a more complicated function there is indeed a minimum here." + }, + { + "text": "But then elsewhere the function drops to a lower value." + }, + { + "text": "We call that just a local minimum to say that it is a minimum if you stick to values that are close enough to that point." + }, + { + "text": "Of course, you also have a local maximum." + }, + { + "text": "Well, I did not plot it, but it is easy to plot." + }, + { + "text": "That is a local maximum." + }, + { + "text": "But there is a third example of critical point, and that is a saddle point." + }, + { + "text": "The saddle point is a new phenomenon that you do not really see in a single variable calculus." + }, + { + "text": "It is a critical point that is neither a minimum nor a maximum because, depending on which direction you look in, it is either one or the other." + }, + { + "text": "The point in the middle at the origin is a saddle point." + }, + { + "text": "If you look at the tangent plane to this graph you will see that it is actually horizontal at the origin." + }, + { + "text": "You have this mountain pass." + }, + { + "text": "At the mountain pass the ground is horizontal." + }, + { + "text": "But, depending on which direction you go, you go up or down." + }, + { + "text": "We say that the point is a saddle point if it is neither a minimum nor a maximum." + }, + { + "text": "OK, so the possibilities could be a local min, a local max, or a saddle." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk8.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..8eebe5d35e57a9bb443552331906178033fbb172 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "Tomorrow we will see how to decide which one it is in general using second derivatives." + }, + { + "text": "For this time let's just try to do it by hand." + }, + { + "text": "I just want to observe." + }, + { + "text": "In fact, I can try to, you know, these examples that I have here, they are x2 y2 y2-x2." + }, + { + "text": "They are sums or differences of squares." + }, + { + "text": "And, if we know that we can put things as a sum of squares, for example, we will be done." + }, + { + "text": "Let's try to express this maybe in terms of a square." + }, + { + "text": "Well, the main problem is this 2xy." + }, + { + "text": "But, observe, we know something that starts with x2 minus 2xy that is actually the square of something else." + }, + { + "text": "It would be x2 minus 2xy, well, plus y2, not plus 3y2." + }, + { + "text": "Let's try to do that." + }, + { + "text": "We are going to complete the square." + }, + { + "text": "I am going to say it is x minus y squared." + }, + { + "text": "That gives me the first two terms and also y squared." + }, + { + "text": "Well, I still need to add two more y squares." + }, + { + "text": "And I also need to add, of course, the 2x minus 2y." + }, + { + "text": "It is simpler." + }, + { + "text": "It is still not simple enough for my taste." + }, + { + "text": "I can actually do better." + }, + { + "text": "See, I mean now what is, so these guys look like a sum of squares." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk9.json b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..2ebab68b48ed9108ed215c21106e93056b697b19 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/UYe98CcxPbs_9_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "But here I have this extra stuff." + }, + { + "text": "But, 2x minus 2y, well, that is twice x minus y." + }, + { + "text": "It looks like maybe we can simplify this and make this into another square." + }, + { + "text": "In fact, I can simplify this further to x minus y plus one squared." + }, + { + "text": "See, that would start like, maybe I should put parentheses here, that would be x minus y squared plus twice x minus y." + }, + { + "text": "And then there is a plus one." + }, + { + "text": "Well, we don't have that plus one, so let's remove it by subtracting one." + }, + { + "text": "Oh, let me find that minus one here." + }, + { + "text": "And I still have my 2y squared." + }, + { + "text": "Do you see why this is the same function as that one?" + }, + { + "text": "Again, if I expand x minus y plus one squared, I get x minus y squared plus twice x minus y, that is those guys, plus one." + }, + { + "text": "But I will have a minus one and that will cancel out." + }, + { + "text": "And then I have a plus 2y squared." + }, + { + "text": "Now what I know, see, this is a sum of two squares minus one." + }, + { + "text": "And this critical point, x, y equals minus one, zero, that is exactly when this is zero and that is zero." + }, + { + "text": "That is the smallest value." + }, + { + "text": "This is always greater or equal to zero, same with that one." + }, + { + "text": "That is always at least minus one." + }, + { + "text": "And minus one happens to be the value at the critical point." + }, + { + "text": "It is a minimum." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk0.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..de88ac001212dfb6b1de182c0b68e842d34b4657 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "Yesterday we have learned about flux and we have seen the first examples of how to set up and compute integrals for flux of a vector field for a surface." + }, + { + "text": "Remember the flux of a vector field F for a surface S is defined by taking the double integral on the surface of F dot n dS where n is the unit normal to the surface and dS is the area element on the surface." + }, + { + "text": "As we have seen, for various surfaces we have various formulas telling us what the normal vector is and what the area element becomes." + }, + { + "text": "For example, on spheres we typically integrate with respect to phi theta the latitude and longitude angles." + }, + { + "text": "On a horizontal plane we would just end up integrating dx dy and so on." + }, + { + "text": "At the end of the lecture we saw a formula." + }, + { + "text": "And a lot of you asked me how did we get it." + }, + { + "text": "Well, we didn't get it yet." + }, + { + "text": "We are going to try to explain where it comes from and why it works." + }, + { + "text": "The case we want to look at is the graph of a function." + }, + { + "text": "It is given by z equals some function in terms of x and y." + }, + { + "text": "Our surface is out here." + }, + { + "text": "z is a function of x and y." + }, + { + "text": "And x and y will range over some domain in the xy plane, namely the region that is the shadow of the surface on the xy plane." + }, + { + "text": "I said that we will have a formula for n ds which will end up being plus minus, minus f sub x minus f sub y one dx dy so that we will set up and evaluate the integral in terms of x and y." + }, + { + "text": "Replacing every time we see z we will replace it by f of xy, whatever the formula for f of xy is." + }, + { + "text": "By the way, if we look at a very easy case where this is just a horizontal plane, so z equals constant, the function is just a constant, well, the partial derivatives become just zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk1.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..83a60f55a64abf7ed3e632f2c0caa0700c633561 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "You get zero, zero, one dx dy." + }, + { + "text": "That is what you would expect for a horizontal plane just from common sense." + }, + { + "text": "This is more interesting, of course, if a function is more interesting." + }, + { + "text": "How do we get that?" + }, + { + "text": "Where does this come from?" + }, + { + "text": "We need to figure out for a small piece of our surface what will be n delta S if you want." + }, + { + "text": "Let's say that we take a small rectangle in here corresponding to the sides delta x and delta y." + }, + { + "text": "And we look at the piece of surface that is above that." + }, + { + "text": "Well, the question we have now is what is the area of this little piece of surface and what is its normal vector?" + }, + { + "text": "Observe this little piece up here." + }, + { + "text": "If it is small enough it will look like a parallelogram." + }, + { + "text": "It might be slightly curvy, but roughly it looks like a parallelogram in space." + }, + { + "text": "And so we have seen how to find the area of a parallelogram in space using cross product." + }, + { + "text": "If we can figure out what are the vectors for this side and that side, then taking the cross product will give us, and taking the magnitude of the cross product will give us the area." + }, + { + "text": "Moreover, the cross product also gives us the normal direction." + }, + { + "text": "In fact, the cross product gives us two in one." + }, + { + "text": "It gives us the normal direction and the area element." + }, + { + "text": "And that is why I said that we will have an easy formula for N dS while N and dS taken separately are more complicated because you would have to actually take the length of a direction of this guy." + }, + { + "text": "Let's carry out this problem." + }, + { + "text": "Let's say I am going to look at a small piece of the xy plane." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk10.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..80ecc53d0640b10ed2fa61964d985138e15dd4dc --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "I think one of you, I forgot, asked yesterday, how would I do it in general?" + }, + { + "text": "Is there a formula like m dx plus n dy?" + }, + { + "text": "Well, that's going to be the formula." + }, + { + "text": "And, you'll see it's a little bit too complicated." + }, + { + "text": "So, the really useful ones are actually the special ones." + }, + { + "text": "So, let's say that we are given a parametric description of a surface S. So, that means we can describe S by formulas saying x is some function of two parameter variables." + }, + { + "text": "I'm going to call them u and v. I hope you don't mind." + }, + { + "text": "You can call them t1 and t2." + }, + { + "text": "You can call them whatever you want." + }, + { + "text": "OK, so one of the basic properties of a surface is because I have only two independent directions to move on, I should be able to express x, y, and z in terms of two variables." + }, + { + "text": "So, now let's say that I know how to do that." + }, + { + "text": "Or, maybe I should instead think of it in terms of a position vector if that helps you." + }, + { + "text": "The position vector, so that's just the vector with components x, y, z is given as a function of u and v. OK, so it works like a parametric curve, but with two parameters." + }, + { + "text": "So, now, how will we actually set up a flux integral on such a surface?" + }, + { + "text": "Well, because we are locating the flux in terms of u and v, we will end up with an integral du dv." + }, + { + "text": "So, we need to figure out how to express n ds in terms of du and dv." + }, + { + "text": "OK, so n ds should be something du dv." + }, + { + "text": "How do we do that?" + }, + { + "text": "Well, we can use the same method that we've actually used over here." + }, + { + "text": "Because if you think for a second, here we used, of course, a rectangle in the x, y plane, and we lifted it to a parallelogram and so on." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk11.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..61d1728a009aa03829fde534d602caecd77a30aa --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "But, more generally, you can think, what happens if I change u by delta u, keeping v constant, or the other way around?" + }, + { + "text": "You will get some sort of mesh grid on your surface, and you will look at a little parallelogram that's an elementary piece of that mesh and figure out what is its area and normal vector." + }, + { + "text": "Well, that will again be given by the cross product of the two sides." + }, + { + "text": "OK, so let's think a little bit about what happens when I move a little bit on my surface." + }, + { + "text": "So, I'm taking a grid on my surface given by the u and v directions." + }, + { + "text": "And, if I take a piece of that corresponding to small changes, delta u and delta v, what's going to be going on here?" + }, + { + "text": "Well, I have to deal with two vectors, one corresponding to changing u, the other one corresponding to changing v. If I change u, how does my point change?" + }, + { + "text": "Well, that's given by the derivative of this with respect to u. OK, so this vector here I will call, so the sides are given by, let me say, partial r over partial u times delta u." + }, + { + "text": "And, if you prefer, maybe I should write it as partial x over partial u delta u partial y." + }, + { + "text": "Well, it's just too boring to write, and so on." + }, + { + "text": "OK, it means just, you know, if I change u a little bit, keep v constant, then how x changes is given by partial x over partial u times delta u." + }, + { + "text": "Same thing with y, same thing with z." + }, + { + "text": "And, I'm just using vector notation to do it this way." + }, + { + "text": "That's the analog of when I said delta r for line integrals along a curve, vector delta r is the velocity vector dr over dt times delta t. OK, now if I look at the other side, OK, so, sorry, so let me start again." + }, + { + "text": "I ran out of space." + }, + { + "text": "One side is partial r partial u times delta u, and the other one would be partial r partial v times delta v because that's how the position of your point changes if you just change u or v and not the other one." + }, + { + "text": "So, now, to find the surface element together with a normal vector, I would just take the cross product between these guys." + }, + { + "text": "So, if you prefer, that's the cross product of partial r partial u with partial r partial v delta u delta v. And so, N dS is this cross product times du dv up to sine." + }, + { + "text": "I mean, also here." + }, + { + "text": "Depends on which choice I make for my normal vector, of course." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk12.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..4edd218fc4799dfc682e96577ad40cb5df2f17ab --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, now, if you, that, of course, is a slightly confusing equation to think of." + }, + { + "text": "So, a good exercise, if you want to really understand what's going on, try this in two good examples to look at." + }, + { + "text": "One good example to look at is the previous one." + }, + { + "text": "What is it?" + }, + { + "text": "It's when u and v are just x and y. OK, so the parametric equations are just x equals x, y equals y, and z is f of x, y." + }, + { + "text": "You should end up with the same formula that we had over there." + }, + { + "text": "And, you should see why because, see, both of them are given by a cross product." + }, + { + "text": "The other case you can look at, just to convince yourselves that it's true, so we don't need to do that because we've seen the formula before." + }, + { + "text": "But, in the case of a sphere, we've seen the formula for N and for dS separately." + }, + { + "text": "So, we know what N dS are in terms of d phi d theta." + }, + { + "text": "Well, you could parametrize a sphere in terms of phi and theta." + }, + { + "text": "Namely, the formulas would be x equals a sine phi cosine theta, y equals a sine phi sine theta, z equals a cosine phi." + }, + { + "text": "The formulas for spherical coordinates setting rho equals a." + }, + { + "text": "So, that's a parametric equation for the sphere." + }, + { + "text": "And then, if you try to use this formula here, you should end up with the same things we've already seen for N dS, just with a lot more pain to actually get there because your cross product is going to be a bit complicated." + }, + { + "text": "But, we're seeing all of these formulas, they all fit together." + }, + { + "text": "Somehow, it's always the same question, just we have different angles of attack on this general problem." + }, + { + "text": "OK, questions?" + }, + { + "text": "No?" + }, + { + "text": "OK, let's look at yet another last way of finding N dS." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk13.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..11d368b6015bc6b9cacbc394c8b399183b51e276 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then, I promise we'll switch to something else because I can feel that you're getting a bit overwhelmed by all these formulas for N dS." + }, + { + "text": "So, OK, so what happens very often is we don't actually know how to parametrize our surface." + }, + { + "text": "Maybe we don't know how to solve for z as a function of x and y, but our surface is given by some equation." + }, + { + "text": "And so, what that means is actually maybe what we know is not really these kinds of formulas, but maybe we know a normal vector." + }, + { + "text": "And, I'm going to call this one capital N because I don't even need it to be a unit vector, you will see." + }, + { + "text": "It can be a normal vector of the surface S. So, why would we ever know a normal vector?" + }, + { + "text": "Well, for example, if our surface is a plane, say it's a slanted plane given by some equation, Ax plus By plus Cz equals D. Well, you know the normal vector." + }, + { + "text": "It's A, B, C. Of course, you could solve for z and then go back to that case, which is why I said that that one is really useful." + }, + { + "text": "But, you can also just stay with a normal vector." + }, + { + "text": "Why else would you know a normal vector?" + }, + { + "text": "Well, let's say that you know an equation that's of a form g of x, y, z equals zero." + }, + { + "text": "Well, then you know that the gradient of g is perpendicular to the level surface." + }, + { + "text": "OK, so let me just give you two examples." + }, + { + "text": "If you have a plane, Ax plus By plus Cz equals D, then the normal vector would just be A, B, C. If you have a surface S given by an equation, g of x, y, z equals zero, then you can take the normal vector to be the gradient of g. We've seen that the gradient is perpendicular to the level surface." + }, + { + "text": "Now, of course, we don't necessarily have to follow what's going to come because if we could solve for z then we might be better off doing what we did over there." + }, + { + "text": "But, let's say that we want to do it this way." + }, + { + "text": "So, then what can we do?" + }, + { + "text": "Well, I'm going to give you a little bit of information about NDS." + }, + { + "text": "So, OK, so let's start by thinking about a slanted plane." + }, + { + "text": "OK, so let's say that my surface is just a slanted plane." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk14.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..8f6af2d2aa3b3d17432ec3b26b0606675c6a7d16 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, my normal vector would be maybe somewhere here." + }, + { + "text": "And, let's say that I'm going to try, you know, I need, of course, some handle on how to set up my integral." + }, + { + "text": "So, maybe I'm going to express this in terms of x and y. OK, so I have my coordinates, and I'll try to use x and y." + }, + { + "text": "So, then I would like to relate delta s, ds, to the area in the xy plane." + }, + { + "text": "So, that means, you know, I want maybe to look at the projection of this guy onto a horizontal plane." + }, + { + "text": "Let's squish it horizontally." + }, + { + "text": "So, then you have here another area." + }, + { + "text": "OK, so the guy on the slanted plane, let's call that delta s, and let's call this guy down here delta a." + }, + { + "text": "So, the question, and, you know, delta a would become ultimately maybe delta x, delta y, or something like that." + }, + { + "text": "The question is, how do we find the conversion rate between these two areas?" + }, + { + "text": "See, I mean, they're not the same." + }, + { + "text": "Visually, I hope it's clear to you that if my plane is actually horizontal, then, of course, they're the same." + }, + { + "text": "But, the more slanted it becomes, the more delta a becomes smaller than delta s, right?" + }, + { + "text": "I mean, if you buy, you know, if you buy land, and it's on the side of a cliff, well, whether you look at it on a map, or whether you look at it on the actual cliff, the area is going to be very different." + }, + { + "text": "I'm not sure if that's a wise thing to do if you want to build a house there, but I've been told you can get really cheap land." + }, + { + "text": "OK, so anyway, OK, so delta s versus delta a depends on how slanted things are." + }, + { + "text": "And, let's try to make that more precise by looking at the angle that our plane makes with the horizontal direction." + }, + { + "text": "OK, so let's call this angle alpha, the angle that our plane makes with the horizontal direction." + }, + { + "text": "See, it's all coming together now." + }, + { + "text": "The first unit about cross products, normal vectors, and so on is actually useful now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk15.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..e90009e6248e5d6a50885b9d3130bf4050ef960c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, I claim that the surface element is related to the area in the plane by delta a equals delta s times the cosine of alpha." + }, + { + "text": "Why is that?" + }, + { + "text": "Well, let's look at this small rectangle with one horizontal side and one slanted side." + }, + { + "text": "Well, when you project, this side doesn't change." + }, + { + "text": "But, this side gets shortened by a factor of cosine alpha." + }, + { + "text": "Whatever this length was, this length here is that one times cosine alpha." + }, + { + "text": "So, that's why the area gets shrunk by cosine alpha." + }, + { + "text": "In one direction, nothing happens." + }, + { + "text": "In the other direction, you squish by cosine alpha." + }, + { + "text": "So, what that means is that, well, OK, so we'll have to deal with this." + }, + { + "text": "And, of course, the one we'll care about actually is delta s expressed in terms of delta a." + }, + { + "text": "But, what are we going to do with this cosine?" + }, + { + "text": "It's not very convenient to have a cosine left in here." + }, + { + "text": "So, remember, the angle between two planes, it's the same thing as the angle between the normal vectors." + }, + { + "text": "So, if you want to see this angle alpha elsewhere, what you can do is you can just take the vertical direction." + }, + { + "text": "Let's take k. Then, here we have our angle alpha again." + }, + { + "text": "So, in particular, cosine of alpha, I can get, well, we know how to find the angle between two vectors." + }, + { + "text": "So, if we have our normal vector n, we'll do n dot k, and we'll divide by length n length k. Well, length k is one." + }, + { + "text": "That's one easy." + }, + { + "text": "OK, so that's how we find the angle." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk16.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..18b8ca6f0e10e19b75db0dabf1ec37a110a6c671 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, now I'm going to say, well, delta s is going to be one over cosine alpha delta a." + }, + { + "text": "And, I can rewrite that as length of n divided by n dot k times delta a." + }, + { + "text": "Now, let's multiply that by the unit normal vector because what I'm multiplying by is not dS, but actually n dS." + }, + { + "text": "So, n delta s will be, I'm just going to multiply by n. Well, let's think for a second." + }, + { + "text": "What happens if I take the unit normal n, and I multiply it by the length of my other normal big N?" + }, + { + "text": "Well, I get big N again, right?" + }, + { + "text": "This is a normal vector of the same length as n, well, up to sine." + }, + { + "text": "But, actually, maybe I should." + }, + { + "text": "The only thing I don't know is whether this guy will be going in the same direction as big N or in the opposite direction." + }, + { + "text": "Say that, for example, my capital N has length, I don't know, length three, for example." + }, + { + "text": "The unit normal vector might be this guy, in which case, indeed, three times little n will be big N. Or, it might be this one, in which case, three times little n will be negative big N. But, up to sine, it's N. And then, I will have N over n dot k delta a." + }, + { + "text": "And so, the final formula, the one that actually we care about in case you don't really like my explanations of how we get there, is that N dS is plus or minus N over N dot k dx dy." + }, + { + "text": "That one is actually kind of useful, so let's box it." + }, + { + "text": "Now, just in case you are wondering, of course, if you didn't want to project to x, y, you would have maybe preferred to project to, say, the plane of a blackboard, yz." + }, + { + "text": "Well, you can do the same thing." + }, + { + "text": "To express N dS in terms of dy dz, you do the same argument." + }, + { + "text": "And simply, the only thing that changes is instead of using the vertical vector k, you use the normal vector i." + }, + { + "text": "So, you would be doing N over N dot i dy dz, and same thing." + }, + { + "text": "Just keep an open mind that this also works with other variables." + }, + { + "text": "But anyway, so that's how you can basically project the vector surface area element onto the x, y plane in a way." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk17.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..09fc575d766fb25a1c29c876fc0a0b29520a15d8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, so let's look at the special case just to see how this fits with stuff we've seen before." + }, + { + "text": "Let's do a special example where our surface is given by the equation z minus f of x, y equals zero." + }, + { + "text": "OK, that's a strange way to write the equation z equals f of x, y that we saw before." + }, + { + "text": "But now, it looks like, well, some function of x, y, z equals zero." + }, + { + "text": "So, let's try to use this new method." + }, + { + "text": "So, let's call this guy g of x, y, z." + }, + { + "text": "Well, so now let's look at the normal vector." + }, + { + "text": "The normal vector would be the gradient of g, we said." + }, + { + "text": "What's the gradient of this function?" + }, + { + "text": "So, gradient of g, well, partial g, partial x, that's just negative partial f, partial x. Gradient g, sorry, the y component, partial g, partial y is going to be negative f sub y." + }, + { + "text": "And, g sub z is just one." + }, + { + "text": "So now, if you take n over n dot k dx dy, well, it looks like that's going to be negative f sub x, negative f sub y, one divided by, well, what's n dot k?" + }, + { + "text": "If you do that with k, you'll get just one." + }, + { + "text": "So, I'm not going to write it, dx dy." + }, + { + "text": "See, that's, again, our favorite formula." + }, + { + "text": "So, this one is actually more general because you don't need to solve for z." + }, + { + "text": "But, if you can solve for z, then it's the same as before." + }, + { + "text": "OK, I think that's enough formulas for n dS." + }, + { + "text": "So, after spending a lot of time telling you how to compute surface integrals, now I'm going to try to tell you how to avoid computing them." + }, + { + "text": "And, that is called the divergence theorem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk18.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..0e5e56886a97cb7eb64b3c2de2f9c304bc0aed75 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And, we'll see the proof and everything and applications on Tuesday, but I want to at least state the theorem and see how it works in one example." + }, + { + "text": "It's also known as the Gauss grain theorem, or just the Gauss theorem depending on who you talk to." + }, + { + "text": "So, the grain here is the same grain as in Green's theorem, OK, because somehow that's a space version of Green's theorem." + }, + { + "text": "So, what does it say?" + }, + { + "text": "It says, so, this is the analog of grain for flux." + }, + { + "text": "What it says is if S is a closed surface, OK, so remember, it's the same as with Green's theorem, we need to have something that's completely enclosed." + }, + { + "text": "So, you have a surface, and there's somehow no gaps in it." + }, + { + "text": "There's no boundary to it." + }, + { + "text": "It's really completely enclosed." + }, + { + "text": "So, I'm choosing a region in space that I will call D. And, I need to choose my orientation." + }, + { + "text": "So, the orientation that will be chosen in this theorem is choosing the normal vector to point outwards." + }, + { + "text": "OK, so, n needs to be outwards." + }, + { + "text": "So, that's one part of the puzzle." + }, + { + "text": "The other part is a vector field." + }, + { + "text": "I need to have a vector field that is defined and differentiable everywhere in D. So, same restrictions as usual." + }, + { + "text": "Then, I don't have, actually, to compute the flux integral." + }, + { + "text": "The integral of F dot n dS of a closed surface S. I need to put a circle just to remind you it's got to be a closed surface." + }, + { + "text": "That's just notation to remind us, closed surface." + }, + { + "text": "I can replace that by the triple integral of the region inside of divergence of F dV." + }, + { + "text": "Now, I need to tell you what's the divergence of a 3D vector field." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk19.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..04bd556506c1a6a0e925cc2b3dd8ba3efad34e8f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, you'll see it's not much of a difference." + }, + { + "text": "In the 2D case, what you do is just, so, say that your vector field has components P, Q, and R. Then, you will take P sub x plus Q sub y plus R sub z. OK, so that's the definition." + }, + { + "text": "It's pretty easy to remember." + }, + { + "text": "You take the x component partial respect to x plus partial respect to y of the y component plus partial respect to z of the z component." + }, + { + "text": "OK, so, for example, last time we saw that the flux of the vector field zk for a sphere of radius a was four-thirds pi a cubed by computing the surface integral." + }, + { + "text": "Well, if we do it more efficiently now by Green's theorem, so we're going to use Green's theorem for this sphere." + }, + { + "text": "Because we're doing the whole sphere, it's fine." + }, + { + "text": "It's a closed surface." + }, + { + "text": "We couldn't do it for, say, a hemisphere or something like that." + }, + { + "text": "We need to, well, I mean, for the hemisphere, we'd need to add maybe the flat face at the bottom or something like that." + }, + { + "text": "So, Green's theorem says that our flux integral can be actually replaced by the triple integral of a solid ball of radius a of the divergence of zk dv." + }, + { + "text": "But now, what's the divergence of this field?" + }, + { + "text": "Well, so you have zero, zero, z." + }, + { + "text": "So, you get zero plus zero plus one." + }, + { + "text": "It looks like it will be one." + }, + { + "text": "So, if you do the triple integral of one dv, you will get just the volume of the region inside, which is four-thirds pi a cubed." + }, + { + "text": "And, so it was no accident." + }, + { + "text": "In fact, before that, we looked at also xi yj zk, and we found three times the volume." + }, + { + "text": "That's because the divergence of that field was actually three." + }, + { + "text": "So, very quickly, let me just say what this means physically." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk2.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..ff983a9074353a930a98538affafbeff51542106 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Here I have delta x, here I have delta y, and I am starting at some point xy." + }, + { + "text": "Now, above that I will have a parallelogram on my surface." + }, + { + "text": "I need to figure out this point here, the point where I start." + }, + { + "text": "I know what it is." + }, + { + "text": "It is just x, y, and z is f of x, y." + }, + { + "text": "Now, what I want to find actually is what are these two vectors, let's call them u and v that correspond to moving a bit in the x direction or in the y direction." + }, + { + "text": "And then u cross v will be, well, in terms of the magnitude of this guy will just be the little piece of surface area delta S. And, in terms of direction, it will be normal to the surface." + }, + { + "text": "Actually, I will get just delta S times my normal vector." + }, + { + "text": "Well, up to sign because depending on whether I do u cross v or v cross u, I might get the normal vector in the direction I want or in the direction I want." + }, + { + "text": "But we will take care of that later." + }, + { + "text": "Up to sign." + }, + { + "text": "OK, so let's find u and v. Actually, in case you have trouble with that small picture, then I have a better one here." + }, + { + "text": "Let's keep it just in case this one gets really too cluttered." + }, + { + "text": "It really represents the same thing." + }, + { + "text": "OK, so let's try to figure out these vectors u and v. So, the vector u starts at the point x, y, f of x, y." + }, + { + "text": "And it goes to, where is its head?" + }, + { + "text": "Well, I'll have moved x by delta x." + }, + { + "text": "So, x plus delta x. y doesn't change." + }, + { + "text": "And, of course, the z coordinate has to change." + }, + { + "text": "It becomes f of x plus delta x and y." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk20.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..f8f4327e9a02af262336ececd46d4897ee00c228 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk20.json @@ -0,0 +1,26 @@ +[ + { + "text": "Physically, see, this guy on the left is the total amount of stuff that goes out of the region per unit time." + }, + { + "text": "So, I want to figure out how much stuff comes out of there." + }, + { + "text": "What does the divergence mean?" + }, + { + "text": "The divergence means, well, it measures how much the flow is expanding things." + }, + { + "text": "It measures how much, I say probably when we understood 2D divergence, it measures the amount of sources or sinks that you have inside your fluid." + }, + { + "text": "So, now it becomes common sense." + }, + { + "text": "If you take a region of space, the total amount of water that flows out of it is the total amount of sources that you have in there minus the sinks." + }, + { + "text": "In spite of this common sense explanation, we are going to see actually how to prove this, and we'll see how it works and the hypothesis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk3.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..4dcc70fd37d899d05e9421b392306604a92d2817 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, how does f change if I change x a little bit?" + }, + { + "text": "Well, we've seen that it's given by the partial derivative f sub x." + }, + { + "text": "So, this is approximately equal to f of x, y plus delta x times f sub x at the given point x, y. I'm not going to add it because notation is already long enough." + }, + { + "text": "So, that means my vector u is, well, approximately, because I'm using this linear approximation, delta x, zero, and f sub x times delta x. OK, is that OK with everyone?" + }, + { + "text": "Good." + }, + { + "text": "Now, what about v?" + }, + { + "text": "Well, v works the same way." + }, + { + "text": "OK, so I'm not going to do all the details." + }, + { + "text": "When I move from here to here, well, x doesn't change, and y changes by delta y." + }, + { + "text": "So, x component, nothing happens." + }, + { + "text": "y component changes by delta y." + }, + { + "text": "What about the z component?" + }, + { + "text": "Well, f changes by f sub y times delta y." + }, + { + "text": "That's how f changes if I increase y by delta y. OK, so I have my two sides." + }, + { + "text": "Now, I can take the cross product." + }, + { + "text": "Well, maybe I will first, sorry, factor something out." + }, + { + "text": "See, I can rewrite this as one zero f sub x times delta x." + }, + { + "text": "And, this one I will rewrite as zero one f sub y delta y." + }, + { + "text": "And so, now the cross product, so n hat delta s up to sine is going to be u cross v. u cross v, well, so we'll have to do the cross product, and we'll have a delta x delta y coming out." + }, + { + "text": "OK, I'm just saving myself the trouble of writing a lot of delta x and delta y's." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk4.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..b0479e4d532bb2675791b9c29b5e2bff581132c7 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "But, if you prefer, you can just do directly this cross product there." + }, + { + "text": "OK, so let's compute this cross product." + }, + { + "text": "Well, the i component is zero minus f sub x." + }, + { + "text": "The y component is going to be, well, f sub y minus zero, but with a minus sign in front of everything, so negative f sub y." + }, + { + "text": "And, the z component will be just one times delta x delta y. OK, does that make sense for, yes, very good." + }, + { + "text": "And so, now, when we just take, we shrink this rectangle, we shrink delta x and delta y down, so that's how we get this formula for n ds equals negative fx negative fy one dx dy." + }, + { + "text": "Well, plus minus because it's up to us to choose whether we want to take the normal vector pointing up or down." + }, + { + "text": "So, see, if you take this convention, then the z component of n ds is positive." + }, + { + "text": "So, that corresponds to normal vector pointing up." + }, + { + "text": "If you take the opposite means, then the z component will be negative." + }, + { + "text": "That means your normal vector points down." + }, + { + "text": "OK, so this one is with n pointing up." + }, + { + "text": "I mean, when I say up, of course, it's still perpendicular to the surface." + }, + { + "text": "You know, if the surface really has a big slope, then it's not really going to go all that much up, but more up than down." + }, + { + "text": "OK, so that's how we get that formula." + }, + { + "text": "Any questions?" + }, + { + "text": "No?" + }, + { + "text": "OK, so that's a really useful formula." + }, + { + "text": "So, you don't really need to remember all the details of how we got it, but please remember that formula." + }, + { + "text": "Let's do an example, actually." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk5.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5b29a7df7e903bf04c8988e8f2436f298193a6d0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, let's say I want to find the flux of the vector field z times k. So, it's a vertical vector point of the paraboloid z equals x squared plus y squared that lives above the unit disk." + }, + { + "text": "OK, so what does that mean?" + }, + { + "text": "z equals x squared plus y squared, well, we've seen it many times." + }, + { + "text": "OK, it's this paraboloid above the unit disk means I only care about, I don't care about this infinite surface." + }, + { + "text": "I will actually stop when I hit a radius of one away from the z axis." + }, + { + "text": "And, so now I have my vector field, which is going to point overall up because, in fact, I'm at z times k. So, the more z is positive, the more your vector field goes up." + }, + { + "text": "Of course, if z were negative, then it would point down, but we live above." + }, + { + "text": "So, actually, a quick opinion poll." + }, + { + "text": "What do you think the flux should be?" + }, + { + "text": "Should it be positive, zero, negative?" + }, + { + "text": "We don't know." + }, + { + "text": "OK, so I see some I don't know." + }, + { + "text": "I see some negative, and I see some positive." + }, + { + "text": "So, of course, I didn't tell you which way I'm orienting my paraboloid." + }, + { + "text": "So, so far, both answers are correct." + }, + { + "text": "The only one that's probably not correct is zero because no matter which way you choose to orient it, you should get something." + }, + { + "text": "It's not looking like it will be zero." + }, + { + "text": "So, let's say that I'm going to do it with a normal pointing upwards." + }, + { + "text": "Second chance." + }, + { + "text": "OK, I see some people changing back and forth between one and two." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk6.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..7d51098b7f0239835af1dceb80b51f4a5d9a519e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, so let's draw a picture." + }, + { + "text": "Which one is pointing upwards?" + }, + { + "text": "Well, let's look at the bottom point, the normal vector pointing up." + }, + { + "text": "Here, we know what it means." + }, + { + "text": "It's this guy." + }, + { + "text": "And so, if you continue to follow your normal vector, see, they're actually pointing up and into the paraboloid." + }, + { + "text": "OK, and I claim that the answer should be positive because the vector field is crossing our paraboloid going upwards, going from the outside out and below to the inside and up side, so in the direction that we are counting positively." + }, + { + "text": "Well, we'll see how it turns out when we do the calculation." + }, + { + "text": "OK, so we have to compute the integral for flux." + }, + { + "text": "The one integral of a surface of F dot n dS is going to be, OK, so what are we going to do?" + }, + { + "text": "Well, F, we said, is 0, 0, z." + }, + { + "text": "What is n dS?" + }, + { + "text": "Well, let's use our brand new formula." + }, + { + "text": "So, it says negative F sub x, negative F sub y, one dx dy." + }, + { + "text": "What is little f in here?" + }, + { + "text": "It's x squared plus y squared, OK?" + }, + { + "text": "So, when we're using this formula, we need to know what little f stands for is whatever the formula is for z as a function of x and y." + }, + { + "text": "So, we take x squared plus y squared, and we take the partial derivatives with minus signs." + }, + { + "text": "We get negative 2x, negative 2y, and one dx dy." + }, + { + "text": "Well, of course, here it didn't really matter because we're going to dot them with zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk7.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..e3524a83e7e3f3457abdd39bd8eb8d13e8d49416 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, actually, even if we had made a mistake, we somehow wouldn't have had to pay the price, still." + }, + { + "text": "OK, so we'll end up with double integral on S of z dx dy." + }, + { + "text": "Now, what do we do with that?" + }, + { + "text": "Well, we have too many things." + }, + { + "text": "We need to get rid of z." + }, + { + "text": "So, let's use z equals x squared plus y squared once more." + }, + { + "text": "OK, so that becomes double integral of x squared plus y squared dx dy." + }, + { + "text": "And here, see, we're using the fact that we're only looking at things that are on the surface." + }, + { + "text": "It's not like in a triple integral, you could never do that because z, x, and y are independent." + }, + { + "text": "Here, they're related by the equation of a surface." + }, + { + "text": "Sorry if I sound like I'm ranting, but I know from experience this is where one of the most sticky and tricky points is, actually." + }, + { + "text": "OK, so now, how will we actually integrate that?" + }, + { + "text": "Well, now that we have just x and y, we should figure out what's the range for x and y?" + }, + { + "text": "Well, the range for x and y is going to be the shadow of our region." + }, + { + "text": "It's going to be this unit disk." + }, + { + "text": "OK, so let me just do that for now." + }, + { + "text": "And see here, this is finally where I've left the world of surface integrals to go back to a usual double integral." + }, + { + "text": "And now, I have to set it up." + }, + { + "text": "Well, I can do it this way with dx dy, but it looks like there's a smarter thing to do." + }, + { + "text": "OK, I'm going to use, actually, polar coordinates." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk8.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..4f11b1ba8efdf54e09dcbd2834634862a1b0e709 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, in fact, I'm going to say this is a double integral of r squared times r dr d theta." + }, + { + "text": "I'm on the unit disk, so r goes zero to one, theta goes zero to two pi." + }, + { + "text": "And, if you do the calculation, you'll find that this is going to be pi over two." + }, + { + "text": "OK, any questions about the example?" + }, + { + "text": "Yes?" + }, + { + "text": "OK, how do I get this negative 2x and negative 2y?" + }, + { + "text": "So, I want to use my formula for n ds." + }, + { + "text": "OK, my surface is given by the graph of a function." + }, + { + "text": "It's the graph of a function x squared plus y squared." + }, + { + "text": "So, I will use this formula that's up here." + }, + { + "text": "I will take the function x squared plus y squared, and I will take its partial derivatives." + }, + { + "text": "So, if I take the partial of f, so, f x squared plus y squared with respect to x, I get 2x." + }, + { + "text": "So, I put negative 2x, and then same thing, negative 2y, one dx dy, yes?" + }, + { + "text": "Which k hat?" + }, + { + "text": "Oh, you mean the vector field?" + }, + { + "text": "Well, so it's a different part of the story, OK?" + }, + { + "text": "So, whenever you do a surface integral for flux, you have two parts of the story." + }, + { + "text": "One is the vector field whose flux you're taking." + }, + { + "text": "The other one is the surface for which you will be taking flux." + }, + { + "text": "So, the vector field only comes as this f in the notation." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk9.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..9fa8c0e63e0fe3808781ed666ef10e0c042b38cb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_1_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And, everything else, the bounds of the double integral and the n ds, they all come from the surface that we are looking at." + }, + { + "text": "OK, so basically, in all of this calculation, this is coming from f equals zk." + }, + { + "text": "Everything else comes from the information paraboloid z equals x squared plus y squared above the disk." + }, + { + "text": "OK, so in particular, if we wanted to now find the flux of any other vector field for the same paraboloid, well, all we have to do is just replace this guy by whatever the new vector field is." + }, + { + "text": "We've learned how to set up flux integrals for this paraboloid." + }, + { + "text": "Not that you should remember this one by heart." + }, + { + "text": "I mean, there's many paraboloids in life and other surfaces, too, so it's better to remember the general method." + }, + { + "text": "OK, any other questions?" + }, + { + "text": "No?" + }, + { + "text": "OK, let's see more ways of tackling flux integrals." + }, + { + "text": "But, just to reassure you, at this point, we've seen the most important ones." + }, + { + "text": "You know, 90% of the problems that we'll be looking at, we can do with what we've seen so far last time and this time." + }, + { + "text": "But, let's look a little bit at a more general situation." + }, + { + "text": "Let's say that my surface is so complicated that I can't actually express z as a function of x and y." + }, + { + "text": "But, let's say that actually I know how to parametrize it." + }, + { + "text": "So, I have a parametric equation for my surface." + }, + { + "text": "That means I can express x, y, z in terms of any two parameter variables that might be relevant for me." + }, + { + "text": "So, if you want, this one here is the special case where you can parametrize things in terms of x and y as your two variables." + }, + { + "text": "So, how would you do it in the fully general case?" + }, + { + "text": "In a way, that will answer your question." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk0.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..de88ac001212dfb6b1de182c0b68e842d34b4657 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "Yesterday we have learned about flux and we have seen the first examples of how to set up and compute integrals for flux of a vector field for a surface." + }, + { + "text": "Remember the flux of a vector field F for a surface S is defined by taking the double integral on the surface of F dot n dS where n is the unit normal to the surface and dS is the area element on the surface." + }, + { + "text": "As we have seen, for various surfaces we have various formulas telling us what the normal vector is and what the area element becomes." + }, + { + "text": "For example, on spheres we typically integrate with respect to phi theta the latitude and longitude angles." + }, + { + "text": "On a horizontal plane we would just end up integrating dx dy and so on." + }, + { + "text": "At the end of the lecture we saw a formula." + }, + { + "text": "And a lot of you asked me how did we get it." + }, + { + "text": "Well, we didn't get it yet." + }, + { + "text": "We are going to try to explain where it comes from and why it works." + }, + { + "text": "The case we want to look at is the graph of a function." + }, + { + "text": "It is given by z equals some function in terms of x and y." + }, + { + "text": "Our surface is out here." + }, + { + "text": "z is a function of x and y." + }, + { + "text": "And x and y will range over some domain in the xy plane, namely the region that is the shadow of the surface on the xy plane." + }, + { + "text": "I said that we will have a formula for n ds which will end up being plus minus, minus f sub x minus f sub y one dx dy so that we will set up and evaluate the integral in terms of x and y." + }, + { + "text": "Replacing every time we see z we will replace it by f of xy, whatever the formula for f of xy is." + }, + { + "text": "By the way, if we look at a very easy case where this is just a horizontal plane, so z equals constant, the function is just a constant, well, the partial derivatives become just zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk1.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..83a60f55a64abf7ed3e632f2c0caa0700c633561 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "You get zero, zero, one dx dy." + }, + { + "text": "That is what you would expect for a horizontal plane just from common sense." + }, + { + "text": "This is more interesting, of course, if a function is more interesting." + }, + { + "text": "How do we get that?" + }, + { + "text": "Where does this come from?" + }, + { + "text": "We need to figure out for a small piece of our surface what will be n delta S if you want." + }, + { + "text": "Let's say that we take a small rectangle in here corresponding to the sides delta x and delta y." + }, + { + "text": "And we look at the piece of surface that is above that." + }, + { + "text": "Well, the question we have now is what is the area of this little piece of surface and what is its normal vector?" + }, + { + "text": "Observe this little piece up here." + }, + { + "text": "If it is small enough it will look like a parallelogram." + }, + { + "text": "It might be slightly curvy, but roughly it looks like a parallelogram in space." + }, + { + "text": "And so we have seen how to find the area of a parallelogram in space using cross product." + }, + { + "text": "If we can figure out what are the vectors for this side and that side, then taking the cross product will give us, and taking the magnitude of the cross product will give us the area." + }, + { + "text": "Moreover, the cross product also gives us the normal direction." + }, + { + "text": "In fact, the cross product gives us two in one." + }, + { + "text": "It gives us the normal direction and the area element." + }, + { + "text": "And that is why I said that we will have an easy formula for N dS while N and dS taken separately are more complicated because you would have to actually take the length of a direction of this guy." + }, + { + "text": "Let's carry out this problem." + }, + { + "text": "Let's say I am going to look at a small piece of the xy plane." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk10.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..80ecc53d0640b10ed2fa61964d985138e15dd4dc --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "I think one of you, I forgot, asked yesterday, how would I do it in general?" + }, + { + "text": "Is there a formula like m dx plus n dy?" + }, + { + "text": "Well, that's going to be the formula." + }, + { + "text": "And, you'll see it's a little bit too complicated." + }, + { + "text": "So, the really useful ones are actually the special ones." + }, + { + "text": "So, let's say that we are given a parametric description of a surface S. So, that means we can describe S by formulas saying x is some function of two parameter variables." + }, + { + "text": "I'm going to call them u and v. I hope you don't mind." + }, + { + "text": "You can call them t1 and t2." + }, + { + "text": "You can call them whatever you want." + }, + { + "text": "OK, so one of the basic properties of a surface is because I have only two independent directions to move on, I should be able to express x, y, and z in terms of two variables." + }, + { + "text": "So, now let's say that I know how to do that." + }, + { + "text": "Or, maybe I should instead think of it in terms of a position vector if that helps you." + }, + { + "text": "The position vector, so that's just the vector with components x, y, z is given as a function of u and v. OK, so it works like a parametric curve, but with two parameters." + }, + { + "text": "So, now, how will we actually set up a flux integral on such a surface?" + }, + { + "text": "Well, because we are locating the flux in terms of u and v, we will end up with an integral du dv." + }, + { + "text": "So, we need to figure out how to express n ds in terms of du and dv." + }, + { + "text": "OK, so n ds should be something du dv." + }, + { + "text": "How do we do that?" + }, + { + "text": "Well, we can use the same method that we've actually used over here." + }, + { + "text": "Because if you think for a second, here we used, of course, a rectangle in the x, y plane, and we lifted it to a parallelogram and so on." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk11.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..61d1728a009aa03829fde534d602caecd77a30aa --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "But, more generally, you can think, what happens if I change u by delta u, keeping v constant, or the other way around?" + }, + { + "text": "You will get some sort of mesh grid on your surface, and you will look at a little parallelogram that's an elementary piece of that mesh and figure out what is its area and normal vector." + }, + { + "text": "Well, that will again be given by the cross product of the two sides." + }, + { + "text": "OK, so let's think a little bit about what happens when I move a little bit on my surface." + }, + { + "text": "So, I'm taking a grid on my surface given by the u and v directions." + }, + { + "text": "And, if I take a piece of that corresponding to small changes, delta u and delta v, what's going to be going on here?" + }, + { + "text": "Well, I have to deal with two vectors, one corresponding to changing u, the other one corresponding to changing v. If I change u, how does my point change?" + }, + { + "text": "Well, that's given by the derivative of this with respect to u. OK, so this vector here I will call, so the sides are given by, let me say, partial r over partial u times delta u." + }, + { + "text": "And, if you prefer, maybe I should write it as partial x over partial u delta u partial y." + }, + { + "text": "Well, it's just too boring to write, and so on." + }, + { + "text": "OK, it means just, you know, if I change u a little bit, keep v constant, then how x changes is given by partial x over partial u times delta u." + }, + { + "text": "Same thing with y, same thing with z." + }, + { + "text": "And, I'm just using vector notation to do it this way." + }, + { + "text": "That's the analog of when I said delta r for line integrals along a curve, vector delta r is the velocity vector dr over dt times delta t. OK, now if I look at the other side, OK, so, sorry, so let me start again." + }, + { + "text": "I ran out of space." + }, + { + "text": "One side is partial r partial u times delta u, and the other one would be partial r partial v times delta v because that's how the position of your point changes if you just change u or v and not the other one." + }, + { + "text": "So, now, to find the surface element together with a normal vector, I would just take the cross product between these guys." + }, + { + "text": "So, if you prefer, that's the cross product of partial r partial u with partial r partial v delta u delta v. And so, N dS is this cross product times du dv up to sine." + }, + { + "text": "I mean, also here." + }, + { + "text": "Depends on which choice I make for my normal vector, of course." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk12.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..4edd218fc4799dfc682e96577ad40cb5df2f17ab --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, now, if you, that, of course, is a slightly confusing equation to think of." + }, + { + "text": "So, a good exercise, if you want to really understand what's going on, try this in two good examples to look at." + }, + { + "text": "One good example to look at is the previous one." + }, + { + "text": "What is it?" + }, + { + "text": "It's when u and v are just x and y. OK, so the parametric equations are just x equals x, y equals y, and z is f of x, y." + }, + { + "text": "You should end up with the same formula that we had over there." + }, + { + "text": "And, you should see why because, see, both of them are given by a cross product." + }, + { + "text": "The other case you can look at, just to convince yourselves that it's true, so we don't need to do that because we've seen the formula before." + }, + { + "text": "But, in the case of a sphere, we've seen the formula for N and for dS separately." + }, + { + "text": "So, we know what N dS are in terms of d phi d theta." + }, + { + "text": "Well, you could parametrize a sphere in terms of phi and theta." + }, + { + "text": "Namely, the formulas would be x equals a sine phi cosine theta, y equals a sine phi sine theta, z equals a cosine phi." + }, + { + "text": "The formulas for spherical coordinates setting rho equals a." + }, + { + "text": "So, that's a parametric equation for the sphere." + }, + { + "text": "And then, if you try to use this formula here, you should end up with the same things we've already seen for N dS, just with a lot more pain to actually get there because your cross product is going to be a bit complicated." + }, + { + "text": "But, we're seeing all of these formulas, they all fit together." + }, + { + "text": "Somehow, it's always the same question, just we have different angles of attack on this general problem." + }, + { + "text": "OK, questions?" + }, + { + "text": "No?" + }, + { + "text": "OK, let's look at yet another last way of finding N dS." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk13.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..11d368b6015bc6b9cacbc394c8b399183b51e276 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then, I promise we'll switch to something else because I can feel that you're getting a bit overwhelmed by all these formulas for N dS." + }, + { + "text": "So, OK, so what happens very often is we don't actually know how to parametrize our surface." + }, + { + "text": "Maybe we don't know how to solve for z as a function of x and y, but our surface is given by some equation." + }, + { + "text": "And so, what that means is actually maybe what we know is not really these kinds of formulas, but maybe we know a normal vector." + }, + { + "text": "And, I'm going to call this one capital N because I don't even need it to be a unit vector, you will see." + }, + { + "text": "It can be a normal vector of the surface S. So, why would we ever know a normal vector?" + }, + { + "text": "Well, for example, if our surface is a plane, say it's a slanted plane given by some equation, Ax plus By plus Cz equals D. Well, you know the normal vector." + }, + { + "text": "It's A, B, C. Of course, you could solve for z and then go back to that case, which is why I said that that one is really useful." + }, + { + "text": "But, you can also just stay with a normal vector." + }, + { + "text": "Why else would you know a normal vector?" + }, + { + "text": "Well, let's say that you know an equation that's of a form g of x, y, z equals zero." + }, + { + "text": "Well, then you know that the gradient of g is perpendicular to the level surface." + }, + { + "text": "OK, so let me just give you two examples." + }, + { + "text": "If you have a plane, Ax plus By plus Cz equals D, then the normal vector would just be A, B, C. If you have a surface S given by an equation, g of x, y, z equals zero, then you can take the normal vector to be the gradient of g. We've seen that the gradient is perpendicular to the level surface." + }, + { + "text": "Now, of course, we don't necessarily have to follow what's going to come because if we could solve for z then we might be better off doing what we did over there." + }, + { + "text": "But, let's say that we want to do it this way." + }, + { + "text": "So, then what can we do?" + }, + { + "text": "Well, I'm going to give you a little bit of information about NDS." + }, + { + "text": "So, OK, so let's start by thinking about a slanted plane." + }, + { + "text": "OK, so let's say that my surface is just a slanted plane." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk14.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..8f6af2d2aa3b3d17432ec3b26b0606675c6a7d16 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, my normal vector would be maybe somewhere here." + }, + { + "text": "And, let's say that I'm going to try, you know, I need, of course, some handle on how to set up my integral." + }, + { + "text": "So, maybe I'm going to express this in terms of x and y. OK, so I have my coordinates, and I'll try to use x and y." + }, + { + "text": "So, then I would like to relate delta s, ds, to the area in the xy plane." + }, + { + "text": "So, that means, you know, I want maybe to look at the projection of this guy onto a horizontal plane." + }, + { + "text": "Let's squish it horizontally." + }, + { + "text": "So, then you have here another area." + }, + { + "text": "OK, so the guy on the slanted plane, let's call that delta s, and let's call this guy down here delta a." + }, + { + "text": "So, the question, and, you know, delta a would become ultimately maybe delta x, delta y, or something like that." + }, + { + "text": "The question is, how do we find the conversion rate between these two areas?" + }, + { + "text": "See, I mean, they're not the same." + }, + { + "text": "Visually, I hope it's clear to you that if my plane is actually horizontal, then, of course, they're the same." + }, + { + "text": "But, the more slanted it becomes, the more delta a becomes smaller than delta s, right?" + }, + { + "text": "I mean, if you buy, you know, if you buy land, and it's on the side of a cliff, well, whether you look at it on a map, or whether you look at it on the actual cliff, the area is going to be very different." + }, + { + "text": "I'm not sure if that's a wise thing to do if you want to build a house there, but I've been told you can get really cheap land." + }, + { + "text": "OK, so anyway, OK, so delta s versus delta a depends on how slanted things are." + }, + { + "text": "And, let's try to make that more precise by looking at the angle that our plane makes with the horizontal direction." + }, + { + "text": "OK, so let's call this angle alpha, the angle that our plane makes with the horizontal direction." + }, + { + "text": "See, it's all coming together now." + }, + { + "text": "The first unit about cross products, normal vectors, and so on is actually useful now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk15.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..e90009e6248e5d6a50885b9d3130bf4050ef960c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, I claim that the surface element is related to the area in the plane by delta a equals delta s times the cosine of alpha." + }, + { + "text": "Why is that?" + }, + { + "text": "Well, let's look at this small rectangle with one horizontal side and one slanted side." + }, + { + "text": "Well, when you project, this side doesn't change." + }, + { + "text": "But, this side gets shortened by a factor of cosine alpha." + }, + { + "text": "Whatever this length was, this length here is that one times cosine alpha." + }, + { + "text": "So, that's why the area gets shrunk by cosine alpha." + }, + { + "text": "In one direction, nothing happens." + }, + { + "text": "In the other direction, you squish by cosine alpha." + }, + { + "text": "So, what that means is that, well, OK, so we'll have to deal with this." + }, + { + "text": "And, of course, the one we'll care about actually is delta s expressed in terms of delta a." + }, + { + "text": "But, what are we going to do with this cosine?" + }, + { + "text": "It's not very convenient to have a cosine left in here." + }, + { + "text": "So, remember, the angle between two planes, it's the same thing as the angle between the normal vectors." + }, + { + "text": "So, if you want to see this angle alpha elsewhere, what you can do is you can just take the vertical direction." + }, + { + "text": "Let's take k. Then, here we have our angle alpha again." + }, + { + "text": "So, in particular, cosine of alpha, I can get, well, we know how to find the angle between two vectors." + }, + { + "text": "So, if we have our normal vector n, we'll do n dot k, and we'll divide by length n length k. Well, length k is one." + }, + { + "text": "That's one easy." + }, + { + "text": "OK, so that's how we find the angle." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk16.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..18b8ca6f0e10e19b75db0dabf1ec37a110a6c671 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, now I'm going to say, well, delta s is going to be one over cosine alpha delta a." + }, + { + "text": "And, I can rewrite that as length of n divided by n dot k times delta a." + }, + { + "text": "Now, let's multiply that by the unit normal vector because what I'm multiplying by is not dS, but actually n dS." + }, + { + "text": "So, n delta s will be, I'm just going to multiply by n. Well, let's think for a second." + }, + { + "text": "What happens if I take the unit normal n, and I multiply it by the length of my other normal big N?" + }, + { + "text": "Well, I get big N again, right?" + }, + { + "text": "This is a normal vector of the same length as n, well, up to sine." + }, + { + "text": "But, actually, maybe I should." + }, + { + "text": "The only thing I don't know is whether this guy will be going in the same direction as big N or in the opposite direction." + }, + { + "text": "Say that, for example, my capital N has length, I don't know, length three, for example." + }, + { + "text": "The unit normal vector might be this guy, in which case, indeed, three times little n will be big N. Or, it might be this one, in which case, three times little n will be negative big N. But, up to sine, it's N. And then, I will have N over n dot k delta a." + }, + { + "text": "And so, the final formula, the one that actually we care about in case you don't really like my explanations of how we get there, is that N dS is plus or minus N over N dot k dx dy." + }, + { + "text": "That one is actually kind of useful, so let's box it." + }, + { + "text": "Now, just in case you are wondering, of course, if you didn't want to project to x, y, you would have maybe preferred to project to, say, the plane of a blackboard, yz." + }, + { + "text": "Well, you can do the same thing." + }, + { + "text": "To express N dS in terms of dy dz, you do the same argument." + }, + { + "text": "And simply, the only thing that changes is instead of using the vertical vector k, you use the normal vector i." + }, + { + "text": "So, you would be doing N over N dot i dy dz, and same thing." + }, + { + "text": "Just keep an open mind that this also works with other variables." + }, + { + "text": "But anyway, so that's how you can basically project the vector surface area element onto the x, y plane in a way." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk17.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..09fc575d766fb25a1c29c876fc0a0b29520a15d8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, so let's look at the special case just to see how this fits with stuff we've seen before." + }, + { + "text": "Let's do a special example where our surface is given by the equation z minus f of x, y equals zero." + }, + { + "text": "OK, that's a strange way to write the equation z equals f of x, y that we saw before." + }, + { + "text": "But now, it looks like, well, some function of x, y, z equals zero." + }, + { + "text": "So, let's try to use this new method." + }, + { + "text": "So, let's call this guy g of x, y, z." + }, + { + "text": "Well, so now let's look at the normal vector." + }, + { + "text": "The normal vector would be the gradient of g, we said." + }, + { + "text": "What's the gradient of this function?" + }, + { + "text": "So, gradient of g, well, partial g, partial x, that's just negative partial f, partial x. Gradient g, sorry, the y component, partial g, partial y is going to be negative f sub y." + }, + { + "text": "And, g sub z is just one." + }, + { + "text": "So now, if you take n over n dot k dx dy, well, it looks like that's going to be negative f sub x, negative f sub y, one divided by, well, what's n dot k?" + }, + { + "text": "If you do that with k, you'll get just one." + }, + { + "text": "So, I'm not going to write it, dx dy." + }, + { + "text": "See, that's, again, our favorite formula." + }, + { + "text": "So, this one is actually more general because you don't need to solve for z." + }, + { + "text": "But, if you can solve for z, then it's the same as before." + }, + { + "text": "OK, I think that's enough formulas for n dS." + }, + { + "text": "So, after spending a lot of time telling you how to compute surface integrals, now I'm going to try to tell you how to avoid computing them." + }, + { + "text": "And, that is called the divergence theorem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk18.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..0e5e56886a97cb7eb64b3c2de2f9c304bc0aed75 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And, we'll see the proof and everything and applications on Tuesday, but I want to at least state the theorem and see how it works in one example." + }, + { + "text": "It's also known as the Gauss grain theorem, or just the Gauss theorem depending on who you talk to." + }, + { + "text": "So, the grain here is the same grain as in Green's theorem, OK, because somehow that's a space version of Green's theorem." + }, + { + "text": "So, what does it say?" + }, + { + "text": "It says, so, this is the analog of grain for flux." + }, + { + "text": "What it says is if S is a closed surface, OK, so remember, it's the same as with Green's theorem, we need to have something that's completely enclosed." + }, + { + "text": "So, you have a surface, and there's somehow no gaps in it." + }, + { + "text": "There's no boundary to it." + }, + { + "text": "It's really completely enclosed." + }, + { + "text": "So, I'm choosing a region in space that I will call D. And, I need to choose my orientation." + }, + { + "text": "So, the orientation that will be chosen in this theorem is choosing the normal vector to point outwards." + }, + { + "text": "OK, so, n needs to be outwards." + }, + { + "text": "So, that's one part of the puzzle." + }, + { + "text": "The other part is a vector field." + }, + { + "text": "I need to have a vector field that is defined and differentiable everywhere in D. So, same restrictions as usual." + }, + { + "text": "Then, I don't have, actually, to compute the flux integral." + }, + { + "text": "The integral of F dot n dS of a closed surface S. I need to put a circle just to remind you it's got to be a closed surface." + }, + { + "text": "That's just notation to remind us, closed surface." + }, + { + "text": "I can replace that by the triple integral of the region inside of divergence of F dV." + }, + { + "text": "Now, I need to tell you what's the divergence of a 3D vector field." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk19.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..04bd556506c1a6a0e925cc2b3dd8ba3efad34e8f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, you'll see it's not much of a difference." + }, + { + "text": "In the 2D case, what you do is just, so, say that your vector field has components P, Q, and R. Then, you will take P sub x plus Q sub y plus R sub z. OK, so that's the definition." + }, + { + "text": "It's pretty easy to remember." + }, + { + "text": "You take the x component partial respect to x plus partial respect to y of the y component plus partial respect to z of the z component." + }, + { + "text": "OK, so, for example, last time we saw that the flux of the vector field zk for a sphere of radius a was four-thirds pi a cubed by computing the surface integral." + }, + { + "text": "Well, if we do it more efficiently now by Green's theorem, so we're going to use Green's theorem for this sphere." + }, + { + "text": "Because we're doing the whole sphere, it's fine." + }, + { + "text": "It's a closed surface." + }, + { + "text": "We couldn't do it for, say, a hemisphere or something like that." + }, + { + "text": "We need to, well, I mean, for the hemisphere, we'd need to add maybe the flat face at the bottom or something like that." + }, + { + "text": "So, Green's theorem says that our flux integral can be actually replaced by the triple integral of a solid ball of radius a of the divergence of zk dv." + }, + { + "text": "But now, what's the divergence of this field?" + }, + { + "text": "Well, so you have zero, zero, z." + }, + { + "text": "So, you get zero plus zero plus one." + }, + { + "text": "It looks like it will be one." + }, + { + "text": "So, if you do the triple integral of one dv, you will get just the volume of the region inside, which is four-thirds pi a cubed." + }, + { + "text": "And, so it was no accident." + }, + { + "text": "In fact, before that, we looked at also xi yj zk, and we found three times the volume." + }, + { + "text": "That's because the divergence of that field was actually three." + }, + { + "text": "So, very quickly, let me just say what this means physically." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk2.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..ff983a9074353a930a98538affafbeff51542106 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Here I have delta x, here I have delta y, and I am starting at some point xy." + }, + { + "text": "Now, above that I will have a parallelogram on my surface." + }, + { + "text": "I need to figure out this point here, the point where I start." + }, + { + "text": "I know what it is." + }, + { + "text": "It is just x, y, and z is f of x, y." + }, + { + "text": "Now, what I want to find actually is what are these two vectors, let's call them u and v that correspond to moving a bit in the x direction or in the y direction." + }, + { + "text": "And then u cross v will be, well, in terms of the magnitude of this guy will just be the little piece of surface area delta S. And, in terms of direction, it will be normal to the surface." + }, + { + "text": "Actually, I will get just delta S times my normal vector." + }, + { + "text": "Well, up to sign because depending on whether I do u cross v or v cross u, I might get the normal vector in the direction I want or in the direction I want." + }, + { + "text": "But we will take care of that later." + }, + { + "text": "Up to sign." + }, + { + "text": "OK, so let's find u and v. Actually, in case you have trouble with that small picture, then I have a better one here." + }, + { + "text": "Let's keep it just in case this one gets really too cluttered." + }, + { + "text": "It really represents the same thing." + }, + { + "text": "OK, so let's try to figure out these vectors u and v. So, the vector u starts at the point x, y, f of x, y." + }, + { + "text": "And it goes to, where is its head?" + }, + { + "text": "Well, I'll have moved x by delta x." + }, + { + "text": "So, x plus delta x. y doesn't change." + }, + { + "text": "And, of course, the z coordinate has to change." + }, + { + "text": "It becomes f of x plus delta x and y." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk20.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..f8f4327e9a02af262336ececd46d4897ee00c228 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk20.json @@ -0,0 +1,26 @@ +[ + { + "text": "Physically, see, this guy on the left is the total amount of stuff that goes out of the region per unit time." + }, + { + "text": "So, I want to figure out how much stuff comes out of there." + }, + { + "text": "What does the divergence mean?" + }, + { + "text": "The divergence means, well, it measures how much the flow is expanding things." + }, + { + "text": "It measures how much, I say probably when we understood 2D divergence, it measures the amount of sources or sinks that you have inside your fluid." + }, + { + "text": "So, now it becomes common sense." + }, + { + "text": "If you take a region of space, the total amount of water that flows out of it is the total amount of sources that you have in there minus the sinks." + }, + { + "text": "In spite of this common sense explanation, we are going to see actually how to prove this, and we'll see how it works and the hypothesis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk3.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..4dcc70fd37d899d05e9421b392306604a92d2817 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, how does f change if I change x a little bit?" + }, + { + "text": "Well, we've seen that it's given by the partial derivative f sub x." + }, + { + "text": "So, this is approximately equal to f of x, y plus delta x times f sub x at the given point x, y. I'm not going to add it because notation is already long enough." + }, + { + "text": "So, that means my vector u is, well, approximately, because I'm using this linear approximation, delta x, zero, and f sub x times delta x. OK, is that OK with everyone?" + }, + { + "text": "Good." + }, + { + "text": "Now, what about v?" + }, + { + "text": "Well, v works the same way." + }, + { + "text": "OK, so I'm not going to do all the details." + }, + { + "text": "When I move from here to here, well, x doesn't change, and y changes by delta y." + }, + { + "text": "So, x component, nothing happens." + }, + { + "text": "y component changes by delta y." + }, + { + "text": "What about the z component?" + }, + { + "text": "Well, f changes by f sub y times delta y." + }, + { + "text": "That's how f changes if I increase y by delta y. OK, so I have my two sides." + }, + { + "text": "Now, I can take the cross product." + }, + { + "text": "Well, maybe I will first, sorry, factor something out." + }, + { + "text": "See, I can rewrite this as one zero f sub x times delta x." + }, + { + "text": "And, this one I will rewrite as zero one f sub y delta y." + }, + { + "text": "And so, now the cross product, so n hat delta s up to sine is going to be u cross v. u cross v, well, so we'll have to do the cross product, and we'll have a delta x delta y coming out." + }, + { + "text": "OK, I'm just saving myself the trouble of writing a lot of delta x and delta y's." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk4.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..b0479e4d532bb2675791b9c29b5e2bff581132c7 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "But, if you prefer, you can just do directly this cross product there." + }, + { + "text": "OK, so let's compute this cross product." + }, + { + "text": "Well, the i component is zero minus f sub x." + }, + { + "text": "The y component is going to be, well, f sub y minus zero, but with a minus sign in front of everything, so negative f sub y." + }, + { + "text": "And, the z component will be just one times delta x delta y. OK, does that make sense for, yes, very good." + }, + { + "text": "And so, now, when we just take, we shrink this rectangle, we shrink delta x and delta y down, so that's how we get this formula for n ds equals negative fx negative fy one dx dy." + }, + { + "text": "Well, plus minus because it's up to us to choose whether we want to take the normal vector pointing up or down." + }, + { + "text": "So, see, if you take this convention, then the z component of n ds is positive." + }, + { + "text": "So, that corresponds to normal vector pointing up." + }, + { + "text": "If you take the opposite means, then the z component will be negative." + }, + { + "text": "That means your normal vector points down." + }, + { + "text": "OK, so this one is with n pointing up." + }, + { + "text": "I mean, when I say up, of course, it's still perpendicular to the surface." + }, + { + "text": "You know, if the surface really has a big slope, then it's not really going to go all that much up, but more up than down." + }, + { + "text": "OK, so that's how we get that formula." + }, + { + "text": "Any questions?" + }, + { + "text": "No?" + }, + { + "text": "OK, so that's a really useful formula." + }, + { + "text": "So, you don't really need to remember all the details of how we got it, but please remember that formula." + }, + { + "text": "Let's do an example, actually." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk5.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5b29a7df7e903bf04c8988e8f2436f298193a6d0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, let's say I want to find the flux of the vector field z times k. So, it's a vertical vector point of the paraboloid z equals x squared plus y squared that lives above the unit disk." + }, + { + "text": "OK, so what does that mean?" + }, + { + "text": "z equals x squared plus y squared, well, we've seen it many times." + }, + { + "text": "OK, it's this paraboloid above the unit disk means I only care about, I don't care about this infinite surface." + }, + { + "text": "I will actually stop when I hit a radius of one away from the z axis." + }, + { + "text": "And, so now I have my vector field, which is going to point overall up because, in fact, I'm at z times k. So, the more z is positive, the more your vector field goes up." + }, + { + "text": "Of course, if z were negative, then it would point down, but we live above." + }, + { + "text": "So, actually, a quick opinion poll." + }, + { + "text": "What do you think the flux should be?" + }, + { + "text": "Should it be positive, zero, negative?" + }, + { + "text": "We don't know." + }, + { + "text": "OK, so I see some I don't know." + }, + { + "text": "I see some negative, and I see some positive." + }, + { + "text": "So, of course, I didn't tell you which way I'm orienting my paraboloid." + }, + { + "text": "So, so far, both answers are correct." + }, + { + "text": "The only one that's probably not correct is zero because no matter which way you choose to orient it, you should get something." + }, + { + "text": "It's not looking like it will be zero." + }, + { + "text": "So, let's say that I'm going to do it with a normal pointing upwards." + }, + { + "text": "Second chance." + }, + { + "text": "OK, I see some people changing back and forth between one and two." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk6.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..7d51098b7f0239835af1dceb80b51f4a5d9a519e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, so let's draw a picture." + }, + { + "text": "Which one is pointing upwards?" + }, + { + "text": "Well, let's look at the bottom point, the normal vector pointing up." + }, + { + "text": "Here, we know what it means." + }, + { + "text": "It's this guy." + }, + { + "text": "And so, if you continue to follow your normal vector, see, they're actually pointing up and into the paraboloid." + }, + { + "text": "OK, and I claim that the answer should be positive because the vector field is crossing our paraboloid going upwards, going from the outside out and below to the inside and up side, so in the direction that we are counting positively." + }, + { + "text": "Well, we'll see how it turns out when we do the calculation." + }, + { + "text": "OK, so we have to compute the integral for flux." + }, + { + "text": "The one integral of a surface of F dot n dS is going to be, OK, so what are we going to do?" + }, + { + "text": "Well, F, we said, is 0, 0, z." + }, + { + "text": "What is n dS?" + }, + { + "text": "Well, let's use our brand new formula." + }, + { + "text": "So, it says negative F sub x, negative F sub y, one dx dy." + }, + { + "text": "What is little f in here?" + }, + { + "text": "It's x squared plus y squared, OK?" + }, + { + "text": "So, when we're using this formula, we need to know what little f stands for is whatever the formula is for z as a function of x and y." + }, + { + "text": "So, we take x squared plus y squared, and we take the partial derivatives with minus signs." + }, + { + "text": "We get negative 2x, negative 2y, and one dx dy." + }, + { + "text": "Well, of course, here it didn't really matter because we're going to dot them with zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk7.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..e3524a83e7e3f3457abdd39bd8eb8d13e8d49416 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, actually, even if we had made a mistake, we somehow wouldn't have had to pay the price, still." + }, + { + "text": "OK, so we'll end up with double integral on S of z dx dy." + }, + { + "text": "Now, what do we do with that?" + }, + { + "text": "Well, we have too many things." + }, + { + "text": "We need to get rid of z." + }, + { + "text": "So, let's use z equals x squared plus y squared once more." + }, + { + "text": "OK, so that becomes double integral of x squared plus y squared dx dy." + }, + { + "text": "And here, see, we're using the fact that we're only looking at things that are on the surface." + }, + { + "text": "It's not like in a triple integral, you could never do that because z, x, and y are independent." + }, + { + "text": "Here, they're related by the equation of a surface." + }, + { + "text": "Sorry if I sound like I'm ranting, but I know from experience this is where one of the most sticky and tricky points is, actually." + }, + { + "text": "OK, so now, how will we actually integrate that?" + }, + { + "text": "Well, now that we have just x and y, we should figure out what's the range for x and y?" + }, + { + "text": "Well, the range for x and y is going to be the shadow of our region." + }, + { + "text": "It's going to be this unit disk." + }, + { + "text": "OK, so let me just do that for now." + }, + { + "text": "And see here, this is finally where I've left the world of surface integrals to go back to a usual double integral." + }, + { + "text": "And now, I have to set it up." + }, + { + "text": "Well, I can do it this way with dx dy, but it looks like there's a smarter thing to do." + }, + { + "text": "OK, I'm going to use, actually, polar coordinates." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk8.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..4f11b1ba8efdf54e09dcbd2834634862a1b0e709 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, in fact, I'm going to say this is a double integral of r squared times r dr d theta." + }, + { + "text": "I'm on the unit disk, so r goes zero to one, theta goes zero to two pi." + }, + { + "text": "And, if you do the calculation, you'll find that this is going to be pi over two." + }, + { + "text": "OK, any questions about the example?" + }, + { + "text": "Yes?" + }, + { + "text": "OK, how do I get this negative 2x and negative 2y?" + }, + { + "text": "So, I want to use my formula for n ds." + }, + { + "text": "OK, my surface is given by the graph of a function." + }, + { + "text": "It's the graph of a function x squared plus y squared." + }, + { + "text": "So, I will use this formula that's up here." + }, + { + "text": "I will take the function x squared plus y squared, and I will take its partial derivatives." + }, + { + "text": "So, if I take the partial of f, so, f x squared plus y squared with respect to x, I get 2x." + }, + { + "text": "So, I put negative 2x, and then same thing, negative 2y, one dx dy, yes?" + }, + { + "text": "Which k hat?" + }, + { + "text": "Oh, you mean the vector field?" + }, + { + "text": "Well, so it's a different part of the story, OK?" + }, + { + "text": "So, whenever you do a surface integral for flux, you have two parts of the story." + }, + { + "text": "One is the vector field whose flux you're taking." + }, + { + "text": "The other one is the surface for which you will be taking flux." + }, + { + "text": "So, the vector field only comes as this f in the notation." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk9.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..9fa8c0e63e0fe3808781ed666ef10e0c042b38cb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_3_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And, everything else, the bounds of the double integral and the n ds, they all come from the surface that we are looking at." + }, + { + "text": "OK, so basically, in all of this calculation, this is coming from f equals zk." + }, + { + "text": "Everything else comes from the information paraboloid z equals x squared plus y squared above the disk." + }, + { + "text": "OK, so in particular, if we wanted to now find the flux of any other vector field for the same paraboloid, well, all we have to do is just replace this guy by whatever the new vector field is." + }, + { + "text": "We've learned how to set up flux integrals for this paraboloid." + }, + { + "text": "Not that you should remember this one by heart." + }, + { + "text": "I mean, there's many paraboloids in life and other surfaces, too, so it's better to remember the general method." + }, + { + "text": "OK, any other questions?" + }, + { + "text": "No?" + }, + { + "text": "OK, let's see more ways of tackling flux integrals." + }, + { + "text": "But, just to reassure you, at this point, we've seen the most important ones." + }, + { + "text": "You know, 90% of the problems that we'll be looking at, we can do with what we've seen so far last time and this time." + }, + { + "text": "But, let's look a little bit at a more general situation." + }, + { + "text": "Let's say that my surface is so complicated that I can't actually express z as a function of x and y." + }, + { + "text": "But, let's say that actually I know how to parametrize it." + }, + { + "text": "So, I have a parametric equation for my surface." + }, + { + "text": "That means I can express x, y, z in terms of any two parameter variables that might be relevant for me." + }, + { + "text": "So, if you want, this one here is the special case where you can parametrize things in terms of x and y as your two variables." + }, + { + "text": "So, how would you do it in the fully general case?" + }, + { + "text": "In a way, that will answer your question." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk0.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..de88ac001212dfb6b1de182c0b68e842d34b4657 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "Yesterday we have learned about flux and we have seen the first examples of how to set up and compute integrals for flux of a vector field for a surface." + }, + { + "text": "Remember the flux of a vector field F for a surface S is defined by taking the double integral on the surface of F dot n dS where n is the unit normal to the surface and dS is the area element on the surface." + }, + { + "text": "As we have seen, for various surfaces we have various formulas telling us what the normal vector is and what the area element becomes." + }, + { + "text": "For example, on spheres we typically integrate with respect to phi theta the latitude and longitude angles." + }, + { + "text": "On a horizontal plane we would just end up integrating dx dy and so on." + }, + { + "text": "At the end of the lecture we saw a formula." + }, + { + "text": "And a lot of you asked me how did we get it." + }, + { + "text": "Well, we didn't get it yet." + }, + { + "text": "We are going to try to explain where it comes from and why it works." + }, + { + "text": "The case we want to look at is the graph of a function." + }, + { + "text": "It is given by z equals some function in terms of x and y." + }, + { + "text": "Our surface is out here." + }, + { + "text": "z is a function of x and y." + }, + { + "text": "And x and y will range over some domain in the xy plane, namely the region that is the shadow of the surface on the xy plane." + }, + { + "text": "I said that we will have a formula for n ds which will end up being plus minus, minus f sub x minus f sub y one dx dy so that we will set up and evaluate the integral in terms of x and y." + }, + { + "text": "Replacing every time we see z we will replace it by f of xy, whatever the formula for f of xy is." + }, + { + "text": "By the way, if we look at a very easy case where this is just a horizontal plane, so z equals constant, the function is just a constant, well, the partial derivatives become just zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk1.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..83a60f55a64abf7ed3e632f2c0caa0700c633561 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "You get zero, zero, one dx dy." + }, + { + "text": "That is what you would expect for a horizontal plane just from common sense." + }, + { + "text": "This is more interesting, of course, if a function is more interesting." + }, + { + "text": "How do we get that?" + }, + { + "text": "Where does this come from?" + }, + { + "text": "We need to figure out for a small piece of our surface what will be n delta S if you want." + }, + { + "text": "Let's say that we take a small rectangle in here corresponding to the sides delta x and delta y." + }, + { + "text": "And we look at the piece of surface that is above that." + }, + { + "text": "Well, the question we have now is what is the area of this little piece of surface and what is its normal vector?" + }, + { + "text": "Observe this little piece up here." + }, + { + "text": "If it is small enough it will look like a parallelogram." + }, + { + "text": "It might be slightly curvy, but roughly it looks like a parallelogram in space." + }, + { + "text": "And so we have seen how to find the area of a parallelogram in space using cross product." + }, + { + "text": "If we can figure out what are the vectors for this side and that side, then taking the cross product will give us, and taking the magnitude of the cross product will give us the area." + }, + { + "text": "Moreover, the cross product also gives us the normal direction." + }, + { + "text": "In fact, the cross product gives us two in one." + }, + { + "text": "It gives us the normal direction and the area element." + }, + { + "text": "And that is why I said that we will have an easy formula for N dS while N and dS taken separately are more complicated because you would have to actually take the length of a direction of this guy." + }, + { + "text": "Let's carry out this problem." + }, + { + "text": "Let's say I am going to look at a small piece of the xy plane." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk10.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..80ecc53d0640b10ed2fa61964d985138e15dd4dc --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "I think one of you, I forgot, asked yesterday, how would I do it in general?" + }, + { + "text": "Is there a formula like m dx plus n dy?" + }, + { + "text": "Well, that's going to be the formula." + }, + { + "text": "And, you'll see it's a little bit too complicated." + }, + { + "text": "So, the really useful ones are actually the special ones." + }, + { + "text": "So, let's say that we are given a parametric description of a surface S. So, that means we can describe S by formulas saying x is some function of two parameter variables." + }, + { + "text": "I'm going to call them u and v. I hope you don't mind." + }, + { + "text": "You can call them t1 and t2." + }, + { + "text": "You can call them whatever you want." + }, + { + "text": "OK, so one of the basic properties of a surface is because I have only two independent directions to move on, I should be able to express x, y, and z in terms of two variables." + }, + { + "text": "So, now let's say that I know how to do that." + }, + { + "text": "Or, maybe I should instead think of it in terms of a position vector if that helps you." + }, + { + "text": "The position vector, so that's just the vector with components x, y, z is given as a function of u and v. OK, so it works like a parametric curve, but with two parameters." + }, + { + "text": "So, now, how will we actually set up a flux integral on such a surface?" + }, + { + "text": "Well, because we are locating the flux in terms of u and v, we will end up with an integral du dv." + }, + { + "text": "So, we need to figure out how to express n ds in terms of du and dv." + }, + { + "text": "OK, so n ds should be something du dv." + }, + { + "text": "How do we do that?" + }, + { + "text": "Well, we can use the same method that we've actually used over here." + }, + { + "text": "Because if you think for a second, here we used, of course, a rectangle in the x, y plane, and we lifted it to a parallelogram and so on." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk11.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..61d1728a009aa03829fde534d602caecd77a30aa --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "But, more generally, you can think, what happens if I change u by delta u, keeping v constant, or the other way around?" + }, + { + "text": "You will get some sort of mesh grid on your surface, and you will look at a little parallelogram that's an elementary piece of that mesh and figure out what is its area and normal vector." + }, + { + "text": "Well, that will again be given by the cross product of the two sides." + }, + { + "text": "OK, so let's think a little bit about what happens when I move a little bit on my surface." + }, + { + "text": "So, I'm taking a grid on my surface given by the u and v directions." + }, + { + "text": "And, if I take a piece of that corresponding to small changes, delta u and delta v, what's going to be going on here?" + }, + { + "text": "Well, I have to deal with two vectors, one corresponding to changing u, the other one corresponding to changing v. If I change u, how does my point change?" + }, + { + "text": "Well, that's given by the derivative of this with respect to u. OK, so this vector here I will call, so the sides are given by, let me say, partial r over partial u times delta u." + }, + { + "text": "And, if you prefer, maybe I should write it as partial x over partial u delta u partial y." + }, + { + "text": "Well, it's just too boring to write, and so on." + }, + { + "text": "OK, it means just, you know, if I change u a little bit, keep v constant, then how x changes is given by partial x over partial u times delta u." + }, + { + "text": "Same thing with y, same thing with z." + }, + { + "text": "And, I'm just using vector notation to do it this way." + }, + { + "text": "That's the analog of when I said delta r for line integrals along a curve, vector delta r is the velocity vector dr over dt times delta t. OK, now if I look at the other side, OK, so, sorry, so let me start again." + }, + { + "text": "I ran out of space." + }, + { + "text": "One side is partial r partial u times delta u, and the other one would be partial r partial v times delta v because that's how the position of your point changes if you just change u or v and not the other one." + }, + { + "text": "So, now, to find the surface element together with a normal vector, I would just take the cross product between these guys." + }, + { + "text": "So, if you prefer, that's the cross product of partial r partial u with partial r partial v delta u delta v. And so, N dS is this cross product times du dv up to sine." + }, + { + "text": "I mean, also here." + }, + { + "text": "Depends on which choice I make for my normal vector, of course." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk12.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..4edd218fc4799dfc682e96577ad40cb5df2f17ab --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, now, if you, that, of course, is a slightly confusing equation to think of." + }, + { + "text": "So, a good exercise, if you want to really understand what's going on, try this in two good examples to look at." + }, + { + "text": "One good example to look at is the previous one." + }, + { + "text": "What is it?" + }, + { + "text": "It's when u and v are just x and y. OK, so the parametric equations are just x equals x, y equals y, and z is f of x, y." + }, + { + "text": "You should end up with the same formula that we had over there." + }, + { + "text": "And, you should see why because, see, both of them are given by a cross product." + }, + { + "text": "The other case you can look at, just to convince yourselves that it's true, so we don't need to do that because we've seen the formula before." + }, + { + "text": "But, in the case of a sphere, we've seen the formula for N and for dS separately." + }, + { + "text": "So, we know what N dS are in terms of d phi d theta." + }, + { + "text": "Well, you could parametrize a sphere in terms of phi and theta." + }, + { + "text": "Namely, the formulas would be x equals a sine phi cosine theta, y equals a sine phi sine theta, z equals a cosine phi." + }, + { + "text": "The formulas for spherical coordinates setting rho equals a." + }, + { + "text": "So, that's a parametric equation for the sphere." + }, + { + "text": "And then, if you try to use this formula here, you should end up with the same things we've already seen for N dS, just with a lot more pain to actually get there because your cross product is going to be a bit complicated." + }, + { + "text": "But, we're seeing all of these formulas, they all fit together." + }, + { + "text": "Somehow, it's always the same question, just we have different angles of attack on this general problem." + }, + { + "text": "OK, questions?" + }, + { + "text": "No?" + }, + { + "text": "OK, let's look at yet another last way of finding N dS." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk13.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..11d368b6015bc6b9cacbc394c8b399183b51e276 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then, I promise we'll switch to something else because I can feel that you're getting a bit overwhelmed by all these formulas for N dS." + }, + { + "text": "So, OK, so what happens very often is we don't actually know how to parametrize our surface." + }, + { + "text": "Maybe we don't know how to solve for z as a function of x and y, but our surface is given by some equation." + }, + { + "text": "And so, what that means is actually maybe what we know is not really these kinds of formulas, but maybe we know a normal vector." + }, + { + "text": "And, I'm going to call this one capital N because I don't even need it to be a unit vector, you will see." + }, + { + "text": "It can be a normal vector of the surface S. So, why would we ever know a normal vector?" + }, + { + "text": "Well, for example, if our surface is a plane, say it's a slanted plane given by some equation, Ax plus By plus Cz equals D. Well, you know the normal vector." + }, + { + "text": "It's A, B, C. Of course, you could solve for z and then go back to that case, which is why I said that that one is really useful." + }, + { + "text": "But, you can also just stay with a normal vector." + }, + { + "text": "Why else would you know a normal vector?" + }, + { + "text": "Well, let's say that you know an equation that's of a form g of x, y, z equals zero." + }, + { + "text": "Well, then you know that the gradient of g is perpendicular to the level surface." + }, + { + "text": "OK, so let me just give you two examples." + }, + { + "text": "If you have a plane, Ax plus By plus Cz equals D, then the normal vector would just be A, B, C. If you have a surface S given by an equation, g of x, y, z equals zero, then you can take the normal vector to be the gradient of g. We've seen that the gradient is perpendicular to the level surface." + }, + { + "text": "Now, of course, we don't necessarily have to follow what's going to come because if we could solve for z then we might be better off doing what we did over there." + }, + { + "text": "But, let's say that we want to do it this way." + }, + { + "text": "So, then what can we do?" + }, + { + "text": "Well, I'm going to give you a little bit of information about NDS." + }, + { + "text": "So, OK, so let's start by thinking about a slanted plane." + }, + { + "text": "OK, so let's say that my surface is just a slanted plane." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk14.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..8f6af2d2aa3b3d17432ec3b26b0606675c6a7d16 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, my normal vector would be maybe somewhere here." + }, + { + "text": "And, let's say that I'm going to try, you know, I need, of course, some handle on how to set up my integral." + }, + { + "text": "So, maybe I'm going to express this in terms of x and y. OK, so I have my coordinates, and I'll try to use x and y." + }, + { + "text": "So, then I would like to relate delta s, ds, to the area in the xy plane." + }, + { + "text": "So, that means, you know, I want maybe to look at the projection of this guy onto a horizontal plane." + }, + { + "text": "Let's squish it horizontally." + }, + { + "text": "So, then you have here another area." + }, + { + "text": "OK, so the guy on the slanted plane, let's call that delta s, and let's call this guy down here delta a." + }, + { + "text": "So, the question, and, you know, delta a would become ultimately maybe delta x, delta y, or something like that." + }, + { + "text": "The question is, how do we find the conversion rate between these two areas?" + }, + { + "text": "See, I mean, they're not the same." + }, + { + "text": "Visually, I hope it's clear to you that if my plane is actually horizontal, then, of course, they're the same." + }, + { + "text": "But, the more slanted it becomes, the more delta a becomes smaller than delta s, right?" + }, + { + "text": "I mean, if you buy, you know, if you buy land, and it's on the side of a cliff, well, whether you look at it on a map, or whether you look at it on the actual cliff, the area is going to be very different." + }, + { + "text": "I'm not sure if that's a wise thing to do if you want to build a house there, but I've been told you can get really cheap land." + }, + { + "text": "OK, so anyway, OK, so delta s versus delta a depends on how slanted things are." + }, + { + "text": "And, let's try to make that more precise by looking at the angle that our plane makes with the horizontal direction." + }, + { + "text": "OK, so let's call this angle alpha, the angle that our plane makes with the horizontal direction." + }, + { + "text": "See, it's all coming together now." + }, + { + "text": "The first unit about cross products, normal vectors, and so on is actually useful now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk15.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..e90009e6248e5d6a50885b9d3130bf4050ef960c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, I claim that the surface element is related to the area in the plane by delta a equals delta s times the cosine of alpha." + }, + { + "text": "Why is that?" + }, + { + "text": "Well, let's look at this small rectangle with one horizontal side and one slanted side." + }, + { + "text": "Well, when you project, this side doesn't change." + }, + { + "text": "But, this side gets shortened by a factor of cosine alpha." + }, + { + "text": "Whatever this length was, this length here is that one times cosine alpha." + }, + { + "text": "So, that's why the area gets shrunk by cosine alpha." + }, + { + "text": "In one direction, nothing happens." + }, + { + "text": "In the other direction, you squish by cosine alpha." + }, + { + "text": "So, what that means is that, well, OK, so we'll have to deal with this." + }, + { + "text": "And, of course, the one we'll care about actually is delta s expressed in terms of delta a." + }, + { + "text": "But, what are we going to do with this cosine?" + }, + { + "text": "It's not very convenient to have a cosine left in here." + }, + { + "text": "So, remember, the angle between two planes, it's the same thing as the angle between the normal vectors." + }, + { + "text": "So, if you want to see this angle alpha elsewhere, what you can do is you can just take the vertical direction." + }, + { + "text": "Let's take k. Then, here we have our angle alpha again." + }, + { + "text": "So, in particular, cosine of alpha, I can get, well, we know how to find the angle between two vectors." + }, + { + "text": "So, if we have our normal vector n, we'll do n dot k, and we'll divide by length n length k. Well, length k is one." + }, + { + "text": "That's one easy." + }, + { + "text": "OK, so that's how we find the angle." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk16.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..18b8ca6f0e10e19b75db0dabf1ec37a110a6c671 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, now I'm going to say, well, delta s is going to be one over cosine alpha delta a." + }, + { + "text": "And, I can rewrite that as length of n divided by n dot k times delta a." + }, + { + "text": "Now, let's multiply that by the unit normal vector because what I'm multiplying by is not dS, but actually n dS." + }, + { + "text": "So, n delta s will be, I'm just going to multiply by n. Well, let's think for a second." + }, + { + "text": "What happens if I take the unit normal n, and I multiply it by the length of my other normal big N?" + }, + { + "text": "Well, I get big N again, right?" + }, + { + "text": "This is a normal vector of the same length as n, well, up to sine." + }, + { + "text": "But, actually, maybe I should." + }, + { + "text": "The only thing I don't know is whether this guy will be going in the same direction as big N or in the opposite direction." + }, + { + "text": "Say that, for example, my capital N has length, I don't know, length three, for example." + }, + { + "text": "The unit normal vector might be this guy, in which case, indeed, three times little n will be big N. Or, it might be this one, in which case, three times little n will be negative big N. But, up to sine, it's N. And then, I will have N over n dot k delta a." + }, + { + "text": "And so, the final formula, the one that actually we care about in case you don't really like my explanations of how we get there, is that N dS is plus or minus N over N dot k dx dy." + }, + { + "text": "That one is actually kind of useful, so let's box it." + }, + { + "text": "Now, just in case you are wondering, of course, if you didn't want to project to x, y, you would have maybe preferred to project to, say, the plane of a blackboard, yz." + }, + { + "text": "Well, you can do the same thing." + }, + { + "text": "To express N dS in terms of dy dz, you do the same argument." + }, + { + "text": "And simply, the only thing that changes is instead of using the vertical vector k, you use the normal vector i." + }, + { + "text": "So, you would be doing N over N dot i dy dz, and same thing." + }, + { + "text": "Just keep an open mind that this also works with other variables." + }, + { + "text": "But anyway, so that's how you can basically project the vector surface area element onto the x, y plane in a way." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk17.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..09fc575d766fb25a1c29c876fc0a0b29520a15d8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, so let's look at the special case just to see how this fits with stuff we've seen before." + }, + { + "text": "Let's do a special example where our surface is given by the equation z minus f of x, y equals zero." + }, + { + "text": "OK, that's a strange way to write the equation z equals f of x, y that we saw before." + }, + { + "text": "But now, it looks like, well, some function of x, y, z equals zero." + }, + { + "text": "So, let's try to use this new method." + }, + { + "text": "So, let's call this guy g of x, y, z." + }, + { + "text": "Well, so now let's look at the normal vector." + }, + { + "text": "The normal vector would be the gradient of g, we said." + }, + { + "text": "What's the gradient of this function?" + }, + { + "text": "So, gradient of g, well, partial g, partial x, that's just negative partial f, partial x. Gradient g, sorry, the y component, partial g, partial y is going to be negative f sub y." + }, + { + "text": "And, g sub z is just one." + }, + { + "text": "So now, if you take n over n dot k dx dy, well, it looks like that's going to be negative f sub x, negative f sub y, one divided by, well, what's n dot k?" + }, + { + "text": "If you do that with k, you'll get just one." + }, + { + "text": "So, I'm not going to write it, dx dy." + }, + { + "text": "See, that's, again, our favorite formula." + }, + { + "text": "So, this one is actually more general because you don't need to solve for z." + }, + { + "text": "But, if you can solve for z, then it's the same as before." + }, + { + "text": "OK, I think that's enough formulas for n dS." + }, + { + "text": "So, after spending a lot of time telling you how to compute surface integrals, now I'm going to try to tell you how to avoid computing them." + }, + { + "text": "And, that is called the divergence theorem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk18.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..0e5e56886a97cb7eb64b3c2de2f9c304bc0aed75 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And, we'll see the proof and everything and applications on Tuesday, but I want to at least state the theorem and see how it works in one example." + }, + { + "text": "It's also known as the Gauss grain theorem, or just the Gauss theorem depending on who you talk to." + }, + { + "text": "So, the grain here is the same grain as in Green's theorem, OK, because somehow that's a space version of Green's theorem." + }, + { + "text": "So, what does it say?" + }, + { + "text": "It says, so, this is the analog of grain for flux." + }, + { + "text": "What it says is if S is a closed surface, OK, so remember, it's the same as with Green's theorem, we need to have something that's completely enclosed." + }, + { + "text": "So, you have a surface, and there's somehow no gaps in it." + }, + { + "text": "There's no boundary to it." + }, + { + "text": "It's really completely enclosed." + }, + { + "text": "So, I'm choosing a region in space that I will call D. And, I need to choose my orientation." + }, + { + "text": "So, the orientation that will be chosen in this theorem is choosing the normal vector to point outwards." + }, + { + "text": "OK, so, n needs to be outwards." + }, + { + "text": "So, that's one part of the puzzle." + }, + { + "text": "The other part is a vector field." + }, + { + "text": "I need to have a vector field that is defined and differentiable everywhere in D. So, same restrictions as usual." + }, + { + "text": "Then, I don't have, actually, to compute the flux integral." + }, + { + "text": "The integral of F dot n dS of a closed surface S. I need to put a circle just to remind you it's got to be a closed surface." + }, + { + "text": "That's just notation to remind us, closed surface." + }, + { + "text": "I can replace that by the triple integral of the region inside of divergence of F dV." + }, + { + "text": "Now, I need to tell you what's the divergence of a 3D vector field." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk19.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..04bd556506c1a6a0e925cc2b3dd8ba3efad34e8f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, you'll see it's not much of a difference." + }, + { + "text": "In the 2D case, what you do is just, so, say that your vector field has components P, Q, and R. Then, you will take P sub x plus Q sub y plus R sub z. OK, so that's the definition." + }, + { + "text": "It's pretty easy to remember." + }, + { + "text": "You take the x component partial respect to x plus partial respect to y of the y component plus partial respect to z of the z component." + }, + { + "text": "OK, so, for example, last time we saw that the flux of the vector field zk for a sphere of radius a was four-thirds pi a cubed by computing the surface integral." + }, + { + "text": "Well, if we do it more efficiently now by Green's theorem, so we're going to use Green's theorem for this sphere." + }, + { + "text": "Because we're doing the whole sphere, it's fine." + }, + { + "text": "It's a closed surface." + }, + { + "text": "We couldn't do it for, say, a hemisphere or something like that." + }, + { + "text": "We need to, well, I mean, for the hemisphere, we'd need to add maybe the flat face at the bottom or something like that." + }, + { + "text": "So, Green's theorem says that our flux integral can be actually replaced by the triple integral of a solid ball of radius a of the divergence of zk dv." + }, + { + "text": "But now, what's the divergence of this field?" + }, + { + "text": "Well, so you have zero, zero, z." + }, + { + "text": "So, you get zero plus zero plus one." + }, + { + "text": "It looks like it will be one." + }, + { + "text": "So, if you do the triple integral of one dv, you will get just the volume of the region inside, which is four-thirds pi a cubed." + }, + { + "text": "And, so it was no accident." + }, + { + "text": "In fact, before that, we looked at also xi yj zk, and we found three times the volume." + }, + { + "text": "That's because the divergence of that field was actually three." + }, + { + "text": "So, very quickly, let me just say what this means physically." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk2.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..ff983a9074353a930a98538affafbeff51542106 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Here I have delta x, here I have delta y, and I am starting at some point xy." + }, + { + "text": "Now, above that I will have a parallelogram on my surface." + }, + { + "text": "I need to figure out this point here, the point where I start." + }, + { + "text": "I know what it is." + }, + { + "text": "It is just x, y, and z is f of x, y." + }, + { + "text": "Now, what I want to find actually is what are these two vectors, let's call them u and v that correspond to moving a bit in the x direction or in the y direction." + }, + { + "text": "And then u cross v will be, well, in terms of the magnitude of this guy will just be the little piece of surface area delta S. And, in terms of direction, it will be normal to the surface." + }, + { + "text": "Actually, I will get just delta S times my normal vector." + }, + { + "text": "Well, up to sign because depending on whether I do u cross v or v cross u, I might get the normal vector in the direction I want or in the direction I want." + }, + { + "text": "But we will take care of that later." + }, + { + "text": "Up to sign." + }, + { + "text": "OK, so let's find u and v. Actually, in case you have trouble with that small picture, then I have a better one here." + }, + { + "text": "Let's keep it just in case this one gets really too cluttered." + }, + { + "text": "It really represents the same thing." + }, + { + "text": "OK, so let's try to figure out these vectors u and v. So, the vector u starts at the point x, y, f of x, y." + }, + { + "text": "And it goes to, where is its head?" + }, + { + "text": "Well, I'll have moved x by delta x." + }, + { + "text": "So, x plus delta x. y doesn't change." + }, + { + "text": "And, of course, the z coordinate has to change." + }, + { + "text": "It becomes f of x plus delta x and y." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk20.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..f8f4327e9a02af262336ececd46d4897ee00c228 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk20.json @@ -0,0 +1,26 @@ +[ + { + "text": "Physically, see, this guy on the left is the total amount of stuff that goes out of the region per unit time." + }, + { + "text": "So, I want to figure out how much stuff comes out of there." + }, + { + "text": "What does the divergence mean?" + }, + { + "text": "The divergence means, well, it measures how much the flow is expanding things." + }, + { + "text": "It measures how much, I say probably when we understood 2D divergence, it measures the amount of sources or sinks that you have inside your fluid." + }, + { + "text": "So, now it becomes common sense." + }, + { + "text": "If you take a region of space, the total amount of water that flows out of it is the total amount of sources that you have in there minus the sinks." + }, + { + "text": "In spite of this common sense explanation, we are going to see actually how to prove this, and we'll see how it works and the hypothesis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk3.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..4dcc70fd37d899d05e9421b392306604a92d2817 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, how does f change if I change x a little bit?" + }, + { + "text": "Well, we've seen that it's given by the partial derivative f sub x." + }, + { + "text": "So, this is approximately equal to f of x, y plus delta x times f sub x at the given point x, y. I'm not going to add it because notation is already long enough." + }, + { + "text": "So, that means my vector u is, well, approximately, because I'm using this linear approximation, delta x, zero, and f sub x times delta x. OK, is that OK with everyone?" + }, + { + "text": "Good." + }, + { + "text": "Now, what about v?" + }, + { + "text": "Well, v works the same way." + }, + { + "text": "OK, so I'm not going to do all the details." + }, + { + "text": "When I move from here to here, well, x doesn't change, and y changes by delta y." + }, + { + "text": "So, x component, nothing happens." + }, + { + "text": "y component changes by delta y." + }, + { + "text": "What about the z component?" + }, + { + "text": "Well, f changes by f sub y times delta y." + }, + { + "text": "That's how f changes if I increase y by delta y. OK, so I have my two sides." + }, + { + "text": "Now, I can take the cross product." + }, + { + "text": "Well, maybe I will first, sorry, factor something out." + }, + { + "text": "See, I can rewrite this as one zero f sub x times delta x." + }, + { + "text": "And, this one I will rewrite as zero one f sub y delta y." + }, + { + "text": "And so, now the cross product, so n hat delta s up to sine is going to be u cross v. u cross v, well, so we'll have to do the cross product, and we'll have a delta x delta y coming out." + }, + { + "text": "OK, I'm just saving myself the trouble of writing a lot of delta x and delta y's." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk4.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..b0479e4d532bb2675791b9c29b5e2bff581132c7 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "But, if you prefer, you can just do directly this cross product there." + }, + { + "text": "OK, so let's compute this cross product." + }, + { + "text": "Well, the i component is zero minus f sub x." + }, + { + "text": "The y component is going to be, well, f sub y minus zero, but with a minus sign in front of everything, so negative f sub y." + }, + { + "text": "And, the z component will be just one times delta x delta y. OK, does that make sense for, yes, very good." + }, + { + "text": "And so, now, when we just take, we shrink this rectangle, we shrink delta x and delta y down, so that's how we get this formula for n ds equals negative fx negative fy one dx dy." + }, + { + "text": "Well, plus minus because it's up to us to choose whether we want to take the normal vector pointing up or down." + }, + { + "text": "So, see, if you take this convention, then the z component of n ds is positive." + }, + { + "text": "So, that corresponds to normal vector pointing up." + }, + { + "text": "If you take the opposite means, then the z component will be negative." + }, + { + "text": "That means your normal vector points down." + }, + { + "text": "OK, so this one is with n pointing up." + }, + { + "text": "I mean, when I say up, of course, it's still perpendicular to the surface." + }, + { + "text": "You know, if the surface really has a big slope, then it's not really going to go all that much up, but more up than down." + }, + { + "text": "OK, so that's how we get that formula." + }, + { + "text": "Any questions?" + }, + { + "text": "No?" + }, + { + "text": "OK, so that's a really useful formula." + }, + { + "text": "So, you don't really need to remember all the details of how we got it, but please remember that formula." + }, + { + "text": "Let's do an example, actually." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk5.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5b29a7df7e903bf04c8988e8f2436f298193a6d0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, let's say I want to find the flux of the vector field z times k. So, it's a vertical vector point of the paraboloid z equals x squared plus y squared that lives above the unit disk." + }, + { + "text": "OK, so what does that mean?" + }, + { + "text": "z equals x squared plus y squared, well, we've seen it many times." + }, + { + "text": "OK, it's this paraboloid above the unit disk means I only care about, I don't care about this infinite surface." + }, + { + "text": "I will actually stop when I hit a radius of one away from the z axis." + }, + { + "text": "And, so now I have my vector field, which is going to point overall up because, in fact, I'm at z times k. So, the more z is positive, the more your vector field goes up." + }, + { + "text": "Of course, if z were negative, then it would point down, but we live above." + }, + { + "text": "So, actually, a quick opinion poll." + }, + { + "text": "What do you think the flux should be?" + }, + { + "text": "Should it be positive, zero, negative?" + }, + { + "text": "We don't know." + }, + { + "text": "OK, so I see some I don't know." + }, + { + "text": "I see some negative, and I see some positive." + }, + { + "text": "So, of course, I didn't tell you which way I'm orienting my paraboloid." + }, + { + "text": "So, so far, both answers are correct." + }, + { + "text": "The only one that's probably not correct is zero because no matter which way you choose to orient it, you should get something." + }, + { + "text": "It's not looking like it will be zero." + }, + { + "text": "So, let's say that I'm going to do it with a normal pointing upwards." + }, + { + "text": "Second chance." + }, + { + "text": "OK, I see some people changing back and forth between one and two." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk6.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..7d51098b7f0239835af1dceb80b51f4a5d9a519e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, so let's draw a picture." + }, + { + "text": "Which one is pointing upwards?" + }, + { + "text": "Well, let's look at the bottom point, the normal vector pointing up." + }, + { + "text": "Here, we know what it means." + }, + { + "text": "It's this guy." + }, + { + "text": "And so, if you continue to follow your normal vector, see, they're actually pointing up and into the paraboloid." + }, + { + "text": "OK, and I claim that the answer should be positive because the vector field is crossing our paraboloid going upwards, going from the outside out and below to the inside and up side, so in the direction that we are counting positively." + }, + { + "text": "Well, we'll see how it turns out when we do the calculation." + }, + { + "text": "OK, so we have to compute the integral for flux." + }, + { + "text": "The one integral of a surface of F dot n dS is going to be, OK, so what are we going to do?" + }, + { + "text": "Well, F, we said, is 0, 0, z." + }, + { + "text": "What is n dS?" + }, + { + "text": "Well, let's use our brand new formula." + }, + { + "text": "So, it says negative F sub x, negative F sub y, one dx dy." + }, + { + "text": "What is little f in here?" + }, + { + "text": "It's x squared plus y squared, OK?" + }, + { + "text": "So, when we're using this formula, we need to know what little f stands for is whatever the formula is for z as a function of x and y." + }, + { + "text": "So, we take x squared plus y squared, and we take the partial derivatives with minus signs." + }, + { + "text": "We get negative 2x, negative 2y, and one dx dy." + }, + { + "text": "Well, of course, here it didn't really matter because we're going to dot them with zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk7.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..e3524a83e7e3f3457abdd39bd8eb8d13e8d49416 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, actually, even if we had made a mistake, we somehow wouldn't have had to pay the price, still." + }, + { + "text": "OK, so we'll end up with double integral on S of z dx dy." + }, + { + "text": "Now, what do we do with that?" + }, + { + "text": "Well, we have too many things." + }, + { + "text": "We need to get rid of z." + }, + { + "text": "So, let's use z equals x squared plus y squared once more." + }, + { + "text": "OK, so that becomes double integral of x squared plus y squared dx dy." + }, + { + "text": "And here, see, we're using the fact that we're only looking at things that are on the surface." + }, + { + "text": "It's not like in a triple integral, you could never do that because z, x, and y are independent." + }, + { + "text": "Here, they're related by the equation of a surface." + }, + { + "text": "Sorry if I sound like I'm ranting, but I know from experience this is where one of the most sticky and tricky points is, actually." + }, + { + "text": "OK, so now, how will we actually integrate that?" + }, + { + "text": "Well, now that we have just x and y, we should figure out what's the range for x and y?" + }, + { + "text": "Well, the range for x and y is going to be the shadow of our region." + }, + { + "text": "It's going to be this unit disk." + }, + { + "text": "OK, so let me just do that for now." + }, + { + "text": "And see here, this is finally where I've left the world of surface integrals to go back to a usual double integral." + }, + { + "text": "And now, I have to set it up." + }, + { + "text": "Well, I can do it this way with dx dy, but it looks like there's a smarter thing to do." + }, + { + "text": "OK, I'm going to use, actually, polar coordinates." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk8.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..4f11b1ba8efdf54e09dcbd2834634862a1b0e709 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, in fact, I'm going to say this is a double integral of r squared times r dr d theta." + }, + { + "text": "I'm on the unit disk, so r goes zero to one, theta goes zero to two pi." + }, + { + "text": "And, if you do the calculation, you'll find that this is going to be pi over two." + }, + { + "text": "OK, any questions about the example?" + }, + { + "text": "Yes?" + }, + { + "text": "OK, how do I get this negative 2x and negative 2y?" + }, + { + "text": "So, I want to use my formula for n ds." + }, + { + "text": "OK, my surface is given by the graph of a function." + }, + { + "text": "It's the graph of a function x squared plus y squared." + }, + { + "text": "So, I will use this formula that's up here." + }, + { + "text": "I will take the function x squared plus y squared, and I will take its partial derivatives." + }, + { + "text": "So, if I take the partial of f, so, f x squared plus y squared with respect to x, I get 2x." + }, + { + "text": "So, I put negative 2x, and then same thing, negative 2y, one dx dy, yes?" + }, + { + "text": "Which k hat?" + }, + { + "text": "Oh, you mean the vector field?" + }, + { + "text": "Well, so it's a different part of the story, OK?" + }, + { + "text": "So, whenever you do a surface integral for flux, you have two parts of the story." + }, + { + "text": "One is the vector field whose flux you're taking." + }, + { + "text": "The other one is the surface for which you will be taking flux." + }, + { + "text": "So, the vector field only comes as this f in the notation." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk9.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..9fa8c0e63e0fe3808781ed666ef10e0c042b38cb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_5_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And, everything else, the bounds of the double integral and the n ds, they all come from the surface that we are looking at." + }, + { + "text": "OK, so basically, in all of this calculation, this is coming from f equals zk." + }, + { + "text": "Everything else comes from the information paraboloid z equals x squared plus y squared above the disk." + }, + { + "text": "OK, so in particular, if we wanted to now find the flux of any other vector field for the same paraboloid, well, all we have to do is just replace this guy by whatever the new vector field is." + }, + { + "text": "We've learned how to set up flux integrals for this paraboloid." + }, + { + "text": "Not that you should remember this one by heart." + }, + { + "text": "I mean, there's many paraboloids in life and other surfaces, too, so it's better to remember the general method." + }, + { + "text": "OK, any other questions?" + }, + { + "text": "No?" + }, + { + "text": "OK, let's see more ways of tackling flux integrals." + }, + { + "text": "But, just to reassure you, at this point, we've seen the most important ones." + }, + { + "text": "You know, 90% of the problems that we'll be looking at, we can do with what we've seen so far last time and this time." + }, + { + "text": "But, let's look a little bit at a more general situation." + }, + { + "text": "Let's say that my surface is so complicated that I can't actually express z as a function of x and y." + }, + { + "text": "But, let's say that actually I know how to parametrize it." + }, + { + "text": "So, I have a parametric equation for my surface." + }, + { + "text": "That means I can express x, y, z in terms of any two parameter variables that might be relevant for me." + }, + { + "text": "So, if you want, this one here is the special case where you can parametrize things in terms of x and y as your two variables." + }, + { + "text": "So, how would you do it in the fully general case?" + }, + { + "text": "In a way, that will answer your question." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk0.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..de88ac001212dfb6b1de182c0b68e842d34b4657 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "Yesterday we have learned about flux and we have seen the first examples of how to set up and compute integrals for flux of a vector field for a surface." + }, + { + "text": "Remember the flux of a vector field F for a surface S is defined by taking the double integral on the surface of F dot n dS where n is the unit normal to the surface and dS is the area element on the surface." + }, + { + "text": "As we have seen, for various surfaces we have various formulas telling us what the normal vector is and what the area element becomes." + }, + { + "text": "For example, on spheres we typically integrate with respect to phi theta the latitude and longitude angles." + }, + { + "text": "On a horizontal plane we would just end up integrating dx dy and so on." + }, + { + "text": "At the end of the lecture we saw a formula." + }, + { + "text": "And a lot of you asked me how did we get it." + }, + { + "text": "Well, we didn't get it yet." + }, + { + "text": "We are going to try to explain where it comes from and why it works." + }, + { + "text": "The case we want to look at is the graph of a function." + }, + { + "text": "It is given by z equals some function in terms of x and y." + }, + { + "text": "Our surface is out here." + }, + { + "text": "z is a function of x and y." + }, + { + "text": "And x and y will range over some domain in the xy plane, namely the region that is the shadow of the surface on the xy plane." + }, + { + "text": "I said that we will have a formula for n ds which will end up being plus minus, minus f sub x minus f sub y one dx dy so that we will set up and evaluate the integral in terms of x and y." + }, + { + "text": "Replacing every time we see z we will replace it by f of xy, whatever the formula for f of xy is." + }, + { + "text": "By the way, if we look at a very easy case where this is just a horizontal plane, so z equals constant, the function is just a constant, well, the partial derivatives become just zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk1.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..83a60f55a64abf7ed3e632f2c0caa0700c633561 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "You get zero, zero, one dx dy." + }, + { + "text": "That is what you would expect for a horizontal plane just from common sense." + }, + { + "text": "This is more interesting, of course, if a function is more interesting." + }, + { + "text": "How do we get that?" + }, + { + "text": "Where does this come from?" + }, + { + "text": "We need to figure out for a small piece of our surface what will be n delta S if you want." + }, + { + "text": "Let's say that we take a small rectangle in here corresponding to the sides delta x and delta y." + }, + { + "text": "And we look at the piece of surface that is above that." + }, + { + "text": "Well, the question we have now is what is the area of this little piece of surface and what is its normal vector?" + }, + { + "text": "Observe this little piece up here." + }, + { + "text": "If it is small enough it will look like a parallelogram." + }, + { + "text": "It might be slightly curvy, but roughly it looks like a parallelogram in space." + }, + { + "text": "And so we have seen how to find the area of a parallelogram in space using cross product." + }, + { + "text": "If we can figure out what are the vectors for this side and that side, then taking the cross product will give us, and taking the magnitude of the cross product will give us the area." + }, + { + "text": "Moreover, the cross product also gives us the normal direction." + }, + { + "text": "In fact, the cross product gives us two in one." + }, + { + "text": "It gives us the normal direction and the area element." + }, + { + "text": "And that is why I said that we will have an easy formula for N dS while N and dS taken separately are more complicated because you would have to actually take the length of a direction of this guy." + }, + { + "text": "Let's carry out this problem." + }, + { + "text": "Let's say I am going to look at a small piece of the xy plane." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk10.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..80ecc53d0640b10ed2fa61964d985138e15dd4dc --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "I think one of you, I forgot, asked yesterday, how would I do it in general?" + }, + { + "text": "Is there a formula like m dx plus n dy?" + }, + { + "text": "Well, that's going to be the formula." + }, + { + "text": "And, you'll see it's a little bit too complicated." + }, + { + "text": "So, the really useful ones are actually the special ones." + }, + { + "text": "So, let's say that we are given a parametric description of a surface S. So, that means we can describe S by formulas saying x is some function of two parameter variables." + }, + { + "text": "I'm going to call them u and v. I hope you don't mind." + }, + { + "text": "You can call them t1 and t2." + }, + { + "text": "You can call them whatever you want." + }, + { + "text": "OK, so one of the basic properties of a surface is because I have only two independent directions to move on, I should be able to express x, y, and z in terms of two variables." + }, + { + "text": "So, now let's say that I know how to do that." + }, + { + "text": "Or, maybe I should instead think of it in terms of a position vector if that helps you." + }, + { + "text": "The position vector, so that's just the vector with components x, y, z is given as a function of u and v. OK, so it works like a parametric curve, but with two parameters." + }, + { + "text": "So, now, how will we actually set up a flux integral on such a surface?" + }, + { + "text": "Well, because we are locating the flux in terms of u and v, we will end up with an integral du dv." + }, + { + "text": "So, we need to figure out how to express n ds in terms of du and dv." + }, + { + "text": "OK, so n ds should be something du dv." + }, + { + "text": "How do we do that?" + }, + { + "text": "Well, we can use the same method that we've actually used over here." + }, + { + "text": "Because if you think for a second, here we used, of course, a rectangle in the x, y plane, and we lifted it to a parallelogram and so on." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk11.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..61d1728a009aa03829fde534d602caecd77a30aa --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "But, more generally, you can think, what happens if I change u by delta u, keeping v constant, or the other way around?" + }, + { + "text": "You will get some sort of mesh grid on your surface, and you will look at a little parallelogram that's an elementary piece of that mesh and figure out what is its area and normal vector." + }, + { + "text": "Well, that will again be given by the cross product of the two sides." + }, + { + "text": "OK, so let's think a little bit about what happens when I move a little bit on my surface." + }, + { + "text": "So, I'm taking a grid on my surface given by the u and v directions." + }, + { + "text": "And, if I take a piece of that corresponding to small changes, delta u and delta v, what's going to be going on here?" + }, + { + "text": "Well, I have to deal with two vectors, one corresponding to changing u, the other one corresponding to changing v. If I change u, how does my point change?" + }, + { + "text": "Well, that's given by the derivative of this with respect to u. OK, so this vector here I will call, so the sides are given by, let me say, partial r over partial u times delta u." + }, + { + "text": "And, if you prefer, maybe I should write it as partial x over partial u delta u partial y." + }, + { + "text": "Well, it's just too boring to write, and so on." + }, + { + "text": "OK, it means just, you know, if I change u a little bit, keep v constant, then how x changes is given by partial x over partial u times delta u." + }, + { + "text": "Same thing with y, same thing with z." + }, + { + "text": "And, I'm just using vector notation to do it this way." + }, + { + "text": "That's the analog of when I said delta r for line integrals along a curve, vector delta r is the velocity vector dr over dt times delta t. OK, now if I look at the other side, OK, so, sorry, so let me start again." + }, + { + "text": "I ran out of space." + }, + { + "text": "One side is partial r partial u times delta u, and the other one would be partial r partial v times delta v because that's how the position of your point changes if you just change u or v and not the other one." + }, + { + "text": "So, now, to find the surface element together with a normal vector, I would just take the cross product between these guys." + }, + { + "text": "So, if you prefer, that's the cross product of partial r partial u with partial r partial v delta u delta v. And so, N dS is this cross product times du dv up to sine." + }, + { + "text": "I mean, also here." + }, + { + "text": "Depends on which choice I make for my normal vector, of course." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk12.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..4edd218fc4799dfc682e96577ad40cb5df2f17ab --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, now, if you, that, of course, is a slightly confusing equation to think of." + }, + { + "text": "So, a good exercise, if you want to really understand what's going on, try this in two good examples to look at." + }, + { + "text": "One good example to look at is the previous one." + }, + { + "text": "What is it?" + }, + { + "text": "It's when u and v are just x and y. OK, so the parametric equations are just x equals x, y equals y, and z is f of x, y." + }, + { + "text": "You should end up with the same formula that we had over there." + }, + { + "text": "And, you should see why because, see, both of them are given by a cross product." + }, + { + "text": "The other case you can look at, just to convince yourselves that it's true, so we don't need to do that because we've seen the formula before." + }, + { + "text": "But, in the case of a sphere, we've seen the formula for N and for dS separately." + }, + { + "text": "So, we know what N dS are in terms of d phi d theta." + }, + { + "text": "Well, you could parametrize a sphere in terms of phi and theta." + }, + { + "text": "Namely, the formulas would be x equals a sine phi cosine theta, y equals a sine phi sine theta, z equals a cosine phi." + }, + { + "text": "The formulas for spherical coordinates setting rho equals a." + }, + { + "text": "So, that's a parametric equation for the sphere." + }, + { + "text": "And then, if you try to use this formula here, you should end up with the same things we've already seen for N dS, just with a lot more pain to actually get there because your cross product is going to be a bit complicated." + }, + { + "text": "But, we're seeing all of these formulas, they all fit together." + }, + { + "text": "Somehow, it's always the same question, just we have different angles of attack on this general problem." + }, + { + "text": "OK, questions?" + }, + { + "text": "No?" + }, + { + "text": "OK, let's look at yet another last way of finding N dS." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk13.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..11d368b6015bc6b9cacbc394c8b399183b51e276 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then, I promise we'll switch to something else because I can feel that you're getting a bit overwhelmed by all these formulas for N dS." + }, + { + "text": "So, OK, so what happens very often is we don't actually know how to parametrize our surface." + }, + { + "text": "Maybe we don't know how to solve for z as a function of x and y, but our surface is given by some equation." + }, + { + "text": "And so, what that means is actually maybe what we know is not really these kinds of formulas, but maybe we know a normal vector." + }, + { + "text": "And, I'm going to call this one capital N because I don't even need it to be a unit vector, you will see." + }, + { + "text": "It can be a normal vector of the surface S. So, why would we ever know a normal vector?" + }, + { + "text": "Well, for example, if our surface is a plane, say it's a slanted plane given by some equation, Ax plus By plus Cz equals D. Well, you know the normal vector." + }, + { + "text": "It's A, B, C. Of course, you could solve for z and then go back to that case, which is why I said that that one is really useful." + }, + { + "text": "But, you can also just stay with a normal vector." + }, + { + "text": "Why else would you know a normal vector?" + }, + { + "text": "Well, let's say that you know an equation that's of a form g of x, y, z equals zero." + }, + { + "text": "Well, then you know that the gradient of g is perpendicular to the level surface." + }, + { + "text": "OK, so let me just give you two examples." + }, + { + "text": "If you have a plane, Ax plus By plus Cz equals D, then the normal vector would just be A, B, C. If you have a surface S given by an equation, g of x, y, z equals zero, then you can take the normal vector to be the gradient of g. We've seen that the gradient is perpendicular to the level surface." + }, + { + "text": "Now, of course, we don't necessarily have to follow what's going to come because if we could solve for z then we might be better off doing what we did over there." + }, + { + "text": "But, let's say that we want to do it this way." + }, + { + "text": "So, then what can we do?" + }, + { + "text": "Well, I'm going to give you a little bit of information about NDS." + }, + { + "text": "So, OK, so let's start by thinking about a slanted plane." + }, + { + "text": "OK, so let's say that my surface is just a slanted plane." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk14.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..8f6af2d2aa3b3d17432ec3b26b0606675c6a7d16 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, my normal vector would be maybe somewhere here." + }, + { + "text": "And, let's say that I'm going to try, you know, I need, of course, some handle on how to set up my integral." + }, + { + "text": "So, maybe I'm going to express this in terms of x and y. OK, so I have my coordinates, and I'll try to use x and y." + }, + { + "text": "So, then I would like to relate delta s, ds, to the area in the xy plane." + }, + { + "text": "So, that means, you know, I want maybe to look at the projection of this guy onto a horizontal plane." + }, + { + "text": "Let's squish it horizontally." + }, + { + "text": "So, then you have here another area." + }, + { + "text": "OK, so the guy on the slanted plane, let's call that delta s, and let's call this guy down here delta a." + }, + { + "text": "So, the question, and, you know, delta a would become ultimately maybe delta x, delta y, or something like that." + }, + { + "text": "The question is, how do we find the conversion rate between these two areas?" + }, + { + "text": "See, I mean, they're not the same." + }, + { + "text": "Visually, I hope it's clear to you that if my plane is actually horizontal, then, of course, they're the same." + }, + { + "text": "But, the more slanted it becomes, the more delta a becomes smaller than delta s, right?" + }, + { + "text": "I mean, if you buy, you know, if you buy land, and it's on the side of a cliff, well, whether you look at it on a map, or whether you look at it on the actual cliff, the area is going to be very different." + }, + { + "text": "I'm not sure if that's a wise thing to do if you want to build a house there, but I've been told you can get really cheap land." + }, + { + "text": "OK, so anyway, OK, so delta s versus delta a depends on how slanted things are." + }, + { + "text": "And, let's try to make that more precise by looking at the angle that our plane makes with the horizontal direction." + }, + { + "text": "OK, so let's call this angle alpha, the angle that our plane makes with the horizontal direction." + }, + { + "text": "See, it's all coming together now." + }, + { + "text": "The first unit about cross products, normal vectors, and so on is actually useful now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk15.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..e90009e6248e5d6a50885b9d3130bf4050ef960c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, I claim that the surface element is related to the area in the plane by delta a equals delta s times the cosine of alpha." + }, + { + "text": "Why is that?" + }, + { + "text": "Well, let's look at this small rectangle with one horizontal side and one slanted side." + }, + { + "text": "Well, when you project, this side doesn't change." + }, + { + "text": "But, this side gets shortened by a factor of cosine alpha." + }, + { + "text": "Whatever this length was, this length here is that one times cosine alpha." + }, + { + "text": "So, that's why the area gets shrunk by cosine alpha." + }, + { + "text": "In one direction, nothing happens." + }, + { + "text": "In the other direction, you squish by cosine alpha." + }, + { + "text": "So, what that means is that, well, OK, so we'll have to deal with this." + }, + { + "text": "And, of course, the one we'll care about actually is delta s expressed in terms of delta a." + }, + { + "text": "But, what are we going to do with this cosine?" + }, + { + "text": "It's not very convenient to have a cosine left in here." + }, + { + "text": "So, remember, the angle between two planes, it's the same thing as the angle between the normal vectors." + }, + { + "text": "So, if you want to see this angle alpha elsewhere, what you can do is you can just take the vertical direction." + }, + { + "text": "Let's take k. Then, here we have our angle alpha again." + }, + { + "text": "So, in particular, cosine of alpha, I can get, well, we know how to find the angle between two vectors." + }, + { + "text": "So, if we have our normal vector n, we'll do n dot k, and we'll divide by length n length k. Well, length k is one." + }, + { + "text": "That's one easy." + }, + { + "text": "OK, so that's how we find the angle." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk16.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..18b8ca6f0e10e19b75db0dabf1ec37a110a6c671 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, now I'm going to say, well, delta s is going to be one over cosine alpha delta a." + }, + { + "text": "And, I can rewrite that as length of n divided by n dot k times delta a." + }, + { + "text": "Now, let's multiply that by the unit normal vector because what I'm multiplying by is not dS, but actually n dS." + }, + { + "text": "So, n delta s will be, I'm just going to multiply by n. Well, let's think for a second." + }, + { + "text": "What happens if I take the unit normal n, and I multiply it by the length of my other normal big N?" + }, + { + "text": "Well, I get big N again, right?" + }, + { + "text": "This is a normal vector of the same length as n, well, up to sine." + }, + { + "text": "But, actually, maybe I should." + }, + { + "text": "The only thing I don't know is whether this guy will be going in the same direction as big N or in the opposite direction." + }, + { + "text": "Say that, for example, my capital N has length, I don't know, length three, for example." + }, + { + "text": "The unit normal vector might be this guy, in which case, indeed, three times little n will be big N. Or, it might be this one, in which case, three times little n will be negative big N. But, up to sine, it's N. And then, I will have N over n dot k delta a." + }, + { + "text": "And so, the final formula, the one that actually we care about in case you don't really like my explanations of how we get there, is that N dS is plus or minus N over N dot k dx dy." + }, + { + "text": "That one is actually kind of useful, so let's box it." + }, + { + "text": "Now, just in case you are wondering, of course, if you didn't want to project to x, y, you would have maybe preferred to project to, say, the plane of a blackboard, yz." + }, + { + "text": "Well, you can do the same thing." + }, + { + "text": "To express N dS in terms of dy dz, you do the same argument." + }, + { + "text": "And simply, the only thing that changes is instead of using the vertical vector k, you use the normal vector i." + }, + { + "text": "So, you would be doing N over N dot i dy dz, and same thing." + }, + { + "text": "Just keep an open mind that this also works with other variables." + }, + { + "text": "But anyway, so that's how you can basically project the vector surface area element onto the x, y plane in a way." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk17.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..09fc575d766fb25a1c29c876fc0a0b29520a15d8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, so let's look at the special case just to see how this fits with stuff we've seen before." + }, + { + "text": "Let's do a special example where our surface is given by the equation z minus f of x, y equals zero." + }, + { + "text": "OK, that's a strange way to write the equation z equals f of x, y that we saw before." + }, + { + "text": "But now, it looks like, well, some function of x, y, z equals zero." + }, + { + "text": "So, let's try to use this new method." + }, + { + "text": "So, let's call this guy g of x, y, z." + }, + { + "text": "Well, so now let's look at the normal vector." + }, + { + "text": "The normal vector would be the gradient of g, we said." + }, + { + "text": "What's the gradient of this function?" + }, + { + "text": "So, gradient of g, well, partial g, partial x, that's just negative partial f, partial x. Gradient g, sorry, the y component, partial g, partial y is going to be negative f sub y." + }, + { + "text": "And, g sub z is just one." + }, + { + "text": "So now, if you take n over n dot k dx dy, well, it looks like that's going to be negative f sub x, negative f sub y, one divided by, well, what's n dot k?" + }, + { + "text": "If you do that with k, you'll get just one." + }, + { + "text": "So, I'm not going to write it, dx dy." + }, + { + "text": "See, that's, again, our favorite formula." + }, + { + "text": "So, this one is actually more general because you don't need to solve for z." + }, + { + "text": "But, if you can solve for z, then it's the same as before." + }, + { + "text": "OK, I think that's enough formulas for n dS." + }, + { + "text": "So, after spending a lot of time telling you how to compute surface integrals, now I'm going to try to tell you how to avoid computing them." + }, + { + "text": "And, that is called the divergence theorem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk18.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..0e5e56886a97cb7eb64b3c2de2f9c304bc0aed75 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And, we'll see the proof and everything and applications on Tuesday, but I want to at least state the theorem and see how it works in one example." + }, + { + "text": "It's also known as the Gauss grain theorem, or just the Gauss theorem depending on who you talk to." + }, + { + "text": "So, the grain here is the same grain as in Green's theorem, OK, because somehow that's a space version of Green's theorem." + }, + { + "text": "So, what does it say?" + }, + { + "text": "It says, so, this is the analog of grain for flux." + }, + { + "text": "What it says is if S is a closed surface, OK, so remember, it's the same as with Green's theorem, we need to have something that's completely enclosed." + }, + { + "text": "So, you have a surface, and there's somehow no gaps in it." + }, + { + "text": "There's no boundary to it." + }, + { + "text": "It's really completely enclosed." + }, + { + "text": "So, I'm choosing a region in space that I will call D. And, I need to choose my orientation." + }, + { + "text": "So, the orientation that will be chosen in this theorem is choosing the normal vector to point outwards." + }, + { + "text": "OK, so, n needs to be outwards." + }, + { + "text": "So, that's one part of the puzzle." + }, + { + "text": "The other part is a vector field." + }, + { + "text": "I need to have a vector field that is defined and differentiable everywhere in D. So, same restrictions as usual." + }, + { + "text": "Then, I don't have, actually, to compute the flux integral." + }, + { + "text": "The integral of F dot n dS of a closed surface S. I need to put a circle just to remind you it's got to be a closed surface." + }, + { + "text": "That's just notation to remind us, closed surface." + }, + { + "text": "I can replace that by the triple integral of the region inside of divergence of F dV." + }, + { + "text": "Now, I need to tell you what's the divergence of a 3D vector field." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk19.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..04bd556506c1a6a0e925cc2b3dd8ba3efad34e8f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, you'll see it's not much of a difference." + }, + { + "text": "In the 2D case, what you do is just, so, say that your vector field has components P, Q, and R. Then, you will take P sub x plus Q sub y plus R sub z. OK, so that's the definition." + }, + { + "text": "It's pretty easy to remember." + }, + { + "text": "You take the x component partial respect to x plus partial respect to y of the y component plus partial respect to z of the z component." + }, + { + "text": "OK, so, for example, last time we saw that the flux of the vector field zk for a sphere of radius a was four-thirds pi a cubed by computing the surface integral." + }, + { + "text": "Well, if we do it more efficiently now by Green's theorem, so we're going to use Green's theorem for this sphere." + }, + { + "text": "Because we're doing the whole sphere, it's fine." + }, + { + "text": "It's a closed surface." + }, + { + "text": "We couldn't do it for, say, a hemisphere or something like that." + }, + { + "text": "We need to, well, I mean, for the hemisphere, we'd need to add maybe the flat face at the bottom or something like that." + }, + { + "text": "So, Green's theorem says that our flux integral can be actually replaced by the triple integral of a solid ball of radius a of the divergence of zk dv." + }, + { + "text": "But now, what's the divergence of this field?" + }, + { + "text": "Well, so you have zero, zero, z." + }, + { + "text": "So, you get zero plus zero plus one." + }, + { + "text": "It looks like it will be one." + }, + { + "text": "So, if you do the triple integral of one dv, you will get just the volume of the region inside, which is four-thirds pi a cubed." + }, + { + "text": "And, so it was no accident." + }, + { + "text": "In fact, before that, we looked at also xi yj zk, and we found three times the volume." + }, + { + "text": "That's because the divergence of that field was actually three." + }, + { + "text": "So, very quickly, let me just say what this means physically." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk2.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..ff983a9074353a930a98538affafbeff51542106 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Here I have delta x, here I have delta y, and I am starting at some point xy." + }, + { + "text": "Now, above that I will have a parallelogram on my surface." + }, + { + "text": "I need to figure out this point here, the point where I start." + }, + { + "text": "I know what it is." + }, + { + "text": "It is just x, y, and z is f of x, y." + }, + { + "text": "Now, what I want to find actually is what are these two vectors, let's call them u and v that correspond to moving a bit in the x direction or in the y direction." + }, + { + "text": "And then u cross v will be, well, in terms of the magnitude of this guy will just be the little piece of surface area delta S. And, in terms of direction, it will be normal to the surface." + }, + { + "text": "Actually, I will get just delta S times my normal vector." + }, + { + "text": "Well, up to sign because depending on whether I do u cross v or v cross u, I might get the normal vector in the direction I want or in the direction I want." + }, + { + "text": "But we will take care of that later." + }, + { + "text": "Up to sign." + }, + { + "text": "OK, so let's find u and v. Actually, in case you have trouble with that small picture, then I have a better one here." + }, + { + "text": "Let's keep it just in case this one gets really too cluttered." + }, + { + "text": "It really represents the same thing." + }, + { + "text": "OK, so let's try to figure out these vectors u and v. So, the vector u starts at the point x, y, f of x, y." + }, + { + "text": "And it goes to, where is its head?" + }, + { + "text": "Well, I'll have moved x by delta x." + }, + { + "text": "So, x plus delta x. y doesn't change." + }, + { + "text": "And, of course, the z coordinate has to change." + }, + { + "text": "It becomes f of x plus delta x and y." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk20.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..f8f4327e9a02af262336ececd46d4897ee00c228 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk20.json @@ -0,0 +1,26 @@ +[ + { + "text": "Physically, see, this guy on the left is the total amount of stuff that goes out of the region per unit time." + }, + { + "text": "So, I want to figure out how much stuff comes out of there." + }, + { + "text": "What does the divergence mean?" + }, + { + "text": "The divergence means, well, it measures how much the flow is expanding things." + }, + { + "text": "It measures how much, I say probably when we understood 2D divergence, it measures the amount of sources or sinks that you have inside your fluid." + }, + { + "text": "So, now it becomes common sense." + }, + { + "text": "If you take a region of space, the total amount of water that flows out of it is the total amount of sources that you have in there minus the sinks." + }, + { + "text": "In spite of this common sense explanation, we are going to see actually how to prove this, and we'll see how it works and the hypothesis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk3.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..4dcc70fd37d899d05e9421b392306604a92d2817 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, how does f change if I change x a little bit?" + }, + { + "text": "Well, we've seen that it's given by the partial derivative f sub x." + }, + { + "text": "So, this is approximately equal to f of x, y plus delta x times f sub x at the given point x, y. I'm not going to add it because notation is already long enough." + }, + { + "text": "So, that means my vector u is, well, approximately, because I'm using this linear approximation, delta x, zero, and f sub x times delta x. OK, is that OK with everyone?" + }, + { + "text": "Good." + }, + { + "text": "Now, what about v?" + }, + { + "text": "Well, v works the same way." + }, + { + "text": "OK, so I'm not going to do all the details." + }, + { + "text": "When I move from here to here, well, x doesn't change, and y changes by delta y." + }, + { + "text": "So, x component, nothing happens." + }, + { + "text": "y component changes by delta y." + }, + { + "text": "What about the z component?" + }, + { + "text": "Well, f changes by f sub y times delta y." + }, + { + "text": "That's how f changes if I increase y by delta y. OK, so I have my two sides." + }, + { + "text": "Now, I can take the cross product." + }, + { + "text": "Well, maybe I will first, sorry, factor something out." + }, + { + "text": "See, I can rewrite this as one zero f sub x times delta x." + }, + { + "text": "And, this one I will rewrite as zero one f sub y delta y." + }, + { + "text": "And so, now the cross product, so n hat delta s up to sine is going to be u cross v. u cross v, well, so we'll have to do the cross product, and we'll have a delta x delta y coming out." + }, + { + "text": "OK, I'm just saving myself the trouble of writing a lot of delta x and delta y's." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk4.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..b0479e4d532bb2675791b9c29b5e2bff581132c7 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "But, if you prefer, you can just do directly this cross product there." + }, + { + "text": "OK, so let's compute this cross product." + }, + { + "text": "Well, the i component is zero minus f sub x." + }, + { + "text": "The y component is going to be, well, f sub y minus zero, but with a minus sign in front of everything, so negative f sub y." + }, + { + "text": "And, the z component will be just one times delta x delta y. OK, does that make sense for, yes, very good." + }, + { + "text": "And so, now, when we just take, we shrink this rectangle, we shrink delta x and delta y down, so that's how we get this formula for n ds equals negative fx negative fy one dx dy." + }, + { + "text": "Well, plus minus because it's up to us to choose whether we want to take the normal vector pointing up or down." + }, + { + "text": "So, see, if you take this convention, then the z component of n ds is positive." + }, + { + "text": "So, that corresponds to normal vector pointing up." + }, + { + "text": "If you take the opposite means, then the z component will be negative." + }, + { + "text": "That means your normal vector points down." + }, + { + "text": "OK, so this one is with n pointing up." + }, + { + "text": "I mean, when I say up, of course, it's still perpendicular to the surface." + }, + { + "text": "You know, if the surface really has a big slope, then it's not really going to go all that much up, but more up than down." + }, + { + "text": "OK, so that's how we get that formula." + }, + { + "text": "Any questions?" + }, + { + "text": "No?" + }, + { + "text": "OK, so that's a really useful formula." + }, + { + "text": "So, you don't really need to remember all the details of how we got it, but please remember that formula." + }, + { + "text": "Let's do an example, actually." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk5.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5b29a7df7e903bf04c8988e8f2436f298193a6d0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, let's say I want to find the flux of the vector field z times k. So, it's a vertical vector point of the paraboloid z equals x squared plus y squared that lives above the unit disk." + }, + { + "text": "OK, so what does that mean?" + }, + { + "text": "z equals x squared plus y squared, well, we've seen it many times." + }, + { + "text": "OK, it's this paraboloid above the unit disk means I only care about, I don't care about this infinite surface." + }, + { + "text": "I will actually stop when I hit a radius of one away from the z axis." + }, + { + "text": "And, so now I have my vector field, which is going to point overall up because, in fact, I'm at z times k. So, the more z is positive, the more your vector field goes up." + }, + { + "text": "Of course, if z were negative, then it would point down, but we live above." + }, + { + "text": "So, actually, a quick opinion poll." + }, + { + "text": "What do you think the flux should be?" + }, + { + "text": "Should it be positive, zero, negative?" + }, + { + "text": "We don't know." + }, + { + "text": "OK, so I see some I don't know." + }, + { + "text": "I see some negative, and I see some positive." + }, + { + "text": "So, of course, I didn't tell you which way I'm orienting my paraboloid." + }, + { + "text": "So, so far, both answers are correct." + }, + { + "text": "The only one that's probably not correct is zero because no matter which way you choose to orient it, you should get something." + }, + { + "text": "It's not looking like it will be zero." + }, + { + "text": "So, let's say that I'm going to do it with a normal pointing upwards." + }, + { + "text": "Second chance." + }, + { + "text": "OK, I see some people changing back and forth between one and two." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk6.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..7d51098b7f0239835af1dceb80b51f4a5d9a519e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, so let's draw a picture." + }, + { + "text": "Which one is pointing upwards?" + }, + { + "text": "Well, let's look at the bottom point, the normal vector pointing up." + }, + { + "text": "Here, we know what it means." + }, + { + "text": "It's this guy." + }, + { + "text": "And so, if you continue to follow your normal vector, see, they're actually pointing up and into the paraboloid." + }, + { + "text": "OK, and I claim that the answer should be positive because the vector field is crossing our paraboloid going upwards, going from the outside out and below to the inside and up side, so in the direction that we are counting positively." + }, + { + "text": "Well, we'll see how it turns out when we do the calculation." + }, + { + "text": "OK, so we have to compute the integral for flux." + }, + { + "text": "The one integral of a surface of F dot n dS is going to be, OK, so what are we going to do?" + }, + { + "text": "Well, F, we said, is 0, 0, z." + }, + { + "text": "What is n dS?" + }, + { + "text": "Well, let's use our brand new formula." + }, + { + "text": "So, it says negative F sub x, negative F sub y, one dx dy." + }, + { + "text": "What is little f in here?" + }, + { + "text": "It's x squared plus y squared, OK?" + }, + { + "text": "So, when we're using this formula, we need to know what little f stands for is whatever the formula is for z as a function of x and y." + }, + { + "text": "So, we take x squared plus y squared, and we take the partial derivatives with minus signs." + }, + { + "text": "We get negative 2x, negative 2y, and one dx dy." + }, + { + "text": "Well, of course, here it didn't really matter because we're going to dot them with zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk7.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..e3524a83e7e3f3457abdd39bd8eb8d13e8d49416 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, actually, even if we had made a mistake, we somehow wouldn't have had to pay the price, still." + }, + { + "text": "OK, so we'll end up with double integral on S of z dx dy." + }, + { + "text": "Now, what do we do with that?" + }, + { + "text": "Well, we have too many things." + }, + { + "text": "We need to get rid of z." + }, + { + "text": "So, let's use z equals x squared plus y squared once more." + }, + { + "text": "OK, so that becomes double integral of x squared plus y squared dx dy." + }, + { + "text": "And here, see, we're using the fact that we're only looking at things that are on the surface." + }, + { + "text": "It's not like in a triple integral, you could never do that because z, x, and y are independent." + }, + { + "text": "Here, they're related by the equation of a surface." + }, + { + "text": "Sorry if I sound like I'm ranting, but I know from experience this is where one of the most sticky and tricky points is, actually." + }, + { + "text": "OK, so now, how will we actually integrate that?" + }, + { + "text": "Well, now that we have just x and y, we should figure out what's the range for x and y?" + }, + { + "text": "Well, the range for x and y is going to be the shadow of our region." + }, + { + "text": "It's going to be this unit disk." + }, + { + "text": "OK, so let me just do that for now." + }, + { + "text": "And see here, this is finally where I've left the world of surface integrals to go back to a usual double integral." + }, + { + "text": "And now, I have to set it up." + }, + { + "text": "Well, I can do it this way with dx dy, but it looks like there's a smarter thing to do." + }, + { + "text": "OK, I'm going to use, actually, polar coordinates." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk8.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..4f11b1ba8efdf54e09dcbd2834634862a1b0e709 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, in fact, I'm going to say this is a double integral of r squared times r dr d theta." + }, + { + "text": "I'm on the unit disk, so r goes zero to one, theta goes zero to two pi." + }, + { + "text": "And, if you do the calculation, you'll find that this is going to be pi over two." + }, + { + "text": "OK, any questions about the example?" + }, + { + "text": "Yes?" + }, + { + "text": "OK, how do I get this negative 2x and negative 2y?" + }, + { + "text": "So, I want to use my formula for n ds." + }, + { + "text": "OK, my surface is given by the graph of a function." + }, + { + "text": "It's the graph of a function x squared plus y squared." + }, + { + "text": "So, I will use this formula that's up here." + }, + { + "text": "I will take the function x squared plus y squared, and I will take its partial derivatives." + }, + { + "text": "So, if I take the partial of f, so, f x squared plus y squared with respect to x, I get 2x." + }, + { + "text": "So, I put negative 2x, and then same thing, negative 2y, one dx dy, yes?" + }, + { + "text": "Which k hat?" + }, + { + "text": "Oh, you mean the vector field?" + }, + { + "text": "Well, so it's a different part of the story, OK?" + }, + { + "text": "So, whenever you do a surface integral for flux, you have two parts of the story." + }, + { + "text": "One is the vector field whose flux you're taking." + }, + { + "text": "The other one is the surface for which you will be taking flux." + }, + { + "text": "So, the vector field only comes as this f in the notation." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk9.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..9fa8c0e63e0fe3808781ed666ef10e0c042b38cb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_7_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And, everything else, the bounds of the double integral and the n ds, they all come from the surface that we are looking at." + }, + { + "text": "OK, so basically, in all of this calculation, this is coming from f equals zk." + }, + { + "text": "Everything else comes from the information paraboloid z equals x squared plus y squared above the disk." + }, + { + "text": "OK, so in particular, if we wanted to now find the flux of any other vector field for the same paraboloid, well, all we have to do is just replace this guy by whatever the new vector field is." + }, + { + "text": "We've learned how to set up flux integrals for this paraboloid." + }, + { + "text": "Not that you should remember this one by heart." + }, + { + "text": "I mean, there's many paraboloids in life and other surfaces, too, so it's better to remember the general method." + }, + { + "text": "OK, any other questions?" + }, + { + "text": "No?" + }, + { + "text": "OK, let's see more ways of tackling flux integrals." + }, + { + "text": "But, just to reassure you, at this point, we've seen the most important ones." + }, + { + "text": "You know, 90% of the problems that we'll be looking at, we can do with what we've seen so far last time and this time." + }, + { + "text": "But, let's look a little bit at a more general situation." + }, + { + "text": "Let's say that my surface is so complicated that I can't actually express z as a function of x and y." + }, + { + "text": "But, let's say that actually I know how to parametrize it." + }, + { + "text": "So, I have a parametric equation for my surface." + }, + { + "text": "That means I can express x, y, z in terms of any two parameter variables that might be relevant for me." + }, + { + "text": "So, if you want, this one here is the special case where you can parametrize things in terms of x and y as your two variables." + }, + { + "text": "So, how would you do it in the fully general case?" + }, + { + "text": "In a way, that will answer your question." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk0.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..de88ac001212dfb6b1de182c0b68e842d34b4657 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "Yesterday we have learned about flux and we have seen the first examples of how to set up and compute integrals for flux of a vector field for a surface." + }, + { + "text": "Remember the flux of a vector field F for a surface S is defined by taking the double integral on the surface of F dot n dS where n is the unit normal to the surface and dS is the area element on the surface." + }, + { + "text": "As we have seen, for various surfaces we have various formulas telling us what the normal vector is and what the area element becomes." + }, + { + "text": "For example, on spheres we typically integrate with respect to phi theta the latitude and longitude angles." + }, + { + "text": "On a horizontal plane we would just end up integrating dx dy and so on." + }, + { + "text": "At the end of the lecture we saw a formula." + }, + { + "text": "And a lot of you asked me how did we get it." + }, + { + "text": "Well, we didn't get it yet." + }, + { + "text": "We are going to try to explain where it comes from and why it works." + }, + { + "text": "The case we want to look at is the graph of a function." + }, + { + "text": "It is given by z equals some function in terms of x and y." + }, + { + "text": "Our surface is out here." + }, + { + "text": "z is a function of x and y." + }, + { + "text": "And x and y will range over some domain in the xy plane, namely the region that is the shadow of the surface on the xy plane." + }, + { + "text": "I said that we will have a formula for n ds which will end up being plus minus, minus f sub x minus f sub y one dx dy so that we will set up and evaluate the integral in terms of x and y." + }, + { + "text": "Replacing every time we see z we will replace it by f of xy, whatever the formula for f of xy is." + }, + { + "text": "By the way, if we look at a very easy case where this is just a horizontal plane, so z equals constant, the function is just a constant, well, the partial derivatives become just zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk1.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..83a60f55a64abf7ed3e632f2c0caa0700c633561 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "You get zero, zero, one dx dy." + }, + { + "text": "That is what you would expect for a horizontal plane just from common sense." + }, + { + "text": "This is more interesting, of course, if a function is more interesting." + }, + { + "text": "How do we get that?" + }, + { + "text": "Where does this come from?" + }, + { + "text": "We need to figure out for a small piece of our surface what will be n delta S if you want." + }, + { + "text": "Let's say that we take a small rectangle in here corresponding to the sides delta x and delta y." + }, + { + "text": "And we look at the piece of surface that is above that." + }, + { + "text": "Well, the question we have now is what is the area of this little piece of surface and what is its normal vector?" + }, + { + "text": "Observe this little piece up here." + }, + { + "text": "If it is small enough it will look like a parallelogram." + }, + { + "text": "It might be slightly curvy, but roughly it looks like a parallelogram in space." + }, + { + "text": "And so we have seen how to find the area of a parallelogram in space using cross product." + }, + { + "text": "If we can figure out what are the vectors for this side and that side, then taking the cross product will give us, and taking the magnitude of the cross product will give us the area." + }, + { + "text": "Moreover, the cross product also gives us the normal direction." + }, + { + "text": "In fact, the cross product gives us two in one." + }, + { + "text": "It gives us the normal direction and the area element." + }, + { + "text": "And that is why I said that we will have an easy formula for N dS while N and dS taken separately are more complicated because you would have to actually take the length of a direction of this guy." + }, + { + "text": "Let's carry out this problem." + }, + { + "text": "Let's say I am going to look at a small piece of the xy plane." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk10.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..80ecc53d0640b10ed2fa61964d985138e15dd4dc --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "I think one of you, I forgot, asked yesterday, how would I do it in general?" + }, + { + "text": "Is there a formula like m dx plus n dy?" + }, + { + "text": "Well, that's going to be the formula." + }, + { + "text": "And, you'll see it's a little bit too complicated." + }, + { + "text": "So, the really useful ones are actually the special ones." + }, + { + "text": "So, let's say that we are given a parametric description of a surface S. So, that means we can describe S by formulas saying x is some function of two parameter variables." + }, + { + "text": "I'm going to call them u and v. I hope you don't mind." + }, + { + "text": "You can call them t1 and t2." + }, + { + "text": "You can call them whatever you want." + }, + { + "text": "OK, so one of the basic properties of a surface is because I have only two independent directions to move on, I should be able to express x, y, and z in terms of two variables." + }, + { + "text": "So, now let's say that I know how to do that." + }, + { + "text": "Or, maybe I should instead think of it in terms of a position vector if that helps you." + }, + { + "text": "The position vector, so that's just the vector with components x, y, z is given as a function of u and v. OK, so it works like a parametric curve, but with two parameters." + }, + { + "text": "So, now, how will we actually set up a flux integral on such a surface?" + }, + { + "text": "Well, because we are locating the flux in terms of u and v, we will end up with an integral du dv." + }, + { + "text": "So, we need to figure out how to express n ds in terms of du and dv." + }, + { + "text": "OK, so n ds should be something du dv." + }, + { + "text": "How do we do that?" + }, + { + "text": "Well, we can use the same method that we've actually used over here." + }, + { + "text": "Because if you think for a second, here we used, of course, a rectangle in the x, y plane, and we lifted it to a parallelogram and so on." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk11.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..61d1728a009aa03829fde534d602caecd77a30aa --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "But, more generally, you can think, what happens if I change u by delta u, keeping v constant, or the other way around?" + }, + { + "text": "You will get some sort of mesh grid on your surface, and you will look at a little parallelogram that's an elementary piece of that mesh and figure out what is its area and normal vector." + }, + { + "text": "Well, that will again be given by the cross product of the two sides." + }, + { + "text": "OK, so let's think a little bit about what happens when I move a little bit on my surface." + }, + { + "text": "So, I'm taking a grid on my surface given by the u and v directions." + }, + { + "text": "And, if I take a piece of that corresponding to small changes, delta u and delta v, what's going to be going on here?" + }, + { + "text": "Well, I have to deal with two vectors, one corresponding to changing u, the other one corresponding to changing v. If I change u, how does my point change?" + }, + { + "text": "Well, that's given by the derivative of this with respect to u. OK, so this vector here I will call, so the sides are given by, let me say, partial r over partial u times delta u." + }, + { + "text": "And, if you prefer, maybe I should write it as partial x over partial u delta u partial y." + }, + { + "text": "Well, it's just too boring to write, and so on." + }, + { + "text": "OK, it means just, you know, if I change u a little bit, keep v constant, then how x changes is given by partial x over partial u times delta u." + }, + { + "text": "Same thing with y, same thing with z." + }, + { + "text": "And, I'm just using vector notation to do it this way." + }, + { + "text": "That's the analog of when I said delta r for line integrals along a curve, vector delta r is the velocity vector dr over dt times delta t. OK, now if I look at the other side, OK, so, sorry, so let me start again." + }, + { + "text": "I ran out of space." + }, + { + "text": "One side is partial r partial u times delta u, and the other one would be partial r partial v times delta v because that's how the position of your point changes if you just change u or v and not the other one." + }, + { + "text": "So, now, to find the surface element together with a normal vector, I would just take the cross product between these guys." + }, + { + "text": "So, if you prefer, that's the cross product of partial r partial u with partial r partial v delta u delta v. And so, N dS is this cross product times du dv up to sine." + }, + { + "text": "I mean, also here." + }, + { + "text": "Depends on which choice I make for my normal vector, of course." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk12.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..4edd218fc4799dfc682e96577ad40cb5df2f17ab --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, now, if you, that, of course, is a slightly confusing equation to think of." + }, + { + "text": "So, a good exercise, if you want to really understand what's going on, try this in two good examples to look at." + }, + { + "text": "One good example to look at is the previous one." + }, + { + "text": "What is it?" + }, + { + "text": "It's when u and v are just x and y. OK, so the parametric equations are just x equals x, y equals y, and z is f of x, y." + }, + { + "text": "You should end up with the same formula that we had over there." + }, + { + "text": "And, you should see why because, see, both of them are given by a cross product." + }, + { + "text": "The other case you can look at, just to convince yourselves that it's true, so we don't need to do that because we've seen the formula before." + }, + { + "text": "But, in the case of a sphere, we've seen the formula for N and for dS separately." + }, + { + "text": "So, we know what N dS are in terms of d phi d theta." + }, + { + "text": "Well, you could parametrize a sphere in terms of phi and theta." + }, + { + "text": "Namely, the formulas would be x equals a sine phi cosine theta, y equals a sine phi sine theta, z equals a cosine phi." + }, + { + "text": "The formulas for spherical coordinates setting rho equals a." + }, + { + "text": "So, that's a parametric equation for the sphere." + }, + { + "text": "And then, if you try to use this formula here, you should end up with the same things we've already seen for N dS, just with a lot more pain to actually get there because your cross product is going to be a bit complicated." + }, + { + "text": "But, we're seeing all of these formulas, they all fit together." + }, + { + "text": "Somehow, it's always the same question, just we have different angles of attack on this general problem." + }, + { + "text": "OK, questions?" + }, + { + "text": "No?" + }, + { + "text": "OK, let's look at yet another last way of finding N dS." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk13.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..11d368b6015bc6b9cacbc394c8b399183b51e276 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then, I promise we'll switch to something else because I can feel that you're getting a bit overwhelmed by all these formulas for N dS." + }, + { + "text": "So, OK, so what happens very often is we don't actually know how to parametrize our surface." + }, + { + "text": "Maybe we don't know how to solve for z as a function of x and y, but our surface is given by some equation." + }, + { + "text": "And so, what that means is actually maybe what we know is not really these kinds of formulas, but maybe we know a normal vector." + }, + { + "text": "And, I'm going to call this one capital N because I don't even need it to be a unit vector, you will see." + }, + { + "text": "It can be a normal vector of the surface S. So, why would we ever know a normal vector?" + }, + { + "text": "Well, for example, if our surface is a plane, say it's a slanted plane given by some equation, Ax plus By plus Cz equals D. Well, you know the normal vector." + }, + { + "text": "It's A, B, C. Of course, you could solve for z and then go back to that case, which is why I said that that one is really useful." + }, + { + "text": "But, you can also just stay with a normal vector." + }, + { + "text": "Why else would you know a normal vector?" + }, + { + "text": "Well, let's say that you know an equation that's of a form g of x, y, z equals zero." + }, + { + "text": "Well, then you know that the gradient of g is perpendicular to the level surface." + }, + { + "text": "OK, so let me just give you two examples." + }, + { + "text": "If you have a plane, Ax plus By plus Cz equals D, then the normal vector would just be A, B, C. If you have a surface S given by an equation, g of x, y, z equals zero, then you can take the normal vector to be the gradient of g. We've seen that the gradient is perpendicular to the level surface." + }, + { + "text": "Now, of course, we don't necessarily have to follow what's going to come because if we could solve for z then we might be better off doing what we did over there." + }, + { + "text": "But, let's say that we want to do it this way." + }, + { + "text": "So, then what can we do?" + }, + { + "text": "Well, I'm going to give you a little bit of information about NDS." + }, + { + "text": "So, OK, so let's start by thinking about a slanted plane." + }, + { + "text": "OK, so let's say that my surface is just a slanted plane." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk14.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..8f6af2d2aa3b3d17432ec3b26b0606675c6a7d16 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, my normal vector would be maybe somewhere here." + }, + { + "text": "And, let's say that I'm going to try, you know, I need, of course, some handle on how to set up my integral." + }, + { + "text": "So, maybe I'm going to express this in terms of x and y. OK, so I have my coordinates, and I'll try to use x and y." + }, + { + "text": "So, then I would like to relate delta s, ds, to the area in the xy plane." + }, + { + "text": "So, that means, you know, I want maybe to look at the projection of this guy onto a horizontal plane." + }, + { + "text": "Let's squish it horizontally." + }, + { + "text": "So, then you have here another area." + }, + { + "text": "OK, so the guy on the slanted plane, let's call that delta s, and let's call this guy down here delta a." + }, + { + "text": "So, the question, and, you know, delta a would become ultimately maybe delta x, delta y, or something like that." + }, + { + "text": "The question is, how do we find the conversion rate between these two areas?" + }, + { + "text": "See, I mean, they're not the same." + }, + { + "text": "Visually, I hope it's clear to you that if my plane is actually horizontal, then, of course, they're the same." + }, + { + "text": "But, the more slanted it becomes, the more delta a becomes smaller than delta s, right?" + }, + { + "text": "I mean, if you buy, you know, if you buy land, and it's on the side of a cliff, well, whether you look at it on a map, or whether you look at it on the actual cliff, the area is going to be very different." + }, + { + "text": "I'm not sure if that's a wise thing to do if you want to build a house there, but I've been told you can get really cheap land." + }, + { + "text": "OK, so anyway, OK, so delta s versus delta a depends on how slanted things are." + }, + { + "text": "And, let's try to make that more precise by looking at the angle that our plane makes with the horizontal direction." + }, + { + "text": "OK, so let's call this angle alpha, the angle that our plane makes with the horizontal direction." + }, + { + "text": "See, it's all coming together now." + }, + { + "text": "The first unit about cross products, normal vectors, and so on is actually useful now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk15.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..e90009e6248e5d6a50885b9d3130bf4050ef960c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, I claim that the surface element is related to the area in the plane by delta a equals delta s times the cosine of alpha." + }, + { + "text": "Why is that?" + }, + { + "text": "Well, let's look at this small rectangle with one horizontal side and one slanted side." + }, + { + "text": "Well, when you project, this side doesn't change." + }, + { + "text": "But, this side gets shortened by a factor of cosine alpha." + }, + { + "text": "Whatever this length was, this length here is that one times cosine alpha." + }, + { + "text": "So, that's why the area gets shrunk by cosine alpha." + }, + { + "text": "In one direction, nothing happens." + }, + { + "text": "In the other direction, you squish by cosine alpha." + }, + { + "text": "So, what that means is that, well, OK, so we'll have to deal with this." + }, + { + "text": "And, of course, the one we'll care about actually is delta s expressed in terms of delta a." + }, + { + "text": "But, what are we going to do with this cosine?" + }, + { + "text": "It's not very convenient to have a cosine left in here." + }, + { + "text": "So, remember, the angle between two planes, it's the same thing as the angle between the normal vectors." + }, + { + "text": "So, if you want to see this angle alpha elsewhere, what you can do is you can just take the vertical direction." + }, + { + "text": "Let's take k. Then, here we have our angle alpha again." + }, + { + "text": "So, in particular, cosine of alpha, I can get, well, we know how to find the angle between two vectors." + }, + { + "text": "So, if we have our normal vector n, we'll do n dot k, and we'll divide by length n length k. Well, length k is one." + }, + { + "text": "That's one easy." + }, + { + "text": "OK, so that's how we find the angle." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk16.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..18b8ca6f0e10e19b75db0dabf1ec37a110a6c671 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, now I'm going to say, well, delta s is going to be one over cosine alpha delta a." + }, + { + "text": "And, I can rewrite that as length of n divided by n dot k times delta a." + }, + { + "text": "Now, let's multiply that by the unit normal vector because what I'm multiplying by is not dS, but actually n dS." + }, + { + "text": "So, n delta s will be, I'm just going to multiply by n. Well, let's think for a second." + }, + { + "text": "What happens if I take the unit normal n, and I multiply it by the length of my other normal big N?" + }, + { + "text": "Well, I get big N again, right?" + }, + { + "text": "This is a normal vector of the same length as n, well, up to sine." + }, + { + "text": "But, actually, maybe I should." + }, + { + "text": "The only thing I don't know is whether this guy will be going in the same direction as big N or in the opposite direction." + }, + { + "text": "Say that, for example, my capital N has length, I don't know, length three, for example." + }, + { + "text": "The unit normal vector might be this guy, in which case, indeed, three times little n will be big N. Or, it might be this one, in which case, three times little n will be negative big N. But, up to sine, it's N. And then, I will have N over n dot k delta a." + }, + { + "text": "And so, the final formula, the one that actually we care about in case you don't really like my explanations of how we get there, is that N dS is plus or minus N over N dot k dx dy." + }, + { + "text": "That one is actually kind of useful, so let's box it." + }, + { + "text": "Now, just in case you are wondering, of course, if you didn't want to project to x, y, you would have maybe preferred to project to, say, the plane of a blackboard, yz." + }, + { + "text": "Well, you can do the same thing." + }, + { + "text": "To express N dS in terms of dy dz, you do the same argument." + }, + { + "text": "And simply, the only thing that changes is instead of using the vertical vector k, you use the normal vector i." + }, + { + "text": "So, you would be doing N over N dot i dy dz, and same thing." + }, + { + "text": "Just keep an open mind that this also works with other variables." + }, + { + "text": "But anyway, so that's how you can basically project the vector surface area element onto the x, y plane in a way." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk17.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..09fc575d766fb25a1c29c876fc0a0b29520a15d8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, so let's look at the special case just to see how this fits with stuff we've seen before." + }, + { + "text": "Let's do a special example where our surface is given by the equation z minus f of x, y equals zero." + }, + { + "text": "OK, that's a strange way to write the equation z equals f of x, y that we saw before." + }, + { + "text": "But now, it looks like, well, some function of x, y, z equals zero." + }, + { + "text": "So, let's try to use this new method." + }, + { + "text": "So, let's call this guy g of x, y, z." + }, + { + "text": "Well, so now let's look at the normal vector." + }, + { + "text": "The normal vector would be the gradient of g, we said." + }, + { + "text": "What's the gradient of this function?" + }, + { + "text": "So, gradient of g, well, partial g, partial x, that's just negative partial f, partial x. Gradient g, sorry, the y component, partial g, partial y is going to be negative f sub y." + }, + { + "text": "And, g sub z is just one." + }, + { + "text": "So now, if you take n over n dot k dx dy, well, it looks like that's going to be negative f sub x, negative f sub y, one divided by, well, what's n dot k?" + }, + { + "text": "If you do that with k, you'll get just one." + }, + { + "text": "So, I'm not going to write it, dx dy." + }, + { + "text": "See, that's, again, our favorite formula." + }, + { + "text": "So, this one is actually more general because you don't need to solve for z." + }, + { + "text": "But, if you can solve for z, then it's the same as before." + }, + { + "text": "OK, I think that's enough formulas for n dS." + }, + { + "text": "So, after spending a lot of time telling you how to compute surface integrals, now I'm going to try to tell you how to avoid computing them." + }, + { + "text": "And, that is called the divergence theorem." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk18.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..0e5e56886a97cb7eb64b3c2de2f9c304bc0aed75 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And, we'll see the proof and everything and applications on Tuesday, but I want to at least state the theorem and see how it works in one example." + }, + { + "text": "It's also known as the Gauss grain theorem, or just the Gauss theorem depending on who you talk to." + }, + { + "text": "So, the grain here is the same grain as in Green's theorem, OK, because somehow that's a space version of Green's theorem." + }, + { + "text": "So, what does it say?" + }, + { + "text": "It says, so, this is the analog of grain for flux." + }, + { + "text": "What it says is if S is a closed surface, OK, so remember, it's the same as with Green's theorem, we need to have something that's completely enclosed." + }, + { + "text": "So, you have a surface, and there's somehow no gaps in it." + }, + { + "text": "There's no boundary to it." + }, + { + "text": "It's really completely enclosed." + }, + { + "text": "So, I'm choosing a region in space that I will call D. And, I need to choose my orientation." + }, + { + "text": "So, the orientation that will be chosen in this theorem is choosing the normal vector to point outwards." + }, + { + "text": "OK, so, n needs to be outwards." + }, + { + "text": "So, that's one part of the puzzle." + }, + { + "text": "The other part is a vector field." + }, + { + "text": "I need to have a vector field that is defined and differentiable everywhere in D. So, same restrictions as usual." + }, + { + "text": "Then, I don't have, actually, to compute the flux integral." + }, + { + "text": "The integral of F dot n dS of a closed surface S. I need to put a circle just to remind you it's got to be a closed surface." + }, + { + "text": "That's just notation to remind us, closed surface." + }, + { + "text": "I can replace that by the triple integral of the region inside of divergence of F dV." + }, + { + "text": "Now, I need to tell you what's the divergence of a 3D vector field." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk19.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..04bd556506c1a6a0e925cc2b3dd8ba3efad34e8f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, you'll see it's not much of a difference." + }, + { + "text": "In the 2D case, what you do is just, so, say that your vector field has components P, Q, and R. Then, you will take P sub x plus Q sub y plus R sub z. OK, so that's the definition." + }, + { + "text": "It's pretty easy to remember." + }, + { + "text": "You take the x component partial respect to x plus partial respect to y of the y component plus partial respect to z of the z component." + }, + { + "text": "OK, so, for example, last time we saw that the flux of the vector field zk for a sphere of radius a was four-thirds pi a cubed by computing the surface integral." + }, + { + "text": "Well, if we do it more efficiently now by Green's theorem, so we're going to use Green's theorem for this sphere." + }, + { + "text": "Because we're doing the whole sphere, it's fine." + }, + { + "text": "It's a closed surface." + }, + { + "text": "We couldn't do it for, say, a hemisphere or something like that." + }, + { + "text": "We need to, well, I mean, for the hemisphere, we'd need to add maybe the flat face at the bottom or something like that." + }, + { + "text": "So, Green's theorem says that our flux integral can be actually replaced by the triple integral of a solid ball of radius a of the divergence of zk dv." + }, + { + "text": "But now, what's the divergence of this field?" + }, + { + "text": "Well, so you have zero, zero, z." + }, + { + "text": "So, you get zero plus zero plus one." + }, + { + "text": "It looks like it will be one." + }, + { + "text": "So, if you do the triple integral of one dv, you will get just the volume of the region inside, which is four-thirds pi a cubed." + }, + { + "text": "And, so it was no accident." + }, + { + "text": "In fact, before that, we looked at also xi yj zk, and we found three times the volume." + }, + { + "text": "That's because the divergence of that field was actually three." + }, + { + "text": "So, very quickly, let me just say what this means physically." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk2.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..ff983a9074353a930a98538affafbeff51542106 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Here I have delta x, here I have delta y, and I am starting at some point xy." + }, + { + "text": "Now, above that I will have a parallelogram on my surface." + }, + { + "text": "I need to figure out this point here, the point where I start." + }, + { + "text": "I know what it is." + }, + { + "text": "It is just x, y, and z is f of x, y." + }, + { + "text": "Now, what I want to find actually is what are these two vectors, let's call them u and v that correspond to moving a bit in the x direction or in the y direction." + }, + { + "text": "And then u cross v will be, well, in terms of the magnitude of this guy will just be the little piece of surface area delta S. And, in terms of direction, it will be normal to the surface." + }, + { + "text": "Actually, I will get just delta S times my normal vector." + }, + { + "text": "Well, up to sign because depending on whether I do u cross v or v cross u, I might get the normal vector in the direction I want or in the direction I want." + }, + { + "text": "But we will take care of that later." + }, + { + "text": "Up to sign." + }, + { + "text": "OK, so let's find u and v. Actually, in case you have trouble with that small picture, then I have a better one here." + }, + { + "text": "Let's keep it just in case this one gets really too cluttered." + }, + { + "text": "It really represents the same thing." + }, + { + "text": "OK, so let's try to figure out these vectors u and v. So, the vector u starts at the point x, y, f of x, y." + }, + { + "text": "And it goes to, where is its head?" + }, + { + "text": "Well, I'll have moved x by delta x." + }, + { + "text": "So, x plus delta x. y doesn't change." + }, + { + "text": "And, of course, the z coordinate has to change." + }, + { + "text": "It becomes f of x plus delta x and y." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk20.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..f8f4327e9a02af262336ececd46d4897ee00c228 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk20.json @@ -0,0 +1,26 @@ +[ + { + "text": "Physically, see, this guy on the left is the total amount of stuff that goes out of the region per unit time." + }, + { + "text": "So, I want to figure out how much stuff comes out of there." + }, + { + "text": "What does the divergence mean?" + }, + { + "text": "The divergence means, well, it measures how much the flow is expanding things." + }, + { + "text": "It measures how much, I say probably when we understood 2D divergence, it measures the amount of sources or sinks that you have inside your fluid." + }, + { + "text": "So, now it becomes common sense." + }, + { + "text": "If you take a region of space, the total amount of water that flows out of it is the total amount of sources that you have in there minus the sinks." + }, + { + "text": "In spite of this common sense explanation, we are going to see actually how to prove this, and we'll see how it works and the hypothesis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk3.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..4dcc70fd37d899d05e9421b392306604a92d2817 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, how does f change if I change x a little bit?" + }, + { + "text": "Well, we've seen that it's given by the partial derivative f sub x." + }, + { + "text": "So, this is approximately equal to f of x, y plus delta x times f sub x at the given point x, y. I'm not going to add it because notation is already long enough." + }, + { + "text": "So, that means my vector u is, well, approximately, because I'm using this linear approximation, delta x, zero, and f sub x times delta x. OK, is that OK with everyone?" + }, + { + "text": "Good." + }, + { + "text": "Now, what about v?" + }, + { + "text": "Well, v works the same way." + }, + { + "text": "OK, so I'm not going to do all the details." + }, + { + "text": "When I move from here to here, well, x doesn't change, and y changes by delta y." + }, + { + "text": "So, x component, nothing happens." + }, + { + "text": "y component changes by delta y." + }, + { + "text": "What about the z component?" + }, + { + "text": "Well, f changes by f sub y times delta y." + }, + { + "text": "That's how f changes if I increase y by delta y. OK, so I have my two sides." + }, + { + "text": "Now, I can take the cross product." + }, + { + "text": "Well, maybe I will first, sorry, factor something out." + }, + { + "text": "See, I can rewrite this as one zero f sub x times delta x." + }, + { + "text": "And, this one I will rewrite as zero one f sub y delta y." + }, + { + "text": "And so, now the cross product, so n hat delta s up to sine is going to be u cross v. u cross v, well, so we'll have to do the cross product, and we'll have a delta x delta y coming out." + }, + { + "text": "OK, I'm just saving myself the trouble of writing a lot of delta x and delta y's." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk4.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..b0479e4d532bb2675791b9c29b5e2bff581132c7 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "But, if you prefer, you can just do directly this cross product there." + }, + { + "text": "OK, so let's compute this cross product." + }, + { + "text": "Well, the i component is zero minus f sub x." + }, + { + "text": "The y component is going to be, well, f sub y minus zero, but with a minus sign in front of everything, so negative f sub y." + }, + { + "text": "And, the z component will be just one times delta x delta y. OK, does that make sense for, yes, very good." + }, + { + "text": "And so, now, when we just take, we shrink this rectangle, we shrink delta x and delta y down, so that's how we get this formula for n ds equals negative fx negative fy one dx dy." + }, + { + "text": "Well, plus minus because it's up to us to choose whether we want to take the normal vector pointing up or down." + }, + { + "text": "So, see, if you take this convention, then the z component of n ds is positive." + }, + { + "text": "So, that corresponds to normal vector pointing up." + }, + { + "text": "If you take the opposite means, then the z component will be negative." + }, + { + "text": "That means your normal vector points down." + }, + { + "text": "OK, so this one is with n pointing up." + }, + { + "text": "I mean, when I say up, of course, it's still perpendicular to the surface." + }, + { + "text": "You know, if the surface really has a big slope, then it's not really going to go all that much up, but more up than down." + }, + { + "text": "OK, so that's how we get that formula." + }, + { + "text": "Any questions?" + }, + { + "text": "No?" + }, + { + "text": "OK, so that's a really useful formula." + }, + { + "text": "So, you don't really need to remember all the details of how we got it, but please remember that formula." + }, + { + "text": "Let's do an example, actually." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk5.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..5b29a7df7e903bf04c8988e8f2436f298193a6d0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, let's say I want to find the flux of the vector field z times k. So, it's a vertical vector point of the paraboloid z equals x squared plus y squared that lives above the unit disk." + }, + { + "text": "OK, so what does that mean?" + }, + { + "text": "z equals x squared plus y squared, well, we've seen it many times." + }, + { + "text": "OK, it's this paraboloid above the unit disk means I only care about, I don't care about this infinite surface." + }, + { + "text": "I will actually stop when I hit a radius of one away from the z axis." + }, + { + "text": "And, so now I have my vector field, which is going to point overall up because, in fact, I'm at z times k. So, the more z is positive, the more your vector field goes up." + }, + { + "text": "Of course, if z were negative, then it would point down, but we live above." + }, + { + "text": "So, actually, a quick opinion poll." + }, + { + "text": "What do you think the flux should be?" + }, + { + "text": "Should it be positive, zero, negative?" + }, + { + "text": "We don't know." + }, + { + "text": "OK, so I see some I don't know." + }, + { + "text": "I see some negative, and I see some positive." + }, + { + "text": "So, of course, I didn't tell you which way I'm orienting my paraboloid." + }, + { + "text": "So, so far, both answers are correct." + }, + { + "text": "The only one that's probably not correct is zero because no matter which way you choose to orient it, you should get something." + }, + { + "text": "It's not looking like it will be zero." + }, + { + "text": "So, let's say that I'm going to do it with a normal pointing upwards." + }, + { + "text": "Second chance." + }, + { + "text": "OK, I see some people changing back and forth between one and two." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk6.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..7d51098b7f0239835af1dceb80b51f4a5d9a519e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, so let's draw a picture." + }, + { + "text": "Which one is pointing upwards?" + }, + { + "text": "Well, let's look at the bottom point, the normal vector pointing up." + }, + { + "text": "Here, we know what it means." + }, + { + "text": "It's this guy." + }, + { + "text": "And so, if you continue to follow your normal vector, see, they're actually pointing up and into the paraboloid." + }, + { + "text": "OK, and I claim that the answer should be positive because the vector field is crossing our paraboloid going upwards, going from the outside out and below to the inside and up side, so in the direction that we are counting positively." + }, + { + "text": "Well, we'll see how it turns out when we do the calculation." + }, + { + "text": "OK, so we have to compute the integral for flux." + }, + { + "text": "The one integral of a surface of F dot n dS is going to be, OK, so what are we going to do?" + }, + { + "text": "Well, F, we said, is 0, 0, z." + }, + { + "text": "What is n dS?" + }, + { + "text": "Well, let's use our brand new formula." + }, + { + "text": "So, it says negative F sub x, negative F sub y, one dx dy." + }, + { + "text": "What is little f in here?" + }, + { + "text": "It's x squared plus y squared, OK?" + }, + { + "text": "So, when we're using this formula, we need to know what little f stands for is whatever the formula is for z as a function of x and y." + }, + { + "text": "So, we take x squared plus y squared, and we take the partial derivatives with minus signs." + }, + { + "text": "We get negative 2x, negative 2y, and one dx dy." + }, + { + "text": "Well, of course, here it didn't really matter because we're going to dot them with zero." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk7.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..e3524a83e7e3f3457abdd39bd8eb8d13e8d49416 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, actually, even if we had made a mistake, we somehow wouldn't have had to pay the price, still." + }, + { + "text": "OK, so we'll end up with double integral on S of z dx dy." + }, + { + "text": "Now, what do we do with that?" + }, + { + "text": "Well, we have too many things." + }, + { + "text": "We need to get rid of z." + }, + { + "text": "So, let's use z equals x squared plus y squared once more." + }, + { + "text": "OK, so that becomes double integral of x squared plus y squared dx dy." + }, + { + "text": "And here, see, we're using the fact that we're only looking at things that are on the surface." + }, + { + "text": "It's not like in a triple integral, you could never do that because z, x, and y are independent." + }, + { + "text": "Here, they're related by the equation of a surface." + }, + { + "text": "Sorry if I sound like I'm ranting, but I know from experience this is where one of the most sticky and tricky points is, actually." + }, + { + "text": "OK, so now, how will we actually integrate that?" + }, + { + "text": "Well, now that we have just x and y, we should figure out what's the range for x and y?" + }, + { + "text": "Well, the range for x and y is going to be the shadow of our region." + }, + { + "text": "It's going to be this unit disk." + }, + { + "text": "OK, so let me just do that for now." + }, + { + "text": "And see here, this is finally where I've left the world of surface integrals to go back to a usual double integral." + }, + { + "text": "And now, I have to set it up." + }, + { + "text": "Well, I can do it this way with dx dy, but it looks like there's a smarter thing to do." + }, + { + "text": "OK, I'm going to use, actually, polar coordinates." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk8.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..4f11b1ba8efdf54e09dcbd2834634862a1b0e709 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "So, in fact, I'm going to say this is a double integral of r squared times r dr d theta." + }, + { + "text": "I'm on the unit disk, so r goes zero to one, theta goes zero to two pi." + }, + { + "text": "And, if you do the calculation, you'll find that this is going to be pi over two." + }, + { + "text": "OK, any questions about the example?" + }, + { + "text": "Yes?" + }, + { + "text": "OK, how do I get this negative 2x and negative 2y?" + }, + { + "text": "So, I want to use my formula for n ds." + }, + { + "text": "OK, my surface is given by the graph of a function." + }, + { + "text": "It's the graph of a function x squared plus y squared." + }, + { + "text": "So, I will use this formula that's up here." + }, + { + "text": "I will take the function x squared plus y squared, and I will take its partial derivatives." + }, + { + "text": "So, if I take the partial of f, so, f x squared plus y squared with respect to x, I get 2x." + }, + { + "text": "So, I put negative 2x, and then same thing, negative 2y, one dx dy, yes?" + }, + { + "text": "Which k hat?" + }, + { + "text": "Oh, you mean the vector field?" + }, + { + "text": "Well, so it's a different part of the story, OK?" + }, + { + "text": "So, whenever you do a surface integral for flux, you have two parts of the story." + }, + { + "text": "One is the vector field whose flux you're taking." + }, + { + "text": "The other one is the surface for which you will be taking flux." + }, + { + "text": "So, the vector field only comes as this f in the notation." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk9.json b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..9fa8c0e63e0fe3808781ed666ef10e0c042b38cb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/WfEQabCGAqI_8_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And, everything else, the bounds of the double integral and the n ds, they all come from the surface that we are looking at." + }, + { + "text": "OK, so basically, in all of this calculation, this is coming from f equals zk." + }, + { + "text": "Everything else comes from the information paraboloid z equals x squared plus y squared above the disk." + }, + { + "text": "OK, so in particular, if we wanted to now find the flux of any other vector field for the same paraboloid, well, all we have to do is just replace this guy by whatever the new vector field is." + }, + { + "text": "We've learned how to set up flux integrals for this paraboloid." + }, + { + "text": "Not that you should remember this one by heart." + }, + { + "text": "I mean, there's many paraboloids in life and other surfaces, too, so it's better to remember the general method." + }, + { + "text": "OK, any other questions?" + }, + { + "text": "No?" + }, + { + "text": "OK, let's see more ways of tackling flux integrals." + }, + { + "text": "But, just to reassure you, at this point, we've seen the most important ones." + }, + { + "text": "You know, 90% of the problems that we'll be looking at, we can do with what we've seen so far last time and this time." + }, + { + "text": "But, let's look a little bit at a more general situation." + }, + { + "text": "Let's say that my surface is so complicated that I can't actually express z as a function of x and y." + }, + { + "text": "But, let's say that actually I know how to parametrize it." + }, + { + "text": "So, I have a parametric equation for my surface." + }, + { + "text": "That means I can express x, y, z in terms of any two parameter variables that might be relevant for me." + }, + { + "text": "So, if you want, this one here is the special case where you can parametrize things in terms of x and y as your two variables." + }, + { + "text": "So, how would you do it in the fully general case?" + }, + { + "text": "In a way, that will answer your question." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk0.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d4554873825c6719ec24d2e3b27b154cb3857640 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "Chapter is a natural capstone chapter for this entire course." + }, + { + "text": "We'll see some of the things we've seen during maximum likelihood and some of the things we've seen during linear regression, some of the things we've seen in terms of the basic modeling that we've had before." + }, + { + "text": "We're not going to go back to much inference questions." + }, + { + "text": "It's really going to be about modeling." + }, + { + "text": "And in a way, generalized linear models, as the word says, are just a generalization of linear models." + }, + { + "text": "And they're actually extremely useful." + }, + { + "text": "They're often forgotten about, and people just jump onto machine learning and sophisticated techniques." + }, + { + "text": "But those things do the job quite well." + }, + { + "text": "So let's see in what sense they are a generalization of the linear model." + }, + { + "text": "So remember, the linear model looked like this." + }, + { + "text": "We said that y was equal to x transpose beta plus epsilon." + }, + { + "text": "That was our linear regression model." + }, + { + "text": "And another way to say this is that if I, let's assume that those were, say, Gaussian with mean 0 and identity covariance matrix, then another way to say this is that the conditional distribution of y given x is a Gaussian with mean x transpose beta and variance, well, we had a sigma square, which I will forget as usual, x transpose beta and then sigma square." + }, + { + "text": "So here, we just assumed that, so what is regression?" + }, + { + "text": "It's just saying I'm trying to explain y as a function of x given x. I'm assuming a distribution for the y." + }, + { + "text": "And this x is just going to be here to help me model what the mean of this Gaussian is." + }, + { + "text": "I mean, I could have something crazy." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk1.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..2c2e721380f9d4710c30835403ae73ceebf39538 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "I could have something that looks like y given x is n0 x transpose beta." + }, + { + "text": "And then this guy could be some other thing, which looks like, I don't know, some x transpose gamma squared times, I don't know, x x transpose plus identity, some crazy thing that depends on x here." + }, + { + "text": "And we deliberately assume that all the thing that depends on x shows up in the mean." + }, + { + "text": "And so what I have here is that y given x is a Gaussian with a mean that depends on x and covariance matrix sigma square identity." + }, + { + "text": "Now, the linear model assumed a very specific form for the mean." + }, + { + "text": "It said, I want the mean to be equal to x transpose beta, which, remember, was the sum from, say, j equals 1 to p of beta j xj, where the xj's are the coordinates of x." + }, + { + "text": "But I could do something also more complicated." + }, + { + "text": "I could have something that looks like, instead, replace this by, I don't know, sum of beta j log of x to the j divided by x to the j squared, or something like this." + }, + { + "text": "I could do this as well." + }, + { + "text": "So there's two things that we've assumed." + }, + { + "text": "The first one is that when I look at the conditional distribution of y given x, x affects only the mean." + }, + { + "text": "I also assumed that it was Gaussian, and that it affects only the mean." + }, + { + "text": "And the mean is affected in a very specific way, which is linear in x." + }, + { + "text": "So this is essentially the things we're going to try to relax." + }, + { + "text": "So the first thing that we assume, the fact that y was Gaussian and had only its mean that depended on x, is what's called the random component." + }, + { + "text": "It just says that the response variables sort of make sense to assume that they're Gaussian." + }, + { + "text": "And everything was essentially captured." + }, + { + "text": "So there's this property of Gaussians that if you tell me if the variance is known, all you need to tell me to understand exactly what the distribution of a Gaussian is, all you need to tell me is its expected value." + }, + { + "text": "So that's this mu of x." + }, + { + "text": "And the second thing is that we had this link that says, well, I need to find a way to use my x's to explain this mu." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk10.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..6a481ea5cb5adb97b455c8bc5c53385e58a31448 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Right?" + }, + { + "text": "I have two parameters." + }, + { + "text": "So what I do here is that I say, well, first, let me transform mu in such a way that I can hope to see something that's linear." + }, + { + "text": "So if I transform mu, I'm going to have log of mu, which is log of this thing." + }, + { + "text": "Right?" + }, + { + "text": "So log of mu of x is equal to log of gamma plus log of exponential delta x, which is delta x. OK?" + }, + { + "text": "And now, this thing is actually linear in x." + }, + { + "text": "So I have that this guy is my first beta 1." + }, + { + "text": "And so that's beta 1 times 1." + }, + { + "text": "And this guy is beta 2 times, sorry, let's say beta 0 times 1." + }, + { + "text": "And this guy is beta 1 times x. OK?" + }, + { + "text": "So that looks like a linear model." + }, + { + "text": "I just have to change my parameters." + }, + { + "text": "My parameters, beta 1 becomes the log of gamma, and beta 2 becomes delta itself." + }, + { + "text": "And the reason why we do this is because, well, the way we put those gamma and those delta was just so that we have some parametrization." + }, + { + "text": "It just so happens that if we want this to be linear, we need to just change the parametrization itself." + }, + { + "text": "This is going to have some effects." + }, + { + "text": "We know that it's going to have some effect in the Fisher information." + }, + { + "text": "It's going to have a bunch of effect to change those things." + }, + { + "text": "But that's what needs to be done to have a generalized linear model." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk11.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b87248456f36363ec8012cc422267e73498f0d65 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, here, the function that I took to turn it into something that's linear is simple." + }, + { + "text": "It came directly from some natural thing it would do here, which is taking the log." + }, + { + "text": "And so the function g, the link that I take, is called the log link, very creatively." + }, + { + "text": "And it's just the function that I apply to mu so that I see something that's linear and that looks like this." + }, + { + "text": "OK?" + }, + { + "text": "So now, this only tells me how to deal with the link function." + }, + { + "text": "But I still have to deal with 0.1." + }, + { + "text": "And this, again, is just some modeling." + }, + { + "text": "Given some data, some random data, what distribution do you choose to explain the randomness?" + }, + { + "text": "And this, I mean, unless there's no choice, it's just a matter of practice." + }, + { + "text": "I mean, why would it be Gaussian and not doubly exponential?" + }, + { + "text": "There's matters of convenience that come into this." + }, + { + "text": "And there's just matter of experience that come into this." + }, + { + "text": "I remember when you chat with engineers, they have a very good notion of what the distribution should be." + }, + { + "text": "They have Weibull distributions." + }, + { + "text": "They do optics and things like this." + }, + { + "text": "So there's some distributions that just come up." + }, + { + "text": "But sometimes, you just have to work." + }, + { + "text": "Now, here, what do we have?" + }, + { + "text": "The thing we're trying to measure y, as we said, so mu is the conditional expectation of y given x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk12.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..af95e1917c846d9d478b143cf28493ff3dd4d7d1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "But y is the number of new cases, right?" + }, + { + "text": "Well, it's a number of." + }, + { + "text": "And the first thing you should think of when you think about number of, if it were bounded above, you would think binomial, baby." + }, + { + "text": "But here, it's just a number." + }, + { + "text": "So you think Poisson." + }, + { + "text": "That's how insurers think." + }, + { + "text": "I have a number of claims per year." + }, + { + "text": "This is a Poisson distribution." + }, + { + "text": "And hopefully, they can model the conditional distribution of the number of claims given everything that they actually ask you in this survey that I hear you now fill in 15 minutes." + }, + { + "text": "All right, so now you have this Poisson distribution." + }, + { + "text": "And that's just a modeling assumption." + }, + { + "text": "There's no particular reason why you should do this, except that that might be a good idea." + }, + { + "text": "And the expected value of your Poisson has to be this mu i at time i." + }, + { + "text": "Any question about this slide?" + }, + { + "text": "So let's switch to another example." + }, + { + "text": "Another example is the so-called prey capture rate." + }, + { + "text": "So here, what you're interested in is the rate capture of prey's Yi for a given prey." + }, + { + "text": "And you have Xi, which is your explanation." + }, + { + "text": "And this is just the density of prey." + }, + { + "text": "So you're trying to explain the rate of captures of preys given the density of the prey." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk13.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..82b4fda8d85deb20289b741cbb4d1b501793ba9c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so you need to find some sort of relationship between the two." + }, + { + "text": "And here again, you talk to experts." + }, + { + "text": "And what they tell you is that, well, it's going to be increasing." + }, + { + "text": "Animals, like predators, are going to just eat more if there's more preys." + }, + { + "text": "But at some point, they're just going to level off because they're just going to be completely full." + }, + { + "text": "And they're going to stop capturing those preys." + }, + { + "text": "And you're just going to have some phenomenon that looks like this." + }, + { + "text": "So here is a curve that sort of makes sense." + }, + { + "text": "As your capture rate goes from 0 to 1, you're increasing." + }, + { + "text": "And then you see you have this concave function that says that at some point, it levels off." + }, + { + "text": "So here, one way I could, I mean, there's again many ways I could just model a function that looks like this." + }, + { + "text": "But a simple one that has only two parameters is this one, where mu i is just this function of Xi, where I have some parameter alpha here and some parameter h here." + }, + { + "text": "So there's clearly, so this function, there's one that essentially tells you." + }, + { + "text": "So this thing starts at 0 for sure." + }, + { + "text": "And essentially, alpha tells you how sharp this thing is." + }, + { + "text": "And h tells you at which point you end here." + }, + { + "text": "It's not exactly what those values are equal to, but it tells you this." + }, + { + "text": "So simple." + }, + { + "text": "And well, no, OK, sorry." + }, + { + "text": "That's actually alpha, which is the maximum capture rate." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk14.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..be9a8b2fcbc0f8c0b1e49f0850eea5b9ab306080 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "And h represents the prey density at which the capture rate is." + }, + { + "text": "So that's the half time." + }, + { + "text": "So there's actual values for this." + }, + { + "text": "So now I have this function." + }, + { + "text": "It's certainly not a function." + }, + { + "text": "I don't see it as a function of x." + }, + { + "text": "So I need to find something that looks like a function of x. OK?" + }, + { + "text": "So now here, there's no log." + }, + { + "text": "There's no, well, I could actually take a log here." + }, + { + "text": "But I would have log of x and log of x plus h. So that would be weird." + }, + { + "text": "So what we propose to do here is to look, rather than looking at mu i, we look at 1 over mu i." + }, + { + "text": "And so since your function was mu i, when you take 1 over mu i, you get h plus xi divided by alpha xi, which is h over alpha times 1 over xi plus 1 over alpha." + }, + { + "text": "And now if I am willing to make this transformation of variables and say, actually, my x, whether it's the density of prey or the inverse density of prey, it really doesn't matter." + }, + { + "text": "I can always make the transformation when the data comes." + }, + { + "text": "Then I'm actually just going to think of this as being some linear function, beta 0 plus beta 1, which is this guy, times 1 over xi." + }, + { + "text": "And now my new variable becomes 1 over xi." + }, + { + "text": "And now it's linear." + }, + { + "text": "And the transformation I had to take was this 1 over x, which is called the reciprocal link." + }, + { + "text": "You can probably guess what the exponential link is going to be and things like this." + }, + { + "text": "So we'll talk about other links that have slightly less obvious names." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk15.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..5d2ed9123f0b6a47840cca2ce477712ca74abf5e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, again, modeling." + }, + { + "text": "So this was the random component." + }, + { + "text": "This was the easy part." + }, + { + "text": "Now I need to just pour in some domain knowledge about how do I think this function, this y, which is the rate of capture of preys." + }, + { + "text": "I want to understand how this thing is actually changing." + }, + { + "text": "What is the randomness of the thing around its mean?" + }, + { + "text": "And something that comes from this textbook, the standard deviation of capture rate might be approximately proportional to the mean rate." + }, + { + "text": "You need to find a distribution that actually has this property." + }, + { + "text": "And it turns out that this happens for gamma distribution." + }, + { + "text": "In gamma distributions, just like, say, for Poisson distribution, for Poisson, the variance and the mean are of the same order." + }, + { + "text": "Here is the standard deviation that's of the same order as the mean for gammas." + }, + { + "text": "And it's a positive distribution as well." + }, + { + "text": "So here is a candidate." + }, + { + "text": "Now, since we're sort of constrained to work under the exponential family of distributions, then you can just go through your list and just decide which one works best for you." + }, + { + "text": "All right, third example." + }, + { + "text": "So here we have binary response." + }, + { + "text": "Here, essentially, the binary response variable indicates the presence or absence of post-covariative deforming for kyphosis on children." + }, + { + "text": "And here, rather than having one covariate, which was before, in the first example, was time, in the second example was the density, here there's three covariates." + }, + { + "text": "So you measure on children." + }, + { + "text": "The first one is age of the child." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk16.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..ef9ff3f87e1e355af4391eaee6e902d9ab157079 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "The second one is the number of vertebrae involved in the operation." + }, + { + "text": "And the third one is the start of the range, so where it is on the spine." + }, + { + "text": "So the response variable here is, did it work or not?" + }, + { + "text": "I mean, that's very simple." + }, + { + "text": "And so here, it's nice, because the random component is the easiest one." + }, + { + "text": "As I said, any random variable that takes only two outcomes must be a Bernoulli." + }, + { + "text": "So that's nice." + }, + { + "text": "There's no modeling going on here." + }, + { + "text": "So you know that y given x is going to be Bernoulli, but of course, all your efforts are going to try to understand what the conditional mean of your Bernoulli, what the conditional probability of being 1 is going to be." + }, + { + "text": "And so in particular, so I'm just here." + }, + { + "text": "I'm spelling it out before we close those examples." + }, + { + "text": "I cannot say that mu of x is x transpose beta for exactly this picture that I drew for you here." + }, + { + "text": "There's just no way here." + }, + { + "text": "The goal of doing this is certainly to be able to extrapolate for yet unseen children whether this is something that we should be doing, and maybe the range of x's is actually going to be slightly out." + }, + { + "text": "And so OK, I don't want to say that I have a negative probability of outcome or a positive one, sorry, or a 1 that's lower than 1, so I need to make this transformation." + }, + { + "text": "What I need to do is to transform mu, which is we know only a number, all we know is a number between 0 and 1, and we need to transform it in such a way that it maps the entire real line, or reciprocally to say that, or inversely I should say, that f of x transpose beta should be a number between 0 and 1." + }, + { + "text": "I need to find a function that takes any real number and maps it into 0 and 1, and we'll see that again, but you have an army of functions that do that for you." + }, + { + "text": "What are those functions?" + }, + { + "text": "I'm sorry?" + }, + { + "text": "AUDIENCE MEMBER 2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk17.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..e618b05cddff9ee23141a82d1f3c33242aeb2d21 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "Trait function." + }, + { + "text": "PHILIPPE RIGOLLET." + }, + { + "text": "Trait?" + }, + { + "text": "AUDIENCE MEMBER 2." + }, + { + "text": "Trait, trait, trait." + }, + { + "text": "PHILIPPE RIGOLLET." + }, + { + "text": "Oh." + }, + { + "text": "Yeah, I want them to be invertible, right?" + }, + { + "text": "AUDIENCE MEMBER 2." + }, + { + "text": "Yeah." + }, + { + "text": "PHILIPPE RIGOLLET." + }, + { + "text": "Yeah." + }, + { + "text": "AUDIENCE MEMBER 2." + }, + { + "text": "Longest trait." + }, + { + "text": "PHILIPPE RIGOLLET." + }, + { + "text": "I have an army of function." + }, + { + "text": "I'm not asking for one soldier in this army." + }, + { + "text": "I want the name of this army." + }, + { + "text": "AUDIENCE MEMBER 2." + }, + { + "text": "They're invertible." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk18.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..f58b1220495ab9dfac97d370ddda29476838a3fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "PHILIPPE RIGOLLET." + }, + { + "text": "Well, they're not really invertible either, right?" + }, + { + "text": "So they're actually in stats textbooks, because remember, statisticians don't know how to integrate functions, but they know how to turn a function into a Gaussian integral, so we know it integrates to 1, and things like this." + }, + { + "text": "Same thing here." + }, + { + "text": "We don't know how to build functions that are invertible and map the entire real line to 0, 1, but there's all the cumulative distribution functions that do that for us." + }, + { + "text": "So I can use any of those guys, and that's what I'm going to be doing, actually." + }, + { + "text": "All right, so just to recap what I just said as we were speaking, so a normal linear model is not appropriate for those examples if only because the response variable is not necessarily Gaussian." + }, + { + "text": "So and also because the linear model has to be, the mean has to be transformed before I can actually apply a linear model for all these plausible nonlinear models that I actually came up with." + }, + { + "text": "So the family we're going to go for is the exponential family of distributions, and we're going to be able to show, so one of the nice part of this is to actually compute maximum likelihood estimators for those, right?" + }, + { + "text": "In the linear model, maximum like, in the Gaussian linear model, maximum likelihood was as nice as it gets, right?" + }, + { + "text": "This actually was the least squares estimator." + }, + { + "text": "We had a closed form, x transpose x inverse x transpose y, and that was it." + }, + { + "text": "We had to just take one derivative." + }, + { + "text": "Here, we're going to have a generally concave likelihood." + }, + { + "text": "We're not going to be able to actually solve this thing directly in closed form unless it's Gaussian, but we will have, we'll see actually how this is not just a black box optimization of a concave function." + }, + { + "text": "We have a lot of properties of this concave function, and we will be able to show some iterative algorithms." + }, + { + "text": "We'll basically see how, when you open the box of convex optimization, you will actually be able to see how things work and actually implement it using least squares." + }, + { + "text": "So each iteration of this iterative algorithm will essentially be a least square, so that's actually quite huge." + }, + { + "text": "It's also very demonstrative of statisticians being pretty ingenious so that they don't have to call in some statistical software, but just can repeatedly call their least squares oracle within a statistical software." + }, + { + "text": "OK, so what is the exponential family?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk19.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..fbe7abc54d0348d4353fcfa16b5a9639e71fe8f7 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "I promised you the exponential family." + }, + { + "text": "Before we go into this, let me just tell you something about exponential families, and what's the only thing that differentiates an exponential family from all possible distributions?" + }, + { + "text": "An exponential family has two parameters, and those are not really parameters, but there's the theta parameter of my distribution." + }, + { + "text": "So it's going to be indexed by some parameter." + }, + { + "text": "Here, I'm only talking about the distribution of, say, some random variable or some random vector." + }, + { + "text": "So here, in this slide, you see that the parameter theta that indexes those distribution is k-dimensional, and the space of the x's that I'm looking at, so that should really be y." + }, + { + "text": "So what I'm going to plug in here is the conditional distribution of y given x, and theta is going to depend on x." + }, + { + "text": "But this really is the y." + }, + { + "text": "That's the distribution of the response variable." + }, + { + "text": "And so this is on q." + }, + { + "text": "So I'm going to assume that y is q-dimensional." + }, + { + "text": "Clearly, soon q is going to be equal to 1, but I can define those things generally." + }, + { + "text": "So I have this." + }, + { + "text": "I have to tell you what this looks like, and let's assume that this is a probability density function." + }, + { + "text": "So this notation, the fact that I just put my theta in subscript, is just for me to remember that this is the variable that indicates the random variable, and this is just the parameter." + }, + { + "text": "But I could just write it as a function of theta and x." + }, + { + "text": "This is just going to be, if you were in multivariable calc, you would have two parameters, theta and x, and you would need to give me a function." + }, + { + "text": "Now, think of x and theta as being one-dimensional at this point." + }, + { + "text": "Think of all the functions that can be depending on theta and x." + }, + { + "text": "There's many of them." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk2.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..4dfa619a62a8cb9f51581c665c6269ca8bec9c50 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the link was exactly mu of x was equal to x transpose beta." + }, + { + "text": "OK?" + }, + { + "text": "Now, we are talking about generalized linear models." + }, + { + "text": "So this part here, where mu of x is of the form, the way I want my beta, my x, to show up is linear." + }, + { + "text": "This will never be questioned." + }, + { + "text": "In principle, I could add a third point, which is just question this part, the fact that mu of x is x transpose beta." + }, + { + "text": "I could have some more complicated nonlinear function of x." + }, + { + "text": "And I will never do that, because we're talking about generalized linear model." + }, + { + "text": "The only thing with generalized are the random component, the conditional distribution of y given x, and the link that just says, well, once you actually tell me that the only thing I need to figure out is the mean, I'm just going to slap it exactly this x transpose beta thing without any transformation of x transpose beta." + }, + { + "text": "OK?" + }, + { + "text": "So those are the two things." + }, + { + "text": "It will become clearer what I mean." + }, + { + "text": "This sounds like a tautology, but let's just see how we could extend that." + }, + { + "text": "So what we're going to do in generalized linear models, so when I talk about GLMs, the first thing I'm going to do with my x is turn it into some x transpose beta." + }, + { + "text": "And that's just the L part." + }, + { + "text": "This I'm not going to be able to change." + }, + { + "text": "That's the way it works." + }, + { + "text": "I'm not going to do anything nonlinear." + }, + { + "text": "But the two things I'm going to change is this random component, which is that y, which used to be some Gaussian with mean mu of x variance sigma squared." + }, + { + "text": "So y given x, sorry." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk20.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..58f979f5cd191f971fd907b961bc1542b84ea77e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And in particular, there's many ways theta and x can interact." + }, + { + "text": "What the exponential family does for you is that it restricts the way these things can actually interact with each other." + }, + { + "text": "It's essentially saying the following." + }, + { + "text": "It's saying this is going to be of the form exponential." + }, + { + "text": "So this exponential is really not much, because I could put a log next to it." + }, + { + "text": "But what I want is that the way theta and x interact has to be of the form theta times x in an exponential." + }, + { + "text": "So that's one of the ways you can think of them interacting." + }, + { + "text": "You just take the product of the two." + }, + { + "text": "Now, clearly, this is not a very rich family." + }, + { + "text": "So what I'm allowing myself is to just slap on some terms that depend only on theta and depend only on x." + }, + { + "text": "So let's just call this thing f of x g of theta." + }, + { + "text": "So here, I've restricted the way theta and x can interact." + }, + { + "text": "So I have something that depends only on x, something that depends only on theta." + }, + { + "text": "And here, I have this very specific interaction." + }, + { + "text": "And that's all that exponential families are doing for you." + }, + { + "text": "So if we go back to this slide, this is much more general." + }, + { + "text": "If I want to go from theta and x in r to theta and x theta in r to theta in rk and x in rq, I cannot take the product of theta and x. I cannot even take the inner product between theta and x, because they're not even of compatible dimensions." + }, + { + "text": "But what I can do is to first map my theta into something and map my x into something so that I actually end up having the same dimensions." + }, + { + "text": "And then I can take the inner product." + }, + { + "text": "That's the natural generalization of this simple product." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk21.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..36059f58796657121c5302bfc6135335368066e7 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what I have is if I want to go from theta to x, what I'm going to first do is I'm going to take theta eta of theta." + }, + { + "text": "So let's say eta 1 of theta to eta k of theta." + }, + { + "text": "And then I'm going to actually take x becomes t1 of x all the way to tk of x." + }, + { + "text": "And what I'm going to do is take the inner product." + }, + { + "text": "So let's call this eta." + }, + { + "text": "And let's call this t. And I'm going to take the inner product of eta and t, which is just the sum from j equal 1 to k of eta j of theta times tj of x." + }, + { + "text": "So that's just a way to say I want this simple interaction." + }, + { + "text": "But in higher dimension, the simplest way I can actually make those things happen is just by taking inner product." + }, + { + "text": "And so now what it's telling me is that the distribution, I want the exponential times something that depends only on theta and something that depends only on x." + }, + { + "text": "And so what it tells me is that when I'm going to take p of theta x, it's just going to be something which is exponential times the sum from j equal 1 to k of eta j theta tj of x." + }, + { + "text": "And then I'm going to have a function that depends only." + }, + { + "text": "So let me write it for now like c of theta." + }, + { + "text": "And then a function that depends only on x." + }, + { + "text": "Let me call it h of x." + }, + { + "text": "And for convenience, there's no particular reason why I do that." + }, + { + "text": "I'm taking this function c of theta, and I'm just actually pushing it in there." + }, + { + "text": "So I can write c of theta as exponential minus log of 1 over c of theta." + }, + { + "text": "And now I have exponential times exponential." + }, + { + "text": "So I push it in, and this thing actually looks like exponential sum from j equal 1 to k of eta j theta tj of x minus log 1 over c of theta times h of x." + }, + { + "text": "And this thing here, log 1 over c of theta, I call actually b of theta." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk22.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..9ce5d204be5cf62e2aafd3d850c84f7dd1eafe0a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because c, I called it c, but I can actually directly call it this guy b, and I don't actually care about c itself." + }, + { + "text": "Now, why don't I put back also h of x in there?" + }, + { + "text": "Because h of x is really here to just, how to put it?" + }, + { + "text": "h of x and b of theta don't play the same role." + }, + { + "text": "b of theta, in many ways, is a normalizing constant." + }, + { + "text": "I want this density to integrate to 1." + }, + { + "text": "If I did not have this guy, I'm not guaranteed that this thing integrates to 1." + }, + { + "text": "But by tweaking this function, b of theta or c of theta, their equivalent, I can actually ensure that this thing integrates to 1." + }, + { + "text": "So b of theta is just a normalizing constant." + }, + { + "text": "h of x is something that's going to be funny for us." + }, + { + "text": "It's going to be something that allows us to be able to treat both discrete and continuous variables within the framework of exponential families." + }, + { + "text": "So for those that are familiar with this, this is essentially saying that h of x is really just a change of measure." + }, + { + "text": "When I actually look at the density of p of theta, this is with respect to some measure, the fact that I just multiply by a function of x just means that I'm not looking that this guy here, without h of theta, is not the density with respect to the original measure, but it's the density with respect to the distribution that has h as a density." + }, + { + "text": "That's all I'm saying." + }, + { + "text": "So I can first transform my x's and then take the density with respect to that." + }, + { + "text": "If you don't want to think about densities or measures, you don't have to." + }, + { + "text": "This is just the way." + }, + { + "text": "This is just the definition." + }, + { + "text": "Is there any question about this definition?" + }, + { + "text": "So it looks complicated, but it's actually essentially the simplest way you could think about it." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk23.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..5eeb518a9d5894bf1eeb94d4fb8a4b81ffe8e5df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "You want to be able to have x and theta interact, and you just say, I want the interaction to be of the form exponential x times theta." + }, + { + "text": "And if they're higher dimensions, I'm going to take the exponential of the function of x inner product for the function of theta." + }, + { + "text": "So I claimed since the beginning that the Gaussian was such an example, so let's just do it." + }, + { + "text": "Is the interaction between theta and x in a Gaussian of the form inner product?" + }, + { + "text": "And the answer is yes." + }, + { + "text": "Actually, whether I know or not what the variance is." + }, + { + "text": "So let's start for the case where I actually do not know what the variance is." + }, + { + "text": "So here I have x is n mu sigma squared." + }, + { + "text": "This is all one dimensional." + }, + { + "text": "And here I'm going to assume that my parameter is both mu and sigma squared." + }, + { + "text": "So what I need to do is to have some function of mu, some function of sigma squared, and take the inner product of some function of x and some other function of x." + }, + { + "text": "So I want to show that p theta of x is what?" + }, + { + "text": "Well, it's 1 over square root sigma 2 pi exponential minus x minus mu squared over 2 sigma squared." + }, + { + "text": "That's just my Gaussian density." + }, + { + "text": "And I want to say that this thing here, so clearly the exponential shows up already." + }, + { + "text": "I want to show that this is something that looks like eta 1 of mu sigma squared." + }, + { + "text": "So I have only two of those guys, so I'm going to need only two etas." + }, + { + "text": "So I want it to be eta 1 of mu and sigma times t1 of x plus eta 2 mu sigma squared times t2 of x." + }, + { + "text": "So I want to have something like that that shows up, and the only things that are left, I want them to depend either only on theta or only on x." + }, + { + "text": "So to find that out, we just need to expand." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk24.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b20dd7faa1dfbea7dd48300ad6e2453578b83cb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I'm going to first put everything into my exponential and expand this guy." + }, + { + "text": "So the first term here is going to be minus x squared over 2 sigma squared." + }, + { + "text": "The second term is going to be minus mu squared over 2 sigma squared." + }, + { + "text": "And then the cross term is going to be plus x mu divided by sigma squared." + }, + { + "text": "And then I'm going to put this guy here, so I have a minus log sigma root 2 pi." + }, + { + "text": "OK, so this term here contains an interaction between x and the parameters." + }, + { + "text": "This term here contains an interaction between x and the parameters." + }, + { + "text": "So let me try to write them in a way that I want." + }, + { + "text": "This guy only depends on the parameters." + }, + { + "text": "This guy only depends on the parameter." + }, + { + "text": "So I'm going to rearrange things." + }, + { + "text": "And so I claim that this is of the form x squared." + }, + { + "text": "Well, let's say, who's getting the minus?" + }, + { + "text": "Eta, OK." + }, + { + "text": "So it's x squared times minus 1 over 2 sigma squared plus x times mu over sigma squared." + }, + { + "text": "So that's this term here." + }, + { + "text": "That's this term here." + }, + { + "text": "Now I need to get this guy here." + }, + { + "text": "And that's minus." + }, + { + "text": "So I'm going to write it like this, minus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk25.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..732b958a14a1b7707a0b37d4bdd107f5be9f2ac5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now I have mu squared over 2 sigma squared plus log sigma square root 2 pi." + }, + { + "text": "OK?" + }, + { + "text": "And now this thing is definitely of the form t1 of x times, did I call them the right way or not?" + }, + { + "text": "Of course not." + }, + { + "text": "OK, so that's going to be t2 of x times eta 2 of x, eta 2 of theta." + }, + { + "text": "This guy is going to be t1 of x times eta 1 of theta." + }, + { + "text": "So just a function of theta times a function of x, just a function of theta times a function of x." + }, + { + "text": "And the way I combine this is just by summing them." + }, + { + "text": "And this is going to be my b of theta." + }, + { + "text": "What is h of x?" + }, + { + "text": "1." + }, + { + "text": "There's one thing I can actually play with." + }, + { + "text": "And this is something you're going to have some free choices." + }, + { + "text": "This is not actually completely determined here." + }, + { + "text": "Is that, for example, when I write the log sigma square root 2 pi, this is just log of sigma plus log square root 2 pi." + }, + { + "text": "So I have two choices here." + }, + { + "text": "Either my b becomes this guy, or so either I have b of theta, which is mu squared over 2 sigma squared plus log sigma square root 2 pi, and h of x is equal to 1." + }, + { + "text": "Or I have that b of theta is mu squared over 2 sigma squared plus log sigma, and h of x is equal to what?" + }, + { + "text": "1." + }, + { + "text": "Well, I can just push this guy out." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk26.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..7128910e23875de6e208c059db4ddc05705e82cc --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk26.json @@ -0,0 +1,62 @@ +[ + { + "text": "I can push it out of the exponential." + }, + { + "text": "And so it's just square root of 2 pi, which is a function of x, technically." + }, + { + "text": "I mean, it's a constant function of x, but it's a function of x." + }, + { + "text": "So you can see that it's not completely clear how you're going to do the trade-off." + }, + { + "text": "So the constant terms can go either in b or in h. But why bother with tracking down b and h when you can actually stuff everything into one and just call h 1 and call it a day?" + }, + { + "text": "So you can just forget about h. It's 1, and think about the rest." + }, + { + "text": "h won't matter, actually, for estimation purposes or anything like this." + }, + { + "text": "All right, so that's basically everything that's written." + }, + { + "text": "When sigma square is known, what's happening is that this guy here is no longer a function of theta, right?" + }, + { + "text": "Agreed?" + }, + { + "text": "This is no longer a parameter." + }, + { + "text": "When sigma square is known, then theta is equal to mu only." + }, + { + "text": "There's no sigma square going on." + }, + { + "text": "So everything that depends on sigma square can be thought as a constant, think 1." + }, + { + "text": "So in particular, this term here does not belong in the interaction between x and theta." + }, + { + "text": "It belongs to h, right?" + }, + { + "text": "So if sigma is known, then this guy is only a function of h of x." + }, + { + "text": "So h of x becomes exponential x squared minus x squared over 2 sigma squared, right?" + }, + { + "text": "That's just a function of x." + }, + { + "text": "Is that clear?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk27.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk27.json new file mode 100644 index 0000000000000000000000000000000000000000..ad5c52c96917f6811fd97391867d647b8dd5d280 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk27.json @@ -0,0 +1,62 @@ +[ + { + "text": "So if you complete this computation, what you're going to get is that your new one parameter thing is that p theta p theta x is not equal to exponential x times mu over sigma squared minus, well, it's still the same thing, and then you have your h of x that comes out, x squared over 2 sigma squared." + }, + { + "text": "So that's my h of x." + }, + { + "text": "That's still my b of theta." + }, + { + "text": "And this is my t1 of x, and this is my eta 1 of theta." + }, + { + "text": "And remember, theta is just equal to mu in this case." + }, + { + "text": "So if I ask you, prove that this distribution belonged to an exponential family, you just have to work it out." + }, + { + "text": "Typically, it's expanding what's in the exponential and just write it in this term and identify all the components, right?" + }, + { + "text": "So here, notice those guys don't even get an index anymore because there's just one of them." + }, + { + "text": "So I wrote theta 1 and t1, but it's really just eta and t. Oh, sorry." + }, + { + "text": "This guy also goes." + }, + { + "text": "This is also a constant, right?" + }, + { + "text": "So it can actually just put sigma divided by sigma squared over 2 pi." + }, + { + "text": "So h of x is what, actually?" + }, + { + "text": "AUDIENCE MEMBER 2." + }, + { + "text": "It's the density of?" + }, + { + "text": "AUDIENCE MEMBER 3." + }, + { + "text": "It's centered." + }, + { + "text": "It's not standard." + }, + { + "text": "It's centered." + }, + { + "text": "It has mean 0, but it has variance sigma squared, right?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk28.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk28.json new file mode 100644 index 0000000000000000000000000000000000000000..e6cd0af7c6a6f3a84bb21243aed86ecb61bec60e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk28.json @@ -0,0 +1,62 @@ +[ + { + "text": "But it's the density of a Gaussian." + }, + { + "text": "And this is what I meant when I said h of x is really just telling you with respect to which distribution, which measure you're taking the density." + }, + { + "text": "And so this thing here is really telling you the density of my Gaussian with mean mu is equal to this with respect to a centered Gaussian is this guy, right?" + }, + { + "text": "That's what it means." + }, + { + "text": "If this thing ends up being a density, it just means that now you just have a new measure, which is this density." + }, + { + "text": "So it's just saying that the density of the Gaussian with mean mu with respect to the Gaussian with mean 0 is just this thing here." + }, + { + "text": "All right, so let's move on." + }, + { + "text": "So here is that I said you can actually do all these computations and forget about the fact that x is continuous." + }, + { + "text": "You can actually do it with PMFs and do it for x is discrete." + }, + { + "text": "This actually also tells you if you can actually get the same form for your density, which is of the form exponential times the product of the interaction between theta and x is just taking this product, and then a function only of theta and a function only of x for the PMF." + }, + { + "text": "It also works." + }, + { + "text": "So I claim that the Bernoulli belongs to this family." + }, + { + "text": "So the PMF of a Bernoulli, we say parameter p, is p to the x 1 minus p to the 1 minus x, right?" + }, + { + "text": "Because we know, so that's only for x equals 0 or 1." + }, + { + "text": "And the reason is because when x is equal to 0, this is 1 minus p. When x is equal to 1, this is p. We've seen that when we were looking at likelihoods for Bernoullis." + }, + { + "text": "This is not clear this is going to look like this at all." + }, + { + "text": "But let's do it." + }, + { + "text": "So what does this thing look like?" + }, + { + "text": "Well, the first thing I want to do is to make an exponential show up." + }, + { + "text": "So what I'm going to write is I'm going to write p to the x as exponential x log p, right?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk29.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk29.json new file mode 100644 index 0000000000000000000000000000000000000000..d713a21eea1b786a7ef3869f97ae02235ce1e655 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk29.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so I'm going to do that for the other one." + }, + { + "text": "So this thing here, so I'm going to get exponential x log p plus 1 minus x log 1 minus p. So what I need to do is to collect my terms in x and my terms in whatever parameters I have." + }, + { + "text": "So here, theta is equal to p. So if I do this, what I end up having is equal to exponential." + }, + { + "text": "So the term in x is log p minus log 1 minus p. So that's x times log p over 1 minus p. And then the term that stays is just 1 times log 1 minus p. But I want to see this as a minus something, right?" + }, + { + "text": "It was minus b of theta." + }, + { + "text": "So I'm going to write it as minus." + }, + { + "text": "Well, I can just keep the plus." + }, + { + "text": "And I'm going to do." + }, + { + "text": "And that's all." + }, + { + "text": "Aha." + }, + { + "text": "Well, this is of the form exponential, something that depends only on x, times something that depends only on theta, minus a function that depends only on theta." + }, + { + "text": "And then h of x is equal to 1 again." + }, + { + "text": "So let's see." + }, + { + "text": "So I have t1 of x is equal to x." + }, + { + "text": "That's this guy." + }, + { + "text": "Eta 1 of theta is equal to log p 1 minus p. And b of theta is equal to log 1 over 1 minus p. And h of x is equal to 1." + }, + { + "text": "You guys want to do Poisson, or you want to have it in homework?" + }, + { + "text": "It's a dilemma, because that's an easy homework versus no homework at all." + }, + { + "text": "That may be something more difficult." + }, + { + "text": "OK, who wants to do it now?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk3.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1b86720582d11cec87b39451799e862944553cac --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "This is going to become y given x follows some distribution." + }, + { + "text": "And I'm not going to allow any distribution." + }, + { + "text": "I want something that comes from the exponential family." + }, + { + "text": "Who knows what the exponential family of distribution is?" + }, + { + "text": "This is not the same thing as the exponential distribution." + }, + { + "text": "It's a family of distribution." + }, + { + "text": "All right, so we'll see that." + }, + { + "text": "What can that be?" + }, + { + "text": "Oh, yeah, that's actually my." + }, + { + "text": "I'm sorry?" + }, + { + "text": "You can mute your laptop." + }, + { + "text": "OK." + }, + { + "text": "I'm in presentation mode." + }, + { + "text": "That should not happen." + }, + { + "text": "OK, so hopefully this is muted." + }, + { + "text": "So essentially, this is going to be a family of distributions." + }, + { + "text": "And what makes them exponential typically is that there's an exponential that shows up in the definition of the density." + }, + { + "text": "We'll see that the Gaussian belongs to the exponential family." + }, + { + "text": "But there are slightly less expected ones, because there's this crazy thing that a to the x is exponential x log a, which makes the exponential show up without being there." + }, + { + "text": "So if there's an exponential of some power, it's going to show up." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk30.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk30.json new file mode 100644 index 0000000000000000000000000000000000000000..d5b105095f9ebc1fa6cd52b7842032b4ff7b8f72 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk30.json @@ -0,0 +1,62 @@ +[ + { + "text": "Who does not want to raise their hand now?" + }, + { + "text": "Who wants to raise their hand now?" + }, + { + "text": "All right." + }, + { + "text": "So let's move on." + }, + { + "text": "I'll just do it." + }, + { + "text": "Do you want to do the gammas instead in the homework?" + }, + { + "text": "That's going to be fun." + }, + { + "text": "I'm not even going to propose to do the gammas." + }, + { + "text": "So this is the gamma distribution." + }, + { + "text": "It's brilliantly called gamma, because it has the gamma function, just like the beta distribution was at the beta function in there." + }, + { + "text": "They look very similar." + }, + { + "text": "One is defined over r plus, the positive real line." + }, + { + "text": "And remember, the beta was defined over the interval 0, 1." + }, + { + "text": "And it's of the form x to some power times exponential minus x to some time something." + }, + { + "text": "So there's a function, a polynomial in x, where the exponent depends on the parameter." + }, + { + "text": "And then there's the exponential minus x times something depends on the parameters." + }, + { + "text": "So this is going to also look like some function of x." + }, + { + "text": "Sorry, like some exponential distribution." + }, + { + "text": "Can somebody guess what is going to be t2 of x?" + }, + { + "text": "Oh, those are the functions of x that show up in this product." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk31.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk31.json new file mode 100644 index 0000000000000000000000000000000000000000..00610d89ea0d6a8998695a3eea0b66796db62411 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk31.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember when we have this, we just need to take some transformations of x, so it looks linear in those things and not in x itself." + }, + { + "text": "Remember, we had x squared and x, for example, in the Gaussian case." + }, + { + "text": "I don't know if it's still there." + }, + { + "text": "Yeah, it's still there, right?" + }, + { + "text": "t2 was x squared." + }, + { + "text": "What do you think x is going to be?" + }, + { + "text": "t2 of x." + }, + { + "text": "So here's a hint." + }, + { + "text": "t1 is going to be x. Yeah, Arjun, what is going to be t2?" + }, + { + "text": "Yeah, you cannot." + }, + { + "text": "This one is taken." + }, + { + "text": "This one is taken." + }, + { + "text": "I don't want to take it." + }, + { + "text": "What?" + }, + { + "text": "Log x, right?" + }, + { + "text": "Because this x to the a minus 1, I'm going to write it as exponential a minus 1 log x." + }, + { + "text": "So basically, eta 1 is going to be a minus 1." + }, + { + "text": "Eta 2 is going to be minus 1 over b." + }, + { + "text": "Well, actually, the opposite." + }, + { + "text": "But this is actually not too complicated." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk32.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk32.json new file mode 100644 index 0000000000000000000000000000000000000000..87cbf659fc56773f52625e97de084ba7714602c8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk32.json @@ -0,0 +1,62 @@ +[ + { + "text": "All right, then those parameters get names." + }, + { + "text": "a is the shape parameter." + }, + { + "text": "b is the scale parameter." + }, + { + "text": "It doesn't really matter." + }, + { + "text": "You have other things that are called the inverse gamma distribution, which has this form." + }, + { + "text": "The difference is that the parameter alpha shows negatively there." + }, + { + "text": "And then the inverse Gaussian distribution, just densities you can come up with." + }, + { + "text": "And it just happened to fall in this family." + }, + { + "text": "And there's other ones that you can actually put it there that we've seen before." + }, + { + "text": "The chi square is actually part of this family." + }, + { + "text": "The beta distribution is part of this family." + }, + { + "text": "The binomial distribution is part of this family." + }, + { + "text": "Well, that's easy because the Bernoulli was." + }, + { + "text": "The negative binomial, which is some stopping time, the first time you hit a certain number of successes when you flip some Bernoulli coins." + }, + { + "text": "So you can check for all of those." + }, + { + "text": "And you will see that you can actually write them as part of the exponential family." + }, + { + "text": "So the main goal of this slide is to convince you that this is actually a pretty broad range of distributions, because it basically includes everything we've seen, but not anything there." + }, + { + "text": "Sorry, plus more." + }, + { + "text": "OK?" + }, + { + "text": "Yeah?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk33.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk33.json new file mode 100644 index 0000000000000000000000000000000000000000..86875d258d1996f3a9c9c903d20c2aaebbe2d921 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk33.json @@ -0,0 +1,62 @@ +[ + { + "text": "Is there any example of a distribution which comes up pretty often that's not in the next exponential family?" + }, + { + "text": "Yeah, like uniform." + }, + { + "text": "Oh, OK. Maybe a bit more complicated than that." + }, + { + "text": "Anything that has a support that depends on the parameter is not going to fall." + }, + { + "text": "It's not going to fit in there." + }, + { + "text": "And you can actually convince yourself why anything that has the support that depends on the parameter is not going to be part of this guy." + }, + { + "text": "It's kind of a hard thing to, if I ask you, prove that it's not, and you wouldn't prove this rule." + }, + { + "text": "It's kind of a little difficult." + }, + { + "text": "But the way you can convince yourself is that, remember, the only interaction between x and theta that I allowed was taking the product of those guys and then the exponential." + }, + { + "text": "If you have something that depends on some parameter, let's say you're going to see something that looks like this." + }, + { + "text": "For uniform, it looks like this." + }, + { + "text": "Well, this is not of the form exponential x times theta." + }, + { + "text": "There's an interaction between x and theta here, but it's actually certainly not of the form x exponential x times theta." + }, + { + "text": "So this is definitely not going to be part of the exponential family." + }, + { + "text": "And every time you start doing things like that, then it's just not going to happen." + }, + { + "text": "Actually, to be fair, I'm not even sure that all these guys, when you allow them to have all their parameters free, are actually going to be part of this." + }, + { + "text": "The beta probably is, but I'm not actually entirely convinced." + }, + { + "text": "There's books on exponential families." + }, + { + "text": "So let's go back." + }, + { + "text": "So here, we've put a lot of effort understanding how big, how much wider than the Gaussian distribution can we think of for the conditional distribution of our response y given x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk34.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk34.json new file mode 100644 index 0000000000000000000000000000000000000000..7d11d0e4f2f489c40ab50852c91946ccd1773a06 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk34.json @@ -0,0 +1,62 @@ +[ + { + "text": "So let's go back to the generalized linear models." + }, + { + "text": "So the generalized linear model said, OK, the random component, y, has to be part of some exponential family distribution." + }, + { + "text": "Check." + }, + { + "text": "We know what this means." + }, + { + "text": "So now I have to understand two things." + }, + { + "text": "I have to understand what is the expectation, because that's actually what I model." + }, + { + "text": "I take the expectation, the conditional expectation of y given x." + }, + { + "text": "So I need to understand, given this guy, it would be nice if it had some simple rules that would tell me exactly what the expectation is, rather than having to do it over and over again." + }, + { + "text": "If I told you, here's a Gaussian, compute the expectation." + }, + { + "text": "Every time you had to use that, it would be slightly painful." + }, + { + "text": "So hopefully, this thing being simple enough, we've actually selected a simple class that's simple enough." + }, + { + "text": "So that we can have rules, whereas as soon as I give you those parameters, t1, t2, eta 1, eta 2, b, and h, you can actually have some simple rules to compute the mean and variance and all the things." + }, + { + "text": "And so in particular, I'm interested in the mean." + }, + { + "text": "And I'm going to have to actually say, well, this mean has to be mapped into the whole real line so I can actually talk about modeling this function of the mean as x transpose beta." + }, + { + "text": "And we saw that for the Kefosis data set or whatever other data sets, you can actually do this using the log of the reciprocal." + }, + { + "text": "Or for the, actually, we didn't do it for the Bernoulli." + }, + { + "text": "We'll come to this." + }, + { + "text": "This is the most important one, and that's called the logit or logistic link." + }, + { + "text": "But before we go there, this was actually a very broad family." + }, + { + "text": "When I wrote this thing on the bottom board, it's gone now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk35.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk35.json new file mode 100644 index 0000000000000000000000000000000000000000..85aa8f3c00dfa505f2dfedae8c76a6308880fbe3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk35.json @@ -0,0 +1,62 @@ +[ + { + "text": "But when I wrote it in the first place, the only thing that I wrote is I wanted x times theta." + }, + { + "text": "Wouldn't it be nice if I have some distribution that was just x times theta, not some function of x times some function of theta?" + }, + { + "text": "The functions seem to be here so that they actually make things a little." + }, + { + "text": "So the functions were here so that I can actually put a lot of functions there." + }, + { + "text": "But first of all, if I actually decide to reparameterize my problem, I can always assume, if I have one dimensional, I can always assume that eta 1 of theta becomes my new theta." + }, + { + "text": "So this thing here, for example, I could say, well, this is actually the parameter of my Bernoulli." + }, + { + "text": "Let me call this guy theta." + }, + { + "text": "I could do that." + }, + { + "text": "Then I could say, well, here I have x that shows up here." + }, + { + "text": "And here, since I'm talking about the response, I cannot really make any transformation." + }, + { + "text": "So here I'm going to actually talk about a specific family for which this guy is not x square or square root of x or log of x or anything I want." + }, + { + "text": "I'm just going to actually look at distributions for which this is x." + }, + { + "text": "These exponential families are called canonical exponential families." + }, + { + "text": "So in the canonical exponential family, what I have is that I have my x times theta." + }, + { + "text": "I'm going to allow myself some normalization factor phi." + }, + { + "text": "And we'll see, for example, that it's very convenient when I talk about the Gaussian." + }, + { + "text": "Because even if I know this guy, which I actually pull into my, oh, that's over here, right?" + }, + { + "text": "I know sigma squared, but I don't want to change my parameter to be mu over sigma squared." + }, + { + "text": "It's kind of painful." + }, + { + "text": "So I just take mu, and I'm going to keep this guy as being this phi over there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk36.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk36.json new file mode 100644 index 0000000000000000000000000000000000000000..89f73402c1fdd2bf2eeed62666de95f3d88a1238 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk36.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's called the dispersion parameter from a clear analogy with the Gaussian." + }, + { + "text": "That's the variance, and that's measuring dispersion." + }, + { + "text": "So here, what I want is I'm going to think throughout this class." + }, + { + "text": "So phi may be known or not." + }, + { + "text": "And when it's not known, this actually might turn into some exponential family, or it might not." + }, + { + "text": "And the main reason is because this b of theta over phi is not necessarily a function of theta over phi." + }, + { + "text": "If I actually have phi unknown, then y theta over phi has to be, this guy has to be my new parameter." + }, + { + "text": "And b might not be a function of this new parameter." + }, + { + "text": "So in a way, it may or may not, but this is not really a concern that we're going to have, because throughout this class, we're going to assume that phi is known." + }, + { + "text": "Phi is going to be known all the time, which means that this is always an exponential family." + }, + { + "text": "And it's just the simplest one you could think of." + }, + { + "text": "One dimensional parameter, one dimensional response, and I just have the product is just y times, or we used to call it x." + }, + { + "text": "Now I've switched to y." + }, + { + "text": "But y times theta divided by phi." + }, + { + "text": "Should I write this, or is this clear to everyone what this is?" + }, + { + "text": "Let me write it somewhere so we actually keep track of it for the 10 minutes." + }, + { + "text": "OK, so this is, we have, remember we had all the distributions." + }, + { + "text": "And then here we had the exponential family." + }, + { + "text": "And now we have the canonical exponential family." + }, + { + "text": "It's actually much, much smaller." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk37.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk37.json new file mode 100644 index 0000000000000000000000000000000000000000..611f08f23a902183ca152ce8cba2cc234c17366b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk37.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, actually, it's probably sort of a good picture." + }, + { + "text": "And what I have is that my density, or my PMF, is just exponential y times theta minus b of theta divided by phi." + }, + { + "text": "And I have plus c of, oh, yeah, plus c of y phi, which means that this is really, if phi is known, h of y is just exponential c of y phi." + }, + { + "text": "Actually, this is the reason why it's not necessarily a canonical family." + }, + { + "text": "It might not be that this depends only on y." + }, + { + "text": "It could depend on y and phi in some annoying way, and I may not be able to break it." + }, + { + "text": "But if phi is known, this is just a function that depends on y." + }, + { + "text": "Agreed?" + }, + { + "text": "In particular, I hope you can convince yourself that this is just a subcase of everything we've seen before." + }, + { + "text": "So for example, the Gaussian, when the variance is known, is indeed of this form." + }, + { + "text": "So we still have it on the board." + }, + { + "text": "So here's my y." + }, + { + "text": "So let me write this as f theta of y." + }, + { + "text": "So every x is replaced with y. Blah, blah, blah." + }, + { + "text": "This is this guy." + }, + { + "text": "And now what I have is that this is going to be my phi." + }, + { + "text": "This is my parameter theta." + }, + { + "text": "So I'm definitely of the form y times theta divided by phi." + }, + { + "text": "And then here, I have a function b that depends only on theta over phi again." + }, + { + "text": "So b of theta is mu squared divided by 2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk38.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk38.json new file mode 100644 index 0000000000000000000000000000000000000000..8580549781bf648098829c5beb6e58f82df064eb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk38.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's divided by sigma square." + }, + { + "text": "And then I have this extra stuff, but I really don't care what it is for now." + }, + { + "text": "It's just something that depends only on y and known stuff." + }, + { + "text": "So it's just a function of y." + }, + { + "text": "Just like my h, I stuff everything in there." + }, + { + "text": "The b, though, this thing here, this is actually what's important." + }, + { + "text": "Because in a canonical family, if you think about it, when you know phi, this is just y times theta scaled by a known constant." + }, + { + "text": "Sorry, y times theta scaled by a known constant is the first term." + }, + { + "text": "The second term is b of theta scaled by some known constant." + }, + { + "text": "But b of theta is what's going to make the difference between Gaussian and Bernoulli's and gammas and betas." + }, + { + "text": "This is all in this b of theta." + }, + { + "text": "b of theta contains everything that's idiosyncratic to this particular distribution." + }, + { + "text": "And so this is going to be important." + }, + { + "text": "And we will see that b of theta is going to capture information about the mean, about the variance, about the likelihood, about everything." + }, + { + "text": "Should I go through this computation?" + }, + { + "text": "I mean, it's the same." + }, + { + "text": "We've just done it." + }, + { + "text": "So maybe it's probably better if you can redo it on your own." + }, + { + "text": "So the canonical exponential family also has other distributions." + }, + { + "text": "So there's the Gaussian, and there's the Poisson, and there's the Bernoulli." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk39.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk39.json new file mode 100644 index 0000000000000000000000000000000000000000..e7503da5bdfd1b43af25b138aa6e92f9d60f5b5b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk39.json @@ -0,0 +1,62 @@ +[ + { + "text": "But the other ones may not be part of this." + }, + { + "text": "In particular, think about the gamma distribution." + }, + { + "text": "We had this log x was one of those things that showed up." + }, + { + "text": "I mean, I cannot get rid of this log x. I mean, that's part of it, except if a is equal to 1." + }, + { + "text": "And I know it for sure." + }, + { + "text": "So if a is equal to 1, then I'm going to have a minus 1, which is equal to 0." + }, + { + "text": "So I'm going to have a minus 1 times log x, which is going to be just 0." + }, + { + "text": "So log x is going to vanish from here." + }, + { + "text": "If a is equal to 1, then this distribution is actually much nicer." + }, + { + "text": "And it actually does not even deserve the name gamma." + }, + { + "text": "What is it if a is equal to 1?" + }, + { + "text": "It's an exponential, right?" + }, + { + "text": "Gamma of 1 is equal to 1. x to the a minus 1 is equal to 1. b, so I have exponential x over b divided by b." + }, + { + "text": "So 1 over b, call it lambda." + }, + { + "text": "And this is just an exponential distribution." + }, + { + "text": "And so every time you're going to see something, so all these guys that don't make it to this table, they could be part of those guys." + }, + { + "text": "But they're just to have another name in this thing." + }, + { + "text": "So you can compute the value of theta for different values." + }, + { + "text": "So again, you still have some continuous or discrete ones." + }, + { + "text": "This is my b of theta." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk4.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..7bcd652938f0899eaa61ff94c0f0810d310b07d7 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "But it's more than that." + }, + { + "text": "So we'll actually come to this particular family of distribution." + }, + { + "text": "Why this particular family?" + }, + { + "text": "Because in a way, everything we've done for the linear model with Gaussian is going to extend fairly naturally to this family." + }, + { + "text": "And it actually also, because it encompasses pretty much everything, all the distributions we've discussed before." + }, + { + "text": "All right, so the second thing that I want to question, so before we just said, well, mu of x was directly equal to this thing." + }, + { + "text": "Mu of x was directly x transpose beta." + }, + { + "text": "So I knew I was going to have an x transpose beta." + }, + { + "text": "And I said, well, I could do something with this x transpose beta before I used it to explain the expected value." + }, + { + "text": "But I'm actually taking it like that." + }, + { + "text": "Here we're going to say, let's extend this to some function is equal to this thing." + }, + { + "text": "Now, admittedly, this is not the most natural way to think about it." + }, + { + "text": "What you would probably feel more comfortable doing is write something like mu of x is a function." + }, + { + "text": "Let's call it f of x transpose beta." + }, + { + "text": "But here I just decide to call f g inverse." + }, + { + "text": "OK, that's just my g inverse, yes." + }, + { + "text": "Is this different than just transforming the x's?" + }, + { + "text": "Yeah." + }, + { + "text": "I mean, what transformation do you want to put on your x's?" + }, + { + "text": "Like, is this equivalent to just applying some function to each individual x component and then multiplying that beta to get the mean?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk40.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk40.json new file mode 100644 index 0000000000000000000000000000000000000000..a4fb0b65f5388522d17114f3d137c0e12fa325f1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk40.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I said this is actually really what captures my theta." + }, + { + "text": "This b is actually called cumulant generating function." + }, + { + "text": "I don't have time." + }, + { + "text": "I could write five slides to explain to you." + }, + { + "text": "But it would just only tell you why it's called cumulant generating function." + }, + { + "text": "It's also known as the log of the moment generating function." + }, + { + "text": "And the way it's called cumulant generating function is because if I start taking successive derivatives and evaluate them at 0, I get the successive cumulants of this distribution, which are some transformation of the moment." + }, + { + "text": "What is the function b?" + }, + { + "text": "The function b." + }, + { + "text": "So this is just normalization." + }, + { + "text": "So this is just to tell you I can compute this, but I really don't care." + }, + { + "text": "And obviously, I don't care about stuff that's complicated." + }, + { + "text": "This is actually cute." + }, + { + "text": "And this is what computes everything." + }, + { + "text": "And the rest is just some general description." + }, + { + "text": "You don't need me to tell you that the range of y is 0 to infinity." + }, + { + "text": "And that is essentially telling me this is going to give me some hints as to which link function I should be using." + }, + { + "text": "Because the range of y tells me what the range of expectation of y is going to be." + }, + { + "text": "Here it tells me that the range of y is between 0 and 1." + }, + { + "text": "So what I want to show you is that this captures a variety of different ranges that you can have." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk41.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk41.json new file mode 100644 index 0000000000000000000000000000000000000000..5bc0529fcb2c87a036825dc5eca45e610158d843 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk41.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I'm going to want to go into the likelihood." + }, + { + "text": "And the likelihood I'm actually going to use to compute the expectations." + }, + { + "text": "But since I actually don't have time to do this now, let's just go quickly through this and give you a spoiler alert to make sure that you all wake up on Thursday and really, really want to think about coming here immediately." + }, + { + "text": "So the thing I'm going to want to do, as I said, is it would be nice if, at least for this canonical family, when I give you b, you would be able to say, oh, here is a simple computation of b that would actually give me the mean and the variance." + }, + { + "text": "The mean and the variance are also known as moments." + }, + { + "text": "b is called cumulant generating function." + }, + { + "text": "So it sounds like moments being related to cumulants might have a path to finding those." + }, + { + "text": "And it might involve taking derivatives of b, as we'll see." + }, + { + "text": "The way we're going to prove this is by using this thing that we've used several times." + }, + { + "text": "So this property we use when we're computing, remember, the Fisher information." + }, + { + "text": "We had two formulas for the Fisher information." + }, + { + "text": "One was the expectation of the second derivative of the likelihood." + }, + { + "text": "And one was negative expectation of the square." + }, + { + "text": "Sorry, expectation of the square." + }, + { + "text": "And the other one was negative the expectation of the second derivative." + }, + { + "text": "The log likelihood is concave." + }, + { + "text": "So this number is negative." + }, + { + "text": "This number is positive." + }, + { + "text": "And the way we did this is by just permuting some derivative and integral here." + }, + { + "text": "And we used the fact that something that looked like this, the log likelihood is log of f theta." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk42.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk42.json new file mode 100644 index 0000000000000000000000000000000000000000..21653facee3fc11ef5000d2beef0a8de5ddfa092 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk42.json @@ -0,0 +1,62 @@ +[ + { + "text": "And when I take the derivative of this guy with respect to theta, then I have something that looks like the derivative divided by f theta." + }, + { + "text": "And if I start taking the integral against f theta of this thing, so the expectation of this thing, those things would cancel." + }, + { + "text": "And then I had just the integral of a derivative, which I would make a leap of faith and say that it's actually the derivative of the integral." + }, + { + "text": "But this was equal to 1." + }, + { + "text": "So this derivative was actually equal to 0." + }, + { + "text": "And so that's how you got that the expectation of the derivative of the log likelihood is equal to 0." + }, + { + "text": "And you do it once again, and you get this guy." + }, + { + "text": "There's just some nice things that happen with taking the derivative of the log." + }, + { + "text": "We've done that." + }, + { + "text": "We'll do that again." + }, + { + "text": "But once you do this, you can actually apply it." + }, + { + "text": "And missing a parenthesis over there." + }, + { + "text": "So when you write the log likelihood, it's just log of an exponential." + }, + { + "text": "That's actually pretty nice." + }, + { + "text": "Just like the least squares came naturally, the least squares criterion came naturally when we took the log likelihood of the Gaussians." + }, + { + "text": "We're going to have the same thing that happens." + }, + { + "text": "When I take the log of the density, the exponential is going to go away." + }, + { + "text": "And then I'm going to use this formula." + }, + { + "text": "But this formula is going to actually give me an equation directly." + }, + { + "text": "Oh, that's where it was." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk43.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk43.json new file mode 100644 index 0000000000000000000000000000000000000000..7f84c7ac778972c0a276af273b35f04b2d19dc71 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk43.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's the one that's missing it there." + }, + { + "text": "So the expectation minus this thing is going to be equal to 0, which tells me that the expectation is just the derivative." + }, + { + "text": "So it's still a function of theta, but it's just the derivative of b." + }, + { + "text": "And the variance is just going to be the second derivative of b." + }, + { + "text": "But remember, this was some sort of a scaling." + }, + { + "text": "It's called the dispersion parameter." + }, + { + "text": "So if I had a Gaussian, and the variance of the Gaussian did not depend on the sigma square, which I stuffed in this phi, that would be certainly weird." + }, + { + "text": "And it cannot depend only on mu." + }, + { + "text": "And so for the Gaussian, this is definitely going to be equal to 1." + }, + { + "text": "And this is just going to be equal to my variance." + }, + { + "text": "So this is just by taking the second derivative." + }, + { + "text": "So basically, the take-home message is that this function b captures, by taking one derivative of the expectation and by taking two derivatives, captures the variance." + }, + { + "text": "Another thing that's actually cool, and we'll come back to this and I want you to think about, is if this second derivative is the variance, what can I say about this thing?" + }, + { + "text": "What do I know about a variance?" + }, + { + "text": "Yeah, it's positive." + }, + { + "text": "So I know that this is positive." + }, + { + "text": "So what does that tell me?" + }, + { + "text": "Positive?" + }, + { + "text": "That's convex, right?" + }, + { + "text": "A function that has positive second derivative is convex." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk44.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk44.json new file mode 100644 index 0000000000000000000000000000000000000000..d5f75378f61eee780be265f51bdebc08ef9bcc39 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk44.json @@ -0,0 +1,11 @@ +[ + { + "text": "So we're going to use that as well." + }, + { + "text": "So yeah, I'll see you on Thursday." + }, + { + "text": "Have your homework." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk5.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..be889780830d4833b3e56baa49edaba9d1277e77 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "Oh, no, certainly not, right?" + }, + { + "text": "I mean, if I force you to work with x1 plus x2, you cannot work with any function of x1 plus any function of x2, right?" + }, + { + "text": "So yeah, this is different." + }, + { + "text": "So yeah, the transformation would be just the simple part of your linear regression problem, where you would take your x's, transform them, and then just apply another linear regression." + }, + { + "text": "This is genuinely new." + }, + { + "text": "Any other question?" + }, + { + "text": "All right, so this function g, and the reason why I sort of have to stick to this slightly less natural way of defining it is because that's g that gets a name, not g inverse that gets a name." + }, + { + "text": "And the name of g is the link function." + }, + { + "text": "So if I want to give you a generalized linear model, I need to give you two ingredients." + }, + { + "text": "The first one is the random component, which is the distribution of y given x." + }, + { + "text": "And it can be anything in what's called the exponential family of distributions." + }, + { + "text": "So for example, I could say y given x is Gaussian with mean ux sigma squared identity." + }, + { + "text": "But I could also tell you y given x is gamma with shape parameter equal to alpha of x. I could do some weird things like this." + }, + { + "text": "And the second thing is I need to give you a link function." + }, + { + "text": "And the link function is going to become very clear how you pick a link function." + }, + { + "text": "And the only reason that you actually pick a link function is because of compatibility." + }, + { + "text": "This mu of x, I call it mu because mu of x is always the conditional expectation of y given x, always, which means that let's think of y as being a Bernoulli random variable." + }, + { + "text": "Where does mu of x live?" + }, + { + "text": "AUDIENCE 2." + }, + { + "text": "0, 1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk6.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..8cb4d97427833f7219b0ac485c9a506b1a3240c9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "0, 1, right?" + }, + { + "text": "That's the expectation of a Bernoulli." + }, + { + "text": "It's just the probability that my coin flip gives me 1." + }, + { + "text": "So it's a number between 0 and 1." + }, + { + "text": "But this guy right here, if my x's are anything, think of any body measurements, plus I take linear combinations with arbitrarily large coefficients, this thing can be any real number." + }, + { + "text": "So the link function, what it's effectively going to do is make those two things compatible." + }, + { + "text": "It's going to take my number, which, for example, is constrained to be between 0 and 1, and map it into the entire real line." + }, + { + "text": "If I have mu, which is forced to be positive, for example, in an exponential distribution, the mean is positive, right?" + }, + { + "text": "That's the, say, I don't know, inter-arrival time for Poisson process." + }, + { + "text": "This thing is known to be positive for an exponential." + }, + { + "text": "I need to map something that's exponential to the entire real line." + }, + { + "text": "I need a function that takes something positive and then tickets everyone." + }, + { + "text": "So we'll see, by the end of this chapter, you will have 100 ways of doing this." + }, + { + "text": "But there are some more traditional ones than other." + }, + { + "text": "So before we go any further, I gave you this example of a Bernoulli random variable." + }, + { + "text": "Let's see a few examples that actually fit there." + }, + { + "text": "Yes?" + }, + { + "text": "AUDIENCE 1 Will it come up later if we already know why the mean distribution is increasing entirely?" + }, + { + "text": "Why can't we do it?" + }, + { + "text": "PHILIPPE RIGOLLET Well, actually, this will not come up later." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk7.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..7a08a1b997a550d2298989615c5c3d9d139188e0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "It should be very clear from here." + }, + { + "text": "Because if I actually have a model, I just want it to be plausible, right?" + }, + { + "text": "I mean, what happens if I suddenly decide that my, so this is what's going to happen." + }, + { + "text": "You're going to have only data to fit this model." + }, + { + "text": "Let's say you actually forget about this thing here." + }, + { + "text": "You can always do this, right?" + }, + { + "text": "You can always say, I'm going to pretend my y's just happen to be the realizations of, say, Gaussians that happen to be 0 or 1 only." + }, + { + "text": "You can always stuff that in some linear model, right?" + }, + { + "text": "You will have some least squares estimator for beta." + }, + { + "text": "But what's going to happen, and it's going to be fine." + }, + { + "text": "For all the points that you see, it will definitely put some number that's actually between 0 and 1." + }, + { + "text": "So this is what your picture is going to look like." + }, + { + "text": "You're going to have a bunch of values for x." + }, + { + "text": "This is your y." + }, + { + "text": "And so these are the values of x that you will get." + }, + { + "text": "And for y, you will see either 0 or 1, right?" + }, + { + "text": "That's what your Bernoulli data set would look like with a one-dimensional x." + }, + { + "text": "Now, if you do least squares on this, you will find this." + }, + { + "text": "And for this guy, this line certainly takes values between 0 and 1." + }, + { + "text": "But let's say now you get an x here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk8.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..dfd389e2603960133ef12ce8ca9c769bb873bedf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "You're going to actually start pretending the probability that it spits out one conditionally in x is like 1.2, and that's going to be weird." + }, + { + "text": "OK?" + }, + { + "text": "Any other questions?" + }, + { + "text": "All right, so let's start with some examples." + }, + { + "text": "Right?" + }, + { + "text": "I mean, you got so used to them throughout this course." + }, + { + "text": "So the first one is all these things are taken." + }, + { + "text": "So there's a few books on generalizing your models, generalize additive models, and there's tons of applications that you can see." + }, + { + "text": "Those are extremely versatile." + }, + { + "text": "And as soon as you want to do modeling to explain some y given x, you sort of need to do that if you want to go beyond linear models." + }, + { + "text": "So this was the disease occurring rate." + }, + { + "text": "So you have a disease epidemic, and you want to basically model the expected number of new cases given at a certain time." + }, + { + "text": "OK?" + }, + { + "text": "So you have time that progresses for each of your reservation." + }, + { + "text": "Each of your relation is a timestamp, say, I don't know, 20th day." + }, + { + "text": "And your response is the number of new cases." + }, + { + "text": "And you're going to actually put your model directly on mu, right?" + }, + { + "text": "When I looked at this, everything here was on mu itself, on the expected, right?" + }, + { + "text": "Mu of x is always the expected, the conditional expectation of y given x." + }, + { + "text": "Right?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk9.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..6cb6e3c31c39383cd65adbaafb2b2ceb06ed1ff3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_0_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So all I need to model is this expected value." + }, + { + "text": "So this mu, I'm going to actually say, so I look at some parameters, and it says, well, it increases exponentially." + }, + { + "text": "So I want to have some sort of exponential trend." + }, + { + "text": "I can parameterize that in several ways." + }, + { + "text": "And the two parameters I want to slap in is some sort of gamma, which is just the coefficient." + }, + { + "text": "And then there's some rate delta that's in the exponential." + }, + { + "text": "OK?" + }, + { + "text": "So if I tell you it's exponential, that's a nice family of functions you might want to think about." + }, + { + "text": "OK, so here, mu of x, if I want to keep the notation x, is gamma exponential delta x, right?" + }, + { + "text": "Except that here, my x are t1, t2, t3, et cetera." + }, + { + "text": "OK?" + }, + { + "text": "And I want to find what the parameters gamma and delta are because I want to be able to maybe compare different epidemics and see if they have the same parameter or maybe just do some prediction based on the data that I have to extrapolate in the future." + }, + { + "text": "OK?" + }, + { + "text": "So here, clearly, mu of x is not of the form x transpose beta." + }, + { + "text": "Right?" + }, + { + "text": "That's not x transpose beta at all." + }, + { + "text": "And it's actually not even a function of x transpose beta." + }, + { + "text": "Right?" + }, + { + "text": "There's two parameters, gamma and delta, and it's not of the form." + }, + { + "text": "So here, I have x, which is 1 and x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk0.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d4554873825c6719ec24d2e3b27b154cb3857640 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "Chapter is a natural capstone chapter for this entire course." + }, + { + "text": "We'll see some of the things we've seen during maximum likelihood and some of the things we've seen during linear regression, some of the things we've seen in terms of the basic modeling that we've had before." + }, + { + "text": "We're not going to go back to much inference questions." + }, + { + "text": "It's really going to be about modeling." + }, + { + "text": "And in a way, generalized linear models, as the word says, are just a generalization of linear models." + }, + { + "text": "And they're actually extremely useful." + }, + { + "text": "They're often forgotten about, and people just jump onto machine learning and sophisticated techniques." + }, + { + "text": "But those things do the job quite well." + }, + { + "text": "So let's see in what sense they are a generalization of the linear model." + }, + { + "text": "So remember, the linear model looked like this." + }, + { + "text": "We said that y was equal to x transpose beta plus epsilon." + }, + { + "text": "That was our linear regression model." + }, + { + "text": "And another way to say this is that if I, let's assume that those were, say, Gaussian with mean 0 and identity covariance matrix, then another way to say this is that the conditional distribution of y given x is a Gaussian with mean x transpose beta and variance, well, we had a sigma square, which I will forget as usual, x transpose beta and then sigma square." + }, + { + "text": "So here, we just assumed that, so what is regression?" + }, + { + "text": "It's just saying I'm trying to explain y as a function of x given x. I'm assuming a distribution for the y." + }, + { + "text": "And this x is just going to be here to help me model what the mean of this Gaussian is." + }, + { + "text": "I mean, I could have something crazy." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk1.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..2c2e721380f9d4710c30835403ae73ceebf39538 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "I could have something that looks like y given x is n0 x transpose beta." + }, + { + "text": "And then this guy could be some other thing, which looks like, I don't know, some x transpose gamma squared times, I don't know, x x transpose plus identity, some crazy thing that depends on x here." + }, + { + "text": "And we deliberately assume that all the thing that depends on x shows up in the mean." + }, + { + "text": "And so what I have here is that y given x is a Gaussian with a mean that depends on x and covariance matrix sigma square identity." + }, + { + "text": "Now, the linear model assumed a very specific form for the mean." + }, + { + "text": "It said, I want the mean to be equal to x transpose beta, which, remember, was the sum from, say, j equals 1 to p of beta j xj, where the xj's are the coordinates of x." + }, + { + "text": "But I could do something also more complicated." + }, + { + "text": "I could have something that looks like, instead, replace this by, I don't know, sum of beta j log of x to the j divided by x to the j squared, or something like this." + }, + { + "text": "I could do this as well." + }, + { + "text": "So there's two things that we've assumed." + }, + { + "text": "The first one is that when I look at the conditional distribution of y given x, x affects only the mean." + }, + { + "text": "I also assumed that it was Gaussian, and that it affects only the mean." + }, + { + "text": "And the mean is affected in a very specific way, which is linear in x." + }, + { + "text": "So this is essentially the things we're going to try to relax." + }, + { + "text": "So the first thing that we assume, the fact that y was Gaussian and had only its mean that depended on x, is what's called the random component." + }, + { + "text": "It just says that the response variables sort of make sense to assume that they're Gaussian." + }, + { + "text": "And everything was essentially captured." + }, + { + "text": "So there's this property of Gaussians that if you tell me if the variance is known, all you need to tell me to understand exactly what the distribution of a Gaussian is, all you need to tell me is its expected value." + }, + { + "text": "So that's this mu of x." + }, + { + "text": "And the second thing is that we had this link that says, well, I need to find a way to use my x's to explain this mu." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk10.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..6a481ea5cb5adb97b455c8bc5c53385e58a31448 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Right?" + }, + { + "text": "I have two parameters." + }, + { + "text": "So what I do here is that I say, well, first, let me transform mu in such a way that I can hope to see something that's linear." + }, + { + "text": "So if I transform mu, I'm going to have log of mu, which is log of this thing." + }, + { + "text": "Right?" + }, + { + "text": "So log of mu of x is equal to log of gamma plus log of exponential delta x, which is delta x. OK?" + }, + { + "text": "And now, this thing is actually linear in x." + }, + { + "text": "So I have that this guy is my first beta 1." + }, + { + "text": "And so that's beta 1 times 1." + }, + { + "text": "And this guy is beta 2 times, sorry, let's say beta 0 times 1." + }, + { + "text": "And this guy is beta 1 times x. OK?" + }, + { + "text": "So that looks like a linear model." + }, + { + "text": "I just have to change my parameters." + }, + { + "text": "My parameters, beta 1 becomes the log of gamma, and beta 2 becomes delta itself." + }, + { + "text": "And the reason why we do this is because, well, the way we put those gamma and those delta was just so that we have some parametrization." + }, + { + "text": "It just so happens that if we want this to be linear, we need to just change the parametrization itself." + }, + { + "text": "This is going to have some effects." + }, + { + "text": "We know that it's going to have some effect in the Fisher information." + }, + { + "text": "It's going to have a bunch of effect to change those things." + }, + { + "text": "But that's what needs to be done to have a generalized linear model." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk11.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b87248456f36363ec8012cc422267e73498f0d65 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, here, the function that I took to turn it into something that's linear is simple." + }, + { + "text": "It came directly from some natural thing it would do here, which is taking the log." + }, + { + "text": "And so the function g, the link that I take, is called the log link, very creatively." + }, + { + "text": "And it's just the function that I apply to mu so that I see something that's linear and that looks like this." + }, + { + "text": "OK?" + }, + { + "text": "So now, this only tells me how to deal with the link function." + }, + { + "text": "But I still have to deal with 0.1." + }, + { + "text": "And this, again, is just some modeling." + }, + { + "text": "Given some data, some random data, what distribution do you choose to explain the randomness?" + }, + { + "text": "And this, I mean, unless there's no choice, it's just a matter of practice." + }, + { + "text": "I mean, why would it be Gaussian and not doubly exponential?" + }, + { + "text": "There's matters of convenience that come into this." + }, + { + "text": "And there's just matter of experience that come into this." + }, + { + "text": "I remember when you chat with engineers, they have a very good notion of what the distribution should be." + }, + { + "text": "They have Weibull distributions." + }, + { + "text": "They do optics and things like this." + }, + { + "text": "So there's some distributions that just come up." + }, + { + "text": "But sometimes, you just have to work." + }, + { + "text": "Now, here, what do we have?" + }, + { + "text": "The thing we're trying to measure y, as we said, so mu is the conditional expectation of y given x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk12.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..af95e1917c846d9d478b143cf28493ff3dd4d7d1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "But y is the number of new cases, right?" + }, + { + "text": "Well, it's a number of." + }, + { + "text": "And the first thing you should think of when you think about number of, if it were bounded above, you would think binomial, baby." + }, + { + "text": "But here, it's just a number." + }, + { + "text": "So you think Poisson." + }, + { + "text": "That's how insurers think." + }, + { + "text": "I have a number of claims per year." + }, + { + "text": "This is a Poisson distribution." + }, + { + "text": "And hopefully, they can model the conditional distribution of the number of claims given everything that they actually ask you in this survey that I hear you now fill in 15 minutes." + }, + { + "text": "All right, so now you have this Poisson distribution." + }, + { + "text": "And that's just a modeling assumption." + }, + { + "text": "There's no particular reason why you should do this, except that that might be a good idea." + }, + { + "text": "And the expected value of your Poisson has to be this mu i at time i." + }, + { + "text": "Any question about this slide?" + }, + { + "text": "So let's switch to another example." + }, + { + "text": "Another example is the so-called prey capture rate." + }, + { + "text": "So here, what you're interested in is the rate capture of prey's Yi for a given prey." + }, + { + "text": "And you have Xi, which is your explanation." + }, + { + "text": "And this is just the density of prey." + }, + { + "text": "So you're trying to explain the rate of captures of preys given the density of the prey." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk13.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..82b4fda8d85deb20289b741cbb4d1b501793ba9c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so you need to find some sort of relationship between the two." + }, + { + "text": "And here again, you talk to experts." + }, + { + "text": "And what they tell you is that, well, it's going to be increasing." + }, + { + "text": "Animals, like predators, are going to just eat more if there's more preys." + }, + { + "text": "But at some point, they're just going to level off because they're just going to be completely full." + }, + { + "text": "And they're going to stop capturing those preys." + }, + { + "text": "And you're just going to have some phenomenon that looks like this." + }, + { + "text": "So here is a curve that sort of makes sense." + }, + { + "text": "As your capture rate goes from 0 to 1, you're increasing." + }, + { + "text": "And then you see you have this concave function that says that at some point, it levels off." + }, + { + "text": "So here, one way I could, I mean, there's again many ways I could just model a function that looks like this." + }, + { + "text": "But a simple one that has only two parameters is this one, where mu i is just this function of Xi, where I have some parameter alpha here and some parameter h here." + }, + { + "text": "So there's clearly, so this function, there's one that essentially tells you." + }, + { + "text": "So this thing starts at 0 for sure." + }, + { + "text": "And essentially, alpha tells you how sharp this thing is." + }, + { + "text": "And h tells you at which point you end here." + }, + { + "text": "It's not exactly what those values are equal to, but it tells you this." + }, + { + "text": "So simple." + }, + { + "text": "And well, no, OK, sorry." + }, + { + "text": "That's actually alpha, which is the maximum capture rate." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk14.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..be9a8b2fcbc0f8c0b1e49f0850eea5b9ab306080 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "And h represents the prey density at which the capture rate is." + }, + { + "text": "So that's the half time." + }, + { + "text": "So there's actual values for this." + }, + { + "text": "So now I have this function." + }, + { + "text": "It's certainly not a function." + }, + { + "text": "I don't see it as a function of x." + }, + { + "text": "So I need to find something that looks like a function of x. OK?" + }, + { + "text": "So now here, there's no log." + }, + { + "text": "There's no, well, I could actually take a log here." + }, + { + "text": "But I would have log of x and log of x plus h. So that would be weird." + }, + { + "text": "So what we propose to do here is to look, rather than looking at mu i, we look at 1 over mu i." + }, + { + "text": "And so since your function was mu i, when you take 1 over mu i, you get h plus xi divided by alpha xi, which is h over alpha times 1 over xi plus 1 over alpha." + }, + { + "text": "And now if I am willing to make this transformation of variables and say, actually, my x, whether it's the density of prey or the inverse density of prey, it really doesn't matter." + }, + { + "text": "I can always make the transformation when the data comes." + }, + { + "text": "Then I'm actually just going to think of this as being some linear function, beta 0 plus beta 1, which is this guy, times 1 over xi." + }, + { + "text": "And now my new variable becomes 1 over xi." + }, + { + "text": "And now it's linear." + }, + { + "text": "And the transformation I had to take was this 1 over x, which is called the reciprocal link." + }, + { + "text": "You can probably guess what the exponential link is going to be and things like this." + }, + { + "text": "So we'll talk about other links that have slightly less obvious names." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk15.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..5d2ed9123f0b6a47840cca2ce477712ca74abf5e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, again, modeling." + }, + { + "text": "So this was the random component." + }, + { + "text": "This was the easy part." + }, + { + "text": "Now I need to just pour in some domain knowledge about how do I think this function, this y, which is the rate of capture of preys." + }, + { + "text": "I want to understand how this thing is actually changing." + }, + { + "text": "What is the randomness of the thing around its mean?" + }, + { + "text": "And something that comes from this textbook, the standard deviation of capture rate might be approximately proportional to the mean rate." + }, + { + "text": "You need to find a distribution that actually has this property." + }, + { + "text": "And it turns out that this happens for gamma distribution." + }, + { + "text": "In gamma distributions, just like, say, for Poisson distribution, for Poisson, the variance and the mean are of the same order." + }, + { + "text": "Here is the standard deviation that's of the same order as the mean for gammas." + }, + { + "text": "And it's a positive distribution as well." + }, + { + "text": "So here is a candidate." + }, + { + "text": "Now, since we're sort of constrained to work under the exponential family of distributions, then you can just go through your list and just decide which one works best for you." + }, + { + "text": "All right, third example." + }, + { + "text": "So here we have binary response." + }, + { + "text": "Here, essentially, the binary response variable indicates the presence or absence of post-covariative deforming for kyphosis on children." + }, + { + "text": "And here, rather than having one covariate, which was before, in the first example, was time, in the second example was the density, here there's three covariates." + }, + { + "text": "So you measure on children." + }, + { + "text": "The first one is age of the child." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk16.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..ef9ff3f87e1e355af4391eaee6e902d9ab157079 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "The second one is the number of vertebrae involved in the operation." + }, + { + "text": "And the third one is the start of the range, so where it is on the spine." + }, + { + "text": "So the response variable here is, did it work or not?" + }, + { + "text": "I mean, that's very simple." + }, + { + "text": "And so here, it's nice, because the random component is the easiest one." + }, + { + "text": "As I said, any random variable that takes only two outcomes must be a Bernoulli." + }, + { + "text": "So that's nice." + }, + { + "text": "There's no modeling going on here." + }, + { + "text": "So you know that y given x is going to be Bernoulli, but of course, all your efforts are going to try to understand what the conditional mean of your Bernoulli, what the conditional probability of being 1 is going to be." + }, + { + "text": "And so in particular, so I'm just here." + }, + { + "text": "I'm spelling it out before we close those examples." + }, + { + "text": "I cannot say that mu of x is x transpose beta for exactly this picture that I drew for you here." + }, + { + "text": "There's just no way here." + }, + { + "text": "The goal of doing this is certainly to be able to extrapolate for yet unseen children whether this is something that we should be doing, and maybe the range of x's is actually going to be slightly out." + }, + { + "text": "And so OK, I don't want to say that I have a negative probability of outcome or a positive one, sorry, or a 1 that's lower than 1, so I need to make this transformation." + }, + { + "text": "What I need to do is to transform mu, which is we know only a number, all we know is a number between 0 and 1, and we need to transform it in such a way that it maps the entire real line, or reciprocally to say that, or inversely I should say, that f of x transpose beta should be a number between 0 and 1." + }, + { + "text": "I need to find a function that takes any real number and maps it into 0 and 1, and we'll see that again, but you have an army of functions that do that for you." + }, + { + "text": "What are those functions?" + }, + { + "text": "I'm sorry?" + }, + { + "text": "AUDIENCE MEMBER 2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk17.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..e618b05cddff9ee23141a82d1f3c33242aeb2d21 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "Trait function." + }, + { + "text": "PHILIPPE RIGOLLET." + }, + { + "text": "Trait?" + }, + { + "text": "AUDIENCE MEMBER 2." + }, + { + "text": "Trait, trait, trait." + }, + { + "text": "PHILIPPE RIGOLLET." + }, + { + "text": "Oh." + }, + { + "text": "Yeah, I want them to be invertible, right?" + }, + { + "text": "AUDIENCE MEMBER 2." + }, + { + "text": "Yeah." + }, + { + "text": "PHILIPPE RIGOLLET." + }, + { + "text": "Yeah." + }, + { + "text": "AUDIENCE MEMBER 2." + }, + { + "text": "Longest trait." + }, + { + "text": "PHILIPPE RIGOLLET." + }, + { + "text": "I have an army of function." + }, + { + "text": "I'm not asking for one soldier in this army." + }, + { + "text": "I want the name of this army." + }, + { + "text": "AUDIENCE MEMBER 2." + }, + { + "text": "They're invertible." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk18.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..f58b1220495ab9dfac97d370ddda29476838a3fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "PHILIPPE RIGOLLET." + }, + { + "text": "Well, they're not really invertible either, right?" + }, + { + "text": "So they're actually in stats textbooks, because remember, statisticians don't know how to integrate functions, but they know how to turn a function into a Gaussian integral, so we know it integrates to 1, and things like this." + }, + { + "text": "Same thing here." + }, + { + "text": "We don't know how to build functions that are invertible and map the entire real line to 0, 1, but there's all the cumulative distribution functions that do that for us." + }, + { + "text": "So I can use any of those guys, and that's what I'm going to be doing, actually." + }, + { + "text": "All right, so just to recap what I just said as we were speaking, so a normal linear model is not appropriate for those examples if only because the response variable is not necessarily Gaussian." + }, + { + "text": "So and also because the linear model has to be, the mean has to be transformed before I can actually apply a linear model for all these plausible nonlinear models that I actually came up with." + }, + { + "text": "So the family we're going to go for is the exponential family of distributions, and we're going to be able to show, so one of the nice part of this is to actually compute maximum likelihood estimators for those, right?" + }, + { + "text": "In the linear model, maximum like, in the Gaussian linear model, maximum likelihood was as nice as it gets, right?" + }, + { + "text": "This actually was the least squares estimator." + }, + { + "text": "We had a closed form, x transpose x inverse x transpose y, and that was it." + }, + { + "text": "We had to just take one derivative." + }, + { + "text": "Here, we're going to have a generally concave likelihood." + }, + { + "text": "We're not going to be able to actually solve this thing directly in closed form unless it's Gaussian, but we will have, we'll see actually how this is not just a black box optimization of a concave function." + }, + { + "text": "We have a lot of properties of this concave function, and we will be able to show some iterative algorithms." + }, + { + "text": "We'll basically see how, when you open the box of convex optimization, you will actually be able to see how things work and actually implement it using least squares." + }, + { + "text": "So each iteration of this iterative algorithm will essentially be a least square, so that's actually quite huge." + }, + { + "text": "It's also very demonstrative of statisticians being pretty ingenious so that they don't have to call in some statistical software, but just can repeatedly call their least squares oracle within a statistical software." + }, + { + "text": "OK, so what is the exponential family?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk19.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..fbe7abc54d0348d4353fcfa16b5a9639e71fe8f7 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "I promised you the exponential family." + }, + { + "text": "Before we go into this, let me just tell you something about exponential families, and what's the only thing that differentiates an exponential family from all possible distributions?" + }, + { + "text": "An exponential family has two parameters, and those are not really parameters, but there's the theta parameter of my distribution." + }, + { + "text": "So it's going to be indexed by some parameter." + }, + { + "text": "Here, I'm only talking about the distribution of, say, some random variable or some random vector." + }, + { + "text": "So here, in this slide, you see that the parameter theta that indexes those distribution is k-dimensional, and the space of the x's that I'm looking at, so that should really be y." + }, + { + "text": "So what I'm going to plug in here is the conditional distribution of y given x, and theta is going to depend on x." + }, + { + "text": "But this really is the y." + }, + { + "text": "That's the distribution of the response variable." + }, + { + "text": "And so this is on q." + }, + { + "text": "So I'm going to assume that y is q-dimensional." + }, + { + "text": "Clearly, soon q is going to be equal to 1, but I can define those things generally." + }, + { + "text": "So I have this." + }, + { + "text": "I have to tell you what this looks like, and let's assume that this is a probability density function." + }, + { + "text": "So this notation, the fact that I just put my theta in subscript, is just for me to remember that this is the variable that indicates the random variable, and this is just the parameter." + }, + { + "text": "But I could just write it as a function of theta and x." + }, + { + "text": "This is just going to be, if you were in multivariable calc, you would have two parameters, theta and x, and you would need to give me a function." + }, + { + "text": "Now, think of x and theta as being one-dimensional at this point." + }, + { + "text": "Think of all the functions that can be depending on theta and x." + }, + { + "text": "There's many of them." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk2.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..4dfa619a62a8cb9f51581c665c6269ca8bec9c50 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the link was exactly mu of x was equal to x transpose beta." + }, + { + "text": "OK?" + }, + { + "text": "Now, we are talking about generalized linear models." + }, + { + "text": "So this part here, where mu of x is of the form, the way I want my beta, my x, to show up is linear." + }, + { + "text": "This will never be questioned." + }, + { + "text": "In principle, I could add a third point, which is just question this part, the fact that mu of x is x transpose beta." + }, + { + "text": "I could have some more complicated nonlinear function of x." + }, + { + "text": "And I will never do that, because we're talking about generalized linear model." + }, + { + "text": "The only thing with generalized are the random component, the conditional distribution of y given x, and the link that just says, well, once you actually tell me that the only thing I need to figure out is the mean, I'm just going to slap it exactly this x transpose beta thing without any transformation of x transpose beta." + }, + { + "text": "OK?" + }, + { + "text": "So those are the two things." + }, + { + "text": "It will become clearer what I mean." + }, + { + "text": "This sounds like a tautology, but let's just see how we could extend that." + }, + { + "text": "So what we're going to do in generalized linear models, so when I talk about GLMs, the first thing I'm going to do with my x is turn it into some x transpose beta." + }, + { + "text": "And that's just the L part." + }, + { + "text": "This I'm not going to be able to change." + }, + { + "text": "That's the way it works." + }, + { + "text": "I'm not going to do anything nonlinear." + }, + { + "text": "But the two things I'm going to change is this random component, which is that y, which used to be some Gaussian with mean mu of x variance sigma squared." + }, + { + "text": "So y given x, sorry." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk20.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..58f979f5cd191f971fd907b961bc1542b84ea77e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And in particular, there's many ways theta and x can interact." + }, + { + "text": "What the exponential family does for you is that it restricts the way these things can actually interact with each other." + }, + { + "text": "It's essentially saying the following." + }, + { + "text": "It's saying this is going to be of the form exponential." + }, + { + "text": "So this exponential is really not much, because I could put a log next to it." + }, + { + "text": "But what I want is that the way theta and x interact has to be of the form theta times x in an exponential." + }, + { + "text": "So that's one of the ways you can think of them interacting." + }, + { + "text": "You just take the product of the two." + }, + { + "text": "Now, clearly, this is not a very rich family." + }, + { + "text": "So what I'm allowing myself is to just slap on some terms that depend only on theta and depend only on x." + }, + { + "text": "So let's just call this thing f of x g of theta." + }, + { + "text": "So here, I've restricted the way theta and x can interact." + }, + { + "text": "So I have something that depends only on x, something that depends only on theta." + }, + { + "text": "And here, I have this very specific interaction." + }, + { + "text": "And that's all that exponential families are doing for you." + }, + { + "text": "So if we go back to this slide, this is much more general." + }, + { + "text": "If I want to go from theta and x in r to theta and x theta in r to theta in rk and x in rq, I cannot take the product of theta and x. I cannot even take the inner product between theta and x, because they're not even of compatible dimensions." + }, + { + "text": "But what I can do is to first map my theta into something and map my x into something so that I actually end up having the same dimensions." + }, + { + "text": "And then I can take the inner product." + }, + { + "text": "That's the natural generalization of this simple product." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk21.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..36059f58796657121c5302bfc6135335368066e7 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what I have is if I want to go from theta to x, what I'm going to first do is I'm going to take theta eta of theta." + }, + { + "text": "So let's say eta 1 of theta to eta k of theta." + }, + { + "text": "And then I'm going to actually take x becomes t1 of x all the way to tk of x." + }, + { + "text": "And what I'm going to do is take the inner product." + }, + { + "text": "So let's call this eta." + }, + { + "text": "And let's call this t. And I'm going to take the inner product of eta and t, which is just the sum from j equal 1 to k of eta j of theta times tj of x." + }, + { + "text": "So that's just a way to say I want this simple interaction." + }, + { + "text": "But in higher dimension, the simplest way I can actually make those things happen is just by taking inner product." + }, + { + "text": "And so now what it's telling me is that the distribution, I want the exponential times something that depends only on theta and something that depends only on x." + }, + { + "text": "And so what it tells me is that when I'm going to take p of theta x, it's just going to be something which is exponential times the sum from j equal 1 to k of eta j theta tj of x." + }, + { + "text": "And then I'm going to have a function that depends only." + }, + { + "text": "So let me write it for now like c of theta." + }, + { + "text": "And then a function that depends only on x." + }, + { + "text": "Let me call it h of x." + }, + { + "text": "And for convenience, there's no particular reason why I do that." + }, + { + "text": "I'm taking this function c of theta, and I'm just actually pushing it in there." + }, + { + "text": "So I can write c of theta as exponential minus log of 1 over c of theta." + }, + { + "text": "And now I have exponential times exponential." + }, + { + "text": "So I push it in, and this thing actually looks like exponential sum from j equal 1 to k of eta j theta tj of x minus log 1 over c of theta times h of x." + }, + { + "text": "And this thing here, log 1 over c of theta, I call actually b of theta." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk22.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..9ce5d204be5cf62e2aafd3d850c84f7dd1eafe0a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because c, I called it c, but I can actually directly call it this guy b, and I don't actually care about c itself." + }, + { + "text": "Now, why don't I put back also h of x in there?" + }, + { + "text": "Because h of x is really here to just, how to put it?" + }, + { + "text": "h of x and b of theta don't play the same role." + }, + { + "text": "b of theta, in many ways, is a normalizing constant." + }, + { + "text": "I want this density to integrate to 1." + }, + { + "text": "If I did not have this guy, I'm not guaranteed that this thing integrates to 1." + }, + { + "text": "But by tweaking this function, b of theta or c of theta, their equivalent, I can actually ensure that this thing integrates to 1." + }, + { + "text": "So b of theta is just a normalizing constant." + }, + { + "text": "h of x is something that's going to be funny for us." + }, + { + "text": "It's going to be something that allows us to be able to treat both discrete and continuous variables within the framework of exponential families." + }, + { + "text": "So for those that are familiar with this, this is essentially saying that h of x is really just a change of measure." + }, + { + "text": "When I actually look at the density of p of theta, this is with respect to some measure, the fact that I just multiply by a function of x just means that I'm not looking that this guy here, without h of theta, is not the density with respect to the original measure, but it's the density with respect to the distribution that has h as a density." + }, + { + "text": "That's all I'm saying." + }, + { + "text": "So I can first transform my x's and then take the density with respect to that." + }, + { + "text": "If you don't want to think about densities or measures, you don't have to." + }, + { + "text": "This is just the way." + }, + { + "text": "This is just the definition." + }, + { + "text": "Is there any question about this definition?" + }, + { + "text": "So it looks complicated, but it's actually essentially the simplest way you could think about it." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk23.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..5eeb518a9d5894bf1eeb94d4fb8a4b81ffe8e5df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "You want to be able to have x and theta interact, and you just say, I want the interaction to be of the form exponential x times theta." + }, + { + "text": "And if they're higher dimensions, I'm going to take the exponential of the function of x inner product for the function of theta." + }, + { + "text": "So I claimed since the beginning that the Gaussian was such an example, so let's just do it." + }, + { + "text": "Is the interaction between theta and x in a Gaussian of the form inner product?" + }, + { + "text": "And the answer is yes." + }, + { + "text": "Actually, whether I know or not what the variance is." + }, + { + "text": "So let's start for the case where I actually do not know what the variance is." + }, + { + "text": "So here I have x is n mu sigma squared." + }, + { + "text": "This is all one dimensional." + }, + { + "text": "And here I'm going to assume that my parameter is both mu and sigma squared." + }, + { + "text": "So what I need to do is to have some function of mu, some function of sigma squared, and take the inner product of some function of x and some other function of x." + }, + { + "text": "So I want to show that p theta of x is what?" + }, + { + "text": "Well, it's 1 over square root sigma 2 pi exponential minus x minus mu squared over 2 sigma squared." + }, + { + "text": "That's just my Gaussian density." + }, + { + "text": "And I want to say that this thing here, so clearly the exponential shows up already." + }, + { + "text": "I want to show that this is something that looks like eta 1 of mu sigma squared." + }, + { + "text": "So I have only two of those guys, so I'm going to need only two etas." + }, + { + "text": "So I want it to be eta 1 of mu and sigma times t1 of x plus eta 2 mu sigma squared times t2 of x." + }, + { + "text": "So I want to have something like that that shows up, and the only things that are left, I want them to depend either only on theta or only on x." + }, + { + "text": "So to find that out, we just need to expand." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk24.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b20dd7faa1dfbea7dd48300ad6e2453578b83cb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I'm going to first put everything into my exponential and expand this guy." + }, + { + "text": "So the first term here is going to be minus x squared over 2 sigma squared." + }, + { + "text": "The second term is going to be minus mu squared over 2 sigma squared." + }, + { + "text": "And then the cross term is going to be plus x mu divided by sigma squared." + }, + { + "text": "And then I'm going to put this guy here, so I have a minus log sigma root 2 pi." + }, + { + "text": "OK, so this term here contains an interaction between x and the parameters." + }, + { + "text": "This term here contains an interaction between x and the parameters." + }, + { + "text": "So let me try to write them in a way that I want." + }, + { + "text": "This guy only depends on the parameters." + }, + { + "text": "This guy only depends on the parameter." + }, + { + "text": "So I'm going to rearrange things." + }, + { + "text": "And so I claim that this is of the form x squared." + }, + { + "text": "Well, let's say, who's getting the minus?" + }, + { + "text": "Eta, OK." + }, + { + "text": "So it's x squared times minus 1 over 2 sigma squared plus x times mu over sigma squared." + }, + { + "text": "So that's this term here." + }, + { + "text": "That's this term here." + }, + { + "text": "Now I need to get this guy here." + }, + { + "text": "And that's minus." + }, + { + "text": "So I'm going to write it like this, minus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk25.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..732b958a14a1b7707a0b37d4bdd107f5be9f2ac5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now I have mu squared over 2 sigma squared plus log sigma square root 2 pi." + }, + { + "text": "OK?" + }, + { + "text": "And now this thing is definitely of the form t1 of x times, did I call them the right way or not?" + }, + { + "text": "Of course not." + }, + { + "text": "OK, so that's going to be t2 of x times eta 2 of x, eta 2 of theta." + }, + { + "text": "This guy is going to be t1 of x times eta 1 of theta." + }, + { + "text": "So just a function of theta times a function of x, just a function of theta times a function of x." + }, + { + "text": "And the way I combine this is just by summing them." + }, + { + "text": "And this is going to be my b of theta." + }, + { + "text": "What is h of x?" + }, + { + "text": "1." + }, + { + "text": "There's one thing I can actually play with." + }, + { + "text": "And this is something you're going to have some free choices." + }, + { + "text": "This is not actually completely determined here." + }, + { + "text": "Is that, for example, when I write the log sigma square root 2 pi, this is just log of sigma plus log square root 2 pi." + }, + { + "text": "So I have two choices here." + }, + { + "text": "Either my b becomes this guy, or so either I have b of theta, which is mu squared over 2 sigma squared plus log sigma square root 2 pi, and h of x is equal to 1." + }, + { + "text": "Or I have that b of theta is mu squared over 2 sigma squared plus log sigma, and h of x is equal to what?" + }, + { + "text": "1." + }, + { + "text": "Well, I can just push this guy out." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk26.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..7128910e23875de6e208c059db4ddc05705e82cc --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk26.json @@ -0,0 +1,62 @@ +[ + { + "text": "I can push it out of the exponential." + }, + { + "text": "And so it's just square root of 2 pi, which is a function of x, technically." + }, + { + "text": "I mean, it's a constant function of x, but it's a function of x." + }, + { + "text": "So you can see that it's not completely clear how you're going to do the trade-off." + }, + { + "text": "So the constant terms can go either in b or in h. But why bother with tracking down b and h when you can actually stuff everything into one and just call h 1 and call it a day?" + }, + { + "text": "So you can just forget about h. It's 1, and think about the rest." + }, + { + "text": "h won't matter, actually, for estimation purposes or anything like this." + }, + { + "text": "All right, so that's basically everything that's written." + }, + { + "text": "When sigma square is known, what's happening is that this guy here is no longer a function of theta, right?" + }, + { + "text": "Agreed?" + }, + { + "text": "This is no longer a parameter." + }, + { + "text": "When sigma square is known, then theta is equal to mu only." + }, + { + "text": "There's no sigma square going on." + }, + { + "text": "So everything that depends on sigma square can be thought as a constant, think 1." + }, + { + "text": "So in particular, this term here does not belong in the interaction between x and theta." + }, + { + "text": "It belongs to h, right?" + }, + { + "text": "So if sigma is known, then this guy is only a function of h of x." + }, + { + "text": "So h of x becomes exponential x squared minus x squared over 2 sigma squared, right?" + }, + { + "text": "That's just a function of x." + }, + { + "text": "Is that clear?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk27.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk27.json new file mode 100644 index 0000000000000000000000000000000000000000..ad5c52c96917f6811fd97391867d647b8dd5d280 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk27.json @@ -0,0 +1,62 @@ +[ + { + "text": "So if you complete this computation, what you're going to get is that your new one parameter thing is that p theta p theta x is not equal to exponential x times mu over sigma squared minus, well, it's still the same thing, and then you have your h of x that comes out, x squared over 2 sigma squared." + }, + { + "text": "So that's my h of x." + }, + { + "text": "That's still my b of theta." + }, + { + "text": "And this is my t1 of x, and this is my eta 1 of theta." + }, + { + "text": "And remember, theta is just equal to mu in this case." + }, + { + "text": "So if I ask you, prove that this distribution belonged to an exponential family, you just have to work it out." + }, + { + "text": "Typically, it's expanding what's in the exponential and just write it in this term and identify all the components, right?" + }, + { + "text": "So here, notice those guys don't even get an index anymore because there's just one of them." + }, + { + "text": "So I wrote theta 1 and t1, but it's really just eta and t. Oh, sorry." + }, + { + "text": "This guy also goes." + }, + { + "text": "This is also a constant, right?" + }, + { + "text": "So it can actually just put sigma divided by sigma squared over 2 pi." + }, + { + "text": "So h of x is what, actually?" + }, + { + "text": "AUDIENCE MEMBER 2." + }, + { + "text": "It's the density of?" + }, + { + "text": "AUDIENCE MEMBER 3." + }, + { + "text": "It's centered." + }, + { + "text": "It's not standard." + }, + { + "text": "It's centered." + }, + { + "text": "It has mean 0, but it has variance sigma squared, right?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk28.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk28.json new file mode 100644 index 0000000000000000000000000000000000000000..e6cd0af7c6a6f3a84bb21243aed86ecb61bec60e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk28.json @@ -0,0 +1,62 @@ +[ + { + "text": "But it's the density of a Gaussian." + }, + { + "text": "And this is what I meant when I said h of x is really just telling you with respect to which distribution, which measure you're taking the density." + }, + { + "text": "And so this thing here is really telling you the density of my Gaussian with mean mu is equal to this with respect to a centered Gaussian is this guy, right?" + }, + { + "text": "That's what it means." + }, + { + "text": "If this thing ends up being a density, it just means that now you just have a new measure, which is this density." + }, + { + "text": "So it's just saying that the density of the Gaussian with mean mu with respect to the Gaussian with mean 0 is just this thing here." + }, + { + "text": "All right, so let's move on." + }, + { + "text": "So here is that I said you can actually do all these computations and forget about the fact that x is continuous." + }, + { + "text": "You can actually do it with PMFs and do it for x is discrete." + }, + { + "text": "This actually also tells you if you can actually get the same form for your density, which is of the form exponential times the product of the interaction between theta and x is just taking this product, and then a function only of theta and a function only of x for the PMF." + }, + { + "text": "It also works." + }, + { + "text": "So I claim that the Bernoulli belongs to this family." + }, + { + "text": "So the PMF of a Bernoulli, we say parameter p, is p to the x 1 minus p to the 1 minus x, right?" + }, + { + "text": "Because we know, so that's only for x equals 0 or 1." + }, + { + "text": "And the reason is because when x is equal to 0, this is 1 minus p. When x is equal to 1, this is p. We've seen that when we were looking at likelihoods for Bernoullis." + }, + { + "text": "This is not clear this is going to look like this at all." + }, + { + "text": "But let's do it." + }, + { + "text": "So what does this thing look like?" + }, + { + "text": "Well, the first thing I want to do is to make an exponential show up." + }, + { + "text": "So what I'm going to write is I'm going to write p to the x as exponential x log p, right?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk29.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk29.json new file mode 100644 index 0000000000000000000000000000000000000000..d713a21eea1b786a7ef3869f97ae02235ce1e655 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk29.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so I'm going to do that for the other one." + }, + { + "text": "So this thing here, so I'm going to get exponential x log p plus 1 minus x log 1 minus p. So what I need to do is to collect my terms in x and my terms in whatever parameters I have." + }, + { + "text": "So here, theta is equal to p. So if I do this, what I end up having is equal to exponential." + }, + { + "text": "So the term in x is log p minus log 1 minus p. So that's x times log p over 1 minus p. And then the term that stays is just 1 times log 1 minus p. But I want to see this as a minus something, right?" + }, + { + "text": "It was minus b of theta." + }, + { + "text": "So I'm going to write it as minus." + }, + { + "text": "Well, I can just keep the plus." + }, + { + "text": "And I'm going to do." + }, + { + "text": "And that's all." + }, + { + "text": "Aha." + }, + { + "text": "Well, this is of the form exponential, something that depends only on x, times something that depends only on theta, minus a function that depends only on theta." + }, + { + "text": "And then h of x is equal to 1 again." + }, + { + "text": "So let's see." + }, + { + "text": "So I have t1 of x is equal to x." + }, + { + "text": "That's this guy." + }, + { + "text": "Eta 1 of theta is equal to log p 1 minus p. And b of theta is equal to log 1 over 1 minus p. And h of x is equal to 1." + }, + { + "text": "You guys want to do Poisson, or you want to have it in homework?" + }, + { + "text": "It's a dilemma, because that's an easy homework versus no homework at all." + }, + { + "text": "That may be something more difficult." + }, + { + "text": "OK, who wants to do it now?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk3.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1b86720582d11cec87b39451799e862944553cac --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "This is going to become y given x follows some distribution." + }, + { + "text": "And I'm not going to allow any distribution." + }, + { + "text": "I want something that comes from the exponential family." + }, + { + "text": "Who knows what the exponential family of distribution is?" + }, + { + "text": "This is not the same thing as the exponential distribution." + }, + { + "text": "It's a family of distribution." + }, + { + "text": "All right, so we'll see that." + }, + { + "text": "What can that be?" + }, + { + "text": "Oh, yeah, that's actually my." + }, + { + "text": "I'm sorry?" + }, + { + "text": "You can mute your laptop." + }, + { + "text": "OK." + }, + { + "text": "I'm in presentation mode." + }, + { + "text": "That should not happen." + }, + { + "text": "OK, so hopefully this is muted." + }, + { + "text": "So essentially, this is going to be a family of distributions." + }, + { + "text": "And what makes them exponential typically is that there's an exponential that shows up in the definition of the density." + }, + { + "text": "We'll see that the Gaussian belongs to the exponential family." + }, + { + "text": "But there are slightly less expected ones, because there's this crazy thing that a to the x is exponential x log a, which makes the exponential show up without being there." + }, + { + "text": "So if there's an exponential of some power, it's going to show up." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk30.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk30.json new file mode 100644 index 0000000000000000000000000000000000000000..d5b105095f9ebc1fa6cd52b7842032b4ff7b8f72 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk30.json @@ -0,0 +1,62 @@ +[ + { + "text": "Who does not want to raise their hand now?" + }, + { + "text": "Who wants to raise their hand now?" + }, + { + "text": "All right." + }, + { + "text": "So let's move on." + }, + { + "text": "I'll just do it." + }, + { + "text": "Do you want to do the gammas instead in the homework?" + }, + { + "text": "That's going to be fun." + }, + { + "text": "I'm not even going to propose to do the gammas." + }, + { + "text": "So this is the gamma distribution." + }, + { + "text": "It's brilliantly called gamma, because it has the gamma function, just like the beta distribution was at the beta function in there." + }, + { + "text": "They look very similar." + }, + { + "text": "One is defined over r plus, the positive real line." + }, + { + "text": "And remember, the beta was defined over the interval 0, 1." + }, + { + "text": "And it's of the form x to some power times exponential minus x to some time something." + }, + { + "text": "So there's a function, a polynomial in x, where the exponent depends on the parameter." + }, + { + "text": "And then there's the exponential minus x times something depends on the parameters." + }, + { + "text": "So this is going to also look like some function of x." + }, + { + "text": "Sorry, like some exponential distribution." + }, + { + "text": "Can somebody guess what is going to be t2 of x?" + }, + { + "text": "Oh, those are the functions of x that show up in this product." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk31.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk31.json new file mode 100644 index 0000000000000000000000000000000000000000..00610d89ea0d6a8998695a3eea0b66796db62411 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk31.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember when we have this, we just need to take some transformations of x, so it looks linear in those things and not in x itself." + }, + { + "text": "Remember, we had x squared and x, for example, in the Gaussian case." + }, + { + "text": "I don't know if it's still there." + }, + { + "text": "Yeah, it's still there, right?" + }, + { + "text": "t2 was x squared." + }, + { + "text": "What do you think x is going to be?" + }, + { + "text": "t2 of x." + }, + { + "text": "So here's a hint." + }, + { + "text": "t1 is going to be x. Yeah, Arjun, what is going to be t2?" + }, + { + "text": "Yeah, you cannot." + }, + { + "text": "This one is taken." + }, + { + "text": "This one is taken." + }, + { + "text": "I don't want to take it." + }, + { + "text": "What?" + }, + { + "text": "Log x, right?" + }, + { + "text": "Because this x to the a minus 1, I'm going to write it as exponential a minus 1 log x." + }, + { + "text": "So basically, eta 1 is going to be a minus 1." + }, + { + "text": "Eta 2 is going to be minus 1 over b." + }, + { + "text": "Well, actually, the opposite." + }, + { + "text": "But this is actually not too complicated." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk32.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk32.json new file mode 100644 index 0000000000000000000000000000000000000000..87cbf659fc56773f52625e97de084ba7714602c8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk32.json @@ -0,0 +1,62 @@ +[ + { + "text": "All right, then those parameters get names." + }, + { + "text": "a is the shape parameter." + }, + { + "text": "b is the scale parameter." + }, + { + "text": "It doesn't really matter." + }, + { + "text": "You have other things that are called the inverse gamma distribution, which has this form." + }, + { + "text": "The difference is that the parameter alpha shows negatively there." + }, + { + "text": "And then the inverse Gaussian distribution, just densities you can come up with." + }, + { + "text": "And it just happened to fall in this family." + }, + { + "text": "And there's other ones that you can actually put it there that we've seen before." + }, + { + "text": "The chi square is actually part of this family." + }, + { + "text": "The beta distribution is part of this family." + }, + { + "text": "The binomial distribution is part of this family." + }, + { + "text": "Well, that's easy because the Bernoulli was." + }, + { + "text": "The negative binomial, which is some stopping time, the first time you hit a certain number of successes when you flip some Bernoulli coins." + }, + { + "text": "So you can check for all of those." + }, + { + "text": "And you will see that you can actually write them as part of the exponential family." + }, + { + "text": "So the main goal of this slide is to convince you that this is actually a pretty broad range of distributions, because it basically includes everything we've seen, but not anything there." + }, + { + "text": "Sorry, plus more." + }, + { + "text": "OK?" + }, + { + "text": "Yeah?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk33.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk33.json new file mode 100644 index 0000000000000000000000000000000000000000..86875d258d1996f3a9c9c903d20c2aaebbe2d921 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk33.json @@ -0,0 +1,62 @@ +[ + { + "text": "Is there any example of a distribution which comes up pretty often that's not in the next exponential family?" + }, + { + "text": "Yeah, like uniform." + }, + { + "text": "Oh, OK. Maybe a bit more complicated than that." + }, + { + "text": "Anything that has a support that depends on the parameter is not going to fall." + }, + { + "text": "It's not going to fit in there." + }, + { + "text": "And you can actually convince yourself why anything that has the support that depends on the parameter is not going to be part of this guy." + }, + { + "text": "It's kind of a hard thing to, if I ask you, prove that it's not, and you wouldn't prove this rule." + }, + { + "text": "It's kind of a little difficult." + }, + { + "text": "But the way you can convince yourself is that, remember, the only interaction between x and theta that I allowed was taking the product of those guys and then the exponential." + }, + { + "text": "If you have something that depends on some parameter, let's say you're going to see something that looks like this." + }, + { + "text": "For uniform, it looks like this." + }, + { + "text": "Well, this is not of the form exponential x times theta." + }, + { + "text": "There's an interaction between x and theta here, but it's actually certainly not of the form x exponential x times theta." + }, + { + "text": "So this is definitely not going to be part of the exponential family." + }, + { + "text": "And every time you start doing things like that, then it's just not going to happen." + }, + { + "text": "Actually, to be fair, I'm not even sure that all these guys, when you allow them to have all their parameters free, are actually going to be part of this." + }, + { + "text": "The beta probably is, but I'm not actually entirely convinced." + }, + { + "text": "There's books on exponential families." + }, + { + "text": "So let's go back." + }, + { + "text": "So here, we've put a lot of effort understanding how big, how much wider than the Gaussian distribution can we think of for the conditional distribution of our response y given x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk34.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk34.json new file mode 100644 index 0000000000000000000000000000000000000000..7d11d0e4f2f489c40ab50852c91946ccd1773a06 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk34.json @@ -0,0 +1,62 @@ +[ + { + "text": "So let's go back to the generalized linear models." + }, + { + "text": "So the generalized linear model said, OK, the random component, y, has to be part of some exponential family distribution." + }, + { + "text": "Check." + }, + { + "text": "We know what this means." + }, + { + "text": "So now I have to understand two things." + }, + { + "text": "I have to understand what is the expectation, because that's actually what I model." + }, + { + "text": "I take the expectation, the conditional expectation of y given x." + }, + { + "text": "So I need to understand, given this guy, it would be nice if it had some simple rules that would tell me exactly what the expectation is, rather than having to do it over and over again." + }, + { + "text": "If I told you, here's a Gaussian, compute the expectation." + }, + { + "text": "Every time you had to use that, it would be slightly painful." + }, + { + "text": "So hopefully, this thing being simple enough, we've actually selected a simple class that's simple enough." + }, + { + "text": "So that we can have rules, whereas as soon as I give you those parameters, t1, t2, eta 1, eta 2, b, and h, you can actually have some simple rules to compute the mean and variance and all the things." + }, + { + "text": "And so in particular, I'm interested in the mean." + }, + { + "text": "And I'm going to have to actually say, well, this mean has to be mapped into the whole real line so I can actually talk about modeling this function of the mean as x transpose beta." + }, + { + "text": "And we saw that for the Kefosis data set or whatever other data sets, you can actually do this using the log of the reciprocal." + }, + { + "text": "Or for the, actually, we didn't do it for the Bernoulli." + }, + { + "text": "We'll come to this." + }, + { + "text": "This is the most important one, and that's called the logit or logistic link." + }, + { + "text": "But before we go there, this was actually a very broad family." + }, + { + "text": "When I wrote this thing on the bottom board, it's gone now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk35.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk35.json new file mode 100644 index 0000000000000000000000000000000000000000..85aa8f3c00dfa505f2dfedae8c76a6308880fbe3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk35.json @@ -0,0 +1,62 @@ +[ + { + "text": "But when I wrote it in the first place, the only thing that I wrote is I wanted x times theta." + }, + { + "text": "Wouldn't it be nice if I have some distribution that was just x times theta, not some function of x times some function of theta?" + }, + { + "text": "The functions seem to be here so that they actually make things a little." + }, + { + "text": "So the functions were here so that I can actually put a lot of functions there." + }, + { + "text": "But first of all, if I actually decide to reparameterize my problem, I can always assume, if I have one dimensional, I can always assume that eta 1 of theta becomes my new theta." + }, + { + "text": "So this thing here, for example, I could say, well, this is actually the parameter of my Bernoulli." + }, + { + "text": "Let me call this guy theta." + }, + { + "text": "I could do that." + }, + { + "text": "Then I could say, well, here I have x that shows up here." + }, + { + "text": "And here, since I'm talking about the response, I cannot really make any transformation." + }, + { + "text": "So here I'm going to actually talk about a specific family for which this guy is not x square or square root of x or log of x or anything I want." + }, + { + "text": "I'm just going to actually look at distributions for which this is x." + }, + { + "text": "These exponential families are called canonical exponential families." + }, + { + "text": "So in the canonical exponential family, what I have is that I have my x times theta." + }, + { + "text": "I'm going to allow myself some normalization factor phi." + }, + { + "text": "And we'll see, for example, that it's very convenient when I talk about the Gaussian." + }, + { + "text": "Because even if I know this guy, which I actually pull into my, oh, that's over here, right?" + }, + { + "text": "I know sigma squared, but I don't want to change my parameter to be mu over sigma squared." + }, + { + "text": "It's kind of painful." + }, + { + "text": "So I just take mu, and I'm going to keep this guy as being this phi over there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk36.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk36.json new file mode 100644 index 0000000000000000000000000000000000000000..89f73402c1fdd2bf2eeed62666de95f3d88a1238 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk36.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's called the dispersion parameter from a clear analogy with the Gaussian." + }, + { + "text": "That's the variance, and that's measuring dispersion." + }, + { + "text": "So here, what I want is I'm going to think throughout this class." + }, + { + "text": "So phi may be known or not." + }, + { + "text": "And when it's not known, this actually might turn into some exponential family, or it might not." + }, + { + "text": "And the main reason is because this b of theta over phi is not necessarily a function of theta over phi." + }, + { + "text": "If I actually have phi unknown, then y theta over phi has to be, this guy has to be my new parameter." + }, + { + "text": "And b might not be a function of this new parameter." + }, + { + "text": "So in a way, it may or may not, but this is not really a concern that we're going to have, because throughout this class, we're going to assume that phi is known." + }, + { + "text": "Phi is going to be known all the time, which means that this is always an exponential family." + }, + { + "text": "And it's just the simplest one you could think of." + }, + { + "text": "One dimensional parameter, one dimensional response, and I just have the product is just y times, or we used to call it x." + }, + { + "text": "Now I've switched to y." + }, + { + "text": "But y times theta divided by phi." + }, + { + "text": "Should I write this, or is this clear to everyone what this is?" + }, + { + "text": "Let me write it somewhere so we actually keep track of it for the 10 minutes." + }, + { + "text": "OK, so this is, we have, remember we had all the distributions." + }, + { + "text": "And then here we had the exponential family." + }, + { + "text": "And now we have the canonical exponential family." + }, + { + "text": "It's actually much, much smaller." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk37.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk37.json new file mode 100644 index 0000000000000000000000000000000000000000..611f08f23a902183ca152ce8cba2cc234c17366b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk37.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, actually, it's probably sort of a good picture." + }, + { + "text": "And what I have is that my density, or my PMF, is just exponential y times theta minus b of theta divided by phi." + }, + { + "text": "And I have plus c of, oh, yeah, plus c of y phi, which means that this is really, if phi is known, h of y is just exponential c of y phi." + }, + { + "text": "Actually, this is the reason why it's not necessarily a canonical family." + }, + { + "text": "It might not be that this depends only on y." + }, + { + "text": "It could depend on y and phi in some annoying way, and I may not be able to break it." + }, + { + "text": "But if phi is known, this is just a function that depends on y." + }, + { + "text": "Agreed?" + }, + { + "text": "In particular, I hope you can convince yourself that this is just a subcase of everything we've seen before." + }, + { + "text": "So for example, the Gaussian, when the variance is known, is indeed of this form." + }, + { + "text": "So we still have it on the board." + }, + { + "text": "So here's my y." + }, + { + "text": "So let me write this as f theta of y." + }, + { + "text": "So every x is replaced with y. Blah, blah, blah." + }, + { + "text": "This is this guy." + }, + { + "text": "And now what I have is that this is going to be my phi." + }, + { + "text": "This is my parameter theta." + }, + { + "text": "So I'm definitely of the form y times theta divided by phi." + }, + { + "text": "And then here, I have a function b that depends only on theta over phi again." + }, + { + "text": "So b of theta is mu squared divided by 2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk38.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk38.json new file mode 100644 index 0000000000000000000000000000000000000000..8580549781bf648098829c5beb6e58f82df064eb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk38.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's divided by sigma square." + }, + { + "text": "And then I have this extra stuff, but I really don't care what it is for now." + }, + { + "text": "It's just something that depends only on y and known stuff." + }, + { + "text": "So it's just a function of y." + }, + { + "text": "Just like my h, I stuff everything in there." + }, + { + "text": "The b, though, this thing here, this is actually what's important." + }, + { + "text": "Because in a canonical family, if you think about it, when you know phi, this is just y times theta scaled by a known constant." + }, + { + "text": "Sorry, y times theta scaled by a known constant is the first term." + }, + { + "text": "The second term is b of theta scaled by some known constant." + }, + { + "text": "But b of theta is what's going to make the difference between Gaussian and Bernoulli's and gammas and betas." + }, + { + "text": "This is all in this b of theta." + }, + { + "text": "b of theta contains everything that's idiosyncratic to this particular distribution." + }, + { + "text": "And so this is going to be important." + }, + { + "text": "And we will see that b of theta is going to capture information about the mean, about the variance, about the likelihood, about everything." + }, + { + "text": "Should I go through this computation?" + }, + { + "text": "I mean, it's the same." + }, + { + "text": "We've just done it." + }, + { + "text": "So maybe it's probably better if you can redo it on your own." + }, + { + "text": "So the canonical exponential family also has other distributions." + }, + { + "text": "So there's the Gaussian, and there's the Poisson, and there's the Bernoulli." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk39.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk39.json new file mode 100644 index 0000000000000000000000000000000000000000..e7503da5bdfd1b43af25b138aa6e92f9d60f5b5b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk39.json @@ -0,0 +1,62 @@ +[ + { + "text": "But the other ones may not be part of this." + }, + { + "text": "In particular, think about the gamma distribution." + }, + { + "text": "We had this log x was one of those things that showed up." + }, + { + "text": "I mean, I cannot get rid of this log x. I mean, that's part of it, except if a is equal to 1." + }, + { + "text": "And I know it for sure." + }, + { + "text": "So if a is equal to 1, then I'm going to have a minus 1, which is equal to 0." + }, + { + "text": "So I'm going to have a minus 1 times log x, which is going to be just 0." + }, + { + "text": "So log x is going to vanish from here." + }, + { + "text": "If a is equal to 1, then this distribution is actually much nicer." + }, + { + "text": "And it actually does not even deserve the name gamma." + }, + { + "text": "What is it if a is equal to 1?" + }, + { + "text": "It's an exponential, right?" + }, + { + "text": "Gamma of 1 is equal to 1. x to the a minus 1 is equal to 1. b, so I have exponential x over b divided by b." + }, + { + "text": "So 1 over b, call it lambda." + }, + { + "text": "And this is just an exponential distribution." + }, + { + "text": "And so every time you're going to see something, so all these guys that don't make it to this table, they could be part of those guys." + }, + { + "text": "But they're just to have another name in this thing." + }, + { + "text": "So you can compute the value of theta for different values." + }, + { + "text": "So again, you still have some continuous or discrete ones." + }, + { + "text": "This is my b of theta." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk4.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..7bcd652938f0899eaa61ff94c0f0810d310b07d7 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "But it's more than that." + }, + { + "text": "So we'll actually come to this particular family of distribution." + }, + { + "text": "Why this particular family?" + }, + { + "text": "Because in a way, everything we've done for the linear model with Gaussian is going to extend fairly naturally to this family." + }, + { + "text": "And it actually also, because it encompasses pretty much everything, all the distributions we've discussed before." + }, + { + "text": "All right, so the second thing that I want to question, so before we just said, well, mu of x was directly equal to this thing." + }, + { + "text": "Mu of x was directly x transpose beta." + }, + { + "text": "So I knew I was going to have an x transpose beta." + }, + { + "text": "And I said, well, I could do something with this x transpose beta before I used it to explain the expected value." + }, + { + "text": "But I'm actually taking it like that." + }, + { + "text": "Here we're going to say, let's extend this to some function is equal to this thing." + }, + { + "text": "Now, admittedly, this is not the most natural way to think about it." + }, + { + "text": "What you would probably feel more comfortable doing is write something like mu of x is a function." + }, + { + "text": "Let's call it f of x transpose beta." + }, + { + "text": "But here I just decide to call f g inverse." + }, + { + "text": "OK, that's just my g inverse, yes." + }, + { + "text": "Is this different than just transforming the x's?" + }, + { + "text": "Yeah." + }, + { + "text": "I mean, what transformation do you want to put on your x's?" + }, + { + "text": "Like, is this equivalent to just applying some function to each individual x component and then multiplying that beta to get the mean?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk40.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk40.json new file mode 100644 index 0000000000000000000000000000000000000000..a4fb0b65f5388522d17114f3d137c0e12fa325f1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk40.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I said this is actually really what captures my theta." + }, + { + "text": "This b is actually called cumulant generating function." + }, + { + "text": "I don't have time." + }, + { + "text": "I could write five slides to explain to you." + }, + { + "text": "But it would just only tell you why it's called cumulant generating function." + }, + { + "text": "It's also known as the log of the moment generating function." + }, + { + "text": "And the way it's called cumulant generating function is because if I start taking successive derivatives and evaluate them at 0, I get the successive cumulants of this distribution, which are some transformation of the moment." + }, + { + "text": "What is the function b?" + }, + { + "text": "The function b." + }, + { + "text": "So this is just normalization." + }, + { + "text": "So this is just to tell you I can compute this, but I really don't care." + }, + { + "text": "And obviously, I don't care about stuff that's complicated." + }, + { + "text": "This is actually cute." + }, + { + "text": "And this is what computes everything." + }, + { + "text": "And the rest is just some general description." + }, + { + "text": "You don't need me to tell you that the range of y is 0 to infinity." + }, + { + "text": "And that is essentially telling me this is going to give me some hints as to which link function I should be using." + }, + { + "text": "Because the range of y tells me what the range of expectation of y is going to be." + }, + { + "text": "Here it tells me that the range of y is between 0 and 1." + }, + { + "text": "So what I want to show you is that this captures a variety of different ranges that you can have." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk41.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk41.json new file mode 100644 index 0000000000000000000000000000000000000000..5bc0529fcb2c87a036825dc5eca45e610158d843 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk41.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I'm going to want to go into the likelihood." + }, + { + "text": "And the likelihood I'm actually going to use to compute the expectations." + }, + { + "text": "But since I actually don't have time to do this now, let's just go quickly through this and give you a spoiler alert to make sure that you all wake up on Thursday and really, really want to think about coming here immediately." + }, + { + "text": "So the thing I'm going to want to do, as I said, is it would be nice if, at least for this canonical family, when I give you b, you would be able to say, oh, here is a simple computation of b that would actually give me the mean and the variance." + }, + { + "text": "The mean and the variance are also known as moments." + }, + { + "text": "b is called cumulant generating function." + }, + { + "text": "So it sounds like moments being related to cumulants might have a path to finding those." + }, + { + "text": "And it might involve taking derivatives of b, as we'll see." + }, + { + "text": "The way we're going to prove this is by using this thing that we've used several times." + }, + { + "text": "So this property we use when we're computing, remember, the Fisher information." + }, + { + "text": "We had two formulas for the Fisher information." + }, + { + "text": "One was the expectation of the second derivative of the likelihood." + }, + { + "text": "And one was negative expectation of the square." + }, + { + "text": "Sorry, expectation of the square." + }, + { + "text": "And the other one was negative the expectation of the second derivative." + }, + { + "text": "The log likelihood is concave." + }, + { + "text": "So this number is negative." + }, + { + "text": "This number is positive." + }, + { + "text": "And the way we did this is by just permuting some derivative and integral here." + }, + { + "text": "And we used the fact that something that looked like this, the log likelihood is log of f theta." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk42.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk42.json new file mode 100644 index 0000000000000000000000000000000000000000..21653facee3fc11ef5000d2beef0a8de5ddfa092 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk42.json @@ -0,0 +1,62 @@ +[ + { + "text": "And when I take the derivative of this guy with respect to theta, then I have something that looks like the derivative divided by f theta." + }, + { + "text": "And if I start taking the integral against f theta of this thing, so the expectation of this thing, those things would cancel." + }, + { + "text": "And then I had just the integral of a derivative, which I would make a leap of faith and say that it's actually the derivative of the integral." + }, + { + "text": "But this was equal to 1." + }, + { + "text": "So this derivative was actually equal to 0." + }, + { + "text": "And so that's how you got that the expectation of the derivative of the log likelihood is equal to 0." + }, + { + "text": "And you do it once again, and you get this guy." + }, + { + "text": "There's just some nice things that happen with taking the derivative of the log." + }, + { + "text": "We've done that." + }, + { + "text": "We'll do that again." + }, + { + "text": "But once you do this, you can actually apply it." + }, + { + "text": "And missing a parenthesis over there." + }, + { + "text": "So when you write the log likelihood, it's just log of an exponential." + }, + { + "text": "That's actually pretty nice." + }, + { + "text": "Just like the least squares came naturally, the least squares criterion came naturally when we took the log likelihood of the Gaussians." + }, + { + "text": "We're going to have the same thing that happens." + }, + { + "text": "When I take the log of the density, the exponential is going to go away." + }, + { + "text": "And then I'm going to use this formula." + }, + { + "text": "But this formula is going to actually give me an equation directly." + }, + { + "text": "Oh, that's where it was." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk43.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk43.json new file mode 100644 index 0000000000000000000000000000000000000000..7f84c7ac778972c0a276af273b35f04b2d19dc71 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk43.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's the one that's missing it there." + }, + { + "text": "So the expectation minus this thing is going to be equal to 0, which tells me that the expectation is just the derivative." + }, + { + "text": "So it's still a function of theta, but it's just the derivative of b." + }, + { + "text": "And the variance is just going to be the second derivative of b." + }, + { + "text": "But remember, this was some sort of a scaling." + }, + { + "text": "It's called the dispersion parameter." + }, + { + "text": "So if I had a Gaussian, and the variance of the Gaussian did not depend on the sigma square, which I stuffed in this phi, that would be certainly weird." + }, + { + "text": "And it cannot depend only on mu." + }, + { + "text": "And so for the Gaussian, this is definitely going to be equal to 1." + }, + { + "text": "And this is just going to be equal to my variance." + }, + { + "text": "So this is just by taking the second derivative." + }, + { + "text": "So basically, the take-home message is that this function b captures, by taking one derivative of the expectation and by taking two derivatives, captures the variance." + }, + { + "text": "Another thing that's actually cool, and we'll come back to this and I want you to think about, is if this second derivative is the variance, what can I say about this thing?" + }, + { + "text": "What do I know about a variance?" + }, + { + "text": "Yeah, it's positive." + }, + { + "text": "So I know that this is positive." + }, + { + "text": "So what does that tell me?" + }, + { + "text": "Positive?" + }, + { + "text": "That's convex, right?" + }, + { + "text": "A function that has positive second derivative is convex." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk44.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk44.json new file mode 100644 index 0000000000000000000000000000000000000000..d5f75378f61eee780be265f51bdebc08ef9bcc39 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk44.json @@ -0,0 +1,11 @@ +[ + { + "text": "So we're going to use that as well." + }, + { + "text": "So yeah, I'll see you on Thursday." + }, + { + "text": "Have your homework." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk5.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..be889780830d4833b3e56baa49edaba9d1277e77 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "Oh, no, certainly not, right?" + }, + { + "text": "I mean, if I force you to work with x1 plus x2, you cannot work with any function of x1 plus any function of x2, right?" + }, + { + "text": "So yeah, this is different." + }, + { + "text": "So yeah, the transformation would be just the simple part of your linear regression problem, where you would take your x's, transform them, and then just apply another linear regression." + }, + { + "text": "This is genuinely new." + }, + { + "text": "Any other question?" + }, + { + "text": "All right, so this function g, and the reason why I sort of have to stick to this slightly less natural way of defining it is because that's g that gets a name, not g inverse that gets a name." + }, + { + "text": "And the name of g is the link function." + }, + { + "text": "So if I want to give you a generalized linear model, I need to give you two ingredients." + }, + { + "text": "The first one is the random component, which is the distribution of y given x." + }, + { + "text": "And it can be anything in what's called the exponential family of distributions." + }, + { + "text": "So for example, I could say y given x is Gaussian with mean ux sigma squared identity." + }, + { + "text": "But I could also tell you y given x is gamma with shape parameter equal to alpha of x. I could do some weird things like this." + }, + { + "text": "And the second thing is I need to give you a link function." + }, + { + "text": "And the link function is going to become very clear how you pick a link function." + }, + { + "text": "And the only reason that you actually pick a link function is because of compatibility." + }, + { + "text": "This mu of x, I call it mu because mu of x is always the conditional expectation of y given x, always, which means that let's think of y as being a Bernoulli random variable." + }, + { + "text": "Where does mu of x live?" + }, + { + "text": "AUDIENCE 2." + }, + { + "text": "0, 1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk6.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..8cb4d97427833f7219b0ac485c9a506b1a3240c9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "0, 1, right?" + }, + { + "text": "That's the expectation of a Bernoulli." + }, + { + "text": "It's just the probability that my coin flip gives me 1." + }, + { + "text": "So it's a number between 0 and 1." + }, + { + "text": "But this guy right here, if my x's are anything, think of any body measurements, plus I take linear combinations with arbitrarily large coefficients, this thing can be any real number." + }, + { + "text": "So the link function, what it's effectively going to do is make those two things compatible." + }, + { + "text": "It's going to take my number, which, for example, is constrained to be between 0 and 1, and map it into the entire real line." + }, + { + "text": "If I have mu, which is forced to be positive, for example, in an exponential distribution, the mean is positive, right?" + }, + { + "text": "That's the, say, I don't know, inter-arrival time for Poisson process." + }, + { + "text": "This thing is known to be positive for an exponential." + }, + { + "text": "I need to map something that's exponential to the entire real line." + }, + { + "text": "I need a function that takes something positive and then tickets everyone." + }, + { + "text": "So we'll see, by the end of this chapter, you will have 100 ways of doing this." + }, + { + "text": "But there are some more traditional ones than other." + }, + { + "text": "So before we go any further, I gave you this example of a Bernoulli random variable." + }, + { + "text": "Let's see a few examples that actually fit there." + }, + { + "text": "Yes?" + }, + { + "text": "AUDIENCE 1 Will it come up later if we already know why the mean distribution is increasing entirely?" + }, + { + "text": "Why can't we do it?" + }, + { + "text": "PHILIPPE RIGOLLET Well, actually, this will not come up later." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk7.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..7a08a1b997a550d2298989615c5c3d9d139188e0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "It should be very clear from here." + }, + { + "text": "Because if I actually have a model, I just want it to be plausible, right?" + }, + { + "text": "I mean, what happens if I suddenly decide that my, so this is what's going to happen." + }, + { + "text": "You're going to have only data to fit this model." + }, + { + "text": "Let's say you actually forget about this thing here." + }, + { + "text": "You can always do this, right?" + }, + { + "text": "You can always say, I'm going to pretend my y's just happen to be the realizations of, say, Gaussians that happen to be 0 or 1 only." + }, + { + "text": "You can always stuff that in some linear model, right?" + }, + { + "text": "You will have some least squares estimator for beta." + }, + { + "text": "But what's going to happen, and it's going to be fine." + }, + { + "text": "For all the points that you see, it will definitely put some number that's actually between 0 and 1." + }, + { + "text": "So this is what your picture is going to look like." + }, + { + "text": "You're going to have a bunch of values for x." + }, + { + "text": "This is your y." + }, + { + "text": "And so these are the values of x that you will get." + }, + { + "text": "And for y, you will see either 0 or 1, right?" + }, + { + "text": "That's what your Bernoulli data set would look like with a one-dimensional x." + }, + { + "text": "Now, if you do least squares on this, you will find this." + }, + { + "text": "And for this guy, this line certainly takes values between 0 and 1." + }, + { + "text": "But let's say now you get an x here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk8.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..dfd389e2603960133ef12ce8ca9c769bb873bedf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "You're going to actually start pretending the probability that it spits out one conditionally in x is like 1.2, and that's going to be weird." + }, + { + "text": "OK?" + }, + { + "text": "Any other questions?" + }, + { + "text": "All right, so let's start with some examples." + }, + { + "text": "Right?" + }, + { + "text": "I mean, you got so used to them throughout this course." + }, + { + "text": "So the first one is all these things are taken." + }, + { + "text": "So there's a few books on generalizing your models, generalize additive models, and there's tons of applications that you can see." + }, + { + "text": "Those are extremely versatile." + }, + { + "text": "And as soon as you want to do modeling to explain some y given x, you sort of need to do that if you want to go beyond linear models." + }, + { + "text": "So this was the disease occurring rate." + }, + { + "text": "So you have a disease epidemic, and you want to basically model the expected number of new cases given at a certain time." + }, + { + "text": "OK?" + }, + { + "text": "So you have time that progresses for each of your reservation." + }, + { + "text": "Each of your relation is a timestamp, say, I don't know, 20th day." + }, + { + "text": "And your response is the number of new cases." + }, + { + "text": "And you're going to actually put your model directly on mu, right?" + }, + { + "text": "When I looked at this, everything here was on mu itself, on the expected, right?" + }, + { + "text": "Mu of x is always the expected, the conditional expectation of y given x." + }, + { + "text": "Right?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk9.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..6cb6e3c31c39383cd65adbaafb2b2ceb06ed1ff3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_2_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So all I need to model is this expected value." + }, + { + "text": "So this mu, I'm going to actually say, so I look at some parameters, and it says, well, it increases exponentially." + }, + { + "text": "So I want to have some sort of exponential trend." + }, + { + "text": "I can parameterize that in several ways." + }, + { + "text": "And the two parameters I want to slap in is some sort of gamma, which is just the coefficient." + }, + { + "text": "And then there's some rate delta that's in the exponential." + }, + { + "text": "OK?" + }, + { + "text": "So if I tell you it's exponential, that's a nice family of functions you might want to think about." + }, + { + "text": "OK, so here, mu of x, if I want to keep the notation x, is gamma exponential delta x, right?" + }, + { + "text": "Except that here, my x are t1, t2, t3, et cetera." + }, + { + "text": "OK?" + }, + { + "text": "And I want to find what the parameters gamma and delta are because I want to be able to maybe compare different epidemics and see if they have the same parameter or maybe just do some prediction based on the data that I have to extrapolate in the future." + }, + { + "text": "OK?" + }, + { + "text": "So here, clearly, mu of x is not of the form x transpose beta." + }, + { + "text": "Right?" + }, + { + "text": "That's not x transpose beta at all." + }, + { + "text": "And it's actually not even a function of x transpose beta." + }, + { + "text": "Right?" + }, + { + "text": "There's two parameters, gamma and delta, and it's not of the form." + }, + { + "text": "So here, I have x, which is 1 and x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk0.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..d4554873825c6719ec24d2e3b27b154cb3857640 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "Chapter is a natural capstone chapter for this entire course." + }, + { + "text": "We'll see some of the things we've seen during maximum likelihood and some of the things we've seen during linear regression, some of the things we've seen in terms of the basic modeling that we've had before." + }, + { + "text": "We're not going to go back to much inference questions." + }, + { + "text": "It's really going to be about modeling." + }, + { + "text": "And in a way, generalized linear models, as the word says, are just a generalization of linear models." + }, + { + "text": "And they're actually extremely useful." + }, + { + "text": "They're often forgotten about, and people just jump onto machine learning and sophisticated techniques." + }, + { + "text": "But those things do the job quite well." + }, + { + "text": "So let's see in what sense they are a generalization of the linear model." + }, + { + "text": "So remember, the linear model looked like this." + }, + { + "text": "We said that y was equal to x transpose beta plus epsilon." + }, + { + "text": "That was our linear regression model." + }, + { + "text": "And another way to say this is that if I, let's assume that those were, say, Gaussian with mean 0 and identity covariance matrix, then another way to say this is that the conditional distribution of y given x is a Gaussian with mean x transpose beta and variance, well, we had a sigma square, which I will forget as usual, x transpose beta and then sigma square." + }, + { + "text": "So here, we just assumed that, so what is regression?" + }, + { + "text": "It's just saying I'm trying to explain y as a function of x given x. I'm assuming a distribution for the y." + }, + { + "text": "And this x is just going to be here to help me model what the mean of this Gaussian is." + }, + { + "text": "I mean, I could have something crazy." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk1.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..2c2e721380f9d4710c30835403ae73ceebf39538 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "I could have something that looks like y given x is n0 x transpose beta." + }, + { + "text": "And then this guy could be some other thing, which looks like, I don't know, some x transpose gamma squared times, I don't know, x x transpose plus identity, some crazy thing that depends on x here." + }, + { + "text": "And we deliberately assume that all the thing that depends on x shows up in the mean." + }, + { + "text": "And so what I have here is that y given x is a Gaussian with a mean that depends on x and covariance matrix sigma square identity." + }, + { + "text": "Now, the linear model assumed a very specific form for the mean." + }, + { + "text": "It said, I want the mean to be equal to x transpose beta, which, remember, was the sum from, say, j equals 1 to p of beta j xj, where the xj's are the coordinates of x." + }, + { + "text": "But I could do something also more complicated." + }, + { + "text": "I could have something that looks like, instead, replace this by, I don't know, sum of beta j log of x to the j divided by x to the j squared, or something like this." + }, + { + "text": "I could do this as well." + }, + { + "text": "So there's two things that we've assumed." + }, + { + "text": "The first one is that when I look at the conditional distribution of y given x, x affects only the mean." + }, + { + "text": "I also assumed that it was Gaussian, and that it affects only the mean." + }, + { + "text": "And the mean is affected in a very specific way, which is linear in x." + }, + { + "text": "So this is essentially the things we're going to try to relax." + }, + { + "text": "So the first thing that we assume, the fact that y was Gaussian and had only its mean that depended on x, is what's called the random component." + }, + { + "text": "It just says that the response variables sort of make sense to assume that they're Gaussian." + }, + { + "text": "And everything was essentially captured." + }, + { + "text": "So there's this property of Gaussians that if you tell me if the variance is known, all you need to tell me to understand exactly what the distribution of a Gaussian is, all you need to tell me is its expected value." + }, + { + "text": "So that's this mu of x." + }, + { + "text": "And the second thing is that we had this link that says, well, I need to find a way to use my x's to explain this mu." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk10.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..6a481ea5cb5adb97b455c8bc5c53385e58a31448 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Right?" + }, + { + "text": "I have two parameters." + }, + { + "text": "So what I do here is that I say, well, first, let me transform mu in such a way that I can hope to see something that's linear." + }, + { + "text": "So if I transform mu, I'm going to have log of mu, which is log of this thing." + }, + { + "text": "Right?" + }, + { + "text": "So log of mu of x is equal to log of gamma plus log of exponential delta x, which is delta x. OK?" + }, + { + "text": "And now, this thing is actually linear in x." + }, + { + "text": "So I have that this guy is my first beta 1." + }, + { + "text": "And so that's beta 1 times 1." + }, + { + "text": "And this guy is beta 2 times, sorry, let's say beta 0 times 1." + }, + { + "text": "And this guy is beta 1 times x. OK?" + }, + { + "text": "So that looks like a linear model." + }, + { + "text": "I just have to change my parameters." + }, + { + "text": "My parameters, beta 1 becomes the log of gamma, and beta 2 becomes delta itself." + }, + { + "text": "And the reason why we do this is because, well, the way we put those gamma and those delta was just so that we have some parametrization." + }, + { + "text": "It just so happens that if we want this to be linear, we need to just change the parametrization itself." + }, + { + "text": "This is going to have some effects." + }, + { + "text": "We know that it's going to have some effect in the Fisher information." + }, + { + "text": "It's going to have a bunch of effect to change those things." + }, + { + "text": "But that's what needs to be done to have a generalized linear model." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk11.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..b87248456f36363ec8012cc422267e73498f0d65 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, here, the function that I took to turn it into something that's linear is simple." + }, + { + "text": "It came directly from some natural thing it would do here, which is taking the log." + }, + { + "text": "And so the function g, the link that I take, is called the log link, very creatively." + }, + { + "text": "And it's just the function that I apply to mu so that I see something that's linear and that looks like this." + }, + { + "text": "OK?" + }, + { + "text": "So now, this only tells me how to deal with the link function." + }, + { + "text": "But I still have to deal with 0.1." + }, + { + "text": "And this, again, is just some modeling." + }, + { + "text": "Given some data, some random data, what distribution do you choose to explain the randomness?" + }, + { + "text": "And this, I mean, unless there's no choice, it's just a matter of practice." + }, + { + "text": "I mean, why would it be Gaussian and not doubly exponential?" + }, + { + "text": "There's matters of convenience that come into this." + }, + { + "text": "And there's just matter of experience that come into this." + }, + { + "text": "I remember when you chat with engineers, they have a very good notion of what the distribution should be." + }, + { + "text": "They have Weibull distributions." + }, + { + "text": "They do optics and things like this." + }, + { + "text": "So there's some distributions that just come up." + }, + { + "text": "But sometimes, you just have to work." + }, + { + "text": "Now, here, what do we have?" + }, + { + "text": "The thing we're trying to measure y, as we said, so mu is the conditional expectation of y given x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk12.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..af95e1917c846d9d478b143cf28493ff3dd4d7d1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "But y is the number of new cases, right?" + }, + { + "text": "Well, it's a number of." + }, + { + "text": "And the first thing you should think of when you think about number of, if it were bounded above, you would think binomial, baby." + }, + { + "text": "But here, it's just a number." + }, + { + "text": "So you think Poisson." + }, + { + "text": "That's how insurers think." + }, + { + "text": "I have a number of claims per year." + }, + { + "text": "This is a Poisson distribution." + }, + { + "text": "And hopefully, they can model the conditional distribution of the number of claims given everything that they actually ask you in this survey that I hear you now fill in 15 minutes." + }, + { + "text": "All right, so now you have this Poisson distribution." + }, + { + "text": "And that's just a modeling assumption." + }, + { + "text": "There's no particular reason why you should do this, except that that might be a good idea." + }, + { + "text": "And the expected value of your Poisson has to be this mu i at time i." + }, + { + "text": "Any question about this slide?" + }, + { + "text": "So let's switch to another example." + }, + { + "text": "Another example is the so-called prey capture rate." + }, + { + "text": "So here, what you're interested in is the rate capture of prey's Yi for a given prey." + }, + { + "text": "And you have Xi, which is your explanation." + }, + { + "text": "And this is just the density of prey." + }, + { + "text": "So you're trying to explain the rate of captures of preys given the density of the prey." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk13.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..82b4fda8d85deb20289b741cbb4d1b501793ba9c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so you need to find some sort of relationship between the two." + }, + { + "text": "And here again, you talk to experts." + }, + { + "text": "And what they tell you is that, well, it's going to be increasing." + }, + { + "text": "Animals, like predators, are going to just eat more if there's more preys." + }, + { + "text": "But at some point, they're just going to level off because they're just going to be completely full." + }, + { + "text": "And they're going to stop capturing those preys." + }, + { + "text": "And you're just going to have some phenomenon that looks like this." + }, + { + "text": "So here is a curve that sort of makes sense." + }, + { + "text": "As your capture rate goes from 0 to 1, you're increasing." + }, + { + "text": "And then you see you have this concave function that says that at some point, it levels off." + }, + { + "text": "So here, one way I could, I mean, there's again many ways I could just model a function that looks like this." + }, + { + "text": "But a simple one that has only two parameters is this one, where mu i is just this function of Xi, where I have some parameter alpha here and some parameter h here." + }, + { + "text": "So there's clearly, so this function, there's one that essentially tells you." + }, + { + "text": "So this thing starts at 0 for sure." + }, + { + "text": "And essentially, alpha tells you how sharp this thing is." + }, + { + "text": "And h tells you at which point you end here." + }, + { + "text": "It's not exactly what those values are equal to, but it tells you this." + }, + { + "text": "So simple." + }, + { + "text": "And well, no, OK, sorry." + }, + { + "text": "That's actually alpha, which is the maximum capture rate." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk14.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..be9a8b2fcbc0f8c0b1e49f0850eea5b9ab306080 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "And h represents the prey density at which the capture rate is." + }, + { + "text": "So that's the half time." + }, + { + "text": "So there's actual values for this." + }, + { + "text": "So now I have this function." + }, + { + "text": "It's certainly not a function." + }, + { + "text": "I don't see it as a function of x." + }, + { + "text": "So I need to find something that looks like a function of x. OK?" + }, + { + "text": "So now here, there's no log." + }, + { + "text": "There's no, well, I could actually take a log here." + }, + { + "text": "But I would have log of x and log of x plus h. So that would be weird." + }, + { + "text": "So what we propose to do here is to look, rather than looking at mu i, we look at 1 over mu i." + }, + { + "text": "And so since your function was mu i, when you take 1 over mu i, you get h plus xi divided by alpha xi, which is h over alpha times 1 over xi plus 1 over alpha." + }, + { + "text": "And now if I am willing to make this transformation of variables and say, actually, my x, whether it's the density of prey or the inverse density of prey, it really doesn't matter." + }, + { + "text": "I can always make the transformation when the data comes." + }, + { + "text": "Then I'm actually just going to think of this as being some linear function, beta 0 plus beta 1, which is this guy, times 1 over xi." + }, + { + "text": "And now my new variable becomes 1 over xi." + }, + { + "text": "And now it's linear." + }, + { + "text": "And the transformation I had to take was this 1 over x, which is called the reciprocal link." + }, + { + "text": "You can probably guess what the exponential link is going to be and things like this." + }, + { + "text": "So we'll talk about other links that have slightly less obvious names." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk15.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..5d2ed9123f0b6a47840cca2ce477712ca74abf5e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, again, modeling." + }, + { + "text": "So this was the random component." + }, + { + "text": "This was the easy part." + }, + { + "text": "Now I need to just pour in some domain knowledge about how do I think this function, this y, which is the rate of capture of preys." + }, + { + "text": "I want to understand how this thing is actually changing." + }, + { + "text": "What is the randomness of the thing around its mean?" + }, + { + "text": "And something that comes from this textbook, the standard deviation of capture rate might be approximately proportional to the mean rate." + }, + { + "text": "You need to find a distribution that actually has this property." + }, + { + "text": "And it turns out that this happens for gamma distribution." + }, + { + "text": "In gamma distributions, just like, say, for Poisson distribution, for Poisson, the variance and the mean are of the same order." + }, + { + "text": "Here is the standard deviation that's of the same order as the mean for gammas." + }, + { + "text": "And it's a positive distribution as well." + }, + { + "text": "So here is a candidate." + }, + { + "text": "Now, since we're sort of constrained to work under the exponential family of distributions, then you can just go through your list and just decide which one works best for you." + }, + { + "text": "All right, third example." + }, + { + "text": "So here we have binary response." + }, + { + "text": "Here, essentially, the binary response variable indicates the presence or absence of post-covariative deforming for kyphosis on children." + }, + { + "text": "And here, rather than having one covariate, which was before, in the first example, was time, in the second example was the density, here there's three covariates." + }, + { + "text": "So you measure on children." + }, + { + "text": "The first one is age of the child." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk16.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..ef9ff3f87e1e355af4391eaee6e902d9ab157079 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "The second one is the number of vertebrae involved in the operation." + }, + { + "text": "And the third one is the start of the range, so where it is on the spine." + }, + { + "text": "So the response variable here is, did it work or not?" + }, + { + "text": "I mean, that's very simple." + }, + { + "text": "And so here, it's nice, because the random component is the easiest one." + }, + { + "text": "As I said, any random variable that takes only two outcomes must be a Bernoulli." + }, + { + "text": "So that's nice." + }, + { + "text": "There's no modeling going on here." + }, + { + "text": "So you know that y given x is going to be Bernoulli, but of course, all your efforts are going to try to understand what the conditional mean of your Bernoulli, what the conditional probability of being 1 is going to be." + }, + { + "text": "And so in particular, so I'm just here." + }, + { + "text": "I'm spelling it out before we close those examples." + }, + { + "text": "I cannot say that mu of x is x transpose beta for exactly this picture that I drew for you here." + }, + { + "text": "There's just no way here." + }, + { + "text": "The goal of doing this is certainly to be able to extrapolate for yet unseen children whether this is something that we should be doing, and maybe the range of x's is actually going to be slightly out." + }, + { + "text": "And so OK, I don't want to say that I have a negative probability of outcome or a positive one, sorry, or a 1 that's lower than 1, so I need to make this transformation." + }, + { + "text": "What I need to do is to transform mu, which is we know only a number, all we know is a number between 0 and 1, and we need to transform it in such a way that it maps the entire real line, or reciprocally to say that, or inversely I should say, that f of x transpose beta should be a number between 0 and 1." + }, + { + "text": "I need to find a function that takes any real number and maps it into 0 and 1, and we'll see that again, but you have an army of functions that do that for you." + }, + { + "text": "What are those functions?" + }, + { + "text": "I'm sorry?" + }, + { + "text": "AUDIENCE MEMBER 2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk17.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..e618b05cddff9ee23141a82d1f3c33242aeb2d21 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "Trait function." + }, + { + "text": "PHILIPPE RIGOLLET." + }, + { + "text": "Trait?" + }, + { + "text": "AUDIENCE MEMBER 2." + }, + { + "text": "Trait, trait, trait." + }, + { + "text": "PHILIPPE RIGOLLET." + }, + { + "text": "Oh." + }, + { + "text": "Yeah, I want them to be invertible, right?" + }, + { + "text": "AUDIENCE MEMBER 2." + }, + { + "text": "Yeah." + }, + { + "text": "PHILIPPE RIGOLLET." + }, + { + "text": "Yeah." + }, + { + "text": "AUDIENCE MEMBER 2." + }, + { + "text": "Longest trait." + }, + { + "text": "PHILIPPE RIGOLLET." + }, + { + "text": "I have an army of function." + }, + { + "text": "I'm not asking for one soldier in this army." + }, + { + "text": "I want the name of this army." + }, + { + "text": "AUDIENCE MEMBER 2." + }, + { + "text": "They're invertible." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk18.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..f58b1220495ab9dfac97d370ddda29476838a3fd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "PHILIPPE RIGOLLET." + }, + { + "text": "Well, they're not really invertible either, right?" + }, + { + "text": "So they're actually in stats textbooks, because remember, statisticians don't know how to integrate functions, but they know how to turn a function into a Gaussian integral, so we know it integrates to 1, and things like this." + }, + { + "text": "Same thing here." + }, + { + "text": "We don't know how to build functions that are invertible and map the entire real line to 0, 1, but there's all the cumulative distribution functions that do that for us." + }, + { + "text": "So I can use any of those guys, and that's what I'm going to be doing, actually." + }, + { + "text": "All right, so just to recap what I just said as we were speaking, so a normal linear model is not appropriate for those examples if only because the response variable is not necessarily Gaussian." + }, + { + "text": "So and also because the linear model has to be, the mean has to be transformed before I can actually apply a linear model for all these plausible nonlinear models that I actually came up with." + }, + { + "text": "So the family we're going to go for is the exponential family of distributions, and we're going to be able to show, so one of the nice part of this is to actually compute maximum likelihood estimators for those, right?" + }, + { + "text": "In the linear model, maximum like, in the Gaussian linear model, maximum likelihood was as nice as it gets, right?" + }, + { + "text": "This actually was the least squares estimator." + }, + { + "text": "We had a closed form, x transpose x inverse x transpose y, and that was it." + }, + { + "text": "We had to just take one derivative." + }, + { + "text": "Here, we're going to have a generally concave likelihood." + }, + { + "text": "We're not going to be able to actually solve this thing directly in closed form unless it's Gaussian, but we will have, we'll see actually how this is not just a black box optimization of a concave function." + }, + { + "text": "We have a lot of properties of this concave function, and we will be able to show some iterative algorithms." + }, + { + "text": "We'll basically see how, when you open the box of convex optimization, you will actually be able to see how things work and actually implement it using least squares." + }, + { + "text": "So each iteration of this iterative algorithm will essentially be a least square, so that's actually quite huge." + }, + { + "text": "It's also very demonstrative of statisticians being pretty ingenious so that they don't have to call in some statistical software, but just can repeatedly call their least squares oracle within a statistical software." + }, + { + "text": "OK, so what is the exponential family?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk19.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..fbe7abc54d0348d4353fcfa16b5a9639e71fe8f7 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "I promised you the exponential family." + }, + { + "text": "Before we go into this, let me just tell you something about exponential families, and what's the only thing that differentiates an exponential family from all possible distributions?" + }, + { + "text": "An exponential family has two parameters, and those are not really parameters, but there's the theta parameter of my distribution." + }, + { + "text": "So it's going to be indexed by some parameter." + }, + { + "text": "Here, I'm only talking about the distribution of, say, some random variable or some random vector." + }, + { + "text": "So here, in this slide, you see that the parameter theta that indexes those distribution is k-dimensional, and the space of the x's that I'm looking at, so that should really be y." + }, + { + "text": "So what I'm going to plug in here is the conditional distribution of y given x, and theta is going to depend on x." + }, + { + "text": "But this really is the y." + }, + { + "text": "That's the distribution of the response variable." + }, + { + "text": "And so this is on q." + }, + { + "text": "So I'm going to assume that y is q-dimensional." + }, + { + "text": "Clearly, soon q is going to be equal to 1, but I can define those things generally." + }, + { + "text": "So I have this." + }, + { + "text": "I have to tell you what this looks like, and let's assume that this is a probability density function." + }, + { + "text": "So this notation, the fact that I just put my theta in subscript, is just for me to remember that this is the variable that indicates the random variable, and this is just the parameter." + }, + { + "text": "But I could just write it as a function of theta and x." + }, + { + "text": "This is just going to be, if you were in multivariable calc, you would have two parameters, theta and x, and you would need to give me a function." + }, + { + "text": "Now, think of x and theta as being one-dimensional at this point." + }, + { + "text": "Think of all the functions that can be depending on theta and x." + }, + { + "text": "There's many of them." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk2.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..4dfa619a62a8cb9f51581c665c6269ca8bec9c50 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the link was exactly mu of x was equal to x transpose beta." + }, + { + "text": "OK?" + }, + { + "text": "Now, we are talking about generalized linear models." + }, + { + "text": "So this part here, where mu of x is of the form, the way I want my beta, my x, to show up is linear." + }, + { + "text": "This will never be questioned." + }, + { + "text": "In principle, I could add a third point, which is just question this part, the fact that mu of x is x transpose beta." + }, + { + "text": "I could have some more complicated nonlinear function of x." + }, + { + "text": "And I will never do that, because we're talking about generalized linear model." + }, + { + "text": "The only thing with generalized are the random component, the conditional distribution of y given x, and the link that just says, well, once you actually tell me that the only thing I need to figure out is the mean, I'm just going to slap it exactly this x transpose beta thing without any transformation of x transpose beta." + }, + { + "text": "OK?" + }, + { + "text": "So those are the two things." + }, + { + "text": "It will become clearer what I mean." + }, + { + "text": "This sounds like a tautology, but let's just see how we could extend that." + }, + { + "text": "So what we're going to do in generalized linear models, so when I talk about GLMs, the first thing I'm going to do with my x is turn it into some x transpose beta." + }, + { + "text": "And that's just the L part." + }, + { + "text": "This I'm not going to be able to change." + }, + { + "text": "That's the way it works." + }, + { + "text": "I'm not going to do anything nonlinear." + }, + { + "text": "But the two things I'm going to change is this random component, which is that y, which used to be some Gaussian with mean mu of x variance sigma squared." + }, + { + "text": "So y given x, sorry." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk20.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..58f979f5cd191f971fd907b961bc1542b84ea77e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "And in particular, there's many ways theta and x can interact." + }, + { + "text": "What the exponential family does for you is that it restricts the way these things can actually interact with each other." + }, + { + "text": "It's essentially saying the following." + }, + { + "text": "It's saying this is going to be of the form exponential." + }, + { + "text": "So this exponential is really not much, because I could put a log next to it." + }, + { + "text": "But what I want is that the way theta and x interact has to be of the form theta times x in an exponential." + }, + { + "text": "So that's one of the ways you can think of them interacting." + }, + { + "text": "You just take the product of the two." + }, + { + "text": "Now, clearly, this is not a very rich family." + }, + { + "text": "So what I'm allowing myself is to just slap on some terms that depend only on theta and depend only on x." + }, + { + "text": "So let's just call this thing f of x g of theta." + }, + { + "text": "So here, I've restricted the way theta and x can interact." + }, + { + "text": "So I have something that depends only on x, something that depends only on theta." + }, + { + "text": "And here, I have this very specific interaction." + }, + { + "text": "And that's all that exponential families are doing for you." + }, + { + "text": "So if we go back to this slide, this is much more general." + }, + { + "text": "If I want to go from theta and x in r to theta and x theta in r to theta in rk and x in rq, I cannot take the product of theta and x. I cannot even take the inner product between theta and x, because they're not even of compatible dimensions." + }, + { + "text": "But what I can do is to first map my theta into something and map my x into something so that I actually end up having the same dimensions." + }, + { + "text": "And then I can take the inner product." + }, + { + "text": "That's the natural generalization of this simple product." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk21.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..36059f58796657121c5302bfc6135335368066e7 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what I have is if I want to go from theta to x, what I'm going to first do is I'm going to take theta eta of theta." + }, + { + "text": "So let's say eta 1 of theta to eta k of theta." + }, + { + "text": "And then I'm going to actually take x becomes t1 of x all the way to tk of x." + }, + { + "text": "And what I'm going to do is take the inner product." + }, + { + "text": "So let's call this eta." + }, + { + "text": "And let's call this t. And I'm going to take the inner product of eta and t, which is just the sum from j equal 1 to k of eta j of theta times tj of x." + }, + { + "text": "So that's just a way to say I want this simple interaction." + }, + { + "text": "But in higher dimension, the simplest way I can actually make those things happen is just by taking inner product." + }, + { + "text": "And so now what it's telling me is that the distribution, I want the exponential times something that depends only on theta and something that depends only on x." + }, + { + "text": "And so what it tells me is that when I'm going to take p of theta x, it's just going to be something which is exponential times the sum from j equal 1 to k of eta j theta tj of x." + }, + { + "text": "And then I'm going to have a function that depends only." + }, + { + "text": "So let me write it for now like c of theta." + }, + { + "text": "And then a function that depends only on x." + }, + { + "text": "Let me call it h of x." + }, + { + "text": "And for convenience, there's no particular reason why I do that." + }, + { + "text": "I'm taking this function c of theta, and I'm just actually pushing it in there." + }, + { + "text": "So I can write c of theta as exponential minus log of 1 over c of theta." + }, + { + "text": "And now I have exponential times exponential." + }, + { + "text": "So I push it in, and this thing actually looks like exponential sum from j equal 1 to k of eta j theta tj of x minus log 1 over c of theta times h of x." + }, + { + "text": "And this thing here, log 1 over c of theta, I call actually b of theta." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk22.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..9ce5d204be5cf62e2aafd3d850c84f7dd1eafe0a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because c, I called it c, but I can actually directly call it this guy b, and I don't actually care about c itself." + }, + { + "text": "Now, why don't I put back also h of x in there?" + }, + { + "text": "Because h of x is really here to just, how to put it?" + }, + { + "text": "h of x and b of theta don't play the same role." + }, + { + "text": "b of theta, in many ways, is a normalizing constant." + }, + { + "text": "I want this density to integrate to 1." + }, + { + "text": "If I did not have this guy, I'm not guaranteed that this thing integrates to 1." + }, + { + "text": "But by tweaking this function, b of theta or c of theta, their equivalent, I can actually ensure that this thing integrates to 1." + }, + { + "text": "So b of theta is just a normalizing constant." + }, + { + "text": "h of x is something that's going to be funny for us." + }, + { + "text": "It's going to be something that allows us to be able to treat both discrete and continuous variables within the framework of exponential families." + }, + { + "text": "So for those that are familiar with this, this is essentially saying that h of x is really just a change of measure." + }, + { + "text": "When I actually look at the density of p of theta, this is with respect to some measure, the fact that I just multiply by a function of x just means that I'm not looking that this guy here, without h of theta, is not the density with respect to the original measure, but it's the density with respect to the distribution that has h as a density." + }, + { + "text": "That's all I'm saying." + }, + { + "text": "So I can first transform my x's and then take the density with respect to that." + }, + { + "text": "If you don't want to think about densities or measures, you don't have to." + }, + { + "text": "This is just the way." + }, + { + "text": "This is just the definition." + }, + { + "text": "Is there any question about this definition?" + }, + { + "text": "So it looks complicated, but it's actually essentially the simplest way you could think about it." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk23.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..5eeb518a9d5894bf1eeb94d4fb8a4b81ffe8e5df --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "You want to be able to have x and theta interact, and you just say, I want the interaction to be of the form exponential x times theta." + }, + { + "text": "And if they're higher dimensions, I'm going to take the exponential of the function of x inner product for the function of theta." + }, + { + "text": "So I claimed since the beginning that the Gaussian was such an example, so let's just do it." + }, + { + "text": "Is the interaction between theta and x in a Gaussian of the form inner product?" + }, + { + "text": "And the answer is yes." + }, + { + "text": "Actually, whether I know or not what the variance is." + }, + { + "text": "So let's start for the case where I actually do not know what the variance is." + }, + { + "text": "So here I have x is n mu sigma squared." + }, + { + "text": "This is all one dimensional." + }, + { + "text": "And here I'm going to assume that my parameter is both mu and sigma squared." + }, + { + "text": "So what I need to do is to have some function of mu, some function of sigma squared, and take the inner product of some function of x and some other function of x." + }, + { + "text": "So I want to show that p theta of x is what?" + }, + { + "text": "Well, it's 1 over square root sigma 2 pi exponential minus x minus mu squared over 2 sigma squared." + }, + { + "text": "That's just my Gaussian density." + }, + { + "text": "And I want to say that this thing here, so clearly the exponential shows up already." + }, + { + "text": "I want to show that this is something that looks like eta 1 of mu sigma squared." + }, + { + "text": "So I have only two of those guys, so I'm going to need only two etas." + }, + { + "text": "So I want it to be eta 1 of mu and sigma times t1 of x plus eta 2 mu sigma squared times t2 of x." + }, + { + "text": "So I want to have something like that that shows up, and the only things that are left, I want them to depend either only on theta or only on x." + }, + { + "text": "So to find that out, we just need to expand." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk24.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..9b20dd7faa1dfbea7dd48300ad6e2453578b83cb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I'm going to first put everything into my exponential and expand this guy." + }, + { + "text": "So the first term here is going to be minus x squared over 2 sigma squared." + }, + { + "text": "The second term is going to be minus mu squared over 2 sigma squared." + }, + { + "text": "And then the cross term is going to be plus x mu divided by sigma squared." + }, + { + "text": "And then I'm going to put this guy here, so I have a minus log sigma root 2 pi." + }, + { + "text": "OK, so this term here contains an interaction between x and the parameters." + }, + { + "text": "This term here contains an interaction between x and the parameters." + }, + { + "text": "So let me try to write them in a way that I want." + }, + { + "text": "This guy only depends on the parameters." + }, + { + "text": "This guy only depends on the parameter." + }, + { + "text": "So I'm going to rearrange things." + }, + { + "text": "And so I claim that this is of the form x squared." + }, + { + "text": "Well, let's say, who's getting the minus?" + }, + { + "text": "Eta, OK." + }, + { + "text": "So it's x squared times minus 1 over 2 sigma squared plus x times mu over sigma squared." + }, + { + "text": "So that's this term here." + }, + { + "text": "That's this term here." + }, + { + "text": "Now I need to get this guy here." + }, + { + "text": "And that's minus." + }, + { + "text": "So I'm going to write it like this, minus." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk25.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..732b958a14a1b7707a0b37d4bdd107f5be9f2ac5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And now I have mu squared over 2 sigma squared plus log sigma square root 2 pi." + }, + { + "text": "OK?" + }, + { + "text": "And now this thing is definitely of the form t1 of x times, did I call them the right way or not?" + }, + { + "text": "Of course not." + }, + { + "text": "OK, so that's going to be t2 of x times eta 2 of x, eta 2 of theta." + }, + { + "text": "This guy is going to be t1 of x times eta 1 of theta." + }, + { + "text": "So just a function of theta times a function of x, just a function of theta times a function of x." + }, + { + "text": "And the way I combine this is just by summing them." + }, + { + "text": "And this is going to be my b of theta." + }, + { + "text": "What is h of x?" + }, + { + "text": "1." + }, + { + "text": "There's one thing I can actually play with." + }, + { + "text": "And this is something you're going to have some free choices." + }, + { + "text": "This is not actually completely determined here." + }, + { + "text": "Is that, for example, when I write the log sigma square root 2 pi, this is just log of sigma plus log square root 2 pi." + }, + { + "text": "So I have two choices here." + }, + { + "text": "Either my b becomes this guy, or so either I have b of theta, which is mu squared over 2 sigma squared plus log sigma square root 2 pi, and h of x is equal to 1." + }, + { + "text": "Or I have that b of theta is mu squared over 2 sigma squared plus log sigma, and h of x is equal to what?" + }, + { + "text": "1." + }, + { + "text": "Well, I can just push this guy out." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk26.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..7128910e23875de6e208c059db4ddc05705e82cc --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk26.json @@ -0,0 +1,62 @@ +[ + { + "text": "I can push it out of the exponential." + }, + { + "text": "And so it's just square root of 2 pi, which is a function of x, technically." + }, + { + "text": "I mean, it's a constant function of x, but it's a function of x." + }, + { + "text": "So you can see that it's not completely clear how you're going to do the trade-off." + }, + { + "text": "So the constant terms can go either in b or in h. But why bother with tracking down b and h when you can actually stuff everything into one and just call h 1 and call it a day?" + }, + { + "text": "So you can just forget about h. It's 1, and think about the rest." + }, + { + "text": "h won't matter, actually, for estimation purposes or anything like this." + }, + { + "text": "All right, so that's basically everything that's written." + }, + { + "text": "When sigma square is known, what's happening is that this guy here is no longer a function of theta, right?" + }, + { + "text": "Agreed?" + }, + { + "text": "This is no longer a parameter." + }, + { + "text": "When sigma square is known, then theta is equal to mu only." + }, + { + "text": "There's no sigma square going on." + }, + { + "text": "So everything that depends on sigma square can be thought as a constant, think 1." + }, + { + "text": "So in particular, this term here does not belong in the interaction between x and theta." + }, + { + "text": "It belongs to h, right?" + }, + { + "text": "So if sigma is known, then this guy is only a function of h of x." + }, + { + "text": "So h of x becomes exponential x squared minus x squared over 2 sigma squared, right?" + }, + { + "text": "That's just a function of x." + }, + { + "text": "Is that clear?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk27.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk27.json new file mode 100644 index 0000000000000000000000000000000000000000..ad5c52c96917f6811fd97391867d647b8dd5d280 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk27.json @@ -0,0 +1,62 @@ +[ + { + "text": "So if you complete this computation, what you're going to get is that your new one parameter thing is that p theta p theta x is not equal to exponential x times mu over sigma squared minus, well, it's still the same thing, and then you have your h of x that comes out, x squared over 2 sigma squared." + }, + { + "text": "So that's my h of x." + }, + { + "text": "That's still my b of theta." + }, + { + "text": "And this is my t1 of x, and this is my eta 1 of theta." + }, + { + "text": "And remember, theta is just equal to mu in this case." + }, + { + "text": "So if I ask you, prove that this distribution belonged to an exponential family, you just have to work it out." + }, + { + "text": "Typically, it's expanding what's in the exponential and just write it in this term and identify all the components, right?" + }, + { + "text": "So here, notice those guys don't even get an index anymore because there's just one of them." + }, + { + "text": "So I wrote theta 1 and t1, but it's really just eta and t. Oh, sorry." + }, + { + "text": "This guy also goes." + }, + { + "text": "This is also a constant, right?" + }, + { + "text": "So it can actually just put sigma divided by sigma squared over 2 pi." + }, + { + "text": "So h of x is what, actually?" + }, + { + "text": "AUDIENCE MEMBER 2." + }, + { + "text": "It's the density of?" + }, + { + "text": "AUDIENCE MEMBER 3." + }, + { + "text": "It's centered." + }, + { + "text": "It's not standard." + }, + { + "text": "It's centered." + }, + { + "text": "It has mean 0, but it has variance sigma squared, right?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk28.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk28.json new file mode 100644 index 0000000000000000000000000000000000000000..e6cd0af7c6a6f3a84bb21243aed86ecb61bec60e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk28.json @@ -0,0 +1,62 @@ +[ + { + "text": "But it's the density of a Gaussian." + }, + { + "text": "And this is what I meant when I said h of x is really just telling you with respect to which distribution, which measure you're taking the density." + }, + { + "text": "And so this thing here is really telling you the density of my Gaussian with mean mu is equal to this with respect to a centered Gaussian is this guy, right?" + }, + { + "text": "That's what it means." + }, + { + "text": "If this thing ends up being a density, it just means that now you just have a new measure, which is this density." + }, + { + "text": "So it's just saying that the density of the Gaussian with mean mu with respect to the Gaussian with mean 0 is just this thing here." + }, + { + "text": "All right, so let's move on." + }, + { + "text": "So here is that I said you can actually do all these computations and forget about the fact that x is continuous." + }, + { + "text": "You can actually do it with PMFs and do it for x is discrete." + }, + { + "text": "This actually also tells you if you can actually get the same form for your density, which is of the form exponential times the product of the interaction between theta and x is just taking this product, and then a function only of theta and a function only of x for the PMF." + }, + { + "text": "It also works." + }, + { + "text": "So I claim that the Bernoulli belongs to this family." + }, + { + "text": "So the PMF of a Bernoulli, we say parameter p, is p to the x 1 minus p to the 1 minus x, right?" + }, + { + "text": "Because we know, so that's only for x equals 0 or 1." + }, + { + "text": "And the reason is because when x is equal to 0, this is 1 minus p. When x is equal to 1, this is p. We've seen that when we were looking at likelihoods for Bernoullis." + }, + { + "text": "This is not clear this is going to look like this at all." + }, + { + "text": "But let's do it." + }, + { + "text": "So what does this thing look like?" + }, + { + "text": "Well, the first thing I want to do is to make an exponential show up." + }, + { + "text": "So what I'm going to write is I'm going to write p to the x as exponential x log p, right?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk29.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk29.json new file mode 100644 index 0000000000000000000000000000000000000000..d713a21eea1b786a7ef3869f97ae02235ce1e655 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk29.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so I'm going to do that for the other one." + }, + { + "text": "So this thing here, so I'm going to get exponential x log p plus 1 minus x log 1 minus p. So what I need to do is to collect my terms in x and my terms in whatever parameters I have." + }, + { + "text": "So here, theta is equal to p. So if I do this, what I end up having is equal to exponential." + }, + { + "text": "So the term in x is log p minus log 1 minus p. So that's x times log p over 1 minus p. And then the term that stays is just 1 times log 1 minus p. But I want to see this as a minus something, right?" + }, + { + "text": "It was minus b of theta." + }, + { + "text": "So I'm going to write it as minus." + }, + { + "text": "Well, I can just keep the plus." + }, + { + "text": "And I'm going to do." + }, + { + "text": "And that's all." + }, + { + "text": "Aha." + }, + { + "text": "Well, this is of the form exponential, something that depends only on x, times something that depends only on theta, minus a function that depends only on theta." + }, + { + "text": "And then h of x is equal to 1 again." + }, + { + "text": "So let's see." + }, + { + "text": "So I have t1 of x is equal to x." + }, + { + "text": "That's this guy." + }, + { + "text": "Eta 1 of theta is equal to log p 1 minus p. And b of theta is equal to log 1 over 1 minus p. And h of x is equal to 1." + }, + { + "text": "You guys want to do Poisson, or you want to have it in homework?" + }, + { + "text": "It's a dilemma, because that's an easy homework versus no homework at all." + }, + { + "text": "That may be something more difficult." + }, + { + "text": "OK, who wants to do it now?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk3.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..1b86720582d11cec87b39451799e862944553cac --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "This is going to become y given x follows some distribution." + }, + { + "text": "And I'm not going to allow any distribution." + }, + { + "text": "I want something that comes from the exponential family." + }, + { + "text": "Who knows what the exponential family of distribution is?" + }, + { + "text": "This is not the same thing as the exponential distribution." + }, + { + "text": "It's a family of distribution." + }, + { + "text": "All right, so we'll see that." + }, + { + "text": "What can that be?" + }, + { + "text": "Oh, yeah, that's actually my." + }, + { + "text": "I'm sorry?" + }, + { + "text": "You can mute your laptop." + }, + { + "text": "OK." + }, + { + "text": "I'm in presentation mode." + }, + { + "text": "That should not happen." + }, + { + "text": "OK, so hopefully this is muted." + }, + { + "text": "So essentially, this is going to be a family of distributions." + }, + { + "text": "And what makes them exponential typically is that there's an exponential that shows up in the definition of the density." + }, + { + "text": "We'll see that the Gaussian belongs to the exponential family." + }, + { + "text": "But there are slightly less expected ones, because there's this crazy thing that a to the x is exponential x log a, which makes the exponential show up without being there." + }, + { + "text": "So if there's an exponential of some power, it's going to show up." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk30.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk30.json new file mode 100644 index 0000000000000000000000000000000000000000..d5b105095f9ebc1fa6cd52b7842032b4ff7b8f72 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk30.json @@ -0,0 +1,62 @@ +[ + { + "text": "Who does not want to raise their hand now?" + }, + { + "text": "Who wants to raise their hand now?" + }, + { + "text": "All right." + }, + { + "text": "So let's move on." + }, + { + "text": "I'll just do it." + }, + { + "text": "Do you want to do the gammas instead in the homework?" + }, + { + "text": "That's going to be fun." + }, + { + "text": "I'm not even going to propose to do the gammas." + }, + { + "text": "So this is the gamma distribution." + }, + { + "text": "It's brilliantly called gamma, because it has the gamma function, just like the beta distribution was at the beta function in there." + }, + { + "text": "They look very similar." + }, + { + "text": "One is defined over r plus, the positive real line." + }, + { + "text": "And remember, the beta was defined over the interval 0, 1." + }, + { + "text": "And it's of the form x to some power times exponential minus x to some time something." + }, + { + "text": "So there's a function, a polynomial in x, where the exponent depends on the parameter." + }, + { + "text": "And then there's the exponential minus x times something depends on the parameters." + }, + { + "text": "So this is going to also look like some function of x." + }, + { + "text": "Sorry, like some exponential distribution." + }, + { + "text": "Can somebody guess what is going to be t2 of x?" + }, + { + "text": "Oh, those are the functions of x that show up in this product." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk31.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk31.json new file mode 100644 index 0000000000000000000000000000000000000000..00610d89ea0d6a8998695a3eea0b66796db62411 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk31.json @@ -0,0 +1,62 @@ +[ + { + "text": "Remember when we have this, we just need to take some transformations of x, so it looks linear in those things and not in x itself." + }, + { + "text": "Remember, we had x squared and x, for example, in the Gaussian case." + }, + { + "text": "I don't know if it's still there." + }, + { + "text": "Yeah, it's still there, right?" + }, + { + "text": "t2 was x squared." + }, + { + "text": "What do you think x is going to be?" + }, + { + "text": "t2 of x." + }, + { + "text": "So here's a hint." + }, + { + "text": "t1 is going to be x. Yeah, Arjun, what is going to be t2?" + }, + { + "text": "Yeah, you cannot." + }, + { + "text": "This one is taken." + }, + { + "text": "This one is taken." + }, + { + "text": "I don't want to take it." + }, + { + "text": "What?" + }, + { + "text": "Log x, right?" + }, + { + "text": "Because this x to the a minus 1, I'm going to write it as exponential a minus 1 log x." + }, + { + "text": "So basically, eta 1 is going to be a minus 1." + }, + { + "text": "Eta 2 is going to be minus 1 over b." + }, + { + "text": "Well, actually, the opposite." + }, + { + "text": "But this is actually not too complicated." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk32.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk32.json new file mode 100644 index 0000000000000000000000000000000000000000..87cbf659fc56773f52625e97de084ba7714602c8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk32.json @@ -0,0 +1,62 @@ +[ + { + "text": "All right, then those parameters get names." + }, + { + "text": "a is the shape parameter." + }, + { + "text": "b is the scale parameter." + }, + { + "text": "It doesn't really matter." + }, + { + "text": "You have other things that are called the inverse gamma distribution, which has this form." + }, + { + "text": "The difference is that the parameter alpha shows negatively there." + }, + { + "text": "And then the inverse Gaussian distribution, just densities you can come up with." + }, + { + "text": "And it just happened to fall in this family." + }, + { + "text": "And there's other ones that you can actually put it there that we've seen before." + }, + { + "text": "The chi square is actually part of this family." + }, + { + "text": "The beta distribution is part of this family." + }, + { + "text": "The binomial distribution is part of this family." + }, + { + "text": "Well, that's easy because the Bernoulli was." + }, + { + "text": "The negative binomial, which is some stopping time, the first time you hit a certain number of successes when you flip some Bernoulli coins." + }, + { + "text": "So you can check for all of those." + }, + { + "text": "And you will see that you can actually write them as part of the exponential family." + }, + { + "text": "So the main goal of this slide is to convince you that this is actually a pretty broad range of distributions, because it basically includes everything we've seen, but not anything there." + }, + { + "text": "Sorry, plus more." + }, + { + "text": "OK?" + }, + { + "text": "Yeah?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk33.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk33.json new file mode 100644 index 0000000000000000000000000000000000000000..86875d258d1996f3a9c9c903d20c2aaebbe2d921 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk33.json @@ -0,0 +1,62 @@ +[ + { + "text": "Is there any example of a distribution which comes up pretty often that's not in the next exponential family?" + }, + { + "text": "Yeah, like uniform." + }, + { + "text": "Oh, OK. Maybe a bit more complicated than that." + }, + { + "text": "Anything that has a support that depends on the parameter is not going to fall." + }, + { + "text": "It's not going to fit in there." + }, + { + "text": "And you can actually convince yourself why anything that has the support that depends on the parameter is not going to be part of this guy." + }, + { + "text": "It's kind of a hard thing to, if I ask you, prove that it's not, and you wouldn't prove this rule." + }, + { + "text": "It's kind of a little difficult." + }, + { + "text": "But the way you can convince yourself is that, remember, the only interaction between x and theta that I allowed was taking the product of those guys and then the exponential." + }, + { + "text": "If you have something that depends on some parameter, let's say you're going to see something that looks like this." + }, + { + "text": "For uniform, it looks like this." + }, + { + "text": "Well, this is not of the form exponential x times theta." + }, + { + "text": "There's an interaction between x and theta here, but it's actually certainly not of the form x exponential x times theta." + }, + { + "text": "So this is definitely not going to be part of the exponential family." + }, + { + "text": "And every time you start doing things like that, then it's just not going to happen." + }, + { + "text": "Actually, to be fair, I'm not even sure that all these guys, when you allow them to have all their parameters free, are actually going to be part of this." + }, + { + "text": "The beta probably is, but I'm not actually entirely convinced." + }, + { + "text": "There's books on exponential families." + }, + { + "text": "So let's go back." + }, + { + "text": "So here, we've put a lot of effort understanding how big, how much wider than the Gaussian distribution can we think of for the conditional distribution of our response y given x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk34.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk34.json new file mode 100644 index 0000000000000000000000000000000000000000..7d11d0e4f2f489c40ab50852c91946ccd1773a06 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk34.json @@ -0,0 +1,62 @@ +[ + { + "text": "So let's go back to the generalized linear models." + }, + { + "text": "So the generalized linear model said, OK, the random component, y, has to be part of some exponential family distribution." + }, + { + "text": "Check." + }, + { + "text": "We know what this means." + }, + { + "text": "So now I have to understand two things." + }, + { + "text": "I have to understand what is the expectation, because that's actually what I model." + }, + { + "text": "I take the expectation, the conditional expectation of y given x." + }, + { + "text": "So I need to understand, given this guy, it would be nice if it had some simple rules that would tell me exactly what the expectation is, rather than having to do it over and over again." + }, + { + "text": "If I told you, here's a Gaussian, compute the expectation." + }, + { + "text": "Every time you had to use that, it would be slightly painful." + }, + { + "text": "So hopefully, this thing being simple enough, we've actually selected a simple class that's simple enough." + }, + { + "text": "So that we can have rules, whereas as soon as I give you those parameters, t1, t2, eta 1, eta 2, b, and h, you can actually have some simple rules to compute the mean and variance and all the things." + }, + { + "text": "And so in particular, I'm interested in the mean." + }, + { + "text": "And I'm going to have to actually say, well, this mean has to be mapped into the whole real line so I can actually talk about modeling this function of the mean as x transpose beta." + }, + { + "text": "And we saw that for the Kefosis data set or whatever other data sets, you can actually do this using the log of the reciprocal." + }, + { + "text": "Or for the, actually, we didn't do it for the Bernoulli." + }, + { + "text": "We'll come to this." + }, + { + "text": "This is the most important one, and that's called the logit or logistic link." + }, + { + "text": "But before we go there, this was actually a very broad family." + }, + { + "text": "When I wrote this thing on the bottom board, it's gone now." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk35.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk35.json new file mode 100644 index 0000000000000000000000000000000000000000..85aa8f3c00dfa505f2dfedae8c76a6308880fbe3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk35.json @@ -0,0 +1,62 @@ +[ + { + "text": "But when I wrote it in the first place, the only thing that I wrote is I wanted x times theta." + }, + { + "text": "Wouldn't it be nice if I have some distribution that was just x times theta, not some function of x times some function of theta?" + }, + { + "text": "The functions seem to be here so that they actually make things a little." + }, + { + "text": "So the functions were here so that I can actually put a lot of functions there." + }, + { + "text": "But first of all, if I actually decide to reparameterize my problem, I can always assume, if I have one dimensional, I can always assume that eta 1 of theta becomes my new theta." + }, + { + "text": "So this thing here, for example, I could say, well, this is actually the parameter of my Bernoulli." + }, + { + "text": "Let me call this guy theta." + }, + { + "text": "I could do that." + }, + { + "text": "Then I could say, well, here I have x that shows up here." + }, + { + "text": "And here, since I'm talking about the response, I cannot really make any transformation." + }, + { + "text": "So here I'm going to actually talk about a specific family for which this guy is not x square or square root of x or log of x or anything I want." + }, + { + "text": "I'm just going to actually look at distributions for which this is x." + }, + { + "text": "These exponential families are called canonical exponential families." + }, + { + "text": "So in the canonical exponential family, what I have is that I have my x times theta." + }, + { + "text": "I'm going to allow myself some normalization factor phi." + }, + { + "text": "And we'll see, for example, that it's very convenient when I talk about the Gaussian." + }, + { + "text": "Because even if I know this guy, which I actually pull into my, oh, that's over here, right?" + }, + { + "text": "I know sigma squared, but I don't want to change my parameter to be mu over sigma squared." + }, + { + "text": "It's kind of painful." + }, + { + "text": "So I just take mu, and I'm going to keep this guy as being this phi over there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk36.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk36.json new file mode 100644 index 0000000000000000000000000000000000000000..89f73402c1fdd2bf2eeed62666de95f3d88a1238 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk36.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it's called the dispersion parameter from a clear analogy with the Gaussian." + }, + { + "text": "That's the variance, and that's measuring dispersion." + }, + { + "text": "So here, what I want is I'm going to think throughout this class." + }, + { + "text": "So phi may be known or not." + }, + { + "text": "And when it's not known, this actually might turn into some exponential family, or it might not." + }, + { + "text": "And the main reason is because this b of theta over phi is not necessarily a function of theta over phi." + }, + { + "text": "If I actually have phi unknown, then y theta over phi has to be, this guy has to be my new parameter." + }, + { + "text": "And b might not be a function of this new parameter." + }, + { + "text": "So in a way, it may or may not, but this is not really a concern that we're going to have, because throughout this class, we're going to assume that phi is known." + }, + { + "text": "Phi is going to be known all the time, which means that this is always an exponential family." + }, + { + "text": "And it's just the simplest one you could think of." + }, + { + "text": "One dimensional parameter, one dimensional response, and I just have the product is just y times, or we used to call it x." + }, + { + "text": "Now I've switched to y." + }, + { + "text": "But y times theta divided by phi." + }, + { + "text": "Should I write this, or is this clear to everyone what this is?" + }, + { + "text": "Let me write it somewhere so we actually keep track of it for the 10 minutes." + }, + { + "text": "OK, so this is, we have, remember we had all the distributions." + }, + { + "text": "And then here we had the exponential family." + }, + { + "text": "And now we have the canonical exponential family." + }, + { + "text": "It's actually much, much smaller." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk37.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk37.json new file mode 100644 index 0000000000000000000000000000000000000000..611f08f23a902183ca152ce8cba2cc234c17366b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk37.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, actually, it's probably sort of a good picture." + }, + { + "text": "And what I have is that my density, or my PMF, is just exponential y times theta minus b of theta divided by phi." + }, + { + "text": "And I have plus c of, oh, yeah, plus c of y phi, which means that this is really, if phi is known, h of y is just exponential c of y phi." + }, + { + "text": "Actually, this is the reason why it's not necessarily a canonical family." + }, + { + "text": "It might not be that this depends only on y." + }, + { + "text": "It could depend on y and phi in some annoying way, and I may not be able to break it." + }, + { + "text": "But if phi is known, this is just a function that depends on y." + }, + { + "text": "Agreed?" + }, + { + "text": "In particular, I hope you can convince yourself that this is just a subcase of everything we've seen before." + }, + { + "text": "So for example, the Gaussian, when the variance is known, is indeed of this form." + }, + { + "text": "So we still have it on the board." + }, + { + "text": "So here's my y." + }, + { + "text": "So let me write this as f theta of y." + }, + { + "text": "So every x is replaced with y. Blah, blah, blah." + }, + { + "text": "This is this guy." + }, + { + "text": "And now what I have is that this is going to be my phi." + }, + { + "text": "This is my parameter theta." + }, + { + "text": "So I'm definitely of the form y times theta divided by phi." + }, + { + "text": "And then here, I have a function b that depends only on theta over phi again." + }, + { + "text": "So b of theta is mu squared divided by 2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk38.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk38.json new file mode 100644 index 0000000000000000000000000000000000000000..8580549781bf648098829c5beb6e58f82df064eb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk38.json @@ -0,0 +1,62 @@ +[ + { + "text": "Then it's divided by sigma square." + }, + { + "text": "And then I have this extra stuff, but I really don't care what it is for now." + }, + { + "text": "It's just something that depends only on y and known stuff." + }, + { + "text": "So it's just a function of y." + }, + { + "text": "Just like my h, I stuff everything in there." + }, + { + "text": "The b, though, this thing here, this is actually what's important." + }, + { + "text": "Because in a canonical family, if you think about it, when you know phi, this is just y times theta scaled by a known constant." + }, + { + "text": "Sorry, y times theta scaled by a known constant is the first term." + }, + { + "text": "The second term is b of theta scaled by some known constant." + }, + { + "text": "But b of theta is what's going to make the difference between Gaussian and Bernoulli's and gammas and betas." + }, + { + "text": "This is all in this b of theta." + }, + { + "text": "b of theta contains everything that's idiosyncratic to this particular distribution." + }, + { + "text": "And so this is going to be important." + }, + { + "text": "And we will see that b of theta is going to capture information about the mean, about the variance, about the likelihood, about everything." + }, + { + "text": "Should I go through this computation?" + }, + { + "text": "I mean, it's the same." + }, + { + "text": "We've just done it." + }, + { + "text": "So maybe it's probably better if you can redo it on your own." + }, + { + "text": "So the canonical exponential family also has other distributions." + }, + { + "text": "So there's the Gaussian, and there's the Poisson, and there's the Bernoulli." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk39.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk39.json new file mode 100644 index 0000000000000000000000000000000000000000..e7503da5bdfd1b43af25b138aa6e92f9d60f5b5b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk39.json @@ -0,0 +1,62 @@ +[ + { + "text": "But the other ones may not be part of this." + }, + { + "text": "In particular, think about the gamma distribution." + }, + { + "text": "We had this log x was one of those things that showed up." + }, + { + "text": "I mean, I cannot get rid of this log x. I mean, that's part of it, except if a is equal to 1." + }, + { + "text": "And I know it for sure." + }, + { + "text": "So if a is equal to 1, then I'm going to have a minus 1, which is equal to 0." + }, + { + "text": "So I'm going to have a minus 1 times log x, which is going to be just 0." + }, + { + "text": "So log x is going to vanish from here." + }, + { + "text": "If a is equal to 1, then this distribution is actually much nicer." + }, + { + "text": "And it actually does not even deserve the name gamma." + }, + { + "text": "What is it if a is equal to 1?" + }, + { + "text": "It's an exponential, right?" + }, + { + "text": "Gamma of 1 is equal to 1. x to the a minus 1 is equal to 1. b, so I have exponential x over b divided by b." + }, + { + "text": "So 1 over b, call it lambda." + }, + { + "text": "And this is just an exponential distribution." + }, + { + "text": "And so every time you're going to see something, so all these guys that don't make it to this table, they could be part of those guys." + }, + { + "text": "But they're just to have another name in this thing." + }, + { + "text": "So you can compute the value of theta for different values." + }, + { + "text": "So again, you still have some continuous or discrete ones." + }, + { + "text": "This is my b of theta." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk4.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..7bcd652938f0899eaa61ff94c0f0810d310b07d7 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "But it's more than that." + }, + { + "text": "So we'll actually come to this particular family of distribution." + }, + { + "text": "Why this particular family?" + }, + { + "text": "Because in a way, everything we've done for the linear model with Gaussian is going to extend fairly naturally to this family." + }, + { + "text": "And it actually also, because it encompasses pretty much everything, all the distributions we've discussed before." + }, + { + "text": "All right, so the second thing that I want to question, so before we just said, well, mu of x was directly equal to this thing." + }, + { + "text": "Mu of x was directly x transpose beta." + }, + { + "text": "So I knew I was going to have an x transpose beta." + }, + { + "text": "And I said, well, I could do something with this x transpose beta before I used it to explain the expected value." + }, + { + "text": "But I'm actually taking it like that." + }, + { + "text": "Here we're going to say, let's extend this to some function is equal to this thing." + }, + { + "text": "Now, admittedly, this is not the most natural way to think about it." + }, + { + "text": "What you would probably feel more comfortable doing is write something like mu of x is a function." + }, + { + "text": "Let's call it f of x transpose beta." + }, + { + "text": "But here I just decide to call f g inverse." + }, + { + "text": "OK, that's just my g inverse, yes." + }, + { + "text": "Is this different than just transforming the x's?" + }, + { + "text": "Yeah." + }, + { + "text": "I mean, what transformation do you want to put on your x's?" + }, + { + "text": "Like, is this equivalent to just applying some function to each individual x component and then multiplying that beta to get the mean?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk40.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk40.json new file mode 100644 index 0000000000000000000000000000000000000000..a4fb0b65f5388522d17114f3d137c0e12fa325f1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk40.json @@ -0,0 +1,62 @@ +[ + { + "text": "And I said this is actually really what captures my theta." + }, + { + "text": "This b is actually called cumulant generating function." + }, + { + "text": "I don't have time." + }, + { + "text": "I could write five slides to explain to you." + }, + { + "text": "But it would just only tell you why it's called cumulant generating function." + }, + { + "text": "It's also known as the log of the moment generating function." + }, + { + "text": "And the way it's called cumulant generating function is because if I start taking successive derivatives and evaluate them at 0, I get the successive cumulants of this distribution, which are some transformation of the moment." + }, + { + "text": "What is the function b?" + }, + { + "text": "The function b." + }, + { + "text": "So this is just normalization." + }, + { + "text": "So this is just to tell you I can compute this, but I really don't care." + }, + { + "text": "And obviously, I don't care about stuff that's complicated." + }, + { + "text": "This is actually cute." + }, + { + "text": "And this is what computes everything." + }, + { + "text": "And the rest is just some general description." + }, + { + "text": "You don't need me to tell you that the range of y is 0 to infinity." + }, + { + "text": "And that is essentially telling me this is going to give me some hints as to which link function I should be using." + }, + { + "text": "Because the range of y tells me what the range of expectation of y is going to be." + }, + { + "text": "Here it tells me that the range of y is between 0 and 1." + }, + { + "text": "So what I want to show you is that this captures a variety of different ranges that you can have." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk41.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk41.json new file mode 100644 index 0000000000000000000000000000000000000000..5bc0529fcb2c87a036825dc5eca45e610158d843 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk41.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I'm going to want to go into the likelihood." + }, + { + "text": "And the likelihood I'm actually going to use to compute the expectations." + }, + { + "text": "But since I actually don't have time to do this now, let's just go quickly through this and give you a spoiler alert to make sure that you all wake up on Thursday and really, really want to think about coming here immediately." + }, + { + "text": "So the thing I'm going to want to do, as I said, is it would be nice if, at least for this canonical family, when I give you b, you would be able to say, oh, here is a simple computation of b that would actually give me the mean and the variance." + }, + { + "text": "The mean and the variance are also known as moments." + }, + { + "text": "b is called cumulant generating function." + }, + { + "text": "So it sounds like moments being related to cumulants might have a path to finding those." + }, + { + "text": "And it might involve taking derivatives of b, as we'll see." + }, + { + "text": "The way we're going to prove this is by using this thing that we've used several times." + }, + { + "text": "So this property we use when we're computing, remember, the Fisher information." + }, + { + "text": "We had two formulas for the Fisher information." + }, + { + "text": "One was the expectation of the second derivative of the likelihood." + }, + { + "text": "And one was negative expectation of the square." + }, + { + "text": "Sorry, expectation of the square." + }, + { + "text": "And the other one was negative the expectation of the second derivative." + }, + { + "text": "The log likelihood is concave." + }, + { + "text": "So this number is negative." + }, + { + "text": "This number is positive." + }, + { + "text": "And the way we did this is by just permuting some derivative and integral here." + }, + { + "text": "And we used the fact that something that looked like this, the log likelihood is log of f theta." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk42.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk42.json new file mode 100644 index 0000000000000000000000000000000000000000..21653facee3fc11ef5000d2beef0a8de5ddfa092 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk42.json @@ -0,0 +1,62 @@ +[ + { + "text": "And when I take the derivative of this guy with respect to theta, then I have something that looks like the derivative divided by f theta." + }, + { + "text": "And if I start taking the integral against f theta of this thing, so the expectation of this thing, those things would cancel." + }, + { + "text": "And then I had just the integral of a derivative, which I would make a leap of faith and say that it's actually the derivative of the integral." + }, + { + "text": "But this was equal to 1." + }, + { + "text": "So this derivative was actually equal to 0." + }, + { + "text": "And so that's how you got that the expectation of the derivative of the log likelihood is equal to 0." + }, + { + "text": "And you do it once again, and you get this guy." + }, + { + "text": "There's just some nice things that happen with taking the derivative of the log." + }, + { + "text": "We've done that." + }, + { + "text": "We'll do that again." + }, + { + "text": "But once you do this, you can actually apply it." + }, + { + "text": "And missing a parenthesis over there." + }, + { + "text": "So when you write the log likelihood, it's just log of an exponential." + }, + { + "text": "That's actually pretty nice." + }, + { + "text": "Just like the least squares came naturally, the least squares criterion came naturally when we took the log likelihood of the Gaussians." + }, + { + "text": "We're going to have the same thing that happens." + }, + { + "text": "When I take the log of the density, the exponential is going to go away." + }, + { + "text": "And then I'm going to use this formula." + }, + { + "text": "But this formula is going to actually give me an equation directly." + }, + { + "text": "Oh, that's where it was." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk43.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk43.json new file mode 100644 index 0000000000000000000000000000000000000000..7f84c7ac778972c0a276af273b35f04b2d19dc71 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk43.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's the one that's missing it there." + }, + { + "text": "So the expectation minus this thing is going to be equal to 0, which tells me that the expectation is just the derivative." + }, + { + "text": "So it's still a function of theta, but it's just the derivative of b." + }, + { + "text": "And the variance is just going to be the second derivative of b." + }, + { + "text": "But remember, this was some sort of a scaling." + }, + { + "text": "It's called the dispersion parameter." + }, + { + "text": "So if I had a Gaussian, and the variance of the Gaussian did not depend on the sigma square, which I stuffed in this phi, that would be certainly weird." + }, + { + "text": "And it cannot depend only on mu." + }, + { + "text": "And so for the Gaussian, this is definitely going to be equal to 1." + }, + { + "text": "And this is just going to be equal to my variance." + }, + { + "text": "So this is just by taking the second derivative." + }, + { + "text": "So basically, the take-home message is that this function b captures, by taking one derivative of the expectation and by taking two derivatives, captures the variance." + }, + { + "text": "Another thing that's actually cool, and we'll come back to this and I want you to think about, is if this second derivative is the variance, what can I say about this thing?" + }, + { + "text": "What do I know about a variance?" + }, + { + "text": "Yeah, it's positive." + }, + { + "text": "So I know that this is positive." + }, + { + "text": "So what does that tell me?" + }, + { + "text": "Positive?" + }, + { + "text": "That's convex, right?" + }, + { + "text": "A function that has positive second derivative is convex." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk44.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk44.json new file mode 100644 index 0000000000000000000000000000000000000000..d5f75378f61eee780be265f51bdebc08ef9bcc39 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk44.json @@ -0,0 +1,11 @@ +[ + { + "text": "So we're going to use that as well." + }, + { + "text": "So yeah, I'll see you on Thursday." + }, + { + "text": "Have your homework." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk5.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..be889780830d4833b3e56baa49edaba9d1277e77 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "Oh, no, certainly not, right?" + }, + { + "text": "I mean, if I force you to work with x1 plus x2, you cannot work with any function of x1 plus any function of x2, right?" + }, + { + "text": "So yeah, this is different." + }, + { + "text": "So yeah, the transformation would be just the simple part of your linear regression problem, where you would take your x's, transform them, and then just apply another linear regression." + }, + { + "text": "This is genuinely new." + }, + { + "text": "Any other question?" + }, + { + "text": "All right, so this function g, and the reason why I sort of have to stick to this slightly less natural way of defining it is because that's g that gets a name, not g inverse that gets a name." + }, + { + "text": "And the name of g is the link function." + }, + { + "text": "So if I want to give you a generalized linear model, I need to give you two ingredients." + }, + { + "text": "The first one is the random component, which is the distribution of y given x." + }, + { + "text": "And it can be anything in what's called the exponential family of distributions." + }, + { + "text": "So for example, I could say y given x is Gaussian with mean ux sigma squared identity." + }, + { + "text": "But I could also tell you y given x is gamma with shape parameter equal to alpha of x. I could do some weird things like this." + }, + { + "text": "And the second thing is I need to give you a link function." + }, + { + "text": "And the link function is going to become very clear how you pick a link function." + }, + { + "text": "And the only reason that you actually pick a link function is because of compatibility." + }, + { + "text": "This mu of x, I call it mu because mu of x is always the conditional expectation of y given x, always, which means that let's think of y as being a Bernoulli random variable." + }, + { + "text": "Where does mu of x live?" + }, + { + "text": "AUDIENCE 2." + }, + { + "text": "0, 1." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk6.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..8cb4d97427833f7219b0ac485c9a506b1a3240c9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "0, 1, right?" + }, + { + "text": "That's the expectation of a Bernoulli." + }, + { + "text": "It's just the probability that my coin flip gives me 1." + }, + { + "text": "So it's a number between 0 and 1." + }, + { + "text": "But this guy right here, if my x's are anything, think of any body measurements, plus I take linear combinations with arbitrarily large coefficients, this thing can be any real number." + }, + { + "text": "So the link function, what it's effectively going to do is make those two things compatible." + }, + { + "text": "It's going to take my number, which, for example, is constrained to be between 0 and 1, and map it into the entire real line." + }, + { + "text": "If I have mu, which is forced to be positive, for example, in an exponential distribution, the mean is positive, right?" + }, + { + "text": "That's the, say, I don't know, inter-arrival time for Poisson process." + }, + { + "text": "This thing is known to be positive for an exponential." + }, + { + "text": "I need to map something that's exponential to the entire real line." + }, + { + "text": "I need a function that takes something positive and then tickets everyone." + }, + { + "text": "So we'll see, by the end of this chapter, you will have 100 ways of doing this." + }, + { + "text": "But there are some more traditional ones than other." + }, + { + "text": "So before we go any further, I gave you this example of a Bernoulli random variable." + }, + { + "text": "Let's see a few examples that actually fit there." + }, + { + "text": "Yes?" + }, + { + "text": "AUDIENCE 1 Will it come up later if we already know why the mean distribution is increasing entirely?" + }, + { + "text": "Why can't we do it?" + }, + { + "text": "PHILIPPE RIGOLLET Well, actually, this will not come up later." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk7.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..7a08a1b997a550d2298989615c5c3d9d139188e0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "It should be very clear from here." + }, + { + "text": "Because if I actually have a model, I just want it to be plausible, right?" + }, + { + "text": "I mean, what happens if I suddenly decide that my, so this is what's going to happen." + }, + { + "text": "You're going to have only data to fit this model." + }, + { + "text": "Let's say you actually forget about this thing here." + }, + { + "text": "You can always do this, right?" + }, + { + "text": "You can always say, I'm going to pretend my y's just happen to be the realizations of, say, Gaussians that happen to be 0 or 1 only." + }, + { + "text": "You can always stuff that in some linear model, right?" + }, + { + "text": "You will have some least squares estimator for beta." + }, + { + "text": "But what's going to happen, and it's going to be fine." + }, + { + "text": "For all the points that you see, it will definitely put some number that's actually between 0 and 1." + }, + { + "text": "So this is what your picture is going to look like." + }, + { + "text": "You're going to have a bunch of values for x." + }, + { + "text": "This is your y." + }, + { + "text": "And so these are the values of x that you will get." + }, + { + "text": "And for y, you will see either 0 or 1, right?" + }, + { + "text": "That's what your Bernoulli data set would look like with a one-dimensional x." + }, + { + "text": "Now, if you do least squares on this, you will find this." + }, + { + "text": "And for this guy, this line certainly takes values between 0 and 1." + }, + { + "text": "But let's say now you get an x here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk8.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..dfd389e2603960133ef12ce8ca9c769bb873bedf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "You're going to actually start pretending the probability that it spits out one conditionally in x is like 1.2, and that's going to be weird." + }, + { + "text": "OK?" + }, + { + "text": "Any other questions?" + }, + { + "text": "All right, so let's start with some examples." + }, + { + "text": "Right?" + }, + { + "text": "I mean, you got so used to them throughout this course." + }, + { + "text": "So the first one is all these things are taken." + }, + { + "text": "So there's a few books on generalizing your models, generalize additive models, and there's tons of applications that you can see." + }, + { + "text": "Those are extremely versatile." + }, + { + "text": "And as soon as you want to do modeling to explain some y given x, you sort of need to do that if you want to go beyond linear models." + }, + { + "text": "So this was the disease occurring rate." + }, + { + "text": "So you have a disease epidemic, and you want to basically model the expected number of new cases given at a certain time." + }, + { + "text": "OK?" + }, + { + "text": "So you have time that progresses for each of your reservation." + }, + { + "text": "Each of your relation is a timestamp, say, I don't know, 20th day." + }, + { + "text": "And your response is the number of new cases." + }, + { + "text": "And you're going to actually put your model directly on mu, right?" + }, + { + "text": "When I looked at this, everything here was on mu itself, on the expected, right?" + }, + { + "text": "Mu of x is always the expected, the conditional expectation of y given x." + }, + { + "text": "Right?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk9.json b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..6cb6e3c31c39383cd65adbaafb2b2ceb06ed1ff3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/X-ix97pw0xY_3_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So all I need to model is this expected value." + }, + { + "text": "So this mu, I'm going to actually say, so I look at some parameters, and it says, well, it increases exponentially." + }, + { + "text": "So I want to have some sort of exponential trend." + }, + { + "text": "I can parameterize that in several ways." + }, + { + "text": "And the two parameters I want to slap in is some sort of gamma, which is just the coefficient." + }, + { + "text": "And then there's some rate delta that's in the exponential." + }, + { + "text": "OK?" + }, + { + "text": "So if I tell you it's exponential, that's a nice family of functions you might want to think about." + }, + { + "text": "OK, so here, mu of x, if I want to keep the notation x, is gamma exponential delta x, right?" + }, + { + "text": "Except that here, my x are t1, t2, t3, et cetera." + }, + { + "text": "OK?" + }, + { + "text": "And I want to find what the parameters gamma and delta are because I want to be able to maybe compare different epidemics and see if they have the same parameter or maybe just do some prediction based on the data that I have to extrapolate in the future." + }, + { + "text": "OK?" + }, + { + "text": "So here, clearly, mu of x is not of the form x transpose beta." + }, + { + "text": "Right?" + }, + { + "text": "That's not x transpose beta at all." + }, + { + "text": "And it's actually not even a function of x transpose beta." + }, + { + "text": "Right?" + }, + { + "text": "There's two parameters, gamma and delta, and it's not of the form." + }, + { + "text": "So here, I have x, which is 1 and x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk0.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..b5d2005486c62ceb6bba16af0971eda159bf4d11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So we're really moving along this review of the highlights of linear algebra." + }, + { + "text": "And today it's matrices Q." + }, + { + "text": "They get that name." + }, + { + "text": "They have orthonormal columns." + }, + { + "text": "So that's what one looks like." + }, + { + "text": "And then the key fact, orthonormal columns translates directly into that simple fact that you just keep remembering." + }, + { + "text": "Every time you see Q transpose Q, you've got the identity matrix." + }, + { + "text": "Let's just see why." + }, + { + "text": "So Q transpose would be, I'll take those columns and make them into rows." + }, + { + "text": "And then I multiply by Q with the columns." + }, + { + "text": "And what do I get?" + }, + { + "text": "Well, hopefully I get the identity matrix." + }, + { + "text": "OK, why?" + }, + { + "text": "Because, oh, yeah, the normal part tells me that the length of each vector, that's the length squared Q transpose Q." + }, + { + "text": "The length squared is 1." + }, + { + "text": "So that gives me the 1 in the identity matrix all along the diagonal." + }, + { + "text": "And then Q transpose times a different Q is 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk1.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..4e5a53f7561a10c59c686c38ce76be1836e60948 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the ortho part." + }, + { + "text": "So that gives me the 0s." + }, + { + "text": "So that's a simple identity." + }, + { + "text": "But it translates from a lot of words into a simple expression." + }, + { + "text": "Now, does that mean that in the other order, Q Q transpose, is that the identity?" + }, + { + "text": "So that's a question to think about." + }, + { + "text": "Is Q Q transpose equal the identity?" + }, + { + "text": "Question." + }, + { + "text": "Sometimes yes, sometimes no." + }, + { + "text": "Easy to tell which." + }, + { + "text": "The answer is yes." + }, + { + "text": "Yes, when Q is square." + }, + { + "text": "The answer is yes." + }, + { + "text": "If Q is a square matrix, a square matrix, this is saying that the square matrix Q has that inverse on its left." + }, + { + "text": "But for square matrices, a left inverse, Q transpose, is also a right inverse." + }, + { + "text": "And for a square matrix, if you have an inverse that works on one side, it will work on the other side." + }, + { + "text": "So the answer is yes in that case." + }, + { + "text": "And then in that case, that's the case when we call Q is, well, we really, I don't know what the right name would be." + }, + { + "text": "But here's the name everybody uses, an orthogonal matrix." + }, + { + "text": "And that's only in the square case, square." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk10.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..49656af3fb9dd19d28412adf515bdcbf6d01baf1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So he started with a unit vector." + }, + { + "text": "Start with a unit vector, u transpose u equal 1." + }, + { + "text": "So the length of the vector is 1." + }, + { + "text": "And then he created, let's name it after him, H. He created this matrix, the identity minus 2 uu transpose." + }, + { + "text": "And I believe that that's a really useful matrix." + }, + { + "text": "So it's just like, I think this review is like going beyond 18.06 into what ones are really worth knowing individually." + }, + { + "text": "Could we just check what are the properties of Householder's reflection of that I minus 2?" + }, + { + "text": "You recognize here a column times a row." + }, + { + "text": "So that's a matrix." + }, + { + "text": "And what could you tell me about that matrix uu transpose?" + }, + { + "text": "It's, yeah." + }, + { + "text": "Or what can we say about H?" + }, + { + "text": "So I guess I'm believing that H is a orthogonal matrix." + }, + { + "text": "Otherwise, it wouldn't be here today." + }, + { + "text": "So I believe that." + }, + { + "text": "And not only is it orthogonal, it is also, have a look at it, symmetric." + }, + { + "text": "It's also symmetric." + }, + { + "text": "The identity is symmetric." + }, + { + "text": "Uu transpose is symmetric." + }, + { + "text": "So this is a family of symmetric orthogonal matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk11.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d1bc347004ae5794bd541685a2530709739f8fb8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "And that was one of them." + }, + { + "text": "That's a symmetric orthogonal matrix." + }, + { + "text": "These matrices are really great to have." + }, + { + "text": "You just, like in using linear algebra, you just get a collection of useful matrices that you can call on." + }, + { + "text": "And these are definitely one family." + }, + { + "text": "Well, it's obviously symmetric." + }, + { + "text": "Shall we check that it's orthogonal?" + }, + { + "text": "So to check that it's orthogonal, I just, so I'm going to check that H transpose H is the identity." + }, + { + "text": "Can I just check that?" + }, + { + "text": "Well, H transpose is the same as H, because it was symmetric." + }, + { + "text": "So I'm going to square this guy." + }, + { + "text": "This is really H times H. I'm squaring it." + }, + { + "text": "And what do I get if I square?" + }, + { + "text": "So I get, I hope I get the identity, but let's see it." + }, + { + "text": "What do I get when I square this?" + }, + { + "text": "Get little, multiply it out." + }, + { + "text": "So I times I is I." + }, + { + "text": "And then I get some number of Uu transposes." + }, + { + "text": "How many do I get from that?" + }, + { + "text": "So I'm squaring this thing, because H transpose H is the same as H times H. So I'm squaring it." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk12.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..25d7b51e680f692a50bab3dc6644564db6a54780 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how many, what do I put here?" + }, + { + "text": "Four, thanks." + }, + { + "text": "And now I've got this guy squared with a plus." + }, + { + "text": "So that's four Uu transpose Uu transpose." + }, + { + "text": "Yeah, I'm totally realizing I've practiced for a lifetime doing these dinky little calculations." + }, + { + "text": "But they are dinky." + }, + { + "text": "And you'll get the hang of it quickly." + }, + { + "text": "Now, what am I hoping out of that bottom line?" + }, + { + "text": "That it is?" + }, + { + "text": "I." + }, + { + "text": "We're hoping to get I." + }, + { + "text": "Do we get I?" + }, + { + "text": "Yes." + }, + { + "text": "Who sees how to get I out of that thing?" + }, + { + "text": "Yeah." + }, + { + "text": "U transpose U in here is a number." + }, + { + "text": "That was U." + }, + { + "text": "That was column times row times column times row." + }, + { + "text": "And I look at the in the middle here is row times column." + }, + { + "text": "And that's the number 1, right?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk13.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2970896b1136ec13f25ac3b1d568b82c5bfd6397 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because it's there." + }, + { + "text": "So that's 1." + }, + { + "text": "And then I have minus 4 of that, plus 4 of that." + }, + { + "text": "They cancel each other." + }, + { + "text": "And I get I." + }, + { + "text": "So those are good matrices." + }, + { + "text": "We'll use them." + }, + { + "text": "We'll use them." + }, + { + "text": "Actually, they're better than Graham-Schmidt." + }, + { + "text": "So we'll use them in making things orthogonal." + }, + { + "text": "So what other orthogonal matrices?" + }, + { + "text": "Let's create some." + }, + { + "text": "Creating good orthogonal matrices, it pays off." + }, + { + "text": "Let's think." + }, + { + "text": "So there's a family named after this French guy who lived to 100." + }, + { + "text": "He was a real old timer." + }, + { + "text": "Well, MIT had a faculty member in math when I came, Professor Struik, who lived to 106." + }, + { + "text": "And I heard him give a lecture at Brown University at age 100." + }, + { + "text": "And it was like perfect." + }, + { + "text": "You could not have done it better." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk14.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7a4761773e251928346e720869f90c17e750fc9c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So he's my inspiration." + }, + { + "text": "I keep going." + }, + { + "text": "I only have like n more years to get there." + }, + { + "text": "And n is, well, it's too many anyway." + }, + { + "text": "OK, Adamard." + }, + { + "text": "All right, Adamard." + }, + { + "text": "So Adamard, he created, well, that's the simplest, the smallest." + }, + { + "text": "Now, the next guy is going to be 4 by 4." + }, + { + "text": "I'm going to put that." + }, + { + "text": "So where I see a 1, I'm going to put Adamard in." + }, + { + "text": "1, 1, 1 minus 1, 1, 1, 1 minus 1." + }, + { + "text": "And then when I see a minus, I'm going to put it in with a minus." + }, + { + "text": "You saw that picture?" + }, + { + "text": "It was a picture of H2, H2, H2, and minus H2." + }, + { + "text": "That's what I've got there." + }, + { + "text": "And I believe those columns are orthogonal." + }, + { + "text": "Now, what could I do?" + }, + { + "text": "Well, it's not quite an orthogonal matrix." + }, + { + "text": "What do I have to do to make it?" + }, + { + "text": "This isn't quite an orthogonal matrix either." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk15.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7c56d46fe9a00c08ec502262a9278c03ce6817ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "What do I do to make that an orthogonal matrix?" + }, + { + "text": "Divide by square root of 2." + }, + { + "text": "I need unit vectors there." + }, + { + "text": "And here, those lengths are 1 squared, 1 squared, 4." + }, + { + "text": "Square root of 4 is 2." + }, + { + "text": "So I better divide by the 2 there." + }, + { + "text": "And now here, I'm up to, yeah, so that was that one." + }, + { + "text": "Tell me the next one up." + }, + { + "text": "What's that going to be?" + }, + { + "text": "8 by 8?" + }, + { + "text": "So this is H4 here." + }, + { + "text": "Oops, 4." + }, + { + "text": "So tell me what I should do for 8 by 8." + }, + { + "text": "You'll think this is simple." + }, + { + "text": "But that's a good thing to say about it." + }, + { + "text": "In coding theory, all sorts of places, you want matrices of 1's and minus 1's." + }, + { + "text": "OK, what's H8?" + }, + { + "text": "I'm going to build it out of H4." + }, + { + "text": "So what's it going to be?" + }, + { + "text": "I'm going to put an H4 there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk16.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..918141f4e0ba694885e6f1ccbc52ab39b4979f98 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "What am I going to put here?" + }, + { + "text": "Another H4." + }, + { + "text": "And up here, another H4." + }, + { + "text": "And finally here, minus H4." + }, + { + "text": "Minus H4, and I think I've got orthogonal columns again." + }, + { + "text": "Because the columns within these, dot products with themselves, give 0 and 0." + }, + { + "text": "The dot products from these columns and these columns obviously have the minus." + }, + { + "text": "And the dot products in here are 0 from that and 0 from that." + }, + { + "text": "Yeah, it works." + }, + { + "text": "And we could keep going to 16 and 32 and 64." + }, + { + "text": "But then up comes a question." + }, + { + "text": "What about H12?" + }, + { + "text": "Is there a 1's and minus 1's matrix of size 12, 12 by 12?" + }, + { + "text": "It doesn't come directly from our little pattern, which is doubling size every time." + }, + { + "text": "But you could still hope." + }, + { + "text": "And it works." + }, + { + "text": "I don't know what it is, but there's a matrix of 1's and minus 1's, 12 orthogonal columns." + }, + { + "text": "So the answer is yes." + }, + { + "text": "OK, so we make an 18.065 conjecture." + }, + { + "text": "Every matrix size, well, not every matrix size, because 3 by 3 is not going to work." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk17.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..424ebae85640980fc86eba92079646d513aa4ab7 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "1 by 1 is not going to work either." + }, + { + "text": "But H12 works, H8, H16." + }, + { + "text": "What's our conjecture?" + }, + { + "text": "We won't be the first to conjecture it." + }, + { + "text": "There is a 1's and minus 1's orthogonal matrix with orthogonal columns of every size n. So always, so I'll start the conjecture." + }, + { + "text": "Always possible if n, which is the size of the matrix, let's say, what would you guess?" + }, + { + "text": "Just take a shot." + }, + { + "text": "You won't be asked for a proof, because nobody has the proof." + }, + { + "text": "Even?" + }, + { + "text": "Well, you could hope for even." + }, + { + "text": "You could look for try 6, I guess, would be the first guy there." + }, + { + "text": "And I don't think it's possible." + }, + { + "text": "I think 6 is not possible." + }, + { + "text": "So every even size is, I think, not going to work." + }, + { + "text": "But it's a natural idea to try." + }, + { + "text": "What's the next thought?" + }, + { + "text": "Every multiple of 4." + }, + { + "text": "If n over 4 is a whole number." + }, + { + "text": "But nobody has a systematic way to create these things." + }, + { + "text": "So like some of them, at this point, we're down to doing it one at a time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk18.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..8b98656b2afa8ad2c2bc10e43f6253f0336687c6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we're up to 668." + }, + { + "text": "But we haven't got that one yet." + }, + { + "text": "Isn't that crazy?" + }, + { + "text": "So all this is coming from Wikipedia, my source of all that's good in mathematics is there on Wikipedia." + }, + { + "text": "Anyway, this is the conjecture." + }, + { + "text": "Conjecture means you don't have any damn idea of whether it's true or not." + }, + { + "text": "Is that divisible by 4?" + }, + { + "text": "Yeah, I guess it would be." + }, + { + "text": "600 certainly is, and 68 certainly is." + }, + { + "text": "So I think that's the first one." + }, + { + "text": "So anybody, if you find one of size 668, just skip the homework and tell us about that one." + }, + { + "text": "But I don't think I'll assign that." + }, + { + "text": "I guess, well, I must have searched for it online." + }, + { + "text": "But yeah, anyway, so those are the Adamard matrices." + }, + { + "text": "Now, where else do I remember orthogonal matrices coming from?" + }, + { + "text": "Well, yeah, really, the biggest source of." + }, + { + "text": "So when I'm looking for orthogonal matrices, I'm looking for a basis of orthogonal vectors." + }, + { + "text": "And where in math am I going to find vectors that come out to be orthogonal?" + }, + { + "text": "We haven't seen that." + }, + { + "text": "It's the next section of the notes, but maybe you're remembering." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk19.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1a1bbc69e93bf8e690780d413ac7692520b39c41 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Where will we sort of like automatically show up with orthogonal vectors?" + }, + { + "text": "They could be the eigenvectors of a symmetric matrix." + }, + { + "text": "And that's where the most important ones come from." + }, + { + "text": "Oh, I could tell you about wavelets, though." + }, + { + "text": "Wavelets are more like this picture." + }, + { + "text": "They're 1's and minus 1's." + }, + { + "text": "Or the simplest wavelets are 1's and minus 1's." + }, + { + "text": "Before I go on to the eigenvector business, can I mention the wavelets matrices?" + }, + { + "text": "Yeah, these are really important, simple and important constructions." + }, + { + "text": "So wavelets, let me draw a picture." + }, + { + "text": "So I'm going to come up with four." + }, + { + "text": "I'll do the 4 by 4 case." + }, + { + "text": "And these are the orthogonal guys." + }, + { + "text": "And then the next one is up and down and 0." + }, + { + "text": "And the last one is 0 and up and down." + }, + { + "text": "So that's four things, but let me show you the matrix." + }, + { + "text": "So I'll call it W for wavelets." + }, + { + "text": "So that guy I'm thinking of as 1, 1, 1, 1." + }, + { + "text": "This guy I'm thinking of as 1, 1, minus 1, minus 1." + }, + { + "text": "It's looking sort of Adhemard way, but there's a difference here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk2.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..fa6e9f79b321740f7bd2a0adca7cc97249c3a10c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Q is an orthogonal matrix." + }, + { + "text": "Right, right." + }, + { + "text": "Do you want to just see an example of how that works?" + }, + { + "text": "And it will not." + }, + { + "text": "So if Q is rectangular, let me do a rectangular Q and a square Q." + }, + { + "text": "So I think there must be a board up there somewhere." + }, + { + "text": "Here." + }, + { + "text": "OK, square." + }, + { + "text": "All right, good to see some orthogonal matrices, because my message is that they're really important in all kinds of applications." + }, + { + "text": "Let's start two by two." + }, + { + "text": "I can think of two different ways to get an orthogonal matrix that's a two by two matrix." + }, + { + "text": "And one of them you will know immediately, cos theta, sine theta." + }, + { + "text": "So that's a unit vector." + }, + { + "text": "It's normalized." + }, + { + "text": "Cos squared plus sine squared is 1." + }, + { + "text": "And this guy has to be orthogonal to it." + }, + { + "text": "So I'll make that minus sine theta and cos theta." + }, + { + "text": "OK. Those are both length 1." + }, + { + "text": "They're orthogonal." + }, + { + "text": "Then this is my Q." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk20.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..3e8bb5de8bf16bf7ce3501ccefb5a330450b8ade --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "This guy is 1, minus 1, 0, 0." + }, + { + "text": "So the wavelets rescale." + }, + { + "text": "That's the difference between Adhemard and wavelets." + }, + { + "text": "Wavelets are self-scaling." + }, + { + "text": "And what's the last guy here?" + }, + { + "text": "What's the fourth column from that fourth wavelet?" + }, + { + "text": "0, 0, 1, minus 1." + }, + { + "text": "So Haar came up with that." + }, + { + "text": "This is the Haar wavelet, which was many years before the word wavelets was invented." + }, + { + "text": "He came up with this construction, the Haar matrix, the Haar functions." + }, + { + "text": "So they're very simple functions, but that makes them usable, the fact that they're so simple." + }, + { + "text": "Now, I don't know if you want to see the pattern in 8 by 8, but let me start the 8 by 8 so you'll know what wavelets are about." + }, + { + "text": "You'll know what these Haar wavelets are about anyway." + }, + { + "text": "They're the ones that were kind of easy to visualize." + }, + { + "text": "So if that's W4, let's just take a minute." + }, + { + "text": "It won't take long for W8." + }, + { + "text": "OK." + }, + { + "text": "So the first column is going to be 8 1's." + }, + { + "text": "And what's the next column going to be?" + }, + { + "text": "4 1's and 4 minus 1's, like so." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk21.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..9e867c07e11ef6d60fe356fac02e997856317ce7 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So 4 1's and 4 minus 1's." + }, + { + "text": "OK, and now the next column." + }, + { + "text": "2 1's, 2 minus 1's, and 0's." + }, + { + "text": "Right?" + }, + { + "text": "1, 1, minus 1, minus 1, and 0." + }, + { + "text": "And the fourth will be 0's and 2 1's and 2 minus 1's." + }, + { + "text": "We've got half a matrix now." + }, + { + "text": "Now, if we just tell me the fifth, what do you think?" + }, + { + "text": "What do I put in the fifth one?" + }, + { + "text": "So again, it's going to squeeze down and rescale." + }, + { + "text": "And what's the fifth column up here that's going to be 1's and minus 1's and 0's now?" + }, + { + "text": "So it's not Adamard." + }, + { + "text": "It's Haar." + }, + { + "text": "And what shall I put?" + }, + { + "text": "1, 1." + }, + { + "text": "Shall I start with 1, 1?" + }, + { + "text": "Oh, 1 minus?" + }, + { + "text": "Yeah." + }, + { + "text": "And then all 0's?" + }, + { + "text": "Oh, yeah, thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk22.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..9c0933bcb3a8da850c610e830d259e286619b663 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Perfect." + }, + { + "text": "1 minus 1, and then all 0's." + }, + { + "text": "And then the next three columns will have the 1 minus 1 here, and the 1 minus 1 here, and the 1 minus 1 here." + }, + { + "text": "And otherwise, all 0's." + }, + { + "text": "So you see the pattern." + }, + { + "text": "It's scaling at every step." + }, + { + "text": "So that matrix has the advantage of being quite sparse." + }, + { + "text": "This, in my mind, is a 4, 1's." + }, + { + "text": "That's involved with taking the average." + }, + { + "text": "Then this guy is like taking the differences, differences between those and those." + }, + { + "text": "And then this is like taking the difference at a smaller scale, and that also at a smaller scale." + }, + { + "text": "So that's what we keep doing." + }, + { + "text": "Yeah." + }, + { + "text": "Yeah." + }, + { + "text": "So that's wavelets." + }, + { + "text": "It looks so simple, right?" + }, + { + "text": "But just a one-minute history of wavelets, so Haar invented this in like 1910." + }, + { + "text": "I mean, along, forever." + }, + { + "text": "But then you wanted wavelets that were a little better, and not just 1's and minus 1's and 0's." + }, + { + "text": "And that took a lot of thinking." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk23.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..2c0478724ed1347c302a19560f09fa22c81860c1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "A lot of people were searching for it." + }, + { + "text": "And Ingrid Dovashy, so I'll just put her name, became famous for finding them." + }, + { + "text": "So in about 1988, she found a whole lot of families of wavelets." + }, + { + "text": "And when I say wavelets, she found a whole lot of orthogonal matrices that had good properties." + }, + { + "text": "So that's the wavelet picture." + }, + { + "text": "Now, to close today and to connect with the next lecture on eigenvalues, eigenvectors, positive definite matrices, we're really getting to the heart of things here." + }, + { + "text": "Let me follow through on that idea." + }, + { + "text": "Idea, so the eigenvectors of a symmetric matrix, but also of an orthogonal matrix are orthogonal." + }, + { + "text": "And that is really where people, where you can invent, because you don't have to work hard." + }, + { + "text": "You just find a symmetric matrix." + }, + { + "text": "Its eigenvectors are automatically orthogonal." + }, + { + "text": "That doesn't mean they're great for use, but some of them are really important." + }, + { + "text": "And maybe the most important of all is the Fourier." + }, + { + "text": "So you probably have seen Fourier series, sines and cosines." + }, + { + "text": "Those guys are orthogonal functions." + }, + { + "text": "But the discrete Fourier series is what everybody computes, and those are orthogonal vectors." + }, + { + "text": "So the orthogonal vectors that go into the discrete Fourier transform, and then they're done at high speed by the fast Fourier transform, those are eigenvectors of Q, eigenvectors of the right Q." + }, + { + "text": "So let me just tell you the right Q, whose eigenvectors." + }, + { + "text": "So here we go." + }, + { + "text": "Eigenvectors of Q." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk24.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..6444776fc980bc4a69fa3b53bb954577f9481f13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "You will just be amazed by how simple this matrix is." + }, + { + "text": "It's just that matrix." + }, + { + "text": "It's called a permutation matrix." + }, + { + "text": "Those are the four Fourier discrete." + }, + { + "text": "Let me put the word discrete up here, transform." + }, + { + "text": "So I really meant to put discrete Fourier transform." + }, + { + "text": "The eigenvectors of that matrix, first of all, they are orthogonal." + }, + { + "text": "And then second and more important, they're tremendously useful." + }, + { + "text": "They're the heart of signal processing." + }, + { + "text": "In signal processing, they just take the discrete Fourier transform of a vector before they even look at it." + }, + { + "text": "I mean, that's the way to see it, is split it into its frequencies." + }, + { + "text": "And that's what the eigenvectors of this will do." + }, + { + "text": "So we're going to see the discrete Fourier transform." + }, + { + "text": "But my point here is to know that they're orthogonal just comes out of this fact that the eigenvectors are orthogonal for any Q." + }, + { + "text": "And that is certainly a Q." + }, + { + "text": "Everybody can see that those columns are orthogonal." + }, + { + "text": "The columns of a permutation matrix, right?" + }, + { + "text": "You've taken the columns of the identity, which are totally orthogonal, and you just put them in a different order." + }, + { + "text": "So a permutation matrix is a reordering of the identity matrix." + }, + { + "text": "It's got to be a Q." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk25.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..8f7ca0deb0b14efd9582bf5072f857c1cf891aae --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And therefore, its eigenvectors are orthogonal." + }, + { + "text": "And they're just the winners." + }, + { + "text": "I mean, the matrix of the Fourier matrix with those four eigenvectors in it, I'll show you now." + }, + { + "text": "So this is really we're finishing today by leading into Wednesday, eigenvectors and eigenvalues." + }, + { + "text": "And we happen to be doing eigenvectors and eigenvalues of a Q, not today of an S. Most of the time, it's a symmetric matrix whose eigenvectors we take." + }, + { + "text": "But here, that happens to be a Q." + }, + { + "text": "Can I show you the eigenvectors, the four eigenvectors of that?" + }, + { + "text": "Now, oh, the complex number I is going to come in." + }, + { + "text": "You have to let it in here." + }, + { + "text": "Sorry." + }, + { + "text": "If S is a real symmetric matrix, its eigenvectors are real." + }, + { + "text": "But if Q is a orthogonal matrix, its eigenvectors, even though you couldn't ask for a more real matrix than that, but its eigenvectors are at least, yeah, the good way are complex numbers." + }, + { + "text": "So can I show you the eigenvectors of?" + }, + { + "text": "OK." + }, + { + "text": "So again, overall, the point today is to see orthogonal matrices." + }, + { + "text": "So I'll just repeat now while I can." + }, + { + "text": "Rotations here, reflections, wavelets, the householder idea of reflections of large matrices that have this form I minus 2 UU transpose are orthogonal." + }, + { + "text": "And now we're going to see the big guys, the eigenvectors of Q." + }, + { + "text": "Right." + }, + { + "text": "Yes?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk26.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..585374b4472c10a27d82558759b1912444ae522b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk26.json @@ -0,0 +1,62 @@ +[ + { + "text": "AUDIENCE 2." + }, + { + "text": "The wavelets, do you want to rescale the column?" + }, + { + "text": "GILBERT STRANG, M.D." + }, + { + "text": "Oh, yeah." + }, + { + "text": "We don't have orthonormal." + }, + { + "text": "That's right." + }, + { + "text": "We don't have orthonormal." + }, + { + "text": "I better divide by square root of 8." + }, + { + "text": "Right." + }, + { + "text": "AUDIENCE 3." + }, + { + "text": "There's different forms for different." + }, + { + "text": "GILBERT STRANG, M.D." + }, + { + "text": "Oh, yes." + }, + { + "text": "Oh, you're right." + }, + { + "text": "Sorry, I thought I'd get away with that, but I didn't." + }, + { + "text": "Yeah." + }, + { + "text": "So these guys are square roots of 8." + }, + { + "text": "So are these." + }, + { + "text": "But these guys are square roots of 4." + }, + { + "text": "And these guys are square roots of 2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk27.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk27.json new file mode 100644 index 0000000000000000000000000000000000000000..fe044f5efd14e48e1d27d0585f9bebef51beb0e8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk27.json @@ -0,0 +1,62 @@ +[ + { + "text": "Thank you." + }, + { + "text": "Absolutely right." + }, + { + "text": "Absolutely." + }, + { + "text": "Yeah." + }, + { + "text": "OK." + }, + { + "text": "So what are the eigenvectors of a permutation?" + }, + { + "text": "This is going to be nice to see." + }, + { + "text": "And I'll use the matrix F for the eigenvector matrix of that Q up there." + }, + { + "text": "And F is for Fourier." + }, + { + "text": "And it'd be the 4 by 4 Fourier matrix." + }, + { + "text": "OK. What are the eigenvectors of Q?" + }, + { + "text": "OK." + }, + { + "text": "So Q is a permutation." + }, + { + "text": "So I'm going to ask you for one eigenvector of every permutation matrix." + }, + { + "text": "What vector can you tell me that actually the eigenvalue will be 1?" + }, + { + "text": "What vector can you tell me where if I permute it, I don't change it?" + }, + { + "text": "1, 1, 1, 1." + }, + { + "text": "It's like it's everywhere here." + }, + { + "text": "1, 1, 1, 1." + }, + { + "text": "So that's the zero frequency Fourier vector, the constant vector, all 1's." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk28.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk28.json new file mode 100644 index 0000000000000000000000000000000000000000..fd0082d001d298314187d0489c0c1333ec2c11ed --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk28.json @@ -0,0 +1,62 @@ +[ + { + "text": "Everybody sees that if I multiply by Q, it doesn't change." + }, + { + "text": "OK. Now the next one, I'll show you the 4 now." + }, + { + "text": "The next one will be 1, i, i squared, and i cubed." + }, + { + "text": "Of course, i squared, I don't know how many course 6j people are in this audience." + }, + { + "text": "But this is a math building, we paid for it." + }, + { + "text": "It's 2, 190, and it's i in this room." + }, + { + "text": "Yeah." + }, + { + "text": "So yeah." + }, + { + "text": "Anyway, i is the first letter in what?" + }, + { + "text": "Imaginary, thank you." + }, + { + "text": "The first letter in imaginary." + }, + { + "text": "You can't say jimaginary." + }, + { + "text": "So that's it." + }, + { + "text": "OK. And then the next one is 1, i squared, i fourth, i sixth." + }, + { + "text": "And the next one is 1, i cubed, i sixth, and i ninth." + }, + { + "text": "Isn't that just beautiful?" + }, + { + "text": "And you could show that every one of those four columns, if you multiply them by Q, you would get the eigenvalues." + }, + { + "text": "And you would see that it's an eigenvector." + }, + { + "text": "And this is just sort of like a discrete Fourier stuff." + }, + { + "text": "And instead of e to the ix, e to the 2ix, e to the 3ix, and so on, we just have vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk29.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk29.json new file mode 100644 index 0000000000000000000000000000000000000000..69ca2b5a6c93f1ff5ff4b1010014d5bbfe4a81fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk29.json @@ -0,0 +1,62 @@ +[ + { + "text": "So those are the four eigenvectors of that permutation." + }, + { + "text": "And those are orthogonal." + }, + { + "text": "Could I just check that?" + }, + { + "text": "How do you know that this first column and the second?" + }, + { + "text": "Well, I should really say zeroth column and first column if I'm talking frequencies." + }, + { + "text": "Do you see that that's orthogonal to that?" + }, + { + "text": "Well, y is 1 plus i plus i squared plus i cubed equals 0." + }, + { + "text": "That's the dot product." + }, + { + "text": "This is column 1 dot column 2." + }, + { + "text": "Yeah." + }, + { + "text": "You're right." + }, + { + "text": "This happens to come out 0." + }, + { + "text": "Is that right?" + }, + { + "text": "Yes, that will come out 0." + }, + { + "text": "That'll come out 0." + }, + { + "text": "But somebody mentioned that this isn't right." + }, + { + "text": "It's true that that came out 0." + }, + { + "text": "But when I have imaginary numbers anywhere around, this isn't the correct dot product to test orthogonal." + }, + { + "text": "If I have complex vectors, if I have complex numbers, complex vectors, I should test column 1 conjugate dotted with column 2." + }, + { + "text": "Column i conjugate." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk3.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..f863ecb71103dd4c79faee118ac276d69bf4817f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the inverse of Q will be the transpose." + }, + { + "text": "The transpose would put the minus sign down here and would produce the inverse matrix." + }, + { + "text": "And what does that particular matrix represent?" + }, + { + "text": "Geometrically, where do we see that matrix?" + }, + { + "text": "It's a rotation." + }, + { + "text": "Thank you." + }, + { + "text": "It's a rotation of the whole plane by theta." + }, + { + "text": "Yeah." + }, + { + "text": "So if I apply that to 1, 0, for example, I get the first column, which is cos theta, sine theta." + }, + { + "text": "And that's just a row." + }, + { + "text": "Let me draw a picture." + }, + { + "text": "That vector 1, 0 has got rotated up to." + }, + { + "text": "So there is the 1, 0." + }, + { + "text": "And there it got rotated through an angle theta." + }, + { + "text": "And similarly, 0, 1 will get rotated through an angle theta to there." + }, + { + "text": "So the whole plane rotates." + }, + { + "text": "Oh, that makes me remember a highly important, very important property of Q." + }, + { + "text": "It doesn't change length." + }, + { + "text": "The length of any vector is the same after you rotate it." + }, + { + "text": "The length of any vector is the same after you multiply by Q." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk30.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk30.json new file mode 100644 index 0000000000000000000000000000000000000000..64bd5e5b732f6ef86ff8d651a31c18dc5d6a7b26 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk30.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, let me take column." + }, + { + "text": "Let's see." + }, + { + "text": "Which one shall I take?" + }, + { + "text": "Maybe that guy and that guy." + }, + { + "text": "Many of them you luck out here." + }, + { + "text": "But really, I should be taking the conjugate." + }, + { + "text": "So these 1's." + }, + { + "text": "But the thing is the complex conjugate of 1 is 1." + }, + { + "text": "So that was OK." + }, + { + "text": "But in general, if I wanted to take column 2 dotted with column, I don't know, maybe 4 would be a little dodgy." + }, + { + "text": "Yeah, look what happens." + }, + { + "text": "Take that column and that column." + }, + { + "text": "Take their dot product." + }, + { + "text": "Do it the wrong way." + }, + { + "text": "So what's the wrong way?" + }, + { + "text": "Forget about the complex conjugate and just do it the usual way." + }, + { + "text": "So 1 times 1 is 1. i times i cube is?" + }, + { + "text": "1. i squared times i6 is?" + }, + { + "text": "1." + }, + { + "text": "I'm getting all 1's." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk31.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk31.json new file mode 100644 index 0000000000000000000000000000000000000000..96f23de58f04372c803c798f245920b0c738af9b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk31.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'm not getting orthogonality there." + }, + { + "text": "And that's because I forgot that I should take the complex conjugate." + }, + { + "text": "Well, of these guys, 1." + }, + { + "text": "I should take minus i." + }, + { + "text": "Minus i squared." + }, + { + "text": "Well, that's real, so it's OK." + }, + { + "text": "Minus there." + }, + { + "text": "So minus i squared is still minus 1." + }, + { + "text": "So now if I do it, it comes out 0." + }, + { + "text": "So let me repeat again." + }, + { + "text": "Let me just make this statement." + }, + { + "text": "If Q transpose Q is i, and Qx is lambda x, and Qy is a different eigenvalue y. OK." + }, + { + "text": "So I'm setting up the main fact that in the last minute, I'm just going to write down." + }, + { + "text": "So I have an orthogonal matrix." + }, + { + "text": "I have an eigenvector with eigenvalue lambda." + }, + { + "text": "I have another eigenvector with a different eigenvalue mu." + }, + { + "text": "Then the claim is that, what is the claim about the eigenvectors?" + }, + { + "text": "So here has one eigen." + }, + { + "text": "This has an eigenvalue." + }, + { + "text": "This has a different eigenvalue." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk32.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk32.json new file mode 100644 index 0000000000000000000000000000000000000000..7b846a742a5f1c49f8285cefa23421fb49501ed2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk32.json @@ -0,0 +1,41 @@ +[ + { + "text": "I need them to be different to really know that the x's and the y's can't be the same." + }, + { + "text": "So what is it that I want to show?" + }, + { + "text": "AUDIENCE 1." + }, + { + "text": "Conjugated x of y minus 1." + }, + { + "text": "Yes." + }, + { + "text": "That x, and I have to remember to do that, x transpose y is 0." + }, + { + "text": "That's orthogonality." + }, + { + "text": "That's orthogonality for complex vectors." + }, + { + "text": "I have to remember to change every i to a minus i in one of the vectors." + }, + { + "text": "And I can prove that fact by playing with these, by playing with starting from here, I can get to that." + }, + { + "text": "OK, that's it." + }, + { + "text": "We've done a lot today, a lot of stuff about orthogonal matrices, important ones and the sources of important ones, eigenvectors." + }, + { + "text": "And so it'll be eigenvectors on Wednesday." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk4.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..2c68625c6da30919ac3c7cd9aa2d38115f88b017 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Can I just do that?" + }, + { + "text": "I claim any x, any vector x, I want to look at the length of Qx." + }, + { + "text": "And I claim that it has the same length as x." + }, + { + "text": "Actually, that's the reason in computations that orthogonal matrix are so much loved, because no overflow can happen with orthogonal matrices." + }, + { + "text": "Lengths don't change." + }, + { + "text": "I can multiply by any number of orthogonal matrices, and the lengths don't change." + }, + { + "text": "Can we just see why that's true?" + }, + { + "text": "How would you show?" + }, + { + "text": "So what do we have to go on?" + }, + { + "text": "What we have to go on is Q transpose Q equal I." + }, + { + "text": "Whatever we're going to prove, it's got to come out of that, because that's all we know." + }, + { + "text": "So how do I use that to get that one?" + }, + { + "text": "Well, we haven't said a whole lot about lengths, but you'll see it all now." + }, + { + "text": "It'll be easier to prove that the squares are the same." + }, + { + "text": "So what's the matrix expression for the length squared?" + }, + { + "text": "What's the right-hand side of that equation?" + }, + { + "text": "X transpose x, right?" + }, + { + "text": "X transpose x gives me the sum of the squares." + }, + { + "text": "Pythagoras says that's the length squared." + }, + { + "text": "So that right-hand side is x transpose x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk5.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..fe88faea55ca7fdbade0e4cf0f0a9f66df2465b8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "What's the left side?" + }, + { + "text": "It's the length squared of this, of Qx." + }, + { + "text": "So it must be the same as Qx, transpose Qx." + }, + { + "text": "And the claim is that that equation holds." + }, + { + "text": "And do you see it?" + }, + { + "text": "Where is it?" + }, + { + "text": "So any property from Q has to just come out directly from that." + }, + { + "text": "Where is it here?" + }, + { + "text": "Do I just push away a little bit at that left-hand side and see it?" + }, + { + "text": "Qx transpose is the same as x transpose Q transpose." + }, + { + "text": "And Qx is Qx." + }, + { + "text": "And now I'm seeing, well, you might say, wait a minute." + }, + { + "text": "The parentheses were there and there." + }, + { + "text": "But I say the most important law for matrix multiplication is you can move parentheses or throw them away." + }, + { + "text": "Let's throw them away." + }, + { + "text": "So in here, I'm seeing Q transpose Q, which is the identity." + }, + { + "text": "So it's true." + }, + { + "text": "So that means that you never underflow or overflow when you're multiplying by Q." + }, + { + "text": "Every numerical algorithm is written to use orthogonal matrices wherever it can." + }, + { + "text": "And here's the first example." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk6.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..962dbdc98b0f27e37ce73e12c9ffbe343c8dddd5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I think it may be good for me to think of other examples or for us to think of other examples of orthogonal matrices." + }, + { + "text": "So I'm using that word orthogonal matrix." + }, + { + "text": "We should really be saying orthonormal." + }, + { + "text": "And I'm really thinking mostly of square ones." + }, + { + "text": "So in the square case, when Q transpose is Q inverse." + }, + { + "text": "Of course, that fact makes it easy to solve all equations that have Q as a coefficient matrix, because you want the inverse and you just use the transpose." + }, + { + "text": "OK, let's just take some minutes to think of examples of Qs, if they're so important there have to be interesting examples." + }, + { + "text": "And that was a first one." + }, + { + "text": "Now, there's one more 2 by 2 example that you should know." + }, + { + "text": "Do you know what that would be?" + }, + { + "text": "So this will be example 2." + }, + { + "text": "And it's also going to be only 2 by 2 and real." + }, + { + "text": "And what possibility have I got left here?" + }, + { + "text": "I'll use the same first column, cos theta, sine theta, because that's more or less any unit vector in two dimensions." + }, + { + "text": "This has got that form." + }, + { + "text": "So what do you propose for the second column?" + }, + { + "text": "Yes?" + }, + { + "text": "Yeah, put the minus sign down here." + }, + { + "text": "So you think, does that make any difference?" + }, + { + "text": "So sine theta and minus cos theta." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk7.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..518d307339e6889aea8a3bded1efa411a6f5745a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "I don't know if you've ever looked at that matrix." + }, + { + "text": "We're trying to collect together a few matrices that are worth knowing, are worth looking at." + }, + { + "text": "OK, now what's happened here?" + }, + { + "text": "You may say that was a trivial change, which it kind of was." + }, + { + "text": "But it's a different matrix now." + }, + { + "text": "It's not a rotation anymore." + }, + { + "text": "That's not a rotation." + }, + { + "text": "And yeah, somehow, now it's symmetric." + }, + { + "text": "And yeah, its eigenvectors must be something or other." + }, + { + "text": "We'll get to those." + }, + { + "text": "But what does that matrix do?" + }, + { + "text": "I don't know if you've seen it." + }, + { + "text": "If you haven't, it doesn't jump out." + }, + { + "text": "But it's an important case." + }, + { + "text": "This is a reflection matrix." + }, + { + "text": "Notice that it's determined it is minus 1." + }, + { + "text": "You have minus cos squared theta minus sine squared theta." + }, + { + "text": "It's determined it is minus 1." + }, + { + "text": "There's some eigenvalue coming up that's got a minus." + }, + { + "text": "Yeah." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk8.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..481458df8b0fa0d4060f8a9ff2fad9395e817b04 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, so what do I mean by a reflection matrix?" + }, + { + "text": "Let me draw the plane." + }, + { + "text": "And I think, so 1, 0." + }, + { + "text": "Let's follow it again." + }, + { + "text": "1, 0, where does that go?" + }, + { + "text": "That gives me the first column." + }, + { + "text": "So as before, it goes to cos theta sine theta." + }, + { + "text": "And when I say reflection, let me put the mirror into the picture." + }, + { + "text": "So you see what reflection it is." + }, + { + "text": "The mirror is along here at angle theta over 2, theta over 2 line." + }, + { + "text": "So sure enough, 1, 0 at angle 0 got reflected into a unit vector at angle theta." + }, + { + "text": "And halfway between was the theta over 2 line." + }, + { + "text": "That's OK. Now, what about the other guy, 0, 1?" + }, + { + "text": "Here's 0, 1." + }, + { + "text": "OK, I multiply that." + }, + { + "text": "Can I put the 0, 1 up here so your eye does the multiplication?" + }, + { + "text": "Where is the result of 0, 1?" + }, + { + "text": "What's the output from Q applied to 0, 1?" + }, + { + "text": "Sine theta minus cos theta, right?" + }, + { + "text": "It's the second column." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk9.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..27a460130a0a8d38fe662c57a511c467a303fbb9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_0_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so where is that?" + }, + { + "text": "Well, it's perpendicular to that guy." + }, + { + "text": "That's what I know, right?" + }, + { + "text": "That was the point, that the two columns are perpendicular." + }, + { + "text": "So it must go down this way, right?" + }, + { + "text": "Sine theta, cos theta." + }, + { + "text": "And it doesn't change length." + }, + { + "text": "All these facts that we just learned are key." + }, + { + "text": "So there's 0, 1, and it goes to this guy, which is whatever that second column is, sine theta minus cos theta." + }, + { + "text": "And if you check that, actually, gosh, this is like plain geometry." + }, + { + "text": "I believe, it's never occurred to me before, but I believe it, that this angle going down to there, that that goes straight through, and that the halfway one is that line." + }, + { + "text": "Yeah, I think that picture has got it, and I think it's in the notes." + }, + { + "text": "So that's a reflection matrix." + }, + { + "text": "Well, that's a 2 by 2 reflection matrix." + }, + { + "text": "Would you like to see some other matrices like this one, but larger?" + }, + { + "text": "They're named after a guy named Householder." + }, + { + "text": "So these are Householder reflections." + }, + { + "text": "What am I doing here?" + }, + { + "text": "I'm collecting together some orthogonal matrices that are useful and important." + }, + { + "text": "And Householder found a whole bunch of them, and his algorithm is a much used part of numerical linear algebra." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk0.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..b5d2005486c62ceb6bba16af0971eda159bf4d11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So we're really moving along this review of the highlights of linear algebra." + }, + { + "text": "And today it's matrices Q." + }, + { + "text": "They get that name." + }, + { + "text": "They have orthonormal columns." + }, + { + "text": "So that's what one looks like." + }, + { + "text": "And then the key fact, orthonormal columns translates directly into that simple fact that you just keep remembering." + }, + { + "text": "Every time you see Q transpose Q, you've got the identity matrix." + }, + { + "text": "Let's just see why." + }, + { + "text": "So Q transpose would be, I'll take those columns and make them into rows." + }, + { + "text": "And then I multiply by Q with the columns." + }, + { + "text": "And what do I get?" + }, + { + "text": "Well, hopefully I get the identity matrix." + }, + { + "text": "OK, why?" + }, + { + "text": "Because, oh, yeah, the normal part tells me that the length of each vector, that's the length squared Q transpose Q." + }, + { + "text": "The length squared is 1." + }, + { + "text": "So that gives me the 1 in the identity matrix all along the diagonal." + }, + { + "text": "And then Q transpose times a different Q is 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk1.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..4e5a53f7561a10c59c686c38ce76be1836e60948 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the ortho part." + }, + { + "text": "So that gives me the 0s." + }, + { + "text": "So that's a simple identity." + }, + { + "text": "But it translates from a lot of words into a simple expression." + }, + { + "text": "Now, does that mean that in the other order, Q Q transpose, is that the identity?" + }, + { + "text": "So that's a question to think about." + }, + { + "text": "Is Q Q transpose equal the identity?" + }, + { + "text": "Question." + }, + { + "text": "Sometimes yes, sometimes no." + }, + { + "text": "Easy to tell which." + }, + { + "text": "The answer is yes." + }, + { + "text": "Yes, when Q is square." + }, + { + "text": "The answer is yes." + }, + { + "text": "If Q is a square matrix, a square matrix, this is saying that the square matrix Q has that inverse on its left." + }, + { + "text": "But for square matrices, a left inverse, Q transpose, is also a right inverse." + }, + { + "text": "And for a square matrix, if you have an inverse that works on one side, it will work on the other side." + }, + { + "text": "So the answer is yes in that case." + }, + { + "text": "And then in that case, that's the case when we call Q is, well, we really, I don't know what the right name would be." + }, + { + "text": "But here's the name everybody uses, an orthogonal matrix." + }, + { + "text": "And that's only in the square case, square." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk10.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..49656af3fb9dd19d28412adf515bdcbf6d01baf1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So he started with a unit vector." + }, + { + "text": "Start with a unit vector, u transpose u equal 1." + }, + { + "text": "So the length of the vector is 1." + }, + { + "text": "And then he created, let's name it after him, H. He created this matrix, the identity minus 2 uu transpose." + }, + { + "text": "And I believe that that's a really useful matrix." + }, + { + "text": "So it's just like, I think this review is like going beyond 18.06 into what ones are really worth knowing individually." + }, + { + "text": "Could we just check what are the properties of Householder's reflection of that I minus 2?" + }, + { + "text": "You recognize here a column times a row." + }, + { + "text": "So that's a matrix." + }, + { + "text": "And what could you tell me about that matrix uu transpose?" + }, + { + "text": "It's, yeah." + }, + { + "text": "Or what can we say about H?" + }, + { + "text": "So I guess I'm believing that H is a orthogonal matrix." + }, + { + "text": "Otherwise, it wouldn't be here today." + }, + { + "text": "So I believe that." + }, + { + "text": "And not only is it orthogonal, it is also, have a look at it, symmetric." + }, + { + "text": "It's also symmetric." + }, + { + "text": "The identity is symmetric." + }, + { + "text": "Uu transpose is symmetric." + }, + { + "text": "So this is a family of symmetric orthogonal matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk11.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d1bc347004ae5794bd541685a2530709739f8fb8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "And that was one of them." + }, + { + "text": "That's a symmetric orthogonal matrix." + }, + { + "text": "These matrices are really great to have." + }, + { + "text": "You just, like in using linear algebra, you just get a collection of useful matrices that you can call on." + }, + { + "text": "And these are definitely one family." + }, + { + "text": "Well, it's obviously symmetric." + }, + { + "text": "Shall we check that it's orthogonal?" + }, + { + "text": "So to check that it's orthogonal, I just, so I'm going to check that H transpose H is the identity." + }, + { + "text": "Can I just check that?" + }, + { + "text": "Well, H transpose is the same as H, because it was symmetric." + }, + { + "text": "So I'm going to square this guy." + }, + { + "text": "This is really H times H. I'm squaring it." + }, + { + "text": "And what do I get if I square?" + }, + { + "text": "So I get, I hope I get the identity, but let's see it." + }, + { + "text": "What do I get when I square this?" + }, + { + "text": "Get little, multiply it out." + }, + { + "text": "So I times I is I." + }, + { + "text": "And then I get some number of Uu transposes." + }, + { + "text": "How many do I get from that?" + }, + { + "text": "So I'm squaring this thing, because H transpose H is the same as H times H. So I'm squaring it." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk12.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..25d7b51e680f692a50bab3dc6644564db6a54780 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how many, what do I put here?" + }, + { + "text": "Four, thanks." + }, + { + "text": "And now I've got this guy squared with a plus." + }, + { + "text": "So that's four Uu transpose Uu transpose." + }, + { + "text": "Yeah, I'm totally realizing I've practiced for a lifetime doing these dinky little calculations." + }, + { + "text": "But they are dinky." + }, + { + "text": "And you'll get the hang of it quickly." + }, + { + "text": "Now, what am I hoping out of that bottom line?" + }, + { + "text": "That it is?" + }, + { + "text": "I." + }, + { + "text": "We're hoping to get I." + }, + { + "text": "Do we get I?" + }, + { + "text": "Yes." + }, + { + "text": "Who sees how to get I out of that thing?" + }, + { + "text": "Yeah." + }, + { + "text": "U transpose U in here is a number." + }, + { + "text": "That was U." + }, + { + "text": "That was column times row times column times row." + }, + { + "text": "And I look at the in the middle here is row times column." + }, + { + "text": "And that's the number 1, right?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk13.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2970896b1136ec13f25ac3b1d568b82c5bfd6397 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because it's there." + }, + { + "text": "So that's 1." + }, + { + "text": "And then I have minus 4 of that, plus 4 of that." + }, + { + "text": "They cancel each other." + }, + { + "text": "And I get I." + }, + { + "text": "So those are good matrices." + }, + { + "text": "We'll use them." + }, + { + "text": "We'll use them." + }, + { + "text": "Actually, they're better than Graham-Schmidt." + }, + { + "text": "So we'll use them in making things orthogonal." + }, + { + "text": "So what other orthogonal matrices?" + }, + { + "text": "Let's create some." + }, + { + "text": "Creating good orthogonal matrices, it pays off." + }, + { + "text": "Let's think." + }, + { + "text": "So there's a family named after this French guy who lived to 100." + }, + { + "text": "He was a real old timer." + }, + { + "text": "Well, MIT had a faculty member in math when I came, Professor Struik, who lived to 106." + }, + { + "text": "And I heard him give a lecture at Brown University at age 100." + }, + { + "text": "And it was like perfect." + }, + { + "text": "You could not have done it better." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk14.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7a4761773e251928346e720869f90c17e750fc9c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So he's my inspiration." + }, + { + "text": "I keep going." + }, + { + "text": "I only have like n more years to get there." + }, + { + "text": "And n is, well, it's too many anyway." + }, + { + "text": "OK, Adamard." + }, + { + "text": "All right, Adamard." + }, + { + "text": "So Adamard, he created, well, that's the simplest, the smallest." + }, + { + "text": "Now, the next guy is going to be 4 by 4." + }, + { + "text": "I'm going to put that." + }, + { + "text": "So where I see a 1, I'm going to put Adamard in." + }, + { + "text": "1, 1, 1 minus 1, 1, 1, 1 minus 1." + }, + { + "text": "And then when I see a minus, I'm going to put it in with a minus." + }, + { + "text": "You saw that picture?" + }, + { + "text": "It was a picture of H2, H2, H2, and minus H2." + }, + { + "text": "That's what I've got there." + }, + { + "text": "And I believe those columns are orthogonal." + }, + { + "text": "Now, what could I do?" + }, + { + "text": "Well, it's not quite an orthogonal matrix." + }, + { + "text": "What do I have to do to make it?" + }, + { + "text": "This isn't quite an orthogonal matrix either." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk15.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7c56d46fe9a00c08ec502262a9278c03ce6817ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "What do I do to make that an orthogonal matrix?" + }, + { + "text": "Divide by square root of 2." + }, + { + "text": "I need unit vectors there." + }, + { + "text": "And here, those lengths are 1 squared, 1 squared, 4." + }, + { + "text": "Square root of 4 is 2." + }, + { + "text": "So I better divide by the 2 there." + }, + { + "text": "And now here, I'm up to, yeah, so that was that one." + }, + { + "text": "Tell me the next one up." + }, + { + "text": "What's that going to be?" + }, + { + "text": "8 by 8?" + }, + { + "text": "So this is H4 here." + }, + { + "text": "Oops, 4." + }, + { + "text": "So tell me what I should do for 8 by 8." + }, + { + "text": "You'll think this is simple." + }, + { + "text": "But that's a good thing to say about it." + }, + { + "text": "In coding theory, all sorts of places, you want matrices of 1's and minus 1's." + }, + { + "text": "OK, what's H8?" + }, + { + "text": "I'm going to build it out of H4." + }, + { + "text": "So what's it going to be?" + }, + { + "text": "I'm going to put an H4 there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk16.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..918141f4e0ba694885e6f1ccbc52ab39b4979f98 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "What am I going to put here?" + }, + { + "text": "Another H4." + }, + { + "text": "And up here, another H4." + }, + { + "text": "And finally here, minus H4." + }, + { + "text": "Minus H4, and I think I've got orthogonal columns again." + }, + { + "text": "Because the columns within these, dot products with themselves, give 0 and 0." + }, + { + "text": "The dot products from these columns and these columns obviously have the minus." + }, + { + "text": "And the dot products in here are 0 from that and 0 from that." + }, + { + "text": "Yeah, it works." + }, + { + "text": "And we could keep going to 16 and 32 and 64." + }, + { + "text": "But then up comes a question." + }, + { + "text": "What about H12?" + }, + { + "text": "Is there a 1's and minus 1's matrix of size 12, 12 by 12?" + }, + { + "text": "It doesn't come directly from our little pattern, which is doubling size every time." + }, + { + "text": "But you could still hope." + }, + { + "text": "And it works." + }, + { + "text": "I don't know what it is, but there's a matrix of 1's and minus 1's, 12 orthogonal columns." + }, + { + "text": "So the answer is yes." + }, + { + "text": "OK, so we make an 18.065 conjecture." + }, + { + "text": "Every matrix size, well, not every matrix size, because 3 by 3 is not going to work." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk17.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..424ebae85640980fc86eba92079646d513aa4ab7 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "1 by 1 is not going to work either." + }, + { + "text": "But H12 works, H8, H16." + }, + { + "text": "What's our conjecture?" + }, + { + "text": "We won't be the first to conjecture it." + }, + { + "text": "There is a 1's and minus 1's orthogonal matrix with orthogonal columns of every size n. So always, so I'll start the conjecture." + }, + { + "text": "Always possible if n, which is the size of the matrix, let's say, what would you guess?" + }, + { + "text": "Just take a shot." + }, + { + "text": "You won't be asked for a proof, because nobody has the proof." + }, + { + "text": "Even?" + }, + { + "text": "Well, you could hope for even." + }, + { + "text": "You could look for try 6, I guess, would be the first guy there." + }, + { + "text": "And I don't think it's possible." + }, + { + "text": "I think 6 is not possible." + }, + { + "text": "So every even size is, I think, not going to work." + }, + { + "text": "But it's a natural idea to try." + }, + { + "text": "What's the next thought?" + }, + { + "text": "Every multiple of 4." + }, + { + "text": "If n over 4 is a whole number." + }, + { + "text": "But nobody has a systematic way to create these things." + }, + { + "text": "So like some of them, at this point, we're down to doing it one at a time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk18.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..8b98656b2afa8ad2c2bc10e43f6253f0336687c6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we're up to 668." + }, + { + "text": "But we haven't got that one yet." + }, + { + "text": "Isn't that crazy?" + }, + { + "text": "So all this is coming from Wikipedia, my source of all that's good in mathematics is there on Wikipedia." + }, + { + "text": "Anyway, this is the conjecture." + }, + { + "text": "Conjecture means you don't have any damn idea of whether it's true or not." + }, + { + "text": "Is that divisible by 4?" + }, + { + "text": "Yeah, I guess it would be." + }, + { + "text": "600 certainly is, and 68 certainly is." + }, + { + "text": "So I think that's the first one." + }, + { + "text": "So anybody, if you find one of size 668, just skip the homework and tell us about that one." + }, + { + "text": "But I don't think I'll assign that." + }, + { + "text": "I guess, well, I must have searched for it online." + }, + { + "text": "But yeah, anyway, so those are the Adamard matrices." + }, + { + "text": "Now, where else do I remember orthogonal matrices coming from?" + }, + { + "text": "Well, yeah, really, the biggest source of." + }, + { + "text": "So when I'm looking for orthogonal matrices, I'm looking for a basis of orthogonal vectors." + }, + { + "text": "And where in math am I going to find vectors that come out to be orthogonal?" + }, + { + "text": "We haven't seen that." + }, + { + "text": "It's the next section of the notes, but maybe you're remembering." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk19.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1a1bbc69e93bf8e690780d413ac7692520b39c41 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Where will we sort of like automatically show up with orthogonal vectors?" + }, + { + "text": "They could be the eigenvectors of a symmetric matrix." + }, + { + "text": "And that's where the most important ones come from." + }, + { + "text": "Oh, I could tell you about wavelets, though." + }, + { + "text": "Wavelets are more like this picture." + }, + { + "text": "They're 1's and minus 1's." + }, + { + "text": "Or the simplest wavelets are 1's and minus 1's." + }, + { + "text": "Before I go on to the eigenvector business, can I mention the wavelets matrices?" + }, + { + "text": "Yeah, these are really important, simple and important constructions." + }, + { + "text": "So wavelets, let me draw a picture." + }, + { + "text": "So I'm going to come up with four." + }, + { + "text": "I'll do the 4 by 4 case." + }, + { + "text": "And these are the orthogonal guys." + }, + { + "text": "And then the next one is up and down and 0." + }, + { + "text": "And the last one is 0 and up and down." + }, + { + "text": "So that's four things, but let me show you the matrix." + }, + { + "text": "So I'll call it W for wavelets." + }, + { + "text": "So that guy I'm thinking of as 1, 1, 1, 1." + }, + { + "text": "This guy I'm thinking of as 1, 1, minus 1, minus 1." + }, + { + "text": "It's looking sort of Adhemard way, but there's a difference here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk2.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..fa6e9f79b321740f7bd2a0adca7cc97249c3a10c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Q is an orthogonal matrix." + }, + { + "text": "Right, right." + }, + { + "text": "Do you want to just see an example of how that works?" + }, + { + "text": "And it will not." + }, + { + "text": "So if Q is rectangular, let me do a rectangular Q and a square Q." + }, + { + "text": "So I think there must be a board up there somewhere." + }, + { + "text": "Here." + }, + { + "text": "OK, square." + }, + { + "text": "All right, good to see some orthogonal matrices, because my message is that they're really important in all kinds of applications." + }, + { + "text": "Let's start two by two." + }, + { + "text": "I can think of two different ways to get an orthogonal matrix that's a two by two matrix." + }, + { + "text": "And one of them you will know immediately, cos theta, sine theta." + }, + { + "text": "So that's a unit vector." + }, + { + "text": "It's normalized." + }, + { + "text": "Cos squared plus sine squared is 1." + }, + { + "text": "And this guy has to be orthogonal to it." + }, + { + "text": "So I'll make that minus sine theta and cos theta." + }, + { + "text": "OK. Those are both length 1." + }, + { + "text": "They're orthogonal." + }, + { + "text": "Then this is my Q." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk20.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..3e8bb5de8bf16bf7ce3501ccefb5a330450b8ade --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "This guy is 1, minus 1, 0, 0." + }, + { + "text": "So the wavelets rescale." + }, + { + "text": "That's the difference between Adhemard and wavelets." + }, + { + "text": "Wavelets are self-scaling." + }, + { + "text": "And what's the last guy here?" + }, + { + "text": "What's the fourth column from that fourth wavelet?" + }, + { + "text": "0, 0, 1, minus 1." + }, + { + "text": "So Haar came up with that." + }, + { + "text": "This is the Haar wavelet, which was many years before the word wavelets was invented." + }, + { + "text": "He came up with this construction, the Haar matrix, the Haar functions." + }, + { + "text": "So they're very simple functions, but that makes them usable, the fact that they're so simple." + }, + { + "text": "Now, I don't know if you want to see the pattern in 8 by 8, but let me start the 8 by 8 so you'll know what wavelets are about." + }, + { + "text": "You'll know what these Haar wavelets are about anyway." + }, + { + "text": "They're the ones that were kind of easy to visualize." + }, + { + "text": "So if that's W4, let's just take a minute." + }, + { + "text": "It won't take long for W8." + }, + { + "text": "OK." + }, + { + "text": "So the first column is going to be 8 1's." + }, + { + "text": "And what's the next column going to be?" + }, + { + "text": "4 1's and 4 minus 1's, like so." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk21.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..9e867c07e11ef6d60fe356fac02e997856317ce7 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So 4 1's and 4 minus 1's." + }, + { + "text": "OK, and now the next column." + }, + { + "text": "2 1's, 2 minus 1's, and 0's." + }, + { + "text": "Right?" + }, + { + "text": "1, 1, minus 1, minus 1, and 0." + }, + { + "text": "And the fourth will be 0's and 2 1's and 2 minus 1's." + }, + { + "text": "We've got half a matrix now." + }, + { + "text": "Now, if we just tell me the fifth, what do you think?" + }, + { + "text": "What do I put in the fifth one?" + }, + { + "text": "So again, it's going to squeeze down and rescale." + }, + { + "text": "And what's the fifth column up here that's going to be 1's and minus 1's and 0's now?" + }, + { + "text": "So it's not Adamard." + }, + { + "text": "It's Haar." + }, + { + "text": "And what shall I put?" + }, + { + "text": "1, 1." + }, + { + "text": "Shall I start with 1, 1?" + }, + { + "text": "Oh, 1 minus?" + }, + { + "text": "Yeah." + }, + { + "text": "And then all 0's?" + }, + { + "text": "Oh, yeah, thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk22.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..9c0933bcb3a8da850c610e830d259e286619b663 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Perfect." + }, + { + "text": "1 minus 1, and then all 0's." + }, + { + "text": "And then the next three columns will have the 1 minus 1 here, and the 1 minus 1 here, and the 1 minus 1 here." + }, + { + "text": "And otherwise, all 0's." + }, + { + "text": "So you see the pattern." + }, + { + "text": "It's scaling at every step." + }, + { + "text": "So that matrix has the advantage of being quite sparse." + }, + { + "text": "This, in my mind, is a 4, 1's." + }, + { + "text": "That's involved with taking the average." + }, + { + "text": "Then this guy is like taking the differences, differences between those and those." + }, + { + "text": "And then this is like taking the difference at a smaller scale, and that also at a smaller scale." + }, + { + "text": "So that's what we keep doing." + }, + { + "text": "Yeah." + }, + { + "text": "Yeah." + }, + { + "text": "So that's wavelets." + }, + { + "text": "It looks so simple, right?" + }, + { + "text": "But just a one-minute history of wavelets, so Haar invented this in like 1910." + }, + { + "text": "I mean, along, forever." + }, + { + "text": "But then you wanted wavelets that were a little better, and not just 1's and minus 1's and 0's." + }, + { + "text": "And that took a lot of thinking." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk23.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..2c0478724ed1347c302a19560f09fa22c81860c1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "A lot of people were searching for it." + }, + { + "text": "And Ingrid Dovashy, so I'll just put her name, became famous for finding them." + }, + { + "text": "So in about 1988, she found a whole lot of families of wavelets." + }, + { + "text": "And when I say wavelets, she found a whole lot of orthogonal matrices that had good properties." + }, + { + "text": "So that's the wavelet picture." + }, + { + "text": "Now, to close today and to connect with the next lecture on eigenvalues, eigenvectors, positive definite matrices, we're really getting to the heart of things here." + }, + { + "text": "Let me follow through on that idea." + }, + { + "text": "Idea, so the eigenvectors of a symmetric matrix, but also of an orthogonal matrix are orthogonal." + }, + { + "text": "And that is really where people, where you can invent, because you don't have to work hard." + }, + { + "text": "You just find a symmetric matrix." + }, + { + "text": "Its eigenvectors are automatically orthogonal." + }, + { + "text": "That doesn't mean they're great for use, but some of them are really important." + }, + { + "text": "And maybe the most important of all is the Fourier." + }, + { + "text": "So you probably have seen Fourier series, sines and cosines." + }, + { + "text": "Those guys are orthogonal functions." + }, + { + "text": "But the discrete Fourier series is what everybody computes, and those are orthogonal vectors." + }, + { + "text": "So the orthogonal vectors that go into the discrete Fourier transform, and then they're done at high speed by the fast Fourier transform, those are eigenvectors of Q, eigenvectors of the right Q." + }, + { + "text": "So let me just tell you the right Q, whose eigenvectors." + }, + { + "text": "So here we go." + }, + { + "text": "Eigenvectors of Q." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk24.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..6444776fc980bc4a69fa3b53bb954577f9481f13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "You will just be amazed by how simple this matrix is." + }, + { + "text": "It's just that matrix." + }, + { + "text": "It's called a permutation matrix." + }, + { + "text": "Those are the four Fourier discrete." + }, + { + "text": "Let me put the word discrete up here, transform." + }, + { + "text": "So I really meant to put discrete Fourier transform." + }, + { + "text": "The eigenvectors of that matrix, first of all, they are orthogonal." + }, + { + "text": "And then second and more important, they're tremendously useful." + }, + { + "text": "They're the heart of signal processing." + }, + { + "text": "In signal processing, they just take the discrete Fourier transform of a vector before they even look at it." + }, + { + "text": "I mean, that's the way to see it, is split it into its frequencies." + }, + { + "text": "And that's what the eigenvectors of this will do." + }, + { + "text": "So we're going to see the discrete Fourier transform." + }, + { + "text": "But my point here is to know that they're orthogonal just comes out of this fact that the eigenvectors are orthogonal for any Q." + }, + { + "text": "And that is certainly a Q." + }, + { + "text": "Everybody can see that those columns are orthogonal." + }, + { + "text": "The columns of a permutation matrix, right?" + }, + { + "text": "You've taken the columns of the identity, which are totally orthogonal, and you just put them in a different order." + }, + { + "text": "So a permutation matrix is a reordering of the identity matrix." + }, + { + "text": "It's got to be a Q." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk25.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..8f7ca0deb0b14efd9582bf5072f857c1cf891aae --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And therefore, its eigenvectors are orthogonal." + }, + { + "text": "And they're just the winners." + }, + { + "text": "I mean, the matrix of the Fourier matrix with those four eigenvectors in it, I'll show you now." + }, + { + "text": "So this is really we're finishing today by leading into Wednesday, eigenvectors and eigenvalues." + }, + { + "text": "And we happen to be doing eigenvectors and eigenvalues of a Q, not today of an S. Most of the time, it's a symmetric matrix whose eigenvectors we take." + }, + { + "text": "But here, that happens to be a Q." + }, + { + "text": "Can I show you the eigenvectors, the four eigenvectors of that?" + }, + { + "text": "Now, oh, the complex number I is going to come in." + }, + { + "text": "You have to let it in here." + }, + { + "text": "Sorry." + }, + { + "text": "If S is a real symmetric matrix, its eigenvectors are real." + }, + { + "text": "But if Q is a orthogonal matrix, its eigenvectors, even though you couldn't ask for a more real matrix than that, but its eigenvectors are at least, yeah, the good way are complex numbers." + }, + { + "text": "So can I show you the eigenvectors of?" + }, + { + "text": "OK." + }, + { + "text": "So again, overall, the point today is to see orthogonal matrices." + }, + { + "text": "So I'll just repeat now while I can." + }, + { + "text": "Rotations here, reflections, wavelets, the householder idea of reflections of large matrices that have this form I minus 2 UU transpose are orthogonal." + }, + { + "text": "And now we're going to see the big guys, the eigenvectors of Q." + }, + { + "text": "Right." + }, + { + "text": "Yes?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk26.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..585374b4472c10a27d82558759b1912444ae522b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk26.json @@ -0,0 +1,62 @@ +[ + { + "text": "AUDIENCE 2." + }, + { + "text": "The wavelets, do you want to rescale the column?" + }, + { + "text": "GILBERT STRANG, M.D." + }, + { + "text": "Oh, yeah." + }, + { + "text": "We don't have orthonormal." + }, + { + "text": "That's right." + }, + { + "text": "We don't have orthonormal." + }, + { + "text": "I better divide by square root of 8." + }, + { + "text": "Right." + }, + { + "text": "AUDIENCE 3." + }, + { + "text": "There's different forms for different." + }, + { + "text": "GILBERT STRANG, M.D." + }, + { + "text": "Oh, yes." + }, + { + "text": "Oh, you're right." + }, + { + "text": "Sorry, I thought I'd get away with that, but I didn't." + }, + { + "text": "Yeah." + }, + { + "text": "So these guys are square roots of 8." + }, + { + "text": "So are these." + }, + { + "text": "But these guys are square roots of 4." + }, + { + "text": "And these guys are square roots of 2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk27.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk27.json new file mode 100644 index 0000000000000000000000000000000000000000..fe044f5efd14e48e1d27d0585f9bebef51beb0e8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk27.json @@ -0,0 +1,62 @@ +[ + { + "text": "Thank you." + }, + { + "text": "Absolutely right." + }, + { + "text": "Absolutely." + }, + { + "text": "Yeah." + }, + { + "text": "OK." + }, + { + "text": "So what are the eigenvectors of a permutation?" + }, + { + "text": "This is going to be nice to see." + }, + { + "text": "And I'll use the matrix F for the eigenvector matrix of that Q up there." + }, + { + "text": "And F is for Fourier." + }, + { + "text": "And it'd be the 4 by 4 Fourier matrix." + }, + { + "text": "OK. What are the eigenvectors of Q?" + }, + { + "text": "OK." + }, + { + "text": "So Q is a permutation." + }, + { + "text": "So I'm going to ask you for one eigenvector of every permutation matrix." + }, + { + "text": "What vector can you tell me that actually the eigenvalue will be 1?" + }, + { + "text": "What vector can you tell me where if I permute it, I don't change it?" + }, + { + "text": "1, 1, 1, 1." + }, + { + "text": "It's like it's everywhere here." + }, + { + "text": "1, 1, 1, 1." + }, + { + "text": "So that's the zero frequency Fourier vector, the constant vector, all 1's." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk28.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk28.json new file mode 100644 index 0000000000000000000000000000000000000000..fd0082d001d298314187d0489c0c1333ec2c11ed --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk28.json @@ -0,0 +1,62 @@ +[ + { + "text": "Everybody sees that if I multiply by Q, it doesn't change." + }, + { + "text": "OK. Now the next one, I'll show you the 4 now." + }, + { + "text": "The next one will be 1, i, i squared, and i cubed." + }, + { + "text": "Of course, i squared, I don't know how many course 6j people are in this audience." + }, + { + "text": "But this is a math building, we paid for it." + }, + { + "text": "It's 2, 190, and it's i in this room." + }, + { + "text": "Yeah." + }, + { + "text": "So yeah." + }, + { + "text": "Anyway, i is the first letter in what?" + }, + { + "text": "Imaginary, thank you." + }, + { + "text": "The first letter in imaginary." + }, + { + "text": "You can't say jimaginary." + }, + { + "text": "So that's it." + }, + { + "text": "OK. And then the next one is 1, i squared, i fourth, i sixth." + }, + { + "text": "And the next one is 1, i cubed, i sixth, and i ninth." + }, + { + "text": "Isn't that just beautiful?" + }, + { + "text": "And you could show that every one of those four columns, if you multiply them by Q, you would get the eigenvalues." + }, + { + "text": "And you would see that it's an eigenvector." + }, + { + "text": "And this is just sort of like a discrete Fourier stuff." + }, + { + "text": "And instead of e to the ix, e to the 2ix, e to the 3ix, and so on, we just have vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk29.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk29.json new file mode 100644 index 0000000000000000000000000000000000000000..69ca2b5a6c93f1ff5ff4b1010014d5bbfe4a81fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk29.json @@ -0,0 +1,62 @@ +[ + { + "text": "So those are the four eigenvectors of that permutation." + }, + { + "text": "And those are orthogonal." + }, + { + "text": "Could I just check that?" + }, + { + "text": "How do you know that this first column and the second?" + }, + { + "text": "Well, I should really say zeroth column and first column if I'm talking frequencies." + }, + { + "text": "Do you see that that's orthogonal to that?" + }, + { + "text": "Well, y is 1 plus i plus i squared plus i cubed equals 0." + }, + { + "text": "That's the dot product." + }, + { + "text": "This is column 1 dot column 2." + }, + { + "text": "Yeah." + }, + { + "text": "You're right." + }, + { + "text": "This happens to come out 0." + }, + { + "text": "Is that right?" + }, + { + "text": "Yes, that will come out 0." + }, + { + "text": "That'll come out 0." + }, + { + "text": "But somebody mentioned that this isn't right." + }, + { + "text": "It's true that that came out 0." + }, + { + "text": "But when I have imaginary numbers anywhere around, this isn't the correct dot product to test orthogonal." + }, + { + "text": "If I have complex vectors, if I have complex numbers, complex vectors, I should test column 1 conjugate dotted with column 2." + }, + { + "text": "Column i conjugate." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk3.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..f863ecb71103dd4c79faee118ac276d69bf4817f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the inverse of Q will be the transpose." + }, + { + "text": "The transpose would put the minus sign down here and would produce the inverse matrix." + }, + { + "text": "And what does that particular matrix represent?" + }, + { + "text": "Geometrically, where do we see that matrix?" + }, + { + "text": "It's a rotation." + }, + { + "text": "Thank you." + }, + { + "text": "It's a rotation of the whole plane by theta." + }, + { + "text": "Yeah." + }, + { + "text": "So if I apply that to 1, 0, for example, I get the first column, which is cos theta, sine theta." + }, + { + "text": "And that's just a row." + }, + { + "text": "Let me draw a picture." + }, + { + "text": "That vector 1, 0 has got rotated up to." + }, + { + "text": "So there is the 1, 0." + }, + { + "text": "And there it got rotated through an angle theta." + }, + { + "text": "And similarly, 0, 1 will get rotated through an angle theta to there." + }, + { + "text": "So the whole plane rotates." + }, + { + "text": "Oh, that makes me remember a highly important, very important property of Q." + }, + { + "text": "It doesn't change length." + }, + { + "text": "The length of any vector is the same after you rotate it." + }, + { + "text": "The length of any vector is the same after you multiply by Q." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk30.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk30.json new file mode 100644 index 0000000000000000000000000000000000000000..64bd5e5b732f6ef86ff8d651a31c18dc5d6a7b26 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk30.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, let me take column." + }, + { + "text": "Let's see." + }, + { + "text": "Which one shall I take?" + }, + { + "text": "Maybe that guy and that guy." + }, + { + "text": "Many of them you luck out here." + }, + { + "text": "But really, I should be taking the conjugate." + }, + { + "text": "So these 1's." + }, + { + "text": "But the thing is the complex conjugate of 1 is 1." + }, + { + "text": "So that was OK." + }, + { + "text": "But in general, if I wanted to take column 2 dotted with column, I don't know, maybe 4 would be a little dodgy." + }, + { + "text": "Yeah, look what happens." + }, + { + "text": "Take that column and that column." + }, + { + "text": "Take their dot product." + }, + { + "text": "Do it the wrong way." + }, + { + "text": "So what's the wrong way?" + }, + { + "text": "Forget about the complex conjugate and just do it the usual way." + }, + { + "text": "So 1 times 1 is 1. i times i cube is?" + }, + { + "text": "1. i squared times i6 is?" + }, + { + "text": "1." + }, + { + "text": "I'm getting all 1's." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk31.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk31.json new file mode 100644 index 0000000000000000000000000000000000000000..96f23de58f04372c803c798f245920b0c738af9b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk31.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'm not getting orthogonality there." + }, + { + "text": "And that's because I forgot that I should take the complex conjugate." + }, + { + "text": "Well, of these guys, 1." + }, + { + "text": "I should take minus i." + }, + { + "text": "Minus i squared." + }, + { + "text": "Well, that's real, so it's OK." + }, + { + "text": "Minus there." + }, + { + "text": "So minus i squared is still minus 1." + }, + { + "text": "So now if I do it, it comes out 0." + }, + { + "text": "So let me repeat again." + }, + { + "text": "Let me just make this statement." + }, + { + "text": "If Q transpose Q is i, and Qx is lambda x, and Qy is a different eigenvalue y. OK." + }, + { + "text": "So I'm setting up the main fact that in the last minute, I'm just going to write down." + }, + { + "text": "So I have an orthogonal matrix." + }, + { + "text": "I have an eigenvector with eigenvalue lambda." + }, + { + "text": "I have another eigenvector with a different eigenvalue mu." + }, + { + "text": "Then the claim is that, what is the claim about the eigenvectors?" + }, + { + "text": "So here has one eigen." + }, + { + "text": "This has an eigenvalue." + }, + { + "text": "This has a different eigenvalue." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk32.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk32.json new file mode 100644 index 0000000000000000000000000000000000000000..7b846a742a5f1c49f8285cefa23421fb49501ed2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk32.json @@ -0,0 +1,41 @@ +[ + { + "text": "I need them to be different to really know that the x's and the y's can't be the same." + }, + { + "text": "So what is it that I want to show?" + }, + { + "text": "AUDIENCE 1." + }, + { + "text": "Conjugated x of y minus 1." + }, + { + "text": "Yes." + }, + { + "text": "That x, and I have to remember to do that, x transpose y is 0." + }, + { + "text": "That's orthogonality." + }, + { + "text": "That's orthogonality for complex vectors." + }, + { + "text": "I have to remember to change every i to a minus i in one of the vectors." + }, + { + "text": "And I can prove that fact by playing with these, by playing with starting from here, I can get to that." + }, + { + "text": "OK, that's it." + }, + { + "text": "We've done a lot today, a lot of stuff about orthogonal matrices, important ones and the sources of important ones, eigenvectors." + }, + { + "text": "And so it'll be eigenvectors on Wednesday." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk4.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..2c68625c6da30919ac3c7cd9aa2d38115f88b017 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Can I just do that?" + }, + { + "text": "I claim any x, any vector x, I want to look at the length of Qx." + }, + { + "text": "And I claim that it has the same length as x." + }, + { + "text": "Actually, that's the reason in computations that orthogonal matrix are so much loved, because no overflow can happen with orthogonal matrices." + }, + { + "text": "Lengths don't change." + }, + { + "text": "I can multiply by any number of orthogonal matrices, and the lengths don't change." + }, + { + "text": "Can we just see why that's true?" + }, + { + "text": "How would you show?" + }, + { + "text": "So what do we have to go on?" + }, + { + "text": "What we have to go on is Q transpose Q equal I." + }, + { + "text": "Whatever we're going to prove, it's got to come out of that, because that's all we know." + }, + { + "text": "So how do I use that to get that one?" + }, + { + "text": "Well, we haven't said a whole lot about lengths, but you'll see it all now." + }, + { + "text": "It'll be easier to prove that the squares are the same." + }, + { + "text": "So what's the matrix expression for the length squared?" + }, + { + "text": "What's the right-hand side of that equation?" + }, + { + "text": "X transpose x, right?" + }, + { + "text": "X transpose x gives me the sum of the squares." + }, + { + "text": "Pythagoras says that's the length squared." + }, + { + "text": "So that right-hand side is x transpose x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk5.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..fe88faea55ca7fdbade0e4cf0f0a9f66df2465b8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "What's the left side?" + }, + { + "text": "It's the length squared of this, of Qx." + }, + { + "text": "So it must be the same as Qx, transpose Qx." + }, + { + "text": "And the claim is that that equation holds." + }, + { + "text": "And do you see it?" + }, + { + "text": "Where is it?" + }, + { + "text": "So any property from Q has to just come out directly from that." + }, + { + "text": "Where is it here?" + }, + { + "text": "Do I just push away a little bit at that left-hand side and see it?" + }, + { + "text": "Qx transpose is the same as x transpose Q transpose." + }, + { + "text": "And Qx is Qx." + }, + { + "text": "And now I'm seeing, well, you might say, wait a minute." + }, + { + "text": "The parentheses were there and there." + }, + { + "text": "But I say the most important law for matrix multiplication is you can move parentheses or throw them away." + }, + { + "text": "Let's throw them away." + }, + { + "text": "So in here, I'm seeing Q transpose Q, which is the identity." + }, + { + "text": "So it's true." + }, + { + "text": "So that means that you never underflow or overflow when you're multiplying by Q." + }, + { + "text": "Every numerical algorithm is written to use orthogonal matrices wherever it can." + }, + { + "text": "And here's the first example." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk6.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..962dbdc98b0f27e37ce73e12c9ffbe343c8dddd5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I think it may be good for me to think of other examples or for us to think of other examples of orthogonal matrices." + }, + { + "text": "So I'm using that word orthogonal matrix." + }, + { + "text": "We should really be saying orthonormal." + }, + { + "text": "And I'm really thinking mostly of square ones." + }, + { + "text": "So in the square case, when Q transpose is Q inverse." + }, + { + "text": "Of course, that fact makes it easy to solve all equations that have Q as a coefficient matrix, because you want the inverse and you just use the transpose." + }, + { + "text": "OK, let's just take some minutes to think of examples of Qs, if they're so important there have to be interesting examples." + }, + { + "text": "And that was a first one." + }, + { + "text": "Now, there's one more 2 by 2 example that you should know." + }, + { + "text": "Do you know what that would be?" + }, + { + "text": "So this will be example 2." + }, + { + "text": "And it's also going to be only 2 by 2 and real." + }, + { + "text": "And what possibility have I got left here?" + }, + { + "text": "I'll use the same first column, cos theta, sine theta, because that's more or less any unit vector in two dimensions." + }, + { + "text": "This has got that form." + }, + { + "text": "So what do you propose for the second column?" + }, + { + "text": "Yes?" + }, + { + "text": "Yeah, put the minus sign down here." + }, + { + "text": "So you think, does that make any difference?" + }, + { + "text": "So sine theta and minus cos theta." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk7.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..518d307339e6889aea8a3bded1efa411a6f5745a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "I don't know if you've ever looked at that matrix." + }, + { + "text": "We're trying to collect together a few matrices that are worth knowing, are worth looking at." + }, + { + "text": "OK, now what's happened here?" + }, + { + "text": "You may say that was a trivial change, which it kind of was." + }, + { + "text": "But it's a different matrix now." + }, + { + "text": "It's not a rotation anymore." + }, + { + "text": "That's not a rotation." + }, + { + "text": "And yeah, somehow, now it's symmetric." + }, + { + "text": "And yeah, its eigenvectors must be something or other." + }, + { + "text": "We'll get to those." + }, + { + "text": "But what does that matrix do?" + }, + { + "text": "I don't know if you've seen it." + }, + { + "text": "If you haven't, it doesn't jump out." + }, + { + "text": "But it's an important case." + }, + { + "text": "This is a reflection matrix." + }, + { + "text": "Notice that it's determined it is minus 1." + }, + { + "text": "You have minus cos squared theta minus sine squared theta." + }, + { + "text": "It's determined it is minus 1." + }, + { + "text": "There's some eigenvalue coming up that's got a minus." + }, + { + "text": "Yeah." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk8.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..481458df8b0fa0d4060f8a9ff2fad9395e817b04 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, so what do I mean by a reflection matrix?" + }, + { + "text": "Let me draw the plane." + }, + { + "text": "And I think, so 1, 0." + }, + { + "text": "Let's follow it again." + }, + { + "text": "1, 0, where does that go?" + }, + { + "text": "That gives me the first column." + }, + { + "text": "So as before, it goes to cos theta sine theta." + }, + { + "text": "And when I say reflection, let me put the mirror into the picture." + }, + { + "text": "So you see what reflection it is." + }, + { + "text": "The mirror is along here at angle theta over 2, theta over 2 line." + }, + { + "text": "So sure enough, 1, 0 at angle 0 got reflected into a unit vector at angle theta." + }, + { + "text": "And halfway between was the theta over 2 line." + }, + { + "text": "That's OK. Now, what about the other guy, 0, 1?" + }, + { + "text": "Here's 0, 1." + }, + { + "text": "OK, I multiply that." + }, + { + "text": "Can I put the 0, 1 up here so your eye does the multiplication?" + }, + { + "text": "Where is the result of 0, 1?" + }, + { + "text": "What's the output from Q applied to 0, 1?" + }, + { + "text": "Sine theta minus cos theta, right?" + }, + { + "text": "It's the second column." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk9.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..27a460130a0a8d38fe662c57a511c467a303fbb9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_1_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so where is that?" + }, + { + "text": "Well, it's perpendicular to that guy." + }, + { + "text": "That's what I know, right?" + }, + { + "text": "That was the point, that the two columns are perpendicular." + }, + { + "text": "So it must go down this way, right?" + }, + { + "text": "Sine theta, cos theta." + }, + { + "text": "And it doesn't change length." + }, + { + "text": "All these facts that we just learned are key." + }, + { + "text": "So there's 0, 1, and it goes to this guy, which is whatever that second column is, sine theta minus cos theta." + }, + { + "text": "And if you check that, actually, gosh, this is like plain geometry." + }, + { + "text": "I believe, it's never occurred to me before, but I believe it, that this angle going down to there, that that goes straight through, and that the halfway one is that line." + }, + { + "text": "Yeah, I think that picture has got it, and I think it's in the notes." + }, + { + "text": "So that's a reflection matrix." + }, + { + "text": "Well, that's a 2 by 2 reflection matrix." + }, + { + "text": "Would you like to see some other matrices like this one, but larger?" + }, + { + "text": "They're named after a guy named Householder." + }, + { + "text": "So these are Householder reflections." + }, + { + "text": "What am I doing here?" + }, + { + "text": "I'm collecting together some orthogonal matrices that are useful and important." + }, + { + "text": "And Householder found a whole bunch of them, and his algorithm is a much used part of numerical linear algebra." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk0.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..b5d2005486c62ceb6bba16af0971eda159bf4d11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So we're really moving along this review of the highlights of linear algebra." + }, + { + "text": "And today it's matrices Q." + }, + { + "text": "They get that name." + }, + { + "text": "They have orthonormal columns." + }, + { + "text": "So that's what one looks like." + }, + { + "text": "And then the key fact, orthonormal columns translates directly into that simple fact that you just keep remembering." + }, + { + "text": "Every time you see Q transpose Q, you've got the identity matrix." + }, + { + "text": "Let's just see why." + }, + { + "text": "So Q transpose would be, I'll take those columns and make them into rows." + }, + { + "text": "And then I multiply by Q with the columns." + }, + { + "text": "And what do I get?" + }, + { + "text": "Well, hopefully I get the identity matrix." + }, + { + "text": "OK, why?" + }, + { + "text": "Because, oh, yeah, the normal part tells me that the length of each vector, that's the length squared Q transpose Q." + }, + { + "text": "The length squared is 1." + }, + { + "text": "So that gives me the 1 in the identity matrix all along the diagonal." + }, + { + "text": "And then Q transpose times a different Q is 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk1.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..4e5a53f7561a10c59c686c38ce76be1836e60948 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the ortho part." + }, + { + "text": "So that gives me the 0s." + }, + { + "text": "So that's a simple identity." + }, + { + "text": "But it translates from a lot of words into a simple expression." + }, + { + "text": "Now, does that mean that in the other order, Q Q transpose, is that the identity?" + }, + { + "text": "So that's a question to think about." + }, + { + "text": "Is Q Q transpose equal the identity?" + }, + { + "text": "Question." + }, + { + "text": "Sometimes yes, sometimes no." + }, + { + "text": "Easy to tell which." + }, + { + "text": "The answer is yes." + }, + { + "text": "Yes, when Q is square." + }, + { + "text": "The answer is yes." + }, + { + "text": "If Q is a square matrix, a square matrix, this is saying that the square matrix Q has that inverse on its left." + }, + { + "text": "But for square matrices, a left inverse, Q transpose, is also a right inverse." + }, + { + "text": "And for a square matrix, if you have an inverse that works on one side, it will work on the other side." + }, + { + "text": "So the answer is yes in that case." + }, + { + "text": "And then in that case, that's the case when we call Q is, well, we really, I don't know what the right name would be." + }, + { + "text": "But here's the name everybody uses, an orthogonal matrix." + }, + { + "text": "And that's only in the square case, square." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk10.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..49656af3fb9dd19d28412adf515bdcbf6d01baf1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So he started with a unit vector." + }, + { + "text": "Start with a unit vector, u transpose u equal 1." + }, + { + "text": "So the length of the vector is 1." + }, + { + "text": "And then he created, let's name it after him, H. He created this matrix, the identity minus 2 uu transpose." + }, + { + "text": "And I believe that that's a really useful matrix." + }, + { + "text": "So it's just like, I think this review is like going beyond 18.06 into what ones are really worth knowing individually." + }, + { + "text": "Could we just check what are the properties of Householder's reflection of that I minus 2?" + }, + { + "text": "You recognize here a column times a row." + }, + { + "text": "So that's a matrix." + }, + { + "text": "And what could you tell me about that matrix uu transpose?" + }, + { + "text": "It's, yeah." + }, + { + "text": "Or what can we say about H?" + }, + { + "text": "So I guess I'm believing that H is a orthogonal matrix." + }, + { + "text": "Otherwise, it wouldn't be here today." + }, + { + "text": "So I believe that." + }, + { + "text": "And not only is it orthogonal, it is also, have a look at it, symmetric." + }, + { + "text": "It's also symmetric." + }, + { + "text": "The identity is symmetric." + }, + { + "text": "Uu transpose is symmetric." + }, + { + "text": "So this is a family of symmetric orthogonal matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk11.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d1bc347004ae5794bd541685a2530709739f8fb8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "And that was one of them." + }, + { + "text": "That's a symmetric orthogonal matrix." + }, + { + "text": "These matrices are really great to have." + }, + { + "text": "You just, like in using linear algebra, you just get a collection of useful matrices that you can call on." + }, + { + "text": "And these are definitely one family." + }, + { + "text": "Well, it's obviously symmetric." + }, + { + "text": "Shall we check that it's orthogonal?" + }, + { + "text": "So to check that it's orthogonal, I just, so I'm going to check that H transpose H is the identity." + }, + { + "text": "Can I just check that?" + }, + { + "text": "Well, H transpose is the same as H, because it was symmetric." + }, + { + "text": "So I'm going to square this guy." + }, + { + "text": "This is really H times H. I'm squaring it." + }, + { + "text": "And what do I get if I square?" + }, + { + "text": "So I get, I hope I get the identity, but let's see it." + }, + { + "text": "What do I get when I square this?" + }, + { + "text": "Get little, multiply it out." + }, + { + "text": "So I times I is I." + }, + { + "text": "And then I get some number of Uu transposes." + }, + { + "text": "How many do I get from that?" + }, + { + "text": "So I'm squaring this thing, because H transpose H is the same as H times H. So I'm squaring it." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk12.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..25d7b51e680f692a50bab3dc6644564db6a54780 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how many, what do I put here?" + }, + { + "text": "Four, thanks." + }, + { + "text": "And now I've got this guy squared with a plus." + }, + { + "text": "So that's four Uu transpose Uu transpose." + }, + { + "text": "Yeah, I'm totally realizing I've practiced for a lifetime doing these dinky little calculations." + }, + { + "text": "But they are dinky." + }, + { + "text": "And you'll get the hang of it quickly." + }, + { + "text": "Now, what am I hoping out of that bottom line?" + }, + { + "text": "That it is?" + }, + { + "text": "I." + }, + { + "text": "We're hoping to get I." + }, + { + "text": "Do we get I?" + }, + { + "text": "Yes." + }, + { + "text": "Who sees how to get I out of that thing?" + }, + { + "text": "Yeah." + }, + { + "text": "U transpose U in here is a number." + }, + { + "text": "That was U." + }, + { + "text": "That was column times row times column times row." + }, + { + "text": "And I look at the in the middle here is row times column." + }, + { + "text": "And that's the number 1, right?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk13.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2970896b1136ec13f25ac3b1d568b82c5bfd6397 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because it's there." + }, + { + "text": "So that's 1." + }, + { + "text": "And then I have minus 4 of that, plus 4 of that." + }, + { + "text": "They cancel each other." + }, + { + "text": "And I get I." + }, + { + "text": "So those are good matrices." + }, + { + "text": "We'll use them." + }, + { + "text": "We'll use them." + }, + { + "text": "Actually, they're better than Graham-Schmidt." + }, + { + "text": "So we'll use them in making things orthogonal." + }, + { + "text": "So what other orthogonal matrices?" + }, + { + "text": "Let's create some." + }, + { + "text": "Creating good orthogonal matrices, it pays off." + }, + { + "text": "Let's think." + }, + { + "text": "So there's a family named after this French guy who lived to 100." + }, + { + "text": "He was a real old timer." + }, + { + "text": "Well, MIT had a faculty member in math when I came, Professor Struik, who lived to 106." + }, + { + "text": "And I heard him give a lecture at Brown University at age 100." + }, + { + "text": "And it was like perfect." + }, + { + "text": "You could not have done it better." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk14.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7a4761773e251928346e720869f90c17e750fc9c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So he's my inspiration." + }, + { + "text": "I keep going." + }, + { + "text": "I only have like n more years to get there." + }, + { + "text": "And n is, well, it's too many anyway." + }, + { + "text": "OK, Adamard." + }, + { + "text": "All right, Adamard." + }, + { + "text": "So Adamard, he created, well, that's the simplest, the smallest." + }, + { + "text": "Now, the next guy is going to be 4 by 4." + }, + { + "text": "I'm going to put that." + }, + { + "text": "So where I see a 1, I'm going to put Adamard in." + }, + { + "text": "1, 1, 1 minus 1, 1, 1, 1 minus 1." + }, + { + "text": "And then when I see a minus, I'm going to put it in with a minus." + }, + { + "text": "You saw that picture?" + }, + { + "text": "It was a picture of H2, H2, H2, and minus H2." + }, + { + "text": "That's what I've got there." + }, + { + "text": "And I believe those columns are orthogonal." + }, + { + "text": "Now, what could I do?" + }, + { + "text": "Well, it's not quite an orthogonal matrix." + }, + { + "text": "What do I have to do to make it?" + }, + { + "text": "This isn't quite an orthogonal matrix either." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk15.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7c56d46fe9a00c08ec502262a9278c03ce6817ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "What do I do to make that an orthogonal matrix?" + }, + { + "text": "Divide by square root of 2." + }, + { + "text": "I need unit vectors there." + }, + { + "text": "And here, those lengths are 1 squared, 1 squared, 4." + }, + { + "text": "Square root of 4 is 2." + }, + { + "text": "So I better divide by the 2 there." + }, + { + "text": "And now here, I'm up to, yeah, so that was that one." + }, + { + "text": "Tell me the next one up." + }, + { + "text": "What's that going to be?" + }, + { + "text": "8 by 8?" + }, + { + "text": "So this is H4 here." + }, + { + "text": "Oops, 4." + }, + { + "text": "So tell me what I should do for 8 by 8." + }, + { + "text": "You'll think this is simple." + }, + { + "text": "But that's a good thing to say about it." + }, + { + "text": "In coding theory, all sorts of places, you want matrices of 1's and minus 1's." + }, + { + "text": "OK, what's H8?" + }, + { + "text": "I'm going to build it out of H4." + }, + { + "text": "So what's it going to be?" + }, + { + "text": "I'm going to put an H4 there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk16.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..918141f4e0ba694885e6f1ccbc52ab39b4979f98 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "What am I going to put here?" + }, + { + "text": "Another H4." + }, + { + "text": "And up here, another H4." + }, + { + "text": "And finally here, minus H4." + }, + { + "text": "Minus H4, and I think I've got orthogonal columns again." + }, + { + "text": "Because the columns within these, dot products with themselves, give 0 and 0." + }, + { + "text": "The dot products from these columns and these columns obviously have the minus." + }, + { + "text": "And the dot products in here are 0 from that and 0 from that." + }, + { + "text": "Yeah, it works." + }, + { + "text": "And we could keep going to 16 and 32 and 64." + }, + { + "text": "But then up comes a question." + }, + { + "text": "What about H12?" + }, + { + "text": "Is there a 1's and minus 1's matrix of size 12, 12 by 12?" + }, + { + "text": "It doesn't come directly from our little pattern, which is doubling size every time." + }, + { + "text": "But you could still hope." + }, + { + "text": "And it works." + }, + { + "text": "I don't know what it is, but there's a matrix of 1's and minus 1's, 12 orthogonal columns." + }, + { + "text": "So the answer is yes." + }, + { + "text": "OK, so we make an 18.065 conjecture." + }, + { + "text": "Every matrix size, well, not every matrix size, because 3 by 3 is not going to work." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk17.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..424ebae85640980fc86eba92079646d513aa4ab7 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "1 by 1 is not going to work either." + }, + { + "text": "But H12 works, H8, H16." + }, + { + "text": "What's our conjecture?" + }, + { + "text": "We won't be the first to conjecture it." + }, + { + "text": "There is a 1's and minus 1's orthogonal matrix with orthogonal columns of every size n. So always, so I'll start the conjecture." + }, + { + "text": "Always possible if n, which is the size of the matrix, let's say, what would you guess?" + }, + { + "text": "Just take a shot." + }, + { + "text": "You won't be asked for a proof, because nobody has the proof." + }, + { + "text": "Even?" + }, + { + "text": "Well, you could hope for even." + }, + { + "text": "You could look for try 6, I guess, would be the first guy there." + }, + { + "text": "And I don't think it's possible." + }, + { + "text": "I think 6 is not possible." + }, + { + "text": "So every even size is, I think, not going to work." + }, + { + "text": "But it's a natural idea to try." + }, + { + "text": "What's the next thought?" + }, + { + "text": "Every multiple of 4." + }, + { + "text": "If n over 4 is a whole number." + }, + { + "text": "But nobody has a systematic way to create these things." + }, + { + "text": "So like some of them, at this point, we're down to doing it one at a time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk18.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..8b98656b2afa8ad2c2bc10e43f6253f0336687c6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we're up to 668." + }, + { + "text": "But we haven't got that one yet." + }, + { + "text": "Isn't that crazy?" + }, + { + "text": "So all this is coming from Wikipedia, my source of all that's good in mathematics is there on Wikipedia." + }, + { + "text": "Anyway, this is the conjecture." + }, + { + "text": "Conjecture means you don't have any damn idea of whether it's true or not." + }, + { + "text": "Is that divisible by 4?" + }, + { + "text": "Yeah, I guess it would be." + }, + { + "text": "600 certainly is, and 68 certainly is." + }, + { + "text": "So I think that's the first one." + }, + { + "text": "So anybody, if you find one of size 668, just skip the homework and tell us about that one." + }, + { + "text": "But I don't think I'll assign that." + }, + { + "text": "I guess, well, I must have searched for it online." + }, + { + "text": "But yeah, anyway, so those are the Adamard matrices." + }, + { + "text": "Now, where else do I remember orthogonal matrices coming from?" + }, + { + "text": "Well, yeah, really, the biggest source of." + }, + { + "text": "So when I'm looking for orthogonal matrices, I'm looking for a basis of orthogonal vectors." + }, + { + "text": "And where in math am I going to find vectors that come out to be orthogonal?" + }, + { + "text": "We haven't seen that." + }, + { + "text": "It's the next section of the notes, but maybe you're remembering." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk19.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1a1bbc69e93bf8e690780d413ac7692520b39c41 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Where will we sort of like automatically show up with orthogonal vectors?" + }, + { + "text": "They could be the eigenvectors of a symmetric matrix." + }, + { + "text": "And that's where the most important ones come from." + }, + { + "text": "Oh, I could tell you about wavelets, though." + }, + { + "text": "Wavelets are more like this picture." + }, + { + "text": "They're 1's and minus 1's." + }, + { + "text": "Or the simplest wavelets are 1's and minus 1's." + }, + { + "text": "Before I go on to the eigenvector business, can I mention the wavelets matrices?" + }, + { + "text": "Yeah, these are really important, simple and important constructions." + }, + { + "text": "So wavelets, let me draw a picture." + }, + { + "text": "So I'm going to come up with four." + }, + { + "text": "I'll do the 4 by 4 case." + }, + { + "text": "And these are the orthogonal guys." + }, + { + "text": "And then the next one is up and down and 0." + }, + { + "text": "And the last one is 0 and up and down." + }, + { + "text": "So that's four things, but let me show you the matrix." + }, + { + "text": "So I'll call it W for wavelets." + }, + { + "text": "So that guy I'm thinking of as 1, 1, 1, 1." + }, + { + "text": "This guy I'm thinking of as 1, 1, minus 1, minus 1." + }, + { + "text": "It's looking sort of Adhemard way, but there's a difference here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk2.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..fa6e9f79b321740f7bd2a0adca7cc97249c3a10c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Q is an orthogonal matrix." + }, + { + "text": "Right, right." + }, + { + "text": "Do you want to just see an example of how that works?" + }, + { + "text": "And it will not." + }, + { + "text": "So if Q is rectangular, let me do a rectangular Q and a square Q." + }, + { + "text": "So I think there must be a board up there somewhere." + }, + { + "text": "Here." + }, + { + "text": "OK, square." + }, + { + "text": "All right, good to see some orthogonal matrices, because my message is that they're really important in all kinds of applications." + }, + { + "text": "Let's start two by two." + }, + { + "text": "I can think of two different ways to get an orthogonal matrix that's a two by two matrix." + }, + { + "text": "And one of them you will know immediately, cos theta, sine theta." + }, + { + "text": "So that's a unit vector." + }, + { + "text": "It's normalized." + }, + { + "text": "Cos squared plus sine squared is 1." + }, + { + "text": "And this guy has to be orthogonal to it." + }, + { + "text": "So I'll make that minus sine theta and cos theta." + }, + { + "text": "OK. Those are both length 1." + }, + { + "text": "They're orthogonal." + }, + { + "text": "Then this is my Q." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk20.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..3e8bb5de8bf16bf7ce3501ccefb5a330450b8ade --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "This guy is 1, minus 1, 0, 0." + }, + { + "text": "So the wavelets rescale." + }, + { + "text": "That's the difference between Adhemard and wavelets." + }, + { + "text": "Wavelets are self-scaling." + }, + { + "text": "And what's the last guy here?" + }, + { + "text": "What's the fourth column from that fourth wavelet?" + }, + { + "text": "0, 0, 1, minus 1." + }, + { + "text": "So Haar came up with that." + }, + { + "text": "This is the Haar wavelet, which was many years before the word wavelets was invented." + }, + { + "text": "He came up with this construction, the Haar matrix, the Haar functions." + }, + { + "text": "So they're very simple functions, but that makes them usable, the fact that they're so simple." + }, + { + "text": "Now, I don't know if you want to see the pattern in 8 by 8, but let me start the 8 by 8 so you'll know what wavelets are about." + }, + { + "text": "You'll know what these Haar wavelets are about anyway." + }, + { + "text": "They're the ones that were kind of easy to visualize." + }, + { + "text": "So if that's W4, let's just take a minute." + }, + { + "text": "It won't take long for W8." + }, + { + "text": "OK." + }, + { + "text": "So the first column is going to be 8 1's." + }, + { + "text": "And what's the next column going to be?" + }, + { + "text": "4 1's and 4 minus 1's, like so." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk21.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..9e867c07e11ef6d60fe356fac02e997856317ce7 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So 4 1's and 4 minus 1's." + }, + { + "text": "OK, and now the next column." + }, + { + "text": "2 1's, 2 minus 1's, and 0's." + }, + { + "text": "Right?" + }, + { + "text": "1, 1, minus 1, minus 1, and 0." + }, + { + "text": "And the fourth will be 0's and 2 1's and 2 minus 1's." + }, + { + "text": "We've got half a matrix now." + }, + { + "text": "Now, if we just tell me the fifth, what do you think?" + }, + { + "text": "What do I put in the fifth one?" + }, + { + "text": "So again, it's going to squeeze down and rescale." + }, + { + "text": "And what's the fifth column up here that's going to be 1's and minus 1's and 0's now?" + }, + { + "text": "So it's not Adamard." + }, + { + "text": "It's Haar." + }, + { + "text": "And what shall I put?" + }, + { + "text": "1, 1." + }, + { + "text": "Shall I start with 1, 1?" + }, + { + "text": "Oh, 1 minus?" + }, + { + "text": "Yeah." + }, + { + "text": "And then all 0's?" + }, + { + "text": "Oh, yeah, thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk22.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..9c0933bcb3a8da850c610e830d259e286619b663 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Perfect." + }, + { + "text": "1 minus 1, and then all 0's." + }, + { + "text": "And then the next three columns will have the 1 minus 1 here, and the 1 minus 1 here, and the 1 minus 1 here." + }, + { + "text": "And otherwise, all 0's." + }, + { + "text": "So you see the pattern." + }, + { + "text": "It's scaling at every step." + }, + { + "text": "So that matrix has the advantage of being quite sparse." + }, + { + "text": "This, in my mind, is a 4, 1's." + }, + { + "text": "That's involved with taking the average." + }, + { + "text": "Then this guy is like taking the differences, differences between those and those." + }, + { + "text": "And then this is like taking the difference at a smaller scale, and that also at a smaller scale." + }, + { + "text": "So that's what we keep doing." + }, + { + "text": "Yeah." + }, + { + "text": "Yeah." + }, + { + "text": "So that's wavelets." + }, + { + "text": "It looks so simple, right?" + }, + { + "text": "But just a one-minute history of wavelets, so Haar invented this in like 1910." + }, + { + "text": "I mean, along, forever." + }, + { + "text": "But then you wanted wavelets that were a little better, and not just 1's and minus 1's and 0's." + }, + { + "text": "And that took a lot of thinking." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk23.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..2c0478724ed1347c302a19560f09fa22c81860c1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "A lot of people were searching for it." + }, + { + "text": "And Ingrid Dovashy, so I'll just put her name, became famous for finding them." + }, + { + "text": "So in about 1988, she found a whole lot of families of wavelets." + }, + { + "text": "And when I say wavelets, she found a whole lot of orthogonal matrices that had good properties." + }, + { + "text": "So that's the wavelet picture." + }, + { + "text": "Now, to close today and to connect with the next lecture on eigenvalues, eigenvectors, positive definite matrices, we're really getting to the heart of things here." + }, + { + "text": "Let me follow through on that idea." + }, + { + "text": "Idea, so the eigenvectors of a symmetric matrix, but also of an orthogonal matrix are orthogonal." + }, + { + "text": "And that is really where people, where you can invent, because you don't have to work hard." + }, + { + "text": "You just find a symmetric matrix." + }, + { + "text": "Its eigenvectors are automatically orthogonal." + }, + { + "text": "That doesn't mean they're great for use, but some of them are really important." + }, + { + "text": "And maybe the most important of all is the Fourier." + }, + { + "text": "So you probably have seen Fourier series, sines and cosines." + }, + { + "text": "Those guys are orthogonal functions." + }, + { + "text": "But the discrete Fourier series is what everybody computes, and those are orthogonal vectors." + }, + { + "text": "So the orthogonal vectors that go into the discrete Fourier transform, and then they're done at high speed by the fast Fourier transform, those are eigenvectors of Q, eigenvectors of the right Q." + }, + { + "text": "So let me just tell you the right Q, whose eigenvectors." + }, + { + "text": "So here we go." + }, + { + "text": "Eigenvectors of Q." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk24.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..6444776fc980bc4a69fa3b53bb954577f9481f13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "You will just be amazed by how simple this matrix is." + }, + { + "text": "It's just that matrix." + }, + { + "text": "It's called a permutation matrix." + }, + { + "text": "Those are the four Fourier discrete." + }, + { + "text": "Let me put the word discrete up here, transform." + }, + { + "text": "So I really meant to put discrete Fourier transform." + }, + { + "text": "The eigenvectors of that matrix, first of all, they are orthogonal." + }, + { + "text": "And then second and more important, they're tremendously useful." + }, + { + "text": "They're the heart of signal processing." + }, + { + "text": "In signal processing, they just take the discrete Fourier transform of a vector before they even look at it." + }, + { + "text": "I mean, that's the way to see it, is split it into its frequencies." + }, + { + "text": "And that's what the eigenvectors of this will do." + }, + { + "text": "So we're going to see the discrete Fourier transform." + }, + { + "text": "But my point here is to know that they're orthogonal just comes out of this fact that the eigenvectors are orthogonal for any Q." + }, + { + "text": "And that is certainly a Q." + }, + { + "text": "Everybody can see that those columns are orthogonal." + }, + { + "text": "The columns of a permutation matrix, right?" + }, + { + "text": "You've taken the columns of the identity, which are totally orthogonal, and you just put them in a different order." + }, + { + "text": "So a permutation matrix is a reordering of the identity matrix." + }, + { + "text": "It's got to be a Q." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk25.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..8f7ca0deb0b14efd9582bf5072f857c1cf891aae --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And therefore, its eigenvectors are orthogonal." + }, + { + "text": "And they're just the winners." + }, + { + "text": "I mean, the matrix of the Fourier matrix with those four eigenvectors in it, I'll show you now." + }, + { + "text": "So this is really we're finishing today by leading into Wednesday, eigenvectors and eigenvalues." + }, + { + "text": "And we happen to be doing eigenvectors and eigenvalues of a Q, not today of an S. Most of the time, it's a symmetric matrix whose eigenvectors we take." + }, + { + "text": "But here, that happens to be a Q." + }, + { + "text": "Can I show you the eigenvectors, the four eigenvectors of that?" + }, + { + "text": "Now, oh, the complex number I is going to come in." + }, + { + "text": "You have to let it in here." + }, + { + "text": "Sorry." + }, + { + "text": "If S is a real symmetric matrix, its eigenvectors are real." + }, + { + "text": "But if Q is a orthogonal matrix, its eigenvectors, even though you couldn't ask for a more real matrix than that, but its eigenvectors are at least, yeah, the good way are complex numbers." + }, + { + "text": "So can I show you the eigenvectors of?" + }, + { + "text": "OK." + }, + { + "text": "So again, overall, the point today is to see orthogonal matrices." + }, + { + "text": "So I'll just repeat now while I can." + }, + { + "text": "Rotations here, reflections, wavelets, the householder idea of reflections of large matrices that have this form I minus 2 UU transpose are orthogonal." + }, + { + "text": "And now we're going to see the big guys, the eigenvectors of Q." + }, + { + "text": "Right." + }, + { + "text": "Yes?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk26.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..585374b4472c10a27d82558759b1912444ae522b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk26.json @@ -0,0 +1,62 @@ +[ + { + "text": "AUDIENCE 2." + }, + { + "text": "The wavelets, do you want to rescale the column?" + }, + { + "text": "GILBERT STRANG, M.D." + }, + { + "text": "Oh, yeah." + }, + { + "text": "We don't have orthonormal." + }, + { + "text": "That's right." + }, + { + "text": "We don't have orthonormal." + }, + { + "text": "I better divide by square root of 8." + }, + { + "text": "Right." + }, + { + "text": "AUDIENCE 3." + }, + { + "text": "There's different forms for different." + }, + { + "text": "GILBERT STRANG, M.D." + }, + { + "text": "Oh, yes." + }, + { + "text": "Oh, you're right." + }, + { + "text": "Sorry, I thought I'd get away with that, but I didn't." + }, + { + "text": "Yeah." + }, + { + "text": "So these guys are square roots of 8." + }, + { + "text": "So are these." + }, + { + "text": "But these guys are square roots of 4." + }, + { + "text": "And these guys are square roots of 2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk27.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk27.json new file mode 100644 index 0000000000000000000000000000000000000000..fe044f5efd14e48e1d27d0585f9bebef51beb0e8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk27.json @@ -0,0 +1,62 @@ +[ + { + "text": "Thank you." + }, + { + "text": "Absolutely right." + }, + { + "text": "Absolutely." + }, + { + "text": "Yeah." + }, + { + "text": "OK." + }, + { + "text": "So what are the eigenvectors of a permutation?" + }, + { + "text": "This is going to be nice to see." + }, + { + "text": "And I'll use the matrix F for the eigenvector matrix of that Q up there." + }, + { + "text": "And F is for Fourier." + }, + { + "text": "And it'd be the 4 by 4 Fourier matrix." + }, + { + "text": "OK. What are the eigenvectors of Q?" + }, + { + "text": "OK." + }, + { + "text": "So Q is a permutation." + }, + { + "text": "So I'm going to ask you for one eigenvector of every permutation matrix." + }, + { + "text": "What vector can you tell me that actually the eigenvalue will be 1?" + }, + { + "text": "What vector can you tell me where if I permute it, I don't change it?" + }, + { + "text": "1, 1, 1, 1." + }, + { + "text": "It's like it's everywhere here." + }, + { + "text": "1, 1, 1, 1." + }, + { + "text": "So that's the zero frequency Fourier vector, the constant vector, all 1's." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk28.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk28.json new file mode 100644 index 0000000000000000000000000000000000000000..fd0082d001d298314187d0489c0c1333ec2c11ed --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk28.json @@ -0,0 +1,62 @@ +[ + { + "text": "Everybody sees that if I multiply by Q, it doesn't change." + }, + { + "text": "OK. Now the next one, I'll show you the 4 now." + }, + { + "text": "The next one will be 1, i, i squared, and i cubed." + }, + { + "text": "Of course, i squared, I don't know how many course 6j people are in this audience." + }, + { + "text": "But this is a math building, we paid for it." + }, + { + "text": "It's 2, 190, and it's i in this room." + }, + { + "text": "Yeah." + }, + { + "text": "So yeah." + }, + { + "text": "Anyway, i is the first letter in what?" + }, + { + "text": "Imaginary, thank you." + }, + { + "text": "The first letter in imaginary." + }, + { + "text": "You can't say jimaginary." + }, + { + "text": "So that's it." + }, + { + "text": "OK. And then the next one is 1, i squared, i fourth, i sixth." + }, + { + "text": "And the next one is 1, i cubed, i sixth, and i ninth." + }, + { + "text": "Isn't that just beautiful?" + }, + { + "text": "And you could show that every one of those four columns, if you multiply them by Q, you would get the eigenvalues." + }, + { + "text": "And you would see that it's an eigenvector." + }, + { + "text": "And this is just sort of like a discrete Fourier stuff." + }, + { + "text": "And instead of e to the ix, e to the 2ix, e to the 3ix, and so on, we just have vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk29.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk29.json new file mode 100644 index 0000000000000000000000000000000000000000..69ca2b5a6c93f1ff5ff4b1010014d5bbfe4a81fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk29.json @@ -0,0 +1,62 @@ +[ + { + "text": "So those are the four eigenvectors of that permutation." + }, + { + "text": "And those are orthogonal." + }, + { + "text": "Could I just check that?" + }, + { + "text": "How do you know that this first column and the second?" + }, + { + "text": "Well, I should really say zeroth column and first column if I'm talking frequencies." + }, + { + "text": "Do you see that that's orthogonal to that?" + }, + { + "text": "Well, y is 1 plus i plus i squared plus i cubed equals 0." + }, + { + "text": "That's the dot product." + }, + { + "text": "This is column 1 dot column 2." + }, + { + "text": "Yeah." + }, + { + "text": "You're right." + }, + { + "text": "This happens to come out 0." + }, + { + "text": "Is that right?" + }, + { + "text": "Yes, that will come out 0." + }, + { + "text": "That'll come out 0." + }, + { + "text": "But somebody mentioned that this isn't right." + }, + { + "text": "It's true that that came out 0." + }, + { + "text": "But when I have imaginary numbers anywhere around, this isn't the correct dot product to test orthogonal." + }, + { + "text": "If I have complex vectors, if I have complex numbers, complex vectors, I should test column 1 conjugate dotted with column 2." + }, + { + "text": "Column i conjugate." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk3.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..f863ecb71103dd4c79faee118ac276d69bf4817f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the inverse of Q will be the transpose." + }, + { + "text": "The transpose would put the minus sign down here and would produce the inverse matrix." + }, + { + "text": "And what does that particular matrix represent?" + }, + { + "text": "Geometrically, where do we see that matrix?" + }, + { + "text": "It's a rotation." + }, + { + "text": "Thank you." + }, + { + "text": "It's a rotation of the whole plane by theta." + }, + { + "text": "Yeah." + }, + { + "text": "So if I apply that to 1, 0, for example, I get the first column, which is cos theta, sine theta." + }, + { + "text": "And that's just a row." + }, + { + "text": "Let me draw a picture." + }, + { + "text": "That vector 1, 0 has got rotated up to." + }, + { + "text": "So there is the 1, 0." + }, + { + "text": "And there it got rotated through an angle theta." + }, + { + "text": "And similarly, 0, 1 will get rotated through an angle theta to there." + }, + { + "text": "So the whole plane rotates." + }, + { + "text": "Oh, that makes me remember a highly important, very important property of Q." + }, + { + "text": "It doesn't change length." + }, + { + "text": "The length of any vector is the same after you rotate it." + }, + { + "text": "The length of any vector is the same after you multiply by Q." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk30.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk30.json new file mode 100644 index 0000000000000000000000000000000000000000..64bd5e5b732f6ef86ff8d651a31c18dc5d6a7b26 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk30.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, let me take column." + }, + { + "text": "Let's see." + }, + { + "text": "Which one shall I take?" + }, + { + "text": "Maybe that guy and that guy." + }, + { + "text": "Many of them you luck out here." + }, + { + "text": "But really, I should be taking the conjugate." + }, + { + "text": "So these 1's." + }, + { + "text": "But the thing is the complex conjugate of 1 is 1." + }, + { + "text": "So that was OK." + }, + { + "text": "But in general, if I wanted to take column 2 dotted with column, I don't know, maybe 4 would be a little dodgy." + }, + { + "text": "Yeah, look what happens." + }, + { + "text": "Take that column and that column." + }, + { + "text": "Take their dot product." + }, + { + "text": "Do it the wrong way." + }, + { + "text": "So what's the wrong way?" + }, + { + "text": "Forget about the complex conjugate and just do it the usual way." + }, + { + "text": "So 1 times 1 is 1. i times i cube is?" + }, + { + "text": "1. i squared times i6 is?" + }, + { + "text": "1." + }, + { + "text": "I'm getting all 1's." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk31.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk31.json new file mode 100644 index 0000000000000000000000000000000000000000..96f23de58f04372c803c798f245920b0c738af9b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk31.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'm not getting orthogonality there." + }, + { + "text": "And that's because I forgot that I should take the complex conjugate." + }, + { + "text": "Well, of these guys, 1." + }, + { + "text": "I should take minus i." + }, + { + "text": "Minus i squared." + }, + { + "text": "Well, that's real, so it's OK." + }, + { + "text": "Minus there." + }, + { + "text": "So minus i squared is still minus 1." + }, + { + "text": "So now if I do it, it comes out 0." + }, + { + "text": "So let me repeat again." + }, + { + "text": "Let me just make this statement." + }, + { + "text": "If Q transpose Q is i, and Qx is lambda x, and Qy is a different eigenvalue y. OK." + }, + { + "text": "So I'm setting up the main fact that in the last minute, I'm just going to write down." + }, + { + "text": "So I have an orthogonal matrix." + }, + { + "text": "I have an eigenvector with eigenvalue lambda." + }, + { + "text": "I have another eigenvector with a different eigenvalue mu." + }, + { + "text": "Then the claim is that, what is the claim about the eigenvectors?" + }, + { + "text": "So here has one eigen." + }, + { + "text": "This has an eigenvalue." + }, + { + "text": "This has a different eigenvalue." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk32.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk32.json new file mode 100644 index 0000000000000000000000000000000000000000..7b846a742a5f1c49f8285cefa23421fb49501ed2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk32.json @@ -0,0 +1,41 @@ +[ + { + "text": "I need them to be different to really know that the x's and the y's can't be the same." + }, + { + "text": "So what is it that I want to show?" + }, + { + "text": "AUDIENCE 1." + }, + { + "text": "Conjugated x of y minus 1." + }, + { + "text": "Yes." + }, + { + "text": "That x, and I have to remember to do that, x transpose y is 0." + }, + { + "text": "That's orthogonality." + }, + { + "text": "That's orthogonality for complex vectors." + }, + { + "text": "I have to remember to change every i to a minus i in one of the vectors." + }, + { + "text": "And I can prove that fact by playing with these, by playing with starting from here, I can get to that." + }, + { + "text": "OK, that's it." + }, + { + "text": "We've done a lot today, a lot of stuff about orthogonal matrices, important ones and the sources of important ones, eigenvectors." + }, + { + "text": "And so it'll be eigenvectors on Wednesday." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk4.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..2c68625c6da30919ac3c7cd9aa2d38115f88b017 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Can I just do that?" + }, + { + "text": "I claim any x, any vector x, I want to look at the length of Qx." + }, + { + "text": "And I claim that it has the same length as x." + }, + { + "text": "Actually, that's the reason in computations that orthogonal matrix are so much loved, because no overflow can happen with orthogonal matrices." + }, + { + "text": "Lengths don't change." + }, + { + "text": "I can multiply by any number of orthogonal matrices, and the lengths don't change." + }, + { + "text": "Can we just see why that's true?" + }, + { + "text": "How would you show?" + }, + { + "text": "So what do we have to go on?" + }, + { + "text": "What we have to go on is Q transpose Q equal I." + }, + { + "text": "Whatever we're going to prove, it's got to come out of that, because that's all we know." + }, + { + "text": "So how do I use that to get that one?" + }, + { + "text": "Well, we haven't said a whole lot about lengths, but you'll see it all now." + }, + { + "text": "It'll be easier to prove that the squares are the same." + }, + { + "text": "So what's the matrix expression for the length squared?" + }, + { + "text": "What's the right-hand side of that equation?" + }, + { + "text": "X transpose x, right?" + }, + { + "text": "X transpose x gives me the sum of the squares." + }, + { + "text": "Pythagoras says that's the length squared." + }, + { + "text": "So that right-hand side is x transpose x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk5.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..fe88faea55ca7fdbade0e4cf0f0a9f66df2465b8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "What's the left side?" + }, + { + "text": "It's the length squared of this, of Qx." + }, + { + "text": "So it must be the same as Qx, transpose Qx." + }, + { + "text": "And the claim is that that equation holds." + }, + { + "text": "And do you see it?" + }, + { + "text": "Where is it?" + }, + { + "text": "So any property from Q has to just come out directly from that." + }, + { + "text": "Where is it here?" + }, + { + "text": "Do I just push away a little bit at that left-hand side and see it?" + }, + { + "text": "Qx transpose is the same as x transpose Q transpose." + }, + { + "text": "And Qx is Qx." + }, + { + "text": "And now I'm seeing, well, you might say, wait a minute." + }, + { + "text": "The parentheses were there and there." + }, + { + "text": "But I say the most important law for matrix multiplication is you can move parentheses or throw them away." + }, + { + "text": "Let's throw them away." + }, + { + "text": "So in here, I'm seeing Q transpose Q, which is the identity." + }, + { + "text": "So it's true." + }, + { + "text": "So that means that you never underflow or overflow when you're multiplying by Q." + }, + { + "text": "Every numerical algorithm is written to use orthogonal matrices wherever it can." + }, + { + "text": "And here's the first example." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk6.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..962dbdc98b0f27e37ce73e12c9ffbe343c8dddd5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I think it may be good for me to think of other examples or for us to think of other examples of orthogonal matrices." + }, + { + "text": "So I'm using that word orthogonal matrix." + }, + { + "text": "We should really be saying orthonormal." + }, + { + "text": "And I'm really thinking mostly of square ones." + }, + { + "text": "So in the square case, when Q transpose is Q inverse." + }, + { + "text": "Of course, that fact makes it easy to solve all equations that have Q as a coefficient matrix, because you want the inverse and you just use the transpose." + }, + { + "text": "OK, let's just take some minutes to think of examples of Qs, if they're so important there have to be interesting examples." + }, + { + "text": "And that was a first one." + }, + { + "text": "Now, there's one more 2 by 2 example that you should know." + }, + { + "text": "Do you know what that would be?" + }, + { + "text": "So this will be example 2." + }, + { + "text": "And it's also going to be only 2 by 2 and real." + }, + { + "text": "And what possibility have I got left here?" + }, + { + "text": "I'll use the same first column, cos theta, sine theta, because that's more or less any unit vector in two dimensions." + }, + { + "text": "This has got that form." + }, + { + "text": "So what do you propose for the second column?" + }, + { + "text": "Yes?" + }, + { + "text": "Yeah, put the minus sign down here." + }, + { + "text": "So you think, does that make any difference?" + }, + { + "text": "So sine theta and minus cos theta." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk7.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..518d307339e6889aea8a3bded1efa411a6f5745a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "I don't know if you've ever looked at that matrix." + }, + { + "text": "We're trying to collect together a few matrices that are worth knowing, are worth looking at." + }, + { + "text": "OK, now what's happened here?" + }, + { + "text": "You may say that was a trivial change, which it kind of was." + }, + { + "text": "But it's a different matrix now." + }, + { + "text": "It's not a rotation anymore." + }, + { + "text": "That's not a rotation." + }, + { + "text": "And yeah, somehow, now it's symmetric." + }, + { + "text": "And yeah, its eigenvectors must be something or other." + }, + { + "text": "We'll get to those." + }, + { + "text": "But what does that matrix do?" + }, + { + "text": "I don't know if you've seen it." + }, + { + "text": "If you haven't, it doesn't jump out." + }, + { + "text": "But it's an important case." + }, + { + "text": "This is a reflection matrix." + }, + { + "text": "Notice that it's determined it is minus 1." + }, + { + "text": "You have minus cos squared theta minus sine squared theta." + }, + { + "text": "It's determined it is minus 1." + }, + { + "text": "There's some eigenvalue coming up that's got a minus." + }, + { + "text": "Yeah." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk8.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..481458df8b0fa0d4060f8a9ff2fad9395e817b04 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, so what do I mean by a reflection matrix?" + }, + { + "text": "Let me draw the plane." + }, + { + "text": "And I think, so 1, 0." + }, + { + "text": "Let's follow it again." + }, + { + "text": "1, 0, where does that go?" + }, + { + "text": "That gives me the first column." + }, + { + "text": "So as before, it goes to cos theta sine theta." + }, + { + "text": "And when I say reflection, let me put the mirror into the picture." + }, + { + "text": "So you see what reflection it is." + }, + { + "text": "The mirror is along here at angle theta over 2, theta over 2 line." + }, + { + "text": "So sure enough, 1, 0 at angle 0 got reflected into a unit vector at angle theta." + }, + { + "text": "And halfway between was the theta over 2 line." + }, + { + "text": "That's OK. Now, what about the other guy, 0, 1?" + }, + { + "text": "Here's 0, 1." + }, + { + "text": "OK, I multiply that." + }, + { + "text": "Can I put the 0, 1 up here so your eye does the multiplication?" + }, + { + "text": "Where is the result of 0, 1?" + }, + { + "text": "What's the output from Q applied to 0, 1?" + }, + { + "text": "Sine theta minus cos theta, right?" + }, + { + "text": "It's the second column." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk9.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..27a460130a0a8d38fe662c57a511c467a303fbb9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_3_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so where is that?" + }, + { + "text": "Well, it's perpendicular to that guy." + }, + { + "text": "That's what I know, right?" + }, + { + "text": "That was the point, that the two columns are perpendicular." + }, + { + "text": "So it must go down this way, right?" + }, + { + "text": "Sine theta, cos theta." + }, + { + "text": "And it doesn't change length." + }, + { + "text": "All these facts that we just learned are key." + }, + { + "text": "So there's 0, 1, and it goes to this guy, which is whatever that second column is, sine theta minus cos theta." + }, + { + "text": "And if you check that, actually, gosh, this is like plain geometry." + }, + { + "text": "I believe, it's never occurred to me before, but I believe it, that this angle going down to there, that that goes straight through, and that the halfway one is that line." + }, + { + "text": "Yeah, I think that picture has got it, and I think it's in the notes." + }, + { + "text": "So that's a reflection matrix." + }, + { + "text": "Well, that's a 2 by 2 reflection matrix." + }, + { + "text": "Would you like to see some other matrices like this one, but larger?" + }, + { + "text": "They're named after a guy named Householder." + }, + { + "text": "So these are Householder reflections." + }, + { + "text": "What am I doing here?" + }, + { + "text": "I'm collecting together some orthogonal matrices that are useful and important." + }, + { + "text": "And Householder found a whole bunch of them, and his algorithm is a much used part of numerical linear algebra." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk0.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..b5d2005486c62ceb6bba16af0971eda159bf4d11 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "So we're really moving along this review of the highlights of linear algebra." + }, + { + "text": "And today it's matrices Q." + }, + { + "text": "They get that name." + }, + { + "text": "They have orthonormal columns." + }, + { + "text": "So that's what one looks like." + }, + { + "text": "And then the key fact, orthonormal columns translates directly into that simple fact that you just keep remembering." + }, + { + "text": "Every time you see Q transpose Q, you've got the identity matrix." + }, + { + "text": "Let's just see why." + }, + { + "text": "So Q transpose would be, I'll take those columns and make them into rows." + }, + { + "text": "And then I multiply by Q with the columns." + }, + { + "text": "And what do I get?" + }, + { + "text": "Well, hopefully I get the identity matrix." + }, + { + "text": "OK, why?" + }, + { + "text": "Because, oh, yeah, the normal part tells me that the length of each vector, that's the length squared Q transpose Q." + }, + { + "text": "The length squared is 1." + }, + { + "text": "So that gives me the 1 in the identity matrix all along the diagonal." + }, + { + "text": "And then Q transpose times a different Q is 0." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk1.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..4e5a53f7561a10c59c686c38ce76be1836e60948 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the ortho part." + }, + { + "text": "So that gives me the 0s." + }, + { + "text": "So that's a simple identity." + }, + { + "text": "But it translates from a lot of words into a simple expression." + }, + { + "text": "Now, does that mean that in the other order, Q Q transpose, is that the identity?" + }, + { + "text": "So that's a question to think about." + }, + { + "text": "Is Q Q transpose equal the identity?" + }, + { + "text": "Question." + }, + { + "text": "Sometimes yes, sometimes no." + }, + { + "text": "Easy to tell which." + }, + { + "text": "The answer is yes." + }, + { + "text": "Yes, when Q is square." + }, + { + "text": "The answer is yes." + }, + { + "text": "If Q is a square matrix, a square matrix, this is saying that the square matrix Q has that inverse on its left." + }, + { + "text": "But for square matrices, a left inverse, Q transpose, is also a right inverse." + }, + { + "text": "And for a square matrix, if you have an inverse that works on one side, it will work on the other side." + }, + { + "text": "So the answer is yes in that case." + }, + { + "text": "And then in that case, that's the case when we call Q is, well, we really, I don't know what the right name would be." + }, + { + "text": "But here's the name everybody uses, an orthogonal matrix." + }, + { + "text": "And that's only in the square case, square." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk10.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..49656af3fb9dd19d28412adf515bdcbf6d01baf1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So he started with a unit vector." + }, + { + "text": "Start with a unit vector, u transpose u equal 1." + }, + { + "text": "So the length of the vector is 1." + }, + { + "text": "And then he created, let's name it after him, H. He created this matrix, the identity minus 2 uu transpose." + }, + { + "text": "And I believe that that's a really useful matrix." + }, + { + "text": "So it's just like, I think this review is like going beyond 18.06 into what ones are really worth knowing individually." + }, + { + "text": "Could we just check what are the properties of Householder's reflection of that I minus 2?" + }, + { + "text": "You recognize here a column times a row." + }, + { + "text": "So that's a matrix." + }, + { + "text": "And what could you tell me about that matrix uu transpose?" + }, + { + "text": "It's, yeah." + }, + { + "text": "Or what can we say about H?" + }, + { + "text": "So I guess I'm believing that H is a orthogonal matrix." + }, + { + "text": "Otherwise, it wouldn't be here today." + }, + { + "text": "So I believe that." + }, + { + "text": "And not only is it orthogonal, it is also, have a look at it, symmetric." + }, + { + "text": "It's also symmetric." + }, + { + "text": "The identity is symmetric." + }, + { + "text": "Uu transpose is symmetric." + }, + { + "text": "So this is a family of symmetric orthogonal matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk11.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..d1bc347004ae5794bd541685a2530709739f8fb8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "And that was one of them." + }, + { + "text": "That's a symmetric orthogonal matrix." + }, + { + "text": "These matrices are really great to have." + }, + { + "text": "You just, like in using linear algebra, you just get a collection of useful matrices that you can call on." + }, + { + "text": "And these are definitely one family." + }, + { + "text": "Well, it's obviously symmetric." + }, + { + "text": "Shall we check that it's orthogonal?" + }, + { + "text": "So to check that it's orthogonal, I just, so I'm going to check that H transpose H is the identity." + }, + { + "text": "Can I just check that?" + }, + { + "text": "Well, H transpose is the same as H, because it was symmetric." + }, + { + "text": "So I'm going to square this guy." + }, + { + "text": "This is really H times H. I'm squaring it." + }, + { + "text": "And what do I get if I square?" + }, + { + "text": "So I get, I hope I get the identity, but let's see it." + }, + { + "text": "What do I get when I square this?" + }, + { + "text": "Get little, multiply it out." + }, + { + "text": "So I times I is I." + }, + { + "text": "And then I get some number of Uu transposes." + }, + { + "text": "How many do I get from that?" + }, + { + "text": "So I'm squaring this thing, because H transpose H is the same as H times H. So I'm squaring it." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk12.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..25d7b51e680f692a50bab3dc6644564db6a54780 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "So how many, what do I put here?" + }, + { + "text": "Four, thanks." + }, + { + "text": "And now I've got this guy squared with a plus." + }, + { + "text": "So that's four Uu transpose Uu transpose." + }, + { + "text": "Yeah, I'm totally realizing I've practiced for a lifetime doing these dinky little calculations." + }, + { + "text": "But they are dinky." + }, + { + "text": "And you'll get the hang of it quickly." + }, + { + "text": "Now, what am I hoping out of that bottom line?" + }, + { + "text": "That it is?" + }, + { + "text": "I." + }, + { + "text": "We're hoping to get I." + }, + { + "text": "Do we get I?" + }, + { + "text": "Yes." + }, + { + "text": "Who sees how to get I out of that thing?" + }, + { + "text": "Yeah." + }, + { + "text": "U transpose U in here is a number." + }, + { + "text": "That was U." + }, + { + "text": "That was column times row times column times row." + }, + { + "text": "And I look at the in the middle here is row times column." + }, + { + "text": "And that's the number 1, right?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk13.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..2970896b1136ec13f25ac3b1d568b82c5bfd6397 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Because it's there." + }, + { + "text": "So that's 1." + }, + { + "text": "And then I have minus 4 of that, plus 4 of that." + }, + { + "text": "They cancel each other." + }, + { + "text": "And I get I." + }, + { + "text": "So those are good matrices." + }, + { + "text": "We'll use them." + }, + { + "text": "We'll use them." + }, + { + "text": "Actually, they're better than Graham-Schmidt." + }, + { + "text": "So we'll use them in making things orthogonal." + }, + { + "text": "So what other orthogonal matrices?" + }, + { + "text": "Let's create some." + }, + { + "text": "Creating good orthogonal matrices, it pays off." + }, + { + "text": "Let's think." + }, + { + "text": "So there's a family named after this French guy who lived to 100." + }, + { + "text": "He was a real old timer." + }, + { + "text": "Well, MIT had a faculty member in math when I came, Professor Struik, who lived to 106." + }, + { + "text": "And I heard him give a lecture at Brown University at age 100." + }, + { + "text": "And it was like perfect." + }, + { + "text": "You could not have done it better." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk14.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7a4761773e251928346e720869f90c17e750fc9c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So he's my inspiration." + }, + { + "text": "I keep going." + }, + { + "text": "I only have like n more years to get there." + }, + { + "text": "And n is, well, it's too many anyway." + }, + { + "text": "OK, Adamard." + }, + { + "text": "All right, Adamard." + }, + { + "text": "So Adamard, he created, well, that's the simplest, the smallest." + }, + { + "text": "Now, the next guy is going to be 4 by 4." + }, + { + "text": "I'm going to put that." + }, + { + "text": "So where I see a 1, I'm going to put Adamard in." + }, + { + "text": "1, 1, 1 minus 1, 1, 1, 1 minus 1." + }, + { + "text": "And then when I see a minus, I'm going to put it in with a minus." + }, + { + "text": "You saw that picture?" + }, + { + "text": "It was a picture of H2, H2, H2, and minus H2." + }, + { + "text": "That's what I've got there." + }, + { + "text": "And I believe those columns are orthogonal." + }, + { + "text": "Now, what could I do?" + }, + { + "text": "Well, it's not quite an orthogonal matrix." + }, + { + "text": "What do I have to do to make it?" + }, + { + "text": "This isn't quite an orthogonal matrix either." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk15.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..7c56d46fe9a00c08ec502262a9278c03ce6817ad --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "What do I do to make that an orthogonal matrix?" + }, + { + "text": "Divide by square root of 2." + }, + { + "text": "I need unit vectors there." + }, + { + "text": "And here, those lengths are 1 squared, 1 squared, 4." + }, + { + "text": "Square root of 4 is 2." + }, + { + "text": "So I better divide by the 2 there." + }, + { + "text": "And now here, I'm up to, yeah, so that was that one." + }, + { + "text": "Tell me the next one up." + }, + { + "text": "What's that going to be?" + }, + { + "text": "8 by 8?" + }, + { + "text": "So this is H4 here." + }, + { + "text": "Oops, 4." + }, + { + "text": "So tell me what I should do for 8 by 8." + }, + { + "text": "You'll think this is simple." + }, + { + "text": "But that's a good thing to say about it." + }, + { + "text": "In coding theory, all sorts of places, you want matrices of 1's and minus 1's." + }, + { + "text": "OK, what's H8?" + }, + { + "text": "I'm going to build it out of H4." + }, + { + "text": "So what's it going to be?" + }, + { + "text": "I'm going to put an H4 there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk16.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..918141f4e0ba694885e6f1ccbc52ab39b4979f98 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "What am I going to put here?" + }, + { + "text": "Another H4." + }, + { + "text": "And up here, another H4." + }, + { + "text": "And finally here, minus H4." + }, + { + "text": "Minus H4, and I think I've got orthogonal columns again." + }, + { + "text": "Because the columns within these, dot products with themselves, give 0 and 0." + }, + { + "text": "The dot products from these columns and these columns obviously have the minus." + }, + { + "text": "And the dot products in here are 0 from that and 0 from that." + }, + { + "text": "Yeah, it works." + }, + { + "text": "And we could keep going to 16 and 32 and 64." + }, + { + "text": "But then up comes a question." + }, + { + "text": "What about H12?" + }, + { + "text": "Is there a 1's and minus 1's matrix of size 12, 12 by 12?" + }, + { + "text": "It doesn't come directly from our little pattern, which is doubling size every time." + }, + { + "text": "But you could still hope." + }, + { + "text": "And it works." + }, + { + "text": "I don't know what it is, but there's a matrix of 1's and minus 1's, 12 orthogonal columns." + }, + { + "text": "So the answer is yes." + }, + { + "text": "OK, so we make an 18.065 conjecture." + }, + { + "text": "Every matrix size, well, not every matrix size, because 3 by 3 is not going to work." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk17.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..424ebae85640980fc86eba92079646d513aa4ab7 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "1 by 1 is not going to work either." + }, + { + "text": "But H12 works, H8, H16." + }, + { + "text": "What's our conjecture?" + }, + { + "text": "We won't be the first to conjecture it." + }, + { + "text": "There is a 1's and minus 1's orthogonal matrix with orthogonal columns of every size n. So always, so I'll start the conjecture." + }, + { + "text": "Always possible if n, which is the size of the matrix, let's say, what would you guess?" + }, + { + "text": "Just take a shot." + }, + { + "text": "You won't be asked for a proof, because nobody has the proof." + }, + { + "text": "Even?" + }, + { + "text": "Well, you could hope for even." + }, + { + "text": "You could look for try 6, I guess, would be the first guy there." + }, + { + "text": "And I don't think it's possible." + }, + { + "text": "I think 6 is not possible." + }, + { + "text": "So every even size is, I think, not going to work." + }, + { + "text": "But it's a natural idea to try." + }, + { + "text": "What's the next thought?" + }, + { + "text": "Every multiple of 4." + }, + { + "text": "If n over 4 is a whole number." + }, + { + "text": "But nobody has a systematic way to create these things." + }, + { + "text": "So like some of them, at this point, we're down to doing it one at a time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk18.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..8b98656b2afa8ad2c2bc10e43f6253f0336687c6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we're up to 668." + }, + { + "text": "But we haven't got that one yet." + }, + { + "text": "Isn't that crazy?" + }, + { + "text": "So all this is coming from Wikipedia, my source of all that's good in mathematics is there on Wikipedia." + }, + { + "text": "Anyway, this is the conjecture." + }, + { + "text": "Conjecture means you don't have any damn idea of whether it's true or not." + }, + { + "text": "Is that divisible by 4?" + }, + { + "text": "Yeah, I guess it would be." + }, + { + "text": "600 certainly is, and 68 certainly is." + }, + { + "text": "So I think that's the first one." + }, + { + "text": "So anybody, if you find one of size 668, just skip the homework and tell us about that one." + }, + { + "text": "But I don't think I'll assign that." + }, + { + "text": "I guess, well, I must have searched for it online." + }, + { + "text": "But yeah, anyway, so those are the Adamard matrices." + }, + { + "text": "Now, where else do I remember orthogonal matrices coming from?" + }, + { + "text": "Well, yeah, really, the biggest source of." + }, + { + "text": "So when I'm looking for orthogonal matrices, I'm looking for a basis of orthogonal vectors." + }, + { + "text": "And where in math am I going to find vectors that come out to be orthogonal?" + }, + { + "text": "We haven't seen that." + }, + { + "text": "It's the next section of the notes, but maybe you're remembering." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk19.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..1a1bbc69e93bf8e690780d413ac7692520b39c41 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Where will we sort of like automatically show up with orthogonal vectors?" + }, + { + "text": "They could be the eigenvectors of a symmetric matrix." + }, + { + "text": "And that's where the most important ones come from." + }, + { + "text": "Oh, I could tell you about wavelets, though." + }, + { + "text": "Wavelets are more like this picture." + }, + { + "text": "They're 1's and minus 1's." + }, + { + "text": "Or the simplest wavelets are 1's and minus 1's." + }, + { + "text": "Before I go on to the eigenvector business, can I mention the wavelets matrices?" + }, + { + "text": "Yeah, these are really important, simple and important constructions." + }, + { + "text": "So wavelets, let me draw a picture." + }, + { + "text": "So I'm going to come up with four." + }, + { + "text": "I'll do the 4 by 4 case." + }, + { + "text": "And these are the orthogonal guys." + }, + { + "text": "And then the next one is up and down and 0." + }, + { + "text": "And the last one is 0 and up and down." + }, + { + "text": "So that's four things, but let me show you the matrix." + }, + { + "text": "So I'll call it W for wavelets." + }, + { + "text": "So that guy I'm thinking of as 1, 1, 1, 1." + }, + { + "text": "This guy I'm thinking of as 1, 1, minus 1, minus 1." + }, + { + "text": "It's looking sort of Adhemard way, but there's a difference here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk2.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..fa6e9f79b321740f7bd2a0adca7cc97249c3a10c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Q is an orthogonal matrix." + }, + { + "text": "Right, right." + }, + { + "text": "Do you want to just see an example of how that works?" + }, + { + "text": "And it will not." + }, + { + "text": "So if Q is rectangular, let me do a rectangular Q and a square Q." + }, + { + "text": "So I think there must be a board up there somewhere." + }, + { + "text": "Here." + }, + { + "text": "OK, square." + }, + { + "text": "All right, good to see some orthogonal matrices, because my message is that they're really important in all kinds of applications." + }, + { + "text": "Let's start two by two." + }, + { + "text": "I can think of two different ways to get an orthogonal matrix that's a two by two matrix." + }, + { + "text": "And one of them you will know immediately, cos theta, sine theta." + }, + { + "text": "So that's a unit vector." + }, + { + "text": "It's normalized." + }, + { + "text": "Cos squared plus sine squared is 1." + }, + { + "text": "And this guy has to be orthogonal to it." + }, + { + "text": "So I'll make that minus sine theta and cos theta." + }, + { + "text": "OK. Those are both length 1." + }, + { + "text": "They're orthogonal." + }, + { + "text": "Then this is my Q." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk20.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..3e8bb5de8bf16bf7ce3501ccefb5a330450b8ade --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "This guy is 1, minus 1, 0, 0." + }, + { + "text": "So the wavelets rescale." + }, + { + "text": "That's the difference between Adhemard and wavelets." + }, + { + "text": "Wavelets are self-scaling." + }, + { + "text": "And what's the last guy here?" + }, + { + "text": "What's the fourth column from that fourth wavelet?" + }, + { + "text": "0, 0, 1, minus 1." + }, + { + "text": "So Haar came up with that." + }, + { + "text": "This is the Haar wavelet, which was many years before the word wavelets was invented." + }, + { + "text": "He came up with this construction, the Haar matrix, the Haar functions." + }, + { + "text": "So they're very simple functions, but that makes them usable, the fact that they're so simple." + }, + { + "text": "Now, I don't know if you want to see the pattern in 8 by 8, but let me start the 8 by 8 so you'll know what wavelets are about." + }, + { + "text": "You'll know what these Haar wavelets are about anyway." + }, + { + "text": "They're the ones that were kind of easy to visualize." + }, + { + "text": "So if that's W4, let's just take a minute." + }, + { + "text": "It won't take long for W8." + }, + { + "text": "OK." + }, + { + "text": "So the first column is going to be 8 1's." + }, + { + "text": "And what's the next column going to be?" + }, + { + "text": "4 1's and 4 minus 1's, like so." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk21.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..9e867c07e11ef6d60fe356fac02e997856317ce7 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "So 4 1's and 4 minus 1's." + }, + { + "text": "OK, and now the next column." + }, + { + "text": "2 1's, 2 minus 1's, and 0's." + }, + { + "text": "Right?" + }, + { + "text": "1, 1, minus 1, minus 1, and 0." + }, + { + "text": "And the fourth will be 0's and 2 1's and 2 minus 1's." + }, + { + "text": "We've got half a matrix now." + }, + { + "text": "Now, if we just tell me the fifth, what do you think?" + }, + { + "text": "What do I put in the fifth one?" + }, + { + "text": "So again, it's going to squeeze down and rescale." + }, + { + "text": "And what's the fifth column up here that's going to be 1's and minus 1's and 0's now?" + }, + { + "text": "So it's not Adamard." + }, + { + "text": "It's Haar." + }, + { + "text": "And what shall I put?" + }, + { + "text": "1, 1." + }, + { + "text": "Shall I start with 1, 1?" + }, + { + "text": "Oh, 1 minus?" + }, + { + "text": "Yeah." + }, + { + "text": "And then all 0's?" + }, + { + "text": "Oh, yeah, thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk22.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..9c0933bcb3a8da850c610e830d259e286619b663 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "Perfect." + }, + { + "text": "1 minus 1, and then all 0's." + }, + { + "text": "And then the next three columns will have the 1 minus 1 here, and the 1 minus 1 here, and the 1 minus 1 here." + }, + { + "text": "And otherwise, all 0's." + }, + { + "text": "So you see the pattern." + }, + { + "text": "It's scaling at every step." + }, + { + "text": "So that matrix has the advantage of being quite sparse." + }, + { + "text": "This, in my mind, is a 4, 1's." + }, + { + "text": "That's involved with taking the average." + }, + { + "text": "Then this guy is like taking the differences, differences between those and those." + }, + { + "text": "And then this is like taking the difference at a smaller scale, and that also at a smaller scale." + }, + { + "text": "So that's what we keep doing." + }, + { + "text": "Yeah." + }, + { + "text": "Yeah." + }, + { + "text": "So that's wavelets." + }, + { + "text": "It looks so simple, right?" + }, + { + "text": "But just a one-minute history of wavelets, so Haar invented this in like 1910." + }, + { + "text": "I mean, along, forever." + }, + { + "text": "But then you wanted wavelets that were a little better, and not just 1's and minus 1's and 0's." + }, + { + "text": "And that took a lot of thinking." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk23.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..2c0478724ed1347c302a19560f09fa22c81860c1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "A lot of people were searching for it." + }, + { + "text": "And Ingrid Dovashy, so I'll just put her name, became famous for finding them." + }, + { + "text": "So in about 1988, she found a whole lot of families of wavelets." + }, + { + "text": "And when I say wavelets, she found a whole lot of orthogonal matrices that had good properties." + }, + { + "text": "So that's the wavelet picture." + }, + { + "text": "Now, to close today and to connect with the next lecture on eigenvalues, eigenvectors, positive definite matrices, we're really getting to the heart of things here." + }, + { + "text": "Let me follow through on that idea." + }, + { + "text": "Idea, so the eigenvectors of a symmetric matrix, but also of an orthogonal matrix are orthogonal." + }, + { + "text": "And that is really where people, where you can invent, because you don't have to work hard." + }, + { + "text": "You just find a symmetric matrix." + }, + { + "text": "Its eigenvectors are automatically orthogonal." + }, + { + "text": "That doesn't mean they're great for use, but some of them are really important." + }, + { + "text": "And maybe the most important of all is the Fourier." + }, + { + "text": "So you probably have seen Fourier series, sines and cosines." + }, + { + "text": "Those guys are orthogonal functions." + }, + { + "text": "But the discrete Fourier series is what everybody computes, and those are orthogonal vectors." + }, + { + "text": "So the orthogonal vectors that go into the discrete Fourier transform, and then they're done at high speed by the fast Fourier transform, those are eigenvectors of Q, eigenvectors of the right Q." + }, + { + "text": "So let me just tell you the right Q, whose eigenvectors." + }, + { + "text": "So here we go." + }, + { + "text": "Eigenvectors of Q." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk24.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..6444776fc980bc4a69fa3b53bb954577f9481f13 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "You will just be amazed by how simple this matrix is." + }, + { + "text": "It's just that matrix." + }, + { + "text": "It's called a permutation matrix." + }, + { + "text": "Those are the four Fourier discrete." + }, + { + "text": "Let me put the word discrete up here, transform." + }, + { + "text": "So I really meant to put discrete Fourier transform." + }, + { + "text": "The eigenvectors of that matrix, first of all, they are orthogonal." + }, + { + "text": "And then second and more important, they're tremendously useful." + }, + { + "text": "They're the heart of signal processing." + }, + { + "text": "In signal processing, they just take the discrete Fourier transform of a vector before they even look at it." + }, + { + "text": "I mean, that's the way to see it, is split it into its frequencies." + }, + { + "text": "And that's what the eigenvectors of this will do." + }, + { + "text": "So we're going to see the discrete Fourier transform." + }, + { + "text": "But my point here is to know that they're orthogonal just comes out of this fact that the eigenvectors are orthogonal for any Q." + }, + { + "text": "And that is certainly a Q." + }, + { + "text": "Everybody can see that those columns are orthogonal." + }, + { + "text": "The columns of a permutation matrix, right?" + }, + { + "text": "You've taken the columns of the identity, which are totally orthogonal, and you just put them in a different order." + }, + { + "text": "So a permutation matrix is a reordering of the identity matrix." + }, + { + "text": "It's got to be a Q." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk25.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..8f7ca0deb0b14efd9582bf5072f857c1cf891aae --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "And therefore, its eigenvectors are orthogonal." + }, + { + "text": "And they're just the winners." + }, + { + "text": "I mean, the matrix of the Fourier matrix with those four eigenvectors in it, I'll show you now." + }, + { + "text": "So this is really we're finishing today by leading into Wednesday, eigenvectors and eigenvalues." + }, + { + "text": "And we happen to be doing eigenvectors and eigenvalues of a Q, not today of an S. Most of the time, it's a symmetric matrix whose eigenvectors we take." + }, + { + "text": "But here, that happens to be a Q." + }, + { + "text": "Can I show you the eigenvectors, the four eigenvectors of that?" + }, + { + "text": "Now, oh, the complex number I is going to come in." + }, + { + "text": "You have to let it in here." + }, + { + "text": "Sorry." + }, + { + "text": "If S is a real symmetric matrix, its eigenvectors are real." + }, + { + "text": "But if Q is a orthogonal matrix, its eigenvectors, even though you couldn't ask for a more real matrix than that, but its eigenvectors are at least, yeah, the good way are complex numbers." + }, + { + "text": "So can I show you the eigenvectors of?" + }, + { + "text": "OK." + }, + { + "text": "So again, overall, the point today is to see orthogonal matrices." + }, + { + "text": "So I'll just repeat now while I can." + }, + { + "text": "Rotations here, reflections, wavelets, the householder idea of reflections of large matrices that have this form I minus 2 UU transpose are orthogonal." + }, + { + "text": "And now we're going to see the big guys, the eigenvectors of Q." + }, + { + "text": "Right." + }, + { + "text": "Yes?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk26.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..585374b4472c10a27d82558759b1912444ae522b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk26.json @@ -0,0 +1,62 @@ +[ + { + "text": "AUDIENCE 2." + }, + { + "text": "The wavelets, do you want to rescale the column?" + }, + { + "text": "GILBERT STRANG, M.D." + }, + { + "text": "Oh, yeah." + }, + { + "text": "We don't have orthonormal." + }, + { + "text": "That's right." + }, + { + "text": "We don't have orthonormal." + }, + { + "text": "I better divide by square root of 8." + }, + { + "text": "Right." + }, + { + "text": "AUDIENCE 3." + }, + { + "text": "There's different forms for different." + }, + { + "text": "GILBERT STRANG, M.D." + }, + { + "text": "Oh, yes." + }, + { + "text": "Oh, you're right." + }, + { + "text": "Sorry, I thought I'd get away with that, but I didn't." + }, + { + "text": "Yeah." + }, + { + "text": "So these guys are square roots of 8." + }, + { + "text": "So are these." + }, + { + "text": "But these guys are square roots of 4." + }, + { + "text": "And these guys are square roots of 2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk27.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk27.json new file mode 100644 index 0000000000000000000000000000000000000000..fe044f5efd14e48e1d27d0585f9bebef51beb0e8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk27.json @@ -0,0 +1,62 @@ +[ + { + "text": "Thank you." + }, + { + "text": "Absolutely right." + }, + { + "text": "Absolutely." + }, + { + "text": "Yeah." + }, + { + "text": "OK." + }, + { + "text": "So what are the eigenvectors of a permutation?" + }, + { + "text": "This is going to be nice to see." + }, + { + "text": "And I'll use the matrix F for the eigenvector matrix of that Q up there." + }, + { + "text": "And F is for Fourier." + }, + { + "text": "And it'd be the 4 by 4 Fourier matrix." + }, + { + "text": "OK. What are the eigenvectors of Q?" + }, + { + "text": "OK." + }, + { + "text": "So Q is a permutation." + }, + { + "text": "So I'm going to ask you for one eigenvector of every permutation matrix." + }, + { + "text": "What vector can you tell me that actually the eigenvalue will be 1?" + }, + { + "text": "What vector can you tell me where if I permute it, I don't change it?" + }, + { + "text": "1, 1, 1, 1." + }, + { + "text": "It's like it's everywhere here." + }, + { + "text": "1, 1, 1, 1." + }, + { + "text": "So that's the zero frequency Fourier vector, the constant vector, all 1's." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk28.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk28.json new file mode 100644 index 0000000000000000000000000000000000000000..fd0082d001d298314187d0489c0c1333ec2c11ed --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk28.json @@ -0,0 +1,62 @@ +[ + { + "text": "Everybody sees that if I multiply by Q, it doesn't change." + }, + { + "text": "OK. Now the next one, I'll show you the 4 now." + }, + { + "text": "The next one will be 1, i, i squared, and i cubed." + }, + { + "text": "Of course, i squared, I don't know how many course 6j people are in this audience." + }, + { + "text": "But this is a math building, we paid for it." + }, + { + "text": "It's 2, 190, and it's i in this room." + }, + { + "text": "Yeah." + }, + { + "text": "So yeah." + }, + { + "text": "Anyway, i is the first letter in what?" + }, + { + "text": "Imaginary, thank you." + }, + { + "text": "The first letter in imaginary." + }, + { + "text": "You can't say jimaginary." + }, + { + "text": "So that's it." + }, + { + "text": "OK. And then the next one is 1, i squared, i fourth, i sixth." + }, + { + "text": "And the next one is 1, i cubed, i sixth, and i ninth." + }, + { + "text": "Isn't that just beautiful?" + }, + { + "text": "And you could show that every one of those four columns, if you multiply them by Q, you would get the eigenvalues." + }, + { + "text": "And you would see that it's an eigenvector." + }, + { + "text": "And this is just sort of like a discrete Fourier stuff." + }, + { + "text": "And instead of e to the ix, e to the 2ix, e to the 3ix, and so on, we just have vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk29.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk29.json new file mode 100644 index 0000000000000000000000000000000000000000..69ca2b5a6c93f1ff5ff4b1010014d5bbfe4a81fe --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk29.json @@ -0,0 +1,62 @@ +[ + { + "text": "So those are the four eigenvectors of that permutation." + }, + { + "text": "And those are orthogonal." + }, + { + "text": "Could I just check that?" + }, + { + "text": "How do you know that this first column and the second?" + }, + { + "text": "Well, I should really say zeroth column and first column if I'm talking frequencies." + }, + { + "text": "Do you see that that's orthogonal to that?" + }, + { + "text": "Well, y is 1 plus i plus i squared plus i cubed equals 0." + }, + { + "text": "That's the dot product." + }, + { + "text": "This is column 1 dot column 2." + }, + { + "text": "Yeah." + }, + { + "text": "You're right." + }, + { + "text": "This happens to come out 0." + }, + { + "text": "Is that right?" + }, + { + "text": "Yes, that will come out 0." + }, + { + "text": "That'll come out 0." + }, + { + "text": "But somebody mentioned that this isn't right." + }, + { + "text": "It's true that that came out 0." + }, + { + "text": "But when I have imaginary numbers anywhere around, this isn't the correct dot product to test orthogonal." + }, + { + "text": "If I have complex vectors, if I have complex numbers, complex vectors, I should test column 1 conjugate dotted with column 2." + }, + { + "text": "Column i conjugate." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk3.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..f863ecb71103dd4c79faee118ac276d69bf4817f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the inverse of Q will be the transpose." + }, + { + "text": "The transpose would put the minus sign down here and would produce the inverse matrix." + }, + { + "text": "And what does that particular matrix represent?" + }, + { + "text": "Geometrically, where do we see that matrix?" + }, + { + "text": "It's a rotation." + }, + { + "text": "Thank you." + }, + { + "text": "It's a rotation of the whole plane by theta." + }, + { + "text": "Yeah." + }, + { + "text": "So if I apply that to 1, 0, for example, I get the first column, which is cos theta, sine theta." + }, + { + "text": "And that's just a row." + }, + { + "text": "Let me draw a picture." + }, + { + "text": "That vector 1, 0 has got rotated up to." + }, + { + "text": "So there is the 1, 0." + }, + { + "text": "And there it got rotated through an angle theta." + }, + { + "text": "And similarly, 0, 1 will get rotated through an angle theta to there." + }, + { + "text": "So the whole plane rotates." + }, + { + "text": "Oh, that makes me remember a highly important, very important property of Q." + }, + { + "text": "It doesn't change length." + }, + { + "text": "The length of any vector is the same after you rotate it." + }, + { + "text": "The length of any vector is the same after you multiply by Q." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk30.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk30.json new file mode 100644 index 0000000000000000000000000000000000000000..64bd5e5b732f6ef86ff8d651a31c18dc5d6a7b26 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk30.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, let me take column." + }, + { + "text": "Let's see." + }, + { + "text": "Which one shall I take?" + }, + { + "text": "Maybe that guy and that guy." + }, + { + "text": "Many of them you luck out here." + }, + { + "text": "But really, I should be taking the conjugate." + }, + { + "text": "So these 1's." + }, + { + "text": "But the thing is the complex conjugate of 1 is 1." + }, + { + "text": "So that was OK." + }, + { + "text": "But in general, if I wanted to take column 2 dotted with column, I don't know, maybe 4 would be a little dodgy." + }, + { + "text": "Yeah, look what happens." + }, + { + "text": "Take that column and that column." + }, + { + "text": "Take their dot product." + }, + { + "text": "Do it the wrong way." + }, + { + "text": "So what's the wrong way?" + }, + { + "text": "Forget about the complex conjugate and just do it the usual way." + }, + { + "text": "So 1 times 1 is 1. i times i cube is?" + }, + { + "text": "1. i squared times i6 is?" + }, + { + "text": "1." + }, + { + "text": "I'm getting all 1's." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk31.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk31.json new file mode 100644 index 0000000000000000000000000000000000000000..96f23de58f04372c803c798f245920b0c738af9b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk31.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'm not getting orthogonality there." + }, + { + "text": "And that's because I forgot that I should take the complex conjugate." + }, + { + "text": "Well, of these guys, 1." + }, + { + "text": "I should take minus i." + }, + { + "text": "Minus i squared." + }, + { + "text": "Well, that's real, so it's OK." + }, + { + "text": "Minus there." + }, + { + "text": "So minus i squared is still minus 1." + }, + { + "text": "So now if I do it, it comes out 0." + }, + { + "text": "So let me repeat again." + }, + { + "text": "Let me just make this statement." + }, + { + "text": "If Q transpose Q is i, and Qx is lambda x, and Qy is a different eigenvalue y. OK." + }, + { + "text": "So I'm setting up the main fact that in the last minute, I'm just going to write down." + }, + { + "text": "So I have an orthogonal matrix." + }, + { + "text": "I have an eigenvector with eigenvalue lambda." + }, + { + "text": "I have another eigenvector with a different eigenvalue mu." + }, + { + "text": "Then the claim is that, what is the claim about the eigenvectors?" + }, + { + "text": "So here has one eigen." + }, + { + "text": "This has an eigenvalue." + }, + { + "text": "This has a different eigenvalue." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk32.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk32.json new file mode 100644 index 0000000000000000000000000000000000000000..7b846a742a5f1c49f8285cefa23421fb49501ed2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk32.json @@ -0,0 +1,41 @@ +[ + { + "text": "I need them to be different to really know that the x's and the y's can't be the same." + }, + { + "text": "So what is it that I want to show?" + }, + { + "text": "AUDIENCE 1." + }, + { + "text": "Conjugated x of y minus 1." + }, + { + "text": "Yes." + }, + { + "text": "That x, and I have to remember to do that, x transpose y is 0." + }, + { + "text": "That's orthogonality." + }, + { + "text": "That's orthogonality for complex vectors." + }, + { + "text": "I have to remember to change every i to a minus i in one of the vectors." + }, + { + "text": "And I can prove that fact by playing with these, by playing with starting from here, I can get to that." + }, + { + "text": "OK, that's it." + }, + { + "text": "We've done a lot today, a lot of stuff about orthogonal matrices, important ones and the sources of important ones, eigenvectors." + }, + { + "text": "And so it'll be eigenvectors on Wednesday." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk4.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..2c68625c6da30919ac3c7cd9aa2d38115f88b017 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Can I just do that?" + }, + { + "text": "I claim any x, any vector x, I want to look at the length of Qx." + }, + { + "text": "And I claim that it has the same length as x." + }, + { + "text": "Actually, that's the reason in computations that orthogonal matrix are so much loved, because no overflow can happen with orthogonal matrices." + }, + { + "text": "Lengths don't change." + }, + { + "text": "I can multiply by any number of orthogonal matrices, and the lengths don't change." + }, + { + "text": "Can we just see why that's true?" + }, + { + "text": "How would you show?" + }, + { + "text": "So what do we have to go on?" + }, + { + "text": "What we have to go on is Q transpose Q equal I." + }, + { + "text": "Whatever we're going to prove, it's got to come out of that, because that's all we know." + }, + { + "text": "So how do I use that to get that one?" + }, + { + "text": "Well, we haven't said a whole lot about lengths, but you'll see it all now." + }, + { + "text": "It'll be easier to prove that the squares are the same." + }, + { + "text": "So what's the matrix expression for the length squared?" + }, + { + "text": "What's the right-hand side of that equation?" + }, + { + "text": "X transpose x, right?" + }, + { + "text": "X transpose x gives me the sum of the squares." + }, + { + "text": "Pythagoras says that's the length squared." + }, + { + "text": "So that right-hand side is x transpose x." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk5.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..fe88faea55ca7fdbade0e4cf0f0a9f66df2465b8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "What's the left side?" + }, + { + "text": "It's the length squared of this, of Qx." + }, + { + "text": "So it must be the same as Qx, transpose Qx." + }, + { + "text": "And the claim is that that equation holds." + }, + { + "text": "And do you see it?" + }, + { + "text": "Where is it?" + }, + { + "text": "So any property from Q has to just come out directly from that." + }, + { + "text": "Where is it here?" + }, + { + "text": "Do I just push away a little bit at that left-hand side and see it?" + }, + { + "text": "Qx transpose is the same as x transpose Q transpose." + }, + { + "text": "And Qx is Qx." + }, + { + "text": "And now I'm seeing, well, you might say, wait a minute." + }, + { + "text": "The parentheses were there and there." + }, + { + "text": "But I say the most important law for matrix multiplication is you can move parentheses or throw them away." + }, + { + "text": "Let's throw them away." + }, + { + "text": "So in here, I'm seeing Q transpose Q, which is the identity." + }, + { + "text": "So it's true." + }, + { + "text": "So that means that you never underflow or overflow when you're multiplying by Q." + }, + { + "text": "Every numerical algorithm is written to use orthogonal matrices wherever it can." + }, + { + "text": "And here's the first example." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk6.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..962dbdc98b0f27e37ce73e12c9ffbe343c8dddd5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I think it may be good for me to think of other examples or for us to think of other examples of orthogonal matrices." + }, + { + "text": "So I'm using that word orthogonal matrix." + }, + { + "text": "We should really be saying orthonormal." + }, + { + "text": "And I'm really thinking mostly of square ones." + }, + { + "text": "So in the square case, when Q transpose is Q inverse." + }, + { + "text": "Of course, that fact makes it easy to solve all equations that have Q as a coefficient matrix, because you want the inverse and you just use the transpose." + }, + { + "text": "OK, let's just take some minutes to think of examples of Qs, if they're so important there have to be interesting examples." + }, + { + "text": "And that was a first one." + }, + { + "text": "Now, there's one more 2 by 2 example that you should know." + }, + { + "text": "Do you know what that would be?" + }, + { + "text": "So this will be example 2." + }, + { + "text": "And it's also going to be only 2 by 2 and real." + }, + { + "text": "And what possibility have I got left here?" + }, + { + "text": "I'll use the same first column, cos theta, sine theta, because that's more or less any unit vector in two dimensions." + }, + { + "text": "This has got that form." + }, + { + "text": "So what do you propose for the second column?" + }, + { + "text": "Yes?" + }, + { + "text": "Yeah, put the minus sign down here." + }, + { + "text": "So you think, does that make any difference?" + }, + { + "text": "So sine theta and minus cos theta." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk7.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..518d307339e6889aea8a3bded1efa411a6f5745a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "I don't know if you've ever looked at that matrix." + }, + { + "text": "We're trying to collect together a few matrices that are worth knowing, are worth looking at." + }, + { + "text": "OK, now what's happened here?" + }, + { + "text": "You may say that was a trivial change, which it kind of was." + }, + { + "text": "But it's a different matrix now." + }, + { + "text": "It's not a rotation anymore." + }, + { + "text": "That's not a rotation." + }, + { + "text": "And yeah, somehow, now it's symmetric." + }, + { + "text": "And yeah, its eigenvectors must be something or other." + }, + { + "text": "We'll get to those." + }, + { + "text": "But what does that matrix do?" + }, + { + "text": "I don't know if you've seen it." + }, + { + "text": "If you haven't, it doesn't jump out." + }, + { + "text": "But it's an important case." + }, + { + "text": "This is a reflection matrix." + }, + { + "text": "Notice that it's determined it is minus 1." + }, + { + "text": "You have minus cos squared theta minus sine squared theta." + }, + { + "text": "It's determined it is minus 1." + }, + { + "text": "There's some eigenvalue coming up that's got a minus." + }, + { + "text": "Yeah." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk8.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..481458df8b0fa0d4060f8a9ff2fad9395e817b04 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, so what do I mean by a reflection matrix?" + }, + { + "text": "Let me draw the plane." + }, + { + "text": "And I think, so 1, 0." + }, + { + "text": "Let's follow it again." + }, + { + "text": "1, 0, where does that go?" + }, + { + "text": "That gives me the first column." + }, + { + "text": "So as before, it goes to cos theta sine theta." + }, + { + "text": "And when I say reflection, let me put the mirror into the picture." + }, + { + "text": "So you see what reflection it is." + }, + { + "text": "The mirror is along here at angle theta over 2, theta over 2 line." + }, + { + "text": "So sure enough, 1, 0 at angle 0 got reflected into a unit vector at angle theta." + }, + { + "text": "And halfway between was the theta over 2 line." + }, + { + "text": "That's OK. Now, what about the other guy, 0, 1?" + }, + { + "text": "Here's 0, 1." + }, + { + "text": "OK, I multiply that." + }, + { + "text": "Can I put the 0, 1 up here so your eye does the multiplication?" + }, + { + "text": "Where is the result of 0, 1?" + }, + { + "text": "What's the output from Q applied to 0, 1?" + }, + { + "text": "Sine theta minus cos theta, right?" + }, + { + "text": "It's the second column." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk9.json b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..27a460130a0a8d38fe662c57a511c467a303fbb9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/Xa2jPbURTjQ_5_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "And so where is that?" + }, + { + "text": "Well, it's perpendicular to that guy." + }, + { + "text": "That's what I know, right?" + }, + { + "text": "That was the point, that the two columns are perpendicular." + }, + { + "text": "So it must go down this way, right?" + }, + { + "text": "Sine theta, cos theta." + }, + { + "text": "And it doesn't change length." + }, + { + "text": "All these facts that we just learned are key." + }, + { + "text": "So there's 0, 1, and it goes to this guy, which is whatever that second column is, sine theta minus cos theta." + }, + { + "text": "And if you check that, actually, gosh, this is like plain geometry." + }, + { + "text": "I believe, it's never occurred to me before, but I believe it, that this angle going down to there, that that goes straight through, and that the halfway one is that line." + }, + { + "text": "Yeah, I think that picture has got it, and I think it's in the notes." + }, + { + "text": "So that's a reflection matrix." + }, + { + "text": "Well, that's a 2 by 2 reflection matrix." + }, + { + "text": "Would you like to see some other matrices like this one, but larger?" + }, + { + "text": "They're named after a guy named Householder." + }, + { + "text": "So these are Householder reflections." + }, + { + "text": "What am I doing here?" + }, + { + "text": "I'm collecting together some orthogonal matrices that are useful and important." + }, + { + "text": "And Householder found a whole bunch of them, and his algorithm is a much used part of numerical linear algebra." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk0.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..aa961d524ea0d1287b995e40358f71afcd69bfb1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "JOHN TSITSIKLIS: Today we're going to finish our discussion of the Poisson process." + }, + { + "text": "We're going to see a few of its properties, do a few interesting problems, some more interesting than others." + }, + { + "text": "So go through a few examples and then we're going to talk about some quite strange things that happen with the Poisson process." + }, + { + "text": "So the first thing is to remember what the Poisson processes is." + }, + { + "text": "It's a model, let's say, of arrivals of customers that are, in some sense, quote unquote, completely random, that is a customer can arrive at any point in time." + }, + { + "text": "All points in time are equally likely." + }, + { + "text": "And different points in time are sort of independent of other points in time." + }, + { + "text": "So the fact that I got an arrival now doesn't tell me anything about whether there's going to be an arrival at some other time." + }, + { + "text": "In some sense, it's a continuous time version of the Bernoulli process." + }, + { + "text": "So the best way to think about the Poisson process is that we divide time into extremely tiny slots." + }, + { + "text": "And in each time slot, there's an independent possibility of having an arrival." + }, + { + "text": "Different time slots are independent of each other." + }, + { + "text": "On the other hand, when the slot is tiny, the probability for obtaining an arrival during that tiny slot is itself going to be tiny." + }, + { + "text": "So we capture these properties into a formal definition what the Poisson process is." + }, + { + "text": "We have a probability mass function for the number of arrivals, k, during an interval of a given length." + }, + { + "text": "So this is the sort of basic description of the distribution of the number of arrivals." + }, + { + "text": "So tau is fixed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk1.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..8ef79a1bbf5e44814915347122880462d60e3970 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And k is the parameter." + }, + { + "text": "So when we add over all k's, the sum of these probabilities has to be equal to 1." + }, + { + "text": "There's a time homogeneity assumption, which is hidden in this, namely, the only thing that matters is the duration of the time interval, not where the time interval sits on the real axis." + }, + { + "text": "Then we have an independence assumption." + }, + { + "text": "Intervals that are disjoint are statistically independent from each other." + }, + { + "text": "So any information you give me about arrivals during this time interval doesn't change my beliefs about what's going to happen during another time interval." + }, + { + "text": "So this is a generalization of the idea that we had in Bernoulli processes that different time slots are independent of each other." + }, + { + "text": "And then to specify this function, the distribution of the number of arrivals, we sort of go in stages." + }, + { + "text": "We first specify this function for the case where the time interval is very small." + }, + { + "text": "And I'm telling you what those probabilities will be." + }, + { + "text": "And based on these then, we do some calculations and to find the formula for the distribution of the number of arrivals for intervals of a general duration." + }, + { + "text": "So for a small duration, delta, the probability of obtaining 1 arrival is lambda delta." + }, + { + "text": "The remaining probability is assigned to the event that we get to no arrivals during that interval." + }, + { + "text": "The probability of obtaining more than 1 arrival in a tiny interval is essentially 0." + }, + { + "text": "And when we say essentially, it's means modular, terms that of order delta squared." + }, + { + "text": "And when delta is very small, anything which is delta squared can be ignored." + }, + { + "text": "So up to delta squared terms, that's what happened during a little interval." + }, + { + "text": "Now if we know the probability distribution for the number of arrivals in a little interval." + }, + { + "text": "We can use this to get the distribution for the number of arrivals over several intervals." + }, + { + "text": "How do we do that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk10.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c993d1aafbcf3de55a33d47639c163aee1857626 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So the expected time is 1 over lambda." + }, + { + "text": "And in our case this, is 1/0.6." + }, + { + "text": "Finally, if I tell you that I have been fishing for 4 hours and nothing has been caught so far, how much do you expect this quantity to be?" + }, + { + "text": "Here is the story that, again, that for the Poisson process used is as good as new." + }, + { + "text": "The process does not have any memory." + }, + { + "text": "Given what happens in the past doesn't matter for the future." + }, + { + "text": "It's as if the process starts new at this point in time." + }, + { + "text": "So this one is going to be, again, the same exponentially distributed random variable with the same parameter lambda." + }, + { + "text": "So expected time until an arrival comes is an exponential distribut -- has an exponential distribution with parameter lambda, no matter what has happened in the past." + }, + { + "text": "Starting from now and looking into the future, it's as if the process has just started." + }, + { + "text": "So it's going to be 1 over lambda, which is 1/0.6." + }, + { + "text": "OK. Now our next example is going to be a little more complicated or subtle." + }, + { + "text": "But before we get to the example, let's refresh our memory about what we discussed last time about merging Poisson independent Poisson processes." + }, + { + "text": "Instead of drawing the picture that way, another way we could draw it could be this." + }, + { + "text": "We have a Poisson process with rate lambda1, and a Poisson process with rate lambda2." + }, + { + "text": "They have, each one of these, have their arrivals." + }, + { + "text": "And then we form the merged process." + }, + { + "text": "And the merged process records an arrival whenever there's an arrival in either of the two processes." + }, + { + "text": "This process in that process are assumed to be independent of each other." + }, + { + "text": "Now different times in this process and that process are independent of each other." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk11.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..98f4de8fc7edf6671add64512cd98e8481dce843 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what happens in these two time intervals is independent from what happens in these two time intervals." + }, + { + "text": "These two time intervals to determine what happens here." + }, + { + "text": "These two time intervals determine what happens there." + }, + { + "text": "So because these are independent from these, this means that this is also independent from that." + }, + { + "text": "So the independence assumption is satisfied for the merged process." + }, + { + "text": "And the merged process turns out to be a Poisson process." + }, + { + "text": "And if you want to find the arrival rate for that process, you argue as follows." + }, + { + "text": "During a little interval of length delta, we have probability lambda1 delta of having an arrival in this process." + }, + { + "text": "We have probability lambda2 delta of an arrival in this process, plus second order terms in delta, which we're ignoring." + }, + { + "text": "And then you do the calculation and you find that in this process, you're going to have an arrival probability, which is lambda1 plus lambda2, again ignoring second order in delta-- terms that are second order in delta." + }, + { + "text": "So the merged process is a Poisson process whose arrival rate is the sum of the arrival rates of the individual processes." + }, + { + "text": "And the calculation we did at the end of the last lecture-- If I tell you that the new arrival happened here, where did that arrival come from?" + }, + { + "text": "Did it come from here or from there?" + }, + { + "text": "If the lambda1 is equal to lambda2, then by symmetry you would say that it's equally likely to have come from here or to come from there." + }, + { + "text": "But if this lambda is much bigger than that lambda, the fact that they saw an arrival is more likely to have come from there." + }, + { + "text": "And the formula that captures this is the following." + }, + { + "text": "This is the probability that my arrival has come from this particular stream rather than that particular stream." + }, + { + "text": "So when an arrival comes and you ask, what is the origin of that arrival?" + }, + { + "text": "It's as if I'm flipping a coin with these odds." + }, + { + "text": "And depending on outcome of that coin, I'm going to tell you came from there or it came from there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk12.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..b81514a3614b4cc14097ef6ee9b3469bf3d09d24 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "So the origin of an arrival is either this stream or that stream." + }, + { + "text": "And this is the probability that the origin of the arrival is that one." + }, + { + "text": "Now if we look at 2 different arrivals, and we ask about their origins-- So let's think about the origin of this arrival and compare it with the origin that arrival." + }, + { + "text": "The origin of this arrival is random." + }, + { + "text": "It could be right be either this or that." + }, + { + "text": "And this is the relevant probability." + }, + { + "text": "The origin of that arrival is random." + }, + { + "text": "It could be either here or is there, and again, with the same relevant probability." + }, + { + "text": "Question." + }, + { + "text": "The origin of this arrival, is it dependent or independent from the origin that arrival?" + }, + { + "text": "And here's how the argument goes." + }, + { + "text": "Separate times are independent." + }, + { + "text": "Whatever has happened in the process during this set of times is independent from whatever happened in the process during that set of times." + }, + { + "text": "Because different times have nothing to do with each other, the origin of this, of an arrival here, has nothing to do with the origin of an arrival there." + }, + { + "text": "So the origins of different arrivals are also independent random variables." + }, + { + "text": "So if I tell you that-- yeah." + }, + { + "text": "OK." + }, + { + "text": "So it as if that each time that you have an arrival in the merge process, it's as if you're flipping a coin to determine where did that arrival came from and these coins are independent of each other." + }, + { + "text": "OK. OK. Now we're going to use this-- what we know about merged processes to solve the problem that would be harder to do, if you were not using ideas from Poisson processes." + }, + { + "text": "So the formulation of the problem has nothing to do with the Poisson process." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk13.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..bf6c66b1e38f68ac6bd19d504f54b3d7f0681a3c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "The formulation is the following." + }, + { + "text": "We have 3 light-bulbs." + }, + { + "text": "And each light bulb is independent and is going to die out at the time that's exponentially distributed." + }, + { + "text": "So 3 light bulbs." + }, + { + "text": "They start their lives and then at some point they die or burn out." + }, + { + "text": "So let's think of this as X, this as Y, and this as Z." + }, + { + "text": "And we're interested in the time until the last light-bulb burns out." + }, + { + "text": "So we're interested in the maximum of the 3 random variables, X, Y, and Z." + }, + { + "text": "And in particular, we want to find the expected value of this maximum." + }, + { + "text": "OK." + }, + { + "text": "So you can do derived distribution, use the expected value rule, anything you want." + }, + { + "text": "You can get this answer using the tools that you already have in your hands." + }, + { + "text": "But now let us see how we can connect to this picture with a Poisson picture and come up with the answer in a very simple way." + }, + { + "text": "What is an exponential random variable?" + }, + { + "text": "An exponential random variable is the first act in the long play that involves a whole Poisson process." + }, + { + "text": "So an exponential random variable is the first act of a Poisson movie." + }, + { + "text": "Same thing here." + }, + { + "text": "You can think of this random variable as being part of some Poisson process that has been running." + }, + { + "text": "So it's part of this bigger picture." + }, + { + "text": "We're still interested in the maximum of the 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk14.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..1a92d35ab267e8941975fcfa559b335f37209c80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "The other arrivals are not going to affect our answers." + }, + { + "text": "It's just, conceptually speaking, we can think of the exponential random variable as being embedded in a bigger Poisson picture." + }, + { + "text": "So we have 3 Poisson process that are running in parallel." + }, + { + "text": "Let us split the expected time until the last burnout into pieces, which is time until the first burnout, time from the first until the second, and time from the second until the third." + }, + { + "text": "And find the expected values of each one of these pieces." + }, + { + "text": "What can we say about the expected value of this?" + }, + { + "text": "This is the first arrival out of all of these 3 Poisson processes." + }, + { + "text": "It's the first event that happens when you look at all of these processes simultaneously." + }, + { + "text": "So 3 Poisson processes running in parallel." + }, + { + "text": "We're interested in the time until one of them, any one of them, gets in arrival." + }, + { + "text": "Rephrase." + }, + { + "text": "We merged the 3 Poisson processes, and we ask for the time until we observe an arrival in the merged process." + }, + { + "text": "When 1 of the 3 gets an arrival for the first time, the merged process gets its first arrival." + }, + { + "text": "So what's the expected value of this time until the first burnout?" + }, + { + "text": "It's going to be the expected value of a Poisson random variable." + }, + { + "text": "So the first burnout is going to have an expected value, which is-- OK." + }, + { + "text": "It's a Poisson process." + }, + { + "text": "The merged process of the 3 has a collective arrival rate, which is 3 times lambda." + }, + { + "text": "So this is the parameter over the exponential distribution that describes the time until the first arrival in the merged process." + }, + { + "text": "And the expected value of this random variable is 1 over that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk15.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..ec2818bb27b6b5b81e6f20bc450cb58a1baac245 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "When you have an exponential random variable with parameter lambda, the expected value of that random variable is 1 over lambda." + }, + { + "text": "Here we're talking about the first arrival time in a process with rate 3 lambda." + }, + { + "text": "The expected time until the first arrival is 1 over (3 lambda)." + }, + { + "text": "Alright." + }, + { + "text": "So at this time, this bulb, this arrival happened, this bulb has been burned." + }, + { + "text": "So we don't care about that bulb anymore." + }, + { + "text": "We start at this time, and we look forward." + }, + { + "text": "This bulb has been burned." + }, + { + "text": "So let's just look forward from now on." + }, + { + "text": "What have we got?" + }, + { + "text": "We have two bulbs that are burning." + }, + { + "text": "We have a Poisson process that's the bigger picture of what could happen to that light bulb, if we were to keep replacing it." + }, + { + "text": "Another Poisson process." + }, + { + "text": "These two processes are, again, independent." + }, + { + "text": "From this time until that time, how long does it take?" + }, + { + "text": "It's the time until either this process records an arrival or that process records and arrival." + }, + { + "text": "That's the same as the time that the merged process of these two records an arrival." + }, + { + "text": "So we're talking about the expected time until the first arrival in a merged process." + }, + { + "text": "The merged process is Poisson." + }, + { + "text": "It's Poisson with rate 2 lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk16.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..6a74ed00548100b2fa7d07c494546d15ecdfac23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that extra time is going to take-- the expected value is going to be 1 over the (rate of that Poisson process)." + }, + { + "text": "So 1 over (2 lambda) is the expected value of this random variable." + }, + { + "text": "So at this point, this bulb now is also burned." + }, + { + "text": "So we start looking from this time on." + }, + { + "text": "That part of the picture disappears." + }, + { + "text": "Starting from this time, what's the expected value until that remaining light-bulb burns out?" + }, + { + "text": "Well, as we said before, in a Poisson process or with exponential random variables, we have memorylessness." + }, + { + "text": "A used bulb is as good as a new one." + }, + { + "text": "So it's as if we're starting from scratch here." + }, + { + "text": "So this is going to be an exponential random variable with parameter lambda." + }, + { + "text": "And the expected value of it is going to be 1 over lambda." + }, + { + "text": "So the beauty of approaching this problem in this particular way is, of course, that we manage to do everything without any calculus at all, without striking an integral, without trying to calculate expectations in any form." + }, + { + "text": "Most of the non-trivial problems that you encounter in the Poisson world basically involve tricks of these kind." + }, + { + "text": "You have a question and you try to rephrase it, trying to think in terms of what might happen in the Poisson setting, use memorylessness, use merging, et cetera, et cetera." + }, + { + "text": "Now we talked about merging." + }, + { + "text": "It turns out that the splitting of Poisson processes also works in a nice way." + }, + { + "text": "The story here is exactly the same as for the Bernoulli process." + }, + { + "text": "So I'm having a Poisson process." + }, + { + "text": "And each time, with some rate lambda, and each time that an arrival comes, I'm going to send it to that stream and the record an arrival here with some probability P. And I'm going to send it to the other stream with some probability 1 minus P. So either of this will happen or that will happen, depending on the outcome of the coin flip that I do." + }, + { + "text": "Each time that then arrival occurs, I flip a coin and I decide whether to record it here or there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk17.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..24ef2d939ecec102e5b0cf66c4aef963c1195410 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "This is called splitting a Poisson process into two pieces." + }, + { + "text": "What kind of process do we get here?" + }, + { + "text": "If you look at the little interval for length delta, what's the probability that this little interval gets an arrival?" + }, + { + "text": "It's the probability that this one gets an arrival, which is lambda delta times the probability that after I get an arrival my coin flip came out to be that way, so that it sends me there." + }, + { + "text": "So this means that this little interval is going to have probability lambda delta P. Or maybe more suggestively, I should write it as lambda P times delta." + }, + { + "text": "So every little interval has a probability of an arrival proportional to delta." + }, + { + "text": "The proportionality factor is lambda P. So lambda P is the rate of that process." + }, + { + "text": "And then you go through the mental exercise that you went through for the Bernoulli process to argue that a different intervals here are independent and so on." + }, + { + "text": "And that completes checking that this process is going to be a Poisson process." + }, + { + "text": "So when you split a Poisson process by doing independent coin flips each time that something happens, the processes that you get is again a Poisson process, but of course with a reduced rate." + }, + { + "text": "So instead of the word splitting, sometimes people also use the words thinning-out." + }, + { + "text": "That is, out of the arrivals that came, you keep a few but throw away a few." + }, + { + "text": "OK." + }, + { + "text": "So now the last topic over this lecture is a quite curious phenomenon that goes under the name of random incidents." + }, + { + "text": "So here's the story." + }, + { + "text": "Buses have been running on Mass Ave. from time immemorial." + }, + { + "text": "And the bus company that runs the buses claims that they come as a Poisson process with some rate, let's say, of 4 buses per hour." + }, + { + "text": "So that the expected time between bus arrivals is going to be 15 minutes." + }, + { + "text": "OK. Alright." + }, + { + "text": "So people have been complaining that they have been showing up there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk18.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..65a62f83b762cf608024e3af374f28f51f49e32f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "They think the buses are taking too long." + }, + { + "text": "So you are asked to investigate." + }, + { + "text": "Is the company-- Does it operate according to its promises or not." + }, + { + "text": "So you send an undercover agent to go and check the interarrival times of the buses." + }, + { + "text": "Are they 15 minutes?" + }, + { + "text": "Or are they longer?" + }, + { + "text": "So you put your dark glasses and you show up at the bus stop at some random time." + }, + { + "text": "And you go and ask the guy in the falafel truck, how long has it been since the last arrival?" + }, + { + "text": "So of course that guy works for the FBI, right?" + }, + { + "text": "So they tell you, well, it's been, let's say, 12 minutes since the last bus arrival." + }, + { + "text": "And then you say, \"Oh, 12 minutes." + }, + { + "text": "Average time is 15." + }, + { + "text": "So a bus should be coming any time now.\"" + }, + { + "text": "Is that correct?" + }, + { + "text": "No, you wouldn't think that way." + }, + { + "text": "It's a Poisson process." + }, + { + "text": "It doesn't matter how long it has been since the last bus arrival." + }, + { + "text": "So you don't go through that fallacy." + }, + { + "text": "Instead of predicting how long it's going to be, you just sit down there and wait and measure the time." + }, + { + "text": "And you find that this is, let's say, 11 minutes." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk19.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..af599f5b8f4c3fc0973b37e81b36088c85eae997 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you go to your boss and report, \"Well, it took-- I went there and the time from the previous bus to the next one was 23 minutes." + }, + { + "text": "It's more than the 15 that they said.\"" + }, + { + "text": "So go and do that again." + }, + { + "text": "You go day after day." + }, + { + "text": "You keep these statistics of the length of this interval." + }, + { + "text": "And you tell your boss it's a lot more than 15." + }, + { + "text": "It tends to be more like 30 or so." + }, + { + "text": "So the bus company is cheating us." + }, + { + "text": "Does the bus company really run Poisson buses at the rate that they have promised?" + }, + { + "text": "Well let's analyze the situation here and figure out what the length of this interval should be, on the average." + }, + { + "text": "The naive argument is that this interval is an interarrival time." + }, + { + "text": "And interarrival times, on the average, are 15 minutes, if the company runs indeed Poisson processes with these interarrival times." + }, + { + "text": "But actually the situation is a little more subtle because this is not a typical interarrival interval." + }, + { + "text": "This interarrival interval consists of two pieces." + }, + { + "text": "Let's call them T1 and T1 prime." + }, + { + "text": "What can you tell me about those two random variables?" + }, + { + "text": "What kind of random variable is T1?" + }, + { + "text": "Starting from this time, with the Poisson process, the past doesn't matter." + }, + { + "text": "It's the time until an arrival happens." + }, + { + "text": "So T1 is going to be an exponential random variable with parameter lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk2.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..ebc6083b4940b3fc27511f672c179a7846abc0b1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "The big interval is composed of many little intervals." + }, + { + "text": "Each little interval is independent from any other little interval, so is it is as if we have a sequence of Bernoulli trials." + }, + { + "text": "Each Bernoulli trial is associated with a little interval and has a small probability of obtaining a success or an arrival during that mini-slot." + }, + { + "text": "On the other hand, when delta is small, and you take a big interval and chop it up, you get a large number of little intervals." + }, + { + "text": "So what we essentially have here is a Bernoulli process, in which is the number of trials is huge but the probability of success during any given trial is tiny." + }, + { + "text": "The average number of trials ends up being proportional to the length of the interval." + }, + { + "text": "If you have twice as large an interval, it's as if you're having twice as many over these mini-trials, so the expected number of arrivals will increase proportionately." + }, + { + "text": "There's also this parameter lambda, which we interpret as expected number of arrivals per unit time." + }, + { + "text": "And it comes in those probabilities here." + }, + { + "text": "When you double lambda, this means that a little interval is twice as likely to get an arrival." + }, + { + "text": "So you would expect to get twice as many arrivals as well." + }, + { + "text": "That's why the expected number of arrivals during an interval of length tau also scales proportional to this parameter lambda." + }, + { + "text": "Somewhat unexpectedly, it turns out that the variance of the number of arrivals is also the same as the mean." + }, + { + "text": "This is a peculiarity that happens in the Poisson process." + }, + { + "text": "So this is one way of thinking about Poisson process, in terms of little intervals, each one of which has a tiny probability of success." + }, + { + "text": "And we think of the distribution associated with that process as being described by this particular PMF." + }, + { + "text": "So this is the PMF for the number of arrivals during an interval of a fixed duration, tau." + }, + { + "text": "It's a PMF that extends all over the entire range of non-negative integers." + }, + { + "text": "So the number of arrivals you can get during an interval for certain length can be anything." + }, + { + "text": "You can get as many arrivals as you want." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk20.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..28349ba5d13c19b16a2957596215f8e4b02bbf01 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "So in particular, the expected value of T1 is going to be 15 by itself." + }, + { + "text": "How about the random variable T1 prime." + }, + { + "text": "What kind of random variable is it?" + }, + { + "text": "This is like the first arrival in a Poisson process that runs backwards in time." + }, + { + "text": "What kind of process is a Poisson process running backwards in time?" + }, + { + "text": "Let's think of coin flips." + }, + { + "text": "Suppose you have a movie of coin flips." + }, + { + "text": "And for some accident, that fascinating movie, you happen to watch it backwards." + }, + { + "text": "Will it look any different statistically?" + }, + { + "text": "No." + }, + { + "text": "It's going to be just the sequence of random coin flips." + }, + { + "text": "So a Bernoulli process that's runs in reverse time is statistically identical to a Bernoulli process in forward time." + }, + { + "text": "The Poisson process is a limit of the Bernoulli." + }, + { + "text": "So, same story with the Poisson process." + }, + { + "text": "If you run it backwards in time it looks the same." + }, + { + "text": "So looking backwards in time, this is a Poisson process." + }, + { + "text": "And T1 prime is the time until the first arrival in this backward process." + }, + { + "text": "So T1 prime is also going to be an exponential random variable with the same parameter, lambda." + }, + { + "text": "And the expected value of T1 prime is 15." + }, + { + "text": "Conclusion is that the expected length of this interval is going to be 30 minutes." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk21.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..e60bcef503b4a0db026939c13f85514e5dcb0817 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the fact that this agent found the average to be something like 30 does not contradict the claims of the bus company that they're running Poisson buses with a rate of lambda equal to 4." + }, + { + "text": "OK." + }, + { + "text": "So maybe the company can this way-- they can defend themselves in court." + }, + { + "text": "But there's something puzzling here." + }, + { + "text": "How long is the interarrival time?" + }, + { + "text": "Is it 15?" + }, + { + "text": "Or is it 30?" + }, + { + "text": "On the average." + }, + { + "text": "The issue is what do we mean by a typical interarrival time." + }, + { + "text": "When we say typical, we mean some kind of average." + }, + { + "text": "But average over what?" + }, + { + "text": "And here's two different ways of thinking about averages." + }, + { + "text": "You number the buses." + }, + { + "text": "And you have bus number 100." + }, + { + "text": "You have bus number 101, bus number 102, bus number 110, and so on." + }, + { + "text": "One way of thinking about averages is that you pick a bus number at random." + }, + { + "text": "I pick, let's say, that bus, all buses being sort of equally likely to be picked." + }, + { + "text": "And I measure this interarrival time." + }, + { + "text": "So for a typical bus." + }, + { + "text": "Then, starting from here until there, the expected time has to be 1 over lambda, for the Poisson process." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk22.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..859fef7a50c29d5a5a9f8517f4db560ee5d550a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But what we did in this experiment was something different." + }, + { + "text": "We didn't pick a bus at random." + }, + { + "text": "We picked a time at random." + }, + { + "text": "And if the picture is, let's say, this way, I'm much more likely to pick this interval and therefore this interarrival time, rather than that interval." + }, + { + "text": "Because, this interval corresponds to very few times." + }, + { + "text": "So if I'm picking a time at random and, in some sense, let's say, uniform, so that all times are equally likely, I'm much more likely to fall inside a big interval rather than a small interval." + }, + { + "text": "So a person who shows up at the bus stop at a random time." + }, + { + "text": "They're selecting an interval in a biased way, with the bias favor of longer intervals." + }, + { + "text": "And that's why what they observe is a random variable that has a larger expected value then the ordinary expected value." + }, + { + "text": "So the subtlety here is to realize that we're talking between two different kinds of experiments." + }, + { + "text": "Picking a bus number at random verses picking an interval at random with a bias in favor of longer intervals." + }, + { + "text": "Lots of paradoxes that one can cook up using Poisson processes and random processes in general often have to do with the story of this kind." + }, + { + "text": "The phenomenon that we had in this particular example also shows up in general, whenever you have other kinds of arrival processes." + }, + { + "text": "So the Poisson process is the simplest arrival process there is, where the interarrival times are exponential random variables." + }, + { + "text": "There's a larger class of models." + }, + { + "text": "They're called renewal processes, in which, again, we have a sequence of successive arrivals, interarrival times are identically distributed and independent, but they may come from a general distribution." + }, + { + "text": "So to make the same point of the previous example but in a much simpler setting, suppose that bus interarrival times are either 5 or 10 minutes apart." + }, + { + "text": "So you get some intervals that are of length 5." + }, + { + "text": "You get some that are of length 10." + }, + { + "text": "And suppose that these are equally likely." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk23.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..0c23f2ec29db9e794aae974425a9309fbc5fa392 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "So we have -- not exactly -- In the long run, we have as many 5 minute intervals as we have 10 minute intervals." + }, + { + "text": "So the average interarrival time is 7 and 1/2." + }, + { + "text": "But if a person shows up at a random time, what are they going to see?" + }, + { + "text": "Do we have as many 5s as 10s?" + }, + { + "text": "But every 10 covers twice as much space." + }, + { + "text": "So if I show up at a random time, I have probability 2/3 falling inside an interval of duration 10." + }, + { + "text": "And I have one 1/3 probability of falling inside an interval of duration 5." + }, + { + "text": "That's because, out of the whole real line, 2/3 of it is covered by intervals of length 10, just because they're longer." + }, + { + "text": "1/3 is covered by the smaller intervals." + }, + { + "text": "Now if I fall inside an interval of length 10 and I measure the length of the interval that I fell into, that's going to be 10." + }, + { + "text": "But if I fall inside an interval of length 5 and I measure how long it is, I'm going to get a 5." + }, + { + "text": "And that, of course, is going to be different than 7.5." + }, + { + "text": "OK. And which number should be bigger?" + }, + { + "text": "It's the second number that's bigger because this one is biased in favor of the longer intervals." + }, + { + "text": "So that's, again, another illustration of the different results that you get when you have this random incidence phenomenon." + }, + { + "text": "So the bottom line, again, is that if you talk about a typical interarrival time, one must be very precise in specifying what we mean typical." + }, + { + "text": "So typical means sort of random." + }, + { + "text": "But to use the word random, you must specify very precisely what is the random experiment that you are using." + }, + { + "text": "And if you're not careful, you can get into apparent puzzles, such as the following." + }, + { + "text": "Suppose somebody tells you the average family size is 4, but the average person lives in a family of size 6." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk24.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..f1454166977d85230e828ad2593835dff01c5eed --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Is that compatible?" + }, + { + "text": "Family size is 4 on the average, but typical people live, on the average, in families of size 6." + }, + { + "text": "Well yes." + }, + { + "text": "There's no contradiction here." + }, + { + "text": "We're talking about two different experiments." + }, + { + "text": "In one experiment, I pick a family at random, and I tell you the average family is 4." + }, + { + "text": "In another experiment, I pick a person at random and I tell you that this person, on the average, will be in their family of size 6." + }, + { + "text": "And what is the catch here?" + }, + { + "text": "That if I pick a person at random, large families are more likely to be picked." + }, + { + "text": "So there's a bias in favor of large families." + }, + { + "text": "Or if you want to survey, let's say, are trains crowded in your city?" + }, + { + "text": "Or are buses crowded?" + }, + { + "text": "One choice is to pick a bus at random and inspect how crowded it is." + }, + { + "text": "Another choice is to pick a typical person and ask them, \"Did you ride the bus today?" + }, + { + "text": "Was it's crowded?\"" + }, + { + "text": "Well suppose that in this city there's one bus that's extremely crowded and all the other buses are completely empty." + }, + { + "text": "If you ask a person." + }, + { + "text": "\"Was your bus crowded?\"" + }, + { + "text": "They will tell you, \"Yes, my bus was crowded.\"" + }, + { + "text": "There's no witness from the empty buses to testify in their favor." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk25.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..5ea6070c380c8c0cc3ed8ff41fe3f0d64a2f6192 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk25.json @@ -0,0 +1,23 @@ +[ + { + "text": "So by sampling people instead of sampling buses, you're going to get different result." + }, + { + "text": "And in the process industry, if your job is to inspect and check cookies, you will be faced with a big dilemma." + }, + { + "text": "Do you want to find out how many chocolate chips there are on a typical cookie?" + }, + { + "text": "Are you going to interview cookies or are you going to interview chocolate chips and ask them how many other chips where there on your cookie?" + }, + { + "text": "And you're going to get different answers in these cases." + }, + { + "text": "So moral is, one has to be very precise on how you formulate the sampling procedure that you have." + }, + { + "text": "And you'll get different answers." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk3.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..65f67102a7086dbc76d65afeddb2720c5b67bdb0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "Of course the probability of getting a zillion arrivals is going to be tiny." + }, + { + "text": "But in principle, this is possible." + }, + { + "text": "And that's because an interval, even if it's a fixed length, consists of an infinite number of mini-slots in some sense." + }, + { + "text": "You can divide, chop it up, into as many mini-slots as you want." + }, + { + "text": "So in principle, it's possible that every mini-slot gets an arrival." + }, + { + "text": "In principle, it's possible to get an arbitrarily large number of arrivals." + }, + { + "text": "So this particular formula here is not very intuitive when you look at it." + }, + { + "text": "But it's a legitimate PMF." + }, + { + "text": "And it's called the Poisson PMF." + }, + { + "text": "It's the PMF that describes the number of arrivals." + }, + { + "text": "So that's one way of thinking about the Poisson process, where the basic object of interest would be this PMF and you try to work with it." + }, + { + "text": "There's another way of thinking about what happens in the Poisson process." + }, + { + "text": "And this has to do with letting things evolve in time." + }, + { + "text": "You start at time 0." + }, + { + "text": "There's going to be a time at which the first arrival occurs, and call that time T1." + }, + { + "text": "This time turns out to have an exponential distribution with parameter lambda." + }, + { + "text": "Once you get an arrival, it's as if the process starts fresh." + }, + { + "text": "The best way to understand why this is the case is by thinking in terms of the analogy with the Bernoulli process." + }, + { + "text": "If you believe that statement for the Bernoulli process, since this is a limiting case, it should also be true." + }, + { + "text": "So starting from this time, we're going to wait a random amount of time until we get the second arrival This random amount of time, let's call it T2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk4.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c5affc1f1a5b3e0305dcd63ee178f3ba1a2da02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "This time, T2 is also going to have an exponential distribution with the same parameter, lambda." + }, + { + "text": "And these two are going to be independent of each other." + }, + { + "text": "OK?" + }, + { + "text": "So the Poisson process has all the same memorylessness properties that the Bernoulli process has." + }, + { + "text": "What's another way of thinking of this property?" + }, + { + "text": "So think of a process where you have a light bulb." + }, + { + "text": "The time at the light bulb burns out, you can model it by an exponential random variable." + }, + { + "text": "And suppose that they tell you that so far, we're are sitting at some time, T. And I tell you that the light bulb has not yet burned out." + }, + { + "text": "What does this tell you about the future of the light bulb?" + }, + { + "text": "Is the fact that they didn't burn out, so far, is it good news or is it bad news?" + }, + { + "text": "Would you rather keep this light bulb that has worked for t times steps and is still OK?" + }, + { + "text": "Or would you rather use a new light bulb that starts new at that point in time?" + }, + { + "text": "Because of the memorylessness property, the past of that light bulb doesn't matter." + }, + { + "text": "So the future of this light bulb is statistically the same as the future of a new light bulb." + }, + { + "text": "For both of them, the time until they burn out is going to be described an exponential distribution." + }, + { + "text": "So one way that people described the situation is to say that used is exactly as good as a new." + }, + { + "text": "So a used on is no worse than a new one." + }, + { + "text": "A used one is no better than a new one." + }, + { + "text": "So a used light bulb that hasn't yet burnt out is exactly as good as a new light bulb." + }, + { + "text": "So that's another way of thinking about the memorylessness that we have in the Poisson process." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk5.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..a8f4593b861f0c6ab6d24f9023bf2c98983b5ab3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "Back to this picture." + }, + { + "text": "The time until the second arrival is the sum of two independent exponential random variables." + }, + { + "text": "So, in principle, you can use the convolution formula to find the distribution of T1 plus T2, and that would be what we call Y2, the time until the second arrival." + }, + { + "text": "But there's also a direct way of obtaining to the distribution of Y2, and this is the calculation that we did last time on the blackboard." + }, + { + "text": "And actually, we did it more generally." + }, + { + "text": "We found the time until the case arrival occurs." + }, + { + "text": "It has a closed form formula, which is called the Erlang distribution with k degrees of freedom." + }, + { + "text": "So let's see what's going on here." + }, + { + "text": "It's a distribution Of what kind?" + }, + { + "text": "It's a continuous distribution." + }, + { + "text": "It's a probability density function." + }, + { + "text": "This is because the time is a continuous random variable." + }, + { + "text": "Time is continuous." + }, + { + "text": "Arrivals can happen at any time." + }, + { + "text": "So we're talking about the PDF." + }, + { + "text": "This k is just the parameter of the distribution." + }, + { + "text": "We're talking about the k-th arrival, so k is a fixed number." + }, + { + "text": "Lambda is another parameter of the distribution, which is the arrival rate So it's a PDF over the Y's, whereas lambda and k are parameters of the distribution." + }, + { + "text": "OK." + }, + { + "text": "So this was what we knew from last time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk6.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..f957b2a1915e0744ba6fb901fba06c158d7e336f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Just to get some practice, let us do a problem that's not too difficult, but just to see how we use the various formulas that we have." + }, + { + "text": "So Poisson was a mathematician, but Poisson also means fish in French." + }, + { + "text": "So Poisson goes fishing." + }, + { + "text": "And let's assume that fish are caught according to a Poisson process." + }, + { + "text": "That's not too bad an assumption." + }, + { + "text": "At any given point in time, you have a little probability that a fish would be caught." + }, + { + "text": "And whether you catch one now is sort of independent about whether at some later time a fish will be caught or not." + }, + { + "text": "So let's just make this assumption." + }, + { + "text": "And suppose that the rules of the game are that you-- Fish are being called it the certain rate of 0.6 per hour." + }, + { + "text": "You fish for 2 hours, no matter what." + }, + { + "text": "And then there are two possibilities." + }, + { + "text": "If I have caught a fish, I stop and go home." + }, + { + "text": "So if some fish have been caught, so there's at least 1 arrival during this interval, I go home." + }, + { + "text": "Or if nothing has being caught, I continue fishing until I catch something." + }, + { + "text": "And then I go home." + }, + { + "text": "So that's the description of what is going to happen." + }, + { + "text": "And now let's starts asking questions of all sorts." + }, + { + "text": "What is the probability that I'm going to be fishing for more than 2 hours?" + }, + { + "text": "I will be fishing for more than 2 hours, if and only if no fish were caught during those 2 hours, in which case, I will have to continue." + }, + { + "text": "Therefore, this is just this quantity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk7.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..d200ba8c85d33ddb01ccd0430f2d344dfd85356f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "The probability of catching 2 fish in-- of catching 0 fish in the next 2 hours, and according to the formula that we have, this is going to be e to the minus lambda times how much time we have." + }, + { + "text": "There's another way of thinking about this." + }, + { + "text": "The probability that I fish for more than 2 hours is the probability that the first catch happens after time 2, which would be the integral from 2 to infinity of the density of the first arrival time." + }, + { + "text": "And that density is an exponential." + }, + { + "text": "So you do the integral of an exponential, and, of course, you would get the same answer." + }, + { + "text": "OK. That's easy." + }, + { + "text": "So what's the probability of fishing for more than 2 but less than 5 hours?" + }, + { + "text": "What does it take for this to happen?" + }, + { + "text": "For this to happen, we need to catch 0 fish from time 0 to 2 and catch the first fish sometime between 2 and 5." + }, + { + "text": "So if you-- one way of thinking about what's happening here might be to say that there's a Poisson process that keeps going on forever." + }, + { + "text": "But as soon as I catch the first fish, instead of continuing fishing and obtaining those other fish I just go home right now." + }, + { + "text": "Now the fact that I go home before time 5 means that, if I were to stay until time 5, I would have caught at least 1 fish." + }, + { + "text": "I might have caught more than 1." + }, + { + "text": "So the event of interest here is that the first catch happens between times 2 and 5." + }, + { + "text": "So one way of calculating this quantity would be-- Its the probability that the first catch happens between times 2 and 5." + }, + { + "text": "Another way to deal with it is to say, this is the probability that I caught 0 fish in the first 2 hours and then the probability that I catch at least 1 fish during the next 3 hours." + }, + { + "text": "This." + }, + { + "text": "What is this?" + }, + { + "text": "The probability of 0 fish in the next 3 hours is the probability of 0 fish during this time." + }, + { + "text": "1 minus this is the probability of catching at least 1 fish, of having at least 1 arrival, between times 2 and 5." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk8.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..63208c3916b0f28860e55ba410e9e8809a2e2618 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "If there's at least 1 arrival between times 2 and 5, then I would have gone home by time 5." + }, + { + "text": "So both of these, if you plug-in numbers and all that, of course, are going to give you the same answer." + }, + { + "text": "Now next, what's the probability that I catch at least 2 fish?" + }, + { + "text": "In which scenario are we?" + }, + { + "text": "Under this scenario, I go home when I catch my first fish." + }, + { + "text": "So in order to catch at least 2 fish, it must be in this case." + }, + { + "text": "So this is the same as the event that I catch at least 2 fish during the first 2 time steps." + }, + { + "text": "So it's going to be the probability from 2 to infinity, the probability that I catch 2 fish, or that I catch 3 fish, or I catch more than that." + }, + { + "text": "So it's this quantity." + }, + { + "text": "k is the number of fish that I catch." + }, + { + "text": "At least 2, so k goes from 2 to infinity." + }, + { + "text": "These are the probabilities of catching a number k of fish during this interval." + }, + { + "text": "And if you want a simpler form without an infinite sum, this would be 1 minus the probability of catching 0 fish, minus the probability of catching 1 fish, during a time interval of length 2." + }, + { + "text": "Another way to think of it." + }, + { + "text": "I'm going to catch 2 fish, at least 2 fish, if and only if the second fish caught in this process happens before time 2." + }, + { + "text": "So that's another way of thinking about the same event." + }, + { + "text": "So it's going to be the probability that the random variable Y2, the arrival time over the second fish, is less than or equal to 2." + }, + { + "text": "OK." + }, + { + "text": "The next one is a little trickier." + }, + { + "text": "Here we need to do a little bit of divide and conquer." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk9.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..438a6aa22ffef63c853416c037d519d661ef6133 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_0_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "Overall, in this expedition, what the expected number of fish to be caught?" + }, + { + "text": "One way to think about it is to try to use the total expectations theorem." + }, + { + "text": "And think of expected number of fish, given this scenario, or expected number of fish, given this scenario." + }, + { + "text": "That's a little more complicated than the way I'm going to do it." + }, + { + "text": "The way I'm going to do is to think as follows-- Expected number of fish is the expected number of fish caught between times 0 and 2 plus expected number of fish caught after time 2." + }, + { + "text": "So what's the expected number caught between time 0 and 2?" + }, + { + "text": "This is lambda t. So lambda is 0.6 times 2." + }, + { + "text": "This is the expected number of fish that are caught between times 0 and 2." + }, + { + "text": "Now let's think about the expected number of fish caught afterwards." + }, + { + "text": "How many fish are being caught afterwards?" + }, + { + "text": "Well it depends on the scenario." + }, + { + "text": "If we're in this scenario, we've gone home and we catch 0." + }, + { + "text": "If we're in this scenario, then we continue fishing until we catch one." + }, + { + "text": "So the expected number of fish to be caught after time 2 is going to be the probability of this scenario times 1." + }, + { + "text": "And the probability of that scenario is the probability that they call it's 0 fish during the first 2 time steps times 1, which is the number of fish I'm going to catch if I continue." + }, + { + "text": "The expected total fishing time we can calculate exactly the same way." + }, + { + "text": "I'm jumping to the last one." + }, + { + "text": "My total fishing time has a period of 2 time steps." + }, + { + "text": "I'm going to fish for 2 time steps no matter what." + }, + { + "text": "And then if I caught 0 fish, which happens with this probability, my expected time is going to be the expected time from here onwards, which is the expected value of this geometric random variable with parameter lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk0.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..aa961d524ea0d1287b995e40358f71afcd69bfb1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "JOHN TSITSIKLIS: Today we're going to finish our discussion of the Poisson process." + }, + { + "text": "We're going to see a few of its properties, do a few interesting problems, some more interesting than others." + }, + { + "text": "So go through a few examples and then we're going to talk about some quite strange things that happen with the Poisson process." + }, + { + "text": "So the first thing is to remember what the Poisson processes is." + }, + { + "text": "It's a model, let's say, of arrivals of customers that are, in some sense, quote unquote, completely random, that is a customer can arrive at any point in time." + }, + { + "text": "All points in time are equally likely." + }, + { + "text": "And different points in time are sort of independent of other points in time." + }, + { + "text": "So the fact that I got an arrival now doesn't tell me anything about whether there's going to be an arrival at some other time." + }, + { + "text": "In some sense, it's a continuous time version of the Bernoulli process." + }, + { + "text": "So the best way to think about the Poisson process is that we divide time into extremely tiny slots." + }, + { + "text": "And in each time slot, there's an independent possibility of having an arrival." + }, + { + "text": "Different time slots are independent of each other." + }, + { + "text": "On the other hand, when the slot is tiny, the probability for obtaining an arrival during that tiny slot is itself going to be tiny." + }, + { + "text": "So we capture these properties into a formal definition what the Poisson process is." + }, + { + "text": "We have a probability mass function for the number of arrivals, k, during an interval of a given length." + }, + { + "text": "So this is the sort of basic description of the distribution of the number of arrivals." + }, + { + "text": "So tau is fixed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk1.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..8ef79a1bbf5e44814915347122880462d60e3970 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And k is the parameter." + }, + { + "text": "So when we add over all k's, the sum of these probabilities has to be equal to 1." + }, + { + "text": "There's a time homogeneity assumption, which is hidden in this, namely, the only thing that matters is the duration of the time interval, not where the time interval sits on the real axis." + }, + { + "text": "Then we have an independence assumption." + }, + { + "text": "Intervals that are disjoint are statistically independent from each other." + }, + { + "text": "So any information you give me about arrivals during this time interval doesn't change my beliefs about what's going to happen during another time interval." + }, + { + "text": "So this is a generalization of the idea that we had in Bernoulli processes that different time slots are independent of each other." + }, + { + "text": "And then to specify this function, the distribution of the number of arrivals, we sort of go in stages." + }, + { + "text": "We first specify this function for the case where the time interval is very small." + }, + { + "text": "And I'm telling you what those probabilities will be." + }, + { + "text": "And based on these then, we do some calculations and to find the formula for the distribution of the number of arrivals for intervals of a general duration." + }, + { + "text": "So for a small duration, delta, the probability of obtaining 1 arrival is lambda delta." + }, + { + "text": "The remaining probability is assigned to the event that we get to no arrivals during that interval." + }, + { + "text": "The probability of obtaining more than 1 arrival in a tiny interval is essentially 0." + }, + { + "text": "And when we say essentially, it's means modular, terms that of order delta squared." + }, + { + "text": "And when delta is very small, anything which is delta squared can be ignored." + }, + { + "text": "So up to delta squared terms, that's what happened during a little interval." + }, + { + "text": "Now if we know the probability distribution for the number of arrivals in a little interval." + }, + { + "text": "We can use this to get the distribution for the number of arrivals over several intervals." + }, + { + "text": "How do we do that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk10.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c993d1aafbcf3de55a33d47639c163aee1857626 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So the expected time is 1 over lambda." + }, + { + "text": "And in our case this, is 1/0.6." + }, + { + "text": "Finally, if I tell you that I have been fishing for 4 hours and nothing has been caught so far, how much do you expect this quantity to be?" + }, + { + "text": "Here is the story that, again, that for the Poisson process used is as good as new." + }, + { + "text": "The process does not have any memory." + }, + { + "text": "Given what happens in the past doesn't matter for the future." + }, + { + "text": "It's as if the process starts new at this point in time." + }, + { + "text": "So this one is going to be, again, the same exponentially distributed random variable with the same parameter lambda." + }, + { + "text": "So expected time until an arrival comes is an exponential distribut -- has an exponential distribution with parameter lambda, no matter what has happened in the past." + }, + { + "text": "Starting from now and looking into the future, it's as if the process has just started." + }, + { + "text": "So it's going to be 1 over lambda, which is 1/0.6." + }, + { + "text": "OK. Now our next example is going to be a little more complicated or subtle." + }, + { + "text": "But before we get to the example, let's refresh our memory about what we discussed last time about merging Poisson independent Poisson processes." + }, + { + "text": "Instead of drawing the picture that way, another way we could draw it could be this." + }, + { + "text": "We have a Poisson process with rate lambda1, and a Poisson process with rate lambda2." + }, + { + "text": "They have, each one of these, have their arrivals." + }, + { + "text": "And then we form the merged process." + }, + { + "text": "And the merged process records an arrival whenever there's an arrival in either of the two processes." + }, + { + "text": "This process in that process are assumed to be independent of each other." + }, + { + "text": "Now different times in this process and that process are independent of each other." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk11.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..98f4de8fc7edf6671add64512cd98e8481dce843 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what happens in these two time intervals is independent from what happens in these two time intervals." + }, + { + "text": "These two time intervals to determine what happens here." + }, + { + "text": "These two time intervals determine what happens there." + }, + { + "text": "So because these are independent from these, this means that this is also independent from that." + }, + { + "text": "So the independence assumption is satisfied for the merged process." + }, + { + "text": "And the merged process turns out to be a Poisson process." + }, + { + "text": "And if you want to find the arrival rate for that process, you argue as follows." + }, + { + "text": "During a little interval of length delta, we have probability lambda1 delta of having an arrival in this process." + }, + { + "text": "We have probability lambda2 delta of an arrival in this process, plus second order terms in delta, which we're ignoring." + }, + { + "text": "And then you do the calculation and you find that in this process, you're going to have an arrival probability, which is lambda1 plus lambda2, again ignoring second order in delta-- terms that are second order in delta." + }, + { + "text": "So the merged process is a Poisson process whose arrival rate is the sum of the arrival rates of the individual processes." + }, + { + "text": "And the calculation we did at the end of the last lecture-- If I tell you that the new arrival happened here, where did that arrival come from?" + }, + { + "text": "Did it come from here or from there?" + }, + { + "text": "If the lambda1 is equal to lambda2, then by symmetry you would say that it's equally likely to have come from here or to come from there." + }, + { + "text": "But if this lambda is much bigger than that lambda, the fact that they saw an arrival is more likely to have come from there." + }, + { + "text": "And the formula that captures this is the following." + }, + { + "text": "This is the probability that my arrival has come from this particular stream rather than that particular stream." + }, + { + "text": "So when an arrival comes and you ask, what is the origin of that arrival?" + }, + { + "text": "It's as if I'm flipping a coin with these odds." + }, + { + "text": "And depending on outcome of that coin, I'm going to tell you came from there or it came from there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk12.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..b81514a3614b4cc14097ef6ee9b3469bf3d09d24 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "So the origin of an arrival is either this stream or that stream." + }, + { + "text": "And this is the probability that the origin of the arrival is that one." + }, + { + "text": "Now if we look at 2 different arrivals, and we ask about their origins-- So let's think about the origin of this arrival and compare it with the origin that arrival." + }, + { + "text": "The origin of this arrival is random." + }, + { + "text": "It could be right be either this or that." + }, + { + "text": "And this is the relevant probability." + }, + { + "text": "The origin of that arrival is random." + }, + { + "text": "It could be either here or is there, and again, with the same relevant probability." + }, + { + "text": "Question." + }, + { + "text": "The origin of this arrival, is it dependent or independent from the origin that arrival?" + }, + { + "text": "And here's how the argument goes." + }, + { + "text": "Separate times are independent." + }, + { + "text": "Whatever has happened in the process during this set of times is independent from whatever happened in the process during that set of times." + }, + { + "text": "Because different times have nothing to do with each other, the origin of this, of an arrival here, has nothing to do with the origin of an arrival there." + }, + { + "text": "So the origins of different arrivals are also independent random variables." + }, + { + "text": "So if I tell you that-- yeah." + }, + { + "text": "OK." + }, + { + "text": "So it as if that each time that you have an arrival in the merge process, it's as if you're flipping a coin to determine where did that arrival came from and these coins are independent of each other." + }, + { + "text": "OK. OK. Now we're going to use this-- what we know about merged processes to solve the problem that would be harder to do, if you were not using ideas from Poisson processes." + }, + { + "text": "So the formulation of the problem has nothing to do with the Poisson process." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk13.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..bf6c66b1e38f68ac6bd19d504f54b3d7f0681a3c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "The formulation is the following." + }, + { + "text": "We have 3 light-bulbs." + }, + { + "text": "And each light bulb is independent and is going to die out at the time that's exponentially distributed." + }, + { + "text": "So 3 light bulbs." + }, + { + "text": "They start their lives and then at some point they die or burn out." + }, + { + "text": "So let's think of this as X, this as Y, and this as Z." + }, + { + "text": "And we're interested in the time until the last light-bulb burns out." + }, + { + "text": "So we're interested in the maximum of the 3 random variables, X, Y, and Z." + }, + { + "text": "And in particular, we want to find the expected value of this maximum." + }, + { + "text": "OK." + }, + { + "text": "So you can do derived distribution, use the expected value rule, anything you want." + }, + { + "text": "You can get this answer using the tools that you already have in your hands." + }, + { + "text": "But now let us see how we can connect to this picture with a Poisson picture and come up with the answer in a very simple way." + }, + { + "text": "What is an exponential random variable?" + }, + { + "text": "An exponential random variable is the first act in the long play that involves a whole Poisson process." + }, + { + "text": "So an exponential random variable is the first act of a Poisson movie." + }, + { + "text": "Same thing here." + }, + { + "text": "You can think of this random variable as being part of some Poisson process that has been running." + }, + { + "text": "So it's part of this bigger picture." + }, + { + "text": "We're still interested in the maximum of the 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk14.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..1a92d35ab267e8941975fcfa559b335f37209c80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "The other arrivals are not going to affect our answers." + }, + { + "text": "It's just, conceptually speaking, we can think of the exponential random variable as being embedded in a bigger Poisson picture." + }, + { + "text": "So we have 3 Poisson process that are running in parallel." + }, + { + "text": "Let us split the expected time until the last burnout into pieces, which is time until the first burnout, time from the first until the second, and time from the second until the third." + }, + { + "text": "And find the expected values of each one of these pieces." + }, + { + "text": "What can we say about the expected value of this?" + }, + { + "text": "This is the first arrival out of all of these 3 Poisson processes." + }, + { + "text": "It's the first event that happens when you look at all of these processes simultaneously." + }, + { + "text": "So 3 Poisson processes running in parallel." + }, + { + "text": "We're interested in the time until one of them, any one of them, gets in arrival." + }, + { + "text": "Rephrase." + }, + { + "text": "We merged the 3 Poisson processes, and we ask for the time until we observe an arrival in the merged process." + }, + { + "text": "When 1 of the 3 gets an arrival for the first time, the merged process gets its first arrival." + }, + { + "text": "So what's the expected value of this time until the first burnout?" + }, + { + "text": "It's going to be the expected value of a Poisson random variable." + }, + { + "text": "So the first burnout is going to have an expected value, which is-- OK." + }, + { + "text": "It's a Poisson process." + }, + { + "text": "The merged process of the 3 has a collective arrival rate, which is 3 times lambda." + }, + { + "text": "So this is the parameter over the exponential distribution that describes the time until the first arrival in the merged process." + }, + { + "text": "And the expected value of this random variable is 1 over that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk15.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..ec2818bb27b6b5b81e6f20bc450cb58a1baac245 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "When you have an exponential random variable with parameter lambda, the expected value of that random variable is 1 over lambda." + }, + { + "text": "Here we're talking about the first arrival time in a process with rate 3 lambda." + }, + { + "text": "The expected time until the first arrival is 1 over (3 lambda)." + }, + { + "text": "Alright." + }, + { + "text": "So at this time, this bulb, this arrival happened, this bulb has been burned." + }, + { + "text": "So we don't care about that bulb anymore." + }, + { + "text": "We start at this time, and we look forward." + }, + { + "text": "This bulb has been burned." + }, + { + "text": "So let's just look forward from now on." + }, + { + "text": "What have we got?" + }, + { + "text": "We have two bulbs that are burning." + }, + { + "text": "We have a Poisson process that's the bigger picture of what could happen to that light bulb, if we were to keep replacing it." + }, + { + "text": "Another Poisson process." + }, + { + "text": "These two processes are, again, independent." + }, + { + "text": "From this time until that time, how long does it take?" + }, + { + "text": "It's the time until either this process records an arrival or that process records and arrival." + }, + { + "text": "That's the same as the time that the merged process of these two records an arrival." + }, + { + "text": "So we're talking about the expected time until the first arrival in a merged process." + }, + { + "text": "The merged process is Poisson." + }, + { + "text": "It's Poisson with rate 2 lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk16.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..6a74ed00548100b2fa7d07c494546d15ecdfac23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that extra time is going to take-- the expected value is going to be 1 over the (rate of that Poisson process)." + }, + { + "text": "So 1 over (2 lambda) is the expected value of this random variable." + }, + { + "text": "So at this point, this bulb now is also burned." + }, + { + "text": "So we start looking from this time on." + }, + { + "text": "That part of the picture disappears." + }, + { + "text": "Starting from this time, what's the expected value until that remaining light-bulb burns out?" + }, + { + "text": "Well, as we said before, in a Poisson process or with exponential random variables, we have memorylessness." + }, + { + "text": "A used bulb is as good as a new one." + }, + { + "text": "So it's as if we're starting from scratch here." + }, + { + "text": "So this is going to be an exponential random variable with parameter lambda." + }, + { + "text": "And the expected value of it is going to be 1 over lambda." + }, + { + "text": "So the beauty of approaching this problem in this particular way is, of course, that we manage to do everything without any calculus at all, without striking an integral, without trying to calculate expectations in any form." + }, + { + "text": "Most of the non-trivial problems that you encounter in the Poisson world basically involve tricks of these kind." + }, + { + "text": "You have a question and you try to rephrase it, trying to think in terms of what might happen in the Poisson setting, use memorylessness, use merging, et cetera, et cetera." + }, + { + "text": "Now we talked about merging." + }, + { + "text": "It turns out that the splitting of Poisson processes also works in a nice way." + }, + { + "text": "The story here is exactly the same as for the Bernoulli process." + }, + { + "text": "So I'm having a Poisson process." + }, + { + "text": "And each time, with some rate lambda, and each time that an arrival comes, I'm going to send it to that stream and the record an arrival here with some probability P. And I'm going to send it to the other stream with some probability 1 minus P. So either of this will happen or that will happen, depending on the outcome of the coin flip that I do." + }, + { + "text": "Each time that then arrival occurs, I flip a coin and I decide whether to record it here or there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk17.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..24ef2d939ecec102e5b0cf66c4aef963c1195410 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "This is called splitting a Poisson process into two pieces." + }, + { + "text": "What kind of process do we get here?" + }, + { + "text": "If you look at the little interval for length delta, what's the probability that this little interval gets an arrival?" + }, + { + "text": "It's the probability that this one gets an arrival, which is lambda delta times the probability that after I get an arrival my coin flip came out to be that way, so that it sends me there." + }, + { + "text": "So this means that this little interval is going to have probability lambda delta P. Or maybe more suggestively, I should write it as lambda P times delta." + }, + { + "text": "So every little interval has a probability of an arrival proportional to delta." + }, + { + "text": "The proportionality factor is lambda P. So lambda P is the rate of that process." + }, + { + "text": "And then you go through the mental exercise that you went through for the Bernoulli process to argue that a different intervals here are independent and so on." + }, + { + "text": "And that completes checking that this process is going to be a Poisson process." + }, + { + "text": "So when you split a Poisson process by doing independent coin flips each time that something happens, the processes that you get is again a Poisson process, but of course with a reduced rate." + }, + { + "text": "So instead of the word splitting, sometimes people also use the words thinning-out." + }, + { + "text": "That is, out of the arrivals that came, you keep a few but throw away a few." + }, + { + "text": "OK." + }, + { + "text": "So now the last topic over this lecture is a quite curious phenomenon that goes under the name of random incidents." + }, + { + "text": "So here's the story." + }, + { + "text": "Buses have been running on Mass Ave. from time immemorial." + }, + { + "text": "And the bus company that runs the buses claims that they come as a Poisson process with some rate, let's say, of 4 buses per hour." + }, + { + "text": "So that the expected time between bus arrivals is going to be 15 minutes." + }, + { + "text": "OK. Alright." + }, + { + "text": "So people have been complaining that they have been showing up there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk18.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..65a62f83b762cf608024e3af374f28f51f49e32f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "They think the buses are taking too long." + }, + { + "text": "So you are asked to investigate." + }, + { + "text": "Is the company-- Does it operate according to its promises or not." + }, + { + "text": "So you send an undercover agent to go and check the interarrival times of the buses." + }, + { + "text": "Are they 15 minutes?" + }, + { + "text": "Or are they longer?" + }, + { + "text": "So you put your dark glasses and you show up at the bus stop at some random time." + }, + { + "text": "And you go and ask the guy in the falafel truck, how long has it been since the last arrival?" + }, + { + "text": "So of course that guy works for the FBI, right?" + }, + { + "text": "So they tell you, well, it's been, let's say, 12 minutes since the last bus arrival." + }, + { + "text": "And then you say, \"Oh, 12 minutes." + }, + { + "text": "Average time is 15." + }, + { + "text": "So a bus should be coming any time now.\"" + }, + { + "text": "Is that correct?" + }, + { + "text": "No, you wouldn't think that way." + }, + { + "text": "It's a Poisson process." + }, + { + "text": "It doesn't matter how long it has been since the last bus arrival." + }, + { + "text": "So you don't go through that fallacy." + }, + { + "text": "Instead of predicting how long it's going to be, you just sit down there and wait and measure the time." + }, + { + "text": "And you find that this is, let's say, 11 minutes." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk19.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..af599f5b8f4c3fc0973b37e81b36088c85eae997 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you go to your boss and report, \"Well, it took-- I went there and the time from the previous bus to the next one was 23 minutes." + }, + { + "text": "It's more than the 15 that they said.\"" + }, + { + "text": "So go and do that again." + }, + { + "text": "You go day after day." + }, + { + "text": "You keep these statistics of the length of this interval." + }, + { + "text": "And you tell your boss it's a lot more than 15." + }, + { + "text": "It tends to be more like 30 or so." + }, + { + "text": "So the bus company is cheating us." + }, + { + "text": "Does the bus company really run Poisson buses at the rate that they have promised?" + }, + { + "text": "Well let's analyze the situation here and figure out what the length of this interval should be, on the average." + }, + { + "text": "The naive argument is that this interval is an interarrival time." + }, + { + "text": "And interarrival times, on the average, are 15 minutes, if the company runs indeed Poisson processes with these interarrival times." + }, + { + "text": "But actually the situation is a little more subtle because this is not a typical interarrival interval." + }, + { + "text": "This interarrival interval consists of two pieces." + }, + { + "text": "Let's call them T1 and T1 prime." + }, + { + "text": "What can you tell me about those two random variables?" + }, + { + "text": "What kind of random variable is T1?" + }, + { + "text": "Starting from this time, with the Poisson process, the past doesn't matter." + }, + { + "text": "It's the time until an arrival happens." + }, + { + "text": "So T1 is going to be an exponential random variable with parameter lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk2.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..ebc6083b4940b3fc27511f672c179a7846abc0b1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "The big interval is composed of many little intervals." + }, + { + "text": "Each little interval is independent from any other little interval, so is it is as if we have a sequence of Bernoulli trials." + }, + { + "text": "Each Bernoulli trial is associated with a little interval and has a small probability of obtaining a success or an arrival during that mini-slot." + }, + { + "text": "On the other hand, when delta is small, and you take a big interval and chop it up, you get a large number of little intervals." + }, + { + "text": "So what we essentially have here is a Bernoulli process, in which is the number of trials is huge but the probability of success during any given trial is tiny." + }, + { + "text": "The average number of trials ends up being proportional to the length of the interval." + }, + { + "text": "If you have twice as large an interval, it's as if you're having twice as many over these mini-trials, so the expected number of arrivals will increase proportionately." + }, + { + "text": "There's also this parameter lambda, which we interpret as expected number of arrivals per unit time." + }, + { + "text": "And it comes in those probabilities here." + }, + { + "text": "When you double lambda, this means that a little interval is twice as likely to get an arrival." + }, + { + "text": "So you would expect to get twice as many arrivals as well." + }, + { + "text": "That's why the expected number of arrivals during an interval of length tau also scales proportional to this parameter lambda." + }, + { + "text": "Somewhat unexpectedly, it turns out that the variance of the number of arrivals is also the same as the mean." + }, + { + "text": "This is a peculiarity that happens in the Poisson process." + }, + { + "text": "So this is one way of thinking about Poisson process, in terms of little intervals, each one of which has a tiny probability of success." + }, + { + "text": "And we think of the distribution associated with that process as being described by this particular PMF." + }, + { + "text": "So this is the PMF for the number of arrivals during an interval of a fixed duration, tau." + }, + { + "text": "It's a PMF that extends all over the entire range of non-negative integers." + }, + { + "text": "So the number of arrivals you can get during an interval for certain length can be anything." + }, + { + "text": "You can get as many arrivals as you want." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk20.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..28349ba5d13c19b16a2957596215f8e4b02bbf01 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "So in particular, the expected value of T1 is going to be 15 by itself." + }, + { + "text": "How about the random variable T1 prime." + }, + { + "text": "What kind of random variable is it?" + }, + { + "text": "This is like the first arrival in a Poisson process that runs backwards in time." + }, + { + "text": "What kind of process is a Poisson process running backwards in time?" + }, + { + "text": "Let's think of coin flips." + }, + { + "text": "Suppose you have a movie of coin flips." + }, + { + "text": "And for some accident, that fascinating movie, you happen to watch it backwards." + }, + { + "text": "Will it look any different statistically?" + }, + { + "text": "No." + }, + { + "text": "It's going to be just the sequence of random coin flips." + }, + { + "text": "So a Bernoulli process that's runs in reverse time is statistically identical to a Bernoulli process in forward time." + }, + { + "text": "The Poisson process is a limit of the Bernoulli." + }, + { + "text": "So, same story with the Poisson process." + }, + { + "text": "If you run it backwards in time it looks the same." + }, + { + "text": "So looking backwards in time, this is a Poisson process." + }, + { + "text": "And T1 prime is the time until the first arrival in this backward process." + }, + { + "text": "So T1 prime is also going to be an exponential random variable with the same parameter, lambda." + }, + { + "text": "And the expected value of T1 prime is 15." + }, + { + "text": "Conclusion is that the expected length of this interval is going to be 30 minutes." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk21.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..e60bcef503b4a0db026939c13f85514e5dcb0817 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the fact that this agent found the average to be something like 30 does not contradict the claims of the bus company that they're running Poisson buses with a rate of lambda equal to 4." + }, + { + "text": "OK." + }, + { + "text": "So maybe the company can this way-- they can defend themselves in court." + }, + { + "text": "But there's something puzzling here." + }, + { + "text": "How long is the interarrival time?" + }, + { + "text": "Is it 15?" + }, + { + "text": "Or is it 30?" + }, + { + "text": "On the average." + }, + { + "text": "The issue is what do we mean by a typical interarrival time." + }, + { + "text": "When we say typical, we mean some kind of average." + }, + { + "text": "But average over what?" + }, + { + "text": "And here's two different ways of thinking about averages." + }, + { + "text": "You number the buses." + }, + { + "text": "And you have bus number 100." + }, + { + "text": "You have bus number 101, bus number 102, bus number 110, and so on." + }, + { + "text": "One way of thinking about averages is that you pick a bus number at random." + }, + { + "text": "I pick, let's say, that bus, all buses being sort of equally likely to be picked." + }, + { + "text": "And I measure this interarrival time." + }, + { + "text": "So for a typical bus." + }, + { + "text": "Then, starting from here until there, the expected time has to be 1 over lambda, for the Poisson process." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk22.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..859fef7a50c29d5a5a9f8517f4db560ee5d550a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But what we did in this experiment was something different." + }, + { + "text": "We didn't pick a bus at random." + }, + { + "text": "We picked a time at random." + }, + { + "text": "And if the picture is, let's say, this way, I'm much more likely to pick this interval and therefore this interarrival time, rather than that interval." + }, + { + "text": "Because, this interval corresponds to very few times." + }, + { + "text": "So if I'm picking a time at random and, in some sense, let's say, uniform, so that all times are equally likely, I'm much more likely to fall inside a big interval rather than a small interval." + }, + { + "text": "So a person who shows up at the bus stop at a random time." + }, + { + "text": "They're selecting an interval in a biased way, with the bias favor of longer intervals." + }, + { + "text": "And that's why what they observe is a random variable that has a larger expected value then the ordinary expected value." + }, + { + "text": "So the subtlety here is to realize that we're talking between two different kinds of experiments." + }, + { + "text": "Picking a bus number at random verses picking an interval at random with a bias in favor of longer intervals." + }, + { + "text": "Lots of paradoxes that one can cook up using Poisson processes and random processes in general often have to do with the story of this kind." + }, + { + "text": "The phenomenon that we had in this particular example also shows up in general, whenever you have other kinds of arrival processes." + }, + { + "text": "So the Poisson process is the simplest arrival process there is, where the interarrival times are exponential random variables." + }, + { + "text": "There's a larger class of models." + }, + { + "text": "They're called renewal processes, in which, again, we have a sequence of successive arrivals, interarrival times are identically distributed and independent, but they may come from a general distribution." + }, + { + "text": "So to make the same point of the previous example but in a much simpler setting, suppose that bus interarrival times are either 5 or 10 minutes apart." + }, + { + "text": "So you get some intervals that are of length 5." + }, + { + "text": "You get some that are of length 10." + }, + { + "text": "And suppose that these are equally likely." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk23.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..0c23f2ec29db9e794aae974425a9309fbc5fa392 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "So we have -- not exactly -- In the long run, we have as many 5 minute intervals as we have 10 minute intervals." + }, + { + "text": "So the average interarrival time is 7 and 1/2." + }, + { + "text": "But if a person shows up at a random time, what are they going to see?" + }, + { + "text": "Do we have as many 5s as 10s?" + }, + { + "text": "But every 10 covers twice as much space." + }, + { + "text": "So if I show up at a random time, I have probability 2/3 falling inside an interval of duration 10." + }, + { + "text": "And I have one 1/3 probability of falling inside an interval of duration 5." + }, + { + "text": "That's because, out of the whole real line, 2/3 of it is covered by intervals of length 10, just because they're longer." + }, + { + "text": "1/3 is covered by the smaller intervals." + }, + { + "text": "Now if I fall inside an interval of length 10 and I measure the length of the interval that I fell into, that's going to be 10." + }, + { + "text": "But if I fall inside an interval of length 5 and I measure how long it is, I'm going to get a 5." + }, + { + "text": "And that, of course, is going to be different than 7.5." + }, + { + "text": "OK. And which number should be bigger?" + }, + { + "text": "It's the second number that's bigger because this one is biased in favor of the longer intervals." + }, + { + "text": "So that's, again, another illustration of the different results that you get when you have this random incidence phenomenon." + }, + { + "text": "So the bottom line, again, is that if you talk about a typical interarrival time, one must be very precise in specifying what we mean typical." + }, + { + "text": "So typical means sort of random." + }, + { + "text": "But to use the word random, you must specify very precisely what is the random experiment that you are using." + }, + { + "text": "And if you're not careful, you can get into apparent puzzles, such as the following." + }, + { + "text": "Suppose somebody tells you the average family size is 4, but the average person lives in a family of size 6." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk24.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..f1454166977d85230e828ad2593835dff01c5eed --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Is that compatible?" + }, + { + "text": "Family size is 4 on the average, but typical people live, on the average, in families of size 6." + }, + { + "text": "Well yes." + }, + { + "text": "There's no contradiction here." + }, + { + "text": "We're talking about two different experiments." + }, + { + "text": "In one experiment, I pick a family at random, and I tell you the average family is 4." + }, + { + "text": "In another experiment, I pick a person at random and I tell you that this person, on the average, will be in their family of size 6." + }, + { + "text": "And what is the catch here?" + }, + { + "text": "That if I pick a person at random, large families are more likely to be picked." + }, + { + "text": "So there's a bias in favor of large families." + }, + { + "text": "Or if you want to survey, let's say, are trains crowded in your city?" + }, + { + "text": "Or are buses crowded?" + }, + { + "text": "One choice is to pick a bus at random and inspect how crowded it is." + }, + { + "text": "Another choice is to pick a typical person and ask them, \"Did you ride the bus today?" + }, + { + "text": "Was it's crowded?\"" + }, + { + "text": "Well suppose that in this city there's one bus that's extremely crowded and all the other buses are completely empty." + }, + { + "text": "If you ask a person." + }, + { + "text": "\"Was your bus crowded?\"" + }, + { + "text": "They will tell you, \"Yes, my bus was crowded.\"" + }, + { + "text": "There's no witness from the empty buses to testify in their favor." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk25.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..5ea6070c380c8c0cc3ed8ff41fe3f0d64a2f6192 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk25.json @@ -0,0 +1,23 @@ +[ + { + "text": "So by sampling people instead of sampling buses, you're going to get different result." + }, + { + "text": "And in the process industry, if your job is to inspect and check cookies, you will be faced with a big dilemma." + }, + { + "text": "Do you want to find out how many chocolate chips there are on a typical cookie?" + }, + { + "text": "Are you going to interview cookies or are you going to interview chocolate chips and ask them how many other chips where there on your cookie?" + }, + { + "text": "And you're going to get different answers in these cases." + }, + { + "text": "So moral is, one has to be very precise on how you formulate the sampling procedure that you have." + }, + { + "text": "And you'll get different answers." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk3.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..65f67102a7086dbc76d65afeddb2720c5b67bdb0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "Of course the probability of getting a zillion arrivals is going to be tiny." + }, + { + "text": "But in principle, this is possible." + }, + { + "text": "And that's because an interval, even if it's a fixed length, consists of an infinite number of mini-slots in some sense." + }, + { + "text": "You can divide, chop it up, into as many mini-slots as you want." + }, + { + "text": "So in principle, it's possible that every mini-slot gets an arrival." + }, + { + "text": "In principle, it's possible to get an arbitrarily large number of arrivals." + }, + { + "text": "So this particular formula here is not very intuitive when you look at it." + }, + { + "text": "But it's a legitimate PMF." + }, + { + "text": "And it's called the Poisson PMF." + }, + { + "text": "It's the PMF that describes the number of arrivals." + }, + { + "text": "So that's one way of thinking about the Poisson process, where the basic object of interest would be this PMF and you try to work with it." + }, + { + "text": "There's another way of thinking about what happens in the Poisson process." + }, + { + "text": "And this has to do with letting things evolve in time." + }, + { + "text": "You start at time 0." + }, + { + "text": "There's going to be a time at which the first arrival occurs, and call that time T1." + }, + { + "text": "This time turns out to have an exponential distribution with parameter lambda." + }, + { + "text": "Once you get an arrival, it's as if the process starts fresh." + }, + { + "text": "The best way to understand why this is the case is by thinking in terms of the analogy with the Bernoulli process." + }, + { + "text": "If you believe that statement for the Bernoulli process, since this is a limiting case, it should also be true." + }, + { + "text": "So starting from this time, we're going to wait a random amount of time until we get the second arrival This random amount of time, let's call it T2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk4.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c5affc1f1a5b3e0305dcd63ee178f3ba1a2da02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "This time, T2 is also going to have an exponential distribution with the same parameter, lambda." + }, + { + "text": "And these two are going to be independent of each other." + }, + { + "text": "OK?" + }, + { + "text": "So the Poisson process has all the same memorylessness properties that the Bernoulli process has." + }, + { + "text": "What's another way of thinking of this property?" + }, + { + "text": "So think of a process where you have a light bulb." + }, + { + "text": "The time at the light bulb burns out, you can model it by an exponential random variable." + }, + { + "text": "And suppose that they tell you that so far, we're are sitting at some time, T. And I tell you that the light bulb has not yet burned out." + }, + { + "text": "What does this tell you about the future of the light bulb?" + }, + { + "text": "Is the fact that they didn't burn out, so far, is it good news or is it bad news?" + }, + { + "text": "Would you rather keep this light bulb that has worked for t times steps and is still OK?" + }, + { + "text": "Or would you rather use a new light bulb that starts new at that point in time?" + }, + { + "text": "Because of the memorylessness property, the past of that light bulb doesn't matter." + }, + { + "text": "So the future of this light bulb is statistically the same as the future of a new light bulb." + }, + { + "text": "For both of them, the time until they burn out is going to be described an exponential distribution." + }, + { + "text": "So one way that people described the situation is to say that used is exactly as good as a new." + }, + { + "text": "So a used on is no worse than a new one." + }, + { + "text": "A used one is no better than a new one." + }, + { + "text": "So a used light bulb that hasn't yet burnt out is exactly as good as a new light bulb." + }, + { + "text": "So that's another way of thinking about the memorylessness that we have in the Poisson process." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk5.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..a8f4593b861f0c6ab6d24f9023bf2c98983b5ab3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "Back to this picture." + }, + { + "text": "The time until the second arrival is the sum of two independent exponential random variables." + }, + { + "text": "So, in principle, you can use the convolution formula to find the distribution of T1 plus T2, and that would be what we call Y2, the time until the second arrival." + }, + { + "text": "But there's also a direct way of obtaining to the distribution of Y2, and this is the calculation that we did last time on the blackboard." + }, + { + "text": "And actually, we did it more generally." + }, + { + "text": "We found the time until the case arrival occurs." + }, + { + "text": "It has a closed form formula, which is called the Erlang distribution with k degrees of freedom." + }, + { + "text": "So let's see what's going on here." + }, + { + "text": "It's a distribution Of what kind?" + }, + { + "text": "It's a continuous distribution." + }, + { + "text": "It's a probability density function." + }, + { + "text": "This is because the time is a continuous random variable." + }, + { + "text": "Time is continuous." + }, + { + "text": "Arrivals can happen at any time." + }, + { + "text": "So we're talking about the PDF." + }, + { + "text": "This k is just the parameter of the distribution." + }, + { + "text": "We're talking about the k-th arrival, so k is a fixed number." + }, + { + "text": "Lambda is another parameter of the distribution, which is the arrival rate So it's a PDF over the Y's, whereas lambda and k are parameters of the distribution." + }, + { + "text": "OK." + }, + { + "text": "So this was what we knew from last time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk6.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..f957b2a1915e0744ba6fb901fba06c158d7e336f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Just to get some practice, let us do a problem that's not too difficult, but just to see how we use the various formulas that we have." + }, + { + "text": "So Poisson was a mathematician, but Poisson also means fish in French." + }, + { + "text": "So Poisson goes fishing." + }, + { + "text": "And let's assume that fish are caught according to a Poisson process." + }, + { + "text": "That's not too bad an assumption." + }, + { + "text": "At any given point in time, you have a little probability that a fish would be caught." + }, + { + "text": "And whether you catch one now is sort of independent about whether at some later time a fish will be caught or not." + }, + { + "text": "So let's just make this assumption." + }, + { + "text": "And suppose that the rules of the game are that you-- Fish are being called it the certain rate of 0.6 per hour." + }, + { + "text": "You fish for 2 hours, no matter what." + }, + { + "text": "And then there are two possibilities." + }, + { + "text": "If I have caught a fish, I stop and go home." + }, + { + "text": "So if some fish have been caught, so there's at least 1 arrival during this interval, I go home." + }, + { + "text": "Or if nothing has being caught, I continue fishing until I catch something." + }, + { + "text": "And then I go home." + }, + { + "text": "So that's the description of what is going to happen." + }, + { + "text": "And now let's starts asking questions of all sorts." + }, + { + "text": "What is the probability that I'm going to be fishing for more than 2 hours?" + }, + { + "text": "I will be fishing for more than 2 hours, if and only if no fish were caught during those 2 hours, in which case, I will have to continue." + }, + { + "text": "Therefore, this is just this quantity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk7.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..d200ba8c85d33ddb01ccd0430f2d344dfd85356f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "The probability of catching 2 fish in-- of catching 0 fish in the next 2 hours, and according to the formula that we have, this is going to be e to the minus lambda times how much time we have." + }, + { + "text": "There's another way of thinking about this." + }, + { + "text": "The probability that I fish for more than 2 hours is the probability that the first catch happens after time 2, which would be the integral from 2 to infinity of the density of the first arrival time." + }, + { + "text": "And that density is an exponential." + }, + { + "text": "So you do the integral of an exponential, and, of course, you would get the same answer." + }, + { + "text": "OK. That's easy." + }, + { + "text": "So what's the probability of fishing for more than 2 but less than 5 hours?" + }, + { + "text": "What does it take for this to happen?" + }, + { + "text": "For this to happen, we need to catch 0 fish from time 0 to 2 and catch the first fish sometime between 2 and 5." + }, + { + "text": "So if you-- one way of thinking about what's happening here might be to say that there's a Poisson process that keeps going on forever." + }, + { + "text": "But as soon as I catch the first fish, instead of continuing fishing and obtaining those other fish I just go home right now." + }, + { + "text": "Now the fact that I go home before time 5 means that, if I were to stay until time 5, I would have caught at least 1 fish." + }, + { + "text": "I might have caught more than 1." + }, + { + "text": "So the event of interest here is that the first catch happens between times 2 and 5." + }, + { + "text": "So one way of calculating this quantity would be-- Its the probability that the first catch happens between times 2 and 5." + }, + { + "text": "Another way to deal with it is to say, this is the probability that I caught 0 fish in the first 2 hours and then the probability that I catch at least 1 fish during the next 3 hours." + }, + { + "text": "This." + }, + { + "text": "What is this?" + }, + { + "text": "The probability of 0 fish in the next 3 hours is the probability of 0 fish during this time." + }, + { + "text": "1 minus this is the probability of catching at least 1 fish, of having at least 1 arrival, between times 2 and 5." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk8.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..63208c3916b0f28860e55ba410e9e8809a2e2618 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "If there's at least 1 arrival between times 2 and 5, then I would have gone home by time 5." + }, + { + "text": "So both of these, if you plug-in numbers and all that, of course, are going to give you the same answer." + }, + { + "text": "Now next, what's the probability that I catch at least 2 fish?" + }, + { + "text": "In which scenario are we?" + }, + { + "text": "Under this scenario, I go home when I catch my first fish." + }, + { + "text": "So in order to catch at least 2 fish, it must be in this case." + }, + { + "text": "So this is the same as the event that I catch at least 2 fish during the first 2 time steps." + }, + { + "text": "So it's going to be the probability from 2 to infinity, the probability that I catch 2 fish, or that I catch 3 fish, or I catch more than that." + }, + { + "text": "So it's this quantity." + }, + { + "text": "k is the number of fish that I catch." + }, + { + "text": "At least 2, so k goes from 2 to infinity." + }, + { + "text": "These are the probabilities of catching a number k of fish during this interval." + }, + { + "text": "And if you want a simpler form without an infinite sum, this would be 1 minus the probability of catching 0 fish, minus the probability of catching 1 fish, during a time interval of length 2." + }, + { + "text": "Another way to think of it." + }, + { + "text": "I'm going to catch 2 fish, at least 2 fish, if and only if the second fish caught in this process happens before time 2." + }, + { + "text": "So that's another way of thinking about the same event." + }, + { + "text": "So it's going to be the probability that the random variable Y2, the arrival time over the second fish, is less than or equal to 2." + }, + { + "text": "OK." + }, + { + "text": "The next one is a little trickier." + }, + { + "text": "Here we need to do a little bit of divide and conquer." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk9.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..438a6aa22ffef63c853416c037d519d661ef6133 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_2_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "Overall, in this expedition, what the expected number of fish to be caught?" + }, + { + "text": "One way to think about it is to try to use the total expectations theorem." + }, + { + "text": "And think of expected number of fish, given this scenario, or expected number of fish, given this scenario." + }, + { + "text": "That's a little more complicated than the way I'm going to do it." + }, + { + "text": "The way I'm going to do is to think as follows-- Expected number of fish is the expected number of fish caught between times 0 and 2 plus expected number of fish caught after time 2." + }, + { + "text": "So what's the expected number caught between time 0 and 2?" + }, + { + "text": "This is lambda t. So lambda is 0.6 times 2." + }, + { + "text": "This is the expected number of fish that are caught between times 0 and 2." + }, + { + "text": "Now let's think about the expected number of fish caught afterwards." + }, + { + "text": "How many fish are being caught afterwards?" + }, + { + "text": "Well it depends on the scenario." + }, + { + "text": "If we're in this scenario, we've gone home and we catch 0." + }, + { + "text": "If we're in this scenario, then we continue fishing until we catch one." + }, + { + "text": "So the expected number of fish to be caught after time 2 is going to be the probability of this scenario times 1." + }, + { + "text": "And the probability of that scenario is the probability that they call it's 0 fish during the first 2 time steps times 1, which is the number of fish I'm going to catch if I continue." + }, + { + "text": "The expected total fishing time we can calculate exactly the same way." + }, + { + "text": "I'm jumping to the last one." + }, + { + "text": "My total fishing time has a period of 2 time steps." + }, + { + "text": "I'm going to fish for 2 time steps no matter what." + }, + { + "text": "And then if I caught 0 fish, which happens with this probability, my expected time is going to be the expected time from here onwards, which is the expected value of this geometric random variable with parameter lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk0.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..aa961d524ea0d1287b995e40358f71afcd69bfb1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "JOHN TSITSIKLIS: Today we're going to finish our discussion of the Poisson process." + }, + { + "text": "We're going to see a few of its properties, do a few interesting problems, some more interesting than others." + }, + { + "text": "So go through a few examples and then we're going to talk about some quite strange things that happen with the Poisson process." + }, + { + "text": "So the first thing is to remember what the Poisson processes is." + }, + { + "text": "It's a model, let's say, of arrivals of customers that are, in some sense, quote unquote, completely random, that is a customer can arrive at any point in time." + }, + { + "text": "All points in time are equally likely." + }, + { + "text": "And different points in time are sort of independent of other points in time." + }, + { + "text": "So the fact that I got an arrival now doesn't tell me anything about whether there's going to be an arrival at some other time." + }, + { + "text": "In some sense, it's a continuous time version of the Bernoulli process." + }, + { + "text": "So the best way to think about the Poisson process is that we divide time into extremely tiny slots." + }, + { + "text": "And in each time slot, there's an independent possibility of having an arrival." + }, + { + "text": "Different time slots are independent of each other." + }, + { + "text": "On the other hand, when the slot is tiny, the probability for obtaining an arrival during that tiny slot is itself going to be tiny." + }, + { + "text": "So we capture these properties into a formal definition what the Poisson process is." + }, + { + "text": "We have a probability mass function for the number of arrivals, k, during an interval of a given length." + }, + { + "text": "So this is the sort of basic description of the distribution of the number of arrivals." + }, + { + "text": "So tau is fixed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk1.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..8ef79a1bbf5e44814915347122880462d60e3970 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And k is the parameter." + }, + { + "text": "So when we add over all k's, the sum of these probabilities has to be equal to 1." + }, + { + "text": "There's a time homogeneity assumption, which is hidden in this, namely, the only thing that matters is the duration of the time interval, not where the time interval sits on the real axis." + }, + { + "text": "Then we have an independence assumption." + }, + { + "text": "Intervals that are disjoint are statistically independent from each other." + }, + { + "text": "So any information you give me about arrivals during this time interval doesn't change my beliefs about what's going to happen during another time interval." + }, + { + "text": "So this is a generalization of the idea that we had in Bernoulli processes that different time slots are independent of each other." + }, + { + "text": "And then to specify this function, the distribution of the number of arrivals, we sort of go in stages." + }, + { + "text": "We first specify this function for the case where the time interval is very small." + }, + { + "text": "And I'm telling you what those probabilities will be." + }, + { + "text": "And based on these then, we do some calculations and to find the formula for the distribution of the number of arrivals for intervals of a general duration." + }, + { + "text": "So for a small duration, delta, the probability of obtaining 1 arrival is lambda delta." + }, + { + "text": "The remaining probability is assigned to the event that we get to no arrivals during that interval." + }, + { + "text": "The probability of obtaining more than 1 arrival in a tiny interval is essentially 0." + }, + { + "text": "And when we say essentially, it's means modular, terms that of order delta squared." + }, + { + "text": "And when delta is very small, anything which is delta squared can be ignored." + }, + { + "text": "So up to delta squared terms, that's what happened during a little interval." + }, + { + "text": "Now if we know the probability distribution for the number of arrivals in a little interval." + }, + { + "text": "We can use this to get the distribution for the number of arrivals over several intervals." + }, + { + "text": "How do we do that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk10.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c993d1aafbcf3de55a33d47639c163aee1857626 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So the expected time is 1 over lambda." + }, + { + "text": "And in our case this, is 1/0.6." + }, + { + "text": "Finally, if I tell you that I have been fishing for 4 hours and nothing has been caught so far, how much do you expect this quantity to be?" + }, + { + "text": "Here is the story that, again, that for the Poisson process used is as good as new." + }, + { + "text": "The process does not have any memory." + }, + { + "text": "Given what happens in the past doesn't matter for the future." + }, + { + "text": "It's as if the process starts new at this point in time." + }, + { + "text": "So this one is going to be, again, the same exponentially distributed random variable with the same parameter lambda." + }, + { + "text": "So expected time until an arrival comes is an exponential distribut -- has an exponential distribution with parameter lambda, no matter what has happened in the past." + }, + { + "text": "Starting from now and looking into the future, it's as if the process has just started." + }, + { + "text": "So it's going to be 1 over lambda, which is 1/0.6." + }, + { + "text": "OK. Now our next example is going to be a little more complicated or subtle." + }, + { + "text": "But before we get to the example, let's refresh our memory about what we discussed last time about merging Poisson independent Poisson processes." + }, + { + "text": "Instead of drawing the picture that way, another way we could draw it could be this." + }, + { + "text": "We have a Poisson process with rate lambda1, and a Poisson process with rate lambda2." + }, + { + "text": "They have, each one of these, have their arrivals." + }, + { + "text": "And then we form the merged process." + }, + { + "text": "And the merged process records an arrival whenever there's an arrival in either of the two processes." + }, + { + "text": "This process in that process are assumed to be independent of each other." + }, + { + "text": "Now different times in this process and that process are independent of each other." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk11.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..98f4de8fc7edf6671add64512cd98e8481dce843 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what happens in these two time intervals is independent from what happens in these two time intervals." + }, + { + "text": "These two time intervals to determine what happens here." + }, + { + "text": "These two time intervals determine what happens there." + }, + { + "text": "So because these are independent from these, this means that this is also independent from that." + }, + { + "text": "So the independence assumption is satisfied for the merged process." + }, + { + "text": "And the merged process turns out to be a Poisson process." + }, + { + "text": "And if you want to find the arrival rate for that process, you argue as follows." + }, + { + "text": "During a little interval of length delta, we have probability lambda1 delta of having an arrival in this process." + }, + { + "text": "We have probability lambda2 delta of an arrival in this process, plus second order terms in delta, which we're ignoring." + }, + { + "text": "And then you do the calculation and you find that in this process, you're going to have an arrival probability, which is lambda1 plus lambda2, again ignoring second order in delta-- terms that are second order in delta." + }, + { + "text": "So the merged process is a Poisson process whose arrival rate is the sum of the arrival rates of the individual processes." + }, + { + "text": "And the calculation we did at the end of the last lecture-- If I tell you that the new arrival happened here, where did that arrival come from?" + }, + { + "text": "Did it come from here or from there?" + }, + { + "text": "If the lambda1 is equal to lambda2, then by symmetry you would say that it's equally likely to have come from here or to come from there." + }, + { + "text": "But if this lambda is much bigger than that lambda, the fact that they saw an arrival is more likely to have come from there." + }, + { + "text": "And the formula that captures this is the following." + }, + { + "text": "This is the probability that my arrival has come from this particular stream rather than that particular stream." + }, + { + "text": "So when an arrival comes and you ask, what is the origin of that arrival?" + }, + { + "text": "It's as if I'm flipping a coin with these odds." + }, + { + "text": "And depending on outcome of that coin, I'm going to tell you came from there or it came from there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk12.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..b81514a3614b4cc14097ef6ee9b3469bf3d09d24 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "So the origin of an arrival is either this stream or that stream." + }, + { + "text": "And this is the probability that the origin of the arrival is that one." + }, + { + "text": "Now if we look at 2 different arrivals, and we ask about their origins-- So let's think about the origin of this arrival and compare it with the origin that arrival." + }, + { + "text": "The origin of this arrival is random." + }, + { + "text": "It could be right be either this or that." + }, + { + "text": "And this is the relevant probability." + }, + { + "text": "The origin of that arrival is random." + }, + { + "text": "It could be either here or is there, and again, with the same relevant probability." + }, + { + "text": "Question." + }, + { + "text": "The origin of this arrival, is it dependent or independent from the origin that arrival?" + }, + { + "text": "And here's how the argument goes." + }, + { + "text": "Separate times are independent." + }, + { + "text": "Whatever has happened in the process during this set of times is independent from whatever happened in the process during that set of times." + }, + { + "text": "Because different times have nothing to do with each other, the origin of this, of an arrival here, has nothing to do with the origin of an arrival there." + }, + { + "text": "So the origins of different arrivals are also independent random variables." + }, + { + "text": "So if I tell you that-- yeah." + }, + { + "text": "OK." + }, + { + "text": "So it as if that each time that you have an arrival in the merge process, it's as if you're flipping a coin to determine where did that arrival came from and these coins are independent of each other." + }, + { + "text": "OK. OK. Now we're going to use this-- what we know about merged processes to solve the problem that would be harder to do, if you were not using ideas from Poisson processes." + }, + { + "text": "So the formulation of the problem has nothing to do with the Poisson process." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk13.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..bf6c66b1e38f68ac6bd19d504f54b3d7f0681a3c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "The formulation is the following." + }, + { + "text": "We have 3 light-bulbs." + }, + { + "text": "And each light bulb is independent and is going to die out at the time that's exponentially distributed." + }, + { + "text": "So 3 light bulbs." + }, + { + "text": "They start their lives and then at some point they die or burn out." + }, + { + "text": "So let's think of this as X, this as Y, and this as Z." + }, + { + "text": "And we're interested in the time until the last light-bulb burns out." + }, + { + "text": "So we're interested in the maximum of the 3 random variables, X, Y, and Z." + }, + { + "text": "And in particular, we want to find the expected value of this maximum." + }, + { + "text": "OK." + }, + { + "text": "So you can do derived distribution, use the expected value rule, anything you want." + }, + { + "text": "You can get this answer using the tools that you already have in your hands." + }, + { + "text": "But now let us see how we can connect to this picture with a Poisson picture and come up with the answer in a very simple way." + }, + { + "text": "What is an exponential random variable?" + }, + { + "text": "An exponential random variable is the first act in the long play that involves a whole Poisson process." + }, + { + "text": "So an exponential random variable is the first act of a Poisson movie." + }, + { + "text": "Same thing here." + }, + { + "text": "You can think of this random variable as being part of some Poisson process that has been running." + }, + { + "text": "So it's part of this bigger picture." + }, + { + "text": "We're still interested in the maximum of the 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk14.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..1a92d35ab267e8941975fcfa559b335f37209c80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "The other arrivals are not going to affect our answers." + }, + { + "text": "It's just, conceptually speaking, we can think of the exponential random variable as being embedded in a bigger Poisson picture." + }, + { + "text": "So we have 3 Poisson process that are running in parallel." + }, + { + "text": "Let us split the expected time until the last burnout into pieces, which is time until the first burnout, time from the first until the second, and time from the second until the third." + }, + { + "text": "And find the expected values of each one of these pieces." + }, + { + "text": "What can we say about the expected value of this?" + }, + { + "text": "This is the first arrival out of all of these 3 Poisson processes." + }, + { + "text": "It's the first event that happens when you look at all of these processes simultaneously." + }, + { + "text": "So 3 Poisson processes running in parallel." + }, + { + "text": "We're interested in the time until one of them, any one of them, gets in arrival." + }, + { + "text": "Rephrase." + }, + { + "text": "We merged the 3 Poisson processes, and we ask for the time until we observe an arrival in the merged process." + }, + { + "text": "When 1 of the 3 gets an arrival for the first time, the merged process gets its first arrival." + }, + { + "text": "So what's the expected value of this time until the first burnout?" + }, + { + "text": "It's going to be the expected value of a Poisson random variable." + }, + { + "text": "So the first burnout is going to have an expected value, which is-- OK." + }, + { + "text": "It's a Poisson process." + }, + { + "text": "The merged process of the 3 has a collective arrival rate, which is 3 times lambda." + }, + { + "text": "So this is the parameter over the exponential distribution that describes the time until the first arrival in the merged process." + }, + { + "text": "And the expected value of this random variable is 1 over that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk15.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..ec2818bb27b6b5b81e6f20bc450cb58a1baac245 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "When you have an exponential random variable with parameter lambda, the expected value of that random variable is 1 over lambda." + }, + { + "text": "Here we're talking about the first arrival time in a process with rate 3 lambda." + }, + { + "text": "The expected time until the first arrival is 1 over (3 lambda)." + }, + { + "text": "Alright." + }, + { + "text": "So at this time, this bulb, this arrival happened, this bulb has been burned." + }, + { + "text": "So we don't care about that bulb anymore." + }, + { + "text": "We start at this time, and we look forward." + }, + { + "text": "This bulb has been burned." + }, + { + "text": "So let's just look forward from now on." + }, + { + "text": "What have we got?" + }, + { + "text": "We have two bulbs that are burning." + }, + { + "text": "We have a Poisson process that's the bigger picture of what could happen to that light bulb, if we were to keep replacing it." + }, + { + "text": "Another Poisson process." + }, + { + "text": "These two processes are, again, independent." + }, + { + "text": "From this time until that time, how long does it take?" + }, + { + "text": "It's the time until either this process records an arrival or that process records and arrival." + }, + { + "text": "That's the same as the time that the merged process of these two records an arrival." + }, + { + "text": "So we're talking about the expected time until the first arrival in a merged process." + }, + { + "text": "The merged process is Poisson." + }, + { + "text": "It's Poisson with rate 2 lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk16.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..6a74ed00548100b2fa7d07c494546d15ecdfac23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that extra time is going to take-- the expected value is going to be 1 over the (rate of that Poisson process)." + }, + { + "text": "So 1 over (2 lambda) is the expected value of this random variable." + }, + { + "text": "So at this point, this bulb now is also burned." + }, + { + "text": "So we start looking from this time on." + }, + { + "text": "That part of the picture disappears." + }, + { + "text": "Starting from this time, what's the expected value until that remaining light-bulb burns out?" + }, + { + "text": "Well, as we said before, in a Poisson process or with exponential random variables, we have memorylessness." + }, + { + "text": "A used bulb is as good as a new one." + }, + { + "text": "So it's as if we're starting from scratch here." + }, + { + "text": "So this is going to be an exponential random variable with parameter lambda." + }, + { + "text": "And the expected value of it is going to be 1 over lambda." + }, + { + "text": "So the beauty of approaching this problem in this particular way is, of course, that we manage to do everything without any calculus at all, without striking an integral, without trying to calculate expectations in any form." + }, + { + "text": "Most of the non-trivial problems that you encounter in the Poisson world basically involve tricks of these kind." + }, + { + "text": "You have a question and you try to rephrase it, trying to think in terms of what might happen in the Poisson setting, use memorylessness, use merging, et cetera, et cetera." + }, + { + "text": "Now we talked about merging." + }, + { + "text": "It turns out that the splitting of Poisson processes also works in a nice way." + }, + { + "text": "The story here is exactly the same as for the Bernoulli process." + }, + { + "text": "So I'm having a Poisson process." + }, + { + "text": "And each time, with some rate lambda, and each time that an arrival comes, I'm going to send it to that stream and the record an arrival here with some probability P. And I'm going to send it to the other stream with some probability 1 minus P. So either of this will happen or that will happen, depending on the outcome of the coin flip that I do." + }, + { + "text": "Each time that then arrival occurs, I flip a coin and I decide whether to record it here or there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk17.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..24ef2d939ecec102e5b0cf66c4aef963c1195410 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "This is called splitting a Poisson process into two pieces." + }, + { + "text": "What kind of process do we get here?" + }, + { + "text": "If you look at the little interval for length delta, what's the probability that this little interval gets an arrival?" + }, + { + "text": "It's the probability that this one gets an arrival, which is lambda delta times the probability that after I get an arrival my coin flip came out to be that way, so that it sends me there." + }, + { + "text": "So this means that this little interval is going to have probability lambda delta P. Or maybe more suggestively, I should write it as lambda P times delta." + }, + { + "text": "So every little interval has a probability of an arrival proportional to delta." + }, + { + "text": "The proportionality factor is lambda P. So lambda P is the rate of that process." + }, + { + "text": "And then you go through the mental exercise that you went through for the Bernoulli process to argue that a different intervals here are independent and so on." + }, + { + "text": "And that completes checking that this process is going to be a Poisson process." + }, + { + "text": "So when you split a Poisson process by doing independent coin flips each time that something happens, the processes that you get is again a Poisson process, but of course with a reduced rate." + }, + { + "text": "So instead of the word splitting, sometimes people also use the words thinning-out." + }, + { + "text": "That is, out of the arrivals that came, you keep a few but throw away a few." + }, + { + "text": "OK." + }, + { + "text": "So now the last topic over this lecture is a quite curious phenomenon that goes under the name of random incidents." + }, + { + "text": "So here's the story." + }, + { + "text": "Buses have been running on Mass Ave. from time immemorial." + }, + { + "text": "And the bus company that runs the buses claims that they come as a Poisson process with some rate, let's say, of 4 buses per hour." + }, + { + "text": "So that the expected time between bus arrivals is going to be 15 minutes." + }, + { + "text": "OK. Alright." + }, + { + "text": "So people have been complaining that they have been showing up there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk18.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..65a62f83b762cf608024e3af374f28f51f49e32f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "They think the buses are taking too long." + }, + { + "text": "So you are asked to investigate." + }, + { + "text": "Is the company-- Does it operate according to its promises or not." + }, + { + "text": "So you send an undercover agent to go and check the interarrival times of the buses." + }, + { + "text": "Are they 15 minutes?" + }, + { + "text": "Or are they longer?" + }, + { + "text": "So you put your dark glasses and you show up at the bus stop at some random time." + }, + { + "text": "And you go and ask the guy in the falafel truck, how long has it been since the last arrival?" + }, + { + "text": "So of course that guy works for the FBI, right?" + }, + { + "text": "So they tell you, well, it's been, let's say, 12 minutes since the last bus arrival." + }, + { + "text": "And then you say, \"Oh, 12 minutes." + }, + { + "text": "Average time is 15." + }, + { + "text": "So a bus should be coming any time now.\"" + }, + { + "text": "Is that correct?" + }, + { + "text": "No, you wouldn't think that way." + }, + { + "text": "It's a Poisson process." + }, + { + "text": "It doesn't matter how long it has been since the last bus arrival." + }, + { + "text": "So you don't go through that fallacy." + }, + { + "text": "Instead of predicting how long it's going to be, you just sit down there and wait and measure the time." + }, + { + "text": "And you find that this is, let's say, 11 minutes." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk19.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..af599f5b8f4c3fc0973b37e81b36088c85eae997 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you go to your boss and report, \"Well, it took-- I went there and the time from the previous bus to the next one was 23 minutes." + }, + { + "text": "It's more than the 15 that they said.\"" + }, + { + "text": "So go and do that again." + }, + { + "text": "You go day after day." + }, + { + "text": "You keep these statistics of the length of this interval." + }, + { + "text": "And you tell your boss it's a lot more than 15." + }, + { + "text": "It tends to be more like 30 or so." + }, + { + "text": "So the bus company is cheating us." + }, + { + "text": "Does the bus company really run Poisson buses at the rate that they have promised?" + }, + { + "text": "Well let's analyze the situation here and figure out what the length of this interval should be, on the average." + }, + { + "text": "The naive argument is that this interval is an interarrival time." + }, + { + "text": "And interarrival times, on the average, are 15 minutes, if the company runs indeed Poisson processes with these interarrival times." + }, + { + "text": "But actually the situation is a little more subtle because this is not a typical interarrival interval." + }, + { + "text": "This interarrival interval consists of two pieces." + }, + { + "text": "Let's call them T1 and T1 prime." + }, + { + "text": "What can you tell me about those two random variables?" + }, + { + "text": "What kind of random variable is T1?" + }, + { + "text": "Starting from this time, with the Poisson process, the past doesn't matter." + }, + { + "text": "It's the time until an arrival happens." + }, + { + "text": "So T1 is going to be an exponential random variable with parameter lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk2.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..ebc6083b4940b3fc27511f672c179a7846abc0b1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "The big interval is composed of many little intervals." + }, + { + "text": "Each little interval is independent from any other little interval, so is it is as if we have a sequence of Bernoulli trials." + }, + { + "text": "Each Bernoulli trial is associated with a little interval and has a small probability of obtaining a success or an arrival during that mini-slot." + }, + { + "text": "On the other hand, when delta is small, and you take a big interval and chop it up, you get a large number of little intervals." + }, + { + "text": "So what we essentially have here is a Bernoulli process, in which is the number of trials is huge but the probability of success during any given trial is tiny." + }, + { + "text": "The average number of trials ends up being proportional to the length of the interval." + }, + { + "text": "If you have twice as large an interval, it's as if you're having twice as many over these mini-trials, so the expected number of arrivals will increase proportionately." + }, + { + "text": "There's also this parameter lambda, which we interpret as expected number of arrivals per unit time." + }, + { + "text": "And it comes in those probabilities here." + }, + { + "text": "When you double lambda, this means that a little interval is twice as likely to get an arrival." + }, + { + "text": "So you would expect to get twice as many arrivals as well." + }, + { + "text": "That's why the expected number of arrivals during an interval of length tau also scales proportional to this parameter lambda." + }, + { + "text": "Somewhat unexpectedly, it turns out that the variance of the number of arrivals is also the same as the mean." + }, + { + "text": "This is a peculiarity that happens in the Poisson process." + }, + { + "text": "So this is one way of thinking about Poisson process, in terms of little intervals, each one of which has a tiny probability of success." + }, + { + "text": "And we think of the distribution associated with that process as being described by this particular PMF." + }, + { + "text": "So this is the PMF for the number of arrivals during an interval of a fixed duration, tau." + }, + { + "text": "It's a PMF that extends all over the entire range of non-negative integers." + }, + { + "text": "So the number of arrivals you can get during an interval for certain length can be anything." + }, + { + "text": "You can get as many arrivals as you want." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk20.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..28349ba5d13c19b16a2957596215f8e4b02bbf01 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "So in particular, the expected value of T1 is going to be 15 by itself." + }, + { + "text": "How about the random variable T1 prime." + }, + { + "text": "What kind of random variable is it?" + }, + { + "text": "This is like the first arrival in a Poisson process that runs backwards in time." + }, + { + "text": "What kind of process is a Poisson process running backwards in time?" + }, + { + "text": "Let's think of coin flips." + }, + { + "text": "Suppose you have a movie of coin flips." + }, + { + "text": "And for some accident, that fascinating movie, you happen to watch it backwards." + }, + { + "text": "Will it look any different statistically?" + }, + { + "text": "No." + }, + { + "text": "It's going to be just the sequence of random coin flips." + }, + { + "text": "So a Bernoulli process that's runs in reverse time is statistically identical to a Bernoulli process in forward time." + }, + { + "text": "The Poisson process is a limit of the Bernoulli." + }, + { + "text": "So, same story with the Poisson process." + }, + { + "text": "If you run it backwards in time it looks the same." + }, + { + "text": "So looking backwards in time, this is a Poisson process." + }, + { + "text": "And T1 prime is the time until the first arrival in this backward process." + }, + { + "text": "So T1 prime is also going to be an exponential random variable with the same parameter, lambda." + }, + { + "text": "And the expected value of T1 prime is 15." + }, + { + "text": "Conclusion is that the expected length of this interval is going to be 30 minutes." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk21.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..e60bcef503b4a0db026939c13f85514e5dcb0817 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the fact that this agent found the average to be something like 30 does not contradict the claims of the bus company that they're running Poisson buses with a rate of lambda equal to 4." + }, + { + "text": "OK." + }, + { + "text": "So maybe the company can this way-- they can defend themselves in court." + }, + { + "text": "But there's something puzzling here." + }, + { + "text": "How long is the interarrival time?" + }, + { + "text": "Is it 15?" + }, + { + "text": "Or is it 30?" + }, + { + "text": "On the average." + }, + { + "text": "The issue is what do we mean by a typical interarrival time." + }, + { + "text": "When we say typical, we mean some kind of average." + }, + { + "text": "But average over what?" + }, + { + "text": "And here's two different ways of thinking about averages." + }, + { + "text": "You number the buses." + }, + { + "text": "And you have bus number 100." + }, + { + "text": "You have bus number 101, bus number 102, bus number 110, and so on." + }, + { + "text": "One way of thinking about averages is that you pick a bus number at random." + }, + { + "text": "I pick, let's say, that bus, all buses being sort of equally likely to be picked." + }, + { + "text": "And I measure this interarrival time." + }, + { + "text": "So for a typical bus." + }, + { + "text": "Then, starting from here until there, the expected time has to be 1 over lambda, for the Poisson process." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk22.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..859fef7a50c29d5a5a9f8517f4db560ee5d550a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But what we did in this experiment was something different." + }, + { + "text": "We didn't pick a bus at random." + }, + { + "text": "We picked a time at random." + }, + { + "text": "And if the picture is, let's say, this way, I'm much more likely to pick this interval and therefore this interarrival time, rather than that interval." + }, + { + "text": "Because, this interval corresponds to very few times." + }, + { + "text": "So if I'm picking a time at random and, in some sense, let's say, uniform, so that all times are equally likely, I'm much more likely to fall inside a big interval rather than a small interval." + }, + { + "text": "So a person who shows up at the bus stop at a random time." + }, + { + "text": "They're selecting an interval in a biased way, with the bias favor of longer intervals." + }, + { + "text": "And that's why what they observe is a random variable that has a larger expected value then the ordinary expected value." + }, + { + "text": "So the subtlety here is to realize that we're talking between two different kinds of experiments." + }, + { + "text": "Picking a bus number at random verses picking an interval at random with a bias in favor of longer intervals." + }, + { + "text": "Lots of paradoxes that one can cook up using Poisson processes and random processes in general often have to do with the story of this kind." + }, + { + "text": "The phenomenon that we had in this particular example also shows up in general, whenever you have other kinds of arrival processes." + }, + { + "text": "So the Poisson process is the simplest arrival process there is, where the interarrival times are exponential random variables." + }, + { + "text": "There's a larger class of models." + }, + { + "text": "They're called renewal processes, in which, again, we have a sequence of successive arrivals, interarrival times are identically distributed and independent, but they may come from a general distribution." + }, + { + "text": "So to make the same point of the previous example but in a much simpler setting, suppose that bus interarrival times are either 5 or 10 minutes apart." + }, + { + "text": "So you get some intervals that are of length 5." + }, + { + "text": "You get some that are of length 10." + }, + { + "text": "And suppose that these are equally likely." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk23.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..0c23f2ec29db9e794aae974425a9309fbc5fa392 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "So we have -- not exactly -- In the long run, we have as many 5 minute intervals as we have 10 minute intervals." + }, + { + "text": "So the average interarrival time is 7 and 1/2." + }, + { + "text": "But if a person shows up at a random time, what are they going to see?" + }, + { + "text": "Do we have as many 5s as 10s?" + }, + { + "text": "But every 10 covers twice as much space." + }, + { + "text": "So if I show up at a random time, I have probability 2/3 falling inside an interval of duration 10." + }, + { + "text": "And I have one 1/3 probability of falling inside an interval of duration 5." + }, + { + "text": "That's because, out of the whole real line, 2/3 of it is covered by intervals of length 10, just because they're longer." + }, + { + "text": "1/3 is covered by the smaller intervals." + }, + { + "text": "Now if I fall inside an interval of length 10 and I measure the length of the interval that I fell into, that's going to be 10." + }, + { + "text": "But if I fall inside an interval of length 5 and I measure how long it is, I'm going to get a 5." + }, + { + "text": "And that, of course, is going to be different than 7.5." + }, + { + "text": "OK. And which number should be bigger?" + }, + { + "text": "It's the second number that's bigger because this one is biased in favor of the longer intervals." + }, + { + "text": "So that's, again, another illustration of the different results that you get when you have this random incidence phenomenon." + }, + { + "text": "So the bottom line, again, is that if you talk about a typical interarrival time, one must be very precise in specifying what we mean typical." + }, + { + "text": "So typical means sort of random." + }, + { + "text": "But to use the word random, you must specify very precisely what is the random experiment that you are using." + }, + { + "text": "And if you're not careful, you can get into apparent puzzles, such as the following." + }, + { + "text": "Suppose somebody tells you the average family size is 4, but the average person lives in a family of size 6." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk24.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..f1454166977d85230e828ad2593835dff01c5eed --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Is that compatible?" + }, + { + "text": "Family size is 4 on the average, but typical people live, on the average, in families of size 6." + }, + { + "text": "Well yes." + }, + { + "text": "There's no contradiction here." + }, + { + "text": "We're talking about two different experiments." + }, + { + "text": "In one experiment, I pick a family at random, and I tell you the average family is 4." + }, + { + "text": "In another experiment, I pick a person at random and I tell you that this person, on the average, will be in their family of size 6." + }, + { + "text": "And what is the catch here?" + }, + { + "text": "That if I pick a person at random, large families are more likely to be picked." + }, + { + "text": "So there's a bias in favor of large families." + }, + { + "text": "Or if you want to survey, let's say, are trains crowded in your city?" + }, + { + "text": "Or are buses crowded?" + }, + { + "text": "One choice is to pick a bus at random and inspect how crowded it is." + }, + { + "text": "Another choice is to pick a typical person and ask them, \"Did you ride the bus today?" + }, + { + "text": "Was it's crowded?\"" + }, + { + "text": "Well suppose that in this city there's one bus that's extremely crowded and all the other buses are completely empty." + }, + { + "text": "If you ask a person." + }, + { + "text": "\"Was your bus crowded?\"" + }, + { + "text": "They will tell you, \"Yes, my bus was crowded.\"" + }, + { + "text": "There's no witness from the empty buses to testify in their favor." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk25.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..5ea6070c380c8c0cc3ed8ff41fe3f0d64a2f6192 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk25.json @@ -0,0 +1,23 @@ +[ + { + "text": "So by sampling people instead of sampling buses, you're going to get different result." + }, + { + "text": "And in the process industry, if your job is to inspect and check cookies, you will be faced with a big dilemma." + }, + { + "text": "Do you want to find out how many chocolate chips there are on a typical cookie?" + }, + { + "text": "Are you going to interview cookies or are you going to interview chocolate chips and ask them how many other chips where there on your cookie?" + }, + { + "text": "And you're going to get different answers in these cases." + }, + { + "text": "So moral is, one has to be very precise on how you formulate the sampling procedure that you have." + }, + { + "text": "And you'll get different answers." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk3.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..65f67102a7086dbc76d65afeddb2720c5b67bdb0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "Of course the probability of getting a zillion arrivals is going to be tiny." + }, + { + "text": "But in principle, this is possible." + }, + { + "text": "And that's because an interval, even if it's a fixed length, consists of an infinite number of mini-slots in some sense." + }, + { + "text": "You can divide, chop it up, into as many mini-slots as you want." + }, + { + "text": "So in principle, it's possible that every mini-slot gets an arrival." + }, + { + "text": "In principle, it's possible to get an arbitrarily large number of arrivals." + }, + { + "text": "So this particular formula here is not very intuitive when you look at it." + }, + { + "text": "But it's a legitimate PMF." + }, + { + "text": "And it's called the Poisson PMF." + }, + { + "text": "It's the PMF that describes the number of arrivals." + }, + { + "text": "So that's one way of thinking about the Poisson process, where the basic object of interest would be this PMF and you try to work with it." + }, + { + "text": "There's another way of thinking about what happens in the Poisson process." + }, + { + "text": "And this has to do with letting things evolve in time." + }, + { + "text": "You start at time 0." + }, + { + "text": "There's going to be a time at which the first arrival occurs, and call that time T1." + }, + { + "text": "This time turns out to have an exponential distribution with parameter lambda." + }, + { + "text": "Once you get an arrival, it's as if the process starts fresh." + }, + { + "text": "The best way to understand why this is the case is by thinking in terms of the analogy with the Bernoulli process." + }, + { + "text": "If you believe that statement for the Bernoulli process, since this is a limiting case, it should also be true." + }, + { + "text": "So starting from this time, we're going to wait a random amount of time until we get the second arrival This random amount of time, let's call it T2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk4.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c5affc1f1a5b3e0305dcd63ee178f3ba1a2da02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "This time, T2 is also going to have an exponential distribution with the same parameter, lambda." + }, + { + "text": "And these two are going to be independent of each other." + }, + { + "text": "OK?" + }, + { + "text": "So the Poisson process has all the same memorylessness properties that the Bernoulli process has." + }, + { + "text": "What's another way of thinking of this property?" + }, + { + "text": "So think of a process where you have a light bulb." + }, + { + "text": "The time at the light bulb burns out, you can model it by an exponential random variable." + }, + { + "text": "And suppose that they tell you that so far, we're are sitting at some time, T. And I tell you that the light bulb has not yet burned out." + }, + { + "text": "What does this tell you about the future of the light bulb?" + }, + { + "text": "Is the fact that they didn't burn out, so far, is it good news or is it bad news?" + }, + { + "text": "Would you rather keep this light bulb that has worked for t times steps and is still OK?" + }, + { + "text": "Or would you rather use a new light bulb that starts new at that point in time?" + }, + { + "text": "Because of the memorylessness property, the past of that light bulb doesn't matter." + }, + { + "text": "So the future of this light bulb is statistically the same as the future of a new light bulb." + }, + { + "text": "For both of them, the time until they burn out is going to be described an exponential distribution." + }, + { + "text": "So one way that people described the situation is to say that used is exactly as good as a new." + }, + { + "text": "So a used on is no worse than a new one." + }, + { + "text": "A used one is no better than a new one." + }, + { + "text": "So a used light bulb that hasn't yet burnt out is exactly as good as a new light bulb." + }, + { + "text": "So that's another way of thinking about the memorylessness that we have in the Poisson process." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk5.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..a8f4593b861f0c6ab6d24f9023bf2c98983b5ab3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "Back to this picture." + }, + { + "text": "The time until the second arrival is the sum of two independent exponential random variables." + }, + { + "text": "So, in principle, you can use the convolution formula to find the distribution of T1 plus T2, and that would be what we call Y2, the time until the second arrival." + }, + { + "text": "But there's also a direct way of obtaining to the distribution of Y2, and this is the calculation that we did last time on the blackboard." + }, + { + "text": "And actually, we did it more generally." + }, + { + "text": "We found the time until the case arrival occurs." + }, + { + "text": "It has a closed form formula, which is called the Erlang distribution with k degrees of freedom." + }, + { + "text": "So let's see what's going on here." + }, + { + "text": "It's a distribution Of what kind?" + }, + { + "text": "It's a continuous distribution." + }, + { + "text": "It's a probability density function." + }, + { + "text": "This is because the time is a continuous random variable." + }, + { + "text": "Time is continuous." + }, + { + "text": "Arrivals can happen at any time." + }, + { + "text": "So we're talking about the PDF." + }, + { + "text": "This k is just the parameter of the distribution." + }, + { + "text": "We're talking about the k-th arrival, so k is a fixed number." + }, + { + "text": "Lambda is another parameter of the distribution, which is the arrival rate So it's a PDF over the Y's, whereas lambda and k are parameters of the distribution." + }, + { + "text": "OK." + }, + { + "text": "So this was what we knew from last time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk6.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..f957b2a1915e0744ba6fb901fba06c158d7e336f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Just to get some practice, let us do a problem that's not too difficult, but just to see how we use the various formulas that we have." + }, + { + "text": "So Poisson was a mathematician, but Poisson also means fish in French." + }, + { + "text": "So Poisson goes fishing." + }, + { + "text": "And let's assume that fish are caught according to a Poisson process." + }, + { + "text": "That's not too bad an assumption." + }, + { + "text": "At any given point in time, you have a little probability that a fish would be caught." + }, + { + "text": "And whether you catch one now is sort of independent about whether at some later time a fish will be caught or not." + }, + { + "text": "So let's just make this assumption." + }, + { + "text": "And suppose that the rules of the game are that you-- Fish are being called it the certain rate of 0.6 per hour." + }, + { + "text": "You fish for 2 hours, no matter what." + }, + { + "text": "And then there are two possibilities." + }, + { + "text": "If I have caught a fish, I stop and go home." + }, + { + "text": "So if some fish have been caught, so there's at least 1 arrival during this interval, I go home." + }, + { + "text": "Or if nothing has being caught, I continue fishing until I catch something." + }, + { + "text": "And then I go home." + }, + { + "text": "So that's the description of what is going to happen." + }, + { + "text": "And now let's starts asking questions of all sorts." + }, + { + "text": "What is the probability that I'm going to be fishing for more than 2 hours?" + }, + { + "text": "I will be fishing for more than 2 hours, if and only if no fish were caught during those 2 hours, in which case, I will have to continue." + }, + { + "text": "Therefore, this is just this quantity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk7.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..d200ba8c85d33ddb01ccd0430f2d344dfd85356f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "The probability of catching 2 fish in-- of catching 0 fish in the next 2 hours, and according to the formula that we have, this is going to be e to the minus lambda times how much time we have." + }, + { + "text": "There's another way of thinking about this." + }, + { + "text": "The probability that I fish for more than 2 hours is the probability that the first catch happens after time 2, which would be the integral from 2 to infinity of the density of the first arrival time." + }, + { + "text": "And that density is an exponential." + }, + { + "text": "So you do the integral of an exponential, and, of course, you would get the same answer." + }, + { + "text": "OK. That's easy." + }, + { + "text": "So what's the probability of fishing for more than 2 but less than 5 hours?" + }, + { + "text": "What does it take for this to happen?" + }, + { + "text": "For this to happen, we need to catch 0 fish from time 0 to 2 and catch the first fish sometime between 2 and 5." + }, + { + "text": "So if you-- one way of thinking about what's happening here might be to say that there's a Poisson process that keeps going on forever." + }, + { + "text": "But as soon as I catch the first fish, instead of continuing fishing and obtaining those other fish I just go home right now." + }, + { + "text": "Now the fact that I go home before time 5 means that, if I were to stay until time 5, I would have caught at least 1 fish." + }, + { + "text": "I might have caught more than 1." + }, + { + "text": "So the event of interest here is that the first catch happens between times 2 and 5." + }, + { + "text": "So one way of calculating this quantity would be-- Its the probability that the first catch happens between times 2 and 5." + }, + { + "text": "Another way to deal with it is to say, this is the probability that I caught 0 fish in the first 2 hours and then the probability that I catch at least 1 fish during the next 3 hours." + }, + { + "text": "This." + }, + { + "text": "What is this?" + }, + { + "text": "The probability of 0 fish in the next 3 hours is the probability of 0 fish during this time." + }, + { + "text": "1 minus this is the probability of catching at least 1 fish, of having at least 1 arrival, between times 2 and 5." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk8.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..63208c3916b0f28860e55ba410e9e8809a2e2618 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "If there's at least 1 arrival between times 2 and 5, then I would have gone home by time 5." + }, + { + "text": "So both of these, if you plug-in numbers and all that, of course, are going to give you the same answer." + }, + { + "text": "Now next, what's the probability that I catch at least 2 fish?" + }, + { + "text": "In which scenario are we?" + }, + { + "text": "Under this scenario, I go home when I catch my first fish." + }, + { + "text": "So in order to catch at least 2 fish, it must be in this case." + }, + { + "text": "So this is the same as the event that I catch at least 2 fish during the first 2 time steps." + }, + { + "text": "So it's going to be the probability from 2 to infinity, the probability that I catch 2 fish, or that I catch 3 fish, or I catch more than that." + }, + { + "text": "So it's this quantity." + }, + { + "text": "k is the number of fish that I catch." + }, + { + "text": "At least 2, so k goes from 2 to infinity." + }, + { + "text": "These are the probabilities of catching a number k of fish during this interval." + }, + { + "text": "And if you want a simpler form without an infinite sum, this would be 1 minus the probability of catching 0 fish, minus the probability of catching 1 fish, during a time interval of length 2." + }, + { + "text": "Another way to think of it." + }, + { + "text": "I'm going to catch 2 fish, at least 2 fish, if and only if the second fish caught in this process happens before time 2." + }, + { + "text": "So that's another way of thinking about the same event." + }, + { + "text": "So it's going to be the probability that the random variable Y2, the arrival time over the second fish, is less than or equal to 2." + }, + { + "text": "OK." + }, + { + "text": "The next one is a little trickier." + }, + { + "text": "Here we need to do a little bit of divide and conquer." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk9.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..438a6aa22ffef63c853416c037d519d661ef6133 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_3_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "Overall, in this expedition, what the expected number of fish to be caught?" + }, + { + "text": "One way to think about it is to try to use the total expectations theorem." + }, + { + "text": "And think of expected number of fish, given this scenario, or expected number of fish, given this scenario." + }, + { + "text": "That's a little more complicated than the way I'm going to do it." + }, + { + "text": "The way I'm going to do is to think as follows-- Expected number of fish is the expected number of fish caught between times 0 and 2 plus expected number of fish caught after time 2." + }, + { + "text": "So what's the expected number caught between time 0 and 2?" + }, + { + "text": "This is lambda t. So lambda is 0.6 times 2." + }, + { + "text": "This is the expected number of fish that are caught between times 0 and 2." + }, + { + "text": "Now let's think about the expected number of fish caught afterwards." + }, + { + "text": "How many fish are being caught afterwards?" + }, + { + "text": "Well it depends on the scenario." + }, + { + "text": "If we're in this scenario, we've gone home and we catch 0." + }, + { + "text": "If we're in this scenario, then we continue fishing until we catch one." + }, + { + "text": "So the expected number of fish to be caught after time 2 is going to be the probability of this scenario times 1." + }, + { + "text": "And the probability of that scenario is the probability that they call it's 0 fish during the first 2 time steps times 1, which is the number of fish I'm going to catch if I continue." + }, + { + "text": "The expected total fishing time we can calculate exactly the same way." + }, + { + "text": "I'm jumping to the last one." + }, + { + "text": "My total fishing time has a period of 2 time steps." + }, + { + "text": "I'm going to fish for 2 time steps no matter what." + }, + { + "text": "And then if I caught 0 fish, which happens with this probability, my expected time is going to be the expected time from here onwards, which is the expected value of this geometric random variable with parameter lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk0.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..aa961d524ea0d1287b995e40358f71afcd69bfb1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "JOHN TSITSIKLIS: Today we're going to finish our discussion of the Poisson process." + }, + { + "text": "We're going to see a few of its properties, do a few interesting problems, some more interesting than others." + }, + { + "text": "So go through a few examples and then we're going to talk about some quite strange things that happen with the Poisson process." + }, + { + "text": "So the first thing is to remember what the Poisson processes is." + }, + { + "text": "It's a model, let's say, of arrivals of customers that are, in some sense, quote unquote, completely random, that is a customer can arrive at any point in time." + }, + { + "text": "All points in time are equally likely." + }, + { + "text": "And different points in time are sort of independent of other points in time." + }, + { + "text": "So the fact that I got an arrival now doesn't tell me anything about whether there's going to be an arrival at some other time." + }, + { + "text": "In some sense, it's a continuous time version of the Bernoulli process." + }, + { + "text": "So the best way to think about the Poisson process is that we divide time into extremely tiny slots." + }, + { + "text": "And in each time slot, there's an independent possibility of having an arrival." + }, + { + "text": "Different time slots are independent of each other." + }, + { + "text": "On the other hand, when the slot is tiny, the probability for obtaining an arrival during that tiny slot is itself going to be tiny." + }, + { + "text": "So we capture these properties into a formal definition what the Poisson process is." + }, + { + "text": "We have a probability mass function for the number of arrivals, k, during an interval of a given length." + }, + { + "text": "So this is the sort of basic description of the distribution of the number of arrivals." + }, + { + "text": "So tau is fixed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk1.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..8ef79a1bbf5e44814915347122880462d60e3970 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And k is the parameter." + }, + { + "text": "So when we add over all k's, the sum of these probabilities has to be equal to 1." + }, + { + "text": "There's a time homogeneity assumption, which is hidden in this, namely, the only thing that matters is the duration of the time interval, not where the time interval sits on the real axis." + }, + { + "text": "Then we have an independence assumption." + }, + { + "text": "Intervals that are disjoint are statistically independent from each other." + }, + { + "text": "So any information you give me about arrivals during this time interval doesn't change my beliefs about what's going to happen during another time interval." + }, + { + "text": "So this is a generalization of the idea that we had in Bernoulli processes that different time slots are independent of each other." + }, + { + "text": "And then to specify this function, the distribution of the number of arrivals, we sort of go in stages." + }, + { + "text": "We first specify this function for the case where the time interval is very small." + }, + { + "text": "And I'm telling you what those probabilities will be." + }, + { + "text": "And based on these then, we do some calculations and to find the formula for the distribution of the number of arrivals for intervals of a general duration." + }, + { + "text": "So for a small duration, delta, the probability of obtaining 1 arrival is lambda delta." + }, + { + "text": "The remaining probability is assigned to the event that we get to no arrivals during that interval." + }, + { + "text": "The probability of obtaining more than 1 arrival in a tiny interval is essentially 0." + }, + { + "text": "And when we say essentially, it's means modular, terms that of order delta squared." + }, + { + "text": "And when delta is very small, anything which is delta squared can be ignored." + }, + { + "text": "So up to delta squared terms, that's what happened during a little interval." + }, + { + "text": "Now if we know the probability distribution for the number of arrivals in a little interval." + }, + { + "text": "We can use this to get the distribution for the number of arrivals over several intervals." + }, + { + "text": "How do we do that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk10.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c993d1aafbcf3de55a33d47639c163aee1857626 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So the expected time is 1 over lambda." + }, + { + "text": "And in our case this, is 1/0.6." + }, + { + "text": "Finally, if I tell you that I have been fishing for 4 hours and nothing has been caught so far, how much do you expect this quantity to be?" + }, + { + "text": "Here is the story that, again, that for the Poisson process used is as good as new." + }, + { + "text": "The process does not have any memory." + }, + { + "text": "Given what happens in the past doesn't matter for the future." + }, + { + "text": "It's as if the process starts new at this point in time." + }, + { + "text": "So this one is going to be, again, the same exponentially distributed random variable with the same parameter lambda." + }, + { + "text": "So expected time until an arrival comes is an exponential distribut -- has an exponential distribution with parameter lambda, no matter what has happened in the past." + }, + { + "text": "Starting from now and looking into the future, it's as if the process has just started." + }, + { + "text": "So it's going to be 1 over lambda, which is 1/0.6." + }, + { + "text": "OK. Now our next example is going to be a little more complicated or subtle." + }, + { + "text": "But before we get to the example, let's refresh our memory about what we discussed last time about merging Poisson independent Poisson processes." + }, + { + "text": "Instead of drawing the picture that way, another way we could draw it could be this." + }, + { + "text": "We have a Poisson process with rate lambda1, and a Poisson process with rate lambda2." + }, + { + "text": "They have, each one of these, have their arrivals." + }, + { + "text": "And then we form the merged process." + }, + { + "text": "And the merged process records an arrival whenever there's an arrival in either of the two processes." + }, + { + "text": "This process in that process are assumed to be independent of each other." + }, + { + "text": "Now different times in this process and that process are independent of each other." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk11.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..98f4de8fc7edf6671add64512cd98e8481dce843 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what happens in these two time intervals is independent from what happens in these two time intervals." + }, + { + "text": "These two time intervals to determine what happens here." + }, + { + "text": "These two time intervals determine what happens there." + }, + { + "text": "So because these are independent from these, this means that this is also independent from that." + }, + { + "text": "So the independence assumption is satisfied for the merged process." + }, + { + "text": "And the merged process turns out to be a Poisson process." + }, + { + "text": "And if you want to find the arrival rate for that process, you argue as follows." + }, + { + "text": "During a little interval of length delta, we have probability lambda1 delta of having an arrival in this process." + }, + { + "text": "We have probability lambda2 delta of an arrival in this process, plus second order terms in delta, which we're ignoring." + }, + { + "text": "And then you do the calculation and you find that in this process, you're going to have an arrival probability, which is lambda1 plus lambda2, again ignoring second order in delta-- terms that are second order in delta." + }, + { + "text": "So the merged process is a Poisson process whose arrival rate is the sum of the arrival rates of the individual processes." + }, + { + "text": "And the calculation we did at the end of the last lecture-- If I tell you that the new arrival happened here, where did that arrival come from?" + }, + { + "text": "Did it come from here or from there?" + }, + { + "text": "If the lambda1 is equal to lambda2, then by symmetry you would say that it's equally likely to have come from here or to come from there." + }, + { + "text": "But if this lambda is much bigger than that lambda, the fact that they saw an arrival is more likely to have come from there." + }, + { + "text": "And the formula that captures this is the following." + }, + { + "text": "This is the probability that my arrival has come from this particular stream rather than that particular stream." + }, + { + "text": "So when an arrival comes and you ask, what is the origin of that arrival?" + }, + { + "text": "It's as if I'm flipping a coin with these odds." + }, + { + "text": "And depending on outcome of that coin, I'm going to tell you came from there or it came from there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk12.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..b81514a3614b4cc14097ef6ee9b3469bf3d09d24 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "So the origin of an arrival is either this stream or that stream." + }, + { + "text": "And this is the probability that the origin of the arrival is that one." + }, + { + "text": "Now if we look at 2 different arrivals, and we ask about their origins-- So let's think about the origin of this arrival and compare it with the origin that arrival." + }, + { + "text": "The origin of this arrival is random." + }, + { + "text": "It could be right be either this or that." + }, + { + "text": "And this is the relevant probability." + }, + { + "text": "The origin of that arrival is random." + }, + { + "text": "It could be either here or is there, and again, with the same relevant probability." + }, + { + "text": "Question." + }, + { + "text": "The origin of this arrival, is it dependent or independent from the origin that arrival?" + }, + { + "text": "And here's how the argument goes." + }, + { + "text": "Separate times are independent." + }, + { + "text": "Whatever has happened in the process during this set of times is independent from whatever happened in the process during that set of times." + }, + { + "text": "Because different times have nothing to do with each other, the origin of this, of an arrival here, has nothing to do with the origin of an arrival there." + }, + { + "text": "So the origins of different arrivals are also independent random variables." + }, + { + "text": "So if I tell you that-- yeah." + }, + { + "text": "OK." + }, + { + "text": "So it as if that each time that you have an arrival in the merge process, it's as if you're flipping a coin to determine where did that arrival came from and these coins are independent of each other." + }, + { + "text": "OK. OK. Now we're going to use this-- what we know about merged processes to solve the problem that would be harder to do, if you were not using ideas from Poisson processes." + }, + { + "text": "So the formulation of the problem has nothing to do with the Poisson process." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk13.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..bf6c66b1e38f68ac6bd19d504f54b3d7f0681a3c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "The formulation is the following." + }, + { + "text": "We have 3 light-bulbs." + }, + { + "text": "And each light bulb is independent and is going to die out at the time that's exponentially distributed." + }, + { + "text": "So 3 light bulbs." + }, + { + "text": "They start their lives and then at some point they die or burn out." + }, + { + "text": "So let's think of this as X, this as Y, and this as Z." + }, + { + "text": "And we're interested in the time until the last light-bulb burns out." + }, + { + "text": "So we're interested in the maximum of the 3 random variables, X, Y, and Z." + }, + { + "text": "And in particular, we want to find the expected value of this maximum." + }, + { + "text": "OK." + }, + { + "text": "So you can do derived distribution, use the expected value rule, anything you want." + }, + { + "text": "You can get this answer using the tools that you already have in your hands." + }, + { + "text": "But now let us see how we can connect to this picture with a Poisson picture and come up with the answer in a very simple way." + }, + { + "text": "What is an exponential random variable?" + }, + { + "text": "An exponential random variable is the first act in the long play that involves a whole Poisson process." + }, + { + "text": "So an exponential random variable is the first act of a Poisson movie." + }, + { + "text": "Same thing here." + }, + { + "text": "You can think of this random variable as being part of some Poisson process that has been running." + }, + { + "text": "So it's part of this bigger picture." + }, + { + "text": "We're still interested in the maximum of the 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk14.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..1a92d35ab267e8941975fcfa559b335f37209c80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "The other arrivals are not going to affect our answers." + }, + { + "text": "It's just, conceptually speaking, we can think of the exponential random variable as being embedded in a bigger Poisson picture." + }, + { + "text": "So we have 3 Poisson process that are running in parallel." + }, + { + "text": "Let us split the expected time until the last burnout into pieces, which is time until the first burnout, time from the first until the second, and time from the second until the third." + }, + { + "text": "And find the expected values of each one of these pieces." + }, + { + "text": "What can we say about the expected value of this?" + }, + { + "text": "This is the first arrival out of all of these 3 Poisson processes." + }, + { + "text": "It's the first event that happens when you look at all of these processes simultaneously." + }, + { + "text": "So 3 Poisson processes running in parallel." + }, + { + "text": "We're interested in the time until one of them, any one of them, gets in arrival." + }, + { + "text": "Rephrase." + }, + { + "text": "We merged the 3 Poisson processes, and we ask for the time until we observe an arrival in the merged process." + }, + { + "text": "When 1 of the 3 gets an arrival for the first time, the merged process gets its first arrival." + }, + { + "text": "So what's the expected value of this time until the first burnout?" + }, + { + "text": "It's going to be the expected value of a Poisson random variable." + }, + { + "text": "So the first burnout is going to have an expected value, which is-- OK." + }, + { + "text": "It's a Poisson process." + }, + { + "text": "The merged process of the 3 has a collective arrival rate, which is 3 times lambda." + }, + { + "text": "So this is the parameter over the exponential distribution that describes the time until the first arrival in the merged process." + }, + { + "text": "And the expected value of this random variable is 1 over that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk15.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..ec2818bb27b6b5b81e6f20bc450cb58a1baac245 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "When you have an exponential random variable with parameter lambda, the expected value of that random variable is 1 over lambda." + }, + { + "text": "Here we're talking about the first arrival time in a process with rate 3 lambda." + }, + { + "text": "The expected time until the first arrival is 1 over (3 lambda)." + }, + { + "text": "Alright." + }, + { + "text": "So at this time, this bulb, this arrival happened, this bulb has been burned." + }, + { + "text": "So we don't care about that bulb anymore." + }, + { + "text": "We start at this time, and we look forward." + }, + { + "text": "This bulb has been burned." + }, + { + "text": "So let's just look forward from now on." + }, + { + "text": "What have we got?" + }, + { + "text": "We have two bulbs that are burning." + }, + { + "text": "We have a Poisson process that's the bigger picture of what could happen to that light bulb, if we were to keep replacing it." + }, + { + "text": "Another Poisson process." + }, + { + "text": "These two processes are, again, independent." + }, + { + "text": "From this time until that time, how long does it take?" + }, + { + "text": "It's the time until either this process records an arrival or that process records and arrival." + }, + { + "text": "That's the same as the time that the merged process of these two records an arrival." + }, + { + "text": "So we're talking about the expected time until the first arrival in a merged process." + }, + { + "text": "The merged process is Poisson." + }, + { + "text": "It's Poisson with rate 2 lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk16.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..6a74ed00548100b2fa7d07c494546d15ecdfac23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that extra time is going to take-- the expected value is going to be 1 over the (rate of that Poisson process)." + }, + { + "text": "So 1 over (2 lambda) is the expected value of this random variable." + }, + { + "text": "So at this point, this bulb now is also burned." + }, + { + "text": "So we start looking from this time on." + }, + { + "text": "That part of the picture disappears." + }, + { + "text": "Starting from this time, what's the expected value until that remaining light-bulb burns out?" + }, + { + "text": "Well, as we said before, in a Poisson process or with exponential random variables, we have memorylessness." + }, + { + "text": "A used bulb is as good as a new one." + }, + { + "text": "So it's as if we're starting from scratch here." + }, + { + "text": "So this is going to be an exponential random variable with parameter lambda." + }, + { + "text": "And the expected value of it is going to be 1 over lambda." + }, + { + "text": "So the beauty of approaching this problem in this particular way is, of course, that we manage to do everything without any calculus at all, without striking an integral, without trying to calculate expectations in any form." + }, + { + "text": "Most of the non-trivial problems that you encounter in the Poisson world basically involve tricks of these kind." + }, + { + "text": "You have a question and you try to rephrase it, trying to think in terms of what might happen in the Poisson setting, use memorylessness, use merging, et cetera, et cetera." + }, + { + "text": "Now we talked about merging." + }, + { + "text": "It turns out that the splitting of Poisson processes also works in a nice way." + }, + { + "text": "The story here is exactly the same as for the Bernoulli process." + }, + { + "text": "So I'm having a Poisson process." + }, + { + "text": "And each time, with some rate lambda, and each time that an arrival comes, I'm going to send it to that stream and the record an arrival here with some probability P. And I'm going to send it to the other stream with some probability 1 minus P. So either of this will happen or that will happen, depending on the outcome of the coin flip that I do." + }, + { + "text": "Each time that then arrival occurs, I flip a coin and I decide whether to record it here or there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk17.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..24ef2d939ecec102e5b0cf66c4aef963c1195410 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "This is called splitting a Poisson process into two pieces." + }, + { + "text": "What kind of process do we get here?" + }, + { + "text": "If you look at the little interval for length delta, what's the probability that this little interval gets an arrival?" + }, + { + "text": "It's the probability that this one gets an arrival, which is lambda delta times the probability that after I get an arrival my coin flip came out to be that way, so that it sends me there." + }, + { + "text": "So this means that this little interval is going to have probability lambda delta P. Or maybe more suggestively, I should write it as lambda P times delta." + }, + { + "text": "So every little interval has a probability of an arrival proportional to delta." + }, + { + "text": "The proportionality factor is lambda P. So lambda P is the rate of that process." + }, + { + "text": "And then you go through the mental exercise that you went through for the Bernoulli process to argue that a different intervals here are independent and so on." + }, + { + "text": "And that completes checking that this process is going to be a Poisson process." + }, + { + "text": "So when you split a Poisson process by doing independent coin flips each time that something happens, the processes that you get is again a Poisson process, but of course with a reduced rate." + }, + { + "text": "So instead of the word splitting, sometimes people also use the words thinning-out." + }, + { + "text": "That is, out of the arrivals that came, you keep a few but throw away a few." + }, + { + "text": "OK." + }, + { + "text": "So now the last topic over this lecture is a quite curious phenomenon that goes under the name of random incidents." + }, + { + "text": "So here's the story." + }, + { + "text": "Buses have been running on Mass Ave. from time immemorial." + }, + { + "text": "And the bus company that runs the buses claims that they come as a Poisson process with some rate, let's say, of 4 buses per hour." + }, + { + "text": "So that the expected time between bus arrivals is going to be 15 minutes." + }, + { + "text": "OK. Alright." + }, + { + "text": "So people have been complaining that they have been showing up there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk18.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..65a62f83b762cf608024e3af374f28f51f49e32f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "They think the buses are taking too long." + }, + { + "text": "So you are asked to investigate." + }, + { + "text": "Is the company-- Does it operate according to its promises or not." + }, + { + "text": "So you send an undercover agent to go and check the interarrival times of the buses." + }, + { + "text": "Are they 15 minutes?" + }, + { + "text": "Or are they longer?" + }, + { + "text": "So you put your dark glasses and you show up at the bus stop at some random time." + }, + { + "text": "And you go and ask the guy in the falafel truck, how long has it been since the last arrival?" + }, + { + "text": "So of course that guy works for the FBI, right?" + }, + { + "text": "So they tell you, well, it's been, let's say, 12 minutes since the last bus arrival." + }, + { + "text": "And then you say, \"Oh, 12 minutes." + }, + { + "text": "Average time is 15." + }, + { + "text": "So a bus should be coming any time now.\"" + }, + { + "text": "Is that correct?" + }, + { + "text": "No, you wouldn't think that way." + }, + { + "text": "It's a Poisson process." + }, + { + "text": "It doesn't matter how long it has been since the last bus arrival." + }, + { + "text": "So you don't go through that fallacy." + }, + { + "text": "Instead of predicting how long it's going to be, you just sit down there and wait and measure the time." + }, + { + "text": "And you find that this is, let's say, 11 minutes." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk19.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..af599f5b8f4c3fc0973b37e81b36088c85eae997 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you go to your boss and report, \"Well, it took-- I went there and the time from the previous bus to the next one was 23 minutes." + }, + { + "text": "It's more than the 15 that they said.\"" + }, + { + "text": "So go and do that again." + }, + { + "text": "You go day after day." + }, + { + "text": "You keep these statistics of the length of this interval." + }, + { + "text": "And you tell your boss it's a lot more than 15." + }, + { + "text": "It tends to be more like 30 or so." + }, + { + "text": "So the bus company is cheating us." + }, + { + "text": "Does the bus company really run Poisson buses at the rate that they have promised?" + }, + { + "text": "Well let's analyze the situation here and figure out what the length of this interval should be, on the average." + }, + { + "text": "The naive argument is that this interval is an interarrival time." + }, + { + "text": "And interarrival times, on the average, are 15 minutes, if the company runs indeed Poisson processes with these interarrival times." + }, + { + "text": "But actually the situation is a little more subtle because this is not a typical interarrival interval." + }, + { + "text": "This interarrival interval consists of two pieces." + }, + { + "text": "Let's call them T1 and T1 prime." + }, + { + "text": "What can you tell me about those two random variables?" + }, + { + "text": "What kind of random variable is T1?" + }, + { + "text": "Starting from this time, with the Poisson process, the past doesn't matter." + }, + { + "text": "It's the time until an arrival happens." + }, + { + "text": "So T1 is going to be an exponential random variable with parameter lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk2.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..ebc6083b4940b3fc27511f672c179a7846abc0b1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "The big interval is composed of many little intervals." + }, + { + "text": "Each little interval is independent from any other little interval, so is it is as if we have a sequence of Bernoulli trials." + }, + { + "text": "Each Bernoulli trial is associated with a little interval and has a small probability of obtaining a success or an arrival during that mini-slot." + }, + { + "text": "On the other hand, when delta is small, and you take a big interval and chop it up, you get a large number of little intervals." + }, + { + "text": "So what we essentially have here is a Bernoulli process, in which is the number of trials is huge but the probability of success during any given trial is tiny." + }, + { + "text": "The average number of trials ends up being proportional to the length of the interval." + }, + { + "text": "If you have twice as large an interval, it's as if you're having twice as many over these mini-trials, so the expected number of arrivals will increase proportionately." + }, + { + "text": "There's also this parameter lambda, which we interpret as expected number of arrivals per unit time." + }, + { + "text": "And it comes in those probabilities here." + }, + { + "text": "When you double lambda, this means that a little interval is twice as likely to get an arrival." + }, + { + "text": "So you would expect to get twice as many arrivals as well." + }, + { + "text": "That's why the expected number of arrivals during an interval of length tau also scales proportional to this parameter lambda." + }, + { + "text": "Somewhat unexpectedly, it turns out that the variance of the number of arrivals is also the same as the mean." + }, + { + "text": "This is a peculiarity that happens in the Poisson process." + }, + { + "text": "So this is one way of thinking about Poisson process, in terms of little intervals, each one of which has a tiny probability of success." + }, + { + "text": "And we think of the distribution associated with that process as being described by this particular PMF." + }, + { + "text": "So this is the PMF for the number of arrivals during an interval of a fixed duration, tau." + }, + { + "text": "It's a PMF that extends all over the entire range of non-negative integers." + }, + { + "text": "So the number of arrivals you can get during an interval for certain length can be anything." + }, + { + "text": "You can get as many arrivals as you want." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk20.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..28349ba5d13c19b16a2957596215f8e4b02bbf01 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "So in particular, the expected value of T1 is going to be 15 by itself." + }, + { + "text": "How about the random variable T1 prime." + }, + { + "text": "What kind of random variable is it?" + }, + { + "text": "This is like the first arrival in a Poisson process that runs backwards in time." + }, + { + "text": "What kind of process is a Poisson process running backwards in time?" + }, + { + "text": "Let's think of coin flips." + }, + { + "text": "Suppose you have a movie of coin flips." + }, + { + "text": "And for some accident, that fascinating movie, you happen to watch it backwards." + }, + { + "text": "Will it look any different statistically?" + }, + { + "text": "No." + }, + { + "text": "It's going to be just the sequence of random coin flips." + }, + { + "text": "So a Bernoulli process that's runs in reverse time is statistically identical to a Bernoulli process in forward time." + }, + { + "text": "The Poisson process is a limit of the Bernoulli." + }, + { + "text": "So, same story with the Poisson process." + }, + { + "text": "If you run it backwards in time it looks the same." + }, + { + "text": "So looking backwards in time, this is a Poisson process." + }, + { + "text": "And T1 prime is the time until the first arrival in this backward process." + }, + { + "text": "So T1 prime is also going to be an exponential random variable with the same parameter, lambda." + }, + { + "text": "And the expected value of T1 prime is 15." + }, + { + "text": "Conclusion is that the expected length of this interval is going to be 30 minutes." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk21.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..e60bcef503b4a0db026939c13f85514e5dcb0817 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the fact that this agent found the average to be something like 30 does not contradict the claims of the bus company that they're running Poisson buses with a rate of lambda equal to 4." + }, + { + "text": "OK." + }, + { + "text": "So maybe the company can this way-- they can defend themselves in court." + }, + { + "text": "But there's something puzzling here." + }, + { + "text": "How long is the interarrival time?" + }, + { + "text": "Is it 15?" + }, + { + "text": "Or is it 30?" + }, + { + "text": "On the average." + }, + { + "text": "The issue is what do we mean by a typical interarrival time." + }, + { + "text": "When we say typical, we mean some kind of average." + }, + { + "text": "But average over what?" + }, + { + "text": "And here's two different ways of thinking about averages." + }, + { + "text": "You number the buses." + }, + { + "text": "And you have bus number 100." + }, + { + "text": "You have bus number 101, bus number 102, bus number 110, and so on." + }, + { + "text": "One way of thinking about averages is that you pick a bus number at random." + }, + { + "text": "I pick, let's say, that bus, all buses being sort of equally likely to be picked." + }, + { + "text": "And I measure this interarrival time." + }, + { + "text": "So for a typical bus." + }, + { + "text": "Then, starting from here until there, the expected time has to be 1 over lambda, for the Poisson process." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk22.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..859fef7a50c29d5a5a9f8517f4db560ee5d550a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But what we did in this experiment was something different." + }, + { + "text": "We didn't pick a bus at random." + }, + { + "text": "We picked a time at random." + }, + { + "text": "And if the picture is, let's say, this way, I'm much more likely to pick this interval and therefore this interarrival time, rather than that interval." + }, + { + "text": "Because, this interval corresponds to very few times." + }, + { + "text": "So if I'm picking a time at random and, in some sense, let's say, uniform, so that all times are equally likely, I'm much more likely to fall inside a big interval rather than a small interval." + }, + { + "text": "So a person who shows up at the bus stop at a random time." + }, + { + "text": "They're selecting an interval in a biased way, with the bias favor of longer intervals." + }, + { + "text": "And that's why what they observe is a random variable that has a larger expected value then the ordinary expected value." + }, + { + "text": "So the subtlety here is to realize that we're talking between two different kinds of experiments." + }, + { + "text": "Picking a bus number at random verses picking an interval at random with a bias in favor of longer intervals." + }, + { + "text": "Lots of paradoxes that one can cook up using Poisson processes and random processes in general often have to do with the story of this kind." + }, + { + "text": "The phenomenon that we had in this particular example also shows up in general, whenever you have other kinds of arrival processes." + }, + { + "text": "So the Poisson process is the simplest arrival process there is, where the interarrival times are exponential random variables." + }, + { + "text": "There's a larger class of models." + }, + { + "text": "They're called renewal processes, in which, again, we have a sequence of successive arrivals, interarrival times are identically distributed and independent, but they may come from a general distribution." + }, + { + "text": "So to make the same point of the previous example but in a much simpler setting, suppose that bus interarrival times are either 5 or 10 minutes apart." + }, + { + "text": "So you get some intervals that are of length 5." + }, + { + "text": "You get some that are of length 10." + }, + { + "text": "And suppose that these are equally likely." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk23.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..0c23f2ec29db9e794aae974425a9309fbc5fa392 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "So we have -- not exactly -- In the long run, we have as many 5 minute intervals as we have 10 minute intervals." + }, + { + "text": "So the average interarrival time is 7 and 1/2." + }, + { + "text": "But if a person shows up at a random time, what are they going to see?" + }, + { + "text": "Do we have as many 5s as 10s?" + }, + { + "text": "But every 10 covers twice as much space." + }, + { + "text": "So if I show up at a random time, I have probability 2/3 falling inside an interval of duration 10." + }, + { + "text": "And I have one 1/3 probability of falling inside an interval of duration 5." + }, + { + "text": "That's because, out of the whole real line, 2/3 of it is covered by intervals of length 10, just because they're longer." + }, + { + "text": "1/3 is covered by the smaller intervals." + }, + { + "text": "Now if I fall inside an interval of length 10 and I measure the length of the interval that I fell into, that's going to be 10." + }, + { + "text": "But if I fall inside an interval of length 5 and I measure how long it is, I'm going to get a 5." + }, + { + "text": "And that, of course, is going to be different than 7.5." + }, + { + "text": "OK. And which number should be bigger?" + }, + { + "text": "It's the second number that's bigger because this one is biased in favor of the longer intervals." + }, + { + "text": "So that's, again, another illustration of the different results that you get when you have this random incidence phenomenon." + }, + { + "text": "So the bottom line, again, is that if you talk about a typical interarrival time, one must be very precise in specifying what we mean typical." + }, + { + "text": "So typical means sort of random." + }, + { + "text": "But to use the word random, you must specify very precisely what is the random experiment that you are using." + }, + { + "text": "And if you're not careful, you can get into apparent puzzles, such as the following." + }, + { + "text": "Suppose somebody tells you the average family size is 4, but the average person lives in a family of size 6." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk24.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..f1454166977d85230e828ad2593835dff01c5eed --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Is that compatible?" + }, + { + "text": "Family size is 4 on the average, but typical people live, on the average, in families of size 6." + }, + { + "text": "Well yes." + }, + { + "text": "There's no contradiction here." + }, + { + "text": "We're talking about two different experiments." + }, + { + "text": "In one experiment, I pick a family at random, and I tell you the average family is 4." + }, + { + "text": "In another experiment, I pick a person at random and I tell you that this person, on the average, will be in their family of size 6." + }, + { + "text": "And what is the catch here?" + }, + { + "text": "That if I pick a person at random, large families are more likely to be picked." + }, + { + "text": "So there's a bias in favor of large families." + }, + { + "text": "Or if you want to survey, let's say, are trains crowded in your city?" + }, + { + "text": "Or are buses crowded?" + }, + { + "text": "One choice is to pick a bus at random and inspect how crowded it is." + }, + { + "text": "Another choice is to pick a typical person and ask them, \"Did you ride the bus today?" + }, + { + "text": "Was it's crowded?\"" + }, + { + "text": "Well suppose that in this city there's one bus that's extremely crowded and all the other buses are completely empty." + }, + { + "text": "If you ask a person." + }, + { + "text": "\"Was your bus crowded?\"" + }, + { + "text": "They will tell you, \"Yes, my bus was crowded.\"" + }, + { + "text": "There's no witness from the empty buses to testify in their favor." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk25.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..5ea6070c380c8c0cc3ed8ff41fe3f0d64a2f6192 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk25.json @@ -0,0 +1,23 @@ +[ + { + "text": "So by sampling people instead of sampling buses, you're going to get different result." + }, + { + "text": "And in the process industry, if your job is to inspect and check cookies, you will be faced with a big dilemma." + }, + { + "text": "Do you want to find out how many chocolate chips there are on a typical cookie?" + }, + { + "text": "Are you going to interview cookies or are you going to interview chocolate chips and ask them how many other chips where there on your cookie?" + }, + { + "text": "And you're going to get different answers in these cases." + }, + { + "text": "So moral is, one has to be very precise on how you formulate the sampling procedure that you have." + }, + { + "text": "And you'll get different answers." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk3.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..65f67102a7086dbc76d65afeddb2720c5b67bdb0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "Of course the probability of getting a zillion arrivals is going to be tiny." + }, + { + "text": "But in principle, this is possible." + }, + { + "text": "And that's because an interval, even if it's a fixed length, consists of an infinite number of mini-slots in some sense." + }, + { + "text": "You can divide, chop it up, into as many mini-slots as you want." + }, + { + "text": "So in principle, it's possible that every mini-slot gets an arrival." + }, + { + "text": "In principle, it's possible to get an arbitrarily large number of arrivals." + }, + { + "text": "So this particular formula here is not very intuitive when you look at it." + }, + { + "text": "But it's a legitimate PMF." + }, + { + "text": "And it's called the Poisson PMF." + }, + { + "text": "It's the PMF that describes the number of arrivals." + }, + { + "text": "So that's one way of thinking about the Poisson process, where the basic object of interest would be this PMF and you try to work with it." + }, + { + "text": "There's another way of thinking about what happens in the Poisson process." + }, + { + "text": "And this has to do with letting things evolve in time." + }, + { + "text": "You start at time 0." + }, + { + "text": "There's going to be a time at which the first arrival occurs, and call that time T1." + }, + { + "text": "This time turns out to have an exponential distribution with parameter lambda." + }, + { + "text": "Once you get an arrival, it's as if the process starts fresh." + }, + { + "text": "The best way to understand why this is the case is by thinking in terms of the analogy with the Bernoulli process." + }, + { + "text": "If you believe that statement for the Bernoulli process, since this is a limiting case, it should also be true." + }, + { + "text": "So starting from this time, we're going to wait a random amount of time until we get the second arrival This random amount of time, let's call it T2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk4.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c5affc1f1a5b3e0305dcd63ee178f3ba1a2da02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "This time, T2 is also going to have an exponential distribution with the same parameter, lambda." + }, + { + "text": "And these two are going to be independent of each other." + }, + { + "text": "OK?" + }, + { + "text": "So the Poisson process has all the same memorylessness properties that the Bernoulli process has." + }, + { + "text": "What's another way of thinking of this property?" + }, + { + "text": "So think of a process where you have a light bulb." + }, + { + "text": "The time at the light bulb burns out, you can model it by an exponential random variable." + }, + { + "text": "And suppose that they tell you that so far, we're are sitting at some time, T. And I tell you that the light bulb has not yet burned out." + }, + { + "text": "What does this tell you about the future of the light bulb?" + }, + { + "text": "Is the fact that they didn't burn out, so far, is it good news or is it bad news?" + }, + { + "text": "Would you rather keep this light bulb that has worked for t times steps and is still OK?" + }, + { + "text": "Or would you rather use a new light bulb that starts new at that point in time?" + }, + { + "text": "Because of the memorylessness property, the past of that light bulb doesn't matter." + }, + { + "text": "So the future of this light bulb is statistically the same as the future of a new light bulb." + }, + { + "text": "For both of them, the time until they burn out is going to be described an exponential distribution." + }, + { + "text": "So one way that people described the situation is to say that used is exactly as good as a new." + }, + { + "text": "So a used on is no worse than a new one." + }, + { + "text": "A used one is no better than a new one." + }, + { + "text": "So a used light bulb that hasn't yet burnt out is exactly as good as a new light bulb." + }, + { + "text": "So that's another way of thinking about the memorylessness that we have in the Poisson process." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk5.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..a8f4593b861f0c6ab6d24f9023bf2c98983b5ab3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "Back to this picture." + }, + { + "text": "The time until the second arrival is the sum of two independent exponential random variables." + }, + { + "text": "So, in principle, you can use the convolution formula to find the distribution of T1 plus T2, and that would be what we call Y2, the time until the second arrival." + }, + { + "text": "But there's also a direct way of obtaining to the distribution of Y2, and this is the calculation that we did last time on the blackboard." + }, + { + "text": "And actually, we did it more generally." + }, + { + "text": "We found the time until the case arrival occurs." + }, + { + "text": "It has a closed form formula, which is called the Erlang distribution with k degrees of freedom." + }, + { + "text": "So let's see what's going on here." + }, + { + "text": "It's a distribution Of what kind?" + }, + { + "text": "It's a continuous distribution." + }, + { + "text": "It's a probability density function." + }, + { + "text": "This is because the time is a continuous random variable." + }, + { + "text": "Time is continuous." + }, + { + "text": "Arrivals can happen at any time." + }, + { + "text": "So we're talking about the PDF." + }, + { + "text": "This k is just the parameter of the distribution." + }, + { + "text": "We're talking about the k-th arrival, so k is a fixed number." + }, + { + "text": "Lambda is another parameter of the distribution, which is the arrival rate So it's a PDF over the Y's, whereas lambda and k are parameters of the distribution." + }, + { + "text": "OK." + }, + { + "text": "So this was what we knew from last time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk6.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..f957b2a1915e0744ba6fb901fba06c158d7e336f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Just to get some practice, let us do a problem that's not too difficult, but just to see how we use the various formulas that we have." + }, + { + "text": "So Poisson was a mathematician, but Poisson also means fish in French." + }, + { + "text": "So Poisson goes fishing." + }, + { + "text": "And let's assume that fish are caught according to a Poisson process." + }, + { + "text": "That's not too bad an assumption." + }, + { + "text": "At any given point in time, you have a little probability that a fish would be caught." + }, + { + "text": "And whether you catch one now is sort of independent about whether at some later time a fish will be caught or not." + }, + { + "text": "So let's just make this assumption." + }, + { + "text": "And suppose that the rules of the game are that you-- Fish are being called it the certain rate of 0.6 per hour." + }, + { + "text": "You fish for 2 hours, no matter what." + }, + { + "text": "And then there are two possibilities." + }, + { + "text": "If I have caught a fish, I stop and go home." + }, + { + "text": "So if some fish have been caught, so there's at least 1 arrival during this interval, I go home." + }, + { + "text": "Or if nothing has being caught, I continue fishing until I catch something." + }, + { + "text": "And then I go home." + }, + { + "text": "So that's the description of what is going to happen." + }, + { + "text": "And now let's starts asking questions of all sorts." + }, + { + "text": "What is the probability that I'm going to be fishing for more than 2 hours?" + }, + { + "text": "I will be fishing for more than 2 hours, if and only if no fish were caught during those 2 hours, in which case, I will have to continue." + }, + { + "text": "Therefore, this is just this quantity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk7.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..d200ba8c85d33ddb01ccd0430f2d344dfd85356f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "The probability of catching 2 fish in-- of catching 0 fish in the next 2 hours, and according to the formula that we have, this is going to be e to the minus lambda times how much time we have." + }, + { + "text": "There's another way of thinking about this." + }, + { + "text": "The probability that I fish for more than 2 hours is the probability that the first catch happens after time 2, which would be the integral from 2 to infinity of the density of the first arrival time." + }, + { + "text": "And that density is an exponential." + }, + { + "text": "So you do the integral of an exponential, and, of course, you would get the same answer." + }, + { + "text": "OK. That's easy." + }, + { + "text": "So what's the probability of fishing for more than 2 but less than 5 hours?" + }, + { + "text": "What does it take for this to happen?" + }, + { + "text": "For this to happen, we need to catch 0 fish from time 0 to 2 and catch the first fish sometime between 2 and 5." + }, + { + "text": "So if you-- one way of thinking about what's happening here might be to say that there's a Poisson process that keeps going on forever." + }, + { + "text": "But as soon as I catch the first fish, instead of continuing fishing and obtaining those other fish I just go home right now." + }, + { + "text": "Now the fact that I go home before time 5 means that, if I were to stay until time 5, I would have caught at least 1 fish." + }, + { + "text": "I might have caught more than 1." + }, + { + "text": "So the event of interest here is that the first catch happens between times 2 and 5." + }, + { + "text": "So one way of calculating this quantity would be-- Its the probability that the first catch happens between times 2 and 5." + }, + { + "text": "Another way to deal with it is to say, this is the probability that I caught 0 fish in the first 2 hours and then the probability that I catch at least 1 fish during the next 3 hours." + }, + { + "text": "This." + }, + { + "text": "What is this?" + }, + { + "text": "The probability of 0 fish in the next 3 hours is the probability of 0 fish during this time." + }, + { + "text": "1 minus this is the probability of catching at least 1 fish, of having at least 1 arrival, between times 2 and 5." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk8.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..63208c3916b0f28860e55ba410e9e8809a2e2618 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "If there's at least 1 arrival between times 2 and 5, then I would have gone home by time 5." + }, + { + "text": "So both of these, if you plug-in numbers and all that, of course, are going to give you the same answer." + }, + { + "text": "Now next, what's the probability that I catch at least 2 fish?" + }, + { + "text": "In which scenario are we?" + }, + { + "text": "Under this scenario, I go home when I catch my first fish." + }, + { + "text": "So in order to catch at least 2 fish, it must be in this case." + }, + { + "text": "So this is the same as the event that I catch at least 2 fish during the first 2 time steps." + }, + { + "text": "So it's going to be the probability from 2 to infinity, the probability that I catch 2 fish, or that I catch 3 fish, or I catch more than that." + }, + { + "text": "So it's this quantity." + }, + { + "text": "k is the number of fish that I catch." + }, + { + "text": "At least 2, so k goes from 2 to infinity." + }, + { + "text": "These are the probabilities of catching a number k of fish during this interval." + }, + { + "text": "And if you want a simpler form without an infinite sum, this would be 1 minus the probability of catching 0 fish, minus the probability of catching 1 fish, during a time interval of length 2." + }, + { + "text": "Another way to think of it." + }, + { + "text": "I'm going to catch 2 fish, at least 2 fish, if and only if the second fish caught in this process happens before time 2." + }, + { + "text": "So that's another way of thinking about the same event." + }, + { + "text": "So it's going to be the probability that the random variable Y2, the arrival time over the second fish, is less than or equal to 2." + }, + { + "text": "OK." + }, + { + "text": "The next one is a little trickier." + }, + { + "text": "Here we need to do a little bit of divide and conquer." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk9.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..438a6aa22ffef63c853416c037d519d661ef6133 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_5_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "Overall, in this expedition, what the expected number of fish to be caught?" + }, + { + "text": "One way to think about it is to try to use the total expectations theorem." + }, + { + "text": "And think of expected number of fish, given this scenario, or expected number of fish, given this scenario." + }, + { + "text": "That's a little more complicated than the way I'm going to do it." + }, + { + "text": "The way I'm going to do is to think as follows-- Expected number of fish is the expected number of fish caught between times 0 and 2 plus expected number of fish caught after time 2." + }, + { + "text": "So what's the expected number caught between time 0 and 2?" + }, + { + "text": "This is lambda t. So lambda is 0.6 times 2." + }, + { + "text": "This is the expected number of fish that are caught between times 0 and 2." + }, + { + "text": "Now let's think about the expected number of fish caught afterwards." + }, + { + "text": "How many fish are being caught afterwards?" + }, + { + "text": "Well it depends on the scenario." + }, + { + "text": "If we're in this scenario, we've gone home and we catch 0." + }, + { + "text": "If we're in this scenario, then we continue fishing until we catch one." + }, + { + "text": "So the expected number of fish to be caught after time 2 is going to be the probability of this scenario times 1." + }, + { + "text": "And the probability of that scenario is the probability that they call it's 0 fish during the first 2 time steps times 1, which is the number of fish I'm going to catch if I continue." + }, + { + "text": "The expected total fishing time we can calculate exactly the same way." + }, + { + "text": "I'm jumping to the last one." + }, + { + "text": "My total fishing time has a period of 2 time steps." + }, + { + "text": "I'm going to fish for 2 time steps no matter what." + }, + { + "text": "And then if I caught 0 fish, which happens with this probability, my expected time is going to be the expected time from here onwards, which is the expected value of this geometric random variable with parameter lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk0.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..aa961d524ea0d1287b995e40358f71afcd69bfb1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "JOHN TSITSIKLIS: Today we're going to finish our discussion of the Poisson process." + }, + { + "text": "We're going to see a few of its properties, do a few interesting problems, some more interesting than others." + }, + { + "text": "So go through a few examples and then we're going to talk about some quite strange things that happen with the Poisson process." + }, + { + "text": "So the first thing is to remember what the Poisson processes is." + }, + { + "text": "It's a model, let's say, of arrivals of customers that are, in some sense, quote unquote, completely random, that is a customer can arrive at any point in time." + }, + { + "text": "All points in time are equally likely." + }, + { + "text": "And different points in time are sort of independent of other points in time." + }, + { + "text": "So the fact that I got an arrival now doesn't tell me anything about whether there's going to be an arrival at some other time." + }, + { + "text": "In some sense, it's a continuous time version of the Bernoulli process." + }, + { + "text": "So the best way to think about the Poisson process is that we divide time into extremely tiny slots." + }, + { + "text": "And in each time slot, there's an independent possibility of having an arrival." + }, + { + "text": "Different time slots are independent of each other." + }, + { + "text": "On the other hand, when the slot is tiny, the probability for obtaining an arrival during that tiny slot is itself going to be tiny." + }, + { + "text": "So we capture these properties into a formal definition what the Poisson process is." + }, + { + "text": "We have a probability mass function for the number of arrivals, k, during an interval of a given length." + }, + { + "text": "So this is the sort of basic description of the distribution of the number of arrivals." + }, + { + "text": "So tau is fixed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk1.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..8ef79a1bbf5e44814915347122880462d60e3970 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And k is the parameter." + }, + { + "text": "So when we add over all k's, the sum of these probabilities has to be equal to 1." + }, + { + "text": "There's a time homogeneity assumption, which is hidden in this, namely, the only thing that matters is the duration of the time interval, not where the time interval sits on the real axis." + }, + { + "text": "Then we have an independence assumption." + }, + { + "text": "Intervals that are disjoint are statistically independent from each other." + }, + { + "text": "So any information you give me about arrivals during this time interval doesn't change my beliefs about what's going to happen during another time interval." + }, + { + "text": "So this is a generalization of the idea that we had in Bernoulli processes that different time slots are independent of each other." + }, + { + "text": "And then to specify this function, the distribution of the number of arrivals, we sort of go in stages." + }, + { + "text": "We first specify this function for the case where the time interval is very small." + }, + { + "text": "And I'm telling you what those probabilities will be." + }, + { + "text": "And based on these then, we do some calculations and to find the formula for the distribution of the number of arrivals for intervals of a general duration." + }, + { + "text": "So for a small duration, delta, the probability of obtaining 1 arrival is lambda delta." + }, + { + "text": "The remaining probability is assigned to the event that we get to no arrivals during that interval." + }, + { + "text": "The probability of obtaining more than 1 arrival in a tiny interval is essentially 0." + }, + { + "text": "And when we say essentially, it's means modular, terms that of order delta squared." + }, + { + "text": "And when delta is very small, anything which is delta squared can be ignored." + }, + { + "text": "So up to delta squared terms, that's what happened during a little interval." + }, + { + "text": "Now if we know the probability distribution for the number of arrivals in a little interval." + }, + { + "text": "We can use this to get the distribution for the number of arrivals over several intervals." + }, + { + "text": "How do we do that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk10.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c993d1aafbcf3de55a33d47639c163aee1857626 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So the expected time is 1 over lambda." + }, + { + "text": "And in our case this, is 1/0.6." + }, + { + "text": "Finally, if I tell you that I have been fishing for 4 hours and nothing has been caught so far, how much do you expect this quantity to be?" + }, + { + "text": "Here is the story that, again, that for the Poisson process used is as good as new." + }, + { + "text": "The process does not have any memory." + }, + { + "text": "Given what happens in the past doesn't matter for the future." + }, + { + "text": "It's as if the process starts new at this point in time." + }, + { + "text": "So this one is going to be, again, the same exponentially distributed random variable with the same parameter lambda." + }, + { + "text": "So expected time until an arrival comes is an exponential distribut -- has an exponential distribution with parameter lambda, no matter what has happened in the past." + }, + { + "text": "Starting from now and looking into the future, it's as if the process has just started." + }, + { + "text": "So it's going to be 1 over lambda, which is 1/0.6." + }, + { + "text": "OK. Now our next example is going to be a little more complicated or subtle." + }, + { + "text": "But before we get to the example, let's refresh our memory about what we discussed last time about merging Poisson independent Poisson processes." + }, + { + "text": "Instead of drawing the picture that way, another way we could draw it could be this." + }, + { + "text": "We have a Poisson process with rate lambda1, and a Poisson process with rate lambda2." + }, + { + "text": "They have, each one of these, have their arrivals." + }, + { + "text": "And then we form the merged process." + }, + { + "text": "And the merged process records an arrival whenever there's an arrival in either of the two processes." + }, + { + "text": "This process in that process are assumed to be independent of each other." + }, + { + "text": "Now different times in this process and that process are independent of each other." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk11.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..98f4de8fc7edf6671add64512cd98e8481dce843 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what happens in these two time intervals is independent from what happens in these two time intervals." + }, + { + "text": "These two time intervals to determine what happens here." + }, + { + "text": "These two time intervals determine what happens there." + }, + { + "text": "So because these are independent from these, this means that this is also independent from that." + }, + { + "text": "So the independence assumption is satisfied for the merged process." + }, + { + "text": "And the merged process turns out to be a Poisson process." + }, + { + "text": "And if you want to find the arrival rate for that process, you argue as follows." + }, + { + "text": "During a little interval of length delta, we have probability lambda1 delta of having an arrival in this process." + }, + { + "text": "We have probability lambda2 delta of an arrival in this process, plus second order terms in delta, which we're ignoring." + }, + { + "text": "And then you do the calculation and you find that in this process, you're going to have an arrival probability, which is lambda1 plus lambda2, again ignoring second order in delta-- terms that are second order in delta." + }, + { + "text": "So the merged process is a Poisson process whose arrival rate is the sum of the arrival rates of the individual processes." + }, + { + "text": "And the calculation we did at the end of the last lecture-- If I tell you that the new arrival happened here, where did that arrival come from?" + }, + { + "text": "Did it come from here or from there?" + }, + { + "text": "If the lambda1 is equal to lambda2, then by symmetry you would say that it's equally likely to have come from here or to come from there." + }, + { + "text": "But if this lambda is much bigger than that lambda, the fact that they saw an arrival is more likely to have come from there." + }, + { + "text": "And the formula that captures this is the following." + }, + { + "text": "This is the probability that my arrival has come from this particular stream rather than that particular stream." + }, + { + "text": "So when an arrival comes and you ask, what is the origin of that arrival?" + }, + { + "text": "It's as if I'm flipping a coin with these odds." + }, + { + "text": "And depending on outcome of that coin, I'm going to tell you came from there or it came from there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk12.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..b81514a3614b4cc14097ef6ee9b3469bf3d09d24 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "So the origin of an arrival is either this stream or that stream." + }, + { + "text": "And this is the probability that the origin of the arrival is that one." + }, + { + "text": "Now if we look at 2 different arrivals, and we ask about their origins-- So let's think about the origin of this arrival and compare it with the origin that arrival." + }, + { + "text": "The origin of this arrival is random." + }, + { + "text": "It could be right be either this or that." + }, + { + "text": "And this is the relevant probability." + }, + { + "text": "The origin of that arrival is random." + }, + { + "text": "It could be either here or is there, and again, with the same relevant probability." + }, + { + "text": "Question." + }, + { + "text": "The origin of this arrival, is it dependent or independent from the origin that arrival?" + }, + { + "text": "And here's how the argument goes." + }, + { + "text": "Separate times are independent." + }, + { + "text": "Whatever has happened in the process during this set of times is independent from whatever happened in the process during that set of times." + }, + { + "text": "Because different times have nothing to do with each other, the origin of this, of an arrival here, has nothing to do with the origin of an arrival there." + }, + { + "text": "So the origins of different arrivals are also independent random variables." + }, + { + "text": "So if I tell you that-- yeah." + }, + { + "text": "OK." + }, + { + "text": "So it as if that each time that you have an arrival in the merge process, it's as if you're flipping a coin to determine where did that arrival came from and these coins are independent of each other." + }, + { + "text": "OK. OK. Now we're going to use this-- what we know about merged processes to solve the problem that would be harder to do, if you were not using ideas from Poisson processes." + }, + { + "text": "So the formulation of the problem has nothing to do with the Poisson process." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk13.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..bf6c66b1e38f68ac6bd19d504f54b3d7f0681a3c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "The formulation is the following." + }, + { + "text": "We have 3 light-bulbs." + }, + { + "text": "And each light bulb is independent and is going to die out at the time that's exponentially distributed." + }, + { + "text": "So 3 light bulbs." + }, + { + "text": "They start their lives and then at some point they die or burn out." + }, + { + "text": "So let's think of this as X, this as Y, and this as Z." + }, + { + "text": "And we're interested in the time until the last light-bulb burns out." + }, + { + "text": "So we're interested in the maximum of the 3 random variables, X, Y, and Z." + }, + { + "text": "And in particular, we want to find the expected value of this maximum." + }, + { + "text": "OK." + }, + { + "text": "So you can do derived distribution, use the expected value rule, anything you want." + }, + { + "text": "You can get this answer using the tools that you already have in your hands." + }, + { + "text": "But now let us see how we can connect to this picture with a Poisson picture and come up with the answer in a very simple way." + }, + { + "text": "What is an exponential random variable?" + }, + { + "text": "An exponential random variable is the first act in the long play that involves a whole Poisson process." + }, + { + "text": "So an exponential random variable is the first act of a Poisson movie." + }, + { + "text": "Same thing here." + }, + { + "text": "You can think of this random variable as being part of some Poisson process that has been running." + }, + { + "text": "So it's part of this bigger picture." + }, + { + "text": "We're still interested in the maximum of the 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk14.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..1a92d35ab267e8941975fcfa559b335f37209c80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "The other arrivals are not going to affect our answers." + }, + { + "text": "It's just, conceptually speaking, we can think of the exponential random variable as being embedded in a bigger Poisson picture." + }, + { + "text": "So we have 3 Poisson process that are running in parallel." + }, + { + "text": "Let us split the expected time until the last burnout into pieces, which is time until the first burnout, time from the first until the second, and time from the second until the third." + }, + { + "text": "And find the expected values of each one of these pieces." + }, + { + "text": "What can we say about the expected value of this?" + }, + { + "text": "This is the first arrival out of all of these 3 Poisson processes." + }, + { + "text": "It's the first event that happens when you look at all of these processes simultaneously." + }, + { + "text": "So 3 Poisson processes running in parallel." + }, + { + "text": "We're interested in the time until one of them, any one of them, gets in arrival." + }, + { + "text": "Rephrase." + }, + { + "text": "We merged the 3 Poisson processes, and we ask for the time until we observe an arrival in the merged process." + }, + { + "text": "When 1 of the 3 gets an arrival for the first time, the merged process gets its first arrival." + }, + { + "text": "So what's the expected value of this time until the first burnout?" + }, + { + "text": "It's going to be the expected value of a Poisson random variable." + }, + { + "text": "So the first burnout is going to have an expected value, which is-- OK." + }, + { + "text": "It's a Poisson process." + }, + { + "text": "The merged process of the 3 has a collective arrival rate, which is 3 times lambda." + }, + { + "text": "So this is the parameter over the exponential distribution that describes the time until the first arrival in the merged process." + }, + { + "text": "And the expected value of this random variable is 1 over that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk15.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..ec2818bb27b6b5b81e6f20bc450cb58a1baac245 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "When you have an exponential random variable with parameter lambda, the expected value of that random variable is 1 over lambda." + }, + { + "text": "Here we're talking about the first arrival time in a process with rate 3 lambda." + }, + { + "text": "The expected time until the first arrival is 1 over (3 lambda)." + }, + { + "text": "Alright." + }, + { + "text": "So at this time, this bulb, this arrival happened, this bulb has been burned." + }, + { + "text": "So we don't care about that bulb anymore." + }, + { + "text": "We start at this time, and we look forward." + }, + { + "text": "This bulb has been burned." + }, + { + "text": "So let's just look forward from now on." + }, + { + "text": "What have we got?" + }, + { + "text": "We have two bulbs that are burning." + }, + { + "text": "We have a Poisson process that's the bigger picture of what could happen to that light bulb, if we were to keep replacing it." + }, + { + "text": "Another Poisson process." + }, + { + "text": "These two processes are, again, independent." + }, + { + "text": "From this time until that time, how long does it take?" + }, + { + "text": "It's the time until either this process records an arrival or that process records and arrival." + }, + { + "text": "That's the same as the time that the merged process of these two records an arrival." + }, + { + "text": "So we're talking about the expected time until the first arrival in a merged process." + }, + { + "text": "The merged process is Poisson." + }, + { + "text": "It's Poisson with rate 2 lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk16.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..6a74ed00548100b2fa7d07c494546d15ecdfac23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that extra time is going to take-- the expected value is going to be 1 over the (rate of that Poisson process)." + }, + { + "text": "So 1 over (2 lambda) is the expected value of this random variable." + }, + { + "text": "So at this point, this bulb now is also burned." + }, + { + "text": "So we start looking from this time on." + }, + { + "text": "That part of the picture disappears." + }, + { + "text": "Starting from this time, what's the expected value until that remaining light-bulb burns out?" + }, + { + "text": "Well, as we said before, in a Poisson process or with exponential random variables, we have memorylessness." + }, + { + "text": "A used bulb is as good as a new one." + }, + { + "text": "So it's as if we're starting from scratch here." + }, + { + "text": "So this is going to be an exponential random variable with parameter lambda." + }, + { + "text": "And the expected value of it is going to be 1 over lambda." + }, + { + "text": "So the beauty of approaching this problem in this particular way is, of course, that we manage to do everything without any calculus at all, without striking an integral, without trying to calculate expectations in any form." + }, + { + "text": "Most of the non-trivial problems that you encounter in the Poisson world basically involve tricks of these kind." + }, + { + "text": "You have a question and you try to rephrase it, trying to think in terms of what might happen in the Poisson setting, use memorylessness, use merging, et cetera, et cetera." + }, + { + "text": "Now we talked about merging." + }, + { + "text": "It turns out that the splitting of Poisson processes also works in a nice way." + }, + { + "text": "The story here is exactly the same as for the Bernoulli process." + }, + { + "text": "So I'm having a Poisson process." + }, + { + "text": "And each time, with some rate lambda, and each time that an arrival comes, I'm going to send it to that stream and the record an arrival here with some probability P. And I'm going to send it to the other stream with some probability 1 minus P. So either of this will happen or that will happen, depending on the outcome of the coin flip that I do." + }, + { + "text": "Each time that then arrival occurs, I flip a coin and I decide whether to record it here or there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk17.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..24ef2d939ecec102e5b0cf66c4aef963c1195410 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "This is called splitting a Poisson process into two pieces." + }, + { + "text": "What kind of process do we get here?" + }, + { + "text": "If you look at the little interval for length delta, what's the probability that this little interval gets an arrival?" + }, + { + "text": "It's the probability that this one gets an arrival, which is lambda delta times the probability that after I get an arrival my coin flip came out to be that way, so that it sends me there." + }, + { + "text": "So this means that this little interval is going to have probability lambda delta P. Or maybe more suggestively, I should write it as lambda P times delta." + }, + { + "text": "So every little interval has a probability of an arrival proportional to delta." + }, + { + "text": "The proportionality factor is lambda P. So lambda P is the rate of that process." + }, + { + "text": "And then you go through the mental exercise that you went through for the Bernoulli process to argue that a different intervals here are independent and so on." + }, + { + "text": "And that completes checking that this process is going to be a Poisson process." + }, + { + "text": "So when you split a Poisson process by doing independent coin flips each time that something happens, the processes that you get is again a Poisson process, but of course with a reduced rate." + }, + { + "text": "So instead of the word splitting, sometimes people also use the words thinning-out." + }, + { + "text": "That is, out of the arrivals that came, you keep a few but throw away a few." + }, + { + "text": "OK." + }, + { + "text": "So now the last topic over this lecture is a quite curious phenomenon that goes under the name of random incidents." + }, + { + "text": "So here's the story." + }, + { + "text": "Buses have been running on Mass Ave. from time immemorial." + }, + { + "text": "And the bus company that runs the buses claims that they come as a Poisson process with some rate, let's say, of 4 buses per hour." + }, + { + "text": "So that the expected time between bus arrivals is going to be 15 minutes." + }, + { + "text": "OK. Alright." + }, + { + "text": "So people have been complaining that they have been showing up there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk18.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..65a62f83b762cf608024e3af374f28f51f49e32f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "They think the buses are taking too long." + }, + { + "text": "So you are asked to investigate." + }, + { + "text": "Is the company-- Does it operate according to its promises or not." + }, + { + "text": "So you send an undercover agent to go and check the interarrival times of the buses." + }, + { + "text": "Are they 15 minutes?" + }, + { + "text": "Or are they longer?" + }, + { + "text": "So you put your dark glasses and you show up at the bus stop at some random time." + }, + { + "text": "And you go and ask the guy in the falafel truck, how long has it been since the last arrival?" + }, + { + "text": "So of course that guy works for the FBI, right?" + }, + { + "text": "So they tell you, well, it's been, let's say, 12 minutes since the last bus arrival." + }, + { + "text": "And then you say, \"Oh, 12 minutes." + }, + { + "text": "Average time is 15." + }, + { + "text": "So a bus should be coming any time now.\"" + }, + { + "text": "Is that correct?" + }, + { + "text": "No, you wouldn't think that way." + }, + { + "text": "It's a Poisson process." + }, + { + "text": "It doesn't matter how long it has been since the last bus arrival." + }, + { + "text": "So you don't go through that fallacy." + }, + { + "text": "Instead of predicting how long it's going to be, you just sit down there and wait and measure the time." + }, + { + "text": "And you find that this is, let's say, 11 minutes." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk19.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..af599f5b8f4c3fc0973b37e81b36088c85eae997 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you go to your boss and report, \"Well, it took-- I went there and the time from the previous bus to the next one was 23 minutes." + }, + { + "text": "It's more than the 15 that they said.\"" + }, + { + "text": "So go and do that again." + }, + { + "text": "You go day after day." + }, + { + "text": "You keep these statistics of the length of this interval." + }, + { + "text": "And you tell your boss it's a lot more than 15." + }, + { + "text": "It tends to be more like 30 or so." + }, + { + "text": "So the bus company is cheating us." + }, + { + "text": "Does the bus company really run Poisson buses at the rate that they have promised?" + }, + { + "text": "Well let's analyze the situation here and figure out what the length of this interval should be, on the average." + }, + { + "text": "The naive argument is that this interval is an interarrival time." + }, + { + "text": "And interarrival times, on the average, are 15 minutes, if the company runs indeed Poisson processes with these interarrival times." + }, + { + "text": "But actually the situation is a little more subtle because this is not a typical interarrival interval." + }, + { + "text": "This interarrival interval consists of two pieces." + }, + { + "text": "Let's call them T1 and T1 prime." + }, + { + "text": "What can you tell me about those two random variables?" + }, + { + "text": "What kind of random variable is T1?" + }, + { + "text": "Starting from this time, with the Poisson process, the past doesn't matter." + }, + { + "text": "It's the time until an arrival happens." + }, + { + "text": "So T1 is going to be an exponential random variable with parameter lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk2.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..ebc6083b4940b3fc27511f672c179a7846abc0b1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "The big interval is composed of many little intervals." + }, + { + "text": "Each little interval is independent from any other little interval, so is it is as if we have a sequence of Bernoulli trials." + }, + { + "text": "Each Bernoulli trial is associated with a little interval and has a small probability of obtaining a success or an arrival during that mini-slot." + }, + { + "text": "On the other hand, when delta is small, and you take a big interval and chop it up, you get a large number of little intervals." + }, + { + "text": "So what we essentially have here is a Bernoulli process, in which is the number of trials is huge but the probability of success during any given trial is tiny." + }, + { + "text": "The average number of trials ends up being proportional to the length of the interval." + }, + { + "text": "If you have twice as large an interval, it's as if you're having twice as many over these mini-trials, so the expected number of arrivals will increase proportionately." + }, + { + "text": "There's also this parameter lambda, which we interpret as expected number of arrivals per unit time." + }, + { + "text": "And it comes in those probabilities here." + }, + { + "text": "When you double lambda, this means that a little interval is twice as likely to get an arrival." + }, + { + "text": "So you would expect to get twice as many arrivals as well." + }, + { + "text": "That's why the expected number of arrivals during an interval of length tau also scales proportional to this parameter lambda." + }, + { + "text": "Somewhat unexpectedly, it turns out that the variance of the number of arrivals is also the same as the mean." + }, + { + "text": "This is a peculiarity that happens in the Poisson process." + }, + { + "text": "So this is one way of thinking about Poisson process, in terms of little intervals, each one of which has a tiny probability of success." + }, + { + "text": "And we think of the distribution associated with that process as being described by this particular PMF." + }, + { + "text": "So this is the PMF for the number of arrivals during an interval of a fixed duration, tau." + }, + { + "text": "It's a PMF that extends all over the entire range of non-negative integers." + }, + { + "text": "So the number of arrivals you can get during an interval for certain length can be anything." + }, + { + "text": "You can get as many arrivals as you want." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk20.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..28349ba5d13c19b16a2957596215f8e4b02bbf01 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "So in particular, the expected value of T1 is going to be 15 by itself." + }, + { + "text": "How about the random variable T1 prime." + }, + { + "text": "What kind of random variable is it?" + }, + { + "text": "This is like the first arrival in a Poisson process that runs backwards in time." + }, + { + "text": "What kind of process is a Poisson process running backwards in time?" + }, + { + "text": "Let's think of coin flips." + }, + { + "text": "Suppose you have a movie of coin flips." + }, + { + "text": "And for some accident, that fascinating movie, you happen to watch it backwards." + }, + { + "text": "Will it look any different statistically?" + }, + { + "text": "No." + }, + { + "text": "It's going to be just the sequence of random coin flips." + }, + { + "text": "So a Bernoulli process that's runs in reverse time is statistically identical to a Bernoulli process in forward time." + }, + { + "text": "The Poisson process is a limit of the Bernoulli." + }, + { + "text": "So, same story with the Poisson process." + }, + { + "text": "If you run it backwards in time it looks the same." + }, + { + "text": "So looking backwards in time, this is a Poisson process." + }, + { + "text": "And T1 prime is the time until the first arrival in this backward process." + }, + { + "text": "So T1 prime is also going to be an exponential random variable with the same parameter, lambda." + }, + { + "text": "And the expected value of T1 prime is 15." + }, + { + "text": "Conclusion is that the expected length of this interval is going to be 30 minutes." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk21.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..e60bcef503b4a0db026939c13f85514e5dcb0817 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the fact that this agent found the average to be something like 30 does not contradict the claims of the bus company that they're running Poisson buses with a rate of lambda equal to 4." + }, + { + "text": "OK." + }, + { + "text": "So maybe the company can this way-- they can defend themselves in court." + }, + { + "text": "But there's something puzzling here." + }, + { + "text": "How long is the interarrival time?" + }, + { + "text": "Is it 15?" + }, + { + "text": "Or is it 30?" + }, + { + "text": "On the average." + }, + { + "text": "The issue is what do we mean by a typical interarrival time." + }, + { + "text": "When we say typical, we mean some kind of average." + }, + { + "text": "But average over what?" + }, + { + "text": "And here's two different ways of thinking about averages." + }, + { + "text": "You number the buses." + }, + { + "text": "And you have bus number 100." + }, + { + "text": "You have bus number 101, bus number 102, bus number 110, and so on." + }, + { + "text": "One way of thinking about averages is that you pick a bus number at random." + }, + { + "text": "I pick, let's say, that bus, all buses being sort of equally likely to be picked." + }, + { + "text": "And I measure this interarrival time." + }, + { + "text": "So for a typical bus." + }, + { + "text": "Then, starting from here until there, the expected time has to be 1 over lambda, for the Poisson process." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk22.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..859fef7a50c29d5a5a9f8517f4db560ee5d550a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But what we did in this experiment was something different." + }, + { + "text": "We didn't pick a bus at random." + }, + { + "text": "We picked a time at random." + }, + { + "text": "And if the picture is, let's say, this way, I'm much more likely to pick this interval and therefore this interarrival time, rather than that interval." + }, + { + "text": "Because, this interval corresponds to very few times." + }, + { + "text": "So if I'm picking a time at random and, in some sense, let's say, uniform, so that all times are equally likely, I'm much more likely to fall inside a big interval rather than a small interval." + }, + { + "text": "So a person who shows up at the bus stop at a random time." + }, + { + "text": "They're selecting an interval in a biased way, with the bias favor of longer intervals." + }, + { + "text": "And that's why what they observe is a random variable that has a larger expected value then the ordinary expected value." + }, + { + "text": "So the subtlety here is to realize that we're talking between two different kinds of experiments." + }, + { + "text": "Picking a bus number at random verses picking an interval at random with a bias in favor of longer intervals." + }, + { + "text": "Lots of paradoxes that one can cook up using Poisson processes and random processes in general often have to do with the story of this kind." + }, + { + "text": "The phenomenon that we had in this particular example also shows up in general, whenever you have other kinds of arrival processes." + }, + { + "text": "So the Poisson process is the simplest arrival process there is, where the interarrival times are exponential random variables." + }, + { + "text": "There's a larger class of models." + }, + { + "text": "They're called renewal processes, in which, again, we have a sequence of successive arrivals, interarrival times are identically distributed and independent, but they may come from a general distribution." + }, + { + "text": "So to make the same point of the previous example but in a much simpler setting, suppose that bus interarrival times are either 5 or 10 minutes apart." + }, + { + "text": "So you get some intervals that are of length 5." + }, + { + "text": "You get some that are of length 10." + }, + { + "text": "And suppose that these are equally likely." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk23.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..0c23f2ec29db9e794aae974425a9309fbc5fa392 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "So we have -- not exactly -- In the long run, we have as many 5 minute intervals as we have 10 minute intervals." + }, + { + "text": "So the average interarrival time is 7 and 1/2." + }, + { + "text": "But if a person shows up at a random time, what are they going to see?" + }, + { + "text": "Do we have as many 5s as 10s?" + }, + { + "text": "But every 10 covers twice as much space." + }, + { + "text": "So if I show up at a random time, I have probability 2/3 falling inside an interval of duration 10." + }, + { + "text": "And I have one 1/3 probability of falling inside an interval of duration 5." + }, + { + "text": "That's because, out of the whole real line, 2/3 of it is covered by intervals of length 10, just because they're longer." + }, + { + "text": "1/3 is covered by the smaller intervals." + }, + { + "text": "Now if I fall inside an interval of length 10 and I measure the length of the interval that I fell into, that's going to be 10." + }, + { + "text": "But if I fall inside an interval of length 5 and I measure how long it is, I'm going to get a 5." + }, + { + "text": "And that, of course, is going to be different than 7.5." + }, + { + "text": "OK. And which number should be bigger?" + }, + { + "text": "It's the second number that's bigger because this one is biased in favor of the longer intervals." + }, + { + "text": "So that's, again, another illustration of the different results that you get when you have this random incidence phenomenon." + }, + { + "text": "So the bottom line, again, is that if you talk about a typical interarrival time, one must be very precise in specifying what we mean typical." + }, + { + "text": "So typical means sort of random." + }, + { + "text": "But to use the word random, you must specify very precisely what is the random experiment that you are using." + }, + { + "text": "And if you're not careful, you can get into apparent puzzles, such as the following." + }, + { + "text": "Suppose somebody tells you the average family size is 4, but the average person lives in a family of size 6." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk24.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..f1454166977d85230e828ad2593835dff01c5eed --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Is that compatible?" + }, + { + "text": "Family size is 4 on the average, but typical people live, on the average, in families of size 6." + }, + { + "text": "Well yes." + }, + { + "text": "There's no contradiction here." + }, + { + "text": "We're talking about two different experiments." + }, + { + "text": "In one experiment, I pick a family at random, and I tell you the average family is 4." + }, + { + "text": "In another experiment, I pick a person at random and I tell you that this person, on the average, will be in their family of size 6." + }, + { + "text": "And what is the catch here?" + }, + { + "text": "That if I pick a person at random, large families are more likely to be picked." + }, + { + "text": "So there's a bias in favor of large families." + }, + { + "text": "Or if you want to survey, let's say, are trains crowded in your city?" + }, + { + "text": "Or are buses crowded?" + }, + { + "text": "One choice is to pick a bus at random and inspect how crowded it is." + }, + { + "text": "Another choice is to pick a typical person and ask them, \"Did you ride the bus today?" + }, + { + "text": "Was it's crowded?\"" + }, + { + "text": "Well suppose that in this city there's one bus that's extremely crowded and all the other buses are completely empty." + }, + { + "text": "If you ask a person." + }, + { + "text": "\"Was your bus crowded?\"" + }, + { + "text": "They will tell you, \"Yes, my bus was crowded.\"" + }, + { + "text": "There's no witness from the empty buses to testify in their favor." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk25.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..5ea6070c380c8c0cc3ed8ff41fe3f0d64a2f6192 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk25.json @@ -0,0 +1,23 @@ +[ + { + "text": "So by sampling people instead of sampling buses, you're going to get different result." + }, + { + "text": "And in the process industry, if your job is to inspect and check cookies, you will be faced with a big dilemma." + }, + { + "text": "Do you want to find out how many chocolate chips there are on a typical cookie?" + }, + { + "text": "Are you going to interview cookies or are you going to interview chocolate chips and ask them how many other chips where there on your cookie?" + }, + { + "text": "And you're going to get different answers in these cases." + }, + { + "text": "So moral is, one has to be very precise on how you formulate the sampling procedure that you have." + }, + { + "text": "And you'll get different answers." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk3.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..65f67102a7086dbc76d65afeddb2720c5b67bdb0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "Of course the probability of getting a zillion arrivals is going to be tiny." + }, + { + "text": "But in principle, this is possible." + }, + { + "text": "And that's because an interval, even if it's a fixed length, consists of an infinite number of mini-slots in some sense." + }, + { + "text": "You can divide, chop it up, into as many mini-slots as you want." + }, + { + "text": "So in principle, it's possible that every mini-slot gets an arrival." + }, + { + "text": "In principle, it's possible to get an arbitrarily large number of arrivals." + }, + { + "text": "So this particular formula here is not very intuitive when you look at it." + }, + { + "text": "But it's a legitimate PMF." + }, + { + "text": "And it's called the Poisson PMF." + }, + { + "text": "It's the PMF that describes the number of arrivals." + }, + { + "text": "So that's one way of thinking about the Poisson process, where the basic object of interest would be this PMF and you try to work with it." + }, + { + "text": "There's another way of thinking about what happens in the Poisson process." + }, + { + "text": "And this has to do with letting things evolve in time." + }, + { + "text": "You start at time 0." + }, + { + "text": "There's going to be a time at which the first arrival occurs, and call that time T1." + }, + { + "text": "This time turns out to have an exponential distribution with parameter lambda." + }, + { + "text": "Once you get an arrival, it's as if the process starts fresh." + }, + { + "text": "The best way to understand why this is the case is by thinking in terms of the analogy with the Bernoulli process." + }, + { + "text": "If you believe that statement for the Bernoulli process, since this is a limiting case, it should also be true." + }, + { + "text": "So starting from this time, we're going to wait a random amount of time until we get the second arrival This random amount of time, let's call it T2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk4.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c5affc1f1a5b3e0305dcd63ee178f3ba1a2da02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "This time, T2 is also going to have an exponential distribution with the same parameter, lambda." + }, + { + "text": "And these two are going to be independent of each other." + }, + { + "text": "OK?" + }, + { + "text": "So the Poisson process has all the same memorylessness properties that the Bernoulli process has." + }, + { + "text": "What's another way of thinking of this property?" + }, + { + "text": "So think of a process where you have a light bulb." + }, + { + "text": "The time at the light bulb burns out, you can model it by an exponential random variable." + }, + { + "text": "And suppose that they tell you that so far, we're are sitting at some time, T. And I tell you that the light bulb has not yet burned out." + }, + { + "text": "What does this tell you about the future of the light bulb?" + }, + { + "text": "Is the fact that they didn't burn out, so far, is it good news or is it bad news?" + }, + { + "text": "Would you rather keep this light bulb that has worked for t times steps and is still OK?" + }, + { + "text": "Or would you rather use a new light bulb that starts new at that point in time?" + }, + { + "text": "Because of the memorylessness property, the past of that light bulb doesn't matter." + }, + { + "text": "So the future of this light bulb is statistically the same as the future of a new light bulb." + }, + { + "text": "For both of them, the time until they burn out is going to be described an exponential distribution." + }, + { + "text": "So one way that people described the situation is to say that used is exactly as good as a new." + }, + { + "text": "So a used on is no worse than a new one." + }, + { + "text": "A used one is no better than a new one." + }, + { + "text": "So a used light bulb that hasn't yet burnt out is exactly as good as a new light bulb." + }, + { + "text": "So that's another way of thinking about the memorylessness that we have in the Poisson process." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk5.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..a8f4593b861f0c6ab6d24f9023bf2c98983b5ab3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "Back to this picture." + }, + { + "text": "The time until the second arrival is the sum of two independent exponential random variables." + }, + { + "text": "So, in principle, you can use the convolution formula to find the distribution of T1 plus T2, and that would be what we call Y2, the time until the second arrival." + }, + { + "text": "But there's also a direct way of obtaining to the distribution of Y2, and this is the calculation that we did last time on the blackboard." + }, + { + "text": "And actually, we did it more generally." + }, + { + "text": "We found the time until the case arrival occurs." + }, + { + "text": "It has a closed form formula, which is called the Erlang distribution with k degrees of freedom." + }, + { + "text": "So let's see what's going on here." + }, + { + "text": "It's a distribution Of what kind?" + }, + { + "text": "It's a continuous distribution." + }, + { + "text": "It's a probability density function." + }, + { + "text": "This is because the time is a continuous random variable." + }, + { + "text": "Time is continuous." + }, + { + "text": "Arrivals can happen at any time." + }, + { + "text": "So we're talking about the PDF." + }, + { + "text": "This k is just the parameter of the distribution." + }, + { + "text": "We're talking about the k-th arrival, so k is a fixed number." + }, + { + "text": "Lambda is another parameter of the distribution, which is the arrival rate So it's a PDF over the Y's, whereas lambda and k are parameters of the distribution." + }, + { + "text": "OK." + }, + { + "text": "So this was what we knew from last time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk6.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..f957b2a1915e0744ba6fb901fba06c158d7e336f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Just to get some practice, let us do a problem that's not too difficult, but just to see how we use the various formulas that we have." + }, + { + "text": "So Poisson was a mathematician, but Poisson also means fish in French." + }, + { + "text": "So Poisson goes fishing." + }, + { + "text": "And let's assume that fish are caught according to a Poisson process." + }, + { + "text": "That's not too bad an assumption." + }, + { + "text": "At any given point in time, you have a little probability that a fish would be caught." + }, + { + "text": "And whether you catch one now is sort of independent about whether at some later time a fish will be caught or not." + }, + { + "text": "So let's just make this assumption." + }, + { + "text": "And suppose that the rules of the game are that you-- Fish are being called it the certain rate of 0.6 per hour." + }, + { + "text": "You fish for 2 hours, no matter what." + }, + { + "text": "And then there are two possibilities." + }, + { + "text": "If I have caught a fish, I stop and go home." + }, + { + "text": "So if some fish have been caught, so there's at least 1 arrival during this interval, I go home." + }, + { + "text": "Or if nothing has being caught, I continue fishing until I catch something." + }, + { + "text": "And then I go home." + }, + { + "text": "So that's the description of what is going to happen." + }, + { + "text": "And now let's starts asking questions of all sorts." + }, + { + "text": "What is the probability that I'm going to be fishing for more than 2 hours?" + }, + { + "text": "I will be fishing for more than 2 hours, if and only if no fish were caught during those 2 hours, in which case, I will have to continue." + }, + { + "text": "Therefore, this is just this quantity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk7.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..d200ba8c85d33ddb01ccd0430f2d344dfd85356f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "The probability of catching 2 fish in-- of catching 0 fish in the next 2 hours, and according to the formula that we have, this is going to be e to the minus lambda times how much time we have." + }, + { + "text": "There's another way of thinking about this." + }, + { + "text": "The probability that I fish for more than 2 hours is the probability that the first catch happens after time 2, which would be the integral from 2 to infinity of the density of the first arrival time." + }, + { + "text": "And that density is an exponential." + }, + { + "text": "So you do the integral of an exponential, and, of course, you would get the same answer." + }, + { + "text": "OK. That's easy." + }, + { + "text": "So what's the probability of fishing for more than 2 but less than 5 hours?" + }, + { + "text": "What does it take for this to happen?" + }, + { + "text": "For this to happen, we need to catch 0 fish from time 0 to 2 and catch the first fish sometime between 2 and 5." + }, + { + "text": "So if you-- one way of thinking about what's happening here might be to say that there's a Poisson process that keeps going on forever." + }, + { + "text": "But as soon as I catch the first fish, instead of continuing fishing and obtaining those other fish I just go home right now." + }, + { + "text": "Now the fact that I go home before time 5 means that, if I were to stay until time 5, I would have caught at least 1 fish." + }, + { + "text": "I might have caught more than 1." + }, + { + "text": "So the event of interest here is that the first catch happens between times 2 and 5." + }, + { + "text": "So one way of calculating this quantity would be-- Its the probability that the first catch happens between times 2 and 5." + }, + { + "text": "Another way to deal with it is to say, this is the probability that I caught 0 fish in the first 2 hours and then the probability that I catch at least 1 fish during the next 3 hours." + }, + { + "text": "This." + }, + { + "text": "What is this?" + }, + { + "text": "The probability of 0 fish in the next 3 hours is the probability of 0 fish during this time." + }, + { + "text": "1 minus this is the probability of catching at least 1 fish, of having at least 1 arrival, between times 2 and 5." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk8.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..63208c3916b0f28860e55ba410e9e8809a2e2618 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "If there's at least 1 arrival between times 2 and 5, then I would have gone home by time 5." + }, + { + "text": "So both of these, if you plug-in numbers and all that, of course, are going to give you the same answer." + }, + { + "text": "Now next, what's the probability that I catch at least 2 fish?" + }, + { + "text": "In which scenario are we?" + }, + { + "text": "Under this scenario, I go home when I catch my first fish." + }, + { + "text": "So in order to catch at least 2 fish, it must be in this case." + }, + { + "text": "So this is the same as the event that I catch at least 2 fish during the first 2 time steps." + }, + { + "text": "So it's going to be the probability from 2 to infinity, the probability that I catch 2 fish, or that I catch 3 fish, or I catch more than that." + }, + { + "text": "So it's this quantity." + }, + { + "text": "k is the number of fish that I catch." + }, + { + "text": "At least 2, so k goes from 2 to infinity." + }, + { + "text": "These are the probabilities of catching a number k of fish during this interval." + }, + { + "text": "And if you want a simpler form without an infinite sum, this would be 1 minus the probability of catching 0 fish, minus the probability of catching 1 fish, during a time interval of length 2." + }, + { + "text": "Another way to think of it." + }, + { + "text": "I'm going to catch 2 fish, at least 2 fish, if and only if the second fish caught in this process happens before time 2." + }, + { + "text": "So that's another way of thinking about the same event." + }, + { + "text": "So it's going to be the probability that the random variable Y2, the arrival time over the second fish, is less than or equal to 2." + }, + { + "text": "OK." + }, + { + "text": "The next one is a little trickier." + }, + { + "text": "Here we need to do a little bit of divide and conquer." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk9.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..438a6aa22ffef63c853416c037d519d661ef6133 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_6_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "Overall, in this expedition, what the expected number of fish to be caught?" + }, + { + "text": "One way to think about it is to try to use the total expectations theorem." + }, + { + "text": "And think of expected number of fish, given this scenario, or expected number of fish, given this scenario." + }, + { + "text": "That's a little more complicated than the way I'm going to do it." + }, + { + "text": "The way I'm going to do is to think as follows-- Expected number of fish is the expected number of fish caught between times 0 and 2 plus expected number of fish caught after time 2." + }, + { + "text": "So what's the expected number caught between time 0 and 2?" + }, + { + "text": "This is lambda t. So lambda is 0.6 times 2." + }, + { + "text": "This is the expected number of fish that are caught between times 0 and 2." + }, + { + "text": "Now let's think about the expected number of fish caught afterwards." + }, + { + "text": "How many fish are being caught afterwards?" + }, + { + "text": "Well it depends on the scenario." + }, + { + "text": "If we're in this scenario, we've gone home and we catch 0." + }, + { + "text": "If we're in this scenario, then we continue fishing until we catch one." + }, + { + "text": "So the expected number of fish to be caught after time 2 is going to be the probability of this scenario times 1." + }, + { + "text": "And the probability of that scenario is the probability that they call it's 0 fish during the first 2 time steps times 1, which is the number of fish I'm going to catch if I continue." + }, + { + "text": "The expected total fishing time we can calculate exactly the same way." + }, + { + "text": "I'm jumping to the last one." + }, + { + "text": "My total fishing time has a period of 2 time steps." + }, + { + "text": "I'm going to fish for 2 time steps no matter what." + }, + { + "text": "And then if I caught 0 fish, which happens with this probability, my expected time is going to be the expected time from here onwards, which is the expected value of this geometric random variable with parameter lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk0.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..aa961d524ea0d1287b995e40358f71afcd69bfb1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "JOHN TSITSIKLIS: Today we're going to finish our discussion of the Poisson process." + }, + { + "text": "We're going to see a few of its properties, do a few interesting problems, some more interesting than others." + }, + { + "text": "So go through a few examples and then we're going to talk about some quite strange things that happen with the Poisson process." + }, + { + "text": "So the first thing is to remember what the Poisson processes is." + }, + { + "text": "It's a model, let's say, of arrivals of customers that are, in some sense, quote unquote, completely random, that is a customer can arrive at any point in time." + }, + { + "text": "All points in time are equally likely." + }, + { + "text": "And different points in time are sort of independent of other points in time." + }, + { + "text": "So the fact that I got an arrival now doesn't tell me anything about whether there's going to be an arrival at some other time." + }, + { + "text": "In some sense, it's a continuous time version of the Bernoulli process." + }, + { + "text": "So the best way to think about the Poisson process is that we divide time into extremely tiny slots." + }, + { + "text": "And in each time slot, there's an independent possibility of having an arrival." + }, + { + "text": "Different time slots are independent of each other." + }, + { + "text": "On the other hand, when the slot is tiny, the probability for obtaining an arrival during that tiny slot is itself going to be tiny." + }, + { + "text": "So we capture these properties into a formal definition what the Poisson process is." + }, + { + "text": "We have a probability mass function for the number of arrivals, k, during an interval of a given length." + }, + { + "text": "So this is the sort of basic description of the distribution of the number of arrivals." + }, + { + "text": "So tau is fixed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk1.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..8ef79a1bbf5e44814915347122880462d60e3970 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And k is the parameter." + }, + { + "text": "So when we add over all k's, the sum of these probabilities has to be equal to 1." + }, + { + "text": "There's a time homogeneity assumption, which is hidden in this, namely, the only thing that matters is the duration of the time interval, not where the time interval sits on the real axis." + }, + { + "text": "Then we have an independence assumption." + }, + { + "text": "Intervals that are disjoint are statistically independent from each other." + }, + { + "text": "So any information you give me about arrivals during this time interval doesn't change my beliefs about what's going to happen during another time interval." + }, + { + "text": "So this is a generalization of the idea that we had in Bernoulli processes that different time slots are independent of each other." + }, + { + "text": "And then to specify this function, the distribution of the number of arrivals, we sort of go in stages." + }, + { + "text": "We first specify this function for the case where the time interval is very small." + }, + { + "text": "And I'm telling you what those probabilities will be." + }, + { + "text": "And based on these then, we do some calculations and to find the formula for the distribution of the number of arrivals for intervals of a general duration." + }, + { + "text": "So for a small duration, delta, the probability of obtaining 1 arrival is lambda delta." + }, + { + "text": "The remaining probability is assigned to the event that we get to no arrivals during that interval." + }, + { + "text": "The probability of obtaining more than 1 arrival in a tiny interval is essentially 0." + }, + { + "text": "And when we say essentially, it's means modular, terms that of order delta squared." + }, + { + "text": "And when delta is very small, anything which is delta squared can be ignored." + }, + { + "text": "So up to delta squared terms, that's what happened during a little interval." + }, + { + "text": "Now if we know the probability distribution for the number of arrivals in a little interval." + }, + { + "text": "We can use this to get the distribution for the number of arrivals over several intervals." + }, + { + "text": "How do we do that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk10.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c993d1aafbcf3de55a33d47639c163aee1857626 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So the expected time is 1 over lambda." + }, + { + "text": "And in our case this, is 1/0.6." + }, + { + "text": "Finally, if I tell you that I have been fishing for 4 hours and nothing has been caught so far, how much do you expect this quantity to be?" + }, + { + "text": "Here is the story that, again, that for the Poisson process used is as good as new." + }, + { + "text": "The process does not have any memory." + }, + { + "text": "Given what happens in the past doesn't matter for the future." + }, + { + "text": "It's as if the process starts new at this point in time." + }, + { + "text": "So this one is going to be, again, the same exponentially distributed random variable with the same parameter lambda." + }, + { + "text": "So expected time until an arrival comes is an exponential distribut -- has an exponential distribution with parameter lambda, no matter what has happened in the past." + }, + { + "text": "Starting from now and looking into the future, it's as if the process has just started." + }, + { + "text": "So it's going to be 1 over lambda, which is 1/0.6." + }, + { + "text": "OK. Now our next example is going to be a little more complicated or subtle." + }, + { + "text": "But before we get to the example, let's refresh our memory about what we discussed last time about merging Poisson independent Poisson processes." + }, + { + "text": "Instead of drawing the picture that way, another way we could draw it could be this." + }, + { + "text": "We have a Poisson process with rate lambda1, and a Poisson process with rate lambda2." + }, + { + "text": "They have, each one of these, have their arrivals." + }, + { + "text": "And then we form the merged process." + }, + { + "text": "And the merged process records an arrival whenever there's an arrival in either of the two processes." + }, + { + "text": "This process in that process are assumed to be independent of each other." + }, + { + "text": "Now different times in this process and that process are independent of each other." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk11.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..98f4de8fc7edf6671add64512cd98e8481dce843 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what happens in these two time intervals is independent from what happens in these two time intervals." + }, + { + "text": "These two time intervals to determine what happens here." + }, + { + "text": "These two time intervals determine what happens there." + }, + { + "text": "So because these are independent from these, this means that this is also independent from that." + }, + { + "text": "So the independence assumption is satisfied for the merged process." + }, + { + "text": "And the merged process turns out to be a Poisson process." + }, + { + "text": "And if you want to find the arrival rate for that process, you argue as follows." + }, + { + "text": "During a little interval of length delta, we have probability lambda1 delta of having an arrival in this process." + }, + { + "text": "We have probability lambda2 delta of an arrival in this process, plus second order terms in delta, which we're ignoring." + }, + { + "text": "And then you do the calculation and you find that in this process, you're going to have an arrival probability, which is lambda1 plus lambda2, again ignoring second order in delta-- terms that are second order in delta." + }, + { + "text": "So the merged process is a Poisson process whose arrival rate is the sum of the arrival rates of the individual processes." + }, + { + "text": "And the calculation we did at the end of the last lecture-- If I tell you that the new arrival happened here, where did that arrival come from?" + }, + { + "text": "Did it come from here or from there?" + }, + { + "text": "If the lambda1 is equal to lambda2, then by symmetry you would say that it's equally likely to have come from here or to come from there." + }, + { + "text": "But if this lambda is much bigger than that lambda, the fact that they saw an arrival is more likely to have come from there." + }, + { + "text": "And the formula that captures this is the following." + }, + { + "text": "This is the probability that my arrival has come from this particular stream rather than that particular stream." + }, + { + "text": "So when an arrival comes and you ask, what is the origin of that arrival?" + }, + { + "text": "It's as if I'm flipping a coin with these odds." + }, + { + "text": "And depending on outcome of that coin, I'm going to tell you came from there or it came from there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk12.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..b81514a3614b4cc14097ef6ee9b3469bf3d09d24 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "So the origin of an arrival is either this stream or that stream." + }, + { + "text": "And this is the probability that the origin of the arrival is that one." + }, + { + "text": "Now if we look at 2 different arrivals, and we ask about their origins-- So let's think about the origin of this arrival and compare it with the origin that arrival." + }, + { + "text": "The origin of this arrival is random." + }, + { + "text": "It could be right be either this or that." + }, + { + "text": "And this is the relevant probability." + }, + { + "text": "The origin of that arrival is random." + }, + { + "text": "It could be either here or is there, and again, with the same relevant probability." + }, + { + "text": "Question." + }, + { + "text": "The origin of this arrival, is it dependent or independent from the origin that arrival?" + }, + { + "text": "And here's how the argument goes." + }, + { + "text": "Separate times are independent." + }, + { + "text": "Whatever has happened in the process during this set of times is independent from whatever happened in the process during that set of times." + }, + { + "text": "Because different times have nothing to do with each other, the origin of this, of an arrival here, has nothing to do with the origin of an arrival there." + }, + { + "text": "So the origins of different arrivals are also independent random variables." + }, + { + "text": "So if I tell you that-- yeah." + }, + { + "text": "OK." + }, + { + "text": "So it as if that each time that you have an arrival in the merge process, it's as if you're flipping a coin to determine where did that arrival came from and these coins are independent of each other." + }, + { + "text": "OK. OK. Now we're going to use this-- what we know about merged processes to solve the problem that would be harder to do, if you were not using ideas from Poisson processes." + }, + { + "text": "So the formulation of the problem has nothing to do with the Poisson process." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk13.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..bf6c66b1e38f68ac6bd19d504f54b3d7f0681a3c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "The formulation is the following." + }, + { + "text": "We have 3 light-bulbs." + }, + { + "text": "And each light bulb is independent and is going to die out at the time that's exponentially distributed." + }, + { + "text": "So 3 light bulbs." + }, + { + "text": "They start their lives and then at some point they die or burn out." + }, + { + "text": "So let's think of this as X, this as Y, and this as Z." + }, + { + "text": "And we're interested in the time until the last light-bulb burns out." + }, + { + "text": "So we're interested in the maximum of the 3 random variables, X, Y, and Z." + }, + { + "text": "And in particular, we want to find the expected value of this maximum." + }, + { + "text": "OK." + }, + { + "text": "So you can do derived distribution, use the expected value rule, anything you want." + }, + { + "text": "You can get this answer using the tools that you already have in your hands." + }, + { + "text": "But now let us see how we can connect to this picture with a Poisson picture and come up with the answer in a very simple way." + }, + { + "text": "What is an exponential random variable?" + }, + { + "text": "An exponential random variable is the first act in the long play that involves a whole Poisson process." + }, + { + "text": "So an exponential random variable is the first act of a Poisson movie." + }, + { + "text": "Same thing here." + }, + { + "text": "You can think of this random variable as being part of some Poisson process that has been running." + }, + { + "text": "So it's part of this bigger picture." + }, + { + "text": "We're still interested in the maximum of the 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk14.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..1a92d35ab267e8941975fcfa559b335f37209c80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "The other arrivals are not going to affect our answers." + }, + { + "text": "It's just, conceptually speaking, we can think of the exponential random variable as being embedded in a bigger Poisson picture." + }, + { + "text": "So we have 3 Poisson process that are running in parallel." + }, + { + "text": "Let us split the expected time until the last burnout into pieces, which is time until the first burnout, time from the first until the second, and time from the second until the third." + }, + { + "text": "And find the expected values of each one of these pieces." + }, + { + "text": "What can we say about the expected value of this?" + }, + { + "text": "This is the first arrival out of all of these 3 Poisson processes." + }, + { + "text": "It's the first event that happens when you look at all of these processes simultaneously." + }, + { + "text": "So 3 Poisson processes running in parallel." + }, + { + "text": "We're interested in the time until one of them, any one of them, gets in arrival." + }, + { + "text": "Rephrase." + }, + { + "text": "We merged the 3 Poisson processes, and we ask for the time until we observe an arrival in the merged process." + }, + { + "text": "When 1 of the 3 gets an arrival for the first time, the merged process gets its first arrival." + }, + { + "text": "So what's the expected value of this time until the first burnout?" + }, + { + "text": "It's going to be the expected value of a Poisson random variable." + }, + { + "text": "So the first burnout is going to have an expected value, which is-- OK." + }, + { + "text": "It's a Poisson process." + }, + { + "text": "The merged process of the 3 has a collective arrival rate, which is 3 times lambda." + }, + { + "text": "So this is the parameter over the exponential distribution that describes the time until the first arrival in the merged process." + }, + { + "text": "And the expected value of this random variable is 1 over that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk15.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..ec2818bb27b6b5b81e6f20bc450cb58a1baac245 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "When you have an exponential random variable with parameter lambda, the expected value of that random variable is 1 over lambda." + }, + { + "text": "Here we're talking about the first arrival time in a process with rate 3 lambda." + }, + { + "text": "The expected time until the first arrival is 1 over (3 lambda)." + }, + { + "text": "Alright." + }, + { + "text": "So at this time, this bulb, this arrival happened, this bulb has been burned." + }, + { + "text": "So we don't care about that bulb anymore." + }, + { + "text": "We start at this time, and we look forward." + }, + { + "text": "This bulb has been burned." + }, + { + "text": "So let's just look forward from now on." + }, + { + "text": "What have we got?" + }, + { + "text": "We have two bulbs that are burning." + }, + { + "text": "We have a Poisson process that's the bigger picture of what could happen to that light bulb, if we were to keep replacing it." + }, + { + "text": "Another Poisson process." + }, + { + "text": "These two processes are, again, independent." + }, + { + "text": "From this time until that time, how long does it take?" + }, + { + "text": "It's the time until either this process records an arrival or that process records and arrival." + }, + { + "text": "That's the same as the time that the merged process of these two records an arrival." + }, + { + "text": "So we're talking about the expected time until the first arrival in a merged process." + }, + { + "text": "The merged process is Poisson." + }, + { + "text": "It's Poisson with rate 2 lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk16.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..6a74ed00548100b2fa7d07c494546d15ecdfac23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that extra time is going to take-- the expected value is going to be 1 over the (rate of that Poisson process)." + }, + { + "text": "So 1 over (2 lambda) is the expected value of this random variable." + }, + { + "text": "So at this point, this bulb now is also burned." + }, + { + "text": "So we start looking from this time on." + }, + { + "text": "That part of the picture disappears." + }, + { + "text": "Starting from this time, what's the expected value until that remaining light-bulb burns out?" + }, + { + "text": "Well, as we said before, in a Poisson process or with exponential random variables, we have memorylessness." + }, + { + "text": "A used bulb is as good as a new one." + }, + { + "text": "So it's as if we're starting from scratch here." + }, + { + "text": "So this is going to be an exponential random variable with parameter lambda." + }, + { + "text": "And the expected value of it is going to be 1 over lambda." + }, + { + "text": "So the beauty of approaching this problem in this particular way is, of course, that we manage to do everything without any calculus at all, without striking an integral, without trying to calculate expectations in any form." + }, + { + "text": "Most of the non-trivial problems that you encounter in the Poisson world basically involve tricks of these kind." + }, + { + "text": "You have a question and you try to rephrase it, trying to think in terms of what might happen in the Poisson setting, use memorylessness, use merging, et cetera, et cetera." + }, + { + "text": "Now we talked about merging." + }, + { + "text": "It turns out that the splitting of Poisson processes also works in a nice way." + }, + { + "text": "The story here is exactly the same as for the Bernoulli process." + }, + { + "text": "So I'm having a Poisson process." + }, + { + "text": "And each time, with some rate lambda, and each time that an arrival comes, I'm going to send it to that stream and the record an arrival here with some probability P. And I'm going to send it to the other stream with some probability 1 minus P. So either of this will happen or that will happen, depending on the outcome of the coin flip that I do." + }, + { + "text": "Each time that then arrival occurs, I flip a coin and I decide whether to record it here or there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk17.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..24ef2d939ecec102e5b0cf66c4aef963c1195410 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "This is called splitting a Poisson process into two pieces." + }, + { + "text": "What kind of process do we get here?" + }, + { + "text": "If you look at the little interval for length delta, what's the probability that this little interval gets an arrival?" + }, + { + "text": "It's the probability that this one gets an arrival, which is lambda delta times the probability that after I get an arrival my coin flip came out to be that way, so that it sends me there." + }, + { + "text": "So this means that this little interval is going to have probability lambda delta P. Or maybe more suggestively, I should write it as lambda P times delta." + }, + { + "text": "So every little interval has a probability of an arrival proportional to delta." + }, + { + "text": "The proportionality factor is lambda P. So lambda P is the rate of that process." + }, + { + "text": "And then you go through the mental exercise that you went through for the Bernoulli process to argue that a different intervals here are independent and so on." + }, + { + "text": "And that completes checking that this process is going to be a Poisson process." + }, + { + "text": "So when you split a Poisson process by doing independent coin flips each time that something happens, the processes that you get is again a Poisson process, but of course with a reduced rate." + }, + { + "text": "So instead of the word splitting, sometimes people also use the words thinning-out." + }, + { + "text": "That is, out of the arrivals that came, you keep a few but throw away a few." + }, + { + "text": "OK." + }, + { + "text": "So now the last topic over this lecture is a quite curious phenomenon that goes under the name of random incidents." + }, + { + "text": "So here's the story." + }, + { + "text": "Buses have been running on Mass Ave. from time immemorial." + }, + { + "text": "And the bus company that runs the buses claims that they come as a Poisson process with some rate, let's say, of 4 buses per hour." + }, + { + "text": "So that the expected time between bus arrivals is going to be 15 minutes." + }, + { + "text": "OK. Alright." + }, + { + "text": "So people have been complaining that they have been showing up there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk18.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..65a62f83b762cf608024e3af374f28f51f49e32f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "They think the buses are taking too long." + }, + { + "text": "So you are asked to investigate." + }, + { + "text": "Is the company-- Does it operate according to its promises or not." + }, + { + "text": "So you send an undercover agent to go and check the interarrival times of the buses." + }, + { + "text": "Are they 15 minutes?" + }, + { + "text": "Or are they longer?" + }, + { + "text": "So you put your dark glasses and you show up at the bus stop at some random time." + }, + { + "text": "And you go and ask the guy in the falafel truck, how long has it been since the last arrival?" + }, + { + "text": "So of course that guy works for the FBI, right?" + }, + { + "text": "So they tell you, well, it's been, let's say, 12 minutes since the last bus arrival." + }, + { + "text": "And then you say, \"Oh, 12 minutes." + }, + { + "text": "Average time is 15." + }, + { + "text": "So a bus should be coming any time now.\"" + }, + { + "text": "Is that correct?" + }, + { + "text": "No, you wouldn't think that way." + }, + { + "text": "It's a Poisson process." + }, + { + "text": "It doesn't matter how long it has been since the last bus arrival." + }, + { + "text": "So you don't go through that fallacy." + }, + { + "text": "Instead of predicting how long it's going to be, you just sit down there and wait and measure the time." + }, + { + "text": "And you find that this is, let's say, 11 minutes." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk19.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..af599f5b8f4c3fc0973b37e81b36088c85eae997 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you go to your boss and report, \"Well, it took-- I went there and the time from the previous bus to the next one was 23 minutes." + }, + { + "text": "It's more than the 15 that they said.\"" + }, + { + "text": "So go and do that again." + }, + { + "text": "You go day after day." + }, + { + "text": "You keep these statistics of the length of this interval." + }, + { + "text": "And you tell your boss it's a lot more than 15." + }, + { + "text": "It tends to be more like 30 or so." + }, + { + "text": "So the bus company is cheating us." + }, + { + "text": "Does the bus company really run Poisson buses at the rate that they have promised?" + }, + { + "text": "Well let's analyze the situation here and figure out what the length of this interval should be, on the average." + }, + { + "text": "The naive argument is that this interval is an interarrival time." + }, + { + "text": "And interarrival times, on the average, are 15 minutes, if the company runs indeed Poisson processes with these interarrival times." + }, + { + "text": "But actually the situation is a little more subtle because this is not a typical interarrival interval." + }, + { + "text": "This interarrival interval consists of two pieces." + }, + { + "text": "Let's call them T1 and T1 prime." + }, + { + "text": "What can you tell me about those two random variables?" + }, + { + "text": "What kind of random variable is T1?" + }, + { + "text": "Starting from this time, with the Poisson process, the past doesn't matter." + }, + { + "text": "It's the time until an arrival happens." + }, + { + "text": "So T1 is going to be an exponential random variable with parameter lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk2.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..ebc6083b4940b3fc27511f672c179a7846abc0b1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "The big interval is composed of many little intervals." + }, + { + "text": "Each little interval is independent from any other little interval, so is it is as if we have a sequence of Bernoulli trials." + }, + { + "text": "Each Bernoulli trial is associated with a little interval and has a small probability of obtaining a success or an arrival during that mini-slot." + }, + { + "text": "On the other hand, when delta is small, and you take a big interval and chop it up, you get a large number of little intervals." + }, + { + "text": "So what we essentially have here is a Bernoulli process, in which is the number of trials is huge but the probability of success during any given trial is tiny." + }, + { + "text": "The average number of trials ends up being proportional to the length of the interval." + }, + { + "text": "If you have twice as large an interval, it's as if you're having twice as many over these mini-trials, so the expected number of arrivals will increase proportionately." + }, + { + "text": "There's also this parameter lambda, which we interpret as expected number of arrivals per unit time." + }, + { + "text": "And it comes in those probabilities here." + }, + { + "text": "When you double lambda, this means that a little interval is twice as likely to get an arrival." + }, + { + "text": "So you would expect to get twice as many arrivals as well." + }, + { + "text": "That's why the expected number of arrivals during an interval of length tau also scales proportional to this parameter lambda." + }, + { + "text": "Somewhat unexpectedly, it turns out that the variance of the number of arrivals is also the same as the mean." + }, + { + "text": "This is a peculiarity that happens in the Poisson process." + }, + { + "text": "So this is one way of thinking about Poisson process, in terms of little intervals, each one of which has a tiny probability of success." + }, + { + "text": "And we think of the distribution associated with that process as being described by this particular PMF." + }, + { + "text": "So this is the PMF for the number of arrivals during an interval of a fixed duration, tau." + }, + { + "text": "It's a PMF that extends all over the entire range of non-negative integers." + }, + { + "text": "So the number of arrivals you can get during an interval for certain length can be anything." + }, + { + "text": "You can get as many arrivals as you want." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk20.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..28349ba5d13c19b16a2957596215f8e4b02bbf01 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "So in particular, the expected value of T1 is going to be 15 by itself." + }, + { + "text": "How about the random variable T1 prime." + }, + { + "text": "What kind of random variable is it?" + }, + { + "text": "This is like the first arrival in a Poisson process that runs backwards in time." + }, + { + "text": "What kind of process is a Poisson process running backwards in time?" + }, + { + "text": "Let's think of coin flips." + }, + { + "text": "Suppose you have a movie of coin flips." + }, + { + "text": "And for some accident, that fascinating movie, you happen to watch it backwards." + }, + { + "text": "Will it look any different statistically?" + }, + { + "text": "No." + }, + { + "text": "It's going to be just the sequence of random coin flips." + }, + { + "text": "So a Bernoulli process that's runs in reverse time is statistically identical to a Bernoulli process in forward time." + }, + { + "text": "The Poisson process is a limit of the Bernoulli." + }, + { + "text": "So, same story with the Poisson process." + }, + { + "text": "If you run it backwards in time it looks the same." + }, + { + "text": "So looking backwards in time, this is a Poisson process." + }, + { + "text": "And T1 prime is the time until the first arrival in this backward process." + }, + { + "text": "So T1 prime is also going to be an exponential random variable with the same parameter, lambda." + }, + { + "text": "And the expected value of T1 prime is 15." + }, + { + "text": "Conclusion is that the expected length of this interval is going to be 30 minutes." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk21.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..e60bcef503b4a0db026939c13f85514e5dcb0817 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the fact that this agent found the average to be something like 30 does not contradict the claims of the bus company that they're running Poisson buses with a rate of lambda equal to 4." + }, + { + "text": "OK." + }, + { + "text": "So maybe the company can this way-- they can defend themselves in court." + }, + { + "text": "But there's something puzzling here." + }, + { + "text": "How long is the interarrival time?" + }, + { + "text": "Is it 15?" + }, + { + "text": "Or is it 30?" + }, + { + "text": "On the average." + }, + { + "text": "The issue is what do we mean by a typical interarrival time." + }, + { + "text": "When we say typical, we mean some kind of average." + }, + { + "text": "But average over what?" + }, + { + "text": "And here's two different ways of thinking about averages." + }, + { + "text": "You number the buses." + }, + { + "text": "And you have bus number 100." + }, + { + "text": "You have bus number 101, bus number 102, bus number 110, and so on." + }, + { + "text": "One way of thinking about averages is that you pick a bus number at random." + }, + { + "text": "I pick, let's say, that bus, all buses being sort of equally likely to be picked." + }, + { + "text": "And I measure this interarrival time." + }, + { + "text": "So for a typical bus." + }, + { + "text": "Then, starting from here until there, the expected time has to be 1 over lambda, for the Poisson process." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk22.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..859fef7a50c29d5a5a9f8517f4db560ee5d550a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But what we did in this experiment was something different." + }, + { + "text": "We didn't pick a bus at random." + }, + { + "text": "We picked a time at random." + }, + { + "text": "And if the picture is, let's say, this way, I'm much more likely to pick this interval and therefore this interarrival time, rather than that interval." + }, + { + "text": "Because, this interval corresponds to very few times." + }, + { + "text": "So if I'm picking a time at random and, in some sense, let's say, uniform, so that all times are equally likely, I'm much more likely to fall inside a big interval rather than a small interval." + }, + { + "text": "So a person who shows up at the bus stop at a random time." + }, + { + "text": "They're selecting an interval in a biased way, with the bias favor of longer intervals." + }, + { + "text": "And that's why what they observe is a random variable that has a larger expected value then the ordinary expected value." + }, + { + "text": "So the subtlety here is to realize that we're talking between two different kinds of experiments." + }, + { + "text": "Picking a bus number at random verses picking an interval at random with a bias in favor of longer intervals." + }, + { + "text": "Lots of paradoxes that one can cook up using Poisson processes and random processes in general often have to do with the story of this kind." + }, + { + "text": "The phenomenon that we had in this particular example also shows up in general, whenever you have other kinds of arrival processes." + }, + { + "text": "So the Poisson process is the simplest arrival process there is, where the interarrival times are exponential random variables." + }, + { + "text": "There's a larger class of models." + }, + { + "text": "They're called renewal processes, in which, again, we have a sequence of successive arrivals, interarrival times are identically distributed and independent, but they may come from a general distribution." + }, + { + "text": "So to make the same point of the previous example but in a much simpler setting, suppose that bus interarrival times are either 5 or 10 minutes apart." + }, + { + "text": "So you get some intervals that are of length 5." + }, + { + "text": "You get some that are of length 10." + }, + { + "text": "And suppose that these are equally likely." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk23.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..0c23f2ec29db9e794aae974425a9309fbc5fa392 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "So we have -- not exactly -- In the long run, we have as many 5 minute intervals as we have 10 minute intervals." + }, + { + "text": "So the average interarrival time is 7 and 1/2." + }, + { + "text": "But if a person shows up at a random time, what are they going to see?" + }, + { + "text": "Do we have as many 5s as 10s?" + }, + { + "text": "But every 10 covers twice as much space." + }, + { + "text": "So if I show up at a random time, I have probability 2/3 falling inside an interval of duration 10." + }, + { + "text": "And I have one 1/3 probability of falling inside an interval of duration 5." + }, + { + "text": "That's because, out of the whole real line, 2/3 of it is covered by intervals of length 10, just because they're longer." + }, + { + "text": "1/3 is covered by the smaller intervals." + }, + { + "text": "Now if I fall inside an interval of length 10 and I measure the length of the interval that I fell into, that's going to be 10." + }, + { + "text": "But if I fall inside an interval of length 5 and I measure how long it is, I'm going to get a 5." + }, + { + "text": "And that, of course, is going to be different than 7.5." + }, + { + "text": "OK. And which number should be bigger?" + }, + { + "text": "It's the second number that's bigger because this one is biased in favor of the longer intervals." + }, + { + "text": "So that's, again, another illustration of the different results that you get when you have this random incidence phenomenon." + }, + { + "text": "So the bottom line, again, is that if you talk about a typical interarrival time, one must be very precise in specifying what we mean typical." + }, + { + "text": "So typical means sort of random." + }, + { + "text": "But to use the word random, you must specify very precisely what is the random experiment that you are using." + }, + { + "text": "And if you're not careful, you can get into apparent puzzles, such as the following." + }, + { + "text": "Suppose somebody tells you the average family size is 4, but the average person lives in a family of size 6." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk24.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..f1454166977d85230e828ad2593835dff01c5eed --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Is that compatible?" + }, + { + "text": "Family size is 4 on the average, but typical people live, on the average, in families of size 6." + }, + { + "text": "Well yes." + }, + { + "text": "There's no contradiction here." + }, + { + "text": "We're talking about two different experiments." + }, + { + "text": "In one experiment, I pick a family at random, and I tell you the average family is 4." + }, + { + "text": "In another experiment, I pick a person at random and I tell you that this person, on the average, will be in their family of size 6." + }, + { + "text": "And what is the catch here?" + }, + { + "text": "That if I pick a person at random, large families are more likely to be picked." + }, + { + "text": "So there's a bias in favor of large families." + }, + { + "text": "Or if you want to survey, let's say, are trains crowded in your city?" + }, + { + "text": "Or are buses crowded?" + }, + { + "text": "One choice is to pick a bus at random and inspect how crowded it is." + }, + { + "text": "Another choice is to pick a typical person and ask them, \"Did you ride the bus today?" + }, + { + "text": "Was it's crowded?\"" + }, + { + "text": "Well suppose that in this city there's one bus that's extremely crowded and all the other buses are completely empty." + }, + { + "text": "If you ask a person." + }, + { + "text": "\"Was your bus crowded?\"" + }, + { + "text": "They will tell you, \"Yes, my bus was crowded.\"" + }, + { + "text": "There's no witness from the empty buses to testify in their favor." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk25.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..5ea6070c380c8c0cc3ed8ff41fe3f0d64a2f6192 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk25.json @@ -0,0 +1,23 @@ +[ + { + "text": "So by sampling people instead of sampling buses, you're going to get different result." + }, + { + "text": "And in the process industry, if your job is to inspect and check cookies, you will be faced with a big dilemma." + }, + { + "text": "Do you want to find out how many chocolate chips there are on a typical cookie?" + }, + { + "text": "Are you going to interview cookies or are you going to interview chocolate chips and ask them how many other chips where there on your cookie?" + }, + { + "text": "And you're going to get different answers in these cases." + }, + { + "text": "So moral is, one has to be very precise on how you formulate the sampling procedure that you have." + }, + { + "text": "And you'll get different answers." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk3.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..65f67102a7086dbc76d65afeddb2720c5b67bdb0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "Of course the probability of getting a zillion arrivals is going to be tiny." + }, + { + "text": "But in principle, this is possible." + }, + { + "text": "And that's because an interval, even if it's a fixed length, consists of an infinite number of mini-slots in some sense." + }, + { + "text": "You can divide, chop it up, into as many mini-slots as you want." + }, + { + "text": "So in principle, it's possible that every mini-slot gets an arrival." + }, + { + "text": "In principle, it's possible to get an arbitrarily large number of arrivals." + }, + { + "text": "So this particular formula here is not very intuitive when you look at it." + }, + { + "text": "But it's a legitimate PMF." + }, + { + "text": "And it's called the Poisson PMF." + }, + { + "text": "It's the PMF that describes the number of arrivals." + }, + { + "text": "So that's one way of thinking about the Poisson process, where the basic object of interest would be this PMF and you try to work with it." + }, + { + "text": "There's another way of thinking about what happens in the Poisson process." + }, + { + "text": "And this has to do with letting things evolve in time." + }, + { + "text": "You start at time 0." + }, + { + "text": "There's going to be a time at which the first arrival occurs, and call that time T1." + }, + { + "text": "This time turns out to have an exponential distribution with parameter lambda." + }, + { + "text": "Once you get an arrival, it's as if the process starts fresh." + }, + { + "text": "The best way to understand why this is the case is by thinking in terms of the analogy with the Bernoulli process." + }, + { + "text": "If you believe that statement for the Bernoulli process, since this is a limiting case, it should also be true." + }, + { + "text": "So starting from this time, we're going to wait a random amount of time until we get the second arrival This random amount of time, let's call it T2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk4.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c5affc1f1a5b3e0305dcd63ee178f3ba1a2da02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "This time, T2 is also going to have an exponential distribution with the same parameter, lambda." + }, + { + "text": "And these two are going to be independent of each other." + }, + { + "text": "OK?" + }, + { + "text": "So the Poisson process has all the same memorylessness properties that the Bernoulli process has." + }, + { + "text": "What's another way of thinking of this property?" + }, + { + "text": "So think of a process where you have a light bulb." + }, + { + "text": "The time at the light bulb burns out, you can model it by an exponential random variable." + }, + { + "text": "And suppose that they tell you that so far, we're are sitting at some time, T. And I tell you that the light bulb has not yet burned out." + }, + { + "text": "What does this tell you about the future of the light bulb?" + }, + { + "text": "Is the fact that they didn't burn out, so far, is it good news or is it bad news?" + }, + { + "text": "Would you rather keep this light bulb that has worked for t times steps and is still OK?" + }, + { + "text": "Or would you rather use a new light bulb that starts new at that point in time?" + }, + { + "text": "Because of the memorylessness property, the past of that light bulb doesn't matter." + }, + { + "text": "So the future of this light bulb is statistically the same as the future of a new light bulb." + }, + { + "text": "For both of them, the time until they burn out is going to be described an exponential distribution." + }, + { + "text": "So one way that people described the situation is to say that used is exactly as good as a new." + }, + { + "text": "So a used on is no worse than a new one." + }, + { + "text": "A used one is no better than a new one." + }, + { + "text": "So a used light bulb that hasn't yet burnt out is exactly as good as a new light bulb." + }, + { + "text": "So that's another way of thinking about the memorylessness that we have in the Poisson process." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk5.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..a8f4593b861f0c6ab6d24f9023bf2c98983b5ab3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "Back to this picture." + }, + { + "text": "The time until the second arrival is the sum of two independent exponential random variables." + }, + { + "text": "So, in principle, you can use the convolution formula to find the distribution of T1 plus T2, and that would be what we call Y2, the time until the second arrival." + }, + { + "text": "But there's also a direct way of obtaining to the distribution of Y2, and this is the calculation that we did last time on the blackboard." + }, + { + "text": "And actually, we did it more generally." + }, + { + "text": "We found the time until the case arrival occurs." + }, + { + "text": "It has a closed form formula, which is called the Erlang distribution with k degrees of freedom." + }, + { + "text": "So let's see what's going on here." + }, + { + "text": "It's a distribution Of what kind?" + }, + { + "text": "It's a continuous distribution." + }, + { + "text": "It's a probability density function." + }, + { + "text": "This is because the time is a continuous random variable." + }, + { + "text": "Time is continuous." + }, + { + "text": "Arrivals can happen at any time." + }, + { + "text": "So we're talking about the PDF." + }, + { + "text": "This k is just the parameter of the distribution." + }, + { + "text": "We're talking about the k-th arrival, so k is a fixed number." + }, + { + "text": "Lambda is another parameter of the distribution, which is the arrival rate So it's a PDF over the Y's, whereas lambda and k are parameters of the distribution." + }, + { + "text": "OK." + }, + { + "text": "So this was what we knew from last time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk6.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..f957b2a1915e0744ba6fb901fba06c158d7e336f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Just to get some practice, let us do a problem that's not too difficult, but just to see how we use the various formulas that we have." + }, + { + "text": "So Poisson was a mathematician, but Poisson also means fish in French." + }, + { + "text": "So Poisson goes fishing." + }, + { + "text": "And let's assume that fish are caught according to a Poisson process." + }, + { + "text": "That's not too bad an assumption." + }, + { + "text": "At any given point in time, you have a little probability that a fish would be caught." + }, + { + "text": "And whether you catch one now is sort of independent about whether at some later time a fish will be caught or not." + }, + { + "text": "So let's just make this assumption." + }, + { + "text": "And suppose that the rules of the game are that you-- Fish are being called it the certain rate of 0.6 per hour." + }, + { + "text": "You fish for 2 hours, no matter what." + }, + { + "text": "And then there are two possibilities." + }, + { + "text": "If I have caught a fish, I stop and go home." + }, + { + "text": "So if some fish have been caught, so there's at least 1 arrival during this interval, I go home." + }, + { + "text": "Or if nothing has being caught, I continue fishing until I catch something." + }, + { + "text": "And then I go home." + }, + { + "text": "So that's the description of what is going to happen." + }, + { + "text": "And now let's starts asking questions of all sorts." + }, + { + "text": "What is the probability that I'm going to be fishing for more than 2 hours?" + }, + { + "text": "I will be fishing for more than 2 hours, if and only if no fish were caught during those 2 hours, in which case, I will have to continue." + }, + { + "text": "Therefore, this is just this quantity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk7.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..d200ba8c85d33ddb01ccd0430f2d344dfd85356f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "The probability of catching 2 fish in-- of catching 0 fish in the next 2 hours, and according to the formula that we have, this is going to be e to the minus lambda times how much time we have." + }, + { + "text": "There's another way of thinking about this." + }, + { + "text": "The probability that I fish for more than 2 hours is the probability that the first catch happens after time 2, which would be the integral from 2 to infinity of the density of the first arrival time." + }, + { + "text": "And that density is an exponential." + }, + { + "text": "So you do the integral of an exponential, and, of course, you would get the same answer." + }, + { + "text": "OK. That's easy." + }, + { + "text": "So what's the probability of fishing for more than 2 but less than 5 hours?" + }, + { + "text": "What does it take for this to happen?" + }, + { + "text": "For this to happen, we need to catch 0 fish from time 0 to 2 and catch the first fish sometime between 2 and 5." + }, + { + "text": "So if you-- one way of thinking about what's happening here might be to say that there's a Poisson process that keeps going on forever." + }, + { + "text": "But as soon as I catch the first fish, instead of continuing fishing and obtaining those other fish I just go home right now." + }, + { + "text": "Now the fact that I go home before time 5 means that, if I were to stay until time 5, I would have caught at least 1 fish." + }, + { + "text": "I might have caught more than 1." + }, + { + "text": "So the event of interest here is that the first catch happens between times 2 and 5." + }, + { + "text": "So one way of calculating this quantity would be-- Its the probability that the first catch happens between times 2 and 5." + }, + { + "text": "Another way to deal with it is to say, this is the probability that I caught 0 fish in the first 2 hours and then the probability that I catch at least 1 fish during the next 3 hours." + }, + { + "text": "This." + }, + { + "text": "What is this?" + }, + { + "text": "The probability of 0 fish in the next 3 hours is the probability of 0 fish during this time." + }, + { + "text": "1 minus this is the probability of catching at least 1 fish, of having at least 1 arrival, between times 2 and 5." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk8.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..63208c3916b0f28860e55ba410e9e8809a2e2618 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "If there's at least 1 arrival between times 2 and 5, then I would have gone home by time 5." + }, + { + "text": "So both of these, if you plug-in numbers and all that, of course, are going to give you the same answer." + }, + { + "text": "Now next, what's the probability that I catch at least 2 fish?" + }, + { + "text": "In which scenario are we?" + }, + { + "text": "Under this scenario, I go home when I catch my first fish." + }, + { + "text": "So in order to catch at least 2 fish, it must be in this case." + }, + { + "text": "So this is the same as the event that I catch at least 2 fish during the first 2 time steps." + }, + { + "text": "So it's going to be the probability from 2 to infinity, the probability that I catch 2 fish, or that I catch 3 fish, or I catch more than that." + }, + { + "text": "So it's this quantity." + }, + { + "text": "k is the number of fish that I catch." + }, + { + "text": "At least 2, so k goes from 2 to infinity." + }, + { + "text": "These are the probabilities of catching a number k of fish during this interval." + }, + { + "text": "And if you want a simpler form without an infinite sum, this would be 1 minus the probability of catching 0 fish, minus the probability of catching 1 fish, during a time interval of length 2." + }, + { + "text": "Another way to think of it." + }, + { + "text": "I'm going to catch 2 fish, at least 2 fish, if and only if the second fish caught in this process happens before time 2." + }, + { + "text": "So that's another way of thinking about the same event." + }, + { + "text": "So it's going to be the probability that the random variable Y2, the arrival time over the second fish, is less than or equal to 2." + }, + { + "text": "OK." + }, + { + "text": "The next one is a little trickier." + }, + { + "text": "Here we need to do a little bit of divide and conquer." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk9.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..438a6aa22ffef63c853416c037d519d661ef6133 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_7_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "Overall, in this expedition, what the expected number of fish to be caught?" + }, + { + "text": "One way to think about it is to try to use the total expectations theorem." + }, + { + "text": "And think of expected number of fish, given this scenario, or expected number of fish, given this scenario." + }, + { + "text": "That's a little more complicated than the way I'm going to do it." + }, + { + "text": "The way I'm going to do is to think as follows-- Expected number of fish is the expected number of fish caught between times 0 and 2 plus expected number of fish caught after time 2." + }, + { + "text": "So what's the expected number caught between time 0 and 2?" + }, + { + "text": "This is lambda t. So lambda is 0.6 times 2." + }, + { + "text": "This is the expected number of fish that are caught between times 0 and 2." + }, + { + "text": "Now let's think about the expected number of fish caught afterwards." + }, + { + "text": "How many fish are being caught afterwards?" + }, + { + "text": "Well it depends on the scenario." + }, + { + "text": "If we're in this scenario, we've gone home and we catch 0." + }, + { + "text": "If we're in this scenario, then we continue fishing until we catch one." + }, + { + "text": "So the expected number of fish to be caught after time 2 is going to be the probability of this scenario times 1." + }, + { + "text": "And the probability of that scenario is the probability that they call it's 0 fish during the first 2 time steps times 1, which is the number of fish I'm going to catch if I continue." + }, + { + "text": "The expected total fishing time we can calculate exactly the same way." + }, + { + "text": "I'm jumping to the last one." + }, + { + "text": "My total fishing time has a period of 2 time steps." + }, + { + "text": "I'm going to fish for 2 time steps no matter what." + }, + { + "text": "And then if I caught 0 fish, which happens with this probability, my expected time is going to be the expected time from here onwards, which is the expected value of this geometric random variable with parameter lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk0.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..aa961d524ea0d1287b995e40358f71afcd69bfb1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "JOHN TSITSIKLIS: Today we're going to finish our discussion of the Poisson process." + }, + { + "text": "We're going to see a few of its properties, do a few interesting problems, some more interesting than others." + }, + { + "text": "So go through a few examples and then we're going to talk about some quite strange things that happen with the Poisson process." + }, + { + "text": "So the first thing is to remember what the Poisson processes is." + }, + { + "text": "It's a model, let's say, of arrivals of customers that are, in some sense, quote unquote, completely random, that is a customer can arrive at any point in time." + }, + { + "text": "All points in time are equally likely." + }, + { + "text": "And different points in time are sort of independent of other points in time." + }, + { + "text": "So the fact that I got an arrival now doesn't tell me anything about whether there's going to be an arrival at some other time." + }, + { + "text": "In some sense, it's a continuous time version of the Bernoulli process." + }, + { + "text": "So the best way to think about the Poisson process is that we divide time into extremely tiny slots." + }, + { + "text": "And in each time slot, there's an independent possibility of having an arrival." + }, + { + "text": "Different time slots are independent of each other." + }, + { + "text": "On the other hand, when the slot is tiny, the probability for obtaining an arrival during that tiny slot is itself going to be tiny." + }, + { + "text": "So we capture these properties into a formal definition what the Poisson process is." + }, + { + "text": "We have a probability mass function for the number of arrivals, k, during an interval of a given length." + }, + { + "text": "So this is the sort of basic description of the distribution of the number of arrivals." + }, + { + "text": "So tau is fixed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk1.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..8ef79a1bbf5e44814915347122880462d60e3970 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And k is the parameter." + }, + { + "text": "So when we add over all k's, the sum of these probabilities has to be equal to 1." + }, + { + "text": "There's a time homogeneity assumption, which is hidden in this, namely, the only thing that matters is the duration of the time interval, not where the time interval sits on the real axis." + }, + { + "text": "Then we have an independence assumption." + }, + { + "text": "Intervals that are disjoint are statistically independent from each other." + }, + { + "text": "So any information you give me about arrivals during this time interval doesn't change my beliefs about what's going to happen during another time interval." + }, + { + "text": "So this is a generalization of the idea that we had in Bernoulli processes that different time slots are independent of each other." + }, + { + "text": "And then to specify this function, the distribution of the number of arrivals, we sort of go in stages." + }, + { + "text": "We first specify this function for the case where the time interval is very small." + }, + { + "text": "And I'm telling you what those probabilities will be." + }, + { + "text": "And based on these then, we do some calculations and to find the formula for the distribution of the number of arrivals for intervals of a general duration." + }, + { + "text": "So for a small duration, delta, the probability of obtaining 1 arrival is lambda delta." + }, + { + "text": "The remaining probability is assigned to the event that we get to no arrivals during that interval." + }, + { + "text": "The probability of obtaining more than 1 arrival in a tiny interval is essentially 0." + }, + { + "text": "And when we say essentially, it's means modular, terms that of order delta squared." + }, + { + "text": "And when delta is very small, anything which is delta squared can be ignored." + }, + { + "text": "So up to delta squared terms, that's what happened during a little interval." + }, + { + "text": "Now if we know the probability distribution for the number of arrivals in a little interval." + }, + { + "text": "We can use this to get the distribution for the number of arrivals over several intervals." + }, + { + "text": "How do we do that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk10.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c993d1aafbcf3de55a33d47639c163aee1857626 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So the expected time is 1 over lambda." + }, + { + "text": "And in our case this, is 1/0.6." + }, + { + "text": "Finally, if I tell you that I have been fishing for 4 hours and nothing has been caught so far, how much do you expect this quantity to be?" + }, + { + "text": "Here is the story that, again, that for the Poisson process used is as good as new." + }, + { + "text": "The process does not have any memory." + }, + { + "text": "Given what happens in the past doesn't matter for the future." + }, + { + "text": "It's as if the process starts new at this point in time." + }, + { + "text": "So this one is going to be, again, the same exponentially distributed random variable with the same parameter lambda." + }, + { + "text": "So expected time until an arrival comes is an exponential distribut -- has an exponential distribution with parameter lambda, no matter what has happened in the past." + }, + { + "text": "Starting from now and looking into the future, it's as if the process has just started." + }, + { + "text": "So it's going to be 1 over lambda, which is 1/0.6." + }, + { + "text": "OK. Now our next example is going to be a little more complicated or subtle." + }, + { + "text": "But before we get to the example, let's refresh our memory about what we discussed last time about merging Poisson independent Poisson processes." + }, + { + "text": "Instead of drawing the picture that way, another way we could draw it could be this." + }, + { + "text": "We have a Poisson process with rate lambda1, and a Poisson process with rate lambda2." + }, + { + "text": "They have, each one of these, have their arrivals." + }, + { + "text": "And then we form the merged process." + }, + { + "text": "And the merged process records an arrival whenever there's an arrival in either of the two processes." + }, + { + "text": "This process in that process are assumed to be independent of each other." + }, + { + "text": "Now different times in this process and that process are independent of each other." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk11.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..98f4de8fc7edf6671add64512cd98e8481dce843 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what happens in these two time intervals is independent from what happens in these two time intervals." + }, + { + "text": "These two time intervals to determine what happens here." + }, + { + "text": "These two time intervals determine what happens there." + }, + { + "text": "So because these are independent from these, this means that this is also independent from that." + }, + { + "text": "So the independence assumption is satisfied for the merged process." + }, + { + "text": "And the merged process turns out to be a Poisson process." + }, + { + "text": "And if you want to find the arrival rate for that process, you argue as follows." + }, + { + "text": "During a little interval of length delta, we have probability lambda1 delta of having an arrival in this process." + }, + { + "text": "We have probability lambda2 delta of an arrival in this process, plus second order terms in delta, which we're ignoring." + }, + { + "text": "And then you do the calculation and you find that in this process, you're going to have an arrival probability, which is lambda1 plus lambda2, again ignoring second order in delta-- terms that are second order in delta." + }, + { + "text": "So the merged process is a Poisson process whose arrival rate is the sum of the arrival rates of the individual processes." + }, + { + "text": "And the calculation we did at the end of the last lecture-- If I tell you that the new arrival happened here, where did that arrival come from?" + }, + { + "text": "Did it come from here or from there?" + }, + { + "text": "If the lambda1 is equal to lambda2, then by symmetry you would say that it's equally likely to have come from here or to come from there." + }, + { + "text": "But if this lambda is much bigger than that lambda, the fact that they saw an arrival is more likely to have come from there." + }, + { + "text": "And the formula that captures this is the following." + }, + { + "text": "This is the probability that my arrival has come from this particular stream rather than that particular stream." + }, + { + "text": "So when an arrival comes and you ask, what is the origin of that arrival?" + }, + { + "text": "It's as if I'm flipping a coin with these odds." + }, + { + "text": "And depending on outcome of that coin, I'm going to tell you came from there or it came from there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk12.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..b81514a3614b4cc14097ef6ee9b3469bf3d09d24 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "So the origin of an arrival is either this stream or that stream." + }, + { + "text": "And this is the probability that the origin of the arrival is that one." + }, + { + "text": "Now if we look at 2 different arrivals, and we ask about their origins-- So let's think about the origin of this arrival and compare it with the origin that arrival." + }, + { + "text": "The origin of this arrival is random." + }, + { + "text": "It could be right be either this or that." + }, + { + "text": "And this is the relevant probability." + }, + { + "text": "The origin of that arrival is random." + }, + { + "text": "It could be either here or is there, and again, with the same relevant probability." + }, + { + "text": "Question." + }, + { + "text": "The origin of this arrival, is it dependent or independent from the origin that arrival?" + }, + { + "text": "And here's how the argument goes." + }, + { + "text": "Separate times are independent." + }, + { + "text": "Whatever has happened in the process during this set of times is independent from whatever happened in the process during that set of times." + }, + { + "text": "Because different times have nothing to do with each other, the origin of this, of an arrival here, has nothing to do with the origin of an arrival there." + }, + { + "text": "So the origins of different arrivals are also independent random variables." + }, + { + "text": "So if I tell you that-- yeah." + }, + { + "text": "OK." + }, + { + "text": "So it as if that each time that you have an arrival in the merge process, it's as if you're flipping a coin to determine where did that arrival came from and these coins are independent of each other." + }, + { + "text": "OK. OK. Now we're going to use this-- what we know about merged processes to solve the problem that would be harder to do, if you were not using ideas from Poisson processes." + }, + { + "text": "So the formulation of the problem has nothing to do with the Poisson process." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk13.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..bf6c66b1e38f68ac6bd19d504f54b3d7f0681a3c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "The formulation is the following." + }, + { + "text": "We have 3 light-bulbs." + }, + { + "text": "And each light bulb is independent and is going to die out at the time that's exponentially distributed." + }, + { + "text": "So 3 light bulbs." + }, + { + "text": "They start their lives and then at some point they die or burn out." + }, + { + "text": "So let's think of this as X, this as Y, and this as Z." + }, + { + "text": "And we're interested in the time until the last light-bulb burns out." + }, + { + "text": "So we're interested in the maximum of the 3 random variables, X, Y, and Z." + }, + { + "text": "And in particular, we want to find the expected value of this maximum." + }, + { + "text": "OK." + }, + { + "text": "So you can do derived distribution, use the expected value rule, anything you want." + }, + { + "text": "You can get this answer using the tools that you already have in your hands." + }, + { + "text": "But now let us see how we can connect to this picture with a Poisson picture and come up with the answer in a very simple way." + }, + { + "text": "What is an exponential random variable?" + }, + { + "text": "An exponential random variable is the first act in the long play that involves a whole Poisson process." + }, + { + "text": "So an exponential random variable is the first act of a Poisson movie." + }, + { + "text": "Same thing here." + }, + { + "text": "You can think of this random variable as being part of some Poisson process that has been running." + }, + { + "text": "So it's part of this bigger picture." + }, + { + "text": "We're still interested in the maximum of the 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk14.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..1a92d35ab267e8941975fcfa559b335f37209c80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "The other arrivals are not going to affect our answers." + }, + { + "text": "It's just, conceptually speaking, we can think of the exponential random variable as being embedded in a bigger Poisson picture." + }, + { + "text": "So we have 3 Poisson process that are running in parallel." + }, + { + "text": "Let us split the expected time until the last burnout into pieces, which is time until the first burnout, time from the first until the second, and time from the second until the third." + }, + { + "text": "And find the expected values of each one of these pieces." + }, + { + "text": "What can we say about the expected value of this?" + }, + { + "text": "This is the first arrival out of all of these 3 Poisson processes." + }, + { + "text": "It's the first event that happens when you look at all of these processes simultaneously." + }, + { + "text": "So 3 Poisson processes running in parallel." + }, + { + "text": "We're interested in the time until one of them, any one of them, gets in arrival." + }, + { + "text": "Rephrase." + }, + { + "text": "We merged the 3 Poisson processes, and we ask for the time until we observe an arrival in the merged process." + }, + { + "text": "When 1 of the 3 gets an arrival for the first time, the merged process gets its first arrival." + }, + { + "text": "So what's the expected value of this time until the first burnout?" + }, + { + "text": "It's going to be the expected value of a Poisson random variable." + }, + { + "text": "So the first burnout is going to have an expected value, which is-- OK." + }, + { + "text": "It's a Poisson process." + }, + { + "text": "The merged process of the 3 has a collective arrival rate, which is 3 times lambda." + }, + { + "text": "So this is the parameter over the exponential distribution that describes the time until the first arrival in the merged process." + }, + { + "text": "And the expected value of this random variable is 1 over that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk15.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..ec2818bb27b6b5b81e6f20bc450cb58a1baac245 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "When you have an exponential random variable with parameter lambda, the expected value of that random variable is 1 over lambda." + }, + { + "text": "Here we're talking about the first arrival time in a process with rate 3 lambda." + }, + { + "text": "The expected time until the first arrival is 1 over (3 lambda)." + }, + { + "text": "Alright." + }, + { + "text": "So at this time, this bulb, this arrival happened, this bulb has been burned." + }, + { + "text": "So we don't care about that bulb anymore." + }, + { + "text": "We start at this time, and we look forward." + }, + { + "text": "This bulb has been burned." + }, + { + "text": "So let's just look forward from now on." + }, + { + "text": "What have we got?" + }, + { + "text": "We have two bulbs that are burning." + }, + { + "text": "We have a Poisson process that's the bigger picture of what could happen to that light bulb, if we were to keep replacing it." + }, + { + "text": "Another Poisson process." + }, + { + "text": "These two processes are, again, independent." + }, + { + "text": "From this time until that time, how long does it take?" + }, + { + "text": "It's the time until either this process records an arrival or that process records and arrival." + }, + { + "text": "That's the same as the time that the merged process of these two records an arrival." + }, + { + "text": "So we're talking about the expected time until the first arrival in a merged process." + }, + { + "text": "The merged process is Poisson." + }, + { + "text": "It's Poisson with rate 2 lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk16.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..6a74ed00548100b2fa7d07c494546d15ecdfac23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that extra time is going to take-- the expected value is going to be 1 over the (rate of that Poisson process)." + }, + { + "text": "So 1 over (2 lambda) is the expected value of this random variable." + }, + { + "text": "So at this point, this bulb now is also burned." + }, + { + "text": "So we start looking from this time on." + }, + { + "text": "That part of the picture disappears." + }, + { + "text": "Starting from this time, what's the expected value until that remaining light-bulb burns out?" + }, + { + "text": "Well, as we said before, in a Poisson process or with exponential random variables, we have memorylessness." + }, + { + "text": "A used bulb is as good as a new one." + }, + { + "text": "So it's as if we're starting from scratch here." + }, + { + "text": "So this is going to be an exponential random variable with parameter lambda." + }, + { + "text": "And the expected value of it is going to be 1 over lambda." + }, + { + "text": "So the beauty of approaching this problem in this particular way is, of course, that we manage to do everything without any calculus at all, without striking an integral, without trying to calculate expectations in any form." + }, + { + "text": "Most of the non-trivial problems that you encounter in the Poisson world basically involve tricks of these kind." + }, + { + "text": "You have a question and you try to rephrase it, trying to think in terms of what might happen in the Poisson setting, use memorylessness, use merging, et cetera, et cetera." + }, + { + "text": "Now we talked about merging." + }, + { + "text": "It turns out that the splitting of Poisson processes also works in a nice way." + }, + { + "text": "The story here is exactly the same as for the Bernoulli process." + }, + { + "text": "So I'm having a Poisson process." + }, + { + "text": "And each time, with some rate lambda, and each time that an arrival comes, I'm going to send it to that stream and the record an arrival here with some probability P. And I'm going to send it to the other stream with some probability 1 minus P. So either of this will happen or that will happen, depending on the outcome of the coin flip that I do." + }, + { + "text": "Each time that then arrival occurs, I flip a coin and I decide whether to record it here or there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk17.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..24ef2d939ecec102e5b0cf66c4aef963c1195410 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "This is called splitting a Poisson process into two pieces." + }, + { + "text": "What kind of process do we get here?" + }, + { + "text": "If you look at the little interval for length delta, what's the probability that this little interval gets an arrival?" + }, + { + "text": "It's the probability that this one gets an arrival, which is lambda delta times the probability that after I get an arrival my coin flip came out to be that way, so that it sends me there." + }, + { + "text": "So this means that this little interval is going to have probability lambda delta P. Or maybe more suggestively, I should write it as lambda P times delta." + }, + { + "text": "So every little interval has a probability of an arrival proportional to delta." + }, + { + "text": "The proportionality factor is lambda P. So lambda P is the rate of that process." + }, + { + "text": "And then you go through the mental exercise that you went through for the Bernoulli process to argue that a different intervals here are independent and so on." + }, + { + "text": "And that completes checking that this process is going to be a Poisson process." + }, + { + "text": "So when you split a Poisson process by doing independent coin flips each time that something happens, the processes that you get is again a Poisson process, but of course with a reduced rate." + }, + { + "text": "So instead of the word splitting, sometimes people also use the words thinning-out." + }, + { + "text": "That is, out of the arrivals that came, you keep a few but throw away a few." + }, + { + "text": "OK." + }, + { + "text": "So now the last topic over this lecture is a quite curious phenomenon that goes under the name of random incidents." + }, + { + "text": "So here's the story." + }, + { + "text": "Buses have been running on Mass Ave. from time immemorial." + }, + { + "text": "And the bus company that runs the buses claims that they come as a Poisson process with some rate, let's say, of 4 buses per hour." + }, + { + "text": "So that the expected time between bus arrivals is going to be 15 minutes." + }, + { + "text": "OK. Alright." + }, + { + "text": "So people have been complaining that they have been showing up there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk18.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..65a62f83b762cf608024e3af374f28f51f49e32f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "They think the buses are taking too long." + }, + { + "text": "So you are asked to investigate." + }, + { + "text": "Is the company-- Does it operate according to its promises or not." + }, + { + "text": "So you send an undercover agent to go and check the interarrival times of the buses." + }, + { + "text": "Are they 15 minutes?" + }, + { + "text": "Or are they longer?" + }, + { + "text": "So you put your dark glasses and you show up at the bus stop at some random time." + }, + { + "text": "And you go and ask the guy in the falafel truck, how long has it been since the last arrival?" + }, + { + "text": "So of course that guy works for the FBI, right?" + }, + { + "text": "So they tell you, well, it's been, let's say, 12 minutes since the last bus arrival." + }, + { + "text": "And then you say, \"Oh, 12 minutes." + }, + { + "text": "Average time is 15." + }, + { + "text": "So a bus should be coming any time now.\"" + }, + { + "text": "Is that correct?" + }, + { + "text": "No, you wouldn't think that way." + }, + { + "text": "It's a Poisson process." + }, + { + "text": "It doesn't matter how long it has been since the last bus arrival." + }, + { + "text": "So you don't go through that fallacy." + }, + { + "text": "Instead of predicting how long it's going to be, you just sit down there and wait and measure the time." + }, + { + "text": "And you find that this is, let's say, 11 minutes." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk19.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..af599f5b8f4c3fc0973b37e81b36088c85eae997 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you go to your boss and report, \"Well, it took-- I went there and the time from the previous bus to the next one was 23 minutes." + }, + { + "text": "It's more than the 15 that they said.\"" + }, + { + "text": "So go and do that again." + }, + { + "text": "You go day after day." + }, + { + "text": "You keep these statistics of the length of this interval." + }, + { + "text": "And you tell your boss it's a lot more than 15." + }, + { + "text": "It tends to be more like 30 or so." + }, + { + "text": "So the bus company is cheating us." + }, + { + "text": "Does the bus company really run Poisson buses at the rate that they have promised?" + }, + { + "text": "Well let's analyze the situation here and figure out what the length of this interval should be, on the average." + }, + { + "text": "The naive argument is that this interval is an interarrival time." + }, + { + "text": "And interarrival times, on the average, are 15 minutes, if the company runs indeed Poisson processes with these interarrival times." + }, + { + "text": "But actually the situation is a little more subtle because this is not a typical interarrival interval." + }, + { + "text": "This interarrival interval consists of two pieces." + }, + { + "text": "Let's call them T1 and T1 prime." + }, + { + "text": "What can you tell me about those two random variables?" + }, + { + "text": "What kind of random variable is T1?" + }, + { + "text": "Starting from this time, with the Poisson process, the past doesn't matter." + }, + { + "text": "It's the time until an arrival happens." + }, + { + "text": "So T1 is going to be an exponential random variable with parameter lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk2.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..ebc6083b4940b3fc27511f672c179a7846abc0b1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "The big interval is composed of many little intervals." + }, + { + "text": "Each little interval is independent from any other little interval, so is it is as if we have a sequence of Bernoulli trials." + }, + { + "text": "Each Bernoulli trial is associated with a little interval and has a small probability of obtaining a success or an arrival during that mini-slot." + }, + { + "text": "On the other hand, when delta is small, and you take a big interval and chop it up, you get a large number of little intervals." + }, + { + "text": "So what we essentially have here is a Bernoulli process, in which is the number of trials is huge but the probability of success during any given trial is tiny." + }, + { + "text": "The average number of trials ends up being proportional to the length of the interval." + }, + { + "text": "If you have twice as large an interval, it's as if you're having twice as many over these mini-trials, so the expected number of arrivals will increase proportionately." + }, + { + "text": "There's also this parameter lambda, which we interpret as expected number of arrivals per unit time." + }, + { + "text": "And it comes in those probabilities here." + }, + { + "text": "When you double lambda, this means that a little interval is twice as likely to get an arrival." + }, + { + "text": "So you would expect to get twice as many arrivals as well." + }, + { + "text": "That's why the expected number of arrivals during an interval of length tau also scales proportional to this parameter lambda." + }, + { + "text": "Somewhat unexpectedly, it turns out that the variance of the number of arrivals is also the same as the mean." + }, + { + "text": "This is a peculiarity that happens in the Poisson process." + }, + { + "text": "So this is one way of thinking about Poisson process, in terms of little intervals, each one of which has a tiny probability of success." + }, + { + "text": "And we think of the distribution associated with that process as being described by this particular PMF." + }, + { + "text": "So this is the PMF for the number of arrivals during an interval of a fixed duration, tau." + }, + { + "text": "It's a PMF that extends all over the entire range of non-negative integers." + }, + { + "text": "So the number of arrivals you can get during an interval for certain length can be anything." + }, + { + "text": "You can get as many arrivals as you want." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk20.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..28349ba5d13c19b16a2957596215f8e4b02bbf01 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "So in particular, the expected value of T1 is going to be 15 by itself." + }, + { + "text": "How about the random variable T1 prime." + }, + { + "text": "What kind of random variable is it?" + }, + { + "text": "This is like the first arrival in a Poisson process that runs backwards in time." + }, + { + "text": "What kind of process is a Poisson process running backwards in time?" + }, + { + "text": "Let's think of coin flips." + }, + { + "text": "Suppose you have a movie of coin flips." + }, + { + "text": "And for some accident, that fascinating movie, you happen to watch it backwards." + }, + { + "text": "Will it look any different statistically?" + }, + { + "text": "No." + }, + { + "text": "It's going to be just the sequence of random coin flips." + }, + { + "text": "So a Bernoulli process that's runs in reverse time is statistically identical to a Bernoulli process in forward time." + }, + { + "text": "The Poisson process is a limit of the Bernoulli." + }, + { + "text": "So, same story with the Poisson process." + }, + { + "text": "If you run it backwards in time it looks the same." + }, + { + "text": "So looking backwards in time, this is a Poisson process." + }, + { + "text": "And T1 prime is the time until the first arrival in this backward process." + }, + { + "text": "So T1 prime is also going to be an exponential random variable with the same parameter, lambda." + }, + { + "text": "And the expected value of T1 prime is 15." + }, + { + "text": "Conclusion is that the expected length of this interval is going to be 30 minutes." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk21.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..e60bcef503b4a0db026939c13f85514e5dcb0817 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the fact that this agent found the average to be something like 30 does not contradict the claims of the bus company that they're running Poisson buses with a rate of lambda equal to 4." + }, + { + "text": "OK." + }, + { + "text": "So maybe the company can this way-- they can defend themselves in court." + }, + { + "text": "But there's something puzzling here." + }, + { + "text": "How long is the interarrival time?" + }, + { + "text": "Is it 15?" + }, + { + "text": "Or is it 30?" + }, + { + "text": "On the average." + }, + { + "text": "The issue is what do we mean by a typical interarrival time." + }, + { + "text": "When we say typical, we mean some kind of average." + }, + { + "text": "But average over what?" + }, + { + "text": "And here's two different ways of thinking about averages." + }, + { + "text": "You number the buses." + }, + { + "text": "And you have bus number 100." + }, + { + "text": "You have bus number 101, bus number 102, bus number 110, and so on." + }, + { + "text": "One way of thinking about averages is that you pick a bus number at random." + }, + { + "text": "I pick, let's say, that bus, all buses being sort of equally likely to be picked." + }, + { + "text": "And I measure this interarrival time." + }, + { + "text": "So for a typical bus." + }, + { + "text": "Then, starting from here until there, the expected time has to be 1 over lambda, for the Poisson process." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk22.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..859fef7a50c29d5a5a9f8517f4db560ee5d550a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But what we did in this experiment was something different." + }, + { + "text": "We didn't pick a bus at random." + }, + { + "text": "We picked a time at random." + }, + { + "text": "And if the picture is, let's say, this way, I'm much more likely to pick this interval and therefore this interarrival time, rather than that interval." + }, + { + "text": "Because, this interval corresponds to very few times." + }, + { + "text": "So if I'm picking a time at random and, in some sense, let's say, uniform, so that all times are equally likely, I'm much more likely to fall inside a big interval rather than a small interval." + }, + { + "text": "So a person who shows up at the bus stop at a random time." + }, + { + "text": "They're selecting an interval in a biased way, with the bias favor of longer intervals." + }, + { + "text": "And that's why what they observe is a random variable that has a larger expected value then the ordinary expected value." + }, + { + "text": "So the subtlety here is to realize that we're talking between two different kinds of experiments." + }, + { + "text": "Picking a bus number at random verses picking an interval at random with a bias in favor of longer intervals." + }, + { + "text": "Lots of paradoxes that one can cook up using Poisson processes and random processes in general often have to do with the story of this kind." + }, + { + "text": "The phenomenon that we had in this particular example also shows up in general, whenever you have other kinds of arrival processes." + }, + { + "text": "So the Poisson process is the simplest arrival process there is, where the interarrival times are exponential random variables." + }, + { + "text": "There's a larger class of models." + }, + { + "text": "They're called renewal processes, in which, again, we have a sequence of successive arrivals, interarrival times are identically distributed and independent, but they may come from a general distribution." + }, + { + "text": "So to make the same point of the previous example but in a much simpler setting, suppose that bus interarrival times are either 5 or 10 minutes apart." + }, + { + "text": "So you get some intervals that are of length 5." + }, + { + "text": "You get some that are of length 10." + }, + { + "text": "And suppose that these are equally likely." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk23.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..0c23f2ec29db9e794aae974425a9309fbc5fa392 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "So we have -- not exactly -- In the long run, we have as many 5 minute intervals as we have 10 minute intervals." + }, + { + "text": "So the average interarrival time is 7 and 1/2." + }, + { + "text": "But if a person shows up at a random time, what are they going to see?" + }, + { + "text": "Do we have as many 5s as 10s?" + }, + { + "text": "But every 10 covers twice as much space." + }, + { + "text": "So if I show up at a random time, I have probability 2/3 falling inside an interval of duration 10." + }, + { + "text": "And I have one 1/3 probability of falling inside an interval of duration 5." + }, + { + "text": "That's because, out of the whole real line, 2/3 of it is covered by intervals of length 10, just because they're longer." + }, + { + "text": "1/3 is covered by the smaller intervals." + }, + { + "text": "Now if I fall inside an interval of length 10 and I measure the length of the interval that I fell into, that's going to be 10." + }, + { + "text": "But if I fall inside an interval of length 5 and I measure how long it is, I'm going to get a 5." + }, + { + "text": "And that, of course, is going to be different than 7.5." + }, + { + "text": "OK. And which number should be bigger?" + }, + { + "text": "It's the second number that's bigger because this one is biased in favor of the longer intervals." + }, + { + "text": "So that's, again, another illustration of the different results that you get when you have this random incidence phenomenon." + }, + { + "text": "So the bottom line, again, is that if you talk about a typical interarrival time, one must be very precise in specifying what we mean typical." + }, + { + "text": "So typical means sort of random." + }, + { + "text": "But to use the word random, you must specify very precisely what is the random experiment that you are using." + }, + { + "text": "And if you're not careful, you can get into apparent puzzles, such as the following." + }, + { + "text": "Suppose somebody tells you the average family size is 4, but the average person lives in a family of size 6." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk24.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..f1454166977d85230e828ad2593835dff01c5eed --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Is that compatible?" + }, + { + "text": "Family size is 4 on the average, but typical people live, on the average, in families of size 6." + }, + { + "text": "Well yes." + }, + { + "text": "There's no contradiction here." + }, + { + "text": "We're talking about two different experiments." + }, + { + "text": "In one experiment, I pick a family at random, and I tell you the average family is 4." + }, + { + "text": "In another experiment, I pick a person at random and I tell you that this person, on the average, will be in their family of size 6." + }, + { + "text": "And what is the catch here?" + }, + { + "text": "That if I pick a person at random, large families are more likely to be picked." + }, + { + "text": "So there's a bias in favor of large families." + }, + { + "text": "Or if you want to survey, let's say, are trains crowded in your city?" + }, + { + "text": "Or are buses crowded?" + }, + { + "text": "One choice is to pick a bus at random and inspect how crowded it is." + }, + { + "text": "Another choice is to pick a typical person and ask them, \"Did you ride the bus today?" + }, + { + "text": "Was it's crowded?\"" + }, + { + "text": "Well suppose that in this city there's one bus that's extremely crowded and all the other buses are completely empty." + }, + { + "text": "If you ask a person." + }, + { + "text": "\"Was your bus crowded?\"" + }, + { + "text": "They will tell you, \"Yes, my bus was crowded.\"" + }, + { + "text": "There's no witness from the empty buses to testify in their favor." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk25.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..5ea6070c380c8c0cc3ed8ff41fe3f0d64a2f6192 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk25.json @@ -0,0 +1,23 @@ +[ + { + "text": "So by sampling people instead of sampling buses, you're going to get different result." + }, + { + "text": "And in the process industry, if your job is to inspect and check cookies, you will be faced with a big dilemma." + }, + { + "text": "Do you want to find out how many chocolate chips there are on a typical cookie?" + }, + { + "text": "Are you going to interview cookies or are you going to interview chocolate chips and ask them how many other chips where there on your cookie?" + }, + { + "text": "And you're going to get different answers in these cases." + }, + { + "text": "So moral is, one has to be very precise on how you formulate the sampling procedure that you have." + }, + { + "text": "And you'll get different answers." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk3.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..65f67102a7086dbc76d65afeddb2720c5b67bdb0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "Of course the probability of getting a zillion arrivals is going to be tiny." + }, + { + "text": "But in principle, this is possible." + }, + { + "text": "And that's because an interval, even if it's a fixed length, consists of an infinite number of mini-slots in some sense." + }, + { + "text": "You can divide, chop it up, into as many mini-slots as you want." + }, + { + "text": "So in principle, it's possible that every mini-slot gets an arrival." + }, + { + "text": "In principle, it's possible to get an arbitrarily large number of arrivals." + }, + { + "text": "So this particular formula here is not very intuitive when you look at it." + }, + { + "text": "But it's a legitimate PMF." + }, + { + "text": "And it's called the Poisson PMF." + }, + { + "text": "It's the PMF that describes the number of arrivals." + }, + { + "text": "So that's one way of thinking about the Poisson process, where the basic object of interest would be this PMF and you try to work with it." + }, + { + "text": "There's another way of thinking about what happens in the Poisson process." + }, + { + "text": "And this has to do with letting things evolve in time." + }, + { + "text": "You start at time 0." + }, + { + "text": "There's going to be a time at which the first arrival occurs, and call that time T1." + }, + { + "text": "This time turns out to have an exponential distribution with parameter lambda." + }, + { + "text": "Once you get an arrival, it's as if the process starts fresh." + }, + { + "text": "The best way to understand why this is the case is by thinking in terms of the analogy with the Bernoulli process." + }, + { + "text": "If you believe that statement for the Bernoulli process, since this is a limiting case, it should also be true." + }, + { + "text": "So starting from this time, we're going to wait a random amount of time until we get the second arrival This random amount of time, let's call it T2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk4.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c5affc1f1a5b3e0305dcd63ee178f3ba1a2da02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "This time, T2 is also going to have an exponential distribution with the same parameter, lambda." + }, + { + "text": "And these two are going to be independent of each other." + }, + { + "text": "OK?" + }, + { + "text": "So the Poisson process has all the same memorylessness properties that the Bernoulli process has." + }, + { + "text": "What's another way of thinking of this property?" + }, + { + "text": "So think of a process where you have a light bulb." + }, + { + "text": "The time at the light bulb burns out, you can model it by an exponential random variable." + }, + { + "text": "And suppose that they tell you that so far, we're are sitting at some time, T. And I tell you that the light bulb has not yet burned out." + }, + { + "text": "What does this tell you about the future of the light bulb?" + }, + { + "text": "Is the fact that they didn't burn out, so far, is it good news or is it bad news?" + }, + { + "text": "Would you rather keep this light bulb that has worked for t times steps and is still OK?" + }, + { + "text": "Or would you rather use a new light bulb that starts new at that point in time?" + }, + { + "text": "Because of the memorylessness property, the past of that light bulb doesn't matter." + }, + { + "text": "So the future of this light bulb is statistically the same as the future of a new light bulb." + }, + { + "text": "For both of them, the time until they burn out is going to be described an exponential distribution." + }, + { + "text": "So one way that people described the situation is to say that used is exactly as good as a new." + }, + { + "text": "So a used on is no worse than a new one." + }, + { + "text": "A used one is no better than a new one." + }, + { + "text": "So a used light bulb that hasn't yet burnt out is exactly as good as a new light bulb." + }, + { + "text": "So that's another way of thinking about the memorylessness that we have in the Poisson process." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk5.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..a8f4593b861f0c6ab6d24f9023bf2c98983b5ab3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "Back to this picture." + }, + { + "text": "The time until the second arrival is the sum of two independent exponential random variables." + }, + { + "text": "So, in principle, you can use the convolution formula to find the distribution of T1 plus T2, and that would be what we call Y2, the time until the second arrival." + }, + { + "text": "But there's also a direct way of obtaining to the distribution of Y2, and this is the calculation that we did last time on the blackboard." + }, + { + "text": "And actually, we did it more generally." + }, + { + "text": "We found the time until the case arrival occurs." + }, + { + "text": "It has a closed form formula, which is called the Erlang distribution with k degrees of freedom." + }, + { + "text": "So let's see what's going on here." + }, + { + "text": "It's a distribution Of what kind?" + }, + { + "text": "It's a continuous distribution." + }, + { + "text": "It's a probability density function." + }, + { + "text": "This is because the time is a continuous random variable." + }, + { + "text": "Time is continuous." + }, + { + "text": "Arrivals can happen at any time." + }, + { + "text": "So we're talking about the PDF." + }, + { + "text": "This k is just the parameter of the distribution." + }, + { + "text": "We're talking about the k-th arrival, so k is a fixed number." + }, + { + "text": "Lambda is another parameter of the distribution, which is the arrival rate So it's a PDF over the Y's, whereas lambda and k are parameters of the distribution." + }, + { + "text": "OK." + }, + { + "text": "So this was what we knew from last time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk6.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..f957b2a1915e0744ba6fb901fba06c158d7e336f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Just to get some practice, let us do a problem that's not too difficult, but just to see how we use the various formulas that we have." + }, + { + "text": "So Poisson was a mathematician, but Poisson also means fish in French." + }, + { + "text": "So Poisson goes fishing." + }, + { + "text": "And let's assume that fish are caught according to a Poisson process." + }, + { + "text": "That's not too bad an assumption." + }, + { + "text": "At any given point in time, you have a little probability that a fish would be caught." + }, + { + "text": "And whether you catch one now is sort of independent about whether at some later time a fish will be caught or not." + }, + { + "text": "So let's just make this assumption." + }, + { + "text": "And suppose that the rules of the game are that you-- Fish are being called it the certain rate of 0.6 per hour." + }, + { + "text": "You fish for 2 hours, no matter what." + }, + { + "text": "And then there are two possibilities." + }, + { + "text": "If I have caught a fish, I stop and go home." + }, + { + "text": "So if some fish have been caught, so there's at least 1 arrival during this interval, I go home." + }, + { + "text": "Or if nothing has being caught, I continue fishing until I catch something." + }, + { + "text": "And then I go home." + }, + { + "text": "So that's the description of what is going to happen." + }, + { + "text": "And now let's starts asking questions of all sorts." + }, + { + "text": "What is the probability that I'm going to be fishing for more than 2 hours?" + }, + { + "text": "I will be fishing for more than 2 hours, if and only if no fish were caught during those 2 hours, in which case, I will have to continue." + }, + { + "text": "Therefore, this is just this quantity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk7.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..d200ba8c85d33ddb01ccd0430f2d344dfd85356f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "The probability of catching 2 fish in-- of catching 0 fish in the next 2 hours, and according to the formula that we have, this is going to be e to the minus lambda times how much time we have." + }, + { + "text": "There's another way of thinking about this." + }, + { + "text": "The probability that I fish for more than 2 hours is the probability that the first catch happens after time 2, which would be the integral from 2 to infinity of the density of the first arrival time." + }, + { + "text": "And that density is an exponential." + }, + { + "text": "So you do the integral of an exponential, and, of course, you would get the same answer." + }, + { + "text": "OK. That's easy." + }, + { + "text": "So what's the probability of fishing for more than 2 but less than 5 hours?" + }, + { + "text": "What does it take for this to happen?" + }, + { + "text": "For this to happen, we need to catch 0 fish from time 0 to 2 and catch the first fish sometime between 2 and 5." + }, + { + "text": "So if you-- one way of thinking about what's happening here might be to say that there's a Poisson process that keeps going on forever." + }, + { + "text": "But as soon as I catch the first fish, instead of continuing fishing and obtaining those other fish I just go home right now." + }, + { + "text": "Now the fact that I go home before time 5 means that, if I were to stay until time 5, I would have caught at least 1 fish." + }, + { + "text": "I might have caught more than 1." + }, + { + "text": "So the event of interest here is that the first catch happens between times 2 and 5." + }, + { + "text": "So one way of calculating this quantity would be-- Its the probability that the first catch happens between times 2 and 5." + }, + { + "text": "Another way to deal with it is to say, this is the probability that I caught 0 fish in the first 2 hours and then the probability that I catch at least 1 fish during the next 3 hours." + }, + { + "text": "This." + }, + { + "text": "What is this?" + }, + { + "text": "The probability of 0 fish in the next 3 hours is the probability of 0 fish during this time." + }, + { + "text": "1 minus this is the probability of catching at least 1 fish, of having at least 1 arrival, between times 2 and 5." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk8.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..63208c3916b0f28860e55ba410e9e8809a2e2618 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "If there's at least 1 arrival between times 2 and 5, then I would have gone home by time 5." + }, + { + "text": "So both of these, if you plug-in numbers and all that, of course, are going to give you the same answer." + }, + { + "text": "Now next, what's the probability that I catch at least 2 fish?" + }, + { + "text": "In which scenario are we?" + }, + { + "text": "Under this scenario, I go home when I catch my first fish." + }, + { + "text": "So in order to catch at least 2 fish, it must be in this case." + }, + { + "text": "So this is the same as the event that I catch at least 2 fish during the first 2 time steps." + }, + { + "text": "So it's going to be the probability from 2 to infinity, the probability that I catch 2 fish, or that I catch 3 fish, or I catch more than that." + }, + { + "text": "So it's this quantity." + }, + { + "text": "k is the number of fish that I catch." + }, + { + "text": "At least 2, so k goes from 2 to infinity." + }, + { + "text": "These are the probabilities of catching a number k of fish during this interval." + }, + { + "text": "And if you want a simpler form without an infinite sum, this would be 1 minus the probability of catching 0 fish, minus the probability of catching 1 fish, during a time interval of length 2." + }, + { + "text": "Another way to think of it." + }, + { + "text": "I'm going to catch 2 fish, at least 2 fish, if and only if the second fish caught in this process happens before time 2." + }, + { + "text": "So that's another way of thinking about the same event." + }, + { + "text": "So it's going to be the probability that the random variable Y2, the arrival time over the second fish, is less than or equal to 2." + }, + { + "text": "OK." + }, + { + "text": "The next one is a little trickier." + }, + { + "text": "Here we need to do a little bit of divide and conquer." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk9.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..438a6aa22ffef63c853416c037d519d661ef6133 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_8_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "Overall, in this expedition, what the expected number of fish to be caught?" + }, + { + "text": "One way to think about it is to try to use the total expectations theorem." + }, + { + "text": "And think of expected number of fish, given this scenario, or expected number of fish, given this scenario." + }, + { + "text": "That's a little more complicated than the way I'm going to do it." + }, + { + "text": "The way I'm going to do is to think as follows-- Expected number of fish is the expected number of fish caught between times 0 and 2 plus expected number of fish caught after time 2." + }, + { + "text": "So what's the expected number caught between time 0 and 2?" + }, + { + "text": "This is lambda t. So lambda is 0.6 times 2." + }, + { + "text": "This is the expected number of fish that are caught between times 0 and 2." + }, + { + "text": "Now let's think about the expected number of fish caught afterwards." + }, + { + "text": "How many fish are being caught afterwards?" + }, + { + "text": "Well it depends on the scenario." + }, + { + "text": "If we're in this scenario, we've gone home and we catch 0." + }, + { + "text": "If we're in this scenario, then we continue fishing until we catch one." + }, + { + "text": "So the expected number of fish to be caught after time 2 is going to be the probability of this scenario times 1." + }, + { + "text": "And the probability of that scenario is the probability that they call it's 0 fish during the first 2 time steps times 1, which is the number of fish I'm going to catch if I continue." + }, + { + "text": "The expected total fishing time we can calculate exactly the same way." + }, + { + "text": "I'm jumping to the last one." + }, + { + "text": "My total fishing time has a period of 2 time steps." + }, + { + "text": "I'm going to fish for 2 time steps no matter what." + }, + { + "text": "And then if I caught 0 fish, which happens with this probability, my expected time is going to be the expected time from here onwards, which is the expected value of this geometric random variable with parameter lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk0.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..aa961d524ea0d1287b995e40358f71afcd69bfb1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "JOHN TSITSIKLIS: Today we're going to finish our discussion of the Poisson process." + }, + { + "text": "We're going to see a few of its properties, do a few interesting problems, some more interesting than others." + }, + { + "text": "So go through a few examples and then we're going to talk about some quite strange things that happen with the Poisson process." + }, + { + "text": "So the first thing is to remember what the Poisson processes is." + }, + { + "text": "It's a model, let's say, of arrivals of customers that are, in some sense, quote unquote, completely random, that is a customer can arrive at any point in time." + }, + { + "text": "All points in time are equally likely." + }, + { + "text": "And different points in time are sort of independent of other points in time." + }, + { + "text": "So the fact that I got an arrival now doesn't tell me anything about whether there's going to be an arrival at some other time." + }, + { + "text": "In some sense, it's a continuous time version of the Bernoulli process." + }, + { + "text": "So the best way to think about the Poisson process is that we divide time into extremely tiny slots." + }, + { + "text": "And in each time slot, there's an independent possibility of having an arrival." + }, + { + "text": "Different time slots are independent of each other." + }, + { + "text": "On the other hand, when the slot is tiny, the probability for obtaining an arrival during that tiny slot is itself going to be tiny." + }, + { + "text": "So we capture these properties into a formal definition what the Poisson process is." + }, + { + "text": "We have a probability mass function for the number of arrivals, k, during an interval of a given length." + }, + { + "text": "So this is the sort of basic description of the distribution of the number of arrivals." + }, + { + "text": "So tau is fixed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk1.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..8ef79a1bbf5e44814915347122880462d60e3970 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And k is the parameter." + }, + { + "text": "So when we add over all k's, the sum of these probabilities has to be equal to 1." + }, + { + "text": "There's a time homogeneity assumption, which is hidden in this, namely, the only thing that matters is the duration of the time interval, not where the time interval sits on the real axis." + }, + { + "text": "Then we have an independence assumption." + }, + { + "text": "Intervals that are disjoint are statistically independent from each other." + }, + { + "text": "So any information you give me about arrivals during this time interval doesn't change my beliefs about what's going to happen during another time interval." + }, + { + "text": "So this is a generalization of the idea that we had in Bernoulli processes that different time slots are independent of each other." + }, + { + "text": "And then to specify this function, the distribution of the number of arrivals, we sort of go in stages." + }, + { + "text": "We first specify this function for the case where the time interval is very small." + }, + { + "text": "And I'm telling you what those probabilities will be." + }, + { + "text": "And based on these then, we do some calculations and to find the formula for the distribution of the number of arrivals for intervals of a general duration." + }, + { + "text": "So for a small duration, delta, the probability of obtaining 1 arrival is lambda delta." + }, + { + "text": "The remaining probability is assigned to the event that we get to no arrivals during that interval." + }, + { + "text": "The probability of obtaining more than 1 arrival in a tiny interval is essentially 0." + }, + { + "text": "And when we say essentially, it's means modular, terms that of order delta squared." + }, + { + "text": "And when delta is very small, anything which is delta squared can be ignored." + }, + { + "text": "So up to delta squared terms, that's what happened during a little interval." + }, + { + "text": "Now if we know the probability distribution for the number of arrivals in a little interval." + }, + { + "text": "We can use this to get the distribution for the number of arrivals over several intervals." + }, + { + "text": "How do we do that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk10.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..c993d1aafbcf3de55a33d47639c163aee1857626 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So the expected time is 1 over lambda." + }, + { + "text": "And in our case this, is 1/0.6." + }, + { + "text": "Finally, if I tell you that I have been fishing for 4 hours and nothing has been caught so far, how much do you expect this quantity to be?" + }, + { + "text": "Here is the story that, again, that for the Poisson process used is as good as new." + }, + { + "text": "The process does not have any memory." + }, + { + "text": "Given what happens in the past doesn't matter for the future." + }, + { + "text": "It's as if the process starts new at this point in time." + }, + { + "text": "So this one is going to be, again, the same exponentially distributed random variable with the same parameter lambda." + }, + { + "text": "So expected time until an arrival comes is an exponential distribut -- has an exponential distribution with parameter lambda, no matter what has happened in the past." + }, + { + "text": "Starting from now and looking into the future, it's as if the process has just started." + }, + { + "text": "So it's going to be 1 over lambda, which is 1/0.6." + }, + { + "text": "OK. Now our next example is going to be a little more complicated or subtle." + }, + { + "text": "But before we get to the example, let's refresh our memory about what we discussed last time about merging Poisson independent Poisson processes." + }, + { + "text": "Instead of drawing the picture that way, another way we could draw it could be this." + }, + { + "text": "We have a Poisson process with rate lambda1, and a Poisson process with rate lambda2." + }, + { + "text": "They have, each one of these, have their arrivals." + }, + { + "text": "And then we form the merged process." + }, + { + "text": "And the merged process records an arrival whenever there's an arrival in either of the two processes." + }, + { + "text": "This process in that process are assumed to be independent of each other." + }, + { + "text": "Now different times in this process and that process are independent of each other." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk11.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..98f4de8fc7edf6671add64512cd98e8481dce843 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what happens in these two time intervals is independent from what happens in these two time intervals." + }, + { + "text": "These two time intervals to determine what happens here." + }, + { + "text": "These two time intervals determine what happens there." + }, + { + "text": "So because these are independent from these, this means that this is also independent from that." + }, + { + "text": "So the independence assumption is satisfied for the merged process." + }, + { + "text": "And the merged process turns out to be a Poisson process." + }, + { + "text": "And if you want to find the arrival rate for that process, you argue as follows." + }, + { + "text": "During a little interval of length delta, we have probability lambda1 delta of having an arrival in this process." + }, + { + "text": "We have probability lambda2 delta of an arrival in this process, plus second order terms in delta, which we're ignoring." + }, + { + "text": "And then you do the calculation and you find that in this process, you're going to have an arrival probability, which is lambda1 plus lambda2, again ignoring second order in delta-- terms that are second order in delta." + }, + { + "text": "So the merged process is a Poisson process whose arrival rate is the sum of the arrival rates of the individual processes." + }, + { + "text": "And the calculation we did at the end of the last lecture-- If I tell you that the new arrival happened here, where did that arrival come from?" + }, + { + "text": "Did it come from here or from there?" + }, + { + "text": "If the lambda1 is equal to lambda2, then by symmetry you would say that it's equally likely to have come from here or to come from there." + }, + { + "text": "But if this lambda is much bigger than that lambda, the fact that they saw an arrival is more likely to have come from there." + }, + { + "text": "And the formula that captures this is the following." + }, + { + "text": "This is the probability that my arrival has come from this particular stream rather than that particular stream." + }, + { + "text": "So when an arrival comes and you ask, what is the origin of that arrival?" + }, + { + "text": "It's as if I'm flipping a coin with these odds." + }, + { + "text": "And depending on outcome of that coin, I'm going to tell you came from there or it came from there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk12.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..b81514a3614b4cc14097ef6ee9b3469bf3d09d24 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "So the origin of an arrival is either this stream or that stream." + }, + { + "text": "And this is the probability that the origin of the arrival is that one." + }, + { + "text": "Now if we look at 2 different arrivals, and we ask about their origins-- So let's think about the origin of this arrival and compare it with the origin that arrival." + }, + { + "text": "The origin of this arrival is random." + }, + { + "text": "It could be right be either this or that." + }, + { + "text": "And this is the relevant probability." + }, + { + "text": "The origin of that arrival is random." + }, + { + "text": "It could be either here or is there, and again, with the same relevant probability." + }, + { + "text": "Question." + }, + { + "text": "The origin of this arrival, is it dependent or independent from the origin that arrival?" + }, + { + "text": "And here's how the argument goes." + }, + { + "text": "Separate times are independent." + }, + { + "text": "Whatever has happened in the process during this set of times is independent from whatever happened in the process during that set of times." + }, + { + "text": "Because different times have nothing to do with each other, the origin of this, of an arrival here, has nothing to do with the origin of an arrival there." + }, + { + "text": "So the origins of different arrivals are also independent random variables." + }, + { + "text": "So if I tell you that-- yeah." + }, + { + "text": "OK." + }, + { + "text": "So it as if that each time that you have an arrival in the merge process, it's as if you're flipping a coin to determine where did that arrival came from and these coins are independent of each other." + }, + { + "text": "OK. OK. Now we're going to use this-- what we know about merged processes to solve the problem that would be harder to do, if you were not using ideas from Poisson processes." + }, + { + "text": "So the formulation of the problem has nothing to do with the Poisson process." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk13.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..bf6c66b1e38f68ac6bd19d504f54b3d7f0681a3c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "The formulation is the following." + }, + { + "text": "We have 3 light-bulbs." + }, + { + "text": "And each light bulb is independent and is going to die out at the time that's exponentially distributed." + }, + { + "text": "So 3 light bulbs." + }, + { + "text": "They start their lives and then at some point they die or burn out." + }, + { + "text": "So let's think of this as X, this as Y, and this as Z." + }, + { + "text": "And we're interested in the time until the last light-bulb burns out." + }, + { + "text": "So we're interested in the maximum of the 3 random variables, X, Y, and Z." + }, + { + "text": "And in particular, we want to find the expected value of this maximum." + }, + { + "text": "OK." + }, + { + "text": "So you can do derived distribution, use the expected value rule, anything you want." + }, + { + "text": "You can get this answer using the tools that you already have in your hands." + }, + { + "text": "But now let us see how we can connect to this picture with a Poisson picture and come up with the answer in a very simple way." + }, + { + "text": "What is an exponential random variable?" + }, + { + "text": "An exponential random variable is the first act in the long play that involves a whole Poisson process." + }, + { + "text": "So an exponential random variable is the first act of a Poisson movie." + }, + { + "text": "Same thing here." + }, + { + "text": "You can think of this random variable as being part of some Poisson process that has been running." + }, + { + "text": "So it's part of this bigger picture." + }, + { + "text": "We're still interested in the maximum of the 3." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk14.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..1a92d35ab267e8941975fcfa559b335f37209c80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "The other arrivals are not going to affect our answers." + }, + { + "text": "It's just, conceptually speaking, we can think of the exponential random variable as being embedded in a bigger Poisson picture." + }, + { + "text": "So we have 3 Poisson process that are running in parallel." + }, + { + "text": "Let us split the expected time until the last burnout into pieces, which is time until the first burnout, time from the first until the second, and time from the second until the third." + }, + { + "text": "And find the expected values of each one of these pieces." + }, + { + "text": "What can we say about the expected value of this?" + }, + { + "text": "This is the first arrival out of all of these 3 Poisson processes." + }, + { + "text": "It's the first event that happens when you look at all of these processes simultaneously." + }, + { + "text": "So 3 Poisson processes running in parallel." + }, + { + "text": "We're interested in the time until one of them, any one of them, gets in arrival." + }, + { + "text": "Rephrase." + }, + { + "text": "We merged the 3 Poisson processes, and we ask for the time until we observe an arrival in the merged process." + }, + { + "text": "When 1 of the 3 gets an arrival for the first time, the merged process gets its first arrival." + }, + { + "text": "So what's the expected value of this time until the first burnout?" + }, + { + "text": "It's going to be the expected value of a Poisson random variable." + }, + { + "text": "So the first burnout is going to have an expected value, which is-- OK." + }, + { + "text": "It's a Poisson process." + }, + { + "text": "The merged process of the 3 has a collective arrival rate, which is 3 times lambda." + }, + { + "text": "So this is the parameter over the exponential distribution that describes the time until the first arrival in the merged process." + }, + { + "text": "And the expected value of this random variable is 1 over that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk15.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..ec2818bb27b6b5b81e6f20bc450cb58a1baac245 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "When you have an exponential random variable with parameter lambda, the expected value of that random variable is 1 over lambda." + }, + { + "text": "Here we're talking about the first arrival time in a process with rate 3 lambda." + }, + { + "text": "The expected time until the first arrival is 1 over (3 lambda)." + }, + { + "text": "Alright." + }, + { + "text": "So at this time, this bulb, this arrival happened, this bulb has been burned." + }, + { + "text": "So we don't care about that bulb anymore." + }, + { + "text": "We start at this time, and we look forward." + }, + { + "text": "This bulb has been burned." + }, + { + "text": "So let's just look forward from now on." + }, + { + "text": "What have we got?" + }, + { + "text": "We have two bulbs that are burning." + }, + { + "text": "We have a Poisson process that's the bigger picture of what could happen to that light bulb, if we were to keep replacing it." + }, + { + "text": "Another Poisson process." + }, + { + "text": "These two processes are, again, independent." + }, + { + "text": "From this time until that time, how long does it take?" + }, + { + "text": "It's the time until either this process records an arrival or that process records and arrival." + }, + { + "text": "That's the same as the time that the merged process of these two records an arrival." + }, + { + "text": "So we're talking about the expected time until the first arrival in a merged process." + }, + { + "text": "The merged process is Poisson." + }, + { + "text": "It's Poisson with rate 2 lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk16.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..6a74ed00548100b2fa7d07c494546d15ecdfac23 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that extra time is going to take-- the expected value is going to be 1 over the (rate of that Poisson process)." + }, + { + "text": "So 1 over (2 lambda) is the expected value of this random variable." + }, + { + "text": "So at this point, this bulb now is also burned." + }, + { + "text": "So we start looking from this time on." + }, + { + "text": "That part of the picture disappears." + }, + { + "text": "Starting from this time, what's the expected value until that remaining light-bulb burns out?" + }, + { + "text": "Well, as we said before, in a Poisson process or with exponential random variables, we have memorylessness." + }, + { + "text": "A used bulb is as good as a new one." + }, + { + "text": "So it's as if we're starting from scratch here." + }, + { + "text": "So this is going to be an exponential random variable with parameter lambda." + }, + { + "text": "And the expected value of it is going to be 1 over lambda." + }, + { + "text": "So the beauty of approaching this problem in this particular way is, of course, that we manage to do everything without any calculus at all, without striking an integral, without trying to calculate expectations in any form." + }, + { + "text": "Most of the non-trivial problems that you encounter in the Poisson world basically involve tricks of these kind." + }, + { + "text": "You have a question and you try to rephrase it, trying to think in terms of what might happen in the Poisson setting, use memorylessness, use merging, et cetera, et cetera." + }, + { + "text": "Now we talked about merging." + }, + { + "text": "It turns out that the splitting of Poisson processes also works in a nice way." + }, + { + "text": "The story here is exactly the same as for the Bernoulli process." + }, + { + "text": "So I'm having a Poisson process." + }, + { + "text": "And each time, with some rate lambda, and each time that an arrival comes, I'm going to send it to that stream and the record an arrival here with some probability P. And I'm going to send it to the other stream with some probability 1 minus P. So either of this will happen or that will happen, depending on the outcome of the coin flip that I do." + }, + { + "text": "Each time that then arrival occurs, I flip a coin and I decide whether to record it here or there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk17.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..24ef2d939ecec102e5b0cf66c4aef963c1195410 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "This is called splitting a Poisson process into two pieces." + }, + { + "text": "What kind of process do we get here?" + }, + { + "text": "If you look at the little interval for length delta, what's the probability that this little interval gets an arrival?" + }, + { + "text": "It's the probability that this one gets an arrival, which is lambda delta times the probability that after I get an arrival my coin flip came out to be that way, so that it sends me there." + }, + { + "text": "So this means that this little interval is going to have probability lambda delta P. Or maybe more suggestively, I should write it as lambda P times delta." + }, + { + "text": "So every little interval has a probability of an arrival proportional to delta." + }, + { + "text": "The proportionality factor is lambda P. So lambda P is the rate of that process." + }, + { + "text": "And then you go through the mental exercise that you went through for the Bernoulli process to argue that a different intervals here are independent and so on." + }, + { + "text": "And that completes checking that this process is going to be a Poisson process." + }, + { + "text": "So when you split a Poisson process by doing independent coin flips each time that something happens, the processes that you get is again a Poisson process, but of course with a reduced rate." + }, + { + "text": "So instead of the word splitting, sometimes people also use the words thinning-out." + }, + { + "text": "That is, out of the arrivals that came, you keep a few but throw away a few." + }, + { + "text": "OK." + }, + { + "text": "So now the last topic over this lecture is a quite curious phenomenon that goes under the name of random incidents." + }, + { + "text": "So here's the story." + }, + { + "text": "Buses have been running on Mass Ave. from time immemorial." + }, + { + "text": "And the bus company that runs the buses claims that they come as a Poisson process with some rate, let's say, of 4 buses per hour." + }, + { + "text": "So that the expected time between bus arrivals is going to be 15 minutes." + }, + { + "text": "OK. Alright." + }, + { + "text": "So people have been complaining that they have been showing up there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk18.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..65a62f83b762cf608024e3af374f28f51f49e32f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "They think the buses are taking too long." + }, + { + "text": "So you are asked to investigate." + }, + { + "text": "Is the company-- Does it operate according to its promises or not." + }, + { + "text": "So you send an undercover agent to go and check the interarrival times of the buses." + }, + { + "text": "Are they 15 minutes?" + }, + { + "text": "Or are they longer?" + }, + { + "text": "So you put your dark glasses and you show up at the bus stop at some random time." + }, + { + "text": "And you go and ask the guy in the falafel truck, how long has it been since the last arrival?" + }, + { + "text": "So of course that guy works for the FBI, right?" + }, + { + "text": "So they tell you, well, it's been, let's say, 12 minutes since the last bus arrival." + }, + { + "text": "And then you say, \"Oh, 12 minutes." + }, + { + "text": "Average time is 15." + }, + { + "text": "So a bus should be coming any time now.\"" + }, + { + "text": "Is that correct?" + }, + { + "text": "No, you wouldn't think that way." + }, + { + "text": "It's a Poisson process." + }, + { + "text": "It doesn't matter how long it has been since the last bus arrival." + }, + { + "text": "So you don't go through that fallacy." + }, + { + "text": "Instead of predicting how long it's going to be, you just sit down there and wait and measure the time." + }, + { + "text": "And you find that this is, let's say, 11 minutes." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk19.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..af599f5b8f4c3fc0973b37e81b36088c85eae997 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you go to your boss and report, \"Well, it took-- I went there and the time from the previous bus to the next one was 23 minutes." + }, + { + "text": "It's more than the 15 that they said.\"" + }, + { + "text": "So go and do that again." + }, + { + "text": "You go day after day." + }, + { + "text": "You keep these statistics of the length of this interval." + }, + { + "text": "And you tell your boss it's a lot more than 15." + }, + { + "text": "It tends to be more like 30 or so." + }, + { + "text": "So the bus company is cheating us." + }, + { + "text": "Does the bus company really run Poisson buses at the rate that they have promised?" + }, + { + "text": "Well let's analyze the situation here and figure out what the length of this interval should be, on the average." + }, + { + "text": "The naive argument is that this interval is an interarrival time." + }, + { + "text": "And interarrival times, on the average, are 15 minutes, if the company runs indeed Poisson processes with these interarrival times." + }, + { + "text": "But actually the situation is a little more subtle because this is not a typical interarrival interval." + }, + { + "text": "This interarrival interval consists of two pieces." + }, + { + "text": "Let's call them T1 and T1 prime." + }, + { + "text": "What can you tell me about those two random variables?" + }, + { + "text": "What kind of random variable is T1?" + }, + { + "text": "Starting from this time, with the Poisson process, the past doesn't matter." + }, + { + "text": "It's the time until an arrival happens." + }, + { + "text": "So T1 is going to be an exponential random variable with parameter lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk2.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..ebc6083b4940b3fc27511f672c179a7846abc0b1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "The big interval is composed of many little intervals." + }, + { + "text": "Each little interval is independent from any other little interval, so is it is as if we have a sequence of Bernoulli trials." + }, + { + "text": "Each Bernoulli trial is associated with a little interval and has a small probability of obtaining a success or an arrival during that mini-slot." + }, + { + "text": "On the other hand, when delta is small, and you take a big interval and chop it up, you get a large number of little intervals." + }, + { + "text": "So what we essentially have here is a Bernoulli process, in which is the number of trials is huge but the probability of success during any given trial is tiny." + }, + { + "text": "The average number of trials ends up being proportional to the length of the interval." + }, + { + "text": "If you have twice as large an interval, it's as if you're having twice as many over these mini-trials, so the expected number of arrivals will increase proportionately." + }, + { + "text": "There's also this parameter lambda, which we interpret as expected number of arrivals per unit time." + }, + { + "text": "And it comes in those probabilities here." + }, + { + "text": "When you double lambda, this means that a little interval is twice as likely to get an arrival." + }, + { + "text": "So you would expect to get twice as many arrivals as well." + }, + { + "text": "That's why the expected number of arrivals during an interval of length tau also scales proportional to this parameter lambda." + }, + { + "text": "Somewhat unexpectedly, it turns out that the variance of the number of arrivals is also the same as the mean." + }, + { + "text": "This is a peculiarity that happens in the Poisson process." + }, + { + "text": "So this is one way of thinking about Poisson process, in terms of little intervals, each one of which has a tiny probability of success." + }, + { + "text": "And we think of the distribution associated with that process as being described by this particular PMF." + }, + { + "text": "So this is the PMF for the number of arrivals during an interval of a fixed duration, tau." + }, + { + "text": "It's a PMF that extends all over the entire range of non-negative integers." + }, + { + "text": "So the number of arrivals you can get during an interval for certain length can be anything." + }, + { + "text": "You can get as many arrivals as you want." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk20.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..28349ba5d13c19b16a2957596215f8e4b02bbf01 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "So in particular, the expected value of T1 is going to be 15 by itself." + }, + { + "text": "How about the random variable T1 prime." + }, + { + "text": "What kind of random variable is it?" + }, + { + "text": "This is like the first arrival in a Poisson process that runs backwards in time." + }, + { + "text": "What kind of process is a Poisson process running backwards in time?" + }, + { + "text": "Let's think of coin flips." + }, + { + "text": "Suppose you have a movie of coin flips." + }, + { + "text": "And for some accident, that fascinating movie, you happen to watch it backwards." + }, + { + "text": "Will it look any different statistically?" + }, + { + "text": "No." + }, + { + "text": "It's going to be just the sequence of random coin flips." + }, + { + "text": "So a Bernoulli process that's runs in reverse time is statistically identical to a Bernoulli process in forward time." + }, + { + "text": "The Poisson process is a limit of the Bernoulli." + }, + { + "text": "So, same story with the Poisson process." + }, + { + "text": "If you run it backwards in time it looks the same." + }, + { + "text": "So looking backwards in time, this is a Poisson process." + }, + { + "text": "And T1 prime is the time until the first arrival in this backward process." + }, + { + "text": "So T1 prime is also going to be an exponential random variable with the same parameter, lambda." + }, + { + "text": "And the expected value of T1 prime is 15." + }, + { + "text": "Conclusion is that the expected length of this interval is going to be 30 minutes." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk21.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..e60bcef503b4a0db026939c13f85514e5dcb0817 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the fact that this agent found the average to be something like 30 does not contradict the claims of the bus company that they're running Poisson buses with a rate of lambda equal to 4." + }, + { + "text": "OK." + }, + { + "text": "So maybe the company can this way-- they can defend themselves in court." + }, + { + "text": "But there's something puzzling here." + }, + { + "text": "How long is the interarrival time?" + }, + { + "text": "Is it 15?" + }, + { + "text": "Or is it 30?" + }, + { + "text": "On the average." + }, + { + "text": "The issue is what do we mean by a typical interarrival time." + }, + { + "text": "When we say typical, we mean some kind of average." + }, + { + "text": "But average over what?" + }, + { + "text": "And here's two different ways of thinking about averages." + }, + { + "text": "You number the buses." + }, + { + "text": "And you have bus number 100." + }, + { + "text": "You have bus number 101, bus number 102, bus number 110, and so on." + }, + { + "text": "One way of thinking about averages is that you pick a bus number at random." + }, + { + "text": "I pick, let's say, that bus, all buses being sort of equally likely to be picked." + }, + { + "text": "And I measure this interarrival time." + }, + { + "text": "So for a typical bus." + }, + { + "text": "Then, starting from here until there, the expected time has to be 1 over lambda, for the Poisson process." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk22.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..859fef7a50c29d5a5a9f8517f4db560ee5d550a9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "But what we did in this experiment was something different." + }, + { + "text": "We didn't pick a bus at random." + }, + { + "text": "We picked a time at random." + }, + { + "text": "And if the picture is, let's say, this way, I'm much more likely to pick this interval and therefore this interarrival time, rather than that interval." + }, + { + "text": "Because, this interval corresponds to very few times." + }, + { + "text": "So if I'm picking a time at random and, in some sense, let's say, uniform, so that all times are equally likely, I'm much more likely to fall inside a big interval rather than a small interval." + }, + { + "text": "So a person who shows up at the bus stop at a random time." + }, + { + "text": "They're selecting an interval in a biased way, with the bias favor of longer intervals." + }, + { + "text": "And that's why what they observe is a random variable that has a larger expected value then the ordinary expected value." + }, + { + "text": "So the subtlety here is to realize that we're talking between two different kinds of experiments." + }, + { + "text": "Picking a bus number at random verses picking an interval at random with a bias in favor of longer intervals." + }, + { + "text": "Lots of paradoxes that one can cook up using Poisson processes and random processes in general often have to do with the story of this kind." + }, + { + "text": "The phenomenon that we had in this particular example also shows up in general, whenever you have other kinds of arrival processes." + }, + { + "text": "So the Poisson process is the simplest arrival process there is, where the interarrival times are exponential random variables." + }, + { + "text": "There's a larger class of models." + }, + { + "text": "They're called renewal processes, in which, again, we have a sequence of successive arrivals, interarrival times are identically distributed and independent, but they may come from a general distribution." + }, + { + "text": "So to make the same point of the previous example but in a much simpler setting, suppose that bus interarrival times are either 5 or 10 minutes apart." + }, + { + "text": "So you get some intervals that are of length 5." + }, + { + "text": "You get some that are of length 10." + }, + { + "text": "And suppose that these are equally likely." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk23.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..0c23f2ec29db9e794aae974425a9309fbc5fa392 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "So we have -- not exactly -- In the long run, we have as many 5 minute intervals as we have 10 minute intervals." + }, + { + "text": "So the average interarrival time is 7 and 1/2." + }, + { + "text": "But if a person shows up at a random time, what are they going to see?" + }, + { + "text": "Do we have as many 5s as 10s?" + }, + { + "text": "But every 10 covers twice as much space." + }, + { + "text": "So if I show up at a random time, I have probability 2/3 falling inside an interval of duration 10." + }, + { + "text": "And I have one 1/3 probability of falling inside an interval of duration 5." + }, + { + "text": "That's because, out of the whole real line, 2/3 of it is covered by intervals of length 10, just because they're longer." + }, + { + "text": "1/3 is covered by the smaller intervals." + }, + { + "text": "Now if I fall inside an interval of length 10 and I measure the length of the interval that I fell into, that's going to be 10." + }, + { + "text": "But if I fall inside an interval of length 5 and I measure how long it is, I'm going to get a 5." + }, + { + "text": "And that, of course, is going to be different than 7.5." + }, + { + "text": "OK. And which number should be bigger?" + }, + { + "text": "It's the second number that's bigger because this one is biased in favor of the longer intervals." + }, + { + "text": "So that's, again, another illustration of the different results that you get when you have this random incidence phenomenon." + }, + { + "text": "So the bottom line, again, is that if you talk about a typical interarrival time, one must be very precise in specifying what we mean typical." + }, + { + "text": "So typical means sort of random." + }, + { + "text": "But to use the word random, you must specify very precisely what is the random experiment that you are using." + }, + { + "text": "And if you're not careful, you can get into apparent puzzles, such as the following." + }, + { + "text": "Suppose somebody tells you the average family size is 4, but the average person lives in a family of size 6." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk24.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..f1454166977d85230e828ad2593835dff01c5eed --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "Is that compatible?" + }, + { + "text": "Family size is 4 on the average, but typical people live, on the average, in families of size 6." + }, + { + "text": "Well yes." + }, + { + "text": "There's no contradiction here." + }, + { + "text": "We're talking about two different experiments." + }, + { + "text": "In one experiment, I pick a family at random, and I tell you the average family is 4." + }, + { + "text": "In another experiment, I pick a person at random and I tell you that this person, on the average, will be in their family of size 6." + }, + { + "text": "And what is the catch here?" + }, + { + "text": "That if I pick a person at random, large families are more likely to be picked." + }, + { + "text": "So there's a bias in favor of large families." + }, + { + "text": "Or if you want to survey, let's say, are trains crowded in your city?" + }, + { + "text": "Or are buses crowded?" + }, + { + "text": "One choice is to pick a bus at random and inspect how crowded it is." + }, + { + "text": "Another choice is to pick a typical person and ask them, \"Did you ride the bus today?" + }, + { + "text": "Was it's crowded?\"" + }, + { + "text": "Well suppose that in this city there's one bus that's extremely crowded and all the other buses are completely empty." + }, + { + "text": "If you ask a person." + }, + { + "text": "\"Was your bus crowded?\"" + }, + { + "text": "They will tell you, \"Yes, my bus was crowded.\"" + }, + { + "text": "There's no witness from the empty buses to testify in their favor." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk25.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..5ea6070c380c8c0cc3ed8ff41fe3f0d64a2f6192 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk25.json @@ -0,0 +1,23 @@ +[ + { + "text": "So by sampling people instead of sampling buses, you're going to get different result." + }, + { + "text": "And in the process industry, if your job is to inspect and check cookies, you will be faced with a big dilemma." + }, + { + "text": "Do you want to find out how many chocolate chips there are on a typical cookie?" + }, + { + "text": "Are you going to interview cookies or are you going to interview chocolate chips and ask them how many other chips where there on your cookie?" + }, + { + "text": "And you're going to get different answers in these cases." + }, + { + "text": "So moral is, one has to be very precise on how you formulate the sampling procedure that you have." + }, + { + "text": "And you'll get different answers." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk3.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..65f67102a7086dbc76d65afeddb2720c5b67bdb0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "Of course the probability of getting a zillion arrivals is going to be tiny." + }, + { + "text": "But in principle, this is possible." + }, + { + "text": "And that's because an interval, even if it's a fixed length, consists of an infinite number of mini-slots in some sense." + }, + { + "text": "You can divide, chop it up, into as many mini-slots as you want." + }, + { + "text": "So in principle, it's possible that every mini-slot gets an arrival." + }, + { + "text": "In principle, it's possible to get an arbitrarily large number of arrivals." + }, + { + "text": "So this particular formula here is not very intuitive when you look at it." + }, + { + "text": "But it's a legitimate PMF." + }, + { + "text": "And it's called the Poisson PMF." + }, + { + "text": "It's the PMF that describes the number of arrivals." + }, + { + "text": "So that's one way of thinking about the Poisson process, where the basic object of interest would be this PMF and you try to work with it." + }, + { + "text": "There's another way of thinking about what happens in the Poisson process." + }, + { + "text": "And this has to do with letting things evolve in time." + }, + { + "text": "You start at time 0." + }, + { + "text": "There's going to be a time at which the first arrival occurs, and call that time T1." + }, + { + "text": "This time turns out to have an exponential distribution with parameter lambda." + }, + { + "text": "Once you get an arrival, it's as if the process starts fresh." + }, + { + "text": "The best way to understand why this is the case is by thinking in terms of the analogy with the Bernoulli process." + }, + { + "text": "If you believe that statement for the Bernoulli process, since this is a limiting case, it should also be true." + }, + { + "text": "So starting from this time, we're going to wait a random amount of time until we get the second arrival This random amount of time, let's call it T2." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk4.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c5affc1f1a5b3e0305dcd63ee178f3ba1a2da02e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "This time, T2 is also going to have an exponential distribution with the same parameter, lambda." + }, + { + "text": "And these two are going to be independent of each other." + }, + { + "text": "OK?" + }, + { + "text": "So the Poisson process has all the same memorylessness properties that the Bernoulli process has." + }, + { + "text": "What's another way of thinking of this property?" + }, + { + "text": "So think of a process where you have a light bulb." + }, + { + "text": "The time at the light bulb burns out, you can model it by an exponential random variable." + }, + { + "text": "And suppose that they tell you that so far, we're are sitting at some time, T. And I tell you that the light bulb has not yet burned out." + }, + { + "text": "What does this tell you about the future of the light bulb?" + }, + { + "text": "Is the fact that they didn't burn out, so far, is it good news or is it bad news?" + }, + { + "text": "Would you rather keep this light bulb that has worked for t times steps and is still OK?" + }, + { + "text": "Or would you rather use a new light bulb that starts new at that point in time?" + }, + { + "text": "Because of the memorylessness property, the past of that light bulb doesn't matter." + }, + { + "text": "So the future of this light bulb is statistically the same as the future of a new light bulb." + }, + { + "text": "For both of them, the time until they burn out is going to be described an exponential distribution." + }, + { + "text": "So one way that people described the situation is to say that used is exactly as good as a new." + }, + { + "text": "So a used on is no worse than a new one." + }, + { + "text": "A used one is no better than a new one." + }, + { + "text": "So a used light bulb that hasn't yet burnt out is exactly as good as a new light bulb." + }, + { + "text": "So that's another way of thinking about the memorylessness that we have in the Poisson process." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk5.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..a8f4593b861f0c6ab6d24f9023bf2c98983b5ab3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "Back to this picture." + }, + { + "text": "The time until the second arrival is the sum of two independent exponential random variables." + }, + { + "text": "So, in principle, you can use the convolution formula to find the distribution of T1 plus T2, and that would be what we call Y2, the time until the second arrival." + }, + { + "text": "But there's also a direct way of obtaining to the distribution of Y2, and this is the calculation that we did last time on the blackboard." + }, + { + "text": "And actually, we did it more generally." + }, + { + "text": "We found the time until the case arrival occurs." + }, + { + "text": "It has a closed form formula, which is called the Erlang distribution with k degrees of freedom." + }, + { + "text": "So let's see what's going on here." + }, + { + "text": "It's a distribution Of what kind?" + }, + { + "text": "It's a continuous distribution." + }, + { + "text": "It's a probability density function." + }, + { + "text": "This is because the time is a continuous random variable." + }, + { + "text": "Time is continuous." + }, + { + "text": "Arrivals can happen at any time." + }, + { + "text": "So we're talking about the PDF." + }, + { + "text": "This k is just the parameter of the distribution." + }, + { + "text": "We're talking about the k-th arrival, so k is a fixed number." + }, + { + "text": "Lambda is another parameter of the distribution, which is the arrival rate So it's a PDF over the Y's, whereas lambda and k are parameters of the distribution." + }, + { + "text": "OK." + }, + { + "text": "So this was what we knew from last time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk6.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..f957b2a1915e0744ba6fb901fba06c158d7e336f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Just to get some practice, let us do a problem that's not too difficult, but just to see how we use the various formulas that we have." + }, + { + "text": "So Poisson was a mathematician, but Poisson also means fish in French." + }, + { + "text": "So Poisson goes fishing." + }, + { + "text": "And let's assume that fish are caught according to a Poisson process." + }, + { + "text": "That's not too bad an assumption." + }, + { + "text": "At any given point in time, you have a little probability that a fish would be caught." + }, + { + "text": "And whether you catch one now is sort of independent about whether at some later time a fish will be caught or not." + }, + { + "text": "So let's just make this assumption." + }, + { + "text": "And suppose that the rules of the game are that you-- Fish are being called it the certain rate of 0.6 per hour." + }, + { + "text": "You fish for 2 hours, no matter what." + }, + { + "text": "And then there are two possibilities." + }, + { + "text": "If I have caught a fish, I stop and go home." + }, + { + "text": "So if some fish have been caught, so there's at least 1 arrival during this interval, I go home." + }, + { + "text": "Or if nothing has being caught, I continue fishing until I catch something." + }, + { + "text": "And then I go home." + }, + { + "text": "So that's the description of what is going to happen." + }, + { + "text": "And now let's starts asking questions of all sorts." + }, + { + "text": "What is the probability that I'm going to be fishing for more than 2 hours?" + }, + { + "text": "I will be fishing for more than 2 hours, if and only if no fish were caught during those 2 hours, in which case, I will have to continue." + }, + { + "text": "Therefore, this is just this quantity." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk7.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..d200ba8c85d33ddb01ccd0430f2d344dfd85356f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "The probability of catching 2 fish in-- of catching 0 fish in the next 2 hours, and according to the formula that we have, this is going to be e to the minus lambda times how much time we have." + }, + { + "text": "There's another way of thinking about this." + }, + { + "text": "The probability that I fish for more than 2 hours is the probability that the first catch happens after time 2, which would be the integral from 2 to infinity of the density of the first arrival time." + }, + { + "text": "And that density is an exponential." + }, + { + "text": "So you do the integral of an exponential, and, of course, you would get the same answer." + }, + { + "text": "OK. That's easy." + }, + { + "text": "So what's the probability of fishing for more than 2 but less than 5 hours?" + }, + { + "text": "What does it take for this to happen?" + }, + { + "text": "For this to happen, we need to catch 0 fish from time 0 to 2 and catch the first fish sometime between 2 and 5." + }, + { + "text": "So if you-- one way of thinking about what's happening here might be to say that there's a Poisson process that keeps going on forever." + }, + { + "text": "But as soon as I catch the first fish, instead of continuing fishing and obtaining those other fish I just go home right now." + }, + { + "text": "Now the fact that I go home before time 5 means that, if I were to stay until time 5, I would have caught at least 1 fish." + }, + { + "text": "I might have caught more than 1." + }, + { + "text": "So the event of interest here is that the first catch happens between times 2 and 5." + }, + { + "text": "So one way of calculating this quantity would be-- Its the probability that the first catch happens between times 2 and 5." + }, + { + "text": "Another way to deal with it is to say, this is the probability that I caught 0 fish in the first 2 hours and then the probability that I catch at least 1 fish during the next 3 hours." + }, + { + "text": "This." + }, + { + "text": "What is this?" + }, + { + "text": "The probability of 0 fish in the next 3 hours is the probability of 0 fish during this time." + }, + { + "text": "1 minus this is the probability of catching at least 1 fish, of having at least 1 arrival, between times 2 and 5." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk8.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..63208c3916b0f28860e55ba410e9e8809a2e2618 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "If there's at least 1 arrival between times 2 and 5, then I would have gone home by time 5." + }, + { + "text": "So both of these, if you plug-in numbers and all that, of course, are going to give you the same answer." + }, + { + "text": "Now next, what's the probability that I catch at least 2 fish?" + }, + { + "text": "In which scenario are we?" + }, + { + "text": "Under this scenario, I go home when I catch my first fish." + }, + { + "text": "So in order to catch at least 2 fish, it must be in this case." + }, + { + "text": "So this is the same as the event that I catch at least 2 fish during the first 2 time steps." + }, + { + "text": "So it's going to be the probability from 2 to infinity, the probability that I catch 2 fish, or that I catch 3 fish, or I catch more than that." + }, + { + "text": "So it's this quantity." + }, + { + "text": "k is the number of fish that I catch." + }, + { + "text": "At least 2, so k goes from 2 to infinity." + }, + { + "text": "These are the probabilities of catching a number k of fish during this interval." + }, + { + "text": "And if you want a simpler form without an infinite sum, this would be 1 minus the probability of catching 0 fish, minus the probability of catching 1 fish, during a time interval of length 2." + }, + { + "text": "Another way to think of it." + }, + { + "text": "I'm going to catch 2 fish, at least 2 fish, if and only if the second fish caught in this process happens before time 2." + }, + { + "text": "So that's another way of thinking about the same event." + }, + { + "text": "So it's going to be the probability that the random variable Y2, the arrival time over the second fish, is less than or equal to 2." + }, + { + "text": "OK." + }, + { + "text": "The next one is a little trickier." + }, + { + "text": "Here we need to do a little bit of divide and conquer." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk9.json b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..438a6aa22ffef63c853416c037d519d661ef6133 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/XsYXACeIklU_9_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "Overall, in this expedition, what the expected number of fish to be caught?" + }, + { + "text": "One way to think about it is to try to use the total expectations theorem." + }, + { + "text": "And think of expected number of fish, given this scenario, or expected number of fish, given this scenario." + }, + { + "text": "That's a little more complicated than the way I'm going to do it." + }, + { + "text": "The way I'm going to do is to think as follows-- Expected number of fish is the expected number of fish caught between times 0 and 2 plus expected number of fish caught after time 2." + }, + { + "text": "So what's the expected number caught between time 0 and 2?" + }, + { + "text": "This is lambda t. So lambda is 0.6 times 2." + }, + { + "text": "This is the expected number of fish that are caught between times 0 and 2." + }, + { + "text": "Now let's think about the expected number of fish caught afterwards." + }, + { + "text": "How many fish are being caught afterwards?" + }, + { + "text": "Well it depends on the scenario." + }, + { + "text": "If we're in this scenario, we've gone home and we catch 0." + }, + { + "text": "If we're in this scenario, then we continue fishing until we catch one." + }, + { + "text": "So the expected number of fish to be caught after time 2 is going to be the probability of this scenario times 1." + }, + { + "text": "And the probability of that scenario is the probability that they call it's 0 fish during the first 2 time steps times 1, which is the number of fish I'm going to catch if I continue." + }, + { + "text": "The expected total fishing time we can calculate exactly the same way." + }, + { + "text": "I'm jumping to the last one." + }, + { + "text": "My total fishing time has a period of 2 time steps." + }, + { + "text": "I'm going to fish for 2 time steps no matter what." + }, + { + "text": "And then if I caught 0 fish, which happens with this probability, my expected time is going to be the expected time from here onwards, which is the expected value of this geometric random variable with parameter lambda." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk0.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..510df1089fd21a6784687fd45af97c7fb5509dfd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "OK, now clustering for graphs." + }, + { + "text": "So this is a topic." + }, + { + "text": "This is one of the important things you can try to do with a graph." + }, + { + "text": "So you have a large graph." + }, + { + "text": "Let me kind of divide it into two clusters." + }, + { + "text": "OK, so you get a giant graph." + }, + { + "text": "And the job is to make some sense out of it." + }, + { + "text": "And one possible step is to be able to subdivide it if, as I see here, there is a cut between two reasonably equal parts of the graph, reasonably same size." + }, + { + "text": "And therefore, that graph could be studied in two pieces." + }, + { + "text": "So the question is, how do you find such a cut by an algorithm?" + }, + { + "text": "What's an algorithm that would find that cut?" + }, + { + "text": "So that's the problem." + }, + { + "text": "Let's say we're looking for two clusters." + }, + { + "text": "We could look for more clusters." + }, + { + "text": "But let's say we want to look for two clusters." + }, + { + "text": "So what are we trying to do?" + }, + { + "text": "We're trying to minimize." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk1.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..b0b4cd43a0d0410163047924f80e639cc1985a55 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So this is the problem, then." + }, + { + "text": "So we look for find positions x and y, let's say, two which will be the centers, so to speak, of the." + }, + { + "text": "And really, it's just these points." + }, + { + "text": "Points." + }, + { + "text": "So the data is the points and the edges, as always, the nodes and the edges." + }, + { + "text": "So the problem is to find x and y so that to minimize." + }, + { + "text": "So it's a distance of points ai from x." + }, + { + "text": "Maybe I should emphasize we're in high dimensions." + }, + { + "text": "Plus the distance of other points." + }, + { + "text": "So the ai will be these points, these nodes." + }, + { + "text": "And the bi will be these nodes plus the sum of bi minus y squared." + }, + { + "text": "And you understand the rule here." + }, + { + "text": "That together, the a's union the b's give me all nodes." + }, + { + "text": "And I guess to be complete, the a's intersect the b's is empty." + }, + { + "text": "Just what you expect." + }, + { + "text": "I'm dividing the a's and the b's into two groups." + }, + { + "text": "And I'm picking an x and a y sort of at the center of those groups." + }, + { + "text": "So that is a minimum." + }, + { + "text": "So I want to minimize." + }, + { + "text": "And also, I probably want to impose some condition that the number of a's is reasonably close to the number of b's." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk10.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..1357e7a698b8cc04b2307b38f9835b26b26cf65d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let's write down the Laplacian." + }, + { + "text": "So if I use the degree minus b, that's easy." + }, + { + "text": "The degrees were 3, 3, 2, and 2." + }, + { + "text": "Now I have these minuses, and those were 0." + }, + { + "text": "So that's a positive semidefinite matrix." + }, + { + "text": "Is it a positive definite matrix?" + }, + { + "text": "So let me ask, is it singular or is it not singular?" + }, + { + "text": "Is there a vector in its null space or is there not a vector in its null space?" + }, + { + "text": "Can you solve dx equals all 0s?" + }, + { + "text": "And of course, you can." + }, + { + "text": "Everybody sees that the vector of all 1s will be a solution to L. I'm sorry." + }, + { + "text": "I should be saying L here." + }, + { + "text": "Lx equals 0." + }, + { + "text": "Lx equals 0 is for a whole line of a one dimensional and the null space of L has dimension 1." + }, + { + "text": "It's got one basis vector, 1, 1, 1, 1." + }, + { + "text": "And that will always happen with the graph setup that I've created." + }, + { + "text": "So that's the first fact, that this positive semidefinite matrix L has lambda 1 equals 0, and the eigenvector is constants, C, C, C, C, the one dimensional eigenspace." + }, + { + "text": "Or 1, 1, 1, 1 is a typical eigenvector." + }, + { + "text": "OK. Now back to graph clustering." + }, + { + "text": "The idea of graph clustering is to look at the Fiedler eigenvector." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk11.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..281caddddde4055024d281f54754cc7d51c84615 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "This is called x2 is the next eigenvector, is the eigenvector for the smallest positive eigenvalue for lambda min excluding 0." + }, + { + "text": "So the smallest eigenvalue of L, the smallest eigenvalue and its eigenvector, this is called the Fiedler vector, named after the Czech mathematician, a great man in linear algebra." + }, + { + "text": "And he studied this vector, this situation." + }, + { + "text": "So everybody who knows about the graph Laplacian is aware that its first eigenvalue is 0, and that the next eigenvalue is important." + }, + { + "text": "Yeah?" + }, + { + "text": "AUDIENCE 2 Is the graph Laplacian named the Laplacian because it has connections?" + }, + { + "text": "GILBERT STRANGSKI-WEISBAUMGESEN To Laplace's equation, yes." + }, + { + "text": "So yeah, that's a good question." + }, + { + "text": "So why the word, the name Laplacian?" + }, + { + "text": "So yeah, that's a good question." + }, + { + "text": "So the familiar thing, so it connects to Laplace's finite difference equation, because we're talking about matrices here and not derivatives, not functions." + }, + { + "text": "So why the word Laplacian?" + }, + { + "text": "Well, so if I have a regular, if my graph is composed of a, so there is a graph with 25 nodes and 4 times 5, 20, about 40." + }, + { + "text": "This probably has about 40 edges and 25 nodes." + }, + { + "text": "And of course, I can construct its graph, all those four matrices for it." + }, + { + "text": "Its incidence matrix, its degree matrix." + }, + { + "text": "So the degree will be 4 at all these inside points." + }, + { + "text": "The degree will be 3 at these boundary points." + }, + { + "text": "The degree will be 2 at these corner points." + }, + { + "text": "But what will the matrix L look like?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk12.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..12daa4372923d18ded725df528b5481880269763 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what is L?" + }, + { + "text": "And that will tell you why it has this name Laplacian." + }, + { + "text": "So the matrix L will have the degree 4, right, will be on the diagonal." + }, + { + "text": "That's coming from D. The other, the minus 1's that come from B, the adjacency matrix will be associated with those nodes and otherwise all 0's." + }, + { + "text": "So this is a typical row of L. This is a typical row of L centered at that node." + }, + { + "text": "So maybe that's node number 5, 10, 13." + }, + { + "text": "That's 13 out of 25 that would show you this." + }, + { + "text": "And sorry, those are minus 1's." + }, + { + "text": "Minus 1's." + }, + { + "text": "So a 4 on the diagonal and 4 minus 1's." + }, + { + "text": "That's the model problem for when the graph is a grid, square grid." + }, + { + "text": "And you associate that with Laplace's equation." + }, + { + "text": "So this is the reason that Laplace, why Laplace gets in it." + }, + { + "text": "Because Laplace's equation, the differential equation, is second derivative with respect to x squared." + }, + { + "text": "And the second derivative with respect to y squared is 0." + }, + { + "text": "And what we have here is Lu equals 0." + }, + { + "text": "It's the discrete Laplacian, the vector Laplacian, the graph Laplacian, where the second x derivative is replaced by minus 1, 2, minus 1." + }, + { + "text": "And the second y derivative is replaced by minus 1, 2, minus 1, second differences in the x and the y directions." + }, + { + "text": "So that's the explanation for Laplace." + }, + { + "text": "It's the discrete Laplace, discrete, or the finite difference Laplace." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk13.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..735b134e5903367fe066cd16a7e4f76a605a7890 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, to finish, I have to tell you what clusters, how do you decide the clusters from L?" + }, + { + "text": "How does L propose two clusters, the A's and the B's?" + }, + { + "text": "And here's the answer." + }, + { + "text": "They come from this eigenvector, the Fiedler eigenvector." + }, + { + "text": "You look at that eigenvector." + }, + { + "text": "It's got some positive and some negative components." + }, + { + "text": "The components with positive numbers of this eigenvector, so the positive components of x, of this eigenvector." + }, + { + "text": "And there are negative components of this eigenvector." + }, + { + "text": "And those are the two clusters." + }, + { + "text": "So the two clusters are decided by the eigenvector, by the signs, plus or minus signs, of the components." + }, + { + "text": "The plus signs go in one, and the minus signs go in another." + }, + { + "text": "And you have to experiment to see that that would succeed." + }, + { + "text": "I don't know what it would do on this, actually, because that's hardly splits up into two." + }, + { + "text": "I suppose maybe the split is along a line like that or something to get." + }, + { + "text": "I don't know what clustering." + }, + { + "text": "This is not a graph that is naturally clustered." + }, + { + "text": "But you could still do k-means on it." + }, + { + "text": "You could still do spectral clustering." + }, + { + "text": "And you would find this eigenvector." + }, + { + "text": "Now, what's the point about this eigenvector?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk14.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d82fbf2e485ffc2071dd7965af955b9488bb4fd3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'll finish in one moment." + }, + { + "text": "What do we know about that eigenvector as compared to that one?" + }, + { + "text": "So here was an eigenvector all 1's." + }, + { + "text": "Let me just make it all 1's." + }, + { + "text": "1, 1, 1, 1." + }, + { + "text": "In that picture, it's 25 1's." + }, + { + "text": "Here's the next eigenvector up." + }, + { + "text": "And what's the relation between those two eigenvectors of L?" + }, + { + "text": "They are orthogonal." + }, + { + "text": "These are eigenvectors of a symmetric matrix." + }, + { + "text": "So they're orthogonal." + }, + { + "text": "So that means to be orthogonal to this guy means that your components add to 0, right?" + }, + { + "text": "A vector is orthogonal to all 1's." + }, + { + "text": "That dot product is just add up the components." + }, + { + "text": "So we have a bunch of positive components and a bunch of negative components." + }, + { + "text": "They have the same sum because the dot product with that is 0." + }, + { + "text": "And those two components, those two sets of components, are your two, tell you the two clusters in spectral clustering." + }, + { + "text": "So it's a pretty nifty algorithm." + }, + { + "text": "It does ask you to compute an eigenvector." + }, + { + "text": "And that, of course, takes time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk15.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..33b314de4bcbf9001b168559a42a59434408ceb9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then there's a third, more direct algorithm to do this optimization problem." + }, + { + "text": "Well, actually, there are many." + }, + { + "text": "This is an important problem." + }, + { + "text": "So there are many proposed algorithms." + }, + { + "text": "Good." + }, + { + "text": "OK, I'm closing up." + }, + { + "text": "Final question?" + }, + { + "text": "Yeah." + }, + { + "text": "AUDIENCE 1 Is it possible to do more than one eigenvector?" + }, + { + "text": "GILBERT STRANGSBERRY Well, certainly for k-means." + }, + { + "text": "Now, if I had to do three clusters with Fiedler, I would look at the first three eigenvectors." + }, + { + "text": "And, well, the first one would be nothing." + }, + { + "text": "And I would look at the next two." + }, + { + "text": "And that would be pretty successful." + }, + { + "text": "If I wanted six clusters, it probably would fall off in the quality of the clustering." + }, + { + "text": "Yeah, but certainly I would look at the lowest six eigenvectors and get somewhere." + }, + { + "text": "Yeah, right." + }, + { + "text": "So OK, so that's a topic, an important topic, a sort of standard topic in applied graph theory." + }, + { + "text": "OK, so see you Wednesday." + }, + { + "text": "I'm hoping on Wednesday." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk16.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..369303b0fe81782847fe72a1f77fa9546a3fe220 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk16.json @@ -0,0 +1,47 @@ +[ + { + "text": "So Professor Edelman has told me a new and optimal way to look at the problem of back propagation." + }, + { + "text": "You remember back propagation?" + }, + { + "text": "If you remember the lecture on it, you don't want to remember the lecture on it." + }, + { + "text": "It's a tricky, messy thing to explain." + }, + { + "text": "But he says, if I explain it using Julia in linear algebra, it's clear." + }, + { + "text": "So we'll give him a chance on Wednesday to show that revolutionary approach to the explanation of back propagation." + }, + { + "text": "And I hope for, I told him he could have half an hour and projects would take some time." + }, + { + "text": "I hope now we've had two with wild applause." + }, + { + "text": "So I hope we get a couple more in our last class." + }, + { + "text": "OK, see you Wednesday." + }, + { + "text": "And if you bring, well, if you have projects ready, send them to me online and maybe a printout as well." + }, + { + "text": "That would be terrific." + }, + { + "text": "If you don't have them ready by the hour, they can go." + }, + { + "text": "The envelope outside my office would receive them." + }, + { + "text": "Good, so I'll see you Wednesday for the final class." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk2.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..33767a0a3dad583cc8f7063e11d58f516d9e5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "In other words, I don't want just that to be the a and all the rest to be the b's." + }, + { + "text": "That would be not a satisfactory clustering." + }, + { + "text": "I'm looking for clusters that are good sized clusters." + }, + { + "text": "So minimize that." + }, + { + "text": "So there are a lot of different algorithms to do it." + }, + { + "text": "But some are more directly attacking this problem." + }, + { + "text": "Others use matrices that we associate with the graph." + }, + { + "text": "So let me tell you about two or three of those algorithms." + }, + { + "text": "And if you've studied, had a course in graph theory, you may already have seen this problem." + }, + { + "text": "First question would be, suppose I decide these are the a's and those are the b's, or some other decision." + }, + { + "text": "Yeah, probably some other decision." + }, + { + "text": "God, I want to solve the problem before I even start." + }, + { + "text": "So some a's and some b's." + }, + { + "text": "What would be the best choice of the x once you've decided on the a's?" + }, + { + "text": "And what would be the best choice of the y once you've decided on the b's?" + }, + { + "text": "So we can answer that question." + }, + { + "text": "Just if we knew the two groups, we could see where they should be centered, where the first group centered at x, the second group centered at y." + }, + { + "text": "And what does centering mean?" + }, + { + "text": "So let's just say." + }, + { + "text": "So I think what I'm saying here is, let me bring that down a little." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk3.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..d50ee5c51dc35b55941a75d0e1fa8771e11923e2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "So given the a's, this is a1 up to, say, ak, what is the best?" + }, + { + "text": "Is the best x?" + }, + { + "text": "Just to make that part right." + }, + { + "text": "And the answer is, do you know geometrically what x should be here?" + }, + { + "text": "x is the." + }, + { + "text": "So if I have a bunch of points and I'm looking for the middle of those points, the point x, a good point x to say, OK, that's the middle." + }, + { + "text": "It'll make the sum of the distances, I think, squared." + }, + { + "text": "I hope I'm right about that." + }, + { + "text": "A minimum." + }, + { + "text": "What is x?" + }, + { + "text": "It is the centroid." + }, + { + "text": "Centroid is the word." + }, + { + "text": "x is the centroid of the a's." + }, + { + "text": "And what is the centroid?" + }, + { + "text": "Let's see." + }, + { + "text": "Oh, maybe I don't know if x and y were a good choice." + }, + { + "text": "But let me see what." + }, + { + "text": "I guess it's the average a." + }, + { + "text": "It's the sum of the a's, of these a's." + }, + { + "text": "Those are vectors, of course, divided by the number of a's." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk4.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..1e80e6b52d8909b62ebd123fe6561cc5be464fc3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "I think." + }, + { + "text": "Actually, I was just quickly reviewing this morning." + }, + { + "text": "So I'm not totally on top of this centroid." + }, + { + "text": "What I'm going to talk, the algorithm that I'm going to talk about is the k, well, k means, it's always called." + }, + { + "text": "And here, it will be the k will be 2." + }, + { + "text": "I just have two partitioning into two sets, a's and b's." + }, + { + "text": "So I just k is just 2." + }, + { + "text": "OK, what's the algorithm?" + }, + { + "text": "Well, if I've chosen a partition, the a's and the b's have separated them, then that tells me what the x and the y should be." + }, + { + "text": "But now, what do I do next?" + }, + { + "text": "So this is going to be a sort of an alternating partition." + }, + { + "text": "Now, I take those two centroids." + }, + { + "text": "So step one is, for a given a's and b's, find the centroids x and y." + }, + { + "text": "And that's elementary." + }, + { + "text": "Then the second step is, given the centroids x and y, given those positions, given x and y, they won't be centroids when you see what happens." + }, + { + "text": "Given x and y, reform the best partition, best clusters." + }, + { + "text": "OK, so step one, we had a guess at what the best clusters were." + }, + { + "text": "And we found their centroids." + }, + { + "text": "Now, we start with the centroids, and we form new clusters again." + }, + { + "text": "And if these clusters are the same as the ones we started with, then the algorithm has converged." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk5.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..7b33825ec164ef11eec503e9bdcbf59f77aba79e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "But probably won't be, these clusters." + }, + { + "text": "So you'll have to tell me what I mean by the best clusters." + }, + { + "text": "If I've got the two points, x and y, I want the points, I want to separate all the points that cluster around x to the ones that cluster around y." + }, + { + "text": "And then they're probably different from my original start." + }, + { + "text": "So now I've got new." + }, + { + "text": "Now I repeat step one." + }, + { + "text": "But let's just think, how do I form the best clusters?" + }, + { + "text": "Well, I take a point, and I have to decide, does it go with x, or does it go in the x cluster, or does it go in the cluster around y?" + }, + { + "text": "So how do I decide that?" + }, + { + "text": "Just whichever one it's closer to." + }, + { + "text": "So each point goes with each node." + }, + { + "text": "I could say each node goes with the closer of x and y." + }, + { + "text": "So points that should have been that are closer to x, now we're going to put them in the cluster around x." + }, + { + "text": "And does that solve the problem?" + }, + { + "text": "No, because, well, it might, but it might not." + }, + { + "text": "We have to come back to step one." + }, + { + "text": "We've now changed the clusters." + }, + { + "text": "They'll have different centroids." + }, + { + "text": "So we repeat step one, find the centroids for the two new clusters." + }, + { + "text": "Then we come to step two, find the ones that should go with the two centroids, and back and forth." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk6.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..c9703db94287ed7629f6d5a0547a4da9b7a456ac --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "I don't know, I don't think there's a nice theory of convergence or rate of convergence, all the questions that this course is always asking." + }, + { + "text": "But it's a very popular algorithm, k-means." + }, + { + "text": "k would be to have k clusters." + }, + { + "text": "So that's a, I'm not going to discuss the, I'd rather discuss some other ways to do this, to solve this problem, but that's one sort of hack that works quite well." + }, + { + "text": "OK, so second approach is what's coming next, second solution method." + }, + { + "text": "And it's called the spectral clustering." + }, + { + "text": "That's the name of the method." + }, + { + "text": "And before I write down what you do, what does the word spectral mean?" + }, + { + "text": "You see spectral graph theory, spectral clustering." + }, + { + "text": "And in other parts of mathematics, you see that word, you see spectral theorem." + }, + { + "text": "I gave you the most, and I described it as the most important, perhaps, theorem in linear algebra, at least one of the top three." + }, + { + "text": "So I'll write it over here, because it's not, it doesn't, this is a, it's the same word spectral." + }, + { + "text": "Well, let me ask the question again." + }, + { + "text": "What's that word spectral about?" + }, + { + "text": "What does that mean?" + }, + { + "text": "That means that if I have a matrix and I want to talk about its spectrum, what is the spectrum of the matrix?" + }, + { + "text": "It is the eigenvalues." + }, + { + "text": "So spectral theory, spectral clustering is using the eigenvalues of some matrix." + }, + { + "text": "That's what that spectral is telling me." + }, + { + "text": "So the spectral theorem, of course, is that for a symmetric matrix S, the eigenvalues are real and the eigenvectors are orthogonal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk7.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..d86e9f9bbdd7d9404d7723410ffb138f3e4560c3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And don't forget what the real full statement is here, because there could be repeated real eigenvalues." + }, + { + "text": "And what does the spectral theorem tell me?" + }, + { + "text": "For symmetric matrices, if lambda equal 5 is repeated four times, if it's a four times solution of the equation that gives eigenvalues, then what's the conclusion?" + }, + { + "text": "Then there are four independent orthogonal eigenvectors to go with it." + }, + { + "text": "We can't say that about matrices, about all matrices, but we can say it about all symmetric matrices." + }, + { + "text": "And in fact, those eigenvectors are orthogonal, so we're even saying more." + }, + { + "text": "We can find four orthogonal eigenvectors that go with a multiplicity for eigenvalue." + }, + { + "text": "OK, that's spectral theorem." + }, + { + "text": "Spectral clustering starts with the graph Laplacian matrix." + }, + { + "text": "Matrix." + }, + { + "text": "May I remember what that matrix is?" + }, + { + "text": "Because that's the key connection of linear algebra to graph theory, is the properties of this graph Laplacian matrix." + }, + { + "text": "OK, so let me say L for Laplacian." + }, + { + "text": "So that matrix, one way to describe it is as a transpose A, where A is the incidence matrix of the graph." + }, + { + "text": "Or another way we'll see is the D, the degree matrix." + }, + { + "text": "That's diagonal." + }, + { + "text": "And I'll do an example just to remind you." + }, + { + "text": "Minus the, I don't know what I'd call this one." + }, + { + "text": "Shall I call it B for the moment?" + }, + { + "text": "And what matrix is B?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk8.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..67236625f07a70f0d7d710097a866d77120c4a81 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the adjacency matrix." + }, + { + "text": "Really, you should know these four matrices." + }, + { + "text": "They're the key four matrices associated with any graph." + }, + { + "text": "The incidence matrix, that's m by n edges and nodes." + }, + { + "text": "Edges and nodes." + }, + { + "text": "So it's rectangular, but I'm forming A transpose A here." + }, + { + "text": "So I'm forming a symmetric positive semi-definite matrix." + }, + { + "text": "So this Laplacian is symmetric positive semi-definite." + }, + { + "text": "Yeah, let me just recall what all these matrices are for a simple graph." + }, + { + "text": "OK, so I'll just draw a graph." + }, + { + "text": "All right." + }, + { + "text": "OK, so the incidence matrix, there are 1, 2, 3, 4, 5 edges, so five rows." + }, + { + "text": "There are four nodes, 1, 2, 3, and 4, so four columns." + }, + { + "text": "And a typical row would be edge 1 going from node 1 to node 2, so it would have a minus 1 and a 1 there." + }, + { + "text": "And let me take edge 2 going from 1 to node 3, so it would have a minus 1 and a 1 there." + }, + { + "text": "So that's the incidence matrix A. OK, what's the degree matrix?" + }, + { + "text": "That's simple." + }, + { + "text": "The degree matrix, well, A transpose A, this is m by n. This is n by m, so it's n by n. OK, in this case, 4 by 4." + }, + { + "text": "So the degree matrix will be 4 by 4, n by n. And it will tell us the degree of that, which means which we just count the edges." + }, + { + "text": "So it's three edges going in, node 2, three edges going in." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk9.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..0b60f0d528f2e4ce2779436b0c9941475e9da813 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_0_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "Node 3 has just two edges, and node 4 has just two edges." + }, + { + "text": "So that's the degree matrix." + }, + { + "text": "And then the adjacency matrix that I've called B is also 4 by 4." + }, + { + "text": "And what is it?" + }, + { + "text": "It tells us which node is connected to which node." + }, + { + "text": "So I don't allow nodes, edges, that connect a node to itself, so 0s on the diagonal." + }, + { + "text": "So which nodes are connected to node 1?" + }, + { + "text": "Well, all of 2 and 4 and 3 are connected to 1, so I have 1s there." + }, + { + "text": "Node 2, all three nodes are connected to node 2." + }, + { + "text": "So I'll have the second column and row will have all three 1s." + }, + { + "text": "How about node 3?" + }, + { + "text": "OK, only two edges are connected." + }, + { + "text": "Only two nodes are connected to 3, 1 and 2, but not 4." + }, + { + "text": "So 1 and 2 I have, but not 4." + }, + { + "text": "So that's the adjacency matrix." + }, + { + "text": "Is that right?" + }, + { + "text": "Think so?" + }, + { + "text": "This is the degree matrix." + }, + { + "text": "This is the incidence matrix." + }, + { + "text": "And that formula gives me the Laplacian." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk0.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..510df1089fd21a6784687fd45af97c7fb5509dfd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation, or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "OK, now clustering for graphs." + }, + { + "text": "So this is a topic." + }, + { + "text": "This is one of the important things you can try to do with a graph." + }, + { + "text": "So you have a large graph." + }, + { + "text": "Let me kind of divide it into two clusters." + }, + { + "text": "OK, so you get a giant graph." + }, + { + "text": "And the job is to make some sense out of it." + }, + { + "text": "And one possible step is to be able to subdivide it if, as I see here, there is a cut between two reasonably equal parts of the graph, reasonably same size." + }, + { + "text": "And therefore, that graph could be studied in two pieces." + }, + { + "text": "So the question is, how do you find such a cut by an algorithm?" + }, + { + "text": "What's an algorithm that would find that cut?" + }, + { + "text": "So that's the problem." + }, + { + "text": "Let's say we're looking for two clusters." + }, + { + "text": "We could look for more clusters." + }, + { + "text": "But let's say we want to look for two clusters." + }, + { + "text": "So what are we trying to do?" + }, + { + "text": "We're trying to minimize." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk1.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..b0b4cd43a0d0410163047924f80e639cc1985a55 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So this is the problem, then." + }, + { + "text": "So we look for find positions x and y, let's say, two which will be the centers, so to speak, of the." + }, + { + "text": "And really, it's just these points." + }, + { + "text": "Points." + }, + { + "text": "So the data is the points and the edges, as always, the nodes and the edges." + }, + { + "text": "So the problem is to find x and y so that to minimize." + }, + { + "text": "So it's a distance of points ai from x." + }, + { + "text": "Maybe I should emphasize we're in high dimensions." + }, + { + "text": "Plus the distance of other points." + }, + { + "text": "So the ai will be these points, these nodes." + }, + { + "text": "And the bi will be these nodes plus the sum of bi minus y squared." + }, + { + "text": "And you understand the rule here." + }, + { + "text": "That together, the a's union the b's give me all nodes." + }, + { + "text": "And I guess to be complete, the a's intersect the b's is empty." + }, + { + "text": "Just what you expect." + }, + { + "text": "I'm dividing the a's and the b's into two groups." + }, + { + "text": "And I'm picking an x and a y sort of at the center of those groups." + }, + { + "text": "So that is a minimum." + }, + { + "text": "So I want to minimize." + }, + { + "text": "And also, I probably want to impose some condition that the number of a's is reasonably close to the number of b's." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk10.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..1357e7a698b8cc04b2307b38f9835b26b26cf65d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let's write down the Laplacian." + }, + { + "text": "So if I use the degree minus b, that's easy." + }, + { + "text": "The degrees were 3, 3, 2, and 2." + }, + { + "text": "Now I have these minuses, and those were 0." + }, + { + "text": "So that's a positive semidefinite matrix." + }, + { + "text": "Is it a positive definite matrix?" + }, + { + "text": "So let me ask, is it singular or is it not singular?" + }, + { + "text": "Is there a vector in its null space or is there not a vector in its null space?" + }, + { + "text": "Can you solve dx equals all 0s?" + }, + { + "text": "And of course, you can." + }, + { + "text": "Everybody sees that the vector of all 1s will be a solution to L. I'm sorry." + }, + { + "text": "I should be saying L here." + }, + { + "text": "Lx equals 0." + }, + { + "text": "Lx equals 0 is for a whole line of a one dimensional and the null space of L has dimension 1." + }, + { + "text": "It's got one basis vector, 1, 1, 1, 1." + }, + { + "text": "And that will always happen with the graph setup that I've created." + }, + { + "text": "So that's the first fact, that this positive semidefinite matrix L has lambda 1 equals 0, and the eigenvector is constants, C, C, C, C, the one dimensional eigenspace." + }, + { + "text": "Or 1, 1, 1, 1 is a typical eigenvector." + }, + { + "text": "OK. Now back to graph clustering." + }, + { + "text": "The idea of graph clustering is to look at the Fiedler eigenvector." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk11.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..281caddddde4055024d281f54754cc7d51c84615 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "This is called x2 is the next eigenvector, is the eigenvector for the smallest positive eigenvalue for lambda min excluding 0." + }, + { + "text": "So the smallest eigenvalue of L, the smallest eigenvalue and its eigenvector, this is called the Fiedler vector, named after the Czech mathematician, a great man in linear algebra." + }, + { + "text": "And he studied this vector, this situation." + }, + { + "text": "So everybody who knows about the graph Laplacian is aware that its first eigenvalue is 0, and that the next eigenvalue is important." + }, + { + "text": "Yeah?" + }, + { + "text": "AUDIENCE 2 Is the graph Laplacian named the Laplacian because it has connections?" + }, + { + "text": "GILBERT STRANGSKI-WEISBAUMGESEN To Laplace's equation, yes." + }, + { + "text": "So yeah, that's a good question." + }, + { + "text": "So why the word, the name Laplacian?" + }, + { + "text": "So yeah, that's a good question." + }, + { + "text": "So the familiar thing, so it connects to Laplace's finite difference equation, because we're talking about matrices here and not derivatives, not functions." + }, + { + "text": "So why the word Laplacian?" + }, + { + "text": "Well, so if I have a regular, if my graph is composed of a, so there is a graph with 25 nodes and 4 times 5, 20, about 40." + }, + { + "text": "This probably has about 40 edges and 25 nodes." + }, + { + "text": "And of course, I can construct its graph, all those four matrices for it." + }, + { + "text": "Its incidence matrix, its degree matrix." + }, + { + "text": "So the degree will be 4 at all these inside points." + }, + { + "text": "The degree will be 3 at these boundary points." + }, + { + "text": "The degree will be 2 at these corner points." + }, + { + "text": "But what will the matrix L look like?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk12.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..12daa4372923d18ded725df528b5481880269763 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "So what is L?" + }, + { + "text": "And that will tell you why it has this name Laplacian." + }, + { + "text": "So the matrix L will have the degree 4, right, will be on the diagonal." + }, + { + "text": "That's coming from D. The other, the minus 1's that come from B, the adjacency matrix will be associated with those nodes and otherwise all 0's." + }, + { + "text": "So this is a typical row of L. This is a typical row of L centered at that node." + }, + { + "text": "So maybe that's node number 5, 10, 13." + }, + { + "text": "That's 13 out of 25 that would show you this." + }, + { + "text": "And sorry, those are minus 1's." + }, + { + "text": "Minus 1's." + }, + { + "text": "So a 4 on the diagonal and 4 minus 1's." + }, + { + "text": "That's the model problem for when the graph is a grid, square grid." + }, + { + "text": "And you associate that with Laplace's equation." + }, + { + "text": "So this is the reason that Laplace, why Laplace gets in it." + }, + { + "text": "Because Laplace's equation, the differential equation, is second derivative with respect to x squared." + }, + { + "text": "And the second derivative with respect to y squared is 0." + }, + { + "text": "And what we have here is Lu equals 0." + }, + { + "text": "It's the discrete Laplacian, the vector Laplacian, the graph Laplacian, where the second x derivative is replaced by minus 1, 2, minus 1." + }, + { + "text": "And the second y derivative is replaced by minus 1, 2, minus 1, second differences in the x and the y directions." + }, + { + "text": "So that's the explanation for Laplace." + }, + { + "text": "It's the discrete Laplace, discrete, or the finite difference Laplace." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk13.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..735b134e5903367fe066cd16a7e4f76a605a7890 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, to finish, I have to tell you what clusters, how do you decide the clusters from L?" + }, + { + "text": "How does L propose two clusters, the A's and the B's?" + }, + { + "text": "And here's the answer." + }, + { + "text": "They come from this eigenvector, the Fiedler eigenvector." + }, + { + "text": "You look at that eigenvector." + }, + { + "text": "It's got some positive and some negative components." + }, + { + "text": "The components with positive numbers of this eigenvector, so the positive components of x, of this eigenvector." + }, + { + "text": "And there are negative components of this eigenvector." + }, + { + "text": "And those are the two clusters." + }, + { + "text": "So the two clusters are decided by the eigenvector, by the signs, plus or minus signs, of the components." + }, + { + "text": "The plus signs go in one, and the minus signs go in another." + }, + { + "text": "And you have to experiment to see that that would succeed." + }, + { + "text": "I don't know what it would do on this, actually, because that's hardly splits up into two." + }, + { + "text": "I suppose maybe the split is along a line like that or something to get." + }, + { + "text": "I don't know what clustering." + }, + { + "text": "This is not a graph that is naturally clustered." + }, + { + "text": "But you could still do k-means on it." + }, + { + "text": "You could still do spectral clustering." + }, + { + "text": "And you would find this eigenvector." + }, + { + "text": "Now, what's the point about this eigenvector?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk14.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d82fbf2e485ffc2071dd7965af955b9488bb4fd3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'll finish in one moment." + }, + { + "text": "What do we know about that eigenvector as compared to that one?" + }, + { + "text": "So here was an eigenvector all 1's." + }, + { + "text": "Let me just make it all 1's." + }, + { + "text": "1, 1, 1, 1." + }, + { + "text": "In that picture, it's 25 1's." + }, + { + "text": "Here's the next eigenvector up." + }, + { + "text": "And what's the relation between those two eigenvectors of L?" + }, + { + "text": "They are orthogonal." + }, + { + "text": "These are eigenvectors of a symmetric matrix." + }, + { + "text": "So they're orthogonal." + }, + { + "text": "So that means to be orthogonal to this guy means that your components add to 0, right?" + }, + { + "text": "A vector is orthogonal to all 1's." + }, + { + "text": "That dot product is just add up the components." + }, + { + "text": "So we have a bunch of positive components and a bunch of negative components." + }, + { + "text": "They have the same sum because the dot product with that is 0." + }, + { + "text": "And those two components, those two sets of components, are your two, tell you the two clusters in spectral clustering." + }, + { + "text": "So it's a pretty nifty algorithm." + }, + { + "text": "It does ask you to compute an eigenvector." + }, + { + "text": "And that, of course, takes time." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk15.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..33b314de4bcbf9001b168559a42a59434408ceb9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "And then there's a third, more direct algorithm to do this optimization problem." + }, + { + "text": "Well, actually, there are many." + }, + { + "text": "This is an important problem." + }, + { + "text": "So there are many proposed algorithms." + }, + { + "text": "Good." + }, + { + "text": "OK, I'm closing up." + }, + { + "text": "Final question?" + }, + { + "text": "Yeah." + }, + { + "text": "AUDIENCE 1 Is it possible to do more than one eigenvector?" + }, + { + "text": "GILBERT STRANGSBERRY Well, certainly for k-means." + }, + { + "text": "Now, if I had to do three clusters with Fiedler, I would look at the first three eigenvectors." + }, + { + "text": "And, well, the first one would be nothing." + }, + { + "text": "And I would look at the next two." + }, + { + "text": "And that would be pretty successful." + }, + { + "text": "If I wanted six clusters, it probably would fall off in the quality of the clustering." + }, + { + "text": "Yeah, but certainly I would look at the lowest six eigenvectors and get somewhere." + }, + { + "text": "Yeah, right." + }, + { + "text": "So OK, so that's a topic, an important topic, a sort of standard topic in applied graph theory." + }, + { + "text": "OK, so see you Wednesday." + }, + { + "text": "I'm hoping on Wednesday." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk16.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..369303b0fe81782847fe72a1f77fa9546a3fe220 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk16.json @@ -0,0 +1,47 @@ +[ + { + "text": "So Professor Edelman has told me a new and optimal way to look at the problem of back propagation." + }, + { + "text": "You remember back propagation?" + }, + { + "text": "If you remember the lecture on it, you don't want to remember the lecture on it." + }, + { + "text": "It's a tricky, messy thing to explain." + }, + { + "text": "But he says, if I explain it using Julia in linear algebra, it's clear." + }, + { + "text": "So we'll give him a chance on Wednesday to show that revolutionary approach to the explanation of back propagation." + }, + { + "text": "And I hope for, I told him he could have half an hour and projects would take some time." + }, + { + "text": "I hope now we've had two with wild applause." + }, + { + "text": "So I hope we get a couple more in our last class." + }, + { + "text": "OK, see you Wednesday." + }, + { + "text": "And if you bring, well, if you have projects ready, send them to me online and maybe a printout as well." + }, + { + "text": "That would be terrific." + }, + { + "text": "If you don't have them ready by the hour, they can go." + }, + { + "text": "The envelope outside my office would receive them." + }, + { + "text": "Good, so I'll see you Wednesday for the final class." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk2.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..33767a0a3dad583cc8f7063e11d58f516d9e5ff5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "In other words, I don't want just that to be the a and all the rest to be the b's." + }, + { + "text": "That would be not a satisfactory clustering." + }, + { + "text": "I'm looking for clusters that are good sized clusters." + }, + { + "text": "So minimize that." + }, + { + "text": "So there are a lot of different algorithms to do it." + }, + { + "text": "But some are more directly attacking this problem." + }, + { + "text": "Others use matrices that we associate with the graph." + }, + { + "text": "So let me tell you about two or three of those algorithms." + }, + { + "text": "And if you've studied, had a course in graph theory, you may already have seen this problem." + }, + { + "text": "First question would be, suppose I decide these are the a's and those are the b's, or some other decision." + }, + { + "text": "Yeah, probably some other decision." + }, + { + "text": "God, I want to solve the problem before I even start." + }, + { + "text": "So some a's and some b's." + }, + { + "text": "What would be the best choice of the x once you've decided on the a's?" + }, + { + "text": "And what would be the best choice of the y once you've decided on the b's?" + }, + { + "text": "So we can answer that question." + }, + { + "text": "Just if we knew the two groups, we could see where they should be centered, where the first group centered at x, the second group centered at y." + }, + { + "text": "And what does centering mean?" + }, + { + "text": "So let's just say." + }, + { + "text": "So I think what I'm saying here is, let me bring that down a little." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk3.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..d50ee5c51dc35b55941a75d0e1fa8771e11923e2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "So given the a's, this is a1 up to, say, ak, what is the best?" + }, + { + "text": "Is the best x?" + }, + { + "text": "Just to make that part right." + }, + { + "text": "And the answer is, do you know geometrically what x should be here?" + }, + { + "text": "x is the." + }, + { + "text": "So if I have a bunch of points and I'm looking for the middle of those points, the point x, a good point x to say, OK, that's the middle." + }, + { + "text": "It'll make the sum of the distances, I think, squared." + }, + { + "text": "I hope I'm right about that." + }, + { + "text": "A minimum." + }, + { + "text": "What is x?" + }, + { + "text": "It is the centroid." + }, + { + "text": "Centroid is the word." + }, + { + "text": "x is the centroid of the a's." + }, + { + "text": "And what is the centroid?" + }, + { + "text": "Let's see." + }, + { + "text": "Oh, maybe I don't know if x and y were a good choice." + }, + { + "text": "But let me see what." + }, + { + "text": "I guess it's the average a." + }, + { + "text": "It's the sum of the a's, of these a's." + }, + { + "text": "Those are vectors, of course, divided by the number of a's." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk4.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..1e80e6b52d8909b62ebd123fe6561cc5be464fc3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "I think." + }, + { + "text": "Actually, I was just quickly reviewing this morning." + }, + { + "text": "So I'm not totally on top of this centroid." + }, + { + "text": "What I'm going to talk, the algorithm that I'm going to talk about is the k, well, k means, it's always called." + }, + { + "text": "And here, it will be the k will be 2." + }, + { + "text": "I just have two partitioning into two sets, a's and b's." + }, + { + "text": "So I just k is just 2." + }, + { + "text": "OK, what's the algorithm?" + }, + { + "text": "Well, if I've chosen a partition, the a's and the b's have separated them, then that tells me what the x and the y should be." + }, + { + "text": "But now, what do I do next?" + }, + { + "text": "So this is going to be a sort of an alternating partition." + }, + { + "text": "Now, I take those two centroids." + }, + { + "text": "So step one is, for a given a's and b's, find the centroids x and y." + }, + { + "text": "And that's elementary." + }, + { + "text": "Then the second step is, given the centroids x and y, given those positions, given x and y, they won't be centroids when you see what happens." + }, + { + "text": "Given x and y, reform the best partition, best clusters." + }, + { + "text": "OK, so step one, we had a guess at what the best clusters were." + }, + { + "text": "And we found their centroids." + }, + { + "text": "Now, we start with the centroids, and we form new clusters again." + }, + { + "text": "And if these clusters are the same as the ones we started with, then the algorithm has converged." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk5.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..7b33825ec164ef11eec503e9bdcbf59f77aba79e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "But probably won't be, these clusters." + }, + { + "text": "So you'll have to tell me what I mean by the best clusters." + }, + { + "text": "If I've got the two points, x and y, I want the points, I want to separate all the points that cluster around x to the ones that cluster around y." + }, + { + "text": "And then they're probably different from my original start." + }, + { + "text": "So now I've got new." + }, + { + "text": "Now I repeat step one." + }, + { + "text": "But let's just think, how do I form the best clusters?" + }, + { + "text": "Well, I take a point, and I have to decide, does it go with x, or does it go in the x cluster, or does it go in the cluster around y?" + }, + { + "text": "So how do I decide that?" + }, + { + "text": "Just whichever one it's closer to." + }, + { + "text": "So each point goes with each node." + }, + { + "text": "I could say each node goes with the closer of x and y." + }, + { + "text": "So points that should have been that are closer to x, now we're going to put them in the cluster around x." + }, + { + "text": "And does that solve the problem?" + }, + { + "text": "No, because, well, it might, but it might not." + }, + { + "text": "We have to come back to step one." + }, + { + "text": "We've now changed the clusters." + }, + { + "text": "They'll have different centroids." + }, + { + "text": "So we repeat step one, find the centroids for the two new clusters." + }, + { + "text": "Then we come to step two, find the ones that should go with the two centroids, and back and forth." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk6.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..c9703db94287ed7629f6d5a0547a4da9b7a456ac --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "I don't know, I don't think there's a nice theory of convergence or rate of convergence, all the questions that this course is always asking." + }, + { + "text": "But it's a very popular algorithm, k-means." + }, + { + "text": "k would be to have k clusters." + }, + { + "text": "So that's a, I'm not going to discuss the, I'd rather discuss some other ways to do this, to solve this problem, but that's one sort of hack that works quite well." + }, + { + "text": "OK, so second approach is what's coming next, second solution method." + }, + { + "text": "And it's called the spectral clustering." + }, + { + "text": "That's the name of the method." + }, + { + "text": "And before I write down what you do, what does the word spectral mean?" + }, + { + "text": "You see spectral graph theory, spectral clustering." + }, + { + "text": "And in other parts of mathematics, you see that word, you see spectral theorem." + }, + { + "text": "I gave you the most, and I described it as the most important, perhaps, theorem in linear algebra, at least one of the top three." + }, + { + "text": "So I'll write it over here, because it's not, it doesn't, this is a, it's the same word spectral." + }, + { + "text": "Well, let me ask the question again." + }, + { + "text": "What's that word spectral about?" + }, + { + "text": "What does that mean?" + }, + { + "text": "That means that if I have a matrix and I want to talk about its spectrum, what is the spectrum of the matrix?" + }, + { + "text": "It is the eigenvalues." + }, + { + "text": "So spectral theory, spectral clustering is using the eigenvalues of some matrix." + }, + { + "text": "That's what that spectral is telling me." + }, + { + "text": "So the spectral theorem, of course, is that for a symmetric matrix S, the eigenvalues are real and the eigenvectors are orthogonal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk7.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..d86e9f9bbdd7d9404d7723410ffb138f3e4560c3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "And don't forget what the real full statement is here, because there could be repeated real eigenvalues." + }, + { + "text": "And what does the spectral theorem tell me?" + }, + { + "text": "For symmetric matrices, if lambda equal 5 is repeated four times, if it's a four times solution of the equation that gives eigenvalues, then what's the conclusion?" + }, + { + "text": "Then there are four independent orthogonal eigenvectors to go with it." + }, + { + "text": "We can't say that about matrices, about all matrices, but we can say it about all symmetric matrices." + }, + { + "text": "And in fact, those eigenvectors are orthogonal, so we're even saying more." + }, + { + "text": "We can find four orthogonal eigenvectors that go with a multiplicity for eigenvalue." + }, + { + "text": "OK, that's spectral theorem." + }, + { + "text": "Spectral clustering starts with the graph Laplacian matrix." + }, + { + "text": "Matrix." + }, + { + "text": "May I remember what that matrix is?" + }, + { + "text": "Because that's the key connection of linear algebra to graph theory, is the properties of this graph Laplacian matrix." + }, + { + "text": "OK, so let me say L for Laplacian." + }, + { + "text": "So that matrix, one way to describe it is as a transpose A, where A is the incidence matrix of the graph." + }, + { + "text": "Or another way we'll see is the D, the degree matrix." + }, + { + "text": "That's diagonal." + }, + { + "text": "And I'll do an example just to remind you." + }, + { + "text": "Minus the, I don't know what I'd call this one." + }, + { + "text": "Shall I call it B for the moment?" + }, + { + "text": "And what matrix is B?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk8.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..67236625f07a70f0d7d710097a866d77120c4a81 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the adjacency matrix." + }, + { + "text": "Really, you should know these four matrices." + }, + { + "text": "They're the key four matrices associated with any graph." + }, + { + "text": "The incidence matrix, that's m by n edges and nodes." + }, + { + "text": "Edges and nodes." + }, + { + "text": "So it's rectangular, but I'm forming A transpose A here." + }, + { + "text": "So I'm forming a symmetric positive semi-definite matrix." + }, + { + "text": "So this Laplacian is symmetric positive semi-definite." + }, + { + "text": "Yeah, let me just recall what all these matrices are for a simple graph." + }, + { + "text": "OK, so I'll just draw a graph." + }, + { + "text": "All right." + }, + { + "text": "OK, so the incidence matrix, there are 1, 2, 3, 4, 5 edges, so five rows." + }, + { + "text": "There are four nodes, 1, 2, 3, and 4, so four columns." + }, + { + "text": "And a typical row would be edge 1 going from node 1 to node 2, so it would have a minus 1 and a 1 there." + }, + { + "text": "And let me take edge 2 going from 1 to node 3, so it would have a minus 1 and a 1 there." + }, + { + "text": "So that's the incidence matrix A. OK, what's the degree matrix?" + }, + { + "text": "That's simple." + }, + { + "text": "The degree matrix, well, A transpose A, this is m by n. This is n by m, so it's n by n. OK, in this case, 4 by 4." + }, + { + "text": "So the degree matrix will be 4 by 4, n by n. And it will tell us the degree of that, which means which we just count the edges." + }, + { + "text": "So it's three edges going in, node 2, three edges going in." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk9.json b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..0b60f0d528f2e4ce2779436b0c9941475e9da813 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/cxTmmasBiC8_1_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "Node 3 has just two edges, and node 4 has just two edges." + }, + { + "text": "So that's the degree matrix." + }, + { + "text": "And then the adjacency matrix that I've called B is also 4 by 4." + }, + { + "text": "And what is it?" + }, + { + "text": "It tells us which node is connected to which node." + }, + { + "text": "So I don't allow nodes, edges, that connect a node to itself, so 0s on the diagonal." + }, + { + "text": "So which nodes are connected to node 1?" + }, + { + "text": "Well, all of 2 and 4 and 3 are connected to 1, so I have 1s there." + }, + { + "text": "Node 2, all three nodes are connected to node 2." + }, + { + "text": "So I'll have the second column and row will have all three 1s." + }, + { + "text": "How about node 3?" + }, + { + "text": "OK, only two edges are connected." + }, + { + "text": "Only two nodes are connected to 3, 1 and 2, but not 4." + }, + { + "text": "So 1 and 2 I have, but not 4." + }, + { + "text": "So that's the adjacency matrix." + }, + { + "text": "Is that right?" + }, + { + "text": "Think so?" + }, + { + "text": "This is the degree matrix." + }, + { + "text": "This is the incidence matrix." + }, + { + "text": "And that formula gives me the Laplacian." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk0.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..afc91322b0d9d5a0ce3bfb215b0940ebb7754749 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "OK, why don't I start?" + }, + { + "text": "So I was hoping that we would have the next online assignment ready, but Julia 6, the new version, is slowing us down." + }, + { + "text": "And it'd probably be next time." + }, + { + "text": "But my lectures, of course, are, well, what I want to say perhaps is this isn't intended to be a course in numerical linear algebra." + }, + { + "text": "But I thought I couldn't let the whole semester go by without saying something about how to compute eigenvalues and singular values." + }, + { + "text": "Of course, you're going to call I or SVD or the equivalent in Python or Julia." + }, + { + "text": "But actually, the QR factorization that we spoke about, that we spoke entirely about last time is the key, unexpectedly, unexpectedly." + }, + { + "text": "You have a matrix A whose eigenvalues you want." + }, + { + "text": "So let's start with eigenvalues." + }, + { + "text": "And it might be a symmetric matrix." + }, + { + "text": "I'll stay with A rather than S because it doesn't have to be." + }, + { + "text": "But you get special always." + }, + { + "text": "You get something special if the matrix is symmetric." + }, + { + "text": "OK, so this method of computing eigenvalues, to me at least, and I think to many people, came like out of the blue a while ago, but not that long ago." + }, + { + "text": "And it worked very well." + }, + { + "text": "So here's the idea." + }, + { + "text": "It's called the QR method because you start by factoring your matrix into QR." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk1.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..f693f6b2ff21648d32a7af5f95cf39d07b0de862 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's A." + }, + { + "text": "Can we call it A0?" + }, + { + "text": "That's the matrix we start with whose eigenvalues we want." + }, + { + "text": "And I'll call these Q0 and R0." + }, + { + "text": "And you remember what that means, what's hiding behind those letters that I've written?" + }, + { + "text": "You have the columns of A, possibly symmetric, as I said, but not orthogonal, usually." + }, + { + "text": "So you find an orthogonal basis." + }, + { + "text": "You orthogonalize them." + }, + { + "text": "You line them up perpendicular to each other." + }, + { + "text": "And then there is a matrix R, which happens to be upper triangular, that connects." + }, + { + "text": "The not orthogonal basis with the orthogonal basis." + }, + { + "text": "Right, we constructed R step by step." + }, + { + "text": "And then the idea is write these in the reverse order." + }, + { + "text": "And that will be A1, the next A. OK, and then do it again, and again, and again." + }, + { + "text": "And so we're hoping, of course, that the eigenvalues didn't change." + }, + { + "text": "We're hoping that we can forget A0, start again with A1, and produce A2, and continue." + }, + { + "text": "So we're hoping two things." + }, + { + "text": "One will not be a hope." + }, + { + "text": "We can see that the eigenvalues of A1 and A0 are the same." + }, + { + "text": "So we have not changed the eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk10.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..6fb2da774bad3a68b507efacec13f9801a995312 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "r0 A0 r0 inverse." + }, + { + "text": "Good." + }, + { + "text": "Minus S. What have I got there?" + }, + { + "text": "From the r0 minus Si r0, what is that?" + }, + { + "text": "That's minus Si." + }, + { + "text": "Look, success." + }, + { + "text": "The r0 cancels the r0 inverse." + }, + { + "text": "So that term from that, that, that is minus Si." + }, + { + "text": "Cancels plus Si." + }, + { + "text": "I'm finished." + }, + { + "text": "And lo and behold, we have the same similarity." + }, + { + "text": "So we messed around by a multiple of the identity, and it actually makes the thing converge faster if we choose the shifts well." + }, + { + "text": "But basically, the same idea is still working." + }, + { + "text": "OK." + }, + { + "text": "So that's the QR method." + }, + { + "text": "Well, that's the method we haven't shown and won't show." + }, + { + "text": "Except for this half-completed example, I don't plan to prove that the lower triangular part begins to disappear, gets smaller and smaller and smaller, and then the eigenvalues pop up on the diagonal." + }, + { + "text": "It's amazing." + }, + { + "text": "Amazing." + }, + { + "text": "OK. Now, is there any other improvement we can make?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk11.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..9e5764513ae4ce678e41ecfcb72a4895642b01f6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's the method." + }, + { + "text": "And where is the work in using that method?" + }, + { + "text": "Because that's what we always focus on." + }, + { + "text": "Where are we spending computer time?" + }, + { + "text": "Well, we're spending computer time in doing the factorization." + }, + { + "text": "So it didn't cost anything to shift by the identity, but then we had to factor that into Q0, R0." + }, + { + "text": "Then it didn't cost much to multiply them in the opposite order." + }, + { + "text": "So the work was in QR." + }, + { + "text": "So could we think of anything to improve that aspect?" + }, + { + "text": "Could we think of anything there?" + }, + { + "text": "And then we've got a really first-class method." + }, + { + "text": "Well, if the matrix A, A0, the matrix we started with, had some zeros that allowed us to skip steps in doing the QR factorization." + }, + { + "text": "So what am I going to say?" + }, + { + "text": "I'm going to say if A or A0, our original matrix, has a bunch of zeros, let's say it's got a whole lot of zeros there." + }, + { + "text": "Maybe it's, well, OK." + }, + { + "text": "I overdid it here." + }, + { + "text": "I know the eigenvalues right off." + }, + { + "text": "But so the truth is I can't, saying that if that, it's not going to happen." + }, + { + "text": "But we can get zeros with one extra diagonal." + }, + { + "text": "That turns out, so here's the main diagonal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk12.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..ab7132ecacaf6cb9786d7b5f399f0082623bd923 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Everybody's got his eye on the main diagonal." + }, + { + "text": "And one diagonal, I can get a lot of zeros." + }, + { + "text": "But I can't by simple computations." + }, + { + "text": "And I'll show you how to get one." + }, + { + "text": "But I can't get all those to be 0, because then I would have the eigenvalues right there." + }, + { + "text": "And that, well, how do I know that I can't?" + }, + { + "text": "In elimination, ordinary solving AX equal B, you really do get to an upper triangular form." + }, + { + "text": "Some operator, some elimination steps, you plug away, and your matrix becomes upper triangular U." + }, + { + "text": "And you're golden." + }, + { + "text": "But that's too much to expect here." + }, + { + "text": "In fact, we know we can't do it by simple steps." + }, + { + "text": "Because if we could do it, if we could get to a U with a whole lower triangular part 0, we would have found the eigenvalues." + }, + { + "text": "And we know that the eigenvalues solve an equation of nth degree." + }, + { + "text": "And we know somebody proved centuries or more ago that you can't solve an nth degree equation by simple little steps." + }, + { + "text": "Right?" + }, + { + "text": "Do you know who that was?" + }, + { + "text": "And you know that fact?" + }, + { + "text": "And what degree does it apply to?" + }, + { + "text": "So that's an important fact that you sort of pick up in math." + }, + { + "text": "Yeah, what do you?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk13.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..5ef254fb5bc0df6883bfe89b2da2433a3da88094 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Fifth degree, yeah." + }, + { + "text": "So 5 by 5 and up would be, this is impossible." + }, + { + "text": "Impossible." + }, + { + "text": "There's no formula to find a simple formula for the lambdas." + }, + { + "text": "And similarly for the sigmas, the singular values." + }, + { + "text": "So the eigenvalues is definitely a level of difficulty beyond Ax equal b, the inverse matrix or something, the pivots." + }, + { + "text": "All that you can do exactly if you do exact arithmetic." + }, + { + "text": "We cannot find the lambdas exactly." + }, + { + "text": "But we can get as close as we like by continuing with the QR method." + }, + { + "text": "So yeah, in other words, we have to settle for, if we want to, at the beginning, improve our matrix before we start doing that stuff." + }, + { + "text": "We can get it with one extra diagonal." + }, + { + "text": "And do you know what kind of a matrix, whose name?" + }, + { + "text": "And I don't know why." + }, + { + "text": "Yeah, say it again." + }, + { + "text": "Upper Hessenberg." + }, + { + "text": "So upper is just like upper triangular." + }, + { + "text": "It's up there." + }, + { + "text": "But the key person's name is Hessenberg." + }, + { + "text": "As I say, that's a Hessenberg matrix." + }, + { + "text": "So Hessenberg matrix is a matrix with one triangular plus one more diagonal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk14.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..890f75c227f0ce9167ef179281769727e008c678 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "But lots of zeros." + }, + { + "text": "Order of n squared, something like almost like half n squared, not quite, but close, zeros." + }, + { + "text": "And you could show that those zeros stay zeros in QR." + }, + { + "text": "So that really pays off." + }, + { + "text": "It cuts the work down significantly." + }, + { + "text": "So the full QR method is step one, reduce A to Hessenberg form with these zeros." + }, + { + "text": "And when I say reduce, I mean find a similarity transformation, of course, because I want the eigenvalues of this to end up the same as the Hessen." + }, + { + "text": "I want to keep the same eigenvalues as I go." + }, + { + "text": "And then step two is QR on this Hessenberg matrix with shifts." + }, + { + "text": "So that's the code that would be programmed in IGAVE." + }, + { + "text": "That's what MATLAB and, well, really, MATLAB is appealing, like other matrix systems, is appealing to LAPAC and LINPAC." + }, + { + "text": "The team of professional numerical analysts really spent a lot of effort and time." + }, + { + "text": "The book LAPAC has 10 authors." + }, + { + "text": "And you can download any of these codes, like the eigenvalue code." + }, + { + "text": "So that's where MATLAB naturally, that's sort of the Bible for codes in linear algebra." + }, + { + "text": "OK, now, I think it's sort of interesting to know." + }, + { + "text": "And there is one more good thing to tell you about this method." + }, + { + "text": "And it applies if the matrix is symmetric." + }, + { + "text": "If the matrix is symmetric, then if we check all this, we could find that the matrices stayed symmetric." + }, + { + "text": "If A0 is symmetric, I can check." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk15.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..1cdfb555c6b2be5bd3044a831ed3f643f560293a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "You could easily check through this, and you would discover that A1 is also symmetric." + }, + { + "text": "It turns out you could rewrite this with a Q0 and a Q0 inverse on the other side." + }, + { + "text": "But that Q0 inverse is the same as Q0 transpose, because it's an orthogonal matrix, and symmetry would fall out." + }, + { + "text": "So if it's symmetric, and it's in Hessenberg form, and it stays symmetric at every step, what can you tell me about a symmetric Hessenberg matrix?" + }, + { + "text": "It's only got, yeah, you just erase all these." + }, + { + "text": "If there are zeros there, and if the matrix is symmetric, then we can safely predict that it will only have one diagonal above, one non-zero diagonal above the main diagonal." + }, + { + "text": "In fact, it'll stay symmetric." + }, + { + "text": "So now I should write symmetric Hessenberg matrix, n equals tri-diagonal matrix." + }, + { + "text": "Yeah, three diagonals." + }, + { + "text": "So now you really have reduced the time to do QR, because you've got a tri-diagonal matrix." + }, + { + "text": "It'll stay tri-diagonal in all these steps." + }, + { + "text": "So you're working with just 3n numbers." + }, + { + "text": "Well, actually, 2n, because the diagonal above and the diagonal below are the same." + }, + { + "text": "You're working with just 2n numbers instead of order n squared, and it just goes like a bomb." + }, + { + "text": "So that's I for symmetric matrices." + }, + { + "text": "And you see that it was all based, that really the heart of the algorithm was QR." + }, + { + "text": "So that's my, it took half the class to report on the favorite way, the EIG way, to find eigenvalues." + }, + { + "text": "Oh, I should say something about singular values." + }, + { + "text": "So singular values, of course, the singular values of the matrix are the eigenvalues of A transpose A, square root of those eigenvalues." + }, + { + "text": "But you wouldn't do it that way." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk16.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..7989fa8939f6d17bfb6b36b82c96bbd76b92a4f6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "You would never form A transpose A. Oh, I didn't mention the other thing you would never, ever, ever do." + }, + { + "text": "So let me just put it here." + }, + { + "text": "This is like in disgrace to solve that equation." + }, + { + "text": "It's like, OK, back to first grade, because that's not, that's very bad." + }, + { + "text": "A determinant, first of all, it's extremely slow, extremely slow." + }, + { + "text": "And the determinant is packing all this n squared pieces of information into n coefficients, and it's hopelessly ill-conditioned." + }, + { + "text": "Yeah, you just, you lose information all the time." + }, + { + "text": "So really, if this is going on camera, it better go on camera with an x, because don't do it." + }, + { + "text": "OK. Yeah." + }, + { + "text": "So where was I?" + }, + { + "text": "Singular values." + }, + { + "text": "So A transpose A." + }, + { + "text": "So again, let's think about what you could do at the beginning before starting on QR for A transpose A, or for the matrix A." + }, + { + "text": "What could you do with orthogonal matrices?" + }, + { + "text": "So I guess, what did we say about symmetric matrices?" + }, + { + "text": "So here's what I said about symmetric matrices." + }, + { + "text": "If you give me a symmetric matrix, I can, in just a simple number of simple steps, make it tridiagonal." + }, + { + "text": "I can't make it diagonal, because then I'd be finding the eigenvalues, and Abel, who was the first person to see that that was impossible, forbids it." + }, + { + "text": "But so let me write down what I'm saying here." + }, + { + "text": "If I have a symmetric matrix S, I can find a bunch of Q's and Q transposes, and I can put them all together into one big Q, and it's transposed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk17.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..08d99076ccc98b0932858bac2de5382359f2d221 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I know about the eigenvalues of that matrix?" + }, + { + "text": "Q is orthogonal always." + }, + { + "text": "So what can you tell me about the, this is the same as Q S Q inverse, and therefore, the eigenvalues are the same." + }, + { + "text": "It's similar to S. And it becomes tridiagonal after I find a good Q." + }, + { + "text": "Now, and therefore, same lambdas, tridiagonal with the same lambdas." + }, + { + "text": "Now, what am I thinking about here?" + }, + { + "text": "I'm thinking about, tell me the corresponding possibility about singular values." + }, + { + "text": "I want to do something to my matrix." + }, + { + "text": "Now, I'm always taking a general matrix A." + }, + { + "text": "And I'm looking for its singular values." + }, + { + "text": "And I'm looking to simplify it." + }, + { + "text": "And what am I allowed to do?" + }, + { + "text": "Yeah, I guess my question is, similarity transformations left the eigenvalues alone." + }, + { + "text": "What can I do that leaves the singular values alone?" + }, + { + "text": "That's a fundamental question, because it was so fundamental for eigenvalues." + }, + { + "text": "By doing this, a matrix and its inverse, I got something similar." + }, + { + "text": "And I checked even in this class that the eigenvalues, same lambdas." + }, + { + "text": "Now I want a whole line that ends up with the same sigmas." + }, + { + "text": "And I want you to tell me what I'm allowed to do to the matrix without changing the sigmas." + }, + { + "text": "So maybe don't shout it out immediately." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk18.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..31cc3c0860684bbd35bab2fb28f2d606a8921e5b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let everybody think." + }, + { + "text": "What am I allowed to do to a matrix?" + }, + { + "text": "Every matrix has got these singular values." + }, + { + "text": "And now I want to make it a better matrix with more 0's or something." + }, + { + "text": "If I do that to it, does that change the sigmas?" + }, + { + "text": "Can I do more than that to it?" + }, + { + "text": "What can I do?" + }, + { + "text": "What group of matrices will have the same sigmas as my starting matrix A?" + }, + { + "text": "So that's a basic, basic question about singular values and the SVD." + }, + { + "text": "So let's think of the answer together." + }, + { + "text": "So it's connected to the SVD." + }, + { + "text": "So let me remember the SVD." + }, + { + "text": "The SVD, I have some orthogonal matrix, then the singular value matrix, SV for singular values, and then another orthogonal matrix." + }, + { + "text": "What could I do to that equation that would not touch this guy?" + }, + { + "text": "So I'm asking what invariance, because not touching it means leaving it not varying." + }, + { + "text": "So I'm looking for under what operations are the singular values invariant?" + }, + { + "text": "When I was looking at eigenvalues, this was the operation." + }, + { + "text": "Well, it didn't have to be orthogonal." + }, + { + "text": "It's something, and it's inverse." + }, + { + "text": "But now what is it up there?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk19.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..01b201f72f3bceb5bd8b70cfc01d55a2e2ff2a71 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "What could I do to that matrix A?" + }, + { + "text": "Could I multiply by Q?" + }, + { + "text": "Could I throw in a Q?" + }, + { + "text": "Maybe not even on the other end." + }, + { + "text": "If I throw in an orthogonal Q, do I change the singular values or do I not change them?" + }, + { + "text": "Fundamental question." + }, + { + "text": "The answer is no, I don't change them." + }, + { + "text": "I'm allowed to do that, because here's an orthogonal matrix, a Q times U." + }, + { + "text": "If both of those are orthogonal, then the product is." + }, + { + "text": "Everybody knows that a product of two orthogonal matrix is still orthogonal." + }, + { + "text": "Better know that." + }, + { + "text": "Better know that." + }, + { + "text": "Yeah." + }, + { + "text": "So if I have an orthogonal matrix Q and an orthogonal matrix U, I claim that this is still orthogonal." + }, + { + "text": "And how do I check it?" + }, + { + "text": "Well, I use some test for orthogonality." + }, + { + "text": "What would be the test you like to use?" + }, + { + "text": "The inverse is the same as the transpose." + }, + { + "text": "You like that test?" + }, + { + "text": "So I'll invert it." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk2.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..49f68a61aecdf81153b85d35f02c4fd1ad64e79f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "How do we see that?" + }, + { + "text": "If you had to show that two matrices had the same eigenvalues, would you compute all the eigenvalues and compare them?" + }, + { + "text": "Certainly not." + }, + { + "text": "What would you do?" + }, + { + "text": "What's the best test, the usual test, the usual thing you would want to show?" + }, + { + "text": "They're similar." + }, + { + "text": "That's right." + }, + { + "text": "So the claim would be that these two matrices are similar." + }, + { + "text": "Right." + }, + { + "text": "So maybe we should show that." + }, + { + "text": "So we want to write A1 in a different way." + }, + { + "text": "So the claim is A1 is similar to A." + }, + { + "text": "So we just have to figure out." + }, + { + "text": "We have to get A1 to A0." + }, + { + "text": "So here's A1." + }, + { + "text": "OK." + }, + { + "text": "So A1, I want to show that that's right." + }, + { + "text": "So that's R0, Q0." + }, + { + "text": "But what is Q0?" + }, + { + "text": "From here, Q0 is what we is R. Q0 is, what do I want?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk20.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..35801c36445d73fe11e2f6274bad6dd29215b8e2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Q U inverse." + }, + { + "text": "Of course, for any matrix, that's U inverse Q inverse." + }, + { + "text": "But these were separately orthogonal, so that's U transpose Q transpose." + }, + { + "text": "And that is the same as Q U transpose." + }, + { + "text": "Yeah." + }, + { + "text": "So I use the orthogonality of U and the orthogonality of Q to conclude that the inverse is the transpose." + }, + { + "text": "So the answer is yes, I could do that." + }, + { + "text": "Now, with singular value, with eigenvalues, I had to multiply on the other side by Q inverse or Q transpose." + }, + { + "text": "Do I have to do that now?" + }, + { + "text": "No." + }, + { + "text": "What can I do on the right-hand side?" + }, + { + "text": "I can multiply by." + }, + { + "text": "I can leave it alone." + }, + { + "text": "Then it has the same singular values because it's the same sigma in there." + }, + { + "text": "If I have a orthogonal matrix times a diagonal times an orthogonal, that diagonal, positive diagonal, is going to be sigma." + }, + { + "text": "So what can I do on this side?" + }, + { + "text": "I could multiply by any orthogonal matrix on that side, too." + }, + { + "text": "So let's call this guy Q1 and this guy Q2." + }, + { + "text": "I still have an orthogonal matrix there, orthogonal matrix there, and the same sigma popped in the middle." + }, + { + "text": "So that's what you're allowed to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk21.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..8733bff8727902ad93fdca4f142729506ca43859 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "That gives us more freedom." + }, + { + "text": "Before, when we had to do similarity transformations with the same guy, we got it to be tridiagonal." + }, + { + "text": "But now we're allowed to do more stuff." + }, + { + "text": "We're allowed to use different orthogonal matrices on the left and right." + }, + { + "text": "And we can reduce it even further from tridiagonal to bidiagonal." + }, + { + "text": "So the first step is getting 0." + }, + { + "text": "The step of getting 0s reduces it all the way to that with all 0s there." + }, + { + "text": "So it's easier." + }, + { + "text": "Then I work on this." + }, + { + "text": "I work on using a QR type idea, some method like that." + }, + { + "text": "So everybody's seeing that our algorithm has got two stages." + }, + { + "text": "One is get a lot of 0s and get them in places that will stay 0 as part 2 of the algorithm gets going." + }, + { + "text": "And then run part 2 of the algorithm." + }, + { + "text": "You're staying with each step is very fast now because doing a QR factorization is fast." + }, + { + "text": "Was there a question?" + }, + { + "text": "Yeah." + }, + { + "text": "So I would call this bidiagonal, of course." + }, + { + "text": "And everybody recognizes that if I have a bidiagonal matrix, call it A or A0 or whatever." + }, + { + "text": "Then what do you think about A transpose A?" + }, + { + "text": "What would A transpose A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk22.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..8562bc4837b9c78d63d64c389d0c913d3dc7d8a2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "If that was A, what could you tell me about A transpose A?" + }, + { + "text": "Could you multiply matrices, like knowing where the non-zeros are, like in your head, and get an idea of where?" + }, + { + "text": "So if I have a bidiagonal matrix A, then sort of implicitly in the SVD, I'm looking at A transpose A." + }, + { + "text": "And what would be true about A transpose A?" + }, + { + "text": "It would be tridiagonal." + }, + { + "text": "So what I've done here and what I've done there just match up." + }, + { + "text": "If you don't want to change singular values, you can get all the way to here." + }, + { + "text": "But then to find those singular values, that would involve A transpose A." + }, + { + "text": "It would be symmetric and tridiagonal." + }, + { + "text": "And then you'd be in that game." + }, + { + "text": "So those are the basic facts of I and SVD." + }, + { + "text": "For matrices of order up to 1,000, say." + }, + { + "text": "I'm not enough of an expert to know where." + }, + { + "text": "Maybe higher, because in perfect math, it's going to take infinitely many steps." + }, + { + "text": "Or Abel would be very surprised." + }, + { + "text": "He would see you solving for eigenvalues and then to re-equation by a whole lot of little steps and getting them exactly right." + }, + { + "text": "That won't happen." + }, + { + "text": "But you get them within epsilon in a number of steps that's like n cubed." + }, + { + "text": "So that's pretty impressive." + }, + { + "text": "The eigenvalue problem is being solved, in quotes, by a fast method that gets you a good answer within a tolerance in n cubed steps." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk23.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..37baceeccac2b563da8271de17d70bb205a69d4d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Right." + }, + { + "text": "So that's great as long as n isn't too big." + }, + { + "text": "And then when n is too big, which of course happens, you have to think again." + }, + { + "text": "So this method is a giant success up to large matrices." + }, + { + "text": "But then you have to think again." + }, + { + "text": "And what is involved in thinking again?" + }, + { + "text": "Well, I guess more thinking." + }, + { + "text": "So what do you do if the matrix is bigger?" + }, + { + "text": "I guess that Krylov would say, use my method." + }, + { + "text": "So Krylov would say, especially if your matrix is sparse." + }, + { + "text": "Can we just remember what Krylov was?" + }, + { + "text": "Krylov started with a vector b, multiplied it by a, multiplied that by a, and got up to, let's say, a to the 999b." + }, + { + "text": "So now Krylov has got 1,000 dimensional space." + }, + { + "text": "He's got a basis for it, 1,000 vectors that span 1,000 dimensional space." + }, + { + "text": "And he'll look at the matrix A only on that space." + }, + { + "text": "In other words, I won't go into detail about that." + }, + { + "text": "He restricts the matrix to this 1,000 dimensional space." + }, + { + "text": "And he hopes that it's captured." + }, + { + "text": "We hope that the eigenvector is virtually in that space." + }, + { + "text": "And actually, I wouldn't go up to, let me take a 9 out of that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk24.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..0f5c17cbd60debd628609f1ccf8848eb0fa9b730 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "100 dimensional would probably catch the eigenvector." + }, + { + "text": "So if the eigenvector is virtually in this space, then we can look at a matrix of order 100." + }, + { + "text": "We can bring A down to just see its action on that space." + }, + { + "text": "So I look at vectors V, which are some combination, C1b plus C2ab plus C3a squared b and C100 a to the 99th b, plus an error." + }, + { + "text": "And I'm going to ignore that error." + }, + { + "text": "Because I've gone up to dimension 100." + }, + { + "text": "I probably say it's pretty safe to ignore that error." + }, + { + "text": "And then in this space, just looking at the matrix A." + }, + { + "text": "So wherever A to the 100th comes in, forget it." + }, + { + "text": "Just think about the matrix A as multiplying vectors of this kind in this space." + }, + { + "text": "Then I have a 100 by 100 eigenvalue problem." + }, + { + "text": "And so the big matrix A is reduced to a matrix of size 100 by, do you see sort of what I'm saying, even though I'm not giving the details?" + }, + { + "text": "Think of a matrix A of size a million." + }, + { + "text": "And you apply it to Krylov vectors." + }, + { + "text": "So I call them little k for a Krylov vector in this 100-dimensional space." + }, + { + "text": "So they have a million minus 100, zero components, you could say, this k. This is in the Krylov space." + }, + { + "text": "This is A, a million, k, 100." + }, + { + "text": "It's a full, it's got a million components, but it's out of just 100-dimensional space." + }, + { + "text": "So when I multiply by A, it'll be mostly in, mostly in, partly in the Krylov space, k 100, and a piece out of k 100." + }, + { + "text": "And I just ignore that part of the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk25.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..41342712fde4874aa3c115a8d909e3bf6f2a0e59 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I have a 100 by 100 problem, and I've solved to find the eigenvalues." + }, + { + "text": "And they're a pretty good approximation to the eigenvalues, to the, hopefully, like the lowest 100 eigenvalues." + }, + { + "text": "I'd like to know that." + }, + { + "text": "But I might not be sure that this idea would give me the lowest 100, the first 100 eigenvalues of the million, of the matrix of size a million." + }, + { + "text": "I'm just taking a few minutes here to sort of wave hands about what Krylov, the Krylov idea would do." + }, + { + "text": "And I probably won't mention Krylov again this semester." + }, + { + "text": "So what it can do is look at this particular type of space, because we can get a basis for it quickly, just multiply again and again by A." + }, + { + "text": "Then we can orthogonalize that basis." + }, + { + "text": "That's Graham-Schmidt in some form." + }, + { + "text": "We're always going back to Graham-Schmidt." + }, + { + "text": "Then I have a 100 by 100." + }, + { + "text": "I have a subspace of size 100." + }, + { + "text": "I look at what the matrix does in that space." + }, + { + "text": "And I could look for, I could find eigenvalues restricted to that space." + }, + { + "text": "They wouldn't be the perfect eigenvalues, but they would be accurate." + }, + { + "text": "OK, so I didn't know it would take one class time to talk about finding eigenvalues and singular values, but we did some important things." + }, + { + "text": "We remembered that similarity is the thing to check, thing to preserve, because it doesn't change the eigenvalues." + }, + { + "text": "And then for singular values, what was the thing?" + }, + { + "text": "You could multiply left and right by different orthogonal matrices." + }, + { + "text": "And somehow, maybe that doesn't have an established name, multiplying left and right by a Q1 and a Q2 transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk26.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..2ce06055331ebe329b68e463d8ac9af5a66e37dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk26.json @@ -0,0 +1,35 @@ +[ + { + "text": "Yeah, but the idea is clear." + }, + { + "text": "And that doesn't change the singular values." + }, + { + "text": "We're ready to move now into maybe our next step, which we don't spend a long time on." + }, + { + "text": "We'll be like random sampling." + }, + { + "text": "What if your matrix is just way too big?" + }, + { + "text": "So that's a new, very new idea, very different idea in numerical linear algebra, is just to sample the matrix." + }, + { + "text": "Could you believe that the answer is going to come out right just for a random sample?" + }, + { + "text": "Well, the odds are in your favor." + }, + { + "text": "OK, so that'll be Wednesday, and then we have lots of new, we'll move onward after that." + }, + { + "text": "OK, see you Wednesday." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk3.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..f5acd4bdba4ba51520fdf921a1fc36684dfeaabb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I want to put R0 inverse over there." + }, + { + "text": "So R0." + }, + { + "text": "Now for Q0, I'm going to substitute." + }, + { + "text": "So what is Q0?" + }, + { + "text": "I multiply both sides of that equation by R0 inverse." + }, + { + "text": "So Q0 is A0 is, sorry, I said A and wrote Q. A0 R0 inverse." + }, + { + "text": "Right." + }, + { + "text": "For Q0, I've put in what it equals." + }, + { + "text": "And that's done it." + }, + { + "text": "That's exactly telling me that A1, which is this, equals this." + }, + { + "text": "And that's a similarity transformation." + }, + { + "text": "I have not changed the eigenvalues." + }, + { + "text": "So that's OK." + }, + { + "text": "The other thing, which is the, like you could say, the miracle in this thing, is that when I continue to do that for almost every matrix, the matrices begin to lose stuff off the diagonal, especially below the diagonal by the ordering that QR is done." + }, + { + "text": "So you tend to start with a matrix A0." + }, + { + "text": "You get a matrix A1, which is like a little smaller here." + }, + { + "text": "This part being not especially smaller." + }, + { + "text": "You do it again." + }, + { + "text": "This is even smaller." + }, + { + "text": "So I put even smaller A2, even smaller." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk4.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..a93c5efe93b5619eae3335916949e5ca1b9c543f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you keep going." + }, + { + "text": "And for most matrices, the result is that I don't know how many steps we want to think of taking, but we get quite small numbers here." + }, + { + "text": "So once we get small numbers here, little epsilons, that's everybody's shorthand for small numbers, what would you expect to see on the diagonal?" + }, + { + "text": "The eigenvalues." + }, + { + "text": "Because this has the same eigenvalues as this, as this, as this." + }, + { + "text": "And these little epsilons are not going to change the eigenvalues too much." + }, + { + "text": "So these will be, on the diagonal, will be close to the eigenvalues." + }, + { + "text": "And actually, what happens is this one comes first." + }, + { + "text": "That one is quite accurate first." + }, + { + "text": "I guess we should probably do a simple example to see this happen." + }, + { + "text": "Actually, I do an example in the notes." + }, + { + "text": "And let me say what happens." + }, + { + "text": "So I do a 2 by 2 example, which has something like cos theta, sine theta." + }, + { + "text": "I don't know what." + }, + { + "text": "I've forgotten what I took." + }, + { + "text": "And I don't have that page of notes here." + }, + { + "text": "Something here." + }, + { + "text": "Something here." + }, + { + "text": "Something here as a 0." + }, + { + "text": "And then a 1, after just one step, has sine cubed theta there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk5.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..2c1c69b5647ae63cfaad8af10731e95f060b6c81 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And numbers there that are getting much closer to the eigenvalues." + }, + { + "text": "Sorry that this isn't a full scale example." + }, + { + "text": "But the point of the example is here, that this off-diagonal entry gets cubed." + }, + { + "text": "And the next step will be its ninth power, and then the 27th power." + }, + { + "text": "So it's really quickly going to 0." + }, + { + "text": "And this happens." + }, + { + "text": "So cubic convergence is a prize." + }, + { + "text": "In numerical linear algebra." + }, + { + "text": "So that happens." + }, + { + "text": "So this arrived on the scene and quickly blew away all other methods that were being used to compute eigenvalues." + }, + { + "text": "But numerical people, being what they are, they wanted to improve it." + }, + { + "text": "Like, is there a way to make it faster?" + }, + { + "text": "And turned out there is." + }, + { + "text": "It turned out that the better way, basically the same idea, but just you're always looking for a simple change." + }, + { + "text": "And the idea of introducing a shift was tried." + }, + { + "text": "And turned out to work extremely well." + }, + { + "text": "So that's the improvement." + }, + { + "text": "So we take a1." + }, + { + "text": "No, so how does the shift work?" + }, + { + "text": "So instead of a0, have I got space here to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk6.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..e081a02643a2181251ac74e36b445d55b6192f14 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Instead of a0, I take a0 minus a shift." + }, + { + "text": "So a shift is some multiple of the identity." + }, + { + "text": "If I just move a matrix by a multiple of the identity, what happens to its eigenvectors?" + }, + { + "text": "What happens to its eigenvalues?" + }, + { + "text": "Something pretty simple, right?" + }, + { + "text": "Because I'm just shifting by si." + }, + { + "text": "What happens to its eigenvectors?" + }, + { + "text": "They're the same." + }, + { + "text": "And what happens to the eigenvalues?" + }, + { + "text": "They change by s. If a0v equals lambda v, then when I multiply this by v, there will be an extra." + }, + { + "text": "It'll be lambda minus s. Because the identity times the v is just v. So it just shifts all the eigenvalues by s. And you try to shift." + }, + { + "text": "You look for a shift." + }, + { + "text": "This would be great." + }, + { + "text": "If you knew lambda n, a shift there, you would be looking for 0 then, if you shifted them all by that lambda." + }, + { + "text": "And it turns out that would speed things up." + }, + { + "text": "So you work instead with this matrix as now, again, I'm factoring in a q0, r0." + }, + { + "text": "So that's the work of the method, is in doing Gram-Schmidt at every step." + }, + { + "text": "And then there's a little work in reversing the order." + }, + { + "text": "And then I want to undo the shift." + }, + { + "text": "So I do that factorization." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk7.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..212c509ec27724246ec3a49d4c24022c4979b516 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, let's see." + }, + { + "text": "You may have to help me to remember what I should do here." + }, + { + "text": "So I factor those." + }, + { + "text": "I reverse those." + }, + { + "text": "And then I think I add back the shift." + }, + { + "text": "And that's my A1." + }, + { + "text": "So I took A0." + }, + { + "text": "I shifted it." + }, + { + "text": "I worked with it, qr, reversed the order, rq, added back the shift to get a matrix." + }, + { + "text": "And what am I, of course, hoping about the matrix A1 and A0?" + }, + { + "text": "I'm hoping they're still similar." + }, + { + "text": "I'm hoping." + }, + { + "text": "So I did a shift." + }, + { + "text": "And I undid a shift." + }, + { + "text": "But of course, after doing a qr, I have to check, are these really still similar?" + }, + { + "text": "So let me just try to check that one again." + }, + { + "text": "Maybe I'll just, it's sitting right there." + }, + { + "text": "So let me do it again." + }, + { + "text": "I'm hoping that something, you know, where did we change?" + }, + { + "text": "Oh, yeah, here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk8.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..4e7fad6f92f20cdf436db6b8933b889b8a6fb34f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We showed that A1 was similar to A0." + }, + { + "text": "And I'm hoping that's probably still true, even, you know, the shift didn't mess that up." + }, + { + "text": "Let's just try." + }, + { + "text": "So A0, that's r0, q0 plus si." + }, + { + "text": "OK. And now what am I going to do?" + }, + { + "text": "I'm going to, what did I do before?" + }, + { + "text": "I figured out what q0 was from this." + }, + { + "text": "You remember?" + }, + { + "text": "So this is r0." + }, + { + "text": "Now I have to put in q0." + }, + { + "text": "But q0 is this thing inverse times this." + }, + { + "text": "Is this going to work?" + }, + { + "text": "I'm like hoping, but I don't think I wanted to get that." + }, + { + "text": "No, it's not q0 there." + }, + { + "text": "What do I put here?" + }, + { + "text": "And if it doesn't work, we'll leave it as an exercise." + }, + { + "text": "OK." + }, + { + "text": "So yeah, because I didn't sort of start right somehow." + }, + { + "text": "OK." + }, + { + "text": "So but let me just push along to see what happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk9.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..f66b5f2f317c991f9ad92b2dc38dd936ae5d8d21 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_0_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I'm plugging in for q0 here." + }, + { + "text": "I'm plugging in this matrix, so it shouldn't have inverted it, times r0 inverse." + }, + { + "text": "Who knows?" + }, + { + "text": "It might work." + }, + { + "text": "Who knows?" + }, + { + "text": "So that's the r0, q0." + }, + { + "text": "Right?" + }, + { + "text": "Is everybody with me?" + }, + { + "text": "Sorry about this." + }, + { + "text": "So r0 inverse." + }, + { + "text": "And then I have to add Si." + }, + { + "text": "So what have I done?" + }, + { + "text": "I've just pushed on, believing that this would work." + }, + { + "text": "Because it's the method that is constantly used." + }, + { + "text": "Now do I have?" + }, + { + "text": "What do I have there?" + }, + { + "text": "Is it working?" + }, + { + "text": "This is r0 A." + }, + { + "text": "That was, of course, A0." + }, + { + "text": "r0 A0 r0 inverse." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk0.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..afc91322b0d9d5a0ce3bfb215b0940ebb7754749 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "OK, why don't I start?" + }, + { + "text": "So I was hoping that we would have the next online assignment ready, but Julia 6, the new version, is slowing us down." + }, + { + "text": "And it'd probably be next time." + }, + { + "text": "But my lectures, of course, are, well, what I want to say perhaps is this isn't intended to be a course in numerical linear algebra." + }, + { + "text": "But I thought I couldn't let the whole semester go by without saying something about how to compute eigenvalues and singular values." + }, + { + "text": "Of course, you're going to call I or SVD or the equivalent in Python or Julia." + }, + { + "text": "But actually, the QR factorization that we spoke about, that we spoke entirely about last time is the key, unexpectedly, unexpectedly." + }, + { + "text": "You have a matrix A whose eigenvalues you want." + }, + { + "text": "So let's start with eigenvalues." + }, + { + "text": "And it might be a symmetric matrix." + }, + { + "text": "I'll stay with A rather than S because it doesn't have to be." + }, + { + "text": "But you get special always." + }, + { + "text": "You get something special if the matrix is symmetric." + }, + { + "text": "OK, so this method of computing eigenvalues, to me at least, and I think to many people, came like out of the blue a while ago, but not that long ago." + }, + { + "text": "And it worked very well." + }, + { + "text": "So here's the idea." + }, + { + "text": "It's called the QR method because you start by factoring your matrix into QR." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk1.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..f693f6b2ff21648d32a7af5f95cf39d07b0de862 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's A." + }, + { + "text": "Can we call it A0?" + }, + { + "text": "That's the matrix we start with whose eigenvalues we want." + }, + { + "text": "And I'll call these Q0 and R0." + }, + { + "text": "And you remember what that means, what's hiding behind those letters that I've written?" + }, + { + "text": "You have the columns of A, possibly symmetric, as I said, but not orthogonal, usually." + }, + { + "text": "So you find an orthogonal basis." + }, + { + "text": "You orthogonalize them." + }, + { + "text": "You line them up perpendicular to each other." + }, + { + "text": "And then there is a matrix R, which happens to be upper triangular, that connects." + }, + { + "text": "The not orthogonal basis with the orthogonal basis." + }, + { + "text": "Right, we constructed R step by step." + }, + { + "text": "And then the idea is write these in the reverse order." + }, + { + "text": "And that will be A1, the next A. OK, and then do it again, and again, and again." + }, + { + "text": "And so we're hoping, of course, that the eigenvalues didn't change." + }, + { + "text": "We're hoping that we can forget A0, start again with A1, and produce A2, and continue." + }, + { + "text": "So we're hoping two things." + }, + { + "text": "One will not be a hope." + }, + { + "text": "We can see that the eigenvalues of A1 and A0 are the same." + }, + { + "text": "So we have not changed the eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk10.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..6fb2da774bad3a68b507efacec13f9801a995312 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "r0 A0 r0 inverse." + }, + { + "text": "Good." + }, + { + "text": "Minus S. What have I got there?" + }, + { + "text": "From the r0 minus Si r0, what is that?" + }, + { + "text": "That's minus Si." + }, + { + "text": "Look, success." + }, + { + "text": "The r0 cancels the r0 inverse." + }, + { + "text": "So that term from that, that, that is minus Si." + }, + { + "text": "Cancels plus Si." + }, + { + "text": "I'm finished." + }, + { + "text": "And lo and behold, we have the same similarity." + }, + { + "text": "So we messed around by a multiple of the identity, and it actually makes the thing converge faster if we choose the shifts well." + }, + { + "text": "But basically, the same idea is still working." + }, + { + "text": "OK." + }, + { + "text": "So that's the QR method." + }, + { + "text": "Well, that's the method we haven't shown and won't show." + }, + { + "text": "Except for this half-completed example, I don't plan to prove that the lower triangular part begins to disappear, gets smaller and smaller and smaller, and then the eigenvalues pop up on the diagonal." + }, + { + "text": "It's amazing." + }, + { + "text": "Amazing." + }, + { + "text": "OK. Now, is there any other improvement we can make?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk11.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..9e5764513ae4ce678e41ecfcb72a4895642b01f6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's the method." + }, + { + "text": "And where is the work in using that method?" + }, + { + "text": "Because that's what we always focus on." + }, + { + "text": "Where are we spending computer time?" + }, + { + "text": "Well, we're spending computer time in doing the factorization." + }, + { + "text": "So it didn't cost anything to shift by the identity, but then we had to factor that into Q0, R0." + }, + { + "text": "Then it didn't cost much to multiply them in the opposite order." + }, + { + "text": "So the work was in QR." + }, + { + "text": "So could we think of anything to improve that aspect?" + }, + { + "text": "Could we think of anything there?" + }, + { + "text": "And then we've got a really first-class method." + }, + { + "text": "Well, if the matrix A, A0, the matrix we started with, had some zeros that allowed us to skip steps in doing the QR factorization." + }, + { + "text": "So what am I going to say?" + }, + { + "text": "I'm going to say if A or A0, our original matrix, has a bunch of zeros, let's say it's got a whole lot of zeros there." + }, + { + "text": "Maybe it's, well, OK." + }, + { + "text": "I overdid it here." + }, + { + "text": "I know the eigenvalues right off." + }, + { + "text": "But so the truth is I can't, saying that if that, it's not going to happen." + }, + { + "text": "But we can get zeros with one extra diagonal." + }, + { + "text": "That turns out, so here's the main diagonal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk12.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..ab7132ecacaf6cb9786d7b5f399f0082623bd923 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Everybody's got his eye on the main diagonal." + }, + { + "text": "And one diagonal, I can get a lot of zeros." + }, + { + "text": "But I can't by simple computations." + }, + { + "text": "And I'll show you how to get one." + }, + { + "text": "But I can't get all those to be 0, because then I would have the eigenvalues right there." + }, + { + "text": "And that, well, how do I know that I can't?" + }, + { + "text": "In elimination, ordinary solving AX equal B, you really do get to an upper triangular form." + }, + { + "text": "Some operator, some elimination steps, you plug away, and your matrix becomes upper triangular U." + }, + { + "text": "And you're golden." + }, + { + "text": "But that's too much to expect here." + }, + { + "text": "In fact, we know we can't do it by simple steps." + }, + { + "text": "Because if we could do it, if we could get to a U with a whole lower triangular part 0, we would have found the eigenvalues." + }, + { + "text": "And we know that the eigenvalues solve an equation of nth degree." + }, + { + "text": "And we know somebody proved centuries or more ago that you can't solve an nth degree equation by simple little steps." + }, + { + "text": "Right?" + }, + { + "text": "Do you know who that was?" + }, + { + "text": "And you know that fact?" + }, + { + "text": "And what degree does it apply to?" + }, + { + "text": "So that's an important fact that you sort of pick up in math." + }, + { + "text": "Yeah, what do you?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk13.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..5ef254fb5bc0df6883bfe89b2da2433a3da88094 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Fifth degree, yeah." + }, + { + "text": "So 5 by 5 and up would be, this is impossible." + }, + { + "text": "Impossible." + }, + { + "text": "There's no formula to find a simple formula for the lambdas." + }, + { + "text": "And similarly for the sigmas, the singular values." + }, + { + "text": "So the eigenvalues is definitely a level of difficulty beyond Ax equal b, the inverse matrix or something, the pivots." + }, + { + "text": "All that you can do exactly if you do exact arithmetic." + }, + { + "text": "We cannot find the lambdas exactly." + }, + { + "text": "But we can get as close as we like by continuing with the QR method." + }, + { + "text": "So yeah, in other words, we have to settle for, if we want to, at the beginning, improve our matrix before we start doing that stuff." + }, + { + "text": "We can get it with one extra diagonal." + }, + { + "text": "And do you know what kind of a matrix, whose name?" + }, + { + "text": "And I don't know why." + }, + { + "text": "Yeah, say it again." + }, + { + "text": "Upper Hessenberg." + }, + { + "text": "So upper is just like upper triangular." + }, + { + "text": "It's up there." + }, + { + "text": "But the key person's name is Hessenberg." + }, + { + "text": "As I say, that's a Hessenberg matrix." + }, + { + "text": "So Hessenberg matrix is a matrix with one triangular plus one more diagonal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk14.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..890f75c227f0ce9167ef179281769727e008c678 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "But lots of zeros." + }, + { + "text": "Order of n squared, something like almost like half n squared, not quite, but close, zeros." + }, + { + "text": "And you could show that those zeros stay zeros in QR." + }, + { + "text": "So that really pays off." + }, + { + "text": "It cuts the work down significantly." + }, + { + "text": "So the full QR method is step one, reduce A to Hessenberg form with these zeros." + }, + { + "text": "And when I say reduce, I mean find a similarity transformation, of course, because I want the eigenvalues of this to end up the same as the Hessen." + }, + { + "text": "I want to keep the same eigenvalues as I go." + }, + { + "text": "And then step two is QR on this Hessenberg matrix with shifts." + }, + { + "text": "So that's the code that would be programmed in IGAVE." + }, + { + "text": "That's what MATLAB and, well, really, MATLAB is appealing, like other matrix systems, is appealing to LAPAC and LINPAC." + }, + { + "text": "The team of professional numerical analysts really spent a lot of effort and time." + }, + { + "text": "The book LAPAC has 10 authors." + }, + { + "text": "And you can download any of these codes, like the eigenvalue code." + }, + { + "text": "So that's where MATLAB naturally, that's sort of the Bible for codes in linear algebra." + }, + { + "text": "OK, now, I think it's sort of interesting to know." + }, + { + "text": "And there is one more good thing to tell you about this method." + }, + { + "text": "And it applies if the matrix is symmetric." + }, + { + "text": "If the matrix is symmetric, then if we check all this, we could find that the matrices stayed symmetric." + }, + { + "text": "If A0 is symmetric, I can check." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk15.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..1cdfb555c6b2be5bd3044a831ed3f643f560293a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "You could easily check through this, and you would discover that A1 is also symmetric." + }, + { + "text": "It turns out you could rewrite this with a Q0 and a Q0 inverse on the other side." + }, + { + "text": "But that Q0 inverse is the same as Q0 transpose, because it's an orthogonal matrix, and symmetry would fall out." + }, + { + "text": "So if it's symmetric, and it's in Hessenberg form, and it stays symmetric at every step, what can you tell me about a symmetric Hessenberg matrix?" + }, + { + "text": "It's only got, yeah, you just erase all these." + }, + { + "text": "If there are zeros there, and if the matrix is symmetric, then we can safely predict that it will only have one diagonal above, one non-zero diagonal above the main diagonal." + }, + { + "text": "In fact, it'll stay symmetric." + }, + { + "text": "So now I should write symmetric Hessenberg matrix, n equals tri-diagonal matrix." + }, + { + "text": "Yeah, three diagonals." + }, + { + "text": "So now you really have reduced the time to do QR, because you've got a tri-diagonal matrix." + }, + { + "text": "It'll stay tri-diagonal in all these steps." + }, + { + "text": "So you're working with just 3n numbers." + }, + { + "text": "Well, actually, 2n, because the diagonal above and the diagonal below are the same." + }, + { + "text": "You're working with just 2n numbers instead of order n squared, and it just goes like a bomb." + }, + { + "text": "So that's I for symmetric matrices." + }, + { + "text": "And you see that it was all based, that really the heart of the algorithm was QR." + }, + { + "text": "So that's my, it took half the class to report on the favorite way, the EIG way, to find eigenvalues." + }, + { + "text": "Oh, I should say something about singular values." + }, + { + "text": "So singular values, of course, the singular values of the matrix are the eigenvalues of A transpose A, square root of those eigenvalues." + }, + { + "text": "But you wouldn't do it that way." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk16.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..7989fa8939f6d17bfb6b36b82c96bbd76b92a4f6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "You would never form A transpose A. Oh, I didn't mention the other thing you would never, ever, ever do." + }, + { + "text": "So let me just put it here." + }, + { + "text": "This is like in disgrace to solve that equation." + }, + { + "text": "It's like, OK, back to first grade, because that's not, that's very bad." + }, + { + "text": "A determinant, first of all, it's extremely slow, extremely slow." + }, + { + "text": "And the determinant is packing all this n squared pieces of information into n coefficients, and it's hopelessly ill-conditioned." + }, + { + "text": "Yeah, you just, you lose information all the time." + }, + { + "text": "So really, if this is going on camera, it better go on camera with an x, because don't do it." + }, + { + "text": "OK. Yeah." + }, + { + "text": "So where was I?" + }, + { + "text": "Singular values." + }, + { + "text": "So A transpose A." + }, + { + "text": "So again, let's think about what you could do at the beginning before starting on QR for A transpose A, or for the matrix A." + }, + { + "text": "What could you do with orthogonal matrices?" + }, + { + "text": "So I guess, what did we say about symmetric matrices?" + }, + { + "text": "So here's what I said about symmetric matrices." + }, + { + "text": "If you give me a symmetric matrix, I can, in just a simple number of simple steps, make it tridiagonal." + }, + { + "text": "I can't make it diagonal, because then I'd be finding the eigenvalues, and Abel, who was the first person to see that that was impossible, forbids it." + }, + { + "text": "But so let me write down what I'm saying here." + }, + { + "text": "If I have a symmetric matrix S, I can find a bunch of Q's and Q transposes, and I can put them all together into one big Q, and it's transposed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk17.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..08d99076ccc98b0932858bac2de5382359f2d221 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I know about the eigenvalues of that matrix?" + }, + { + "text": "Q is orthogonal always." + }, + { + "text": "So what can you tell me about the, this is the same as Q S Q inverse, and therefore, the eigenvalues are the same." + }, + { + "text": "It's similar to S. And it becomes tridiagonal after I find a good Q." + }, + { + "text": "Now, and therefore, same lambdas, tridiagonal with the same lambdas." + }, + { + "text": "Now, what am I thinking about here?" + }, + { + "text": "I'm thinking about, tell me the corresponding possibility about singular values." + }, + { + "text": "I want to do something to my matrix." + }, + { + "text": "Now, I'm always taking a general matrix A." + }, + { + "text": "And I'm looking for its singular values." + }, + { + "text": "And I'm looking to simplify it." + }, + { + "text": "And what am I allowed to do?" + }, + { + "text": "Yeah, I guess my question is, similarity transformations left the eigenvalues alone." + }, + { + "text": "What can I do that leaves the singular values alone?" + }, + { + "text": "That's a fundamental question, because it was so fundamental for eigenvalues." + }, + { + "text": "By doing this, a matrix and its inverse, I got something similar." + }, + { + "text": "And I checked even in this class that the eigenvalues, same lambdas." + }, + { + "text": "Now I want a whole line that ends up with the same sigmas." + }, + { + "text": "And I want you to tell me what I'm allowed to do to the matrix without changing the sigmas." + }, + { + "text": "So maybe don't shout it out immediately." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk18.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..31cc3c0860684bbd35bab2fb28f2d606a8921e5b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let everybody think." + }, + { + "text": "What am I allowed to do to a matrix?" + }, + { + "text": "Every matrix has got these singular values." + }, + { + "text": "And now I want to make it a better matrix with more 0's or something." + }, + { + "text": "If I do that to it, does that change the sigmas?" + }, + { + "text": "Can I do more than that to it?" + }, + { + "text": "What can I do?" + }, + { + "text": "What group of matrices will have the same sigmas as my starting matrix A?" + }, + { + "text": "So that's a basic, basic question about singular values and the SVD." + }, + { + "text": "So let's think of the answer together." + }, + { + "text": "So it's connected to the SVD." + }, + { + "text": "So let me remember the SVD." + }, + { + "text": "The SVD, I have some orthogonal matrix, then the singular value matrix, SV for singular values, and then another orthogonal matrix." + }, + { + "text": "What could I do to that equation that would not touch this guy?" + }, + { + "text": "So I'm asking what invariance, because not touching it means leaving it not varying." + }, + { + "text": "So I'm looking for under what operations are the singular values invariant?" + }, + { + "text": "When I was looking at eigenvalues, this was the operation." + }, + { + "text": "Well, it didn't have to be orthogonal." + }, + { + "text": "It's something, and it's inverse." + }, + { + "text": "But now what is it up there?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk19.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..01b201f72f3bceb5bd8b70cfc01d55a2e2ff2a71 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "What could I do to that matrix A?" + }, + { + "text": "Could I multiply by Q?" + }, + { + "text": "Could I throw in a Q?" + }, + { + "text": "Maybe not even on the other end." + }, + { + "text": "If I throw in an orthogonal Q, do I change the singular values or do I not change them?" + }, + { + "text": "Fundamental question." + }, + { + "text": "The answer is no, I don't change them." + }, + { + "text": "I'm allowed to do that, because here's an orthogonal matrix, a Q times U." + }, + { + "text": "If both of those are orthogonal, then the product is." + }, + { + "text": "Everybody knows that a product of two orthogonal matrix is still orthogonal." + }, + { + "text": "Better know that." + }, + { + "text": "Better know that." + }, + { + "text": "Yeah." + }, + { + "text": "So if I have an orthogonal matrix Q and an orthogonal matrix U, I claim that this is still orthogonal." + }, + { + "text": "And how do I check it?" + }, + { + "text": "Well, I use some test for orthogonality." + }, + { + "text": "What would be the test you like to use?" + }, + { + "text": "The inverse is the same as the transpose." + }, + { + "text": "You like that test?" + }, + { + "text": "So I'll invert it." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk2.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..49f68a61aecdf81153b85d35f02c4fd1ad64e79f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "How do we see that?" + }, + { + "text": "If you had to show that two matrices had the same eigenvalues, would you compute all the eigenvalues and compare them?" + }, + { + "text": "Certainly not." + }, + { + "text": "What would you do?" + }, + { + "text": "What's the best test, the usual test, the usual thing you would want to show?" + }, + { + "text": "They're similar." + }, + { + "text": "That's right." + }, + { + "text": "So the claim would be that these two matrices are similar." + }, + { + "text": "Right." + }, + { + "text": "So maybe we should show that." + }, + { + "text": "So we want to write A1 in a different way." + }, + { + "text": "So the claim is A1 is similar to A." + }, + { + "text": "So we just have to figure out." + }, + { + "text": "We have to get A1 to A0." + }, + { + "text": "So here's A1." + }, + { + "text": "OK." + }, + { + "text": "So A1, I want to show that that's right." + }, + { + "text": "So that's R0, Q0." + }, + { + "text": "But what is Q0?" + }, + { + "text": "From here, Q0 is what we is R. Q0 is, what do I want?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk20.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..35801c36445d73fe11e2f6274bad6dd29215b8e2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Q U inverse." + }, + { + "text": "Of course, for any matrix, that's U inverse Q inverse." + }, + { + "text": "But these were separately orthogonal, so that's U transpose Q transpose." + }, + { + "text": "And that is the same as Q U transpose." + }, + { + "text": "Yeah." + }, + { + "text": "So I use the orthogonality of U and the orthogonality of Q to conclude that the inverse is the transpose." + }, + { + "text": "So the answer is yes, I could do that." + }, + { + "text": "Now, with singular value, with eigenvalues, I had to multiply on the other side by Q inverse or Q transpose." + }, + { + "text": "Do I have to do that now?" + }, + { + "text": "No." + }, + { + "text": "What can I do on the right-hand side?" + }, + { + "text": "I can multiply by." + }, + { + "text": "I can leave it alone." + }, + { + "text": "Then it has the same singular values because it's the same sigma in there." + }, + { + "text": "If I have a orthogonal matrix times a diagonal times an orthogonal, that diagonal, positive diagonal, is going to be sigma." + }, + { + "text": "So what can I do on this side?" + }, + { + "text": "I could multiply by any orthogonal matrix on that side, too." + }, + { + "text": "So let's call this guy Q1 and this guy Q2." + }, + { + "text": "I still have an orthogonal matrix there, orthogonal matrix there, and the same sigma popped in the middle." + }, + { + "text": "So that's what you're allowed to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk21.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..8733bff8727902ad93fdca4f142729506ca43859 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "That gives us more freedom." + }, + { + "text": "Before, when we had to do similarity transformations with the same guy, we got it to be tridiagonal." + }, + { + "text": "But now we're allowed to do more stuff." + }, + { + "text": "We're allowed to use different orthogonal matrices on the left and right." + }, + { + "text": "And we can reduce it even further from tridiagonal to bidiagonal." + }, + { + "text": "So the first step is getting 0." + }, + { + "text": "The step of getting 0s reduces it all the way to that with all 0s there." + }, + { + "text": "So it's easier." + }, + { + "text": "Then I work on this." + }, + { + "text": "I work on using a QR type idea, some method like that." + }, + { + "text": "So everybody's seeing that our algorithm has got two stages." + }, + { + "text": "One is get a lot of 0s and get them in places that will stay 0 as part 2 of the algorithm gets going." + }, + { + "text": "And then run part 2 of the algorithm." + }, + { + "text": "You're staying with each step is very fast now because doing a QR factorization is fast." + }, + { + "text": "Was there a question?" + }, + { + "text": "Yeah." + }, + { + "text": "So I would call this bidiagonal, of course." + }, + { + "text": "And everybody recognizes that if I have a bidiagonal matrix, call it A or A0 or whatever." + }, + { + "text": "Then what do you think about A transpose A?" + }, + { + "text": "What would A transpose A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk22.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..8562bc4837b9c78d63d64c389d0c913d3dc7d8a2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "If that was A, what could you tell me about A transpose A?" + }, + { + "text": "Could you multiply matrices, like knowing where the non-zeros are, like in your head, and get an idea of where?" + }, + { + "text": "So if I have a bidiagonal matrix A, then sort of implicitly in the SVD, I'm looking at A transpose A." + }, + { + "text": "And what would be true about A transpose A?" + }, + { + "text": "It would be tridiagonal." + }, + { + "text": "So what I've done here and what I've done there just match up." + }, + { + "text": "If you don't want to change singular values, you can get all the way to here." + }, + { + "text": "But then to find those singular values, that would involve A transpose A." + }, + { + "text": "It would be symmetric and tridiagonal." + }, + { + "text": "And then you'd be in that game." + }, + { + "text": "So those are the basic facts of I and SVD." + }, + { + "text": "For matrices of order up to 1,000, say." + }, + { + "text": "I'm not enough of an expert to know where." + }, + { + "text": "Maybe higher, because in perfect math, it's going to take infinitely many steps." + }, + { + "text": "Or Abel would be very surprised." + }, + { + "text": "He would see you solving for eigenvalues and then to re-equation by a whole lot of little steps and getting them exactly right." + }, + { + "text": "That won't happen." + }, + { + "text": "But you get them within epsilon in a number of steps that's like n cubed." + }, + { + "text": "So that's pretty impressive." + }, + { + "text": "The eigenvalue problem is being solved, in quotes, by a fast method that gets you a good answer within a tolerance in n cubed steps." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk23.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..37baceeccac2b563da8271de17d70bb205a69d4d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Right." + }, + { + "text": "So that's great as long as n isn't too big." + }, + { + "text": "And then when n is too big, which of course happens, you have to think again." + }, + { + "text": "So this method is a giant success up to large matrices." + }, + { + "text": "But then you have to think again." + }, + { + "text": "And what is involved in thinking again?" + }, + { + "text": "Well, I guess more thinking." + }, + { + "text": "So what do you do if the matrix is bigger?" + }, + { + "text": "I guess that Krylov would say, use my method." + }, + { + "text": "So Krylov would say, especially if your matrix is sparse." + }, + { + "text": "Can we just remember what Krylov was?" + }, + { + "text": "Krylov started with a vector b, multiplied it by a, multiplied that by a, and got up to, let's say, a to the 999b." + }, + { + "text": "So now Krylov has got 1,000 dimensional space." + }, + { + "text": "He's got a basis for it, 1,000 vectors that span 1,000 dimensional space." + }, + { + "text": "And he'll look at the matrix A only on that space." + }, + { + "text": "In other words, I won't go into detail about that." + }, + { + "text": "He restricts the matrix to this 1,000 dimensional space." + }, + { + "text": "And he hopes that it's captured." + }, + { + "text": "We hope that the eigenvector is virtually in that space." + }, + { + "text": "And actually, I wouldn't go up to, let me take a 9 out of that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk24.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..0f5c17cbd60debd628609f1ccf8848eb0fa9b730 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "100 dimensional would probably catch the eigenvector." + }, + { + "text": "So if the eigenvector is virtually in this space, then we can look at a matrix of order 100." + }, + { + "text": "We can bring A down to just see its action on that space." + }, + { + "text": "So I look at vectors V, which are some combination, C1b plus C2ab plus C3a squared b and C100 a to the 99th b, plus an error." + }, + { + "text": "And I'm going to ignore that error." + }, + { + "text": "Because I've gone up to dimension 100." + }, + { + "text": "I probably say it's pretty safe to ignore that error." + }, + { + "text": "And then in this space, just looking at the matrix A." + }, + { + "text": "So wherever A to the 100th comes in, forget it." + }, + { + "text": "Just think about the matrix A as multiplying vectors of this kind in this space." + }, + { + "text": "Then I have a 100 by 100 eigenvalue problem." + }, + { + "text": "And so the big matrix A is reduced to a matrix of size 100 by, do you see sort of what I'm saying, even though I'm not giving the details?" + }, + { + "text": "Think of a matrix A of size a million." + }, + { + "text": "And you apply it to Krylov vectors." + }, + { + "text": "So I call them little k for a Krylov vector in this 100-dimensional space." + }, + { + "text": "So they have a million minus 100, zero components, you could say, this k. This is in the Krylov space." + }, + { + "text": "This is A, a million, k, 100." + }, + { + "text": "It's a full, it's got a million components, but it's out of just 100-dimensional space." + }, + { + "text": "So when I multiply by A, it'll be mostly in, mostly in, partly in the Krylov space, k 100, and a piece out of k 100." + }, + { + "text": "And I just ignore that part of the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk25.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..41342712fde4874aa3c115a8d909e3bf6f2a0e59 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I have a 100 by 100 problem, and I've solved to find the eigenvalues." + }, + { + "text": "And they're a pretty good approximation to the eigenvalues, to the, hopefully, like the lowest 100 eigenvalues." + }, + { + "text": "I'd like to know that." + }, + { + "text": "But I might not be sure that this idea would give me the lowest 100, the first 100 eigenvalues of the million, of the matrix of size a million." + }, + { + "text": "I'm just taking a few minutes here to sort of wave hands about what Krylov, the Krylov idea would do." + }, + { + "text": "And I probably won't mention Krylov again this semester." + }, + { + "text": "So what it can do is look at this particular type of space, because we can get a basis for it quickly, just multiply again and again by A." + }, + { + "text": "Then we can orthogonalize that basis." + }, + { + "text": "That's Graham-Schmidt in some form." + }, + { + "text": "We're always going back to Graham-Schmidt." + }, + { + "text": "Then I have a 100 by 100." + }, + { + "text": "I have a subspace of size 100." + }, + { + "text": "I look at what the matrix does in that space." + }, + { + "text": "And I could look for, I could find eigenvalues restricted to that space." + }, + { + "text": "They wouldn't be the perfect eigenvalues, but they would be accurate." + }, + { + "text": "OK, so I didn't know it would take one class time to talk about finding eigenvalues and singular values, but we did some important things." + }, + { + "text": "We remembered that similarity is the thing to check, thing to preserve, because it doesn't change the eigenvalues." + }, + { + "text": "And then for singular values, what was the thing?" + }, + { + "text": "You could multiply left and right by different orthogonal matrices." + }, + { + "text": "And somehow, maybe that doesn't have an established name, multiplying left and right by a Q1 and a Q2 transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk26.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..2ce06055331ebe329b68e463d8ac9af5a66e37dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk26.json @@ -0,0 +1,35 @@ +[ + { + "text": "Yeah, but the idea is clear." + }, + { + "text": "And that doesn't change the singular values." + }, + { + "text": "We're ready to move now into maybe our next step, which we don't spend a long time on." + }, + { + "text": "We'll be like random sampling." + }, + { + "text": "What if your matrix is just way too big?" + }, + { + "text": "So that's a new, very new idea, very different idea in numerical linear algebra, is just to sample the matrix." + }, + { + "text": "Could you believe that the answer is going to come out right just for a random sample?" + }, + { + "text": "Well, the odds are in your favor." + }, + { + "text": "OK, so that'll be Wednesday, and then we have lots of new, we'll move onward after that." + }, + { + "text": "OK, see you Wednesday." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk3.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..f5acd4bdba4ba51520fdf921a1fc36684dfeaabb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I want to put R0 inverse over there." + }, + { + "text": "So R0." + }, + { + "text": "Now for Q0, I'm going to substitute." + }, + { + "text": "So what is Q0?" + }, + { + "text": "I multiply both sides of that equation by R0 inverse." + }, + { + "text": "So Q0 is A0 is, sorry, I said A and wrote Q. A0 R0 inverse." + }, + { + "text": "Right." + }, + { + "text": "For Q0, I've put in what it equals." + }, + { + "text": "And that's done it." + }, + { + "text": "That's exactly telling me that A1, which is this, equals this." + }, + { + "text": "And that's a similarity transformation." + }, + { + "text": "I have not changed the eigenvalues." + }, + { + "text": "So that's OK." + }, + { + "text": "The other thing, which is the, like you could say, the miracle in this thing, is that when I continue to do that for almost every matrix, the matrices begin to lose stuff off the diagonal, especially below the diagonal by the ordering that QR is done." + }, + { + "text": "So you tend to start with a matrix A0." + }, + { + "text": "You get a matrix A1, which is like a little smaller here." + }, + { + "text": "This part being not especially smaller." + }, + { + "text": "You do it again." + }, + { + "text": "This is even smaller." + }, + { + "text": "So I put even smaller A2, even smaller." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk4.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..a93c5efe93b5619eae3335916949e5ca1b9c543f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you keep going." + }, + { + "text": "And for most matrices, the result is that I don't know how many steps we want to think of taking, but we get quite small numbers here." + }, + { + "text": "So once we get small numbers here, little epsilons, that's everybody's shorthand for small numbers, what would you expect to see on the diagonal?" + }, + { + "text": "The eigenvalues." + }, + { + "text": "Because this has the same eigenvalues as this, as this, as this." + }, + { + "text": "And these little epsilons are not going to change the eigenvalues too much." + }, + { + "text": "So these will be, on the diagonal, will be close to the eigenvalues." + }, + { + "text": "And actually, what happens is this one comes first." + }, + { + "text": "That one is quite accurate first." + }, + { + "text": "I guess we should probably do a simple example to see this happen." + }, + { + "text": "Actually, I do an example in the notes." + }, + { + "text": "And let me say what happens." + }, + { + "text": "So I do a 2 by 2 example, which has something like cos theta, sine theta." + }, + { + "text": "I don't know what." + }, + { + "text": "I've forgotten what I took." + }, + { + "text": "And I don't have that page of notes here." + }, + { + "text": "Something here." + }, + { + "text": "Something here." + }, + { + "text": "Something here as a 0." + }, + { + "text": "And then a 1, after just one step, has sine cubed theta there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk5.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..2c1c69b5647ae63cfaad8af10731e95f060b6c81 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And numbers there that are getting much closer to the eigenvalues." + }, + { + "text": "Sorry that this isn't a full scale example." + }, + { + "text": "But the point of the example is here, that this off-diagonal entry gets cubed." + }, + { + "text": "And the next step will be its ninth power, and then the 27th power." + }, + { + "text": "So it's really quickly going to 0." + }, + { + "text": "And this happens." + }, + { + "text": "So cubic convergence is a prize." + }, + { + "text": "In numerical linear algebra." + }, + { + "text": "So that happens." + }, + { + "text": "So this arrived on the scene and quickly blew away all other methods that were being used to compute eigenvalues." + }, + { + "text": "But numerical people, being what they are, they wanted to improve it." + }, + { + "text": "Like, is there a way to make it faster?" + }, + { + "text": "And turned out there is." + }, + { + "text": "It turned out that the better way, basically the same idea, but just you're always looking for a simple change." + }, + { + "text": "And the idea of introducing a shift was tried." + }, + { + "text": "And turned out to work extremely well." + }, + { + "text": "So that's the improvement." + }, + { + "text": "So we take a1." + }, + { + "text": "No, so how does the shift work?" + }, + { + "text": "So instead of a0, have I got space here to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk6.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..e081a02643a2181251ac74e36b445d55b6192f14 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Instead of a0, I take a0 minus a shift." + }, + { + "text": "So a shift is some multiple of the identity." + }, + { + "text": "If I just move a matrix by a multiple of the identity, what happens to its eigenvectors?" + }, + { + "text": "What happens to its eigenvalues?" + }, + { + "text": "Something pretty simple, right?" + }, + { + "text": "Because I'm just shifting by si." + }, + { + "text": "What happens to its eigenvectors?" + }, + { + "text": "They're the same." + }, + { + "text": "And what happens to the eigenvalues?" + }, + { + "text": "They change by s. If a0v equals lambda v, then when I multiply this by v, there will be an extra." + }, + { + "text": "It'll be lambda minus s. Because the identity times the v is just v. So it just shifts all the eigenvalues by s. And you try to shift." + }, + { + "text": "You look for a shift." + }, + { + "text": "This would be great." + }, + { + "text": "If you knew lambda n, a shift there, you would be looking for 0 then, if you shifted them all by that lambda." + }, + { + "text": "And it turns out that would speed things up." + }, + { + "text": "So you work instead with this matrix as now, again, I'm factoring in a q0, r0." + }, + { + "text": "So that's the work of the method, is in doing Gram-Schmidt at every step." + }, + { + "text": "And then there's a little work in reversing the order." + }, + { + "text": "And then I want to undo the shift." + }, + { + "text": "So I do that factorization." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk7.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..212c509ec27724246ec3a49d4c24022c4979b516 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, let's see." + }, + { + "text": "You may have to help me to remember what I should do here." + }, + { + "text": "So I factor those." + }, + { + "text": "I reverse those." + }, + { + "text": "And then I think I add back the shift." + }, + { + "text": "And that's my A1." + }, + { + "text": "So I took A0." + }, + { + "text": "I shifted it." + }, + { + "text": "I worked with it, qr, reversed the order, rq, added back the shift to get a matrix." + }, + { + "text": "And what am I, of course, hoping about the matrix A1 and A0?" + }, + { + "text": "I'm hoping they're still similar." + }, + { + "text": "I'm hoping." + }, + { + "text": "So I did a shift." + }, + { + "text": "And I undid a shift." + }, + { + "text": "But of course, after doing a qr, I have to check, are these really still similar?" + }, + { + "text": "So let me just try to check that one again." + }, + { + "text": "Maybe I'll just, it's sitting right there." + }, + { + "text": "So let me do it again." + }, + { + "text": "I'm hoping that something, you know, where did we change?" + }, + { + "text": "Oh, yeah, here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk8.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..4e7fad6f92f20cdf436db6b8933b889b8a6fb34f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We showed that A1 was similar to A0." + }, + { + "text": "And I'm hoping that's probably still true, even, you know, the shift didn't mess that up." + }, + { + "text": "Let's just try." + }, + { + "text": "So A0, that's r0, q0 plus si." + }, + { + "text": "OK. And now what am I going to do?" + }, + { + "text": "I'm going to, what did I do before?" + }, + { + "text": "I figured out what q0 was from this." + }, + { + "text": "You remember?" + }, + { + "text": "So this is r0." + }, + { + "text": "Now I have to put in q0." + }, + { + "text": "But q0 is this thing inverse times this." + }, + { + "text": "Is this going to work?" + }, + { + "text": "I'm like hoping, but I don't think I wanted to get that." + }, + { + "text": "No, it's not q0 there." + }, + { + "text": "What do I put here?" + }, + { + "text": "And if it doesn't work, we'll leave it as an exercise." + }, + { + "text": "OK." + }, + { + "text": "So yeah, because I didn't sort of start right somehow." + }, + { + "text": "OK." + }, + { + "text": "So but let me just push along to see what happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk9.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..f66b5f2f317c991f9ad92b2dc38dd936ae5d8d21 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_1_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I'm plugging in for q0 here." + }, + { + "text": "I'm plugging in this matrix, so it shouldn't have inverted it, times r0 inverse." + }, + { + "text": "Who knows?" + }, + { + "text": "It might work." + }, + { + "text": "Who knows?" + }, + { + "text": "So that's the r0, q0." + }, + { + "text": "Right?" + }, + { + "text": "Is everybody with me?" + }, + { + "text": "Sorry about this." + }, + { + "text": "So r0 inverse." + }, + { + "text": "And then I have to add Si." + }, + { + "text": "So what have I done?" + }, + { + "text": "I've just pushed on, believing that this would work." + }, + { + "text": "Because it's the method that is constantly used." + }, + { + "text": "Now do I have?" + }, + { + "text": "What do I have there?" + }, + { + "text": "Is it working?" + }, + { + "text": "This is r0 A." + }, + { + "text": "That was, of course, A0." + }, + { + "text": "r0 A0 r0 inverse." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk0.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..afc91322b0d9d5a0ce3bfb215b0940ebb7754749 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "OK, why don't I start?" + }, + { + "text": "So I was hoping that we would have the next online assignment ready, but Julia 6, the new version, is slowing us down." + }, + { + "text": "And it'd probably be next time." + }, + { + "text": "But my lectures, of course, are, well, what I want to say perhaps is this isn't intended to be a course in numerical linear algebra." + }, + { + "text": "But I thought I couldn't let the whole semester go by without saying something about how to compute eigenvalues and singular values." + }, + { + "text": "Of course, you're going to call I or SVD or the equivalent in Python or Julia." + }, + { + "text": "But actually, the QR factorization that we spoke about, that we spoke entirely about last time is the key, unexpectedly, unexpectedly." + }, + { + "text": "You have a matrix A whose eigenvalues you want." + }, + { + "text": "So let's start with eigenvalues." + }, + { + "text": "And it might be a symmetric matrix." + }, + { + "text": "I'll stay with A rather than S because it doesn't have to be." + }, + { + "text": "But you get special always." + }, + { + "text": "You get something special if the matrix is symmetric." + }, + { + "text": "OK, so this method of computing eigenvalues, to me at least, and I think to many people, came like out of the blue a while ago, but not that long ago." + }, + { + "text": "And it worked very well." + }, + { + "text": "So here's the idea." + }, + { + "text": "It's called the QR method because you start by factoring your matrix into QR." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk1.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..f693f6b2ff21648d32a7af5f95cf39d07b0de862 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's A." + }, + { + "text": "Can we call it A0?" + }, + { + "text": "That's the matrix we start with whose eigenvalues we want." + }, + { + "text": "And I'll call these Q0 and R0." + }, + { + "text": "And you remember what that means, what's hiding behind those letters that I've written?" + }, + { + "text": "You have the columns of A, possibly symmetric, as I said, but not orthogonal, usually." + }, + { + "text": "So you find an orthogonal basis." + }, + { + "text": "You orthogonalize them." + }, + { + "text": "You line them up perpendicular to each other." + }, + { + "text": "And then there is a matrix R, which happens to be upper triangular, that connects." + }, + { + "text": "The not orthogonal basis with the orthogonal basis." + }, + { + "text": "Right, we constructed R step by step." + }, + { + "text": "And then the idea is write these in the reverse order." + }, + { + "text": "And that will be A1, the next A. OK, and then do it again, and again, and again." + }, + { + "text": "And so we're hoping, of course, that the eigenvalues didn't change." + }, + { + "text": "We're hoping that we can forget A0, start again with A1, and produce A2, and continue." + }, + { + "text": "So we're hoping two things." + }, + { + "text": "One will not be a hope." + }, + { + "text": "We can see that the eigenvalues of A1 and A0 are the same." + }, + { + "text": "So we have not changed the eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk10.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..6fb2da774bad3a68b507efacec13f9801a995312 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "r0 A0 r0 inverse." + }, + { + "text": "Good." + }, + { + "text": "Minus S. What have I got there?" + }, + { + "text": "From the r0 minus Si r0, what is that?" + }, + { + "text": "That's minus Si." + }, + { + "text": "Look, success." + }, + { + "text": "The r0 cancels the r0 inverse." + }, + { + "text": "So that term from that, that, that is minus Si." + }, + { + "text": "Cancels plus Si." + }, + { + "text": "I'm finished." + }, + { + "text": "And lo and behold, we have the same similarity." + }, + { + "text": "So we messed around by a multiple of the identity, and it actually makes the thing converge faster if we choose the shifts well." + }, + { + "text": "But basically, the same idea is still working." + }, + { + "text": "OK." + }, + { + "text": "So that's the QR method." + }, + { + "text": "Well, that's the method we haven't shown and won't show." + }, + { + "text": "Except for this half-completed example, I don't plan to prove that the lower triangular part begins to disappear, gets smaller and smaller and smaller, and then the eigenvalues pop up on the diagonal." + }, + { + "text": "It's amazing." + }, + { + "text": "Amazing." + }, + { + "text": "OK. Now, is there any other improvement we can make?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk11.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..9e5764513ae4ce678e41ecfcb72a4895642b01f6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's the method." + }, + { + "text": "And where is the work in using that method?" + }, + { + "text": "Because that's what we always focus on." + }, + { + "text": "Where are we spending computer time?" + }, + { + "text": "Well, we're spending computer time in doing the factorization." + }, + { + "text": "So it didn't cost anything to shift by the identity, but then we had to factor that into Q0, R0." + }, + { + "text": "Then it didn't cost much to multiply them in the opposite order." + }, + { + "text": "So the work was in QR." + }, + { + "text": "So could we think of anything to improve that aspect?" + }, + { + "text": "Could we think of anything there?" + }, + { + "text": "And then we've got a really first-class method." + }, + { + "text": "Well, if the matrix A, A0, the matrix we started with, had some zeros that allowed us to skip steps in doing the QR factorization." + }, + { + "text": "So what am I going to say?" + }, + { + "text": "I'm going to say if A or A0, our original matrix, has a bunch of zeros, let's say it's got a whole lot of zeros there." + }, + { + "text": "Maybe it's, well, OK." + }, + { + "text": "I overdid it here." + }, + { + "text": "I know the eigenvalues right off." + }, + { + "text": "But so the truth is I can't, saying that if that, it's not going to happen." + }, + { + "text": "But we can get zeros with one extra diagonal." + }, + { + "text": "That turns out, so here's the main diagonal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk12.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..ab7132ecacaf6cb9786d7b5f399f0082623bd923 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Everybody's got his eye on the main diagonal." + }, + { + "text": "And one diagonal, I can get a lot of zeros." + }, + { + "text": "But I can't by simple computations." + }, + { + "text": "And I'll show you how to get one." + }, + { + "text": "But I can't get all those to be 0, because then I would have the eigenvalues right there." + }, + { + "text": "And that, well, how do I know that I can't?" + }, + { + "text": "In elimination, ordinary solving AX equal B, you really do get to an upper triangular form." + }, + { + "text": "Some operator, some elimination steps, you plug away, and your matrix becomes upper triangular U." + }, + { + "text": "And you're golden." + }, + { + "text": "But that's too much to expect here." + }, + { + "text": "In fact, we know we can't do it by simple steps." + }, + { + "text": "Because if we could do it, if we could get to a U with a whole lower triangular part 0, we would have found the eigenvalues." + }, + { + "text": "And we know that the eigenvalues solve an equation of nth degree." + }, + { + "text": "And we know somebody proved centuries or more ago that you can't solve an nth degree equation by simple little steps." + }, + { + "text": "Right?" + }, + { + "text": "Do you know who that was?" + }, + { + "text": "And you know that fact?" + }, + { + "text": "And what degree does it apply to?" + }, + { + "text": "So that's an important fact that you sort of pick up in math." + }, + { + "text": "Yeah, what do you?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk13.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..5ef254fb5bc0df6883bfe89b2da2433a3da88094 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Fifth degree, yeah." + }, + { + "text": "So 5 by 5 and up would be, this is impossible." + }, + { + "text": "Impossible." + }, + { + "text": "There's no formula to find a simple formula for the lambdas." + }, + { + "text": "And similarly for the sigmas, the singular values." + }, + { + "text": "So the eigenvalues is definitely a level of difficulty beyond Ax equal b, the inverse matrix or something, the pivots." + }, + { + "text": "All that you can do exactly if you do exact arithmetic." + }, + { + "text": "We cannot find the lambdas exactly." + }, + { + "text": "But we can get as close as we like by continuing with the QR method." + }, + { + "text": "So yeah, in other words, we have to settle for, if we want to, at the beginning, improve our matrix before we start doing that stuff." + }, + { + "text": "We can get it with one extra diagonal." + }, + { + "text": "And do you know what kind of a matrix, whose name?" + }, + { + "text": "And I don't know why." + }, + { + "text": "Yeah, say it again." + }, + { + "text": "Upper Hessenberg." + }, + { + "text": "So upper is just like upper triangular." + }, + { + "text": "It's up there." + }, + { + "text": "But the key person's name is Hessenberg." + }, + { + "text": "As I say, that's a Hessenberg matrix." + }, + { + "text": "So Hessenberg matrix is a matrix with one triangular plus one more diagonal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk14.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..890f75c227f0ce9167ef179281769727e008c678 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "But lots of zeros." + }, + { + "text": "Order of n squared, something like almost like half n squared, not quite, but close, zeros." + }, + { + "text": "And you could show that those zeros stay zeros in QR." + }, + { + "text": "So that really pays off." + }, + { + "text": "It cuts the work down significantly." + }, + { + "text": "So the full QR method is step one, reduce A to Hessenberg form with these zeros." + }, + { + "text": "And when I say reduce, I mean find a similarity transformation, of course, because I want the eigenvalues of this to end up the same as the Hessen." + }, + { + "text": "I want to keep the same eigenvalues as I go." + }, + { + "text": "And then step two is QR on this Hessenberg matrix with shifts." + }, + { + "text": "So that's the code that would be programmed in IGAVE." + }, + { + "text": "That's what MATLAB and, well, really, MATLAB is appealing, like other matrix systems, is appealing to LAPAC and LINPAC." + }, + { + "text": "The team of professional numerical analysts really spent a lot of effort and time." + }, + { + "text": "The book LAPAC has 10 authors." + }, + { + "text": "And you can download any of these codes, like the eigenvalue code." + }, + { + "text": "So that's where MATLAB naturally, that's sort of the Bible for codes in linear algebra." + }, + { + "text": "OK, now, I think it's sort of interesting to know." + }, + { + "text": "And there is one more good thing to tell you about this method." + }, + { + "text": "And it applies if the matrix is symmetric." + }, + { + "text": "If the matrix is symmetric, then if we check all this, we could find that the matrices stayed symmetric." + }, + { + "text": "If A0 is symmetric, I can check." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk15.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..1cdfb555c6b2be5bd3044a831ed3f643f560293a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "You could easily check through this, and you would discover that A1 is also symmetric." + }, + { + "text": "It turns out you could rewrite this with a Q0 and a Q0 inverse on the other side." + }, + { + "text": "But that Q0 inverse is the same as Q0 transpose, because it's an orthogonal matrix, and symmetry would fall out." + }, + { + "text": "So if it's symmetric, and it's in Hessenberg form, and it stays symmetric at every step, what can you tell me about a symmetric Hessenberg matrix?" + }, + { + "text": "It's only got, yeah, you just erase all these." + }, + { + "text": "If there are zeros there, and if the matrix is symmetric, then we can safely predict that it will only have one diagonal above, one non-zero diagonal above the main diagonal." + }, + { + "text": "In fact, it'll stay symmetric." + }, + { + "text": "So now I should write symmetric Hessenberg matrix, n equals tri-diagonal matrix." + }, + { + "text": "Yeah, three diagonals." + }, + { + "text": "So now you really have reduced the time to do QR, because you've got a tri-diagonal matrix." + }, + { + "text": "It'll stay tri-diagonal in all these steps." + }, + { + "text": "So you're working with just 3n numbers." + }, + { + "text": "Well, actually, 2n, because the diagonal above and the diagonal below are the same." + }, + { + "text": "You're working with just 2n numbers instead of order n squared, and it just goes like a bomb." + }, + { + "text": "So that's I for symmetric matrices." + }, + { + "text": "And you see that it was all based, that really the heart of the algorithm was QR." + }, + { + "text": "So that's my, it took half the class to report on the favorite way, the EIG way, to find eigenvalues." + }, + { + "text": "Oh, I should say something about singular values." + }, + { + "text": "So singular values, of course, the singular values of the matrix are the eigenvalues of A transpose A, square root of those eigenvalues." + }, + { + "text": "But you wouldn't do it that way." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk16.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..7989fa8939f6d17bfb6b36b82c96bbd76b92a4f6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "You would never form A transpose A. Oh, I didn't mention the other thing you would never, ever, ever do." + }, + { + "text": "So let me just put it here." + }, + { + "text": "This is like in disgrace to solve that equation." + }, + { + "text": "It's like, OK, back to first grade, because that's not, that's very bad." + }, + { + "text": "A determinant, first of all, it's extremely slow, extremely slow." + }, + { + "text": "And the determinant is packing all this n squared pieces of information into n coefficients, and it's hopelessly ill-conditioned." + }, + { + "text": "Yeah, you just, you lose information all the time." + }, + { + "text": "So really, if this is going on camera, it better go on camera with an x, because don't do it." + }, + { + "text": "OK. Yeah." + }, + { + "text": "So where was I?" + }, + { + "text": "Singular values." + }, + { + "text": "So A transpose A." + }, + { + "text": "So again, let's think about what you could do at the beginning before starting on QR for A transpose A, or for the matrix A." + }, + { + "text": "What could you do with orthogonal matrices?" + }, + { + "text": "So I guess, what did we say about symmetric matrices?" + }, + { + "text": "So here's what I said about symmetric matrices." + }, + { + "text": "If you give me a symmetric matrix, I can, in just a simple number of simple steps, make it tridiagonal." + }, + { + "text": "I can't make it diagonal, because then I'd be finding the eigenvalues, and Abel, who was the first person to see that that was impossible, forbids it." + }, + { + "text": "But so let me write down what I'm saying here." + }, + { + "text": "If I have a symmetric matrix S, I can find a bunch of Q's and Q transposes, and I can put them all together into one big Q, and it's transposed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk17.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..08d99076ccc98b0932858bac2de5382359f2d221 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I know about the eigenvalues of that matrix?" + }, + { + "text": "Q is orthogonal always." + }, + { + "text": "So what can you tell me about the, this is the same as Q S Q inverse, and therefore, the eigenvalues are the same." + }, + { + "text": "It's similar to S. And it becomes tridiagonal after I find a good Q." + }, + { + "text": "Now, and therefore, same lambdas, tridiagonal with the same lambdas." + }, + { + "text": "Now, what am I thinking about here?" + }, + { + "text": "I'm thinking about, tell me the corresponding possibility about singular values." + }, + { + "text": "I want to do something to my matrix." + }, + { + "text": "Now, I'm always taking a general matrix A." + }, + { + "text": "And I'm looking for its singular values." + }, + { + "text": "And I'm looking to simplify it." + }, + { + "text": "And what am I allowed to do?" + }, + { + "text": "Yeah, I guess my question is, similarity transformations left the eigenvalues alone." + }, + { + "text": "What can I do that leaves the singular values alone?" + }, + { + "text": "That's a fundamental question, because it was so fundamental for eigenvalues." + }, + { + "text": "By doing this, a matrix and its inverse, I got something similar." + }, + { + "text": "And I checked even in this class that the eigenvalues, same lambdas." + }, + { + "text": "Now I want a whole line that ends up with the same sigmas." + }, + { + "text": "And I want you to tell me what I'm allowed to do to the matrix without changing the sigmas." + }, + { + "text": "So maybe don't shout it out immediately." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk18.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..31cc3c0860684bbd35bab2fb28f2d606a8921e5b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let everybody think." + }, + { + "text": "What am I allowed to do to a matrix?" + }, + { + "text": "Every matrix has got these singular values." + }, + { + "text": "And now I want to make it a better matrix with more 0's or something." + }, + { + "text": "If I do that to it, does that change the sigmas?" + }, + { + "text": "Can I do more than that to it?" + }, + { + "text": "What can I do?" + }, + { + "text": "What group of matrices will have the same sigmas as my starting matrix A?" + }, + { + "text": "So that's a basic, basic question about singular values and the SVD." + }, + { + "text": "So let's think of the answer together." + }, + { + "text": "So it's connected to the SVD." + }, + { + "text": "So let me remember the SVD." + }, + { + "text": "The SVD, I have some orthogonal matrix, then the singular value matrix, SV for singular values, and then another orthogonal matrix." + }, + { + "text": "What could I do to that equation that would not touch this guy?" + }, + { + "text": "So I'm asking what invariance, because not touching it means leaving it not varying." + }, + { + "text": "So I'm looking for under what operations are the singular values invariant?" + }, + { + "text": "When I was looking at eigenvalues, this was the operation." + }, + { + "text": "Well, it didn't have to be orthogonal." + }, + { + "text": "It's something, and it's inverse." + }, + { + "text": "But now what is it up there?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk19.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..01b201f72f3bceb5bd8b70cfc01d55a2e2ff2a71 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "What could I do to that matrix A?" + }, + { + "text": "Could I multiply by Q?" + }, + { + "text": "Could I throw in a Q?" + }, + { + "text": "Maybe not even on the other end." + }, + { + "text": "If I throw in an orthogonal Q, do I change the singular values or do I not change them?" + }, + { + "text": "Fundamental question." + }, + { + "text": "The answer is no, I don't change them." + }, + { + "text": "I'm allowed to do that, because here's an orthogonal matrix, a Q times U." + }, + { + "text": "If both of those are orthogonal, then the product is." + }, + { + "text": "Everybody knows that a product of two orthogonal matrix is still orthogonal." + }, + { + "text": "Better know that." + }, + { + "text": "Better know that." + }, + { + "text": "Yeah." + }, + { + "text": "So if I have an orthogonal matrix Q and an orthogonal matrix U, I claim that this is still orthogonal." + }, + { + "text": "And how do I check it?" + }, + { + "text": "Well, I use some test for orthogonality." + }, + { + "text": "What would be the test you like to use?" + }, + { + "text": "The inverse is the same as the transpose." + }, + { + "text": "You like that test?" + }, + { + "text": "So I'll invert it." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk2.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..49f68a61aecdf81153b85d35f02c4fd1ad64e79f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "How do we see that?" + }, + { + "text": "If you had to show that two matrices had the same eigenvalues, would you compute all the eigenvalues and compare them?" + }, + { + "text": "Certainly not." + }, + { + "text": "What would you do?" + }, + { + "text": "What's the best test, the usual test, the usual thing you would want to show?" + }, + { + "text": "They're similar." + }, + { + "text": "That's right." + }, + { + "text": "So the claim would be that these two matrices are similar." + }, + { + "text": "Right." + }, + { + "text": "So maybe we should show that." + }, + { + "text": "So we want to write A1 in a different way." + }, + { + "text": "So the claim is A1 is similar to A." + }, + { + "text": "So we just have to figure out." + }, + { + "text": "We have to get A1 to A0." + }, + { + "text": "So here's A1." + }, + { + "text": "OK." + }, + { + "text": "So A1, I want to show that that's right." + }, + { + "text": "So that's R0, Q0." + }, + { + "text": "But what is Q0?" + }, + { + "text": "From here, Q0 is what we is R. Q0 is, what do I want?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk20.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..35801c36445d73fe11e2f6274bad6dd29215b8e2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Q U inverse." + }, + { + "text": "Of course, for any matrix, that's U inverse Q inverse." + }, + { + "text": "But these were separately orthogonal, so that's U transpose Q transpose." + }, + { + "text": "And that is the same as Q U transpose." + }, + { + "text": "Yeah." + }, + { + "text": "So I use the orthogonality of U and the orthogonality of Q to conclude that the inverse is the transpose." + }, + { + "text": "So the answer is yes, I could do that." + }, + { + "text": "Now, with singular value, with eigenvalues, I had to multiply on the other side by Q inverse or Q transpose." + }, + { + "text": "Do I have to do that now?" + }, + { + "text": "No." + }, + { + "text": "What can I do on the right-hand side?" + }, + { + "text": "I can multiply by." + }, + { + "text": "I can leave it alone." + }, + { + "text": "Then it has the same singular values because it's the same sigma in there." + }, + { + "text": "If I have a orthogonal matrix times a diagonal times an orthogonal, that diagonal, positive diagonal, is going to be sigma." + }, + { + "text": "So what can I do on this side?" + }, + { + "text": "I could multiply by any orthogonal matrix on that side, too." + }, + { + "text": "So let's call this guy Q1 and this guy Q2." + }, + { + "text": "I still have an orthogonal matrix there, orthogonal matrix there, and the same sigma popped in the middle." + }, + { + "text": "So that's what you're allowed to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk21.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..8733bff8727902ad93fdca4f142729506ca43859 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "That gives us more freedom." + }, + { + "text": "Before, when we had to do similarity transformations with the same guy, we got it to be tridiagonal." + }, + { + "text": "But now we're allowed to do more stuff." + }, + { + "text": "We're allowed to use different orthogonal matrices on the left and right." + }, + { + "text": "And we can reduce it even further from tridiagonal to bidiagonal." + }, + { + "text": "So the first step is getting 0." + }, + { + "text": "The step of getting 0s reduces it all the way to that with all 0s there." + }, + { + "text": "So it's easier." + }, + { + "text": "Then I work on this." + }, + { + "text": "I work on using a QR type idea, some method like that." + }, + { + "text": "So everybody's seeing that our algorithm has got two stages." + }, + { + "text": "One is get a lot of 0s and get them in places that will stay 0 as part 2 of the algorithm gets going." + }, + { + "text": "And then run part 2 of the algorithm." + }, + { + "text": "You're staying with each step is very fast now because doing a QR factorization is fast." + }, + { + "text": "Was there a question?" + }, + { + "text": "Yeah." + }, + { + "text": "So I would call this bidiagonal, of course." + }, + { + "text": "And everybody recognizes that if I have a bidiagonal matrix, call it A or A0 or whatever." + }, + { + "text": "Then what do you think about A transpose A?" + }, + { + "text": "What would A transpose A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk22.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..8562bc4837b9c78d63d64c389d0c913d3dc7d8a2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "If that was A, what could you tell me about A transpose A?" + }, + { + "text": "Could you multiply matrices, like knowing where the non-zeros are, like in your head, and get an idea of where?" + }, + { + "text": "So if I have a bidiagonal matrix A, then sort of implicitly in the SVD, I'm looking at A transpose A." + }, + { + "text": "And what would be true about A transpose A?" + }, + { + "text": "It would be tridiagonal." + }, + { + "text": "So what I've done here and what I've done there just match up." + }, + { + "text": "If you don't want to change singular values, you can get all the way to here." + }, + { + "text": "But then to find those singular values, that would involve A transpose A." + }, + { + "text": "It would be symmetric and tridiagonal." + }, + { + "text": "And then you'd be in that game." + }, + { + "text": "So those are the basic facts of I and SVD." + }, + { + "text": "For matrices of order up to 1,000, say." + }, + { + "text": "I'm not enough of an expert to know where." + }, + { + "text": "Maybe higher, because in perfect math, it's going to take infinitely many steps." + }, + { + "text": "Or Abel would be very surprised." + }, + { + "text": "He would see you solving for eigenvalues and then to re-equation by a whole lot of little steps and getting them exactly right." + }, + { + "text": "That won't happen." + }, + { + "text": "But you get them within epsilon in a number of steps that's like n cubed." + }, + { + "text": "So that's pretty impressive." + }, + { + "text": "The eigenvalue problem is being solved, in quotes, by a fast method that gets you a good answer within a tolerance in n cubed steps." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk23.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..37baceeccac2b563da8271de17d70bb205a69d4d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Right." + }, + { + "text": "So that's great as long as n isn't too big." + }, + { + "text": "And then when n is too big, which of course happens, you have to think again." + }, + { + "text": "So this method is a giant success up to large matrices." + }, + { + "text": "But then you have to think again." + }, + { + "text": "And what is involved in thinking again?" + }, + { + "text": "Well, I guess more thinking." + }, + { + "text": "So what do you do if the matrix is bigger?" + }, + { + "text": "I guess that Krylov would say, use my method." + }, + { + "text": "So Krylov would say, especially if your matrix is sparse." + }, + { + "text": "Can we just remember what Krylov was?" + }, + { + "text": "Krylov started with a vector b, multiplied it by a, multiplied that by a, and got up to, let's say, a to the 999b." + }, + { + "text": "So now Krylov has got 1,000 dimensional space." + }, + { + "text": "He's got a basis for it, 1,000 vectors that span 1,000 dimensional space." + }, + { + "text": "And he'll look at the matrix A only on that space." + }, + { + "text": "In other words, I won't go into detail about that." + }, + { + "text": "He restricts the matrix to this 1,000 dimensional space." + }, + { + "text": "And he hopes that it's captured." + }, + { + "text": "We hope that the eigenvector is virtually in that space." + }, + { + "text": "And actually, I wouldn't go up to, let me take a 9 out of that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk24.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..0f5c17cbd60debd628609f1ccf8848eb0fa9b730 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "100 dimensional would probably catch the eigenvector." + }, + { + "text": "So if the eigenvector is virtually in this space, then we can look at a matrix of order 100." + }, + { + "text": "We can bring A down to just see its action on that space." + }, + { + "text": "So I look at vectors V, which are some combination, C1b plus C2ab plus C3a squared b and C100 a to the 99th b, plus an error." + }, + { + "text": "And I'm going to ignore that error." + }, + { + "text": "Because I've gone up to dimension 100." + }, + { + "text": "I probably say it's pretty safe to ignore that error." + }, + { + "text": "And then in this space, just looking at the matrix A." + }, + { + "text": "So wherever A to the 100th comes in, forget it." + }, + { + "text": "Just think about the matrix A as multiplying vectors of this kind in this space." + }, + { + "text": "Then I have a 100 by 100 eigenvalue problem." + }, + { + "text": "And so the big matrix A is reduced to a matrix of size 100 by, do you see sort of what I'm saying, even though I'm not giving the details?" + }, + { + "text": "Think of a matrix A of size a million." + }, + { + "text": "And you apply it to Krylov vectors." + }, + { + "text": "So I call them little k for a Krylov vector in this 100-dimensional space." + }, + { + "text": "So they have a million minus 100, zero components, you could say, this k. This is in the Krylov space." + }, + { + "text": "This is A, a million, k, 100." + }, + { + "text": "It's a full, it's got a million components, but it's out of just 100-dimensional space." + }, + { + "text": "So when I multiply by A, it'll be mostly in, mostly in, partly in the Krylov space, k 100, and a piece out of k 100." + }, + { + "text": "And I just ignore that part of the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk25.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..41342712fde4874aa3c115a8d909e3bf6f2a0e59 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I have a 100 by 100 problem, and I've solved to find the eigenvalues." + }, + { + "text": "And they're a pretty good approximation to the eigenvalues, to the, hopefully, like the lowest 100 eigenvalues." + }, + { + "text": "I'd like to know that." + }, + { + "text": "But I might not be sure that this idea would give me the lowest 100, the first 100 eigenvalues of the million, of the matrix of size a million." + }, + { + "text": "I'm just taking a few minutes here to sort of wave hands about what Krylov, the Krylov idea would do." + }, + { + "text": "And I probably won't mention Krylov again this semester." + }, + { + "text": "So what it can do is look at this particular type of space, because we can get a basis for it quickly, just multiply again and again by A." + }, + { + "text": "Then we can orthogonalize that basis." + }, + { + "text": "That's Graham-Schmidt in some form." + }, + { + "text": "We're always going back to Graham-Schmidt." + }, + { + "text": "Then I have a 100 by 100." + }, + { + "text": "I have a subspace of size 100." + }, + { + "text": "I look at what the matrix does in that space." + }, + { + "text": "And I could look for, I could find eigenvalues restricted to that space." + }, + { + "text": "They wouldn't be the perfect eigenvalues, but they would be accurate." + }, + { + "text": "OK, so I didn't know it would take one class time to talk about finding eigenvalues and singular values, but we did some important things." + }, + { + "text": "We remembered that similarity is the thing to check, thing to preserve, because it doesn't change the eigenvalues." + }, + { + "text": "And then for singular values, what was the thing?" + }, + { + "text": "You could multiply left and right by different orthogonal matrices." + }, + { + "text": "And somehow, maybe that doesn't have an established name, multiplying left and right by a Q1 and a Q2 transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk26.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..2ce06055331ebe329b68e463d8ac9af5a66e37dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk26.json @@ -0,0 +1,35 @@ +[ + { + "text": "Yeah, but the idea is clear." + }, + { + "text": "And that doesn't change the singular values." + }, + { + "text": "We're ready to move now into maybe our next step, which we don't spend a long time on." + }, + { + "text": "We'll be like random sampling." + }, + { + "text": "What if your matrix is just way too big?" + }, + { + "text": "So that's a new, very new idea, very different idea in numerical linear algebra, is just to sample the matrix." + }, + { + "text": "Could you believe that the answer is going to come out right just for a random sample?" + }, + { + "text": "Well, the odds are in your favor." + }, + { + "text": "OK, so that'll be Wednesday, and then we have lots of new, we'll move onward after that." + }, + { + "text": "OK, see you Wednesday." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk3.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..f5acd4bdba4ba51520fdf921a1fc36684dfeaabb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I want to put R0 inverse over there." + }, + { + "text": "So R0." + }, + { + "text": "Now for Q0, I'm going to substitute." + }, + { + "text": "So what is Q0?" + }, + { + "text": "I multiply both sides of that equation by R0 inverse." + }, + { + "text": "So Q0 is A0 is, sorry, I said A and wrote Q. A0 R0 inverse." + }, + { + "text": "Right." + }, + { + "text": "For Q0, I've put in what it equals." + }, + { + "text": "And that's done it." + }, + { + "text": "That's exactly telling me that A1, which is this, equals this." + }, + { + "text": "And that's a similarity transformation." + }, + { + "text": "I have not changed the eigenvalues." + }, + { + "text": "So that's OK." + }, + { + "text": "The other thing, which is the, like you could say, the miracle in this thing, is that when I continue to do that for almost every matrix, the matrices begin to lose stuff off the diagonal, especially below the diagonal by the ordering that QR is done." + }, + { + "text": "So you tend to start with a matrix A0." + }, + { + "text": "You get a matrix A1, which is like a little smaller here." + }, + { + "text": "This part being not especially smaller." + }, + { + "text": "You do it again." + }, + { + "text": "This is even smaller." + }, + { + "text": "So I put even smaller A2, even smaller." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk4.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..a93c5efe93b5619eae3335916949e5ca1b9c543f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you keep going." + }, + { + "text": "And for most matrices, the result is that I don't know how many steps we want to think of taking, but we get quite small numbers here." + }, + { + "text": "So once we get small numbers here, little epsilons, that's everybody's shorthand for small numbers, what would you expect to see on the diagonal?" + }, + { + "text": "The eigenvalues." + }, + { + "text": "Because this has the same eigenvalues as this, as this, as this." + }, + { + "text": "And these little epsilons are not going to change the eigenvalues too much." + }, + { + "text": "So these will be, on the diagonal, will be close to the eigenvalues." + }, + { + "text": "And actually, what happens is this one comes first." + }, + { + "text": "That one is quite accurate first." + }, + { + "text": "I guess we should probably do a simple example to see this happen." + }, + { + "text": "Actually, I do an example in the notes." + }, + { + "text": "And let me say what happens." + }, + { + "text": "So I do a 2 by 2 example, which has something like cos theta, sine theta." + }, + { + "text": "I don't know what." + }, + { + "text": "I've forgotten what I took." + }, + { + "text": "And I don't have that page of notes here." + }, + { + "text": "Something here." + }, + { + "text": "Something here." + }, + { + "text": "Something here as a 0." + }, + { + "text": "And then a 1, after just one step, has sine cubed theta there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk5.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..2c1c69b5647ae63cfaad8af10731e95f060b6c81 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And numbers there that are getting much closer to the eigenvalues." + }, + { + "text": "Sorry that this isn't a full scale example." + }, + { + "text": "But the point of the example is here, that this off-diagonal entry gets cubed." + }, + { + "text": "And the next step will be its ninth power, and then the 27th power." + }, + { + "text": "So it's really quickly going to 0." + }, + { + "text": "And this happens." + }, + { + "text": "So cubic convergence is a prize." + }, + { + "text": "In numerical linear algebra." + }, + { + "text": "So that happens." + }, + { + "text": "So this arrived on the scene and quickly blew away all other methods that were being used to compute eigenvalues." + }, + { + "text": "But numerical people, being what they are, they wanted to improve it." + }, + { + "text": "Like, is there a way to make it faster?" + }, + { + "text": "And turned out there is." + }, + { + "text": "It turned out that the better way, basically the same idea, but just you're always looking for a simple change." + }, + { + "text": "And the idea of introducing a shift was tried." + }, + { + "text": "And turned out to work extremely well." + }, + { + "text": "So that's the improvement." + }, + { + "text": "So we take a1." + }, + { + "text": "No, so how does the shift work?" + }, + { + "text": "So instead of a0, have I got space here to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk6.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..e081a02643a2181251ac74e36b445d55b6192f14 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Instead of a0, I take a0 minus a shift." + }, + { + "text": "So a shift is some multiple of the identity." + }, + { + "text": "If I just move a matrix by a multiple of the identity, what happens to its eigenvectors?" + }, + { + "text": "What happens to its eigenvalues?" + }, + { + "text": "Something pretty simple, right?" + }, + { + "text": "Because I'm just shifting by si." + }, + { + "text": "What happens to its eigenvectors?" + }, + { + "text": "They're the same." + }, + { + "text": "And what happens to the eigenvalues?" + }, + { + "text": "They change by s. If a0v equals lambda v, then when I multiply this by v, there will be an extra." + }, + { + "text": "It'll be lambda minus s. Because the identity times the v is just v. So it just shifts all the eigenvalues by s. And you try to shift." + }, + { + "text": "You look for a shift." + }, + { + "text": "This would be great." + }, + { + "text": "If you knew lambda n, a shift there, you would be looking for 0 then, if you shifted them all by that lambda." + }, + { + "text": "And it turns out that would speed things up." + }, + { + "text": "So you work instead with this matrix as now, again, I'm factoring in a q0, r0." + }, + { + "text": "So that's the work of the method, is in doing Gram-Schmidt at every step." + }, + { + "text": "And then there's a little work in reversing the order." + }, + { + "text": "And then I want to undo the shift." + }, + { + "text": "So I do that factorization." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk7.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..212c509ec27724246ec3a49d4c24022c4979b516 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, let's see." + }, + { + "text": "You may have to help me to remember what I should do here." + }, + { + "text": "So I factor those." + }, + { + "text": "I reverse those." + }, + { + "text": "And then I think I add back the shift." + }, + { + "text": "And that's my A1." + }, + { + "text": "So I took A0." + }, + { + "text": "I shifted it." + }, + { + "text": "I worked with it, qr, reversed the order, rq, added back the shift to get a matrix." + }, + { + "text": "And what am I, of course, hoping about the matrix A1 and A0?" + }, + { + "text": "I'm hoping they're still similar." + }, + { + "text": "I'm hoping." + }, + { + "text": "So I did a shift." + }, + { + "text": "And I undid a shift." + }, + { + "text": "But of course, after doing a qr, I have to check, are these really still similar?" + }, + { + "text": "So let me just try to check that one again." + }, + { + "text": "Maybe I'll just, it's sitting right there." + }, + { + "text": "So let me do it again." + }, + { + "text": "I'm hoping that something, you know, where did we change?" + }, + { + "text": "Oh, yeah, here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk8.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..4e7fad6f92f20cdf436db6b8933b889b8a6fb34f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We showed that A1 was similar to A0." + }, + { + "text": "And I'm hoping that's probably still true, even, you know, the shift didn't mess that up." + }, + { + "text": "Let's just try." + }, + { + "text": "So A0, that's r0, q0 plus si." + }, + { + "text": "OK. And now what am I going to do?" + }, + { + "text": "I'm going to, what did I do before?" + }, + { + "text": "I figured out what q0 was from this." + }, + { + "text": "You remember?" + }, + { + "text": "So this is r0." + }, + { + "text": "Now I have to put in q0." + }, + { + "text": "But q0 is this thing inverse times this." + }, + { + "text": "Is this going to work?" + }, + { + "text": "I'm like hoping, but I don't think I wanted to get that." + }, + { + "text": "No, it's not q0 there." + }, + { + "text": "What do I put here?" + }, + { + "text": "And if it doesn't work, we'll leave it as an exercise." + }, + { + "text": "OK." + }, + { + "text": "So yeah, because I didn't sort of start right somehow." + }, + { + "text": "OK." + }, + { + "text": "So but let me just push along to see what happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk9.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..f66b5f2f317c991f9ad92b2dc38dd936ae5d8d21 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_2_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I'm plugging in for q0 here." + }, + { + "text": "I'm plugging in this matrix, so it shouldn't have inverted it, times r0 inverse." + }, + { + "text": "Who knows?" + }, + { + "text": "It might work." + }, + { + "text": "Who knows?" + }, + { + "text": "So that's the r0, q0." + }, + { + "text": "Right?" + }, + { + "text": "Is everybody with me?" + }, + { + "text": "Sorry about this." + }, + { + "text": "So r0 inverse." + }, + { + "text": "And then I have to add Si." + }, + { + "text": "So what have I done?" + }, + { + "text": "I've just pushed on, believing that this would work." + }, + { + "text": "Because it's the method that is constantly used." + }, + { + "text": "Now do I have?" + }, + { + "text": "What do I have there?" + }, + { + "text": "Is it working?" + }, + { + "text": "This is r0 A." + }, + { + "text": "That was, of course, A0." + }, + { + "text": "r0 A0 r0 inverse." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk0.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..afc91322b0d9d5a0ce3bfb215b0940ebb7754749 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "OK, why don't I start?" + }, + { + "text": "So I was hoping that we would have the next online assignment ready, but Julia 6, the new version, is slowing us down." + }, + { + "text": "And it'd probably be next time." + }, + { + "text": "But my lectures, of course, are, well, what I want to say perhaps is this isn't intended to be a course in numerical linear algebra." + }, + { + "text": "But I thought I couldn't let the whole semester go by without saying something about how to compute eigenvalues and singular values." + }, + { + "text": "Of course, you're going to call I or SVD or the equivalent in Python or Julia." + }, + { + "text": "But actually, the QR factorization that we spoke about, that we spoke entirely about last time is the key, unexpectedly, unexpectedly." + }, + { + "text": "You have a matrix A whose eigenvalues you want." + }, + { + "text": "So let's start with eigenvalues." + }, + { + "text": "And it might be a symmetric matrix." + }, + { + "text": "I'll stay with A rather than S because it doesn't have to be." + }, + { + "text": "But you get special always." + }, + { + "text": "You get something special if the matrix is symmetric." + }, + { + "text": "OK, so this method of computing eigenvalues, to me at least, and I think to many people, came like out of the blue a while ago, but not that long ago." + }, + { + "text": "And it worked very well." + }, + { + "text": "So here's the idea." + }, + { + "text": "It's called the QR method because you start by factoring your matrix into QR." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk1.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..f693f6b2ff21648d32a7af5f95cf39d07b0de862 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's A." + }, + { + "text": "Can we call it A0?" + }, + { + "text": "That's the matrix we start with whose eigenvalues we want." + }, + { + "text": "And I'll call these Q0 and R0." + }, + { + "text": "And you remember what that means, what's hiding behind those letters that I've written?" + }, + { + "text": "You have the columns of A, possibly symmetric, as I said, but not orthogonal, usually." + }, + { + "text": "So you find an orthogonal basis." + }, + { + "text": "You orthogonalize them." + }, + { + "text": "You line them up perpendicular to each other." + }, + { + "text": "And then there is a matrix R, which happens to be upper triangular, that connects." + }, + { + "text": "The not orthogonal basis with the orthogonal basis." + }, + { + "text": "Right, we constructed R step by step." + }, + { + "text": "And then the idea is write these in the reverse order." + }, + { + "text": "And that will be A1, the next A. OK, and then do it again, and again, and again." + }, + { + "text": "And so we're hoping, of course, that the eigenvalues didn't change." + }, + { + "text": "We're hoping that we can forget A0, start again with A1, and produce A2, and continue." + }, + { + "text": "So we're hoping two things." + }, + { + "text": "One will not be a hope." + }, + { + "text": "We can see that the eigenvalues of A1 and A0 are the same." + }, + { + "text": "So we have not changed the eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk10.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..6fb2da774bad3a68b507efacec13f9801a995312 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "r0 A0 r0 inverse." + }, + { + "text": "Good." + }, + { + "text": "Minus S. What have I got there?" + }, + { + "text": "From the r0 minus Si r0, what is that?" + }, + { + "text": "That's minus Si." + }, + { + "text": "Look, success." + }, + { + "text": "The r0 cancels the r0 inverse." + }, + { + "text": "So that term from that, that, that is minus Si." + }, + { + "text": "Cancels plus Si." + }, + { + "text": "I'm finished." + }, + { + "text": "And lo and behold, we have the same similarity." + }, + { + "text": "So we messed around by a multiple of the identity, and it actually makes the thing converge faster if we choose the shifts well." + }, + { + "text": "But basically, the same idea is still working." + }, + { + "text": "OK." + }, + { + "text": "So that's the QR method." + }, + { + "text": "Well, that's the method we haven't shown and won't show." + }, + { + "text": "Except for this half-completed example, I don't plan to prove that the lower triangular part begins to disappear, gets smaller and smaller and smaller, and then the eigenvalues pop up on the diagonal." + }, + { + "text": "It's amazing." + }, + { + "text": "Amazing." + }, + { + "text": "OK. Now, is there any other improvement we can make?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk11.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..9e5764513ae4ce678e41ecfcb72a4895642b01f6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's the method." + }, + { + "text": "And where is the work in using that method?" + }, + { + "text": "Because that's what we always focus on." + }, + { + "text": "Where are we spending computer time?" + }, + { + "text": "Well, we're spending computer time in doing the factorization." + }, + { + "text": "So it didn't cost anything to shift by the identity, but then we had to factor that into Q0, R0." + }, + { + "text": "Then it didn't cost much to multiply them in the opposite order." + }, + { + "text": "So the work was in QR." + }, + { + "text": "So could we think of anything to improve that aspect?" + }, + { + "text": "Could we think of anything there?" + }, + { + "text": "And then we've got a really first-class method." + }, + { + "text": "Well, if the matrix A, A0, the matrix we started with, had some zeros that allowed us to skip steps in doing the QR factorization." + }, + { + "text": "So what am I going to say?" + }, + { + "text": "I'm going to say if A or A0, our original matrix, has a bunch of zeros, let's say it's got a whole lot of zeros there." + }, + { + "text": "Maybe it's, well, OK." + }, + { + "text": "I overdid it here." + }, + { + "text": "I know the eigenvalues right off." + }, + { + "text": "But so the truth is I can't, saying that if that, it's not going to happen." + }, + { + "text": "But we can get zeros with one extra diagonal." + }, + { + "text": "That turns out, so here's the main diagonal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk12.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..ab7132ecacaf6cb9786d7b5f399f0082623bd923 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Everybody's got his eye on the main diagonal." + }, + { + "text": "And one diagonal, I can get a lot of zeros." + }, + { + "text": "But I can't by simple computations." + }, + { + "text": "And I'll show you how to get one." + }, + { + "text": "But I can't get all those to be 0, because then I would have the eigenvalues right there." + }, + { + "text": "And that, well, how do I know that I can't?" + }, + { + "text": "In elimination, ordinary solving AX equal B, you really do get to an upper triangular form." + }, + { + "text": "Some operator, some elimination steps, you plug away, and your matrix becomes upper triangular U." + }, + { + "text": "And you're golden." + }, + { + "text": "But that's too much to expect here." + }, + { + "text": "In fact, we know we can't do it by simple steps." + }, + { + "text": "Because if we could do it, if we could get to a U with a whole lower triangular part 0, we would have found the eigenvalues." + }, + { + "text": "And we know that the eigenvalues solve an equation of nth degree." + }, + { + "text": "And we know somebody proved centuries or more ago that you can't solve an nth degree equation by simple little steps." + }, + { + "text": "Right?" + }, + { + "text": "Do you know who that was?" + }, + { + "text": "And you know that fact?" + }, + { + "text": "And what degree does it apply to?" + }, + { + "text": "So that's an important fact that you sort of pick up in math." + }, + { + "text": "Yeah, what do you?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk13.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..5ef254fb5bc0df6883bfe89b2da2433a3da88094 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Fifth degree, yeah." + }, + { + "text": "So 5 by 5 and up would be, this is impossible." + }, + { + "text": "Impossible." + }, + { + "text": "There's no formula to find a simple formula for the lambdas." + }, + { + "text": "And similarly for the sigmas, the singular values." + }, + { + "text": "So the eigenvalues is definitely a level of difficulty beyond Ax equal b, the inverse matrix or something, the pivots." + }, + { + "text": "All that you can do exactly if you do exact arithmetic." + }, + { + "text": "We cannot find the lambdas exactly." + }, + { + "text": "But we can get as close as we like by continuing with the QR method." + }, + { + "text": "So yeah, in other words, we have to settle for, if we want to, at the beginning, improve our matrix before we start doing that stuff." + }, + { + "text": "We can get it with one extra diagonal." + }, + { + "text": "And do you know what kind of a matrix, whose name?" + }, + { + "text": "And I don't know why." + }, + { + "text": "Yeah, say it again." + }, + { + "text": "Upper Hessenberg." + }, + { + "text": "So upper is just like upper triangular." + }, + { + "text": "It's up there." + }, + { + "text": "But the key person's name is Hessenberg." + }, + { + "text": "As I say, that's a Hessenberg matrix." + }, + { + "text": "So Hessenberg matrix is a matrix with one triangular plus one more diagonal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk14.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..890f75c227f0ce9167ef179281769727e008c678 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "But lots of zeros." + }, + { + "text": "Order of n squared, something like almost like half n squared, not quite, but close, zeros." + }, + { + "text": "And you could show that those zeros stay zeros in QR." + }, + { + "text": "So that really pays off." + }, + { + "text": "It cuts the work down significantly." + }, + { + "text": "So the full QR method is step one, reduce A to Hessenberg form with these zeros." + }, + { + "text": "And when I say reduce, I mean find a similarity transformation, of course, because I want the eigenvalues of this to end up the same as the Hessen." + }, + { + "text": "I want to keep the same eigenvalues as I go." + }, + { + "text": "And then step two is QR on this Hessenberg matrix with shifts." + }, + { + "text": "So that's the code that would be programmed in IGAVE." + }, + { + "text": "That's what MATLAB and, well, really, MATLAB is appealing, like other matrix systems, is appealing to LAPAC and LINPAC." + }, + { + "text": "The team of professional numerical analysts really spent a lot of effort and time." + }, + { + "text": "The book LAPAC has 10 authors." + }, + { + "text": "And you can download any of these codes, like the eigenvalue code." + }, + { + "text": "So that's where MATLAB naturally, that's sort of the Bible for codes in linear algebra." + }, + { + "text": "OK, now, I think it's sort of interesting to know." + }, + { + "text": "And there is one more good thing to tell you about this method." + }, + { + "text": "And it applies if the matrix is symmetric." + }, + { + "text": "If the matrix is symmetric, then if we check all this, we could find that the matrices stayed symmetric." + }, + { + "text": "If A0 is symmetric, I can check." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk15.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..1cdfb555c6b2be5bd3044a831ed3f643f560293a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "You could easily check through this, and you would discover that A1 is also symmetric." + }, + { + "text": "It turns out you could rewrite this with a Q0 and a Q0 inverse on the other side." + }, + { + "text": "But that Q0 inverse is the same as Q0 transpose, because it's an orthogonal matrix, and symmetry would fall out." + }, + { + "text": "So if it's symmetric, and it's in Hessenberg form, and it stays symmetric at every step, what can you tell me about a symmetric Hessenberg matrix?" + }, + { + "text": "It's only got, yeah, you just erase all these." + }, + { + "text": "If there are zeros there, and if the matrix is symmetric, then we can safely predict that it will only have one diagonal above, one non-zero diagonal above the main diagonal." + }, + { + "text": "In fact, it'll stay symmetric." + }, + { + "text": "So now I should write symmetric Hessenberg matrix, n equals tri-diagonal matrix." + }, + { + "text": "Yeah, three diagonals." + }, + { + "text": "So now you really have reduced the time to do QR, because you've got a tri-diagonal matrix." + }, + { + "text": "It'll stay tri-diagonal in all these steps." + }, + { + "text": "So you're working with just 3n numbers." + }, + { + "text": "Well, actually, 2n, because the diagonal above and the diagonal below are the same." + }, + { + "text": "You're working with just 2n numbers instead of order n squared, and it just goes like a bomb." + }, + { + "text": "So that's I for symmetric matrices." + }, + { + "text": "And you see that it was all based, that really the heart of the algorithm was QR." + }, + { + "text": "So that's my, it took half the class to report on the favorite way, the EIG way, to find eigenvalues." + }, + { + "text": "Oh, I should say something about singular values." + }, + { + "text": "So singular values, of course, the singular values of the matrix are the eigenvalues of A transpose A, square root of those eigenvalues." + }, + { + "text": "But you wouldn't do it that way." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk16.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..7989fa8939f6d17bfb6b36b82c96bbd76b92a4f6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "You would never form A transpose A. Oh, I didn't mention the other thing you would never, ever, ever do." + }, + { + "text": "So let me just put it here." + }, + { + "text": "This is like in disgrace to solve that equation." + }, + { + "text": "It's like, OK, back to first grade, because that's not, that's very bad." + }, + { + "text": "A determinant, first of all, it's extremely slow, extremely slow." + }, + { + "text": "And the determinant is packing all this n squared pieces of information into n coefficients, and it's hopelessly ill-conditioned." + }, + { + "text": "Yeah, you just, you lose information all the time." + }, + { + "text": "So really, if this is going on camera, it better go on camera with an x, because don't do it." + }, + { + "text": "OK. Yeah." + }, + { + "text": "So where was I?" + }, + { + "text": "Singular values." + }, + { + "text": "So A transpose A." + }, + { + "text": "So again, let's think about what you could do at the beginning before starting on QR for A transpose A, or for the matrix A." + }, + { + "text": "What could you do with orthogonal matrices?" + }, + { + "text": "So I guess, what did we say about symmetric matrices?" + }, + { + "text": "So here's what I said about symmetric matrices." + }, + { + "text": "If you give me a symmetric matrix, I can, in just a simple number of simple steps, make it tridiagonal." + }, + { + "text": "I can't make it diagonal, because then I'd be finding the eigenvalues, and Abel, who was the first person to see that that was impossible, forbids it." + }, + { + "text": "But so let me write down what I'm saying here." + }, + { + "text": "If I have a symmetric matrix S, I can find a bunch of Q's and Q transposes, and I can put them all together into one big Q, and it's transposed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk17.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..08d99076ccc98b0932858bac2de5382359f2d221 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I know about the eigenvalues of that matrix?" + }, + { + "text": "Q is orthogonal always." + }, + { + "text": "So what can you tell me about the, this is the same as Q S Q inverse, and therefore, the eigenvalues are the same." + }, + { + "text": "It's similar to S. And it becomes tridiagonal after I find a good Q." + }, + { + "text": "Now, and therefore, same lambdas, tridiagonal with the same lambdas." + }, + { + "text": "Now, what am I thinking about here?" + }, + { + "text": "I'm thinking about, tell me the corresponding possibility about singular values." + }, + { + "text": "I want to do something to my matrix." + }, + { + "text": "Now, I'm always taking a general matrix A." + }, + { + "text": "And I'm looking for its singular values." + }, + { + "text": "And I'm looking to simplify it." + }, + { + "text": "And what am I allowed to do?" + }, + { + "text": "Yeah, I guess my question is, similarity transformations left the eigenvalues alone." + }, + { + "text": "What can I do that leaves the singular values alone?" + }, + { + "text": "That's a fundamental question, because it was so fundamental for eigenvalues." + }, + { + "text": "By doing this, a matrix and its inverse, I got something similar." + }, + { + "text": "And I checked even in this class that the eigenvalues, same lambdas." + }, + { + "text": "Now I want a whole line that ends up with the same sigmas." + }, + { + "text": "And I want you to tell me what I'm allowed to do to the matrix without changing the sigmas." + }, + { + "text": "So maybe don't shout it out immediately." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk18.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..31cc3c0860684bbd35bab2fb28f2d606a8921e5b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let everybody think." + }, + { + "text": "What am I allowed to do to a matrix?" + }, + { + "text": "Every matrix has got these singular values." + }, + { + "text": "And now I want to make it a better matrix with more 0's or something." + }, + { + "text": "If I do that to it, does that change the sigmas?" + }, + { + "text": "Can I do more than that to it?" + }, + { + "text": "What can I do?" + }, + { + "text": "What group of matrices will have the same sigmas as my starting matrix A?" + }, + { + "text": "So that's a basic, basic question about singular values and the SVD." + }, + { + "text": "So let's think of the answer together." + }, + { + "text": "So it's connected to the SVD." + }, + { + "text": "So let me remember the SVD." + }, + { + "text": "The SVD, I have some orthogonal matrix, then the singular value matrix, SV for singular values, and then another orthogonal matrix." + }, + { + "text": "What could I do to that equation that would not touch this guy?" + }, + { + "text": "So I'm asking what invariance, because not touching it means leaving it not varying." + }, + { + "text": "So I'm looking for under what operations are the singular values invariant?" + }, + { + "text": "When I was looking at eigenvalues, this was the operation." + }, + { + "text": "Well, it didn't have to be orthogonal." + }, + { + "text": "It's something, and it's inverse." + }, + { + "text": "But now what is it up there?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk19.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..01b201f72f3bceb5bd8b70cfc01d55a2e2ff2a71 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "What could I do to that matrix A?" + }, + { + "text": "Could I multiply by Q?" + }, + { + "text": "Could I throw in a Q?" + }, + { + "text": "Maybe not even on the other end." + }, + { + "text": "If I throw in an orthogonal Q, do I change the singular values or do I not change them?" + }, + { + "text": "Fundamental question." + }, + { + "text": "The answer is no, I don't change them." + }, + { + "text": "I'm allowed to do that, because here's an orthogonal matrix, a Q times U." + }, + { + "text": "If both of those are orthogonal, then the product is." + }, + { + "text": "Everybody knows that a product of two orthogonal matrix is still orthogonal." + }, + { + "text": "Better know that." + }, + { + "text": "Better know that." + }, + { + "text": "Yeah." + }, + { + "text": "So if I have an orthogonal matrix Q and an orthogonal matrix U, I claim that this is still orthogonal." + }, + { + "text": "And how do I check it?" + }, + { + "text": "Well, I use some test for orthogonality." + }, + { + "text": "What would be the test you like to use?" + }, + { + "text": "The inverse is the same as the transpose." + }, + { + "text": "You like that test?" + }, + { + "text": "So I'll invert it." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk2.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..49f68a61aecdf81153b85d35f02c4fd1ad64e79f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "How do we see that?" + }, + { + "text": "If you had to show that two matrices had the same eigenvalues, would you compute all the eigenvalues and compare them?" + }, + { + "text": "Certainly not." + }, + { + "text": "What would you do?" + }, + { + "text": "What's the best test, the usual test, the usual thing you would want to show?" + }, + { + "text": "They're similar." + }, + { + "text": "That's right." + }, + { + "text": "So the claim would be that these two matrices are similar." + }, + { + "text": "Right." + }, + { + "text": "So maybe we should show that." + }, + { + "text": "So we want to write A1 in a different way." + }, + { + "text": "So the claim is A1 is similar to A." + }, + { + "text": "So we just have to figure out." + }, + { + "text": "We have to get A1 to A0." + }, + { + "text": "So here's A1." + }, + { + "text": "OK." + }, + { + "text": "So A1, I want to show that that's right." + }, + { + "text": "So that's R0, Q0." + }, + { + "text": "But what is Q0?" + }, + { + "text": "From here, Q0 is what we is R. Q0 is, what do I want?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk20.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..35801c36445d73fe11e2f6274bad6dd29215b8e2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Q U inverse." + }, + { + "text": "Of course, for any matrix, that's U inverse Q inverse." + }, + { + "text": "But these were separately orthogonal, so that's U transpose Q transpose." + }, + { + "text": "And that is the same as Q U transpose." + }, + { + "text": "Yeah." + }, + { + "text": "So I use the orthogonality of U and the orthogonality of Q to conclude that the inverse is the transpose." + }, + { + "text": "So the answer is yes, I could do that." + }, + { + "text": "Now, with singular value, with eigenvalues, I had to multiply on the other side by Q inverse or Q transpose." + }, + { + "text": "Do I have to do that now?" + }, + { + "text": "No." + }, + { + "text": "What can I do on the right-hand side?" + }, + { + "text": "I can multiply by." + }, + { + "text": "I can leave it alone." + }, + { + "text": "Then it has the same singular values because it's the same sigma in there." + }, + { + "text": "If I have a orthogonal matrix times a diagonal times an orthogonal, that diagonal, positive diagonal, is going to be sigma." + }, + { + "text": "So what can I do on this side?" + }, + { + "text": "I could multiply by any orthogonal matrix on that side, too." + }, + { + "text": "So let's call this guy Q1 and this guy Q2." + }, + { + "text": "I still have an orthogonal matrix there, orthogonal matrix there, and the same sigma popped in the middle." + }, + { + "text": "So that's what you're allowed to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk21.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..8733bff8727902ad93fdca4f142729506ca43859 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "That gives us more freedom." + }, + { + "text": "Before, when we had to do similarity transformations with the same guy, we got it to be tridiagonal." + }, + { + "text": "But now we're allowed to do more stuff." + }, + { + "text": "We're allowed to use different orthogonal matrices on the left and right." + }, + { + "text": "And we can reduce it even further from tridiagonal to bidiagonal." + }, + { + "text": "So the first step is getting 0." + }, + { + "text": "The step of getting 0s reduces it all the way to that with all 0s there." + }, + { + "text": "So it's easier." + }, + { + "text": "Then I work on this." + }, + { + "text": "I work on using a QR type idea, some method like that." + }, + { + "text": "So everybody's seeing that our algorithm has got two stages." + }, + { + "text": "One is get a lot of 0s and get them in places that will stay 0 as part 2 of the algorithm gets going." + }, + { + "text": "And then run part 2 of the algorithm." + }, + { + "text": "You're staying with each step is very fast now because doing a QR factorization is fast." + }, + { + "text": "Was there a question?" + }, + { + "text": "Yeah." + }, + { + "text": "So I would call this bidiagonal, of course." + }, + { + "text": "And everybody recognizes that if I have a bidiagonal matrix, call it A or A0 or whatever." + }, + { + "text": "Then what do you think about A transpose A?" + }, + { + "text": "What would A transpose A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk22.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..8562bc4837b9c78d63d64c389d0c913d3dc7d8a2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "If that was A, what could you tell me about A transpose A?" + }, + { + "text": "Could you multiply matrices, like knowing where the non-zeros are, like in your head, and get an idea of where?" + }, + { + "text": "So if I have a bidiagonal matrix A, then sort of implicitly in the SVD, I'm looking at A transpose A." + }, + { + "text": "And what would be true about A transpose A?" + }, + { + "text": "It would be tridiagonal." + }, + { + "text": "So what I've done here and what I've done there just match up." + }, + { + "text": "If you don't want to change singular values, you can get all the way to here." + }, + { + "text": "But then to find those singular values, that would involve A transpose A." + }, + { + "text": "It would be symmetric and tridiagonal." + }, + { + "text": "And then you'd be in that game." + }, + { + "text": "So those are the basic facts of I and SVD." + }, + { + "text": "For matrices of order up to 1,000, say." + }, + { + "text": "I'm not enough of an expert to know where." + }, + { + "text": "Maybe higher, because in perfect math, it's going to take infinitely many steps." + }, + { + "text": "Or Abel would be very surprised." + }, + { + "text": "He would see you solving for eigenvalues and then to re-equation by a whole lot of little steps and getting them exactly right." + }, + { + "text": "That won't happen." + }, + { + "text": "But you get them within epsilon in a number of steps that's like n cubed." + }, + { + "text": "So that's pretty impressive." + }, + { + "text": "The eigenvalue problem is being solved, in quotes, by a fast method that gets you a good answer within a tolerance in n cubed steps." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk23.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..37baceeccac2b563da8271de17d70bb205a69d4d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Right." + }, + { + "text": "So that's great as long as n isn't too big." + }, + { + "text": "And then when n is too big, which of course happens, you have to think again." + }, + { + "text": "So this method is a giant success up to large matrices." + }, + { + "text": "But then you have to think again." + }, + { + "text": "And what is involved in thinking again?" + }, + { + "text": "Well, I guess more thinking." + }, + { + "text": "So what do you do if the matrix is bigger?" + }, + { + "text": "I guess that Krylov would say, use my method." + }, + { + "text": "So Krylov would say, especially if your matrix is sparse." + }, + { + "text": "Can we just remember what Krylov was?" + }, + { + "text": "Krylov started with a vector b, multiplied it by a, multiplied that by a, and got up to, let's say, a to the 999b." + }, + { + "text": "So now Krylov has got 1,000 dimensional space." + }, + { + "text": "He's got a basis for it, 1,000 vectors that span 1,000 dimensional space." + }, + { + "text": "And he'll look at the matrix A only on that space." + }, + { + "text": "In other words, I won't go into detail about that." + }, + { + "text": "He restricts the matrix to this 1,000 dimensional space." + }, + { + "text": "And he hopes that it's captured." + }, + { + "text": "We hope that the eigenvector is virtually in that space." + }, + { + "text": "And actually, I wouldn't go up to, let me take a 9 out of that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk24.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..0f5c17cbd60debd628609f1ccf8848eb0fa9b730 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "100 dimensional would probably catch the eigenvector." + }, + { + "text": "So if the eigenvector is virtually in this space, then we can look at a matrix of order 100." + }, + { + "text": "We can bring A down to just see its action on that space." + }, + { + "text": "So I look at vectors V, which are some combination, C1b plus C2ab plus C3a squared b and C100 a to the 99th b, plus an error." + }, + { + "text": "And I'm going to ignore that error." + }, + { + "text": "Because I've gone up to dimension 100." + }, + { + "text": "I probably say it's pretty safe to ignore that error." + }, + { + "text": "And then in this space, just looking at the matrix A." + }, + { + "text": "So wherever A to the 100th comes in, forget it." + }, + { + "text": "Just think about the matrix A as multiplying vectors of this kind in this space." + }, + { + "text": "Then I have a 100 by 100 eigenvalue problem." + }, + { + "text": "And so the big matrix A is reduced to a matrix of size 100 by, do you see sort of what I'm saying, even though I'm not giving the details?" + }, + { + "text": "Think of a matrix A of size a million." + }, + { + "text": "And you apply it to Krylov vectors." + }, + { + "text": "So I call them little k for a Krylov vector in this 100-dimensional space." + }, + { + "text": "So they have a million minus 100, zero components, you could say, this k. This is in the Krylov space." + }, + { + "text": "This is A, a million, k, 100." + }, + { + "text": "It's a full, it's got a million components, but it's out of just 100-dimensional space." + }, + { + "text": "So when I multiply by A, it'll be mostly in, mostly in, partly in the Krylov space, k 100, and a piece out of k 100." + }, + { + "text": "And I just ignore that part of the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk25.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..41342712fde4874aa3c115a8d909e3bf6f2a0e59 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I have a 100 by 100 problem, and I've solved to find the eigenvalues." + }, + { + "text": "And they're a pretty good approximation to the eigenvalues, to the, hopefully, like the lowest 100 eigenvalues." + }, + { + "text": "I'd like to know that." + }, + { + "text": "But I might not be sure that this idea would give me the lowest 100, the first 100 eigenvalues of the million, of the matrix of size a million." + }, + { + "text": "I'm just taking a few minutes here to sort of wave hands about what Krylov, the Krylov idea would do." + }, + { + "text": "And I probably won't mention Krylov again this semester." + }, + { + "text": "So what it can do is look at this particular type of space, because we can get a basis for it quickly, just multiply again and again by A." + }, + { + "text": "Then we can orthogonalize that basis." + }, + { + "text": "That's Graham-Schmidt in some form." + }, + { + "text": "We're always going back to Graham-Schmidt." + }, + { + "text": "Then I have a 100 by 100." + }, + { + "text": "I have a subspace of size 100." + }, + { + "text": "I look at what the matrix does in that space." + }, + { + "text": "And I could look for, I could find eigenvalues restricted to that space." + }, + { + "text": "They wouldn't be the perfect eigenvalues, but they would be accurate." + }, + { + "text": "OK, so I didn't know it would take one class time to talk about finding eigenvalues and singular values, but we did some important things." + }, + { + "text": "We remembered that similarity is the thing to check, thing to preserve, because it doesn't change the eigenvalues." + }, + { + "text": "And then for singular values, what was the thing?" + }, + { + "text": "You could multiply left and right by different orthogonal matrices." + }, + { + "text": "And somehow, maybe that doesn't have an established name, multiplying left and right by a Q1 and a Q2 transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk26.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..2ce06055331ebe329b68e463d8ac9af5a66e37dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk26.json @@ -0,0 +1,35 @@ +[ + { + "text": "Yeah, but the idea is clear." + }, + { + "text": "And that doesn't change the singular values." + }, + { + "text": "We're ready to move now into maybe our next step, which we don't spend a long time on." + }, + { + "text": "We'll be like random sampling." + }, + { + "text": "What if your matrix is just way too big?" + }, + { + "text": "So that's a new, very new idea, very different idea in numerical linear algebra, is just to sample the matrix." + }, + { + "text": "Could you believe that the answer is going to come out right just for a random sample?" + }, + { + "text": "Well, the odds are in your favor." + }, + { + "text": "OK, so that'll be Wednesday, and then we have lots of new, we'll move onward after that." + }, + { + "text": "OK, see you Wednesday." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk3.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..f5acd4bdba4ba51520fdf921a1fc36684dfeaabb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I want to put R0 inverse over there." + }, + { + "text": "So R0." + }, + { + "text": "Now for Q0, I'm going to substitute." + }, + { + "text": "So what is Q0?" + }, + { + "text": "I multiply both sides of that equation by R0 inverse." + }, + { + "text": "So Q0 is A0 is, sorry, I said A and wrote Q. A0 R0 inverse." + }, + { + "text": "Right." + }, + { + "text": "For Q0, I've put in what it equals." + }, + { + "text": "And that's done it." + }, + { + "text": "That's exactly telling me that A1, which is this, equals this." + }, + { + "text": "And that's a similarity transformation." + }, + { + "text": "I have not changed the eigenvalues." + }, + { + "text": "So that's OK." + }, + { + "text": "The other thing, which is the, like you could say, the miracle in this thing, is that when I continue to do that for almost every matrix, the matrices begin to lose stuff off the diagonal, especially below the diagonal by the ordering that QR is done." + }, + { + "text": "So you tend to start with a matrix A0." + }, + { + "text": "You get a matrix A1, which is like a little smaller here." + }, + { + "text": "This part being not especially smaller." + }, + { + "text": "You do it again." + }, + { + "text": "This is even smaller." + }, + { + "text": "So I put even smaller A2, even smaller." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk4.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..a93c5efe93b5619eae3335916949e5ca1b9c543f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you keep going." + }, + { + "text": "And for most matrices, the result is that I don't know how many steps we want to think of taking, but we get quite small numbers here." + }, + { + "text": "So once we get small numbers here, little epsilons, that's everybody's shorthand for small numbers, what would you expect to see on the diagonal?" + }, + { + "text": "The eigenvalues." + }, + { + "text": "Because this has the same eigenvalues as this, as this, as this." + }, + { + "text": "And these little epsilons are not going to change the eigenvalues too much." + }, + { + "text": "So these will be, on the diagonal, will be close to the eigenvalues." + }, + { + "text": "And actually, what happens is this one comes first." + }, + { + "text": "That one is quite accurate first." + }, + { + "text": "I guess we should probably do a simple example to see this happen." + }, + { + "text": "Actually, I do an example in the notes." + }, + { + "text": "And let me say what happens." + }, + { + "text": "So I do a 2 by 2 example, which has something like cos theta, sine theta." + }, + { + "text": "I don't know what." + }, + { + "text": "I've forgotten what I took." + }, + { + "text": "And I don't have that page of notes here." + }, + { + "text": "Something here." + }, + { + "text": "Something here." + }, + { + "text": "Something here as a 0." + }, + { + "text": "And then a 1, after just one step, has sine cubed theta there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk5.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..2c1c69b5647ae63cfaad8af10731e95f060b6c81 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And numbers there that are getting much closer to the eigenvalues." + }, + { + "text": "Sorry that this isn't a full scale example." + }, + { + "text": "But the point of the example is here, that this off-diagonal entry gets cubed." + }, + { + "text": "And the next step will be its ninth power, and then the 27th power." + }, + { + "text": "So it's really quickly going to 0." + }, + { + "text": "And this happens." + }, + { + "text": "So cubic convergence is a prize." + }, + { + "text": "In numerical linear algebra." + }, + { + "text": "So that happens." + }, + { + "text": "So this arrived on the scene and quickly blew away all other methods that were being used to compute eigenvalues." + }, + { + "text": "But numerical people, being what they are, they wanted to improve it." + }, + { + "text": "Like, is there a way to make it faster?" + }, + { + "text": "And turned out there is." + }, + { + "text": "It turned out that the better way, basically the same idea, but just you're always looking for a simple change." + }, + { + "text": "And the idea of introducing a shift was tried." + }, + { + "text": "And turned out to work extremely well." + }, + { + "text": "So that's the improvement." + }, + { + "text": "So we take a1." + }, + { + "text": "No, so how does the shift work?" + }, + { + "text": "So instead of a0, have I got space here to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk6.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..e081a02643a2181251ac74e36b445d55b6192f14 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Instead of a0, I take a0 minus a shift." + }, + { + "text": "So a shift is some multiple of the identity." + }, + { + "text": "If I just move a matrix by a multiple of the identity, what happens to its eigenvectors?" + }, + { + "text": "What happens to its eigenvalues?" + }, + { + "text": "Something pretty simple, right?" + }, + { + "text": "Because I'm just shifting by si." + }, + { + "text": "What happens to its eigenvectors?" + }, + { + "text": "They're the same." + }, + { + "text": "And what happens to the eigenvalues?" + }, + { + "text": "They change by s. If a0v equals lambda v, then when I multiply this by v, there will be an extra." + }, + { + "text": "It'll be lambda minus s. Because the identity times the v is just v. So it just shifts all the eigenvalues by s. And you try to shift." + }, + { + "text": "You look for a shift." + }, + { + "text": "This would be great." + }, + { + "text": "If you knew lambda n, a shift there, you would be looking for 0 then, if you shifted them all by that lambda." + }, + { + "text": "And it turns out that would speed things up." + }, + { + "text": "So you work instead with this matrix as now, again, I'm factoring in a q0, r0." + }, + { + "text": "So that's the work of the method, is in doing Gram-Schmidt at every step." + }, + { + "text": "And then there's a little work in reversing the order." + }, + { + "text": "And then I want to undo the shift." + }, + { + "text": "So I do that factorization." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk7.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..212c509ec27724246ec3a49d4c24022c4979b516 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, let's see." + }, + { + "text": "You may have to help me to remember what I should do here." + }, + { + "text": "So I factor those." + }, + { + "text": "I reverse those." + }, + { + "text": "And then I think I add back the shift." + }, + { + "text": "And that's my A1." + }, + { + "text": "So I took A0." + }, + { + "text": "I shifted it." + }, + { + "text": "I worked with it, qr, reversed the order, rq, added back the shift to get a matrix." + }, + { + "text": "And what am I, of course, hoping about the matrix A1 and A0?" + }, + { + "text": "I'm hoping they're still similar." + }, + { + "text": "I'm hoping." + }, + { + "text": "So I did a shift." + }, + { + "text": "And I undid a shift." + }, + { + "text": "But of course, after doing a qr, I have to check, are these really still similar?" + }, + { + "text": "So let me just try to check that one again." + }, + { + "text": "Maybe I'll just, it's sitting right there." + }, + { + "text": "So let me do it again." + }, + { + "text": "I'm hoping that something, you know, where did we change?" + }, + { + "text": "Oh, yeah, here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk8.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..4e7fad6f92f20cdf436db6b8933b889b8a6fb34f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We showed that A1 was similar to A0." + }, + { + "text": "And I'm hoping that's probably still true, even, you know, the shift didn't mess that up." + }, + { + "text": "Let's just try." + }, + { + "text": "So A0, that's r0, q0 plus si." + }, + { + "text": "OK. And now what am I going to do?" + }, + { + "text": "I'm going to, what did I do before?" + }, + { + "text": "I figured out what q0 was from this." + }, + { + "text": "You remember?" + }, + { + "text": "So this is r0." + }, + { + "text": "Now I have to put in q0." + }, + { + "text": "But q0 is this thing inverse times this." + }, + { + "text": "Is this going to work?" + }, + { + "text": "I'm like hoping, but I don't think I wanted to get that." + }, + { + "text": "No, it's not q0 there." + }, + { + "text": "What do I put here?" + }, + { + "text": "And if it doesn't work, we'll leave it as an exercise." + }, + { + "text": "OK." + }, + { + "text": "So yeah, because I didn't sort of start right somehow." + }, + { + "text": "OK." + }, + { + "text": "So but let me just push along to see what happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk9.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..f66b5f2f317c991f9ad92b2dc38dd936ae5d8d21 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_3_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I'm plugging in for q0 here." + }, + { + "text": "I'm plugging in this matrix, so it shouldn't have inverted it, times r0 inverse." + }, + { + "text": "Who knows?" + }, + { + "text": "It might work." + }, + { + "text": "Who knows?" + }, + { + "text": "So that's the r0, q0." + }, + { + "text": "Right?" + }, + { + "text": "Is everybody with me?" + }, + { + "text": "Sorry about this." + }, + { + "text": "So r0 inverse." + }, + { + "text": "And then I have to add Si." + }, + { + "text": "So what have I done?" + }, + { + "text": "I've just pushed on, believing that this would work." + }, + { + "text": "Because it's the method that is constantly used." + }, + { + "text": "Now do I have?" + }, + { + "text": "What do I have there?" + }, + { + "text": "Is it working?" + }, + { + "text": "This is r0 A." + }, + { + "text": "That was, of course, A0." + }, + { + "text": "r0 A0 r0 inverse." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk0.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..afc91322b0d9d5a0ce3bfb215b0940ebb7754749 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "OK, why don't I start?" + }, + { + "text": "So I was hoping that we would have the next online assignment ready, but Julia 6, the new version, is slowing us down." + }, + { + "text": "And it'd probably be next time." + }, + { + "text": "But my lectures, of course, are, well, what I want to say perhaps is this isn't intended to be a course in numerical linear algebra." + }, + { + "text": "But I thought I couldn't let the whole semester go by without saying something about how to compute eigenvalues and singular values." + }, + { + "text": "Of course, you're going to call I or SVD or the equivalent in Python or Julia." + }, + { + "text": "But actually, the QR factorization that we spoke about, that we spoke entirely about last time is the key, unexpectedly, unexpectedly." + }, + { + "text": "You have a matrix A whose eigenvalues you want." + }, + { + "text": "So let's start with eigenvalues." + }, + { + "text": "And it might be a symmetric matrix." + }, + { + "text": "I'll stay with A rather than S because it doesn't have to be." + }, + { + "text": "But you get special always." + }, + { + "text": "You get something special if the matrix is symmetric." + }, + { + "text": "OK, so this method of computing eigenvalues, to me at least, and I think to many people, came like out of the blue a while ago, but not that long ago." + }, + { + "text": "And it worked very well." + }, + { + "text": "So here's the idea." + }, + { + "text": "It's called the QR method because you start by factoring your matrix into QR." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk1.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..f693f6b2ff21648d32a7af5f95cf39d07b0de862 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's A." + }, + { + "text": "Can we call it A0?" + }, + { + "text": "That's the matrix we start with whose eigenvalues we want." + }, + { + "text": "And I'll call these Q0 and R0." + }, + { + "text": "And you remember what that means, what's hiding behind those letters that I've written?" + }, + { + "text": "You have the columns of A, possibly symmetric, as I said, but not orthogonal, usually." + }, + { + "text": "So you find an orthogonal basis." + }, + { + "text": "You orthogonalize them." + }, + { + "text": "You line them up perpendicular to each other." + }, + { + "text": "And then there is a matrix R, which happens to be upper triangular, that connects." + }, + { + "text": "The not orthogonal basis with the orthogonal basis." + }, + { + "text": "Right, we constructed R step by step." + }, + { + "text": "And then the idea is write these in the reverse order." + }, + { + "text": "And that will be A1, the next A. OK, and then do it again, and again, and again." + }, + { + "text": "And so we're hoping, of course, that the eigenvalues didn't change." + }, + { + "text": "We're hoping that we can forget A0, start again with A1, and produce A2, and continue." + }, + { + "text": "So we're hoping two things." + }, + { + "text": "One will not be a hope." + }, + { + "text": "We can see that the eigenvalues of A1 and A0 are the same." + }, + { + "text": "So we have not changed the eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk10.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..6fb2da774bad3a68b507efacec13f9801a995312 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "r0 A0 r0 inverse." + }, + { + "text": "Good." + }, + { + "text": "Minus S. What have I got there?" + }, + { + "text": "From the r0 minus Si r0, what is that?" + }, + { + "text": "That's minus Si." + }, + { + "text": "Look, success." + }, + { + "text": "The r0 cancels the r0 inverse." + }, + { + "text": "So that term from that, that, that is minus Si." + }, + { + "text": "Cancels plus Si." + }, + { + "text": "I'm finished." + }, + { + "text": "And lo and behold, we have the same similarity." + }, + { + "text": "So we messed around by a multiple of the identity, and it actually makes the thing converge faster if we choose the shifts well." + }, + { + "text": "But basically, the same idea is still working." + }, + { + "text": "OK." + }, + { + "text": "So that's the QR method." + }, + { + "text": "Well, that's the method we haven't shown and won't show." + }, + { + "text": "Except for this half-completed example, I don't plan to prove that the lower triangular part begins to disappear, gets smaller and smaller and smaller, and then the eigenvalues pop up on the diagonal." + }, + { + "text": "It's amazing." + }, + { + "text": "Amazing." + }, + { + "text": "OK. Now, is there any other improvement we can make?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk11.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..9e5764513ae4ce678e41ecfcb72a4895642b01f6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's the method." + }, + { + "text": "And where is the work in using that method?" + }, + { + "text": "Because that's what we always focus on." + }, + { + "text": "Where are we spending computer time?" + }, + { + "text": "Well, we're spending computer time in doing the factorization." + }, + { + "text": "So it didn't cost anything to shift by the identity, but then we had to factor that into Q0, R0." + }, + { + "text": "Then it didn't cost much to multiply them in the opposite order." + }, + { + "text": "So the work was in QR." + }, + { + "text": "So could we think of anything to improve that aspect?" + }, + { + "text": "Could we think of anything there?" + }, + { + "text": "And then we've got a really first-class method." + }, + { + "text": "Well, if the matrix A, A0, the matrix we started with, had some zeros that allowed us to skip steps in doing the QR factorization." + }, + { + "text": "So what am I going to say?" + }, + { + "text": "I'm going to say if A or A0, our original matrix, has a bunch of zeros, let's say it's got a whole lot of zeros there." + }, + { + "text": "Maybe it's, well, OK." + }, + { + "text": "I overdid it here." + }, + { + "text": "I know the eigenvalues right off." + }, + { + "text": "But so the truth is I can't, saying that if that, it's not going to happen." + }, + { + "text": "But we can get zeros with one extra diagonal." + }, + { + "text": "That turns out, so here's the main diagonal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk12.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..ab7132ecacaf6cb9786d7b5f399f0082623bd923 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Everybody's got his eye on the main diagonal." + }, + { + "text": "And one diagonal, I can get a lot of zeros." + }, + { + "text": "But I can't by simple computations." + }, + { + "text": "And I'll show you how to get one." + }, + { + "text": "But I can't get all those to be 0, because then I would have the eigenvalues right there." + }, + { + "text": "And that, well, how do I know that I can't?" + }, + { + "text": "In elimination, ordinary solving AX equal B, you really do get to an upper triangular form." + }, + { + "text": "Some operator, some elimination steps, you plug away, and your matrix becomes upper triangular U." + }, + { + "text": "And you're golden." + }, + { + "text": "But that's too much to expect here." + }, + { + "text": "In fact, we know we can't do it by simple steps." + }, + { + "text": "Because if we could do it, if we could get to a U with a whole lower triangular part 0, we would have found the eigenvalues." + }, + { + "text": "And we know that the eigenvalues solve an equation of nth degree." + }, + { + "text": "And we know somebody proved centuries or more ago that you can't solve an nth degree equation by simple little steps." + }, + { + "text": "Right?" + }, + { + "text": "Do you know who that was?" + }, + { + "text": "And you know that fact?" + }, + { + "text": "And what degree does it apply to?" + }, + { + "text": "So that's an important fact that you sort of pick up in math." + }, + { + "text": "Yeah, what do you?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk13.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..5ef254fb5bc0df6883bfe89b2da2433a3da88094 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Fifth degree, yeah." + }, + { + "text": "So 5 by 5 and up would be, this is impossible." + }, + { + "text": "Impossible." + }, + { + "text": "There's no formula to find a simple formula for the lambdas." + }, + { + "text": "And similarly for the sigmas, the singular values." + }, + { + "text": "So the eigenvalues is definitely a level of difficulty beyond Ax equal b, the inverse matrix or something, the pivots." + }, + { + "text": "All that you can do exactly if you do exact arithmetic." + }, + { + "text": "We cannot find the lambdas exactly." + }, + { + "text": "But we can get as close as we like by continuing with the QR method." + }, + { + "text": "So yeah, in other words, we have to settle for, if we want to, at the beginning, improve our matrix before we start doing that stuff." + }, + { + "text": "We can get it with one extra diagonal." + }, + { + "text": "And do you know what kind of a matrix, whose name?" + }, + { + "text": "And I don't know why." + }, + { + "text": "Yeah, say it again." + }, + { + "text": "Upper Hessenberg." + }, + { + "text": "So upper is just like upper triangular." + }, + { + "text": "It's up there." + }, + { + "text": "But the key person's name is Hessenberg." + }, + { + "text": "As I say, that's a Hessenberg matrix." + }, + { + "text": "So Hessenberg matrix is a matrix with one triangular plus one more diagonal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk14.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..890f75c227f0ce9167ef179281769727e008c678 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "But lots of zeros." + }, + { + "text": "Order of n squared, something like almost like half n squared, not quite, but close, zeros." + }, + { + "text": "And you could show that those zeros stay zeros in QR." + }, + { + "text": "So that really pays off." + }, + { + "text": "It cuts the work down significantly." + }, + { + "text": "So the full QR method is step one, reduce A to Hessenberg form with these zeros." + }, + { + "text": "And when I say reduce, I mean find a similarity transformation, of course, because I want the eigenvalues of this to end up the same as the Hessen." + }, + { + "text": "I want to keep the same eigenvalues as I go." + }, + { + "text": "And then step two is QR on this Hessenberg matrix with shifts." + }, + { + "text": "So that's the code that would be programmed in IGAVE." + }, + { + "text": "That's what MATLAB and, well, really, MATLAB is appealing, like other matrix systems, is appealing to LAPAC and LINPAC." + }, + { + "text": "The team of professional numerical analysts really spent a lot of effort and time." + }, + { + "text": "The book LAPAC has 10 authors." + }, + { + "text": "And you can download any of these codes, like the eigenvalue code." + }, + { + "text": "So that's where MATLAB naturally, that's sort of the Bible for codes in linear algebra." + }, + { + "text": "OK, now, I think it's sort of interesting to know." + }, + { + "text": "And there is one more good thing to tell you about this method." + }, + { + "text": "And it applies if the matrix is symmetric." + }, + { + "text": "If the matrix is symmetric, then if we check all this, we could find that the matrices stayed symmetric." + }, + { + "text": "If A0 is symmetric, I can check." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk15.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..1cdfb555c6b2be5bd3044a831ed3f643f560293a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "You could easily check through this, and you would discover that A1 is also symmetric." + }, + { + "text": "It turns out you could rewrite this with a Q0 and a Q0 inverse on the other side." + }, + { + "text": "But that Q0 inverse is the same as Q0 transpose, because it's an orthogonal matrix, and symmetry would fall out." + }, + { + "text": "So if it's symmetric, and it's in Hessenberg form, and it stays symmetric at every step, what can you tell me about a symmetric Hessenberg matrix?" + }, + { + "text": "It's only got, yeah, you just erase all these." + }, + { + "text": "If there are zeros there, and if the matrix is symmetric, then we can safely predict that it will only have one diagonal above, one non-zero diagonal above the main diagonal." + }, + { + "text": "In fact, it'll stay symmetric." + }, + { + "text": "So now I should write symmetric Hessenberg matrix, n equals tri-diagonal matrix." + }, + { + "text": "Yeah, three diagonals." + }, + { + "text": "So now you really have reduced the time to do QR, because you've got a tri-diagonal matrix." + }, + { + "text": "It'll stay tri-diagonal in all these steps." + }, + { + "text": "So you're working with just 3n numbers." + }, + { + "text": "Well, actually, 2n, because the diagonal above and the diagonal below are the same." + }, + { + "text": "You're working with just 2n numbers instead of order n squared, and it just goes like a bomb." + }, + { + "text": "So that's I for symmetric matrices." + }, + { + "text": "And you see that it was all based, that really the heart of the algorithm was QR." + }, + { + "text": "So that's my, it took half the class to report on the favorite way, the EIG way, to find eigenvalues." + }, + { + "text": "Oh, I should say something about singular values." + }, + { + "text": "So singular values, of course, the singular values of the matrix are the eigenvalues of A transpose A, square root of those eigenvalues." + }, + { + "text": "But you wouldn't do it that way." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk16.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..7989fa8939f6d17bfb6b36b82c96bbd76b92a4f6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "You would never form A transpose A. Oh, I didn't mention the other thing you would never, ever, ever do." + }, + { + "text": "So let me just put it here." + }, + { + "text": "This is like in disgrace to solve that equation." + }, + { + "text": "It's like, OK, back to first grade, because that's not, that's very bad." + }, + { + "text": "A determinant, first of all, it's extremely slow, extremely slow." + }, + { + "text": "And the determinant is packing all this n squared pieces of information into n coefficients, and it's hopelessly ill-conditioned." + }, + { + "text": "Yeah, you just, you lose information all the time." + }, + { + "text": "So really, if this is going on camera, it better go on camera with an x, because don't do it." + }, + { + "text": "OK. Yeah." + }, + { + "text": "So where was I?" + }, + { + "text": "Singular values." + }, + { + "text": "So A transpose A." + }, + { + "text": "So again, let's think about what you could do at the beginning before starting on QR for A transpose A, or for the matrix A." + }, + { + "text": "What could you do with orthogonal matrices?" + }, + { + "text": "So I guess, what did we say about symmetric matrices?" + }, + { + "text": "So here's what I said about symmetric matrices." + }, + { + "text": "If you give me a symmetric matrix, I can, in just a simple number of simple steps, make it tridiagonal." + }, + { + "text": "I can't make it diagonal, because then I'd be finding the eigenvalues, and Abel, who was the first person to see that that was impossible, forbids it." + }, + { + "text": "But so let me write down what I'm saying here." + }, + { + "text": "If I have a symmetric matrix S, I can find a bunch of Q's and Q transposes, and I can put them all together into one big Q, and it's transposed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk17.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..08d99076ccc98b0932858bac2de5382359f2d221 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I know about the eigenvalues of that matrix?" + }, + { + "text": "Q is orthogonal always." + }, + { + "text": "So what can you tell me about the, this is the same as Q S Q inverse, and therefore, the eigenvalues are the same." + }, + { + "text": "It's similar to S. And it becomes tridiagonal after I find a good Q." + }, + { + "text": "Now, and therefore, same lambdas, tridiagonal with the same lambdas." + }, + { + "text": "Now, what am I thinking about here?" + }, + { + "text": "I'm thinking about, tell me the corresponding possibility about singular values." + }, + { + "text": "I want to do something to my matrix." + }, + { + "text": "Now, I'm always taking a general matrix A." + }, + { + "text": "And I'm looking for its singular values." + }, + { + "text": "And I'm looking to simplify it." + }, + { + "text": "And what am I allowed to do?" + }, + { + "text": "Yeah, I guess my question is, similarity transformations left the eigenvalues alone." + }, + { + "text": "What can I do that leaves the singular values alone?" + }, + { + "text": "That's a fundamental question, because it was so fundamental for eigenvalues." + }, + { + "text": "By doing this, a matrix and its inverse, I got something similar." + }, + { + "text": "And I checked even in this class that the eigenvalues, same lambdas." + }, + { + "text": "Now I want a whole line that ends up with the same sigmas." + }, + { + "text": "And I want you to tell me what I'm allowed to do to the matrix without changing the sigmas." + }, + { + "text": "So maybe don't shout it out immediately." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk18.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..31cc3c0860684bbd35bab2fb28f2d606a8921e5b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let everybody think." + }, + { + "text": "What am I allowed to do to a matrix?" + }, + { + "text": "Every matrix has got these singular values." + }, + { + "text": "And now I want to make it a better matrix with more 0's or something." + }, + { + "text": "If I do that to it, does that change the sigmas?" + }, + { + "text": "Can I do more than that to it?" + }, + { + "text": "What can I do?" + }, + { + "text": "What group of matrices will have the same sigmas as my starting matrix A?" + }, + { + "text": "So that's a basic, basic question about singular values and the SVD." + }, + { + "text": "So let's think of the answer together." + }, + { + "text": "So it's connected to the SVD." + }, + { + "text": "So let me remember the SVD." + }, + { + "text": "The SVD, I have some orthogonal matrix, then the singular value matrix, SV for singular values, and then another orthogonal matrix." + }, + { + "text": "What could I do to that equation that would not touch this guy?" + }, + { + "text": "So I'm asking what invariance, because not touching it means leaving it not varying." + }, + { + "text": "So I'm looking for under what operations are the singular values invariant?" + }, + { + "text": "When I was looking at eigenvalues, this was the operation." + }, + { + "text": "Well, it didn't have to be orthogonal." + }, + { + "text": "It's something, and it's inverse." + }, + { + "text": "But now what is it up there?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk19.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..01b201f72f3bceb5bd8b70cfc01d55a2e2ff2a71 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "What could I do to that matrix A?" + }, + { + "text": "Could I multiply by Q?" + }, + { + "text": "Could I throw in a Q?" + }, + { + "text": "Maybe not even on the other end." + }, + { + "text": "If I throw in an orthogonal Q, do I change the singular values or do I not change them?" + }, + { + "text": "Fundamental question." + }, + { + "text": "The answer is no, I don't change them." + }, + { + "text": "I'm allowed to do that, because here's an orthogonal matrix, a Q times U." + }, + { + "text": "If both of those are orthogonal, then the product is." + }, + { + "text": "Everybody knows that a product of two orthogonal matrix is still orthogonal." + }, + { + "text": "Better know that." + }, + { + "text": "Better know that." + }, + { + "text": "Yeah." + }, + { + "text": "So if I have an orthogonal matrix Q and an orthogonal matrix U, I claim that this is still orthogonal." + }, + { + "text": "And how do I check it?" + }, + { + "text": "Well, I use some test for orthogonality." + }, + { + "text": "What would be the test you like to use?" + }, + { + "text": "The inverse is the same as the transpose." + }, + { + "text": "You like that test?" + }, + { + "text": "So I'll invert it." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk2.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..49f68a61aecdf81153b85d35f02c4fd1ad64e79f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "How do we see that?" + }, + { + "text": "If you had to show that two matrices had the same eigenvalues, would you compute all the eigenvalues and compare them?" + }, + { + "text": "Certainly not." + }, + { + "text": "What would you do?" + }, + { + "text": "What's the best test, the usual test, the usual thing you would want to show?" + }, + { + "text": "They're similar." + }, + { + "text": "That's right." + }, + { + "text": "So the claim would be that these two matrices are similar." + }, + { + "text": "Right." + }, + { + "text": "So maybe we should show that." + }, + { + "text": "So we want to write A1 in a different way." + }, + { + "text": "So the claim is A1 is similar to A." + }, + { + "text": "So we just have to figure out." + }, + { + "text": "We have to get A1 to A0." + }, + { + "text": "So here's A1." + }, + { + "text": "OK." + }, + { + "text": "So A1, I want to show that that's right." + }, + { + "text": "So that's R0, Q0." + }, + { + "text": "But what is Q0?" + }, + { + "text": "From here, Q0 is what we is R. Q0 is, what do I want?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk20.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..35801c36445d73fe11e2f6274bad6dd29215b8e2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Q U inverse." + }, + { + "text": "Of course, for any matrix, that's U inverse Q inverse." + }, + { + "text": "But these were separately orthogonal, so that's U transpose Q transpose." + }, + { + "text": "And that is the same as Q U transpose." + }, + { + "text": "Yeah." + }, + { + "text": "So I use the orthogonality of U and the orthogonality of Q to conclude that the inverse is the transpose." + }, + { + "text": "So the answer is yes, I could do that." + }, + { + "text": "Now, with singular value, with eigenvalues, I had to multiply on the other side by Q inverse or Q transpose." + }, + { + "text": "Do I have to do that now?" + }, + { + "text": "No." + }, + { + "text": "What can I do on the right-hand side?" + }, + { + "text": "I can multiply by." + }, + { + "text": "I can leave it alone." + }, + { + "text": "Then it has the same singular values because it's the same sigma in there." + }, + { + "text": "If I have a orthogonal matrix times a diagonal times an orthogonal, that diagonal, positive diagonal, is going to be sigma." + }, + { + "text": "So what can I do on this side?" + }, + { + "text": "I could multiply by any orthogonal matrix on that side, too." + }, + { + "text": "So let's call this guy Q1 and this guy Q2." + }, + { + "text": "I still have an orthogonal matrix there, orthogonal matrix there, and the same sigma popped in the middle." + }, + { + "text": "So that's what you're allowed to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk21.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..8733bff8727902ad93fdca4f142729506ca43859 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "That gives us more freedom." + }, + { + "text": "Before, when we had to do similarity transformations with the same guy, we got it to be tridiagonal." + }, + { + "text": "But now we're allowed to do more stuff." + }, + { + "text": "We're allowed to use different orthogonal matrices on the left and right." + }, + { + "text": "And we can reduce it even further from tridiagonal to bidiagonal." + }, + { + "text": "So the first step is getting 0." + }, + { + "text": "The step of getting 0s reduces it all the way to that with all 0s there." + }, + { + "text": "So it's easier." + }, + { + "text": "Then I work on this." + }, + { + "text": "I work on using a QR type idea, some method like that." + }, + { + "text": "So everybody's seeing that our algorithm has got two stages." + }, + { + "text": "One is get a lot of 0s and get them in places that will stay 0 as part 2 of the algorithm gets going." + }, + { + "text": "And then run part 2 of the algorithm." + }, + { + "text": "You're staying with each step is very fast now because doing a QR factorization is fast." + }, + { + "text": "Was there a question?" + }, + { + "text": "Yeah." + }, + { + "text": "So I would call this bidiagonal, of course." + }, + { + "text": "And everybody recognizes that if I have a bidiagonal matrix, call it A or A0 or whatever." + }, + { + "text": "Then what do you think about A transpose A?" + }, + { + "text": "What would A transpose A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk22.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..8562bc4837b9c78d63d64c389d0c913d3dc7d8a2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "If that was A, what could you tell me about A transpose A?" + }, + { + "text": "Could you multiply matrices, like knowing where the non-zeros are, like in your head, and get an idea of where?" + }, + { + "text": "So if I have a bidiagonal matrix A, then sort of implicitly in the SVD, I'm looking at A transpose A." + }, + { + "text": "And what would be true about A transpose A?" + }, + { + "text": "It would be tridiagonal." + }, + { + "text": "So what I've done here and what I've done there just match up." + }, + { + "text": "If you don't want to change singular values, you can get all the way to here." + }, + { + "text": "But then to find those singular values, that would involve A transpose A." + }, + { + "text": "It would be symmetric and tridiagonal." + }, + { + "text": "And then you'd be in that game." + }, + { + "text": "So those are the basic facts of I and SVD." + }, + { + "text": "For matrices of order up to 1,000, say." + }, + { + "text": "I'm not enough of an expert to know where." + }, + { + "text": "Maybe higher, because in perfect math, it's going to take infinitely many steps." + }, + { + "text": "Or Abel would be very surprised." + }, + { + "text": "He would see you solving for eigenvalues and then to re-equation by a whole lot of little steps and getting them exactly right." + }, + { + "text": "That won't happen." + }, + { + "text": "But you get them within epsilon in a number of steps that's like n cubed." + }, + { + "text": "So that's pretty impressive." + }, + { + "text": "The eigenvalue problem is being solved, in quotes, by a fast method that gets you a good answer within a tolerance in n cubed steps." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk23.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..37baceeccac2b563da8271de17d70bb205a69d4d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Right." + }, + { + "text": "So that's great as long as n isn't too big." + }, + { + "text": "And then when n is too big, which of course happens, you have to think again." + }, + { + "text": "So this method is a giant success up to large matrices." + }, + { + "text": "But then you have to think again." + }, + { + "text": "And what is involved in thinking again?" + }, + { + "text": "Well, I guess more thinking." + }, + { + "text": "So what do you do if the matrix is bigger?" + }, + { + "text": "I guess that Krylov would say, use my method." + }, + { + "text": "So Krylov would say, especially if your matrix is sparse." + }, + { + "text": "Can we just remember what Krylov was?" + }, + { + "text": "Krylov started with a vector b, multiplied it by a, multiplied that by a, and got up to, let's say, a to the 999b." + }, + { + "text": "So now Krylov has got 1,000 dimensional space." + }, + { + "text": "He's got a basis for it, 1,000 vectors that span 1,000 dimensional space." + }, + { + "text": "And he'll look at the matrix A only on that space." + }, + { + "text": "In other words, I won't go into detail about that." + }, + { + "text": "He restricts the matrix to this 1,000 dimensional space." + }, + { + "text": "And he hopes that it's captured." + }, + { + "text": "We hope that the eigenvector is virtually in that space." + }, + { + "text": "And actually, I wouldn't go up to, let me take a 9 out of that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk24.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..0f5c17cbd60debd628609f1ccf8848eb0fa9b730 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "100 dimensional would probably catch the eigenvector." + }, + { + "text": "So if the eigenvector is virtually in this space, then we can look at a matrix of order 100." + }, + { + "text": "We can bring A down to just see its action on that space." + }, + { + "text": "So I look at vectors V, which are some combination, C1b plus C2ab plus C3a squared b and C100 a to the 99th b, plus an error." + }, + { + "text": "And I'm going to ignore that error." + }, + { + "text": "Because I've gone up to dimension 100." + }, + { + "text": "I probably say it's pretty safe to ignore that error." + }, + { + "text": "And then in this space, just looking at the matrix A." + }, + { + "text": "So wherever A to the 100th comes in, forget it." + }, + { + "text": "Just think about the matrix A as multiplying vectors of this kind in this space." + }, + { + "text": "Then I have a 100 by 100 eigenvalue problem." + }, + { + "text": "And so the big matrix A is reduced to a matrix of size 100 by, do you see sort of what I'm saying, even though I'm not giving the details?" + }, + { + "text": "Think of a matrix A of size a million." + }, + { + "text": "And you apply it to Krylov vectors." + }, + { + "text": "So I call them little k for a Krylov vector in this 100-dimensional space." + }, + { + "text": "So they have a million minus 100, zero components, you could say, this k. This is in the Krylov space." + }, + { + "text": "This is A, a million, k, 100." + }, + { + "text": "It's a full, it's got a million components, but it's out of just 100-dimensional space." + }, + { + "text": "So when I multiply by A, it'll be mostly in, mostly in, partly in the Krylov space, k 100, and a piece out of k 100." + }, + { + "text": "And I just ignore that part of the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk25.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..41342712fde4874aa3c115a8d909e3bf6f2a0e59 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I have a 100 by 100 problem, and I've solved to find the eigenvalues." + }, + { + "text": "And they're a pretty good approximation to the eigenvalues, to the, hopefully, like the lowest 100 eigenvalues." + }, + { + "text": "I'd like to know that." + }, + { + "text": "But I might not be sure that this idea would give me the lowest 100, the first 100 eigenvalues of the million, of the matrix of size a million." + }, + { + "text": "I'm just taking a few minutes here to sort of wave hands about what Krylov, the Krylov idea would do." + }, + { + "text": "And I probably won't mention Krylov again this semester." + }, + { + "text": "So what it can do is look at this particular type of space, because we can get a basis for it quickly, just multiply again and again by A." + }, + { + "text": "Then we can orthogonalize that basis." + }, + { + "text": "That's Graham-Schmidt in some form." + }, + { + "text": "We're always going back to Graham-Schmidt." + }, + { + "text": "Then I have a 100 by 100." + }, + { + "text": "I have a subspace of size 100." + }, + { + "text": "I look at what the matrix does in that space." + }, + { + "text": "And I could look for, I could find eigenvalues restricted to that space." + }, + { + "text": "They wouldn't be the perfect eigenvalues, but they would be accurate." + }, + { + "text": "OK, so I didn't know it would take one class time to talk about finding eigenvalues and singular values, but we did some important things." + }, + { + "text": "We remembered that similarity is the thing to check, thing to preserve, because it doesn't change the eigenvalues." + }, + { + "text": "And then for singular values, what was the thing?" + }, + { + "text": "You could multiply left and right by different orthogonal matrices." + }, + { + "text": "And somehow, maybe that doesn't have an established name, multiplying left and right by a Q1 and a Q2 transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk26.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..2ce06055331ebe329b68e463d8ac9af5a66e37dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk26.json @@ -0,0 +1,35 @@ +[ + { + "text": "Yeah, but the idea is clear." + }, + { + "text": "And that doesn't change the singular values." + }, + { + "text": "We're ready to move now into maybe our next step, which we don't spend a long time on." + }, + { + "text": "We'll be like random sampling." + }, + { + "text": "What if your matrix is just way too big?" + }, + { + "text": "So that's a new, very new idea, very different idea in numerical linear algebra, is just to sample the matrix." + }, + { + "text": "Could you believe that the answer is going to come out right just for a random sample?" + }, + { + "text": "Well, the odds are in your favor." + }, + { + "text": "OK, so that'll be Wednesday, and then we have lots of new, we'll move onward after that." + }, + { + "text": "OK, see you Wednesday." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk3.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..f5acd4bdba4ba51520fdf921a1fc36684dfeaabb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I want to put R0 inverse over there." + }, + { + "text": "So R0." + }, + { + "text": "Now for Q0, I'm going to substitute." + }, + { + "text": "So what is Q0?" + }, + { + "text": "I multiply both sides of that equation by R0 inverse." + }, + { + "text": "So Q0 is A0 is, sorry, I said A and wrote Q. A0 R0 inverse." + }, + { + "text": "Right." + }, + { + "text": "For Q0, I've put in what it equals." + }, + { + "text": "And that's done it." + }, + { + "text": "That's exactly telling me that A1, which is this, equals this." + }, + { + "text": "And that's a similarity transformation." + }, + { + "text": "I have not changed the eigenvalues." + }, + { + "text": "So that's OK." + }, + { + "text": "The other thing, which is the, like you could say, the miracle in this thing, is that when I continue to do that for almost every matrix, the matrices begin to lose stuff off the diagonal, especially below the diagonal by the ordering that QR is done." + }, + { + "text": "So you tend to start with a matrix A0." + }, + { + "text": "You get a matrix A1, which is like a little smaller here." + }, + { + "text": "This part being not especially smaller." + }, + { + "text": "You do it again." + }, + { + "text": "This is even smaller." + }, + { + "text": "So I put even smaller A2, even smaller." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk4.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..a93c5efe93b5619eae3335916949e5ca1b9c543f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you keep going." + }, + { + "text": "And for most matrices, the result is that I don't know how many steps we want to think of taking, but we get quite small numbers here." + }, + { + "text": "So once we get small numbers here, little epsilons, that's everybody's shorthand for small numbers, what would you expect to see on the diagonal?" + }, + { + "text": "The eigenvalues." + }, + { + "text": "Because this has the same eigenvalues as this, as this, as this." + }, + { + "text": "And these little epsilons are not going to change the eigenvalues too much." + }, + { + "text": "So these will be, on the diagonal, will be close to the eigenvalues." + }, + { + "text": "And actually, what happens is this one comes first." + }, + { + "text": "That one is quite accurate first." + }, + { + "text": "I guess we should probably do a simple example to see this happen." + }, + { + "text": "Actually, I do an example in the notes." + }, + { + "text": "And let me say what happens." + }, + { + "text": "So I do a 2 by 2 example, which has something like cos theta, sine theta." + }, + { + "text": "I don't know what." + }, + { + "text": "I've forgotten what I took." + }, + { + "text": "And I don't have that page of notes here." + }, + { + "text": "Something here." + }, + { + "text": "Something here." + }, + { + "text": "Something here as a 0." + }, + { + "text": "And then a 1, after just one step, has sine cubed theta there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk5.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..2c1c69b5647ae63cfaad8af10731e95f060b6c81 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And numbers there that are getting much closer to the eigenvalues." + }, + { + "text": "Sorry that this isn't a full scale example." + }, + { + "text": "But the point of the example is here, that this off-diagonal entry gets cubed." + }, + { + "text": "And the next step will be its ninth power, and then the 27th power." + }, + { + "text": "So it's really quickly going to 0." + }, + { + "text": "And this happens." + }, + { + "text": "So cubic convergence is a prize." + }, + { + "text": "In numerical linear algebra." + }, + { + "text": "So that happens." + }, + { + "text": "So this arrived on the scene and quickly blew away all other methods that were being used to compute eigenvalues." + }, + { + "text": "But numerical people, being what they are, they wanted to improve it." + }, + { + "text": "Like, is there a way to make it faster?" + }, + { + "text": "And turned out there is." + }, + { + "text": "It turned out that the better way, basically the same idea, but just you're always looking for a simple change." + }, + { + "text": "And the idea of introducing a shift was tried." + }, + { + "text": "And turned out to work extremely well." + }, + { + "text": "So that's the improvement." + }, + { + "text": "So we take a1." + }, + { + "text": "No, so how does the shift work?" + }, + { + "text": "So instead of a0, have I got space here to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk6.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..e081a02643a2181251ac74e36b445d55b6192f14 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Instead of a0, I take a0 minus a shift." + }, + { + "text": "So a shift is some multiple of the identity." + }, + { + "text": "If I just move a matrix by a multiple of the identity, what happens to its eigenvectors?" + }, + { + "text": "What happens to its eigenvalues?" + }, + { + "text": "Something pretty simple, right?" + }, + { + "text": "Because I'm just shifting by si." + }, + { + "text": "What happens to its eigenvectors?" + }, + { + "text": "They're the same." + }, + { + "text": "And what happens to the eigenvalues?" + }, + { + "text": "They change by s. If a0v equals lambda v, then when I multiply this by v, there will be an extra." + }, + { + "text": "It'll be lambda minus s. Because the identity times the v is just v. So it just shifts all the eigenvalues by s. And you try to shift." + }, + { + "text": "You look for a shift." + }, + { + "text": "This would be great." + }, + { + "text": "If you knew lambda n, a shift there, you would be looking for 0 then, if you shifted them all by that lambda." + }, + { + "text": "And it turns out that would speed things up." + }, + { + "text": "So you work instead with this matrix as now, again, I'm factoring in a q0, r0." + }, + { + "text": "So that's the work of the method, is in doing Gram-Schmidt at every step." + }, + { + "text": "And then there's a little work in reversing the order." + }, + { + "text": "And then I want to undo the shift." + }, + { + "text": "So I do that factorization." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk7.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..212c509ec27724246ec3a49d4c24022c4979b516 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, let's see." + }, + { + "text": "You may have to help me to remember what I should do here." + }, + { + "text": "So I factor those." + }, + { + "text": "I reverse those." + }, + { + "text": "And then I think I add back the shift." + }, + { + "text": "And that's my A1." + }, + { + "text": "So I took A0." + }, + { + "text": "I shifted it." + }, + { + "text": "I worked with it, qr, reversed the order, rq, added back the shift to get a matrix." + }, + { + "text": "And what am I, of course, hoping about the matrix A1 and A0?" + }, + { + "text": "I'm hoping they're still similar." + }, + { + "text": "I'm hoping." + }, + { + "text": "So I did a shift." + }, + { + "text": "And I undid a shift." + }, + { + "text": "But of course, after doing a qr, I have to check, are these really still similar?" + }, + { + "text": "So let me just try to check that one again." + }, + { + "text": "Maybe I'll just, it's sitting right there." + }, + { + "text": "So let me do it again." + }, + { + "text": "I'm hoping that something, you know, where did we change?" + }, + { + "text": "Oh, yeah, here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk8.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..4e7fad6f92f20cdf436db6b8933b889b8a6fb34f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We showed that A1 was similar to A0." + }, + { + "text": "And I'm hoping that's probably still true, even, you know, the shift didn't mess that up." + }, + { + "text": "Let's just try." + }, + { + "text": "So A0, that's r0, q0 plus si." + }, + { + "text": "OK. And now what am I going to do?" + }, + { + "text": "I'm going to, what did I do before?" + }, + { + "text": "I figured out what q0 was from this." + }, + { + "text": "You remember?" + }, + { + "text": "So this is r0." + }, + { + "text": "Now I have to put in q0." + }, + { + "text": "But q0 is this thing inverse times this." + }, + { + "text": "Is this going to work?" + }, + { + "text": "I'm like hoping, but I don't think I wanted to get that." + }, + { + "text": "No, it's not q0 there." + }, + { + "text": "What do I put here?" + }, + { + "text": "And if it doesn't work, we'll leave it as an exercise." + }, + { + "text": "OK." + }, + { + "text": "So yeah, because I didn't sort of start right somehow." + }, + { + "text": "OK." + }, + { + "text": "So but let me just push along to see what happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk9.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..f66b5f2f317c991f9ad92b2dc38dd936ae5d8d21 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_4_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I'm plugging in for q0 here." + }, + { + "text": "I'm plugging in this matrix, so it shouldn't have inverted it, times r0 inverse." + }, + { + "text": "Who knows?" + }, + { + "text": "It might work." + }, + { + "text": "Who knows?" + }, + { + "text": "So that's the r0, q0." + }, + { + "text": "Right?" + }, + { + "text": "Is everybody with me?" + }, + { + "text": "Sorry about this." + }, + { + "text": "So r0 inverse." + }, + { + "text": "And then I have to add Si." + }, + { + "text": "So what have I done?" + }, + { + "text": "I've just pushed on, believing that this would work." + }, + { + "text": "Because it's the method that is constantly used." + }, + { + "text": "Now do I have?" + }, + { + "text": "What do I have there?" + }, + { + "text": "Is it working?" + }, + { + "text": "This is r0 A." + }, + { + "text": "That was, of course, A0." + }, + { + "text": "r0 A0 r0 inverse." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk0.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..afc91322b0d9d5a0ce3bfb215b0940ebb7754749 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "OK, why don't I start?" + }, + { + "text": "So I was hoping that we would have the next online assignment ready, but Julia 6, the new version, is slowing us down." + }, + { + "text": "And it'd probably be next time." + }, + { + "text": "But my lectures, of course, are, well, what I want to say perhaps is this isn't intended to be a course in numerical linear algebra." + }, + { + "text": "But I thought I couldn't let the whole semester go by without saying something about how to compute eigenvalues and singular values." + }, + { + "text": "Of course, you're going to call I or SVD or the equivalent in Python or Julia." + }, + { + "text": "But actually, the QR factorization that we spoke about, that we spoke entirely about last time is the key, unexpectedly, unexpectedly." + }, + { + "text": "You have a matrix A whose eigenvalues you want." + }, + { + "text": "So let's start with eigenvalues." + }, + { + "text": "And it might be a symmetric matrix." + }, + { + "text": "I'll stay with A rather than S because it doesn't have to be." + }, + { + "text": "But you get special always." + }, + { + "text": "You get something special if the matrix is symmetric." + }, + { + "text": "OK, so this method of computing eigenvalues, to me at least, and I think to many people, came like out of the blue a while ago, but not that long ago." + }, + { + "text": "And it worked very well." + }, + { + "text": "So here's the idea." + }, + { + "text": "It's called the QR method because you start by factoring your matrix into QR." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk1.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..f693f6b2ff21648d32a7af5f95cf39d07b0de862 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's A." + }, + { + "text": "Can we call it A0?" + }, + { + "text": "That's the matrix we start with whose eigenvalues we want." + }, + { + "text": "And I'll call these Q0 and R0." + }, + { + "text": "And you remember what that means, what's hiding behind those letters that I've written?" + }, + { + "text": "You have the columns of A, possibly symmetric, as I said, but not orthogonal, usually." + }, + { + "text": "So you find an orthogonal basis." + }, + { + "text": "You orthogonalize them." + }, + { + "text": "You line them up perpendicular to each other." + }, + { + "text": "And then there is a matrix R, which happens to be upper triangular, that connects." + }, + { + "text": "The not orthogonal basis with the orthogonal basis." + }, + { + "text": "Right, we constructed R step by step." + }, + { + "text": "And then the idea is write these in the reverse order." + }, + { + "text": "And that will be A1, the next A. OK, and then do it again, and again, and again." + }, + { + "text": "And so we're hoping, of course, that the eigenvalues didn't change." + }, + { + "text": "We're hoping that we can forget A0, start again with A1, and produce A2, and continue." + }, + { + "text": "So we're hoping two things." + }, + { + "text": "One will not be a hope." + }, + { + "text": "We can see that the eigenvalues of A1 and A0 are the same." + }, + { + "text": "So we have not changed the eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk10.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..6fb2da774bad3a68b507efacec13f9801a995312 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "r0 A0 r0 inverse." + }, + { + "text": "Good." + }, + { + "text": "Minus S. What have I got there?" + }, + { + "text": "From the r0 minus Si r0, what is that?" + }, + { + "text": "That's minus Si." + }, + { + "text": "Look, success." + }, + { + "text": "The r0 cancels the r0 inverse." + }, + { + "text": "So that term from that, that, that is minus Si." + }, + { + "text": "Cancels plus Si." + }, + { + "text": "I'm finished." + }, + { + "text": "And lo and behold, we have the same similarity." + }, + { + "text": "So we messed around by a multiple of the identity, and it actually makes the thing converge faster if we choose the shifts well." + }, + { + "text": "But basically, the same idea is still working." + }, + { + "text": "OK." + }, + { + "text": "So that's the QR method." + }, + { + "text": "Well, that's the method we haven't shown and won't show." + }, + { + "text": "Except for this half-completed example, I don't plan to prove that the lower triangular part begins to disappear, gets smaller and smaller and smaller, and then the eigenvalues pop up on the diagonal." + }, + { + "text": "It's amazing." + }, + { + "text": "Amazing." + }, + { + "text": "OK. Now, is there any other improvement we can make?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk11.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..9e5764513ae4ce678e41ecfcb72a4895642b01f6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's the method." + }, + { + "text": "And where is the work in using that method?" + }, + { + "text": "Because that's what we always focus on." + }, + { + "text": "Where are we spending computer time?" + }, + { + "text": "Well, we're spending computer time in doing the factorization." + }, + { + "text": "So it didn't cost anything to shift by the identity, but then we had to factor that into Q0, R0." + }, + { + "text": "Then it didn't cost much to multiply them in the opposite order." + }, + { + "text": "So the work was in QR." + }, + { + "text": "So could we think of anything to improve that aspect?" + }, + { + "text": "Could we think of anything there?" + }, + { + "text": "And then we've got a really first-class method." + }, + { + "text": "Well, if the matrix A, A0, the matrix we started with, had some zeros that allowed us to skip steps in doing the QR factorization." + }, + { + "text": "So what am I going to say?" + }, + { + "text": "I'm going to say if A or A0, our original matrix, has a bunch of zeros, let's say it's got a whole lot of zeros there." + }, + { + "text": "Maybe it's, well, OK." + }, + { + "text": "I overdid it here." + }, + { + "text": "I know the eigenvalues right off." + }, + { + "text": "But so the truth is I can't, saying that if that, it's not going to happen." + }, + { + "text": "But we can get zeros with one extra diagonal." + }, + { + "text": "That turns out, so here's the main diagonal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk12.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..ab7132ecacaf6cb9786d7b5f399f0082623bd923 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Everybody's got his eye on the main diagonal." + }, + { + "text": "And one diagonal, I can get a lot of zeros." + }, + { + "text": "But I can't by simple computations." + }, + { + "text": "And I'll show you how to get one." + }, + { + "text": "But I can't get all those to be 0, because then I would have the eigenvalues right there." + }, + { + "text": "And that, well, how do I know that I can't?" + }, + { + "text": "In elimination, ordinary solving AX equal B, you really do get to an upper triangular form." + }, + { + "text": "Some operator, some elimination steps, you plug away, and your matrix becomes upper triangular U." + }, + { + "text": "And you're golden." + }, + { + "text": "But that's too much to expect here." + }, + { + "text": "In fact, we know we can't do it by simple steps." + }, + { + "text": "Because if we could do it, if we could get to a U with a whole lower triangular part 0, we would have found the eigenvalues." + }, + { + "text": "And we know that the eigenvalues solve an equation of nth degree." + }, + { + "text": "And we know somebody proved centuries or more ago that you can't solve an nth degree equation by simple little steps." + }, + { + "text": "Right?" + }, + { + "text": "Do you know who that was?" + }, + { + "text": "And you know that fact?" + }, + { + "text": "And what degree does it apply to?" + }, + { + "text": "So that's an important fact that you sort of pick up in math." + }, + { + "text": "Yeah, what do you?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk13.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..5ef254fb5bc0df6883bfe89b2da2433a3da88094 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Fifth degree, yeah." + }, + { + "text": "So 5 by 5 and up would be, this is impossible." + }, + { + "text": "Impossible." + }, + { + "text": "There's no formula to find a simple formula for the lambdas." + }, + { + "text": "And similarly for the sigmas, the singular values." + }, + { + "text": "So the eigenvalues is definitely a level of difficulty beyond Ax equal b, the inverse matrix or something, the pivots." + }, + { + "text": "All that you can do exactly if you do exact arithmetic." + }, + { + "text": "We cannot find the lambdas exactly." + }, + { + "text": "But we can get as close as we like by continuing with the QR method." + }, + { + "text": "So yeah, in other words, we have to settle for, if we want to, at the beginning, improve our matrix before we start doing that stuff." + }, + { + "text": "We can get it with one extra diagonal." + }, + { + "text": "And do you know what kind of a matrix, whose name?" + }, + { + "text": "And I don't know why." + }, + { + "text": "Yeah, say it again." + }, + { + "text": "Upper Hessenberg." + }, + { + "text": "So upper is just like upper triangular." + }, + { + "text": "It's up there." + }, + { + "text": "But the key person's name is Hessenberg." + }, + { + "text": "As I say, that's a Hessenberg matrix." + }, + { + "text": "So Hessenberg matrix is a matrix with one triangular plus one more diagonal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk14.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..890f75c227f0ce9167ef179281769727e008c678 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "But lots of zeros." + }, + { + "text": "Order of n squared, something like almost like half n squared, not quite, but close, zeros." + }, + { + "text": "And you could show that those zeros stay zeros in QR." + }, + { + "text": "So that really pays off." + }, + { + "text": "It cuts the work down significantly." + }, + { + "text": "So the full QR method is step one, reduce A to Hessenberg form with these zeros." + }, + { + "text": "And when I say reduce, I mean find a similarity transformation, of course, because I want the eigenvalues of this to end up the same as the Hessen." + }, + { + "text": "I want to keep the same eigenvalues as I go." + }, + { + "text": "And then step two is QR on this Hessenberg matrix with shifts." + }, + { + "text": "So that's the code that would be programmed in IGAVE." + }, + { + "text": "That's what MATLAB and, well, really, MATLAB is appealing, like other matrix systems, is appealing to LAPAC and LINPAC." + }, + { + "text": "The team of professional numerical analysts really spent a lot of effort and time." + }, + { + "text": "The book LAPAC has 10 authors." + }, + { + "text": "And you can download any of these codes, like the eigenvalue code." + }, + { + "text": "So that's where MATLAB naturally, that's sort of the Bible for codes in linear algebra." + }, + { + "text": "OK, now, I think it's sort of interesting to know." + }, + { + "text": "And there is one more good thing to tell you about this method." + }, + { + "text": "And it applies if the matrix is symmetric." + }, + { + "text": "If the matrix is symmetric, then if we check all this, we could find that the matrices stayed symmetric." + }, + { + "text": "If A0 is symmetric, I can check." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk15.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..1cdfb555c6b2be5bd3044a831ed3f643f560293a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "You could easily check through this, and you would discover that A1 is also symmetric." + }, + { + "text": "It turns out you could rewrite this with a Q0 and a Q0 inverse on the other side." + }, + { + "text": "But that Q0 inverse is the same as Q0 transpose, because it's an orthogonal matrix, and symmetry would fall out." + }, + { + "text": "So if it's symmetric, and it's in Hessenberg form, and it stays symmetric at every step, what can you tell me about a symmetric Hessenberg matrix?" + }, + { + "text": "It's only got, yeah, you just erase all these." + }, + { + "text": "If there are zeros there, and if the matrix is symmetric, then we can safely predict that it will only have one diagonal above, one non-zero diagonal above the main diagonal." + }, + { + "text": "In fact, it'll stay symmetric." + }, + { + "text": "So now I should write symmetric Hessenberg matrix, n equals tri-diagonal matrix." + }, + { + "text": "Yeah, three diagonals." + }, + { + "text": "So now you really have reduced the time to do QR, because you've got a tri-diagonal matrix." + }, + { + "text": "It'll stay tri-diagonal in all these steps." + }, + { + "text": "So you're working with just 3n numbers." + }, + { + "text": "Well, actually, 2n, because the diagonal above and the diagonal below are the same." + }, + { + "text": "You're working with just 2n numbers instead of order n squared, and it just goes like a bomb." + }, + { + "text": "So that's I for symmetric matrices." + }, + { + "text": "And you see that it was all based, that really the heart of the algorithm was QR." + }, + { + "text": "So that's my, it took half the class to report on the favorite way, the EIG way, to find eigenvalues." + }, + { + "text": "Oh, I should say something about singular values." + }, + { + "text": "So singular values, of course, the singular values of the matrix are the eigenvalues of A transpose A, square root of those eigenvalues." + }, + { + "text": "But you wouldn't do it that way." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk16.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..7989fa8939f6d17bfb6b36b82c96bbd76b92a4f6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "You would never form A transpose A. Oh, I didn't mention the other thing you would never, ever, ever do." + }, + { + "text": "So let me just put it here." + }, + { + "text": "This is like in disgrace to solve that equation." + }, + { + "text": "It's like, OK, back to first grade, because that's not, that's very bad." + }, + { + "text": "A determinant, first of all, it's extremely slow, extremely slow." + }, + { + "text": "And the determinant is packing all this n squared pieces of information into n coefficients, and it's hopelessly ill-conditioned." + }, + { + "text": "Yeah, you just, you lose information all the time." + }, + { + "text": "So really, if this is going on camera, it better go on camera with an x, because don't do it." + }, + { + "text": "OK. Yeah." + }, + { + "text": "So where was I?" + }, + { + "text": "Singular values." + }, + { + "text": "So A transpose A." + }, + { + "text": "So again, let's think about what you could do at the beginning before starting on QR for A transpose A, or for the matrix A." + }, + { + "text": "What could you do with orthogonal matrices?" + }, + { + "text": "So I guess, what did we say about symmetric matrices?" + }, + { + "text": "So here's what I said about symmetric matrices." + }, + { + "text": "If you give me a symmetric matrix, I can, in just a simple number of simple steps, make it tridiagonal." + }, + { + "text": "I can't make it diagonal, because then I'd be finding the eigenvalues, and Abel, who was the first person to see that that was impossible, forbids it." + }, + { + "text": "But so let me write down what I'm saying here." + }, + { + "text": "If I have a symmetric matrix S, I can find a bunch of Q's and Q transposes, and I can put them all together into one big Q, and it's transposed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk17.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..08d99076ccc98b0932858bac2de5382359f2d221 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I know about the eigenvalues of that matrix?" + }, + { + "text": "Q is orthogonal always." + }, + { + "text": "So what can you tell me about the, this is the same as Q S Q inverse, and therefore, the eigenvalues are the same." + }, + { + "text": "It's similar to S. And it becomes tridiagonal after I find a good Q." + }, + { + "text": "Now, and therefore, same lambdas, tridiagonal with the same lambdas." + }, + { + "text": "Now, what am I thinking about here?" + }, + { + "text": "I'm thinking about, tell me the corresponding possibility about singular values." + }, + { + "text": "I want to do something to my matrix." + }, + { + "text": "Now, I'm always taking a general matrix A." + }, + { + "text": "And I'm looking for its singular values." + }, + { + "text": "And I'm looking to simplify it." + }, + { + "text": "And what am I allowed to do?" + }, + { + "text": "Yeah, I guess my question is, similarity transformations left the eigenvalues alone." + }, + { + "text": "What can I do that leaves the singular values alone?" + }, + { + "text": "That's a fundamental question, because it was so fundamental for eigenvalues." + }, + { + "text": "By doing this, a matrix and its inverse, I got something similar." + }, + { + "text": "And I checked even in this class that the eigenvalues, same lambdas." + }, + { + "text": "Now I want a whole line that ends up with the same sigmas." + }, + { + "text": "And I want you to tell me what I'm allowed to do to the matrix without changing the sigmas." + }, + { + "text": "So maybe don't shout it out immediately." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk18.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..31cc3c0860684bbd35bab2fb28f2d606a8921e5b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let everybody think." + }, + { + "text": "What am I allowed to do to a matrix?" + }, + { + "text": "Every matrix has got these singular values." + }, + { + "text": "And now I want to make it a better matrix with more 0's or something." + }, + { + "text": "If I do that to it, does that change the sigmas?" + }, + { + "text": "Can I do more than that to it?" + }, + { + "text": "What can I do?" + }, + { + "text": "What group of matrices will have the same sigmas as my starting matrix A?" + }, + { + "text": "So that's a basic, basic question about singular values and the SVD." + }, + { + "text": "So let's think of the answer together." + }, + { + "text": "So it's connected to the SVD." + }, + { + "text": "So let me remember the SVD." + }, + { + "text": "The SVD, I have some orthogonal matrix, then the singular value matrix, SV for singular values, and then another orthogonal matrix." + }, + { + "text": "What could I do to that equation that would not touch this guy?" + }, + { + "text": "So I'm asking what invariance, because not touching it means leaving it not varying." + }, + { + "text": "So I'm looking for under what operations are the singular values invariant?" + }, + { + "text": "When I was looking at eigenvalues, this was the operation." + }, + { + "text": "Well, it didn't have to be orthogonal." + }, + { + "text": "It's something, and it's inverse." + }, + { + "text": "But now what is it up there?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk19.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..01b201f72f3bceb5bd8b70cfc01d55a2e2ff2a71 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "What could I do to that matrix A?" + }, + { + "text": "Could I multiply by Q?" + }, + { + "text": "Could I throw in a Q?" + }, + { + "text": "Maybe not even on the other end." + }, + { + "text": "If I throw in an orthogonal Q, do I change the singular values or do I not change them?" + }, + { + "text": "Fundamental question." + }, + { + "text": "The answer is no, I don't change them." + }, + { + "text": "I'm allowed to do that, because here's an orthogonal matrix, a Q times U." + }, + { + "text": "If both of those are orthogonal, then the product is." + }, + { + "text": "Everybody knows that a product of two orthogonal matrix is still orthogonal." + }, + { + "text": "Better know that." + }, + { + "text": "Better know that." + }, + { + "text": "Yeah." + }, + { + "text": "So if I have an orthogonal matrix Q and an orthogonal matrix U, I claim that this is still orthogonal." + }, + { + "text": "And how do I check it?" + }, + { + "text": "Well, I use some test for orthogonality." + }, + { + "text": "What would be the test you like to use?" + }, + { + "text": "The inverse is the same as the transpose." + }, + { + "text": "You like that test?" + }, + { + "text": "So I'll invert it." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk2.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..49f68a61aecdf81153b85d35f02c4fd1ad64e79f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "How do we see that?" + }, + { + "text": "If you had to show that two matrices had the same eigenvalues, would you compute all the eigenvalues and compare them?" + }, + { + "text": "Certainly not." + }, + { + "text": "What would you do?" + }, + { + "text": "What's the best test, the usual test, the usual thing you would want to show?" + }, + { + "text": "They're similar." + }, + { + "text": "That's right." + }, + { + "text": "So the claim would be that these two matrices are similar." + }, + { + "text": "Right." + }, + { + "text": "So maybe we should show that." + }, + { + "text": "So we want to write A1 in a different way." + }, + { + "text": "So the claim is A1 is similar to A." + }, + { + "text": "So we just have to figure out." + }, + { + "text": "We have to get A1 to A0." + }, + { + "text": "So here's A1." + }, + { + "text": "OK." + }, + { + "text": "So A1, I want to show that that's right." + }, + { + "text": "So that's R0, Q0." + }, + { + "text": "But what is Q0?" + }, + { + "text": "From here, Q0 is what we is R. Q0 is, what do I want?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk20.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..35801c36445d73fe11e2f6274bad6dd29215b8e2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Q U inverse." + }, + { + "text": "Of course, for any matrix, that's U inverse Q inverse." + }, + { + "text": "But these were separately orthogonal, so that's U transpose Q transpose." + }, + { + "text": "And that is the same as Q U transpose." + }, + { + "text": "Yeah." + }, + { + "text": "So I use the orthogonality of U and the orthogonality of Q to conclude that the inverse is the transpose." + }, + { + "text": "So the answer is yes, I could do that." + }, + { + "text": "Now, with singular value, with eigenvalues, I had to multiply on the other side by Q inverse or Q transpose." + }, + { + "text": "Do I have to do that now?" + }, + { + "text": "No." + }, + { + "text": "What can I do on the right-hand side?" + }, + { + "text": "I can multiply by." + }, + { + "text": "I can leave it alone." + }, + { + "text": "Then it has the same singular values because it's the same sigma in there." + }, + { + "text": "If I have a orthogonal matrix times a diagonal times an orthogonal, that diagonal, positive diagonal, is going to be sigma." + }, + { + "text": "So what can I do on this side?" + }, + { + "text": "I could multiply by any orthogonal matrix on that side, too." + }, + { + "text": "So let's call this guy Q1 and this guy Q2." + }, + { + "text": "I still have an orthogonal matrix there, orthogonal matrix there, and the same sigma popped in the middle." + }, + { + "text": "So that's what you're allowed to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk21.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..8733bff8727902ad93fdca4f142729506ca43859 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "That gives us more freedom." + }, + { + "text": "Before, when we had to do similarity transformations with the same guy, we got it to be tridiagonal." + }, + { + "text": "But now we're allowed to do more stuff." + }, + { + "text": "We're allowed to use different orthogonal matrices on the left and right." + }, + { + "text": "And we can reduce it even further from tridiagonal to bidiagonal." + }, + { + "text": "So the first step is getting 0." + }, + { + "text": "The step of getting 0s reduces it all the way to that with all 0s there." + }, + { + "text": "So it's easier." + }, + { + "text": "Then I work on this." + }, + { + "text": "I work on using a QR type idea, some method like that." + }, + { + "text": "So everybody's seeing that our algorithm has got two stages." + }, + { + "text": "One is get a lot of 0s and get them in places that will stay 0 as part 2 of the algorithm gets going." + }, + { + "text": "And then run part 2 of the algorithm." + }, + { + "text": "You're staying with each step is very fast now because doing a QR factorization is fast." + }, + { + "text": "Was there a question?" + }, + { + "text": "Yeah." + }, + { + "text": "So I would call this bidiagonal, of course." + }, + { + "text": "And everybody recognizes that if I have a bidiagonal matrix, call it A or A0 or whatever." + }, + { + "text": "Then what do you think about A transpose A?" + }, + { + "text": "What would A transpose A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk22.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..8562bc4837b9c78d63d64c389d0c913d3dc7d8a2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "If that was A, what could you tell me about A transpose A?" + }, + { + "text": "Could you multiply matrices, like knowing where the non-zeros are, like in your head, and get an idea of where?" + }, + { + "text": "So if I have a bidiagonal matrix A, then sort of implicitly in the SVD, I'm looking at A transpose A." + }, + { + "text": "And what would be true about A transpose A?" + }, + { + "text": "It would be tridiagonal." + }, + { + "text": "So what I've done here and what I've done there just match up." + }, + { + "text": "If you don't want to change singular values, you can get all the way to here." + }, + { + "text": "But then to find those singular values, that would involve A transpose A." + }, + { + "text": "It would be symmetric and tridiagonal." + }, + { + "text": "And then you'd be in that game." + }, + { + "text": "So those are the basic facts of I and SVD." + }, + { + "text": "For matrices of order up to 1,000, say." + }, + { + "text": "I'm not enough of an expert to know where." + }, + { + "text": "Maybe higher, because in perfect math, it's going to take infinitely many steps." + }, + { + "text": "Or Abel would be very surprised." + }, + { + "text": "He would see you solving for eigenvalues and then to re-equation by a whole lot of little steps and getting them exactly right." + }, + { + "text": "That won't happen." + }, + { + "text": "But you get them within epsilon in a number of steps that's like n cubed." + }, + { + "text": "So that's pretty impressive." + }, + { + "text": "The eigenvalue problem is being solved, in quotes, by a fast method that gets you a good answer within a tolerance in n cubed steps." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk23.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..37baceeccac2b563da8271de17d70bb205a69d4d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Right." + }, + { + "text": "So that's great as long as n isn't too big." + }, + { + "text": "And then when n is too big, which of course happens, you have to think again." + }, + { + "text": "So this method is a giant success up to large matrices." + }, + { + "text": "But then you have to think again." + }, + { + "text": "And what is involved in thinking again?" + }, + { + "text": "Well, I guess more thinking." + }, + { + "text": "So what do you do if the matrix is bigger?" + }, + { + "text": "I guess that Krylov would say, use my method." + }, + { + "text": "So Krylov would say, especially if your matrix is sparse." + }, + { + "text": "Can we just remember what Krylov was?" + }, + { + "text": "Krylov started with a vector b, multiplied it by a, multiplied that by a, and got up to, let's say, a to the 999b." + }, + { + "text": "So now Krylov has got 1,000 dimensional space." + }, + { + "text": "He's got a basis for it, 1,000 vectors that span 1,000 dimensional space." + }, + { + "text": "And he'll look at the matrix A only on that space." + }, + { + "text": "In other words, I won't go into detail about that." + }, + { + "text": "He restricts the matrix to this 1,000 dimensional space." + }, + { + "text": "And he hopes that it's captured." + }, + { + "text": "We hope that the eigenvector is virtually in that space." + }, + { + "text": "And actually, I wouldn't go up to, let me take a 9 out of that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk24.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..0f5c17cbd60debd628609f1ccf8848eb0fa9b730 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "100 dimensional would probably catch the eigenvector." + }, + { + "text": "So if the eigenvector is virtually in this space, then we can look at a matrix of order 100." + }, + { + "text": "We can bring A down to just see its action on that space." + }, + { + "text": "So I look at vectors V, which are some combination, C1b plus C2ab plus C3a squared b and C100 a to the 99th b, plus an error." + }, + { + "text": "And I'm going to ignore that error." + }, + { + "text": "Because I've gone up to dimension 100." + }, + { + "text": "I probably say it's pretty safe to ignore that error." + }, + { + "text": "And then in this space, just looking at the matrix A." + }, + { + "text": "So wherever A to the 100th comes in, forget it." + }, + { + "text": "Just think about the matrix A as multiplying vectors of this kind in this space." + }, + { + "text": "Then I have a 100 by 100 eigenvalue problem." + }, + { + "text": "And so the big matrix A is reduced to a matrix of size 100 by, do you see sort of what I'm saying, even though I'm not giving the details?" + }, + { + "text": "Think of a matrix A of size a million." + }, + { + "text": "And you apply it to Krylov vectors." + }, + { + "text": "So I call them little k for a Krylov vector in this 100-dimensional space." + }, + { + "text": "So they have a million minus 100, zero components, you could say, this k. This is in the Krylov space." + }, + { + "text": "This is A, a million, k, 100." + }, + { + "text": "It's a full, it's got a million components, but it's out of just 100-dimensional space." + }, + { + "text": "So when I multiply by A, it'll be mostly in, mostly in, partly in the Krylov space, k 100, and a piece out of k 100." + }, + { + "text": "And I just ignore that part of the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk25.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..41342712fde4874aa3c115a8d909e3bf6f2a0e59 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I have a 100 by 100 problem, and I've solved to find the eigenvalues." + }, + { + "text": "And they're a pretty good approximation to the eigenvalues, to the, hopefully, like the lowest 100 eigenvalues." + }, + { + "text": "I'd like to know that." + }, + { + "text": "But I might not be sure that this idea would give me the lowest 100, the first 100 eigenvalues of the million, of the matrix of size a million." + }, + { + "text": "I'm just taking a few minutes here to sort of wave hands about what Krylov, the Krylov idea would do." + }, + { + "text": "And I probably won't mention Krylov again this semester." + }, + { + "text": "So what it can do is look at this particular type of space, because we can get a basis for it quickly, just multiply again and again by A." + }, + { + "text": "Then we can orthogonalize that basis." + }, + { + "text": "That's Graham-Schmidt in some form." + }, + { + "text": "We're always going back to Graham-Schmidt." + }, + { + "text": "Then I have a 100 by 100." + }, + { + "text": "I have a subspace of size 100." + }, + { + "text": "I look at what the matrix does in that space." + }, + { + "text": "And I could look for, I could find eigenvalues restricted to that space." + }, + { + "text": "They wouldn't be the perfect eigenvalues, but they would be accurate." + }, + { + "text": "OK, so I didn't know it would take one class time to talk about finding eigenvalues and singular values, but we did some important things." + }, + { + "text": "We remembered that similarity is the thing to check, thing to preserve, because it doesn't change the eigenvalues." + }, + { + "text": "And then for singular values, what was the thing?" + }, + { + "text": "You could multiply left and right by different orthogonal matrices." + }, + { + "text": "And somehow, maybe that doesn't have an established name, multiplying left and right by a Q1 and a Q2 transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk26.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..2ce06055331ebe329b68e463d8ac9af5a66e37dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk26.json @@ -0,0 +1,35 @@ +[ + { + "text": "Yeah, but the idea is clear." + }, + { + "text": "And that doesn't change the singular values." + }, + { + "text": "We're ready to move now into maybe our next step, which we don't spend a long time on." + }, + { + "text": "We'll be like random sampling." + }, + { + "text": "What if your matrix is just way too big?" + }, + { + "text": "So that's a new, very new idea, very different idea in numerical linear algebra, is just to sample the matrix." + }, + { + "text": "Could you believe that the answer is going to come out right just for a random sample?" + }, + { + "text": "Well, the odds are in your favor." + }, + { + "text": "OK, so that'll be Wednesday, and then we have lots of new, we'll move onward after that." + }, + { + "text": "OK, see you Wednesday." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk3.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..f5acd4bdba4ba51520fdf921a1fc36684dfeaabb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I want to put R0 inverse over there." + }, + { + "text": "So R0." + }, + { + "text": "Now for Q0, I'm going to substitute." + }, + { + "text": "So what is Q0?" + }, + { + "text": "I multiply both sides of that equation by R0 inverse." + }, + { + "text": "So Q0 is A0 is, sorry, I said A and wrote Q. A0 R0 inverse." + }, + { + "text": "Right." + }, + { + "text": "For Q0, I've put in what it equals." + }, + { + "text": "And that's done it." + }, + { + "text": "That's exactly telling me that A1, which is this, equals this." + }, + { + "text": "And that's a similarity transformation." + }, + { + "text": "I have not changed the eigenvalues." + }, + { + "text": "So that's OK." + }, + { + "text": "The other thing, which is the, like you could say, the miracle in this thing, is that when I continue to do that for almost every matrix, the matrices begin to lose stuff off the diagonal, especially below the diagonal by the ordering that QR is done." + }, + { + "text": "So you tend to start with a matrix A0." + }, + { + "text": "You get a matrix A1, which is like a little smaller here." + }, + { + "text": "This part being not especially smaller." + }, + { + "text": "You do it again." + }, + { + "text": "This is even smaller." + }, + { + "text": "So I put even smaller A2, even smaller." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk4.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..a93c5efe93b5619eae3335916949e5ca1b9c543f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you keep going." + }, + { + "text": "And for most matrices, the result is that I don't know how many steps we want to think of taking, but we get quite small numbers here." + }, + { + "text": "So once we get small numbers here, little epsilons, that's everybody's shorthand for small numbers, what would you expect to see on the diagonal?" + }, + { + "text": "The eigenvalues." + }, + { + "text": "Because this has the same eigenvalues as this, as this, as this." + }, + { + "text": "And these little epsilons are not going to change the eigenvalues too much." + }, + { + "text": "So these will be, on the diagonal, will be close to the eigenvalues." + }, + { + "text": "And actually, what happens is this one comes first." + }, + { + "text": "That one is quite accurate first." + }, + { + "text": "I guess we should probably do a simple example to see this happen." + }, + { + "text": "Actually, I do an example in the notes." + }, + { + "text": "And let me say what happens." + }, + { + "text": "So I do a 2 by 2 example, which has something like cos theta, sine theta." + }, + { + "text": "I don't know what." + }, + { + "text": "I've forgotten what I took." + }, + { + "text": "And I don't have that page of notes here." + }, + { + "text": "Something here." + }, + { + "text": "Something here." + }, + { + "text": "Something here as a 0." + }, + { + "text": "And then a 1, after just one step, has sine cubed theta there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk5.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..2c1c69b5647ae63cfaad8af10731e95f060b6c81 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And numbers there that are getting much closer to the eigenvalues." + }, + { + "text": "Sorry that this isn't a full scale example." + }, + { + "text": "But the point of the example is here, that this off-diagonal entry gets cubed." + }, + { + "text": "And the next step will be its ninth power, and then the 27th power." + }, + { + "text": "So it's really quickly going to 0." + }, + { + "text": "And this happens." + }, + { + "text": "So cubic convergence is a prize." + }, + { + "text": "In numerical linear algebra." + }, + { + "text": "So that happens." + }, + { + "text": "So this arrived on the scene and quickly blew away all other methods that were being used to compute eigenvalues." + }, + { + "text": "But numerical people, being what they are, they wanted to improve it." + }, + { + "text": "Like, is there a way to make it faster?" + }, + { + "text": "And turned out there is." + }, + { + "text": "It turned out that the better way, basically the same idea, but just you're always looking for a simple change." + }, + { + "text": "And the idea of introducing a shift was tried." + }, + { + "text": "And turned out to work extremely well." + }, + { + "text": "So that's the improvement." + }, + { + "text": "So we take a1." + }, + { + "text": "No, so how does the shift work?" + }, + { + "text": "So instead of a0, have I got space here to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk6.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..e081a02643a2181251ac74e36b445d55b6192f14 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Instead of a0, I take a0 minus a shift." + }, + { + "text": "So a shift is some multiple of the identity." + }, + { + "text": "If I just move a matrix by a multiple of the identity, what happens to its eigenvectors?" + }, + { + "text": "What happens to its eigenvalues?" + }, + { + "text": "Something pretty simple, right?" + }, + { + "text": "Because I'm just shifting by si." + }, + { + "text": "What happens to its eigenvectors?" + }, + { + "text": "They're the same." + }, + { + "text": "And what happens to the eigenvalues?" + }, + { + "text": "They change by s. If a0v equals lambda v, then when I multiply this by v, there will be an extra." + }, + { + "text": "It'll be lambda minus s. Because the identity times the v is just v. So it just shifts all the eigenvalues by s. And you try to shift." + }, + { + "text": "You look for a shift." + }, + { + "text": "This would be great." + }, + { + "text": "If you knew lambda n, a shift there, you would be looking for 0 then, if you shifted them all by that lambda." + }, + { + "text": "And it turns out that would speed things up." + }, + { + "text": "So you work instead with this matrix as now, again, I'm factoring in a q0, r0." + }, + { + "text": "So that's the work of the method, is in doing Gram-Schmidt at every step." + }, + { + "text": "And then there's a little work in reversing the order." + }, + { + "text": "And then I want to undo the shift." + }, + { + "text": "So I do that factorization." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk7.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..212c509ec27724246ec3a49d4c24022c4979b516 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, let's see." + }, + { + "text": "You may have to help me to remember what I should do here." + }, + { + "text": "So I factor those." + }, + { + "text": "I reverse those." + }, + { + "text": "And then I think I add back the shift." + }, + { + "text": "And that's my A1." + }, + { + "text": "So I took A0." + }, + { + "text": "I shifted it." + }, + { + "text": "I worked with it, qr, reversed the order, rq, added back the shift to get a matrix." + }, + { + "text": "And what am I, of course, hoping about the matrix A1 and A0?" + }, + { + "text": "I'm hoping they're still similar." + }, + { + "text": "I'm hoping." + }, + { + "text": "So I did a shift." + }, + { + "text": "And I undid a shift." + }, + { + "text": "But of course, after doing a qr, I have to check, are these really still similar?" + }, + { + "text": "So let me just try to check that one again." + }, + { + "text": "Maybe I'll just, it's sitting right there." + }, + { + "text": "So let me do it again." + }, + { + "text": "I'm hoping that something, you know, where did we change?" + }, + { + "text": "Oh, yeah, here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk8.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..4e7fad6f92f20cdf436db6b8933b889b8a6fb34f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We showed that A1 was similar to A0." + }, + { + "text": "And I'm hoping that's probably still true, even, you know, the shift didn't mess that up." + }, + { + "text": "Let's just try." + }, + { + "text": "So A0, that's r0, q0 plus si." + }, + { + "text": "OK. And now what am I going to do?" + }, + { + "text": "I'm going to, what did I do before?" + }, + { + "text": "I figured out what q0 was from this." + }, + { + "text": "You remember?" + }, + { + "text": "So this is r0." + }, + { + "text": "Now I have to put in q0." + }, + { + "text": "But q0 is this thing inverse times this." + }, + { + "text": "Is this going to work?" + }, + { + "text": "I'm like hoping, but I don't think I wanted to get that." + }, + { + "text": "No, it's not q0 there." + }, + { + "text": "What do I put here?" + }, + { + "text": "And if it doesn't work, we'll leave it as an exercise." + }, + { + "text": "OK." + }, + { + "text": "So yeah, because I didn't sort of start right somehow." + }, + { + "text": "OK." + }, + { + "text": "So but let me just push along to see what happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk9.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..f66b5f2f317c991f9ad92b2dc38dd936ae5d8d21 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_6_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I'm plugging in for q0 here." + }, + { + "text": "I'm plugging in this matrix, so it shouldn't have inverted it, times r0 inverse." + }, + { + "text": "Who knows?" + }, + { + "text": "It might work." + }, + { + "text": "Who knows?" + }, + { + "text": "So that's the r0, q0." + }, + { + "text": "Right?" + }, + { + "text": "Is everybody with me?" + }, + { + "text": "Sorry about this." + }, + { + "text": "So r0 inverse." + }, + { + "text": "And then I have to add Si." + }, + { + "text": "So what have I done?" + }, + { + "text": "I've just pushed on, believing that this would work." + }, + { + "text": "Because it's the method that is constantly used." + }, + { + "text": "Now do I have?" + }, + { + "text": "What do I have there?" + }, + { + "text": "Is it working?" + }, + { + "text": "This is r0 A." + }, + { + "text": "That was, of course, A0." + }, + { + "text": "r0 A0 r0 inverse." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk0.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..afc91322b0d9d5a0ce3bfb215b0940ebb7754749 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "OK, why don't I start?" + }, + { + "text": "So I was hoping that we would have the next online assignment ready, but Julia 6, the new version, is slowing us down." + }, + { + "text": "And it'd probably be next time." + }, + { + "text": "But my lectures, of course, are, well, what I want to say perhaps is this isn't intended to be a course in numerical linear algebra." + }, + { + "text": "But I thought I couldn't let the whole semester go by without saying something about how to compute eigenvalues and singular values." + }, + { + "text": "Of course, you're going to call I or SVD or the equivalent in Python or Julia." + }, + { + "text": "But actually, the QR factorization that we spoke about, that we spoke entirely about last time is the key, unexpectedly, unexpectedly." + }, + { + "text": "You have a matrix A whose eigenvalues you want." + }, + { + "text": "So let's start with eigenvalues." + }, + { + "text": "And it might be a symmetric matrix." + }, + { + "text": "I'll stay with A rather than S because it doesn't have to be." + }, + { + "text": "But you get special always." + }, + { + "text": "You get something special if the matrix is symmetric." + }, + { + "text": "OK, so this method of computing eigenvalues, to me at least, and I think to many people, came like out of the blue a while ago, but not that long ago." + }, + { + "text": "And it worked very well." + }, + { + "text": "So here's the idea." + }, + { + "text": "It's called the QR method because you start by factoring your matrix into QR." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk1.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..f693f6b2ff21648d32a7af5f95cf39d07b0de862 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here's A." + }, + { + "text": "Can we call it A0?" + }, + { + "text": "That's the matrix we start with whose eigenvalues we want." + }, + { + "text": "And I'll call these Q0 and R0." + }, + { + "text": "And you remember what that means, what's hiding behind those letters that I've written?" + }, + { + "text": "You have the columns of A, possibly symmetric, as I said, but not orthogonal, usually." + }, + { + "text": "So you find an orthogonal basis." + }, + { + "text": "You orthogonalize them." + }, + { + "text": "You line them up perpendicular to each other." + }, + { + "text": "And then there is a matrix R, which happens to be upper triangular, that connects." + }, + { + "text": "The not orthogonal basis with the orthogonal basis." + }, + { + "text": "Right, we constructed R step by step." + }, + { + "text": "And then the idea is write these in the reverse order." + }, + { + "text": "And that will be A1, the next A. OK, and then do it again, and again, and again." + }, + { + "text": "And so we're hoping, of course, that the eigenvalues didn't change." + }, + { + "text": "We're hoping that we can forget A0, start again with A1, and produce A2, and continue." + }, + { + "text": "So we're hoping two things." + }, + { + "text": "One will not be a hope." + }, + { + "text": "We can see that the eigenvalues of A1 and A0 are the same." + }, + { + "text": "So we have not changed the eigenvalues." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk10.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..6fb2da774bad3a68b507efacec13f9801a995312 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "r0 A0 r0 inverse." + }, + { + "text": "Good." + }, + { + "text": "Minus S. What have I got there?" + }, + { + "text": "From the r0 minus Si r0, what is that?" + }, + { + "text": "That's minus Si." + }, + { + "text": "Look, success." + }, + { + "text": "The r0 cancels the r0 inverse." + }, + { + "text": "So that term from that, that, that is minus Si." + }, + { + "text": "Cancels plus Si." + }, + { + "text": "I'm finished." + }, + { + "text": "And lo and behold, we have the same similarity." + }, + { + "text": "So we messed around by a multiple of the identity, and it actually makes the thing converge faster if we choose the shifts well." + }, + { + "text": "But basically, the same idea is still working." + }, + { + "text": "OK." + }, + { + "text": "So that's the QR method." + }, + { + "text": "Well, that's the method we haven't shown and won't show." + }, + { + "text": "Except for this half-completed example, I don't plan to prove that the lower triangular part begins to disappear, gets smaller and smaller and smaller, and then the eigenvalues pop up on the diagonal." + }, + { + "text": "It's amazing." + }, + { + "text": "Amazing." + }, + { + "text": "OK. Now, is there any other improvement we can make?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk11.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..9e5764513ae4ce678e41ecfcb72a4895642b01f6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "So that's the method." + }, + { + "text": "And where is the work in using that method?" + }, + { + "text": "Because that's what we always focus on." + }, + { + "text": "Where are we spending computer time?" + }, + { + "text": "Well, we're spending computer time in doing the factorization." + }, + { + "text": "So it didn't cost anything to shift by the identity, but then we had to factor that into Q0, R0." + }, + { + "text": "Then it didn't cost much to multiply them in the opposite order." + }, + { + "text": "So the work was in QR." + }, + { + "text": "So could we think of anything to improve that aspect?" + }, + { + "text": "Could we think of anything there?" + }, + { + "text": "And then we've got a really first-class method." + }, + { + "text": "Well, if the matrix A, A0, the matrix we started with, had some zeros that allowed us to skip steps in doing the QR factorization." + }, + { + "text": "So what am I going to say?" + }, + { + "text": "I'm going to say if A or A0, our original matrix, has a bunch of zeros, let's say it's got a whole lot of zeros there." + }, + { + "text": "Maybe it's, well, OK." + }, + { + "text": "I overdid it here." + }, + { + "text": "I know the eigenvalues right off." + }, + { + "text": "But so the truth is I can't, saying that if that, it's not going to happen." + }, + { + "text": "But we can get zeros with one extra diagonal." + }, + { + "text": "That turns out, so here's the main diagonal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk12.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..ab7132ecacaf6cb9786d7b5f399f0082623bd923 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "Everybody's got his eye on the main diagonal." + }, + { + "text": "And one diagonal, I can get a lot of zeros." + }, + { + "text": "But I can't by simple computations." + }, + { + "text": "And I'll show you how to get one." + }, + { + "text": "But I can't get all those to be 0, because then I would have the eigenvalues right there." + }, + { + "text": "And that, well, how do I know that I can't?" + }, + { + "text": "In elimination, ordinary solving AX equal B, you really do get to an upper triangular form." + }, + { + "text": "Some operator, some elimination steps, you plug away, and your matrix becomes upper triangular U." + }, + { + "text": "And you're golden." + }, + { + "text": "But that's too much to expect here." + }, + { + "text": "In fact, we know we can't do it by simple steps." + }, + { + "text": "Because if we could do it, if we could get to a U with a whole lower triangular part 0, we would have found the eigenvalues." + }, + { + "text": "And we know that the eigenvalues solve an equation of nth degree." + }, + { + "text": "And we know somebody proved centuries or more ago that you can't solve an nth degree equation by simple little steps." + }, + { + "text": "Right?" + }, + { + "text": "Do you know who that was?" + }, + { + "text": "And you know that fact?" + }, + { + "text": "And what degree does it apply to?" + }, + { + "text": "So that's an important fact that you sort of pick up in math." + }, + { + "text": "Yeah, what do you?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk13.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..5ef254fb5bc0df6883bfe89b2da2433a3da88094 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "Fifth degree, yeah." + }, + { + "text": "So 5 by 5 and up would be, this is impossible." + }, + { + "text": "Impossible." + }, + { + "text": "There's no formula to find a simple formula for the lambdas." + }, + { + "text": "And similarly for the sigmas, the singular values." + }, + { + "text": "So the eigenvalues is definitely a level of difficulty beyond Ax equal b, the inverse matrix or something, the pivots." + }, + { + "text": "All that you can do exactly if you do exact arithmetic." + }, + { + "text": "We cannot find the lambdas exactly." + }, + { + "text": "But we can get as close as we like by continuing with the QR method." + }, + { + "text": "So yeah, in other words, we have to settle for, if we want to, at the beginning, improve our matrix before we start doing that stuff." + }, + { + "text": "We can get it with one extra diagonal." + }, + { + "text": "And do you know what kind of a matrix, whose name?" + }, + { + "text": "And I don't know why." + }, + { + "text": "Yeah, say it again." + }, + { + "text": "Upper Hessenberg." + }, + { + "text": "So upper is just like upper triangular." + }, + { + "text": "It's up there." + }, + { + "text": "But the key person's name is Hessenberg." + }, + { + "text": "As I say, that's a Hessenberg matrix." + }, + { + "text": "So Hessenberg matrix is a matrix with one triangular plus one more diagonal." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk14.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..890f75c227f0ce9167ef179281769727e008c678 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "But lots of zeros." + }, + { + "text": "Order of n squared, something like almost like half n squared, not quite, but close, zeros." + }, + { + "text": "And you could show that those zeros stay zeros in QR." + }, + { + "text": "So that really pays off." + }, + { + "text": "It cuts the work down significantly." + }, + { + "text": "So the full QR method is step one, reduce A to Hessenberg form with these zeros." + }, + { + "text": "And when I say reduce, I mean find a similarity transformation, of course, because I want the eigenvalues of this to end up the same as the Hessen." + }, + { + "text": "I want to keep the same eigenvalues as I go." + }, + { + "text": "And then step two is QR on this Hessenberg matrix with shifts." + }, + { + "text": "So that's the code that would be programmed in IGAVE." + }, + { + "text": "That's what MATLAB and, well, really, MATLAB is appealing, like other matrix systems, is appealing to LAPAC and LINPAC." + }, + { + "text": "The team of professional numerical analysts really spent a lot of effort and time." + }, + { + "text": "The book LAPAC has 10 authors." + }, + { + "text": "And you can download any of these codes, like the eigenvalue code." + }, + { + "text": "So that's where MATLAB naturally, that's sort of the Bible for codes in linear algebra." + }, + { + "text": "OK, now, I think it's sort of interesting to know." + }, + { + "text": "And there is one more good thing to tell you about this method." + }, + { + "text": "And it applies if the matrix is symmetric." + }, + { + "text": "If the matrix is symmetric, then if we check all this, we could find that the matrices stayed symmetric." + }, + { + "text": "If A0 is symmetric, I can check." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk15.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..1cdfb555c6b2be5bd3044a831ed3f643f560293a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "You could easily check through this, and you would discover that A1 is also symmetric." + }, + { + "text": "It turns out you could rewrite this with a Q0 and a Q0 inverse on the other side." + }, + { + "text": "But that Q0 inverse is the same as Q0 transpose, because it's an orthogonal matrix, and symmetry would fall out." + }, + { + "text": "So if it's symmetric, and it's in Hessenberg form, and it stays symmetric at every step, what can you tell me about a symmetric Hessenberg matrix?" + }, + { + "text": "It's only got, yeah, you just erase all these." + }, + { + "text": "If there are zeros there, and if the matrix is symmetric, then we can safely predict that it will only have one diagonal above, one non-zero diagonal above the main diagonal." + }, + { + "text": "In fact, it'll stay symmetric." + }, + { + "text": "So now I should write symmetric Hessenberg matrix, n equals tri-diagonal matrix." + }, + { + "text": "Yeah, three diagonals." + }, + { + "text": "So now you really have reduced the time to do QR, because you've got a tri-diagonal matrix." + }, + { + "text": "It'll stay tri-diagonal in all these steps." + }, + { + "text": "So you're working with just 3n numbers." + }, + { + "text": "Well, actually, 2n, because the diagonal above and the diagonal below are the same." + }, + { + "text": "You're working with just 2n numbers instead of order n squared, and it just goes like a bomb." + }, + { + "text": "So that's I for symmetric matrices." + }, + { + "text": "And you see that it was all based, that really the heart of the algorithm was QR." + }, + { + "text": "So that's my, it took half the class to report on the favorite way, the EIG way, to find eigenvalues." + }, + { + "text": "Oh, I should say something about singular values." + }, + { + "text": "So singular values, of course, the singular values of the matrix are the eigenvalues of A transpose A, square root of those eigenvalues." + }, + { + "text": "But you wouldn't do it that way." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk16.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..7989fa8939f6d17bfb6b36b82c96bbd76b92a4f6 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "You would never form A transpose A. Oh, I didn't mention the other thing you would never, ever, ever do." + }, + { + "text": "So let me just put it here." + }, + { + "text": "This is like in disgrace to solve that equation." + }, + { + "text": "It's like, OK, back to first grade, because that's not, that's very bad." + }, + { + "text": "A determinant, first of all, it's extremely slow, extremely slow." + }, + { + "text": "And the determinant is packing all this n squared pieces of information into n coefficients, and it's hopelessly ill-conditioned." + }, + { + "text": "Yeah, you just, you lose information all the time." + }, + { + "text": "So really, if this is going on camera, it better go on camera with an x, because don't do it." + }, + { + "text": "OK. Yeah." + }, + { + "text": "So where was I?" + }, + { + "text": "Singular values." + }, + { + "text": "So A transpose A." + }, + { + "text": "So again, let's think about what you could do at the beginning before starting on QR for A transpose A, or for the matrix A." + }, + { + "text": "What could you do with orthogonal matrices?" + }, + { + "text": "So I guess, what did we say about symmetric matrices?" + }, + { + "text": "So here's what I said about symmetric matrices." + }, + { + "text": "If you give me a symmetric matrix, I can, in just a simple number of simple steps, make it tridiagonal." + }, + { + "text": "I can't make it diagonal, because then I'd be finding the eigenvalues, and Abel, who was the first person to see that that was impossible, forbids it." + }, + { + "text": "But so let me write down what I'm saying here." + }, + { + "text": "If I have a symmetric matrix S, I can find a bunch of Q's and Q transposes, and I can put them all together into one big Q, and it's transposed." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk17.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..08d99076ccc98b0932858bac2de5382359f2d221 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "And what do I know about the eigenvalues of that matrix?" + }, + { + "text": "Q is orthogonal always." + }, + { + "text": "So what can you tell me about the, this is the same as Q S Q inverse, and therefore, the eigenvalues are the same." + }, + { + "text": "It's similar to S. And it becomes tridiagonal after I find a good Q." + }, + { + "text": "Now, and therefore, same lambdas, tridiagonal with the same lambdas." + }, + { + "text": "Now, what am I thinking about here?" + }, + { + "text": "I'm thinking about, tell me the corresponding possibility about singular values." + }, + { + "text": "I want to do something to my matrix." + }, + { + "text": "Now, I'm always taking a general matrix A." + }, + { + "text": "And I'm looking for its singular values." + }, + { + "text": "And I'm looking to simplify it." + }, + { + "text": "And what am I allowed to do?" + }, + { + "text": "Yeah, I guess my question is, similarity transformations left the eigenvalues alone." + }, + { + "text": "What can I do that leaves the singular values alone?" + }, + { + "text": "That's a fundamental question, because it was so fundamental for eigenvalues." + }, + { + "text": "By doing this, a matrix and its inverse, I got something similar." + }, + { + "text": "And I checked even in this class that the eigenvalues, same lambdas." + }, + { + "text": "Now I want a whole line that ends up with the same sigmas." + }, + { + "text": "And I want you to tell me what I'm allowed to do to the matrix without changing the sigmas." + }, + { + "text": "So maybe don't shout it out immediately." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk18.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..31cc3c0860684bbd35bab2fb28f2d606a8921e5b --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "Let everybody think." + }, + { + "text": "What am I allowed to do to a matrix?" + }, + { + "text": "Every matrix has got these singular values." + }, + { + "text": "And now I want to make it a better matrix with more 0's or something." + }, + { + "text": "If I do that to it, does that change the sigmas?" + }, + { + "text": "Can I do more than that to it?" + }, + { + "text": "What can I do?" + }, + { + "text": "What group of matrices will have the same sigmas as my starting matrix A?" + }, + { + "text": "So that's a basic, basic question about singular values and the SVD." + }, + { + "text": "So let's think of the answer together." + }, + { + "text": "So it's connected to the SVD." + }, + { + "text": "So let me remember the SVD." + }, + { + "text": "The SVD, I have some orthogonal matrix, then the singular value matrix, SV for singular values, and then another orthogonal matrix." + }, + { + "text": "What could I do to that equation that would not touch this guy?" + }, + { + "text": "So I'm asking what invariance, because not touching it means leaving it not varying." + }, + { + "text": "So I'm looking for under what operations are the singular values invariant?" + }, + { + "text": "When I was looking at eigenvalues, this was the operation." + }, + { + "text": "Well, it didn't have to be orthogonal." + }, + { + "text": "It's something, and it's inverse." + }, + { + "text": "But now what is it up there?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk19.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..01b201f72f3bceb5bd8b70cfc01d55a2e2ff2a71 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "What could I do to that matrix A?" + }, + { + "text": "Could I multiply by Q?" + }, + { + "text": "Could I throw in a Q?" + }, + { + "text": "Maybe not even on the other end." + }, + { + "text": "If I throw in an orthogonal Q, do I change the singular values or do I not change them?" + }, + { + "text": "Fundamental question." + }, + { + "text": "The answer is no, I don't change them." + }, + { + "text": "I'm allowed to do that, because here's an orthogonal matrix, a Q times U." + }, + { + "text": "If both of those are orthogonal, then the product is." + }, + { + "text": "Everybody knows that a product of two orthogonal matrix is still orthogonal." + }, + { + "text": "Better know that." + }, + { + "text": "Better know that." + }, + { + "text": "Yeah." + }, + { + "text": "So if I have an orthogonal matrix Q and an orthogonal matrix U, I claim that this is still orthogonal." + }, + { + "text": "And how do I check it?" + }, + { + "text": "Well, I use some test for orthogonality." + }, + { + "text": "What would be the test you like to use?" + }, + { + "text": "The inverse is the same as the transpose." + }, + { + "text": "You like that test?" + }, + { + "text": "So I'll invert it." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk2.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..49f68a61aecdf81153b85d35f02c4fd1ad64e79f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "How do we see that?" + }, + { + "text": "If you had to show that two matrices had the same eigenvalues, would you compute all the eigenvalues and compare them?" + }, + { + "text": "Certainly not." + }, + { + "text": "What would you do?" + }, + { + "text": "What's the best test, the usual test, the usual thing you would want to show?" + }, + { + "text": "They're similar." + }, + { + "text": "That's right." + }, + { + "text": "So the claim would be that these two matrices are similar." + }, + { + "text": "Right." + }, + { + "text": "So maybe we should show that." + }, + { + "text": "So we want to write A1 in a different way." + }, + { + "text": "So the claim is A1 is similar to A." + }, + { + "text": "So we just have to figure out." + }, + { + "text": "We have to get A1 to A0." + }, + { + "text": "So here's A1." + }, + { + "text": "OK." + }, + { + "text": "So A1, I want to show that that's right." + }, + { + "text": "So that's R0, Q0." + }, + { + "text": "But what is Q0?" + }, + { + "text": "From here, Q0 is what we is R. Q0 is, what do I want?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk20.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..35801c36445d73fe11e2f6274bad6dd29215b8e2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "Q U inverse." + }, + { + "text": "Of course, for any matrix, that's U inverse Q inverse." + }, + { + "text": "But these were separately orthogonal, so that's U transpose Q transpose." + }, + { + "text": "And that is the same as Q U transpose." + }, + { + "text": "Yeah." + }, + { + "text": "So I use the orthogonality of U and the orthogonality of Q to conclude that the inverse is the transpose." + }, + { + "text": "So the answer is yes, I could do that." + }, + { + "text": "Now, with singular value, with eigenvalues, I had to multiply on the other side by Q inverse or Q transpose." + }, + { + "text": "Do I have to do that now?" + }, + { + "text": "No." + }, + { + "text": "What can I do on the right-hand side?" + }, + { + "text": "I can multiply by." + }, + { + "text": "I can leave it alone." + }, + { + "text": "Then it has the same singular values because it's the same sigma in there." + }, + { + "text": "If I have a orthogonal matrix times a diagonal times an orthogonal, that diagonal, positive diagonal, is going to be sigma." + }, + { + "text": "So what can I do on this side?" + }, + { + "text": "I could multiply by any orthogonal matrix on that side, too." + }, + { + "text": "So let's call this guy Q1 and this guy Q2." + }, + { + "text": "I still have an orthogonal matrix there, orthogonal matrix there, and the same sigma popped in the middle." + }, + { + "text": "So that's what you're allowed to do." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk21.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..8733bff8727902ad93fdca4f142729506ca43859 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "That gives us more freedom." + }, + { + "text": "Before, when we had to do similarity transformations with the same guy, we got it to be tridiagonal." + }, + { + "text": "But now we're allowed to do more stuff." + }, + { + "text": "We're allowed to use different orthogonal matrices on the left and right." + }, + { + "text": "And we can reduce it even further from tridiagonal to bidiagonal." + }, + { + "text": "So the first step is getting 0." + }, + { + "text": "The step of getting 0s reduces it all the way to that with all 0s there." + }, + { + "text": "So it's easier." + }, + { + "text": "Then I work on this." + }, + { + "text": "I work on using a QR type idea, some method like that." + }, + { + "text": "So everybody's seeing that our algorithm has got two stages." + }, + { + "text": "One is get a lot of 0s and get them in places that will stay 0 as part 2 of the algorithm gets going." + }, + { + "text": "And then run part 2 of the algorithm." + }, + { + "text": "You're staying with each step is very fast now because doing a QR factorization is fast." + }, + { + "text": "Was there a question?" + }, + { + "text": "Yeah." + }, + { + "text": "So I would call this bidiagonal, of course." + }, + { + "text": "And everybody recognizes that if I have a bidiagonal matrix, call it A or A0 or whatever." + }, + { + "text": "Then what do you think about A transpose A?" + }, + { + "text": "What would A transpose A?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk22.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..8562bc4837b9c78d63d64c389d0c913d3dc7d8a2 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "If that was A, what could you tell me about A transpose A?" + }, + { + "text": "Could you multiply matrices, like knowing where the non-zeros are, like in your head, and get an idea of where?" + }, + { + "text": "So if I have a bidiagonal matrix A, then sort of implicitly in the SVD, I'm looking at A transpose A." + }, + { + "text": "And what would be true about A transpose A?" + }, + { + "text": "It would be tridiagonal." + }, + { + "text": "So what I've done here and what I've done there just match up." + }, + { + "text": "If you don't want to change singular values, you can get all the way to here." + }, + { + "text": "But then to find those singular values, that would involve A transpose A." + }, + { + "text": "It would be symmetric and tridiagonal." + }, + { + "text": "And then you'd be in that game." + }, + { + "text": "So those are the basic facts of I and SVD." + }, + { + "text": "For matrices of order up to 1,000, say." + }, + { + "text": "I'm not enough of an expert to know where." + }, + { + "text": "Maybe higher, because in perfect math, it's going to take infinitely many steps." + }, + { + "text": "Or Abel would be very surprised." + }, + { + "text": "He would see you solving for eigenvalues and then to re-equation by a whole lot of little steps and getting them exactly right." + }, + { + "text": "That won't happen." + }, + { + "text": "But you get them within epsilon in a number of steps that's like n cubed." + }, + { + "text": "So that's pretty impressive." + }, + { + "text": "The eigenvalue problem is being solved, in quotes, by a fast method that gets you a good answer within a tolerance in n cubed steps." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk23.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..37baceeccac2b563da8271de17d70bb205a69d4d --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "Right." + }, + { + "text": "So that's great as long as n isn't too big." + }, + { + "text": "And then when n is too big, which of course happens, you have to think again." + }, + { + "text": "So this method is a giant success up to large matrices." + }, + { + "text": "But then you have to think again." + }, + { + "text": "And what is involved in thinking again?" + }, + { + "text": "Well, I guess more thinking." + }, + { + "text": "So what do you do if the matrix is bigger?" + }, + { + "text": "I guess that Krylov would say, use my method." + }, + { + "text": "So Krylov would say, especially if your matrix is sparse." + }, + { + "text": "Can we just remember what Krylov was?" + }, + { + "text": "Krylov started with a vector b, multiplied it by a, multiplied that by a, and got up to, let's say, a to the 999b." + }, + { + "text": "So now Krylov has got 1,000 dimensional space." + }, + { + "text": "He's got a basis for it, 1,000 vectors that span 1,000 dimensional space." + }, + { + "text": "And he'll look at the matrix A only on that space." + }, + { + "text": "In other words, I won't go into detail about that." + }, + { + "text": "He restricts the matrix to this 1,000 dimensional space." + }, + { + "text": "And he hopes that it's captured." + }, + { + "text": "We hope that the eigenvector is virtually in that space." + }, + { + "text": "And actually, I wouldn't go up to, let me take a 9 out of that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk24.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..0f5c17cbd60debd628609f1ccf8848eb0fa9b730 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "100 dimensional would probably catch the eigenvector." + }, + { + "text": "So if the eigenvector is virtually in this space, then we can look at a matrix of order 100." + }, + { + "text": "We can bring A down to just see its action on that space." + }, + { + "text": "So I look at vectors V, which are some combination, C1b plus C2ab plus C3a squared b and C100 a to the 99th b, plus an error." + }, + { + "text": "And I'm going to ignore that error." + }, + { + "text": "Because I've gone up to dimension 100." + }, + { + "text": "I probably say it's pretty safe to ignore that error." + }, + { + "text": "And then in this space, just looking at the matrix A." + }, + { + "text": "So wherever A to the 100th comes in, forget it." + }, + { + "text": "Just think about the matrix A as multiplying vectors of this kind in this space." + }, + { + "text": "Then I have a 100 by 100 eigenvalue problem." + }, + { + "text": "And so the big matrix A is reduced to a matrix of size 100 by, do you see sort of what I'm saying, even though I'm not giving the details?" + }, + { + "text": "Think of a matrix A of size a million." + }, + { + "text": "And you apply it to Krylov vectors." + }, + { + "text": "So I call them little k for a Krylov vector in this 100-dimensional space." + }, + { + "text": "So they have a million minus 100, zero components, you could say, this k. This is in the Krylov space." + }, + { + "text": "This is A, a million, k, 100." + }, + { + "text": "It's a full, it's got a million components, but it's out of just 100-dimensional space." + }, + { + "text": "So when I multiply by A, it'll be mostly in, mostly in, partly in the Krylov space, k 100, and a piece out of k 100." + }, + { + "text": "And I just ignore that part of the matrix." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk25.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..41342712fde4874aa3c115a8d909e3bf6f2a0e59 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I have a 100 by 100 problem, and I've solved to find the eigenvalues." + }, + { + "text": "And they're a pretty good approximation to the eigenvalues, to the, hopefully, like the lowest 100 eigenvalues." + }, + { + "text": "I'd like to know that." + }, + { + "text": "But I might not be sure that this idea would give me the lowest 100, the first 100 eigenvalues of the million, of the matrix of size a million." + }, + { + "text": "I'm just taking a few minutes here to sort of wave hands about what Krylov, the Krylov idea would do." + }, + { + "text": "And I probably won't mention Krylov again this semester." + }, + { + "text": "So what it can do is look at this particular type of space, because we can get a basis for it quickly, just multiply again and again by A." + }, + { + "text": "Then we can orthogonalize that basis." + }, + { + "text": "That's Graham-Schmidt in some form." + }, + { + "text": "We're always going back to Graham-Schmidt." + }, + { + "text": "Then I have a 100 by 100." + }, + { + "text": "I have a subspace of size 100." + }, + { + "text": "I look at what the matrix does in that space." + }, + { + "text": "And I could look for, I could find eigenvalues restricted to that space." + }, + { + "text": "They wouldn't be the perfect eigenvalues, but they would be accurate." + }, + { + "text": "OK, so I didn't know it would take one class time to talk about finding eigenvalues and singular values, but we did some important things." + }, + { + "text": "We remembered that similarity is the thing to check, thing to preserve, because it doesn't change the eigenvalues." + }, + { + "text": "And then for singular values, what was the thing?" + }, + { + "text": "You could multiply left and right by different orthogonal matrices." + }, + { + "text": "And somehow, maybe that doesn't have an established name, multiplying left and right by a Q1 and a Q2 transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk26.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..2ce06055331ebe329b68e463d8ac9af5a66e37dd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk26.json @@ -0,0 +1,35 @@ +[ + { + "text": "Yeah, but the idea is clear." + }, + { + "text": "And that doesn't change the singular values." + }, + { + "text": "We're ready to move now into maybe our next step, which we don't spend a long time on." + }, + { + "text": "We'll be like random sampling." + }, + { + "text": "What if your matrix is just way too big?" + }, + { + "text": "So that's a new, very new idea, very different idea in numerical linear algebra, is just to sample the matrix." + }, + { + "text": "Could you believe that the answer is going to come out right just for a random sample?" + }, + { + "text": "Well, the odds are in your favor." + }, + { + "text": "OK, so that'll be Wednesday, and then we have lots of new, we'll move onward after that." + }, + { + "text": "OK, see you Wednesday." + }, + { + "text": "Thanks." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk3.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..f5acd4bdba4ba51520fdf921a1fc36684dfeaabb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I want to put R0 inverse over there." + }, + { + "text": "So R0." + }, + { + "text": "Now for Q0, I'm going to substitute." + }, + { + "text": "So what is Q0?" + }, + { + "text": "I multiply both sides of that equation by R0 inverse." + }, + { + "text": "So Q0 is A0 is, sorry, I said A and wrote Q. A0 R0 inverse." + }, + { + "text": "Right." + }, + { + "text": "For Q0, I've put in what it equals." + }, + { + "text": "And that's done it." + }, + { + "text": "That's exactly telling me that A1, which is this, equals this." + }, + { + "text": "And that's a similarity transformation." + }, + { + "text": "I have not changed the eigenvalues." + }, + { + "text": "So that's OK." + }, + { + "text": "The other thing, which is the, like you could say, the miracle in this thing, is that when I continue to do that for almost every matrix, the matrices begin to lose stuff off the diagonal, especially below the diagonal by the ordering that QR is done." + }, + { + "text": "So you tend to start with a matrix A0." + }, + { + "text": "You get a matrix A1, which is like a little smaller here." + }, + { + "text": "This part being not especially smaller." + }, + { + "text": "You do it again." + }, + { + "text": "This is even smaller." + }, + { + "text": "So I put even smaller A2, even smaller." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk4.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..a93c5efe93b5619eae3335916949e5ca1b9c543f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "And you keep going." + }, + { + "text": "And for most matrices, the result is that I don't know how many steps we want to think of taking, but we get quite small numbers here." + }, + { + "text": "So once we get small numbers here, little epsilons, that's everybody's shorthand for small numbers, what would you expect to see on the diagonal?" + }, + { + "text": "The eigenvalues." + }, + { + "text": "Because this has the same eigenvalues as this, as this, as this." + }, + { + "text": "And these little epsilons are not going to change the eigenvalues too much." + }, + { + "text": "So these will be, on the diagonal, will be close to the eigenvalues." + }, + { + "text": "And actually, what happens is this one comes first." + }, + { + "text": "That one is quite accurate first." + }, + { + "text": "I guess we should probably do a simple example to see this happen." + }, + { + "text": "Actually, I do an example in the notes." + }, + { + "text": "And let me say what happens." + }, + { + "text": "So I do a 2 by 2 example, which has something like cos theta, sine theta." + }, + { + "text": "I don't know what." + }, + { + "text": "I've forgotten what I took." + }, + { + "text": "And I don't have that page of notes here." + }, + { + "text": "Something here." + }, + { + "text": "Something here." + }, + { + "text": "Something here as a 0." + }, + { + "text": "And then a 1, after just one step, has sine cubed theta there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk5.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..2c1c69b5647ae63cfaad8af10731e95f060b6c81 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "And numbers there that are getting much closer to the eigenvalues." + }, + { + "text": "Sorry that this isn't a full scale example." + }, + { + "text": "But the point of the example is here, that this off-diagonal entry gets cubed." + }, + { + "text": "And the next step will be its ninth power, and then the 27th power." + }, + { + "text": "So it's really quickly going to 0." + }, + { + "text": "And this happens." + }, + { + "text": "So cubic convergence is a prize." + }, + { + "text": "In numerical linear algebra." + }, + { + "text": "So that happens." + }, + { + "text": "So this arrived on the scene and quickly blew away all other methods that were being used to compute eigenvalues." + }, + { + "text": "But numerical people, being what they are, they wanted to improve it." + }, + { + "text": "Like, is there a way to make it faster?" + }, + { + "text": "And turned out there is." + }, + { + "text": "It turned out that the better way, basically the same idea, but just you're always looking for a simple change." + }, + { + "text": "And the idea of introducing a shift was tried." + }, + { + "text": "And turned out to work extremely well." + }, + { + "text": "So that's the improvement." + }, + { + "text": "So we take a1." + }, + { + "text": "No, so how does the shift work?" + }, + { + "text": "So instead of a0, have I got space here to do this?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk6.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..e081a02643a2181251ac74e36b445d55b6192f14 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "Instead of a0, I take a0 minus a shift." + }, + { + "text": "So a shift is some multiple of the identity." + }, + { + "text": "If I just move a matrix by a multiple of the identity, what happens to its eigenvectors?" + }, + { + "text": "What happens to its eigenvalues?" + }, + { + "text": "Something pretty simple, right?" + }, + { + "text": "Because I'm just shifting by si." + }, + { + "text": "What happens to its eigenvectors?" + }, + { + "text": "They're the same." + }, + { + "text": "And what happens to the eigenvalues?" + }, + { + "text": "They change by s. If a0v equals lambda v, then when I multiply this by v, there will be an extra." + }, + { + "text": "It'll be lambda minus s. Because the identity times the v is just v. So it just shifts all the eigenvalues by s. And you try to shift." + }, + { + "text": "You look for a shift." + }, + { + "text": "This would be great." + }, + { + "text": "If you knew lambda n, a shift there, you would be looking for 0 then, if you shifted them all by that lambda." + }, + { + "text": "And it turns out that would speed things up." + }, + { + "text": "So you work instead with this matrix as now, again, I'm factoring in a q0, r0." + }, + { + "text": "So that's the work of the method, is in doing Gram-Schmidt at every step." + }, + { + "text": "And then there's a little work in reversing the order." + }, + { + "text": "And then I want to undo the shift." + }, + { + "text": "So I do that factorization." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk7.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..212c509ec27724246ec3a49d4c24022c4979b516 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now, let's see." + }, + { + "text": "You may have to help me to remember what I should do here." + }, + { + "text": "So I factor those." + }, + { + "text": "I reverse those." + }, + { + "text": "And then I think I add back the shift." + }, + { + "text": "And that's my A1." + }, + { + "text": "So I took A0." + }, + { + "text": "I shifted it." + }, + { + "text": "I worked with it, qr, reversed the order, rq, added back the shift to get a matrix." + }, + { + "text": "And what am I, of course, hoping about the matrix A1 and A0?" + }, + { + "text": "I'm hoping they're still similar." + }, + { + "text": "I'm hoping." + }, + { + "text": "So I did a shift." + }, + { + "text": "And I undid a shift." + }, + { + "text": "But of course, after doing a qr, I have to check, are these really still similar?" + }, + { + "text": "So let me just try to check that one again." + }, + { + "text": "Maybe I'll just, it's sitting right there." + }, + { + "text": "So let me do it again." + }, + { + "text": "I'm hoping that something, you know, where did we change?" + }, + { + "text": "Oh, yeah, here." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk8.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..4e7fad6f92f20cdf436db6b8933b889b8a6fb34f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "We showed that A1 was similar to A0." + }, + { + "text": "And I'm hoping that's probably still true, even, you know, the shift didn't mess that up." + }, + { + "text": "Let's just try." + }, + { + "text": "So A0, that's r0, q0 plus si." + }, + { + "text": "OK. And now what am I going to do?" + }, + { + "text": "I'm going to, what did I do before?" + }, + { + "text": "I figured out what q0 was from this." + }, + { + "text": "You remember?" + }, + { + "text": "So this is r0." + }, + { + "text": "Now I have to put in q0." + }, + { + "text": "But q0 is this thing inverse times this." + }, + { + "text": "Is this going to work?" + }, + { + "text": "I'm like hoping, but I don't think I wanted to get that." + }, + { + "text": "No, it's not q0 there." + }, + { + "text": "What do I put here?" + }, + { + "text": "And if it doesn't work, we'll leave it as an exercise." + }, + { + "text": "OK." + }, + { + "text": "So yeah, because I didn't sort of start right somehow." + }, + { + "text": "OK." + }, + { + "text": "So but let me just push along to see what happens." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk9.json b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..f66b5f2f317c991f9ad92b2dc38dd936ae5d8d21 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/d32WV1rKoVk_7_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I'm plugging in for q0 here." + }, + { + "text": "I'm plugging in this matrix, so it shouldn't have inverted it, times r0 inverse." + }, + { + "text": "Who knows?" + }, + { + "text": "It might work." + }, + { + "text": "Who knows?" + }, + { + "text": "So that's the r0, q0." + }, + { + "text": "Right?" + }, + { + "text": "Is everybody with me?" + }, + { + "text": "Sorry about this." + }, + { + "text": "So r0 inverse." + }, + { + "text": "And then I have to add Si." + }, + { + "text": "So what have I done?" + }, + { + "text": "I've just pushed on, believing that this would work." + }, + { + "text": "Because it's the method that is constantly used." + }, + { + "text": "Now do I have?" + }, + { + "text": "What do I have there?" + }, + { + "text": "Is it working?" + }, + { + "text": "This is r0 A." + }, + { + "text": "That was, of course, A0." + }, + { + "text": "r0 A0 r0 inverse." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk0.json b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..50f904d9ed28821087f331bf1edfa222ba655b95 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " The following content is provided under a Creative Commons license." + }, + { + "text": "Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free." + }, + { + "text": "To make a donation or to view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu." + }, + { + "text": "OK, here we go." + }, + { + "text": "All set." + }, + { + "text": "And two topics for today." + }, + { + "text": "One is to go back to Professor Sra's lecture." + }, + { + "text": "That was last Friday." + }, + { + "text": "And he promised a theorem and proof." + }, + { + "text": "And this morning, he sent it to me." + }, + { + "text": "So it's the convergence." + }, + { + "text": "It's proving the convergence of stochastic gradient descent." + }, + { + "text": "And really, what's important, maybe, and useful is not so much the details of the proof, which I'm just learning, but the assumptions." + }, + { + "text": "You know, what's the logic here?" + }, + { + "text": "What do you have to assume about the gradient and about the algorithm to get the answer?" + }, + { + "text": "But now, I actually look back at the video of his lecture." + }, + { + "text": "And it was excellent." + }, + { + "text": "And as I looked at it, there were a couple of things later in the lecture that I thought would make good projects." + }, + { + "text": "So I don't know if anybody is still open to what to do on a project." + }, + { + "text": "But here are my two ideas." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk1.json b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..b2f543dcb487306c505bf7c12405ca2c0240a0b1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "And if you've already finished your project, well, get an A-plus by considering one of these." + }, + { + "text": "So you remember, and this will remind you of the lecture, which is a good thing." + }, + { + "text": "So do you remember that question one was whether in the stochastic part, after you've sampled one or some mini batch, but let's just say one of the loss functions coming from one sample, you remember the whole point is that if we do all zillion samples at every iteration, we're really, really slow." + }, + { + "text": "So the stochastic idea is to randomly pick one or a mini batch of the samples and just reduce their loss, just deal with the loss, say the square loss, or later we'll see cross-entropy loss." + }, + { + "text": "But whatever the cost is, just do a few or one." + }, + { + "text": "And then the question was, after you've done that one, do you put it back in the pot and every time you sample over the whole collection, but that's expensive, or do you just make a list of random list of random order of all the samples and go through them, which is then without replacement, which is sort of semi-illegal." + }, + { + "text": "That is, the logic in the randomization asks you to replace every time, but nobody does it." + }, + { + "text": "It costs a lot, probably not worth it." + }, + { + "text": "So the project would be, suppose you take 1,000, or say just 100, 100 random numbers." + }, + { + "text": "Say you use MATLAB, just the command rand." + }, + { + "text": "So you get numbers whose average is 1 by 2 from rand." + }, + { + "text": "They're between 0 and 1." + }, + { + "text": "So we know what the average is." + }, + { + "text": "So let's compute it two ways." + }, + { + "text": "One is by not replacing, and that's the interesting one." + }, + { + "text": "So take 100 samples." + }, + { + "text": "Well, I guess we know that after we've got through the full 100, we're going to get exactly the right answer." + }, + { + "text": "But anyway, my question would be, how much difference do you see in the eventual approach?" + }, + { + "text": "So the law of large numbers, I guess, would tell us we get an average of 1 half for these numbers with uniform distribution between 0 and 1." + }, + { + "text": "Should I be writing anything here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk10.json b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..4a8e5cd6efc22313e3a4384dca0293be5a09a7bd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I have to use the fact that the derivative of x cubed with respect to x. Oh, I better do partial derivative." + }, + { + "text": "Partial derivatives of x cubed with respect to x is 3x squared." + }, + { + "text": "So now I'll put maybe a formula and then a number, so that gives 3 times 4, 12." + }, + { + "text": "And the derivative of x cubed with respect to y gives 0." + }, + { + "text": "Clearly, that's 0." + }, + { + "text": "And then the derivative." + }, + { + "text": "So I'm doing the x derivative." + }, + { + "text": "So the derivative of y with respect to x is, you get to tell me, if I'm computing partial derivatives, is 0." + }, + { + "text": "Is 0. y and x are independent." + }, + { + "text": "And this is the reason, in my view, that the forward method is wasteful, because I'm going to have to do another whole graph for the y derivative." + }, + { + "text": "In other words, tracking the x derivatives, a whole lot of stuff never got off the ground." + }, + { + "text": "So we never should have looked at it." + }, + { + "text": "So anyway." + }, + { + "text": "But I do need, I have this x plus 3y." + }, + { + "text": "Maybe, I don't know whether to erase that." + }, + { + "text": "I think I will, just because I don't know what to do with it there." + }, + { + "text": "So now let me take the ones that I really need." + }, + { + "text": "So this is the derivative with respect to x of x plus 3y, which is 1." + }, + { + "text": "And so that gives me the answer 1 for any x, actually." + }, + { + "text": "And now what?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk11.json b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..25c22d3c6330903728719d34f0cbb2c658deeb44 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "Oh, yeah." + }, + { + "text": "I'm really, I don't need these." + }, + { + "text": "This is a waste of time, isn't it?" + }, + { + "text": "Is it only x derivatives I want?" + }, + { + "text": "Anyway, let's just keep going." + }, + { + "text": "You can see this takes a little organization, and I'm not practiced with it." + }, + { + "text": "So what am I going to do?" + }, + { + "text": "I'm looking for the x derivative of, I've got to use a product rule now." + }, + { + "text": "I found the x derivative of that factor was 12." + }, + { + "text": "The x derivative of this factor is 1." + }, + { + "text": "And now the x derivative of the product." + }, + { + "text": "So now I'm going to do somehow a product rule." + }, + { + "text": "The x derivative of this product." + }, + { + "text": "I should have given these two terms a name." + }, + { + "text": "Let me call that first term x cubed and the second term x plus 3y." + }, + { + "text": "Call it s. So I'll call the two terms c and s. So I now need to get, so that's dc ds." + }, + { + "text": "This is dc dx." + }, + { + "text": "This is dc dx." + }, + { + "text": "And this one is ds dx." + }, + { + "text": "And dc dy, do I need to know that?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk12.json b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..a832d1c060cb6f1ea599c9552f8cba6846f76fe3 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'm sorry." + }, + { + "text": "This computational graph has thrown me." + }, + { + "text": "But now I want to use the product rule." + }, + { + "text": "And I'm taking x derivatives, right?" + }, + { + "text": "So I should have computed c and s. Yes, I see I've got to need those in the product rule." + }, + { + "text": "So I should have computed c as being 8 and s as being 5." + }, + { + "text": "Is that right?" + }, + { + "text": "2 plus 3 is 11." + }, + { + "text": "Yeah, I needed the 8 and the 11." + }, + { + "text": "Is that our?" + }, + { + "text": "What's up?" + }, + { + "text": "I've just been running along here without getting myself in the whole picture." + }, + { + "text": "Yeah, 8 and 11 is right." + }, + { + "text": "But now I'm looking for the derivatives, right?" + }, + { + "text": "So I don't multiply those." + }, + { + "text": "That's not the product rule." + }, + { + "text": "So the product rule is what?" + }, + { + "text": "s times, so this product rule, I have to do this combination of this is now the product rule for the derivative of c times s. So I want c ds dx plus s dc dx." + }, + { + "text": "I think I'm on track now." + }, + { + "text": "And now I want to put in numbers." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk13.json b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..606e74b64e9dc92c469d46b50ec4e5b83c3e4e7f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "So c is 8. ds dx, have we computed ds dx?" + }, + { + "text": "Yes, ds dx is 1." + }, + { + "text": "And now s itself is computed as 11." + }, + { + "text": "And dc dx, we compute it as 12." + }, + { + "text": "I don't dare look." + }, + { + "text": "Have I?" + }, + { + "text": "Am I?" + }, + { + "text": "I don't think I'm going to get." + }, + { + "text": "Oh, no, I don't know the answer yet." + }, + { + "text": "Sorry, I'm not trying to get 88, right?" + }, + { + "text": "You guys are not helping." + }, + { + "text": "You see, I'm in trouble." + }, + { + "text": "But what I imagine here is that's 8 and that's 132." + }, + { + "text": "So I'm getting 140." + }, + { + "text": "Is there any possibility that that's the right answer for df dx?" + }, + { + "text": "This is df dx I computed." + }, + { + "text": "By watching me struggle here, you're seeing the idea." + }, + { + "text": "Every step, I take the derivative of each step." + }, + { + "text": "So it was a power step, x cubed." + }, + { + "text": "So I had a 3x squared and a sum step." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk14.json b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..d9bce8eb5124ebbfa7340250ad365f47df2e0c70 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "So I had a 1." + }, + { + "text": "Then the next step was a multiplication." + }, + { + "text": "So I needed the product rule for that." + }, + { + "text": "I have these separate numbers." + }, + { + "text": "So I put them in." + }, + { + "text": "And so the computational graph finished." + }, + { + "text": "We only needed two levels." + }, + { + "text": "And we got 8 and 132, 140." + }, + { + "text": "But we didn't get df dy yet." + }, + { + "text": "And for that, I'd need to redo this again." + }, + { + "text": "And I don't want to do that." + }, + { + "text": "I would rather do the reverse mode and do them both at once." + }, + { + "text": "That's the point of the reverse mode." + }, + { + "text": "It's very efficient." + }, + { + "text": "It's very efficient, actually." + }, + { + "text": "Computing the gradient after you've done the work for the function, computing first derivatives, you could compute n first derivatives with about four or five times the cost, not n times." + }, + { + "text": "That's amazing to me." + }, + { + "text": "That is amazing that I can compute the gradient very efficiently by the back prop." + }, + { + "text": "So I have to show you the backwards way." + }, + { + "text": "I'm just going to follow all the paths backwards so that I get both df dx and df dy." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk15.json b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..c7ce6b4fd47a17150f8e8bd50717b43addb07584 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "You see the idea is to take the derivative of each step, each small step." + }, + { + "text": "That's really what we do in calculus." + }, + { + "text": "If you think about the start of a calculus course, what derivatives do we actually know?" + }, + { + "text": "Do we actually use xf at x plus delta x minus f?" + }, + { + "text": "What derivatives do we grind out?" + }, + { + "text": "We do the derivatives of x to the n. Every calculus book starts with x squared and then finds the derivative of x to the n. Then you do sine x and cos x." + }, + { + "text": "Then what others?" + }, + { + "text": "Are there any more?" + }, + { + "text": "Even e to the x, good, e to the x." + }, + { + "text": "And it's the inverse function log." + }, + { + "text": "In freshman calculus, you always write ln just to be out of date." + }, + { + "text": "And now that may be the list, is it?" + }, + { + "text": "And then the chain rule." + }, + { + "text": "Are there others that you actually do a computation of?" + }, + { + "text": "Actually, e to the x is defined by the property that its derivative is e to the x." + }, + { + "text": "And then you discover what log x has to be." + }, + { + "text": "And sine x, how do you do sine of x plus delta x?" + }, + { + "text": "Well, minus sine of x, how do you find the hard way, once and for all way?" + }, + { + "text": "You draw a little unit circle and mess with some angles." + }, + { + "text": "And you discover that the derivative of the sine is the cosine." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk16.json b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..c98c82abd3e50580cd9ca74496036de3494d54b8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's if you've defined the sine as a ratio of sides in a right triangle." + }, + { + "text": "Of course, you could define it as an infinite series." + }, + { + "text": "And then you would be back to just using that." + }, + { + "text": "OK." + }, + { + "text": "So calculus does exactly what we're doing here." + }, + { + "text": "Finds all derivatives by the chain rule applied to a few ones that it has worked out in detail." + }, + { + "text": "But tangent of x, we would use the quotient rule." + }, + { + "text": "Secant of x, we would use the quotient rule, 1 over cosine." + }, + { + "text": "And the products, we use the product rule." + }, + { + "text": "So really, calculus tends to seem fairly simple when you look back to see what actually you did." + }, + { + "text": "And then integration, what is integral calculus about?" + }, + { + "text": "More or less, guessing the answer." + }, + { + "text": "You have to integrate f of x dx." + }, + { + "text": "And so really, what you have to do is sort of think, OK, what had this derivative?" + }, + { + "text": "What function had that derivative?" + }, + { + "text": "And mess around and get it." + }, + { + "text": "So really, it's a freshman course, I guess." + }, + { + "text": "OK." + }, + { + "text": "So where am I?" + }, + { + "text": "Backward, right." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk17.json b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..da912f3fb942e524e31ca2eb3b8ad7dc207e6267 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's the thing still to do." + }, + { + "text": "How does the backward system work?" + }, + { + "text": "OK, I'll try my best." + }, + { + "text": "OK." + }, + { + "text": "So here's the big goal." + }, + { + "text": "Back." + }, + { + "text": "So reverse mode AD." + }, + { + "text": "Right." + }, + { + "text": "And let me make myself a little note." + }, + { + "text": "The little note is to give you another example where the order that you do the computations makes a big difference." + }, + { + "text": "And that's not obvious that it will, right?" + }, + { + "text": "There are many things in math that you could do in either order." + }, + { + "text": "And it seems like logically, you've done the same thing." + }, + { + "text": "So another and simpler example, which shows how one way could be way faster than another way, is when I'm multiplying two matrices, three matrices." + }, + { + "text": "So I'm multiplying three matrices, A times B times C. And the question is, do I do BC first and then multiply by A?" + }, + { + "text": "Or do I do AB first and then multiply that by C?" + }, + { + "text": "And of course, I kept them in order, in the order ABC." + }, + { + "text": "But the order of computations can be different." + }, + { + "text": "You get the same." + }, + { + "text": "You get the right answer both ways." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk18.json b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..c546999eea8721142b1753c43f29e9691e987a64 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "But those can be completely, completely different." + }, + { + "text": "One can be 1,000 times faster than the other." + }, + { + "text": "So that's just to show." + }, + { + "text": "Actually, it kind of connects to this." + }, + { + "text": "And there is also another." + }, + { + "text": "So I'll do that too." + }, + { + "text": "And there's also this." + }, + { + "text": "So this is example 2, where this is meant to be example 1." + }, + { + "text": "And example 3 would be, leads to something called the adjoint method in differential equations or in optimization." + }, + { + "text": "In computing optimum, in maximizing." + }, + { + "text": "And that has the same, really, the underlying reason it gives a speed up is it makes the right choice in a product of three things." + }, + { + "text": "So it'll be enough to do example 1 and example 2." + }, + { + "text": "Let me go with example 1." + }, + { + "text": "Our, this is now back propagation." + }, + { + "text": "Finally, we got to it." + }, + { + "text": "OK." + }, + { + "text": "So how do I, well, I look at my notes." + }, + { + "text": "This is how I do it." + }, + { + "text": "So the notes, this is section 7.2, does these computational graphs." + }, + { + "text": "And then here is reverse mode." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk19.json b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..cdad0d4b861e94ad0f6e49ee9cd59adab1539990 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "So it starts over here with, so I'm going to use the chain rule." + }, + { + "text": "So df df is 1." + }, + { + "text": "And then I go in backwards." + }, + { + "text": "And I have to use, of course, I have to take the derivatives." + }, + { + "text": "I have to use the right rule." + }, + { + "text": "So I have to use the product rule." + }, + { + "text": "And then soon I'll have to use these power rule and linear rule." + }, + { + "text": "So of course, no change there." + }, + { + "text": "The change is that by going backwards, oh, I don't know if I completed that sentence, that I could find 100 partial derivatives if the function depended on 100 variables in about 5 times the cost of one variable, 3 to 5 times the cost of 1." + }, + { + "text": "So you would expect 100 chain rules would cost 100 times." + }, + { + "text": "But you see, we're reusing the pieces in the chain and just having a larger." + }, + { + "text": "Our chain is wider, but it's not longer and it's not repeated." + }, + { + "text": "Anyway, so here I'm going to use whatever it is, df dc, and df ds." + }, + { + "text": "And I'm remembering that." + }, + { + "text": "So df dc is s, and df ds is c. That was because f started out as c times s. It was a product." + }, + { + "text": "Then we've got to evaluate those." + }, + { + "text": "I'll look again to see that I'm hopefully writing down some of the correct things." + }, + { + "text": "So now what I've written down next is df dc is 5." + }, + { + "text": "Or no, 5 on that example." + }, + { + "text": "What is it here?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk2.json b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..878917065ea5801ef56c24af14fd04e84dc68985 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "Maybe I should." + }, + { + "text": "So this is project 1." + }, + { + "text": "So you pick numbers a, k, which is rand from rand, so uniformly on 0, 1, on 0, 0, 1." + }, + { + "text": "And then my question is, what about convergence to the average is 1 half?" + }, + { + "text": "And so this may be too simple an example, but could we see what happens for the convergence of the average as you either do replacements or don't do replacements?" + }, + { + "text": "And then, in fact, I would like to see a figure that looks like those in his lecture." + }, + { + "text": "He started it somewhere." + }, + { + "text": "Start." + }, + { + "text": "And then here's the finish." + }, + { + "text": "But you remember that stochastic gradient descent was kind of pretty effective at the beginning." + }, + { + "text": "Well, the beginning, those might be 100 iterations each, one epoch, one run through the full number." + }, + { + "text": "But then when it got to here, got closer, it started oscillating." + }, + { + "text": "You remember he identified the region of confusion around the thing." + }, + { + "text": "Well, my suggestion is just I think those videos should be accessible to you on, are they on Stellar?" + }, + { + "text": "Yeah." + }, + { + "text": "So I'd love to see that behavior in some good examples of that behavior and some pictures to use." + }, + { + "text": "So that would be one idea." + }, + { + "text": "With and with." + }, + { + "text": "Oh, yeah, that's also idea two." + }, + { + "text": "Idea two is the good start and then the bad finish for stochastic gradient descent." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk20.json b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..55bd4ae57d8e01aa671bebe4ed5e3215777b3dda --- /dev/null +++ b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "df dc is c is x cubed." + }, + { + "text": "So df dc, yeah, I want s. I'm looking for s here." + }, + { + "text": "I'm looking for s. So I'm looking for s, and that's x plus 3y." + }, + { + "text": "Am I doing this well?" + }, + { + "text": "No." + }, + { + "text": "I want, in the end, to get the derivatives with respect to x and y, the whole gradient." + }, + { + "text": "OK, I think we're started right." + }, + { + "text": "The first derivatives is to write c and s. And then let me leave these boxes open just to get the picture." + }, + { + "text": "Then I'm going to do, then I'll need dc dx, dc dy, ds dx, and ds dy." + }, + { + "text": "I think that's right." + }, + { + "text": "Here I had a product of c and s. So I needed two, I had two derivatives." + }, + { + "text": "Here I have c and s each to differentiate." + }, + { + "text": "So I have an x and a y derivative, x and a y derivative." + }, + { + "text": "And now it's just a matter of putting in those numbers and following the chain backwards." + }, + { + "text": "Maybe I'm not going to put those numbers in, because if I didn't reach 140, you wouldn't believe in back propagation." + }, + { + "text": "And that would be like an unhappy outcome." + }, + { + "text": "So I'll leave you to put them in, maybe." + }, + { + "text": "Or the notes have a separate example that you can see." + }, + { + "text": "But do you see the point?" + }, + { + "text": "That I'm going to find all the, in the end, I'm going to find df dx and df dy from the chain, from one chain and not from a separate chain for x and a separate chain for y." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk21.json b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..a133a0477be520bc2d01965dd8c23837c8c87e36 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "To me, that's the point of reverse mode." + }, + { + "text": "It's a little bit of magic." + }, + { + "text": "But you see the steps, the ingredient." + }, + { + "text": "And some of you have seen this before and maybe know a better exposition." + }, + { + "text": "I found this blog by Christopher Ola clear." + }, + { + "text": "And these very simple things you'll see are clear in the notes." + }, + { + "text": "But maybe another blog brings out other points to make here." + }, + { + "text": "It's not obvious, maybe, that I could have 100 variables and do the calculation in four or five times the cost, four or five times being instead of 100." + }, + { + "text": "But it's possible." + }, + { + "text": "So could I close today with this one?" + }, + { + "text": "No." + }, + { + "text": "How could those be different?" + }, + { + "text": "You're computing the same numbers, the same aij, bjk, ckls, and doing this sums." + }, + { + "text": "But it certainly is different." + }, + { + "text": "So let's just do that." + }, + { + "text": "OK, I'll do it here." + }, + { + "text": "And then after my time, and I guess it'll be after Professor Rao on Friday and Monday, I'll come back to Professor Sra's short proof of the convergence of stochastic gradient descent." + }, + { + "text": "The whole point is to show you what assumptions do you need." + }, + { + "text": "You need some assumptions on the gradient, some assumptions on the step size." + }, + { + "text": "And for a good proof, all the assumptions fit together, and dong, out comes the conclusion." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk22.json b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..27f37d86ab2fb6d10c86c23d8dd16163decbf246 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk22.json @@ -0,0 +1,62 @@ +[ + { + "text": "And the conclusion would be how fast it converges, stochastic gradient descent." + }, + { + "text": "So there's some expected things, because it's stochastic." + }, + { + "text": "We expect some assumptions about the mean and the variance to go into the proof." + }, + { + "text": "So you'll see that, but maybe it's too much for today." + }, + { + "text": "So for today, I'll just come back to that." + }, + { + "text": "I might even put it on Stellar and just close with this." + }, + { + "text": "So suppose A is m by n, B is n by p, and C is p by q." + }, + { + "text": "How many steps does it take to find A times B times C, the product of those three matrices?" + }, + { + "text": "Well, if I go this way, I have to multiply A. I have to do BC first, so BC costs." + }, + { + "text": "How many operations to multiply that times that?" + }, + { + "text": "npq." + }, + { + "text": "Nice formula, npq." + }, + { + "text": "Why is that?" + }, + { + "text": "Well, I could say that the answer is n by q, and every number in there was an inner product of a row and column of length p. So I have nq inner product, and each one costs p multiply add." + }, + { + "text": "And then, so now I have BC, which will be now." + }, + { + "text": "So now I have m by n. And then I have m by n, which is the A, times B by C, which is now n by q." + }, + { + "text": "That's BC." + }, + { + "text": "This is ABC." + }, + { + "text": "So this one costs, what's the cost here?" + }, + { + "text": "m by n, n by q." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk23.json b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk23.json new file mode 100644 index 0000000000000000000000000000000000000000..7963693435949bb1667422ed03a6e7890707e272 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk23.json @@ -0,0 +1,62 @@ +[ + { + "text": "By the same rule, it'll be mnq." + }, + { + "text": "Good." + }, + { + "text": "That's the first way, A times BC." + }, + { + "text": "Now, the second way is AB times C. And let me write in again, m by n, n by p, p by q." + }, + { + "text": "So now I'm doing this first." + }, + { + "text": "So AB costs." + }, + { + "text": "Tell me again now, what's the rule for the cost of a matrix multiplication?" + }, + { + "text": "Mnp, mnp." + }, + { + "text": "And then I'm multiplying m by p. That's AB times p by q." + }, + { + "text": "That's C. So I have mpq." + }, + { + "text": "So I have that together with that, or that together with that." + }, + { + "text": "That sum, those two, or these two." + }, + { + "text": "And they're different." + }, + { + "text": "And let's just recognize the most important example." + }, + { + "text": "Suppose C is a column vector." + }, + { + "text": "C for a column vector." + }, + { + "text": "So q is 1." + }, + { + "text": "There's only one column." + }, + { + "text": "So if q is 1, this way did np." + }, + { + "text": "Let's just specialize to that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk24.json b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk24.json new file mode 100644 index 0000000000000000000000000000000000000000..83fb6be49ecbb1aaf0a6b7a0eaa34a0ea19c5985 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk24.json @@ -0,0 +1,62 @@ +[ + { + "text": "So specialize to C equal a column vector, which means that q is 1." + }, + { + "text": "I only have one column." + }, + { + "text": "So then A times BC is versus AB times C. So let's just figure that out when q is 1." + }, + { + "text": "So npq is just np." + }, + { + "text": "And mnq is just mn, where AB is mnp." + }, + { + "text": "Oh, that's a bad one." + }, + { + "text": "Disaster already." + }, + { + "text": "Multiplying, those are potentially two big matrices." + }, + { + "text": "Multiplying a column vector." + }, + { + "text": "So here I've done a matrix multiplication." + }, + { + "text": "I never should have done that." + }, + { + "text": "This is a matrix vector." + }, + { + "text": "It gives me a vector." + }, + { + "text": "And then this is a matrix vector." + }, + { + "text": "So I get nice numbers here." + }, + { + "text": "But I get a terrible number for AB." + }, + { + "text": "And then I multiply that by C. So that's mpq." + }, + { + "text": "mpq." + }, + { + "text": "So mp is factoring out." + }, + { + "text": "So if I write it as n times m plus p versus this one is m that's factoring out times m. No." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk25.json b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk25.json new file mode 100644 index 0000000000000000000000000000000000000000..9cf5018ff9826febbc12329440a539defec3aae0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk25.json @@ -0,0 +1,62 @@ +[ + { + "text": "Yeah." + }, + { + "text": "What's up here?" + }, + { + "text": "Sorry." + }, + { + "text": "What am I doing?" + }, + { + "text": "Yeah." + }, + { + "text": "Is it p that factors out from this one?" + }, + { + "text": "OK. p times m plus n, I guess." + }, + { + "text": "Sorry." + }, + { + "text": "Anyway, the difference is." + }, + { + "text": "AUDIENCE 1." + }, + { + "text": "I think it's mp times p plus q." + }, + { + "text": "Sorry." + }, + { + "text": "Shall I go over it again or write?" + }, + { + "text": "Let me do just this thinking again." + }, + { + "text": "If q is 1, if I go this way, was that my final total when q was 1?" + }, + { + "text": "And that's this." + }, + { + "text": "That's no." + }, + { + "text": "m factors out times n plus p. Whoops." + }, + { + "text": "Let's just get that right." + }, + { + "text": "This is." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk26.json b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk26.json new file mode 100644 index 0000000000000000000000000000000000000000..af8728538347bd6b63877035b9cf8c3f0b930ea5 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk26.json @@ -0,0 +1,62 @@ +[ + { + "text": "Oh, no." + }, + { + "text": "n factors out." + }, + { + "text": "Sorry." + }, + { + "text": "n factors out times n plus p. And this way was all these things." + }, + { + "text": "Both the m and the p factor out." + }, + { + "text": "Both the m and the p factor out." + }, + { + "text": "Thanks." + }, + { + "text": "Times n plus q. n plus q was 1." + }, + { + "text": "The whole point is we've got this horrible multiplication of three big numbers." + }, + { + "text": "And this only had two big numbers." + }, + { + "text": "So this is orders of magnitude faster than that." + }, + { + "text": "And of course, you would have done the calculation that way." + }, + { + "text": "You would have multiplied the column vector by a matrix to get another column vector." + }, + { + "text": "And you would have multiplied that by a matrix to get another column vector." + }, + { + "text": "Where here, you crazily multiplied two big matrices together and then got a column vector." + }, + { + "text": "So there's the bad move." + }, + { + "text": "OK, thanks." + }, + { + "text": "So we're past the time on this ABC." + }, + { + "text": "It's just to show that on a very familiar calculation, you have to do it in the right order." + }, + { + "text": "And back propagation is the right order for partial derivatives." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk27.json b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk27.json new file mode 100644 index 0000000000000000000000000000000000000000..6bd79ffad5f75893c8c2be466a93853bc1d4f528 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk27.json @@ -0,0 +1,14 @@ +[ + { + "text": "OK, thank you." + }, + { + "text": "And so bring laptops Friday." + }, + { + "text": "And look forward to Professor Rao." + }, + { + "text": "Give him a good welcome." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk3.json b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..049d777e0014a035a8356a9617411b90e4f8d7eb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "And of course, the magic words in, even without this, the magic words in computations is early stopping." + }, + { + "text": "We don't overfit." + }, + { + "text": "So we wanted to stop early anyway." + }, + { + "text": "And early stopping just is like a good idea for if that's what the approach to the x star that you're looking for." + }, + { + "text": "This would be the place where the, this is where, that's x star where grad f at x star is 0." + }, + { + "text": "That's the minimum point." + }, + { + "text": "That's arg min." + }, + { + "text": "Arg min." + }, + { + "text": "Exactly what we're looking for." + }, + { + "text": "And we don't find it very well, but we get close to it fast." + }, + { + "text": "OK. Two ideas on projects." + }, + { + "text": "So just, so maybe I'll go to the main topic of today, the topic I promised, the idea of back propagation." + }, + { + "text": "To compute, this is all to compute grad f, the gradient, all the derivatives." + }, + { + "text": "This is the df dx1 to df dxm, maybe I'll say, where I have m features for the sample." + }, + { + "text": "OK." + }, + { + "text": "So that's back propagation." + }, + { + "text": "And that's the thing whose discovery or rediscovery put neural nets on the map." + }, + { + "text": "That's the key calculation, of course, to find the gradient in the steepest descent algorithm." + }, + { + "text": "Every step needs a gradient." + }, + { + "text": "And if you can't compute it quickly, you're in bad shape." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk4.json b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..53e77122198a04f3cb82fd768bfdbc4e82f828af --- /dev/null +++ b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "But you can compute it quickly by this automatic differentiation in reverse mode, which is otherwise known." + }, + { + "text": "I don't think the people, maybe Hinton was the first, was the leader in developing deep neural nets, deep learning." + }, + { + "text": "And he realized, so I give him big credit for that, that back propagation would work and would give him fast gradients." + }, + { + "text": "But it actually had been studied before under the name AD, automatic differentiation." + }, + { + "text": "So may I just tell you that idea?" + }, + { + "text": "Some of you may know it, may know about it, may know more than I, and might know a good website to see this description." + }, + { + "text": "There'll be, of course, a section of the book, of the notes." + }, + { + "text": "Already, you already have it." + }, + { + "text": "This is section 7.2." + }, + { + "text": "So this is the chapter on deep learning." + }, + { + "text": "And the first section was about the structure of f of x." + }, + { + "text": "And you remember the key point about the structure of f of x is that I start with x and apply some function f1 of x." + }, + { + "text": "And to that, I apply some function f2 of x." + }, + { + "text": "And to that, I apply some function of f3 of f2 of f1 of x." + }, + { + "text": "And that's the thing whose derivative I need." + }, + { + "text": "So I'll just take ordinary derivative." + }, + { + "text": "Well, partial derivatives, really, because I better say partial derivatives." + }, + { + "text": "So suppose x is a pair xy." + }, + { + "text": "Example." + }, + { + "text": "Let me show you by example." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk5.json b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..0e6e60110990797810cbe4bea31ce7cad31fa0cd --- /dev/null +++ b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "So suppose f of x is, let me take a simple example, x cubed times x plus 2y." + }, + { + "text": "So I want to think of that function the way anybody would, as being built as a product of two functions." + }, + { + "text": "So there is a product rule to get into the derivative." + }, + { + "text": "And then we need the derivatives of each piece." + }, + { + "text": "So there's a power rule and a linear combination rule." + }, + { + "text": "So it's got a few of the rules that we use." + }, + { + "text": "And the point is to think about the computation of f of x and the computation of df dx and the computation of df dy." + }, + { + "text": "Those are the derivatives that we need." + }, + { + "text": "This is the function we need." + }, + { + "text": "And how to do those computations quickly." + }, + { + "text": "OK." + }, + { + "text": "So and this is section 7.2, which benefited a lot from a blog." + }, + { + "text": "I'm not a blog reader or a blog writer, but somehow I found this blog." + }, + { + "text": "So let me put." + }, + { + "text": "It's Christopher Olwa is his name." + }, + { + "text": "And he really writes clear things." + }, + { + "text": "So he contributes." + }, + { + "text": "He works for one of the big companies and does the deeper research." + }, + { + "text": "But he's also a really good expositor." + }, + { + "text": "And the website that he now uses is called distill.something." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk6.json b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..09a6a97e822ff6cb7ccd34628dde0b0d507689cb --- /dev/null +++ b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "But I think maybe this blog was earlier before the start of distill." + }, + { + "text": "But it might be loaded onto distil." + }, + { + "text": "Anyway, that's where I got this simple description of backpropagation." + }, + { + "text": "And let's just do calculus first of all." + }, + { + "text": "If I just have a function of maybe even one variable, what's the derivative?" + }, + { + "text": "What is df dx here?" + }, + { + "text": "Just to remember what calculation we have to do." + }, + { + "text": "So df dx, this is with n equal 1, one variable." + }, + { + "text": "So I'll use ordinary derivative and not partial derivative." + }, + { + "text": "But this is then what I, that's what really has to be done." + }, + { + "text": "But just what's the derivative of that, of a chain of functions?" + }, + { + "text": "Well, of course, the chain rule." + }, + { + "text": "So what does the chain rule say?" + }, + { + "text": "I differentiate F3." + }, + { + "text": "I don't know, what do I put that it's differentiated with respect to?" + }, + { + "text": "F3, df3, df2, is that what I should put?" + }, + { + "text": "OK. And where do I evaluate that derivative?" + }, + { + "text": "So yeah, I don't evaluate it at x, right?" + }, + { + "text": "I'm differentiating with respect to F2." + }, + { + "text": "So do I evaluate it at F2 of F1 of x?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk7.json b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..29ccdff3dd56902e813ac485477ec46596a83daf --- /dev/null +++ b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "This is where the chain rule gets sort of a little chainy, a little." + }, + { + "text": "OK, then we know that df2, df1." + }, + { + "text": "And again, that's now evaluated at F1 of x." + }, + { + "text": "And then the final factor is df1, dx, evaluated at x." + }, + { + "text": "That's somehow what we have to do." + }, + { + "text": "And that's just for an ordinary one variable function." + }, + { + "text": "And I have here a two variable function." + }, + { + "text": "And deep learning has a million variable function." + }, + { + "text": "So let's, I think we won't go to a million, but two we could manage." + }, + { + "text": "So let's compute those." + }, + { + "text": "Let's compute the function, first of all." + }, + { + "text": "Compute F. So I'm given x equals, say, 2, and y equals, say, 3." + }, + { + "text": "And I'm going to create a computational graph." + }, + { + "text": "So this is to draw." + }, + { + "text": "So I'm actually going to draw the computational graph to compute for F. And then it'll be a variation of that graph to find the derivatives." + }, + { + "text": "So let's just start with the graph, first of all, for the function, because we're going to need that." + }, + { + "text": "So again, it's x cubed plus." + }, + { + "text": "So can I write that function again?" + }, + { + "text": "x cubed times x plus 2y." + }, + { + "text": "So I think we're going to, the first step will be to find x plus x cubed, that factor, which will be 8." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk8.json b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..6a84d34b12e1bbcfabf591a6880e487aafa13fee --- /dev/null +++ b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "And we have to find the other factor, x plus 2y." + }, + { + "text": "So then I'm going to, that uses y and x." + }, + { + "text": "So it's a directed graph going forward with this computation." + }, + { + "text": "So x plus 2y equals whatever it is, 2 and 6." + }, + { + "text": "Oh, 8 again, not brilliant." + }, + { + "text": "What shall I change here?" + }, + { + "text": "Make it 3y, 3y, just to get a different number here." + }, + { + "text": "So now x is 2, y is 3." + }, + { + "text": "I get 11." + }, + { + "text": "That's a good number, 11." + }, + { + "text": "OK, so far so good?" + }, + { + "text": "And now the next step on this graph will be to, I have a product of those." + }, + { + "text": "So that will go to the product." + }, + { + "text": "Product F equals 8 times 11, 88." + }, + { + "text": "OK, so we got the answer, 88." + }, + { + "text": "Which math, normally I wouldn't take that much of a book to compute F. I would have said 2 cubed times 2 plus 3 times 3." + }, + { + "text": "And I'd have simplified that to 8 times 11." + }, + { + "text": "And I would have got 88." + }, + { + "text": "So if we were just writing normally, that would do it." + }, + { + "text": "But this is the picture of the computational graph." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk9.json b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..b10119ee042fb282c85c49ac60ccc9e74b2ae980 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/lZrIPRnoGQQ_0_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK, good, good, good." + }, + { + "text": "Now it's the derivatives, two derivatives to find, dF dx and dF dy." + }, + { + "text": "Suppose we go forward first." + }, + { + "text": "My point is going to be, or the great point is that backward is better." + }, + { + "text": "Reverse mode is better." + }, + { + "text": "But we don't know what that means until we've gone forward." + }, + { + "text": "So let me go forward." + }, + { + "text": "So now I'm going to go forward." + }, + { + "text": "Forward." + }, + { + "text": "So what do we?" + }, + { + "text": "Let's do dF dx, OK?" + }, + { + "text": "Everybody's up for dF dx, the partial derivative with respect to x." + }, + { + "text": "So here we have x equal 2 and y equal 3." + }, + { + "text": "OK?" + }, + { + "text": "And then I've got to take the derivative of that step." + }, + { + "text": "The first step was x to x cubed." + }, + { + "text": "So I need the derivative." + }, + { + "text": "The whole point of AD is that the computation, every computation of a derivative breaks down like this into very simple pieces." + }, + { + "text": "And the derivatives of those simple pieces are also simple pieces." + }, + { + "text": "So the whole point is to replace appropriately those intermediate steps with derivatives, so as to compute the x derivative." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk0.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6b8bcce949e11c9807b49a56c5ca68fdb459f818 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay, here is lecture ten in linear algebra." + }, + { + "text": "Two important things to do in this lecture." + }, + { + "text": "One is to correct an error from lecture nine." + }, + { + "text": "So the blackboard with that awful error is still with us." + }, + { + "text": "And the second, the big thing to do is to tell you about the four subspaces that come with a matrix." + }, + { + "text": "We've seen two subspaces, the column space and the null space, there's two to go." + }, + { + "text": "Okay." + }, + { + "text": "First of all, and this is a great way to recap and correct the previous lecture." + }, + { + "text": "So you remember I was just doing R3." + }, + { + "text": "I couldn't have taken a simpler example than R3." + }, + { + "text": "And I wrote down the standard basis." + }, + { + "text": "That's the standard basis." + }, + { + "text": "The basis, the obvious basis for the whole three-dimensional space." + }, + { + "text": "And then I wanted to make the point that there was nothing special, nothing about that basis that another basis couldn't have." + }, + { + "text": "It could have linear independence, it could span a space, there's lots of other bases." + }, + { + "text": "So I started with these vectors one one two and two two five, and those were independent." + }, + { + "text": "And then I said three three seven wouldn't do, because three three seven is the sum of those." + }, + { + "text": "So in my innocence, I put in three three eight." + }, + { + "text": "I figured probably if three three seven is on the plane, is, which I know, it's in the plane with these two, then probably three three eight sticks a little bit out of the plane." + }, + { + "text": "And it's independent and it gives a basis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk1.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..97d9d72b29a5aa923aae0ba9c0fb0da57e9db2ed --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "But after class, to my sorrow, student tells me, wait a minute, that third vector three three eight is not independent." + }, + { + "text": "And why did she say that?" + }, + { + "text": "She didn't actually take the time, didn't have to, to find what combination of this one and this one gives three three eight." + }, + { + "text": "She did something else." + }, + { + "text": "In other words, she looked ahead because she said, wait a minute, if I look at that matrix, it's not invertible." + }, + { + "text": "That third column can't be independent of the first two, because when I look at that matrix, it's got two identical rows." + }, + { + "text": "I have a square matrix." + }, + { + "text": "Its rows are obviously dependent." + }, + { + "text": "And that makes the columns dependent." + }, + { + "text": "So there's my error." + }, + { + "text": "When I look at the matrix A that has those three columns, those three columns can't be independent because that matrix is not invertible because it's got two equal rows." + }, + { + "text": "And today's lecture will reach the conclusion, the great conclusion, that connects the column space with the row space." + }, + { + "text": "So those are the row space is now going to be another one of my fundamental subspaces." + }, + { + "text": "The row space of this matrix or of this one, well, the row space of this one is okay." + }, + { + "text": "But the row space of this one, I'm looking at the rows of the matrix, oh, anyway, I'll have two equal rows and the row space will be only two-dimensional." + }, + { + "text": "The rank of the matrix with these columns will only be two, so only two of those columns can be independent too." + }, + { + "text": "The rows tell me something about the columns, in other words." + }, + { + "text": "Something that I should have noticed and I didn't." + }, + { + "text": "Okay." + }, + { + "text": "So now let me pin down these four fundamental subspaces." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk10.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..8f428ebe86b1b4488558f6fa55b8940ef758b264 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "Okay." + }, + { + "text": "What about its row space?" + }, + { + "text": "What happened to its row space?" + }, + { + "text": "Well, what happened, let me first ask, just because this is, sometimes something does happen." + }, + { + "text": "Its column space changed." + }, + { + "text": "The column space of R is not the column space of A, right?" + }, + { + "text": "Because one one one is certainly in the column space of A and certainly not in the column space of R. I did row operations." + }, + { + "text": "Those row operations preserved the row space, so the row so the column spaces are different." + }, + { + "text": "Different column spaces." + }, + { + "text": "Different column spaces." + }, + { + "text": "But I believe that they have the same row space." + }, + { + "text": "Same row space." + }, + { + "text": "I believe that the row space of that matrix and the row space of this matrix are identical." + }, + { + "text": "They have exactly the same vectors in them." + }, + { + "text": "Those vectors are vectors with four components, right?" + }, + { + "text": "They're all combinations of those rows." + }, + { + "text": "Or I believe you get the same thing by taking all combinations of these rows." + }, + { + "text": "And if true, what's a basis?" + }, + { + "text": "What's a basis for the row space of R?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk11.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..258e5999dbb0aea67696256511eb6b999136132a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it'll be a basis for the row space of the original A." + }, + { + "text": "But it's obviously a basis for the row space of R. What's a basis for the row space of that matrix?" + }, + { + "text": "The first two rows." + }, + { + "text": "So a basis for the row so a basis is for the row space of A or of R is the first R rows of R, not of A." + }, + { + "text": "Sometimes it's true for A, but not necessarily." + }, + { + "text": "But R, we definitely have a matrix here whose row space we can identify." + }, + { + "text": "The row space is spanned by the three rows." + }, + { + "text": "But if we want a basis, we want independence." + }, + { + "text": "So out goes row three." + }, + { + "text": "The row space is also spanned by the first two rows." + }, + { + "text": "This guy didn't contribute anything." + }, + { + "text": "And of course, over here, this one, two, three, one in the bottom didn't contribute anything." + }, + { + "text": "We had it already." + }, + { + "text": "So this, here's a basis, one zero one one and zero one one zero." + }, + { + "text": "I believe those are in the row space." + }, + { + "text": "I know they're independent." + }, + { + "text": "Why are they in the row space?" + }, + { + "text": "Why are those two vectors in the row space?" + }, + { + "text": "Because all those operations we did, which started with these rows and took combinations of them." + }, + { + "text": "I took this row minus this row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk12.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..d05a7eb6e4998c4acd748e3bb7087c68e6e29a80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "That gave me something that's still in the row space." + }, + { + "text": "That's the point." + }, + { + "text": "When I took a row minus a multiple of another row, I'm staying in the row space." + }, + { + "text": "The row space is not changing." + }, + { + "text": "My little basis for it is changing, and I've ended up with, sort of, the best basis." + }, + { + "text": "If the columns of the identity matrix are the best basis for R3 or Rn, the rows of this matrix are the best basis for the row space." + }, + { + "text": "Best in the sense of being as clean as I can make it." + }, + { + "text": "Starting off with the identity and then finishing up with whatever has to be in there." + }, + { + "text": "OK. Do you see, then, that the dimension is R?" + }, + { + "text": "For sure." + }, + { + "text": "Because we've got R pivots, R nonzero rows, we've got the right number of vectors, R. They're in the row space, they're independent, that's it." + }, + { + "text": "They are a basis for the row space." + }, + { + "text": "And we can even pin that down further." + }, + { + "text": "How do I know that every row of A is a combination?" + }, + { + "text": "How do I know they span the row space?" + }, + { + "text": "Oh, well, somebody says I've got the right number of them, so they must, but that's true." + }, + { + "text": "But let me just say, how do I know that this row is a combination of these?" + }, + { + "text": "By just reversing the steps of row reduction." + }, + { + "text": "If I just reverse the steps and go from A, from R back to A, then what do I, what am I doing?" + }, + { + "text": "I'm starting with these rows, I'm taking combinations of them, after a couple of steps, undoing the subtractions that I did before, I'm back to these rows." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk13.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..7b0edabbd24233827c7692f63429589952dac1bc --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "So these rows are combinations of those rows, those rows are combinations of those rows, the two row spaces are the same, the bases are the same, and the natural basis is this guy." + }, + { + "text": "Is that all right for the row space?" + }, + { + "text": "The row space is sitting there in R, in its cleanest possible form." + }, + { + "text": "OK. Now what about the fourth guy, the null space of A transpose?" + }, + { + "text": "First of all, why do I call that the left null space?" + }, + { + "text": "So let me save that and bring that down." + }, + { + "text": "OK." + }, + { + "text": "So the fourth space is the null space of A transpose." + }, + { + "text": "So it has in it vectors, let me call them y, so that A transpose y equals zero." + }, + { + "text": "If A transpose y equals zero, then y is in the null space of A transpose, of course." + }, + { + "text": "So this is a matrix times a column equaling zero." + }, + { + "text": "And now, because I want y to sit on the left, and I want A instead of A transpose, I'll just transpose that equation." + }, + { + "text": "Can I just transpose that?" + }, + { + "text": "On the right, it makes the zero vector lie down." + }, + { + "text": "And on the left, it's a product, A transpose times y." + }, + { + "text": "If I take the transpose, then they come in opposite order, right?" + }, + { + "text": "So it's y transpose times A transpose transpose, but nobody's going to leave it like that." + }, + { + "text": "That's A transpose transpose is just A, of course." + }, + { + "text": "When I transposed A transpose, I got back to A." + }, + { + "text": "Now, do you see what I have now?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk14.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7a889f79409e9a95fbd4cc01518da4b9706c49d1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "I have a row vector, y transpose, multiplying A and multiplying from the left." + }, + { + "text": "That's why I call it the left null space." + }, + { + "text": "But by making it, putting it on the left, I had to make it into a row instead of a column vector." + }, + { + "text": "And so my convention is I usually don't do that, I usually stay with A transpose y equals zero." + }, + { + "text": "OK. And you might ask, how do we get a basis, or I might ask, how do we get a basis for this fourth space, this left null space?" + }, + { + "text": "OK." + }, + { + "text": "I'll do it the example." + }, + { + "text": "As always, ah, not that one." + }, + { + "text": "The left null space is not jumping out at me here." + }, + { + "text": "I know which are the free variables, the special solutions, but those are special solutions to Ax equals zero, and now I'm looking at A transpose and I'm not seeing it here." + }, + { + "text": "So, but somehow you feel that the work that you did, which simplified A to R, should have revealed the left null space too." + }, + { + "text": "And it's slightly less immediate, but it's there." + }, + { + "text": "So from A to R, I took some steps, and I guess I'm interested in what were those steps, or what were all of them together." + }, + { + "text": "I don't want to -- I'm not interested in what particular ones they were." + }, + { + "text": "I'm interested in what was the whole matrix that took me from A to R. How would you find that?" + }, + { + "text": "Do you remember Gauss-Jordan, where you tack on the identity matrix?" + }, + { + "text": "Let's do that again." + }, + { + "text": "So I'll do it above here." + }, + { + "text": "So this is now the idea of I take the matrix A, which is m by n. In Gauss-Jordan, when we saw him before, A was a square invertible matrix and we were finding its inverse." + }, + { + "text": "Now the matrix isn't square, it's probably rectangular." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk15.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3c045b6d07a6635d896789ba37b0d578bd175e92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "But I'll still tack on the identity matrix, and of course, since these have length m, it better be m by m. And now I'll do the reduced row echelon form of this matrix." + }, + { + "text": "And what do I get?" + }, + { + "text": "The reduced row echelon form starts with these columns, starts with the first columns, works like mad, and produces R. Of course, still the same size, m by n, and we did it before." + }, + { + "text": "And then whatever it did to get R, something else is going to show up here." + }, + { + "text": "Let me call it E, m by m. It's whatever you see that E is just going to contain a record of what we did." + }, + { + "text": "We did whatever it took to get A to become R. And at the same time, we were doing it to the identity matrix." + }, + { + "text": "So we started with the identity matrix, we buzzed along." + }, + { + "text": "So we took some -- all this row reduction amounted to multiplying on the left by some matrix, some series of elementary matrices that all together gave us one matrix, and that matrix is E. So all this row reduction stuff amounted to multiplying by E. How do I know that?" + }, + { + "text": "It certainly amounted to multiplying by something, and that something took I to E, so that something was E. So now look at the first part, E A is R. No big deal." + }, + { + "text": "All I've said is that the row reduction steps that we all know well, taking A to R, are in a- in some matrix, and I can find out what that matrix is by just tacking I on and seeing what comes out." + }, + { + "text": "What comes out is E. Let's just review the invertible square case." + }, + { + "text": "What happened then?" + }, + { + "text": "Because I was interested in it in chapter two also." + }, + { + "text": "When A was square and invertible, I took A I, I did row elimination, what was the R that came out?" + }, + { + "text": "It was I." + }, + { + "text": "So in chapter two, in chapter two, R was I." + }, + { + "text": "The row- the reduced row echelon form of a nice invertible square matrix is the identity." + }, + { + "text": "So if R was I in that case, then E was A inverse, because E A is I." + }, + { + "text": "Good." + }, + { + "text": "That's- that was good and easy." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk16.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..c5a8adc4741aeb68371eb235609b24dad795df03 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now what I'm saying is that there still is an E, it's not A inverse anymore, because A is a rectangular, it hasn't got an inverse." + }, + { + "text": "But there is still some matrix E that connected this to this." + }, + { + "text": "Oh, I should have figured out in advance what it was." + }, + { + "text": "Shoot." + }, + { + "text": "I didn't- I did those steps and sort of erased as I went, and, I should have done them to the identity, too." + }, + { + "text": "Can I do that?" + }, + { + "text": "Can I do that?" + }, + { + "text": "I'll keep the identity matrix, like I'm supposed to do, and I'll do the same operations on it and see what I end up with." + }, + { + "text": "Okay." + }, + { + "text": "So I'm starting with the identity, which I'll write in light, light enough, but okay, what did I do?" + }, + { + "text": "I subtracted that row from that one and that row from that one." + }, + { + "text": "Okay, I'll do that to the identity." + }, + { + "text": "So I subtract that first row from row two and row three." + }, + { + "text": "Good." + }, + { + "text": "Then I think I multiply, do you remember, I multiplied row two by minus one?" + }, + { + "text": "Let me just do that." + }, + { + "text": "Then what did I do?" + }, + { + "text": "I subtracted two of row two away from row one." + }, + { + "text": "I better do that." + }, + { + "text": "Subtract two of this away from this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk17.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..368775ffcdaa5a9fe2c24f8c85bcb4963097a79c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's minus one, two of these away leaves a plus two and zero." + }, + { + "text": "I believe that's E. The way to check is to see, multiply that E by this A, just to see, did I do it right?" + }, + { + "text": "So I believe E was minus one, two, zero, one minus one, zero, and minus one, zero, one." + }, + { + "text": "Okay." + }, + { + "text": "That's my E, that's my A, and that's R. All right." + }, + { + "text": "All I'm struggling to do is write the reason I wanted this blasted E was so that I could figure out the left null space." + }, + { + "text": "Not only its dimension, which I know." + }, + { + "text": "Actually, what is the dimension of the left null space?" + }, + { + "text": "Here's my matrix." + }, + { + "text": "What's the rank of the matrix?" + }, + { + "text": "Two." + }, + { + "text": "And the dimension of the left null space is supposed to be M minus R, three minus two, one." + }, + { + "text": "I believe that the left null space is one-dimensional." + }, + { + "text": "There is one combination of those three rows that produces the zero row." + }, + { + "text": "There is a basis." + }, + { + "text": "A basis for the left null space has only got one vector in it." + }, + { + "text": "And what is that vector?" + }, + { + "text": "It's here in the last row of E. But, ah, we could have seen it earlier." + }, + { + "text": "What combination of those rows gives the zero row?" + }, + { + "text": "Minus one of that, plus one of that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk18.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..9f5e8b1fcc2242dbdc56d379cbc7126ada792e31 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a basis for the left null space of this matrix, I'm looking for combinations of rows that give the zero row, if I'm looking at the left null space." + }, + { + "text": "For the null space, I'm looking at combinations of columns to get the zero column." + }, + { + "text": "Now I'm looking at combinations of these three rows to get the zero row, and of course, there is my zero row, and here is my vector that produced it." + }, + { + "text": "Minus one of that row and one of that row." + }, + { + "text": "Obvious." + }, + { + "text": "Okay." + }, + { + "text": "So in that example, and actually in all examples, we have seen how to produce a basis for the left null space." + }, + { + "text": "I won't ask you that all the time." + }, + { + "text": "Because it didn't come out immediately from R, we had to keep track of E for that left null space." + }, + { + "text": "But at least it didn't require us to transpose the matrix and start all over again." + }, + { + "text": "Okay." + }, + { + "text": "Those are the four subspaces." + }, + { + "text": "Can I review them?" + }, + { + "text": "The row space and the null space are in Rn." + }, + { + "text": "Their dimensions add to n. The column space and the left null space are in Rm, and their dimensions add to m. Okay." + }, + { + "text": "So let me close these last minutes by pushing you a little bit more to a new type of vector space." + }, + { + "text": "All our vector spaces, all the ones that we took seriously, have been subspaces of some real three- or n-dimensional space." + }, + { + "text": "Now I'm going to write down another vector space, a new vector space." + }, + { + "text": "Say all three by three matrices." + }, + { + "text": "My matrices are the vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk19.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..c1658ee474fcf6206f54d67e4dededa02a1ef92c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Is that all right?" + }, + { + "text": "I'm just naming them." + }, + { + "text": "You can put quotes around vectors." + }, + { + "text": "Every three by three matrix is one of my vectors." + }, + { + "text": "Now how am I entitled to call those things vectors?" + }, + { + "text": "I mean, they look very much like matrices." + }, + { + "text": "But they're vectors in my vector space because they obey the rules." + }, + { + "text": "All I'm supposed to be able to do with vectors is add them." + }, + { + "text": "I can add matrices." + }, + { + "text": "I'm supposed to be able to multiply them by scalar numbers, like seven." + }, + { + "text": "Well, I can multiply a matrix by seven." + }, + { + "text": "And I can take combinations of matrices." + }, + { + "text": "I can take three of one matrix minus five of another matrix." + }, + { + "text": "And those combinations, there's a zero matrix, the matrix that has all zeros in it." + }, + { + "text": "If I add that to another matrix, it doesn't change it." + }, + { + "text": "All the good stuff." + }, + { + "text": "If I multiply a matrix by one, it doesn't change it." + }, + { + "text": "All those eight rules for a vector space that we never wrote down, all easily satisfied." + }, + { + "text": "So now we have a different --." + }, + { + "text": "Now, of course, you can say you can multiply those matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk2.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..b92bd923d792a0f92ab4de95b7867006e9880f71 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here are the four fundamental subspaces." + }, + { + "text": "This is really the heart of this approach to linear algebra, to see these four subspaces, how they're related." + }, + { + "text": "So what are they?" + }, + { + "text": "The column space, C of A." + }, + { + "text": "The null space, N of A." + }, + { + "text": "And now comes the row space, something new." + }, + { + "text": "The row space, what's in that?" + }, + { + "text": "It's all combinations of the rows." + }, + { + "text": "That's natural." + }, + { + "text": "We want a space, so we have to take all combinations and we start with the rows." + }, + { + "text": "So the rows span the row space." + }, + { + "text": "Are the rows a basis for the row space?" + }, + { + "text": "Maybe so, maybe no." + }, + { + "text": "The rows are a basis for the row space when they're independent." + }, + { + "text": "But if they're dependent, as in this example, my error from last time, they're not, those three rows are not a basis, the row space would only be two-dimensional, I only need two rows for a basis." + }, + { + "text": "So the row space, now what's in it?" + }, + { + "text": "It's all combinations of the rows of A." + }, + { + "text": "All combinations of the rows of A." + }, + { + "text": "But I don't like working with row vectors." + }, + { + "text": "All my vectors have been column vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk20.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..56956e8347a8f8c1f8522690db77860dcc6953b9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "I don't care." + }, + { + "text": "For the moment, I'm only thinking of these matrices as forming a vector space, so I am only doing A plus B and C times A. I'm not interested in A, B for now." + }, + { + "text": "The fact that I can multiply is not relevant to a vector space." + }, + { + "text": "OK, so I have three by three matrices." + }, + { + "text": "And how about subspaces?" + }, + { + "text": "What's, tell me a subspace of this matrix space." + }, + { + "text": "Let me call this matrix space M. That's my matrix space, my space of all three by three matrices." + }, + { + "text": "Tell me a subspace of it." + }, + { + "text": "OK, what about the upper triangular matrices?" + }, + { + "text": "So subspaces, subspaces of M. All upper triangular matrices." + }, + { + "text": "Another subspace." + }, + { + "text": "All symmetric matrices." + }, + { + "text": "The intersection of two subspaces is supposed to be a subspace." + }, + { + "text": "We gave a little effort to the proof of that fact." + }, + { + "text": "If I look at the matrices that are in this subspace, they're symmetric, and they're also in this subspace, they're upper triangular." + }, + { + "text": "What do they look like?" + }, + { + "text": "Well, if they're symmetric, but they have zeros below the diagonal, they better have zeros above the diagonal." + }, + { + "text": "So the intersection would be diagonal matrices." + }, + { + "text": "That's another subspace, smaller than those." + }, + { + "text": "How can I use the word smaller?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk21.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..ffcdd44ed2f644726e04b27114327cb30bc7fb92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, I'm now entitled to use the word smaller." + }, + { + "text": "I mean, well, one way to say is, OK, these are contained in those." + }, + { + "text": "These are contained in those." + }, + { + "text": "But more precisely, I could give the dimension of these spaces." + }, + { + "text": "So I could, we can compute, let's compute it next time." + }, + { + "text": "The dimension of all upper, of the subspace of upper triangular three by three matrices." + }, + { + "text": "The dimension of symmetric three by three matrices." + }, + { + "text": "The dimension of diagonal three by three matrices." + }, + { + "text": "Well, to produce dimension, that means I'm supposed to produce a basis." + }, + { + "text": "And then I just count how many I needed in the basis." + }, + { + "text": "Let me give you the answer for this one." + }, + { + "text": "What's the dimension?" + }, + { + "text": "The dimension of this, say, this subspace, let me call it D, all diagonal matrices." + }, + { + "text": "The dimension of this subspace is, as I write, you're working it out, three." + }, + { + "text": "Because here's a matrix in this, it's a diagonal matrix." + }, + { + "text": "Here's another one." + }, + { + "text": "Here's another one." + }, + { + "text": "Better make it diagonal, let me put a seven there." + }, + { + "text": "That was not a very great choice, but it's three diagonal matrices, and I believe that they're a basis." + }, + { + "text": "I believe that those three matrices are independent, and I believe that any diagonal matrix is a combination of those three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk22.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..8c6bce8cf8085e6544c31ae6926bb7ccf18b983e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk22.json @@ -0,0 +1,20 @@ +[ + { + "text": "So they span the subspace of diagonal matrices." + }, + { + "text": "Do you see that idea?" + }, + { + "text": "It's like stretching the idea from Rn to Rn by n, three by three, but we can still add, we can still multiply by numbers, and we just ignore the fact that we can multiply two matrices together." + }, + { + "text": "Okay." + }, + { + "text": "Thank you." + }, + { + "text": "That's lecture ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk3.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..25f31647b76274f9088c60d1292bcc43915d3fb0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'd like to stay with column vectors." + }, + { + "text": "How can I get to column vectors out of these rows?" + }, + { + "text": "I transpose the matrix." + }, + { + "text": "So if that's OK with you, I'm going to transpose the matrix, I'm going to say all combinations of the columns of A transpose." + }, + { + "text": "And that allows me to use the convenient notation, the column space of A transpose." + }, + { + "text": "Nothing, no mathematics went on there, we just got some vectors that were lying down to stand up." + }, + { + "text": "But it means that we can use this column space of A transpose, that's telling me in a nice matrix notation what the row space is." + }, + { + "text": "OK. And finally is another null space." + }, + { + "text": "The fourth fundamental space will be the null space of A transpose." + }, + { + "text": "The fourth guy is the null space of A transpose." + }, + { + "text": "And of course, my notation is N of A transpose." + }, + { + "text": "That's the null space of A transpose." + }, + { + "text": "Now, we don't have a perfect name for this space as a, as a, connecting with A, but our usual name is the left null space, and I'll show you why in a moment." + }, + { + "text": "So often I call this the, just to write that word, the left null space of A." + }, + { + "text": "So just the way we have the row space of A and we switch it to the column space of A transpose, so we have this space of guys that I call the left null space of A, but the good notation is it's the null space of A transpose." + }, + { + "text": "OK. Those are four spaces." + }, + { + "text": "Where are those spaces?" + }, + { + "text": "What big space are they in for when A is m by n?" + }, + { + "text": "In that case, the null space of A, what's in the null space of A?" + }, + { + "text": "Vectors with n components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk4.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c2575473d88ff4598107e190483f0484b6558678 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Solutions to Ax equals zero." + }, + { + "text": "So the null space of A is n R n. What's in the column space of A?" + }, + { + "text": "Well, columns." + }, + { + "text": "How many components do those columns have?" + }, + { + "text": "m. So this column space is n R m. What about the column space of A transpose, which are just a disguised way of saying the rows of A?" + }, + { + "text": "The rows of A in this three by six matrix have six components, n components." + }, + { + "text": "The column space is n R n. And the null space of A transpose, I see that this fourth space is already getting second, you know, second class citizen treatment and it doesn't deserve it." + }, + { + "text": "It's, it should be there, it is there, and shouldn't be squeezed." + }, + { + "text": "The null space of A transpose, well, if the null space of A had vectors with n components, the null space of A transpose will be n R m. I want to draw a picture of the four spaces." + }, + { + "text": "OK. OK." + }, + { + "text": "Here are the four spaces." + }, + { + "text": "OK, let me put n dimensional space over on this side." + }, + { + "text": "Then which were the subspaces in R n?" + }, + { + "text": "The null space was and the row space was." + }, + { + "text": "So here we have the can I make that picture of the row space?" + }, + { + "text": "And can I make this kind of picture of the null space?" + }, + { + "text": "That's just meant to be a sketch, to remind you that they're in this which, you know, how, what type of vectors are in it?" + }, + { + "text": "Vectors with n components." + }, + { + "text": "Over here, inside consisting of vectors with m components is the column space and what I'm calling the null space of A transpose." + }, + { + "text": "Those are the ones with m components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk5.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..f4e64e208c1a1d8e07a9a66a6a6c59f8c4cbcec8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. To understand these spaces is our job now." + }, + { + "text": "Because by understanding those spaces, we know everything about this half of linear algebra." + }, + { + "text": "What do I mean by understanding those spaces?" + }, + { + "text": "I would like to know a basis for those spaces." + }, + { + "text": "For each one of those spaces, how would I create, construct a basis?" + }, + { + "text": "What systematic way would produce a basis?" + }, + { + "text": "And what's their dimension?" + }, + { + "text": "OK." + }, + { + "text": "So for each of the four spaces, I have to answer those questions." + }, + { + "text": "How do I produce a basis?" + }, + { + "text": "And then, which has a somewhat long answer, and what's the dimension, which is just a number, so it has a real short answer?" + }, + { + "text": "Can I give you the short answer first?" + }, + { + "text": "I shouldn't do it, but here it is." + }, + { + "text": "I can tell you the dimension of the column space." + }, + { + "text": "Let me start with this guy." + }, + { + "text": "What's its dimension?" + }, + { + "text": "I have an m by n matrix." + }, + { + "text": "The dimension of the column space is the rank, R. We actually got to that at the end of the last lecture, but only for an example." + }, + { + "text": "So I really have to say, OK, what's going on there?" + }, + { + "text": "I should produce a basis, and then I just look to see how many vectors I needed in that basis, and the answer will be R. Actually, I'll do that before I get on to the others." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk6.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..ac7425fbe27a77a7e448b576483b4c179e9a31f1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "What's a basis for the column space?" + }, + { + "text": "We've done all the work of row reduction, identifying the pivot columns, the ones that have pivots, the ones that end up with pivots, but now I the pivot columns I'm interested in are columns of A, the original A." + }, + { + "text": "And those pivot columns, there are R of them, the rank R counts those, those are a basis." + }, + { + "text": "So if I answer this question for the column space, the answer will be a basis is the pivot columns, and the dimension is the rank R. And there are pivot columns and everything great." + }, + { + "text": "OK, so that space we pretty well understand." + }, + { + "text": "I probably have a little going back to see that, to prove that this is a right answer, but you know it's the right answer." + }, + { + "text": "Now let me look at the row space." + }, + { + "text": "OK. Shall I tell you the dimension of the row space?" + }, + { + "text": "Yes." + }, + { + "text": "Before we do even an example, let me tell you the dimension of the row space." + }, + { + "text": "Its dimension is also R. The row space and the column space have the same dimension." + }, + { + "text": "That's a wonderful fact." + }, + { + "text": "The dimension of the column space of A transpose, that's the row space, is R. That space is R-dimensional." + }, + { + "text": "And so is this one." + }, + { + "text": "OK. That's the, that's the sort of insight that got used in this example." + }, + { + "text": "If those, if those, if those, are the three columns of a matrix, let me make them the three columns of a matrix by just erasing some brackets, OK, those are the three columns of a matrix, the rank of that matrix, if I look at the columns, it wasn't obvious to me anyway." + }, + { + "text": "But if I look at the rows, it's, now it's obvious." + }, + { + "text": "The row space of that matrix obviously is two-dimensional, because I can, I see a basis for the row space, this row and that row." + }, + { + "text": "And of course, strictly speaking, I'm supposed to transpose those guys, make them stand up." + }, + { + "text": "But the rank is two, and therefore the column space is two-dimensional by this wonderful fact that the row space and column space have the same dimension, and therefore there are only two pivot columns, not three, and, those, the three columns are dependent." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk7.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..7d55c74913379543a71fcc53c971f787baf12a92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, let me bury that error and talk about the row space." + }, + { + "text": "Well, I'm going to give you the dimensions of all the spaces, because that's the, such a nice answer." + }, + { + "text": "OK." + }, + { + "text": "So let me come back here." + }, + { + "text": "So we have this great fact to establish, that the row space, its dimension is also the rank." + }, + { + "text": "OK. What about the null space?" + }, + { + "text": "What's a basis for the null space?" + }, + { + "text": "What's the dimension of the null space?" + }, + { + "text": "Let me, I'll put that answer up here, for the null space." + }, + { + "text": "Well, how have we constructed the null space?" + }, + { + "text": "We took the matrix A, we did those row operations to get it into a form U or even further, we got it into the reduced form R, and then we read off special solutions." + }, + { + "text": "Special solutions, and every special solution came from a free variable." + }, + { + "text": "And those special solutions are in the null space, and the great thing is, they're a basis for it." + }, + { + "text": "So for the null space, a basis will be the special solutions." + }, + { + "text": "And there's one for every free variable, right?" + }, + { + "text": "For each free variable, we give that variable the value one, the other free variable zero." + }, + { + "text": "We get the pivot variables, we get a vector in the -- we get a special solution." + }, + { + "text": "So we get all together n minus R of them, because that's the number of free variables." + }, + { + "text": "If we have R, this is, the dimension is R, is the number of pivot variables, this is the number of free variables." + }, + { + "text": "So the beauty is that those special solutions do form a basis and tell us immediately that the dimension of the null space is n -- I'd better write this well, because it's so nice, n minus R. And you see the nice thing, that the two dimensions in this n-dimensional space, one subspace is R-dimensional, to be proved, that's the row space." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk8.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f4c70532a641ef630aa1f7bca077776017097cd4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "The other subspace is n minus R-dimensional, that's the null space." + }, + { + "text": "And the two dimensions, like, together, give n. The sum of R and n minus R is n. And that's just great." + }, + { + "text": "It's really copying the fact that we have n variables, R of them are pivot variables and n minus R are free variables and n all together." + }, + { + "text": "OK. And now what's the dimension of this poor misbegotten fourth subspace?" + }, + { + "text": "It's got to be m minus R. The dimension of this left null space, left out practically, is m minus R. Well, that's really just saying that this, again, the sum of that plus that is m. And m is correct." + }, + { + "text": "It's the number of columns in A transpose." + }, + { + "text": "A transpose is just as good a matrix as A." + }, + { + "text": "It just happens to be n by m. It happens to have m columns, so it will have m variables, when I go to Ax equals zero, and m of them and R of them will be pivot variables and m minus R will be free variables." + }, + { + "text": "A transpose is as good a matrix as A." + }, + { + "text": "It follows the same rule that this plus the dimension, this dimension plus this dimension adds up to the number of columns." + }, + { + "text": "And over here, A transpose has m columns." + }, + { + "text": "Okay." + }, + { + "text": "Okay, so I gave you the easy answer, the dimensions." + }, + { + "text": "Now can I go back to check on a basis?" + }, + { + "text": "We would like to think that, say, the row space." + }, + { + "text": "Because we've got a basis for the column space." + }, + { + "text": "The pivot columns give a basis for the column space." + }, + { + "text": "Now I'm asking you to look at the row space." + }, + { + "text": "And I you could say, okay, I can produce a basis for the row space by transposing my matrix, making those columns, then doing elimination, row reduction, and checking out the pivot columns in this transposed matrix." + }, + { + "text": "But that means you had to do all that row reduction on A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk9.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..8be162da3ff089e5c511aa65ea7d801c64cad56f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_0_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It ought to be possible, if we take a matrix A, let me take the matrix, maybe we had this matrix in the last lecture, one one one, two one two, three two three, one one one." + }, + { + "text": "Okay." + }, + { + "text": "That, that matrix was so easy, we spotted its pivot columns, one and two, without actually doing row reduction." + }, + { + "text": "But now let's do the job properly." + }, + { + "text": "So I subtract this away from this to produce a zero." + }, + { + "text": "So one two three one is fine." + }, + { + "text": "Subtracting that away leaves me minus one minus one zero, right?" + }, + { + "text": "And subtracting that from the last row, oh, well, that's easy." + }, + { + "text": "Okay, I'm doing row reduction." + }, + { + "text": "Now I've, the first column is all set." + }, + { + "text": "The second column, I now see the pivot, and I can clean up, if I, actually, okay, why don't I make the pivot into a one?" + }, + { + "text": "I'll multiply that row through by minus one, and then I have one one." + }, + { + "text": "That was an elementary operation, I'm allowed." + }, + { + "text": "Multiply a row by a number." + }, + { + "text": "And now I'll do elimination." + }, + { + "text": "Two of those away from that will knock this guy out and make this into a one." + }, + { + "text": "So that's now a zero and that's a one." + }, + { + "text": "Okay." + }, + { + "text": "Done." + }, + { + "text": "That's R. I'm seeing the identity matrix here, I'm seeing zeros below, and I'm seeing F there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk0.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6b8bcce949e11c9807b49a56c5ca68fdb459f818 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay, here is lecture ten in linear algebra." + }, + { + "text": "Two important things to do in this lecture." + }, + { + "text": "One is to correct an error from lecture nine." + }, + { + "text": "So the blackboard with that awful error is still with us." + }, + { + "text": "And the second, the big thing to do is to tell you about the four subspaces that come with a matrix." + }, + { + "text": "We've seen two subspaces, the column space and the null space, there's two to go." + }, + { + "text": "Okay." + }, + { + "text": "First of all, and this is a great way to recap and correct the previous lecture." + }, + { + "text": "So you remember I was just doing R3." + }, + { + "text": "I couldn't have taken a simpler example than R3." + }, + { + "text": "And I wrote down the standard basis." + }, + { + "text": "That's the standard basis." + }, + { + "text": "The basis, the obvious basis for the whole three-dimensional space." + }, + { + "text": "And then I wanted to make the point that there was nothing special, nothing about that basis that another basis couldn't have." + }, + { + "text": "It could have linear independence, it could span a space, there's lots of other bases." + }, + { + "text": "So I started with these vectors one one two and two two five, and those were independent." + }, + { + "text": "And then I said three three seven wouldn't do, because three three seven is the sum of those." + }, + { + "text": "So in my innocence, I put in three three eight." + }, + { + "text": "I figured probably if three three seven is on the plane, is, which I know, it's in the plane with these two, then probably three three eight sticks a little bit out of the plane." + }, + { + "text": "And it's independent and it gives a basis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk1.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..97d9d72b29a5aa923aae0ba9c0fb0da57e9db2ed --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "But after class, to my sorrow, student tells me, wait a minute, that third vector three three eight is not independent." + }, + { + "text": "And why did she say that?" + }, + { + "text": "She didn't actually take the time, didn't have to, to find what combination of this one and this one gives three three eight." + }, + { + "text": "She did something else." + }, + { + "text": "In other words, she looked ahead because she said, wait a minute, if I look at that matrix, it's not invertible." + }, + { + "text": "That third column can't be independent of the first two, because when I look at that matrix, it's got two identical rows." + }, + { + "text": "I have a square matrix." + }, + { + "text": "Its rows are obviously dependent." + }, + { + "text": "And that makes the columns dependent." + }, + { + "text": "So there's my error." + }, + { + "text": "When I look at the matrix A that has those three columns, those three columns can't be independent because that matrix is not invertible because it's got two equal rows." + }, + { + "text": "And today's lecture will reach the conclusion, the great conclusion, that connects the column space with the row space." + }, + { + "text": "So those are the row space is now going to be another one of my fundamental subspaces." + }, + { + "text": "The row space of this matrix or of this one, well, the row space of this one is okay." + }, + { + "text": "But the row space of this one, I'm looking at the rows of the matrix, oh, anyway, I'll have two equal rows and the row space will be only two-dimensional." + }, + { + "text": "The rank of the matrix with these columns will only be two, so only two of those columns can be independent too." + }, + { + "text": "The rows tell me something about the columns, in other words." + }, + { + "text": "Something that I should have noticed and I didn't." + }, + { + "text": "Okay." + }, + { + "text": "So now let me pin down these four fundamental subspaces." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk10.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..8f428ebe86b1b4488558f6fa55b8940ef758b264 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "Okay." + }, + { + "text": "What about its row space?" + }, + { + "text": "What happened to its row space?" + }, + { + "text": "Well, what happened, let me first ask, just because this is, sometimes something does happen." + }, + { + "text": "Its column space changed." + }, + { + "text": "The column space of R is not the column space of A, right?" + }, + { + "text": "Because one one one is certainly in the column space of A and certainly not in the column space of R. I did row operations." + }, + { + "text": "Those row operations preserved the row space, so the row so the column spaces are different." + }, + { + "text": "Different column spaces." + }, + { + "text": "Different column spaces." + }, + { + "text": "But I believe that they have the same row space." + }, + { + "text": "Same row space." + }, + { + "text": "I believe that the row space of that matrix and the row space of this matrix are identical." + }, + { + "text": "They have exactly the same vectors in them." + }, + { + "text": "Those vectors are vectors with four components, right?" + }, + { + "text": "They're all combinations of those rows." + }, + { + "text": "Or I believe you get the same thing by taking all combinations of these rows." + }, + { + "text": "And if true, what's a basis?" + }, + { + "text": "What's a basis for the row space of R?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk11.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..258e5999dbb0aea67696256511eb6b999136132a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it'll be a basis for the row space of the original A." + }, + { + "text": "But it's obviously a basis for the row space of R. What's a basis for the row space of that matrix?" + }, + { + "text": "The first two rows." + }, + { + "text": "So a basis for the row so a basis is for the row space of A or of R is the first R rows of R, not of A." + }, + { + "text": "Sometimes it's true for A, but not necessarily." + }, + { + "text": "But R, we definitely have a matrix here whose row space we can identify." + }, + { + "text": "The row space is spanned by the three rows." + }, + { + "text": "But if we want a basis, we want independence." + }, + { + "text": "So out goes row three." + }, + { + "text": "The row space is also spanned by the first two rows." + }, + { + "text": "This guy didn't contribute anything." + }, + { + "text": "And of course, over here, this one, two, three, one in the bottom didn't contribute anything." + }, + { + "text": "We had it already." + }, + { + "text": "So this, here's a basis, one zero one one and zero one one zero." + }, + { + "text": "I believe those are in the row space." + }, + { + "text": "I know they're independent." + }, + { + "text": "Why are they in the row space?" + }, + { + "text": "Why are those two vectors in the row space?" + }, + { + "text": "Because all those operations we did, which started with these rows and took combinations of them." + }, + { + "text": "I took this row minus this row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk12.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..d05a7eb6e4998c4acd748e3bb7087c68e6e29a80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "That gave me something that's still in the row space." + }, + { + "text": "That's the point." + }, + { + "text": "When I took a row minus a multiple of another row, I'm staying in the row space." + }, + { + "text": "The row space is not changing." + }, + { + "text": "My little basis for it is changing, and I've ended up with, sort of, the best basis." + }, + { + "text": "If the columns of the identity matrix are the best basis for R3 or Rn, the rows of this matrix are the best basis for the row space." + }, + { + "text": "Best in the sense of being as clean as I can make it." + }, + { + "text": "Starting off with the identity and then finishing up with whatever has to be in there." + }, + { + "text": "OK. Do you see, then, that the dimension is R?" + }, + { + "text": "For sure." + }, + { + "text": "Because we've got R pivots, R nonzero rows, we've got the right number of vectors, R. They're in the row space, they're independent, that's it." + }, + { + "text": "They are a basis for the row space." + }, + { + "text": "And we can even pin that down further." + }, + { + "text": "How do I know that every row of A is a combination?" + }, + { + "text": "How do I know they span the row space?" + }, + { + "text": "Oh, well, somebody says I've got the right number of them, so they must, but that's true." + }, + { + "text": "But let me just say, how do I know that this row is a combination of these?" + }, + { + "text": "By just reversing the steps of row reduction." + }, + { + "text": "If I just reverse the steps and go from A, from R back to A, then what do I, what am I doing?" + }, + { + "text": "I'm starting with these rows, I'm taking combinations of them, after a couple of steps, undoing the subtractions that I did before, I'm back to these rows." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk13.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..7b0edabbd24233827c7692f63429589952dac1bc --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "So these rows are combinations of those rows, those rows are combinations of those rows, the two row spaces are the same, the bases are the same, and the natural basis is this guy." + }, + { + "text": "Is that all right for the row space?" + }, + { + "text": "The row space is sitting there in R, in its cleanest possible form." + }, + { + "text": "OK. Now what about the fourth guy, the null space of A transpose?" + }, + { + "text": "First of all, why do I call that the left null space?" + }, + { + "text": "So let me save that and bring that down." + }, + { + "text": "OK." + }, + { + "text": "So the fourth space is the null space of A transpose." + }, + { + "text": "So it has in it vectors, let me call them y, so that A transpose y equals zero." + }, + { + "text": "If A transpose y equals zero, then y is in the null space of A transpose, of course." + }, + { + "text": "So this is a matrix times a column equaling zero." + }, + { + "text": "And now, because I want y to sit on the left, and I want A instead of A transpose, I'll just transpose that equation." + }, + { + "text": "Can I just transpose that?" + }, + { + "text": "On the right, it makes the zero vector lie down." + }, + { + "text": "And on the left, it's a product, A transpose times y." + }, + { + "text": "If I take the transpose, then they come in opposite order, right?" + }, + { + "text": "So it's y transpose times A transpose transpose, but nobody's going to leave it like that." + }, + { + "text": "That's A transpose transpose is just A, of course." + }, + { + "text": "When I transposed A transpose, I got back to A." + }, + { + "text": "Now, do you see what I have now?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk14.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7a889f79409e9a95fbd4cc01518da4b9706c49d1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "I have a row vector, y transpose, multiplying A and multiplying from the left." + }, + { + "text": "That's why I call it the left null space." + }, + { + "text": "But by making it, putting it on the left, I had to make it into a row instead of a column vector." + }, + { + "text": "And so my convention is I usually don't do that, I usually stay with A transpose y equals zero." + }, + { + "text": "OK. And you might ask, how do we get a basis, or I might ask, how do we get a basis for this fourth space, this left null space?" + }, + { + "text": "OK." + }, + { + "text": "I'll do it the example." + }, + { + "text": "As always, ah, not that one." + }, + { + "text": "The left null space is not jumping out at me here." + }, + { + "text": "I know which are the free variables, the special solutions, but those are special solutions to Ax equals zero, and now I'm looking at A transpose and I'm not seeing it here." + }, + { + "text": "So, but somehow you feel that the work that you did, which simplified A to R, should have revealed the left null space too." + }, + { + "text": "And it's slightly less immediate, but it's there." + }, + { + "text": "So from A to R, I took some steps, and I guess I'm interested in what were those steps, or what were all of them together." + }, + { + "text": "I don't want to -- I'm not interested in what particular ones they were." + }, + { + "text": "I'm interested in what was the whole matrix that took me from A to R. How would you find that?" + }, + { + "text": "Do you remember Gauss-Jordan, where you tack on the identity matrix?" + }, + { + "text": "Let's do that again." + }, + { + "text": "So I'll do it above here." + }, + { + "text": "So this is now the idea of I take the matrix A, which is m by n. In Gauss-Jordan, when we saw him before, A was a square invertible matrix and we were finding its inverse." + }, + { + "text": "Now the matrix isn't square, it's probably rectangular." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk15.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3c045b6d07a6635d896789ba37b0d578bd175e92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "But I'll still tack on the identity matrix, and of course, since these have length m, it better be m by m. And now I'll do the reduced row echelon form of this matrix." + }, + { + "text": "And what do I get?" + }, + { + "text": "The reduced row echelon form starts with these columns, starts with the first columns, works like mad, and produces R. Of course, still the same size, m by n, and we did it before." + }, + { + "text": "And then whatever it did to get R, something else is going to show up here." + }, + { + "text": "Let me call it E, m by m. It's whatever you see that E is just going to contain a record of what we did." + }, + { + "text": "We did whatever it took to get A to become R. And at the same time, we were doing it to the identity matrix." + }, + { + "text": "So we started with the identity matrix, we buzzed along." + }, + { + "text": "So we took some -- all this row reduction amounted to multiplying on the left by some matrix, some series of elementary matrices that all together gave us one matrix, and that matrix is E. So all this row reduction stuff amounted to multiplying by E. How do I know that?" + }, + { + "text": "It certainly amounted to multiplying by something, and that something took I to E, so that something was E. So now look at the first part, E A is R. No big deal." + }, + { + "text": "All I've said is that the row reduction steps that we all know well, taking A to R, are in a- in some matrix, and I can find out what that matrix is by just tacking I on and seeing what comes out." + }, + { + "text": "What comes out is E. Let's just review the invertible square case." + }, + { + "text": "What happened then?" + }, + { + "text": "Because I was interested in it in chapter two also." + }, + { + "text": "When A was square and invertible, I took A I, I did row elimination, what was the R that came out?" + }, + { + "text": "It was I." + }, + { + "text": "So in chapter two, in chapter two, R was I." + }, + { + "text": "The row- the reduced row echelon form of a nice invertible square matrix is the identity." + }, + { + "text": "So if R was I in that case, then E was A inverse, because E A is I." + }, + { + "text": "Good." + }, + { + "text": "That's- that was good and easy." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk16.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..c5a8adc4741aeb68371eb235609b24dad795df03 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now what I'm saying is that there still is an E, it's not A inverse anymore, because A is a rectangular, it hasn't got an inverse." + }, + { + "text": "But there is still some matrix E that connected this to this." + }, + { + "text": "Oh, I should have figured out in advance what it was." + }, + { + "text": "Shoot." + }, + { + "text": "I didn't- I did those steps and sort of erased as I went, and, I should have done them to the identity, too." + }, + { + "text": "Can I do that?" + }, + { + "text": "Can I do that?" + }, + { + "text": "I'll keep the identity matrix, like I'm supposed to do, and I'll do the same operations on it and see what I end up with." + }, + { + "text": "Okay." + }, + { + "text": "So I'm starting with the identity, which I'll write in light, light enough, but okay, what did I do?" + }, + { + "text": "I subtracted that row from that one and that row from that one." + }, + { + "text": "Okay, I'll do that to the identity." + }, + { + "text": "So I subtract that first row from row two and row three." + }, + { + "text": "Good." + }, + { + "text": "Then I think I multiply, do you remember, I multiplied row two by minus one?" + }, + { + "text": "Let me just do that." + }, + { + "text": "Then what did I do?" + }, + { + "text": "I subtracted two of row two away from row one." + }, + { + "text": "I better do that." + }, + { + "text": "Subtract two of this away from this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk17.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..368775ffcdaa5a9fe2c24f8c85bcb4963097a79c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's minus one, two of these away leaves a plus two and zero." + }, + { + "text": "I believe that's E. The way to check is to see, multiply that E by this A, just to see, did I do it right?" + }, + { + "text": "So I believe E was minus one, two, zero, one minus one, zero, and minus one, zero, one." + }, + { + "text": "Okay." + }, + { + "text": "That's my E, that's my A, and that's R. All right." + }, + { + "text": "All I'm struggling to do is write the reason I wanted this blasted E was so that I could figure out the left null space." + }, + { + "text": "Not only its dimension, which I know." + }, + { + "text": "Actually, what is the dimension of the left null space?" + }, + { + "text": "Here's my matrix." + }, + { + "text": "What's the rank of the matrix?" + }, + { + "text": "Two." + }, + { + "text": "And the dimension of the left null space is supposed to be M minus R, three minus two, one." + }, + { + "text": "I believe that the left null space is one-dimensional." + }, + { + "text": "There is one combination of those three rows that produces the zero row." + }, + { + "text": "There is a basis." + }, + { + "text": "A basis for the left null space has only got one vector in it." + }, + { + "text": "And what is that vector?" + }, + { + "text": "It's here in the last row of E. But, ah, we could have seen it earlier." + }, + { + "text": "What combination of those rows gives the zero row?" + }, + { + "text": "Minus one of that, plus one of that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk18.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..9f5e8b1fcc2242dbdc56d379cbc7126ada792e31 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a basis for the left null space of this matrix, I'm looking for combinations of rows that give the zero row, if I'm looking at the left null space." + }, + { + "text": "For the null space, I'm looking at combinations of columns to get the zero column." + }, + { + "text": "Now I'm looking at combinations of these three rows to get the zero row, and of course, there is my zero row, and here is my vector that produced it." + }, + { + "text": "Minus one of that row and one of that row." + }, + { + "text": "Obvious." + }, + { + "text": "Okay." + }, + { + "text": "So in that example, and actually in all examples, we have seen how to produce a basis for the left null space." + }, + { + "text": "I won't ask you that all the time." + }, + { + "text": "Because it didn't come out immediately from R, we had to keep track of E for that left null space." + }, + { + "text": "But at least it didn't require us to transpose the matrix and start all over again." + }, + { + "text": "Okay." + }, + { + "text": "Those are the four subspaces." + }, + { + "text": "Can I review them?" + }, + { + "text": "The row space and the null space are in Rn." + }, + { + "text": "Their dimensions add to n. The column space and the left null space are in Rm, and their dimensions add to m. Okay." + }, + { + "text": "So let me close these last minutes by pushing you a little bit more to a new type of vector space." + }, + { + "text": "All our vector spaces, all the ones that we took seriously, have been subspaces of some real three- or n-dimensional space." + }, + { + "text": "Now I'm going to write down another vector space, a new vector space." + }, + { + "text": "Say all three by three matrices." + }, + { + "text": "My matrices are the vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk19.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..c1658ee474fcf6206f54d67e4dededa02a1ef92c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Is that all right?" + }, + { + "text": "I'm just naming them." + }, + { + "text": "You can put quotes around vectors." + }, + { + "text": "Every three by three matrix is one of my vectors." + }, + { + "text": "Now how am I entitled to call those things vectors?" + }, + { + "text": "I mean, they look very much like matrices." + }, + { + "text": "But they're vectors in my vector space because they obey the rules." + }, + { + "text": "All I'm supposed to be able to do with vectors is add them." + }, + { + "text": "I can add matrices." + }, + { + "text": "I'm supposed to be able to multiply them by scalar numbers, like seven." + }, + { + "text": "Well, I can multiply a matrix by seven." + }, + { + "text": "And I can take combinations of matrices." + }, + { + "text": "I can take three of one matrix minus five of another matrix." + }, + { + "text": "And those combinations, there's a zero matrix, the matrix that has all zeros in it." + }, + { + "text": "If I add that to another matrix, it doesn't change it." + }, + { + "text": "All the good stuff." + }, + { + "text": "If I multiply a matrix by one, it doesn't change it." + }, + { + "text": "All those eight rules for a vector space that we never wrote down, all easily satisfied." + }, + { + "text": "So now we have a different --." + }, + { + "text": "Now, of course, you can say you can multiply those matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk2.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..b92bd923d792a0f92ab4de95b7867006e9880f71 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here are the four fundamental subspaces." + }, + { + "text": "This is really the heart of this approach to linear algebra, to see these four subspaces, how they're related." + }, + { + "text": "So what are they?" + }, + { + "text": "The column space, C of A." + }, + { + "text": "The null space, N of A." + }, + { + "text": "And now comes the row space, something new." + }, + { + "text": "The row space, what's in that?" + }, + { + "text": "It's all combinations of the rows." + }, + { + "text": "That's natural." + }, + { + "text": "We want a space, so we have to take all combinations and we start with the rows." + }, + { + "text": "So the rows span the row space." + }, + { + "text": "Are the rows a basis for the row space?" + }, + { + "text": "Maybe so, maybe no." + }, + { + "text": "The rows are a basis for the row space when they're independent." + }, + { + "text": "But if they're dependent, as in this example, my error from last time, they're not, those three rows are not a basis, the row space would only be two-dimensional, I only need two rows for a basis." + }, + { + "text": "So the row space, now what's in it?" + }, + { + "text": "It's all combinations of the rows of A." + }, + { + "text": "All combinations of the rows of A." + }, + { + "text": "But I don't like working with row vectors." + }, + { + "text": "All my vectors have been column vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk20.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..56956e8347a8f8c1f8522690db77860dcc6953b9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "I don't care." + }, + { + "text": "For the moment, I'm only thinking of these matrices as forming a vector space, so I am only doing A plus B and C times A. I'm not interested in A, B for now." + }, + { + "text": "The fact that I can multiply is not relevant to a vector space." + }, + { + "text": "OK, so I have three by three matrices." + }, + { + "text": "And how about subspaces?" + }, + { + "text": "What's, tell me a subspace of this matrix space." + }, + { + "text": "Let me call this matrix space M. That's my matrix space, my space of all three by three matrices." + }, + { + "text": "Tell me a subspace of it." + }, + { + "text": "OK, what about the upper triangular matrices?" + }, + { + "text": "So subspaces, subspaces of M. All upper triangular matrices." + }, + { + "text": "Another subspace." + }, + { + "text": "All symmetric matrices." + }, + { + "text": "The intersection of two subspaces is supposed to be a subspace." + }, + { + "text": "We gave a little effort to the proof of that fact." + }, + { + "text": "If I look at the matrices that are in this subspace, they're symmetric, and they're also in this subspace, they're upper triangular." + }, + { + "text": "What do they look like?" + }, + { + "text": "Well, if they're symmetric, but they have zeros below the diagonal, they better have zeros above the diagonal." + }, + { + "text": "So the intersection would be diagonal matrices." + }, + { + "text": "That's another subspace, smaller than those." + }, + { + "text": "How can I use the word smaller?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk21.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..ffcdd44ed2f644726e04b27114327cb30bc7fb92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, I'm now entitled to use the word smaller." + }, + { + "text": "I mean, well, one way to say is, OK, these are contained in those." + }, + { + "text": "These are contained in those." + }, + { + "text": "But more precisely, I could give the dimension of these spaces." + }, + { + "text": "So I could, we can compute, let's compute it next time." + }, + { + "text": "The dimension of all upper, of the subspace of upper triangular three by three matrices." + }, + { + "text": "The dimension of symmetric three by three matrices." + }, + { + "text": "The dimension of diagonal three by three matrices." + }, + { + "text": "Well, to produce dimension, that means I'm supposed to produce a basis." + }, + { + "text": "And then I just count how many I needed in the basis." + }, + { + "text": "Let me give you the answer for this one." + }, + { + "text": "What's the dimension?" + }, + { + "text": "The dimension of this, say, this subspace, let me call it D, all diagonal matrices." + }, + { + "text": "The dimension of this subspace is, as I write, you're working it out, three." + }, + { + "text": "Because here's a matrix in this, it's a diagonal matrix." + }, + { + "text": "Here's another one." + }, + { + "text": "Here's another one." + }, + { + "text": "Better make it diagonal, let me put a seven there." + }, + { + "text": "That was not a very great choice, but it's three diagonal matrices, and I believe that they're a basis." + }, + { + "text": "I believe that those three matrices are independent, and I believe that any diagonal matrix is a combination of those three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk22.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..8c6bce8cf8085e6544c31ae6926bb7ccf18b983e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk22.json @@ -0,0 +1,20 @@ +[ + { + "text": "So they span the subspace of diagonal matrices." + }, + { + "text": "Do you see that idea?" + }, + { + "text": "It's like stretching the idea from Rn to Rn by n, three by three, but we can still add, we can still multiply by numbers, and we just ignore the fact that we can multiply two matrices together." + }, + { + "text": "Okay." + }, + { + "text": "Thank you." + }, + { + "text": "That's lecture ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk3.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..25f31647b76274f9088c60d1292bcc43915d3fb0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'd like to stay with column vectors." + }, + { + "text": "How can I get to column vectors out of these rows?" + }, + { + "text": "I transpose the matrix." + }, + { + "text": "So if that's OK with you, I'm going to transpose the matrix, I'm going to say all combinations of the columns of A transpose." + }, + { + "text": "And that allows me to use the convenient notation, the column space of A transpose." + }, + { + "text": "Nothing, no mathematics went on there, we just got some vectors that were lying down to stand up." + }, + { + "text": "But it means that we can use this column space of A transpose, that's telling me in a nice matrix notation what the row space is." + }, + { + "text": "OK. And finally is another null space." + }, + { + "text": "The fourth fundamental space will be the null space of A transpose." + }, + { + "text": "The fourth guy is the null space of A transpose." + }, + { + "text": "And of course, my notation is N of A transpose." + }, + { + "text": "That's the null space of A transpose." + }, + { + "text": "Now, we don't have a perfect name for this space as a, as a, connecting with A, but our usual name is the left null space, and I'll show you why in a moment." + }, + { + "text": "So often I call this the, just to write that word, the left null space of A." + }, + { + "text": "So just the way we have the row space of A and we switch it to the column space of A transpose, so we have this space of guys that I call the left null space of A, but the good notation is it's the null space of A transpose." + }, + { + "text": "OK. Those are four spaces." + }, + { + "text": "Where are those spaces?" + }, + { + "text": "What big space are they in for when A is m by n?" + }, + { + "text": "In that case, the null space of A, what's in the null space of A?" + }, + { + "text": "Vectors with n components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk4.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c2575473d88ff4598107e190483f0484b6558678 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Solutions to Ax equals zero." + }, + { + "text": "So the null space of A is n R n. What's in the column space of A?" + }, + { + "text": "Well, columns." + }, + { + "text": "How many components do those columns have?" + }, + { + "text": "m. So this column space is n R m. What about the column space of A transpose, which are just a disguised way of saying the rows of A?" + }, + { + "text": "The rows of A in this three by six matrix have six components, n components." + }, + { + "text": "The column space is n R n. And the null space of A transpose, I see that this fourth space is already getting second, you know, second class citizen treatment and it doesn't deserve it." + }, + { + "text": "It's, it should be there, it is there, and shouldn't be squeezed." + }, + { + "text": "The null space of A transpose, well, if the null space of A had vectors with n components, the null space of A transpose will be n R m. I want to draw a picture of the four spaces." + }, + { + "text": "OK. OK." + }, + { + "text": "Here are the four spaces." + }, + { + "text": "OK, let me put n dimensional space over on this side." + }, + { + "text": "Then which were the subspaces in R n?" + }, + { + "text": "The null space was and the row space was." + }, + { + "text": "So here we have the can I make that picture of the row space?" + }, + { + "text": "And can I make this kind of picture of the null space?" + }, + { + "text": "That's just meant to be a sketch, to remind you that they're in this which, you know, how, what type of vectors are in it?" + }, + { + "text": "Vectors with n components." + }, + { + "text": "Over here, inside consisting of vectors with m components is the column space and what I'm calling the null space of A transpose." + }, + { + "text": "Those are the ones with m components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk5.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..f4e64e208c1a1d8e07a9a66a6a6c59f8c4cbcec8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. To understand these spaces is our job now." + }, + { + "text": "Because by understanding those spaces, we know everything about this half of linear algebra." + }, + { + "text": "What do I mean by understanding those spaces?" + }, + { + "text": "I would like to know a basis for those spaces." + }, + { + "text": "For each one of those spaces, how would I create, construct a basis?" + }, + { + "text": "What systematic way would produce a basis?" + }, + { + "text": "And what's their dimension?" + }, + { + "text": "OK." + }, + { + "text": "So for each of the four spaces, I have to answer those questions." + }, + { + "text": "How do I produce a basis?" + }, + { + "text": "And then, which has a somewhat long answer, and what's the dimension, which is just a number, so it has a real short answer?" + }, + { + "text": "Can I give you the short answer first?" + }, + { + "text": "I shouldn't do it, but here it is." + }, + { + "text": "I can tell you the dimension of the column space." + }, + { + "text": "Let me start with this guy." + }, + { + "text": "What's its dimension?" + }, + { + "text": "I have an m by n matrix." + }, + { + "text": "The dimension of the column space is the rank, R. We actually got to that at the end of the last lecture, but only for an example." + }, + { + "text": "So I really have to say, OK, what's going on there?" + }, + { + "text": "I should produce a basis, and then I just look to see how many vectors I needed in that basis, and the answer will be R. Actually, I'll do that before I get on to the others." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk6.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..ac7425fbe27a77a7e448b576483b4c179e9a31f1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "What's a basis for the column space?" + }, + { + "text": "We've done all the work of row reduction, identifying the pivot columns, the ones that have pivots, the ones that end up with pivots, but now I the pivot columns I'm interested in are columns of A, the original A." + }, + { + "text": "And those pivot columns, there are R of them, the rank R counts those, those are a basis." + }, + { + "text": "So if I answer this question for the column space, the answer will be a basis is the pivot columns, and the dimension is the rank R. And there are pivot columns and everything great." + }, + { + "text": "OK, so that space we pretty well understand." + }, + { + "text": "I probably have a little going back to see that, to prove that this is a right answer, but you know it's the right answer." + }, + { + "text": "Now let me look at the row space." + }, + { + "text": "OK. Shall I tell you the dimension of the row space?" + }, + { + "text": "Yes." + }, + { + "text": "Before we do even an example, let me tell you the dimension of the row space." + }, + { + "text": "Its dimension is also R. The row space and the column space have the same dimension." + }, + { + "text": "That's a wonderful fact." + }, + { + "text": "The dimension of the column space of A transpose, that's the row space, is R. That space is R-dimensional." + }, + { + "text": "And so is this one." + }, + { + "text": "OK. That's the, that's the sort of insight that got used in this example." + }, + { + "text": "If those, if those, if those, are the three columns of a matrix, let me make them the three columns of a matrix by just erasing some brackets, OK, those are the three columns of a matrix, the rank of that matrix, if I look at the columns, it wasn't obvious to me anyway." + }, + { + "text": "But if I look at the rows, it's, now it's obvious." + }, + { + "text": "The row space of that matrix obviously is two-dimensional, because I can, I see a basis for the row space, this row and that row." + }, + { + "text": "And of course, strictly speaking, I'm supposed to transpose those guys, make them stand up." + }, + { + "text": "But the rank is two, and therefore the column space is two-dimensional by this wonderful fact that the row space and column space have the same dimension, and therefore there are only two pivot columns, not three, and, those, the three columns are dependent." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk7.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..7d55c74913379543a71fcc53c971f787baf12a92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, let me bury that error and talk about the row space." + }, + { + "text": "Well, I'm going to give you the dimensions of all the spaces, because that's the, such a nice answer." + }, + { + "text": "OK." + }, + { + "text": "So let me come back here." + }, + { + "text": "So we have this great fact to establish, that the row space, its dimension is also the rank." + }, + { + "text": "OK. What about the null space?" + }, + { + "text": "What's a basis for the null space?" + }, + { + "text": "What's the dimension of the null space?" + }, + { + "text": "Let me, I'll put that answer up here, for the null space." + }, + { + "text": "Well, how have we constructed the null space?" + }, + { + "text": "We took the matrix A, we did those row operations to get it into a form U or even further, we got it into the reduced form R, and then we read off special solutions." + }, + { + "text": "Special solutions, and every special solution came from a free variable." + }, + { + "text": "And those special solutions are in the null space, and the great thing is, they're a basis for it." + }, + { + "text": "So for the null space, a basis will be the special solutions." + }, + { + "text": "And there's one for every free variable, right?" + }, + { + "text": "For each free variable, we give that variable the value one, the other free variable zero." + }, + { + "text": "We get the pivot variables, we get a vector in the -- we get a special solution." + }, + { + "text": "So we get all together n minus R of them, because that's the number of free variables." + }, + { + "text": "If we have R, this is, the dimension is R, is the number of pivot variables, this is the number of free variables." + }, + { + "text": "So the beauty is that those special solutions do form a basis and tell us immediately that the dimension of the null space is n -- I'd better write this well, because it's so nice, n minus R. And you see the nice thing, that the two dimensions in this n-dimensional space, one subspace is R-dimensional, to be proved, that's the row space." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk8.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f4c70532a641ef630aa1f7bca077776017097cd4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "The other subspace is n minus R-dimensional, that's the null space." + }, + { + "text": "And the two dimensions, like, together, give n. The sum of R and n minus R is n. And that's just great." + }, + { + "text": "It's really copying the fact that we have n variables, R of them are pivot variables and n minus R are free variables and n all together." + }, + { + "text": "OK. And now what's the dimension of this poor misbegotten fourth subspace?" + }, + { + "text": "It's got to be m minus R. The dimension of this left null space, left out practically, is m minus R. Well, that's really just saying that this, again, the sum of that plus that is m. And m is correct." + }, + { + "text": "It's the number of columns in A transpose." + }, + { + "text": "A transpose is just as good a matrix as A." + }, + { + "text": "It just happens to be n by m. It happens to have m columns, so it will have m variables, when I go to Ax equals zero, and m of them and R of them will be pivot variables and m minus R will be free variables." + }, + { + "text": "A transpose is as good a matrix as A." + }, + { + "text": "It follows the same rule that this plus the dimension, this dimension plus this dimension adds up to the number of columns." + }, + { + "text": "And over here, A transpose has m columns." + }, + { + "text": "Okay." + }, + { + "text": "Okay, so I gave you the easy answer, the dimensions." + }, + { + "text": "Now can I go back to check on a basis?" + }, + { + "text": "We would like to think that, say, the row space." + }, + { + "text": "Because we've got a basis for the column space." + }, + { + "text": "The pivot columns give a basis for the column space." + }, + { + "text": "Now I'm asking you to look at the row space." + }, + { + "text": "And I you could say, okay, I can produce a basis for the row space by transposing my matrix, making those columns, then doing elimination, row reduction, and checking out the pivot columns in this transposed matrix." + }, + { + "text": "But that means you had to do all that row reduction on A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk9.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..8be162da3ff089e5c511aa65ea7d801c64cad56f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_11_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It ought to be possible, if we take a matrix A, let me take the matrix, maybe we had this matrix in the last lecture, one one one, two one two, three two three, one one one." + }, + { + "text": "Okay." + }, + { + "text": "That, that matrix was so easy, we spotted its pivot columns, one and two, without actually doing row reduction." + }, + { + "text": "But now let's do the job properly." + }, + { + "text": "So I subtract this away from this to produce a zero." + }, + { + "text": "So one two three one is fine." + }, + { + "text": "Subtracting that away leaves me minus one minus one zero, right?" + }, + { + "text": "And subtracting that from the last row, oh, well, that's easy." + }, + { + "text": "Okay, I'm doing row reduction." + }, + { + "text": "Now I've, the first column is all set." + }, + { + "text": "The second column, I now see the pivot, and I can clean up, if I, actually, okay, why don't I make the pivot into a one?" + }, + { + "text": "I'll multiply that row through by minus one, and then I have one one." + }, + { + "text": "That was an elementary operation, I'm allowed." + }, + { + "text": "Multiply a row by a number." + }, + { + "text": "And now I'll do elimination." + }, + { + "text": "Two of those away from that will knock this guy out and make this into a one." + }, + { + "text": "So that's now a zero and that's a one." + }, + { + "text": "Okay." + }, + { + "text": "Done." + }, + { + "text": "That's R. I'm seeing the identity matrix here, I'm seeing zeros below, and I'm seeing F there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk0.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6b8bcce949e11c9807b49a56c5ca68fdb459f818 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay, here is lecture ten in linear algebra." + }, + { + "text": "Two important things to do in this lecture." + }, + { + "text": "One is to correct an error from lecture nine." + }, + { + "text": "So the blackboard with that awful error is still with us." + }, + { + "text": "And the second, the big thing to do is to tell you about the four subspaces that come with a matrix." + }, + { + "text": "We've seen two subspaces, the column space and the null space, there's two to go." + }, + { + "text": "Okay." + }, + { + "text": "First of all, and this is a great way to recap and correct the previous lecture." + }, + { + "text": "So you remember I was just doing R3." + }, + { + "text": "I couldn't have taken a simpler example than R3." + }, + { + "text": "And I wrote down the standard basis." + }, + { + "text": "That's the standard basis." + }, + { + "text": "The basis, the obvious basis for the whole three-dimensional space." + }, + { + "text": "And then I wanted to make the point that there was nothing special, nothing about that basis that another basis couldn't have." + }, + { + "text": "It could have linear independence, it could span a space, there's lots of other bases." + }, + { + "text": "So I started with these vectors one one two and two two five, and those were independent." + }, + { + "text": "And then I said three three seven wouldn't do, because three three seven is the sum of those." + }, + { + "text": "So in my innocence, I put in three three eight." + }, + { + "text": "I figured probably if three three seven is on the plane, is, which I know, it's in the plane with these two, then probably three three eight sticks a little bit out of the plane." + }, + { + "text": "And it's independent and it gives a basis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk1.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..97d9d72b29a5aa923aae0ba9c0fb0da57e9db2ed --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "But after class, to my sorrow, student tells me, wait a minute, that third vector three three eight is not independent." + }, + { + "text": "And why did she say that?" + }, + { + "text": "She didn't actually take the time, didn't have to, to find what combination of this one and this one gives three three eight." + }, + { + "text": "She did something else." + }, + { + "text": "In other words, she looked ahead because she said, wait a minute, if I look at that matrix, it's not invertible." + }, + { + "text": "That third column can't be independent of the first two, because when I look at that matrix, it's got two identical rows." + }, + { + "text": "I have a square matrix." + }, + { + "text": "Its rows are obviously dependent." + }, + { + "text": "And that makes the columns dependent." + }, + { + "text": "So there's my error." + }, + { + "text": "When I look at the matrix A that has those three columns, those three columns can't be independent because that matrix is not invertible because it's got two equal rows." + }, + { + "text": "And today's lecture will reach the conclusion, the great conclusion, that connects the column space with the row space." + }, + { + "text": "So those are the row space is now going to be another one of my fundamental subspaces." + }, + { + "text": "The row space of this matrix or of this one, well, the row space of this one is okay." + }, + { + "text": "But the row space of this one, I'm looking at the rows of the matrix, oh, anyway, I'll have two equal rows and the row space will be only two-dimensional." + }, + { + "text": "The rank of the matrix with these columns will only be two, so only two of those columns can be independent too." + }, + { + "text": "The rows tell me something about the columns, in other words." + }, + { + "text": "Something that I should have noticed and I didn't." + }, + { + "text": "Okay." + }, + { + "text": "So now let me pin down these four fundamental subspaces." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk10.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..8f428ebe86b1b4488558f6fa55b8940ef758b264 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "Okay." + }, + { + "text": "What about its row space?" + }, + { + "text": "What happened to its row space?" + }, + { + "text": "Well, what happened, let me first ask, just because this is, sometimes something does happen." + }, + { + "text": "Its column space changed." + }, + { + "text": "The column space of R is not the column space of A, right?" + }, + { + "text": "Because one one one is certainly in the column space of A and certainly not in the column space of R. I did row operations." + }, + { + "text": "Those row operations preserved the row space, so the row so the column spaces are different." + }, + { + "text": "Different column spaces." + }, + { + "text": "Different column spaces." + }, + { + "text": "But I believe that they have the same row space." + }, + { + "text": "Same row space." + }, + { + "text": "I believe that the row space of that matrix and the row space of this matrix are identical." + }, + { + "text": "They have exactly the same vectors in them." + }, + { + "text": "Those vectors are vectors with four components, right?" + }, + { + "text": "They're all combinations of those rows." + }, + { + "text": "Or I believe you get the same thing by taking all combinations of these rows." + }, + { + "text": "And if true, what's a basis?" + }, + { + "text": "What's a basis for the row space of R?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk11.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..258e5999dbb0aea67696256511eb6b999136132a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it'll be a basis for the row space of the original A." + }, + { + "text": "But it's obviously a basis for the row space of R. What's a basis for the row space of that matrix?" + }, + { + "text": "The first two rows." + }, + { + "text": "So a basis for the row so a basis is for the row space of A or of R is the first R rows of R, not of A." + }, + { + "text": "Sometimes it's true for A, but not necessarily." + }, + { + "text": "But R, we definitely have a matrix here whose row space we can identify." + }, + { + "text": "The row space is spanned by the three rows." + }, + { + "text": "But if we want a basis, we want independence." + }, + { + "text": "So out goes row three." + }, + { + "text": "The row space is also spanned by the first two rows." + }, + { + "text": "This guy didn't contribute anything." + }, + { + "text": "And of course, over here, this one, two, three, one in the bottom didn't contribute anything." + }, + { + "text": "We had it already." + }, + { + "text": "So this, here's a basis, one zero one one and zero one one zero." + }, + { + "text": "I believe those are in the row space." + }, + { + "text": "I know they're independent." + }, + { + "text": "Why are they in the row space?" + }, + { + "text": "Why are those two vectors in the row space?" + }, + { + "text": "Because all those operations we did, which started with these rows and took combinations of them." + }, + { + "text": "I took this row minus this row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk12.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..d05a7eb6e4998c4acd748e3bb7087c68e6e29a80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "That gave me something that's still in the row space." + }, + { + "text": "That's the point." + }, + { + "text": "When I took a row minus a multiple of another row, I'm staying in the row space." + }, + { + "text": "The row space is not changing." + }, + { + "text": "My little basis for it is changing, and I've ended up with, sort of, the best basis." + }, + { + "text": "If the columns of the identity matrix are the best basis for R3 or Rn, the rows of this matrix are the best basis for the row space." + }, + { + "text": "Best in the sense of being as clean as I can make it." + }, + { + "text": "Starting off with the identity and then finishing up with whatever has to be in there." + }, + { + "text": "OK. Do you see, then, that the dimension is R?" + }, + { + "text": "For sure." + }, + { + "text": "Because we've got R pivots, R nonzero rows, we've got the right number of vectors, R. They're in the row space, they're independent, that's it." + }, + { + "text": "They are a basis for the row space." + }, + { + "text": "And we can even pin that down further." + }, + { + "text": "How do I know that every row of A is a combination?" + }, + { + "text": "How do I know they span the row space?" + }, + { + "text": "Oh, well, somebody says I've got the right number of them, so they must, but that's true." + }, + { + "text": "But let me just say, how do I know that this row is a combination of these?" + }, + { + "text": "By just reversing the steps of row reduction." + }, + { + "text": "If I just reverse the steps and go from A, from R back to A, then what do I, what am I doing?" + }, + { + "text": "I'm starting with these rows, I'm taking combinations of them, after a couple of steps, undoing the subtractions that I did before, I'm back to these rows." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk13.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..7b0edabbd24233827c7692f63429589952dac1bc --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "So these rows are combinations of those rows, those rows are combinations of those rows, the two row spaces are the same, the bases are the same, and the natural basis is this guy." + }, + { + "text": "Is that all right for the row space?" + }, + { + "text": "The row space is sitting there in R, in its cleanest possible form." + }, + { + "text": "OK. Now what about the fourth guy, the null space of A transpose?" + }, + { + "text": "First of all, why do I call that the left null space?" + }, + { + "text": "So let me save that and bring that down." + }, + { + "text": "OK." + }, + { + "text": "So the fourth space is the null space of A transpose." + }, + { + "text": "So it has in it vectors, let me call them y, so that A transpose y equals zero." + }, + { + "text": "If A transpose y equals zero, then y is in the null space of A transpose, of course." + }, + { + "text": "So this is a matrix times a column equaling zero." + }, + { + "text": "And now, because I want y to sit on the left, and I want A instead of A transpose, I'll just transpose that equation." + }, + { + "text": "Can I just transpose that?" + }, + { + "text": "On the right, it makes the zero vector lie down." + }, + { + "text": "And on the left, it's a product, A transpose times y." + }, + { + "text": "If I take the transpose, then they come in opposite order, right?" + }, + { + "text": "So it's y transpose times A transpose transpose, but nobody's going to leave it like that." + }, + { + "text": "That's A transpose transpose is just A, of course." + }, + { + "text": "When I transposed A transpose, I got back to A." + }, + { + "text": "Now, do you see what I have now?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk14.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7a889f79409e9a95fbd4cc01518da4b9706c49d1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "I have a row vector, y transpose, multiplying A and multiplying from the left." + }, + { + "text": "That's why I call it the left null space." + }, + { + "text": "But by making it, putting it on the left, I had to make it into a row instead of a column vector." + }, + { + "text": "And so my convention is I usually don't do that, I usually stay with A transpose y equals zero." + }, + { + "text": "OK. And you might ask, how do we get a basis, or I might ask, how do we get a basis for this fourth space, this left null space?" + }, + { + "text": "OK." + }, + { + "text": "I'll do it the example." + }, + { + "text": "As always, ah, not that one." + }, + { + "text": "The left null space is not jumping out at me here." + }, + { + "text": "I know which are the free variables, the special solutions, but those are special solutions to Ax equals zero, and now I'm looking at A transpose and I'm not seeing it here." + }, + { + "text": "So, but somehow you feel that the work that you did, which simplified A to R, should have revealed the left null space too." + }, + { + "text": "And it's slightly less immediate, but it's there." + }, + { + "text": "So from A to R, I took some steps, and I guess I'm interested in what were those steps, or what were all of them together." + }, + { + "text": "I don't want to -- I'm not interested in what particular ones they were." + }, + { + "text": "I'm interested in what was the whole matrix that took me from A to R. How would you find that?" + }, + { + "text": "Do you remember Gauss-Jordan, where you tack on the identity matrix?" + }, + { + "text": "Let's do that again." + }, + { + "text": "So I'll do it above here." + }, + { + "text": "So this is now the idea of I take the matrix A, which is m by n. In Gauss-Jordan, when we saw him before, A was a square invertible matrix and we were finding its inverse." + }, + { + "text": "Now the matrix isn't square, it's probably rectangular." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk15.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3c045b6d07a6635d896789ba37b0d578bd175e92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "But I'll still tack on the identity matrix, and of course, since these have length m, it better be m by m. And now I'll do the reduced row echelon form of this matrix." + }, + { + "text": "And what do I get?" + }, + { + "text": "The reduced row echelon form starts with these columns, starts with the first columns, works like mad, and produces R. Of course, still the same size, m by n, and we did it before." + }, + { + "text": "And then whatever it did to get R, something else is going to show up here." + }, + { + "text": "Let me call it E, m by m. It's whatever you see that E is just going to contain a record of what we did." + }, + { + "text": "We did whatever it took to get A to become R. And at the same time, we were doing it to the identity matrix." + }, + { + "text": "So we started with the identity matrix, we buzzed along." + }, + { + "text": "So we took some -- all this row reduction amounted to multiplying on the left by some matrix, some series of elementary matrices that all together gave us one matrix, and that matrix is E. So all this row reduction stuff amounted to multiplying by E. How do I know that?" + }, + { + "text": "It certainly amounted to multiplying by something, and that something took I to E, so that something was E. So now look at the first part, E A is R. No big deal." + }, + { + "text": "All I've said is that the row reduction steps that we all know well, taking A to R, are in a- in some matrix, and I can find out what that matrix is by just tacking I on and seeing what comes out." + }, + { + "text": "What comes out is E. Let's just review the invertible square case." + }, + { + "text": "What happened then?" + }, + { + "text": "Because I was interested in it in chapter two also." + }, + { + "text": "When A was square and invertible, I took A I, I did row elimination, what was the R that came out?" + }, + { + "text": "It was I." + }, + { + "text": "So in chapter two, in chapter two, R was I." + }, + { + "text": "The row- the reduced row echelon form of a nice invertible square matrix is the identity." + }, + { + "text": "So if R was I in that case, then E was A inverse, because E A is I." + }, + { + "text": "Good." + }, + { + "text": "That's- that was good and easy." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk16.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..c5a8adc4741aeb68371eb235609b24dad795df03 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now what I'm saying is that there still is an E, it's not A inverse anymore, because A is a rectangular, it hasn't got an inverse." + }, + { + "text": "But there is still some matrix E that connected this to this." + }, + { + "text": "Oh, I should have figured out in advance what it was." + }, + { + "text": "Shoot." + }, + { + "text": "I didn't- I did those steps and sort of erased as I went, and, I should have done them to the identity, too." + }, + { + "text": "Can I do that?" + }, + { + "text": "Can I do that?" + }, + { + "text": "I'll keep the identity matrix, like I'm supposed to do, and I'll do the same operations on it and see what I end up with." + }, + { + "text": "Okay." + }, + { + "text": "So I'm starting with the identity, which I'll write in light, light enough, but okay, what did I do?" + }, + { + "text": "I subtracted that row from that one and that row from that one." + }, + { + "text": "Okay, I'll do that to the identity." + }, + { + "text": "So I subtract that first row from row two and row three." + }, + { + "text": "Good." + }, + { + "text": "Then I think I multiply, do you remember, I multiplied row two by minus one?" + }, + { + "text": "Let me just do that." + }, + { + "text": "Then what did I do?" + }, + { + "text": "I subtracted two of row two away from row one." + }, + { + "text": "I better do that." + }, + { + "text": "Subtract two of this away from this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk17.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..368775ffcdaa5a9fe2c24f8c85bcb4963097a79c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's minus one, two of these away leaves a plus two and zero." + }, + { + "text": "I believe that's E. The way to check is to see, multiply that E by this A, just to see, did I do it right?" + }, + { + "text": "So I believe E was minus one, two, zero, one minus one, zero, and minus one, zero, one." + }, + { + "text": "Okay." + }, + { + "text": "That's my E, that's my A, and that's R. All right." + }, + { + "text": "All I'm struggling to do is write the reason I wanted this blasted E was so that I could figure out the left null space." + }, + { + "text": "Not only its dimension, which I know." + }, + { + "text": "Actually, what is the dimension of the left null space?" + }, + { + "text": "Here's my matrix." + }, + { + "text": "What's the rank of the matrix?" + }, + { + "text": "Two." + }, + { + "text": "And the dimension of the left null space is supposed to be M minus R, three minus two, one." + }, + { + "text": "I believe that the left null space is one-dimensional." + }, + { + "text": "There is one combination of those three rows that produces the zero row." + }, + { + "text": "There is a basis." + }, + { + "text": "A basis for the left null space has only got one vector in it." + }, + { + "text": "And what is that vector?" + }, + { + "text": "It's here in the last row of E. But, ah, we could have seen it earlier." + }, + { + "text": "What combination of those rows gives the zero row?" + }, + { + "text": "Minus one of that, plus one of that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk18.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..9f5e8b1fcc2242dbdc56d379cbc7126ada792e31 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a basis for the left null space of this matrix, I'm looking for combinations of rows that give the zero row, if I'm looking at the left null space." + }, + { + "text": "For the null space, I'm looking at combinations of columns to get the zero column." + }, + { + "text": "Now I'm looking at combinations of these three rows to get the zero row, and of course, there is my zero row, and here is my vector that produced it." + }, + { + "text": "Minus one of that row and one of that row." + }, + { + "text": "Obvious." + }, + { + "text": "Okay." + }, + { + "text": "So in that example, and actually in all examples, we have seen how to produce a basis for the left null space." + }, + { + "text": "I won't ask you that all the time." + }, + { + "text": "Because it didn't come out immediately from R, we had to keep track of E for that left null space." + }, + { + "text": "But at least it didn't require us to transpose the matrix and start all over again." + }, + { + "text": "Okay." + }, + { + "text": "Those are the four subspaces." + }, + { + "text": "Can I review them?" + }, + { + "text": "The row space and the null space are in Rn." + }, + { + "text": "Their dimensions add to n. The column space and the left null space are in Rm, and their dimensions add to m. Okay." + }, + { + "text": "So let me close these last minutes by pushing you a little bit more to a new type of vector space." + }, + { + "text": "All our vector spaces, all the ones that we took seriously, have been subspaces of some real three- or n-dimensional space." + }, + { + "text": "Now I'm going to write down another vector space, a new vector space." + }, + { + "text": "Say all three by three matrices." + }, + { + "text": "My matrices are the vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk19.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..c1658ee474fcf6206f54d67e4dededa02a1ef92c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Is that all right?" + }, + { + "text": "I'm just naming them." + }, + { + "text": "You can put quotes around vectors." + }, + { + "text": "Every three by three matrix is one of my vectors." + }, + { + "text": "Now how am I entitled to call those things vectors?" + }, + { + "text": "I mean, they look very much like matrices." + }, + { + "text": "But they're vectors in my vector space because they obey the rules." + }, + { + "text": "All I'm supposed to be able to do with vectors is add them." + }, + { + "text": "I can add matrices." + }, + { + "text": "I'm supposed to be able to multiply them by scalar numbers, like seven." + }, + { + "text": "Well, I can multiply a matrix by seven." + }, + { + "text": "And I can take combinations of matrices." + }, + { + "text": "I can take three of one matrix minus five of another matrix." + }, + { + "text": "And those combinations, there's a zero matrix, the matrix that has all zeros in it." + }, + { + "text": "If I add that to another matrix, it doesn't change it." + }, + { + "text": "All the good stuff." + }, + { + "text": "If I multiply a matrix by one, it doesn't change it." + }, + { + "text": "All those eight rules for a vector space that we never wrote down, all easily satisfied." + }, + { + "text": "So now we have a different --." + }, + { + "text": "Now, of course, you can say you can multiply those matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk2.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..b92bd923d792a0f92ab4de95b7867006e9880f71 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here are the four fundamental subspaces." + }, + { + "text": "This is really the heart of this approach to linear algebra, to see these four subspaces, how they're related." + }, + { + "text": "So what are they?" + }, + { + "text": "The column space, C of A." + }, + { + "text": "The null space, N of A." + }, + { + "text": "And now comes the row space, something new." + }, + { + "text": "The row space, what's in that?" + }, + { + "text": "It's all combinations of the rows." + }, + { + "text": "That's natural." + }, + { + "text": "We want a space, so we have to take all combinations and we start with the rows." + }, + { + "text": "So the rows span the row space." + }, + { + "text": "Are the rows a basis for the row space?" + }, + { + "text": "Maybe so, maybe no." + }, + { + "text": "The rows are a basis for the row space when they're independent." + }, + { + "text": "But if they're dependent, as in this example, my error from last time, they're not, those three rows are not a basis, the row space would only be two-dimensional, I only need two rows for a basis." + }, + { + "text": "So the row space, now what's in it?" + }, + { + "text": "It's all combinations of the rows of A." + }, + { + "text": "All combinations of the rows of A." + }, + { + "text": "But I don't like working with row vectors." + }, + { + "text": "All my vectors have been column vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk20.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..56956e8347a8f8c1f8522690db77860dcc6953b9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "I don't care." + }, + { + "text": "For the moment, I'm only thinking of these matrices as forming a vector space, so I am only doing A plus B and C times A. I'm not interested in A, B for now." + }, + { + "text": "The fact that I can multiply is not relevant to a vector space." + }, + { + "text": "OK, so I have three by three matrices." + }, + { + "text": "And how about subspaces?" + }, + { + "text": "What's, tell me a subspace of this matrix space." + }, + { + "text": "Let me call this matrix space M. That's my matrix space, my space of all three by three matrices." + }, + { + "text": "Tell me a subspace of it." + }, + { + "text": "OK, what about the upper triangular matrices?" + }, + { + "text": "So subspaces, subspaces of M. All upper triangular matrices." + }, + { + "text": "Another subspace." + }, + { + "text": "All symmetric matrices." + }, + { + "text": "The intersection of two subspaces is supposed to be a subspace." + }, + { + "text": "We gave a little effort to the proof of that fact." + }, + { + "text": "If I look at the matrices that are in this subspace, they're symmetric, and they're also in this subspace, they're upper triangular." + }, + { + "text": "What do they look like?" + }, + { + "text": "Well, if they're symmetric, but they have zeros below the diagonal, they better have zeros above the diagonal." + }, + { + "text": "So the intersection would be diagonal matrices." + }, + { + "text": "That's another subspace, smaller than those." + }, + { + "text": "How can I use the word smaller?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk21.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..ffcdd44ed2f644726e04b27114327cb30bc7fb92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, I'm now entitled to use the word smaller." + }, + { + "text": "I mean, well, one way to say is, OK, these are contained in those." + }, + { + "text": "These are contained in those." + }, + { + "text": "But more precisely, I could give the dimension of these spaces." + }, + { + "text": "So I could, we can compute, let's compute it next time." + }, + { + "text": "The dimension of all upper, of the subspace of upper triangular three by three matrices." + }, + { + "text": "The dimension of symmetric three by three matrices." + }, + { + "text": "The dimension of diagonal three by three matrices." + }, + { + "text": "Well, to produce dimension, that means I'm supposed to produce a basis." + }, + { + "text": "And then I just count how many I needed in the basis." + }, + { + "text": "Let me give you the answer for this one." + }, + { + "text": "What's the dimension?" + }, + { + "text": "The dimension of this, say, this subspace, let me call it D, all diagonal matrices." + }, + { + "text": "The dimension of this subspace is, as I write, you're working it out, three." + }, + { + "text": "Because here's a matrix in this, it's a diagonal matrix." + }, + { + "text": "Here's another one." + }, + { + "text": "Here's another one." + }, + { + "text": "Better make it diagonal, let me put a seven there." + }, + { + "text": "That was not a very great choice, but it's three diagonal matrices, and I believe that they're a basis." + }, + { + "text": "I believe that those three matrices are independent, and I believe that any diagonal matrix is a combination of those three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk22.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..8c6bce8cf8085e6544c31ae6926bb7ccf18b983e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk22.json @@ -0,0 +1,20 @@ +[ + { + "text": "So they span the subspace of diagonal matrices." + }, + { + "text": "Do you see that idea?" + }, + { + "text": "It's like stretching the idea from Rn to Rn by n, three by three, but we can still add, we can still multiply by numbers, and we just ignore the fact that we can multiply two matrices together." + }, + { + "text": "Okay." + }, + { + "text": "Thank you." + }, + { + "text": "That's lecture ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk3.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..25f31647b76274f9088c60d1292bcc43915d3fb0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'd like to stay with column vectors." + }, + { + "text": "How can I get to column vectors out of these rows?" + }, + { + "text": "I transpose the matrix." + }, + { + "text": "So if that's OK with you, I'm going to transpose the matrix, I'm going to say all combinations of the columns of A transpose." + }, + { + "text": "And that allows me to use the convenient notation, the column space of A transpose." + }, + { + "text": "Nothing, no mathematics went on there, we just got some vectors that were lying down to stand up." + }, + { + "text": "But it means that we can use this column space of A transpose, that's telling me in a nice matrix notation what the row space is." + }, + { + "text": "OK. And finally is another null space." + }, + { + "text": "The fourth fundamental space will be the null space of A transpose." + }, + { + "text": "The fourth guy is the null space of A transpose." + }, + { + "text": "And of course, my notation is N of A transpose." + }, + { + "text": "That's the null space of A transpose." + }, + { + "text": "Now, we don't have a perfect name for this space as a, as a, connecting with A, but our usual name is the left null space, and I'll show you why in a moment." + }, + { + "text": "So often I call this the, just to write that word, the left null space of A." + }, + { + "text": "So just the way we have the row space of A and we switch it to the column space of A transpose, so we have this space of guys that I call the left null space of A, but the good notation is it's the null space of A transpose." + }, + { + "text": "OK. Those are four spaces." + }, + { + "text": "Where are those spaces?" + }, + { + "text": "What big space are they in for when A is m by n?" + }, + { + "text": "In that case, the null space of A, what's in the null space of A?" + }, + { + "text": "Vectors with n components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk4.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c2575473d88ff4598107e190483f0484b6558678 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Solutions to Ax equals zero." + }, + { + "text": "So the null space of A is n R n. What's in the column space of A?" + }, + { + "text": "Well, columns." + }, + { + "text": "How many components do those columns have?" + }, + { + "text": "m. So this column space is n R m. What about the column space of A transpose, which are just a disguised way of saying the rows of A?" + }, + { + "text": "The rows of A in this three by six matrix have six components, n components." + }, + { + "text": "The column space is n R n. And the null space of A transpose, I see that this fourth space is already getting second, you know, second class citizen treatment and it doesn't deserve it." + }, + { + "text": "It's, it should be there, it is there, and shouldn't be squeezed." + }, + { + "text": "The null space of A transpose, well, if the null space of A had vectors with n components, the null space of A transpose will be n R m. I want to draw a picture of the four spaces." + }, + { + "text": "OK. OK." + }, + { + "text": "Here are the four spaces." + }, + { + "text": "OK, let me put n dimensional space over on this side." + }, + { + "text": "Then which were the subspaces in R n?" + }, + { + "text": "The null space was and the row space was." + }, + { + "text": "So here we have the can I make that picture of the row space?" + }, + { + "text": "And can I make this kind of picture of the null space?" + }, + { + "text": "That's just meant to be a sketch, to remind you that they're in this which, you know, how, what type of vectors are in it?" + }, + { + "text": "Vectors with n components." + }, + { + "text": "Over here, inside consisting of vectors with m components is the column space and what I'm calling the null space of A transpose." + }, + { + "text": "Those are the ones with m components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk5.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..f4e64e208c1a1d8e07a9a66a6a6c59f8c4cbcec8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. To understand these spaces is our job now." + }, + { + "text": "Because by understanding those spaces, we know everything about this half of linear algebra." + }, + { + "text": "What do I mean by understanding those spaces?" + }, + { + "text": "I would like to know a basis for those spaces." + }, + { + "text": "For each one of those spaces, how would I create, construct a basis?" + }, + { + "text": "What systematic way would produce a basis?" + }, + { + "text": "And what's their dimension?" + }, + { + "text": "OK." + }, + { + "text": "So for each of the four spaces, I have to answer those questions." + }, + { + "text": "How do I produce a basis?" + }, + { + "text": "And then, which has a somewhat long answer, and what's the dimension, which is just a number, so it has a real short answer?" + }, + { + "text": "Can I give you the short answer first?" + }, + { + "text": "I shouldn't do it, but here it is." + }, + { + "text": "I can tell you the dimension of the column space." + }, + { + "text": "Let me start with this guy." + }, + { + "text": "What's its dimension?" + }, + { + "text": "I have an m by n matrix." + }, + { + "text": "The dimension of the column space is the rank, R. We actually got to that at the end of the last lecture, but only for an example." + }, + { + "text": "So I really have to say, OK, what's going on there?" + }, + { + "text": "I should produce a basis, and then I just look to see how many vectors I needed in that basis, and the answer will be R. Actually, I'll do that before I get on to the others." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk6.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..ac7425fbe27a77a7e448b576483b4c179e9a31f1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "What's a basis for the column space?" + }, + { + "text": "We've done all the work of row reduction, identifying the pivot columns, the ones that have pivots, the ones that end up with pivots, but now I the pivot columns I'm interested in are columns of A, the original A." + }, + { + "text": "And those pivot columns, there are R of them, the rank R counts those, those are a basis." + }, + { + "text": "So if I answer this question for the column space, the answer will be a basis is the pivot columns, and the dimension is the rank R. And there are pivot columns and everything great." + }, + { + "text": "OK, so that space we pretty well understand." + }, + { + "text": "I probably have a little going back to see that, to prove that this is a right answer, but you know it's the right answer." + }, + { + "text": "Now let me look at the row space." + }, + { + "text": "OK. Shall I tell you the dimension of the row space?" + }, + { + "text": "Yes." + }, + { + "text": "Before we do even an example, let me tell you the dimension of the row space." + }, + { + "text": "Its dimension is also R. The row space and the column space have the same dimension." + }, + { + "text": "That's a wonderful fact." + }, + { + "text": "The dimension of the column space of A transpose, that's the row space, is R. That space is R-dimensional." + }, + { + "text": "And so is this one." + }, + { + "text": "OK. That's the, that's the sort of insight that got used in this example." + }, + { + "text": "If those, if those, if those, are the three columns of a matrix, let me make them the three columns of a matrix by just erasing some brackets, OK, those are the three columns of a matrix, the rank of that matrix, if I look at the columns, it wasn't obvious to me anyway." + }, + { + "text": "But if I look at the rows, it's, now it's obvious." + }, + { + "text": "The row space of that matrix obviously is two-dimensional, because I can, I see a basis for the row space, this row and that row." + }, + { + "text": "And of course, strictly speaking, I'm supposed to transpose those guys, make them stand up." + }, + { + "text": "But the rank is two, and therefore the column space is two-dimensional by this wonderful fact that the row space and column space have the same dimension, and therefore there are only two pivot columns, not three, and, those, the three columns are dependent." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk7.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..7d55c74913379543a71fcc53c971f787baf12a92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, let me bury that error and talk about the row space." + }, + { + "text": "Well, I'm going to give you the dimensions of all the spaces, because that's the, such a nice answer." + }, + { + "text": "OK." + }, + { + "text": "So let me come back here." + }, + { + "text": "So we have this great fact to establish, that the row space, its dimension is also the rank." + }, + { + "text": "OK. What about the null space?" + }, + { + "text": "What's a basis for the null space?" + }, + { + "text": "What's the dimension of the null space?" + }, + { + "text": "Let me, I'll put that answer up here, for the null space." + }, + { + "text": "Well, how have we constructed the null space?" + }, + { + "text": "We took the matrix A, we did those row operations to get it into a form U or even further, we got it into the reduced form R, and then we read off special solutions." + }, + { + "text": "Special solutions, and every special solution came from a free variable." + }, + { + "text": "And those special solutions are in the null space, and the great thing is, they're a basis for it." + }, + { + "text": "So for the null space, a basis will be the special solutions." + }, + { + "text": "And there's one for every free variable, right?" + }, + { + "text": "For each free variable, we give that variable the value one, the other free variable zero." + }, + { + "text": "We get the pivot variables, we get a vector in the -- we get a special solution." + }, + { + "text": "So we get all together n minus R of them, because that's the number of free variables." + }, + { + "text": "If we have R, this is, the dimension is R, is the number of pivot variables, this is the number of free variables." + }, + { + "text": "So the beauty is that those special solutions do form a basis and tell us immediately that the dimension of the null space is n -- I'd better write this well, because it's so nice, n minus R. And you see the nice thing, that the two dimensions in this n-dimensional space, one subspace is R-dimensional, to be proved, that's the row space." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk8.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f4c70532a641ef630aa1f7bca077776017097cd4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "The other subspace is n minus R-dimensional, that's the null space." + }, + { + "text": "And the two dimensions, like, together, give n. The sum of R and n minus R is n. And that's just great." + }, + { + "text": "It's really copying the fact that we have n variables, R of them are pivot variables and n minus R are free variables and n all together." + }, + { + "text": "OK. And now what's the dimension of this poor misbegotten fourth subspace?" + }, + { + "text": "It's got to be m minus R. The dimension of this left null space, left out practically, is m minus R. Well, that's really just saying that this, again, the sum of that plus that is m. And m is correct." + }, + { + "text": "It's the number of columns in A transpose." + }, + { + "text": "A transpose is just as good a matrix as A." + }, + { + "text": "It just happens to be n by m. It happens to have m columns, so it will have m variables, when I go to Ax equals zero, and m of them and R of them will be pivot variables and m minus R will be free variables." + }, + { + "text": "A transpose is as good a matrix as A." + }, + { + "text": "It follows the same rule that this plus the dimension, this dimension plus this dimension adds up to the number of columns." + }, + { + "text": "And over here, A transpose has m columns." + }, + { + "text": "Okay." + }, + { + "text": "Okay, so I gave you the easy answer, the dimensions." + }, + { + "text": "Now can I go back to check on a basis?" + }, + { + "text": "We would like to think that, say, the row space." + }, + { + "text": "Because we've got a basis for the column space." + }, + { + "text": "The pivot columns give a basis for the column space." + }, + { + "text": "Now I'm asking you to look at the row space." + }, + { + "text": "And I you could say, okay, I can produce a basis for the row space by transposing my matrix, making those columns, then doing elimination, row reduction, and checking out the pivot columns in this transposed matrix." + }, + { + "text": "But that means you had to do all that row reduction on A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk9.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..8be162da3ff089e5c511aa65ea7d801c64cad56f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_13_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It ought to be possible, if we take a matrix A, let me take the matrix, maybe we had this matrix in the last lecture, one one one, two one two, three two three, one one one." + }, + { + "text": "Okay." + }, + { + "text": "That, that matrix was so easy, we spotted its pivot columns, one and two, without actually doing row reduction." + }, + { + "text": "But now let's do the job properly." + }, + { + "text": "So I subtract this away from this to produce a zero." + }, + { + "text": "So one two three one is fine." + }, + { + "text": "Subtracting that away leaves me minus one minus one zero, right?" + }, + { + "text": "And subtracting that from the last row, oh, well, that's easy." + }, + { + "text": "Okay, I'm doing row reduction." + }, + { + "text": "Now I've, the first column is all set." + }, + { + "text": "The second column, I now see the pivot, and I can clean up, if I, actually, okay, why don't I make the pivot into a one?" + }, + { + "text": "I'll multiply that row through by minus one, and then I have one one." + }, + { + "text": "That was an elementary operation, I'm allowed." + }, + { + "text": "Multiply a row by a number." + }, + { + "text": "And now I'll do elimination." + }, + { + "text": "Two of those away from that will knock this guy out and make this into a one." + }, + { + "text": "So that's now a zero and that's a one." + }, + { + "text": "Okay." + }, + { + "text": "Done." + }, + { + "text": "That's R. I'm seeing the identity matrix here, I'm seeing zeros below, and I'm seeing F there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk0.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6b8bcce949e11c9807b49a56c5ca68fdb459f818 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay, here is lecture ten in linear algebra." + }, + { + "text": "Two important things to do in this lecture." + }, + { + "text": "One is to correct an error from lecture nine." + }, + { + "text": "So the blackboard with that awful error is still with us." + }, + { + "text": "And the second, the big thing to do is to tell you about the four subspaces that come with a matrix." + }, + { + "text": "We've seen two subspaces, the column space and the null space, there's two to go." + }, + { + "text": "Okay." + }, + { + "text": "First of all, and this is a great way to recap and correct the previous lecture." + }, + { + "text": "So you remember I was just doing R3." + }, + { + "text": "I couldn't have taken a simpler example than R3." + }, + { + "text": "And I wrote down the standard basis." + }, + { + "text": "That's the standard basis." + }, + { + "text": "The basis, the obvious basis for the whole three-dimensional space." + }, + { + "text": "And then I wanted to make the point that there was nothing special, nothing about that basis that another basis couldn't have." + }, + { + "text": "It could have linear independence, it could span a space, there's lots of other bases." + }, + { + "text": "So I started with these vectors one one two and two two five, and those were independent." + }, + { + "text": "And then I said three three seven wouldn't do, because three three seven is the sum of those." + }, + { + "text": "So in my innocence, I put in three three eight." + }, + { + "text": "I figured probably if three three seven is on the plane, is, which I know, it's in the plane with these two, then probably three three eight sticks a little bit out of the plane." + }, + { + "text": "And it's independent and it gives a basis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk1.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..97d9d72b29a5aa923aae0ba9c0fb0da57e9db2ed --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "But after class, to my sorrow, student tells me, wait a minute, that third vector three three eight is not independent." + }, + { + "text": "And why did she say that?" + }, + { + "text": "She didn't actually take the time, didn't have to, to find what combination of this one and this one gives three three eight." + }, + { + "text": "She did something else." + }, + { + "text": "In other words, she looked ahead because she said, wait a minute, if I look at that matrix, it's not invertible." + }, + { + "text": "That third column can't be independent of the first two, because when I look at that matrix, it's got two identical rows." + }, + { + "text": "I have a square matrix." + }, + { + "text": "Its rows are obviously dependent." + }, + { + "text": "And that makes the columns dependent." + }, + { + "text": "So there's my error." + }, + { + "text": "When I look at the matrix A that has those three columns, those three columns can't be independent because that matrix is not invertible because it's got two equal rows." + }, + { + "text": "And today's lecture will reach the conclusion, the great conclusion, that connects the column space with the row space." + }, + { + "text": "So those are the row space is now going to be another one of my fundamental subspaces." + }, + { + "text": "The row space of this matrix or of this one, well, the row space of this one is okay." + }, + { + "text": "But the row space of this one, I'm looking at the rows of the matrix, oh, anyway, I'll have two equal rows and the row space will be only two-dimensional." + }, + { + "text": "The rank of the matrix with these columns will only be two, so only two of those columns can be independent too." + }, + { + "text": "The rows tell me something about the columns, in other words." + }, + { + "text": "Something that I should have noticed and I didn't." + }, + { + "text": "Okay." + }, + { + "text": "So now let me pin down these four fundamental subspaces." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk10.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..8f428ebe86b1b4488558f6fa55b8940ef758b264 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "Okay." + }, + { + "text": "What about its row space?" + }, + { + "text": "What happened to its row space?" + }, + { + "text": "Well, what happened, let me first ask, just because this is, sometimes something does happen." + }, + { + "text": "Its column space changed." + }, + { + "text": "The column space of R is not the column space of A, right?" + }, + { + "text": "Because one one one is certainly in the column space of A and certainly not in the column space of R. I did row operations." + }, + { + "text": "Those row operations preserved the row space, so the row so the column spaces are different." + }, + { + "text": "Different column spaces." + }, + { + "text": "Different column spaces." + }, + { + "text": "But I believe that they have the same row space." + }, + { + "text": "Same row space." + }, + { + "text": "I believe that the row space of that matrix and the row space of this matrix are identical." + }, + { + "text": "They have exactly the same vectors in them." + }, + { + "text": "Those vectors are vectors with four components, right?" + }, + { + "text": "They're all combinations of those rows." + }, + { + "text": "Or I believe you get the same thing by taking all combinations of these rows." + }, + { + "text": "And if true, what's a basis?" + }, + { + "text": "What's a basis for the row space of R?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk11.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..258e5999dbb0aea67696256511eb6b999136132a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it'll be a basis for the row space of the original A." + }, + { + "text": "But it's obviously a basis for the row space of R. What's a basis for the row space of that matrix?" + }, + { + "text": "The first two rows." + }, + { + "text": "So a basis for the row so a basis is for the row space of A or of R is the first R rows of R, not of A." + }, + { + "text": "Sometimes it's true for A, but not necessarily." + }, + { + "text": "But R, we definitely have a matrix here whose row space we can identify." + }, + { + "text": "The row space is spanned by the three rows." + }, + { + "text": "But if we want a basis, we want independence." + }, + { + "text": "So out goes row three." + }, + { + "text": "The row space is also spanned by the first two rows." + }, + { + "text": "This guy didn't contribute anything." + }, + { + "text": "And of course, over here, this one, two, three, one in the bottom didn't contribute anything." + }, + { + "text": "We had it already." + }, + { + "text": "So this, here's a basis, one zero one one and zero one one zero." + }, + { + "text": "I believe those are in the row space." + }, + { + "text": "I know they're independent." + }, + { + "text": "Why are they in the row space?" + }, + { + "text": "Why are those two vectors in the row space?" + }, + { + "text": "Because all those operations we did, which started with these rows and took combinations of them." + }, + { + "text": "I took this row minus this row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk12.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..d05a7eb6e4998c4acd748e3bb7087c68e6e29a80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "That gave me something that's still in the row space." + }, + { + "text": "That's the point." + }, + { + "text": "When I took a row minus a multiple of another row, I'm staying in the row space." + }, + { + "text": "The row space is not changing." + }, + { + "text": "My little basis for it is changing, and I've ended up with, sort of, the best basis." + }, + { + "text": "If the columns of the identity matrix are the best basis for R3 or Rn, the rows of this matrix are the best basis for the row space." + }, + { + "text": "Best in the sense of being as clean as I can make it." + }, + { + "text": "Starting off with the identity and then finishing up with whatever has to be in there." + }, + { + "text": "OK. Do you see, then, that the dimension is R?" + }, + { + "text": "For sure." + }, + { + "text": "Because we've got R pivots, R nonzero rows, we've got the right number of vectors, R. They're in the row space, they're independent, that's it." + }, + { + "text": "They are a basis for the row space." + }, + { + "text": "And we can even pin that down further." + }, + { + "text": "How do I know that every row of A is a combination?" + }, + { + "text": "How do I know they span the row space?" + }, + { + "text": "Oh, well, somebody says I've got the right number of them, so they must, but that's true." + }, + { + "text": "But let me just say, how do I know that this row is a combination of these?" + }, + { + "text": "By just reversing the steps of row reduction." + }, + { + "text": "If I just reverse the steps and go from A, from R back to A, then what do I, what am I doing?" + }, + { + "text": "I'm starting with these rows, I'm taking combinations of them, after a couple of steps, undoing the subtractions that I did before, I'm back to these rows." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk13.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..7b0edabbd24233827c7692f63429589952dac1bc --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "So these rows are combinations of those rows, those rows are combinations of those rows, the two row spaces are the same, the bases are the same, and the natural basis is this guy." + }, + { + "text": "Is that all right for the row space?" + }, + { + "text": "The row space is sitting there in R, in its cleanest possible form." + }, + { + "text": "OK. Now what about the fourth guy, the null space of A transpose?" + }, + { + "text": "First of all, why do I call that the left null space?" + }, + { + "text": "So let me save that and bring that down." + }, + { + "text": "OK." + }, + { + "text": "So the fourth space is the null space of A transpose." + }, + { + "text": "So it has in it vectors, let me call them y, so that A transpose y equals zero." + }, + { + "text": "If A transpose y equals zero, then y is in the null space of A transpose, of course." + }, + { + "text": "So this is a matrix times a column equaling zero." + }, + { + "text": "And now, because I want y to sit on the left, and I want A instead of A transpose, I'll just transpose that equation." + }, + { + "text": "Can I just transpose that?" + }, + { + "text": "On the right, it makes the zero vector lie down." + }, + { + "text": "And on the left, it's a product, A transpose times y." + }, + { + "text": "If I take the transpose, then they come in opposite order, right?" + }, + { + "text": "So it's y transpose times A transpose transpose, but nobody's going to leave it like that." + }, + { + "text": "That's A transpose transpose is just A, of course." + }, + { + "text": "When I transposed A transpose, I got back to A." + }, + { + "text": "Now, do you see what I have now?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk14.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7a889f79409e9a95fbd4cc01518da4b9706c49d1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "I have a row vector, y transpose, multiplying A and multiplying from the left." + }, + { + "text": "That's why I call it the left null space." + }, + { + "text": "But by making it, putting it on the left, I had to make it into a row instead of a column vector." + }, + { + "text": "And so my convention is I usually don't do that, I usually stay with A transpose y equals zero." + }, + { + "text": "OK. And you might ask, how do we get a basis, or I might ask, how do we get a basis for this fourth space, this left null space?" + }, + { + "text": "OK." + }, + { + "text": "I'll do it the example." + }, + { + "text": "As always, ah, not that one." + }, + { + "text": "The left null space is not jumping out at me here." + }, + { + "text": "I know which are the free variables, the special solutions, but those are special solutions to Ax equals zero, and now I'm looking at A transpose and I'm not seeing it here." + }, + { + "text": "So, but somehow you feel that the work that you did, which simplified A to R, should have revealed the left null space too." + }, + { + "text": "And it's slightly less immediate, but it's there." + }, + { + "text": "So from A to R, I took some steps, and I guess I'm interested in what were those steps, or what were all of them together." + }, + { + "text": "I don't want to -- I'm not interested in what particular ones they were." + }, + { + "text": "I'm interested in what was the whole matrix that took me from A to R. How would you find that?" + }, + { + "text": "Do you remember Gauss-Jordan, where you tack on the identity matrix?" + }, + { + "text": "Let's do that again." + }, + { + "text": "So I'll do it above here." + }, + { + "text": "So this is now the idea of I take the matrix A, which is m by n. In Gauss-Jordan, when we saw him before, A was a square invertible matrix and we were finding its inverse." + }, + { + "text": "Now the matrix isn't square, it's probably rectangular." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk15.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3c045b6d07a6635d896789ba37b0d578bd175e92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "But I'll still tack on the identity matrix, and of course, since these have length m, it better be m by m. And now I'll do the reduced row echelon form of this matrix." + }, + { + "text": "And what do I get?" + }, + { + "text": "The reduced row echelon form starts with these columns, starts with the first columns, works like mad, and produces R. Of course, still the same size, m by n, and we did it before." + }, + { + "text": "And then whatever it did to get R, something else is going to show up here." + }, + { + "text": "Let me call it E, m by m. It's whatever you see that E is just going to contain a record of what we did." + }, + { + "text": "We did whatever it took to get A to become R. And at the same time, we were doing it to the identity matrix." + }, + { + "text": "So we started with the identity matrix, we buzzed along." + }, + { + "text": "So we took some -- all this row reduction amounted to multiplying on the left by some matrix, some series of elementary matrices that all together gave us one matrix, and that matrix is E. So all this row reduction stuff amounted to multiplying by E. How do I know that?" + }, + { + "text": "It certainly amounted to multiplying by something, and that something took I to E, so that something was E. So now look at the first part, E A is R. No big deal." + }, + { + "text": "All I've said is that the row reduction steps that we all know well, taking A to R, are in a- in some matrix, and I can find out what that matrix is by just tacking I on and seeing what comes out." + }, + { + "text": "What comes out is E. Let's just review the invertible square case." + }, + { + "text": "What happened then?" + }, + { + "text": "Because I was interested in it in chapter two also." + }, + { + "text": "When A was square and invertible, I took A I, I did row elimination, what was the R that came out?" + }, + { + "text": "It was I." + }, + { + "text": "So in chapter two, in chapter two, R was I." + }, + { + "text": "The row- the reduced row echelon form of a nice invertible square matrix is the identity." + }, + { + "text": "So if R was I in that case, then E was A inverse, because E A is I." + }, + { + "text": "Good." + }, + { + "text": "That's- that was good and easy." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk16.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..c5a8adc4741aeb68371eb235609b24dad795df03 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now what I'm saying is that there still is an E, it's not A inverse anymore, because A is a rectangular, it hasn't got an inverse." + }, + { + "text": "But there is still some matrix E that connected this to this." + }, + { + "text": "Oh, I should have figured out in advance what it was." + }, + { + "text": "Shoot." + }, + { + "text": "I didn't- I did those steps and sort of erased as I went, and, I should have done them to the identity, too." + }, + { + "text": "Can I do that?" + }, + { + "text": "Can I do that?" + }, + { + "text": "I'll keep the identity matrix, like I'm supposed to do, and I'll do the same operations on it and see what I end up with." + }, + { + "text": "Okay." + }, + { + "text": "So I'm starting with the identity, which I'll write in light, light enough, but okay, what did I do?" + }, + { + "text": "I subtracted that row from that one and that row from that one." + }, + { + "text": "Okay, I'll do that to the identity." + }, + { + "text": "So I subtract that first row from row two and row three." + }, + { + "text": "Good." + }, + { + "text": "Then I think I multiply, do you remember, I multiplied row two by minus one?" + }, + { + "text": "Let me just do that." + }, + { + "text": "Then what did I do?" + }, + { + "text": "I subtracted two of row two away from row one." + }, + { + "text": "I better do that." + }, + { + "text": "Subtract two of this away from this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk17.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..368775ffcdaa5a9fe2c24f8c85bcb4963097a79c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's minus one, two of these away leaves a plus two and zero." + }, + { + "text": "I believe that's E. The way to check is to see, multiply that E by this A, just to see, did I do it right?" + }, + { + "text": "So I believe E was minus one, two, zero, one minus one, zero, and minus one, zero, one." + }, + { + "text": "Okay." + }, + { + "text": "That's my E, that's my A, and that's R. All right." + }, + { + "text": "All I'm struggling to do is write the reason I wanted this blasted E was so that I could figure out the left null space." + }, + { + "text": "Not only its dimension, which I know." + }, + { + "text": "Actually, what is the dimension of the left null space?" + }, + { + "text": "Here's my matrix." + }, + { + "text": "What's the rank of the matrix?" + }, + { + "text": "Two." + }, + { + "text": "And the dimension of the left null space is supposed to be M minus R, three minus two, one." + }, + { + "text": "I believe that the left null space is one-dimensional." + }, + { + "text": "There is one combination of those three rows that produces the zero row." + }, + { + "text": "There is a basis." + }, + { + "text": "A basis for the left null space has only got one vector in it." + }, + { + "text": "And what is that vector?" + }, + { + "text": "It's here in the last row of E. But, ah, we could have seen it earlier." + }, + { + "text": "What combination of those rows gives the zero row?" + }, + { + "text": "Minus one of that, plus one of that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk18.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..9f5e8b1fcc2242dbdc56d379cbc7126ada792e31 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a basis for the left null space of this matrix, I'm looking for combinations of rows that give the zero row, if I'm looking at the left null space." + }, + { + "text": "For the null space, I'm looking at combinations of columns to get the zero column." + }, + { + "text": "Now I'm looking at combinations of these three rows to get the zero row, and of course, there is my zero row, and here is my vector that produced it." + }, + { + "text": "Minus one of that row and one of that row." + }, + { + "text": "Obvious." + }, + { + "text": "Okay." + }, + { + "text": "So in that example, and actually in all examples, we have seen how to produce a basis for the left null space." + }, + { + "text": "I won't ask you that all the time." + }, + { + "text": "Because it didn't come out immediately from R, we had to keep track of E for that left null space." + }, + { + "text": "But at least it didn't require us to transpose the matrix and start all over again." + }, + { + "text": "Okay." + }, + { + "text": "Those are the four subspaces." + }, + { + "text": "Can I review them?" + }, + { + "text": "The row space and the null space are in Rn." + }, + { + "text": "Their dimensions add to n. The column space and the left null space are in Rm, and their dimensions add to m. Okay." + }, + { + "text": "So let me close these last minutes by pushing you a little bit more to a new type of vector space." + }, + { + "text": "All our vector spaces, all the ones that we took seriously, have been subspaces of some real three- or n-dimensional space." + }, + { + "text": "Now I'm going to write down another vector space, a new vector space." + }, + { + "text": "Say all three by three matrices." + }, + { + "text": "My matrices are the vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk19.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..c1658ee474fcf6206f54d67e4dededa02a1ef92c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Is that all right?" + }, + { + "text": "I'm just naming them." + }, + { + "text": "You can put quotes around vectors." + }, + { + "text": "Every three by three matrix is one of my vectors." + }, + { + "text": "Now how am I entitled to call those things vectors?" + }, + { + "text": "I mean, they look very much like matrices." + }, + { + "text": "But they're vectors in my vector space because they obey the rules." + }, + { + "text": "All I'm supposed to be able to do with vectors is add them." + }, + { + "text": "I can add matrices." + }, + { + "text": "I'm supposed to be able to multiply them by scalar numbers, like seven." + }, + { + "text": "Well, I can multiply a matrix by seven." + }, + { + "text": "And I can take combinations of matrices." + }, + { + "text": "I can take three of one matrix minus five of another matrix." + }, + { + "text": "And those combinations, there's a zero matrix, the matrix that has all zeros in it." + }, + { + "text": "If I add that to another matrix, it doesn't change it." + }, + { + "text": "All the good stuff." + }, + { + "text": "If I multiply a matrix by one, it doesn't change it." + }, + { + "text": "All those eight rules for a vector space that we never wrote down, all easily satisfied." + }, + { + "text": "So now we have a different --." + }, + { + "text": "Now, of course, you can say you can multiply those matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk2.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..b92bd923d792a0f92ab4de95b7867006e9880f71 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here are the four fundamental subspaces." + }, + { + "text": "This is really the heart of this approach to linear algebra, to see these four subspaces, how they're related." + }, + { + "text": "So what are they?" + }, + { + "text": "The column space, C of A." + }, + { + "text": "The null space, N of A." + }, + { + "text": "And now comes the row space, something new." + }, + { + "text": "The row space, what's in that?" + }, + { + "text": "It's all combinations of the rows." + }, + { + "text": "That's natural." + }, + { + "text": "We want a space, so we have to take all combinations and we start with the rows." + }, + { + "text": "So the rows span the row space." + }, + { + "text": "Are the rows a basis for the row space?" + }, + { + "text": "Maybe so, maybe no." + }, + { + "text": "The rows are a basis for the row space when they're independent." + }, + { + "text": "But if they're dependent, as in this example, my error from last time, they're not, those three rows are not a basis, the row space would only be two-dimensional, I only need two rows for a basis." + }, + { + "text": "So the row space, now what's in it?" + }, + { + "text": "It's all combinations of the rows of A." + }, + { + "text": "All combinations of the rows of A." + }, + { + "text": "But I don't like working with row vectors." + }, + { + "text": "All my vectors have been column vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk20.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..56956e8347a8f8c1f8522690db77860dcc6953b9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "I don't care." + }, + { + "text": "For the moment, I'm only thinking of these matrices as forming a vector space, so I am only doing A plus B and C times A. I'm not interested in A, B for now." + }, + { + "text": "The fact that I can multiply is not relevant to a vector space." + }, + { + "text": "OK, so I have three by three matrices." + }, + { + "text": "And how about subspaces?" + }, + { + "text": "What's, tell me a subspace of this matrix space." + }, + { + "text": "Let me call this matrix space M. That's my matrix space, my space of all three by three matrices." + }, + { + "text": "Tell me a subspace of it." + }, + { + "text": "OK, what about the upper triangular matrices?" + }, + { + "text": "So subspaces, subspaces of M. All upper triangular matrices." + }, + { + "text": "Another subspace." + }, + { + "text": "All symmetric matrices." + }, + { + "text": "The intersection of two subspaces is supposed to be a subspace." + }, + { + "text": "We gave a little effort to the proof of that fact." + }, + { + "text": "If I look at the matrices that are in this subspace, they're symmetric, and they're also in this subspace, they're upper triangular." + }, + { + "text": "What do they look like?" + }, + { + "text": "Well, if they're symmetric, but they have zeros below the diagonal, they better have zeros above the diagonal." + }, + { + "text": "So the intersection would be diagonal matrices." + }, + { + "text": "That's another subspace, smaller than those." + }, + { + "text": "How can I use the word smaller?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk21.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..ffcdd44ed2f644726e04b27114327cb30bc7fb92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, I'm now entitled to use the word smaller." + }, + { + "text": "I mean, well, one way to say is, OK, these are contained in those." + }, + { + "text": "These are contained in those." + }, + { + "text": "But more precisely, I could give the dimension of these spaces." + }, + { + "text": "So I could, we can compute, let's compute it next time." + }, + { + "text": "The dimension of all upper, of the subspace of upper triangular three by three matrices." + }, + { + "text": "The dimension of symmetric three by three matrices." + }, + { + "text": "The dimension of diagonal three by three matrices." + }, + { + "text": "Well, to produce dimension, that means I'm supposed to produce a basis." + }, + { + "text": "And then I just count how many I needed in the basis." + }, + { + "text": "Let me give you the answer for this one." + }, + { + "text": "What's the dimension?" + }, + { + "text": "The dimension of this, say, this subspace, let me call it D, all diagonal matrices." + }, + { + "text": "The dimension of this subspace is, as I write, you're working it out, three." + }, + { + "text": "Because here's a matrix in this, it's a diagonal matrix." + }, + { + "text": "Here's another one." + }, + { + "text": "Here's another one." + }, + { + "text": "Better make it diagonal, let me put a seven there." + }, + { + "text": "That was not a very great choice, but it's three diagonal matrices, and I believe that they're a basis." + }, + { + "text": "I believe that those three matrices are independent, and I believe that any diagonal matrix is a combination of those three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk22.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..8c6bce8cf8085e6544c31ae6926bb7ccf18b983e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk22.json @@ -0,0 +1,20 @@ +[ + { + "text": "So they span the subspace of diagonal matrices." + }, + { + "text": "Do you see that idea?" + }, + { + "text": "It's like stretching the idea from Rn to Rn by n, three by three, but we can still add, we can still multiply by numbers, and we just ignore the fact that we can multiply two matrices together." + }, + { + "text": "Okay." + }, + { + "text": "Thank you." + }, + { + "text": "That's lecture ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk3.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..25f31647b76274f9088c60d1292bcc43915d3fb0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'd like to stay with column vectors." + }, + { + "text": "How can I get to column vectors out of these rows?" + }, + { + "text": "I transpose the matrix." + }, + { + "text": "So if that's OK with you, I'm going to transpose the matrix, I'm going to say all combinations of the columns of A transpose." + }, + { + "text": "And that allows me to use the convenient notation, the column space of A transpose." + }, + { + "text": "Nothing, no mathematics went on there, we just got some vectors that were lying down to stand up." + }, + { + "text": "But it means that we can use this column space of A transpose, that's telling me in a nice matrix notation what the row space is." + }, + { + "text": "OK. And finally is another null space." + }, + { + "text": "The fourth fundamental space will be the null space of A transpose." + }, + { + "text": "The fourth guy is the null space of A transpose." + }, + { + "text": "And of course, my notation is N of A transpose." + }, + { + "text": "That's the null space of A transpose." + }, + { + "text": "Now, we don't have a perfect name for this space as a, as a, connecting with A, but our usual name is the left null space, and I'll show you why in a moment." + }, + { + "text": "So often I call this the, just to write that word, the left null space of A." + }, + { + "text": "So just the way we have the row space of A and we switch it to the column space of A transpose, so we have this space of guys that I call the left null space of A, but the good notation is it's the null space of A transpose." + }, + { + "text": "OK. Those are four spaces." + }, + { + "text": "Where are those spaces?" + }, + { + "text": "What big space are they in for when A is m by n?" + }, + { + "text": "In that case, the null space of A, what's in the null space of A?" + }, + { + "text": "Vectors with n components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk4.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c2575473d88ff4598107e190483f0484b6558678 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Solutions to Ax equals zero." + }, + { + "text": "So the null space of A is n R n. What's in the column space of A?" + }, + { + "text": "Well, columns." + }, + { + "text": "How many components do those columns have?" + }, + { + "text": "m. So this column space is n R m. What about the column space of A transpose, which are just a disguised way of saying the rows of A?" + }, + { + "text": "The rows of A in this three by six matrix have six components, n components." + }, + { + "text": "The column space is n R n. And the null space of A transpose, I see that this fourth space is already getting second, you know, second class citizen treatment and it doesn't deserve it." + }, + { + "text": "It's, it should be there, it is there, and shouldn't be squeezed." + }, + { + "text": "The null space of A transpose, well, if the null space of A had vectors with n components, the null space of A transpose will be n R m. I want to draw a picture of the four spaces." + }, + { + "text": "OK. OK." + }, + { + "text": "Here are the four spaces." + }, + { + "text": "OK, let me put n dimensional space over on this side." + }, + { + "text": "Then which were the subspaces in R n?" + }, + { + "text": "The null space was and the row space was." + }, + { + "text": "So here we have the can I make that picture of the row space?" + }, + { + "text": "And can I make this kind of picture of the null space?" + }, + { + "text": "That's just meant to be a sketch, to remind you that they're in this which, you know, how, what type of vectors are in it?" + }, + { + "text": "Vectors with n components." + }, + { + "text": "Over here, inside consisting of vectors with m components is the column space and what I'm calling the null space of A transpose." + }, + { + "text": "Those are the ones with m components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk5.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..f4e64e208c1a1d8e07a9a66a6a6c59f8c4cbcec8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. To understand these spaces is our job now." + }, + { + "text": "Because by understanding those spaces, we know everything about this half of linear algebra." + }, + { + "text": "What do I mean by understanding those spaces?" + }, + { + "text": "I would like to know a basis for those spaces." + }, + { + "text": "For each one of those spaces, how would I create, construct a basis?" + }, + { + "text": "What systematic way would produce a basis?" + }, + { + "text": "And what's their dimension?" + }, + { + "text": "OK." + }, + { + "text": "So for each of the four spaces, I have to answer those questions." + }, + { + "text": "How do I produce a basis?" + }, + { + "text": "And then, which has a somewhat long answer, and what's the dimension, which is just a number, so it has a real short answer?" + }, + { + "text": "Can I give you the short answer first?" + }, + { + "text": "I shouldn't do it, but here it is." + }, + { + "text": "I can tell you the dimension of the column space." + }, + { + "text": "Let me start with this guy." + }, + { + "text": "What's its dimension?" + }, + { + "text": "I have an m by n matrix." + }, + { + "text": "The dimension of the column space is the rank, R. We actually got to that at the end of the last lecture, but only for an example." + }, + { + "text": "So I really have to say, OK, what's going on there?" + }, + { + "text": "I should produce a basis, and then I just look to see how many vectors I needed in that basis, and the answer will be R. Actually, I'll do that before I get on to the others." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk6.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..ac7425fbe27a77a7e448b576483b4c179e9a31f1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "What's a basis for the column space?" + }, + { + "text": "We've done all the work of row reduction, identifying the pivot columns, the ones that have pivots, the ones that end up with pivots, but now I the pivot columns I'm interested in are columns of A, the original A." + }, + { + "text": "And those pivot columns, there are R of them, the rank R counts those, those are a basis." + }, + { + "text": "So if I answer this question for the column space, the answer will be a basis is the pivot columns, and the dimension is the rank R. And there are pivot columns and everything great." + }, + { + "text": "OK, so that space we pretty well understand." + }, + { + "text": "I probably have a little going back to see that, to prove that this is a right answer, but you know it's the right answer." + }, + { + "text": "Now let me look at the row space." + }, + { + "text": "OK. Shall I tell you the dimension of the row space?" + }, + { + "text": "Yes." + }, + { + "text": "Before we do even an example, let me tell you the dimension of the row space." + }, + { + "text": "Its dimension is also R. The row space and the column space have the same dimension." + }, + { + "text": "That's a wonderful fact." + }, + { + "text": "The dimension of the column space of A transpose, that's the row space, is R. That space is R-dimensional." + }, + { + "text": "And so is this one." + }, + { + "text": "OK. That's the, that's the sort of insight that got used in this example." + }, + { + "text": "If those, if those, if those, are the three columns of a matrix, let me make them the three columns of a matrix by just erasing some brackets, OK, those are the three columns of a matrix, the rank of that matrix, if I look at the columns, it wasn't obvious to me anyway." + }, + { + "text": "But if I look at the rows, it's, now it's obvious." + }, + { + "text": "The row space of that matrix obviously is two-dimensional, because I can, I see a basis for the row space, this row and that row." + }, + { + "text": "And of course, strictly speaking, I'm supposed to transpose those guys, make them stand up." + }, + { + "text": "But the rank is two, and therefore the column space is two-dimensional by this wonderful fact that the row space and column space have the same dimension, and therefore there are only two pivot columns, not three, and, those, the three columns are dependent." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk7.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..7d55c74913379543a71fcc53c971f787baf12a92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, let me bury that error and talk about the row space." + }, + { + "text": "Well, I'm going to give you the dimensions of all the spaces, because that's the, such a nice answer." + }, + { + "text": "OK." + }, + { + "text": "So let me come back here." + }, + { + "text": "So we have this great fact to establish, that the row space, its dimension is also the rank." + }, + { + "text": "OK. What about the null space?" + }, + { + "text": "What's a basis for the null space?" + }, + { + "text": "What's the dimension of the null space?" + }, + { + "text": "Let me, I'll put that answer up here, for the null space." + }, + { + "text": "Well, how have we constructed the null space?" + }, + { + "text": "We took the matrix A, we did those row operations to get it into a form U or even further, we got it into the reduced form R, and then we read off special solutions." + }, + { + "text": "Special solutions, and every special solution came from a free variable." + }, + { + "text": "And those special solutions are in the null space, and the great thing is, they're a basis for it." + }, + { + "text": "So for the null space, a basis will be the special solutions." + }, + { + "text": "And there's one for every free variable, right?" + }, + { + "text": "For each free variable, we give that variable the value one, the other free variable zero." + }, + { + "text": "We get the pivot variables, we get a vector in the -- we get a special solution." + }, + { + "text": "So we get all together n minus R of them, because that's the number of free variables." + }, + { + "text": "If we have R, this is, the dimension is R, is the number of pivot variables, this is the number of free variables." + }, + { + "text": "So the beauty is that those special solutions do form a basis and tell us immediately that the dimension of the null space is n -- I'd better write this well, because it's so nice, n minus R. And you see the nice thing, that the two dimensions in this n-dimensional space, one subspace is R-dimensional, to be proved, that's the row space." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk8.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f4c70532a641ef630aa1f7bca077776017097cd4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "The other subspace is n minus R-dimensional, that's the null space." + }, + { + "text": "And the two dimensions, like, together, give n. The sum of R and n minus R is n. And that's just great." + }, + { + "text": "It's really copying the fact that we have n variables, R of them are pivot variables and n minus R are free variables and n all together." + }, + { + "text": "OK. And now what's the dimension of this poor misbegotten fourth subspace?" + }, + { + "text": "It's got to be m minus R. The dimension of this left null space, left out practically, is m minus R. Well, that's really just saying that this, again, the sum of that plus that is m. And m is correct." + }, + { + "text": "It's the number of columns in A transpose." + }, + { + "text": "A transpose is just as good a matrix as A." + }, + { + "text": "It just happens to be n by m. It happens to have m columns, so it will have m variables, when I go to Ax equals zero, and m of them and R of them will be pivot variables and m minus R will be free variables." + }, + { + "text": "A transpose is as good a matrix as A." + }, + { + "text": "It follows the same rule that this plus the dimension, this dimension plus this dimension adds up to the number of columns." + }, + { + "text": "And over here, A transpose has m columns." + }, + { + "text": "Okay." + }, + { + "text": "Okay, so I gave you the easy answer, the dimensions." + }, + { + "text": "Now can I go back to check on a basis?" + }, + { + "text": "We would like to think that, say, the row space." + }, + { + "text": "Because we've got a basis for the column space." + }, + { + "text": "The pivot columns give a basis for the column space." + }, + { + "text": "Now I'm asking you to look at the row space." + }, + { + "text": "And I you could say, okay, I can produce a basis for the row space by transposing my matrix, making those columns, then doing elimination, row reduction, and checking out the pivot columns in this transposed matrix." + }, + { + "text": "But that means you had to do all that row reduction on A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk9.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..8be162da3ff089e5c511aa65ea7d801c64cad56f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_14_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It ought to be possible, if we take a matrix A, let me take the matrix, maybe we had this matrix in the last lecture, one one one, two one two, three two three, one one one." + }, + { + "text": "Okay." + }, + { + "text": "That, that matrix was so easy, we spotted its pivot columns, one and two, without actually doing row reduction." + }, + { + "text": "But now let's do the job properly." + }, + { + "text": "So I subtract this away from this to produce a zero." + }, + { + "text": "So one two three one is fine." + }, + { + "text": "Subtracting that away leaves me minus one minus one zero, right?" + }, + { + "text": "And subtracting that from the last row, oh, well, that's easy." + }, + { + "text": "Okay, I'm doing row reduction." + }, + { + "text": "Now I've, the first column is all set." + }, + { + "text": "The second column, I now see the pivot, and I can clean up, if I, actually, okay, why don't I make the pivot into a one?" + }, + { + "text": "I'll multiply that row through by minus one, and then I have one one." + }, + { + "text": "That was an elementary operation, I'm allowed." + }, + { + "text": "Multiply a row by a number." + }, + { + "text": "And now I'll do elimination." + }, + { + "text": "Two of those away from that will knock this guy out and make this into a one." + }, + { + "text": "So that's now a zero and that's a one." + }, + { + "text": "Okay." + }, + { + "text": "Done." + }, + { + "text": "That's R. I'm seeing the identity matrix here, I'm seeing zeros below, and I'm seeing F there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk0.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6b8bcce949e11c9807b49a56c5ca68fdb459f818 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay, here is lecture ten in linear algebra." + }, + { + "text": "Two important things to do in this lecture." + }, + { + "text": "One is to correct an error from lecture nine." + }, + { + "text": "So the blackboard with that awful error is still with us." + }, + { + "text": "And the second, the big thing to do is to tell you about the four subspaces that come with a matrix." + }, + { + "text": "We've seen two subspaces, the column space and the null space, there's two to go." + }, + { + "text": "Okay." + }, + { + "text": "First of all, and this is a great way to recap and correct the previous lecture." + }, + { + "text": "So you remember I was just doing R3." + }, + { + "text": "I couldn't have taken a simpler example than R3." + }, + { + "text": "And I wrote down the standard basis." + }, + { + "text": "That's the standard basis." + }, + { + "text": "The basis, the obvious basis for the whole three-dimensional space." + }, + { + "text": "And then I wanted to make the point that there was nothing special, nothing about that basis that another basis couldn't have." + }, + { + "text": "It could have linear independence, it could span a space, there's lots of other bases." + }, + { + "text": "So I started with these vectors one one two and two two five, and those were independent." + }, + { + "text": "And then I said three three seven wouldn't do, because three three seven is the sum of those." + }, + { + "text": "So in my innocence, I put in three three eight." + }, + { + "text": "I figured probably if three three seven is on the plane, is, which I know, it's in the plane with these two, then probably three three eight sticks a little bit out of the plane." + }, + { + "text": "And it's independent and it gives a basis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk1.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..97d9d72b29a5aa923aae0ba9c0fb0da57e9db2ed --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "But after class, to my sorrow, student tells me, wait a minute, that third vector three three eight is not independent." + }, + { + "text": "And why did she say that?" + }, + { + "text": "She didn't actually take the time, didn't have to, to find what combination of this one and this one gives three three eight." + }, + { + "text": "She did something else." + }, + { + "text": "In other words, she looked ahead because she said, wait a minute, if I look at that matrix, it's not invertible." + }, + { + "text": "That third column can't be independent of the first two, because when I look at that matrix, it's got two identical rows." + }, + { + "text": "I have a square matrix." + }, + { + "text": "Its rows are obviously dependent." + }, + { + "text": "And that makes the columns dependent." + }, + { + "text": "So there's my error." + }, + { + "text": "When I look at the matrix A that has those three columns, those three columns can't be independent because that matrix is not invertible because it's got two equal rows." + }, + { + "text": "And today's lecture will reach the conclusion, the great conclusion, that connects the column space with the row space." + }, + { + "text": "So those are the row space is now going to be another one of my fundamental subspaces." + }, + { + "text": "The row space of this matrix or of this one, well, the row space of this one is okay." + }, + { + "text": "But the row space of this one, I'm looking at the rows of the matrix, oh, anyway, I'll have two equal rows and the row space will be only two-dimensional." + }, + { + "text": "The rank of the matrix with these columns will only be two, so only two of those columns can be independent too." + }, + { + "text": "The rows tell me something about the columns, in other words." + }, + { + "text": "Something that I should have noticed and I didn't." + }, + { + "text": "Okay." + }, + { + "text": "So now let me pin down these four fundamental subspaces." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk10.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..8f428ebe86b1b4488558f6fa55b8940ef758b264 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "Okay." + }, + { + "text": "What about its row space?" + }, + { + "text": "What happened to its row space?" + }, + { + "text": "Well, what happened, let me first ask, just because this is, sometimes something does happen." + }, + { + "text": "Its column space changed." + }, + { + "text": "The column space of R is not the column space of A, right?" + }, + { + "text": "Because one one one is certainly in the column space of A and certainly not in the column space of R. I did row operations." + }, + { + "text": "Those row operations preserved the row space, so the row so the column spaces are different." + }, + { + "text": "Different column spaces." + }, + { + "text": "Different column spaces." + }, + { + "text": "But I believe that they have the same row space." + }, + { + "text": "Same row space." + }, + { + "text": "I believe that the row space of that matrix and the row space of this matrix are identical." + }, + { + "text": "They have exactly the same vectors in them." + }, + { + "text": "Those vectors are vectors with four components, right?" + }, + { + "text": "They're all combinations of those rows." + }, + { + "text": "Or I believe you get the same thing by taking all combinations of these rows." + }, + { + "text": "And if true, what's a basis?" + }, + { + "text": "What's a basis for the row space of R?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk11.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..258e5999dbb0aea67696256511eb6b999136132a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it'll be a basis for the row space of the original A." + }, + { + "text": "But it's obviously a basis for the row space of R. What's a basis for the row space of that matrix?" + }, + { + "text": "The first two rows." + }, + { + "text": "So a basis for the row so a basis is for the row space of A or of R is the first R rows of R, not of A." + }, + { + "text": "Sometimes it's true for A, but not necessarily." + }, + { + "text": "But R, we definitely have a matrix here whose row space we can identify." + }, + { + "text": "The row space is spanned by the three rows." + }, + { + "text": "But if we want a basis, we want independence." + }, + { + "text": "So out goes row three." + }, + { + "text": "The row space is also spanned by the first two rows." + }, + { + "text": "This guy didn't contribute anything." + }, + { + "text": "And of course, over here, this one, two, three, one in the bottom didn't contribute anything." + }, + { + "text": "We had it already." + }, + { + "text": "So this, here's a basis, one zero one one and zero one one zero." + }, + { + "text": "I believe those are in the row space." + }, + { + "text": "I know they're independent." + }, + { + "text": "Why are they in the row space?" + }, + { + "text": "Why are those two vectors in the row space?" + }, + { + "text": "Because all those operations we did, which started with these rows and took combinations of them." + }, + { + "text": "I took this row minus this row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk12.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..d05a7eb6e4998c4acd748e3bb7087c68e6e29a80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "That gave me something that's still in the row space." + }, + { + "text": "That's the point." + }, + { + "text": "When I took a row minus a multiple of another row, I'm staying in the row space." + }, + { + "text": "The row space is not changing." + }, + { + "text": "My little basis for it is changing, and I've ended up with, sort of, the best basis." + }, + { + "text": "If the columns of the identity matrix are the best basis for R3 or Rn, the rows of this matrix are the best basis for the row space." + }, + { + "text": "Best in the sense of being as clean as I can make it." + }, + { + "text": "Starting off with the identity and then finishing up with whatever has to be in there." + }, + { + "text": "OK. Do you see, then, that the dimension is R?" + }, + { + "text": "For sure." + }, + { + "text": "Because we've got R pivots, R nonzero rows, we've got the right number of vectors, R. They're in the row space, they're independent, that's it." + }, + { + "text": "They are a basis for the row space." + }, + { + "text": "And we can even pin that down further." + }, + { + "text": "How do I know that every row of A is a combination?" + }, + { + "text": "How do I know they span the row space?" + }, + { + "text": "Oh, well, somebody says I've got the right number of them, so they must, but that's true." + }, + { + "text": "But let me just say, how do I know that this row is a combination of these?" + }, + { + "text": "By just reversing the steps of row reduction." + }, + { + "text": "If I just reverse the steps and go from A, from R back to A, then what do I, what am I doing?" + }, + { + "text": "I'm starting with these rows, I'm taking combinations of them, after a couple of steps, undoing the subtractions that I did before, I'm back to these rows." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk13.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..7b0edabbd24233827c7692f63429589952dac1bc --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "So these rows are combinations of those rows, those rows are combinations of those rows, the two row spaces are the same, the bases are the same, and the natural basis is this guy." + }, + { + "text": "Is that all right for the row space?" + }, + { + "text": "The row space is sitting there in R, in its cleanest possible form." + }, + { + "text": "OK. Now what about the fourth guy, the null space of A transpose?" + }, + { + "text": "First of all, why do I call that the left null space?" + }, + { + "text": "So let me save that and bring that down." + }, + { + "text": "OK." + }, + { + "text": "So the fourth space is the null space of A transpose." + }, + { + "text": "So it has in it vectors, let me call them y, so that A transpose y equals zero." + }, + { + "text": "If A transpose y equals zero, then y is in the null space of A transpose, of course." + }, + { + "text": "So this is a matrix times a column equaling zero." + }, + { + "text": "And now, because I want y to sit on the left, and I want A instead of A transpose, I'll just transpose that equation." + }, + { + "text": "Can I just transpose that?" + }, + { + "text": "On the right, it makes the zero vector lie down." + }, + { + "text": "And on the left, it's a product, A transpose times y." + }, + { + "text": "If I take the transpose, then they come in opposite order, right?" + }, + { + "text": "So it's y transpose times A transpose transpose, but nobody's going to leave it like that." + }, + { + "text": "That's A transpose transpose is just A, of course." + }, + { + "text": "When I transposed A transpose, I got back to A." + }, + { + "text": "Now, do you see what I have now?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk14.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7a889f79409e9a95fbd4cc01518da4b9706c49d1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "I have a row vector, y transpose, multiplying A and multiplying from the left." + }, + { + "text": "That's why I call it the left null space." + }, + { + "text": "But by making it, putting it on the left, I had to make it into a row instead of a column vector." + }, + { + "text": "And so my convention is I usually don't do that, I usually stay with A transpose y equals zero." + }, + { + "text": "OK. And you might ask, how do we get a basis, or I might ask, how do we get a basis for this fourth space, this left null space?" + }, + { + "text": "OK." + }, + { + "text": "I'll do it the example." + }, + { + "text": "As always, ah, not that one." + }, + { + "text": "The left null space is not jumping out at me here." + }, + { + "text": "I know which are the free variables, the special solutions, but those are special solutions to Ax equals zero, and now I'm looking at A transpose and I'm not seeing it here." + }, + { + "text": "So, but somehow you feel that the work that you did, which simplified A to R, should have revealed the left null space too." + }, + { + "text": "And it's slightly less immediate, but it's there." + }, + { + "text": "So from A to R, I took some steps, and I guess I'm interested in what were those steps, or what were all of them together." + }, + { + "text": "I don't want to -- I'm not interested in what particular ones they were." + }, + { + "text": "I'm interested in what was the whole matrix that took me from A to R. How would you find that?" + }, + { + "text": "Do you remember Gauss-Jordan, where you tack on the identity matrix?" + }, + { + "text": "Let's do that again." + }, + { + "text": "So I'll do it above here." + }, + { + "text": "So this is now the idea of I take the matrix A, which is m by n. In Gauss-Jordan, when we saw him before, A was a square invertible matrix and we were finding its inverse." + }, + { + "text": "Now the matrix isn't square, it's probably rectangular." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk15.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3c045b6d07a6635d896789ba37b0d578bd175e92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "But I'll still tack on the identity matrix, and of course, since these have length m, it better be m by m. And now I'll do the reduced row echelon form of this matrix." + }, + { + "text": "And what do I get?" + }, + { + "text": "The reduced row echelon form starts with these columns, starts with the first columns, works like mad, and produces R. Of course, still the same size, m by n, and we did it before." + }, + { + "text": "And then whatever it did to get R, something else is going to show up here." + }, + { + "text": "Let me call it E, m by m. It's whatever you see that E is just going to contain a record of what we did." + }, + { + "text": "We did whatever it took to get A to become R. And at the same time, we were doing it to the identity matrix." + }, + { + "text": "So we started with the identity matrix, we buzzed along." + }, + { + "text": "So we took some -- all this row reduction amounted to multiplying on the left by some matrix, some series of elementary matrices that all together gave us one matrix, and that matrix is E. So all this row reduction stuff amounted to multiplying by E. How do I know that?" + }, + { + "text": "It certainly amounted to multiplying by something, and that something took I to E, so that something was E. So now look at the first part, E A is R. No big deal." + }, + { + "text": "All I've said is that the row reduction steps that we all know well, taking A to R, are in a- in some matrix, and I can find out what that matrix is by just tacking I on and seeing what comes out." + }, + { + "text": "What comes out is E. Let's just review the invertible square case." + }, + { + "text": "What happened then?" + }, + { + "text": "Because I was interested in it in chapter two also." + }, + { + "text": "When A was square and invertible, I took A I, I did row elimination, what was the R that came out?" + }, + { + "text": "It was I." + }, + { + "text": "So in chapter two, in chapter two, R was I." + }, + { + "text": "The row- the reduced row echelon form of a nice invertible square matrix is the identity." + }, + { + "text": "So if R was I in that case, then E was A inverse, because E A is I." + }, + { + "text": "Good." + }, + { + "text": "That's- that was good and easy." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk16.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..c5a8adc4741aeb68371eb235609b24dad795df03 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now what I'm saying is that there still is an E, it's not A inverse anymore, because A is a rectangular, it hasn't got an inverse." + }, + { + "text": "But there is still some matrix E that connected this to this." + }, + { + "text": "Oh, I should have figured out in advance what it was." + }, + { + "text": "Shoot." + }, + { + "text": "I didn't- I did those steps and sort of erased as I went, and, I should have done them to the identity, too." + }, + { + "text": "Can I do that?" + }, + { + "text": "Can I do that?" + }, + { + "text": "I'll keep the identity matrix, like I'm supposed to do, and I'll do the same operations on it and see what I end up with." + }, + { + "text": "Okay." + }, + { + "text": "So I'm starting with the identity, which I'll write in light, light enough, but okay, what did I do?" + }, + { + "text": "I subtracted that row from that one and that row from that one." + }, + { + "text": "Okay, I'll do that to the identity." + }, + { + "text": "So I subtract that first row from row two and row three." + }, + { + "text": "Good." + }, + { + "text": "Then I think I multiply, do you remember, I multiplied row two by minus one?" + }, + { + "text": "Let me just do that." + }, + { + "text": "Then what did I do?" + }, + { + "text": "I subtracted two of row two away from row one." + }, + { + "text": "I better do that." + }, + { + "text": "Subtract two of this away from this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk17.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..368775ffcdaa5a9fe2c24f8c85bcb4963097a79c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's minus one, two of these away leaves a plus two and zero." + }, + { + "text": "I believe that's E. The way to check is to see, multiply that E by this A, just to see, did I do it right?" + }, + { + "text": "So I believe E was minus one, two, zero, one minus one, zero, and minus one, zero, one." + }, + { + "text": "Okay." + }, + { + "text": "That's my E, that's my A, and that's R. All right." + }, + { + "text": "All I'm struggling to do is write the reason I wanted this blasted E was so that I could figure out the left null space." + }, + { + "text": "Not only its dimension, which I know." + }, + { + "text": "Actually, what is the dimension of the left null space?" + }, + { + "text": "Here's my matrix." + }, + { + "text": "What's the rank of the matrix?" + }, + { + "text": "Two." + }, + { + "text": "And the dimension of the left null space is supposed to be M minus R, three minus two, one." + }, + { + "text": "I believe that the left null space is one-dimensional." + }, + { + "text": "There is one combination of those three rows that produces the zero row." + }, + { + "text": "There is a basis." + }, + { + "text": "A basis for the left null space has only got one vector in it." + }, + { + "text": "And what is that vector?" + }, + { + "text": "It's here in the last row of E. But, ah, we could have seen it earlier." + }, + { + "text": "What combination of those rows gives the zero row?" + }, + { + "text": "Minus one of that, plus one of that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk18.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..9f5e8b1fcc2242dbdc56d379cbc7126ada792e31 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a basis for the left null space of this matrix, I'm looking for combinations of rows that give the zero row, if I'm looking at the left null space." + }, + { + "text": "For the null space, I'm looking at combinations of columns to get the zero column." + }, + { + "text": "Now I'm looking at combinations of these three rows to get the zero row, and of course, there is my zero row, and here is my vector that produced it." + }, + { + "text": "Minus one of that row and one of that row." + }, + { + "text": "Obvious." + }, + { + "text": "Okay." + }, + { + "text": "So in that example, and actually in all examples, we have seen how to produce a basis for the left null space." + }, + { + "text": "I won't ask you that all the time." + }, + { + "text": "Because it didn't come out immediately from R, we had to keep track of E for that left null space." + }, + { + "text": "But at least it didn't require us to transpose the matrix and start all over again." + }, + { + "text": "Okay." + }, + { + "text": "Those are the four subspaces." + }, + { + "text": "Can I review them?" + }, + { + "text": "The row space and the null space are in Rn." + }, + { + "text": "Their dimensions add to n. The column space and the left null space are in Rm, and their dimensions add to m. Okay." + }, + { + "text": "So let me close these last minutes by pushing you a little bit more to a new type of vector space." + }, + { + "text": "All our vector spaces, all the ones that we took seriously, have been subspaces of some real three- or n-dimensional space." + }, + { + "text": "Now I'm going to write down another vector space, a new vector space." + }, + { + "text": "Say all three by three matrices." + }, + { + "text": "My matrices are the vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk19.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..c1658ee474fcf6206f54d67e4dededa02a1ef92c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Is that all right?" + }, + { + "text": "I'm just naming them." + }, + { + "text": "You can put quotes around vectors." + }, + { + "text": "Every three by three matrix is one of my vectors." + }, + { + "text": "Now how am I entitled to call those things vectors?" + }, + { + "text": "I mean, they look very much like matrices." + }, + { + "text": "But they're vectors in my vector space because they obey the rules." + }, + { + "text": "All I'm supposed to be able to do with vectors is add them." + }, + { + "text": "I can add matrices." + }, + { + "text": "I'm supposed to be able to multiply them by scalar numbers, like seven." + }, + { + "text": "Well, I can multiply a matrix by seven." + }, + { + "text": "And I can take combinations of matrices." + }, + { + "text": "I can take three of one matrix minus five of another matrix." + }, + { + "text": "And those combinations, there's a zero matrix, the matrix that has all zeros in it." + }, + { + "text": "If I add that to another matrix, it doesn't change it." + }, + { + "text": "All the good stuff." + }, + { + "text": "If I multiply a matrix by one, it doesn't change it." + }, + { + "text": "All those eight rules for a vector space that we never wrote down, all easily satisfied." + }, + { + "text": "So now we have a different --." + }, + { + "text": "Now, of course, you can say you can multiply those matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk2.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..b92bd923d792a0f92ab4de95b7867006e9880f71 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here are the four fundamental subspaces." + }, + { + "text": "This is really the heart of this approach to linear algebra, to see these four subspaces, how they're related." + }, + { + "text": "So what are they?" + }, + { + "text": "The column space, C of A." + }, + { + "text": "The null space, N of A." + }, + { + "text": "And now comes the row space, something new." + }, + { + "text": "The row space, what's in that?" + }, + { + "text": "It's all combinations of the rows." + }, + { + "text": "That's natural." + }, + { + "text": "We want a space, so we have to take all combinations and we start with the rows." + }, + { + "text": "So the rows span the row space." + }, + { + "text": "Are the rows a basis for the row space?" + }, + { + "text": "Maybe so, maybe no." + }, + { + "text": "The rows are a basis for the row space when they're independent." + }, + { + "text": "But if they're dependent, as in this example, my error from last time, they're not, those three rows are not a basis, the row space would only be two-dimensional, I only need two rows for a basis." + }, + { + "text": "So the row space, now what's in it?" + }, + { + "text": "It's all combinations of the rows of A." + }, + { + "text": "All combinations of the rows of A." + }, + { + "text": "But I don't like working with row vectors." + }, + { + "text": "All my vectors have been column vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk20.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..56956e8347a8f8c1f8522690db77860dcc6953b9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "I don't care." + }, + { + "text": "For the moment, I'm only thinking of these matrices as forming a vector space, so I am only doing A plus B and C times A. I'm not interested in A, B for now." + }, + { + "text": "The fact that I can multiply is not relevant to a vector space." + }, + { + "text": "OK, so I have three by three matrices." + }, + { + "text": "And how about subspaces?" + }, + { + "text": "What's, tell me a subspace of this matrix space." + }, + { + "text": "Let me call this matrix space M. That's my matrix space, my space of all three by three matrices." + }, + { + "text": "Tell me a subspace of it." + }, + { + "text": "OK, what about the upper triangular matrices?" + }, + { + "text": "So subspaces, subspaces of M. All upper triangular matrices." + }, + { + "text": "Another subspace." + }, + { + "text": "All symmetric matrices." + }, + { + "text": "The intersection of two subspaces is supposed to be a subspace." + }, + { + "text": "We gave a little effort to the proof of that fact." + }, + { + "text": "If I look at the matrices that are in this subspace, they're symmetric, and they're also in this subspace, they're upper triangular." + }, + { + "text": "What do they look like?" + }, + { + "text": "Well, if they're symmetric, but they have zeros below the diagonal, they better have zeros above the diagonal." + }, + { + "text": "So the intersection would be diagonal matrices." + }, + { + "text": "That's another subspace, smaller than those." + }, + { + "text": "How can I use the word smaller?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk21.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..ffcdd44ed2f644726e04b27114327cb30bc7fb92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, I'm now entitled to use the word smaller." + }, + { + "text": "I mean, well, one way to say is, OK, these are contained in those." + }, + { + "text": "These are contained in those." + }, + { + "text": "But more precisely, I could give the dimension of these spaces." + }, + { + "text": "So I could, we can compute, let's compute it next time." + }, + { + "text": "The dimension of all upper, of the subspace of upper triangular three by three matrices." + }, + { + "text": "The dimension of symmetric three by three matrices." + }, + { + "text": "The dimension of diagonal three by three matrices." + }, + { + "text": "Well, to produce dimension, that means I'm supposed to produce a basis." + }, + { + "text": "And then I just count how many I needed in the basis." + }, + { + "text": "Let me give you the answer for this one." + }, + { + "text": "What's the dimension?" + }, + { + "text": "The dimension of this, say, this subspace, let me call it D, all diagonal matrices." + }, + { + "text": "The dimension of this subspace is, as I write, you're working it out, three." + }, + { + "text": "Because here's a matrix in this, it's a diagonal matrix." + }, + { + "text": "Here's another one." + }, + { + "text": "Here's another one." + }, + { + "text": "Better make it diagonal, let me put a seven there." + }, + { + "text": "That was not a very great choice, but it's three diagonal matrices, and I believe that they're a basis." + }, + { + "text": "I believe that those three matrices are independent, and I believe that any diagonal matrix is a combination of those three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk22.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..8c6bce8cf8085e6544c31ae6926bb7ccf18b983e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk22.json @@ -0,0 +1,20 @@ +[ + { + "text": "So they span the subspace of diagonal matrices." + }, + { + "text": "Do you see that idea?" + }, + { + "text": "It's like stretching the idea from Rn to Rn by n, three by three, but we can still add, we can still multiply by numbers, and we just ignore the fact that we can multiply two matrices together." + }, + { + "text": "Okay." + }, + { + "text": "Thank you." + }, + { + "text": "That's lecture ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk3.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..25f31647b76274f9088c60d1292bcc43915d3fb0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'd like to stay with column vectors." + }, + { + "text": "How can I get to column vectors out of these rows?" + }, + { + "text": "I transpose the matrix." + }, + { + "text": "So if that's OK with you, I'm going to transpose the matrix, I'm going to say all combinations of the columns of A transpose." + }, + { + "text": "And that allows me to use the convenient notation, the column space of A transpose." + }, + { + "text": "Nothing, no mathematics went on there, we just got some vectors that were lying down to stand up." + }, + { + "text": "But it means that we can use this column space of A transpose, that's telling me in a nice matrix notation what the row space is." + }, + { + "text": "OK. And finally is another null space." + }, + { + "text": "The fourth fundamental space will be the null space of A transpose." + }, + { + "text": "The fourth guy is the null space of A transpose." + }, + { + "text": "And of course, my notation is N of A transpose." + }, + { + "text": "That's the null space of A transpose." + }, + { + "text": "Now, we don't have a perfect name for this space as a, as a, connecting with A, but our usual name is the left null space, and I'll show you why in a moment." + }, + { + "text": "So often I call this the, just to write that word, the left null space of A." + }, + { + "text": "So just the way we have the row space of A and we switch it to the column space of A transpose, so we have this space of guys that I call the left null space of A, but the good notation is it's the null space of A transpose." + }, + { + "text": "OK. Those are four spaces." + }, + { + "text": "Where are those spaces?" + }, + { + "text": "What big space are they in for when A is m by n?" + }, + { + "text": "In that case, the null space of A, what's in the null space of A?" + }, + { + "text": "Vectors with n components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk4.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c2575473d88ff4598107e190483f0484b6558678 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Solutions to Ax equals zero." + }, + { + "text": "So the null space of A is n R n. What's in the column space of A?" + }, + { + "text": "Well, columns." + }, + { + "text": "How many components do those columns have?" + }, + { + "text": "m. So this column space is n R m. What about the column space of A transpose, which are just a disguised way of saying the rows of A?" + }, + { + "text": "The rows of A in this three by six matrix have six components, n components." + }, + { + "text": "The column space is n R n. And the null space of A transpose, I see that this fourth space is already getting second, you know, second class citizen treatment and it doesn't deserve it." + }, + { + "text": "It's, it should be there, it is there, and shouldn't be squeezed." + }, + { + "text": "The null space of A transpose, well, if the null space of A had vectors with n components, the null space of A transpose will be n R m. I want to draw a picture of the four spaces." + }, + { + "text": "OK. OK." + }, + { + "text": "Here are the four spaces." + }, + { + "text": "OK, let me put n dimensional space over on this side." + }, + { + "text": "Then which were the subspaces in R n?" + }, + { + "text": "The null space was and the row space was." + }, + { + "text": "So here we have the can I make that picture of the row space?" + }, + { + "text": "And can I make this kind of picture of the null space?" + }, + { + "text": "That's just meant to be a sketch, to remind you that they're in this which, you know, how, what type of vectors are in it?" + }, + { + "text": "Vectors with n components." + }, + { + "text": "Over here, inside consisting of vectors with m components is the column space and what I'm calling the null space of A transpose." + }, + { + "text": "Those are the ones with m components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk5.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..f4e64e208c1a1d8e07a9a66a6a6c59f8c4cbcec8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. To understand these spaces is our job now." + }, + { + "text": "Because by understanding those spaces, we know everything about this half of linear algebra." + }, + { + "text": "What do I mean by understanding those spaces?" + }, + { + "text": "I would like to know a basis for those spaces." + }, + { + "text": "For each one of those spaces, how would I create, construct a basis?" + }, + { + "text": "What systematic way would produce a basis?" + }, + { + "text": "And what's their dimension?" + }, + { + "text": "OK." + }, + { + "text": "So for each of the four spaces, I have to answer those questions." + }, + { + "text": "How do I produce a basis?" + }, + { + "text": "And then, which has a somewhat long answer, and what's the dimension, which is just a number, so it has a real short answer?" + }, + { + "text": "Can I give you the short answer first?" + }, + { + "text": "I shouldn't do it, but here it is." + }, + { + "text": "I can tell you the dimension of the column space." + }, + { + "text": "Let me start with this guy." + }, + { + "text": "What's its dimension?" + }, + { + "text": "I have an m by n matrix." + }, + { + "text": "The dimension of the column space is the rank, R. We actually got to that at the end of the last lecture, but only for an example." + }, + { + "text": "So I really have to say, OK, what's going on there?" + }, + { + "text": "I should produce a basis, and then I just look to see how many vectors I needed in that basis, and the answer will be R. Actually, I'll do that before I get on to the others." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk6.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..ac7425fbe27a77a7e448b576483b4c179e9a31f1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "What's a basis for the column space?" + }, + { + "text": "We've done all the work of row reduction, identifying the pivot columns, the ones that have pivots, the ones that end up with pivots, but now I the pivot columns I'm interested in are columns of A, the original A." + }, + { + "text": "And those pivot columns, there are R of them, the rank R counts those, those are a basis." + }, + { + "text": "So if I answer this question for the column space, the answer will be a basis is the pivot columns, and the dimension is the rank R. And there are pivot columns and everything great." + }, + { + "text": "OK, so that space we pretty well understand." + }, + { + "text": "I probably have a little going back to see that, to prove that this is a right answer, but you know it's the right answer." + }, + { + "text": "Now let me look at the row space." + }, + { + "text": "OK. Shall I tell you the dimension of the row space?" + }, + { + "text": "Yes." + }, + { + "text": "Before we do even an example, let me tell you the dimension of the row space." + }, + { + "text": "Its dimension is also R. The row space and the column space have the same dimension." + }, + { + "text": "That's a wonderful fact." + }, + { + "text": "The dimension of the column space of A transpose, that's the row space, is R. That space is R-dimensional." + }, + { + "text": "And so is this one." + }, + { + "text": "OK. That's the, that's the sort of insight that got used in this example." + }, + { + "text": "If those, if those, if those, are the three columns of a matrix, let me make them the three columns of a matrix by just erasing some brackets, OK, those are the three columns of a matrix, the rank of that matrix, if I look at the columns, it wasn't obvious to me anyway." + }, + { + "text": "But if I look at the rows, it's, now it's obvious." + }, + { + "text": "The row space of that matrix obviously is two-dimensional, because I can, I see a basis for the row space, this row and that row." + }, + { + "text": "And of course, strictly speaking, I'm supposed to transpose those guys, make them stand up." + }, + { + "text": "But the rank is two, and therefore the column space is two-dimensional by this wonderful fact that the row space and column space have the same dimension, and therefore there are only two pivot columns, not three, and, those, the three columns are dependent." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk7.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..7d55c74913379543a71fcc53c971f787baf12a92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, let me bury that error and talk about the row space." + }, + { + "text": "Well, I'm going to give you the dimensions of all the spaces, because that's the, such a nice answer." + }, + { + "text": "OK." + }, + { + "text": "So let me come back here." + }, + { + "text": "So we have this great fact to establish, that the row space, its dimension is also the rank." + }, + { + "text": "OK. What about the null space?" + }, + { + "text": "What's a basis for the null space?" + }, + { + "text": "What's the dimension of the null space?" + }, + { + "text": "Let me, I'll put that answer up here, for the null space." + }, + { + "text": "Well, how have we constructed the null space?" + }, + { + "text": "We took the matrix A, we did those row operations to get it into a form U or even further, we got it into the reduced form R, and then we read off special solutions." + }, + { + "text": "Special solutions, and every special solution came from a free variable." + }, + { + "text": "And those special solutions are in the null space, and the great thing is, they're a basis for it." + }, + { + "text": "So for the null space, a basis will be the special solutions." + }, + { + "text": "And there's one for every free variable, right?" + }, + { + "text": "For each free variable, we give that variable the value one, the other free variable zero." + }, + { + "text": "We get the pivot variables, we get a vector in the -- we get a special solution." + }, + { + "text": "So we get all together n minus R of them, because that's the number of free variables." + }, + { + "text": "If we have R, this is, the dimension is R, is the number of pivot variables, this is the number of free variables." + }, + { + "text": "So the beauty is that those special solutions do form a basis and tell us immediately that the dimension of the null space is n -- I'd better write this well, because it's so nice, n minus R. And you see the nice thing, that the two dimensions in this n-dimensional space, one subspace is R-dimensional, to be proved, that's the row space." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk8.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f4c70532a641ef630aa1f7bca077776017097cd4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "The other subspace is n minus R-dimensional, that's the null space." + }, + { + "text": "And the two dimensions, like, together, give n. The sum of R and n minus R is n. And that's just great." + }, + { + "text": "It's really copying the fact that we have n variables, R of them are pivot variables and n minus R are free variables and n all together." + }, + { + "text": "OK. And now what's the dimension of this poor misbegotten fourth subspace?" + }, + { + "text": "It's got to be m minus R. The dimension of this left null space, left out practically, is m minus R. Well, that's really just saying that this, again, the sum of that plus that is m. And m is correct." + }, + { + "text": "It's the number of columns in A transpose." + }, + { + "text": "A transpose is just as good a matrix as A." + }, + { + "text": "It just happens to be n by m. It happens to have m columns, so it will have m variables, when I go to Ax equals zero, and m of them and R of them will be pivot variables and m minus R will be free variables." + }, + { + "text": "A transpose is as good a matrix as A." + }, + { + "text": "It follows the same rule that this plus the dimension, this dimension plus this dimension adds up to the number of columns." + }, + { + "text": "And over here, A transpose has m columns." + }, + { + "text": "Okay." + }, + { + "text": "Okay, so I gave you the easy answer, the dimensions." + }, + { + "text": "Now can I go back to check on a basis?" + }, + { + "text": "We would like to think that, say, the row space." + }, + { + "text": "Because we've got a basis for the column space." + }, + { + "text": "The pivot columns give a basis for the column space." + }, + { + "text": "Now I'm asking you to look at the row space." + }, + { + "text": "And I you could say, okay, I can produce a basis for the row space by transposing my matrix, making those columns, then doing elimination, row reduction, and checking out the pivot columns in this transposed matrix." + }, + { + "text": "But that means you had to do all that row reduction on A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk9.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..8be162da3ff089e5c511aa65ea7d801c64cad56f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_16_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It ought to be possible, if we take a matrix A, let me take the matrix, maybe we had this matrix in the last lecture, one one one, two one two, three two three, one one one." + }, + { + "text": "Okay." + }, + { + "text": "That, that matrix was so easy, we spotted its pivot columns, one and two, without actually doing row reduction." + }, + { + "text": "But now let's do the job properly." + }, + { + "text": "So I subtract this away from this to produce a zero." + }, + { + "text": "So one two three one is fine." + }, + { + "text": "Subtracting that away leaves me minus one minus one zero, right?" + }, + { + "text": "And subtracting that from the last row, oh, well, that's easy." + }, + { + "text": "Okay, I'm doing row reduction." + }, + { + "text": "Now I've, the first column is all set." + }, + { + "text": "The second column, I now see the pivot, and I can clean up, if I, actually, okay, why don't I make the pivot into a one?" + }, + { + "text": "I'll multiply that row through by minus one, and then I have one one." + }, + { + "text": "That was an elementary operation, I'm allowed." + }, + { + "text": "Multiply a row by a number." + }, + { + "text": "And now I'll do elimination." + }, + { + "text": "Two of those away from that will knock this guy out and make this into a one." + }, + { + "text": "So that's now a zero and that's a one." + }, + { + "text": "Okay." + }, + { + "text": "Done." + }, + { + "text": "That's R. I'm seeing the identity matrix here, I'm seeing zeros below, and I'm seeing F there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk0.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6b8bcce949e11c9807b49a56c5ca68fdb459f818 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay, here is lecture ten in linear algebra." + }, + { + "text": "Two important things to do in this lecture." + }, + { + "text": "One is to correct an error from lecture nine." + }, + { + "text": "So the blackboard with that awful error is still with us." + }, + { + "text": "And the second, the big thing to do is to tell you about the four subspaces that come with a matrix." + }, + { + "text": "We've seen two subspaces, the column space and the null space, there's two to go." + }, + { + "text": "Okay." + }, + { + "text": "First of all, and this is a great way to recap and correct the previous lecture." + }, + { + "text": "So you remember I was just doing R3." + }, + { + "text": "I couldn't have taken a simpler example than R3." + }, + { + "text": "And I wrote down the standard basis." + }, + { + "text": "That's the standard basis." + }, + { + "text": "The basis, the obvious basis for the whole three-dimensional space." + }, + { + "text": "And then I wanted to make the point that there was nothing special, nothing about that basis that another basis couldn't have." + }, + { + "text": "It could have linear independence, it could span a space, there's lots of other bases." + }, + { + "text": "So I started with these vectors one one two and two two five, and those were independent." + }, + { + "text": "And then I said three three seven wouldn't do, because three three seven is the sum of those." + }, + { + "text": "So in my innocence, I put in three three eight." + }, + { + "text": "I figured probably if three three seven is on the plane, is, which I know, it's in the plane with these two, then probably three three eight sticks a little bit out of the plane." + }, + { + "text": "And it's independent and it gives a basis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk1.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..97d9d72b29a5aa923aae0ba9c0fb0da57e9db2ed --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "But after class, to my sorrow, student tells me, wait a minute, that third vector three three eight is not independent." + }, + { + "text": "And why did she say that?" + }, + { + "text": "She didn't actually take the time, didn't have to, to find what combination of this one and this one gives three three eight." + }, + { + "text": "She did something else." + }, + { + "text": "In other words, she looked ahead because she said, wait a minute, if I look at that matrix, it's not invertible." + }, + { + "text": "That third column can't be independent of the first two, because when I look at that matrix, it's got two identical rows." + }, + { + "text": "I have a square matrix." + }, + { + "text": "Its rows are obviously dependent." + }, + { + "text": "And that makes the columns dependent." + }, + { + "text": "So there's my error." + }, + { + "text": "When I look at the matrix A that has those three columns, those three columns can't be independent because that matrix is not invertible because it's got two equal rows." + }, + { + "text": "And today's lecture will reach the conclusion, the great conclusion, that connects the column space with the row space." + }, + { + "text": "So those are the row space is now going to be another one of my fundamental subspaces." + }, + { + "text": "The row space of this matrix or of this one, well, the row space of this one is okay." + }, + { + "text": "But the row space of this one, I'm looking at the rows of the matrix, oh, anyway, I'll have two equal rows and the row space will be only two-dimensional." + }, + { + "text": "The rank of the matrix with these columns will only be two, so only two of those columns can be independent too." + }, + { + "text": "The rows tell me something about the columns, in other words." + }, + { + "text": "Something that I should have noticed and I didn't." + }, + { + "text": "Okay." + }, + { + "text": "So now let me pin down these four fundamental subspaces." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk10.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..8f428ebe86b1b4488558f6fa55b8940ef758b264 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "Okay." + }, + { + "text": "What about its row space?" + }, + { + "text": "What happened to its row space?" + }, + { + "text": "Well, what happened, let me first ask, just because this is, sometimes something does happen." + }, + { + "text": "Its column space changed." + }, + { + "text": "The column space of R is not the column space of A, right?" + }, + { + "text": "Because one one one is certainly in the column space of A and certainly not in the column space of R. I did row operations." + }, + { + "text": "Those row operations preserved the row space, so the row so the column spaces are different." + }, + { + "text": "Different column spaces." + }, + { + "text": "Different column spaces." + }, + { + "text": "But I believe that they have the same row space." + }, + { + "text": "Same row space." + }, + { + "text": "I believe that the row space of that matrix and the row space of this matrix are identical." + }, + { + "text": "They have exactly the same vectors in them." + }, + { + "text": "Those vectors are vectors with four components, right?" + }, + { + "text": "They're all combinations of those rows." + }, + { + "text": "Or I believe you get the same thing by taking all combinations of these rows." + }, + { + "text": "And if true, what's a basis?" + }, + { + "text": "What's a basis for the row space of R?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk11.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..258e5999dbb0aea67696256511eb6b999136132a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it'll be a basis for the row space of the original A." + }, + { + "text": "But it's obviously a basis for the row space of R. What's a basis for the row space of that matrix?" + }, + { + "text": "The first two rows." + }, + { + "text": "So a basis for the row so a basis is for the row space of A or of R is the first R rows of R, not of A." + }, + { + "text": "Sometimes it's true for A, but not necessarily." + }, + { + "text": "But R, we definitely have a matrix here whose row space we can identify." + }, + { + "text": "The row space is spanned by the three rows." + }, + { + "text": "But if we want a basis, we want independence." + }, + { + "text": "So out goes row three." + }, + { + "text": "The row space is also spanned by the first two rows." + }, + { + "text": "This guy didn't contribute anything." + }, + { + "text": "And of course, over here, this one, two, three, one in the bottom didn't contribute anything." + }, + { + "text": "We had it already." + }, + { + "text": "So this, here's a basis, one zero one one and zero one one zero." + }, + { + "text": "I believe those are in the row space." + }, + { + "text": "I know they're independent." + }, + { + "text": "Why are they in the row space?" + }, + { + "text": "Why are those two vectors in the row space?" + }, + { + "text": "Because all those operations we did, which started with these rows and took combinations of them." + }, + { + "text": "I took this row minus this row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk12.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..d05a7eb6e4998c4acd748e3bb7087c68e6e29a80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "That gave me something that's still in the row space." + }, + { + "text": "That's the point." + }, + { + "text": "When I took a row minus a multiple of another row, I'm staying in the row space." + }, + { + "text": "The row space is not changing." + }, + { + "text": "My little basis for it is changing, and I've ended up with, sort of, the best basis." + }, + { + "text": "If the columns of the identity matrix are the best basis for R3 or Rn, the rows of this matrix are the best basis for the row space." + }, + { + "text": "Best in the sense of being as clean as I can make it." + }, + { + "text": "Starting off with the identity and then finishing up with whatever has to be in there." + }, + { + "text": "OK. Do you see, then, that the dimension is R?" + }, + { + "text": "For sure." + }, + { + "text": "Because we've got R pivots, R nonzero rows, we've got the right number of vectors, R. They're in the row space, they're independent, that's it." + }, + { + "text": "They are a basis for the row space." + }, + { + "text": "And we can even pin that down further." + }, + { + "text": "How do I know that every row of A is a combination?" + }, + { + "text": "How do I know they span the row space?" + }, + { + "text": "Oh, well, somebody says I've got the right number of them, so they must, but that's true." + }, + { + "text": "But let me just say, how do I know that this row is a combination of these?" + }, + { + "text": "By just reversing the steps of row reduction." + }, + { + "text": "If I just reverse the steps and go from A, from R back to A, then what do I, what am I doing?" + }, + { + "text": "I'm starting with these rows, I'm taking combinations of them, after a couple of steps, undoing the subtractions that I did before, I'm back to these rows." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk13.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..7b0edabbd24233827c7692f63429589952dac1bc --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "So these rows are combinations of those rows, those rows are combinations of those rows, the two row spaces are the same, the bases are the same, and the natural basis is this guy." + }, + { + "text": "Is that all right for the row space?" + }, + { + "text": "The row space is sitting there in R, in its cleanest possible form." + }, + { + "text": "OK. Now what about the fourth guy, the null space of A transpose?" + }, + { + "text": "First of all, why do I call that the left null space?" + }, + { + "text": "So let me save that and bring that down." + }, + { + "text": "OK." + }, + { + "text": "So the fourth space is the null space of A transpose." + }, + { + "text": "So it has in it vectors, let me call them y, so that A transpose y equals zero." + }, + { + "text": "If A transpose y equals zero, then y is in the null space of A transpose, of course." + }, + { + "text": "So this is a matrix times a column equaling zero." + }, + { + "text": "And now, because I want y to sit on the left, and I want A instead of A transpose, I'll just transpose that equation." + }, + { + "text": "Can I just transpose that?" + }, + { + "text": "On the right, it makes the zero vector lie down." + }, + { + "text": "And on the left, it's a product, A transpose times y." + }, + { + "text": "If I take the transpose, then they come in opposite order, right?" + }, + { + "text": "So it's y transpose times A transpose transpose, but nobody's going to leave it like that." + }, + { + "text": "That's A transpose transpose is just A, of course." + }, + { + "text": "When I transposed A transpose, I got back to A." + }, + { + "text": "Now, do you see what I have now?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk14.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7a889f79409e9a95fbd4cc01518da4b9706c49d1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "I have a row vector, y transpose, multiplying A and multiplying from the left." + }, + { + "text": "That's why I call it the left null space." + }, + { + "text": "But by making it, putting it on the left, I had to make it into a row instead of a column vector." + }, + { + "text": "And so my convention is I usually don't do that, I usually stay with A transpose y equals zero." + }, + { + "text": "OK. And you might ask, how do we get a basis, or I might ask, how do we get a basis for this fourth space, this left null space?" + }, + { + "text": "OK." + }, + { + "text": "I'll do it the example." + }, + { + "text": "As always, ah, not that one." + }, + { + "text": "The left null space is not jumping out at me here." + }, + { + "text": "I know which are the free variables, the special solutions, but those are special solutions to Ax equals zero, and now I'm looking at A transpose and I'm not seeing it here." + }, + { + "text": "So, but somehow you feel that the work that you did, which simplified A to R, should have revealed the left null space too." + }, + { + "text": "And it's slightly less immediate, but it's there." + }, + { + "text": "So from A to R, I took some steps, and I guess I'm interested in what were those steps, or what were all of them together." + }, + { + "text": "I don't want to -- I'm not interested in what particular ones they were." + }, + { + "text": "I'm interested in what was the whole matrix that took me from A to R. How would you find that?" + }, + { + "text": "Do you remember Gauss-Jordan, where you tack on the identity matrix?" + }, + { + "text": "Let's do that again." + }, + { + "text": "So I'll do it above here." + }, + { + "text": "So this is now the idea of I take the matrix A, which is m by n. In Gauss-Jordan, when we saw him before, A was a square invertible matrix and we were finding its inverse." + }, + { + "text": "Now the matrix isn't square, it's probably rectangular." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk15.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3c045b6d07a6635d896789ba37b0d578bd175e92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "But I'll still tack on the identity matrix, and of course, since these have length m, it better be m by m. And now I'll do the reduced row echelon form of this matrix." + }, + { + "text": "And what do I get?" + }, + { + "text": "The reduced row echelon form starts with these columns, starts with the first columns, works like mad, and produces R. Of course, still the same size, m by n, and we did it before." + }, + { + "text": "And then whatever it did to get R, something else is going to show up here." + }, + { + "text": "Let me call it E, m by m. It's whatever you see that E is just going to contain a record of what we did." + }, + { + "text": "We did whatever it took to get A to become R. And at the same time, we were doing it to the identity matrix." + }, + { + "text": "So we started with the identity matrix, we buzzed along." + }, + { + "text": "So we took some -- all this row reduction amounted to multiplying on the left by some matrix, some series of elementary matrices that all together gave us one matrix, and that matrix is E. So all this row reduction stuff amounted to multiplying by E. How do I know that?" + }, + { + "text": "It certainly amounted to multiplying by something, and that something took I to E, so that something was E. So now look at the first part, E A is R. No big deal." + }, + { + "text": "All I've said is that the row reduction steps that we all know well, taking A to R, are in a- in some matrix, and I can find out what that matrix is by just tacking I on and seeing what comes out." + }, + { + "text": "What comes out is E. Let's just review the invertible square case." + }, + { + "text": "What happened then?" + }, + { + "text": "Because I was interested in it in chapter two also." + }, + { + "text": "When A was square and invertible, I took A I, I did row elimination, what was the R that came out?" + }, + { + "text": "It was I." + }, + { + "text": "So in chapter two, in chapter two, R was I." + }, + { + "text": "The row- the reduced row echelon form of a nice invertible square matrix is the identity." + }, + { + "text": "So if R was I in that case, then E was A inverse, because E A is I." + }, + { + "text": "Good." + }, + { + "text": "That's- that was good and easy." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk16.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..c5a8adc4741aeb68371eb235609b24dad795df03 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now what I'm saying is that there still is an E, it's not A inverse anymore, because A is a rectangular, it hasn't got an inverse." + }, + { + "text": "But there is still some matrix E that connected this to this." + }, + { + "text": "Oh, I should have figured out in advance what it was." + }, + { + "text": "Shoot." + }, + { + "text": "I didn't- I did those steps and sort of erased as I went, and, I should have done them to the identity, too." + }, + { + "text": "Can I do that?" + }, + { + "text": "Can I do that?" + }, + { + "text": "I'll keep the identity matrix, like I'm supposed to do, and I'll do the same operations on it and see what I end up with." + }, + { + "text": "Okay." + }, + { + "text": "So I'm starting with the identity, which I'll write in light, light enough, but okay, what did I do?" + }, + { + "text": "I subtracted that row from that one and that row from that one." + }, + { + "text": "Okay, I'll do that to the identity." + }, + { + "text": "So I subtract that first row from row two and row three." + }, + { + "text": "Good." + }, + { + "text": "Then I think I multiply, do you remember, I multiplied row two by minus one?" + }, + { + "text": "Let me just do that." + }, + { + "text": "Then what did I do?" + }, + { + "text": "I subtracted two of row two away from row one." + }, + { + "text": "I better do that." + }, + { + "text": "Subtract two of this away from this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk17.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..368775ffcdaa5a9fe2c24f8c85bcb4963097a79c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's minus one, two of these away leaves a plus two and zero." + }, + { + "text": "I believe that's E. The way to check is to see, multiply that E by this A, just to see, did I do it right?" + }, + { + "text": "So I believe E was minus one, two, zero, one minus one, zero, and minus one, zero, one." + }, + { + "text": "Okay." + }, + { + "text": "That's my E, that's my A, and that's R. All right." + }, + { + "text": "All I'm struggling to do is write the reason I wanted this blasted E was so that I could figure out the left null space." + }, + { + "text": "Not only its dimension, which I know." + }, + { + "text": "Actually, what is the dimension of the left null space?" + }, + { + "text": "Here's my matrix." + }, + { + "text": "What's the rank of the matrix?" + }, + { + "text": "Two." + }, + { + "text": "And the dimension of the left null space is supposed to be M minus R, three minus two, one." + }, + { + "text": "I believe that the left null space is one-dimensional." + }, + { + "text": "There is one combination of those three rows that produces the zero row." + }, + { + "text": "There is a basis." + }, + { + "text": "A basis for the left null space has only got one vector in it." + }, + { + "text": "And what is that vector?" + }, + { + "text": "It's here in the last row of E. But, ah, we could have seen it earlier." + }, + { + "text": "What combination of those rows gives the zero row?" + }, + { + "text": "Minus one of that, plus one of that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk18.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..9f5e8b1fcc2242dbdc56d379cbc7126ada792e31 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a basis for the left null space of this matrix, I'm looking for combinations of rows that give the zero row, if I'm looking at the left null space." + }, + { + "text": "For the null space, I'm looking at combinations of columns to get the zero column." + }, + { + "text": "Now I'm looking at combinations of these three rows to get the zero row, and of course, there is my zero row, and here is my vector that produced it." + }, + { + "text": "Minus one of that row and one of that row." + }, + { + "text": "Obvious." + }, + { + "text": "Okay." + }, + { + "text": "So in that example, and actually in all examples, we have seen how to produce a basis for the left null space." + }, + { + "text": "I won't ask you that all the time." + }, + { + "text": "Because it didn't come out immediately from R, we had to keep track of E for that left null space." + }, + { + "text": "But at least it didn't require us to transpose the matrix and start all over again." + }, + { + "text": "Okay." + }, + { + "text": "Those are the four subspaces." + }, + { + "text": "Can I review them?" + }, + { + "text": "The row space and the null space are in Rn." + }, + { + "text": "Their dimensions add to n. The column space and the left null space are in Rm, and their dimensions add to m. Okay." + }, + { + "text": "So let me close these last minutes by pushing you a little bit more to a new type of vector space." + }, + { + "text": "All our vector spaces, all the ones that we took seriously, have been subspaces of some real three- or n-dimensional space." + }, + { + "text": "Now I'm going to write down another vector space, a new vector space." + }, + { + "text": "Say all three by three matrices." + }, + { + "text": "My matrices are the vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk19.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..c1658ee474fcf6206f54d67e4dededa02a1ef92c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Is that all right?" + }, + { + "text": "I'm just naming them." + }, + { + "text": "You can put quotes around vectors." + }, + { + "text": "Every three by three matrix is one of my vectors." + }, + { + "text": "Now how am I entitled to call those things vectors?" + }, + { + "text": "I mean, they look very much like matrices." + }, + { + "text": "But they're vectors in my vector space because they obey the rules." + }, + { + "text": "All I'm supposed to be able to do with vectors is add them." + }, + { + "text": "I can add matrices." + }, + { + "text": "I'm supposed to be able to multiply them by scalar numbers, like seven." + }, + { + "text": "Well, I can multiply a matrix by seven." + }, + { + "text": "And I can take combinations of matrices." + }, + { + "text": "I can take three of one matrix minus five of another matrix." + }, + { + "text": "And those combinations, there's a zero matrix, the matrix that has all zeros in it." + }, + { + "text": "If I add that to another matrix, it doesn't change it." + }, + { + "text": "All the good stuff." + }, + { + "text": "If I multiply a matrix by one, it doesn't change it." + }, + { + "text": "All those eight rules for a vector space that we never wrote down, all easily satisfied." + }, + { + "text": "So now we have a different --." + }, + { + "text": "Now, of course, you can say you can multiply those matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk2.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..b92bd923d792a0f92ab4de95b7867006e9880f71 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here are the four fundamental subspaces." + }, + { + "text": "This is really the heart of this approach to linear algebra, to see these four subspaces, how they're related." + }, + { + "text": "So what are they?" + }, + { + "text": "The column space, C of A." + }, + { + "text": "The null space, N of A." + }, + { + "text": "And now comes the row space, something new." + }, + { + "text": "The row space, what's in that?" + }, + { + "text": "It's all combinations of the rows." + }, + { + "text": "That's natural." + }, + { + "text": "We want a space, so we have to take all combinations and we start with the rows." + }, + { + "text": "So the rows span the row space." + }, + { + "text": "Are the rows a basis for the row space?" + }, + { + "text": "Maybe so, maybe no." + }, + { + "text": "The rows are a basis for the row space when they're independent." + }, + { + "text": "But if they're dependent, as in this example, my error from last time, they're not, those three rows are not a basis, the row space would only be two-dimensional, I only need two rows for a basis." + }, + { + "text": "So the row space, now what's in it?" + }, + { + "text": "It's all combinations of the rows of A." + }, + { + "text": "All combinations of the rows of A." + }, + { + "text": "But I don't like working with row vectors." + }, + { + "text": "All my vectors have been column vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk20.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..56956e8347a8f8c1f8522690db77860dcc6953b9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "I don't care." + }, + { + "text": "For the moment, I'm only thinking of these matrices as forming a vector space, so I am only doing A plus B and C times A. I'm not interested in A, B for now." + }, + { + "text": "The fact that I can multiply is not relevant to a vector space." + }, + { + "text": "OK, so I have three by three matrices." + }, + { + "text": "And how about subspaces?" + }, + { + "text": "What's, tell me a subspace of this matrix space." + }, + { + "text": "Let me call this matrix space M. That's my matrix space, my space of all three by three matrices." + }, + { + "text": "Tell me a subspace of it." + }, + { + "text": "OK, what about the upper triangular matrices?" + }, + { + "text": "So subspaces, subspaces of M. All upper triangular matrices." + }, + { + "text": "Another subspace." + }, + { + "text": "All symmetric matrices." + }, + { + "text": "The intersection of two subspaces is supposed to be a subspace." + }, + { + "text": "We gave a little effort to the proof of that fact." + }, + { + "text": "If I look at the matrices that are in this subspace, they're symmetric, and they're also in this subspace, they're upper triangular." + }, + { + "text": "What do they look like?" + }, + { + "text": "Well, if they're symmetric, but they have zeros below the diagonal, they better have zeros above the diagonal." + }, + { + "text": "So the intersection would be diagonal matrices." + }, + { + "text": "That's another subspace, smaller than those." + }, + { + "text": "How can I use the word smaller?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk21.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..ffcdd44ed2f644726e04b27114327cb30bc7fb92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, I'm now entitled to use the word smaller." + }, + { + "text": "I mean, well, one way to say is, OK, these are contained in those." + }, + { + "text": "These are contained in those." + }, + { + "text": "But more precisely, I could give the dimension of these spaces." + }, + { + "text": "So I could, we can compute, let's compute it next time." + }, + { + "text": "The dimension of all upper, of the subspace of upper triangular three by three matrices." + }, + { + "text": "The dimension of symmetric three by three matrices." + }, + { + "text": "The dimension of diagonal three by three matrices." + }, + { + "text": "Well, to produce dimension, that means I'm supposed to produce a basis." + }, + { + "text": "And then I just count how many I needed in the basis." + }, + { + "text": "Let me give you the answer for this one." + }, + { + "text": "What's the dimension?" + }, + { + "text": "The dimension of this, say, this subspace, let me call it D, all diagonal matrices." + }, + { + "text": "The dimension of this subspace is, as I write, you're working it out, three." + }, + { + "text": "Because here's a matrix in this, it's a diagonal matrix." + }, + { + "text": "Here's another one." + }, + { + "text": "Here's another one." + }, + { + "text": "Better make it diagonal, let me put a seven there." + }, + { + "text": "That was not a very great choice, but it's three diagonal matrices, and I believe that they're a basis." + }, + { + "text": "I believe that those three matrices are independent, and I believe that any diagonal matrix is a combination of those three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk22.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..8c6bce8cf8085e6544c31ae6926bb7ccf18b983e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk22.json @@ -0,0 +1,20 @@ +[ + { + "text": "So they span the subspace of diagonal matrices." + }, + { + "text": "Do you see that idea?" + }, + { + "text": "It's like stretching the idea from Rn to Rn by n, three by three, but we can still add, we can still multiply by numbers, and we just ignore the fact that we can multiply two matrices together." + }, + { + "text": "Okay." + }, + { + "text": "Thank you." + }, + { + "text": "That's lecture ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk3.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..25f31647b76274f9088c60d1292bcc43915d3fb0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'd like to stay with column vectors." + }, + { + "text": "How can I get to column vectors out of these rows?" + }, + { + "text": "I transpose the matrix." + }, + { + "text": "So if that's OK with you, I'm going to transpose the matrix, I'm going to say all combinations of the columns of A transpose." + }, + { + "text": "And that allows me to use the convenient notation, the column space of A transpose." + }, + { + "text": "Nothing, no mathematics went on there, we just got some vectors that were lying down to stand up." + }, + { + "text": "But it means that we can use this column space of A transpose, that's telling me in a nice matrix notation what the row space is." + }, + { + "text": "OK. And finally is another null space." + }, + { + "text": "The fourth fundamental space will be the null space of A transpose." + }, + { + "text": "The fourth guy is the null space of A transpose." + }, + { + "text": "And of course, my notation is N of A transpose." + }, + { + "text": "That's the null space of A transpose." + }, + { + "text": "Now, we don't have a perfect name for this space as a, as a, connecting with A, but our usual name is the left null space, and I'll show you why in a moment." + }, + { + "text": "So often I call this the, just to write that word, the left null space of A." + }, + { + "text": "So just the way we have the row space of A and we switch it to the column space of A transpose, so we have this space of guys that I call the left null space of A, but the good notation is it's the null space of A transpose." + }, + { + "text": "OK. Those are four spaces." + }, + { + "text": "Where are those spaces?" + }, + { + "text": "What big space are they in for when A is m by n?" + }, + { + "text": "In that case, the null space of A, what's in the null space of A?" + }, + { + "text": "Vectors with n components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk4.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c2575473d88ff4598107e190483f0484b6558678 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Solutions to Ax equals zero." + }, + { + "text": "So the null space of A is n R n. What's in the column space of A?" + }, + { + "text": "Well, columns." + }, + { + "text": "How many components do those columns have?" + }, + { + "text": "m. So this column space is n R m. What about the column space of A transpose, which are just a disguised way of saying the rows of A?" + }, + { + "text": "The rows of A in this three by six matrix have six components, n components." + }, + { + "text": "The column space is n R n. And the null space of A transpose, I see that this fourth space is already getting second, you know, second class citizen treatment and it doesn't deserve it." + }, + { + "text": "It's, it should be there, it is there, and shouldn't be squeezed." + }, + { + "text": "The null space of A transpose, well, if the null space of A had vectors with n components, the null space of A transpose will be n R m. I want to draw a picture of the four spaces." + }, + { + "text": "OK. OK." + }, + { + "text": "Here are the four spaces." + }, + { + "text": "OK, let me put n dimensional space over on this side." + }, + { + "text": "Then which were the subspaces in R n?" + }, + { + "text": "The null space was and the row space was." + }, + { + "text": "So here we have the can I make that picture of the row space?" + }, + { + "text": "And can I make this kind of picture of the null space?" + }, + { + "text": "That's just meant to be a sketch, to remind you that they're in this which, you know, how, what type of vectors are in it?" + }, + { + "text": "Vectors with n components." + }, + { + "text": "Over here, inside consisting of vectors with m components is the column space and what I'm calling the null space of A transpose." + }, + { + "text": "Those are the ones with m components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk5.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..f4e64e208c1a1d8e07a9a66a6a6c59f8c4cbcec8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. To understand these spaces is our job now." + }, + { + "text": "Because by understanding those spaces, we know everything about this half of linear algebra." + }, + { + "text": "What do I mean by understanding those spaces?" + }, + { + "text": "I would like to know a basis for those spaces." + }, + { + "text": "For each one of those spaces, how would I create, construct a basis?" + }, + { + "text": "What systematic way would produce a basis?" + }, + { + "text": "And what's their dimension?" + }, + { + "text": "OK." + }, + { + "text": "So for each of the four spaces, I have to answer those questions." + }, + { + "text": "How do I produce a basis?" + }, + { + "text": "And then, which has a somewhat long answer, and what's the dimension, which is just a number, so it has a real short answer?" + }, + { + "text": "Can I give you the short answer first?" + }, + { + "text": "I shouldn't do it, but here it is." + }, + { + "text": "I can tell you the dimension of the column space." + }, + { + "text": "Let me start with this guy." + }, + { + "text": "What's its dimension?" + }, + { + "text": "I have an m by n matrix." + }, + { + "text": "The dimension of the column space is the rank, R. We actually got to that at the end of the last lecture, but only for an example." + }, + { + "text": "So I really have to say, OK, what's going on there?" + }, + { + "text": "I should produce a basis, and then I just look to see how many vectors I needed in that basis, and the answer will be R. Actually, I'll do that before I get on to the others." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk6.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..ac7425fbe27a77a7e448b576483b4c179e9a31f1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "What's a basis for the column space?" + }, + { + "text": "We've done all the work of row reduction, identifying the pivot columns, the ones that have pivots, the ones that end up with pivots, but now I the pivot columns I'm interested in are columns of A, the original A." + }, + { + "text": "And those pivot columns, there are R of them, the rank R counts those, those are a basis." + }, + { + "text": "So if I answer this question for the column space, the answer will be a basis is the pivot columns, and the dimension is the rank R. And there are pivot columns and everything great." + }, + { + "text": "OK, so that space we pretty well understand." + }, + { + "text": "I probably have a little going back to see that, to prove that this is a right answer, but you know it's the right answer." + }, + { + "text": "Now let me look at the row space." + }, + { + "text": "OK. Shall I tell you the dimension of the row space?" + }, + { + "text": "Yes." + }, + { + "text": "Before we do even an example, let me tell you the dimension of the row space." + }, + { + "text": "Its dimension is also R. The row space and the column space have the same dimension." + }, + { + "text": "That's a wonderful fact." + }, + { + "text": "The dimension of the column space of A transpose, that's the row space, is R. That space is R-dimensional." + }, + { + "text": "And so is this one." + }, + { + "text": "OK. That's the, that's the sort of insight that got used in this example." + }, + { + "text": "If those, if those, if those, are the three columns of a matrix, let me make them the three columns of a matrix by just erasing some brackets, OK, those are the three columns of a matrix, the rank of that matrix, if I look at the columns, it wasn't obvious to me anyway." + }, + { + "text": "But if I look at the rows, it's, now it's obvious." + }, + { + "text": "The row space of that matrix obviously is two-dimensional, because I can, I see a basis for the row space, this row and that row." + }, + { + "text": "And of course, strictly speaking, I'm supposed to transpose those guys, make them stand up." + }, + { + "text": "But the rank is two, and therefore the column space is two-dimensional by this wonderful fact that the row space and column space have the same dimension, and therefore there are only two pivot columns, not three, and, those, the three columns are dependent." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk7.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..7d55c74913379543a71fcc53c971f787baf12a92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, let me bury that error and talk about the row space." + }, + { + "text": "Well, I'm going to give you the dimensions of all the spaces, because that's the, such a nice answer." + }, + { + "text": "OK." + }, + { + "text": "So let me come back here." + }, + { + "text": "So we have this great fact to establish, that the row space, its dimension is also the rank." + }, + { + "text": "OK. What about the null space?" + }, + { + "text": "What's a basis for the null space?" + }, + { + "text": "What's the dimension of the null space?" + }, + { + "text": "Let me, I'll put that answer up here, for the null space." + }, + { + "text": "Well, how have we constructed the null space?" + }, + { + "text": "We took the matrix A, we did those row operations to get it into a form U or even further, we got it into the reduced form R, and then we read off special solutions." + }, + { + "text": "Special solutions, and every special solution came from a free variable." + }, + { + "text": "And those special solutions are in the null space, and the great thing is, they're a basis for it." + }, + { + "text": "So for the null space, a basis will be the special solutions." + }, + { + "text": "And there's one for every free variable, right?" + }, + { + "text": "For each free variable, we give that variable the value one, the other free variable zero." + }, + { + "text": "We get the pivot variables, we get a vector in the -- we get a special solution." + }, + { + "text": "So we get all together n minus R of them, because that's the number of free variables." + }, + { + "text": "If we have R, this is, the dimension is R, is the number of pivot variables, this is the number of free variables." + }, + { + "text": "So the beauty is that those special solutions do form a basis and tell us immediately that the dimension of the null space is n -- I'd better write this well, because it's so nice, n minus R. And you see the nice thing, that the two dimensions in this n-dimensional space, one subspace is R-dimensional, to be proved, that's the row space." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk8.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f4c70532a641ef630aa1f7bca077776017097cd4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "The other subspace is n minus R-dimensional, that's the null space." + }, + { + "text": "And the two dimensions, like, together, give n. The sum of R and n minus R is n. And that's just great." + }, + { + "text": "It's really copying the fact that we have n variables, R of them are pivot variables and n minus R are free variables and n all together." + }, + { + "text": "OK. And now what's the dimension of this poor misbegotten fourth subspace?" + }, + { + "text": "It's got to be m minus R. The dimension of this left null space, left out practically, is m minus R. Well, that's really just saying that this, again, the sum of that plus that is m. And m is correct." + }, + { + "text": "It's the number of columns in A transpose." + }, + { + "text": "A transpose is just as good a matrix as A." + }, + { + "text": "It just happens to be n by m. It happens to have m columns, so it will have m variables, when I go to Ax equals zero, and m of them and R of them will be pivot variables and m minus R will be free variables." + }, + { + "text": "A transpose is as good a matrix as A." + }, + { + "text": "It follows the same rule that this plus the dimension, this dimension plus this dimension adds up to the number of columns." + }, + { + "text": "And over here, A transpose has m columns." + }, + { + "text": "Okay." + }, + { + "text": "Okay, so I gave you the easy answer, the dimensions." + }, + { + "text": "Now can I go back to check on a basis?" + }, + { + "text": "We would like to think that, say, the row space." + }, + { + "text": "Because we've got a basis for the column space." + }, + { + "text": "The pivot columns give a basis for the column space." + }, + { + "text": "Now I'm asking you to look at the row space." + }, + { + "text": "And I you could say, okay, I can produce a basis for the row space by transposing my matrix, making those columns, then doing elimination, row reduction, and checking out the pivot columns in this transposed matrix." + }, + { + "text": "But that means you had to do all that row reduction on A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk9.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..8be162da3ff089e5c511aa65ea7d801c64cad56f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_17_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It ought to be possible, if we take a matrix A, let me take the matrix, maybe we had this matrix in the last lecture, one one one, two one two, three two three, one one one." + }, + { + "text": "Okay." + }, + { + "text": "That, that matrix was so easy, we spotted its pivot columns, one and two, without actually doing row reduction." + }, + { + "text": "But now let's do the job properly." + }, + { + "text": "So I subtract this away from this to produce a zero." + }, + { + "text": "So one two three one is fine." + }, + { + "text": "Subtracting that away leaves me minus one minus one zero, right?" + }, + { + "text": "And subtracting that from the last row, oh, well, that's easy." + }, + { + "text": "Okay, I'm doing row reduction." + }, + { + "text": "Now I've, the first column is all set." + }, + { + "text": "The second column, I now see the pivot, and I can clean up, if I, actually, okay, why don't I make the pivot into a one?" + }, + { + "text": "I'll multiply that row through by minus one, and then I have one one." + }, + { + "text": "That was an elementary operation, I'm allowed." + }, + { + "text": "Multiply a row by a number." + }, + { + "text": "And now I'll do elimination." + }, + { + "text": "Two of those away from that will knock this guy out and make this into a one." + }, + { + "text": "So that's now a zero and that's a one." + }, + { + "text": "Okay." + }, + { + "text": "Done." + }, + { + "text": "That's R. I'm seeing the identity matrix here, I'm seeing zeros below, and I'm seeing F there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk0.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6b8bcce949e11c9807b49a56c5ca68fdb459f818 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay, here is lecture ten in linear algebra." + }, + { + "text": "Two important things to do in this lecture." + }, + { + "text": "One is to correct an error from lecture nine." + }, + { + "text": "So the blackboard with that awful error is still with us." + }, + { + "text": "And the second, the big thing to do is to tell you about the four subspaces that come with a matrix." + }, + { + "text": "We've seen two subspaces, the column space and the null space, there's two to go." + }, + { + "text": "Okay." + }, + { + "text": "First of all, and this is a great way to recap and correct the previous lecture." + }, + { + "text": "So you remember I was just doing R3." + }, + { + "text": "I couldn't have taken a simpler example than R3." + }, + { + "text": "And I wrote down the standard basis." + }, + { + "text": "That's the standard basis." + }, + { + "text": "The basis, the obvious basis for the whole three-dimensional space." + }, + { + "text": "And then I wanted to make the point that there was nothing special, nothing about that basis that another basis couldn't have." + }, + { + "text": "It could have linear independence, it could span a space, there's lots of other bases." + }, + { + "text": "So I started with these vectors one one two and two two five, and those were independent." + }, + { + "text": "And then I said three three seven wouldn't do, because three three seven is the sum of those." + }, + { + "text": "So in my innocence, I put in three three eight." + }, + { + "text": "I figured probably if three three seven is on the plane, is, which I know, it's in the plane with these two, then probably three three eight sticks a little bit out of the plane." + }, + { + "text": "And it's independent and it gives a basis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk1.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..97d9d72b29a5aa923aae0ba9c0fb0da57e9db2ed --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "But after class, to my sorrow, student tells me, wait a minute, that third vector three three eight is not independent." + }, + { + "text": "And why did she say that?" + }, + { + "text": "She didn't actually take the time, didn't have to, to find what combination of this one and this one gives three three eight." + }, + { + "text": "She did something else." + }, + { + "text": "In other words, she looked ahead because she said, wait a minute, if I look at that matrix, it's not invertible." + }, + { + "text": "That third column can't be independent of the first two, because when I look at that matrix, it's got two identical rows." + }, + { + "text": "I have a square matrix." + }, + { + "text": "Its rows are obviously dependent." + }, + { + "text": "And that makes the columns dependent." + }, + { + "text": "So there's my error." + }, + { + "text": "When I look at the matrix A that has those three columns, those three columns can't be independent because that matrix is not invertible because it's got two equal rows." + }, + { + "text": "And today's lecture will reach the conclusion, the great conclusion, that connects the column space with the row space." + }, + { + "text": "So those are the row space is now going to be another one of my fundamental subspaces." + }, + { + "text": "The row space of this matrix or of this one, well, the row space of this one is okay." + }, + { + "text": "But the row space of this one, I'm looking at the rows of the matrix, oh, anyway, I'll have two equal rows and the row space will be only two-dimensional." + }, + { + "text": "The rank of the matrix with these columns will only be two, so only two of those columns can be independent too." + }, + { + "text": "The rows tell me something about the columns, in other words." + }, + { + "text": "Something that I should have noticed and I didn't." + }, + { + "text": "Okay." + }, + { + "text": "So now let me pin down these four fundamental subspaces." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk10.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..8f428ebe86b1b4488558f6fa55b8940ef758b264 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "Okay." + }, + { + "text": "What about its row space?" + }, + { + "text": "What happened to its row space?" + }, + { + "text": "Well, what happened, let me first ask, just because this is, sometimes something does happen." + }, + { + "text": "Its column space changed." + }, + { + "text": "The column space of R is not the column space of A, right?" + }, + { + "text": "Because one one one is certainly in the column space of A and certainly not in the column space of R. I did row operations." + }, + { + "text": "Those row operations preserved the row space, so the row so the column spaces are different." + }, + { + "text": "Different column spaces." + }, + { + "text": "Different column spaces." + }, + { + "text": "But I believe that they have the same row space." + }, + { + "text": "Same row space." + }, + { + "text": "I believe that the row space of that matrix and the row space of this matrix are identical." + }, + { + "text": "They have exactly the same vectors in them." + }, + { + "text": "Those vectors are vectors with four components, right?" + }, + { + "text": "They're all combinations of those rows." + }, + { + "text": "Or I believe you get the same thing by taking all combinations of these rows." + }, + { + "text": "And if true, what's a basis?" + }, + { + "text": "What's a basis for the row space of R?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk11.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..258e5999dbb0aea67696256511eb6b999136132a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it'll be a basis for the row space of the original A." + }, + { + "text": "But it's obviously a basis for the row space of R. What's a basis for the row space of that matrix?" + }, + { + "text": "The first two rows." + }, + { + "text": "So a basis for the row so a basis is for the row space of A or of R is the first R rows of R, not of A." + }, + { + "text": "Sometimes it's true for A, but not necessarily." + }, + { + "text": "But R, we definitely have a matrix here whose row space we can identify." + }, + { + "text": "The row space is spanned by the three rows." + }, + { + "text": "But if we want a basis, we want independence." + }, + { + "text": "So out goes row three." + }, + { + "text": "The row space is also spanned by the first two rows." + }, + { + "text": "This guy didn't contribute anything." + }, + { + "text": "And of course, over here, this one, two, three, one in the bottom didn't contribute anything." + }, + { + "text": "We had it already." + }, + { + "text": "So this, here's a basis, one zero one one and zero one one zero." + }, + { + "text": "I believe those are in the row space." + }, + { + "text": "I know they're independent." + }, + { + "text": "Why are they in the row space?" + }, + { + "text": "Why are those two vectors in the row space?" + }, + { + "text": "Because all those operations we did, which started with these rows and took combinations of them." + }, + { + "text": "I took this row minus this row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk12.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..d05a7eb6e4998c4acd748e3bb7087c68e6e29a80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "That gave me something that's still in the row space." + }, + { + "text": "That's the point." + }, + { + "text": "When I took a row minus a multiple of another row, I'm staying in the row space." + }, + { + "text": "The row space is not changing." + }, + { + "text": "My little basis for it is changing, and I've ended up with, sort of, the best basis." + }, + { + "text": "If the columns of the identity matrix are the best basis for R3 or Rn, the rows of this matrix are the best basis for the row space." + }, + { + "text": "Best in the sense of being as clean as I can make it." + }, + { + "text": "Starting off with the identity and then finishing up with whatever has to be in there." + }, + { + "text": "OK. Do you see, then, that the dimension is R?" + }, + { + "text": "For sure." + }, + { + "text": "Because we've got R pivots, R nonzero rows, we've got the right number of vectors, R. They're in the row space, they're independent, that's it." + }, + { + "text": "They are a basis for the row space." + }, + { + "text": "And we can even pin that down further." + }, + { + "text": "How do I know that every row of A is a combination?" + }, + { + "text": "How do I know they span the row space?" + }, + { + "text": "Oh, well, somebody says I've got the right number of them, so they must, but that's true." + }, + { + "text": "But let me just say, how do I know that this row is a combination of these?" + }, + { + "text": "By just reversing the steps of row reduction." + }, + { + "text": "If I just reverse the steps and go from A, from R back to A, then what do I, what am I doing?" + }, + { + "text": "I'm starting with these rows, I'm taking combinations of them, after a couple of steps, undoing the subtractions that I did before, I'm back to these rows." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk13.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..7b0edabbd24233827c7692f63429589952dac1bc --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "So these rows are combinations of those rows, those rows are combinations of those rows, the two row spaces are the same, the bases are the same, and the natural basis is this guy." + }, + { + "text": "Is that all right for the row space?" + }, + { + "text": "The row space is sitting there in R, in its cleanest possible form." + }, + { + "text": "OK. Now what about the fourth guy, the null space of A transpose?" + }, + { + "text": "First of all, why do I call that the left null space?" + }, + { + "text": "So let me save that and bring that down." + }, + { + "text": "OK." + }, + { + "text": "So the fourth space is the null space of A transpose." + }, + { + "text": "So it has in it vectors, let me call them y, so that A transpose y equals zero." + }, + { + "text": "If A transpose y equals zero, then y is in the null space of A transpose, of course." + }, + { + "text": "So this is a matrix times a column equaling zero." + }, + { + "text": "And now, because I want y to sit on the left, and I want A instead of A transpose, I'll just transpose that equation." + }, + { + "text": "Can I just transpose that?" + }, + { + "text": "On the right, it makes the zero vector lie down." + }, + { + "text": "And on the left, it's a product, A transpose times y." + }, + { + "text": "If I take the transpose, then they come in opposite order, right?" + }, + { + "text": "So it's y transpose times A transpose transpose, but nobody's going to leave it like that." + }, + { + "text": "That's A transpose transpose is just A, of course." + }, + { + "text": "When I transposed A transpose, I got back to A." + }, + { + "text": "Now, do you see what I have now?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk14.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7a889f79409e9a95fbd4cc01518da4b9706c49d1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "I have a row vector, y transpose, multiplying A and multiplying from the left." + }, + { + "text": "That's why I call it the left null space." + }, + { + "text": "But by making it, putting it on the left, I had to make it into a row instead of a column vector." + }, + { + "text": "And so my convention is I usually don't do that, I usually stay with A transpose y equals zero." + }, + { + "text": "OK. And you might ask, how do we get a basis, or I might ask, how do we get a basis for this fourth space, this left null space?" + }, + { + "text": "OK." + }, + { + "text": "I'll do it the example." + }, + { + "text": "As always, ah, not that one." + }, + { + "text": "The left null space is not jumping out at me here." + }, + { + "text": "I know which are the free variables, the special solutions, but those are special solutions to Ax equals zero, and now I'm looking at A transpose and I'm not seeing it here." + }, + { + "text": "So, but somehow you feel that the work that you did, which simplified A to R, should have revealed the left null space too." + }, + { + "text": "And it's slightly less immediate, but it's there." + }, + { + "text": "So from A to R, I took some steps, and I guess I'm interested in what were those steps, or what were all of them together." + }, + { + "text": "I don't want to -- I'm not interested in what particular ones they were." + }, + { + "text": "I'm interested in what was the whole matrix that took me from A to R. How would you find that?" + }, + { + "text": "Do you remember Gauss-Jordan, where you tack on the identity matrix?" + }, + { + "text": "Let's do that again." + }, + { + "text": "So I'll do it above here." + }, + { + "text": "So this is now the idea of I take the matrix A, which is m by n. In Gauss-Jordan, when we saw him before, A was a square invertible matrix and we were finding its inverse." + }, + { + "text": "Now the matrix isn't square, it's probably rectangular." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk15.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3c045b6d07a6635d896789ba37b0d578bd175e92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "But I'll still tack on the identity matrix, and of course, since these have length m, it better be m by m. And now I'll do the reduced row echelon form of this matrix." + }, + { + "text": "And what do I get?" + }, + { + "text": "The reduced row echelon form starts with these columns, starts with the first columns, works like mad, and produces R. Of course, still the same size, m by n, and we did it before." + }, + { + "text": "And then whatever it did to get R, something else is going to show up here." + }, + { + "text": "Let me call it E, m by m. It's whatever you see that E is just going to contain a record of what we did." + }, + { + "text": "We did whatever it took to get A to become R. And at the same time, we were doing it to the identity matrix." + }, + { + "text": "So we started with the identity matrix, we buzzed along." + }, + { + "text": "So we took some -- all this row reduction amounted to multiplying on the left by some matrix, some series of elementary matrices that all together gave us one matrix, and that matrix is E. So all this row reduction stuff amounted to multiplying by E. How do I know that?" + }, + { + "text": "It certainly amounted to multiplying by something, and that something took I to E, so that something was E. So now look at the first part, E A is R. No big deal." + }, + { + "text": "All I've said is that the row reduction steps that we all know well, taking A to R, are in a- in some matrix, and I can find out what that matrix is by just tacking I on and seeing what comes out." + }, + { + "text": "What comes out is E. Let's just review the invertible square case." + }, + { + "text": "What happened then?" + }, + { + "text": "Because I was interested in it in chapter two also." + }, + { + "text": "When A was square and invertible, I took A I, I did row elimination, what was the R that came out?" + }, + { + "text": "It was I." + }, + { + "text": "So in chapter two, in chapter two, R was I." + }, + { + "text": "The row- the reduced row echelon form of a nice invertible square matrix is the identity." + }, + { + "text": "So if R was I in that case, then E was A inverse, because E A is I." + }, + { + "text": "Good." + }, + { + "text": "That's- that was good and easy." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk16.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..c5a8adc4741aeb68371eb235609b24dad795df03 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now what I'm saying is that there still is an E, it's not A inverse anymore, because A is a rectangular, it hasn't got an inverse." + }, + { + "text": "But there is still some matrix E that connected this to this." + }, + { + "text": "Oh, I should have figured out in advance what it was." + }, + { + "text": "Shoot." + }, + { + "text": "I didn't- I did those steps and sort of erased as I went, and, I should have done them to the identity, too." + }, + { + "text": "Can I do that?" + }, + { + "text": "Can I do that?" + }, + { + "text": "I'll keep the identity matrix, like I'm supposed to do, and I'll do the same operations on it and see what I end up with." + }, + { + "text": "Okay." + }, + { + "text": "So I'm starting with the identity, which I'll write in light, light enough, but okay, what did I do?" + }, + { + "text": "I subtracted that row from that one and that row from that one." + }, + { + "text": "Okay, I'll do that to the identity." + }, + { + "text": "So I subtract that first row from row two and row three." + }, + { + "text": "Good." + }, + { + "text": "Then I think I multiply, do you remember, I multiplied row two by minus one?" + }, + { + "text": "Let me just do that." + }, + { + "text": "Then what did I do?" + }, + { + "text": "I subtracted two of row two away from row one." + }, + { + "text": "I better do that." + }, + { + "text": "Subtract two of this away from this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk17.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..368775ffcdaa5a9fe2c24f8c85bcb4963097a79c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's minus one, two of these away leaves a plus two and zero." + }, + { + "text": "I believe that's E. The way to check is to see, multiply that E by this A, just to see, did I do it right?" + }, + { + "text": "So I believe E was minus one, two, zero, one minus one, zero, and minus one, zero, one." + }, + { + "text": "Okay." + }, + { + "text": "That's my E, that's my A, and that's R. All right." + }, + { + "text": "All I'm struggling to do is write the reason I wanted this blasted E was so that I could figure out the left null space." + }, + { + "text": "Not only its dimension, which I know." + }, + { + "text": "Actually, what is the dimension of the left null space?" + }, + { + "text": "Here's my matrix." + }, + { + "text": "What's the rank of the matrix?" + }, + { + "text": "Two." + }, + { + "text": "And the dimension of the left null space is supposed to be M minus R, three minus two, one." + }, + { + "text": "I believe that the left null space is one-dimensional." + }, + { + "text": "There is one combination of those three rows that produces the zero row." + }, + { + "text": "There is a basis." + }, + { + "text": "A basis for the left null space has only got one vector in it." + }, + { + "text": "And what is that vector?" + }, + { + "text": "It's here in the last row of E. But, ah, we could have seen it earlier." + }, + { + "text": "What combination of those rows gives the zero row?" + }, + { + "text": "Minus one of that, plus one of that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk18.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..9f5e8b1fcc2242dbdc56d379cbc7126ada792e31 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a basis for the left null space of this matrix, I'm looking for combinations of rows that give the zero row, if I'm looking at the left null space." + }, + { + "text": "For the null space, I'm looking at combinations of columns to get the zero column." + }, + { + "text": "Now I'm looking at combinations of these three rows to get the zero row, and of course, there is my zero row, and here is my vector that produced it." + }, + { + "text": "Minus one of that row and one of that row." + }, + { + "text": "Obvious." + }, + { + "text": "Okay." + }, + { + "text": "So in that example, and actually in all examples, we have seen how to produce a basis for the left null space." + }, + { + "text": "I won't ask you that all the time." + }, + { + "text": "Because it didn't come out immediately from R, we had to keep track of E for that left null space." + }, + { + "text": "But at least it didn't require us to transpose the matrix and start all over again." + }, + { + "text": "Okay." + }, + { + "text": "Those are the four subspaces." + }, + { + "text": "Can I review them?" + }, + { + "text": "The row space and the null space are in Rn." + }, + { + "text": "Their dimensions add to n. The column space and the left null space are in Rm, and their dimensions add to m. Okay." + }, + { + "text": "So let me close these last minutes by pushing you a little bit more to a new type of vector space." + }, + { + "text": "All our vector spaces, all the ones that we took seriously, have been subspaces of some real three- or n-dimensional space." + }, + { + "text": "Now I'm going to write down another vector space, a new vector space." + }, + { + "text": "Say all three by three matrices." + }, + { + "text": "My matrices are the vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk19.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..c1658ee474fcf6206f54d67e4dededa02a1ef92c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Is that all right?" + }, + { + "text": "I'm just naming them." + }, + { + "text": "You can put quotes around vectors." + }, + { + "text": "Every three by three matrix is one of my vectors." + }, + { + "text": "Now how am I entitled to call those things vectors?" + }, + { + "text": "I mean, they look very much like matrices." + }, + { + "text": "But they're vectors in my vector space because they obey the rules." + }, + { + "text": "All I'm supposed to be able to do with vectors is add them." + }, + { + "text": "I can add matrices." + }, + { + "text": "I'm supposed to be able to multiply them by scalar numbers, like seven." + }, + { + "text": "Well, I can multiply a matrix by seven." + }, + { + "text": "And I can take combinations of matrices." + }, + { + "text": "I can take three of one matrix minus five of another matrix." + }, + { + "text": "And those combinations, there's a zero matrix, the matrix that has all zeros in it." + }, + { + "text": "If I add that to another matrix, it doesn't change it." + }, + { + "text": "All the good stuff." + }, + { + "text": "If I multiply a matrix by one, it doesn't change it." + }, + { + "text": "All those eight rules for a vector space that we never wrote down, all easily satisfied." + }, + { + "text": "So now we have a different --." + }, + { + "text": "Now, of course, you can say you can multiply those matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk2.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..b92bd923d792a0f92ab4de95b7867006e9880f71 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here are the four fundamental subspaces." + }, + { + "text": "This is really the heart of this approach to linear algebra, to see these four subspaces, how they're related." + }, + { + "text": "So what are they?" + }, + { + "text": "The column space, C of A." + }, + { + "text": "The null space, N of A." + }, + { + "text": "And now comes the row space, something new." + }, + { + "text": "The row space, what's in that?" + }, + { + "text": "It's all combinations of the rows." + }, + { + "text": "That's natural." + }, + { + "text": "We want a space, so we have to take all combinations and we start with the rows." + }, + { + "text": "So the rows span the row space." + }, + { + "text": "Are the rows a basis for the row space?" + }, + { + "text": "Maybe so, maybe no." + }, + { + "text": "The rows are a basis for the row space when they're independent." + }, + { + "text": "But if they're dependent, as in this example, my error from last time, they're not, those three rows are not a basis, the row space would only be two-dimensional, I only need two rows for a basis." + }, + { + "text": "So the row space, now what's in it?" + }, + { + "text": "It's all combinations of the rows of A." + }, + { + "text": "All combinations of the rows of A." + }, + { + "text": "But I don't like working with row vectors." + }, + { + "text": "All my vectors have been column vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk20.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..56956e8347a8f8c1f8522690db77860dcc6953b9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "I don't care." + }, + { + "text": "For the moment, I'm only thinking of these matrices as forming a vector space, so I am only doing A plus B and C times A. I'm not interested in A, B for now." + }, + { + "text": "The fact that I can multiply is not relevant to a vector space." + }, + { + "text": "OK, so I have three by three matrices." + }, + { + "text": "And how about subspaces?" + }, + { + "text": "What's, tell me a subspace of this matrix space." + }, + { + "text": "Let me call this matrix space M. That's my matrix space, my space of all three by three matrices." + }, + { + "text": "Tell me a subspace of it." + }, + { + "text": "OK, what about the upper triangular matrices?" + }, + { + "text": "So subspaces, subspaces of M. All upper triangular matrices." + }, + { + "text": "Another subspace." + }, + { + "text": "All symmetric matrices." + }, + { + "text": "The intersection of two subspaces is supposed to be a subspace." + }, + { + "text": "We gave a little effort to the proof of that fact." + }, + { + "text": "If I look at the matrices that are in this subspace, they're symmetric, and they're also in this subspace, they're upper triangular." + }, + { + "text": "What do they look like?" + }, + { + "text": "Well, if they're symmetric, but they have zeros below the diagonal, they better have zeros above the diagonal." + }, + { + "text": "So the intersection would be diagonal matrices." + }, + { + "text": "That's another subspace, smaller than those." + }, + { + "text": "How can I use the word smaller?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk21.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..ffcdd44ed2f644726e04b27114327cb30bc7fb92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, I'm now entitled to use the word smaller." + }, + { + "text": "I mean, well, one way to say is, OK, these are contained in those." + }, + { + "text": "These are contained in those." + }, + { + "text": "But more precisely, I could give the dimension of these spaces." + }, + { + "text": "So I could, we can compute, let's compute it next time." + }, + { + "text": "The dimension of all upper, of the subspace of upper triangular three by three matrices." + }, + { + "text": "The dimension of symmetric three by three matrices." + }, + { + "text": "The dimension of diagonal three by three matrices." + }, + { + "text": "Well, to produce dimension, that means I'm supposed to produce a basis." + }, + { + "text": "And then I just count how many I needed in the basis." + }, + { + "text": "Let me give you the answer for this one." + }, + { + "text": "What's the dimension?" + }, + { + "text": "The dimension of this, say, this subspace, let me call it D, all diagonal matrices." + }, + { + "text": "The dimension of this subspace is, as I write, you're working it out, three." + }, + { + "text": "Because here's a matrix in this, it's a diagonal matrix." + }, + { + "text": "Here's another one." + }, + { + "text": "Here's another one." + }, + { + "text": "Better make it diagonal, let me put a seven there." + }, + { + "text": "That was not a very great choice, but it's three diagonal matrices, and I believe that they're a basis." + }, + { + "text": "I believe that those three matrices are independent, and I believe that any diagonal matrix is a combination of those three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk22.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..8c6bce8cf8085e6544c31ae6926bb7ccf18b983e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk22.json @@ -0,0 +1,20 @@ +[ + { + "text": "So they span the subspace of diagonal matrices." + }, + { + "text": "Do you see that idea?" + }, + { + "text": "It's like stretching the idea from Rn to Rn by n, three by three, but we can still add, we can still multiply by numbers, and we just ignore the fact that we can multiply two matrices together." + }, + { + "text": "Okay." + }, + { + "text": "Thank you." + }, + { + "text": "That's lecture ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk3.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..25f31647b76274f9088c60d1292bcc43915d3fb0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'd like to stay with column vectors." + }, + { + "text": "How can I get to column vectors out of these rows?" + }, + { + "text": "I transpose the matrix." + }, + { + "text": "So if that's OK with you, I'm going to transpose the matrix, I'm going to say all combinations of the columns of A transpose." + }, + { + "text": "And that allows me to use the convenient notation, the column space of A transpose." + }, + { + "text": "Nothing, no mathematics went on there, we just got some vectors that were lying down to stand up." + }, + { + "text": "But it means that we can use this column space of A transpose, that's telling me in a nice matrix notation what the row space is." + }, + { + "text": "OK. And finally is another null space." + }, + { + "text": "The fourth fundamental space will be the null space of A transpose." + }, + { + "text": "The fourth guy is the null space of A transpose." + }, + { + "text": "And of course, my notation is N of A transpose." + }, + { + "text": "That's the null space of A transpose." + }, + { + "text": "Now, we don't have a perfect name for this space as a, as a, connecting with A, but our usual name is the left null space, and I'll show you why in a moment." + }, + { + "text": "So often I call this the, just to write that word, the left null space of A." + }, + { + "text": "So just the way we have the row space of A and we switch it to the column space of A transpose, so we have this space of guys that I call the left null space of A, but the good notation is it's the null space of A transpose." + }, + { + "text": "OK. Those are four spaces." + }, + { + "text": "Where are those spaces?" + }, + { + "text": "What big space are they in for when A is m by n?" + }, + { + "text": "In that case, the null space of A, what's in the null space of A?" + }, + { + "text": "Vectors with n components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk4.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c2575473d88ff4598107e190483f0484b6558678 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Solutions to Ax equals zero." + }, + { + "text": "So the null space of A is n R n. What's in the column space of A?" + }, + { + "text": "Well, columns." + }, + { + "text": "How many components do those columns have?" + }, + { + "text": "m. So this column space is n R m. What about the column space of A transpose, which are just a disguised way of saying the rows of A?" + }, + { + "text": "The rows of A in this three by six matrix have six components, n components." + }, + { + "text": "The column space is n R n. And the null space of A transpose, I see that this fourth space is already getting second, you know, second class citizen treatment and it doesn't deserve it." + }, + { + "text": "It's, it should be there, it is there, and shouldn't be squeezed." + }, + { + "text": "The null space of A transpose, well, if the null space of A had vectors with n components, the null space of A transpose will be n R m. I want to draw a picture of the four spaces." + }, + { + "text": "OK. OK." + }, + { + "text": "Here are the four spaces." + }, + { + "text": "OK, let me put n dimensional space over on this side." + }, + { + "text": "Then which were the subspaces in R n?" + }, + { + "text": "The null space was and the row space was." + }, + { + "text": "So here we have the can I make that picture of the row space?" + }, + { + "text": "And can I make this kind of picture of the null space?" + }, + { + "text": "That's just meant to be a sketch, to remind you that they're in this which, you know, how, what type of vectors are in it?" + }, + { + "text": "Vectors with n components." + }, + { + "text": "Over here, inside consisting of vectors with m components is the column space and what I'm calling the null space of A transpose." + }, + { + "text": "Those are the ones with m components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk5.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..f4e64e208c1a1d8e07a9a66a6a6c59f8c4cbcec8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. To understand these spaces is our job now." + }, + { + "text": "Because by understanding those spaces, we know everything about this half of linear algebra." + }, + { + "text": "What do I mean by understanding those spaces?" + }, + { + "text": "I would like to know a basis for those spaces." + }, + { + "text": "For each one of those spaces, how would I create, construct a basis?" + }, + { + "text": "What systematic way would produce a basis?" + }, + { + "text": "And what's their dimension?" + }, + { + "text": "OK." + }, + { + "text": "So for each of the four spaces, I have to answer those questions." + }, + { + "text": "How do I produce a basis?" + }, + { + "text": "And then, which has a somewhat long answer, and what's the dimension, which is just a number, so it has a real short answer?" + }, + { + "text": "Can I give you the short answer first?" + }, + { + "text": "I shouldn't do it, but here it is." + }, + { + "text": "I can tell you the dimension of the column space." + }, + { + "text": "Let me start with this guy." + }, + { + "text": "What's its dimension?" + }, + { + "text": "I have an m by n matrix." + }, + { + "text": "The dimension of the column space is the rank, R. We actually got to that at the end of the last lecture, but only for an example." + }, + { + "text": "So I really have to say, OK, what's going on there?" + }, + { + "text": "I should produce a basis, and then I just look to see how many vectors I needed in that basis, and the answer will be R. Actually, I'll do that before I get on to the others." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk6.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..ac7425fbe27a77a7e448b576483b4c179e9a31f1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "What's a basis for the column space?" + }, + { + "text": "We've done all the work of row reduction, identifying the pivot columns, the ones that have pivots, the ones that end up with pivots, but now I the pivot columns I'm interested in are columns of A, the original A." + }, + { + "text": "And those pivot columns, there are R of them, the rank R counts those, those are a basis." + }, + { + "text": "So if I answer this question for the column space, the answer will be a basis is the pivot columns, and the dimension is the rank R. And there are pivot columns and everything great." + }, + { + "text": "OK, so that space we pretty well understand." + }, + { + "text": "I probably have a little going back to see that, to prove that this is a right answer, but you know it's the right answer." + }, + { + "text": "Now let me look at the row space." + }, + { + "text": "OK. Shall I tell you the dimension of the row space?" + }, + { + "text": "Yes." + }, + { + "text": "Before we do even an example, let me tell you the dimension of the row space." + }, + { + "text": "Its dimension is also R. The row space and the column space have the same dimension." + }, + { + "text": "That's a wonderful fact." + }, + { + "text": "The dimension of the column space of A transpose, that's the row space, is R. That space is R-dimensional." + }, + { + "text": "And so is this one." + }, + { + "text": "OK. That's the, that's the sort of insight that got used in this example." + }, + { + "text": "If those, if those, if those, are the three columns of a matrix, let me make them the three columns of a matrix by just erasing some brackets, OK, those are the three columns of a matrix, the rank of that matrix, if I look at the columns, it wasn't obvious to me anyway." + }, + { + "text": "But if I look at the rows, it's, now it's obvious." + }, + { + "text": "The row space of that matrix obviously is two-dimensional, because I can, I see a basis for the row space, this row and that row." + }, + { + "text": "And of course, strictly speaking, I'm supposed to transpose those guys, make them stand up." + }, + { + "text": "But the rank is two, and therefore the column space is two-dimensional by this wonderful fact that the row space and column space have the same dimension, and therefore there are only two pivot columns, not three, and, those, the three columns are dependent." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk7.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..7d55c74913379543a71fcc53c971f787baf12a92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, let me bury that error and talk about the row space." + }, + { + "text": "Well, I'm going to give you the dimensions of all the spaces, because that's the, such a nice answer." + }, + { + "text": "OK." + }, + { + "text": "So let me come back here." + }, + { + "text": "So we have this great fact to establish, that the row space, its dimension is also the rank." + }, + { + "text": "OK. What about the null space?" + }, + { + "text": "What's a basis for the null space?" + }, + { + "text": "What's the dimension of the null space?" + }, + { + "text": "Let me, I'll put that answer up here, for the null space." + }, + { + "text": "Well, how have we constructed the null space?" + }, + { + "text": "We took the matrix A, we did those row operations to get it into a form U or even further, we got it into the reduced form R, and then we read off special solutions." + }, + { + "text": "Special solutions, and every special solution came from a free variable." + }, + { + "text": "And those special solutions are in the null space, and the great thing is, they're a basis for it." + }, + { + "text": "So for the null space, a basis will be the special solutions." + }, + { + "text": "And there's one for every free variable, right?" + }, + { + "text": "For each free variable, we give that variable the value one, the other free variable zero." + }, + { + "text": "We get the pivot variables, we get a vector in the -- we get a special solution." + }, + { + "text": "So we get all together n minus R of them, because that's the number of free variables." + }, + { + "text": "If we have R, this is, the dimension is R, is the number of pivot variables, this is the number of free variables." + }, + { + "text": "So the beauty is that those special solutions do form a basis and tell us immediately that the dimension of the null space is n -- I'd better write this well, because it's so nice, n minus R. And you see the nice thing, that the two dimensions in this n-dimensional space, one subspace is R-dimensional, to be proved, that's the row space." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk8.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f4c70532a641ef630aa1f7bca077776017097cd4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "The other subspace is n minus R-dimensional, that's the null space." + }, + { + "text": "And the two dimensions, like, together, give n. The sum of R and n minus R is n. And that's just great." + }, + { + "text": "It's really copying the fact that we have n variables, R of them are pivot variables and n minus R are free variables and n all together." + }, + { + "text": "OK. And now what's the dimension of this poor misbegotten fourth subspace?" + }, + { + "text": "It's got to be m minus R. The dimension of this left null space, left out practically, is m minus R. Well, that's really just saying that this, again, the sum of that plus that is m. And m is correct." + }, + { + "text": "It's the number of columns in A transpose." + }, + { + "text": "A transpose is just as good a matrix as A." + }, + { + "text": "It just happens to be n by m. It happens to have m columns, so it will have m variables, when I go to Ax equals zero, and m of them and R of them will be pivot variables and m minus R will be free variables." + }, + { + "text": "A transpose is as good a matrix as A." + }, + { + "text": "It follows the same rule that this plus the dimension, this dimension plus this dimension adds up to the number of columns." + }, + { + "text": "And over here, A transpose has m columns." + }, + { + "text": "Okay." + }, + { + "text": "Okay, so I gave you the easy answer, the dimensions." + }, + { + "text": "Now can I go back to check on a basis?" + }, + { + "text": "We would like to think that, say, the row space." + }, + { + "text": "Because we've got a basis for the column space." + }, + { + "text": "The pivot columns give a basis for the column space." + }, + { + "text": "Now I'm asking you to look at the row space." + }, + { + "text": "And I you could say, okay, I can produce a basis for the row space by transposing my matrix, making those columns, then doing elimination, row reduction, and checking out the pivot columns in this transposed matrix." + }, + { + "text": "But that means you had to do all that row reduction on A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk9.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..8be162da3ff089e5c511aa65ea7d801c64cad56f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_20_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It ought to be possible, if we take a matrix A, let me take the matrix, maybe we had this matrix in the last lecture, one one one, two one two, three two three, one one one." + }, + { + "text": "Okay." + }, + { + "text": "That, that matrix was so easy, we spotted its pivot columns, one and two, without actually doing row reduction." + }, + { + "text": "But now let's do the job properly." + }, + { + "text": "So I subtract this away from this to produce a zero." + }, + { + "text": "So one two three one is fine." + }, + { + "text": "Subtracting that away leaves me minus one minus one zero, right?" + }, + { + "text": "And subtracting that from the last row, oh, well, that's easy." + }, + { + "text": "Okay, I'm doing row reduction." + }, + { + "text": "Now I've, the first column is all set." + }, + { + "text": "The second column, I now see the pivot, and I can clean up, if I, actually, okay, why don't I make the pivot into a one?" + }, + { + "text": "I'll multiply that row through by minus one, and then I have one one." + }, + { + "text": "That was an elementary operation, I'm allowed." + }, + { + "text": "Multiply a row by a number." + }, + { + "text": "And now I'll do elimination." + }, + { + "text": "Two of those away from that will knock this guy out and make this into a one." + }, + { + "text": "So that's now a zero and that's a one." + }, + { + "text": "Okay." + }, + { + "text": "Done." + }, + { + "text": "That's R. I'm seeing the identity matrix here, I'm seeing zeros below, and I'm seeing F there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk0.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6b8bcce949e11c9807b49a56c5ca68fdb459f818 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay, here is lecture ten in linear algebra." + }, + { + "text": "Two important things to do in this lecture." + }, + { + "text": "One is to correct an error from lecture nine." + }, + { + "text": "So the blackboard with that awful error is still with us." + }, + { + "text": "And the second, the big thing to do is to tell you about the four subspaces that come with a matrix." + }, + { + "text": "We've seen two subspaces, the column space and the null space, there's two to go." + }, + { + "text": "Okay." + }, + { + "text": "First of all, and this is a great way to recap and correct the previous lecture." + }, + { + "text": "So you remember I was just doing R3." + }, + { + "text": "I couldn't have taken a simpler example than R3." + }, + { + "text": "And I wrote down the standard basis." + }, + { + "text": "That's the standard basis." + }, + { + "text": "The basis, the obvious basis for the whole three-dimensional space." + }, + { + "text": "And then I wanted to make the point that there was nothing special, nothing about that basis that another basis couldn't have." + }, + { + "text": "It could have linear independence, it could span a space, there's lots of other bases." + }, + { + "text": "So I started with these vectors one one two and two two five, and those were independent." + }, + { + "text": "And then I said three three seven wouldn't do, because three three seven is the sum of those." + }, + { + "text": "So in my innocence, I put in three three eight." + }, + { + "text": "I figured probably if three three seven is on the plane, is, which I know, it's in the plane with these two, then probably three three eight sticks a little bit out of the plane." + }, + { + "text": "And it's independent and it gives a basis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk1.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..97d9d72b29a5aa923aae0ba9c0fb0da57e9db2ed --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "But after class, to my sorrow, student tells me, wait a minute, that third vector three three eight is not independent." + }, + { + "text": "And why did she say that?" + }, + { + "text": "She didn't actually take the time, didn't have to, to find what combination of this one and this one gives three three eight." + }, + { + "text": "She did something else." + }, + { + "text": "In other words, she looked ahead because she said, wait a minute, if I look at that matrix, it's not invertible." + }, + { + "text": "That third column can't be independent of the first two, because when I look at that matrix, it's got two identical rows." + }, + { + "text": "I have a square matrix." + }, + { + "text": "Its rows are obviously dependent." + }, + { + "text": "And that makes the columns dependent." + }, + { + "text": "So there's my error." + }, + { + "text": "When I look at the matrix A that has those three columns, those three columns can't be independent because that matrix is not invertible because it's got two equal rows." + }, + { + "text": "And today's lecture will reach the conclusion, the great conclusion, that connects the column space with the row space." + }, + { + "text": "So those are the row space is now going to be another one of my fundamental subspaces." + }, + { + "text": "The row space of this matrix or of this one, well, the row space of this one is okay." + }, + { + "text": "But the row space of this one, I'm looking at the rows of the matrix, oh, anyway, I'll have two equal rows and the row space will be only two-dimensional." + }, + { + "text": "The rank of the matrix with these columns will only be two, so only two of those columns can be independent too." + }, + { + "text": "The rows tell me something about the columns, in other words." + }, + { + "text": "Something that I should have noticed and I didn't." + }, + { + "text": "Okay." + }, + { + "text": "So now let me pin down these four fundamental subspaces." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk10.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..8f428ebe86b1b4488558f6fa55b8940ef758b264 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "Okay." + }, + { + "text": "What about its row space?" + }, + { + "text": "What happened to its row space?" + }, + { + "text": "Well, what happened, let me first ask, just because this is, sometimes something does happen." + }, + { + "text": "Its column space changed." + }, + { + "text": "The column space of R is not the column space of A, right?" + }, + { + "text": "Because one one one is certainly in the column space of A and certainly not in the column space of R. I did row operations." + }, + { + "text": "Those row operations preserved the row space, so the row so the column spaces are different." + }, + { + "text": "Different column spaces." + }, + { + "text": "Different column spaces." + }, + { + "text": "But I believe that they have the same row space." + }, + { + "text": "Same row space." + }, + { + "text": "I believe that the row space of that matrix and the row space of this matrix are identical." + }, + { + "text": "They have exactly the same vectors in them." + }, + { + "text": "Those vectors are vectors with four components, right?" + }, + { + "text": "They're all combinations of those rows." + }, + { + "text": "Or I believe you get the same thing by taking all combinations of these rows." + }, + { + "text": "And if true, what's a basis?" + }, + { + "text": "What's a basis for the row space of R?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk11.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..258e5999dbb0aea67696256511eb6b999136132a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it'll be a basis for the row space of the original A." + }, + { + "text": "But it's obviously a basis for the row space of R. What's a basis for the row space of that matrix?" + }, + { + "text": "The first two rows." + }, + { + "text": "So a basis for the row so a basis is for the row space of A or of R is the first R rows of R, not of A." + }, + { + "text": "Sometimes it's true for A, but not necessarily." + }, + { + "text": "But R, we definitely have a matrix here whose row space we can identify." + }, + { + "text": "The row space is spanned by the three rows." + }, + { + "text": "But if we want a basis, we want independence." + }, + { + "text": "So out goes row three." + }, + { + "text": "The row space is also spanned by the first two rows." + }, + { + "text": "This guy didn't contribute anything." + }, + { + "text": "And of course, over here, this one, two, three, one in the bottom didn't contribute anything." + }, + { + "text": "We had it already." + }, + { + "text": "So this, here's a basis, one zero one one and zero one one zero." + }, + { + "text": "I believe those are in the row space." + }, + { + "text": "I know they're independent." + }, + { + "text": "Why are they in the row space?" + }, + { + "text": "Why are those two vectors in the row space?" + }, + { + "text": "Because all those operations we did, which started with these rows and took combinations of them." + }, + { + "text": "I took this row minus this row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk12.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..d05a7eb6e4998c4acd748e3bb7087c68e6e29a80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "That gave me something that's still in the row space." + }, + { + "text": "That's the point." + }, + { + "text": "When I took a row minus a multiple of another row, I'm staying in the row space." + }, + { + "text": "The row space is not changing." + }, + { + "text": "My little basis for it is changing, and I've ended up with, sort of, the best basis." + }, + { + "text": "If the columns of the identity matrix are the best basis for R3 or Rn, the rows of this matrix are the best basis for the row space." + }, + { + "text": "Best in the sense of being as clean as I can make it." + }, + { + "text": "Starting off with the identity and then finishing up with whatever has to be in there." + }, + { + "text": "OK. Do you see, then, that the dimension is R?" + }, + { + "text": "For sure." + }, + { + "text": "Because we've got R pivots, R nonzero rows, we've got the right number of vectors, R. They're in the row space, they're independent, that's it." + }, + { + "text": "They are a basis for the row space." + }, + { + "text": "And we can even pin that down further." + }, + { + "text": "How do I know that every row of A is a combination?" + }, + { + "text": "How do I know they span the row space?" + }, + { + "text": "Oh, well, somebody says I've got the right number of them, so they must, but that's true." + }, + { + "text": "But let me just say, how do I know that this row is a combination of these?" + }, + { + "text": "By just reversing the steps of row reduction." + }, + { + "text": "If I just reverse the steps and go from A, from R back to A, then what do I, what am I doing?" + }, + { + "text": "I'm starting with these rows, I'm taking combinations of them, after a couple of steps, undoing the subtractions that I did before, I'm back to these rows." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk13.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..7b0edabbd24233827c7692f63429589952dac1bc --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "So these rows are combinations of those rows, those rows are combinations of those rows, the two row spaces are the same, the bases are the same, and the natural basis is this guy." + }, + { + "text": "Is that all right for the row space?" + }, + { + "text": "The row space is sitting there in R, in its cleanest possible form." + }, + { + "text": "OK. Now what about the fourth guy, the null space of A transpose?" + }, + { + "text": "First of all, why do I call that the left null space?" + }, + { + "text": "So let me save that and bring that down." + }, + { + "text": "OK." + }, + { + "text": "So the fourth space is the null space of A transpose." + }, + { + "text": "So it has in it vectors, let me call them y, so that A transpose y equals zero." + }, + { + "text": "If A transpose y equals zero, then y is in the null space of A transpose, of course." + }, + { + "text": "So this is a matrix times a column equaling zero." + }, + { + "text": "And now, because I want y to sit on the left, and I want A instead of A transpose, I'll just transpose that equation." + }, + { + "text": "Can I just transpose that?" + }, + { + "text": "On the right, it makes the zero vector lie down." + }, + { + "text": "And on the left, it's a product, A transpose times y." + }, + { + "text": "If I take the transpose, then they come in opposite order, right?" + }, + { + "text": "So it's y transpose times A transpose transpose, but nobody's going to leave it like that." + }, + { + "text": "That's A transpose transpose is just A, of course." + }, + { + "text": "When I transposed A transpose, I got back to A." + }, + { + "text": "Now, do you see what I have now?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk14.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7a889f79409e9a95fbd4cc01518da4b9706c49d1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "I have a row vector, y transpose, multiplying A and multiplying from the left." + }, + { + "text": "That's why I call it the left null space." + }, + { + "text": "But by making it, putting it on the left, I had to make it into a row instead of a column vector." + }, + { + "text": "And so my convention is I usually don't do that, I usually stay with A transpose y equals zero." + }, + { + "text": "OK. And you might ask, how do we get a basis, or I might ask, how do we get a basis for this fourth space, this left null space?" + }, + { + "text": "OK." + }, + { + "text": "I'll do it the example." + }, + { + "text": "As always, ah, not that one." + }, + { + "text": "The left null space is not jumping out at me here." + }, + { + "text": "I know which are the free variables, the special solutions, but those are special solutions to Ax equals zero, and now I'm looking at A transpose and I'm not seeing it here." + }, + { + "text": "So, but somehow you feel that the work that you did, which simplified A to R, should have revealed the left null space too." + }, + { + "text": "And it's slightly less immediate, but it's there." + }, + { + "text": "So from A to R, I took some steps, and I guess I'm interested in what were those steps, or what were all of them together." + }, + { + "text": "I don't want to -- I'm not interested in what particular ones they were." + }, + { + "text": "I'm interested in what was the whole matrix that took me from A to R. How would you find that?" + }, + { + "text": "Do you remember Gauss-Jordan, where you tack on the identity matrix?" + }, + { + "text": "Let's do that again." + }, + { + "text": "So I'll do it above here." + }, + { + "text": "So this is now the idea of I take the matrix A, which is m by n. In Gauss-Jordan, when we saw him before, A was a square invertible matrix and we were finding its inverse." + }, + { + "text": "Now the matrix isn't square, it's probably rectangular." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk15.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3c045b6d07a6635d896789ba37b0d578bd175e92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "But I'll still tack on the identity matrix, and of course, since these have length m, it better be m by m. And now I'll do the reduced row echelon form of this matrix." + }, + { + "text": "And what do I get?" + }, + { + "text": "The reduced row echelon form starts with these columns, starts with the first columns, works like mad, and produces R. Of course, still the same size, m by n, and we did it before." + }, + { + "text": "And then whatever it did to get R, something else is going to show up here." + }, + { + "text": "Let me call it E, m by m. It's whatever you see that E is just going to contain a record of what we did." + }, + { + "text": "We did whatever it took to get A to become R. And at the same time, we were doing it to the identity matrix." + }, + { + "text": "So we started with the identity matrix, we buzzed along." + }, + { + "text": "So we took some -- all this row reduction amounted to multiplying on the left by some matrix, some series of elementary matrices that all together gave us one matrix, and that matrix is E. So all this row reduction stuff amounted to multiplying by E. How do I know that?" + }, + { + "text": "It certainly amounted to multiplying by something, and that something took I to E, so that something was E. So now look at the first part, E A is R. No big deal." + }, + { + "text": "All I've said is that the row reduction steps that we all know well, taking A to R, are in a- in some matrix, and I can find out what that matrix is by just tacking I on and seeing what comes out." + }, + { + "text": "What comes out is E. Let's just review the invertible square case." + }, + { + "text": "What happened then?" + }, + { + "text": "Because I was interested in it in chapter two also." + }, + { + "text": "When A was square and invertible, I took A I, I did row elimination, what was the R that came out?" + }, + { + "text": "It was I." + }, + { + "text": "So in chapter two, in chapter two, R was I." + }, + { + "text": "The row- the reduced row echelon form of a nice invertible square matrix is the identity." + }, + { + "text": "So if R was I in that case, then E was A inverse, because E A is I." + }, + { + "text": "Good." + }, + { + "text": "That's- that was good and easy." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk16.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..c5a8adc4741aeb68371eb235609b24dad795df03 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now what I'm saying is that there still is an E, it's not A inverse anymore, because A is a rectangular, it hasn't got an inverse." + }, + { + "text": "But there is still some matrix E that connected this to this." + }, + { + "text": "Oh, I should have figured out in advance what it was." + }, + { + "text": "Shoot." + }, + { + "text": "I didn't- I did those steps and sort of erased as I went, and, I should have done them to the identity, too." + }, + { + "text": "Can I do that?" + }, + { + "text": "Can I do that?" + }, + { + "text": "I'll keep the identity matrix, like I'm supposed to do, and I'll do the same operations on it and see what I end up with." + }, + { + "text": "Okay." + }, + { + "text": "So I'm starting with the identity, which I'll write in light, light enough, but okay, what did I do?" + }, + { + "text": "I subtracted that row from that one and that row from that one." + }, + { + "text": "Okay, I'll do that to the identity." + }, + { + "text": "So I subtract that first row from row two and row three." + }, + { + "text": "Good." + }, + { + "text": "Then I think I multiply, do you remember, I multiplied row two by minus one?" + }, + { + "text": "Let me just do that." + }, + { + "text": "Then what did I do?" + }, + { + "text": "I subtracted two of row two away from row one." + }, + { + "text": "I better do that." + }, + { + "text": "Subtract two of this away from this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk17.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..368775ffcdaa5a9fe2c24f8c85bcb4963097a79c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's minus one, two of these away leaves a plus two and zero." + }, + { + "text": "I believe that's E. The way to check is to see, multiply that E by this A, just to see, did I do it right?" + }, + { + "text": "So I believe E was minus one, two, zero, one minus one, zero, and minus one, zero, one." + }, + { + "text": "Okay." + }, + { + "text": "That's my E, that's my A, and that's R. All right." + }, + { + "text": "All I'm struggling to do is write the reason I wanted this blasted E was so that I could figure out the left null space." + }, + { + "text": "Not only its dimension, which I know." + }, + { + "text": "Actually, what is the dimension of the left null space?" + }, + { + "text": "Here's my matrix." + }, + { + "text": "What's the rank of the matrix?" + }, + { + "text": "Two." + }, + { + "text": "And the dimension of the left null space is supposed to be M minus R, three minus two, one." + }, + { + "text": "I believe that the left null space is one-dimensional." + }, + { + "text": "There is one combination of those three rows that produces the zero row." + }, + { + "text": "There is a basis." + }, + { + "text": "A basis for the left null space has only got one vector in it." + }, + { + "text": "And what is that vector?" + }, + { + "text": "It's here in the last row of E. But, ah, we could have seen it earlier." + }, + { + "text": "What combination of those rows gives the zero row?" + }, + { + "text": "Minus one of that, plus one of that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk18.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..9f5e8b1fcc2242dbdc56d379cbc7126ada792e31 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a basis for the left null space of this matrix, I'm looking for combinations of rows that give the zero row, if I'm looking at the left null space." + }, + { + "text": "For the null space, I'm looking at combinations of columns to get the zero column." + }, + { + "text": "Now I'm looking at combinations of these three rows to get the zero row, and of course, there is my zero row, and here is my vector that produced it." + }, + { + "text": "Minus one of that row and one of that row." + }, + { + "text": "Obvious." + }, + { + "text": "Okay." + }, + { + "text": "So in that example, and actually in all examples, we have seen how to produce a basis for the left null space." + }, + { + "text": "I won't ask you that all the time." + }, + { + "text": "Because it didn't come out immediately from R, we had to keep track of E for that left null space." + }, + { + "text": "But at least it didn't require us to transpose the matrix and start all over again." + }, + { + "text": "Okay." + }, + { + "text": "Those are the four subspaces." + }, + { + "text": "Can I review them?" + }, + { + "text": "The row space and the null space are in Rn." + }, + { + "text": "Their dimensions add to n. The column space and the left null space are in Rm, and their dimensions add to m. Okay." + }, + { + "text": "So let me close these last minutes by pushing you a little bit more to a new type of vector space." + }, + { + "text": "All our vector spaces, all the ones that we took seriously, have been subspaces of some real three- or n-dimensional space." + }, + { + "text": "Now I'm going to write down another vector space, a new vector space." + }, + { + "text": "Say all three by three matrices." + }, + { + "text": "My matrices are the vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk19.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..c1658ee474fcf6206f54d67e4dededa02a1ef92c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Is that all right?" + }, + { + "text": "I'm just naming them." + }, + { + "text": "You can put quotes around vectors." + }, + { + "text": "Every three by three matrix is one of my vectors." + }, + { + "text": "Now how am I entitled to call those things vectors?" + }, + { + "text": "I mean, they look very much like matrices." + }, + { + "text": "But they're vectors in my vector space because they obey the rules." + }, + { + "text": "All I'm supposed to be able to do with vectors is add them." + }, + { + "text": "I can add matrices." + }, + { + "text": "I'm supposed to be able to multiply them by scalar numbers, like seven." + }, + { + "text": "Well, I can multiply a matrix by seven." + }, + { + "text": "And I can take combinations of matrices." + }, + { + "text": "I can take three of one matrix minus five of another matrix." + }, + { + "text": "And those combinations, there's a zero matrix, the matrix that has all zeros in it." + }, + { + "text": "If I add that to another matrix, it doesn't change it." + }, + { + "text": "All the good stuff." + }, + { + "text": "If I multiply a matrix by one, it doesn't change it." + }, + { + "text": "All those eight rules for a vector space that we never wrote down, all easily satisfied." + }, + { + "text": "So now we have a different --." + }, + { + "text": "Now, of course, you can say you can multiply those matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk2.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..b92bd923d792a0f92ab4de95b7867006e9880f71 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here are the four fundamental subspaces." + }, + { + "text": "This is really the heart of this approach to linear algebra, to see these four subspaces, how they're related." + }, + { + "text": "So what are they?" + }, + { + "text": "The column space, C of A." + }, + { + "text": "The null space, N of A." + }, + { + "text": "And now comes the row space, something new." + }, + { + "text": "The row space, what's in that?" + }, + { + "text": "It's all combinations of the rows." + }, + { + "text": "That's natural." + }, + { + "text": "We want a space, so we have to take all combinations and we start with the rows." + }, + { + "text": "So the rows span the row space." + }, + { + "text": "Are the rows a basis for the row space?" + }, + { + "text": "Maybe so, maybe no." + }, + { + "text": "The rows are a basis for the row space when they're independent." + }, + { + "text": "But if they're dependent, as in this example, my error from last time, they're not, those three rows are not a basis, the row space would only be two-dimensional, I only need two rows for a basis." + }, + { + "text": "So the row space, now what's in it?" + }, + { + "text": "It's all combinations of the rows of A." + }, + { + "text": "All combinations of the rows of A." + }, + { + "text": "But I don't like working with row vectors." + }, + { + "text": "All my vectors have been column vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk20.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..56956e8347a8f8c1f8522690db77860dcc6953b9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "I don't care." + }, + { + "text": "For the moment, I'm only thinking of these matrices as forming a vector space, so I am only doing A plus B and C times A. I'm not interested in A, B for now." + }, + { + "text": "The fact that I can multiply is not relevant to a vector space." + }, + { + "text": "OK, so I have three by three matrices." + }, + { + "text": "And how about subspaces?" + }, + { + "text": "What's, tell me a subspace of this matrix space." + }, + { + "text": "Let me call this matrix space M. That's my matrix space, my space of all three by three matrices." + }, + { + "text": "Tell me a subspace of it." + }, + { + "text": "OK, what about the upper triangular matrices?" + }, + { + "text": "So subspaces, subspaces of M. All upper triangular matrices." + }, + { + "text": "Another subspace." + }, + { + "text": "All symmetric matrices." + }, + { + "text": "The intersection of two subspaces is supposed to be a subspace." + }, + { + "text": "We gave a little effort to the proof of that fact." + }, + { + "text": "If I look at the matrices that are in this subspace, they're symmetric, and they're also in this subspace, they're upper triangular." + }, + { + "text": "What do they look like?" + }, + { + "text": "Well, if they're symmetric, but they have zeros below the diagonal, they better have zeros above the diagonal." + }, + { + "text": "So the intersection would be diagonal matrices." + }, + { + "text": "That's another subspace, smaller than those." + }, + { + "text": "How can I use the word smaller?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk21.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..ffcdd44ed2f644726e04b27114327cb30bc7fb92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, I'm now entitled to use the word smaller." + }, + { + "text": "I mean, well, one way to say is, OK, these are contained in those." + }, + { + "text": "These are contained in those." + }, + { + "text": "But more precisely, I could give the dimension of these spaces." + }, + { + "text": "So I could, we can compute, let's compute it next time." + }, + { + "text": "The dimension of all upper, of the subspace of upper triangular three by three matrices." + }, + { + "text": "The dimension of symmetric three by three matrices." + }, + { + "text": "The dimension of diagonal three by three matrices." + }, + { + "text": "Well, to produce dimension, that means I'm supposed to produce a basis." + }, + { + "text": "And then I just count how many I needed in the basis." + }, + { + "text": "Let me give you the answer for this one." + }, + { + "text": "What's the dimension?" + }, + { + "text": "The dimension of this, say, this subspace, let me call it D, all diagonal matrices." + }, + { + "text": "The dimension of this subspace is, as I write, you're working it out, three." + }, + { + "text": "Because here's a matrix in this, it's a diagonal matrix." + }, + { + "text": "Here's another one." + }, + { + "text": "Here's another one." + }, + { + "text": "Better make it diagonal, let me put a seven there." + }, + { + "text": "That was not a very great choice, but it's three diagonal matrices, and I believe that they're a basis." + }, + { + "text": "I believe that those three matrices are independent, and I believe that any diagonal matrix is a combination of those three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk22.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..8c6bce8cf8085e6544c31ae6926bb7ccf18b983e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk22.json @@ -0,0 +1,20 @@ +[ + { + "text": "So they span the subspace of diagonal matrices." + }, + { + "text": "Do you see that idea?" + }, + { + "text": "It's like stretching the idea from Rn to Rn by n, three by three, but we can still add, we can still multiply by numbers, and we just ignore the fact that we can multiply two matrices together." + }, + { + "text": "Okay." + }, + { + "text": "Thank you." + }, + { + "text": "That's lecture ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk3.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..25f31647b76274f9088c60d1292bcc43915d3fb0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'd like to stay with column vectors." + }, + { + "text": "How can I get to column vectors out of these rows?" + }, + { + "text": "I transpose the matrix." + }, + { + "text": "So if that's OK with you, I'm going to transpose the matrix, I'm going to say all combinations of the columns of A transpose." + }, + { + "text": "And that allows me to use the convenient notation, the column space of A transpose." + }, + { + "text": "Nothing, no mathematics went on there, we just got some vectors that were lying down to stand up." + }, + { + "text": "But it means that we can use this column space of A transpose, that's telling me in a nice matrix notation what the row space is." + }, + { + "text": "OK. And finally is another null space." + }, + { + "text": "The fourth fundamental space will be the null space of A transpose." + }, + { + "text": "The fourth guy is the null space of A transpose." + }, + { + "text": "And of course, my notation is N of A transpose." + }, + { + "text": "That's the null space of A transpose." + }, + { + "text": "Now, we don't have a perfect name for this space as a, as a, connecting with A, but our usual name is the left null space, and I'll show you why in a moment." + }, + { + "text": "So often I call this the, just to write that word, the left null space of A." + }, + { + "text": "So just the way we have the row space of A and we switch it to the column space of A transpose, so we have this space of guys that I call the left null space of A, but the good notation is it's the null space of A transpose." + }, + { + "text": "OK. Those are four spaces." + }, + { + "text": "Where are those spaces?" + }, + { + "text": "What big space are they in for when A is m by n?" + }, + { + "text": "In that case, the null space of A, what's in the null space of A?" + }, + { + "text": "Vectors with n components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk4.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c2575473d88ff4598107e190483f0484b6558678 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Solutions to Ax equals zero." + }, + { + "text": "So the null space of A is n R n. What's in the column space of A?" + }, + { + "text": "Well, columns." + }, + { + "text": "How many components do those columns have?" + }, + { + "text": "m. So this column space is n R m. What about the column space of A transpose, which are just a disguised way of saying the rows of A?" + }, + { + "text": "The rows of A in this three by six matrix have six components, n components." + }, + { + "text": "The column space is n R n. And the null space of A transpose, I see that this fourth space is already getting second, you know, second class citizen treatment and it doesn't deserve it." + }, + { + "text": "It's, it should be there, it is there, and shouldn't be squeezed." + }, + { + "text": "The null space of A transpose, well, if the null space of A had vectors with n components, the null space of A transpose will be n R m. I want to draw a picture of the four spaces." + }, + { + "text": "OK. OK." + }, + { + "text": "Here are the four spaces." + }, + { + "text": "OK, let me put n dimensional space over on this side." + }, + { + "text": "Then which were the subspaces in R n?" + }, + { + "text": "The null space was and the row space was." + }, + { + "text": "So here we have the can I make that picture of the row space?" + }, + { + "text": "And can I make this kind of picture of the null space?" + }, + { + "text": "That's just meant to be a sketch, to remind you that they're in this which, you know, how, what type of vectors are in it?" + }, + { + "text": "Vectors with n components." + }, + { + "text": "Over here, inside consisting of vectors with m components is the column space and what I'm calling the null space of A transpose." + }, + { + "text": "Those are the ones with m components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk5.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..f4e64e208c1a1d8e07a9a66a6a6c59f8c4cbcec8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. To understand these spaces is our job now." + }, + { + "text": "Because by understanding those spaces, we know everything about this half of linear algebra." + }, + { + "text": "What do I mean by understanding those spaces?" + }, + { + "text": "I would like to know a basis for those spaces." + }, + { + "text": "For each one of those spaces, how would I create, construct a basis?" + }, + { + "text": "What systematic way would produce a basis?" + }, + { + "text": "And what's their dimension?" + }, + { + "text": "OK." + }, + { + "text": "So for each of the four spaces, I have to answer those questions." + }, + { + "text": "How do I produce a basis?" + }, + { + "text": "And then, which has a somewhat long answer, and what's the dimension, which is just a number, so it has a real short answer?" + }, + { + "text": "Can I give you the short answer first?" + }, + { + "text": "I shouldn't do it, but here it is." + }, + { + "text": "I can tell you the dimension of the column space." + }, + { + "text": "Let me start with this guy." + }, + { + "text": "What's its dimension?" + }, + { + "text": "I have an m by n matrix." + }, + { + "text": "The dimension of the column space is the rank, R. We actually got to that at the end of the last lecture, but only for an example." + }, + { + "text": "So I really have to say, OK, what's going on there?" + }, + { + "text": "I should produce a basis, and then I just look to see how many vectors I needed in that basis, and the answer will be R. Actually, I'll do that before I get on to the others." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk6.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..ac7425fbe27a77a7e448b576483b4c179e9a31f1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "What's a basis for the column space?" + }, + { + "text": "We've done all the work of row reduction, identifying the pivot columns, the ones that have pivots, the ones that end up with pivots, but now I the pivot columns I'm interested in are columns of A, the original A." + }, + { + "text": "And those pivot columns, there are R of them, the rank R counts those, those are a basis." + }, + { + "text": "So if I answer this question for the column space, the answer will be a basis is the pivot columns, and the dimension is the rank R. And there are pivot columns and everything great." + }, + { + "text": "OK, so that space we pretty well understand." + }, + { + "text": "I probably have a little going back to see that, to prove that this is a right answer, but you know it's the right answer." + }, + { + "text": "Now let me look at the row space." + }, + { + "text": "OK. Shall I tell you the dimension of the row space?" + }, + { + "text": "Yes." + }, + { + "text": "Before we do even an example, let me tell you the dimension of the row space." + }, + { + "text": "Its dimension is also R. The row space and the column space have the same dimension." + }, + { + "text": "That's a wonderful fact." + }, + { + "text": "The dimension of the column space of A transpose, that's the row space, is R. That space is R-dimensional." + }, + { + "text": "And so is this one." + }, + { + "text": "OK. That's the, that's the sort of insight that got used in this example." + }, + { + "text": "If those, if those, if those, are the three columns of a matrix, let me make them the three columns of a matrix by just erasing some brackets, OK, those are the three columns of a matrix, the rank of that matrix, if I look at the columns, it wasn't obvious to me anyway." + }, + { + "text": "But if I look at the rows, it's, now it's obvious." + }, + { + "text": "The row space of that matrix obviously is two-dimensional, because I can, I see a basis for the row space, this row and that row." + }, + { + "text": "And of course, strictly speaking, I'm supposed to transpose those guys, make them stand up." + }, + { + "text": "But the rank is two, and therefore the column space is two-dimensional by this wonderful fact that the row space and column space have the same dimension, and therefore there are only two pivot columns, not three, and, those, the three columns are dependent." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk7.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..7d55c74913379543a71fcc53c971f787baf12a92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, let me bury that error and talk about the row space." + }, + { + "text": "Well, I'm going to give you the dimensions of all the spaces, because that's the, such a nice answer." + }, + { + "text": "OK." + }, + { + "text": "So let me come back here." + }, + { + "text": "So we have this great fact to establish, that the row space, its dimension is also the rank." + }, + { + "text": "OK. What about the null space?" + }, + { + "text": "What's a basis for the null space?" + }, + { + "text": "What's the dimension of the null space?" + }, + { + "text": "Let me, I'll put that answer up here, for the null space." + }, + { + "text": "Well, how have we constructed the null space?" + }, + { + "text": "We took the matrix A, we did those row operations to get it into a form U or even further, we got it into the reduced form R, and then we read off special solutions." + }, + { + "text": "Special solutions, and every special solution came from a free variable." + }, + { + "text": "And those special solutions are in the null space, and the great thing is, they're a basis for it." + }, + { + "text": "So for the null space, a basis will be the special solutions." + }, + { + "text": "And there's one for every free variable, right?" + }, + { + "text": "For each free variable, we give that variable the value one, the other free variable zero." + }, + { + "text": "We get the pivot variables, we get a vector in the -- we get a special solution." + }, + { + "text": "So we get all together n minus R of them, because that's the number of free variables." + }, + { + "text": "If we have R, this is, the dimension is R, is the number of pivot variables, this is the number of free variables." + }, + { + "text": "So the beauty is that those special solutions do form a basis and tell us immediately that the dimension of the null space is n -- I'd better write this well, because it's so nice, n minus R. And you see the nice thing, that the two dimensions in this n-dimensional space, one subspace is R-dimensional, to be proved, that's the row space." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk8.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f4c70532a641ef630aa1f7bca077776017097cd4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "The other subspace is n minus R-dimensional, that's the null space." + }, + { + "text": "And the two dimensions, like, together, give n. The sum of R and n minus R is n. And that's just great." + }, + { + "text": "It's really copying the fact that we have n variables, R of them are pivot variables and n minus R are free variables and n all together." + }, + { + "text": "OK. And now what's the dimension of this poor misbegotten fourth subspace?" + }, + { + "text": "It's got to be m minus R. The dimension of this left null space, left out practically, is m minus R. Well, that's really just saying that this, again, the sum of that plus that is m. And m is correct." + }, + { + "text": "It's the number of columns in A transpose." + }, + { + "text": "A transpose is just as good a matrix as A." + }, + { + "text": "It just happens to be n by m. It happens to have m columns, so it will have m variables, when I go to Ax equals zero, and m of them and R of them will be pivot variables and m minus R will be free variables." + }, + { + "text": "A transpose is as good a matrix as A." + }, + { + "text": "It follows the same rule that this plus the dimension, this dimension plus this dimension adds up to the number of columns." + }, + { + "text": "And over here, A transpose has m columns." + }, + { + "text": "Okay." + }, + { + "text": "Okay, so I gave you the easy answer, the dimensions." + }, + { + "text": "Now can I go back to check on a basis?" + }, + { + "text": "We would like to think that, say, the row space." + }, + { + "text": "Because we've got a basis for the column space." + }, + { + "text": "The pivot columns give a basis for the column space." + }, + { + "text": "Now I'm asking you to look at the row space." + }, + { + "text": "And I you could say, okay, I can produce a basis for the row space by transposing my matrix, making those columns, then doing elimination, row reduction, and checking out the pivot columns in this transposed matrix." + }, + { + "text": "But that means you had to do all that row reduction on A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk9.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..8be162da3ff089e5c511aa65ea7d801c64cad56f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_21_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It ought to be possible, if we take a matrix A, let me take the matrix, maybe we had this matrix in the last lecture, one one one, two one two, three two three, one one one." + }, + { + "text": "Okay." + }, + { + "text": "That, that matrix was so easy, we spotted its pivot columns, one and two, without actually doing row reduction." + }, + { + "text": "But now let's do the job properly." + }, + { + "text": "So I subtract this away from this to produce a zero." + }, + { + "text": "So one two three one is fine." + }, + { + "text": "Subtracting that away leaves me minus one minus one zero, right?" + }, + { + "text": "And subtracting that from the last row, oh, well, that's easy." + }, + { + "text": "Okay, I'm doing row reduction." + }, + { + "text": "Now I've, the first column is all set." + }, + { + "text": "The second column, I now see the pivot, and I can clean up, if I, actually, okay, why don't I make the pivot into a one?" + }, + { + "text": "I'll multiply that row through by minus one, and then I have one one." + }, + { + "text": "That was an elementary operation, I'm allowed." + }, + { + "text": "Multiply a row by a number." + }, + { + "text": "And now I'll do elimination." + }, + { + "text": "Two of those away from that will knock this guy out and make this into a one." + }, + { + "text": "So that's now a zero and that's a one." + }, + { + "text": "Okay." + }, + { + "text": "Done." + }, + { + "text": "That's R. I'm seeing the identity matrix here, I'm seeing zeros below, and I'm seeing F there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk0.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6b8bcce949e11c9807b49a56c5ca68fdb459f818 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay, here is lecture ten in linear algebra." + }, + { + "text": "Two important things to do in this lecture." + }, + { + "text": "One is to correct an error from lecture nine." + }, + { + "text": "So the blackboard with that awful error is still with us." + }, + { + "text": "And the second, the big thing to do is to tell you about the four subspaces that come with a matrix." + }, + { + "text": "We've seen two subspaces, the column space and the null space, there's two to go." + }, + { + "text": "Okay." + }, + { + "text": "First of all, and this is a great way to recap and correct the previous lecture." + }, + { + "text": "So you remember I was just doing R3." + }, + { + "text": "I couldn't have taken a simpler example than R3." + }, + { + "text": "And I wrote down the standard basis." + }, + { + "text": "That's the standard basis." + }, + { + "text": "The basis, the obvious basis for the whole three-dimensional space." + }, + { + "text": "And then I wanted to make the point that there was nothing special, nothing about that basis that another basis couldn't have." + }, + { + "text": "It could have linear independence, it could span a space, there's lots of other bases." + }, + { + "text": "So I started with these vectors one one two and two two five, and those were independent." + }, + { + "text": "And then I said three three seven wouldn't do, because three three seven is the sum of those." + }, + { + "text": "So in my innocence, I put in three three eight." + }, + { + "text": "I figured probably if three three seven is on the plane, is, which I know, it's in the plane with these two, then probably three three eight sticks a little bit out of the plane." + }, + { + "text": "And it's independent and it gives a basis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk1.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..97d9d72b29a5aa923aae0ba9c0fb0da57e9db2ed --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "But after class, to my sorrow, student tells me, wait a minute, that third vector three three eight is not independent." + }, + { + "text": "And why did she say that?" + }, + { + "text": "She didn't actually take the time, didn't have to, to find what combination of this one and this one gives three three eight." + }, + { + "text": "She did something else." + }, + { + "text": "In other words, she looked ahead because she said, wait a minute, if I look at that matrix, it's not invertible." + }, + { + "text": "That third column can't be independent of the first two, because when I look at that matrix, it's got two identical rows." + }, + { + "text": "I have a square matrix." + }, + { + "text": "Its rows are obviously dependent." + }, + { + "text": "And that makes the columns dependent." + }, + { + "text": "So there's my error." + }, + { + "text": "When I look at the matrix A that has those three columns, those three columns can't be independent because that matrix is not invertible because it's got two equal rows." + }, + { + "text": "And today's lecture will reach the conclusion, the great conclusion, that connects the column space with the row space." + }, + { + "text": "So those are the row space is now going to be another one of my fundamental subspaces." + }, + { + "text": "The row space of this matrix or of this one, well, the row space of this one is okay." + }, + { + "text": "But the row space of this one, I'm looking at the rows of the matrix, oh, anyway, I'll have two equal rows and the row space will be only two-dimensional." + }, + { + "text": "The rank of the matrix with these columns will only be two, so only two of those columns can be independent too." + }, + { + "text": "The rows tell me something about the columns, in other words." + }, + { + "text": "Something that I should have noticed and I didn't." + }, + { + "text": "Okay." + }, + { + "text": "So now let me pin down these four fundamental subspaces." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk10.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..8f428ebe86b1b4488558f6fa55b8940ef758b264 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "Okay." + }, + { + "text": "What about its row space?" + }, + { + "text": "What happened to its row space?" + }, + { + "text": "Well, what happened, let me first ask, just because this is, sometimes something does happen." + }, + { + "text": "Its column space changed." + }, + { + "text": "The column space of R is not the column space of A, right?" + }, + { + "text": "Because one one one is certainly in the column space of A and certainly not in the column space of R. I did row operations." + }, + { + "text": "Those row operations preserved the row space, so the row so the column spaces are different." + }, + { + "text": "Different column spaces." + }, + { + "text": "Different column spaces." + }, + { + "text": "But I believe that they have the same row space." + }, + { + "text": "Same row space." + }, + { + "text": "I believe that the row space of that matrix and the row space of this matrix are identical." + }, + { + "text": "They have exactly the same vectors in them." + }, + { + "text": "Those vectors are vectors with four components, right?" + }, + { + "text": "They're all combinations of those rows." + }, + { + "text": "Or I believe you get the same thing by taking all combinations of these rows." + }, + { + "text": "And if true, what's a basis?" + }, + { + "text": "What's a basis for the row space of R?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk11.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..258e5999dbb0aea67696256511eb6b999136132a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it'll be a basis for the row space of the original A." + }, + { + "text": "But it's obviously a basis for the row space of R. What's a basis for the row space of that matrix?" + }, + { + "text": "The first two rows." + }, + { + "text": "So a basis for the row so a basis is for the row space of A or of R is the first R rows of R, not of A." + }, + { + "text": "Sometimes it's true for A, but not necessarily." + }, + { + "text": "But R, we definitely have a matrix here whose row space we can identify." + }, + { + "text": "The row space is spanned by the three rows." + }, + { + "text": "But if we want a basis, we want independence." + }, + { + "text": "So out goes row three." + }, + { + "text": "The row space is also spanned by the first two rows." + }, + { + "text": "This guy didn't contribute anything." + }, + { + "text": "And of course, over here, this one, two, three, one in the bottom didn't contribute anything." + }, + { + "text": "We had it already." + }, + { + "text": "So this, here's a basis, one zero one one and zero one one zero." + }, + { + "text": "I believe those are in the row space." + }, + { + "text": "I know they're independent." + }, + { + "text": "Why are they in the row space?" + }, + { + "text": "Why are those two vectors in the row space?" + }, + { + "text": "Because all those operations we did, which started with these rows and took combinations of them." + }, + { + "text": "I took this row minus this row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk12.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..d05a7eb6e4998c4acd748e3bb7087c68e6e29a80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "That gave me something that's still in the row space." + }, + { + "text": "That's the point." + }, + { + "text": "When I took a row minus a multiple of another row, I'm staying in the row space." + }, + { + "text": "The row space is not changing." + }, + { + "text": "My little basis for it is changing, and I've ended up with, sort of, the best basis." + }, + { + "text": "If the columns of the identity matrix are the best basis for R3 or Rn, the rows of this matrix are the best basis for the row space." + }, + { + "text": "Best in the sense of being as clean as I can make it." + }, + { + "text": "Starting off with the identity and then finishing up with whatever has to be in there." + }, + { + "text": "OK. Do you see, then, that the dimension is R?" + }, + { + "text": "For sure." + }, + { + "text": "Because we've got R pivots, R nonzero rows, we've got the right number of vectors, R. They're in the row space, they're independent, that's it." + }, + { + "text": "They are a basis for the row space." + }, + { + "text": "And we can even pin that down further." + }, + { + "text": "How do I know that every row of A is a combination?" + }, + { + "text": "How do I know they span the row space?" + }, + { + "text": "Oh, well, somebody says I've got the right number of them, so they must, but that's true." + }, + { + "text": "But let me just say, how do I know that this row is a combination of these?" + }, + { + "text": "By just reversing the steps of row reduction." + }, + { + "text": "If I just reverse the steps and go from A, from R back to A, then what do I, what am I doing?" + }, + { + "text": "I'm starting with these rows, I'm taking combinations of them, after a couple of steps, undoing the subtractions that I did before, I'm back to these rows." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk13.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..7b0edabbd24233827c7692f63429589952dac1bc --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "So these rows are combinations of those rows, those rows are combinations of those rows, the two row spaces are the same, the bases are the same, and the natural basis is this guy." + }, + { + "text": "Is that all right for the row space?" + }, + { + "text": "The row space is sitting there in R, in its cleanest possible form." + }, + { + "text": "OK. Now what about the fourth guy, the null space of A transpose?" + }, + { + "text": "First of all, why do I call that the left null space?" + }, + { + "text": "So let me save that and bring that down." + }, + { + "text": "OK." + }, + { + "text": "So the fourth space is the null space of A transpose." + }, + { + "text": "So it has in it vectors, let me call them y, so that A transpose y equals zero." + }, + { + "text": "If A transpose y equals zero, then y is in the null space of A transpose, of course." + }, + { + "text": "So this is a matrix times a column equaling zero." + }, + { + "text": "And now, because I want y to sit on the left, and I want A instead of A transpose, I'll just transpose that equation." + }, + { + "text": "Can I just transpose that?" + }, + { + "text": "On the right, it makes the zero vector lie down." + }, + { + "text": "And on the left, it's a product, A transpose times y." + }, + { + "text": "If I take the transpose, then they come in opposite order, right?" + }, + { + "text": "So it's y transpose times A transpose transpose, but nobody's going to leave it like that." + }, + { + "text": "That's A transpose transpose is just A, of course." + }, + { + "text": "When I transposed A transpose, I got back to A." + }, + { + "text": "Now, do you see what I have now?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk14.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7a889f79409e9a95fbd4cc01518da4b9706c49d1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "I have a row vector, y transpose, multiplying A and multiplying from the left." + }, + { + "text": "That's why I call it the left null space." + }, + { + "text": "But by making it, putting it on the left, I had to make it into a row instead of a column vector." + }, + { + "text": "And so my convention is I usually don't do that, I usually stay with A transpose y equals zero." + }, + { + "text": "OK. And you might ask, how do we get a basis, or I might ask, how do we get a basis for this fourth space, this left null space?" + }, + { + "text": "OK." + }, + { + "text": "I'll do it the example." + }, + { + "text": "As always, ah, not that one." + }, + { + "text": "The left null space is not jumping out at me here." + }, + { + "text": "I know which are the free variables, the special solutions, but those are special solutions to Ax equals zero, and now I'm looking at A transpose and I'm not seeing it here." + }, + { + "text": "So, but somehow you feel that the work that you did, which simplified A to R, should have revealed the left null space too." + }, + { + "text": "And it's slightly less immediate, but it's there." + }, + { + "text": "So from A to R, I took some steps, and I guess I'm interested in what were those steps, or what were all of them together." + }, + { + "text": "I don't want to -- I'm not interested in what particular ones they were." + }, + { + "text": "I'm interested in what was the whole matrix that took me from A to R. How would you find that?" + }, + { + "text": "Do you remember Gauss-Jordan, where you tack on the identity matrix?" + }, + { + "text": "Let's do that again." + }, + { + "text": "So I'll do it above here." + }, + { + "text": "So this is now the idea of I take the matrix A, which is m by n. In Gauss-Jordan, when we saw him before, A was a square invertible matrix and we were finding its inverse." + }, + { + "text": "Now the matrix isn't square, it's probably rectangular." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk15.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3c045b6d07a6635d896789ba37b0d578bd175e92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "But I'll still tack on the identity matrix, and of course, since these have length m, it better be m by m. And now I'll do the reduced row echelon form of this matrix." + }, + { + "text": "And what do I get?" + }, + { + "text": "The reduced row echelon form starts with these columns, starts with the first columns, works like mad, and produces R. Of course, still the same size, m by n, and we did it before." + }, + { + "text": "And then whatever it did to get R, something else is going to show up here." + }, + { + "text": "Let me call it E, m by m. It's whatever you see that E is just going to contain a record of what we did." + }, + { + "text": "We did whatever it took to get A to become R. And at the same time, we were doing it to the identity matrix." + }, + { + "text": "So we started with the identity matrix, we buzzed along." + }, + { + "text": "So we took some -- all this row reduction amounted to multiplying on the left by some matrix, some series of elementary matrices that all together gave us one matrix, and that matrix is E. So all this row reduction stuff amounted to multiplying by E. How do I know that?" + }, + { + "text": "It certainly amounted to multiplying by something, and that something took I to E, so that something was E. So now look at the first part, E A is R. No big deal." + }, + { + "text": "All I've said is that the row reduction steps that we all know well, taking A to R, are in a- in some matrix, and I can find out what that matrix is by just tacking I on and seeing what comes out." + }, + { + "text": "What comes out is E. Let's just review the invertible square case." + }, + { + "text": "What happened then?" + }, + { + "text": "Because I was interested in it in chapter two also." + }, + { + "text": "When A was square and invertible, I took A I, I did row elimination, what was the R that came out?" + }, + { + "text": "It was I." + }, + { + "text": "So in chapter two, in chapter two, R was I." + }, + { + "text": "The row- the reduced row echelon form of a nice invertible square matrix is the identity." + }, + { + "text": "So if R was I in that case, then E was A inverse, because E A is I." + }, + { + "text": "Good." + }, + { + "text": "That's- that was good and easy." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk16.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..c5a8adc4741aeb68371eb235609b24dad795df03 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now what I'm saying is that there still is an E, it's not A inverse anymore, because A is a rectangular, it hasn't got an inverse." + }, + { + "text": "But there is still some matrix E that connected this to this." + }, + { + "text": "Oh, I should have figured out in advance what it was." + }, + { + "text": "Shoot." + }, + { + "text": "I didn't- I did those steps and sort of erased as I went, and, I should have done them to the identity, too." + }, + { + "text": "Can I do that?" + }, + { + "text": "Can I do that?" + }, + { + "text": "I'll keep the identity matrix, like I'm supposed to do, and I'll do the same operations on it and see what I end up with." + }, + { + "text": "Okay." + }, + { + "text": "So I'm starting with the identity, which I'll write in light, light enough, but okay, what did I do?" + }, + { + "text": "I subtracted that row from that one and that row from that one." + }, + { + "text": "Okay, I'll do that to the identity." + }, + { + "text": "So I subtract that first row from row two and row three." + }, + { + "text": "Good." + }, + { + "text": "Then I think I multiply, do you remember, I multiplied row two by minus one?" + }, + { + "text": "Let me just do that." + }, + { + "text": "Then what did I do?" + }, + { + "text": "I subtracted two of row two away from row one." + }, + { + "text": "I better do that." + }, + { + "text": "Subtract two of this away from this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk17.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..368775ffcdaa5a9fe2c24f8c85bcb4963097a79c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's minus one, two of these away leaves a plus two and zero." + }, + { + "text": "I believe that's E. The way to check is to see, multiply that E by this A, just to see, did I do it right?" + }, + { + "text": "So I believe E was minus one, two, zero, one minus one, zero, and minus one, zero, one." + }, + { + "text": "Okay." + }, + { + "text": "That's my E, that's my A, and that's R. All right." + }, + { + "text": "All I'm struggling to do is write the reason I wanted this blasted E was so that I could figure out the left null space." + }, + { + "text": "Not only its dimension, which I know." + }, + { + "text": "Actually, what is the dimension of the left null space?" + }, + { + "text": "Here's my matrix." + }, + { + "text": "What's the rank of the matrix?" + }, + { + "text": "Two." + }, + { + "text": "And the dimension of the left null space is supposed to be M minus R, three minus two, one." + }, + { + "text": "I believe that the left null space is one-dimensional." + }, + { + "text": "There is one combination of those three rows that produces the zero row." + }, + { + "text": "There is a basis." + }, + { + "text": "A basis for the left null space has only got one vector in it." + }, + { + "text": "And what is that vector?" + }, + { + "text": "It's here in the last row of E. But, ah, we could have seen it earlier." + }, + { + "text": "What combination of those rows gives the zero row?" + }, + { + "text": "Minus one of that, plus one of that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk18.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..9f5e8b1fcc2242dbdc56d379cbc7126ada792e31 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a basis for the left null space of this matrix, I'm looking for combinations of rows that give the zero row, if I'm looking at the left null space." + }, + { + "text": "For the null space, I'm looking at combinations of columns to get the zero column." + }, + { + "text": "Now I'm looking at combinations of these three rows to get the zero row, and of course, there is my zero row, and here is my vector that produced it." + }, + { + "text": "Minus one of that row and one of that row." + }, + { + "text": "Obvious." + }, + { + "text": "Okay." + }, + { + "text": "So in that example, and actually in all examples, we have seen how to produce a basis for the left null space." + }, + { + "text": "I won't ask you that all the time." + }, + { + "text": "Because it didn't come out immediately from R, we had to keep track of E for that left null space." + }, + { + "text": "But at least it didn't require us to transpose the matrix and start all over again." + }, + { + "text": "Okay." + }, + { + "text": "Those are the four subspaces." + }, + { + "text": "Can I review them?" + }, + { + "text": "The row space and the null space are in Rn." + }, + { + "text": "Their dimensions add to n. The column space and the left null space are in Rm, and their dimensions add to m. Okay." + }, + { + "text": "So let me close these last minutes by pushing you a little bit more to a new type of vector space." + }, + { + "text": "All our vector spaces, all the ones that we took seriously, have been subspaces of some real three- or n-dimensional space." + }, + { + "text": "Now I'm going to write down another vector space, a new vector space." + }, + { + "text": "Say all three by three matrices." + }, + { + "text": "My matrices are the vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk19.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..c1658ee474fcf6206f54d67e4dededa02a1ef92c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Is that all right?" + }, + { + "text": "I'm just naming them." + }, + { + "text": "You can put quotes around vectors." + }, + { + "text": "Every three by three matrix is one of my vectors." + }, + { + "text": "Now how am I entitled to call those things vectors?" + }, + { + "text": "I mean, they look very much like matrices." + }, + { + "text": "But they're vectors in my vector space because they obey the rules." + }, + { + "text": "All I'm supposed to be able to do with vectors is add them." + }, + { + "text": "I can add matrices." + }, + { + "text": "I'm supposed to be able to multiply them by scalar numbers, like seven." + }, + { + "text": "Well, I can multiply a matrix by seven." + }, + { + "text": "And I can take combinations of matrices." + }, + { + "text": "I can take three of one matrix minus five of another matrix." + }, + { + "text": "And those combinations, there's a zero matrix, the matrix that has all zeros in it." + }, + { + "text": "If I add that to another matrix, it doesn't change it." + }, + { + "text": "All the good stuff." + }, + { + "text": "If I multiply a matrix by one, it doesn't change it." + }, + { + "text": "All those eight rules for a vector space that we never wrote down, all easily satisfied." + }, + { + "text": "So now we have a different --." + }, + { + "text": "Now, of course, you can say you can multiply those matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk2.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..b92bd923d792a0f92ab4de95b7867006e9880f71 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here are the four fundamental subspaces." + }, + { + "text": "This is really the heart of this approach to linear algebra, to see these four subspaces, how they're related." + }, + { + "text": "So what are they?" + }, + { + "text": "The column space, C of A." + }, + { + "text": "The null space, N of A." + }, + { + "text": "And now comes the row space, something new." + }, + { + "text": "The row space, what's in that?" + }, + { + "text": "It's all combinations of the rows." + }, + { + "text": "That's natural." + }, + { + "text": "We want a space, so we have to take all combinations and we start with the rows." + }, + { + "text": "So the rows span the row space." + }, + { + "text": "Are the rows a basis for the row space?" + }, + { + "text": "Maybe so, maybe no." + }, + { + "text": "The rows are a basis for the row space when they're independent." + }, + { + "text": "But if they're dependent, as in this example, my error from last time, they're not, those three rows are not a basis, the row space would only be two-dimensional, I only need two rows for a basis." + }, + { + "text": "So the row space, now what's in it?" + }, + { + "text": "It's all combinations of the rows of A." + }, + { + "text": "All combinations of the rows of A." + }, + { + "text": "But I don't like working with row vectors." + }, + { + "text": "All my vectors have been column vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk20.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..56956e8347a8f8c1f8522690db77860dcc6953b9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "I don't care." + }, + { + "text": "For the moment, I'm only thinking of these matrices as forming a vector space, so I am only doing A plus B and C times A. I'm not interested in A, B for now." + }, + { + "text": "The fact that I can multiply is not relevant to a vector space." + }, + { + "text": "OK, so I have three by three matrices." + }, + { + "text": "And how about subspaces?" + }, + { + "text": "What's, tell me a subspace of this matrix space." + }, + { + "text": "Let me call this matrix space M. That's my matrix space, my space of all three by three matrices." + }, + { + "text": "Tell me a subspace of it." + }, + { + "text": "OK, what about the upper triangular matrices?" + }, + { + "text": "So subspaces, subspaces of M. All upper triangular matrices." + }, + { + "text": "Another subspace." + }, + { + "text": "All symmetric matrices." + }, + { + "text": "The intersection of two subspaces is supposed to be a subspace." + }, + { + "text": "We gave a little effort to the proof of that fact." + }, + { + "text": "If I look at the matrices that are in this subspace, they're symmetric, and they're also in this subspace, they're upper triangular." + }, + { + "text": "What do they look like?" + }, + { + "text": "Well, if they're symmetric, but they have zeros below the diagonal, they better have zeros above the diagonal." + }, + { + "text": "So the intersection would be diagonal matrices." + }, + { + "text": "That's another subspace, smaller than those." + }, + { + "text": "How can I use the word smaller?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk21.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..ffcdd44ed2f644726e04b27114327cb30bc7fb92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, I'm now entitled to use the word smaller." + }, + { + "text": "I mean, well, one way to say is, OK, these are contained in those." + }, + { + "text": "These are contained in those." + }, + { + "text": "But more precisely, I could give the dimension of these spaces." + }, + { + "text": "So I could, we can compute, let's compute it next time." + }, + { + "text": "The dimension of all upper, of the subspace of upper triangular three by three matrices." + }, + { + "text": "The dimension of symmetric three by three matrices." + }, + { + "text": "The dimension of diagonal three by three matrices." + }, + { + "text": "Well, to produce dimension, that means I'm supposed to produce a basis." + }, + { + "text": "And then I just count how many I needed in the basis." + }, + { + "text": "Let me give you the answer for this one." + }, + { + "text": "What's the dimension?" + }, + { + "text": "The dimension of this, say, this subspace, let me call it D, all diagonal matrices." + }, + { + "text": "The dimension of this subspace is, as I write, you're working it out, three." + }, + { + "text": "Because here's a matrix in this, it's a diagonal matrix." + }, + { + "text": "Here's another one." + }, + { + "text": "Here's another one." + }, + { + "text": "Better make it diagonal, let me put a seven there." + }, + { + "text": "That was not a very great choice, but it's three diagonal matrices, and I believe that they're a basis." + }, + { + "text": "I believe that those three matrices are independent, and I believe that any diagonal matrix is a combination of those three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk22.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..8c6bce8cf8085e6544c31ae6926bb7ccf18b983e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk22.json @@ -0,0 +1,20 @@ +[ + { + "text": "So they span the subspace of diagonal matrices." + }, + { + "text": "Do you see that idea?" + }, + { + "text": "It's like stretching the idea from Rn to Rn by n, three by three, but we can still add, we can still multiply by numbers, and we just ignore the fact that we can multiply two matrices together." + }, + { + "text": "Okay." + }, + { + "text": "Thank you." + }, + { + "text": "That's lecture ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk3.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..25f31647b76274f9088c60d1292bcc43915d3fb0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'd like to stay with column vectors." + }, + { + "text": "How can I get to column vectors out of these rows?" + }, + { + "text": "I transpose the matrix." + }, + { + "text": "So if that's OK with you, I'm going to transpose the matrix, I'm going to say all combinations of the columns of A transpose." + }, + { + "text": "And that allows me to use the convenient notation, the column space of A transpose." + }, + { + "text": "Nothing, no mathematics went on there, we just got some vectors that were lying down to stand up." + }, + { + "text": "But it means that we can use this column space of A transpose, that's telling me in a nice matrix notation what the row space is." + }, + { + "text": "OK. And finally is another null space." + }, + { + "text": "The fourth fundamental space will be the null space of A transpose." + }, + { + "text": "The fourth guy is the null space of A transpose." + }, + { + "text": "And of course, my notation is N of A transpose." + }, + { + "text": "That's the null space of A transpose." + }, + { + "text": "Now, we don't have a perfect name for this space as a, as a, connecting with A, but our usual name is the left null space, and I'll show you why in a moment." + }, + { + "text": "So often I call this the, just to write that word, the left null space of A." + }, + { + "text": "So just the way we have the row space of A and we switch it to the column space of A transpose, so we have this space of guys that I call the left null space of A, but the good notation is it's the null space of A transpose." + }, + { + "text": "OK. Those are four spaces." + }, + { + "text": "Where are those spaces?" + }, + { + "text": "What big space are they in for when A is m by n?" + }, + { + "text": "In that case, the null space of A, what's in the null space of A?" + }, + { + "text": "Vectors with n components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk4.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c2575473d88ff4598107e190483f0484b6558678 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Solutions to Ax equals zero." + }, + { + "text": "So the null space of A is n R n. What's in the column space of A?" + }, + { + "text": "Well, columns." + }, + { + "text": "How many components do those columns have?" + }, + { + "text": "m. So this column space is n R m. What about the column space of A transpose, which are just a disguised way of saying the rows of A?" + }, + { + "text": "The rows of A in this three by six matrix have six components, n components." + }, + { + "text": "The column space is n R n. And the null space of A transpose, I see that this fourth space is already getting second, you know, second class citizen treatment and it doesn't deserve it." + }, + { + "text": "It's, it should be there, it is there, and shouldn't be squeezed." + }, + { + "text": "The null space of A transpose, well, if the null space of A had vectors with n components, the null space of A transpose will be n R m. I want to draw a picture of the four spaces." + }, + { + "text": "OK. OK." + }, + { + "text": "Here are the four spaces." + }, + { + "text": "OK, let me put n dimensional space over on this side." + }, + { + "text": "Then which were the subspaces in R n?" + }, + { + "text": "The null space was and the row space was." + }, + { + "text": "So here we have the can I make that picture of the row space?" + }, + { + "text": "And can I make this kind of picture of the null space?" + }, + { + "text": "That's just meant to be a sketch, to remind you that they're in this which, you know, how, what type of vectors are in it?" + }, + { + "text": "Vectors with n components." + }, + { + "text": "Over here, inside consisting of vectors with m components is the column space and what I'm calling the null space of A transpose." + }, + { + "text": "Those are the ones with m components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk5.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..f4e64e208c1a1d8e07a9a66a6a6c59f8c4cbcec8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. To understand these spaces is our job now." + }, + { + "text": "Because by understanding those spaces, we know everything about this half of linear algebra." + }, + { + "text": "What do I mean by understanding those spaces?" + }, + { + "text": "I would like to know a basis for those spaces." + }, + { + "text": "For each one of those spaces, how would I create, construct a basis?" + }, + { + "text": "What systematic way would produce a basis?" + }, + { + "text": "And what's their dimension?" + }, + { + "text": "OK." + }, + { + "text": "So for each of the four spaces, I have to answer those questions." + }, + { + "text": "How do I produce a basis?" + }, + { + "text": "And then, which has a somewhat long answer, and what's the dimension, which is just a number, so it has a real short answer?" + }, + { + "text": "Can I give you the short answer first?" + }, + { + "text": "I shouldn't do it, but here it is." + }, + { + "text": "I can tell you the dimension of the column space." + }, + { + "text": "Let me start with this guy." + }, + { + "text": "What's its dimension?" + }, + { + "text": "I have an m by n matrix." + }, + { + "text": "The dimension of the column space is the rank, R. We actually got to that at the end of the last lecture, but only for an example." + }, + { + "text": "So I really have to say, OK, what's going on there?" + }, + { + "text": "I should produce a basis, and then I just look to see how many vectors I needed in that basis, and the answer will be R. Actually, I'll do that before I get on to the others." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk6.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..ac7425fbe27a77a7e448b576483b4c179e9a31f1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "What's a basis for the column space?" + }, + { + "text": "We've done all the work of row reduction, identifying the pivot columns, the ones that have pivots, the ones that end up with pivots, but now I the pivot columns I'm interested in are columns of A, the original A." + }, + { + "text": "And those pivot columns, there are R of them, the rank R counts those, those are a basis." + }, + { + "text": "So if I answer this question for the column space, the answer will be a basis is the pivot columns, and the dimension is the rank R. And there are pivot columns and everything great." + }, + { + "text": "OK, so that space we pretty well understand." + }, + { + "text": "I probably have a little going back to see that, to prove that this is a right answer, but you know it's the right answer." + }, + { + "text": "Now let me look at the row space." + }, + { + "text": "OK. Shall I tell you the dimension of the row space?" + }, + { + "text": "Yes." + }, + { + "text": "Before we do even an example, let me tell you the dimension of the row space." + }, + { + "text": "Its dimension is also R. The row space and the column space have the same dimension." + }, + { + "text": "That's a wonderful fact." + }, + { + "text": "The dimension of the column space of A transpose, that's the row space, is R. That space is R-dimensional." + }, + { + "text": "And so is this one." + }, + { + "text": "OK. That's the, that's the sort of insight that got used in this example." + }, + { + "text": "If those, if those, if those, are the three columns of a matrix, let me make them the three columns of a matrix by just erasing some brackets, OK, those are the three columns of a matrix, the rank of that matrix, if I look at the columns, it wasn't obvious to me anyway." + }, + { + "text": "But if I look at the rows, it's, now it's obvious." + }, + { + "text": "The row space of that matrix obviously is two-dimensional, because I can, I see a basis for the row space, this row and that row." + }, + { + "text": "And of course, strictly speaking, I'm supposed to transpose those guys, make them stand up." + }, + { + "text": "But the rank is two, and therefore the column space is two-dimensional by this wonderful fact that the row space and column space have the same dimension, and therefore there are only two pivot columns, not three, and, those, the three columns are dependent." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk7.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..7d55c74913379543a71fcc53c971f787baf12a92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, let me bury that error and talk about the row space." + }, + { + "text": "Well, I'm going to give you the dimensions of all the spaces, because that's the, such a nice answer." + }, + { + "text": "OK." + }, + { + "text": "So let me come back here." + }, + { + "text": "So we have this great fact to establish, that the row space, its dimension is also the rank." + }, + { + "text": "OK. What about the null space?" + }, + { + "text": "What's a basis for the null space?" + }, + { + "text": "What's the dimension of the null space?" + }, + { + "text": "Let me, I'll put that answer up here, for the null space." + }, + { + "text": "Well, how have we constructed the null space?" + }, + { + "text": "We took the matrix A, we did those row operations to get it into a form U or even further, we got it into the reduced form R, and then we read off special solutions." + }, + { + "text": "Special solutions, and every special solution came from a free variable." + }, + { + "text": "And those special solutions are in the null space, and the great thing is, they're a basis for it." + }, + { + "text": "So for the null space, a basis will be the special solutions." + }, + { + "text": "And there's one for every free variable, right?" + }, + { + "text": "For each free variable, we give that variable the value one, the other free variable zero." + }, + { + "text": "We get the pivot variables, we get a vector in the -- we get a special solution." + }, + { + "text": "So we get all together n minus R of them, because that's the number of free variables." + }, + { + "text": "If we have R, this is, the dimension is R, is the number of pivot variables, this is the number of free variables." + }, + { + "text": "So the beauty is that those special solutions do form a basis and tell us immediately that the dimension of the null space is n -- I'd better write this well, because it's so nice, n minus R. And you see the nice thing, that the two dimensions in this n-dimensional space, one subspace is R-dimensional, to be proved, that's the row space." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk8.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f4c70532a641ef630aa1f7bca077776017097cd4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "The other subspace is n minus R-dimensional, that's the null space." + }, + { + "text": "And the two dimensions, like, together, give n. The sum of R and n minus R is n. And that's just great." + }, + { + "text": "It's really copying the fact that we have n variables, R of them are pivot variables and n minus R are free variables and n all together." + }, + { + "text": "OK. And now what's the dimension of this poor misbegotten fourth subspace?" + }, + { + "text": "It's got to be m minus R. The dimension of this left null space, left out practically, is m minus R. Well, that's really just saying that this, again, the sum of that plus that is m. And m is correct." + }, + { + "text": "It's the number of columns in A transpose." + }, + { + "text": "A transpose is just as good a matrix as A." + }, + { + "text": "It just happens to be n by m. It happens to have m columns, so it will have m variables, when I go to Ax equals zero, and m of them and R of them will be pivot variables and m minus R will be free variables." + }, + { + "text": "A transpose is as good a matrix as A." + }, + { + "text": "It follows the same rule that this plus the dimension, this dimension plus this dimension adds up to the number of columns." + }, + { + "text": "And over here, A transpose has m columns." + }, + { + "text": "Okay." + }, + { + "text": "Okay, so I gave you the easy answer, the dimensions." + }, + { + "text": "Now can I go back to check on a basis?" + }, + { + "text": "We would like to think that, say, the row space." + }, + { + "text": "Because we've got a basis for the column space." + }, + { + "text": "The pivot columns give a basis for the column space." + }, + { + "text": "Now I'm asking you to look at the row space." + }, + { + "text": "And I you could say, okay, I can produce a basis for the row space by transposing my matrix, making those columns, then doing elimination, row reduction, and checking out the pivot columns in this transposed matrix." + }, + { + "text": "But that means you had to do all that row reduction on A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk9.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..8be162da3ff089e5c511aa65ea7d801c64cad56f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_22_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It ought to be possible, if we take a matrix A, let me take the matrix, maybe we had this matrix in the last lecture, one one one, two one two, three two three, one one one." + }, + { + "text": "Okay." + }, + { + "text": "That, that matrix was so easy, we spotted its pivot columns, one and two, without actually doing row reduction." + }, + { + "text": "But now let's do the job properly." + }, + { + "text": "So I subtract this away from this to produce a zero." + }, + { + "text": "So one two three one is fine." + }, + { + "text": "Subtracting that away leaves me minus one minus one zero, right?" + }, + { + "text": "And subtracting that from the last row, oh, well, that's easy." + }, + { + "text": "Okay, I'm doing row reduction." + }, + { + "text": "Now I've, the first column is all set." + }, + { + "text": "The second column, I now see the pivot, and I can clean up, if I, actually, okay, why don't I make the pivot into a one?" + }, + { + "text": "I'll multiply that row through by minus one, and then I have one one." + }, + { + "text": "That was an elementary operation, I'm allowed." + }, + { + "text": "Multiply a row by a number." + }, + { + "text": "And now I'll do elimination." + }, + { + "text": "Two of those away from that will knock this guy out and make this into a one." + }, + { + "text": "So that's now a zero and that's a one." + }, + { + "text": "Okay." + }, + { + "text": "Done." + }, + { + "text": "That's R. I'm seeing the identity matrix here, I'm seeing zeros below, and I'm seeing F there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk0.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6b8bcce949e11c9807b49a56c5ca68fdb459f818 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay, here is lecture ten in linear algebra." + }, + { + "text": "Two important things to do in this lecture." + }, + { + "text": "One is to correct an error from lecture nine." + }, + { + "text": "So the blackboard with that awful error is still with us." + }, + { + "text": "And the second, the big thing to do is to tell you about the four subspaces that come with a matrix." + }, + { + "text": "We've seen two subspaces, the column space and the null space, there's two to go." + }, + { + "text": "Okay." + }, + { + "text": "First of all, and this is a great way to recap and correct the previous lecture." + }, + { + "text": "So you remember I was just doing R3." + }, + { + "text": "I couldn't have taken a simpler example than R3." + }, + { + "text": "And I wrote down the standard basis." + }, + { + "text": "That's the standard basis." + }, + { + "text": "The basis, the obvious basis for the whole three-dimensional space." + }, + { + "text": "And then I wanted to make the point that there was nothing special, nothing about that basis that another basis couldn't have." + }, + { + "text": "It could have linear independence, it could span a space, there's lots of other bases." + }, + { + "text": "So I started with these vectors one one two and two two five, and those were independent." + }, + { + "text": "And then I said three three seven wouldn't do, because three three seven is the sum of those." + }, + { + "text": "So in my innocence, I put in three three eight." + }, + { + "text": "I figured probably if three three seven is on the plane, is, which I know, it's in the plane with these two, then probably three three eight sticks a little bit out of the plane." + }, + { + "text": "And it's independent and it gives a basis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk1.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..97d9d72b29a5aa923aae0ba9c0fb0da57e9db2ed --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "But after class, to my sorrow, student tells me, wait a minute, that third vector three three eight is not independent." + }, + { + "text": "And why did she say that?" + }, + { + "text": "She didn't actually take the time, didn't have to, to find what combination of this one and this one gives three three eight." + }, + { + "text": "She did something else." + }, + { + "text": "In other words, she looked ahead because she said, wait a minute, if I look at that matrix, it's not invertible." + }, + { + "text": "That third column can't be independent of the first two, because when I look at that matrix, it's got two identical rows." + }, + { + "text": "I have a square matrix." + }, + { + "text": "Its rows are obviously dependent." + }, + { + "text": "And that makes the columns dependent." + }, + { + "text": "So there's my error." + }, + { + "text": "When I look at the matrix A that has those three columns, those three columns can't be independent because that matrix is not invertible because it's got two equal rows." + }, + { + "text": "And today's lecture will reach the conclusion, the great conclusion, that connects the column space with the row space." + }, + { + "text": "So those are the row space is now going to be another one of my fundamental subspaces." + }, + { + "text": "The row space of this matrix or of this one, well, the row space of this one is okay." + }, + { + "text": "But the row space of this one, I'm looking at the rows of the matrix, oh, anyway, I'll have two equal rows and the row space will be only two-dimensional." + }, + { + "text": "The rank of the matrix with these columns will only be two, so only two of those columns can be independent too." + }, + { + "text": "The rows tell me something about the columns, in other words." + }, + { + "text": "Something that I should have noticed and I didn't." + }, + { + "text": "Okay." + }, + { + "text": "So now let me pin down these four fundamental subspaces." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk10.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..8f428ebe86b1b4488558f6fa55b8940ef758b264 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "Okay." + }, + { + "text": "What about its row space?" + }, + { + "text": "What happened to its row space?" + }, + { + "text": "Well, what happened, let me first ask, just because this is, sometimes something does happen." + }, + { + "text": "Its column space changed." + }, + { + "text": "The column space of R is not the column space of A, right?" + }, + { + "text": "Because one one one is certainly in the column space of A and certainly not in the column space of R. I did row operations." + }, + { + "text": "Those row operations preserved the row space, so the row so the column spaces are different." + }, + { + "text": "Different column spaces." + }, + { + "text": "Different column spaces." + }, + { + "text": "But I believe that they have the same row space." + }, + { + "text": "Same row space." + }, + { + "text": "I believe that the row space of that matrix and the row space of this matrix are identical." + }, + { + "text": "They have exactly the same vectors in them." + }, + { + "text": "Those vectors are vectors with four components, right?" + }, + { + "text": "They're all combinations of those rows." + }, + { + "text": "Or I believe you get the same thing by taking all combinations of these rows." + }, + { + "text": "And if true, what's a basis?" + }, + { + "text": "What's a basis for the row space of R?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk11.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..258e5999dbb0aea67696256511eb6b999136132a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it'll be a basis for the row space of the original A." + }, + { + "text": "But it's obviously a basis for the row space of R. What's a basis for the row space of that matrix?" + }, + { + "text": "The first two rows." + }, + { + "text": "So a basis for the row so a basis is for the row space of A or of R is the first R rows of R, not of A." + }, + { + "text": "Sometimes it's true for A, but not necessarily." + }, + { + "text": "But R, we definitely have a matrix here whose row space we can identify." + }, + { + "text": "The row space is spanned by the three rows." + }, + { + "text": "But if we want a basis, we want independence." + }, + { + "text": "So out goes row three." + }, + { + "text": "The row space is also spanned by the first two rows." + }, + { + "text": "This guy didn't contribute anything." + }, + { + "text": "And of course, over here, this one, two, three, one in the bottom didn't contribute anything." + }, + { + "text": "We had it already." + }, + { + "text": "So this, here's a basis, one zero one one and zero one one zero." + }, + { + "text": "I believe those are in the row space." + }, + { + "text": "I know they're independent." + }, + { + "text": "Why are they in the row space?" + }, + { + "text": "Why are those two vectors in the row space?" + }, + { + "text": "Because all those operations we did, which started with these rows and took combinations of them." + }, + { + "text": "I took this row minus this row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk12.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..d05a7eb6e4998c4acd748e3bb7087c68e6e29a80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "That gave me something that's still in the row space." + }, + { + "text": "That's the point." + }, + { + "text": "When I took a row minus a multiple of another row, I'm staying in the row space." + }, + { + "text": "The row space is not changing." + }, + { + "text": "My little basis for it is changing, and I've ended up with, sort of, the best basis." + }, + { + "text": "If the columns of the identity matrix are the best basis for R3 or Rn, the rows of this matrix are the best basis for the row space." + }, + { + "text": "Best in the sense of being as clean as I can make it." + }, + { + "text": "Starting off with the identity and then finishing up with whatever has to be in there." + }, + { + "text": "OK. Do you see, then, that the dimension is R?" + }, + { + "text": "For sure." + }, + { + "text": "Because we've got R pivots, R nonzero rows, we've got the right number of vectors, R. They're in the row space, they're independent, that's it." + }, + { + "text": "They are a basis for the row space." + }, + { + "text": "And we can even pin that down further." + }, + { + "text": "How do I know that every row of A is a combination?" + }, + { + "text": "How do I know they span the row space?" + }, + { + "text": "Oh, well, somebody says I've got the right number of them, so they must, but that's true." + }, + { + "text": "But let me just say, how do I know that this row is a combination of these?" + }, + { + "text": "By just reversing the steps of row reduction." + }, + { + "text": "If I just reverse the steps and go from A, from R back to A, then what do I, what am I doing?" + }, + { + "text": "I'm starting with these rows, I'm taking combinations of them, after a couple of steps, undoing the subtractions that I did before, I'm back to these rows." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk13.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..7b0edabbd24233827c7692f63429589952dac1bc --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "So these rows are combinations of those rows, those rows are combinations of those rows, the two row spaces are the same, the bases are the same, and the natural basis is this guy." + }, + { + "text": "Is that all right for the row space?" + }, + { + "text": "The row space is sitting there in R, in its cleanest possible form." + }, + { + "text": "OK. Now what about the fourth guy, the null space of A transpose?" + }, + { + "text": "First of all, why do I call that the left null space?" + }, + { + "text": "So let me save that and bring that down." + }, + { + "text": "OK." + }, + { + "text": "So the fourth space is the null space of A transpose." + }, + { + "text": "So it has in it vectors, let me call them y, so that A transpose y equals zero." + }, + { + "text": "If A transpose y equals zero, then y is in the null space of A transpose, of course." + }, + { + "text": "So this is a matrix times a column equaling zero." + }, + { + "text": "And now, because I want y to sit on the left, and I want A instead of A transpose, I'll just transpose that equation." + }, + { + "text": "Can I just transpose that?" + }, + { + "text": "On the right, it makes the zero vector lie down." + }, + { + "text": "And on the left, it's a product, A transpose times y." + }, + { + "text": "If I take the transpose, then they come in opposite order, right?" + }, + { + "text": "So it's y transpose times A transpose transpose, but nobody's going to leave it like that." + }, + { + "text": "That's A transpose transpose is just A, of course." + }, + { + "text": "When I transposed A transpose, I got back to A." + }, + { + "text": "Now, do you see what I have now?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk14.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7a889f79409e9a95fbd4cc01518da4b9706c49d1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "I have a row vector, y transpose, multiplying A and multiplying from the left." + }, + { + "text": "That's why I call it the left null space." + }, + { + "text": "But by making it, putting it on the left, I had to make it into a row instead of a column vector." + }, + { + "text": "And so my convention is I usually don't do that, I usually stay with A transpose y equals zero." + }, + { + "text": "OK. And you might ask, how do we get a basis, or I might ask, how do we get a basis for this fourth space, this left null space?" + }, + { + "text": "OK." + }, + { + "text": "I'll do it the example." + }, + { + "text": "As always, ah, not that one." + }, + { + "text": "The left null space is not jumping out at me here." + }, + { + "text": "I know which are the free variables, the special solutions, but those are special solutions to Ax equals zero, and now I'm looking at A transpose and I'm not seeing it here." + }, + { + "text": "So, but somehow you feel that the work that you did, which simplified A to R, should have revealed the left null space too." + }, + { + "text": "And it's slightly less immediate, but it's there." + }, + { + "text": "So from A to R, I took some steps, and I guess I'm interested in what were those steps, or what were all of them together." + }, + { + "text": "I don't want to -- I'm not interested in what particular ones they were." + }, + { + "text": "I'm interested in what was the whole matrix that took me from A to R. How would you find that?" + }, + { + "text": "Do you remember Gauss-Jordan, where you tack on the identity matrix?" + }, + { + "text": "Let's do that again." + }, + { + "text": "So I'll do it above here." + }, + { + "text": "So this is now the idea of I take the matrix A, which is m by n. In Gauss-Jordan, when we saw him before, A was a square invertible matrix and we were finding its inverse." + }, + { + "text": "Now the matrix isn't square, it's probably rectangular." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk15.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3c045b6d07a6635d896789ba37b0d578bd175e92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "But I'll still tack on the identity matrix, and of course, since these have length m, it better be m by m. And now I'll do the reduced row echelon form of this matrix." + }, + { + "text": "And what do I get?" + }, + { + "text": "The reduced row echelon form starts with these columns, starts with the first columns, works like mad, and produces R. Of course, still the same size, m by n, and we did it before." + }, + { + "text": "And then whatever it did to get R, something else is going to show up here." + }, + { + "text": "Let me call it E, m by m. It's whatever you see that E is just going to contain a record of what we did." + }, + { + "text": "We did whatever it took to get A to become R. And at the same time, we were doing it to the identity matrix." + }, + { + "text": "So we started with the identity matrix, we buzzed along." + }, + { + "text": "So we took some -- all this row reduction amounted to multiplying on the left by some matrix, some series of elementary matrices that all together gave us one matrix, and that matrix is E. So all this row reduction stuff amounted to multiplying by E. How do I know that?" + }, + { + "text": "It certainly amounted to multiplying by something, and that something took I to E, so that something was E. So now look at the first part, E A is R. No big deal." + }, + { + "text": "All I've said is that the row reduction steps that we all know well, taking A to R, are in a- in some matrix, and I can find out what that matrix is by just tacking I on and seeing what comes out." + }, + { + "text": "What comes out is E. Let's just review the invertible square case." + }, + { + "text": "What happened then?" + }, + { + "text": "Because I was interested in it in chapter two also." + }, + { + "text": "When A was square and invertible, I took A I, I did row elimination, what was the R that came out?" + }, + { + "text": "It was I." + }, + { + "text": "So in chapter two, in chapter two, R was I." + }, + { + "text": "The row- the reduced row echelon form of a nice invertible square matrix is the identity." + }, + { + "text": "So if R was I in that case, then E was A inverse, because E A is I." + }, + { + "text": "Good." + }, + { + "text": "That's- that was good and easy." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk16.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..c5a8adc4741aeb68371eb235609b24dad795df03 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now what I'm saying is that there still is an E, it's not A inverse anymore, because A is a rectangular, it hasn't got an inverse." + }, + { + "text": "But there is still some matrix E that connected this to this." + }, + { + "text": "Oh, I should have figured out in advance what it was." + }, + { + "text": "Shoot." + }, + { + "text": "I didn't- I did those steps and sort of erased as I went, and, I should have done them to the identity, too." + }, + { + "text": "Can I do that?" + }, + { + "text": "Can I do that?" + }, + { + "text": "I'll keep the identity matrix, like I'm supposed to do, and I'll do the same operations on it and see what I end up with." + }, + { + "text": "Okay." + }, + { + "text": "So I'm starting with the identity, which I'll write in light, light enough, but okay, what did I do?" + }, + { + "text": "I subtracted that row from that one and that row from that one." + }, + { + "text": "Okay, I'll do that to the identity." + }, + { + "text": "So I subtract that first row from row two and row three." + }, + { + "text": "Good." + }, + { + "text": "Then I think I multiply, do you remember, I multiplied row two by minus one?" + }, + { + "text": "Let me just do that." + }, + { + "text": "Then what did I do?" + }, + { + "text": "I subtracted two of row two away from row one." + }, + { + "text": "I better do that." + }, + { + "text": "Subtract two of this away from this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk17.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..368775ffcdaa5a9fe2c24f8c85bcb4963097a79c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's minus one, two of these away leaves a plus two and zero." + }, + { + "text": "I believe that's E. The way to check is to see, multiply that E by this A, just to see, did I do it right?" + }, + { + "text": "So I believe E was minus one, two, zero, one minus one, zero, and minus one, zero, one." + }, + { + "text": "Okay." + }, + { + "text": "That's my E, that's my A, and that's R. All right." + }, + { + "text": "All I'm struggling to do is write the reason I wanted this blasted E was so that I could figure out the left null space." + }, + { + "text": "Not only its dimension, which I know." + }, + { + "text": "Actually, what is the dimension of the left null space?" + }, + { + "text": "Here's my matrix." + }, + { + "text": "What's the rank of the matrix?" + }, + { + "text": "Two." + }, + { + "text": "And the dimension of the left null space is supposed to be M minus R, three minus two, one." + }, + { + "text": "I believe that the left null space is one-dimensional." + }, + { + "text": "There is one combination of those three rows that produces the zero row." + }, + { + "text": "There is a basis." + }, + { + "text": "A basis for the left null space has only got one vector in it." + }, + { + "text": "And what is that vector?" + }, + { + "text": "It's here in the last row of E. But, ah, we could have seen it earlier." + }, + { + "text": "What combination of those rows gives the zero row?" + }, + { + "text": "Minus one of that, plus one of that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk18.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..9f5e8b1fcc2242dbdc56d379cbc7126ada792e31 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a basis for the left null space of this matrix, I'm looking for combinations of rows that give the zero row, if I'm looking at the left null space." + }, + { + "text": "For the null space, I'm looking at combinations of columns to get the zero column." + }, + { + "text": "Now I'm looking at combinations of these three rows to get the zero row, and of course, there is my zero row, and here is my vector that produced it." + }, + { + "text": "Minus one of that row and one of that row." + }, + { + "text": "Obvious." + }, + { + "text": "Okay." + }, + { + "text": "So in that example, and actually in all examples, we have seen how to produce a basis for the left null space." + }, + { + "text": "I won't ask you that all the time." + }, + { + "text": "Because it didn't come out immediately from R, we had to keep track of E for that left null space." + }, + { + "text": "But at least it didn't require us to transpose the matrix and start all over again." + }, + { + "text": "Okay." + }, + { + "text": "Those are the four subspaces." + }, + { + "text": "Can I review them?" + }, + { + "text": "The row space and the null space are in Rn." + }, + { + "text": "Their dimensions add to n. The column space and the left null space are in Rm, and their dimensions add to m. Okay." + }, + { + "text": "So let me close these last minutes by pushing you a little bit more to a new type of vector space." + }, + { + "text": "All our vector spaces, all the ones that we took seriously, have been subspaces of some real three- or n-dimensional space." + }, + { + "text": "Now I'm going to write down another vector space, a new vector space." + }, + { + "text": "Say all three by three matrices." + }, + { + "text": "My matrices are the vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk19.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..c1658ee474fcf6206f54d67e4dededa02a1ef92c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Is that all right?" + }, + { + "text": "I'm just naming them." + }, + { + "text": "You can put quotes around vectors." + }, + { + "text": "Every three by three matrix is one of my vectors." + }, + { + "text": "Now how am I entitled to call those things vectors?" + }, + { + "text": "I mean, they look very much like matrices." + }, + { + "text": "But they're vectors in my vector space because they obey the rules." + }, + { + "text": "All I'm supposed to be able to do with vectors is add them." + }, + { + "text": "I can add matrices." + }, + { + "text": "I'm supposed to be able to multiply them by scalar numbers, like seven." + }, + { + "text": "Well, I can multiply a matrix by seven." + }, + { + "text": "And I can take combinations of matrices." + }, + { + "text": "I can take three of one matrix minus five of another matrix." + }, + { + "text": "And those combinations, there's a zero matrix, the matrix that has all zeros in it." + }, + { + "text": "If I add that to another matrix, it doesn't change it." + }, + { + "text": "All the good stuff." + }, + { + "text": "If I multiply a matrix by one, it doesn't change it." + }, + { + "text": "All those eight rules for a vector space that we never wrote down, all easily satisfied." + }, + { + "text": "So now we have a different --." + }, + { + "text": "Now, of course, you can say you can multiply those matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk2.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..b92bd923d792a0f92ab4de95b7867006e9880f71 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here are the four fundamental subspaces." + }, + { + "text": "This is really the heart of this approach to linear algebra, to see these four subspaces, how they're related." + }, + { + "text": "So what are they?" + }, + { + "text": "The column space, C of A." + }, + { + "text": "The null space, N of A." + }, + { + "text": "And now comes the row space, something new." + }, + { + "text": "The row space, what's in that?" + }, + { + "text": "It's all combinations of the rows." + }, + { + "text": "That's natural." + }, + { + "text": "We want a space, so we have to take all combinations and we start with the rows." + }, + { + "text": "So the rows span the row space." + }, + { + "text": "Are the rows a basis for the row space?" + }, + { + "text": "Maybe so, maybe no." + }, + { + "text": "The rows are a basis for the row space when they're independent." + }, + { + "text": "But if they're dependent, as in this example, my error from last time, they're not, those three rows are not a basis, the row space would only be two-dimensional, I only need two rows for a basis." + }, + { + "text": "So the row space, now what's in it?" + }, + { + "text": "It's all combinations of the rows of A." + }, + { + "text": "All combinations of the rows of A." + }, + { + "text": "But I don't like working with row vectors." + }, + { + "text": "All my vectors have been column vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk20.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..56956e8347a8f8c1f8522690db77860dcc6953b9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "I don't care." + }, + { + "text": "For the moment, I'm only thinking of these matrices as forming a vector space, so I am only doing A plus B and C times A. I'm not interested in A, B for now." + }, + { + "text": "The fact that I can multiply is not relevant to a vector space." + }, + { + "text": "OK, so I have three by three matrices." + }, + { + "text": "And how about subspaces?" + }, + { + "text": "What's, tell me a subspace of this matrix space." + }, + { + "text": "Let me call this matrix space M. That's my matrix space, my space of all three by three matrices." + }, + { + "text": "Tell me a subspace of it." + }, + { + "text": "OK, what about the upper triangular matrices?" + }, + { + "text": "So subspaces, subspaces of M. All upper triangular matrices." + }, + { + "text": "Another subspace." + }, + { + "text": "All symmetric matrices." + }, + { + "text": "The intersection of two subspaces is supposed to be a subspace." + }, + { + "text": "We gave a little effort to the proof of that fact." + }, + { + "text": "If I look at the matrices that are in this subspace, they're symmetric, and they're also in this subspace, they're upper triangular." + }, + { + "text": "What do they look like?" + }, + { + "text": "Well, if they're symmetric, but they have zeros below the diagonal, they better have zeros above the diagonal." + }, + { + "text": "So the intersection would be diagonal matrices." + }, + { + "text": "That's another subspace, smaller than those." + }, + { + "text": "How can I use the word smaller?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk21.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..ffcdd44ed2f644726e04b27114327cb30bc7fb92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, I'm now entitled to use the word smaller." + }, + { + "text": "I mean, well, one way to say is, OK, these are contained in those." + }, + { + "text": "These are contained in those." + }, + { + "text": "But more precisely, I could give the dimension of these spaces." + }, + { + "text": "So I could, we can compute, let's compute it next time." + }, + { + "text": "The dimension of all upper, of the subspace of upper triangular three by three matrices." + }, + { + "text": "The dimension of symmetric three by three matrices." + }, + { + "text": "The dimension of diagonal three by three matrices." + }, + { + "text": "Well, to produce dimension, that means I'm supposed to produce a basis." + }, + { + "text": "And then I just count how many I needed in the basis." + }, + { + "text": "Let me give you the answer for this one." + }, + { + "text": "What's the dimension?" + }, + { + "text": "The dimension of this, say, this subspace, let me call it D, all diagonal matrices." + }, + { + "text": "The dimension of this subspace is, as I write, you're working it out, three." + }, + { + "text": "Because here's a matrix in this, it's a diagonal matrix." + }, + { + "text": "Here's another one." + }, + { + "text": "Here's another one." + }, + { + "text": "Better make it diagonal, let me put a seven there." + }, + { + "text": "That was not a very great choice, but it's three diagonal matrices, and I believe that they're a basis." + }, + { + "text": "I believe that those three matrices are independent, and I believe that any diagonal matrix is a combination of those three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk22.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..8c6bce8cf8085e6544c31ae6926bb7ccf18b983e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk22.json @@ -0,0 +1,20 @@ +[ + { + "text": "So they span the subspace of diagonal matrices." + }, + { + "text": "Do you see that idea?" + }, + { + "text": "It's like stretching the idea from Rn to Rn by n, three by three, but we can still add, we can still multiply by numbers, and we just ignore the fact that we can multiply two matrices together." + }, + { + "text": "Okay." + }, + { + "text": "Thank you." + }, + { + "text": "That's lecture ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk3.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..25f31647b76274f9088c60d1292bcc43915d3fb0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'd like to stay with column vectors." + }, + { + "text": "How can I get to column vectors out of these rows?" + }, + { + "text": "I transpose the matrix." + }, + { + "text": "So if that's OK with you, I'm going to transpose the matrix, I'm going to say all combinations of the columns of A transpose." + }, + { + "text": "And that allows me to use the convenient notation, the column space of A transpose." + }, + { + "text": "Nothing, no mathematics went on there, we just got some vectors that were lying down to stand up." + }, + { + "text": "But it means that we can use this column space of A transpose, that's telling me in a nice matrix notation what the row space is." + }, + { + "text": "OK. And finally is another null space." + }, + { + "text": "The fourth fundamental space will be the null space of A transpose." + }, + { + "text": "The fourth guy is the null space of A transpose." + }, + { + "text": "And of course, my notation is N of A transpose." + }, + { + "text": "That's the null space of A transpose." + }, + { + "text": "Now, we don't have a perfect name for this space as a, as a, connecting with A, but our usual name is the left null space, and I'll show you why in a moment." + }, + { + "text": "So often I call this the, just to write that word, the left null space of A." + }, + { + "text": "So just the way we have the row space of A and we switch it to the column space of A transpose, so we have this space of guys that I call the left null space of A, but the good notation is it's the null space of A transpose." + }, + { + "text": "OK. Those are four spaces." + }, + { + "text": "Where are those spaces?" + }, + { + "text": "What big space are they in for when A is m by n?" + }, + { + "text": "In that case, the null space of A, what's in the null space of A?" + }, + { + "text": "Vectors with n components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk4.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c2575473d88ff4598107e190483f0484b6558678 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Solutions to Ax equals zero." + }, + { + "text": "So the null space of A is n R n. What's in the column space of A?" + }, + { + "text": "Well, columns." + }, + { + "text": "How many components do those columns have?" + }, + { + "text": "m. So this column space is n R m. What about the column space of A transpose, which are just a disguised way of saying the rows of A?" + }, + { + "text": "The rows of A in this three by six matrix have six components, n components." + }, + { + "text": "The column space is n R n. And the null space of A transpose, I see that this fourth space is already getting second, you know, second class citizen treatment and it doesn't deserve it." + }, + { + "text": "It's, it should be there, it is there, and shouldn't be squeezed." + }, + { + "text": "The null space of A transpose, well, if the null space of A had vectors with n components, the null space of A transpose will be n R m. I want to draw a picture of the four spaces." + }, + { + "text": "OK. OK." + }, + { + "text": "Here are the four spaces." + }, + { + "text": "OK, let me put n dimensional space over on this side." + }, + { + "text": "Then which were the subspaces in R n?" + }, + { + "text": "The null space was and the row space was." + }, + { + "text": "So here we have the can I make that picture of the row space?" + }, + { + "text": "And can I make this kind of picture of the null space?" + }, + { + "text": "That's just meant to be a sketch, to remind you that they're in this which, you know, how, what type of vectors are in it?" + }, + { + "text": "Vectors with n components." + }, + { + "text": "Over here, inside consisting of vectors with m components is the column space and what I'm calling the null space of A transpose." + }, + { + "text": "Those are the ones with m components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk5.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..f4e64e208c1a1d8e07a9a66a6a6c59f8c4cbcec8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. To understand these spaces is our job now." + }, + { + "text": "Because by understanding those spaces, we know everything about this half of linear algebra." + }, + { + "text": "What do I mean by understanding those spaces?" + }, + { + "text": "I would like to know a basis for those spaces." + }, + { + "text": "For each one of those spaces, how would I create, construct a basis?" + }, + { + "text": "What systematic way would produce a basis?" + }, + { + "text": "And what's their dimension?" + }, + { + "text": "OK." + }, + { + "text": "So for each of the four spaces, I have to answer those questions." + }, + { + "text": "How do I produce a basis?" + }, + { + "text": "And then, which has a somewhat long answer, and what's the dimension, which is just a number, so it has a real short answer?" + }, + { + "text": "Can I give you the short answer first?" + }, + { + "text": "I shouldn't do it, but here it is." + }, + { + "text": "I can tell you the dimension of the column space." + }, + { + "text": "Let me start with this guy." + }, + { + "text": "What's its dimension?" + }, + { + "text": "I have an m by n matrix." + }, + { + "text": "The dimension of the column space is the rank, R. We actually got to that at the end of the last lecture, but only for an example." + }, + { + "text": "So I really have to say, OK, what's going on there?" + }, + { + "text": "I should produce a basis, and then I just look to see how many vectors I needed in that basis, and the answer will be R. Actually, I'll do that before I get on to the others." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk6.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..ac7425fbe27a77a7e448b576483b4c179e9a31f1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "What's a basis for the column space?" + }, + { + "text": "We've done all the work of row reduction, identifying the pivot columns, the ones that have pivots, the ones that end up with pivots, but now I the pivot columns I'm interested in are columns of A, the original A." + }, + { + "text": "And those pivot columns, there are R of them, the rank R counts those, those are a basis." + }, + { + "text": "So if I answer this question for the column space, the answer will be a basis is the pivot columns, and the dimension is the rank R. And there are pivot columns and everything great." + }, + { + "text": "OK, so that space we pretty well understand." + }, + { + "text": "I probably have a little going back to see that, to prove that this is a right answer, but you know it's the right answer." + }, + { + "text": "Now let me look at the row space." + }, + { + "text": "OK. Shall I tell you the dimension of the row space?" + }, + { + "text": "Yes." + }, + { + "text": "Before we do even an example, let me tell you the dimension of the row space." + }, + { + "text": "Its dimension is also R. The row space and the column space have the same dimension." + }, + { + "text": "That's a wonderful fact." + }, + { + "text": "The dimension of the column space of A transpose, that's the row space, is R. That space is R-dimensional." + }, + { + "text": "And so is this one." + }, + { + "text": "OK. That's the, that's the sort of insight that got used in this example." + }, + { + "text": "If those, if those, if those, are the three columns of a matrix, let me make them the three columns of a matrix by just erasing some brackets, OK, those are the three columns of a matrix, the rank of that matrix, if I look at the columns, it wasn't obvious to me anyway." + }, + { + "text": "But if I look at the rows, it's, now it's obvious." + }, + { + "text": "The row space of that matrix obviously is two-dimensional, because I can, I see a basis for the row space, this row and that row." + }, + { + "text": "And of course, strictly speaking, I'm supposed to transpose those guys, make them stand up." + }, + { + "text": "But the rank is two, and therefore the column space is two-dimensional by this wonderful fact that the row space and column space have the same dimension, and therefore there are only two pivot columns, not three, and, those, the three columns are dependent." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk7.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..7d55c74913379543a71fcc53c971f787baf12a92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, let me bury that error and talk about the row space." + }, + { + "text": "Well, I'm going to give you the dimensions of all the spaces, because that's the, such a nice answer." + }, + { + "text": "OK." + }, + { + "text": "So let me come back here." + }, + { + "text": "So we have this great fact to establish, that the row space, its dimension is also the rank." + }, + { + "text": "OK. What about the null space?" + }, + { + "text": "What's a basis for the null space?" + }, + { + "text": "What's the dimension of the null space?" + }, + { + "text": "Let me, I'll put that answer up here, for the null space." + }, + { + "text": "Well, how have we constructed the null space?" + }, + { + "text": "We took the matrix A, we did those row operations to get it into a form U or even further, we got it into the reduced form R, and then we read off special solutions." + }, + { + "text": "Special solutions, and every special solution came from a free variable." + }, + { + "text": "And those special solutions are in the null space, and the great thing is, they're a basis for it." + }, + { + "text": "So for the null space, a basis will be the special solutions." + }, + { + "text": "And there's one for every free variable, right?" + }, + { + "text": "For each free variable, we give that variable the value one, the other free variable zero." + }, + { + "text": "We get the pivot variables, we get a vector in the -- we get a special solution." + }, + { + "text": "So we get all together n minus R of them, because that's the number of free variables." + }, + { + "text": "If we have R, this is, the dimension is R, is the number of pivot variables, this is the number of free variables." + }, + { + "text": "So the beauty is that those special solutions do form a basis and tell us immediately that the dimension of the null space is n -- I'd better write this well, because it's so nice, n minus R. And you see the nice thing, that the two dimensions in this n-dimensional space, one subspace is R-dimensional, to be proved, that's the row space." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk8.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f4c70532a641ef630aa1f7bca077776017097cd4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "The other subspace is n minus R-dimensional, that's the null space." + }, + { + "text": "And the two dimensions, like, together, give n. The sum of R and n minus R is n. And that's just great." + }, + { + "text": "It's really copying the fact that we have n variables, R of them are pivot variables and n minus R are free variables and n all together." + }, + { + "text": "OK. And now what's the dimension of this poor misbegotten fourth subspace?" + }, + { + "text": "It's got to be m minus R. The dimension of this left null space, left out practically, is m minus R. Well, that's really just saying that this, again, the sum of that plus that is m. And m is correct." + }, + { + "text": "It's the number of columns in A transpose." + }, + { + "text": "A transpose is just as good a matrix as A." + }, + { + "text": "It just happens to be n by m. It happens to have m columns, so it will have m variables, when I go to Ax equals zero, and m of them and R of them will be pivot variables and m minus R will be free variables." + }, + { + "text": "A transpose is as good a matrix as A." + }, + { + "text": "It follows the same rule that this plus the dimension, this dimension plus this dimension adds up to the number of columns." + }, + { + "text": "And over here, A transpose has m columns." + }, + { + "text": "Okay." + }, + { + "text": "Okay, so I gave you the easy answer, the dimensions." + }, + { + "text": "Now can I go back to check on a basis?" + }, + { + "text": "We would like to think that, say, the row space." + }, + { + "text": "Because we've got a basis for the column space." + }, + { + "text": "The pivot columns give a basis for the column space." + }, + { + "text": "Now I'm asking you to look at the row space." + }, + { + "text": "And I you could say, okay, I can produce a basis for the row space by transposing my matrix, making those columns, then doing elimination, row reduction, and checking out the pivot columns in this transposed matrix." + }, + { + "text": "But that means you had to do all that row reduction on A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk9.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..8be162da3ff089e5c511aa65ea7d801c64cad56f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_24_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It ought to be possible, if we take a matrix A, let me take the matrix, maybe we had this matrix in the last lecture, one one one, two one two, three two three, one one one." + }, + { + "text": "Okay." + }, + { + "text": "That, that matrix was so easy, we spotted its pivot columns, one and two, without actually doing row reduction." + }, + { + "text": "But now let's do the job properly." + }, + { + "text": "So I subtract this away from this to produce a zero." + }, + { + "text": "So one two three one is fine." + }, + { + "text": "Subtracting that away leaves me minus one minus one zero, right?" + }, + { + "text": "And subtracting that from the last row, oh, well, that's easy." + }, + { + "text": "Okay, I'm doing row reduction." + }, + { + "text": "Now I've, the first column is all set." + }, + { + "text": "The second column, I now see the pivot, and I can clean up, if I, actually, okay, why don't I make the pivot into a one?" + }, + { + "text": "I'll multiply that row through by minus one, and then I have one one." + }, + { + "text": "That was an elementary operation, I'm allowed." + }, + { + "text": "Multiply a row by a number." + }, + { + "text": "And now I'll do elimination." + }, + { + "text": "Two of those away from that will knock this guy out and make this into a one." + }, + { + "text": "So that's now a zero and that's a one." + }, + { + "text": "Okay." + }, + { + "text": "Done." + }, + { + "text": "That's R. I'm seeing the identity matrix here, I'm seeing zeros below, and I'm seeing F there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk0.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6b8bcce949e11c9807b49a56c5ca68fdb459f818 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay, here is lecture ten in linear algebra." + }, + { + "text": "Two important things to do in this lecture." + }, + { + "text": "One is to correct an error from lecture nine." + }, + { + "text": "So the blackboard with that awful error is still with us." + }, + { + "text": "And the second, the big thing to do is to tell you about the four subspaces that come with a matrix." + }, + { + "text": "We've seen two subspaces, the column space and the null space, there's two to go." + }, + { + "text": "Okay." + }, + { + "text": "First of all, and this is a great way to recap and correct the previous lecture." + }, + { + "text": "So you remember I was just doing R3." + }, + { + "text": "I couldn't have taken a simpler example than R3." + }, + { + "text": "And I wrote down the standard basis." + }, + { + "text": "That's the standard basis." + }, + { + "text": "The basis, the obvious basis for the whole three-dimensional space." + }, + { + "text": "And then I wanted to make the point that there was nothing special, nothing about that basis that another basis couldn't have." + }, + { + "text": "It could have linear independence, it could span a space, there's lots of other bases." + }, + { + "text": "So I started with these vectors one one two and two two five, and those were independent." + }, + { + "text": "And then I said three three seven wouldn't do, because three three seven is the sum of those." + }, + { + "text": "So in my innocence, I put in three three eight." + }, + { + "text": "I figured probably if three three seven is on the plane, is, which I know, it's in the plane with these two, then probably three three eight sticks a little bit out of the plane." + }, + { + "text": "And it's independent and it gives a basis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk1.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..97d9d72b29a5aa923aae0ba9c0fb0da57e9db2ed --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "But after class, to my sorrow, student tells me, wait a minute, that third vector three three eight is not independent." + }, + { + "text": "And why did she say that?" + }, + { + "text": "She didn't actually take the time, didn't have to, to find what combination of this one and this one gives three three eight." + }, + { + "text": "She did something else." + }, + { + "text": "In other words, she looked ahead because she said, wait a minute, if I look at that matrix, it's not invertible." + }, + { + "text": "That third column can't be independent of the first two, because when I look at that matrix, it's got two identical rows." + }, + { + "text": "I have a square matrix." + }, + { + "text": "Its rows are obviously dependent." + }, + { + "text": "And that makes the columns dependent." + }, + { + "text": "So there's my error." + }, + { + "text": "When I look at the matrix A that has those three columns, those three columns can't be independent because that matrix is not invertible because it's got two equal rows." + }, + { + "text": "And today's lecture will reach the conclusion, the great conclusion, that connects the column space with the row space." + }, + { + "text": "So those are the row space is now going to be another one of my fundamental subspaces." + }, + { + "text": "The row space of this matrix or of this one, well, the row space of this one is okay." + }, + { + "text": "But the row space of this one, I'm looking at the rows of the matrix, oh, anyway, I'll have two equal rows and the row space will be only two-dimensional." + }, + { + "text": "The rank of the matrix with these columns will only be two, so only two of those columns can be independent too." + }, + { + "text": "The rows tell me something about the columns, in other words." + }, + { + "text": "Something that I should have noticed and I didn't." + }, + { + "text": "Okay." + }, + { + "text": "So now let me pin down these four fundamental subspaces." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk10.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..8f428ebe86b1b4488558f6fa55b8940ef758b264 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "Okay." + }, + { + "text": "What about its row space?" + }, + { + "text": "What happened to its row space?" + }, + { + "text": "Well, what happened, let me first ask, just because this is, sometimes something does happen." + }, + { + "text": "Its column space changed." + }, + { + "text": "The column space of R is not the column space of A, right?" + }, + { + "text": "Because one one one is certainly in the column space of A and certainly not in the column space of R. I did row operations." + }, + { + "text": "Those row operations preserved the row space, so the row so the column spaces are different." + }, + { + "text": "Different column spaces." + }, + { + "text": "Different column spaces." + }, + { + "text": "But I believe that they have the same row space." + }, + { + "text": "Same row space." + }, + { + "text": "I believe that the row space of that matrix and the row space of this matrix are identical." + }, + { + "text": "They have exactly the same vectors in them." + }, + { + "text": "Those vectors are vectors with four components, right?" + }, + { + "text": "They're all combinations of those rows." + }, + { + "text": "Or I believe you get the same thing by taking all combinations of these rows." + }, + { + "text": "And if true, what's a basis?" + }, + { + "text": "What's a basis for the row space of R?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk11.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..258e5999dbb0aea67696256511eb6b999136132a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it'll be a basis for the row space of the original A." + }, + { + "text": "But it's obviously a basis for the row space of R. What's a basis for the row space of that matrix?" + }, + { + "text": "The first two rows." + }, + { + "text": "So a basis for the row so a basis is for the row space of A or of R is the first R rows of R, not of A." + }, + { + "text": "Sometimes it's true for A, but not necessarily." + }, + { + "text": "But R, we definitely have a matrix here whose row space we can identify." + }, + { + "text": "The row space is spanned by the three rows." + }, + { + "text": "But if we want a basis, we want independence." + }, + { + "text": "So out goes row three." + }, + { + "text": "The row space is also spanned by the first two rows." + }, + { + "text": "This guy didn't contribute anything." + }, + { + "text": "And of course, over here, this one, two, three, one in the bottom didn't contribute anything." + }, + { + "text": "We had it already." + }, + { + "text": "So this, here's a basis, one zero one one and zero one one zero." + }, + { + "text": "I believe those are in the row space." + }, + { + "text": "I know they're independent." + }, + { + "text": "Why are they in the row space?" + }, + { + "text": "Why are those two vectors in the row space?" + }, + { + "text": "Because all those operations we did, which started with these rows and took combinations of them." + }, + { + "text": "I took this row minus this row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk12.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..d05a7eb6e4998c4acd748e3bb7087c68e6e29a80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "That gave me something that's still in the row space." + }, + { + "text": "That's the point." + }, + { + "text": "When I took a row minus a multiple of another row, I'm staying in the row space." + }, + { + "text": "The row space is not changing." + }, + { + "text": "My little basis for it is changing, and I've ended up with, sort of, the best basis." + }, + { + "text": "If the columns of the identity matrix are the best basis for R3 or Rn, the rows of this matrix are the best basis for the row space." + }, + { + "text": "Best in the sense of being as clean as I can make it." + }, + { + "text": "Starting off with the identity and then finishing up with whatever has to be in there." + }, + { + "text": "OK. Do you see, then, that the dimension is R?" + }, + { + "text": "For sure." + }, + { + "text": "Because we've got R pivots, R nonzero rows, we've got the right number of vectors, R. They're in the row space, they're independent, that's it." + }, + { + "text": "They are a basis for the row space." + }, + { + "text": "And we can even pin that down further." + }, + { + "text": "How do I know that every row of A is a combination?" + }, + { + "text": "How do I know they span the row space?" + }, + { + "text": "Oh, well, somebody says I've got the right number of them, so they must, but that's true." + }, + { + "text": "But let me just say, how do I know that this row is a combination of these?" + }, + { + "text": "By just reversing the steps of row reduction." + }, + { + "text": "If I just reverse the steps and go from A, from R back to A, then what do I, what am I doing?" + }, + { + "text": "I'm starting with these rows, I'm taking combinations of them, after a couple of steps, undoing the subtractions that I did before, I'm back to these rows." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk13.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..7b0edabbd24233827c7692f63429589952dac1bc --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "So these rows are combinations of those rows, those rows are combinations of those rows, the two row spaces are the same, the bases are the same, and the natural basis is this guy." + }, + { + "text": "Is that all right for the row space?" + }, + { + "text": "The row space is sitting there in R, in its cleanest possible form." + }, + { + "text": "OK. Now what about the fourth guy, the null space of A transpose?" + }, + { + "text": "First of all, why do I call that the left null space?" + }, + { + "text": "So let me save that and bring that down." + }, + { + "text": "OK." + }, + { + "text": "So the fourth space is the null space of A transpose." + }, + { + "text": "So it has in it vectors, let me call them y, so that A transpose y equals zero." + }, + { + "text": "If A transpose y equals zero, then y is in the null space of A transpose, of course." + }, + { + "text": "So this is a matrix times a column equaling zero." + }, + { + "text": "And now, because I want y to sit on the left, and I want A instead of A transpose, I'll just transpose that equation." + }, + { + "text": "Can I just transpose that?" + }, + { + "text": "On the right, it makes the zero vector lie down." + }, + { + "text": "And on the left, it's a product, A transpose times y." + }, + { + "text": "If I take the transpose, then they come in opposite order, right?" + }, + { + "text": "So it's y transpose times A transpose transpose, but nobody's going to leave it like that." + }, + { + "text": "That's A transpose transpose is just A, of course." + }, + { + "text": "When I transposed A transpose, I got back to A." + }, + { + "text": "Now, do you see what I have now?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk14.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7a889f79409e9a95fbd4cc01518da4b9706c49d1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "I have a row vector, y transpose, multiplying A and multiplying from the left." + }, + { + "text": "That's why I call it the left null space." + }, + { + "text": "But by making it, putting it on the left, I had to make it into a row instead of a column vector." + }, + { + "text": "And so my convention is I usually don't do that, I usually stay with A transpose y equals zero." + }, + { + "text": "OK. And you might ask, how do we get a basis, or I might ask, how do we get a basis for this fourth space, this left null space?" + }, + { + "text": "OK." + }, + { + "text": "I'll do it the example." + }, + { + "text": "As always, ah, not that one." + }, + { + "text": "The left null space is not jumping out at me here." + }, + { + "text": "I know which are the free variables, the special solutions, but those are special solutions to Ax equals zero, and now I'm looking at A transpose and I'm not seeing it here." + }, + { + "text": "So, but somehow you feel that the work that you did, which simplified A to R, should have revealed the left null space too." + }, + { + "text": "And it's slightly less immediate, but it's there." + }, + { + "text": "So from A to R, I took some steps, and I guess I'm interested in what were those steps, or what were all of them together." + }, + { + "text": "I don't want to -- I'm not interested in what particular ones they were." + }, + { + "text": "I'm interested in what was the whole matrix that took me from A to R. How would you find that?" + }, + { + "text": "Do you remember Gauss-Jordan, where you tack on the identity matrix?" + }, + { + "text": "Let's do that again." + }, + { + "text": "So I'll do it above here." + }, + { + "text": "So this is now the idea of I take the matrix A, which is m by n. In Gauss-Jordan, when we saw him before, A was a square invertible matrix and we were finding its inverse." + }, + { + "text": "Now the matrix isn't square, it's probably rectangular." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk15.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3c045b6d07a6635d896789ba37b0d578bd175e92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "But I'll still tack on the identity matrix, and of course, since these have length m, it better be m by m. And now I'll do the reduced row echelon form of this matrix." + }, + { + "text": "And what do I get?" + }, + { + "text": "The reduced row echelon form starts with these columns, starts with the first columns, works like mad, and produces R. Of course, still the same size, m by n, and we did it before." + }, + { + "text": "And then whatever it did to get R, something else is going to show up here." + }, + { + "text": "Let me call it E, m by m. It's whatever you see that E is just going to contain a record of what we did." + }, + { + "text": "We did whatever it took to get A to become R. And at the same time, we were doing it to the identity matrix." + }, + { + "text": "So we started with the identity matrix, we buzzed along." + }, + { + "text": "So we took some -- all this row reduction amounted to multiplying on the left by some matrix, some series of elementary matrices that all together gave us one matrix, and that matrix is E. So all this row reduction stuff amounted to multiplying by E. How do I know that?" + }, + { + "text": "It certainly amounted to multiplying by something, and that something took I to E, so that something was E. So now look at the first part, E A is R. No big deal." + }, + { + "text": "All I've said is that the row reduction steps that we all know well, taking A to R, are in a- in some matrix, and I can find out what that matrix is by just tacking I on and seeing what comes out." + }, + { + "text": "What comes out is E. Let's just review the invertible square case." + }, + { + "text": "What happened then?" + }, + { + "text": "Because I was interested in it in chapter two also." + }, + { + "text": "When A was square and invertible, I took A I, I did row elimination, what was the R that came out?" + }, + { + "text": "It was I." + }, + { + "text": "So in chapter two, in chapter two, R was I." + }, + { + "text": "The row- the reduced row echelon form of a nice invertible square matrix is the identity." + }, + { + "text": "So if R was I in that case, then E was A inverse, because E A is I." + }, + { + "text": "Good." + }, + { + "text": "That's- that was good and easy." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk16.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..c5a8adc4741aeb68371eb235609b24dad795df03 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now what I'm saying is that there still is an E, it's not A inverse anymore, because A is a rectangular, it hasn't got an inverse." + }, + { + "text": "But there is still some matrix E that connected this to this." + }, + { + "text": "Oh, I should have figured out in advance what it was." + }, + { + "text": "Shoot." + }, + { + "text": "I didn't- I did those steps and sort of erased as I went, and, I should have done them to the identity, too." + }, + { + "text": "Can I do that?" + }, + { + "text": "Can I do that?" + }, + { + "text": "I'll keep the identity matrix, like I'm supposed to do, and I'll do the same operations on it and see what I end up with." + }, + { + "text": "Okay." + }, + { + "text": "So I'm starting with the identity, which I'll write in light, light enough, but okay, what did I do?" + }, + { + "text": "I subtracted that row from that one and that row from that one." + }, + { + "text": "Okay, I'll do that to the identity." + }, + { + "text": "So I subtract that first row from row two and row three." + }, + { + "text": "Good." + }, + { + "text": "Then I think I multiply, do you remember, I multiplied row two by minus one?" + }, + { + "text": "Let me just do that." + }, + { + "text": "Then what did I do?" + }, + { + "text": "I subtracted two of row two away from row one." + }, + { + "text": "I better do that." + }, + { + "text": "Subtract two of this away from this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk17.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..368775ffcdaa5a9fe2c24f8c85bcb4963097a79c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's minus one, two of these away leaves a plus two and zero." + }, + { + "text": "I believe that's E. The way to check is to see, multiply that E by this A, just to see, did I do it right?" + }, + { + "text": "So I believe E was minus one, two, zero, one minus one, zero, and minus one, zero, one." + }, + { + "text": "Okay." + }, + { + "text": "That's my E, that's my A, and that's R. All right." + }, + { + "text": "All I'm struggling to do is write the reason I wanted this blasted E was so that I could figure out the left null space." + }, + { + "text": "Not only its dimension, which I know." + }, + { + "text": "Actually, what is the dimension of the left null space?" + }, + { + "text": "Here's my matrix." + }, + { + "text": "What's the rank of the matrix?" + }, + { + "text": "Two." + }, + { + "text": "And the dimension of the left null space is supposed to be M minus R, three minus two, one." + }, + { + "text": "I believe that the left null space is one-dimensional." + }, + { + "text": "There is one combination of those three rows that produces the zero row." + }, + { + "text": "There is a basis." + }, + { + "text": "A basis for the left null space has only got one vector in it." + }, + { + "text": "And what is that vector?" + }, + { + "text": "It's here in the last row of E. But, ah, we could have seen it earlier." + }, + { + "text": "What combination of those rows gives the zero row?" + }, + { + "text": "Minus one of that, plus one of that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk18.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..9f5e8b1fcc2242dbdc56d379cbc7126ada792e31 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a basis for the left null space of this matrix, I'm looking for combinations of rows that give the zero row, if I'm looking at the left null space." + }, + { + "text": "For the null space, I'm looking at combinations of columns to get the zero column." + }, + { + "text": "Now I'm looking at combinations of these three rows to get the zero row, and of course, there is my zero row, and here is my vector that produced it." + }, + { + "text": "Minus one of that row and one of that row." + }, + { + "text": "Obvious." + }, + { + "text": "Okay." + }, + { + "text": "So in that example, and actually in all examples, we have seen how to produce a basis for the left null space." + }, + { + "text": "I won't ask you that all the time." + }, + { + "text": "Because it didn't come out immediately from R, we had to keep track of E for that left null space." + }, + { + "text": "But at least it didn't require us to transpose the matrix and start all over again." + }, + { + "text": "Okay." + }, + { + "text": "Those are the four subspaces." + }, + { + "text": "Can I review them?" + }, + { + "text": "The row space and the null space are in Rn." + }, + { + "text": "Their dimensions add to n. The column space and the left null space are in Rm, and their dimensions add to m. Okay." + }, + { + "text": "So let me close these last minutes by pushing you a little bit more to a new type of vector space." + }, + { + "text": "All our vector spaces, all the ones that we took seriously, have been subspaces of some real three- or n-dimensional space." + }, + { + "text": "Now I'm going to write down another vector space, a new vector space." + }, + { + "text": "Say all three by three matrices." + }, + { + "text": "My matrices are the vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk19.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..c1658ee474fcf6206f54d67e4dededa02a1ef92c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Is that all right?" + }, + { + "text": "I'm just naming them." + }, + { + "text": "You can put quotes around vectors." + }, + { + "text": "Every three by three matrix is one of my vectors." + }, + { + "text": "Now how am I entitled to call those things vectors?" + }, + { + "text": "I mean, they look very much like matrices." + }, + { + "text": "But they're vectors in my vector space because they obey the rules." + }, + { + "text": "All I'm supposed to be able to do with vectors is add them." + }, + { + "text": "I can add matrices." + }, + { + "text": "I'm supposed to be able to multiply them by scalar numbers, like seven." + }, + { + "text": "Well, I can multiply a matrix by seven." + }, + { + "text": "And I can take combinations of matrices." + }, + { + "text": "I can take three of one matrix minus five of another matrix." + }, + { + "text": "And those combinations, there's a zero matrix, the matrix that has all zeros in it." + }, + { + "text": "If I add that to another matrix, it doesn't change it." + }, + { + "text": "All the good stuff." + }, + { + "text": "If I multiply a matrix by one, it doesn't change it." + }, + { + "text": "All those eight rules for a vector space that we never wrote down, all easily satisfied." + }, + { + "text": "So now we have a different --." + }, + { + "text": "Now, of course, you can say you can multiply those matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk2.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..b92bd923d792a0f92ab4de95b7867006e9880f71 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here are the four fundamental subspaces." + }, + { + "text": "This is really the heart of this approach to linear algebra, to see these four subspaces, how they're related." + }, + { + "text": "So what are they?" + }, + { + "text": "The column space, C of A." + }, + { + "text": "The null space, N of A." + }, + { + "text": "And now comes the row space, something new." + }, + { + "text": "The row space, what's in that?" + }, + { + "text": "It's all combinations of the rows." + }, + { + "text": "That's natural." + }, + { + "text": "We want a space, so we have to take all combinations and we start with the rows." + }, + { + "text": "So the rows span the row space." + }, + { + "text": "Are the rows a basis for the row space?" + }, + { + "text": "Maybe so, maybe no." + }, + { + "text": "The rows are a basis for the row space when they're independent." + }, + { + "text": "But if they're dependent, as in this example, my error from last time, they're not, those three rows are not a basis, the row space would only be two-dimensional, I only need two rows for a basis." + }, + { + "text": "So the row space, now what's in it?" + }, + { + "text": "It's all combinations of the rows of A." + }, + { + "text": "All combinations of the rows of A." + }, + { + "text": "But I don't like working with row vectors." + }, + { + "text": "All my vectors have been column vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk20.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..56956e8347a8f8c1f8522690db77860dcc6953b9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "I don't care." + }, + { + "text": "For the moment, I'm only thinking of these matrices as forming a vector space, so I am only doing A plus B and C times A. I'm not interested in A, B for now." + }, + { + "text": "The fact that I can multiply is not relevant to a vector space." + }, + { + "text": "OK, so I have three by three matrices." + }, + { + "text": "And how about subspaces?" + }, + { + "text": "What's, tell me a subspace of this matrix space." + }, + { + "text": "Let me call this matrix space M. That's my matrix space, my space of all three by three matrices." + }, + { + "text": "Tell me a subspace of it." + }, + { + "text": "OK, what about the upper triangular matrices?" + }, + { + "text": "So subspaces, subspaces of M. All upper triangular matrices." + }, + { + "text": "Another subspace." + }, + { + "text": "All symmetric matrices." + }, + { + "text": "The intersection of two subspaces is supposed to be a subspace." + }, + { + "text": "We gave a little effort to the proof of that fact." + }, + { + "text": "If I look at the matrices that are in this subspace, they're symmetric, and they're also in this subspace, they're upper triangular." + }, + { + "text": "What do they look like?" + }, + { + "text": "Well, if they're symmetric, but they have zeros below the diagonal, they better have zeros above the diagonal." + }, + { + "text": "So the intersection would be diagonal matrices." + }, + { + "text": "That's another subspace, smaller than those." + }, + { + "text": "How can I use the word smaller?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk21.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..ffcdd44ed2f644726e04b27114327cb30bc7fb92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, I'm now entitled to use the word smaller." + }, + { + "text": "I mean, well, one way to say is, OK, these are contained in those." + }, + { + "text": "These are contained in those." + }, + { + "text": "But more precisely, I could give the dimension of these spaces." + }, + { + "text": "So I could, we can compute, let's compute it next time." + }, + { + "text": "The dimension of all upper, of the subspace of upper triangular three by three matrices." + }, + { + "text": "The dimension of symmetric three by three matrices." + }, + { + "text": "The dimension of diagonal three by three matrices." + }, + { + "text": "Well, to produce dimension, that means I'm supposed to produce a basis." + }, + { + "text": "And then I just count how many I needed in the basis." + }, + { + "text": "Let me give you the answer for this one." + }, + { + "text": "What's the dimension?" + }, + { + "text": "The dimension of this, say, this subspace, let me call it D, all diagonal matrices." + }, + { + "text": "The dimension of this subspace is, as I write, you're working it out, three." + }, + { + "text": "Because here's a matrix in this, it's a diagonal matrix." + }, + { + "text": "Here's another one." + }, + { + "text": "Here's another one." + }, + { + "text": "Better make it diagonal, let me put a seven there." + }, + { + "text": "That was not a very great choice, but it's three diagonal matrices, and I believe that they're a basis." + }, + { + "text": "I believe that those three matrices are independent, and I believe that any diagonal matrix is a combination of those three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk22.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..8c6bce8cf8085e6544c31ae6926bb7ccf18b983e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk22.json @@ -0,0 +1,20 @@ +[ + { + "text": "So they span the subspace of diagonal matrices." + }, + { + "text": "Do you see that idea?" + }, + { + "text": "It's like stretching the idea from Rn to Rn by n, three by three, but we can still add, we can still multiply by numbers, and we just ignore the fact that we can multiply two matrices together." + }, + { + "text": "Okay." + }, + { + "text": "Thank you." + }, + { + "text": "That's lecture ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk3.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..25f31647b76274f9088c60d1292bcc43915d3fb0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'd like to stay with column vectors." + }, + { + "text": "How can I get to column vectors out of these rows?" + }, + { + "text": "I transpose the matrix." + }, + { + "text": "So if that's OK with you, I'm going to transpose the matrix, I'm going to say all combinations of the columns of A transpose." + }, + { + "text": "And that allows me to use the convenient notation, the column space of A transpose." + }, + { + "text": "Nothing, no mathematics went on there, we just got some vectors that were lying down to stand up." + }, + { + "text": "But it means that we can use this column space of A transpose, that's telling me in a nice matrix notation what the row space is." + }, + { + "text": "OK. And finally is another null space." + }, + { + "text": "The fourth fundamental space will be the null space of A transpose." + }, + { + "text": "The fourth guy is the null space of A transpose." + }, + { + "text": "And of course, my notation is N of A transpose." + }, + { + "text": "That's the null space of A transpose." + }, + { + "text": "Now, we don't have a perfect name for this space as a, as a, connecting with A, but our usual name is the left null space, and I'll show you why in a moment." + }, + { + "text": "So often I call this the, just to write that word, the left null space of A." + }, + { + "text": "So just the way we have the row space of A and we switch it to the column space of A transpose, so we have this space of guys that I call the left null space of A, but the good notation is it's the null space of A transpose." + }, + { + "text": "OK. Those are four spaces." + }, + { + "text": "Where are those spaces?" + }, + { + "text": "What big space are they in for when A is m by n?" + }, + { + "text": "In that case, the null space of A, what's in the null space of A?" + }, + { + "text": "Vectors with n components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk4.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c2575473d88ff4598107e190483f0484b6558678 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Solutions to Ax equals zero." + }, + { + "text": "So the null space of A is n R n. What's in the column space of A?" + }, + { + "text": "Well, columns." + }, + { + "text": "How many components do those columns have?" + }, + { + "text": "m. So this column space is n R m. What about the column space of A transpose, which are just a disguised way of saying the rows of A?" + }, + { + "text": "The rows of A in this three by six matrix have six components, n components." + }, + { + "text": "The column space is n R n. And the null space of A transpose, I see that this fourth space is already getting second, you know, second class citizen treatment and it doesn't deserve it." + }, + { + "text": "It's, it should be there, it is there, and shouldn't be squeezed." + }, + { + "text": "The null space of A transpose, well, if the null space of A had vectors with n components, the null space of A transpose will be n R m. I want to draw a picture of the four spaces." + }, + { + "text": "OK. OK." + }, + { + "text": "Here are the four spaces." + }, + { + "text": "OK, let me put n dimensional space over on this side." + }, + { + "text": "Then which were the subspaces in R n?" + }, + { + "text": "The null space was and the row space was." + }, + { + "text": "So here we have the can I make that picture of the row space?" + }, + { + "text": "And can I make this kind of picture of the null space?" + }, + { + "text": "That's just meant to be a sketch, to remind you that they're in this which, you know, how, what type of vectors are in it?" + }, + { + "text": "Vectors with n components." + }, + { + "text": "Over here, inside consisting of vectors with m components is the column space and what I'm calling the null space of A transpose." + }, + { + "text": "Those are the ones with m components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk5.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..f4e64e208c1a1d8e07a9a66a6a6c59f8c4cbcec8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. To understand these spaces is our job now." + }, + { + "text": "Because by understanding those spaces, we know everything about this half of linear algebra." + }, + { + "text": "What do I mean by understanding those spaces?" + }, + { + "text": "I would like to know a basis for those spaces." + }, + { + "text": "For each one of those spaces, how would I create, construct a basis?" + }, + { + "text": "What systematic way would produce a basis?" + }, + { + "text": "And what's their dimension?" + }, + { + "text": "OK." + }, + { + "text": "So for each of the four spaces, I have to answer those questions." + }, + { + "text": "How do I produce a basis?" + }, + { + "text": "And then, which has a somewhat long answer, and what's the dimension, which is just a number, so it has a real short answer?" + }, + { + "text": "Can I give you the short answer first?" + }, + { + "text": "I shouldn't do it, but here it is." + }, + { + "text": "I can tell you the dimension of the column space." + }, + { + "text": "Let me start with this guy." + }, + { + "text": "What's its dimension?" + }, + { + "text": "I have an m by n matrix." + }, + { + "text": "The dimension of the column space is the rank, R. We actually got to that at the end of the last lecture, but only for an example." + }, + { + "text": "So I really have to say, OK, what's going on there?" + }, + { + "text": "I should produce a basis, and then I just look to see how many vectors I needed in that basis, and the answer will be R. Actually, I'll do that before I get on to the others." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk6.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..ac7425fbe27a77a7e448b576483b4c179e9a31f1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "What's a basis for the column space?" + }, + { + "text": "We've done all the work of row reduction, identifying the pivot columns, the ones that have pivots, the ones that end up with pivots, but now I the pivot columns I'm interested in are columns of A, the original A." + }, + { + "text": "And those pivot columns, there are R of them, the rank R counts those, those are a basis." + }, + { + "text": "So if I answer this question for the column space, the answer will be a basis is the pivot columns, and the dimension is the rank R. And there are pivot columns and everything great." + }, + { + "text": "OK, so that space we pretty well understand." + }, + { + "text": "I probably have a little going back to see that, to prove that this is a right answer, but you know it's the right answer." + }, + { + "text": "Now let me look at the row space." + }, + { + "text": "OK. Shall I tell you the dimension of the row space?" + }, + { + "text": "Yes." + }, + { + "text": "Before we do even an example, let me tell you the dimension of the row space." + }, + { + "text": "Its dimension is also R. The row space and the column space have the same dimension." + }, + { + "text": "That's a wonderful fact." + }, + { + "text": "The dimension of the column space of A transpose, that's the row space, is R. That space is R-dimensional." + }, + { + "text": "And so is this one." + }, + { + "text": "OK. That's the, that's the sort of insight that got used in this example." + }, + { + "text": "If those, if those, if those, are the three columns of a matrix, let me make them the three columns of a matrix by just erasing some brackets, OK, those are the three columns of a matrix, the rank of that matrix, if I look at the columns, it wasn't obvious to me anyway." + }, + { + "text": "But if I look at the rows, it's, now it's obvious." + }, + { + "text": "The row space of that matrix obviously is two-dimensional, because I can, I see a basis for the row space, this row and that row." + }, + { + "text": "And of course, strictly speaking, I'm supposed to transpose those guys, make them stand up." + }, + { + "text": "But the rank is two, and therefore the column space is two-dimensional by this wonderful fact that the row space and column space have the same dimension, and therefore there are only two pivot columns, not three, and, those, the three columns are dependent." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk7.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..7d55c74913379543a71fcc53c971f787baf12a92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, let me bury that error and talk about the row space." + }, + { + "text": "Well, I'm going to give you the dimensions of all the spaces, because that's the, such a nice answer." + }, + { + "text": "OK." + }, + { + "text": "So let me come back here." + }, + { + "text": "So we have this great fact to establish, that the row space, its dimension is also the rank." + }, + { + "text": "OK. What about the null space?" + }, + { + "text": "What's a basis for the null space?" + }, + { + "text": "What's the dimension of the null space?" + }, + { + "text": "Let me, I'll put that answer up here, for the null space." + }, + { + "text": "Well, how have we constructed the null space?" + }, + { + "text": "We took the matrix A, we did those row operations to get it into a form U or even further, we got it into the reduced form R, and then we read off special solutions." + }, + { + "text": "Special solutions, and every special solution came from a free variable." + }, + { + "text": "And those special solutions are in the null space, and the great thing is, they're a basis for it." + }, + { + "text": "So for the null space, a basis will be the special solutions." + }, + { + "text": "And there's one for every free variable, right?" + }, + { + "text": "For each free variable, we give that variable the value one, the other free variable zero." + }, + { + "text": "We get the pivot variables, we get a vector in the -- we get a special solution." + }, + { + "text": "So we get all together n minus R of them, because that's the number of free variables." + }, + { + "text": "If we have R, this is, the dimension is R, is the number of pivot variables, this is the number of free variables." + }, + { + "text": "So the beauty is that those special solutions do form a basis and tell us immediately that the dimension of the null space is n -- I'd better write this well, because it's so nice, n minus R. And you see the nice thing, that the two dimensions in this n-dimensional space, one subspace is R-dimensional, to be proved, that's the row space." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk8.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f4c70532a641ef630aa1f7bca077776017097cd4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "The other subspace is n minus R-dimensional, that's the null space." + }, + { + "text": "And the two dimensions, like, together, give n. The sum of R and n minus R is n. And that's just great." + }, + { + "text": "It's really copying the fact that we have n variables, R of them are pivot variables and n minus R are free variables and n all together." + }, + { + "text": "OK. And now what's the dimension of this poor misbegotten fourth subspace?" + }, + { + "text": "It's got to be m minus R. The dimension of this left null space, left out practically, is m minus R. Well, that's really just saying that this, again, the sum of that plus that is m. And m is correct." + }, + { + "text": "It's the number of columns in A transpose." + }, + { + "text": "A transpose is just as good a matrix as A." + }, + { + "text": "It just happens to be n by m. It happens to have m columns, so it will have m variables, when I go to Ax equals zero, and m of them and R of them will be pivot variables and m minus R will be free variables." + }, + { + "text": "A transpose is as good a matrix as A." + }, + { + "text": "It follows the same rule that this plus the dimension, this dimension plus this dimension adds up to the number of columns." + }, + { + "text": "And over here, A transpose has m columns." + }, + { + "text": "Okay." + }, + { + "text": "Okay, so I gave you the easy answer, the dimensions." + }, + { + "text": "Now can I go back to check on a basis?" + }, + { + "text": "We would like to think that, say, the row space." + }, + { + "text": "Because we've got a basis for the column space." + }, + { + "text": "The pivot columns give a basis for the column space." + }, + { + "text": "Now I'm asking you to look at the row space." + }, + { + "text": "And I you could say, okay, I can produce a basis for the row space by transposing my matrix, making those columns, then doing elimination, row reduction, and checking out the pivot columns in this transposed matrix." + }, + { + "text": "But that means you had to do all that row reduction on A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk9.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..8be162da3ff089e5c511aa65ea7d801c64cad56f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_26_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It ought to be possible, if we take a matrix A, let me take the matrix, maybe we had this matrix in the last lecture, one one one, two one two, three two three, one one one." + }, + { + "text": "Okay." + }, + { + "text": "That, that matrix was so easy, we spotted its pivot columns, one and two, without actually doing row reduction." + }, + { + "text": "But now let's do the job properly." + }, + { + "text": "So I subtract this away from this to produce a zero." + }, + { + "text": "So one two three one is fine." + }, + { + "text": "Subtracting that away leaves me minus one minus one zero, right?" + }, + { + "text": "And subtracting that from the last row, oh, well, that's easy." + }, + { + "text": "Okay, I'm doing row reduction." + }, + { + "text": "Now I've, the first column is all set." + }, + { + "text": "The second column, I now see the pivot, and I can clean up, if I, actually, okay, why don't I make the pivot into a one?" + }, + { + "text": "I'll multiply that row through by minus one, and then I have one one." + }, + { + "text": "That was an elementary operation, I'm allowed." + }, + { + "text": "Multiply a row by a number." + }, + { + "text": "And now I'll do elimination." + }, + { + "text": "Two of those away from that will knock this guy out and make this into a one." + }, + { + "text": "So that's now a zero and that's a one." + }, + { + "text": "Okay." + }, + { + "text": "Done." + }, + { + "text": "That's R. I'm seeing the identity matrix here, I'm seeing zeros below, and I'm seeing F there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk0.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6b8bcce949e11c9807b49a56c5ca68fdb459f818 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay, here is lecture ten in linear algebra." + }, + { + "text": "Two important things to do in this lecture." + }, + { + "text": "One is to correct an error from lecture nine." + }, + { + "text": "So the blackboard with that awful error is still with us." + }, + { + "text": "And the second, the big thing to do is to tell you about the four subspaces that come with a matrix." + }, + { + "text": "We've seen two subspaces, the column space and the null space, there's two to go." + }, + { + "text": "Okay." + }, + { + "text": "First of all, and this is a great way to recap and correct the previous lecture." + }, + { + "text": "So you remember I was just doing R3." + }, + { + "text": "I couldn't have taken a simpler example than R3." + }, + { + "text": "And I wrote down the standard basis." + }, + { + "text": "That's the standard basis." + }, + { + "text": "The basis, the obvious basis for the whole three-dimensional space." + }, + { + "text": "And then I wanted to make the point that there was nothing special, nothing about that basis that another basis couldn't have." + }, + { + "text": "It could have linear independence, it could span a space, there's lots of other bases." + }, + { + "text": "So I started with these vectors one one two and two two five, and those were independent." + }, + { + "text": "And then I said three three seven wouldn't do, because three three seven is the sum of those." + }, + { + "text": "So in my innocence, I put in three three eight." + }, + { + "text": "I figured probably if three three seven is on the plane, is, which I know, it's in the plane with these two, then probably three three eight sticks a little bit out of the plane." + }, + { + "text": "And it's independent and it gives a basis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk1.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..97d9d72b29a5aa923aae0ba9c0fb0da57e9db2ed --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "But after class, to my sorrow, student tells me, wait a minute, that third vector three three eight is not independent." + }, + { + "text": "And why did she say that?" + }, + { + "text": "She didn't actually take the time, didn't have to, to find what combination of this one and this one gives three three eight." + }, + { + "text": "She did something else." + }, + { + "text": "In other words, she looked ahead because she said, wait a minute, if I look at that matrix, it's not invertible." + }, + { + "text": "That third column can't be independent of the first two, because when I look at that matrix, it's got two identical rows." + }, + { + "text": "I have a square matrix." + }, + { + "text": "Its rows are obviously dependent." + }, + { + "text": "And that makes the columns dependent." + }, + { + "text": "So there's my error." + }, + { + "text": "When I look at the matrix A that has those three columns, those three columns can't be independent because that matrix is not invertible because it's got two equal rows." + }, + { + "text": "And today's lecture will reach the conclusion, the great conclusion, that connects the column space with the row space." + }, + { + "text": "So those are the row space is now going to be another one of my fundamental subspaces." + }, + { + "text": "The row space of this matrix or of this one, well, the row space of this one is okay." + }, + { + "text": "But the row space of this one, I'm looking at the rows of the matrix, oh, anyway, I'll have two equal rows and the row space will be only two-dimensional." + }, + { + "text": "The rank of the matrix with these columns will only be two, so only two of those columns can be independent too." + }, + { + "text": "The rows tell me something about the columns, in other words." + }, + { + "text": "Something that I should have noticed and I didn't." + }, + { + "text": "Okay." + }, + { + "text": "So now let me pin down these four fundamental subspaces." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk10.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..8f428ebe86b1b4488558f6fa55b8940ef758b264 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "Okay." + }, + { + "text": "What about its row space?" + }, + { + "text": "What happened to its row space?" + }, + { + "text": "Well, what happened, let me first ask, just because this is, sometimes something does happen." + }, + { + "text": "Its column space changed." + }, + { + "text": "The column space of R is not the column space of A, right?" + }, + { + "text": "Because one one one is certainly in the column space of A and certainly not in the column space of R. I did row operations." + }, + { + "text": "Those row operations preserved the row space, so the row so the column spaces are different." + }, + { + "text": "Different column spaces." + }, + { + "text": "Different column spaces." + }, + { + "text": "But I believe that they have the same row space." + }, + { + "text": "Same row space." + }, + { + "text": "I believe that the row space of that matrix and the row space of this matrix are identical." + }, + { + "text": "They have exactly the same vectors in them." + }, + { + "text": "Those vectors are vectors with four components, right?" + }, + { + "text": "They're all combinations of those rows." + }, + { + "text": "Or I believe you get the same thing by taking all combinations of these rows." + }, + { + "text": "And if true, what's a basis?" + }, + { + "text": "What's a basis for the row space of R?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk11.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..258e5999dbb0aea67696256511eb6b999136132a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it'll be a basis for the row space of the original A." + }, + { + "text": "But it's obviously a basis for the row space of R. What's a basis for the row space of that matrix?" + }, + { + "text": "The first two rows." + }, + { + "text": "So a basis for the row so a basis is for the row space of A or of R is the first R rows of R, not of A." + }, + { + "text": "Sometimes it's true for A, but not necessarily." + }, + { + "text": "But R, we definitely have a matrix here whose row space we can identify." + }, + { + "text": "The row space is spanned by the three rows." + }, + { + "text": "But if we want a basis, we want independence." + }, + { + "text": "So out goes row three." + }, + { + "text": "The row space is also spanned by the first two rows." + }, + { + "text": "This guy didn't contribute anything." + }, + { + "text": "And of course, over here, this one, two, three, one in the bottom didn't contribute anything." + }, + { + "text": "We had it already." + }, + { + "text": "So this, here's a basis, one zero one one and zero one one zero." + }, + { + "text": "I believe those are in the row space." + }, + { + "text": "I know they're independent." + }, + { + "text": "Why are they in the row space?" + }, + { + "text": "Why are those two vectors in the row space?" + }, + { + "text": "Because all those operations we did, which started with these rows and took combinations of them." + }, + { + "text": "I took this row minus this row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk12.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..d05a7eb6e4998c4acd748e3bb7087c68e6e29a80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "That gave me something that's still in the row space." + }, + { + "text": "That's the point." + }, + { + "text": "When I took a row minus a multiple of another row, I'm staying in the row space." + }, + { + "text": "The row space is not changing." + }, + { + "text": "My little basis for it is changing, and I've ended up with, sort of, the best basis." + }, + { + "text": "If the columns of the identity matrix are the best basis for R3 or Rn, the rows of this matrix are the best basis for the row space." + }, + { + "text": "Best in the sense of being as clean as I can make it." + }, + { + "text": "Starting off with the identity and then finishing up with whatever has to be in there." + }, + { + "text": "OK. Do you see, then, that the dimension is R?" + }, + { + "text": "For sure." + }, + { + "text": "Because we've got R pivots, R nonzero rows, we've got the right number of vectors, R. They're in the row space, they're independent, that's it." + }, + { + "text": "They are a basis for the row space." + }, + { + "text": "And we can even pin that down further." + }, + { + "text": "How do I know that every row of A is a combination?" + }, + { + "text": "How do I know they span the row space?" + }, + { + "text": "Oh, well, somebody says I've got the right number of them, so they must, but that's true." + }, + { + "text": "But let me just say, how do I know that this row is a combination of these?" + }, + { + "text": "By just reversing the steps of row reduction." + }, + { + "text": "If I just reverse the steps and go from A, from R back to A, then what do I, what am I doing?" + }, + { + "text": "I'm starting with these rows, I'm taking combinations of them, after a couple of steps, undoing the subtractions that I did before, I'm back to these rows." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk13.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..7b0edabbd24233827c7692f63429589952dac1bc --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "So these rows are combinations of those rows, those rows are combinations of those rows, the two row spaces are the same, the bases are the same, and the natural basis is this guy." + }, + { + "text": "Is that all right for the row space?" + }, + { + "text": "The row space is sitting there in R, in its cleanest possible form." + }, + { + "text": "OK. Now what about the fourth guy, the null space of A transpose?" + }, + { + "text": "First of all, why do I call that the left null space?" + }, + { + "text": "So let me save that and bring that down." + }, + { + "text": "OK." + }, + { + "text": "So the fourth space is the null space of A transpose." + }, + { + "text": "So it has in it vectors, let me call them y, so that A transpose y equals zero." + }, + { + "text": "If A transpose y equals zero, then y is in the null space of A transpose, of course." + }, + { + "text": "So this is a matrix times a column equaling zero." + }, + { + "text": "And now, because I want y to sit on the left, and I want A instead of A transpose, I'll just transpose that equation." + }, + { + "text": "Can I just transpose that?" + }, + { + "text": "On the right, it makes the zero vector lie down." + }, + { + "text": "And on the left, it's a product, A transpose times y." + }, + { + "text": "If I take the transpose, then they come in opposite order, right?" + }, + { + "text": "So it's y transpose times A transpose transpose, but nobody's going to leave it like that." + }, + { + "text": "That's A transpose transpose is just A, of course." + }, + { + "text": "When I transposed A transpose, I got back to A." + }, + { + "text": "Now, do you see what I have now?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk14.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7a889f79409e9a95fbd4cc01518da4b9706c49d1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "I have a row vector, y transpose, multiplying A and multiplying from the left." + }, + { + "text": "That's why I call it the left null space." + }, + { + "text": "But by making it, putting it on the left, I had to make it into a row instead of a column vector." + }, + { + "text": "And so my convention is I usually don't do that, I usually stay with A transpose y equals zero." + }, + { + "text": "OK. And you might ask, how do we get a basis, or I might ask, how do we get a basis for this fourth space, this left null space?" + }, + { + "text": "OK." + }, + { + "text": "I'll do it the example." + }, + { + "text": "As always, ah, not that one." + }, + { + "text": "The left null space is not jumping out at me here." + }, + { + "text": "I know which are the free variables, the special solutions, but those are special solutions to Ax equals zero, and now I'm looking at A transpose and I'm not seeing it here." + }, + { + "text": "So, but somehow you feel that the work that you did, which simplified A to R, should have revealed the left null space too." + }, + { + "text": "And it's slightly less immediate, but it's there." + }, + { + "text": "So from A to R, I took some steps, and I guess I'm interested in what were those steps, or what were all of them together." + }, + { + "text": "I don't want to -- I'm not interested in what particular ones they were." + }, + { + "text": "I'm interested in what was the whole matrix that took me from A to R. How would you find that?" + }, + { + "text": "Do you remember Gauss-Jordan, where you tack on the identity matrix?" + }, + { + "text": "Let's do that again." + }, + { + "text": "So I'll do it above here." + }, + { + "text": "So this is now the idea of I take the matrix A, which is m by n. In Gauss-Jordan, when we saw him before, A was a square invertible matrix and we were finding its inverse." + }, + { + "text": "Now the matrix isn't square, it's probably rectangular." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk15.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3c045b6d07a6635d896789ba37b0d578bd175e92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "But I'll still tack on the identity matrix, and of course, since these have length m, it better be m by m. And now I'll do the reduced row echelon form of this matrix." + }, + { + "text": "And what do I get?" + }, + { + "text": "The reduced row echelon form starts with these columns, starts with the first columns, works like mad, and produces R. Of course, still the same size, m by n, and we did it before." + }, + { + "text": "And then whatever it did to get R, something else is going to show up here." + }, + { + "text": "Let me call it E, m by m. It's whatever you see that E is just going to contain a record of what we did." + }, + { + "text": "We did whatever it took to get A to become R. And at the same time, we were doing it to the identity matrix." + }, + { + "text": "So we started with the identity matrix, we buzzed along." + }, + { + "text": "So we took some -- all this row reduction amounted to multiplying on the left by some matrix, some series of elementary matrices that all together gave us one matrix, and that matrix is E. So all this row reduction stuff amounted to multiplying by E. How do I know that?" + }, + { + "text": "It certainly amounted to multiplying by something, and that something took I to E, so that something was E. So now look at the first part, E A is R. No big deal." + }, + { + "text": "All I've said is that the row reduction steps that we all know well, taking A to R, are in a- in some matrix, and I can find out what that matrix is by just tacking I on and seeing what comes out." + }, + { + "text": "What comes out is E. Let's just review the invertible square case." + }, + { + "text": "What happened then?" + }, + { + "text": "Because I was interested in it in chapter two also." + }, + { + "text": "When A was square and invertible, I took A I, I did row elimination, what was the R that came out?" + }, + { + "text": "It was I." + }, + { + "text": "So in chapter two, in chapter two, R was I." + }, + { + "text": "The row- the reduced row echelon form of a nice invertible square matrix is the identity." + }, + { + "text": "So if R was I in that case, then E was A inverse, because E A is I." + }, + { + "text": "Good." + }, + { + "text": "That's- that was good and easy." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk16.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..c5a8adc4741aeb68371eb235609b24dad795df03 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now what I'm saying is that there still is an E, it's not A inverse anymore, because A is a rectangular, it hasn't got an inverse." + }, + { + "text": "But there is still some matrix E that connected this to this." + }, + { + "text": "Oh, I should have figured out in advance what it was." + }, + { + "text": "Shoot." + }, + { + "text": "I didn't- I did those steps and sort of erased as I went, and, I should have done them to the identity, too." + }, + { + "text": "Can I do that?" + }, + { + "text": "Can I do that?" + }, + { + "text": "I'll keep the identity matrix, like I'm supposed to do, and I'll do the same operations on it and see what I end up with." + }, + { + "text": "Okay." + }, + { + "text": "So I'm starting with the identity, which I'll write in light, light enough, but okay, what did I do?" + }, + { + "text": "I subtracted that row from that one and that row from that one." + }, + { + "text": "Okay, I'll do that to the identity." + }, + { + "text": "So I subtract that first row from row two and row three." + }, + { + "text": "Good." + }, + { + "text": "Then I think I multiply, do you remember, I multiplied row two by minus one?" + }, + { + "text": "Let me just do that." + }, + { + "text": "Then what did I do?" + }, + { + "text": "I subtracted two of row two away from row one." + }, + { + "text": "I better do that." + }, + { + "text": "Subtract two of this away from this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk17.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..368775ffcdaa5a9fe2c24f8c85bcb4963097a79c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's minus one, two of these away leaves a plus two and zero." + }, + { + "text": "I believe that's E. The way to check is to see, multiply that E by this A, just to see, did I do it right?" + }, + { + "text": "So I believe E was minus one, two, zero, one minus one, zero, and minus one, zero, one." + }, + { + "text": "Okay." + }, + { + "text": "That's my E, that's my A, and that's R. All right." + }, + { + "text": "All I'm struggling to do is write the reason I wanted this blasted E was so that I could figure out the left null space." + }, + { + "text": "Not only its dimension, which I know." + }, + { + "text": "Actually, what is the dimension of the left null space?" + }, + { + "text": "Here's my matrix." + }, + { + "text": "What's the rank of the matrix?" + }, + { + "text": "Two." + }, + { + "text": "And the dimension of the left null space is supposed to be M minus R, three minus two, one." + }, + { + "text": "I believe that the left null space is one-dimensional." + }, + { + "text": "There is one combination of those three rows that produces the zero row." + }, + { + "text": "There is a basis." + }, + { + "text": "A basis for the left null space has only got one vector in it." + }, + { + "text": "And what is that vector?" + }, + { + "text": "It's here in the last row of E. But, ah, we could have seen it earlier." + }, + { + "text": "What combination of those rows gives the zero row?" + }, + { + "text": "Minus one of that, plus one of that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk18.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..9f5e8b1fcc2242dbdc56d379cbc7126ada792e31 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a basis for the left null space of this matrix, I'm looking for combinations of rows that give the zero row, if I'm looking at the left null space." + }, + { + "text": "For the null space, I'm looking at combinations of columns to get the zero column." + }, + { + "text": "Now I'm looking at combinations of these three rows to get the zero row, and of course, there is my zero row, and here is my vector that produced it." + }, + { + "text": "Minus one of that row and one of that row." + }, + { + "text": "Obvious." + }, + { + "text": "Okay." + }, + { + "text": "So in that example, and actually in all examples, we have seen how to produce a basis for the left null space." + }, + { + "text": "I won't ask you that all the time." + }, + { + "text": "Because it didn't come out immediately from R, we had to keep track of E for that left null space." + }, + { + "text": "But at least it didn't require us to transpose the matrix and start all over again." + }, + { + "text": "Okay." + }, + { + "text": "Those are the four subspaces." + }, + { + "text": "Can I review them?" + }, + { + "text": "The row space and the null space are in Rn." + }, + { + "text": "Their dimensions add to n. The column space and the left null space are in Rm, and their dimensions add to m. Okay." + }, + { + "text": "So let me close these last minutes by pushing you a little bit more to a new type of vector space." + }, + { + "text": "All our vector spaces, all the ones that we took seriously, have been subspaces of some real three- or n-dimensional space." + }, + { + "text": "Now I'm going to write down another vector space, a new vector space." + }, + { + "text": "Say all three by three matrices." + }, + { + "text": "My matrices are the vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk19.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..c1658ee474fcf6206f54d67e4dededa02a1ef92c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Is that all right?" + }, + { + "text": "I'm just naming them." + }, + { + "text": "You can put quotes around vectors." + }, + { + "text": "Every three by three matrix is one of my vectors." + }, + { + "text": "Now how am I entitled to call those things vectors?" + }, + { + "text": "I mean, they look very much like matrices." + }, + { + "text": "But they're vectors in my vector space because they obey the rules." + }, + { + "text": "All I'm supposed to be able to do with vectors is add them." + }, + { + "text": "I can add matrices." + }, + { + "text": "I'm supposed to be able to multiply them by scalar numbers, like seven." + }, + { + "text": "Well, I can multiply a matrix by seven." + }, + { + "text": "And I can take combinations of matrices." + }, + { + "text": "I can take three of one matrix minus five of another matrix." + }, + { + "text": "And those combinations, there's a zero matrix, the matrix that has all zeros in it." + }, + { + "text": "If I add that to another matrix, it doesn't change it." + }, + { + "text": "All the good stuff." + }, + { + "text": "If I multiply a matrix by one, it doesn't change it." + }, + { + "text": "All those eight rules for a vector space that we never wrote down, all easily satisfied." + }, + { + "text": "So now we have a different --." + }, + { + "text": "Now, of course, you can say you can multiply those matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk2.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..b92bd923d792a0f92ab4de95b7867006e9880f71 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here are the four fundamental subspaces." + }, + { + "text": "This is really the heart of this approach to linear algebra, to see these four subspaces, how they're related." + }, + { + "text": "So what are they?" + }, + { + "text": "The column space, C of A." + }, + { + "text": "The null space, N of A." + }, + { + "text": "And now comes the row space, something new." + }, + { + "text": "The row space, what's in that?" + }, + { + "text": "It's all combinations of the rows." + }, + { + "text": "That's natural." + }, + { + "text": "We want a space, so we have to take all combinations and we start with the rows." + }, + { + "text": "So the rows span the row space." + }, + { + "text": "Are the rows a basis for the row space?" + }, + { + "text": "Maybe so, maybe no." + }, + { + "text": "The rows are a basis for the row space when they're independent." + }, + { + "text": "But if they're dependent, as in this example, my error from last time, they're not, those three rows are not a basis, the row space would only be two-dimensional, I only need two rows for a basis." + }, + { + "text": "So the row space, now what's in it?" + }, + { + "text": "It's all combinations of the rows of A." + }, + { + "text": "All combinations of the rows of A." + }, + { + "text": "But I don't like working with row vectors." + }, + { + "text": "All my vectors have been column vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk20.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..56956e8347a8f8c1f8522690db77860dcc6953b9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "I don't care." + }, + { + "text": "For the moment, I'm only thinking of these matrices as forming a vector space, so I am only doing A plus B and C times A. I'm not interested in A, B for now." + }, + { + "text": "The fact that I can multiply is not relevant to a vector space." + }, + { + "text": "OK, so I have three by three matrices." + }, + { + "text": "And how about subspaces?" + }, + { + "text": "What's, tell me a subspace of this matrix space." + }, + { + "text": "Let me call this matrix space M. That's my matrix space, my space of all three by three matrices." + }, + { + "text": "Tell me a subspace of it." + }, + { + "text": "OK, what about the upper triangular matrices?" + }, + { + "text": "So subspaces, subspaces of M. All upper triangular matrices." + }, + { + "text": "Another subspace." + }, + { + "text": "All symmetric matrices." + }, + { + "text": "The intersection of two subspaces is supposed to be a subspace." + }, + { + "text": "We gave a little effort to the proof of that fact." + }, + { + "text": "If I look at the matrices that are in this subspace, they're symmetric, and they're also in this subspace, they're upper triangular." + }, + { + "text": "What do they look like?" + }, + { + "text": "Well, if they're symmetric, but they have zeros below the diagonal, they better have zeros above the diagonal." + }, + { + "text": "So the intersection would be diagonal matrices." + }, + { + "text": "That's another subspace, smaller than those." + }, + { + "text": "How can I use the word smaller?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk21.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..ffcdd44ed2f644726e04b27114327cb30bc7fb92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, I'm now entitled to use the word smaller." + }, + { + "text": "I mean, well, one way to say is, OK, these are contained in those." + }, + { + "text": "These are contained in those." + }, + { + "text": "But more precisely, I could give the dimension of these spaces." + }, + { + "text": "So I could, we can compute, let's compute it next time." + }, + { + "text": "The dimension of all upper, of the subspace of upper triangular three by three matrices." + }, + { + "text": "The dimension of symmetric three by three matrices." + }, + { + "text": "The dimension of diagonal three by three matrices." + }, + { + "text": "Well, to produce dimension, that means I'm supposed to produce a basis." + }, + { + "text": "And then I just count how many I needed in the basis." + }, + { + "text": "Let me give you the answer for this one." + }, + { + "text": "What's the dimension?" + }, + { + "text": "The dimension of this, say, this subspace, let me call it D, all diagonal matrices." + }, + { + "text": "The dimension of this subspace is, as I write, you're working it out, three." + }, + { + "text": "Because here's a matrix in this, it's a diagonal matrix." + }, + { + "text": "Here's another one." + }, + { + "text": "Here's another one." + }, + { + "text": "Better make it diagonal, let me put a seven there." + }, + { + "text": "That was not a very great choice, but it's three diagonal matrices, and I believe that they're a basis." + }, + { + "text": "I believe that those three matrices are independent, and I believe that any diagonal matrix is a combination of those three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk22.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..8c6bce8cf8085e6544c31ae6926bb7ccf18b983e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk22.json @@ -0,0 +1,20 @@ +[ + { + "text": "So they span the subspace of diagonal matrices." + }, + { + "text": "Do you see that idea?" + }, + { + "text": "It's like stretching the idea from Rn to Rn by n, three by three, but we can still add, we can still multiply by numbers, and we just ignore the fact that we can multiply two matrices together." + }, + { + "text": "Okay." + }, + { + "text": "Thank you." + }, + { + "text": "That's lecture ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk3.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..25f31647b76274f9088c60d1292bcc43915d3fb0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'd like to stay with column vectors." + }, + { + "text": "How can I get to column vectors out of these rows?" + }, + { + "text": "I transpose the matrix." + }, + { + "text": "So if that's OK with you, I'm going to transpose the matrix, I'm going to say all combinations of the columns of A transpose." + }, + { + "text": "And that allows me to use the convenient notation, the column space of A transpose." + }, + { + "text": "Nothing, no mathematics went on there, we just got some vectors that were lying down to stand up." + }, + { + "text": "But it means that we can use this column space of A transpose, that's telling me in a nice matrix notation what the row space is." + }, + { + "text": "OK. And finally is another null space." + }, + { + "text": "The fourth fundamental space will be the null space of A transpose." + }, + { + "text": "The fourth guy is the null space of A transpose." + }, + { + "text": "And of course, my notation is N of A transpose." + }, + { + "text": "That's the null space of A transpose." + }, + { + "text": "Now, we don't have a perfect name for this space as a, as a, connecting with A, but our usual name is the left null space, and I'll show you why in a moment." + }, + { + "text": "So often I call this the, just to write that word, the left null space of A." + }, + { + "text": "So just the way we have the row space of A and we switch it to the column space of A transpose, so we have this space of guys that I call the left null space of A, but the good notation is it's the null space of A transpose." + }, + { + "text": "OK. Those are four spaces." + }, + { + "text": "Where are those spaces?" + }, + { + "text": "What big space are they in for when A is m by n?" + }, + { + "text": "In that case, the null space of A, what's in the null space of A?" + }, + { + "text": "Vectors with n components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk4.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c2575473d88ff4598107e190483f0484b6558678 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Solutions to Ax equals zero." + }, + { + "text": "So the null space of A is n R n. What's in the column space of A?" + }, + { + "text": "Well, columns." + }, + { + "text": "How many components do those columns have?" + }, + { + "text": "m. So this column space is n R m. What about the column space of A transpose, which are just a disguised way of saying the rows of A?" + }, + { + "text": "The rows of A in this three by six matrix have six components, n components." + }, + { + "text": "The column space is n R n. And the null space of A transpose, I see that this fourth space is already getting second, you know, second class citizen treatment and it doesn't deserve it." + }, + { + "text": "It's, it should be there, it is there, and shouldn't be squeezed." + }, + { + "text": "The null space of A transpose, well, if the null space of A had vectors with n components, the null space of A transpose will be n R m. I want to draw a picture of the four spaces." + }, + { + "text": "OK. OK." + }, + { + "text": "Here are the four spaces." + }, + { + "text": "OK, let me put n dimensional space over on this side." + }, + { + "text": "Then which were the subspaces in R n?" + }, + { + "text": "The null space was and the row space was." + }, + { + "text": "So here we have the can I make that picture of the row space?" + }, + { + "text": "And can I make this kind of picture of the null space?" + }, + { + "text": "That's just meant to be a sketch, to remind you that they're in this which, you know, how, what type of vectors are in it?" + }, + { + "text": "Vectors with n components." + }, + { + "text": "Over here, inside consisting of vectors with m components is the column space and what I'm calling the null space of A transpose." + }, + { + "text": "Those are the ones with m components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk5.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..f4e64e208c1a1d8e07a9a66a6a6c59f8c4cbcec8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. To understand these spaces is our job now." + }, + { + "text": "Because by understanding those spaces, we know everything about this half of linear algebra." + }, + { + "text": "What do I mean by understanding those spaces?" + }, + { + "text": "I would like to know a basis for those spaces." + }, + { + "text": "For each one of those spaces, how would I create, construct a basis?" + }, + { + "text": "What systematic way would produce a basis?" + }, + { + "text": "And what's their dimension?" + }, + { + "text": "OK." + }, + { + "text": "So for each of the four spaces, I have to answer those questions." + }, + { + "text": "How do I produce a basis?" + }, + { + "text": "And then, which has a somewhat long answer, and what's the dimension, which is just a number, so it has a real short answer?" + }, + { + "text": "Can I give you the short answer first?" + }, + { + "text": "I shouldn't do it, but here it is." + }, + { + "text": "I can tell you the dimension of the column space." + }, + { + "text": "Let me start with this guy." + }, + { + "text": "What's its dimension?" + }, + { + "text": "I have an m by n matrix." + }, + { + "text": "The dimension of the column space is the rank, R. We actually got to that at the end of the last lecture, but only for an example." + }, + { + "text": "So I really have to say, OK, what's going on there?" + }, + { + "text": "I should produce a basis, and then I just look to see how many vectors I needed in that basis, and the answer will be R. Actually, I'll do that before I get on to the others." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk6.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..ac7425fbe27a77a7e448b576483b4c179e9a31f1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "What's a basis for the column space?" + }, + { + "text": "We've done all the work of row reduction, identifying the pivot columns, the ones that have pivots, the ones that end up with pivots, but now I the pivot columns I'm interested in are columns of A, the original A." + }, + { + "text": "And those pivot columns, there are R of them, the rank R counts those, those are a basis." + }, + { + "text": "So if I answer this question for the column space, the answer will be a basis is the pivot columns, and the dimension is the rank R. And there are pivot columns and everything great." + }, + { + "text": "OK, so that space we pretty well understand." + }, + { + "text": "I probably have a little going back to see that, to prove that this is a right answer, but you know it's the right answer." + }, + { + "text": "Now let me look at the row space." + }, + { + "text": "OK. Shall I tell you the dimension of the row space?" + }, + { + "text": "Yes." + }, + { + "text": "Before we do even an example, let me tell you the dimension of the row space." + }, + { + "text": "Its dimension is also R. The row space and the column space have the same dimension." + }, + { + "text": "That's a wonderful fact." + }, + { + "text": "The dimension of the column space of A transpose, that's the row space, is R. That space is R-dimensional." + }, + { + "text": "And so is this one." + }, + { + "text": "OK. That's the, that's the sort of insight that got used in this example." + }, + { + "text": "If those, if those, if those, are the three columns of a matrix, let me make them the three columns of a matrix by just erasing some brackets, OK, those are the three columns of a matrix, the rank of that matrix, if I look at the columns, it wasn't obvious to me anyway." + }, + { + "text": "But if I look at the rows, it's, now it's obvious." + }, + { + "text": "The row space of that matrix obviously is two-dimensional, because I can, I see a basis for the row space, this row and that row." + }, + { + "text": "And of course, strictly speaking, I'm supposed to transpose those guys, make them stand up." + }, + { + "text": "But the rank is two, and therefore the column space is two-dimensional by this wonderful fact that the row space and column space have the same dimension, and therefore there are only two pivot columns, not three, and, those, the three columns are dependent." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk7.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..7d55c74913379543a71fcc53c971f787baf12a92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, let me bury that error and talk about the row space." + }, + { + "text": "Well, I'm going to give you the dimensions of all the spaces, because that's the, such a nice answer." + }, + { + "text": "OK." + }, + { + "text": "So let me come back here." + }, + { + "text": "So we have this great fact to establish, that the row space, its dimension is also the rank." + }, + { + "text": "OK. What about the null space?" + }, + { + "text": "What's a basis for the null space?" + }, + { + "text": "What's the dimension of the null space?" + }, + { + "text": "Let me, I'll put that answer up here, for the null space." + }, + { + "text": "Well, how have we constructed the null space?" + }, + { + "text": "We took the matrix A, we did those row operations to get it into a form U or even further, we got it into the reduced form R, and then we read off special solutions." + }, + { + "text": "Special solutions, and every special solution came from a free variable." + }, + { + "text": "And those special solutions are in the null space, and the great thing is, they're a basis for it." + }, + { + "text": "So for the null space, a basis will be the special solutions." + }, + { + "text": "And there's one for every free variable, right?" + }, + { + "text": "For each free variable, we give that variable the value one, the other free variable zero." + }, + { + "text": "We get the pivot variables, we get a vector in the -- we get a special solution." + }, + { + "text": "So we get all together n minus R of them, because that's the number of free variables." + }, + { + "text": "If we have R, this is, the dimension is R, is the number of pivot variables, this is the number of free variables." + }, + { + "text": "So the beauty is that those special solutions do form a basis and tell us immediately that the dimension of the null space is n -- I'd better write this well, because it's so nice, n minus R. And you see the nice thing, that the two dimensions in this n-dimensional space, one subspace is R-dimensional, to be proved, that's the row space." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk8.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f4c70532a641ef630aa1f7bca077776017097cd4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "The other subspace is n minus R-dimensional, that's the null space." + }, + { + "text": "And the two dimensions, like, together, give n. The sum of R and n minus R is n. And that's just great." + }, + { + "text": "It's really copying the fact that we have n variables, R of them are pivot variables and n minus R are free variables and n all together." + }, + { + "text": "OK. And now what's the dimension of this poor misbegotten fourth subspace?" + }, + { + "text": "It's got to be m minus R. The dimension of this left null space, left out practically, is m minus R. Well, that's really just saying that this, again, the sum of that plus that is m. And m is correct." + }, + { + "text": "It's the number of columns in A transpose." + }, + { + "text": "A transpose is just as good a matrix as A." + }, + { + "text": "It just happens to be n by m. It happens to have m columns, so it will have m variables, when I go to Ax equals zero, and m of them and R of them will be pivot variables and m minus R will be free variables." + }, + { + "text": "A transpose is as good a matrix as A." + }, + { + "text": "It follows the same rule that this plus the dimension, this dimension plus this dimension adds up to the number of columns." + }, + { + "text": "And over here, A transpose has m columns." + }, + { + "text": "Okay." + }, + { + "text": "Okay, so I gave you the easy answer, the dimensions." + }, + { + "text": "Now can I go back to check on a basis?" + }, + { + "text": "We would like to think that, say, the row space." + }, + { + "text": "Because we've got a basis for the column space." + }, + { + "text": "The pivot columns give a basis for the column space." + }, + { + "text": "Now I'm asking you to look at the row space." + }, + { + "text": "And I you could say, okay, I can produce a basis for the row space by transposing my matrix, making those columns, then doing elimination, row reduction, and checking out the pivot columns in this transposed matrix." + }, + { + "text": "But that means you had to do all that row reduction on A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk9.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..8be162da3ff089e5c511aa65ea7d801c64cad56f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_27_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It ought to be possible, if we take a matrix A, let me take the matrix, maybe we had this matrix in the last lecture, one one one, two one two, three two three, one one one." + }, + { + "text": "Okay." + }, + { + "text": "That, that matrix was so easy, we spotted its pivot columns, one and two, without actually doing row reduction." + }, + { + "text": "But now let's do the job properly." + }, + { + "text": "So I subtract this away from this to produce a zero." + }, + { + "text": "So one two three one is fine." + }, + { + "text": "Subtracting that away leaves me minus one minus one zero, right?" + }, + { + "text": "And subtracting that from the last row, oh, well, that's easy." + }, + { + "text": "Okay, I'm doing row reduction." + }, + { + "text": "Now I've, the first column is all set." + }, + { + "text": "The second column, I now see the pivot, and I can clean up, if I, actually, okay, why don't I make the pivot into a one?" + }, + { + "text": "I'll multiply that row through by minus one, and then I have one one." + }, + { + "text": "That was an elementary operation, I'm allowed." + }, + { + "text": "Multiply a row by a number." + }, + { + "text": "And now I'll do elimination." + }, + { + "text": "Two of those away from that will knock this guy out and make this into a one." + }, + { + "text": "So that's now a zero and that's a one." + }, + { + "text": "Okay." + }, + { + "text": "Done." + }, + { + "text": "That's R. I'm seeing the identity matrix here, I'm seeing zeros below, and I'm seeing F there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk0.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6b8bcce949e11c9807b49a56c5ca68fdb459f818 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay, here is lecture ten in linear algebra." + }, + { + "text": "Two important things to do in this lecture." + }, + { + "text": "One is to correct an error from lecture nine." + }, + { + "text": "So the blackboard with that awful error is still with us." + }, + { + "text": "And the second, the big thing to do is to tell you about the four subspaces that come with a matrix." + }, + { + "text": "We've seen two subspaces, the column space and the null space, there's two to go." + }, + { + "text": "Okay." + }, + { + "text": "First of all, and this is a great way to recap and correct the previous lecture." + }, + { + "text": "So you remember I was just doing R3." + }, + { + "text": "I couldn't have taken a simpler example than R3." + }, + { + "text": "And I wrote down the standard basis." + }, + { + "text": "That's the standard basis." + }, + { + "text": "The basis, the obvious basis for the whole three-dimensional space." + }, + { + "text": "And then I wanted to make the point that there was nothing special, nothing about that basis that another basis couldn't have." + }, + { + "text": "It could have linear independence, it could span a space, there's lots of other bases." + }, + { + "text": "So I started with these vectors one one two and two two five, and those were independent." + }, + { + "text": "And then I said three three seven wouldn't do, because three three seven is the sum of those." + }, + { + "text": "So in my innocence, I put in three three eight." + }, + { + "text": "I figured probably if three three seven is on the plane, is, which I know, it's in the plane with these two, then probably three three eight sticks a little bit out of the plane." + }, + { + "text": "And it's independent and it gives a basis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk1.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..97d9d72b29a5aa923aae0ba9c0fb0da57e9db2ed --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "But after class, to my sorrow, student tells me, wait a minute, that third vector three three eight is not independent." + }, + { + "text": "And why did she say that?" + }, + { + "text": "She didn't actually take the time, didn't have to, to find what combination of this one and this one gives three three eight." + }, + { + "text": "She did something else." + }, + { + "text": "In other words, she looked ahead because she said, wait a minute, if I look at that matrix, it's not invertible." + }, + { + "text": "That third column can't be independent of the first two, because when I look at that matrix, it's got two identical rows." + }, + { + "text": "I have a square matrix." + }, + { + "text": "Its rows are obviously dependent." + }, + { + "text": "And that makes the columns dependent." + }, + { + "text": "So there's my error." + }, + { + "text": "When I look at the matrix A that has those three columns, those three columns can't be independent because that matrix is not invertible because it's got two equal rows." + }, + { + "text": "And today's lecture will reach the conclusion, the great conclusion, that connects the column space with the row space." + }, + { + "text": "So those are the row space is now going to be another one of my fundamental subspaces." + }, + { + "text": "The row space of this matrix or of this one, well, the row space of this one is okay." + }, + { + "text": "But the row space of this one, I'm looking at the rows of the matrix, oh, anyway, I'll have two equal rows and the row space will be only two-dimensional." + }, + { + "text": "The rank of the matrix with these columns will only be two, so only two of those columns can be independent too." + }, + { + "text": "The rows tell me something about the columns, in other words." + }, + { + "text": "Something that I should have noticed and I didn't." + }, + { + "text": "Okay." + }, + { + "text": "So now let me pin down these four fundamental subspaces." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk10.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..8f428ebe86b1b4488558f6fa55b8940ef758b264 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "Okay." + }, + { + "text": "What about its row space?" + }, + { + "text": "What happened to its row space?" + }, + { + "text": "Well, what happened, let me first ask, just because this is, sometimes something does happen." + }, + { + "text": "Its column space changed." + }, + { + "text": "The column space of R is not the column space of A, right?" + }, + { + "text": "Because one one one is certainly in the column space of A and certainly not in the column space of R. I did row operations." + }, + { + "text": "Those row operations preserved the row space, so the row so the column spaces are different." + }, + { + "text": "Different column spaces." + }, + { + "text": "Different column spaces." + }, + { + "text": "But I believe that they have the same row space." + }, + { + "text": "Same row space." + }, + { + "text": "I believe that the row space of that matrix and the row space of this matrix are identical." + }, + { + "text": "They have exactly the same vectors in them." + }, + { + "text": "Those vectors are vectors with four components, right?" + }, + { + "text": "They're all combinations of those rows." + }, + { + "text": "Or I believe you get the same thing by taking all combinations of these rows." + }, + { + "text": "And if true, what's a basis?" + }, + { + "text": "What's a basis for the row space of R?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk11.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..258e5999dbb0aea67696256511eb6b999136132a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it'll be a basis for the row space of the original A." + }, + { + "text": "But it's obviously a basis for the row space of R. What's a basis for the row space of that matrix?" + }, + { + "text": "The first two rows." + }, + { + "text": "So a basis for the row so a basis is for the row space of A or of R is the first R rows of R, not of A." + }, + { + "text": "Sometimes it's true for A, but not necessarily." + }, + { + "text": "But R, we definitely have a matrix here whose row space we can identify." + }, + { + "text": "The row space is spanned by the three rows." + }, + { + "text": "But if we want a basis, we want independence." + }, + { + "text": "So out goes row three." + }, + { + "text": "The row space is also spanned by the first two rows." + }, + { + "text": "This guy didn't contribute anything." + }, + { + "text": "And of course, over here, this one, two, three, one in the bottom didn't contribute anything." + }, + { + "text": "We had it already." + }, + { + "text": "So this, here's a basis, one zero one one and zero one one zero." + }, + { + "text": "I believe those are in the row space." + }, + { + "text": "I know they're independent." + }, + { + "text": "Why are they in the row space?" + }, + { + "text": "Why are those two vectors in the row space?" + }, + { + "text": "Because all those operations we did, which started with these rows and took combinations of them." + }, + { + "text": "I took this row minus this row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk12.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..d05a7eb6e4998c4acd748e3bb7087c68e6e29a80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "That gave me something that's still in the row space." + }, + { + "text": "That's the point." + }, + { + "text": "When I took a row minus a multiple of another row, I'm staying in the row space." + }, + { + "text": "The row space is not changing." + }, + { + "text": "My little basis for it is changing, and I've ended up with, sort of, the best basis." + }, + { + "text": "If the columns of the identity matrix are the best basis for R3 or Rn, the rows of this matrix are the best basis for the row space." + }, + { + "text": "Best in the sense of being as clean as I can make it." + }, + { + "text": "Starting off with the identity and then finishing up with whatever has to be in there." + }, + { + "text": "OK. Do you see, then, that the dimension is R?" + }, + { + "text": "For sure." + }, + { + "text": "Because we've got R pivots, R nonzero rows, we've got the right number of vectors, R. They're in the row space, they're independent, that's it." + }, + { + "text": "They are a basis for the row space." + }, + { + "text": "And we can even pin that down further." + }, + { + "text": "How do I know that every row of A is a combination?" + }, + { + "text": "How do I know they span the row space?" + }, + { + "text": "Oh, well, somebody says I've got the right number of them, so they must, but that's true." + }, + { + "text": "But let me just say, how do I know that this row is a combination of these?" + }, + { + "text": "By just reversing the steps of row reduction." + }, + { + "text": "If I just reverse the steps and go from A, from R back to A, then what do I, what am I doing?" + }, + { + "text": "I'm starting with these rows, I'm taking combinations of them, after a couple of steps, undoing the subtractions that I did before, I'm back to these rows." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk13.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..7b0edabbd24233827c7692f63429589952dac1bc --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "So these rows are combinations of those rows, those rows are combinations of those rows, the two row spaces are the same, the bases are the same, and the natural basis is this guy." + }, + { + "text": "Is that all right for the row space?" + }, + { + "text": "The row space is sitting there in R, in its cleanest possible form." + }, + { + "text": "OK. Now what about the fourth guy, the null space of A transpose?" + }, + { + "text": "First of all, why do I call that the left null space?" + }, + { + "text": "So let me save that and bring that down." + }, + { + "text": "OK." + }, + { + "text": "So the fourth space is the null space of A transpose." + }, + { + "text": "So it has in it vectors, let me call them y, so that A transpose y equals zero." + }, + { + "text": "If A transpose y equals zero, then y is in the null space of A transpose, of course." + }, + { + "text": "So this is a matrix times a column equaling zero." + }, + { + "text": "And now, because I want y to sit on the left, and I want A instead of A transpose, I'll just transpose that equation." + }, + { + "text": "Can I just transpose that?" + }, + { + "text": "On the right, it makes the zero vector lie down." + }, + { + "text": "And on the left, it's a product, A transpose times y." + }, + { + "text": "If I take the transpose, then they come in opposite order, right?" + }, + { + "text": "So it's y transpose times A transpose transpose, but nobody's going to leave it like that." + }, + { + "text": "That's A transpose transpose is just A, of course." + }, + { + "text": "When I transposed A transpose, I got back to A." + }, + { + "text": "Now, do you see what I have now?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk14.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7a889f79409e9a95fbd4cc01518da4b9706c49d1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "I have a row vector, y transpose, multiplying A and multiplying from the left." + }, + { + "text": "That's why I call it the left null space." + }, + { + "text": "But by making it, putting it on the left, I had to make it into a row instead of a column vector." + }, + { + "text": "And so my convention is I usually don't do that, I usually stay with A transpose y equals zero." + }, + { + "text": "OK. And you might ask, how do we get a basis, or I might ask, how do we get a basis for this fourth space, this left null space?" + }, + { + "text": "OK." + }, + { + "text": "I'll do it the example." + }, + { + "text": "As always, ah, not that one." + }, + { + "text": "The left null space is not jumping out at me here." + }, + { + "text": "I know which are the free variables, the special solutions, but those are special solutions to Ax equals zero, and now I'm looking at A transpose and I'm not seeing it here." + }, + { + "text": "So, but somehow you feel that the work that you did, which simplified A to R, should have revealed the left null space too." + }, + { + "text": "And it's slightly less immediate, but it's there." + }, + { + "text": "So from A to R, I took some steps, and I guess I'm interested in what were those steps, or what were all of them together." + }, + { + "text": "I don't want to -- I'm not interested in what particular ones they were." + }, + { + "text": "I'm interested in what was the whole matrix that took me from A to R. How would you find that?" + }, + { + "text": "Do you remember Gauss-Jordan, where you tack on the identity matrix?" + }, + { + "text": "Let's do that again." + }, + { + "text": "So I'll do it above here." + }, + { + "text": "So this is now the idea of I take the matrix A, which is m by n. In Gauss-Jordan, when we saw him before, A was a square invertible matrix and we were finding its inverse." + }, + { + "text": "Now the matrix isn't square, it's probably rectangular." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk15.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3c045b6d07a6635d896789ba37b0d578bd175e92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "But I'll still tack on the identity matrix, and of course, since these have length m, it better be m by m. And now I'll do the reduced row echelon form of this matrix." + }, + { + "text": "And what do I get?" + }, + { + "text": "The reduced row echelon form starts with these columns, starts with the first columns, works like mad, and produces R. Of course, still the same size, m by n, and we did it before." + }, + { + "text": "And then whatever it did to get R, something else is going to show up here." + }, + { + "text": "Let me call it E, m by m. It's whatever you see that E is just going to contain a record of what we did." + }, + { + "text": "We did whatever it took to get A to become R. And at the same time, we were doing it to the identity matrix." + }, + { + "text": "So we started with the identity matrix, we buzzed along." + }, + { + "text": "So we took some -- all this row reduction amounted to multiplying on the left by some matrix, some series of elementary matrices that all together gave us one matrix, and that matrix is E. So all this row reduction stuff amounted to multiplying by E. How do I know that?" + }, + { + "text": "It certainly amounted to multiplying by something, and that something took I to E, so that something was E. So now look at the first part, E A is R. No big deal." + }, + { + "text": "All I've said is that the row reduction steps that we all know well, taking A to R, are in a- in some matrix, and I can find out what that matrix is by just tacking I on and seeing what comes out." + }, + { + "text": "What comes out is E. Let's just review the invertible square case." + }, + { + "text": "What happened then?" + }, + { + "text": "Because I was interested in it in chapter two also." + }, + { + "text": "When A was square and invertible, I took A I, I did row elimination, what was the R that came out?" + }, + { + "text": "It was I." + }, + { + "text": "So in chapter two, in chapter two, R was I." + }, + { + "text": "The row- the reduced row echelon form of a nice invertible square matrix is the identity." + }, + { + "text": "So if R was I in that case, then E was A inverse, because E A is I." + }, + { + "text": "Good." + }, + { + "text": "That's- that was good and easy." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk16.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..c5a8adc4741aeb68371eb235609b24dad795df03 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now what I'm saying is that there still is an E, it's not A inverse anymore, because A is a rectangular, it hasn't got an inverse." + }, + { + "text": "But there is still some matrix E that connected this to this." + }, + { + "text": "Oh, I should have figured out in advance what it was." + }, + { + "text": "Shoot." + }, + { + "text": "I didn't- I did those steps and sort of erased as I went, and, I should have done them to the identity, too." + }, + { + "text": "Can I do that?" + }, + { + "text": "Can I do that?" + }, + { + "text": "I'll keep the identity matrix, like I'm supposed to do, and I'll do the same operations on it and see what I end up with." + }, + { + "text": "Okay." + }, + { + "text": "So I'm starting with the identity, which I'll write in light, light enough, but okay, what did I do?" + }, + { + "text": "I subtracted that row from that one and that row from that one." + }, + { + "text": "Okay, I'll do that to the identity." + }, + { + "text": "So I subtract that first row from row two and row three." + }, + { + "text": "Good." + }, + { + "text": "Then I think I multiply, do you remember, I multiplied row two by minus one?" + }, + { + "text": "Let me just do that." + }, + { + "text": "Then what did I do?" + }, + { + "text": "I subtracted two of row two away from row one." + }, + { + "text": "I better do that." + }, + { + "text": "Subtract two of this away from this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk17.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..368775ffcdaa5a9fe2c24f8c85bcb4963097a79c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's minus one, two of these away leaves a plus two and zero." + }, + { + "text": "I believe that's E. The way to check is to see, multiply that E by this A, just to see, did I do it right?" + }, + { + "text": "So I believe E was minus one, two, zero, one minus one, zero, and minus one, zero, one." + }, + { + "text": "Okay." + }, + { + "text": "That's my E, that's my A, and that's R. All right." + }, + { + "text": "All I'm struggling to do is write the reason I wanted this blasted E was so that I could figure out the left null space." + }, + { + "text": "Not only its dimension, which I know." + }, + { + "text": "Actually, what is the dimension of the left null space?" + }, + { + "text": "Here's my matrix." + }, + { + "text": "What's the rank of the matrix?" + }, + { + "text": "Two." + }, + { + "text": "And the dimension of the left null space is supposed to be M minus R, three minus two, one." + }, + { + "text": "I believe that the left null space is one-dimensional." + }, + { + "text": "There is one combination of those three rows that produces the zero row." + }, + { + "text": "There is a basis." + }, + { + "text": "A basis for the left null space has only got one vector in it." + }, + { + "text": "And what is that vector?" + }, + { + "text": "It's here in the last row of E. But, ah, we could have seen it earlier." + }, + { + "text": "What combination of those rows gives the zero row?" + }, + { + "text": "Minus one of that, plus one of that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk18.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..9f5e8b1fcc2242dbdc56d379cbc7126ada792e31 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a basis for the left null space of this matrix, I'm looking for combinations of rows that give the zero row, if I'm looking at the left null space." + }, + { + "text": "For the null space, I'm looking at combinations of columns to get the zero column." + }, + { + "text": "Now I'm looking at combinations of these three rows to get the zero row, and of course, there is my zero row, and here is my vector that produced it." + }, + { + "text": "Minus one of that row and one of that row." + }, + { + "text": "Obvious." + }, + { + "text": "Okay." + }, + { + "text": "So in that example, and actually in all examples, we have seen how to produce a basis for the left null space." + }, + { + "text": "I won't ask you that all the time." + }, + { + "text": "Because it didn't come out immediately from R, we had to keep track of E for that left null space." + }, + { + "text": "But at least it didn't require us to transpose the matrix and start all over again." + }, + { + "text": "Okay." + }, + { + "text": "Those are the four subspaces." + }, + { + "text": "Can I review them?" + }, + { + "text": "The row space and the null space are in Rn." + }, + { + "text": "Their dimensions add to n. The column space and the left null space are in Rm, and their dimensions add to m. Okay." + }, + { + "text": "So let me close these last minutes by pushing you a little bit more to a new type of vector space." + }, + { + "text": "All our vector spaces, all the ones that we took seriously, have been subspaces of some real three- or n-dimensional space." + }, + { + "text": "Now I'm going to write down another vector space, a new vector space." + }, + { + "text": "Say all three by three matrices." + }, + { + "text": "My matrices are the vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk19.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..c1658ee474fcf6206f54d67e4dededa02a1ef92c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Is that all right?" + }, + { + "text": "I'm just naming them." + }, + { + "text": "You can put quotes around vectors." + }, + { + "text": "Every three by three matrix is one of my vectors." + }, + { + "text": "Now how am I entitled to call those things vectors?" + }, + { + "text": "I mean, they look very much like matrices." + }, + { + "text": "But they're vectors in my vector space because they obey the rules." + }, + { + "text": "All I'm supposed to be able to do with vectors is add them." + }, + { + "text": "I can add matrices." + }, + { + "text": "I'm supposed to be able to multiply them by scalar numbers, like seven." + }, + { + "text": "Well, I can multiply a matrix by seven." + }, + { + "text": "And I can take combinations of matrices." + }, + { + "text": "I can take three of one matrix minus five of another matrix." + }, + { + "text": "And those combinations, there's a zero matrix, the matrix that has all zeros in it." + }, + { + "text": "If I add that to another matrix, it doesn't change it." + }, + { + "text": "All the good stuff." + }, + { + "text": "If I multiply a matrix by one, it doesn't change it." + }, + { + "text": "All those eight rules for a vector space that we never wrote down, all easily satisfied." + }, + { + "text": "So now we have a different --." + }, + { + "text": "Now, of course, you can say you can multiply those matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk2.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..b92bd923d792a0f92ab4de95b7867006e9880f71 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here are the four fundamental subspaces." + }, + { + "text": "This is really the heart of this approach to linear algebra, to see these four subspaces, how they're related." + }, + { + "text": "So what are they?" + }, + { + "text": "The column space, C of A." + }, + { + "text": "The null space, N of A." + }, + { + "text": "And now comes the row space, something new." + }, + { + "text": "The row space, what's in that?" + }, + { + "text": "It's all combinations of the rows." + }, + { + "text": "That's natural." + }, + { + "text": "We want a space, so we have to take all combinations and we start with the rows." + }, + { + "text": "So the rows span the row space." + }, + { + "text": "Are the rows a basis for the row space?" + }, + { + "text": "Maybe so, maybe no." + }, + { + "text": "The rows are a basis for the row space when they're independent." + }, + { + "text": "But if they're dependent, as in this example, my error from last time, they're not, those three rows are not a basis, the row space would only be two-dimensional, I only need two rows for a basis." + }, + { + "text": "So the row space, now what's in it?" + }, + { + "text": "It's all combinations of the rows of A." + }, + { + "text": "All combinations of the rows of A." + }, + { + "text": "But I don't like working with row vectors." + }, + { + "text": "All my vectors have been column vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk20.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..56956e8347a8f8c1f8522690db77860dcc6953b9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "I don't care." + }, + { + "text": "For the moment, I'm only thinking of these matrices as forming a vector space, so I am only doing A plus B and C times A. I'm not interested in A, B for now." + }, + { + "text": "The fact that I can multiply is not relevant to a vector space." + }, + { + "text": "OK, so I have three by three matrices." + }, + { + "text": "And how about subspaces?" + }, + { + "text": "What's, tell me a subspace of this matrix space." + }, + { + "text": "Let me call this matrix space M. That's my matrix space, my space of all three by three matrices." + }, + { + "text": "Tell me a subspace of it." + }, + { + "text": "OK, what about the upper triangular matrices?" + }, + { + "text": "So subspaces, subspaces of M. All upper triangular matrices." + }, + { + "text": "Another subspace." + }, + { + "text": "All symmetric matrices." + }, + { + "text": "The intersection of two subspaces is supposed to be a subspace." + }, + { + "text": "We gave a little effort to the proof of that fact." + }, + { + "text": "If I look at the matrices that are in this subspace, they're symmetric, and they're also in this subspace, they're upper triangular." + }, + { + "text": "What do they look like?" + }, + { + "text": "Well, if they're symmetric, but they have zeros below the diagonal, they better have zeros above the diagonal." + }, + { + "text": "So the intersection would be diagonal matrices." + }, + { + "text": "That's another subspace, smaller than those." + }, + { + "text": "How can I use the word smaller?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk21.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..ffcdd44ed2f644726e04b27114327cb30bc7fb92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, I'm now entitled to use the word smaller." + }, + { + "text": "I mean, well, one way to say is, OK, these are contained in those." + }, + { + "text": "These are contained in those." + }, + { + "text": "But more precisely, I could give the dimension of these spaces." + }, + { + "text": "So I could, we can compute, let's compute it next time." + }, + { + "text": "The dimension of all upper, of the subspace of upper triangular three by three matrices." + }, + { + "text": "The dimension of symmetric three by three matrices." + }, + { + "text": "The dimension of diagonal three by three matrices." + }, + { + "text": "Well, to produce dimension, that means I'm supposed to produce a basis." + }, + { + "text": "And then I just count how many I needed in the basis." + }, + { + "text": "Let me give you the answer for this one." + }, + { + "text": "What's the dimension?" + }, + { + "text": "The dimension of this, say, this subspace, let me call it D, all diagonal matrices." + }, + { + "text": "The dimension of this subspace is, as I write, you're working it out, three." + }, + { + "text": "Because here's a matrix in this, it's a diagonal matrix." + }, + { + "text": "Here's another one." + }, + { + "text": "Here's another one." + }, + { + "text": "Better make it diagonal, let me put a seven there." + }, + { + "text": "That was not a very great choice, but it's three diagonal matrices, and I believe that they're a basis." + }, + { + "text": "I believe that those three matrices are independent, and I believe that any diagonal matrix is a combination of those three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk22.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..8c6bce8cf8085e6544c31ae6926bb7ccf18b983e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk22.json @@ -0,0 +1,20 @@ +[ + { + "text": "So they span the subspace of diagonal matrices." + }, + { + "text": "Do you see that idea?" + }, + { + "text": "It's like stretching the idea from Rn to Rn by n, three by three, but we can still add, we can still multiply by numbers, and we just ignore the fact that we can multiply two matrices together." + }, + { + "text": "Okay." + }, + { + "text": "Thank you." + }, + { + "text": "That's lecture ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk3.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..25f31647b76274f9088c60d1292bcc43915d3fb0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'd like to stay with column vectors." + }, + { + "text": "How can I get to column vectors out of these rows?" + }, + { + "text": "I transpose the matrix." + }, + { + "text": "So if that's OK with you, I'm going to transpose the matrix, I'm going to say all combinations of the columns of A transpose." + }, + { + "text": "And that allows me to use the convenient notation, the column space of A transpose." + }, + { + "text": "Nothing, no mathematics went on there, we just got some vectors that were lying down to stand up." + }, + { + "text": "But it means that we can use this column space of A transpose, that's telling me in a nice matrix notation what the row space is." + }, + { + "text": "OK. And finally is another null space." + }, + { + "text": "The fourth fundamental space will be the null space of A transpose." + }, + { + "text": "The fourth guy is the null space of A transpose." + }, + { + "text": "And of course, my notation is N of A transpose." + }, + { + "text": "That's the null space of A transpose." + }, + { + "text": "Now, we don't have a perfect name for this space as a, as a, connecting with A, but our usual name is the left null space, and I'll show you why in a moment." + }, + { + "text": "So often I call this the, just to write that word, the left null space of A." + }, + { + "text": "So just the way we have the row space of A and we switch it to the column space of A transpose, so we have this space of guys that I call the left null space of A, but the good notation is it's the null space of A transpose." + }, + { + "text": "OK. Those are four spaces." + }, + { + "text": "Where are those spaces?" + }, + { + "text": "What big space are they in for when A is m by n?" + }, + { + "text": "In that case, the null space of A, what's in the null space of A?" + }, + { + "text": "Vectors with n components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk4.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c2575473d88ff4598107e190483f0484b6558678 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Solutions to Ax equals zero." + }, + { + "text": "So the null space of A is n R n. What's in the column space of A?" + }, + { + "text": "Well, columns." + }, + { + "text": "How many components do those columns have?" + }, + { + "text": "m. So this column space is n R m. What about the column space of A transpose, which are just a disguised way of saying the rows of A?" + }, + { + "text": "The rows of A in this three by six matrix have six components, n components." + }, + { + "text": "The column space is n R n. And the null space of A transpose, I see that this fourth space is already getting second, you know, second class citizen treatment and it doesn't deserve it." + }, + { + "text": "It's, it should be there, it is there, and shouldn't be squeezed." + }, + { + "text": "The null space of A transpose, well, if the null space of A had vectors with n components, the null space of A transpose will be n R m. I want to draw a picture of the four spaces." + }, + { + "text": "OK. OK." + }, + { + "text": "Here are the four spaces." + }, + { + "text": "OK, let me put n dimensional space over on this side." + }, + { + "text": "Then which were the subspaces in R n?" + }, + { + "text": "The null space was and the row space was." + }, + { + "text": "So here we have the can I make that picture of the row space?" + }, + { + "text": "And can I make this kind of picture of the null space?" + }, + { + "text": "That's just meant to be a sketch, to remind you that they're in this which, you know, how, what type of vectors are in it?" + }, + { + "text": "Vectors with n components." + }, + { + "text": "Over here, inside consisting of vectors with m components is the column space and what I'm calling the null space of A transpose." + }, + { + "text": "Those are the ones with m components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk5.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..f4e64e208c1a1d8e07a9a66a6a6c59f8c4cbcec8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. To understand these spaces is our job now." + }, + { + "text": "Because by understanding those spaces, we know everything about this half of linear algebra." + }, + { + "text": "What do I mean by understanding those spaces?" + }, + { + "text": "I would like to know a basis for those spaces." + }, + { + "text": "For each one of those spaces, how would I create, construct a basis?" + }, + { + "text": "What systematic way would produce a basis?" + }, + { + "text": "And what's their dimension?" + }, + { + "text": "OK." + }, + { + "text": "So for each of the four spaces, I have to answer those questions." + }, + { + "text": "How do I produce a basis?" + }, + { + "text": "And then, which has a somewhat long answer, and what's the dimension, which is just a number, so it has a real short answer?" + }, + { + "text": "Can I give you the short answer first?" + }, + { + "text": "I shouldn't do it, but here it is." + }, + { + "text": "I can tell you the dimension of the column space." + }, + { + "text": "Let me start with this guy." + }, + { + "text": "What's its dimension?" + }, + { + "text": "I have an m by n matrix." + }, + { + "text": "The dimension of the column space is the rank, R. We actually got to that at the end of the last lecture, but only for an example." + }, + { + "text": "So I really have to say, OK, what's going on there?" + }, + { + "text": "I should produce a basis, and then I just look to see how many vectors I needed in that basis, and the answer will be R. Actually, I'll do that before I get on to the others." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk6.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..ac7425fbe27a77a7e448b576483b4c179e9a31f1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "What's a basis for the column space?" + }, + { + "text": "We've done all the work of row reduction, identifying the pivot columns, the ones that have pivots, the ones that end up with pivots, but now I the pivot columns I'm interested in are columns of A, the original A." + }, + { + "text": "And those pivot columns, there are R of them, the rank R counts those, those are a basis." + }, + { + "text": "So if I answer this question for the column space, the answer will be a basis is the pivot columns, and the dimension is the rank R. And there are pivot columns and everything great." + }, + { + "text": "OK, so that space we pretty well understand." + }, + { + "text": "I probably have a little going back to see that, to prove that this is a right answer, but you know it's the right answer." + }, + { + "text": "Now let me look at the row space." + }, + { + "text": "OK. Shall I tell you the dimension of the row space?" + }, + { + "text": "Yes." + }, + { + "text": "Before we do even an example, let me tell you the dimension of the row space." + }, + { + "text": "Its dimension is also R. The row space and the column space have the same dimension." + }, + { + "text": "That's a wonderful fact." + }, + { + "text": "The dimension of the column space of A transpose, that's the row space, is R. That space is R-dimensional." + }, + { + "text": "And so is this one." + }, + { + "text": "OK. That's the, that's the sort of insight that got used in this example." + }, + { + "text": "If those, if those, if those, are the three columns of a matrix, let me make them the three columns of a matrix by just erasing some brackets, OK, those are the three columns of a matrix, the rank of that matrix, if I look at the columns, it wasn't obvious to me anyway." + }, + { + "text": "But if I look at the rows, it's, now it's obvious." + }, + { + "text": "The row space of that matrix obviously is two-dimensional, because I can, I see a basis for the row space, this row and that row." + }, + { + "text": "And of course, strictly speaking, I'm supposed to transpose those guys, make them stand up." + }, + { + "text": "But the rank is two, and therefore the column space is two-dimensional by this wonderful fact that the row space and column space have the same dimension, and therefore there are only two pivot columns, not three, and, those, the three columns are dependent." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk7.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..7d55c74913379543a71fcc53c971f787baf12a92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, let me bury that error and talk about the row space." + }, + { + "text": "Well, I'm going to give you the dimensions of all the spaces, because that's the, such a nice answer." + }, + { + "text": "OK." + }, + { + "text": "So let me come back here." + }, + { + "text": "So we have this great fact to establish, that the row space, its dimension is also the rank." + }, + { + "text": "OK. What about the null space?" + }, + { + "text": "What's a basis for the null space?" + }, + { + "text": "What's the dimension of the null space?" + }, + { + "text": "Let me, I'll put that answer up here, for the null space." + }, + { + "text": "Well, how have we constructed the null space?" + }, + { + "text": "We took the matrix A, we did those row operations to get it into a form U or even further, we got it into the reduced form R, and then we read off special solutions." + }, + { + "text": "Special solutions, and every special solution came from a free variable." + }, + { + "text": "And those special solutions are in the null space, and the great thing is, they're a basis for it." + }, + { + "text": "So for the null space, a basis will be the special solutions." + }, + { + "text": "And there's one for every free variable, right?" + }, + { + "text": "For each free variable, we give that variable the value one, the other free variable zero." + }, + { + "text": "We get the pivot variables, we get a vector in the -- we get a special solution." + }, + { + "text": "So we get all together n minus R of them, because that's the number of free variables." + }, + { + "text": "If we have R, this is, the dimension is R, is the number of pivot variables, this is the number of free variables." + }, + { + "text": "So the beauty is that those special solutions do form a basis and tell us immediately that the dimension of the null space is n -- I'd better write this well, because it's so nice, n minus R. And you see the nice thing, that the two dimensions in this n-dimensional space, one subspace is R-dimensional, to be proved, that's the row space." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk8.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f4c70532a641ef630aa1f7bca077776017097cd4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "The other subspace is n minus R-dimensional, that's the null space." + }, + { + "text": "And the two dimensions, like, together, give n. The sum of R and n minus R is n. And that's just great." + }, + { + "text": "It's really copying the fact that we have n variables, R of them are pivot variables and n minus R are free variables and n all together." + }, + { + "text": "OK. And now what's the dimension of this poor misbegotten fourth subspace?" + }, + { + "text": "It's got to be m minus R. The dimension of this left null space, left out practically, is m minus R. Well, that's really just saying that this, again, the sum of that plus that is m. And m is correct." + }, + { + "text": "It's the number of columns in A transpose." + }, + { + "text": "A transpose is just as good a matrix as A." + }, + { + "text": "It just happens to be n by m. It happens to have m columns, so it will have m variables, when I go to Ax equals zero, and m of them and R of them will be pivot variables and m minus R will be free variables." + }, + { + "text": "A transpose is as good a matrix as A." + }, + { + "text": "It follows the same rule that this plus the dimension, this dimension plus this dimension adds up to the number of columns." + }, + { + "text": "And over here, A transpose has m columns." + }, + { + "text": "Okay." + }, + { + "text": "Okay, so I gave you the easy answer, the dimensions." + }, + { + "text": "Now can I go back to check on a basis?" + }, + { + "text": "We would like to think that, say, the row space." + }, + { + "text": "Because we've got a basis for the column space." + }, + { + "text": "The pivot columns give a basis for the column space." + }, + { + "text": "Now I'm asking you to look at the row space." + }, + { + "text": "And I you could say, okay, I can produce a basis for the row space by transposing my matrix, making those columns, then doing elimination, row reduction, and checking out the pivot columns in this transposed matrix." + }, + { + "text": "But that means you had to do all that row reduction on A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk9.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..8be162da3ff089e5c511aa65ea7d801c64cad56f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_28_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It ought to be possible, if we take a matrix A, let me take the matrix, maybe we had this matrix in the last lecture, one one one, two one two, three two three, one one one." + }, + { + "text": "Okay." + }, + { + "text": "That, that matrix was so easy, we spotted its pivot columns, one and two, without actually doing row reduction." + }, + { + "text": "But now let's do the job properly." + }, + { + "text": "So I subtract this away from this to produce a zero." + }, + { + "text": "So one two three one is fine." + }, + { + "text": "Subtracting that away leaves me minus one minus one zero, right?" + }, + { + "text": "And subtracting that from the last row, oh, well, that's easy." + }, + { + "text": "Okay, I'm doing row reduction." + }, + { + "text": "Now I've, the first column is all set." + }, + { + "text": "The second column, I now see the pivot, and I can clean up, if I, actually, okay, why don't I make the pivot into a one?" + }, + { + "text": "I'll multiply that row through by minus one, and then I have one one." + }, + { + "text": "That was an elementary operation, I'm allowed." + }, + { + "text": "Multiply a row by a number." + }, + { + "text": "And now I'll do elimination." + }, + { + "text": "Two of those away from that will knock this guy out and make this into a one." + }, + { + "text": "So that's now a zero and that's a one." + }, + { + "text": "Okay." + }, + { + "text": "Done." + }, + { + "text": "That's R. I'm seeing the identity matrix here, I'm seeing zeros below, and I'm seeing F there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk0.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6b8bcce949e11c9807b49a56c5ca68fdb459f818 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay, here is lecture ten in linear algebra." + }, + { + "text": "Two important things to do in this lecture." + }, + { + "text": "One is to correct an error from lecture nine." + }, + { + "text": "So the blackboard with that awful error is still with us." + }, + { + "text": "And the second, the big thing to do is to tell you about the four subspaces that come with a matrix." + }, + { + "text": "We've seen two subspaces, the column space and the null space, there's two to go." + }, + { + "text": "Okay." + }, + { + "text": "First of all, and this is a great way to recap and correct the previous lecture." + }, + { + "text": "So you remember I was just doing R3." + }, + { + "text": "I couldn't have taken a simpler example than R3." + }, + { + "text": "And I wrote down the standard basis." + }, + { + "text": "That's the standard basis." + }, + { + "text": "The basis, the obvious basis for the whole three-dimensional space." + }, + { + "text": "And then I wanted to make the point that there was nothing special, nothing about that basis that another basis couldn't have." + }, + { + "text": "It could have linear independence, it could span a space, there's lots of other bases." + }, + { + "text": "So I started with these vectors one one two and two two five, and those were independent." + }, + { + "text": "And then I said three three seven wouldn't do, because three three seven is the sum of those." + }, + { + "text": "So in my innocence, I put in three three eight." + }, + { + "text": "I figured probably if three three seven is on the plane, is, which I know, it's in the plane with these two, then probably three three eight sticks a little bit out of the plane." + }, + { + "text": "And it's independent and it gives a basis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk1.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..97d9d72b29a5aa923aae0ba9c0fb0da57e9db2ed --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "But after class, to my sorrow, student tells me, wait a minute, that third vector three three eight is not independent." + }, + { + "text": "And why did she say that?" + }, + { + "text": "She didn't actually take the time, didn't have to, to find what combination of this one and this one gives three three eight." + }, + { + "text": "She did something else." + }, + { + "text": "In other words, she looked ahead because she said, wait a minute, if I look at that matrix, it's not invertible." + }, + { + "text": "That third column can't be independent of the first two, because when I look at that matrix, it's got two identical rows." + }, + { + "text": "I have a square matrix." + }, + { + "text": "Its rows are obviously dependent." + }, + { + "text": "And that makes the columns dependent." + }, + { + "text": "So there's my error." + }, + { + "text": "When I look at the matrix A that has those three columns, those three columns can't be independent because that matrix is not invertible because it's got two equal rows." + }, + { + "text": "And today's lecture will reach the conclusion, the great conclusion, that connects the column space with the row space." + }, + { + "text": "So those are the row space is now going to be another one of my fundamental subspaces." + }, + { + "text": "The row space of this matrix or of this one, well, the row space of this one is okay." + }, + { + "text": "But the row space of this one, I'm looking at the rows of the matrix, oh, anyway, I'll have two equal rows and the row space will be only two-dimensional." + }, + { + "text": "The rank of the matrix with these columns will only be two, so only two of those columns can be independent too." + }, + { + "text": "The rows tell me something about the columns, in other words." + }, + { + "text": "Something that I should have noticed and I didn't." + }, + { + "text": "Okay." + }, + { + "text": "So now let me pin down these four fundamental subspaces." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk10.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..8f428ebe86b1b4488558f6fa55b8940ef758b264 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "Okay." + }, + { + "text": "What about its row space?" + }, + { + "text": "What happened to its row space?" + }, + { + "text": "Well, what happened, let me first ask, just because this is, sometimes something does happen." + }, + { + "text": "Its column space changed." + }, + { + "text": "The column space of R is not the column space of A, right?" + }, + { + "text": "Because one one one is certainly in the column space of A and certainly not in the column space of R. I did row operations." + }, + { + "text": "Those row operations preserved the row space, so the row so the column spaces are different." + }, + { + "text": "Different column spaces." + }, + { + "text": "Different column spaces." + }, + { + "text": "But I believe that they have the same row space." + }, + { + "text": "Same row space." + }, + { + "text": "I believe that the row space of that matrix and the row space of this matrix are identical." + }, + { + "text": "They have exactly the same vectors in them." + }, + { + "text": "Those vectors are vectors with four components, right?" + }, + { + "text": "They're all combinations of those rows." + }, + { + "text": "Or I believe you get the same thing by taking all combinations of these rows." + }, + { + "text": "And if true, what's a basis?" + }, + { + "text": "What's a basis for the row space of R?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk11.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..258e5999dbb0aea67696256511eb6b999136132a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it'll be a basis for the row space of the original A." + }, + { + "text": "But it's obviously a basis for the row space of R. What's a basis for the row space of that matrix?" + }, + { + "text": "The first two rows." + }, + { + "text": "So a basis for the row so a basis is for the row space of A or of R is the first R rows of R, not of A." + }, + { + "text": "Sometimes it's true for A, but not necessarily." + }, + { + "text": "But R, we definitely have a matrix here whose row space we can identify." + }, + { + "text": "The row space is spanned by the three rows." + }, + { + "text": "But if we want a basis, we want independence." + }, + { + "text": "So out goes row three." + }, + { + "text": "The row space is also spanned by the first two rows." + }, + { + "text": "This guy didn't contribute anything." + }, + { + "text": "And of course, over here, this one, two, three, one in the bottom didn't contribute anything." + }, + { + "text": "We had it already." + }, + { + "text": "So this, here's a basis, one zero one one and zero one one zero." + }, + { + "text": "I believe those are in the row space." + }, + { + "text": "I know they're independent." + }, + { + "text": "Why are they in the row space?" + }, + { + "text": "Why are those two vectors in the row space?" + }, + { + "text": "Because all those operations we did, which started with these rows and took combinations of them." + }, + { + "text": "I took this row minus this row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk12.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..d05a7eb6e4998c4acd748e3bb7087c68e6e29a80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "That gave me something that's still in the row space." + }, + { + "text": "That's the point." + }, + { + "text": "When I took a row minus a multiple of another row, I'm staying in the row space." + }, + { + "text": "The row space is not changing." + }, + { + "text": "My little basis for it is changing, and I've ended up with, sort of, the best basis." + }, + { + "text": "If the columns of the identity matrix are the best basis for R3 or Rn, the rows of this matrix are the best basis for the row space." + }, + { + "text": "Best in the sense of being as clean as I can make it." + }, + { + "text": "Starting off with the identity and then finishing up with whatever has to be in there." + }, + { + "text": "OK. Do you see, then, that the dimension is R?" + }, + { + "text": "For sure." + }, + { + "text": "Because we've got R pivots, R nonzero rows, we've got the right number of vectors, R. They're in the row space, they're independent, that's it." + }, + { + "text": "They are a basis for the row space." + }, + { + "text": "And we can even pin that down further." + }, + { + "text": "How do I know that every row of A is a combination?" + }, + { + "text": "How do I know they span the row space?" + }, + { + "text": "Oh, well, somebody says I've got the right number of them, so they must, but that's true." + }, + { + "text": "But let me just say, how do I know that this row is a combination of these?" + }, + { + "text": "By just reversing the steps of row reduction." + }, + { + "text": "If I just reverse the steps and go from A, from R back to A, then what do I, what am I doing?" + }, + { + "text": "I'm starting with these rows, I'm taking combinations of them, after a couple of steps, undoing the subtractions that I did before, I'm back to these rows." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk13.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..7b0edabbd24233827c7692f63429589952dac1bc --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "So these rows are combinations of those rows, those rows are combinations of those rows, the two row spaces are the same, the bases are the same, and the natural basis is this guy." + }, + { + "text": "Is that all right for the row space?" + }, + { + "text": "The row space is sitting there in R, in its cleanest possible form." + }, + { + "text": "OK. Now what about the fourth guy, the null space of A transpose?" + }, + { + "text": "First of all, why do I call that the left null space?" + }, + { + "text": "So let me save that and bring that down." + }, + { + "text": "OK." + }, + { + "text": "So the fourth space is the null space of A transpose." + }, + { + "text": "So it has in it vectors, let me call them y, so that A transpose y equals zero." + }, + { + "text": "If A transpose y equals zero, then y is in the null space of A transpose, of course." + }, + { + "text": "So this is a matrix times a column equaling zero." + }, + { + "text": "And now, because I want y to sit on the left, and I want A instead of A transpose, I'll just transpose that equation." + }, + { + "text": "Can I just transpose that?" + }, + { + "text": "On the right, it makes the zero vector lie down." + }, + { + "text": "And on the left, it's a product, A transpose times y." + }, + { + "text": "If I take the transpose, then they come in opposite order, right?" + }, + { + "text": "So it's y transpose times A transpose transpose, but nobody's going to leave it like that." + }, + { + "text": "That's A transpose transpose is just A, of course." + }, + { + "text": "When I transposed A transpose, I got back to A." + }, + { + "text": "Now, do you see what I have now?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk14.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7a889f79409e9a95fbd4cc01518da4b9706c49d1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "I have a row vector, y transpose, multiplying A and multiplying from the left." + }, + { + "text": "That's why I call it the left null space." + }, + { + "text": "But by making it, putting it on the left, I had to make it into a row instead of a column vector." + }, + { + "text": "And so my convention is I usually don't do that, I usually stay with A transpose y equals zero." + }, + { + "text": "OK. And you might ask, how do we get a basis, or I might ask, how do we get a basis for this fourth space, this left null space?" + }, + { + "text": "OK." + }, + { + "text": "I'll do it the example." + }, + { + "text": "As always, ah, not that one." + }, + { + "text": "The left null space is not jumping out at me here." + }, + { + "text": "I know which are the free variables, the special solutions, but those are special solutions to Ax equals zero, and now I'm looking at A transpose and I'm not seeing it here." + }, + { + "text": "So, but somehow you feel that the work that you did, which simplified A to R, should have revealed the left null space too." + }, + { + "text": "And it's slightly less immediate, but it's there." + }, + { + "text": "So from A to R, I took some steps, and I guess I'm interested in what were those steps, or what were all of them together." + }, + { + "text": "I don't want to -- I'm not interested in what particular ones they were." + }, + { + "text": "I'm interested in what was the whole matrix that took me from A to R. How would you find that?" + }, + { + "text": "Do you remember Gauss-Jordan, where you tack on the identity matrix?" + }, + { + "text": "Let's do that again." + }, + { + "text": "So I'll do it above here." + }, + { + "text": "So this is now the idea of I take the matrix A, which is m by n. In Gauss-Jordan, when we saw him before, A was a square invertible matrix and we were finding its inverse." + }, + { + "text": "Now the matrix isn't square, it's probably rectangular." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk15.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3c045b6d07a6635d896789ba37b0d578bd175e92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "But I'll still tack on the identity matrix, and of course, since these have length m, it better be m by m. And now I'll do the reduced row echelon form of this matrix." + }, + { + "text": "And what do I get?" + }, + { + "text": "The reduced row echelon form starts with these columns, starts with the first columns, works like mad, and produces R. Of course, still the same size, m by n, and we did it before." + }, + { + "text": "And then whatever it did to get R, something else is going to show up here." + }, + { + "text": "Let me call it E, m by m. It's whatever you see that E is just going to contain a record of what we did." + }, + { + "text": "We did whatever it took to get A to become R. And at the same time, we were doing it to the identity matrix." + }, + { + "text": "So we started with the identity matrix, we buzzed along." + }, + { + "text": "So we took some -- all this row reduction amounted to multiplying on the left by some matrix, some series of elementary matrices that all together gave us one matrix, and that matrix is E. So all this row reduction stuff amounted to multiplying by E. How do I know that?" + }, + { + "text": "It certainly amounted to multiplying by something, and that something took I to E, so that something was E. So now look at the first part, E A is R. No big deal." + }, + { + "text": "All I've said is that the row reduction steps that we all know well, taking A to R, are in a- in some matrix, and I can find out what that matrix is by just tacking I on and seeing what comes out." + }, + { + "text": "What comes out is E. Let's just review the invertible square case." + }, + { + "text": "What happened then?" + }, + { + "text": "Because I was interested in it in chapter two also." + }, + { + "text": "When A was square and invertible, I took A I, I did row elimination, what was the R that came out?" + }, + { + "text": "It was I." + }, + { + "text": "So in chapter two, in chapter two, R was I." + }, + { + "text": "The row- the reduced row echelon form of a nice invertible square matrix is the identity." + }, + { + "text": "So if R was I in that case, then E was A inverse, because E A is I." + }, + { + "text": "Good." + }, + { + "text": "That's- that was good and easy." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk16.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..c5a8adc4741aeb68371eb235609b24dad795df03 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now what I'm saying is that there still is an E, it's not A inverse anymore, because A is a rectangular, it hasn't got an inverse." + }, + { + "text": "But there is still some matrix E that connected this to this." + }, + { + "text": "Oh, I should have figured out in advance what it was." + }, + { + "text": "Shoot." + }, + { + "text": "I didn't- I did those steps and sort of erased as I went, and, I should have done them to the identity, too." + }, + { + "text": "Can I do that?" + }, + { + "text": "Can I do that?" + }, + { + "text": "I'll keep the identity matrix, like I'm supposed to do, and I'll do the same operations on it and see what I end up with." + }, + { + "text": "Okay." + }, + { + "text": "So I'm starting with the identity, which I'll write in light, light enough, but okay, what did I do?" + }, + { + "text": "I subtracted that row from that one and that row from that one." + }, + { + "text": "Okay, I'll do that to the identity." + }, + { + "text": "So I subtract that first row from row two and row three." + }, + { + "text": "Good." + }, + { + "text": "Then I think I multiply, do you remember, I multiplied row two by minus one?" + }, + { + "text": "Let me just do that." + }, + { + "text": "Then what did I do?" + }, + { + "text": "I subtracted two of row two away from row one." + }, + { + "text": "I better do that." + }, + { + "text": "Subtract two of this away from this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk17.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..368775ffcdaa5a9fe2c24f8c85bcb4963097a79c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's minus one, two of these away leaves a plus two and zero." + }, + { + "text": "I believe that's E. The way to check is to see, multiply that E by this A, just to see, did I do it right?" + }, + { + "text": "So I believe E was minus one, two, zero, one minus one, zero, and minus one, zero, one." + }, + { + "text": "Okay." + }, + { + "text": "That's my E, that's my A, and that's R. All right." + }, + { + "text": "All I'm struggling to do is write the reason I wanted this blasted E was so that I could figure out the left null space." + }, + { + "text": "Not only its dimension, which I know." + }, + { + "text": "Actually, what is the dimension of the left null space?" + }, + { + "text": "Here's my matrix." + }, + { + "text": "What's the rank of the matrix?" + }, + { + "text": "Two." + }, + { + "text": "And the dimension of the left null space is supposed to be M minus R, three minus two, one." + }, + { + "text": "I believe that the left null space is one-dimensional." + }, + { + "text": "There is one combination of those three rows that produces the zero row." + }, + { + "text": "There is a basis." + }, + { + "text": "A basis for the left null space has only got one vector in it." + }, + { + "text": "And what is that vector?" + }, + { + "text": "It's here in the last row of E. But, ah, we could have seen it earlier." + }, + { + "text": "What combination of those rows gives the zero row?" + }, + { + "text": "Minus one of that, plus one of that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk18.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..9f5e8b1fcc2242dbdc56d379cbc7126ada792e31 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a basis for the left null space of this matrix, I'm looking for combinations of rows that give the zero row, if I'm looking at the left null space." + }, + { + "text": "For the null space, I'm looking at combinations of columns to get the zero column." + }, + { + "text": "Now I'm looking at combinations of these three rows to get the zero row, and of course, there is my zero row, and here is my vector that produced it." + }, + { + "text": "Minus one of that row and one of that row." + }, + { + "text": "Obvious." + }, + { + "text": "Okay." + }, + { + "text": "So in that example, and actually in all examples, we have seen how to produce a basis for the left null space." + }, + { + "text": "I won't ask you that all the time." + }, + { + "text": "Because it didn't come out immediately from R, we had to keep track of E for that left null space." + }, + { + "text": "But at least it didn't require us to transpose the matrix and start all over again." + }, + { + "text": "Okay." + }, + { + "text": "Those are the four subspaces." + }, + { + "text": "Can I review them?" + }, + { + "text": "The row space and the null space are in Rn." + }, + { + "text": "Their dimensions add to n. The column space and the left null space are in Rm, and their dimensions add to m. Okay." + }, + { + "text": "So let me close these last minutes by pushing you a little bit more to a new type of vector space." + }, + { + "text": "All our vector spaces, all the ones that we took seriously, have been subspaces of some real three- or n-dimensional space." + }, + { + "text": "Now I'm going to write down another vector space, a new vector space." + }, + { + "text": "Say all three by three matrices." + }, + { + "text": "My matrices are the vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk19.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..c1658ee474fcf6206f54d67e4dededa02a1ef92c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Is that all right?" + }, + { + "text": "I'm just naming them." + }, + { + "text": "You can put quotes around vectors." + }, + { + "text": "Every three by three matrix is one of my vectors." + }, + { + "text": "Now how am I entitled to call those things vectors?" + }, + { + "text": "I mean, they look very much like matrices." + }, + { + "text": "But they're vectors in my vector space because they obey the rules." + }, + { + "text": "All I'm supposed to be able to do with vectors is add them." + }, + { + "text": "I can add matrices." + }, + { + "text": "I'm supposed to be able to multiply them by scalar numbers, like seven." + }, + { + "text": "Well, I can multiply a matrix by seven." + }, + { + "text": "And I can take combinations of matrices." + }, + { + "text": "I can take three of one matrix minus five of another matrix." + }, + { + "text": "And those combinations, there's a zero matrix, the matrix that has all zeros in it." + }, + { + "text": "If I add that to another matrix, it doesn't change it." + }, + { + "text": "All the good stuff." + }, + { + "text": "If I multiply a matrix by one, it doesn't change it." + }, + { + "text": "All those eight rules for a vector space that we never wrote down, all easily satisfied." + }, + { + "text": "So now we have a different --." + }, + { + "text": "Now, of course, you can say you can multiply those matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk2.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..b92bd923d792a0f92ab4de95b7867006e9880f71 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here are the four fundamental subspaces." + }, + { + "text": "This is really the heart of this approach to linear algebra, to see these four subspaces, how they're related." + }, + { + "text": "So what are they?" + }, + { + "text": "The column space, C of A." + }, + { + "text": "The null space, N of A." + }, + { + "text": "And now comes the row space, something new." + }, + { + "text": "The row space, what's in that?" + }, + { + "text": "It's all combinations of the rows." + }, + { + "text": "That's natural." + }, + { + "text": "We want a space, so we have to take all combinations and we start with the rows." + }, + { + "text": "So the rows span the row space." + }, + { + "text": "Are the rows a basis for the row space?" + }, + { + "text": "Maybe so, maybe no." + }, + { + "text": "The rows are a basis for the row space when they're independent." + }, + { + "text": "But if they're dependent, as in this example, my error from last time, they're not, those three rows are not a basis, the row space would only be two-dimensional, I only need two rows for a basis." + }, + { + "text": "So the row space, now what's in it?" + }, + { + "text": "It's all combinations of the rows of A." + }, + { + "text": "All combinations of the rows of A." + }, + { + "text": "But I don't like working with row vectors." + }, + { + "text": "All my vectors have been column vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk20.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..56956e8347a8f8c1f8522690db77860dcc6953b9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "I don't care." + }, + { + "text": "For the moment, I'm only thinking of these matrices as forming a vector space, so I am only doing A plus B and C times A. I'm not interested in A, B for now." + }, + { + "text": "The fact that I can multiply is not relevant to a vector space." + }, + { + "text": "OK, so I have three by three matrices." + }, + { + "text": "And how about subspaces?" + }, + { + "text": "What's, tell me a subspace of this matrix space." + }, + { + "text": "Let me call this matrix space M. That's my matrix space, my space of all three by three matrices." + }, + { + "text": "Tell me a subspace of it." + }, + { + "text": "OK, what about the upper triangular matrices?" + }, + { + "text": "So subspaces, subspaces of M. All upper triangular matrices." + }, + { + "text": "Another subspace." + }, + { + "text": "All symmetric matrices." + }, + { + "text": "The intersection of two subspaces is supposed to be a subspace." + }, + { + "text": "We gave a little effort to the proof of that fact." + }, + { + "text": "If I look at the matrices that are in this subspace, they're symmetric, and they're also in this subspace, they're upper triangular." + }, + { + "text": "What do they look like?" + }, + { + "text": "Well, if they're symmetric, but they have zeros below the diagonal, they better have zeros above the diagonal." + }, + { + "text": "So the intersection would be diagonal matrices." + }, + { + "text": "That's another subspace, smaller than those." + }, + { + "text": "How can I use the word smaller?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk21.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..ffcdd44ed2f644726e04b27114327cb30bc7fb92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, I'm now entitled to use the word smaller." + }, + { + "text": "I mean, well, one way to say is, OK, these are contained in those." + }, + { + "text": "These are contained in those." + }, + { + "text": "But more precisely, I could give the dimension of these spaces." + }, + { + "text": "So I could, we can compute, let's compute it next time." + }, + { + "text": "The dimension of all upper, of the subspace of upper triangular three by three matrices." + }, + { + "text": "The dimension of symmetric three by three matrices." + }, + { + "text": "The dimension of diagonal three by three matrices." + }, + { + "text": "Well, to produce dimension, that means I'm supposed to produce a basis." + }, + { + "text": "And then I just count how many I needed in the basis." + }, + { + "text": "Let me give you the answer for this one." + }, + { + "text": "What's the dimension?" + }, + { + "text": "The dimension of this, say, this subspace, let me call it D, all diagonal matrices." + }, + { + "text": "The dimension of this subspace is, as I write, you're working it out, three." + }, + { + "text": "Because here's a matrix in this, it's a diagonal matrix." + }, + { + "text": "Here's another one." + }, + { + "text": "Here's another one." + }, + { + "text": "Better make it diagonal, let me put a seven there." + }, + { + "text": "That was not a very great choice, but it's three diagonal matrices, and I believe that they're a basis." + }, + { + "text": "I believe that those three matrices are independent, and I believe that any diagonal matrix is a combination of those three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk22.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..8c6bce8cf8085e6544c31ae6926bb7ccf18b983e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk22.json @@ -0,0 +1,20 @@ +[ + { + "text": "So they span the subspace of diagonal matrices." + }, + { + "text": "Do you see that idea?" + }, + { + "text": "It's like stretching the idea from Rn to Rn by n, three by three, but we can still add, we can still multiply by numbers, and we just ignore the fact that we can multiply two matrices together." + }, + { + "text": "Okay." + }, + { + "text": "Thank you." + }, + { + "text": "That's lecture ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk3.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..25f31647b76274f9088c60d1292bcc43915d3fb0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'd like to stay with column vectors." + }, + { + "text": "How can I get to column vectors out of these rows?" + }, + { + "text": "I transpose the matrix." + }, + { + "text": "So if that's OK with you, I'm going to transpose the matrix, I'm going to say all combinations of the columns of A transpose." + }, + { + "text": "And that allows me to use the convenient notation, the column space of A transpose." + }, + { + "text": "Nothing, no mathematics went on there, we just got some vectors that were lying down to stand up." + }, + { + "text": "But it means that we can use this column space of A transpose, that's telling me in a nice matrix notation what the row space is." + }, + { + "text": "OK. And finally is another null space." + }, + { + "text": "The fourth fundamental space will be the null space of A transpose." + }, + { + "text": "The fourth guy is the null space of A transpose." + }, + { + "text": "And of course, my notation is N of A transpose." + }, + { + "text": "That's the null space of A transpose." + }, + { + "text": "Now, we don't have a perfect name for this space as a, as a, connecting with A, but our usual name is the left null space, and I'll show you why in a moment." + }, + { + "text": "So often I call this the, just to write that word, the left null space of A." + }, + { + "text": "So just the way we have the row space of A and we switch it to the column space of A transpose, so we have this space of guys that I call the left null space of A, but the good notation is it's the null space of A transpose." + }, + { + "text": "OK. Those are four spaces." + }, + { + "text": "Where are those spaces?" + }, + { + "text": "What big space are they in for when A is m by n?" + }, + { + "text": "In that case, the null space of A, what's in the null space of A?" + }, + { + "text": "Vectors with n components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk4.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c2575473d88ff4598107e190483f0484b6558678 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Solutions to Ax equals zero." + }, + { + "text": "So the null space of A is n R n. What's in the column space of A?" + }, + { + "text": "Well, columns." + }, + { + "text": "How many components do those columns have?" + }, + { + "text": "m. So this column space is n R m. What about the column space of A transpose, which are just a disguised way of saying the rows of A?" + }, + { + "text": "The rows of A in this three by six matrix have six components, n components." + }, + { + "text": "The column space is n R n. And the null space of A transpose, I see that this fourth space is already getting second, you know, second class citizen treatment and it doesn't deserve it." + }, + { + "text": "It's, it should be there, it is there, and shouldn't be squeezed." + }, + { + "text": "The null space of A transpose, well, if the null space of A had vectors with n components, the null space of A transpose will be n R m. I want to draw a picture of the four spaces." + }, + { + "text": "OK. OK." + }, + { + "text": "Here are the four spaces." + }, + { + "text": "OK, let me put n dimensional space over on this side." + }, + { + "text": "Then which were the subspaces in R n?" + }, + { + "text": "The null space was and the row space was." + }, + { + "text": "So here we have the can I make that picture of the row space?" + }, + { + "text": "And can I make this kind of picture of the null space?" + }, + { + "text": "That's just meant to be a sketch, to remind you that they're in this which, you know, how, what type of vectors are in it?" + }, + { + "text": "Vectors with n components." + }, + { + "text": "Over here, inside consisting of vectors with m components is the column space and what I'm calling the null space of A transpose." + }, + { + "text": "Those are the ones with m components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk5.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..f4e64e208c1a1d8e07a9a66a6a6c59f8c4cbcec8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. To understand these spaces is our job now." + }, + { + "text": "Because by understanding those spaces, we know everything about this half of linear algebra." + }, + { + "text": "What do I mean by understanding those spaces?" + }, + { + "text": "I would like to know a basis for those spaces." + }, + { + "text": "For each one of those spaces, how would I create, construct a basis?" + }, + { + "text": "What systematic way would produce a basis?" + }, + { + "text": "And what's their dimension?" + }, + { + "text": "OK." + }, + { + "text": "So for each of the four spaces, I have to answer those questions." + }, + { + "text": "How do I produce a basis?" + }, + { + "text": "And then, which has a somewhat long answer, and what's the dimension, which is just a number, so it has a real short answer?" + }, + { + "text": "Can I give you the short answer first?" + }, + { + "text": "I shouldn't do it, but here it is." + }, + { + "text": "I can tell you the dimension of the column space." + }, + { + "text": "Let me start with this guy." + }, + { + "text": "What's its dimension?" + }, + { + "text": "I have an m by n matrix." + }, + { + "text": "The dimension of the column space is the rank, R. We actually got to that at the end of the last lecture, but only for an example." + }, + { + "text": "So I really have to say, OK, what's going on there?" + }, + { + "text": "I should produce a basis, and then I just look to see how many vectors I needed in that basis, and the answer will be R. Actually, I'll do that before I get on to the others." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk6.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..ac7425fbe27a77a7e448b576483b4c179e9a31f1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "What's a basis for the column space?" + }, + { + "text": "We've done all the work of row reduction, identifying the pivot columns, the ones that have pivots, the ones that end up with pivots, but now I the pivot columns I'm interested in are columns of A, the original A." + }, + { + "text": "And those pivot columns, there are R of them, the rank R counts those, those are a basis." + }, + { + "text": "So if I answer this question for the column space, the answer will be a basis is the pivot columns, and the dimension is the rank R. And there are pivot columns and everything great." + }, + { + "text": "OK, so that space we pretty well understand." + }, + { + "text": "I probably have a little going back to see that, to prove that this is a right answer, but you know it's the right answer." + }, + { + "text": "Now let me look at the row space." + }, + { + "text": "OK. Shall I tell you the dimension of the row space?" + }, + { + "text": "Yes." + }, + { + "text": "Before we do even an example, let me tell you the dimension of the row space." + }, + { + "text": "Its dimension is also R. The row space and the column space have the same dimension." + }, + { + "text": "That's a wonderful fact." + }, + { + "text": "The dimension of the column space of A transpose, that's the row space, is R. That space is R-dimensional." + }, + { + "text": "And so is this one." + }, + { + "text": "OK. That's the, that's the sort of insight that got used in this example." + }, + { + "text": "If those, if those, if those, are the three columns of a matrix, let me make them the three columns of a matrix by just erasing some brackets, OK, those are the three columns of a matrix, the rank of that matrix, if I look at the columns, it wasn't obvious to me anyway." + }, + { + "text": "But if I look at the rows, it's, now it's obvious." + }, + { + "text": "The row space of that matrix obviously is two-dimensional, because I can, I see a basis for the row space, this row and that row." + }, + { + "text": "And of course, strictly speaking, I'm supposed to transpose those guys, make them stand up." + }, + { + "text": "But the rank is two, and therefore the column space is two-dimensional by this wonderful fact that the row space and column space have the same dimension, and therefore there are only two pivot columns, not three, and, those, the three columns are dependent." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk7.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..7d55c74913379543a71fcc53c971f787baf12a92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, let me bury that error and talk about the row space." + }, + { + "text": "Well, I'm going to give you the dimensions of all the spaces, because that's the, such a nice answer." + }, + { + "text": "OK." + }, + { + "text": "So let me come back here." + }, + { + "text": "So we have this great fact to establish, that the row space, its dimension is also the rank." + }, + { + "text": "OK. What about the null space?" + }, + { + "text": "What's a basis for the null space?" + }, + { + "text": "What's the dimension of the null space?" + }, + { + "text": "Let me, I'll put that answer up here, for the null space." + }, + { + "text": "Well, how have we constructed the null space?" + }, + { + "text": "We took the matrix A, we did those row operations to get it into a form U or even further, we got it into the reduced form R, and then we read off special solutions." + }, + { + "text": "Special solutions, and every special solution came from a free variable." + }, + { + "text": "And those special solutions are in the null space, and the great thing is, they're a basis for it." + }, + { + "text": "So for the null space, a basis will be the special solutions." + }, + { + "text": "And there's one for every free variable, right?" + }, + { + "text": "For each free variable, we give that variable the value one, the other free variable zero." + }, + { + "text": "We get the pivot variables, we get a vector in the -- we get a special solution." + }, + { + "text": "So we get all together n minus R of them, because that's the number of free variables." + }, + { + "text": "If we have R, this is, the dimension is R, is the number of pivot variables, this is the number of free variables." + }, + { + "text": "So the beauty is that those special solutions do form a basis and tell us immediately that the dimension of the null space is n -- I'd better write this well, because it's so nice, n minus R. And you see the nice thing, that the two dimensions in this n-dimensional space, one subspace is R-dimensional, to be proved, that's the row space." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk8.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f4c70532a641ef630aa1f7bca077776017097cd4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "The other subspace is n minus R-dimensional, that's the null space." + }, + { + "text": "And the two dimensions, like, together, give n. The sum of R and n minus R is n. And that's just great." + }, + { + "text": "It's really copying the fact that we have n variables, R of them are pivot variables and n minus R are free variables and n all together." + }, + { + "text": "OK. And now what's the dimension of this poor misbegotten fourth subspace?" + }, + { + "text": "It's got to be m minus R. The dimension of this left null space, left out practically, is m minus R. Well, that's really just saying that this, again, the sum of that plus that is m. And m is correct." + }, + { + "text": "It's the number of columns in A transpose." + }, + { + "text": "A transpose is just as good a matrix as A." + }, + { + "text": "It just happens to be n by m. It happens to have m columns, so it will have m variables, when I go to Ax equals zero, and m of them and R of them will be pivot variables and m minus R will be free variables." + }, + { + "text": "A transpose is as good a matrix as A." + }, + { + "text": "It follows the same rule that this plus the dimension, this dimension plus this dimension adds up to the number of columns." + }, + { + "text": "And over here, A transpose has m columns." + }, + { + "text": "Okay." + }, + { + "text": "Okay, so I gave you the easy answer, the dimensions." + }, + { + "text": "Now can I go back to check on a basis?" + }, + { + "text": "We would like to think that, say, the row space." + }, + { + "text": "Because we've got a basis for the column space." + }, + { + "text": "The pivot columns give a basis for the column space." + }, + { + "text": "Now I'm asking you to look at the row space." + }, + { + "text": "And I you could say, okay, I can produce a basis for the row space by transposing my matrix, making those columns, then doing elimination, row reduction, and checking out the pivot columns in this transposed matrix." + }, + { + "text": "But that means you had to do all that row reduction on A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk9.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..8be162da3ff089e5c511aa65ea7d801c64cad56f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_2_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It ought to be possible, if we take a matrix A, let me take the matrix, maybe we had this matrix in the last lecture, one one one, two one two, three two three, one one one." + }, + { + "text": "Okay." + }, + { + "text": "That, that matrix was so easy, we spotted its pivot columns, one and two, without actually doing row reduction." + }, + { + "text": "But now let's do the job properly." + }, + { + "text": "So I subtract this away from this to produce a zero." + }, + { + "text": "So one two three one is fine." + }, + { + "text": "Subtracting that away leaves me minus one minus one zero, right?" + }, + { + "text": "And subtracting that from the last row, oh, well, that's easy." + }, + { + "text": "Okay, I'm doing row reduction." + }, + { + "text": "Now I've, the first column is all set." + }, + { + "text": "The second column, I now see the pivot, and I can clean up, if I, actually, okay, why don't I make the pivot into a one?" + }, + { + "text": "I'll multiply that row through by minus one, and then I have one one." + }, + { + "text": "That was an elementary operation, I'm allowed." + }, + { + "text": "Multiply a row by a number." + }, + { + "text": "And now I'll do elimination." + }, + { + "text": "Two of those away from that will knock this guy out and make this into a one." + }, + { + "text": "So that's now a zero and that's a one." + }, + { + "text": "Okay." + }, + { + "text": "Done." + }, + { + "text": "That's R. I'm seeing the identity matrix here, I'm seeing zeros below, and I'm seeing F there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk0.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6b8bcce949e11c9807b49a56c5ca68fdb459f818 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay, here is lecture ten in linear algebra." + }, + { + "text": "Two important things to do in this lecture." + }, + { + "text": "One is to correct an error from lecture nine." + }, + { + "text": "So the blackboard with that awful error is still with us." + }, + { + "text": "And the second, the big thing to do is to tell you about the four subspaces that come with a matrix." + }, + { + "text": "We've seen two subspaces, the column space and the null space, there's two to go." + }, + { + "text": "Okay." + }, + { + "text": "First of all, and this is a great way to recap and correct the previous lecture." + }, + { + "text": "So you remember I was just doing R3." + }, + { + "text": "I couldn't have taken a simpler example than R3." + }, + { + "text": "And I wrote down the standard basis." + }, + { + "text": "That's the standard basis." + }, + { + "text": "The basis, the obvious basis for the whole three-dimensional space." + }, + { + "text": "And then I wanted to make the point that there was nothing special, nothing about that basis that another basis couldn't have." + }, + { + "text": "It could have linear independence, it could span a space, there's lots of other bases." + }, + { + "text": "So I started with these vectors one one two and two two five, and those were independent." + }, + { + "text": "And then I said three three seven wouldn't do, because three three seven is the sum of those." + }, + { + "text": "So in my innocence, I put in three three eight." + }, + { + "text": "I figured probably if three three seven is on the plane, is, which I know, it's in the plane with these two, then probably three three eight sticks a little bit out of the plane." + }, + { + "text": "And it's independent and it gives a basis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk1.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..97d9d72b29a5aa923aae0ba9c0fb0da57e9db2ed --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "But after class, to my sorrow, student tells me, wait a minute, that third vector three three eight is not independent." + }, + { + "text": "And why did she say that?" + }, + { + "text": "She didn't actually take the time, didn't have to, to find what combination of this one and this one gives three three eight." + }, + { + "text": "She did something else." + }, + { + "text": "In other words, she looked ahead because she said, wait a minute, if I look at that matrix, it's not invertible." + }, + { + "text": "That third column can't be independent of the first two, because when I look at that matrix, it's got two identical rows." + }, + { + "text": "I have a square matrix." + }, + { + "text": "Its rows are obviously dependent." + }, + { + "text": "And that makes the columns dependent." + }, + { + "text": "So there's my error." + }, + { + "text": "When I look at the matrix A that has those three columns, those three columns can't be independent because that matrix is not invertible because it's got two equal rows." + }, + { + "text": "And today's lecture will reach the conclusion, the great conclusion, that connects the column space with the row space." + }, + { + "text": "So those are the row space is now going to be another one of my fundamental subspaces." + }, + { + "text": "The row space of this matrix or of this one, well, the row space of this one is okay." + }, + { + "text": "But the row space of this one, I'm looking at the rows of the matrix, oh, anyway, I'll have two equal rows and the row space will be only two-dimensional." + }, + { + "text": "The rank of the matrix with these columns will only be two, so only two of those columns can be independent too." + }, + { + "text": "The rows tell me something about the columns, in other words." + }, + { + "text": "Something that I should have noticed and I didn't." + }, + { + "text": "Okay." + }, + { + "text": "So now let me pin down these four fundamental subspaces." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk10.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..8f428ebe86b1b4488558f6fa55b8940ef758b264 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "Okay." + }, + { + "text": "What about its row space?" + }, + { + "text": "What happened to its row space?" + }, + { + "text": "Well, what happened, let me first ask, just because this is, sometimes something does happen." + }, + { + "text": "Its column space changed." + }, + { + "text": "The column space of R is not the column space of A, right?" + }, + { + "text": "Because one one one is certainly in the column space of A and certainly not in the column space of R. I did row operations." + }, + { + "text": "Those row operations preserved the row space, so the row so the column spaces are different." + }, + { + "text": "Different column spaces." + }, + { + "text": "Different column spaces." + }, + { + "text": "But I believe that they have the same row space." + }, + { + "text": "Same row space." + }, + { + "text": "I believe that the row space of that matrix and the row space of this matrix are identical." + }, + { + "text": "They have exactly the same vectors in them." + }, + { + "text": "Those vectors are vectors with four components, right?" + }, + { + "text": "They're all combinations of those rows." + }, + { + "text": "Or I believe you get the same thing by taking all combinations of these rows." + }, + { + "text": "And if true, what's a basis?" + }, + { + "text": "What's a basis for the row space of R?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk11.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..258e5999dbb0aea67696256511eb6b999136132a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it'll be a basis for the row space of the original A." + }, + { + "text": "But it's obviously a basis for the row space of R. What's a basis for the row space of that matrix?" + }, + { + "text": "The first two rows." + }, + { + "text": "So a basis for the row so a basis is for the row space of A or of R is the first R rows of R, not of A." + }, + { + "text": "Sometimes it's true for A, but not necessarily." + }, + { + "text": "But R, we definitely have a matrix here whose row space we can identify." + }, + { + "text": "The row space is spanned by the three rows." + }, + { + "text": "But if we want a basis, we want independence." + }, + { + "text": "So out goes row three." + }, + { + "text": "The row space is also spanned by the first two rows." + }, + { + "text": "This guy didn't contribute anything." + }, + { + "text": "And of course, over here, this one, two, three, one in the bottom didn't contribute anything." + }, + { + "text": "We had it already." + }, + { + "text": "So this, here's a basis, one zero one one and zero one one zero." + }, + { + "text": "I believe those are in the row space." + }, + { + "text": "I know they're independent." + }, + { + "text": "Why are they in the row space?" + }, + { + "text": "Why are those two vectors in the row space?" + }, + { + "text": "Because all those operations we did, which started with these rows and took combinations of them." + }, + { + "text": "I took this row minus this row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk12.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..d05a7eb6e4998c4acd748e3bb7087c68e6e29a80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "That gave me something that's still in the row space." + }, + { + "text": "That's the point." + }, + { + "text": "When I took a row minus a multiple of another row, I'm staying in the row space." + }, + { + "text": "The row space is not changing." + }, + { + "text": "My little basis for it is changing, and I've ended up with, sort of, the best basis." + }, + { + "text": "If the columns of the identity matrix are the best basis for R3 or Rn, the rows of this matrix are the best basis for the row space." + }, + { + "text": "Best in the sense of being as clean as I can make it." + }, + { + "text": "Starting off with the identity and then finishing up with whatever has to be in there." + }, + { + "text": "OK. Do you see, then, that the dimension is R?" + }, + { + "text": "For sure." + }, + { + "text": "Because we've got R pivots, R nonzero rows, we've got the right number of vectors, R. They're in the row space, they're independent, that's it." + }, + { + "text": "They are a basis for the row space." + }, + { + "text": "And we can even pin that down further." + }, + { + "text": "How do I know that every row of A is a combination?" + }, + { + "text": "How do I know they span the row space?" + }, + { + "text": "Oh, well, somebody says I've got the right number of them, so they must, but that's true." + }, + { + "text": "But let me just say, how do I know that this row is a combination of these?" + }, + { + "text": "By just reversing the steps of row reduction." + }, + { + "text": "If I just reverse the steps and go from A, from R back to A, then what do I, what am I doing?" + }, + { + "text": "I'm starting with these rows, I'm taking combinations of them, after a couple of steps, undoing the subtractions that I did before, I'm back to these rows." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk13.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..7b0edabbd24233827c7692f63429589952dac1bc --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "So these rows are combinations of those rows, those rows are combinations of those rows, the two row spaces are the same, the bases are the same, and the natural basis is this guy." + }, + { + "text": "Is that all right for the row space?" + }, + { + "text": "The row space is sitting there in R, in its cleanest possible form." + }, + { + "text": "OK. Now what about the fourth guy, the null space of A transpose?" + }, + { + "text": "First of all, why do I call that the left null space?" + }, + { + "text": "So let me save that and bring that down." + }, + { + "text": "OK." + }, + { + "text": "So the fourth space is the null space of A transpose." + }, + { + "text": "So it has in it vectors, let me call them y, so that A transpose y equals zero." + }, + { + "text": "If A transpose y equals zero, then y is in the null space of A transpose, of course." + }, + { + "text": "So this is a matrix times a column equaling zero." + }, + { + "text": "And now, because I want y to sit on the left, and I want A instead of A transpose, I'll just transpose that equation." + }, + { + "text": "Can I just transpose that?" + }, + { + "text": "On the right, it makes the zero vector lie down." + }, + { + "text": "And on the left, it's a product, A transpose times y." + }, + { + "text": "If I take the transpose, then they come in opposite order, right?" + }, + { + "text": "So it's y transpose times A transpose transpose, but nobody's going to leave it like that." + }, + { + "text": "That's A transpose transpose is just A, of course." + }, + { + "text": "When I transposed A transpose, I got back to A." + }, + { + "text": "Now, do you see what I have now?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk14.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7a889f79409e9a95fbd4cc01518da4b9706c49d1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "I have a row vector, y transpose, multiplying A and multiplying from the left." + }, + { + "text": "That's why I call it the left null space." + }, + { + "text": "But by making it, putting it on the left, I had to make it into a row instead of a column vector." + }, + { + "text": "And so my convention is I usually don't do that, I usually stay with A transpose y equals zero." + }, + { + "text": "OK. And you might ask, how do we get a basis, or I might ask, how do we get a basis for this fourth space, this left null space?" + }, + { + "text": "OK." + }, + { + "text": "I'll do it the example." + }, + { + "text": "As always, ah, not that one." + }, + { + "text": "The left null space is not jumping out at me here." + }, + { + "text": "I know which are the free variables, the special solutions, but those are special solutions to Ax equals zero, and now I'm looking at A transpose and I'm not seeing it here." + }, + { + "text": "So, but somehow you feel that the work that you did, which simplified A to R, should have revealed the left null space too." + }, + { + "text": "And it's slightly less immediate, but it's there." + }, + { + "text": "So from A to R, I took some steps, and I guess I'm interested in what were those steps, or what were all of them together." + }, + { + "text": "I don't want to -- I'm not interested in what particular ones they were." + }, + { + "text": "I'm interested in what was the whole matrix that took me from A to R. How would you find that?" + }, + { + "text": "Do you remember Gauss-Jordan, where you tack on the identity matrix?" + }, + { + "text": "Let's do that again." + }, + { + "text": "So I'll do it above here." + }, + { + "text": "So this is now the idea of I take the matrix A, which is m by n. In Gauss-Jordan, when we saw him before, A was a square invertible matrix and we were finding its inverse." + }, + { + "text": "Now the matrix isn't square, it's probably rectangular." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk15.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3c045b6d07a6635d896789ba37b0d578bd175e92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "But I'll still tack on the identity matrix, and of course, since these have length m, it better be m by m. And now I'll do the reduced row echelon form of this matrix." + }, + { + "text": "And what do I get?" + }, + { + "text": "The reduced row echelon form starts with these columns, starts with the first columns, works like mad, and produces R. Of course, still the same size, m by n, and we did it before." + }, + { + "text": "And then whatever it did to get R, something else is going to show up here." + }, + { + "text": "Let me call it E, m by m. It's whatever you see that E is just going to contain a record of what we did." + }, + { + "text": "We did whatever it took to get A to become R. And at the same time, we were doing it to the identity matrix." + }, + { + "text": "So we started with the identity matrix, we buzzed along." + }, + { + "text": "So we took some -- all this row reduction amounted to multiplying on the left by some matrix, some series of elementary matrices that all together gave us one matrix, and that matrix is E. So all this row reduction stuff amounted to multiplying by E. How do I know that?" + }, + { + "text": "It certainly amounted to multiplying by something, and that something took I to E, so that something was E. So now look at the first part, E A is R. No big deal." + }, + { + "text": "All I've said is that the row reduction steps that we all know well, taking A to R, are in a- in some matrix, and I can find out what that matrix is by just tacking I on and seeing what comes out." + }, + { + "text": "What comes out is E. Let's just review the invertible square case." + }, + { + "text": "What happened then?" + }, + { + "text": "Because I was interested in it in chapter two also." + }, + { + "text": "When A was square and invertible, I took A I, I did row elimination, what was the R that came out?" + }, + { + "text": "It was I." + }, + { + "text": "So in chapter two, in chapter two, R was I." + }, + { + "text": "The row- the reduced row echelon form of a nice invertible square matrix is the identity." + }, + { + "text": "So if R was I in that case, then E was A inverse, because E A is I." + }, + { + "text": "Good." + }, + { + "text": "That's- that was good and easy." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk16.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..c5a8adc4741aeb68371eb235609b24dad795df03 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now what I'm saying is that there still is an E, it's not A inverse anymore, because A is a rectangular, it hasn't got an inverse." + }, + { + "text": "But there is still some matrix E that connected this to this." + }, + { + "text": "Oh, I should have figured out in advance what it was." + }, + { + "text": "Shoot." + }, + { + "text": "I didn't- I did those steps and sort of erased as I went, and, I should have done them to the identity, too." + }, + { + "text": "Can I do that?" + }, + { + "text": "Can I do that?" + }, + { + "text": "I'll keep the identity matrix, like I'm supposed to do, and I'll do the same operations on it and see what I end up with." + }, + { + "text": "Okay." + }, + { + "text": "So I'm starting with the identity, which I'll write in light, light enough, but okay, what did I do?" + }, + { + "text": "I subtracted that row from that one and that row from that one." + }, + { + "text": "Okay, I'll do that to the identity." + }, + { + "text": "So I subtract that first row from row two and row three." + }, + { + "text": "Good." + }, + { + "text": "Then I think I multiply, do you remember, I multiplied row two by minus one?" + }, + { + "text": "Let me just do that." + }, + { + "text": "Then what did I do?" + }, + { + "text": "I subtracted two of row two away from row one." + }, + { + "text": "I better do that." + }, + { + "text": "Subtract two of this away from this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk17.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..368775ffcdaa5a9fe2c24f8c85bcb4963097a79c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's minus one, two of these away leaves a plus two and zero." + }, + { + "text": "I believe that's E. The way to check is to see, multiply that E by this A, just to see, did I do it right?" + }, + { + "text": "So I believe E was minus one, two, zero, one minus one, zero, and minus one, zero, one." + }, + { + "text": "Okay." + }, + { + "text": "That's my E, that's my A, and that's R. All right." + }, + { + "text": "All I'm struggling to do is write the reason I wanted this blasted E was so that I could figure out the left null space." + }, + { + "text": "Not only its dimension, which I know." + }, + { + "text": "Actually, what is the dimension of the left null space?" + }, + { + "text": "Here's my matrix." + }, + { + "text": "What's the rank of the matrix?" + }, + { + "text": "Two." + }, + { + "text": "And the dimension of the left null space is supposed to be M minus R, three minus two, one." + }, + { + "text": "I believe that the left null space is one-dimensional." + }, + { + "text": "There is one combination of those three rows that produces the zero row." + }, + { + "text": "There is a basis." + }, + { + "text": "A basis for the left null space has only got one vector in it." + }, + { + "text": "And what is that vector?" + }, + { + "text": "It's here in the last row of E. But, ah, we could have seen it earlier." + }, + { + "text": "What combination of those rows gives the zero row?" + }, + { + "text": "Minus one of that, plus one of that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk18.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..9f5e8b1fcc2242dbdc56d379cbc7126ada792e31 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a basis for the left null space of this matrix, I'm looking for combinations of rows that give the zero row, if I'm looking at the left null space." + }, + { + "text": "For the null space, I'm looking at combinations of columns to get the zero column." + }, + { + "text": "Now I'm looking at combinations of these three rows to get the zero row, and of course, there is my zero row, and here is my vector that produced it." + }, + { + "text": "Minus one of that row and one of that row." + }, + { + "text": "Obvious." + }, + { + "text": "Okay." + }, + { + "text": "So in that example, and actually in all examples, we have seen how to produce a basis for the left null space." + }, + { + "text": "I won't ask you that all the time." + }, + { + "text": "Because it didn't come out immediately from R, we had to keep track of E for that left null space." + }, + { + "text": "But at least it didn't require us to transpose the matrix and start all over again." + }, + { + "text": "Okay." + }, + { + "text": "Those are the four subspaces." + }, + { + "text": "Can I review them?" + }, + { + "text": "The row space and the null space are in Rn." + }, + { + "text": "Their dimensions add to n. The column space and the left null space are in Rm, and their dimensions add to m. Okay." + }, + { + "text": "So let me close these last minutes by pushing you a little bit more to a new type of vector space." + }, + { + "text": "All our vector spaces, all the ones that we took seriously, have been subspaces of some real three- or n-dimensional space." + }, + { + "text": "Now I'm going to write down another vector space, a new vector space." + }, + { + "text": "Say all three by three matrices." + }, + { + "text": "My matrices are the vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk19.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..c1658ee474fcf6206f54d67e4dededa02a1ef92c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Is that all right?" + }, + { + "text": "I'm just naming them." + }, + { + "text": "You can put quotes around vectors." + }, + { + "text": "Every three by three matrix is one of my vectors." + }, + { + "text": "Now how am I entitled to call those things vectors?" + }, + { + "text": "I mean, they look very much like matrices." + }, + { + "text": "But they're vectors in my vector space because they obey the rules." + }, + { + "text": "All I'm supposed to be able to do with vectors is add them." + }, + { + "text": "I can add matrices." + }, + { + "text": "I'm supposed to be able to multiply them by scalar numbers, like seven." + }, + { + "text": "Well, I can multiply a matrix by seven." + }, + { + "text": "And I can take combinations of matrices." + }, + { + "text": "I can take three of one matrix minus five of another matrix." + }, + { + "text": "And those combinations, there's a zero matrix, the matrix that has all zeros in it." + }, + { + "text": "If I add that to another matrix, it doesn't change it." + }, + { + "text": "All the good stuff." + }, + { + "text": "If I multiply a matrix by one, it doesn't change it." + }, + { + "text": "All those eight rules for a vector space that we never wrote down, all easily satisfied." + }, + { + "text": "So now we have a different --." + }, + { + "text": "Now, of course, you can say you can multiply those matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk2.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..b92bd923d792a0f92ab4de95b7867006e9880f71 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here are the four fundamental subspaces." + }, + { + "text": "This is really the heart of this approach to linear algebra, to see these four subspaces, how they're related." + }, + { + "text": "So what are they?" + }, + { + "text": "The column space, C of A." + }, + { + "text": "The null space, N of A." + }, + { + "text": "And now comes the row space, something new." + }, + { + "text": "The row space, what's in that?" + }, + { + "text": "It's all combinations of the rows." + }, + { + "text": "That's natural." + }, + { + "text": "We want a space, so we have to take all combinations and we start with the rows." + }, + { + "text": "So the rows span the row space." + }, + { + "text": "Are the rows a basis for the row space?" + }, + { + "text": "Maybe so, maybe no." + }, + { + "text": "The rows are a basis for the row space when they're independent." + }, + { + "text": "But if they're dependent, as in this example, my error from last time, they're not, those three rows are not a basis, the row space would only be two-dimensional, I only need two rows for a basis." + }, + { + "text": "So the row space, now what's in it?" + }, + { + "text": "It's all combinations of the rows of A." + }, + { + "text": "All combinations of the rows of A." + }, + { + "text": "But I don't like working with row vectors." + }, + { + "text": "All my vectors have been column vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk20.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..56956e8347a8f8c1f8522690db77860dcc6953b9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "I don't care." + }, + { + "text": "For the moment, I'm only thinking of these matrices as forming a vector space, so I am only doing A plus B and C times A. I'm not interested in A, B for now." + }, + { + "text": "The fact that I can multiply is not relevant to a vector space." + }, + { + "text": "OK, so I have three by three matrices." + }, + { + "text": "And how about subspaces?" + }, + { + "text": "What's, tell me a subspace of this matrix space." + }, + { + "text": "Let me call this matrix space M. That's my matrix space, my space of all three by three matrices." + }, + { + "text": "Tell me a subspace of it." + }, + { + "text": "OK, what about the upper triangular matrices?" + }, + { + "text": "So subspaces, subspaces of M. All upper triangular matrices." + }, + { + "text": "Another subspace." + }, + { + "text": "All symmetric matrices." + }, + { + "text": "The intersection of two subspaces is supposed to be a subspace." + }, + { + "text": "We gave a little effort to the proof of that fact." + }, + { + "text": "If I look at the matrices that are in this subspace, they're symmetric, and they're also in this subspace, they're upper triangular." + }, + { + "text": "What do they look like?" + }, + { + "text": "Well, if they're symmetric, but they have zeros below the diagonal, they better have zeros above the diagonal." + }, + { + "text": "So the intersection would be diagonal matrices." + }, + { + "text": "That's another subspace, smaller than those." + }, + { + "text": "How can I use the word smaller?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk21.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..ffcdd44ed2f644726e04b27114327cb30bc7fb92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, I'm now entitled to use the word smaller." + }, + { + "text": "I mean, well, one way to say is, OK, these are contained in those." + }, + { + "text": "These are contained in those." + }, + { + "text": "But more precisely, I could give the dimension of these spaces." + }, + { + "text": "So I could, we can compute, let's compute it next time." + }, + { + "text": "The dimension of all upper, of the subspace of upper triangular three by three matrices." + }, + { + "text": "The dimension of symmetric three by three matrices." + }, + { + "text": "The dimension of diagonal three by three matrices." + }, + { + "text": "Well, to produce dimension, that means I'm supposed to produce a basis." + }, + { + "text": "And then I just count how many I needed in the basis." + }, + { + "text": "Let me give you the answer for this one." + }, + { + "text": "What's the dimension?" + }, + { + "text": "The dimension of this, say, this subspace, let me call it D, all diagonal matrices." + }, + { + "text": "The dimension of this subspace is, as I write, you're working it out, three." + }, + { + "text": "Because here's a matrix in this, it's a diagonal matrix." + }, + { + "text": "Here's another one." + }, + { + "text": "Here's another one." + }, + { + "text": "Better make it diagonal, let me put a seven there." + }, + { + "text": "That was not a very great choice, but it's three diagonal matrices, and I believe that they're a basis." + }, + { + "text": "I believe that those three matrices are independent, and I believe that any diagonal matrix is a combination of those three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk22.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..8c6bce8cf8085e6544c31ae6926bb7ccf18b983e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk22.json @@ -0,0 +1,20 @@ +[ + { + "text": "So they span the subspace of diagonal matrices." + }, + { + "text": "Do you see that idea?" + }, + { + "text": "It's like stretching the idea from Rn to Rn by n, three by three, but we can still add, we can still multiply by numbers, and we just ignore the fact that we can multiply two matrices together." + }, + { + "text": "Okay." + }, + { + "text": "Thank you." + }, + { + "text": "That's lecture ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk3.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..25f31647b76274f9088c60d1292bcc43915d3fb0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'd like to stay with column vectors." + }, + { + "text": "How can I get to column vectors out of these rows?" + }, + { + "text": "I transpose the matrix." + }, + { + "text": "So if that's OK with you, I'm going to transpose the matrix, I'm going to say all combinations of the columns of A transpose." + }, + { + "text": "And that allows me to use the convenient notation, the column space of A transpose." + }, + { + "text": "Nothing, no mathematics went on there, we just got some vectors that were lying down to stand up." + }, + { + "text": "But it means that we can use this column space of A transpose, that's telling me in a nice matrix notation what the row space is." + }, + { + "text": "OK. And finally is another null space." + }, + { + "text": "The fourth fundamental space will be the null space of A transpose." + }, + { + "text": "The fourth guy is the null space of A transpose." + }, + { + "text": "And of course, my notation is N of A transpose." + }, + { + "text": "That's the null space of A transpose." + }, + { + "text": "Now, we don't have a perfect name for this space as a, as a, connecting with A, but our usual name is the left null space, and I'll show you why in a moment." + }, + { + "text": "So often I call this the, just to write that word, the left null space of A." + }, + { + "text": "So just the way we have the row space of A and we switch it to the column space of A transpose, so we have this space of guys that I call the left null space of A, but the good notation is it's the null space of A transpose." + }, + { + "text": "OK. Those are four spaces." + }, + { + "text": "Where are those spaces?" + }, + { + "text": "What big space are they in for when A is m by n?" + }, + { + "text": "In that case, the null space of A, what's in the null space of A?" + }, + { + "text": "Vectors with n components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk4.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c2575473d88ff4598107e190483f0484b6558678 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Solutions to Ax equals zero." + }, + { + "text": "So the null space of A is n R n. What's in the column space of A?" + }, + { + "text": "Well, columns." + }, + { + "text": "How many components do those columns have?" + }, + { + "text": "m. So this column space is n R m. What about the column space of A transpose, which are just a disguised way of saying the rows of A?" + }, + { + "text": "The rows of A in this three by six matrix have six components, n components." + }, + { + "text": "The column space is n R n. And the null space of A transpose, I see that this fourth space is already getting second, you know, second class citizen treatment and it doesn't deserve it." + }, + { + "text": "It's, it should be there, it is there, and shouldn't be squeezed." + }, + { + "text": "The null space of A transpose, well, if the null space of A had vectors with n components, the null space of A transpose will be n R m. I want to draw a picture of the four spaces." + }, + { + "text": "OK. OK." + }, + { + "text": "Here are the four spaces." + }, + { + "text": "OK, let me put n dimensional space over on this side." + }, + { + "text": "Then which were the subspaces in R n?" + }, + { + "text": "The null space was and the row space was." + }, + { + "text": "So here we have the can I make that picture of the row space?" + }, + { + "text": "And can I make this kind of picture of the null space?" + }, + { + "text": "That's just meant to be a sketch, to remind you that they're in this which, you know, how, what type of vectors are in it?" + }, + { + "text": "Vectors with n components." + }, + { + "text": "Over here, inside consisting of vectors with m components is the column space and what I'm calling the null space of A transpose." + }, + { + "text": "Those are the ones with m components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk5.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..f4e64e208c1a1d8e07a9a66a6a6c59f8c4cbcec8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. To understand these spaces is our job now." + }, + { + "text": "Because by understanding those spaces, we know everything about this half of linear algebra." + }, + { + "text": "What do I mean by understanding those spaces?" + }, + { + "text": "I would like to know a basis for those spaces." + }, + { + "text": "For each one of those spaces, how would I create, construct a basis?" + }, + { + "text": "What systematic way would produce a basis?" + }, + { + "text": "And what's their dimension?" + }, + { + "text": "OK." + }, + { + "text": "So for each of the four spaces, I have to answer those questions." + }, + { + "text": "How do I produce a basis?" + }, + { + "text": "And then, which has a somewhat long answer, and what's the dimension, which is just a number, so it has a real short answer?" + }, + { + "text": "Can I give you the short answer first?" + }, + { + "text": "I shouldn't do it, but here it is." + }, + { + "text": "I can tell you the dimension of the column space." + }, + { + "text": "Let me start with this guy." + }, + { + "text": "What's its dimension?" + }, + { + "text": "I have an m by n matrix." + }, + { + "text": "The dimension of the column space is the rank, R. We actually got to that at the end of the last lecture, but only for an example." + }, + { + "text": "So I really have to say, OK, what's going on there?" + }, + { + "text": "I should produce a basis, and then I just look to see how many vectors I needed in that basis, and the answer will be R. Actually, I'll do that before I get on to the others." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk6.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..ac7425fbe27a77a7e448b576483b4c179e9a31f1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "What's a basis for the column space?" + }, + { + "text": "We've done all the work of row reduction, identifying the pivot columns, the ones that have pivots, the ones that end up with pivots, but now I the pivot columns I'm interested in are columns of A, the original A." + }, + { + "text": "And those pivot columns, there are R of them, the rank R counts those, those are a basis." + }, + { + "text": "So if I answer this question for the column space, the answer will be a basis is the pivot columns, and the dimension is the rank R. And there are pivot columns and everything great." + }, + { + "text": "OK, so that space we pretty well understand." + }, + { + "text": "I probably have a little going back to see that, to prove that this is a right answer, but you know it's the right answer." + }, + { + "text": "Now let me look at the row space." + }, + { + "text": "OK. Shall I tell you the dimension of the row space?" + }, + { + "text": "Yes." + }, + { + "text": "Before we do even an example, let me tell you the dimension of the row space." + }, + { + "text": "Its dimension is also R. The row space and the column space have the same dimension." + }, + { + "text": "That's a wonderful fact." + }, + { + "text": "The dimension of the column space of A transpose, that's the row space, is R. That space is R-dimensional." + }, + { + "text": "And so is this one." + }, + { + "text": "OK. That's the, that's the sort of insight that got used in this example." + }, + { + "text": "If those, if those, if those, are the three columns of a matrix, let me make them the three columns of a matrix by just erasing some brackets, OK, those are the three columns of a matrix, the rank of that matrix, if I look at the columns, it wasn't obvious to me anyway." + }, + { + "text": "But if I look at the rows, it's, now it's obvious." + }, + { + "text": "The row space of that matrix obviously is two-dimensional, because I can, I see a basis for the row space, this row and that row." + }, + { + "text": "And of course, strictly speaking, I'm supposed to transpose those guys, make them stand up." + }, + { + "text": "But the rank is two, and therefore the column space is two-dimensional by this wonderful fact that the row space and column space have the same dimension, and therefore there are only two pivot columns, not three, and, those, the three columns are dependent." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk7.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..7d55c74913379543a71fcc53c971f787baf12a92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, let me bury that error and talk about the row space." + }, + { + "text": "Well, I'm going to give you the dimensions of all the spaces, because that's the, such a nice answer." + }, + { + "text": "OK." + }, + { + "text": "So let me come back here." + }, + { + "text": "So we have this great fact to establish, that the row space, its dimension is also the rank." + }, + { + "text": "OK. What about the null space?" + }, + { + "text": "What's a basis for the null space?" + }, + { + "text": "What's the dimension of the null space?" + }, + { + "text": "Let me, I'll put that answer up here, for the null space." + }, + { + "text": "Well, how have we constructed the null space?" + }, + { + "text": "We took the matrix A, we did those row operations to get it into a form U or even further, we got it into the reduced form R, and then we read off special solutions." + }, + { + "text": "Special solutions, and every special solution came from a free variable." + }, + { + "text": "And those special solutions are in the null space, and the great thing is, they're a basis for it." + }, + { + "text": "So for the null space, a basis will be the special solutions." + }, + { + "text": "And there's one for every free variable, right?" + }, + { + "text": "For each free variable, we give that variable the value one, the other free variable zero." + }, + { + "text": "We get the pivot variables, we get a vector in the -- we get a special solution." + }, + { + "text": "So we get all together n minus R of them, because that's the number of free variables." + }, + { + "text": "If we have R, this is, the dimension is R, is the number of pivot variables, this is the number of free variables." + }, + { + "text": "So the beauty is that those special solutions do form a basis and tell us immediately that the dimension of the null space is n -- I'd better write this well, because it's so nice, n minus R. And you see the nice thing, that the two dimensions in this n-dimensional space, one subspace is R-dimensional, to be proved, that's the row space." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk8.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f4c70532a641ef630aa1f7bca077776017097cd4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "The other subspace is n minus R-dimensional, that's the null space." + }, + { + "text": "And the two dimensions, like, together, give n. The sum of R and n minus R is n. And that's just great." + }, + { + "text": "It's really copying the fact that we have n variables, R of them are pivot variables and n minus R are free variables and n all together." + }, + { + "text": "OK. And now what's the dimension of this poor misbegotten fourth subspace?" + }, + { + "text": "It's got to be m minus R. The dimension of this left null space, left out practically, is m minus R. Well, that's really just saying that this, again, the sum of that plus that is m. And m is correct." + }, + { + "text": "It's the number of columns in A transpose." + }, + { + "text": "A transpose is just as good a matrix as A." + }, + { + "text": "It just happens to be n by m. It happens to have m columns, so it will have m variables, when I go to Ax equals zero, and m of them and R of them will be pivot variables and m minus R will be free variables." + }, + { + "text": "A transpose is as good a matrix as A." + }, + { + "text": "It follows the same rule that this plus the dimension, this dimension plus this dimension adds up to the number of columns." + }, + { + "text": "And over here, A transpose has m columns." + }, + { + "text": "Okay." + }, + { + "text": "Okay, so I gave you the easy answer, the dimensions." + }, + { + "text": "Now can I go back to check on a basis?" + }, + { + "text": "We would like to think that, say, the row space." + }, + { + "text": "Because we've got a basis for the column space." + }, + { + "text": "The pivot columns give a basis for the column space." + }, + { + "text": "Now I'm asking you to look at the row space." + }, + { + "text": "And I you could say, okay, I can produce a basis for the row space by transposing my matrix, making those columns, then doing elimination, row reduction, and checking out the pivot columns in this transposed matrix." + }, + { + "text": "But that means you had to do all that row reduction on A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk9.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..8be162da3ff089e5c511aa65ea7d801c64cad56f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_32_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It ought to be possible, if we take a matrix A, let me take the matrix, maybe we had this matrix in the last lecture, one one one, two one two, three two three, one one one." + }, + { + "text": "Okay." + }, + { + "text": "That, that matrix was so easy, we spotted its pivot columns, one and two, without actually doing row reduction." + }, + { + "text": "But now let's do the job properly." + }, + { + "text": "So I subtract this away from this to produce a zero." + }, + { + "text": "So one two three one is fine." + }, + { + "text": "Subtracting that away leaves me minus one minus one zero, right?" + }, + { + "text": "And subtracting that from the last row, oh, well, that's easy." + }, + { + "text": "Okay, I'm doing row reduction." + }, + { + "text": "Now I've, the first column is all set." + }, + { + "text": "The second column, I now see the pivot, and I can clean up, if I, actually, okay, why don't I make the pivot into a one?" + }, + { + "text": "I'll multiply that row through by minus one, and then I have one one." + }, + { + "text": "That was an elementary operation, I'm allowed." + }, + { + "text": "Multiply a row by a number." + }, + { + "text": "And now I'll do elimination." + }, + { + "text": "Two of those away from that will knock this guy out and make this into a one." + }, + { + "text": "So that's now a zero and that's a one." + }, + { + "text": "Okay." + }, + { + "text": "Done." + }, + { + "text": "That's R. I'm seeing the identity matrix here, I'm seeing zeros below, and I'm seeing F there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk0.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6b8bcce949e11c9807b49a56c5ca68fdb459f818 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay, here is lecture ten in linear algebra." + }, + { + "text": "Two important things to do in this lecture." + }, + { + "text": "One is to correct an error from lecture nine." + }, + { + "text": "So the blackboard with that awful error is still with us." + }, + { + "text": "And the second, the big thing to do is to tell you about the four subspaces that come with a matrix." + }, + { + "text": "We've seen two subspaces, the column space and the null space, there's two to go." + }, + { + "text": "Okay." + }, + { + "text": "First of all, and this is a great way to recap and correct the previous lecture." + }, + { + "text": "So you remember I was just doing R3." + }, + { + "text": "I couldn't have taken a simpler example than R3." + }, + { + "text": "And I wrote down the standard basis." + }, + { + "text": "That's the standard basis." + }, + { + "text": "The basis, the obvious basis for the whole three-dimensional space." + }, + { + "text": "And then I wanted to make the point that there was nothing special, nothing about that basis that another basis couldn't have." + }, + { + "text": "It could have linear independence, it could span a space, there's lots of other bases." + }, + { + "text": "So I started with these vectors one one two and two two five, and those were independent." + }, + { + "text": "And then I said three three seven wouldn't do, because three three seven is the sum of those." + }, + { + "text": "So in my innocence, I put in three three eight." + }, + { + "text": "I figured probably if three three seven is on the plane, is, which I know, it's in the plane with these two, then probably three three eight sticks a little bit out of the plane." + }, + { + "text": "And it's independent and it gives a basis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk1.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..97d9d72b29a5aa923aae0ba9c0fb0da57e9db2ed --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "But after class, to my sorrow, student tells me, wait a minute, that third vector three three eight is not independent." + }, + { + "text": "And why did she say that?" + }, + { + "text": "She didn't actually take the time, didn't have to, to find what combination of this one and this one gives three three eight." + }, + { + "text": "She did something else." + }, + { + "text": "In other words, she looked ahead because she said, wait a minute, if I look at that matrix, it's not invertible." + }, + { + "text": "That third column can't be independent of the first two, because when I look at that matrix, it's got two identical rows." + }, + { + "text": "I have a square matrix." + }, + { + "text": "Its rows are obviously dependent." + }, + { + "text": "And that makes the columns dependent." + }, + { + "text": "So there's my error." + }, + { + "text": "When I look at the matrix A that has those three columns, those three columns can't be independent because that matrix is not invertible because it's got two equal rows." + }, + { + "text": "And today's lecture will reach the conclusion, the great conclusion, that connects the column space with the row space." + }, + { + "text": "So those are the row space is now going to be another one of my fundamental subspaces." + }, + { + "text": "The row space of this matrix or of this one, well, the row space of this one is okay." + }, + { + "text": "But the row space of this one, I'm looking at the rows of the matrix, oh, anyway, I'll have two equal rows and the row space will be only two-dimensional." + }, + { + "text": "The rank of the matrix with these columns will only be two, so only two of those columns can be independent too." + }, + { + "text": "The rows tell me something about the columns, in other words." + }, + { + "text": "Something that I should have noticed and I didn't." + }, + { + "text": "Okay." + }, + { + "text": "So now let me pin down these four fundamental subspaces." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk10.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..8f428ebe86b1b4488558f6fa55b8940ef758b264 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "Okay." + }, + { + "text": "What about its row space?" + }, + { + "text": "What happened to its row space?" + }, + { + "text": "Well, what happened, let me first ask, just because this is, sometimes something does happen." + }, + { + "text": "Its column space changed." + }, + { + "text": "The column space of R is not the column space of A, right?" + }, + { + "text": "Because one one one is certainly in the column space of A and certainly not in the column space of R. I did row operations." + }, + { + "text": "Those row operations preserved the row space, so the row so the column spaces are different." + }, + { + "text": "Different column spaces." + }, + { + "text": "Different column spaces." + }, + { + "text": "But I believe that they have the same row space." + }, + { + "text": "Same row space." + }, + { + "text": "I believe that the row space of that matrix and the row space of this matrix are identical." + }, + { + "text": "They have exactly the same vectors in them." + }, + { + "text": "Those vectors are vectors with four components, right?" + }, + { + "text": "They're all combinations of those rows." + }, + { + "text": "Or I believe you get the same thing by taking all combinations of these rows." + }, + { + "text": "And if true, what's a basis?" + }, + { + "text": "What's a basis for the row space of R?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk11.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..258e5999dbb0aea67696256511eb6b999136132a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it'll be a basis for the row space of the original A." + }, + { + "text": "But it's obviously a basis for the row space of R. What's a basis for the row space of that matrix?" + }, + { + "text": "The first two rows." + }, + { + "text": "So a basis for the row so a basis is for the row space of A or of R is the first R rows of R, not of A." + }, + { + "text": "Sometimes it's true for A, but not necessarily." + }, + { + "text": "But R, we definitely have a matrix here whose row space we can identify." + }, + { + "text": "The row space is spanned by the three rows." + }, + { + "text": "But if we want a basis, we want independence." + }, + { + "text": "So out goes row three." + }, + { + "text": "The row space is also spanned by the first two rows." + }, + { + "text": "This guy didn't contribute anything." + }, + { + "text": "And of course, over here, this one, two, three, one in the bottom didn't contribute anything." + }, + { + "text": "We had it already." + }, + { + "text": "So this, here's a basis, one zero one one and zero one one zero." + }, + { + "text": "I believe those are in the row space." + }, + { + "text": "I know they're independent." + }, + { + "text": "Why are they in the row space?" + }, + { + "text": "Why are those two vectors in the row space?" + }, + { + "text": "Because all those operations we did, which started with these rows and took combinations of them." + }, + { + "text": "I took this row minus this row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk12.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..d05a7eb6e4998c4acd748e3bb7087c68e6e29a80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "That gave me something that's still in the row space." + }, + { + "text": "That's the point." + }, + { + "text": "When I took a row minus a multiple of another row, I'm staying in the row space." + }, + { + "text": "The row space is not changing." + }, + { + "text": "My little basis for it is changing, and I've ended up with, sort of, the best basis." + }, + { + "text": "If the columns of the identity matrix are the best basis for R3 or Rn, the rows of this matrix are the best basis for the row space." + }, + { + "text": "Best in the sense of being as clean as I can make it." + }, + { + "text": "Starting off with the identity and then finishing up with whatever has to be in there." + }, + { + "text": "OK. Do you see, then, that the dimension is R?" + }, + { + "text": "For sure." + }, + { + "text": "Because we've got R pivots, R nonzero rows, we've got the right number of vectors, R. They're in the row space, they're independent, that's it." + }, + { + "text": "They are a basis for the row space." + }, + { + "text": "And we can even pin that down further." + }, + { + "text": "How do I know that every row of A is a combination?" + }, + { + "text": "How do I know they span the row space?" + }, + { + "text": "Oh, well, somebody says I've got the right number of them, so they must, but that's true." + }, + { + "text": "But let me just say, how do I know that this row is a combination of these?" + }, + { + "text": "By just reversing the steps of row reduction." + }, + { + "text": "If I just reverse the steps and go from A, from R back to A, then what do I, what am I doing?" + }, + { + "text": "I'm starting with these rows, I'm taking combinations of them, after a couple of steps, undoing the subtractions that I did before, I'm back to these rows." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk13.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..7b0edabbd24233827c7692f63429589952dac1bc --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "So these rows are combinations of those rows, those rows are combinations of those rows, the two row spaces are the same, the bases are the same, and the natural basis is this guy." + }, + { + "text": "Is that all right for the row space?" + }, + { + "text": "The row space is sitting there in R, in its cleanest possible form." + }, + { + "text": "OK. Now what about the fourth guy, the null space of A transpose?" + }, + { + "text": "First of all, why do I call that the left null space?" + }, + { + "text": "So let me save that and bring that down." + }, + { + "text": "OK." + }, + { + "text": "So the fourth space is the null space of A transpose." + }, + { + "text": "So it has in it vectors, let me call them y, so that A transpose y equals zero." + }, + { + "text": "If A transpose y equals zero, then y is in the null space of A transpose, of course." + }, + { + "text": "So this is a matrix times a column equaling zero." + }, + { + "text": "And now, because I want y to sit on the left, and I want A instead of A transpose, I'll just transpose that equation." + }, + { + "text": "Can I just transpose that?" + }, + { + "text": "On the right, it makes the zero vector lie down." + }, + { + "text": "And on the left, it's a product, A transpose times y." + }, + { + "text": "If I take the transpose, then they come in opposite order, right?" + }, + { + "text": "So it's y transpose times A transpose transpose, but nobody's going to leave it like that." + }, + { + "text": "That's A transpose transpose is just A, of course." + }, + { + "text": "When I transposed A transpose, I got back to A." + }, + { + "text": "Now, do you see what I have now?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk14.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7a889f79409e9a95fbd4cc01518da4b9706c49d1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "I have a row vector, y transpose, multiplying A and multiplying from the left." + }, + { + "text": "That's why I call it the left null space." + }, + { + "text": "But by making it, putting it on the left, I had to make it into a row instead of a column vector." + }, + { + "text": "And so my convention is I usually don't do that, I usually stay with A transpose y equals zero." + }, + { + "text": "OK. And you might ask, how do we get a basis, or I might ask, how do we get a basis for this fourth space, this left null space?" + }, + { + "text": "OK." + }, + { + "text": "I'll do it the example." + }, + { + "text": "As always, ah, not that one." + }, + { + "text": "The left null space is not jumping out at me here." + }, + { + "text": "I know which are the free variables, the special solutions, but those are special solutions to Ax equals zero, and now I'm looking at A transpose and I'm not seeing it here." + }, + { + "text": "So, but somehow you feel that the work that you did, which simplified A to R, should have revealed the left null space too." + }, + { + "text": "And it's slightly less immediate, but it's there." + }, + { + "text": "So from A to R, I took some steps, and I guess I'm interested in what were those steps, or what were all of them together." + }, + { + "text": "I don't want to -- I'm not interested in what particular ones they were." + }, + { + "text": "I'm interested in what was the whole matrix that took me from A to R. How would you find that?" + }, + { + "text": "Do you remember Gauss-Jordan, where you tack on the identity matrix?" + }, + { + "text": "Let's do that again." + }, + { + "text": "So I'll do it above here." + }, + { + "text": "So this is now the idea of I take the matrix A, which is m by n. In Gauss-Jordan, when we saw him before, A was a square invertible matrix and we were finding its inverse." + }, + { + "text": "Now the matrix isn't square, it's probably rectangular." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk15.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3c045b6d07a6635d896789ba37b0d578bd175e92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "But I'll still tack on the identity matrix, and of course, since these have length m, it better be m by m. And now I'll do the reduced row echelon form of this matrix." + }, + { + "text": "And what do I get?" + }, + { + "text": "The reduced row echelon form starts with these columns, starts with the first columns, works like mad, and produces R. Of course, still the same size, m by n, and we did it before." + }, + { + "text": "And then whatever it did to get R, something else is going to show up here." + }, + { + "text": "Let me call it E, m by m. It's whatever you see that E is just going to contain a record of what we did." + }, + { + "text": "We did whatever it took to get A to become R. And at the same time, we were doing it to the identity matrix." + }, + { + "text": "So we started with the identity matrix, we buzzed along." + }, + { + "text": "So we took some -- all this row reduction amounted to multiplying on the left by some matrix, some series of elementary matrices that all together gave us one matrix, and that matrix is E. So all this row reduction stuff amounted to multiplying by E. How do I know that?" + }, + { + "text": "It certainly amounted to multiplying by something, and that something took I to E, so that something was E. So now look at the first part, E A is R. No big deal." + }, + { + "text": "All I've said is that the row reduction steps that we all know well, taking A to R, are in a- in some matrix, and I can find out what that matrix is by just tacking I on and seeing what comes out." + }, + { + "text": "What comes out is E. Let's just review the invertible square case." + }, + { + "text": "What happened then?" + }, + { + "text": "Because I was interested in it in chapter two also." + }, + { + "text": "When A was square and invertible, I took A I, I did row elimination, what was the R that came out?" + }, + { + "text": "It was I." + }, + { + "text": "So in chapter two, in chapter two, R was I." + }, + { + "text": "The row- the reduced row echelon form of a nice invertible square matrix is the identity." + }, + { + "text": "So if R was I in that case, then E was A inverse, because E A is I." + }, + { + "text": "Good." + }, + { + "text": "That's- that was good and easy." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk16.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..c5a8adc4741aeb68371eb235609b24dad795df03 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now what I'm saying is that there still is an E, it's not A inverse anymore, because A is a rectangular, it hasn't got an inverse." + }, + { + "text": "But there is still some matrix E that connected this to this." + }, + { + "text": "Oh, I should have figured out in advance what it was." + }, + { + "text": "Shoot." + }, + { + "text": "I didn't- I did those steps and sort of erased as I went, and, I should have done them to the identity, too." + }, + { + "text": "Can I do that?" + }, + { + "text": "Can I do that?" + }, + { + "text": "I'll keep the identity matrix, like I'm supposed to do, and I'll do the same operations on it and see what I end up with." + }, + { + "text": "Okay." + }, + { + "text": "So I'm starting with the identity, which I'll write in light, light enough, but okay, what did I do?" + }, + { + "text": "I subtracted that row from that one and that row from that one." + }, + { + "text": "Okay, I'll do that to the identity." + }, + { + "text": "So I subtract that first row from row two and row three." + }, + { + "text": "Good." + }, + { + "text": "Then I think I multiply, do you remember, I multiplied row two by minus one?" + }, + { + "text": "Let me just do that." + }, + { + "text": "Then what did I do?" + }, + { + "text": "I subtracted two of row two away from row one." + }, + { + "text": "I better do that." + }, + { + "text": "Subtract two of this away from this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk17.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..368775ffcdaa5a9fe2c24f8c85bcb4963097a79c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's minus one, two of these away leaves a plus two and zero." + }, + { + "text": "I believe that's E. The way to check is to see, multiply that E by this A, just to see, did I do it right?" + }, + { + "text": "So I believe E was minus one, two, zero, one minus one, zero, and minus one, zero, one." + }, + { + "text": "Okay." + }, + { + "text": "That's my E, that's my A, and that's R. All right." + }, + { + "text": "All I'm struggling to do is write the reason I wanted this blasted E was so that I could figure out the left null space." + }, + { + "text": "Not only its dimension, which I know." + }, + { + "text": "Actually, what is the dimension of the left null space?" + }, + { + "text": "Here's my matrix." + }, + { + "text": "What's the rank of the matrix?" + }, + { + "text": "Two." + }, + { + "text": "And the dimension of the left null space is supposed to be M minus R, three minus two, one." + }, + { + "text": "I believe that the left null space is one-dimensional." + }, + { + "text": "There is one combination of those three rows that produces the zero row." + }, + { + "text": "There is a basis." + }, + { + "text": "A basis for the left null space has only got one vector in it." + }, + { + "text": "And what is that vector?" + }, + { + "text": "It's here in the last row of E. But, ah, we could have seen it earlier." + }, + { + "text": "What combination of those rows gives the zero row?" + }, + { + "text": "Minus one of that, plus one of that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk18.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..9f5e8b1fcc2242dbdc56d379cbc7126ada792e31 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a basis for the left null space of this matrix, I'm looking for combinations of rows that give the zero row, if I'm looking at the left null space." + }, + { + "text": "For the null space, I'm looking at combinations of columns to get the zero column." + }, + { + "text": "Now I'm looking at combinations of these three rows to get the zero row, and of course, there is my zero row, and here is my vector that produced it." + }, + { + "text": "Minus one of that row and one of that row." + }, + { + "text": "Obvious." + }, + { + "text": "Okay." + }, + { + "text": "So in that example, and actually in all examples, we have seen how to produce a basis for the left null space." + }, + { + "text": "I won't ask you that all the time." + }, + { + "text": "Because it didn't come out immediately from R, we had to keep track of E for that left null space." + }, + { + "text": "But at least it didn't require us to transpose the matrix and start all over again." + }, + { + "text": "Okay." + }, + { + "text": "Those are the four subspaces." + }, + { + "text": "Can I review them?" + }, + { + "text": "The row space and the null space are in Rn." + }, + { + "text": "Their dimensions add to n. The column space and the left null space are in Rm, and their dimensions add to m. Okay." + }, + { + "text": "So let me close these last minutes by pushing you a little bit more to a new type of vector space." + }, + { + "text": "All our vector spaces, all the ones that we took seriously, have been subspaces of some real three- or n-dimensional space." + }, + { + "text": "Now I'm going to write down another vector space, a new vector space." + }, + { + "text": "Say all three by three matrices." + }, + { + "text": "My matrices are the vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk19.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..c1658ee474fcf6206f54d67e4dededa02a1ef92c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Is that all right?" + }, + { + "text": "I'm just naming them." + }, + { + "text": "You can put quotes around vectors." + }, + { + "text": "Every three by three matrix is one of my vectors." + }, + { + "text": "Now how am I entitled to call those things vectors?" + }, + { + "text": "I mean, they look very much like matrices." + }, + { + "text": "But they're vectors in my vector space because they obey the rules." + }, + { + "text": "All I'm supposed to be able to do with vectors is add them." + }, + { + "text": "I can add matrices." + }, + { + "text": "I'm supposed to be able to multiply them by scalar numbers, like seven." + }, + { + "text": "Well, I can multiply a matrix by seven." + }, + { + "text": "And I can take combinations of matrices." + }, + { + "text": "I can take three of one matrix minus five of another matrix." + }, + { + "text": "And those combinations, there's a zero matrix, the matrix that has all zeros in it." + }, + { + "text": "If I add that to another matrix, it doesn't change it." + }, + { + "text": "All the good stuff." + }, + { + "text": "If I multiply a matrix by one, it doesn't change it." + }, + { + "text": "All those eight rules for a vector space that we never wrote down, all easily satisfied." + }, + { + "text": "So now we have a different --." + }, + { + "text": "Now, of course, you can say you can multiply those matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk2.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..b92bd923d792a0f92ab4de95b7867006e9880f71 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here are the four fundamental subspaces." + }, + { + "text": "This is really the heart of this approach to linear algebra, to see these four subspaces, how they're related." + }, + { + "text": "So what are they?" + }, + { + "text": "The column space, C of A." + }, + { + "text": "The null space, N of A." + }, + { + "text": "And now comes the row space, something new." + }, + { + "text": "The row space, what's in that?" + }, + { + "text": "It's all combinations of the rows." + }, + { + "text": "That's natural." + }, + { + "text": "We want a space, so we have to take all combinations and we start with the rows." + }, + { + "text": "So the rows span the row space." + }, + { + "text": "Are the rows a basis for the row space?" + }, + { + "text": "Maybe so, maybe no." + }, + { + "text": "The rows are a basis for the row space when they're independent." + }, + { + "text": "But if they're dependent, as in this example, my error from last time, they're not, those three rows are not a basis, the row space would only be two-dimensional, I only need two rows for a basis." + }, + { + "text": "So the row space, now what's in it?" + }, + { + "text": "It's all combinations of the rows of A." + }, + { + "text": "All combinations of the rows of A." + }, + { + "text": "But I don't like working with row vectors." + }, + { + "text": "All my vectors have been column vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk20.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..56956e8347a8f8c1f8522690db77860dcc6953b9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "I don't care." + }, + { + "text": "For the moment, I'm only thinking of these matrices as forming a vector space, so I am only doing A plus B and C times A. I'm not interested in A, B for now." + }, + { + "text": "The fact that I can multiply is not relevant to a vector space." + }, + { + "text": "OK, so I have three by three matrices." + }, + { + "text": "And how about subspaces?" + }, + { + "text": "What's, tell me a subspace of this matrix space." + }, + { + "text": "Let me call this matrix space M. That's my matrix space, my space of all three by three matrices." + }, + { + "text": "Tell me a subspace of it." + }, + { + "text": "OK, what about the upper triangular matrices?" + }, + { + "text": "So subspaces, subspaces of M. All upper triangular matrices." + }, + { + "text": "Another subspace." + }, + { + "text": "All symmetric matrices." + }, + { + "text": "The intersection of two subspaces is supposed to be a subspace." + }, + { + "text": "We gave a little effort to the proof of that fact." + }, + { + "text": "If I look at the matrices that are in this subspace, they're symmetric, and they're also in this subspace, they're upper triangular." + }, + { + "text": "What do they look like?" + }, + { + "text": "Well, if they're symmetric, but they have zeros below the diagonal, they better have zeros above the diagonal." + }, + { + "text": "So the intersection would be diagonal matrices." + }, + { + "text": "That's another subspace, smaller than those." + }, + { + "text": "How can I use the word smaller?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk21.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..ffcdd44ed2f644726e04b27114327cb30bc7fb92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, I'm now entitled to use the word smaller." + }, + { + "text": "I mean, well, one way to say is, OK, these are contained in those." + }, + { + "text": "These are contained in those." + }, + { + "text": "But more precisely, I could give the dimension of these spaces." + }, + { + "text": "So I could, we can compute, let's compute it next time." + }, + { + "text": "The dimension of all upper, of the subspace of upper triangular three by three matrices." + }, + { + "text": "The dimension of symmetric three by three matrices." + }, + { + "text": "The dimension of diagonal three by three matrices." + }, + { + "text": "Well, to produce dimension, that means I'm supposed to produce a basis." + }, + { + "text": "And then I just count how many I needed in the basis." + }, + { + "text": "Let me give you the answer for this one." + }, + { + "text": "What's the dimension?" + }, + { + "text": "The dimension of this, say, this subspace, let me call it D, all diagonal matrices." + }, + { + "text": "The dimension of this subspace is, as I write, you're working it out, three." + }, + { + "text": "Because here's a matrix in this, it's a diagonal matrix." + }, + { + "text": "Here's another one." + }, + { + "text": "Here's another one." + }, + { + "text": "Better make it diagonal, let me put a seven there." + }, + { + "text": "That was not a very great choice, but it's three diagonal matrices, and I believe that they're a basis." + }, + { + "text": "I believe that those three matrices are independent, and I believe that any diagonal matrix is a combination of those three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk22.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..8c6bce8cf8085e6544c31ae6926bb7ccf18b983e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk22.json @@ -0,0 +1,20 @@ +[ + { + "text": "So they span the subspace of diagonal matrices." + }, + { + "text": "Do you see that idea?" + }, + { + "text": "It's like stretching the idea from Rn to Rn by n, three by three, but we can still add, we can still multiply by numbers, and we just ignore the fact that we can multiply two matrices together." + }, + { + "text": "Okay." + }, + { + "text": "Thank you." + }, + { + "text": "That's lecture ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk3.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..25f31647b76274f9088c60d1292bcc43915d3fb0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'd like to stay with column vectors." + }, + { + "text": "How can I get to column vectors out of these rows?" + }, + { + "text": "I transpose the matrix." + }, + { + "text": "So if that's OK with you, I'm going to transpose the matrix, I'm going to say all combinations of the columns of A transpose." + }, + { + "text": "And that allows me to use the convenient notation, the column space of A transpose." + }, + { + "text": "Nothing, no mathematics went on there, we just got some vectors that were lying down to stand up." + }, + { + "text": "But it means that we can use this column space of A transpose, that's telling me in a nice matrix notation what the row space is." + }, + { + "text": "OK. And finally is another null space." + }, + { + "text": "The fourth fundamental space will be the null space of A transpose." + }, + { + "text": "The fourth guy is the null space of A transpose." + }, + { + "text": "And of course, my notation is N of A transpose." + }, + { + "text": "That's the null space of A transpose." + }, + { + "text": "Now, we don't have a perfect name for this space as a, as a, connecting with A, but our usual name is the left null space, and I'll show you why in a moment." + }, + { + "text": "So often I call this the, just to write that word, the left null space of A." + }, + { + "text": "So just the way we have the row space of A and we switch it to the column space of A transpose, so we have this space of guys that I call the left null space of A, but the good notation is it's the null space of A transpose." + }, + { + "text": "OK. Those are four spaces." + }, + { + "text": "Where are those spaces?" + }, + { + "text": "What big space are they in for when A is m by n?" + }, + { + "text": "In that case, the null space of A, what's in the null space of A?" + }, + { + "text": "Vectors with n components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk4.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c2575473d88ff4598107e190483f0484b6558678 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Solutions to Ax equals zero." + }, + { + "text": "So the null space of A is n R n. What's in the column space of A?" + }, + { + "text": "Well, columns." + }, + { + "text": "How many components do those columns have?" + }, + { + "text": "m. So this column space is n R m. What about the column space of A transpose, which are just a disguised way of saying the rows of A?" + }, + { + "text": "The rows of A in this three by six matrix have six components, n components." + }, + { + "text": "The column space is n R n. And the null space of A transpose, I see that this fourth space is already getting second, you know, second class citizen treatment and it doesn't deserve it." + }, + { + "text": "It's, it should be there, it is there, and shouldn't be squeezed." + }, + { + "text": "The null space of A transpose, well, if the null space of A had vectors with n components, the null space of A transpose will be n R m. I want to draw a picture of the four spaces." + }, + { + "text": "OK. OK." + }, + { + "text": "Here are the four spaces." + }, + { + "text": "OK, let me put n dimensional space over on this side." + }, + { + "text": "Then which were the subspaces in R n?" + }, + { + "text": "The null space was and the row space was." + }, + { + "text": "So here we have the can I make that picture of the row space?" + }, + { + "text": "And can I make this kind of picture of the null space?" + }, + { + "text": "That's just meant to be a sketch, to remind you that they're in this which, you know, how, what type of vectors are in it?" + }, + { + "text": "Vectors with n components." + }, + { + "text": "Over here, inside consisting of vectors with m components is the column space and what I'm calling the null space of A transpose." + }, + { + "text": "Those are the ones with m components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk5.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..f4e64e208c1a1d8e07a9a66a6a6c59f8c4cbcec8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. To understand these spaces is our job now." + }, + { + "text": "Because by understanding those spaces, we know everything about this half of linear algebra." + }, + { + "text": "What do I mean by understanding those spaces?" + }, + { + "text": "I would like to know a basis for those spaces." + }, + { + "text": "For each one of those spaces, how would I create, construct a basis?" + }, + { + "text": "What systematic way would produce a basis?" + }, + { + "text": "And what's their dimension?" + }, + { + "text": "OK." + }, + { + "text": "So for each of the four spaces, I have to answer those questions." + }, + { + "text": "How do I produce a basis?" + }, + { + "text": "And then, which has a somewhat long answer, and what's the dimension, which is just a number, so it has a real short answer?" + }, + { + "text": "Can I give you the short answer first?" + }, + { + "text": "I shouldn't do it, but here it is." + }, + { + "text": "I can tell you the dimension of the column space." + }, + { + "text": "Let me start with this guy." + }, + { + "text": "What's its dimension?" + }, + { + "text": "I have an m by n matrix." + }, + { + "text": "The dimension of the column space is the rank, R. We actually got to that at the end of the last lecture, but only for an example." + }, + { + "text": "So I really have to say, OK, what's going on there?" + }, + { + "text": "I should produce a basis, and then I just look to see how many vectors I needed in that basis, and the answer will be R. Actually, I'll do that before I get on to the others." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk6.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..ac7425fbe27a77a7e448b576483b4c179e9a31f1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "What's a basis for the column space?" + }, + { + "text": "We've done all the work of row reduction, identifying the pivot columns, the ones that have pivots, the ones that end up with pivots, but now I the pivot columns I'm interested in are columns of A, the original A." + }, + { + "text": "And those pivot columns, there are R of them, the rank R counts those, those are a basis." + }, + { + "text": "So if I answer this question for the column space, the answer will be a basis is the pivot columns, and the dimension is the rank R. And there are pivot columns and everything great." + }, + { + "text": "OK, so that space we pretty well understand." + }, + { + "text": "I probably have a little going back to see that, to prove that this is a right answer, but you know it's the right answer." + }, + { + "text": "Now let me look at the row space." + }, + { + "text": "OK. Shall I tell you the dimension of the row space?" + }, + { + "text": "Yes." + }, + { + "text": "Before we do even an example, let me tell you the dimension of the row space." + }, + { + "text": "Its dimension is also R. The row space and the column space have the same dimension." + }, + { + "text": "That's a wonderful fact." + }, + { + "text": "The dimension of the column space of A transpose, that's the row space, is R. That space is R-dimensional." + }, + { + "text": "And so is this one." + }, + { + "text": "OK. That's the, that's the sort of insight that got used in this example." + }, + { + "text": "If those, if those, if those, are the three columns of a matrix, let me make them the three columns of a matrix by just erasing some brackets, OK, those are the three columns of a matrix, the rank of that matrix, if I look at the columns, it wasn't obvious to me anyway." + }, + { + "text": "But if I look at the rows, it's, now it's obvious." + }, + { + "text": "The row space of that matrix obviously is two-dimensional, because I can, I see a basis for the row space, this row and that row." + }, + { + "text": "And of course, strictly speaking, I'm supposed to transpose those guys, make them stand up." + }, + { + "text": "But the rank is two, and therefore the column space is two-dimensional by this wonderful fact that the row space and column space have the same dimension, and therefore there are only two pivot columns, not three, and, those, the three columns are dependent." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk7.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..7d55c74913379543a71fcc53c971f787baf12a92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, let me bury that error and talk about the row space." + }, + { + "text": "Well, I'm going to give you the dimensions of all the spaces, because that's the, such a nice answer." + }, + { + "text": "OK." + }, + { + "text": "So let me come back here." + }, + { + "text": "So we have this great fact to establish, that the row space, its dimension is also the rank." + }, + { + "text": "OK. What about the null space?" + }, + { + "text": "What's a basis for the null space?" + }, + { + "text": "What's the dimension of the null space?" + }, + { + "text": "Let me, I'll put that answer up here, for the null space." + }, + { + "text": "Well, how have we constructed the null space?" + }, + { + "text": "We took the matrix A, we did those row operations to get it into a form U or even further, we got it into the reduced form R, and then we read off special solutions." + }, + { + "text": "Special solutions, and every special solution came from a free variable." + }, + { + "text": "And those special solutions are in the null space, and the great thing is, they're a basis for it." + }, + { + "text": "So for the null space, a basis will be the special solutions." + }, + { + "text": "And there's one for every free variable, right?" + }, + { + "text": "For each free variable, we give that variable the value one, the other free variable zero." + }, + { + "text": "We get the pivot variables, we get a vector in the -- we get a special solution." + }, + { + "text": "So we get all together n minus R of them, because that's the number of free variables." + }, + { + "text": "If we have R, this is, the dimension is R, is the number of pivot variables, this is the number of free variables." + }, + { + "text": "So the beauty is that those special solutions do form a basis and tell us immediately that the dimension of the null space is n -- I'd better write this well, because it's so nice, n minus R. And you see the nice thing, that the two dimensions in this n-dimensional space, one subspace is R-dimensional, to be proved, that's the row space." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk8.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f4c70532a641ef630aa1f7bca077776017097cd4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "The other subspace is n minus R-dimensional, that's the null space." + }, + { + "text": "And the two dimensions, like, together, give n. The sum of R and n minus R is n. And that's just great." + }, + { + "text": "It's really copying the fact that we have n variables, R of them are pivot variables and n minus R are free variables and n all together." + }, + { + "text": "OK. And now what's the dimension of this poor misbegotten fourth subspace?" + }, + { + "text": "It's got to be m minus R. The dimension of this left null space, left out practically, is m minus R. Well, that's really just saying that this, again, the sum of that plus that is m. And m is correct." + }, + { + "text": "It's the number of columns in A transpose." + }, + { + "text": "A transpose is just as good a matrix as A." + }, + { + "text": "It just happens to be n by m. It happens to have m columns, so it will have m variables, when I go to Ax equals zero, and m of them and R of them will be pivot variables and m minus R will be free variables." + }, + { + "text": "A transpose is as good a matrix as A." + }, + { + "text": "It follows the same rule that this plus the dimension, this dimension plus this dimension adds up to the number of columns." + }, + { + "text": "And over here, A transpose has m columns." + }, + { + "text": "Okay." + }, + { + "text": "Okay, so I gave you the easy answer, the dimensions." + }, + { + "text": "Now can I go back to check on a basis?" + }, + { + "text": "We would like to think that, say, the row space." + }, + { + "text": "Because we've got a basis for the column space." + }, + { + "text": "The pivot columns give a basis for the column space." + }, + { + "text": "Now I'm asking you to look at the row space." + }, + { + "text": "And I you could say, okay, I can produce a basis for the row space by transposing my matrix, making those columns, then doing elimination, row reduction, and checking out the pivot columns in this transposed matrix." + }, + { + "text": "But that means you had to do all that row reduction on A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk9.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..8be162da3ff089e5c511aa65ea7d801c64cad56f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_3_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It ought to be possible, if we take a matrix A, let me take the matrix, maybe we had this matrix in the last lecture, one one one, two one two, three two three, one one one." + }, + { + "text": "Okay." + }, + { + "text": "That, that matrix was so easy, we spotted its pivot columns, one and two, without actually doing row reduction." + }, + { + "text": "But now let's do the job properly." + }, + { + "text": "So I subtract this away from this to produce a zero." + }, + { + "text": "So one two three one is fine." + }, + { + "text": "Subtracting that away leaves me minus one minus one zero, right?" + }, + { + "text": "And subtracting that from the last row, oh, well, that's easy." + }, + { + "text": "Okay, I'm doing row reduction." + }, + { + "text": "Now I've, the first column is all set." + }, + { + "text": "The second column, I now see the pivot, and I can clean up, if I, actually, okay, why don't I make the pivot into a one?" + }, + { + "text": "I'll multiply that row through by minus one, and then I have one one." + }, + { + "text": "That was an elementary operation, I'm allowed." + }, + { + "text": "Multiply a row by a number." + }, + { + "text": "And now I'll do elimination." + }, + { + "text": "Two of those away from that will knock this guy out and make this into a one." + }, + { + "text": "So that's now a zero and that's a one." + }, + { + "text": "Okay." + }, + { + "text": "Done." + }, + { + "text": "That's R. I'm seeing the identity matrix here, I'm seeing zeros below, and I'm seeing F there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk0.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6b8bcce949e11c9807b49a56c5ca68fdb459f818 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay, here is lecture ten in linear algebra." + }, + { + "text": "Two important things to do in this lecture." + }, + { + "text": "One is to correct an error from lecture nine." + }, + { + "text": "So the blackboard with that awful error is still with us." + }, + { + "text": "And the second, the big thing to do is to tell you about the four subspaces that come with a matrix." + }, + { + "text": "We've seen two subspaces, the column space and the null space, there's two to go." + }, + { + "text": "Okay." + }, + { + "text": "First of all, and this is a great way to recap and correct the previous lecture." + }, + { + "text": "So you remember I was just doing R3." + }, + { + "text": "I couldn't have taken a simpler example than R3." + }, + { + "text": "And I wrote down the standard basis." + }, + { + "text": "That's the standard basis." + }, + { + "text": "The basis, the obvious basis for the whole three-dimensional space." + }, + { + "text": "And then I wanted to make the point that there was nothing special, nothing about that basis that another basis couldn't have." + }, + { + "text": "It could have linear independence, it could span a space, there's lots of other bases." + }, + { + "text": "So I started with these vectors one one two and two two five, and those were independent." + }, + { + "text": "And then I said three three seven wouldn't do, because three three seven is the sum of those." + }, + { + "text": "So in my innocence, I put in three three eight." + }, + { + "text": "I figured probably if three three seven is on the plane, is, which I know, it's in the plane with these two, then probably three three eight sticks a little bit out of the plane." + }, + { + "text": "And it's independent and it gives a basis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk1.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..97d9d72b29a5aa923aae0ba9c0fb0da57e9db2ed --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "But after class, to my sorrow, student tells me, wait a minute, that third vector three three eight is not independent." + }, + { + "text": "And why did she say that?" + }, + { + "text": "She didn't actually take the time, didn't have to, to find what combination of this one and this one gives three three eight." + }, + { + "text": "She did something else." + }, + { + "text": "In other words, she looked ahead because she said, wait a minute, if I look at that matrix, it's not invertible." + }, + { + "text": "That third column can't be independent of the first two, because when I look at that matrix, it's got two identical rows." + }, + { + "text": "I have a square matrix." + }, + { + "text": "Its rows are obviously dependent." + }, + { + "text": "And that makes the columns dependent." + }, + { + "text": "So there's my error." + }, + { + "text": "When I look at the matrix A that has those three columns, those three columns can't be independent because that matrix is not invertible because it's got two equal rows." + }, + { + "text": "And today's lecture will reach the conclusion, the great conclusion, that connects the column space with the row space." + }, + { + "text": "So those are the row space is now going to be another one of my fundamental subspaces." + }, + { + "text": "The row space of this matrix or of this one, well, the row space of this one is okay." + }, + { + "text": "But the row space of this one, I'm looking at the rows of the matrix, oh, anyway, I'll have two equal rows and the row space will be only two-dimensional." + }, + { + "text": "The rank of the matrix with these columns will only be two, so only two of those columns can be independent too." + }, + { + "text": "The rows tell me something about the columns, in other words." + }, + { + "text": "Something that I should have noticed and I didn't." + }, + { + "text": "Okay." + }, + { + "text": "So now let me pin down these four fundamental subspaces." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk10.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..8f428ebe86b1b4488558f6fa55b8940ef758b264 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "Okay." + }, + { + "text": "What about its row space?" + }, + { + "text": "What happened to its row space?" + }, + { + "text": "Well, what happened, let me first ask, just because this is, sometimes something does happen." + }, + { + "text": "Its column space changed." + }, + { + "text": "The column space of R is not the column space of A, right?" + }, + { + "text": "Because one one one is certainly in the column space of A and certainly not in the column space of R. I did row operations." + }, + { + "text": "Those row operations preserved the row space, so the row so the column spaces are different." + }, + { + "text": "Different column spaces." + }, + { + "text": "Different column spaces." + }, + { + "text": "But I believe that they have the same row space." + }, + { + "text": "Same row space." + }, + { + "text": "I believe that the row space of that matrix and the row space of this matrix are identical." + }, + { + "text": "They have exactly the same vectors in them." + }, + { + "text": "Those vectors are vectors with four components, right?" + }, + { + "text": "They're all combinations of those rows." + }, + { + "text": "Or I believe you get the same thing by taking all combinations of these rows." + }, + { + "text": "And if true, what's a basis?" + }, + { + "text": "What's a basis for the row space of R?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk11.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..258e5999dbb0aea67696256511eb6b999136132a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it'll be a basis for the row space of the original A." + }, + { + "text": "But it's obviously a basis for the row space of R. What's a basis for the row space of that matrix?" + }, + { + "text": "The first two rows." + }, + { + "text": "So a basis for the row so a basis is for the row space of A or of R is the first R rows of R, not of A." + }, + { + "text": "Sometimes it's true for A, but not necessarily." + }, + { + "text": "But R, we definitely have a matrix here whose row space we can identify." + }, + { + "text": "The row space is spanned by the three rows." + }, + { + "text": "But if we want a basis, we want independence." + }, + { + "text": "So out goes row three." + }, + { + "text": "The row space is also spanned by the first two rows." + }, + { + "text": "This guy didn't contribute anything." + }, + { + "text": "And of course, over here, this one, two, three, one in the bottom didn't contribute anything." + }, + { + "text": "We had it already." + }, + { + "text": "So this, here's a basis, one zero one one and zero one one zero." + }, + { + "text": "I believe those are in the row space." + }, + { + "text": "I know they're independent." + }, + { + "text": "Why are they in the row space?" + }, + { + "text": "Why are those two vectors in the row space?" + }, + { + "text": "Because all those operations we did, which started with these rows and took combinations of them." + }, + { + "text": "I took this row minus this row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk12.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..d05a7eb6e4998c4acd748e3bb7087c68e6e29a80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "That gave me something that's still in the row space." + }, + { + "text": "That's the point." + }, + { + "text": "When I took a row minus a multiple of another row, I'm staying in the row space." + }, + { + "text": "The row space is not changing." + }, + { + "text": "My little basis for it is changing, and I've ended up with, sort of, the best basis." + }, + { + "text": "If the columns of the identity matrix are the best basis for R3 or Rn, the rows of this matrix are the best basis for the row space." + }, + { + "text": "Best in the sense of being as clean as I can make it." + }, + { + "text": "Starting off with the identity and then finishing up with whatever has to be in there." + }, + { + "text": "OK. Do you see, then, that the dimension is R?" + }, + { + "text": "For sure." + }, + { + "text": "Because we've got R pivots, R nonzero rows, we've got the right number of vectors, R. They're in the row space, they're independent, that's it." + }, + { + "text": "They are a basis for the row space." + }, + { + "text": "And we can even pin that down further." + }, + { + "text": "How do I know that every row of A is a combination?" + }, + { + "text": "How do I know they span the row space?" + }, + { + "text": "Oh, well, somebody says I've got the right number of them, so they must, but that's true." + }, + { + "text": "But let me just say, how do I know that this row is a combination of these?" + }, + { + "text": "By just reversing the steps of row reduction." + }, + { + "text": "If I just reverse the steps and go from A, from R back to A, then what do I, what am I doing?" + }, + { + "text": "I'm starting with these rows, I'm taking combinations of them, after a couple of steps, undoing the subtractions that I did before, I'm back to these rows." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk13.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..7b0edabbd24233827c7692f63429589952dac1bc --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "So these rows are combinations of those rows, those rows are combinations of those rows, the two row spaces are the same, the bases are the same, and the natural basis is this guy." + }, + { + "text": "Is that all right for the row space?" + }, + { + "text": "The row space is sitting there in R, in its cleanest possible form." + }, + { + "text": "OK. Now what about the fourth guy, the null space of A transpose?" + }, + { + "text": "First of all, why do I call that the left null space?" + }, + { + "text": "So let me save that and bring that down." + }, + { + "text": "OK." + }, + { + "text": "So the fourth space is the null space of A transpose." + }, + { + "text": "So it has in it vectors, let me call them y, so that A transpose y equals zero." + }, + { + "text": "If A transpose y equals zero, then y is in the null space of A transpose, of course." + }, + { + "text": "So this is a matrix times a column equaling zero." + }, + { + "text": "And now, because I want y to sit on the left, and I want A instead of A transpose, I'll just transpose that equation." + }, + { + "text": "Can I just transpose that?" + }, + { + "text": "On the right, it makes the zero vector lie down." + }, + { + "text": "And on the left, it's a product, A transpose times y." + }, + { + "text": "If I take the transpose, then they come in opposite order, right?" + }, + { + "text": "So it's y transpose times A transpose transpose, but nobody's going to leave it like that." + }, + { + "text": "That's A transpose transpose is just A, of course." + }, + { + "text": "When I transposed A transpose, I got back to A." + }, + { + "text": "Now, do you see what I have now?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk14.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7a889f79409e9a95fbd4cc01518da4b9706c49d1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "I have a row vector, y transpose, multiplying A and multiplying from the left." + }, + { + "text": "That's why I call it the left null space." + }, + { + "text": "But by making it, putting it on the left, I had to make it into a row instead of a column vector." + }, + { + "text": "And so my convention is I usually don't do that, I usually stay with A transpose y equals zero." + }, + { + "text": "OK. And you might ask, how do we get a basis, or I might ask, how do we get a basis for this fourth space, this left null space?" + }, + { + "text": "OK." + }, + { + "text": "I'll do it the example." + }, + { + "text": "As always, ah, not that one." + }, + { + "text": "The left null space is not jumping out at me here." + }, + { + "text": "I know which are the free variables, the special solutions, but those are special solutions to Ax equals zero, and now I'm looking at A transpose and I'm not seeing it here." + }, + { + "text": "So, but somehow you feel that the work that you did, which simplified A to R, should have revealed the left null space too." + }, + { + "text": "And it's slightly less immediate, but it's there." + }, + { + "text": "So from A to R, I took some steps, and I guess I'm interested in what were those steps, or what were all of them together." + }, + { + "text": "I don't want to -- I'm not interested in what particular ones they were." + }, + { + "text": "I'm interested in what was the whole matrix that took me from A to R. How would you find that?" + }, + { + "text": "Do you remember Gauss-Jordan, where you tack on the identity matrix?" + }, + { + "text": "Let's do that again." + }, + { + "text": "So I'll do it above here." + }, + { + "text": "So this is now the idea of I take the matrix A, which is m by n. In Gauss-Jordan, when we saw him before, A was a square invertible matrix and we were finding its inverse." + }, + { + "text": "Now the matrix isn't square, it's probably rectangular." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk15.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3c045b6d07a6635d896789ba37b0d578bd175e92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "But I'll still tack on the identity matrix, and of course, since these have length m, it better be m by m. And now I'll do the reduced row echelon form of this matrix." + }, + { + "text": "And what do I get?" + }, + { + "text": "The reduced row echelon form starts with these columns, starts with the first columns, works like mad, and produces R. Of course, still the same size, m by n, and we did it before." + }, + { + "text": "And then whatever it did to get R, something else is going to show up here." + }, + { + "text": "Let me call it E, m by m. It's whatever you see that E is just going to contain a record of what we did." + }, + { + "text": "We did whatever it took to get A to become R. And at the same time, we were doing it to the identity matrix." + }, + { + "text": "So we started with the identity matrix, we buzzed along." + }, + { + "text": "So we took some -- all this row reduction amounted to multiplying on the left by some matrix, some series of elementary matrices that all together gave us one matrix, and that matrix is E. So all this row reduction stuff amounted to multiplying by E. How do I know that?" + }, + { + "text": "It certainly amounted to multiplying by something, and that something took I to E, so that something was E. So now look at the first part, E A is R. No big deal." + }, + { + "text": "All I've said is that the row reduction steps that we all know well, taking A to R, are in a- in some matrix, and I can find out what that matrix is by just tacking I on and seeing what comes out." + }, + { + "text": "What comes out is E. Let's just review the invertible square case." + }, + { + "text": "What happened then?" + }, + { + "text": "Because I was interested in it in chapter two also." + }, + { + "text": "When A was square and invertible, I took A I, I did row elimination, what was the R that came out?" + }, + { + "text": "It was I." + }, + { + "text": "So in chapter two, in chapter two, R was I." + }, + { + "text": "The row- the reduced row echelon form of a nice invertible square matrix is the identity." + }, + { + "text": "So if R was I in that case, then E was A inverse, because E A is I." + }, + { + "text": "Good." + }, + { + "text": "That's- that was good and easy." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk16.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..c5a8adc4741aeb68371eb235609b24dad795df03 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now what I'm saying is that there still is an E, it's not A inverse anymore, because A is a rectangular, it hasn't got an inverse." + }, + { + "text": "But there is still some matrix E that connected this to this." + }, + { + "text": "Oh, I should have figured out in advance what it was." + }, + { + "text": "Shoot." + }, + { + "text": "I didn't- I did those steps and sort of erased as I went, and, I should have done them to the identity, too." + }, + { + "text": "Can I do that?" + }, + { + "text": "Can I do that?" + }, + { + "text": "I'll keep the identity matrix, like I'm supposed to do, and I'll do the same operations on it and see what I end up with." + }, + { + "text": "Okay." + }, + { + "text": "So I'm starting with the identity, which I'll write in light, light enough, but okay, what did I do?" + }, + { + "text": "I subtracted that row from that one and that row from that one." + }, + { + "text": "Okay, I'll do that to the identity." + }, + { + "text": "So I subtract that first row from row two and row three." + }, + { + "text": "Good." + }, + { + "text": "Then I think I multiply, do you remember, I multiplied row two by minus one?" + }, + { + "text": "Let me just do that." + }, + { + "text": "Then what did I do?" + }, + { + "text": "I subtracted two of row two away from row one." + }, + { + "text": "I better do that." + }, + { + "text": "Subtract two of this away from this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk17.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..368775ffcdaa5a9fe2c24f8c85bcb4963097a79c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's minus one, two of these away leaves a plus two and zero." + }, + { + "text": "I believe that's E. The way to check is to see, multiply that E by this A, just to see, did I do it right?" + }, + { + "text": "So I believe E was minus one, two, zero, one minus one, zero, and minus one, zero, one." + }, + { + "text": "Okay." + }, + { + "text": "That's my E, that's my A, and that's R. All right." + }, + { + "text": "All I'm struggling to do is write the reason I wanted this blasted E was so that I could figure out the left null space." + }, + { + "text": "Not only its dimension, which I know." + }, + { + "text": "Actually, what is the dimension of the left null space?" + }, + { + "text": "Here's my matrix." + }, + { + "text": "What's the rank of the matrix?" + }, + { + "text": "Two." + }, + { + "text": "And the dimension of the left null space is supposed to be M minus R, three minus two, one." + }, + { + "text": "I believe that the left null space is one-dimensional." + }, + { + "text": "There is one combination of those three rows that produces the zero row." + }, + { + "text": "There is a basis." + }, + { + "text": "A basis for the left null space has only got one vector in it." + }, + { + "text": "And what is that vector?" + }, + { + "text": "It's here in the last row of E. But, ah, we could have seen it earlier." + }, + { + "text": "What combination of those rows gives the zero row?" + }, + { + "text": "Minus one of that, plus one of that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk18.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..9f5e8b1fcc2242dbdc56d379cbc7126ada792e31 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a basis for the left null space of this matrix, I'm looking for combinations of rows that give the zero row, if I'm looking at the left null space." + }, + { + "text": "For the null space, I'm looking at combinations of columns to get the zero column." + }, + { + "text": "Now I'm looking at combinations of these three rows to get the zero row, and of course, there is my zero row, and here is my vector that produced it." + }, + { + "text": "Minus one of that row and one of that row." + }, + { + "text": "Obvious." + }, + { + "text": "Okay." + }, + { + "text": "So in that example, and actually in all examples, we have seen how to produce a basis for the left null space." + }, + { + "text": "I won't ask you that all the time." + }, + { + "text": "Because it didn't come out immediately from R, we had to keep track of E for that left null space." + }, + { + "text": "But at least it didn't require us to transpose the matrix and start all over again." + }, + { + "text": "Okay." + }, + { + "text": "Those are the four subspaces." + }, + { + "text": "Can I review them?" + }, + { + "text": "The row space and the null space are in Rn." + }, + { + "text": "Their dimensions add to n. The column space and the left null space are in Rm, and their dimensions add to m. Okay." + }, + { + "text": "So let me close these last minutes by pushing you a little bit more to a new type of vector space." + }, + { + "text": "All our vector spaces, all the ones that we took seriously, have been subspaces of some real three- or n-dimensional space." + }, + { + "text": "Now I'm going to write down another vector space, a new vector space." + }, + { + "text": "Say all three by three matrices." + }, + { + "text": "My matrices are the vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk19.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..c1658ee474fcf6206f54d67e4dededa02a1ef92c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Is that all right?" + }, + { + "text": "I'm just naming them." + }, + { + "text": "You can put quotes around vectors." + }, + { + "text": "Every three by three matrix is one of my vectors." + }, + { + "text": "Now how am I entitled to call those things vectors?" + }, + { + "text": "I mean, they look very much like matrices." + }, + { + "text": "But they're vectors in my vector space because they obey the rules." + }, + { + "text": "All I'm supposed to be able to do with vectors is add them." + }, + { + "text": "I can add matrices." + }, + { + "text": "I'm supposed to be able to multiply them by scalar numbers, like seven." + }, + { + "text": "Well, I can multiply a matrix by seven." + }, + { + "text": "And I can take combinations of matrices." + }, + { + "text": "I can take three of one matrix minus five of another matrix." + }, + { + "text": "And those combinations, there's a zero matrix, the matrix that has all zeros in it." + }, + { + "text": "If I add that to another matrix, it doesn't change it." + }, + { + "text": "All the good stuff." + }, + { + "text": "If I multiply a matrix by one, it doesn't change it." + }, + { + "text": "All those eight rules for a vector space that we never wrote down, all easily satisfied." + }, + { + "text": "So now we have a different --." + }, + { + "text": "Now, of course, you can say you can multiply those matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk2.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..b92bd923d792a0f92ab4de95b7867006e9880f71 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here are the four fundamental subspaces." + }, + { + "text": "This is really the heart of this approach to linear algebra, to see these four subspaces, how they're related." + }, + { + "text": "So what are they?" + }, + { + "text": "The column space, C of A." + }, + { + "text": "The null space, N of A." + }, + { + "text": "And now comes the row space, something new." + }, + { + "text": "The row space, what's in that?" + }, + { + "text": "It's all combinations of the rows." + }, + { + "text": "That's natural." + }, + { + "text": "We want a space, so we have to take all combinations and we start with the rows." + }, + { + "text": "So the rows span the row space." + }, + { + "text": "Are the rows a basis for the row space?" + }, + { + "text": "Maybe so, maybe no." + }, + { + "text": "The rows are a basis for the row space when they're independent." + }, + { + "text": "But if they're dependent, as in this example, my error from last time, they're not, those three rows are not a basis, the row space would only be two-dimensional, I only need two rows for a basis." + }, + { + "text": "So the row space, now what's in it?" + }, + { + "text": "It's all combinations of the rows of A." + }, + { + "text": "All combinations of the rows of A." + }, + { + "text": "But I don't like working with row vectors." + }, + { + "text": "All my vectors have been column vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk20.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..56956e8347a8f8c1f8522690db77860dcc6953b9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "I don't care." + }, + { + "text": "For the moment, I'm only thinking of these matrices as forming a vector space, so I am only doing A plus B and C times A. I'm not interested in A, B for now." + }, + { + "text": "The fact that I can multiply is not relevant to a vector space." + }, + { + "text": "OK, so I have three by three matrices." + }, + { + "text": "And how about subspaces?" + }, + { + "text": "What's, tell me a subspace of this matrix space." + }, + { + "text": "Let me call this matrix space M. That's my matrix space, my space of all three by three matrices." + }, + { + "text": "Tell me a subspace of it." + }, + { + "text": "OK, what about the upper triangular matrices?" + }, + { + "text": "So subspaces, subspaces of M. All upper triangular matrices." + }, + { + "text": "Another subspace." + }, + { + "text": "All symmetric matrices." + }, + { + "text": "The intersection of two subspaces is supposed to be a subspace." + }, + { + "text": "We gave a little effort to the proof of that fact." + }, + { + "text": "If I look at the matrices that are in this subspace, they're symmetric, and they're also in this subspace, they're upper triangular." + }, + { + "text": "What do they look like?" + }, + { + "text": "Well, if they're symmetric, but they have zeros below the diagonal, they better have zeros above the diagonal." + }, + { + "text": "So the intersection would be diagonal matrices." + }, + { + "text": "That's another subspace, smaller than those." + }, + { + "text": "How can I use the word smaller?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk21.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..ffcdd44ed2f644726e04b27114327cb30bc7fb92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, I'm now entitled to use the word smaller." + }, + { + "text": "I mean, well, one way to say is, OK, these are contained in those." + }, + { + "text": "These are contained in those." + }, + { + "text": "But more precisely, I could give the dimension of these spaces." + }, + { + "text": "So I could, we can compute, let's compute it next time." + }, + { + "text": "The dimension of all upper, of the subspace of upper triangular three by three matrices." + }, + { + "text": "The dimension of symmetric three by three matrices." + }, + { + "text": "The dimension of diagonal three by three matrices." + }, + { + "text": "Well, to produce dimension, that means I'm supposed to produce a basis." + }, + { + "text": "And then I just count how many I needed in the basis." + }, + { + "text": "Let me give you the answer for this one." + }, + { + "text": "What's the dimension?" + }, + { + "text": "The dimension of this, say, this subspace, let me call it D, all diagonal matrices." + }, + { + "text": "The dimension of this subspace is, as I write, you're working it out, three." + }, + { + "text": "Because here's a matrix in this, it's a diagonal matrix." + }, + { + "text": "Here's another one." + }, + { + "text": "Here's another one." + }, + { + "text": "Better make it diagonal, let me put a seven there." + }, + { + "text": "That was not a very great choice, but it's three diagonal matrices, and I believe that they're a basis." + }, + { + "text": "I believe that those three matrices are independent, and I believe that any diagonal matrix is a combination of those three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk22.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..8c6bce8cf8085e6544c31ae6926bb7ccf18b983e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk22.json @@ -0,0 +1,20 @@ +[ + { + "text": "So they span the subspace of diagonal matrices." + }, + { + "text": "Do you see that idea?" + }, + { + "text": "It's like stretching the idea from Rn to Rn by n, three by three, but we can still add, we can still multiply by numbers, and we just ignore the fact that we can multiply two matrices together." + }, + { + "text": "Okay." + }, + { + "text": "Thank you." + }, + { + "text": "That's lecture ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk3.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..25f31647b76274f9088c60d1292bcc43915d3fb0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'd like to stay with column vectors." + }, + { + "text": "How can I get to column vectors out of these rows?" + }, + { + "text": "I transpose the matrix." + }, + { + "text": "So if that's OK with you, I'm going to transpose the matrix, I'm going to say all combinations of the columns of A transpose." + }, + { + "text": "And that allows me to use the convenient notation, the column space of A transpose." + }, + { + "text": "Nothing, no mathematics went on there, we just got some vectors that were lying down to stand up." + }, + { + "text": "But it means that we can use this column space of A transpose, that's telling me in a nice matrix notation what the row space is." + }, + { + "text": "OK. And finally is another null space." + }, + { + "text": "The fourth fundamental space will be the null space of A transpose." + }, + { + "text": "The fourth guy is the null space of A transpose." + }, + { + "text": "And of course, my notation is N of A transpose." + }, + { + "text": "That's the null space of A transpose." + }, + { + "text": "Now, we don't have a perfect name for this space as a, as a, connecting with A, but our usual name is the left null space, and I'll show you why in a moment." + }, + { + "text": "So often I call this the, just to write that word, the left null space of A." + }, + { + "text": "So just the way we have the row space of A and we switch it to the column space of A transpose, so we have this space of guys that I call the left null space of A, but the good notation is it's the null space of A transpose." + }, + { + "text": "OK. Those are four spaces." + }, + { + "text": "Where are those spaces?" + }, + { + "text": "What big space are they in for when A is m by n?" + }, + { + "text": "In that case, the null space of A, what's in the null space of A?" + }, + { + "text": "Vectors with n components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk4.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c2575473d88ff4598107e190483f0484b6558678 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Solutions to Ax equals zero." + }, + { + "text": "So the null space of A is n R n. What's in the column space of A?" + }, + { + "text": "Well, columns." + }, + { + "text": "How many components do those columns have?" + }, + { + "text": "m. So this column space is n R m. What about the column space of A transpose, which are just a disguised way of saying the rows of A?" + }, + { + "text": "The rows of A in this three by six matrix have six components, n components." + }, + { + "text": "The column space is n R n. And the null space of A transpose, I see that this fourth space is already getting second, you know, second class citizen treatment and it doesn't deserve it." + }, + { + "text": "It's, it should be there, it is there, and shouldn't be squeezed." + }, + { + "text": "The null space of A transpose, well, if the null space of A had vectors with n components, the null space of A transpose will be n R m. I want to draw a picture of the four spaces." + }, + { + "text": "OK. OK." + }, + { + "text": "Here are the four spaces." + }, + { + "text": "OK, let me put n dimensional space over on this side." + }, + { + "text": "Then which were the subspaces in R n?" + }, + { + "text": "The null space was and the row space was." + }, + { + "text": "So here we have the can I make that picture of the row space?" + }, + { + "text": "And can I make this kind of picture of the null space?" + }, + { + "text": "That's just meant to be a sketch, to remind you that they're in this which, you know, how, what type of vectors are in it?" + }, + { + "text": "Vectors with n components." + }, + { + "text": "Over here, inside consisting of vectors with m components is the column space and what I'm calling the null space of A transpose." + }, + { + "text": "Those are the ones with m components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk5.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..f4e64e208c1a1d8e07a9a66a6a6c59f8c4cbcec8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. To understand these spaces is our job now." + }, + { + "text": "Because by understanding those spaces, we know everything about this half of linear algebra." + }, + { + "text": "What do I mean by understanding those spaces?" + }, + { + "text": "I would like to know a basis for those spaces." + }, + { + "text": "For each one of those spaces, how would I create, construct a basis?" + }, + { + "text": "What systematic way would produce a basis?" + }, + { + "text": "And what's their dimension?" + }, + { + "text": "OK." + }, + { + "text": "So for each of the four spaces, I have to answer those questions." + }, + { + "text": "How do I produce a basis?" + }, + { + "text": "And then, which has a somewhat long answer, and what's the dimension, which is just a number, so it has a real short answer?" + }, + { + "text": "Can I give you the short answer first?" + }, + { + "text": "I shouldn't do it, but here it is." + }, + { + "text": "I can tell you the dimension of the column space." + }, + { + "text": "Let me start with this guy." + }, + { + "text": "What's its dimension?" + }, + { + "text": "I have an m by n matrix." + }, + { + "text": "The dimension of the column space is the rank, R. We actually got to that at the end of the last lecture, but only for an example." + }, + { + "text": "So I really have to say, OK, what's going on there?" + }, + { + "text": "I should produce a basis, and then I just look to see how many vectors I needed in that basis, and the answer will be R. Actually, I'll do that before I get on to the others." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk6.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..ac7425fbe27a77a7e448b576483b4c179e9a31f1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "What's a basis for the column space?" + }, + { + "text": "We've done all the work of row reduction, identifying the pivot columns, the ones that have pivots, the ones that end up with pivots, but now I the pivot columns I'm interested in are columns of A, the original A." + }, + { + "text": "And those pivot columns, there are R of them, the rank R counts those, those are a basis." + }, + { + "text": "So if I answer this question for the column space, the answer will be a basis is the pivot columns, and the dimension is the rank R. And there are pivot columns and everything great." + }, + { + "text": "OK, so that space we pretty well understand." + }, + { + "text": "I probably have a little going back to see that, to prove that this is a right answer, but you know it's the right answer." + }, + { + "text": "Now let me look at the row space." + }, + { + "text": "OK. Shall I tell you the dimension of the row space?" + }, + { + "text": "Yes." + }, + { + "text": "Before we do even an example, let me tell you the dimension of the row space." + }, + { + "text": "Its dimension is also R. The row space and the column space have the same dimension." + }, + { + "text": "That's a wonderful fact." + }, + { + "text": "The dimension of the column space of A transpose, that's the row space, is R. That space is R-dimensional." + }, + { + "text": "And so is this one." + }, + { + "text": "OK. That's the, that's the sort of insight that got used in this example." + }, + { + "text": "If those, if those, if those, are the three columns of a matrix, let me make them the three columns of a matrix by just erasing some brackets, OK, those are the three columns of a matrix, the rank of that matrix, if I look at the columns, it wasn't obvious to me anyway." + }, + { + "text": "But if I look at the rows, it's, now it's obvious." + }, + { + "text": "The row space of that matrix obviously is two-dimensional, because I can, I see a basis for the row space, this row and that row." + }, + { + "text": "And of course, strictly speaking, I'm supposed to transpose those guys, make them stand up." + }, + { + "text": "But the rank is two, and therefore the column space is two-dimensional by this wonderful fact that the row space and column space have the same dimension, and therefore there are only two pivot columns, not three, and, those, the three columns are dependent." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk7.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..7d55c74913379543a71fcc53c971f787baf12a92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, let me bury that error and talk about the row space." + }, + { + "text": "Well, I'm going to give you the dimensions of all the spaces, because that's the, such a nice answer." + }, + { + "text": "OK." + }, + { + "text": "So let me come back here." + }, + { + "text": "So we have this great fact to establish, that the row space, its dimension is also the rank." + }, + { + "text": "OK. What about the null space?" + }, + { + "text": "What's a basis for the null space?" + }, + { + "text": "What's the dimension of the null space?" + }, + { + "text": "Let me, I'll put that answer up here, for the null space." + }, + { + "text": "Well, how have we constructed the null space?" + }, + { + "text": "We took the matrix A, we did those row operations to get it into a form U or even further, we got it into the reduced form R, and then we read off special solutions." + }, + { + "text": "Special solutions, and every special solution came from a free variable." + }, + { + "text": "And those special solutions are in the null space, and the great thing is, they're a basis for it." + }, + { + "text": "So for the null space, a basis will be the special solutions." + }, + { + "text": "And there's one for every free variable, right?" + }, + { + "text": "For each free variable, we give that variable the value one, the other free variable zero." + }, + { + "text": "We get the pivot variables, we get a vector in the -- we get a special solution." + }, + { + "text": "So we get all together n minus R of them, because that's the number of free variables." + }, + { + "text": "If we have R, this is, the dimension is R, is the number of pivot variables, this is the number of free variables." + }, + { + "text": "So the beauty is that those special solutions do form a basis and tell us immediately that the dimension of the null space is n -- I'd better write this well, because it's so nice, n minus R. And you see the nice thing, that the two dimensions in this n-dimensional space, one subspace is R-dimensional, to be proved, that's the row space." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk8.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f4c70532a641ef630aa1f7bca077776017097cd4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "The other subspace is n minus R-dimensional, that's the null space." + }, + { + "text": "And the two dimensions, like, together, give n. The sum of R and n minus R is n. And that's just great." + }, + { + "text": "It's really copying the fact that we have n variables, R of them are pivot variables and n minus R are free variables and n all together." + }, + { + "text": "OK. And now what's the dimension of this poor misbegotten fourth subspace?" + }, + { + "text": "It's got to be m minus R. The dimension of this left null space, left out practically, is m minus R. Well, that's really just saying that this, again, the sum of that plus that is m. And m is correct." + }, + { + "text": "It's the number of columns in A transpose." + }, + { + "text": "A transpose is just as good a matrix as A." + }, + { + "text": "It just happens to be n by m. It happens to have m columns, so it will have m variables, when I go to Ax equals zero, and m of them and R of them will be pivot variables and m minus R will be free variables." + }, + { + "text": "A transpose is as good a matrix as A." + }, + { + "text": "It follows the same rule that this plus the dimension, this dimension plus this dimension adds up to the number of columns." + }, + { + "text": "And over here, A transpose has m columns." + }, + { + "text": "Okay." + }, + { + "text": "Okay, so I gave you the easy answer, the dimensions." + }, + { + "text": "Now can I go back to check on a basis?" + }, + { + "text": "We would like to think that, say, the row space." + }, + { + "text": "Because we've got a basis for the column space." + }, + { + "text": "The pivot columns give a basis for the column space." + }, + { + "text": "Now I'm asking you to look at the row space." + }, + { + "text": "And I you could say, okay, I can produce a basis for the row space by transposing my matrix, making those columns, then doing elimination, row reduction, and checking out the pivot columns in this transposed matrix." + }, + { + "text": "But that means you had to do all that row reduction on A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk9.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..8be162da3ff089e5c511aa65ea7d801c64cad56f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_5_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It ought to be possible, if we take a matrix A, let me take the matrix, maybe we had this matrix in the last lecture, one one one, two one two, three two three, one one one." + }, + { + "text": "Okay." + }, + { + "text": "That, that matrix was so easy, we spotted its pivot columns, one and two, without actually doing row reduction." + }, + { + "text": "But now let's do the job properly." + }, + { + "text": "So I subtract this away from this to produce a zero." + }, + { + "text": "So one two three one is fine." + }, + { + "text": "Subtracting that away leaves me minus one minus one zero, right?" + }, + { + "text": "And subtracting that from the last row, oh, well, that's easy." + }, + { + "text": "Okay, I'm doing row reduction." + }, + { + "text": "Now I've, the first column is all set." + }, + { + "text": "The second column, I now see the pivot, and I can clean up, if I, actually, okay, why don't I make the pivot into a one?" + }, + { + "text": "I'll multiply that row through by minus one, and then I have one one." + }, + { + "text": "That was an elementary operation, I'm allowed." + }, + { + "text": "Multiply a row by a number." + }, + { + "text": "And now I'll do elimination." + }, + { + "text": "Two of those away from that will knock this guy out and make this into a one." + }, + { + "text": "So that's now a zero and that's a one." + }, + { + "text": "Okay." + }, + { + "text": "Done." + }, + { + "text": "That's R. I'm seeing the identity matrix here, I'm seeing zeros below, and I'm seeing F there." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk0.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk0.json new file mode 100644 index 0000000000000000000000000000000000000000..6b8bcce949e11c9807b49a56c5ca68fdb459f818 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk0.json @@ -0,0 +1,62 @@ +[ + { + "text": " Okay, here is lecture ten in linear algebra." + }, + { + "text": "Two important things to do in this lecture." + }, + { + "text": "One is to correct an error from lecture nine." + }, + { + "text": "So the blackboard with that awful error is still with us." + }, + { + "text": "And the second, the big thing to do is to tell you about the four subspaces that come with a matrix." + }, + { + "text": "We've seen two subspaces, the column space and the null space, there's two to go." + }, + { + "text": "Okay." + }, + { + "text": "First of all, and this is a great way to recap and correct the previous lecture." + }, + { + "text": "So you remember I was just doing R3." + }, + { + "text": "I couldn't have taken a simpler example than R3." + }, + { + "text": "And I wrote down the standard basis." + }, + { + "text": "That's the standard basis." + }, + { + "text": "The basis, the obvious basis for the whole three-dimensional space." + }, + { + "text": "And then I wanted to make the point that there was nothing special, nothing about that basis that another basis couldn't have." + }, + { + "text": "It could have linear independence, it could span a space, there's lots of other bases." + }, + { + "text": "So I started with these vectors one one two and two two five, and those were independent." + }, + { + "text": "And then I said three three seven wouldn't do, because three three seven is the sum of those." + }, + { + "text": "So in my innocence, I put in three three eight." + }, + { + "text": "I figured probably if three three seven is on the plane, is, which I know, it's in the plane with these two, then probably three three eight sticks a little bit out of the plane." + }, + { + "text": "And it's independent and it gives a basis." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk1.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk1.json new file mode 100644 index 0000000000000000000000000000000000000000..97d9d72b29a5aa923aae0ba9c0fb0da57e9db2ed --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk1.json @@ -0,0 +1,62 @@ +[ + { + "text": "But after class, to my sorrow, student tells me, wait a minute, that third vector three three eight is not independent." + }, + { + "text": "And why did she say that?" + }, + { + "text": "She didn't actually take the time, didn't have to, to find what combination of this one and this one gives three three eight." + }, + { + "text": "She did something else." + }, + { + "text": "In other words, she looked ahead because she said, wait a minute, if I look at that matrix, it's not invertible." + }, + { + "text": "That third column can't be independent of the first two, because when I look at that matrix, it's got two identical rows." + }, + { + "text": "I have a square matrix." + }, + { + "text": "Its rows are obviously dependent." + }, + { + "text": "And that makes the columns dependent." + }, + { + "text": "So there's my error." + }, + { + "text": "When I look at the matrix A that has those three columns, those three columns can't be independent because that matrix is not invertible because it's got two equal rows." + }, + { + "text": "And today's lecture will reach the conclusion, the great conclusion, that connects the column space with the row space." + }, + { + "text": "So those are the row space is now going to be another one of my fundamental subspaces." + }, + { + "text": "The row space of this matrix or of this one, well, the row space of this one is okay." + }, + { + "text": "But the row space of this one, I'm looking at the rows of the matrix, oh, anyway, I'll have two equal rows and the row space will be only two-dimensional." + }, + { + "text": "The rank of the matrix with these columns will only be two, so only two of those columns can be independent too." + }, + { + "text": "The rows tell me something about the columns, in other words." + }, + { + "text": "Something that I should have noticed and I didn't." + }, + { + "text": "Okay." + }, + { + "text": "So now let me pin down these four fundamental subspaces." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk10.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk10.json new file mode 100644 index 0000000000000000000000000000000000000000..8f428ebe86b1b4488558f6fa55b8940ef758b264 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk10.json @@ -0,0 +1,62 @@ +[ + { + "text": "Okay." + }, + { + "text": "Okay." + }, + { + "text": "What about its row space?" + }, + { + "text": "What happened to its row space?" + }, + { + "text": "Well, what happened, let me first ask, just because this is, sometimes something does happen." + }, + { + "text": "Its column space changed." + }, + { + "text": "The column space of R is not the column space of A, right?" + }, + { + "text": "Because one one one is certainly in the column space of A and certainly not in the column space of R. I did row operations." + }, + { + "text": "Those row operations preserved the row space, so the row so the column spaces are different." + }, + { + "text": "Different column spaces." + }, + { + "text": "Different column spaces." + }, + { + "text": "But I believe that they have the same row space." + }, + { + "text": "Same row space." + }, + { + "text": "I believe that the row space of that matrix and the row space of this matrix are identical." + }, + { + "text": "They have exactly the same vectors in them." + }, + { + "text": "Those vectors are vectors with four components, right?" + }, + { + "text": "They're all combinations of those rows." + }, + { + "text": "Or I believe you get the same thing by taking all combinations of these rows." + }, + { + "text": "And if true, what's a basis?" + }, + { + "text": "What's a basis for the row space of R?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk11.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk11.json new file mode 100644 index 0000000000000000000000000000000000000000..258e5999dbb0aea67696256511eb6b999136132a --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk11.json @@ -0,0 +1,62 @@ +[ + { + "text": "And it'll be a basis for the row space of the original A." + }, + { + "text": "But it's obviously a basis for the row space of R. What's a basis for the row space of that matrix?" + }, + { + "text": "The first two rows." + }, + { + "text": "So a basis for the row so a basis is for the row space of A or of R is the first R rows of R, not of A." + }, + { + "text": "Sometimes it's true for A, but not necessarily." + }, + { + "text": "But R, we definitely have a matrix here whose row space we can identify." + }, + { + "text": "The row space is spanned by the three rows." + }, + { + "text": "But if we want a basis, we want independence." + }, + { + "text": "So out goes row three." + }, + { + "text": "The row space is also spanned by the first two rows." + }, + { + "text": "This guy didn't contribute anything." + }, + { + "text": "And of course, over here, this one, two, three, one in the bottom didn't contribute anything." + }, + { + "text": "We had it already." + }, + { + "text": "So this, here's a basis, one zero one one and zero one one zero." + }, + { + "text": "I believe those are in the row space." + }, + { + "text": "I know they're independent." + }, + { + "text": "Why are they in the row space?" + }, + { + "text": "Why are those two vectors in the row space?" + }, + { + "text": "Because all those operations we did, which started with these rows and took combinations of them." + }, + { + "text": "I took this row minus this row." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk12.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk12.json new file mode 100644 index 0000000000000000000000000000000000000000..d05a7eb6e4998c4acd748e3bb7087c68e6e29a80 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk12.json @@ -0,0 +1,62 @@ +[ + { + "text": "That gave me something that's still in the row space." + }, + { + "text": "That's the point." + }, + { + "text": "When I took a row minus a multiple of another row, I'm staying in the row space." + }, + { + "text": "The row space is not changing." + }, + { + "text": "My little basis for it is changing, and I've ended up with, sort of, the best basis." + }, + { + "text": "If the columns of the identity matrix are the best basis for R3 or Rn, the rows of this matrix are the best basis for the row space." + }, + { + "text": "Best in the sense of being as clean as I can make it." + }, + { + "text": "Starting off with the identity and then finishing up with whatever has to be in there." + }, + { + "text": "OK. Do you see, then, that the dimension is R?" + }, + { + "text": "For sure." + }, + { + "text": "Because we've got R pivots, R nonzero rows, we've got the right number of vectors, R. They're in the row space, they're independent, that's it." + }, + { + "text": "They are a basis for the row space." + }, + { + "text": "And we can even pin that down further." + }, + { + "text": "How do I know that every row of A is a combination?" + }, + { + "text": "How do I know they span the row space?" + }, + { + "text": "Oh, well, somebody says I've got the right number of them, so they must, but that's true." + }, + { + "text": "But let me just say, how do I know that this row is a combination of these?" + }, + { + "text": "By just reversing the steps of row reduction." + }, + { + "text": "If I just reverse the steps and go from A, from R back to A, then what do I, what am I doing?" + }, + { + "text": "I'm starting with these rows, I'm taking combinations of them, after a couple of steps, undoing the subtractions that I did before, I'm back to these rows." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk13.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk13.json new file mode 100644 index 0000000000000000000000000000000000000000..7b0edabbd24233827c7692f63429589952dac1bc --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk13.json @@ -0,0 +1,62 @@ +[ + { + "text": "So these rows are combinations of those rows, those rows are combinations of those rows, the two row spaces are the same, the bases are the same, and the natural basis is this guy." + }, + { + "text": "Is that all right for the row space?" + }, + { + "text": "The row space is sitting there in R, in its cleanest possible form." + }, + { + "text": "OK. Now what about the fourth guy, the null space of A transpose?" + }, + { + "text": "First of all, why do I call that the left null space?" + }, + { + "text": "So let me save that and bring that down." + }, + { + "text": "OK." + }, + { + "text": "So the fourth space is the null space of A transpose." + }, + { + "text": "So it has in it vectors, let me call them y, so that A transpose y equals zero." + }, + { + "text": "If A transpose y equals zero, then y is in the null space of A transpose, of course." + }, + { + "text": "So this is a matrix times a column equaling zero." + }, + { + "text": "And now, because I want y to sit on the left, and I want A instead of A transpose, I'll just transpose that equation." + }, + { + "text": "Can I just transpose that?" + }, + { + "text": "On the right, it makes the zero vector lie down." + }, + { + "text": "And on the left, it's a product, A transpose times y." + }, + { + "text": "If I take the transpose, then they come in opposite order, right?" + }, + { + "text": "So it's y transpose times A transpose transpose, but nobody's going to leave it like that." + }, + { + "text": "That's A transpose transpose is just A, of course." + }, + { + "text": "When I transposed A transpose, I got back to A." + }, + { + "text": "Now, do you see what I have now?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk14.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk14.json new file mode 100644 index 0000000000000000000000000000000000000000..7a889f79409e9a95fbd4cc01518da4b9706c49d1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk14.json @@ -0,0 +1,62 @@ +[ + { + "text": "I have a row vector, y transpose, multiplying A and multiplying from the left." + }, + { + "text": "That's why I call it the left null space." + }, + { + "text": "But by making it, putting it on the left, I had to make it into a row instead of a column vector." + }, + { + "text": "And so my convention is I usually don't do that, I usually stay with A transpose y equals zero." + }, + { + "text": "OK. And you might ask, how do we get a basis, or I might ask, how do we get a basis for this fourth space, this left null space?" + }, + { + "text": "OK." + }, + { + "text": "I'll do it the example." + }, + { + "text": "As always, ah, not that one." + }, + { + "text": "The left null space is not jumping out at me here." + }, + { + "text": "I know which are the free variables, the special solutions, but those are special solutions to Ax equals zero, and now I'm looking at A transpose and I'm not seeing it here." + }, + { + "text": "So, but somehow you feel that the work that you did, which simplified A to R, should have revealed the left null space too." + }, + { + "text": "And it's slightly less immediate, but it's there." + }, + { + "text": "So from A to R, I took some steps, and I guess I'm interested in what were those steps, or what were all of them together." + }, + { + "text": "I don't want to -- I'm not interested in what particular ones they were." + }, + { + "text": "I'm interested in what was the whole matrix that took me from A to R. How would you find that?" + }, + { + "text": "Do you remember Gauss-Jordan, where you tack on the identity matrix?" + }, + { + "text": "Let's do that again." + }, + { + "text": "So I'll do it above here." + }, + { + "text": "So this is now the idea of I take the matrix A, which is m by n. In Gauss-Jordan, when we saw him before, A was a square invertible matrix and we were finding its inverse." + }, + { + "text": "Now the matrix isn't square, it's probably rectangular." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk15.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk15.json new file mode 100644 index 0000000000000000000000000000000000000000..3c045b6d07a6635d896789ba37b0d578bd175e92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk15.json @@ -0,0 +1,62 @@ +[ + { + "text": "But I'll still tack on the identity matrix, and of course, since these have length m, it better be m by m. And now I'll do the reduced row echelon form of this matrix." + }, + { + "text": "And what do I get?" + }, + { + "text": "The reduced row echelon form starts with these columns, starts with the first columns, works like mad, and produces R. Of course, still the same size, m by n, and we did it before." + }, + { + "text": "And then whatever it did to get R, something else is going to show up here." + }, + { + "text": "Let me call it E, m by m. It's whatever you see that E is just going to contain a record of what we did." + }, + { + "text": "We did whatever it took to get A to become R. And at the same time, we were doing it to the identity matrix." + }, + { + "text": "So we started with the identity matrix, we buzzed along." + }, + { + "text": "So we took some -- all this row reduction amounted to multiplying on the left by some matrix, some series of elementary matrices that all together gave us one matrix, and that matrix is E. So all this row reduction stuff amounted to multiplying by E. How do I know that?" + }, + { + "text": "It certainly amounted to multiplying by something, and that something took I to E, so that something was E. So now look at the first part, E A is R. No big deal." + }, + { + "text": "All I've said is that the row reduction steps that we all know well, taking A to R, are in a- in some matrix, and I can find out what that matrix is by just tacking I on and seeing what comes out." + }, + { + "text": "What comes out is E. Let's just review the invertible square case." + }, + { + "text": "What happened then?" + }, + { + "text": "Because I was interested in it in chapter two also." + }, + { + "text": "When A was square and invertible, I took A I, I did row elimination, what was the R that came out?" + }, + { + "text": "It was I." + }, + { + "text": "So in chapter two, in chapter two, R was I." + }, + { + "text": "The row- the reduced row echelon form of a nice invertible square matrix is the identity." + }, + { + "text": "So if R was I in that case, then E was A inverse, because E A is I." + }, + { + "text": "Good." + }, + { + "text": "That's- that was good and easy." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk16.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk16.json new file mode 100644 index 0000000000000000000000000000000000000000..c5a8adc4741aeb68371eb235609b24dad795df03 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk16.json @@ -0,0 +1,62 @@ +[ + { + "text": "Now what I'm saying is that there still is an E, it's not A inverse anymore, because A is a rectangular, it hasn't got an inverse." + }, + { + "text": "But there is still some matrix E that connected this to this." + }, + { + "text": "Oh, I should have figured out in advance what it was." + }, + { + "text": "Shoot." + }, + { + "text": "I didn't- I did those steps and sort of erased as I went, and, I should have done them to the identity, too." + }, + { + "text": "Can I do that?" + }, + { + "text": "Can I do that?" + }, + { + "text": "I'll keep the identity matrix, like I'm supposed to do, and I'll do the same operations on it and see what I end up with." + }, + { + "text": "Okay." + }, + { + "text": "So I'm starting with the identity, which I'll write in light, light enough, but okay, what did I do?" + }, + { + "text": "I subtracted that row from that one and that row from that one." + }, + { + "text": "Okay, I'll do that to the identity." + }, + { + "text": "So I subtract that first row from row two and row three." + }, + { + "text": "Good." + }, + { + "text": "Then I think I multiply, do you remember, I multiplied row two by minus one?" + }, + { + "text": "Let me just do that." + }, + { + "text": "Then what did I do?" + }, + { + "text": "I subtracted two of row two away from row one." + }, + { + "text": "I better do that." + }, + { + "text": "Subtract two of this away from this." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk17.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk17.json new file mode 100644 index 0000000000000000000000000000000000000000..368775ffcdaa5a9fe2c24f8c85bcb4963097a79c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk17.json @@ -0,0 +1,62 @@ +[ + { + "text": "That's minus one, two of these away leaves a plus two and zero." + }, + { + "text": "I believe that's E. The way to check is to see, multiply that E by this A, just to see, did I do it right?" + }, + { + "text": "So I believe E was minus one, two, zero, one minus one, zero, and minus one, zero, one." + }, + { + "text": "Okay." + }, + { + "text": "That's my E, that's my A, and that's R. All right." + }, + { + "text": "All I'm struggling to do is write the reason I wanted this blasted E was so that I could figure out the left null space." + }, + { + "text": "Not only its dimension, which I know." + }, + { + "text": "Actually, what is the dimension of the left null space?" + }, + { + "text": "Here's my matrix." + }, + { + "text": "What's the rank of the matrix?" + }, + { + "text": "Two." + }, + { + "text": "And the dimension of the left null space is supposed to be M minus R, three minus two, one." + }, + { + "text": "I believe that the left null space is one-dimensional." + }, + { + "text": "There is one combination of those three rows that produces the zero row." + }, + { + "text": "There is a basis." + }, + { + "text": "A basis for the left null space has only got one vector in it." + }, + { + "text": "And what is that vector?" + }, + { + "text": "It's here in the last row of E. But, ah, we could have seen it earlier." + }, + { + "text": "What combination of those rows gives the zero row?" + }, + { + "text": "Minus one of that, plus one of that." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk18.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk18.json new file mode 100644 index 0000000000000000000000000000000000000000..9f5e8b1fcc2242dbdc56d379cbc7126ada792e31 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk18.json @@ -0,0 +1,62 @@ +[ + { + "text": "So a basis for the left null space of this matrix, I'm looking for combinations of rows that give the zero row, if I'm looking at the left null space." + }, + { + "text": "For the null space, I'm looking at combinations of columns to get the zero column." + }, + { + "text": "Now I'm looking at combinations of these three rows to get the zero row, and of course, there is my zero row, and here is my vector that produced it." + }, + { + "text": "Minus one of that row and one of that row." + }, + { + "text": "Obvious." + }, + { + "text": "Okay." + }, + { + "text": "So in that example, and actually in all examples, we have seen how to produce a basis for the left null space." + }, + { + "text": "I won't ask you that all the time." + }, + { + "text": "Because it didn't come out immediately from R, we had to keep track of E for that left null space." + }, + { + "text": "But at least it didn't require us to transpose the matrix and start all over again." + }, + { + "text": "Okay." + }, + { + "text": "Those are the four subspaces." + }, + { + "text": "Can I review them?" + }, + { + "text": "The row space and the null space are in Rn." + }, + { + "text": "Their dimensions add to n. The column space and the left null space are in Rm, and their dimensions add to m. Okay." + }, + { + "text": "So let me close these last minutes by pushing you a little bit more to a new type of vector space." + }, + { + "text": "All our vector spaces, all the ones that we took seriously, have been subspaces of some real three- or n-dimensional space." + }, + { + "text": "Now I'm going to write down another vector space, a new vector space." + }, + { + "text": "Say all three by three matrices." + }, + { + "text": "My matrices are the vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk19.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk19.json new file mode 100644 index 0000000000000000000000000000000000000000..c1658ee474fcf6206f54d67e4dededa02a1ef92c --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk19.json @@ -0,0 +1,62 @@ +[ + { + "text": "Is that all right?" + }, + { + "text": "I'm just naming them." + }, + { + "text": "You can put quotes around vectors." + }, + { + "text": "Every three by three matrix is one of my vectors." + }, + { + "text": "Now how am I entitled to call those things vectors?" + }, + { + "text": "I mean, they look very much like matrices." + }, + { + "text": "But they're vectors in my vector space because they obey the rules." + }, + { + "text": "All I'm supposed to be able to do with vectors is add them." + }, + { + "text": "I can add matrices." + }, + { + "text": "I'm supposed to be able to multiply them by scalar numbers, like seven." + }, + { + "text": "Well, I can multiply a matrix by seven." + }, + { + "text": "And I can take combinations of matrices." + }, + { + "text": "I can take three of one matrix minus five of another matrix." + }, + { + "text": "And those combinations, there's a zero matrix, the matrix that has all zeros in it." + }, + { + "text": "If I add that to another matrix, it doesn't change it." + }, + { + "text": "All the good stuff." + }, + { + "text": "If I multiply a matrix by one, it doesn't change it." + }, + { + "text": "All those eight rules for a vector space that we never wrote down, all easily satisfied." + }, + { + "text": "So now we have a different --." + }, + { + "text": "Now, of course, you can say you can multiply those matrices." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk2.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk2.json new file mode 100644 index 0000000000000000000000000000000000000000..b92bd923d792a0f92ab4de95b7867006e9880f71 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk2.json @@ -0,0 +1,62 @@ +[ + { + "text": "So here are the four fundamental subspaces." + }, + { + "text": "This is really the heart of this approach to linear algebra, to see these four subspaces, how they're related." + }, + { + "text": "So what are they?" + }, + { + "text": "The column space, C of A." + }, + { + "text": "The null space, N of A." + }, + { + "text": "And now comes the row space, something new." + }, + { + "text": "The row space, what's in that?" + }, + { + "text": "It's all combinations of the rows." + }, + { + "text": "That's natural." + }, + { + "text": "We want a space, so we have to take all combinations and we start with the rows." + }, + { + "text": "So the rows span the row space." + }, + { + "text": "Are the rows a basis for the row space?" + }, + { + "text": "Maybe so, maybe no." + }, + { + "text": "The rows are a basis for the row space when they're independent." + }, + { + "text": "But if they're dependent, as in this example, my error from last time, they're not, those three rows are not a basis, the row space would only be two-dimensional, I only need two rows for a basis." + }, + { + "text": "So the row space, now what's in it?" + }, + { + "text": "It's all combinations of the rows of A." + }, + { + "text": "All combinations of the rows of A." + }, + { + "text": "But I don't like working with row vectors." + }, + { + "text": "All my vectors have been column vectors." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk20.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk20.json new file mode 100644 index 0000000000000000000000000000000000000000..56956e8347a8f8c1f8522690db77860dcc6953b9 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk20.json @@ -0,0 +1,62 @@ +[ + { + "text": "I don't care." + }, + { + "text": "For the moment, I'm only thinking of these matrices as forming a vector space, so I am only doing A plus B and C times A. I'm not interested in A, B for now." + }, + { + "text": "The fact that I can multiply is not relevant to a vector space." + }, + { + "text": "OK, so I have three by three matrices." + }, + { + "text": "And how about subspaces?" + }, + { + "text": "What's, tell me a subspace of this matrix space." + }, + { + "text": "Let me call this matrix space M. That's my matrix space, my space of all three by three matrices." + }, + { + "text": "Tell me a subspace of it." + }, + { + "text": "OK, what about the upper triangular matrices?" + }, + { + "text": "So subspaces, subspaces of M. All upper triangular matrices." + }, + { + "text": "Another subspace." + }, + { + "text": "All symmetric matrices." + }, + { + "text": "The intersection of two subspaces is supposed to be a subspace." + }, + { + "text": "We gave a little effort to the proof of that fact." + }, + { + "text": "If I look at the matrices that are in this subspace, they're symmetric, and they're also in this subspace, they're upper triangular." + }, + { + "text": "What do they look like?" + }, + { + "text": "Well, if they're symmetric, but they have zeros below the diagonal, they better have zeros above the diagonal." + }, + { + "text": "So the intersection would be diagonal matrices." + }, + { + "text": "That's another subspace, smaller than those." + }, + { + "text": "How can I use the word smaller?" + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk21.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk21.json new file mode 100644 index 0000000000000000000000000000000000000000..ffcdd44ed2f644726e04b27114327cb30bc7fb92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk21.json @@ -0,0 +1,62 @@ +[ + { + "text": "Well, I'm now entitled to use the word smaller." + }, + { + "text": "I mean, well, one way to say is, OK, these are contained in those." + }, + { + "text": "These are contained in those." + }, + { + "text": "But more precisely, I could give the dimension of these spaces." + }, + { + "text": "So I could, we can compute, let's compute it next time." + }, + { + "text": "The dimension of all upper, of the subspace of upper triangular three by three matrices." + }, + { + "text": "The dimension of symmetric three by three matrices." + }, + { + "text": "The dimension of diagonal three by three matrices." + }, + { + "text": "Well, to produce dimension, that means I'm supposed to produce a basis." + }, + { + "text": "And then I just count how many I needed in the basis." + }, + { + "text": "Let me give you the answer for this one." + }, + { + "text": "What's the dimension?" + }, + { + "text": "The dimension of this, say, this subspace, let me call it D, all diagonal matrices." + }, + { + "text": "The dimension of this subspace is, as I write, you're working it out, three." + }, + { + "text": "Because here's a matrix in this, it's a diagonal matrix." + }, + { + "text": "Here's another one." + }, + { + "text": "Here's another one." + }, + { + "text": "Better make it diagonal, let me put a seven there." + }, + { + "text": "That was not a very great choice, but it's three diagonal matrices, and I believe that they're a basis." + }, + { + "text": "I believe that those three matrices are independent, and I believe that any diagonal matrix is a combination of those three." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk22.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk22.json new file mode 100644 index 0000000000000000000000000000000000000000..8c6bce8cf8085e6544c31ae6926bb7ccf18b983e --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk22.json @@ -0,0 +1,20 @@ +[ + { + "text": "So they span the subspace of diagonal matrices." + }, + { + "text": "Do you see that idea?" + }, + { + "text": "It's like stretching the idea from Rn to Rn by n, three by three, but we can still add, we can still multiply by numbers, and we just ignore the fact that we can multiply two matrices together." + }, + { + "text": "Okay." + }, + { + "text": "Thank you." + }, + { + "text": "That's lecture ten." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk3.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk3.json new file mode 100644 index 0000000000000000000000000000000000000000..25f31647b76274f9088c60d1292bcc43915d3fb0 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk3.json @@ -0,0 +1,62 @@ +[ + { + "text": "I'd like to stay with column vectors." + }, + { + "text": "How can I get to column vectors out of these rows?" + }, + { + "text": "I transpose the matrix." + }, + { + "text": "So if that's OK with you, I'm going to transpose the matrix, I'm going to say all combinations of the columns of A transpose." + }, + { + "text": "And that allows me to use the convenient notation, the column space of A transpose." + }, + { + "text": "Nothing, no mathematics went on there, we just got some vectors that were lying down to stand up." + }, + { + "text": "But it means that we can use this column space of A transpose, that's telling me in a nice matrix notation what the row space is." + }, + { + "text": "OK. And finally is another null space." + }, + { + "text": "The fourth fundamental space will be the null space of A transpose." + }, + { + "text": "The fourth guy is the null space of A transpose." + }, + { + "text": "And of course, my notation is N of A transpose." + }, + { + "text": "That's the null space of A transpose." + }, + { + "text": "Now, we don't have a perfect name for this space as a, as a, connecting with A, but our usual name is the left null space, and I'll show you why in a moment." + }, + { + "text": "So often I call this the, just to write that word, the left null space of A." + }, + { + "text": "So just the way we have the row space of A and we switch it to the column space of A transpose, so we have this space of guys that I call the left null space of A, but the good notation is it's the null space of A transpose." + }, + { + "text": "OK. Those are four spaces." + }, + { + "text": "Where are those spaces?" + }, + { + "text": "What big space are they in for when A is m by n?" + }, + { + "text": "In that case, the null space of A, what's in the null space of A?" + }, + { + "text": "Vectors with n components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk4.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk4.json new file mode 100644 index 0000000000000000000000000000000000000000..c2575473d88ff4598107e190483f0484b6558678 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk4.json @@ -0,0 +1,62 @@ +[ + { + "text": "Solutions to Ax equals zero." + }, + { + "text": "So the null space of A is n R n. What's in the column space of A?" + }, + { + "text": "Well, columns." + }, + { + "text": "How many components do those columns have?" + }, + { + "text": "m. So this column space is n R m. What about the column space of A transpose, which are just a disguised way of saying the rows of A?" + }, + { + "text": "The rows of A in this three by six matrix have six components, n components." + }, + { + "text": "The column space is n R n. And the null space of A transpose, I see that this fourth space is already getting second, you know, second class citizen treatment and it doesn't deserve it." + }, + { + "text": "It's, it should be there, it is there, and shouldn't be squeezed." + }, + { + "text": "The null space of A transpose, well, if the null space of A had vectors with n components, the null space of A transpose will be n R m. I want to draw a picture of the four spaces." + }, + { + "text": "OK. OK." + }, + { + "text": "Here are the four spaces." + }, + { + "text": "OK, let me put n dimensional space over on this side." + }, + { + "text": "Then which were the subspaces in R n?" + }, + { + "text": "The null space was and the row space was." + }, + { + "text": "So here we have the can I make that picture of the row space?" + }, + { + "text": "And can I make this kind of picture of the null space?" + }, + { + "text": "That's just meant to be a sketch, to remind you that they're in this which, you know, how, what type of vectors are in it?" + }, + { + "text": "Vectors with n components." + }, + { + "text": "Over here, inside consisting of vectors with m components is the column space and what I'm calling the null space of A transpose." + }, + { + "text": "Those are the ones with m components." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk5.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk5.json new file mode 100644 index 0000000000000000000000000000000000000000..f4e64e208c1a1d8e07a9a66a6a6c59f8c4cbcec8 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk5.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. To understand these spaces is our job now." + }, + { + "text": "Because by understanding those spaces, we know everything about this half of linear algebra." + }, + { + "text": "What do I mean by understanding those spaces?" + }, + { + "text": "I would like to know a basis for those spaces." + }, + { + "text": "For each one of those spaces, how would I create, construct a basis?" + }, + { + "text": "What systematic way would produce a basis?" + }, + { + "text": "And what's their dimension?" + }, + { + "text": "OK." + }, + { + "text": "So for each of the four spaces, I have to answer those questions." + }, + { + "text": "How do I produce a basis?" + }, + { + "text": "And then, which has a somewhat long answer, and what's the dimension, which is just a number, so it has a real short answer?" + }, + { + "text": "Can I give you the short answer first?" + }, + { + "text": "I shouldn't do it, but here it is." + }, + { + "text": "I can tell you the dimension of the column space." + }, + { + "text": "Let me start with this guy." + }, + { + "text": "What's its dimension?" + }, + { + "text": "I have an m by n matrix." + }, + { + "text": "The dimension of the column space is the rank, R. We actually got to that at the end of the last lecture, but only for an example." + }, + { + "text": "So I really have to say, OK, what's going on there?" + }, + { + "text": "I should produce a basis, and then I just look to see how many vectors I needed in that basis, and the answer will be R. Actually, I'll do that before I get on to the others." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk6.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk6.json new file mode 100644 index 0000000000000000000000000000000000000000..ac7425fbe27a77a7e448b576483b4c179e9a31f1 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk6.json @@ -0,0 +1,62 @@ +[ + { + "text": "What's a basis for the column space?" + }, + { + "text": "We've done all the work of row reduction, identifying the pivot columns, the ones that have pivots, the ones that end up with pivots, but now I the pivot columns I'm interested in are columns of A, the original A." + }, + { + "text": "And those pivot columns, there are R of them, the rank R counts those, those are a basis." + }, + { + "text": "So if I answer this question for the column space, the answer will be a basis is the pivot columns, and the dimension is the rank R. And there are pivot columns and everything great." + }, + { + "text": "OK, so that space we pretty well understand." + }, + { + "text": "I probably have a little going back to see that, to prove that this is a right answer, but you know it's the right answer." + }, + { + "text": "Now let me look at the row space." + }, + { + "text": "OK. Shall I tell you the dimension of the row space?" + }, + { + "text": "Yes." + }, + { + "text": "Before we do even an example, let me tell you the dimension of the row space." + }, + { + "text": "Its dimension is also R. The row space and the column space have the same dimension." + }, + { + "text": "That's a wonderful fact." + }, + { + "text": "The dimension of the column space of A transpose, that's the row space, is R. That space is R-dimensional." + }, + { + "text": "And so is this one." + }, + { + "text": "OK. That's the, that's the sort of insight that got used in this example." + }, + { + "text": "If those, if those, if those, are the three columns of a matrix, let me make them the three columns of a matrix by just erasing some brackets, OK, those are the three columns of a matrix, the rank of that matrix, if I look at the columns, it wasn't obvious to me anyway." + }, + { + "text": "But if I look at the rows, it's, now it's obvious." + }, + { + "text": "The row space of that matrix obviously is two-dimensional, because I can, I see a basis for the row space, this row and that row." + }, + { + "text": "And of course, strictly speaking, I'm supposed to transpose those guys, make them stand up." + }, + { + "text": "But the rank is two, and therefore the column space is two-dimensional by this wonderful fact that the row space and column space have the same dimension, and therefore there are only two pivot columns, not three, and, those, the three columns are dependent." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk7.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk7.json new file mode 100644 index 0000000000000000000000000000000000000000..7d55c74913379543a71fcc53c971f787baf12a92 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk7.json @@ -0,0 +1,62 @@ +[ + { + "text": "OK. Now, let me bury that error and talk about the row space." + }, + { + "text": "Well, I'm going to give you the dimensions of all the spaces, because that's the, such a nice answer." + }, + { + "text": "OK." + }, + { + "text": "So let me come back here." + }, + { + "text": "So we have this great fact to establish, that the row space, its dimension is also the rank." + }, + { + "text": "OK. What about the null space?" + }, + { + "text": "What's a basis for the null space?" + }, + { + "text": "What's the dimension of the null space?" + }, + { + "text": "Let me, I'll put that answer up here, for the null space." + }, + { + "text": "Well, how have we constructed the null space?" + }, + { + "text": "We took the matrix A, we did those row operations to get it into a form U or even further, we got it into the reduced form R, and then we read off special solutions." + }, + { + "text": "Special solutions, and every special solution came from a free variable." + }, + { + "text": "And those special solutions are in the null space, and the great thing is, they're a basis for it." + }, + { + "text": "So for the null space, a basis will be the special solutions." + }, + { + "text": "And there's one for every free variable, right?" + }, + { + "text": "For each free variable, we give that variable the value one, the other free variable zero." + }, + { + "text": "We get the pivot variables, we get a vector in the -- we get a special solution." + }, + { + "text": "So we get all together n minus R of them, because that's the number of free variables." + }, + { + "text": "If we have R, this is, the dimension is R, is the number of pivot variables, this is the number of free variables." + }, + { + "text": "So the beauty is that those special solutions do form a basis and tell us immediately that the dimension of the null space is n -- I'd better write this well, because it's so nice, n minus R. And you see the nice thing, that the two dimensions in this n-dimensional space, one subspace is R-dimensional, to be proved, that's the row space." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk8.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk8.json new file mode 100644 index 0000000000000000000000000000000000000000..f4c70532a641ef630aa1f7bca077776017097cd4 --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk8.json @@ -0,0 +1,62 @@ +[ + { + "text": "The other subspace is n minus R-dimensional, that's the null space." + }, + { + "text": "And the two dimensions, like, together, give n. The sum of R and n minus R is n. And that's just great." + }, + { + "text": "It's really copying the fact that we have n variables, R of them are pivot variables and n minus R are free variables and n all together." + }, + { + "text": "OK. And now what's the dimension of this poor misbegotten fourth subspace?" + }, + { + "text": "It's got to be m minus R. The dimension of this left null space, left out practically, is m minus R. Well, that's really just saying that this, again, the sum of that plus that is m. And m is correct." + }, + { + "text": "It's the number of columns in A transpose." + }, + { + "text": "A transpose is just as good a matrix as A." + }, + { + "text": "It just happens to be n by m. It happens to have m columns, so it will have m variables, when I go to Ax equals zero, and m of them and R of them will be pivot variables and m minus R will be free variables." + }, + { + "text": "A transpose is as good a matrix as A." + }, + { + "text": "It follows the same rule that this plus the dimension, this dimension plus this dimension adds up to the number of columns." + }, + { + "text": "And over here, A transpose has m columns." + }, + { + "text": "Okay." + }, + { + "text": "Okay, so I gave you the easy answer, the dimensions." + }, + { + "text": "Now can I go back to check on a basis?" + }, + { + "text": "We would like to think that, say, the row space." + }, + { + "text": "Because we've got a basis for the column space." + }, + { + "text": "The pivot columns give a basis for the column space." + }, + { + "text": "Now I'm asking you to look at the row space." + }, + { + "text": "And I you could say, okay, I can produce a basis for the row space by transposing my matrix, making those columns, then doing elimination, row reduction, and checking out the pivot columns in this transposed matrix." + }, + { + "text": "But that means you had to do all that row reduction on A transpose." + } +] \ No newline at end of file diff --git a/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk9.json b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk9.json new file mode 100644 index 0000000000000000000000000000000000000000..8be162da3ff089e5c511aa65ea7d801c64cad56f --- /dev/null +++ b/sight/sources/annotated_chunks_window20/nHlE7EgJFds_9_chunk9.json @@ -0,0 +1,62 @@ +[ + { + "text": "It ought to be possible, if we take a matrix A, let me take the matrix, maybe we had this matrix in the last lecture, one one one, two one two, three two three, one one one." + }, + { + "text": "Okay." + }, + { + "text": "That, that matrix was so easy, we spotted its pivot columns, one and two, without actually doing row reduction." + }, + { + "text": "But now let's do the job properly." + }, + { + "text": "So I subtract this away from this to produce a zero." + }, + { + "text": "So one two three one is fine." + }, + { + "text": "Subtracting that away leaves me minus one minus one zero, right?" + }, + { + "text": "And subtracting that from the last row, oh, well, that's easy." + }, + { + "text": "Okay, I'm doing row reduction." + }, + { + "text": "Now I've, the first column is all set." + }, + { + "text": "The second column, I now see the pivot, and I can clean up, if I, actually, okay, why don't I make the pivot into a one?" + }, + { + "text": "I'll multiply that row through by minus one, and then I have one one." + }, + { + "text": "That was an elementary operation, I'm allowed." + }, + { + "text": "Multiply a row by a number." + }, + { + "text": "And now I'll do elimination." + }, + { + "text": "Two of those away from that will knock this guy out and make this into a one." + }, + { + "text": "So that's now a zero and that's a one." + }, + { + "text": "Okay." + }, + { + "text": "Done." + }, + { + "text": "That's R. I'm seeing the identity matrix here, I'm seeing zeros below, and I'm seeing F there." + } +] \ No newline at end of file